diff --git a/.gitattributes b/.gitattributes index ed877487a..98603d9fe 100644 --- a/.gitattributes +++ b/.gitattributes @@ -5,4 +5,19 @@ *.Gen linguist-language=Mathematica *.conf linguist-language=Mathematica *.Fac linguist-language=Mathematica - +Tests export-ignore +FeynCalc/DocSource export-ignore +FeynCalc/DocOutput export-ignore +FeynCalc/Phi export-ignore +install.m export-ignore +.project export-ignore +.gitignore export-ignore +.gitattributes export-ignore +docbuild.xml export-ignore +issue_template.md export-ignore +SUPPORT.md export-ignore +README.MD export-ignore +.WolframResources export-ignore +edit_documentation.sh export-ignore +use_documentation.sh export-ignore +LICENSE export-ignore diff --git a/.gitignore b/.gitignore index 7ad209fab..ab2783f81 100644 --- a/.gitignore +++ b/.gitignore @@ -2,14 +2,23 @@ FeynCalc/FeynArts FeynCalc/FeynArts/* FeynCalc/Database/*.db FeynCalc/Examples/Temp +FeynCalc/Examples/*/WIP +FeynCalc/Examples/WIP FeynCalc/Database/*.start FeynCalc/Database/*.m +FeynCalc/Database/*.nb FeynCalc/Tarcer/*.mx FeynCalc/AddOns/* FeynCalc/Documentation FeynCalc/Documentation/* +FeynCalc/DocOutputHold +FeynCalc/DocOutput/SearchIndex/* +FeynCalc/DocOutput/English/SearchIndex/* +FeynCalc/Ignore* FeynCalc/FCConfig.m build/* .settings/* .amateras +/.DS_Store +/.gitignore diff --git a/.project b/.project index d73fea635..42e4e5cc7 100644 --- a/.project +++ b/.project @@ -16,7 +16,7 @@ - 1446741392778 + 1537241074983 26 @@ -25,12 +25,75 @@ - 1446741392779 + 1537241074984 26 org.eclipse.ui.ide.multiFilter - 1.0-name-matches-false-false-FeynArts + 1.0-name-matches-true-false-FeynArts + + + + 1537241074986 + + 26 + + org.eclipse.ui.ide.multiFilter + 1.0-name-matches-true-false-Phi + + + + 1537241074987 + + 26 + + org.eclipse.ui.ide.multiFilter + 1.0-name-matches-true-false-Tests + + + + 1537241074989 + + 26 + + org.eclipse.ui.ide.multiFilter + 1.0-name-matches-true-false-build + + + + 1537241074990 + + 26 + + org.eclipse.ui.ide.multiFilter + 1.0-name-matches-true-false-DocOutput + + + + 1537241074997 + + 26 + + org.eclipse.ui.ide.multiFilter + 1.0-name-matches-true-false-Examples + + + + 1537241074999 + + 26 + + org.eclipse.ui.ide.multiFilter + 1.0-name-matches-true-false-AddOns + + + + 1537241075001 + + 26 + + org.eclipse.ui.ide.multiFilter + 1.0-name-matches-true-false-Database diff --git a/FeynCalc/AddOns/FUnitTools/FUnitTools.m b/FeynCalc/AddOns/FUnitTools/FUnitTools.m index 9e3fc3428..c142638a2 100644 --- a/FeynCalc/AddOns/FUnitTools/FUnitTools.m +++ b/FeynCalc/AddOns/FUnitTools/FUnitTools.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Tools for working with FeynCalc's unit tests *) @@ -31,7 +31,10 @@ FUnitCreateUnitTestsTypesetting::usage = \ "FUnitCreateUnitTestsTypesetting[TestName,Tests] is like FUnitCreateUnitTests \ but with the sole purpose of creating unit tests for typesetting, \ -i.e. the TraditionalForm output." +i.e. the TraditionalForm output. Notice that when creating typesetting tests, \ +the list elements must not be strings, i.e. li = {FV[p,mu], FV[q,nu]}. Then \ +FUnitCreateUnitTestsTypesetting[fcstFV,li] does the job and the output (copied as\ +Input Text) can be directly pasted into the test file." AddMakeBoxes::usage = "AddMakeBoxes is an option for FUnitCreateUnitTestsTypesetting, which \ @@ -43,22 +46,44 @@ Begin["`FUnitTools`Private`"]; -$FUnitToolsVersion="0.1"; +$FUnitToolsVersion="0.2"; $FUnitToolsDirectory = ToFileName[{$FeynCalcDirectory, "AddOns", "FUnitTools"}]; Options[FUnitCreateUnitTestsTypesetting] = { - AddMakeBoxes -> True + AddMakeBoxes -> True, + "ZeroIDValue" -> 0 }; -FUnitCreateUnitTests[n_String, l_List] := - MapIndexed[{n <> "-ID" <> ToString[First[#2]], #, ToString[ToExpression[#], FormatType -> InputForm]} &, l]; +Options[FUnitCreateUnitTests] = { + AddMakeBoxes -> True, + "ZeroIDValue" -> 0 +}; + +Options[FUnitExtractUnitTests] = { + Names -> False +}; + +FUnitCreateUnitTests[n_String, l_List, OptionsPattern[]] := + MapIndexed[{n <> "-ID" <> + If[ StringQ[OptionValue["ZeroIDValue"]], + ToString[OptionValue["ZeroIDValue"]]<>ToString[First[#2]], + ToString[OptionValue["ZeroIDValue"]+First[#2]] + ], + #, ToString[ToExpression[#], FormatType -> InputForm]} &, l] + + FUnitCreateUnitTestsTypesetting[n_String, l_List, OptionsPattern[]] := - MapIndexed[{n <> "-ID" <> ToString[First[#2]], + MapIndexed[{n <> "-ID" <> + + If[ StringQ[OptionValue["ZeroIDValue"]], + ToString[OptionValue["ZeroIDValue"]]<>ToString[First[#2]], + ToString[OptionValue["ZeroIDValue"]+First[#2]] + ], If[OptionValue[AddMakeBoxes], - StringReplace[ToString[System`MakeBoxees[#, TraditionalForm]], + StringReplace[ToString[System`MakeBoxees[#, TraditionalForm], InputForm], "MakeBoxees" -> "MakeBoxes"], ToString[#] ], @@ -69,17 +94,20 @@ ], InputForm, CharacterEncoding -> "Unicode"]} &, l]; -FUnitExtractUnitTests[{dir__, file_}, testVar_] := +FUnitExtractUnitTests[{dir__, file_}, testVar_, OptionsPattern[]] := Module[{li}, Get[FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", dir, file <> ".test"}]]; li = "Tests`" <> First[{dir}] <> "`" <> testVar; li = ToExpression[li]; - Map[#[[2]] &, li] + If[ OptionValue[Names], + Map[#[[1;;2]] &, li], + Map[#[[2]] &, li] + ] ]; (* Print startup message *) -If[ Global`$FeynCalcStartupMessages =!= False, +If[ $FeynCalcStartupMessages =!= False, Print[Style["FUnitTools ", "Text", Bold], Style[$FUnitToolsVersion <> " loaded.", "Text"]] ]; diff --git a/FeynCalc/AddOns/FVProjection/Examples/Vectors.m b/FeynCalc/AddOns/FVProjection/Examples/Vectors.m index 8c8d92346..49be42152 100644 --- a/FeynCalc/AddOns/FVProjection/Examples/Vectors.m +++ b/FeynCalc/AddOns/FVProjection/Examples/Vectors.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Simple operations with 4-vectors using FVProjection *) diff --git a/FeynCalc/AddOns/FVProjection/FVProjection.m b/FeynCalc/AddOns/FVProjection/FVProjection.m index c780b110e..deb034b0e 100644 --- a/FeynCalc/AddOns/FVProjection/FVProjection.m +++ b/FeynCalc/AddOns/FVProjection/FVProjection.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Toy add-on for FeynCalc for obtaining transverse and @@ -19,19 +19,19 @@ FVProjectionT::usage= "FVProjectionT[x_,mu_,p_] returns the transverse component of the 4-vector \ -x^mu with respect to the the 4-vector p"; +x^mu with respect to the 4-vector p"; FVProjectionL::usage= "FVProjectionL[x_,mu_,p_] returns the longitudinal component of the 4-vector \ -x^mu with respect to the the 4-vector p"; +x^mu with respect to the 4-vector p"; FVProjectorT::usage= "FVProjectorT[mu,nu,p] returns the transverse projector with respect to \ -the the 4-vector p"; +the 4-vector p"; FVProjectorL::usage= "FVProjectorL[mu,nu,p] returns the longitudinal projector with respect to \ -the the 4-vector p"; +the 4-vector p"; $FVProjectionVersion::usage= "$FVProjectionVersion is the string that represents the version of FVProjection"; @@ -126,7 +126,7 @@ (* Print startup message *) -If[ Global`$FeynCalcStartupMessages =!= False, +If[ $FeynCalcStartupMessages =!= False, Print[Style["FVProjector ", "Text", Bold], Style[$FVProjectionVersion <> " loaded.", "Text"]] ]; diff --git a/FeynCalc/AddOns/FVProjection/Tests/General/General.mt b/FeynCalc/AddOns/FVProjection/Tests/General/General.mt index 244026e9e..a3b851844 100644 --- a/FeynCalc/AddOns/FVProjection/Tests/General/General.mt +++ b/FeynCalc/AddOns/FVProjection/Tests/General/General.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for FVProjection *) diff --git a/FeynCalc/AddOns/FVProjection/Tests/General/General.test b/FeynCalc/AddOns/FVProjection/Tests/General/General.test index 3c3b7c6df..2f924cf3f 100644 --- a/FeynCalc/AddOns/FVProjection/Tests/General/General.test +++ b/FeynCalc/AddOns/FVProjection/Tests/General/General.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) diff --git a/FeynCalc/AddOns/FVProjection/Tests/MUnitTestSuite.mt b/FeynCalc/AddOns/FVProjection/Tests/MUnitTestSuite.mt index 46859cfac..90624d327 100644 --- a/FeynCalc/AddOns/FVProjection/Tests/MUnitTestSuite.mt +++ b/FeynCalc/AddOns/FVProjection/Tests/MUnitTestSuite.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Test Suite for FVProjection via MUnit *) diff --git a/FeynCalc/AddOns/FeynArtsLoader/FeynArtsLoader.m b/FeynCalc/AddOns/FeynArtsLoader/FeynArtsLoader.m new file mode 100644 index 000000000..cbf38e65a --- /dev/null +++ b/FeynCalc/AddOns/FeynArtsLoader/FeynArtsLoader.m @@ -0,0 +1,82 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FeynArtsLoader *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: A simple loader to load the patched FeynArts from + $FeynArtsDirectory *) + +(* ------------------------------------------------------------------------ *) + + +Begin["`Package`"] +End[] + +Begin["`FeynArtsLoader`Private`"]; + + +If[ $FeynCalcStartupMessages, + PrintTemporary[Style["Loading FeynArts from " <> $FeynArtsDirectory, "Text"]]; +]; + +(* Load the .m files *) +Block[ {loadfa, fafiles, strm, patch=True, str}, + If[ $FAPatch, + (* Check if FeynArts needs to be patched *) + If[(fafiles = FileNames["FeynArts.m", $FeynArtsDirectory])=!={}, + strm = OpenRead[First[fafiles]]; + If[ Head[strm] =!= InputStream, + Message[General::noopen, First[fafiles]]; + Abort[] + ]; + While[ ToString[str] != "EndOfFile", + str = Read[strm, String]; + If[ StringMatchQ[ToString[str], "*patched for use with FeynCalc*", IgnoreCase -> True], + patch = False + ] + ]; + Close[First[fafiles]], + Message[General::noopen, FileNameJoin[{$FeynArtsDirectory, "FeynArts.m"}]]; + Message[FeynCalc::faerror, $FeynArtsDirectory]; + patch = False + ]; + (* Apply the patch *) + If[ patch, + FAPatch[] + ] + ]; + loadfa=Block[ {Print= System`Print},Get[FileNameJoin[{$FeynArtsDirectory, "FeynArts.m"}]]]; + If[loadfa =!=$Failed, + (* If everything went fine *) + If[ $FeynCalcStartupMessages, + Print[ Style["FeynArts ", "Text", Bold], + Style[StringReplace[ToString[FeynArts`$FeynArtsVersion],"FeynArts "->""] <>" patched for use with FeynCalc, for documentation see the ", + "Text"], + Style[DisplayForm@ButtonBox["manual", BaseStyle -> "Hyperlink", ButtonFunction :> + SystemOpen[First@FileNames[{"*.pdf", "*.PDF"}, FileNameJoin[{$FeynArtsDirectory, "manual"}]]], + Evaluator -> Automatic, Method -> "Preemptive"], "Text"], + Style[" or visit ", "Text"], + Style[DisplayForm@ButtonBox["www.feynarts.de.", ButtonData :> {URL["http://www.feynarts.de/"], None}, + BaseStyle -> "Hyperlink", ButtonNote -> "www.feynarts.de/"],"Text"] + ]; + Print[ Style["If you use FeynArts in your research, please cite","Text"]]; + Print [Style[" \[Bullet] T. Hahn, Comput. Phys. Commun., 140, 418-431, 2001, arXiv:hep-ph/0012260","Text"]]; + ], + (* If FeynArts didn't load *) + Message[FeynCalc::faerror, $FeynArtsDirectory]; + ]; +]; + +FeynCalc`Private`AddToTheContextPath = Join[FeynCalc`Private`AddToTheContextPath,{"FeynArts`"}]; + +End[] + + diff --git a/FeynCalc/AddOns/TARCER/9801383.pdf b/FeynCalc/AddOns/TARCER/9801383.pdf new file mode 100644 index 000000000..28519f5ff Binary files /dev/null and b/FeynCalc/AddOns/TARCER/9801383.pdf differ diff --git a/FeynCalc/AddOns/TARCER/README.MD b/FeynCalc/AddOns/TARCER/README.MD new file mode 100755 index 000000000..f54af363b --- /dev/null +++ b/FeynCalc/AddOns/TARCER/README.MD @@ -0,0 +1,24 @@ +# Description +TARCER is a Mathematica program for the reduction of two-loop propagator integrals . + +# Requirements + +The latest versions of TARCER are designed as an addon for FeynCalc. To use TARCER you need FeynCalc and Mathematica (at least version 8). + +# Installation + +TARCER is bundled with FeynCalc. When you install FeynCalc using the automatic installer, TARCER will be installed as well. + +# Usage + +For usage information see the accompanying paper [arXiv:hep-ph/9801383](https://arxiv.org/abs/hep-ph/9801383) and the supplied examples. + +# Acknowledgments + +If you use TARCER in you work, please cite + +* R. Mertig and R. Scharf, Comput. Phys. Commun., 111, 265-273, 1998, arXiv:hep-ph/9801383 + +# License + +* As the rest of the FeynCalc code, the code of TARCER is licensed under GNU GPLv3. diff --git a/FeynCalc/AddOns/TARCER/TARCER.m b/FeynCalc/AddOns/TARCER/TARCER.m new file mode 100644 index 000000000..132f7875c --- /dev/null +++ b/FeynCalc/AddOns/TARCER/TARCER.m @@ -0,0 +1,102 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: TARCER *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1998-2018 Rolf Mertig + Copyright (C) 1998-2018 Rainer Scharf + Copyright (C) 1998-2018 Frederik Orellana + Copyright (C) 2014-2018 Vladyslav Shtabovenko +*) + +(* :Summary: Loader for TARCER *) + +(* ------------------------------------------------------------------------ *) + +$TARCERVersion::usage= +"$FeynHelpersVersion is the string that represents the version of TARCER"; + +$TARCERDirectory::usage= +"$TARCERDirectory is the string that represents the full path to the TARCER \ +directory"; + +GenerateTarcerMX::usage = +"GenerateTarcerMX creates the *.mx file for TARCER. This is necessary to use +TARCER and has to be done only once. The evaluation usually takes a +couple of minutes." + +TARCER::taerror = +"TARCER*.mx file not found or damaged. Please evaluate the command \ +GenerateTarcerMX[] to create it and then restart Mathematica."; + +Begin["`Package`"] + + + +End[] + +Begin["`TARCER`Private`"]; + +$TARCERVersion = "2.0"; + +$TARCERDirectory = ToFileName[{$FeynCalcDirectory, "AddOns", "TARCER"}]; + +tarcerfilenames = FileNames["tarcer"<> StringReplace[$System,{"-"->"","Microsoft"->"","("->"",")"->""," "->""}] <>"*.mx", $TARCERDirectory,IgnoreCase->True]; + +TarcerDialogText = "TARCER*.mx file not found or damaged. Creating a new \ +file can take couple of minutes, but this has to be done only once. \ +After the new file is generated you need to restart Mathematica. Should \ +we generate the new TARCER*.mx now?" + +GenerateTarcerMX[]:= + If[ Get@ToFileName[$TARCERDirectory, "TARCERSource.m"]=!= $Failed, + Print["Succesfully created ", Last@FileNames["*.mx", $TARCERDirectory]] + ] + +needNewTarcerMX[]:= + If[ TrueQ[$Notebooks], + + If[ ChoiceDialog[TarcerDialogText], + GenerateTarcerMX[] + ] + ]; + +If[ tarcerfilenames==={}, + Message[TARCER::taerror]; + needNewTarcerMX[] +]; + +If[ Length[tarcerfilenames]>1, + Print[Style["Found multiple versions of TARCER: ", "Text"]]; + Print[TableForm[tarcerfilenames]]; + Print[Style["FeynCalc will load ","Text"], Last[tarcerfilenames]] +]; + +If[ tarcerfilenames=!={}, + If[ Get[Last[tarcerfilenames]]===$Failed, + Message[TARCER::taerror]; + needNewTarcerMX[] + ]; + + FeynCalc`Private`AddToTheContextPath = Join[FeynCalc`Private`AddToTheContextPath,{"Tarcer`"}]; + + + (* Print startup message *) + If[ $FeynCalcStartupMessages, + Print[ Style["TARCER ", "Text", Bold], + Style[$TARCERVersion <> ", for more information see the accompanying ", "Text"], + Style[DisplayForm@ButtonBox["publication.", BaseStyle -> "Hyperlink", ButtonFunction :> + SystemOpen[ToFileName[{$TARCERDirectory},"9801383.pdf"]], + Evaluator -> Automatic, Method -> "Preemptive"], "Text"], + Style[" If you use TARCER in your research, please cite","Text"] + ]; + Print [Style[" \[Bullet] R. Mertig and R. Scharf, Comput. Phys. Commun., 111, 265-273, 1998, arXiv:hep-ph/9801383","Text"]]; + ] +] + +End[] + + diff --git a/FeynCalc/AddOns/TARCER/TARCERSource.m b/FeynCalc/AddOns/TARCER/TARCERSource.m new file mode 100644 index 000000000..7b21b08bf --- /dev/null +++ b/FeynCalc/AddOns/TARCER/TARCERSource.m @@ -0,0 +1,4255 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: TARCER *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1998-2018 Rolf Mertig + Copyright (C) 1998-2018 Rainer Scharf + Copyright (C) 1998-2018 Frederik Orellana + Copyright (C) 2014-2018 Vladyslav Shtabovenko +*) + +(* :Summary: TARCER is a Mathematica program for the reduction + of two-loop propagator integrals *) + +(* ------------------------------------------------------------------------ *) + +(* + +COMMENTS (VS 04.8.2011) changed typsetting for SEpsilon +COMMENTS (RM 19.8.2011) changed typsetting for SEpsilon +COMMENTS (RM 20.7.2011) changed the way .mx files are named +COMMENTS (RM 14.3..2004) uncommented a global variable assignement.changed default setting of $RankLimit to {2,5}. +COMMENTS (RM 31.10.2003) Change default settings of TarcerExpand, modify $BasisIntegras for massless integrals, +changed default setting of $RankLimit to {1,6}. +COMMENTS (RM 28.10.2003) Fixed a bug in TarcerExpand (only introduced recently), +changed default setting of $RankLimit to {1,5}. +COMMENTS (RM 24.9.2003) Relaxed a condition in equation (61) and (6153) +COMMENTS (RM 18.9.2003): Fixed things for 5.0, eliminated a TVI symmetry (causing infinite recursion) and added +TFI decomposition into products of TAI's (was somehow missing but shows up in, e.g., the 2-loop Higss selfenergy). +Putting TFI back into the Tarcer context, because the fcloops context created trouble ... +Changed default of $Comment to False. +COMMENTS (FO 8.9.2002.): Changed context of TFI to HighEnergyPhysics`fcloops`TFI` and updated other HighEnergyPhysics`* + contexts. +COMMENTS (FO 15.3.2001.): Changed PreFactor into Prefactor1 to avoid conflict with FeynArts and FeynCalc. +COMMENTS (FO 15.3.2001.): Changed context of Zeta2 and made definition dependent on not having loaded FeynCalc. +COMMENTS (RM 25.4.): TFISimplify (like TFIRecurse, but without trule[9]). +COMMENTS (RM 23.4.): bug fixed in tlrule[17]. +COMMENTS (RM 6.4.): special TVR relations added to TVR. +COMMENTS (RM 22.3.): TVI Symmetry added to TVR. +COMMENTS (RM 18.3.): More rules added to $TTable. +COMMENTS (RM 18.2.): More rules added to $TTable. +COMMENTS (RM 21.2.): Included $TTable. added tlrule[25] +COMMENTS (RM 20.2.): $RankLimit = {0,6} ; Changed TarcerRecurse such that special TJR and TVR + (reducing D -> D-2) are used first. +COMMENTS (RM 15.2.): $RankLimit = {0,8} ; +The following test now works: + + Print["test 1 : TFI[D, pp, {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1,MW}}] = ", + Timing[t1 =TarcerRecurse[TFI[D, pp, {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1,MW}}]] + ] // InputForm + ] + + Print["test 2 : TFI[d, pp, 0, {0, 0, 0, 0, 4},{{1, m1}, {1, m2}, 0, 0, 0}] = ", + Timing[t2 =TarcerRecurse[TFI[D, pp, 0, {0, 0, 0, 0, 4},{{1, m1}, {1, m2}, 0, 0, 0}]]; + ] // InputForm + ] + +COMMENTS (RM 13.2.): tlrule[11] and trule[12] made more restrictive: inhibiting thus a recursion if {n5,m5} equals {0,0}. +COMMENTS (RM 12.2.): tlrule[15] made safer (in order to not get 0 :> 0 ); + TFIRecurse made safer (to not get into a recursion); + There is still something wrong with the tlrule's ; since + TFIRecurse[TFI[D, pp, {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1, MW}}]] + doesn't work .. +COMMENTS (RM 5.2.): tlrule[10] slightly changed to cover more cases. +COMMENTS (RM 2.2.): FunctionExpand added in tlrule[9]. Option TimeConstraint added to + TarcerRecurse (because TimeConstrained is buggy under Linux). +COMMENTS (RM 1.2.): Changed TarcerRecurse. New TLR definition. + default $RankLimit={0,6}; +$Remember=True; +COMMENTS (RM 19.1.): changes are: tlrule[22] and tlrule[23], minor efficiency changes (Expand3 = Identity) + and other small programming optimizations. +COMMENTS (RM 22.1.): changes are: bug in tlrule[23] fixed, new tlrule[24], new option Factor to + TarcerReduce (doesn't change anything by default, but allows for improved Factoring). + +See also: hep-ph/9801383, published in Comput. Phys. Commun. 111 (1998) 265-273 *) + + +Unset[$Post]; +$Post = (#;) &; +If[$Notebooks =!= True, $Post = (#;) &]; + +$HistoryLength = 0; + +BeginPackage["Tarcer`",{"FeynCalc`"}]; + +TarcerRecurse::usage = +"TarcerRecurse[expr] applies recurrence relations for all TFI's \ +(and TVI, TJI, TBI, TAI) in expr. For evaluation and Laurent \ +expansion of the resulting basis integrals use TarcerExpand."; + +TarcerExpand::usage = +"TarcerExpand[expr, d -> (4+e), order] or TarcerExpand[epxr, d -> \ +(4-e), order] or TarcerExpand[expr, d -> (4 - 2 om)substitutes \ +integrals as specified by the option TarcerRules, and does a Laurent \ +expansion in the variable around 0 at the right hand side of the \ +second argument (i.e., you can use whatever convention you like ...). \ +The same effect as TarcerExpand[TarcerRecurse[expr], ...] can be \ +achieved by setting the option TarcerRecurse of TarcerExpand to True. \ +TarcerExpand[expr, d -> (4+e)] is equivalent to TarcerExpand[expr, d -> \ +(4+e), 0]."; + +TarcerReduce::usage = +"TarcerReduce is an option to TarcerExpand. It should be set to a \ +list of basic integrals."; + +Cayley::usage = +"Cayley[m1,m2,m3,m4,m5,Sqrt[pp]] is the Cayley determinant."; + +Cayleyu::usage = +"Cayleyu are the sub-Cayley-determinants as described in Tarasov's \ +paper."; + +CayleyD::usage = +"CayleyD are the sub-Cayley-determinants as described in Tarasov's \ +paper."; + +Prefactor1::usage = +"Prefactor1[expr] may be used to prohibit TarcerExpand from \ +Taylor-expanding expr."; + +SEpsilon::usage = +"Sepsilon[d] is an abbreviation for Exp[(d-4)/2 EulerGamma]."; + +TFI::usage = +"TFI[d, pp, {{n1,m1},{n2,m2},{n3,m3},{n4,m4},{n5,m5}}] is + the 2-loop d-dimensional integral + 1/( (q1^2 - m1^2)^n1 (q2^2 - m2^2)^n2 ((q1-p)^2 - m3^2)^n3 * + ((q2-p)^2 - m4^2)^n4 ((q1-q2)^2 - m5^2)^n5 ) . + + TFI[d, pp, {x,y,z,v,w}, {{n1,m1},{n2,m2},{n3,m3},{n4,m4},{n5,m5}}] + has as additional factors in the numerator \ +(q1^2)^x*(q2^2)^y*(q1.p)^z* + (q2.p)^v*(q1.q2)^w . + + TFI[d, pp, dp, {a,b}, {{n1,m1},{n2,m2},{n3,m3},{n4,m4},{n5,m5}}] + has as additional factors in the numerator (OPEDelta.q1)^a * \ +(OPEDelta.q2)^b; + dp is (OPEDelta.p)."; + +TFIRecurse::usage = +"TFIRecurse[expr] applies the recursion algorithm implemented in \ +TARCER.nb (following Tarasov) to TFI's (and TVI's, TJI's, TBI's, \ +TAI's in expr."; + +TFISimplify::usage = +"TFISimplify[expr] applies the recursion algorithm implemented in \ +TARCER.nb (following Tarasov) to TFI's (and TVI's, TJI's, TBI's, \ +TAI's in expr, except k1.k2."; + +TVI::usage = +"TVI[d,pp,{ {n1,m1},{n2,m2},{n3,m3},{n4,m4}}] is the massive 2-loop \ +integral with four propagators in d dimensions. "; + +TJI::usage = +"TJI[d, pp, { {n1,m1},{n2,m2},{n3,m3} }] is the massive 2-loop \ +integral with three propagators in d dimensions. "; + +TKI::usage = +"TKI[d, 0, { {n1,m1},{n2,m2},{n3,m3} }] is the bubble massive \ +2-loop selfenergy type integral with three propagators in d \ +dimensions. "; + +TBI::usage = +"TBI[d, pp, { {n1,m1},{n2,m2} }] is the massive 1-loop selfenergy \ +type integral with two propagators in d dimensions."; + +TAI::usage = +"TAI[d, pp, { {n1,m1} }] is the massive 1-loop selfenergy type \ +integral with one propagator in d dimensions."; + +TFR::usage = +"TFR is similar in syntax to TFI but applies once the recurrence \ +relations derived for TFI."; + +TVR::usage = +"TVR is similar in syntax to TVI but applies once the recurrence \ +relations derived for TVI."; + +TJR::usage = +"TJR is similar in syntax to TJI but applies once the recurrence \ +relations derived for TJI."; + +TBR::usage = +"TBR is similar in syntax to TBI but applies once the recurrence \ +relations derived for TBI."; + +TAR::usage = +"TAR is similar in syntax to TAI but applies once the recurrence \ +relations derived for TAI."; + +$RankLimit::usage = +"$RankLimit is the list of integers specifying the highest possible \ +sums of exponents of scalar products; i.e., {a+b, r+s} means that at \ +most (Delta.k1)^a * (Delta.k2)^2 * (p.k1)^r * (p.k2)^s in the \ +numerator will be calculated (a,b,r,s have to be non-negative \ +integares). $RankLimit has to be set in the TARCER.nb notebook. In \ +the tarcer.mx file this is not possible anymore."; + +$TarcerRecursed::usage = +"If $Comment is set to True all integrals\n\t\twhich are reduced \ +are collected in the global variable $TarcerRecured."; + +$BasisIntegrals::usage = +"$BasisIntegrals is a list of some basis integrals. It is the \ +default setting of TarcerReduce of TarcerExpand."; + +$Comment::usage = +"$Comment can be set to True or False. If set to False no comments \ +are generated."; + +$CommentNotebook::usage = +"$Comment can be set to True or False. Setting it to True will \ +generate a separate notebook (if and only if $Comment is True) where \ +the used recursion relations are displayed."; + +$RecursionStop::usage = +"$RecursionStop sets an upper limit on the total number of \ +recursion levels. Its purpose is to inhibit erroneous infinite \ +recursions."; + +$TTable::usage = +"$TTable is a list of precomputed reductions. $TTable is the \ +default setting of the option Table of TarcerRecurse. "; + +$TarcerVersion::usage= +"contains the version of TARCER." + +Begin["`Private`"]; +trVerbose::usage=""; +pal1::usage=""; +pal2::usage=""; + +m1::usage=""; +m2::usage=""; +m3::usage=""; +m4::usage=""; +m5::usage=""; +hCayley::usage=""; +hCayleyD::usage=""; +cD::usage=""; +cu::usage=""; +setd::usage=""; +notnecessaryf::usage=""; +gamma::usage=""; +test::usage=""; +ia::usage=""; +ib::usage=""; +ir::usage=""; +es::usage=""; +top::usage=""; +set::usage=""; +factor::usage=""; + +$TarcerVersion = "2.0"; + +If[ !ValueQ[$RankLimit], + $RankLimit = {2, 5}; +]; + +Expand3 = Identity; +$CheckRecursion = False; +$PutPalettes = False; +atime = AbsoluteTime[]; + + +SEpsilon /: + MakeBoxes[SEpsilon[d_], fmt_] := + InterpretationBox @@ {StyleBox[SubscriptBox["S", ToBoxes[First[Variables[d]], fmt]], FontWeight -> "Bold"], SEpsilon[d], Editable -> False} + +MakeBoxes[SEpsilon[d_]^n_, fmt_] := + InterpretationBox @@ {StyleBox[SubsuperscriptBox["S", ToBoxes[First[Variables[d]], fmt], n], FontWeight -> "Bold"], SEpsilon[d], Editable -> False} + +Prefactor1 /: + MakeBoxes[Prefactor1[d_], fmt_] := + InterpretationBox @@ {MakeBoxes[d, fmt], Prefactor1[d], Editable -> False} + +MakeBoxes[Schiebe[i_, pm_String] , _] := + InterpretationBox[StyleBox[SuperscriptBox[i, pm], FontWeight -> "Bold"], Schiebe[i, pm], Editable -> True] + +CayleyD /: + MakeBoxes[CayleyD[i_Integer][_], _] := + FractionBox[SubscriptBox["\[CapitalDelta]", i], "\[CapitalDelta]"]; + +CayleyD /: + MakeBoxes[CayleyD[i_Integer, j_Integer][_], _] := + FractionBox[SubscriptBox["\[CapitalDelta]", 10 i + j], "\[CapitalDelta]"]; + +CayleyD /: + MakeBoxes[CayleyD[i_Integer, j_Integer, k_Integer][_], _] := + FractionBox[SubscriptBox["\[CapitalDelta]", 100 i + 10 j + k], "\[CapitalDelta]"]; + +Cayley /: + MakeBoxes[Cayley[i_Integer][_], _] := + SubscriptBox["\[CapitalDelta]", i]; + +Cayley /: + MakeBoxes[Cayley[i_Integer, j_Integer][_], _] := + SubscriptBox["\[CapitalDelta]", 10 i + j]; + +Cayley /: + MakeBoxes[Cayley[i_Integer, j_Integer, k_Integer][_], _] := + SubscriptBox["\[CapitalDelta]", 100 i + 10 j + k]; + +Cayleyu /: + MakeBoxes[Cayleyu[i_Integer, j_Integer, k_Integer][_], _] := + SubscriptBox["u", 100 i + 10 j + k]; + +MakeBoxes[PP, _] := + InterpretationBox[SuperscriptBox[p, 2], PP]; + +MakeBoxes[m1^(p_), _] := + InterpretationBox[SubsuperscriptBox[m, 1, p], m1^p]; + +MakeBoxes[m2^(p_), _] := + InterpretationBox[SubsuperscriptBox[m, 2, p], m2^p]; + +MakeBoxes[m3^(p_), _] := + InterpretationBox[SubsuperscriptBox[m, 3, p], m3^p]; + +MakeBoxes[m4^(p_), _] := + InterpretationBox[SubsuperscriptBox[m, 4, p], m4^p]; + +MakeBoxes[m5^(p_), _] := + InterpretationBox[SubsuperscriptBox[m, 5, p], m5^p]; + +m6 = Sqrt[PP]; + +MakeBoxes[m1, _] := + InterpretationBox[SubscriptBox[m, 1], m1]; + +MakeBoxes[m2, _] := + InterpretationBox[SubscriptBox[m, 2], m2]; + +MakeBoxes[m3, _] := + InterpretationBox[SubscriptBox[m, 3], m3]; + +MakeBoxes[m4, _] := + InterpretationBox[SubscriptBox[m, 4], m4]; + +MakeBoxes[m5, _] := + InterpretationBox[SubscriptBox[m, 5], m5]; + +mbt[z_] := + ToBoxes[z, TraditionalForm]; + +redblue[z_ /; Head[z] =!= Plus] := + mbt[z]; + +redblue[z_ - 1] := + StyleBox[mbt[z], FontColor -> RGBColor[1, 0, 0]]; + +redblue[z_Subscript - 2] := + StyleBox[SubscriptBox[OverscriptBox[z[[1]], "_"], z[[2]]], FontColor -> RGBColor[1, 0, 0]]; + +redblue[z_ - 2] := + StyleBox[OverscriptBox[mbt[z], "_"], FontColor -> RGBColor[1, 0, 0]]; +redblue[z_ - 3] := + StyleBox[UnderscriptBox[OverscriptBox[mbt[z], "_"], "_"], FontColor -> RGBColor[1, 0, 0]]; + +redblue[z_ + 1] := + StyleBox[mbt[z], FontColor -> RGBColor[0, 0, 1]]; + +redblue[z_ + 2] := + StyleBox[OverscriptBox[mbt[z], "_"], FontColor -> RGBColor[0, 0, 1]]; + +redblue[z_Subscript + 2] := + StyleBox[SubscriptBox[OverscriptBox[z[[1]], "_"], z[[2]]], FontColor -> RGBColor[0, 0, 1]]; + +TFI /: + MakeBoxes[TFI[d_, pp_, {ur__}, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", ur}]], TFI[d, pp, {ur}, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TFI /: + MakeBoxes[TFI[d_, pp_, dp_, any__, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", Apply[Sequence, Flatten[{any}]]}]], TFI[d, pp, dp, any, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] /; Head[dp] =!= List; + +TFI /: + MakeBoxes[TFI[dpp__, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[First[{dpp}], TraditionalForm], ")"}]], TFI[dpp, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; + +TVI /: + MakeBoxes[TVI[dpp__, {den__}], fmt_] := + ( + (InterpretationBox @@ {SubsuperscriptBox[StyleBox["V", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TVI][dpp, {den}], Editable -> True}) /. Hold[TVI] -> TVI + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; + +TJI /: + MakeBoxes[TJI[d_, 0, {den__}], fmt_] := + ( + (InterpretationBox @@ {SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], Hold[TJI][d, 0, {den}], Editable -> True}) /. Hold[TJI] -> TJI + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TJI /: + MakeBoxes[TJI[dpp__, {den__}], fmt_] := + ( + (InterpretationBox @@ {SubsuperscriptBox[StyleBox["J", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TJI][dpp, {den}], Editable -> True}) /. Hold[TJI] -> TJI + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TKI /: + MakeBoxes[TKI[d_, ___, {den__}], fmt_] := + ( + SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]] + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TKI /: + MakeBoxes[TKI[dpp__, {den__}], fmt_] := + ( + (InterpretationBox @@ {SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TKI][dpp, {den}], Editable -> True}) /. Hold[TKI] -> TKI + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TBI /: + MakeBoxes[TBI[d_, ___, {den__}], fmt_] := + ( + SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]] + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TBI /: + MakeBoxes[TBI[d_, pp___, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TBI[d, pp, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TAI /: + MakeBoxes[TAI[d_, ___, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["A", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TAI[d, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TFIC /: + MakeBoxes[TFIC[d_, pp_, {0, 0, i_, 0, 0}, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", i, "0"}]], TFIC[d, pp, {0, 0, i, 0, 0}, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TFIC /: + MakeBoxes[TFIC[d_, pp_, {0, 0, 0, i_, 0}, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", "0", i}]], TFIC[d, pp, {0, 0, 0, i, 0}, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TFIC /: + MakeBoxes[TFIC[dpp__, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[First[{dpp}], TraditionalForm], ")"}]], TFIC[dpp, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; + +TVIC /: + MakeBoxes[TVIC[dpp__, {den__}], fmt_] := + ( + (InterpretationBox @@ {SubsuperscriptBox[StyleBox["V", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TVIC][dpp, {den}], Editable -> True}) /. Hold[TVIC] -> TVIC + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; + +TJIC /: + MakeBoxes[TJIC[d_, 0, {den__}], fmt_] := + ((InterpretationBox @@ {SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], Hold[TJIC][d, 0, {den}], Editable -> True}) /. Hold[TJIC] -> TJIC + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] + +TJIC /: + MakeBoxes[TJIC[dpp__, {den__}], fmt_] := + ((InterpretationBox @@ {SubsuperscriptBox[StyleBox["J", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TJIC][dpp, {den}], Editable -> True}) /. Hold[TJIC] -> TJIC + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] + +TBIC /: + MakeBoxes[TBIC[d_, ___, {den__}], fmt_] := + ( + SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]] + ) /;MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TBIC /: + MakeBoxes[TBIC[d_, pp___, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TBIC[d, pp, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TAIC /: + MakeBoxes[TAIC[d_, ___, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["A", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TAIC[d, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TFR /: + MakeBoxes[TFR[d_, pp_, {0, 0, i_, 0, 0}, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", i, "0"}]], TFR[d, pp, {0, 0, i, 0, 0}, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TFR /: + MakeBoxes[TFR[d_, pp_, {0, 0, 0, i_, 0}, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", "0", i}]], TFR[d, pp, {0, 0, 0, i, 0}, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TFR /: + MakeBoxes[TFR[dpp__, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[First[{dpp}], TraditionalForm], ")"}]], TFR[dpp, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; + +TVR /: + MakeBoxes[TVR[dpp__, {den__}], fmt_] := + ( + (InterpretationBox @@ {SubsuperscriptBox[StyleBox["V", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TVR][dpp, {den}], Editable -> True}) /. Hold[TVR] -> TVR + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; + +TJR /: + MakeBoxes[TJR[d_, 0, {den__}], fmt_] := + ( + (InterpretationBox @@ {SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], Hold[TJR][d, 0, {den}], Editable -> True}) /. Hold[TJR] -> TJR + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] + +TJR /: + MakeBoxes[TJR[dpp__, {den__}], fmt_] := + ( + (InterpretationBox @@ {SubsuperscriptBox[StyleBox["J", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TJR][dpp, {den}], Editable -> True}) /. Hold[TJR] -> TJR + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TBR /: + MakeBoxes[TBR[d_, ___, {den__}], fmt_] := + ( + SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]] + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TBR /: + MakeBoxes[TBR[d_, pp___, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TBR[d, pp, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +TAR /: + MakeBoxes[TAR[d_, ___, {den__}], fmt_] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["A", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TAR[d, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; + +n1 /: + MakeBoxes[n1, TraditionalForm] := + SubscriptBox["\[Nu]", 1]; +n2 /: + MakeBoxes[n2, TraditionalForm] := + SubscriptBox["\[Nu]", 2]; +n3 /: + MakeBoxes[n3, TraditionalForm] := + SubscriptBox["\[Nu]", 3]; +n4 /: + MakeBoxes[n4, TraditionalForm] := + SubscriptBox["\[Nu]", 4]; +n5 /: + MakeBoxes[n5, TraditionalForm] := + SubscriptBox["\[Nu]", 5]; + +MakeBoxes[ParD[i_]^j_, TraditionalForm] := + SubsuperscriptBox["\[PartialD]", i, j]; + +MakeBoxes[ParD[i_], TraditionalForm] ^= + SubscriptBox["\[PartialD]", i]; + +MakeBoxes[DPlus, TraditionalForm] := + StyleBox[SuperscriptBox["d", "+"], FontWeight -> "Bold", SingleLetterItalics -> False]; + +MakeBoxes[TpD[_, b_], TraditionalForm] := + MakeBoxes[b, TraditionalForm] + +If[ $PutPalettes === True, + tobut[a_] := + ButtonBox[ToBoxes[a, StandardForm], ButtonStyle -> "Paste"]; + If[ Head[pal1] === NotebookObject, + NotebookClose[pal1]]; + pal1 = NotebookPut[ + Notebook[{Cell[BoxData[GridBox[Join[Transpose@{ + Table[tobut@(Subscript[m, j]^2), {j, 5}], + Table[tobut@Subscript[\[Nu], j], {j, 5}], + Table[tobut@Schiebe[i, "+"], {i, 5}], + Table[tobut@Schiebe[i, "-"], {i, 5}]}, { + tobut /@ {PP, Subscript[\[CapitalDelta], \[Placeholder]], Subscript[u, \[Placeholder]], \[ScriptCapitalC] }}], + RowSpacings -> 0, ColumnSpacings -> 0]], NotebookDefault]}, + Editable -> True, + WindowToolbars -> {}, + WindowSize -> {Fit, Fit}, + WindowMargins -> {{0, Automatic}, {0, Automatic}}, + WindowFrame -> "Palette", + WindowElements -> {}, + WindowFrameElements -> "CloseBox", + WindowClickSelect -> False, + ScrollingOptions -> {"PagewiseScrolling" -> True}, + ShowCellBracket -> False, + CellMargins -> {{0, 0}, {0, 0}}, + Active -> True, + CellOpen -> True, + ShowCellLabel -> False, + ShowCellTags -> False, + ImageMargins -> {{0, 0}, {0, 0}}, + Magnification -> 2, Visible -> True] + ]; + SetOptions[pal1, WindowMargins -> {{0, Automatic}, {Automatic, 0}}]; + SetOptions[pal1, Visible -> True, WindowSize -> {Fit, Fit}]; + + If[ Head[pal2] === NotebookObject, + NotebookClose[pal2] + ]; + + pal2 = NotebookPut[Notebook[{Cell[BoxData[GridBox[ + + JJJ = Join[ + {tobut /@ { + TFI[d + 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}], + TVI[d + 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}], + TJI[d + 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}], + TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}], + TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}], + TAI[d, {Subscript[\[Nu], 1]}]}}, + {tobut /@ { + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}], + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}], + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}], + TKI[d - 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}], + TBI[d - 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}], + TAI[d - 2, {Subscript[\[Nu], 1]}]}} + ], RowSpacings -> 0, ColumnSpacings -> 0]], NotebookDefault]}, + + Editable -> True, + WindowToolbars -> {}, + WindowSize -> {FitAll, FitAll}, + WindowMargins -> {{0, Automatic}, {0, Automatic}}, + WindowFrame -> "Palette", + WindowElements -> {}, + WindowFrameElements -> "CloseBox", + WindowClickSelect -> False, + ScrollingOptions -> {"PagewiseScrolling" -> True}, + ShowCellBracket -> False, + CellMargins -> {{0, 0}, {0, 0}}, + Active -> True, + CellOpen -> True, + ShowCellLabel -> False, + ShowCellTags -> False, + ImageMargins -> {{0, 0}, {0, 0}}, + Magnification -> 2, Visible -> True] + ]; + SetOptions[pal2, WindowMargins -> {{Automatic, 15}, {Automatic, 4}}]; + SetOptions[pal2, Visible -> True, WindowSize -> {Fit, Fit}]; + SetOptions[pal2, WindowSize -> {Fit, Fit}] +]; + +OperatorApplyF[x_ == y_] := + Block[{sch}, + sch = { + Schiebe[i_, "+"]^ni_. TFI[d_, {n15__}] :> + TFI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], + Schiebe[i_, "-"]^ni_. TFI[d_, {n15__}] :> + TFI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] + }; + Map[Collect[Expand[#] //. sch, TFI[__], Factor] &, x == y] + ]; + +OperatorApplyV[x_ == y_] := + Block[{sch}, + sch = { + Schiebe[i_, "+"]^ni_. TVI[d_, {n15__}] :> + TVI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], + Schiebe[i_, "-"]^ni_. TVI[d_, {n15__}] :> + TVI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] + }; + Map[Collect[Expand[#] //. sch, TVI[__], Factor] &, x == y] + ]; + +OperatorApplyJ[x_ == y_] := + Block[{sch}, + sch = { + Schiebe[i_, "+"]^ni_. TJI[d_, {n15__}] :> + TJI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], + Schiebe[i_, "-"]^ni_. TJI[d_, {n15__}] :> + TJI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] + }; + Map[Collect[Expand[#] //. sch, TJI[__], Factor] &, x == y] + ]; + +OperatorApplyK[x_ == y_] := + Block[{sch}, + sch = { + Schiebe[i_, "+"]^ni_. TKI[d_, {n15__}] :> + TKI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], + Schiebe[i_, "-"]^ni_. TKI[d_, {n15__}] :> + TKI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] + }; + Map[Collect[Expand[#] //. sch, TKI[__], Factor] &, x == y] + ]; + +OperatorApplyK[x_ == y_] := + Block[{sch}, + sch = { + Schiebe[i_, "+"]^ni_. TKI[d_, {n15__}] :> + TKI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], + Schiebe[i_, "-"]^ni_. TKI[d_, {n15__}] :> + TKI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] + }; + Map[Collect[Expand[#] //. sch, TKI[__], Factor] &, x == y] + ]; + +OperatorApplyB[x_ == y_] := + Block[{sch}, + sch = { + Schiebe[i_, "+"]^ni_. TBI[d_, {n15__}] :> + TBI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], + Schiebe[i_, "-"]^ni_. TBI[d_, {n15__}] :> + TBI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] + }; + Map[Collect[Expand[#] //. sch, TBI[__], Factor] &, x == y] + ]; + +OperatorApplyA[x_ == y_] := + Block[{sch}, + sch = { + Schiebe[i_, "+"]^ni_. TAI[d_, {n15__}] :> + TAI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], + Schiebe[i_, "-"]^ni_. TAI[d_, {n15__}] :> + TAI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] + }; + Map[Collect[Expand[#] //. sch, TAI[__], Factor] &, x == y] + ]; + +MassDerivative[STLI[any__, { {al_, m1_}, {be_, m2_}, {ga_, m3_}, {de_, m4_}, {ep_, m5_}}], {{0, d1_}, {0, d2_}, {0, d3_}, {0, d4_}, {0, d5_}}] := + Pochhammer[al, d1] Pochhammer[be, d2] Pochhammer[ga, d3] Pochhammer[de, d4] Pochhammer[ep, d5] * + STLI[any, {{al + d1, m1}, {be + d2, m2}, {ga + d3, m3}, {de + d4, m4}, {ep + d5, m5}}]; + +TarasovT[abrs__, qq_ /; Head[qq] =!= List] := + TarasovT[abrs, qq, {"g", "g", "g", "g", "g"}] + +TarasovT[r_, s_, qq_, {alp1_, alp2_, alp3_, alp4_, alp5_}] := + Block[{ al1, al2, al3, al4, al5, alrul, new, Q1, Q11, Q12, Q2, Q22, dum1, dum2, be1, be2, ga1, ga2, rho}, + + If[ alp1 === 0, + al1 = 0 + ]; + + If[ alp2 === 0, + al2 = 0 + ]; + + If[ alp3 === 0, + al3 = 0 + ]; + + If[ alp4 === 0, + al4 = 0 + ]; + + If[ alp5 === 0, + al5 = 0 + ]; + + alrul = Select[{ al1 :> I ParD[1], al2 :> I ParD[2], al3 :> I ParD[3], al4 :> I ParD[4], al5 :> I ParD[5]}, ! MatchQ[#, 0 :> _] &]; + + Q1 = al3 al5 + al4 al5 + al2 al3 + al3 al4; + Q2 = al4 al5 + al3 al5 + al1 al4 + al3 al4; + Q11 = 1/(-4) ( al2 + al4 + al5 ); + Q22 = 1/(-4) ( al1 + al3 + al5 ); + Q12 = 1/(-2) al5; + new = + I^(-r-s) ( D[ Exp[ I qq ( be1 Q1 + be2 Q2 + be1^2 Q11 + be2^2 Q22 + be1 be2 Q12 ) rho ], {be1, r}, {be2, s}] ) /. + Join[alrul, {be1 :> 0, be2 :> 0, rho :> -Pi^2/Pi^2 DPlus}]; + + Map[(Select[#, (FreeQ[#, ParD] && FreeQ[#, DPlus]) &] TpD[qq, Select[#, (! (FreeQ[#, ParD] && FreeQ[#, DPlus])) &]]) &, + (Expand[new, ParD] + dum1 dum2)] /. {dum1 :> 0, dum2 :> 0} + ]; + +TarasovT[r_, s_, pp_, dp_ /; Head[dp] =!= List] := + TarasovT[r, s, pp, dp, {"g", "g", "g", "g", "g"}] + +TarasovT[a_, b_, r_, s_, pp_, dp_, {alp1_, alp2_, alp3_, alp4_, alp5_}] := + Block[{al1, al2, al3, al4, al5, alrul, new, Q1, Q11, Q12, Q2, Q22, dum1, dum2, be1, be2, ga1, ga2, rho}, + + If[alp1 === 0, al1 = 0]; If[alp2 === 0, al2 = 0]; + If[alp3 === 0, al3 = 0]; If[alp4 === 0, al4 = 0]; + If[alp5 === 0, al5 = 0]; + + alrul = Select[{al1 :> I ParD[1], al2 :> I ParD[2], al3 :> I ParD[3], al4 :> I ParD[4], al5 :> I ParD[5]}, !(MatchQ[#1, 0 :> _]) &]; + + Q1 = al3 al5 + al4 al5 + al2 al3 + al3 al4; + Q2 = al4 al5 + al3 al5 + al1 al4 + al3 al4; + Q11 = -(1/4) (al2 + al4 + al5); Q22 = -(1/4) (al1 + al3 + al5); + Q12 = -(al5/2); + new = + I^(-r - s - a - b) * + D[Exp[I ((be1 pp + ga1 dp) Q1 + (be2 pp + ga2 dp) Q2 + be1 (be1 pp + 2 ga1 dp) Q11 + be2 (be2 pp + 2 ga2 dp) Q22 + (be1 be2 pp + (be1 ga2 + be2 ga1) dp) Q12) rho], + {be1, r}, {be2, s}, {ga1, a}, {ga2, b}] /. Join[alrul, {be1 :> 0, be2 :> 0, ga1 :> 0, ga2 :> 0, rho :> -((Pi^2 DPlus)/Pi^2)}]; + + (Select[#1, FreeQ[#1, ParD] && FreeQ[#1, DPlus] &] TpD[pp, Select[#1, ! (FreeQ[#1, ParD] && FreeQ[#1, DPlus]) &]] &) /@ (Expand[new] + dum1 dum2) /. + {dum1 :> 0, dum2 :> 0} + ]; + +ApplyTarasovT[tij_, exp_] := + Block[{dump}, + dump = Product[ParD[j]^dummy, {j, 5}]; + + Expand[tij exp] /. (STLI[de_, pp_, pe__List] TpD[_, DPlus^i_. t_]) :> + MassDerivative[STLI[ de /. de :> (de + 2 i), pp, pe], t dump /. Times -> List /. Power[_, n_] :> {0, n} /. dummy -> 0] + ]; + +Prefactor1 /: + Prefactor1[a_]^n_ := + Prefactor1[a^n]; + +MakeBoxes[Block, StandardForm] := + StyleBox["Block", FontSize -> 16, FontWeight -> "Bold", FontColor -> RGBColor[1, 0.2, 0.2]]; + +MakeBoxes[Cayley, StandardForm] := + StyleBox["Cayley", FontColor -> RGBColor[1, 0, 0.4]]; + +MakeBoxes[CayleyD, StandardForm] := + StyleBox["CayleyD", FontColor -> RGBColor[1, 0.2, 1]]; + +MakeBoxes[Cayleyu, StandardForm] := + StyleBox["Cayleyu", FontColor -> RGBColor[0.8, 0.8, 0.4]]; + +MakeBoxes[IFF, StandardForm] := + StyleBox["IFF", FontColor -> RGBColor[0.6, 0.4, 1]]; + +MakeBoxes[MakeFun, StandardForm] := + StyleBox["MakeFun", FontColor -> RGBColor[1, 0.6, 0.6]]; + +MakeBoxes[TFI, StandardForm] := + StyleBox["TFI", FontColor -> RGBColor[1, 0.6, 0]]; + +MakeBoxes[TFR, StandardForm] := + StyleBox["TFR", FontColor -> RGBColor[0, 0.6, 0]]; + +MakeBoxes[ToArgs, StandardForm] := + StyleBox["ToArgs", FontColor -> RGBColor[0.2, 0.6, 1]]; + +MakeBoxes[TVI, StandardForm] := + StyleBox["TVI", FontColor -> RGBColor[0.2, 0.4, 0.8]]; + +MakeBoxes[TVR, StandardForm] := + StyleBox["TVR", FontColor -> RGBColor[0.2, 0.8, 1]]; + +PQ[_Integer?Positive] := + True; + +PNQ[0] = + True; + +PNQ[_Integer?Positive] := + True; + +FactorC[z_] := + FactorC[z] = Factor[z] + +TFI[depp__, {a___, b_Integer, c___}] := + TFI[depp, {a, {b, 0}, c}]; + +TFI[depp__, {a___, {0, m_ /; m =!= 0}, b___}] := + TFI[depp, {a, {0, 0}, b}]; + +TFI[a__, {0, 0}, b__List] := TFI[a, b]; + +TFI[d_, pp_, _, {0, 0}, {x1_, x2_, x3_, x4_, x5_}, list_List] := + TFI[d, pp, {x1, x2, x3, x4, x5}, list]; + +TFI[d_, pp_, dp_, {a_, b_}, {0, 0, 0, 0, 0}, list_List] := + TFI[d, pp, dp, {a, b}, list]; + +TFI[d_, pp_, dp_ /; Head[dp] =!= List, {0, 0, 0, 0, 0}, list_List] := + TFI[d, pp, list]; + +TFI[d_, pp_, dp_ /; Head[dp] =!= List, list_List] := + TFI[d, pp, list]; + +TFI[d_, pp_, dp_ /; Head[dp] =!= List, {x1_, x2_, x3_, x4_, x5_}, list_List] := + TFI[d, pp, {x1, x2, x3, x4, x5}, list]; + +TFI[__, {{_, _}, {0, 0}, {_, _}, {0, 0}, {_, 0}}] := + 0; + +TFI[__, {{0, 0}, {_, _}, {0, 0}, {_, _}, {_, 0}}] := + 0; + +TFI[__, {{0, 0}, {_, _}, {_, 0}, {_, _}, {0, 0}}] := + 0; + +TFI[__, {{_, 0}, {_, _}, {0, 0}, {_, _}, {0, 0}}] := + 0; + +TFI[__, {{_, _}, {_, 0}, {_, _}, {0, 0}, {0, 0}}] := + 0; + +TFI[__, {{_, _}, {0, 0}, {_, _}, {_, 0}, {0, 0}}] := + 0; + +TFI[__, {{0, 0}, {0, 0}, {0, 0}, {_, 0}, {_, _}}] := + 0; + +TFI[__, {{0, 0}, {0, 0}, {_, 0}, {0, 0}, {_, _}}] := + 0; + +TFI[__, {{0, 0}, {_, 0}, {0, 0}, {0, 0}, {_, _}}] := + 0; + +TFI[__, {{_, 0}, {0, 0}, {0, 0}, {0, 0}, {_, _}}] := + 0; + +TFI[__, {{_, _}, {_, 0}, {0, 0}, {0, 0}, {0, 0}}] := + 0; + +TFI[__, {{_, 0}, {_, _}, {0, 0}, {0, 0}, {0, 0}}] := + 0; + +TFI[__, {{_, _}, {0, 0}, {0, 0}, {_, 0}, {0, 0}}] := + 0; + +TFI[__, {{_, 0}, {0, 0}, {0, 0}, {_, _}, {0, 0}}] := + 0; + +TFI[__, {{0, 0}, {_, 0}, {_, _}, {0, 0}, {0, 0}}] := + 0; + +TFI[__, {{0, 0}, {_, _}, {_, 0}, {0, 0}, {0, 0}}] := + 0; + +TFI[__, {{0, 0}, {0, 0}, {_, _}, {_, 0}, {0, 0}}] := + 0; + +TFI[__, {{0, 0}, {0, 0}, {_, 0}, {_, _}, {0, 0}}] := + 0; + +If[ $Notebooks, + + mbt[z_] := + ToBoxes[z, TraditionalForm]; + + redblue[z_ /; Head[z] =!= Plus] := + mbt[z]; + + redblue[(z_) - 1] := + StyleBox[mbt[z], FontColor -> RGBColor[1, 0, 0]]; + + redblue[(z_Subscript) - 2] := + StyleBox[SubscriptBox[OverscriptBox[z[[1]], "_"], z[[2]]], FontColor -> RGBColor[1, 0, 0]]; + + redblue[(z_) - 2] := + StyleBox[OverscriptBox[mbt[z], "_"], FontColor -> RGBColor[1, 0, 0]]; + + redblue[(z_) - 3] := + StyleBox[UnderscriptBox[OverscriptBox[mbt[z], "_"], "_"], FontColor -> RGBColor[1, 0, 0]]; + + redblue[(z_) + 1] := + StyleBox[mbt[z], FontColor -> RGBColor[0, 0, 1]]; + + redblue[(z_) + 2] := + StyleBox[OverscriptBox[mbt[z], "_"], FontColor -> RGBColor[0, 0, 1]]; + + redblue[(z_Subscript) + 2] := + StyleBox[SubscriptBox[OverscriptBox[z[[1]], "_"], z[[2]]], FontColor -> RGBColor[0, 0, 1]]; + + TFI /: + MakeBoxes[TFI[d_, pp_, {ur__}, {den__}], TraditionalForm] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", Rule[SingleLetterItalics, False], + Rule[FontWeight, "Bold"]], RowBox @@ {redblue /@ {den}}, + RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", ur}]], TFI[d, pp, {ur}, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, TraditionalForm]; + + TFI /: + MakeBoxes[TFI[d_, pp_, dp_, any__, {den__}], TraditionalForm] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", Rule[SingleLetterItalics, False], + Rule[FontWeight, "Bold"]], RowBox @@ {redblue /@ {den}}, RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", + Sequence @@ Flatten[{any}]}]], TFI[d, pp, dp, any, {den}], Editable -> True} + ) /; Head[dp] =!= List; + + TFI /: + MakeBoxes[TFI[dpp__, {den__}], TraditionalForm] := + ( + InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", Rule[SingleLetterItalics, False], Rule[FontWeight, "Bold"]], + RowBox @@ {redblue /@ {den}}, RowBox[{"(", ToBoxes[First[{dpp}], TraditionalForm], ")"}]], TFI[dpp, {den}], Editable -> True} + ) /; MemberQ[{StandardForm, TraditionalForm}, TraditionalForm] && Head[Last[{dpp}]] =!= List; +]; + + +TJI[de_, pp_, {{n1_Integer, m1_}, {n2_Integer, m2_}, {n3_Integer, m3_}}] := + ( + TJI[de, pp, {{n1, m1}, {n2, m2}, {n3, m3}}] = + TJI[de, pp, Reverse[Sort[{{n1, m1}, {n2, m2}, {n3, m3}}]]] + ) /; !OrderedQ[{{n3, m3}, {n2, m2}, {n1, m1}}]; + +TJI[_, 0, {{_, 0}, {_, 0}, {_, 0}}] := + 0 + +TBI[de_, pp_, {{n1_Integer, m1_}, {n2_Integer, m2_}}] := + ( + TJI[de, pp, {{n1, m1}, {n2, m2}}] = + TBI[de, pp, Reverse[Sort[{{n1, m1}, {n2, m2}}]]] + ) /; !OrderedQ[{{n2, m2}, {n1, m1}}]; + +TBI[_, 0, {{_, 0}, {_, 0}}] := + 0; + +TAI[_, _, {{_Integer, 0}}] := + 0; + +\[CapitalDelta]\[ScriptCapitalC] = + (-(1/2)) Det[{ + {0, 1, 1, 1, 1}, + {1, 0, Subscript[\[Mu], 6], Subscript[\[Mu], 4], Subscript[\[Mu], 3]}, + {1, Subscript[\[Mu], 6], 0, Subscript[\[Mu], 2], Subscript[\[Mu], 1]}, + {1, Subscript[\[Mu], 4], Subscript[\[Mu], 2], 0, Subscript[\[Mu], 5]}, + {1, Subscript[\[Mu], 3], Subscript[\[Mu], 1], Subscript[\[Mu], 5], 0}} +]; + +checkli = { + \[ScriptCapitalC] -> + \[CapitalDelta]\[ScriptCapitalC], + + Subscript[\[CapitalDelta], i_] :> + D[\[CapitalDelta]\[ScriptCapitalC], Subscript[\[Mu], i]], + + Subscript[\[Mu], 6] :> PP, + Subscript[\[Mu], i_] :> ToExpression[StringJoin["m", ToString[i]]]^2, + Subscript[m, 1] :> Sqrt[m1^2], + Subscript[m, 2] :> Sqrt[m2^2], Subscript[m, 3] :> Sqrt[m3^2], + Subscript[m, 4] :> Sqrt[m4^2], + Subscript[m, 5] :> Sqrt[m5^2], + + Subscript[\[CapitalDelta], i_, j_, k_] :> + Subscript[\[Mu], i]^2 + Subscript[\[Mu], j]^2 + Subscript[\[Mu], k]^2 - 2*(Subscript[\[Mu], i]*Subscript[\[Mu], j] + + Subscript[\[Mu], j]*Subscript[\[Mu], k] + Subscript[\[Mu], k]*Subscript[\[Mu], i]), + + Subscript[u, i_, j_, k_] :> + Subscript[\[Mu], i] - Subscript[\[Mu], j] - Subscript[\[Mu], k], + + Subscript[\[CapitalSigma], i_] :> + 3*d - 2*Sum[Subscript[\[Nu], j], {j, 1, i}] - 2, + + Subscript[\[Nu], 1] :> n1, + Subscript[\[Nu], 2] :> n2, + Subscript[\[Nu], 3] :> n3, + Subscript[\[Nu], 4] :> n4, + Subscript[\[Nu], 5] :> n5 +}; + + +Subscript[\[CapitalDelta], i_, j_, k_] := + Subscript[\[CapitalDelta], Sequence @@ Sort[{i, j, k}]] /; !OrderedQ[{i, j, k}]; + +ToArgs[z_] := + Expand[z //. checkli]; + +setd[hCayley[m1_, m2_, m3_, m4_, m5_, p_], set[hCayley[m1, m2, m3, m4, m5, p], + factor[ToArgs[\[ScriptCapitalC]] /. PP -> p^2]] +] /. { hCayley :> Cayley, setd :> SetDelayed, set :> Set, factor :> Factor}; + +Do[ setd[hCayley[i][{m1_, m2_, m3_, m4_, m5_, p_}], + set[hCayley[i][{m1, m2, m3, m4, m5, p}], + factor[ToArgs[Subscript[\[CapitalDelta], i]] /. PP -> p^2]]] /. { + hCayley :> Cayley, setd :> SetDelayed, set :> Set, factor :> Factor}, {i, 6} +]; + + +Cayley[i_, j_, k_][m_List] := + Cayley[i, j, k][m] = + Block[{mm = m}, + While[ + Length[mm] < 7, + AppendTo[mm, Last[mm]] + ]; + + FactorC[mm[[i]]^4 - 2*mm[[j]]^2*mm[[i]]^2 - 2*mm[[k]]^2*mm[[i]]^2 + mm[[j]]^4 + mm[[k]]^4 - 2*mm[[j]]^2*mm[[k]]^2] + ]; + +Cayleyu[i_, j_, k_][m_List] := + Cayleyu[i, j, k][mm] = + Block[{mm = m}, + While[ + Length[mm] < 7, + AppendTo[mm, Last[mm]] + ]; + + FactorC[mm[[i]]^2 - mm[[j]]^2 - mm[[k]]^2] + ]; + +Do[setd[hCayleyD[i][{m1_, m2_, m3_, m4_, m5_, p_}], + set[hCayleyD[i][{m1, m2, m3, m4, m5, p}], + factor[(ToArgs[Subscript[\[CapitalDelta], i]] /. PP -> p^2)/\[ScriptCapitalC][m1, m2, m3, m4, m5, p]]]] /. + {hCayleyD :> CayleyD, setd :> SetDelayed, set :> Set, factor :> Factor, \[ScriptCapitalC] :> Cayley}, {i, 6} +]; + +setd[hCayleyD[1, 2, 5][{m1_, m2_, m3_, m4_, m5_, p_}], + set[hCayleyD[1, 2, 5][{m1, m2, m3, m4, m5, p}], + factor[(ToArgs[Subscript[\[CapitalDelta], 1, 2, 5]] /. PP -> p^2)/\[ScriptCapitalC][m1, m2, m3, m4, m5, p]]] +] /. {hCayleyD :> CayleyD, setd :> SetDelayed, set :> Set, factor :> Factor, \[ScriptCapitalC] :> Cayley}; + +setd[hCayleyD[1, 3, 6][{m1_, m2_, m3_, m4_, m5_, p_}], + set[hCayleyD[1, 3, 6][{m1, m2, m3, m4, m5, p}], + factor[(ToArgs[Subscript[\[CapitalDelta], 1, 3, 6]] /. PP -> p^2)/\[ScriptCapitalC][m1, m2, m3, m4, m5, p]]] +] /. {hCayleyD :> CayleyD, setd :> SetDelayed, set :> Set, factor :> Factor, \[ScriptCapitalC] :> Cayley}; + +setd[hCayleyD[3, 4, 5][{m1_, m2_, m3_, m4_, m5_, p_}], + set[hCayleyD[3, 4, 5][{m1, m2, m3, m4, m5, p}], + factor[(ToArgs[Subscript[\[CapitalDelta], 3, 4, 5]] /. PP -> p^2)/\[ScriptCapitalC][m1, m2, m3, m4, m5, p]]] +] /. {hCayleyD :> CayleyD, setd :> SetDelayed, set :> Set, factor :> Factor, \[ScriptCapitalC] :> Cayley}; + +nutonandDelta[w_, 5] := + w /. { + Subscript[\[Nu], 1] :> n1, + Subscript[\[Nu], 2] :> n2, + Subscript[\[Nu], 3] :> n3, + Subscript[\[Nu], 4] :> n4, + Subscript[\[Nu], 5] :> n5, + Subscript[\[CapitalDelta], ijk__] :> \[ScriptCapitalC]*cD[ijk], + Subscript[u, ijk__] :> cu[ijk], + Subscript[D, ijk__] :> TA[D, ijk], + Subscript[\[Rho], ijk__] :> TA[\[Rho], ijk], + Subscript[\[Phi], ijk__] :> TA[\[Phi], ijk], + Subscript[\[Sigma], i_, j_, k_] :> TA[\[Sigma], d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], Subscript[\[Nu], k]], + Subscript[h, i_, j_, k_] :> TA[h, d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], Subscript[\[Nu], k]], + Subscript[S, i_, j_, k_] :> TA[S, d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], Subscript[\[Nu], k]], + Subscript[\[CapitalSigma], i_] :> ToArgs[Subscript[\[CapitalSigma], i]]} /. { + + Subscript[\[Nu], 1] :> n1, + Subscript[\[Nu], 2] :> n2, + Subscript[\[Nu], 3] :> n3, + Subscript[\[Nu], 4] :> n4, + Subscript[\[Nu], 5] :> n5, + Subscript[m, 1] :> m1, + Subscript[m, 2] :> m2, + Subscript[m, 3] :> m3, + Subscript[m, 4] :> m4, + Subscript[m, 5] :> m5 + }; + +nutonandDelta[w_] := + w /. { + Subscript[\[Nu], 1] :> n1, + Subscript[\[Nu], 2] :> n2, + Subscript[\[Nu], 3] :> n3, + Subscript[\[Nu], 4] :> n4, + Subscript[\[Nu], 5] :> n5, + Subscript[\[CapitalDelta], ijk__] :> cD[ijk], + Subscript[u, ijk__] :> cu[ijk], + Subscript[D, ijk__] :> TA[D, ijk], + Subscript[\[Rho], ijk__] :> TA[\[Rho], ijk], + Subscript[\[Phi], ijk__] :> TA[\[Phi], ijk], + Subscript[\[Sigma], i_, j_, k_] :> TA[\[Sigma], d, i, j, k, Subscript[\[Nu], i], + Subscript[\[Nu], j], Subscript[\[Nu], k]], + Subscript[h, i_, j_, k_] :> TA[h, d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], Subscript[\[Nu], k]], + Subscript[S, i_, j_, k_] :> TA[S, d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], + Subscript[\[Nu], k]], + Subscript[\[CapitalSigma], i_] :> ToArgs[Subscript[\[CapitalSigma], i]]} /. { + + Subscript[\[Nu], 1] :> n1, + Subscript[\[Nu], 2] :> n2, + Subscript[\[Nu], 3] :> n3, + Subscript[\[Nu], 4] :> n4, + Subscript[\[Nu], 5] :> n5, + Subscript[m, 1] :> m1, + Subscript[m, 2] :> m2, + Subscript[m, 3] :> m3, + Subscript[m, 4] :> m4, + Subscript[m, 5] :> m5 + }; + +addPeP[TFR[d_, pp_, li1_, rest_]] := + TFR[d, pp, li1, rest]; + +addPeP[TFI[d_, pp_, li1_List]] := + TFI[d, pp, li1]; + +addPeP[TFR[d_, pp_, dp_Symbol, li1_, rest_]] := + TFR[d, pp, dp, li1, rest]; + +addPeP[TFI[d_, pp_, dp_Symbol, li1_List]] := + TFI[d, pp, dp, li1]; + +addPeP[TVI[d_, pp_, li1_List]] := + TVI[d, pp, li1]; + +(* TODO ??? *) +nnnnnaddPeP[(any_)[d_, pp_, li1_List, rest__List]] := + any[d, pp, li1, rest] /; any =!= List + +addPeP[z_List] := Append[z, Sqrt[PP]]; + +addPeP[TFI[d_, z_List]] := + TFI[d, PP, z]; + +addPeP[TVI[d_, z_List]] := + TVI[d, PP, z]; + +addPeP[TJI[d_, z_List]] := + TJI[d, PP, z]; + +addPeP[TFR[d_, z_List]] := + TFR[d, PP_, z]; + +addPeP[TFR[d_, pl_List, z_List]] := + TFR[d, PP_, pl, z]; + +addPeP[TVR[d_, z__List]] := + TVR[d, PP_, z]; + +addPeP[TJR[d_, z__List]] := + TJR[d, PP_, z]; + +nutomass[w_] := + w /. { + Subscript[\[Nu], 1] + (i1_.) :> {n1 + i1, m1}, + Subscript[\[Nu], 2] + (i2_.) :> {n2 + i2, m2}, + Subscript[\[Nu], 3] + (i3_.) :> {n3 + i3, m3}, + Subscript[\[Nu], 4] + (i4_.) :> {n4 + i4, m4}, + Subscript[\[Nu], 5] + (i5_.) :> {n5 + i5, m5}} /. + {in1_Integer, in2_Integer, in3_Integer, in4_Integer} :> {{in1, m1}, {in2, m2}, {in3, m3}, {in4, m4}} /. + {in1_Integer, in2_Integer, in3_Integer} :> {{in1, m1}, {in2, m2}, {in3, m3}}; + +Clear[maybeF]; + +maybeF[z_Times] := + FactorC[z] /; FreeQ[z, TFI] && FreeQ[z, TVI] && FreeQ[z, TJI] && Length[Cases[z, cD[__], -1]] > 1; + +maybeF[z_] := z; + +SetAttributes[top, Listable]; +SetAttributes[IFF, HoldAll]; + +Clear[MakeFun]; + +MakeFun[(c_.) TFI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := + Block[{nm, nmrel, setdel, pat, blank, pattern, patternTest, identitL}, + nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; + HoldForm @@ {setdel[ + addPeP[TFR @@ top /@ nutomass[{t}]] /. nmrel, + Hold[Condition][Hold[CompoundExpression][ + Hold[TComment][eqn, addPeP[nutomass[TFR[t]]] /. + TFR -> TFIC /. {Pattern :> pat, Blank :> blank} /. pat[PP, blank[]] :> PP /. nmrel], + + Collect[ TT = Expand3[nutonandDelta[(1/c) (rhs /. TFI[te__] :> addPeP[nutomass[TFI[te]]]), 5]], + TFI[__], maybeF[(Collect[Numerator[#1], cD[__], Factor]/Collect[Denominator[#1], cD[__], Factor] & ) /@ + Factor[#1]] & ] /. nmrel + ], + + nutonandDelta[IFF[conds], 5]]] /. top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. + patternTest[pattern[dm_ /; MemberQ[{d, PP, DP, m1, m2, m3, m4, m5}, dm], blank[]], _] :> + pattern[dm, blank[]] /. {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. + cD[ijk__] -> Hold[CayleyD[ijk]][addPeP[BLA = nutomass[Last[{t}]] /. nmrel /. {_, ma_} :> ma]] /. + addPeP -> Identity /. Hold[CompoundExpression] -> CompoundExpression /. Hold[Condition][a_, IFF[b_]] -> a /; b /. + Hold[Set] -> Set /. Hold[TComment] -> TComment /. Hold[CayleyD[ijk__]] -> CayleyD[ijk] /. {setdel :> SetDelayed} /. + Identity -> identit /. identit[a_] -> a + ]; + +MakeFun[(c_.) TFI[t__] == (rhs_), eqn_String, mrel_: {}] := + Block[{nm, nmrel, setdel, pat, blank, pattern, patternTest, identit}, + nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; + + HoldForm @@ {setdel[ + addPeP[TFR @@ top /@ nutomass[{t}]] /. nmrel, + + Hold[CompoundExpression][Hold[TComment][eqn, addPeP[nutomass[TFR[t]]] /. TFR -> TFIC /. {Pattern :> pat, Blank :> blank} /. + pat[PP, blank[]] :> PP /. nmrel], + Collect[TT = Expand3[nutonandDelta[(1/c)*(rhs /. TFI[te__] :> addPeP[nutomass[TFI[te]]])]], TFI[__], + maybeF[(Collect[Numerator[#1], cD[__], Factor] / Collect[Denominator[#1], cD[__], Factor] & ) /@ Factor[#1]] & ] /. nmrel] + ] /. top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. + patternTest[ pattern[dm_ /; MemberQ[{d, PP, DP, m1, m2, m3, m4, m5}, dm], blank[]], _] :> pattern[dm, blank[]] /. + {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. + cD[ijk__] -> Hold[CayleyD[ijk]][addPeP[nutomass[Last[{t}]] /. addPeP -> Identity /. nmrel /. + {nuu_, ma_} :> ma]] /. Hold[CompoundExpression] -> CompoundExpression /. Hold[Condition][a_, IFF[b_]] -> a /; b /. + Hold[Set] -> Set /. Hold[TComment] -> TComment /. Hold[CayleyD[ijk__]] -> CayleyD[ijk] /. {setdel :> SetDelayed} /. + addPeP -> Identity /. Identity -> identit /. identit[a_] -> a + ] /; Head[mrel] =!= IFF; + +MakeFun[(c_.) TVI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := + Block[{nm, nmrel, setdel, pat, blank, pattern, patternTest, identit}, + nmrel = + Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; + + nmrel = + Join[nmrel, { + Subscript[m, 1] :> m1, + Subscript[m, 2] :> m2, + Subscript[m, 3] :> m3, + Subscript[m, 4] :> m4, + Subscript[\[CapitalSigma], i_] :> + ToArgs[Subscript[\[CapitalSigma], i]]} + ]; + HoldForm @@ {setdel[ + addPeP[TVR @@ top /@ nutomass[{t}]] /. nmrel, + + Hold[Condition][Hold[CompoundExpression][Hold[TComment][eqn, addPeP[nutomass[TVR[t]]] /. + TVR -> TVIC /. {Pattern :> pat, Blank :> blank} /. pat[PP, blank[]] :> PP /. nmrel], + + Collect[TT = Expand3[nutonandDelta[(1/c) (rhs /. TVI[te__] :> addPeP[nutomass[TVI[te]]])]], + TVI[__], maybeF[(Collect[Numerator[#1], cu[__], Factor]/ Collect[Denominator[#1], cu[__], Factor] & ) /@ + Factor[#1]] & ] /. \[ScriptCapitalC] -> 1 /. nmrel], nutonandDelta[IFF[conds]]] + ] /. + top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. + patternTest[pattern[dm_ /; MemberQ[{d, PP, m1, m2, m3, m4}, dm], blank[]], _] :> + pattern[dm, blank[]] /. {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. + HoldPattern[TA[aijk__]] -> Hold[TA[aijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_} :> ma]] /. + cD[ijk__] -> Hold[Cayley[ijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_} :> ma]] /. cu[ijk__] -> + Hold[Cayleyu[ijk]][addPeP[nutomass[Last[{t}]] /. addPeP -> Identity /. nmrel /. {_, ma_} :> ma]] /. + Hold[CompoundExpression] -> CompoundExpression /. Hold[Condition][a_, IFF[b_]] -> a /; b /. Hold[Set] -> Set /. + Hold[TComment] -> TComment /. addPeP -> Identity /. Hold[Cayleyu[ijk__]] -> Cayleyu[ijk] /. + Hold[Cayley[ijk__]] -> Cayley[ijk] /. Hold[TA] -> TA /. {setdel :> SetDelayed} /. Identity -> identit /. identit[a_] -> a + ]; + +MakeFun[(c_.) TVI[t__] == (rhs_), eqn_String, mrel_: {}] := + Block[{nm, nmrel, setdel, pat, blank, pattern, patternTest}, + nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; + + nmrel = Join[nmrel, { + Subscript[m, 1] :> m1, + Subscript[m, 2] :> m2, + Subscript[m, 3] :> m3, + Subscript[m, 4] :> m4, + Subscript[\[CapitalSigma], i_] :> ToArgs[Subscript[\[CapitalSigma], i]]}]; + + HoldForm @@ {setdel[ + addPeP[TVR @@ top /@ nutomass[{t}]] /. nmrel, + + Hold[CompoundExpression][Hold[TComment][eqn, addPeP[nutomass[TVR[t]]] /. + TVR -> TVIC /. {Pattern :> pat, Blank :> blank} /. pat[PP, blank[]] :> PP /. nmrel], + + Collect[TT = Expand3[nutonandDelta[(1/c)*(rhs /. TVI[te__] :> addPeP[nutomass[TVI[te]]])]], + TVI[__], maybeF[(Collect[Numerator[#1], cu[__], Factor]/ Collect[Denominator[#1], cu[__], Factor] & ) /@ + Factor[#1]] & ] /. nmrel /. \[ScriptCapitalC] -> 1] + ] /. + top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. + patternTest[pattern[dm_ /; MemberQ[{d, PP, m1, m2, m3, m4}, dm], blank[]], _] :> pattern[dm, blank[]] /. + {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. cD[ijk__] -> + Hold[Cayley[ijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {nuu_, ma_Symbol} :> ma]] /. + cu[ijk__] -> Hold[Cayleyu[ijk]][addPeP[nutomass[Last[{t}]] /. + nmrel /. {nuu_, ma_Symbol} :> ma]] /. Hold[CompoundExpression] -> CompoundExpression /. + Hold[Set] -> Set /. Hold[TComment] -> TComment /. addPeP -> Identity /. Hold[Cayleyu[ijk__]] -> Cayleyu[ijk] /. + Hold[Cayley[ijk__]] -> Cayley[ijk] /. {setdel :> SetDelayed} /. Identity -> identit /. identit[a_] -> a + ] /; Head[mrel] =!= IFF; + +MakeFun[(c_.) TJI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := + Block[{nm, nmrel, result, setdel, pat, blank, pattern, patternTest, tT}, + + \[ScriptCapitalC] = 1; + + nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; + + nmrel = + Join[nmrel, { + Subscript[m, 1] :> m1, + Subscript[m, 2] :> m2, + Subscript[m, 3] :> m3, + Subscript[m, 4] :> m4, + Subscript[\[CapitalSigma], i_] :> + ToArgs[Subscript[\[CapitalSigma], i]]} + ]; + + result = + HoldForm @@ {setdel[ + addPeP[TJR @@ top /@ nutomass[{tT = t}]] /. nmrel, + + Hold[Condition][Hold[CompoundExpression][Hold[TComment][eqn, addPeP[nutomass[TJR[t]]] /. TJR -> TJIC /. + {Pattern :> pat, Blank :> blank} /. pat[PP, blank[]] :> PP /. nmrel], + TJ = Collect[ TT = Expand3[nutonandDelta[(1/c) (rhs /. TJI[te__] :> addPeP[nutomass[TJI[te]]])]], TJI[__], + maybeF[(Collect[Numerator[#1], cu[__], Factor]/Collect[Denominator[#1], cu[__], Factor] & ) /@ Factor[#1]] & ] /. + \[ScriptCapitalC] -> 1 /. nmrel], nutonandDelta[IFF[conds]]] + ] /. + top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. + patternTest[pattern[dm_ /; MemberQ[{d, PP, m1, m2, m3, m4}, dm], blank[]], _] :> + pattern[dm, blank[]] /. {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. + HoldPattern[TA[aijk__]] -> Hold[TA][aijk][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_} :> ma]] /. cD[ijk__] -> + Hold[Cayley[ijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_Symbol} :> ma]] /. cu[ijk__] -> + Hold[Cayleyu[ijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_Symbol} :> ma]] /. + Hold[CompoundExpression] -> CompoundExpression /. Hold[Condition][a_, IFF[b_]] -> a /; b /. + Hold[Set] -> Set /. Hold[TComment] -> TComment /. Hold[Cayleyu[ijk__]] -> Cayleyu[ijk] /. + Hold[Cayley[ijk__]] -> Cayley[ijk] /. Hold[TA] -> TA /. {setdel :> SetDelayed}; \[ScriptCapitalC] =. ; + + result + ]; + +SetAttributes[paTT, HoldFirst]; + +MakeFun[(c_.) TKI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := + MakeFun[c TJI[t] == rhs /. TKI -> TJI, eqn, IFF[conds], mrel] /. + {PP :> 0, Sqrt[PP] :> 0, Pattern :> paTT} /. paTT[0, _] -> 0 /. paTT -> Pattern /. TJIC[d_, li_List] :> TJIC[d, 0, li]; + +MakeFun[(c_.) TBI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := + MakeFun[c TJI[t] == rhs /. TBI -> TJI, eqn, IFF[conds], mrel] /. + {TJI :> TBI, TJR :> TBR, TJIC :> TBIC}; + +MakeFun[(c_.) TAI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := + MakeFun[c TJI[t] == rhs /. TAI -> TJI, eqn, IFF[conds], mrel] /. {TJI :> TAI, TJR :> TAR, TJIC :> TAIC}; + +Interchange[z_, (i_) \[LeftRightArrow] (j_)] := + nuExplicit[z] /. { + + Subscript[\[Nu], i] :> Subscript[\[Nu], j], + Subscript[\[Nu], j] :> Subscript[\[Nu], i], + Subscript[m, i] :> Subscript[m, j], + Subscript[m, j] :> Subscript[m, i], + Subscript[\[CapitalDelta], ij__] :> + Subscript[\[CapitalDelta], ij] /. {i :> j, j :> i}, + Subscript[u, ij__] :> (Subscript[u, ij] /. {i :> j, j :> i}), + Subscript[h, ij__] :> (Subscript[h, ij] /. {i :> j, j :> i}), + Subscript[\[Phi], ij__] :> (Subscript[\[Phi], ij] /. {i :> j, j :> i}), + Subscript[\[Rho], ij__] :> (Subscript[\[Rho], ij] /. {i :> j, j :> i}), + Subscript[\[Sigma], ij__] :> (Subscript[\[Sigma], ij] /. {i :> j, j :> i}), + Subscript[D, ij__] :> (Subscript[D, ij] /. {i :> j, j :> i})} /. { + + TFI[depp__, args_List] :> TFI[depp, Sort[args]] /; ! OrderedQ[args], + TVI[depp__, args_List] :> TVI[depp, Sort[args]] /; ! OrderedQ[args], + TJI[depp__, args_List] :> TJI[depp, Sort[args]] /; ! OrderedQ[args], + TBI[depp__, args_List] :> TBI[depp, Sort[args]] /; ! OrderedQ[args] + }; + +Interchange[z_, (i_) \[LeftRightArrow] (j_), vw__] := + Interchange[Interchange[z, i \[LeftRightArrow] j], vw]; + +Interchange[z_, {(i_) \[LeftRightArrow] (j_)}] := + Interchange[Interchange[z, i \[LeftRightArrow] j]]; + +Interchange[z_, {(i_) \[LeftRightArrow] (j_), vw__}] := + Interchange[Interchange[z, i \[LeftRightArrow] j], vw]; + + +nuExplicit[z_] := + z /. + Subscript[\[CapitalSigma], i_] :> + Expand[3*d - 2 - 2*Sum[Subscript[\[Nu], j], {j, 1, i}]] /. { + + Subscript[\[Sigma], i_, j_, k_] :> + (-(1/4))*(d - Subscript[\[Nu], i] - 2*Subscript[\[Nu], j])*Subscript[\[Phi], i, j, k] - + (1/4)*(d - 2*Subscript[\[Nu], i] - Subscript[\[Nu], j])*Subscript[\[Phi], j, i, k] - + (1/4)*(2*d - 2*Subscript[\[Nu], i] - 2*Subscript[\[Nu], j] - Subscript[\[Nu], k] - 1)*Subscript[\[Phi], k, i, j], + + Subscript[h, i_, j_, k_] :> + (-(1/2))*(d - 2*Subscript[\[Nu], j] - Subscript[\[Nu], k])*Subscript[m, k]^2* + Subscript[\[Phi], i, j, k] - (1/2)*(2*d - Subscript[\[Nu], i] - 2*Subscript[\[Nu], j] - + 2*Subscript[\[Nu], k] - 1)*Subscript[m, i]^2*Subscript[\[Phi], k, i, j] + (d - Subscript[\[Nu], j] - + 2*Subscript[\[Nu], k]) Subscript[\[Rho], i, j, k], + Subscript[S, i_, j_, k_] :> + (-(d - 2*Subscript[\[Nu], j] - Subscript[\[Nu], k])) Subscript[m, k]^2* + Subscript[\[Phi], j, i, k] - (d - Subscript[\[Nu], j] - 2*Subscript[\[Nu], k])* + Subscript[m, j]^2 Subscript[\[Phi], k, i, j] + 2*(2*d - Subscript[\[Nu], i] - 2*Subscript[\[Nu], j] - + 2*Subscript[\[Nu], k] - 1)*Subscript[\[Rho], i, j, k] + }; + +MakeBoxes[TA[a_, ___Symbol, ijk___Integer][__], _] := + SubscriptBox[a, RowBox[{ijk}]] + +MakeBoxes[TA[a_, ___Symbol, ijk___Integer, ___Symbol][__], _] := + SubscriptBox[a, RowBox[{ijk}]] + +TA[args__][mar_List] := + TA[args][mar] = ta[args][mar]; + +ta[D, i_Integer, j_Integer, k_Integer][{em__}] := + With[ + {q = Last[{em}], mi = {em}[[i]], mj = {em}[[j]], mk = {em}[[k]]}, + + Factor[ + q^8 - 4*q^6*(mi^2 + mj^2 + mk^2) + q^4*(6*(mi^4 + mj^4 + mk^4) + 4*(mi^2*mj^2 + mk^2*mi^2 + mk^2*mj^2)) - + 4*q^2*(mi^6 + mj^6 + mk^6 - mi^2*(mj^4 + mk^4) - mj^2*(mi^4 + mk^4) - mk^2*(mi^4 + mj^4) + + 10*mi^2*mj^2*mk^2) + Cayley[i, j, k][{em}]^2 + ] + ]; + +ta[\[Rho], i_Integer, j_Integer, k_Integer][{em__}] := + With[ + {q = Last[{em}], mi = {em}[[i]], mj = {em}[[j]], mk = {em}[[k]]}, + + Factor[ + -q^6 + 3*q^4*(mi^2 + mj^2 + mk^2) - q^2*(3*(mi^4 + mj^4 + mk^4) + + 2*(mi^2*mj^2 + mk^2*mi^2 + mk^2*mj^2)) + (mi^6 + mj^6 + + mk^6 - mi^2*(mj^4 + mk^4) - mj^2*(mi^4 + mk^4) - mk^2*(mi^4 + mj^4) + 10*mi^2*mj^2*mk^2)] + ]; + +ta[\[Phi], i_Integer, j_Integer, k_Integer][{em__}] := + With[ + {q = Last[{em}], mi = {em}[[i]], mj = {em}[[j]], mk = {em}[[k]]}, + + 4*Factor[q^4 + 2*q^2*(mi^2 - mj^2 - mk^2) + (mj^2 - mk^2)^2 + mi^2*(2*mj^2 + 2*mk^2 - 3*mi^2)] + ]; + +ta[\[Sigma], d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer][{em__}] := + Factor[ + (-(1/4))*(d - \[Nu]i - 2*\[Nu]j)* + TA[\[Phi], i, j, k][{em}] - (1/4)*(d - 2*\[Nu]i - \[Nu]j)* + TA[\[Phi], j, i, k][{em}] - (1/4)*(2*d - 2*\[Nu]i - 2*\[Nu]j - \[Nu]k - 1)*TA[\[Phi], k, i, j][{em}] + ]; + +ta[h, d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer][{em__}] := + With[ + {mk = {em}[[k]]}, + + Factor[ + (-(1/2))*(d - 2*\[Nu]j - \[Nu]k)*mk^2* + TA[\[Phi], i, j, k][{em}] - (1/2)*(2*d - \[Nu]i - 2*\[Nu]j - 2*\[Nu]k - 1)*mi^2* + TA[\[Phi], k, i, j][{em}] + (d - \[Nu]j - 2 \[Nu]k) TA[\[Rho], i, j, k][{em}] + ] + ]; + +ta[S, d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer][{em__}] := + With[ + {mj = {em}[[j]], mk = {em}[[k]]}, + + Factor[ + (-(d - 2*\[Nu]j - \[Nu]k))*mk^2* TA[\[Phi], j, i, k][{em}] - (d - \[Nu]j - 2*\[Nu]k)*mj^2* + TA[\[Phi], k, i, j][{em}]*test* + test*2*(2*d - \[Nu]i - 2*\[Nu]j - 2*\[Nu]k - 1)* + TA[\[Rho], i, j, k][{em}] + ] + ]; + +TVIKernel[d_, PP, lis_] := + (-PP)^(d - n1 - n2 - n3 - n4)*(m1^2/(-PP))^s1*(m2^2/(-PP))^s2*(m3^2/(-PP))^s3*(m4^2/(-PP))^s4*TVIpsi[d, lis /. {m1 -> s1, m2 -> s2, m3 -> s3, m4 -> s4}]; + +TVIPsi[d_, {{n1_, s1_}, {n2_, s2_}, {n3_, s3_}, {n4_, s4_}}] := + (-1)^(n1 + n2 + n3 + n4 + 1)*((gamma[-s1]*gamma[d/2 - n1 - s1])/gamma[n1])* + ((gamma[-s2]*gamma[d/2 - n2 - s2])/gamma[n2])* + ((gamma[-s3]*gamma[d/2 - n3 - s3])/gamma[n3])* + ((gamma[-s4]*gamma[n4 + s4])/gamma[n4])* + (gamma[n1 + n2 + n3 + n4 + s1 + s2 + s3 + s4 - d]/gamma[3*(d/2) - n1 - n2 - n3 - n4 - s1 - s2 - s3 - s4])* + (gamma[n1 + n3 + s1 + s3 - d/2]/gamma[n1 + n3 + n4 + s1 + s3 + s4 - d/2])* + (gamma[d - n1 - n3 - n4 - s1 - s3 - s4]/gamma[d - n1 - n3 - s1 - s3]); + +CheckTVIRecursion[expr_] := + If[ $CheckRecursion === True, + + Block[{rel, kern, nkern, z1, z2, z3, z4}, + rel = Extract[expr /. TVIC -> TVIkernel, {1, 2, 1, 1, 2}] - + Extract[expr /. TVI -> TVIkernel, {1, 2, 1, 2}]; + + If[ {TVIkernel} === Union[Head /@ Cases[rel, (ff_)[__] /; Context[ff] =!= "System`", 4]], + rel = Collect[Numerator[Together[rel]], TVI[__], Factor]; + kern = rel /. TVIkernel -> TVIKernel; + + kern = kern /. {PP -> -1, m1 -> Sqrt[z1], m2 -> Sqrt[z2], m3 -> Sqrt[z3], m4 -> Sqrt[z4]}; kern = PowerExpand[kern]; + kern = Expand[kern]; + + kern = kern /. {z1^(s1 + (w1_.))*z2^(s2 + (w2_.))*z3^(s3 + (w3_.))*z4^(s4 + (w4_.))*(fac_) :> (fac /. { + s1 -> s1 - w1, s2 -> s2 - w2, s3 -> s3 - w3, s4 -> s4 - w4})}; + + kern = kern /. TVIpsi -> TVIPsi /. {gamma[zz_] :> gamma[Expand[zz]]} /. {gamma[(zz_) + (nn_Integer)] :> + gamma[zz] Pochhammer[zz, nn]}; + + kern = kern /. {gamma[_] :> 1}; + + kern = kern /. {(-1)^((_) + (ww_Integer)) :> (-1)^ww} /. {(-1)^(_) :> 1}; + + nkern = Table[kern /. Thread[{d, n1, n2, n3, n4, s1, s2, s3, s4} -> Table[Random[], {9}]], {3}]; + nkern, + + Print["Matching Error"] + ] + ], + + If[$Notebooks, FCPrint[1,"Off"]] + ]; + +TJIKernel[d_, PP, lis_] := + (-PP)^(d - n1 - n2 - n3) (m1^2/(-PP))^s1 (m2^2/(-PP))^s2*(m3^2/(-PP))^s3 TJIpsi[d, lis /. {m1 -> s1, m2 -> s2, m3 -> s3}]; + +TJIPsi[d_, {{n1_, s1_}, {n2_, s2_}, {n3_, s3_}}] := + Evaluate[TVIPsi[d, {{n1, s1}, {n2, s2}, {n3, s3}, {0, 0}}]/gamma[0]]; + +Clear[CheckTJIRecursion]; + +CheckTJIRecursion[expr_] := + If[$CheckRecursion === True, + Block[ {rel, kern, nkern, z1, z2, z3}, + rel = Extract[expr /. TJIC -> TJIkernel, {1, 2, 1, 1, 2}] - Extract[expr /. TJI -> TJIkernel, {1, 2, 1, 2}]; + REL = rel; + If[{TJIkernel} === Union[Head /@ Cases[rel, (ff_)[__] /; Context[ff] =!= "System`", 4]], + rel = Collect[Numerator[Together[rel]], TJI[__], Factor]; + kern = rel /. TJIkernel -> TJIKernel; + kern = kern /. {PP -> -1, m1 -> Sqrt[z1], m2 -> Sqrt[z2], m3 -> Sqrt[z3]}; + kern = PowerExpand[kern]; + kern = Expand[kern]; + kern = kern /. {z1^(s1 + (w1_.)) z2^(s2 + (w2_.))*z3^(s3 + (w3_.)) (fac_) :> (fac /. {s1 -> s1 - w1, s2 -> s2 - w2, s3 -> s3 - w3})}; + kern = kern /. TJIpsi -> TJIPsi /. {gamma[zz_] :> gamma[Expand[zz]]} /. {gamma[(zz_) + (nn_Integer)] :> gamma[zz] Pochhammer[zz, nn]}; + kern = kern /. {gamma[_] :> 1}; + kern = kern /. {(-1)^((_) + (ww_Integer)) :> (-1)^ww} /. {(-1)^(_) :> 1}; + nkern = Table[ kern /. Thread[{d, n1, n2, n3, s1, s2, s3} -> Table[Random[], {7}]], {3}]; + nkern, + + Print["Matching Error"]] + ], + + If[$Notebooks, FCPrint[1,"Off"]] + ]; + +TFR[d_, pp_, {{n1_, m1_}, {n2_, m2_}, {0, 0}, {0, 0}, {0, 0}}] := + TAI[d, pp, {{n1, m1}}]*TAI[d, {{n2, m2}}]; + +Subscript[e, 35] = + 2*Subscript[\[Nu], 1]*\[ScriptCapitalC]*Schiebe[1, "+"]* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == + ( + (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - Subscript[\[Nu], 5])*Subscript[\[CapitalDelta], 1] + + Subscript[\[CapitalDelta], 3, 4, 5]*(Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[2, "-"] - Schiebe[1, "-"]) - + Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"]) + Subscript[\[CapitalDelta], 2]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*(Schiebe[5, "-"] - Schiebe[2, "-"]) + + Subscript[\[Nu], 3]*Schiebe[3, "+"]*(Schiebe[5, "-"] - Schiebe[4, "-"]) + Subscript[\[Nu], 5] - Subscript[\[Nu], 1]) + + Subscript[\[CapitalDelta], 6]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*Schiebe[3, "-"] + + Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"]) + Subscript[\[Nu], 3] - Subscript[\[Nu], 1]) + ) * TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; + +Subscript[s, 35] = + OperatorApplyF[Subscript[e, 35]]; + +Subscript[h, 351] = + Subscript[s, 35] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 351] = +MakeFun[Subscript[h, 351], "(35_1)", IFF[Subscript[\[Nu], 1] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; + +Subscript[f, 352] = +MakeFun[Interchange[Subscript[h, 351], 1 \[LeftRightArrow] 2, 3 \[LeftRightArrow] 4], "(35_2)", + IFF[Subscript[\[Nu], 2] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; + +Subscript[f, 353] = +MakeFun[Interchange[Subscript[h, 351], 1 \[LeftRightArrow] 3, 2 \[LeftRightArrow] 4], "(35_3)", + IFF[Subscript[\[Nu], 3] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; + +Subscript[f, 354] = +MakeFun[Interchange[Subscript[h, 351], 1 \[LeftRightArrow] 4, 2 \[LeftRightArrow] 3], "(35_4)", + IFF[Subscript[\[Nu], 4] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; + +Subscript[e, 3501] = + (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - Subscript[\[Nu], 5])* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == + (Subscript[\[Nu], 5]*(Schiebe[1, "-"] - Schiebe[2, "-"]) Schiebe[5, "+"] + + Subscript[\[Nu], 3]*Schiebe[1, "-"]*Schiebe[3, "+"])*TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], + Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; + +Subscript[s, 3501] = + OperatorApplyF[Subscript[e, 3501]]; + +Subscript[h, 3501] = + Subscript[s, 3501]; + +Subscript[f, 3501] = + MakeFun[Subscript[s, 3501], "(3501)", IFF[PP === m5^2], {m1 :> 0, m2 :> m5, m3 :> m5}] + +Subscript[e, 3502] = + (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - Subscript[\[Nu], 5])* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == + (Subscript[\[Nu], 5]*(Schiebe[1, "-"] - Schiebe[2, "-"])*Schiebe[5, "+"] + Subscript[\[Nu], 3]*Schiebe[1, "-"]*Schiebe[3, "+"])* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; + +Subscript[s, 3502] = + OperatorApplyF[Subscript[e, 3502]]; + +Subscript[h, 3502] = + Subscript[s, 3502]; + +Subscript[f, 3502] = + MakeFun[Subscript[h, 3502], "(3502)", IFF[PP === m5^2], {m4 :> 0, m2 :> m5, m3 :> m5}]; + +Subscript[h, 3503] = + Interchange[Subscript[s, 3502], 1 \[LeftRightArrow] 2, 3 \[LeftRightArrow] 4]; + +Subscript[f, 3503] = + MakeFun[Subscript[h, 3503], "(3503)", IFF[PP === m5^2], {m2 :> 0, m1 :> m5, m4 :> m5}]; + + +Subscript[h, 3504] = +Interchange[Subscript[s, 3502], 1 \[LeftRightArrow] 3, 2 \[LeftRightArrow] 4]; + +Subscript[f, 3504] = +MakeFun[Subscript[h, 3504], "(3504)", IFF[PP === m5^2], {m3 :> 0, m1 :> m5, m4 :> m5}]; + +Subscript[e, 41] = + 2*Subscript[\[Nu], 5]*\[ScriptCapitalC]*Schiebe[5, "+"]* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == + (Subscript[\[CapitalDelta], 1, 3, 6]*(Subscript[\[Nu], 3] Schiebe[3, "+"]*(Schiebe[4, "-"] - Schiebe[5, "-"]) + + Subscript[\[Nu], 1] Schiebe[1, "+"]*(Schiebe[2, "-"] - Schiebe[5, "-"])) + + (d - Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - 2 Subscript[\[Nu], 5])*Subscript[\[CapitalDelta], 5] + + Subscript[\[CapitalDelta], 2]*(Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[1, "-"] - Schiebe[2, "-"]) + + Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + Subscript[\[Nu], 1] - Subscript[\[Nu], 5]) + + Subscript[\[CapitalDelta], 4]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*Schiebe[3, "-"] + + Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"]) + + Subscript[\[Nu], 3] - Subscript[\[Nu], 5]))* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; + +Subscript[s, 41] = + OperatorApplyF[Subscript[e, 41]]; + +Subscript[h, 41] = + Subscript[s, 41] /. Subscript[\[Nu], 5] -> Subscript[\[Nu], 5] - 1; + +Subscript[f, 41] = + MakeFun[Subscript[h, 41], "(41)", IFF[Subscript[\[Nu], 5] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; + +Subscript[e, 43] = (d - Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - 2*Subscript[\[Nu], 5])* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == + (Subscript[\[Nu], 1] Schiebe[1, "+"]*(Schiebe[5, "-"] - Schiebe[2, "-"]) + + Subscript[\[Nu], 3] Schiebe[3, "+"]*(Schiebe[5, "-"] - Schiebe[4, "-"]))* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; + +Subscript[s, 43] = + OperatorApplyF[Subscript[e, 43]]; + +Subscript[e,44] = + (d - Subscript[\[Nu], 2] - Subscript[\[Nu], 4] - 2*Subscript[\[Nu], 5])* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == + (Subscript[\[Nu], 2] Schiebe[2, "+"]*(Schiebe[5, "-"] - Schiebe[1, "-"]) + Subscript[\[Nu], 4]* + Schiebe[4, "+"]*(Schiebe[5, "-"] - Schiebe[3, "-"]))* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; + +Subscript[s, 44] = + OperatorApplyF[Subscript[e, 44]]; + +Subscript[e, 45] = + Subscript[\[CapitalDelta], 1, 3, 6]* + Schiebe[1, "+"] TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == + (Subscript[u, 6, 1, 3]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*Schiebe[3, "-"] + Subscript[\[Nu], 5]*Schiebe[5, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"])) - + + 2*Subscript[u, 1, 3, 6]*(Subscript[\[Nu], 2]* Schiebe[2, "+"]*(Schiebe[5, "-"] - Schiebe[1, "-"]) + + Subscript[\[Nu], 4] Schiebe[4, "+"]*(Schiebe[5, "-"] - Schiebe[3, "-"]) - + Subscript[\[CapitalSigma], 5] - Subscript[\[Nu], 1] + 3*Subscript[\[Nu], 3]) + + 2*Subscript[m, 3]^2*(Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[1, "-"] - Schiebe[2, "-"]) + + Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + Subscript[\[Nu], 1] - Subscript[\[Nu], 3]))* + TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; + +Subscript[s, 45] = + OperatorApplyF[Subscript[e, 45]]; + +Subscript[f, 43] = +MakeFun[Subscript[s, 43], "(43)", IFF[Subscript[\[Nu], 1] + Subscript[\[Nu], 3] + 2*Subscript[\[Nu], 5] - (d /. _Symbol :> 4) =!= 0], + {m5 :> 0, m4 :> m3, m2 :> m1}]; + +Subscript[f, 44] = + MakeFun[Subscript[s, 44], "(44)", {m5 :> 0, m4 :> m3, m2 :> m1}]; + +Subscript[f, 50] = + HoldForm[TFR[d_, PP_, {{(n1_)?PQ, m1_}, {(n2_)?PQ, m2_}, {(n3_)?PQ, m3_}, {(n4_)?PQ, m4_}, {(n5_)?PQ, m5_}}] := + ( + TComment["(50)", TFIC[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {n4, m4}, {n5, m5}}]]; + Block[{ + + r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, + r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, + r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, + r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, + r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, + r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, + r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, + r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, + r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, + r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, + r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, + r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, + r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, + r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, + r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, + r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, + r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, + r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, + r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, + r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, + r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, + r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, + r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, + r276, r277, r278, r279, r280, r281, r282, r283, r284, r285, r286, + r287, r288, r289, r290, r291, r292, r293, r294, r295, r296, r297, + r298, r299, r300, r301, r302, r303, r304, r305, r306}, + + + r1 = 3 - d; + r2 = 4 - d; + r3 = -(m1^2*m2^2*m3^2) + m2^4*m3^2 + m2^2*m3^4 + m1^4*m4^2 - m1^2*m2^2*m4^2 - m1^2*m3^2*m4^2 - m2^2*m3^2*m4^2 + + m1^2*m4^4 + m1^2*m2^2*m5^2 - m2^2*m3^2*m5^2 - m1^2*m4^2*m5^2 + m3^2*m4^2*m5^2 + m1^2*m3^2*PP - + m2^2*m3^2*PP - m1^2*m4^2*PP + m2^2*m4^2*PP - m1^2*m5^2*PP - m2^2*m5^2*PP - m3^2*m5^2*PP - m4^2*m5^2*PP + m5^4*PP + + m5^2*PP^2; + r4 = -4 + d; + r5 = -3 + d; + r6 = -7 + 2*d; + r7 = -(m2^2*r4) + m3^2*r5 - m5^2*r5 + m4^2*r6; + r8 = -10 + 3*d; + r9 = -m3^2 + m4^2; + r10 = -11 + 3*d; + r11 = -(m4^2*r10) - 3*m5^2*r5 + m3^2*r6; + r12 = m2^2*r11 + m5^4*r5 + m2^4*r8 + m4^2*r4*r9 + m5^2*r5*r9; + r13 = -6 + d; + r14 = -(m4^2*r13) + m5^2*r5; + r15 = -3*m3^2 - m4^2*r10 + m5^2*r5; + r16 = m3^2*r14 + m2^2*r15 + m2^4*r4 - 2*m3^4*r5 - 3*m4^2*m5^2*r5 + m5^4*r5 + m4^4*r8; + r17 = m3^2 + 2*m4^2; + r18 = -1 + d; + r19 = -(m3^2*r13) - 2*m4^2*r18 + 2*m5^2*r5; + r20 = 2*m2^4 - 3*m3^4 + d*m3^4 - 3*m3^2*m4^2 + 2*m4^4 + m2^2*r19 - 2*m5^4*r5 + m5^2*r17*r5; + r21 = 2 + d; + r22 = 2*m5^2 - m4^2*r21 + m2^2*r4 - m3^2*r4; + r23 = -7 + d; + r24 = 6*m4^2 - 4*m5^2; + r25 = 3*m3^2 + m4^2*r18 + m5^2*r23; + r26 = -6*m4^4 - 2*m4^2*m5^2*r23 + m3^2*r24 + 2*m2^2*r25 - 2*m2^4*r4 - m3^4*r4; + r27 = m3^4 + m3^2*m4^2 - 2*m4^4; + r28 = m3^2 + m4^2*r23; + r29 = -2*m4^2*r18 + m3^2*r21 + 2*m5^2*r23; + r30 = -6*m2^4 + 2*m5^2*r28 - m2^2*r29 + r27*r4; + r31 = m1^4*r22 + m1^2*r26 + m3^2*r30 + m1^6*r4; + r32 = m3 - m4; + r33 = m3 + m4; + r34 = 2*m3^2 + m4^2; + r35 = -17 + 3*d; + r36 = m3^2*r23 + m4^2*r35; + r37 = -9 + d; + r38 = 17 - 3*d; + r39 = 5*m3^2 + m4^2*r37 + m5^2*r38; + r40 = 1 + d; + r41 = 5*m4^2 - m5^2*r23 + m2^2*r4 - m3^2*r40; + r42 = m5^4*r35 - m5^2*r36 + m2^2*r39 - 2*m1^4*r4 + m2^4*r4 - r32*r33*r34*r4 + m1^2*r41; + r43 = m1^2 - m2^2 + m3^2 - m4^2; + r44 = 2*m5^2*r13 + r4*r43; + r45 = m3^4*r12 + m1^4*r16 + m1^2*m3^2*r20 + PP*r31 + PP^2*r42 + PP^3*r44 + m1^6*r7; + r46 = m2^2 + m4^2; + r47 = 13 - 3*d; + r48 = m4^2*r47 - m5^2*r5 + m3^2*r6; + r49 = m5^4*r5 + m5^2*r32*r33*r5 + m4^2*r4*r9; + r50 = -18 + 4*d; + r51 = -(m4^2*r13) - 3*m5^2*r5; + r52 = 2*m3^4*r5 + m4^2*m5^2*r5 + m5^4*r5 + m4^4*r50 + m3^2*r51; + r53 = -3*m4^2 + 2*m5^2*r5; + r54 = m4^4*r47 + 2*m3^4*r5 + m4^2*m5^2*r5 - 2*m5^4*r5 + m3^2*r53; + r55 = m4^2*r13 + 6*m3^2*r5 - 2*m5^2*r5; + r56 = 3*m4^2 + m3^2*r5 - m5^2*r5; + r57 = 7 - 2*d; + r58 = m3^2*r5 + 3*m5^2*r5 + m4^2*r57; + r59 = m2^6*r4 + m2^2*m4^2*r55 + m2^4*r56 + m4^4*r58; + r60 = m4^2 - m3^2*r5; + r61 = 10 - 3*d; + r62 = 2*m5^2 + 3*m4^2*r4 + m3^2*r61; + r63 = m4^2 + m5^2*r5; + r64 = -4*m4^2*m5^2 + 3*m4^4*r4 - 2*m3^4*r5 + 2*m3^2*r63; + r65 = m4^2 + m3^2*r5 - m5^2*r5; + r66 = 2*m3^2*r5 + 2*m5^2*r5 + m4^2*r61; + r67 = 3*m2^4*r4 + 2*m2^2*r65 + m4^2*r66; + r68 = -3*m2^6*r4 - 2*m1^4*m4^2*r5 + 2*m4^2*m5^2*r60 + m2^4*r62 + m2^2*r64 + m1^2*r67 - 3*m4^4*r4*r9; + r69 = -13 + 3*d; + r70 = m3^2*r5 + m4^2*r69; + r71 = m4^2 - 3*m2^2*r4 - m3^2*r5 + m5^2*r5; + r72 = -5 + d; + r73 = m3^2 + m5^2*r69 + m4^2*r72; + r74 = 3*m2^4*r4 - m5^4*r5 + m5^2*r70 + m1^2*r71 + m2^2*r73 + 3*m4^2*r4*r9; + r75 = m1^2 - m2^2 + m3^2 - m4^2 - 2*m5^2; + r76 = m2^8*r4 + m2^6*r48 + m4^4*r49 + 2*m1^4*m4^2*r46*r5 + m2^4*r52 + m2^2*m4^2*r54 - m1^2*r59 + PP*r68 + PP^2*r74 + PP^3*r4*r75; + r77 = m3^2 - m4^2 + m5^2; + r78 = -2*m2^2 + m4^2 + m5^2; + r79 = -2*m1^2 - m3^2 - m4^2 + m5^2; + r80 = m1^4 + PP^2 - m1^2*r77 + m3^2*r78 + PP*r79; + r81 = m3^2 + m4^2; + r82 = m3^2 + m4^2 + m5^2; + r83 = m1^2 + m3^2 - m5^2; + r84 = m1^4 + 2*m3^2*m4^2 - m4^4 + PP^2 - m2^2*r77 + m5^2*r81 - m1^2*r82 - 2*PP*r83; + r85 = m1 - m3; + r86 = -PP + r85^2; + r87 = m1 + m3; + r88 = -PP + r87^2; + r89 = m2 - m4; + r90 = m2 + m4; + r91 = -m1^2 - m2^2 - m3^2 - m4^2 + 2*m5^2; + r92 = PP^2 + r85*r87*r89*r90 + PP*r91; + r93 = m2^2 - 3*m4^2; + r94 = m4 - m5; + r95 = m4 + m5; + r96 = 2*m3^2 - m4^2 + m5^2; + r97 = -m1^2 - m2^2 - 2*m3^2 + 3*m5^2; + r98 = PP^2 + m1^2*r93 + m2^2*r94*r95 + m4^2*r96 + PP*r97; + r99 = -2 + d; + r100 = -m1^2 + m2^2; + r101 = m2^2 + m1^2*r72; + r102 = m3^2*r101 - 2*m3^4*r4 + m2^2*r100*r4; + r103 = 9 - 2*d; + r104 = m2^2*r23 + m3^2*r72; + r105 = 2*m1^4 + m2^4*r103 + m1^2*r104 + m2^2*m3^2*r5; + r106 = -9 + 2*d; + r107 = m1 - m2; + r108 = m1 + m2; + r109 = -(r106*r107*r108) + m3^2*r4; + r110 = m2^2*r102 + m4^2*r105 + m4^4*r109 - m4^6*r4; + r111 = m1^2 + m2^2; + r112 = m2^2*r4 - 2*m1^2*r72; + r113 = -19 + 5*d; + r114 = m3^2*r112 + m3^4*r113 + m2^2*r111*r4; + r115 = m3^2*r5 + m2^2*r6; + r116 = 2*m1^4 + 2*m1^2*r115 + m2^4*r13 + m3^4*r72 - 2*m2^2*m3^2*r99; + r117 = m2^2*r106 + m3^2*r4 - m1^2*r99; + r118 = m2^2*r114 - m4^2*r116 + m4^4*r117 - m4^6*r6; + r119 = -(m2^2*r5) + 2*m3^2*r57 + m1^2*r72; + r120 = m1^2*r18 + 2*m3^2*r4 - m2^2*r5; + r121 = m2^2*r119 + m4^2*r120 + 2*m4^4*r5; + r122 = m3^2*r5 + m4^2*r72; + r123 = -2*m2^2*r4 - m4^2*r69 + m3^2*r72; + r124 = m2^2*r122 + m1^2*r123 + 2*m2^4*r4 + 2*m4^2*r32*r33*r4; + r125 = -3*m4^2 + m2^2*r4 - m3^2*r72; + r126 = m3^2 - m4^2*r72; + r127 = -2*m3^2*m4^2 - 2*m1^2*r125 - 2*m2^2*r126 + m4^4*r18 - 4*m2^4*r4 + m3^4*r72; + r128 = -(m2^2*r18) + 2*m4^2*r5 + m1^2*r72 + 2*m3^2*r72; + r129 = m5^2*r127 - m5^4*r128 - r124*r32*r33 + m5^6*r72; + r130 = -m1^2 + m2^2 + m3^2 - m4^2; + r131 = -14 + 3*d; + r132 = -(m3^2*r13) + m4^2*r131 + m1^2*r4 + 5*m2^2*r4; + r133 = -2*m5^4 + m5^2*r132 + r130*r32*r33*r4; + r134 = m5^2*r118 + m5^4*r121 + PP*r129 + PP^2*r133 + r110*r32*r33 - 2*m5^2*PP^3*r4 + m5^6*r5*r89*r90; + r135 = m3 - m4 - m5; + r136 = m3 + m4 - m5; + r137 = m3 - m4 + m5; + r138 = m3 + m4 + m5; + r139 = -10 + d; + r140 = 13 - 2*d; + r141 = d*m4^2 + 2*m3^2*r5; + r142 = -8 + d; + r143 = m4^2*r142 - m3^2*r99 + m5^2*r99; + r144 = m3^2*m4^2*r139 + m4^4*r140 - m5^2*r141 + m2^2*r143 + m3^4*r5 + m5^4*r5; + r145 = 3*m3^4 - 12*m3^2*m4^2 + 7*m4^4; + r146 = 3*m3^2 + 4*m4^2; + r147 = m3^2 - 11*m4^2; + r148 = 7*m3^4 + 10*m3^2*m4^2 - 17*m4^4 - 5*m5^4 - 2*m5^2*r147; + r149 = m2^2 + 2*m3^2 + m4^2; + r150 = -m2^4 + m2^2*m3^2 + m3^4 + 3*m2^2*m4^2 + m3^2*m4^2 - m4^4 + m5^4 - m5^2*r149; + r151 = 3*m3^6 + 6*m3^4*m4^2 - 17*m3^2*m4^4 + 8*m4^6 + 3*m5^6 - m5^2*r145 - m5^4*r146 + m2^2*r148 - d*r150*r77 + 6*m2^4*r94*r95; + r152 = -(m3^2*m4) + m4^3; + r153 = 11 - 2*d; + r154 = -(d*m3^2*m4^2) + m4^4*r153 + m3^4*r5; + r155 = m4^2 + m3^2*r5; + r156 = r142*r32*r33 + m5^2*r99; + r157 = 11 - 3*d; + r158 = -8 + 3*d; + r159 = m5^2*r158 + m4^2*r21; + r160 = -3*m3^4 + 2*m4^2*m5^2*r106 + m5^4*r157 + m3^2*r159 - m4^4*r18; + r161 = -2*m2^6 + m5^2*r154 - 2*m5^4*r155 + m2^4*r156 + m2^2*r160 + r152^2*r4 + m5^6*r5; + r162 = m4^2*r23 - 3*m3^2*r72; + r163 = -4*m2^2 + m4^2*r18 + m3^2*r23; + r164 = -m3^4 + m4^4; + r165 = -(m2^4*r13) + m2^2*r162 + m1^2*r163 + r164*r4 + m1^4*r99; + r166 = -19 + 4*d; + r167 = m4^2 + m3^2*r72; + r168 = m3^2 + m4^2*r69; + r169 = -2*r168 + 4*m2^2*r4; + r170 = -m3^4 + m2^4*r13 - m4^4*r166 + 2*m2^2*r167 + m1^2*r169 + 2*m3^2*m4^2*r72 + m1^4*r99; + r171 = m1^2 - m2^2 + 4*m4^2; + r172 = -(m5^2*r170) + r165*r32*r33 + m5^6*r72 - m5^4*r171*r72; + r173 = m2^2 + m3^2; + r174 = -(m4^2*r13) + r131*r173 + m1^2*r8; + r175 = m5^2*r174 - 2*m5^4*r4 + r130*r32*r33*r4; + r176 = 2*m1^6*m4^2 + m1^4*r144 + m1^2*r151 + m3^2*r161 + PP*r172 + PP^2*r175 - 2*m5^2*PP^3*r4; + r177 = m3^2 + m4^2 - m5^2; + r178 = -2*m1^2 + m3^2 - m4^2 + m5^2; + r179 = -m3^2 + m4^2 + m5^2; + r180 = m2^2*r177 + m4^2*r178 + PP*r179; + r181 = -2*m2^2 - m3^2 + m4^2 + m5^2; + r182 = m1^2*r177 + m3^2*r181 + PP*r77; + r183 = -(m2^2*r13) - 2*m3^2*r5; + r184 = m1^2*r183 - 2*m3^4*r4 + m2^4*r57 + m1^4*r72 - m2^2*m3^2*r99; + r185 = 3*m2^2*r4 + m3^2*r72; + r186 = m2^4*r106 + 2*m1^2*r185 + m1^4*r40 - 2*m2^2*m3^2*r6; + r187 = r111*r13 - m3^2*r4; + r188 = m2^2*r184 + m4^2*r186 - m4^4*r187 + m4^6*r4; + r189 = 2*m1^2 + m3^2*r10 + 2*m2^2*r5; + r190 = m2^2*r5 + m3^2*r72 + 2*m1^2*r99; + r191 = m2^2*r189 - m4^2*r190 - m4^4*r5; + r192 = -(m3^2*r5) - m4^2*r72; + r193 = 2*m2^2*r4 + m4^2*r69 - m3^2*r72; + r194 = m2^2*r192 + m1^2*r193 - 2*m2^4*r4 + 2*m4^2*r4*r9; + r195 = m2^2 + m4^2 + m3^2*r72; + r196 = -(m3^2*r6) - m4^2*r72; + r197 = m2^4*r157 + 2*m1^2*r195 + 2*m2^2*r196 + 2*m4^2*r17*r4 + m1^4*r72; + r198 = m4^2*r10 - 2*m2^2*r5 + 2*m1^2*r72 + m3^2*r72; + r199 = r107*r108*r194 + m5^2*r197 - m5^4*r198 + m5^6*r72; + r200 = m1^2 - m2^2 - m3^2 + m4^2; + r201 = m1^2 + m2^2 + m3^2 + 5*m4^2; + r202 = 2*m5^4 - r107*r108*r200 - m5^2*r201; + r203 = r107*r108*r110 - m5^2*r188 - m5^4*r191 + PP*r199 + 2*m5^2*PP^3*r4 + PP^2*r202*r4 + m5^6*r5*r89*r90; + r204 = m4^2 + m5^2; + r205 = -2*m5^2*r5 + m4^2*r99; + r206 = 18 - 5*d; + r207 = m4^2*r206 + m5^2*r8 - 2*m3^2*r99; + r208 = m2^2*r207 + 2*m2^4*r4 - m3^4*r5 - m3^2*r204*r5 + r205*r94*r95; + r209 = 2*m3^2*m4^2 + m4^4*r142 + 2*m3^4*r5; + r210 = -(m4^2*r18) + m3^2*r5; + r211 = 3 - 2*d; + r212 = m5^2 + m4^2*r157 + m3^2*r211; + r213 = m4^2*r106 + m3^2*r4; + r214 = -(d*m3^4) + 10*m3^2*m4^2 - 2*d*m3^2*m4^2 - 2*m4^4 + d*m4^4 + 2*m5^2*r213 - 2*m5^4*r4; + r215 = d*m3^2*m4^4 - 2*m4^6 - m5^2*r209 + m5^4*r210 + m2^4*r212 + m2^2*r214 + m2^6*r4 + m5^6*r5 - m3^4*m4^2*r99; + r216 = m4^2*r13 + m3^2*r99; + r217 = m3^2*r5 - m4^2*r72; + r218 = 13 - 4*d; + r219 = 3*m3^2 + m5^2*r218 + m4^2*r23; + r220 = m4^2*r142 + m5^2*r61; + r221 = 2*m3^4 + 2*m4^2*m5^2 - m4^4*r13 + m3^2*r220 + 2*m5^4*r6; + r222 = m4^2*m5^2*r216 + m5^4*r217 + m2^4*r219 + m2^2*r221 - m5^6*r5 + m2^6*r99; + r223 = -(m3^2*r10) + m4^2*r5; + r224 = 4*m3^2*m4^2 + m1^2*r122 + m4^4*r13 + m2^2*r223 + m1^4*r4 - m2^4*r4 - m3^4*r99; + r225 = -m3^2 + m2^2*r72 - m4^2*r72; + r226 = -2*m4^2*r106 + 2*m3^2*r69; + r227 = m1^4*r106 + m2^4*r106 - m4^4*r13 - 2*m1^2*r225 + m2^2*r226 - 4*m3^2*m4^2*r4 - m3^4*r99; + r228 = m3^2 + 3*m4^2; + r229 = r107*r108*r224 - m5^2*r227 + m5^6*r72 - m5^4*r228*r72; + r230 = m4^2*r131 + m1^2*r4 + m2^2*r4 + m3^2*r8; + r231 = 2*m5^4*r106 - m5^2*r230 - r107*r108*r200*r4; + r232 = m1^4*r208 - m1^2*r215 - m3^2*r222 + PP*r229 + PP^2*r231 + 2*m5^2*PP^3*r4 + m1^6*r7; + r233 = -2*m3^2 + m4^2; + r234 = -m2^2 + m4^2 - 2*m5^2; + r235 = -m1^2 + m2^2 + m5^2; + r236 = m1^4 + m5^4 + m2^2*r233 + m1^2*r234 + PP*r235 - m5^2*r46; + r237 = -m2^2 + m5^2; + r238 = m2^2 + m3^2 - 2*m4^2 + m5^2; + r239 = -m1^2 + m2^2 - m5^2; + r240 = m1^4 + m3^2*r237 - m1^2*r238 + PP*r239; + r241 = m3^2 + 3*m4^2 - m5^2; r242 = -3*m3^2 - m4^2 + m5^2; + r243 = m5^4 - m5^2*r228 + m1^2*r241 + m2^2*r242 + 2*PP*r32*r33 + 2*m4^2*r9; + r244 = 2*m1^2 + m2^2 + m4^2; + r245 = -2*m1^2 - m3^2 - m4^2 + 3*m5^2; + r246 = m1^4 - 3*m2^2*m3^2 + m5^4 + PP^2 + m4^2*r173 - m5^2*r244 + PP*r245; + r247 = -2*m3^2 + m4^2 + m5^2; + r248 = -m2^4 - m4^2*m5^2 + PP*r235 + m2^2*r247 + m1^2*r46; + r249 = m2^2*r153 + m1^2*r5; r250 = 2*m1^2 + m2^2*r4; + r251 = m2^2*r13 + m1^2*r139; + r252 = r107*r108*r250 + m3^2*r251 - m3^4*r4; + r253 = m1^2*r140 + 2*m3^2*r4 + m2^2*r72; + r254 = m3^4*r249 + m4^2*r252 + m4^4*r253 - m4^6*r4 + m2^2*m3^2*r100*r99; + r255 = 2*m3^2 + m4^2*r13; + r256 = -2*m3^2*r5 + m2^2*r99 - m4^2*r99; + r257 = -11 + 2*d; + r258 = -(m4^4*r106) + 2*m3^2*m4^2*r23 - m3^4*r257; + r259 = 4*m4^2 + m3^2*r13; + r260 = -2*m2^4 + 6*m3^2*m4^2 + 2*m2^2*r259 + m4^4*r37 + m3^4*r5; + r261 = -5*m3^4*m4^2 + m2^4*r255 + m1^4*r256 + m2^2*r258 + m1^2*r260 - m2^6*r4 + m3^6*r5 + m4^6*r6 - 3*m3^2*m4^4*r72; + r262 = m3^4 + m3^2*m4^2 + m4^4; + r263 = m1^4 + m2^4 - 2*r262 + m1^2*r81 + m2^2*r81; + r264 = m1^2 + m2^2 - m3^2 - m4^2; + r265 = -(r13*r32*r33) + m2^2*r99; + r266 = -2*m1^2*r265 - r32^2*r33^2*r4 + 2*m2^2*r13*r9 + m1^4*r99 + m2^4*r99; + r267 = m3^2*r13 + m4^2*r4; + r268 = -16 + 3*d; + r269 = m3^2*r13 - m4^2*r268 + m2^2*r4; + r270 = 2*m2^2*r267 + 2*m1^2*r269 + r13*r228*r32*r33 + m2^4*r61 + m1^4*r99; + r271 = 2*m2^2 + m4^2*r23 - m3^2*r72; + r272 = -(m5^2*r270) - 2*m5^4*r271 + r266*r32*r33; + r273 = 2*m3^2 - 2*m4^2 - m5^2; + r274 = m1^2*r5 - m2^2*r5 + r273*r72; + r275 = r200*r254 + m5^2*r261 + PP*r272 + 2*m5^2*PP^2*r274 + m5^4*r263*r5 - m5^6*r264*r5; + r276 = -2*m2^2*m3^2 - 2*m3^4 + 3*m3^2*m4^2 - m4^4 + 3*m3^2*m5^2 + 2*m4^2*m5^2 - m5^4 + m1^2*r177 + PP*r77; + r277 = -(m4^2*r106) + m2^2*r4 - m3^2*r5; + r278 = -2*m3^4 - m3^2*m4^2*r13 + m2^2*r196 + m2^4*r4 + m4^4*r4; + r279 = m4^2*r131 + m3^2*r8; + r280 = m2^2*r279 - 2*m2^4*r4 + m4^2*r32*r33*r99; + r281 = m1^4*r277 + m2^2*r278 + m1^2*r280; + r282 = 11*m3^2 - 3*d*m3^2 + 9*m4^2 - 2*d*m4^2; + r283 = 15 - 4*d; + r284 = m4^2*r106 + m2^2*r283 + m3^2*r5; + r285 = m4^4*r13 + 4*m3^2*m4^2*r5 - m3^4*r99; + r286 = -m4^2 + m3^2*r5; + r287 = -(m4^2*r5) + m3^2*r6; + r288 = 2*m2^2*r287 + m2^4*r72 - 2*r286*r81; + r289 = -2*m3^2*m4^4 + m2^4*r282 + m1^4*r284 + m2^2*r285 + m1^2*r288 - m4^6*r4 + m1^6*r5 + m2^6*r6 + m3^4*m4^2*r99; + r290 = 2*m2^2 - m3^2 - m4^2; + r291 = 2*m1^4 + 2*m2^4 - m3^4 - m4^4 + m1^2*r290 - m2^2*r81; + r292 = m2^2 - m3^2 + m4^2; + r293 = m1^4*r4 + m2^4*r4 - 2*m1^2*r292*r4 + 2*m2^2*r4*r9 - r32^2*r33^2*r99; r294 = m3^2*r13 - m4^2*r131; + r295 = m2^2*r13 - r4*r81; + r296 = m1^4*r131 + 2*m2^2*r294 - 2*m1^2*r295 - 2*m3^2*m4^2*r4 + m4^4*r8 - m2^4*r99 - m3^4*r99; + r297 = 2*m4^2 - m2^2*r5 + m1^2*r72; + r298 = r107*r108*r293 - m5^2*r296 + 2*m5^4*r297; + r299 = -2*m5^2*r32*r33*r5 + 2*m5^4*r72; + r300 = r130*r281 - m5^2*r289 + PP*r298 + PP^2*r299 - m5^6*r264*r5 + m5^4*r291*r5; + r301 = -2*m2^2*m3^2 - m3^2*m4^2 + m4^4 + m5^4 - m5^2*r17 + m1^2*r177 + PP*r77; + r302 = m2^2 + 2*m3^2 - 3*m4^2; + r303 = -m1^2 + m2^2 - 3*m5^2; + r304 = m1^4 - m2^2*m4^2 - m5^4 + m5^2*r149 - m1^2*r302 + PP*r303; + r305 = -( + (r45 TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{2, m1}, {1, m3}}])/(4*r3)) + + (r76 TBI[d, PP, {{1, m3}, {1, m1}}] TBI[d, PP, {{2, m2}, {1, m4}}])/(4*r3) - + (r80 TBI[d, PP, {{2, m1}, {1, m3}}] TBI[d, PP, {{2, m2}, {1, m4}}])/2 - + (r45 TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{2, m3}, {1, m1}}])/(4*r3) - + (r84 TBI[d, PP, {{2, m2}, {1, m4}}] TBI[d, PP, {{2, m3}, {1, m1}}])/2 - + r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{2, m3}, {2, m1}}] + + (r76 TBI[d, PP, {{1, m3}, {1, m1}}] TBI[d, PP, {{2, m4}, {1, m2}}])/(4*r3) - + (r92*TBI[d, PP, {{2, m1}, {1, m3}}] TBI[d, PP, {{2, m4}, {1, m2}}])/2 - + (r98*TBI[d, PP, {{2, m3}, {1, m1}}] TBI[d, PP, {{2, m4}, {1, m2}}])/2 - + r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{3, m1}, {1, m3}}] - + r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{3, m3}, {1, m1}}] - + r3*TFI[r99, PP, {{1, m1}, {1, m2}, {1, m3}, {1, m4}, {1, m5}}] - + (r134*TVI[d, PP, {{1, m5}, {1, m1}, {2, m4}, {1, m3}}])/(4*r3) - + (r135*r136*r137*r138*TVI[d, PP, {{1, m5}, {1, m1}, {2, m4}, {2, m3}}])/2 - + (r176*TVI[d, PP, {{1, m5}, {1, m2}, {2, m3}, {1, m4}}])/(4*r3) + + (r180*TVI[d, PP, {{1, m5}, {1, m2}, {2, m3}, {2, m4}}])/2 - + r182*TVI[d, PP, {{1, m5}, {1, m2}, {3, m3}, {1, m4}}] + + (r203 TVI[d, PP, {{1, m5}, {1, m3}, {2, m2}, {1, m1}}])/(4*r3) + + (r232*TVI[d, PP, {{1, m5}, {1, m4}, {2, m1}, {1, m2}}])/(4*r3) + + (r236*TVI[d, PP, {{1, m5}, {1, m4}, {2, m1}, {2, m2}}])/2 + + r240*TVI[d, PP, {{1, m5}, {1, m4}, {3, m1}, {1, m2}}] + + (r45*TVI[d, PP, {{1, m5}, {2, m1}, {1, m4}, {1, m3}}])/(4*r3) + + (r86*r88*TVI[d, PP, {{1, m5}, {2, m1}, {1, m4}, {2, m3}}])/2 + + (r92*TVI[d, PP, {{1, m5}, {2, m1}, {2, m4}, {1, m3}}])/2 - + (r76*TVI[d, PP, {{1, m5}, {2, m2}, {1, m3}, {1, m4}}])/(4*r3) - + (r243*TVI[d, PP, {{1, m5}, {2, m2}, {2, m3}, {1, m4}}])/2 + + (r45*TVI[d, PP, {{1, m5}, {2, m3}, {1, m2}, {1, m1}}])/(4*r3) + + (r86*r88*TVI[d, PP, {{1, m5}, {2, m3}, {1, m2}, {2, m1}}])/2 + + (r246*TVI[d, PP, {{1, m5}, {2, m3}, {2, m2}, {1, m1}}])/2 - + (r76*TVI[d, PP, {{1, m5}, {2, m4}, {1, m1}, {1, m2}}])/(4*r3) + + (r248*TVI[d, PP, {{1, m5}, {2, m4}, {2, m1}, {1, m2}}])/2 + + r86*r88*TVI[d, PP, {{1, m5}, {3, m1}, {1, m4}, {1, m3}}] + + r86*r88*TVI[d, PP, {{1, m5}, {3, m3}, {1, m2}, {1, m1}}] + + (r275*TVI[d, PP, {{2, m5}, {1, m1}, {1, m4}, {1, m3}}])/(4*r3) + + (r276*TVI[d, PP, {{2, m5}, {1, m1}, {1, m4}, {2, m3}}])/2 - + (r180*TVI[d, PP, {{2, m5}, {1, m1}, {2, m4}, {1, m3}}])/2 - + (r275*TVI[d, PP, {{2, m5}, {1, m2}, {1, m3}, {1, m4}}])/(4*r3) + + (r180*TVI[d, PP, {{2, m5}, {1, m2}, {1, m3}, {2, m4}}])/2 - + (r276*TVI[d, PP, {{2, m5}, {1, m2}, {2, m3}, {1, m4}}])/2 - + (r300*TVI[d, PP, {{2, m5}, {1, m3}, {1, m2}, {1, m1}}])/(4*r3) - + (r240*TVI[d, PP, {{2, m5}, {1, m3}, {1, m2}, {2, m1}}])/2 - + (r236*TVI[d, PP, {{2, m5}, {1, m3}, {2, m2}, {1, m1}}])/2 + + (r300*TVI[d, PP, {{2, m5}, {1, m4}, {1, m1}, {1, m2}}])/(4*r3) + + (r236*TVI[d, PP, {{2, m5}, {1, m4}, {1, m1}, {2, m2}}])/2 + + (r240*TVI[d, PP, {{2, m5}, {1, m4}, {2, m1}, {1, m2}}])/2 + + (r182*TVI[d, PP, {{2, m5}, {2, m1}, {1, m4}, {1, m3}}])/2 - + (r301*TVI[d, PP, {{2, m5}, {2, m2}, {1, m3}, {1, m4}}])/2 - + (r304*TVI[d, PP, {{2, m5}, {2, m3}, {1, m2}, {1, m1}}])/2 + + (r248*TVI[d, PP, {{2, m5}, {2, m4}, {1, m1}, {1, m2}}])/2; + + + + r306 = Factor /@ r305/(PP*r1*r2); r306]) /; + n1 === 1 && n2 === 1 && n3 === 1 && n4 === 1 && n5 === 1 && MatchQ[d, _Symbol + _Integer?Positive] && PP =!= 0 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0 + ]; + +Subscript[e, 51] = + Subscript[\[CapitalDelta], 1, 3, 4]*Subscript[\[Nu], 1]* + Schiebe[1, "+"] TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (2*Subscript[m, 3]^2*Subscript[\[Nu], 3]* + Schiebe[3, "+"]*(Schiebe[1, "-"] - Schiebe[4, "-"]) + Subscript[u, 4, 1, 3]*Subscript[\[Nu], 1]* + Schiebe[1, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"]) + Subscript[u, 1, 3, 4]*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3]) + + 2*Subscript[m, 3]^2*(Subscript[\[Nu], 1] - Subscript[\[Nu], 3]))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2],Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 51] = + OperatorApplyV[Subscript[e, 51]]; + +Subscript[h, 51] = + Subscript[s, 51] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 + +Subscript[f, 51] = + MakeFun[Subscript[h, 51], "(51)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[\[CapitalDelta], 1, 3, 4] =!= 0]]; + +CheckTVIRecursion[Subscript[f, 51]] + +Subscript[e, 52] = + Subscript[\[CapitalDelta], 2, 4, 6]*Subscript[\[Nu], 2]* + Schiebe[2, "+"]* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (2*Subscript[m, 1]^2*Subscript[\[Nu], 1] Schiebe[1, "+"]*(Schiebe[4, "-"] - Schiebe[2, "-"]) + + 2*Subscript[m, 3]^2*Subscript[\[Nu], 3]* Schiebe[3, "+"]*(Schiebe[4, "-"] - Schiebe[2, "-"]) - + 2*Subscript[m, 4]^2*Subscript[\[Nu], 4]*Schiebe[4, "+"]*Schiebe[2, "-"] + + (2*Subscript[m, 2]^2 - Subscript[u, 4, 2, 6])*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[4, "-"] - + (Subscript[\[CapitalSigma], 4] + 2)*(Schiebe[4, "-"] - Schiebe[2, "-"]) + + Subscript[u, 2, 4, 6]*(d - 3*Subscript[\[Nu], 2]) + 2*Subscript[m, 4]^2*(Subscript[\[Nu], 4] - Subscript[\[Nu], 2]))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 52] = + OperatorApplyV[Subscript[e, 52]] + +Subscript[h, 52] = + nuExplicit[Subscript[s, 52]] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1; + +Subscript[f, 52] = + MakeFun[Subscript[h, 52], "(52)", IFF[Subscript[\[Nu], 2] > 1 && Subscript[\[CapitalDelta], 2, 4, 6] =!= 0]]; + + +Subscript[h, 53] = + Interchange[Subscript[s, 51], 1 \[LeftRightArrow] 3] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; + +Subscript[f, 53] = + MakeFun[Subscript[h, 53], "(53)", IFF[Subscript[\[Nu], 3] > 1 && Subscript[\[CapitalDelta], 3, 1, 4] =!= 0]]; + + +Subscript[e, 54] = + 2*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"]* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (Subscript[u, 4, 1, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + Subscript[\[Nu], 1]* + Schiebe[1, "+"]*(Schiebe[4, "-"] - Schiebe[3, "-"]) + (d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3]))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 54] = + OperatorApplyV[Subscript[e, 54]]; + +Subscript[h, 54] = + Subscript[s, 54] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; + +Subscript[f, 54] = +MakeFun[Subscript[h, 54], "(54)", IFF[Subscript[\[Nu], 3] > 1 && m3 =!= 0]]; + +Subscript[e, 55] = + 2*Subscript[m, 4]^2*Subscript[\[Nu], 4]*Schiebe[4, "+"]* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (Subscript[u, 3, 1, 4]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + Subscript[u, 6, 2, 4]*Subscript[\[Nu], 2]*Schiebe[2, "+"] + + Subscript[\[Nu], 1]*Schiebe[1, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"]) - + Subscript[\[Nu], 2]*Schiebe[2, "+"] Schiebe[4, "-"] + (d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 4]))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 55] = + OperatorApplyV[Subscript[e, 55]]; + +Subscript[h, 55] = + Subscript[s, 55] /. Subscript[\[Nu], 4] -> Subscript[\[Nu], 4] - 1; + +Subscript[f, 55] = + MakeFun[Subscript[h, 55], "(55)", IFF[Subscript[\[Nu], 4] > 1 && m4 =!= 0 && Subscript[\[Nu], 3] > 1]]; + +Subscript[e, 56] = + 2*Subscript[m, 4]^2*Subscript[\[Nu], 4]*Schiebe[4, "+"]* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (-2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] + Subscript[u, 6, 2, 4]*Subscript[\[Nu], 2]*Schiebe[2, "+"] - + 2*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] - Subscript[\[Nu], 2]*Schiebe[2, "+"]* + Schiebe[4, "-"] + (2*d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3] - + 2*Subscript[\[Nu], 4]))*TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 56] = + OperatorApplyV[Subscript[e, 56]]; + +Subscript[h, 56] = + Subscript[s, 56] /. Subscript[\[Nu], 4] -> Subscript[\[Nu], 4] - 1; + +Subscript[f, 56] = + MakeFun[Subscript[h, 56], "(56)", IFF[Subscript[\[Nu], 4] > 1 && m4 =!= 0 && Subscript[\[Nu], 3] === 1]]; + +Subscript[e, 59] = + (2*Subscript[m, 1]^2*Subscript[u, 1, 3, 4]*(d - Subscript[\[Nu], 1] - + 2*Subscript[\[Nu], 3]) + (Subscript[\[Nu], 3] - 1)*Subscript[u, 4, 1, 3]^2 + 4*Subscript[m, 1]^2* + Subscript[m, 3]^2*(Subscript[\[Nu], 1] - Subscript[\[Nu], 3]))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (Subscript[u, 4, 1, 3]*Subscript[\[Nu], 3]*Schiebe[3, "+"]* + Schiebe[4, "-"]*(Schiebe[4, "-"] - Schiebe[1, "-"]) - + 4*Subscript[m, 1]^2*Subscript[m, 3]^2*Subscript[\[Nu], 3] Schiebe[3, "+"]* + Schiebe[1, "-"] + (4*Subscript[m, 1]^2*Subscript[m, 3]^2 + + Subscript[u, 4, 1, 3]^2)*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[4, "-"] + + Subscript[u, 4, 1, 3]*(Subscript[\[Nu], 3] - 1)*Schiebe[1, "-"] - + (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] + 1)*Subscript[u, 4, 1, 3]*Schiebe[3, "-"] + + (d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3] + 1)*Subscript[u, 4, 1, 3]*Schiebe[4, "-"])* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 59] = + OperatorApplyV[Subscript[e, 59]]; + +Subscript[h, 59] = + Subscript[s, 59]; + +Subscript[f, 59] = + MakeFun[Subscript[h, 59], "(59)", + IFF[Subscript[\[CapitalDelta], 1, 3, 4] == 0 && 4*Subscript[m, 3]^2*Subscript[m, 1]^2 - 4*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Subscript[m, 1]^2 + + 2*d*Subscript[u, 1, 3, 4]*Subscript[m, 1]^2 - 4*Subscript[\[Nu], 3]*Subscript[u, 1, 3, 4]*Subscript[m, 1]^2 - + 2*Subscript[u, 1, 3, 4]*Subscript[m, 1]^2 + Subscript[\[Nu], 3]*Subscript[u, 4, 1, 3]^2 - Subscript[u, 4, 1, 3]^2 =!= 0 && + n1 === 1 && n2 === 1 && n4 === 1 && MatchQ[d, _Integer]]]; + +Subscript[e, 60] = + 2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"]* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (Subscript[u, 4, 1, 3]*Subscript[\[Nu], 3]*Schiebe[3, "+"] + Subscript[\[Nu], 3]*Schiebe[3, "+"]*(Schiebe[4, "-"] - Schiebe[1, "-"]) + + (d - Subscript[\[Nu], 3] - 2*Subscript[\[Nu], 1]))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 60] = + OperatorApplyV[Subscript[e, 60]]; + +Subscript[h, 60] = + Subscript[s, 60] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[notnecessaryf, 60] = + MakeFun[Subscript[h, 60], "(60)", IFF[Subscript[\[Nu], 1] > 1 && m1 =!= 0]]; + +Subscript[e, 61] = + (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3])* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + Subscript[\[Nu], 3]* Schiebe[3, "+"]*(Schiebe[1, "-"] - Schiebe[4, "-"])* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 61] = + OperatorApplyV[Subscript[e, 61]]; + +Subscript[h, 61] = + Subscript[s, 61]; + +Subscript[f, 61] = + MakeFun[Subscript[h, 61], "(61)", IFF[m1 === 0 && m3 === m4]]; + +Subscript[h, 6153] = + Interchange[Subscript[s, 61], 1 \[LeftRightArrow] 3]; + +Subscript[f, 6153] = + MakeFun[Subscript[h, 6153], "(6153)", IFF[m3 === 0 && m1 === m4]]; + +Subscript[e, 62] = + (PP - Subscript[m, 2]^2)*(Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] + 2*Subscript[\[Nu], 4] + 2)* + Schiebe[4, "+"]* TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + ((Subscript[m, 1]^2 - Subscript[u, 6, 1, 2])*Subscript[\[Nu], 1]*Schiebe[1, "+"] + + 4*Subscript[m, 2]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"] + + 2*Subscript[m, 1]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + + (Subscript[\[CapitalSigma], 4] - 2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] - + 2*Subscript[m, 1]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"])* + Schiebe[2, "-"]*Schiebe[4, "+"] + (PP - Subscript[m, 2]^2)*Subscript[\[Nu], 1]* Schiebe[1, "+"]*Schiebe[4, "+"]*Schiebe[3, "-"] - + Subscript[\[CapitalSigma], 4])* TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 62] = + OperatorApplyV[Subscript[e, 62]]; + +Subscript[h, 62] = + nuExplicit[Subscript[s, 62]] /. Subscript[\[Nu], 4] -> Subscript[\[Nu], 4] - 1; + +Subscript[f, 62] = + MakeFun[Subscript[h, 62], "(62)", IFF[PP =!= m2^2 && Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] + 2*Subscript[\[Nu], 4] =!= 0], {m4 :> 0, m3 :> m1, n2 :> 1}]; +Subscript[e, 63] = + (PP - Subscript[m, 2]^2)*((Subscript[m, 3]^2 - Subscript[m, 1]^2)*(d - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3] + + 2*Subscript[\[Nu], 4]) + 2*Subscript[m, 3]^2*(Subscript[\[Nu], 3] - Subscript[\[Nu], 1]))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + ((Subscript[m, 1]^2 - Subscript[m, 3]^2)*((2*Subscript[m, 1]^2*Subscript[\[Nu], 1] Schiebe[1, "+"] + + 2*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] - Subscript[\[CapitalSigma], 4] - 2)* + (Schiebe[2, "-"] - Schiebe[4, "-"]) - 4*Subscript[m, 2]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"] Schiebe[4, "-"]) + + + 2*(PP - Subscript[m, 2]^2)*(Subscript[m, 3]^2*Subscript[\[Nu], 3]* + Schiebe[3, "+"]*(Schiebe[1, "-"] - Schiebe[4, "-"]) + Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"]* + (Schiebe[4, "-"] - Schiebe[3, "-"])))* TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 63] = + OperatorApplyV[Subscript[e, 63]]; + +Subscript[h, 63] = + nuExplicit[Subscript[s, 63]]; + +Subscript[f, 63] = + MakeFun[Subscript[h, 63], "(63)", IFF[PP =!= m2^2 && Cayley[1, 3, 4][{m1, m2, m3, m4}] =!= 0], {m4 :>0}]; + +Subscript[f, 63] = + MakeFun[Subscript[h, 63], "(63)", IFF[PP =!= m2^2 && Cayley[1, 3, 4][{m1, m2, m3, m4}] =!= 0], {m4 :> 0, n1 :> 1, n3 :> 1}]; + +Subscript[r, 6552] = + nuExplicit[Subscript[e, 52]] /. Subscript[\[CapitalDelta], 2, 4, 6] -> 0; + +formal = + Solve[Subscript[e, 55] /. TVI[__] -> 1, Schiebe[4, "+"]][[1, 1]] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1; + +Subscript[n, 6552] = + OperatorApplyV[Subscript[r, 6552] /. formal]; + +Subscript[s, 6552] = + -Subscript[n, 6552][[2, 4]] == Subscript[n, 6552][[2]] - Subscript[n, 6552][[2, 4]]; + +Subscript[f, 6552] = + MakeFun[Subscript[s, 6552], "(6552)", IFF[Subscript[\[CapitalDelta], 2, 4, 6] === 0 && + Expand[2*(Subscript[\[Nu], 2] - Subscript[\[Nu], 4])* m4^2 + (3*Subscript[\[Nu], 2] - d)* + Subscript[u, 2, 4, 6] + Subscript[\[Nu], 2]*Subscript[u, 6, 2, 4]] =!= 0] + ]; + +Subscript[r, 6552] = + nuExplicit[Subscript[e, 52]] /. Subscript[\[CapitalDelta], 2, 4, 6] -> 0; + +Subscript[n, 6552] = + OperatorApplyV[Subscript[r, 6552]]; + + +Subscript[s, 6552] = + -Subscript[n, 6552][[2, 5]] == Subscript[n, 6552][[2]] - Subscript[n, 6552][[2, 5]]; + +Subscript[f, 6552] = + MakeFun[Subscript[s, 6552], "(6552)", IFF[Subscript[\[CapitalDelta], 2, 4, 6] === 0 && + Expand[-2*Subscript[\[Nu], 2]*Subscript[m, 4]^2 + 2*Subscript[\[Nu], 4]*Subscript[m, 4]^2 + d*Subscript[u, 2, 4, 6] - + 3*Subscript[\[Nu], 2]*Subscript[u, 2, 4, 6]] =!= 0]]; + +Subscript[r, 6553] = + nuExplicit[Subscript[s, 55]] /. Subscript[u, 3, 1, 4] -> 0 /. Subscript[u, 6, 2, 4] -> 0 /. Subscript[m, 4] -> 0; + +Subscript[h, 6553] = + -Subscript[r, 6553][[2, 1]] == Subscript[r, 6553][[2]] - Subscript[r, 6553][[2, 1]]; + +Subscript[f, 6553] = + MakeFun[Subscript[h, 6553], "(6553)", IFF[Subscript[u, 6, 2, 4] === 0 && Subscript[u, 1, 3, 4] === 0], m4 :> 0]; + +Subscript[e, 66] = + 4*PP*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]* + TVI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (-((6*d - 6*Subscript[\[Nu], 1] - 5*Subscript[\[Nu], 2] - 6*Subscript[\[Nu], 3] - 4*Subscript[\[Nu], 4] - + 6*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"]) + (Subscript[u, 6, 2, 4] - 4*Subscript[m, 2]^2)* + Subscript[\[Nu], 2]*Schiebe[2, "+"] - 6*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + + 2*(Subscript[u, 6, 2, 4] - Subscript[m, 4]^2)*Subscript[\[Nu], 4]*Schiebe[4, "+"] - + Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[4, "-"] - 2*Subscript[\[Nu], 4]*Schiebe[4, "+"]*Schiebe[2, "-"]))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 66] = + OperatorApplyV[Subscript[e, 66]]; + +Subscript[h, 66] = + Subscript[s, 66] /. { + Subscript[\[Nu], 1] :> Subscript[\[Nu], 1] - 1, + Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 1, + Subscript[\[Nu], 3] :> Subscript[\[Nu], 3] - 1, d :> d - 2 + }; + +Subscript[f, 66] = + MakeFun[Subscript[h, 66], "(66)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 2] > 1 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 67] = + 4*PP*Subscript[\[Nu], 1]*(Subscript[\[Nu], 1] + 1)*Schiebe[1, "+"] Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]* + TVI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + ((6*d - 6*Subscript[\[Nu], 1] - 5*Subscript[\[Nu], 2] - 6*Subscript[\[Nu], 3] - 4*Subscript[\[Nu], 4]) - + 2*(Subscript[u, 2, 4, 6] + 3*Subscript[m, 1]^2)*Subscript[\[Nu], 1] Schiebe[1, "+"] + + (Subscript[u, 6, 2, 4] - 4*Subscript[m, 2]^2) Subscript[\[Nu], 2]*Schiebe[2, "+"] - + 6*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + 2*(Subscript[u, 6, 2, 4] - Subscript[m, 4]^2) Subscript[\[Nu], 4]*Schiebe[4, "+"] + + 2*Subscript[\[Nu], 1] Schiebe[1, "+"]*(Schiebe[4, "-"] - Schiebe[2, "-"]) - + Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[4, "-"] - 2*Subscript[\[Nu], 4]*Schiebe[4, "+"]*Schiebe[2, "-"])* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 67] = + OperatorApplyV[Subscript[e, 67]]; + +Subscript[e, 67] = + 4*PP*Subscript[\[Nu], 1]*(Subscript[\[Nu], 1] + 1)*Schiebe[1, "+"] Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]* + TVI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (2*(2*d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3] - Subscript[\[Nu], 4]) - + 2*(Subscript[u, 2, 4, 6] + 2*Subscript[m, 1]^2)*Subscript[\[Nu], 1]*Schiebe[1, "+"] - + 4*Subscript[m, 2]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"] - 4*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + + 2*Subscript[u, 6, 2, 4]*Subscript[\[Nu], 4]*Schiebe[4, "+"] + 2*Subscript[\[Nu], 1]* + Schiebe[1, "+"]*(Schiebe[4, "-"] - Schiebe[2, "-"]) - 2*Subscript[\[Nu], 4]*Schiebe[4, "+"]*Schiebe[2, "-"])* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 67] = + OperatorApplyV[Subscript[e, 67]]; + +Subscript[h, 67] = + Subscript[s, 67] /. {Subscript[\[Nu], 1] :> Subscript[\[Nu], 1] - 2, Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 1, d :> d - 2}; + +Subscript[f, 67] = + MakeFun[Subscript[h, 67], "(67)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 2 && Subscript[\[Nu], 2] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[h, 6713] = + Interchange[Subscript[s, 67], 1 \[LeftRightArrow] 3] /. {Subscript[\[Nu], 3] :> Subscript[\[Nu], 3] - 2, Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 1, d :> d - 2}; + +Subscript[f, 6713] = + MakeFun[Subscript[h, 6713], "(6713)", IFF[PP =!= 0 && Subscript[\[Nu], 3] > 2 && Subscript[\[Nu], 2] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 68] = + 4*PP*Subscript[m, 4]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*(Subscript[\[Nu], 2] + 1)*Schiebe[2, "+"]* + Schiebe[2, "+"]*TVI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == + (-(((Subscript[m, 1]^2 - Subscript[m, 3]^2)*(2*d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - + 2*Subscript[\[Nu], 3] - 2*Subscript[\[Nu], 4]) + Subscript[m, 4]^2*(2*Subscript[\[Nu], 1] + + Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3])) - Subscript[u, 1, 3, 4]*(2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] + + Subscript[u, 2, 4, 6]*Subscript[\[Nu], 2]*Schiebe[2, "+"]) + + Subscript[u, 3, 1, 4]*(2*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[4, "-"]) - + 2*Subscript[m, 4]^2*(Subscript[\[Nu], 2]*Schiebe[2, "+"] + Subscript[\[Nu], 4]*Schiebe[4, "+"])*(Schiebe[3, "-"] - Schiebe[1, "-"])))* + TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; + +Subscript[s, 68] = + OperatorApplyV[Subscript[e, 68]]; + +Subscript[h, 68] = + Subscript[s, 68] /. {Subscript[\[Nu], 1] :> Subscript[\[Nu], 1] - 1, Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 2, d :> d - 2}; + +Subscript[f, 68] = + MakeFun[Subscript[h, 68], "(68)", IFF[PP =!= 0 && m4 =!= 0 && Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 2] > 2 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[h, 6813] = + Interchange[Subscript[s, 68], 1 \[LeftRightArrow] 3] /. {Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 2, Subscript[\[Nu], 3] :> Subscript[\[Nu], 3] - 1, d :> d - 2}; + +Subscript[f, 6813] = + MakeFun[Subscript[h, 6813], "(6813)", IFF[PP =!= 0 && m4 =!= 0 && Subscript[\[Nu], 2] > 2 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 70] = + (3*d - 10)*(d - 3)^2*Subscript[m, 4]^2 TVI[d, {1, 1, 1, 1}] == + (1/(4*PP))*((3*d - 10)*Subscript[\[CapitalDelta], 1, 3, 4]*(Subscript[\[CapitalDelta], 2, 4, 6] + Subscript[u, 2, 4, 6]*(Schiebe[2, "-"] - Schiebe[4, "-"])) - + 8*(d - 4)^2*PP*Subscript[m, 3]^2*Subscript[m, 4]^2*Schiebe[4, "-"])*TVI[-2 + d, {1, 1, 1,1}] + ((d - 3)* + Subscript[m, 4]^2*(4*Subscript[m, 1]^2*(d - 4)*Schiebe[1, "+"]* + Schiebe[1, "+"] - 8*(d - 3)*Subscript[m, 2]^2*Schiebe[2, "+"] Schiebe[2, "+"] + (3*d - 10)*(d - 3)*Schiebe[2, "+"]) + + Subscript[u, 6, 2, 4]*((1/2)*(3*d - 10)* Subscript[u, 1, 3, 4]*(Schiebe[1, "+"] - Schiebe[3, "+"]) + (d - 2)*(d - 3)* + Subscript[m, 4]^2*Schiebe[1, "+"])*Schiebe[2, "+"] - Subscript[m, 4]^2*((d - 4)^2*Subscript[u, 1, 3, 4]* Schiebe[2, "+"] + + (3*d - 10)*Subscript[u, 4, 1, 3]* Schiebe[3, "+"])*Schiebe[1, "+"])*Schiebe[4, "-"]* + TVI[d, {1, 1, 1, 1}] - (d - 3)* Subscript[m, 4]^2*(4*(d - 4)*Subscript[m, 1]^2*Schiebe[1, "+"] + (d - 2)*(Subscript[u, 6, 2, 4]*Schiebe[2, "+"] - + 2*Subscript[m, 4]^2*Schiebe[4, "+"]))*Schiebe[1, "+"]* Schiebe[3, "-"]* TVI[d, {1, 1, 1, 1}] + (1/2)*(3*d - 10)* + Subscript[u, 1, 3, 4]*(Subscript[u, 6, 2, 4]*Schiebe[2, "+"] - 2*Subscript[m, 4]^2*Schiebe[4, "+"])* + (Schiebe[3, "+"]*Schiebe[1, "-"] - Schiebe[1, "+"]*Schiebe[3, "-"])*TVI[d, {1, 1, 1, 1}]; + +Subscript[s, 70] = + OperatorApplyV[Subscript[e, 70]]; + +Subscript[h, 70] = + Subscript[s, 70]; + +Subscript[f, 70] = + MakeFun[Subscript[h, 70], "(70)", IFF[m4 =!= 0 && PP =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 71] = + 2*Subscript[D, 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (2*Subscript[h, 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + + 2*Subscript[h, 2, 1, 3]*Subscript[\[Nu], 2]*Schiebe[2, "+"] + + 4*Subscript[m, 3]^2*Subscript[\[Sigma], 1, 2, 3]*Subscript[\[Nu], 3]* Schiebe[3, "+"] + + Subscript[m, 3]^2*Subscript[\[Phi], 2, 1, 3]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + + Subscript[m, 3]^2*Subscript[\[Phi], 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[2, "-"] - + 2*Subscript[\[Rho], 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[3, "-"] + + (1/2)*Subscript[\[CapitalSigma], 3]*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])*Subscript[\[Phi], 3, 2, 1])* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 71] = + OperatorApplyJ[Subscript[e, 71]]; + +Subscript[h, 71] = + nuExplicit[Subscript[s, 71]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1; + +Subscript[f, 71] = + MakeFun[Subscript[h, 71], "(71)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 2] > 1 && Subscript[D, 1, 2, 3] =!= 0]]; + + +Subscript[h, 7123] = + Interchange[Subscript[s, 71], 2 \[LeftRightArrow] 3] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; + +Subscript[f, 7123] = + MakeFun[Subscript[h, 7123], "(7123)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 3] > 1 && Subscript[D, 1, 3, 2] =!= 0]]; + + +Subscript[h, 7113] = + Interchange[Subscript[s, 71], 1 \[LeftRightArrow] 3] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; + +Subscript[f, 7113] = + MakeFun[Subscript[h, 7113], "(7113)", IFF[Subscript[\[Nu], 2] > 1 && Subscript[\[Nu], 3] > 1 && Subscript[D, 3, 2, 1] =!= 0]]; + +Subscript[e, 78] = + 2*Subscript[m, 1]^2*Subscript[D, 1, 2, 3]* + Subscript[\[Nu], 1]*(Subscript[\[Nu], 1] + 1)*Schiebe[1, "+"]* + Schiebe[1, "+"]* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + ((-Subscript[\[CapitalSigma], 3])*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])*Subscript[\[Rho], 1, 2, 3] + + Subscript[m, 2]^2*Subscript[m, 3]^2*Subscript[\[Phi], 1, 2, 3]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + + Subscript[m, 1]^2*Subscript[m, 3]^2*Subscript[\[Phi], 2, 1, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[2, "-"] + + Subscript[m, 1]^2*Subscript[m, 2]^2*Subscript[\[Phi], 3, 1, 2]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[3, "-"] + + (d - 2 - 2*Subscript[\[Nu], 1])*Subscript[D, 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + + Subscript[m, 1]^2*Subscript[S, 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + Subscript[m, 2]^2*Subscript[S, 2, 1, 3]*Subscript[\[Nu], 2]*Schiebe[2, "+"] + + Subscript[m, 3]^2*Subscript[S, 3, 1, 2]*Subscript[\[Nu], 3]*Schiebe[3, "+"])* TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 78] = + OperatorApplyJ[Subscript[e, 78]]; + +Subscript[h, 78] = + nuExplicit[Subscript[s, 78]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 2; + +Subscript[f, 78] = + MakeFun[Subscript[h, 78], "(78)", IFF[Subscript[\[Nu], 1] > 2 && m1 =!= 0 && Subscript[D, 1, 2, 3] =!= 0]]; + +Subscript[e, 80] = + Subscript[\[Nu], 1]*(d - 2*Subscript[\[Nu], 1] - 2)* + Subscript[\[CapitalDelta], 2, 3, 6]*Schiebe[1, "+"]* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], + Subscript[\[Nu], 3]}] == + (-4*Subscript[m, 2]^2*Subscript[m, 3]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + + 2*Subscript[m, 2]^2*((PP - Subscript[m, 2]^2)*(2*d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - + 2*Subscript[\[Nu], 3] - 1) - Subscript[m, 3]^2*(2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 1))*Subscript[\[Nu], 2]*Schiebe[2, "+"] + + 2*Subscript[m, 3]^2*((PP - Subscript[m, 3]^2)*(2*d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - Subscript[\[Nu], 3] - 1) - + Subscript[m, 2]^2*(2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - 1))*Subscript[\[Nu], 3]*Schiebe[3, "+"] - + Subscript[\[CapitalSigma], 3]*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - + Subscript[\[Nu], 3])*Subscript[u, 6, 2, 3])*TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 80] = + OperatorApplyJ[Subscript[e, 80]]; + +Subscript[h, 80] = + nuExplicit[Subscript[s, 80]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 80] = + MakeFun[Subscript[h, 80], "(80)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[\[CapitalDelta], 2, 3, 6] =!= 0], m1 :> 0]; + +Subscript[e, 81] = + PP*(Subscript[\[CapitalSigma], 3] + 2)*Subscript[\[Nu], 1]* + Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*TJI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (PP*(d - 2*Subscript[\[Nu], 3]) + Subscript[m, 1]^2*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2]) + + Subscript[m, 2]^2*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2]) - + 2*Subscript[m, 3]^2*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3]) - + 2*Subscript[m, 3]^2*(PP - Subscript[m, 3]^2)*Subscript[\[Nu], 3]*Schiebe[3, "+"] + + Subscript[m, 1]^2*(PP - Subscript[m, 1]^2 - + 3*Subscript[m, 2]^2 + 3*Subscript[m, 3]^2 - + Schiebe[2, "-"] + Schiebe[3, "-"])*Subscript[\[Nu], 1]*Schiebe[1, "+"] + + Subscript[m, 2]^2*(PP - 3*Subscript[m, 1]^2 - Subscript[m, 2]^2 + 3*Subscript[m, 3]^2 - Schiebe[1, "-"] + + Schiebe[3, "-"])*Subscript[\[Nu], 2]*Schiebe[2, "+"])* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 81] = + OperatorApplyJ[Subscript[e, 81]]; + +Subscript[h, 81] = + nuExplicit[Subscript[s, 81]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1 /. d -> d - 2; + +Subscript[f, 81] = + MakeFun[Subscript[h, 81], "(81)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 2] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + + +Subscript[h, 8123] = + Interchange[Subscript[s, 81], 2 \[LeftRightArrow] 3] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1 /. d -> d - 2; + +Subscript[f, 8123] = + MakeFun[Subscript[h, 8123], "(8123)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[h, 8113] = + Interchange[Subscript[s, 81], 1 \[LeftRightArrow] 3] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1 /. d -> d - 2; + +Subscript[f, 8113] = + MakeFun[Subscript[h, 8113], "(8113)", IFF[PP =!= 0 && Subscript[\[Nu], 2] > 1 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + + +Subscript[e, 82] = + (-PP)*Subscript[m, 1]^2*(Subscript[\[CapitalSigma], 3] + 2)* + Subscript[\[Nu], 1]*(Subscript[\[Nu], 1] + 1)*Schiebe[1, "+"]*Schiebe[1, "+"]*TJI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] + + (1/2)*PP*(Subscript[\[CapitalSigma], 3] + 2)*(Subscript[\[CapitalSigma], 3] + 4)*Subscript[\[Nu], 1]*Schiebe[1, "+"]* + TJI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + ((-(1/2))*PP^2*(d + 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3]) + + (1/2)* + PP*(Subscript[m, 1]^2*(6*Subscript[\[Nu], 1] + 6*Subscript[\[Nu], 2] + 6*Subscript[\[Nu], 3] - 7*d) + + Subscript[m, 2]^2*(7*d - 2*Subscript[\[Nu], 1] - 4*Subscript[\[Nu], 2] - 10*Subscript[\[Nu], 3]) + + Subscript[m, 3]^2*(7*d - 2*Subscript[\[Nu], 1] - 10*Subscript[\[Nu], 2] - 4*Subscript[\[Nu], 3])) + + (Subscript[m, 2]^2)^2*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2]) + (Subscript[m, 3]^2)^2* + (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3]) + + Subscript[m, 1]^2* Subscript[m, 2]^2*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2]) + + + Subscript[m, 1]^2*Subscript[m, 3]^2*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3]) - 4*Subscript[m, 2]^2* + Subscript[m, 3]^2*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3]) - + Subscript[m, 1]^2*(2*PP^2 - PP*(2*Subscript[m, 1]^2 + Subscript[m, 2]^2 + Subscript[m, 3]^2) + + Subscript[m, 1]^2*(Subscript[m, 2]^2 + Subscript[m, 3]^2) + 3*(Subscript[m, 2]^2 - Subscript[m, 3]^2)^2)*Subscript[\[Nu], 1]*Schiebe[1, "+"] + + + Subscript[m, 2]^2*(PP^2 + (PP - Subscript[m, 2]^2)*(3*Subscript[m, 1]^2 - 5*Subscript[m, 3]^2 + Schiebe[1, "-"] - + Schiebe[3, "-"]) - (Subscript[m, 2]^2)^2)*Subscript[\[Nu], 2]*Schiebe[2, "+"] + + + Subscript[m, 3]^2*(PP^2 + (PP - Subscript[m, 3]^2)*(3*Subscript[m, 1]^2 - 5*Subscript[m, 2]^2 + Schiebe[1, "-"] - + Schiebe[2, "-"]) - (Subscript[m, 3]^2)^2)*Subscript[\[Nu], 3]*Schiebe[3, "+"] - + (1/2)*PP*(Subscript[\[CapitalSigma], 3] + 2)*(Schiebe[1, "-"] - Schiebe[2, "-"] - Schiebe[3, "-"]) - + Subscript[m, 1]^2*(Subscript[m, 2]^2 - Subscript[m, 3]^2)*Subscript[\[Nu], 1]*Schiebe[1, "+"]*(Schiebe[2, "-"] - Schiebe[3, "-"]))* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[r, 82] = + OperatorApplyJ[Subscript[e, 82]]; + +Subscript[s, 82] = + Subscript[r, 82][[1, 2]] == -Subscript[r, 82][[1, 1]] + Subscript[r, 82][[2]]; + +Subscript[h, 82] = nuExplicit[Subscript[s, 82]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 2 /. d -> d - 2; + +Subscript[f, 82] = + MakeFun[Subscript[h, 82], "(82)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 2 && m1 =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; + + +Subscript[h, 8213] = + Interchange[Subscript[s, 82], 1 \[LeftRightArrow] 3] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 2 /. d -> d - 2; + +Subscript[f, 8213] = + MakeFun[Subscript[h, 8213], "(8213)", IFF[PP =!= 0 && m3 =!= 0 && Subscript[\[Nu], 3] > 2 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[h, 8212] = + Interchange[Subscript[s, 82], 1 \[LeftRightArrow] 2] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 2 /. d -> d - 2; + +Subscript[f, 8212] = + MakeFun[Subscript[h, 8212], "(8212)", IFF[PP =!= 0 && Subscript[\[Nu], 2] > 2 && m2 =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 83] = + PP*(Subscript[\[CapitalSigma], 3] + 2)*(Subscript[\[CapitalSigma], 3] + 4)*Subscript[\[Nu], 1]* + Schiebe[1, "+"]*TJI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + ((-PP^2)*(d + 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3]) + + PP*(Subscript[m, 2]^2*(7*d - 2*Subscript[\[Nu], 1] - 4*Subscript[\[Nu], 2] - 10*Subscript[\[Nu], 3]) + + Subscript[m, 3]^2*(7*d - 2*Subscript[\[Nu], 1] - 10*Subscript[\[Nu], 2] - 4*Subscript[\[Nu], 3])) + + 2*(Subscript[m, 2]^2)^2*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2]) + + 2*(Subscript[m, 3]^2)^2*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3]) - + 8*Subscript[m, 2]^2*Subscript[m, 3]^2*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3]) + + 2*Subscript[m, 2]^2*(PP^2 - (PP - Subscript[m, 2]^2)*(5*Subscript[m, 3]^2 - + Schiebe[1, "-"] + Schiebe[3, "-"]) - (Subscript[m, 2]^2)^2)*Subscript[\[Nu], 2]*Schiebe[2, "+"] + + 2*Subscript[m, 3]^2*(PP^2 - (PP - Subscript[m, 3]^2)*(5*Subscript[m, 2]^2 - Schiebe[1, "-"] + Schiebe[2, "-"]) - + (Subscript[m, 3]^2)^2)*Subscript[\[Nu], 3]*Schiebe[3, "+"] - + PP*(Subscript[\[CapitalSigma], 3] + 2)*(Schiebe[1, "-"] - Schiebe[2, "-"] - Schiebe[3, "-"]))* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 83] = + OperatorApplyJ[Subscript[e, 83]]; + +Subscript[h, 83] = + nuExplicit[Subscript[s, 83]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. d -> d - 2; + +Subscript[f, 83] = + MakeFun[Subscript[h, 83], "(83)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol + _Integer?Positive]], m1 :> 0]; + +Subscript[t, 1] = + Subscript[m, 1]^2 + Subscript[m, 2]^2 + Subscript[m, 3]^2; + +Subscript[t, 2] = + 3*(Subscript[m, 1]^4 + Subscript[m, 2]^4 + Subscript[m, 3]^4) + + 2*(Subscript[m, 1]^2*Subscript[m, 2]^2 + Subscript[m, 1]^2*Subscript[m, 3]^2 + + Subscript[m, 2]^2*Subscript[m, 3]^2); + +Subscript[t, 3] = + Subscript[m, 1]^2*(Subscript[m, 1]^4 - Subscript[m, 2]^4 - Subscript[m, 3]^4) + + Subscript[m, 2]^2*(Subscript[m, 2]^4 - Subscript[m, 1]^4 - Subscript[m, 3]^4) + + Subscript[m, 3]^2*(Subscript[m, 3]^4 - Subscript[m, 1]^4 - Subscript[m, 2]^4) + + 10*Subscript[m, 1]^2*Subscript[m, 2]^2*Subscript[m, 3]^2; + +f[\[Mu]1_, \[Mu]2_, \[Mu]3_] := + \[Mu]1*(PP - \[Mu]1)*(-2*(d - 4)*PP^2 + PP*(4*Subscript[t, 1]*(5*d - 18) - 24*\[Mu]1*(2*d - 7)) - + 2*(4*d - 13)*Subscript[t, 1]^2 + 2*(9*d - 31)*Subscript[t, 2] - 24*\[Mu]2*\[Mu]3*(4*d - 13) - 24*\[Mu]1^2*(2*d - 7)); + +Subscript[f, 1, 2, 3] = + f[Subscript[m, 1]^2, Subscript[m, 2]^2, Subscript[m, 3]^2]; + +Subscript[f, 2, 1, 3] = + f[Subscript[m, 2]^2, Subscript[m, 1]^2, Subscript[m, 3]^2]; + +Subscript[f, 3, 2, 1] = + f[Subscript[m, 3]^2, Subscript[m, 2]^2, Subscript[m, 1]^2]; + +g[\[Mu]1_, \[Mu]2_, \[Mu]3_] := + ((\[Mu]1*\[Mu]2)/(d - 4))*(4*(d - 4)*PP^2 - 4*(7*d - 24)*PP*(3*\[Mu]3 - 2*Subscript[t, 1]) - + Subscript[t, 1]^2*(23*d - 80) + Subscript[t, 2]*(9*d - 32) - 12*\[Mu]3^2*(d - 4) + 12*\[Mu]1*\[Mu]2*(7*d - 24)); + +Subscript[g, 1, 2, 3] = + g[Subscript[m, 1]^2, Subscript[m, 2]^2, Subscript[m, 3]^2]; + +Subscript[g, 1, 3, 2] = + g[Subscript[m, 1]^2, Subscript[m, 3]^2, Subscript[m, 2]^2]; + +Subscript[g, 2, 3, 1] = + g[Subscript[m, 2]^2, Subscript[m, 3]^2, Subscript[m, 1]^2]; + + +Subscript[e, 87] = + 3*PP*(d - 3)*(d - 4)*(3*d - 8)*(3*d - 10)*TJI[d, {1, 1, 1}] == + ((d - 4)^2*PP^3 - 2*PP^2*Subscript[t, 1]*(d - 4)*(6*d - 23) + + PP*(5*Subscript[t, 1]^2*(15*d^2 - 117*d + 224) - + Subscript[t, 2]*(42*d^2 - 331*d + 640)) - (1/4)*(d - 5)*(Subscript[t, 3]*(27*d - 90) - + Subscript[t, 1]*Subscript[t, 2]*(3*d - 2) - 2*Subscript[t, 1]^3*(5*d - 26)) + + Subscript[f, 1, 2, 3]*Schiebe[1, "+"] + + Subscript[f, 2, 1, 3]*Schiebe[2, "+"] + + Subscript[f, 3, 2, 1]*Schiebe[3, "+"] + + Subscript[g, 1, 2, 3]*Schiebe[1, "+"]*Schiebe[2, "+"]*Schiebe[3, "-"] + + Subscript[g, 1, 3, 2]*Schiebe[1, "+"]*Schiebe[2, "-"]*Schiebe[3, "+"] + + Subscript[g, 2, 3, 1]*Schiebe[1, "-"]*Schiebe[2, "+"]*Schiebe[3, "+"])*TJI[-2 + d, {1, 1, 1}]; + +Subscript[s, 87] = + OperatorApplyJ[Subscript[e, 87]]; + +Subscript[h, 87] = + Subscript[s, 87]; + +Subscript[f, 87] = + MakeFun[Subscript[h, 87], "(87)", IFF[PP =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 90] = + 3*PP*(d - 3)*(d - 4)*(3*d - 10)*Schiebe[1, "+"]*TJI[d, {1, 1, 1}] == + ((-Subscript[m, 1]^2)*(PP^2*(7*d - 24) - 2*PP*((4*d - 15)*Subscript[t, 1] - (d - 5)* + Subscript[m, 1]^2) + (3/2)*(d - 5)*Subscript[t, 1]^2 + (5/2)*(d - 3)*Subscript[t, 2] - + 2*(5*d - 17)*(Subscript[m, 1]^2)^2 - 2*(13*d - 45)*Subscript[m, 2]^2*Subscript[m, 3]^2)* + Schiebe[1, "+"] + 2*Subscript[m, 2]^2*(PP - Subscript[m, 2]^2)*((d - 3)*(PP + Subscript[m, 2]^2 - + 5*Subscript[m, 3]^2) + (7*d - 25)*Subscript[m, 1]^2)*Schiebe[2, "+"] + + 2*Subscript[m, 3]^2*(PP - Subscript[m, 3]^2)*((d - 3)*(PP - 5*Subscript[m, 2]^2 + + Subscript[m, 3]^2) + (7*d - 25)*Subscript[m, 1]^2)*Schiebe[3, "+"] - (d - 3)*(d - 4)*PP^2 + + + PP*((7*d - 30)*(d - 3)*Subscript[t, 1] - (7*d - 31)*(3*d - 10)*Subscript[m, 1]^2) + + (1/4)*(d - 5)*((17*d - 66)*Subscript[t, 1]^2 - (3*d - 14)*Subscript[t, 2] - + 4*(3*d - 10)*((Subscript[m, 1]^2)^2 + 5*Subscript[m, 2]^2*Subscript[m, 3]^2)) + + (2/(d - 4))*(((PP + Subscript[m, 2]^2)*(7*d - 24) + (d - 4)*Subscript[m, 1]^2 - + (5*d - 18)*Subscript[m, 3]^2)*Subscript[m, 1]^2*Subscript[m, 2]^2*Schiebe[1, "+"]*Schiebe[2, "+"]*Schiebe[3,"-"] + + ((PP + Subscript[m, 3]^2)*(7*d - 24) + (d - 4)*Subscript[m, 1]^2 - + (5*d - 18)*Subscript[m, 2]^2)*Subscript[m, 1]^2*Subscript[m, 3]^2*Schiebe[1, "+"]*Schiebe[2, "-"]*Schiebe[3, "+"] - + 2*((PP + Subscript[m, 2]^2 + Subscript[m, 3]^2)*(d - 3) + + (d - 4)*Subscript[m, 1]^2)*Subscript[m, 2]^2*Subscript[m, 3]^2*Schiebe[1, "-"]*Schiebe[2, "+"]*Schiebe[3, "+"]))*TJI[-2 + d, {1, 1, 1}]; + +Subscript[s, 90] = + OperatorApplyJ[Subscript[e, 90]]; + +Subscript[h, 90] = + Subscript[s, 90]; + +Subscript[f, 90] = + MakeFun[Subscript[h, 90], "(90)", IFF[PP =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 91.1] = + (d - 2)*Subscript[\[Nu], 1]*Schiebe[1, "+"]*TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (-Subscript[u, 1, 2, 3] - Schiebe[1, "-"] + Schiebe[2, "-"] + Schiebe[3, "-"])* + TKI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 91.1] = + OperatorApplyK[Subscript[e, 91.1]]; + +Subscript[e, 91.2] = + (d - 2)*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]* + TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2],Subscript[\[Nu], 3]}] == + (-2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] + (d - 2 - 2*Subscript[\[Nu], 1]))* + TKI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 91.2] = + OperatorApplyK[Subscript[e, 91.2]]; + +Subscript[e, 91.3] = + (d - 2)*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])* + TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (-(Subscript[\[CapitalDelta], 1, 2, 3] + Subscript[u, 1, 2, 3]*Schiebe[1, "-"] + Subscript[u, 2, 1, 3]*Schiebe[2, "-"] + + Subscript[u, 3, 1, 2]*Schiebe[3, "-"])) TKI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 91.3] = + OperatorApplyK[Subscript[e, 91.3]]; + +Subscript[e, 91.4] = + Subscript[\[CapitalDelta], 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (Subscript[u, 1, 2, 3]*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2]) + + 2*Subscript[m, 2]^2*(Subscript[\[Nu], 1] - Subscript[\[Nu], 2]) + + Subscript[u, 3, 1, 2]*Subscript[\[Nu], 1]*Schiebe[1, "+"] (Schiebe[2, "-"] - Schiebe[3, "-"]) + + 2*Subscript[m, 2]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"]*(Schiebe[1, "-"] - Schiebe[3, "-"]))* + TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 91.4] = + OperatorApplyK[Subscript[e, 91.4]]; + +Subscript[h, 911] = + Subscript[s, 91.1] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 911] = + MakeFun[Subscript[h, 911], "(911)", IFF[Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[h, 912] = + Subscript[s, 91.2] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; + +Subscript[f, 912] = + MakeFun[Subscript[h, 912], "(912)", IFF[Subscript[\[Nu], 2] > 1 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[h, 913] = + Subscript[s, 91.3]; + +Subscript[f, 913] = + MakeFun[Subscript[h, 913], "(913)", IFF[(n2 === 1 || n3 === 1) && MatchQ[d, _Symbol + _Integer?Positive]], n1 :> 1]; + +Subscript[h, 914] = + Subscript[s, 91.4] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 914] = + MakeFun[Subscript[h, 914], "(914)", IFF[Subscript[\[CapitalDelta], 1, 2, 3] =!= 0 && Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol]]]; + + +Subscript[e, 92] = + 2*Subscript[m, 2]*Subscript[m,3]*(Subscript[m, 2] + Subscript[m, 3])*(d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - + 2*Subscript[\[Nu], 3] - 1)*Schiebe[1, "+"] TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (Subscript[m, 2]*((d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3] - 1)*(Schiebe[1, "+"]*Schiebe[2, "-"] -1) + + (Subscript[\[Nu], 1] - Subscript[\[Nu], 2] + 1)*Schiebe[1, "+"]*Schiebe[3, "-"]) + + Subscript[m, 3]*((d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - Subscript[\[Nu], 3] - 1)*(Schiebe[1, "+"]*Schiebe[3, "-"] - 1) + + (Subscript[\[Nu], 1] - Subscript[\[Nu], 3] + 1)*Schiebe[1, "+"]*Schiebe[2, "-"]))* + TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 92] = + OperatorApplyK[Subscript[e, 92]]; + +Subscript[e, 93] = + 2*Subscript[m, 2]^2*(d - 2*Subscript[\[Nu], 1] - 2)*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - + Subscript[\[Nu], 3] - 1)*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])*Schiebe[1, "+"]* + TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3])*(d - 2*Subscript[\[Nu], 1] - + 2*Subscript[\[Nu], 2])*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])* + TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 93] = + OperatorApplyK[Subscript[e, 93]]; + +Subscript[h, 93] = + Subscript[s, 93] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 93] = + MakeFun[Subscript[h, 93], "(93)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[m, 2] =!= 0], {m1 :> 0, m3 :> m2}]; + +Subscript[e, 94] = + Subscript[\[CapitalDelta], 1, 2, 6]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}] == + (Subscript[u, 6, 1, 2]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*Schiebe[2, "-"] - d + Subscript[\[Nu], 1] + 2*Subscript[\[Nu], 2]) + + 2*Subscript[m, 2]^2*(Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[1, "-"] - d + 2*Subscript[\[Nu], 1] + Subscript[\[Nu], 2]))* + TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}]; + +Subscript[s, 94] = + OperatorApplyB[Subscript[e, 94]]; + +Subscript[h, 94] = + Subscript[s, 94] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 94] = + MakeFun[Subscript[h, 94], "(94)", IFF[Subscript[\[CapitalDelta], 1, 2, 6] =!= 0 && Subscript[\[Nu], 1] > 1]]; + +Subscript[n, 9401] = + Subscript[s, 94] /. Subscript[\[CapitalDelta], 1, 2, 6] -> 0 /. Subscript[u, 6, 1, 2] -> 0; + +Subscript[h, 9401] = + -Subscript[n, 9401][[2, 2]] == Subscript[n, 9401][[2, 1]]; + +Subscript[f, 9401] = + MakeFun[Subscript[h, 9401], "(9401)", IFF[Subscript[\[CapitalDelta], 1, 2, 6] === 0 && Subscript[u, 6, 1, 2] === 0 && m2 =!= 0]]; + +Subscript[n, 9402] = +Interchange[Subscript[s, 94] /. Subscript[\[CapitalDelta], 1, 2, 6] -> 0 /. Subscript[u, 6, 1, 2] -> 0, 1 \[LeftRightArrow] 2]; + +Subscript[h, 9402] = + -Subscript[n, 9402][[2, 1]] == Subscript[n, 9402][[2, 2]]; + +Subscript[f, 9402] = + MakeFun[Subscript[h, 9402], "(9402)", IFF[Subscript[\[CapitalDelta], 1, 2, 6] === 0 && Subscript[u, 6, 1, 2] === 0 && m1 =!= 0]]; + +Subscript[e, 95] = + 2*PP*Subscript[\[Nu], 1]*Schiebe[1, "+"] TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}] == (Subscript[u, 1, 2, 6] + + Schiebe[1, "-"] - Schiebe[2, "-"])*TBI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}]; + +Subscript[s, 95] = + OperatorApplyB[Subscript[e, 95]]; + +Subscript[h, 95] = + Subscript[s, 95] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 95] = + MakeFun[Subscript[h, 95], "(95)", IFF[Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 96] = + 2*PP*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 1)*TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}] == + (Subscript[\[CapitalDelta], 1, 2, 6] + Subscript[u, 1, 2, 6]*Schiebe[1, "-"] + Subscript[u, 2, 1, 6]*Schiebe[2, "-"])* + TBI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}]; + +Subscript[s, 96] = + OperatorApplyB[Subscript[e, 96]]; + +Subscript[h, 96] = + Subscript[s, 96]; + +Subscript[f, 96] = + MakeFun[Subscript[h, 96], "(96)", IFF[MatchQ[d, _Symbol + _Integer?Positive]], n1 :> 1]; + +Subscript[e, 97] = + 2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] TAI[d, {Subscript[\[Nu], 1]}] == + (d - 2*Subscript[\[Nu], 1]) TAI[d, {Subscript[\[Nu], 1]}]; + +Subscript[s, 97] = + OperatorApplyA[Subscript[e, 97]]; + +Subscript[h, 97] = + Subscript[s, 97] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 97] = + MakeFun[Subscript[h, 97], "(97)", IFF[Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol]]]; + +Subscript[e, 98] = + (d - 2*Subscript[\[Nu], 1])*TAI[d, {Subscript[\[Nu], 1]}] == -2*Subscript[m, 1]^2* + TAI[-2 + d, {Subscript[\[Nu], 1]}]; + +Subscript[s, 98] = + OperatorApplyA[Subscript[e, 98]]; + +Subscript[h, 98] = + Subscript[s, 98]; + +Subscript[f, 98] = + MakeFun[Subscript[h, 98], "(98)", IFF[MatchQ[d, _Symbol + _Integer?Positive]]]; + +Subscript[e, 99] = + Subscript[\[Nu], 1]*(d - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3])*(d - Subscript[\[Nu], 2] - + Subscript[\[Nu], 3] - 1)*Schiebe[1, "+"]*TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (-Subscript[\[Nu], 2])*(-d + 2*Subscript[\[Nu], 2] + 2)*(-2*d + Subscript[\[Nu], 1] + 2*Subscript[\[Nu], 2] + 2*Subscript[\[Nu], 3] + 2)* + Schiebe[2, "+"]*TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 99] = + OperatorApplyJ[Subscript[e, 99]]; + +Subscript[h, 99] = + Subscript[s, 99] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; + +Subscript[f, 99] = + MakeFun[Subscript[h, 99], "(99)", IFF[m1^2 === PP && Subscript[\[Nu], 1] > 1], {m2 :> 0, m3 :> 0}]; + +Subscript[h, 9912] = + Interchange[ Subscript[s, 99] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1, 1 \[LeftRightArrow] 2]; + +Subscript[f, 9912] = + MakeFun[Subscript[h, 9912], "(9912)", IFF[m2^2 === PP && Subscript[\[Nu], 2] > 1], {m1 :> 0, m3 :> 0}]; + +Subscript[h, 9913] = + Interchange[Subscript[s, 99] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1, 1 \[LeftRightArrow] 3]; + +Subscript[f, 9913] = + MakeFun[Subscript[h, 9913], "(9913)", IFF[m3^2 === PP && Subscript[\[Nu], 3] > 1], {m1 :> 0, m2 :> 0}]; + +Subscript[e, 100] = + 2*Subscript[m, 2]^2*(1 - Subscript[\[Nu], 2])*Subscript[\[Nu], 2]*Schiebe[2, "+"]* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == + (d - 2*Subscript[\[Nu], 2])*(1 - Subscript[\[Nu], 2])*TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] - + Subscript[\[Nu], 1]*(-d + 2*Subscript[\[Nu], 1] + 2)*Schiebe[1, "+"]*Schiebe[2, "-"]* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; + +Subscript[s, 100] = + OperatorApplyJ[Subscript[e, 100]]; + +Subscript[h, 100] = + Subscript[s, 100]; + +Subscript[f, 100] = + MakeFun[Subscript[h, 100] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1, "(100)", IFF[Subscript[\[Nu], 2] > 2 && m2 =!= 0], m1 :> 0]; + +Subscript[h, 1002] = + Interchange[Subscript[s, 100], 1 \[LeftRightArrow] 3]; + +Subscript[f, 1002] = + MakeFun[Subscript[h, 1002] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1, "(1002)", IFF[Subscript[\[Nu], 2] > 2 && m2 =!= 0], m3 :> 0]; + +Subscript[h, 1003] = + Interchange[Subscript[s, 100], 1 \[LeftRightArrow] 3, 1 \[LeftRightArrow] 2]; + +Subscript[f, 1003] = + MakeFun[Subscript[h, 1003] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1, "(1003)", IFF[Subscript[\[Nu], 1] > 2 && m1 =!= 0], m3 :> 0]; + +Subscript[h, 1004] = + Interchange[Subscript[s, 100], 1 \[LeftRightArrow] 2]; + +Subscript[f, 1004] = + MakeFun[Subscript[h, 1004] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1, "(1004)", IFF[Subscript[\[Nu], 1] > 2 && m1 =!= 0], m2 :> 0]; + +Subscript[h, 1005] = + Interchange[Subscript[s, 100], 2 \[LeftRightArrow] 3]; + +Subscript[f, 1005] = + MakeFun[Subscript[h, 1005] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1, "(1005)", + IFF[Subscript[\[Nu], 3] > 2 && m3 =!= 0], m1 :> 0]; + +Subscript[h, 1006] = + Interchange[Subscript[s, 100], 2 \[LeftRightArrow] 3, 1 \[LeftRightArrow] 2]; + +Subscript[f, 1006] = + MakeFun[Subscript[h, 1006] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1, "(1006)", IFF[Subscript[\[Nu], 3] > 2 && m3 =!= 0], m2 :> 0]; + +Subscript[s, 150] = + TFI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {-1, m4}, {n5, m5}}] == + TFI[d, PP, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}, {n5, m5}}] - + 2*TFI[d, PP, {0, 0, 0, 1, 0}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}] + (PP + m2^2 - m4^2)* + TFI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}]; + +Subscript[h, 150] = + Subscript[s, 150]; + +Subscript[f, 150] = + MakeFun[Subscript[h, 150], "(150)"]; + +Subscript[s, 151] = + TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2, m2}, {n3, m3}, {-1, m4}, {n5, m5}}] == + TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}, {n5, m5}}] - + 2*TFI[d, PP, DP, {a, b}, {0, 0, 0, 1, 0}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}] + + (PP + m2^2 - m4^2)*TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}]; + +Subscript[h, 151] = + Subscript[s, 151]; + +Subscript[f, 151] = + ReplacePart[MakeFun[Subscript[h, 151], "(151)"], {a_, b_}, {1, 1, 4}]; + +Subscript[s, 152] = + TVI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {-1, m4}}] == + TVI[d, PP, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}}] - + 2*TFI[d, PP, {0, 0, 0, 1, 0}, {{0, 0}, {n2, m2}, {n3, m3}, {0, 0}, {n1, m1}}] + + (PP + m2^2 - m4^2)*TVI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}}]; + +Subscript[h, 152] = + Subscript[s, 152]; + +Subscript[f, 152] = + MakeFun[Subscript[h, 152], "(152)"]; + +Subscript[s, 153] = + TVI[d, PP, {{n1, m1}, {-1, m2}, {n3, m3}, {n4, m4}}] == + TFI[d, PP, {0, 1, 0, 0, 0}, {{0, 0}, {0, 0}, {n3, m3}, {n4, m4}, {n1, m1}}] + + m2^2*TVI[d, PP, {{n1, m1}, {0, 0}, {n3, m3}, {n4, m4}}]; + +Subscript[h, 153] = + Subscript[s, 153]; + +Subscript[f, 153] = + MakeFun[Subscript[h, 153], "(153)"]; + +Subscript[s, 200] = + 16*Subscript[m, 1]^2* + Subscript[\[Nu], + 1]*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - + Subscript[\[Nu], 3])* + TJI[d, {1 + Subscript[\[Nu], 1], Subscript[\[Nu], 2], + Subscript[\[Nu], 3]}] == + (-(1 + 3*d - 3*Subscript[\[Nu], 1] - 4*Subscript[\[Nu], 2]))* + Subscript[\[Nu], 3]* + TJI[d, {-1 + Subscript[\[Nu], 1], Subscript[\[Nu], 2], + 1 + Subscript[\[Nu], 3]}] - + Subscript[\[Nu], + 2]*(1 + 3*d - 3*Subscript[\[Nu], 1] - 4*Subscript[\[Nu], 3])* + TJI[d, {-1 + Subscript[\[Nu], 1], 1 + Subscript[\[Nu], 2], + Subscript[\[Nu], 3]}] + + (-1 + 2*d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2])* + Subscript[\[Nu], 3]* + TJI[d, {Subscript[\[Nu], 1], -1 + Subscript[\[Nu], 2], + 1 + Subscript[\[Nu], 3]}] - + (-6*d^2 + 22*d*Subscript[\[Nu], 1] - + 16*Subscript[\[Nu], 1]^2 - Subscript[\[Nu], 2] + + 6*d*Subscript[\[Nu], 2] - + 13*Subscript[\[Nu], 1]*Subscript[\[Nu], 2] - + Subscript[\[Nu], 3] + 6*d*Subscript[\[Nu], 3] - + 13*Subscript[\[Nu], 1]*Subscript[\[Nu], 3] - + 4*Subscript[\[Nu], 2]*Subscript[\[Nu], 3])* + TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], + Subscript[\[Nu], 3]}] + + Subscript[\[Nu], + 2]*(-1 + 2*d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3])* + TJI[d, {Subscript[\[Nu], 1], + 1 + Subscript[\[Nu], 2], -1 + Subscript[\[Nu], 3]}]; +Subscript[h, 200] = +Subscript[s, 200] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 +Subscript[f, 200] = +MakeFun[Subscript[h, 200], "(200)", + IFF[Subscript[\[Nu], 1] > 1 && m1 =!= 0 && PP === m1^2], {m2 :> m1, m3 :> m1}]; + +Subscript[f, 201] = + HoldForm[TJR[d_, PP_, {{(n1_)?PQ, 0}, {(n2_)?PQ, 0}, {(n3_)?PQ, m3_}}] := + ( + TComment["(201)", TJIC[d, {{n1, 0}, {n2, 0}, {n3, m3}}]]; + -(((d - n1 - n2)*(-2 - d + 2*n1 + 2*n2)*(3*d - 2*n1 - 2*n2 - 2*n3)*(-1 - d + n1 + n2 + n3)* + TJI[d, PP, {{-1 + n1, 0}, {n2, 0}, {n3, m3}}])/(2*m3^2*(d - 2*n1)*(-1 + n1)*(2*d - 2*n1 - 2*n2 - n3)*(1 + + 2*d - 2*n1 - 2*n2 - n3))) + ) /; n1 > 1 && m3 =!= 0 && PP === m3^2]; + +Subscript[f, 202] = + HoldForm[TJR[d_, PP_, {{(n1_)?PQ, 0}, {(n3_)?PQ, m3_}, {(n2_)?PQ, 0}}] := + ( + TComment["(202)", TJIC[d, {{n1, 0}, {n2, 0}, {n3, m3}}]]; + -(((d - n1 - n2)*(-2 - d + 2*n1 + 2*n2)*(3*d - 2*n1 - 2*n2 - 2*n3)*(-1 - d + n1 + n2 + n3)* + TJI[d, m3^2, {{-1 + n1, 0}, {n2, 0}, {n3, m3}}])/(2*m3^2*(d - 2*n1)*(-1 + n1)*(2*d - 2*n1 - 2*n2 - n3)*(1 + + 2*d - 2*n1 - 2*n2 - n3)))) /; n1 > 1 && m3 =!= 0 && PP === m3^2]; + +Subscript[f, 203] = + HoldForm[TJR[d_, 0, {{(n1_)?PQ, 0}, {(n2_)?PQ, m2_}, {(n3_)?PQ, m2_}}] := + ( + TComment["(203)", TJIC[d, 0, {{n1, 0}, {n2, m2}, {n3, m2}}]]; + ((d - 2*(-1 + n1 + n2))*(1 + d - n1 - n2 - n3)*(d - 2*(-1 + n1 + n3))* + TJR[d, 0, {{-1 + n1, 0}, {n2, m2}, {n3, m2}}])/(2*m2^2*(d - 2*n1)*(1 + d - 2*n1 - n2 - n3)*(2 + d - 2*n1 - n2 - n3)))]; + + +Subscript[f, 204] = + HoldForm[TJR[d_, 0, {{(n2_)?PQ, m2_}, {(n1_)?PQ, 0}, {(n3_)?PQ, m2_}}] := + ( + TComment["(204)", TJIC[d, 0, {{n2, m2}, {n1, 0}, {n3, m2}}]]; + ((d - 2*(-1 + n1 + n2))*(1 + d - n1 - n2 - n3)*(d - 2*(-1 + n1 + n3))* + TJR[d, 0, {{-1 + n1, 0}, {n2, m2}, {n3, m2}}])/(2*m2^2*(d - 2*n1)*(1 + d - 2*n1 - n2 - n3)*(2 + d - 2*n1 - n2 - n3)))]; + +Subscript[f, 205] = + HoldForm[TJR[d_, + 0, {{(n2_)?PQ, m2_}, {(n3_)?PQ, m2_}, {(n1_)?PQ, 0}}] := + ( + TComment["(205)", TJIC[d, 0, {{n2, m2}, {n3, m2}, {n1, 0}}]]; + ((d - 2*(-1 + n1 + n2))*(1 + d - n1 - n2 - n3)*(d - 2*(-1 + n1 + n3))* + TJR[d, 0, {{-1 + n1, 0}, {n2, m2}, {n3, m2}}])/(2* m2^2*(d - 2*n1)*(1 + d - 2*n1 - n2 - n3)*(2 + d - 2*n1 - n2 - n3)))]; + +If[ MatchQ[$RankLimit, {_Integer?NonNegative, _Integer? NonNegative}], + $TarasovTdeltaplimit = $RankLimit[[1]]; + $TarasovTplimit = $RankLimit[[2]], + + $TarasovTdeltaplimit = 2; + $TarasovTplimit = 2 +]; + +tarti = + Timing[ + ia = 0; + ib = 0; + ir = 0; + es = 0; + Do[ + If[ 0 < ia + ib + ir + es, + WriteString["stdout", {ia, ib, ir, es}]; + Set @@ {Subscript[s, 10^4 + 1000*ia + 100*ib + 10*ir + es], + + TFI[d, PP, DP, {ia, ib}, {0, 0, ir, es, 0}, {{n1, m1}, {n2, m2}, {n3, m3}, {n4, m4}, {n5, m5}}] == + ApplyTarasovT[TarasovT[ia, ib, ir, es, PP, DP], + + STLI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {n4, m4}, {n5, m5}}]] /. STLI -> TFI} + ], + {ia, 0, $TarasovTdeltaplimit}, {ib, 0, $TarasovTdeltaplimit - ia}, {ir, 0, $TarasovTplimit}, {es, 0, $TarasovTplimit - ir} + ] + ]; + +matarti = + Timing[ + ia = 0; + ib = 0; + ir = 0; + es = 0; + Do[ + If[0 < ia + ib + ir + es, + WriteString["stdout", {ia, ib, ir, es}]; + Subscript[f, 10^4 + 1000*ia + 100*ib + 10*ir + es] = + MakeFun[Subscript[s, 10^4 + 1000*ia + 100*ib + 10*ir + es], + StringJoin["(1", ToString[ia], ToString[ib], ToString[ir], ToString[es], ")"]] /. PQ :> PNQ + ], + {ia, 0, $TarasovTdeltaplimit}, {ib, 0, $TarasovTdeltaplimit - ia}, {ir, 0, $TarasovTplimit}, {es, 0, $TarasovTplimit - ir} + ] + ] + +(*TODO ...*) +Share[] + +TVR[2 + (d_Symbol), pp_, {{1, m1_}, {1, m1_}, {2, 0}, {1, m1_}}] := + ((-6*m1^2 + 2*d*m1^2 + 3*pp)*TAI[d, 0, {{1, m1}}]^2)/(12*(-3 + d)*(-1 + d)*m1^2*pp) + + ((4*m1^2 - pp)*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/(4*(-3 + d)*(-1 + d)* m1^2) - + ((6*m1^2 - 2*d*m1^2 - 7*pp + 2*d*pp)*TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(6*(-2 + d)*(-1 + d)*pp) + + ((-4*m1^2 + pp)*(-6*m1^2 + 2*d*m1^2 + 3*pp)*TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(6*(-3 + d)*(-2 + d)*(-1 + d)*pp) /; m1 =!= 0 && pp =!= 0; + +TVR[4 + (d_Symbol), pp_, {{1, m1_}, {1, m1_}, {2, 0}, {1, m1_}}] := + -((-96*d*m1^6 + 352*d^2*m1^6 - 384*d^3*m1^6 + 128*d^4*m1^6 - + 192*m1^4*pp + 1008*d*m1^4*pp - 1632*d^2*m1^4*pp + + 912*d^3*m1^4*pp - 144*d^4*m1^4*pp + 288*m1^2*pp^2 - + 1536*d*m1^2*pp^2 + 2316*d^2*m1^2*pp^2 - 1086*d^3*m1^2*pp^2 + 66*d^4*m1^2*pp^2 + 72*d*pp^3 - 166*d^2*pp^3 + 81*d^3*pp^3 + + 4*d^4*pp^3)*TAI[d, 0, {{1, m1}}]^2)/ (36*(-1 + d)^2*d^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)* pp^2) + + ((4*m1^2 - pp)^2*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/(4*(-1 + d)^2*d*(1 + d)) - + ((288*m1^8 - 1152*d*m1^8 + 1504*d^2*m1^8 - 768*d^3*m1^8 + 128*d^4*m1^8 - 816*m1^6*pp + 2480*d*m1^6*pp - + 2224*d^2*m1^6*pp + 736*d^3*m1^6*pp - 80*d^4*m1^6*pp + 864*m1^4*pp^2 - 2196*d*m1^4*pp^2 + + 1446*d^2*m1^4*pp^2 - 252*d^3*m1^4*pp^2 - 6*d^4*m1^4*pp^2 - 432*m1^2*pp^3 + 1086*d*m1^2*pp^3 - + 895*d^2*m1^2*pp^3 + 315*d^3*m1^2*pp^3 - 44*d^4*m1^2*pp^3 + 4*d*pp^4 - 2*d^2*pp^4 - 4*d^3*pp^4 + 2*d^4*pp^4)* + TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(18*(-2 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) + + (m1^2*(4*m1^2 - pp)*(-96*m1^6 + 352*d*m1^6 - 384*d^2*m1^6 + 128*d^3*m1^6 + 240*m1^4*pp - 624*d*m1^4*pp + + 384*d^2*m1^4*pp - 48*d^3*m1^4*pp - 192*m1^2*pp^2 + 420*d*m1^2*pp^2 - 162*d^2*m1^2*pp^2 - + 18*d^3*m1^2*pp^2 + 72*pp^3 - 154*d*pp^3 + 81*d^2*pp^3 - 8*d^3*pp^3)* + TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(18*(-2 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) /; m1 =!= 0 && pp =!= 0; + +TVR[4 + (d_Symbol), pp_, {{1, m1_}, {1, m1_}, {3, 0}, {1, m1_}}] := + ((-72*d^2*m1^6 + 144*d^3*m1^6 - 88*d^4*m1^6 + 16*d^5*m1^6 - + 240*d*m1^4*pp + 572*d^2*m1^4*pp - 398*d^3*m1^4*pp + + 84*d^4*m1^4*pp - 2*d^5*m1^4*pp - 96*m1^2*pp^2 + 480*d*m1^2*pp^2 - + 744*d^2*m1^2*pp^2 + 390*d^3*m1^2*pp^2 - 50*d^4*m1^2*pp^2 + 4*d^5*m1^2*pp^2 - 24*d*pp^3 + + 54*d^2*pp^3 - 27*d^3*pp^3)*TAI[d, 0, {{1, m1}}]^2)/ (24*(-3 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)* + m1^2*pp^2) + ((4*m1^2 - pp)^2*TAI[d, 0, {{1, m1}}]* TBI[d, pp, {{1, m1}, {1, m1}}])/(8*(-3 + d)*(-1 + d)^2*(1 + d)* m1^2) + + ((-72*d*m1^6 + 144*d^2*m1^6 - 88*d^3*m1^6 + 16*d^4*m1^6 - 96*m1^4*pp + 260*d*m1^4*pp - 166*d^2*m1^4*pp + + 12*d^3*m1^4*pp + 6*d^4*m1^4*pp + 160*m1^2*pp^2 - 300*d*m1^2*pp^2 + 50*d^2*m1^2*pp^2 + + 90*d^3*m1^2*pp^2 - 24*d^4*m1^2*pp^2 - 48*pp^3 + 114*d*pp^3 - 67*d^2*pp^3 + 4*d^3*pp^3 + 2*d^4*pp^3)* + TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ (12*(-2 + d)*(-1 + d)^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)* pp^2) - + ((-4*m1^2 + pp)*(72*d*m1^6 - 144*d^2*m1^6 + 88*d^3*m1^6 - 16*d^4*m1^6 + 96*m1^4*pp - 236*d*m1^4*pp + + 122*d^2*m1^4*pp + 12*d^3*m1^4*pp - 10*d^4*m1^4*pp - 96*m1^2*pp^2 + + 180*d*m1^2*pp^2 - 30*d^2*m1^2*pp^2 - 46*d^3*m1^2*pp^2 + 8*d^4*m1^2*pp^2 + 24*pp^3 - 54*d*pp^3 + 27*d^2*pp^3)* + TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(12*(-3 + d)*(-2 + d)*(-1 + d)^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) /; m1 =!= 0 && pp =!= 0; + +TVR[6 + (d_Symbol), pp_, {{1, m1_}, {1, m1_}, {4, 0}, {1, m1_}}] := + ((2304*d*m1^10 - 4608*d^2*m1^10 - 3520*d^3*m1^10 + 6976*d^4*m1^10 + 1472*d^5*m1^10 - 2624*d^6*m1^10 - + 256*d^7*m1^10 + 256*d^8*m1^10 + 4608*m1^8*pp - + 9600*d*m1^8*pp - 7680*d^2*m1^8*pp + 9312*d^3*m1^8*pp + 11680*d^4*m1^8*pp - + 6560*d^5*m1^8*pp - 2880*d^6*m1^8*pp + 1088*d^7*m1^8*pp + + 32*d^8*m1^8*pp + 6912*m1^6*pp^2 - 35712*d*m1^6*pp^2 + 1056*d^2*m1^6*pp^2 + + 85296*d^3*m1^6*pp^2 - 37032*d^4*m1^6*pp^2 - 20484*d^5*m1^6*pp^2 + 8700*d^6*m1^6*pp^2 - + 12*d^7*m1^6*pp^2 - 84*d^8*m1^6*pp^2 - 20736*m1^4*pp^3 + 58752*d*m1^4*pp^3 + 40560*d^2*m1^4*pp^3 - + 150536*d^3*m1^4*pp^3 + 18980*d^4*m1^4*pp^3 + 48946*d^5*m1^4*pp^3 - 6748*d^6*m1^4*pp^3 - + 146*d^7*m1^4*pp^3 + 128*d^8*m1^4*pp^3 + 3456*m1^2*pp^4 - 13824*d*m1^2*pp^4 - 4176*d^2*m1^2*pp^4 + + 35784*d^3*m1^2*pp^4 - 8332*d^4*m1^2*pp^4 - 10162*d^5*m1^2*pp^4 + 1122*d^6*m1^2*pp^4 - + 80*d^7*m1^2*pp^4 - 8*d^8*m1^2*pp^4 + 864*d*pp^5 - 216*d^2*pp^5 - 2268*d^3*pp^5 + 486*d^4*pp^5 + 729*d^5*pp^5)* + TAI[d, 0, {{1, m1}}]^2)/(432*(-3 + d)*(-1 + d)^2* d^2*(1 + d)*(2 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)* m1^2*pp^3) + + ((4*m1^2 - pp)^3*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/(16*(-3 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*m1^2) - + ((-1152*m1^10 + 2880*d*m1^10 + 320*d^2*m1^10 - 3648*d^3*m1^10 + 1088*d^4*m1^10 + 768*d^5*m1^10 - + 256*d^6*m1^10 - 192*m1^8*pp + 1312*d*m1^8*pp + 2080*d^2*m1^8*pp - 6880*d^3*m1^8*pp + 4032*d^4*m1^8*pp - 192*d^5*m1^8*pp - + 160*d^6*m1^8*pp + 6336*m1^6*pp^2 - 6960*d*m1^6*pp^2 - 16960*d^2*m1^6*pp^2 + 17292*d^3*m1^6*pp^2 - + 1828*d^4*m1^6*pp^2 - 828*d^5*m1^6*pp^2 + 68*d^6*m1^6*pp^2 - 9504*m1^4*pp^3 + + 3624*d*m1^4*pp^3 + 26104*d^2*m1^4*pp^3 - 10938*d^3*m1^4*pp^3 - 4976*d^4*m1^4*pp^3 + + 330*d^5*m1^4*pp^3 + 400*d^6*m1^4*pp^3 + 6336*m1^2*pp^4 - 3640*d*m1^2*pp^4 - 14584*d^2*m1^2*pp^4 + + 9190*d^3*m1^2*pp^4 + 1374*d^4*m1^2*pp^4 - 600*d^5*m1^2*pp^4 - 56*d^6*m1^2*pp^4 - 864*pp^5 + + 732*d*pp^5 + 1864*d^2*pp^5 - 1695*d^3*pp^5 + 148*d^4*pp^5 + 36*d^5*pp^5 + 4*d^6*pp^5)* + TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(216*(-2 + d)*(-1 + d)^2* + d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)*pp^3) + + ((-4*m1^2 + pp)*(1152*m1^10 - 2880*d*m1^10 - 320*d^2*m1^10 + + 3648*d^3*m1^10 - 1088*d^4*m1^10 - 768*d^5*m1^10 + + 256*d^6*m1^10 + 576*m1^8*pp - 2208*d*m1^8*pp - 2304*d^2*m1^8*pp + + 8000*d^3*m1^8*pp - 4256*d^4*m1^8*pp - 32*d^5*m1^8*pp + 224*d^6*m1^8*pp - 6336*m1^6*pp^2 + + 6288*d*m1^6*pp^2 + 16320*d^2*m1^6*pp^2 - 14868*d^3*m1^6*pp^2 + 684*d^4*m1^6*pp^2 + + 804*d^5*m1^6*pp^2 - 12*d^6*m1^6*pp^2 + 6912*m1^4*pp^3 - 3192*d*m1^4*pp^3 - 18160*d^2*m1^4*pp^3 + + 7950*d^3*m1^4*pp^3 + 3128*d^4*m1^4*pp^3 - 78*d^5*m1^4*pp^3 - 160*d^6*m1^4*pp^3 - + 3456*m1^2*pp^4 + 1800*d*m1^2*pp^4 + 8136*d^2*m1^2*pp^4 - 4322*d^3*m1^2*pp^4 - + 1042*d^4*m1^2*pp^4 + 128*d^5*m1^2*pp^4 + 16*d^6*m1^2*pp^4 + 432*pp^5 - 324*d*pp^5 - 972*d^2*pp^5 + 729*d^3*pp^5)* + TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(216*(-3 + d)*(-2 + d)*(-1 + d)^2* + d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)*pp^3) /; m1 =!= 0 && pp =!= 0; + +TVR[6 + (d_Symbol), pp_, {{2, m1_}, {1, m1_}, {3, 0}, {1, m1_}}] := + -((-1536*d*m1^10 + 2560*d^2*m1^10 + 3200*d^3*m1^10 - + 3584*d^4*m1^10 - 2176*d^5*m1^10 + 1024*d^6*m1^10 + + 512*d^7*m1^10 - 3072*m1^8*pp + 6528*d*m1^8*pp + 5376*d^2*m1^8*pp - 7520*d^3*m1^8*pp - + 5568*d^4*m1^8*pp + 3232*d^5*m1^8*pp + 1344*d^6*m1^8*pp - 320*d^7*m1^8*pp - 2304*m1^6*pp^2 + + 13824*d*m1^6*pp^2 + 192*d^2*m1^6*pp^2 - 31584*d^3*m1^6*pp^2 + 11232*d^4*m1^6*pp^2 + + 8088*d^5*m1^6*pp^2 - 2304*d^6*m1^6*pp^2 - 24*d^7*m1^6*pp^2 + 6912*m1^4*pp^3 - 19584*d*m1^4*pp^3 - + 12688*d^2*m1^4*pp^3 + 50584*d^3*m1^4*pp^3 - 7516*d^4*m1^4*pp^3 - 16982*d^5*m1^4*pp^3 + + 2564*d^6*m1^4*pp^3 + 310*d^7*m1^4*pp^3 - 1152*m1^2*pp^4 + 4608*d*m1^2*pp^4 + 1392*d^2*m1^2*pp^4 - + 11896*d^3*m1^2*pp^4 + 2820*d^4*m1^2*pp^4 + 3374*d^5*m1^2*pp^4 - 414*d^6*m1^2*pp^4 + + 8*d^7*m1^2*pp^4 - 288*d*pp^5 + 72*d^2*pp^5 + 756*d^3*pp^5 - 162*d^4*pp^5 - 243*d^5*pp^5)* + TAI[d, 0, {{1, m1}}]^2)/(144*(-1 + d)^2*d^2*(1 + d)*(2 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)* + m1^2*pp^3) + ((4*m1^2 - pp)^3*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/(16*(-1 + d)^2* + d*(1 + d)*(3 + d)*m1^2) - ((2304*m1^10 - 5760*d*m1^10 - 640*d^2*m1^10 + 7296*d^3*m1^10 - 2176*d^4*m1^10 - 1536*d^5*m1^10 + + 512*d^6*m1^10 - 1344*m1^8*pp + 1120*d*m1^8*pp - 1376*d^2*m1^8*pp + 5280*d^3*m1^8*pp - 4896*d^4*m1^8*pp + 1280*d^5*m1^8*pp - + 64*d^6*m1^8*pp - 5184*m1^6*pp^2 + 7584*d*m1^6*pp^2 + 14800*d^2*m1^6*pp^2 - 21496*d^3*m1^6*pp^2 + + 6120*d^4*m1^6*pp^2 + 280*d^5*m1^6*pp^2 - 184*d^6*m1^6*pp^2 + 9504*m1^4*pp^3 - + 3720*d*m1^4*pp^3 - 27296*d^2*m1^4*pp^3 + 15378*d^3*m1^4*pp^3 + 4114*d^4*m1^4*pp^3 - + 666*d^5*m1^4*pp^3 - 674*d^6*m1^4*pp^3 - 6336*m1^2*pp^4 + 5720*d*m1^2*pp^4 + 13712*d^2*m1^2*pp^4 - + 13926*d^3*m1^2*pp^4 + 1284*d^4*m1^2*pp^4 + 946*d^5*m1^2*pp^4 - 80*d^6*m1^2*pp^4 + 864*pp^5 - + 1020*d*pp^5 - 1636*d^2*pp^5 + 2311*d^3*pp^5 - 693*d^4*pp^5 + 20*d^5*pp^5 + 4*d^6*pp^5)* + TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(72*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)*pp^3) + + ((4*m1^2 - pp)*(-768*m1^10 + 1664*d*m1^10 + 768*d^2*m1^10 - 2176*d^3*m1^10 + 512*d^5*m1^10 + 192*m1^8*pp + + 288*d*m1^8*pp + 704*d^2*m1^8*pp - 2272*d^3*m1^8*pp + 1024*d^4*m1^8*pp + + 64*d^5*m1^8*pp + 1920*m1^6*pp^2 - 1824*d*m1^6*pp^2 - 5472*d^2*m1^6*pp^2 + 4584*d^3*m1^6*pp^2 - + 168*d^5*m1^6*pp^2 - 2304*m1^4*pp^3 + 616*d*m1^4*pp^3 + 6192*d^2*m1^4*pp^3 - + 1946*d^3*m1^4*pp^3 - 1128*d^4*m1^4*pp^3 - 230*d^5*m1^4*pp^3 + 1152*m1^2*pp^4 - 600*d*m1^2*pp^4 - + 2744*d^2*m1^2*pp^4 + 1414*d^3*m1^2*pp^4 + 374*d^4*m1^2*pp^4 - 16*d^5*m1^2*pp^4 - 144*pp^5 + + 108*d*pp^5 + 324*d^2*pp^5 - 243*d^3*pp^5)*TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(72*(-2 + d)*(-1 + d)^2* + d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)*pp^3) /; m1 =!= 0 && pp =!= 0; + +TFR[d_, PP_ /; Head[PP] =!= List, {{0, _}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] := + TVI[d, PP, {{n5, m5}, {n2, m2}, {n3, m3}, {n4, m4}}]; + +TFR[d_, PP_ /; Head[PP] =!= List, {{n2_, m2_}, {0, _}, {n4_, m4_}, {n3_, m3_}, {n5_, m5_}}] := + TVI[d, PP, {{n5, m5}, {n2, m2}, {n3, m3}, {n4, m4}}]; + +TFR[d_, PP_ /; Head[PP] =!= List, {{n3_, m3_}, {n4_, m4_}, {0, _}, {n2_, m2_}, {n5_, m5_}}] := + TVI[d, PP, {{n5, m5}, {n2, m2}, {n3, m3}, {n4, m4}}]; + +TFR[d_, PP_ /; Head[PP] =!= List, {{n4_, m4_}, {n3_, m3_}, {n2_, m2_}, {0, _}, {n5_, m5_}}] := + TVI[d, PP, {{n5, m5}, {n2, m2}, {n3, m3}, {n4, m4}}]; + +TFR[d_, PP_ /; Head[PP] =!= List, {{n1_, m1_}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}, {0, _}}] := + TBI[d, PP, {{n1, m1}, {n3, m3}}]*TBI[d, PP, {{n2, m2}, {n4, m4}}]; + +TVI[d_, PP_, {{0, _}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}}] := + TAI[d, 0, {{n3, m3}}]*TBI[d, PP, {{n2, m2}, {n4, m4}}]; + +TVI[d_, PP_, {{n1_, m1_}, {n2_, m2_}, {0, _}, {n4_, m4_}}] := + TAI[d, 0, {{n1, m1}}]*TBI[d, PP, {{n2, m2}, {n4, m4}}]; + +TVI[d_, _, {{n1_, m1_}, {0, _}, {n3_, m3_}, {n4_, m4_}}] := + TJI[d, 0, {{n1, m1}, {n3, m3}, {n4, m4}}]; + +TVI[d_, PP_, {{n1_, m1_}, {n2_, m2_}, {n3_, m3_}, {0, _}}] := + TJI[d, PP, {{n2, m2}, {n1, m1}, {n3, m3}}]; + +TJI[d_, _, {{0, _}, {n2_, m2_}, {n3_, m3_}}] := + TAI[d, 0, {{n2, m2}}]*TAI[d, 0, {{n3, m3}}]; + +TJI[d_, _, {{n1_, m1_}, {0, _}, {n3_, m3_}}] := + TAI[d, 0, {{n1, m1}}]*TAI[d, 0, {{n3, m3}}]; + +TJI[d_, _, {{n1_, m1_}, {n2_, m2_}, {0, _}}] := + TAI[d, 0, {{n1, m1}}]*TAI[d, 0, {{n2, m2}}]; + +TBI[d_, _, {{0, _}, {n2_, m2_}}] := + TAI[d, 0, {{n2, m2}}]; + +TBI[d_, _, {{n1_, m1_}, {0, _}}] := + TAI[d, 0, {{n1, m1}}]; + +TAI[d_, {{n_Integer, m_}}] := + TAI[d, 0, {{n, m}}]; + +TAI[d_, {n_Integer, m_}] := + TAI[d, 0, {{n, m}}]; + +TAI[d_, 0, {n_Integer, m_}] := + TAI[d, 0, {{n, m}}]; + +$TLRComment = False; +TLRComment[s_String] := + WriteString["stdout", s, " "] /; $TLRComment === True; + +applytlrules[y_, fun_] := + fun[y /. TFI -> TLR /. TLRules /. TLR -> TFI]; + +TFIRecurse[z_, f_: Identity] := + (FixedPoint[(applytlrules[#1, f] ) & , z, 1000] /. TAI[dim_, pp_, list_List]/;pp=!=0:>TAI[dim,0,list]); + +applytlrules2[y_, fun_] := + fun[y /. TFI -> TLR /. TLRules2 /. TLR -> TFI]; + +TFISimplify[z_, f_: Identity] := + (FixedPoint[applytlrules2[#1, f] & , z, 1000]/. TAI[dim_, pp_, list_List]/;pp=!=0:>TAI[dim,0,list]); + +ExpandMaybe = + Identity; + +fN[li_List] := fN[li] = li /. {0, _} :> {0, 0}; +TLR[depp__, {a___, b_Integer, c___}] := TLR[depp, {a, {b, 0}, c}]; + +tlrule[1] = + TLR[d_, pp_, {0, 0, 0, 0, 0}, pr_] :> (NoTLRComment["tlrule1"]; TFI[d, pp, pr /. {0, _} :> {0, 0}] ); + +tlrule[2] = + TLR[dpp__, {(v_)?PQ, w_, x_, y_, z_}, {{(n1_)?PQ, m1_}, nm2_, nm3_, nm4_, nm5_}] :> + ( + TLRComment["tlrule2"]; + ExpandMaybe[ + If[ v <= n1, + If[ m1 === 0, + TLR[dpp, {0, w, x, y, z}, {{n1 - v, 0}, nm2, nm3, nm4, nm5}], + Sum[Binomial[v, i] TLR[dpp, {0, w, x, y, z}, {fN[{n1 - i, m1}], nm2, nm3, nm4, nm5}]*(m1^2)^(v - i), {i, 0, v}] + ], + If[ m1 === 0, + TLR[dpp, {v - n1, w, x, y, z}, {{0, 0}, nm2, nm3, nm4, nm5}], + Sum[Binomial[n1, i] TLR[dpp, {v - n1, w, x, y, z}, {fN[{n1 - i, m1}], nm2, nm3, nm4, nm5}]*(m1^2)^(n1 - i), {i, 0, n1}] + ] + ] + ] + ); + +tlrule[3] = + TLR[dpp__, {v_, (w_)?PQ, x_, y_, z_}, {nm1_, {(n2_)?PQ, m2_}, nm3_, nm4_, nm5_}] :> + ( + TLRComment["tlrule3"]; + ExpandMaybe[ + If[ w <= n2, + If[ m2 === 0, + TLR[dpp, {v, 0, x, y, z}, {nm1, {n2 - w, 0}, nm3, nm4, nm5}], + Sum[Binomial[w, i] TLR[dpp, {v, 0, x, y, z}, {nm1, fN[{n2 - i, m2}], nm3, nm4, nm5}]*(m2^2)^(w - i), {i, 0, w}] + ], + If[ m2 === 0, + TLR[dpp, {v, w - n2, x, y, z}, {nm1, {0, 0}, nm3, nm4, nm5}], + Sum[Binomial[n2, i] TLR[dpp, {v, w - n2, x, y, z}, {nm1, fN[{n2 - i, m2}], nm3, nm4, nm5}]*(m2^2)^(n2 - i), {i, 0, n2}]]]] + ); + +tlrule[4] = + TLR[dpp__, {v_, w_, (x_)?PQ, y_, z_}, {{(n1_)?PQ, m1_}, nm2_, {(n3_)?PQ, m3_}, nm4_, nm5_}] :> + ( + TLRComment["tlrule4"]; + ExpandMaybe[ + (1/2)*TLR[dpp, {v + 1, w, x - 1, y, z}, {{n1, m1}, nm2, {n3, m3}, nm4, nm5}] - + (1/2)*TLR[dpp, {v, w, x - 1, y, z}, {{n1, m1}, nm2, fN[{n3 - 1, m3}], nm4, nm5}] + + (1/2)*({dpp}[[2]] - m3^2)*TLR[dpp, {v, w, x - 1, y, z}, {{n1, m1}, nm2, {n3, m3}, nm4, nm5}]] + ); + +tlrule[5] = + TLR[dpp__, {v_, w_, x_, (y_)?PQ, z_}, {{n1_, m1_}, {(n2_)?PQ, m2_}, nm3_, {(n4_)?PQ, m4_}, nm5_}] :> + ( + TLRComment["tlrule5"]; + ExpandMaybe[ + (1/2)*TLR[dpp, {v, w + 1, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, {n4, m4}, nm5}] - + (1/2)*TLR[dpp, {v, w, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, fN[{n4 - 1, m4}], nm5}] + + (1/2)*({dpp}[[2]] - m4^2) TLR[dpp, {v, w, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, {n4, m4}, nm5}]] + ); + +tlrule[6] = + TLR[dpp__, {v_, w_, x_, y_, (z_)?PQ}, {{n1_, m1_}, {n2_, m2_}, nm3_, nm4_, {(n5_)?PQ, m5_}}] :> + ( + TLRComment["tlrule6"]; + ExpandMaybe[ + (1/2)*TLR[dpp, {v + 1, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}] - + (1/2)*TLR[dpp, {v, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, fN[{n5 - 1, m5}]}] + + (1/2)*TLR[dpp, {v, w + 1, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}] - + (1/2)*m5^2*TLR[dpp, {v, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}]] + ); + +tlrule[7] = + TLR[d_, pp_, dp___, {(v_)?PQ, w_, x_, y_, z_}, {{0, _}, nm2_, {(n3_)?PQ, m3_}, nm4_, nm5_}] :> + ( + TLRComment["tlrule7"]; + ExpandMaybe[ + TLR[d, pp, dp, {v - 1, w, x, y, z}, {{0, 0}, nm2, fN[{n3 - 1, m3}], nm4, nm5}] + + 2*TLR[d, pp, dp, {v - 1, w, x + 1, y, z}, {{0, 0}, nm2, {n3, m3}, nm4, nm5}] - + (pp - m3^2)*TLR[d, pp, dp, {v - 1, w, x, y, z}, {{0, 0}, nm2, {n3, m3}, nm4, nm5}] + ] + ); + +tlrule[8] = + TLR[d_, pp_, dp___, {v_, (w_)?PQ, x_, y_, z_}, {nm1_, {0, _}, nm3_, {(n4_)?PQ, m4_}, nm5_}] :> + ( + TLRComment["tlrule8"]; + ExpandMaybe[ + TLR[d, pp, dp, {v, w - 1, x, y, z}, {nm1, {0, 0}, nm3, fN[{n4 - 1, m4}], nm5}] + + 2*TLR[d, pp, dp, {v, w - 1, x, y + 1, z}, {nm1, {0, 0}, nm3, {n4, m4}, nm5}] - (pp - m4^2)* + TLR[d, pp, dp, {v, w - 1, x, y, z}, {nm1, {0, 0}, nm3, {n4, m4}, nm5}] + ] + ); + +tlrule[9] = + TLR[d_, pp_, {v_, w_, x_, y_, (z_)?PQ}, {nm1_, nm2_, nm3_, nm4_, {0, _}}] :> + ( + TLRComment["tlrule9"]; + FunctionExpand[ + ExpandMaybe[ + Sum[(Gamma[k + 1/2]*Gamma[d/2 - 1/2]*Binomial[z, 2*k]*Binomial[k, i]*Binomial[k, j]*(-1)^(i + j)*pp^(i + j - z)* + TLR[d, pp, {v + i, w + j, x + z - 2*i, y + z - 2*j, 0}, {nm1, nm2, nm3, nm4, {0, 0}}])/(Gamma[1/2]* + Gamma[k + d/2 - 1/2]), {k, 0, Floor[z/2]}, {i, 0, k}, {j, 0, k}] + ] + ] + ); + +tlrule[10] = + TLR[_, _, {_, _, (x_)?PNQ, (y_)?PNQ, _}, {{(_)?PQ, _}, {(_)?PQ, _}, {0, _}, {0, _}, _}] :> (TLRComment["tlrule10"]; 0 /; OddQ[x + y]); + +tlrule[11] = + TLR[d_, pp_, {v_, w_, (x_)?PQ, (y_)?PQ, z_}, {nm1_, nm2_, {0, _}, {0, _}, {(n5_)?PQ, m5_}}] :> + ( + TLRComment["tlrule11"]; + ExpandMaybe[(pp/(d + x + y - 2))*((x - 1)*TLR[d, pp, {v + 1, w, x - 2, y, z}, {nm1, nm2, {0, 0}, {0, 0}, {n5, m5}}] + + y*TLR[d, pp, {v, w, x - 1, y - 1, z + 1}, {nm1, nm2, {0, 0}, {0, 0}, {n5, m5}}])] /; EvenQ[x + y] && x > 1); + +tlrule[12] = + TLR[d_, pp_, {v_, w_, (x_)?PQ, (y_)?PQ, z_}, {nm1_, nm2_, {0, _}, {0, _}, {(n5_)?PQ, m5_}}] :> + ( + TLRComment["tlrule12"]; + ExpandMaybe[ + (pp/(d + x + y - 2))*((y - 1)*TLR[d, pp, {v, w + 1, x, y - 2, z}, {nm1, nm2, {0, 0}, {0, 0}, {n5, m5}}] + + x*TLR[d, pp, {v, w, x - 1, y - 1, z + 1}, {nm1, nm2, {0, 0}, {0, 0}, {n5, m5}}])] /; EvenQ[x + y] && y > 1 + ); + +tlrule[13] = + TLR[d_, pp_, {0, 0, 0, (y_)?PQ, 0}, {nm1_, {0, 0}, nm3_, {(n4_)?PQ, m4_}, nm5_}] :> + ( + TLRComment["tlrule13"]; + Sum[Binomial[y, i]*pp^(y - i)*(-1)^i*TLR[d, pp, {0, 0, 0, i, 0}, {nm3, {n4, m4}, nm1, {0, 0}, nm5}], {i, 0, y}] + ); + +tlrule[14] = + TLR[d_, pp_, {0, 0, (x_)?PQ, 0, 0}, {{0, 0}, nm2_, {(n3_)?PQ, m3_}, nm4_, nm5_}] :> + ( + TLRComment["tlrule14"]; + Sum[Binomial[x, i]*pp^(x - i)*(-1)^i* TLR[d, pp, {0, 0, i, 0, 0}, {{n3, m3}, nm4, {0, 0}, nm2, nm5}], {i, 0, x}]); + +tlrule[15] = + HoldPattern[TLR[_, _, {_, _, _, _, _}, {{_, 0}, {_, 0}, {0, _}, {0, _}, {0, _}}]] :> (TLRComment["tlrule15"]; 0); + +tlrule[16] = + TLR[_, _, {0, 0, (x_)?PQ, (y_)?PQ, 0}, {{_, _}, {_, _}, {0, _}, {0, _}, {0, _}}] :> (TLRComment["tlrule16"]; 0 /; OddQ[x] || OddQ[y]); + +tlrule[17] = + TLR[d_, pp_, {(a_)?PQ, b_, 0, de_, 0}, {{0, _}, {n2_, m2_}, {0, _}, {n4_, m4_}, {n5_, m5_}}] :> + ( + TLRComment["tlrule17"]; + Sum[Binomial[a, i]*Binomial[i, j]*(1 + (-1)^j)*2^(j - 1)* + TLR[d, pp, {a - i, b + i - j, 0, de,j}, {{n5, m5}, {n2, m2}, {0, 0}, {n4, m4}, {0, 0}}], {i, 0, a}, {j, 0, i}] + ); + +tlrule[18] = + TLR[d_, pp_, dp_, {(a_)?PNQ, (b_)?PNQ}, {1, 0, 0, 0, 0}, {{0, 0}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] :> + ( + TLRComment["tlrule18"]; + Sum[Binomial[a, i]*Binomial[b,j]*((pp + m3^2)*TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}] + + TLR[d, pp, dp, {i, j}, {{n3 - 1, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}] - + 2*TLR[d, pp, dp, {i, j}, {0, 0, 1, 0, 0}, {{n3, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}])*(-1)^(i + j)*dp^(a + b - i - j), {i, 0, a}, {j, 0, b}] + ); + +tlrule[19] = + TLR[d_, pp_, dp_, {(a_)?PNQ, (b_)?PNQ}, {0, 1, 0, 0, 0}, {{n1_, m1_}, {0, 0}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] :> + ( + TLRComment["tlrule18"]; + Sum[Binomial[a, i]*Binomial[b, j]*((pp + m4^2)* TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4, m4}, {n1, m1}, {0, 0}, {n5, m5}}] + + TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4 - 1, m4}, {n1, m1}, {0, 0}, {n5, m5}}] - + 2*TLR[d, pp, dp, {i, j}, {0, 0, 0, 1, 0}, {{n3, m3}, {n4, m4}, {n1, m1}, {0, 0}, {n5, m5}}])*(-1)^(i + j)*dp^(a + b - i - j), {i, 0, a}, {j, 0, b}] + ); + +tlrule[20] = + TLR[d_, pp_, {(v_)?PQ, w_, x_, y_, 0}, {{0, _}, nm2_, {0, _}, nm4_, {(n5_)?PQ, m5_}}] :> + ( + TLRComment["tlrule20"]; + Sum[Binomial[i, r]*Binomial[v, i]*Binomial[x, j]*2^r*TLR[d, pp, {v - i, -r + i + w, j, x - j + y, r}, {{n5, m5}, nm2, 0, nm4, 0}], {j, 0, x}, {i, 0, v}, {r, 0, i}] + ); + +tlrule[21] = + TLR[d_, pp_, {v_, (w_)?PQ, x_, y_, 0}, {nm1_, {0, _}, nm3_, {0, _}, nm5_}] :> + ( + TLRComment["tlrule21"]; + TLR[d, pp, {w, v, y, x, 0}, {{0, 0}, nm1, {0, 0}, nm3, nm5}] + ); + +tlrule[22] = + TLR[d_, pp_, dp_, {0, (b_)?PNQ}, {0, (w_)?PNQ, 0, (y_)?PNQ, 1}, {nm1_, nm2_, nm3_, nm4_, {0, 0}}] :> + ( + TLRComment["tlrule22"]; (1/pp)* + TLR[d, pp, dp, {0, b}, {0, w, 1, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] + ); + +tlrule[23] = + TLR[d_, pp_, dp_, {1, (b_)?PNQ}, {0, (w_)?PNQ, 0, (y_)?PNQ, 1}, {nm1_, nm2_, nm3_, nm4_, {0, 0}}] :> + ( + TLRComment["tlrule23"]; + (1/((1 - d)*pp))*TLR[d, pp, dp, {0, b + 1}, {0, w, 2, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - + ((d*dp)/((1 - d)*pp^2))*TLR[d, pp, dp, {0, b}, {0, w, 2, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - (1/(1 - d))* + TLR[d, pp, dp, {0, b + 1}, {1, w, 0, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] + (dp/((1 - d)*pp))* + TLR[d, pp, dp, {0, b}, {1, w, 0, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] + ); + +tlrule[24] = + TLR[d_, pp_, dp_, {2, (b_)?PNQ}, {0, (w_)?PNQ, 0, (y_)?PNQ, 1}, {nm1_, nm2_, nm3_, nm4_, {0, 0}}] :> + ( + TLRComment["tlrule24"]; + 2*dp*(1/((1 - d)*pp^2))* TLR[d, pp, dp, {0, b + 1}, {0, w, 3, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - + (((d + 2)*dp^2)/((1 - d)*pp^3))*TLR[d, pp, dp, {0, b}, {0, w, 3, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - + ((2*dp)/((1 - d)*pp))*TLR[d, pp, dp, {0, b + 1}, {1, w, 1, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] + ((3*dp^2)/((1 - d)*pp^2))* + TLR[d, pp, dp, {0, b}, {1, w, 1, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] + ); + +tlrule[25] = + TLR[dim_, pp_, {a_, b_, (c_)?PNQ, (d_)?PQ, 0}, {nm1_, nm2_, nm3_, {0, _}, nm5_}] :> + ( + TLRComment["tlrule25"]; + TLR[dim, pp, {b, a, d, c, 0}, {nm2, nm1, {0, 0}, nm3, nm5}] + ) /; d > c; + +TLRules = Array[tlrule, 25]; + +TLRules2 = Drop[TLRules, {9, 9}]; + +TLR[__, {{_, _}, {0, _}, {_, _}, {0, _}, {_, 0}}] := + 0; +TLR[__, {{0, _}, {_, _}, {0, _}, {_, _}, {_, 0}}] := + 0; +TLR[__, {{0, _}, {_, _}, {_, 0}, {_, _}, {0, _}}] := + 0; +TLR[__, {{_, 0}, {_, _}, {0, _}, {_, _}, {0, _}}] := + 0; +TLR[__, {{_, _}, {_, 0}, {_, _}, {0, _}, {0, _}}] := + 0; +TLR[__, {{_, _}, {0, _}, {_, _}, {_, 0}, {0, _}}] := + 0; + +SetAttributes[seeetDelayed, HoldAll]; + +seeetDelayed[TLR[a__], b_] := + SetDelayed @@ {TLR[a], b}; + +lis1 = + Permutations[{{0, _}, {0, _}, {0, _}, {_, _}, {_, 0}}]; + +lis2 = + Table[TLR[__, lis1[[i]]] :> 0, {i, Length[lis1]}] /. RuleDelayed -> seeetDelayed; + +Clear[lis1, lis2]; + +TJIS[d_, (M_)^2, {{\[Alpha]_, 0}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := + SMu^2*(((-1)^(\[Alpha] + \[Beta] + \[Gamma] + 1)/(-M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4))* + Exp[(-I)*Pi*(d - 4)]*(Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]/Gamma[(3/2)*d - \[Alpha] - \[Beta] - \[Gamma]])* + (Gamma[d/2 - \[Alpha]]/Gamma[\[Alpha]])*(Gamma[d/2 - \[Beta]]/ Gamma[\[Beta]])*(Gamma[d/2 - \[Gamma]]/Gamma[\[Gamma]])); + +TJIS[d_, (M_)^2, {{\[Beta]_, 0}, {\[Gamma]_, 0}, {\[Alpha]_, M_}}] := + TJIS[d, M^2, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]; + +TJIS[d_, (M_)^2, {{\[Beta]_, 0}, {\[Alpha]_, M_}, {\[Gamma]_, 0}}] := + TJIS[d, M^2, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]; + +TJIS[d_, (M_)^2, {{\[Alpha]_, M_}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := + (SMu^2/(M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4))*(-1)^(\[Alpha] + \[Beta] + \[Gamma] +1)* + (Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]/(Gamma[\[Alpha]]* Gamma[\[Beta]]*Gamma[\[Gamma]]))* + ((Gamma[d/2 - \[Gamma]]*Gamma[d/2 - \[Beta]])/ Gamma[d - \[Beta] - \[Gamma]])*((Gamma[\[Beta] + \[Gamma] - d/2]* + Gamma[2*d - \[Alpha] - 2*\[Beta] - 2*\[Gamma]])/ Gamma[(3*d)/2 - \[Alpha] - \[Beta] - \[Gamma]]); + +TJIS[d_, 0, {{\[Beta]_, 0}, {\[Alpha]_, M_}, {\[Gamma]_, 0}}] := + TJIS[d, 0, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]; + +TJIS[d_, 0, {{\[Beta]_, 0}, {\[Gamma]_, 0}, {\[Alpha]_, M_}}] := + TJIS[d, 0, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]; + +TJIS[d_, 0, {{\[Alpha]_, M_}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := + (SMu^2/(M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4))*(-1)^(\[Alpha] + \[Beta] + \[Gamma] + 1)* + (Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]/(Gamma[\[Alpha]]* Gamma[\[Beta]]*Gamma[\[Gamma]]))* + ((Gamma[\[Beta] + \[Gamma] - d/2]*Gamma[d/2 - \[Beta]]* Gamma[d/2 - \[Gamma]])/Gamma[d/2]); + +TJIS[d_, 0, {{\[Beta]_, M_}, {\[Alpha]_, 0}, {\[Gamma]_, M_}}] := + TJIS[d, 0, {{\[Alpha], 0}, {\[Beta], M}, {\[Gamma], M}}]; + +TJIS[d_, 0, {{\[Beta]_, M_}, {\[Gamma]_, M_}, {\[Alpha]_, 0}}] := + TJIS[d, 0, {{\[Alpha], 0}, {\[Beta], M}, {\[Gamma], M}}]; + +TJIS[d_, 0, {{\[Alpha]_, 0}, {\[Beta]_, M_}, {\[Gamma]_, M_}}] := + (SMu^2/(M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4))*(-1)^(\[Alpha] + \[Beta] + \[Gamma] + 1)* + (Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]/(Gamma[\[Beta]]* Gamma[\[Gamma]]))*(Gamma[d/2 - \[Alpha]]/Gamma[d/2])* + ((Gamma[\[Alpha] + \[Gamma] - d/2]*Gamma[\[Alpha] + \[Beta] - d/2])/ Gamma[2*\[Alpha] + \[Beta] + \[Gamma] - d]); + +TJIS[d_, 0, {{\[Alpha]_, 0}, {\[Beta]_, M_}, {\[Gamma]_, M_}}] := + (SMu^2*(-1)^(\[Alpha] + \[Beta] + \[Gamma] + 1)*Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]*Gamma[d/2 - \[Alpha]]* + (Gamma[\[Alpha] + \[Gamma] - d/2]*Gamma[\[Alpha] + \[Beta] - d/2]))/((M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4)*(Gamma[\[Beta]]* + Gamma[\[Gamma]])*Gamma[d/2]*Gamma[2*\[Alpha] + \[Beta] + \[Gamma] - d]); + +TAIS[d_, 0, {{1, M_}}] := + (-I)*M^2*SMu*Gamma[(4 - d)/2 - 1] + +TBIS[_, 0, {{_, 0}, {_, 0}}] := + 0; + +TBIS[d_, (M_)^2, {{\[Alpha]_, 0}, {\[Beta]_, 0}}] := + I*SMu*(((-1)^(\[Alpha] + \[Beta])/(-M^2)^(\[Alpha] + \[Beta] - 2))* + Exp[(-I)*Pi*((d - 4)/2)]*(Gamma[\[Alpha] + \[Beta] - d/2]/(Gamma[\[Alpha]]*Gamma[\[Beta]]))* + ((Gamma[d/2 - \[Alpha]]*Gamma[d/2 - \[Beta]])/ Gamma[d - \[Alpha] - \[Beta]])); + +TJIS[d_Symbol, (M_)^2, {{1, M_}, {1, M_}, {1, M_}}] := + M^2*SMu^2*(-(6/(-4 + d)^2) + 17/(2*(-4 + d)) + (1/8)*(-59 - 2*Pi^2) + (-4 + d)^3*FCGV["TJI111e"] + + (1/ 1920)*((-4 + d)^2*(16755 - 4750*Pi^2 - 14*Pi^4 + 3840*Pi^2*Log[2] - 12080*Zeta[3])) + + (1/96)*(-4 + d)*(195 + 98*Pi^2 - 48*Zeta[3])); + +$CommentNotebook = True; + +TComment[s_String, b_] := + If[ + If[ !ValueQ[$TarcerRecursed], $TarcerRecursed = {}]; !MemberQ[$TarcerRecursed, {s, b}], + AppendTo[$TarcerRecursed, {s, b}]; + + If[ $Notebooks && $CommentNotebook === True, + + If[ $commentnb === False, + $commentnb = True; + $cnb = NotebookCreate[StyleDefinitions -> "NaturalColor.nb", Magnification -> 1.5]; + SetOptions[$cnb, WindowMargins -> {{0, Automatic}, {Automatic, 0}}]; SetOptions[$cnb, WindowSize -> {500, 300}]; + NotebookWrite[$cnb, Cell[BoxData[ToBoxes[b /. Rule[TFIC, TFI], StandardForm]], "Input", CellDingbat -> StringJoin[s, " "]]], + + NotebookWrite[$cnb, Cell[BoxData[ToBoxes[b /. Rule[TFIC, TFI], StandardForm]], "Input", CellDingbat -> StringJoin[s, " "]]] + ], + + Print[s, b /. {TFIC :> TFI, TVIC :> TVI, TJIC :> TJI, TBIC :> TBI, TAIC :> TAI}] + ] + ] /; $Comment === True; + +$TTable = {}; + +FEPrint[a__String] := + Print[a] /; $Notebooks === False; + +FEPrint[a__String] := + If[ Head[$cnb] === NotebookObject, + NotebookWrite[$cnb, Cell[StringJoin @@ {a}, "SmallText"]]; + SelectionMove[$cnb, After, Cell] + ] /; $Notebooks === True; + +Options[TarcerRecurse] = { + FCVerbose -> False, + Factor -> Factor, + TimeConstraint -> Infinity, + Table :> $TTable, + Together -> Together, + Replace -> {} +}; + +TarcerRecurse[expr_, OptionsPattern[]] := + Catch[ + Block[{ basisdone, factorfun, fertig, dummm1, dummm2, getvars, + te, time, cutoff, tog, ttable, facfun, nexp, oldexpr, rec, + special, sti, tl, tcheck, tjrd, tvrd, together, vars, $cc = 0, + $cv, t0, tvars, time0}, + + time0 = AbsoluteTime[]; + + If [OptionValue[FCVerbose]===False, + trVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + trVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "TarcerRecurse: Entering.", FCDoControl->trVerbose]; + FCPrint[3, "TarcerRecurse: Entering with", expr, FCDoControl->trVerbose]; + + + If[ !MatchQ[ttable, + {__RuleDelayed}], + ttable = {} + ]; + + ttable = OptionValue[Table]; + + special = OptionValue[Replace]; + cutoff = OptionValue[TimeConstraint]; + together = OptionValue[Together]; + factorfun = OptionValue[Factor]; + + $commentnb = False; + + tog = + ((If[ #1 > 1001, + If[ $Comment, + FEPrint[ + StringJoin[ + "coefficient # ", + If[ ValueQ[$cv], + ToString[$cc], + "" + ], + If[ ValueQ[$cv], + StringJoin[" (", ToString[$cv], ")"], + "" + ], + " simplified, " + ], ToString[#1]]]]; #2) & + )[LeafCount[#1], $cc++; together[#1]]&; + + If[ !ValueQ[$TarcerRecursed], + $TarcerRecursed = {} + ]; + + $TarcerRecursed = {}; + + FCPrint[1, "TarcerRecurse: Applying ToTFi.", FCDoControl->trVerbose]; + time=AbsoluteTime[]; + t0 = ToTFi[expr] /. {TFi :> TFI, ToTFi :> Identity}; + FCPrint[1, "TarcerRecurse: ToFi done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->trVerbose]; + FCPrint[3, "TarcerRecurse: After ToTFi: ", t0, FCDoControl->trVerbose]; + + If[ ttable =!= {}, + FCPrint[1, "TarcerRecurse: Applying custom reduction rules (Table).", FCDoControl->trVerbose]; + time=AbsoluteTime[]; + t0 = t0 /. ttable; + FCPrint[1, "TarcerRecurse: Done applying custom reduction rules , timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->trVerbose]; + FCPrint[3, "TarcerRecurse: After applying custom reduction rules: ", t0, FCDoControl->trVerbose] + ]; + + getvars = Select[Variables[#1], MatchQ[#1, TFI[__] | TVI[__] | TJI[__] | TBI[__] | TAI[__]] & ] & ; + + If[ !FreeQ[t0, TFI], + + FCPrint[1, "TarcerRecurse: Applying TFIRecuse.", FCDoControl->trVerbose]; + time=AbsoluteTime[]; + t0 = TFIRecurse[t0]; + FCPrint[1, "TarcerRecurse: TFIRecuse done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->trVerbose]; + FCPrint[3, "TarcerRecurse: After TFIRecuse: ", t0, FCDoControl->trVerbose]; + + + If[ ttable =!= {}, + FCPrint[1, "TarcerRecurse: Applying custom reduction rules (Table).", FCDoControl->trVerbose]; + time=AbsoluteTime[]; + t0 = t0 /. ttable; + FCPrint[1, "TarcerRecurse: Done applying custom reduction rules , timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->trVerbose]; + FCPrint[3, "TarcerRecurse: After applying custom reduction rules: ", t0, FCDoControl->trVerbose] + ]; + + + t0 = Collect[t0, getvars[t0], tog] + ]; + + If[ !FreeQ[t0, TVI[_Plus, __]], + + tvrd = Select[DownValues[TVR], !FreeQ[#1, TVI[_ - 2, __]]&] /. TVR -> TVI; + FCPrint[3, "TarcerRecurse: Available rules for TVR: ", t0, FCDoControl->trVerbose]; + + + t0 = t0 /. tvrd /. tvrd /. tvrd /. tvrd; + + + t0 = Collect[t0, getvars[t0], tog]; + + If[ !FreeQ[t0, TVI[_Plus, __]], + t0 = Collect[t0 = t0 //. tvrd, getvars[t0], tog] + ] + ]; + + + tjrd = Select[DownValues[TJR], ! FreeQ[#1, TJI[_ - 2, __]] & ] /. TJR -> TJI; + + If[ !FreeQ[t0, TJI[_Plus, __]], + (*tjrd = Select[DownValues[TJR], ! FreeQ[#1, TJI[_ - 2, __]] & ] /. TJR -> TJI;*) + t0 = Collect[t0 = t0 /. tjrd /. tjrd /. tjrd /. tjrd, getvars[t0], tog]; + + If[ !FreeQ[t0, TJI[_Plus, __]], + t0 = Collect[t0 = t0 //. tjrd, getvars[t0], tog] + ] + ]; + + rec[exp_, {ti_, tr_}] := + ( + sti = ToString[ti]; + + FCPrint[4, "TarcerRecurse: rec: Entering with ", exp ," ",{ti,tr}, FCDoControl->trVerbose]; + + If[ FreeQ[exp, ti], + exp, + nexp = exp; + + If[ $Comment, + ( + If[ #1 === 1, + FEPrint[StringJoin[sti, " level, there is 1 ", sti]], + FEPrint[StringJoin[sti, " level, there are "], ToString[#1], StringJoin[" ", sti, "'s "]]] & ) + [Count[nexp, ti[__], -1]] + ]; + + nexp = nexp /. ti -> tr /. tr -> ti; + FCPrint[4, "TarcerRecurse: rec: After ti -> tr replacements ", nexp , FCDoControl->trVerbose]; + + If[ !FreeQ[nexp, TJI[_Plus, __]], + nexp = nexp //. tjrd; + FCPrint[4, "TarcerRecurse: rec: After tjrd replacements ", nexp , FCDoControl->trVerbose]; + ]; + + tvars = getvars[nexp]; $cc = 0; $cv = Length[tvars]; + nexp = Collect[nexp, tvars, tog]; + + If[ cutoff =!= Infinity, + If[ AbsoluteTime[] - time0 > cutoff, + Throw[$Failed]] + ]; + nexp + ] + ); + basisdone = 0; + + tl = {{TFI, TFR}, {TVI, TVR}, {TJI, TJR}, {TBI, TBR}, {TAI, TAR}}; + + FCPrint[3, "TarcerRecurse: Intermediate result: ", t0, FCDoControl->trVerbose]; + + + FCPrint[1, "TarcerRecurse: Doing the final recursion.", FCDoControl->trVerbose]; + time=AbsoluteTime[]; + Do[ + FCPrint[4, "TarcerRecurse: Iteration: ", i , FCDoControl->trVerbose]; + t0 = FixedPoint[rec[#1, tl[[i]]] & , t0, 100]; + FCPrint[4, "TarcerRecurse: After rec: ", t0 , FCDoControl->trVerbose]; + + + If[ Head[t0] === Plus, + fertig = Select[t0, ! FreeQ[#1, tl[[i, 1]]]]; + basisdone = basisdone + fertig; t0 = t0 - fertig + ], {i, Length[tl]} + ]; + FCPrint[1, "TarcerRecurse: Final recursion done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->trVerbose]; + FCPrint[3, "TarcerRecurse: After the final recursion: ", t0, FCDoControl->trVerbose]; + + t0 = t0 + basisdone; + $cv =. ; + + t0 = Collect[t0, {TAI[__], TAI[a1__]*TAI[a2__], TAI[__], TBI[__], TJI[__], TVI[__], TFI[__]}, factorfun]; + + If[ $Comment, + FEPrint["the result has ", ToString[Length[t0 + dummm1 + dummm2] - 2], " terms"] + ]; + + If[ $Notebooks, + SetSelectedNotebook[EvaluationNotebook[]] + ]; + + t0 = t0 /. TAI[dim_, pp_, list_List]/;pp=!=0:>TAI[dim,0,list]; + + FCPrint[1, "TarcerRecurse: Leaving.", FCDoControl->trVerbose]; + FCPrint[3, "TarcerRecurse: Leaving with: ", t0, FCDoControl->trVerbose]; + + t0 + ] + ]; + +Options[TarcerExpand] = { + TarcerReduce :> $BasisIntegrals, + TarcerRecurse -> False, Zeta -> True, + Replace -> {Prefactor1 -> Identity, EulerGamma -> 0} +}; + +TarcerExpand[expr_, d_Symbol -> fe_ /; Length[Variables[fe]] === 1, ru___Rule] := + TarcerExpand[expr, d -> fe, 0, ru]; + +TarcerExpand[expr_, d_Symbol -> fe_, (order_Integer)?NonNegative, opts___Rule] := + Block[{ + t1, t2, t3, t4, numfa, z2rule, restfa, ta0, tarcNumericalFactor, tarcFactor1, eeps, ints, vars, + t0, recurse, zeta2replace}, + + eeps = Variables[fe][[1]]; + tarcNumericalFactor[x_] := + If[ NumberQ[x], + x, + If[ Head[x] === Times, + If[ NumberQ[First[x]], + First[x], + 1 + ], + 1 + ] + ]; + + tarcFactor1[x_] := + Block[{factor1t1, factor1t2, factor1t3, mt, mi, m1, mp1, nx = x, iIii}, + + mt = #1 /. Plus -> mi /. mi -> Plus /. m1 -> -1 /. mp1 -> (-(Plus[##1]) & ) /. iIii -> I &; + + mi[y_, z__] := + m1*mp1[y, z] /; ( + If[ Head[#1] === Complex, + False, + If[ #1 < 0, + True, + False] + ]&)[tarcNumericalFactor[y]]; + + nx = x /. Complex[0, b_] -> b*iIii; + + If[ Head[nx] =!= Plus, + mt[nx /. Plus -> (Factor1[Plus[##1]] & )], + + factor1t1 = List @@ (#1 /. Plus -> factor1t3 & ) /@ nx; + factor1t2 = PolynomialGCD @@ factor1t1 /. factor1t3 -> Plus; + mt[factor1t2 Plus @@ ((#1 /. factor1t3 -> Plus)/factor1t2 & ) /@ factor1t1] + ] + ]; + + + Catch[ + e = eeps; + {ints, recurse, zeta2replace} = {TarcerReduce, TarcerRecurse, Zeta} /. Flatten[{opts, Options[TarcerExpand]}]; + + If[ zeta2replace =!= True, + z2rule = {}, + z2rule = Pi^2 :> 6*ToExpression["Zeta2"] + ]; + + ints = Flatten[ints]; + + If[ recurse =!= True, + ta0 = expr, + ta0 = TarcerRecurse[expr] + ]; + + t1 = ta0 /. ints /. { + SEpsilon[de_] :> SEpsilon[ToString[d]], + Prefactor1[de_] :> Prefactor1[ToString[de, InputForm]] + }; + + vars = Select[Variables[t1], Length[#1] > 0 & ]; + + If[ !FreeQ[vars, TFI | TVI | TJI | TKI | TBI | TAI], + Print["Returning the list of remaining integrals."]; + Throw[Select[vars, !FreeQ[#1, TFI | TVI | TJI | TKI | TBI | TAI] & ]] + ]; + + t1 = t1 /. d -> fe; polygafu[2, 1] = -2*Zeta[3]; + + polygafu[2, 2] = 2 - 2*Zeta[3]; + + polygafu[x_, y_] := + polygafu[x, y] = FunctionExpand[PolyGamma[x, y]]; + + t2 = Normal[t1 + O[e]^(order + 1)] /. PolyGamma -> polygafu /. (Replace /. {opts} /. Options[TarcerExpand]); + + t3 = Collect[t2, e, Expand[#1] /. z2rule & ]; + t3 = t2 /. ToString[d] :> fe; + + t4 = tarcFactor1[Expand[t3]] //. pre : (Prefactor1 | SEpsilon)[a_]*Prefactor1[b_] :> Prefactor1[a*b] /. Prefactor1[1] :> + 1 /. Prefactor1[xy_] :> Prefactor1[xy /. st_String :> ToExpression[st]] /. Prefactor1[(m_)^e*(xx_)]*(m_)^(any_) :> + Prefactor1[m^(e + any)*xx] /. z2rule; + + + If[ Head[t4] === Times, + numfa = tarcNumericalFactor[t4]; + restfa = Select[t4, FreeQ[#1, eeps | Log | Zeta] & ]; + + extracoll[z_, e] := + Block[{}, + If[ Head[z] === Plus, + (extracoll[#1, e] & ) /@ z, + z /. xy_Plus :> + If[ Length[Variables[xy]] === 0, + xy, + Collect[xy, Complement[Variables[xy], {e}]] + ] + ] + ]; + + (Select[t4, !FreeQ[#1, Prefactor1] & ]*(restfa/numfa)) . extracoll[Collect[Expand[(numfa*Select[t4, FreeQ[#1, Prefactor1] & ])/restfa], e], e], + + t4 + ] /. s_String :> ToExpression[s] /. d -> fe /. (Replace /. {opts} /. Options[TarcerExpand])]] /; Length[Variables[fe]] === 1; + +tfch = { + TFR :> Hold[TFR], + TVR :> Hold[TVR], + TJR :> Hold[TJR], + TBR :> Hold[TBR], + TAR :> Hold[TAR], + TComment :> Hold[TComment] +}; + +rtfch = + Reverse /@ tfch; + +SetAttributes[condrest, HoldRest]; + +Clear[remember]; +remember[zi_HoldForm] := + Block[{z = zi /. tfch}, + If[ !FreeQ[z, Condition], + Hold[HoldForm][ + Hold[SetDelayed][z[[1, 1]], ReplacePart[z[[1, 2]], Prepend[Extract[z, {1, 2, 1}, Hold], + z[[1, 1]] /. PatternTest -> pt /. pt[a_, _] :> a /. Pattern -> pat /. pat[a_, _] :> a], 1]] + ] /. Hold[HoldForm] -> HoldForm /. rtfch /. Hold[SetDelayed] -> SetDelayed /. Hold -> Set, + Hold[HoldForm][ + Hold[SetDelayed][z[[1, 1]], Prepend[Extract[z, {1, 2}, Hold], z[[1, 1]] /. PatternTest -> pt /. + pt[a_, _] :> a /. Pattern -> pat /. pat[a_, _] :> a]] + ] /. + Hold[HoldForm] -> HoldForm /. rtfch /. Hold[SetDelayed] -> SetDelayed /. Hold -> Set] + ]; + +$TarasovTdeltaplimit + +aa2 = Array[Subscript[f, #1] &, 10000 + ($TarasovTdeltaplimit + 1)*1000]; + +bb12 = Select[aa2, Head[#1] =!= Subscript &]; +Clear[aa2]; + +Print["there are ", Length[bb12], " recursion equations for $RankLimit = ", $RankLimit]; + +If[ $Remember === True, + + RCHECK = True; + nb = remember /@ bb12, + nb = bb12 +]; + +Clear[bb12]; + + +(* Checks of the recursion relations *) +CheckTVIRecursion[Subscript[f, 52]]; +CheckTVIRecursion[Subscript[f, 53]]; +CheckTVIRecursion[Subscript[f, 51]]; +CheckTVIRecursion[Subscript[f, 54]]; +CheckTVIRecursion[Subscript[f, 55]]; +CheckTVIRecursion[Subscript[f, 56]] +CheckTVIRecursion[Subscript[notnecessaryf, 60]]; +CheckTVIRecursion[Subscript[f, 63]]; +CheckTVIRecursion[Subscript[f, 66]]; +CheckTVIRecursion[Subscript[f, 67]]; +CheckTVIRecursion[Subscript[f, 6713]]; +CheckTVIRecursion[Subscript[f, 68]]; +CheckTVIRecursion[Subscript[f, 6813]]; +CheckTJIRecursion[Subscript[f, 7113]]; +CheckTJIRecursion[Subscript[f, 71]]; +CheckTJIRecursion[Subscript[f, 7123]]; +CheckTJIRecursion[Subscript[f, 78]]; +CheckTJIRecursion[Subscript[f, 80]]; +CheckTJIRecursion[Subscript[f, 81]]; +CheckTJIRecursion[Subscript[f, 8113]]; +CheckTJIRecursion[Subscript[f, 8123]]; +CheckTJIRecursion[Subscript[f, 82]]; +CheckTJIRecursion[Subscript[f, 8213]]; +CheckTJIRecursion[Subscript[f, 8212]]; +CheckTJIRecursion[Subscript[f, 83]]; +CheckTJIRecursion[Subscript[f, 100]]; +CheckTJIRecursion[Subscript[f, 1002]]; +CheckTJIRecursion[Subscript[f, 1003]]; +CheckTJIRecursion[Subscript[f, 1004]]; +CheckTJIRecursion[Subscript[f, 1005]]; +CheckTJIRecursion[Subscript[f, 1006]]; + + + +$Post =. +ReleaseHold[nb]; +$Comment = False; +End[]; +EndPackage[]; + + +$BasisIntegrals = { + TAI[d_, 0, {{1, M_}}] -> + -I*E^(1/2*(4 - d)*EulerGamma)*M^2*Gamma[-1 + (4 - d)/2]*Prefactor1[(M^2)^(1/2*(-4 + d))*SEpsilon[d]], + + TBI[d_, pp_, {{1, 0},{1, 0}}] -> + (I*E^(((4 - d)*EulerGamma)/2)*Gamma[2 - d/2]*Gamma[-1 + d/2]^2*Prefactor1[ (-pp)^((-4 + d)/2)*SEpsilon[d]])/Gamma[-2 + d], + + TJI[d_, pp_, {{1,0},{1,0},{1,0}}] -> + -((pp*Gamma[3 - d]*Gamma[-1 + d/2]^3*E^((4 - d)*EulerGamma)*Prefactor1[(-pp)^(-4 + d)*SEpsilon[d]^2])/(Gamma[-3 + (3*d)/2] )), + + TJI[d_, M_^2, {{1,M_},{1,0},{1,0}}] -> + (M^2*Gamma[3 - d]*Gamma[2 - d/2]*Gamma[-1 + d/2]^2*Gamma[-5 + 2*d]*E^((4 - d)*EulerGamma) Prefactor1[(M^2)^(-4 + d)*SEpsilon[d]^2])/(Gamma[-2 + d]*Gamma[-3 + (3*d)/2]), + + TJI[d_Symbol, (M_)^2, {{1, M_}, {1, M_}, {1, M_}}]-> + M^2*Prefactor1[(M^2)^(-4 + d)*SEpsilon[d]^2]*(-6/(-4 + d)^2 + 17/(2*(-4 + d)) + (-59 - 2*Pi^2)/8 + (-4 + d)^3*FCGV["TJI111e"] + + ((-4 + d)^2*(16755 - 4750*Pi^2 - 14*Pi^4 + 3840*Pi^2*Log[2] - 12080*Zeta[3]))/1920 + ((-4 + d)*(195 + 98*Pi^2 - 48*Zeta[3]))/96), + + TJI[d_, 0, {{1, M_}, {1, M_}, {1, 0}}]->(M^2*Gamma[3 - d]*Gamma[2 - d/2]^2*Gamma[-1 + d/2]*E^((4 - d)*EulerGamma)* + Prefactor1[(M^2)^(-4 + d)*SEpsilon[d]^2])/(Gamma[4 - d]*Gamma[d/2]), + + TJI[d_, 0, {{1,M_},{1,0},{1,0}}] ->(M^2*Gamma[3 - d]*Gamma[2 - d/2]*Gamma[-1 + d/2]^2*E^((4 - d)*EulerGamma)*Prefactor1[(M^2)^(-4 + d)*SEpsilon[d]^2])/Gamma[d/2] +}; + +filename= ToFileName[{$TARCERDirectory},StringJoin["tarcer", StringReplace[$System,{"-"->"","Microsoft"->"","("->"",")"->""," "->""}], StringJoin @@ + ToString /@ $RankLimit, ".mx"]]; + +DumpSave[filename, { + Tarcer`Cayley, + Tarcer`CayleyD, + Tarcer`Cayleyu, + Tarcer`Prefactor1, + Tarcer`TarcerRecurse, + Tarcer`TFIRecurse, + Tarcer`TFISimplify, + Tarcer`SEpsilon, + Tarcer`TarcerExpand, + Tarcer`TarcerReduce, + Tarcer`TAI, + Tarcer`TAR, + Tarcer`TBI, + Tarcer`TBR, + Tarcer`TFI, + Tarcer`TFR, + Tarcer`TJI, + Tarcer`TJR, + Tarcer`TKI, + Tarcer`TVI, + Tarcer`TVR, + Tarcer`$BasisIntegrals, + Tarcer`$Comment, + Tarcer`$CommentNotebook, + Tarcer`$RankLimit, + Tarcer`$RecursionStop, + Tarcer`$TTable, + Tarcer`Private`applytlrules, + Tarcer`Private`applytlrules2, + Tarcer`Private`ExpandMaybe, + Tarcer`Private`FactorC, + Tarcer`Private`FEPrint, + Tarcer`Private`fN, + Tarcer`Private`mbt, + Tarcer`Private`PNQ, + Tarcer`Private`PQ, + Tarcer`Private`ta, + Tarcer`Private`TA, + Tarcer`Private`TAIC, + Tarcer`Private`TBIC, + Tarcer`Private`TComment, + Tarcer`Private`TLRComment, + Tarcer`Private`TFIC, + Tarcer`Private`TJIC, + Tarcer`Private`TLR, + Tarcer`Private`tlrule, + Tarcer`Private`redblue, + Tarcer`Private`TLRules, + Tarcer`Private`TLRules2, + Tarcer`Private`TVIC, + Tarcer`Private`$TLRComment, + Tarcer`$TarcerVersion +}]; + + + + +$HistoryLength = \[Infinity]; + +Print["Elapsed time: ", Round[AbsoluteTime[] - Tarcer`Private`atime]/60. min]; +Print["File size: ", Round[FileByteCount[filename]/1024.^2], "MB"]; diff --git a/FeynCalc/Changelog.md b/FeynCalc/Changelog.md index 72d98d35d..c0e6e6601 100644 --- a/FeynCalc/Changelog.md +++ b/FeynCalc/Changelog.md @@ -1,1080 +1,1281 @@ -### Version 9.2.0 (November 2016) - -#### Important changes - * New handy functions `FCAbbreviate`, `FCHideEpsilon`, `FCShowEpsilon`, `FCLoopIBPReducableQ`, `FCFactorOut`, `SelectFree2`, `SelectNotFree2` - * Finally we have shortcuts for spinors with D-dimensional momenta: `SpinorUD`, `SpinorUBarD`, `SpinorVD`, `SpinorVBarD` - * New option `$KeepLogDivergentScalelessIntegrals` permits consistent 1-loop computations, where UV and IR divergences are regularized with different epsilons. - * `Examples/FeynRules` now contains several FeynRules models (with more to come) with additional scripts that show how such models can be used with patched `FeynArts`. This should be useful for new users. - * `DiracTrace` has received a lot of internfal refactoring and should be now faster and much more stable. Thanks to Peng Sun for motivating me to do so. I hope to get `DiracSimplify` refactored as well in the next release. - - - -#### Commit log - -* Added an example calculation to the test-suite. (a4cdd648) -* Fixed wrong option name in FCDiracIsolate. (202f3e2) -* Added some missing unit tests for FCLoop-functions. (c81660f1) -* Added few tree-level electroweak examples. (4909891) -* Added FCAbbreviate, a new function that introduces abbreviations for FeynCalc expressions that should be exported to other tools. (a7a27e5); Example: - - ``` - FCAbbreviate[SPD[p, k] FAD[{q, SMP["m_e"]}, {q + p, m}], {q}, {p, k}, Head -> spd] - ``` - -* Now FCLoopBasisFindCompletion can complete the basis using a list of user-supplied propagators given as the value of the Method option (4b70dcb) - - ``` - FCLoopBasisFindCompletion[FAD[q1 + p, +q2 - k] SPD[q1, q2], {q1, q2}, Method -> {FAD[{q2 + k, m}], FAD[{q1 - p, m}], +SPD[p, q2], SPD[k, q1]}] - ``` - -* Added new option FCLoopIBPReducableQ to FCLoopExtract and FCLoopIsolate. This allows to extract/isolate only those loop integrals that are IBP reducable. (20af417) - - ``` - FCLoopExtract[a FCI[FAD[{q, 0, 2}]] + b FCI[FAD[{q, 0, 1}]], {q},loop, FCLoopIBPReducableQ -> True] - FCLoopIsolate[a FCI[FAD[{q, 0, 2}]] + b FCI[FAD[{q, 0, 1}]], {q}, Head -> loop, FCLoopIBPReducableQ -> True] - - ``` -* Added new function FCLoopIBPReducableQ for a quick check if the given loop integrals has propagators raised to integer powers. (b699150); Example: - - ``` - FCLoopIBPReducableQ[FCI[SPD[q,q]^2FAD[{q,0,1}]]] - - ``` -* Some minor refactoring in FDS. (681ef0e) -* Improved FCLoopBasisFindCompletion to use scalar products as extra propagators. The old behavior can be achieved via the option Method->NullSpace. The new default is however Method->ScalarProduct. (38386fa); Example: - - ``` - FCLoopBasisFindCompletion[FAD[{q1, m, 2}, {q1 + q3, m}, {q2 \[Minus] q3}, q2], {q1, q2, q3}] - FCLoopBasisFindCompletion[FAD[{q1, m, 2}, {q1 + q3, m}, {q2 \[Minus] q3}, q2], {q1, q2, q3}, Method -> NullSpace] - ``` - -* Version bump to 9.2 (c8c8cfb) -* Fixed a bug in FDS related to $KeepLogDivergentScaleless set to True. (a411e67) -* Improved debugging output in FDS. (fe21cbe) -* Fixed a bug with D-dim Eps not disappearing when indices are the same. (906cac6) -* Fixed a small bug in FCShowEpsilon. (0c25ba0) -* Improved FCHideEpsilon and FCShowEpsilon to work also for D=4-Epsilon via the option D. (16b814e) -* Fixed a bug in FourDivergence related to the differentiation of FADs. (b372e2b) -* Added new shortcuts for spinors with D-dimensional momenta: SpinorUD, SpinorUBarD, SpinorVD, SpinorVBarD. (201b058); Example: - - ``` - SpinorUD[p, m] // FCI // StandardForm - SpinorVD[p, m] // FCI // StandardForm - SpinorUBarD[p, m] // FCI // StandardForm - SpinorVBarD[p, m] // FCI // StandardForm - ``` - -* Some cross-checks in ToPaVe, SPC, OneLoop,OneLoopSimplify. (0d832c2) -* Improved typesetting of the SMP's for renormalization. (1c7b512) -* Added FeynRules model for pure QED with counterterms following Bohm, Denner and Joos. (fc14872) -* Added new SMP objects for renormalization calculations. (f2eabd6) -* Perofrmance improvement in DiracTrace. (3c40740) -* Added two convenience functions FCHideEpsilon and FCShowEpsilon for doing the substitution 1/Eps - EulerGamma + Log[4Pi] -> Delta. (6cddeb0); Example: - - ``` - FCHideEpsilon[1/Epsilon - EulerGamma + Log[4 Pi]] - FCShowEpsilon[SMP["Delta"]] - ``` - -* Fixed a bug in FCReplaceD, so that DiracGamma does not loose the dimension anymore. (9544275) -* Fixed a bug in FourDivergence related to the differentiation of D-dim Dirac matrices. (dad4b85) -* Added FCFactorOut option to Collect2. Currently this only allows to factor out a global prefactor. (54f513a); Example: - - ``` - Collect2[Together[a (1 + x) + 4 b (1 + y)], {a, b}, FCFactorOut -> 4] - ``` - -* Added FCFactorOut, a small convenience function for factoring out user-specified prefactors. (31f3543); Example: - - ``` - FCFactorOut[(a + 3 b), 3 b] - ``` - -* Added SelectFree2 and SelectNotFree2. They act like SelectFree and SelectNotFree, but with an Expand2 before the selection. (d6fb941); Example: - - ``` - SelectFree2[a (b + c) + d, b] - SelectFree[a (b + c) + d, b] - SelectNotFree2[a (b + c) + d, b] - SelectNotFree[a (b + c) + d, b] - ``` - -* Added FeynArts model (generated with FeynRules) for QCD in the background field formalism. The reason is that this model is missing in the standard FeynArts. (991e340) -* Fixed a small bug in DiracTrick. (f567f82) -* Added an extra check for DiracTrick. (75466d4) -* Made DotSimplify finish faster if there is nothing to simplify. (db0a586) -* Added new option DiracSigmaExplicit to FCDiracIsolate. (9cf7654) -* Some improvements in TID for the BMHV scheme. In particular, unless BMHV scheme has been explicitly selected, amplitudes that are partly 4-dim and partly D-dim will not be tolerated anymore. (aa89a44) -* Refactoring DiracSimplify. (7f3dc3d) -* DiracTrick: Adjusted Larin's scheme (12fd5ac) -* Made DiracTrick a bit faster by evaluating simple traces before entering the main loop. (f419c0d) -* Added option FCDiracIsolate to DiracTrick. This is for calling DiracTrick from internal functions. (f40ec42) -* Cleaning up the code of DiracTrace. (ab363ab) -* Some more adjustments for DiracTrace and DiracTrick. (edc954a) -* Improved performance of DiracTrace on big traces. (64f5120) -* Some more refactoring in DiracTrick. (2be6dd4) -* Improved performance of DiracTrace for West->False. (972c7c9) -* DiracTrick: Finally separated rules for different schemes. (8bb589a) -* DirackTrick: Cleaned up the rules for moving g^5. (1a63162) -* DiracTrick: Use cached FCFastContract instead of coneins. (d4ed905) -* DiracTrick: Get rid of scev in favor of FCUseCache. (7446399) -* DiracTrick: Refactoring continues 2. (7a37313) -* DirackTrick: Refactoring continues. (f026c48) -* Continuing refactoring in DiracTrick. (3a743a1) -* Added option LorentzIndex to FCDiracIsolate that allows inclusion of Lorezntz tensors into isolated heads.dch[GS[p].GS[l]] + dch[GA[i].GA[j].GA[k] MT[mu, nu]] (beb0713; Example: - - ``` - FCDiracIsolate[ MT[mu, nu] GA[i, j, k] + GS[p, l] + MT[mu, nu] GA[mu, j, k], LorentzIndex -> True, Head -> dch] - ``` - -* Fixed in a bug in the handling of unknown non-commutative objects by DiracTrick. (fe1e459) -* DiracTrick: Splitting of DiracChains is now handled by FCDiracIsolate. (4e269d0) -* DiracTrick: Fatoring out of SUNT matrices is now handled by FCDiracIsolate. Moreover, gamma5Present checks if g^5 is present at all. (d60406a) -* Improved InsideDiracTrace simplifications of DiracTrick. (2d550c6) -* DiracTrick refactoring in progress. (b6db370) -* Improved test suite to show time required to run single tests. (2689240) -* Started refactoring of DiracTrick. (a552eaa) -* Fixed handling of Larin's scheme in Anti5. (174bb74) -* Updated description of Larin's scheme. (174f98e) -* Minor cleanups in FCI and FCE. (e86d145) -* Added example for the computation of the self-energy diagrams in pure Yang-Mills using background field formalism according to Abbott. (2845af6) -* Improved handling of Dirac traces that contain unknown non-commutative objects. (1aa3f96) -* DiracTrace improvement with Expand. (b1ff3f7) -* Rempoved some old code from DiracTrace (981ab92) -* Implemented new trace function in DiracTrace. (c6025e4) -* Test (2941b9e) -* Some more improvements in DiracTrace. (dfe1dc5) -* Some fixes in DiracTrace plus now we it uses DiracTrick instead of DiracSimplify. (57b1b2a) -* More refactoring in DiracTrace. (685a1c4) -* Even more refactoring in DiracTrace. (6be8f53) -* More refactoring in DiracTrace (1dcb5bb) -* More refactoring in DiracTrace. (a06533e) -* Some more refactoring in DiracTrace. (5187efd) -* Some more refactoring in DiracTrace. (b185f3c) -* Some fixes for Larin's scheme in DiracTrace. (cda3f15) -* Improved splitting between SUNT and DiracGamma in DotSimplify. (45ebe1e) -* Fixed a bug in the new InsideDiracTrace simplification of DiracTrick. (da94751) -* Added new option InsideDiracTrace to DiracTrick. (a5b63dc) -* Added new option DiracGammaCombine to DiracTrick and improved handling of chiral projectors. (5416c72) -* Some refactoring in DiracTrick. (87f3d4b) -* Fixed typo in the description of TarcerToFC (6abb381) -* Added new option DiracGammaCombine to FCDiracIsolate. (2d5e8aa); Example: -* - ``` - FCDiracIsolate[GA[nu].(GS[p] + GS[q] + GS[k] + m).GA[mu], Head -> dch] - - FCDiracIsolate[GA[nu].(GS[p] + GS[q] + GS[k] + m).GA[mu], Head -> dch, - DiracGammaCombine -> False] - ``` - -* Some refactoring in FCDiracIsolate. (79fdd36) -* Improved the muon decay example. (b79005d) -* Added an example for using Tdec to compute some multi-loop decompositions that appear in the renormalization of the Gross-Neveu model at 4-loops. (de1cf3b) -* Fixed a bug in Tdec related to wrong determination of symmetries in multi-loop integrals. (f4bb647) -* Added several new SMP typesettings: m_qu and m_qd for up- and down-type quark masses m_l for lepton masses Q_u and Q_D for up- and down-type quark charges g_W and g'_W for the weak couplings (5a1c91c); Example: - - ``` - ?SMP - SMP[] - ``` - -* Added the option PaVeIntegralHeads to FCLoopCanonicalize, FCLoopIsolate and FCLoopSplit. This allows to specify extra heads that should be treated as PaVe integrals. (b5ee87b); Example: - - ``` - FCLoopSplit[Foobar[x], {}, PaVeIntegralHeads -> Join[OptionValue[FCLoopIsolate, PaVeIntegralHeads], {Foobar}]] - - FCLoopIsolate[Foobar[x], {}, PaVeIntegralHeads -> Join[OptionValue[FCLoopIsolate, PaVeIntegralHeads], - {Foobar}],Head -> loop] - ``` - -* Added new !experimental! global option $KeepLogDivergentScalelessIntegrals that forces FeynCalc not to put log divergent scaleless integral 1/q^4 to zero. This is important e.g. for EFTs, where IR and UV divergences must be distinguished. (d1610d0); Example: - - ``` - $KeepLogDivergentScalelessIntegrals=True; - TID[FVD[q,mu]FVD[q,nu]FAD[{q,0,3}],q] - ``` - -* Fixed typos in the description of the ABJ example. (5262505) -* Small refactoring in OneLoop. (4d53ccd) -* Fixed a small bug (just caused a warning) in PaVeReduce when PaVe functions have user-defined options. (40f3338) -* Improved automatic installer to allow installing FeynCalc and FeynArts from local tarballs. For example: (e2a13c0) - -### Version 9.1.0 (August 2016) - -#### Important changes -* Many new hadndy functions: `FCTraceExpand`, `FCTraceFactor`, `FCGetDimensions`, `FCCanonicalizeDummyIndices`, `TarcerToFC`, `FCReplaceD`, `FCColorIsolate`, `FCDiracIsolate`, `DeclareFCTensor`, `UnDeclareFCTensor`, `CommutatorOrder` -* Improved support for using `FeynCalc` with custom `FeynRules`-models (see http://www.feyncalc.org/forum/1042.html for more details) -* `$LimitTo4` is now disabled by default. Even when set to `True`, it is applied only to 1- and 2-point functions (see http://www.feyncalc.org/forum/1077.html for more details). - -#### Commits log -* Added g-2 calculation to the examples testsuite (a3e66b1) -* Paclet version updated to 9.1 (fa6c7e7) -* Rebuilt the documentation. (31f3710) -* Fixed a small typo in the documentation. (9262470) -* Updated the changelog for FeynCalc 9.1 (91ae94d) -* Updated `README.MD` (9e99cd) -* Fixed a bug in the computation of chiral traces, when West's formula is not used. (0a25312); Example: - ``` - $BreitMaison = True; - (DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True] - DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True, West -> False]) // Simplify - ``` -* Fixed usage information of `GluonGhostVertex` (thanks to H. Patel). (16a6cbf) -* For now commented out syntax check in `DataType` (leads to problems with FeynHelpers). (1c534a8) -* Added an example for the g-2 calculation in QED at 1-loop and corrected few spelling errors. (96aa208) See `Examples/QED/QEDElectronGMinusTwoOneLoop.m` -* Added several new unit tests for `TARCER` . (c2be321) -* Small cleanups in `FeynCalc.m` and `SUNTrace` to prevent unnecessary pollution of the Global context. (ee76da2) -* Some improvements in `FCTraceExpand` and `FCTraceFactor`. In particular, now `FCTraceFactor` can properly treat nested Dirac traces. (f985c16); Example: - ``` - FCTraceExpand[DiracTrace[GA[i, i] + GA[j, j] DiracTrace[GA[a] + GA[b] DiracTrace[GA[x]]]]] - ``` -* Added option CustomIndexNames to `FCCanonicalizeDummyIndices` and made many improvements to the code. Now one can use `FCCanonicalizeDummyIndices` with arbitrary custom indices, which are treated on the same footing as the built-in indices LorentzIndex, `SUNIndex` und `SUNFIndex`. Einstein's convention is always assumed, though. (1403efe); Example: - ``` - FCCanonicalizeDummyIndices[ T1[MyIndex2[a], MyIndex1[b]] v1[MyIndex1[b]] v2[MyIndex2[a]] + T1[MyIndex2[c], MyIndex1[f]] v1[MyIndex1[f]] v2[MyIndex2[c]], Head -> {MyIndex1, MyIndex2}, CustomIndexNames -> {{MyIndex1, {i1}}, {MyIndex2, {i2}}}] - ``` -* Made automatic expansion of `DiracGamma[Momentum[a]+...]` work also for dimensions other than 4. (4f6169c); Example: - ``` - DiracGamma[Momentum[a, D] + Momentum[b, D] + Momentum[c, D], D] - ``` -* Added checks against predefined scalar products involving loop momenta. This should prevent some stupid mistakes (6fd45b0); Example - ``` - SP[q, q] = 0; - Tdec[{q, mu}, {p}] - ``` -* Added a global variable `$ScalarProducts` that keeps track of vector pairs for which a scalar product has been defined. This is useful e.g. if one needs to check if the given variable can be used as a general 4-vector (i.e. loop momentum) or if it already has some rules attached to it. (d15191f) -* Added new function CommutatorOrder that orders any `Commutator` and `AntiCommutator` lexicographically. (3039650); Example: - ``` - CommutatorOrder[Commutator[a, b] + Commutator[b, a]] - ``` -* Small refactoring in `DotSimplify`. (6e6b01e) -* Improved `ExpandScalarProduct` to work on arbitrary tensor declared via `DeclareFCTensor`. (fc05a8e); Example - - ``` - DeclareFCTensor[myTens]; - ExpandScalarProduct[myTens[z, Momentum[a + b], Momentum[c + d]]] - UnDeclareFCTensor[myTens]; - ``` - -* Added `DeclareFCTensor` and `UnDeclareFCTensor`. Now it is possible to declare new tensor heads, just like this done for new non-commutative objects. (bbbe8af) -* Improved error messages for several function. (d5a0572) -* Added `TensorArgsList`, an internal list of possible heads that may appear as arguments of tensors. (d815c58) - -* Updated list of publications. (12d4b27) -* Added options `EpsEvaluate` to `ExpandScalarProduct`. This way one can now do both operations via `ExpandScalarProduct[expr, EpsEvaluate->True]`. (a83592d); Example: - ``` - ExpandScalarProduct[SP[a + b, c] LC[e, f][g + h, j] LC[][i1, i2, i3, i4 + i5], EpsEvaluate -> True, Momentum -> {a, g}] - ``` -* Improved `FCCanonicalizeDummyIndices` to allow exclusion of certain index heads (via the `Head` option) and definition of own renaming functions (via the `Function` option). (065ad89) -* Added `FCColorIsolate`, a handy helper function to extract color structures. (5cf9f56); Example: - ``` - FCColorIsolate[SUNF[x, y, z]^2 SUNT[a, b] x + SUNT[c] SUND[i, j, k]] - ``` -* Added `SUNHeadsList`, an internal list of colored objects. (9bfd660) -* Added `ToDiracSigma` which is essentialy the inverse of `DiracSigmaExplicit`. (2098ee5); Example: - ``` - ToDiracSigma[GA[i, j], GA[i], GA[j]] - ``` -* Added `Chisholm2` that applies Chisholm identity to eliminate terms of type `GA[i,j,5]`. (7a5c381); Example: - ``` - Chisholm2[GA[i, j, 5]] - ``` -* Fixed a bug in `EpsChisholm`. (0819112); Example: - ``` - EpsChisholm[(SpinorUBar[p1, m1].SpinorV[p2, m2] + SpinorUBar[p1,m1].GS[k].SpinorV[p2, m2])] - ``` -* Fixed a small bug in `Collect2`. (e08933a); Example: - ``` - Collect2[Sum[xa[i], {i, 1, 10}] + VAR Sum[xb[i], {i, 1, 10}] + VAR Sum[xx[i], {i, 1, 10}] + VAR^2 Sum[xy[i], {i, 1, 10}] + VAR^2 Sum[xz[i], {i, 1, 10}], VAR, Factoring -> False, IsolateFast -> True, IsolateNames -> KK] // FRH - ``` -* Refactored `FermionSpinSum` and added treatment of D-dimensional Dirac spinors (thanks to O. Gituliar). (bc9ce8d); Example: - ``` - FermionSpinSum[ChangeDimension[Spinor[p1, m1].GA[i].GA[5].Spinor[p2, m2] Spinor[p2, +m2].GA[5].GA[i].Spinor[p1, m1], D], Momentum -> {p1, p2}] - ``` -* Removed obsolete option `SUNFToTraces`. (a9e729e) -* Added `FCDiracIsolate`, a handy helper function to extract Dirac structures. (ad6af8b); Example: - ``` - FCDiracIsolate[ yy GA[i] + xx SpinorUBar[p1, m1].GA[5].SpinorVBar[p2, m2] + zz + DiracTrace[GA[i, j]]] - ``` -* Added an option to disable `DiracSimplify` in `Chisholm` and `DiracReduce`. (0e4093a) -* Small performance improvement in `Collect2`. (c0db8ab); Example - ``` - Collect2[yy (xx*Sum[p[i] i^2, {i, 1, 100000}] + abc) + abc2, {abc, abc2}, Factoring -> False] // AbsoluteTiming // First - ``` -* Improved `FCPrepareFAAmp` to handle `FASclarProduct` (thanks to Francesco S). (16671c9) -* Refactored `EpsChisholm`. (8287f45) -* Removed `LeviCivitaSign` option from `DiracTrace`, `TR` and `Chisholm`. Instead the value should be set through `$LeviCivitaSign`. A more user-friendly configuration might be added in future. (0551b73) -* Fixed inconsistent treatment of `$LeviCivitaSign` when it set not to the default value (thanks to Christopher Lester). (e05ed33); Example: - ``` - $LeviCivitaSign = -I; - DiracReduce[GA[i1, i2, 5]] - ``` -* Refactored `Chisholm` and added the `LeviCivitaSign` option (thanks to Christopher Lester). (cb44558); -* Version number bump to 9.1; Development versions are now extra indicated to avoid confustion with stable versions. (e0c75a6) -* `Eps` should not evaluate to explicit values when it has integer arguments. The result is not-well defined when no distinction between upper and lower indices is made (thanks to Christopher Lester). (a4699d4); Example: - ``` - Eps[0, 1, 2, 3] - ``` - -* Fixed a bug in `ApartFF` related to singular kinematica (thanks to Shaowu Zhang). (329d5d2); Example: - ``` - FCClearScalarProducts[]; - ScalarProduct[k, k] = 0; - ScalarProduct[p, p] = m^2; - ApartFF[FAD[{q1, m}, {q1 - p}, {q1 - 2 p, m}, {q1 - k - 2 p, m}], {q1}] - ``` -* Improved `FAPatch` to recognize that a `FeynArts`/`FeynRules` model have already been patched. (21f5783) -* Fixed a bug (#issue 9) in `DoPolarizationsSums` (thanks to Luca Mantani). (8944ff3); Example - ``` - ScalarProduct[p1, p1] = 0; - DoPolarizationSums[Pair[Momentum[Polarization[p1, -I], D], Momentum[Polarization[p1, I], D]], p1, 0] - ``` -* Fixed a small bug in `FCE` when applied to metric tensors with explicit Lorentz indices (thanks to Wen Chen). (a7d66ff); Example: - ``` - FCE[Pair[ExplicitLorentzIndex[0], LorentzIndex[a]]] - ``` -* Small fix in `Write2`. (b618ce9) -* Introduced automatic ordering of masses in `B0` in the `PaVe` notation. (0fc0088); Example: - ``` - PaVeReduce[PaVe[2, {p10, p12, p20}, {m1^2, m2^2, m3^2}]] - ``` -* More debugging output in `OneLoop`. (e2ae9c9) -* Fixed a bug in the definition of `A00`. (a8c783f); Example: - ``` - $LimitTo4 = True; - A00[m1^2] - ``` -* Fixed a bug in `PaVeReduce` that prevented detection of zero Gram deteriminants in C and D functions. (55080de); Example - ``` - PaVeReduce[PaVe[1, 2, {(p1 - p2)^2, p1^2, p2^2}, {m2^2, m1^2, m0^2}]] - ``` -* Added `ToPaVe2`, a function that converts direct Passarino-Veltman functions like `A0`, `B1` etc. to `PaVe` ones. (913a50d); Example: - ``` - B0[p^2,m1^2,m2^2]//ToPaVe2 - ``` -* Added an extra test to `SUNSimplify`. Confirms the result from (a355845) -* Adjusted and extended `PaVe` related unit tests. (13987d1) -* More cleanups in `PaVeIntegrals.m` (0bf24e7) -* Moved extra simplifications of `B0` functions into `PaVeReduce`. (d21e164) -* Cleanups in `PaVeIntegrals.m` (faf1f86) -* Moved all the `$LimitTo4=True` simplifications out of `PaVe`. They are not applied, unless `PaVeAutoReduce` is set to `True`. (64cd9a4) -* Added `A00`. (1c75e8b) -* `PaVeAutoReduce` for `PaVe` functions is set to `False` by default. (4163a13) -* `$LimitTo4` is splitted into `$LimitTo4` (for tadpoles and bubbles) and `$LimitTo4IRUnsafe` (for triangles and boxes). Also, the description of the option is now much less cryptic. (fcfe3e7) -* Added the option `A0ToB0` directly to `PaVeReduce`. (547dacb) -* Added some extra `B0`-cases to `PaVeReduce`. (bb535ec) -* Added the option `PaVeAutoReduce` to `PaVeReduce`. (9ab155e) -* Improved `PaVeReduce` to handle more different cases (also with zero Gram determinants). (18dcc4d) -* Fixed a bug in `FCLoopSplit`. (961960b); Example: - ``` - FCLoopSplit[+1/6 (m1^2 + m2^2) + A0[m2^2]/6 + 1/3 m1^2 B0[0, m1^2, m2^2] + +1/6 (m1^2 - m2^2) B1[0, m1^2, m2^2], {}] - ``` -* Added `FCReplaceD`, a function that facilitates taking the limit D->4 without unwanted effects on the FeynCalc functions. (a49487e); Example: - ``` - FCReplaceD[ScaleMu^(D - 4) SPD[p, p]*D, D -> 4 - 2 Epsilon] - ``` -* Small fix in `FUnitTools` related to the recreation of typesetting tests. (c409a14) -* Added a `CovariantD` with explicit fundamental color indices. Although it can't be used in FeynRule, it is still very useful when deriving Feynman rules by hand. (732a6a9); Example: - ``` - CovariantD[i, SUNFIndex[a], SUNFIndex[b], Explicit -> True] - ``` -* Improved typesetting of `QuantumFields`. Now it is possible to add more (custom) indices that will be typeset correctly. (4659077) -* Added four new field types to be put into `QuantumField`: `QuarkFieldPsi`, `QuarkFieldPsiDagger`, `QuarkFieldChi`, `QuarkFieldChiDagger`. Currently, only typesetting is attached to them. (562d408) -* `FCCanonicalizeDummyIndices` can now work also with SU(N) indices, as well as one custom index head (via `Head` option). (6eebc67); Example: - ``` - FCCanonicalizeDummyIndices[T1[MyIndex[a], MyIndex[b]] v1[MyIndex[b]] v2[MyIndex[c]], Head -> MyIndex] - ``` -* `FCFAConvert` can now rename also SU(N) indices by supplying the index names via `SUNIndexNames` and `SUNFIndexNames`. (90e3b59) -* Adjusted `FDS` to be a bit smarter on 1-loop integrals with same masses. (ed92327); Example: - ``` - FDS[Apart2[FAD[{qp, m}, {qp - q}, {qp, M, 2}, {qp - q, M, 2}]] - ApartFF[FAD[{qp, m}, {qp - q}, {qp, M, 2}, {qp - q, M, 2}], {qp}], qp] - ``` -* Let `FCTraceExpand` set the PreservePropagatorStructures of internal `DotSimplify`. This (together with `DiracGammaExpand` set to `False`) seems to be the most convenient and sensible way to do expansions of `DiracTraces`. (b155314); Example: - ``` - DiracTrace[((GSD[k + p] + M).GA[5].GSD[l - p].GAD[nu].(GSD[l] + M).GAD[la].GSD[k + l] + (GSD[k1 + p1] + M).GA[6].GSD[l1 - p1].GAD[nu].(GSD[l] + M).GAD[la].GSD[k1 + l1]).(GSD[x] + M)] // FCTraceExpand[#, DiracGammaExpand -> False] & - ``` -* Some refactoring in `DiracSimplify`. Also `InsideDiracTrace` simplifications are now applied agagin after `DiracTrick`. (cd9d228); Example - ``` - DiracSimplify[GA[i].(GS[p] + M).GA[j].GA[6].GA[k].GA[j],InsideDiracTrace -> True] - ``` -* Added new option `PreservePropagatorStructures` to `DotSimplify`. If set to `True`, numerators of fermionic propagators like `(GS[p]+m)` that appear in chains of Dirac matrices will not be expanded. (4d9f34d); Example: - ``` - DotSimplify[(GA[i].SUNT[a] (GS[p] + M).GA[j].GA[6].GA[k].GA[j] FAD[p + k, M] + - GA[i].(GS[p1] + M).GA[j].GA[7].GA[j].GA[k] FAD[p1 + k, M]).(GS[q] + m).(GA[l].(GS[p] + M).GA[n] + GA[n].(GS[p] + M).GA[l]), PreservePropagatorStructures -> True] - ``` -* Corrected a typo in `FeynCalc.m` (f840d00) -* Improved debugging output in `OneLoop`. (ce133d6) -* Added new option `FCCheckSyntax`. As checking the syntax in `DiracSimplify` slows things down a lot on big expressions, it is better to make it optional and turned off by default. (34e6aeb); Example - ``` - DiracSimplify[SUNT[a] SUNT[b]] - DiracSimplify[SUNT[a] SUNT[b], FCCheckSyntax -> True] - ``` -* Fixed a bug in `DiracTrick` related to `$Larin=True` (thanks to Steffen Schwertfeger ) (03756b2); Example: - ``` - $BreitMaison = False; - $Larin = True; - DiracTrick[GAD[a, b, c].GA[5].GAD[b, a, m]] - ``` -* Fixed a minor bug in `TarcerToFC`. (cbf6334) -* Added `TarcerToFC`, a small tool to convert integrals in the `Tarcer` notation to the `FeynCalc` notation. (fb06f22); Example: - ``` - TarcerToFC[ Tarcer`TFI[D,Pair[Momentum[p, D], Momentum[p, D]], {0, 0, 3, 2,0}, {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}], {q1, q2}] - ``` -* Moved `FromTFI` to the `QCD` directory. (1fd22cf) -* Fixed treatment of `FAD`'s with propagator powers equal to zero, i.e. `FAD[{q,m,0}]` now evaluates to `1`. (654f569); Example: - ``` - FAD[{q1 - p, 0, 0}] - ``` -* More debugging output in `PaVeReduce`. (cd4f508) -* Some more cleanups in the source code of `TARCER`. (fc6851c) -* Fixed a bug in `TARCER` related to wrong `tlrules` (thanks to Yan, http://www.feyncalc.org/forum/1060.html) (19a53ff); Example: - ``` - TarcerRecurse[ - TFI[D, Pair[Momentum[p, D], Momentum[p, D]], {0, 0, 3, 2, 0}, {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}]] - ``` -* Small cleanups in tlrules in `TARCER`. (1be65e1) -* Fixed a small bug in `FeynRule`. (87315c0) Example: - ``` - FeynRule[2*(QuantumField[AntiQuarkField].LeftRightPartialD[ - + i1].QuantumField[QuarkField]), {QuantumField[QuarkField][p1], - +QuantumField[AntiQuarkField][p2]}] - ``` - -* Updated the `FeynCalc` startup message. (ac87b5d) -* Removed the `eps(l)^mu eps(l)_mu = -1` rule, which is not compatible with D-dimensional polarization vectors (thanks to keith-hamilton for reporting Issue #8). (56482a9); Example: - ``` - SPD[p1, p1] = 0; - SPD[p2, p2] = 0; - Pair[LorentzIndex[Subscript[\[Alpha], 1], D], Momentum[Polarization[p1, I, Transversality -> True], D]] Pair[LorentzIndex[Subscript[\[Alpha], 1], D], Momentum[Polarization[p1, -I, Transversality -> True], D]] Pair[LorentzIndex[Subscript[\[Alpha], 2], D], Momentum[Polarization[p2, I, Transversality -> True], D]] Pair[LorentzIndex[Subscript[\[Alpha], 2], D], Momentum[Polarization[p2, -I, Transversality -> True], D]] // DoPolarizationSums[#, p1, n, Contract -> False] & // DoPolarizationSums[#, p2, n, Contract -> False] & // Contract - ``` -* Added a unit test for `OneLoop` (thanks to Yi-Bo Yang). (1d0f03e) -* Added unit tests for `PairContract`. (a578fb1) -* Set `PairContract[0,x]` to `0`. (e588312) -* Fixed a bug in the handling of `PairContract` heads in the input of `Contract`. (f1cd4a5); Example: - ``` - Contract[PairContract[LorentzIndex[i, D], Momentum[p, D]]] - ``` -* Some extra debuggin output for `OneLoop`. (a7aefb7) -* Modified the syntax of `DiracGamma`. From now we have `DiracGamma[0] === 0`. It is also forbidden to enter things like `DiracGamma[1]`, `DiracGamma[2]`, `DiracGamma[3]` etc. Instead, one should use `DiracGamma[ExplicitLorentzIndex[1]]` etc. Of course, `DiracGamma[5]`, `DiracGamma[6]` and `DiracGamma[7]` are still allowed. (537e019) -* All model parameters like masses, coupling constants and mixing angles can be now represented via `SMP[par]`. `FeynArts` patching was updated accordingly. `FCFAConvert` will introduce `SMP` objects if the option `SMP` is set to `True`. (29b8535) -* Refactored `FAPatch`. Also added the option `PatchModelsOnly` to patch only the model files in the `FeynArts` `Models` directory (thanks to Xing-Bo Yuan for the suggestion). (da16d74) -* Adjusted `FCFAConvert` and `FCPrepareFAAmp` to work with amplitudes generated by unpatched `FeynArts`. (0826e85) -* Fixed `DiracSpinor` to `Spinor` conversion. (1aeca0a); Example - ``` - DiracSpinor[p, m] - ``` -* Updated `.gitignore`. (701faa9) -* Added 3 more tree level QCD examples for photon gluon, photon quark and quark antiquark processes. (ae26f38); See `Examples/QCD/QCDGammaStarGToQiQBari.m`, `Examples/QCD/QCDQiGammaStarToQiGTree.m`, `Examples/QCD/QCDQiQBariToGammaStarGTree.m` - -* Added `FCCanonicalizeDummyIndices`, a function that canonicalizes dummy Lorentz indices. (0c877bd); Example - ``` - FCCanonicalizeDummyIndices[Uncontract[SP[q, p]^4, q, p, Pair -> All], LorentzIndexNames -> {mu, nu, rho, si}] - ``` - -* Added ABJ anomaly example to the test suite. (36fae9b) -* Some improvements in the documentation. (479b773) -* Added an extra Contract to `FCMultiLoopTID`. (41b84b3); Example - ``` - FCMultiLoopTID[FVD[q1, mu] FVD[q2, nu] LCD[mu, nu][a,b] FAD[{q1 - p1, m1}, {q2 - p2, m2}, {q1 - q2}], {q1, q2}] - ``` -* Improved Documentation for `TID`. (0aff5ff) -* Added a unit test for `ToPaVe` in `TID`. (8d072c0) -* Add an option `Head` to `Collect2` that allows to wrap prefactors into the given Head. (57decb6); Examples: - ``` - Collect2[Expand[(a + b + c)^2 (b + d)^3], {a, d}, Head -> hh] - ``` -* Improved `ApartFF` (actually `FCApart`) to set loop integrals that vanish in DR to zero by default. Not having this was an omission in the original implementation. The "old" behavior can be recovered by setting the option `DropScaleless` to `False`. (8e859cb) ; Examples: - - ``` - FCApart[FAD[{p, m0}, {-k1 + p, m1}] SPD[k1, p]^2 SPD[p, p], {p}, FDS -> False] - FCApart[FAD[{p, m0}, {-k1 + p, m1}] SPD[k1, p]^2 SPD[p, p], {p}, FDS -> False, DropScaleless -> False] - ``` - -* Block wrong syntax in `ApartFF`. (d48a409); Examples: - ``` - ApartFF[SPD[q, q] FAD[{q, m}], q] - ApartFF[SPD[q, q] FAD[{q, m}], {q}] - ``` -* Minor improvement in `FCLoopIsolate`. (3a75ac2) -* Even more improvements for the options parsing in `Contract`. (0431062) -* Improved `Contract` to contract multiple occurence of Eps tensors in a more efficient way. Thanks to Jos Vermaseren for the useful explanation. (5b28976); Example: - ``` - Contract[LC[i1, i2, i3, dum1] LC[i4, i5, i6, dum1] LC[i10, i11, i12, dum2] LC[i7, i8, i9, dum2]] // FCE - ``` -* Some cleanups in `Contract.m` (mostly just spacing.) (5ce91d9) -* Some more improvements in the options parsing and debugging output in `Contract`. (61506cb) -* Some improvement in the options parsing in `Contract`. (b2e94a5) -* Small fix in `Isolate`. (ac994f3) -* Fixed a bug in `DiracSimplify` with `DiracSubstitute67` not being applied to spinor chains. (7f9204c); Examples: - ``` - DiracSimplify[Spinor[-Momentum[p2], 0, 1].GS[Polarization[k1, -I]].GS[k1].GS[Polarization[k2, -I]].GA[7].Spinor[Momentum[p1], 0, 1], DiracSubstitute67 -> True] - ``` -* Refactored `ToLarin`. (f937c6b) -* Removed premature memoization in `DiracTrace`. This doesn't really give a performance gain but rather causes a lot of problems with different gamma^5 schemes. Now we memoize only where it is necessary and safe. (b96cbe9) -* Added an example for the calcuation of the Adler-Bell-Jackiw anomaly in QED. (8d28e06); See `Examples/QED/QEDABJAxialAnomaly.m` -* Some refactoring and performance improvements in `Contract`. (ccb705b) -* Improved calculation of chiral traces in 4 dimensions. (0ab7ee4) -* Degraded `$West` to `West`, which is now an option of `DiracTrace` and `TR`. Also, `West` has now no effect on the calculations of the chiral traces in 4 dimensions. (033bd54); Examples: - ``` - $BreitMaison = True; - DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True] // Factor2 - DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True, West -> False] // Factor2 - DiracTrace[GA[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True] // Factor2 - DiracTrace[GA[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True, West -> False] // Factor2 - ``` -* Some performance improvements in `DiracTrace`. (d9748c9) -* Some refactoring and better debugging output in `DiracTrace` and `TR`. (0ccf4d9) -* Some refactoring and better option parsing in `DiracSimplify`. (beffe33) -* Ensured that Tr[T^a]=0 where T^a is a single color matrix in the fundamental rep is always applied on the level of SUNTFs. (b1e777e); Example: - ``` - FCI[SUNTF[a,x,x]] - ``` -* Added the options `EpsEvaluate` and `ToPaVe` to `TID`. (69539b9) -* Fixed a bug in `TID` (missing `Contract` at the beginning) reported by YI-Bo Yang. (b78bb62); Example: - ``` - TID[FAD[{q, m}] FV[q, i]^2 FV[q, j] FV[q, k], q] - ``` -* Fixed a bug in `FCE` related to `ExplicitLorentzIndex` (thanks to Wen Chern). (ab5f6c1); Example: - ``` - Eps[ExplicitLorentzIndex[0], ExplicitLorentzIndex[1], Momentum[p],Momentum[q]]//FCE - ``` -* Added the option `BReduce` to `PaVeReduce`. Set to `False` by default. (e11575); Example: - ``` - Factor2[(B1[p^2, m0^2, m1^2] // PaVeReduce[#, BReduce -> True] &)] - ``` -* Improved `FCTraceExpand` to use `DiracGammaExpand` and `FCTraceFactor`. (770810d); Examples: - ``` - FCTraceExpand[DiracTrace[GS[p + b]]] - FCTraceExpand[DiracTrace[GS[p + b]], DiracGammaExpand -> False] - ``` -* Fixed mixing of dimensions in shifts of `FDS` (affected `Eps` tensors contracted with loop momentum). (7840801); Example: - ``` - FDS[LC[][p1, p2, p3, l] FAD[{l - p, m}, {l + q, m}, l - t], l] // FCE - ``` -* Set `$LimitTo4=False` as default. Otherwise, IR divergent C-functions might lead to inconsistencies. (2629530) -* Added `EpsilonUV` and `EpsilonIR` to be able to distinguish between UV and IR divergences in dim reg, when this is needed. Currently those are just placeholders with attached typesetting. (c391187) -* Added a new option `IsolateFast` to `Isolate`. This way one can isolate special types of very large expressions in a much faster way. (1c0c0e6); Examples: - ``` - Isolate[Total[Table[Sqrt[TZ[i] + 2 ZZ[i]]/+HH[ToString[i] + ToString[i + 2] + ToString[i + 4]], {i, 1,100}]]] // AbsoluteTiming - Isolate[Total[Table[Sqrt[TZ[i] + 2 ZZ[i]]/+HH[ToString[i] + ToString[i + 2] + ToString[i + 4]], {i, 1,100}]], IsolateFast -> True] // AbsoluteTiming - Isolate[Total[Table[Sqrt[TZ[i] + 2 ZZ[i]]/+HH[ToString[i] + ToString[i + 2] + ToString[i + 4]], {i, 1, 10000}]], IsolateFast -> True] // AbsoluteTiming - ``` -* Added the option `FinalSubstitutions` to `FCFAConvert`. (183e102) -* Made `MT`, `MTD` and `MTE` orderless. (bb49ab6); Example: - ``` - MT[a, b] === MT[b, a] - ``` -* Fixed a small bug in `Isolate`. (d8de71b); Example: - ``` - Isolate[-1 x] - ``` -* Made `Expand2` faster recognize that the expression is already fully expanded. (37a5728) -* Refactored `Collect2` and improved the performance on large expressions by switching to `CoefficientArrays`. (bff4790) -* Fixed a small bug in `FeynmanParametrize`. (2c44965) -* Refactored the unit testing framework to work as a bash script without Wolfram Workbench. Mathematica 8 and 9 require `MUnit` that can be pulled out of the WWB files. (ee7068c); Examples (under Linux): - ``` - inttetsts.sh math - inttetsts.sh math Lorentz - inttetsts.sh math Dirac - inttetsts.sh math Loop - examples.sh - ``` -* Improved `FCApart`'s internal algorithm and added new option `MaxIterations` to break the fractioning after a given number of iterations. (1225fe1); Example: - ``` - FCApart[SPD[k1, p] SPD[p, p] FAD[{p, m0}], {p}, MaxIterations -> 1, FDS -> False] - FCApart[SPD[k1, p] SPD[p, p] FAD[{p, m0}], {p}, MaxIterations -> 2, FDS -> False] - ``` -* Added `FCGetDimensions`, an auxiliary function for checking the dimensionality of the expression. (fd5621b); Example: - ``` - FCGetDimensions[{FV[p, mu], FVD[p, mu], FVE[p, mu]}] - ``` - -* Fixed wrong context in the unit tests for `FourLaplacian`. (b8562dd) -* Added `FCTraceFactor` for factoring constants out of `Dirac` traces. (a04902b); Example: - ``` - FCTraceFactor[DiracTrace[(a + b).(a - b).DiracTrace[GA[i].c.GA[j]].(a + b)]] - ``` -* Fixed a bug in `Write2` related to `FortranFormatDoublePrecision` (thanks to Wen-Long Sang). (ea03857); Example: - ``` - Write2["sang.abc", abc = 0.6*(-8 + 12 Log[5 + y[1]]), abc1 = 1/x^(2/3), FormatType -> FortranForm, Precision -> 10]; - Import["sang.abc", "Text"] - - Write2["sang.abc", abc = 0.6*(-8 + 12 Log[5 + y[1]]), abc1 = 1/x^(2/3), FormatType -> FortranForm, Precision -> 3]; - Import["sang.abc", "Text"] - - Write2["sang.abc", abc = 0.6*(-8 + 12 Log[5 + y[1]]), abc1 = 1/x^(2/3), FormatType -> FortranForm, FortranFormatDoublePrecision -> False]; - Import["sang.abc", "Text"] - ``` - - -* Improved `FCI` convertion of `FeynAmpDenominator`'s with dimensions other than `D`. (fa58485); Example: - ``` - FCI[FCI[FAD[q1, {-p + q1, m}, Dimension -> 4]]] - ``` - -* Added `FCTraceExpand`, a function that expands traces without evaluating them. (a9e8745); Example - ``` - FCTraceExpand[DiracTrace[GA[i, i] + GA[j, j].DiracTrace[GA[a] + GA[b]]]] - ``` -* Integrated FeynCalcManual.nb into main documentation. (10c5210) -* Catch wrong expressions like `Momentum[LorentzIndex[mu]]` or `LorentzIndex[Momentum[p]]` and warn the user immediately. (15fa095) - -### Version 9.0.1 (2016) - * For publishing reasons, the license has been changed from LGPL 3 to GPL 3 - * Fixed bugs that were discovered since the relese of FeynCalc 9.0.0 - * Converted an example of using Integrate2 from FeynCalcManual.nb to a proper .m file - -### Version 9.0.0 (2016) - - * Introduced `FCFAConvert` for automatic conversion of the CreateFeynAmp - output into FeynCalc input. - * Added `FCMultiLoopTID` for tensor decomposition of multiloop integrals. - * Documentation ported from the old HelpBrowser to the new Documentation Center. - * Make entering of `FAD`'s with propagators that have exponents simpler. - Now to enter e.g. `FAD[q,{q,m},{q,m},q-p,q-p,q-p]` one can simply write `FAD[q,{q,m,2},{q-p,0,3}]`. - * `ApartFF` is the new powerful replacement for `SPC` and `Apart2`. It uses `FCApart` as a backend and works for multiloop integrals. The "FF" in the name of the function is to honour Feng Feng, the author (arXiv:1204.2314) of the algorithm used in `FCApart`. - * Added Added `FCApart` for partial fractioning loop integrals with linearly dependent propagators. The algorithm comes from the work of Feng Feng (arXiv:1204.2314). - * Added `FCLoopExtract`, a new helper function for extracting loop integrals from the given expression. - * Added `FCLoopBasisIncompleteQ`, `FCLoopBasisOverdeterminedQ` and `FCLoopBasisFindCompletion` for studying the space formed by the propagators of the given loop integral. - * Now it is finally possible to enter `FAD`s also like `FAD[{q, m}, {q, m}, {q + p - k}]` where the last propagator is massless. - * Improved `PaVe` to set scaleless integrals to zero. - * New add-on `FUnitTools` for working with unit tests. - * Added possibility to set scalar products directly via `SP`, `SPD` and `SPE`. - * Added `TFIOrder` that can exploit some symmetries between Tarcer's scalar 2-loop integrals `TFI`. - * Many improvements to `ToTFI` (thanks to Anne Ernst!) - * Add new option `MultiLoop` to `FCLoopIsolate`. This allows to isolate only those integrals that depend on all of the loop momenta. - * `$DisableMemSet` can be used to deactivate `MemSet`, - * New option `PDEHeads` for `PropagatorDenominatorExplicit`. It allows to wrap what used to be `FAD` into used defined heads, so that one can can - better keep track of scalar products that come from the denominator. - * Spinors can be now D-dimensional - * Added `$FCCheckProgress` to activate `FCMonitor` when needed. Note that `FCMonitor` slows things down for simple calculations, so it is better to activate it only for large expressions. Here is an example of activating FCMonitor (curently only TID supports it) - ``` - int = -EL^3 Spinor[Momentum[p2, D], ME, 1].GAD[Lor3].(ME + GSD[p2 + q]).GAD[Lor1].(ME + - GSD[p1 + q]).GAD[Lor3].Spinor[Momentum[p1, D], ME, 1] FAD[{p1 + q, ME}, {p2 + q, ME}, q]; - $FCCheckProgress = True; - TID[int, q] - ``` - - * Added `FCSplit` for splitting expressions into pieces that contain given variables and pieces that do not. `FCSplit[expr,{v1, v2, ...}]` splits `expr` into pieces that are free of any occurence of `v1`, `v2`, ... and pieces that contain those variables. This works both on sums and products. The output is provided in the form of a two element list. One can recover the original expression by applying `Total` to that list. For example - ``` - FCSplit[(z + a)^2 + (z + b)^2, {z}] - FCSplit[(z + a)^2 + (z + b)^2, {a}] - FCSplit[(z + a)^2 + (z + b)^2, {b}] - ``` - - - * Introduced `$DisableMemSet` for deactivating `MemSet`, which is often needed for debugging. - * Added a new option `PDEHeads` to `PropagatorDenominatorExplicit`. It allows to wrap what used to be `FAD` into user defined heads, so that one can better keep track of scalar products that come from the denominator. - * Allowed spinors to depend on D-dimensional external momenta to be compatible with the CDR scheme. `ChangeDimension` now doesn't force the spinors to depend only on 4-dimensional momenta. - * Introduced `FCLoopCanonicalize` and `FCLoopSolutionList`, that are useful for canonicalizing free Lorentz indices of 1-loop tensor integrals. See [https://github.com/FeynCalc/feyncalc/blob/master/Tests/LoopIntegrals/FCLoopCanonicalize.test] and - [https://github.com/FeynCalc/feyncalc/blob/master/Tests/LoopIntegrals/FCLoopSolutionList.test] for examples. - - * Introduced `FCLoopIsolate` and `FCLoopSplit`. These two functions should facilitate manipulation, separation and sorting of arbitrary loop integrals in the given expressions. `FCLoopSplit[expr,{q1,q2,...}]` separates `expr` into following four pieces: - * terms that are free of loop integrals - * terms with scalar loop integrals - * terms with tensor loop integrals, where all loop momenta are contracted - * terms with tensor loop integrals, where at least some loop momenta have free indices - The result is returned as a list with the 4 above elements. For example - - ``` - FCLoopSplit[zzz + (FVD[q, mu] FVD[p, mu] a + SPD[p, q] b) FAD[q, q + p] + yyy FAD[{q, m}], {q}] - ``` - - `FCLoopIsolate[expr,{q1,q2,...}]` wraps loop integrals into heads specified by the user. This is useful when you want to know which loop integrals appear appear in the given expression. For example, - - ``` - FCLoopIsolate[zzz + (FVD[q, mu] FVD[p, mu] a + SPD[p, q] b) FAD[q, q + p] + yyy FAD[{q, m}], {q}] - ``` - - * Added new options `PaVeAutoReduce` and `PaVeAutoOrder` that can be used to inhibit automatic reduction of A and B coefficient functions into `A0` and `B0`. Compare e.g. - ``` - PaVe[0, 0, {p}, {m, m}] - ``` - - to - - ``` - PaVe[0, 0, {p}, {m, m}, PaVeAutoReduce -> False] - - ``` - - * New function `FCDeclareHeader` to be used for FeynCalc add-ons that go into the `AddOn` directory. - - * Some functions now support a new function `FCVerbose` that allows a more concise debugging output as compared to using `$VeryVerbose`. For example - ``` - TID[FVD[q, mu] FVD[q, nu] FAD[q, {q + p, m}], q, FCVerbose -> 3] - ``` - - * Added an option `IsolateNames` to `FRH` to enable applying `ReleaseHold` only on specified `HoldForm` expressions. Compare e.g. - ``` - iso = Isolate[(a + b) F[q], q, IsolateNames -> KK1] + Isolate[(c + d) F[q1], q1, IsolateNames -> KK2]; - FRH[iso] - ``` - with - ``` - FRH[iso, IsolateNames -> KK1] - FRH[iso, IsolateNames -> KK2] - FRH[iso, IsolateNames -> {KK1, KK2}] - ``` - - * Added new option `ExcludeMasses` for `Apart2` to disable factoring and not to apply partial fractoning on propagators that contain specified masses. This gives you a more fine - grained control of partial fractioning. Compare e.g. - ``` - Apart2[FAD[p, {p, m1}, {p, m2}]] - ``` - - to - - ``` - Apart2[FAD[p, {p, m1}, {p, m2}], ExcludeMasses -> {m1}] - ``` - - * Added options `$TypesettingDim4`, `$TypesettingDimE` and `$TypesettingDimD` to modify the typesetting of momenta, Dirac matrices, metric tensors and polarization vectors in `4`, `D-4`, and `D`-dimensions. - For example, now you can do `$TypesettingDim4="";` to remove bars from 4-dimensional objects. Thanks to Yu Lu for the suggestion. - - * You might have been wondering, why FeynCalc must be installed to the directory `HighEnergyPhysics` and not just `FeynCalc`. Well, this used to be liked that for some legacy reasons but is actually not necessary nowadays. From now on FeynCalc lives in `FeynCalc` and it is started simply via ```<ToExpression[x]}`. We understand that this additional step may pose some inconveniences to you, but from the point of view of Mathematica programming and interoperability between different packages, this solution seems to be the cleanest way to avoid troubles in future. + FCGetDiracGammaScheme[] - For example, ```Lagrangian["QCD"]``` now returns -``` --(1/4) FieldStrength[FCGV["\[Alpha]"], FCGV["\[Beta]"], - FCGV["a"]].FieldStrength[FCGV["\[Alpha]"], - FCGV["\[Beta]"], FCGV["a"]] -``` - instead of -``` --(1/4) FieldStrength[\[Alpha], \[Beta], a].FieldStrength[\[Alpha], \[Beta], a] -``` - as it used to be. Now suppose that before invoking Lagrangian["QCD"] you defined \[Alpha] = 1/137. With the new output using FCGV nothing changes. With the old output - you would have got -``` --(1/4) FieldStrength[1/137, \[Beta], a].FieldStrength[1/137, \[Beta], a] -``` - which is clearly not what you want. + * Example: Show available g^5 schemes - * To circumvent problems related to the patching of FeynArts, from now on FeynCalc will look for FeynArts only in the directory `FeynArts` -inside `FeynCal`. Nevertheless, it is still possible to specify an alternative directory by setting ```FeynCalc`$FeynArtsDirectory="path"``` before loading FeynCalc. The patching code was moved to FeynCalc, i.e. now it will run even when Phi is not loaded. + ?FCSetDiracGammaScheme[] - * The TARCER notebook have been converted into a source file (`TARCER.m`). Furthermore, generated TARCER*.mx files are not distributed anymore with the source code. When you first try to load TARCER, a dialog will appear with the suggestion to generate the .mx file now. This process has to be done only once and takes only a couple of minutes. After that, the generated .mx will be automatically loaded whenever you want to use TARCER. + * Example: Switch to the BMHV scheme - * Prior to this commit FeynCalc used to switch the format of output cells to `TraditionalForm`. Now it will only issue a warning message suggesting the user to do this by himself or herself. Such messages can be disabled by setting `$FCAdvice` to False. So if you despise all the fancy typesetting and prefer to work with `StandardForm`, FeynCalc will respect your decision. + FCSetDiracGammaScheme["BMHV"] - * To avoid clashes with built-in functions of recent Mathematica versions, we had to rename some FeynCalc functions: - * `PartialD` -> `FCPartialD` - * `Symmetrize` -> `FCSymmetrize` - * `AntiSymmetrize` -> `FCAntiSymmetrize` + * Example: Switch to the NDR scheme -* To avoid further confusion about the handling of Dirac Gamma 5 in FeynCalc, it is now forbidden to enter -g^5 or the chiral projectors g^6 and g^7 as D-dimensional objects. Hence,`GAD[5]` or `DiracGamma[5,D]` will now generate error messages. This is not really a significant change, since before FeynCalc would silently convert `GAD[5]` to `GA[5]` without issuing any warnings, contrary to what the user might have expected from entering `GAD[5]`. The thing is that internally, FeynCalc always works with `DiracGamma[5]`. As far as dimensional regularization is concerned, the scheme to handle g^5 is determined by the values of `$BreitMaison` and `$Larin` and not by the dimension of g^5. Even in NDR, where g^5 is normally assumed to be D-dimensional, FeynCalc uses just `DiracGamma[5]`. Note that this is just a technicality of the implementation, nothing really related to physics. + FCSetDiracGammaScheme["NDR"] -* Tensor decomposition routines have been updated to improve performance and usability. Before actually performing the decomposition, `Tdec` will now first check `TIDL` (Tensor Integral Decomposition Library) to see if the required integral is already contained there. If yes, the formula will be fetched from there. This behavior is controlled by the new option `UseTIDL` which is set to `True` by default. Furthermore, `Tdec` can now recognize symmetries in the indices of 1-loop integrals which significantly speeds up the computations. For multiloop integrals the symmetries recognition is not implemented yet. Another turbo for `Tdec` is the option `UseParallelization` (`True` by default) that activates parallelization code in the solver of linear equations `Solve3`. This can make things up to 40% faster and works for all kinds of integrals. Last but not least, a couple of new decompositions have been added to TIDL, just in case. +* Added a new scheme for handling g^5: `"NDR-Drop"`. It is like `"NDR"` but all the remaining traces with one g^5 (that NDR can't evaluate) are set to zero. It is meant to be applied in calculations where we know in advance that g^5 does not pose any issues. (031368f5) -* Fixed a bug in `DoPolarizationSums` [reported](http://www.feyncalc.org/forum/0853.html) by Kyrylo Bondarenko. +* Modified `ComplexConjugate` to automatically apply `FCRenameDummyIndices`. This can be turned off using the option named the same way. (d7708286) -* Adjusted the typesetting of SU(N) objects such that adjoint indices are now always upstairs while the fundamental indices are downstairs. -* Added additional SU(N) objects to work with SU(N) T-matrices that have explicit fundamental indices. See -the [announcement](http://www.feyncalc.org/forum/0843.html) on the mailing list for more details. -* Added examples for computing 2->2 tree level parton processes in QCD. -* Imporved DoPolarizationSums to handle massive and massless vector bosons in a proper way. See -the [announcement](http://www.feyncalc.org/forum/0843.html) on the mailing list for more details. -* Updated `FCPrepareFAAmp` to handle the main steps in converting the output of FeynArts to FeynCalc. See the updated wiki [page](https://github.com/FeynCalc/feyncalc/wiki/FeynArts#fatofc) for more details. +* The default behavior of `DiracSimplify` was changed to automatically evaluate Dirac traces. Now there is no need to use the replacement `DiracTrace->Tr` (b74b4c20) -* Fixed a bug in `FourDivergence` (actually in `Contract`) [reported](http://www.feyncalc.org/forum/0755.html) by Sun. + * Example: Evaluate a Dirac trace using `DiracSimplify` -* Added typesetting for `AlphaStrong` (QCD coupling constant) and `AlphaFS` (fine-structure constant). + DiracTrace[GA[a,b,c,d]] // DiracSimplify -* Handling of algebraic simplifications for Dirac matrices in `DiracTrick` has been reworked to improve performance and provide better support for the Breitenlohner-Maison-'t Hooft-Veltman scheme. +* Vectors in the `FeynCalcExternal` representation that contain a minus sign will have it factored out automatically, so that e.g. `FV[-p,mu]` will become `-FV[p,mu]`. (249d8b22) -* Fixed a bug in `PowerSimplify` [reported](http://www.feyncalc.org/forum/0815.html) by Sun Qingfeng +* Changed the handling of the output format type to address the issue #30 (9f409e1f). In particular, `FeynCalc` will now change only the output format of the current front end session, not the global `Mathematica` option as before. This behavior is controlled by the new global option `$FCTraditionalFormOutput`. The default value is `False`. One can load `FeynCalc` with the `TraditionalForm` typesetting via -* * Improved `EpsEvaluate` to always expand sums of momenta as [requested](http://www.feyncalc.org/forum/0812.html) by Lingxiao Xu. + $FCTraditionalFormOutput = True; + << FeynCalc` -* Improved TraditionalForm formatting of metric tensors, vectors, Dirac matrices, Dirac slashes and scalar products. Now all 4- and D-4-dimensional quantities are displayed with a bar or a hat respectively on top of the symbol. The D-dimensional quantities remain as they are. This change allows to easily distinguish between D- , 4- and D-4-dimensional objects without deactivating TraditionalForm. + Or one can also write `$FCTraditionalFormOutput = True` to `FCConfig.m` so that this value will be set each time `FeynCalc` is loaded. Finally two new functions `FCDisableTraditionalFormOutput[]` and `FCEnableTraditionalFormOutput[]` allow to switch between `StandardForm` and `TraditionalForm` on the fly -* Introduced `FeynCalcInternal` shortcuts for D-4-dimensional metric tensors (`MTE`), vectors (`FVE`), Dirac matrices (`GAE`), Dirac slashes (`GSE`) and scalar products (`SPE`). + * Example: Switch between different output formats in a `FeynCalc` session -* Extended polarization vectors to allow for vectors that are not transverse, i.e. not orthogonal to their momentum. This behavior is controlled by the option `Transversality` that applies to `Polarization` and `PolarizationVector`. + < "FCMetricTensor", "Factor1" -> "FCFactor1", "Factor2" -> "FCFactor2"}; + << FeynCalc` + + FCDisableTraditionalFormOutput[] + (* Output format changed to StandardForm for the current session *) + +* Moved the loader of `TARCER` into a separate file. So we can (and should) load `TARCER` via `$LoadAddOns={"TARCER"}`. The old `$LoadTARCER` is now deprecated. Reason: More consistency when loading additional packages that interact with `FeynCalc` (851efb72) -### Version 8.2.0 (2012) + * Example: Load `FeynCalc` and `TARCER` -* Added **FeynArts 3.7** - unpatched. On first load it will be patched automatically. -* When running the first time set *$LoadPHI=True* before executing - Needs``` [HighEnergyPhysics`FeynCalc`]```, then it will be patched automatically. -* Updated **PHI** to work with **FeynArts 3.7**, which can now be kept in a subdir. + $LoadAddOns={"TARCER"} + <2`. (45496b34) +* Removed `$SpinorChainMinimal` and `ChisholmSpinor`. (153c344d) +* Removed the option `Dimension` in `Eps`. Reason: `Eps` is an `FCI` object so that the dimension of the indices or momenta is always unambiguous (a82bb76e) +* Removed `MomentumCombine2`. Reason: it only duplicated `MomentumCombine`. (4233f90e) +* Removed `Upper`, `Lower`, `Contract1`, `$Covariant` and `$LorentzIndices`. Reason: With the introduction of Cartesian tensors in `FeynCalc` 9.3, there is no more ambiguity regarding the positions of the indices. Moreover, `Upper` and `Lower` never were fully integrated into `FeynCalc`. (76a6ae59) (9a3ba199) +* Removed `CrossProduct`, `DotProduct` and `ThreeVector`. Reason: Now that we have native support for symbolic Cartesian vectors, they are not needed anymore. (4c7ff29a) +* Removed the typesetting option `$PairBrackets`. Reason: The option is obsolete. Once a scalar product is multiplied by something else, it will automatically have brackets around it, so that setting `$PairBrackets=True` is never needed. (7d3e6eef) +* Removed `DiracSimplify2`. Reason: All settings related to gamma_5 should be handled by setting a suitable scheme. Otherwise, inconsistencies are unavoidable. (80f64f83) +* Removed `UVPart`. Reason: In the current form it is useless and wrong (thanks to M. Beneke for the suggestion). It was replaced by `PaVeUVPart` (cebaf7a5) +* Eliminated `TemporalIndex[]`. Reason: There is really no point to reinvent the wheel and use this peculiar object instead of just `LorentzIndex[0]`. No harm done, since the name `TemporalIndex` never maid it into a stable version (3be9fee8) +* Removed the option `DenominatorOrder` option from `OneLoop`. Reason: ongoing progress in the attempts to refactor `OneLoop` (26641c4c) +* Removed the option `ChangeDimension` from `TID`. Reason: Automatic or implicit changes of the dimension are dangerous and may easily to unwanted side effects or even inconsistent results. It is better to avoid that completely. (6fbd3f22) +* Removed `FCMonitor` and `FCMonitorStub`. Reason: They are not used in `TID` anymore. (8e4b3ffa) +* Removed `MakeFeynCalcPrivateContext` and `$IndexPrefix`. Reason: Some very old routines that were largely obsolete already in the version 9. (c7510662) +* Removed the legacy syntax of `DiracTrick`, where one could enter Dirac matrices without `DOT`s. (69957a9f) +* Removed the unfinished experimental function `SquareAmplitude2`. Reason: It never became sufficiently stable and ready to be used and hence was also never mentioned in the documentation. (ee1149f7) -* Minimal updates for **Mathematica 8.0**. -* Added a patched o **FeynArts 3.4**. +--- -### Version 7.0.0 (2009/2010) +* Renamed the option `DiracSimpCombine` of `DiracSimplify` to `DiracGammaCombine`. (6da10564) +* Renamed the `DiracCanonical` option of `DiracSimplify` to `DiracOrder`. (7fc6846e) +* Renamed the option `SpinPolarizationSum` of `FermionSpinSum` to `Head`. (c56581f6) +* Renamed `MemoryAvailable` and `$MemoryAvailable` to `FCMemoryAvailable` and `$FCMemoryAvailable`. Reason: `MemoryAvailable` is a system variable since `Mathematica` 11.0. (3c18c338) +* Renamed `PropagatorDenominatorExplicit` to `FeynAmpDenominatorExplicit`. Reason: more consistent naming scheme. This way it fits to other functions that start with `FeynAmpDenominator`. Of course, `PropagatorDenominatorExplicit` still works in order not to break the existing codes. (8bfefcda) +* Renamed `SquareAmplitude` to `SquareAmplitude2`. Reason: `SquareAmplitude2` is an experimental function that never became sufficiently stable. The name `SquareAmplitude` will be used for a different function. (23667615) +* Removed a call to `ChangeDimension` from `Explicit`. Reason: The `Dimension` option should already handle this, so that we don't need to call another function. (d1dd1def) +* Renamed the `PDEHead` option in `FeynAmpDenominatorExplicit` to `Head`. (51fc4da4) -* Bug fixes. -* Updates for **Mathematica 7.0** and new **FeynArts**. - -### Version 6.0.0 (2007) - -* Bug fixes. -* Updates for **Mathematica 6.0** and new **FeynArts**. -* For **Mathematica 6** only. Rolf patched **FeynCalc** to be compatible with **Mathematica 6** (not **PHI**, not **FeynArts**) and zipped it together, including fully evaluated documentation notebooks in *HighEnergyPhysics/Documentation/English/*. Notice that this version does not load **PHI** nor **FeynArts** by default. Notice also that the changes are not entered into CVS yet, due to lack of time. - -### Version 5.1.0 (2006) - -* Bug fixes. -* Updates for **Mathematica 5.2** and new **FeynArts**. - -### Version 5.0.0b (2003) - -* Bug fixes. -* Adjustments for **Mathematica 5.0**. -* More reorganization by Frederik Orellana. -* Inclusion of help system, **PHI** and **FeynArts**. - -### Version 4.9.beta (2002) - -* Improved *DiracOrder*. -* Added *FeynCalcToLaTeX*. -* Fixed the cyclicity problem with *Gamma[5]*. -* Simplified installation mechanism. -* Fixed things for **Mathematica 5.0** and **FeynArts** and patching and all that. -* Other bugfixes. - -### Version 4.2.0 (2002) - -* Changed to use *DOT* everywhere instead of *DOT*. -* **FeynArts 3** support: Exclude *ShapeData* from autoloading. -* Keep *PolarizationVector* unevaluated when given **FeynArts** arguments. -* Added support for other multiplications than *DOT*. -* Added *FieldDerivative* and *CovariantFieldDerivative*. -* Added *$Multiplications*, *$DistributiveFunctions* and *$Containers* to allow customization of *FieldDerivative*. -* *DOT* moved into main context. -* Have *ExpandScalarProduct* expand also *Pair[LorentzIndex[mu], Momentum[a] * Momentum [b] +...]*. -* Small bug fix of *FourVector*: *fci* not defined. -* *IsolateHead* dropped. *IsolateNames* used instead everwhere. -* Some more box definitions for *PartialD*. -* Split *FeynCalcBook.nb* in two. -* New directory *fcdevel* with files under development (or just unfinished). -* New directory *fcloops* with (1,2) loop related files. -* Changed usage into *"usage"*. -* Had *Contract* contract also denominators. -* Moved *Vectors* into context ```FORM2FeynCalc` ```. -* Moved *FORMEpilog*, *FORMProlog* and *TraceDimension* into context *FeynCalc2FORM* -* Fixed Breit-Maison problem of *FeynCalcInternal*. -* Had *FeynRule* and *FunctionalD* know about *ExplicitSUNIndex*. -* Dropped ```Global` ``` symbols in *SquareAmplitude*. -* Small bug fix in *Uncontract*. -* Let Uncontract accept option *Dimension -> Automatic*. -* Have *Uncontract* uncontract also denominators. -* Changed option of *A0* *A0ToB0* from *True* to *False*. -* Code moved from *FeynCalc.m* to new files; should improve maintainability. -* Moved *SUNSimplify.m* and *SUNTrace.m* from *qcd* to *fctools*, -*qcd/InverseMellin.m* -> *fctables/InverseMellin.m* and -*qcd/ToLarin.m* -> *fctools/ToLarin.m* (corrections of Rolf). -* Moved a few more files to more logical places. -* Changed usage to *"usage"* everywhere. -* Moved *IsolagePrint* and *IsolateSplit* into context *Isolate*. -* Changed *QCDScaleMu* into *ScaleMu*. -* Dropped *SUNF2*. -* Changed option of *SUNSimplify* *SUNTrace* from *True* to *False*. -* Made *SUNSimplify* trace also term proportional to the identity matrix when -* *SUNTrace* is set to *True*. -* *FeynCalc.m*: - * Added support for *:>* to *OptionsSelect*. - * Placed *FDr* and *CDr* in correct contexts. - * Bugfixed check for integer arguments in *SUND* and *SUNDeltaContract: Added ExplicitSUNIndex*. - * *SUND*: No longer set all *SUND[a,a,b]* to *0* if a is not an integer, only when - a has head *SUNIndex*. -* *DiracSimplify.m*: * Defined *print1*, *print2*, *print3* -* *OneLoop.m*: Changed a few debug printing statements. -* Fixed *SumOver* to comply with **FeynArts 3**. -* **PHI**: - * As far as possible dropped using explicit contexts, use *MakeContext* instead. - * Small fix of *ArgumentsSupply*. - * Moved *FieldDerivative* and *CovariantFieldDerivative* (and *CDr* and *FDr*) into *HighEnergyPhysics/fctools/*. - * Implemented compatibility with **FeynCalc**'s *PartialD*-operator notation. - * Removed many comments. They don't give useful information and clutter things. - * Changed the possible settings of *B0Evaluation* to strings to facilitate extensibility and reduce the number of defined symbols. - * Introduced *LeutwylerJBarEvaluation* instead of *ExplicitLeutwylerJBar*. - * Implemented above-threshold evaluation of *VeltmanB0* (and *LeutwylerJBar*). - * Dropped *FANonCommutative*, *FAMetricTensorm*, *FAPolarizationVector*, *FAFourVector*, *FADiracMatrix*, *FAIndices* in favour of *NonCommutative* in consistence with *FAPatch.m*. - * Had *FAPatch.m* add *$FermionHeads* to *$NonCommuting* in *Setup.m*, - as well as set *FeynCalcInternal -> False* for *FourVector*, *MetricTensor*, - *DiracSlash*. - * End all usage definitions with a full stop. - * Changed *Dot* to *DOT*. -* *Objects.m*: - * Dropped *RemoveIntegerIndices*. - * Changed to have head *ExplicitSUNIndex* on integers (instead of nothing) in compliance with **FeynCalc**. - * *setLeftRightComponents* fixed to have *Explicit* in right context. - * Fixed bug in *WriteOutUMatrices* causing *NM[a[x], UMatrix[b]] + UMatrix[UIdentity]* not to work (reported by P.Buettiker). - * Fixed bug in *UIndicesSupply*, putting *DOT* in correct context. - * Fixed bug in *UExp* (reported by Paul Buettiker): - When zeros were in *$UExpansionCoefficients MM*, *UFieldMatrix* didn't work. -* *Utilities.m*: - * Added support for *WFFactor* in *DiscardOrders* (Don't discard if order is not known). - * *MandelstamReduce* now has renormalized masses as default. - * Added first sketch of *PHIToLaTeX*. -* Palettes.m: LoadLagrangian now keeps lagrangians given as strings in context ``` Global` ``` (instead of ``` HighEnergyPhysics`PHI`Objects` ``` ). -* *Renormalization.m*: - * Fixed small bug causing LeutwylerJBar causing problem with LeutwylerSigma. - * Readded *C0Evaluation -> "none"*, *D0Evaluation -> "none"* to *Options[VeltmanExpand]*. -* *Couplings.m*: - * Added *PHIModel* as option of *WFFactor*, *PMFactor*, *DCFactor*. - * Added *Drop* as option of *DoSumOver*. - * Fixed problem with *FCToFA* causing possible substitution of multiple pairs of identical indices in a product. - * Added *DiracSlash* to *FCToFA*. - * Dropped *Projection* in *FCToFA*, since *RemoveIntegerIndices* has been dropped. - * Fixed bug in *XName* causing existing coupling vectors not to be found. - * Fixed bug in *VerticesSpecifications*. Multiple order of a coupling are now correctly merged into e.g. one coupling with orders {2, 4} instead of two couplings. (*orderJoin*). - * Fixed problem with *DiscardCT* and **FeynArts 3** . - * Fixed bug in *FixCouplingIndices*. *SUNDelta*, *SUND* and *SUNF* are now also supported in coupling vectors. - * Updated *DoSumOver* to comply with **FeynArts 3**. - * Improved *WFFactor*, *DCFactor* and *PMFactor* to behave better if a file is not there. - * *DCRenormalize* now correctly uses the inverse factor. - -* *Channels.m* - * Dropped *RemoveIntegerIndices* and *Projection*. - * Fixed bug with *SU2F* in *SUNReduce*. - * Added support for *ExplicitSUNIndex*. -* *PHIStart.m* - * Dropped *RemoveIntegerIndices*. - * Switched to *UNablaHatDelta* with "scalar weak source", remember to switch back if vectors or axial-vectors are needed. -* *ChPTW34.m*: Fix missing comma in N29. -* *ChPTW32.m*: Fix Typo (``` QuantumField` ``` instead of ```QuantumField```). - - -### Version 4.1.1 (2001) -* Help System: Following the instructions above, the FeynCalc Book is now viewable via the -Mathematica help browser. It is possible to look up help pages on individual -functions by selecting them in a notebook with the cursor and then clicking -on AddOns in the help browser. -* **PHI/FeynArts**: Support for **FeynArts** through the new sub-package **PHI**, which is now fully integrated in **FeynCalc**. **PHI** adds support for Chiral Perturbation Theory including tools for dealing with a large number of Feynman rules, derivative couplings, field expansion, etc. Moreover, some examples of using **PHI** are provided which should also be generally instructive. The examples can be found at -http://www.feyncalc.org/examples/index.html. Information about **PHI** can be found at http://www.feyncalc.org/examples/phi/index.html. -* The *ReadProtected* Attribute has been removed from all functions. -* Moved the file *FeynCalcBook.nb* into the new directory *English* and -added the file *BrowserCategories.m* to allow lookup via the -Mathematica help browser. -* Changes in *FeynCalc.m*: - * All **FeynCalc** definitions are now cleared upon reload, - hopefully improved the way filenames and paths are determined, - * Added support for loading from *~/.Mathematica*. - * Added support for loading **PHI** and **FeynArts**. - * Added *$Abbreviations*. - * Added a few definitions to *DeltaFunction*. - * Fixed bug in *DiracTrace* reported by A. Kyrieleis. - * Fixed bug in *DiracTrace* causing *Tr[DiracSlash[p,p]]* to give p^2 instead of 4 p^2 (reported by W. Broniowski and L. Trueman and A. Krishna). - * Fixed small display bug of *Spinor* reported by A. Krishna. - * Added *FCIntegrate* and *FCNIntegrate* which are options of the new - (still experimental) function *FeynmanDoIntegrals* fixed bug in the display definition for *Pair* causing infinite recursion. - * Added two new functions (still very experimental) *FeynmanReduce* and *FeynmanDoIntegrals*. - * Very small addition to *Integrate2*. - * Added option *InitialFunction* to *FeynRule*. - * Fixed bug in *ComplexConjugate*'s treatment of *DiracGamma[5]*, -reported by T.Rashba and V. Khotilovich. - * Fixed bugs related to Mac OS's filesystem in *FeynCalc.m*, *FORM2FeynCalc.m*, *FeynCalc2FORM.m*, *OneLoop.m*, *PaVeReduce.m*, *RHI.m*, *SquareAmplitude.m*, *Write2.m*. - * Fixed bug in *FeynCalc2FORM.m* reported by V. Khotilovich. - * Fixed forgotten small bugs in *FeynCalcExternal.m*. - * Changed *FeynCalcExternal.m*, *OneLoopSimplify.m*, *TID.m* - to allow other symbols for *Dimension* than *D*. - * Completely rewrote *FeynmanParametrize1.m*. It is still experimental, but in progress and intended to be much more general than *FeynmanParametrize.m*. - * Small changes in *OneLoop.m*, *PaVeReduce.m* to write out to more readable file names. - * Fixed forgotten Blank in *SimplifyPolyLog.m*. - * Added the following new general utility functions: -*NumericQ1*, *Combinations*, *MLimit*, *TimedIntegrate*, *SelectSplit*. - * Added check for integers in SU(N) related functions. - * Small change in *TARCER.nb* to avoid name conflict with **FeynCalc** and **FeynArts**. - * Various very small spelling fixes etc. - -### Version 4.0 (2000) - * Reorganized for open-source and extensibility. - -### Version 3.0.1.1 - * Two bug-fixes for *OneLoop*. - -### Version 3.0 (1998) - * Typesetting features of **Mathematica 3.0**. - -### Version 2.2beta9 (1995) -* Updated version of **FeynCalc** compatible with **Mathematica 2.2**. - -### Version 2.2 - -### Version 1.13 (1992) - -### Version 1.0 (1991) - * Initial release written by Rolf Mertig. \ No newline at end of file +* Modified the syntax of `FCLoopBasisExtract` so that the dimensions are now given via the `SetDimensions` option. Reason: This unifies the behavior among the other `FCLoopBasis*` functions. Furthermore, the new `FCTopology` option allows to include loop momenta that are not actually present in the input expression. This is useful when working with integral topologies. (8ab84fdd) + +## New functions and symbols + + +### Noncommutative algebra + +* Added new function `FCMatrixIsolate` that combines the application of `FCDiracIsolate`, `FCColorIsolate` and `FCPauliIsolate`. This is very useful for amplitude manipulations that affect the matrix structure of the expression, i.e. for taking the complex conjugate. (20030293) + +* Added new function `DiracSigmaExpand` that handles expansions of `DiracSigma`s. (2ed72ef9) + + * Example: Expand a suitable `DiracSigma` + + DiracSigma[GSD[p]+GSD[q],GSD[r]]//DiracSigmaExpand + +* Outsourced `DiracSubstitute67` out of `DiracSimplify`. Now it is a proper function for replacing chirality projectors with their definitions. (9efa4451) + + * Example: Substitute chirality projectors with their explicit definitions + + SpinorUBar[p1].GA[6].SpinorU[p2] // DiracSubstitute67 + + SpinorUBar[p1].GA[7].SpinorU[p2] // DiracSubstitute67 + +* Added `DiracSubstitute5`. It is a small auxiliary function that replaces `GA[5]` with `GA[6]-GA[7]`. This can be useful, e.g. if the spinor chains should be written in a particular way, always involving chiral projectors. (7b234636) + + * Example: Rewrite a spinor chain with g^5 in terms of chirality projectors + + SpinorUBar[p1].GA[5].SpinorU[p2] // DiracSubstitute5 + +* Introduced `ToDiracGamma67`, which is an inverse of `DiracSubstitute67`. By default, only terms that can be directly converted to a chirality projector are taken into account. If the options `All` is set to `True`, every occurrence of g^5 will be converted to chirality projectors (ce5c3f8f) + + * Example: Introduce chirality projectors in suitable Dirac matrix chains + + ToDiracGamma67[GA[mu].(1/2 + GA[5]/2).GA[nu]] + + ToDiracGamma67[GA[mu, 5, nu], All -> True] + + +* Added `SirlinSimplify`, a dedicated function for applying Sirlin's relations to Dirac spinor chains. Previously these relations were encoded in the code of `DiracSimplify` but now they can be applied using a separate function (9f74883b) + + * Example: Apply Sirlin's relations to a suitable spinor chain + + SirlinSimplify[SpinorUBar[p3, m3].GA[mu, rho, nu, 7].SpinorU[p1, m1] SpinorUBar[p4, m4]. + GA[mu, tau, nu, 7].SpinorU[p2, m2]] + +* Added `SpinorChainTrick`, an analogon of `DiracTrick` for products of spinor chains. This is an auxiliary function that will be called by higher level functions that deal with the Dirac algebra. (f0ead943) + + * Example: Combine two spinor chains by canonicalizing the Lorentz indices + + SpinorChainTrick[a SpinorUBar[p1, m1].GA[mu].SpinorU[p2, m2] SpinorVBar[p1, m1]. + GA[mu].SpinorV[p4, m4] + b SpinorUBar[p1, m1].GA[nu].SpinorU[p2, m2] SpinorVBar[p1, m1].GA[nu]. + SpinorV[p4, m4]] + + +* Added `SpinorChainChiralSplit`, a function that introduces chiral projectors in spinor chains that contain no gamma^5 or chiral projectors. Could be useful for working with chiral theories. (7cc4169f) + + * Example: Rewrite a spinor chain free of g^5 in terms of chains with chirality projectors + + SpinorChainChiralSplit[SpinorUBar[p1, m1].GSD[p].SpinorV[p2, m2]] + +* Added new function `SpinorChainTranspose`. It transposes the closed spinor chains in the expression, thus effectively switching `u` and `v` spinors. The `Select` option can be used for a flexible choice of chains that should be transposed. (7b832a61) + + * Example: Transpose some spinor chains + + SpinorChainTranspose[SpinorVBarD[p1, m1].GAD[mu].(GSD[p] + m).GAD[mu].SpinorUD[p2, m2]] + + SpinorChainTranspose[SpinorUBarD[p1, m1].GAD[mu].(GSD[p] + m).GAD[mu].SpinorVD[p2, m2]] + + SpinorChainTranspose[SpinorUBarD[p1, m1].GAD[mu].(GSD[p] + m).GAD[mu].SpinorVD[p2, m2], Select -> {{SpinorUBarD[_, _], SpinorVD[_, _]}}] + + +* Added new function `FCChargeConjugateTransposed` (a shortcut is just `FCCCT`). Given an expression in the Dirac space x, it obtains C x^T C^(-1), where C is the charge conjugation matrix. This is handy when dealing with Majorana spinors. (16e51495) + + * Example: Apply charge conjugation to some Dirac matrix chains + + FCChargeConjugateTransposed[GA[mu, nu, rho], Explicit -> True] + + FCChargeConjugateTransposed[GA[5], Explicit -> True] + +* Added `UnDeclareCommutator` and `UnDeclareAntiCommutator` that can remove the previously set values of commutators and anticommutators. (eccb96ca) + + * Example: Specify that `A`-fields commute with each other and remove this property later on + + Commutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A], QuantumField[A]] = 0; + DotSimplify[ExpandPartialD[QuantumField[A].QuantumField[A].LeftPartialD[nu]]] + + UnDeclareCommutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A], QuantumField[A]]; + DotSimplify[ExpandPartialD[QuantumField[A].QuantumField[A].LeftPartialD[nu]]] + +* Introduced initial support for Dirac matrix chains with explicit Dirac indices (via `DiracChain`). This particularly useful when importing amplitudes from `QGRAF` (fd49dd63) (4468a00e) (a6b577d9) (5799b97b) + + * Example: Some expressions with open Dirac indices that are now possible + + (* A Kronecker delta in the Dirac space*) + DIDelta[i, j] + + (* A standalone Dirac matrix with open Dirac indices *) + DCHN[GAD[mu], i, j] + + (* A chain of Dirac matrices with open Dirac indices *) + DCHN[GAD[mu].GAD[nu], i, j] + + (* A single UBar spinor with an open Dirac index *) + DCHN[SpinorUBar[p, m], i] + + (* A single VBar spinor with an open Dirac index *) + DCHN[SpinorVBar[p, m], i] + + (* A single U spinor with an open Dirac index *) + DCHN[i, SpinorU[p, m]] + + (* A single V spinor with an open Dirac index *) + DCHN[i, SpinorV[p, m]] + + (* UBar spinor contracted with a chain of Dirac matrices *) + DCHN[GAD[mu].GAD[nu], SpinorUBar[p, m], j] + + (* VBar spinor contracted with a chain of Dirac matrices *) + DCHN[GAD[mu].GAD[nu], SpinorVBar[p, m], j] + + (* U spinor contracted with a chain of Dirac matrices *) + DCHN[GAD[mu].GAD[nu], i, SpinorU[p, m]] + + (* V spinor contracted with a chain of Dirac matrices *) + DCHN[GAD[mu].GAD[nu], i, SpinorV[p, m]] + +* Introduced `DiracChainJoin` to handle contractions of the Dirac indices (4d3649a6) (18ac295d) (0575c06f) + + * Example: Contract the Dirac indices to obtain a closed spin chain + + DCHN[SpinorUBar[p1, m1], i] DCHN[GAD[mu].GAD[nu], i, j] DCHN[j, SpinorV[p2, m2]] // + DiracChainJoin + +* Added DiracChainExpand, a function to expand Dirac chains with explicit indices using linearity. (4e938efe) + +* Added DiracChainFactor, an auxiliary function to factor out commutative objects out of DiracChains. (97b47b24) + +* Added new function DiracChainCombine, which is an inverse operation to DiracChainExpand. (90431dfc) + +* Added `PauliSigmaExpand` and `PauliSigmaCombine` which are essentially analogons of `DiracGammaExpand` and `DiracSigmaCombine` for Pauli matrices. (a99b9882) + + * Example: Perform some expansions of Pauli matrices or undo them + + PauliSigmaExpand[SIS[q].SIS[p - q]] + + PauliSigmaExpand[SIS[a + b].SIS[c + d], Momentum -> {a}] + + PauliSigmaExpand[CSIS[a + b].CSIS[c + d], Momentum -> All] + + PauliSigmaCombine[SIS[p] + SIS[q]] +* Added `FCPauliIsolate`. It is like `FCDiracIsolate`, but for Pauli matrices. (20a1af91) + + * Example: Isolate Pauli matrices and spinors in the expression + + FCPauliIsolate[c1 SI[i] + c2 PauliXi[-I].SIS[p].PauliEta[I]] + +* Added new function `PauliOrder`. It is like `DiracOrder` but for Pauli matrices. (2759035e) + + * Example: Change the order of Pauli matrices using their commutation/anticommutation properties + + PauliOrder[CSI[i, j], {j, i}] + +* Added `PauliTrick` to have initial support for simplifying chains of Pauli matrices. As far as `D-1` dimensional Pauli matrices are concerned one can use `FCSetPauliSigmaScheme` to specify whether the 3D anticommutator relation should be used in D-1 dimensions. (498504f0) + + * Example: Simplify some chains of Pauli matrices + + CSIS[p1].CSI[i].CSIS[p2] // PauliTrick // Contract + + CSID[i, j, i] // PauliTrick // Contract + +* Added new option `PauliReduce` to `PauliTrick`. It specifies whether a chain of Pauli matrices should be reduced to at most one matrix by rewriting every pair of matrices in terms of commutator and anticommutator. When set to False, `PauliTrick` will try to use anticommutation relations to simplify Pauli chains. (e2299af2) + + * Example: Simplify a chain of Pauli matrices without the full reduction + + CSIS[p].CSI[j].CSIS[p].CSIS[i] // PauliTrick[#, PauliReduce -> False] & + +* Added `PauliSimplify`, an analogon of `DiracSimplify` but for Pauli matrices. (c8039c5c) + +### Loop integrals + +* Added `FCTopology`. Although currently it is just a placeholder for topologies, it is enormously useful in real calculations. (7239fd6f) + +* Introduced new propagator heads to support many new types of integral previously not available in `FeynCalc`. Covariant integrals that appear in such EFTs as HQET, NRQCD or SCET can be entered using the new `SFAD` (Standard FeynAmp denominator) head. The Cartesian analogon of `SFAD` is called `CFAD` (Cartesian FeynAmp denominator). Nonstandard integrals that cannot be represented via `SFAD` or `CFAD` can be introduced using `GFAD` (Generic FeynAmp denominator). +The support for the manipulation of the new integral is still somewhat experimental but will be improved in the future versions of the package + + + * Example: New propagators now available in `FeynCalc` + + (* The standard covariant propagator, corresponds to FAD[{p,m}]*) + SFAD[{{p, 0}, m^2}] + + (* The standard covariant propagator with the opposite I eta prescription*) + SFAD[{{p, 0}, {m^2, -1}}] + + (* Covariant Euclidean propagator in 4D *) + SFAD[{{p, 0}, {-m^2, -1}}] + + (* Massive covariant eikonal propagator *) + SFAD[{{0, p.q}, m^2}] + + (* Massless covariant eikonal propagator *) + SFAD[{{0, p.q}, m^2}] + + (* The standard Cartesian propagator *) + CFAD[{{p, 0}, m^2}] + + (* The standard Cartesian propagator with the opposite I eta prescription*) + CFAD[{{p, 0}, {m^2, 1}}] + + (* Cartesian propagator with a different mass term sign *) + CFAD[{{p, 0}, -m^2}] + + (* Massive Cartesian eikonal propagator *) + CFAD[{{0, p.q}, m^2}] + + (* Massless Cartesian eikonal propagator *) + CFAD[{{0, p.q}}] + + (* A special nonlinear propagator*) + GFAD[SPD[p1, q] SPD[p2, q] + x SPD[p1, p2]] + + +* Added some new placeholders: `Zeta4`, `Zeta6`, `Zeta8`, `Zeta10` and `Li4`. Those are mainly to be used in conjunction with `SimplifyPolyLog`. The `Conjugate` of a `ZetaX` is the object itself (44cdfef7) (966c8004) (d25f1125) (13ceb2a9) + + * Example: Simplify an expression using `SimplifyPolyLog` + + c1 Pi^4 + c2 Pi^6 + c4 Pi^8 + c5 Pi^10 // SimplifyPolyLog + + +* Added `FCGramMatrix` and `FCGramDeterminant` that compute the Gramian out of the given list of momenta. (d3009020) + + + * Example: Compute the Gramian for the 4-momenta `p1`, `p2` and `p3` + + FCGramMatrix[{p1, p2, p3}] + + * Example: Compute the Gramian for the 3-momenta `p1`, `p2` and `p3`. This is needed when doing tensor reduction of Cartesian integrals + + FCGramMatrix[{p1, p2, p3}, Head -> {CartesianPair, CartesianMomentum}, Dimension -> D - 1] + +* Extracted `N`-point to 4-point reduction from `OneLoop` and moved it to a separate function `NPointTo4Point`. (fd8949d3) + + * Example: Rewrite a massless scalar pentagon in terms of boxes + + FCClearScalarProducts[]; + NPointTo4Point[ FCI@FAD[{q, m0}, {q + p1, 0}, {q + p2, 0}, {q + p3, 0}, {q + p4, 0}], q, FCE -> True, FCVerbose -> -1] + + +* Added `PaVeUVPart`. This function returns UV divergent parts of arbitrary Passarino-Veltman functions. The algorithm is courtesy of G. Sulyok, cf. Phys. Part. Nuclei Lett. (2017) 14:631, arXiv:hep-ph/0609282. (03d50607) + + * Example: Obtain the UV-pole of the massive `B1111` Passarino-Veltman coefficient function + + FCClearScalarProducts[]; + PaVeUVPart[PaVe[1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]] + +* Added `FCLoopBasisGetSize`, a tiny convenience function that returns the number of linearly independent propagators for a topology with the given number of loop of external momenta. (33ce898a) + + * Example: Get the number of linearly independent propagators (size of the topology) for a topology with 4 loop momenta and one external momentum + + FCLoopBasisGetSize[4, 1] + +* Added `FCLoopBasisSplit` an auxiliary function for identifying multi-loop integrals that factorize. (9e22d22a) + + * Example: Separate some factorizable multiloop integrals into separate pieces + + FCLoopBasisSplit[FCI@FAD[{q1, m}, {q2 - q3, m}], {q1, q2}, Head -> loopInt] + + FCLoopBasisSplit[ FCI@FAD[{q1, m}, {q2, m}, {q3 - q4, 0}, {q3 - p, m}, {q5}], {q1, q2, q3, q4, q5}, Head -> loopInt] + +* Added `FCLoopBasisIntegralToPropagators`, a handy auxiliary function that converts the given loop integral into a list of the corresponding propagators and scalar products. The powers of propagators can be counted if the options `Tally` is set to `True`. (2db802f3) + + * Example: Convert the given integrals to a list of propagators as required e.g. for topology identification or IBP reduction + + FCLoopBasisIntegralToPropagators[SPD[p, q]^2 FCI[SPD[p, q]] SFAD[q, p - q], {q}, Tally -> True, Negative -> True, Pair -> True] + + FCLoopBasisIntegralToPropagators[GFAD[{p1.q p2.q + x, 2}] SFAD[p1], {p1, p2}, Tally -> True] + +* Added new auxiliary function `FCLoopBasisPropagatorsToTopology` to facilitate the extraction of the topologies from the expressions with loop integrals. (9b3cd7e1) + + * Example: Convert the given list of propagators to a list `Pair`'s + + FCLoopBasisPropagatorsToTopology[{SFAD[{q, m}], SPD[q, p]}] + + +* Added `ToSFAD`, a function that converts `FAD`s and `PropagatorDenominator`s to `SFAD`s and `StandardPropagatorDenominator`s. (f300d7f6) + + * Example: Convert some integrals in the `FAD`-notation to the `SFAD`-notation + + ToSFAD[FAD[p]] + + ToSFAD[x + FAD[{p, m}, q] FAD[{p, m1}, q, {r - q, m2, 2}]] + +* Added `CTdec`, a Cartesian version of `Tdec`. (d77968e0) + + * Example: Calculate some tensor reductions for Cartesian integrals + + CTdec[{{l, i1}, {l, i2}}, {p1}] + + CTdec[{{l1, i1}, {l2, i2}}, {p1, p2}, List -> False] + +* Added `FCLoopMixedToCartesianAndTemporal`. The purpose of this function is to rewrite (when possible) integrals with both Lorentz and Cartesian or temporal indices to integrals that are free of Lorentz indices (448de342) + + * Example: Rewrite some integrals + + FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{q, q.p}, m^2}], {q}] + + FCLoopMixedToCartesianAndTemporal[ FCI[TC[k] FVD[k, mu] FAD[k, k + p]], {k}] + +* Added `FCLoopPropagatorPowersCombine`, `FCLoopPropagatorPowersExpand`, `FCLoopRemoveNegativePropagatorPowers` and `FCLoopNonIntegerPropagatorsFreeQ` to manage the propagator powers of `CFADs`, `SFADs` and `GFADs`. These functions were mainly introduced to manage various new propagators inside `FeynCalc`. They are probably not very useful for the normal users but can be handy when writing codes on top of `FeynCalc` (ff57f617) + + * Example: Combine identical propagators of a loop integral raised to different powers into one propagator + + FCLoopPropagatorPowersCombine[ SFAD[{{q, 0}, {m, 1}, 3}, {{q, 0}, {m, 1}, 4}]] + + + * Example: Rewrite propagators raised to an integer power as a list inside `FeynAmpDenominator` (relevant only for the `FCI` representation) + + FCLoopPropagatorPowersExpand[FCI[SFAD[{q, m, 2}, q + p]]] + + + * Example: Rewrite propagators raised to negative integer powers as scalar products + + FCLoopRemoveNegativePropagatorPowers[SFAD[{q, m}, q + p, {q, m, -2}]] + + * Example: Check if the given integral is free of propagator raised to noninteger (e.g. fractional or symbolic) powers + + FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q + p, mm, 2}]] + (* True *) + + FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q + p, mm, n}]] + (* False *) + + FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q + p, mm, 0.5}]] + (* False *) + +* Added new function `FCLoopSamePropagatorHeadsQ` to detect integrals that simultaneously contain both purely Cartesian and purely Lorentzian propagators. Currently, those cannot be properly handled in `FeynCalc` (bc9a42f2) + + * Example: Check if the given integral is free of propagators with different `Head`s + + FCLoopSamePropagatorHeadsQ[FCI[SFAD[q,q-p]]] + (* True *) + + FCLoopSamePropagatorHeadsQ[FeynAmpDenominatorCombine[CFAD[q, q - p] SFAD[l, l + k]]] + (* False *) + + FCLoopSamePropagatorHeadsQ[FeynAmpDenominatorCombine[FAD[q, q - p] SFAD[l, l + k]]] + (* False *) + + +* Added new function `FCLoopMixedIntegralQ` to detect mixed Lorentz-Cartesian integrals. (3c6863cc) + + * Example: Check if the given integral is a mixed one + + FCLoopMixedIntegralQ[FCI[FVD[p, mu] SFAD[q, q - p]]] + (* False *) + + FCLoopMixedIntegralQ[FeynAmpDenominatorCombine[GFAD[TC[q] + EN] SFAD[q]]] + (* True *) + + +* Added new function `FCLoopEikonalPropagatorFreeQ` to detect eikonal propagators. (9f31f2fb) + + * Example: Check if the given integral is free of eikonal propagators + + FCLoopEikonalPropagatorFreeQ[FCI@SFAD[p, p - q]] + (* True *) + + FCLoopEikonalPropagatorFreeQ[FCI@CFAD[{{0, p.q}}]] + (* False *) + + +* Added `FCLoopBasisCreateScalarProducts`, an auxiliary function that creates a list of all loop-momentum dependent scalar products from the given lists of loop and external momenta. (8778efb7) + + * Example: Generate all `D`-dimensional scalar products for 2-loop 3-point function + + FCLoopBasisCreateScalarProducts[{l1, l2}, {p1, p2, p3}, {D}, Pair] + (* True *) + +* Added `$FCShowIEta` to control whether the `I Eta` should be explicitly shown in the `TraditionalForm` typesetting or not. If it is clear that all propagators have `+ I Eta`, it is more useful to set `$FCShowIEta=False`. (300bfb08) + + +### Kinematics and amplitudes + +* Introduced `FCRerouteMomenta`, a handy function that can automatically change the routing of the external momenta to make the amplitudes look simpler. It uses the supplied 4-momentum conservation and tries to minimize the number of momenta in propagators, 4-vectors, scalar products, Dirac slashes etc. (bcabba99) (26814232) + + * Example: Rewrite the amplitude in a more compact way using the momentum conservation relation `l1+l2=p1+p2+kp` + + amp = (-I)*Spinor[-Momentum[l2], ME, 1].GA[Lor3].Spinor[Momentum[l1], ME, 1]*Spinor[Momentum[p1], SMP["m_Q"], 1] . + GS[Polarization[kp, -I, Transversality -> True]].(GS[kp + p1] + SMP["m_Q"]) . GA[Lor3] . Spinor[-Momentum[p2], SMP["m_Q"], 1]* + FAD[kp + p1 + p2, Dimension -> 4]*FAD[{-l1 - l2 - p2, SMP["m_Q"]}, Dimension -> 4]*SDF[cq, cqbar]*SMP["e"]^3*SMP["Q_u"]^2 + + FCRerouteMomenta[amp, {l1, l2}, {p1, p2, kp}] + + +* Added new function `FCPermuteMomentaRules`, a convenience function for generating replacement rules for all possible permutations (renamings) of the given set of momenta. (9ff9423e) + + * Example: Give a set of rules for all possible permutations of the momenta `p1`, `p2` and `p3` + + FCPermuteMomentaRules[{p1, p2, p3}] + +* Added `FCReplaceMomenta`, a convenience function for replacing 4-momenta and 3-momenta in the given expressions. (3c5c8ae3) (d00dc59f) (28123ca9) + + * Example: Apply the substitutions `p1 -> P + 1/2 q` and `p2 -> P - 1/2 q` to the given amplitude + + amp = (-I)*Spinor[-Momentum[l2], ME, 1].GA[Lor3].Spinor[Momentum[l1], ME, 1]*Spinor[Momentum[p1], SMP["m_Q"], 1] . + GS[Polarization[kp, -I, Transversality -> True]].(GS[kp + p1] + SMP["m_Q"]) . GA[Lor3] . Spinor[-Momentum[p2], SMP["m_Q"], 1]* + FAD[kp + p1 + p2, Dimension -> 4]*FAD[{-l1 - l2 - p2, SMP["m_Q"]}, Dimension -> 4]*SDF[cq, cqbar]*SMP["e"]^3*SMP["Q_u"]^2 + + FCReplaceMomenta[amp, {p1 -> P + 1/2 q, p2 -> P - 1/2 q}] + + + * Notice that `FCReplaceMomenta` is not suitable for expanding in 4-momenta (soft limits etc.) as it does not check for cases where a particular substitution yields a singularity. For example, the following code obviously returns a nonsensical result + + FCClearScalarProducts[]; + SPD[q] = 0; + FCReplaceMomenta[FAD[q + p], {p -> 0}] + + +* Added new `DataType` `FCVariable` so that symbols marked as `FCVariable` will be pulled out from `Momentum`, `CartesianMomentum` and `TemporalMomentum`. (d0754e8b) (955fb6f2) + + * Example: For `SPD[c1 p1 + c2 p2, q]` with `c1` and `c2` being some constants (not 4-momenta), `ExpandScalarProduct` does not work properly + + SPD[c1 p1 + c2 p2, q] // ExpandScalarProduct + + Prior to `FeynCalc` 9.3 the only solution was to write the expression explicitly using the FCI notation + + Pair[c1 Momentum[ p1, D] + c2 Momentum[ p2, D], Momentum[q, D]] // ExpandScalarProduct + + Now we can explicitly declare `c1` and `c2` to be of the type `FCVariable` so that everything works as expected + + DataType[c1, FCVariable] = True; + DataType[c2, FCVariable] = True; + SPD[c1 p1 + c2 p2, q] // ExpandScalarProduct + + Notice that this also works for propagators, e.g. in `FAD[{q + c1 p1, m}]` as well as Dirac and Pauli matrices. Use `DataType[c1, FCVariable] = False` etc. to undo the declaration for a particular variable. + +* Added `ToStandardMatrixElement`. This function wraps spinor chains, color strutctures and polarization vectors into head `StandardMatrixElement`. This functionality was previously available only via `OneLoop`. The idea of having standard matrix elements is described in Denner's famous paper in Fortschritte der Physik, Vol. 41, Nummer 4, 1991, Section 5. (d456057a) (15238e61) (f70658ae) + + * Example: Decompose the given product of spinor chains into pieces with different chiral projectors + + + exp = Spinor[Momentum[k2, D], 0, 1].GAD[mu].Spinor[-Momentum[k1, D], 0, 1] * + Spinor[-Momentum[ps, D], SMP["m_s"], 1].GAD[mu].Spinor[Momentum[pd, D], SMP["m_d"], 1] + + ToStandardMatrixElement[exp] + +* Added `SquareAmplitude`, a simple function that multiplies amplitudes with their complex conjugates and returns the result without doing any evaluations. This function is particularly useful when some amplitudes evaluated with `FeynCalc` should be passed to `FORM` for calculating the amplitude squared (8165ef48) + + * Example: Construct the squared matrix element for a sum of three amplitudes `M1`, `M2` and `M3` + + + exp = SquareAmplitude[{M1, M2, M3}, {M1cc, M2cc, M3cc}] + + Total[exp] + + If the sum of the amplitudes corresponds to real corrections, i.e. the amplitudes are purely real, we can obtain a shorter expression + + SquareAmplitude[{M1, M2, M3}, {M1cc, M2cc, M3cc}, Real->True,List->False] + +### Tensors and vectors + +* Added new function FreeIndexFreeQ for checking whether the expression contains free (i.e. uncontracted) indices. (0e75d46c) + +* Added new objects for non-relativistic calculations. (a82bb76e) + + * Example: Following new tensor objects are now available + + + (* Temporal component of the 4-vector p^mu *) + TC[p] + + (* Cartesian 3-vectors *) + {CV[p, i], CVD[p, i], CVE[p, i]} + + (* Cartesian scalar products *) + {CSP[p, q], CSPD[p, q], CSPE[p, q]} + + (* Cartesian Kronecker deltas *) + {KD[i, j], KDD[i, j], KDE[i, j]} + + (* Cartesian Levi-Civita tensors *) + {CLC[i, j, k], CLCD[i, j, k], CLC[][p1, p2, p3], CLCD[][p1, p2, p3]} + + (* Dirac matrices with a spatial index *) + {CGA[i], CGAD[i], CGAE[i]} + + (* Dirac matrices contracted with a 3-vector *) + {CGS[p], CGSD[p], CGSE[p]} + + (* Dirac matrix with a temporal index *) + TGA[] + + (* Pauli matrices with a Lorentz index *) + {SI[mu], SID[mu], SIE[mu]} + + (* Pauli matrices contracted with a 4-vector *) + {SIS[p], SISD[p], SISE[p]} + + (* Pauli matrices with a spatial index *) + {CSI[i], CSID[i], CSIE[i]} + + (* Pauli matrices contracted with a 3-vector *) + {CSIS[p], CSISD[p], CSISE[p]} + + * Notice that the support for nonrelativistic calculations is still somewhat experimental and will be improved in the future versions of `FeynCalc`. + +* Added `ThreeDivergence` to differentiate w.r.t Cartesian vectors. It is essentialy the 3D analogon of `FourDivergence` (88d0213e) + + + * Example: Differentiate the given expression w.r.t `p^i` + + + ThreeDivergence[CSPD[p, r] CFAD[{p + q, m}], CVD[p, i]] + + +* Introduced `CartesianScalarProduct` to set scalar products of Cartesian vectors and `SetTemporalComponent` to set values of the temporal components of 4-vectors. (3b0c4b1b) + + * Example: Specify the value of the Cartesian scalar product `p.q` + + FCClearScalarProducts[]; + CSP[p, q] = mm; + ExpandScalarProduct[CSP[p + r, q + s]] + + * Example: Specify the value of the temporal component of `p^mu` + + FCClearScalarProducts[]; + TC[p] = x; + ExpandScalarProduct[TC[p + r]] + +* Added `EpsContractFreeQ` that can quickly check if the given expression contains epsilon tensors that can be contracted with each other. This is an auxiliary function that is useful when writing involved codes on top of `FeynCalc` (5b02fd19) + + * Example: Check some expressions + + + EpsContractFreeQ[FCI[LC[p1, p2, p3, p4]]] + (* True *) + + EpsContractFreeQ[FCI[LC[p1, p2, p3, mu] LC[q1, q2, q3, q4]]] + (* False *) + +* Added `DummyIndexFreeQ` that can quickly check if the given expression contains dummy indices. This is an auxiliary function that is useful when writing involved codes on top of `FeynCalc` (f0547fb9) (db47ddf0) + + * Example: Check some expressions + + + DummyIndexFreeQ[FCI[FV[p, mu] FV[q, nu]], {LorentzIndex}] + (* True *) + + DummyIndexFreeQ[FCI[FV[p, mu] FV[q, mu]], {LorentzIndex}] + (* False *) + + DummyIndexFreeQ[FCI[SUNT[a, b]], {SUNIndex}] + (* True *) + + DummyIndexFreeQ[FCI[SUNT[a, a]], {SUNIndex}] + (* False *) + +* Added `CartesianToLorentz`, a function that replaces Cartesian Dirac slashes and Cartesian scalar products with corresponding Lorentz tensors and temporal components. (44a6e961) + + * Example: Eliminate `ga^i p^i` in favor of `ga^mu p_mu` and `ga^0 p^0` + + CGS[p] // CartesianToLorentz + + + * Example: Eliminate `p^i q^i` in favor of `p^mu q_mu` and `p^0 q^0` + + CSP[p, q] // CartesianToLorentz + +* Added `LorentzToCartesian`, a function that decomposes selected Lorentz tensors into their Cartesian and temporal components. (1430daf2) + + + * Example: Decompose `p^mu q_mu` into its temporal and spatial components + + SPD[p, q] // LorentzToCartesian + + + * Example: Rewrite `eps^{mu nu rho si} p_rho q_si` as a linear combination of 3D Levi-Civita tensors + + LC[mu, nu][p, q] // LorentzToCartesian + + + +* Added `FCSetMetricSignature` and `FCGetMetricSignature`. Notice that currently the metric signature is mainly used by the functions `CartesianToLorentz` and `LorentzToCartesian`. It is e.g. not possible to set the signature to `{1,1}` and have Euclidean Dirac matrices (30c2c217) + + * Example: Get the current metric signature + + FCGetMetricSignature[] + (* {1,-1} i.e. mostly minus *) + + * Example: Changing the metric signature to mostly plus naturally modifies the output of `LorentzToCartesian` + + FCSetMetricSignature[{-1, 1}] + SPD[p, q] // LorentzToCartesian + + +* Added `FCSchoutenBruteForce`, a function that attempts to automatically simplify the given expression by applying Schouten's identity. Notice that what this function does is pure heuristics so that there is no warranty that it can achieve all possible simplifications (f23523b6) (21092852) + + * Example: Simplify the given expression using Schouten's identity + + exp = LC[][p1, p2, p3, p4] SP[p5, p6] + + LC[][p2, p3, p4, p5] SP[p1, p6] + LC[][p3, p4, p5, p1] SP[p2, p6] + + LC[][p4, p5, p1, p2] SP[p3, p6] + + FCSchoutenBruteForce[exp, {}, {}, Rule -> False] + + + +* Outsourced contractions of epsilon tensors to `EpsContract`. (2d1d8f6f) + + * Example: Calculate some contractions of epsilon tensors + + LC[][p1, p2, p3, p4] LC[][p1, p2, p5, p6] // EpsContract + + CLC[][p1, p2, p3] CLC[][p1, p2, p4] // EpsContract + +### Miscellaneous + +* Added new function `FCCheckVersion` that can abort the evaluation if the current `FeynCalc` version is too old. + +* Added `SMPToSymbol`, a small function for converting `SMP`s to symbols. (e473b3a4) + +* Introduced `FCSubsetQ`, a cheap replacement for the standard `SubsetQ`, which is unfortunately not available in `Mathematica` 8 and 9. The syntax is identical to that of `SubsetQ` (5a4eca2c) + +* Introduced `FCDuplicateFreeQ`, a cheap replacement for the standard `DuplicateFreeQ`, which is unfortunately not available in `Mathematica` 8 and 9. The syntax is identical to that of `DuplicateFreeQ` (b44bd2f7) + +* Added new auxiliary function `FCProductSplit` for splitting products into lists w.r.t a list of the given variables. (efedef66) + + + * Example: Fish out `a` and `b` from the product `a*b*c*d` + + FCProductSplit[a b c d, {a, b}] + + +* Added `FCReplaceAll` and `FCReplaceRepeated`, two handy functions for applying replacement rules sequentially. This avoid writing long chains of `ex /. rule1 /. rule2 /. rule3` etc. (00a34b65) + + + * Example: Apply a sequence of replacement rules to `a*c` + + FCReplaceRepeated[a c, {a -> b}, {c -> d}, {d -> e}, {b -> f}] + +* Introduced `FCPatternFreeQ`. It is just a convenience function that makes it easier to check for patterns in the arguments of `FeynCalc` functions and helps to avoid duplicated code. (212c2cba) + + * Example: Check some expressions + + + FCPatternFreeQ[{FV[p, mu]}] + (* True *) + + FCPatternFreeQ[{FV[p, _]}] + (* False *) + +* Added `FCCheckSyntax`, a helper function that attempts to identify errors in the user input. Notice that such checks are very expensive performance-wise, so they should not be used on a regular basis. Furthermore, `FCCheckSyntax` is not guaranteed to detect all possible syntax errors (6541e10d) (41b8b8eb) + + * Example: Check some expressions + + + FCCheckSyntax[GA[mu]*GA[nu]] + (* Typical mistake, using Times instead of Dot in noncommutative products *) + + FCCheckSyntax[FV[p, mu]*FV[q, mu]*FV[r, mu]] + (* Another common mistake, Einstein summation convention violated *) + + +* Added a new function `FCCompareResults`. It offers a convenient way to compare intermediate of final results to the known values. This function was originally written for example calculations to compare the final results with the literature. (1dab575b) (6287947b) + + * Example: Compare some expressions + + + FCCompareResults[{4, 4}, {2^2, 8/2}] + (* The results agree *) + + FCCompareResults[{3, 5}, {2^2, 8/2}] + (* The results disagree *) + + + +* Added `ExpandAll2` for fast expansions of very large expressions (like in Dirac traces). It is a very special auxiliary +function that is probably useful only in very special cases. The syntax is identical to that of `ExpandAll` (089eb9e6) + + * Example: Benchmark against `ExpandAll` + + + exp = Sum[p[i], {i, 1, 100}] Sum[q[i], {i, 1, 1000}]; + + AbsoluteTiming[ExpandAll[exp];] + + AbsoluteTiming[ExpandAll2[exp];] + (* In `Mathematica` 11.0 ExpandAll2 is almost 60% faster than ExpandAll! *) + + +* Added `FCMakeIndex`. It is a small convenience function for generating indices, i.e. `LorentzIndex`, `SUNIndex` etc. from the output of diagram generators such as `FeynArts` and `QGRAF`. Notice that `FeynCalc` currently does not offer a native interface to `QGRAF`. This is planned for future versions of the package. (2fad0817) + + * Example: Generate some indices + + FCMakeIndex["Lor", "1"] + + FCMakeIndex["Lor", {3, 1, 4}, LorentzIndex] + + FCMakeIndex["Sun", {"a", 1, -4}] + + +* Added new `SMP` objects. (d53496a9) (da890b9f) (f4bb3b73) (eaf5339f) + + * Example: Show all available `SMP`'s + + SMP[] + +* Added `FCShowReferenceCard` and a sample reference card for `FeynArts`. (a1d90ef2) + + + * Example: Show the reference card for `FeynArts` + + + FCShowReferenceCard[{"FeynArts"}] + + +* Added `TypesettingExplicitLorentzIndex` to allow user defined typesetting of explicit Lorentz indices. This was essentially added as a reaction to a request for MSE ([https://mathematica.stackexchange.com/questions/133114/how-to-differentiate-between-superscript-indices-and-powers-in-the-output/134146#134146](URL)) (8b1102de) + + + * Example: Make explicit Lorentz indices look red + + TypesettingExplicitLorentzIndex = Function[x, Style[x, Red]]; + + exp = 4 M^2 u FV[k, 0]^2 - 4 M^2 u FV[k, 3]^2 - + 4 M SP[k, k] - 2 M u FV[k, 0] FV[k, 3]^2 + + 4 M u FV[k, 0] FV[k, 2] - u^2 FV[k, 2]^2 + +* Added `FCGetNotebookDirectory[]`, a simple convenience function that is like `NotebookDirectory[]`, but works also when the Front End is not available. This is especially useful when running some .m scripts from the terminal (600c95ba) + +* Added `FCReloadFunctionFromFile`, an auxiliary function that is useful for debugging the existing `FeynCalc` functions without reloading the kernel. This is a helper function for developers that is not meant to be employed by the users (c51fe7d0) + + + * Example: Reload the definition of `Collect2` + + FCReloadFunctionFromFile[Collect2, FileNameJoin[{$FeynCalcDirectory, "Shared", "Collect.m"}]] + +* Introduced `FCProgressBar`. It is a small auxiliary function that can be used to show the current progress of processing a list of objects with a given function. (d72b205e) + + * Example: Show the progress of some calculation + + FCProgressBar["Calculating something ", i, 10], {i, 1, 10}] + + +## New options, features and other improvements + +#### Miscellaneous + +* Improved `FCUseCache` to take NR quantitites into account when caching. (ca446ee4) +* Allowed `SquareAmplitude` to handle amplitudes of different length (e.g. RV- contributions). (ba642612) +* Modified the debugging interface to have negative values of `FCVerbose` parsed correctly. (0771fa6e) +* Improved factoring of momenta arguments in `DotSimplify`. (bacfa855) +* Improved `Cases2` not to generate erroneous messages when handling functions that must have more than one argument (e.g. `PolyLog`s) (d34a9e64) +* Modified the behavior of `ComplexConjugate` not to abort the evaluation if the expression cannot be strictly factored into Dirac, Pauli and color parts. This should fix Issue #51. (e53bdc0d) +* Improved `FCRenameDummyIndices` and `FCCanonicalizeDummyIndices` to work with `DiracIndex`. (74540c36) +* Added new internal variable ```FeynCalc`Private`AddToTheWhiteListedContextAdditions```. It is meant for packages that add stuff to the `Global` context so that there will be no warning messages when `$FCCheckContext` is set to `True`. (d57682f4) +* Added new option `FreeQ` to `FCGetDimensions` that allows to specify objects to be ignored when extraction dimensions present in the expression. (32aff18b) +* Made `FC{Dirac,Color,Pauli,Matrix}Isolate` listable. (14d5ac71) +* Improved `FCRenamingDummyIndices`. (0f1ecb94) +* Added new option `DiracIndexNames` to `FCCanonicalizeDummyIndices`. (53fec02e) +* Improved the `Conjugate` option of `ComplexConjugate` following the suggestion of JP-Ellis from https://github.com/FeynCalc/feyncalc/pull/48 (4327daf7) +* Completely refactored ComplexConjugate, adding support for DiracChains and PauliSigmas. (82bdedc9) +* Added the `TimeConstrained` option to FCColorIsolate. (0c29d439) +* Improved `Uncontract` to handle `DiracChain`s. (ba756e9c) +* Improved `FCCanonicalizeDummyIndices` to handle `DiracChain`s. (4801967e) +* Improved `DotSimplify` to apply DiracChainFactor when the input contains `DiracChain` symbols. (9f268817) +* Various functions now support the option `FCE -> True` to convert the output to the `FeynCalcExternal` form. +* Added new option `Expand` to `NTerms`. (e8cc7378) +* Moved `OptionsSelect` and `$Gauge` from `FeynCalc.m` to `Phi`. (7bc5d54d) +* Added an option `Conjugate` to `ComplexConjugate`. Now it is possible to wrap arbitrary variables into `Conjugate` heads, i.e. coupling constants. (cc79324f) +* Improved `MomentumCombine` to work also on `Eps` tensors. This can be disabled via the option `LC->False` (thanks to Pablo Sanchez Puertas for the suggestion) (4bfe6e59) +* Added a new option `ChangeDimension` to `FCGetDimensions`. When set to true, the dimensions of Cartesian objects will be determined with respect to the Lorentz objects from which they originate. In this case the dimension of `CV[p,i]` will be 4 and not 3. This is mainly required for functions related to the Dirac algebra, which need to check the dimensions in order to be conistent with different gamma_5 schemes. (d231c3ec) +* Added new option `Head` to `FCFactorOut` (e508b29b) +* Added new option `Full` to `ExpandScalarProduct`. Together with the momentum options it allows even more fine-grained expansions, e.g. for `ExpandScalarProduct[SP[l+p1+p2+p3,q1+q2+q3+q4],Momentum->l,Full->False]`. This helps to avoid an unnecessary proliferation of terms. (64c6e504) +* Added a new option `ExpandScalarProduct` to `Contract`. When set to `False`, scalar product will not be expanded which should give a speed up on QCD diagrams with 3- and 4-gluon vertices. (50e860b1) +* Changed the behavior of `Collect2` on expressions that contain none of the specified monomials. Now such expressions will be factored (according to the `Factoring` option) in the output. This is a more consistent behavior compared to what we had before. (c9219af6) +* Improved `Collect2` so that it can now thread over (lists of) replacement rules. This is particularly useful when applying `Collect2` to the output of `Solve`. (5c334b7d) +* Changed the ordering of InitialFunction and `FCFactorOut` in `Collect2`. It is better to first factor out the overall coefficient and then apply the `InitialFunction` (e.g. `Expand`). (3dc17555) +* Modified the option `Factoring` of `Collect2` so that one can specify the maximal `LeafCount`. Terms that are more complicated than that will not be factorized. (f9a12d59) + +* New options added to `Collect2` + * `TimeConstrained`, specifies the maximal amount of seconds that can be spent on factoring a single term. Default value: `Infinity` (958d5536) + * `Head->{h1,h2}`, will wrap the product of the monomial and the coefficient into `h2` (cba0b153) + * `InitialFunction -> fun`, applies `fun` to the expression before collecting the monomials (cba0b153) + * `IntermediateSubstitutions`, specifies a set of replacement rules to applies to the expressions after applying `InitialFunction` (cba0b153) + * `Numerator` and `FactoringDenominator`. These options are meant for cases where `Collect2` is used on fractions, i.e. `Collect2[(....)/(....),...]`. With `Numerator->True` `Collect2` will be applied only to the numerator but not the denominator. `FactoringDenominator` allows to specify a function that will applied to the denominator, e.g. `Factor2`. (1e48d104) + +* Miscellaneous improvements and optimizations in various functions + * `Contract`: (f1538e4e) + * `ExpandScalarProduct`: (7bb494c4) (358365b3) + * `FourDivergence`: (f00d8584) + * `SUNSimplify`: (ef8500a5) + * `PairContract`: (b538f4eb) + * `MomentumCombine`: (f2da34ad) + * `ChangeDimension`: (262aa4b0) + * `DoPolarizationSums`: (40710e25) + * `EpsEvaluate`: (3627da9b) + * `FCSplit`: (5c42c5f6) + * `Collect2`: (4573748f) + +#### Typesetting + +* Improved typesetting of `Eps` to have explicit distinction between `4`- and `D`-dimensional Levi-Civita tensors. (38151c96) +* Improved the typesetting rules to avoid unnecessary calls to `FCI` and `MomentumExpand`. (e11aa3ae) +* Improved typesetting of `FAD`s so that now objects like `FAD[p,Dimension->4]` or `FAD[{p+q,m}, Dimension->D-4]` will have the momenta displayed with the correct bars and hats. This way now one can immediately see the dimension of a `FAD`. (30542a78) +* Improved typesetting of `FeynAmpDenominator`. (1e802f06) +* Improved typesetting of four vectors. (87fab6da) + +#### `FeynArts` + +* Improved `FCPrepareFAAmp` to support the new `PropagatorDenominator` syntax of `FeynArts` 3.12 (thanks to Will, ) (6946116f) +* Improved `FCPrepareFAAmp` to handle the input from `FeynArts` with explicit Dirac indices (issue # 46). (7eed481b) +* Added new option `FAModelsDirectory` to `FAPatch` so that we can also patch models that are not in `FeynArts/Models`. (9341acea) +* Patch `FCFAConvert` to support empty diagram lists (#43) (e01b3b8b) +* Updated `FCPrepareFAAmp` to handle Majorana spinors. (a84199f2) +* Improved `FCFAConvert` to handle `FeynArts` models with `SUND`s in the Feynman rules (thanks to A. Hayreter). (59002150) +* Added a new option `Prefactor` to `FCFAConvert`. (8e8d0b96) +* Added new option `Contract` to `FCFAConvert`. Sometimes it is convenient to carry out all the Lorentz contractions immediately after generating the amplitudes. (c5e593bd) +* Improved handling of CKM matrix element when converting from `FeynArts` to `FeynCalc`. (90d42d47) +* Updated `FeynArts` patching function to protect the `SI` shortcut. (b818e820) + +#### Dirac algebra + +* Modified the behavior of `DiracReduce` not to output DiracSigmas with `FCE` applied to their arguments. (2c4793f5) +* Improved performance of `DiracSimplify` on contractions from large traces. (834cefa9) +* Improved formulas used in `PauliTrick`. (e687d04c) +* Updated `FCPauliIsolate` to have similar features as `FCDiracIsolate`. (096a12c0) +* Added new option `FeynAmpDenominatorCombine` to `FCFAConvert`. When set to False, propagators raised to integer powers will be returned e.g. as `FAD[p1+p2]^2` instead of `FAD[p1+p2,p1+p2]`. This should emulate the old behavior of `FeynArts` before the change that occurred on the 19.03.2019. (ec976f75) +* Improved `DiracSimplify` on expressions with Cartesian tensors. (8921a977) +* Added new option `CartesianIndex` to `FCDiracIsolate`. (006f65f2) +* Added new options `LorentzIndexNames` and `CartesianIndexNames` to `ToStandardMatrixElement`. This way we can choose nicer looking indices when applying the function. (9020ffe5) +* Improved the parsing of `FeynArts` amplitudes with 4-fermions when using the `UndoChiralSplittings` option. (6f018947) (221af0f3) +* Improved handling of 4-fermion diagrams in `DiracSimplify` and `ToStandardMatrixElement`. (d6699ac3) +* Improved BMHV algebra in `DiracTrick` so that chiral structures of the expression (`GA[6]` and `GA[7]`) do not get messed up when moving chiral projectors past other matrices. (081fb5e0) +* Added new options `DiracSimplify` and `DiracEquation` to `ToStandardMatrixElement` to have more fine grained control over the process. (f43caece) +* Added new options `LorentzIndexNames` and `CartesianIndexNames` to `DiracSimplify`. This can help to avoid additional index canonicalizations when applying DiracSimplify to a list of amplitudes. (50f01060) +* Small optimization in `DiracSimplify` regarding Sirlin relations. (69cb590d) +* Made `DiracSimplify` listable. (61872d54) +* Added new options `LorentzIndexNames` and `CartesianIndexNames` to `SpinorChainTrick`. (a63eb61b) +* Added new option `FCTraceExpand` to `FCDiracIsolate` and changed the default value of the factoring option to `{Factor2, 5000}`. (21235227) +* Improved `DiracTrace` to evaluate simple traces before entering the main evaluation function via `DiracTrick`. (d60a0b6b) +* Improved `DiracSimplify` not to miss certain contractions. (6a01f4dd) +* Allowed `DiracChain` symbols to factor out an overall numerical coefficient. (e71bf706) +* Added additional simplifications in `DiracTrick` for the `NDR-Drop` scheme. (021c5030) +* Added fast mode to `DiracTrace`. (53d2e07a) +* Modified `DiracEquation` not to mess up the chiral structure of the input expressions. (43799615) +* Refactored `Anti5` to call `DiracTrick` for all g^5-related manipulations. (f3a23a7f) +* Improved `DiracSimplify` to try to repeat the attempt to calculate the trace at a latter stage. This is mainly relevant for NDR, where the trace might become simpler at a latter stage. (64ea28f3) +* Improved `Chisholm`, `DiracOrder`, `EspChisholm`, `FCChargeConjugateTransposed` and `SpinorChainTranspose` to handle `DiraChain` objects. (3c48b725) +* Improved `FCDiracIsolate`, `FCPauliIsolate` and `FCColorIsolat` to wrap the prefactor of the matrix chain into a user-specified head via the Head option. (47f48b2f) +* Improved `DiracSimplify` to handle `DiracChain`s. (1b1b1d1d) +* Improved `DiracTrick` to support `DiracChain`s. (553ff9c4) +* Added a fast mode to `DiracChainJoin`. (a327b9d4) +* Improved `FermionSpinSum` to handle amplitudes squared that involve Majorana spinors. The reordering of spinors in the corresponding chains can be turned off via the option `SpinorChainTranspose`. (71b9d256) +* Added a new option `FCJoinDOTs` to `DotSimplify`. This allows to inhibit the joining of DOTs when `Expanding` is set to False. The same option is now also available in `FCDiracIsolate`, `DiracTrick`, `Chisholm`, `DiracOrder` and `EpsChisholm`. (34f08996) (c280442e) + +* New options added to `FCDiracIsolate` + * `Polarization`, when set to `True`, also tensors contracted with polarization vectors will be isolated together with the Dirac structures. Default value: `False` (bae9eadd) + * `Spinor->Join`, when the already existing option `Spinor` is set to `Join`, products of spinor chains will be wrapped into one head, which is useful for a range of special identities. (fbdfcecf) + * `TimeConstrained`, specifies the maximal amount of seconds that can be spent on factoring a single term in the application of `Collect2`. Default value: `3` (fcf27e17) + +* New options added to `DiracSimplify` + * `DiracSubstitute5`, when set to `True`, the function `DiracSubstitute5` will be applied to the input expression . Default value: `False` (7de810df) + * `DiracTrace`, when set to `False`, `DiracSimplify` will completely ignore all Dirac traces in the expression. Default value: `True`. (3a439bbe) + * `Expand2`, when set to `False`, `Expand2` will not be applied to the final result. Default value: `True`. (ac506e16) + +* Miscellaneous improvements and optimizations in various functions + * `DotSimplify`: (f66d9973) (f3accd1d) (e7830814) (9d622473) + * `DiracTrick`: (4212b34c) (d8d8a496) (e3097739) (a72ac349) (3ab2aa76) (748255e6) (92a7db05) (45e04933) (86517dda) + * `DiracOrder`: (7fd172af) (a9af59b3) + * `DiracEquation`: (86517dda) + * `DiracTrace`: (f9457758) (60eee612) + * `DiracReduce`: (389021fd) + * `Chisholm`: (5208ffb2) (a9af59b3) (d3030b84) + * `DiracGammaCombine`: (a9af59b3) + * `DiracGammaExpand`: (a9af59b3) (53fbf542) + * `EpsChhisholm`: (a9af59b3) + * `FCDiracIsolate`: (4b2f7ed9) (86517dda) + * `FCTraceExpand`: (9d622473) + * `DiracSimplify`: (153c344d) (6e74bd96) (47faf5eb) (86517dda) + * `DiracTrace`: (78f8de5a) (bb826aa8) (47faf5eb) (f1538e4e) + +#### Cartesian tensors + +* Improvemenets of various functions to support Cartesian tensors: `Contract`, `DiracSigmaExplicit`, `DiracTrace`, `DiracOrder`, `DiracSimplify`, `DiracOrder`, `DiracTrick`, `ToDiracSigma`, `DiracEquation`, `DotSimplify`, `DiracSigmaExplicit`, `DiracGammaCombine`, `DiracGammaExpand`, `FCDiracIsolate`, `FCTraceExpand`, `FCTraceFactor`, `ToLarin`, `EpsChisholm`, `Chisholm`, `EpsEvaluate`, `ExpandScalarProduct`, `FCGetDimensions`, `MomentumCombine`, `MomentumExpand`, `FeynAmpDenominatorSplit`, `FCCanonicalizeDummyIndices`, `FCLoopIsolate`, `FCGramDeterminant`, `FCGramMatrix`, `PaVeReduce`, `FCLoopSolutionList`, `FCLoopCanonicalize`, `ChangeDimension`, `FCRenameDummyIndices`, `ComplexConjugate`, `FCReplaceD`, `PropagatorDenominatorExplicit`, `FeynAmpDenominatorCombine`, `Calc`, `Tr2`, `Trick`, `Anti5`, `DoPolarizationSums`, `PolarizationSums`, `Uncontract`, `FermionSpinSum` `FCClearScalarProducts` `Eps` (4827b5d3) (f7797f05) (aed41980) (209de41e) (4202cc6c) (265cd258) (c229666e) (98cbefc3) (f7c77b20) (2839e4b4) (0f4e03b4) (265638e9) (0cd763c8) (ed5b7c53) (789da180) (23b138d8) (a374b2fd) (081f2ec5) (b20b55f5) (108702ee) (112f2707) (d1feae49) (ac18f860) (36148aca) (afeb7f22) (75f1091e) (b40a399c) (4fb85670) (ca8f1396) (b572d81e) (3d3923d0) (ddd968e0) (51477c4e) (2caa6cfb) (1aa319d4) (17ce0a3f) (2d42c7c3) (cc8221dc) (518d4cd4) (0829849d) (626114ab) (2d1d8f6f) (123c5e52) (5c43cf49) (6ad513ec) + +#### Loop integrals + +* Improved performance in `FCLoopExtract`, `FCLoopIsolate` and `FCMultiLoopTID` (98a10039). +* Improved performance of `FCApart` by using memoization. (9f19c326) +* Added new option `MaxIterations` to `PaVeReduce`, so that one can limit the depth of the reduction. (4d32be8c) +* Improved `FCLoopBasisIntegralToPropagators` and `FCLoopBasisIntegralToPropagators` to allow for lists of propagators in the input. (b48a10e9) +* Added new option `PaVeOrder` to `ToPaVe`. When used together with `PaVeAutoOrder` this will completely disable the reordering of the arguments using symmetries of the `PaVe` functions. (0938f7d4) +* Improved `TarcerToFC` to properly recover the external momentum from scalar products using the new option ScalarProduct. (a2af7454) +* Added some additional rank 4 2-loop tensor decompositions to `TIDL`. (d83b42e6) +* Improved `PaVeReduce` not to remove external isolations. (69225bad) +* Improved `FCApart` to handle nonlinear loop integrals. (f5b0f90a) +* Improved `FCMultiLoopTID` to handle NR integrals. (dd56a002) +* Improved `FCLoopBasisExtract` and `FCLoopBasisOverdeterminedQ` not to freak out on nonlinear/nonstandard integrals. (bc886f6d) +* Improved `ApartFF` and `FCApart` to avoid issues with `Collect2` never finishing due to bugs in ` Mathematica` 's `Factor`. The option `Factoring` is now given as a list, e.g. `{Factor2, 5000}`. The second value is the maximal `LeafCount`. Coefficients that have a higher LeafCount value will not be factored but left as they are. The option `TimeConstrained` is passed to `Collect2`. Here we set `3` seconds as a safe default. If the user exprects more compact results when facotrization is allowed to try harder, he or she should modify the options `Factoring` and `TimeConstrained` accordingly. (bbc38955) +* Improved `TID` and `FCMultiLoopTID` to handle input with `DiracChains`. (69481170) +* Added an option `Collecting` to `PaVeReduce` to prevent some reductions from never terminating (thanks to C. Bobeth). (0eea4f8f) +* Added new option `Momentum` to `FeynAmpDenominatorCombine`. It makes it possible to combine only those `FADs` that depend on the given set of momenta. (ee4245e4) +* Added new option `Head` to `Tdec`. (b1e2b5bd) +* Added new option `TID` to `ToTFI` (thanks to P. Schicho for the suggestion). (231d64a0) +* Added new option `Subtract` to `FCHideEpsilon` and `FCShowEpsilon`. This allows one to specify what will be abbreviated together with `1/Eps`, i.e. we are not limited to `1/Eps - EulerGamma + Log[4Pi]` anymore. (0c70248a) +* Modified `FCApart` not to mess with the propagators when `FDS` is set to `False` and to apply `FCE` (when needed) even to expressions that do not require partial fractioning. (37214903) +* Added new option `List` to `FeynAmpDenominatorSplit`. Now we can also obtain a splitted `FAD` as a list of single denominators. (e60fe5e6) +* Improved `TID` to avoid issues with `Collect2` never finishing due to bugs in `Mathematica`'s `Factor`. The option `Factoring` is now given as a list, e.g. `{Factor2, 5000}`. The second value is the maximal `LeafCount`. Coefficients that have a higher `LeafCount` value will not be factored but left as they are. The option `TimeConstrained` is passed to `Collect2`. Here we set 3 seconds as a safe default. If the user expects more compact results when factorization is allowed to try harder, he or she should modify the options `Factoring` and `TimeConstrained` accordingly. (21c9c3d0) + +* New options added to `FCLoopIsolate` and `FCLoopExtract` + * `FAD`, `SFAD`, `CFAD`, `GFAD`. When set to `False` the corresponding denominator will be ignored. Default values: `True` (57d8f075) + * `Numerator`, when set to `False` only denominators will be isolated. This is meant for the cases when we are interested only in propagators but not in the scalar products (e.g. when we are doing a topology identification). Default value: `True` (54c14e95) + +* New options added to `FCLoopBasisFindCompletion` + * `Check`, when set to `False`, we can also supply less propagators than needed to complete the basis via `Method`. As long as those propagators fit properly, they will be accepted. Default value `True` (2defcf3f) + * `Abort`, when we have a user supplied list of propagators and `Abort` is set to `True`, `FCLoopBasisFindCompletion` will immediately stop once it encounters a propagator that cannot be used to complete the basis. This options makes sense only when `Check` is set to `False`. Default value: `False` (4cd8c36f) + * `ExpandScalarProduct`. Internally we need to apply `ExpandScalarProduct` to check the basis completion, but sometimes we want to custom propagators to be returned unexpanded. Now this is possible when `ExpandScalarProduct` is set to `False`. Default value: `True` (6e1219da) + +* New options added to `FeynAmpDenominatorExplicit` + * `Denominator`, to wrap propagator denominators in the given head. Default value: `Identity`. (51fc4da4) + * `ExpandScalarProduct`, when set to `False`, `ExpandScalarProduct` will not be applied to the result. Default value `True`. (3572db28) + * `MomentumCombine`, when set to `False`, `MomentumCombine` will not be applied to the result. Default value `True`. (3572db28) + * `SmallVariable`, when set to `True`, `SmallVariable`'s in the propagator denominators will be set to zero. Default value `False`. (cdbc121b) + + * `Mandelstam`, when set to a non-empty list that is a valid second argument of `TrickMandelstam`, this function will be applied to the result. Default value: `{}`. (cdbc121b) + +* New options added to `SimplifyPolyLog` + * `EulerGamma`, when set to `True`, all `EulerGamma` will be dropped when simplifying `PolyGamma` functions. Default value: `False` (dde6afdd) + * `Sqrt`, when set to `False`, functions with square roots in their arguments will not be simplified. Default value: `True` (0bc92d2a) + * `Log`, when set to `False`, `Log`s will not be simplified. Default value: `True` (8d750492) + * `Trig`, when set to `False`, trigonometric functions (`ArcSihn`, `ArcCosh`, `ArcTanh`) will not be simplified. Default value: `True` (7fb37a60) + * `PolyLog`, when set to `False`, polylogs will not be simplified. Default value: `True` (28168962) + * `Nielsen`, when set to `False`, `Nielsen` will be converted to `PolyLogs` in the final result. Default value: `True` (5bb8131a) + +* New options added to `ApartFF` + * `MaxIterations`, determines the maximal number of interations to achieve full partial fractioning. Default value: `Infinity` (47a532c9) + * `Numerator`, when set to `False`, partial fractioning will be applied only to the propagator denominators, but not numerators. This is sometimes more useful when dealing with multiloop integrals. Default value: `True` (8918b220) + + +* Miscellaneous improvements and optimizations in various functions + * `FCLoopBasisOverdeterminedQ`: (52bf243d) (1d5d7271) (207b7f76) + * `FCLoopBasisIncompleteQ`: (52bf243d) + * `FCLoopBasisIntegralToPropagators`: (467e86cb) (11b153be) (6195d440) (a2e5485d) (8ce4ac38) (20676a4b) (b28b0d2b) + * `FCLoopIsolate`: (4d641b95) (d9f4ed15) + * `FCLoopBasisExtract`: (467e86cb) (05085495) (1bada3da) (05732bb0) (207b7f76) + * `FCLoopExtract`: (c6443ae3) + * `OneLoopSimplify`: (a7a28ff2) + * `OneLoop`: (51a658bf) (46f15431) + * `FCMultiLoopTID`: (46c78f0f) (d3ea5b04) (ea1f0769) + * `TID`: (cb109c2a) (97f9fe6c) (1a1c13b8) (278d2b28) (d0ab6d53) (43cd70fa) (ab863779) (aa8e6bf4) + * `FDS`: (fed3b259) (1a1c13b8) (4763a181) (6e0f5c7c) (81df755e) (2c671abf) (bf4dcd4e) (427c4434) (d5d68b15) (f62cc928) (3d41a694) + * `SimplifyPolyLog`: (4429da9a) (bd2f788f) (e4d9bb99) (357463ec) (615022b1) (925e489f) (29135ecc) + * `ToPaVe`: (3299a73d) (3395a452) + * `ToPaVe2`: (e360de81) + * `ApartFF`: (1a1c13b8) (278d2b28) (06de9161) (5a2b39ab) (d8e70625) + * `FeynAmpDenominatorSplit`: (92f81fd1) + * `FeynAmpDenominatorCombine`: (7a7493c2) (9bd0eccf) (95529a5a) (0d764f97) + + +## Bug fixes + +* Fixed `DCHN` typesetting for spinors with D-dimensional momenta. (b08e3edd) +* Fix an infinite loop in `ExpandAll2[]`. (#45) (22628122) +* Fixed `UndoChiralSplittings` in `FCPrepareFAAmp` for explicit Dirac indices. (2d2904f2) +* Fixed a bug in `GhostPropagator`, where the sign from `QCDFeynmanRuleConvention` was ignored. (b79b3573) +* Fixed/improved some descriptions of the functions. (f5a6900d) +* Fixed a bug in `DiracSimplify` not recognizing traces free of Dirac matrices. (a186d537) +* Fixed a bug in `ComplexConjugate` regarding the conjugation of `FCChargeConjugateTransposed` expressions. (348918b4) +* Corrected EW examples where the gauge terms of weak bosons were missing in the unitarity gauge. Thanks to N. Steinberg. (b9338605) +* Fixed a bug in `DiracChainCombine` that did not take into account products of `DCHN`s in the input. (bac01220) +* Cleaned up the source code following the WWB warnings. (4d8715ad) +* Fixed a performance issue in `FCDiracIsolate` that made `FCFADiraChain` join painfully slow at 2-loops. (4360a634) +* Fixed not working cases of `diracTrickEvalFast` in `DiracTrick`. The new debugging option Evaluate should help in catching such cases via unit tests. (b563a17b) +* Fixed a small bug in `DiracTrace` when traces of `DOT[1,1]` and alike are not fully evaluated. (555a1739) +* Fixed bugs in `TID` and `FCMultiLoopTID` when we have loop momenta inside Dirac traces that cannot or should not be evaluated. (e638daba) +* Fixed a bug in `FCPrepareFAAmp` when specyfing explicit SU(N) indices in the FA input. (3d34989e) +* Fixed multiple typos (thanks to Hermès BÉLUSCA - MAÏTO). (eca73ac6) +* Fixed the option `ExceptHeads` in `FCColorIsolate` so that it can be used to filter out `SU(N)` constants in `StandardMatrixElement`. (55d97635) +* Fixed a typo in `FeynCalc.m` (66d4b984) +* Fixed a bug in `Tr2`. (b7e8be20) +* Rebuild the new documentation for `FeynCalc` 9.3. This should solve Issue #20, Issue #25, Issue #36 and Issue #44 (c6d41ea8) +* Fix the renormalization example. (f1639276) +* Reworked error messages in mixed dimensions in schemes other than BMHV. This way the user should better understand what is going wrong. (45363084) +* `TID`: Do not fail with weird error messages when the loop momentum is inside a list. (8ee8b593) +* Fixed a bug in the detection of variables leaking into the `Global` context. (97d0e853) +* Fixed an issue with `$SystemMemory` missing in `Mathematica` 8 and 9. (1b7cb9cf) +* Disabled automatic expansion of momenta in Dirac spinors. Otherwise it is impossible to apply `MomentumCombine` when needed. (7ba7fcfd) +* Do not allow `Uncontract` act on expressions with symbolic or negative powers: this inevitably generates wrong results. (ea32f1e1) +* Blocked obviously illegal `SUNIndex` and `SUNFIndex` objects. (44002e8f) +* Fixed a bug when `FCSplit` would not immediately abort the evaluation although the second argument is not a list. (76a8b277) +* Fixed a bug, where a conversion rule was missing in `TarcerToFC`. (428f4d18) +* Fixed several bugs in `DotSimplify` that prevented an efficient application of predefined commutation and anticommutation rules. (eff659e1) +* Added a workaround for products of non-commutative objects in DOTs to be handled by `DotSimplify` (GitHub Issue #42). (0ebd271b) +* Fixed a bug in `FCProductSplit`. (347fab47) +* Fix for the accidental removal of the `PropagatorDenominatorExplicit` compatibility mode. (e235e369) +* Fixed wrong factoring option in `Solve3`. (15b624ac) +* Fixed a bug in `FCCanonicalizeDummyIndices` when it would erroneously rename free indices. (3fb80784) +* Fixed a bug when `FCLoopBasis` functions would not abort the evaluation when applied to expressions free of the loop momenta. (4163772a) +* Removed obsolete rules for Polarization that did not honor the `Transversality` option (thanks to ChiMaoShuPhy, GitHub Issue #41). (357cac41) +* Resolved possible issues with Cartesian quantities in `FourDivergence`. (fbac6b35) +* When a Cartesian scalar product of type p^2 is set to zero, the corresponding `CartesianMomentum` must be set to zero as well. (2e588be6) +* `Collect2` should abort if the input contains `SeriesData`. This usually happens when one forgets to apply `Normal` after a series expansion. (ac08a472) +* Fixed another small bug in `TID` for NR integrals. (81faa558) +* Fixed some bugs in the treatment of NR integrals. (b0804303) +* Fixed some bugs in the typesetting. (ca7a9743) +* Fixed a small bug in `DiracEquation`. (3d3c9921) +* Fixed a bug in `Spinor` with `HoldForm` in the momentum slot. (df57486c) +* Fixed some more bugs related to the reduction of integrals with temporal components. (3f9d6b7c) +* Fixed a bug in `FCApart`. (bff5237f) +* Fixed a bug in `FCApart` related to `SFADs` and `CFADs`. (6777a01e) +* Fixed another bug in `Write2` (thanks to F. Saturnino). (e312281d) +* Fixed another bug in `Write2` (thanks to F. Saturnino). (62d395fa) +* Fixed missing link to `FCCanonicalizeDummyIndices`. (e003b3fe) +* Fixed a bug in `Write2` (thanks to F. Saturnino). (23625442) +* Make `FCLoopBasisIntegralToPropagators` be less strict on integrals with linear combinations of scalar products in the numerators (thanks to H. BÉLUSCA - MAÏTO, GitHub Issue #38). (7cc253f8) +* Fixed some more bugs in the symmetrizer of `Tdec` (thanks to H. BÉLUSCA - MAÏTO, GitHub Issue #37) (25e17ce2) +* Fixed a small bug in `FCReplaceMomenta`. (95ff78d9) +* Fixed a bug in `Tdec` related to the missing symmetrizations for multiloop integrals (thanks to H. BÉLUSCA - MAÏTO, GitHub Issue #35). (6cbbffbe) +* Fixed some tests. (b3a0226a) +* Fixed a small bug in `FCLoopBasisIntegralToPropagatorsFCLoopBasisIntegralToPropagators`. (46ff60a2) +* Fixed a small bug in FDS related to the handling of `SFADs`. (14be10b9) +* Fixed a bug in `FCLoopBasisIntegralToTopology` related to a wrong extraction of propagator powers. (8014a58c) +* Fixed a bug in `FCCanonicalizeDummyIndices` that Lorentz indices were always canonicalized, even when this was turned off via the `Head` option. (808ca5b5) +* Fixed a bug in `FCApart`, where `f` was wrongly assumed to be nonzero. (405023b2) +* Fixed a bug in `FCCanonicalizeDummyIndices` in conjunction with Dirac traces. (676407b7) +* Fixed a bug in `FCLoopBasisFindCompletion` when the list of user-supplied propagators contains duplicate entries. (a6adb95a) +* Fixed a bug with wrong propagator powers reported by `FCLoopBasisExtract` for `SFAD`s and `CFAD`s. (3f2b6e3b) +* Fixed a performance regression in the typesetting of `FeynAmpDenominator` (`FCI` version). (4c5351ff) +* Fixed `FCFAConvert` to properly handle `FeynArts` models with an explicit `Eps` (thanks to Gang Li). (4496d289) +* `OneLoop`: Fix typos. (c272ef8e) +* Fixed some issues with `Mathematica` 9 and 8 (thanks to Gang Li). (6ee20946) +* Fixed inconsistent behavior of `FDS`. If a loop integral factorizes into a product of loop integtrals, `FDS` can often detect that and give the result in such a way, that a single `FAD` is rewritten as a product of `FAD`s. This behavior is controlled by the option `FeynAmpDenominatorCombine`. The default value is `False` (to be compatible with the old behavior). Setting this option to `True` activates the factorization. (8a7553f4) +* Small fix in `Solve3`. (c7a74d74) +* Fixed a small bug in `FCPrepareFAAmp`. (84ca61dc) +* Small fix in `FeynAmpDenominatorSimplify` to handle cases like `FAD[{p,m}]^2 - FAD[{p,m},{p,m}]` when no loop momentum is specified. (e9bae655) +* Small fix in `FUnitTools`. (2523f6fd) +* Small fix in the automatic installer. (54065442) +* Fixed several bugs in `FeynCalc2FORM`. (43b6352e) +* Do not call `SirlinSimplify` from `DiracSimplify` if the expression is not strictly 4-dimensional. (a2a18a42) +* `FCCanonicalizeDummyIndices`: Do not expand the expression if there is nothing to canonicalize. (d6feaa03) +* Disabled memoization in `TrickMandelstam` to prevent problems with `ScalarProduct[x,y]=z`. (82b4d8fc) +* Do not generate nrfail messages, if the expression contains only an `ExplicitLorentzIndex[0]`. (ae8c109f) +* Do not automatically project all `ExplicitLorentzIndex` objects to 4 dimensions. (edffee97) +* Disabled `SimplifyPolyLog` on expression that contain patterns. This often leads to wrong and/or unpredictable results. (aabe103f) +* Removed memoization in `PairContract`. Otherwise one gets issues with many other functions after changing definitions of the scalar product. (b70704d4) +* Fixed issues with `TID` when `Dimension` is not `D`. (0bd9c1ec) +* Some more fixes in `SimplifyPolyLog`. (b468ad64) +* Small fix in the `FeynArts` patcher (thanks to Will). (e0b620f3) +* Fixed a bug in `FCAbbreviate`. (0e58c3ae) +* Fixed the two loop QCD ghost example. (01fedaef) +* Fixed improper blocking of non-scalar 5-point functions in `NPointTo4Point`. (d88303fb) +* Fixed wrong sign in `NPointTo4Point` (thanks to Pablo Sanchez Puertas). (37d80c7f) +* Fixed handling of BMHV in `FCMultiLoopTID` and blocked input in wrong dimensions. (0a394469) +* Fixed a small bug in `DiracTrick`, where an internal variable entered the final result (thanks to Graczyk Krzysztof). (a29eebf0) +* Fixed a small bug in `TID` with some indices remaining uncontracted in the final output. (c50521df) +* Fixed a bug in `TID` related to the BMHV scheme. (d26489e8) +* Fixed missing `PartialD -> FCPartialD` replacements in PHI. (090eb50d) +* Fixed a bug in `ExpandScalarProduct` (thanks to Simone Biondini). (7d72b11e) +* Added another check against incorrect `Pair` expressions. (2de6c8c0) +* Fixed a bug in `FCLoopMixedToCartesianAndTemporal` when the input contains `FADs`. (7b863558) +* Fixed a bug in `SUNTF` related to the pattern matching. (0cb39274) +* Fixed a bug in `DiracReduce` when too complicated Dirac structures could not be reduced to `SPVAT`. (e2e3d2ed) +* Fixed `Chisholm` and `DiracReduce` failing on spinor chains. (28d942a7) +* Fixed another bug in `FCLoopBasisIntegralToPropagators`. (62130671) +* Fixed a bug in `FCGetNotebookDirectory`. (dd014f8d) +* Fixed a small bug in the `FeynRules` QCD model. (e92ae81f) +* Minor fixes in the bundled add-ons. (ddbe1247) +* Fixed some leakage of `FeynCalc` internal symbols into the `Global` context after loading `FeynCalc`. Furthermore, the file `.testing` in the `FeynCalc` directory now allows `FeynCalc` to decide whether the current version is a development or a stable version. (0e1fc2cd) +* Added a fix to `FCLoopSplit` to work around a bug in Factor in `Mathematica` 11.0.1 (c.f. ) (7efbbacc) +* Small fix in `TR`. (81b862dd) +* Fixed a bug in `SpinorChainTrick` related to the canonicalization of Lorentz indices in spinor chains. (7a79835c) +* Fixed a bug in `OneLoopSimplify` related to an excessive use of `Isolate` that leads to issues with noncommutative objects (thanks to Adrian). (60ef0c62) +* Small fix in `README.md` for the examples. (52d25d50) +* Fixed possible memoization issues in `SimplifyPolyLog`. (fa423bee) +* Fixed an issue with `FDS` when it is used with specifying loop momenta. (e7f5308d) +* Minor fixes in `FCCompareResults`. (95478e03) +* Fixed a small bug in `FCLoopIsolate`. (46a2de4a) +* Fixed a bug when `FCMultiLoopTID` would ignore tensor integrals that depend on a smaller number of loop momenta then given in the second argument of the function (thanks to P. Schicho). (9a0a9834) +* A tiny fix in `PaVeReduce`. (e6a76e46) +* Small improvements in `FAPatch` (better text output). (2e1a3b5b) +* Minor corrections in the `FeynRules` models. (eff81a4a) +* Fixed some false warnings in `PolarizationSum` when working with `D`-dimensional polarization vectors. (be849046) +* Fixed a small bug in `ComplexConjugate` (`SUNDeltaContract` not converted back into `SUNDelta`). (6d80a841) +* Small fix in `FCCheckSyntax`. (d93d0c08) +* Fixed a small bug in `DiracTrick` (`Eps` has no options anymore). (4753508e) +* Fixed an issue with user defined `$RankLimit` when generating `Tarcer.mx` (4a472353) +* Fixed a bug in `FCPrepareFAAmp` related to the convestion of the SU(N) Kronecker delta. (ebaa2504) +* Fixed a bug in the definition of `TFR` in `Tarcer` (thanks to P. Schicho). (4abdafda) +* Some minor corrections to `PaVeUVPart`. (fb4c8255) +* Several minor corrections in `DiracTrick`. (ba08afba) +* Fixed a small bug in `TarcerToFC` regarding nonstandard dimensions. (4222c8aa) +* Fixed a bug in the typesetting of `FAD`s. (c809f4a4) +* Fixed a bug in the typesetting of `TemporalPair`. (fc044986) +* Fixed a regression bug in `TarasovT` (thanks to Zhang). (33641020) +* Fixed a bug in `FCCanonicalizeDummyIndices` related to contractions of Lorentz and Cartesian indices in different dimensions. (df50e5ae) +* Fixed some issues in `DotSimplify` related to the new `FCJoinDots` option. (998d8081) +* Fixed a bug in `FCE` related to issues with `FAD`'s having nonstandard dimensions. (b59338a8) +* Fixed a bug in `DiracTrick` regarding the cyclicity simplifications of traces with chiral projections (thanks to Ula). (4b5ca9bd) +* Fixed a bug in `DiracTrick` regarding wrong anticommutation properties of combinations of chiral projectors (thanks to Ula). (3d446a33) +* Fixed a bug with premature memoization in `ToTFI` (thanks to Philipp Schicho) (88ea81c8) +* Fixed an infinite recursion bug in `PaVe` (thanks to Xiaonu Xiong). (c4c0c644) +* Fixed a bug where `DiracSimplify` was ignoring products of `D`-dimensional spinors (thanks to James McKay). (46710a7e) +* Fixed a minor bug in `EpsEvaluate` (thanks to Pablo Sanchez Puertas). (5f3031ee) +* Fixed a bug that `SP[p]=p2` was not setting the value of `SP[p,p]` likeweise for `CSP` and other dimensions. (233af78a) +* Fixed a bug with `DiracTrace` ignoring the change of `$LeviCivitaSign` (thanks to James G.). (e1553275) +* Fixed a small bug in `Uncontract`. (d6eb09eb) +* Fixed a small bug in the definition of `Eps`. (1797ce4f) +* Small fix in `SetMandelstam` for more than 4 momenta. (4abb8e06) +* Fixed a small bug in `MomentumCombine`. (2b64ab92) +* Fixed two example files to work with `FeynArts` using unitarity gauge. (e70fc629) +* Fixed a bug in `FCRenameDummyIndices` (thanks to Luigi Delle Rose). (4853e427) +* Fixed a bug in `ChangeDimension` related to `Eps` tensors. (1cf89752) +* Fixed a bug with missing `DiracSigmaExplicit` in DiracTrace (Issue #23, thanks to sbilmis). (341e27ea) +* Fixed a bug in `Contract` related to the BMHV scheme (thanks to H.Patel). (88739e50) +* Small fix for `PD` in `FCE` and `FCI`. (9811355c) +* Minor fixes in `MomentumExpand`, `FourDivergence`, `ToTFI`, `FCLoopBasis` and `NPointTo4Point`. (f136eaad) +* Minor fix in `FCPrepareFAAmp`. (e065592f) +* Fixed a bug in the new definition of `Pair`. (b9e787ad) +* Fixed a bug in `MomentumCombine`. (867bf9f3) +* Small fix in `Contract`. (b7e3bd13) +* Fixed a bug with `PropagatorDenominator[0,0]` (c6335b6e) +* Blocked some malformed `Pair` arguments. (6376f481) +* Fixed premature memoization in `ToPaVe` (thanks to Michael Park, ). (b78c3c4c) +* Improved `PaVe` to block functions that have wrong number of kinematic invariants. (a2f7280c) +* Improved typesetting of four vectors raised to powers. (6947b64d) +* Fixed `FCCanonicalizeDummyIndices` not canonicalizing some combinations of dummy indices. (381d019a) +* Fixed a bug in `OneLoop` when the number of propagators is too high (thanks to Jongping Hsu). (cf9da445) +* Fixed a small bug in the definition of scaleless `PaVe`s (2528ca9b) +* Fixed wrong definiton of `E0` in ToPaVe. (41ca39d5) +* Fixed a bug related to `$KeepLogDivergentScalelessIntegrals`. (0ea126eb) +* Fixed an infinite recursion bug in the symmetry of `D`-functions. (8aca4503) +* Fixed a bug in `FCReplaceD`. (2ad3c226) +* Fixed a bug in `DiracTrick` (related to issue #18). (468d9627) +* Fixed a bug in `DotSimplify` (related to issue #18). (a5670f24) +* Fixed an infinite recursion bug with `B0`. (59618b02) +* Blocked further wrong/inconsistent arguments for `GA`, `GAD`, `GAE`, `GS`, `GSD`, `GSE`, `DiracGamma`, `DiracMatrix` and `DiracSlash`. (7e95dc01) +* Fixed incorrect behavior of `DiracMatrix[mu,nu,...]`. (f988e5a7) +* Fixed another bug in `ApartFF` (thanks again to Zhang Shao Wu). (5b98e326) +* Fixed issue #19 (Documentation doesn't work until restart). Thanks to Szabolcs Horvát. (d399819e) +* Fixed a bug in `ApartFF` (thanks to Zhang Shao Wu). (6d77c2e1) +* Fixed a small bug in `OneLoop` related to terms free of loop integrals. (a484bc08) +* Fixed remaining issue with `FAD[{0,0}]` (c4a9b299) diff --git a/FeynCalc/ChangelogOld.md b/FeynCalc/ChangelogOld.md new file mode 100644 index 000000000..8b42ea535 --- /dev/null +++ b/FeynCalc/ChangelogOld.md @@ -0,0 +1,1080 @@ +### Version 9.2.0 (November 2016) + +#### Important changes + * New handy functions `FCAbbreviate`, `FCHideEpsilon`, `FCShowEpsilon`, `FCLoopIBPReducableQ`, `FCFactorOut`, `SelectFree2`, `SelectNotFree2` + * Finally we have shortcuts for spinors with D-dimensional momenta: `SpinorUD`, `SpinorUBarD`, `SpinorVD`, `SpinorVBarD` + * New option `$KeepLogDivergentScalelessIntegrals` permits consistent 1-loop computations, where UV and IR divergences are regularized with different epsilons. + * `Examples/FeynRules` now contains several FeynRules models (with more to come) with additional scripts that show how such models can be used with patched `FeynArts`. This should be useful for new users. + * `DiracTrace` has received a lot of internfal refactoring and should be now faster and much more stable. Thanks to Peng Sun for motivating me to do so. I hope to get `DiracSimplify` refactored as well in the next release. + + + +#### Commit log + +* Added an example calculation to the test-suite. (a4cdd648) +* Fixed wrong option name in FCDiracIsolate. (202f3e2) +* Added some missing unit tests for FCLoop-functions. (c81660f1) +* Added few tree-level electroweak examples. (4909891) +* Added FCAbbreviate, a new function that introduces abbreviations for FeynCalc expressions that should be exported to other tools. (a7a27e5); Example: + + ``` + FCAbbreviate[SPD[p, k] FAD[{q, SMP["m_e"]}, {q + p, m}], {q}, {p, k}, Head -> spd] + ``` + +* Now FCLoopBasisFindCompletion can complete the basis using a list of user-supplied propagators given as the value of the Method option (4b70dcb) + + ``` + FCLoopBasisFindCompletion[FAD[q1 + p, +q2 - k] SPD[q1, q2], {q1, q2}, Method -> {FAD[{q2 + k, m}], FAD[{q1 - p, m}], +SPD[p, q2], SPD[k, q1]}] + ``` + +* Added new option FCLoopIBPReducableQ to FCLoopExtract and FCLoopIsolate. This allows to extract/isolate only those loop integrals that are IBP reducable. (20af417) + + ``` + FCLoopExtract[a FCI[FAD[{q, 0, 2}]] + b FCI[FAD[{q, 0, 1}]], {q},loop, FCLoopIBPReducableQ -> True] + FCLoopIsolate[a FCI[FAD[{q, 0, 2}]] + b FCI[FAD[{q, 0, 1}]], {q}, Head -> loop, FCLoopIBPReducableQ -> True] + + ``` +* Added new function FCLoopIBPReducableQ for a quick check if the given loop integrals has propagators raised to integer powers. (b699150); Example: + + ``` + FCLoopIBPReducableQ[FCI[SPD[q,q]^2FAD[{q,0,1}]]] + + ``` +* Some minor refactoring in FDS. (681ef0e) +* Improved FCLoopBasisFindCompletion to use scalar products as extra propagators. The old behavior can be achieved via the option Method->NullSpace. The new default is however Method->ScalarProduct. (38386fa); Example: + + ``` + FCLoopBasisFindCompletion[FAD[{q1, m, 2}, {q1 + q3, m}, {q2 \[Minus] q3}, q2], {q1, q2, q3}] + FCLoopBasisFindCompletion[FAD[{q1, m, 2}, {q1 + q3, m}, {q2 \[Minus] q3}, q2], {q1, q2, q3}, Method -> NullSpace] + ``` + +* Version bump to 9.2 (c8c8cfb) +* Fixed a bug in FDS related to $KeepLogDivergentScaleless set to True. (a411e67) +* Improved debugging output in FDS. (fe21cbe) +* Fixed a bug with D-dim Eps not disappearing when indices are the same. (906cac6) +* Fixed a small bug in FCShowEpsilon. (0c25ba0) +* Improved FCHideEpsilon and FCShowEpsilon to work also for D=4-Epsilon via the option D. (16b814e) +* Fixed a bug in FourDivergence related to the differentiation of FADs. (b372e2b) +* Added new shortcuts for spinors with D-dimensional momenta: SpinorUD, SpinorUBarD, SpinorVD, SpinorVBarD. (201b058); Example: + + ``` + SpinorUD[p, m] // FCI // StandardForm + SpinorVD[p, m] // FCI // StandardForm + SpinorUBarD[p, m] // FCI // StandardForm + SpinorVBarD[p, m] // FCI // StandardForm + ``` + +* Some cross-checks in ToPaVe, SPC, OneLoop,OneLoopSimplify. (0d832c2) +* Improved typesetting of the SMP's for renormalization. (1c7b512) +* Added FeynRules model for pure QED with counterterms following Bohm, Denner and Joos. (fc14872) +* Added new SMP objects for renormalization calculations. (f2eabd6) +* Perofrmance improvement in DiracTrace. (3c40740) +* Added two convenience functions FCHideEpsilon and FCShowEpsilon for doing the substitution 1/Eps - EulerGamma + Log[4Pi] -> Delta. (6cddeb0); Example: + + ``` + FCHideEpsilon[1/Epsilon - EulerGamma + Log[4 Pi]] + FCShowEpsilon[SMP["Delta"]] + ``` + +* Fixed a bug in FCReplaceD, so that DiracGamma does not loose the dimension anymore. (9544275) +* Fixed a bug in FourDivergence related to the differentiation of D-dim Dirac matrices. (dad4b85) +* Added FCFactorOut option to Collect2. Currently this only allows to factor out a global prefactor. (54f513a); Example: + + ``` + Collect2[Together[a (1 + x) + 4 b (1 + y)], {a, b}, FCFactorOut -> 4] + ``` + +* Added FCFactorOut, a small convenience function for factoring out user-specified prefactors. (31f3543); Example: + + ``` + FCFactorOut[(a + 3 b), 3 b] + ``` + +* Added SelectFree2 and SelectNotFree2. They act like SelectFree and SelectNotFree, but with an Expand2 before the selection. (d6fb941); Example: + + ``` + SelectFree2[a (b + c) + d, b] + SelectFree[a (b + c) + d, b] + SelectNotFree2[a (b + c) + d, b] + SelectNotFree[a (b + c) + d, b] + ``` + +* Added FeynArts model (generated with FeynRules) for QCD in the background field formalism. The reason is that this model is missing in the standard FeynArts. (991e340) +* Fixed a small bug in DiracTrick. (f567f82) +* Added an extra check for DiracTrick. (75466d4) +* Made DotSimplify finish faster if there is nothing to simplify. (db0a586) +* Added new option DiracSigmaExplicit to FCDiracIsolate. (9cf7654) +* Some improvements in TID for the BMHV scheme. In particular, unless BMHV scheme has been explicitly selected, amplitudes that are partly 4-dim and partly D-dim will not be tolerated anymore. (aa89a44) +* Refactoring DiracSimplify. (7f3dc3d) +* DiracTrick: Adjusted Larin's scheme (12fd5ac) +* Made DiracTrick a bit faster by evaluating simple traces before entering the main loop. (f419c0d) +* Added option FCDiracIsolate to DiracTrick. This is for calling DiracTrick from internal functions. (f40ec42) +* Cleaning up the code of DiracTrace. (ab363ab) +* Some more adjustments for DiracTrace and DiracTrick. (edc954a) +* Improved performance of DiracTrace on big traces. (64f5120) +* Some more refactoring in DiracTrick. (2be6dd4) +* Improved performance of DiracTrace for West->False. (972c7c9) +* DiracTrick: Finally separated rules for different schemes. (8bb589a) +* DirackTrick: Cleaned up the rules for moving g^5. (1a63162) +* DiracTrick: Use cached FCFastContract instead of coneins. (d4ed905) +* DiracTrick: Get rid of scev in favor of FCUseCache. (7446399) +* DiracTrick: Refactoring continues 2. (7a37313) +* DirackTrick: Refactoring continues. (f026c48) +* Continuing refactoring in DiracTrick. (3a743a1) +* Added option LorentzIndex to FCDiracIsolate that allows inclusion of Lorezntz tensors into isolated heads.dch[GS[p].GS[l]] + dch[GA[i].GA[j].GA[k] MT[mu, nu]] (beb0713; Example: + + ``` + FCDiracIsolate[ MT[mu, nu] GA[i, j, k] + GS[p, l] + MT[mu, nu] GA[mu, j, k], LorentzIndex -> True, Head -> dch] + ``` + +* Fixed in a bug in the handling of unknown non-commutative objects by DiracTrick. (fe1e459) +* DiracTrick: Splitting of DiracChains is now handled by FCDiracIsolate. (4e269d0) +* DiracTrick: Fatoring out of SUNT matrices is now handled by FCDiracIsolate. Moreover, gamma5Present checks if g^5 is present at all. (d60406a) +* Improved InsideDiracTrace simplifications of DiracTrick. (2d550c6) +* DiracTrick refactoring in progress. (b6db370) +* Improved test suite to show time required to run single tests. (2689240) +* Started refactoring of DiracTrick. (a552eaa) +* Fixed handling of Larin's scheme in Anti5. (174bb74) +* Updated description of Larin's scheme. (174f98e) +* Minor cleanups in FCI and FCE. (e86d145) +* Added example for the computation of the self-energy diagrams in pure Yang-Mills using background field formalism according to Abbott. (2845af6) +* Improved handling of Dirac traces that contain unknown non-commutative objects. (1aa3f96) +* DiracTrace improvement with Expand. (b1ff3f7) +* Rempoved some old code from DiracTrace (981ab92) +* Implemented new trace function in DiracTrace. (c6025e4) +* Test (2941b9e) +* Some more improvements in DiracTrace. (dfe1dc5) +* Some fixes in DiracTrace plus now we it uses DiracTrick instead of DiracSimplify. (57b1b2a) +* More refactoring in DiracTrace. (685a1c4) +* Even more refactoring in DiracTrace. (6be8f53) +* More refactoring in DiracTrace (1dcb5bb) +* More refactoring in DiracTrace. (a06533e) +* Some more refactoring in DiracTrace. (5187efd) +* Some more refactoring in DiracTrace. (b185f3c) +* Some fixes for Larin's scheme in DiracTrace. (cda3f15) +* Improved splitting between SUNT and DiracGamma in DotSimplify. (45ebe1e) +* Fixed a bug in the new InsideDiracTrace simplification of DiracTrick. (da94751) +* Added new option InsideDiracTrace to DiracTrick. (a5b63dc) +* Added new option DiracGammaCombine to DiracTrick and improved handling of chiral projectors. (5416c72) +* Some refactoring in DiracTrick. (87f3d4b) +* Fixed typo in the description of TarcerToFC (6abb381) +* Added new option DiracGammaCombine to FCDiracIsolate. (2d5e8aa); Example: +* + ``` + FCDiracIsolate[GA[nu].(GS[p] + GS[q] + GS[k] + m).GA[mu], Head -> dch] + + FCDiracIsolate[GA[nu].(GS[p] + GS[q] + GS[k] + m).GA[mu], Head -> dch, + DiracGammaCombine -> False] + ``` + +* Some refactoring in FCDiracIsolate. (79fdd36) +* Improved the muon decay example. (b79005d) +* Added an example for using Tdec to compute some multi-loop decompositions that appear in the renormalization of the Gross-Neveu model at 4-loops. (de1cf3b) +* Fixed a bug in Tdec related to wrong determination of symmetries in multi-loop integrals. (f4bb647) +* Added several new SMP typesettings: m_qu and m_qd for up- and down-type quark masses m_l for lepton masses Q_u and Q_D for up- and down-type quark charges g_W and g'_W for the weak couplings (5a1c91c); Example: + + ``` + ?SMP + SMP[] + ``` + +* Added the option PaVeIntegralHeads to FCLoopCanonicalize, FCLoopIsolate and FCLoopSplit. This allows to specify extra heads that should be treated as PaVe integrals. (b5ee87b); Example: + + ``` + FCLoopSplit[Foobar[x], {}, PaVeIntegralHeads -> Join[OptionValue[FCLoopIsolate, PaVeIntegralHeads], {Foobar}]] + + FCLoopIsolate[Foobar[x], {}, PaVeIntegralHeads -> Join[OptionValue[FCLoopIsolate, PaVeIntegralHeads], + {Foobar}],Head -> loop] + ``` + +* Added new !experimental! global option $KeepLogDivergentScalelessIntegrals that forces FeynCalc not to put log divergent scaleless integral 1/q^4 to zero. This is important e.g. for EFTs, where IR and UV divergences must be distinguished. (d1610d0); Example: + + ``` + $KeepLogDivergentScalelessIntegrals=True; + TID[FVD[q,mu]FVD[q,nu]FAD[{q,0,3}],q] + ``` + +* Fixed typos in the description of the ABJ example. (5262505) +* Small refactoring in OneLoop. (4d53ccd) +* Fixed a small bug (just caused a warning) in PaVeReduce when PaVe functions have user-defined options. (40f3338) +* Improved automatic installer to allow installing FeynCalc and FeynArts from local tarballs. For example: (e2a13c0) + +### Version 9.1.0 (August 2016) + +#### Important changes +* Many new hadndy functions: `FCTraceExpand`, `FCTraceFactor`, `FCGetDimensions`, `FCCanonicalizeDummyIndices`, `TarcerToFC`, `FCReplaceD`, `FCColorIsolate`, `FCDiracIsolate`, `DeclareFCTensor`, `UnDeclareFCTensor`, `CommutatorOrder` +* Improved support for using `FeynCalc` with custom `FeynRules`-models (see http://www.feyncalc.org/forum/1042.html for more details) +* `$LimitTo4` is now disabled by default. Even when set to `True`, it is applied only to 1- and 2-point functions (see http://www.feyncalc.org/forum/1077.html for more details). + +#### Commits log +* Added g-2 calculation to the examples testsuite (a3e66b1) +* Paclet version updated to 9.1 (fa6c7e7) +* Rebuilt the documentation. (31f3710) +* Fixed a small typo in the documentation. (9262470) +* Updated the changelog for FeynCalc 9.1 (91ae94d) +* Updated `README.MD` (9e99cd) +* Fixed a bug in the computation of chiral traces, when West's formula is not used. (0a25312); Example: + ``` + $BreitMaison = True; + (DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True] - DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True, West -> False]) // Simplify + ``` +* Fixed usage information of `GluonGhostVertex` (thanks to H. Patel). (16a6cbf) +* For now commented out syntax check in `DataType` (leads to problems with FeynHelpers). (1c534a8) +* Added an example for the g-2 calculation in QED at 1-loop and corrected few spelling errors. (96aa208) See `Examples/QED/QEDElectronGMinusTwoOneLoop.m` +* Added several new unit tests for `TARCER` . (c2be321) +* Small cleanups in `FeynCalc.m` and `SUNTrace` to prevent unnecessary pollution of the Global context. (ee76da2) +* Some improvements in `FCTraceExpand` and `FCTraceFactor`. In particular, now `FCTraceFactor` can properly treat nested Dirac traces. (f985c16); Example: + ``` + FCTraceExpand[DiracTrace[GA[i, i] + GA[j, j] DiracTrace[GA[a] + GA[b] DiracTrace[GA[x]]]]] + ``` +* Added option CustomIndexNames to `FCCanonicalizeDummyIndices` and made many improvements to the code. Now one can use `FCCanonicalizeDummyIndices` with arbitrary custom indices, which are treated on the same footing as the built-in indices LorentzIndex, `SUNIndex` und `SUNFIndex`. Einstein's convention is always assumed, though. (1403efe); Example: + ``` + FCCanonicalizeDummyIndices[ T1[MyIndex2[a], MyIndex1[b]] v1[MyIndex1[b]] v2[MyIndex2[a]] + T1[MyIndex2[c], MyIndex1[f]] v1[MyIndex1[f]] v2[MyIndex2[c]], Head -> {MyIndex1, MyIndex2}, CustomIndexNames -> {{MyIndex1, {i1}}, {MyIndex2, {i2}}}] + ``` +* Made automatic expansion of `DiracGamma[Momentum[a]+...]` work also for dimensions other than 4. (4f6169c); Example: + ``` + DiracGamma[Momentum[a, D] + Momentum[b, D] + Momentum[c, D], D] + ``` +* Added checks against predefined scalar products involving loop momenta. This should prevent some stupid mistakes (6fd45b0); Example + ``` + SP[q, q] = 0; + Tdec[{q, mu}, {p}] + ``` +* Added a global variable `$ScalarProducts` that keeps track of vector pairs for which a scalar product has been defined. This is useful e.g. if one needs to check if the given variable can be used as a general 4-vector (i.e. loop momentum) or if it already has some rules attached to it. (d15191f) +* Added new function CommutatorOrder that orders any `Commutator` and `AntiCommutator` lexicographically. (3039650); Example: + ``` + CommutatorOrder[Commutator[a, b] + Commutator[b, a]] + ``` +* Small refactoring in `DotSimplify`. (6e6b01e) +* Improved `ExpandScalarProduct` to work on arbitrary tensor declared via `DeclareFCTensor`. (fc05a8e); Example + + ``` + DeclareFCTensor[myTens]; + ExpandScalarProduct[myTens[z, Momentum[a + b], Momentum[c + d]]] + UnDeclareFCTensor[myTens]; + ``` + +* Added `DeclareFCTensor` and `UnDeclareFCTensor`. Now it is possible to declare new tensor heads, just like this done for new non-commutative objects. (bbbe8af) +* Improved error messages for several function. (d5a0572) +* Added `TensorArgsList`, an internal list of possible heads that may appear as arguments of tensors. (d815c58) + +* Updated list of publications. (12d4b27) +* Added options `EpsEvaluate` to `ExpandScalarProduct`. This way one can now do both operations via `ExpandScalarProduct[expr, EpsEvaluate->True]`. (a83592d); Example: + ``` + ExpandScalarProduct[SP[a + b, c] LC[e, f][g + h, j] LC[][i1, i2, i3, i4 + i5], EpsEvaluate -> True, Momentum -> {a, g}] + ``` +* Improved `FCCanonicalizeDummyIndices` to allow exclusion of certain index heads (via the `Head` option) and definition of own renaming functions (via the `Function` option). (065ad89) +* Added `FCColorIsolate`, a handy helper function to extract color structures. (5cf9f56); Example: + ``` + FCColorIsolate[SUNF[x, y, z]^2 SUNT[a, b] x + SUNT[c] SUND[i, j, k]] + ``` +* Added `SUNHeadsList`, an internal list of colored objects. (9bfd660) +* Added `ToDiracSigma` which is essentialy the inverse of `DiracSigmaExplicit`. (2098ee5); Example: + ``` + ToDiracSigma[GA[i, j], GA[i], GA[j]] + ``` +* Added `Chisholm2` that applies Chisholm identity to eliminate terms of type `GA[i,j,5]`. (7a5c381); Example: + ``` + Chisholm2[GA[i, j, 5]] + ``` +* Fixed a bug in `EpsChisholm`. (0819112); Example: + ``` + EpsChisholm[(SpinorUBar[p1, m1].SpinorV[p2, m2] + SpinorUBar[p1,m1].GS[k].SpinorV[p2, m2])] + ``` +* Fixed a small bug in `Collect2`. (e08933a); Example: + ``` + Collect2[Sum[xa[i], {i, 1, 10}] + VAR Sum[xb[i], {i, 1, 10}] + VAR Sum[xx[i], {i, 1, 10}] + VAR^2 Sum[xy[i], {i, 1, 10}] + VAR^2 Sum[xz[i], {i, 1, 10}], VAR, Factoring -> False, IsolateFast -> True, IsolateNames -> KK] // FRH + ``` +* Refactored `FermionSpinSum` and added treatment of D-dimensional Dirac spinors (thanks to O. Gituliar). (bc9ce8d); Example: + ``` + FermionSpinSum[ChangeDimension[Spinor[p1, m1].GA[i].GA[5].Spinor[p2, m2] Spinor[p2, +m2].GA[5].GA[i].Spinor[p1, m1], D], Momentum -> {p1, p2}] + ``` +* Removed obsolete option `SUNFToTraces`. (a9e729e) +* Added `FCDiracIsolate`, a handy helper function to extract Dirac structures. (ad6af8b); Example: + ``` + FCDiracIsolate[ yy GA[i] + xx SpinorUBar[p1, m1].GA[5].SpinorVBar[p2, m2] + zz + DiracTrace[GA[i, j]]] + ``` +* Added an option to disable `DiracSimplify` in `Chisholm` and `DiracReduce`. (0e4093a) +* Small performance improvement in `Collect2`. (c0db8ab); Example + ``` + Collect2[yy (xx*Sum[p[i] i^2, {i, 1, 100000}] + abc) + abc2, {abc, abc2}, Factoring -> False] // AbsoluteTiming // First + ``` +* Improved `FCPrepareFAAmp` to handle `FASclarProduct` (thanks to Francesco S). (16671c9) +* Refactored `EpsChisholm`. (8287f45) +* Removed `LeviCivitaSign` option from `DiracTrace`, `TR` and `Chisholm`. Instead the value should be set through `$LeviCivitaSign`. A more user-friendly configuration might be added in future. (0551b73) +* Fixed inconsistent treatment of `$LeviCivitaSign` when it set not to the default value (thanks to Christopher Lester). (e05ed33); Example: + ``` + $LeviCivitaSign = -I; + DiracReduce[GA[i1, i2, 5]] + ``` +* Refactored `Chisholm` and added the `LeviCivitaSign` option (thanks to Christopher Lester). (cb44558); +* Version number bump to 9.1; Development versions are now extra indicated to avoid confustion with stable versions. (e0c75a6) +* `Eps` should not evaluate to explicit values when it has integer arguments. The result is not-well defined when no distinction between upper and lower indices is made (thanks to Christopher Lester). (a4699d4); Example: + ``` + Eps[0, 1, 2, 3] + ``` + +* Fixed a bug in `ApartFF` related to singular kinematica (thanks to Shaowu Zhang). (329d5d2); Example: + ``` + FCClearScalarProducts[]; + ScalarProduct[k, k] = 0; + ScalarProduct[p, p] = m^2; + ApartFF[FAD[{q1, m}, {q1 - p}, {q1 - 2 p, m}, {q1 - k - 2 p, m}], {q1}] + ``` +* Improved `FAPatch` to recognize that a `FeynArts`/`FeynRules` model have already been patched. (21f5783) +* Fixed a bug (#issue 9) in `DoPolarizationsSums` (thanks to Luca Mantani). (8944ff3); Example + ``` + ScalarProduct[p1, p1] = 0; + DoPolarizationSums[Pair[Momentum[Polarization[p1, -I], D], Momentum[Polarization[p1, I], D]], p1, 0] + ``` +* Fixed a small bug in `FCE` when applied to metric tensors with explicit Lorentz indices (thanks to Wen Chen). (a7d66ff); Example: + ``` + FCE[Pair[ExplicitLorentzIndex[0], LorentzIndex[a]]] + ``` +* Small fix in `Write2`. (b618ce9) +* Introduced automatic ordering of masses in `B0` in the `PaVe` notation. (0fc0088); Example: + ``` + PaVeReduce[PaVe[2, {p10, p12, p20}, {m1^2, m2^2, m3^2}]] + ``` +* More debugging output in `OneLoop`. (e2ae9c9) +* Fixed a bug in the definition of `A00`. (a8c783f); Example: + ``` + $LimitTo4 = True; + A00[m1^2] + ``` +* Fixed a bug in `PaVeReduce` that prevented detection of zero Gram deteriminants in C and D functions. (55080de); Example + ``` + PaVeReduce[PaVe[1, 2, {(p1 - p2)^2, p1^2, p2^2}, {m2^2, m1^2, m0^2}]] + ``` +* Added `ToPaVe2`, a function that converts direct Passarino-Veltman functions like `A0`, `B1` etc. to `PaVe` ones. (913a50d); Example: + ``` + B0[p^2,m1^2,m2^2]//ToPaVe2 + ``` +* Added an extra test to `SUNSimplify`. Confirms the result from (a355845) +* Adjusted and extended `PaVe` related unit tests. (13987d1) +* More cleanups in `PaVeIntegrals.m` (0bf24e7) +* Moved extra simplifications of `B0` functions into `PaVeReduce`. (d21e164) +* Cleanups in `PaVeIntegrals.m` (faf1f86) +* Moved all the `$LimitTo4=True` simplifications out of `PaVe`. They are not applied, unless `PaVeAutoReduce` is set to `True`. (64cd9a4) +* Added `A00`. (1c75e8b) +* `PaVeAutoReduce` for `PaVe` functions is set to `False` by default. (4163a13) +* `$LimitTo4` is splitted into `$LimitTo4` (for tadpoles and bubbles) and `$LimitTo4IRUnsafe` (for triangles and boxes). Also, the description of the option is now much less cryptic. (fcfe3e7) +* Added the option `A0ToB0` directly to `PaVeReduce`. (547dacb) +* Added some extra `B0`-cases to `PaVeReduce`. (bb535ec) +* Added the option `PaVeAutoReduce` to `PaVeReduce`. (9ab155e) +* Improved `PaVeReduce` to handle more different cases (also with zero Gram determinants). (18dcc4d) +* Fixed a bug in `FCLoopSplit`. (961960b); Example: + ``` + FCLoopSplit[+1/6 (m1^2 + m2^2) + A0[m2^2]/6 + 1/3 m1^2 B0[0, m1^2, m2^2] + +1/6 (m1^2 - m2^2) B1[0, m1^2, m2^2], {}] + ``` +* Added `FCReplaceD`, a function that facilitates taking the limit D->4 without unwanted effects on the FeynCalc functions. (a49487e); Example: + ``` + FCReplaceD[ScaleMu^(D - 4) SPD[p, p]*D, D -> 4 - 2 Epsilon] + ``` +* Small fix in `FUnitTools` related to the recreation of typesetting tests. (c409a14) +* Added a `CovariantD` with explicit fundamental color indices. Although it can't be used in FeynRule, it is still very useful when deriving Feynman rules by hand. (732a6a9); Example: + ``` + CovariantD[i, SUNFIndex[a], SUNFIndex[b], Explicit -> True] + ``` +* Improved typesetting of `QuantumFields`. Now it is possible to add more (custom) indices that will be typeset correctly. (4659077) +* Added four new field types to be put into `QuantumField`: `QuarkFieldPsi`, `QuarkFieldPsiDagger`, `QuarkFieldChi`, `QuarkFieldChiDagger`. Currently, only typesetting is attached to them. (562d408) +* `FCCanonicalizeDummyIndices` can now work also with SU(N) indices, as well as one custom index head (via `Head` option). (6eebc67); Example: + ``` + FCCanonicalizeDummyIndices[T1[MyIndex[a], MyIndex[b]] v1[MyIndex[b]] v2[MyIndex[c]], Head -> MyIndex] + ``` +* `FCFAConvert` can now rename also SU(N) indices by supplying the index names via `SUNIndexNames` and `SUNFIndexNames`. (90e3b59) +* Adjusted `FDS` to be a bit smarter on 1-loop integrals with same masses. (ed92327); Example: + ``` + FDS[Apart2[FAD[{qp, m}, {qp - q}, {qp, M, 2}, {qp - q, M, 2}]] - ApartFF[FAD[{qp, m}, {qp - q}, {qp, M, 2}, {qp - q, M, 2}], {qp}], qp] + ``` +* Let `FCTraceExpand` set the PreservePropagatorStructures of internal `DotSimplify`. This (together with `DiracGammaExpand` set to `False`) seems to be the most convenient and sensible way to do expansions of `DiracTraces`. (b155314); Example: + ``` + DiracTrace[((GSD[k + p] + M).GA[5].GSD[l - p].GAD[nu].(GSD[l] + M).GAD[la].GSD[k + l] + (GSD[k1 + p1] + M).GA[6].GSD[l1 - p1].GAD[nu].(GSD[l] + M).GAD[la].GSD[k1 + l1]).(GSD[x] + M)] // FCTraceExpand[#, DiracGammaExpand -> False] & + ``` +* Some refactoring in `DiracSimplify`. Also `InsideDiracTrace` simplifications are now applied agagin after `DiracTrick`. (cd9d228); Example + ``` + DiracSimplify[GA[i].(GS[p] + M).GA[j].GA[6].GA[k].GA[j],InsideDiracTrace -> True] + ``` +* Added new option `PreservePropagatorStructures` to `DotSimplify`. If set to `True`, numerators of fermionic propagators like `(GS[p]+m)` that appear in chains of Dirac matrices will not be expanded. (4d9f34d); Example: + ``` + DotSimplify[(GA[i].SUNT[a] (GS[p] + M).GA[j].GA[6].GA[k].GA[j] FAD[p + k, M] + + GA[i].(GS[p1] + M).GA[j].GA[7].GA[j].GA[k] FAD[p1 + k, M]).(GS[q] + m).(GA[l].(GS[p] + M).GA[n] + GA[n].(GS[p] + M).GA[l]), PreservePropagatorStructures -> True] + ``` +* Corrected a typo in `FeynCalc.m` (f840d00) +* Improved debugging output in `OneLoop`. (ce133d6) +* Added new option `FCCheckSyntax`. As checking the syntax in `DiracSimplify` slows things down a lot on big expressions, it is better to make it optional and turned off by default. (34e6aeb); Example + ``` + DiracSimplify[SUNT[a] SUNT[b]] + DiracSimplify[SUNT[a] SUNT[b], FCCheckSyntax -> True] + ``` +* Fixed a bug in `DiracTrick` related to `$Larin=True` (thanks to Steffen Schwertfeger ) (03756b2); Example: + ``` + $BreitMaison = False; + $Larin = True; + DiracTrick[GAD[a, b, c].GA[5].GAD[b, a, m]] + ``` +* Fixed a minor bug in `TarcerToFC`. (cbf6334) +* Added `TarcerToFC`, a small tool to convert integrals in the `Tarcer` notation to the `FeynCalc` notation. (fb06f22); Example: + ``` + TarcerToFC[ Tarcer`TFI[D,Pair[Momentum[p, D], Momentum[p, D]], {0, 0, 3, 2,0}, {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}], {q1, q2}] + ``` +* Moved `FromTFI` to the `QCD` directory. (1fd22cf) +* Fixed treatment of `FAD`'s with propagator powers equal to zero, i.e. `FAD[{q,m,0}]` now evaluates to `1`. (654f569); Example: + ``` + FAD[{q1 - p, 0, 0}] + ``` +* More debugging output in `PaVeReduce`. (cd4f508) +* Some more cleanups in the source code of `TARCER`. (fc6851c) +* Fixed a bug in `TARCER` related to wrong `tlrules` (thanks to Yan, http://www.feyncalc.org/forum/1060.html) (19a53ff); Example: + ``` + TarcerRecurse[ + TFI[D, Pair[Momentum[p, D], Momentum[p, D]], {0, 0, 3, 2, 0}, {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}]] + ``` +* Small cleanups in tlrules in `TARCER`. (1be65e1) +* Fixed a small bug in `FeynRule`. (87315c0) Example: + ``` + FeynRule[2*(QuantumField[AntiQuarkField].LeftRightPartialD[ + + i1].QuantumField[QuarkField]), {QuantumField[QuarkField][p1], + +QuantumField[AntiQuarkField][p2]}] + ``` + +* Updated the `FeynCalc` startup message. (ac87b5d) +* Removed the `eps(l)^mu eps(l)_mu = -1` rule, which is not compatible with D-dimensional polarization vectors (thanks to keith-hamilton for reporting Issue #8). (56482a9); Example: + ``` + SPD[p1, p1] = 0; + SPD[p2, p2] = 0; + Pair[LorentzIndex[Subscript[\[Alpha], 1], D], Momentum[Polarization[p1, I, Transversality -> True], D]] Pair[LorentzIndex[Subscript[\[Alpha], 1], D], Momentum[Polarization[p1, -I, Transversality -> True], D]] Pair[LorentzIndex[Subscript[\[Alpha], 2], D], Momentum[Polarization[p2, I, Transversality -> True], D]] Pair[LorentzIndex[Subscript[\[Alpha], 2], D], Momentum[Polarization[p2, -I, Transversality -> True], D]] // DoPolarizationSums[#, p1, n, Contract -> False] & // DoPolarizationSums[#, p2, n, Contract -> False] & // Contract + ``` +* Added a unit test for `OneLoop` (thanks to Yi-Bo Yang). (1d0f03e) +* Added unit tests for `PairContract`. (a578fb1) +* Set `PairContract[0,x]` to `0`. (e588312) +* Fixed a bug in the handling of `PairContract` heads in the input of `Contract`. (f1cd4a5); Example: + ``` + Contract[PairContract[LorentzIndex[i, D], Momentum[p, D]]] + ``` +* Some extra debuggin output for `OneLoop`. (a7aefb7) +* Modified the syntax of `DiracGamma`. From now we have `DiracGamma[0] === 0`. It is also forbidden to enter things like `DiracGamma[1]`, `DiracGamma[2]`, `DiracGamma[3]` etc. Instead, one should use `DiracGamma[ExplicitLorentzIndex[1]]` etc. Of course, `DiracGamma[5]`, `DiracGamma[6]` and `DiracGamma[7]` are still allowed. (537e019) +* All model parameters like masses, coupling constants and mixing angles can be now represented via `SMP[par]`. `FeynArts` patching was updated accordingly. `FCFAConvert` will introduce `SMP` objects if the option `SMP` is set to `True`. (29b8535) +* Refactored `FAPatch`. Also added the option `PatchModelsOnly` to patch only the model files in the `FeynArts` `Models` directory (thanks to Xing-Bo Yuan for the suggestion). (da16d74) +* Adjusted `FCFAConvert` and `FCPrepareFAAmp` to work with amplitudes generated by unpatched `FeynArts`. (0826e85) +* Fixed `DiracSpinor` to `Spinor` conversion. (1aeca0a); Example + ``` + DiracSpinor[p, m] + ``` +* Updated `.gitignore`. (701faa9) +* Added 3 more tree level QCD examples for photon gluon, photon quark and quark antiquark processes. (ae26f38); See `Examples/QCD/QCDGammaStarGToQiQBari.m`, `Examples/QCD/QCDQiGammaStarToQiGTree.m`, `Examples/QCD/QCDQiQBariToGammaStarGTree.m` + +* Added `FCCanonicalizeDummyIndices`, a function that canonicalizes dummy Lorentz indices. (0c877bd); Example + ``` + FCCanonicalizeDummyIndices[Uncontract[SP[q, p]^4, q, p, Pair -> All], LorentzIndexNames -> {mu, nu, rho, si}] + ``` + +* Added ABJ anomaly example to the test suite. (36fae9b) +* Some improvements in the documentation. (479b773) +* Added an extra Contract to `FCMultiLoopTID`. (41b84b3); Example + ``` + FCMultiLoopTID[FVD[q1, mu] FVD[q2, nu] LCD[mu, nu][a,b] FAD[{q1 - p1, m1}, {q2 - p2, m2}, {q1 - q2}], {q1, q2}] + ``` +* Improved Documentation for `TID`. (0aff5ff) +* Added a unit test for `ToPaVe` in `TID`. (8d072c0) +* Add an option `Head` to `Collect2` that allows to wrap prefactors into the given Head. (57decb6); Examples: + ``` + Collect2[Expand[(a + b + c)^2 (b + d)^3], {a, d}, Head -> hh] + ``` +* Improved `ApartFF` (actually `FCApart`) to set loop integrals that vanish in DR to zero by default. Not having this was an omission in the original implementation. The "old" behavior can be recovered by setting the option `DropScaleless` to `False`. (8e859cb) ; Examples: + + ``` + FCApart[FAD[{p, m0}, {-k1 + p, m1}] SPD[k1, p]^2 SPD[p, p], {p}, FDS -> False] + FCApart[FAD[{p, m0}, {-k1 + p, m1}] SPD[k1, p]^2 SPD[p, p], {p}, FDS -> False, DropScaleless -> False] + ``` + +* Block wrong syntax in `ApartFF`. (d48a409); Examples: + ``` + ApartFF[SPD[q, q] FAD[{q, m}], q] + ApartFF[SPD[q, q] FAD[{q, m}], {q}] + ``` +* Minor improvement in `FCLoopIsolate`. (3a75ac2) +* Even more improvements for the options parsing in `Contract`. (0431062) +* Improved `Contract` to contract multiple occurence of Eps tensors in a more efficient way. Thanks to Jos Vermaseren for the useful explanation. (5b28976); Example: + ``` + Contract[LC[i1, i2, i3, dum1] LC[i4, i5, i6, dum1] LC[i10, i11, i12, dum2] LC[i7, i8, i9, dum2]] // FCE + ``` +* Some cleanups in `Contract.m` (mostly just spacing.) (5ce91d9) +* Some more improvements in the options parsing and debugging output in `Contract`. (61506cb) +* Some improvement in the options parsing in `Contract`. (b2e94a5) +* Small fix in `Isolate`. (ac994f3) +* Fixed a bug in `DiracSimplify` with `DiracSubstitute67` not being applied to spinor chains. (7f9204c); Examples: + ``` + DiracSimplify[Spinor[-Momentum[p2], 0, 1].GS[Polarization[k1, -I]].GS[k1].GS[Polarization[k2, -I]].GA[7].Spinor[Momentum[p1], 0, 1], DiracSubstitute67 -> True] + ``` +* Refactored `ToLarin`. (f937c6b) +* Removed premature memoization in `DiracTrace`. This doesn't really give a performance gain but rather causes a lot of problems with different gamma^5 schemes. Now we memoize only where it is necessary and safe. (b96cbe9) +* Added an example for the calcuation of the Adler-Bell-Jackiw anomaly in QED. (8d28e06); See `Examples/QED/QEDABJAxialAnomaly.m` +* Some refactoring and performance improvements in `Contract`. (ccb705b) +* Improved calculation of chiral traces in 4 dimensions. (0ab7ee4) +* Degraded `$West` to `West`, which is now an option of `DiracTrace` and `TR`. Also, `West` has now no effect on the calculations of the chiral traces in 4 dimensions. (033bd54); Examples: + ``` + $BreitMaison = True; + DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True] // Factor2 + DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True, West -> False] // Factor2 + DiracTrace[GA[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True] // Factor2 + DiracTrace[GA[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True, West -> False] // Factor2 + ``` +* Some performance improvements in `DiracTrace`. (d9748c9) +* Some refactoring and better debugging output in `DiracTrace` and `TR`. (0ccf4d9) +* Some refactoring and better option parsing in `DiracSimplify`. (beffe33) +* Ensured that Tr[T^a]=0 where T^a is a single color matrix in the fundamental rep is always applied on the level of SUNTFs. (b1e777e); Example: + ``` + FCI[SUNTF[a,x,x]] + ``` +* Added the options `EpsEvaluate` and `ToPaVe` to `TID`. (69539b9) +* Fixed a bug in `TID` (missing `Contract` at the beginning) reported by YI-Bo Yang. (b78bb62); Example: + ``` + TID[FAD[{q, m}] FV[q, i]^2 FV[q, j] FV[q, k], q] + ``` +* Fixed a bug in `FCE` related to `ExplicitLorentzIndex` (thanks to Wen Chern). (ab5f6c1); Example: + ``` + Eps[ExplicitLorentzIndex[0], ExplicitLorentzIndex[1], Momentum[p],Momentum[q]]//FCE + ``` +* Added the option `BReduce` to `PaVeReduce`. Set to `False` by default. (e11575); Example: + ``` + Factor2[(B1[p^2, m0^2, m1^2] // PaVeReduce[#, BReduce -> True] &)] + ``` +* Improved `FCTraceExpand` to use `DiracGammaExpand` and `FCTraceFactor`. (770810d); Examples: + ``` + FCTraceExpand[DiracTrace[GS[p + b]]] + FCTraceExpand[DiracTrace[GS[p + b]], DiracGammaExpand -> False] + ``` +* Fixed mixing of dimensions in shifts of `FDS` (affected `Eps` tensors contracted with loop momentum). (7840801); Example: + ``` + FDS[LC[][p1, p2, p3, l] FAD[{l - p, m}, {l + q, m}, l - t], l] // FCE + ``` +* Set `$LimitTo4=False` as default. Otherwise, IR divergent C-functions might lead to inconsistencies. (2629530) +* Added `EpsilonUV` and `EpsilonIR` to be able to distinguish between UV and IR divergences in dim reg, when this is needed. Currently those are just placeholders with attached typesetting. (c391187) +* Added a new option `IsolateFast` to `Isolate`. This way one can isolate special types of very large expressions in a much faster way. (1c0c0e6); Examples: + ``` + Isolate[Total[Table[Sqrt[TZ[i] + 2 ZZ[i]]/+HH[ToString[i] + ToString[i + 2] + ToString[i + 4]], {i, 1,100}]]] // AbsoluteTiming + Isolate[Total[Table[Sqrt[TZ[i] + 2 ZZ[i]]/+HH[ToString[i] + ToString[i + 2] + ToString[i + 4]], {i, 1,100}]], IsolateFast -> True] // AbsoluteTiming + Isolate[Total[Table[Sqrt[TZ[i] + 2 ZZ[i]]/+HH[ToString[i] + ToString[i + 2] + ToString[i + 4]], {i, 1, 10000}]], IsolateFast -> True] // AbsoluteTiming + ``` +* Added the option `FinalSubstitutions` to `FCFAConvert`. (183e102) +* Made `MT`, `MTD` and `MTE` orderless. (bb49ab6); Example: + ``` + MT[a, b] === MT[b, a] + ``` +* Fixed a small bug in `Isolate`. (d8de71b); Example: + ``` + Isolate[-1 x] + ``` +* Made `Expand2` faster recognize that the expression is already fully expanded. (37a5728) +* Refactored `Collect2` and improved the performance on large expressions by switching to `CoefficientArrays`. (bff4790) +* Fixed a small bug in `FeynmanParametrize`. (2c44965) +* Refactored the unit testing framework to work as a bash script without Wolfram Workbench. Mathematica 8 and 9 require `MUnit` that can be pulled out of the WWB files. (ee7068c); Examples (under Linux): + ``` + inttetsts.sh math + inttetsts.sh math Lorentz + inttetsts.sh math Dirac + inttetsts.sh math Loop + examples.sh + ``` +* Improved `FCApart`'s internal algorithm and added new option `MaxIterations` to break the fractioning after a given number of iterations. (1225fe1); Example: + ``` + FCApart[SPD[k1, p] SPD[p, p] FAD[{p, m0}], {p}, MaxIterations -> 1, FDS -> False] + FCApart[SPD[k1, p] SPD[p, p] FAD[{p, m0}], {p}, MaxIterations -> 2, FDS -> False] + ``` +* Added `FCGetDimensions`, an auxiliary function for checking the dimensionality of the expression. (fd5621b); Example: + ``` + FCGetDimensions[{FV[p, mu], FVD[p, mu], FVE[p, mu]}] + ``` + +* Fixed wrong context in the unit tests for `FourLaplacian`. (b8562dd) +* Added `FCTraceFactor` for factoring constants out of `Dirac` traces. (a04902b); Example: + ``` + FCTraceFactor[DiracTrace[(a + b).(a - b).DiracTrace[GA[i].c.GA[j]].(a + b)]] + ``` +* Fixed a bug in `Write2` related to `FortranFormatDoublePrecision` (thanks to Wen-Long Sang). (ea03857); Example: + ``` + Write2["sang.abc", abc = 0.6*(-8 + 12 Log[5 + y[1]]), abc1 = 1/x^(2/3), FormatType -> FortranForm, Precision -> 10]; + Import["sang.abc", "Text"] + + Write2["sang.abc", abc = 0.6*(-8 + 12 Log[5 + y[1]]), abc1 = 1/x^(2/3), FormatType -> FortranForm, Precision -> 3]; + Import["sang.abc", "Text"] + + Write2["sang.abc", abc = 0.6*(-8 + 12 Log[5 + y[1]]), abc1 = 1/x^(2/3), FormatType -> FortranForm, FortranFormatDoublePrecision -> False]; + Import["sang.abc", "Text"] + ``` + + +* Improved `FCI` convertion of `FeynAmpDenominator`'s with dimensions other than `D`. (fa58485); Example: + ``` + FCI[FCI[FAD[q1, {-p + q1, m}, Dimension -> 4]]] + ``` + +* Added `FCTraceExpand`, a function that expands traces without evaluating them. (a9e8745); Example + ``` + FCTraceExpand[DiracTrace[GA[i, i] + GA[j, j].DiracTrace[GA[a] + GA[b]]]] + ``` +* Integrated FeynCalcManual.nb into main documentation. (10c5210) +* Catch wrong expressions like `Momentum[LorentzIndex[mu]]` or `LorentzIndex[Momentum[p]]` and warn the user immediately. (15fa095) + +### Version 9.0.1 (2016) + * For publishing reasons, the license has been changed from LGPL 3 to GPL 3 + * Fixed bugs that were discovered since the relese of FeynCalc 9.0.0 + * Converted an example of using Integrate2 from FeynCalcManual.nb to a proper .m file + +### Version 9.0.0 (2016) + + * Introduced `FCFAConvert` for automatic conversion of the CreateFeynAmp + output into FeynCalc input. + * Added `FCMultiLoopTID` for tensor decomposition of multiloop integrals. + * Documentation ported from the old HelpBrowser to the new Documentation Center. + * Make entering of `FAD`'s with propagators that have exponents simpler. + Now to enter e.g. `FAD[q,{q,m},{q,m},q-p,q-p,q-p]` one can simply write `FAD[q,{q,m,2},{q-p,0,3}]`. + * `ApartFF` is the new powerful replacement for `SPC` and `Apart2`. It uses `FCApart` as a backend and works for multiloop integrals. The "FF" in the name of the function is to honour Feng Feng, the author (arXiv:1204.2314) of the algorithm used in `FCApart`. + * Added `FCApart` for partial fractioning loop integrals with linearly dependent propagators. The algorithm comes from the work of Feng Feng (arXiv:1204.2314). + * Added `FCLoopExtract`, a new helper function for extracting loop integrals from the given expression. + * Added `FCLoopBasisIncompleteQ`, `FCLoopBasisOverdeterminedQ` and `FCLoopBasisFindCompletion` for studying the space formed by the propagators of the given loop integral. + * Now it is finally possible to enter `FAD`s also like `FAD[{q, m}, {q, m}, {q + p - k}]` where the last propagator is massless. + * Improved `PaVe` to set scaleless integrals to zero. + * New add-on `FUnitTools` for working with unit tests. + * Added possibility to set scalar products directly via `SP`, `SPD` and `SPE`. + * Added `TFIOrder` that can exploit some symmetries between Tarcer's scalar 2-loop integrals `TFI`. + * Many improvements to `ToTFI` (thanks to Anne Ernst!) + * Add new option `MultiLoop` to `FCLoopIsolate`. This allows to isolate only those integrals that depend on all of the loop momenta. + * `$DisableMemSet` can be used to deactivate `MemSet`, + * New option `PDEHeads` for `PropagatorDenominatorExplicit`. It allows to wrap what used to be `FAD` into used defined heads, so that one can + better keep track of scalar products that come from the denominator. + * Spinors can be now D-dimensional + * Added `$FCCheckProgress` to activate `FCMonitor` when needed. Note that `FCMonitor` slows things down for simple calculations, so it is better to activate it only for large expressions. Here is an example of activating FCMonitor (curently only TID supports it) + ``` + int = -EL^3 Spinor[Momentum[p2, D], ME, 1].GAD[Lor3].(ME + GSD[p2 + q]).GAD[Lor1].(ME + + GSD[p1 + q]).GAD[Lor3].Spinor[Momentum[p1, D], ME, 1] FAD[{p1 + q, ME}, {p2 + q, ME}, q]; + $FCCheckProgress = True; + TID[int, q] + ``` + + * Added `FCSplit` for splitting expressions into pieces that contain given variables and pieces that do not. `FCSplit[expr,{v1, v2, ...}]` splits `expr` into pieces that are free of any occurence of `v1`, `v2`, ... and pieces that contain those variables. This works both on sums and products. The output is provided in the form of a two element list. One can recover the original expression by applying `Total` to that list. For example + ``` + FCSplit[(z + a)^2 + (z + b)^2, {z}] + FCSplit[(z + a)^2 + (z + b)^2, {a}] + FCSplit[(z + a)^2 + (z + b)^2, {b}] + ``` + + + * Introduced `$DisableMemSet` for deactivating `MemSet`, which is often needed for debugging. + * Added a new option `PDEHeads` to `PropagatorDenominatorExplicit`. It allows to wrap what used to be `FAD` into user defined heads, so that one can better keep track of scalar products that come from the denominator. + * Allowed spinors to depend on D-dimensional external momenta to be compatible with the CDR scheme. `ChangeDimension` now doesn't force the spinors to depend only on 4-dimensional momenta. + * Introduced `FCLoopCanonicalize` and `FCLoopSolutionList`, that are useful for canonicalizing free Lorentz indices of 1-loop tensor integrals. See [https://github.com/FeynCalc/feyncalc/blob/master/Tests/LoopIntegrals/FCLoopCanonicalize.test] and + [https://github.com/FeynCalc/feyncalc/blob/master/Tests/LoopIntegrals/FCLoopSolutionList.test] for examples. + + * Introduced `FCLoopIsolate` and `FCLoopSplit`. These two functions should facilitate manipulation, separation and sorting of arbitrary loop integrals in the given expressions. `FCLoopSplit[expr,{q1,q2,...}]` separates `expr` into following four pieces: + * terms that are free of loop integrals + * terms with scalar loop integrals + * terms with tensor loop integrals, where all loop momenta are contracted + * terms with tensor loop integrals, where at least some loop momenta have free indices + The result is returned as a list with the 4 above elements. For example + + ``` + FCLoopSplit[zzz + (FVD[q, mu] FVD[p, mu] a + SPD[p, q] b) FAD[q, q + p] + yyy FAD[{q, m}], {q}] + ``` + + `FCLoopIsolate[expr,{q1,q2,...}]` wraps loop integrals into heads specified by the user. This is useful when you want to know which loop integrals appear in the given expression. For example, + + ``` + FCLoopIsolate[zzz + (FVD[q, mu] FVD[p, mu] a + SPD[p, q] b) FAD[q, q + p] + yyy FAD[{q, m}], {q}] + ``` + + * Added new options `PaVeAutoReduce` and `PaVeAutoOrder` that can be used to inhibit automatic reduction of A and B coefficient functions into `A0` and `B0`. Compare e.g. + ``` + PaVe[0, 0, {p}, {m, m}] + ``` + + to + + ``` + PaVe[0, 0, {p}, {m, m}, PaVeAutoReduce -> False] + + ``` + + * New function `FCDeclareHeader` to be used for FeynCalc add-ons that go into the `AddOn` directory. + + * Some functions now support a new function `FCVerbose` that allows a more concise debugging output as compared to using `$VeryVerbose`. For example + ``` + TID[FVD[q, mu] FVD[q, nu] FAD[q, {q + p, m}], q, FCVerbose -> 3] + ``` + + * Added an option `IsolateNames` to `FRH` to enable applying `ReleaseHold` only on specified `HoldForm` expressions. Compare e.g. + ``` + iso = Isolate[(a + b) F[q], q, IsolateNames -> KK1] + Isolate[(c + d) F[q1], q1, IsolateNames -> KK2]; + FRH[iso] + ``` + with + ``` + FRH[iso, IsolateNames -> KK1] + FRH[iso, IsolateNames -> KK2] + FRH[iso, IsolateNames -> {KK1, KK2}] + ``` + + * Added new option `ExcludeMasses` for `Apart2` to disable factoring and not to apply partial fractoning on propagators that contain specified masses. This gives you a more fine + grained control of partial fractioning. Compare e.g. + ``` + Apart2[FAD[p, {p, m1}, {p, m2}]] + ``` + + to + + ``` + Apart2[FAD[p, {p, m1}, {p, m2}], ExcludeMasses -> {m1}] + ``` + + * Added options `$TypesettingDim4`, `$TypesettingDimE` and `$TypesettingDimD` to modify the typesetting of momenta, Dirac matrices, metric tensors and polarization vectors in `4`, `D-4`, and `D`-dimensions. + For example, now you can do `$TypesettingDim4="";` to remove bars from 4-dimensional objects. Thanks to Yu Lu for the suggestion. + + * You might have been wondering, why FeynCalc must be installed to the directory `HighEnergyPhysics` and not just `FeynCalc`. Well, this used to be liked that for some legacy reasons but is actually not necessary nowadays. From now on FeynCalc lives in `FeynCalc` and it is started simply via ```<ToExpression[x]}`. We understand that this additional step may pose some inconveniences to you, but from the point of view of Mathematica programming and interoperability between different packages, this solution seems to be the cleanest way to avoid troubles in future. + + For example, ```Lagrangian["QCD"]``` now returns +``` +-(1/4) FieldStrength[FCGV["\[Alpha]"], FCGV["\[Beta]"], + FCGV["a"]].FieldStrength[FCGV["\[Alpha]"], + FCGV["\[Beta]"], FCGV["a"]] +``` + instead of +``` +-(1/4) FieldStrength[\[Alpha], \[Beta], a].FieldStrength[\[Alpha], \[Beta], a] +``` + as it used to be. Now suppose that before invoking Lagrangian["QCD"] you defined \[Alpha] = 1/137. With the new output using FCGV nothing changes. With the old output + you would have got +``` +-(1/4) FieldStrength[1/137, \[Beta], a].FieldStrength[1/137, \[Beta], a] +``` + which is clearly not what you want. + + * To circumvent problems related to the patching of FeynArts, from now on FeynCalc will look for FeynArts only in the directory `FeynArts` +inside `FeynCal`. Nevertheless, it is still possible to specify an alternative directory by setting ```FeynCalc`$FeynArtsDirectory="path"``` before loading FeynCalc. The patching code was moved to FeynCalc, i.e. now it will run even when Phi is not loaded. + + * The TARCER notebook have been converted into a source file (`TARCER.m`). Furthermore, generated TARCER*.mx files are not distributed anymore with the source code. When you first try to load TARCER, a dialog will appear with the suggestion to generate the .mx file now. This process has to be done only once and takes only a couple of minutes. After that, the generated .mx will be automatically loaded whenever you want to use TARCER. + + * Prior to this commit FeynCalc used to switch the format of output cells to `TraditionalForm`. Now it will only issue a warning message suggesting the user to do this by himself or herself. Such messages can be disabled by setting `$FCAdvice` to False. So if you despise all the fancy typesetting and prefer to work with `StandardForm`, FeynCalc will respect your decision. + + * To avoid clashes with built-in functions of recent Mathematica versions, we had to rename some FeynCalc functions: + * `PartialD` -> `FCPartialD` + * `Symmetrize` -> `FCSymmetrize` + * `AntiSymmetrize` -> `FCAntiSymmetrize` + +* To avoid further confusion about the handling of Dirac Gamma 5 in FeynCalc, it is now forbidden to enter +g^5 or the chiral projectors g^6 and g^7 as D-dimensional objects. Hence,`GAD[5]` or `DiracGamma[5,D]` will now generate error messages. This is not really a significant change, since before FeynCalc would silently convert `GAD[5]` to `GA[5]` without issuing any warnings, contrary to what the user might have expected from entering `GAD[5]`. The thing is that internally, FeynCalc always works with `DiracGamma[5]`. As far as dimensional regularization is concerned, the scheme to handle g^5 is determined by the values of `$BreitMaison` and `$Larin` and not by the dimension of g^5. Even in NDR, where g^5 is normally assumed to be D-dimensional, FeynCalc uses just `DiracGamma[5]`. Note that this is just a technicality of the implementation, nothing really related to physics. + +* Tensor decomposition routines have been updated to improve performance and usability. Before actually performing the decomposition, `Tdec` will now first check `TIDL` (Tensor Integral Decomposition Library) to see if the required integral is already contained there. If yes, the formula will be fetched from there. This behavior is controlled by the new option `UseTIDL` which is set to `True` by default. Furthermore, `Tdec` can now recognize symmetries in the indices of 1-loop integrals which significantly speeds up the computations. For multiloop integrals the symmetries recognition is not implemented yet. Another turbo for `Tdec` is the option `UseParallelization` (`True` by default) that activates parallelization code in the solver of linear equations `Solve3`. This can make things up to 40% faster and works for all kinds of integrals. Last but not least, a couple of new decompositions have been added to TIDL, just in case. + +* Fixed a bug in `DoPolarizationSums` [reported](http://www.feyncalc.org/forum/0853.html) by Kyrylo Bondarenko. + +* Adjusted the typesetting of SU(N) objects such that adjoint indices are now always upstairs while the fundamental indices are downstairs. +* Added additional SU(N) objects to work with SU(N) T-matrices that have explicit fundamental indices. See +the [announcement](http://www.feyncalc.org/forum/0843.html) on the mailing list for more details. +* Added examples for computing 2->2 tree level parton processes in QCD. +* Imporved DoPolarizationSums to handle massive and massless vector bosons in a proper way. See +the [announcement](http://www.feyncalc.org/forum/0843.html) on the mailing list for more details. +* Updated `FCPrepareFAAmp` to handle the main steps in converting the output of FeynArts to FeynCalc. See the updated wiki [page](https://github.com/FeynCalc/feyncalc/wiki/FeynArts#fatofc) for more details. + +* Fixed a bug in `FourDivergence` (actually in `Contract`) [reported](http://www.feyncalc.org/forum/0755.html) by Sun. + +* Added typesetting for `AlphaStrong` (QCD coupling constant) and `AlphaFS` (fine-structure constant). + +* Handling of algebraic simplifications for Dirac matrices in `DiracTrick` has been reworked to improve performance and provide better support for the Breitenlohner-Maison-'t Hooft-Veltman scheme. + +* Fixed a bug in `PowerSimplify` [reported](http://www.feyncalc.org/forum/0815.html) by Sun Qingfeng + +* Improved `EpsEvaluate` to always expand sums of momenta as [requested](http://www.feyncalc.org/forum/0812.html) by Lingxiao Xu. + +* Improved TraditionalForm formatting of metric tensors, vectors, Dirac matrices, Dirac slashes and scalar products. Now all 4- and D-4-dimensional quantities are displayed with a bar or a hat respectively on top of the symbol. The D-dimensional quantities remain as they are. This change allows to easily distinguish between D- , 4- and D-4-dimensional objects without deactivating TraditionalForm. + +* Introduced `FeynCalcInternal` shortcuts for D-4-dimensional metric tensors (`MTE`), vectors (`FVE`), Dirac matrices (`GAE`), Dirac slashes (`GSE`) and scalar products (`SPE`). + +* Extended polarization vectors to allow for vectors that are not transverse, i.e. not orthogonal to their momentum. This behavior is controlled by the option `Transversality` that applies to `Polarization` and `PolarizationVector`. + +* Added examples of computing QCD quark self-energy at one loop and explicitly verifying Furrry's theorem in QED at one loop for one and three photons. + +* Introduced a new experimental function `FCRenameDummyIndices` that can rename dummy Lorentz and SU(N) indices wihtout invoking `Contract` or `DiracSimplify`. + +* Introduced `FCPrint`, a new universal function for debug output. +* Added a new option `SirlinRelations` that controls whether `DiracSimplify` uses Sirlin's relations to simplify spinor chains. + +* Started to implement unit tests (via MUnit). + +* Fixed a bug in `ComplexConjugate` [reported](http://www.feyncalc.org/forum/0773.html) by Sun. + + +### Version 8.2.0 (2012) + +* Added **FeynArts 3.7** - unpatched. On first load it will be patched automatically. +* When running the first time set *$LoadPHI=True* before executing + Needs``` [HighEnergyPhysics`FeynCalc`]```, then it will be patched automatically. +* Updated **PHI** to work with **FeynArts 3.7**, which can now be kept in a subdir. + +###Version 8.1.0.1 (2012) + +* Updated **PHI** to work with **FeynArts 3.7**, which can now be kept in a subdir. + +### Version 8.1.0. (2012) + +* Fixed *DiracTrick*. +* Improved *SUNSimplify*, *DiracEquation*. +* Fixed Hyperlinks in *FeynCalc8.nb*. +* Fixed Tarcer .mx loading. + +### Version 8.0.3 (2011) + +* Added ClearAttributes *[FeynAmpDenominator,Orderless]* +* Added Momentum in *DiracSimplify* + +### Version 8.0.2 (2011) + +* Fixed more problems. +* Working on documentation. + +### Version 8.0.1 (2011) + +* Fixed a problem in *DiracTrace.* + +### Version 8.0.0beta3 (2011) + +* Fixed a bug in *OneLoop*. +* Changed *Uncontract*, *TID*. + +### Version 8.0.0 (2011) + +* Fixed some bugs reported by ibedir. + +### Version 8.0.0 (2010) + +* Minimal updates for **Mathematica 8.0**. +* Added a patched o **FeynArts 3.4**. + +### Version 7.0.0 (2009/2010) + +* Bug fixes. +* Updates for **Mathematica 7.0** and new **FeynArts**. + +### Version 6.0.0 (2007) + +* Bug fixes. +* Updates for **Mathematica 6.0** and new **FeynArts**. +* For **Mathematica 6** only. Rolf patched **FeynCalc** to be compatible with **Mathematica 6** (not **PHI**, not **FeynArts**) and zipped it together, including fully evaluated documentation notebooks in *HighEnergyPhysics/Documentation/English/*. Notice that this version does not load **PHI** nor **FeynArts** by default. Notice also that the changes are not entered into CVS yet, due to lack of time. + +### Version 5.1.0 (2006) + +* Bug fixes. +* Updates for **Mathematica 5.2** and new **FeynArts**. + +### Version 5.0.0b (2003) + +* Bug fixes. +* Adjustments for **Mathematica 5.0**. +* More reorganization by Frederik Orellana. +* Inclusion of help system, **PHI** and **FeynArts**. + +### Version 4.9.beta (2002) + +* Improved *DiracOrder*. +* Added *FeynCalcToLaTeX*. +* Fixed the cyclicity problem with *Gamma[5]*. +* Simplified installation mechanism. +* Fixed things for **Mathematica 5.0** and **FeynArts** and patching and all that. +* Other bugfixes. + +### Version 4.2.0 (2002) + +* Changed to use *DOT* everywhere instead of *DOT*. +* **FeynArts 3** support: Exclude *ShapeData* from autoloading. +* Keep *PolarizationVector* unevaluated when given **FeynArts** arguments. +* Added support for other multiplications than *DOT*. +* Added *FieldDerivative* and *CovariantFieldDerivative*. +* Added *$Multiplications*, *$DistributiveFunctions* and *$Containers* to allow customization of *FieldDerivative*. +* *DOT* moved into main context. +* Have *ExpandScalarProduct* expand also *Pair[LorentzIndex[mu], Momentum[a] * Momentum [b] +...]*. +* Small bug fix of *FourVector*: *fci* not defined. +* *IsolateHead* dropped. *IsolateNames* used instead everwhere. +* Some more box definitions for *PartialD*. +* Split *FeynCalcBook.nb* in two. +* New directory *fcdevel* with files under development (or just unfinished). +* New directory *fcloops* with (1,2) loop related files. +* Changed usage into *"usage"*. +* Had *Contract* contract also denominators. +* Moved *Vectors* into context ```FORM2FeynCalc` ```. +* Moved *FORMEpilog*, *FORMProlog* and *TraceDimension* into context *FeynCalc2FORM* +* Fixed Breit-Maison problem of *FeynCalcInternal*. +* Had *FeynRule* and *FunctionalD* know about *ExplicitSUNIndex*. +* Dropped ```Global` ``` symbols in *SquareAmplitude*. +* Small bug fix in *Uncontract*. +* Let Uncontract accept option *Dimension -> Automatic*. +* Have *Uncontract* uncontract also denominators. +* Changed option of *A0* *A0ToB0* from *True* to *False*. +* Code moved from *FeynCalc.m* to new files; should improve maintainability. +* Moved *SUNSimplify.m* and *SUNTrace.m* from *qcd* to *fctools*, +*qcd/InverseMellin.m* -> *fctables/InverseMellin.m* and +*qcd/ToLarin.m* -> *fctools/ToLarin.m* (corrections of Rolf). +* Moved a few more files to more logical places. +* Changed usage to *"usage"* everywhere. +* Moved *IsolagePrint* and *IsolateSplit* into context *Isolate*. +* Changed *QCDScaleMu* into *ScaleMu*. +* Dropped *SUNF2*. +* Changed option of *SUNSimplify* *SUNTrace* from *True* to *False*. +* Made *SUNSimplify* trace also term proportional to the identity matrix when +* *SUNTrace* is set to *True*. +* *FeynCalc.m*: + * Added support for *:>* to *OptionsSelect*. + * Placed *FDr* and *CDr* in correct contexts. + * Bugfixed check for integer arguments in *SUND* and *SUNDeltaContract: Added ExplicitSUNIndex*. + * *SUND*: No longer set all *SUND[a,a,b]* to *0* if a is not an integer, only when + a has head *SUNIndex*. +* *DiracSimplify.m*: * Defined *print1*, *print2*, *print3* +* *OneLoop.m*: Changed a few debug printing statements. +* Fixed *SumOver* to comply with **FeynArts 3**. +* **PHI**: + * As far as possible dropped using explicit contexts, use *MakeContext* instead. + * Small fix of *ArgumentsSupply*. + * Moved *FieldDerivative* and *CovariantFieldDerivative* (and *CDr* and *FDr*) into *HighEnergyPhysics/fctools/*. + * Implemented compatibility with **FeynCalc**'s *PartialD*-operator notation. + * Removed many comments. They don't give useful information and clutter things. + * Changed the possible settings of *B0Evaluation* to strings to facilitate extensibility and reduce the number of defined symbols. + * Introduced *LeutwylerJBarEvaluation* instead of *ExplicitLeutwylerJBar*. + * Implemented above-threshold evaluation of *VeltmanB0* (and *LeutwylerJBar*). + * Dropped *FANonCommutative*, *FAMetricTensorm*, *FAPolarizationVector*, *FAFourVector*, *FADiracMatrix*, *FAIndices* in favour of *NonCommutative* in consistence with *FAPatch.m*. + * Had *FAPatch.m* add *$FermionHeads* to *$NonCommuting* in *Setup.m*, + as well as set *FeynCalcInternal -> False* for *FourVector*, *MetricTensor*, + *DiracSlash*. + * End all usage definitions with a full stop. + * Changed *Dot* to *DOT*. +* *Objects.m*: + * Dropped *RemoveIntegerIndices*. + * Changed to have head *ExplicitSUNIndex* on integers (instead of nothing) in compliance with **FeynCalc**. + * *setLeftRightComponents* fixed to have *Explicit* in right context. + * Fixed bug in *WriteOutUMatrices* causing *NM[a[x], UMatrix[b]] + UMatrix[UIdentity]* not to work (reported by P.Buettiker). + * Fixed bug in *UIndicesSupply*, putting *DOT* in correct context. + * Fixed bug in *UExp* (reported by Paul Buettiker): + When zeros were in *$UExpansionCoefficients MM*, *UFieldMatrix* didn't work. +* *Utilities.m*: + * Added support for *WFFactor* in *DiscardOrders* (Don't discard if order is not known). + * *MandelstamReduce* now has renormalized masses as default. + * Added first sketch of *PHIToLaTeX*. +* Palettes.m: LoadLagrangian now keeps lagrangians given as strings in context ``` Global` ``` (instead of ``` HighEnergyPhysics`PHI`Objects` ``` ). +* *Renormalization.m*: + * Fixed small bug causing LeutwylerJBar causing problem with LeutwylerSigma. + * Readded *C0Evaluation -> "none"*, *D0Evaluation -> "none"* to *Options[VeltmanExpand]*. +* *Couplings.m*: + * Added *PHIModel* as option of *WFFactor*, *PMFactor*, *DCFactor*. + * Added *Drop* as option of *DoSumOver*. + * Fixed problem with *FCToFA* causing possible substitution of multiple pairs of identical indices in a product. + * Added *DiracSlash* to *FCToFA*. + * Dropped *Projection* in *FCToFA*, since *RemoveIntegerIndices* has been dropped. + * Fixed bug in *XName* causing existing coupling vectors not to be found. + * Fixed bug in *VerticesSpecifications*. Multiple order of a coupling are now correctly merged into e.g. one coupling with orders {2, 4} instead of two couplings. (*orderJoin*). + * Fixed problem with *DiscardCT* and **FeynArts 3** . + * Fixed bug in *FixCouplingIndices*. *SUNDelta*, *SUND* and *SUNF* are now also supported in coupling vectors. + * Updated *DoSumOver* to comply with **FeynArts 3**. + * Improved *WFFactor*, *DCFactor* and *PMFactor* to behave better if a file is not there. + * *DCRenormalize* now correctly uses the inverse factor. + +* *Channels.m* + * Dropped *RemoveIntegerIndices* and *Projection*. + * Fixed bug with *SU2F* in *SUNReduce*. + * Added support for *ExplicitSUNIndex*. +* *PHIStart.m* + * Dropped *RemoveIntegerIndices*. + * Switched to *UNablaHatDelta* with "scalar weak source", remember to switch back if vectors or axial-vectors are needed. +* *ChPTW34.m*: Fix missing comma in N29. +* *ChPTW32.m*: Fix Typo (``` QuantumField` ``` instead of ```QuantumField```). + + +### Version 4.1.1 (2001) +* Help System: Following the instructions above, the FeynCalc Book is now viewable via the +Mathematica help browser. It is possible to look up help pages on individual +functions by selecting them in a notebook with the cursor and then clicking +on AddOns in the help browser. +* **PHI/FeynArts**: Support for **FeynArts** through the new sub-package **PHI**, which is now fully integrated in **FeynCalc**. **PHI** adds support for Chiral Perturbation Theory including tools for dealing with a large number of Feynman rules, derivative couplings, field expansion, etc. Moreover, some examples of using **PHI** are provided which should also be generally instructive. The examples can be found at +http://www.feyncalc.org/examples/index.html. Information about **PHI** can be found at http://www.feyncalc.org/examples/phi/index.html. +* The *ReadProtected* Attribute has been removed from all functions. +* Moved the file *FeynCalcBook.nb* into the new directory *English* and +added the file *BrowserCategories.m* to allow lookup via the +Mathematica help browser. +* Changes in *FeynCalc.m*: + * All **FeynCalc** definitions are now cleared upon reload, + hopefully improved the way filenames and paths are determined, + * Added support for loading from *~/.Mathematica*. + * Added support for loading **PHI** and **FeynArts**. + * Added *$Abbreviations*. + * Added a few definitions to *DeltaFunction*. + * Fixed bug in *DiracTrace* reported by A. Kyrieleis. + * Fixed bug in *DiracTrace* causing *Tr[DiracSlash[p,p]]* to give p^2 instead of 4 p^2 (reported by W. Broniowski and L. Trueman and A. Krishna). + * Fixed small display bug of *Spinor* reported by A. Krishna. + * Added *FCIntegrate* and *FCNIntegrate* which are options of the new + (still experimental) function *FeynmanDoIntegrals* fixed bug in the display definition for *Pair* causing infinite recursion. + * Added two new functions (still very experimental) *FeynmanReduce* and *FeynmanDoIntegrals*. + * Very small addition to *Integrate2*. + * Added option *InitialFunction* to *FeynRule*. + * Fixed bug in *ComplexConjugate*'s treatment of *DiracGamma[5]*, +reported by T.Rashba and V. Khotilovich. + * Fixed bugs related to Mac OS's filesystem in *FeynCalc.m*, *FORM2FeynCalc.m*, *FeynCalc2FORM.m*, *OneLoop.m*, *PaVeReduce.m*, *RHI.m*, *SquareAmplitude.m*, *Write2.m*. + * Fixed bug in *FeynCalc2FORM.m* reported by V. Khotilovich. + * Fixed forgotten small bugs in *FeynCalcExternal.m*. + * Changed *FeynCalcExternal.m*, *OneLoopSimplify.m*, *TID.m* + to allow other symbols for *Dimension* than *D*. + * Completely rewrote *FeynmanParametrize1.m*. It is still experimental, but in progress and intended to be much more general than *FeynmanParametrize.m*. + * Small changes in *OneLoop.m*, *PaVeReduce.m* to write out to more readable file names. + * Fixed forgotten Blank in *SimplifyPolyLog.m*. + * Added the following new general utility functions: +*NumericQ1*, *Combinations*, *MLimit*, *TimedIntegrate*, *SelectSplit*. + * Added check for integers in SU(N) related functions. + * Small change in *TARCER.nb* to avoid name conflict with **FeynCalc** and **FeynArts**. + * Various very small spelling fixes etc. + +### Version 4.0 (2000) + * Reorganized for open-source and extensibility. + +### Version 3.0.1.1 + * Two bug-fixes for *OneLoop*. + +### Version 3.0 (1998) + * Typesetting features of **Mathematica 3.0**. + +### Version 2.2beta9 (1995) +* Updated version of **FeynCalc** compatible with **Mathematica 2.2**. + +### Version 2.2 + +### Version 1.13 (1992) + +### Version 1.0 (1991) + * Initial release written by Rolf Mertig. diff --git a/FeynCalc/Dirac/Anti5.m b/FeynCalc/Dirac/Anti5.m index e649438a4..589622cad 100644 --- a/FeynCalc/Dirac/Anti5.m +++ b/FeynCalc/Dirac/Anti5.m @@ -2,23 +2,27 @@ -(* :Title: Anti5 *) +(* :Title: Anti5 *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) -(* :Summary: Anti5 anticommutes gamma5's right or left *) +(* :Summary: Anti5 anticommutes g^5 to the right or the left *) (* ------------------------------------------------------------------------ *) Anti5::usage = -"Anti5[exp] anticommutes all gamma5 one time to the right. \ -Anti5[exp, n] anticommutes all gamma5 n times to the right. \ -Anti5[exp, -n] anticommutes all gamma5 n times to the left."; +"Anti5[exp] anticommutes all g^5 one time to the right. \ +Anti5[exp, n] anticommutes all g^5 n times to the right. \ +Anti5[exp, -n] anticommutes all g^5 n times to the left."; + +Anti5::failmsg = +"Error! Anti5 has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" (* ------------------------------------------------------------------------ *) @@ -28,107 +32,250 @@ Begin["`Anti5`Private`"] -Anti5[expr_Plus, n_] := - Map[Anti5[#,n]&,expr]; -Anti5[expr_, _] := - expr /; FreeQ2[FeynCalcInternal[expr], {DiracGamma[5],DiracGamma[6],DiracGamma[7]}]; -Anti5[expr_, Infinity] := - FixedPoint[Anti5, expr, $RecursionLimit]; -Anti5[expr_, -Infinity] := - FixedPoint[Anti5[#,-1]&, expr, $RecursionLimit]; -Anti5[expr_, n_Integer?Positive] := - Nest[Anti5, expr, n]/; (n =!= 1); -Anti5[expr_, n_Integer?Negative] := - Nest[Anti5[#,-1]&, expr, -n] /; (n =!= -1); -Anti5[expr_] := - Anti5[expr, 1]; - -Anti5[xx_, n_] := - Block[ {HoldDOT, ruleBMHVRight, ruleAnticommute, ruleNaiveRight, - ruleBMHVLeft, ruleNaiveLeft, temp, result}, - temp = FeynCalcInternal[xx] /. {1/2+DiracGamma[5]/2:>DiracGamma[6],1/2-DiracGamma[5]/2:>DiracGamma[7]} /. DOT -> HoldDOT; - HoldDOT[] := - 1; - HoldDOT[a___, DiracGamma[5], DiracGamma[5], b___ ] := - HoldDOT[a,b]; - HoldDOT[a___, DiracGamma[6], DiracGamma[6], b___ ] := - HoldDOT[a,b]; - HoldDOT[a___, DiracGamma[7], DiracGamma[7], b___ ] := - HoldDOT[a,b]; - - HoldDOT[a___, DiracGamma[6], b___]:= - (1/2)HoldDOT[a, DiracGamma[5], b] + (1/2)*HoldDOT[a, b]/; - !MatchQ[{b},{DiracGamma[5],___}|{DiracGamma[6],___}|{DiracGamma[7],___}] && - !MatchQ[{a},{___,DiracGamma[5]}|{___,DiracGamma[6]}|{___,DiracGamma[7]}]; - HoldDOT[a___, DiracGamma[7], b___]:= - -(1/2)HoldDOT[a, DiracGamma[5], b] + (1/2)*HoldDOT[a, b]/; - !MatchQ[{b},{DiracGamma[5],___}|{DiracGamma[6],___}|{DiracGamma[7],___}] && - !MatchQ[{a},{___,DiracGamma[5]}|{___,DiracGamma[6]}|{___,DiracGamma[7]}]; - - HoldDOT[a___, DiracGamma[5], DiracGamma[6], b___]:= - HoldDOT[a, DiracGamma[6], b]; - HoldDOT[a___, DiracGamma[5], DiracGamma[7], b___]:= - -HoldDOT[a, DiracGamma[7], b]; - HoldDOT[a___, DiracGamma[6], DiracGamma[5], b___]:= - HoldDOT[a, DiracGamma[6], b]; - HoldDOT[a___, DiracGamma[7], DiracGamma[5], b___]:= - -HoldDOT[a, DiracGamma[5], b]; - HoldDOT[a___, DiracGamma[6], DiracGamma[6], b___]:= - HoldDOT[a, DiracGamma[6], b]; - HoldDOT[a___, DiracGamma[6], DiracGamma[7], b___]:= - 0; - HoldDOT[a___, DiracGamma[7], DiracGamma[7], b___]:= - HoldDOT[a, DiracGamma[7], b]; - HoldDOT[a___, DiracGamma[7], DiracGamma[6], b___]:= - 0; - FCPrint[3,"Entering Anti5 with ", FeynCalcInternal[xx]]; - ruleAnticommute = { - - (* Every scheme, 4 dimensions, move gamma^5 to the right *) - HoldDOT[a___, DiracGamma[5], DiracGamma[(y: LorentzIndex | ExplicitLorentzIndex | Momentum)[x_]], - b___]/; (n===1) :> (-HoldDOT[a, DiracGamma[y[x]], DiracGamma[5],b]), - - (* Naive scheme, D dimensions, move gamma^5 to the right *) - HoldDOT[a___, DiracGamma[5], DiracGamma[(y: LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, - dim_Symbol], dim_Symbol], b___]/; (n===1) && !$BreitMaison && !$Larin :> - -HoldDOT[a, DiracGamma[y[x, dim], dim], DiracGamma[5],b], - - (* BMHV scheme, D dimensions, move gamma^5 to the right *) - HoldDOT[a___, DiracGamma[5], DiracGamma[(y: LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, - dim_Symbol], dim_Symbol ], b___ ]/; (n===1) && $BreitMaison && !$Larin :> - -HoldDOT[a, DiracGamma[y[x, dim], dim], DiracGamma[5], b] + - 2 HoldDOT[a, DiracGamma[y[x, dim-4], dim-4], DiracGamma[5],b], - - (* BMHV scheme, D-4 dimensions, move gamma^5 to the right *) - HoldDOT[a___, DiracGamma[5], DiracGamma[(y: LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, - dim_Symbol - 4], dim_Symbol - 4], b___ ]/; (n===1) && $BreitMaison && !$Larin :> - HoldDOT[a, DiracGamma[y[x, dim-4], dim - 4], DiracGamma[5], b], - (*-------------------------------------------------------------------------------------*) - - (* Every scheme, 4 dimensions, move gamma^5 to the left *) - HoldDOT[a___, DiracGamma[(y: LorentzIndex | ExplicitLorentzIndex | Momentum)[x_]], DiracGamma[5], - b___]/; (n===-1) :> -HoldDOT[a, DiracGamma[5], DiracGamma[y[x]], b], - - (* Naive scheme, D dimensions, move gamma^5 to the left *) - HoldDOT[a___, DiracGamma[(y: LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, - dim_Symbol], dim_Symbol], DiracGamma[5], b___]/; (n===-1) && !$BreitMaison && !$Larin :> - -HoldDOT[a, DiracGamma[5], DiracGamma[y[x, dim], dim], b], - - (* BMHV scheme, D dimensions, move gamma^5 to the left *) - HoldDOT[a___, DiracGamma[(y: LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, - dim_Symbol], dim_Symbol ], DiracGamma[5], b___ ]/; (n===-1) && $BreitMaison && !$Larin :> - -HoldDOT[a, DiracGamma[5], DiracGamma[y[x, dim], dim], b] + - 2 HoldDOT[a, DiracGamma[5], DiracGamma[y[x, dim-4], dim-4], b], - - (* BMHV scheme, D-4 dimensions, move gamma^5 to the left *) - HoldDOT[a___, DiracGamma[(y: LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, - dim_Symbol - 4], dim_Symbol - 4], DiracGamma[5], b___ ]/; (n===-1) && $BreitMaison && !$Larin :> - HoldDOT[a, DiracGamma[5], DiracGamma[y[x, dim-4], dim - 4], b] - }; - result = temp /. ruleAnticommute /. HoldDOT -> DOT; - FCPrint[3,"Leaving Anti5 with ", result]; - result - ]/; (n===1 || n===-1); +a5Verbose::usage=""; +anti5MoveLeft::usage=""; +anti5MoveRight::usage=""; +max::usage=""; + + +commonGamma5Properties = FeynCalc`DiracTrick`Private`commonGamma5Properties; +chiralTrickAnticommuting4DimRight = FeynCalc`DiracTrick`Private`chiralTrickAnticommuting4DimRight; +chiralTrickAnticommuting4DimLeft = FeynCalc`DiracTrick`Private`chiralTrickAnticommuting4DimLeft; +chiralTrickAnticommutingDDimRight = FeynCalc`DiracTrick`Private`chiralTrickAnticommutingDDimRight; +chiralTrickAnticommutingDDimLeft = FeynCalc`DiracTrick`Private`chiralTrickAnticommutingDDimLeft; +gamma5MoveBMHVRight = FeynCalc`DiracTrick`Private`gamma5MoveBMHVRight; +gamma5MoveBMHVLeft = FeynCalc`DiracTrick`Private`gamma5MoveBMHVLeft; +holdDOT = commonGamma5Properties; + +Options[Anti5] = { + FCDiracIsolate -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False +}; + +Anti5[expr_, opts:OptionsPattern[]] := + Anti5[expr, 1, opts]; + +Anti5[expr_, n_/; !OptionQ[n] && MatchQ[n, Infinity | -Infinity | _Integer], OptionsPattern[]] := + Block[ {new = 0,ex,terms,rest,res, eps, freePart, dsPart, diracObjects, + diracObjectsEval, null1, null2, dsHead, time, repRule}, + + If [OptionValue[FCVerbose]===False, + a5Verbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + a5Verbose=OptionValue[FCVerbose] + ]; + ]; + + max = n; + + FCPrint[1, "Anti5: Entering Anti5", FCDoControl->a5Verbose]; + FCPrint[3, "Anti5: Entering with, ", expr , FCDoControl->a5Verbose]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ2[ex, {DiracGamma[5],DiracGamma[6],DiracGamma[7]}], + Return[ex] + ]; + + + If[ OptionValue[FCDiracIsolate], + + (* This is the normal mode which works well both for large and small expressions *) + FCPrint[1, "Anti5: Normal mode.", FCDoControl->a5Verbose]; + time=AbsoluteTime[]; + FCPrint[1, "Anti5: Extracting Dirac objects.", FCDoControl->a5Verbose]; + ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, DiracGammaCombine->True, LorentzIndex->False, DiracChain->True]; + ex = ex /. h_dsHead/; FreeQ2[h,{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] :> Identity@@h; + + {freePart,dsPart} = FCSplit[ex,{dsHead}]; + diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//DeleteDuplicates//Sort; + FCPrint[1, "Anti5: Done extracting Dirac objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->a5Verbose], + + (* This is the fast mode for single expressions *) + FCPrint[1, "Anti5: Fast mode.", FCDoControl->a5Verbose]; + freePart = 0; + dsPart = dsHead[ex]; + diracObjects = {dsPart} + ]; + FCPrint[3,"Anti5: dsPart: ",dsPart , FCDoControl->a5Verbose]; + FCPrint[3,"Anti5: freePart: ",freePart , FCDoControl->a5Verbose]; + FCPrint[3,"Anti5: diracObjects: ",diracObjects , FCDoControl->a5Verbose]; + + FCPrint[1, "Anti5: Moving g^5.", FCDoControl->a5Verbose]; + time=AbsoluteTime[]; + + diracObjectsEval = (diracObjects /. DOT->holdDOT /. dsHead->Identity); + Switch[n, + + _Integer?Positive, + diracObjectsEval = Map[anti5MoveRight[#,0]&,diracObjectsEval], + Infinity, + diracObjectsEval = Map[anti5MoveRight[#,Infinity]&,diracObjectsEval], + _Integer?Negative, + diracObjectsEval = Map[anti5MoveLeft[#,0]&,diracObjectsEval], + -Infinity, + diracObjectsEval = Map[anti5MoveLeft[#,-Infinity]&,diracObjectsEval], + _, + Message[Anti5::failmsg,"Failed to identify the requested number of iterations."]; + Abort[] + ]; + + FCPrint[1, "Anti5: Done moving g^5, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->a5Verbose]; + + FCPrint[3, "Anti5: diracObjectsEval: ", diracObjectsEval , FCDoControl->a5Verbose]; + + time=AbsoluteTime[]; + FCPrint[1, "Anti5: Inserting Dirac objects back.", FCDoControl->a5Verbose]; + + diracObjectsEval = diracObjectsEval /. { + holdDOT->DOT + } /. (anti5MoveLeft|anti5MoveRight)[z_,_]-> z; + repRule = Thread[Rule[diracObjects,diracObjectsEval]]; + FCPrint[3,"Anti5: repRule: ", repRule, FCDoControl->a5Verbose]; + res = freePart + ( dsPart/. Dispatch[repRule]); + FCPrint[1, "Anti5: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->a5Verbose]; + FCPrint[3,"Anti5: Intermediate result: ", res, FCDoControl->a5Verbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + + FCPrint[1, "Anti5: Leaving.", FCDoControl->a5Verbose]; + FCPrint[3, "Anti5: Leaving with ", res, FCDoControl->a5Verbose]; + + res + ]; + + +(* ------------------------------------------------------------------------------ *) +(* ------------------------------------------------------------------------------ *) +(* -------------- Right movers ---------------------- *) +(* ------------------------------------------------------------------------------ *) +(* ------------------------------------------------------------------------------ *) + +anti5MoveRight[0, _]:= + 0; + +anti5MoveRight[DiracChain[ex_, i_, j_], c_]:= + DiracChain[anti5MoveRight[ex, c],i,j]; + +anti5MoveRight[c1_. a_holdDOT + c2_. b_holdDOT + c3_:0, i_]:= + anti5MoveRight[c1 a,i] + anti5MoveRight[c2 b,i] + anti5MoveRight[c3,i]; + +(* 4-dimensions, any scheme, move to the right *) +anti5MoveRight[r_. ch:holdDOT[___, (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), d__], Infinity] := + r anti5MoveRight[FixedPoint[(# /. chiralTrickAnticommuting4DimRight -> commonGamma5Properties /. commonGamma5Properties -> chiralTrickAnticommuting4DimRight)&, + chiralTrickAnticommuting4DimRight@@ch]/. chiralTrickAnticommuting4DimRight->holdDOT, Infinity]/; FreeQ[r,holdDOT] && + MatchQ[FCGetDimensions[{d}, ChangeDimension->True],{4}]; + +(* -> Limited number of rearrangements *) +anti5MoveRight[r_. holdDOT[b___, ch: (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), c_, d___], n_Integer?NonNegative] := + r anti5MoveRight[FixedPoint[(# /. chiralTrickAnticommuting4DimRight -> commonGamma5Properties /. commonGamma5Properties -> chiralTrickAnticommuting4DimRight)&, + chiralTrickAnticommuting4DimRight@@Join[{b}/. DiracGamma->diga,{ch,c}, {d} /. DiracGamma->diga]]/. + chiralTrickAnticommuting4DimRight->holdDOT /.diga->DiracGamma, n+1]/; FreeQ[r,holdDOT] && (n+1<=max) && + MatchQ[FCGetDimensions[{c}, ChangeDimension->True],{4}]; + +(* ------------------------------------------------------------------------------ *) + +(* D-dimensions, NDR scheme, move to the right *) +anti5MoveRight[r_. ch:holdDOT[___, (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), d__], Infinity] := + r anti5MoveRight[FixedPoint[(# /. chiralTrickAnticommutingDDimRight -> commonGamma5Properties /. commonGamma5Properties -> chiralTrickAnticommutingDDimRight)&, + chiralTrickAnticommutingDDimRight@@ch]/. chiralTrickAnticommutingDDimRight->holdDOT, Infinity]/; + MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && FreeQ[r,holdDOT] && + (MatchQ[FCGetDimensions[{d}, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True],{_Symbol}]); + +(* -> Limited number of rearrangements *) +anti5MoveRight[r_. holdDOT[b___, ch: (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), c_, d___], n_Integer?NonNegative] := + r anti5MoveRight[FixedPoint[(# /. chiralTrickAnticommutingDDimRight -> commonGamma5Properties /. commonGamma5Properties -> chiralTrickAnticommutingDDimRight)&, + chiralTrickAnticommutingDDimRight@@Join[{b}/. DiracGamma->diga,{ch,c}, {d} /. DiracGamma->diga]]/. + chiralTrickAnticommutingDDimRight->holdDOT /.diga->DiracGamma, n+1]/; + MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && FreeQ[r,holdDOT] && (n+1<=max) && + MatchQ[FCGetDimensions[{c}, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True],{_Symbol}]; + +(* ------------------------------------------------------------------------------ *) + +(* BMHV scheme, D or D-4 dimensions, move to the right *) +anti5MoveRight[r_. ch:holdDOT[___, (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), d__], Infinity] := + r anti5MoveRight[FixedPoint[(# /. gamma5MoveBMHVRight -> commonGamma5Properties /. commonGamma5Properties -> gamma5MoveBMHVRight)&, + gamma5MoveBMHVRight@@ch]/. gamma5MoveBMHVRight->holdDOT, Infinity]/; + MemberQ[{"BMHV"},FeynCalc`Package`DiracGammaScheme] && FreeQ[r,holdDOT] && + (!MatchQ[FCGetDimensions[{d}, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True],{4}]); + +(* -> Limited number of rearrangements *) +anti5MoveRight[r_. holdDOT[b___, ch: (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), c_, d___], n_Integer?NonNegative] := + r anti5MoveRight[FixedPoint[(# /. gamma5MoveBMHVRight -> commonGamma5Properties /. commonGamma5Properties -> gamma5MoveBMHVRight)&, + gamma5MoveBMHVRight@@Join[{b}/. DiracGamma->diga,{ch,c}, {d} /. DiracGamma->diga]]/. + gamma5MoveBMHVRight->holdDOT /.diga->DiracGamma, n+1]/; + MemberQ[{"BMHV"},FeynCalc`Package`DiracGammaScheme] && FreeQ[r,holdDOT] && (n+1<=max) && + (!MatchQ[FCGetDimensions[{d}, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True],{4}]); + +(* ------------------------------------------------------------------------------ *) +(* ------------------------------------------------------------------------------ *) +(* -------------- Left movers ---------------------- *) +(* ------------------------------------------------------------------------------ *) +(* ------------------------------------------------------------------------------ *) + + +anti5MoveLeft[0, _]:= + 0; + +anti5MoveLeft[DiracChain[ex_, i_, j_], c_]:= + DiracChain[anti5MoveLeft[ex, c],i,j]; + +anti5MoveLeft[c1_. a_holdDOT + c2_. b_holdDOT + c3_:0, i_]:= + anti5MoveLeft[c1 a,i] + anti5MoveLeft[c2 b,i] + anti5MoveLeft[c3,i]; + +(* 4-dimensions, any scheme, move to the left *) +anti5MoveLeft[r_. ch:holdDOT[d__, (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), ___], -Infinity] := + r anti5MoveLeft[FixedPoint[(# /. chiralTrickAnticommuting4DimLeft -> commonGamma5Properties /. commonGamma5Properties -> chiralTrickAnticommuting4DimLeft)&, + chiralTrickAnticommuting4DimLeft@@ch]/. chiralTrickAnticommuting4DimLeft->holdDOT, -Infinity]/; FreeQ[r,holdDOT] && + (MatchQ[FCGetDimensions[{d}, ChangeDimension->True],{4}]); + +(* -> Limited number of rearrangements *) +anti5MoveLeft[r_. holdDOT[b___, c_, ch:(DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), d___], n_Integer?NonPositive] := + r anti5MoveLeft[FixedPoint[(# /. chiralTrickAnticommuting4DimLeft -> commonGamma5Properties /. commonGamma5Properties -> chiralTrickAnticommuting4DimLeft)&, + chiralTrickAnticommuting4DimLeft@@Join[{b}/. DiracGamma->diga,{c,ch}, {d} /. DiracGamma->diga]]/. + chiralTrickAnticommuting4DimLeft->holdDOT /.diga->DiracGamma, n-1]/; FreeQ[r,holdDOT] && (max<=n-1) && MatchQ[FCGetDimensions[{c}, ChangeDimension->True],{4}]; + +(* ------------------------------------------------------------------------------ *) +(* D-dimensions, NDR scheme, move to the left *) +anti5MoveLeft[r_. ch:holdDOT[d__, (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), ___], -Infinity] := + r anti5MoveLeft[FixedPoint[(# /. chiralTrickAnticommutingDDimLeft -> commonGamma5Properties /. commonGamma5Properties -> chiralTrickAnticommutingDDimLeft)&, + chiralTrickAnticommutingDDimLeft@@ch]/. chiralTrickAnticommutingDDimLeft->holdDOT, -Infinity]/; + MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && FreeQ[r,holdDOT] && + (MatchQ[FCGetDimensions[{d}, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True],{_Symbol}]); + +(* -> Limited number of rearrangements *) +anti5MoveLeft[r_. holdDOT[b___, c_, ch:(DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), d___], n_Integer?NonPositive] := + r anti5MoveLeft[FixedPoint[(# /. chiralTrickAnticommutingDDimLeft -> commonGamma5Properties /. commonGamma5Properties -> chiralTrickAnticommutingDDimLeft)&, + chiralTrickAnticommutingDDimLeft@@Join[{b}/. DiracGamma->diga,{c,ch}, {d} /. DiracGamma->diga]]/. + chiralTrickAnticommutingDDimLeft->holdDOT /.diga->DiracGamma, n-1]/; + MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && FreeQ[r,holdDOT] && (max<=n-1) && + MatchQ[FCGetDimensions[{c}, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True],{_Symbol}]; + +(* ------------------------------------------------------------------------------ *) + +(* BMHV scheme, D oder D-4 dimensions, move to the left *) +anti5MoveLeft[r_. ch:holdDOT[d__, (DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), ___], -Infinity] := + r anti5MoveLeft[FixedPoint[(# /. gamma5MoveBMHVLeft -> commonGamma5Properties /. commonGamma5Properties -> gamma5MoveBMHVLeft)&, + gamma5MoveBMHVLeft@@ch]/. gamma5MoveBMHVLeft->holdDOT, -Infinity]/; + MemberQ[{"BMHV"},FeynCalc`Package`DiracGammaScheme] && FreeQ[r,holdDOT] && + !MatchQ[FCGetDimensions[{d}, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True],{4}]; + + +(* -> Limited number of rearrangements *) +anti5MoveLeft[r_. holdDOT[b___, c_, ch:(DiracGamma[5|6|7] | (_. DiracGamma[6] + _. DiracGamma[7])), d___], n_Integer?NonPositive] := + r anti5MoveLeft[FixedPoint[(# /. gamma5MoveBMHVLeft -> commonGamma5Properties /. commonGamma5Properties -> gamma5MoveBMHVLeft)&, + gamma5MoveBMHVLeft@@Join[{b}/. DiracGamma->diga,{c,ch}, {d} /. DiracGamma->diga]]/. + gamma5MoveBMHVLeft->holdDOT /.diga->DiracGamma, n-1]/; + MemberQ[{"BMHV"},FeynCalc`Package`DiracGammaScheme] && FreeQ[r,holdDOT] && (max<=n-1) && + !MatchQ[FCGetDimensions[{d}, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True],{4}]; FCPrint[1,"Anti5.m loaded."]; End[] diff --git a/FeynCalc/Dirac/Chisholm.m b/FeynCalc/Dirac/Chisholm.m index 6fc985185..37a518bc4 100755 --- a/FeynCalc/Dirac/Chisholm.m +++ b/FeynCalc/Dirac/Chisholm.m @@ -7,9 +7,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Applies the Chisholm identity *) @@ -17,9 +17,13 @@ (* ------------------------------------------------------------------------ *) Chisholm::usage = -"Chisholm[x] substitutes products of three Dirac matrices or \ +"Chisholm[exp] substitutes products of three Dirac matrices or \ slashes by the Chisholm identity."; +Chisholm::failmsg = +"Error! Chisholm has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -27,13 +31,82 @@ Begin["`Chisholm`Private`"] +chVerbose::usage=""; + Options[Chisholm] = { - DiracSimplify -> True, - FCI -> False + Contract -> True, + DiracSigmaExplicit -> False, + DiracSimplify -> True, + DotSimplify -> True, + FCDiracIsolate -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCVerbose -> False, + InsideDiracTrace -> False, + MaxIterations -> Infinity, + Mode -> 1, + NonCommutative -> True }; Chisholm[expr_, OptionsPattern[]] := - Block[{ex}, + Block[{ex, tmp, tmpli, tmpli1, tmpli2, terms,rest,res, holdDOT, eps, freePart, dsPart, diracObjects, + diracObjectsEval, null1, null2, dsHead, time, repRule, mode, chisholmRule1, chisholmRule2, maxIterations, + nonComm, chisholmRuleInsideTrace}, + + mode = OptionValue[Mode]; + maxIterations = OptionValue[MaxIterations]; + nonComm = OptionValue[NonCommutative]; + + chisholmRule1 = { + dsHead[holdDOT[a___,DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], + DiracGamma[(lv3:(LorentzIndex|Momentum)[_])]]] :> + (tmpli= LorentzIndex[$MU[Unique[]]]; ( + Pair[lv1, lv2] dsHead[holdDOT[a,DiracGamma[lv3]]] - + Pair[lv1, lv3] dsHead[holdDOT[a,DiracGamma[lv2]]] + + Pair[lv2, lv3] dsHead[holdDOT[a,DiracGamma[lv1]]] - + $LeviCivitaSign I Eps[lv1,lv2,lv3, tmpli] dsHead[holdDOT[a,DiracGamma[tmpli],DiracGamma[5]]] + )), + dsHead[holdDOT[a___, DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], + DiracGamma[(lv3:(LorentzIndex|Momentum)[_])], DiracGamma[5]]] :> + (tmpli= LorentzIndex[$MU[Unique[]]]; ( + Pair[lv1, lv2] dsHead[holdDOT[a, DiracGamma[lv3],DiracGamma[5]]] - + Pair[lv1, lv3] dsHead[holdDOT[a, DiracGamma[lv2],DiracGamma[5]]] + + Pair[lv2, lv3] dsHead[holdDOT[a, DiracGamma[lv1],DiracGamma[5]]] - + $LeviCivitaSign I Eps[lv1,lv2,lv3, tmpli] dsHead[holdDOT[a,DiracGamma[tmpli]]])), + + (*The same with the spinors*) + dsHead[holdDOT[a___,DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], + DiracGamma[(lv3:(LorentzIndex|Momentum)[_])], b_Spinor]] :> + (tmpli= LorentzIndex[$MU[Unique[]]]; ( + Pair[lv1, lv2] dsHead[holdDOT[a,DiracGamma[lv3], b]] - + Pair[lv1, lv3] dsHead[holdDOT[a,DiracGamma[lv2], b]] + + Pair[lv2, lv3] dsHead[holdDOT[a,DiracGamma[lv1], b]] - + $LeviCivitaSign I Eps[lv1,lv2,lv3, tmpli] dsHead[holdDOT[a,DiracGamma[tmpli],DiracGamma[5], b]] + )), + dsHead[holdDOT[a___, DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], + DiracGamma[(lv3:(LorentzIndex|Momentum)[_])], DiracGamma[5], b_Spinor]] :> + (tmpli= LorentzIndex[$MU[Unique[]]]; ( + Pair[lv1, lv2] dsHead[holdDOT[a, DiracGamma[lv3],DiracGamma[5], b]] - + Pair[lv1, lv3] dsHead[holdDOT[a, DiracGamma[lv2],DiracGamma[5], b]] + + Pair[lv2, lv3] dsHead[holdDOT[a, DiracGamma[lv1],DiracGamma[5], b]] - + $LeviCivitaSign I Eps[lv1,lv2,lv3, tmpli] dsHead[holdDOT[a,DiracGamma[tmpli],b]])) + }; + + chisholmRuleInsideTrace = { + dsHead[holdDOT[x___DiracGamma, DiracGamma[5]]]/; Length[{x}]<4 && FreeQ2[{x},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] :> 0 + }; + + + chisholmRule2 = { + dsHead[holdDOT[a___, DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], + DiracGamma[(lv3:(LorentzIndex|Momentum)[_])], b___]] :> + (tmpli= LorentzIndex[$MU[Unique[]]]; ( + Pair[lv1, lv2] dsHead[holdDOT[a, DiracGamma[lv3], b]] - + Pair[lv1, lv3] dsHead[holdDOT[a, DiracGamma[lv2], b]] + + Pair[lv2, lv3] dsHead[holdDOT[a, DiracGamma[lv1], b]] - + $LeviCivitaSign I Eps[lv1,lv2,lv3, tmpli] dsHead[holdDOT[a, DiracGamma[tmpli], DiracGamma[5], b]])) + }; If[ OptionValue[FCI], ex = expr, @@ -44,30 +117,158 @@ Return[ex] ]; + If[ OptionValue[FCVerbose]===False, + chVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + chVerbose=OptionValue[FCVerbose] + ]; + ]; + + + FCPrint[1, "Chisholm. Entering.", FCDoControl->chVerbose]; + FCPrint[3, "Chisholm: Entering with ", ex, FCDoControl->chVerbose]; + + If[ OptionValue[FCDiracIsolate], + (* This is the normal mode which works well both for large and small expressions *) + FCPrint[1, "Chisholm: Normal mode.", FCDoControl->chVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "Chisholm: Extracting Dirac objects.", FCDoControl->chVerbose]; + + If[ !FreeQ[ex, DiracChain], + ex = DiracChainExpand[ex, FCI->True]; + ]; + + ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, DiracChain->True, + DotSimplify->OptionValue[DotSimplify], FCJoinDOTs -> OptionValue[FCJoinDOTs], DiracGammaCombine-> False]; + + If[ !FreeQ[ex, DiracChain], + ex = ex /. dsHead[DiracChain[x_,i_,j_]] :> DiracChain[dsHead[x],i,j] + ]; + + {freePart,dsPart} = FCSplit[ex,{dsHead}]; + FCPrint[3,"Chisholm: dsPart: ",dsPart , FCDoControl->chVerbose]; + FCPrint[3,"Chisholm: freePart: ",freePart , FCDoControl->chVerbose]; + + diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//DeleteDuplicates//Sort; + FCPrint[1, "Chisholm: Done extracting Dirac objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->chVerbose]; + + time=AbsoluteTime[]; + Which[ + mode===1, + FCPrint[1, "Chisholm: Applying Chisholm identity (mode 1).", FCDoControl->chVerbose]; + + diracObjectsEval = diracObjects /. DOT->holdDOT; + + diracObjectsEval = FixedPoint[(# /. chisholmRule1)&,diracObjectsEval, maxIterations]; + If[ nonComm, + diracObjectsEval = FixedPoint[(# /. chisholmRule2)&,diracObjectsEval, maxIterations] + ]; + + If [OptionValue[InsideDiracTrace], + diracObjectsEval = diracObjectsEval/.chisholmRuleInsideTrace; + ]; + + FCPrint[1, "Done applying Chisholm identity (mode 1), timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->chVerbose], + + mode===2, + FCPrint[1, "Chisholm: Applying Chisholm identity (mode 2).", FCDoControl->chVerbose]; + diracObjectsEval = diracObjects /. DOT->holdDOT //. {dsHead[holdDOT[DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], + DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], DiracGamma[5], b___]] :> + (tmpli1= LorentzIndex[$MU[Unique[]]]; tmpli2= LorentzIndex[$MU[Unique[]]]; ( + - $LeviCivitaSign/2 Eps[lv1, lv2, tmpli1, tmpli2] dsHead[holdDOT[DiracSigma[DiracGamma[tmpli1], DiracGamma[tmpli2]],b]] + + Pair[lv1, lv2] dsHead[holdDOT[DiracGamma[5],b]]))} //. { + + dsHead[holdDOT[a___, DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], DiracGamma[5], b___]] :> + ( + tmpli1= LorentzIndex[$MU[Unique[]]]; + tmpli2= LorentzIndex[$MU[Unique[]]]; + - $LeviCivitaSign/2 Eps[lv1, lv2, tmpli1, tmpli2] dsHead[holdDOT[a,DiracSigma[DiracGamma[tmpli1], DiracGamma[tmpli2]],b]] + + Pair[lv1, lv2] dsHead[holdDOT[a,DiracGamma[5],b]]) + } //. { + dsHead[holdDOT[a___, DiracSigma[DiracGamma[lv1_], DiracGamma[lv2_]], DiracGamma[5], b___]] :> + ( + tmpli1= LorentzIndex[$MU[Unique[]]]; + tmpli2= LorentzIndex[$MU[Unique[]]]; + -I*$LeviCivitaSign (1/2) dsHead[holdDOT[a,DiracSigma[DiracGamma[tmpli1], DiracGamma[tmpli2]],b]] Eps[lv1, lv2, tmpli1, tmpli2] + ) + }; + FCPrint[1, "Done applying Chisholm identity (mode 2), timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->chVerbose], + True, + Message[Chisholm::failmsg, "Unknown operation mode."]; + Abort[] + ]; + time=AbsoluteTime[]; + FCPrint[1, "Chisholm: Inserting Dirac objects back.", FCDoControl->chVerbose]; + + diracObjectsEval = diracObjectsEval /. holdDOT[]->1 /.holdDOT->DOT /. dsHead->Identity; + repRule = Thread[Rule[diracObjects,diracObjectsEval]]; + FCPrint[3,"Chisholm: repRule: ",repRule , FCDoControl->chVerbose]; + tmp = freePart + (dsPart/. Dispatch[repRule]); + FCPrint[1, "Chisholm: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->chVerbose]; + FCPrint[3,"Chisholm: Intermediate result: ", tmp, FCDoControl->chVerbose], + + (* This is the fast mode for standalone Dirac chains *) + FCPrint[1, "Chisholm: Fast mode.", FCDoControl->chVerbose]; + time=AbsoluteTime[]; + + Which[ + mode===1, + FCPrint[1, "Chisholm: Applying Chisholm identity (mode 1).", FCDoControl->chVerbose]; + tmp = ex /. DOT -> holdDOT /. holdDOT[z__] :> dsHead[holdDOT[z]]; + + tmp = FixedPoint[(# /. chisholmRule1)&, tmp, maxIterations]; + If[ nonComm, + tmp = FixedPoint[(# /. chisholmRule2)&, tmp, maxIterations] + ]; + FCPrint[1, "Done applying Chisholm identity (mode 1), timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->chVerbose], + + mode===2, + FCPrint[1, "Chisholm: Applying Chisholm identity (mode 2).", FCDoControl->chVerbose]; + tmp = ex /. DOT -> holdDOT //. {holdDOT[DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], + DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], DiracGamma[5], b___] :> + (tmpli1= LorentzIndex[$MU[Unique[]]]; tmpli2= LorentzIndex[$MU[Unique[]]]; ( + - $LeviCivitaSign/2 Eps[lv1, lv2, tmpli1, tmpli2] holdDOT[DiracSigma[DiracGamma[tmpli1], DiracGamma[tmpli2]],b] + + Pair[lv1, lv2] holdDOT[DiracGamma[5],b]))} //. {holdDOT[a___, DiracGamma[(lv1:(LorentzIndex|Momentum)[_])], + DiracGamma[(lv2:(LorentzIndex|Momentum)[_])], DiracGamma[5], b___] :> + (tmpli1= LorentzIndex[$MU[Unique[]]]; tmpli2= LorentzIndex[$MU[Unique[]]]; ( + - $LeviCivitaSign/2 Eps[lv1, lv2, tmpli1, tmpli2] holdDOT[a,DiracSigma[DiracGamma[tmpli1], DiracGamma[tmpli2]],b] + + Pair[lv1, lv2] holdDOT[a,DiracGamma[5],b]))}; + FCPrint[1, "Done applying Chisholm identity (mode 2), timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->chVerbose], + + + True, + Message[Chisholm::failmsg, "Unknown operation mode."]; + Abort[] + ]; + tmp = tmp/. holdDOT[]->1 /.holdDOT->DOT /. dsHead->Identity + ]; + + res = tmp; + + If[ OptionValue[Contract], + time=AbsoluteTime[]; + FCPrint[1, "Chisholm: Applying Contract.", FCDoControl->chVerbose]; + res = Contract[res, FCI->True]; + FCPrint[1, "Chisholm: Done applying Contract, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->chVerbose] + ]; + If[ OptionValue[DiracSimplify], - ex = Contract[DiracSimplify[ex //. chish1 //. chish2]], - ex = Contract[ex //. chish1 //. chish2] + time=AbsoluteTime[]; + FCPrint[1, "Chisholm: Applying DiracSimplify.", FCDoControl->chVerbose]; + res = DiracSimplify[res, FCI->True, DiracSigmaExplicit->OptionValue[DiracSigmaExplicit]]; + FCPrint[1, "Chisholm: Done applying DiracSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->chVerbose] ]; - ex + FCPrint[1, "Chisholm: Leaving.", FCDoControl->chVerbose]; + FCPrint[3, "Chisholm: Leaving with ", res, FCDoControl->chVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res ]; -chish1 = (f_. DOT[a_DiracGamma, b_DiracGamma, c_DiracGamma, - d_DiracGamma, e_DiracGamma, f_DiracGamma, g___]) :> - Chisholm[Contract[DiracSimplify[DOT[Chisholm[f DOT[a,b,c]] ,Chisholm[d,e,f,g]]],Rename->False]]; - -chish2 = DOT[a___, DiracGamma[lv1_[pe1_]],DiracGamma[lv2_[pe2_]], DiracGamma[lv3_[pe3_]],b___] :> - Block[ {index}, - index = Unique[$MU]; - Contract[DiracSimplify[ - ( - Pair[lv1[pe1], lv2[pe2]] DOT[a, DiracGamma[lv3[pe3]], b] - - Pair[lv1[pe1], lv3[pe3]] DOT[a, DiracGamma[lv2[pe2]], b] + - Pair[lv2[pe2], lv3[pe3]] DOT[a, DiracGamma[lv1[pe1]], b] - - $LeviCivitaSign I Eps[ lv1[pe1],lv2[pe2],lv3[pe3],LorentzIndex[index] ]* - DOT[a, DiracGamma[LorentzIndex[index]].DiracGamma[5], b] - )], EpsContract->True, Rename->False] - ]; FCPrint[1,"Chisholm.m loaded"]; End[] diff --git a/FeynCalc/Dirac/Chisholm2.m b/FeynCalc/Dirac/Chisholm2.m deleted file mode 100755 index 246a0b8f9..000000000 --- a/FeynCalc/Dirac/Chisholm2.m +++ /dev/null @@ -1,66 +0,0 @@ -(* ::Package:: *) - - -(* :Title: Chisholm2 *) - -(* :Title: Chisholm2 *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Applies the Chisholm2 identity *) - -(* ------------------------------------------------------------------------ *) - -Chisholm2::usage = -"Chisholm2[x] elininates products of two Dirac matrices and the 5th Dirac matrix \ -by applying the Chisholm identity."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`Chisholm2`Private`"] - -Options[Chisholm2] = { - DiracSimplify -> True, - FCI -> False, - DiracSigmaExplicit -> False -}; - -Chisholm2[expr_, OptionsPattern[]] := - Block[{ex}, - - If[ OptionValue[FCI], - ex = expr, - ex = FCI[expr] - ]; - - If[ FreeQ[ex,DiracGamma], - Return[ex] - ]; - - If[ OptionValue[DiracSimplify], - ex = FCRenameDummyIndices[Contract[DiracSimplify[ex //. chish,DiracSigmaExplicit->OptionValue[DiracSigmaExplicit]]]], - ex = FCRenameDummyIndices[Contract[ex //. chish]] - ]; - - ex - - ]; - -chish = DOT[a___, DiracGamma[lv1_[pe1_]],DiracGamma[lv2_[pe2_]], DiracGamma[5],b___] :> - (un1 = Unique[mU1]; - un2 = Unique[mU2]; - Expand[1/2 ( - $LeviCivitaSign Eps[lv1[pe1], lv2[pe2], LorentzIndex[un1], - LorentzIndex[un2]] DOT[a,DiracSigma[DiracGamma[LorentzIndex[un1]], - DiracGamma[LorentzIndex[un2]]],b] + - 2 Pair[lv1[pe1], lv2[pe2]] DOT[a,DiracGamma[5],b])]); - -FCPrint[1,"Chisholm2.m loaded"]; -End[] diff --git a/FeynCalc/Dirac/DiracChainCombine.m b/FeynCalc/Dirac/DiracChainCombine.m new file mode 100644 index 000000000..be50bbc3e --- /dev/null +++ b/FeynCalc/Dirac/DiracChainCombine.m @@ -0,0 +1,83 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: DiracChainCombine *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: DiracChainCombine *) + +(* ------------------------------------------------------------------------ *) + +DiracChainCombine::usage = +"DiracChainCombine[expr] is (nearly) the inverse operation to DiracChainExpand."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`DiracChainCombine`Private`"]; + +optDiracGammaCombine::usage=""; +mark::usage=""; + +rulesMain = { + (n1_. DiracChain[x_, i1: (_DiracIndex| _ExplicitDiracIndex| _Spinor), i2: (_DiracIndex| _ExplicitDiracIndex| _Spinor)] + + n2_. DiracChain[y_, i1: (_DiracIndex| _ExplicitDiracIndex| _Spinor), i2: (_DiracIndex| _ExplicitDiracIndex| _Spinor)])/; + Denominator[n1]===1 && Denominator[n2]===1 && NonCommFreeQ[{n1,n2}] && FreeQ[{n1,n2}, DiracChain] :> + DiracChain[mark (n1 x + n2 y), i1, i2], + + (n_. DiracChain[x_, i1: (DiracIndex|ExplicitDiracIndex|Spinor)[__], i2: (DiracIndex|ExplicitDiracIndex|Spinor)[__]] + + n_. DiracChain[y_, i1: (DiracIndex|ExplicitDiracIndex|Spinor)[__], i2: (DiracIndex|ExplicitDiracIndex|Spinor)[__]])/; + !(Denominator[n]===1 && NonCommFreeQ[n] && FreeQ[n, DiracChain]) :> + n DiracChain[mark (x + y), i1, i2], + + (* Works also for Expand[DiracChainExpand[DCHN[1 + GA5, i, j] DCHN[1 + GA5, k, l]]]*) + (n1_. DiracChain[x_, i1: (DiracIndex|ExplicitDiracIndex|Spinor)[__], i2: (DiracIndex|ExplicitDiracIndex|Spinor)[__]] + + n2_. DiracChain[y_, i1: (DiracIndex|ExplicitDiracIndex|Spinor)[__], i2: (DiracIndex|ExplicitDiracIndex|Spinor)[__]])/; + !(Denominator[n1]===1 && Denominator[n2]===1 && NonCommFreeQ[{n1,n2}] && FreeQ[{n1,n2}, DiracChain]) && Expand[(n1-n2)]==0 :> + n1 DiracChain[mark (x - y), i1, i2] +}; + + + +Options[DiracChainCombine] = { + DiracGammaCombine -> False, + FCE -> False, + FCI -> False +}; + +DiracChainCombine[expr_, OptionsPattern[]] := + Block[{ex, res, rules=rulesMain}, + + optDiracGammaCombine = OptionValue[DiracGammaCombine]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + res = ex //. Dispatch[rules]; + + If[ OptionValue[DiracGammaCombine], + res = res /. DiracChain[x_,i_,j_]/; !FreeQ[x,mark] :> DiracChain[DiracGammaCombine[x/.mark->1],i,j] + ]; + res = res /. mark -> 1; + + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + +FCPrint["DiracChainCombine.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/DiracChainExpand.m b/FeynCalc/Dirac/DiracChainExpand.m new file mode 100644 index 000000000..d996c8a25 --- /dev/null +++ b/FeynCalc/Dirac/DiracChainExpand.m @@ -0,0 +1,127 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: DiracChainExpand *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Expands Dirac chains with explicit indices *) + +(* ------------------------------------------------------------------------ *) + +DiracChainExpand::usage = +"DiracChainExpand[exp] expands all Dirac chains with explicit indices \ +using linearity, e.g. DCHN[GA[p1]+GA[p2]+m,i,j] becomes \ +DCHN[GA[p1],i,j]+DCHN[GA[p2],i,j]+m*DCHN[1,i,j]."; + +DiracChainExpand::fail = +"Something went wrong while expanding Dirach chains with explicit indices. +Evaluation aborted! " + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`DiracChainExpand`Private`"] + +optDiracGammaExpand::usage=""; +optDotSimplify::usage=""; + +null1::usage=""; +null2::usage=""; +chLinExp::usage=""; +chLin::usage=""; +tmp::usage=""; +momList::usage=""; + +Options[DiracChainExpand] = { + DiracChainFactor -> True, + DiracGammaExpand -> True, + DotSimplify -> True, + FCE -> False, + FCI -> False, + Momentum -> All +}; + +DiracChainExpand[expr_, OptionsPattern[]] := + Block[{ex, null1, null2, uniqList, solsList, repRule, ruleDelayed, res, rhs}, + + momList = OptionValue[Momentum]; + optDotSimplify = OptionValue[DotSimplify]; + optDiracGammaExpand = OptionValue[DiracGammaExpand]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + (* Nothing to do... *) + If[ FreeQ[ex,DiracChain], + Return[ex] + ]; + + (* List of all the unique Dirac chains *) + uniqList = Cases[ex+null1+null2, DiracChain[__], Infinity]//DeleteDuplicates//Sort; + + (* If the user specified to perform expansion only for some + special momenta, let's do it *) + If[ momList=!=All && Head[momList]===List, + uniqList = Select[uniqList, !FreeQ2[#, momList]&] + ]; + rhs = uniqList /. DiracChain -> chLin /. chLinExp -> DiracChain; + + If[ OptionValue[DiracChainFactor], + rhs = DiracChainFactor[rhs, FCI->True] + ]; + + (* Final replacement rule *) + repRule = Thread[ruleDelayed[uniqList, rhs]] /. ruleDelayed->RuleDelayed; + + (* Simple cross check *) + If[ !FreeQ2[repRule,{chLin,chLinExp}], + Message[DiracChainExpand::fail]; + Abort[] + ]; + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + +chLinExp[null1|null2,__]:=0; + +(* For spinors there is nothing to expand *) +chLin[xx_, i_]:= + chLinExp[xx, i]; + +chLin[xx_, i : (_DiracIndex | _ExplicitDiracIndex | _Spinor), j : (_DiracIndex | _ExplicitDiracIndex | _Spinor)] := + Map[chLinExp[#,i,j]&,expandFu[xx]+null1+null2]; + +expandFu[xx_]:= + ( + tmp = Expand[xx]; + + If[optDiracGammaExpand, + tmp = DiracGammaExpand[tmp,FCI->True, Momentum->momList]; + ]; + + If[optDotSimplify, + tmp = DotSimplify[tmp,FCI->True]; + ]; + tmp + ); + +FCPrint[1,"DiracChainExpand.m loaded."]; +End[] diff --git a/FeynCalc/Dirac/DiracChainFactor.m b/FeynCalc/Dirac/DiracChainFactor.m new file mode 100644 index 000000000..4d33f819b --- /dev/null +++ b/FeynCalc/Dirac/DiracChainFactor.m @@ -0,0 +1,83 @@ +(* Wolfram Language package *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: DiracChainFactor *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Factors Dirac chains with explicit indices using linearity *) + +(* ------------------------------------------------------------------------ *) + +DiracChainFactor::usage = +"DiracChainFactor[expr] factors out all expressions inside a DiracChain to which the \ +chain doesn't apply. For example, all objects that are not Dirac matrices can be \ +safely factrored out from every Dirac chain."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`DiracChainFactor`Private`"] + +Options[DiracChainFactor] = { + FCI -> False, + FCE -> False +}; + +DiracChainFactor[expr_, OptionsPattern[]] := + Block[ {ex, moms,res, diracChains}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex, DiracChain], + Return[ex] + ]; + + + + diracChains = Cases2[ex, DiracChain]; + + If[ diracChains =!= {}, + res = ex /. Dispatch[Thread[diracChains -> chainFactor[diracChains]]] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + +chainFactor[x_] := + x /. DOT -> holdDOT /. DiracChain -> factorDirac /. holdDOT[] -> 1 /. + factorDirac -> DiracChain /. holdDOT->DOT; + +holdDOT[a___,b_,c___]:= + b holdDOT[a,c]/; NonCommFreeQ[b]; + +holdDOT[a___,b1_ b2_,c___]:= + b1 holdDOT[a,b2,c]/; NonCommFreeQ[b1] && !NonCommFreeQ[b2]; + +factorDirac[a_,i_,j_] := + a DiracChain[1,i,j]/; NonCommFreeQ[a]; + +factorDirac[a_DiracTrace b_., i_,j_] := + a factorDirac[b,i,j]; + +factorDirac[a_ b_,i_,j_] := + a factorDirac[b,i,j]/; NonCommFreeQ[a] && !NonCommFreeQ[b]; + + +FCPrint[1,"DiracChainFactor.m loaded."]; +End[] diff --git a/FeynCalc/Dirac/DiracChainJoin.m b/FeynCalc/Dirac/DiracChainJoin.m new file mode 100644 index 000000000..b1d733ee8 --- /dev/null +++ b/FeynCalc/Dirac/DiracChainJoin.m @@ -0,0 +1,198 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: DiracChainJoin *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2018 Rolf Mertig + Copyright (C) 1997-2018 Frederik Orellana + Copyright (C) 2014-2018 Vladyslav Shtabovenko +*) + +(* :Summary: Joins chains of Dirac matrices with explicit Dirac + indices into index free chains *) + +(* ------------------------------------------------------------------------ *) + +DiracChainJoin::usage = +"DiracChainJoin[exp] joins chains of Dirac matrices with explicit \ +Dirac indices wrapped with a head DiracChain. \n +Notice that DiracChainJoin is not suitable for creating closed Dirac \ +chains out of the FeynArts output with explicit Dirac indices, e.g. when \ +the model contains 4-fermion operators. Use FCFADiracChainJoin for that."; + +DiracChainJoin::failmsg = +"Error! DiracChainJoin has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`DiracChainJoin`Private`"] + +dchjVerbose::usage=""; +li::usage=""; +li1::usage=""; +li2::usage=""; +li3::usage=""; +li4::usage=""; + +holdDOT::usage=""; +optTraceOfOne::usage=""; + +Options[DiracChainJoin] = { + Drop -> True, + FCDiracIsolate -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> True, + TraceOfOne -> 4 +}; + +DiracChainJoin[expr_, OptionsPattern[]] := + Block[{ ex, tmp, res, diracObjects, diracObjectsEval, null1, null2, + dsHead, time, repRule}, + + optTraceOfOne = OptionValue[TraceOfOne]; + + If [OptionValue[FCVerbose]===False, + dchjVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + dchjVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "DiracChainJoin. Entering.", FCDoControl->dchjVerbose]; + FCPrint[3, "DiracChainJoin: Entering with ", expr, FCDoControl->dchjVerbose]; + + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ2[ex,{DiracChain,DiracIndexDelta}], + Return[ex] + ]; + + If[ OptionValue[FCVerbose]===False, + dchjVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + dchjVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "DiracChainJoin: Isolating Dirac chains.", FCDoControl->dchjVerbose]; + time=AbsoluteTime[]; + + If[ OptionValue[FCDiracIsolate], + + tmp = FCDiracIsolate[ex,FCI->True,Head->dsHead, DotSimplify->False, DiracGammaCombine->False, FCJoinDOTs-> False, + DiracSigmaExplicit->False, LorentzIndex->False, Spinor->False, DiracGamma->False, DiracChain->True, + Factoring -> OptionValue[Factoring]]; + diracObjects = Cases[tmp+null1+null2, dsHead[_], Infinity]//Sort//DeleteDuplicates; + + FCPrint[1, "DiracChainJoin: Done isolating spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dchjVerbose]; + FCPrint[3, "DiracChainJoin: After FCDiracIsolate ", tmp, FCDoControl->dchjVerbose]; + + + + FCPrint[3,"DiracChainJoin: diracObjects: ", diracObjects , FCDoControl->dchjVerbose]; + + + FCPrint[1, "DiracChainJoin: Simplifying Dirac chains.", FCDoControl->dchjVerbose]; + time=AbsoluteTime[]; + diracObjectsEval = Map[(diracChainEval[#])&, (diracObjects/.dsHead->Identity/. DOT->holdDOT)]/. + diracChainEval -> Identity /. holdDOT->DOT; + + FCPrint[1, "DiracChainJoin: Done simplifying Dirac chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dchjVerbose]; + FCPrint[3, "DiracChainJoin: diracObjectsEval: ", diracObjectsEval, FCDoControl->dchjVerbose]; + + If[ !FreeQ2[diracObjectsEval,{diracChainEval,holdDOT}], + Message[DiracChainJoin::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ]; + + FCPrint[1, "DiracChainJoin: Inserting Dirac objects back.", FCDoControl->dchjVerbose]; + time=AbsoluteTime[]; + repRule = MapThread[Rule[#1,#2]&,{diracObjects,diracObjectsEval}]; + FCPrint[3,"DiracChainJoin: repRule: ",repRule , FCDoControl->dchjVerbose]; + res = ( tmp/.repRule); + FCPrint[1, "DiracChainJoin: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dchjVerbose], + + (*Fast mode*) + FCPrint[1, "DiracChainJoin: Using the fast mode.", FCDoControl->dchjVerbose]; + res = diracChainEval[ex/. DOT->holdDOT] /. diracChainEval -> Identity /. holdDOT->DOT ; + FCPrint[3, "DiracChainJoin: Result of the evaluation: ", res, FCDoControl->dchjVerbose] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "DiracChainJoin: Leaving.", FCDoControl->dchjVerbose]; + FCPrint[3, "DiracChainJoin: Leaving with ", res, FCDoControl->dchjVerbose]; + + + + res + +]; + +(* sbar_i A_ij*) +diracChainEval[rest_. DiracChain[spinor_Spinor, i_DiracIndex] DiracChain[chain_, i_DiracIndex, j_]]:= + diracChainEval[rest DiracChain[chain,spinor,j]]; + +(* ... A_ij s_j *) +diracChainEval[rest_. DiracChain[chain_, i:(_DiracIndex|_ExplicitDiracIndex|_Spinor), j_DiracIndex] DiracChain[j_DiracIndex, spinor_Spinor]]:= + diracChainEval[rest DiracChain[chain,i,spinor]]; + +(* sbar_i A_ij s'_j *) +diracChainEval[rest_. DiracChain[chain_, spinor1_Spinor, spinor2_Spinor]]:= + holdDOT[spinor1,chain,spinor2] diracChainEval[rest]; + +(* (sbar.A)_i (B.s')_i -> sbar.A.B.s' *) +diracChainEval[rest_. DiracChain[spinor1_Spinor, i_DiracIndex] DiracChain[i_DiracIndex, spinor2_Spinor]]:= + holdDOT[spinor1,spinor2] diracChainEval[rest]; + +(* A_ii -> Tr(A) *) +diracChainEval[rest_. DiracChain[chain_/;chain=!=1,i_DiracIndex,i_DiracIndex]]:= + DiracTrace[chain] diracChainEval[rest]; + +diracChainEval[rest_. DiracChain[1,i_DiracIndex,i_DiracIndex]]:= + optTraceOfOne diracChainEval[rest]; + +(* A_*i* d_ij *) +diracChainEval[rest_. DiracChain[a__,i_DiracIndex,b___] DiracIndexDelta[i_DiracIndex,j_DiracIndex]]:= + diracChainEval[rest DiracChain[a,j,b]]; + +(* A_ij B_jk -> (A.B)_ik *) +diracChainEval[rest_. DiracChain[chain1_,a:(_DiracIndex|_ExplicitDiracIndex|_Spinor),i_DiracIndex] * + DiracChain[chain2_,i_DiracIndex,b: (_DiracIndex|_ExplicitDiracIndex|_Spinor)]]:= + diracChainEval[rest DiracChain[holdDOT[chain1,chain2],a,b]]/; a=!=i && b=!=i; + +(* d_ii -> Tr(1) *) +diracChainEval[rest_. DiracIndexDelta[i_DiracIndex,i_DiracIndex]]:= + optTraceOfOne diracChainEval[rest]; + +(* d_ij d_jk -> d_ik *) +diracChainEval[rest_. DiracIndexDelta[i_DiracIndex,j_DiracIndex] DiracIndexDelta[j_DiracIndex,k_DiracIndex]]:= + diracChainEval[rest DiracIndexDelta[i,k]]; + +(* d_ij^2 -> Tr(1) *) +diracChainEval[rest_. DiracIndexDelta[i_DiracIndex, j_DiracIndex]^2]:= + optTraceOfOne diracChainEval[rest]/; i=!=j; + +holdDOT[a___,1,b___]:= + holdDOT[a,b]; + +holdDOT[]:= + 1; + +FCPrint[1,"DiracChainJoin.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/DiracEquation.m b/FeynCalc/Dirac/DiracEquation.m index 253907982..925fd3ddc 100644 --- a/FeynCalc/Dirac/DiracEquation.m +++ b/FeynCalc/Dirac/DiracEquation.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Applies Dirac equation to simplify spinor chains *) @@ -18,7 +18,7 @@ DiracEquation::usage = "DiracEquation[exp] applies the Dirac equation without \ -expanding exp. If that is needed, use DiracSimplify."; +expanding exp. If expansions are necessary, use DiracSimplify."; (* ------------------------------------------------------------------------ *) @@ -27,10 +27,12 @@ Begin["`DiracEquation`Private`"] -HoldDOT; +HoldDOT::usage=""; +tmp::usage=""; Options[DiracEquation] = { - FeynCalcInternal -> False + FCI -> False, + FCE -> False }; DiracEquation[ex_, OptionsPattern[]] := @@ -42,11 +44,15 @@ ]; (* If there are no spinors or no Dirac matrices, then we can't apply the Dirac equation *) - If[ FreeQ[expr,Spinor] || FreeQ[expr,DiracGamma], + If[ FreeQ2[expr, {Spinor,DiracGamma}], Return[expr]; ]; - res = DotSimplify[diraceq[expr], Expanding->False]; + res = DotSimplify[FixedPoint[diraceq,expr,5]/.PairContract->Pair, Expanding->False]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; res @@ -59,9 +65,7 @@ diraceq[x_] := x/;FreeQ[x,Spinor]; diraceq[x_] := - Expand[ x/. dirac67back /. DOT->HoldDOT //.spCDieqRules /.HoldDOT->DOT, DOT ]; - -dirac67back = {1/2+DiracGamma[5]/2:>DiracGamma[6],1/2-DiracGamma[5]/2:>DiracGamma[7]}; + Expand[x/. DOT->HoldDOT //. spCDieqRules /.HoldDOT->DOT, DOT ]; HoldDOT[a___,HoldDOT[b___],c___]:= HoldDOT[a,b,c]; HoldDOT[a___,b1_HoldDOT + b2_HoldDOT + b3_:0 ,c___]:= @@ -77,7 +81,8 @@ 0, 1/n HoldDOT[ z, Spinor[n Momentum[p,dim] + k,m,op], DiracGamma[k,dim],a] ] - ])/; last[n Momentum[p,dim]+k]===Momentum[p,dim], + ] + )/; last[n Momentum[p,dim]+k]===Momentum[p,dim], HoldDOT[ a___,DiracGamma[Momentum[p_, dim_ : 4],dim_ : 4], Spinor[n_. Momentum[p_, dim_ : 4] + k_. ,m_,op___],z___] :> (m/n HoldDOT[ a,Spinor[ n Momentum[p, dim] + k,m,op ],z] - If[ (k===0), @@ -89,7 +94,7 @@ ]) /; last[n Momentum[p]+k]===Momentum[p], HoldDOT[ a___,DiracGamma[Momentum[y_,dim_:4],dim_:4], DiracGamma[Momentum[y_,dim_:4],dim_:4],b___] :> - ExpandScalarProduct[Momentum[y,dim],Momentum[y,dim]] HoldDOT[a,b], + ExpandScalarProduct[Pair[Momentum[y,dim],Momentum[y,dim]]] HoldDOT[a,b], (* Here the situation is more complicated since we need to move the slash through a certain number of other Dirac matrices before we reach the spinor. Note that the matrices @@ -97,16 +102,19 @@ (* reaching the first spinor, if we need to anticommute past another Dirac gamma (not gamma 5) *) HoldDOT[ z___, s: Spinor[n_. Momentum[p_, dim_ : 4] + k_. ,___], - a : DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_, _ :4] | 5 | 6 | 7, _ : 4] ..., - DiracGamma[(x : LorentzIndex | ExplicitLorentzIndex | Momentum)[y_,di_:4],di_:4], - DiracGamma[Momentum[p_,dim_ : 4],dim_ : 4],b___] :> - -HoldDOT[ z,s,a, DiracGamma[Momentum[p,dim],dim],DiracGamma[x[y,di],di],b] + - 2(PairContract[x[y,di],Momentum[p,dim]] /. PairContract -> Pair)*HoldDOT[ z,s,a,b]/; + a___DiracGamma, + DiracGamma[x: (_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum),di_:4], + DiracGamma[Momentum[p_,dim_ : 4],dim_ : 4],b___] :> ( tmp = + -HoldDOT[ z,s,a, DiracGamma[Momentum[p,dim],dim],DiracGamma[x,di],b] + + 2*((PairContract[x,Momentum[p,dim]]*HoldDOT[ z,s,a,b]) ) + )/; last[n Momentum[p,dim]+k] === Momentum[p,dim], + + (* reaching the first spinor, if we need to anticommute past a Dirac gamma 5 *) HoldDOT[ z___, s: Spinor[n_. Momentum[p_, dim_ : 4] + k_. ,___], - a : DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_, _ :4] | 5 | 6 | 7, _ : 4] ..., + a___DiracGamma, DiracGamma[(u:5|6|7)], DiracGamma[Momentum[p_,dim_ : 4],dim_ : 4],b___] :> HoldDOT[ z,s,a, Anti5[DiracGamma[u].DiracGamma[Momentum[p,dim],dim]]/.DOT|Times->HoldDOT,b]/; @@ -114,17 +122,17 @@ (* reaching the last spinor, if we need to anticommute past another Dirac gamma (not gamma 5) *) HoldDOT[ a___, DiracGamma[Momentum[p_,dim_:4],dim_:4], - DiracGamma[(x : LorentzIndex | ExplicitLorentzIndex | Momentum)[y_,di_:4],di_:4], - b : DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_, _ :4] | 5 | 6 | 7, _ : 4] ..., + DiracGamma[x: (_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum),di_:4], + b___DiracGamma, s: Spinor[n_. Momentum[p_, dim_: 4] + k_.,___],z___] :> - (-HoldDOT[a,DiracGamma[x[y,di],di],DiracGamma[Momentum[p,dim],dim],b,s,z]+ - 2(PairContract[x[y,di],Momentum[p,dim]] /. PairContract -> Pair)*HoldDOT[a,b,s,z])/; + (-HoldDOT[a,DiracGamma[x,di],DiracGamma[Momentum[p,dim],dim],b,s,z]+ + 2*((PairContract[x,Momentum[p,dim]]*HoldDOT[a,b,s,z]) ))/; last[n Momentum[p,dim]+k]===Momentum[p,dim], (* reaching the last spinor, if we need to anticommute past a Dirac gamma 5 *) HoldDOT[ a___, DiracGamma[Momentum[p_,dim_:4],dim_:4], DiracGamma[(u:5|6|7)], - b : DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_, _ :4] | 5 | 6 | 7, _ : 4] ..., + b___DiracGamma, s: Spinor[n_. Momentum[p_, dim_: 4] + k_.,___],z___] :> HoldDOT[a, Anti5[DiracGamma[Momentum[p,dim],dim].DiracGamma[u],-1]/.DOT|Times->HoldDOT,b,s,z]/; last[n Momentum[p,dim]+k] === Momentum[p,dim] diff --git a/FeynCalc/Dirac/DiracGammaCombine.m b/FeynCalc/Dirac/DiracGammaCombine.m index 297feecaf..a7db427e8 100644 --- a/FeynCalc/Dirac/DiracGammaCombine.m +++ b/FeynCalc/Dirac/DiracGammaCombine.m @@ -1,13 +1,22 @@ -(* ------------------------------------------------------------------------ *) -(* ------------------------------------------------------------------------ *) +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Summary: The inverse of DiracGammaExpand *) +(* :Title: DiracGammaCombine *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: The inverse of DiracGammaExpand *) (* ------------------------------------------------------------------------ *) DiracGammaCombine::usage = -"DiracGammaCombine[exp] is (nearly) the inverse operation to \ -DiracGammaExpand."; +"DiracGammaCombine[exp] is (nearly) the inverse operation to DiracGammaExpand."; (* ------------------------------------------------------------------------ *) @@ -16,33 +25,55 @@ Begin["`DiracGammaCombine`Private`"] -DiracGammaCombine[y_] := - If[ !FreeQ2[y,{GS, GSD, GSE}], - FeynCalcInternal[y]//dircg, - y//dircg - ]; - -dircg[x_Plus] := - If[ Length[x] > 8, - Map[DiracGammaCombine, x], - x //. gasumrules - ]; +dgcVerbose::usage=""; -dircg[exp_] := - exp //. gasumrules; - -(* merge sums of DiracGamma's into one *) -gasumrules = { - n1_. DiracGamma[Momentum[x_,di___],di___] + - n2_. DiracGamma[Momentum[y_,di___],di___] :> - DiracGamma[ Momentum[n1 x + n2 y,di], di ] /; - (NumberQ[n1] && NumberQ[n2]), - (n1_. DiracGamma[Momentum[x_, di___], di___] + - n2_. DiracGamma[Momentum[x_, di___], di___] ):> - (n1+n2) DiracGamma[Momentum[x, di], di], - (n3_. Momentum[x_,di___] + n4_. Momentum[y_,di___]):> - Momentum[ Expand[n3 x + n4 y],di]/;(NumberQ[n3]&&NumberQ[n4]) +Options[DiracGammaCombine] = { + FCE -> False, + FCI -> False }; +DiracGammaCombine[expr_, OptionsPattern[]] := + Block[{ ex, tmp, res, holdDOT, freePart, diracPart, holdPlus, diracList, diracListEval, repRule, + null1, null2}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex, DiracGamma], + Return[ex] + ]; + + ex = (ex/. Plus -> holdPlus); + diracList = (Cases[ex+null1+null2,holdPlus[z__]/; !FreeQ[{z},DiracGamma], Infinity])//DeleteDuplicates//Sort; + + diracListEval = diracList /. p_holdPlus :> holdPlus@@Sort[List@@p] //. { + holdPlus[a___, n1_. DiracGamma[Momentum[x_,dim_:4],dim_:4], n2_. DiracGamma[Momentum[y_, dim_:4], dim_:4], b___]/;(NumberQ[n1] && NumberQ[n2]) :> + holdPlus[a, DiracGamma[Momentum[n1 x + n2 y, dim], dim], b], + holdPlus[a___, n1_. DiracGamma[Momentum[x_,dim_:4],dim_:4], n2_. DiracGamma[Momentum[x_, dim_:4], dim_:4], b___]/;(NumberQ[n1] && NumberQ[n2]) :> + holdPlus[a, (n1+n2)DiracGamma[Momentum[x, dim], dim], b], + + holdPlus[a___, n1_. DiracGamma[CartesianMomentum[x_,dim1_:3],dim2_:4], n2_. DiracGamma[CartesianMomentum[y_, dim1_:3], dim2_:4], b___]/;(NumberQ[n1] && NumberQ[n2]) :> + holdPlus[a, DiracGamma[CartesianMomentum[n1 x + n2 y, dim1], dim2], b], + + holdPlus[a___, n1_. DiracGamma[CartesianMomentum[x_,dim1_:3],dim2_:4], n2_. DiracGamma[CartesianMomentum[x_, dim1_:3], dim2_:4], b___]/;(NumberQ[n1] && NumberQ[n2]) :> + holdPlus[a, (n1+n2)DiracGamma[CartesianMomentum[x, dim1], dim2], b] + + + } /. holdPlus -> Plus; + + repRule = Thread[Rule[diracList,diracListEval]]; + + res = ex /. Dispatch[repRule] /. holdPlus -> Plus; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + FCPrint[1,"DiracGammaCombine.m loaded"]; End[] diff --git a/FeynCalc/Dirac/DiracGammaExpand.m b/FeynCalc/Dirac/DiracGammaExpand.m index 5123836f2..12da60a48 100644 --- a/FeynCalc/Dirac/DiracGammaExpand.m +++ b/FeynCalc/Dirac/DiracGammaExpand.m @@ -2,13 +2,13 @@ (* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Title: DiracGamma *) +(* :Title: DiracGammaExpand *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Expands Feynman slashes *) @@ -20,7 +20,7 @@ exp into (DiracGamma[Momentum[a]] + DiracGamma[Momentum[b]] + ...)."; DiracGammaExpand::fail = -"Something went while expanding momenta contracted with Dirac matrices. +"Something went wrong while expanding momenta contracted with Dirac matrices. Evaluation aborted! " (* ------------------------------------------------------------------------ *) @@ -31,34 +31,29 @@ Begin["`DiracGammaExpand`Private`"] Options[DiracGammaExpand] = { + DiracSigmaExpand -> True, + FCE -> False, FCI -> False, Momentum -> All }; DiracGammaExpand[expr_, OptionsPattern[]] := - Block[{x,null1,null2, uniqList, solsList, repRule, momList,gaev,gaevlin,rud}, - - gaev[xx_,di_:4] := - gaevlin[Expand[xx//MomentumExpand, Momentum], di]; - - gaevlin[xx_Plus, di_:4] := - Map[gaevlin[#, di]&, xx]; + Block[{ex, null1, null2, uniqList, solsList, repRule, momList, ruleDelayed, res}, momList = OptionValue[Momentum]; - If[ !OptionValue[FCI], - x = FCI[expr], - x = expr + ex = FCI[expr], + ex = expr ]; (* Nothing to do... *) - If[ FreeQ[x,DiracGamma], - Return[x] + If[ FreeQ[ex,DiracGamma], + Return[ex] ]; (* List of all the unique Feynman slashes *) - uniqList = Cases[x+null1+null2, DiracGamma[arg_ /; ! FreeQ[{arg}, Momentum],_:4], Infinity]//Union; + uniqList = Cases[ex+null1+null2, DiracGamma[arg_ /; ! FreeQ2[{arg}, {Momentum,CartesianMomentum}],___], Infinity]//DeleteDuplicates//Sort; (* If the user specified to perform expansion only for some special slashed momenta, let's do it *) @@ -67,7 +62,7 @@ ]; (* Final replacement rule *) - repRule = Thread[rud[uniqList, uniqList/.DiracGamma -> gaev /. gaevlin -> DiracGamma]] /. rud->RuleDelayed; + repRule = Thread[ruleDelayed[uniqList, uniqList /.DiracGamma -> gaev /. gaevlin -> DiracGamma]] /. ruleDelayed->RuleDelayed; (* Simple cross check *) If[ !FreeQ2[repRule,{gaev,gaevlin}], @@ -75,9 +70,25 @@ Abort[] ]; - x /. Dispatch[repRule] + res = ex /. Dispatch[repRule]; + + If[ OptionValue[DiracSigmaExpand], + res = DiracSigmaExpand[res, FCI->True, DiracGammaExpand->False, Momentum -> momList] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res ]; +gaev[xx_,di_:4] := + gaevlin[Expand[MomentumExpand[xx], Momentum], di]; + +gaevlin[xx_Plus, di_:4] := + Map[gaevlin[#, di]&, xx]; + FCPrint[1,"DiracGammaExpand.m loaded."]; End[] diff --git a/FeynCalc/Dirac/DiracOrder.m b/FeynCalc/Dirac/DiracOrder.m index b8ddd6ba9..5a16c52fa 100644 --- a/FeynCalc/Dirac/DiracOrder.m +++ b/FeynCalc/Dirac/DiracOrder.m @@ -1,13 +1,32 @@ -(* ------------------------------------------------------------------------ *) +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: DiracOrder *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* :Summary: *) +(* :Summary: Lexicographic ordering of Dirac matrices *) (* ------------------------------------------------------------------------ *) DiracOrder::usage = -"DiracOrder[expr] orders the Dirac matrices in expr alphabetically. \ -DiracOrder[expr, orderlist] orders the Dirac matrices in expr according \ -to orderlist."; +"DiracOrder[exp] orders the Dirac matrices in exp lexicographically. \ +DiracOrder[exp, orderlist] orders the Dirac matrices in exp according \ +to orderlist.\n +DiracOrder is also an option of DiracSimplify and some other functions dealing \ +with Dirac algebra. If set to True, the function DiracOrder will be applied to \ +the intermediate result to reorder the Dirac matrices lexicographically. +"; + +DiracOrder::failmsg = +"Error! DiracOrder has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" (* ------------------------------------------------------------------------ *) @@ -16,59 +35,187 @@ Begin["`DiracOrder`Private`"]; -dotLin[z_] := - DotSimplify[z, Expanding -> False]; - -dicomm[a___,DiracGamma[vl_[y__],di___], - DiracGamma[lv_[z__],dim___],b___] := - MemSet[dicomm[a, DiracGamma[vl[y], di], DiracGamma[lv[z], dim], b], - ((-DiracTrick[a,DiracGamma[lv[z],dim], DiracGamma[vl[y],di],b] + - ((2 PairContract[vl[y],lv[z]] DiracTrick[a,b])/.PairContract->Pair) - )/.PairContract->Pair)]/;!OrderedQ[{lv[y],vl[z]}]; - -dessav[x__] := - MemSet[dessav[x], DiracTrick[x]]; - -diraccanonical[ x_,y__ ] := - diraccanonical[x.y]; - -diraccanonical[x_] := - MemSet[diraccanonical[x], - Block[ {diraccanres}, (*diraccanonicaldef*) - diraccanres = x //. DOT -> dicomm /. dicomm -> DOT /. - DOT-> dessav /. DiracTrick -> DOT; - diraccanres = Expand[dotLin[ diraccanres ], DiracGamma] /. - Pair -> PairContract /. PairContract->Pair; - diraccanres - ] - ]; +doVerbose::usage=""; +holdDOT::usage=""; +tmp::usage=""; + +Options[DiracOrder] = { + DiracGammaCombine -> False, + DiracTrick -> True, + FCDiracIsolate -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCVerbose -> False, + MaxIterations -> Infinity +}; + +DiracOrder[expr_, (opts:OptionsPattern[])/;opts=!={}] := + DiracOrder[expr, {}, opts]; + +DiracOrder[expr_, orderList_List/; (!OptionQ[orderList] || orderList==={}), OptionsPattern[]]:= + Block[{ex,res,dsHead,dsPart,freePart,null1,null2,diracObjects,tmp, maxIterations, diracObjectsEval, repRule,time}, + + maxIterations = OptionValue[MaxIterations]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ2[ex,DiracHeadsList], + Return[ex] + ]; + + If[ OptionValue[FCVerbose]===False, + doVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + doVerbose=OptionValue[FCVerbose] + ]; + ]; -DiracOrder[x__] := - diracord@@FCI[{x}]; - -diracord[x_] := - FixedPoint[diraccanonical, x, 42]; -diracord[x_,y___,z_] := - FixedPoint[diraccanonical, DOT[x,y,z], 42]/;Head[z]=!=List; - -diracord[x_,y__,ord_List] := - diracord[DOT[x,y],ord]; - -diracord[x_,ord_List] := - MemSet[diracord[x,ord], - Block[ {diracordrev = Reverse[ord], diracordz, diracordres = x,diracordi}, - Do[ diracordz = diracordrev[[diracordi]]; - diracordres = diracordres//. - {_[a___,DiracGamma[vl_[y__],di___], - DiracGamma[lv_[diracordz0_,dime___],dim___],b___] :> - ((-DiracTrick[a,DiracGamma[lv[diracordz0,dime],dim], - DiracGamma[vl[y],di],b]+ - (2 PairContract[vl[y],lv[diracordz0,dime]] DiracTrick[a,b] )/.PairContract->Pair))/; - !FreeQ[lv[diracordz0, dime], diracordz]} /. DOT -> DiracTrick /. DiracTrick -> DOT, - {diracordi,1,Length[ord]} + FCPrint[1, "DiracOrder. Entering.", FCDoControl->doVerbose]; + FCPrint[3, "DiracOrder: Entering with ", ex, FCDoControl->doVerbose]; + + If[ OptionValue[FCDiracIsolate], + (* This is the normal mode which works well both for large and small expressions *) + FCPrint[1, "DiracOrder: Normal mode.", FCDoControl->doVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "DiracOrder: Extracting Dirac objects.", FCDoControl->doVerbose]; + ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, DotSimplify->True, DiracChain->True, + DiracGammaCombine->OptionValue[DiracGammaCombine], FCJoinDOTs->OptionValue[FCJoinDOTs]]; + + + {freePart,dsPart} = FCSplit[ex,{dsHead}]; + FCPrint[3,"DiracOrder: dsPart: ",dsPart , FCDoControl->doVerbose]; + FCPrint[3,"DiracOrder: freePart: ",freePart , FCDoControl->doVerbose]; + + diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//DeleteDuplicates//Sort; + FCPrint[1, "DiracOrder: Done extracting Dirac objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->doVerbose]; + + time=AbsoluteTime[]; + If[orderList=!={}, + FCPrint[1, "DiracOrder: Ordering according to: ", orderList, FCDoControl->doVerbose]; + diracObjectsEval = Map[diracOrderCustom[#,orderList]&, (diracObjects/. DOT -> holdDOT/.dsHead->Identity)]; + FCPrint[1, "DiracOrder: Ordering done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->doVerbose], + + FCPrint[1, "DiracOrder. Using lexicographic ordering.", FCDoControl->doVerbose]; + diracObjectsEval = Map[diracOrderLex[#,maxIterations]&, (diracObjects/. DOT -> holdDOT/.dsHead->Identity)]; + FCPrint[1, "DiracOrder: Ordering done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->doVerbose] + ]; + + time=AbsoluteTime[]; + FCPrint[1, "DiracOrder: Inserting Dirac objects back.", FCDoControl->doVerbose]; + + diracObjectsEval = diracObjectsEval /. holdDOT[]->1 /.holdDOT->DOT /. PairContract -> Pair; + If[ !FreeQ[diracObjectsEval,CartesianPair], + diracObjectsEval = diracObjectsEval/. CartesianPair->CartesianPairContract /. CartesianPairContract->CartesianPair ]; - (Expand[dotLin[diracordres], DiracGamma])/.Pair->PairContract/.PairContract->Pair - ] + + repRule = Thread[Rule[diracObjects, diracObjectsEval]]; + FCPrint[3,"DiracOrder: repRule: ",repRule , FCDoControl->doVerbose]; + tmp = freePart + (dsPart/. Dispatch[repRule]); + FCPrint[1, "DiracOrder: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->doVerbose]; + FCPrint[3,"DiracOrder: Intermediate result: ", tmp, FCDoControl->doVerbose], + + (* This is the fast mode for standalone Dirac chains *) + FCPrint[1, "DiracOrder: Fast mode.", FCDoControl->doVerbose]; + time=AbsoluteTime[]; + tmp = ex /. DOT -> holdDOT; + + If[orderList=!={}, + FCPrint[1, "DiracOrder: Ordering according to: ", orderList, FCDoControl->doVerbose]; + tmp = diracOrderCustom[tmp, orderList]; + FCPrint[1, "DiracOrder: Ordering done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->doVerbose], + + FCPrint[1, "DiracOrder. Using lexicographic ordering.", FCDoControl->doVerbose]; + tmp = diracOrderLex[tmp, maxIterations]; + FCPrint[1, "DiracOrder: Ordering done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->doVerbose] + + ]; + tmp = tmp/. holdDOT[]->1 /.holdDOT->DOT /. PairContract -> Pair; + If[ !FreeQ[diracObjectsEval,CartesianPair], + diracObjectsEval = diracObjectsEval/. CartesianPair->CartesianPairContract /. CartesianPairContract->CartesianPair + ]; + + ]; + + + res = tmp; + + (* If orderingList contains an ExplicitLorentzIndex[0], do not apply DiracTrick, since it would mess up the ordering! *) + If[ OptionValue[DiracTrick] && FreeQ[orderList,ExplicitLorentzIndex[0]], + time=AbsoluteTime[]; + FCPrint[1, "DiracOrder: Applying DiracTrick.", FCDoControl->doVerbose]; + res = DiracTrick[res, FCI->True]; + FCPrint[1, "DiracOrder: Done applying DiracTrick,timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->doVerbose] + ]; + + FCPrint[1, "DiracOrder: Leaving.", FCDoControl->doVerbose]; + FCPrint[3, "DiracOrder: Leaving with ", res, FCDoControl->doVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + +diracOrderLex[x_, maxIterations_]:= + FixedPoint[(# /. { + holdDOT[a___,DiracGamma[(h1:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[ar1__], dim1_:4],DiracGamma[(h2:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[ar2__], dim2_:4],b___]/; + !OrderedQ[{h1[First[{ar1}],dim1],h2[First[{ar2}],dim2]}] && h1[First[{ar1}],dim1]=!=h2[First[{ar2}],dim2] :> + -holdDOT[a, DiracGamma[h2[ar2],dim2], DiracGamma[h1[ar1],dim1] ,b] + + 2 PairContract[h1[ar1],h2[ar2]] holdDOT[a,b], + + (* The g^0 matrices are moved to the very right *) + holdDOT[a___,DiracGamma[ExplicitLorentzIndex[0]],DiracGamma[(h2:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[ar2__], dim2_:4],b___] :> + -holdDOT[a, DiracGamma[h2[ar2],dim2], DiracGamma[ExplicitLorentzIndex[0]] ,b] + + 2 PairContract[ExplicitLorentzIndex[0],h2[ar2]] holdDOT[a,b], + + holdDOT[a___,DiracGamma[(h:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum|ExplicitLorentzIndex)[ar___], dim_:4], + DiracGamma[(h:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum|ExplicitLorentzIndex)[ar___], dim_:4],b___] :> + holdDOT[a,b] DiracTrick[DOT[DiracGamma[h[ar],dim].DiracGamma[h[ar],dim]],FCI->True,FCDiracIsolate->False] + + + })&, x, maxIterations] + +customOrdering[x_, currentElement_]:= + x //. { + holdDOT[a___,DiracGamma[(h1:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[ar1__], dim1_:4], + DiracGamma[(h2:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[ar2__], dim2_:4],b___]/; + !FreeQ[h2[First[{ar2}],dim2],currentElement] && h1[First[{ar1}],dim1]=!=h2[First[{ar2}],dim2] :> + -holdDOT[a, DiracGamma[h2[ar2],dim2], DiracGamma[h1[ar1],dim1] ,b] + + 2 PairContract[h1[ar1],h2[ar2]] holdDOT[a,b], + + holdDOT[a___,DiracGamma[(h1:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[ar1__], dim1_:4],DiracGamma[ExplicitLorentzIndex[0]],b___]/; + !FreeQ[ExplicitLorentzIndex[0],currentElement] && h1[First[{ar1}],dim1]=!=ExplicitLorentzIndex[0] :> + -holdDOT[a, DiracGamma[ExplicitLorentzIndex[0]], DiracGamma[h1[ar1],dim1] ,b] + + 2 PairContract[h1[ar1],ExplicitLorentzIndex[0]] holdDOT[a,b], + + holdDOT[a___,DiracGamma[ExplicitLorentzIndex[0]],DiracGamma[(h2:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[ar2__], dim2_:4],b___]/; + !FreeQ[h2[First[{ar2}],dim2],currentElement] && ExplicitLorentzIndex[0]=!=h2[First[{ar2}],dim2] :> + -holdDOT[a, DiracGamma[h2[ar2],dim2], DiracGamma[ExplicitLorentzIndex[0]] ,b] + + 2 PairContract[ExplicitLorentzIndex[0],h2[ar2]] holdDOT[a,b], + + + holdDOT[a___,DiracGamma[(h:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum|ExplicitLorentzIndex)[ar___], dim_:4], + DiracGamma[(h:LorentzIndex|Momentum|CartesianIndex|CartesianMomentum|ExplicitLorentzIndex)[ar___], dim_:4],b___] :> + holdDOT[a,b] DiracTrick[DOT[DiracGamma[h[ar],dim].DiracGamma[h[ar],dim]],FCI->True,FCDiracIsolate->False] +}; + + + +diracOrderCustom[x_, orderList_List]:= + ( + tmp=x; + Scan[(tmp = customOrdering[tmp,#])&, Reverse[orderList]]; + tmp + ); + + + + FCPrint[1,"DiracOrder.m loaded."]; End[] diff --git a/FeynCalc/Dirac/DiracReduce.m b/FeynCalc/Dirac/DiracReduce.m index 766cfd3ea..91493877e 100644 --- a/FeynCalc/Dirac/DiracReduce.m +++ b/FeynCalc/Dirac/DiracReduce.m @@ -1,14 +1,17 @@ +(* ::Package:: *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Title: DiracReduce *) +(* :Title: DiracReduce *) -(* :Author: Rolf Mertig *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* ------------------------------------------------------------------------ *) -(* :History: Last changed July 19th 2000 *) -(* ------------------------------------------------------------------------ *) - -(* :Summary: contraction and simplification rules for gamma matrices *) +(* :Summary: SPVAT decomposition of Dirac matrix chains *) (* ------------------------------------------------------------------------ *) @@ -18,9 +21,9 @@ to the standard basis (S,P,V,A,T) using the Chisholm identity (see Chisholm). \ In the result the basic Dirac structures are wrapped with a head \ DiracBasis. I.e.: S corresponds to DiracBasis[1], \ -P : DiracBasis[DiracMatrix[5]], \ -V : DiracBasis[DiracMatrix[mu]], A: DiracBasis[DiracMatrix[mu, 5]], \ -T: DiracBasis[DiracSigma[DiracMatrix[mu, nu]]]. \ +P : DiracBasis[GA[5]], \ +V : DiracBasis[GA[mu]], A: DiracBasis[GA[mu, 5]], \ +T: DiracBasis[DiracSigma[GA[mu, nu]]]. \ By default DiracBasis is substituted to Identity. \n Notice that the result of DiracReduce is given in the FeynCalcExternal-way, \ i.e., evtl. you may have to use FeynCalcInternal on result."; @@ -32,63 +35,85 @@ to the standard basis (S,P,V,A,T) using the Chisholm identity (see Chisholm). \ Begin["`DiracReduce`Private`"] +drVerbose::usage=""; + Options[DiracReduce] = { - DiracSimplify -> True, - Factoring -> False, - FinalSubstitutions -> {DiracBasis -> Identity} + Contract -> True, + DiracGammaCombine -> True, + DiracSimplify -> False, + DotSimplify -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> False, + FinalSubstitutions -> {DiracBasis -> Identity} }; -DiracReduce[x_, {ops___Rule}] := - DiracReduce[x, ops]; - -DiracReduce[x_, ops___Rule] := - Block[ {temp = FCI[x], spart, n1, n2, ddb, res, finsub,finsub1,factoring,diracSimplify}, - finsub1 = - If[ Length[{ops}] === 0, - {}, - If[ !FreeQ[{ops}, FinalSubstitutions], - FinalSubstitutions /. {ops}, - Select[Flatten[{ops}], FreeQ[#,Factoring]&] - ] + +DiracReduce[expr_List, opts:OptionsPattern[]] := + Map[DiracReduce[#,opts]&,expr]; + +DiracReduce[expr_, OptionsPattern[]] := + Block[ {ex, tmp, spart, null1, null2, res, finsub, factoring,diracSimplify, li1, li2}, + + finsub = OptionValue[FinalSubstitutions]; + factoring = OptionValue[Factoring]; + diracSimplify = OptionValue[DiracSimplify]; + + If[ OptionValue[FCVerbose]===False, + drVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + drVerbose=OptionValue[FCVerbose] ]; - finsub = Join[finsub1, FinalSubstitutions /. Options[DiracReduce]]; - factoring = Factoring /. {ops} /. Options[DiracReduce]; - diracSimplify = DiracSimplify /. {ops} /. Options[DiracReduce]; + ]; - (* do first usual DiracSimplify *) - If[ diracSimplify, - temp = DiracSimplify[temp, DiracSubstitute67 -> True, DiracSigmaExplicit -> False]; - FCPrint[2,"DiracSimplify done"]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + FCPrint[1, "DiracReduce. Entering.", FCDoControl->drVerbose]; + FCPrint[3, "DiracReduce: Entering with ", ex, FCDoControl->drVerbose]; + + If[ FreeQ2[ex,DiracHeadsList], + Return[ex] + ]; + + tmp = ex /. {DiracGamma[6] :> (1/2 + DiracGamma[5]/2), DiracGamma[7] :> (1/2 - DiracGamma[5]/2)}; + + If[ OptionValue[DiracGammaCombine], + tmp = DiracGammaCombine[tmp,FCI->True] ]; + + If[ OptionValue[DotSimplify], + tmp = DotSimplify[tmp,FCI->True] + ]; + (* Chisholm identity recursively *) - temp = Chisholm[temp,FCI->True, DiracSimplify -> diracSimplify]//DiracOrder; - FCPrint[2,"Chisholm done"]; - temp = Expand[temp, DiracGamma]; - (* introduce DiracSigma *) - (* use gamma[m,n, 5] = 1/2 ( eps[m,n,r,s] sig[r,s] + 2 g[m,n] gamma[5] ) - *) - temp = temp /. DOT[DiracGamma[a_[xx_]], DiracGamma[b_[yy_]], DiracGamma[5]] :> - (un1 = Unique[mU1]; - un2 = Unique[mU2]; - Expand[1/2 ( - $LeviCivitaSign Eps[a[xx], b[yy], LorentzIndex[un1], - LorentzIndex[un2]](I/2) (FCI[ DiracMatrix[un1, un2] - DiracMatrix[un2, un1]]) + - 2 Pair[a[xx], b[yy]] DiracGamma[5])]); - (* for the renaming of dummy indices *) - temp = FCRenameDummyIndices[Contract[temp, Rename-> True]]; - (* XXX *) - temp = temp /. DOT[DiracGamma[a_[xx_]], DiracGamma[b_[yy_]]] :> - ( -I DiracSigma[DiracGamma[a[xx]], DiracGamma[b[yy]]]+Pair[b[yy], a[xx]]); + tmp = Chisholm[tmp,FCI->True, DiracSimplify -> False]; + FCPrint[3, "DiracReduce: After Chisholm: ", tmp, FCDoControl->drVerbose]; + + tmp = DiracOrder[tmp, FCI->True]; + FCPrint[3, "DiracReduce: After DiracOrder: ", tmp, FCDoControl->drVerbose]; + + tmp = Chisholm[tmp,FCI->True,DiracSimplify->False,Mode->2]; + FCPrint[3, "DiracReduce: After Chisholm: ", tmp, FCDoControl->drVerbose]; + + tmp = tmp /. DOT[DiracGamma[a_[xx_]], DiracGamma[b_[yy_]]] :> (-I DiracSigma[DiracGamma[a[xx]], DiracGamma[b[yy]]]+Pair[b[yy], a[xx]]); + FCPrint[3, "DiracReduce: After introducing DiracSigma: ", tmp, FCDoControl->drVerbose]; If[ diracSimplify, - temp = Contract[DiracSimplify[temp, DiracSigmaExplicit -> False]], - temp = Contract[temp] + tmp = DiracSimplify[tmp, DiracSigmaExplicit -> False, FCI->True]; + FCPrint[3, "DiracReduce: After DiracSimplify: ", tmp, FCDoControl->drVerbose] ]; - temp = Collect2[temp, DiracGamma, Factoring -> factoring]; + tmp = Collect2[tmp, DiracGamma, Factoring -> factoring]; FCPrint[2,"collecting done"]; (* get the S - part *) - spart = Select[temp + n1 + n2, FreeQ[#, DiracGamma]&] /. {n1 :> 0, n2 :> 0}; - temp = temp - spart; + spart = SelectFree[tmp + null1 + null2, DiracGamma] /. null1|null2 :> 0; + tmp = tmp - spart; + If[ factoring === False, spart = Expand[spart] DiracBasis[1], If[ factoring === True, @@ -96,15 +121,26 @@ to the standard basis (S,P,V,A,T) using the Chisholm identity (see Chisholm). \ spart = factoring[spart] DiracBasis[1] ] ]; - ddb[y__] := - DiracBasis[DOT[y]]; - res = spart + (temp /. DiracSigma[a__] :> DiracBasis[FCE[DiracSigma[a]]] /. + + + res = spart + (tmp /. DiracSigma[a__] :> DiracBasis[DiracSigma[a]] /. DOT[DiracGamma[a_], DiracGamma[5]] :> - DiracBasis[FCE[DOT[DiracGamma[a], DiracGamma[5]]]] /. - DiracGamma[a_] :> DiracBasis[FCE[DiracGamma[a]]]); - res = res /. finsub /. finsub; - res = FCE[res]; + DiracBasis[DOT[DiracGamma[a], DiracGamma[5]]] /. + DiracGamma[a_] :> DiracBasis[DiracGamma[a]]); res = res /. finsub /. finsub; + + If[ OptionValue[DotSimplify], + res = DotSimplify[res,FCI->True] + ]; + + If[ OptionValue[Contract], + res = Contract[res,FCI->True] + ]; + + If[OptionValue[FCE], + res = FCE[res] + ]; + res ]; diff --git a/FeynCalc/Dirac/DiracSigmaExpand.m b/FeynCalc/Dirac/DiracSigmaExpand.m new file mode 100644 index 000000000..6b8a1558f --- /dev/null +++ b/FeynCalc/Dirac/DiracSigmaExpand.m @@ -0,0 +1,85 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: DiracSigma *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Expands Feynman slashes inside DiracSigma *) + +(* ------------------------------------------------------------------------ *) + +DiracSigmaExpand::usage = +"DiracSigmaExpand[exp] expands all DiracSigma[DiracGamma[Momentum[a]]+ \ +DiracGamma[Momentum[b]] + ..., ...] into (DiracSigma[DiracGamma[Momentum[a]],\ +...] + DiracSigma[DiracGamma[Momentum[b]], ...] + ...)."; + +DiracSigmaExpand::fail = +"Something went wrong while expanding DiracSigma's. Evaluation aborted! " + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`DiracSigmaExpand`Private`"] + +Options[DiracSigmaExpand] = { + DiracGammaExpand -> False, + FCE -> False, + FCI -> False, + Momentum -> All +}; + +DiracSigmaExpand[expr_, OptionsPattern[]] := + Block[{ex,null1,null2, uniqList, repRule, momList,rud, uniqListEval,res}, + + momList = OptionValue[Momentum]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + (* Nothing to do... *) + If[ FreeQ[ex,DiracSigma], + Return[ex] + ]; + + (* List of all the unique Feynman slashes *) + uniqList = Cases[ex+null1+null2, DiracSigma[arg__ /; ! FreeQ2[{arg}, {Momentum,CartesianMomentum}]], Infinity]//DeleteDuplicates//Sort; + + (* If the user specified to perform expansion only for some + special slashed momenta, let's do it *) + If[ momList=!=All && Head[momList]===List, + uniqList = Select[uniqList, !FreeQ2[#, momList]&] + ]; + + If[ OptionValue[DiracGammaExpand], + uniqListEval = DiracGammaExpand[uniqList,FCI->True, Momentum->momList, DiracSigmaExpand->False], + uniqListEval = uniqList; + ]; + + uniqListEval = uniqListEval /. z_DiracSigma :> Distribute[z]; + + (* Final replacement rule *) + repRule = Thread[rud[uniqList, uniqListEval]] /. rud->RuleDelayed; + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + +FCPrint[1,"DiracSigmaExpand.m loaded."]; +End[] diff --git a/FeynCalc/Dirac/DiracSigmaExplicit.m b/FeynCalc/Dirac/DiracSigmaExplicit.m index 6d60b026f..c1abe4045 100644 --- a/FeynCalc/Dirac/DiracSigmaExplicit.m +++ b/FeynCalc/Dirac/DiracSigmaExplicit.m @@ -1,14 +1,28 @@ -(* ------------------------------------------------------------------------ *) -(* ------------------------------------------------------------------------ *) +(* ::Package:: *) + + +(* :Title: DiracSigmaExplicit *) -(* :Summary: substitute DiracSigma in terms of DiracGamma's *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Substitute DiracSigma in terms of DiracGamma's *) (* ------------------------------------------------------------------------ *) DiracSigmaExplicit::usage = "DiracSigmaExplicit[exp] inserts in exp the definition of \ -DiracSigma. DiracSigmaExplict is also an option of \ -DiracSimplify."; +DiracSigma. \n +DiracSigmaExplict is also an option of various FeynCalc functions \ +that handle the Dirac algebra."; + +DiracSigmaExplicit::failmsg = +"Error! DiracSigmaExplicit has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" (* ------------------------------------------------------------------------ *) @@ -17,19 +31,85 @@ Begin["`DiracSigmaExplicit`Private`"]; -dirsigex[a_DiracGamma, b_DiracGamma] := - dirsigex[a,b] = I/2 (DOT[a, b] - DOT[b, a]); +dsiVerbose::usage=""; + +Options[DiracSigmaExplicit] = { + FCE -> False, + FCI -> False, + FCVerbose -> False +}; + +DiracSigmaExplicit[expr_, OptionsPattern[]] := + Block[{ex, res, holdDOT, tmp}, + + If [OptionValue[FCVerbose]===False, + dsiVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + dsiVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1,"DiracSigmaExplicit: Entering. ", FCDoControl->dsiVerbose]; + FCPrint[3,"DiracSigmaExplicit: Entering DiracSigmaExplicit with: ", ex, FCDoControl->dsiVerbose]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex, DiracSigma], + Return[ex] + ]; + + tmp = ex /. DOT->holdDOT; + + tmp = tmp //. { + holdDOT[x___, c_. DiracSigma[DiracGamma[ExplicitLorentzIndex[0]], (a: DiracGamma[(_CartesianIndex| _CartesianMomentum), ___])],y___]/; NonCommFreeQ[c] :> + I c (holdDOT[x,DiracGamma[ExplicitLorentzIndex[0]],a,y]), + holdDOT[x___, c_. DiracSigma[(a: DiracGamma[(_CartesianIndex| _CartesianMomentum), ___]),DiracGamma[ExplicitLorentzIndex[0]]],y___]/; NonCommFreeQ[c] :> + -I c (holdDOT[x,DiracGamma[ExplicitLorentzIndex[0]], a,y]), + holdDOT[x___, c_. DiracSigma[(a: DiracGamma[(_CartesianIndex| _CartesianMomentum), ___]), (b: DiracGamma[(_CartesianIndex| _CartesianMomentum), ___])],y___]/; NonCommFreeQ[c] :> + I c (holdDOT[x,a,b,y] + CartesianPair[First[a],First[b]] holdDOT[x,y]) + + }; + + FCPrint[3,"DiracSigmaExplicit: After applying the 1st set of rules: ", tmp, FCDoControl->dsiVerbose]; + + tmp = tmp //. { + DiracSigma[DiracGamma[ExplicitLorentzIndex[0]], (a: DiracGamma[(_CartesianIndex| _CartesianMomentum), ___])] :> I holdDOT[DiracGamma[ExplicitLorentzIndex[0]], a], + DiracSigma[(a: DiracGamma[(_CartesianIndex| _CartesianMomentum), ___]),DiracGamma[ExplicitLorentzIndex[0]]] :> - I holdDOT[DiracGamma[ExplicitLorentzIndex[0]], a], + DiracSigma[(a: DiracGamma[(_CartesianIndex| _CartesianMomentum), ___]), (b: DiracGamma[(_CartesianIndex| _CartesianMomentum), ___])] :> I (holdDOT[a,b] + CartesianPair[First[a],First[b]]) + }; + + FCPrint[3,"DiracSigmaExplicit: After applying the 2nd set of rules: ", tmp, FCDoControl->dsiVerbose]; + + tmp = tmp //. { + holdDOT[x___, c_. DiracSigma[a_DiracGamma,b_DiracGamma],y___]/; NonCommFreeQ[c] :> I/2 c (holdDOT[x,a,b,y] - holdDOT[x,b,a,y]) + }; + + + FCPrint[3,"DiracSigmaExplicit: After applying the 3rd set of rules: ", tmp, FCDoControl->dsiVerbose]; + + tmp = tmp //. { + DiracSigma[a_DiracGamma,b_DiracGamma]:> I/2 (DOT[a, b] - DOT[b, a]) + } /. holdDOT->DOT; + + FCPrint[3,"DiracSigmaExplicit: After applying the final set of rules: ", tmp, FCDoControl->dsiVerbose]; + + res = tmp; + + If[ !FreeQ[res,DiracSigma], + Message[DiracSigmaExplicit::failmsg,"Failed to eliminate all occurences of DiracSigma."]; + Abort[] + ]; -dirsigex[DiracMatrix[a_, b_]] := - dirsigex[DiracMatrix[a,b]] = - I/2 (DiracMatrix[a, b] - DiracMatrix[b, a]); + If[ OptionValue[FCE], + res = FCE[res] + ]; -dirsigex[DiracSlash[a_, b_]] := - dirsigex[DiracSlash[a,b]] = - I/2 (DiracSlash[a, b] - DiracSlash[b, a]); + res -DiracSigmaExplicit[x_] := - FCI[x]/. DiracSigma -> dirsigex; + ]; FCPrint[1,"DiracSigmaExplicit.m loaded"]; End[] diff --git a/FeynCalc/Dirac/DiracSimplify.m b/FeynCalc/Dirac/DiracSimplify.m index 7f9b556ac..a0576e769 100755 --- a/FeynCalc/Dirac/DiracSimplify.m +++ b/FeynCalc/Dirac/DiracSimplify.m @@ -1,82 +1,32 @@ +(* ::Package:: *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Title: DiracSimplify *) +(* :Title: DiracSimplify *) -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 20 December '98 at 23:00 *) -(* ------------------------------------------------------------------------ *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* :Summary: like DiracTrick, but including non-commutative expansion *) +(* :Summary: Like DiracTrick, but including non-commutative expansions + and simplifications of spinor chains *) (* ------------------------------------------------------------------------ *) -(* NonCommQ replaced with NonCommFreeQ everywhere due to change (fix) of - definitions of these functions. F.Orellana, 13/9-2002 *) - - -ChisholmSpinor::usage = -"ChisholmSpinor[x] uses the Chisholm identity on a DiraGamma between spinors. \ -As an optional second argument 1 or 2 may be \ -given, indicating that ChisholmSpinor should only act on the first \ -resp. second part of a product of spinor chains."; - -DiracCanonical::usage = -"DiracCanonical is an option for DiracSimplify. \ -If set to True DiracSimplify uses the function DiracOrder \ -internally."; - -InsideDiracTrace::usage = -"InsideDiracTrace is an option of DiracSimplify. \ -If set to True, DiracSimplify assumes to operate \ -inside a DiracTrace, i.e., products of an odd number \ -of Dirac matrices are discarded. Furthermore simple \ -traces are calculated (but divided by a factor 4, \ -i.e. : DiracSimplify[DiracMatrix[a,b], InsideDiracTrace->True] \ -yields ScalarProduct[a,b]) \n -Traces involving more than \ -four DiracGammas and DiracGamma[5] are not performed."; - DiracSimplify::usage = -"DiracSimplify[expr] simplifies products of Dirac matrices \ -in expr and expands non-commutative products. \ +"DiracSimplify[exp] simplifies products of Dirac matrices \ +and expands non-commutative products. \ Double Lorentz indices and four vectors are contracted. \ The Dirac equation is applied. \ -All DiracMatrix[5], DiracMatrix[6] and DiracMatrix[7] are moved to \ +All DiracGamma[5], DiracGamma[6] and DiracGamma[7] are moved to \ the right. The order of the Dirac matrices is not changed."; -$SpinorMinimal::usage = -"$SpinorMinimal is a global switch for an additional simplification \ -attempt in DiracSimplify for more than one Spinor-line. \ -The default is False, since otherwise it costs too much time."; - -DiracSimpCombine::usage = -"DiracSimpCombine is an option for DiracSimplify. If set to \ -True, sums of DiracGamma's will be merged as much as \ -possible in DiracGamma[ .. + .. + ]'s."; - -DiracSubstitute67::usage = -"DiracSubstitute67 is an option for DiracSimplify. If set to \ -True the chirality-projectors DiracGamma[6] and DiracGamma[7] are \ -substituted by their definitions."; - -SirlinRelations::usage = -"SirlinRelations is an option for DiracSimplify. If set to\ -True the spinor chains that contain Dirac matrices are simplified \ -using relations derived by Sirlin in Nuclear Physics B192 (1981) 93-99 \ -Contrary to the original paper, the sign of the Levi-Civita tensor is \ -choosen as epsilon^{0123} = 1 which is the standard choice in FeynCalc."; - -DiracSimplify::noncom = -"Wrong syntax! `1` contains Dirac or SU(N) matrices multiplied via \ -Times (commutative multiplication) instead of DOT (non-commutative multiplication). \ -Evaluation aborted!"; - -DiracSimplify2::usage = -"DiracSimplify2[exp] simplifies the Dirac structure but leaves \ -any DiracGamma[5] untouched. \ -DiracGamma[6] and DiracGamma[7] are inserted by their definitions."; +DiracSimplify::failmsg = +"Error! DiracSimplify encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" (* ------------------------------------------------------------------------ *) @@ -86,100 +36,103 @@ using relations derived by Sirlin in Nuclear Physics B192 (1981) 93-99 \ Begin["`DiracSimplify`Private`"] dsVerbose::usage=""; -insideDiracTrace::usage=""; - -DiracSimplify2[exp_] := - Block[ {nn,tt}, - If[ FreeQ[exp,DOT], - exp, - nn = DotSimplify[DiracGammaExpand[FeynCalcInternal[exp]] /. - DiracGamma[6] -> (1/2 + DiracGamma[5]/2) /. - DiracGamma[7] -> (1/2 - DiracGamma[5]/2)]; - If[ FreeQ[nn, DiracGamma[5]], - DiracSimplify[nn], - tt = Cases2[nn, DOT]; - nn/.(Table[tt[[ij]] -> DotSimplify[ - Contract[ tt[[ij]] //. - {doot[a__, DiracGamma[5], b__] :> - If[ FreeQ[{a}, DiracGamma[5]], - DiracSimplify[DOT[a]], - DiracSimplify2[DOT[b]] - ].DiracGamma[5]. - If[ FreeQ[{b}, DiracGamma[5] ], - DiracSimplify2[DOT[a]], - DiracSimplify[DOT[b]] - ] - }]], {ij,Length[tt]}]) - ] - ] - ]; +optInsideDiracTrace::usage=""; +optExpanding::usage=""; +optExpandScalarProduct::usage=""; +optDiracGammaCombine::usage=""; +optDiracSubstitute67::usage=""; +optDiracSubstitute5::usage=""; +optDiracSigmaExplicit::usage=""; +optDiracTraceEvaluate::usage=""; +optDiracEquation::usage=""; +optDiracOrder::usage=""; +optFactoring::usage=""; +optEpsContract::usage=""; +optContract::usage=""; +optToDiracGamma67::usage=""; Options[DiracSimplify] = { - DiracCanonical -> False, + Contract -> True, + DiracChain -> True, + DiracChainJoin -> True, DiracEquation -> True, + DiracGammaCombine -> False, + DiracOrder -> False, DiracSigmaExplicit -> True, - DiracSimpCombine -> False, + DiracSubstitute5 -> False, DiracSubstitute67 -> False, + DiracTrace -> True, + DiracTraceEvaluate -> True, + EpsContract -> True, + Expand2 -> True, + ExpandScalarProduct -> True, Expanding -> True, FCCheckSyntax -> False, FCDiracIsolate -> True, + FCE -> False, + FCI -> False, FCVerbose -> False, Factoring -> False, - FeynCalcInternal -> False, InsideDiracTrace -> False, - SirlinRelations -> True + LorentzIndexNames -> {}, + CartesianIndexNames -> {}, + SirlinSimplify -> True, + SpinorChainTrick -> True, + ToDiracGamma67 -> True }; +DiracSimplify[expr_List, opts:OptionsPattern[]] := + DiracSimplify[#, opts]&/@expr; -(*TODO: This syntax is really bad and should be blacklisted! *) -DiracSimplify[x_,y__, z___?OptionQ] := - DiracSimplify[DOT[x,y], z] /; FreeQ[{x,y}, Rule] && FreeQ[{x,y}, RuleDelayed]; - - -DiracSimplify[expr_, opts:OptionsPattern[]] := - Block[{ex,res,time, null1, null2, holdDOT, freePart, dsPart, diracObjects, - diracObjectsEval, repRule}, +DiracSimplify[expr_/;Head[expr]=!=List, OptionsPattern[]] := + Block[{ex,res,time, null1, null2, holdDOT, freePart=0, dsPart, diracObjects, + diracObjectsEval, repRule, tmp, tmpHead}, If [OptionValue[FCVerbose]===False, dsVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], dsVerbose=OptionValue[FCVerbose] ]; ]; + optContract = OptionValue[Contract]; + optDiracEquation = OptionValue[DiracEquation]; + optDiracGammaCombine = OptionValue[DiracGammaCombine]; + optDiracOrder = OptionValue[DiracOrder]; + optDiracSigmaExplicit = OptionValue[DiracSigmaExplicit]; + optDiracSubstitute5 = OptionValue[DiracSubstitute5]; + optDiracSubstitute67 = OptionValue[DiracSubstitute67]; + optDiracTraceEvaluate = OptionValue[DiracTraceEvaluate]; + optEpsContract = OptionValue[EpsContract]; + optExpandScalarProduct = OptionValue[ExpandScalarProduct]; + optExpanding = OptionValue[Expanding]; + optInsideDiracTrace = OptionValue[InsideDiracTrace]; + optToDiracGamma67 = OptionValue[ToDiracGamma67]; + + If[ OptionValue[Factoring] === Automatic, + optFactoring = + Function[x, If[ LeafCount[x] < 5000, + Factor[x], + x + ] + ], + optFactoring = OptionValue[Factoring] + ]; + FCPrint[1, "DiracSimplify: Entering.", FCDoControl->dsVerbose]; - FCPrint[3, "DiracSimplify: Entering with ", ex, FCDoControl->dsVerbose]; + FCPrint[3, "DiracSimplify: Entering with ", expr, FCDoControl->dsVerbose]; If[ OptionValue[FCI], ex = expr, ex = FCI[expr] ]; - If[ OptionValue[InsideDiracTrace], - insideDiracTrace = True, - insideDiracTrace = False - ]; - - If [OptionValue[FCCheckSyntax], + If[ OptionValue[FCCheckSyntax], time=AbsoluteTime[]; FCPrint[1, "DiracSimplify: Checking the syntax", FCDoControl->dsVerbose]; - - If[ !FreeQ2[DotExpand[Expand2[DiracSigmaExplicit[ex],{DiracGamma,Spinor,SUNT}]],{ - DiracGamma[a__]*DiracGamma[b__], - DOT[a:Except[_Spinor]...,DiracGamma[b__],c:Except[_Spinor]...]* - DOT[d:Except[_Spinor]...,DiracGamma[e__],f:Except[_Spinor]...], - DOT[a:Except[_Spinor]...,DiracGamma[b__],c:Except[_Spinor]...]*DiracGamma[d__], - SUNT[a__]*SUNT[b__], - DOT[a:Except[_Spinor]...,SUNT[b__],c:Except[_Spinor]...]*DOT[d:Except[_Spinor]...,SUNT[e__],f:Except[_Spinor]...], - DOT[a___,SUNT[b__],c___]*SUNT[d__] - }], - Block[{$MessagePrePrint}, - Message[DiracSimplify::noncom, ToString[expr,FormatType->InputForm]]]; - Abort[] - ]; - + FCCheckSyntax[ex,FCI->True]; FCPrint[1, "DiracSimplify: Checking the syntax done", FCDoControl->dsVerbose]; FCPrint[1,"DiracSimplify: Done checking the syntax, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose] ]; @@ -187,1295 +140,358 @@ using relations derived by Sirlin in Nuclear Physics B192 (1981) 93-99 \ If[ FreeQ2[ex,DiracHeadsList], Return[ex] ]; -(* + + (* Here we separately simplify each chain of Dirac matrices *) If[ OptionValue[FCDiracIsolate], (* This is the standard mode for calling DiracSimplify *) - + FCPrint[1,"DiracSimplify: Normal mode.", FCDoControl->dsVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "DiracSimplify: Extracting Dirac objects.", FCDoControl->dsVerbose]; (* First of all we need to extract all the Dirac structures in the input. *) - ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, DotSimplify->True, DiracGammaCombine->OptionValue[DiracSimpCombine],Lorentz->True]; + ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, DotSimplify->True, DiracGammaCombine->OptionValue[DiracGammaCombine], + DiracSigmaExplicit->OptionValue[DiracSigmaExplicit], LorentzIndex->True, CartesianIndex->True, + ToDiracGamma67->optToDiracGamma67, DiracChain->OptionValue[DiracChain]]; + + If[ !FreeQ[ex,DiracTrace] && !OptionValue[DiracTrace], + ex = ex /. dsHead[zz_]/; !FreeQ[zz,DiracTrace] :> zz + ]; {freePart,dsPart} = FCSplit[ex,{dsHead}]; FCPrint[3,"DiracSimplify: dsPart: ",dsPart , FCDoControl->dsVerbose]; FCPrint[3,"DiracSimplify: freePart: ",freePart , FCDoControl->dsVerbose]; + FCPrint[1, "DiracSimplify: Done extracting Dirac objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; - diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//Union; - FCPrint[3,"DiracSimplify: diracObjects: ",diracObjects , FCDoControl->dsVerbose]; - - time=AbsoluteTime[]; - FCPrint[1, "DiracSimplify: Applying diracTrickEval", FCDoControl->dsVerbose]; - diracObjectsEval = Map[(diracTrickEvalFast[#]/. diracTrickEvalFast->diracTrickEval)&, (diracObjects/.dsHead->Identity)]; - FCPrint[1,"DiracTrace: diracTrickEval done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; - - If[ !FreeQ2[diracObjectsEval,{diracTrickEvalFast,diracTrickEval}], - Message[DiracTrick::failmsg,"Evaluation of isolated objects failed."]; - Abort[] - ]; - - repRule = MapThread[Rule[#1,#2]&,{diracObjects,diracObjectsEval}]; - FCPrint[3,"DiracSimplify: repRule: ",repRule , FCDoControl->dsVerbose]; - res = freePart + ( dsPart/.repRule), - - (* This is a fast mode for input that is already isolated, e.g. for calling DiracTrick/@exprList - from internal functions *) - res = diracTrickEvalFast[ex] /. diracTrickEvalFast->diracTrickEval - ];*) + diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//Sort//DeleteDuplicates; + diracObjectsEval = diracObjects; + FCPrint[3,"DiracSimplify: diracObjects: ", diracObjects , FCDoControl->dsVerbose]; + If[ optDiracTraceEvaluate, + time=AbsoluteTime[]; + FCPrint[1, "DiracSimplify: Calculating Dirac traces.", FCDoControl->dsVerbose]; + diracObjectsEval = diracObjectsEval /. DiracTrace[zz_, opts:OptionsPattern[]] :> DiracTrace[zz, + DiracTraceEvaluate->True, Expand-> optExpandScalarProduct, opts]; + FCPrint[1, "DiracSimplify: Done calculating Dirac traces, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: diracObjects after calcuating Dirac traces: ", diracObjectsEval , FCDoControl->dsVerbose]; + diracObjectsEval - If[ !OptionValue[Expanding], - (* If Expanding is set to False, just use the Dirac equation and apply DotSimplify.*) - If[ OptionValue[DiracSigmaExplicit], - ex = DiracSigmaExplicit[ex] ]; - ex = dotLin[ex]; - If[ OptionValue[DiracEquation] && !FreeQ[ex,Spinor], - ex = diracEq[ex] - ], - (*If Expanding is set to True, the main simplification function (oldDiracSimplify) is applied.*) - time=AbsoluteTime[]; - FCPrint[1, "DiracSimplify: Applying PairContract.", FCDoControl->dsVerbose]; - FCPrint[3,"DiracSimplify: Doing contractions on ", ex, FCDoControl->dsVerbose]; - ex = ex /. Pair -> PairContract; - If[ OptionValue[DiracSigmaExplicit], - ex = DiracSigmaExplicit[ex] + + If[ OptionValue[DiracChainJoin], + time=AbsoluteTime[]; + FCPrint[1, "DiracSimplify: Contracting Dirac indices.", FCDoControl->dsVerbose]; + diracObjectsEval = diracObjectsEval /. dsHead[x_]/;!FreeQ[x,DiracChain] :> + DiracChainJoin[x, FCI->True, FCDiracIsolate->False]; + FCPrint[1, "DiracSimplify: Done calculating Dirac traces, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: diracObjects after calcuating Dirac traces: ", diracObjects , FCDoControl->dsVerbose] ]; - FCPrint[1,"DiracSimplify: Done applying PairContract, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + time=AbsoluteTime[]; - FCPrint[1, "DiracSimplify: Starting oldDiracSimplify", FCDoControl->dsVerbose]; - FCPrint[3,"DiracSimplify: Doing oldDiracSimplify on ", ex, FCDoControl->dsVerbose]; - ex = oldDiracSimplify[ex,Flatten[Join[{opts}, FilterRules[Options[DiracSimplify], Except[{opts}]]]]]/. PairContract -> Pair; - FCPrint[1,"DiracSimplify: Done doing oldDiracSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; - ]; + FCPrint[1, "DiracSimplify: Applying diracSimplifyEval", FCDoControl->dsVerbose]; + diracObjectsEval = FeynCalc`Package`diracTrickEvalFastFromDiracSimplifyList[(diracObjectsEval/.dsHead->Identity), {optInsideDiracTrace,optDiracOrder}]; + diracObjectsEval = diracSimplifyEval/@diracObjectsEval; - (* Covariant normalization of ubar.u or vbar.v (as in Peskin and Schroeder). - The combinations ubar.v and vbar.u are orthogonal and hence vanish *) - If[ !FreeQ[ex,Spinor], - FCPrint[2,"DiracSimplify: Applying spinor normalization on ", ex, FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: After diracSimplifyEval: ", diracObjectsEval, FCDoControl->dsVerbose]; + FCPrint[1,"DiracSimplify: diracSimplifyEval done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; - ex = ex/. DOT->holdDOT //. - { holdDOT[Spinor[s_. Momentum[p__],m_, 1],Spinor[s_. Momentum[p__],m_, 1]] -> s 2 m, - holdDOT[Spinor[- Momentum[p__],m_, 1],Spinor[Momentum[p__],m_, 1]] -> 0, - holdDOT[Spinor[Momentum[p__],m_, 1],Spinor[- Momentum[p__],m_, 1]] -> 0} /. - holdDOT -> DOT - ]; + If[ !FreeQ2[diracObjectsEval,{FeynCalc`Package`diracTrickEvalFastFromDiracSimplifyList,diracSimplifyEval,holdDOT}], + Message[DiracSimplify::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ]; - res = ex; - FCPrint[3,"DiracSimplify: Leaving with ", res, FCDoControl->dsVerbose]; - res - ]; + FCPrint[1, "DiracSimplify: Inserting Dirac objects back.", FCDoControl->dsVerbose]; + time=AbsoluteTime[]; + repRule = Thread[Rule[diracObjects,diracObjectsEval]]; + FCPrint[3,"DiracSimplify: repRule: ", repRule, FCDoControl->dsVerbose]; + tmp = (dsPart /. Dispatch[repRule]); + FCPrint[1, "DiracSimplify: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose], -(*if the expression contains non-commutative objects, apply DotSimplify*) -dotLin[x_] := - If[ FreeQ[x, DOT], - x, - DotSimplify[x, Expanding -> False] - ]; -(*if the expression contains spinors, apply the Dirac equation*) -diracEq[x_] := - If[ FreeQ[x, Spinor], - x, - DiracEquation[x] - ]; + (* + This is a fast mode for input that is already isolated, e.g. for calling DiracSimplify/@exprList + from internal functions + *) + FCPrint[1,"DiracSimplify: Fast mode.", FCDoControl->dsVerbose]; -dit[x_,ops___Rule] := - DiracTrace[diracSimplify@@Join[{x},{ops}, - Flatten[Prepend[{Options[DiracSimplify]}, - InsideDiracTrace -> True]]] - ]; + tmp = FeynCalc`Package`diracTrickEvalFastFromDiracSimplifySingle[ex, {tmpHead,optInsideDiracTrace,optDiracOrder}]; -diracSimplify[z_, OptionsPattern[]] := - (Contract[z]/.DiracTrace->dit)/;!FreeQ[z,DiracTrace]; + (* It might happen that after diracTrickEvalFast there are no Dirac matrices left.*) -dS[x___] := - If[ $BreitMaison === True, - dSBM[x], - dSNV[x] - ]; + FCPrint[3,"DiracSimplify: After diracTrickEvalFast: ", tmp , FCDoControl->dsVerbose]; -dSBM[x___] := - MemSet[dSBM[x], DiracTrick[x]]; -dSNV[x___] := - MemSet[dSNV[x], DiracTrick[x]]; + If[ OptionValue[ToDiracGamma67], + res = res /. tmpHead[zzz_]/;!FreeQ[{zzz}, DiracGamma[5]] :> tmpHead[ToDiracGamma67[zzz,FCI->True]] + ]; + If[ !FreeQ2[tmp,{DiracHeadsList,tmpHead}], + tmp = tmp /. tmpHead -> diracSimplifyEval + ]; + If[ !FreeQ2[tmp,{FeynCalc`Package`diracTrickEvalFastFromDiracSimplifySingle,diracSimplifyEval,holdDOT}], + Message[DiracSimplify::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ] + ]; -(* ****************************************************************** *) + FCPrint[3, "DiracSimplify: Intermediate result: ", tmp, FCDoControl->dsVerbose]; -(*this is oldDiracSimplify for spinor free expressions*) -oldDiracSimplify[x_, opts:OptionsPattern[]] := - diracSimplify[x, opts] /; FreeQ[x, Spinor]; + (* To simplify products of spinor chains we need to work with the full expression *) + If[ !FreeQ[tmp,Spinor], -(*this is oldDiracSimplify for expressions that contain spinors*) -oldDiracSimplify[x_,opts:OptionsPattern[]] := - Block[ {ex=x,dre, factoring,dooo,diracga67}, - FCPrint[2,"DiracSimplify: oldDiracSimplify: Entering with ", ex, FCDoControl->dsVerbose]; - factoring = OptionValue[DiracSimplify,{opts},Factoring]; - diracga67 = OptionValue[DiracSimplify,{opts},DiracSubstitute67]; - If[ factoring === True, - factoring = Factor2 - ]; + If[ OptionValue[SpinorChainTrick], - If[ diracga67, - ex = DiracSubstitute67[ex]; - ]; + FCPrint[1, "DiracSimplify: Applying SpinorChainTrick.", FCDoControl->dsVerbose]; + time=AbsoluteTime[]; + tmp = SpinorChainTrick[tmp, FCI->True,DiracGammaCombine->optDiracGammaCombine, DiracSigmaExplicit->False, + LorentzIndexNames->OptionValue[LorentzIndexNames], CartesianIndexNames->OptionValue[CartesianIndexNames]]; - dre = Collect[DotSimplify[DiracTrick[DiracGammaCombine[ex]]]/. - DOT->dooo,dooo[__]]/.dooo->DOT; - dre = FixedPoint[ SpinorChainEvaluate[#,opts]&, dre, 142]; - If[ !FreeQ[dre, Eps], - dre = Contract[dre, EpsContract -> True]; - dre = FixedPoint[ SpinorChainEvaluate[#,opts]&, dre, 142], - If[ !FreeQ[dre, LorentzIndex], - dre = Contract[dre, Expanding -> False] + FCPrint[1,"DiracSimplify: Done applying SpinorChainTrick, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3, "DiracSimplify: After SpinorChainTrick: ", tmp, FCDoControl->dsVerbose]; ]; - dre = FixedPoint[ SpinorChainEvaluate[#,opts]&, dre, 142]; - ]; - FCPrint[2,"DiracSimplify: oldDiracSimplify: Doing contractions in ", dre, FCDoControl->dsVerbose]; - If[ !FreeQ[dre, LorentzIndex], - FCPrint[2,"contracting in oldDiracSimpify"]; - dre = Contract[dre]; - FCPrint[2,"contracting in oldDiracSimpify done"] - ]; + If [ OptionValue[SirlinSimplify] && FCGetDimensions[tmp]==={4}, - If[ Length[DownValues[SpinorsandPairs]] > 1, - dre = (dre /. DOT -> SpinorsandPairs/. SpinorsandPairs->DOT)//dotLin - ]; + FCPrint[1, "DiracSimplify: Applying SirlinSimplify.", FCDoControl->dsVerbose]; + time=AbsoluteTime[]; + tmp = SirlinSimplify[tmp, FCI->True,DiracGammaCombine->optDiracGammaCombine, DiracSigmaExplicit->False, SpinorChainTrick->False]; - If[ !FreeQ[dre, DiracGamma], - dre = Expand2[dre, DiracGamma] - ]; + FCPrint[1,"DiracSimplify: Done applying SirlinSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3, "DiracSimplify: AfteSirlinSimplify: ", tmp, FCDoControl->dsVerbose] + ] - If[ factoring =!= False, - dre = factoring[dre] ]; - FCPrint[2,"DiracSimplify: oldDiracSimplify: Leaving with ", dre, FCDoControl->dsVerbose]; - - dre - ]/; !FreeQ[x,Spinor]; - -DiracSubstitute67[x_] := - x/. {DiracGamma[6] :> (1/2 + DiracGamma[5]/2), - DiracGamma[7] :> (1/2 - DiracGamma[5]/2)}; - -contractli[x_] := - MemSet[contractli[x], - Contract[ x, Expanding -> True, Factoring -> False, EpsContract -> False] - ]; - -(*if the expression doesn't contain any non-commutative objects, return it unevaluated*) -diracSimplify[x_, OptionsPattern[]] := - x /; NonCommFreeQ[x]; - -(*CHANGE 1298 *) - -diracSimplify[x_, in:OptionsPattern[]] := - If[ $BreitMaison === True, - diracSimplifyBM[x,in], - diracSimplifyNV[x,in] - ]; - -diracSimplifyBM[x_,in:OptionsPattern[]] := - MemSet[diracSimplifyBM[x,in], diracSimplifyGEN[x,in]]; -diracSimplifyNV[x_,in:OptionsPattern[]] := - MemSet[diracSimplifyNV[x,in], diracSimplifyGEN[x,in]]; -dirfun[exp_] := - Collect2[exp/.DOT->dS, DOT, Factoring -> False]; + res = freePart + tmp; -diracSimplifyInsideTrace[ex_] := - Block[{diracdt=ex,holdDOT}, - (* bug fix 2005-02-05: this is a problem because of Flat and OneIdentity of Dot ... *) - (* diracdt = diracdt/.DOT->trIC/. *) - (* only do cyclicity simplification if there is a simple structure of Dirac matrices *) - If[ FreeQ[diracdt/. DOT -> holdDOT, holdDOT[a__/; !FreeQ[{a}, holdDOT]]], - diracdt = diracdt/.DOT->trIC/. - (* bug fix on September 25th 2003 (RM): due to earlier changes this was overseen:*) - {trI:>dS, spursav:> dS}; + If[ optExpanding && OptionValue[Expand2], + time=AbsoluteTime[]; + FCPrint[1, "DiracSimplify: Expanding the result.", FCDoControl->dsVerbose]; + res = Expand2[res]; + FCPrint[1,"DiracSimplify: Expanding done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3, "DiracSimplify: After expanding: ", res, FCDoControl->dsVerbose] ]; - (* careful: can run into infinite loop ..., adding a cut in FixedPoint, 10.9.2003 *) - (* even be more careful: and get rid of cyclic simplifications hrere ... *) - diracdt = - FixedPoint[dirfun, diracdt, 5](*/.DOT ->trIC/.trI->dS*); - FCPrint[2,"dir2done, diracdt=", FullForm[diracdt]]; - If[ FreeQ[ diracdt, DOT ], - diracdt = diracdt/.DiracGamma[_[__],___]->0; - diracpag = PartitHead[diracdt,DiracGamma]; - If[ diracpag[[2]] === DiracGamma[5], - diracdt = 0 - ]; - If[ diracpag[[2]] === DiracGamma[6] || diracpag[[2]] === DiracGamma[7], - diracdt = 1/2 diracpag[[1]] - ] + If[ OptionValue[FCE], + res = FCE[res] ]; - diracdt - ]; - - -diracSimplifyGEN[x_, opts:OptionsPattern[]] := - If[ FreeQ[x, DiracGamma], - x, - Block[ {diracopt,diracdt,diracndt = 0,diraccanopt,diracpdt,diracgasu, - diracldt,diracjj = 0,diractrlabel,diracga67,diracsifac, - diracpag,colle, dooT,time}, - (* There are several options *) - - - FCPrint[1, "DiracSimplify: diracSimplifyGEN: Entering", FCDoControl->dsVerbose]; - - - diraccanopt = OptionValue[DiracSimplify,{opts},DiracCanonical]; - diractrlabel = OptionValue[DiracSimplify,{opts},InsideDiracTrace]; - diracga67 = OptionValue[DiracSimplify,{opts},DiracSubstitute67]; - diracgasu = OptionValue[DiracSimplify,{opts},DiracSimpCombine]; - diracsifac = OptionValue[DiracSimplify,{opts},Factoring]; + (*res = ex;*) + FCPrint[1,"DiracSimplify: Leaving.", FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: Leaving with ", res, FCDoControl->dsVerbose]; + res + ]; - time=AbsoluteTime[]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Applying DotSimplify.", FCDoControl->dsVerbose]; - FCPrint[3,"DiracSimplify: diracSimplifyGEN: Applying DotSimplify to ", x, FCDoControl->dsVerbose]; - diracdt = dotLin[ x//DiracGammaExpand ]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Done applying DotSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; +(*TODO Figure out some way to treat spinors as well! *) +diracSimplifyEval[DiracChain[expr_,i_,j_]]:= + DiracChain[diracSimplifyEval[expr],i,j]/; !optExpanding +diracSimplifyEval[DiracChain[expr_,i_,j_]]:= + DiracChainExpand[DiracChain[diracSimplifyEval[expr],i,j], FCI->True]/; optExpanding - time=AbsoluteTime[]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Doing index contractions.", FCDoControl->dsVerbose]; - FCPrint[3,"DiracSimplify: diracSimplifyGEN: Contract indices in ", diracdt, FCDoControl->dsVerbose]; - If[ diracgasu === True, - diracdt = contractli[DiracGammaCombine[diracdt/.Pair->PairContract]](*/. DOT -> dS*)(*Commented out 27/3-2003, see above*), - diracdt = contractli[ diracdt ] - (*/. DOT->dS*) - ]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Done doing index contractions, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; +diracSimplifyEval[expr_]:= + Block[{tmp=expr, time, time2, res}, + (* General algorithm of diracSimplifyEval: - (* Commented out Sept. 9 203 by RM, in order to fix the 27/3 2003 bug - diracdt = Expand2[ ExpandScalarProduct[diracdt//fEx], {Pair, DOT}]; *) + 1) Apply DiracTrick to the unexpanded expression + 2) Expand the expression using DotSimplify and apply DiracTrick again + 3) If there are uncontracted indices, contract them + 4) If needed, expand scalar products + 5) If needed, replace chiral projectors by their explicit values and apply DotSimplify + afterwards - If[ diractrlabel===True, - FCPrint[2,"DiracSimplify: diracSimplifyGEN: Simplifications inside a Dirac trace.", FCDoControl->dsVerbose]; - FCPrint[3,"DiracSimplify: diracSimplifyGEN: Applying simplifications that are valid only inside a Dirac trace", FCDoControl->dsVerbose]; - diracdt=diracSimplifyInsideTrace[diracdt] - ]; - (* Change 27/3-2003 by Rolf Mertig, see above (27/3-2003)*) - FCPrint[2,"dir2a, diracdt=", FullForm[diracdt]]; - (* diracdt = Expand2[ ExpandScalarProduct[diracdt//fEx], {Pair, DOT}]; *) + 6) If the expression contains spinors + 6.1) If needed, apply the Dirac equation + 6.2) If needed, apply Sirlin's relations - FCPrint[2,"DiracSimplify: diracSimplifyGEN: Expanding scalar products", FCDoControl->dsVerbose]; - diracdt = - Expand[ ExpandScalarProduct[diracdt//fEx], DOT | Pair]; + 7) If needed, order the remaining Dirac matrices canonically + 8) If needed, factor the result + *) - FCPrint[2,"dir3, diracdt=", FullForm[diracdt]]; - If[ FreeQ[diracdt,DOT], - diracndt = Expand[(diracdt/.PairContract->ExpandScalarProduct)//DiracGammaExpand]; - If[ diracga67 === True, - diracndt = Expand[diracndt//DiracSubstitute67] - ], - FCPrint[2,"dir3 expanding "]; - (* diracdt = Expand[ diracdt ]; *) - diracdt = Expand[ diracdt, DOT ]; - FCPrint[2,"dir3 expanding done ", Length[diracdt]]; - If[ Head[diracdt] === Plus, - diracldt = Length[diracdt], - If[ diracdt===0, - diracldt = 0, - diracldt = 1 - ] - ]; - diracpdt = diracdt; - - (* TODO: Here we would need cyclicity simplifications *) - (*If[ diractrlabel, - (* change 2005-02-05 - diracpdt = diracpdt/.DOT->trIC/.trI->dS//. DOT -> trIC/.trI->dS; *) - diracpdt = DiracTrick[diracpdt] - ];*) -(* - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Expanding scalar products", FCDoControl->dsVerbose]; - diracpdt = ExpandScalarProduct[diracpdt]//Expand;*) - - - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Subsituting chiral projectors", FCDoControl->dsVerbose]; - If[ diracga67, - If[!FreeQ2[diracpdt,{DiracGamma[6],DiracGamma[7]}], - diracpdt = DiracSubstitute67[diracpdt] - ]; - If[!FreeQ2[diracndt,{DiracGamma[6],DiracGamma[7]}], - diracndt = DiracSubstitute67[diracndt] - ] - ]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: Entering", FCDoControl->dsVerbose]; + FCPrint[3, "DiracSimplify: diracSimplifyEval: Entering with: ", tmp, FCDoControl->dsVerbose]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Applying DiracTrick", FCDoControl->dsVerbose]; - diracpdt = fEx[DiracGammaExpand[diracpdt]]//DiracTrick; - If[ diractrlabel===True, - FCPrint[2,"DiracSimplify: diracSimplifyGEN: Simplifications inside a Dirac trace.", FCDoControl->dsVerbose]; - FCPrint[3,"DiracSimplify: diracSimplifyGEN: Applying simplifications that are valid only inside a Dirac trace", FCDoControl->dsVerbose]; - diracpdt=diracSimplifyInsideTrace[diracpdt] - ]; + (* First application of DiracTrick, no expansions so far *) + If[ !FreeQ[tmp, DiracGamma], + time=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Applying DiracTrick.", FCDoControl->dsVerbose]; + tmp = DiracTrick[tmp, FCI -> True, InsideDiracTrace-> optInsideDiracTrace, FCDiracIsolate->False, ToDiracGamma67->optToDiracGamma67]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: DiracTrick done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: diracSimplifyEval: After DiracTrick: ", tmp, FCDoControl->dsVerbose] + ]; - (*If[ diractrlabel, - diracpdt = fEx[(diracpdt//DiracGammaExpand)//DiracTrick](*/. - DOT->trIC/.trI->dS//.DOT->dS/. - DOT->trIC/.trI->dS *) , - diracpdt = fEx[DiracGammaExpand[diracpdt]//DiracTrick]//DiracTrick - ];*) + (* + This is mainly relevant for products of traces when using NDR, so that despite of + DiracTraceEvaluate->True we may end up with unevaluated traces here, like with + DiracSimplify[DiracTrace[GAD[al, be, mu, nu, 5]] DiracTrace[GAD[al, be, mu, nu]]] + *) + If[ !FreeQ[tmp, DiracTrace] && optDiracTraceEvaluate, + tmp = tmp /. DiracTrace[z_, o:OptionsPattern[]] :> DiracTrace[z, + DiracTraceEvaluate->True, Expand-> optExpandScalarProduct, o]; + ]; - (*FCPrint[1,"DiracSimplify: diracSimplifyGEN: Subsituting chiral projectors", FCDoControl->dsVerbose]; - If[ diracga67, - diracpdt = DiracSubstitute67[ diracpdt/.DOT->dr67 ], - diracpdt = fEx[ diracpdt ] - ];*) + (* Expansion of Dirac slashes *) + If[ !optDiracGammaCombine && !FreeQ[tmp, DiracGamma], + tmp = DiracGammaExpand[tmp,FCI->True]; + ]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Expanding scalar products and other things", FCDoControl->dsVerbose]; - diracndt = diracndt + Expand2[ExpandScalarProduct[diracpdt], DOT]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Doing contractions", FCDoControl->dsVerbose]; - diracndt = diracndt /. PairContract->ExpandScalarProduct; + If[ optExpanding && !FreeQ[tmp, DiracGamma], + time2=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Applying Dotsimplify.", FCDoControl->dsVerbose]; + tmp = DotSimplify[tmp, FCI->True, Expanding -> True, FCJoinDOTs->False]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Dotsimplify done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: diracSimplifyEval: After Dotsimplify: ", tmp, FCDoControl->dsVerbose]; + ]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Applying DotSimplify", FCDoControl->dsVerbose]; - diracndt = Expand[dotLin[diracndt]]; + If[ !FreeQ[tmp, DiracGamma], + If[ optContract=!=False && !DummyIndexFreeQ[tmp,{LorentzIndex,CartesianIndex}], + time2=AbsoluteTime[]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: Applying Contract.", FCDoControl->dsVerbose]; + tmp = Contract[tmp, Expanding->True, EpsContract-> False, Factoring->False]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: Contract done, timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->dsVerbose]; + FCPrint[3, "DiracSimplify: diracSimplifyEval: After Contract: ", tmp, FCDoControl->dsVerbose]; - If[ diraccanopt===True, - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Applying canonical ordering", FCDoControl->dsVerbose]; - diracndt = DiracOrder[ diracndt ]; - diracndt = Expand[dotLin[diracndt]] + time2=AbsoluteTime[]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: Applying EpsContract.", FCDoControl->dsVerbose]; + If[ optEpsContract, + tmp = EpsContract[tmp,FCI->True] ]; - ]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: EpsContract done, timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->dsVerbose]; + FCPrint[3, "DiracSimplify: diracSimplifyEval: After EpsContract: ", tmp, FCDoControl->dsVerbose]; - If[ diracsifac, - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Factoring the result", FCDoControl->dsVerbose]; - diracndt = Factor2[ diracndt ] ]; - FCPrint[1,"DiracSimplify: diracSimplifyGEN: Leaving DiracSimplify", FCDoControl->dsVerbose]; - - diracndt/.spursav:> DOT - ] - ]; (* end of diracSimplify *) - - -dr67[ b___ ] := - dS[ b ]/;FreeQ2[{b},{DiracGamma[6],DiracGamma[7]}]; - -dr67[ b___,DiracGamma[6],z___ ] := - 1/2 dS[b,z] + 1/2 dS[ b,DiracGamma[5],z]; - -dr67[ b___,DiracGamma[7],z___ ] := - 1/2 dS[b,z] - 1/2 dS[ b,DiracGamma[5],z]; - -dIex[ a___,x_ + y_, b___] := - dS[a,x,b] + dS[a,y,b]; - -dix[y_] := - y/.DOT->dIex/.dIex->dS; - -(* This is the tricky function which does the expansion of the dr's *) -fEx[z_] := - FixedPoint[ dix, z/.DOT -> dS ]; - -(* cyclic property *) (* Changed by F.Orellana, 14/1-2002. - Dropped Kreimer scheme. According to - Rolf it's wrong *) -trIC[y___] := - tris @@ cyclic[y]; - -cyclic[x__] := - RotateLeft[{x},Position[{x},First[Sort[{x}]]][[1,1]]]; -cyclic[] := - {}; - -(* ************************************************************** *) -(* fr567def, frlivcdef : two special FreeQ - checking functions *) - fr567[x__] := - True /; FreeQ2[FixedPoint[ReleaseHold, {x}],{DiracGamma[5],DiracGamma[6],DiracGamma[7]}]; - -(* Properties and special cases of traces (up to a factor 4) *) -tris[x___] := - tris[x] = trI[x]; - -trI[a_Plus] := - Map[tris, a]; -trI[] = - 1; -trI[ DiracGamma[5] ] = - 0; -trI[ DiracGamma[6] ] = - 1/2; -trI[ DiracGamma[7] ] = - 1/2; - -trI[ a:DiracGamma[_[__]].. ,DiracGamma[n_] ] := - 0 /;(OddQ[Length[{a}]]&&(n==5 || n==6 || n==7)); - -trI[ a:DiracGamma[_[__],___].. ,DiracGamma[n_] ] := - 0 /;(OddQ[Length[{a}]]&&(n==5 || n==6 || n==7)) && ($BreitMaison === False); - -trI[ d:DiracGamma[__].. ] := - 0/;(OddQ[Length[{d}]] && fr567[ d ]); - -trI[ d:DiracGamma[_[__],___].. ,DiracGamma[5] ] := - 0/;Length[{d}]<4; - -trI[x_] := - x /; FreeQ[ {x},DiracGamma ]; - -trI[ DiracGamma[a_[b__],___],DiracGamma[c_[d__],___], DiracGamma[6] ] := - 1/2 ExpandScalarProduct[ a[b],c[d] ]; - -trI[ DiracGamma[a_[b__],___],DiracGamma[c_[d__],___], DiracGamma[7] ] := - 1/2 ExpandScalarProduct[ a[b],c[d] ]; - -trI[ x__] := - spursav[x]/; - ( Length[{x}] < 11 && fr567[x]) || ( Length[{x}] < 6 && (!fr567[x])); - -(* #################################################################### *) + time2=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Applying DiracTrick.", FCDoControl->dsVerbose]; + tmp = DiracTrick[tmp, FCI -> True, InsideDiracTrace-> optInsideDiracTrace, FCJoinDOTs->False, ToDiracGamma67->optToDiracGamma67]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: DiracTrick done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: diracSimplifyEval: After DiracTrick: ", tmp, FCDoControl->dsVerbose]; + ]; + (* Doing index contractions *) + If[ optContract=!=False && !DummyIndexFreeQ[tmp,{LorentzIndex,CartesianIndex}], + time2=AbsoluteTime[]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: Applying Contract.", FCDoControl->dsVerbose]; + tmp = Contract[tmp, EpsContract-> False]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: Contract done, timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->dsVerbose]; + + time2=AbsoluteTime[]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: Applying EpsContract.", FCDoControl->dsVerbose]; + If[ optEpsContract, + tmp = EpsContract[tmp,FCI->True] + ]; + FCPrint[2, "DiracSimplify: diracSimplifyEval: EpsContract done, timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->dsVerbose]; + FCPrint[3, "DiracSimplify: diracSimplifyEval: After EpsContract: ", tmp, FCDoControl->dsVerbose]; + ]; -(* SpinorChainEvaluatedef *) + (* Expansion of the scalar products. *) + If[ optExpandScalarProduct && !FreeQ[tmp,Momentum], + time2=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Expanding scalar products", FCDoControl->dsVerbose]; + tmp = ExpandScalarProduct[tmp,FCI->False]; + FCPrint[2,"DiracSimplify:diracSimplifyEvale: Done expanding the result, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->dsVerbose] + ]; -(* #################################################################### *) -(* Main43 *) -(* #################################################################### *) + (* Substituting the explicit values of Dirac sigma *) + If [ optDiracSigmaExplicit && !FreeQ[tmp,DiracSigma], + FCPrint[2,"DiracSimplify: diracSimplifyEval: Substituting the explicit values of the Dirac sigma.", FCDoControl->dsVerbose]; + tmp = DiracSigmaExplicit[tmp,FCI->True] + ]; -spinlin[x_Plus] := - spinlin/@x; -spinlin[a_] := - ((a/.DOT->ddot)//.{ - ddot[x___,z_ b__,c___] :> z ddot[x,b,c]/;NonCommFreeQ[z]===True, - ddot[x___,z_ ,c___] :> z ddot[x,c]/;NonCommFreeQ[z]===True, - ddot[x_Spinor,b___,c_Spinor,d_Spinor,e___,f_Spinor,g___]:> ddot[x,b,c] ddot[d,e,f,g] - })/.ddot[]->1/.ddot->DOT; + (* Canonical ordering of the Dirac matrices. *) + If[ optDiracOrder, + time2=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Applying DiracOrder.", FCDoControl->dsVerbose]; + tmp = DiracOrder[tmp, FCI->True, FCJoinDOTs->OptionValue[Expanding]]; + FCPrint[2,"DiracSimplify:diracSimplifyEvale: Done applying DiracOrder, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->dsVerbose] + ]; -(*SetAttributes[ SpinorChainEvaluate, Listable ];*) -SpinorChainEvaluate[y_, OptionsPattern[]] := - y /; FreeQ[y,Spinor]; + (* Expansion of Dirac slashes *) + (* + If[ optDiracGammaExpand, + FCPrint[1,"DiracSimplify: diracSimplifyEval: Expanding Dirac slashes.", FCDoControl->dsVerbose]; + tmp = DiracGammaExpand[tmp,FCI->True]; -(* #################################################################### *) -(* Main44 *) -(* #################################################################### *) + ];*) -SpinorChainEvaluate[z_Plus,opts:OptionsPattern[]] := - Block[ {nz,useSirlin}, - useSirlin = OptionValue[DiracSimplify,{opts},SirlinRelations]; - FCPrint[3,"DiracSimplify: SpinorChainEvaluate: Entering with ", z, FCDoControl->dsVerbose]; - nz = DotSimplify[z]; - If[ Length[nz]>20, - nz = Collect2[ nz, Spinor,Factoring -> False] - ]; - If[ Head[nz]=!=Plus, - nz = SpinorChainEvaluate[nz,opts], - If[ !useSirlin, - nz = Map[ spcev0, nz ], - If[ FreeQ[nz, DOT[Spinor[p1__], (a__ /; FreeQ[{a}, DiracGamma[_,_]]), - Spinor[p2__]] DOT[Spinor[p3__], - (b__ /; FreeQ[{b}, DiracGamma[_,_]]) , Spinor[p4__]]], - nz = Map[ spcev0,nz ], - (* added ,Spinor, Nov. 2003 , RM*) - nz = sirlin00[ Expand[Map[ spcev0,z//sirlin0 ], Spinor] ] - ] - ] - ]; - FCPrint[3,"DiracSimplify: SpinorChainEvaluate: Leaving with ", nz, FCDoControl->dsVerbose]; - nz - ]; -SpinorChainEvaluate[x_,opts:OptionsPattern[]] := - Block[ {nz,useSirlin}, - useSirlin = OptionValue[DiracSimplify,{opts},SirlinRelations]; - FCPrint[3,"DiracSimplify: SpinorChainEvaluate: Entering with ", x, FCDoControl->dsVerbose]; - If[ !useSirlin, - nz = Expand[spcev0[x], - Spinor - ], - If[ FreeQ[x//DotSimplify, - DOT[Spinor[p1__], (a__ /; FreeQ[{a}, DiracGamma[_,_]]), - Spinor[p2__]] DOT[Spinor[p3__] , - (b__ /; FreeQ[{b}, DiracGamma[_,_]]) , Spinor[p4__]]], - (* added ,Spinor, Nov. 2003 , RM*) - nz = Expand[spcev0[x], Spinor], - nz = sirlin00[ Expand[FixedPoint[spcev0, x//sirlin0, 3 ], Spinor]]; - ] - ]; - FCPrint[3,"DiracSimplify: SpinorChainEvaluate: Leaving with ", FullForm[nz], FCDoControl->dsVerbose]; - nz - ]/; !Head[x]===Plus && Head[x]=!=List; -(* #################################################################### *) -(* Main45 *) -(* #################################################################### *) - -spcev0[x_] := - spcev000[x]/.spcev000->spcev0ev; -(* - spcev000[ a_ b_ ] := a spcev000[b] /; NonCommFreeQ[a] === True; -*) -spcev000[y_] := - y /; NonCommFreeQ[y] === True; -spcev000[y_Times] := - Select[y, FreeQ[#, Spinor]& ] spcev0ev[Select[y,!FreeQ[#, Spinor]&]]; - -spcev0ev[x_] := - ExpandScalarProduct[Contract[Expand[spinlin[x](*, Spinor*)]/.DOT->spcevs/. - spcev->DOT, Expanding->False]](*//Expand*); - -spcevs[xx___] := - MemSet[ spcevs[xx], FixedPoint[ spcev,{xx},4 ] ]; -(*spcevsdef*) - -(*spcevdef*) -spcev[y_List] := - spcev@@y; - -spcev[a___,b_ /; FreeQ2[b,{Pattern, BlankSequence, BlankNullSequence}],c___] := - b spcev[a,c] /; NonCommFreeQ[b] === True; - -(*added to allow nested structures like phi.(gamm1.gamm2+gamma3.gamma4).phi -F.Orellana, 26/9-2002*) - -spcev[a__] := - DOT[a] /; FreeQ[{a}, Spinor]; -(**) -spcev[] = - 1; - -spcev[x___,Spinor[a__],y___] := - Expand[ DiracOrder[ DiracEquation[fEx[DiracGammaExpand[ - DOT[x,Spinor[a],y]]](*/.dR->DOT*)]]]/; FreeQ[{x,y},Spinor]; - -spcev[x___,Spinor[a__],b___,Spinor[c__],y___] := - Block[ {spcevdi,spcevre,spcevj}, - FCPrint[2,"entering spcev with ", InputForm[DOT@@{x,Spinor[a],b,Spinor[c],y}]]; - spcevdi = diracSimplify[DOT[Spinor[a],b,Spinor[c]], InsideDiracTrace->False, - DiracCanonical->False, Factoring->False, DiracSimpCombine->True]; - spcevdi = Expand[ExpandScalarProduct[spcevdi]]; - spcevdi = Expand[spcevdi]; - If[ !(Head[spcevdi]===Plus), - spcevre = spinlin[ spcevdi ]; - spcevre = DiracEquation[ spcevre ];, - spcevre = Sum[DiracEquation[ spinlin[ spcevdi[[spcevj]] ] ], - {spcevj,1,Length[spcevdi]}]; - ]; - spcevre = DotSimplify[DOT[spcevs[x],spcevre,spcevs[y]]]; - If[ !FreeQ[spcevre, SUNT], - spcevre = (spcevre/.DOT->dS) + (* Substituting the explicit values of the chiral projectors *) + If[ optDiracSubstitute67 && !FreeQ2[tmp,{DiracGamma[6],DiracGamma[7]}], + FCPrint[2,"DiracSimplify: diracSimplifyEval: Substituting the explicit values of the chiral projectors.", FCDoControl->dsVerbose]; + tmp = DiracSubstitute67[tmp, FCI->True] ]; - spcevre = spcevre//DotSimplify; - FCPrint[2,"exiting spcev with ",InputForm[spcevre]]; - spcevre - ] /; FreeQ[{b}, Spinor]; - -(* Reference of Sirlin-relations: Nuclear Physics B192 (1981) 93-99; - Note that we take another sign in front of the Levi-Civita tensor - in eq. (7), since we take (implicitly) \varepsilon^{0123} = 1 -*) -(* #################################################################### *) -(* Main441 *) -(* #################################################################### *) - -$SpinorMinimal = False; - -sirlin00[x_] := - x/;$SpinorMinimal === False; - -sirlin00[x_] := - MemSet[sirlin00[x], - Block[ {te, tg5, ntg5, test}, - FCPrint[3,"sirlin001"]; - (* te = sirlin0[x]//ExpandAll; *) - te = sirlin0[x]//Expand; - FCPrint[3,"sirlin002"]; - If[ FreeQ2[te,{DiracGamma[6],DiracGamma[7]}]&& - Head[te]===Plus && !FreeQ[te,DiracGamma[5]], - tg5 = Select[te, !FreeQ[#,DiracGamma[5]]& ]; - ntg5 = te - tg5; -(*i.e. te = tg5 + ntg5 *) - test = Expand[tg5 + ChisholmSpinor[ntg5], Spinor]; - If[ nterms[test] < Length[te], - te = test - ] - ]; - FCPrint[3,"exiting sirlin00"]; - te - ] - ]/; $SpinorMinimal === True; - -ident3[a_,_] := - a; - -(* #################################################################### *) -(* Main442 *) -(* #################################################################### *) -(* canonize different dummy indices *) (*sirlin3def*) -sirlin3a[x_] := - ((sirlin3[Expand[Contract[x](*,Spinor*)]/. - $MU->dum$y]/.dum$y->$MU)/. sirlin3 -> Identity)//Contract; - -sirlin3[a_Plus] := - sirlin3 /@ a; - -sirlin3[ m_. DOT[Spinor[p1__] , (ga1___) , DiracGamma[ LorentzIndex[la_] ] , (ga2___), -Spinor[p2__]] DOT[Spinor[p3__], (ga3___) , DiracGamma[ LorentzIndex[la_] ], (ga4___), -Spinor[p4__]]] := - Block[ {counter}, - counter = 1; - While[!FreeQ2[{m,ga1,ga2,ga3,ga4}, {$MU[counter], dum$y[counter]}], - counter = counter + 1 + (* Rewriting DiracGamma[5] in terms of the chiral projectors *) + If[ optDiracSubstitute5 && !FreeQ[tmp,DiracGamma[5]], + FCPrint[2,"DiracSimplify: diracSimplifyEval: Rewriting DiracGamma[5] in terms of the chiral projectors.", FCDoControl->dsVerbose]; + tmp = DiracSubstitute5[tmp, FCI->True] ]; - sirlin3[m DOT[Spinor[p1], ga1, DiracGamma[ LorentzIndex[$MU[counter]]], - ga2, Spinor[p2]] DOT[Spinor[p3] , ga3 , DiracGamma[ LorentzIndex[$MU[counter]]], - ga4, Spinor[p4]]] - ]/; FreeQ[la, $MU]; -sirlin3[ m_. DOT[Spinor[p1__],(ga1___), DiracGamma[ LorentzIndex[la_,di_],di_ ], (ga2___), -Spinor[p2__]] DOT[Spinor[p3__],(ga3___), DiracGamma[ LorentzIndex[la_,di_],di_ ], (ga4___), -Spinor[p4__]]] := - (m DOT[Spinor[p1], ga1, DiracGamma[ LorentzIndex[$MU[1], di],di ], ga2, - Spinor[p2]] DOT[Spinor[p3], ga3, DiracGamma[LorentzIndex[$MU[1], di], di], ga4, - Spinor[p4]])/; FreeQ2[{ga1,ga2,ga3,ga4}, DiracGamma[_,_]]; + If[ optExpanding && (!optDiracGammaCombine || optDiracSubstitute67), + time2=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Applying Dotsimplify.", FCDoControl->dsVerbose]; + tmp = DotSimplify[tmp, FCI->True, Expanding -> True]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Dotsimplify done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: diracSimplifyEval: After Dotsimplify: ", tmp, FCDoControl->dsVerbose]; + ]; -(* #################################################################### *) -(* Main443 *) -(* #################################################################### *) -(* The Sirlin - identities are only valid in 4 dimensions and are -only needed, if Dirac matrices are around -*) -sirlin0[x_] := - If[ FreeQ2[x, {LorentzIndex, Momentum}], - x, - If[ FreeQ[x, Spinor], - x, - If[ !FreeQ[x, DiracGamma[_,_]], - sirlin3[x]/.sirlin3->Identity, - sirlin0doit[(x//sirlin2)/.sirlin2->Identity] - ] - ] - ]; + (* Dirac equation *) + If[ !FreeQ[tmp,Spinor] && optDiracEquation, + time2=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Applying DiracEquation.", FCDoControl->dsVerbose]; + tmp = DiracEquation[tmp, FCI->True]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: DiracEquation done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->dsVerbose]; + FCPrint[3,"DiracSimplify: diracSimplifyEval: After DiracEquation: ", tmp, FCDoControl->dsVerbose]; + ]; -$sirlintime = 242; - -SetAttributes[timeconstrained, HoldAll]; - -If[ $OperatingSystem === "Unix", - timeconstrained[x__] := - TimeConstrained[x], - timeconstrained[x_,__] := - x -]; - -sirlin0doit[a_Plus] := - timeconstrained[sirlin3a[Contract[ - (Expand[Map[sirlin1, a](*, DOT*)]/. - sirlin1->sirlin2) /. - sirlin2 -> sirlin1/.sirlin1->sirlin2/. - sirlin2 -> Identity,EpsContract->True]] // spcev0, - 2 $sirlintime, a]; - -sirlin0doit[a_] := - timeconstrained[(sirlin3a[sirlin1[a]/.sirlin1->sirlin2/. - sirlin2 -> Identity] // spcev0), $sirlintime, a] /;Head[a]=!=Plus; - -sirlin2[a_Plus] := - sirlin2/@a; - - -sirlin2[m_. DOT[ - Spinor[pa__], - DiracGamma[Momentum[pj_]], - DiracGamma[Momentum[pi_]], - DiracGamma[LorentzIndex[mu_]], - (vg5___), - Spinor[pb__] - ] * - DOT[ - Spinor[Momentum[pi_],0,qf___] , - DiracGamma[LorentzIndex[mu_]] , - (vg5___), - Spinor[Momentum[pj_],0,qf___] - ] -] := - (-sirlin2[m DOT[ - Spinor[pa] , - DiracSlash[pi,pj], - DiracMatrix[mu], - vg5 , - Spinor[pb] - ] * - DOT[ - Spinor[Momentum[pi],0,qf] , - DiracMatrix[mu], vg5 , - Spinor[Momentum[pj],0,qf] - ]] + - 2 m ExpandScalarProduct[Momentum[pi],Momentum[pj]] * - DOT[ - Spinor[pa], - DiracMatrix[mu], - vg5 , - Spinor[pb]] * - DOT[ - Spinor[Momentum[pi],0,qf] , - DiracMatrix[mu] , vg5 , - Spinor[Momentum[pj],0,qf]])/; - ({vg5}==={}) || ({vg5}==={DiracGamma[5]}); - -sirlin22[m_. DOT[ - Spinor[pa__], - DiracGamma[Momentum[pj_]], - DiracGamma[Momentum[pi_]], - DiracGamma[LorentzIndex[mu_]], - (vg5___), - Spinor[pb__]] * - DOT[ - Spinor[Momentum[pi_],0,qf___], - DiracGamma[LorentzIndex[mu_]], - (vg5___), - Spinor[Momentum[pj_],0,qf___] - ] -] := - (-sirlin2[m DOT[ - Spinor[pa], - DiracSlash[pi,pj], - DiracMatrix[mu], - vg5, - Spinor[pb]] * - DOT[ - Spinor[Momentum[pi],0,qf] , - DiracMatrix[mu] , vg5 , - Spinor[Momentum[pj],0,qf]]] + - 2 m ExpandScalarProduct[Momentum[pi],Momentum[pj]] * - DOT[ - Spinor[pa] , - DiracMatrix[mu] , - vg5, - Spinor[pb]] * - DOT[ - Spinor[Momentum[pi],0,qf] , - DiracMatrix[mu], - vg5, - Spinor[Momentum[pj],0,qf] - ])/; ({vg5}==={}) || ({vg5}==={DiracGamma[5]}); - - -sirlin2[m_. DOT[ - Spinor[pa__] , - DiracGamma[Momentum[pi_]] , - DiracGamma[Momentum[pj_]] , - DiracGamma[LorentzIndex[mu_]], - (vg5___), - Spinor[pb__]] * - DOT[ - Spinor[Momentum[pi_],0,qf___], - DiracGamma[LorentzIndex[mu_]], - (vg5___), - Spinor[Momentum[pj_],0,qf___] - ]] := - (m ExpandScalarProduct[Momentum[pi], Momentum[pj]] * - DOT[ - Spinor[pa], - DiracMatrix[$MU[1]], - Spinor[pb]] * - DOT[ - Spinor[Momentum[pi],0,qf], - DiracMatrix[$MU[1]] , - Spinor[Momentum[pj],0,qf] - ] + m ExpandScalarProduct[Momentum[pi], Momentum[pj]] * - DOT[ - Spinor[pa] , - DiracMatrix[$MU[1]], - DiracGamma[5], - Spinor[pb]] * - DOT[ - Spinor[Momentum[pi],0,qf] , - DiracMatrix[$MU[1]], - DiracGamma[5], - Spinor[Momentum[pj],0,qf] - ]) /; ({vg5}==={}) || ({vg5}==={DiracGamma[5]}); - - -sirlin2[m_. DOT[ - Spinor[p1__], - (ga1___) , - DiracGamma[ LorentzIndex[la_] ], - DiracGamma[ LorentzIndex[nu_] ], - DiracGamma[6] , - Spinor[p2__]] * - DOT[ - Spinor[p3__], - (ga2___) , - DiracGamma[ LorentzIndex[la_] ], - DiracGamma[ LorentzIndex[nu_] ], - DiracGamma[7] , - Spinor[p4__]]] := - (m 4 DOT[Spinor[p1] , ga1 , DiracGamma[6] , Spinor[p2] * - Spinor[p3] , ga2 , DiracGamma[7] , Spinor[p4]]); - -sirlin2[m_. DOT[ - Spinor[p1__], - (ga1___) , - DiracGamma[ LorentzIndex[la_] ], - DiracGamma[ LorentzIndex[nu_] ], - DiracGamma[7] , - Spinor[p2__]] * - DOT[ - Spinor[p3__], - (ga2___) , - DiracGamma[ LorentzIndex[la_] ], - DiracGamma[ LorentzIndex[nu_] ], - DiracGamma[6] , - Spinor[p4__]]] := - ( - m 4 DOT[Spinor[p1] , ga1 , DiracGamma[7] , Spinor[p2] * - Spinor[p3] , ga2 , DiracGamma[6] , Spinor[p4]] ); -(* #################################################################### *) -(* Main444 *) -(* #################################################################### *) - - -(* eq. (8) *) -sirlin2[m_. DOT[ - Spinor[p1__], (ga1___) , - DiracGamma[ LorentzIndex[mu_] ], - DiracGamma[ lv_[rho_] ] , - DiracGamma[ LorentzIndex[nu_] ], (ga2___) , - Spinor[p2__]] * - DOT[ - Spinor[p3__], (ga3___) , - DiracGamma[ LorentzIndex[mu_] ], - DiracGamma[ lvt_[tau_] ] , - DiracGamma[ LorentzIndex[nu_] ], (ga4___) , - Spinor[p4__]] -] := - Block[ {ii = 1, ind, la, grho, gtau, gam5}, - While[!FreeQ[{ga1,rho,ga2,ga3,tau,ga4}, - $MU[ii]], - ii++ + (* Covariant normalization of ubar.u or vbar.v (as in Peskin and Schroeder). + The combinations ubar.v and vbar.u are orthogonal and hence vanish *) + If[ !FreeQ[tmp,Spinor], + time2=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: Applying spinor normalization on ", tmp, FCDoControl->dsVerbose]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Spinor normalization done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->dsVerbose]; + tmp = tmp/. DOT->holdDOT //. + { holdDOT[Spinor[s_. Momentum[p__],m_, 1],Spinor[s_. Momentum[p__],m_, 1]] -> s 2 m, + holdDOT[Spinor[- Momentum[p__],m_, 1],Spinor[Momentum[p__],m_, 1]] -> 0, + holdDOT[Spinor[Momentum[p__],m_, 1],Spinor[- Momentum[p__],m_, 1]] -> 0} /. + holdDOT -> DOT; + FCPrint[3,"DiracSimplify: diracSimplifyEval: After spinor normalization: ", tmp, FCDoControl->dsVerbose]; ]; - la = DiracGamma[LorentzIndex[$MU[ii]]]; - grho = DiracGamma[lv[rho]]; - gtau = DiracGamma[lvt[tau]]; - gam5 = DiracGamma[5]; - Contract[ - 2 m Pair[lv[rho], lvt[tau]] * - DOT[Spinor[p1] , ga1 , la , ga2 , Spinor[p2]] * - DOT[Spinor[p3] , ga3 , la , ga4 , Spinor[p4]] + - 2 m * - DOT[Spinor[p1] , ga1 , gtau , ga2 , Spinor[p2]] * - DOT[Spinor[p3] , ga3 , grho , ga4 , Spinor[p4]] + - 2 m Pair[lv[rho], lvt[tau]] * - DOT[Spinor[p1] , ga1 , la , ga2 , gam5 , Spinor[p2]] * - DOT[Spinor[p3] , ga3 , la , ga4 , gam5 , Spinor[p4]] - - 2 m * - DOT[Spinor[p1] , ga1 , gtau , ga2 , gam5 , Spinor[p2]] * - DOT[Spinor[p3] , ga3 , grho , ga4 , gam5 , Spinor[p4]] - ] - ]; -(* eq. (12) of Sirlin *) - -sirlin2[m_. DOT[ - Spinor[p1__], - DiracGamma[LorentzIndex[mu_]], - DiracGamma[lv_[rho_] ] , - DiracGamma[LorentzIndex[sigma_]], - DiracGamma[lvt_[tau_]], - DiracGamma[LorentzIndex[nu_]], - om_ , - Spinor[p2__]] * - DOT[Spinor[p3__], - DiracGamma[LorentzIndex[mu_]], - DiracGamma[lva_[alpha_] ] , - DiracGamma[LorentzIndex[sigma_]], - DiracGamma[lvb_[beta_]], - DiracGamma[ LorentzIndex[nu_]], - om_ , - Spinor[p4__]] -] := - Contract[ m 16 Pair[lvt[tau],lvb[beta]] Pair[lv[rho], lva[alpha]] * - DOT[ - Spinor[p1], - DiracMatrix[mu], - om, - Spinor[p2]] * - DOT[ - Spinor[p3], - DiracMatrix[mu], - om , - Spinor[p4]] - ]/; (om===DiracGamma[6]) || (om===DiracGamma[7]); - -(* eq. (13) of Sirlin *) -sirlin2[m_. DOT[ - Spinor[p1__], - DiracGamma[LorentzIndex[mu_]], - DiracGamma[lv_[rho_] ] , - DiracGamma[LorentzIndex[sigma_]], - DiracGamma[lvt_[tau_] ], - DiracGamma[LorentzIndex[nu_]], - om1_ , - Spinor[p2__]] * - DOT[ - Spinor[p3__], - DiracGamma[LorentzIndex[mu_]], - DiracGamma[lva_[alpha_] ] , - DiracGamma[LorentzIndex[sigma_]], - DiracGamma[lvb_[beta_] ], - DiracGamma[LorentzIndex[nu_]], om2_ , - Spinor[p4__]] -] := - (m 4 DOT[ - Spinor[p1], - DiracMatrix[mu], - DiracGamma[lv[rho]], - DiracGamma[lvb[beta]], - om1 , - Spinor[p2]] * - DOT[ - Spinor[p3], - DiracMatrix[mu], - DiracGamma[lva[alpha]], - DiracGamma[lvt[tau]], - om2, - Spinor[p4]]) /; ( (om1===DiracGamma[6])&& (om2===DiracGamma[7]) )|| - ((om1===DiracGamma[7])&& (om2===DiracGamma[6]) ); -(* #################################################################### *) -(* Main445 *) -(* #################################################################### *) - - -(* in case if no chiral projectors are present: *) -sirlin2[m_. DOT[ - Spinor[p1__], - DiracGamma[LorentzIndex[mu_]], - DiracGamma[lv_[rho_] ] , - DiracGamma[LorentzIndex[sigma_]], - DiracGamma[lvt_[tau_] ], - DiracGamma[LorentzIndex[nu_]], - Spinor[p2__]] * - DOT[ - Spinor[p3__], - DiracGamma[ LorentzIndex[mu_] ], - DiracGamma[ lva_[alpha_] ] , - DiracGamma[ LorentzIndex[sigma_] ], - DiracGamma[ lvb_[beta_] ], - DiracGamma[ LorentzIndex[nu_] ], - Spinor[p4__]] -] := - Block[ {tmp,re}, - tmp[ome1_,ome2_] := - sirlin2[m DOT[ - Spinor[p1], - DiracMatrix[mu], - DiracGamma[lv[rho]], - DiracMatrix[sigma], - DiracGamma[lvt[tau]], - DiracMatrix[nu], - DiracGamma[ome1], - Spinor[p2]] * - DOT[ - Spinor[p3], - DiracMatrix[mu], - DiracGamma[lva[alpha]], - DiracMatrix[sigma], - DiracGamma[lvb[beta]], - DiracMatrix[nu], - DiracGamma[ome2], - Spinor[p4]]]; - re = tmp[6,6] + tmp[6,7] + tmp[7,6] + tmp[7,7]; - re - ]; + (* Factoring *) + If[ optFactoring=!=False, + time2=AbsoluteTime[]; + FCPrint[2,"DiracSimplify: diracSimplifyEval: Factoring the result.", FCDoControl->dsVerbose]; + tmp = optFactoring[tmp]; + FCPrint[2,"DiracSimplify:diracSimplifyEvale: Done factoring, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->dsVerbose] + ]; -(* #################################################################### *) -(* Main446 *) -(* #################################################################### *) - -(* These are the ones calculated by FeynCalc *) - -sirlin2[m_. DOT[ - Spinor[pi__] , - x1___ , - DiracGamma[ LorentzIndex[mu_] ] , - DiracGamma[ LorentzIndex[nu_] ] , - x2___ , - Spinor[pj__]] * - DOT[ - Spinor[pk__] , - x3___ , - DiracGamma[ vm_[a_] ] , - DiracGamma[ LorentzIndex[mu_] ] , - DiracGamma[ LorentzIndex[nu_] ] , - x4___ , - Spinor[pl__] - ] -] := - Contract[ m (2 DOT[ - Spinor[pi], - x1, - x2, - Spinor[pj] - ]* - DOT[ - Spinor[pk], - x3 , - DiracGamma[vm[a]], - x4, - Spinor[pl] - ] + - 2 DOT[ - Spinor[pk], - x3, - DiracGamma[LorentzIndex[al$mu]], - x4, - Spinor[pl] - ]* - DOT[ - Spinor[pi], - x1, - DiracGamma[vm[a]], - DiracGamma[LorentzIndex[al$mu]], - x2, - Spinor[pj] - ] - 2 * - DOT[ - Spinor[pi], - x1, - DiracGamma[5], - x2, - Spinor[pj] - ]* - DOT[ - Spinor[pk] , - x3 , - DiracGamma[vm[a]], - DiracGamma[5], - x4, - Spinor[pl] - ] + 2* - DOT[ - Spinor[pk], - x3, - DiracGamma[LorentzIndex[al$mu]] , - DiracGamma[5], - x4, - Spinor[pl]]* - DOT[ - Spinor[pi], - x1, - DiracGamma[vm[a]] , - DiracGamma[LorentzIndex[al$mu]], - DiracGamma[5] , - x2, - Spinor[pj] - ]) - ]; + res = tmp; -sirlin2[m_. DOT[Spinor[Momentum[pi_], 0, fq___] , DiracGamma[Momentum[pk_]], Spinor[Momentum[pj_], 0, fq___]]* - DOT[Spinor[Momentum[pl_], 0, fq___] , DiracGamma[Momentum[pj_]], Spinor[Momentum[pk_], 0, fq___]]] := - Contract[m (-(( DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pl]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pi]], Spinor[Momentum[pk], 0, fq]]* - Pair[Momentum[pj], Momentum[pk]])/Pair[Momentum[pi], Momentum[pl]]) + - ( DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], DiracGamma[5] , Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], DiracGamma[5] , Spinor[Momentum[pk], 0, fq]]* - (-(Pair[Momentum[pi], Momentum[pl]]*Pair[Momentum[pj], Momentum[pk]]) + Pair[Momentum[pi], Momentum[pk]]* - Pair[Momentum[pj], Momentum[pl]] - Pair[Momentum[pi], Momentum[pj]]*Pair[Momentum[pk], Momentum[pl]]))/ - (2 Pair[Momentum[pi], Momentum[pl]]) + - ( DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pk], 0, fq]]* - (3 Pair[Momentum[pi], Momentum[pl]] Pair[Momentum[pj], Momentum[pk]] + Pair[Momentum[pi], Momentum[pk]]* - Pair[Momentum[pj], Momentum[pl]] - Pair[Momentum[pi], Momentum[pj]]*Pair[Momentum[pk], Momentum[pl]]))/ - (2 Pair[Momentum[pi], Momentum[pl]]) - )]; - -sirlin2[m_. DOT[Spinor[Momentum[pi_], 0, fq___] , DiracGamma[Momentum[pk_]], Spinor[Momentum[pj_], 0, fq___]]* - DOT[Spinor[Momentum[pl_], 0, fq___] , DiracGamma[Momentum[pi_]], Spinor[Momentum[pk_], 0, fq___]]] := - Contract[m (-(( DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pl]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pj]], Spinor[Momentum[pk], 0, fq]]* - Pair[Momentum[pi], Momentum[pk]])/ Pair[Momentum[pj], Momentum[pl]]) + - ( DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pk], 0, fq]]* - (Pair[Momentum[pi], Momentum[pl]] Pair[Momentum[pj], Momentum[pk]] + 3 Pair[Momentum[pi], Momentum[pk]]* - Pair[Momentum[pj], Momentum[pl]] - Pair[Momentum[pi], Momentum[pj]]*Pair[Momentum[pk], Momentum[pl]]))/ - (2 Pair[Momentum[pj], Momentum[pl]]) + - ( DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], DiracGamma[5], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], DiracGamma[5] , Spinor[Momentum[pk], 0, fq]]* - (-(Pair[Momentum[pi], Momentum[pl]] Pair[Momentum[pj], Momentum[pk]]) + - Pair[Momentum[pi], Momentum[pk]]*Pair[Momentum[pj], Momentum[pl]] + Pair[Momentum[pi], Momentum[pj]]* - Pair[Momentum[pk], Momentum[pl]]))/(2*Pair[Momentum[pj], Momentum[pl]]))] /; - First[ DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pk]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pi]] , Spinor[Momentum[pk], 0, fq]]]=== - DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pk]], Spinor[Momentum[pj], 0, fq]]; - -sirlin2[ m_. DOT[Spinor[Momentum[pi_], 0, fq___] , DiracGamma[Momentum[pk_]], DiracGamma[5], Spinor[Momentum[pj_], 0, fq___]]* - DOT[Spinor[Momentum[pl_], 0, fq___] , DiracGamma[Momentum[pj_]], DiracGamma[5], Spinor[Momentum[pk_], 0, fq___]]] := - Contract[ m(DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pk]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pj]], Spinor[Momentum[pk], 0, fq]] - - DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pk], 0, fq]]* - Pair[Momentum[pj], Momentum[pk]] + - DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], DiracGamma[5], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], DiracGamma[5], Spinor[Momentum[pk], 0, fq]]* - Pair[Momentum[pj], Momentum[pk]])]; - -sirlin2[m_. DOT[Spinor[Momentum[pi_], 0, fq___] , DiracGamma[Momentum[pk_]], DiracGamma[5], Spinor[Momentum[pj_], 0, fq___]]* - DOT[Spinor[Momentum[pl_], 0,fq___], DiracGamma[Momentum[pi_]], DiracGamma[5], Spinor[Momentum[pk_], 0, fq___]]] := - Contract[ m (-( DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pk]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pi]], Spinor[Momentum[pk], 0, fq]]) + - DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pk], 0, fq]]* - Pair[Momentum[pi], Momentum[pk]] + - DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], DiracGamma[5] , Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], DiracGamma[5] , Spinor[Momentum[pk], 0, fq]]* - Pair[Momentum[pi], Momentum[pk]]) - ]; + FCPrint[3,"DiracSimplify: diracSimplifyEval: Leaving with: ", res, FCDoControl->dsVerbose]; -sirlin2[m_. DOT[Spinor[Momentum[pi_], 0, fq___], DiracGamma[Momentum[pl_]], DiracGamma[5], Spinor[Momentum[pj_], 0, fq___]]* - DOT[Spinor[Momentum[pl_], 0, fq___] , DiracGamma[Momentum[pj_]], DiracGamma[5], Spinor[Momentum[pk_], 0, fq___]]] := - Contract[ m (-( - DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pl]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pj]], Spinor[Momentum[pk], 0, fq]]) + - DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]], Spinor[Momentum[pk], 0, fq]]* - Pair[Momentum[pj], Momentum[pl]] + - DOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[la]] , - DiracGamma[5] , Spinor[Momentum[pj], 0, fq]]* - DOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[la]] , - DiracGamma[5] , Spinor[Momentum[pk], 0, fq]]* Pair[Momentum[pj], Momentum[pl]])]; - -(* #################################################################### *) -(* Main447 *) -(* #################################################################### *) - -dig[LorentzIndex[a_,___]] := - a; -dig[Momentum[a_,___]] := - a; -dig[x_] := - x/;(Head[x]=!=LorentzIndex)&&(Head[x]=!=Momentum); -dig[_?NumberQ] := - {}; -getV[x_List] := - Select[Flatten[{x}/.DOT->List]/.DiracGamma -> dige, Head[#]===dige&]/.dige->dig; - -(* Get a list of equal gamma matrices *) -schnitt[x___][y___] := - Intersection[ - Select[Flatten[{x}/.DOT->List],!FreeQ[#,LorentzIndex]&], - Select[Flatten[{y}/.DOT->List],!FreeQ[#,LorentzIndex]&] - ]; + res -(* get a list of not equal slashes and matrices *) -comp[x___][y___] := - Select[Complement[Flatten[Union[{x},{y}]/.DOT->List], - schnitt[x][y] ], - !FreeQ2[#, {LorentzIndex, Momentum}]&]; - -(* sirlin1def *) -(* do some ordering with sirlin1 ... *) -sirlin1[m_. DOT[Spinor[p1__], (gam1__) , Spinor[p2__]] DOT[Spinor[p3__], (gam2__) , Spinor[p4__]]] := - MemSet[sirlin1[m DOT[Spinor[p1],gam1,Spinor[p2]] DOT[Spinor[p3],gam2,Spinor[p4]]], - Block[ {schnittmenge, compmenge, result,order, orderl,orderr, leftind, rightind}, - schnittmenge = schnitt[gam1][gam2]; - compmenge = comp[gam1][gam2]; - leftind = comp[gam1][schnittmenge]; - rightind = comp[gam2][schnittmenge]; - FCPrint[3,"entering sirlin1"]; - (* We need at least two dummy indices for the sirlin relations *) - If[ Length[schnittmenge] > 1, - (* Test for eq. (12) *) - If[ (Length[schnittmenge] === 3) && (Length[compmenge] > 3), - orderl = Join[ Drop[leftind, {1,2}], {schnittmenge[[1]], - leftind[[1]], schnittmenge[[2]], - leftind[[2]], schnittmenge[[3]]}] // getV; - orderr = Join[ Drop[rightind, {1,2}], {schnittmenge[[1]], - rightind[[1]], schnittmenge[[2]], - rightind[[2]], schnittmenge[[3]]}] // getV; - result = - Expand[m Contract[ - DiracOrder[ DOT[Spinor[p1],gam1,Spinor[p2]], orderl ]* - DiracOrder[ DOT[Spinor[p3],gam2,Spinor[p4]], orderr ] ] - ]//sirlin2 - ]; - (* ... *) - (* Test for eq. (8) *) - If[ (Length[schnittmenge] === 2) && (Length[compmenge] > 1), - order = Join[{First[schnittmenge]}, compmenge, - {Last[schnittmenge]} ] // getV; - result = sirlin2[ Expand[ m DiracOrder[ - DOT[Spinor[p1],gam1,Spinor[p2]] * - DOT[Spinor[p3],gam2,Spinor[p4]], order]]//Contract] - ]; - ]; - If[ !ValueQ[result], - result = sirlin2[m * - DOT[Spinor[p1],gam1,Spinor[p2]] * - DOT[Spinor[p3],gam2,Spinor[p4]]] - ]; - FCPrint[3,"exiting sirlin1"]; - result - ] - ] /; !FreeQ[{gam1}, LorentzIndex]; - - -(*ChisholmSpinordef*) -dsimp[x_] := - sirlin0[spcev0[x]]; -ChisholmSpinor[x_, choice_:0] := - MemSet[ChisholmSpinor[x,choice], - Block[ {new = x, indi}, - FCPrint[3,"entering ChisholmSpinor "]; - new = DotSimplify[new]; - If[ choice===1, - new = new/.{ DOT[Spinor[a__],b__ ,Spinor[c__]] * - DOT[Spinor[d__],e__ ,Spinor[f__]]:> - DOT[nospinor[a],b,nospinor[c]] * - DOT[Spinor[d],e,Spinor[f]]} - ]; - If[ choice===2, - new = new/.{ DOT[Spinor[a__],b__ ,Spinor[c__]] * - DOT[Spinor[d__],e__ ,Spinor[f__]]:> - DOT[Spinor[a],b,Spinor[c]] * - DOT[nospinor[d],e,nospinor[f]]} - ]; - dsimp[Contract[dsimp[new/.{(DOT[Spinor[pe1_, m_, ql___], - DiracGamma[lv_[k_]] , h___ , Spinor[pe2_, m2_, ql___]]) :> - Block[ {indi}, - indi = Unique["alpha"]; - -1/Pair[pe1,pe2] ( DOT[Spinor[pe1, m, ql], DiracGamma[pe1], - DiracGamma[lv[k]] , DiracGamma[pe2],h, - Spinor[pe2, m2, ql]] - - Pair[pe1,lv[k]] DOT[Spinor[pe1, m, ql], - DiracGamma[pe2], h , Spinor[pe2, m2, ql]] - - Pair[lv[k],pe2] DOT[Spinor[pe1, m, ql], - DiracGamma[pe1] , h , Spinor[pe2, m2, ql]]- - I Eps[pe1,lv[k],pe2,LorentzIndex[indi]] * - DOT[Spinor[pe1, m, ql], - DiracGamma[LorentzIndex[indi]], - DiracGamma[5],h, - Spinor[pe2, m2, ql]] - ) - ]}/.nospinor->Spinor], EpsContract->True] - ] - ] - ]; + ]/;Head[expr]=!=DiracChain; FCPrint[1,"DiracSimplify.m loaded."]; End[] diff --git a/FeynCalc/Dirac/DiracSubstitute5.m b/FeynCalc/Dirac/DiracSubstitute5.m new file mode 100644 index 000000000..94f6fde3c --- /dev/null +++ b/FeynCalc/Dirac/DiracSubstitute5.m @@ -0,0 +1,69 @@ +(* ::Package:: *) + + +(* :Title: DiracSubstitute5 *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Substitutes DiracGamma[6] and DiracGamma[7] in terms of + DiracGamma[5] *) + +(* ------------------------------------------------------------------------ *) + +DiracSubstitute5::usage = +"DiracSubstitute5[exp] rewrites DiracGamma[5] in exp in terms of \ +the chirality projectors DiracGamma[6] and DiracGamma[7]. \ +DiracSubstitute5 is also an option of various FeynCalc functions \ +that handle Dirac algebra."; + +DiracSubstitute5::failmsg = +"Error! DiracSubstitute5 has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`DiracSubstitute5`Private`"]; + +Options[DiracSubstitute5] = { + FCE -> False, + FCI -> False +}; + +DiracSubstitute5[expr_, OptionsPattern[]] := + Block[{ex, res, holdDOT}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ2[ex, {DiracGamma[5]}], + Return[ex] + ]; + + res = ex /. DiracGamma[5] :> DiracGamma[6]-DiracGamma[7]; + + + If[ !FreeQ2[res,{DiracGamma[5]}], + Message[DiracSubstitute5::failmsg,"Failed to eliminate all occurences of DiracGamma[5]."]; + Abort[] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + +FCPrint[1,"DiracSubstitute5.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/DiracSubstitute67.m b/FeynCalc/Dirac/DiracSubstitute67.m new file mode 100644 index 000000000..15469cb3b --- /dev/null +++ b/FeynCalc/Dirac/DiracSubstitute67.m @@ -0,0 +1,72 @@ +(* ::Package:: *) + + +(* :Title: DiracSubstitute67 *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Substitutes DiracGamma[6] and DiracGamma[7] in terms of + DiracGamma[5] *) + +(* ------------------------------------------------------------------------ *) + +DiracSubstitute67::usage = +"DiracSubstitute67[exp] inserts the explicit definitions of \ +the chirality projectors DiracGamma[6] and DiracGamma[7]. \ +DiracSubstitute67 is also an option of various FeynCalc functions \ +that handle Dirac algebra."; + +DiracSubstitute67::failmsg = +"Error! DiracSubstitute67 has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`DiracSubstitute67`Private`"]; + +Options[DiracSubstitute67] = { + FCE -> False, + FCI -> False +}; + +DiracSubstitute67[expr_, OptionsPattern[]] := + Block[{ex, res, holdDOT}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ2[ex, {DiracGamma[6],DiracGamma[7]}], + Return[ex] + ]; + + res = ex /. { + DiracGamma[6] :> (1/2 + DiracGamma[5]/2), + DiracGamma[7] :> (1/2 - DiracGamma[5]/2) + }; + + + If[ !FreeQ2[res,{DiracGamma[6],DiracGamma[7]}], + Message[DiracSubstitute67::failmsg,"Failed to eliminate all occurences of chirality projectors."]; + Abort[] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + +FCPrint[1,"DiracSubstitute67.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/DiracTrace.m b/FeynCalc/Dirac/DiracTrace.m index 95c922574..41ca4c04c 100755 --- a/FeynCalc/Dirac/DiracTrace.m +++ b/FeynCalc/Dirac/DiracTrace.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Dirac trace calculation *) @@ -17,37 +17,23 @@ DiracTrace::usage = -"DiracTrace[expr] is the head of Dirac traces. \ -Whether the trace is evaluated depends on the option \ -DiracTraceEvaluate. See also TR. \ -The argument expr may be a product of Dirac matrices or slashes \ -separated by the Mathematica Dot \".\" (assuming DOT has been set to Dot). -The option Factoring determines the final function to be applied. If \ -it is set to False no simplification is done. \ -It might be set to, e.g., Factor or Factor2 to get simpler results. \ -With the default setting Factoring -> Automatic factorization is performed on \ -not too long (LeafCount[ ] < 5000 ) expressions. -"; - -DiracTrace::noncom = -"Wrong syntax! The Dirac trace of `1` contains Dirac matrices multiplied via \ -Times (commutative multiplication) instead of DOT (non-commutative multiplication). \ -Evaluation aborted!"; - -DiracTrace::ndranomaly = -"You are using naive dimensional regularization (NDR), such that in D dimensions \ -gamma^5 anticommutes with all other Dirac matrices. In this scheme \ -(without additional prescriptions) it is not possible to compute traces with an \ -odd number of gamma^5 unambiguously. Evaluation aborted!"; - -DiracTrace::ilsch = -"The settings $BreitMaison=`1`, $Larin=`2` do not describe a valid \ -scheme for treating gamma^5 in D dimensions. Evaluation aborted!."; +"DiracTrace[exp] is the head of Dirac traces. \ +By default the trace is not evaluated. The evaluation occurs only when \ +the option DiracTraceEvaluate is set to True. It is recommended to use \ +DiracSimplify, which will automatically evaluate all Dirac traces in the \ +input expression."; DiracTrace::failmsg = "Error! DiracTrace has encountered a fatal problem and must abort the computation. \ The problem reads: `1`" +DiracTrace::mixmsg = "Expressions that mix D-, 4- and D-4-dimensional quantities are forbidden \ +in Dirac matrix chains unless you are using the t'Hooft-Veltman scheme. For every other scheme, please \ +recheck your input expressions and ensure that all matrices, spinors and tensors are purely \ +D-dimensional. You might want to use FCGetDimensions[exp] to find the offending terms and fix them \ +by hand or ChangeDimension[exp,D] to convert the whole expression to D-dimensions. If you explicitly \ +intend to use the t'Hooft-Veltman scheme, please activate it via FCSetDiracGammaScheme[\"BMHV\"]." + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -61,21 +47,25 @@ not too long (LeafCount[ ] < 5000 ) expressions. traceNo5Fun::usage=""; trace5Fun::usage=""; noSpur::usage=""; +leviCivitaSign::usage=""; +optSort::usage=""; Options[DiracTrace] = { - Contract -> 400000, - DiracTraceEvaluate-> False, - EpsContract -> False, - Expand -> True, - FCVerbose -> False, - Factoring -> Automatic, - FeynCalcExternal -> False, - FeynCalcInternal -> False, - Mandelstam -> {}, - PairCollect -> False, - Schouten-> 0, - TraceOfOne -> 4, - West -> True + Contract -> True, + DiracTraceEvaluate -> False, + EpsContract -> False, + Expand -> True, + FCVerbose -> False, + Factoring -> Automatic, + FCDiracIsolate -> True, + FeynCalcExternal -> False, + FeynCalcInternal -> False, + Mandelstam -> {}, + PairCollect -> False, + Schouten -> 0, + Sort -> True, + TraceOfOne -> 4, + West -> True }; @@ -83,32 +73,27 @@ not too long (LeafCount[ ] < 5000 ) expressions. MakeBoxes[DiracTrace[expr__, OptionsPattern[]], TraditionalForm]:= RowBox[{"tr","(",TBox[expr], ")"}] - -(* gamma67backdef: reinsertion of gamma6 and gamm7 *) -gamma67back[x_] := - x/.DiracGamma[6]->( 1/2 + DiracGamma[5]/2 )/. DiracGamma[7]->( 1/2 - DiracGamma[5]/2 ); - DiracTrace[0, OptionsPattern[]] := 0; -DiracTrace[a_ /; (FreeQ[a, DiracGamma] && !FreeQ[a, DiracGammaT]), b:OptionsPattern[]] := - DiracTrace[(a//Transpose)//Reverse, b]; - DiracTrace[a:Except[_HoldAll]..., x_,y_, z___] := - DiracTrace[a,x.y,z]/;FreeQ2[y,{Rule,BlankNullSequence}]&& FreeQ2[x,{Rule,BlankNullSequence}]; + DiracTrace[a,x.y,z]/;FCPatternFreeQ[{x,y},{Rule}]; DiracTrace[expr_, op:OptionsPattern[]] := - Block[ {diTres, ex, tr1,tr2,tr3,time,dsHead,diracObjects,diracObjectsEval,null1,null2,freePart,dsPart,repRule,diTr}, + Block[{ diTres, ex, tr1, tr2, tr3, time, dsHead, diracObjects, + diracObjectsEval, null1, null2, freePart, dsPart, repRule, + diTr, holdDOT, insideDiracTrace}, If [OptionValue[FCVerbose]===False, diTrVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], diTrVerbose=OptionValue[FCVerbose] ]; ]; unitMatrixTrace = OptionValue[TraceOfOne]; + optSort = OptionValue[Sort]; FCPrint[1, "DiracTrace. Entering.", FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrace: Entering with ", expr, FCDoControl->diTrVerbose]; @@ -118,71 +103,94 @@ not too long (LeafCount[ ] < 5000 ) expressions. ex = expr, ex = FCI[expr] ]; - (* - time=AbsoluteTime[]; - FCPrint[1, "DiracTrace. Checking the syntax.", FCDoControl->diTrVerbose]; - If [ !FreeQ2[ex, - { - (*Times instead of DOT between two Dirac or SU(N) matrices*) - (DiracGamma | DiracGammaT)[a__]*(DiracGamma | DiracGammaT)[b__], - SUNT[a__]*SUNT[b__], - (*Two DOT objects multiplied with each other via Times, unless those are closed spinor chains*) - DOT[a:Except[_Spinor]...,(DiracGamma | DiracGammaT )[b__],c:Except[_Spinor]...]* - DOT[d:Except[_Spinor]...,(DiracGamma | DiracGammaT)[e__],f:Except[_Spinor]...], - (*Open spinor chains*) - DOT[a_Spinor,b:Except[_Spinor]...], - (*DOT object multiplied by a Dirac or SU(N) matrix via Times*) - DOT[a:Except[_Spinor]...,(DiracGamma | DiracGammaT)[b__],c:Except[_Spinor]...]* - (DiracGamma | DiracGammaT)[d__]}], - Message[DiracTrace::noncom, InputForm[ex]]; - Abort[] - ]; - FCPrint[1,"DiracTrace: Syntax check done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->diTrVerbose]; - *) (* Doing contractions can often simplify the underlying expression *) time=AbsoluteTime[]; - FCPrint[1, "DiracTrace. Applying Contract.", FCDoControl->diTrVerbose]; - If[ Contract=!=False, + + If[ OptionValue[Contract]=!=False && !DummyIndexFreeQ[ex,{LorentzIndex,CartesianIndex}], + FCPrint[1, "DiracTrace. Applying Contract.", FCDoControl->diTrVerbose]; ex = Contract[ex, Expanding->True, EpsContract-> OptionValue[EpsContract], Factoring->False]; + FCPrint[1,"DiracTrace: Contract done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->diTrVerbose] ]; - FCPrint[1,"DiracTrace: Contract done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->diTrVerbose]; - (* First of all we need to extract all the Dirac structures inside the trace. *) - ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, Spinor->False, DiracTrace -> False, DiracSigmaExplicit->True]; - ex = ex /. DiracTrace -> diTr; + If[ OptionValue[FCDiracIsolate], + FCPrint[1, "DiracTrace: Standard mode.", FCDoControl->diTrVerbose]; + (* First of all we need to extract all the Dirac structures inside the trace. *) + ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, Spinor->False, DiracTrace -> False, DiracSigmaExplicit->True]; + ex = ex /. DiracTrace -> diTr; - {freePart,dsPart} = FCSplit[ex,{dsHead}]; - FCPrint[3,"DiracTrace: dsPart: ",dsPart , FCDoControl->diTrVerbose]; - FCPrint[3,"DiracTrace: freePart: ",freePart , FCDoControl->diTrVerbose]; - If [ dsPart=!=0, - (* Check that there is only one dsHead per term and no nested dsHeads *) - Scan[ - If[ !MatchQ[#, a_. dsHead[b_]/; (FreeQ[{a,b}, dsHead] && !FreeQ[b,DiracGamma])], - Message[DiracTrace::failmsg, "Irregular trace structure in", InputForm[#]]; - Print[#]; - Abort[] - ]&, dsPart+dsHead[DiracGamma] ]; - ]; + {freePart,dsPart} = FCSplit[ex,{dsHead}]; + FCPrint[3,"DiracTrace: dsPart: ",dsPart , FCDoControl->diTrVerbose]; + FCPrint[3,"DiracTrace: freePart: ",freePart , FCDoControl->diTrVerbose]; + If [ dsPart=!=0, + (* Check that there is only one dsHead per term and no nested dsHeads *) + Scan[ + If[ !MatchQ[#, a_. dsHead[b_]/; (FreeQ[{a,b}, dsHead] && !FreeQ[b,DiracGamma])], + Message[DiracTrace::failmsg, "Irregular trace structure in", InputForm[#]]; + Print[#]; + Abort[] + ]&, dsPart+dsHead[DiracGamma] ]; + ]; + + (* Now it is guaranteed that dsPart is of the form a*dsHead[x]+b*dsHead[y]+c*dsHead[z]+... + So it is safe to extract all the dsHead objects and handle them separately *) + diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//Union, + + + FCPrint[1, "DiracTrace: Fast mode.", FCDoControl->diTrVerbose]; + (* Fast mode for simple traces *) + If[ !FreeQ[ex,DiracGamma], + freePart=0; + If[ !FreeQ[ex,DiracSigma], + ex = DiracSigmaExplicit[ex,FCI->True] + ]; - (* Now it is guaranteed that dsPart is of the form a*dsHead[x]+b*dsHead[y]+c*dsHead[z]+... - So it is safe to extract all the dsHead objects and handle them separately *) - diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//Union; + dsPart=dsHead[ex]/. DiracTrace -> diTr; + diracObjects = {dsPart}, + + freePart=ex; + dsPart=0; + diracObjects = {} + ]; + + + + ]; time=AbsoluteTime[]; - FCPrint[1, "DiracTrace. Applying diracTraceEvaluate.", FCDoControl->diTrVerbose]; + FCPrint[1, "DiracTrace. Applying diracTrickEvalFast.", FCDoControl->diTrVerbose]; + + (* Here we try to compute some very simple traces in a faster way *) + + insideDiracTrace = FeynCalc`DiracTrick`Private`insideDiracTrace; + FeynCalc`DiracTrick`Private`insideDiracTrace = True; + + diracObjectsEval = Map[FeynCalc`DiracTrick`Private`diracTrickEvalFast[#]&, (diracObjects/.dsHead->Identity)] /. FeynCalc`DiracTrick`Private`diracTrickEvalFast->Identity; + + FeynCalc`DiracTrick`Private`insideDiracTrace = insideDiracTrace; + + + FCPrint[1,"DiracTrace: After diracTrickEvalFast: ", diracObjectsEval, FCDoControl->diTrVerbose]; diracObjectsEval = Map[diracTraceEvaluate[#, Flatten[Join[{op}, FilterRules[Options[DiracTrace], Except[{op}]]]]]&, - (diracObjects/.dsHead->Identity)]; + diracObjectsEval]; diracObjectsEval = diracObjectsEval/. noSpur[x__]:> diTr[DOT[x]]/unitMatrixTrace; - repRule = MapThread[Rule[#1,#2]&,{diracObjects,diracObjectsEval}]; + FCPrint[1,"DiracTrace: diracTraceEvaluate finished, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->diTrVerbose]; + + repRule = Thread[Rule[diracObjects,diracObjectsEval]]; FCPrint[3,"DiracTrace: repRule: ",repRule , FCDoControl->diTrVerbose]; - tr3 = (unitMatrixTrace freePart) + ( dsPart/.repRule); + If[ !FreeQ[freePart,DOT], + freePart = freePart /. DOT->holdDOT /. holdDOT[a__]/;NonCommFreeQ[{a}] :> Times[a] /. holdDOT -> DOT + ]; + + tr3 = (unitMatrixTrace freePart) + ( dsPart /. Dispatch[repRule]); + + (* If the result should contain Mandelstam variables *) If[ Length[OptionValue[Mandelstam]] > 0, @@ -200,20 +208,24 @@ not too long (LeafCount[ ] < 5000 ) expressions. ]; diTres = diTres/. diTr->DiracTrace; + diTrVerbose=$VeryVerbose; + FCPrint[1, "DiracTrace: Leaving.", FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrace: Leaving with", diTres, FCDoControl->diTrVerbose]; diTres ]/; OptionValue[DiracTraceEvaluate]; -diracTraceEvaluate[expr_,opts:OptionsPattern[]] := + +diracTraceEvaluate[expr_/;FreeQ[expr,DiracGamma], OptionsPattern[]] := + unitMatrixTrace expr; + +diracTraceEvaluate[expr_/;!FreeQ[expr,DiracGamma], opts:OptionsPattern[]] := Block[ { diractrres, tmp = expr, diractrfact, diractrcoll, schoutenopt, - dtmp,dWrap,dtWrap,wrapRule,prepSpur,time,time2,contract,spurHeadList,spurHeadListChiral,spurHeadListNonChiral, + dtmp,dWrap,wrapRule,prepSpur,time,time2,contract,spurHeadList,spurHeadListChiral,spurHeadListNonChiral, gammaFree,gammaPart, - traceListChiral,traceListNonChiral,repRule,null1,null2 - - }, + traceListChiral,traceListNonChiral,repRule,null1,null2,dummyIndexFreeQ}, wrapRule = {dWrap[5]->0, dWrap[6]->1/2, dWrap[7]->1/2, dWrap[LorentzIndex[_,_:4],___]->0, dWrap[_. Momentum[_,_:4]+_:0,___]->0}; @@ -234,6 +246,16 @@ not too long (LeafCount[ ] < 5000 ) expressions. FCPrint[1,"DiracTrace: diracTraceEvaluate: Entering", FCDoControl->diTrVerbose]; FCPrint[3,"DiracTrace: diracTraceEvaluate: Entering with: ",expr, FCDoControl->diTrVerbose]; + (* Even before we compute the trace, we can already decide if the expression contains dummy + indices. It is clearly better to do it here, while the expression is still in the most + compact form! *) + time=AbsoluteTime[]; + FCPrint[1,"DiracTrace: diracTraceEvaluate: Checking if there are indices that need to be contracted. ", FCDoControl->diTrVerbose]; + dummyIndexFreeQ = DummyIndexFreeQ[tmp,{LorentzIndex,CartesianIndex}]; + FCPrint[1,"DiracTrace: diracTraceEvaluate: Check done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + + + time=AbsoluteTime[]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Applying DiracTrick.", FCDoControl->diTrVerbose]; @@ -244,7 +266,7 @@ not too long (LeafCount[ ] < 5000 ) expressions. time=AbsoluteTime[]; If[ !FreeQ[tmp, DiracGamma], - (* If the output of DiracSimplify still contains Dirac matrices, apply DotSimplify and use DiracTrick again *) + (* If the output of DiracTrick still contains Dirac matrices, apply DotSimplify and use DiracTrick again *) (* We need to consider standalone Dirac matrices separately: With the following all of them will be wrapped inside dWrap or dtWrap *) FCPrint[1,"DiracTrace: diracTraceEvaluate: Calculating the trace.", FCDoControl->diTrVerbose]; @@ -258,13 +280,12 @@ not too long (LeafCount[ ] < 5000 ) expressions. time2=AbsoluteTime[]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Applying DiracTrick.", FCDoControl->diTrVerbose]; - tmp = DiracTrick[tmp, FCI -> True, InsideDiracTrace->True]; + tmp = DiracTrick[tmp, FCI -> True, InsideDiracTrace->True, FCJoinDOTs->False]; FCPrint[1,"DiracTrace: diracTraceEvaluate: DiracTrick done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->diTrVerbose]; FCPrint[3,"DiracTrace: diracTraceEvaluate: After DiracTrick: ", tmp, FCDoControl->diTrVerbose]; - - tmp = tmp /. {DiracGamma -> dWrap,DiracGammaT -> dtWrap} /. DOT -> prepSpur; - tmp = tmp /. prepSpur[zzz__] :> spurHead@@({zzz} /. {dWrap -> DiracGamma,dtWrap->DiracGammaT}); + tmp = tmp /. {DiracGamma -> dWrap} /. DOT -> prepSpur; + tmp = tmp /. prepSpur[zzz__] :> spurHead@@({zzz} /. {dWrap -> DiracGamma}); FCPrint[3,"DiracTrace: diracTraceEvaluate: Wrapped in spurHead: ",tmp, FCDoControl->diTrVerbose]; @@ -283,6 +304,21 @@ not too long (LeafCount[ ] < 5000 ) expressions. Abort[] ]; + (* Sort the matrices in the traces lexicographically using the cyclicity of the trace*) + + If[ optSort, + time2=AbsoluteTime[]; + FCPrint[1,"DiracTrace: diracTraceEvaluate: Applying the cyclicity of the trace to sort the matrices lexicographically.", FCDoControl->diTrVerbose]; + tmp = tmp /. spurHead[x__]/;(FCGetDimensions[{x},ChangeDimension->True]==={4})-> orderSpurHead[x]; + + If[ !FreeQ[tmp,orderSpurHead], + Message[DiracTrace::failmsg,"Sorting matrices inside Dirac traces failed."]; + Abort[] + ]; + + FCPrint[1,"DiracTrace: diracTraceEvaluate: Done sorting matrices lexicographically, timing:", N[AbsoluteTime[] - time2, 4], FCDoControl->diTrVerbose]; + FCPrint[3,"DiracTrace: diracTraceEvaluate: After sorting matrices lexicographically: ", tmp, FCDoControl->diTrVerbose] + ]; (* After all the simplifications we need to split terms that still containd Dirac matrices from those that don't. *) {gammaFree,gammaPart} = FCSplit[tmp,{spurHead}]; @@ -318,10 +354,10 @@ not too long (LeafCount[ ] < 5000 ) expressions. ]; (* One more check: Traces with mixed dimensions are forbidden in NDR and Larin's scheme, so we abort the computation if this is the case *) - If [ !$BreitMaison, + If [ (FeynCalc`Package`DiracGammaScheme =!= "BMHV"), Scan[ - If[ Length[FCGetDimensions[#/.DiracGamma[5]->1]]=!=1, - Message[DiracTrace::failmsg, "Traces with mixed dimensions are forbidden in this g^5 scheme."]; + If[ Length[FCGetDimensions[#, FreeQ->{DiracGamma[5]},ChangeDimension->True]]=!=1, + Message[DiracTrace::mixmsg]; Abort[] ]&, spurHeadListChiral ] @@ -352,30 +388,37 @@ not too long (LeafCount[ ] < 5000 ) expressions. FCPrint[1,"DiracTrace: diracTraceEvaluate: Calculating chiral traces.", FCDoControl->diTrVerbose]; (* Purely 4 dimensional traces are always computed in the same way, regardless of the chosen scheme: Eq 2.18 of R. Mertig, M. Boehm, A. Denner. Comp. Phys. Commun., 64 (1991)) *) - traceListChiral = spurHeadListChiral/. spurHead[x__]/;(FCGetDimensions[{x}]==={4}) :> spur5In4Dim[x]; + traceListChiral = spurHeadListChiral/. spurHead[x__]/;(FCGetDimensions[{x},ChangeDimension->True]==={4}) :> spur5In4Dim[x]; (* Choice of the scheme for D-dimensional g^5 *) If[ !FreeQ[traceListChiral,spurHead], - Which[ + Switch[FeynCalc`Package`DiracGammaScheme, + (* NDR *) - !$Larin && !$BreitMaison, - Message[DiracTrace::ndranomaly]; - Abort[], + "NDR", + traceListChiral = traceListChiral/. spurHead -> noSpur, + + (* NDR-Discard *) + "NDR-Drop", + traceListChiral = ConstantArray[0, Length[traceListChiral]], + (* Larin *) - $Larin && !$BreitMaison, + "Larin", FCPrint[3,"DiracTrace: diracTraceEvaluate: Chiral traces will be computed using Larin's scheme", FCDoControl->diTrVerbose]; traceListChiral = traceListChiral/. spurHead -> spur5Larin, + (* BMHV *) - !$Larin && $BreitMaison, + "BMHV", If[ west, (* BMHV, West's trace formula *) traceListChiral = traceListChiral/. spurHead -> spur5BMHVWest, (* BMHV, standard (slow!) trace formula *) traceListChiral = traceListChiral/. spurHead -> spur5BMHVNoWest ], - (* Any other combination of $Larin and $BreitMaison doesn't describe a valid scheme *) - True, - Message[DiracTrace::ilsch, $BreitMaison, $Larin]; + + (* unknown scheme *) + _, + Message[DiracTrace::failmsg, "Unknown scheme for handling Dirac matrices in dimensional regularization."]; Abort[] ] ]; @@ -384,7 +427,8 @@ not too long (LeafCount[ ] < 5000 ) expressions. FCPrint[3,"DiracTrace: diracTraceEvaluate: traceListChiral", traceListChiral, FCDoControl->diTrVerbose]; (* Check that there are no uncomputed traces left *) - If[ !FreeQ2[traceListChiral,{spurHead,DiracGamma,trace5}], + If[ !FreeQ2[traceListChiral /. _noSpur:>1 ,{spurHead,DiracGamma,trace5}], + Print[traceListChiral]; Message[DiracTrace::failmsg, "Not all chiral traces were evaluated."]; Abort[] ]; @@ -394,59 +438,63 @@ not too long (LeafCount[ ] < 5000 ) expressions. (* Expansion of scalar products. If some of the scalar products were arlready defined, they will be inserted here. *) - If[ OptionValue[DiracTrace,{opts},Expand], + If[ OptionValue[DiracTrace,{opts},Expand] && !FreeQ[{traceListNonChiral,traceListChiral,gammaFree,gammaPart}, Momentum], time2=AbsoluteTime[]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Expanding scalar products", FCDoControl->diTrVerbose]; - traceListNonChiral=Map[ExpandScalarProduct[#,FCI->False]&,traceListNonChiral]; - traceListChiral=Map[ExpandScalarProduct[#,FCI->False]&,traceListChiral]; - gammaFree=ExpandScalarProduct[gammaFree,FCI->False]; - gammaPart=ExpandScalarProduct[gammaPart,FCI->False]; + traceListNonChiral=Map[ExpandScalarProduct[#,FCI->True]&,traceListNonChiral]; + traceListChiral=Map[ExpandScalarProduct[#,FCI->True]&,traceListChiral]; + gammaFree=ExpandScalarProduct[gammaFree,FCI->True]; + gammaPart=ExpandScalarProduct[gammaPart,FCI->True]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Done expanding the result, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->diTrVerbose] ]; (* Create the substitution rule*) - repRule = MapThread[Rule[#1,#2]&,{spurHeadListChiral,traceListChiral}]; - repRule = Join[repRule,MapThread[Rule[#1,#2]&,{spurHeadListNonChiral,traceListNonChiral}]]; + time2=AbsoluteTime[]; + FCPrint[1,"DiracTrace: diracTraceEvaluate: Rebuilding the full result.", FCDoControl->diTrVerbose]; + repRule = Thread[Rule[spurHeadListChiral,traceListChiral]]; + repRule = Join[repRule, Thread[Rule[spurHeadListNonChiral,traceListNonChiral]]]; FCPrint[3,"DiracTrace: diracTraceEvaluate: repRule: ", traceListChiral, FCDoControl->diTrVerbose]; (* The trace of any standalone Dirac matrix is zero, g^6 and g^7 are of course special *) - tmp = (gammaFree/. wrapRule) + (gammaPart/.repRule); + tmp = (gammaFree/. wrapRule) + (gammaPart /. Dispatch[repRule]); + FCPrint[1,"DiracTrace: diracTraceEvaluate: Full result ready, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->diTrVerbose]; FCPrint[3,"DiracTrace: diracTraceEvaluate: tmp: ", tmp, FCDoControl->diTrVerbose]; - If[ !FreeQ2[tmp /. noSpur[__]:>1,{spurHead,DiracGamma}], + If[ !FreeQ2[tmp /. _noSpur:>1,{spurHead,DiracGamma}], Message[DiracTrace::failmsg, "Something went wrong while substituting trace results."]; Abort[] ]; ]; - FCPrint[1,"DiracTrace: diracTraceEvaluate: Main part finished, timing:",N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + FCPrint[1,"DiracTrace: diracTraceEvaluate: Main part finished, timing: ",N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; (* At this point there should be no Dirac matrices left, by definition. The only allowed exception are objects wrapped into noSpur *) - If[ !FreeQ[tmp /. noSpur[__]:>1 ,DiracGamma], + + If[ !FreeQ[tmp /. _noSpur:>1, DiracGamma], Message[DiracTrace::failmsg,"The output still contains Dirac matrices"]; Abort[] ]; (* If there are uncontracted Lorentz indices, try to contract them *) - If[ (contract===True || (NumberQ[contract] && LeafCount[tmp] < contract)) && !FreeQ[tmp, LorentzIndex], + If[ contract===True && !dummyIndexFreeQ, time=AbsoluteTime[]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Contracting Lorentz indices. ", FCDoControl->diTrVerbose]; - tmp=Contract[tmp]; + tmp=Contract[tmp,FCI->True]; FCPrint[3,"DiracTrace: diracTraceEvaluate: After Contract: ", tmp, FCDoControl->diTrVerbose]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Contract done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose] ]; - (* Special expansion for expressions that contain Levi-Civita tensors*) If[ !FreeQ[tmp, Eps], time=AbsoluteTime[]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Treating Eps tensors.", FCDoControl->diTrVerbose]; - tmp = EpsEvaluate[tmp]//Expand; - tmp = Contract[ tmp, EpsContract -> OptionValue[DiracTrace,{opts},EpsContract], - Schouten->schoutenopt, Expanding -> False ]; - FCPrint[1,"DiracTrace: diracTraceEvaluate: Done with Eps tensors, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose] + tmp = EpsEvaluate[tmp,FCI->True]//Expand; + If[ (contract===True || (NumberQ[contract] && LeafCount[tmp] < contract)), + tmp = Contract[ tmp, EpsContract -> OptionValue[DiracTrace,{opts},EpsContract], + Schouten->schoutenopt, Expanding -> False, FCI->True]; + ]; ]; (* Factor the result, if requested; This is where we put back the prefactor of 4. *) @@ -459,7 +507,7 @@ not too long (LeafCount[ ] < 5000 ) expressions. diractrres = diractrfact[unitMatrixTrace tmp] ] ]; - FCPrint[3,"DiracTrace: diracTraceEvaluate: After factoring: ", tmp, FCDoControl->diTrVerbose]; + FCPrint[3,"DiracTrace: diracTraceEvaluate: After factoring: ", diractrres, FCDoControl->diTrVerbose]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Factoring done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; diractrpc[x__] := @@ -477,10 +525,44 @@ not too long (LeafCount[ ] < 5000 ) expressions. ]; FCPrint[1,"DiracTrace: diracTraceEvaluate: Leaving.", FCDoControl->diTrVerbose]; - + FCPrint[3,"DiracTrace: diracTraceEvaluate: Leaving with: ", diractrres, FCDoControl->diTrVerbose]; diractrres ]; +(* since the cyclicity of the trace is respected in all the Gamma^5 schemes + used in FeynCalc and the sorting does not depend on the values of the scalar + products, orderSpurHead is safe for memoization. This might change if we would + implement Kreimer's scheme in the future. *) + +orderSpurHead[x__DiracGamma, DiracGamma[5]] := + Block[{p1, p2, tmpSpur, li = {x}, pos, tab}, + tab = + Table[ + ( + p1 = li[[;; i]]; + p2 = li[[i + 1 ;;]]; + {((-1)^Length[p2]), tmpSpur[Sequence @@ p2, Sequence @@ p1]} + ), {i, 1,Length[li] - 1}]; + tab = Join[{{1, tmpSpur[x]}}, tab]; + pos = First[Ordering[tab /. {_, tmpSpur[b__]} :> List[b]]]; + tab[[pos]][[1]] spurHead[Sequence @@ (tab[[pos]][[2]]), DiracGamma[5]] + ]; + + +orderSpurHead[x__DiracGamma,y_DiracGamma/;(y=!=DiracGamma[5] && y=!=DiracGamma[6] && y=!=DiracGamma[7])] := + Block[{p1, p2, tmpSpur, li = {x,y}, pos, tab}, + tab = + Table[ + ( + p1 = li[[;; i]]; + p2 = li[[i + 1 ;;]]; + {1, tmpSpur[Sequence @@ p2, Sequence @@ p1]} + ), {i, 1,Length[li] - 1}]; + tab = Join[{{1, tmpSpur[x,y]}}, tab]; + pos = First[Ordering[tab /. {_, tmpSpur[b__]} :> List[b]]]; + spurHead[Sequence @@ (tab[[pos]][[2]])] + ]; + fastExpand[xx_] := Replace[xx, p_. Times[a__, x_Plus] :> Distribute[p a*x, Plus], 1]; @@ -493,7 +575,7 @@ not too long (LeafCount[ ] < 5000 ) expressions. (* traceNo5Wrap is a higher level function that handles the computation of traces without gamma 5, all indices different. The trick here is that as soon as we compute a trace for a given number of Dirac matrices, - we define it is a function (traceNo5fun) so that the result can be retrieved very fast. Combined with the the fast expansion + we define it is a function (traceNo5fun) so that the result can be retrieved very fast. Combined with the fast expansion using fastExpand this provides a rather quick way to obtain Dirac traces. The bottlenecks here are the amount of RAM required for caching and the general slowness of Mathematica on very large expressions. Traces with up to 14 Dirac matrices should be fine, after that it becomes too slow *) @@ -506,7 +588,7 @@ we define it is a function (traceNo5fun) so that the result can be retrieved ver If[Head[finalRes] === traceNo5Fun, (* The trace needs to be computed *) tmpRes = traceNo5 @@ tab; - If[ ($MemoryAvailable - MemoryInUse[]/1000000.) >1. , + If[ ($FCMemoryAvailable - MemoryInUse[]/1000000.) >1. , (* If there is enough memory, we save the computed result as a function *) args = Sequence @@ (Pattern[#, _] & /@ tab); setDel[traceNo5Fun[args], fastExpand[tmpRes]] /. setDel -> SetDelayed; @@ -551,7 +633,7 @@ we define it is a function (traceNo5fun) so that the result can be retrieved ver If[Head[realRes] === trace5Fun, (* The trace needs to be computed *) tmpRes = trace5 @@ (Join[tab, {5}]); - If[ ($MemoryAvailable - MemoryInUse[]/1000000.) >1. , + If[ ($FCMemoryAvailable - MemoryInUse[]/1000000.) >1. , (* If there is enough memory, we save the computed result as a function *) args = Sequence @@ Join[(Pattern[#, _] & /@ tab), {5}]; setDel[trace5Fun[args], fastExpand[tmpRes]] /. setDel -> SetDelayed; @@ -597,12 +679,12 @@ we define it is a function (traceNo5fun) so that the result can be retrieved ver spur5Larin[x__DiracGamma, y:DiracGamma[_[_,dim_],dim_], DiracGamma[5]]:= Block[{li1,li2,li3, res}, {li1,li2,li3} = LorentzIndex[#,dim]& /@ Unique[{"larLia","larLib","larLic"}]; - If[ FCGetDimensions[{x}]=!={dim}, - Message[DiracTrace::failmsg, "Traces with mixed dimensions are forbidden in Larin's scheme."]; + If[ FCGetDimensions[{x},ChangeDimension->True]=!={dim}, + Message[DiracTrace::mixmsg]; Abort[] ]; - res = I/6 leviCivitaSign Eps[y[[1]], li1, li2, li3, Dimension->dim] spurNo5[x,DiracGamma[li1,dim],DiracGamma[li2,dim], DiracGamma[li3,dim]]; - If[ FCGetDimensions[{res}]=!={dim}, + res = I/6 leviCivitaSign Eps[y[[1]], li1, li2, li3] spurNo5[x,DiracGamma[li1,dim],DiracGamma[li2,dim], DiracGamma[li3,dim]]; + If[ FCGetDimensions[{res},ChangeDimension->True]=!={dim}, Message[DiracTrace::failmsg, "Something went wrong while computing trace in Larin's scheme."]; Abort[] ]; @@ -617,9 +699,12 @@ we define it is a function (traceNo5fun) so that the result can be retrieved ver res ]/; EvenQ[Length[{x}]] && Length[{x}]>4; -spur5BMHVWest[x_DiracGamma,y_DiracGamma,r_DiracGamma,z_DiracGamma, DiracGamma[5]] := - EpsEvaluate[leviCivitaSign I Eps[x[[1]],y[[1]],r[[1]],z[[1]]]]; +spur5BMHVWest[DiracGamma[x_,___],DiracGamma[y_,___],DiracGamma[r_,___],DiracGamma[z_,___], DiracGamma[5]] := + EpsEvaluate[leviCivitaSign I Eps[Take[x,1], Take[y,1], Take[r,1], Take[z,1]], FCI->True]/; + !MatchQ[FCGetDimensions[{x,y,r,z},ChangeDimension->True],{___,_Symbol-4,___}]; +spur5BMHVWest[DiracGamma[x_,___],DiracGamma[y_,___],DiracGamma[r_,___],DiracGamma[z_,___], DiracGamma[5]] := + 0/; MatchQ[FCGetDimensions[{x,y,r,z},ChangeDimension->True],{___,_Symbol-4,___}]; spur5BMHVNoWest[x__DiracGamma, DiracGamma[5]]:= Block[{li1,li2,li3,li4, res}, diff --git a/FeynCalc/Dirac/DiracTrick.m b/FeynCalc/Dirac/DiracTrick.m index ddab39869..39f594692 100755 --- a/FeynCalc/Dirac/DiracTrick.m +++ b/FeynCalc/Dirac/DiracTrick.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Contraction and simplification rules for Dirac matrices *) @@ -16,8 +16,10 @@ (* ------------------------------------------------------------------------ *) DiracTrick::usage = -"DiracTrick[exp] contracts gamma matrices with each other and \ -performs several simplifications (no expansion, use DiracSimplify for this)."; +"DiracTrick[exp] contracts Dirac matrices with each other and \ +performs several simplifications but no expansions. There are not many \ +cases when a user will need to call this function directly. Use DiracSimplify \ +to achieve maximal simplification of Dirac matrix chains."; DiracTrick::failmsg = "Error! DiracTrick has encountered a fatal problem and must abort the computation. \ @@ -27,6 +29,10 @@ (* ------------------------------------------------------------------------ *) Begin["`Package`"] + +diracTrickEvalFastFromDiracSimplifyList; +diracTrickEvalFastFromDiracSimplifySingle; +(*TODO: Need to add an option for moving all g^5 to the left!*) End[] Begin["`DiracTrick`Private`"] @@ -34,22 +40,51 @@ diTrVerbose::usage=""; diracTraceSimplify::usage=""; insideDiracTrace::usage=""; +diracOrder::usage=""; +optJoin::usage=""; diga::usage=""; +tmpli::usage=""; Options[DiracTrick] = { - DiracGammaCombine -> False, - Expanding -> False, - FCDiracIsolate -> True, - FCI -> False, - FCVerbose -> False, - InsideDiracTrace -> False + Evaluate -> True, + DiracChain -> True, + DiracGammaCombine -> False, + Expanding -> False, + FCDiracIsolate -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> False, + FCVerbose -> False, + InsideDiracTrace -> False, + ToDiracGamma67 -> True }; -(* TODO: Bad syntax that one should get rid off*) -DiracTrick[] = 1; +diracTrickEvalFastFromDiracSimplifyList[diracObjects_List, {optInsideDiracTrace_, optDiracOrder_}]:= + Block[{tmp1,tmp2,res}, + tmp1 = insideDiracTrace; + tmp2 = diracOrder; + insideDiracTrace = optInsideDiracTrace; + diracOrder = optDiracOrder; + res = (diracTrickEvalFast/@diracObjects) /. diracTrickEvalFast->Identity; + insideDiracTrace = tmp1; + diracOrder = tmp2; + res + ]; -DiracTrick[y__ /; FreeQ[{y}, Rule, 1],z_/;Head[z]=!=Rule] := - DiracTrick[DOT[y,z],FCI->True]; +diracTrickEvalFastFromDiracSimplifySingle[diracObject_, {tmpHead_, optInsideDiracTrace_, optDiracOrder_}]:= + Block[{tmp1,tmp2,res}, + tmp1 = insideDiracTrace; + tmp2 = diracOrder; + insideDiracTrace = optInsideDiracTrace; + diracOrder = optDiracOrder; + res = diracTrickEvalFast[diracObject] /. diracTrickEvalFast->tmpHead; + insideDiracTrace = tmp1; + diracOrder = tmp2; + res + ]/; Head[diracObject]=!=DiracChain; + +diracTrickEvalFastFromDiracSimplifySingle[DiracChain[diracObject_,i_,j_], {tmpHead_, optInsideDiracTrace_, optDiracOrder_}]:= + DiracChain[diracTrickEvalFastFromDiracSimplifySingle[diracObject, {tmpHead, optInsideDiracTrace, optDiracOrder}],i,j] DiracTrick[expr_,OptionsPattern[]] := Block[{ res, tmp, ex, null1, null2, holdDOT, freePart, dsPart, diracObjects, @@ -93,9 +128,11 @@ create replacement rules (standard) and substitute the results back. *) + optJoin = OptionValue[FCJoinDOTs]; + If [OptionValue[FCVerbose]===False, diTrVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], diTrVerbose=OptionValue[FCVerbose] ]; ]; @@ -121,51 +158,93 @@ create replacement rules (standard) and substitute the results back. If[ OptionValue[FCDiracIsolate], (* This is the standard mode for calling DiracTrick *) - + FCPrint[1,"DiracTrick: Normal mode.", FCDoControl->diTrVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "DiracTrick: Extracting Dirac objects.", FCDoControl->diTrVerbose]; (* First of all we need to extract all the Dirac structures in the input. *) - ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, DotSimplify->True, DiracGammaCombine->OptionValue[DiracGammaCombine],LorentzIndex->True]; + ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, DotSimplify->True, DiracGammaCombine->OptionValue[DiracGammaCombine], + FCJoinDOTs -> optJoin, LorentzIndex->True, ToDiracGamma67-> OptionValue[ToDiracGamma67], DiracChain->OptionValue[DiracChain]]; {freePart,dsPart} = FCSplit[ex,{dsHead}]; FCPrint[3,"DiracTrick: dsPart: ",dsPart , FCDoControl->diTrVerbose]; FCPrint[3,"DiracTrick: freePart: ",freePart , FCDoControl->diTrVerbose]; + FCPrint[1, "DiracTrick: Done extracting Dirac objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//Union; FCPrint[3,"DiracTrick: diracObjects: ",diracObjects , FCDoControl->diTrVerbose]; time=AbsoluteTime[]; - FCPrint[1, "DiracTrick: Applying diracTrickEval", FCDoControl->diTrVerbose]; - (* diracObjectsEval = Map[(diracTrickEvalFast[#]/. diracTrickEvalFast->diracTrickEval)&, (diracObjects/.dsHead->Identity)];*) + FCPrint[1, "DiracTrick: Applying diracTrickEvalFast", FCDoControl->diTrVerbose]; diracObjectsEval = diracTrickEvalFast/@(diracObjects/.dsHead->Identity); + FCPrint[1,"DiracTrick: diracTrickEvalFast done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + FCPrint[3,"DiracTrick: After diracTrickEvalFast: ", diracObjectsEval, FCDoControl->diTrVerbose]; + + + time=AbsoluteTime[]; + FCPrint[1, "DiracTrick: Doing contractions", FCDoControl->diTrVerbose]; + If[ !FreeQ[diracObjectsEval,Pair], diracObjectsEval = diracObjectsEval /. diracTrickEvalFast[zzz_] :> diracTrickEvalFast[Expand2[zzz,Pair]/. Pair->PairContract /. PairContract->Pair] ]; - diracObjectsEval = diracObjectsEval /. diracTrickEvalFast -> diracTrickEval; + If[ !FreeQ[diracObjectsEval,CartesianPair], + diracObjectsEval = diracObjectsEval /. diracTrickEvalFast[zzz_] :> diracTrickEvalFast[Expand2[zzz,CartesianPair]/. + CartesianPair->CartesianPairContract /. CartesianPairContract->CartesianPair] + ]; + + FCPrint[1,"DiracTrick: Contractions done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + FCPrint[3,"DiracTrick: After contractions: ", diracObjectsEval, FCDoControl->diTrVerbose]; - FCPrint[3,"DiracTrace: After diracTrickEval: ", diracObjectsEval, FCDoControl->diTrVerbose]; - FCPrint[1,"DiracTrace: diracTrickEval done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "DiracTrick: Applying diracTrickEval", FCDoControl->diTrVerbose]; + + If[ OptionValue[Evaluate], + diracObjectsEval = diracObjectsEval /. diracTrickEvalFast -> diracTrickEval, + diracObjectsEval = diracObjectsEval /. diracTrickEvalFast -> Identity + ]; + + FCPrint[3,"DiracTrick: After diracTrickEval: ", diracObjectsEval, FCDoControl->diTrVerbose]; + FCPrint[1,"DiracTrick: diracTrickEval done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + If[ !FreeQ2[diracObjectsEval,{diracTrickEvalFast,diracTrickEval,holdDOT}], Message[DiracTrick::failmsg,"Evaluation of isolated objects failed."]; Abort[] ]; - repRule = MapThread[Rule[#1,#2]&,{diracObjects,diracObjectsEval}]; + FCPrint[1, "DiracTrick: Inserting Dirac objects back.", FCDoControl->diTrVerbose]; + time=AbsoluteTime[]; + repRule = Thread[Rule[diracObjects,diracObjectsEval]]; FCPrint[3,"DiracTrick: repRule: ",repRule , FCDoControl->diTrVerbose]; - res = freePart + ( dsPart/.repRule), + res = freePart + ( dsPart /. Dispatch[repRule]); + FCPrint[1, "DiracTrick: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose], + + FCPrint[1,"DiracTrick: Fast mode.", FCDoControl->diTrVerbose]; (* This is a fast mode for input that is already isolated, e.g. for calling DiracTrick/@exprList from internal functions *) - res = diracTrickEvalFast[ex]; If[ !FreeQ[diracObjectsEval,Pair], res = res /. diracTrickEvalFast[zzz_] :> diracTrickEvalFast[Expand2[zzz,Pair]/. Pair->PairContract /. PairContract->Pair] ]; + If[ !FreeQ[diracObjectsEval,CartesianPair], + res = res /. diracTrickEvalFast[zzz_] :> diracTrickEvalFast[Expand2[zzz,CartesianPair]/. + CartesianPair->CartesianPairContract /. CartesianPairContract->CartesianPair] + ]; + + (* It might happen that after diracTrickEvalFast there are no Dirac matrices left.*) + + FCPrint[3,"DiracTrick: After diracTrickEvalFast: ", res , FCDoControl->diTrVerbose]; + + If[ OptionValue[ToDiracGamma67], + res = res /. diracTrickEvalFast[zzz_]/;!FreeQ[{zzz}, DiracGamma[5]] :> diracTrickEvalFast[ToDiracGamma67[zzz,FCI->True]] + ]; + If[ !FreeQ2[res,{DiracHeadsList,diracTrickEvalFast}], res = res /. diracTrickEvalFast -> diracTrickEval ]; @@ -181,21 +260,71 @@ create replacement rules (standard) and substitute the results back. time=AbsoluteTime[]; FCPrint[1, "DiracTrick: Expanding the result.", FCDoControl->diTrVerbose]; res = Expand[res]; - FCPrint[1,"DiracTrace: Expanding done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + FCPrint[1,"DiracTrick: Expanding done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: After expanding: ", res, FCDoControl->diTrVerbose] ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + FCPrint[1, "DiracTrick. Leaving.", FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: Leaving with ", res, FCDoControl->diTrVerbose]; res ]; -diracTrickEvalFast[ex:DiracGamma[__]]:= - ex/; !insideDiracTrace +(* Here we can quickly handle trivial contractions of short expressions. Usually such expressions appear + when we call DiracTrick from DiracTrace after DotSimplify. Hence, the rules should be as simple, as possible *) + + +diracTrickEvalFast[DiracChain[x_, i_, j_]]:= + DiracChain[diracTrickEvalFast[x],i,j]; + +diracTrickEvalFast[x_DiracGamma]:= + x/; !insideDiracTrace && !diracOrder; + + +diracTrickEvalFast[x_DiracGamma]:= + 0/; insideDiracTrace && FreeQ2[x, {DiracGamma[6],DiracGamma[7]}]; + +diracTrickEvalFast[DiracGamma[6|7]]:= + (1/2)/; insideDiracTrace; + + +diracTrickEvalFast[DOT[DiracGamma[ExplicitLorentzIndex[0]],DiracGamma[ExplicitLorentzIndex[0]]]]:= + 1; + + +diracTrickEvalFast[DOT[x_DiracGamma,y__DiracGamma]]:= + DOT[x,y]/; FreeQ2[{x,y},{DiracGamma[5],DiracGamma[6],DiracGamma[7], ExplicitLorentzIndex[0]}] && + (Sort[Cases[{x,y}, (LorentzIndex | Momentum | CartesianIndex | CartesianMomentum)[a_, ___] :> a, Infinity]] === + Union[Cases[{x,y}, (LorentzIndex | Momentum | CartesianIndex | CartesianMomentum)[a_, ___] :> a, Infinity]])/; !insideDiracTrace && !diracOrder; + +(* Dirac trace related simplifications *) + +diracTrickEvalFast[DOT[b___DiracGamma,di_DiracGamma,c__DiracGamma]] := + diracTrickEvalFast[DOT[c,b, di]]/; !FreeQ2[{di},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && + FreeQ2[{b,c},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}]/; insideDiracTrace; + + +diracTrickEvalFast[DOT[x__DiracGamma, DiracGamma[5]]]:= + 0/; FreeQ2[{x},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && EvenQ[Length[{x}]] && insideDiracTrace && + MatchQ[FCGetDimensions[{x}],{_Symbol}] && (FeynCalc`Package`DiracGammaScheme === "NDR-Drop"); + + +diracTrickEvalFast[DOT[x__DiracGamma, DiracGamma[6|7]]]:= + 1/2 diracTrickEvalFast[DOT[x]]/; FreeQ2[{x},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && EvenQ[Length[{x}]] && insideDiracTrace && + MatchQ[FCGetDimensions[{x}],{_Symbol}] && (FeynCalc`Package`DiracGammaScheme === "NDR-Drop"); + +diracTrickEvalFast[DOT[DiracGamma[(arg1:_[_, dim1___]),dim1___], DiracGamma[(arg2:_[_, dim2___]), dim2___]]] := + FCUseCache[ExpandScalarProduct,{PairContract[arg1,arg2] /. PairContract->Pair},{}]/; insideDiracTrace; -diracTrickEvalFast[DOT[x__DiracGamma]]:= - 0/; FreeQ2[{x},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && OddQ[Length[{x}]] && insideDiracTrace; +diracTrickEvalFast[DOT[DiracGamma[(arg1:_[_, dim1___]),dim1___], DiracGamma[(arg2:_[_, dim2___]), dim2___], DiracGamma[6|7]]]:= + 1/2 FCUseCache[ExpandScalarProduct,{PairContract[arg1,arg2] /. PairContract->Pair},{}]/; insideDiracTrace; + +diracTrickEvalFast[DOT[x_DiracGamma,y__DiracGamma]]:= + 0/; FreeQ2[{x,y},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && OddQ[Length[{x,y}]] && insideDiracTrace; diracTrickEvalFast[DOT[x___DiracGamma,DiracGamma[5],y___DiracGamma]]:= 0/; Length[{x,y}]<4 && FreeQ2[{x,y},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && insideDiracTrace; @@ -209,32 +338,146 @@ create replacement rules (standard) and substitute the results back. diracTrickEvalFast[DiracGamma[6|7]]:= 1/2/; insideDiracTrace; +diracTrickEvalFast[DOT[DiracGamma[(a:6|7)],b___,DiracGamma[(a:6|7)]]] := + diracTrickEvalFast[DOT[b,DiracGamma[a]]]/; insideDiracTrace; + +diracTrickEvalFast[DOT[DiracGamma[(h1:5|6|7)],b___,DiracGamma[(h2:5|6|7)]]] := + ga67MatSign[h1,h2] diracTrickEvalFast[DOT[b,ga67Mat[h1,h2]]]/; h1=!=h2 && insideDiracTrace; + +(* Generic simplifications *) + +diracTrickEvalFast[DOT[b___,DiracGamma[l_LorentzIndex], DiracGamma[l_LorentzIndex], d___]] := + 4 diracTrickEvalFast[DOT[ b,d ]]; + +diracTrickEvalFast[DOT[b___,DiracGamma[l_LorentzIndex, dim_], DiracGamma[l_LorentzIndex, dim_], d___]] := + dim diracTrickEvalFast[DOT[ b,d ]]; + +diracTrickEvalFast[DOT[]]:= + 1; + +diracTrickEvalFast[DOT[b___,DiracGamma[c_Momentum], DiracGamma[c_Momentum], d___ ]] := + FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracTrickEvalFast[DOT[b,d]]; + +diracTrickEvalFast[DOT[b___,DiracGamma[c_Momentum, dim_], DiracGamma[c_Momentum, dim_], d___]] := + FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracTrickEvalFast[DOT[b,d]]; + +diracTrickEvalFast[DOT[b___,DiracGamma[l_LorentzIndex, dim_:4], DiracGamma[c_Momentum, dim_:4], DiracGamma[l_LorentzIndex, dim_:4], d___]] := + (2 - dim) diracTrickEvalFast[DOT[ b, DiracGamma[c, dim], d ]]; + +diracTrickEvalFast[DOT[b___,DiracGamma[5], DiracGamma[5], d___]] := + diracTrickEvalFast[DOT[ b,d ]]; + +diracTrickEvalFast[DOT[b___, DiracGamma[5], DiracGamma[(hh:6|7)], c___]] := + ga67Val1[hh] diracTrickEvalFast[DOT[b,DiracGamma[hh],c]]; + +diracTrickEvalFast[DOT[b___, DiracGamma[(hh:6|7)], DiracGamma[5], c___]] := + ga67Val1[hh] diracTrickEvalFast[DOT[b,DiracGamma[hh],c]]; + +diracTrickEvalFast[DOT[b___, DiracGamma[(hh1:6|7)],DiracGamma[(hh2:6|7)], c___]] := + ga67Val2[hh1,hh2] diracTrickEvalFast[DOT[b, DiracGamma[hh2], c]]; + + +diracTrickEvalFast[DOT[b___,DiracGamma[5], c:DiracGamma[_[_,_],_].. , d___]] := + (-1)^Length[{c}] diracTrickEvalFast[DOT[ b,c,DiracGamma[5],d]]/; MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && + MatchQ[FCGetDimensions[{c}],{_Symbol}]; + +diracTrickEvalFast[DOT[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_,_],_].. ,d___]] := + diracTrickEvalFast[DOT[ b,c,DiracGamma[h],d]]/; EvenQ[Length[{c}]] && MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && + MatchQ[FCGetDimensions[{c}],{_Symbol}]; + +diracTrickEvalFast[DOT[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_,_],_].. ,d___]] := + diracTrickEvalFast[DOT[ b,c,DiracGamma[ga67Switch1[h]],d]]/; OddQ[Length[{c}]] && MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && + MatchQ[FCGetDimensions[{c}],{_Symbol}]; + +diracTrickEvalFast[DOT[___,DiracGamma[(h:6|7)],DiracGamma[_[_,_],_], DiracGamma[(h:6|7)], ___]] := + 0/; MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme]; + +diracTrickEvalFast[DOT[b___,DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]), DiracGamma[(h2:6|7)], c___]] := + diracTrickEvalFast[DOT[b, dg, DiracGamma[h2], c]]/; h1=!=h2 && MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && + MatchQ[FCGetDimensions[{dg}],{_Symbol}]; + +diracTrickEvalFast[DOT[b___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]), xy:DiracGamma[_[_] ].. , DiracGamma[(h2:6|7)], c___]] := + diracTrickEvalFast[DOT[b, dg, xy, DiracGamma[h2], c]]/; EvenQ[Length[{xy}]] && h1=!=h2 && MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && + MatchQ[FCGetDimensions[{dg,xy}],{_Symbol}]; + +diracTrickEvalFast[DOT[___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_,_],_]), xy:DiracGamma[_[_] ].. , DiracGamma[(h:6|7)], ___]] := + 0/; EvenQ[Length[{xy}]] && MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && + MatchQ[FCGetDimensions[{dg,xy}],{_Symbol}]; + + +diracTrickEvalFast[DOT[___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]), xy:DiracGamma[_[_,_],_].. , DiracGamma[(h2:6|7)], ___]] := + 0/; OddQ[Length[{xy}]] && h1=!=h2 && MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && + MatchQ[FCGetDimensions[{dg,xy}],{_Symbol}]; + +diracTrickEvalFast[DOT[b___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_,_],_]), xy:DiracGamma[_[_,_],_].. , DiracGamma[(h:6|7)], c___]] := + diracTrickEvalFast[DOT[b, dg, xy, DiracGamma[h], c]]/; OddQ[Length[{xy}]] && MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && + MatchQ[FCGetDimensions[{dg,xy}],{_Symbol}]; + + +diracTrickEvalFast[DOT[b___,DiracGamma[5], c:DiracGamma[_[_]].. , d___]] := + (-1)^Length[{c}] diracTrickEvalFast[DOT[ b,c,DiracGamma[5],d]]; + +diracTrickEvalFast[DOT[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_]].. ,d___]] := + diracTrickEvalFast[DOT[ b,c,DiracGamma[h],d]]/; EvenQ[Length[{c}]]; + +diracTrickEvalFast[DOT[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_]].. ,d___]] := + diracTrickEvalFast[DOT[ b,c,DiracGamma[ga67Switch1[h]],d]]/; OddQ[Length[{c}]]; + +diracTrickEvalFast[DOT[___,DiracGamma[(h:6|7)],DiracGamma[_[_]], DiracGamma[(h:6|7)], ___]] := + 0; + +diracTrickEvalFast[DOT[b___,DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_]]), DiracGamma[(h2:6|7)], c___]] := + diracTrickEvalFast[DOT[b, dg, DiracGamma[h2], c]]/; h1=!=h2; + +diracTrickEvalFast[DOT[b___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_]]), xy:DiracGamma[_[_] ].. , DiracGamma[(h2:6|7)], c___]] := + diracTrickEvalFast[DOT[b, dg, xy, DiracGamma[h2], c]]/; EvenQ[Length[{xy}]] && h1=!=h2; + +diracTrickEvalFast[DOT[___, DiracGamma[(h:6|7)],DiracGamma[_[_]], xy:DiracGamma[_[_] ].. , DiracGamma[(h:6|7)], ___]] := + 0/; EvenQ[Length[{xy}]]; + +diracTrickEvalFast[DOT[___, DiracGamma[(h1:6|7)],DiracGamma[_[_]], xy:DiracGamma[_[_]].. , DiracGamma[(h2:6|7)], ___]] := + 0/; OddQ[Length[{xy}]] && h1=!=h2; + +diracTrickEvalFast[DOT[b___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_]]), xy:DiracGamma[_[_]].. , DiracGamma[(h:6|7)], c___]] := + diracTrickEvalFast[DOT[b, dg, xy, DiracGamma[h], c]]/; OddQ[Length[{xy}]]; + +diracTrickEval[0]:= + 0; + +diracTrickEval[ex_DiracGamma]:= + ex/; !insideDiracTrace; + +diracTrickEval[ex_DiracGamma]:= + 0/; insideDiracTrace && !MatchQ[ex,DiracGamma[6|7]]; + +diracTrickEval[ex_DiracGamma]:= + 1/2/; insideDiracTrace && MatchQ[ex, DiracGamma[6|7]]; diracTrickEval[ex_/;Head[ex]=!=DiracGamma]:= Which[ (* NDR, inside Trace *) - !$BreitMaison && !$Larin && insideDiracTrace, + MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme] && insideDiracTrace, diracTrickEvalCachedNDRInsideTrace[ex], (* Larin, inside Trace *) - !$BreitMaison && $Larin && insideDiracTrace, + (FeynCalc`Package`DiracGammaScheme === "Larin") && insideDiracTrace, diracTrickEvalCachedLarinInsideTrace[ex], (* BMHV, inside Trace *) - $BreitMaison && !$Larin && insideDiracTrace, + (FeynCalc`Package`DiracGammaScheme === "BMHV") && insideDiracTrace, diracTrickEvalCachedBMHVInsideTrace[ex], (* NDR *) - !$BreitMaison && !$Larin, + MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme], diracTrickEvalCachedNDR[ex], (* Larin *) - !$BreitMaison && $Larin, + (FeynCalc`Package`DiracGammaScheme === "Larin"), diracTrickEvalCachedLarin[ex], (* BMHV *) - $BreitMaison && !$Larin, + (FeynCalc`Package`DiracGammaScheme === "BMHV"), diracTrickEvalCachedBMHV[ex], (* Else *) True, - Message[DiracTrick::failmsg,"Incorrect combination of dimensions and g^5 scheme!"]; + Message[DiracTrace::mixmsg]; Abort[] - ]; + ]/; ex=!=0; diracTrickEvalCachedNDRInsideTrace[x_] := diracTrickEvalInternal[x]; @@ -277,12 +520,11 @@ create replacement rules (standard) and substitute the results back. diracTrickEvalInternal[ex_/;Head[ex]=!=DiracGamma]:= Block[{res=ex, holdDOT, time, dim, gamma5Present,noncommPresent,null1,null2,dsHead}, - FCPrint[1, "DiracTrick: diracTrickEval: Entering.", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Entering.", FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: diracTrickEval: Entering with", ex , FCDoControl->diTrVerbose]; gamma5Present = !FreeQ2[ex,{DiracGamma[5],DiracGamma[6],DiracGamma[7]}]; noncommPresent = !NonCommFreeQ[ex/.DiracGamma->diga]; - dim = FCGetDimensions[ex/.DiracGamma[5|6|7]:>diga]; FCPrint[3, "DiracTrick: diracTrickEval: g^5 present:", gamma5Present, FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: diracTrickEval: unknown non-commutative objects present:", noncommPresent, FCDoControl->diTrVerbose]; @@ -301,10 +543,10 @@ create replacement rules (standard) and substitute the results back. If[ insideDiracTrace, time=AbsoluteTime[]; - FCPrint[1, "DiracTrick: diracTrickEval: Applying diracTraceSimplify ", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Applying diracTraceSimplify ", FCDoControl->diTrVerbose]; res = diracTraceSimplify[res] /. DOT -> holdDOT /. diracTraceSimplify[holdDOT[x__]] :> diracTraceSimplify[x]/. diracTraceSimplify -> commonGamma5Properties /. commonGamma5Properties -> holdDOT; - FCPrint[1,"DiracTrace: diracTrickEval: diracTraceSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + FCPrint[1,"DiracTrick: diracTrickEval: diracTraceSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: diracTrickEval: After diracTraceSimplify ", res, FCDoControl->diTrVerbose], res = res /. DOT -> holdDOT; ]; @@ -313,11 +555,18 @@ create replacement rules (standard) and substitute the results back. res = Expand2[res,Pair]/. Pair->PairContract /. PairContract->Pair; ]; + If[ !FreeQ[res,CartesianPair], + res = Expand2[res,CartesianPair]/. CartesianPair->CartesianPairContract /. CartesianPairContract->CartesianPair; + ]; + + If[ FreeQ2[res,DiracHeadsList], Return[res] ]; - dim = FCGetDimensions[res/.DiracGamma[5|6|7]:>diga]; + dim = FCGetDimensions[res, FreeQ->{DiracGamma[5],DiracGamma[6],DiracGamma[7]}, ChangeDimension->True]; + + noncommPresent = !NonCommFreeQ[res/.DiracGamma->diga]; FCPrint[3, "DiracTrick: diracTrickEval: Dimensions:", dim, FCDoControl->diTrVerbose]; @@ -325,83 +574,89 @@ create replacement rules (standard) and substitute the results back. If[ gamma5Present, time=AbsoluteTime[]; - FCPrint[1, "DiracTrick: diracTrickEval: Applying chiralTrick ", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Applying chiralTrick ", FCDoControl->diTrVerbose]; Which[ (* Purely 4-dimensional -> use anticommuting g^5 *) - dim==={4}, - FCPrint[1, "DiracTrick: diracTrickEval: Purely 4-dim.", FCDoControl->diTrVerbose]; - res = res /. holdDOT -> chiralTrickAnticommuting4Dim; - res = FixedPoint[(# /. chiralTrickAnticommuting4Dim -> commonGamma5Properties /. - commonGamma5Properties -> chiralTrickAnticommuting4Dim)&,res]; - res = res /. chiralTrickAnticommuting4Dim -> holdDOT, + MatchQ[dim,{4}], + FCPrint[2, "DiracTrick: diracTrickEval: Purely 4-dim.", FCDoControl->diTrVerbose]; + res = res /. holdDOT -> chiralTrickAnticommuting4DimRight; + res = FixedPoint[(# /. chiralTrickAnticommuting4DimRight -> commonGamma5Properties /. + commonGamma5Properties -> chiralTrickAnticommuting4DimRight)&,res]; + res = res /. chiralTrickAnticommuting4DimRight -> holdDOT, (* Purely D-dimensional and NDR -> use anticommuting g^5 *) - MatchQ[dim,{_Symbol}] && !$BreitMaison && !$Larin, - FCPrint[1, "DiracTrick: diracTrickEval: Purely D-dim, NDR.", FCDoControl->diTrVerbose]; - res = res /. holdDOT -> chiralTrickAnticommutingDDim; - res = FixedPoint[(# /. chiralTrickAnticommutingDDim -> commonGamma5Properties /. - commonGamma5Properties -> chiralTrickAnticommutingDDim)&,res]; - res = res /. chiralTrickAnticommutingDDim -> holdDOT, + MatchQ[dim,{_Symbol}] && MemberQ[{"NDR","NDR-Drop"},FeynCalc`Package`DiracGammaScheme], + FCPrint[2, "DiracTrick: diracTrickEval: Purely D-dim, NDR.", FCDoControl->diTrVerbose]; + res = res /. holdDOT -> chiralTrickAnticommutingDDimRight; + res = FixedPoint[(# /. chiralTrickAnticommutingDDimRight -> commonGamma5Properties /. + commonGamma5Properties -> chiralTrickAnticommutingDDimRight)&,res]; + res = res /. chiralTrickAnticommutingDDimRight -> holdDOT, (* Purely D-dimensional and BMHV -> don't move anything around *) - MatchQ[dim,{_Symbol}] && ($BreitMaison && !$Larin), - FCPrint[1, "DiracTrick: diracTrickEval: Purely D-dim and Larin.", FCDoControl->diTrVerbose]; + MatchQ[dim,{_Symbol}] && (FeynCalc`Package`DiracGammaScheme === "BMHV"), + FCPrint[2, "DiracTrick: diracTrickEval: Purely D-dim and BMHV.", FCDoControl->diTrVerbose]; Null, (* Purely D-dimensional and Larin use the substitution rule to eliminate g^5 that are not on the left of the trace *) - MatchQ[dim,{_Symbol}] && (!$BreitMaison && $Larin), - FCPrint[1, "DiracTrick: diracTrickEval: Purely D-dim and Larin.", FCDoControl->diTrVerbose]; + MatchQ[dim,{_Symbol}] && (FeynCalc`Package`DiracGammaScheme === "Larin"), + FCPrint[2, "DiracTrick: diracTrickEval: Purely D-dim and Larin.", FCDoControl->diTrVerbose]; res = res /. holdDOT -> chiralTrickLarin /. chiralTrickLarin -> holdDOT, (* Mixed and BMHV -> don't move g^5 around *) - MatchQ[dim, {_Symbol - 4} | {4, _Symbol} | {4, _Symbol-4} | {_Symbol-4, _Symbol} | {4, _Symbol-4, _Symbol}] && $BreitMaison && !$Larin, + dim=!={} && (FeynCalc`Package`DiracGammaScheme === "BMHV"), FCPrint[1, "DiracTrick: diracTrickEval: Mixed and BMHV.", FCDoControl->diTrVerbose], - (* special case that the expression contains only chiral matrices*) - dim==={} !FreeQ2[res,{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && FreeQ[(res/.DiracGamma[5|6|7]:>diga),DiracGamma], - FCPrint[1, "DiracTrick: diracTrickEval: Chiral only.", FCDoControl->diTrVerbose], + (* special case that the expression contains only chiral or g^0 matrices*) + dim==={} && !FreeQ2[res,{DiracGamma[5],DiracGamma[6],DiracGamma[7],DiracGamma[ExplicitLorentzIndex[0]]}] && FreeQ[(res/.DiracGamma[5|6|7|ExplicitLorentzIndex[0]]:>diga),DiracGamma], + FCPrint[2, "DiracTrick: diracTrickEval: Chiral or g^0 only.", FCDoControl->diTrVerbose], (* Anything else is most likely an error *) True, - Message[DiracTrick::failmsg,"Incorrect combination of dimensions and g^5 scheme!"]; + Message[DiracTrace::mixmsg]; Abort[] ]; - FCPrint[1,"DiracTrace: diracTrickEval: chiralTrick done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + FCPrint[2,"DiracTrick: diracTrickEval: chiralTrick done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: diracTrickEval: After chiralTrick ", res, FCDoControl->diTrVerbose]; gamma5Present = !FreeQ2[res,{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] ]; (* Here we do all the simplifications not realted to g^5 *) - FCPrint[1, "DiracTrick: diracTrickEval: Doing simplifications unrelated to g^5.", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Doing simplifications unrelated to g^5.", FCDoControl->diTrVerbose]; Which[ (* Purely 4-dimensional *) - dim==={4}, - FCPrint[1, "DiracTrick: diracTrickEval: Purely 4-dim.", FCDoControl->diTrVerbose]; - FCPrint[1, "DiracTrick: diracTrickEval: Applying diracology4Dim.", FCDoControl->diTrVerbose]; + MatchQ[dim,{4}], + FCPrint[2, "DiracTrick: diracTrickEval: Purely 4-dim.", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Applying diracology4Dim.", FCDoControl->diTrVerbose]; res = res /. holdDOT -> diracology4Dim /. diracology4Dim -> holdDOT; FCPrint[3, "DiracTrick: diracTrickEval: After diracology4Dim: ", res, FCDoControl->diTrVerbose], (* Purely D-dimensional *) MatchQ[dim,{_Symbol}], - FCPrint[1, "DiracTrick: diracTrickEval: Purely D-dim.", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Purely D-dim.", FCDoControl->diTrVerbose]; res = res /. holdDOT -> diracologyDDim; res = FixedPoint[(# /. diracologyDDim -> diracologyDDim2 /. diracologyDDim2 -> diracologyDDim)&,res]; res = res /. diracologyDDim -> holdDOT, (* Purely D-4-dimensional and BMHV *) - MatchQ[dim,{_Symbol - 4}] && $BreitMaison && !$Larin, - FCPrint[1, "DiracTrick: diracTrickEval: Purely D-4-dim.", FCDoControl->diTrVerbose]; + MatchQ[dim,{_Symbol - 4}] && (FeynCalc`Package`DiracGammaScheme === "BMHV"), + FCPrint[2, "DiracTrick: diracTrickEval: Purely D-4-dim.", FCDoControl->diTrVerbose]; res = res /. holdDOT -> diracologyDDim; res = FixedPoint[(# /. diracologyDDim -> diracologyDDim2 /. diracologyDDim2 -> diracologyDDim)&,res]; res = res /. diracologyDDim -> holdDOT, (* Mixed and BMHV *) - MatchQ[dim, {4, _Symbol} | {4, _Symbol-4} | {_Symbol-4, _Symbol} | {4, _Symbol-4, _Symbol}] && $BreitMaison && !$Larin, - FCPrint[1, "DiracTrick: diracTrickEval: Mixed and BMHV.", FCDoControl->diTrVerbose]; + dim=!={} && (FeynCalc`Package`DiracGammaScheme === "BMHV"), + FCPrint[2, "DiracTrick: diracTrickEval: Mixed and BMHV.", FCDoControl->diTrVerbose]; res = res /. holdDOT -> diracologyBMHV1; res = FixedPoint[(# /. diracologyBMHV1 -> diracologyBMHV2 /. diracologyBMHV2 -> diracologyBMHV1)&,res]; res = res /. diracologyBMHV1 -> holdDOT, - (* special case that the expression contains only chiral matrices*) - dim==={} !FreeQ2[res,{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && FreeQ[(res/.DiracGamma[5|6|7]:>diga),DiracGamma], - FCPrint[1, "DiracTrick: diracTrickEval: Chiral only.", FCDoControl->diTrVerbose], - (* Anything else is most likely an error *) - True, - Message[DiracTrick::failmsg,"Incorrect combination of dimensions and g^5 scheme!"]; - Abort[] + (* special case that the expression contains only g^0 matrices*) + dim==={} && !FreeQ2[res,{DiracGamma[ExplicitLorentzIndex[0]]}] && FreeQ[(res/.DiracGamma[ExplicitLorentzIndex[0]]:>diga),DiracGamma], + FCPrint[2, "DiracTrick: diracTrickEval: Only g^0 matrices.", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Applying diracology4Dim.", FCDoControl->diTrVerbose]; + res = res /. holdDOT -> diracology4Dim /. diracology4Dim -> holdDOT; + FCPrint[3, "DiracTrick: diracTrickEval: After diracology4Dim: ", res, FCDoControl->diTrVerbose], + (* special case that the expression contains only chiral or g^0 matrices*) + dim==={} !FreeQ2[res,{DiracGamma[5],DiracGamma[6],DiracGamma[7],DiracGamma[ExplicitLorentzIndex[0]]}] && FreeQ[(res/.DiracGamma[5|6|7|ExplicitLorentzIndex[0]]:>diga),DiracGamma], + FCPrint[2, "DiracTrick: diracTrickEval: Chiral or g^0 only.", FCDoControl->diTrVerbose], + (* Anything else is most likely an error *) + True, + Message[DiracTrace::mixmsg]; + Abort[] ]; - FCPrint[1, "DiracTrick: diracTrickEval: Done with simplifications unrelated to g^5.", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Done with simplifications unrelated to g^5.", FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: diracTrickEval: After simplifications unrelated to g^5: ", res , FCDoControl->diTrVerbose]; If[ FreeQ2[res,DiracHeadsList], @@ -409,16 +664,16 @@ create replacement rules (standard) and substitute the results back. ]; (* For BMHV we need to handle g^5 again here*) - If[ gamma5Present && $BreitMaison && !$Larin, - FCPrint[1, "DiracTrick: diracTrickEval: Doing special simplifications for the BMHV scheme.", FCDoControl->diTrVerbose]; - res = res /. holdDOT -> gamma5MoveBMHV; - res = FixedPoint[(# /. gamma5MoveBMHV -> commonGamma5Properties /. - commonGamma5Properties -> chiralTrickAnticommuting4Dim /. chiralTrickAnticommuting4Dim -> gamma5MoveBMHV)&,res]; - FCPrint[1, "DiracTrick: diracTrickEval: Additional simplifications of g^5 in BMHV.", FCDoControl->diTrVerbose]; - res = res /. gamma5MoveBMHV -> diracologyBMHV1; + If[ gamma5Present && (FeynCalc`Package`DiracGammaScheme === "BMHV"), + FCPrint[2, "DiracTrick: diracTrickEval: Doing special simplifications for the BMHV scheme.", FCDoControl->diTrVerbose]; + res = res /. holdDOT -> gamma5MoveBMHVRight; + res = FixedPoint[(# /. gamma5MoveBMHVRight -> commonGamma5Properties /. + commonGamma5Properties -> chiralTrickAnticommuting4DimRight /. chiralTrickAnticommuting4DimRight -> gamma5MoveBMHVRight)&,res]; + FCPrint[2, "DiracTrick: diracTrickEval: Additional simplifications of g^5 in BMHV.", FCDoControl->diTrVerbose]; + res = res /. gamma5MoveBMHVRight -> diracologyBMHV1; res = FixedPoint[(# /. diracologyBMHV1 -> diracologyBMHV2 /. diracologyBMHV2 -> diracologyBMHV1)&,res]; res = res /. diracologyBMHV1 -> holdDOT; - FCPrint[1, "DiracTrick: diracTrickEval: Done with special simplifications for the BMHV scheme.", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Done with special simplifications for the BMHV scheme.", FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: diracTrickEval: After special simplifications for the BMHV scheme: ", res , FCDoControl->diTrVerbose]; ]; @@ -430,16 +685,16 @@ create replacement rules (standard) and substitute the results back. If[ insideDiracTrace && res=!=0, time=AbsoluteTime[]; - FCPrint[1, "DiracTrick: diracTrickEval: Applying diracTraceSimplify again ", FCDoControl->diTrVerbose]; - res = FCDiracIsolate[res,DotSimplify->False,FCI->True,DiracGammaCombine->False,Head->dsHead]; + FCPrint[2, "DiracTrick: diracTrickEval: Applying diracTraceSimplify again ", FCDoControl->diTrVerbose]; + res = FCDiracIsolate[res, DotSimplify->False, FCI->True, DiracGammaCombine->False, FCJoinDOTs->optJoin, Head->dsHead]; res = res /. {dsHead[DiracGamma[5]] :> 0, dsHead[DiracGamma[6|7]] :> 1/2 } /. DOT-> holdDOT/. dsHead[holdDOT[x__]] :> diracTraceSimplify[x]; res = res /. diracTraceSimplify -> DOT /. dsHead-> Identity /. holdDOT -> DOT; - FCPrint[1,"DiracTrace: diracTrickEval: diracTraceSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; + FCPrint[2,"DiracTrick: diracTrickEval: diracTraceSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: diracTrickEval: After diracTraceSimplify ", res, FCDoControl->diTrVerbose] ]; - FCPrint[1, "DiracTrick: diracTrickEval: Leaving.", FCDoControl->diTrVerbose]; + FCPrint[2, "DiracTrick: diracTrickEval: Leaving.", FCDoControl->diTrVerbose]; FCPrint[3, "DiracTrick: diracTrickEval: Leaving with ", res, FCDoControl->diTrVerbose]; res ]; @@ -450,64 +705,91 @@ create replacement rules (standard) and substitute the results back. diracology4Dim[]:= 1; -(* g^mu g^mu *) +(* g^mu g_mu *) diracology4Dim[b___,DiracGamma[l_LorentzIndex], DiracGamma[l_LorentzIndex], d___] := 4 diracology4Dim[ b,d ]; +(* g^i g^i *) +diracology4Dim[b___,DiracGamma[l_CartesianIndex], DiracGamma[l_CartesianIndex], d___] := + 3 FeynCalc`Package`MetricS diracology4Dim[ b,d ]; + +(* g^0 g^0 *) +diracology4Dim[b___,DiracGamma[ExplicitLorentzIndex[0]], DiracGamma[ExplicitLorentzIndex[0]], d___] := + diracology4Dim[ b,d ]; + +(* g^0 g^i_1 ... g^i_n -> (-1)^n g^i_1 ... g^i_n g^0 *) +diracology4Dim[ b___, DiracGamma[ExplicitLorentzIndex[0]], Longest[ch : DiracGamma[(_CartesianIndex | _CartesianMomentum)]..], f___ ] := + (-1)^Length[{ch}] diracology4Dim[b,ch,DiracGamma[ExplicitLorentzIndex[0]],f]; + (* g^mu g^nu g_mu *) diracology4Dim[b___ , DiracGamma[c_LorentzIndex], - DiracGamma[(x: LorentzIndex | ExplicitLorentzIndex | Momentum)[y_]], + DiracGamma[x: (_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)], DiracGamma[c_LorentzIndex], d___] := - - 2 diracology4Dim[b,DiracGamma[x[y]], d]; + - 2 diracology4Dim[b,DiracGamma[x], d]; (* g^mu g^nu g^rho g_mu *) diracology4Dim[b___ , DiracGamma[c_LorentzIndex], - DiracGamma[(x1: LorentzIndex | ExplicitLorentzIndex | Momentum)[y1_]], - DiracGamma[(x2: LorentzIndex | ExplicitLorentzIndex | Momentum)[y2_]], + DiracGamma[x1: (_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)], + DiracGamma[x2: (_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)], DiracGamma[c_LorentzIndex], d___] := - 4 FCUseCache[FCFastContract,{Pair[x1[y1],x2[y2]] diracology4Dim[b, d]},{}]; + 4 FCUseCache[FCFastContract,{Pair[x1,x2] diracology4Dim[b, d]},{}]; (* g^mu g^nu g^rho g^sigma g_mu *) diracology4Dim[b___ , DiracGamma[c_LorentzIndex], - (dg1: DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]]), - (dg2: DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]]), - (dg3: DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]]), DiracGamma[c_LorentzIndex], d___] := + (dg1: DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)]), + (dg2: DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)]), + (dg3: DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)]), DiracGamma[c_LorentzIndex], d___] := - 2 diracology4Dim[b, dg3, dg2, dg1, d]; diracology4Dim[b___ , DiracGamma[c_LorentzIndex], - (dg1: DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]]), - (dg2: DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]]), - (dg3: DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]]), - (dg4: DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]]), + (dg1: DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)]), + (dg2: DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)]), + (dg3: DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)]), + (dg4: DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)]), DiracGamma[c_LorentzIndex], d___] := 2 diracology4Dim[b, dg3, dg2, dg1, dg4, d] + 2 diracology4Dim[b, dg4, dg1, dg2, dg3, d]; (* g^mu g^nu_1 ... g^nu_i g_mu -> -2 g^nu_i ... g^nu_1, where i is odd *) diracology4Dim[ b___, DiracGamma[c_LorentzIndex], - ch : DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]].., DiracGamma[c_LorentzIndex], f___ ] := + ch : DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)].., DiracGamma[c_LorentzIndex], f___ ] := -2 diracology4Dim @@ Join[ {b},Reverse[{ch}],{f} ] /; OddQ[Length[{ch}]] && Length[{ch}]>3; (* g^mu g^nu_1 ... g^nu_i g_mu -> 2 g^nu_i-1 ... g^nu_1 g^nu_i + 2 g^nu_i g^nu_1 ... g^nu_i-1, where i is even *) diracology4Dim[ b___, DiracGamma[c_LorentzIndex], - ch : DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]].., - end : DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]], + ch : DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)].., + end : DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)], DiracGamma[c_LorentzIndex], f___ ] := (2 diracology4Dim @@ Join[ {b},Reverse[{ch}],{end}, {f}] + 2 diracology4Dim[ b,end,ch,f ])/; OddQ[Length[{ch}]] && Length[{ch}]>4; +(* g^0 g^nu_1 ... g^nu_i g^0 -> ... *) +(* This is rather simplistic and inefficient, but for the time being ... *) +diracology4Dim[ b___, DiracGamma[ExplicitLorentzIndex[0]], + ch : DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)].., DiracGamma[ExplicitLorentzIndex[0]], f___ ] := + Block[{len=Length[{ch}],iVar}, + (-1)^len diracology4Dim[b,ch,f] + Sum[2 (-1)^(iVar+1) Pair[ExplicitLorentzIndex[0],({ch}[[iVar]])[[1]]] * + diracology4Dim@@Join[{b},Drop[{ch}, {iVar, iVar}],{DiracGamma[ExplicitLorentzIndex[0]],f}],{iVar,1,len}] + ]; + +(* g^i g^nu_1 ... g^nu_i g^i -> s ( g^mu g^nu_1 ... g^nu_i g_mu - t g^0 g^nu_1 ... g^nu_i g^0 ) *) +diracology4Dim[ b___, DiracGamma[c_CartesianIndex], + ch : DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)].., DiracGamma[c_CartesianIndex], f___ ] := + ( + tmpli= LorentzIndex[$MU[Unique[]]]; + FeynCalc`Package`MetricS (diracology4Dim[b,DiracGamma[tmpli],ch,DiracGamma[tmpli],f] - + FeynCalc`Package`MetricT diracology4Dim[b,DiracGamma[ExplicitLorentzIndex[0]],ch,DiracGamma[ExplicitLorentzIndex[0]],f] ) + ); + (* Slash(p).Slash(p) *) diracology4Dim[b___,DiracGamma[c_Momentum], DiracGamma[c_Momentum], d___ ] := FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracology4Dim[b,d]; - - - (* Slash(p) g^nu Slash(p) *) -diracology4Dim[b___ , DiracGamma[c_Momentum], DiracGamma[(x: LorentzIndex | ExplicitLorentzIndex | Momentum)[y_]], +diracology4Dim[b___ , DiracGamma[c_Momentum], DiracGamma[x: (_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)], DiracGamma[c_Momentum], d___] := - - FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracology4Dim[b,DiracGamma[x[y]], d] + 2 FCUseCache[FCFastContract,{Pair[c,x[y]] diracology4Dim[b, DiracGamma[c], d]},{}]; + - FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracology4Dim[b,DiracGamma[x], d] + 2 FCUseCache[FCFastContract,{Pair[c,x] diracology4Dim[b, DiracGamma[c], d]},{}]; (* Slash(p) g^nu_1 ... g^nu_n Slash(p), purely 4-dim; Eq 2.10 of R. Mertig, M. Boehm, A. Denner. Comp. Phys. Commun., 64 (1991) *) -diracology4Dim[b___, DiracGamma[c_Momentum],ch:DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]].., +diracology4Dim[b___, DiracGamma[c_Momentum],ch:DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)].., DiracGamma[c_Momentum],f___ ] := Block[ {iVar, len = Length[{ch}]}, (-1)^len FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracology4Dim[b,ch,f] @@ -515,6 +797,19 @@ create replacement rules (standard) and substitute the results back. Drop[{ch},{iVar, iVar}],{DiracGamma[c],f}]},{}],{iVar, 1,len}] ]/; (Length[{ch}]>0); +(* g^i g^i p^i p^j *) +diracology4Dim[b___,DiracGamma[c_CartesianMomentum], DiracGamma[c_CartesianMomentum], d___ ] := + FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracology4Dim[b,d]; + +(* g^i g^nu_1 ... g^nu_n g^i p^i p^j *) +diracology4Dim[b___, DiracGamma[c_CartesianMomentum],ch:DiracGamma[(_LorentzIndex | _ExplicitLorentzIndex | _Momentum | _CartesianIndex | _CartesianMomentum)].., + DiracGamma[c_CartesianMomentum],f___ ] := + Block[{len=Length[{ch}],iVar}, + (-1)^len FeynCalc`Package`MetricS CartesianPair[c,c] diracology4Dim[b,ch,f] + + Sum[2 (-1)^(iVar+1) Pair[c,({ch}[[iVar]])[[1]]] * + diracology4Dim@@Join[{b},Drop[{ch}, {iVar, iVar}],{DiracGamma[c],f}],{iVar,1,len}] + ]; + (* ------------------------------------------------------------------------ *) @@ -525,6 +820,11 @@ create replacement rules (standard) and substitute the results back. diracologyDDim[b___,DiracGamma[l_LorentzIndex, dim_], DiracGamma[l_LorentzIndex, dim_], d___] := dim diracologyDDim[ b,d ]; +(* g^i g^i *) +diracologyDDim[b___,DiracGamma[l_CartesianIndex, dim_], DiracGamma[l_CartesianIndex, dim_], d___] := + (dim-1) FeynCalc`Package`MetricS diracologyDDim[ b,d ]; + + (* g^mu g^nu g_mu *) diracologyDDim[b___ , DiracGamma[c_LorentzIndex, dim_], DiracGamma[(x: LorentzIndex | ExplicitLorentzIndex | Momentum)[y_, dim_], dim_], @@ -569,13 +869,17 @@ create replacement rules (standard) and substitute the results back. Block[ {iVar,jVar,len = Length[{ch}],dsTemp}, FCUseCache[FCFastContract,{(-1)^len ( dim - 2 len ) dsTemp[b,ch,f] - 4 (-1)^len Sum[ (-1)^(jVar-iVar) * Pair[{ch}[[iVar,1]], {ch}[[jVar,1]] ]*dsTemp@@Join[{b}, Delete[{ch}, {{iVar},{jVar}}], {f}],{iVar,1,len-1},{jVar,iVar+1,len}]},{}]/. - dsTemp->diracologyDDim/. Pair[aa__]/;!FreeQ[{a},Momentum] :> FCUseCache[ExpandScalarProduct,{Pair[aa]},{}] + dsTemp->diracologyDDim/. Pair[z__]/;!FreeQ[{z},Momentum] :> FCUseCache[ExpandScalarProduct,{Pair[z]},{}] ] /; (Length[{ch}]>4); (* Slash(p) Slash(p) *) diracologyDDim[b___,DiracGamma[c_Momentum, dim_], DiracGamma[c_Momentum, dim_], d___] := FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracologyDDim[b,d]; +(* g^i g^i p^i p^j *) +diracologyDDim[b___,DiracGamma[c_CartesianMomentum, dim_], DiracGamma[c_CartesianMomentum, dim_], d___ ] := + FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] diracologyDDim[b,d]; + (* Slash(p) g^nu Slash(p) *) diracologyDDim[b___ , DiracGamma[c_Momentum, dim_], DiracGamma[(x: LorentzIndex | ExplicitLorentzIndex | Momentum)[y_, dim_] ,dim_], @@ -629,7 +933,7 @@ create replacement rules (standard) and substitute the results back. ga67MatSign[6,5]= 1; -ga67MatSignt[6,7]= +ga67MatSign[6,7]= 0; ga67MatSign[7,5]= @@ -654,6 +958,10 @@ create replacement rules (standard) and substitute the results back. diracTraceSimplify[DOT[x__DiracGamma]]:= 0/; FreeQ2[{x},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && OddQ[Length[{x}]] + +diracTraceSimplify[DiracGamma[(arg1:_[_, dim1___]),dim1___], DiracGamma[(arg2:_[_, dim2___]), dim2___]] := + FCUseCache[ExpandScalarProduct,{Pair[arg1,arg2]},{}]; + diracTraceSimplify[DOT[x___DiracGamma,DiracGamma[6|7],y___DiracGamma]]:= 0/; OddQ[Length[{x,y}]] && FreeQ2[{x,y},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}]; @@ -680,8 +988,11 @@ create replacement rules (standard) and substitute the results back. diracTraceSimplify[cc1_. DiracGamma[6] + cc2_. DiracGamma[7]]:= 1/2 (cc1+cc2)/; NonCommFreeQ[{cc1,cc2}]; +diracTraceSimplify[cc_. DiracGamma[6|7]]:= + 1/2 cc/; NonCommFreeQ[{cc}]; -(* ------------------------------------------------------------------------ *) +diracTraceSimplify[cc1_. DiracGamma[6] + cc2_. DiracGamma[7]]:= + 1/2 (cc1+cc2)/; NonCommFreeQ[{cc1,cc2}]; ga67Val1[7]= -1; @@ -734,7 +1045,8 @@ create replacement rules (standard) and substitute the results back. commonGamma5Properties[b___,cc_. DiracGamma[6]+ cc_. DiracGamma[7],c___] := cc commonGamma5Properties[b, c]/; NonCommFreeQ[{cc}]; -(* ------------------------------------------------------------------------ *) +commonGamma5Properties[___,0,___]:= + 0; ga67Switch1[7]= 6; @@ -742,110 +1054,243 @@ create replacement rules (standard) and substitute the results back. ga67Switch1[6]= 7; -chiralTrickAnticommuting4Dim[b___,DiracGamma[5], c:DiracGamma[_[_]].. , d___] := - (-1)^Length[{c}] chiralTrickAnticommuting4Dim[ b,c,DiracGamma[5],d]; +(* Move g^5 to the right: *) + +chiralTrickAnticommuting4DimRight[b___,DiracGamma[5], c:DiracGamma[_[_]].. , d___] := + (-1)^Length[{c}] chiralTrickAnticommuting4DimRight[ b,c,DiracGamma[5],d]; + +chiralTrickAnticommuting4DimRight[b___, DiracGamma[5], (dd1_. (dg:DiracGamma[_[_]]) + dd2_:0 ),d___ ] := + chiralTrickAnticommuting4DimRight[b,(- dd1 dg + dd2), DiracGamma[5],d ]/; NonCommFreeQ[{dd1,dd2}]; + +chiralTrickAnticommuting4DimRight[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_]].. ,d___] := + chiralTrickAnticommuting4DimRight[ b,c,DiracGamma[h],d]/; EvenQ[Length[{c}]]; + +chiralTrickAnticommuting4DimRight[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_]].. ,d___] := + chiralTrickAnticommuting4DimRight[ b,c,DiracGamma[ga67Switch1[h]],d]/; OddQ[Length[{c}]]; + +chiralTrickAnticommuting4DimRight[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), (dd1_. DiracGamma[6] + dd2_. DiracGamma[7]),d___ ] := + chiralTrickAnticommuting4DimRight[b, (cc1 dd1 DiracGamma[6] + cc2 dd2 DiracGamma[7]),d ]/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; + +chiralTrickAnticommuting4DimRight[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), dd1_. (c:DiracGamma[_[_]]) + dd2_:0, d___ ] := + ( + dd1 chiralTrickAnticommuting4DimRight[b, c, (cc1 DiracGamma[7] + cc2 DiracGamma[6]), d] + + dd2 chiralTrickAnticommuting4DimRight[b, (cc1 DiracGamma[6] + cc2 DiracGamma[7]), d] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; + +chiralTrickAnticommuting4DimRight[b___, (cc1_. + cc2_. DiracGamma[5]), dd1_. (c:DiracGamma[_[_]]) + dd2_:0, d___ ] := + ( + cc1 chiralTrickAnticommuting4DimRight[b, dd1 c + dd2 , d] - + cc2 chiralTrickAnticommuting4DimRight[b, dd1 c - dd2 , DiracGamma[5], d] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; + +chiralTrickAnticommuting4DimRight[b___,(cc2_. DiracGamma[(h:6|7)] + cc1_:0),(dd1_. (dg:DiracGamma[_[_]]) + dd2_:0),d___ ] := + ( + dd1 chiralTrickAnticommuting4DimRight[b,dg, (cc1 + cc2 DiracGamma[ga67Switch1[h]]),d ] + + dd2 chiralTrickAnticommuting4DimRight[b, (cc1 + cc2 DiracGamma[h]),d ] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}] + +chiralTrickAnticommuting4DimRight[b___, DiracGamma[(h1:6|7)],DiracGamma[_[_]] + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h2:6|7)], c___] := + mass chiralTrickAnticommuting4DimRight[b, xy, DiracGamma[h2], c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; + +chiralTrickAnticommuting4DimRight[b___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h:6|7)], c___] := + chiralTrickAnticommuting4DimRight[b, dg, xy, DiracGamma[h], c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass]; + +chiralTrickAnticommuting4DimRight[b___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h2:6|7)], c___] := + chiralTrickAnticommuting4DimRight[b, dg, xy, DiracGamma[h2], c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; + +chiralTrickAnticommuting4DimRight[b___, DiracGamma[(h:6|7)],DiracGamma[_[_]] + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h:6|7)], c___] := + mass chiralTrickAnticommuting4DimRight[b, xy, DiracGamma[h], c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass]; + +chiralTrickAnticommuting4DimRight[b___,DiracGamma[(h:6|7)],DiracGamma[_[_]] + mass_:0, DiracGamma[(h:6|7)], c___] := + mass chiralTrickAnticommuting4DimRight[b, DiracGamma[h], c]/; NonCommFreeQ[mass]; -chiralTrickAnticommuting4Dim[b___, DiracGamma[5], (dd1_. (dg:DiracGamma[_[_]]) + dd2_:0 ),d___ ] := - chiralTrickAnticommuting4Dim[b,(- dd1 dg + dd2), DiracGamma[5],d ]/; NonCommFreeQ[{dd1,dd2}]; +chiralTrickAnticommuting4DimRight[b___,DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, DiracGamma[(h2:6|7)], c___] := + chiralTrickAnticommuting4DimRight[b, dg, DiracGamma[h2], c]/; NonCommFreeQ[mass] && h1=!=h2; -chiralTrickAnticommuting4Dim[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_]].. ,d___] := - chiralTrickAnticommuting4Dim[ b,c,DiracGamma[h],d]/; EvenQ[Length[{c}]]; +chiralTrickAnticommuting4DimRight[b___,DiracGamma[(h:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, c___] := + (chiralTrickAnticommuting4DimRight[b, dg, DiracGamma[ga67Switch1[h]], c] + + mass chiralTrickAnticommuting4DimRight[b, DiracGamma[h], c])/; NonCommFreeQ[mass]; -chiralTrickAnticommuting4Dim[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_]].. ,d___] := - chiralTrickAnticommuting4Dim[ b,c,DiracGamma[ga67Switch1[h]],d]/; OddQ[Length[{c}]]; -chiralTrickAnticommuting4Dim[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), (dd1_. DiracGamma[6] + dd2_. DiracGamma[7]),d___ ] := - chiralTrickAnticommuting4Dim[b, (cc1 dd1 DiracGamma[6] + cc2 dd2 DiracGamma[7]),d ]/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; +(* Move g^5 to the left: *) -chiralTrickAnticommuting4Dim[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), dd1_. (c:DiracGamma[_[_]]) + dd2_:0, d___ ] := +chiralTrickAnticommuting4DimLeft[b___, c:DiracGamma[_[_]].. , DiracGamma[5], d___] := + (-1)^Length[{c}] chiralTrickAnticommuting4DimLeft[ b,DiracGamma[5],c,d]; + +chiralTrickAnticommuting4DimLeft[b___, (dd1_. (dg:DiracGamma[_[_]]) + dd2_:0 ), DiracGamma[5], d___ ] := + chiralTrickAnticommuting4DimLeft[b, DiracGamma[5], (- dd1 dg + dd2), d ]/; NonCommFreeQ[{dd1,dd2}]; + +chiralTrickAnticommuting4DimLeft[b___, c:DiracGamma[_[_]].. , DiracGamma[(h:6|7)], d___] := + chiralTrickAnticommuting4DimLeft[ b,DiracGamma[h],c,d]/; EvenQ[Length[{c}]]; + +chiralTrickAnticommuting4DimLeft[b___, c:DiracGamma[_[_]].. , DiracGamma[(h:6|7)], d___] := + chiralTrickAnticommuting4DimLeft[ b,DiracGamma[ga67Switch1[h]],c,d]/; OddQ[Length[{c}]]; + +chiralTrickAnticommuting4DimLeft[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), (dd1_. DiracGamma[6] + dd2_. DiracGamma[7]),d___ ] := + chiralTrickAnticommuting4DimLeft[b, (cc1 dd1 DiracGamma[6] + cc2 dd2 DiracGamma[7]),d ]/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; + +chiralTrickAnticommuting4DimLeft[b___, dd1_. (c:DiracGamma[_[_]]) + dd2_:0, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), d___ ] := ( - dd1 chiralTrickAnticommuting4Dim[b, c, (cc1 DiracGamma[7] + cc2 DiracGamma[6]), d] + - dd2 chiralTrickAnticommuting4Dim[b, (cc1 DiracGamma[6] + cc2 DiracGamma[7]), d] + dd1 chiralTrickAnticommuting4DimLeft[b, (cc1 DiracGamma[7] + cc2 DiracGamma[6]), c, d] + + dd2 chiralTrickAnticommuting4DimLeft[b, (cc1 DiracGamma[6] + cc2 DiracGamma[7]), d] )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; -Off[Optional::opdef]; -chiralTrickAnticommuting4Dim[b___, (cc1_:0 + cc2_. DiracGamma[(h:6|7)]),(dd1_. (dg:DiracGamma[_[_]]) + dd2_:0),d___ ] := - chiralTrickAnticommuting4Dim[b,(dd1 dg + dd2), (cc1 + cc2 DiracGamma[ga67Switch1[h]]),d ]/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; -On[Optional::opdef]; +chiralTrickAnticommuting4DimLeft[b___, dd1_. (c:DiracGamma[_[_]]) + dd2_:0, (cc1_. + cc2_. DiracGamma[5]), d___ ] := + ( + cc1 chiralTrickAnticommuting4DimLeft[b, dd1 c + dd2 , d] - + cc2 chiralTrickAnticommuting4DimLeft[b, DiracGamma[5], dd1 c - dd2, d] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; -chiralTrickAnticommuting4Dim[b___, DiracGamma[(h1:6|7)],DiracGamma[_[_]] + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h2:6|7)], c___] := - mass chiralTrickAnticommuting4Dim[b, xy, DiracGamma[h2], c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; +chiralTrickAnticommuting4DimLeft[b___,(dd1_. (dg:DiracGamma[_[_]]) + dd2_:0),(cc2_. DiracGamma[(h:6|7)] + cc1_:0),d___ ] := + ( + dd1 chiralTrickAnticommuting4DimLeft[b,(cc1 + cc2 DiracGamma[ga67Switch1[h]]), dg, d ] + + dd2 chiralTrickAnticommuting4DimLeft[b, (cc1 + cc2 DiracGamma[h]),d ] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}] + +chiralTrickAnticommuting4DimLeft[b___, DiracGamma[(h1:6|7)],DiracGamma[_[_]] + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h2:6|7)], c___] := + mass chiralTrickAnticommuting4DimLeft[b, DiracGamma[h1], xy, c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; + +chiralTrickAnticommuting4DimLeft[b___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h:6|7)], c___] := + chiralTrickAnticommuting4DimLeft[b, DiracGamma[h], dg, xy, c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass]; -chiralTrickAnticommuting4Dim[b___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h:6|7)], c___] := - chiralTrickAnticommuting4Dim[b, dg, xy, DiracGamma[h], c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass]; +chiralTrickAnticommuting4DimLeft[b___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h2:6|7)], c___] := + chiralTrickAnticommuting4DimLeft[b, DiracGamma[h1], dg, xy, c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; -chiralTrickAnticommuting4Dim[b___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, xy:DiracGamma[_[_] ].. , DiracGamma[(h2:6|7)], c___] := - chiralTrickAnticommuting4Dim[b, dg, xy, DiracGamma[h2], c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; +chiralTrickAnticommuting4DimLeft[b___, DiracGamma[(h:6|7)],DiracGamma[_[_]] + mass_:0, xy:DiracGamma[_[_]].. , DiracGamma[(h:6|7)], c___] := + mass chiralTrickAnticommuting4DimLeft[b, DiracGamma[h], xy, c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass]; -chiralTrickAnticommuting4Dim[b___, DiracGamma[(h:6|7)],DiracGamma[_[_]] + mass_:0, xy:DiracGamma[_[_] ].. , DiracGamma[(h:6|7)], c___] := - mass chiralTrickAnticommuting4Dim[b, xy, DiracGamma[h], c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass]; +chiralTrickAnticommuting4DimLeft[b___,DiracGamma[(h:6|7)],DiracGamma[_[_]] + mass_:0, DiracGamma[(h:6|7)], c___] := + mass chiralTrickAnticommuting4DimLeft[b, DiracGamma[h], c]/; NonCommFreeQ[mass]; -chiralTrickAnticommuting4Dim[b___,DiracGamma[(h:6|7)],DiracGamma[_[_]] + mass_:0, DiracGamma[(h:6|7)], c___] := - mass chiralTrickAnticommuting4Dim[b, DiracGamma[h], c]/; NonCommFreeQ[mass]; +chiralTrickAnticommuting4DimLeft[b___,DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, DiracGamma[(h2:6|7)], c___] := + chiralTrickAnticommuting4DimLeft[b, DiracGamma[h1], dg, c]/; NonCommFreeQ[mass] && h1=!=h2; -chiralTrickAnticommuting4Dim[b___,DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, DiracGamma[(h2:6|7)], c___] := - chiralTrickAnticommuting4Dim[b, dg, DiracGamma[h2], c]/; NonCommFreeQ[mass] && h1=!=h2; +chiralTrickAnticommuting4DimLeft[b___,(dg:DiracGamma[_[_]]) + mass_:0, DiracGamma[(h:6|7)], c___] := + (chiralTrickAnticommuting4DimLeft[b, DiracGamma[ga67Switch1[h]], dg, c] + + mass chiralTrickAnticommuting4DimLeft[b, DiracGamma[h], c])/; NonCommFreeQ[mass]; -chiralTrickAnticommuting4Dim[b___,DiracGamma[(h:6|7)],(dg:DiracGamma[_[_]]) + mass_:0, c___] := - (chiralTrickAnticommuting4Dim[b, dg, DiracGamma[ga67Switch1[h]], c] + - mass chiralTrickAnticommuting4Dim[b, DiracGamma[h], c])/; NonCommFreeQ[mass]; (* ------------------------------------------------------------------------ *) -chiralTrickAnticommutingDDim[b___,DiracGamma[5], c:DiracGamma[_[_,_],_].. , d___] := - (-1)^Length[{c}] chiralTrickAnticommutingDDim[ b,c,DiracGamma[5],d]; +(* Move g^5 to the right: *) -chiralTrickAnticommutingDDim[b___, DiracGamma[5], (dd1_. (dg:DiracGamma[_[_,_],_]) + dd2_:0 ),d___ ] := - chiralTrickAnticommutingDDim[b,(- dd1 dg + dd2), DiracGamma[5],d ]/; NonCommFreeQ[{dd1,dd2}]; +chiralTrickAnticommutingDDimRight[b___,DiracGamma[5], c:DiracGamma[_[_,_],_].. , d___] := + (-1)^Length[{c}] chiralTrickAnticommutingDDimRight[ b,c,DiracGamma[5],d]; -chiralTrickAnticommutingDDim[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_,_],_].. ,d___] := - chiralTrickAnticommutingDDim[ b,c,DiracGamma[h],d]/; EvenQ[Length[{c}]]; +chiralTrickAnticommutingDDimRight[b___, DiracGamma[5], (dd1_. (dg:DiracGamma[_[_,_],_]) + dd2_:0 ),d___ ] := + chiralTrickAnticommutingDDimRight[b,(- dd1 dg + dd2), DiracGamma[5],d ]/; NonCommFreeQ[{dd1,dd2}]; -chiralTrickAnticommutingDDim[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_,_],_].. ,d___] := - chiralTrickAnticommutingDDim[ b,c,DiracGamma[ga67Switch1[h]],d]/; OddQ[Length[{c}]]; +chiralTrickAnticommutingDDimRight[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_,_],_].. ,d___] := + chiralTrickAnticommutingDDimRight[ b,c,DiracGamma[h],d]/; EvenQ[Length[{c}]]; -chiralTrickAnticommutingDDim[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), (dd1_. DiracGamma[6] + dd2_. DiracGamma[7]),d___ ] := - chiralTrickAnticommutingDDim[b, (cc1 dd1 DiracGamma[6] + cc2 dd2 DiracGamma[7]),d ]/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; +chiralTrickAnticommutingDDimRight[b___,DiracGamma[(h:6|7)], c:DiracGamma[_[_,_],_].. ,d___] := + chiralTrickAnticommutingDDimRight[ b,c,DiracGamma[ga67Switch1[h]],d]/; OddQ[Length[{c}]]; + +chiralTrickAnticommutingDDimRight[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), (dd1_. DiracGamma[6] + dd2_. DiracGamma[7]),d___ ] := + chiralTrickAnticommutingDDimRight[b, (cc1 dd1 DiracGamma[6] + cc2 dd2 DiracGamma[7]),d ]/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; + +chiralTrickAnticommutingDDimRight[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), dd1_. (c:DiracGamma[_[_,_],_]) + dd2_:0, d___ ] := + ( + dd1 chiralTrickAnticommutingDDimRight[b, c, (cc1 DiracGamma[7] + cc2 DiracGamma[6]), d] + + dd2 chiralTrickAnticommutingDDimRight[b, (cc1 DiracGamma[6] + cc2 DiracGamma[7]), d] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; -chiralTrickAnticommutingDDim[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), dd1_. (c:DiracGamma[_[_,_],_]) + dd2_:0, d___ ] := +chiralTrickAnticommutingDDimRight[b___, (cc1_. + cc2_. DiracGamma[5]), dd1_. (c:DiracGamma[_[_,_],_]) + dd2_:0, d___ ] := ( - dd1 chiralTrickAnticommutingDDim[b, c, (cc1 DiracGamma[7] + cc2 DiracGamma[6]), d] + - dd2 chiralTrickAnticommutingDDim[b, (cc1 DiracGamma[6] + cc2 DiracGamma[7]), d] + cc1 chiralTrickAnticommutingDDimRight[b, dd1 c + dd2 , d] - cc2 chiralTrickAnticommutingDDimRight[b, dd1 c - dd2 , DiracGamma[5], d] )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; -Off[Optional::opdef]; -chiralTrickAnticommutingDDim[b___, (cc1_:0 + cc2_. DiracGamma[(h:6|7)]),(dd1_. (dg:DiracGamma[_[_,_],_]) + dd2_:0),d___ ] := - chiralTrickAnticommutingDDim[b,(dd1 dg + dd2), (cc1 + cc2 DiracGamma[ga67Switch1[h]]),d ]/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; -On[Optional::opdef]; +chiralTrickAnticommutingDDimRight[b___, (cc2_. DiracGamma[(h:6|7)] + cc1_:0),(dd1_. (dg:DiracGamma[_[_,_],_]) + dd2_:0),d___ ] := + ( + dd1 chiralTrickAnticommutingDDimRight[b,dg, (cc1 + cc2 DiracGamma[ga67Switch1[h]]),d ] + + dd2 chiralTrickAnticommutingDDimRight[b, (cc1 + cc2 DiracGamma[h]),d ] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}] + +chiralTrickAnticommutingDDimRight[b___, DiracGamma[(h1:6|7)],DiracGamma[_[_,_],_] + mass_:0, xy:DiracGamma[_[_,_],_].. , DiracGamma[(h2:6|7)], c___] := + mass chiralTrickAnticommutingDDimRight[b, xy, DiracGamma[h2], c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; + +chiralTrickAnticommutingDDimRight[b___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, xy:DiracGamma[_[_,_],_].. , DiracGamma[(h:6|7)], c___] := + chiralTrickAnticommutingDDimRight[b, dg, xy, DiracGamma[h], c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass]; + +chiralTrickAnticommutingDDimRight[b___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, xy:DiracGamma[_[_] ].. , DiracGamma[(h2:6|7)], c___] := + chiralTrickAnticommutingDDimRight[b, dg, xy, DiracGamma[h2], c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; + +chiralTrickAnticommutingDDimRight[b___, DiracGamma[(h:6|7)],DiracGamma[_[_,_],_] + mass_:0, xy:DiracGamma[_[_] ].. , DiracGamma[(h:6|7)], c___] := + mass chiralTrickAnticommutingDDimRight[b, xy, DiracGamma[h], c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass]; + +chiralTrickAnticommutingDDimRight[b___,DiracGamma[(h:6|7)],DiracGamma[_[_,_],_] + mass_:0, DiracGamma[(h:6|7)], c___] := + mass chiralTrickAnticommutingDDimRight[b, DiracGamma[h], c]/; NonCommFreeQ[mass]; -chiralTrickAnticommutingDDim[b___, DiracGamma[(h1:6|7)],DiracGamma[_[_,_],_] + mass_:0, xy:DiracGamma[_[_,_],_].. , DiracGamma[(h2:6|7)], c___] := - mass chiralTrickAnticommutingDDim[b, xy, DiracGamma[h2], c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; +chiralTrickAnticommutingDDimRight[b___,DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, DiracGamma[(h2:6|7)], c___] := + chiralTrickAnticommutingDDimRight[b, dg, DiracGamma[h2], c]/; NonCommFreeQ[mass] && h1=!=h2; -chiralTrickAnticommutingDDim[b___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, xy:DiracGamma[_[_,_],_].. , DiracGamma[(h:6|7)], c___] := - chiralTrickAnticommutingDDim[b, dg, xy, DiracGamma[h], c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass]; +chiralTrickAnticommutingDDimRight[b___,DiracGamma[(h:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, c___] := + (chiralTrickAnticommutingDDimRight[b, dg, DiracGamma[ga67Switch1[h]], c] + + mass chiralTrickAnticommutingDDimRight[b, DiracGamma[h], c])/; NonCommFreeQ[mass]; -chiralTrickAnticommutingDDim[b___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, xy:DiracGamma[_[_] ].. , DiracGamma[(h2:6|7)], c___] := - chiralTrickAnticommutingDDim[b, dg, xy, DiracGamma[h2], c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; +(* Move g^5 to the left: *) -chiralTrickAnticommutingDDim[b___, DiracGamma[(h:6|7)],DiracGamma[_[_,_],_] + mass_:0, xy:DiracGamma[_[_] ].. , DiracGamma[(h:6|7)], c___] := - mass chiralTrickAnticommutingDDim[b, xy, DiracGamma[h], c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass]; +chiralTrickAnticommutingDDimLeft[b___, c:DiracGamma[_[_,_],_].. , DiracGamma[5], d___] := + (-1)^Length[{c}] chiralTrickAnticommutingDDimLeft[ b,DiracGamma[5],c,d]; -chiralTrickAnticommutingDDim[b___,DiracGamma[(h:6|7)],DiracGamma[_[_,_],_] + mass_:0, DiracGamma[(h:6|7)], c___] := - mass chiralTrickAnticommutingDDim[b, DiracGamma[h], c]/; NonCommFreeQ[mass]; +chiralTrickAnticommutingDDimLeft[b___, (dd1_. (dg:DiracGamma[_[_,_],_]) + dd2_:0 ), DiracGamma[5], d___ ] := + chiralTrickAnticommutingDDimLeft[b, DiracGamma[5], (- dd1 dg + dd2), d ]/; NonCommFreeQ[{dd1,dd2}]; -chiralTrickAnticommutingDDim[b___,DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, DiracGamma[(h2:6|7)], c___] := - chiralTrickAnticommutingDDim[b, dg, DiracGamma[h2], c]/; NonCommFreeQ[mass] && h1=!=h2; +chiralTrickAnticommutingDDimLeft[b___, c:DiracGamma[_[_,_],_].. , DiracGamma[(h:6|7)], d___] := + chiralTrickAnticommutingDDimLeft[ b,DiracGamma[h],c,d]/; EvenQ[Length[{c}]]; -chiralTrickAnticommutingDDim[b___,DiracGamma[(h:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, c___] := - (chiralTrickAnticommutingDDim[b, dg, DiracGamma[ga67Switch1[h]], c] + - mass chiralTrickAnticommutingDDim[b, DiracGamma[h], c])/; NonCommFreeQ[mass]; +chiralTrickAnticommutingDDimLeft[b___, c:DiracGamma[_[_,_],_].. , DiracGamma[(h:6|7)], d___] := + chiralTrickAnticommutingDDimLeft[ b,DiracGamma[ga67Switch1[h]],c,d]/; OddQ[Length[{c}]]; + +chiralTrickAnticommutingDDimLeft[b___, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), (dd1_. DiracGamma[6] + dd2_. DiracGamma[7]),d___ ] := + chiralTrickAnticommutingDDimLeft[b, (cc1 dd1 DiracGamma[6] + cc2 dd2 DiracGamma[7]),d ]/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; + +chiralTrickAnticommutingDDimLeft[b___, dd1_. (c:DiracGamma[_[_,_],_]) + dd2_:0, (cc1_. DiracGamma[6] + cc2_. DiracGamma[7]), d___ ] := + ( + dd1 chiralTrickAnticommutingDDimLeft[b, (cc1 DiracGamma[7] + cc2 DiracGamma[6]), c, d] + + dd2 chiralTrickAnticommutingDDimLeft[b, (cc1 DiracGamma[6] + cc2 DiracGamma[7]), d] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; + +chiralTrickAnticommutingDDimLeft[b___, dd1_. (c:DiracGamma[_[_,_],_]) + dd2_:0, (cc1_. + cc2_. DiracGamma[5]), d___ ] := + ( + cc1 chiralTrickAnticommutingDDimLeft[b, dd1 c + dd2 , d] - + cc2 chiralTrickAnticommutingDDimLeft[b, DiracGamma[5], dd1 c - dd2 , d] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}]; + +chiralTrickAnticommutingDDimLeft[b___, (dd1_. (dg:DiracGamma[_[_,_],_]) + dd2_:0), (cc2_. DiracGamma[(h:6|7)] + cc1_:0), d___ ] := + ( + dd1 chiralTrickAnticommutingDDimLeft[b, (cc1 + cc2 DiracGamma[ga67Switch1[h]]), dg,d ] + + dd2 chiralTrickAnticommutingDDimLeft[b, (cc1 + cc2 DiracGamma[h]),d ] + )/; NonCommFreeQ[{cc1,cc2,dd1,dd2}] + +chiralTrickAnticommutingDDimLeft[b___, DiracGamma[(h1:6|7)],DiracGamma[_[_,_],_] + mass_:0, xy:DiracGamma[_[_,_],_].. , DiracGamma[(h2:6|7)], c___] := + mass chiralTrickAnticommutingDDimLeft[b, DiracGamma[h1], xy, c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; + +chiralTrickAnticommutingDDimLeft[b___, DiracGamma[(h:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, xy:DiracGamma[_[_,_],_].. , DiracGamma[(h:6|7)], c___] := + chiralTrickAnticommutingDDimLeft[b, DiracGamma[h], dg, xy, c]/; OddQ[Length[{xy}]] && NonCommFreeQ[mass]; + +chiralTrickAnticommutingDDimLeft[b___, DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, xy:DiracGamma[_[_] ].. , DiracGamma[(h2:6|7)], c___] := + chiralTrickAnticommutingDDimLeft[b, DiracGamma[h1], dg, xy, c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass] && h1=!=h2; + +chiralTrickAnticommutingDDimLeft[b___, DiracGamma[(h:6|7)],DiracGamma[_[_,_],_] + mass_:0, xy:DiracGamma[_[_] ].. , DiracGamma[(h:6|7)], c___] := + mass chiralTrickAnticommutingDDimLeft[b, DiracGamma[h], xy, c]/; EvenQ[Length[{xy}]] && NonCommFreeQ[mass]; + +chiralTrickAnticommutingDDimLeft[b___,DiracGamma[(h:6|7)],DiracGamma[_[_,_],_] + mass_:0, DiracGamma[(h:6|7)], c___] := + mass chiralTrickAnticommutingDDimLeft[b, DiracGamma[h], c]/; NonCommFreeQ[mass]; + +chiralTrickAnticommutingDDimLeft[b___,DiracGamma[(h1:6|7)],(dg:DiracGamma[_[_,_],_]) + mass_:0, DiracGamma[(h2:6|7)], c___] := + chiralTrickAnticommutingDDimLeft[b, DiracGamma[h1], dg, c]/; NonCommFreeQ[mass] && h1=!=h2; + +chiralTrickAnticommutingDDimLeft[b___,(dg:DiracGamma[_[_,_],_]) + mass_:0, DiracGamma[(h:6|7)], c___] := + (chiralTrickAnticommutingDDimLeft[b, DiracGamma[ga67Switch1[h]], dg, c] + + mass chiralTrickAnticommutingDDimLeft[b, DiracGamma[h], c])/; NonCommFreeQ[mass]; (* ------------------------------------------------------------------------ *) chiralTrickLarin[b___,((dg:DiracGamma[_[_,_], dim_]) + mass_:0),DiracGamma[5],d__] := Block[{li1,li2,li3}, {li1,li2,li3} = LorentzIndex[#,dim]& /@ Unique[{"dtlarLia","dtlarLib","dtlarLic"}]; - I/6 $LeviCivitaSign Eps[dg[[1]], li1, li2, li3, Dimension->dim] chiralTrickLarin[b,DiracGamma[li1,dim], + I/6 $LeviCivitaSign Eps[dg[[1]], li1, li2, li3] chiralTrickLarin[b,DiracGamma[li1,dim], DiracGamma[li2,dim],DiracGamma[li3,dim],d] + mass chiralTrickLarin[b,DiracGamma[5],d] ]/; !FreeQ2[{d},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && NonCommFreeQ[mass]; @@ -854,7 +1299,7 @@ create replacement rules (standard) and substitute the results back. {li1,li2,li3} = LorentzIndex[#,dim]& /@ Unique[{"dtlarLia","dtlarLib","dtlarLic"}]; mass chiralTrickLarin[b,DiracGamma[6],d] + 1/2 chiralTrickLarin[b,dg,d] + - I/12 $LeviCivitaSign Eps[dg[[1]], li1, li2, li3, Dimension->dim] chiralTrickLarin[b,DiracGamma[li1,dim],DiracGamma[li2,dim],DiracGamma[li3,dim],d] + I/12 $LeviCivitaSign Eps[dg[[1]], li1, li2, li3] chiralTrickLarin[b,DiracGamma[li1,dim],DiracGamma[li2,dim],DiracGamma[li3,dim],d] ]/; !FreeQ2[{d},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && NonCommFreeQ[mass]; chiralTrickLarin[b___,((dg:DiracGamma[_[_,_], dim_]) + mass_:0),DiracGamma[7],d__] := @@ -862,35 +1307,54 @@ create replacement rules (standard) and substitute the results back. {li1,li2,li3} = LorentzIndex[#,dim]& /@ Unique[{"dtlarLia","dtlarLib","dtlarLic"}]; mass chiralTrickLarin[b,DiracGamma[7],d] + 1/2 chiralTrickLarin[b,dg,d] + - I/12 $LeviCivitaSign Eps[dg[[1]], li1, li2, li3, Dimension->dim] chiralTrickLarin[b,DiracGamma[li1,dim],DiracGamma[li2,dim],DiracGamma[li3,dim],d] + I/12 $LeviCivitaSign Eps[dg[[1]], li1, li2, li3] chiralTrickLarin[b,DiracGamma[li1,dim],DiracGamma[li2,dim],DiracGamma[li3,dim],d] ]/; !FreeQ2[{d},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] && NonCommFreeQ[mass]; (* ------------------------------------------------------------------------ *) -gamma5MoveBMHV[]:= +(* Move g^5 to the right: *) + +gamma5MoveBMHVRight[]:= 1; -gamma5MoveBMHV[b___,DiracGamma[(h:5|6|7)],DiracGamma[x_[y__],d_Symbol -4] + mass_:0,f___] := - gamma5MoveBMHV[ b,mass + DiracGamma[x[y],d-4],DiracGamma[h],f ]/; NonCommFreeQ[mass]; +gamma5MoveBMHVRight[b___, DiracGamma[(h:5|6|7)],DiracGamma[x_[y__],d_Symbol -4] + mass_:0,f___] := + gamma5MoveBMHVRight[ b,mass + DiracGamma[x[y],d-4],DiracGamma[h],f ]/; NonCommFreeQ[mass]; -gamma5MoveBMHV[b___,DiracGamma[5],DiracGamma[x_[y__],d_Symbol], f___] := - 2 gamma5MoveBMHV[b,DiracGamma[x[y],d-4],DiracGamma[5],f] - - gamma5MoveBMHV[b,DiracGamma[x[y],d],DiracGamma[5],f]; +gamma5MoveBMHVRight[b___,DiracGamma[5],DiracGamma[x_[y__],d_Symbol], f___] := + 2 gamma5MoveBMHVRight[b,DiracGamma[x[y],d-4],DiracGamma[5],f] - + gamma5MoveBMHVRight[b,DiracGamma[x[y],d],DiracGamma[5],f]; -gamma5MoveBMHV[b___,DiracGamma[5],DiracGamma[x_[y__],d_Symbol] + mass_, f___] := - 2 gamma5MoveBMHV[b,DiracGamma[x[y],d-4],DiracGamma[5],f] + - gamma5MoveBMHV[b,(mass - DiracGamma[x[y],d]),DiracGamma[5],f]/; NonCommFreeQ[mass]; +gamma5MoveBMHVRight[b___,DiracGamma[5],DiracGamma[x_[y__],d_Symbol] + mass_, f___] := + 2 gamma5MoveBMHVRight[b,DiracGamma[x[y],d-4],DiracGamma[5],f] + + gamma5MoveBMHVRight[b,(mass - DiracGamma[x[y],d]),DiracGamma[5],f]/; NonCommFreeQ[mass]; -gamma5MoveBMHV[b___,DiracGamma[6],DiracGamma[x_[y__],d_Symbol] + mass_:0, f___] := - (gamma5MoveBMHV[b,DiracGamma[x[y],d-4],DiracGamma[5],f] + - gamma5MoveBMHV[b,DiracGamma[x[y],d],DiracGamma[7],f] + - mass gamma5MoveBMHV[b,DiracGamma[6],f])/; NonCommFreeQ[mass]; +gamma5MoveBMHVRight[b___,DiracGamma[(h:6|7)],DiracGamma[x_[y_,_],d_Symbol] + mass_:0, f___] := + ( + gamma5MoveBMHVRight[b,DiracGamma[x[y,d-4],d-4] + mass,DiracGamma[h],f] + + gamma5MoveBMHVRight[b,DiracGamma[x[y]],DiracGamma[ga67Switch1[h]],f] + )/; NonCommFreeQ[mass]; -gamma5MoveBMHV[b___,DiracGamma[7],DiracGamma[x_[y__],d_Symbol] + mass_:0, f___] := - (- gamma5MoveBMHV[b,DiracGamma[x[y],d-4],DiracGamma[5],f] + - gamma5MoveBMHV[b,DiracGamma[x[y],d],DiracGamma[6],f] + - mass gamma5MoveBMHV[b,DiracGamma[7],f])/; NonCommFreeQ[mass]; +(* Move g^5 to the left: *) +gamma5MoveBMHVLeft[]:= + 1; + +gamma5MoveBMHVLeft[b___, DiracGamma[x_[y__],d_Symbol -4] + mass_:0, DiracGamma[(h:5|6|7)], f___] := + gamma5MoveBMHVLeft[ b,DiracGamma[h], mass + DiracGamma[x[y],d-4],f ]/; NonCommFreeQ[mass]; + +gamma5MoveBMHVLeft[b___,DiracGamma[x_[y__],d_Symbol], DiracGamma[5], f___] := + 2 gamma5MoveBMHVLeft[b,DiracGamma[5],DiracGamma[x[y],d-4],f] - + gamma5MoveBMHVLeft[b,DiracGamma[5],DiracGamma[x[y],d],f] + +gamma5MoveBMHVLeft[b___,DiracGamma[x_[y__],d_Symbol] + mass_, DiracGamma[5], f___] := + 2 gamma5MoveBMHVLeft[b,DiracGamma[5],DiracGamma[x[y],d-4],f] + + gamma5MoveBMHVLeft[b,DiracGamma[5],(mass - DiracGamma[x[y],d]),f]/; NonCommFreeQ[mass]; + +gamma5MoveBMHVLeft[b___,DiracGamma[x_[y_,_],d_Symbol] + mass_:0, DiracGamma[(h:6|7)], f___] := + ( + gamma5MoveBMHVLeft[b,DiracGamma[h],DiracGamma[x[y,d-4],d-4] + mass,f] + + gamma5MoveBMHVLeft[b,DiracGamma[ga67Switch1[h]],DiracGamma[x[y]],f] + )/; NonCommFreeQ[mass]; (* ------------------------------------------------------------------------ *) @@ -908,29 +1372,49 @@ create replacement rules (standard) and substitute the results back. DiracGamma[LorentzIndex[c_]], f___ ] := diracologyBMHV1[b, DiracGamma[LorentzIndex[c]], d, DiracGamma[LorentzIndex[c]], f]; +(* D-1 and 3 -> 3 *) +diracologyBMHV1[ b___, DiracGamma[CartesianIndex[c_, dimD_Symbol-1], dimD_Symbol], d:DiracGamma[__].. , + DiracGamma[CartesianIndex[c_]], f___ ] := + diracologyBMHV1[b, DiracGamma[CartesianIndex[c]], d, DiracGamma[CartesianIndex[c]], f]; + (* 4 and D -> 4 *) diracologyBMHV1[ b___, DiracGamma[LorentzIndex[c_]], d:DiracGamma[__].. , DiracGamma[LorentzIndex[c_, dimD_Symbol], dimD_Symbol], f___ ] := diracologyBMHV1[b, DiracGamma[LorentzIndex[c]], d, DiracGamma[LorentzIndex[c]], f]; +(* 3 and D-1 -> 3 *) +diracologyBMHV1[ b___, DiracGamma[CartesianIndex[c_]], d:DiracGamma[__].. , + DiracGamma[CartesianIndex[c_, dimD_Symbol-1], dimD_Symbol], f___ ] := + diracologyBMHV1[b, DiracGamma[CartesianIndex[c]], d, DiracGamma[CartesianIndex[c]], f]; + (* D and D-4 -> D-4 *) diracologyBMHV1[ b___, DiracGamma[LorentzIndex[c_, dimD_Symbol], dimD_Symbol], d:DiracGamma[__].. , DiracGamma[LorentzIndex[c_, dimD_Symbol-4], dimD_Symbol-4], f___ ] := diracologyBMHV1[b,DiracGamma[LorentzIndex[c, dimD-4], dimD-4], d,DiracGamma[LorentzIndex[c, dimD-4], dimD-4], f]; +(* D-1 and D-4 -> D-4 *) +diracologyBMHV1[ b___, DiracGamma[CartesianIndex[c_, dimD_Symbol-1], dimD_Symbol], d:DiracGamma[__].. , + DiracGamma[CartesianIndex[c_, dimD_Symbol-4], dimD_Symbol-4], f___ ] := + diracologyBMHV1[b,DiracGamma[CartesianIndex[c, dimD-4], dimD-4], d,DiracGamma[CartesianIndex[c, dimD-4], dimD-4], f]; + (* D-4 and D -> D-4 *) diracologyBMHV1[ b___, DiracGamma[LorentzIndex[c_, dimD_Symbol-4], dimD_Symbol-4], d:DiracGamma[__].. , DiracGamma[LorentzIndex[c_, dimD_Symbol],dimD_Symbol],f___ ] := diracologyBMHV1[b,DiracGamma[LorentzIndex[c, dimD-4], dimD-4], d, DiracGamma[LorentzIndex[c, dimD-4], dimD-4],f]; +(* D-4 and D-1 -> D-4 *) +diracologyBMHV1[ b___, DiracGamma[CartesianIndex[c_, dimD_Symbol-4], dimD_Symbol-4], d:DiracGamma[__].. , + DiracGamma[CartesianIndex[c_, dimD_Symbol-1],dimD_Symbol],f___ ] := + diracologyBMHV1[b,DiracGamma[CartesianIndex[c, dimD-4], dimD-4], d, DiracGamma[CartesianIndex[c, dimD-4], dimD-4],f]; + (* 4 and D-4 -> 0 *) -diracologyBMHV1[ ___, DiracGamma[LorentzIndex[c_, dimD_Symbol-4], dimD_Symbol-4], DiracGamma[__].. , - DiracGamma[LorentzIndex[c_]], ___ ] := +diracologyBMHV1[ ___, DiracGamma[(h:LorentzIndex|CartesianIndex)[c_, dimD_Symbol-4], dimD_Symbol-4], DiracGamma[__].. , + DiracGamma[(h:LorentzIndex|CartesianIndex)[c_]], ___ ] := 0; (* D-4 and 4 -> 0 *) -diracologyBMHV1[ ___, DiracGamma[LorentzIndex[c_]], DiracGamma[__].. , - DiracGamma[LorentzIndex[c_, dimD_Symbol-4], dimD_Symbol-4], ___ ] := +diracologyBMHV1[ ___, DiracGamma[(h:LorentzIndex|CartesianIndex)[c_]], DiracGamma[__].. , + DiracGamma[(h:LorentzIndex|CartesianIndex)[c_, dimD_Symbol-4], dimD_Symbol-4], ___ ] := 0; (* Contractions of neighbouring Dirac matrices in D, 4 and D-4 dimensions *) @@ -940,6 +1424,10 @@ create replacement rules (standard) and substitute the results back. DiracGamma[LorentzIndex[c_, dim2_ : 4], dim2_: 4], d___] := (PairContract[LorentzIndex[c, dim1],LorentzIndex[c, dim2]]/. PairContract->Pair) diracologyBMHV2[ b,d ]; +diracologyBMHV2[b___,DiracGamma[CartesianIndex[c_, dim1_ : 3], ___], + DiracGamma[CartesianIndex[c_, dim2_ : 3], ___], d___] := + (FeynCalc`Package`MetricS CartesianPairContract[CartesianIndex[c, dim1],CartesianIndex[c, dim2]]/. CartesianPairContract->CartesianPair) diracologyBMHV2[ b,d ]; + (* Simplifications for g^mu g^nu_1 ... g^nu_n g_mu where g^mu is in 4 and g^nu_i are in D-4 dimensions or vice versa. *) (* ------------------------------------------------------------------------ *) @@ -952,13 +1440,15 @@ create replacement rules (standard) and substitute the results back. (* D-4, (... 4 ... ), D-4 *) diracologyBMHV2[b___ , DiracGamma[LorentzIndex[c_, dim_Symbol-4], dim_Symbol-4], - ch : DiracGamma[(LorentzIndex | ExplicitLorentzIndex | Momentum)[_]].., + ch : DiracGamma[((LorentzIndex | ExplicitLorentzIndex | Momentum)[_])].., DiracGamma[LorentzIndex[c_, dim_Symbol-4], dim_Symbol-4], d___] := (dim - 4) (-1)^Length[{ch}] diracologyBMHV2[b,ch, d]; +(* D, (... 4 ... ), D *) (* Simplification for g^mu g^nu_1 ... g^nu_n g_mu where g^mu is in D and g^nu_i are in 4 dimensions. Applies for n>4, since for n<=4 we have - explicit expressions in the code *) + explicit expressions in the code. However, if g^nu_i contain g^0, we + apply this formula independently of the length of the chain. *) (* ------------------------------------------------------------------------ *) diracologyBMHV2[b___ , DiracGamma[LorentzIndex[c_, dim_Symbol], dim_Symbol], @@ -967,6 +1457,7 @@ create replacement rules (standard) and substitute the results back. diracologyBMHV2[b,DiracGamma[LorentzIndex[c]], ch, DiracGamma[LorentzIndex[c]], d] + (dim - 4) (-1)^Length[{ch}] diracologyBMHV2[b,ch, d]/; Length[{ch}]>4; +(* D, (... D-4 ... ), D *) (* Simplification for g^mu g^nu_1 ... g^nu_n g_mu where g^mu is in D and g^nu_i are in D-4 dimensions. Applies for n>4, since for n<=4 we have explicit expressions in the code *) @@ -1220,7 +1711,7 @@ create replacement rules (standard) and substitute the results back. Sum[ (-1)^(jVar-iVar) * Pair[{ch}[[iVar,1]], {ch}[[jVar,1]] ]*dsTemp@@Join[{b}, Delete[{ch}, {{iVar},{jVar}}], {f}],{iVar,1,len-1},{jVar,iVar+1,len} - ]},{}]/.dsTemp->diracologyBMHV2/. Pair[aa__] :> FCUseCache[ExpandScalarProduct,{Pair[aa]},{}] + ]},{}]/.dsTemp->diracologyBMHV2 /. Pair[z__] :> FCUseCache[ExpandScalarProduct,{Pair[z]},{}] ] /;(Length[{ch}]>4) && MatchQ[dim, _Symbol | _Symbol-4 ]; diff --git a/FeynCalc/Dirac/EpsChisholm.m b/FeynCalc/Dirac/EpsChisholm.m index 4140e868f..8e6075bf3 100755 --- a/FeynCalc/Dirac/EpsChisholm.m +++ b/FeynCalc/Dirac/EpsChisholm.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Applies the Chisholm identity backwards *) @@ -16,8 +16,8 @@ (* ------------------------------------------------------------------------ *) EpsChisholm::usage = -"EpsChisholm[expr] substitutes for a gamma matrix contracted with \ -a Levi Civita tensor (Eps) the Chisholm identity."; +"EpsChisholm[exp] applies the Chisholm identiy to a Dirac matrix \ +contracted with a Levi-Civita tensor."; (* ------------------------------------------------------------------------ *) @@ -27,20 +27,25 @@ Begin["`EpsChisholm`Private`"] esVerbose::usage=""; +eeps::usage=""; Options[EpsChisholm] = { - FCI -> False, - FCVerbose -> False + DiracTrick -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCVerbose -> False }; EpsChisholm[expr_, OptionsPattern[]] := - Block[ {new = 0,ex,terms,rest,res}, + Block[ {new = 0,ex,terms,rest,res, holdDOT, eps, freePart, dsPart, diracObjects, + diracObjectsEval, null1, null2, dsHead, time, repRule}, If [OptionValue[FCVerbose]===False, esVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], esVerbose=OptionValue[FCVerbose] ]; ]; @@ -57,50 +62,78 @@ Return[ex] ]; - {rest, terms} = FCSplit[ex,{DiracGamma,Eps}]; - FCPrint[3, "EpsChisholm: Relevant part of the expression, ", terms , FCDoControl->esVerbose]; - FCPrint[3, "EpsChisholm: Irrelevant part of the expression, ", rest , FCDoControl->esVerbose]; + (* This is the normal mode which works well both for large and small expressions *) + FCPrint[1, "EpsChisholm: Normal mode.", FCDoControl->esVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "EpsChisholm: Extracting Dirac objects.", FCDoControl->esVerbose]; + ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, DiracGammaCombine->False, LorentzIndex->True, FCJoinDOTs -> OptionValue[FCJoinDOTs], + DiracChain->True]; + ex = ex /. h_dsHead/; FreeQ[h,Eps] :> Identity@@h; - new = terms /. {Eps[a_,b_,c_,d_]->eeps[a,b,c,d]}//.eepsOrder; - FCPrint[3, "EpsChisholm: After properly ordering eps tensors: ", - new , FCDoControl->esVerbose]; + {freePart,dsPart} = FCSplit[ex,{dsHead}]; + FCPrint[3,"EpsChisholm: dsPart: ",dsPart , FCDoControl->esVerbose]; + FCPrint[3,"EpsChisholm: freePart: ",freePart , FCDoControl->esVerbose]; - new = Expand2[new,{eeps,DiracGamma}]; - new = Expand2[new//.epsspcrule,{eeps,DiracGamma}]; + diracObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//DeleteDuplicates//Sort; - FCPrint[3, "EpsChisholm: After applying Chisholm identity backwards: ", - new , FCDoControl->esVerbose]; + FCPrint[1, "EpsChisholm: Done extracting Dirac objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->esVerbose]; - res = (new/.eeps->Eps) + rest; - FCPrint[3, "EpsChisholm: Leaving with: ", res , FCDoControl->esVerbose]; + time=AbsoluteTime[]; + + diracObjectsEval = diracObjects/. Eps->eeps /. DOT->holdDOT //. { + dsHead[m_. holdDOT[x__] eeps[a___, LorentzIndex[in_], b__]]/;!FreeQ[{x},in] :> + (-1^Length[{b}]) dsHead[m eeps2[a, b, LorentzIndex[in]] holdDOT[x]], + + dsHead[m_. DiracChain[holdDOT[x__],z1_, z2_] eeps[a___, LorentzIndex[in_], b__]]/;!FreeQ[{x},in] :> + (-1^Length[{b}]) dsHead[m eeps2[a, b, LorentzIndex[in]] DiracChain[holdDOT[x],z1,z2]] + }; + + diracObjectsEval = diracObjectsEval/.eeps2->eeps; + + diracObjectsEval = diracObjectsEval //. dsHead[m_. holdDOT[x___, DiracGamma[in_LorentzIndex],y___] eeps[a_,b_,c_,in_LorentzIndex]] :> + (Conjugate[$LeviCivitaSign] I ( dsHead[m holdDOT[x,DiracGamma[a], DiracGamma[b], DiracGamma[c], DiracGamma[5],y]] + - dsHead[m ExpandScalarProduct[Pair[a,b],FCI->True] holdDOT[x,DiracGamma[c],DiracGamma[5],y]] + - dsHead[m ExpandScalarProduct[Pair[b,c],FCI->True] holdDOT[x,DiracGamma[a].DiracGamma[5],y]] + + dsHead[m ExpandScalarProduct[Pair[a,c],FCI->True] holdDOT[x,DiracGamma[b],DiracGamma[5],y]])); + + If[ !FreeQ[diracObjectsEval,DiracChain], + + diracObjectsEval = diracObjectsEval //. dsHead[m_. DiracChain[holdDOT[x___, DiracGamma[in_LorentzIndex],y___], z1_, z2_] eeps[a_,b_,c_,in_LorentzIndex]] :> + (Conjugate[$LeviCivitaSign] I ( dsHead[m DiracChain[holdDOT[x,DiracGamma[a], DiracGamma[b], DiracGamma[c], DiracGamma[5],y],z1,z2]] + - dsHead[m ExpandScalarProduct[Pair[a,b],FCI->True] DiracChain[holdDOT[x,DiracGamma[c],DiracGamma[5],y],z1,z2]] + - dsHead[m ExpandScalarProduct[Pair[b,c],FCI->True] DiracChain[holdDOT[x,DiracGamma[a].DiracGamma[5],y],z1,z2]] + + dsHead[m ExpandScalarProduct[Pair[a,c],FCI->True] DiracChain[holdDOT[x,DiracGamma[b],DiracGamma[5],y],z1,z2]])) + ]; + + time=AbsoluteTime[]; + FCPrint[1, "EpsChisholm: Inserting Dirac objects back.", FCDoControl->esVerbose]; + + diracObjectsEval = diracObjectsEval /. holdDOT->DOT /. dsHead->Identity /. eeps->Eps; + repRule = Thread[Rule[diracObjects,diracObjectsEval]]; + FCPrint[3,"EpsChisholm: repRule: ", repRule, FCDoControl->esVerbose]; + res = freePart + ( dsPart/. Dispatch[repRule]); + FCPrint[1, "EpsChisholm: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->esVerbose]; + FCPrint[3,"EpsChisholm: Intermediate result: ", res, FCDoControl->esVerbose]; + + If[ OptionValue[DiracTrick], + time=AbsoluteTime[]; + FCPrint[1, "EpsChisholm: Applying DiracTrick.", FCDoControl->esVerbose]; + res = DiracTrick[res, FCI->True]; + FCPrint[1, "EpsChisholm: Done applying DiracTrick,timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->esVerbose] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + + FCPrint[1, "EpsChisholm: Leaving.", FCDoControl->esVerbose]; + FCPrint[3, "EpsChisholm: Leaving with ", res, FCDoControl->esVerbose]; res ] -(* change maybe later *) -SpinorChainEvaluate = DiracSimplify; -scev = ExpandScalarProduct; - - -eepsOrder = {m_. DOT[x___, DiracGamma[LorentzIndex[in_]], y___] * - eeps[a___, LorentzIndex[in_], b__] :> - (-1^Length[{b}]) m DOT[x, DiracGamma[LorentzIndex[in]], y] eeps[a, b, LorentzIndex[in]]}; - -epsspcrule = { - (* Inside DOT *) - m_. DOT[ x___,DiracGamma[LorentzIndex[in_]],y___] eeps[a_,b_,c_,LorentzIndex[in_]] :> - ( Conjugate[$LeviCivitaSign]* I m ( DOT[x,DiracGamma[a], DiracGamma[b], DiracGamma[c], DiracGamma[5],y] - - scev[a,b] DOT[x,DiracGamma[c],DiracGamma[5],y] -scev[b,c] DOT[x,DiracGamma[a].DiracGamma[5],y] + - scev[a,c] DOT[x,DiracGamma[b],DiracGamma[5],y])//SpinorChainEvaluate)//Expand2[#,{DiracGamma,eeps}]&, - (* Standalone *) - DiracGamma[LorentzIndex[in_]] eeps[a_,b_,c_,LorentzIndex[in_]] :> - ( Conjugate[$LeviCivitaSign]* I ( DOT[x,DiracGamma[a],DiracGamma[b],DiracGamma[c], DiracGamma[5],y] - - scev[a,b] DOT[x,DiracGamma[c],DiracGamma[5],y] - - scev[b,c] DOT[x,DiracGamma[a],DiracGamma[5],y] + - scev[a,c] DOT[x,DiracGamma[b],DiracGamma[5],y])//SpinorChainEvaluate)//Expand2[#,{DiracGamma,eeps}]& -}; - FCPrint[1,"EpsChisholm.m loaded."]; End[] diff --git a/FeynCalc/Dirac/FCChargeConjugateTransposed.m b/FeynCalc/Dirac/FCChargeConjugateTransposed.m new file mode 100755 index 000000000..d17a4cbe5 --- /dev/null +++ b/FeynCalc/Dirac/FCChargeConjugateTransposed.m @@ -0,0 +1,215 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCChargeConjugateTransposed *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: C x^T C^(-1) for Dirac matrices *) + +(* ------------------------------------------------------------------------ *) + +FCCCT::usage = +"FCCCT is an alias for FCChargeConjugateTransposed."; + +FCChargeConjugateTransposed::usage = +"FCChargeConjugateTransposed[exp] represents the application of the charge \ +conjugation operator to the transposed of exp, i.e. C exp^T C^(-1). Here exp \ +is understood to be a single Dirac matrix or a chain thereof. \n +The option Explicit determines whether to substitute the explicit result or \ +to leave the expression in the unevaluated form. This form will be \ +also maintained if the function does not know how to obtain C exp^T C^(-1) \ +from the given exp."; + +FCChargeConjugateTransposed::failmsg = +"Error! SpinorChainTranspose has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCChargeConjugateTransposed`Private`"] + +fcctVerbose::usage=""; + +DeclareNonCommutative[FCChargeConjugateTransposed]; + +Options[FCChargeConjugateTransposed] = { + DotSimplify -> True, + Explicit -> False, + FCDiracIsolate -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False +}; + +FCCCT = FCChargeConjugateTransposed; +Abbreviation[FCChargeConjugateTransposed] = HoldForm[FCCCT]; + +FCChargeConjugateTransposed /: + MakeBoxes[FCChargeConjugateTransposed[ex_, OptionsPattern[]], TraditionalForm] := + RowBox[{"C", SuperscriptBox[RowBox[{"(", TBox[ex], ")"}], "T"], SuperscriptBox["C", "-1"]}]; + +FCChargeConjugateTransposed[ex_, OptionsPattern[]]:= + ex/; NonCommFreeQ[ex] && FCPatternFreeQ[{ex}]; + + +FCChargeConjugateTransposed[expr_, opts:OptionsPattern[]] := + Block[ {ex, time,dsHead,nonDsHead,diracObjects, + nonDiracObjects,diracObjectsEval,nonDiracObjectsEval,null1,null2, repRule1,repRule2,res}, + + If [OptionValue[FCVerbose]===False, + fcctVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fcctVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "FCChargeConjugateTransposed. Entering.", FCDoControl->fcctVerbose]; + FCPrint[3, "FCChargeConjugateTransposed: Entering with ", expr, FCDoControl->fcctVerbose]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ !FreeQ[ex,DiracSigma], + ex = ex/. d_DiracSigma/; !FreeQ2[d,{DiracGamma[5],DiracGamma[6],DiracGamma[7]}] :> DiracSigmaExplicit[d,FCI->True] + ]; + + If[ OptionValue[FCDiracIsolate], + (* Extract all the Dirac structures inside the operator. *) + + If[ !FreeQ[ex, DiracChain], + ex = DiracChainExpand[ex, FCI->True]; + ]; + + ex = FCDiracIsolate[ex,FCI->True,Head->dsHead, Factoring-> nonDsHead, DiracChain->True]; + ex = ex /. dsHead[z_]/;!FreeQ[z,Spinor] :> nonDsHead[z]; + + If[ !FreeQ[ex, DiracChain], + (* Switch the indices, since it is a transpose *) + ex = ex /. dsHead[DiracChain[x_,i_,j_]] :> DiracChain[dsHead[x],j,i] + ]; + + diracObjects = Cases[ex+null1+null2, dsHead[_], Infinity]//Union; + nonDiracObjects = Cases[ex+null1+null2, nonDsHead[_], Infinity]//Union, + + + (* The operator contains only Dirac structures (fast mode). *) + + If[ TrueQ[FreeQ[ex,Spinor]], + ex = dsHead[ex]; + diracObjects = {ex}; + nonDiracObjects = {}, + + ex = nonDsHead[ex]; + diracObjects = {}; + nonDiracObjects = {ex} + + ]; + + ]; + + + If[ nonDiracObjects=!={}, + time=AbsoluteTime[]; + nonDiracObjectsEval = Map[FCChargeConjugateTransposed[#,Explicit->False,Sequence@@FilterRules[{opts}, Except[Explicit]]]&, + nonDiracObjects /. nonDsHead->Identity]; + FCPrint[1,"FCChargeConjugateTransposed: nonDiracObjectsEval finished, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->fcctVerbose]; + FCPrint[3,"FCChargeConjugateTransposed: nonDiracObjectsEval: ", nonDiracObjectsEval, FCDoControl->fcctVerbose]; + repRule2 = Thread[Rule[nonDiracObjects,nonDiracObjectsEval]]; + FCPrint[3,"FCChargeConjugateTransposed: repRule: ",repRule2 , FCDoControl->fcctVerbose], + + repRule2 = {} + ]; + + If[ diracObjects=!={}, + time=AbsoluteTime[]; + diracObjectsEval = Map[cctEvaluateSingle[#]&, diracObjects /. dsHead->Identity /. DOT-> dotHold]; + (* at this point the chain is already reversed (a.b.c)^T -> c^T.b^T.a^T *) + + FCPrint[3,"FCChargeConjugateTransposed: diracObjectsEval after cctEvaluateSingle: ", diracObjectsEval, FCDoControl->fcctVerbose]; + + diracObjectsEval = diracObjectsEval /. cctEvaluateSingle[dotHold[z__]] :> cctEvaluateMultiple[dotHold@@(Reverse[{z}])]; + + FCPrint[3,"FCChargeConjugateTransposed: diracObjectsEval after cctEvaluateMultiple: ", diracObjectsEval, FCDoControl->fcctVerbose]; + + diracObjectsEval = diracObjectsEval /. cctEvaluateMultiple -> cctEvaluateSplit; + + FCPrint[3,"FCChargeConjugateTransposed: diracObjectsEval after cctEvaluateSplit: ", diracObjectsEval, FCDoControl->fcctVerbose]; + + diracObjectsEval = diracObjectsEval/. cctEvaluateSingle[z_] :> + FCChargeConjugateTransposed[z,Explicit->False,Sequence@@FilterRules[{opts}, Except[Explicit]]] /. dotHold->DOT; + + FCPrint[1,"FCChargeConjugateTransposed: diracObjectsEval finished, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->fcctVerbose]; + + If[ OptionValue[DotSimplify], + diracObjectsEval = DotSimplify[#,FCI->True,Expanding->False]&/@diracObjectsEval + ]; + + repRule1 = Thread[Rule[diracObjects,diracObjectsEval]]; + FCPrint[3,"FCChargeConjugateTransposed: repRule: ",repRule1 , FCDoControl->fcctVerbose], + + repRule1 = {} + ]; + + + + + res = ex /. Dispatch[repRule2] /. Dispatch[repRule1]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "FCChargeConjugateTransposed: Leaving.", FCDoControl->fcctVerbose]; + FCPrint[3, "FCChargeConjugateTransposed: Leaving with", res, FCDoControl->fcctVerbose]; + + res + + ]/; OptionValue[Explicit]; + +dotHold[]:= + 1; + +dotHold[a___, cctEvaluateMultiple[1], b___]:= + dotHold[a,b]; + +(* C (si^{mu nu})^T C^(-1) = - si^{mu nu} *) +cctEvaluateSingle[d_DiracSigma]:= + - d/; FreeQ2[d,{DiracGamma[5],DiracGamma[6],DiracGamma[7]}]; + +(* C (g^mu)^T C^(-1) = - g^mu *) +cctEvaluateSingle[d_DiracGamma]:= + - d/; !MatchQ[d,DiracGamma[5|6|7]]; + +(* C g^(5|6|7)^T C^(-1) = g^(5|6|7)*) +cctEvaluateSingle[(d:DiracGamma[5|6|7])]:= + d; + +(* C (g^mu p_mu +/- m)^T C^(-1) = (-g^mu p_mu +/- m) *) +cctEvaluateSingle[c1_. d_DiracGamma + c2_:0]:= + (- c1 d + c2)/; NonCommFreeQ[{c1,c2}] && FreeQ[{c1,c2}, dotHold] && !MatchQ[d,DiracGamma[5|6|7]]; + +cctEvaluateMultiple[dotHold[a_]]:= + cctEvaluateSingle[a]; + +cctEvaluateMultiple[dotHold[rest1___, Longest[d: DiracGamma[__]..], + rest2___]]:= + ((-1)^Length[{d}]) dotHold[cctEvaluateMultiple[dotHold[rest1]], d, cctEvaluateMultiple[dotHold[rest2]]]/; Length[{d}]>1 && + FreeQ2[{d},{DiracGamma[5],DiracGamma[6],DiracGamma[7]}]; + +cctEvaluateSplit[dotHold[a__]]:= + dotHold@@(cctEvaluateSingle/@{a}); + +FCPrint[1,"FCChargeConjugateTransposed.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/FCDiracIsolate.m b/FeynCalc/Dirac/FCDiracIsolate.m index 146c9a83c..f90cee42b 100755 --- a/FeynCalc/Dirac/FCDiracIsolate.m +++ b/FeynCalc/Dirac/FCDiracIsolate.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Isolates chains of Dirac matrices *) @@ -16,7 +16,7 @@ (* ------------------------------------------------------------------------ *) FCDiracIsolate::usage = -"FCDiracIsolate[expr,{q1,q2,...}] wraps chains of Dirac matrices into heads specified \ +"FCDiracIsolate[exp] wraps chains of Dirac matrices into heads specified \ by the user " <> ToString[ Hyperlink[Style["\[RightSkeleton]", "SR"], "paclet:FeynCalc/ref/FCDiracIsolate"], StandardForm]; @@ -30,118 +30,258 @@ Begin["`FCDiracIsolate`Private`"] Options[FCDiracIsolate] = { - ClearHeads -> {FCGV["DiracChain"]}, - Collecting -> True, - DotSimplify -> True, - DiracGammaCombine -> True, - DiracSigmaExplicit -> False, - ExceptHeads -> {}, - Expanding -> True, - FCI -> False, - Factoring -> Factor, - LorentzIndex -> False, - Head -> FCGV["DiracChain"], - Split -> True, - Isolate -> False, - IsolateNames -> KK, - IsolateFast -> False, - DiracGamma -> True, - Spinor -> True, - DiracTrace -> True + CartesianIndex -> False, + ClearHeads -> {FCGV["DiracChain"]}, + Collecting -> True, + DiracChain -> False, + DiracGamma -> True, + DiracGammaCombine -> True, + DiracSigmaExplicit -> False, + DiracTrace -> True, + DotSimplify -> True, + ExceptHeads -> {}, + Expanding -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCTraceExpand -> False, + FCVerbose -> False, + Factoring -> {Factor2, 5000}, + Head -> FCGV["DiracChain"], + Isolate -> False, + IsolateFast -> False, + IsolateNames -> KK, + LorentzIndex -> False, + Polarization -> False, + Spinor -> True, + Split -> True, + TimeConstrained -> 3, + ToDiracGamma67 -> False }; makeSelectionList[expr_,heads_List]:= MemSet[makeSelectionList[expr,heads], - Join[heads,Intersection[Cases[SelectFree[expr, heads],l_LorentzIndex:>l[[1]],Infinity], - Cases[SelectNotFree[expr, heads],l_LorentzIndex:>l[[1]],Infinity]]] + Join[heads,Intersection[Cases[SelectFree[expr, heads], l: (_LorentzIndex| _CartesianIndex) :> l[[1]] ,Infinity], + Cases[SelectNotFree[expr, heads], l: (_LorentzIndex| _CartesianIndex) :> l[[1]] ,Infinity]]] ]; -FCDiracIsolate[expr_, OptionsPattern[]] := - Block[ {res, null1, null2, ex,tmp, head, restHead,selectionList,lorHead,tmpHead,tmpHead2}, +holdDOT[]=1; - head = OptionValue[Head]; +FCDiracIsolate[expr_List, opts:OptionsPattern[]]:= + FCDiracIsolate[#, opts]&/@expr; + +FCDiracIsolate[expr_/; Head[expr]=!=List, OptionsPattern[]] := + Block[{ res, null1, null2, ex,tmp, head, selectionList, + time, fcdiVerbose, headsList, headsOrig, optTimeConstrained, + optHead, headR, allHeads, allHeadsEval, headNoMatrix}, + + If [OptionValue[FCVerbose]===False, + fcdiVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fcdiVerbose=OptionValue[FCVerbose] + ]; + ]; + + optTimeConstrained = OptionValue[TimeConstrained]; + headsOrig = Complement[DiracHeadsList,OptionValue[ExceptHeads]]; + headsList = headsOrig; + + If[ OptionValue[Polarization], + headsList = Join[headsList,{Polarization}]; + ]; + + If[ OptionValue[LorentzIndex]===All, + headsList = Join[headsList,{LorentzIndex}]; + ]; + + If[ OptionValue[CartesianIndex]===All, + headsList = Join[headsList,{CartesianIndex}]; + ]; + + optHead = OptionValue[Head]; + + If[MatchQ[optHead,{_,_}], + {head, headR} = optHead, + + head = optHead; + headR = Identity + ]; If[OptionValue[FCI], ex = expr/. (Map[Rule[#, Identity] &, OptionValue[ClearHeads]]), ex = FCI[expr]/. (Map[Rule[#, Identity] &, OptionValue[ClearHeads]]) ]; + FCPrint[3, "FCDiracIsolate: Entering with: ", ex, FCDoControl->fcdiVerbose]; - If[ FreeQ2[ex,DiracHeadsList], - Return[ex] + If[ FreeQ2[ex,headsList], + Return[restHead[ex] /. restHead -> headR] ]; If[ OptionValue[DiracSigmaExplicit], - ex = DiracSigmaExplicit[ex] + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Applying DiracSigmaExplicit.", FCDoControl->fcdiVerbose]; + ex = DiracSigmaExplicit[ex, FCI->True]; + FCPrint[1, "FCDiracIsolate: Done applying DiracSigmaExplicit timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; + FCPrint[3, "FCDiracIsolate: After DiracSigmaExplicit: ", ex, FCDoControl->fcdiVerbose] + ]; + + If[ OptionValue[ToDiracGamma67], + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Applying ToDiracGamma67.", FCDoControl->fcdiVerbose]; + ex = ToDiracGamma67[ex, FCI->True]; + FCPrint[1, "FCDiracIsolate: Done applying ToDiracGamma67 timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; + FCPrint[3, "FCDiracIsolate: After ToDiracGamma67: ", ex, FCDoControl->fcdiVerbose] ]; If[ OptionValue[DiracGammaCombine], - ex = DiracGammaCombine[ex]; + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Applying DiracGammaCombine.", FCDoControl->fcdiVerbose]; + ex = DiracGammaCombine[ex, FCI->True]; + FCPrint[1, "FCDiracIsolate: Done applying DiracGammaCombine, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; + FCPrint[3, "FCDiracIsolate: After DiracGammaCombine: ", ex, FCDoControl->fcdiVerbose] ]; If[ OptionValue[Expanding], - ex = Expand2[ex, DiracHeadsList]; + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Applying Expand2.", FCDoControl->fcdiVerbose]; + ex = Expand2[ex, headsList]; + FCPrint[1, "FCDiracIsolate: Done applying Expand2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; + FCPrint[3, "FCDiracIsolate: After Expand2: ", ex, FCDoControl->fcdiVerbose] ]; If[ OptionValue[DotSimplify] && !FreeQ[ex,DOT], - tmp = FCSplit[ex, DiracHeadsList, Expanding->OptionValue[Expanding]]; - ex = tmp[[1]]+ DotSimplify[tmp[[2]],Expanding->False] + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Applying DotSimplify.", FCDoControl->fcdiVerbose]; + tmp = FCSplit[ex, headsList, Expanding->OptionValue[Expanding]]; + ex = tmp[[1]]+ DotSimplify[tmp[[2]],Expanding->False,FCI->True, FCJoinDOTs->OptionValue[FCJoinDOTs]]; + FCPrint[1, "FCDiracIsolate: Done applying DotSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; + FCPrint[3, "FCDiracIsolate: After DotSimplify: ", ex, FCDoControl->fcdiVerbose] + ]; + + If[ OptionValue[FCTraceExpand], + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Applying FCTraceExpand.", FCDoControl->fcdiVerbose]; + ex = FCTraceExpand[ex, FCI->True, SUNTrace->False]; + FCPrint[1, "FCDiracIsolate: Done applying FCTraceExpand, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; + FCPrint[3, "FCDiracIsolate: After FCTraceExpand: ", ex, FCDoControl->fcdiVerbose] ]; If[ OptionValue[Collecting], - ex = Collect2[ex,DiracHeadsList,Factoring->OptionValue[Factoring]]; + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Applying Collect2.", FCDoControl->fcdiVerbose]; + ex = Collect2[ex,headsList,Factoring->OptionValue[Factoring],TimeConstrained->optTimeConstrained]; + FCPrint[1, "FCDiracIsolate: Done applying Collect2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose] ]; - If[ OptionValue[LorentzIndex], - res = (Map[(selectionList=makeSelectionList[#,DiracHeadsList]; restHead[SelectFree[#, selectionList]] head[SelectNotFree[#, selectionList]])&, + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Handling Lorentz and Cartesian indices.", FCDoControl->fcdiVerbose]; + If[ OptionValue[LorentzIndex]===True || OptionValue[CartesianIndex]===True, + res = (Map[(selectionList=makeSelectionList[#,headsList]; restHead[SelectFree[#, selectionList]] head[SelectNotFree[#, selectionList]])&, ex + null1 + null2] /. {null1 | null2 -> 0} /. head[1] -> 1), - res = (Map[(restHead[SelectFree[#, DiracHeadsList]] head[SelectNotFree[#, DiracHeadsList]]) &, + + res = (Map[(restHead[SelectFree[#, headsList]] head[SelectNotFree[#, headsList]]) &, ex + null1 + null2] /. {null1 | null2 -> 0} /. head[1] -> 1) ]; + FCPrint[1, "FCDiracIsolate: Done handling Lorentz and Cartesian indices, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; - res = res /. {head[x_] /; !FreeQ2[x, OptionValue[ExceptHeads]] :> x}; - - If[ Together[(res /. restHead|head|tmpHead|lorHead|tmpHead2 -> Identity)-ex] =!= 0, + If[ Together[(res /. restHead|head -> Identity)-ex] =!= 0, Message[FCDiracIsolate::fail, ex]; Abort[] ]; + allHeads = Cases2[res,head]; + allHeadsEval = allHeads /. DOT->holdDOT; + + allHeadsEval = allHeadsEval /. {head[x_] /; !FreeQ2[x, OptionValue[ExceptHeads]] :> x}; + If[ OptionValue[Split], - res = res /. DOT->holdDOT //. {head[a_holdDOT b_holdDOT c_.] :> head[a]head[b c], - head[holdDOT[r1___,a_Spinor,b___,c_Spinor, d_Spinor, e___, f_Spinor, r2___]]/;FreeQ[{r1,b,e,r2}, Spinor] :> - head[holdDOT[a,b,c]] head[holdDOT[d,e,f]] head[holdDOT[r1,r2]] }/. holdDOT[] ->1 /. holdDOT -> DOT + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Doing splittings.", FCDoControl->fcdiVerbose]; + + allHeadsEval = allHeadsEval //. head[a_holdDOT b_]/; !FreeQ[b, holdDOT] :> head[a] head[b]; + + If[ !FreeQ[allHeadsEval,Spinor], + allHeadsEval = allHeadsEval /. { + head[holdDOT[r1___,a_Spinor,b___,c_Spinor, d_Spinor, e___, f_Spinor, r2___]]/;FreeQ[{r1,b,e,r2}, Spinor] :> + head[holdDOT[a,b,c]] head[holdDOT[d,e,f]] head[holdDOT[r1,r2]]} + ]; + FCPrint[1, "FCDiracIsolate: Splittings done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose] ]; + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Removing unneeded isolations.", FCDoControl->fcdiVerbose]; (* Here we unisolate objects that are not needed *) If[ !OptionValue[DiracTrace], - res = res //. head[x_DiracTrace y_.] :> x head[y]; + allHeadsEval = allHeadsEval //. head[x_DiracTrace y_.] :> x head[y] + ]; + + If[ !OptionValue[DiracChain], + allHeadsEval = allHeadsEval //. head[x_DiracChain y_.] :> x head[y] //. + head[holdDOT[x__] y_.]/; !FreeQ[{x},DiracChain] :> holdDOT[x] head[y] ]; If[ !OptionValue[DiracGamma], - res = res //. head[x_DiracGamma y_.] :> x head[y] //. - head[DOT[x__] y_.]/; FreeQ[{x},Spinor] && !FreeQ[{x},DiracGamma] :> DOT[x] head[y]; + allHeadsEval = allHeadsEval //. head[x_DiracGamma y_.] :> x head[y] //. + head[holdDOT[x__] y_.]/; FreeQ[{x},Spinor] && !FreeQ[{x},DiracGamma] :> holdDOT[x] head[y] ]; - If[ !OptionValue[Spinor], - res = res //. head[DOT[x__] y_.]/; !FreeQ[{x},Spinor] :> DOT[x] head[y]; + If[ OptionValue[Spinor]===False, + allHeadsEval = allHeadsEval //. head[holdDOT[x__] y_.]/; !FreeQ[{x},Spinor] :> holdDOT[x] head[y], + + + If[ OptionValue[Spinor]===Join, + allHeadsEval = allHeadsEval //. + head[holdDOT[a_Spinor,b___,c_Spinor] x_.] head[holdDOT[d_Spinor,e___,f_Spinor] y_.]/; FreeQ[{b,e},Spinor] :> + head[holdDOT[a,b,c] holdDOT[d,e,f] x y] + ] + ]; - res = res //. head[x_]/; FreeQ2[x,DiracHeadsList] :> x; + + allHeadsEval = allHeadsEval /. holdDOT->DOT //. head[x_]/; FreeQ2[x,headsList] :> x; + + res = res /. Dispatch[Thread[Rule[allHeads,allHeadsEval]]]; + + FCPrint[1, "FCDiracIsolate: Done removing unneeded isolations, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; If[ OptionValue[Isolate], + time=AbsoluteTime[]; + FCPrint[1, "FCDiracIsolate: Applying Isolate.", FCDoControl->fcdiVerbose]; res = res/. restHead[x_]:> Isolate[x,IsolateNames->OptionValue[IsolateNames],IsolateFast->OptionValue[IsolateFast]], - res = res /. restHead -> Identity + res = res /. restHead[0]->0 /. restHead -> headR; + FCPrint[1, "FCDiracIsolate: Done applying Isolate, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcdiVerbose]; + ]; + + tmp = headsList; + + If[ OptionValue[LorentzIndex]===True, + tmp = Join[tmp,{LorentzIndex}] + ]; + + If[ OptionValue[CartesianIndex]===True, + tmp = Join[tmp,{CartesianIndex}] ]; - If [ !FreeQ[res/. head[__] :> 1, DiracHeadsList] & || !FreeQ[res,head[]], + (* If LorentzIndex/CartesianIndex is set to true, this check guarantees that all Lorentz/Cartesian tensors are inside head *) + If [ !FreeQ2[res/. head[__] :> 1, tmp] & || !FreeQ[res,head[]], Message[FCDiracIsolate::fail, ex]; Abort[] ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "FCDiracIsolate: Leaving.", FCDoControl->fcdiVerbose]; + res ]; +restHead[0]= + 0; + FCPrint[1,"FCDiracIsolate.m loaded."]; End[] diff --git a/FeynCalc/Dirac/Schouten.m b/FeynCalc/Dirac/Schouten.m deleted file mode 100755 index fa1ad3ea4..000000000 --- a/FeynCalc/Dirac/Schouten.m +++ /dev/null @@ -1,158 +0,0 @@ - - -(* :Title: Schouten *) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 22 June '97 at 23:00 *) -(* ------------------------------------------------------------------------ *) - -(* :Summary: Option and Function *) - -(* ------------------------------------------------------------------------ *) - -Schouten::usage = -"Schouten[expr] applies the Schouten identity for four-vectors on at most \ -42 terms in a sum. If Schouten should operate on larger expression you \ -can give a second argument, e.g.: \ -Schouten[expr, 4711] which will work \ -on sums with less than 4711 terms.\n\n - -Schouten is also an option of Contract and \ -DiracTrace. It may be set to an integer \ -indicating the maximum number of terms onto which the \ -function Schouten will be applied ."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`Schouten`Private`"] - -Schouten[y_, 0] := - y; -Schouten[y_, oparg_:42] := - FixedPoint[schouten[#, oparg]&, FeynCalcInternal[y], 14]; - -liget[_. Eps[x1_[y1_], x2_[y2_], x3_[y3_], x4_[y4_]] Pair[x5_[y5_], -x6_[y6_]]] := - {x1[y1],x2[y2],x3[y3],x4[y4],x5[y5],x6[y6]}; - -lisch[{a1_,a2_,a3_,a4_,a5_,a6_}] := - Pair[a5,a6] Eps[a1,a2,a3,a4]; - -schouten[x_,opar_:42] := - MemSet[schouten[x, opar], - Block[ {i,nx,temp0,temp,lind,ltemp,ntemp,dummIlabel = False,DUMMI, - schou,sor, all,result,epc, epsnterms,numberofli, optarg = opar, - temp1, nxf = 1}, - epc[a_, b_] := - If[ Length[Position[PartitHead[a, Eps][[2]], - LorentzIndex]] False]; - If[ Head[tem]===Plus, - Length[tem], - 1 - ] - ]; - nx = EpsEvaluate[ExpandScalarProduct[x]//Expand]//Expand; - (* Split the sum into two parts *) - result = nx; - If[ (optarg === I) && (Head[nx] === Times), - nxf = Select[nx, !FreeQ[#, _^(a_/;Head[a] =!= Integer)]&]; - nx = nx/nxf + DUMMI; - dummIlabel = True; - optarg = 6 - ]; - all = PartitHead[nx, Eps]; - If[ Head[all[[2]]]===Plus || dummIlabel === True, - If[ dummIlabel === True, - temp0 = {0,all[[2]]}, - temp0 = PartitHead[all[[2]], Pair]; - ]; - temp = temp0[[2]]; - If[ ((Head[temp]===Plus) && Length[temp] > 1 && - If[ IntegerQ[optarg], - Length[temp] < optarg, - False - ]) || dummIlabel === True, - ltemp = Length[temp]; - If[ dummIlabel =!= True, - temp1 = temp[[1]], - temp1 = temp; - ltemp = 7 - ]; - numberofli = Length[Position[temp1, LorentzIndex]]; - i = 0; - temp = - If[ dummIlabel === True, - Catch[ - lind = liget[ temp ]; - If[ Length[lind]===6, - schou = lisch /@ - Map[Append[#, Last[lind]]&, - NestList[RotateLeft,Take[lind,5],4]]; - sor = schou; - Do[ - If[ FreeQ[temp, sor[[1]]], - sor = RotateLeft[sor] - ], - {6} - ]; - If[ !FreeQ[temp, sor[[1]]], - ntemp = Expand[EpsEvaluate[temp/.sor[[1]]-> - (-Apply[Plus, Drop[sor,1]])]]; - Throw[ntemp] - ] - ]; - ], - Catch[ - While[i < Length[temp], i++; - If[ !FreeQ2[temp[[i]],{Eps,Pair}], - lind = liget[ temp[[i]] ]; - If[ Length[lind]===6, - (* create a list of 5 possible arrangements of terms of Schouten ident. *) - schou = lisch /@ Map[Append[#, Last[lind]]&, - NestList[RotateLeft,Take[lind,5],4]]; - sor = Sort[ schou, epc ]//Reverse; - Do[ - If[ FreeQ[temp, sor[[1]]], - sor = RotateLeft[sor] - ], - {6} - ]; - FCPrint[2,"sor = ", sor]; - If[ !FreeQ[temp, sor[[1]]], - ntemp = Expand[EpsEvaluate[temp/.sor[[1]]-> - (-Apply[Plus, Drop[sor,1]])]]; - (* or all LorentzIndices are inside all Eps's *) - If[ (epsnterms[ntemp] < ltemp) || (Union[Length[ Position[#, LorentzIndex] ]& /@ - Select[ Variables[ntemp], Head[#]===Eps& ]] === {numberofli}), - Throw[temp = ntemp] - ] - ] - ] - ] - ]; - temp - ] - ]; - result = (all[[1]]/.DUMMI->0) + temp0[[1]] + temp - ] - ]; - result nxf - ] - ]; - -FCPrint[1,"Schouten.m loaded."]; -End[] diff --git a/FeynCalc/Dirac/SirlinSimplify.m b/FeynCalc/Dirac/SirlinSimplify.m new file mode 100755 index 000000000..0d396a514 --- /dev/null +++ b/FeynCalc/Dirac/SirlinSimplify.m @@ -0,0 +1,549 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: SirlinSimplify *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Applies Sirlin identities for spinor chain products *) + +(* ------------------------------------------------------------------------ *) + +SirlinSimplify::usage = +"SirlinSimplify[exp] simplifies spinor chains that contain Dirac matrices \ +using relations derived by Sirlin in Nuclear Physics B192 (1981) 93-99. \ +Contrary to the original paper, the sign of the Levi-Civita tensor is \ +choosen as epsilon^{0123} = 1 which is the standard choice in FeynCalc."; + +SirlinSimplify::failmsg = +"Error! SirlinSimplify has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`SirlinSimplify`Private`"] + +sisVerbose::usage=""; +li::usage=""; +li1::usage=""; +li2::usage=""; +li3::usage=""; +li4::usage=""; + +holdDOT::usage=""; + +Options[SirlinSimplify] = { + Contract -> True, + DiracGammaCombine -> True, + DiracSigmaExplicit -> False, + DiracTrick -> True, + FCCanonicalizeDummyIndices -> True, + FCDiracIsolate -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCVerbose -> False, + Factoring -> True, + SpinorChainTrick -> True +}; + +SirlinSimplify[expr_, OptionsPattern[]] := + Block[{ex, tmp, res, diracObjects, diracObjectsEval, null1, null2, dsHead, time, repRule, mode, + optDiracSigmaExplicit, optDiracGammaCombine, optContract, optFCCanonicalizeDummyIndices + }, + + optDiracSigmaExplicit = OptionValue[DiracSigmaExplicit]; + optDiracGammaCombine = OptionValue[DiracGammaCombine]; + optContract = OptionValue[Contract]; + optFCCanonicalizeDummyIndices = OptionValue[FCCanonicalizeDummyIndices]; + + FCPrint[1, "SirlinSimplify. Entering.", FCDoControl->sisVerbose]; + FCPrint[3, "SirlinSimplify: Entering with ", expr, FCDoControl->sisVerbose]; + + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex,Spinor], + Return[ex] + ]; + + If[ OptionValue[FCVerbose]===False, + sisVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + sisVerbose=OptionValue[FCVerbose] + ]; + ]; + + If[ OptionValue[SpinorChainTrick], + + FCPrint[1, "SirlinSimplify: Applying SpinorChainTrick.", FCDoControl->sisVerbose]; + time=AbsoluteTime[]; + tmp = SpinorChainTrick[ex, FCI->True,DiracGammaCombine->optDiracGammaCombine, DiracSigmaExplicit->optDiracSigmaExplicit, + Contract -> optContract, FCCanonicalizeDummyIndices -> optFCCanonicalizeDummyIndices, FCJoinDOTs-> OptionValue[FCJoinDOTs]]; + + FCPrint[1, "SirlinSimplify: Done applying SpinorChainTrick, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->sisVerbose]; + FCPrint[3, "SirlinSimplify: After SpinorChainTrick: ", tmp, FCDoControl->sisVerbose], + + tmp = ex + ]; + + + + FCPrint[1, "SirlinSimplify: Isolating spinor chains.", FCDoControl->sisVerbose]; + time=AbsoluteTime[]; + + tmp = FCDiracIsolate[tmp,FCI->True,Head->dsHead, DotSimplify->False, DiracGammaCombine->optDiracGammaCombine, FCJoinDOTs-> OptionValue[FCJoinDOTs], + DiracSigmaExplicit->optDiracSigmaExplicit, LorentzIndex->False, Spinor->Join, DiracGamma->False, Factoring -> OptionValue[Factoring]]; + + FCPrint[1, "SirlinSimplify: Done isolating spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->sisVerbose]; + FCPrint[3, "SirlinSimplify: After FCDiracIsolate ", tmp, FCDoControl->sisVerbose]; + + + + diracObjects = Cases[tmp+null1+null2, dsHead[_], Infinity]//Sort//DeleteDuplicates; + FCPrint[3,"SirlinSimplify: diracObjects: ", diracObjects , FCDoControl->sisVerbose]; + + + FCPrint[1, "SirlinSimplify: Simplifying products of spinor chains.", FCDoControl->sisVerbose]; + time=AbsoluteTime[]; + diracObjectsEval = Map[(spinorChainSirlinEvalSpecial[#])&, (diracObjects/.dsHead->Identity/. DOT->holdDOT)]/. + spinorChainSirlinEvalSpecial -> spinorChainSirlinEval /. holdDOT->DOT; + FCPrint[1, "SirlinSimplify: Done simplifying products of spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->sisVerbose]; + FCPrint[3, "SirlinSimplify: diracObjectsEval: ", tmp, FCDoControl->sisVerbose]; + + If[ OptionValue[DiracTrick], + + FCPrint[1, "SirlinSimplify: Applying DiracTrick to the simplified relations.", FCDoControl->sisVerbose]; + time=AbsoluteTime[]; + diracObjectsEval = diracObjectsEval /. spinorChainSirlinEval[] -> 1 /. zzz_spinorChainSirlinEval :> DiracTrick[First[zzz],FCI->True, FCDiracIsolate->False], + diracObjectsEval = diracObjectsEval /. spinorChainSirlinEval -> Identity; + FCPrint[1, "SirlinSimplify: DiracTrick done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->sisVerbose] + ]; + + + If[ !FreeQ2[diracObjectsEval,{spinorChainSirlinEval,holdDOT}], + Message[SirlinSimplify::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ]; + + FCPrint[1, "SirlinSimplify: Inserting Dirac objects back.", FCDoControl->sisVerbose]; + time=AbsoluteTime[]; + repRule = Thread[Rule[diracObjects,diracObjectsEval]]; + FCPrint[3,"SirlinSimplify: repRule: ",repRule , FCDoControl->sisVerbose]; + res = (tmp/. Dispatch[repRule]); + FCPrint[1, "SirlinSimplify: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->sisVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "SirlinSimplify: Leaving.", FCDoControl->sisVerbose]; + FCPrint[3, "SirlinSimplify: Leaving with ", res, FCDoControl->sisVerbose]; + + + + res + + + + + + + ]; + + +(* [mu nu] [mu nu] ; [mu nu] [nu mu] *) +(* ----------------------------------------------------------------------------------------------------------------- *) + +(* Sirlin's very useful relations, 4th page of Sirlin's paper *) +spinorChainSirlinEval[m_. holdDOT[ Spinor[p1__], (ga1___), DiracGamma[LorentzIndex[mu_]], DiracGamma[LorentzIndex[nu_]], DiracGamma[(n1:6|7)], Spinor[p2__]]* + holdDOT[ Spinor[p3__], (ga2___), DiracGamma[LorentzIndex[mu_]], DiracGamma[LorentzIndex[nu_]], DiracGamma[(n2:6|7)], Spinor[p4__]]] := + 4 spinorChainSirlinEval[m holdDOT[Spinor[p1] , ga1, DiracGamma[n1], Spinor[p2]] holdDOT[Spinor[p3], ga2, DiracGamma[n2], Spinor[p4]]]/; n1=!=n2; + +spinorChainSirlinEval[m_. holdDOT[ Spinor[p1__], (ga1___), DiracGamma[LorentzIndex[mu_]], DiracGamma[LorentzIndex[nu_]], DiracGamma[(n1:6|7)], Spinor[p2__]]* + holdDOT[ Spinor[p3__], (ga2___), DiracGamma[LorentzIndex[nu_]], DiracGamma[LorentzIndex[mu_]], DiracGamma[(n2:6|7)], Spinor[p4__]]] := + 4 spinorChainSirlinEval[m holdDOT[Spinor[p1] , ga1, DiracGamma[n1], Spinor[p2]] holdDOT[Spinor[p3], ga2, DiracGamma[n2], Spinor[p4]]]/; n1=!=n2; + + + + +(* These are simiar to Sirlin's very useful relations, except for the fact that the chiral projectors are identical *) +spinorChainSirlinEval[m_. holdDOT[Spinor[p1__],DiracGamma[LorentzIndex[mu_]],DiracGamma[LorentzIndex[nu_]],DiracGamma[(n:6|7)],Spinor[p2__]]* + holdDOT[Spinor[p3__],DiracGamma[LorentzIndex[mu_]],DiracGamma[LorentzIndex[nu_]],DiracGamma[(n:6|7)],Spinor[p4__]]]:= + ( + li1 = LorentzIndex[Unique["liS"]]; + li2 = LorentzIndex[Unique["liS"]]; + li3 = LorentzIndex[Unique["liS"]]; + li4 = LorentzIndex[Unique["liS"]]; + + (4 spinorChainSirlinEval[holdDOT[Spinor[p1], DiracGamma[n], Spinor[p2]] holdDOT[Spinor[p3], DiracGamma[n], Spinor[p4]]] - + + 1/2 spinorChainSirlinEval[m holdDOT[Spinor[p1], DiracSigma[DiracGamma[li1], DiracGamma[li2]], Spinor[p2]] * + holdDOT[ Spinor[p3], DiracSigma[DiracGamma[li1], DiracGamma[li2]], Spinor[p4]]] + + 1/4 I (-1)^n $LeviCivitaSign Eps[li1, li2, li3, li4] spinorChainSirlinEval[m holdDOT[Spinor[p1], DiracSigma[DiracGamma[li1], DiracGamma[li2]], Spinor[p2]] * + holdDOT[ Spinor[p3], DiracSigma[DiracGamma[li3], DiracGamma[li4]], Spinor[p4]]]) + ); + +spinorChainSirlinEval[m_. holdDOT[Spinor[p1__],DiracGamma[LorentzIndex[mu_]],DiracGamma[LorentzIndex[nu_]],DiracGamma[(n:6|7)],Spinor[p2__]]* + holdDOT[Spinor[p3__],DiracGamma[LorentzIndex[nu_]],DiracGamma[LorentzIndex[mu_]],DiracGamma[(n:6|7)],Spinor[p4__]]]:= + ( + li1 = LorentzIndex[Unique["liS"]]; + li2 = LorentzIndex[Unique["liS"]]; + li3 = LorentzIndex[Unique["liS"]]; + li4 = LorentzIndex[Unique["liS"]]; + + (4 spinorChainSirlinEval[holdDOT[Spinor[p1], DiracGamma[n], Spinor[p2]] holdDOT[Spinor[p3], DiracGamma[n], Spinor[p4]]] + + + 1/2 spinorChainSirlinEval[m holdDOT[Spinor[p1], DiracSigma[DiracGamma[li1], DiracGamma[li2]], Spinor[p2]] * + holdDOT[ Spinor[p3], DiracSigma[DiracGamma[li1], DiracGamma[li2]], Spinor[p4]]] + + - 1/4 I (-1)^n $LeviCivitaSign Eps[li1, li2, li3, li4] spinorChainSirlinEval[m holdDOT[Spinor[p1], DiracSigma[DiracGamma[li1], DiracGamma[li2]], Spinor[p2]] * + holdDOT[ Spinor[p3], DiracSigma[DiracGamma[li3], DiracGamma[li4]], Spinor[p4]]]) + ); + + + +(* [mu rho nu] [mu tau nu] ; [mu rho nu] [nu tau mu] *) +(* ----------------------------------------------------------------------------------------------------------------- *) + +(* eq. (8) of Sirlin, the result is independent of $LeviCivitaSign. This implements Eqs. 1-2 of Sirlin. Notice that ga1, ga2, ga3 and ga4 are arbitrary. *) +spinorChainSirlinEval[m_. holdDOT[sp1_Spinor, ga1___, DiracGamma[LorentzIndex[mu_]], DiracGamma[h1_[rho_]], DiracGamma[LorentzIndex[nu_]], ga2___, sp2_Spinor]* + holdDOT[sp3_Spinor, ga3___, DiracGamma[LorentzIndex[mu_]], DiracGamma[h2_[tau_]], DiracGamma[LorentzIndex[nu_]], ga4___, sp4_Spinor]] := + Block[ {la, grho, gtau}, + li = LorentzIndex[Unique["liS"]]; + la = DiracGamma[li]; + grho = DiracGamma[h1[rho]]; + gtau = DiracGamma[h2[tau]]; + + 2 Pair[h1[rho], h2[tau]] spinorChainSirlinEval[m holdDOT[sp1, ga1, la, ga2, sp2] holdDOT[sp3, ga3, la, ga4, sp4]] + + 2 spinorChainSirlinEval[m holdDOT[sp1, ga1, gtau, ga2, sp2] holdDOT[sp3, ga3, grho, ga4, sp4]] + + 2 Pair[h1[rho], h2[tau]] spinorChainSirlinEval[ m holdDOT[sp1 , ga1 , la , ga2 , DiracGamma[5] , sp2] holdDOT[sp3, ga3, la, ga4, DiracGamma[5], sp4]] - + 2 spinorChainSirlinEval[m holdDOT[sp1, ga1 , gtau, ga2, DiracGamma[5], sp2] holdDOT[sp3, ga3, grho, ga4, DiracGamma[5], sp4]] + + ]; + +(* eq. (9) of Sirlin, the result is independent of $LeviCivitaSign. This implements Eqs. 3-4 of Sirlin. Notice that ga1, ga2, ga3 and ga4 are arbitrary. *) +spinorChainSirlinEval[m_. holdDOT[sp1_Spinor, ga1___, DiracGamma[LorentzIndex[nu_]], DiracGamma[h1_[rho_]], DiracGamma[LorentzIndex[mu_]], ga2___, sp2_Spinor]* + holdDOT[sp3_Spinor, ga3___, DiracGamma[LorentzIndex[mu_]], DiracGamma[h2_[tau_]], DiracGamma[LorentzIndex[nu_]], ga4___, sp4_Spinor]] := + Block[ {la, grho, gtau}, + li = LorentzIndex[Unique["liS"]]; + la = DiracGamma[li]; + grho = DiracGamma[h1[rho]]; + gtau = DiracGamma[h2[tau]]; + + 2 Pair[h1[rho], h2[tau]] spinorChainSirlinEval[m holdDOT[sp1, ga1, la, ga2, sp2] holdDOT[sp3, ga3, la, ga4, sp4]] + + 2 spinorChainSirlinEval[m holdDOT[sp1, ga1, gtau, ga2, sp2] holdDOT[sp3, ga3, grho, ga4, sp4]] - + 2 Pair[h1[rho], h2[tau]] spinorChainSirlinEval[ m holdDOT[sp1 , ga1 , la , ga2 , DiracGamma[5] , sp2] holdDOT[sp3, ga3, la, ga4, DiracGamma[5], sp4]] + + 2 spinorChainSirlinEval[m holdDOT[sp1, ga1 , gtau, ga2, DiracGamma[5], sp2] holdDOT[sp3, ga3, grho, ga4, DiracGamma[5], sp4]] + + ]; + +(* [mu rho si tau nu] [mu rho si tau nu] ; [mu rho si tau nu] [nu rho si tau mu] *) +(* ----------------------------------------------------------------------------------------------------------------- *) + +(* This covers the cases where we have more Dirac matrices between mu and nu... +i.e. Eqs 10a, 10b, 11, 12, 13 and alike +spinorChainSirlinEval. *) + +(* eq. (12) of Sirlin *) +spinorChainSirlinEvalSpecial[m_. holdDOT[Spinor[p1__], DiracGamma[LorentzIndex[mu_]], DiracGamma[lv_[rho_]], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvt_[tau_]], DiracGamma[LorentzIndex[nu_]], DiracGamma[(n:6|7)] , Spinor[p2__]]* + holdDOT[Spinor[p3__], DiracGamma[LorentzIndex[mu_]], DiracGamma[lva_[alpha_] ], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvb_[beta_]], DiracGamma[ LorentzIndex[nu_]], DiracGamma[(n:6|7)] , Spinor[p4__]]] := + 16 Pair[lvt[tau],lvb[beta]] Pair[lv[rho], lva[alpha]] * + spinorChainSirlinEvalSpecial[ m holdDOT[ Spinor[p1], DiracGamma[LorentzIndex[mu]], DiracGamma[n], Spinor[p2]] * + holdDOT[ Spinor[p3], DiracGamma[LorentzIndex[mu]], DiracGamma[n], Spinor[p4]]]; + +(* reversed version of eq. (12) from Sirlin *) +spinorChainSirlinEvalSpecial[m_. holdDOT[Spinor[p1__], DiracGamma[LorentzIndex[mu_]], DiracGamma[lv_[rho_]], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvt_[tau_]], DiracGamma[LorentzIndex[nu_]], DiracGamma[(n:6|7)] , Spinor[p2__]]* + holdDOT[Spinor[p3__], DiracGamma[LorentzIndex[nu_]], DiracGamma[lva_[alpha_]], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvb_[beta_]], DiracGamma[ LorentzIndex[mu_]], DiracGamma[(n:6|7)] , Spinor[p4__]]] := + ( + li = LorentzIndex[Unique["liS"]]; + 4 spinorChainSirlinEvalSpecial[m holdDOT[Spinor[p1],DiracGamma[lvb[beta]],DiracGamma[lvt[tau]],DiracGamma[li],DiracGamma[n],Spinor[p2]] * + holdDOT[Spinor[p3],DiracGamma[li],DiracGamma[lva[alpha]],DiracGamma[lv[rho]],DiracGamma[n],Spinor[p4]]] + ) + + +(* eq. (13) of Sirlin *) +spinorChainSirlinEvalSpecial[m_. holdDOT[Spinor[p1__], DiracGamma[LorentzIndex[mu_]], DiracGamma[lv_[rho_] ], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvt_[tau_]], DiracGamma[LorentzIndex[nu_]], DiracGamma[(n1:6|7)] , Spinor[p2__]]* + holdDOT[Spinor[p3__], DiracGamma[LorentzIndex[mu_]], DiracGamma[lva_[alpha_] ], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvb_[beta_] ], DiracGamma[LorentzIndex[nu_]], DiracGamma[(n2:6|7)] , Spinor[p4__]]] := + (4 spinorChainSirlinEvalSpecial[m holdDOT[Spinor[p1], DiracGamma[LorentzIndex[mu]], DiracGamma[lv[rho]], DiracGamma[lvb[beta]], DiracGamma[n1], Spinor[p2]] * + holdDOT[Spinor[p3], DiracGamma[LorentzIndex[mu]], DiracGamma[lva[alpha]], DiracGamma[lvt[tau]], DiracGamma[n2], Spinor[p4]]]); + +(* reversed version of eq. (13) from Sirlin *) +spinorChainSirlinEvalSpecial[m_. holdDOT[Spinor[p1__], DiracGamma[LorentzIndex[mu_]], DiracGamma[lv_[rho_]], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvt_[tau_]], DiracGamma[LorentzIndex[nu_]], DiracGamma[(n1:6|7)] , Spinor[p2__]]* + holdDOT[Spinor[p3__], DiracGamma[LorentzIndex[nu_]], DiracGamma[lva_[alpha_]], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvb_[beta_]], DiracGamma[LorentzIndex[mu_]], DiracGamma[(n2:6|7)] , Spinor[p4__]]] := + ( + li = LorentzIndex[Unique["liS"]]; + 16 Pair[LorentzIndex[lva[alpha]], LorentzIndex[lvt[tau]]] Pair[LorentzIndex[lvb[beta]], lv[rho]] * + spinorChainSirlinEvalSpecial[m holdDOT[Spinor[p1],DiracGamma[li],DiracGamma[n1],Spinor[p2]] holdDOT[Spinor[p3],DiracGamma[li],DiracGamma[n2],Spinor[p4]]] + ) + + +(* Eq. 5 of Sirlin *) +spinorChainSirlinEvalSpecial[m_. holdDOT[sp1_Spinor, DiracGamma[LorentzIndex[mu_]], DiracGamma[h1_[rho_]], DiracGamma[LorentzIndex[nu_]], 1/2 + la1_. DiracGamma[5], sp2_Spinor]* + holdDOT[sp3_Spinor, DiracGamma[LorentzIndex[mu_]], DiracGamma[h2_[tau_]], DiracGamma[LorentzIndex[nu_]], 1/2 + la2_. DiracGamma[5], sp4_Spinor]] := + ( + li = LorentzIndex[Unique["liS"]]; + + (1 + 2 la1) (1 + 2 la2) Pair[h1[rho], h2[tau]] spinorChainSirlinEvalSpecial[m holdDOT[sp1, DiracGamma[li], DiracGamma[6], sp2] holdDOT[sp3, DiracGamma[li], DiracGamma[6], sp4]] + + + (1 - 2 la1) (1 - 2 la2) Pair[h1[rho], h2[tau]] spinorChainSirlinEvalSpecial[m holdDOT[sp1, DiracGamma[li], DiracGamma[7], sp2] holdDOT[sp3, DiracGamma[li], DiracGamma[7], sp4]] + + + (1 + 2 la1) (1 - 2 la2) spinorChainSirlinEvalSpecial[m holdDOT[sp1, DiracGamma[h2[tau]], DiracGamma[6], sp2] holdDOT[sp3, DiracGamma[h1[rho]], DiracGamma[7], sp4]] + + + (1 - 2 la1) (1 + 2 la2) spinorChainSirlinEvalSpecial[m holdDOT[sp1, DiracGamma[h2[tau]], DiracGamma[7], sp2] holdDOT[sp3, DiracGamma[h1[rho]], DiracGamma[6], sp4]] + + )/; NonCommFreeQ[{la1,la2}] + + +(* Eq. 6 of Sirlin *) +spinorChainSirlinEvalSpecial[m_. holdDOT[sp1_Spinor, DiracGamma[LorentzIndex[nu_]], DiracGamma[h1_[rho_]], DiracGamma[LorentzIndex[mu_]], 1/2 + la1_. DiracGamma[5], sp2_Spinor]* + holdDOT[sp3_Spinor, DiracGamma[LorentzIndex[mu_]], DiracGamma[h2_[tau_]], DiracGamma[LorentzIndex[nu_]], 1/2 + la2_. DiracGamma[5], sp4_Spinor]] := + ( + li = LorentzIndex[Unique["liS"]]; + + (1 + 2 la1) (1 + 2 la2) spinorChainSirlinEvalSpecial[m holdDOT[sp1, DiracGamma[h2[tau]], DiracGamma[6], sp2] holdDOT[sp3, DiracGamma[h1[rho]], DiracGamma[6], sp4]] + + + (1 - 2 la1) (1 - 2 la2) spinorChainSirlinEvalSpecial[m holdDOT[sp1, DiracGamma[h2[tau]], DiracGamma[7], sp2] holdDOT[sp3, DiracGamma[h1[rho]], DiracGamma[7], sp4]] + + + (1 + 2 la1) (1 - 2 la2) Pair[h1[rho], h2[tau]] spinorChainSirlinEvalSpecial[m holdDOT[sp1, DiracGamma[li], DiracGamma[6], sp2] holdDOT[sp3, DiracGamma[li], DiracGamma[7], sp4]] + + + (1 - 2 la1) (1 + 2 la2) Pair[h1[rho], h2[tau]] spinorChainSirlinEvalSpecial[m holdDOT[sp1, DiracGamma[li], DiracGamma[7], sp2] holdDOT[sp3, DiracGamma[li], DiracGamma[6], sp4]] + + )/; NonCommFreeQ[{la1,la2}] + + + + + +(* [mu i1 i2 i3 ... nu] [mu i1 i2 i3 ... nu] ; [mu i1 i2 i3 ... nu] [nu i1 i2 i3 ... mu] *) +(* ----------------------------------------------------------------------------------------------------------------- *) + + + + + +(* ??? *) +(* +m=0 +spinorChainSirlinEval[m_. holdDOT[Spinor[pa__], DiracGamma[Momentum[pj_]], DiracGamma[Momentum[pi_]], DiracGamma[LorentzIndex[mu_]], (vg5___), Spinor[pb__]]* + holdDOT[Spinor[Momentum[pi_], 0, qf___], DiracGamma[LorentzIndex[mu_]], (vg5___), Spinor[Momentum[pj_],0,qf___]]] := + ( + - spinorChainSirlinEval[ m holdDOT[Spinor[pa] , DiracGamma[Momentum[pi]], DiracGamma[Momentum[pj]], DiracGamma[LorentzIndex[mu]], vg5 , Spinor[pb]] * + holdDOT[Spinor[Momentum[pi],0,qf], DiracGamma[LorentzIndex[mu]], vg5 , Spinor[Momentum[pj],0,qf]] + ] + + + 2 Pair[Momentum[pi], Momentum[pj]] spinorChainSirlinEval[ m holdDOT[Spinor[pa], DiracGamma[LorentzIndex[mu]], vg5, Spinor[pb]] * + holdDOT[Spinor[Momentum[pi],0,qf], DiracGamma[LorentzIndex[mu]], vg5, Spinor[Momentum[pj],0,qf]] + ] + ) /; ({vg5}==={}) || ({vg5}==={DiracGamma[5]}); +*) + +(* +m=0 +spinorChainSirlinEval[m_. holdDOT[Spinor[pa__], DiracGamma[Momentum[pi_]], DiracGamma[Momentum[pj_]], DiracGamma[LorentzIndex[mu_]], (vg5___), Spinor[pb__]]* + holdDOT[Spinor[Momentum[pi_],0,qf___], DiracGamma[LorentzIndex[mu_]], (vg5___), Spinor[Momentum[pj_],0,qf___]]] := + ( + li = LorentzIndex[Unique["liS"]]; + + Pair[Momentum[pi], Momentum[pj]] spinorChainSirlinEval[ m holdDOT[ Spinor[pa], DiracGamma[li], Spinor[pb]] * + holdDOT[ Spinor[Momentum[pi],0,qf], DiracGamma[li], Spinor[Momentum[pj],0,qf]] + ] + + + Pair[Momentum[pi], Momentum[pj]] spinorChainSirlinEval[ m holdDOT[ Spinor[pa], DiracGamma[li], DiracGamma[5], Spinor[pb]] * + holdDOT[ Spinor[Momentum[pi],0,qf], DiracGamma[li], DiracGamma[5], Spinor[Momentum[pj],0,qf]] + ] + + + ) /; ({vg5}==={}) || ({vg5}==={DiracGamma[5]}); +*) + + + + + + + +(* If the chains do not contain g_5, would need an extra option + +*) +(*spinorChainSirlinEval[m_. holdDOT[Spinor[p1__], DiracGamma[LorentzIndex[mu_]], DiracGamma[lv_[rho_]], + DiracGamma[LorentzIndex[sigma_]], DiracGamma[lvt_[tau_] ], DiracGamma[LorentzIndex[nu_]], Spinor[p2__]]* + holdDOT[Spinor[p3__], DiracGamma[LorentzIndex[mu_]], DiracGamma[lva_[alpha_]], + DiracGamma[ LorentzIndex[sigma_]], DiracGamma[lvb_[beta_]], DiracGamma[LorentzIndex[nu_] ], Spinor[p4__]]] := + Block[ {tmp,re}, + tmp[ome1_,ome2_] := + spinorChainSirlinEval[m holdDOT[Spinor[p1], DiracGamma[LorentzIndex[mu]], DiracGamma[lv[rho]], + DiracGamma[LorentzIndex[sigma]], DiracGamma[lvt[tau]], DiracGamma[LorentzIndex[nu]], DiracGamma[ome1], Spinor[p2]] * + holdDOT[Spinor[p3], DiracGamma[LorentzIndex[mu]], DiracGamma[lva[alpha]], + DiracGamma[LorentzIndex[sigma]], DiracGamma[lvb[beta]], DiracGamma[LorentzIndex[nu]], DiracGamma[ome2], Spinor[p4]] + ]; + re = tmp[6,6] + tmp[6,7] + tmp[7,6] + tmp[7,7]; + re + + ]; +*) + + +(* These are the ones calculated by FeynCalc *) + +(* This one is for the case that there is nothing between mu and nu, btw mu nu and nu mu should +equally work ...*) +(* eventually PairContract is needed here!!! *) +(* +spinorChainSirlinEval[m_. holdDOT[Spinor[pi__], x1___, DiracGamma[LorentzIndex[mu_]], DiracGamma[LorentzIndex[nu_]], x2___ , Spinor[pj__]]* + holdDOT[Spinor[pk__], x3___, DiracGamma[vm_[a_]], DiracGamma[LorentzIndex[mu_]], DiracGamma[LorentzIndex[nu_]], x4___, Spinor[pl__]]] := + ( + li = LorentzIndex[Unique["liS"]]; + 2 spinorChainSirlinEval[m holdDOT[Spinor[pi], x1, x2, Spinor[pj]] holdDOT[Spinor[pk], x3, DiracGamma[vm[a]], x4, Spinor[pl]]] + + 2 spinorChainSirlinEval[m holdDOT[Spinor[pk], x3, DiracGamma[li], x4, Spinor[pl]] holdDOT[Spinor[pi], x1, DiracGamma[vm[a]], DiracGamma[li], x2, Spinor[pj]]] - + 2 spinorChainSirlinEval[m holdDOT[Spinor[pi], x1, DiracGamma[5], x2, Spinor[pj]] holdDOT[Spinor[pk], x3, DiracGamma[vm[a]], DiracGamma[5], x4, Spinor[pl]]] + + 2 spinorChainSirlinEval[m holdDOT[Spinor[pk], x3, DiracGamma[li] , DiracGamma[5], x4, Spinor[pl]]* + holdDOT[Spinor[pi], x1, DiracGamma[vm[a]], DiracGamma[li], DiracGamma[5], x2, Spinor[pj]]] + ); +*) +(* +(*???? *) +spinorChainSirlinEval[m_. holdDOT[Spinor[Momentum[pi_], 0, fq___] , DiracGamma[Momentum[pk_]], Spinor[Momentum[pj_], 0, fq___]]* + holdDOT[Spinor[Momentum[pl_], 0, fq___] , DiracGamma[Momentum[pj_]], Spinor[Momentum[pk_], 0, fq___]]] := + ( + li = LorentzIndex[Unique["liS"]]; + -Pair[Momentum[pj], Momentum[pk]]/Pair[Momentum[pi], Momentum[pl]] * + spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq], DiracGamma[Momentum[pl]], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq], DiracGamma[Momentum[pi]], Spinor[Momentum[pk], 0, fq]] + ] + + + (-Pair[Momentum[pi], Momentum[pl]] Pair[Momentum[pj], Momentum[pk]] + + Pair[Momentum[pi], Momentum[pk]] Pair[Momentum[pj], Momentum[pl]] - + Pair[Momentum[pi], Momentum[pj]] Pair[Momentum[pk], Momentum[pl]])/(2 Pair[Momentum[pi], Momentum[pl]])* + spinorChainSirlinEval[ m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[li]], DiracGamma[5] , Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[li]], DiracGamma[5] , Spinor[Momentum[pk], 0, fq]] + ] + + + (3 Pair[Momentum[pi], Momentum[pl]] Pair[Momentum[pj], Momentum[pk]] + + Pair[Momentum[pi], Momentum[pk]] Pair[Momentum[pj], Momentum[pl]] - + Pair[Momentum[pi], Momentum[pj]]*Pair[Momentum[pk], Momentum[pl]])/(2 Pair[Momentum[pi], Momentum[pl]])* + spinorChainSirlinEval[ m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[li]], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[li]], Spinor[Momentum[pk], 0, fq]] + ] + ); + +(*???? *) +spinorChainSirlinEval[m_. holdDOT[Spinor[Momentum[pi_], 0, fq___] , DiracGamma[Momentum[pk_]], Spinor[Momentum[pj_], 0, fq___]]* + holdDOT[Spinor[Momentum[pl_], 0, fq___] , DiracGamma[Momentum[pi_]], Spinor[Momentum[pk_], 0, fq___]]] := + ( + li = LorentzIndex[Unique["liS"]]; + - Pair[Momentum[pi], Momentum[pk]]/ Pair[Momentum[pj], Momentum[pl]] * + spinorChainSirlinEval[ m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pl]], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pj]], Spinor[Momentum[pk], 0, fq]] + ] + + + (Pair[Momentum[pi], Momentum[pl]] Pair[Momentum[pj], Momentum[pk]] + + 3 Pair[Momentum[pi], Momentum[pk]] Pair[Momentum[pj], Momentum[pl]] - + Pair[Momentum[pi], Momentum[pj]]*Pair[Momentum[pk], Momentum[pl]])/(2 Pair[Momentum[pj], Momentum[pl]])* + spinorChainSirlinEval[ m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[li]], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[li]], Spinor[Momentum[pk], 0, fq]] + ] + + + ( - Pair[Momentum[pi], Momentum[pl]] Pair[Momentum[pj], Momentum[pk]] + + Pair[Momentum[pi], Momentum[pk]]*Pair[Momentum[pj], Momentum[pl]] + + Pair[Momentum[pi], Momentum[pj]]*Pair[Momentum[pk], Momentum[pl]])/(2 Pair[Momentum[pj], Momentum[pl]])* + spinorChainSirlinEval[ m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[LorentzIndex[li]], DiracGamma[5], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[LorentzIndex[li]], DiracGamma[5], Spinor[Momentum[pk], 0, fq]] + ] + + )/; + First[holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pk]], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pi]] , Spinor[Momentum[pk], 0, fq]]]=== + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pk]], Spinor[Momentum[pj], 0, fq]]; + + +(*???? *) +spinorChainSirlinEval[m_. holdDOT[Spinor[Momentum[pi_], 0, fq___] , DiracGamma[Momentum[pk_]], DiracGamma[5], Spinor[Momentum[pj_], 0, fq___]]* + holdDOT[Spinor[Momentum[pl_], 0, fq___] , DiracGamma[Momentum[pj_]], DiracGamma[5], Spinor[Momentum[pk_], 0, fq___]]] := + ( + li = LorentzIndex[Unique["liS"]]; + spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pk]], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pj]], Spinor[Momentum[pk], 0, fq]] + ] - + + Pair[Momentum[pj], Momentum[pk]] spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[li], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[li], Spinor[Momentum[pk], 0, fq]] + ] + + + Pair[Momentum[pj], Momentum[pk]] spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[li], DiracGamma[5], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[li], DiracGamma[5], Spinor[Momentum[pk], 0, fq]] + ] + ); + +(*???? *) +spinorChainSirlinEval[m_. holdDOT[Spinor[Momentum[pi_], 0, fq___] , DiracGamma[Momentum[pk_]], DiracGamma[5], Spinor[Momentum[pj_], 0, fq___]]* + holdDOT[Spinor[Momentum[pl_], 0,fq___], DiracGamma[Momentum[pi_]], DiracGamma[5], Spinor[Momentum[pk_], 0, fq___]]] := + ( + li = LorentzIndex[Unique["liS"]]; + - spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[Momentum[pk]], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[Momentum[pi]], Spinor[Momentum[pk], 0, fq]] + ] + + + Pair[Momentum[pi], Momentum[pk]] spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[li], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[li], Spinor[Momentum[pk], 0, fq]] + ] + + + Pair[Momentum[pi], Momentum[pk]] spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq] , DiracGamma[li], DiracGamma[5] , Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq] , DiracGamma[li], DiracGamma[5] , Spinor[Momentum[pk], 0, fq]] + ] + ); + +(*???? *) +spinorChainSirlinEval[m_. holdDOT[Spinor[Momentum[pi_], 0, fq___], DiracGamma[Momentum[pl_]], DiracGamma[5], Spinor[Momentum[pj_], 0, fq___]]* + holdDOT[Spinor[Momentum[pl_], 0, fq___] , DiracGamma[Momentum[pj_]], DiracGamma[5], Spinor[Momentum[pk_], 0, fq___]]] := + ( + li = LorentzIndex[Unique["liS"]]; + - spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq], DiracGamma[Momentum[pl]], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq], DiracGamma[Momentum[pj]], Spinor[Momentum[pk], 0, fq]] + ] + + + Pair[Momentum[pj], Momentum[pl]] spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq], DiracGamma[li], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq], DiracGamma[li], Spinor[Momentum[pk], 0, fq]] + ] + + + Pair[Momentum[pj], Momentum[pl]] spinorChainSirlinEval[m * + holdDOT[Spinor[Momentum[pi], 0, fq], DiracGamma[li], DiracGamma[5], Spinor[Momentum[pj], 0, fq]]* + holdDOT[Spinor[Momentum[pl], 0, fq], DiracGamma[li], DiracGamma[5], Spinor[Momentum[pk], 0, fq]] + ] + ); +*) +FCPrint[1,"SirlinSimplify.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/SpinorChainChiralSplit.m b/FeynCalc/Dirac/SpinorChainChiralSplit.m new file mode 100755 index 000000000..28576f9af --- /dev/null +++ b/FeynCalc/Dirac/SpinorChainChiralSplit.m @@ -0,0 +1,122 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: SpinorChainChiralSplit *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Simplification rules for products of spinor chains *) + +(* ------------------------------------------------------------------------ *) + +SpinorChainChiralSplit::usage = +"SpinorChainChiralSplit[exp] introduces chirality projectors in spinor chains \ +that contain no GA[5]."; + +SpinorChainChiralSplit::failmsg = +"Error! SpinorChainChiralSplit has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`SpinorChainChiralSplit`Private`"] + +holdDOT::usage=""; +spchchspVerbose::usage=""; + +Options[SpinorChainChiralSplit] = { + Collecting -> True, + DiracSubstitute5 -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> Factor, + Head -> Identity +}; + +SpinorChainChiralSplit[expr_, OptionsPattern[]] := + Block[{ex, tmp, dsHead, dsIso, freePart,dsPart, null1, null2, time, diracObjects, diracObjectsEval, repRule, res, optHead}, + + optHead = OptionValue[Head]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex,Spinor], + Return[ex] + ]; + + If[ OptionValue[FCVerbose]===False, + spchchspVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + spchchspVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "SpinorChainChiralSplit. Entering.", FCDoControl->spchchspVerbose]; + FCPrint[3, "SpinorChainChiralSplit: Entering with ", ex, FCDoControl->spchchspVerbose]; + + If[ MatchQ[ex/.DOT->holdDOT, holdDOT[a_Spinor,b___,c_Spinor]/;FreeQ[{b},Spinor]], + + FCPrint[1, "SpinorChainChiralSplit: Recognized standalone expression.", FCDoControl->spchchspVerbose]; + tmp = dsHead[ex]; + diracObjects = {dsHead[ex]}, + + FCPrint[1, "SpinorChainChiralSplit: Isolating spinor chains.", FCDoControl->spchchspVerbose]; + time=AbsoluteTime[]; + tmp = FCDiracIsolate[ex,FCI->True, Head->dsHead, Spinor->True, Collecting-> OptionValue[Collecting], DiracGamma->False, Factoring -> OptionValue[Factoring]]; + FCPrint[1, "SpinorChainChiralSplit: Done isolating spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchchspVerbose]; + FCPrint[3, "SpinorChainChiralSplit: After FCDiracIsolate ", tmp, FCDoControl->spchchspVerbose]; + + diracObjects = Cases[tmp+null1+null2, dsHead[_], Infinity]//Sort//DeleteDuplicates; + + ]; + + FCPrint[3,"SpinorChainChiralSplit: diracObjects: ", diracObjects , FCDoControl->spchchspVerbose]; + + + FCPrint[1, "SpinorChainChiralSplit: Rewriting products of spinor chains.", FCDoControl->spchchspVerbose]; + time=AbsoluteTime[]; + diracObjectsEval = (diracObjects/.dsHead->Identity/. DOT->holdDOT)/. holdDOT[a_Spinor, b___, c_Spinor]/; + FreeQ2[{b},{DiracGamma[5],DiracGamma[6],DiracGamma[7],Spinor}] :> optHead[holdDOT[a,b,DiracGamma[6],c]] + optHead[holdDOT[a,b,DiracGamma[7],c]]; + + If[ OptionValue[DiracSubstitute5] && !FreeQ[diracObjectsEval,DiracGamma[5]], + + diracObjectsEval = diracObjectsEval/. holdDOT[a_Spinor, b___,DiracGamma[5],c___, d_Spinor]:> + optHead[holdDOT[a, b,DiracGamma[6],c, d]] - optHead[holdDOT[a, b, DiracGamma[7], c, d]] + ]; + + FCPrint[1, "SpinorChainChiralSplit: Done rewriting products of spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchchspVerbose]; + FCPrint[3, "SpinorChainChiralSplit: diracObjectsEval: ", diracObjectsEval, FCDoControl->spchchspVerbose]; + + FCPrint[1, "SpinorChainChiralSplit: Inserting Dirac objects back.", FCDoControl->spchchspVerbose]; + time=AbsoluteTime[]; + repRule = Thread[Rule[diracObjects,(diracObjectsEval/.holdDOT->DOT)]]; + FCPrint[3,"SpinorChainChiralSplit: repRule: ",repRule , FCDoControl->spchchspVerbose]; + res = (tmp /. Dispatch[repRule]); + FCPrint[1, "SpinorChainChiralSplit: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchchspVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "SpinorChainChiralSplit: Leaving.", FCDoControl->spchchspVerbose]; + FCPrint[3, "SpinorChainChiralSplit: Leaving with ", res, FCDoControl->spchchspVerbose]; + + res + + ]; + +FCPrint[1,"SpinorChainChiralSplit.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/SpinorChainTranspose.m b/FeynCalc/Dirac/SpinorChainTranspose.m new file mode 100755 index 000000000..d7baebd7c --- /dev/null +++ b/FeynCalc/Dirac/SpinorChainTranspose.m @@ -0,0 +1,156 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: SpinorChainTranspose *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Switch u and v spinors in a spinor chain *) + +(* ------------------------------------------------------------------------ *) + +SpinorChainTranspose::usage = +"SpinorChainTranspose[exp] tranposes particular spinor chains in exp, \ +which effectively switches the u and v spinors and reverses the order of \ +the Dirac matrices using charge conjugation operator. This operation is \ +often required in calculations that involve Majorana particles. By default, \ +the function will tranpose all chains of the form vbar.x.u and vbar.x.v. \ +A different or more fine grained choice can be obtained via the option Select."; + +SpinorChainTranspose::failmsg = +"Error! SpinorChainTranspose has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`SpinorChainTranspose`Private`"] + +holdDOT::usage=""; +sctrVerbose::usage=""; + +Options[SpinorChainTranspose] = { + Collecting -> True, + DotSimplify -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> Factor, + Head -> Identity, + Select -> { + {SpinorVBar[_,_], SpinorU[_,_]}, + {SpinorVBar[_,_], SpinorV[_,_]}, + {SpinorVBarD[_,_], SpinorUD[_,_]}, + {SpinorVBarD[_,_], SpinorVD[_,_]} + }, + TimeConstrained -> 3 +}; + +SpinorChainTranspose[expr_, OptionsPattern[]] := + Block[{ex, tmp, dsHead, freePart,dsPart, null1, null2, time, diracObjects, diracObjectsEval, + repRule, res, optHead, optSelect, chainPatterns}, + + optHead = OptionValue[Head]; + optSelect = FCI[OptionValue[Select]]; + + If[ !MatchQ[optSelect, {{Spinor[__], Spinor[__]}..}], + Message[SpinorChainTranspose::failmsg,"The value of the Select option is not a valid list of filters."]; + Abort[] + ]; + + chainPatterns = Map[holdDOT[#[[1]], ___, #[[2]]] &, optSelect]; + + If[ Length[chainPatterns]===1, + chainPatterns = First[chainPatterns], + chainPatterns = Alternatives@@chainPatterns + ]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex,Spinor], + Return[ex] + ]; + + If[ OptionValue[FCVerbose]===False, + sctrVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + sctrVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "SpinorChainTranspose. Entering.", FCDoControl->sctrVerbose]; + FCPrint[3, "SpinorChainTranspose: Entering with ", ex, FCDoControl->sctrVerbose]; + + If[ !FreeQ[ex,DiracChain], + ex = ex//. DiracChain[x___, a_Spinor, b_Spinor] :> DOT[a,x,b] + ]; + + If[ MatchQ[ex/.DOT->holdDOT, holdDOT[a_Spinor,b___,c_Spinor]/;FreeQ[{b},Spinor]], + + FCPrint[1, "SpinorChainTranspose: Recognized standalone expression.", FCDoControl->sctrVerbose]; + tmp = dsHead[ex]; + tmp = tmp /. { + dsHead[DOT[a_Spinor,b___,c_Spinor]]/;!MatchQ[holdDOT[a,b,c],chainPatterns] :> DOT[a,b,c] + }, + + FCPrint[1, "SpinorChainTranspose: Isolating spinor chains.", FCDoControl->sctrVerbose]; + time=AbsoluteTime[]; + tmp = FCDiracIsolate[ex,FCI->True, Head->dsHead, Spinor->True, Collecting-> OptionValue[Collecting], DiracGamma->False, + Factoring -> OptionValue[Factoring], TimeConstrained -> OptionValue[TimeConstrained]]; + FCPrint[1, "SpinorChainTranspose: Done isolating spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->sctrVerbose]; + FCPrint[3, "SpinorChainTranspose: After FCDiracIsolate ", tmp, FCDoControl->sctrVerbose]; + + tmp = tmp /. { + dsHead[DOT[a_Spinor,b___,c_Spinor]]/;!MatchQ[holdDOT[a,b,c],chainPatterns] :> DOT[a,b,c] + }; + ]; + + diracObjects = Cases[tmp+null1+null2, dsHead[_], Infinity]//Sort//DeleteDuplicates; + + FCPrint[3,"SpinorChainTranspose: diracObjects: ", diracObjects , FCDoControl->sctrVerbose]; + FCPrint[1, "SpinorChainTranspose: Trasnposing spinor chains.", FCDoControl->sctrVerbose]; + + time=AbsoluteTime[]; + diracObjectsEval = (diracObjects/.dsHead->Identity /. DOT->holdDOT)/. { + holdDOT[Spinor[p1_,r1__], b___, Spinor[p2_,r2__]] :> + -1*optHead[DOT[Spinor[-p2,r2], FCChargeConjugateTransposed[DOT[b],FCI->True,Explicit->True,DotSimplify->False],Spinor[-p1,r1]]] + } /. holdDOT -> DOT; + + FCPrint[1, "SpinorChainTranspose: Done transposing spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->sctrVerbose]; + FCPrint[3, "SpinorChainTranspose: diracObjectsEval: ", diracObjectsEval, FCDoControl->sctrVerbose]; + + If[ OptionValue[DotSimplify], + diracObjectsEval = DotSimplify[#,FCI->True,Expanding->False]&/@diracObjectsEval + ]; + + FCPrint[1, "SpinorChainTranspose: Inserting Dirac objects back.", FCDoControl->sctrVerbose]; + time=AbsoluteTime[]; + repRule = Thread[Rule[diracObjects,diracObjectsEval]]; + FCPrint[3,"SpinorChainTranspose: repRule: ",repRule , FCDoControl->sctrVerbose]; + res = (tmp /. Dispatch[repRule]); + FCPrint[1, "SpinorChainTranspose: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->sctrVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "SpinorChainTranspose: Leaving.", FCDoControl->sctrVerbose]; + FCPrint[3, "SpinorChainTranspose: Leaving with ", res, FCDoControl->sctrVerbose]; + + res + + ]; + +FCPrint[1,"SpinorChainTranspose.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/SpinorChainTrick.m b/FeynCalc/Dirac/SpinorChainTrick.m new file mode 100755 index 000000000..9851687e5 --- /dev/null +++ b/FeynCalc/Dirac/SpinorChainTrick.m @@ -0,0 +1,182 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: SpinorChainTrick *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Simplification rules for products of spinor chains *) + +(* ------------------------------------------------------------------------ *) + +SpinorChainTrick::usage = +"SpinorChainTrick[exp] applies several simplifications to products of spinor \ +chains."; + +SpinorChainTrick::failmsg = +"Error! SpinorChainTrick has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`SpinorChainTrick`Private`"] + +holdDOT::usage=""; +spchtrVerbose::usage=""; + +Options[SpinorChainTrick] = { + CartesianIndexNames -> {}, + Contract -> True, + DiracEquation -> True, + DiracGammaCombine -> False, + DiracSigmaExplicit -> True, + DiracTrick -> True, + DotSimplify -> True, + FCCanonicalizeDummyIndices -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCVerbose -> False, + Factoring -> {Factor2, 5000}, + LorentzIndexNames -> {} +}; + +SpinorChainTrick[expr_, OptionsPattern[]] := + Block[{ex, tmp, dsHead, dsIso, freePart,dsPart, null1, null2, time, diracObjects, optDiracSigmaExplicit, + optDiracGammaCombine, diracObjectsEval, repRule, res}, + + optDiracSigmaExplicit = OptionValue[DiracSigmaExplicit]; + optDiracGammaCombine = OptionValue[DiracGammaCombine]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex,Spinor], + Return[ex] + ]; + + If[ OptionValue[FCVerbose]===False, + spchtrVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + spchtrVerbose=OptionValue[FCVerbose] + ]; + ]; + + + FCPrint[1, "SpinorChainTrick. Entering.", FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: Entering with ", ex, FCDoControl->spchtrVerbose]; + + FCPrint[1, "SpinorChainTrick: Isolating spinor chains.", FCDoControl->spchtrVerbose]; + time=AbsoluteTime[]; + tmp = FCDiracIsolate[ex,FCI->True, Head->dsHead, DotSimplify->True, DiracGammaCombine->optDiracGammaCombine, + DiracSigmaExplicit->optDiracSigmaExplicit, LorentzIndex->All, Spinor->Join, DiracGamma->False, FCJoinDOTs-> OptionValue[FCJoinDOTs], + Isolate->True, IsolateNames->dsIso, Factoring -> False, FCTraceExpand->True](* /. dsHead->Identity*); + FCPrint[1, "SpinorChainTrick: Done isolating spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: After FCDiracIsolate ", tmp, FCDoControl->spchtrVerbose]; + + If[ OptionValue[FCCanonicalizeDummyIndices], + FCPrint[1, "SpinorChainTrick: Canonicalize dummy Lorentz and Cartesian indices.", FCDoControl->spchtrVerbose]; + time=AbsoluteTime[]; + + tmp = FCCanonicalizeDummyIndices[tmp , FCI->True, Head->{LorentzIndex,CartesianIndex}, DotSimplify->False, + LorentzIndexNames-> OptionValue[LorentzIndexNames], CartesianIndexNames-> OptionValue[CartesianIndexNames]]; + FCPrint[1, "SpinorChainTrick: Done canonicalize dummy Lorentz and Cartesian indices, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: After FCCanonicalizeDummyIndices ", tmp, FCDoControl->spchtrVerbose] + ]; + + + If[ OptionValue[Contract], + FCPrint[1, "SpinorChainTrick: Applying Contract.", FCDoControl->spchtrVerbose]; + time=AbsoluteTime[]; + tmp = tmp /. dsHead[x_] :> Contract[x, FCI->True]; + FCPrint[1, "SpinorChainTrick: Contract done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: After Contract ", tmp, FCDoControl->spchtrVerbose] + ]; + + tmp = FRH[tmp, IsolateNames->dsIso]; + + FCPrint[1, "SpinorChainTrick: Isolating spinor chains (again).", FCDoControl->spchtrVerbose]; + time=AbsoluteTime[]; + tmp = FCDiracIsolate[tmp,FCI->True,Head->dsHead, DotSimplify->False, DiracGammaCombine->optDiracGammaCombine, FCJoinDOTs-> OptionValue[FCJoinDOTs], + DiracSigmaExplicit->False, LorentzIndex->All, Spinor->Join, DiracGamma->False, Factoring -> OptionValue[Factoring]]; + FCPrint[1, "SpinorChainTrick: Done isolating spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: After second FCDiracIsolate ", tmp, FCDoControl->spchtrVerbose]; + + + diracObjects = Cases[tmp+null1+null2, dsHead[_], Infinity]//Sort//DeleteDuplicates; + FCPrint[3,"SpinorChainTrick: diracObjects: ", diracObjects , FCDoControl->spchtrVerbose]; + + + FCPrint[1, "SpinorChainTrick: Simplifying products of spinor chains.", FCDoControl->spchtrVerbose]; + time=AbsoluteTime[]; + diracObjectsEval = Map[(spinorChainTrickEval[#])&, (diracObjects/.dsHead->Identity/. DOT->holdDOT)] /. spinorChainTrickEval -> Identity /. holdDOT->DOT; + FCPrint[1, "SpinorChainTrick: Done simplifying products of spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: diracObjectsEval: ", diracObjectsEval, FCDoControl->spchtrVerbose]; + + + If[ OptionValue[DiracEquation], + FCPrint[1, "SpinorChainTrick: Applying Dirac equation to the products of spinor chains.", FCDoControl->spchtrVerbose]; + time=AbsoluteTime[]; + diracObjectsEval = Map[DiracEquation[#,FCI->True]&, diracObjectsEval]; + FCPrint[1, "SpinorChainTrick: Done applying Dirac equation, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: diracObjectsEval: ", diracObjectsEval, FCDoControl->spchtrVerbose]; + ]; + + If[ OptionValue[DiracTrick], + FCPrint[1, "SpinorChainTrick: Applying DiracTrick to the products of spinor chains.", FCDoControl->spchtrVerbose]; + time=AbsoluteTime[]; + diracObjectsEval = Map[DiracTrick[#,FCI->True]&, diracObjectsEval]; + FCPrint[1, "SpinorChainTrick: Done applying DiracTrick, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: diracObjectsEval: ", diracObjectsEval, FCDoControl->spchtrVerbose]; + ]; + + If[ !FreeQ2[diracObjectsEval,{spinorChainTrickEval,holdDOT}], + Message[SpinorChainTrick::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ]; + + FCPrint[1, "SpinorChainTrick: Inserting Dirac objects back.", FCDoControl->spchtrVerbose]; + time=AbsoluteTime[]; + repRule = Thread[Rule[diracObjects, diracObjectsEval]]; + FCPrint[3,"SpinorChainTrick: repRule: ",repRule , FCDoControl->spchtrVerbose]; + res = ( tmp/. Dispatch[repRule]); + FCPrint[1, "SpinorChainTrick: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->spchtrVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "SpinorChainTrick: Leaving.", FCDoControl->spchtrVerbose]; + FCPrint[3, "SpinorChainTrick: Leaving with ", res, FCDoControl->spchtrVerbose]; + + + + res + + ]; + +(* 4 and D *) +spinorChainTrickEval[c_. holdDOT[a1___, DiracGamma[LorentzIndex[arg_]], b1___] holdDOT[a2___, DiracGamma[LorentzIndex[arg_, dim_Symbol], dim_Symbol], b2___]]:= + spinorChainTrickEval[c holdDOT[a1, DiracGamma[LorentzIndex[arg]], b1] holdDOT[a2, DiracGamma[LorentzIndex[arg]], b2]]; + +(* 4 and D-4 *) +spinorChainTrickEval[_. holdDOT[___, DiracGamma[LorentzIndex[arg_]], ___] holdDOT[___, DiracGamma[LorentzIndex[arg_, dim_Symbol-4], dim_Symbol-4], ___]]:= + 0; + +(* D and D - 4 *) +spinorChainTrickEval[c_. holdDOT[a1___, DiracGamma[LorentzIndex[arg_, dim_Symbol], dim_Symbol], b1___] holdDOT[a2___, DiracGamma[LorentzIndex[arg_, dim_Symbol-4], dim_Symbol-4], b2___]]:= + spinorChainTrickEval[c holdDOT[a1, DiracGamma[LorentzIndex[arg, dim-4], dim-4], b1] holdDOT[a2, DiracGamma[LorentzIndex[arg, dim-4], dim-4], b2]]; + +FCPrint[1,"SpinorChainTrick.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/ToDiracGamma67.m b/FeynCalc/Dirac/ToDiracGamma67.m new file mode 100755 index 000000000..b404ee0dc --- /dev/null +++ b/FeynCalc/Dirac/ToDiracGamma67.m @@ -0,0 +1,67 @@ +(* ::Package:: *) + + +(* :Title: ToDiracGamma67 *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Introduces chirality projectors *) + +(* ------------------------------------------------------------------------ *) + +ToDiracGamma67::usage = +"ToDiracGamma67[exp] substitutes 1/2(1 + GA[5]) and 1/2(1 - GA[5]) by \ +the chirality projectors DiracGamma[6] and DiracGamma[7]."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`ToDiracGamma67`Private`"] + +Options[ToDiracGamma67] = { + All -> False, + DotSimplify -> False, + FCE -> False, + FCI -> False +} + +ToDiracGamma67[expr_, OptionsPattern[]] := + Block[{ex}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + ex = ex /.{ + 1/2+DiracGamma[5]/2 -> DiracGamma[6], + 1/2-DiracGamma[5]/2 -> DiracGamma[7], + 1+DiracGamma[5] -> 2 DiracGamma[6], + 1-DiracGamma[5] -> 2 DiracGamma[7] + }; + + If[ OptionValue[All], + ex = ex /. DiracGamma[5] -> DiracGamma[6] - DiracGamma[7] + ]; + + If[ OptionValue[DotSimplify], + ex = DotSimplify[ex, FCI->True] + ]; + + If[ OptionValue[FCE], + ex = FCE[ex] + ]; + + ex + +] + +FCPrint[1,"ToDiracGamma67.m loaded"]; +End[] diff --git a/FeynCalc/Dirac/ToDiracSigma.m b/FeynCalc/Dirac/ToDiracSigma.m index a628b58bb..e91a2910c 100755 --- a/FeynCalc/Dirac/ToDiracSigma.m +++ b/FeynCalc/Dirac/ToDiracSigma.m @@ -5,9 +5,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Introduces DiracSigma *) @@ -15,13 +15,13 @@ (* ------------------------------------------------------------------------ *) ToDiracSigma::usage = -"ToDiracSigma[ex,x,y] substitutes the neighboring Gamma matrices x and y by \ -DiracSigma and the metric tensor, e.g. ToDiracSigma[GA[i,j],GA[i],GA[j]] \ -gives MT[i, j] - I DiracSigma[GA[i], GA[j]]."; +"ToDiracSigma[exp,x,y] substitutes the neighboring Dirac matrices x and y by \ +DiracSigma and the metric tensor."; + +ToDiracSigma::failmsg = +"Error! ToDiracSigma has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" -ToDiracSigma::noddim = -"Error. ToDiracSigma does not work with Dirac matrices in other dimensions than 4. \ -Evaluation aborted."; (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -30,32 +30,42 @@ Begin["`ToDiracSigma`Private`"] Options[ToDiracSigma] = { - FCI -> False, - DotSimplify -> True + DotSimplify -> True, + FCE -> False, + FCI -> False } ToDiracSigma[expr_, xx_, yy_, OptionsPattern[]] := - Block[{x = FCI[xx], y = FCI[yy], ex}, + Block[{x, y, ex, holdDOT}, + + If[ OptionValue[FCI], + ex = expr; + {x,y} = FCI[{xx,yy}], + {ex,x,y} = FCI[{expr,xx,yy}] + ]; + + If[ !MatchQ[x,DiracGamma[_]] || !MatchQ[y,DiracGamma[_]], + Message[ToDiracSigma::failmsg,"Only Dirac matrices in 4 dimensions are supported."]; + Abort[] + ]; + + ex = ex /. DOT -> holdDOT; - If[ OptionValue[FCI], - ex = expr, - ex = FCI[expr] - ]; + ex = (ex //. holdDOT[a___, x, y, b___] :> (- I holdDOT[a, DiracSigma[x, y], b] + Pair[First[x], First[y]] holdDOT[a, b])); - If[ !MatchQ[x,DiracGamma[_]] || !MatchQ[y,DiracGamma[_]], - Message[ToDiracSigma::noddim]; - Abort[] - ]; + ex = ex /. holdDOT[] -> 1 /. holdDOT -> DOT; - ex = (ex /. DOT[a___, x, y, b___] :> (- I DOT[a, DiracSigma[x, y], b] + Pair[First[x], First[y]] DOT[a, b]) /. DOT[] -> 1); + If[ OptionValue[DotSimplify], + ex = DotSimplify[ex, FCI->True] + ]; - If[ OptionValue[DotSimplify], - ex = DotSimplify[ex] - ]; + If[ OptionValue[FCE], + ex = FCE[ex] + ]; - ex + ex -] + ] FCPrint[1,"ToDiracSigma.m loaded"]; End[] diff --git a/FeynCalc/Dirac/ToLarin.m b/FeynCalc/Dirac/ToLarin.m index 8d72df6e2..b887051e6 100644 --- a/FeynCalc/Dirac/ToLarin.m +++ b/FeynCalc/Dirac/ToLarin.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Rewrites chiral traces according to Larin's prescription *) @@ -16,8 +16,7 @@ (* ------------------------------------------------------------------------ *) ToLarin::usage = -"ToLarin[exp] translates gamma[mu].gamma[5] into \ --I/6 Eps[mu,nu,la,si] gamma[nu,la,si]."; +"ToLarin[exp] substitutes GAD[mu].GA[5] with -I/6 LC[mu,nu,la,si] GAD[nu,la,si]."; (* ------------------------------------------------------------------------ *) @@ -27,15 +26,16 @@ Begin["`ToLarin`Private`"] Options[ToLarin] = { - Dimension -> D, - FCI -> False + Dimension -> D, + FCE -> False, + FCI -> False }; ToLarin[expr_, OptionsPattern[]] := Block[ {ex,fi1,fi2,fi3,drsi,res, dotHold, dim}, - dim = OptionValue[Dimension]; - drsi = $LeviCivitaSign; + dim = OptionValue[Dimension]; + drsi = $LeviCivitaSign; (*drsi is usually -1 *) If[ OptionValue[FCI], @@ -44,11 +44,16 @@ ]; ex = ex /. DOT->dotHold; - ex = ex //. dotHold[a___, DiracGamma[mUU_, dim], DiracGamma[5], b___] :> + ex = ex //. dotHold[a___, DiracGamma[mUU: (_LorentzIndex | _Momentum), dim], DiracGamma[5], b___] :> ({fi1, fi2, fi3} = LorentzIndex[#,dim]& /@ Unique[{"du","du","du"}]; - (drsi I/6 Eps[mUU, fi1, fi2, fi3, Dimension->dim] dotHold[a,DiracGamma[fi1,dim],DiracGamma[fi2,dim],DiracGamma[fi3,dim],b])); + (drsi I/6 Eps[mUU, fi1, fi2, fi3] dotHold[a,DiracGamma[fi1,dim],DiracGamma[fi2,dim],DiracGamma[fi3,dim],b])); res = ex /. dotHold -> DOT; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + res ]; diff --git a/FeynCalc/DocOutput/English/Guides/FeynCalc.nb b/FeynCalc/DocOutput/English/Guides/FeynCalc.nb index 1ecd38954..57dd534f5 100644 --- a/FeynCalc/DocOutput/English/Guides/FeynCalc.nb +++ b/FeynCalc/DocOutput/English/Guides/FeynCalc.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 149253, 4807] -NotebookOptionsPosition[ 131654, 4273] -NotebookOutlinePosition[ 133200, 4313] -CellTagsIndexPosition[ 133157, 4310] +NotebookDataLength[ 219130, 6920] +NotebookOptionsPosition[ 195011, 6190] +NotebookOutlinePosition[ 196601, 6230] +CellTagsIndexPosition[ 196558, 6227] WindowTitle->FeynCalc WindowFrame->Normal*) @@ -35,7 +35,11 @@ Cell[BoxData[GridBox[{ StripOnInput->False], {"\<\"A0\"\>":>Documentation`HelpLookup[ "paclet:FeynCalc/ref/A0"], "\<\"Abbreviation\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Abbreviation"], "\<\"Amplitude\"\>":> + "paclet:FeynCalc/ref/Abbreviation"], "\<\"AlphaFS\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/AlphaFS"], "\<\"AlphaStrong\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/AlphaStrong"], "\<\"Amplitude\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/Amplitude"], "\<\"Amputate\"\>":> Documentation`HelpLookup[ @@ -63,23 +67,39 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/Calc"], "\<\"CalcColorFactor\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/CalcColorFactor"], "\<\"Cases\"\>":> + "paclet:FeynCalc/ref/CalcColorFactor"], "\<\"CartesianIndex\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CartesianIndex"], "\<\"CartesianMomentum\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CartesianMomentum"], "\<\"CartesianPair\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CartesianPair"], \ +"\<\"CartesianPropagatorDenominator\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CartesianPropagatorDenominator"], \ +"\<\"CartesianToLorentz\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CartesianToLorentz"], "\<\"Cases\"\>":> Documentation`HelpLookup["paclet:ref/Cases"], "\<\"Cases2\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/Cases2"], "\<\"CF\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CF"], "\<\"CFAD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CFAD"], "\<\"CGA\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CGA"], "\<\"CGAD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CGAD"], "\<\"CGAE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CGAE"], "\<\"CGS\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CGS"], "\<\"CGSD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CGSD"], "\<\"CGSE\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/CF"], "\<\"ChangeDimension\"\>":> + "paclet:FeynCalc/ref/CGSE"], "\<\"ChangeDimension\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/ChangeDimension"], "\<\"ChargeConjugationMatrix\"\ -\>":>Documentation`HelpLookup[ - "paclet:FeynCalc/ref/ChargeConjugationMatrix"], \ -"\<\"ChargeConjugationMatrixInv\"\>":>Documentation`HelpLookup[ - "paclet:FeynCalc/ref/ChargeConjugationMatrixInv"], "\<\"CheckDB\"\>":> + "paclet:FeynCalc/ref/ChangeDimension"], "\<\"CheckDB\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/CheckDB"], "\<\"ChiralityProjector\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/ChiralityProjector"], "\<\"Chisholm\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Chisholm"], "\<\"Collect\"\>":> + "paclet:FeynCalc/ref/Chisholm"], "\<\"CLC\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CLC"], "\<\"CLCD\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CLCD"], "\<\"Collect\"\>":> Documentation`HelpLookup["paclet:ref/Collect"], "\<\"Collect2\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/Collect2"], "\<\"Collect3\"\>":> @@ -92,7 +112,9 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/CommutatorExplicit"], "\<\"Complement\"\>":> Documentation`HelpLookup[ - "paclet:ref/Complement"], "\<\"CompleteSquare\"\>":> + "paclet:ref/Complement"], "\<\"Complement1\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Complement1"], "\<\"CompleteSquare\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/CompleteSquare"], "\<\"ComplexConjugate\"\>":> Documentation`HelpLookup[ @@ -108,21 +130,49 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/CovariantD"], "\<\"CovariantFieldDerivative\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/CovariantFieldDerivative"], "\<\"D0\"\>":> + "paclet:FeynCalc/ref/CovariantFieldDerivative"], "\<\"CSI\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSI"], "\<\"CSID\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSID"], "\<\"CSIE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSIE"], "\<\"CSIS\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSIS"], "\<\"CSISD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSISD"], "\<\"CSISE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSISE"], "\<\"CSP\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSP"], "\<\"CSPD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSPD"], "\<\"CSPE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CSPE"], "\<\"CTdec\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CTdec"], "\<\"CV\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CV"], "\<\"CVD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CVD"], "\<\"CVE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CVE"], "\<\"D0\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/D0"], "\<\"DataType\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/DataType"], "\<\"DB0\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/DB0"], "\<\"DB1\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/DB1"], "\<\"DCHN\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/DB1"], "\<\"DeclareNonCommutative\"\>":> + "paclet:FeynCalc/ref/DCHN"], "\<\"DeclareFCTensor\"\>":> Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DeclareFCTensor"], \ +"\<\"DeclareNonCommutative\"\>":>Documentation`HelpLookup[ "paclet:FeynCalc/ref/DeclareNonCommutative"], "\<\"DeltaFunction\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/DeltaFunction"], \ "\<\"DeltaFunctionDoublePrime\"\>":>Documentation`HelpLookup[ "paclet:FeynCalc/ref/DeltaFunctionDoublePrime"], \ "\<\"DeltaFunctionPrime\"\>":>Documentation`HelpLookup[ - "paclet:FeynCalc/ref/DeltaFunctionPrime"], "\<\"DiracEquation\"\>":> + "paclet:FeynCalc/ref/DeltaFunctionPrime"], "\<\"DIDelta\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DIDelta"], "\<\"DiracChain\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracChain"], "\<\"DiracChainCombine\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracChainCombine"], "\<\"DiracChainExpand\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracChainExpand"], "\<\"DiracChainFactor\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracChainFactor"], "\<\"DiracChainJoin\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracChainJoin"], "\<\"DiracEquation\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/DiracEquation"], "\<\"DiracGamma\"\>":> Documentation`HelpLookup[ @@ -130,9 +180,11 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/DiracGammaCombine"], "\<\"DiracGammaExpand\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/DiracGammaExpand"], "\<\"DiracGammaT\"\>":> + "paclet:FeynCalc/ref/DiracGammaExpand"], "\<\"DiracIndex\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/DiracGammaT"], "\<\"DiracMatrix\"\>":> + "paclet:FeynCalc/ref/DiracIndex"], "\<\"DiracIndexDelta\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracIndexDelta"], "\<\"DiracMatrix\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/DiracMatrix"], "\<\"DiracOrder\"\>":> Documentation`HelpLookup[ @@ -140,15 +192,19 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/DiracReduce"], "\<\"DiracSigma\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/DiracSigma"], "\<\"DiracSigmaExplicit\"\>":> + "paclet:FeynCalc/ref/DiracSigma"], "\<\"DiracSigmaExpand\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracSigmaExpand"], "\<\"DiracSigmaExplicit\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/DiracSigmaExplicit"], "\<\"DiracSimplify\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/DiracSimplify"], "\<\"DiracSlash\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/DiracSlash"], "\<\"DiracSpinor\"\>":> + "paclet:FeynCalc/ref/DiracSlash"], "\<\"DiracSubstitute5\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/DiracSpinor"], "\<\"DiracTrace\"\>":> + "paclet:FeynCalc/ref/DiracSubstitute5"], "\<\"DiracSubstitute67\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracSubstitute67"], "\<\"DiracTrace\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/DiracTrace"], "\<\"DiracTrick\"\>":> Documentation`HelpLookup[ @@ -159,63 +215,208 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/DotExpand"], "\<\"DotSimplify\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/DotSimplify"], "\<\"Eps\"\>":> + "paclet:FeynCalc/ref/DotSimplify"], "\<\"DummyIndexFreeQ\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DummyIndexFreeQ"], "\<\"DuplicateFreeQ\"\>":> + Documentation`HelpLookup["paclet:ref/DuplicateFreeQ"], "\<\"Eps\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/Eps"], "\<\"EpsChisholm\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/EpsChisholm"], "\<\"EpsEvaluate\"\>":> + "paclet:FeynCalc/ref/EpsChisholm"], "\<\"EpsContract\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/EpsContract"], "\<\"EpsContractFreeQ\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/EpsContractFreeQ"], "\<\"EpsEvaluate\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/EpsEvaluate"], "\<\"Epsilon\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Epsilon"], "\<\"Expand\"\>":> + "paclet:FeynCalc/ref/Epsilon"], "\<\"EpsilonIR\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/EpsilonIR"], "\<\"EpsilonUV\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/EpsilonUV"], "\<\"Expand\"\>":> Documentation`HelpLookup["paclet:ref/Expand"], "\<\"Expand2\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Expand2"], "\<\"ExpandPartialD\"\>":> + "paclet:FeynCalc/ref/Expand2"], "\<\"ExpandAll\"\>":> + Documentation`HelpLookup["paclet:ref/ExpandAll"], "\<\"ExpandAll2\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ExpandAll2"], "\<\"ExpandPartialD\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/ExpandPartialD"], "\<\"ExpandScalarProduct\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/ExpandScalarProduct"], "\<\"Explicit\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Explicit"], "\<\"ExplicitLorentzIndex\"\>":> + "paclet:FeynCalc/ref/Explicit"], "\<\"ExplicitDiracIndex\"\>":> Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ExplicitDiracIndex"], "\<\"ExplicitLorentzIndex\"\ +\>":>Documentation`HelpLookup[ "paclet:FeynCalc/ref/ExplicitLorentzIndex"], \ "\<\"ExplicitPartialD\"\>":>Documentation`HelpLookup[ - "paclet:FeynCalc/ref/ExplicitPartialD"], "\<\"ExplicitSUNIndex\"\>":> + "paclet:FeynCalc/ref/ExplicitPartialD"], "\<\"ExplicitSUNFIndex\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ExplicitSUNFIndex"], "\<\"ExplicitSUNIndex\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/ExplicitSUNIndex"], "\<\"Factor\"\>":> Documentation`HelpLookup["paclet:ref/Factor"], "\<\"Factor1\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/Factor1"], "\<\"Factor2\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/Factor2"], "\<\"FAD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FAD"], "\<\"FAPatch\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FAPatch"], "\<\"FCAbbreviate\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FAD"], "\<\"FCAntiSymmetrize\"\>":> + "paclet:FeynCalc/ref/FCAbbreviate"], "\<\"FCAntiSymmetrize\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/FCAntiSymmetrize"], "\<\"FCApart\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FCApart"], "\<\"FCClearScalarProducts\"\>":> + "paclet:FeynCalc/ref/FCApart"], "\<\"FCCanonicalizeDummyIndices\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FCClearScalarProducts"], "\<\"FCE\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/FCE"], "\<\"FCI\"\>":> + "paclet:FeynCalc/ref/FCCanonicalizeDummyIndices"], "\<\"FCCCT\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FCI"], "\<\"FCIntegral\"\>":> + "paclet:FeynCalc/ref/FCCCT"], "\<\"FCChargeConjugateTransposed\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCChargeConjugateTransposed"], "\<\"FCCheckSyntax\ +\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCCheckSyntax"], "\<\"FCCheckVersion\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCCheckVersion"], "\<\"FCClearScalarProducts\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCClearScalarProducts"], \ +"\<\"FCCompareResults\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCCompareResults"], "\<\"FCDiracIsolate\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCDiracIsolate"], "\<\"FCDuplicateFreeQ\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCDuplicateFreeQ"], "\<\"FCE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FCE"], "\<\"FCF\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FCIntegral"], "\<\"FCLoopExtract\"\>":> + "paclet:FeynCalc/ref/FCF"], "\<\"FCFAConvert\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FCLoopExtract"], "\<\"FCLoopIsolate\"\>":> + "paclet:FeynCalc/ref/FCFAConvert"], "\<\"FCFactorOut\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FCLoopIsolate"], "\<\"FCMultiLoopTID\"\>":> + "paclet:FeynCalc/ref/FCFactorOut"], "\<\"FCFADiracChainJoin\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCFADiracChainJoin"], "\<\"FCGetDimensions\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCGetDimensions"], \ +"\<\"FCGetDiracGammaScheme\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCGetDiracGammaScheme"], \ +"\<\"FCGetNotebookDirectory\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCGetNotebookDirectory"], \ +"\<\"FCGetPauliSigmaScheme\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCGetPauliSigmaScheme"], "\<\"FCGramDeterminant\"\ +\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCGramDeterminant"], "\<\"FCGramMatrix\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCGramMatrix"], "\<\"FCHideEpsilon\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCHideEpsilon"], "\<\"FCI\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCI"], "\<\"FCIntegral\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCIntegral"], \ +"\<\"FCLoopBasisCreateScalarProducts\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopBasisCreateScalarProducts"], \ +"\<\"FCLoopBasisExtract\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopBasisExtract"], \ +"\<\"FCLoopBasisGetSize\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopBasisGetSize"], "\<\"FCLoopBasisIncompleteQ\ +\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopBasisIncompleteQ"], \ +"\<\"FCLoopBasisIntegralToPropagators\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopBasisIntegralToPropagators"], \ +"\<\"FCLoopBasisOverdeterminedQ\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopBasisOverdeterminedQ"], \ +"\<\"FCLoopBasisPropagatorsToTopology\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopBasisPropagatorsToTopology"], \ +"\<\"FCLoopBasisSplit\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopBasisSplit"], "\<\"FCLoopCanonicalize\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopCanonicalize"], \ +"\<\"FCLoopEikonalPropagatorFreeQ\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopEikonalPropagatorFreeQ"], \ +"\<\"FCLoopExtract\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopExtract"], "\<\"FCLoopIBPReducableQ\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopIBPReducableQ"], "\<\"FCLoopIsolate\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopIsolate"], "\<\"FCLoopMixedIntegralQ\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopMixedIntegralQ"], \ +"\<\"FCLoopMixedToCartesianAndTemporal\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopMixedToCartesianAndTemporal"], \ +"\<\"FCLoopNonIntegerPropagatorPowersFreeQ\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopNonIntegerPropagatorPowersFreeQ"], \ +"\<\"FCLoopPropagatorPowersCombine\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopPropagatorPowersCombine"], \ +"\<\"FCLoopPropagatorPowersExpand\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopPropagatorPowersExpand"], \ +"\<\"FCLoopRemoveNegativePropagatorPowers\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopRemoveNegativePropagatorPowers"], \ +"\<\"FCLoopSamePropagatorHeadsQ\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopSamePropagatorHeadsQ"], \ +"\<\"FCLoopSolutionList\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopSolutionList"], "\<\"FCLoopSplit\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCLoopSplit"], "\<\"FCMakeIndex\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCMakeIndex"], "\<\"FCMatrixIsolate\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCMatrixIsolate"], "\<\"FCMultiLoopTID\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/FCMultiLoopTID"], "\<\"FCPartialD\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FCPartialD"], "\<\"FCSymmetrize\"\>":> + "paclet:FeynCalc/ref/FCPartialD"], "\<\"FCPatternFreeQ\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCPatternFreeQ"], "\<\"FCPauliIsolate\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCPauliIsolate"], "\<\"FCPermuteMomentaRules\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCPermuteMomentaRules"], "\<\"FCPrepareFAAmp\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCPrepareFAAmp"], "\<\"FCProductSplit\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCProductSplit"], "\<\"FCProgressBar\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCProgressBar"], "\<\"FCRenameDummyIndices\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCRenameDummyIndices"], "\<\"FCReplaceAll\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCReplaceAll"], "\<\"FCReplaceMomenta\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FCSymmetrize"], "\<\"FermionSpinSum\"\>":> + "paclet:FeynCalc/ref/FCReplaceMomenta"], "\<\"FCReplaceRepeated\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCReplaceRepeated"], "\<\"FCRerouteMomenta\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCRerouteMomenta"], \ +"\<\"FCSchoutenBruteForce\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCSchoutenBruteForce"], \ +"\<\"FCSetDiracGammaScheme\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCSetDiracGammaScheme"], \ +"\<\"FCSetPauliSigmaScheme\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCSetPauliSigmaScheme"], "\<\"FCShowEpsilon\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCShowEpsilon"], "\<\"FCSplit\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCSplit"], "\<\"FCSubsetQ\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCSubsetQ"], "\<\"FCSymmetrize\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCSymmetrize"], "\<\"FCTopology\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCTopology"], "\<\"FCTraceExpand\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCTraceExpand"], "\<\"FCTraceFactor\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCTraceFactor"], "\<\"FermionSpinSum\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/FermionSpinSum"], "\<\"FeynAmpDenominator\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/FeynAmpDenominator"], \ "\<\"FeynAmpDenominatorCombine\"\>":>Documentation`HelpLookup[ "paclet:FeynCalc/ref/FeynAmpDenominatorCombine"], \ +"\<\"FeynAmpDenominatorExplicit\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FeynAmpDenominatorExplicit"], \ "\<\"FeynAmpDenominatorSimplify\"\>":>Documentation`HelpLookup[ "paclet:FeynCalc/ref/FeynAmpDenominatorSimplify"], \ "\<\"FeynAmpDenominatorSplit\"\>":>Documentation`HelpLookup[ @@ -245,7 +446,9 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/FourLaplacian"], "\<\"FourVector\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/FourVector"], "\<\"FreeQ\"\>":> + "paclet:FeynCalc/ref/FourVector"], "\<\"FreeIndexFreeQ\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FreeIndexFreeQ"], "\<\"FreeQ\"\>":> Documentation`HelpLookup["paclet:ref/FreeQ"], "\<\"FreeQ2\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/FreeQ2"], "\<\"FRH\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/FRH"], "\<\"FromTFI\"\>":> @@ -254,10 +457,12 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/FunctionalD"], "\<\"FV\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/FV"], "\<\"FVD\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/FVD"], "\<\"GA\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FVD"], "\<\"FVE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FVE"], "\<\"GA\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/GA"], "\<\"GA5\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/GA5"], "\<\"GAD\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/GAD"], "\<\"Gamma\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/GAD"], "\<\"GAE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/GAE"], "\<\"Gamma\"\>":> Documentation`HelpLookup["paclet:ref/Gamma"], "\<\"Gamma1\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/Gamma1"], "\<\"Gamma2\"\>":> @@ -272,7 +477,13 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/GaugeField"], "\<\"GaugeXi\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/GaugeXi"], "\<\"GhostPropagator\"\>":> + "paclet:FeynCalc/ref/GaugeXi"], "\<\"GenericPropagatorDenominator\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/GenericPropagatorDenominator"], "\<\"GenPaVe\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/GenPaVe"], "\<\"GFAD\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/GFAD"], "\<\"GhostPropagator\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/GhostPropagator"], "\<\"GluonField\"\>":> Documentation`HelpLookup[ @@ -286,7 +497,8 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/GluonVertex"], "\<\"GS\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/GS"], "\<\"GSD\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/GSD"], "\<\"Gstrong\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/GSD"], "\<\"GSE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/GSE"], "\<\"Gstrong\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/Gstrong"], "\<\"Hill\"\>":> Documentation`HelpLookup[ @@ -322,8 +534,10 @@ Cell[BoxData[GridBox[{ "paclet:FeynCalc/ref/IntegrateByParts"], "\<\"InverseMellin\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/InverseMellin"], "\<\"Isolate\"\>":> - Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Isolate"], "\<\"Kummer\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Isolate"], "\<\"KD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/KD"], "\<\"KDD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/KDD"], "\<\"KDE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/KDE"], "\<\"Kummer\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/Kummer"], "\<\"Lagrangian\"\>":> Documentation`HelpLookup[ @@ -341,10 +555,13 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/LeviCivita"], "\<\"Li2\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/Li2"], "\<\"Li3\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/Li3"], "\<\"Log\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Li3"], "\<\"Li4\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Li4"], "\<\"Log\"\>":> Documentation`HelpLookup["paclet:ref/Log"], "\<\"LorentzIndex\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/LorentzIndex"], "\<\"Map\"\>":> + "paclet:FeynCalc/ref/LorentzIndex"], "\<\"LorentzToCartesian\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/LorentzToCartesian"], "\<\"Map\"\>":> Documentation`HelpLookup["paclet:ref/Map"], "\<\"Map2\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/Map2"], "\<\"MemSet\"\>":> Documentation`HelpLookup[ @@ -366,7 +583,11 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/NonCommFreeQ"], "\<\"NonCommQ\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/NonCommQ"], "\<\"NTerms\"\>":> + "paclet:FeynCalc/ref/NonCommQ"], "\<\"NotebookDirectory\"\>":> + Documentation`HelpLookup[ + "paclet:ref/NotebookDirectory"], "\<\"NPointTo4Point\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/NPointTo4Point"], "\<\"NTerms\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/NTerms"], "\<\"NumericalFactor\"\>":> Documentation`HelpLookup[ @@ -389,11 +610,31 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/PartialIntegrate"], "\<\"PartitHead\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/PartitHead"], "\<\"PaVe\"\>":> + "paclet:FeynCalc/ref/PartitHead"], "\<\"PauliEta\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PauliEta"], "\<\"PauliOrder\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PauliOrder"], "\<\"PauliSigma\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PauliSigma"], "\<\"PauliSigmaCombine\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PauliSigmaCombine"], "\<\"PauliSigmaExpand\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PauliSigmaExpand"], "\<\"PauliSimplify\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PauliSimplify"], "\<\"PauliTrick\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PauliTrick"], "\<\"PauliXi\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/PaVe"], "\<\"PaVeReduce\"\>":> + "paclet:FeynCalc/ref/PauliXi"], "\<\"PaVe\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/PaVeReduce"], "\<\"PD\"\>":> + "paclet:FeynCalc/ref/PaVe"], "\<\"PaVeOrder\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PaVeOrder"], "\<\"PaVeReduce\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PaVeReduce"], "\<\"PaVeUVPart\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PaVeUVPart"], "\<\"PD\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/PD"], "\<\"PlusDistribution\"\>":> Documentation`HelpLookup[ @@ -413,19 +654,29 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/PowerSimplify"], "\<\"PropagatorDenominator\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/PropagatorDenominator"], \ -"\<\"PropagatorDenominatorExplicit\"\>":>Documentation`HelpLookup[ - "paclet:FeynCalc/ref/PropagatorDenominatorExplicit"], \ -"\<\"QuantumField\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PropagatorDenominator"], "\<\"QuantumField\"\>":> + Documentation`HelpLookup[ "paclet:FeynCalc/ref/QuantumField"], "\<\"QuarkField\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/QuarkField"], "\<\"QuarkGluonVertex\"\>":> + "paclet:FeynCalc/ref/QuarkField"], "\<\"QuarkFieldChi\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/QuarkFieldChi"], "\<\"QuarkFieldChiDagger\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/QuarkFieldChiDagger"], "\<\"QuarkFieldPsi\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/QuarkFieldPsi"], "\<\"QuarkFieldPsiDagger\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/QuarkFieldPsiDagger"], "\<\"QuarkGluonVertex\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/QuarkGluonVertex"], "\<\"QuarkPropagator\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/QuarkPropagator"], "\<\"ReleaseHold\"\>":> Documentation`HelpLookup[ - "paclet:ref/ReleaseHold"], "\<\"RightPartialD\"\>":> + "paclet:ref/ReleaseHold"], "\<\"ReplaceAll\"\>":> + Documentation`HelpLookup[ + "paclet:ref/ReplaceAll"], "\<\"ReplaceRepeated\"\>":> + Documentation`HelpLookup[ + "paclet:ref/ReplaceRepeated"], "\<\"RightPartialD\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/RightPartialD"], "\<\"RussianTrick\"\>":> Documentation`HelpLookup[ @@ -439,7 +690,8 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/ScaleMu"], "\<\"Schouten\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/Schouten"], "\<\"SD\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/SD"], "\<\"Select\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SD"], "\<\"SDF\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SDF"], "\<\"Select\"\>":> Documentation`HelpLookup["paclet:ref/Select"], "\<\"SelectFree\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/SelectFree"], "\<\"SelectNotFree\"\>":> @@ -451,11 +703,22 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/Series3"], "\<\"SetMandelstam\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SetMandelstam"], "\<\"SimplifyDeltaFunction\"\>":> + "paclet:FeynCalc/ref/SetMandelstam"], "\<\"SFAD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SFAD"], "\<\"SI\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SI"], "\<\"SID\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SID"], "\<\"SIE\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SIE"], "\<\"SimplifyDeltaFunction\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/SimplifyDeltaFunction"], \ "\<\"SimplifyPolyLog\"\>":>Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SimplifyPolyLog"], "\<\"SmallDelta\"\>":> + "paclet:FeynCalc/ref/SimplifyPolyLog"], "\<\"SirlinSimplify\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SirlinSimplify"], "\<\"SIS\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SIS"], "\<\"SISD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SISD"], "\<\"SISE\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SISE"], "\<\"SmallDelta\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/SmallDelta"], "\<\"SmallEpsilon\"\>":> Documentation`HelpLookup[ @@ -463,7 +726,9 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/SmallVariable"], "\<\"SMP\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SMP"], "\<\"SMVertex\"\>":> + "paclet:FeynCalc/ref/SMP"], "\<\"SMPToSymbol\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SMPToSymbol"], "\<\"SMVertex\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/SMVertex"], "\<\"Sn\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/Sn"], "\<\"Solve\"\>":> Documentation`HelpLookup["paclet:ref/Solve"], "\<\"Solve2\"\>":> @@ -471,19 +736,41 @@ Cell[BoxData[GridBox[{ "paclet:FeynCalc/ref/Solve2"], "\<\"Solve3\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/Solve3"], "\<\"SP\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/SP"], "\<\"SPD\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/SPD"], "\<\"Spinor\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SPD"], "\<\"SPE\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SPE"], "\<\"Spinor\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Spinor"], "\<\"SpinorU\"\>":> + "paclet:FeynCalc/ref/Spinor"], "\<\"SpinorChainChiralSplit\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SpinorChainChiralSplit"], \ +"\<\"SpinorChainTranspose\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SpinorChainTranspose"], \ +"\<\"SpinorChainTrick\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SpinorChainTrick"], "\<\"SpinorU\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/SpinorU"], "\<\"SpinorUBar\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SpinorUBar"], "\<\"SpinorV\"\>":> + "paclet:FeynCalc/ref/SpinorUBar"], "\<\"SpinorUBarD\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SpinorUBarD"], "\<\"SpinorUD\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SpinorUD"], "\<\"SpinorV\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/SpinorV"], "\<\"SpinorVBar\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SpinorVBar"], "\<\"SplittingFunction\"\>":> + "paclet:FeynCalc/ref/SpinorVBar"], "\<\"SpinorVBarD\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SpinorVBarD"], "\<\"SpinorVD\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SpinorVD"], "\<\"SplittingFunction\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SplittingFunction"], "\<\"SquareAmplitude\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SplittingFunction"], "\<\"SumP\"\>":> + "paclet:FeynCalc/ref/SquareAmplitude"], \ +"\<\"StandardPropagatorDenominator\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/StandardPropagatorDenominator"], "\<\"StringChomp\ +\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/StringChomp"], "\<\"SubsetQ\"\>":> + Documentation`HelpLookup["paclet:ref/SubsetQ"], "\<\"SumP\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/SumP"], "\<\"SumS\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/SumS"], "\<\"SumT\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/SumT"], "\<\"SUND\"\>":> @@ -494,35 +781,66 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/SUNDeltaContract"], "\<\"SUNF\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SUNF"], "\<\"SUNFDeltaContract\"\>":> + "paclet:FeynCalc/ref/SUNF"], "\<\"SUNFDelta\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SUNDeltaContract"], "\<\"SUNIndex\"\>":> + "paclet:FeynCalc/ref/SUNFDelta"], "\<\"SUNFDeltaContract\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SUNFDeltaContract"], "\<\"SUNFIndex\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SUNFIndex"], "\<\"SUNFSimplify\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SUNFSimplify"], "\<\"SUNIndex\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/SUNIndex"], "\<\"SUNN\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/SUNN"], "\<\"SUNSimplify\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/SUNSimplify"], "\<\"SUNT\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SUNT"], "\<\"SUNTF\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SUNTF"], "\<\"SUNTrace\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SUNTrace"], "\<\"TC\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/TC"], "\<\"Tdec\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SUNT"], "\<\"SUNTrace\"\>":> + "paclet:FeynCalc/ref/Tdec"], "\<\"TemporalMomentum\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/SUNTrace"], "\<\"Tdec\"\>":> + "paclet:FeynCalc/ref/TemporalMomentum"], "\<\"TemporalPair\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Tdec"], "\<\"TensorFunction\"\>":> + "paclet:FeynCalc/ref/TemporalPair"], "\<\"TensorFunction\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/TensorFunction"], "\<\"Tf\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/Tf"], "\<\"TID\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Tf"], "\<\"TFIOrder\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/TFIOrder"], "\<\"TGA\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CGA"], "\<\"ThreeDivergence\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ThreeDivergence"], "\<\"TID\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/TID"], "\<\"TIDL\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/TIDL"], "\<\"ToDistribution\"\>":> + "paclet:FeynCalc/ref/TIDL"], "\<\"ToDiracGamma67\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ToDiracGamma67"], "\<\"ToDiracSigma\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/ToDistribution"], "\<\"Together\"\>":> + "paclet:FeynCalc/ref/ToDiracSigma"], "\<\"ToDistribution\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ToDistribution"], "\<\"ToFI\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ToFI"], "\<\"Together\"\>":> Documentation`HelpLookup[ "paclet:ref/Together"], "\<\"ToHypergeometric\"\>":> Documentation`HelpLookup[ "paclet:FeynCalc/ref/ToHypergeometric"], "\<\"ToLarin\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/ToLarin"], "\<\"ToTFI\"\>":> + "paclet:FeynCalc/ref/ToLarin"], "\<\"ToPaVe\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ToPaVe"], "\<\"ToPaVe2\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ToPaVe2"], "\<\"ToSFAD\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ToSFAD"], "\<\"ToStandardMatrixElement\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ToStandardMatrixElement"], "\<\"ToTFI\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/ToTFI"], "\<\"TR\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/TR"], "\<\"Tr2\"\>":> Documentation`HelpLookup["paclet:FeynCalc/ref/Tr2"], "\<\"Trick\"\>":> @@ -533,14 +851,23 @@ Cell[BoxData[GridBox[{ Documentation`HelpLookup[ "paclet:FeynCalc/ref/TrickMandelstam"], "\<\"Uncontract\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Uncontract"], "\<\"UnDeclareNonCommutative\"\>":> + "paclet:FeynCalc/ref/Uncontract"], "\<\"UnDeclareAntiCommutator\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/UnDeclareNonCommutative"], "\<\"UVPart\"\>":> + "paclet:FeynCalc/ref/UnDeclareAntiCommutator"], \ +"\<\"UnDeclareCommutator\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/UnDeclareCommutator"], \ +"\<\"UnDeclareFCTensor\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/UnDeclareFCTensor"], "\<\"UnDeclareNonCommutative\ +\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/UnDeclareNonCommutative"], "\<\"Write2\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/UVPart"], "\<\"Write2\"\>":> + "paclet:FeynCalc/ref/Write2"], "\<\"Zeta10\"\>":> Documentation`HelpLookup[ - "paclet:FeynCalc/ref/Write2"], "\<\"Zeta2\"\>":> - Documentation`HelpLookup["paclet:FeynCalc/ref/Zeta2"]}, + "paclet:FeynCalc/ref/Zeta10"], "\<\"Zeta2\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Zeta2"], "\<\"Zeta4\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Zeta4"], "\<\"Zeta6\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Zeta6"], "\<\"Zeta8\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Zeta8"]}, Appearance->None, MenuAppearance->Automatic, MenuStyle->"GuideFunction"]], @@ -559,7 +886,7 @@ Cell[BoxData[GridBox[{ Row[{"Tutorials", Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], StripOnInput->False], {"\<\"Short 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CellID->1224892054], +Cell[TextData[{ + Cell["$Abbreviations", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -139,9 +179,7 @@ Cell[TextData[{ ButtonNote->"WriteOutPaVe"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"$Abbreviations", - CellID->1391380109] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -158,10 +196,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 57.525452}", + "built" -> "{2020, 1, 5, 19, 4, 10.988118}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -170,11 +208,12 @@ TaggingRules->{ "$Abbreviations are a list of string substitution rules used when \ generating names for storing intermediate results. 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/$\ BreitMaison.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$167474], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/$BreitMaison", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; 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Use FCSetDiracGammaScheme to \ +specify a scheme for handling Dirac matrices in dimensional regularization \ +and FCGetDiracGammaScheme to check the current setting." }]]} }]], "Usage", GridBoxOptions->{ @@ -112,27 +143,19 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["Tr", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/Tr", - ButtonNote->"Tr"], - FontFamily->"Verdana"], - ", ", - StyleBox[ButtonBox["$Larin", + StyleBox[ButtonBox["FCSetDiracGammaScheme", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/$Larin", - ButtonNote->"$Larin"], + ButtonData->"paclet:FeynCalc/ref/FCSetDiracGammaScheme", + ButtonNote->"FCSetDiracGammaScheme"], FontFamily->"Verdana"], ", ", - StyleBox[ButtonBox["West", + StyleBox[ButtonBox["FCGetDiracGammaScheme", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/West", - ButtonNote->"West"], + ButtonData->"paclet:FeynCalc/ref/FCGetDiracGammaScheme", + ButtonNote->"FCGetDiracGammaScheme"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"$BreitMaison", - CellID->1928344928] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -149,22 +172,24 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 0.635216}", + "built" -> "{2020, 1, 5, 19, 4, 12.967783}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "$BreitMaison The Breitenlohner-Maison \\[Gamma]5 scheme is currently not \ -supported by the Dirac algebra functions.Use Tracer if you need it (PHI \ -supplies the functions FCToTracer and TracerToFC).", "synonyms" -> {}, - "title" -> "$BreitMaison", "titlemodifier" -> "", "windowtitle" -> - "$BreitMaison", "type" -> "Symbol", "uri" -> "FeynCalc/ref/$BreitMaison"}}, + "$BreitMaison is a legacy switch for the \ +Breitenlohner-Maison-t'Hooft-Veltman scheme. 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The default is 128. It \ +should be increased if possible. The higher $FCMemoryAvailable can be, the \ +more intermediate steps do not have to be repeated by FeynCalc.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "$FCMemoryAvailable", + "titlemodifier" -> "", "windowtitle" -> "$FCMemoryAvailable", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/$FCMemoryAvailable"}, + "SearchTextTranslated" -> ""}, +CellContext->"Global`", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> "Global`"], + Cell[ + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", + StyleDefinitions -> "Default.nb"] +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{ + "PrimaryExamplesSection"->{ + Cell[3932, 112, 386, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->78056813]}, + "$FCMemoryAvailable"->{ + Cell[4563, 141, 120, 3, 27, "Input", + CellTags->"$FCMemoryAvailable", + CellID->695439641], + Cell[4686, 146, 202, 6, 35, "Output", + CellTags->"$FCMemoryAvailable"]} + } +*) +(*CellTagsIndex +CellTagsIndex->{ + {"PrimaryExamplesSection", 7064, 207}, + {"$FCMemoryAvailable", 7208, 211} + } +*) +(*NotebookFileOutline +Notebook[{ +Cell[590, 21, 2314, 53, 53, "AnchorBarGrid", + CellID->1], +Cell[2907, 76, 295, 11, 45, "ObjectNameGrid"], +Cell[3205, 89, 702, 19, 119, "Usage", + CellID->982511436], +Cell[CellGroupData[{ +Cell[3932, 112, 386, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->78056813], +Cell[CellGroupData[{ +Cell[4343, 131, 195, 6, 26, "ExampleSection", + CellID->512569663], +Cell[CellGroupData[{ +Cell[4563, 141, 120, 3, 27, "Input", + CellTags->"$FCMemoryAvailable", + CellID->695439641], +Cell[4686, 146, 202, 6, 35, "Output", + CellTags->"$FCMemoryAvailable"] +}, Open ]] +}, Open ]] +}, Open ]], +Cell[4927, 157, 23, 0, 41, "FooterCell"] +} +] +*) + +(* End of internal cache information *) + diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FCS.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FCS.nb index ad68cbfcd..5d2249f79 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FCS.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FCS.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 8036, 249] -NotebookOptionsPosition[ 5110, 159] -NotebookOutlinePosition[ 7439, 225] -CellTagsIndexPosition[ 7333, 219] +NotebookDataLength[ 8271, 259] +NotebookOptionsPosition[ 5372, 170] +NotebookOutlinePosition[ 7688, 236] +CellTagsIndexPosition[ 7582, 230] WindowTitle->$FCS WindowFrame->Normal*) @@ -59,12 +59,13 @@ Cell[BoxData[GridBox[{ URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$168169], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$292286], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/$FCS", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["$FCS", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["$FCS", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +118,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->275219115], + CellID->361639652], Cell[TextData[{ "Basic Examples", @@ -115,7 +126,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->318828667], + CellID->353242586], Cell[CellGroupData[{ @@ -145,7 +156,7 @@ Cell[BoxData[ ",", "\<\"SDF\"\>", ",", "\<\"SOD\"\>", ",", "\<\"SP\"\>", ",", "\<\"SPC\"\>", ",", "\<\"SPD\"\>", ",", "\<\"SPE\"\>", ",", "\<\"SPL\"\>"}], "}"}], TraditionalForm]], "Output", - ImageSize->{412, 54}, + ImageSize->{428, 52}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"$FCS", @@ -160,7 +171,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"$FCS", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -169,21 +180,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 3.627449}", + "built" -> "{2020, 1, 5, 19, 4, 15.989055}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "$FCS is a list of functions with a short name. 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$168508], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$292719], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/$FCT", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["$FCT", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["$FCT", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +118,9 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->700707134], + CellID->1799296695], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -115,13 +128,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1464216787], - -Cell[CellGroupData[{ - -Cell["Examples", "Subsubsection", - CellTags->"$FCT", - CellID->1394179374], + CellID->1539302137], Cell[BoxData[ RowBox[{ @@ -159,7 +166,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{45, 17}, + ImageSize->{49, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"$FCT", @@ -203,7 +210,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{45, 17}, + ImageSize->{49, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"$FCT", @@ -227,10 +234,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 5.100052}", + "built" -> "{2020, 1, 5, 19, 4, 16.995257}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -238,11 +245,11 @@ TaggingRules->{ "None", "summary" -> "$FCT Setting the global variable $FCT to True changes the default \ typesetting rules for the noncommutative multiplication operator Dot[].", - "synonyms" -> {}, "title" -> "$FCT", "titlemodifier" -> "", "windowtitle" -> - "$FCT", "type" -> "Symbol", "uri" -> "FeynCalc/ref/$FCT"}, - "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "$FCT", "titlemodifier" -> + "", "windowtitle" -> "$FCT", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/$FCT"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -250,8 +257,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - 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If set to True, FeynCalc will activate the \ +TraditionalForm output. Otherwise, the StandardForm output (Mathematica's \ +default) will be used. This setting only changes the output format of the \ +current notebook, i.e. it is not persistent and will not modify the global \ +options of Mathematica. If unsure, it is recommended to set \ +$FCTraditionalFormOutput to True, so that you can benefit from the nice \ +FeynCalc typesetting for various QFT quantities." + }]]} + }]], "Usage", + GridBoxOptions->{ + GridBoxBackground->{ + "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, + "RowsIndexed" -> {}}}, + CellID->982511436], + +Cell[CellGroupData[{ + +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->455133749], + +Cell["", "SectionHeaderSpacer"], + +Cell[CellGroupData[{ + +Cell[BoxData["$FCTraditionalFormOutput"], "Input", + CellLabel->"In[13]:=", + CellID->1499223899], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + ImageSize->{34, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[13]=", + CellID->825857747] +}, Open ]] +}, Closed]] +}, Open ]], + +Cell[" ", "FooterCell"] +}, +Saveable->False, +ScreenStyleEnvironment->"Working", +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, +WindowTitle->"$FCTraditionalFormOutput", +TaggingRules->{ + "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> + GridBox[{{ + RowBox[{ + ButtonBox[ + "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", + BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", + "Metadata" -> { + "built" -> "{2020, 1, 5, 19, 4, 18.096385}", + "history" -> {"9.3", "", "", ""}, "context" -> "FeynCalc`", + "keywords" -> {}, "specialkeywords" -> {}, + "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> + "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> + "None", "summary" -> + "$FCTraditionalFormOutput The boolean setting of $FCTraditionalFormOutput \ +determines which output format type should be used in the notebook front end \ +when FeynCalc is loaded. If set to True, FeynCalc will activate the \ +TraditionalForm output. Otherwise, the StandardForm output (Mathematica's \ +default) will be used. This setting only changes the output format of the \ +current notebook, i.e. it is not persistent and will not modify the global \ +options of Mathematica. If unsure, it is recommended to set \ +$FCTraditionalFormOutput to True, so that you can benefit from the nice \ +FeynCalc typesetting for various QFT quantities.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "$FCTraditionalFormOutput", "titlemodifier" -> + "", "windowtitle" -> "$FCTraditionalFormOutput", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/$FCTraditionalFormOutput"}, "SearchTextTranslated" -> + ""}, +CellContext->"Global`", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> "Global`"], + Cell[ + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", + StyleDefinitions -> "Default.nb"] +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{} +*) +(*CellTagsIndex +CellTagsIndex->{} +*) +(*NotebookFileOutline +Notebook[{ +Cell[596, 21, 2351, 54, 53, "AnchorBarGrid", + CellID->1], +Cell[2950, 77, 301, 11, 45, "ObjectNameGrid"], +Cell[CellGroupData[{ +Cell[3276, 92, 930, 18, 171, "Usage", + CellID->982511436], +Cell[CellGroupData[{ +Cell[4231, 114, 738, 24, 31, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->455133749], +Cell[4972, 140, 31, 0, 70, "SectionHeaderSpacer"], +Cell[CellGroupData[{ +Cell[5028, 144, 95, 2, 70, "Input", + CellID->1499223899], +Cell[5126, 148, 191, 6, 35, "Output", + CellID->825857747] +}, Open ]] +}, Closed]] +}, Open ]], +Cell[5356, 159, 23, 0, 41, "FooterCell"] +} +] +*) + +(* End of internal cache information *) + diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FeynCalcStuff.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FeynCalcStuff.nb index be46d3514..277bcc52f 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FeynCalcStuff.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FeynCalcStuff.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 5203, 145] -NotebookOptionsPosition[ 3308, 93] -NotebookOutlinePosition[ 5125, 141] -CellTagsIndexPosition[ 5082, 138] +NotebookDataLength[ 5445, 155] +NotebookOptionsPosition[ 3570, 104] +NotebookOutlinePosition[ 5381, 152] +CellTagsIndexPosition[ 5338, 149] WindowTitle->$FeynCalcStuff WindowFrame->Normal*) @@ -59,12 +59,13 @@ FeynCalcStuff.html"], StandardForm]], "Input", TextClipboardType -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$168842], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$302809], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/$FeynCalcStuff", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ FeynCalcStuff.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["$FeynCalcStuff", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["$FeynCalcStuff", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -103,19 +114,19 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 6.762475}", + "built" -> "{2019, 3, 29, 17, 55, 47.588952}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "$FeynCalcStuff is the list of availabe stuff in FeynCalc.", - "synonyms" -> {}, "title" -> "$FeynCalcStuff", "titlemodifier" -> "", - "windowtitle" -> "$FeynCalcStuff", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/$FeynCalcStuff"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "$FeynCalcStuff", + "titlemodifier" -> "", "windowtitle" -> "$FeynCalcStuff", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/$FeynCalcStuff"}}, CellContext->"Global`", FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->Notebook[{ @@ -140,13 +151,12 @@ CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[586, 21, 2270, 52, 70, "AnchorBarGrid", +Cell[586, 21, 2298, 53, 70, "AnchorBarGrid", CellID->1], -Cell[2859, 75, 57, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2919, 78, 359, 11, 70, "Usage", +Cell[2887, 76, 291, 11, 70, "ObjectNameGrid"], +Cell[3181, 89, 359, 11, 70, "Usage", CellID->982511436], -Cell[3281, 91, 23, 0, 70, "FooterCell"] +Cell[3543, 102, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FeynCalcVersion.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FeynCalcVersion.nb index 2c8f24089..5c9d89e67 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FeynCalcVersion.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$FeynCalcVersion.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 7512, 235] -NotebookOptionsPosition[ 4463, 145] -NotebookOutlinePosition[ 6877, 211] -CellTagsIndexPosition[ 6759, 205] +NotebookDataLength[ 7451, 234] +NotebookOptionsPosition[ 4615, 151] +NotebookOutlinePosition[ 6949, 215] +CellTagsIndexPosition[ 6831, 209] WindowTitle->$FeynCalcVersion WindowFrame->Normal*) @@ -59,12 +59,13 @@ FeynCalcVersion.html"], StandardForm]], "Input", TextClipboardType -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$169186], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$293576], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/$FeynCalcVersion", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ FeynCalcVersion.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["$FeynCalcVersion", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["$FeynCalcVersion", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -106,7 +117,9 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1421813232], + CellID->614101205], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -114,13 +127,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->753980873], - -Cell[CellGroupData[{ - -Cell["Examples", "Subsubsection", - CellTags->"$FeynCalcVersion", - CellID->1483320671], + CellID->211792166], Cell[CellGroupData[{ @@ -130,13 +137,12 @@ Cell[BoxData["$FeynCalcVersion"], "Input", CellID->806604709], Cell[BoxData[ - FormBox["\<\"9.0.0\"\>", TraditionalForm]], "Output", - ImageSize->{33, 15}, + FormBox["\<\"9.3.0\"\>", TraditionalForm]], "Output", + ImageSize->{34, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"$FeynCalcVersion", - CellLabel->"Out[1]=", - CellID->1396918294] + CellLabel->"Out[1]="] }, Open ]] }, Open ]] }, Open ]], @@ -146,7 +152,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"$FeynCalcVersion", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -155,21 +161,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 8.183592}", + "built" -> "{2020, 1, 5, 19, 4, 19.178713}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "$FeynCalcVersion is a string that represents the version of FeynCalc.", - "synonyms" -> {}, "title" -> "$FeynCalcVersion", "titlemodifier" -> "", - "windowtitle" -> "$FeynCalcVersion", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/$FeynCalcVersion"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "$FeynCalcVersion", + "titlemodifier" -> "", "windowtitle" -> "$FeynCalcVersion", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/$FeynCalcVersion"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -177,8 +184,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -187,56 +195,47 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3327, 93, 388, 15, 31, "PrimaryExamplesSection", + Cell[3589, 104, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1421813232]}, + CellID->614101205]}, "$FeynCalcVersion"->{ - Cell[3938, 120, 85, 2, 35, "Subsubsection", - CellTags->"$FeynCalcVersion", - CellID->1483320671], - Cell[4048, 126, 116, 3, 27, "Input", + Cell[4221, 133, 116, 3, 27, "Input", CellTags->"$FeynCalcVersion", CellID->806604709], - Cell[4167, 131, 230, 7, 36, "Output", - 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Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/$\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"Write2\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Write2"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput-> + False], {"\<\"FeynCalc/ref/$FortranContinuationCharacter\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/$FortranContinuationCharacter"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/$\ FortranContinuationCharacter.html"], StandardForm]], "Input", - 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CellID->1224892054], +Cell[TextData[{ + Cell["$Gauge", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -114,9 +146,7 @@ Cell[TextData[{ ButtonNote->"Gauge"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"$Gauge", - CellID->1591453554] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -133,10 +163,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 11.276561}", + "built" -> "{2020, 1, 5, 19, 4, 21.229034}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -145,11 +175,11 @@ TaggingRules->{ "$Gauge (= 1/xi) is a constant specifying the gauge fixing parameter of \ QED in Lorentz gauge. 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Notice \ that $Gauge is used by some functions, the option Gauge by others.", - "synonyms" -> {}, "title" -> "$Gauge", "titlemodifier" -> "", - "windowtitle" -> "$Gauge", "type" -> "Symbol", "uri" -> + "synonyms" -> {}, "tabletags" -> {}, "title" -> "$Gauge", "titlemodifier" -> + "", "windowtitle" -> "$Gauge", "type" -> "Symbol", "uri" -> "FeynCalc/ref/$Gauge"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -158,41 +188,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "$Gauge"->{ - Cell[3686, 109, 217, 9, 70, "Text", - CellTags->"$Gauge", - CellID->1591453554]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"$Gauge", 5837, 168} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[578, 21, 2237, 52, 70, "AnchorBarGrid", +Cell[578, 21, 2987, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2818, 75, 49, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2870, 78, 518, 13, 70, "Usage", +Cell[3568, 97, 283, 11, 70, "ObjectNameGrid"], +Cell[3854, 110, 518, 13, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3413, 95, 270, 12, 70, "SeeAlsoSection", +Cell[4397, 127, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3686, 109, 217, 9, 70, "Text", - CellTags->"$Gauge", - CellID->1591453554] +Cell[4670, 141, 178, 7, 70, "SeeAlso"] }, Open ]], -Cell[3918, 121, 23, 0, 70, "FooterCell"] +Cell[4863, 151, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$Larin.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$Larin.nb index d9f67a4cb..3134a35aa 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$Larin.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$Larin.nb @@ -3,69 +3,94 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 10223, 324] -NotebookOptionsPosition[ 6342, 215] -NotebookOutlinePosition[ 9381, 292] -CellTagsIndexPosition[ 9273, 286] +NotebookDataLength[ 7514, 222] +NotebookOptionsPosition[ 5330, 163] +NotebookOutlinePosition[ 7305, 214] +CellTagsIndexPosition[ 7262, 211] WindowTitle->$Larin WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/$Larin\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/$Larin"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/$Larin.\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FCSetDiracGammaScheme\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCSetDiracGammaScheme"], \ +"\<\"FCGetDiracGammaScheme\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCGetDiracGammaScheme"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/$Larin\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/$Larin"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/$Larin.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$170198], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/$Larin", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$294880], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/$Larin", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,41 +98,27 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["$Larin", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["$Larin", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData["$Larin"], "InlineFormula"], - " \[LineSeparator]", - "If set to True, the Larin-Gorishny-Atkyampo-DelBurgo-scheme for ", - Cell[BoxData[ - FormBox[ - SubscriptBox["\[Gamma]", "5"], TraditionalForm]]], - " in ", - StyleBox["D", - FontSlant->"Italic"], - "-dimensions is used, i.e. before evaluating traces (but after moving ", - Cell[BoxData[ - FormBox[ - SubscriptBox["\[Gamma]", "5"], TraditionalForm]]], - " anticommuting in all dimensions to the right of the Dirac string) a \ -product gamma[mu].gamma5 is substituted to -I/6 Eps[mu,al,be,si] \ -gamma[al,be,si], where all indices live in ", - StyleBox["D", - FontSlant->"Italic"], - "-dimensions now. 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The modern way is to use \ +FCSetDiracGammaScheme to specify a scheme for handling Dirac matrices in \ +dimensional regularization and FCGetDiracGammaScheme to check the current \ +setting." }]]} }]], "Usage", GridBoxOptions->{ @@ -118,60 +129,6 @@ this scheme also works for more than one fermion line involving ", Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", - WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->1471140951], - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->1585615479], - -Cell[CellGroupData[{ - -Cell["Examples", "Subsubsection", - CellTags->"$Larin", - CellID->1690224764], - -Cell[CellGroupData[{ - -Cell[BoxData["$Larin"], "Input", - CellTags->"$Larin", - CellLabel->"In[1]:=", - CellID->1245299015], - -Cell[BoxData[ - FormBox["True", TraditionalForm]], "Output", - ImageSize->{33, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"$Larin", - CellLabel->"Out[1]=", - CellID->1660409352] -}, Open ]], - -Cell["", "SectionFooterSpacer"] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -186,29 +143,20 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[RawData["\<\ Cell[TextData[{ - ButtonBox[\"Tr\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/Tr\", - ButtonNote->\"Tr\"], - \", \", - ButtonBox[\"$BreitMaison\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/$BreitMaison\", - ButtonNote->\"$BreitMaison\"], - \", \", - ButtonBox[\"West\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/West\", - ButtonNote->\"West\"], - \".\" -}], \"Text\", - CellTags->\"$Larin\", - CellID->181403197]\ -\>"], "Text", - CellTags->"$Larin", - CellID->181403197] + StyleBox[ButtonBox["FCSetDiracGammaScheme", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/FCSetDiracGammaScheme", + ButtonNote->"FCSetDiracGammaScheme"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["FCGetDiracGammaScheme", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/FCGetDiracGammaScheme", + ButtonNote->"FCGetDiracGammaScheme"], + FontFamily->"Verdana"], + "." +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -216,7 +164,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, WindowTitle->"$Larin", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -225,29 +173,24 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 12.606587}", + "built" -> "{2020, 1, 5, 19, 4, 22.087028}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "$Larin If set to True, the Larin-Gorishny-Atkyampo-DelBurgo-scheme for \ -\\[Gamma]5 in D-dimensions is used, i.e. before evaluating traces (but after \ -moving \\[Gamma]5 anticommuting in all dimensions to the right of the Dirac \ -string) a product gamma[mu].gamma5 is substituted to -I/6 Eps[mu,al,be,si] \ -gamma[al,be,si], where all indices live in D-dimensions now. Especially the \ -Levic-Civita tensor is taken to be D-dimensional, i.e., contraction of two \ -Eps's results in D's. This has (FOR ONE AXIAL-VECTOR-CURRENT ONLY, it is not \ -so clear if this scheme also works for more than one fermion line involving \ -\\[Gamma]5) the same effect as the Breitenlohner-Maison-'t Hooft-Veltman \ -scheme.", "synonyms" -> {}, "title" -> "$Larin", "titlemodifier" -> "", + "$Larin is a legacy switch for the Larin-Gorishny-Atkyampo-DelBurgo \ +scheme. The modern way is to use FCSetDiracGammaScheme to specify a scheme \ +for handling Dirac matrices in dimensional regularization and \ +FCGetDiracGammaScheme to check the current setting.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "$Larin", "titlemodifier" -> "", "windowtitle" -> "$Larin", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/$Larin"}, "SearchTextTranslated" -> ""}, + "FeynCalc/ref/$Larin"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -256,79 +199,33 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$170533], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$295326], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/$LeviCivitaSign", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,17 +74,27 @@ LeviCivitaSign.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["$LeviCivitaSign", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["$LeviCivitaSign", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData["$LeviCivitaSign"], "InlineFormula"], " \[LineSeparator]is a global variable that determines the sign in the \ result of a Dirac trace of four gamma matrices and gamma5. $LeviCivitaSign \ -is by default set to -1 which corresponds to the convention \ -Tr[LeviCivita[a,b,c,d,5]] = -4*I*Eps[a,b,c,d]. Setting $LeviCivitaSign=-I \ -will switch to the FORM-convention." +is by default set to -1 which corresponds to the convention Tr[LC[a,b,c,d,5]] \ += -4*I*Eps[a,b,c,d]. Setting $LeviCivitaSign=-I will switch to the \ +FORM-convention." }]]} }]], "Usage", GridBoxOptions->{ @@ -109,7 +120,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->62338071], + CellID->887122515], Cell[CellGroupData[{ @@ -119,7 +130,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1709334668], + CellID->1894416738], Cell[CellGroupData[{ @@ -130,7 +141,7 @@ Cell[BoxData["$LeviCivitaSign"], "Input", Cell[BoxData[ FormBox[ RowBox[{"-", "1"}], TraditionalForm]], "Output", - ImageSize->{21, 15}, + ImageSize->{22, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellLabel->"Out[1]=", @@ -169,7 +180,7 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", - ImageSize->{87, 18}, + ImageSize->{85, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellLabel->"Out[2]=", @@ -213,7 +224,7 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", - ImageSize->{66, 18}, + ImageSize->{64, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellLabel->"Out[3]=", @@ -237,7 +248,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"$LeviCivitaSign", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -246,10 +257,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 14.224707}", + "built" -> "{2020, 1, 5, 19, 4, 23.052180}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -257,14 +268,14 @@ TaggingRules->{ "None", "summary" -> "$LeviCivitaSign is a global variable that determines the sign in the \ result of a Dirac trace of four gamma matrices and gamma5. $LeviCivitaSign is \ -by default set to -1 which corresponds to the convention \ -Tr[LeviCivita[a,b,c,d,5]] = -4*I*Eps[a,b,c,d]. Setting $LeviCivitaSign=-I \ -will switch to the FORM-convention.", "synonyms" -> {}, "title" -> +by default set to -1 which corresponds to the convention Tr[LC[a,b,c,d,5]] = \ +-4*I*Eps[a,b,c,d]. Setting $LeviCivitaSign=-I will switch to the \ +FORM-convention.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "$LeviCivitaSign", "titlemodifier" -> "", "windowtitle" -> "$LeviCivitaSign", "type" -> "Symbol", "uri" -> "FeynCalc/ref/$LeviCivitaSign"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -272,8 +283,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -282,58 +294,57 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3566, 96, 386, 15, 31, "PrimaryExamplesSection", + Cell[3820, 107, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->62338071]} + CellID->887122515]} } *) (*CellTagsIndex CellTagsIndex->{ - {"PrimaryExamplesSection", 8778, 283} + {"PrimaryExamplesSection", 9065, 295} } *) (*NotebookFileOutline Notebook[{ -Cell[587, 21, 2274, 52, 51, "AnchorBarGrid", +Cell[587, 21, 2302, 53, 53, "AnchorBarGrid", CellID->1], -Cell[2864, 75, 58, 1, 42, "ObjectName", - CellID->1224892054], -Cell[2925, 78, 616, 14, 130, "Usage", +Cell[2892, 76, 292, 11, 45, "ObjectNameGrid"], +Cell[3187, 89, 608, 14, 119, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3566, 96, 386, 15, 31, "PrimaryExamplesSection", +Cell[3820, 107, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->62338071], + CellID->887122515], Cell[CellGroupData[{ -Cell[3977, 115, 196, 6, 25, "ExampleSection", - CellID->1709334668], +Cell[4232, 126, 196, 6, 26, "ExampleSection", + CellID->1894416738], Cell[CellGroupData[{ -Cell[4198, 125, 85, 2, 27, "Input", +Cell[4453, 136, 85, 2, 27, "Input", CellID->1712420789], -Cell[4286, 129, 205, 7, 36, "Output", +Cell[4541, 140, 205, 7, 35, "Output", CellID->2017735240] }, Open ]], Cell[CellGroupData[{ -Cell[4528, 141, 205, 6, 27, "Input", +Cell[4783, 152, 205, 6, 27, "Input", CellID->722943498], -Cell[4736, 149, 645, 26, 39, "Output", +Cell[4991, 160, 645, 26, 35, "Output", CellID->24019145] }, Open ]], -Cell[5396, 178, 78, 1, 31, "Notes", +Cell[5651, 189, 78, 1, 32, "Notes", CellID->1734027625], Cell[CellGroupData[{ -Cell[5499, 183, 309, 9, 45, "Input", +Cell[5754, 194, 309, 9, 45, "Input", CellID->1075951969], -Cell[5811, 194, 606, 25, 39, "Output", +Cell[6066, 205, 606, 25, 35, "Output", CellID->1430392236] }, Open ]], -Cell[6432, 222, 63, 1, 31, "Notes", +Cell[6687, 233, 63, 1, 32, "Notes", CellID->223764811], -Cell[6498, 225, 143, 5, 27, "Input", +Cell[6753, 236, 143, 5, 27, "Input", CellID->955635605] }, Open ]] }, Open ]], -Cell[6668, 234, 23, 0, 42, "FooterCell"] +Cell[6923, 245, 23, 0, 41, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$LimitTo4.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$LimitTo4.nb index 3094d765c..fdfbb0bfa 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/$LimitTo4.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/$LimitTo4.nb @@ -3,69 +3,94 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 8706, 290] -NotebookOptionsPosition[ 5343, 188] -NotebookOutlinePosition[ 7857, 258] -CellTagsIndexPosition[ 7746, 252] +NotebookDataLength[ 9460, 308] +NotebookOptionsPosition[ 6384, 217] +NotebookOutlinePosition[ 8755, 282] +CellTagsIndexPosition[ 8644, 276] WindowTitle->$LimitTo4 WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/$LimitTo4\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/$LimitTo4"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/$LimitTo4.\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"PaVe\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PaVe"], "\<\"PaVeReduce\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PaVeReduce"], "\<\"OneLoop\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/OneLoop"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/$LimitTo4\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/$LimitTo4"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/$LimitTo4.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$170872], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/$LimitTo4", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$295759], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/$LimitTo4", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +98,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["$LimitTo4", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["$LimitTo4", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +142,9 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1772191243], + CellID->336697932], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -115,13 +152,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->199274007], - -Cell[CellGroupData[{ - -Cell["Examples", "Subsubsection", - CellTags->"$LimitTo4", - CellID->1433837082], + CellID->269137595], Cell[CellGroupData[{ @@ -132,16 +163,16 @@ Cell[BoxData["$LimitTo4"], "Input", Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", - ImageSize->{33, 15}, + ImageSize->{31, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"$LimitTo4", CellLabel->"Out[1]=", CellID->477908355] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] -}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -179,9 +210,7 @@ Cell[TextData[{ ButtonNote->"OneLoop"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"$LimitTo4", - CellID->1267840867] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -198,10 +227,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 15.736072}", + "built" -> "{2020, 1, 5, 19, 4, 24.101436}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -209,11 +238,11 @@ TaggingRules->{ "None", "summary" -> "$LimitTo4 is a variable with default setting True. If set to False, no \ limit Dimension -> 4 is performed after tensor integral decomposition.", - "synonyms" -> {}, "title" -> "$LimitTo4", "titlemodifier" -> "", - "windowtitle" -> "$LimitTo4", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/$LimitTo4"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "$LimitTo4", + "titlemodifier" -> "", "windowtitle" -> "$LimitTo4", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/$LimitTo4"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -221,8 +250,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -231,67 +261,55 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -233,73 +249,55 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3366, 96, 388, 15, 31, "PrimaryExamplesSection", + Cell[4375, 128, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1773590494]}, + CellID->613466333]}, "$MIntegrate"->{ - Cell[3977, 123, 79, 2, 35, "Subsubsection", - CellTags->"$MIntegrate", - CellID->896374065], - Cell[4081, 129, 107, 3, 27, "Input", + Cell[5007, 157, 107, 3, 27, "Input", CellTags->"$MIntegrate", CellID->1439168966], - Cell[4191, 134, 231, 8, 36, "Output", + Cell[5117, 162, 231, 8, 35, "Output", CellTags->"$MIntegrate", - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$173585], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$298379], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/$VeryVerbose", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ VeryVerbose.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["$VeryVerbose", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["$VeryVerbose", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,7 +119,9 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1051520274], + CellID->1852257957], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -116,13 +129,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->313296919], - -Cell[CellGroupData[{ - -Cell["Examples", "Subsubsection", - CellTags->"$VeryVerbose", - CellID->61376549], + CellID->1682360856], Cell[CellGroupData[{ @@ -133,7 +140,7 @@ Cell[BoxData["$VeryVerbose"], "Input", Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"$VeryVerbose", @@ -286,7 +293,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"$VeryVerbose", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -295,10 +302,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - 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CellTags->"A0", - CellID->1026580483], +}], "Notes"], Cell[CellGroupData[{ @@ -177,7 +210,7 @@ Cell[BoxData[ SuperscriptBox["m", "2"], ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - ImageSize->{58, 21}, + ImageSize->{59, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"A0", @@ -220,7 +253,7 @@ Cell[BoxData[ HoldForm], TraditionalForm]}], "+", SuperscriptBox["m", "2"]}], TraditionalForm]], "Output", - ImageSize->{164, 21}, + ImageSize->{172, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"A0", @@ -244,9 +277,7 @@ Cell[TextData[{ RowBox[{ SubscriptBox["A", "0"], "(", "0", ")"}], TraditionalForm]]], " is set to 0." -}], "Text", - CellTags->"A0", - CellID->1221823578], +}], "Notes"], Cell[CellGroupData[{ @@ -258,7 +289,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"A0", @@ -278,7 +309,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"A0", @@ -331,9 +362,7 @@ Cell[TextData[{ ButtonNote->"PaVe"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"A0", - CellID->70965860] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -350,21 +379,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 15, 58.864970}", + "built" -> "{2020, 1, 5, 18, 52, 25.309540}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "A0[m^2] is the Passarino-Veltman one-point integral A0.", - 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"HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 7.428216}", + "built" -> "{2020, 1, 5, 18, 52, 32.078733}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -1643,11 +772,12 @@ defined names is obtained with Amplitude[]. New amplitudes can be added to \ the file \"Amplitude.m\". It is strongly recommended to use names that \ reflect the process. The option Gauge -> 1 means `t Hooft Feynman gauge; \ Polarization -> 0 gives unpolarized OPE-type amplitudes, Polarization -> 1 \ -the polarized ones.", "synonyms" -> {}, "title" -> "Amplitude", - "titlemodifier" -> "", "windowtitle" -> "Amplitude", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/Amplitude"}, "SearchTextTranslated" -> ""}, +the polarized ones.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "Amplitude", "titlemodifier" -> "", "windowtitle" -> "Amplitude", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/Amplitude"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -1655,8 +785,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -1665,115 +796,80 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellLabel->"Out[2]=", - CellID->1732499360] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -190,27 +265,23 @@ Cell[BoxData[ RowBox[{"Amputate", "[", RowBox[{"%", ",", "q"}], "]"}]], "Input", CellTags->"Amputate", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1612122659], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["q", - TraditionalForm], - TraditionalForm], + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], + FormBox[ FormBox[ - FormBox[ - FormBox[ - RowBox[{"$AL$2188", "\[InvisibleApplication]", - RowBox[{"(", "1", ")"}]}], - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", + RowBox[{"$AL$41318", "\[InvisibleApplication]", + RowBox[{"(", "1", ")"}]}], + TraditionalForm], + TraditionalForm]], " ", RowBox[{ RowBox[{"(", RowBox[{ @@ -223,16 +294,15 @@ Cell[BoxData[ SuperscriptBox["\[Gamma]", FormBox[ FormBox[ - RowBox[{"$AL$2188", "\[InvisibleApplication]", + RowBox[{"$AL$41318", "\[InvisibleApplication]", RowBox[{"(", "1", ")"}]}], TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", - ImageSize->{197, 23}, + ImageSize->{214, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Amputate", - CellLabel->"Out[3]=", - CellID->42958207] + CellLabel->"Out[2]="] }, Open ]] }, Open ]], @@ -262,10 +332,10 @@ Cell[TextData[{ ButtonNote->"DiracGamma"], FontFamily->"Verdana"], ", ", - StyleBox[ButtonBox["DiracMatrix", + StyleBox[ButtonBox["GA", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData->"paclet:FeynCalc/ref/GA", + ButtonNote->"GA"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["DiracSimplify", @@ -274,10 +344,10 @@ Cell[TextData[{ ButtonNote->"DiracSimplify"], FontFamily->"Verdana"], ", ", - StyleBox[ButtonBox["DiracSlash", + StyleBox[ButtonBox["GS", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], + ButtonData->"paclet:FeynCalc/ref/GS", + ButtonNote->"GS"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["DiracTrick", @@ -286,9 +356,7 @@ Cell[TextData[{ ButtonNote->"DiracTrick"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Amputate", - CellID->1266124166] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -305,10 +373,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 9.030852}", + "built" -> "{2020, 1, 5, 18, 52, 33.254118}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -316,11 +384,11 @@ TaggingRules->{ "None", "summary" -> "Amputate[exp, q1, q2, ...] amputates Eps and DiracGamma. \ Amputate[exp,q1,q2,Pair->{p}] amputates also p.q1 and p.q2; Pair->All \ -amputates all except OPEDelta.", "synonyms" -> {}, "title" -> "Amputate", - "titlemodifier" -> "", "windowtitle" -> "Amputate", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/Amputate"}, "SearchTextTranslated" -> ""}, +amputates all except OPEDelta.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "Amputate", "titlemodifier" -> "", "windowtitle" -> "Amputate", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/Amputate"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -329,7 +397,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -337,90 +405,86 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"Anti5", "[", RowBox[{"%", ",", RowBox[{"-", "1"}]}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[3]:=", + CellLabel->"In[1]:=", CellID->1609506190], Cell[BoxData[ @@ -207,37 +320,70 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{45, 18}, + ImageSize->{49, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Anti5", - CellLabel->"Out[3]=", - CellID->741917191] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracMatrix", "[", + RowBox[{"GA", "[", RowBox[{ "5", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[4]:=", + CellLabel->"In[2]:=", CellID->1286690073], Cell[BoxData[ FormBox[ - RowBox[{"DiracMatrix", "(", - RowBox[{ - "5", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], - ")"}], TraditionalForm]], "Output", - ImageSize->{171, 15}, + RowBox[{ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Gamma]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Delta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm]}], TraditionalForm]], "Output", + ImageSize->{124, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Anti5", - CellLabel->"Out[4]=", - CellID->733245772] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -246,7 +392,7 @@ Cell[BoxData[ RowBox[{"Anti5", "[", RowBox[{"%", ",", "2"}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[5]:=", + CellLabel->"In[3]:=", CellID->197831622], Cell[BoxData[ @@ -280,12 +426,11 @@ Cell[BoxData[ FormBox["\[Delta]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{116, 19}, + ImageSize->{124, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Anti5", - CellLabel->"Out[5]=", - CellID->446711059] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -294,7 +439,7 @@ Cell[BoxData[ RowBox[{"Anti5", "[", RowBox[{"%%", ",", "Infinity"}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[6]:=", + CellLabel->"In[4]:=", CellID->1010214576], Cell[BoxData[ @@ -328,12 +473,11 @@ Cell[BoxData[ OverscriptBox["\[Gamma]", "_"], FormBox["5", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{116, 19}, + ImageSize->{124, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Anti5", - CellLabel->"Out[6]=", - CellID->1568263833] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -343,7 +487,7 @@ Cell[BoxData[ RowBox[{"%", ",", RowBox[{"-", "Infinity"}]}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[7]:=", + CellLabel->"In[5]:=", CellID->1359760692], Cell[BoxData[ @@ -377,30 +521,33 @@ Cell[BoxData[ FormBox["\[Delta]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{116, 19}, + ImageSize->{124, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Anti5", - CellLabel->"Out[7]=", - CellID->177899299] + CellLabel->"Out[5]="] +}, Open ]] }, Open ]], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + Cell[TextData[{ "In the naive ", Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], - "- scheme D-dimensional ", + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + "-scheme ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional ", + Cell[BoxData["\[Gamma]"], "InlineFormula"], + "-matrices anticommute with", Cell[BoxData[ - FormBox["\[Gamma]", TraditionalForm]]], - "-matrices anticommute with ", - Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], "." -}], "Text", - CellTags->"Anti5", - CellID->1633748802], +}], "Notes"], Cell[CellGroupData[{ @@ -408,7 +555,7 @@ Cell[BoxData[ RowBox[{"GA5", ".", RowBox[{"GAD", "[", "\[Mu]", "]"}]}]], "Input", CellTags->"Anti5", - CellLabel->"In[8]:=", + CellLabel->"In[1]:=", CellID->1799781971], Cell[BoxData[ @@ -425,12 +572,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{44, 18}, + ImageSize->{48, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Anti5", - CellLabel->"Out[8]=", - CellID->1994871864] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -438,7 +584,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Anti5", "[", "%", "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[9]:=", + CellLabel->"In[2]:=", CellID->42617734], Cell[BoxData[ @@ -454,12 +600,78 @@ Cell[BoxData[ OverscriptBox["\[Gamma]", "_"], FormBox["5", TraditionalForm]]}]}], TraditionalForm]], "Output", - ImageSize->{54, 18}, + ImageSize->{59, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Anti5", - CellLabel->"Out[9]=", - CellID->1660721309] + CellLabel->"Out[2]="] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; 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Anti5[exp, -n] \ +anticommutes all \\[Gamma]^5 n-times to the left.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "Anti5", "titlemodifier" -> "", + "windowtitle" -> "Anti5", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/Anti5"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -543,8 +754,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -553,179 +765,178 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["Apart2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -93,6 +130,60 @@ Please use ApartFF instead." 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CellID->1089764331], + CellID->1660425432], Cell[CellGroupData[{ @@ -118,30 +209,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1867734952], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "Apart2", "]"}]], "Input", - CellTags->"Apart2", - CellLabel->"In[1]:=", - CellID->1571464480], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Factoring", "\[Rule]", "True"}], ",", - RowBox[{"ExcludeMasses", "\[Rule]", - RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{266, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Apart2", - CellLabel->"Out[1]=", - CellID->1842118848] -}, Open ]], + CellID->29687880], Cell[CellGroupData[{ @@ -154,7 +222,7 @@ Cell[BoxData[ RowBox[{"q", ",", "M"}], "}"}], ",", RowBox[{"q", "-", "p"}]}], "]"}]], "Input", CellTags->"Apart2", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1580962822], Cell[BoxData[ @@ -163,35 +231,60 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["q", "2"], "\[InvisibleSpace]", "\<\"-\"\>", + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", "\[InvisibleSpace]", - SuperscriptBox["m", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`q^2, "-", $CellContext`m^2, "]"], + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]], "-", $CellContext`m^2], Editable->False], ")"}], ".", RowBox[{"(", InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["q", "2"], "\[InvisibleSpace]", "\<\"-\"\>", + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", "\[InvisibleSpace]", - SuperscriptBox["M", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`q^2, "-", $CellContext`M^2, "]"], + SuperscriptBox["M", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]], "-", $CellContext`M^2], Editable->False], ")"}], ".", - 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CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->867958772], Cell[BoxData[ FormBox[ FractionBox[ RowBox[{ - FractionBox["1", - RowBox[{ - RowBox[{"(", - RowBox[{ - SuperscriptBox[ - FormBox["q", - TraditionalForm], "2"], "-", - SuperscriptBox["m", "2"]}], ")"}], ".", - SuperscriptBox[ + FormBox[ + FractionBox["1", + RowBox[{ RowBox[{"(", - RowBox[{ - FormBox["q", - TraditionalForm], "-", - FormBox["p", - TraditionalForm]}], ")"}], "2"]}]], "-", - FractionBox["1", - RowBox[{ - RowBox[{"(", - RowBox[{ + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]], "-", $CellContext`m^2], + Editable->False], ")"}], ".", + InterpretationBox[ SuperscriptBox[ - FormBox["q", - TraditionalForm], "2"], "-", - SuperscriptBox["M", "2"]}], ")"}], ".", - 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+ FeynCalc`Momentum[$CellContext`p, D] + + FeynCalc`Momentum[$CellContext`q, D]]], + Editable->False]}]], + TraditionalForm]}], RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["M", "2"]}]], TraditionalForm]], "Output", - ImageSize->{234, 61}, + ImageSize->{306, 63}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Apart2", - CellLabel->"Out[3]=", - CellID->496976710] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -253,7 +397,7 @@ Cell[BoxData[ RowBox[{"StandardForm", "[", RowBox[{"FCE", "[", "%", "]"}], "]"}]], "Input", CellTags->"Apart2", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->168515472], Cell[BoxData[ @@ -274,12 +418,11 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["M", "2"]}]]], "Output", - ImageSize->{315, 40}, + ImageSize->{317, 34}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Apart2", - CellLabel->"Out[4]//StandardForm=", - CellID->638625530] + CellLabel->"Out[3]//StandardForm="] }, Open ]] }, Open ]], @@ -321,9 +464,7 @@ Cell[TextData[{ ButtonNote->"ApartFF"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Apart2", - CellID->1960323984] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -331,7 +472,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"Apart2", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -340,10 +481,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 18.319132}", + "built" -> "{2020, 1, 5, 18, 52, 40.594627}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -351,11 +492,11 @@ TaggingRules->{ "None", "summary" -> "Apart2[expr] partial fractions very simple 1-loop integrals of the form \ 1/[(q^2-m1^2)(q^2-m2^2)]. Since FeynCalc 9 this function is deprecated. \ -Please use ApartFF instead.", "synonyms" -> {}, "title" -> "Apart2", - "titlemodifier" -> "", "windowtitle" -> "Apart2", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/Apart2"}, "SearchTextTranslated" -> ""}, +Please use ApartFF instead.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "Apart2", "titlemodifier" -> "", "windowtitle" -> "Apart2", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/Apart2"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -363,8 +504,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -372,104 +514,98 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CellID->1395703577], + CellID->2020340374], Cell["", "SectionHeaderSpacer"], @@ -167,7 +178,34 @@ multivariate polynomials,\t\t\t\t", " objects, i.e. it is less general. 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 21.039238}", + "built" -> "{2020, 1, 5, 18, 52, 42.751459}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -1102,11 +3287,11 @@ decomposing them into simpler integrals that contain only linearly \ independent propagators. 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ApartFF effectively replaces the older \ function Apart2 and ScalarProductCancel which are now considered legacy.", - "synonyms" -> {}, "title" -> "ApartFF", "titlemodifier" -> "", - "windowtitle" -> "ApartFF", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/ApartFF"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "ApartFF", + "titlemodifier" -> "", "windowtitle" -> "ApartFF", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/ApartFF"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -1114,8 +3299,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -1124,89 +3310,140 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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ImageSize->{114, 21}, + ImageSize->{120, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"B0", - CellLabel->"Out[2]=", - CellID->1350980966] + CellLabel->"Out[1]="] }, Open ]], -Cell[BoxData[ - RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"B0", ",", - RowBox[{"B0Unique", "\[Rule]", "True"}], ",", - RowBox[{"B0Real", "\[Rule]", "True"}]}], "]"}], ";"}]], "Input", - CellTags->"B0", - CellLabel->"In[3]:=", - CellID->643767668], - Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{"0", ",", "0", ",", - SuperscriptBox["m", "2"]}], "]"}]], "Input", + SuperscriptBox["m", "2"], ",", + RowBox[{"B0Unique", "\[Rule]", "True"}], ",", + RowBox[{"B0Real", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"B0", - CellLabel->"In[4]:=", + CellLabel->"In[2]:=", CellID->510341898], Cell[BoxData[ @@ -226,12 +285,11 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm], "+", "1"}], TraditionalForm]], "Output", - ImageSize->{124, 21}, + ImageSize->{130, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"B0", - CellLabel->"Out[4]=", - CellID->170690020] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -240,9 +298,11 @@ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{ SuperscriptBox["m", "2"], ",", "0", ",", - SuperscriptBox["m", "2"]}], "]"}]], "Input", + SuperscriptBox["m", "2"], ",", + RowBox[{"B0Unique", "\[Rule]", "True"}], ",", + RowBox[{"B0Real", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"B0", - CellLabel->"In[5]:=", + CellLabel->"In[3]:=", CellID->1178094654], Cell[BoxData[ @@ -259,12 +319,11 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm], "+", "2"}], TraditionalForm]], "Output", - ImageSize->{125, 21}, + ImageSize->{132, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"B0", - CellLabel->"Out[5]=", - CellID->2121507054] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -275,7 +334,7 @@ Cell[BoxData[ RowBox[{"m", "^", "2"}], ",", RowBox[{"m", "^", "2"}]}], "]"}]], "Input", CellTags->"B0", - CellLabel->"In[6]:=", + CellLabel->"In[4]:=", CellID->828170126], Cell[BoxData[ @@ -289,12 +348,11 @@ Cell[BoxData[ SuperscriptBox["m", "2"]}], ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - 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CellID->1224892054], +Cell[TextData[{ + Cell["B0Real", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +139,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->955343210], + CellID->953528149], Cell[CellGroupData[{ @@ -117,11 +149,9 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1561501857], + CellID->434066379], -Cell["By default the arguments are not assumed real.", "Text", - CellTags->"B0Real", - CellID->130288840], +Cell["By default the arguments are not assumed real.", "Notes"], Cell[CellGroupData[{ @@ -134,60 +164,31 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - RowBox[{ + TagBox[ FormBox[ - 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"See also: ", StyleBox[ButtonBox["B0", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/B0", ButtonNote->"B0"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"B0Real", - CellID->1839543320] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -248,7 +245,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"B0Real", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -257,10 +254,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 25.763973}", + "built" -> "{2020, 1, 5, 18, 52, 46.578599}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -268,11 +265,11 @@ TaggingRules->{ "None", "summary" -> "B0Real is an option of B0 (default False). 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CellID->1224892054], +Cell[TextData[{ + Cell["B0Unique", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +139,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1380979473], + CellID->1501296835], Cell[CellGroupData[{ @@ -117,11 +149,9 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->318683481], + CellID->791572088], -Cell["By default transformation is done.", "Text", - CellTags->"B0Unique", - CellID->1633725722], +Cell["By default no transformation is done.", "Notes"], Cell[CellGroupData[{ @@ -134,77 +164,49 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - RowBox[{ + TagBox[ FormBox[ - TagBox[ - FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{"0", ",", "s", ",", "s"}], ")"}], - TraditionalForm], - HoldForm], - TraditionalForm], "+", "1"}], TraditionalForm]], "Output", - ImageSize->{95, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"B0Unique", - CellLabel->"Out[1]=", - CellID->2030362910] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "B0", "]"}]], "Input", - CellTags->"B0Unique", - CellLabel->"In[2]:=", - CellID->1904628151], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"BReduce", "\[Rule]", "False"}], ",", - RowBox[{"B0Unique", "\[Rule]", "True"}], ",", - RowBox[{"B0Real", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - ImageSize->{350, 15}, + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{"0", ",", "0", ",", "s"}], ")"}], + TraditionalForm], + HoldForm], TraditionalForm]], "Output", + ImageSize->{79, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"B0Unique", - CellLabel->"Out[2]=", - CellID->226407255] + CellLabel->"Out[1]="] }, Open ]], -Cell["With B0Real\[Rule]False, nothing happens.", "Text", - CellTags->"B0Unique", - CellID->1308469818], +Cell["With B0Real\[Rule]True following transformation is applied", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{"0", ",", "0", ",", "s", ",", - RowBox[{"B0Unique", "\[Rule]", "False"}]}], "]"}]], "Input", + RowBox[{"B0Unique", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"B0Unique", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->224258616], Cell[BoxData[ FormBox[ - TagBox[ + RowBox[{ FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{"0", ",", "0", ",", "s"}], ")"}], - TraditionalForm], - HoldForm], TraditionalForm]], "Output", - ImageSize->{72, 15}, + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{"0", ",", "s", ",", "s"}], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm], "+", "1"}], TraditionalForm]], "Output", + ImageSize->{102, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"B0Unique", - CellLabel->"Out[3]=", - CellID->1908481089] + CellLabel->"Out[2]="] }, Open ]] }, Open ]], @@ -228,16 +230,13 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["B0", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/B0", ButtonNote->"B0"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"B0Unique", - CellID->993329416] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -254,10 +253,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 27.234711}", + "built" -> "{2020, 1, 5, 18, 52, 47.637956}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -265,11 +264,11 @@ TaggingRules->{ "None", "summary" -> "B0Unique is an option of B0. If set to True, B0[0,0,m2] is replaced with \ (B0[0,m2,m2]+1) and B0[m2,0,m2] simplifies to (B0[0,m2,m2]+2).", - "synonyms" -> {}, "title" -> "B0Unique", "titlemodifier" -> "", - "windowtitle" -> "B0Unique", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/B0Unique"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "B0Unique", + "titlemodifier" -> "", "windowtitle" -> "B0Unique", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/B0Unique"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -278,7 +277,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -287,101 +286,67 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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Note that \ -Abbot's coupling constant convention is consistent with the default setting \ -of GluonVertex." + " \[LineSeparator]yields the 3-gluon vertex in the background field \ +gauge, where the first set of arguments corresponds to the external \ +background field." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"BackgroundGluonVertex", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "mu", ",", "a"}], "}"}], ",", + RowBox[{"{", + RowBox[{"q", ",", "nu", ",", "b"}], "}"}], ",", + RowBox[{"{", + RowBox[{"k", ",", "la", ",", "c"}], "}"}], ",", + RowBox[{"{", + RowBox[{"s", ",", "si", ",", "d"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]yields the 4-gluon vertex, with ", + Cell[BoxData[ + RowBox[{"{", + RowBox[{"p", ",", "mu", ",", "a"}], "}"}]], "InlineFormula"], + " and ", + Cell[BoxData[ + RowBox[{"{", + RowBox[{"k", ",", "la", ",", "c"}], "}"}]], "InlineFormula"], + " denoting the external background fields." }]]} }]], "Usage", GridBoxOptions->{ GridBoxBackground->{ - "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, + "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {None, {None}}, "RowsIndexed" -> {}}}, - CellID->982511436], + CellID->2010081510], Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->582436831], + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1132022700], -Cell[CellGroupData[{ +Cell["", "SectionHeaderSpacer"], Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->666479760], + "The gauge, dimension and the name of the coupling constant are determined \ +by the options ", + ButtonBox["Gauge", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/Gauge", + ButtonNote->"Gauge"], + ", ", + ButtonBox["Dimension", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/Dimension", + ButtonNote->"Dimension"], + " and ", + ButtonBox["CouplingConstant", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/CouplingConstant", + ButtonNote->"CouplingConstant"], + ". 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CellLabel->"Out[5]=", - CellID->686414429] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -1299,16 +1140,11 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[TextData[{ - StyleBox[ButtonBox["GluonVertex", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/GluonVertex", - ButtonNote->"GluonVertex"], - FontFamily->"Verdana"], - "." -}], "Text", - CellTags->"BackgroundGluonVertex", - CellID->648308599] +Cell[TextData[StyleBox[ButtonBox["GluonVertex", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/GluonVertex", + ButtonNote->"GluonVertex"], + FontFamily->"Verdana"]], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -1325,33 +1161,26 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 32.025409}", + "built" -> "{2020, 1, 5, 18, 52, 51.452845}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "BackgroundGluonVertex[{p, mu, a}, {q, nu, b}, {k, la, c}] or \ -BackgroundGluonVertex[p,mu,a , q,nu,b , k,la,c ] yields the 3-gluon vertex in \ -the background field gauge, where the first set of arguments corresponds to \ -the external background field. BackgroundGluonVertex[{p,mu,a}, {q,nu,b}, \ -{k,la,c}, {s,si,d}] or BackgroundGluonVertex[{mu,a}, {nu,b}, {la,c}, {si,d}] \ -or BackgroundGluonVertex[p,mu,a , q,nu,b , k,la,c , s,si,d] or \ -BackgroundGluonVertex[mu,a , nu,b , la,c , si,d ] yields the 4-gluon vertex, \ -with {p,mu,a} and {k,la,c} denoting the external background fields. The \ -gauge, dimension and the name of the coupling constant are determined by the \ -options Gauge, Dimension and CouplingConstant. The Feynman rules are taken \ -from L.Abbot NPB 185 (1981), 189-203; except that all momenta are incoming. \ -Note that Abbot's coupling constant convention is consistent with the default \ -setting of GluonVertex.", "synonyms" -> {}, "title" -> + "BackgroundGluonVertex[{p, mu, a}, {q, nu, b}, {k, la, c}] yields the \ +3-gluon vertex in the background field gauge, where the first set of \ +arguments corresponds to the external background field. \ +BackgroundGluonVertex[{p, mu, a}, {q, nu, b}, {k, la, c}, {s, si, d}] yields \ +the 4-gluon vertex, with {p, mu, a} and {k, la, c} denoting the external \ +background fields.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "BackgroundGluonVertex", "titlemodifier" -> "", "windowtitle" -> "BackgroundGluonVertex", "type" -> "Symbol", "uri" -> "FeynCalc/ref/BackgroundGluonVertex"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -1360,7 +1189,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - 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CellID->1224892054], +Cell[TextData[{ + Cell["Bracket", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -113,9 +145,7 @@ Cell[TextData[{ ButtonNote->"Convolute"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Bracket", - CellID->442526235] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -132,21 +162,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 34.001575}", + "built" -> "{2020, 1, 5, 18, 52, 52.749365}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "Bracket is an option of Convolute, specifying the variable with respect \ -to which the result is collected.", "synonyms" -> {}, "title" -> "Bracket", - "titlemodifier" -> "", "windowtitle" -> "Bracket", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/Bracket"}}, +to which the result is collected.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "Bracket", "titlemodifier" -> "", "windowtitle" -> "Bracket", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/Bracket"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -155,41 +185,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "Bracket"->{ - Cell[3582, 108, 229, 9, 70, "Text", - 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CellID->1224892054], +Cell[TextData[{ + Cell["C0", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -118,7 +153,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1857092055], + CellID->1362566519], Cell[CellGroupData[{ @@ -128,7 +163,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->2101311426], + CellID->2034063019], Cell[CellGroupData[{ @@ -150,12 +185,11 @@ Cell[BoxData[ ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - ImageSize->{182, 15}, + ImageSize->{190, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"C0", - CellLabel->"Out[1]=", - CellID->370674132] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -179,12 +213,11 @@ Cell[BoxData[ ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - ImageSize->{182, 15}, + ImageSize->{190, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"C0", - CellLabel->"Out[2]=", - CellID->240939187] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -212,12 +245,11 @@ Cell[BoxData[ ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - ImageSize->{182, 15}, + ImageSize->{190, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"C0", - CellLabel->"Out[3]=", - CellID->1857619476] + CellLabel->"Out[3]="] }, Open ]] }, Open ]], @@ -265,9 +297,7 @@ Cell[TextData[{ ButtonNote->"PaVeOrder"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"C0", - CellID->1972879175] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -284,10 +314,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - 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False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -319,89 +349,77 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3789, 105, 388, 15, 31, "PrimaryExamplesSection", + Cell[5009, 140, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1857092055]}, + CellID->1362566519]}, "C0"->{ - Cell[4423, 134, 192, 6, 27, "Input", + Cell[5643, 169, 192, 6, 27, "Input", CellTags->"C0", CellID->929768353], - Cell[4618, 142, 411, 15, 36, "Output", - CellTags->"C0", - CellID->370674132], - Cell[5066, 162, 221, 7, 27, "Input", + Cell[5838, 177, 391, 14, 37, "Output", + CellTags->"C0"], + Cell[6266, 196, 221, 7, 27, "Input", CellTags->"C0", CellID->281164286], - Cell[5290, 171, 411, 15, 36, "Output", - CellTags->"C0", - CellID->240939187], - Cell[5738, 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TextClipboardType -> "PlainText"]}, + Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$31673], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/CA", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +96,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["CA", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["CA", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,7 +145,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->698490347], + CellID->1253702121], Cell[CellGroupData[{ @@ -122,7 +155,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->518889655], + CellID->1260543835], Cell[CellGroupData[{ @@ -134,12 +167,11 @@ Cell[BoxData["CA"], "Input", Cell[BoxData[ FormBox[ SubscriptBox["C", "A"], TraditionalForm]], "Output", - ImageSize->{23, 15}, + ImageSize->{28, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"CA", - CellLabel->"Out[1]=", - CellID->1618948920] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -154,12 +186,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["N", TraditionalForm]], "Output", - ImageSize->{19, 15}, + ImageSize->{19, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"CA", - CellLabel->"Out[2]=", - CellID->2112958244] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -171,12 +202,11 @@ Cell[BoxData["SUNN"], "Input", Cell[BoxData[ FormBox["N", TraditionalForm]], "Output", - ImageSize->{19, 15}, + ImageSize->{19, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"CA", - CellLabel->"Out[3]=", - CellID->981411080] + CellLabel->"Out[3]="] }, Open ]] }, Open ]], @@ -212,17 +242,15 @@ Cell[TextData[{ ButtonNote->"SUNSimplify"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"CA", - CellID->831413788] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, 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{}, "title" -> "CA", "titlemodifier" -> "", "windowtitle" -> - "CA", "type" -> "Symbol", "uri" -> "FeynCalc/ref/CA"}, - "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "CA", "titlemodifier" -> + "", "windowtitle" -> "CA", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/CA"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -254,7 +282,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -263,89 +291,77 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline 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CellID->2016701578], + CellID->1884678991], Cell[CellGroupData[{ @@ -126,7 +159,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1606023489], + CellID->2080959042], Cell[CellGroupData[{ @@ -138,12 +171,11 @@ Cell[BoxData["CF"], "Input", Cell[BoxData[ FormBox[ SubscriptBox["C", "F"], TraditionalForm]], "Output", - ImageSize->{24, 15}, + ImageSize->{26, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"CF", - CellLabel->"Out[1]=", - CellID->1771246704] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -162,12 +194,11 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["N", "2"], "-", "1"}], RowBox[{"2", " ", "N"}]], TraditionalForm]], "Output", - ImageSize->{54, 45}, + ImageSize->{54, 38}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"CF", - CellLabel->"Out[2]=", - CellID->1827752058] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -179,12 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{"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 45.677246}", + "built" -> "{2020, 1, 5, 18, 53, 10.624337}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "CF is one of the Casimir operator eigenvalues of SU(N) (CF = (N^2-1)/(2 \ -N)).", "synonyms" -> {}, "title" -> "CF", "titlemodifier" -> "", - "windowtitle" -> "CF", "type" -> "Symbol", "uri" -> "FeynCalc/ref/CF"}, - "SearchTextTranslated" -> ""}, +N)).", "synonyms" -> {}, "tabletags" -> {}, "title" -> "CF", "titlemodifier" -> + "", 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CellID->419675880], + CellID->292765766], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -119,13 +132,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->831323002], - -Cell[CellGroupData[{ - -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"Cases2", - CellID->645978510], + CellID->1337546765], Cell[CellGroupData[{ @@ -150,12 +157,11 @@ Cell[BoxData[ RowBox[{"f", "(", "b", ")"}], ",", RowBox[{"f", "(", RowBox[{"c", ",", "d"}], ")"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{143, 15}, + ImageSize->{156, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Cases2", - CellLabel->"Out[1]=", - CellID->1245535704] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -181,12 +187,11 @@ Cell[BoxData[ RowBox[{"sin", "(", "x", ")"}], ",", RowBox[{"sin", "(", RowBox[{"y", "-", "z"}], ")"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{169, 15}, + ImageSize->{179, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Cases2", - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 47.147097}", + "built" -> "{2020, 1, 5, 18, 53, 19.013365}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -639,11 +602,12 @@ TaggingRules->{ "None", "summary" -> "ChangeDimension[exp, dim] changes all LorentzIndex and Momenta in exp to \ dimension dim (and also Levi-Civita-tensors, Dirac slashes and Dirac \ -matrices).", "synonyms" -> {}, "title" -> "ChangeDimension", "titlemodifier" -> - "", "windowtitle" -> "ChangeDimension", "type" -> "Symbol", "uri" -> +matrices).", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "ChangeDimension", "titlemodifier" -> "", "windowtitle" -> + "ChangeDimension", "type" -> "Symbol", "uri" -> "FeynCalc/ref/ChangeDimension"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -651,8 +615,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$26279], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$39265], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/CheckDB", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,29 +74,35 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["CheckDB", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["CheckDB", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ RowBox[{"CheckDB", "[", RowBox[{"exp", ",", " ", "fil"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "saves [with Put] or retrieves [with Get] exp from a file fil. 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If fil is a file name with full path, the setting \ -of Directory is also ignored." + " \[LineSeparator]saves [with Put] or retrieves [with Get] exp from a \ +file fil. It checks if the setting of the option Directory is a valid \ +directory name and if fil is a valid file name and does exist. If it does, \ +Get[fil] is executed. If fil does not exist, exp gets evaluated and saved to \ +fil. Saving and evaluating can be further controlled with the options \ +ForceSave and NoSave. If the option Check is set to False the return value \ +is what is evaluated [see above]. If Check is set to True the return value is \ +True or False depending on whether the evaluation of exp agrees with what is \ +loaded from fil or fil does not exist. Default value of Check : False." }]]} }]], "Usage", GridBoxOptions->{ @@ -106,44 +113,48 @@ of Directory is also ignored." 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If fil \ +ends with \".Fac\", the setting of Directory is ignored and fil is saved in \ +the \"Factors\" subdirectory of \"Phi\". If fil is a file name with full \ +path, the setting of Directory is also ignored.\ +\>", "Notes", + CellID->1067943069], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "CheckDB", "]"}]], "Input", - CellTags->"CheckDB", - CellLabel->"In[1]:=", - CellID->2004487562], + CellLabel->"In[305]:="], Cell[BoxData[ FormBox[ @@ -158,39 +169,62 @@ Cell[BoxData[ RowBox[{"NoSave", "\[Rule]", "False"}], ",", RowBox[{"Check", "\[Rule]", "False"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{384, 35}, + ImageSize->{355, 34}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"CheckDB", - CellLabel->"Out[1]=", - CellID->1735070400] + CellLabel->"Out[305]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Attributes", "[", "CheckDB", "]"}]], "Input", - CellTags->"CheckDB", - CellLabel->"In[2]:=", - CellID->62116505], + CellLabel->"In[306]:="], Cell[BoxData[ FormBox[ RowBox[{"{", "HoldFirst", "}"}], TraditionalForm]], "Output", - ImageSize->{77, 15}, + ImageSize->{70, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"CheckDB", - CellLabel->"Out[2]=", - CellID->393414258] + CellLabel->"Out[306]="] +}, Open ]] +}, Closed]] }, Open ]], +Cell[CellGroupData[{ + +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->470154859], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->1371204916], + Cell["\<\ The first time the Table function is evaluated and the result saved into the \ test.s file.\ -\>", "Text", - CellTags->"CheckDB", - CellID->1632453918], +\>", "Notes"], Cell[CellGroupData[{ @@ -207,32 +241,28 @@ Cell[BoxData[ RowBox[{"i", ",", "2"}], "}"}]}], "]"}], ",", "\"\\""}], "]"}]], "Input", CellTags->"CheckDB", - 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CellLabel->"In[6]:=", + CellLabel->"In[4]:=", CellID->1720430951] }, Open ]] }, Open ]], @@ -309,8 +335,8 @@ Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"CheckDB", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -319,10 +345,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 51.595649}", + "built" -> "{2020, 1, 5, 18, 53, 20.271790}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -336,17 +362,12 @@ fil. 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Default value of Check : False.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "CheckDB", + "titlemodifier" -> "", "windowtitle" -> "CheckDB", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/CheckDB"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -355,7 +376,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -364,142 +385,102 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[4319, 108, 388, 15, 31, "PrimaryExamplesSection", + Cell[6456, 196, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/ChiralityProjector\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/ChiralityProjector"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"GA\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/GA"], "\<\"FCI\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCI"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/ChiralityProjector\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/ChiralityProjector"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ ChiralityProjector.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$26618], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/ChiralityProjector", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$39702], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/ChiralityProjector", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +96,20 @@ ChiralityProjector.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["ChiralityProjector", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["ChiralityProjector", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -109,6 +144,44 @@ Cell[BoxData[GridBox[{ Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->723076214], + +Cell["", "SectionHeaderSpacer"], + +Cell["\<\ +The shortcut ChiralityProjector is deprecated, please use GA[6] and GA[7] \ +instead!\ +\>", "Notes", + CellID->1067943069] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -124,7 +197,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->489332914], + CellID->1872745401], Cell[CellGroupData[{ @@ -134,7 +207,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->807211662], + CellID->1538912494], Cell[CellGroupData[{ @@ -161,20 +234,22 @@ Cell[BoxData[ OverscriptBox["\[Gamma]", "_"], FormBox["7", TraditionalForm]]}], "}"}], TraditionalForm]], "Output", - ImageSize->{62, 21}, + ImageSize->{64, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"ChiralityProjector", - CellLabel->"Out[1]=", - CellID->1252517379] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracSimplify", "[", - RowBox[{"%", ",", - RowBox[{"DiracSubstitute67", "\[Rule]", "True"}]}], "]"}]], "Input", + RowBox[{ + RowBox[{ + RowBox[{"DiracSimplify", "[", + RowBox[{"#", ",", + RowBox[{"DiracSubstitute67", "\[Rule]", "True"}]}], "]"}], "&"}], "/@", + "%"}]], "Input", CellTags->"ChiralityProjector", CellLabel->"In[2]:=", CellID->2102778570], @@ -197,12 +272,83 @@ Cell[BoxData[ OverscriptBox["\[Gamma]", "_"], FormBox["5", TraditionalForm]], "2"]}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{130, 45}, + ImageSize->{133, 39}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"ChiralityProjector", - CellLabel->"Out[2]=", - CellID->1744568026] + CellLabel->"Out[2]="] +}, Open ]], + +Cell["\<\ +ChiralityProjector is scheduled for removal in the future versions of \ +FeynCalc. The safe alternative is to use GA[6] and GA[7].\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{"GA", "[", "6", "]"}], ",", + RowBox[{"GA", "[", "7", "]"}]}], "}"}]], "Input", + CellLabel->"In[3]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["6", + TraditionalForm]], + TraditionalForm], ",", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["7", + TraditionalForm]], + TraditionalForm]}], "}"}], TraditionalForm]], "Output", + ImageSize->{64, 21}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[3]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"GA", "[", "6", "]"}], "]"}], "===", + RowBox[{"ChiralityProjector", "[", + RowBox[{"+", "1"}], "]"}]}]], "Input", + CellLabel->"In[4]:="], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + ImageSize->{31, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[4]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"GA", "[", "7", "]"}], "]"}], "===", + RowBox[{"ChiralityProjector", "[", + RowBox[{"-", "1"}], "]"}]}]], "Input", + CellLabel->"In[5]:="], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + ImageSize->{31, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[5]="] }, Open ]] }, Open ]], @@ -226,16 +372,10 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["DiracGamma", + StyleBox[ButtonBox["GA", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracGamma", - ButtonNote->"DiracGamma"], - FontFamily->"Verdana"], - ", ", - StyleBox[ButtonBox["DiracMatrix", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData->"paclet:FeynCalc/ref/GA", + ButtonNote->"GA"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["FCI", @@ -244,9 +384,7 @@ Cell[TextData[{ ButtonNote->"FCI"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"ChiralityProjector", - CellID->326424545] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -254,7 +392,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"ChiralityProjector", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -263,10 +401,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 16, 53.037247}", + "built" -> "{2020, 1, 5, 18, 53, 21.485586}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -274,11 +412,11 @@ TaggingRules->{ "None", "summary" -> "ChiralityProjector[+1] denotes 1/2 (1 + \\[Gamma]^5). \ ChiralityProjector[-1] denotes 1/2 (1 + \\[Gamma]^5).", "synonyms" -> {}, - "title" -> "ChiralityProjector", "titlemodifier" -> "", "windowtitle" -> - "ChiralityProjector", "type" -> "Symbol", "uri" -> + "tabletags" -> {}, "title" -> "ChiralityProjector", "titlemodifier" -> "", + "windowtitle" -> "ChiralityProjector", "type" -> "Symbol", "uri" -> "FeynCalc/ref/ChiralityProjector"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -286,8 +424,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -296,75 +435,88 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3819, 111, 387, 15, 31, "PrimaryExamplesSection", + Cell[5850, 184, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->489332914]}, + CellID->1872745401]}, "ChiralityProjector"->{ - Cell[4451, 140, 280, 9, 27, "Input", + Cell[6484, 213, 280, 9, 27, "Input", CellTags->"ChiralityProjector", CellID->336937517], - Cell[4734, 151, 461, 17, 42, "Output", - CellTags->"ChiralityProjector", - CellID->1252517379], - Cell[5232, 173, 215, 6, 27, "Input", + Cell[6767, 224, 440, 16, 42, "Output", + CellTags->"ChiralityProjector"], + Cell[7244, 245, 265, 9, 27, "Input", CellTags->"ChiralityProjector", CellID->2102778570], - 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An option Factor -> True/False can be given, which \ factors the coefficients. The option Head (default Plus) determines the \ applied function to the list of monomials mulitplied by their coefficients.", - "synonyms" -> {}, "title" -> "Collect3", "titlemodifier" -> "", - "windowtitle" -> "Collect3", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/Collect3"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "Collect3", + "titlemodifier" -> "", "windowtitle" -> "Collect3", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/Collect3"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -446,7 +508,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -454,90 +516,86 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["Collecting", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -126,9 +161,7 @@ Cell[TextData[{ ButtonNote->"TID"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Collecting", - CellID->782318945] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -145,10 +178,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 1.040744}", + "built" -> "{2020, 1, 5, 18, 53, 29.305607}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -156,11 +189,11 @@ TaggingRules->{ "None", "summary" -> "Collecting is an option of ScalarProductCancel, Series2, TID and related \ functions. 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CellID->1555962841], + CellID->1626179003], Cell[CellGroupData[{ @@ -120,28 +206,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1898342962], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "Combine", "]"}]], "Input", - CellTags->"Combine", - CellLabel->"In[1]:=", - CellID->194899276], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Expanding", "\[Rule]", "False"}], "}"}], - TraditionalForm]], "Output", - ImageSize->{138, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Combine", - CellLabel->"Out[1]=", - CellID->1836728683] -}, Open ]], + CellID->1194284115], Cell[CellGroupData[{ @@ -155,7 +220,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"c", "-", "d"}], ")"}]}], "e"], "+", "g"}], "]"}]], "Input", CellTags->"Combine", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->809742744], Cell[BoxData[ @@ -168,19 +233,16 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"c", "-", "d"}], ")"}]}], "+", RowBox[{"e", " ", "g"}]}], "e"], TraditionalForm]], "Output", - ImageSize->{139, 43}, + ImageSize->{152, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Combine", - CellLabel->"Out[2]=", - CellID->1151883280] + CellLabel->"Out[1]="] }, Open ]], Cell["\<\ Here the result from Together where the numerator is automatically expanded.\ -\>", "Text", - CellTags->"Combine", - CellID->18145815], +\>", "Notes"], Cell[CellGroupData[{ @@ -194,7 +256,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"c", "-", "d"}], ")"}]}], "e"], "+", "g"}], "]"}]], "Input", CellTags->"Combine", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->990215666], Cell[BoxData[ @@ -206,20 +268,17 @@ Cell[BoxData[ RowBox[{"b", " ", "c"}], "+", RowBox[{"b", " ", "d"}], "+", RowBox[{"e", " ", "g"}]}], "e"], TraditionalForm]], "Output", - ImageSize->{175, 43}, + ImageSize->{197, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Combine", - CellLabel->"Out[3]=", - CellID->1980431254] + CellLabel->"Out[2]="] }, Open ]], Cell["\<\ If the option Expanding is set to True, the result of Combine is the same as \ Together, but uses a slightly different algorithm.\ -\>", "Text", - CellTags->"Combine", - CellID->484864717], +\>", "Notes"], Cell[CellGroupData[{ @@ -235,7 +294,7 @@ Cell[BoxData[ RowBox[{"c", "-", "d"}], ")"}]}], "e"], "+", "g"}], ",", RowBox[{"Expanding", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Combine", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->758144630], Cell[BoxData[ @@ -247,12 +306,11 @@ Cell[BoxData[ RowBox[{"b", " ", "c"}], "+", RowBox[{"b", " ", "d"}], "+", RowBox[{"e", " ", "g"}]}], "e"], TraditionalForm]], "Output", - ImageSize->{175, 43}, + ImageSize->{197, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Combine", - CellLabel->"Out[4]=", - CellID->1932335260] + CellLabel->"Out[3]="] }, Open ]] }, Open ]], @@ -282,9 +340,7 @@ Cell[TextData[{ ButtonNote->"Factor2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Combine", - CellID->2027442052] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -292,7 +348,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"Combine", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -301,10 +357,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 3.435623}", + "built" -> "{2020, 1, 5, 18, 53, 31.336054}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -313,12 +369,12 @@ TaggingRules->{ "Combine[expr] puts terms in a sum over a common denominator,and cancels \ factors in the result. Combine is similar to Together, but accepts the option \ Expanding and works usually better than Together for polynomials involving \ -rationals with sums in the denominator.", "synonyms" -> {}, "title" -> - "Combine", "titlemodifier" -> "", "windowtitle" -> "Combine", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/Combine"}, "SearchTextTranslated" -> - ""}, +rationals with sums in the denominator.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "Combine", "titlemodifier" -> "", "windowtitle" -> "Combine", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/Combine"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -327,7 +383,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -335,116 +391,100 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CompleteSquare[a p^2+b p+c, p] -> -b^2/(4 a)+c+a (b/(2 a)+x)^2. \ CompleteSquare[a p^2+b p+c, p, q] -> {-b^2/(4 a)+c+a q^2, q->b/(2 a)+p}.", - "synonyms" -> {}, "title" -> "Completes", "titlemodifier" -> "", - "windowtitle" -> "Completes", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/Completes"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "CompleteSquare", + "titlemodifier" -> "", "windowtitle" -> "CompleteSquare", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/CompleteSquare"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -389,8 +386,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -399,90 +397,76 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/Contract\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/Contract"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/Contract.\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"Pair\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Pair"], "\<\"CartesianPair\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CartesianPair"], "\<\"DiracSimplify\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/DiracSimplify"], "\<\"MomentumCombine\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/MomentumCombine"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/Contract\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/Contract"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/Contract.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - 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CellID->1224892054], +Cell[TextData[{ + Cell["Contract", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -96,40 +135,39 @@ products of sums of metric tensors and 4-vectors. 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CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->26500400], Cell[BoxData[ @@ -224,39 +286,38 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], + FormBox["\[Nu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{23, 19}, + ImageSize->{26, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Contract", - CellLabel->"Out[3]=", - CellID->246386443] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}], - RowBox[{"DiracMatrix", "[", "\[Mu]", "]"}]}]], "Input", + RowBox[{"GA", "[", "\[Mu]", "]"}]}]], "Input", CellTags->"Contract", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->2005973076], Cell[BoxData[ FormBox[ RowBox[{ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], " ", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], " ", FormBox[ SuperscriptBox[ FormBox[ @@ -265,18 +326,15 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - 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CellLabel->"Out[12]=", - CellID->1318550208] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + FractionBox[ + RowBox[{"Log", "[", + RowBox[{"1", "-", "x"}], "]"}], + RowBox[{"1", "-", "x"}]], ",", "x"}], "]"}], "/.", RowBox[{ - FractionBox[ - RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}], - RowBox[{"1", "-", "x"}]], ",", "x"}], "]"}]], "Input", + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[13]:=", + CellLabel->"In[12]:=", CellID->2055743895], Cell[BoxData[ @@ -511,53 +599,57 @@ Cell[BoxData[ RowBox[{"x", " ", RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], + RowBox[{"log", "(", "x", ")"}]}], RowBox[{"x", "-", "1"}]], TraditionalForm]], "Output", - ImageSize->{182, 42}, + ImageSize->{134, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Convolute", - 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CellLabel->"Out[14]=", - CellID->278611380] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Log", "[", + RowBox[{"1", "-", "x"}], "]"}], ",", "x"}], "]"}], "/.", RowBox[{ - RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}], ",", "x"}], "]"}]], "Input", + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[15]:=", + CellLabel->"In[14]:=", CellID->342391696], Cell[BoxData[ @@ -566,29 +658,30 @@ Cell[BoxData[ RowBox[{"-", "x"}], " ", RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], - TraditionalForm]], "Output", - ImageSize->{187, 15}, + RowBox[{"log", "(", "x", ")"}]}], TraditionalForm]], "Output", + ImageSize->{141, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Convolute", - CellLabel->"Out[15]=", - CellID->1414596566] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + FractionBox["1", + RowBox[{"1", "-", "x"}]], ",", + FractionBox[ + RowBox[{"Log", "[", "x", "]"}], + RowBox[{"1", "-", "x"}]]}], "]"}], "/.", RowBox[{ - FractionBox["1", - RowBox[{"1", "-", "x"}]], ",", - FractionBox[ - RowBox[{"Log", "[", "x", "]"}], - RowBox[{"1", "-", "x"}]]}], "]"}]], "Input", + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[16]:=", + CellLabel->"In[15]:=", CellID->1164478774], Cell[BoxData[ @@ -596,55 +689,57 @@ Cell[BoxData[ RowBox[{"-", FractionBox[ RowBox[{ - RowBox[{"log", "(", "x", ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], + SuperscriptBox["log", "2"], "(", "x", ")"}], SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "2"]]}], TraditionalForm]], "Output", - 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CellLabel->"Out[17]=", - CellID->552984683] + CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", - RowBox[{"x", ",", " ", - RowBox[{"x", " ", - RowBox[{"Log", "[", "x", "]"}]}]}], "]"}]], "Input", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{"x", ",", " ", + RowBox[{"x", " ", + RowBox[{"Log", "[", "x", "]"}]}]}], "]"}], "/.", + RowBox[{ + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[18]:=", + CellLabel->"In[17]:=", CellID->935305016], Cell[BoxData[ @@ -652,197 +747,209 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", SuperscriptBox["x", "2"]}], " ", - RowBox[{"log", "(", "x", ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], - TraditionalForm]], "Output", - ImageSize->{173, 18}, + RowBox[{ + SuperscriptBox["log", "2"], "(", "x", ")"}]}], TraditionalForm]], "Output",\ + + ImageSize->{87, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Convolute", - 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CellLabel->"Out[23]=", - CellID->1394422583] + CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Log", "[", "x", "]"}], ",", "x"}], "]"}], "/.", RowBox[{ - RowBox[{"Log", "[", "x", "]"}], ",", "x"}], "]"}]], "Input", + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[24]:=", + CellLabel->"In[23]:=", CellID->1760428538], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"-", "x"}], " ", - RowBox[{"log", "(", "x", ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], - TraditionalForm]], "Output", - ImageSize->{165, 15}, + RowBox[{ + SuperscriptBox["log", "2"], "(", "x", ")"}]}], TraditionalForm]], "Output",\ + + ImageSize->{79, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Convolute", - CellLabel->"Out[24]=", - CellID->395731069] + CellLabel->"Out[23]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + FractionBox["1", + RowBox[{"1", "-", "x"}]], ",", + FractionBox[ + RowBox[{"Log", "[", + RowBox[{"1", "-", "x"}], "]"}], + RowBox[{"1", "-", "x"}]]}], "]"}], "/.", RowBox[{ - FractionBox["1", - RowBox[{"1", "-", "x"}]], ",", - FractionBox[ - RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}], - RowBox[{"1", "-", "x"}]]}], "]"}]], "Input", + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[25]:=", + CellLabel->"In[24]:=", CellID->379553048], Cell[BoxData[ @@ -852,32 +959,34 @@ Cell[BoxData[ RowBox[{ RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], + RowBox[{"log", "(", "x", ")"}]}], SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "2"]]}], TraditionalForm]], "Output", - ImageSize->{180, 47}, + ImageSize->{131, 40}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Convolute", - CellLabel->"Out[25]=", - CellID->1955426678] + CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", - RowBox[{ - FractionBox[ + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + FractionBox[ + RowBox[{"Log", "[", + RowBox[{"1", "-", "x"}], "]"}], + RowBox[{"1", "-", "x"}]], ",", RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}], - RowBox[{"1", "-", "x"}]], ",", - RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}]}], "]"}]], "Input", + RowBox[{"1", "-", "x"}], "]"}]}], "]"}], "/.", + RowBox[{ + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[26]:=", + CellLabel->"In[25]:=", CellID->1743318528], Cell[BoxData[ @@ -887,45 +996,13 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["log", "2"], "(", RowBox[{"1", "-", "x"}], ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], + RowBox[{"log", "(", "x", ")"}]}], RowBox[{"x", "-", "1"}]], TraditionalForm]], "Output", - ImageSize->{176, 45}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Convolute", - CellLabel->"Out[26]=", - CellID->2109333521] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"ConvoluteTable", "[", - RowBox[{ - FractionBox[ - RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}], - RowBox[{"1", "-", "x"}]], ",", "1"}], "]"}]], "Input", - CellTags->"Convolute", - CellLabel->"In[27]:=", - CellID->1987067231], - -Cell[BoxData[ - FormBox[ - RowBox[{"False", "[", - RowBox[{ - FractionBox[ - RowBox[{"log", "(", - RowBox[{"1", "-", "x"}], ")"}], - RowBox[{"1", "-", "x"}]], ",", "1"}], "]"}], TraditionalForm]], "Output",\ - - ImageSize->{135, 42}, + ImageSize->{127, 38}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Convolute", - CellLabel->"Out[27]=", - CellID->1326268935] + CellLabel->"Out[25]="] }, Open ]] }, Open ]], @@ -961,9 +1038,7 @@ Cell[TextData[{ ButtonNote->"ConvoluteTable"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Convolute", - CellID->573828711] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -980,10 +1055,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 14.110151}", + "built" -> "{2020, 1, 5, 18, 53, 40.194292}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -994,11 +1069,11 @@ TaggingRules->{ Convolute[f, g] is equivalent to Convolute[f, g, x]. Convolute[exp, {x1, x2}] \ assumes that exp is polynomial in x1 and x2. 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CellLabel->"Out[3]=", - CellID->289063823] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ConvoluteTable", "[", - RowBox[{"1", ",", "x"}], "]"}]], "Input", + RowBox[{"1", ",", "x", ",", "x"}], "]"}]], "Input", CellTags->"ConvoluteTable", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->1430786364], Cell[BoxData[ FormBox[ - RowBox[{"False", "[", - RowBox[{"1", ",", "x"}], "]"}], TraditionalForm]], "Output", - ImageSize->{72, 15}, + RowBox[{"1", "-", "x"}], TraditionalForm]], "Output", + ImageSize->{38, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"ConvoluteTable", - CellLabel->"Out[4]=", - CellID->1781441936] + CellLabel->"Out[3]="] }, Open ]] }, Open ]], @@ -247,9 +308,7 @@ Cell[TextData[{ ButtonNote->"Convolute"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"ConvoluteTable", - CellID->538606169] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -266,22 +325,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - 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False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$32472], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/CounterT", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$47766], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/CounterT", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +99,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["CounterT", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["CounterT", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +143,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->771362176], + CellID->236252029], Cell[CellGroupData[{ @@ -117,7 +153,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1163533640], + CellID->2042467455], Cell[CellGroupData[{ @@ -155,32 +191,24 @@ Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{"10", " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - 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CellLabel->"Out[1]=", - CellID->1579672535] + CellLabel->"Out[1]="] }, Open ]] }, Open ]], @@ -354,9 +365,7 @@ Cell[TextData[{ ButtonNote->"QuarkPropagator"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"CounterT", - CellID->1128461713] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -373,21 +382,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 18.762961}", + "built" -> "{2020, 1, 5, 18, 53, 43.977584}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "CounterT is a factor used by GluonPropagator and QuarkPropagator when \ -CounterTerms is set to All.", "synonyms" -> {}, "title" -> "CounterT", - "titlemodifier" -> "", "windowtitle" -> "CounterT", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/CounterT"}, "SearchTextTranslated" -> ""}, +CounterTerms is set to All.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "CounterT", "titlemodifier" -> "", "windowtitle" -> "CounterT", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/CounterT"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -396,7 +405,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -405,61 +414,53 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["CounterTerm", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -93,6 +132,64 @@ Feynman rule functions QuarkGluonVertex, GluonPropagator, QuarkPropagator." 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CounterTerm is also an \ option for the Feynman rule functions QuarkGluonVertex, GluonPropagator, \ -QuarkPropagator.", "synonyms" -> {}, "title" -> "CounterTerm", - "titlemodifier" -> "", "windowtitle" -> "CounterTerm", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/CounterTerm"}, "SearchTextTranslated" -> ""}, +QuarkPropagator.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "CounterTerm", "titlemodifier" -> "", "windowtitle" -> "CounterTerm", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/CounterTerm"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -274,8 +369,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -284,61 +380,65 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["CouplingConstant", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData["CouplingConstant"], "InlineFormula"], - " \[LineSeparator]", - "is an option for several Feynman rule functions and for CovariantD and \ -FieldStrength.\nIn the convention of the subpackage PHI, CouplingConstant is \ -also the head of coupling constants. 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CouplingConstant takes three extra optional arguments, \ +with head RenormalizationState, RenormalizationScheme and ExpansionState \ +respectively. E.g. CouplingConstant[QED[1]] is the unit charge, \ +CouplingConstant[ChPT2[4],1] is the first of the coupling constants of the \ +lagrangian ChPT2[4]. CouplingConstant[a_,b_,c___][i_] := \ +CouplingConstant[a,b,RenormalizationState[i],c].\ +\>", "Notes", + CellID->1067943069] +}, Closed]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -124,16 +192,8 @@ Cell[TextData[{ ButtonData->"paclet:FeynCalc/ref/FieldStrength", ButtonNote->"FieldStrength"], FontFamily->"Verdana"], - ", ", - StyleBox[ButtonBox["\"PHI - A Mathematica package for ChPT calculations\"", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/phi", - ButtonNote->"phi"], - FontFamily->"Verdana"], "." -}], "Text", - CellTags->"CouplingConstant", - CellID->1805142582] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -150,29 +210,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 20.280403}", + "built" -> "{2020, 1, 5, 18, 53, 45.220402}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "CouplingConstant is an option for several Feynman rule functions and for \ -CovariantD and FieldStrength. In the convention of the subpackage PHI, \ -CouplingConstant is also the head of coupling constants. CouplingConstant \ -takes three extra optional arguments, with head RenormalizationState, \ -RenormalizationScheme and ExpansionState respectively. E.g. \ -CouplingConstant[QED[1]] is the unit charge, CouplingConstant[ChPT2[4],1] is \ -the first of the coupling constants of the lagrangian ChPT2[4]. \ -CouplingConstant[a_,b_,c___][i_] := \ -CouplingConstant[a,b,RenormalizationState[i],c].", "synonyms" -> {}, "title" -> +CovariantD and FieldStrength.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "CouplingConstant", "titlemodifier" -> "", "windowtitle" -> "CouplingConstant", "type" -> "Symbol", "uri" -> "FeynCalc/ref/CouplingConstant"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -181,41 +234,39 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "CouplingConstant"->{ - Cell[4121, 114, 610, 21, 70, "Text", - CellTags->"CouplingConstant", - CellID->1805142582]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"CouplingConstant", 7089, 191} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[588, 21, 2277, 52, 70, "AnchorBarGrid", +Cell[588, 21, 3134, 75, 70, "AnchorBarGrid", CellID->1], -Cell[2868, 75, 59, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2930, 78, 893, 18, 70, "Usage", +Cell[3725, 98, 293, 11, 70, "ObjectNameGrid"], +Cell[4021, 111, 397, 11, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3848, 100, 270, 12, 70, "SeeAlsoSection", +Cell[4443, 126, 730, 24, 70, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], +Cell[5176, 152, 31, 0, 70, "SectionHeaderSpacer"], +Cell[5210, 154, 531, 9, 70, "Notes", + CellID->1067943069] +}, Closed]], +Cell[CellGroupData[{ +Cell[5778, 168, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[4121, 114, 610, 21, 70, "Text", - CellTags->"CouplingConstant", - CellID->1805142582] +Cell[6051, 182, 367, 13, 70, "SeeAlso"] }, Open ]], -Cell[4746, 138, 23, 0, 70, "FooterCell"] +Cell[6433, 198, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/CovariantD.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/CovariantD.nb index 3ce4b7da9..1212a9291 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/CovariantD.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/CovariantD.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 44038, 1552] -NotebookOptionsPosition[ 33192, 1206] -NotebookOutlinePosition[ 39872, 1391] -CellTagsIndexPosition[ 39756, 1385] +NotebookDataLength[ 46324, 1621] +NotebookOptionsPosition[ 36914, 1328] +NotebookOutlinePosition[ 42415, 1476] +CellTagsIndexPosition[ 42299, 1470] WindowTitle->CovariantD WindowFrame->Normal*) @@ -59,12 +59,13 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$33159], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$48725], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/CovariantD", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,75 +74,180 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["CovariantD", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["CovariantD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"CovariantD", "[", "mu", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is a generic covariant derivative with Lorentz index mu. With the \ -option-setting Explicit \[Rule] True, an explicit expression for a fermionic \ -field is returned, depending on the setting on the other options.\n\ -CovariantD[x, mu] is a generic covariant derivative with respect to x^mu.\n\ -CovariantD[mu, a, b] is a covariant derivative for a bosonic field; acting on \ -QuantumField[f,{},{a,b}], where f is some field name and a and b are two \ -SU(N) indices. Again, with the option-setting Explicit \[Rule] True, an \ -explicit expression is returned, depending on the setting on the other \ -options.\nCovariantD[OPEDelta, a, b] is a short form for \ -CovariantD[mu,a,b]*FourVector[OPEDelta, mu]. CovariantD[{OPEDelta, a, b}, \ -{n}] yields the product of n operators, where n is an integer. \ -CovariantD[OPEDelta, a, b, {m, n}] gives the expanded form of \ -CovariantD[OPEDelta, a, b]^m up to order g^n for the gluon, where n is an \ -integer and g the coupling constant indicated by the setting of the option \ -CouplingConstant. CovariantD[OPEDelta, {m, n}] gives the expanded form of \ -CovariantD[OPEDelta]^m up to order g^n of the fermionic field.\n\n Possible \ -settings of PartialD are: LeftPartialD, LeftRigthPartialD, RightPartialD. The \ -default setting of QuantumField is GaugeField." + RowBox[{"CovariantD", "[", "\[Mu]", "]"}]], "InlineFormula"], + " \[LineSeparator]is a generic covariant derivative with Lorentz index \ +\[Mu]." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"CovariantD", "[", + RowBox[{"x", ",", "\[Mu]"}], "]"}]], "InlineFormula"], + " \[LineSeparator]is a generic covariant derivative with respect to ", + Cell[BoxData[ + SuperscriptBox["x", "\[Mu]"]], "InlineFormula"], + "." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"CovariantD", "[", + RowBox[{"\[Mu]", ",", "a", ",", "b"}], "]"}]], "InlineFormula"], + " \[LineSeparator]is a covariant derivative for a bosonic field that \ +acts on ", + Cell[BoxData[ + RowBox[{"QuantumField", "[", + RowBox[{"f", ",", + RowBox[{"{", "}"}], ",", + RowBox[{"{", + RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "InlineFormula"], + ", where ", + Cell[BoxData["f"], "InlineFormula"], + " is some field name and ", + Cell[BoxData["a"], "InlineFormula"], + " and ", + Cell[BoxData["b"], "InlineFormula"], + " are two ", + Cell[BoxData[ + RowBox[{"SU", + RowBox[{"(", "N", ")"}]}]], "InlineFormula"], + " indices in the adjoint representation." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"CovariantD", "[", + RowBox[{"OPEDelta", ",", "a", ",", "b"}], "]"}]], "InlineFormula"], + " \[LineSeparator]is a short form for ", + Cell[BoxData[ + RowBox[{ + RowBox[{"CovariantD", "[", + RowBox[{"\[Mu]", ",", "a", ",", "b"}], "]"}], " ", + RowBox[{"FV", "[", + RowBox[{"OPEDelta", ",", " ", "\[Mu]"}], "]"}]}]], "InlineFormula"], + "." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"CovariantD", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"OPEDelta", ",", "a", ",", "b"}], "}"}], ",", + RowBox[{"{", "n", "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]yields the product of ", + Cell[BoxData["n"], "InlineFormula"], + " operators, where ", + Cell[BoxData["n"], "InlineFormula"], + " is an integer." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"CovariantD", "[", + RowBox[{"OPEDelta", ",", "a", ",", "b", ",", + RowBox[{"{", + RowBox[{"m", ",", "n"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]gives the expanded form of ", + Cell[BoxData[ + RowBox[{ + RowBox[{"CovariantD", "[", + RowBox[{"OPEDelta", ",", " ", "a", ",", " ", "b"}], "]"}], "^", + "m"}]], "InlineFormula"], + " up to order ", + Cell[BoxData[ + RowBox[{"g", "^", "n"}]], "InlineFormula"], + " for the gluon, where ", + Cell[BoxData["n"], "InlineFormula"], + " is an integer and ", + Cell[BoxData["g"], "InlineFormula"], + " the coupling constant indicated by the setting of the option ", + ButtonBox["CouplingConstant.", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/CouplingConstant", + ButtonNote->"CouplingConstant"] + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"CovariantD", "[", + RowBox[{"OPEDelta", ",", + RowBox[{"{", + RowBox[{"m", ",", "n"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]gives the expanded form of ", + Cell[BoxData[ + RowBox[{ + RowBox[{"CovariantD", "[", "OPEDelta", "]"}], "^", "m"}]], + "InlineFormula"], + " up to order ", + Cell[BoxData[ + RowBox[{"g", "^", "n"}]], "InlineFormula"], + " of the fermionic field." }]]} }]], "Usage", GridBoxOptions->{ GridBoxBackground->{ - 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"CovariantD[mu] is a generic covariant derivative with Lorentz index mu. \ -With the option-setting Explicit -> True, an explicit expression for a \ -fermionic field is returned, depending on the setting on the other options. \ -CovariantD[x, mu] is a generic covariant derivative with respect to x^mu. \ -CovariantD[mu, a, b] is a covariant derivative for a bosonic field; acting on \ -QuantumField[f,{},{a,b}], where f is some field name and a and b are two \ -SU(N) indices. Again, with the option-setting Explicit -> True, an explicit \ -expression is returned, depending on the setting on the other options. \ -CovariantD[OPEDelta, a, b] is a short form for \ -CovariantD[mu,a,b]*FourVector[OPEDelta, mu]. CovariantD[{OPEDelta, a, b}, \ -{n}] yields the product of n operators, where n is an integer. \ -CovariantD[OPEDelta, a, b, {m, n}] gives the expanded form of \ -CovariantD[OPEDelta, a, b]^m up to order g^n for the gluon, where n is an \ -integer and g the coupling constant indicated by the setting of the option \ -CouplingConstant. CovariantD[OPEDelta, {m, n}] gives the expanded form of \ -CovariantD[OPEDelta]^m up to order g^n of the fermionic field. Possible \ -settings of PartialD are: LeftPartialD, LeftRigthPartialD, RightPartialD. The \ -default setting of QuantumField is GaugeField.", "synonyms" -> {}, "title" -> - "CovariantD", "titlemodifier" -> "", "windowtitle" -> "CovariantD", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/CovariantD"}, - "SearchTextTranslated" -> ""}, + "CovariantD[\\[Mu]] is a generic covariant derivative with Lorentz index \ +\\[Mu]. CovariantD[x, \\[Mu]] is a generic covariant derivative with respect \ +to x^\\[Mu]. CovariantD[\\[Mu], a, b] is a covariant derivative for a bosonic \ +field that acts on QuantumField[f, {}, {a, b}], where f is some field name \ +and a and b are two SU (N) indices in the adjoint representation. \ +CovariantD[OPEDelta, a, b] is a short form for CovariantD[\\[Mu], a, b] \ +FV[OPEDelta, \\[Mu]]. CovariantD[{OPEDelta, a, b}, {n}] yields the product of \ +n operators, where n is an integer. CovariantD[OPEDelta, a, b, {m, n}] gives \ +the expanded form of CovariantD[OPEDelta, a, b]^m up to order g^n for the \ +gluon, where n is an integer and g the coupling constant indicated by the \ +setting of the option CouplingConstant. 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CovariantFieldDerivative has only typesetting \ +indices li1, li2, .... CovariantFieldDerivative has only typesetting \ definitions by default. 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CellID->2083359639] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -203,12 +237,11 @@ Cell[BoxData[ SuperscriptBox["m3", "2"]}], ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - ImageSize->{358, 21}, + ImageSize->{357, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"D0", - CellLabel->"Out[2]=", - CellID->1336389725] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -233,12 +266,11 @@ Cell[BoxData[ SuperscriptBox["m4", "2"]}], ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - ImageSize->{358, 21}, + ImageSize->{357, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"D0", - CellLabel->"Out[3]=", - CellID->871188946] + CellLabel->"Out[3]="] }, Open ]] }, Open ]], @@ -286,9 +318,7 @@ Cell[TextData[{ ButtonNote->"PaVeOrder"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"D0", - CellID->1437823057] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -296,7 +326,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"D0", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -305,10 +335,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 27.348210}", + "built" -> "{2020, 1, 5, 18, 54, 5.753406}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -319,11 +349,11 @@ Passarino-Veltman D0 function. The convention for the arguments is that if \ the denominator of the integrand has the form ([q^2-m1^2] [(q+p1)^2-m2^2] \ [(q+p2)^2-m3^2] [(q+p3)^2-m4^2] ), the first six arguments of D0 are the \ scalar products p10 = p1^2, p12 = (p1-p2)^2, p23 = (p2-p3)^2, p30 = p3^2, p20 \ -= p2^2, p13 = (p1-p3)^2.", "synonyms" -> {}, "title" -> "D0", "titlemodifier" -> - "", "windowtitle" -> "D0", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/D0"}, "SearchTextTranslated" -> ""}, += p2^2, p13 = (p1-p3)^2.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "D0", "titlemodifier" -> "", "windowtitle" -> "D0", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/D0"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -332,7 +362,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -341,89 +371,77 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3958, 109, 388, 15, 31, "PrimaryExamplesSection", + Cell[5178, 144, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1996953412]}, + CellID->1842826744]}, "D0"->{ - Cell[4591, 138, 334, 10, 27, "Input", + Cell[5812, 173, 334, 10, 27, "Input", CellTags->"D0", CellID->1703594627], - Cell[4928, 150, 574, 19, 42, "Output", - CellTags->"D0", - CellID->2083359639], - Cell[5539, 174, 502, 15, 45, "Input", + Cell[6149, 185, 553, 18, 42, "Output", + CellTags->"D0"], + Cell[6739, 208, 502, 15, 45, "Input", CellTags->"D0", CellID->493215523], - Cell[6044, 191, 574, 19, 42, "Output", - CellTags->"D0", - CellID->1336389725], - Cell[6655, 215, 123, 4, 27, "Input", + Cell[7244, 225, 553, 18, 42, "Output", + CellTags->"D0"], + Cell[7834, 248, 123, 4, 27, "Input", CellTags->"D0", CellID->1818800785], - Cell[6781, 221, 573, 19, 42, "Output", - CellTags->"D0", - CellID->871188946], - Cell[7722, 263, 654, 27, 31, "Text", - CellTags->"D0", - CellID->1437823057]} + Cell[7960, 254, 553, 18, 42, "Output", + CellTags->"D0"]} } *) (*CellTagsIndex CellTagsIndex->{ - {"PrimaryExamplesSection", 10522, 342}, - {"D0", 10652, 346} + {"PrimaryExamplesSection", 11629, 372}, + {"D0", 11759, 376} } *) (*NotebookFileOutline Notebook[{ -Cell[574, 21, 2233, 52, 51, "AnchorBarGrid", +Cell[574, 21, 3219, 77, 53, "AnchorBarGrid", CellID->1], -Cell[2810, 75, 45, 1, 42, "ObjectName", - CellID->1224892054], -Cell[2858, 78, 1075, 27, 132, "Usage", +Cell[3796, 100, 279, 11, 45, "ObjectNameGrid"], +Cell[4078, 113, 1075, 27, 137, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3958, 109, 388, 15, 31, "PrimaryExamplesSection", +Cell[5178, 144, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1996953412], + CellID->1842826744], Cell[CellGroupData[{ -Cell[4371, 128, 195, 6, 25, "ExampleSection", - 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CellID->1224892054], +Cell[TextData[{ + Cell["D0Convention", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -109,7 +143,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["D0", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/D0", @@ -122,9 +155,7 @@ Cell[TextData[{ ButtonNote->"Write2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"D0Convention", - CellID->1599988993] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -141,10 +172,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 25.958800}", + "built" -> "{2020, 1, 5, 18, 54, 4.819720}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -153,11 +184,11 @@ TaggingRules->{ "D0Convention is an option for Write2. 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}], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->396336563], + CellID->2095234350], Cell[CellGroupData[{ @@ -147,12 +179,11 @@ Cell[BoxData[ SubscriptBox["p", "2"], ",", SubsuperscriptBox["m", "1", "2"], ",", SubsuperscriptBox["m", "2", "2"]}], ")"}], TraditionalForm]], "Output", - ImageSize->{121, 21}, + ImageSize->{125, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DB0", - CellLabel->"Out[1]=", - CellID->758313713] + CellLabel->"Out[1]="] }, Open ]] }, Open ]], @@ -182,17 +213,15 @@ Cell[TextData[{ ButtonNote->"B0"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"DB0", - CellID->1206126123] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"DB0", TaggingRules->{ "ModificationHighlight" -> 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By default it is set to the Mathematica Dot function. This \ -can in principle be disabled by setting DOT=. (or by commenting out \"DOT = \ -Dot;\" in the file \"FeynCalc.m\"), but then non-commutative products should \ -to be entered like DOT[DiracMatrix[mu], m + DiracSlash[p], DiracMatrix[mu] ] \ -etc.", "synonyms" -> {}, "title" -> "DOT", "titlemodifier" -> "", - "windowtitle" -> "DOT", "type" -> "Symbol", "uri" -> +multiplication. By default it is set to the Mathematica Dot function. ", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DOT", "titlemodifier" -> + "", "windowtitle" -> "DOT", "type" -> "Symbol", "uri" -> "FeynCalc/ref/DOT"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -166,41 +229,39 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "DOT"->{ - Cell[3958, 114, 247, 10, 70, "Text", - CellTags->"DOT", - CellID->1131348229]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"DOT", 6283, 176} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[575, 21, 2237, 52, 70, "AnchorBarGrid", +Cell[575, 21, 2987, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2815, 75, 46, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2864, 78, 796, 18, 70, "Usage", +Cell[3565, 97, 280, 11, 70, "ObjectNameGrid"], +Cell[3848, 110, 551, 16, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3685, 100, 270, 12, 70, "SeeAlsoSection", +Cell[4424, 130, 730, 24, 70, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], +Cell[5157, 156, 31, 0, 70, "SectionHeaderSpacer"], +Cell[5191, 158, 309, 6, 70, "Notes", + CellID->1067943069] +}, Closed]], +Cell[CellGroupData[{ +Cell[5537, 169, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3958, 114, 247, 10, 70, "Text", - CellTags->"DOT", - CellID->1131348229] +Cell[5810, 183, 196, 7, 70, "SeeAlso"] }, Open ]], -Cell[4220, 127, 23, 0, 70, "FooterCell"] +Cell[6021, 193, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/DataType.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/DataType.nb index 387b5f7ef..8fd0d2b6b 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/DataType.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/DataType.nb @@ -3,69 +3,92 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 25472, 942] -NotebookOptionsPosition[ 16187, 632] -NotebookOutlinePosition[ 21760, 799] -CellTagsIndexPosition[ 21648, 793] +NotebookDataLength[ 25911, 961] +NotebookOptionsPosition[ 17435, 683] +NotebookOutlinePosition[ 22260, 826] +CellTagsIndexPosition[ 22148, 820] WindowTitle->DataType WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/DataType\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/DataType"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/DataType.\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"DeclareNonCommutative\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/DeclareNonCommutative"]}, + + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/DataType\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/DataType"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/DataType.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$34891], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/DataType", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$56303], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/DataType", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,60 +96,32 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["DataType", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["DataType", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"DataType", "[", - RowBox[{"exp", ",", " ", "type"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "= True defines the object exp to have data-type type. DataType[exp1, \ -exp2, ..., type] defines the objects exp1, exp2, ...to have data-type type. \ -The default setting is DataType[__, _] := False. 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The default setting is DataType[__, _] := False. To assign a \ +certain data-type, do, e.g., DataType[x, PositiveInteger] = True." }]]} }]], "Usage", GridBoxOptions->{ @@ -137,6 +132,86 @@ DataTypes: ", Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1205239117], + +Cell["", "SectionHeaderSpacer"], + +Cell[TextData[{ + "Currently used DataTypes: ", + ButtonBox["NonCommutative", + BaseStyle->"AddOnsLink", + ButtonData:>"NonCommutative", + ButtonNote->"NonCommutative"], + ", ", + ButtonBox["PositiveInteger", + BaseStyle->"AddOnsLink", + ButtonData:>"PositiveInteger", + ButtonNote->"PositiveInteger"], + ", ", + ButtonBox["NegativeInteger", + BaseStyle->"AddOnsLink", + ButtonData:>"NegativeInteger", + ButtonNote->"NegativeInteger"], + ", ", + ButtonBox["PositiveNumber", + BaseStyle->"AddOnsLink", + ButtonData:>"PositiveNumber", + ButtonNote->"PositiveNumber"], + ", ", + ButtonBox["FreeIndex", + BaseStyle->"AddOnsLink", + ButtonData:>"FreeIndex", + ButtonNote->"FreeIndex"], + ", ", + ButtonBox["GrassmannParity", + BaseStyle->"AddOnsLink", + ButtonData:>"GrassmannParity", + ButtonNote->"GrassmannParity"] +}], "Notes", + CellID->1067943069], + +Cell[TextData[{ + "If loaded, PHI adds the DataTypes: ", + ButtonBox["UMatrix", + BaseStyle->"AddOnsLink", + ButtonData:>"UMatrix", + ButtonNote->"UMatrix"], + ", ", + ButtonBox["UScalar", + BaseStyle->"AddOnsLink", + ButtonData:>"UScalar", + ButtonNote->"UScalar"], + "." +}], "Notes"] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -152,7 +227,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1824112295], + CellID->1658663371], Cell[CellGroupData[{ @@ -162,11 +237,9 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->576268529], + CellID->28126502], -Cell["NonCommutative is just a data-type.", "Text", - CellTags->"DataType", - CellID->1046565146], +Cell["NonCommutative is just a data-type.", "Notes"], Cell[BoxData[ RowBox[{ @@ -199,18 +272,17 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"2", " ", "a"}], ")"}], ".", "f"}]}], TraditionalForm]], "Output",\ - ImageSize->{105, 15}, + ImageSize->{115, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[2]=", - CellID->353088944] + CellLabel->"Out[2]="] }, Open ]], Cell["\<\ Since \"f \"and \"g\" have DataType NonCommutative the function DotSimplify \ extracts only \"a\" out of the noncommutative product.\ -\>", "Text", +\>", "Notes", CellTags->"DataType", CellID->2142748174], @@ -228,12 +300,11 @@ Cell[BoxData[ RowBox[{"f", ".", "g"}], "-", RowBox[{"2", " ", "a", " ", RowBox[{"g", ".", "f"}]}]}], TraditionalForm]], "Output", - ImageSize->{92, 15}, + ImageSize->{101, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[3]=", - CellID->1728093744] + CellLabel->"Out[3]="] }, Open ]], Cell[BoxData[ @@ -312,12 +383,11 @@ Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "z"]}], TraditionalForm]], "Output", - ImageSize->{152, 15}, + ImageSize->{159, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[7]=", - CellID->538518934] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -338,12 +408,11 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "z"], "-", "1"}], TraditionalForm]], "Output",\ - ImageSize->{117, 15}, + ImageSize->{123, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[8]=", - CellID->1174286962] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -359,12 +428,11 @@ Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "z"], TraditionalForm]], "Output", - ImageSize->{42, 15}, + ImageSize->{44, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[9]=", - CellID->1170774235] + CellLabel->"Out[9]="] }, Open ]], Cell[BoxData[ @@ -380,7 +448,7 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"DataType", "[", - RowBox[{"m", ",", "ganzeZahl"}], "]"}], "=", "True"}], ";"}]], "Input", + RowBox[{"m", ",", "integer"}], "]"}], "=", "True"}], ";"}]], "Input", CellTags->"DataType", CellLabel->"In[11]:=", CellID->585585082], @@ -397,7 +465,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "^", "p_"}], "/;", RowBox[{"DataType", "[", - RowBox[{"p", ",", "ganzeZahl"}], "]"}]}], "\[RuleDelayed]", "1"}], + RowBox[{"p", ",", "integer"}], "]"}]}], "\[RuleDelayed]", "1"}], "}"}]}]}], ";"}]], "Input", CellTags->"DataType", CellLabel->"In[12]:=", @@ -430,12 +498,11 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "n"], " ", "x"}]}], TraditionalForm]], "Output", - ImageSize->{112, 15}, + ImageSize->{118, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[13]=", - CellID->41432149] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -454,12 +521,11 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "n"], " ", "x"}], "+", "1"}], TraditionalForm]], "Output", - ImageSize->{77, 15}, + ImageSize->{82, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[14]=", - CellID->1117139634] + CellLabel->"Out[14]="] }, Open ]], Cell[BoxData[ @@ -494,9 +560,7 @@ Cell[BoxData[ Cell["\<\ Certain FeynCalc objects have DataType PositiveInteger set to True.\ -\>", "Text", - CellTags->"DataType", - CellID->1789811013], +\>", "Notes"], Cell[CellGroupData[{ @@ -509,17 +573,14 @@ Cell[BoxData[ Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", - ImageSize->{33, 15}, + ImageSize->{31, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[18]=", - CellID->1327437721] + CellLabel->"Out[18]="] }, Open ]], -Cell["PowerSimplify uses the DataType information.", "Text", - CellTags->"DataType", - CellID->2130197226], +Cell["PowerSimplify uses the DataType information.", "Notes"], Cell[CellGroupData[{ @@ -536,12 +597,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{11, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[19]=", - CellID->410693850] + CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ @@ -582,12 +642,11 @@ Cell[BoxData[ "Floor"]}], "+", RowBox[{"\[ImaginaryI]", " ", "\[Pi]", " ", "m"}]}]]}], TraditionalForm]], "Output", - ImageSize->{233, 36}, + ImageSize->{229, 27}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DataType", - CellLabel->"Out[20]=", - CellID->359212449] + CellLabel->"Out[20]="] }, Open ]] }, Open ]], @@ -616,16 +675,8 @@ Cell[TextData[{ ButtonData->"paclet:FeynCalc/ref/DeclareNonCommutative", ButtonNote->"DeclareNonCommutative"], FontFamily->"Verdana"], - ", ", - StyleBox[ButtonBox["\"PHI - A Mathematica package for ChPT calculations\"", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/phi", - ButtonNote->"phi"], - FontFamily->"Verdana"], "." -}], "Text", - CellTags->"DataType", - CellID->1742681066] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -633,7 +684,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"DataType", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -642,10 +693,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 29.100598}", + "built" -> "{2020, 1, 5, 18, 54, 6.998476}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -654,14 +705,12 @@ TaggingRules->{ "DataType[exp, type] = True defines the object exp to have data-type \ type. DataType[exp1, exp2, ..., type] defines the objects exp1, exp2, ...to \ have data-type type. The default setting is DataType[__, _] := False. To \ -assign a certain data-type, do, e.g., DataType[x, PositiveInteger] = True. \ -Currently used DataTypes: NonCommutative, PositiveInteger, NegativeInteger, \ -PositiveNumber, FreeIndex, GrassmannParity PHI adds the DataTypes: UMatrix, \ -UScalar.", "synonyms" -> {}, "title" -> "DataType", "titlemodifier" -> "", - "windowtitle" -> "DataType", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/DataType"}, "SearchTextTranslated" -> ""}, +assign a certain data-type, do, e.g., DataType[x, PositiveInteger] = True.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DataType", + "titlemodifier" -> "", "windowtitle" -> "DataType", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/DataType"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -670,7 +719,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -679,271 +728,241 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[4757, 139, 388, 15, 31, "PrimaryExamplesSection", + Cell[6576, 214, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1824112295]}, + CellID->1658663371]}, "DataType"->{ - Cell[5368, 166, 95, 2, 32, "Text", - CellTags->"DataType", - CellID->1046565146], - Cell[5466, 170, 240, 8, 27, "Input", + Cell[7241, 243, 240, 8, 27, "Input", CellTags->"DataType", CellID->1643430273], - Cell[5731, 182, 242, 9, 27, "Input", + Cell[7506, 255, 242, 9, 27, "Input", CellTags->"DataType", CellID->370505351], - Cell[5976, 193, 344, 13, 36, "Output", 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+Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -114,7 +191,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->164674075], + CellID->1801745377], Cell[CellGroupData[{ @@ -124,7 +201,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->986793998], + CellID->1300323557], Cell[CellGroupData[{ @@ -141,12 +218,11 @@ Cell[BoxData[ FormBox[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{57, 15}, + ImageSize->{59, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DeltaFunction", - CellLabel->"Out[1]=", - CellID->1935055166] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -167,12 +243,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{"f", "(", "1", ")"}], TraditionalForm]], "Output", - ImageSize->{33, 15}, + ImageSize->{34, 16}, 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NOTICE: After \ -version 4 of Mathematica there is a built-in function, DiracDelta, with \ -comparable properties.", "synonyms" -> {}, "title" -> "DeltaFunction", + "DeltaFunction[x] is the Dirac delta-function \\[Delta](x).", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DeltaFunction", "titlemodifier" -> "", "windowtitle" -> "DeltaFunction", "type" -> "Symbol", "uri" -> "FeynCalc/ref/DeltaFunction"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -344,8 +415,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -354,117 +426,111 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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Eventually you want to substitute \ -DiracBasis by Identity (or set: DiracBasis[1] = S; \ -DiracBasis[DiracMatrix[mu]] = P; etc.)." + " \[LineSeparator]is a head which is wrapped around Dirac structures \ +(and the 1) as a result of the function ", + ButtonBox["DiracReduce", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracReduce", + ButtonNote->"DiracReduce"], + "." }]]} }]], "Usage", GridBoxOptions->{ @@ -95,6 +129,47 @@ DiracBasis[DiracMatrix[mu]] = P; etc.)." 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OverscriptBox[ + RowBox[{"-", FormBox["p", - TraditionalForm], "_"], + TraditionalForm]}], TraditionalForm], FormBox["\<\",\"\>", TraditionalForm], @@ -197,12 +457,10 @@ Cell[BoxData[ TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{100, 18}, + ImageSize->{125, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"DiracEquation", - CellLabel->"Out[2]=", - CellID->1802781574] + CellLabel->"Out[8]="] }, Open ]] }, Open ]], @@ -225,16 +483,11 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[TextData[{ - StyleBox[ButtonBox["DiracSimplify", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], - FontFamily->"Verdana"], - "." -}], "Text", - CellTags->"DiracEquation", - CellID->1088896111] +Cell[TextData[StyleBox[ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + FontFamily->"Verdana"]], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -242,7 +495,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"DiracEquation", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -251,22 +504,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - 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ImageSize->{135, 18}, + ImageSize->{151, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DiracGamma", - CellLabel->"Out[7]=", - CellID->754251999] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a3", "=", - RowBox[{ - RowBox[{"GAD", "[", "\[Mu]", "]"}], ".", - RowBox[{"GSD", "[", - RowBox[{"p", "-", "q"}], "]"}], ".", - RowBox[{"GSD", "[", "q", "]"}], ".", - RowBox[{"GAD", "[", "\[Mu]", "]"}]}]}]], "Input", + RowBox[{ + RowBox[{"GAD", "[", "\[Mu]", "]"}], ".", + RowBox[{"GSD", "[", + RowBox[{"p", "-", "q"}], "]"}], ".", + RowBox[{"GSD", "[", "q", "]"}], ".", + RowBox[{"GAD", "[", "\[Mu]", "]"}]}]], "Input", CellTags->"DiracGamma", CellLabel->"In[8]:=", CellID->667969280], @@ -450,19 +522,17 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{165, 19}, + ImageSize->{185, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DiracGamma", - CellLabel->"Out[8]=", - CellID->712838090] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a4", "=", - RowBox[{"DiracTrick", "[", "a3", "]"}]}]], "Input", + RowBox[{"DiracTrick", "[", "%", "]"}]], "Input", CellTags->"DiracGamma", CellLabel->"In[9]:=", CellID->1907296195], @@ -476,11 +546,13 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - FormBox["p", - TraditionalForm], "-", - FormBox["q", - TraditionalForm]}], + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -511,19 +583,17 @@ Cell[BoxData[ FormBox["q", TraditionalForm], TraditionalForm]}], ")"}]}]}]}], TraditionalForm]], "Output", - ImageSize->{282, 17}, + ImageSize->{311, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DiracGamma", - CellLabel->"Out[9]=", - CellID->1654426864] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - 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StyleBox[ButtonBox["DiracMatrix", + StyleBox[ButtonBox["GA", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData->"paclet:FeynCalc/ref/GA", + ButtonNote->"GA"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["DiracSimplify", @@ -633,10 +845,10 @@ Cell[TextData[{ ButtonNote->"DiracSimplify"], FontFamily->"Verdana"], ", ", - StyleBox[ButtonBox["DiracSlash", + StyleBox[ButtonBox["GS", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], + ButtonData->"paclet:FeynCalc/ref/GS", + ButtonNote->"GS"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["DiracTrick", @@ -645,9 +857,7 @@ Cell[TextData[{ ButtonNote->"DiracTrick"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"DiracGamma", - CellID->1692507192] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -664,25 +874,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 17, 51.472111}", + "built" -> "{2020, 1, 5, 18, 54, 30.446317}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "DiracGamma[x, dim] is the head of all Dirac matrices and slashes (in the \ -internal representation). Use DiracMatrix (or GA, GAD) and DiracSlash (or GS, \ -GSD) for manual (short) input. DiracGamma[x, 4] simplifies to DiracGamma[x]. \ -DiracGamma[5] is \\[Gamma]^5. DiracGamma[6] is (1 + \\[Gamma]^5)/2. \ -DiracGamma[7] is (1 - \\[Gamma]^5)/2.", "synonyms" -> {}, "title" -> - "DiracGamma", "titlemodifier" -> "", "windowtitle" -> "DiracGamma", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/DiracGamma"}, - "SearchTextTranslated" -> ""}, +internal representation). Use GA, GAD, GS or GSD for manual (short) input.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DiracGamma", + "titlemodifier" -> "", "windowtitle" -> "DiracGamma", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/DiracGamma"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -691,7 +898,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -700,199 +907,197 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[4065, 117, 387, 15, 31, "PrimaryExamplesSection", + Cell[6293, 201, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - 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The ", StyleBox["Mathematica", FontSlant->"Italic"], " Dot \".\" is used as non-commutative multiplication operator." -}], "Text", +}], "Notes", CellTags->"DiracMatrix", CellID->477550014], @@ -228,7 +295,7 @@ Cell[BoxData[ RowBox[{"DiracMatrix", "[", "\[Mu]", "]"}], ".", RowBox[{"DiracMatrix", "[", "\[Nu]", "]"}]}]], "Input", CellTags->"DiracMatrix", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->216003987], Cell[BoxData[ @@ -246,12 +313,11 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{45, 17}, + ImageSize->{49, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DiracMatrix", - CellLabel->"Out[3]=", - CellID->527384282] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -261,7 +327,7 @@ Cell[BoxData[ RowBox[{"DiracMatrix", "[", "\[Alpha]", "]"}], "//", "StandardForm"}]], "Input", CellTags->"DiracMatrix", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->1775640770], Cell[BoxData[ @@ -271,18 +337,19 @@ Cell[BoxData[ ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DiracMatrix", - CellLabel->"Out[4]//StandardForm=", - CellID->209169397] + CellLabel->"Out[3]//StandardForm="] }, Open ]], +Cell["\<\ +DiracMatrix is scheduled for removal in the future versions of FeynCalc. 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"language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "DiracReduce[exp] reduces all four-dimensional Dirac matrices in exp to \ -the standard basis (S,P,V,A,T) using the Chisholm identity (see Chisholm). In \ -the result the basic Dirac structures are wrapped with a head DiracBasis. \ -I.e., S corresponds to DiracBasis[1], P : DiracBasis[DiracMatrix[5]], V: \ -DiracBasis[DiracMatrix[mu]], A: DiracBasis[DiracMatrix[mu, 5]], T: \ -DiracBasis[DiracSigma[DiracMatrix[mu, nu]]]. By default DiracBasis is \ -substituted to Identity. Notice that the result of DiracReduce is given in \ -the FeynCalcExternal-way, i.e.,evtl. you may have to use FeynCalcInternal on \ -the result.", "synonyms" -> {}, "title" -> "DiracReduce", "titlemodifier" -> - "", "windowtitle" -> "DiracReduce", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/DiracReduce"}, "SearchTextTranslated" -> ""}, + "DiracReduce[exp] reduces all 4-dimensional Dirac matrices in exp to the \ +standard basis (S, P, V, A, T) using the Chisholm identity. ", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DiracReduce", + "titlemodifier" -> "", "windowtitle" -> "DiracReduce", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/DiracReduce"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -638,8 +1168,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -648,184 +1179,180 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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DiracSigmaExplict is also an option of DiracSimplify.", - "synonyms" -> {}, "title" -> "DiracSigmaExplicit", "titlemodifier" -> "", - "windowtitle" -> "DiracSigmaExplicit", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/DiracSigmaExplicit"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DiracSigmaExplicit", + "titlemodifier" -> "", "windowtitle" -> "DiracSigmaExplicit", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/DiracSigmaExplicit"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -264,8 +473,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -274,75 +484,90 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["DiracSimpCombine", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData["DiracSimpCombine"], "InlineFormula"], - " \[LineSeparator]", - "is an option for DiracSimplify. If set to True, sums of DiracGamma's \ -will be merged as much as possible in DiracGamma[ .. + .. + ]'s." + " \[LineSeparator]is an option for ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + ". If set to ", + Cell[BoxData["True"], "InlineFormula"], + ", ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + " uses the function ", + ButtonBox["DiracGammaCombine", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracGammaCombine", + ButtonNote->"DiracGammaCombine"], + " internally." }]]} }]], "Usage", GridBoxOptions->{ @@ -92,6 +139,47 @@ will be merged as much as possible in DiracGamma[ .. + .. + ]'s." 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If set to True, sums of \ -DiracGamma's will be merged as much as possible in DiracGamma[ .. + .. + \ -]'s.", "synonyms" -> {}, "title" -> "DiracSimpCombine", "titlemodifier" -> "", - "windowtitle" -> "DiracSimpCombine", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/DiracSimpCombine"}}, + "DiracSimpCombine is an option for DiracSimplify. If set to True, \ +DiracSimplify uses the function DiracGammaCombine internally.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DiracSimpCombine", + "titlemodifier" -> "", "windowtitle" -> "DiracSimpCombine", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/DiracSimpCombine"}}, CellContext->"Global`", FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->Notebook[{ @@ -164,34 +246,32 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "DiracSimpCombine"->{ - Cell[3682, 108, 266, 10, 70, "Text", - CellTags->"DiracSimpCombine", - CellID->1079786131]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"DiracSimpCombine", 5865, 167} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[588, 21, 2277, 52, 70, "AnchorBarGrid", +Cell[588, 21, 3044, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2868, 75, 59, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2930, 78, 454, 12, 70, "Usage", +Cell[3635, 97, 293, 11, 70, "ObjectNameGrid"], +Cell[3931, 110, 909, 27, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3409, 94, 270, 12, 70, "SeeAlsoSection", +Cell[4865, 141, 730, 24, 70, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], +Cell[5598, 167, 31, 0, 70, "SectionHeaderSpacer"], +Cell[5632, 169, 235, 8, 70, "Notes", + CellID->1067943069] +}, Closed]], +Cell[CellGroupData[{ +Cell[5904, 182, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3682, 108, 266, 10, 70, "Text", - CellTags->"DiracSimpCombine", - CellID->1079786131] +Cell[6177, 196, 187, 4, 70, "SeeAlso"] }, Open ]], -Cell[3963, 121, 23, 0, 70, "FooterCell"] +Cell[6379, 203, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/DiracSimplify.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/DiracSimplify.nb index f2f6e2520..7cba1b08a 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/DiracSimplify.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/DiracSimplify.nb @@ -3,69 +3,118 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 48297, 1682] -NotebookOptionsPosition[ 36204, 1284] -NotebookOutlinePosition[ 43105, 1488] -CellTagsIndexPosition[ 42950, 1481] +NotebookDataLength[ 172610, 6280] +NotebookOptionsPosition[ 157236, 5783] +NotebookOutlinePosition[ 160902, 5887] +CellTagsIndexPosition[ 160744, 5880] WindowTitle->DiracSimplify WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/DiracSimplify\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/DiracSimplify"]}, Visible -> False]]; 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For every other scheme, please recheck your input expressions and \ +ensure that all matrices, spinors and tensors are purely D-dimensional. You \ +might want to use FCGetDimensions[exp] to find the offending terms and fix \ +them by hand or ChangeDimension[exp,D] to convert the whole expression to \ +D-dimensions. If you explicitly intend to use the t'Hooft-Veltman scheme, \ +please activate it via FCSetDiracGammaScheme[\\\"BMHV\\\"]. \ +\\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ +ButtonFrame->None, ButtonData:>\\\"paclet:FeynCalc/ref/DiracTrace\\\", \ +ButtonNote -> \\\"FeynCalc`DiracTrace::mixmsg\\\"]\\)\"\>"}], + TraditionalForm]], "Message", "MSG", + CellLabel->"During evaluation of In[2]:="], + +Cell[BoxData[ + FormBox["$Aborted", TraditionalForm]], "Output", + ImageSize->{58, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[2]="] +}, Open ]], + +Cell[TextData[{ + "By default, FeynCalc uses the naive dimensional regularization (NDR) \ +scheme, where all Dirac matrices are taken to be ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional. Therefore, in NDR you may not have mixtures of Dirac matrices \ +living in ", + Cell[BoxData["D"], "InlineFormula"], + " and 4 dimensions. However, such expressions are possible in the \ +t'Hooft-Veltman-Breitenlohner-Maison (BMHV) scheme." +}], "Notes"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}], ";"}]], "Input",\ + + CellLabel->"In[3]:="], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSimplify", "[", + RowBox[{ + RowBox[{"GAD", "[", "\[Mu]", "]"}], ".", + RowBox[{"(", + RowBox[{ + RowBox[{"GA", "[", "p", "]"}], "+", "m"}], ")"}], ".", + RowBox[{"GAD", "[", "\[Mu]", "]"}]}], "]"}]], "Input", + CellLabel->"In[4]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"-", + RowBox[{"D", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]]}]}], "+", + RowBox[{"2", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]]}], "+", + RowBox[{"D", " ", "m"}]}], TraditionalForm]], "Output", + ImageSize->{154, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[4]="] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}], ";"}]], "Input",\ + + CellLabel->"In[5]:="], + +Cell[TextData[{ + "The BMHV scheme is a special prescription for handling ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " in dimensional regularization. Do not activate this scheme mindlessly just \ +to get rid of errors from ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + "! If you are doing a calculation in NDR or a calculation that does not \ +involve ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + ", better make sure that your input expressions are correctly written to be ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional objects." +}], "Notes"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[TextData[{ + "Traces that contain an odd number of ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " or chirality projectors cannot be calculated unambigously in NDR. To \ +avoid inconsistencies, ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + " will refuse to evaluate such traces in NDR." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracTrace", "[", + RowBox[{ + RowBox[{"GAD", "[", + RowBox[{ + "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "\[Alpha]", + ",", "\[Beta]"}], "]"}], ".", + RowBox[{"GA", "[", "5", "]"}]}], "]"}]], "Input", + CellLabel->"In[1]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox[ + RowBox[{ + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], + TraditionalForm]}], + TraditionalForm], ")"}], TraditionalForm]], "Output", + ImageSize->{193, 22}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[1]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[2]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox[ + RowBox[{ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]]}], + TraditionalForm], ")"}], TraditionalForm]], "Output", + ImageSize->{193, 22}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[2]="] +}, Open ]], + +Cell["\<\ +Such traces can be consistently calculated in the BMHV scheme. 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Whether the trace is \ -evaluated depends on the option DiracTraceEvaluate. Direct trace evaluation \ -should be performed with TR (or Tr). The argument expr may be a product of \ -Dirac matrices or slashes separated by the Mathematica Dot (.). For comments \ -regarding \\[Gamma]^5schemes see the notes for TR.", "synonyms" -> {}, - "title" -> "DiracTrace", "titlemodifier" -> "", "windowtitle" -> - "DiracTrace", "type" -> "Symbol", "uri" -> "FeynCalc/ref/DiracTrace"}, - "SearchTextTranslated" -> ""}, + "DiracTrace[exp] is the head of Dirac traces. By default the trace is not \ +evaluated. The evaluation occurs only when the option DiracTraceEvaluate is \ +set to True. 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If set to False, Dirac traces remain unevaluated.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DiracTraceEvaluate", + "titlemodifier" -> "", "windowtitle" -> "DiracTraceEvaluate", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/DiracTraceEvaluate"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -163,41 +249,39 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "DiracTraceEvaluate"->{ - Cell[3647, 108, 400, 16, 70, "Text", - CellTags->"DiracTraceEvaluate", - CellID->1627432666]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"DiracTraceEvaluate", 5931, 173} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[590, 21, 2285, 52, 70, "AnchorBarGrid", +Cell[590, 21, 3150, 76, 70, "AnchorBarGrid", CellID->1], -Cell[2878, 75, 61, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2942, 78, 407, 12, 70, "Usage", +Cell[3743, 99, 295, 11, 70, "ObjectNameGrid"], +Cell[4041, 112, 762, 22, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3374, 94, 270, 12, 70, "SeeAlsoSection", +Cell[4828, 138, 730, 24, 70, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], +Cell[5561, 164, 31, 0, 70, "SectionHeaderSpacer"], +Cell[5595, 166, 368, 13, 70, "Notes", + CellID->1067943069] +}, Closed]], +Cell[CellGroupData[{ +Cell[6000, 184, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3647, 108, 400, 16, 70, "Text", - CellTags->"DiracTraceEvaluate", - CellID->1627432666] +Cell[6273, 198, 361, 12, 70, "SeeAlso"] }, Open ]], -Cell[4062, 127, 23, 0, 70, "FooterCell"] +Cell[6649, 213, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/DiracTrick.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/DiracTrick.nb index e1a3bdea2..9e667faaf 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/DiracTrick.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/DiracTrick.nb @@ -3,69 +3,102 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 41960, 1355] -NotebookOptionsPosition[ 32968, 1054] -NotebookOutlinePosition[ 38270, 1213] -CellTagsIndexPosition[ 38118, 1206] +NotebookDataLength[ 23155, 844] +NotebookOptionsPosition[ 18871, 711] +NotebookOutlinePosition[ 20942, 767] +CellTagsIndexPosition[ 20857, 762] WindowTitle->DiracTrick WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/DiracTrick\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/DiracTrick"]}, Visible -> False]]; 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CellID->1224892054], +Cell[TextData[{ + Cell["DotExpand", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"DotExpand", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "expands DOT products in expr." + RowBox[{"DotExpand", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]expands dot products in ", + Cell[BoxData["exp"], "InlineFormula"], + "." }]]} }]], "Usage", GridBoxOptions->{ @@ -103,35 +142,56 @@ Cell[TextData[{ Spacer[6]]]], "Examples", "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] + Cell["(3)", "ExampleCount"] }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->2006956772], + CellID->173805481], Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] + Cell["(3)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1248977172], + CellID->404488661], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DotExpand", "[", - RowBox[{"DOT", "[", + RowBox[{"DOT", "[", + RowBox[{ RowBox[{ + RowBox[{"a", " ", "x"}], "+", + RowBox[{"b", " ", "y"}], "+", + RowBox[{"c", " ", "z"}]}], ",", + RowBox[{"d", "+", "e", "+", "f"}]}], "]"}]], "Input", + CellLabel->"In[1]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"(", RowBox[{ RowBox[{"a", " ", "x"}], "+", RowBox[{"b", " ", "y"}], "+", - RowBox[{"c", " ", "z"}]}], ",", - RowBox[{"d", "+", "e", "+", "f"}]}], "]"}], "]"}]], "Input", + RowBox[{"c", " ", "z"}]}], ")"}], ".", + RowBox[{"(", + RowBox[{"d", "+", "e", "+", "f"}], ")"}]}], TraditionalForm]], "Output", + ImageSize->{204, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[1]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DotExpand", "[", "%", "]"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[1]:=", + CellLabel->"In[2]:=", CellID->407288908], Cell[BoxData[ @@ -146,14 +206,19 @@ Cell[BoxData[ RowBox[{"c", " ", "d", " ", "z"}], "+", RowBox[{"c", " ", "e", " ", "z"}], "+", RowBox[{"c", " ", "f", " ", "z"}]}], TraditionalForm]], "Output", - ImageSize->{421, 15}, + ImageSize->{480, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DotExpand", - CellLabel->"Out[1]=", - CellID->887725401] + CellLabel->"Out[2]="] }, Open ]], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + Cell[BoxData[ RowBox[{ RowBox[{"DeclareNonCommutative", "/@", @@ -161,7 +226,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "f"}], "}"}]}], ";"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1021626920], Cell[CellGroupData[{ @@ -176,7 +241,7 @@ Cell[BoxData[ RowBox[{"c", " ", "z"}]}], ",", RowBox[{"d", "+", "e", "+", "f"}]}], "]"}], "]"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->587871772], Cell[BoxData[ @@ -200,12 +265,11 @@ Cell[BoxData[ RowBox[{"c", ".", "e"}]}], "+", RowBox[{"z", " ", RowBox[{"c", ".", "f"}]}]}], TraditionalForm]], "Output", - ImageSize->{430, 15}, + ImageSize->{498, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DotExpand", - CellLabel->"Out[3]=", - CellID->70533327] + CellLabel->"Out[2]="] }, Open ]], Cell[BoxData[ @@ -215,8 +279,15 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "f"}], "}"}]}], ";"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[4]:=", - CellID->1926968700], + CellLabel->"In[3]:=", + CellID->1926968700] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], Cell[CellGroupData[{ @@ -230,7 +301,7 @@ Cell[BoxData[ RowBox[{"c", " ", "z"}]}], ",", RowBox[{"d", "+", "e", "+", "f"}]}], "]"}], "]"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[5]:=", + CellLabel->"In[1]:=", CellID->1551070412], Cell[BoxData[ @@ -245,12 +316,12 @@ Cell[BoxData[ RowBox[{"c", " ", "d", " ", "z"}], "+", RowBox[{"c", " ", "e", " ", "z"}], "+", RowBox[{"c", " ", "f", " ", "z"}]}], TraditionalForm]], "Output", - ImageSize->{421, 15}, + ImageSize->{480, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"DotExpand", - CellLabel->"Out[5]=", - CellID->283503340] + CellLabel->"Out[1]="] +}, Open ]] }, Open ]] }, Open ]], @@ -274,7 +345,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["DOT", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/DOT", @@ -292,16 +362,13 @@ Cell[TextData[{ ButtonData->"paclet:FeynCalc/ref/DeclareNonCommutative", ButtonNote->"DeclareNonCommutative"], FontFamily->"Verdana"], - ", ", StyleBox[ButtonBox["UnDeclareNonCommutative", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/UnDeclareNonCommutative", ButtonNote->"UnDeclareNonCommutative"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"DotExpand", - CellID->631413415] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -318,20 +385,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 17.990763}", + "built" -> "{2020, 1, 5, 18, 54, 55.545277}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> - "None", "summary" -> "DotExpand[expr] expands DOT products in expr.", - "synonyms" -> {}, "title" -> "DotExpand", "titlemodifier" -> "", - "windowtitle" -> "DotExpand", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/DotExpand"}, "SearchTextTranslated" -> ""}, + "None", "summary" -> "DotExpand[exp] expands dot products in exp.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "DotExpand", + "titlemodifier" -> "", "windowtitle" -> "DotExpand", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/DotExpand"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -340,7 +407,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -349,101 +416,99 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["EpsContract", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ - Cell[BoxData["EpsContract"], "InlineFormula"], - " \[LineSeparator]", - "is an option of Contract specifying whether Levi-Civita tensors \ -Eps[...] will be contracted, i.e., products of two Eps are replaced via the \ -determinant formula." + Cell[BoxData[ + RowBox[{"EpsContract", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]handles contractions of two Levi-Civita tensors. It is \ +also an option of Contract and other functions that specifies whether such \ +contractions should be done or not." }]]} }]], "Usage", GridBoxOptions->{ @@ -108,7 +142,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1783233241], + CellID->1606407450], Cell[CellGroupData[{ @@ -118,29 +152,20 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1533026957], + CellID->698680576], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a1", " ", "=", - RowBox[{"Eps", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Sigma]", ",", "D"}], "]"}]}], "]"}]}]], "Input", - CellTags->"EpsContract", - CellLabel->"In[1]:=", - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 28.981206}", + "built" -> "{2020, 1, 5, 18, 55, 6.061578}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "EpsContract is an option of Contract specifying whether Levi-Civita \ -tensors Eps[...] will be contracted, i.e., products of two Eps are replaced \ -via the determinant formula.", "synonyms" -> {}, "title" -> "EpsContract", - "titlemodifier" -> "", "windowtitle" -> "EpsContract", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/EpsContract"}, "SearchTextTranslated" -> ""}, + "EpsContract[exp] handles contractions of two Levi-Civita tensors. 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ EpsEvaluate.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$49731], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/EpsEvaluate", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$78925], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/EpsEvaluate", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,16 +98,27 @@ EpsEvaluate.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["EpsEvaluate", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["EpsEvaluate", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ RowBox[{"EpsEvaluate", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "applies total antisymmetry and linearity (w.r.t. Momentum's) to all \ -Levi-Civita tensors (Eps') in expr." + " \[LineSeparator]applies total antisymmetry and linearity (w.r.t. \ +momenta) to all Levi-Civita tensors (Eps') in expr." }]]} }]], "Usage", GridBoxOptions->{ @@ -93,6 +129,57 @@ Levi-Civita tensors (Eps') in expr." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1134527267], + +Cell["", "SectionHeaderSpacer"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "EpsEvaluate", "]"}]], "Input", + CellLabel->"In[705]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"Momentum", "\[Rule]", "All"}]}], "}"}], + TraditionalForm]], "Output", + ImageSize->{275, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[705]="] +}, Open ]] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -108,7 +195,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1157327986], + CellID->1045845675], Cell[CellGroupData[{ @@ -118,26 +205,29 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->2006863315], + CellID->227360342], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Trick", "[", - RowBox[{ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], - " ", - RowBox[{"FourVector", "[", - RowBox[{ - RowBox[{"p", "+", "q"}], ",", "\[Sigma]"}], "]"}]}], "]"}]], "Input", + RowBox[{ + RowBox[{"Contract", "[", + RowBox[{ + RowBox[{"LC", "[", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], + " ", + RowBox[{"FV", "[", + RowBox[{ + RowBox[{"p", "+", "q"}], ",", "\[Sigma]"}], "]"}]}], "]"}], "//", + "MomentumCombine"}]], "Input", CellTags->"EpsEvaluate", CellLabel->"In[1]:=", CellID->684764895], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -162,12 +252,11 @@ Cell[BoxData[ TraditionalForm], "_"]}], TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{70, 21}, + ImageSize->{77, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"EpsEvaluate", - CellLabel->"Out[1]=", - CellID->440945173] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -181,7 +270,8 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -200,7 +290,8 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm]}]], "+", - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -219,12 +310,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm]}]]}], TraditionalForm]], "Output", - ImageSize->{117, 21}, + ImageSize->{125, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"EpsEvaluate", - CellLabel->"Out[2]=", - CellID->352429971] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -239,30 +329,21 @@ Cell[BoxData[ RowBox[{ RowBox[{"Eps", "[", RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", - RowBox[{"Momentum", "[", "p", "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "+", + RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", + RowBox[{"Momentum", "[", "p", "]"}]}], "]"}], "+", RowBox[{"Eps", "[", RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", - RowBox[{"Momentum", "[", "q", "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]}]], "Output", - ImageSize->{408, 67}, + RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", + RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]}]], "Output", + ImageSize->{559, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"EpsEvaluate", - CellLabel->"Out[3]//StandardForm=", - CellID->746268781] + CellLabel->"Out[3]//StandardForm="] }, Open ]] }, Open ]], @@ -298,10 +379,10 @@ Cell[TextData[{ ButtonNote->"Eps"], FontFamily->"Verdana"], ", ", - StyleBox[ButtonBox["LeviCivita", + StyleBox[ButtonBox["LC", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/LeviCivita", - ButtonNote->"LeviCivita"], + ButtonData->"paclet:FeynCalc/ref/LC", + ButtonNote->"LC"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["Trick", @@ -310,9 +391,7 @@ Cell[TextData[{ ButtonNote->"Trick"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"EpsEvaluate", - CellID->1755604338] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -329,22 +408,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 31.633847}", + "built" -> "{2020, 1, 5, 18, 55, 8.290141}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "EpsEvaluate[expr] applies total antisymmetry and linearity (w.r.t. \ -Momentum's) to all Levi-Civita tensors (Eps') in expr.", "synonyms" -> {}, - "title" -> "EpsEvaluate", "titlemodifier" -> "", "windowtitle" -> - "EpsEvaluate", "type" -> "Symbol", "uri" -> "FeynCalc/ref/EpsEvaluate"}, - "SearchTextTranslated" -> ""}, +momenta) to all Levi-Civita tensors (Eps') in expr.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "EpsEvaluate", "titlemodifier" -> "", + "windowtitle" -> "EpsEvaluate", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/EpsEvaluate"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -353,7 +432,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - 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CellID->1628615596], + CellID->1019186291], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -116,36 +211,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1724408364], - -Cell[CellGroupData[{ - -Cell["Examples", "Subsubsection", - CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellID->2116782470], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "ExpandScalarProduct", "]"}]], "Input", - CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[1]:=", - CellID->668026966], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"FeynCalcInternal", "\[Rule]", "True"}], ",", - RowBox[{"Momentum", "\[Rule]", - RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{292, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[1]=", - CellID->4871317] -}, Open ]], + CellID->1652478564], Cell[CellGroupData[{ @@ -156,7 +222,7 @@ Cell[BoxData[ RowBox[{"p1", "+", "p2", "+", "p3"}], ",", RowBox[{"p4", "+", "p5", "+", "p6"}]}], "]"}]}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - 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ExpandScalarProduct does not use Expand on expr. \ -ScalarProductExpand=ExpandScalarProduct.", "synonyms" -> {}, "title" -> - "ExpandScalarProduct", "titlemodifier" -> "", "windowtitle" -> - "ExpandScalarProduct", "type" -> "Symbol", "uri" -> +expr. ExpandScalarProduct does not use Expand on expr.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "ExpandScalarProduct", "titlemodifier" -> + "", "windowtitle" -> "ExpandScalarProduct", "type" -> "Symbol", "uri" -> "FeynCalc/ref/ExpandScalarProduct"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -706,7 +746,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -714,242 +754,205 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - "PrimaryExamplesSection"->{ - 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a10c244cb..815c4f5b3 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/ExplicitPartialD.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/ExplicitPartialD.nb @@ -3,69 +3,95 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 13924, 484] -NotebookOptionsPosition[ 9059, 332] -NotebookOutlinePosition[ 12283, 423] -CellTagsIndexPosition[ 12163, 417] +NotebookDataLength[ 16817, 595] +NotebookOptionsPosition[ 11969, 445] +NotebookOutlinePosition[ 14843, 524] +CellTagsIndexPosition[ 14723, 518] WindowTitle->ExplicitPartialD WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - 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\[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/ExplicitPartialD\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/ExplicitPartialD"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ ExplicitPartialD.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, 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Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ExplicitPartialD", "[", " ", - RowBox[{"LeftRightPartialD", "[", "OPEDelta", "]"}], " ", "]"}]], "Input", + RowBox[{"ExplicitPartialD", "[", "%", "]"}]], "Input", CellTags->"ExplicitPartialD", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1791671183], Cell[BoxData[ @@ -214,23 +325,29 @@ Cell[BoxData[ FormBox["\[CapitalDelta]", TraditionalForm], TraditionalForm]]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{87, 41}, + ImageSize->{83, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"ExplicitPartialD", - CellLabel->"Out[3]=", - CellID->490499430] + CellLabel->"Out[2]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"16", " ", RowBox[{ RowBox[{"LeftRightPartialD", "[", "OPEDelta", "]"}], "^", "4"}]}]], "Input",\ CellTags->"ExplicitPartialD", - CellLabel->"In[4]:=", + CellLabel->"In[1]:=", CellID->2120633580], Cell[BoxData[ @@ -242,12 +359,11 @@ Cell[BoxData[ FormBox["\[CapitalDelta]", TraditionalForm], TraditionalForm], "4"]}], TraditionalForm]], "Output", - ImageSize->{43, 26}, + ImageSize->{42, 23}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"ExplicitPartialD", - CellLabel->"Out[4]=", - CellID->962398275] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -255,7 +371,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExplicitPartialD", "[", "%", "]"}]], "Input", CellTags->"ExplicitPartialD", - CellLabel->"In[5]:=", + CellLabel->"In[2]:=", CellID->1962668305], Cell[BoxData[ @@ -275,12 +391,12 @@ Cell[BoxData[ FormBox["\[CapitalDelta]", TraditionalForm], TraditionalForm]]}], ")"}], "4"], TraditionalForm]], "Output", - ImageSize->{80, 34}, + ImageSize->{75, 27}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"ExplicitPartialD", - CellLabel->"Out[5]=", - CellID->2132998296] + CellLabel->"Out[2]="] +}, Open ]] }, Open ]] }, Open ]], @@ -304,7 +420,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["ExpandPartialD", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/ExpandPartialD", @@ -323,9 +438,7 @@ Cell[TextData[{ ButtonNote->"LeftRightPartialD2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"ExplicitPartialD", - CellID->1172851554] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -333,7 +446,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"ExplicitPartialD", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -342,22 +455,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 47.997611}", + "built" -> "{2020, 1, 5, 18, 55, 24.804064}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "ExplicitPartialD[exp] inserts in exp the definition for \ -LeftRightPartialD[z] (and LeftRightPartialD2[z]).", "synonyms" -> {}, "title" -> + "ExplicitPartialD[exp] inserts the definitions for LeftRightPartialD and \ +LeftRightPartialD2.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "ExplicitPartialD", "titlemodifier" -> "", "windowtitle" -> "ExplicitPartialD", 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ ExtraVariables.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$54535], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/ExtraVariables", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$86914], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/ExtraVariables", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +96,18 @@ ExtraVariables.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["ExtraVariables", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["ExtraVariables", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -119,9 +152,7 @@ Cell[TextData[{ ButtonNote->"OneLoopSum"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"ExtraVariables", - CellID->908293507] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -138,10 +169,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 52.292898}", + "built" -> "{2020, 1, 5, 18, 55, 29.244505}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -149,11 +180,11 @@ TaggingRules->{ "None", "summary" -> "ExtraVariables is an option for OneLoopSum; it may be set to a list of \ variables which are also bracketed out in the result, just like B0, C0, D0 \ -and PaVe.", "synonyms" -> {}, "title" -> "ExtraVariables", "titlemodifier" -> - "", "windowtitle" -> "ExtraVariables", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/ExtraVariables"}}, +and PaVe.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "ExtraVariables", + "titlemodifier" -> "", "windowtitle" -> "ExtraVariables", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/ExtraVariables"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -162,41 +193,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "ExtraVariables"->{ - Cell[3676, 108, 395, 15, 70, "Text", - CellTags->"ExtraVariables", - CellID->908293507]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"ExtraVariables", 5984, 172} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[586, 21, 2269, 52, 70, "AnchorBarGrid", +Cell[586, 21, 3114, 75, 70, "AnchorBarGrid", CellID->1], -Cell[2858, 75, 57, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2918, 78, 460, 12, 70, "Usage", +Cell[3703, 98, 291, 11, 70, "ObjectNameGrid"], +Cell[3997, 111, 460, 12, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3403, 94, 270, 12, 70, "SeeAlsoSection", +Cell[4482, 127, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3676, 108, 395, 15, 70, "Text", - CellTags->"ExtraVariables", - CellID->908293507] +Cell[4755, 141, 349, 13, 70, "SeeAlso"] }, Open ]], -Cell[4086, 126, 23, 0, 70, "FooterCell"] +Cell[5119, 157, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FAD.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FAD.nb index bd1b82eca..edeecdb4f 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FAD.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FAD.nb @@ -3,69 +3,99 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 14902, 518] -NotebookOptionsPosition[ 10225, 364] -NotebookOutlinePosition[ 13406, 457] -CellTagsIndexPosition[ 13299, 451] +NotebookDataLength[ 18903, 657] +NotebookOptionsPosition[ 14365, 514] +NotebookOutlinePosition[ 17262, 595] +CellTagsIndexPosition[ 17155, 589] WindowTitle->FAD WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FAD\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FAD"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/FAD.html"], - StandardForm]], "Input", TextClipboardType -> "PlainText"]}, - Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$56607], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/FAD", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FAD\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FAD"], "\<\"FCE\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCE"], "\<\"FCI\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCI"], "\<\"FeynAmpDenominator\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FeynAmpDenominator"], \ +"\<\"FeynAmpDenominatorSimplify\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FeynAmpDenominatorSimplify"], \ +"\<\"PropagatorDenominator\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PropagatorDenominator"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/FAD\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/FAD"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/FAD.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$89576], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/FAD", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +103,20 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["FAD", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FAD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -94,6 +136,54 @@ Translation into FeynCalc internal form is performed by FeynCalcInternal." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1808684290], + +Cell["", "SectionHeaderSpacer"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FAD", "]"}]], "Input", + CellLabel->"In[751]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Dimension", "\[Rule]", "D"}], "}"}], TraditionalForm]], "Output", + ImageSize->{112, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[751]="] +}, Open ]] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -109,7 +199,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1002001349], + CellID->1958456365], Cell[CellGroupData[{ @@ -119,7 +209,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->2046427822], + CellID->1301223188], Cell[CellGroupData[{ @@ -135,27 +225,43 @@ Cell[BoxData[ FormBox[ FractionBox["1", RowBox[{ - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["q", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`q^2, "]"], - Editable->False], ")"}], ".", - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox[ - RowBox[{"(", - RowBox[{"p", "-", "q"}], ")"}], "2"], - "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", ($CellContext`p - $CellContext`q)^2, "]"], - Editable->False], ")"}]}]], TraditionalForm]], "Output", - ImageSize->{132, 48}, + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D], + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D]]], + Editable->False]}]], TraditionalForm]], "Output", + ImageSize->{99, 40}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FAD", - CellLabel->"Out[1]=", - CellID->574537865] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -174,55 +280,110 @@ Cell[BoxData[ FormBox[ FractionBox["1", RowBox[{ + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False], ".", RowBox[{"(", InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["p", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`p^2, "]"], - Editable->False], ")"}], ".", - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", + RowBox[{ SuperscriptBox[ - RowBox[{"(", - RowBox[{"p", "-", "q"}], ")"}], "2"], - 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$CellContext`q, D], + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D]], + "-", $CellContext`m^2], + Editable->False], ")"}], "3"]}]], TraditionalForm]], "Output", + ImageSize->{172, 43}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"FAD", - CellLabel->"Out[3]//StandardForm=", - CellID->1226815761] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -257,8 +418,7 @@ Cell[BoxData[ ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FAD", - CellLabel->"Out[4]//StandardForm=", - CellID->962460787] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -270,32 +430,24 @@ Cell[BoxData[ RowBox[{"FAD", "[", "p", "]"}], " ", RowBox[{"FAD", "[", RowBox[{"p", "-", "q"}], "]"}]}], " ", "//", " ", - "FeynAmpDenominatorCombine"}], "//", "StandardForm"}]], "Input", + RowBox[{ + RowBox[{"FeynAmpDenominatorCombine", "[", + RowBox[{"#", ",", + RowBox[{"FCE", "\[Rule]", "True"}]}], "]"}], "&"}]}], "//", + "StandardForm"}]], "Input", CellTags->"FAD", CellLabel->"In[5]:=", CellID->844291899], Cell[BoxData[ - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 0.354281}", + "built" -> "{2020, 1, 5, 18, 55, 35.478507}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -387,11 +537,11 @@ TaggingRules->{ inverse propagator. FAD[q, q-p, ...] is 1/(q^2 (q-p)^2 ...). FAD[{q1,m}, \ {q1-p,m}, q2, ...] is 1/( (q1^2 - m^2) ( (q1-p)^2 - m^2 ) q2^2 ... ). \ Translation into FeynCalc internal form is performed by FeynCalcInternal.", - "synonyms" -> {}, "title" -> "FAD", "titlemodifier" -> "", "windowtitle" -> - "FAD", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FAD"}, - "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FAD", "titlemodifier" -> + "", "windowtitle" -> "FAD", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FAD"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -399,8 +549,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], 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@@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1619831617], + CellID->2062751557], Cell[BoxData["FI"], "Input", CellTags->"FC", @@ -141,8 +179,7 @@ Cell["{DiracGamma[5], DiracGamma[Momentum[p]]}", "Output", ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FC", - CellLabel->"Out[2]=", - CellID->914835770] + CellLabel->"Out[2]="] }, Open ]], Cell[BoxData["FC"], "Input", @@ -177,12 +214,11 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm]}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{73, 21}, + ImageSize->{79, 22}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FC", - CellLabel->"Out[4]=", - CellID->832664174] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -230,9 +266,7 @@ Cell[TextData[{ ButtonNote->"FeynCalcInternal"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FC", - CellID->121401811] +}], "SeeAlso"] }, Open ]], 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To change to InputForm use \ -FI.", "synonyms" -> {}, "title" -> "FC", "titlemodifier" -> "", "windowtitle" -> - "FC", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FC"}, - "SearchTextTranslated" -> ""}, +FI.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "FC", "titlemodifier" -> + "", "windowtitle" -> "FC", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FC"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -271,8 +305,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -281,87 +316,77 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$56955], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/FC2RHI", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$90464], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/FC2RHI", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FC2RHI", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FC2RHI", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -97,39 +131,40 @@ IncludePair governs the inclusion of scalar products p.k1, p.k2 and k1.k2 \ Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->163322982], + CellGroupingRules->{"SectionGrouping", 50}, + CellID->2033600335], -Cell[CellGroupData[{ - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->1794007483], +Cell["", "SectionHeaderSpacer"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "FC2RHI", "]"}]], "Input", CellTags->"FC2RHI", - CellLabel->"In[1]:=", + CellLabel->"In[756]:=", CellID->744239659], Cell[BoxData[ @@ -139,16 +174,13 @@ Cell[BoxData[ RowBox[{"Dimension", "\[Rule]", "D"}], ",", RowBox[{"IncludePair", "\[Rule]", "True"}], ",", RowBox[{"Do", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{327, 15}, + ImageSize->{306, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FC2RHI", - CellLabel->"Out[1]=", - CellID->283717471] + CellLabel->"Out[756]="] }, Open ]] -}, Open ]], - -Cell["", "SectionFooterSpacer"] +}, Closed]] }, Open ]], Cell[CellGroupData[{ @@ -174,9 +206,7 @@ Cell[TextData[{ ButtonNote->"RHI"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FC2RHI", - CellID->2109849659] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -184,7 +214,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, WindowTitle->"FC2RHI", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -193,10 +223,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 1.918910}", + "built" -> "{2020, 1, 5, 18, 55, 37.608336}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -205,11 +235,12 @@ TaggingRules->{ "FC2RHI[exp, k1, k2] transforms all 2-loop OPE-integrals in \ FeynAmpDenominator form to the RHI-integrals. FC2RHI[exp] is equivalent to \ FC2RHI[exp,q1,q2]. The option IncludePair governs the inclusion of scalar \ -products p.k1, p.k2 and k1.k2 (setting True).", "synonyms" -> {}, "title" -> - "FC2RHI", "titlemodifier" -> "", "windowtitle" -> "FC2RHI", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/FC2RHI"}, "SearchTextTranslated" -> ""}, +products p.k1, p.k2 and k1.k2 (setting True).", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "FC2RHI", "titlemodifier" -> "", + "windowtitle" -> "FC2RHI", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FC2RHI"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -217,8 +248,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -226,62 +258,47 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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-79,12 +79,13 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$57963], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$92237], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/FCApart", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}] }], "AnchorBar"]} }]], "AnchorBarGrid", @@ -94,8 +95,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FCApart", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FCApart", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[CellGroupData[{ @@ -147,7 +158,7 @@ Cell[TextData[Cell[BoxData[ Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, CellGroupingRules->{"SectionGrouping", 50}, - CellID->32159945], + CellID->1559637087], Cell["", "SectionHeaderSpacer"], @@ -156,7 +167,38 @@ There is actually no reason, why one would want to apply FCApart instead of \ ApartFF, except for cases, where FCApart is called from a different package \ that interacts with FeynCalc.\ \>", "Notes", - CellID->1067943069] + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FCApart", "]"}]], "Input", + CellLabel->"In[763]:=", + CellID->466656637], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Check", "\[Rule]", "True"}], ",", + RowBox[{"Collecting", "\[Rule]", "True"}], ",", + RowBox[{"DropScaleless", "\[Rule]", "True"}], ",", + RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", 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MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ FCClearScalarProducts.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$58641], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/FCClearScalarProducts", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$94886], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/FCClearScalarProducts", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +99,18 @@ FCClearScalarProducts.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FCClearScalarProducts[]", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FCClearScalarProducts[]", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +143,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->224266882], + CellID->1957370991], Cell[CellGroupData[{ @@ -117,7 +153,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->595250500], + CellID->780051132], Cell[CellGroupData[{ @@ -133,12 +169,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ SuperscriptBox["m", "2"], TraditionalForm]], "Output", - ImageSize->{26, 18}, + ImageSize->{27, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FCClearScalarProducts", - CellLabel->"Out[1]=", - CellID->29501459] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -155,12 +190,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ SuperscriptBox["m", "2"], TraditionalForm]], "Output", - ImageSize->{26, 18}, + ImageSize->{27, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FCClearScalarProducts", - CellLabel->"Out[2]=", - CellID->988927941] + CellLabel->"Out[2]="] }, Open ]], Cell[BoxData[ @@ -188,18 +222,17 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm], "2"], TraditionalForm]], "Output", - ImageSize->{23, 20}, + ImageSize->{26, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FCClearScalarProducts", - CellLabel->"Out[4]=", - CellID->975498131] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ScalarProduct", "[", + RowBox[{"SP", "[", RowBox[{"p", ",", "p"}], "]"}]], "Input", CellTags->"FCClearScalarProducts", CellLabel->"In[5]:=", @@ -213,12 +246,11 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm], "2"], TraditionalForm]], "Output", - ImageSize->{23, 20}, + ImageSize->{26, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FCClearScalarProducts", - 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The only reason for introducing \ +FCDuplicateFreeQ is that DuplicateFreeQ is not available in Mathematica 8 and \ +9, which are still supported by FeynCalc.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "FCDuplicateFreeQ", "titlemodifier" -> "", + "windowtitle" -> "FCDuplicateFreeQ", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FCDuplicateFreeQ"}, "SearchTextTranslated" -> ""}, +CellContext->"Global`", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> "Global`"], + Cell[ + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", + StyleDefinitions -> "Default.nb"] +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{ + "PrimaryExamplesSection"->{ + Cell[3964, 109, 387, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->210388594]} + } +*) +(*CellTagsIndex +CellTagsIndex->{ + {"PrimaryExamplesSection", 8892, 277} + } +*) +(*NotebookFileOutline +Notebook[{ +Cell[588, 21, 2305, 53, 53, "AnchorBarGrid", + CellID->1], +Cell[2896, 76, 293, 11, 45, "ObjectNameGrid"], +Cell[3192, 89, 747, 16, 136, "Usage", + CellID->982511436], +Cell[CellGroupData[{ +Cell[3964, 109, 387, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->210388594], +Cell[CellGroupData[{ +Cell[4376, 128, 196, 6, 26, "ExampleSection", + CellID->1201668591], +Cell[CellGroupData[{ +Cell[4597, 138, 170, 5, 27, "Input", + CellID->1365347863], +Cell[4770, 145, 190, 6, 35, "Output", + CellID->1783991330] +}, Open ]], +Cell[CellGroupData[{ +Cell[4997, 156, 179, 5, 27, "Input", + CellID->484757087], +Cell[5179, 163, 188, 6, 35, "Output", + CellID->2639087] +}, Open ]], +Cell[CellGroupData[{ +Cell[5404, 174, 262, 9, 27, "Input", + CellID->1576732881], +Cell[5669, 185, 188, 6, 35, "Output", + CellID->52773390] +}, Open ]], +Cell[CellGroupData[{ +Cell[5894, 196, 504, 17, 45, "Input", + CellID->800569343], +Cell[6401, 215, 191, 6, 35, "Output", + CellID->1930688687] +}, Open ]] +}, Open ]] +}, Open ]], +Cell[6631, 226, 23, 0, 41, "FooterCell"] +} +] +*) + +(* End of internal cache information *) + diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FCE.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FCE.nb index d459e1ee3..70012b4e5 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FCE.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FCE.nb @@ -3,69 +3,95 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 18538, 690] -NotebookOptionsPosition[ 13302, 511] -NotebookOutlinePosition[ 16655, 613] -CellTagsIndexPosition[ 16548, 607] +NotebookDataLength[ 19816, 724] +NotebookOptionsPosition[ 14718, 554] +NotebookOutlinePosition[ 17836, 647] +CellTagsIndexPosition[ 17729, 641] WindowTitle->FCE WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FCE\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FCE"]}, Visible -> False]]; 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CellLabel->"Out[3]=", - CellID->1056453085] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -305,12 +364,11 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], ",", RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", - ImageSize->{416, 15}, + ImageSize->{424, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FCE", - CellLabel->"Out[4]//StandardForm=", - CellID->2003071088] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -356,43 +414,32 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm]}], ",", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], ",", - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - 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CellLabel->"Out[6]//StandardForm=", - CellID->394450163] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -455,12 +501,11 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], ",", RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", - ImageSize->{416, 15}, + ImageSize->{424, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FCE", - CellLabel->"Out[7]//StandardForm=", - CellID->1313014770] + CellLabel->"Out[7]//StandardForm="] }, Open ]] }, Open ]], @@ -502,9 +547,7 @@ Cell[TextData[{ ButtonNote->"FeynCalcInternal"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FCE", - CellID->141332597] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -512,7 +555,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"FCE", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -521,21 +564,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - 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The result is returned as a list, e.g. {4}, {D} or {4,D,D-4} \ -etc. This is useful if one want to be sure that all quantities inside a \ -particular expression are purely 4-dimensional or purely D-dimensional." +dimensions in which 4-momenta and Dirac matrices of the given expression are \ +defined. " }]]} }]], "Usage", GridBoxOptions->{ @@ -95,6 +106,63 @@ particular expression are purely 4-dimensional or purely D-dimensional." 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If the option First is set to False, \ +propagators that have both a quadratic and linear piece, e.g. \ +1/[(q-p)^2+q.r+x] will also count as eikonal propagators. The option Momentum \ +can be used to check for the presence of eikonal propagators only with \ +respect to particular momenta. 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 18.316417}", + "built" -> "{2020, 1, 5, 18, 56, 30.447330}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -317,12 +1367,12 @@ loop integrals. 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StandardForm]], "Input", TextClipboardType -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$61028], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$110595], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/FCLoopIsolate", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,20 @@ FCLoopIsolate.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FCLoopIsolate", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FCLoopIsolate", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], 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PlotRange->{{0, 366}, {0, 193}}]], "Output", + ImageSize->{370, 193}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellLabel->"Out[1]=", - CellID->1111325861] + CellTags->"RasterizedOutput", + CellLabel->"Out[2]=", + CellID->618109214] }, Open ]] }, Open ]] }, Open ]], @@ -551,7 +549,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"FCMultiLoopTID", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -560,10 +558,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 21.615738}", + "built" -> "{2020, 1, 5, 18, 56, 50.903800}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -573,11 +571,12 @@ TaggingRules->{ decomposition, transforming the Lorentz indices away from the loop momenta \ q1,q2,... 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 25.795460}", + "built" -> "{2020, 1, 5, 18, 56, 54.192687}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -316,11 +346,11 @@ TaggingRules->{ \\[PartialD]TraditionalForm\\`TraditionalForm\\`\\[Mu]. 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Instead of doing exp /. ru1 /. \ +ru2 /. ru3 one can just write FCReplaceAll[exp, ru1, ru2, ru3]", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FCReplaceAll", + "titlemodifier" -> "", "windowtitle" -> "FCReplaceAll", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/FCReplaceAll"}, "SearchTextTranslated" -> + ""}, +CellContext->"Global`", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> "Global`"], + Cell[ + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 0}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", + StyleDefinitions -> "Default.nb"] +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{ + "PrimaryExamplesSection"->{ + Cell[3779, 108, 388, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->2137324929]} + } +*) +(*CellTagsIndex +CellTagsIndex->{ + {"PrimaryExamplesSection", 7912, 250} + } +*) +(*NotebookFileOutline +Notebook[{ +Cell[584, 21, 2290, 53, 53, "AnchorBarGrid", + CellID->1], +Cell[2877, 76, 289, 11, 45, "ObjectNameGrid"], +Cell[3169, 89, 585, 15, 102, "Usage", + CellID->982511436], +Cell[CellGroupData[{ +Cell[3779, 108, 388, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->2137324929], +Cell[CellGroupData[{ +Cell[4192, 127, 196, 6, 26, "ExampleSection", + CellID->1901306597], +Cell[CellGroupData[{ +Cell[4413, 137, 160, 5, 27, "Input", + CellID->52762404], +Cell[4576, 144, 187, 6, 35, "Output", + CellID->1612762649] +}, Open ]], +Cell[CellGroupData[{ +Cell[4800, 155, 269, 9, 27, "Input", + CellID->1810816466], +Cell[5072, 166, 210, 7, 35, "Output", + CellID->2011322610] +}, Open ]], +Cell[CellGroupData[{ +Cell[5319, 178, 306, 9, 27, "Input", + CellID->1366564949], +Cell[5628, 189, 210, 7, 35, "Output", + CellID->2023491188] +}, Open ]] +}, Open ]] +}, Open ]], +Cell[5877, 201, 23, 0, 41, "FooterCell"] +} +] +*) + +(* End of internal cache information *) + diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FCReplaceD.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FCReplaceD.nb index e971ae44a..aa2d53b13 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FCReplaceD.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FCReplaceD.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 11444, 394] -NotebookOptionsPosition[ 8288, 303] -NotebookOutlinePosition[ 10561, 361] -CellTagsIndexPosition[ 10476, 356] +NotebookDataLength[ 12820, 450] +NotebookOptionsPosition[ 9291, 346] +NotebookOutlinePosition[ 11609, 406] +CellTagsIndexPosition[ 11524, 401] WindowTitle->FCReplaceD WindowFrame->Normal*) @@ -59,12 +59,13 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$62730], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$121883], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/FCReplaceD", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FCReplaceD", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FCReplaceD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -96,6 +109,58 @@ ChangeDimension." 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This is mainly relevant to the treatment of the \ +fifth Dirac matrix ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + ", which is not well-defined in dimensional regularization." + }]]} + }]], "Usage", + GridBoxOptions->{ + GridBoxBackground->{ + "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, + "RowsIndexed" -> {}}}, + CellID->982511436], + +Cell[CellGroupData[{ + +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->36733847], + +Cell["", "SectionHeaderSpacer"], + +Cell["Following schemes are supported: ", "Notes", + CellID->1067943069], + +Cell[TextData[{ + "\"NDR\" - This is the default value. In the naive dimensional \ +regularization (also known as conventional dimensional regularization or CDR) \ +", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + " is assumed to anticommute with all Dirac matrices in ", + Cell[BoxData["D"], "InlineFormula"], + " dimensions. Hence, every Dirac trace can be rewritten in such a way, that \ +it contains either just one or not a single ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + " matrix. The latter traces are obviously unambiguous. The traces with one \ +", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + " are not well-defined in this scheme. It usually depends on the physics of \ +the process, whether and how they can contribute to the final result. \ +Therefore, FeynCalc will keep such traces unevaluated, leaving it to the user \ +to decide how to treat them. " +}], "Notes", + CellID->190401776], + +Cell[TextData[{ + "Notice that traces with an odd number of the usual Dirac matrices and one \ +", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + ", that vanish in 4 dimensions, will be also put to zero in this scheme." +}], "Notes", + CellID->1784502655], + +Cell[TextData[{ + "\"NDR-Discard\" - This is a special version of the NDR scheme. The Dirac \ +algebra is\nevaluated in the same way as with \"NDR\", but the remaining \ +traces with one ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + "\nare put to zero. This assumes that such traces do not contribute to the \ +final result,\nwhich is obviously true only for specific calculations." +}], "Notes", + CellID->665441283], + +Cell[TextData[{ + "\"BMHV\" - The Breitenlohner-Maison extension of the t'Hooft-Veltman \ +scheme. This scheme introduces Dirac and Lorentz tensors living in ", + Cell[BoxData["4"], "InlineFormula"], + ", ", + Cell[BoxData["D"], "InlineFormula"], + " or ", + Cell[BoxData[ + RowBox[{"D", "-", "4"}]], "InlineFormula"], + " dimensions, while ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " is a purely ", + Cell[BoxData["4"], "InlineFormula"], + "-dimensional object. BMHV is algebraically consistent but often suffers \ +from nonconservation of currents in the final results. The conservation must \ +be then enfornced by introducing finite counter-terms. The counter-terms are \ +to be supplied by the users, FeynCalc does not do this automatically." +}], "Notes", + CellID->2003509557], + +Cell[TextData[{ + "\"Larin\" - Special prescription developed by Larin, also known as the \ +Larin-Gorishny-Atkyampo-DelBurgo scheme. Essentially, it is a shortcut \ +(mostly used in QCD) for obtaining the same results as in BMHV but without \ +the necessity to deal with tensors from different dimensions. That is, before \ +evaluating traces (but after moving gamma5 anticommuting in D-dimensions to \ +the right of the Dirac string inside a trace) a product gamma[mu].gamma5 is \ +substituted to -I/6 Eps[mu,al,be,si] gamma[al,be,si], where all indices live \ +in D-dimensions now. The Levi-Civita tensor is taken to be", + StyleBox[" ", "Tutorials"], + Cell[BoxData["D"], "InlineFormula"], + StyleBox["-", "Tutorials"], + "dimensional, i.e., contraction of two Eps's results in D's. \\\nThis scheme \ +is often used for performance reasons and is assumed to give the same results \ +as the Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme. However, ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " is not anticommuting inside closed fermion loops and it is not so clear if \ +this scheme works for more than one fermion line involving ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " When in doubt, it might be better to use BMHV instead." +}], "Notes", + CellID->93561036] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->82917860], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->32234158], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}]], "Input", + CellLabel->"In[1]:=", + CellID->1948773281], + +Cell[BoxData[ + FormBox["\<\"NDR\"\>", TraditionalForm]], "Output", + ImageSize->{35, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[1]=", + CellID->1851033209] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracTrace", "[", + RowBox[{"GAD", "[", + RowBox[{ + "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "\[Tau]", ",", + "\[Kappa]", ",", "5"}], "]"}], "]"}]], "Input", + CellLabel->"In[2]:=", + CellID->98306849], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox[ + RowBox[{ + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Tau]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Kappa]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], + TraditionalForm]}], + TraditionalForm], ")"}], TraditionalForm]], "Output", + ImageSize->{189, 22}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[2]=", + CellID->319736968] +}, Open ]], + +Cell["\<\ +In NDR chiral traces remain unevaluated. You decide how to treat them.\ +\>", "ExampleText", + CellID->1475497628], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[3]:=", + CellID->933234494], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox[ + RowBox[{ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Tau]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Kappa]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + 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FormBox["nu", + FormBox["\[Nu]", TraditionalForm], TraditionalForm]]}], TraditionalForm], ")"}]}]}], TraditionalForm]], "Output", - ImageSize->{480, 21}, + ImageSize->{442, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellLabel->"Out[6]=", - CellID->1128579487] + CellLabel->"Out[2]="] +}, Open ]] }, Open ]], -Cell["\<\ -At the moment SUNTrace automatically expands its content, so here \ -FCTraceExpand is not needed. 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The traces themselves are not evaluated.", - "synonyms" -> {}, "title" -> "FCTraceExpand", "titlemodifier" -> "", - "windowtitle" -> "FCTraceExpand", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/FCTraceExpand"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FCTraceExpand", + "titlemodifier" -> "", "windowtitle" -> "FCTraceExpand", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/FCTraceExpand"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -960,8 +1050,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -970,97 +1061,104 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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DataType[z, FCVariable] = True.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FCVariable", + "titlemodifier" -> "", "windowtitle" -> "FCVariable", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/FCVariable"}, "SearchTextTranslated" -> ""}, +CellContext->"Global`", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> "Global`"], + Cell[ + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 0}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", + StyleDefinitions -> "Default.nb"] +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{ + "PrimaryExamplesSection"->{ + Cell[3547, 104, 388, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->1731146497]} + } +*) +(*CellTagsIndex +CellTagsIndex->{ + {"PrimaryExamplesSection", 15205, 542} + } +*) +(*NotebookFileOutline +Notebook[{ +Cell[582, 21, 2281, 53, 53, "AnchorBarGrid", + CellID->1], +Cell[2866, 76, 287, 11, 45, "ObjectNameGrid"], +Cell[3156, 89, 366, 11, 85, "Usage", + CellID->982511436], +Cell[CellGroupData[{ +Cell[3547, 104, 388, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->1731146497], +Cell[CellGroupData[{ +Cell[3960, 123, 196, 6, 26, "ExampleSection", + CellID->1672467737], +Cell[4159, 131, 140, 4, 32, "Notes", + CellID->247520490], +Cell[CellGroupData[{ +Cell[4324, 139, 250, 9, 27, "Input", + CellID->1215664914], +Cell[4577, 150, 721, 31, 37, "Output", + CellID->63183590] +}, Open ]], +Cell[5313, 184, 155, 4, 48, "Notes", + CellID->1683370483], +Cell[CellGroupData[{ +Cell[5493, 192, 502, 17, 62, "Input", + CellID->1946914218], +Cell[5998, 211, 810, 33, 37, "Output", + CellID->425164179] +}, Open ]], +Cell[6823, 247, 92, 1, 32, "Notes", + CellID->84688361], +Cell[CellGroupData[{ +Cell[6940, 252, 301, 10, 45, "Input", + CellID->228259200], +Cell[7244, 264, 728, 21, 61, "Output", + CellID->365749151], +Cell[7975, 287, 574, 17, 69, "Output", + CellID->1642692538] +}, Open ]], +Cell[CellGroupData[{ +Cell[8586, 309, 373, 11, 45, "Input", + CellID->1015735328], +Cell[8962, 322, 648, 25, 37, "Output", + CellID->2133407116], +Cell[9613, 349, 679, 21, 86, "Output", + CellID->2114556516] +}, Open ]], +Cell[CellGroupData[{ +Cell[10329, 375, 312, 9, 45, "Input", + CellID->897525840], +Cell[10644, 386, 1292, 52, 40, "Output", + CellID->825817380], +Cell[11939, 440, 496, 14, 69, "Output", + CellID->19578284] +}, Open ]], +Cell[12450, 457, 65, 1, 32, "Notes", + CellID->874852462], +Cell[CellGroupData[{ +Cell[12540, 462, 293, 9, 45, "Input", + CellID->219796287], +Cell[12836, 473, 191, 6, 35, "Output", + CellID->1930979781], +Cell[13030, 481, 191, 6, 35, "Output", + CellID->1284707712] +}, Open ]], +Cell[13236, 490, 68, 2, 27, "Input", + CellID->58122944] +}, Open ]] +}, Open ]], +Cell[13331, 496, 23, 0, 41, "FooterCell"] +} +] +*) + +(* End of internal cache information *) + diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FDS.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FDS.nb index 571f59f1e..5810117d0 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FDS.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FDS.nb @@ -3,69 +3,92 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 5955, 185] -NotebookOptionsPosition[ 3830, 121] -NotebookOutlinePosition[ 5700, 174] -CellTagsIndexPosition[ 5635, 169] +NotebookDataLength[ 6771, 207] +NotebookOptionsPosition[ 4818, 152] +NotebookOutlinePosition[ 6564, 199] +CellTagsIndexPosition[ 6521, 196] WindowTitle->FDS WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["FDS", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +145,7 @@ Cell[TextData[{ ButtonNote->"FeynAmpDenominatorSimplify"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FDS", - CellID->429222179] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,19 +162,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 33.487746}", + "built" -> "{2020, 1, 5, 18, 57, 24.526755}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "FDS is shorthand for FeynAmpDenominatorSimplify.", - "synonyms" -> {}, "title" -> "FDS", "titlemodifier" -> "", "windowtitle" -> - "FDS", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FDS"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FDS", "titlemodifier" -> + "", "windowtitle" -> "FDS", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FDS"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -152,41 +184,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "FDS"->{ - Cell[3512, 107, 276, 9, 70, "Text", - CellTags->"FDS", - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FI\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FI"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/FI.html"], - StandardForm]], "Input", TextClipboardType -> "PlainText"]}, - Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$72316], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/FI", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalcForm\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FeynCalcForm"], "\<\"FC\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FC"], "\<\"FeynCalcExternal\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FeynCalcExternal"], "\<\"FeynCalcInternal\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FeynCalcInternal"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/FI\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/FI"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/FI.html"], + StandardForm]], "Input", TextClipboardType -> "PlainText"]}, + Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$140577], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/FI", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +101,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["FI", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FI", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -132,9 +170,7 @@ Cell[TextData[{ ButtonNote->"FeynCalcInternal"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FI", - CellID->1056689858] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -151,10 +187,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 8.723866}", + "built" -> "{2020, 1, 5, 18, 57, 53.943509}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -162,10 +198,11 @@ TaggingRules->{ "None", "summary" -> "FI changes the output format to InputForm. This is useful to see the \ internal representation of FeynCalc objects. To change back to FeynCalcForm \ -use FC.", "synonyms" -> {}, "title" -> "FI", "titlemodifier" -> "", - "windowtitle" -> "FI", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FI"}}, +use FC.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "FI", + "titlemodifier" -> "", "windowtitle" -> "FI", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FI"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -174,41 +211,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "FI"->{ - Cell[3614, 109, 741, 27, 70, "Text", - CellTags->"FI", - CellID->1056689858]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"FI", 6199, 184} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[574, 21, 2233, 52, 70, "AnchorBarGrid", +Cell[574, 21, 3302, 80, 70, "AnchorBarGrid", CellID->1], -Cell[2810, 75, 45, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2858, 78, 458, 13, 70, "Usage", +Cell[3879, 103, 279, 11, 70, "ObjectNameGrid"], +Cell[4161, 116, 458, 13, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3341, 95, 270, 12, 70, "SeeAlsoSection", +Cell[4644, 133, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3614, 109, 741, 27, 70, "Text", - CellTags->"FI", - CellID->1056689858] +Cell[4917, 147, 706, 25, 70, "SeeAlso"] }, Open ]], -Cell[4370, 139, 23, 0, 70, "FooterCell"] +Cell[5638, 175, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORM.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORM.nb index 301cbfb9c..bbb63b223 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORM.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORM.nb @@ -3,69 +3,93 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6298, 196] -NotebookOptionsPosition[ 4043, 129] -NotebookOutlinePosition[ 6040, 185] -CellTagsIndexPosition[ 5974, 180] +NotebookDataLength[ 7172, 218] +NotebookOptionsPosition[ 5101, 161] +NotebookOutlinePosition[ 6964, 210] +CellTagsIndexPosition[ 6921, 207] WindowTitle->FORM WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FORM\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FORM"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/FORM.html"]\ -, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$73361], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/FORM", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"RHI\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/RHI"], "\<\"FeynCalc2FORM\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FeynCalc2FORM"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/FORM\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/FORM"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + + "http://reference.wolfram.com/language/FeynCalc/ref/FORM.\ +html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$141944], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/FORM", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +97,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["FORM", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FORM", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -120,9 +154,7 @@ Cell[TextData[{ ButtonNote->"FeynCalc2FORM"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FORM", - CellID->2094325907] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -139,10 +171,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 12.802762}", + "built" -> "{2020, 1, 5, 18, 57, 57.250397}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -150,11 +182,11 @@ TaggingRules->{ "None", "summary" -> "FORM is an option for RHI. If set to True a FORM file is generated and \ run from Mathematica (provided R. Hamberg's FORM-program is installed \ -correctly ... ).", "synonyms" -> {}, "title" -> "FORM", "titlemodifier" -> "", - "windowtitle" -> "FORM", "type" -> "Symbol", "uri" -> +correctly ... ).", "synonyms" -> {}, "tabletags" -> {}, "title" -> "FORM", + "titlemodifier" -> "", "windowtitle" -> "FORM", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FORM"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -163,41 +195,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "FORM"->{ - Cell[3618, 109, 383, 15, 70, "Text", - CellTags->"FORM", - CellID->2094325907]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"FORM", 5866, 173} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[576, 21, 2228, 52, 70, "AnchorBarGrid", +Cell[576, 21, 3089, 76, 70, "AnchorBarGrid", CellID->1], -Cell[2807, 75, 47, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2857, 78, 463, 13, 70, "Usage", +Cell[3668, 99, 281, 11, 70, "ObjectNameGrid"], +Cell[3952, 112, 463, 13, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3345, 95, 270, 12, 70, "SeeAlsoSection", +Cell[4440, 129, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3618, 109, 383, 15, 70, "Text", - CellTags->"FORM", - CellID->2094325907] +Cell[4713, 143, 346, 13, 70, "SeeAlso"] }, Open ]], -Cell[4016, 127, 23, 0, 70, "FooterCell"] +Cell[5074, 159, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORM2FeynCalc.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORM2FeynCalc.nb index 9bf916c47..d3b79aff8 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORM2FeynCalc.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORM2FeynCalc.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 21579, 771] -NotebookOptionsPosition[ 13924, 525] -NotebookOutlinePosition[ 18626, 659] -CellTagsIndexPosition[ 18509, 653] +NotebookDataLength[ 23333, 824] +NotebookOptionsPosition[ 16156, 599] +NotebookOutlinePosition[ 20313, 715] +CellTagsIndexPosition[ 20196, 709] WindowTitle->FORM2FeynCalc WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FORM2FeynCalc\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FORM2FeynCalc"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc2FORM\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FeynCalc2FORM"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/FORM2FeynCalc\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/FORM2FeynCalc"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ FORM2FeynCalc.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$72665], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/FORM2FeynCalc", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$141050], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/FORM2FeynCalc", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,63 +95,107 @@ FORM2FeynCalc.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FORM2FeynCalc", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FORM2FeynCalc", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"FORM2FeynCalc", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "translates the FORM expr into FeynCalc notation. FORM2FeynCalc[file] \ -translates the FORM expresssions in file into FeynCalcnotation. \ -FORM2FeynCalc[file, x1, x2, ...] reads in a file in FORM-format and \ -translates the assignments for the variables a, b, ... into FeynCalc syntax. \ -If the option Set is True, the variables x1, x2 are assigned to the right \ -hand sides defined in the FORM-file." + RowBox[{"FORM2FeynCalc", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]translates the FORM ", + Cell[BoxData["exp"], "InlineFormula"], + " into FeynCalc notation." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"FORM2FeynCalc", "[", "file", "]"}]], "InlineFormula"], + " \[LineSeparator] translates the FORM expresssions in ", + Cell[BoxData["file"], "InlineFormula"], + " into FeynCalc notation." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"FORM2FeynCalc", "[", + RowBox[{"file", ",", "x1", ",", "x2", ",", "..."}], "]"}]], + "InlineFormula"], + " \[LineSeparator]reads in a file in FORM-format and translates the \ +assignments for the variables ", + Cell[BoxData[ + RowBox[{"a", ",", " ", "b", ",", " ", "..."}]], "InlineFormula"], + " into FeynCalc syntax." }]]} }]], "Usage", GridBoxOptions->{ GridBoxBackground->{ - "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, - "RowsIndexed" -> {}}}, - CellID->982511436], + "Columns" -> {{None}}, "ColumnsIndexed" -> {}, + "Rows" -> {None, None, {None}}, "RowsIndexed" -> {}}}, + CellID->2010081510], Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->1208601621], + CellGroupingRules->{"SectionGrouping", 50}, + CellID->376987914], -Cell[CellGroupData[{ +Cell["", "SectionHeaderSpacer"], Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->1619789030], + "If the option ", + Cell[BoxData["Set"], "InlineFormula"], + " is ", + Cell[BoxData["True"], "InlineFormula"], + ", the variables ", + Cell[BoxData["x1"], "InlineFormula"], + ", ", + Cell[BoxData["x2"], "InlineFormula"], + " are assigned to the right hand sides defined in the FORM-file." +}], "Notes"], + +Cell["\<\ +The capabilities of this function are very limited, so that you should not \ +expect it to easily handle large and compicated expressions.\ +\>", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "FORM2FeynCalc", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[1]:=", + CellLabel->"In[136]:=", CellID->1139385107], Cell[BoxData[ @@ -153,20 +219,50 @@ Cell[BoxData[ RowBox[{"{", "}"}]}], ",", RowBox[{"Vectors", "\[Rule]", "Automatic"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{472, 54}, + ImageSize->{435, 53}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[1]=", - CellID->1509057543] + CellLabel->"Out[136]="] +}, Open ]] +}, Closed]] }, Open ]], Cell[CellGroupData[{ +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(2)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->1071045998], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(2)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->1307185854], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"FORM2FeynCalc", "[", "\"\\"", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1971183578], Cell[BoxData[ @@ -190,12 +286,11 @@ Cell[BoxData[ RowBox[{"2", " ", RowBox[{"x", ".", SuperscriptBox["m", "2"]}]}]}], TraditionalForm]], "Output", - ImageSize->{96, 20}, + ImageSize->{110, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[2]=", - CellID->437204044] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -203,7 +298,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1292875249], Cell[BoxData[ @@ -213,20 +308,23 @@ Cell[BoxData[ SuperscriptBox["m", "2"]}]}], "+", RowBox[{"SP", "[", RowBox[{"p", ",", "q"}], "]"}]}]], "Output", - ImageSize->{129, 15}, + ImageSize->{132, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[3]//StandardForm=", - CellID->1525941930] + CellLabel->"Out[2]//StandardForm="] }, Open ]], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + Cell["\<\ Functions are automatically converted right, but bracketed expressions need \ to be substituted explicitly.\ -\>", "Text", - CellTags->"FORM2FeynCalc", - CellID->1823304465], +\>", "Notes"], Cell[CellGroupData[{ @@ -238,7 +336,7 @@ Cell[BoxData[ RowBox[{"\"\<[li2(1-x)]\>\"", "\[Rule]", "\"\\""}], "}"}]}]}], "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[4]:=", + CellLabel->"In[1]:=", CellID->1620741920], Cell[BoxData[ @@ -250,12 +348,11 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["log", "2"], "(", "x", ")"}]}], TraditionalForm]], "Output",\ - ImageSize->{202, 18}, + ImageSize->{213, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[4]=", - CellID->827693663] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -263,7 +360,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[5]:=", + CellLabel->"In[2]:=", CellID->1897584456], Cell[BoxData[ @@ -274,12 +371,11 @@ Cell[BoxData[ RowBox[{"PolyLog", "[", RowBox[{"2", ",", RowBox[{"1", "-", "x"}]}], "]"}]}]], "Output", - ImageSize->{273, 15}, + ImageSize->{275, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[5]//StandardForm=", - CellID->879638641] + CellLabel->"Out[2]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -288,7 +384,7 @@ Cell[BoxData[ RowBox[{"FORM2FeynCalc", "[", "\"\\"", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[6]:=", + CellLabel->"In[3]:=", CellID->1533060910], Cell[BoxData[ @@ -302,12 +398,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"Hold", "[", "1", "]"}], ".", "y"}], "+", "x"}], TraditionalForm]], "Output", - ImageSize->{205, 18}, + ImageSize->{207, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[6]=", - CellID->1027470118] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -315,7 +410,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ReleaseHold", "[", "%", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[7]:=", + CellLabel->"In[4]:=", CellID->1512515442], Cell[BoxData[ @@ -326,12 +421,11 @@ Cell[BoxData[ RowBox[{"-", "1"}], ")"}], RowBox[{"m", "+", "1"}]], "+", "x", "+", RowBox[{"1", ".", "y"}]}], TraditionalForm]], "Output", - ImageSize->{120, 18}, + ImageSize->{128, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[7]=", - CellID->1640354437] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -340,40 +434,33 @@ Cell[BoxData[ RowBox[{"FORM2FeynCalc", "[", "\"\\"", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[8]:=", + CellLabel->"In[5]:=", CellID->2089442701], Cell[BoxData[ FormBox[ RowBox[{ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["nu", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["nu", + TraditionalForm], + TraditionalForm]}]], TraditionalForm], "+", RowBox[{ RowBox[{"p", "(", "mu", ")"}], ".", RowBox[{"q", "(", "nu", ")"}]}]}], TraditionalForm]], "Output", - ImageSize->{154, 19}, + ImageSize->{152, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[8]=", - CellID->758219802] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -381,7 +468,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[9]:=", + CellLabel->"In[6]:=", CellID->1054646204], Cell[BoxData[ @@ -391,12 +478,11 @@ Cell[BoxData[ RowBox[{"q", "[", "nu", "]"}]}], "+", RowBox[{"MT", "[", RowBox[{"mu", ",", "nu"}], "]"}]}]], "Output", - ImageSize->{203, 15}, + ImageSize->{197, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[9]//StandardForm=", - CellID->11165984] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -410,40 +496,33 @@ Cell[BoxData[ RowBox[{"mu", "\[Rule]", "\[Mu]"}], ",", RowBox[{"nu", "\[Rule]", "\[Nu]"}]}], "}"}]}]}], "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[10]:=", + CellLabel->"In[7]:=", CellID->1352382070], Cell[BoxData[ FormBox[ RowBox[{ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm], "+", RowBox[{ RowBox[{"p", "(", "\[Mu]", ")"}], ".", RowBox[{"q", "(", "\[Nu]", ")"}]}]}], TraditionalForm]], "Output", - ImageSize->{116, 19}, + ImageSize->{125, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[10]=", - CellID->291792517] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -453,7 +532,7 @@ Cell[BoxData[ "\"\\"", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[11]:=", + CellLabel->"In[8]:=", CellID->476542838], Cell[BoxData[ @@ -481,12 +560,12 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm], ")"}], ".", "blam"}], TraditionalForm]], "Output", - ImageSize->{446, 25}, + ImageSize->{432, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FORM2FeynCalc", - CellLabel->"Out[11]=", - CellID->276944378] + CellLabel->"Out[8]="] +}, Open ]] }, Open ]] }, Open ]], @@ -509,24 +588,19 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[TextData[{ - StyleBox[ButtonBox["FeynCalc2FORM", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/FeynCalc2FORM", - ButtonNote->"FeynCalc2FORM"], - FontFamily->"Verdana"], - "." -}], "Text", - CellTags->"FORM2FeynCalc", - CellID->1782635377] +Cell[TextData[StyleBox[ButtonBox["FeynCalc2FORM", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/FeynCalc2FORM", + ButtonNote->"FeynCalc2FORM"], + FontFamily->"Verdana"]], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"FORM2FeynCalc", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -535,26 +609,25 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 10.034466}", + "built" -> "{2020, 1, 5, 18, 57, 54.917912}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "FORM2FeynCalc[expr] translates the FORM expr into FeynCalc notation. \ -FORM2FeynCalc[file] translates the FORM expresssions in file into \ -FeynCalcnotation. FORM2FeynCalc[file, x1, x2, ...] reads in a file in \ -FORM-format and translates the assignments for the variables a, b, ... into \ -FeynCalc syntax. If the option Set is True, the variables x1, x2 are assigned \ -to the right hand sides defined in the FORM-file.", "synonyms" -> {}, "title" -> - "FORM2FeynCalc", "titlemodifier" -> "", "windowtitle" -> "FORM2FeynCalc", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/FORM2FeynCalc"}, - "SearchTextTranslated" -> ""}, + "FORM2FeynCalc[exp] translates the FORM exp into FeynCalc notation. \ +FORM2FeynCalc[file] translates the FORM expresssions in file into FeynCalc \ +notation. FORM2FeynCalc[file, x1, x2, ...] reads in a file in FORM-format and \ +translates the assignments for the variables a, b, ... into FeynCalc syntax.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FORM2FeynCalc", + "titlemodifier" -> "", "windowtitle" -> "FORM2FeynCalc", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/FORM2FeynCalc"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -563,7 +636,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -571,208 +644,188 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FORMEpilog\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FORMEpilog"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/FORMEpilog.\ -html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$73009], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/FORMEpilog", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc2FORM\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FeynCalc2FORM"], "\<\"FORMProlog\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FORMProlog"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/FORMEpilog\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/FORMEpilog"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ +FORMEpilog.html"], StandardForm]], "Input", TextClipboardType -> + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$141494], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/FORMEpilog", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +97,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FORMEpilog", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FORMEpilog", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -119,9 +153,7 @@ Cell[TextData[{ ButtonNote->"FORMProlog"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FORMEpilog", - CellID->703276888] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -138,21 +170,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 11.561638}", + "built" -> "{2020, 1, 5, 18, 57, 56.228565}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "FORMEpilog is an option for FeynCalc2FORM. It may be set to a string \ -which is put at the end of the FORM-file.", "synonyms" -> {}, "title" -> - "FORMEpilog", "titlemodifier" -> "", "windowtitle" -> "FORMEpilog", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/FORMEpilog"}}, +which is put at the end of the FORM-file.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "FORMEpilog", "titlemodifier" -> "", + "windowtitle" -> "FORMEpilog", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FORMEpilog"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -161,41 +194,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "FORMEpilog"->{ - Cell[3605, 108, 409, 15, 70, "Text", - CellTags->"FORMEpilog", - CellID->703276888]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"FORMEpilog", 5860, 171} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[582, 21, 2252, 52, 70, "AnchorBarGrid", +Cell[582, 21, 3119, 76, 70, "AnchorBarGrid", CellID->1], -Cell[2837, 75, 53, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2893, 78, 414, 12, 70, "Usage", +Cell[3704, 99, 287, 11, 70, "ObjectNameGrid"], +Cell[3994, 112, 414, 12, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3332, 94, 270, 12, 70, "SeeAlsoSection", +Cell[4433, 128, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3605, 108, 409, 15, 70, "Text", - CellTags->"FORMEpilog", - CellID->703276888] +Cell[4706, 142, 367, 13, 70, "SeeAlso"] }, Open ]], -Cell[4029, 126, 23, 0, 70, "FooterCell"] +Cell[5088, 158, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORMProlog.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORMProlog.nb index c7e83e0fd..bd1262b5c 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORMProlog.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FORMProlog.nb @@ -3,69 +3,93 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6342, 194] -NotebookOptionsPosition[ 4073, 128] -NotebookOutlinePosition[ 6079, 183] -CellTagsIndexPosition[ 6007, 178] +NotebookDataLength[ 7200, 217] +NotebookOptionsPosition[ 5132, 160] +NotebookOutlinePosition[ 6992, 209] +CellTagsIndexPosition[ 6949, 206] WindowTitle->FORMProlog WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FORMProlog\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FORMProlog"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/FORMProlog.\ -html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$73707], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/FORMProlog", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc2FORM\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FeynCalc2FORM"], "\<\"FORMEpilog\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FORMEpilog"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/FORMProlog\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/FORMProlog"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ +FORMProlog.html"], StandardForm]], "Input", TextClipboardType -> + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$142388], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/FORMProlog", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +97,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FORMProlog", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FORMProlog", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -119,9 +153,7 @@ Cell[TextData[{ ButtonNote->"FORMEpilog"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FORMProlog", - CellID->553964491] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -138,10 +170,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 14.092232}", + "built" -> "{2020, 1, 5, 18, 57, 58.143261}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -149,10 +181,11 @@ TaggingRules->{ "None", "summary" -> "FORMProlog is an option for FeynCalc2FORM. It may be set to a string \ which is put after the type declarations of the FORM-file.", "synonyms" -> {}, - "title" -> "FORMProlog", "titlemodifier" -> "", "windowtitle" -> - "FORMProlog", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FORMProlog"}}, + "tabletags" -> {}, "title" -> "FORMProlog", "titlemodifier" -> "", + "windowtitle" -> "FORMProlog", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FORMProlog"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -161,41 +194,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["FRH", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,7 +140,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1462863261], + CellID->277173287], Cell[CellGroupData[{ @@ -118,7 +150,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1933653438], + CellID->726842935], Cell[CellGroupData[{ @@ -139,12 +171,11 @@ Cell[BoxData[ RowBox[{"Hold", "[", RowBox[{"2", "-", "2"}], "]"}]}], "+", "1", "-", "1"}], "]"}], TraditionalForm]], "Output", - ImageSize->{177, 15}, + ImageSize->{177, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FRH", - CellLabel->"Out[1]=", - CellID->1110463745] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -157,12 +188,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FRH", - CellLabel->"Out[2]=", - CellID->313757423] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -175,7 +205,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"x", "^", "3"}], "-", "x", "-", "1"}], "==", "0"}], "]"}], ",", "x", ",", - RowBox[{"IsolateNames", "\[Rule]", "hh"}]}], "]"}]], "Input", + RowBox[{"IsolateNames", "\[Rule]", "KK"}]}], "]"}]], "Input", CellTags->"FRH", CellLabel->"In[3]:=", CellID->971664034], @@ -187,51 +217,126 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", "\[Rule]", TagBox[ - RowBox[{"hh", "(", "670", ")"}], + RowBox[{"KK", "(", "510", ")"}], HoldForm]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", TagBox[ - RowBox[{"hh", "(", "673", ")"}], + RowBox[{"KK", "(", "513", ")"}], HoldForm]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", TagBox[ - RowBox[{"hh", "(", "674", ")"}], + RowBox[{"KK", "(", "514", ")"}], HoldForm]}], "}"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{316, 15}, + ImageSize->{330, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FRH", - CellLabel->"Out[3]=", - CellID->529538815] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"FRH", "[", - RowBox[{"hh", "[", "3", "]"}], "]"}]], "Input", + RowBox[{"FRH", "[", "%", "]"}]], "Input", CellTags->"FRH", CellLabel->"In[4]:=", CellID->866394763], Cell[BoxData[ FormBox[ - RowBox[{"hh", "(", "3", ")"}], TraditionalForm]], "Output", - ImageSize->{42, 15}, + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"x", "\[Rule]", + RowBox[{ + RowBox[{ + FractionBox["1", "3"], " ", + RadicalBox[ + RowBox[{ + FractionBox["27", "2"], "-", + FractionBox[ + RowBox[{"3", " ", + SqrtBox["69"]}], "2"]}], "3"]}], "+", + FractionBox[ + RadicalBox[ + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"(", + RowBox[{"9", "+", + SqrtBox["69"]}], ")"}]}], "3"], + SuperscriptBox["3", + RowBox[{"2", "/", "3"}]]]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", "\[Rule]", + RowBox[{ + RowBox[{"-", + RowBox[{ + FractionBox["1", "6"], " ", + RowBox[{"(", + RowBox[{"1", "+", + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}]}], ")"}], " ", + RadicalBox[ + RowBox[{ + FractionBox["27", "2"], "-", + FractionBox[ + RowBox[{"3", " ", + SqrtBox["69"]}], "2"]}], "3"]}]}], "-", + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "-", + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}]}], ")"}], " ", + RadicalBox[ + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"(", + RowBox[{"9", "+", + SqrtBox["69"]}], ")"}]}], "3"]}], + RowBox[{"2", " ", + SuperscriptBox["3", + RowBox[{"2", "/", "3"}]]}]]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", "\[Rule]", + RowBox[{ + RowBox[{"-", + RowBox[{ + FractionBox["1", "6"], " ", + RowBox[{"(", + RowBox[{"1", "-", + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}]}], ")"}], " ", + RadicalBox[ + RowBox[{ + FractionBox["27", "2"], "-", + FractionBox[ + RowBox[{"3", " ", + SqrtBox["69"]}], "2"]}], "3"]}]}], "-", + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "+", + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}]}], ")"}], " ", + RadicalBox[ + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"(", + RowBox[{"9", "+", + SqrtBox["69"]}], ")"}]}], "3"]}], + RowBox[{"2", " ", + SuperscriptBox["3", + RowBox[{"2", "/", "3"}]]}]]}]}], "}"}]}], "}"}], + TraditionalForm]], "Output", + ImageSize->{484, 232}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FRH", - 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CellID->1224892054], +Cell[TextData[{ + Cell["FUNCTION", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -115,9 +147,7 @@ Cell[TextData[{ ButtonNote->"Write2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FUNCTION", - CellID->234059656] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -134,21 +164,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 28.134756}", + "built" -> "{2020, 1, 5, 18, 58, 10.454556}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "FUNCTION[exp, string] is a head of an expression to be declared a \ -function (of type string), if used in Write2.", "synonyms" -> {}, "title" -> - "FUNCTION", "titlemodifier" -> "", "windowtitle" -> "FUNCTION", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/FUNCTION"}}, +function (of type string), if used in Write2.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "FUNCTION", "titlemodifier" -> "", + "windowtitle" -> "FUNCTION", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FUNCTION"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -157,41 +188,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "FUNCTION"->{ - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FV\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FV"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/FV.html"], - StandardForm]], "Input", TextClipboardType -> "PlainText"]}, - Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$77532], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/FV", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FCE\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCE"], "\<\"FCI\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCI"], "\<\"FVD\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FVD"], "\<\"Pair\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Pair"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/FV\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/FV"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/FV.html"], + StandardForm]], "Input", TextClipboardType -> "PlainText"]}, + Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$148242], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/FV", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +98,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["FV", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FV", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,7 +147,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->2064034391], + CellID->1196530961], Cell[CellGroupData[{ @@ -122,7 +157,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1940107799], + CellID->792562904], Cell[CellGroupData[{ @@ -135,26 +170,21 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], TraditionalForm]], "Output", - ImageSize->{24, 19}, + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + ImageSize->{28, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FV", - CellLabel->"Out[1]=", - CellID->1773215925] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -169,33 +199,28 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm], TraditionalForm]], "Output", - ImageSize->{62, 20}, + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + ImageSize->{70, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FV", - CellLabel->"Out[2]=", - CellID->1009721662] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -211,12 +236,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Output", - ImageSize->{70, 15}, + ImageSize->{71, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FV", - CellLabel->"Out[3]//StandardForm=", - CellID->732230663] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -236,20 +260,15 @@ Cell[BoxData[ RowBox[{ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]], "Output", - ImageSize->{281, 15}, + ImageSize->{283, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FV", - CellLabel->"Out[4]//StandardForm=", - CellID->1070070718] + CellLabel->"Out[4]//StandardForm="] }, Open ]], -Cell["\<\ -There is no special function to expand momenta in FV; ExpandScalarProduct \ -does the job.\ -\>", "Text", - CellTags->"FV", - CellID->1859479702], +Cell["ExpandScalarProduct is used to expand momenta in FV", "Notes", + CellID->97927264], Cell[CellGroupData[{ @@ -258,73 +277,36 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{ RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}], "]"}]], "Input", - CellTags->"FV", CellLabel->"In[5]:=", - CellID->260687674], + CellID->1140711302], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], "-", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - 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CellTags->"FV", - CellLabel->"Out[6]//StandardForm=", - CellID->1086258444] + CellLabel->"Out[5]="] }, Open ]] }, Open ]], @@ -366,21 +348,13 @@ Cell[TextData[{ ButtonNote->"FVD"], FontFamily->"Verdana"], ", ", - StyleBox[ButtonBox["FourVector", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], - FontFamily->"Verdana"], - ", ", StyleBox[ButtonBox["Pair", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/Pair", ButtonNote->"Pair"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FV", - CellID->449809030] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -388,7 +362,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"FV", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -397,20 +371,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 31.033352}", + "built" -> "{2020, 1, 5, 18, 58, 13.893687}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "FV[p, mu] is the four-dimensional vector p^\\[Mu]. 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DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/Factor1.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$54880], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/Factor1", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$87357], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/Factor1", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Factor1", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Factor1", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,7 +140,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1743631578], + CellID->256108941], Cell[CellGroupData[{ @@ -118,17 +150,16 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->442500656], + CellID->1116701667], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{ - RowBox[{"(", - RowBox[{"a", "-", "x"}], ")"}], - RowBox[{"(", - RowBox[{"b", "-", "x"}], ")"}]}]}]], "Input", + RowBox[{ + RowBox[{"(", + RowBox[{"a", "-", "x"}], ")"}], + RowBox[{"(", + RowBox[{"b", "-", "x"}], ")"}]}]], "Input", CellTags->"Factor1", CellLabel->"In[1]:=", CellID->106113384], @@ -140,22 +171,20 @@ Cell[BoxData[ RowBox[{"a", "-", "x"}], ")"}], " ", RowBox[{"(", RowBox[{"b", "-", "x"}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{97, 15}, + ImageSize->{107, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Factor1", - CellLabel->"Out[1]=", - CellID->705307377] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"Factor1", "[", "t1", "]"}], ",", " ", - RowBox[{"Factor", "[", "t1", "]"}]}], "}"}]}]], "Input", + RowBox[{"{", + RowBox[{ + RowBox[{"Factor1", "[", "%", "]"}], ",", " ", + RowBox[{"Factor", "[", "%", "]"}]}], "}"}]], "Input", CellTags->"Factor1", CellLabel->"In[2]:=", CellID->1501862951], @@ -175,24 +204,22 @@ Cell[BoxData[ RowBox[{"a", "-", "x"}], ")"}]}], " ", RowBox[{"(", RowBox[{"x", "-", "b"}], ")"}]}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{221, 15}, + ImageSize->{242, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Factor1", - CellLabel->"Out[2]=", - CellID->1528620346] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t3", "=", - RowBox[{"Expand", "[", - RowBox[{ - RowBox[{"(", - RowBox[{"a", "-", "b"}], ")"}], - RowBox[{"(", - RowBox[{"a", "+", "b"}], ")"}]}], "]"}]}]], "Input", + RowBox[{"Expand", "[", + RowBox[{ + RowBox[{"(", + RowBox[{"a", "-", "b"}], ")"}], + RowBox[{"(", + RowBox[{"a", "+", "b"}], ")"}]}], "]"}]], "Input", CellTags->"Factor1", CellLabel->"In[3]:=", CellID->641613489], @@ -202,18 +229,17 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], TraditionalForm]], "Output", - ImageSize->{53, 18}, + ImageSize->{58, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Factor1", - CellLabel->"Out[3]=", - CellID->2030611853] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Factor", "[", "t3", "]"}]], "Input", + RowBox[{"Factor", "[", "%", "]"}]], "Input", CellTags->"Factor1", CellLabel->"In[4]:=", CellID->916389340], @@ -225,18 +251,17 @@ Cell[BoxData[ RowBox[{"a", "-", "b"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{97, 15}, + ImageSize->{107, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Factor1", - CellLabel->"Out[4]=", - CellID->865327707] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Factor1", "[", "t3", "]"}]], "Input", + RowBox[{"Factor1", "[", "%%", "]"}]], "Input", CellTags->"Factor1", CellLabel->"In[5]:=", CellID->892191531], @@ -246,20 +271,12 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], TraditionalForm]], "Output", - ImageSize->{53, 18}, + ImageSize->{58, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Factor1", - CellLabel->"Out[5]=", - CellID->1139945824] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2", ",", "t3"}], "]"}]], "Input", - CellTags->"Factor1", - CellLabel->"In[6]:=", - CellID->1482315372] + CellLabel->"Out[5]="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] @@ -288,9 +305,7 @@ Cell[TextData[{ ButtonNote->"Factor2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Factor1", - CellID->73262209] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -298,7 +313,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"Factor1", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -307,21 +322,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 53.580150}", + "built" -> "{2020, 1, 5, 18, 55, 30.104899}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "Factor1[poly] factorizes common terms in the summands of poly. It uses \ -basically PolynomialGCD.", "synonyms" -> {}, "title" -> "Factor1", - "titlemodifier" -> "", "windowtitle" -> "Factor1", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/Factor1"}, "SearchTextTranslated" -> ""}, +basically PolynomialGCD.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "Factor1", "titlemodifier" -> "", "windowtitle" -> "Factor1", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/Factor1"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -329,8 +345,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -339,123 +356,101 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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RowBox[{"Factor", "[", "t3", "]"}]], "Input", + RowBox[{"Factor", "[", "%", "]"}]], "Input", CellTags->"Factor2", - CellLabel->"In[5]:=", + CellLabel->"In[4]:=", CellID->791609042], Cell[BoxData[ @@ -250,20 +306,19 @@ Cell[BoxData[ RowBox[{"a", "-", "b"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{97, 15}, + ImageSize->{107, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Factor2", - CellLabel->"Out[5]=", - CellID->2074352994] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Factor2", "[", "t3", "]"}]], "Input", + RowBox[{"Factor2", "[", "%%", "]"}]], "Input", CellTags->"Factor2", - CellLabel->"In[6]:=", + CellLabel->"In[5]:=", CellID->880415397], Cell[BoxData[ @@ -271,22 +326,21 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], TraditionalForm]], "Output", - ImageSize->{53, 18}, + ImageSize->{58, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Factor2", - CellLabel->"Out[6]=", - CellID->611482702] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor2", "[", - RowBox[{"t3", ",", + RowBox[{"%%%", ",", RowBox[{"FactorFull", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Factor2", - CellLabel->"In[7]:=", + CellLabel->"In[6]:=", CellID->17862753], Cell[BoxData[ @@ -296,20 +350,12 @@ Cell[BoxData[ RowBox[{"a", "-", "b"}], ")"}], " ", RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{97, 15}, + ImageSize->{107, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Factor2", - CellLabel->"Out[7]=", - CellID->1886805891] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2", ",", "t3"}], "]"}]], "Input", - CellTags->"Factor2", - CellLabel->"In[8]:=", - CellID->2010909365] + CellLabel->"Out[6]="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] @@ -338,17 +384,15 @@ Cell[TextData[{ ButtonNote->"Collect2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Factor2", - CellID->1336134208] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"Factor2", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -357,10 +401,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 55.029800}", + "built" -> "{2020, 1, 5, 18, 55, 31.306495}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -370,12 +414,12 @@ TaggingRules->{ sometimes better than Factor on polynomials involving rationals with sums in \ the denominator. Factor2 uses Factor internally and is in general slower than \ Factor. There are four possible settings of the option Method (0,1,2,3). In \ -general Factor will work faster than Factor2.", "synonyms" -> {}, "title" -> - "Factor2", "titlemodifier" -> "", "windowtitle" -> "Factor2", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/Factor2"}, "SearchTextTranslated" -> - ""}, +general Factor will work faster than Factor2.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "Factor2", "titlemodifier" -> "", + "windowtitle" -> "Factor2", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/Factor2"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -383,8 +427,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -393,151 +438,125 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["FactorFull", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -133,9 +165,7 @@ Cell[TextData[{ ButtonNote->"Factor2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FactorFull", - CellID->1018782586] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -152,10 +182,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 56.603925}", + "built" -> "{2020, 1, 5, 18, 55, 32.525318}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -163,10 +193,11 @@ TaggingRules->{ "None", "summary" -> "FactorFull is an option of Factor2 (default False). If set to False, \ products like (a-b) (a+b) will be replaced by (a^2-b^2).", "synonyms" -> {}, - "title" -> "FactorFull", "titlemodifier" -> "", "windowtitle" -> - "FactorFull", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FactorFull"}}, + "tabletags" -> {}, "title" -> "FactorFull", "titlemodifier" -> "", + "windowtitle" -> "FactorFull", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FactorFull"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -175,41 +206,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "FactorFull"->{ - Cell[4026, 128, 227, 9, 70, "Text", - CellTags->"FactorFull", - CellID->1018782586]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"FactorFull", 6114, 185} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[582, 21, 2252, 52, 70, "AnchorBarGrid", +Cell[582, 21, 3008, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2837, 75, 53, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2893, 78, 835, 32, 70, "Usage", +Cell[3593, 97, 287, 11, 70, "ObjectNameGrid"], +Cell[3883, 110, 835, 32, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3753, 114, 270, 12, 70, "SeeAlsoSection", +Cell[4743, 146, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[4026, 128, 227, 9, 70, "Text", - CellTags->"FactorFull", - CellID->1018782586] +Cell[5016, 160, 184, 7, 70, "SeeAlso"] }, Open ]], -Cell[4268, 140, 23, 0, 70, "FooterCell"] +Cell[5215, 170, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Factoring.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Factoring.nb index b00b92400..3cfebd87e 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Factoring.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Factoring.nb @@ -3,69 +3,93 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6566, 202] -NotebookOptionsPosition[ 4245, 135] -NotebookOutlinePosition[ 6303, 191] -CellTagsIndexPosition[ 6232, 186] +NotebookDataLength[ 7471, 224] +NotebookOptionsPosition[ 5354, 167] +NotebookOutlinePosition[ 7263, 216] +CellTagsIndexPosition[ 7220, 213] WindowTitle->Factoring WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/Factoring\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/Factoring"]}, Visible -> False]]; 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SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$88677], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/Factoring", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +97,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Factoring", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Factoring", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -126,9 +160,7 @@ Cell[TextData[{ ButtonNote->"Tr"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Factoring", - CellID->1376974355] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -145,10 +177,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 18, 57.884378}", + "built" -> "{2020, 1, 5, 18, 55, 33.553768}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -156,11 +188,11 @@ TaggingRules->{ "None", "summary" -> "Factoring is an option for Collect2, Contract, Tr and more functions. 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There are \ +however special typesetting rules attached.\ +\>", "Notes", + CellID->1067943069] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -112,7 +181,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1464467340], + CellID->618300883], Cell[CellGroupData[{ @@ -122,14 +191,12 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->652924101], + CellID->493798849], Cell["\<\ This is a 1-loop gluon self-energy amplitude (ignoring factors of (2 \[Pi])).\ \ -\>", "Text", - CellTags->"FeynAmp", - CellID->1803940715], +\>", "Notes"], Cell[CellGroupData[{ @@ -302,17 +369,14 @@ Cell[BoxData[ RowBox[{"p", "-", "q"}], TraditionalForm], ")"}]}], TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{574, 33}, + ImageSize->{449, 69}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynAmp", - CellLabel->"Out[1]=", - CellID->1301141355] + CellLabel->"Out[1]="] }, Open ]], -Cell["This is a generic 2-loop amplitude.", "Text", - CellTags->"FeynAmp", - CellID->311938840], +Cell["This is a generic 2-loop amplitude.", "Notes"], Cell[CellGroupData[{ @@ -332,12 +396,11 @@ Cell[BoxData[ SubscriptBox["q", "1"], ",", SubscriptBox["q", "2"], ",", "anyexpression"}], ")"}], TraditionalForm]], "Output", - ImageSize->{209, 17}, + ImageSize->{203, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynAmp", - CellLabel->"Out[2]=", - CellID->1833982253] + CellLabel->"Out[2]="] }, Open ]] }, Open ]], @@ -367,9 +430,7 @@ Cell[TextData[{ ButtonNote->"Amplitude"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FeynAmp", - CellID->1771618737] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -386,10 +447,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 43.798937}", + "built" -> "{2020, 1, 5, 18, 57, 34.080536}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -397,13 +458,12 @@ TaggingRules->{ "None", "summary" -> "FeynAmp[q, amp] is the head of a Feynman amplitude, where amp denotes \ the analytical expression for the amplitude and q is the integration \ -variable. FeynAmp[q1, q2, amp] denotes a two-loop amplitude. FeynAmp has no \ -functional properties and serves just as a head. There are however special \ -typesetting rules attached.", "synonyms" -> {}, "title" -> "FeynAmp", +variable. FeynAmp[q1, q2, amp] denotes a two-loop amplitude.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FeynAmp", "titlemodifier" -> "", "windowtitle" -> "FeynAmp", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FeynAmp"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -412,7 +472,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -421,87 +481,77 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3589, 99, 388, 15, 31, "PrimaryExamplesSection", + Cell[5461, 168, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - 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FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"", + SuperscriptBox["m", "2"],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + ImageSize->{102, 40}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"FeynAmpDenominator", - CellLabel->"Out[4]//StandardForm=", - CellID->1126645796] + CellLabel->"Out[5]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", "MM", ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[6]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"","MM", + "\"+\"",RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + ImageSize->{105, 40}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[6]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"SPD", "[", + RowBox[{"q", ",", "q"}], "]"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[7]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"",FormBox[ + SuperscriptBox[ + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm], 2], TraditionalForm], + "\"+\"",RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + ImageSize->{99, 40}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[7]="] +}, Open ]], + +Cell[TextData[{ + "One can also change the sign of the ", + Cell[BoxData[ + RowBox[{"I", " ", "\[Eta]"}]], "InlineFormula"], + "- prescription, although currently no internal functions make use of it" +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{"-", "1"}]}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[8]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\"-\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + ImageSize->{103, 40}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[8]="] +}, Open ]], + +Cell["The propagator may be raised to integer or symbolic powers", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{"3", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[9]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + SuperscriptBox[ + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"", + SuperscriptBox["m", "2"],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"], "3"]], TraditionalForm]], "Output", + ImageSize->{110, 40}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[9]="] +}, Open ]], + 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"0", ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{"n", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[11]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"", + SuperscriptBox["m", "2"],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"], + RowBox[{"-", "n"}]], TraditionalForm]], "Output", + ImageSize->{117, 18}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[11]="] +}, Open ]], + +Cell["Eikonal propagators are also supported", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}], ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[12]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",RowBox[{ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm]}],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + ImageSize->{118, 40}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[12]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}], ",", "0", ",", 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This is where the ", + Cell[BoxData[ + RowBox[{"I", " ", "\[Eta]"}]], "InlineFormula"], + "- prescription may come handy" +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"-", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}]}], ",", "0", ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[14]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"","\"-\"",RowBox[{ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + ImageSize->{94, 38}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"t", "//", "FCE"}], "]"}]], "Input", + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}], ",", "0", ",", + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{"-", "1"}]}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[15]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",RowBox[{ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm]}],"\"-\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + ImageSize->{84, 38}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[15]="] +}, Open ]], + +Cell["\<\ +The shortcut to enter FeynAmpDenominators with StandardPropagatorDenominators \ +is SFAD\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}], "//", "FCE"}], "//", + "StandardForm"}]], "Input", CellTags->"FeynAmpDenominator", - CellLabel->"In[5]:=", - CellID->1592188506], + CellLabel->"In[16]:=", + CellID->484409356], Cell[BoxData[ - RowBox[{"FAD", "[", + RowBox[{"SFAD", "[", RowBox[{"{", - RowBox[{"p", ",", "m"}], "}"}], "]"}]], "Output", - ImageSize->{94, 15}, + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + SuperscriptBox["m", "2"], ",", "1"}], "}"}], ",", "1"}], "}"}], + "]"}]], "Output", + ImageSize->{205, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynAmpDenominator", - CellLabel->"Out[5]//StandardForm=", - CellID->1536013774] + CellLabel->"Out[16]//StandardForm="] }, Open ]], +Cell["\<\ +Eikonal propagators are entered using the dot (\".\") as in noncommutative \ +products\ +\>", "Notes"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ - RowBox[{"Clear", "[", "t", "]"}], ";"}]], "Input", - CellTags->"FeynAmpDenominator", - CellLabel->"In[6]:=", - CellID->1230382152] + RowBox[{ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}], ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}], "//", "FCE"}], "//", + "StandardForm"}]], "Input", + CellLabel->"In[17]:="], + +Cell[BoxData[ + RowBox[{"SFAD", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"p", ".", "q"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + SuperscriptBox["m", "2"], ",", "1"}], "}"}], ",", "1"}], "}"}], + "]"}]], "Output", + ImageSize->{223, 21}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[17]//StandardForm="] +}, Open ]], + +Cell["\<\ +The Cartesian version of StandardPropagatorDenominator is called \ +CartesianPropagatorDenominator. 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Different propagator \ +denominators are represented using special heads such as \ +PropagatorDenominator, StandardPropagatorDenominator, \ +CartesianPropagatorDenominator etc.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "FeynAmpDenominator", "titlemodifier" -> "", "windowtitle" -> "FeynAmpDenominator", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FeynAmpDenominator"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -319,7 +1158,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -328,115 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"RowsIndexed" -> {}}}, CellID->1], -Cell["FeynAmpDenominatorSimplify", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FeynAmpDenominatorSimplify", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ RowBox[{"FeynAmpDenominatorSimplify", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "tries to simplify each PropagatorDenominator in a canonical way. \ -FeynAmpDenominatorSimplify[exp, q1] simplifies all FeynAmpDenominator's in \ -exp in a canonical way, including some translation of momenta. \ -FeynAmpDenominatorSimplify[exp, q1, q2] additionally removes integrals with \ -no mass scale.\n\nFDS can be used as an alias." + " \[LineSeparator]tries to simplify each PropagatorDenominator in a \ +canonical way. FeynAmpDenominatorSimplify[exp, q1] simplifies all \ +FeynAmpDenominator's in exp in a canonical way, including some translation of \ +momenta. FeynAmpDenominatorSimplify[exp, q1, q2] additionally removes \ +integrals with no mass scale." }]]} }]], "Usage", GridBoxOptions->{ @@ -99,6 +132,41 @@ no mass scale.\n\nFDS can be used as an alias." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1104034988], + +Cell["", "SectionHeaderSpacer"], + +Cell["FDS can be used as an alias.", "Notes", + CellID->1067943069] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -114,7 +182,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->865391719], + CellID->1330700296], Cell[CellGroupData[{ @@ -124,7 +192,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1544574464], + CellID->690731379], Cell[CellGroupData[{ @@ -135,12 +203,11 @@ Cell[BoxData["FDS"], "Input", Cell[BoxData[ FormBox["FeynAmpDenominatorSimplify", TraditionalForm]], "Output", - ImageSize->{196, 15}, + ImageSize->{179, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"Out[1]=", - CellID->1554505245] + CellLabel->"Out[1]="] }, Open ]], Cell[TextData[{ @@ -156,9 +223,7 @@ Cell[TextData[{ SuperscriptBox["k", RowBox[{"2", "m"}]]}]}]}], "=", " ", RowBox[{"0", " ", "."}]}], TraditionalForm]]] -}], "Text", - CellTags->"FeynAmpDenominatorSimplify", - CellID->652878159], +}], "Notes"], Cell[CellGroupData[{ @@ -175,12 +240,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"Out[2]=", - CellID->1407968210] + CellLabel->"Out[2]="] }, Open ]], Cell[TextData[{ @@ -200,9 +264,7 @@ Cell[TextData[{ SubscriptBox["p", "2"]}], ")"}], "2"]}], ")"}]}], TraditionalForm]]], " into a standard form." -}], "Text", - CellTags->"FeynAmpDenominatorSimplify", - CellID->2080676792], +}], "Notes"], Cell[CellGroupData[{ @@ -223,34 +285,58 @@ Cell[BoxData[ FormBox[ FractionBox["1", RowBox[{ - SuperscriptBox[ - FormBox["k", - TraditionalForm], "2"], ".", - SuperscriptBox[ - RowBox[{"(", - RowBox[{ + InterpretationBox[ + SuperscriptBox[ + FormBox[ FormBox["k", - TraditionalForm], "-", - SubscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox["1", - TraditionalForm]], "+", - SubscriptBox[ + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`k, D], + FeynCalc`Momentum[$CellContext`k, D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ FormBox[ - 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FeynCalc`Momentum[ + Subscript[$CellContext`p, 1], D] + FeynCalc`Momentum[ + Subscript[$CellContext`p, 2], D]]], + Editable->False]}]], TraditionalForm]], "Output", + ImageSize->{136, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"Out[8]=", - CellID->1920009759] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -654,32 +805,50 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]}], ")"}], "2"], RowBox[{ - SuperscriptBox[ - FormBox["k", - TraditionalForm], "2"], ".", - SuperscriptBox[ - RowBox[{"(", - RowBox[{ + InterpretationBox[ + SuperscriptBox[ + FormBox[ FormBox["k", - TraditionalForm], "-", - FormBox["p1", - TraditionalForm], "+", - FormBox["p2", - TraditionalForm]}], ")"}], "2"]}]], TraditionalForm]], "Output", - ImageSize->{121, 50}, + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`k, D], + FeynCalc`Momentum[$CellContext`k, D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["k", + TraditionalForm], "-", + FormBox["p1", + TraditionalForm], "+", + FormBox["p2", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`k, D] - + FeynCalc`Momentum[$CellContext`p1, D] + + FeynCalc`Momentum[$CellContext`p2, D], + FeynCalc`Momentum[$CellContext`k, D] - + FeynCalc`Momentum[$CellContext`p1, D] + + FeynCalc`Momentum[$CellContext`p2, D]]], + Editable->False]}]], TraditionalForm]], "Output", + ImageSize->{134, 43}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"Out[9]=", - CellID->1092598212] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"t", ",", "r"}], "]"}]], "Input", - CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"In[10]:=", - CellID->1443488055] + CellLabel->"Out[9]="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] @@ -702,23 +871,21 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["OneLoopSimplify", + StyleBox[ButtonBox["TID", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/OneLoopSimplify", - ButtonNote->"OneLoopSimplify"], + ButtonData->"paclet:FeynCalc/ref/TID", + ButtonNote->"TID"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FeynAmpDenominatorSimplify", - CellID->1104174358] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"FeynAmpDenominatorSimplify", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -727,10 +894,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 39.446097}", + "built" -> "{2020, 1, 5, 18, 57, 30.673972}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -740,13 +907,13 @@ TaggingRules->{ PropagatorDenominator in a canonical way. FeynAmpDenominatorSimplify[exp, q1] \ simplifies all FeynAmpDenominator's in exp in a canonical way, including some \ translation of momenta. FeynAmpDenominatorSimplify[exp, q1, q2] additionally \ -removes integrals with no mass scale. 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CellTags->"FeynAmpDenominatorSplit", - CellID->1583918878] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -383,10 +609,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 40.992096}", + "built" -> "{2020, 1, 5, 18, 57, 31.865841}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -396,11 +622,12 @@ TaggingRules->{ expr into FeynAmpDenominator[a]*FeynAmpDenominator[b] ... . \ FeynAmpDenominatorSplit[expr, q1] splits all FeynAmpDenominator in expr into \ a product of two, one containing q1 and other momenta, the second without \ -q1.", "synonyms" -> {}, "title" -> "FeynAmpDenominatorSplit", "titlemodifier" -> - 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CellID->1224892054], +Cell[TextData[{ + Cell["FeynAmpList", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -85,9 +117,7 @@ Cell[BoxData[GridBox[{ RowBox[{"FeynAmp", "[", "...", "]"}], ",", " ", RowBox[{"FeynAmp", "[", "...", "]"}], ",", " ", "..."}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is a head of a list of Feynman amplitudes.\nFeynAmpList has no \ -functional properties and serves just as a head." + " \[LineSeparator]is a head of a list of Feynman amplitudes." }]]} }]], "Usage", GridBoxOptions->{ @@ -98,6 +128,42 @@ functional properties and serves just as a head." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], + +Cell["", "SectionHeaderSpacer"], + +Cell["\<\ +FeynAmpList has no functional properties and serves just as a head.\ +\>", "Notes", + CellID->1067943069] +}, Closed]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -119,9 +185,7 @@ Cell[TextData[{ ButtonNote->"FeynAmp"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FeynAmpList", - CellID->1636179239] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -138,22 +202,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 42.510512}", + "built" -> "{2020, 1, 5, 18, 57, 33.138252}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "FeynAmpList[info][FeynAmp[ ...], FeynAmp[ ...], ...] is a head of a list \ -of Feynman amplitudes. FeynAmpList has no functional properties and serves \ -just as a head.", "synonyms" -> {}, "title" -> "FeynAmpList", "titlemodifier" -> - "", "windowtitle" -> "FeynAmpList", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/FeynAmpList"}}, +of Feynman amplitudes.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "FeynAmpList", "titlemodifier" -> "", "windowtitle" -> "FeynAmpList", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/FeynAmpList"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -162,41 +225,39 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "FeynAmpList"->{ - Cell[3834, 114, 228, 9, 70, "Text", - CellTags->"FeynAmpList", - CellID->1636179239]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"FeynAmpList", 5968, 172} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[583, 21, 2257, 52, 70, "AnchorBarGrid", +Cell[583, 21, 3013, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2843, 75, 54, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2900, 78, 636, 18, 70, "Usage", +Cell[3599, 97, 288, 11, 70, "ObjectNameGrid"], +Cell[3890, 110, 556, 16, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3561, 100, 270, 12, 70, "SeeAlsoSection", +Cell[4471, 130, 730, 24, 70, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], +Cell[5204, 156, 31, 0, 70, "SectionHeaderSpacer"], +Cell[5238, 158, 113, 3, 70, "Notes", + CellID->1067943069] +}, Closed]], +Cell[CellGroupData[{ +Cell[5388, 166, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3834, 114, 228, 9, 70, "Text", - CellTags->"FeynAmpList", - CellID->1636179239] +Cell[5661, 180, 184, 7, 70, "SeeAlso"] }, Open ]], -Cell[4077, 126, 23, 0, 70, "FooterCell"] +Cell[5860, 190, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FeynCalc.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FeynCalc.nb index ba96a9cd5..83c3d8722 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FeynCalc.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FeynCalc.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 8094, 245] -NotebookOptionsPosition[ 4884, 151] -NotebookOutlinePosition[ 7453, 221] -CellTagsIndexPosition[ 7284, 214] +NotebookDataLength[ 7864, 240] +NotebookOptionsPosition[ 4927, 155] +NotebookOutlinePosition[ 7347, 221] +CellTagsIndexPosition[ 7178, 214] WindowTitle->FeynCalc WindowFrame->Normal*) @@ -59,12 +59,13 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$68207], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$135222], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/FeynCalc", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FeynCalc", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FeynCalc", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -118,10 +129,6 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1], -Cell["Examples", "Subsubsection", - CellTags->"FeynCalc", - CellID->1788950203], - Cell[CellGroupData[{ Cell[BoxData[ @@ -131,18 +138,15 @@ Cell[BoxData[ CellID->1258876634], Cell[BoxData[ - StyleBox["\<\"For installation notes visit www.feyncalc.org\\n\\nFor a list \ -of availabe objects type $FeynCalcStuff, which contains a list of all \ -functions and options in StringForm. 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You can \ +get on-line information by ?function, e.g. ?Contract.\\n\\nThere are several \ +useful functions for short input, type $FCS for a list of short commands. \ +Then type, e.g., ?GA.\\n\\n\\nTo enable/disable start-up messages, put the \ line\\n\\n$FeynCalcStartupMessages = \ True;\\n\\nor\\n\\n$FeynCalcStartupMessages = False;\\n\\ninto your \ \\\"init.m\\\" file or into your \\\"FCConfig.m\\\" file.\"\>", "MSG"]], "Print", "PrintUsage", - CellTags->{"FeynCalc", "Info-1d55ee43-67b8-4d8b-8c35-3f3a2bc368ed"}, - CellID->144621555] + CellTags->{"FeynCalc", "Info-d5d5947c-0e52-48a8-b6a9-37ad11b1e404"}] }, Open ]] }, Open ]] }, Open ]], @@ -161,20 +165,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 51.643140}", + "built" -> "{2020, 1, 5, 18, 57, 40.058823}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "FeynCalc is simply a symbol with a usage definition.", "synonyms" -> {}, - "title" -> "FeynCalc", "titlemodifier" -> "", "windowtitle" -> "FeynCalc", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/FeynCalc"}}, + "tabletags" -> {}, "title" -> "FeynCalc", "titlemodifier" -> "", + "windowtitle" -> "FeynCalc", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FeynCalc"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -183,7 +188,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - 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CellID->1224892054], +Cell[TextData[{ + Cell["FeynCalc2FORM", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"FeynCalc2FORM", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "displays expr in FORM syntax. FeynCalc2FORM[file, x] writes x in FORM \ -syntax to a file. FeynCalc2FORM[file, x==y] writes x=y to a file in FORM \ -syntax." + RowBox[{"FeynCalc2FORM", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]displays ", + Cell[BoxData["exp"], "InlineFormula"], + " in FORM syntax." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"FeynCalc2FORM", "[", + RowBox[{"file", ",", "x"}], "]"}]], "InlineFormula"], + " \[LineSeparator]writes ", + Cell[BoxData["x"], "InlineFormula"], + " in FORM syntax to a file." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"FeynCalc2FORM", "[", + RowBox[{"file", ",", + RowBox[{"x", "\[Equal]", "y"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]writes ", + Cell[BoxData[ + RowBox[{"x", "=", "y"}]], "InlineFormula"], + " to a file in FORM syntax." }]]} }]], "Usage", GridBoxOptions->{ GridBoxBackground->{ - "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, - "RowsIndexed" -> {}}}, - CellID->982511436], + "Columns" -> {{None}}, "ColumnsIndexed" -> {}, + "Rows" -> {None, None, 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RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"FORMAbbreviations", "\[Rule]", + RowBox[{"{", + RowBox[{"\<\"syFC\"\>", ",", "\<\"vFC\"\>"}], "}"}]}], ",", + RowBox[{"FORMEpilog", "\[Rule]", + RowBox[{"{", + RowBox[{"\<\"print;\"\>", ",", "\<\".end\"\>"}], "}"}]}], ",", + RowBox[{"FORMIdStatements", "\[Rule]", "True"}], ",", RowBox[{"FORMProlog", "\[Rule]", "\<\"write statistics;\"\>"}], ",", RowBox[{"Replace", "\[Rule]", RowBox[{"{", @@ -150,16 +216,46 @@ Cell[BoxData[ ",", RowBox[{"TraceDimension", "\[Rule]", "4"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{524, 54}, + ImageSize->{492, 92}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalc2FORM", - CellLabel->"Out[1]=", - CellID->490814627] + CellLabel->"Out[135]="] +}, Open ]] +}, Closed]] }, Open ]], Cell[CellGroupData[{ +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(4)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->1372230660], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(4)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->504486489], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ RowBox[{"MT", "[", @@ -169,7 +265,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"y", "^", "2"}], "/", "d"}]}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1451127405], Cell[BoxData[ @@ -178,46 +274,35 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["y", "2"], " ", FormBox[ - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], " ", + FormBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Mu]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], + FormBox["\[Nu]", TraditionalForm], - TraditionalForm]], - TraditionalForm], - TraditionalForm], " ", - FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + TraditionalForm]}]], TraditionalForm]}], "d"], TraditionalForm]], "Output", - ImageSize->{83, 45}, + ImageSize->{90, 38}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalc2FORM", - CellLabel->"Out[2]=", - CellID->1238649149] + 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CellLabel->"In[8]:=", + CellLabel->"In[3]:=", CellID->2088847593], Cell[BoxData[ @@ -418,12 +505,11 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", - ImageSize->{140, 20}, + ImageSize->{144, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalc2FORM", - CellLabel->"Out[8]=", - CellID->1720680077] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -432,15 +518,21 @@ Cell[BoxData[ RowBox[{ RowBox[{"FeynCalc2FORM", "[", "%", "]"}], ";"}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[9]:=", + CellLabel->"In[4]:=", CellID->1981124799], Cell["g_(0,mu)*g_(0,nu)*g_(1,mu)*g_(1,ro)", "Print", CellTags->"FeynCalc2FORM", - CellLabel->"During evaluation of In[9]:=", - CellID->1021911992] + CellLabel->"During evaluation of In[119]:="] +}, Open ]] }, Open ]], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], 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"[", "t", "]"}], ";"}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[16]:=", + CellLabel->"In[5]:=", CellID->261285927] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] @@ -763,16 +796,11 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[TextData[{ - StyleBox[ButtonBox["FORM2FeynCalc", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/FORM2FeynCalc", - ButtonNote->"FORM2FeynCalc"], - FontFamily->"Verdana"], - "." -}], "Text", - CellTags->"FeynCalc2FORM", - CellID->610402838] +Cell[TextData[StyleBox[ButtonBox["FORM2FeynCalc", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/FORM2FeynCalc", + ButtonNote->"FORM2FeynCalc"], + FontFamily->"Verdana"]], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -789,23 +817,23 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 45.277886}", + "built" -> "{2020, 1, 5, 18, 57, 35.290011}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "FeynCalc2FORM[expr] displays expr in FORM syntax. FeynCalc2FORM[file, x] \ -writes x in FORM syntax to a file. FeynCalc2FORM[file, x==y] writes x=y to a \ -file in FORM syntax.", "synonyms" -> {}, "title" -> "FeynCalc2FORM", - "titlemodifier" -> "", "windowtitle" -> "FeynCalc2FORM", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/FeynCalc2FORM"}, "SearchTextTranslated" -> - ""}, + "FeynCalc2FORM[exp] displays exp in FORM syntax. FeynCalc2FORM[file, x] \ +writes x in FORM syntax to a file. FeynCalc2FORM[file, x == y] writes x = y \ +to a file in FORM syntax.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "FeynCalc2FORM", "titlemodifier" -> "", "windowtitle" -> "FeynCalc2FORM", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/FeynCalc2FORM"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -813,8 +841,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -822,245 +851,235 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], - TraditionalForm]], - TraditionalForm], + TraditionalForm]}]], + TraditionalForm], ",", + FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]}], "}"}], TraditionalForm]], "Output", - ImageSize->{213, 25}, + ImageSize->{234, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcExternal", - CellLabel->"Out[3]=", - CellID->1438725943] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -285,12 +304,11 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], ",", RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", - ImageSize->{416, 15}, + ImageSize->{424, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcExternal", - CellLabel->"Out[4]//StandardForm=", - 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CellLabel->"Out[5]=", - CellID->16755113] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -406,12 +413,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}], "}"}]], "Output", - ImageSize->{521, 67}, + ImageSize->{523, 67}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcExternal", - CellLabel->"Out[6]//StandardForm=", - CellID->1797900650] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -436,12 +442,11 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], ",", RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", - ImageSize->{416, 15}, + ImageSize->{424, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcExternal", - CellLabel->"Out[7]//StandardForm=", - CellID->1902701879] + CellLabel->"Out[7]//StandardForm="] }, Open ]] }, Open ]], @@ -471,17 +476,15 @@ Cell[TextData[{ ButtonNote->"FeynCalcInternal"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FeynCalcExternal", - CellID->35172117] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"FeynCalcExternal", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -490,22 +493,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 46.839073}", + "built" -> "{2020, 1, 5, 18, 57, 36.479239}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "FeynCalcExternal[exp] translates exp from the internal FeynCalc \ -representation to a shorthand form.", "synonyms" -> {}, "title" -> - "FeynCalcExternal", "titlemodifier" -> "", "windowtitle" -> +representation to a shorthand form.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "FeynCalcExternal", "titlemodifier" -> "", "windowtitle" -> "FeynCalcExternal", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FeynCalcExternal"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -513,8 +516,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -523,145 +527,125 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["FeynCalcForm", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -114,7 +149,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->693458567], + CellID->1276139522], Cell[CellGroupData[{ @@ -124,11 +159,9 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1231677925], + CellID->318448114], -Cell["This is the normal notebook display:", "Text", - CellTags->"FeynCalcForm", - CellID->1383220456], +Cell["This is the normal notebook display:", "Notes"], Cell[CellGroupData[{ @@ -169,19 +202,16 @@ Cell[BoxData[ TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{104, 19}, + ImageSize->{116, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcForm", - CellLabel->"Out[1]=", - CellID->2135875157] + CellLabel->"Out[1]="] }, Open ]], Cell["\<\ This is the shorthand (terminal) display (easy-to-read form):\ -\>", "Text", - CellTags->"FeynCalcForm", - CellID->981626969], +\>", "Notes"], Cell[BoxData[ RowBox[{ @@ -193,14 +223,15 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{ RowBox[{"SetOptions", "[", - RowBox[{"$FrontEnd", ",", + RowBox[{"$FrontEndSession", ",", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Options", "[", - RowBox[{"$FrontEnd", ",", "\"\\""}], - "]"}], "/.", + RowBox[{ + "$FrontEndSession", ",", "\"\\""}], "]"}], + "/.", RowBox[{ RowBox[{"(", RowBox[{"\"\\"", "\[Rule]", "_"}], ")"}], "\[Rule]", @@ -228,19 +259,19 @@ Cell[OutputFormData["\<\ SUNTrace[SUNT[SUNIndex[a]] . SUNT[SUNIndex[b]] . SUNT[SUNIndex[c]]]\ \>", "\<\ -tr[T[a] T[b] T[c]]\ +SUNTrace[SUNT[SUNIndex[a]] . SUNT[SUNIndex[b]] . + + + SUNT[SUNIndex[c]]]\ \>"], "Output", - ImageSize->{144, 20}, + ImageSize->{392, 50}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcForm", - CellLabel->"Out[4]=", - CellID->1930690446] + CellLabel->"Out[4]="] }, Open ]], -Cell["Reset to normal notebook display:", "Text", - CellTags->"FeynCalcForm", - CellID->1776666281], +Cell["Reset to normal notebook display:", "Notes"], Cell[BoxData[ RowBox[{ @@ -252,14 +283,15 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{ RowBox[{"SetOptions", "[", - RowBox[{"$FrontEnd", ",", + RowBox[{"$FrontEndSession", ",", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Options", "[", - RowBox[{"$FrontEnd", ",", "\"\\""}], - "]"}], "/.", + RowBox[{ + "$FrontEndSession", ",", "\"\\""}], "]"}], + "/.", RowBox[{ RowBox[{"(", RowBox[{"\"\\"", "\[Rule]", "_"}], ")"}], "\[Rule]", @@ -269,7 +301,50 @@ Cell[BoxData[ RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "]"}], ";"}]], "Input", CellTags->"FeynCalcForm", CellLabel->"In[6]:=", - CellID->803099917] + CellID->803099917], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNTrace", "[", + RowBox[{ + RowBox[{"SUNT", "[", "a", "]"}], ".", + RowBox[{"SUNT", "[", "b", "]"}], ".", + RowBox[{"SUNT", "[", "c", "]"}]}], "]"}]], "Input", + CellLabel->"In[7]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + FormBox["\<\"tr\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + RowBox[{ + SuperscriptBox["T", + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["T", + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["T", + FormBox[ + FormBox["c", + TraditionalForm], + TraditionalForm]]}], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], TraditionalForm]], "Output", + ImageSize->{116, 19}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[7]="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] @@ -310,9 +385,7 @@ Cell[TextData[{ ButtonNote->"FeynCalcInternal"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FeynCalcForm", - CellID->1584845220] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -320,7 +393,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"FeynCalcForm", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -329,10 +402,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 48.450259}", + "built" -> "{2020, 1, 5, 18, 57, 37.694365}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -344,11 +417,12 @@ session. Whether the result of FeynCalcForm[expr] is displayed or not, \ depends on the setting of $PrePrint. $PrePrint = FeynCalcForm forces \ displaying everything after applying FeynCalcForm. 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CellID->1224892054], +Cell[TextData[{ + Cell["FeynCalcInternal", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,7 +143,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1620212646], + CellID->688688892], Cell[CellGroupData[{ @@ -118,7 +153,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1845158141], + CellID->915609596], Cell[CellGroupData[{ @@ -182,46 +217,35 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ",", FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - 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ImageSize->{416, 15}, + ImageSize->{424, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcInternal", - CellLabel->"Out[2]//StandardForm=", - CellID->603554670] + CellLabel->"Out[2]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -295,43 +318,32 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm]}], ",", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], ",", - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Alpha]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "}"}], TraditionalForm]], "Output", - ImageSize->{213, 25}, + TraditionalForm]}]], ",", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], "}"}], TraditionalForm]], "Output", + ImageSize->{234, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcInternal", - CellLabel->"Out[3]=", - CellID->618861015] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -365,12 +377,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}], "}"}]], "Output", - ImageSize->{521, 67}, + ImageSize->{523, 67}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcInternal", - CellLabel->"Out[4]//StandardForm=", - CellID->1678932419] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -395,12 +406,11 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], ",", RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", - ImageSize->{416, 15}, + ImageSize->{424, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcInternal", - CellLabel->"Out[5]//StandardForm=", - CellID->44863235] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -465,11 +475,22 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]}]], ",", - FractionBox["1", - SuperscriptBox[ - FormBox["q", - TraditionalForm], "2"]], ",", - SuperscriptBox["\[Epsilon]", + FormBox[ + FractionBox["1", + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]]], + Editable->False]], + TraditionalForm], ",", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -487,12 +508,11 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]]}], "}"}], TraditionalForm]], "Output", - ImageSize->{231, 47}, + ImageSize->{249, 40}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcInternal", - CellLabel->"Out[6]=", - CellID->164140775] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -530,14 +550,13 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", - RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "4"}]}], "]"}]}], "}"}]], "Output", - ImageSize->{505, 101}, + RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}]}], "]"}]}], + "}"}]], "Output", + ImageSize->{573, 84}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FeynCalcInternal", - CellLabel->"Out[7]//StandardForm=", - CellID->700854959] + CellLabel->"Out[7]//StandardForm="] }, Open ]] }, Open ]], @@ -579,17 +598,15 @@ Cell[TextData[{ ButtonNote->"FCE"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"FeynCalcInternal", - CellID->1416834624] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"FeynCalcInternal", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -598,22 +615,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 49.988209}", + "built" -> "{2020, 1, 5, 18, 57, 38.810751}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "FeynCalcInternal[exp] translates exp into the internal FeynCalc \ -(abstract data-type) representation.", "synonyms" -> {}, "title" -> - "FeynCalcInternal", "titlemodifier" -> "", "windowtitle" -> +(abstract data-type) representation.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "FeynCalcInternal", "titlemodifier" -> "", "windowtitle" -> "FeynCalcInternal", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FeynCalcInternal"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -621,8 +638,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -631,145 +649,125 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$68550], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$135667], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/FeynCalcToLaTeX", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,24 +74,82 @@ FeynCalcToLaTeX.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FeynCalcToLaTeX", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FeynCalcToLaTeX", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"FeynCalcToLaTeX", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "generates LaTeX with line-breaking for expr. \nFeynCalcToLaTeX[expr, \ -500] generates LaTeX for expr where 500 is the Window width setting for the \ -Mathematica frontend. Increasing its value will generate less line breaks." + RowBox[{"FeynCalcToLaTeX", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]generates LaTeX with line-breaking for ", + Cell[BoxData["exp"], "InlineFormula"], + "." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"FeynCalcToLaTeX", "[", + RowBox[{"expr", ",", "500"}], "]"}]], "InlineFormula"], + " \[LineSeparator]generates LaTeX for ", + Cell[BoxData["exp"], "InlineFormula"], + " where 500 is the Window width setting for the Mathematica frontend. \ +Increasing its value will generate less line breaks." }]]} }]], "Usage", GridBoxOptions->{ GridBoxBackground->{ - "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, + "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {None, {None}}, "RowsIndexed" -> {}}}, - CellID->982511436], + CellID->2010081510], + +Cell[CellGroupData[{ + +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], + +Cell["", "SectionHeaderSpacer"], + +Cell[TextData[{ + "This function appears to be broken in the recent ", + StyleBox["Mathematica", + FontSlant->"Italic"], + " versions, most likely it will be rewritten from scratch in a future \ +version of FeynCalc." +}], "Notes", + CellID->1067943069] +}, Closed]], Cell[" ", "FooterCell"] }, @@ -106,23 +165,24 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 19, 52.976412}", + "built" -> "{2020, 1, 5, 18, 57, 41.035316}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "FeynCalcToLaTeX[expr] generates LaTeX with line-breaking for expr. \ -FeynCalcToLaTeX[expr, 500] generates LaTeX for expr where 500 is the Window \ + "FeynCalcToLaTeX[exp] generates LaTeX with line-breaking for exp. \ +FeynCalcToLaTeX[expr, 500] generates LaTeX for exp where 500 is the Window \ width setting for the Mathematica frontend. Increasing its value will \ -generate less line breaks.", "synonyms" -> {}, "title" -> "FeynCalcToLaTeX", - "titlemodifier" -> "", "windowtitle" -> "FeynCalcToLaTeX", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/FeynCalcToLaTeX"}}, +generate less line breaks.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "FeynCalcToLaTeX", "titlemodifier" -> "", "windowtitle" -> + "FeynCalcToLaTeX", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FeynCalcToLaTeX"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -131,7 +191,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -145,13 +205,20 @@ CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[587, 21, 2273, 52, 70, "AnchorBarGrid", +Cell[587, 21, 2302, 53, 70, "AnchorBarGrid", + CellID->1], +Cell[2892, 76, 292, 11, 70, "ObjectNameGrid"], +Cell[3187, 89, 821, 22, 70, "Usage", + CellID->2010081510], +Cell[CellGroupData[{ +Cell[4033, 115, 730, 24, 70, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, CellID->1], -Cell[2863, 75, 58, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2924, 78, 578, 14, 70, "Usage", - CellID->982511436], -Cell[3505, 94, 23, 0, 70, "FooterCell"] +Cell[4766, 141, 31, 0, 70, "SectionHeaderSpacer"], +Cell[4800, 143, 247, 7, 70, "Notes", + CellID->1067943069] +}, Closed]], +Cell[5062, 153, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FeynRule.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FeynRule.nb index fcc95a3a0..d1447977f 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/FeynRule.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/FeynRule.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 108718, 4060] -NotebookOptionsPosition[ 94644, 3573] -NotebookOutlinePosition[ 102339, 3812] -CellTagsIndexPosition[ 102225, 3806] +NotebookDataLength[ 100307, 3704] +NotebookOptionsPosition[ 93137, 3475] +NotebookOutlinePosition[ 95412, 3538] +CellTagsIndexPosition[ 95298, 3532] WindowTitle->FeynRule WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/FeynRule\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/FeynRule"]}, Visible -> False]]; 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SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$138323], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/FeynRule", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["FeynRule", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["FeynRule", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -82,11 +116,12 @@ Cell[BoxData[GridBox[{ RowBox[{"FeynRule", "[", RowBox[{"lag", ",", " ", RowBox[{"{", "fields", "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "derives the Feynman rule corresponding to the field configuration \ -fields of the lagrangian lag.\n\nFeynRule does not calculate propagator \ -Feynman rules.\n\nThe option ZeroMomentumInsertion can be used for twist-2 \ -and higher twist operators." + " \[LineSeparator]derives the Feynman rule corresponding to the field \ +configuration ", + Cell[BoxData["fields"], "InlineFormula"], + " of the lagrangian ", + Cell[BoxData["lag"], "InlineFormula"], + "." }]]} }]], "Usage", GridBoxOptions->{ @@ -97,6 +132,105 @@ and higher twist operators." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->290293433], + +Cell["", "SectionHeaderSpacer"], + +Cell[TextData[{ + ButtonBox["FeynRule", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/FeynRule", + ButtonNote->"FeynRule"], + " does not calculate propagator Feynman rules." +}], "Notes"], + +Cell[TextData[{ + "The option ", + ButtonBox["ZeroMomentumInsertion", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/ZeroMomentumInsertion", + ButtonNote->"ZeroMomentumInsertion"], + " can be used for twist-2 and higher twist operators." +}], "Notes"], + +Cell[TextData[{ + ButtonBox["FeynRule", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/FeynRule", + ButtonNote->"FeynRule"], + " is not very versatile and was primarily developed for QCD calculations. It \ +is often more useful when dealing with bosonic fields than with fermions. 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If \ -the space-time derivative of other objects is wanted, the corresponding rule \ -must be specified.", "synonyms" -> {}, "title" -> "FieldDerivative", - "titlemodifier" -> "", "windowtitle" -> "FieldDerivative", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/FieldDerivative"}, - "SearchTextTranslated" -> ""}, +where li1, li2, ... have head LorentzIndex.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "FieldDerivative", "titlemodifier" -> "", + "windowtitle" -> "FieldDerivative", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/FieldDerivative"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -562,8 +549,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -572,89 +560,87 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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RowBox[{"-", "Gstrong"}]}], ",", + RowBox[{"-", + RowBox[{"SMP", "[", "\"\\"", "]"}]}]}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"FieldStrength", - CellLabel->"In[8]:=", + CellLabel->"In[5]:=", CellID->1847448290], Cell[BoxData[ @@ -459,9 +481,9 @@ Cell[BoxData[ RowBox[{ FormBox["a", TraditionalForm], - FormBox["b665", + FormBox["b853", TraditionalForm], - FormBox["c666", + FormBox["c854", TraditionalForm]}]], " ", RowBox[{ SubsuperscriptBox[ @@ -472,7 +494,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["b665", + FormBox["b853", TraditionalForm], TraditionalForm]], ".", SubsuperscriptBox[ @@ -483,11 +505,12 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["c666", + FormBox["c854", TraditionalForm], TraditionalForm]]}]}]}], "+", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], @@ -502,9 +525,10 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], @@ -519,13 +543,12 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}]}], TraditionalForm]], "Output", - ImageSize->{282, 23}, + TraditionalForm]], ")"}]}], TraditionalForm]], "Output", + ImageSize->{337, 22}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FieldStrength", - CellLabel->"Out[8]=", - CellID->865013743] + CellLabel->"Out[5]="] }, Open ]] }, Open ]], @@ -548,24 +571,19 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[TextData[{ - StyleBox[ButtonBox["QuantumField", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/QuantumField", - ButtonNote->"QuantumField"], - FontFamily->"Verdana"], - "." -}], "Text", - CellTags->"FieldStrength", - CellID->830418848] +Cell[TextData[StyleBox[ButtonBox["QuantumField", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/QuantumField", + ButtonNote->"QuantumField"], + FontFamily->"Verdana"]], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"FieldStrength", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -574,10 +592,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 4.548584}", + "built" -> "{2020, 1, 5, 18, 57, 50.417948}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -585,17 +603,14 @@ TaggingRules->{ "None", "summary" -> "FieldStrength[\\[Mu], \\[Nu], a] is the field strength tensor \ \\[PartialD]\\[Mu] A_\\[Nu]^a - \\[PartialD]\\[Nu] \\ A_\\[Mu]^a + gs \ -A_\\[Mu]^b1 A_\\[Nu]^c1 f a b1 c1. FieldStrength[\\[Mu], \\[Nu]] is the field \ -strength tensor \\[PartialD]\\[Mu] A_\\[Nu]^\\[Null] - \\ \\[PartialD]\\[Nu] \ -A_\\[Mu]^\\[Null]. The name of the field (A) and the coupling constant (g) \ -can be set through the options or by additional arguments. The first two \ -indices are interpreted as type LorentzIndex, except OPEDelta, which is \ -converted to Momentum[OPEDelta].", "synonyms" -> {}, "title" -> - "FieldStrength", "titlemodifier" -> "", "windowtitle" -> "FieldStrength", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/FieldStrength"}, - "SearchTextTranslated" -> ""}, +A_\\[Mu]^b A_\\[Nu]^c f^abc. FieldStrength[\\[Mu], \\[Nu]] is the field \ +strength tensor \\[PartialD]\\[Mu] A\\[Nu] - \\[PartialD]\\[Nu] A\\[Mu].", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FieldStrength", + "titlemodifier" -> "", "windowtitle" -> "FieldStrength", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/FieldStrength"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -604,7 +619,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -612,160 +627,124 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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"synonyms" -> {}, "title" -> "FinalFunction", "titlemodifier" -> "", - "windowtitle" -> "FinalFunction", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/FinalFunction"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "FinalFunction", + "titlemodifier" -> "", "windowtitle" -> "FinalFunction", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/FinalFunction"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -153,41 +183,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellTags->"FourDivergence", - CellID->1618281503] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -312,7 +447,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"FourDivergence", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -321,23 +456,23 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 15.433986}", + "built" -> "{2020, 1, 5, 18, 57, 59.174858}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - 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FourDivergence[exp, FourVector[p, mu], FourVector[p,nu], \ -...]gives the multiple derivative.", "synonyms" -> {}, "title" -> + "FourDivergence[exp, FV[p, mu]] calculates the partial derivative of exp \ +w.r.t p^\\[Mu]. FourDivergence[exp, FV[p, mu], FV[p,nu], ...] gives the \ +multiple derivative.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "FourDivergence", "titlemodifier" -> "", "windowtitle" -> "FourDivergence", "type" -> "Symbol", "uri" -> "FeynCalc/ref/FourDivergence"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -345,8 +480,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -355,109 +491,109 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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As always in FeynCalc, Einstein summation convention is implicitly \ +assumed. 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See the TARCER documentation on TFI \ -for details on the conventions.", "synonyms" -> {}, "title" -> "FromTFI", - "titlemodifier" -> "", "windowtitle" -> "FromTFI", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/FromTFI"}, "SearchTextTranslated" -> ""}, +for details on the conventions.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "FromTFI", "titlemodifier" -> "", "windowtitle" -> "FromTFI", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/FromTFI"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -396,7 +335,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -405,89 +344,66 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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FormBox["a", - TraditionalForm], - TraditionalForm]]}], "+", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["F", - TraditionalForm], - RowBox[{ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]}], - FormBox[ - FormBox["g", + FormBox["c", TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", - ImageSize->{158, 22}, + ImageSize->{187, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FunctionalD", - CellLabel->"Out[17]=", - CellID->1369525226] + CellLabel->"Out[12]="] }, Open ]], Cell[TextData[{ - "Since the variational derivative vanishes t4 implies that 0 = ", + "Since the variational derivative vanishes ", + Cell[BoxData["t4"], "InlineFormula"], + " implies that ", Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["D", "\[Mu]"], - SubsuperscriptBox["F", "g", "\[Mu]\[Sigma]"]}], TraditionalForm]]], - " ." -}], "Text", - CellTags->"FunctionalD", - CellID->1366711149], + RowBox[{"0", "=", + FormBox[ + RowBox[{ + SubscriptBox["D", "\[Mu]"], + SubsuperscriptBox["F", "g", "\[Mu]\[Sigma]"]}], + TraditionalForm]}]], "InlineFormula"], + "." +}], "Notes"], -Cell[TextData[StyleBox["Second approach", - FontWeight->"Bold"]], "Text", - CellTags->"FunctionalD", - CellID->1672341951], +Cell["Second approach:", "Notes"], -Cell["\<\ -It is of course also possible to do the functional deriviate on the S[A] with \ -both field strength tensors inserted.\ -\>", "Text", - CellTags->"FunctionalD", - CellID->680079191], +Cell[TextData[{ + "It is of course also possible to do the functional deriviate on the ", + Cell[BoxData[ + RowBox[{"S", "[", "A", "]"}]], "InlineFormula"], + " with both field strength tensors inserted." +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"S", "[", "A", "]"}]], "Input", CellTags->"FunctionalD", - CellLabel->"In[18]:=", + CellLabel->"In[13]:=", CellID->1996431184], Cell[BoxData[ @@ -1776,7 +1825,8 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], "+", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], @@ -1791,9 +1841,10 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], @@ -1808,7 +1859,7 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}]}], ")"}], ".", + TraditionalForm]], ")"}]}], ")"}], ".", RowBox[{"(", RowBox[{ RowBox[{ @@ -1844,7 +1895,8 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], "+", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], @@ -1859,9 +1911,10 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], @@ -1876,13 +1929,12 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}]}], ")"}]}]}], TraditionalForm]], "Output", - ImageSize->{435, 41}, + TraditionalForm]], ")"}]}], ")"}]}]}], TraditionalForm]], "Output", + ImageSize->{564, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"FunctionalD", - CellLabel->"Out[18]=", - CellID->745422332] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -1893,7 +1945,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"S", "[", "A", "]"}], ",", "Ag"}], "]"}]}]], "Input", CellTags->"FunctionalD", - CellLabel->"In[19]:=", + CellLabel->"In[14]:=", CellID->1238326201], Cell[BoxData[ @@ -1946,22 +1998,22 @@ Cell[BoxData[ FormBox["A", TraditionalForm], FormBox[ - FormBox["\[Sigma]", + FormBox["\[Mu]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["c", + FormBox["d", TraditionalForm], TraditionalForm]], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], FormBox[ - FormBox["\[Mu]", + FormBox["\[Sigma]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["d", + FormBox["c", TraditionalForm], TraditionalForm]]}]}]}], "+", RowBox[{ @@ -1999,11 +2051,11 @@ Cell[BoxData[ FormBox["A", TraditionalForm], FormBox[ - FormBox["\[Sigma]", + FormBox["\[Nu]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["b", + FormBox["c", TraditionalForm], TraditionalForm]], ".", SubsuperscriptBox[ @@ -2014,18 +2066,18 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["c", + FormBox["e", TraditionalForm], TraditionalForm]], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], FormBox[ - FormBox["\[Nu]", + FormBox["\[Sigma]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["e", + FormBox["b", TraditionalForm], TraditionalForm]]}]}], "-", RowBox[{ @@ -2120,23 +2172,25 @@ Cell[BoxData[ FormBox["b", TraditionalForm], TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}]}]}], "+", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "+", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2165,23 +2219,25 @@ Cell[BoxData[ FormBox["b", TraditionalForm], TraditionalForm]], ".", - 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FormBox["\[Nu]", + FormBox["\[Sigma]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["e", + FormBox["d", TraditionalForm], TraditionalForm]]}]}], "-", RowBox[{ @@ -2274,23 +2330,25 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}]}]}], "+", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "+", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2319,23 +2377,25 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}]}]}], "-", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "-", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2353,23 +2413,6 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - 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FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ -2425,41 +2470,43 @@ Cell[BoxData[ FormBox[ FormBox["d", TraditionalForm], - TraditionalForm]]}]}], "-", - RowBox[{ - FractionBox["1", "4"], " ", - SuperscriptBox["f", - RowBox[{ - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["e", - TraditionalForm], - TraditionalForm], - FormBox[ + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "-", + RowBox[{ + FractionBox["1", "4"], " ", + SuperscriptBox["f", + RowBox[{ + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["e", + TraditionalForm], + TraditionalForm], + FormBox[ FormBox["g", TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ -2470,7 +2517,26 @@ Cell[BoxData[ FormBox[ FormBox["e", TraditionalForm], - TraditionalForm]]}]}], "+", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "+", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2488,23 +2554,6 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - 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TraditionalForm]]}]}], "-", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["d", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "-", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2807,30 +2887,32 @@ Cell[BoxData[ FormBox["A", TraditionalForm], FormBox[ - FormBox["\[Sigma]", + FormBox["\[Nu]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["d", + FormBox["e", TraditionalForm], TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["e", - TraditionalForm], - TraditionalForm]]}]}]}], "-", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["d", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "-", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2848,272 +2930,252 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - 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CellLabel->"Out[19]=", - CellID->1475699650] + CellLabel->"Out[14]="] }, Open ]], Cell["\<\ This is just funcional derivation and partial integration and simple \ -contraction of indices. No attempt is made to rename dummy indices (since \ -this is difficult in general).\ -\>", "Text", - CellTags->"FunctionalD", - CellID->1367707502], +contraction of indices. At first no attempt is made to rename dummy indices \ +(since this is difficult in general).\ +\>", "Notes"], Cell["\<\ With a general replacement rule only valid for commuting fields the color \ indices can be canonicalized a bit more. The idea is to use the commutative \ properties of the vector fields, and canonicalize the color indices by a \ -trick. 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"AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,19 +97,29 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["GA", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["GA", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"GA", "[", "mu", "]"}]], "InlineFormula"], + RowBox[{"GA", "[", "\[Mu]", "]"}]], "InlineFormula"], " \[LineSeparator]", "can be used as input for a 4-dimensional ", Cell[BoxData[ FormBox[ - SubscriptBox["\[Gamma]", - RowBox[{"\[Mu]", " "}]], TraditionalForm]]], + SubscriptBox[ + SuperscriptBox["\[Gamma]", "\[Mu]"], " "], TraditionalForm]]], "and is transformed into DiracGamma[LorentzIndex[", Cell[BoxData[ FormBox["\[Mu]", TraditionalForm]]], @@ -125,7 +159,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1937257617], + CellID->1166659898], Cell[CellGroupData[{ @@ -135,7 +169,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1143751957], + CellID->731692333], Cell[CellGroupData[{ @@ -153,12 +187,11 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{23, 17}, + ImageSize->{25, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GA", - CellLabel->"Out[1]=", - CellID->1620727253] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -210,12 +243,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}]}], TraditionalForm]], "Output", - ImageSize->{101, 17}, + ImageSize->{110, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GA", - CellLabel->"Out[2]=", - CellID->751580324] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -231,12 +263,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}]], "Output", - ImageSize->{225, 15}, + ImageSize->{226, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GA", - CellLabel->"Out[3]//StandardForm=", - CellID->1671355959] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -284,12 +315,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{93, 18}, + ImageSize->{100, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GA", - CellLabel->"Out[4]=", - CellID->973003462] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -309,12 +339,11 @@ Cell[BoxData[ RowBox[{"GA", "[", "\[Nu]", "]"}], ".", RowBox[{"GA", "[", "\[Rho]", "]"}], ".", RowBox[{"GA", "[", "\[Sigma]", "]"}]}]], "Output", - ImageSize->{199, 15}, + ImageSize->{205, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GA", - CellLabel->"Out[5]//StandardForm=", - CellID->390738149] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -360,12 +389,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{123, 22}, + ImageSize->{133, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GA", - CellLabel->"Out[6]=", - CellID->1420363209] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -389,10 +417,10 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["DiracMatrix", + StyleBox[ButtonBox["DiracGamma", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData->"paclet:FeynCalc/ref/DiracGamma", + ButtonNote->"DiracGamma"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["GAD", @@ -407,9 +435,7 @@ Cell[TextData[{ ButtonNote->"GS"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GA", - CellID->1423338362] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -417,7 +443,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"GA", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -426,23 +452,23 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 43.060317}", + "built" -> "{2020, 1, 5, 18, 58, 23.715243}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "GA[mu] can be used as input for a 4-dimensional \\[Gamma] \\[Mu] and is \ -transformed into DiracGamma[LorentzIndex[\\[Mu]]] by FeynCalcInternal \ + "GA[\\[Mu]] can be used as input for a 4-dimensional \\[Gamma]^\\[Mu]and \ +is transformed into DiracGamma[LorentzIndex[\\[Mu]]] by FeynCalcInternal \ (=FCI).GA[\\[Mu], \\[Nu], ...] is a short form for GA[\\[Mu]].GA[\\[Nu]].", - "synonyms" -> {}, "title" -> "GA", "titlemodifier" -> "", "windowtitle" -> - "GA", "type" -> "Symbol", "uri" -> "FeynCalc/ref/GA"}, - "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "GA", "titlemodifier" -> + "", "windowtitle" -> "GA", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/GA"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -450,8 +476,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -460,131 +487,113 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3829, 112, 388, 15, 31, "PrimaryExamplesSection", + Cell[4985, 146, 388, 15, 31, "PrimaryExamplesSection", 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Documentation`HelpLookup["paclet:FeynCalc/ref/GA"], "\<\"GS\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/GS"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/GA5\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/GA5"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + 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FormBox["5", TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{22, 18}, + ImageSize->{23, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GA5", - CellLabel->"Out[1]=", - CellID->26317546] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"%", "//", "Tr"}]], "Input", + RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"GA5", CellLabel->"In[2]:=", CellID->306400430], Cell[BoxData[ - FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + RowBox[{"DiracGamma", "[", "5", "]"}]], "Output", + ImageSize->{110, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GA5", - CellLabel->"Out[2]=", - CellID->223026079] + CellLabel->"Out[2]//StandardForm="] }, Open ]] }, Open ]], @@ -196,9 +228,7 @@ Cell[TextData[{ ButtonNote->"GS"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GA5", - CellID->1140253619] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -215,21 +245,21 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"synonyms" -> {}, "tabletags" -> {}, "title" -> "GA5", "titlemodifier" -> + "", "windowtitle" -> "GA5", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/GA5"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -237,8 +267,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -247,75 +278,65 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ 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Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/GAD.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$149134], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/GAD", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,19 +97,29 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["GAD", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["GAD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"GAD", "[", "mu", "]"}]], "InlineFormula"], + RowBox[{"GAD", "[", "\[Mu]", "]"}]], "InlineFormula"], " \[LineSeparator]", "can be used as input for a D-dimensional ", Cell[BoxData[ FormBox[ - SubscriptBox["\[Gamma]", - RowBox[{"\[Mu]", " "}]], TraditionalForm]]], + SubscriptBox[ + SuperscriptBox["\[Gamma]", "\[Mu]"], " "], TraditionalForm]]], "and is transformed into DiracGamma[LorentzIndex[", Cell[BoxData[ FormBox["\[Mu]", TraditionalForm]]], @@ -125,7 +159,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->995390804], + CellID->1169550819], Cell[CellGroupData[{ @@ -135,7 +169,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1450127099], + CellID->585030036], Cell[CellGroupData[{ @@ -152,12 +186,11 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{22, 17}, + ImageSize->{24, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GAD", - CellLabel->"Out[1]=", - CellID->1066808251] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -205,12 +238,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}]}], TraditionalForm]], "Output", - ImageSize->{97, 17}, + ImageSize->{106, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GAD", - CellLabel->"Out[2]=", - CellID->1547742824] + CellLabel->"Out[2]="] }, 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ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GAD", - CellLabel->"Out[5]//StandardForm=", - CellID->20038506] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -349,12 +378,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{118, 21}, + ImageSize->{128, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GAD", - CellLabel->"Out[6]=", - CellID->1687383827] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -378,10 +406,10 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["DiracMatrix", + StyleBox[ButtonBox["DiracGamma", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData->"paclet:FeynCalc/ref/DiracGamma", + ButtonNote->"DiracGamma"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["GA", @@ -396,9 +424,7 @@ Cell[TextData[{ ButtonNote->"GS"], 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CellID->1224892054], +Cell[TextData[{ + Cell["GGV", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +144,7 @@ Cell[TextData[{ ButtonNote->"GluonGhostVertex"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GGV", - CellID->535760603] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,19 +161,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 49.141458}", + "built" -> "{2020, 1, 5, 18, 58, 30.938984}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "GGV is equivalent to GluonGhostVertex.", - 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CellID->1224892054], +Cell[TextData[{ + Cell["GHP", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -114,7 +150,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->99090036], + CellID->1853416107], Cell[CellGroupData[{ @@ -124,7 +160,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->261177431], + CellID->1687938001], Cell[CellGroupData[{ @@ -146,12 +182,11 @@ Cell[BoxData[ TraditionalForm]}]], "(", FormBox["p", TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{54, 17}, + ImageSize->{61, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GHP", - CellLabel->"Out[1]=", - CellID->798549713] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -166,22 +201,29 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ FractionBox["\[ImaginaryI]", - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"]], TraditionalForm]], "Output", - ImageSize->{27, 48}, + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False]], TraditionalForm]], "Output", + ImageSize->{28, 39}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GHP", - CellLabel->"Out[2]=", - CellID->1879723497] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GHP", "[", - RowBox[{"p", ",", "1", ",", "2"}], "]"}]], "Input", + RowBox[{"p", ",", "c1", ",", "c2"}], "]"}]], "Input", CellTags->"GHP", CellLabel->"In[3]:=", CellID->1429235603], @@ -191,18 +233,17 @@ Cell[BoxData[ RowBox[{ SubscriptBox["\[CapitalPi]", RowBox[{ - FormBox["ci1", + FormBox["c1", TraditionalForm], - FormBox["ci2", + FormBox["c2", TraditionalForm]}]], "(", FormBox["p", TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{68, 17}, + ImageSize->{66, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GHP", - CellLabel->"Out[3]=", - CellID->1586595147] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -213,7 +254,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"GHP", "[", RowBox[{ - RowBox[{"-", "k"}], ",", "3", ",", "4"}], "]"}], "//", "Explicit"}], + RowBox[{"-", "k"}], ",", "c3", ",", "c4"}], "]"}], "//", "Explicit"}], "]"}], "]"}]], "Input", CellTags->"GHP", CellLabel->"In[4]:=", @@ -223,13 +264,12 @@ Cell[BoxData[ RowBox[{"\[ImaginaryI]", " ", RowBox[{"FAD", "[", "k", "]"}], " ", RowBox[{"SD", "[", - RowBox[{"ci3", ",", "ci4"}], "]"}]}]], "Output", - ImageSize->{164, 15}, + RowBox[{"c3", ",", "c4"}], "]"}]}]], "Output", + ImageSize->{152, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GHP", - CellLabel->"Out[4]//StandardForm=", - CellID->1550998879] + CellLabel->"Out[4]//StandardForm="] }, Open ]] }, Open ]], @@ -271,9 +311,7 @@ Cell[TextData[{ ButtonNote->"GluonGhostVertex"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GHP", - CellID->269539325] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -281,7 +319,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"GHP", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -290,21 +328,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - 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GHP[p] omits the \\[Delta] ab.", "synonyms" -> {}, "title" -> - "GHP", "titlemodifier" -> "", "windowtitle" -> "GHP", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/GHP"}, "SearchTextTranslated" -> ""}, +color indices. GHP[p] omits the \\[Delta] ab.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "GHP", "titlemodifier" -> "", "windowtitle" -> + "GHP", "type" -> "Symbol", "uri" -> "FeynCalc/ref/GHP"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -312,8 +351,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -322,103 +362,89 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["GP", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData["GP"], "InlineFormula"], - " \[LineSeparator]", - "is equivalent to GluonPropagator." + " \[LineSeparator]is equivalent to GluonPropagator." }]]} }]], "Usage", GridBoxOptions->{ @@ -112,9 +143,7 @@ Cell[TextData[{ ButtonNote->"GluonPropagator"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GP", - CellID->444986205] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,19 +160,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - 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CellID->1224892054], +Cell[TextData[{ + Cell["GS", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -122,7 +156,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1189847232], + CellID->1090110818], Cell[CellGroupData[{ @@ -132,7 +166,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->232924120], + CellID->808016956], Cell[CellGroupData[{ @@ -151,12 +185,11 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{33, 17}, + ImageSize->{38, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GS", - CellLabel->"Out[1]=", - CellID->682141754] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -173,12 +206,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"Momentum", "[", "p", "]"}], "]"}]], "Output", - ImageSize->{195, 15}, + ImageSize->{194, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GS", - CellLabel->"Out[2]//StandardForm=", - CellID->1007084382] + CellLabel->"Out[2]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -233,12 +265,11 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", - ImageSize->{179, 18}, + ImageSize->{197, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GS", - CellLabel->"Out[3]=", - CellID->1827181467] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +289,11 @@ Cell[BoxData[ RowBox[{"GS", "[", "q", "]"}], ".", RowBox[{"GS", "[", "r", "]"}], ".", RowBox[{"GS", "[", "s", "]"}]}]], "Output", - ImageSize->{194, 15}, + ImageSize->{197, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GS", - CellLabel->"Out[4]//StandardForm=", - CellID->451922065] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -313,12 +343,11 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", - ImageSize->{165, 18}, + ImageSize->{183, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GS", - CellLabel->"Out[5]=", - CellID->373152039] + CellLabel->"Out[5]="] }, Open ]] }, Open ]], @@ -348,12 +377,6 @@ Cell[TextData[{ ButtonNote->"DiracGamma"], FontFamily->"Verdana"], ", ", - StyleBox[ButtonBox["DiracSlash", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], - FontFamily->"Verdana"], - ", ", StyleBox[ButtonBox["GA", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/GA", @@ -366,9 +389,7 @@ Cell[TextData[{ ButtonNote->"GAD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GS", - CellID->1515784011] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -376,7 +397,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"GS", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -385,10 +406,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 7.553793}", + "built" -> "{2020, 1, 5, 18, 58, 45.520183}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -398,11 +419,11 @@ TaggingRules->{ \\[NegativeMediumSpace]\\[NegativeMediumSpace]\\ \\[NegativeMediumSpace]/ (= \ \\[Gamma].p = \\[Gamma]\\[Mu] p^\\[Mu]) and is transformed into \ DiracGamma[Momentum[p]] by FeynCalcInternal (=FCI). 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+Cell[TextData[{ + Cell["GTI", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +144,7 @@ Cell[TextData[{ ButtonNote->"RHI"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GTI", - CellID->1799992921] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,20 +161,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 11.120337}", + "built" -> 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False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "GTI"->{ - Cell[3515, 107, 208, 9, 70, "Text", - CellTags->"GTI", - CellID->1799992921]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"GTI", 5473, 163} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[575, 21, 2237, 52, 70, "AnchorBarGrid", +Cell[575, 21, 2971, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2815, 75, 46, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2864, 78, 353, 11, 70, "Usage", +Cell[3549, 97, 280, 11, 70, "ObjectNameGrid"], +Cell[3832, 110, 353, 11, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3242, 93, 270, 12, 70, "SeeAlsoSection", +Cell[4210, 125, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3515, 107, 208, 9, 70, "Text", 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SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/GV.html"], + StandardForm]], "Input", TextClipboardType -> "PlainText"]}, + Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$162559], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/GV", + ".html"]], None}]}]}, + 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FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + + "http://reference.wolfram.com/language/FeynCalc/ref/Gamma3.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$79259], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/Gamma3", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$150921], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/Gamma3", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +97,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Gamma3", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Gamma3", "ObjectName"], + Cell[BoxData[ + 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"", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -153,11 +185,12 @@ TaggingRules->{ "None", "summary" -> "Gamma3[al, be, ga, ep] is a special product of Gamma functions expanded \ up to order Epsilon^n when positive integer arguments are given (the order n \ -is determined by the option EpsilonOrder).", "synonyms" -> {}, "title" -> - "Gamma3", "titlemodifier" -> "", "windowtitle" -> "Gamma3", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/Gamma3"}}, +is determined by the option EpsilonOrder).", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "Gamma3", "titlemodifier" -> "", + "windowtitle" -> "Gamma3", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/Gamma3"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -166,41 +199,31 @@ 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DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ GammaEpsilon.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$79609], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/GammaEpsilon", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$151369], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/GammaEpsilon", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +97,18 @@ GammaEpsilon.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["GammaEpsilon", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["GammaEpsilon", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,7 +142,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1663045079], + CellID->76090078], Cell[CellGroupData[{ @@ -118,14 +152,12 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1035397999], + CellID->1264124567], Cell["\<\ If the argument is of the form (1+a Epsilon) the result is not calculated but \ tabulated.\ -\>", "Text", - CellTags->"GammaEpsilon", - CellID->1418061835], +\>", "Notes"], Cell[CellGroupData[{ @@ -180,16 +212,15 @@ Cell[BoxData[ SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "2"]}], "+", - RowBox[{"C$23297", " ", + RowBox[{"C$44993", " ", SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "6"]}], "+", "1"}], TraditionalForm]], "Output", - ImageSize->{335, 98}, + ImageSize->{410, 88}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GammaEpsilon", - CellLabel->"Out[1]=", - CellID->1401166400] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -205,7 +236,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{"C$23317", " ", + RowBox[{"C$45019", " ", SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "6"]}], "+", @@ -242,17 +273,14 @@ Cell[BoxData[ TraditionalForm], "3"], " ", TemplateBox[{"3"}, "Zeta"]}], "24"], "+", "1"}], TraditionalForm]], "Output", - ImageSize->{450, 49}, + ImageSize->{435, 40}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GammaEpsilon", - CellLabel->"Out[2]=", - CellID->924354653] + CellLabel->"Out[2]="] }, Open ]], -Cell["For other arguments the expansion is calculated.", "Text", - CellTags->"GammaEpsilon", - CellID->185068189], +Cell["For other arguments the expansion is calculated.", "Notes"], Cell[CellGroupData[{ @@ -265,7 +293,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{"C$24452", " ", + RowBox[{"C$46162", " ", SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "6"]}], "+", @@ -336,12 +364,11 @@ Cell[BoxData[ RowBox[{"288", " ", TemplateBox[{"5"}, "Zeta"]}]}], ")"}]}], "1440"]}], TraditionalForm]], "Output", - ImageSize->{561, 112}, + ImageSize->{545, 90}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GammaEpsilon", - CellLabel->"Out[3]=", - CellID->208287808] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -356,12 +383,11 @@ Cell[BoxData[ FormBox[ TemplateBox[{"x"}, "Gamma"], TraditionalForm]], "Output", - ImageSize->{33, 15}, + ImageSize->{37, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GammaEpsilon", - CellLabel->"Out[4]=", - CellID->460537482] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -397,9 +423,7 @@ Cell[TextData[{ ButtonNote->"Series2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GammaEpsilon", - CellID->1891061042] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -416,22 +440,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 40.038799}", + "built" -> "{2020, 1, 5, 18, 58, 21.513053}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "GammaEpsilon[exp] gives a series expansion of Gamma[exp] in Epsilon up \ -to order 6 (where EulerGamma is neglected).", "synonyms" -> {}, "title" -> - "GammaEpsilon", "titlemodifier" -> "", "windowtitle" -> "GammaEpsilon", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/GammaEpsilon"}, - "SearchTextTranslated" -> ""}, +to order 6 (where EulerGamma is neglected).", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "GammaEpsilon", "titlemodifier" -> "", + "windowtitle" -> "GammaEpsilon", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/GammaEpsilon"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -439,8 +463,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> 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@@ Cell[TextData[{ ButtonNote->"GammaEpsilon"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"GammaExpand", - CellID->1346477755] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -247,7 +274,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"GammaExpand", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -256,21 +283,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 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"http://reference.wolfram.com/language/"], "FeynCalc/ref/Gauge", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +96,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Gauge", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Gauge", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -119,9 +152,7 @@ Cell[TextData[{ ButtonNote->"GluonProgagator"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Gauge", - CellID->1660814530] +}], "SeeAlso"] }, Open ]], Cell[" ", 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If set to 1 the 't Hooft Feynman \ -gauge is used.", "synonyms" -> {}, "title" -> "Gauge", "titlemodifier" -> "", - "windowtitle" -> "Gauge", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/Gauge"}}, +gauge is used.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "Gauge", + "titlemodifier" -> "", "windowtitle" -> "Gauge", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/Gauge"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -161,41 +192,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "Gauge"->{ - Cell[3552, 108, 399, 15, 70, "Text", - CellTags->"Gauge", - CellID->1660814530]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"Gauge", 5749, 171} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[577, 21, 2232, 52, 70, "AnchorBarGrid", +Cell[577, 21, 3086, 75, 70, "AnchorBarGrid", CellID->1], -Cell[2812, 75, 48, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2863, 78, 391, 12, 70, "Usage", +Cell[3666, 98, 282, 11, 70, "ObjectNameGrid"], +Cell[3951, 111, 391, 12, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3279, 94, 270, 12, 70, "SeeAlsoSection", +Cell[4367, 127, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3552, 108, 399, 15, 70, "Text", - CellTags->"Gauge", - CellID->1660814530] +Cell[4640, 141, 361, 13, 70, "SeeAlso"] }, Open ]], -Cell[3966, 126, 23, 0, 70, "FooterCell"] +Cell[5016, 157, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/GaugeField.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/GaugeField.nb index 741828209..1acc49d58 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/GaugeField.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/GaugeField.nb @@ -3,69 +3,93 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 9467, 321] -NotebookOptionsPosition[ 5878, 211] -NotebookOutlinePosition[ 8502, 284] -CellTagsIndexPosition[ 8390, 278] +NotebookDataLength[ 10303, 342] +NotebookOptionsPosition[ 6900, 241] +NotebookOutlinePosition[ 9433, 310] +CellTagsIndexPosition[ 9321, 304] WindowTitle->GaugeField WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/GaugeField\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/GaugeField"]}, Visible -> False]]; 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CellLabel->"In[3]:=", + CellLabel->"In[1]:=", CellID->357152074], Cell[BoxData[ @@ -203,74 +315,38 @@ Cell[BoxData[ SubscriptBox["\[CapitalPi]", "u"], "(", FormBox["p", TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{44, 17}, + ImageSize->{49, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"GhostPropagator", - CellLabel->"Out[3]=", - CellID->1092778903] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"GhostPropagator", "[", - RowBox[{"p", ",", "1", ",", "2"}], "]"}], "//", "Explicit"}]], "Input", - CellTags->"GhostPropagator", - CellLabel->"In[4]:=", - CellID->1361525951], + RowBox[{"Explicit", "[", "%", "]"}]], "Input", + CellLabel->"In[2]:="], Cell[BoxData[ FormBox[ - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SuperscriptBox["\[Delta]", - RowBox[{ - FormBox[ - FormBox["ci1", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["ci2", - TraditionalForm], - TraditionalForm]}]]}], - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"]], TraditionalForm]], "Output", - ImageSize->{63, 52}, + FractionBox["\[ImaginaryI]", + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False]], TraditionalForm]], "Output", + ImageSize->{28, 39}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"GhostPropagator", - CellLabel->"Out[4]=", - CellID->190043121] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"GhostPropagator", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", "3", ",", "4"}], "]"}], "//", "Explicit"}], "//", - " ", "FCE"}], "//", "StandardForm"}]], "Input", - CellTags->"GhostPropagator", - CellLabel->"In[5]:=", - CellID->160188204], - -Cell[BoxData[ - RowBox[{"\[ImaginaryI]", " ", - RowBox[{"FAD", "[", "k", "]"}], " ", - 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CellTags->"GhostPropagator", - CellID->495663945] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -331,22 +405,23 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 20, 50.542135}", + "built" -> "{2020, 1, 5, 18, 58, 31.985995}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "GhostPropagator[p, a, b] gives the ghost propagator where \"a\" and \ -\"b\" are the color indices. 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The dimension and the name of the \ -coupling constant are determined by the options Dimension and \ -CouplingConstant.", "synonyms" -> {}, "title" -> "GluonGhostVertex", - "titlemodifier" -> "", "windowtitle" -> "GluonGhostVertex", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/GluonGhostVertex"}, - "SearchTextTranslated" -> ""}, +GluonGhostVertex[p, mu, a , q, nu, b , k, rho, c ] yields the Gluon-Ghost \ +vertex. The first argument represents the gluon and the third argument the \ +outgoing ghost field (but incoming 4-momentum).", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "GluonGhostVertex", "titlemodifier" -> "", + "windowtitle" -> "GluonGhostVertex", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/GluonGhostVertex"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -368,8 +440,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -377,104 +450,81 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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GluonPropagator[p, {mu}, {nu}] or \ -GluonPropagator[p, mu, nu] omits the SUNDelta. The gauge and the dimension is \ -determined by the option Gauge and Dimension. The following settings of Gauge \ -are possible: 1 for the Feynman gauge; \\[Alpha] for the general covariant \ -gauge; {Momentum[n] ,1} for the axial gauge. GP can be used as an \ -abbreviation of GluonPropagator.", "synonyms" -> {}, "title" -> - "GluonPropagator", "titlemodifier" -> "", "windowtitle" -> - "GluonPropagator", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/GluonPropagator"}, "SearchTextTranslated" -> ""}, + "GluonPropagator[p, {\\[Mu], a}, {\\[Nu], b}] or GluonPropagator[p, \ +\\[Mu], a, \\[Nu], b] yields the gluon propagator. 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Only a typesetting rule is defined.\ -\>", "Text", - CellTags->"Gstrong", - CellID->1604993747], + CellID->321004010], Cell[CellGroupData[{ @@ -134,12 +207,25 @@ Cell[BoxData["Gstrong"], "Input", Cell[BoxData[ FormBox[ SubscriptBox["g", "s"], TraditionalForm]], "Output", - ImageSize->{20, 15}, + ImageSize->{22, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Gstrong", - CellLabel->"Out[1]=", - CellID->50548467] + CellLabel->"Out[1]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "StandardForm"}]], "Input", + CellLabel->"In[2]:="], + +Cell[BoxData[ + RowBox[{"SMP", "[", "\<\"g_s\"\>", "]"}]], "Output", + ImageSize->{70, 15}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[2]//StandardForm="] }, Open ]] }, Open ]], @@ -163,7 +249,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["CovariantD", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/CovariantD"], @@ -179,9 +264,7 @@ Cell[TextData[{ ButtonData->"paclet:FeynCalc/ref/GluonVertex"], FontFamily->"Verdana"], "." -}], "Text", - 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CellID->1638895535], + CellID->1163149135], Cell[CellGroupData[{ @@ -120,7 +131,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1480924129], + CellID->1258941768], Cell[CellGroupData[{ @@ -135,12 +146,11 @@ Cell[BoxData[ FormBox[ TemplateBox[{"a","b","c","z"}, "Hypergeometric2F1"], TraditionalForm]], "Output", - ImageSize->{101, 15}, + ImageSize->{104, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"HypInt", - CellLabel->"Out[1]=", - CellID->1455067917] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -187,12 +197,11 @@ Cell[BoxData[ "Gamma"], " ", TemplateBox[{RowBox[{"c", "-", "b"}]}, "Gamma"]}]], TraditionalForm]], "Output", - ImageSize->{280, 52}, + ImageSize->{300, 56}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"HypInt", - CellLabel->"Out[2]=", - CellID->1838289676] + CellLabel->"Out[2]="] }, Open ]] }, Open ]] }, Open ]], @@ -202,7 +211,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"HypInt", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -211,10 +220,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 19.209123}", + "built" -> "{2020, 1, 5, 18, 58, 53.261201}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -294,12 +355,12 @@ TaggingRules->{ "None", "summary" -> "HypergeometricSE[exp, nu] expresses Hypergeometric functions by their \ series expansion in terms of a sum (the Sum is omitted and nu, running from 0 \ -to \\[Infinity], is the summation index).", "synonyms" -> {}, "title" -> - "HypergeometricSE", "titlemodifier" -> "", "windowtitle" -> - "HypergeometricSE", "type" -> "Symbol", "uri" -> +to \\[Infinity], is the summation index).", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "HypergeometricSE", "titlemodifier" -> "", + "windowtitle" -> "HypergeometricSE", "type" -> "Symbol", "uri" -> "FeynCalc/ref/HypergeometricSE"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -307,8 +368,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - 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CellID->1224892054], +Cell[TextData[{ + Cell["IFPDOff", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -110,7 +143,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->2145771835], + CellID->243646067], Cell[CellGroupData[{ @@ -120,7 +153,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1904573923], + CellID->117025203], Cell[CellGroupData[{ @@ -150,12 +183,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{86, 20}, + ImageSize->{91, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"IFPDOff", - CellLabel->"Out[1]=", - CellID->784861447] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -170,12 +202,11 @@ Cell[BoxData[ RowBox[{"IFPD", "[", RowBox[{ RowBox[{"Momentum", "[", "p", "]"}], ",", "m"}], "]"}]], "Output", - ImageSize->{167, 15}, + ImageSize->{168, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"IFPDOff", - CellLabel->"Out[2]//StandardForm=", - CellID->690906879] + CellLabel->"Out[2]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -197,12 +228,11 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"], "-", SuperscriptBox["m", "2"]}], TraditionalForm]], "Output", - ImageSize->{60, 20}, + ImageSize->{65, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"IFPDOff", - CellLabel->"Out[3]=", - CellID->2145155528] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -221,12 +251,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"Momentum", "[", "p", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}]], "Output", - ImageSize->{291, 15}, + ImageSize->{292, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"IFPDOff", - CellLabel->"Out[4]//StandardForm=", - CellID->128477436] + CellLabel->"Out[4]//StandardForm="] }, Open ]] }, Open ]], @@ -262,9 +291,7 @@ Cell[TextData[{ ButtonNote->"IFPDOn"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"IFPDOff", - CellID->1144166368] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -281,10 +308,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 25.194704}", + "built" -> "{2020, 1, 5, 18, 58, 57.265956}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -292,11 +319,11 @@ TaggingRules->{ "None", "summary" -> "IFPDOff[exp_, q1_, q2_, ...] changes from IFPD representation to \ FeynAmpDenominator[ ...]. The q1, q2, ... are the integration momenta.", - "synonyms" -> {}, "title" -> "IFPDOff", "titlemodifier" -> "", - "windowtitle" -> "IFPDOff", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/IFPDOff"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "IFPDOff", + "titlemodifier" -> "", "windowtitle" -> "IFPDOff", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/IFPDOff"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -305,7 +332,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -314,103 +341,89 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["IFPDOn", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -124,9 +157,7 @@ Cell[TextData[{ ButtonNote->"IFPDOff"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"IFPDOn", - CellID->168214064] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -143,10 +174,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 26.848069}", + "built" -> "{2020, 1, 5, 18, 58, 58.342273}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -156,11 +187,11 @@ TaggingRules->{ representation to the IFPD one (Inverse Feynman Propagator Denominator). \ I.e., FeynAmpDenominator[PropagatorDenominator[a,b]] is replaced by \ 1/IFPD[a,b] and The q1, q2, ... are the integration momenta.", - "synonyms" -> {}, "title" -> "IFPDOn", "titlemodifier" -> "", - "windowtitle" -> "IFPDOn", "type" -> "Symbol", "uri" -> + "synonyms" -> {}, "tabletags" -> {}, "title" -> "IFPDOn", "titlemodifier" -> + "", "windowtitle" -> "IFPDOn", "type" -> "Symbol", "uri" -> "FeynCalc/ref/IFPDOn"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -169,41 +200,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "IFPDOn"->{ - Cell[3827, 113, 369, 15, 70, "Text", - CellTags->"IFPDOn", - 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CellID->1224892054], +Cell[TextData[{ + Cell["IncludePair", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -125,9 +161,7 @@ Cell[TextData[{ ButtonNote->"FeynAmpDenominatorSimplify"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"IncludePair", - CellID->419229587] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -144,10 +178,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 28.279098}", + "built" -> "{2020, 1, 5, 18, 58, 59.292807}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -155,11 +189,11 @@ TaggingRules->{ "None", "summary" -> "IncludePair is an option for FC2RHI, FC2TLI and \ FeynAmpDenominatorSimplify. Possible settings are True and False.", - "synonyms" -> {}, "title" -> "IncludePair", "titlemodifier" -> "", - "windowtitle" -> "IncludePair", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/IncludePair"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "IncludePair", + "titlemodifier" -> "", "windowtitle" -> "IncludePair", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/IncludePair"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -168,41 +202,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["IndexPosition", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +144,7 @@ Cell[TextData[{ ButtonNote->"FieldStrength"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"IndexPosition", - CellID->976822558] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,20 +161,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 29.541064}", + "built" -> "{2020, 1, 5, 18, 59, 0.291510}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "IndexPosition is an option for FieldStrength.", - "synonyms" -> {}, "title" -> "IndexPosition", "titlemodifier" -> "", - "windowtitle" -> "IndexPosition", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/IndexPosition"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "IndexPosition", + "titlemodifier" -> "", "windowtitle" -> "IndexPosition", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/IndexPosition"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -153,41 +183,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["InitialFunction", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -113,9 +145,7 @@ Cell[TextData[{ ButtonNote->"FeynRule"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"InitialFunction", - CellID->1858355403] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -132,10 +162,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 30.911262}", + "built" -> "{2020, 1, 5, 18, 59, 1.298241}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -143,11 +173,11 @@ TaggingRules->{ "None", "summary" -> "InitialFunction is an option of FeynRule the setting of which is applied \ to the first argument of FeynRule before anything else", "synonyms" -> {}, - "title" -> "InitialFunction", "titlemodifier" -> "", "windowtitle" -> - "InitialFunction", "type" -> "Symbol", "uri" -> + "tabletags" -> {}, "title" -> "InitialFunction", "titlemodifier" -> "", + "windowtitle" -> "InitialFunction", "type" -> "Symbol", "uri" -> "FeynCalc/ref/InitialFunction"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -156,41 +186,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "InitialFunction"->{ - Cell[3653, 108, 235, 9, 70, "Text", - 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Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], + +Cell["", "SectionHeaderSpacer"], + +Cell[TextData[{ + "For more details, see the documentation for ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + "." +}], "Notes", + CellID->1067943069] +}, Closed]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -110,22 +185,11 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[TextData[{ - StyleBox[ButtonBox["DiracSimplify", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], - FontFamily->"Verdana"], - ", ", - StyleBox[ButtonBox["DiracTrace", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/DiracTrace", - ButtonNote->"DiracTrace"], - FontFamily->"Verdana"], - "." -}], "Text", - CellTags->"InsideDiracTrace", - CellID->1537569404] +Cell[TextData[StyleBox[ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + FontFamily->"Verdana"]], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -142,26 +206,24 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 33.462754}", + "built" -> "{2020, 1, 5, 18, 59, 3.316695}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "InsideDiracTrace is and option of DiracSimplify. If set to True, \ -DiracSimplify assumes to operate inside a DiracTrace, i.e., products of an \ -odd number of Dirac matrices are discarded. Furthermore simple traces are \ -calculated (but divided by a factor 4, i.e. : DiracSimplify[DiracMatrix[a,b], \ -InsideDiracTrace->True] yields ScalarProduct[a,b]) Traces involving more than \ -four DiracGamma's and DiracGamma[5] are not performed.", "synonyms" -> {}, - "title" -> "InsideDiracTrace", "titlemodifier" -> "", "windowtitle" -> + "InsideDiracTrace is an option of DiracSimplify and some other functions \ +dealing with Dirac algebra. If set to True, the function assumes to operate \ +inside a Dirac trace, i.e., products of an odd number of Dirac matrices are \ +discarded.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "InsideDiracTrace", "titlemodifier" -> "", "windowtitle" -> "InsideDiracTrace", "type" -> "Symbol", "uri" -> "FeynCalc/ref/InsideDiracTrace"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -170,41 +232,39 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "InsideDiracTrace"->{ - Cell[3971, 112, 416, 15, 70, "Text", - CellTags->"InsideDiracTrace", - CellID->1537569404]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"InsideDiracTrace", 6590, 180} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[588, 21, 2277, 52, 70, "AnchorBarGrid", +Cell[588, 21, 3045, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2868, 75, 59, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2930, 78, 743, 16, 70, "Usage", +Cell[3636, 97, 293, 11, 70, "ObjectNameGrid"], +Cell[3932, 110, 723, 18, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3698, 98, 270, 12, 70, "SeeAlsoSection", +Cell[4680, 132, 730, 24, 70, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], +Cell[5413, 158, 31, 0, 70, "SectionHeaderSpacer"], +Cell[5447, 160, 235, 8, 70, "Notes", + CellID->1067943069] +}, Closed]], +Cell[CellGroupData[{ +Cell[5719, 173, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3971, 112, 416, 15, 70, "Text", - CellTags->"InsideDiracTrace", - CellID->1537569404] +Cell[5992, 187, 187, 4, 70, "SeeAlso"] }, Open ]], -Cell[4402, 130, 23, 0, 70, "FooterCell"] +Cell[6194, 194, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/IntegralTable.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/IntegralTable.nb index bbc262f65..1e970e633 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/IntegralTable.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/IntegralTable.nb @@ -3,69 +3,96 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6714, 202] -NotebookOptionsPosition[ 4381, 135] -NotebookOutlinePosition[ 6448, 191] -CellTagsIndexPosition[ 6373, 186] +NotebookDataLength[ 7702, 228] +NotebookOptionsPosition[ 5582, 170] +NotebookOutlinePosition[ 7493, 220] +CellTagsIndexPosition[ 7450, 217] WindowTitle->IntegralTable WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/IntegralTable\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/IntegralTable"]}, Visible -> False]]; 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It may be set to a list of the form : \ -{FCIntegral[ ... ] :> bla, ...}.", "synonyms" -> {}, "title" -> - "IntegralTable", "titlemodifier" -> "", "windowtitle" -> "IntegralTable", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/IntegralTable"}}, +{FCIntegral[ ... ] :> bla, ...}.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "IntegralTable", "titlemodifier" -> "", "windowtitle" -> + "IntegralTable", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/IntegralTable"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -169,41 +205,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "IntegralTable"->{ - Cell[3693, 109, 646, 21, 70, "Text", - CellTags->"IntegralTable", - CellID->498155720]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"IntegralTable", 6257, 179} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[585, 21, 2265, 52, 70, "AnchorBarGrid", +Cell[585, 21, 3277, 79, 70, "AnchorBarGrid", CellID->1], -Cell[2853, 75, 56, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2912, 78, 483, 13, 70, "Usage", +Cell[3865, 102, 290, 11, 70, "ObjectNameGrid"], +Cell[4158, 115, 483, 13, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3420, 95, 270, 12, 70, "SeeAlsoSection", +Cell[4666, 132, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3693, 109, 646, 21, 70, "Text", - CellTags->"IntegralTable", - CellID->498155720] +Cell[4939, 146, 601, 19, 70, "SeeAlso"] }, Open ]], -Cell[4354, 133, 23, 0, 70, "FooterCell"] +Cell[5555, 168, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Integrate2.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Integrate2.nb index d90886ab6..8c7bd1e12 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Integrate2.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Integrate2.nb @@ -3,69 +3,100 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 120460, 3982] -NotebookOptionsPosition[ 103951, 3432] -NotebookOutlinePosition[ 113194, 3703] -CellTagsIndexPosition[ 113076, 3697] +NotebookDataLength[ 82809, 2951] +NotebookOptionsPosition[ 68414, 2482] +NotebookOutlinePosition[ 76050, 2701] +CellTagsIndexPosition[ 75934, 2695] WindowTitle->Integrate2 WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/Integrate2\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/Integrate2"]}, Visible -> False]]; 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Integrate2[f[x] DeltaFunction[a + b \ -x], x] \[Rule] Integrate[f[x] (1/Abs[b]) DeltaFunction[a/b + x], x], where \ -abs[b] \[Rule] b, if b is a Symbol, and if b = -c, then abs[-c] \[Rule] c, \ -i.e., the variable contained in b is supposed to be positive. ", + " \[LineSeparator]is like Integrate, but : Integrate2[a_Plus, b__] := \ +Map[Integrate2[#, b]&, a] ( more linear algebra and partial fraction \ +decomposition is done) Integrate2[f[x] DeltaFunction[x], x] \[Rule] f[0] \ +Integrate2[f[x] DeltaFunction[x0-x], x] \[Rule] f[x0]. Integrate2[f[x] \ +DeltaFunction[a + b x], x] \[Rule] Integrate[f[x] (1/Abs[b]) \ +DeltaFunction[a/b + x], x], where abs[b] \[Rule] b, if b is a Symbol, and if \ +b = -c, then abs[-c] \[Rule] c, i.e., the variable contained in b is supposed \ +to be positive. ", Cell[BoxData[ FormBox[ RowBox[{" ", SuperscriptBox["\[Pi]", "2"]}], TraditionalForm]]], " is replaced by 6 Zeta2. Integrate2[1/(1-y),{y,x,1}] is intepreted as \ distribution, i.e. as Integrate2[-1/(1-y)],{y, 0, x}] \[Rule] Log[1-y]. \ -Integrate2[1/(1-x),{x,0,1}] \[Rule] 0.\n\nNOTE: Since Integrate2 does do a \ -reordering and partial fraction decomposition before calling the integral \ -table of Integrate3 it will in general be slower compared to Integrate3 for \ -sums of integrals. I.e., if the integrand has already an expanded form and if \ -partial fraction decomposition is not necessary it is more effective to use \ -Integrate3." +Integrate2[1/(1-x),{x,0,1}] \[Rule] 0." }]]} }]], "Usage", GridBoxOptions->{ @@ -109,6 +147,47 @@ Integrate3." 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I.e., if the integrand has \ +already an expanded form and if partial fraction decomposition is not \ +necessary it is more effective to use Integrate3.\ +\>", "Notes", + CellID->1067943069] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -124,7 +203,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1621069730], + CellID->1066608491], Cell[CellGroupData[{ @@ -134,7 +213,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->756384805], + CellID->656544217], Cell[CellGroupData[{ @@ -159,7 +238,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{"{", - RowBox[{"0.006734`", ",", + RowBox[{"0.028933`", ",", RowBox[{ TemplateBox[{"3"}, "Zeta"], "-", @@ -168,12 +247,11 @@ Cell[BoxData[ RowBox[{"\[Zeta]", "(", "2", ")"}], " ", RowBox[{"log", "(", "2", ")"}]}]}]}], "}"}], TraditionalForm]], 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CellLabel->"In[18]:=", + CellLabel->"In[17]:=", CellID->1975519554], Cell[BoxData[ @@ -756,12 +771,11 @@ Cell[BoxData[ RowBox[{"log", "(", RowBox[{"1", "-", "y"}], ")"}]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{282, 42}, + ImageSize->{288, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"InverseMellin", - CellLabel->"Out[18]=", - CellID->2023526209] + CellLabel->"Out[17]="] }, Open ]], Cell[CellGroupData[{ @@ -776,7 +790,7 @@ Cell[BoxData[ RowBox[{"-", "1"}], "+", "OPEm"}]}], "]"}], "^", "2"}], "/", "OPEm"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[19]:=", + CellLabel->"In[18]:=", CellID->1312317430], Cell[BoxData[ @@ -809,12 +823,11 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["log", "2"], "(", "y", ")"}], "2"]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{517, 48}, + ImageSize->{540, 40}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"InverseMellin", - CellLabel->"Out[19]=", - CellID->1387073931] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -825,7 +838,7 @@ Cell[BoxData[ RowBox[{"2", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[20]:=", + CellLabel->"In[19]:=", CellID->1086751012], Cell[BoxData[ @@ -852,12 +865,11 @@ Cell[BoxData[ RowBox[{"log", "(", "y", ")"}], RowBox[{"1", "-", "y"}]]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{307, 45}, + ImageSize->{315, 38}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"InverseMellin", - CellLabel->"Out[20]=", - CellID->229974260] + CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ @@ -869,7 +881,7 @@ Cell[BoxData[ RowBox[{"2", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "/", "OPEm"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[21]:=", + CellLabel->"In[20]:=", CellID->410476681], Cell[BoxData[ @@ -895,12 +907,11 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["log", "2"], "(", "y", ")"}]}]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$95484], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$173667], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/Isolate", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Isolate", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Isolate", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -96,39 +109,40 @@ abbreviations may be specified with the option IsolateNames." Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->1728614717], + CellGroupingRules->{"SectionGrouping", 50}, + CellID->773008384], -Cell[CellGroupData[{ - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->1400364295], +Cell["", "SectionHeaderSpacer"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "Isolate", "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[1]:=", + CellLabel->"In[79]:=", CellID->2088060696], Cell[BoxData[ @@ -137,39 +151,69 @@ Cell[BoxData[ RowBox[{ RowBox[{"IsolateNames", "\[Rule]", "KK"}], ",", RowBox[{"IsolatePrint", "\[Rule]", "False"}], ",", + RowBox[{"IsolateFast", "\[Rule]", "False"}], ",", RowBox[{"IsolateSplit", "\[Rule]", "\[Infinity]"}], ",", RowBox[{"IsolateTimes", "\[Rule]", "False"}], ",", RowBox[{"IsolatePlus", "\[Rule]", "False"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{402, 35}, + ImageSize->{371, 34}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Isolate", - CellLabel->"Out[1]=", - CellID->2033547322] + CellLabel->"Out[79]="] +}, Open ]] +}, Closed]] }, Open ]], Cell[CellGroupData[{ +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->476043383], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->704436246], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"t0", "=", RowBox[{"Isolate", "[", RowBox[{"a", "+", "b"}], "]"}]}]], "Input", CellTags->"Isolate", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1761911845], Cell[BoxData[ FormBox[ TagBox[ - RowBox[{"KK", "(", "682", ")"}], + RowBox[{"KK", "(", "24", ")"}], HoldForm], TraditionalForm]], "Output", - ImageSize->{57, 15}, + ImageSize->{54, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Isolate", - CellLabel->"Out[2]=", - CellID->2009964510] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -187,7 +231,7 @@ Cell[BoxData[ RowBox[{"c", "+", "d"}], ")"}], " ", "f"}], " ", "+", " ", "e"}], ",", "f"}], "]"}]}]], "Input", CellTags->"Isolate", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1164516818], Cell[BoxData[ @@ -195,18 +239,17 @@ Cell[BoxData[ RowBox[{"e", "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "(", "682", ")"}], + RowBox[{"KK", "(", "24", ")"}], HoldForm]}], "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "(", "683", ")"}], + RowBox[{"KK", "(", "25", ")"}], HoldForm]}]}], TraditionalForm]], "Output", - ImageSize->{174, 15}, + ImageSize->{173, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Isolate", - CellLabel->"Out[3]=", - CellID->416280036] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -214,25 +257,24 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"StandardForm", "[", "t1", "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->810104736], Cell[BoxData[ RowBox[{"e", "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "[", "682", "]"}], + RowBox[{"KK", "[", "24", "]"}], HoldForm]}], "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "[", "683", "]"}], + RowBox[{"KK", "[", "25", "]"}], HoldForm]}]}]], "Output", - ImageSize->{183, 15}, + ImageSize->{166, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Isolate", - CellLabel->"Out[4]//StandardForm=", - CellID->1069603345] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -242,7 +284,7 @@ Cell[BoxData[ RowBox[{"t0", ",", " ", "t1", ",", " ", RowBox[{"ReleaseHold", "[", "t1", "]"}]}], "}"}]], "Input", CellTags->"Isolate", - CellLabel->"In[5]:=", + CellLabel->"In[4]:=", CellID->113729976], Cell[BoxData[ @@ -250,16 +292,16 @@ Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[ - RowBox[{"KK", "(", "682", ")"}], + RowBox[{"KK", "(", "24", ")"}], HoldForm], ",", RowBox[{"e", "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "(", "682", ")"}], + RowBox[{"KK", "(", "24", ")"}], HoldForm]}], "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "(", "683", ")"}], + RowBox[{"KK", "(", "25", ")"}], HoldForm]}]}], ",", RowBox[{ RowBox[{"f", " ", @@ -269,12 +311,11 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"c", "+", "d"}], ")"}]}], "+", "e"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{410, 15}, + ImageSize->{423, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Isolate", - CellLabel->"Out[5]=", - CellID->743594287] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -298,7 +339,7 @@ Cell[BoxData[ RowBox[{"a", ",", "d"}], "}"}], ",", RowBox[{"IsolateNames", "\[Rule]", "fF"}]}], "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[6]:=", + CellLabel->"In[5]:=", CellID->689489417], Cell[BoxData[ @@ -306,20 +347,19 @@ Cell[BoxData[ RowBox[{ RowBox[{ TagBox[ - RowBox[{"fF", "(", "685", ")"}], + RowBox[{"fF", "(", "27", ")"}], HoldForm], " ", RowBox[{"a", "(", "z", ")"}]}], "+", RowBox[{ TagBox[ - RowBox[{"fF", "(", "684", ")"}], + RowBox[{"fF", "(", "26", ")"}], HoldForm], " ", RowBox[{"d", "(", "z", ")"}]}]}], TraditionalForm]], "Output", - ImageSize->{183, 15}, + ImageSize->{175, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Isolate", - CellLabel->"Out[6]=", - CellID->2124185985] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -327,30 +367,29 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"??", "fF"}]], "Input", CellTags->"Isolate", - CellLabel->"In[7]:=", + CellLabel->"In[6]:=", CellID->1089652184], Cell[CellGroupData[{ Cell["Global`fF", "Print", "PrintUsage", - CellTags->{"Info-5c3dc742-bd47-47d4-be3e-c64284c792e1", "Isolate"}, - CellID->811343181], + CellTags->{"Info-e2b39ee4-0424-4b02-a1ac-880dc8e10ae5", "Isolate"}], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ { RowBox[{ - RowBox[{"fF", "[", "684", "]"}], "=", + RowBox[{"fF", "[", "26", "]"}], "=", RowBox[{"y", "+", "z"}]}]}, {" "}, { RowBox[{ - RowBox[{"fF", "[", "685", "]"}], "=", + RowBox[{"fF", "[", "27", "]"}], "=", RowBox[{"b", "+", RowBox[{"c", " ", RowBox[{"\<\"HoldForm\"\>", "[", - RowBox[{"fF", "[", "684", "]"}], "]"}]}]}]}]} + RowBox[{"fF", "[", "26", "]"}], "]"}]}]}]}]} }, BaselinePosition->{Baseline, {1, 1}}, GridBoxAlignment->{ @@ -366,8 +405,7 @@ Cell[BoxData[ "RowsIndexed" -> {}}], Definition[$CellContext`fF], Editable->False]], "Print", - CellTags->{"Info-5c3dc742-bd47-47d4-be3e-c64284c792e1", "Isolate"}, - CellID->1424099393] + CellTags->{"Info-e2b39ee4-0424-4b02-a1ac-880dc8e10ae5", "Isolate"}] }, Open ]] }, Open ]], @@ -380,52 +418,26 @@ Cell[BoxData[ RowBox[{"IsolateNames", "\[Rule]", "l"}], ",", RowBox[{"IsolateSplit", "\[Rule]", "15"}]}], "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[8]:=", + CellLabel->"In[7]:=", CellID->2019918870], Cell[BoxData[ FormBox[ TagBox[ - RowBox[{"l", "(", "687", ")"}], + RowBox[{"l", "(", "29", ")"}], HoldForm], TraditionalForm]], "Output", - ImageSize->{45, 15}, + ImageSize->{41, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Isolate", - CellLabel->"Out[8]=", - CellID->1344566773] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"{", - RowBox[{ - RowBox[{"l", "[", "2", "]"}], ",", - RowBox[{"l", "[", "1", "]"}]}], "}"}]], "Input", - CellTags->"Isolate", - CellLabel->"In[9]:=", - CellID->727095247], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"l", "(", "2", ")"}], ",", - RowBox[{"l", "(", "1", ")"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{78, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Isolate", - CellLabel->"Out[9]=", - CellID->1999836335] + CellLabel->"Out[7]="] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"t0", ",", "t1", ",", "l", ",", "fF"}], "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[10]:=", + CellLabel->"In[8]:=", CellID->808271947] }, Open ]] }, Open ]], @@ -444,10 +456,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 50.343751}", + "built" -> "{2020, 1, 5, 18, 59, 15.670179}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -458,11 +470,11 @@ TaggingRules->{ varlist] substitutes KK[i] for all subsums in expr which are free of any \ occurence of a member of the list varlist. Instead of KK any other head or a \ list of names of the abbreviations may be specified with the option \ -IsolateNames.", "synonyms" -> {}, "title" -> "Isolate", "titlemodifier" -> "", - "windowtitle" -> "Isolate", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/Isolate"}, "SearchTextTranslated" -> ""}, +IsolateNames.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "Isolate", + "titlemodifier" -> "", "windowtitle" -> "Isolate", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/Isolate"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -470,8 +482,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -479,185 +492,158 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["IsolateNames", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -120,9 +153,7 @@ Cell[TextData[{ ButtonNote->"Collect2"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"IsolateNames", - CellID->641552758] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -139,10 +170,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 49.124161}", + "built" -> "{2020, 1, 5, 18, 59, 14.676198}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -150,11 +181,11 @@ TaggingRules->{ "None", "summary" -> "IsolateNames is an option for Isolate and Collect2. 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$174103], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/IsolatePrint", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ IsolatePrint.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["IsolatePrint", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["IsolatePrint", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -114,9 +146,7 @@ Cell[TextData[{ ButtonNote->"Isolate"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"IsolatePrint", - CellID->1589107046] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -133,10 +163,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 51.943620}", + "built" -> "{2020, 1, 5, 18, 59, 16.772533}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -145,11 +175,11 @@ TaggingRules->{ "IsolatePrint is an option of Isolate. If it is set to OutputForm (or any \ other *Form) the definitions of the abbreviations are printed during the \ operation of Isolate. The setting IsolatePrint -> False suppresses printing.", - "synonyms" -> {}, "title" -> "IsolatePrint", "titlemodifier" -> "", - "windowtitle" -> "IsolatePrint", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/IsolatePrint"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "IsolatePrint", + "titlemodifier" -> "", "windowtitle" -> "IsolatePrint", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/IsolatePrint"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -158,41 +188,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "IsolatePrint"->{ - Cell[3737, 109, 229, 9, 70, "Text", - CellTags->"IsolatePrint", - CellID->1589107046]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"IsolatePrint", 5941, 168} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[584, 21, 2261, 52, 70, "AnchorBarGrid", +Cell[584, 21, 3017, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2848, 75, 55, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2906, 78, 533, 13, 70, "Usage", +Cell[3604, 97, 289, 11, 70, "ObjectNameGrid"], +Cell[3896, 110, 533, 13, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3464, 95, 270, 12, 70, "SeeAlsoSection", +Cell[4454, 127, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3737, 109, 229, 9, 70, "Text", - CellTags->"IsolatePrint", - CellID->1589107046] +Cell[4727, 141, 184, 7, 70, "SeeAlso"] }, Open ]], -Cell[3981, 121, 23, 0, 70, "FooterCell"] +Cell[4926, 151, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/IsolateSplit.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/IsolateSplit.nb index 18bd41556..ce270e0fb 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/IsolateSplit.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/IsolateSplit.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6652, 194] -NotebookOptionsPosition[ 4139, 125] -NotebookOutlinePosition[ 6387, 183] -CellTagsIndexPosition[ 6313, 178] +NotebookDataLength[ 7387, 215] +NotebookOptionsPosition[ 5084, 155] +NotebookOutlinePosition[ 7180, 207] +CellTagsIndexPosition[ 7137, 204] WindowTitle->IsolateSplit WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/IsolateSplit\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/IsolateSplit"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"Isolate\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Isolate"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/IsolateSplit\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/IsolateSplit"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ IsolateSplit.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$96169], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/IsolateSplit", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$174545], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/IsolateSplit", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ IsolateSplit.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["IsolateSplit", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["IsolateSplit", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -116,9 +148,7 @@ Cell[TextData[{ ButtonNote->"Isolate"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"IsolateSplit", - CellID->1638104774] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -135,10 +165,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 53.138397}", + "built" -> "{2020, 1, 5, 18, 59, 17.568794}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -149,10 +179,11 @@ maximum number of characters of FortranForm[expr] which are abbreviated by \ Isolate. If the expression is larger than the indicated number, it is split \ into smaller pieces and onto each subsum Isolate is applied. With the default \ setting IsolateSplit -> Infinity no splitting is done.", "synonyms" -> {}, - "title" -> "IsolateSplit", "titlemodifier" -> "", "windowtitle" -> - "IsolateSplit", "type" -> "Symbol", "uri" -> "FeynCalc/ref/IsolateSplit"}}, + "tabletags" -> {}, "title" -> "IsolateSplit", "titlemodifier" -> "", + "windowtitle" -> "IsolateSplit", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/IsolateSplit"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -161,41 +192,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* 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CellID->1224892054], +Cell[TextData[{ + Cell["Kummer", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -110,7 +142,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->451429310], + CellID->1622183496], Cell[CellGroupData[{ @@ -120,7 +152,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->22536900], + CellID->842763816], Cell[CellGroupData[{ @@ -149,12 +181,11 @@ Cell[BoxData[ RowBox[{"-", "a"}], "-", "b", "+", "c"}]], " ", TemplateBox[{RowBox[{"c", "-", "a"}],RowBox[{"c", "-", "b"}],"c","z"}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{357, 19}, + ImageSize->{375, 20}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[1]=", - CellID->780995976] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -185,12 +216,11 @@ Cell[BoxData[ FractionBox["z", RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{342, 39}, + ImageSize->{354, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[2]=", - CellID->334128730] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -221,12 +251,11 @@ Cell[BoxData[ FractionBox["z", RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{342, 39}, + ImageSize->{355, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[3]=", - CellID->1379521301] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +287,11 @@ Cell[BoxData[ RowBox[{"c", "-", "a"}],RowBox[{"c", "-", "b"}],"c", RowBox[{"1", "-", "z"}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{367, 19}, + ImageSize->{386, 20}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[4]=", - CellID->1681078809] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -298,12 +326,11 @@ Cell[BoxData[ RowBox[{"a", "-", "c", "+", "1"}],RowBox[{"b", "-", "c", "+", "1"}], RowBox[{"a", "+", "b", "-", "c", "+", "1"}],RowBox[{"1", "-", "z"}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{526, 18}, + ImageSize->{557, 20}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[5]=", - CellID->583730114] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -334,12 +361,11 @@ Cell[BoxData[ FractionBox[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{330, 43}, + ImageSize->{342, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[6]=", - CellID->282378053] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -376,12 +402,11 @@ Cell[BoxData[ FractionBox[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{492, 43}, + ImageSize->{517, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[7]=", - CellID->593894309] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -412,12 +437,11 @@ Cell[BoxData[ FractionBox[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{330, 43}, + ImageSize->{343, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[8]=", - CellID->658206917] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -454,12 +478,11 @@ Cell[BoxData[ FractionBox[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{492, 43}, + ImageSize->{522, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[9]=", - CellID->884891760] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -501,12 +524,11 @@ Cell[BoxData[ RowBox[{"c", "-", "a"}],RowBox[{"c", "-", "b"}],"c",FractionBox[ "1", "z"]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{444, 43}, + ImageSize->{468, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[10]=", - CellID->1201929686] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -554,12 +576,11 @@ Cell[BoxData[ RowBox[{"1", "-", "b"}],RowBox[{"c", "-", "b"}], RowBox[{"a", "-", "b", "+", "1"}],FractionBox["1", "z"]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{380, 93}, + ImageSize->{405, 78}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[11]=", - CellID->1407407771] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -600,12 +621,11 @@ Cell[BoxData[ TemplateBox[{"a",RowBox[{"c", "-", "b"}],"c",FractionBox["1", RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{397, 42}, + ImageSize->{412, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[12]=", - CellID->171828604] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -654,12 +674,11 @@ Cell[BoxData[ FractionBox["1", RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{536, 42}, + ImageSize->{561, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[13]=", - CellID->1340266483] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -699,12 +718,11 @@ Cell[BoxData[ TemplateBox[{"b",RowBox[{"c", "-", "a"}],"c",FractionBox["1", RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{397, 43}, + ImageSize->{414, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[14]=", - CellID->1878402139] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ @@ -753,12 +771,11 @@ Cell[BoxData[ RowBox[{"a", "-", "b", "+", "1"}],FractionBox["1", RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{406, 93}, + ImageSize->{424, 78}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[15]=", - CellID->1646537872] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ @@ -800,12 +817,11 @@ Cell[BoxData[ RowBox[{"c", "-", "a"}],RowBox[{"c", "-", "b"}],"c",FractionBox[ "1", "z"]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{444, 43}, + ImageSize->{468, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[16]=", - CellID->976219709] + CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ @@ -852,12 +868,11 @@ Cell[BoxData[ TemplateBox[{RowBox[{"1", "-", "a"}],RowBox[{"c", "-", "a"}],RowBox[{ RowBox[{"-", "a"}], "+", "b", "+", "1"}],FractionBox["1", "z"]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{390, 93}, + ImageSize->{412, 78}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[17]=", - CellID->922572585] + CellLabel->"Out[17]="] }, Open ]], Cell[CellGroupData[{ @@ -896,12 +911,11 @@ Cell[BoxData[ TemplateBox[{"b",RowBox[{"c", "-", "a"}],"c",FractionBox["1", RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{381, 43}, + ImageSize->{397, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[18]=", - CellID->1393980026] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -950,12 +964,11 @@ Cell[BoxData[ RowBox[{"-", "a"}], "+", "b", "+", "1"}],FractionBox["1", RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{432, 93}, + ImageSize->{454, 78}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[19]=", - CellID->1288498782] + CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ @@ -994,12 +1007,11 @@ Cell[BoxData[ TemplateBox[{"a",RowBox[{"c", "-", "b"}],"c",FractionBox["1", RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{381, 43}, + ImageSize->{395, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[20]=", - CellID->2121590638] + CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ @@ -1045,12 +1057,11 @@ Cell[BoxData[ RowBox[{"-", "a"}], "+", "b", "+", "1"}],FractionBox["1", RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{540, 43}, + ImageSize->{572, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[21]=", - CellID->1992183596] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ @@ -1090,12 +1101,11 @@ Cell[BoxData[ RowBox[{"1", "-", "a"}],RowBox[{"1", "-", "b"}],RowBox[{"2", "-", "c"}], "z"}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{491, 19}, + ImageSize->{517, 20}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[22]=", - CellID->652936361] + CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ @@ -1125,12 +1135,11 @@ Cell[BoxData[ RowBox[{"-", "a"}], "-", "b", "+", "c"}]], " ", TemplateBox[{RowBox[{"c", "-", "a"}],RowBox[{"c", "-", "b"}],"c","z"}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{357, 19}, + ImageSize->{375, 20}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[23]=", - CellID->1706021647] + CellLabel->"Out[23]="] }, Open ]], Cell[CellGroupData[{ @@ -1171,12 +1180,11 @@ Cell[BoxData[ RowBox[{"2", "-", "c"}],FractionBox["z", RowBox[{"z", "-", "1"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{542, 39}, + ImageSize->{568, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[24]=", - CellID->378032271] + CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ @@ -1206,12 +1214,11 @@ Cell[BoxData[ TemplateBox[{"a",RowBox[{"c", "-", "b"}],"c",FractionBox["z", RowBox[{"z", "-", "1"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{332, 39}, + ImageSize->{343, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[25]=", - CellID->2057626251] + CellLabel->"Out[25]="] }, Open ]], Cell[CellGroupData[{ @@ -1252,12 +1259,11 @@ Cell[BoxData[ RowBox[{"2", "-", "c"}],FractionBox["z", RowBox[{"z", "-", "1"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{542, 39}, + ImageSize->{569, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[26]=", - CellID->129109138] + CellLabel->"Out[26]="] }, Open ]], Cell[CellGroupData[{ @@ -1287,12 +1293,11 @@ Cell[BoxData[ TemplateBox[{"b",RowBox[{"c", "-", "a"}],"c",FractionBox["z", RowBox[{"z", "-", "1"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{332, 39}, + ImageSize->{344, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[27]=", - CellID->149180370] + CellLabel->"Out[27]="] }, Open ]], Cell[CellGroupData[{ @@ -1332,12 +1337,11 @@ Cell[BoxData[ RowBox[{"-", "a"}], "-", "b", "+", "c", "+", "1"}], RowBox[{"1", "-", "z"}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{546, 18}, + ImageSize->{579, 20}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[28]=", - CellID->1291617006] + CellLabel->"Out[28]="] }, Open ]], Cell[CellGroupData[{ @@ -1369,12 +1373,11 @@ Cell[BoxData[ RowBox[{"c", "-", "a"}],RowBox[{"c", "-", "b"}],"c", RowBox[{"1", "-", "z"}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{367, 19}, + ImageSize->{386, 20}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[29]=", - CellID->467825582] + CellLabel->"Out[29]="] }, Open ]], Cell[CellGroupData[{ @@ -1417,12 +1420,11 @@ Cell[BoxData[ FractionBox["1", RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{359, 63}, + ImageSize->{377, 57}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[30]=", - CellID->1418885380] + CellLabel->"Out[30]="] }, Open ]], Cell[CellGroupData[{ @@ -1455,12 +1457,11 @@ Cell[BoxData[ FractionBox["1", RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{376, 43}, + ImageSize->{389, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[31]=", - CellID->1820473911] + CellLabel->"Out[31]="] }, Open ]], Cell[CellGroupData[{ @@ -1501,12 +1502,11 @@ Cell[BoxData[ FractionBox[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{565, 43}, + ImageSize->{335, 57}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[32]=", - CellID->1271802490] + CellLabel->"Out[32]="] }, Open ]], Cell[CellGroupData[{ @@ -1537,12 +1537,11 @@ Cell[BoxData[ FractionBox[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", - ImageSize->{330, 43}, + ImageSize->{343, 36}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[33]=", - CellID->1670296832] + CellLabel->"Out[33]="] }, Open ]], Cell[CellGroupData[{ @@ -1601,12 +1600,11 @@ Cell[BoxData[ "Gamma"], " ", TemplateBox[{RowBox[{"c", "-", "b"}]}, "Gamma"]}]]}]}], TraditionalForm]], "Output", - ImageSize->{482, 125}, + ImageSize->{520, 112}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Kummer", - CellLabel->"Out[34]=", - CellID->1552242027] + CellLabel->"Out[34]="] }, Open ]], Cell[CellGroupData[{ @@ -1668,12 +1666,11 @@ Cell[BoxData[ "Gamma"], " ", TemplateBox[{RowBox[{"c", "-", "b"}]}, "Gamma"]}]]}]}], TraditionalForm]], "Output", - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 55.649152}", + "built" -> "{2020, 1, 5, 18, 59, 23.123162}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -1801,11 +1795,11 @@ TaggingRules->{ "Kummer[i][exp] applies Kummer relation number i (i =1, ... 24, 94,95,96) \ to all Hypergeometric2F1 in exp. i = 94 corresponds to eq. 9.131.2, i = 95 to \ eq. 9.132.1 and i = 96 to eq. 9.132.2 in Gradsteyn & Ryzhik.", - "synonyms" -> {}, "title" -> "Kummer", "titlemodifier" -> "", - "windowtitle" -> "Kummer", "type" -> "Symbol", "uri" -> + "synonyms" -> {}, "tabletags" -> {}, "title" -> "Kummer", "titlemodifier" -> + "", "windowtitle" -> "Kummer", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Kummer"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -1814,7 +1808,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - 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CellID->1224892054], +Cell[TextData[{ + Cell["LC", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ RowBox[{"LC", "[", RowBox[{"m", ",", "n", ",", "r", ",", "s"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "evaluates to 4-dimensional LeviCivita[m,n,r,s] by virtue of applying \ -FeynCalcInternal. LC[m,...][p, ...] evaluates to 4-dimensional \ -LeviCivita[m,...][p,...] applying FeynCalcInternal." + " \[LineSeparator]evaluates to 4-dimensional ", + Cell[BoxData[ + SuperscriptBox["\[Epsilon]", + RowBox[{"m", " ", "n", " ", "r", " ", "s"}]]], "InlineFormula"], + " by virtue of applying FeynCalcInternal. LC[m,...][p, ...] evaluates to \ +4-dimensional ", + Cell[BoxData[ + RowBox[{ + SuperscriptBox["\[Epsilon]", + RowBox[{ + RowBox[{ + RowBox[{"m", " ", ".."}], " ", "\[Mu]"}], " ", ".."}]], + SubscriptBox["p", + RowBox[{"\[Mu]", " ", ".."}]]}]], "InlineFormula"], + " applying FeynCalcInternal." }]]} }]], "Usage", GridBoxOptions->{ @@ -110,7 +154,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->151617198], + CellID->2053325263], Cell[CellGroupData[{ @@ -120,7 +164,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1072283782], + CellID->427460382], Cell[CellGroupData[{ @@ -134,7 +178,8 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -152,12 +197,11 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{54, 18}, + ImageSize->{53, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LC", - CellLabel->"Out[1]=", - CellID->1184653612] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -170,7 +214,8 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -188,12 +233,11 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{54, 18}, + ImageSize->{53, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LC", - CellLabel->"Out[2]=", - CellID->513333789] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -211,12 +255,11 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}]}], "]"}]], "Output", - ImageSize->{575, 15}, + ImageSize->{306, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LC", - CellLabel->"Out[3]//StandardForm=", - CellID->979116929] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -232,7 +275,8 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -252,12 +296,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{54, 21}, + ImageSize->{61, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LC", - CellLabel->"Out[4]=", - CellID->1590586499] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -276,12 +319,11 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}], ",", RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]], "Output", - ImageSize->{513, 15}, + ImageSize->{516, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LC", - CellLabel->"Out[5]//StandardForm=", - CellID->1014807484] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -320,12 +362,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{68, 18}, + ImageSize->{78, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LC", - CellLabel->"Out[6]=", - CellID->218829035] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -349,10 +390,10 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["LeviCivita", + StyleBox[ButtonBox["Eps", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/LeviCivita", - ButtonNote->"LeviCivita"], + ButtonData->"paclet:FeynCalc/ref/Eps", + ButtonNote->"Eps"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["LCD", @@ -361,9 +402,7 @@ Cell[TextData[{ ButtonNote->"LCD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"LC", - CellID->283409041] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -380,22 +419,23 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 0.751151}", + "built" -> "{2020, 1, 5, 18, 59, 26.975298}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "LC[m, n, r, s] evaluates to 4-dimensional LeviCivita[m,n,r,s] by virtue \ + "LC[m, n, r, s] evaluates to 4-dimensional \\[Epsilon] m n r s by virtue \ of applying FeynCalcInternal. LC[m,...][p, ...] evaluates to 4-dimensional \ -LeviCivita[m,...][p,...] applying FeynCalcInternal.", "synonyms" -> {}, - "title" -> "LC", "titlemodifier" -> "", "windowtitle" -> "LC", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/LC"}, "SearchTextTranslated" -> ""}, +\\[Epsilon] m .. \\[Mu] .. p \\[Mu] .. applying FeynCalcInternal.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "LC", "titlemodifier" -> + "", "windowtitle" -> "LC", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/LC"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -403,8 +443,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -413,131 +454,113 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["LCD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ RowBox[{"LCD", "[", RowBox[{"m", ",", "n", ",", "r", ",", "s"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "evaluates to D-dimensional LeviCivita[m,n,r,s] by virtue of \ -FeynCalcInternal. LCD[m,...][p, ...] evaluates to D-dimensional \ -LeviCivita[m,...][p,...] applying FeynCalcInternal.\n\nYou need to do \ -SetOptions[Eps, Dimension\[Rule]D] before LCD can be used as D-dimensional \ -Levi-Civita input function." + " \[LineSeparator]evaluates to D-dimensional ", + Cell[BoxData[ + SuperscriptBox["\[Epsilon]", + RowBox[{"m", " ", "n", " ", "r", " ", "s"}]]], "InlineFormula"], + " by virtue of FeynCalcInternal. LCD[m,...][p, ...] evaluates to \ +D-dimensional ", + Cell[BoxData[ + RowBox[{ + SuperscriptBox["\[Epsilon]", + RowBox[{ + RowBox[{ + RowBox[{"m", " ", ".."}], " ", "\[Mu]"}], " ", ".."}]], + SubscriptBox["p", + RowBox[{"\[Mu]", " ", ".."}]]}]], "InlineFormula"], + " applying FeynCalcInternal." }]]} }]], "Usage", GridBoxOptions->{ @@ -112,7 +154,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1729963782], + CellID->288407350], Cell[CellGroupData[{ @@ -122,16 +164,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1361724083], - -Cell[BoxData[ - RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], ";"}]], "Input", - CellTags->"LCD", - CellLabel->"In[1]:=", - CellID->246917287], + CellID->1781901275], Cell[CellGroupData[{ @@ -140,12 +173,13 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}]], "Input", CellTags->"LCD", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->163498575], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -163,58 +197,22 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{54, 18}, + ImageSize->{52, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LCD", - CellLabel->"Out[2]=", - CellID->1669873163] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"%", "//", "FCI"}]], "Input", + RowBox[{ + RowBox[{"%", "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"LCD", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->950730684], -Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Epsilon]", - RowBox[{ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{54, 18}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"LCD", - CellLabel->"Out[3]=", - CellID->774559606] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"%", "//", "StandardForm"}]], "Input", - CellTags->"LCD", - CellLabel->"In[4]:=", - CellID->1738716456], - Cell[BoxData[ RowBox[{"Eps", "[", RowBox[{ @@ -225,14 +223,12 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", RowBox[{"LorentzIndex", "[", - RowBox[{"\[Sigma]", ",", "D"}], "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]], "Output", - ImageSize->{444, 33}, + RowBox[{"\[Sigma]", ",", "D"}], "]"}]}], "]"}]], "Output", + ImageSize->{352, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LCD", - CellLabel->"Out[4]//StandardForm=", - CellID->1281931789] + CellLabel->"Out[2]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -243,12 +239,13 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "[", RowBox[{"p", ",", "q"}], "]"}]], "Input", CellTags->"LCD", - CellLabel->"In[5]:=", + CellLabel->"In[3]:=", CellID->1568724284], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -266,12 +263,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{52, 17}, + ImageSize->{56, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LCD", - CellLabel->"Out[5]=", - CellID->474988897] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -280,7 +276,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"%", "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"LCD", - CellLabel->"In[6]:=", + CellLabel->"In[4]:=", CellID->531209658], Cell[BoxData[ @@ -293,14 +289,12 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "D"}], "]"}], ",", RowBox[{"Momentum", "[", - RowBox[{"q", ",", "D"}], "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]], "Output", - ImageSize->{382, 33}, + RowBox[{"q", ",", "D"}], "]"}]}], "]"}]], "Output", + ImageSize->{608, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LCD", - CellLabel->"Out[6]//StandardForm=", - CellID->1647742492] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -318,7 +312,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], "[", "q", "]"}]}], "]"}], "]"}]], "Input", CellTags->"LCD", - CellLabel->"In[7]:=", + CellLabel->"In[5]:=", CellID->173575058], Cell[BoxData[ @@ -342,34 +336,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{194, 17}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"LCD", - CellLabel->"Out[7]=", - CellID->932361259] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "4"}]}], "]"}]], "Input", - CellTags->"LCD", - CellLabel->"In[8]:=", - CellID->1229900885], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Dimension", "\[Rule]", "4"}], "}"}], TraditionalForm]], "Output", - ImageSize->{116, 15}, + ImageSize->{213, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LCD", - CellLabel->"Out[8]=", - CellID->1904977628] + CellLabel->"Out[5]="] }, Open ]] }, Open ]], @@ -393,10 +364,10 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["LeviCivita", + StyleBox[ButtonBox["Eps", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/LeviCivita", - ButtonNote->"LeviCivita"], + ButtonData->"paclet:FeynCalc/ref/Eps", + ButtonNote->"Eps"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["LC", @@ -405,17 +376,15 @@ Cell[TextData[{ ButtonNote->"LC"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"LCD", - CellID->552899823] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"LCD", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -424,24 +393,23 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 21, 59.254051}", + "built" -> "{2020, 1, 5, 18, 59, 25.757254}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "LCD[m, n, r, s] evaluates to D-dimensional LeviCivita[m,n,r,s] by virtue \ + "LCD[m, n, r, s] evaluates to D-dimensional \\[Epsilon] m n r s by virtue \ of FeynCalcInternal. LCD[m,...][p, ...] evaluates to D-dimensional \ -LeviCivita[m,...][p,...] applying FeynCalcInternal. You need to do \ -SetOptions[Eps, Dimension->D] before LCD can be used as D-dimensional \ -Levi-Civita input function.", "synonyms" -> {}, "title" -> "LCD", - "titlemodifier" -> "", "windowtitle" -> "LCD", "type" -> "Symbol", "uri" -> +\\[Epsilon] m .. \\[Mu] .. p \\[Mu] .. applying FeynCalcInternal.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "LCD", "titlemodifier" -> + "", "windowtitle" -> "LCD", "type" -> "Symbol", "uri" -> "FeynCalc/ref/LCD"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -449,8 +417,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -459,151 +428,101 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["LeftPartialD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -116,7 +154,9 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->635621775], + CellID->797566762], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -124,13 +164,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1554178979], - -Cell[CellGroupData[{ - -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"LeftPartialD", - CellID->112576831], + CellID->1164783384], Cell[CellGroupData[{ @@ -158,12 +192,11 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{45, 27}, + ImageSize->{47, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftPartialD", - CellLabel->"Out[1]=", - CellID->830365091] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -177,24 +210,24 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Mu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], TraditionalForm]], "Output", - ImageSize->{39, 19}, + TraditionalForm]], ")"}], TraditionalForm]], "Output", + ImageSize->{57, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftPartialD", - CellLabel->"Out[2]=", - CellID->1758698798] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -211,12 +244,11 @@ Cell[BoxData[ RowBox[{"FCPartialD", "[", RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], "]"}], ",", "A", ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]], "Output", - ImageSize->{497, 15}, + ImageSize->{500, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftPartialD", - CellLabel->"Out[3]//StandardForm=", - CellID->1222822570] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -231,12 +263,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"LeftPartialD", "[", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}]], "Output", - ImageSize->{239, 15}, + ImageSize->{242, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftPartialD", - CellLabel->"Out[4]//StandardForm=", - CellID->2010768027] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -273,12 +304,11 @@ Cell[BoxData[ FormBox["\[Rho]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{67, 27}, + ImageSize->{72, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftPartialD", - CellLabel->"Out[5]=", - CellID->1721340260] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -298,44 +328,47 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}]}], "+", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}], "+", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}], ".", SubscriptBox[ FormBox["A", TraditionalForm], FormBox["\[Nu]", TraditionalForm]]}]}], TraditionalForm]], "Output", - ImageSize->{133, 19}, + ImageSize->{200, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftPartialD", - CellLabel->"Out[6]=", - CellID->1229859500] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -366,16 +399,15 @@ Cell[BoxData[ RowBox[{"QuantumField", "[", RowBox[{"A", ",", RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}]}], "]"}]}]}]], "Output", - ImageSize->{525, 67}, + ImageSize->{528, 67}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftPartialD", - CellLabel->"Out[7]//StandardForm=", - CellID->296675662] + CellLabel->"Out[7]//StandardForm="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] -}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -419,9 +451,7 @@ Cell[TextData[{ ButtonNote->"RightPartialD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"LeftPartialD", - CellID->333878293] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -429,7 +459,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"LeftPartialD", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -438,10 +468,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 2.268600}", + "built" -> "{2020, 1, 5, 18, 59, 28.174638}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -449,11 +479,12 @@ TaggingRules->{ "None", "summary" -> "LeftPartialD[\\[Mu]] denotes OverscriptBox[\\[PartialD], \\ \ \\[LeftArrow]]TraditionalForm\\`TraditionalForm\\`\\[Mu]acting to the left.", - "synonyms" -> {}, "title" -> "LeftPartialD", "titlemodifier" -> "", - "windowtitle" -> "LeftPartialD", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/LeftPartialD"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "LeftPartialD", + "titlemodifier" -> "", "windowtitle" -> "LeftPartialD", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/LeftPartialD"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -461,8 +492,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -471,151 +503,125 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3547, 103, 387, 15, 31, "PrimaryExamplesSection", + Cell[4865, 141, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->635621775]}, + CellID->797566762]}, "LeftPartialD"->{ - Cell[4158, 130, 89, 2, 35, "Subsubsection", - CellTags->"LeftPartialD", - CellID->112576831], - Cell[4272, 136, 271, 8, 27, "Input", + Cell[5498, 170, 271, 8, 27, "Input", CellTags->"LeftPartialD", CellID->1505949422], - Cell[4546, 146, 482, 19, 48, "Output", - CellTags->"LeftPartialD", - 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CellID->1224892054], +Cell[TextData[{ + Cell["LeftRightPartialD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -125,7 +167,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1628042135], + CellID->679018927], Cell[CellGroupData[{ @@ -135,7 +177,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1062363671], + CellID->1737714940], Cell[CellGroupData[{ @@ -153,12 +195,11 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{25, 27}, + ImageSize->{24, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD", - CellLabel->"Out[1]=", - CellID->1132769852] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -187,12 +228,11 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{85, 41}, + ImageSize->{83, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD", - CellLabel->"Out[2]=", - CellID->215900493] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -221,12 +261,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Nu]", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{47, 27}, + ImageSize->{49, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD", - CellLabel->"Out[3]=", - CellID->1398421327] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -244,18 +283,19 @@ Cell[BoxData[ RowBox[{"(", RowBox[{ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Nu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ SubscriptBox[ OverscriptBox["\[PartialD]", "\[LeftArrow]"], @@ -268,12 +308,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Nu]", TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{126, 41}, + ImageSize->{146, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD", - CellLabel->"Out[4]=", - CellID->1245680526] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -310,12 +349,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Rho]", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{69, 27}, + ImageSize->{74, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD", - CellLabel->"Out[5]=", - CellID->488945383] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -338,44 +376,47 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], "\[Null]"]}]}], "-", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}], "-", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}], ".", SubscriptBox[ FormBox["A", TraditionalForm], FormBox["\[Rho]", TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{162, 41}, + ImageSize->{228, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD", - CellLabel->"Out[6]=", - CellID->1968825715] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -399,7 +440,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["ExplicitPartialD", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/ExplicitPartialD", @@ -436,9 +476,7 @@ Cell[TextData[{ ButtonNote->"RightPartialD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"LeftRightPartialD", - CellID->2130291841] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -455,10 +493,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 5.391576}", + "built" -> "{2020, 1, 5, 18, 59, 30.726278}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -467,12 +505,12 @@ TaggingRules->{ "LeftRightPartialD[mu] denotes OverscriptBox[\\[PartialD], \\ \ \\[LeftRightArrow]]TraditionalForm\\`TraditionalForm\\`\\[Mu]\\ , acting to \ the left and right. ExplicitPartialD[LeftRightPartialD[\\[Mu]]] gives 1/2 \ -(RightPartialD[\\[Mu]] - LeftPartialD[\\[Mu]]).", "synonyms" -> {}, "title" -> - "LeftRightPartialD", "titlemodifier" -> "", "windowtitle" -> - "LeftRightPartialD", "type" -> "Symbol", "uri" -> +(RightPartialD[\\[Mu]] - LeftPartialD[\\[Mu]]).", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "LeftRightPartialD", "titlemodifier" -> "", + "windowtitle" -> "LeftRightPartialD", "type" -> "Symbol", "uri" -> "FeynCalc/ref/LeftRightPartialD"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -481,7 +519,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -490,131 +528,113 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellLabel->"Out[1]=", - CellID->1370534562] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -184,12 +223,11 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{55, 27}, + ImageSize->{54, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD2", - CellLabel->"Out[2]=", - CellID->1797023804] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -220,12 +258,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Nu]", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{47, 27}, + ImageSize->{49, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD2", - CellLabel->"Out[3]=", - CellID->334849476] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -240,18 +277,19 @@ Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Nu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], "+", + TraditionalForm]], ")"}], "+", RowBox[{ SubscriptBox[ OverscriptBox["\[PartialD]", "\[LeftArrow]"], @@ -264,12 +302,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Nu]", TraditionalForm]]}]}], TraditionalForm]], "Output", - ImageSize->{96, 27}, + ImageSize->{117, 25}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD2", - CellLabel->"Out[4]=", - CellID->412944908] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -308,12 +345,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Rho]", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{69, 27}, + ImageSize->{74, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD2", - CellLabel->"Out[5]=", - CellID->637341112] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -333,44 +369,47 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], "\[Null]"]}]}], "+", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}], "+", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}], ".", SubscriptBox[ FormBox["A", TraditionalForm], FormBox["\[Rho]", TraditionalForm]]}]}], TraditionalForm]], "Output", - ImageSize->{133, 19}, + ImageSize->{200, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeftRightPartialD2", - CellLabel->"Out[6]=", - CellID->545682027] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -424,17 +463,15 @@ Cell[TextData[{ ButtonNote->"RightPartialD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"LeftRightPartialD2", - CellID->1097237675] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"LeftRightPartialD2", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -443,10 +480,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 3.777881}", + "built" -> "{2020, 1, 5, 18, 59, 29.444730}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -455,12 +492,12 @@ TaggingRules->{ "LeftRightPartialD2[mu] denotes OverscriptBox[\\[PartialD], \\ \ \\[LeftRightArrow]]TraditionalForm\\`TraditionalForm\\`\\[Mu]\\ , acting to \ the left and right. 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CellTags->"LeftRightPartialD2", - CellID->1097237675] +Cell[11791, 434, 898, 31, 56, "SeeAlso"] }, Open ]], -Cell[11349, 431, 23, 0, 42, "FooterCell"] +Cell[12704, 468, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/LeviCivita.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/LeviCivita.nb index aa43cd11b..beb31b7d4 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/LeviCivita.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/LeviCivita.nb @@ -3,69 +3,92 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 22699, 839] -NotebookOptionsPosition[ 15166, 594] -NotebookOutlinePosition[ 19846, 729] -CellTagsIndexPosition[ 19732, 723] +NotebookDataLength[ 23521, 882] +NotebookOptionsPosition[ 17307, 689] +NotebookOutlinePosition[ 20806, 783] +CellTagsIndexPosition[ 20692, 777] WindowTitle->LeviCivita WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - 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False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$99308], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/LeviCivita", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"LC\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FV"], "\<\"FCI\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FCI"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/LeviCivita\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/LeviCivita"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ +LeviCivita.html"], StandardForm]], "Input", TextClipboardType -> + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$179892], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/LeviCivita", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +96,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["LeviCivita", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["LeviCivita", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -116,6 +151,62 @@ Dimension of LeviCivita is changed). LeviCivita[", Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1571136183], + +Cell["", "SectionHeaderSpacer"], + +Cell["\<\ +The shortcut LeviCivita is deprecated, please use LC instead!\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "LeviCivita", "]"}]], "Input", + CellLabel->"In[356]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + ImageSize->{257, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[356]="] +}, Open ]] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -131,7 +222,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->646864681], + CellID->672121972], Cell[CellGroupData[{ @@ -141,30 +232,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->440823594], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "LeviCivita", "]"}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[1]:=", - CellID->2141079579], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - ImageSize->{284, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"LeviCivita", - CellLabel->"Out[1]=", - CellID->1665927785] -}, Open ]], + CellID->596443126], Cell[CellGroupData[{ @@ -173,12 +241,13 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], "]"}]], "Input", CellTags->"LeviCivita", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->970809287], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Alpha]", @@ -196,104 +265,131 @@ Cell[BoxData[ FormBox["\[Delta]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{55, 19}, + ImageSize->{53, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeviCivita", - CellLabel->"Out[2]=", - CellID->1096309803] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "[", - RowBox[{"OPEDelta", ",", "p"}], "]"}]], "Input", + RowBox[{"LeviCivita", "[", "]"}], "[", + RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}]], "Input", CellTags->"LeviCivita", - CellLabel->"In[3]:=", - CellID->972968542], + CellLabel->"In[2]:=", + CellID->1735126440], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox["\[Nu]", - TraditionalForm], + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], + OverscriptBox[ + FormBox["r", + TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox["p", - TraditionalForm], + OverscriptBox[ + FormBox["s", + TraditionalForm], "_"], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{53, 19}, + ImageSize->{65, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeviCivita", - CellLabel->"Out[3]=", - CellID->657040186] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"LeviCivita", "[", "]"}], "[", - RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[4]:=", - CellID->1735126440], + RowBox[{"LeviCivita", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "[", + RowBox[{"p", ",", "q"}], "]"}]], "Input", + CellLabel->"In[3]:="], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ - FormBox["p", + FormBox["\[Alpha]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["q", + FormBox["\[Beta]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["r", - TraditionalForm], + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox["s", - TraditionalForm], + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{51, 15}, + ImageSize->{63, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"LeviCivita", - CellLabel->"Out[4]=", - CellID->986206459] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Beta]", ",", "\[Delta]"}], + RowBox[{"StandardForm", "[", "%", "]"}]], "Input", + CellLabel->"In[4]:="], + +Cell[BoxData[ + RowBox[{"Eps", "[", + RowBox[{ + RowBox[{"LorentzIndex", "[", "\[Alpha]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Beta]", "]"}], ",", + RowBox[{"Momentum", "[", "p", "]"}], ",", + RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]], "Output", + ImageSize->{516, 15}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[4]//StandardForm="] +}, Open ]], + +Cell["\<\ +LeviCivita is scheduled for removal in the future versions of FeynCalc. The \ +safe alternative is to use LC.\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"LC", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], "]"}]], "Input", CellTags->"LeviCivita", CellLabel->"In[5]:=", - CellID->1409243674], + CellID->2075117917], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Alpha]", @@ -304,211 +400,189 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["\[Beta]", + FormBox["\[Gamma]", TraditionalForm], TraditionalForm], FormBox[ FormBox["\[Delta]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{57, 19}, + ImageSize->{53, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"LeviCivita", - CellLabel->"Out[5]=", - CellID->1898302846] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{ - RowBox[{"LeviCivita", "[", - 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Cell["FeynCalc/ref/Li3"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/Li3.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$180773], + "http://reference.wolfram.com/system-modeler/", + 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ImageSize->{70, 15}, + ImageSize->{71, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MT", - CellLabel->"Out[3]//StandardForm=", - CellID->2108634469] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -216,12 +244,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"LorentzIndex", "[", "a", "]"}], ",", RowBox[{"LorentzIndex", "[", "b", "]"}]}], "]"}]], "Output", - ImageSize->{312, 15}, + ImageSize->{315, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MT", - CellLabel->"Out[4]//StandardForm=", - CellID->1337434264] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -240,12 +267,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"MT", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", - ImageSize->{70, 15}, + ImageSize->{71, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MT", - CellLabel->"Out[5]//StandardForm=", - CellID->62630223] + CellLabel->"Out[5]//StandardForm="] }, Open ]] }, Open ]], @@ -287,12 +313,6 @@ Cell[TextData[{ ButtonNote->"FCI"], FontFamily->"Verdana"], ", ", - 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CellID->1224892054], +Cell[TextData[{ + Cell["MTD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,7 +145,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->61949600], + CellID->1942422787], Cell[CellGroupData[{ @@ -118,7 +155,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1930410875], + CellID->1624809085], Cell[CellGroupData[{ @@ -131,28 +168,21 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], TraditionalForm]], "Output", - ImageSize->{36, 19}, + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", + ImageSize->{37, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[1]=", - CellID->1640321247] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -170,12 +200,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["D", TraditionalForm]], "Output", - ImageSize->{16, 15}, + ImageSize->{19, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[2]=", - CellID->366701652] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -192,12 +221,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"MTD", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Output", - ImageSize->{78, 15}, + ImageSize->{79, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[3]//StandardForm=", - CellID->842419980] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -219,12 +247,11 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "D"}], "]"}], ",", RowBox[{"LorentzIndex", "[", RowBox[{"\[Beta]", ",", "D"}], "]"}]}], "]"}]], "Output", - ImageSize->{359, 15}, + ImageSize->{361, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[4]//StandardForm=", - CellID->255141216] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -243,12 +270,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"MTD", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Output", - ImageSize->{77, 15}, + ImageSize->{79, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[5]//StandardForm=", - CellID->141115701] + CellLabel->"Out[5]//StandardForm="] }, Open ]] }, Open ]], @@ -271,44 +297,38 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[RawData["\<\ Cell[TextData[{ - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 30.820672}", + "built" -> "{2020, 1, 5, 18, 59, 48.745138}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "MTD[mu, nu] is the metric tensor in D dimensions.", - "synonyms" -> {}, "title" -> "MTD", "titlemodifier" -> "", "windowtitle" -> - "MTD", "type" -> "Symbol", "uri" -> "FeynCalc/ref/MTD"}, - "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "MTD", "titlemodifier" -> + "", "windowtitle" -> "MTD", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/MTD"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -346,8 +366,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - 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CellID->1224892054], +Cell[TextData[{ + Cell["MTE", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,7 +145,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1554798484], + CellID->1903374112], Cell[CellGroupData[{ @@ -118,7 +155,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1048770762], + CellID->1366075322], Cell[CellGroupData[{ @@ -131,29 +168,22 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "^"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - 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ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellLabel->"Out[3]=", - CellID->40801765] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -216,11 +244,10 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{"D", "-", "4"}], TraditionalForm]], "Output", - ImageSize->{40, 15}, + ImageSize->{44, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellLabel->"Out[4]=", - CellID->509955041] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -237,12 +264,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"MTE", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Output", - ImageSize->{78, 15}, + ImageSize->{79, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[5]//StandardForm=", - CellID->1333611151] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -256,29 +282,22 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "^"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], TraditionalForm]], "Output", - ImageSize->{36, 20}, + SuperscriptBox[ + OverscriptBox["g", "^"], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", + ImageSize->{37, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[6]=", - CellID->869554807] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -304,12 +323,11 @@ Cell[BoxData[ RowBox[{"\[Beta]", ",", RowBox[{ RowBox[{"-", "4"}], "+", "D"}]}], "]"}]}], "]"}]], "Output", - ImageSize->{421, 15}, + ImageSize->{425, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[7]//StandardForm=", - CellID->369801037] + CellLabel->"Out[7]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -328,12 +346,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"MTE", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Output", - ImageSize->{77, 15}, + ImageSize->{79, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[8]//StandardForm=", - CellID->1143698797] + CellLabel->"Out[8]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -347,29 +364,22 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "^"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], TraditionalForm]], "Output", - ImageSize->{33, 19}, + SuperscriptBox[ + OverscriptBox["g", "^"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", + ImageSize->{35, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MTD", - CellLabel->"Out[9]=", - CellID->1588832862] + CellLabel->"Out[9]="] }, Open ]] }, Open ]], @@ -411,12 +421,6 @@ Cell[TextData[{ ButtonNote->"FCI"], FontFamily->"Verdana"], ", ", - StyleBox[ButtonBox["MetricTensor", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/MetricTensor", - ButtonNote->"MetricTensor"], - FontFamily->"Verdana"], - ", ", StyleBox[ButtonBox["MT", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/MT", @@ -429,9 +433,7 @@ Cell[TextData[{ ButtonNote->"MTD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"MTD", - CellID->310039993] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -448,20 +450,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 32.366168}", + "built" -> "{2020, 1, 5, 18, 59, 49.855256}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "MTE[mu, nu] is the metric tensor in D-4 dimensions.", "synonyms" -> {}, - "title" -> "MTE", "titlemodifier" -> "", "windowtitle" -> "MTE", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/MTE"}, "SearchTextTranslated" -> ""}, + "tabletags" -> {}, "title" -> "MTE", "titlemodifier" -> "", "windowtitle" -> + "MTE", "type" -> "Symbol", "uri" -> "FeynCalc/ref/MTE"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -469,8 +472,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -479,157 +483,135 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3297, 95, 388, 15, 31, "PrimaryExamplesSection", + Cell[4601, 132, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1554798484]}, + CellID->1903374112]}, "MTD"->{ - Cell[3931, 124, 154, 5, 27, "Input", + Cell[5235, 161, 154, 5, 27, "Input", CellTags->"MTD", CellID->1680977301], - Cell[4088, 131, 560, 24, 41, "Output", - CellTags->"MTD", - CellID->1958039632], - Cell[4685, 160, 284, 9, 27, "Input", + Cell[5392, 168, 412, 17, 39, "Output", + CellTags->"MTD"], + Cell[5841, 190, 284, 9, 27, "Input", CellTags->"MTD", CellID->2085004373], - 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CellID->1224892054], +Cell[TextData[{ + Cell["Mandelstam", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -146,9 +187,7 @@ Cell[TextData[{ ButtonNote->"SetMandelstam"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Mandelstam", - CellID->817062959] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -165,10 +204,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 15.798194}", + "built" -> "{2020, 1, 5, 18, 59, 39.625434}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -178,11 +217,11 @@ TaggingRules->{ TrickMandelstam. A typical setting is Mandelstam -> {s, t, u, \ m1^2+m2^2+m3^2+m4^2}, which implies s + t + u = m1^2+m2^2+m3^2+m4^2. If other \ than four-particle processes are calculated, the setting should be: \ -Mandelstam -> {}.", "synonyms" -> {}, "title" -> "Mandelstam", - "titlemodifier" -> "", "windowtitle" -> "Mandelstam", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/Mandelstam"}}, +Mandelstam -> {}.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "Mandelstam", "titlemodifier" -> "", "windowtitle" -> "Mandelstam", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/Mandelstam"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -191,41 +230,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["Map2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -109,7 +141,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1245800203], + CellID->1935818076], Cell[CellGroupData[{ @@ -119,7 +151,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->211987111], + CellID->83404821], Cell[CellGroupData[{ @@ -137,12 +169,11 @@ Cell[BoxData[ RowBox[{"f", "(", "a", ")"}], "+", RowBox[{"f", "(", RowBox[{"-", "b"}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{91, 15}, + ImageSize->{99, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Map2", - CellLabel->"Out[1]=", - CellID->979511779] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -157,12 +188,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{"f", "(", "x", ")"}], TraditionalForm]], "Output", - ImageSize->{35, 15}, + ImageSize->{38, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Map2", - CellLabel->"Out[2]=", - CellID->1491769424] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -182,12 +212,11 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], ")"}], TraditionalForm]], "Output", - ImageSize->{81, 15}, + ImageSize->{89, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Map2", - CellLabel->"Out[3]=", - CellID->1614084211] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -202,12 +231,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{"f", "(", "1", ")"}], TraditionalForm]], "Output", - ImageSize->{33, 15}, + ImageSize->{34, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Map2", - CellLabel->"Out[4]=", - CellID->1998194589] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -237,9 +265,7 @@ Cell[TextData[{ ButtonNote->"NTerms"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Map2", - CellID->435233862] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -256,21 +282,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 17.128632}", + "built" -> "{2020, 1, 5, 18, 59, 40.661048}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "Map2[f, exp] is equivalent to Map if Nterms[exp] > 0, otherwise Map2[f, \ -exp] gives f[exp].", "synonyms" -> {}, "title" -> "Map2", "titlemodifier" -> - "", "windowtitle" -> "Map2", "type" -> "Symbol", "uri" -> +exp] gives f[exp].", "synonyms" -> {}, "tabletags" -> {}, "title" -> "Map2", + "titlemodifier" -> "", "windowtitle" -> "Map2", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Map2"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -278,8 +304,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -288,103 +315,89 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["MetricTensor", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -93,6 +129,63 @@ Cell[BoxData[GridBox[{ Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->45285396], + +Cell["", "SectionHeaderSpacer"], + +Cell["\<\ +The shortcut MetricTensor is deprecated, please use MT instead!\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "MetricTensor", "]"}]], "Input", + CellLabel->"In[25]:=", + CellID->1215792887], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + ImageSize->{257, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[25]="] +}, Open ]] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -108,7 +201,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1369115102], + CellID->1410517924], Cell[CellGroupData[{ @@ -118,7 +211,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->343685928], + CellID->926168638], Cell[CellGroupData[{ @@ -135,23 +228,18 @@ Cell[BoxData[ OverscriptBox["g", "_"], RowBox[{ FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], + FormBox["\[Alpha]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{38, 19}, + ImageSize->{39, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MetricTensor", - CellLabel->"Out[1]=", - CellID->1323519245] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -159,18 +247,14 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Contract", "[", RowBox[{"%", " ", "%"}], "]"}]], "Input", - CellTags->"MetricTensor", - CellLabel->"In[2]:=", - CellID->888467606], + CellLabel->"In[2]:="], Cell[BoxData[ FormBox["4", TraditionalForm]], "Output", - ImageSize->{13, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"MetricTensor", - CellLabel->"Out[2]=", - CellID->116818789] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -178,7 +262,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MetricTensor", "[", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", - RowBox[{"Dimension", "\[Rule]", "n"}]}], "]"}]], "Input", + RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]], "Input", CellTags->"MetricTensor", CellLabel->"In[3]:=", CellID->524835668], @@ -188,23 +272,18 @@ Cell[BoxData[ SuperscriptBox["g", RowBox[{ FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], + FormBox["\[Alpha]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{36, 19}, + ImageSize->{37, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"MetricTensor", - 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The \ +safe alternative is to use MT.\ +\>", "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"MetricTensor", "[", - RowBox[{"a", ",", "b", ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "]"}]], "Input", - CellTags->"MetricTensor", - CellLabel->"In[6]:=", - CellID->1544242781], + RowBox[{"MT", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Input", + CellLabel->"In[6]:="], Cell[BoxData[ - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"a", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"b", ",", "D"}], "]"}]}], "]"}]], "Output", - ImageSize->{358, 15}, + FormBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", + ImageSize->{37, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"MetricTensor", - CellLabel->"Out[6]//StandardForm=", - CellID->2135349923] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"FCE", "[", - RowBox[{"MetricTensor", "[", - RowBox[{"a", ",", "b"}], "]"}], "]"}], "]"}]], "Input", - CellTags->"MetricTensor", - CellLabel->"In[7]:=", - CellID->912797684], + RowBox[{"MTD", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Input", + CellLabel->"In[7]:="], Cell[BoxData[ - RowBox[{"MT", "[", - RowBox[{"a", ",", "b"}], "]"}]], "Output", - ImageSize->{70, 15}, + FormBox[ + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", + ImageSize->{35, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"MetricTensor", - CellLabel->"Out[7]//StandardForm=", - CellID->489293900] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - 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"http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/NTerms", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["NTerms", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["NTerms", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,7 +119,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->39215680], + CellID->1272617833], Cell[CellGroupData[{ @@ -118,7 +129,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->376720262], + CellID->381699119], Cell[CellGroupData[{ @@ -131,12 +142,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["2", TraditionalForm]], "Output", - ImageSize->{12, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"NTerms", - CellLabel->"Out[1]=", - CellID->306409458] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -150,12 +160,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{11, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"NTerms", - CellLabel->"Out[2]=", - CellID->730102974] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -168,12 +177,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{11, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"NTerms", - CellLabel->"Out[3]=", - CellID->313925848] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -186,12 +194,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"NTerms", - CellLabel->"Out[4]=", - CellID->2111597694] + CellLabel->"Out[4]="] }, Open ]] }, Open ]] }, Open ]], @@ -200,8 +207,8 @@ Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"NTerms", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -210,21 +217,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 43.857945}", + "built" -> "{2020, 1, 5, 19, 0, 0.130174}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "NTerms[x] is equivalent to Length if x is a sum; otherwise NTerms[x] \ -returns 1, except NTerms[0] -> 0.", "synonyms" -> {}, "title" -> "NTerms", - "titlemodifier" -> "", "windowtitle" -> "NTerms", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/NTerms"}, "SearchTextTranslated" -> ""}, +returns 1, except NTerms[0] -> 0.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "NTerms", "titlemodifier" -> "", "windowtitle" -> "NTerms", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/NTerms"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -232,8 +240,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -242,92 +251,83 @@ StyleDefinitions->Notebook[{ 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Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ NegativeInteger.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$105856], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/NegativeInteger", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + 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CellID->1224892054], +Cell[TextData[{ + Cell["Nf", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -136,9 +175,7 @@ Cell[TextData[{ ButtonNote->"SplittingFunction"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Nf", - CellID->822571614] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -155,19 +192,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 36.821328}", + "built" -> "{2020, 1, 5, 18, 59, 52.983164}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "Nf denotes the number of flavors.", - "synonyms" -> {}, "title" -> "Nf", "titlemodifier" -> "", "windowtitle" -> - "Nf", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Nf"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "Nf", "titlemodifier" -> + "", "windowtitle" -> "Nf", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/Nf"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -176,41 +214,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "Nf"->{ - Cell[3492, 107, 929, 33, 70, "Text", - CellTags->"Nf", - 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CellID->1054756312], + CellID->1354488895], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -116,34 +204,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1326836899], - -Cell[CellGroupData[{ - -Cell["Examples", "Subsubsection", - CellTags->"Nielsen", - CellID->108447826], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "Nielsen", "]"}]], "Input", - CellTags->"Nielsen", - CellLabel->"In[1]:=", - CellID->393617069], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"PolyLog", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output",\ - - ImageSize->{124, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Nielsen", - CellLabel->"Out[1]=", - CellID->61376182] -}, Open ]], + CellID->913768145], Cell[CellGroupData[{ @@ -151,7 +212,7 @@ Cell[BoxData[ RowBox[{"Nielsen", "[", RowBox[{"1", ",", "2", ",", "x"}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1266057514], Cell[BoxData[ @@ -165,20 +226,17 @@ Cell[BoxData[ TraditionalForm]}]], "(", FormBox["x", TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{49, 15}, + ImageSize->{51, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Nielsen", - CellLabel->"Out[2]=", - CellID->1282400495] + CellLabel->"Out[1]="] }, Open ]], Cell["\<\ Numerical evaluation is done via N[Nielsen[n_,p_,x_]] := \ (-1)^(n+p-1)/(n-1)!/p! NIntegrate[Log[1-x t]^p Log[t]^(n-1)/t,{t,0,1}];\ -\>", "Text", - CellTags->"Nielsen", - CellID->826105795], +\>", "Notes"], Cell[CellGroupData[{ @@ -187,22 +245,19 @@ Cell[BoxData[ RowBox[{"Nielsen", "[", RowBox[{"1", ",", "2", ",", ".45"}], "]"}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1539557957], Cell[BoxData[ FormBox["0.07287162612104658`", TraditionalForm]], "Output", - ImageSize->{64, 15}, + ImageSize->{65, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Nielsen", - CellLabel->"Out[3]=", - CellID->233293253] + CellLabel->"Out[2]="] }, Open ]], -Cell["Some special values are built in.", "Text", - CellTags->"Nielsen", - CellID->76431912], +Cell["Some special values are built in.", "Notes"], Cell[CellGroupData[{ @@ -220,7 +275,7 @@ Cell[BoxData[ RowBox[{"Nielsen", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "}"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->1900952317], Cell[BoxData[ @@ -235,12 +290,11 @@ Cell[BoxData[ "Zeta"], "8"], ",", TemplateBox[{"3"}, "Zeta"]}], "}"}], TraditionalForm]], "Output", - ImageSize->{155, 42}, + ImageSize->{151, 34}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Nielsen", - CellLabel->"Out[4]=", - CellID->488179787] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -250,7 +304,7 @@ Cell[BoxData[ RowBox[{"1", ",", "2", ",", "x", ",", RowBox[{"PolyLog", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[5]:=", + CellLabel->"In[4]:=", CellID->1917228474], Cell[BoxData[ @@ -272,12 +326,11 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], ")"}]}], "+", TemplateBox[{"3"}, "Zeta"]}], TraditionalForm]], "Output", - ImageSize->{419, 41}, + ImageSize->{430, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Nielsen", - CellLabel->"Out[5]=", - CellID->552589005] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -287,7 +340,7 @@ Cell[BoxData[ RowBox[{"1", ",", "3", ",", "x", ",", RowBox[{"PolyLog", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[6]:=", + CellLabel->"In[5]:=", CellID->2065085174], Cell[BoxData[ @@ -316,12 +369,11 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], ")"}]}], "+", FractionBox[ SuperscriptBox["\[Pi]", "4"], "90"]}], TraditionalForm]], "Output", - 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CellID->1224892054], +Cell[TextData[{ + Cell["NonCommQ", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -132,9 +169,7 @@ Cell[TextData[{ ButtonNote->"SUNTrace"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"NonCommQ", - CellID->303191409] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -151,10 +186,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 41.128276}", + "built" -> "{2020, 1, 5, 18, 59, 56.297267}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -162,11 +197,11 @@ TaggingRules->{ "None", "summary" -> "NonCommQ[exp] yields True if exp contains non-commutative objects (i.e. \ those objects which are listed in $NonComm) not inside DiracTrace's or \ -SUNTrace's.", "synonyms" -> {}, "title" -> "NonCommQ", "titlemodifier" -> "", - "windowtitle" -> "NonCommQ", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/NonCommQ"}}, +SUNTrace's.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "NonCommQ", + "titlemodifier" -> "", "windowtitle" -> "NonCommQ", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/NonCommQ"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -175,41 +210,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "NonCommQ"->{ - Cell[3667, 109, 722, 27, 70, "Text", - CellTags->"NonCommQ", - 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CellID->1224892054], +Cell[TextData[{ + Cell["NonCommutative", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -119,9 +153,7 @@ Cell[TextData[{ ButtonNote->"DeclareNonCommutative"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"NonCommutative", - CellID->776574018] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -138,21 +170,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 42.499841}", + "built" -> "{2020, 1, 5, 18, 59, 57.292137}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "NonCommutative is a data type which may be used, e.g., as: DataType[x, \ -NonCommutative] = True.", "synonyms" -> {}, "title" -> "NonCommutative", - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$108618], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$191821], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/NumericQ1", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["NumericQ1", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["NumericQ1", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -110,7 +121,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1531988954], + CellID->395669097], Cell[CellGroupData[{ @@ -120,7 +131,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->146669933], + CellID->711952792], Cell[CellGroupData[{ @@ -136,12 +147,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["False", TraditionalForm]], "Output", - ImageSize->{37, 15}, + ImageSize->{34, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"NumericQ1", - CellLabel->"Out[1]=", - CellID->583048133] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -160,12 +170,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["False", TraditionalForm]], "Output", - ImageSize->{37, 15}, + ImageSize->{34, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"NumericQ1", - CellLabel->"Out[2]=", - CellID->1595713370] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -185,12 +194,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", - ImageSize->{33, 15}, + ImageSize->{31, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"NumericQ1", - CellLabel->"Out[3]=", - CellID->397430963] + CellLabel->"Out[3]="] }, Open ]] }, Open ]] }, Open ]], @@ -209,21 +217,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 47.013464}", + "built" -> "{2020, 1, 5, 19, 0, 2.361565}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "NumericQ1[x, {a, b, ..}] is like NumericQ, but assumes that {a,b,..} are \ -numeric quantities.", "synonyms" -> {}, "title" -> "NumericQ1", - 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$195338], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/OPEIntegrateDelta", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ OPEIntegrateDelta.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["OPEIntegrateDelta", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["OPEIntegrateDelta", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -82,14 +114,12 @@ Cell[BoxData[GridBox[{ RowBox[{"OPEIntegrateDelta", "[", RowBox[{"expr", ",", " ", "x", ",", " ", "m"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "introduces the \[Delta](1-x) (DeltaFunction[1-x]). The ", + " \[LineSeparator]introduces the \[Delta](1-x) (DeltaFunction[1-x]). The \ +", StyleBox["Mathematica", FontSlant->"Italic"], " Integrate function is called and each integration (from 0 to 1) is \ -recorded for reference (and bug-checking) in the list $MIntegrate. \nNotice \ -that the dimension specified by the option should also be the dimension used \ -in expr. It is replaced in OPEIntegrateDelta by (4+Epsilon)." +recorded for reference (and bug-checking) in the list $MIntegrate." }]]} }]], "Usage", GridBoxOptions->{ @@ -100,44 +130,43 @@ in expr. It is replaced in OPEIntegrateDelta by (4+Epsilon)." Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", + CellGroupingRules->{"SectionGrouping", 50}, CellID->1], -Cell[CellGroupData[{ - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->1], +Cell["", "SectionHeaderSpacer"], -Cell[BoxData[""], "Input", - CellTags->"OPEIntegrateDelta", - CellLabel->"In[1]:=", - CellID->1585063282] -}, Open ]] -}, Open ]], +Cell["\<\ +Notice that the dimension specified by the option should also be the \ +dimension used in expr. It is replaced in OPEIntegrateDelta by (4+Epsilon).\ +\>", "Notes", + CellID->1067943069] +}, Closed]], Cell[CellGroupData[{ -Cell["", "SectionFooterSpacer"], - Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -159,9 +188,7 @@ Cell[TextData[{ ButtonNote->"RHI"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"OPEIntegrateDelta", - CellID->2121617043] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -178,10 +205,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 59.392024}", + "built" -> "{2020, 1, 5, 19, 0, 11.069400}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -190,13 +217,12 @@ TaggingRules->{ "OPEIntegrateDelta[expr, x, m] introduces the \\[Delta](1-x) \ (DeltaFunction[1-x]). 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It is replaced in OPEIntegrateDelta by \ -(4+Epsilon).", "synonyms" -> {}, "title" -> "OPEIntegrateDelta", - "titlemodifier" -> "", "windowtitle" -> "OPEIntegrateDelta", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/OPEIntegrateDelta"}}, +list $MIntegrate.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "OPEIntegrateDelta", "titlemodifier" -> "", "windowtitle" -> + "OPEIntegrateDelta", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/OPEIntegrateDelta"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -205,62 +231,39 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["OPESum", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -111,7 +145,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->515601059], + CellID->1624710317], Cell[CellGroupData[{ @@ -121,24 +155,23 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1756004996], + CellID->1809286407], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{"OPESum", "[", + RowBox[{"OPESum", "[", + RowBox[{ RowBox[{ RowBox[{ - RowBox[{ - RowBox[{"SO", "[", "p", "]"}], "^", "OPEi"}], - RowBox[{ - RowBox[{"SO", "[", "k", "]"}], "^", - RowBox[{"(", - RowBox[{"OPEm", "-", "OPEi", "-", "3"}], ")"}]}]}], ",", - RowBox[{"{", - RowBox[{"OPEi", ",", "0", ",", - RowBox[{"OPEm", "-", "3"}]}], "}"}]}], "]"}]}]], "Input", + RowBox[{"SO", "[", "p", "]"}], "^", "OPEi"}], + RowBox[{ + RowBox[{"SO", "[", "k", "]"}], "^", + RowBox[{"(", + RowBox[{"OPEm", "-", "OPEi", "-", "3"}], ")"}]}]}], ",", + RowBox[{"{", + RowBox[{"OPEi", ",", "0", ",", + RowBox[{"OPEm", "-", "3"}]}], "}"}]}], "]"}]], "Input", CellTags->"OPESum", CellLabel->"In[1]:=", CellID->448625968], @@ -173,18 +206,17 @@ Cell[BoxData[ FormBox["p", TraditionalForm]}], ")"}], "i"]}]}], HoldForm], TraditionalForm]], "Output", - ImageSize->{183, 47}, + ImageSize->{197, 46}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"OPESum", - CellLabel->"Out[1]=", - CellID->1323502805] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"OPESumExplicit", "[", "t1", "]"}]], "Input", + RowBox[{"OPESumExplicit", "[", "%", "]"}]], "Input", CellTags->"OPESum", CellLabel->"In[2]:=", CellID->575960405], @@ -248,18 +280,17 @@ Cell[BoxData[ TraditionalForm], FormBox["p", TraditionalForm]}]}]]}], TraditionalForm]], "Output", - ImageSize->{180, 49}, + ImageSize->{196, 41}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"OPESum", - CellLabel->"Out[2]=", - CellID->988725801] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", " ", "=", " ", + RowBox[{" ", RowBox[{"OPESum", "[", RowBox[{ RowBox[{ @@ -305,18 +336,17 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "j"}], "+", "m", "-", "4"}]]}], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{200, 49}, + ImageSize->{221, 48}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"OPESum", - CellLabel->"Out[3]=", - CellID->1408007149] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"OPESumExplicit", "[", "t2", "]"}]], "Input", + RowBox[{"OPESumExplicit", "[", "%", "]"}]], "Input", CellTags->"OPESum", CellLabel->"In[4]:=", CellID->1712949576], @@ -386,21 +416,12 @@ Cell[BoxData[ RowBox[{"a", "-", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"b", "-", "c"}], ")"}]}]]}], TraditionalForm]], "Output", - ImageSize->{477, 105}, + ImageSize->{521, 90}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"OPESum", - CellLabel->"Out[4]=", - CellID->1163635134] -}, Open ]], - -Cell[BoxData[ - RowBox[{" ", - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2"}], "]"}]}]], "Input", - CellTags->"OPESum", - CellLabel->"In[5]:=", - CellID->790847648] + CellLabel->"Out[4]="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] @@ -435,9 +456,7 @@ Cell[TextData[{ ButtonNote->"OPESumSimplify"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"OPESum", - CellID->1162371524] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -445,7 +464,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"OPESum", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -454,21 +473,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 6.159074}", + "built" -> "{2020, 1, 5, 19, 0, 15.999798}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "OPESum[exp, {i, 0, m}] denotes a symbolic sum.The syntax is the same as \ -for Sum.", "synonyms" -> {}, "title" -> "OPESum", "titlemodifier" -> "", - "windowtitle" -> "OPESum", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/OPESum"}, "SearchTextTranslated" -> ""}, +for Sum.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "OPESum", + "titlemodifier" -> "", "windowtitle" -> "OPESum", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/OPESum"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -476,8 +495,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - 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ImageSize->{119, 45}, + ImageSize->{142, 44}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"OPESumSimplify", @@ -349,7 +433,7 @@ Cell[BoxData[ RowBox[{"i", ",", "0", ",", "m"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "i"}], "}"}]}], "]"}]], "Output", - ImageSize->{291, 20}, + ImageSize->{292, 25}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"OPESumSimplify", @@ -390,17 +474,15 @@ Cell[TextData[{ ButtonNote->"OPESumExplicit"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"OPESumSimplify", - CellID->189414120] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"OPESumSimplify", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -409,20 +491,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$111017], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$194903], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/OPEi", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["OPEi", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["OPEi", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +118,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->36494890], + CellID->463695855], Cell[CellGroupData[{ @@ -117,7 +128,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1892922609], + CellID->35029913], Cell[CellGroupData[{ @@ -128,12 +139,11 @@ Cell[BoxData["OPEi"], "Input", Cell[BoxData[ FormBox["i", TraditionalForm]], "Output", - ImageSize->{9, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"OPEi", - CellLabel->"Out[1]=", - CellID->1058262689] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -154,12 +164,11 @@ Cell[BoxData[ RowBox[{ "True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True"}], "}"}], TraditionalForm]], "Output", - ImageSize->{268, 15}, + ImageSize->{259, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"OPEi", - CellLabel->"Out[2]=", - CellID->1847732928] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -212,17 +221,14 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1"}], "}"}], TraditionalForm]], "Output", - 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OneLoop[name, q, amplitude] has as first argument a \ -name of the amplitude. If the second argument has head FeynAmp then \ -OneLoop[q, FeynAmp[name, k, expr]] and OneLoop[FeynAmp[name, k, expr]] \ -tranform to OneLoop[name, k, expr].\n\nNOTICE: While OneLoop is restricted to \ -'t Hooft Feynman gauge, the function ", - ButtonBox["OneLoopSimplify", - BaseStyle->"AddOnsLink", - ButtonData:>"OneLoopSimplify", - ButtonNote->"OneLoopSimplify"], - " does not have this restriction (but is usually slower).\n\nWARNING: If \ -you encounter anomalies: The default setting of West is True, i.e., the way ", - - Cell[BoxData[ - FormBox[ - RowBox[{" ", - RowBox[{"tr", "(", - RowBox[{ - SuperscriptBox["\[Gamma]", "\[Mu]"], - SuperscriptBox["\[Gamma]", "\[Nu]"], - SuperscriptBox["\[Gamma]", "\[Rho]"], - SuperscriptBox["\[Gamma]", "\[Sigma]"], - SuperscriptBox["\[Gamma]", "\[Tau]"], - SuperscriptBox["\[Gamma]", "\[Lambda]"], - SuperscriptBox["\[Gamma]", "5"]}], ")"}]}], TraditionalForm]]], - " is calculated in D dimensions has changed compared to the old FeynCalc \ -version. Please keep in mind that the issue of ", - Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], - "schemes is inherintly tricky." + " \[LineSeparator]calculates the one-loop Feynman diagram amplitude. The \ +argument q denotes the integration variable, i.e., the loop momentum. \ +OneLoop[name, q, amplitude] has as first argument a name of the amplitude. If \ +the second argument has head FeynAmp then OneLoop[q, FeynAmp[name, k, expr]] \ +and OneLoop[FeynAmp[name, k, expr]] tranform to OneLoop[name, k, expr]." }]]} }]], "Usage", GridBoxOptions->{ @@ -130,51 +136,56 @@ version. 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CellLabel->"Out[1]=", - CellID->353873485] + CellLabel->"Out[41]="] +}, Open ]] +}, Closed]] }, Open ]], Cell[CellGroupData[{ +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->479073918], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->757238189], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ RowBox[{ - RowBox[{ - RowBox[{"-", "I"}], "/", - RowBox[{"Pi", "^", "2"}]}], " ", - RowBox[{"FAD", "[", - RowBox[{"{", - RowBox[{"q", ",", "m"}], "}"}], "]"}]}], "//", "FCI"}]], "Input", + RowBox[{"-", "I"}], "/", + RowBox[{"Pi", "^", "2"}]}], " ", + RowBox[{"FAD", "[", + RowBox[{"{", + RowBox[{"q", ",", "m"}], "}"}], "]"}]}]], "Input", CellTags->"OneLoop", - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 48.682794}", + "built" -> "{2020, 1, 5, 19, 0, 3.482634}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "OneLoop[q, amplitude] calculates the one-loop Feynman diagram amplitude \ -(n-point, where n<=4 and the highest tensor rank of the integration momenta \ -(after cancellation of scalar products) may be up to 3; unless \ -OneLoopSimplify is used). The argument q denotes the integration variable, \ -i.e., the loop momentum. OneLoop[name, q, amplitude] has as first argument a \ -name of the amplitude. If the second argument has head FeynAmp then \ -OneLoop[q, FeynAmp[name, k, expr]] and OneLoop[FeynAmp[name, k, expr]] \ -tranform to OneLoop[name, k, expr]. NOTICE: While OneLoop is restricted to 't \ -Hooft Feynman gauge, the function OneLoopSimplify does not have this \ -restriction (but is usually slower). WARNING: If you encounter anomalies: The \ -default setting of West is True, i.e., the way tr(\\[Gamma]^\\[Mu] \\[Gamma]^\ -\\[Nu] \\[Gamma]^\\[Rho] \\[Gamma]^\\[Sigma] \\ \\[Gamma]^\\[Tau] \ -\\[Gamma]^\\[Lambda] \\[Gamma]^5) is calculated in D dimensions has changed \ -compared to the old FeynCalc version. Please keep in mind that the issue of \ -\\[Gamma]^5schemes is inherintly tricky.", "synonyms" -> {}, "title" -> - "OneLoop", "titlemodifier" -> "", "windowtitle" -> "OneLoop", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/OneLoop"}, "SearchTextTranslated" -> - ""}, + "OneLoop[q, amplitude] calculates the one-loop Feynman diagram amplitude. \ +The argument q denotes the integration variable, i.e., the loop momentum. \ +OneLoop[name, q, amplitude] has as first argument a name of the amplitude. If \ +the second argument has head FeynAmp then OneLoop[q, FeynAmp[name, k, expr]] \ +and OneLoop[FeynAmp[name, k, expr]] tranform to OneLoop[name, k, expr].", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "OneLoop", + "titlemodifier" -> "", "windowtitle" -> "OneLoop", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/OneLoop"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -978,8 +644,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -987,184 +654,104 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["OneLoopSum", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -114,9 +146,7 @@ Cell[TextData[{ ButtonNote->"OneLoop"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"OneLoopSum", - CellID->702509014] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -133,10 +163,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 22, 52.079224}", + "built" -> "{2020, 1, 5, 19, 0, 5.777966}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -144,11 +174,11 @@ TaggingRules->{ "None", "summary" -> "OneLoopSum[FeynAmp[ ... ], FeynAmp[ ... ] , ...] will calculate a list \ of Feynman amplitudes by replacing FeynAmp step by step by OneLoop.", - "synonyms" -> {}, "title" -> "OneLoopSum", "titlemodifier" -> "", - "windowtitle" -> "OneLoopSum", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/OneLoopSum"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "OneLoopSum", + "titlemodifier" -> "", "windowtitle" -> "OneLoopSum", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/OneLoopSum"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -157,41 +187,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "OneLoopSum"->{ - Cell[3656, 109, 226, 9, 70, "Text", - CellTags->"OneLoopSum", - CellID->702509014]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"OneLoopSum", 5761, 167} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[582, 21, 2253, 52, 70, "AnchorBarGrid", +Cell[582, 21, 3009, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2838, 75, 53, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2894, 78, 464, 13, 70, "Usage", +Cell[3594, 97, 287, 11, 70, "ObjectNameGrid"], +Cell[3884, 110, 464, 13, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3383, 95, 270, 12, 70, "SeeAlsoSection", +Cell[4373, 127, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3656, 109, 226, 9, 70, "Text", - CellTags->"OneLoopSum", - CellID->702509014] +Cell[4646, 141, 184, 7, 70, "SeeAlso"] }, Open ]], -Cell[3897, 121, 23, 0, 70, "FooterCell"] +Cell[4845, 151, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/OptionsSelect.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/OptionsSelect.nb index 1489a50e2..540cf0282 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/OptionsSelect.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/OptionsSelect.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 5461, 149] -NotebookOptionsPosition[ 3465, 96] -NotebookOutlinePosition[ 5383, 145] -CellTagsIndexPosition[ 5340, 142] +NotebookDataLength[ 5695, 159] +NotebookOptionsPosition[ 3727, 107] +NotebookOutlinePosition[ 5631, 156] +CellTagsIndexPosition[ 5588, 153] WindowTitle->OptionsSelect WindowFrame->Normal*) @@ -59,12 +59,13 @@ OptionsSelect.html"], StandardForm]], "Input", TextClipboardType -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$113759], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$198427], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/OptionsSelect", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ OptionsSelect.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["OptionsSelect", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["OptionsSelect", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -106,10 +117,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 9.366529}", + "built" -> "{2020, 1, 5, 19, 0, 18.257683}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -117,11 +128,11 @@ TaggingRules->{ "None", "summary" -> "OptionsSelect[function, opts] returns the option settings of opts \ accepted by function. When an option occurs several times in opts, the first \ -setting is selected.", "synonyms" -> {}, "title" -> "OptionsSelect", - "titlemodifier" -> "", "windowtitle" -> "OptionsSelect", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/OptionsSelect"}}, +setting is selected.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "OptionsSelect", "titlemodifier" -> "", "windowtitle" -> "OptionsSelect", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/OptionsSelect"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -130,7 +141,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -144,13 +155,12 @@ CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[585, 21, 2266, 52, 70, "AnchorBarGrid", +Cell[585, 21, 2294, 53, 70, "AnchorBarGrid", CellID->1], -Cell[2854, 75, 56, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2913, 78, 522, 14, 70, "Usage", +Cell[2882, 76, 290, 11, 70, "ObjectNameGrid"], +Cell[3175, 89, 522, 14, 70, "Usage", CellID->982511436], -Cell[3438, 94, 23, 0, 70, "FooterCell"] +Cell[3700, 105, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/PD.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/PD.nb index eca938497..39ec57b35 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/PD.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/PD.nb @@ -3,69 +3,93 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6075, 191] -NotebookOptionsPosition[ 3956, 127] -NotebookOutlinePosition[ 5820, 180] -CellTagsIndexPosition[ 5756, 175] +NotebookDataLength[ 6975, 214] +NotebookOptionsPosition[ 5026, 159] +NotebookOutlinePosition[ 6767, 206] +CellTagsIndexPosition[ 6724, 203] WindowTitle->PD WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - 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StandardForm]], "Input", TextClipboardType -> "PlainText"]}, - Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$118581], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/PD", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"PropagatorDenominator\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PropagatorDenominator"], "\<\"IFPD\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/IFPD"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/PD\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/PD"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/PD.html"], + StandardForm]], "Input", TextClipboardType -> "PlainText"]}, + Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$208542], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/PD", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +97,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["PD", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["PD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -118,9 +152,7 @@ Cell[TextData[{ ButtonNote->"IFPD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PD", - CellID->155972299] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -137,19 +169,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 28.660122}", + "built" -> "{2020, 1, 5, 19, 0, 44.167261}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "PD is an abbreviation for PropagatorDenominator.", - "synonyms" -> {}, "title" -> "PD", "titlemodifier" -> "", "windowtitle" -> - "PD", "type" -> "Symbol", "uri" -> "FeynCalc/ref/PD"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "PD", "titlemodifier" -> + "", "windowtitle" -> "PD", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/PD"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -158,41 +191,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "PD"->{ - Cell[3507, 107, 407, 15, 70, "Text", - CellTags->"PD", - 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ImageSize->{553, 166}, + ImageSize->{481, 96}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"PaVe", - CellLabel->"Out[2]=", - CellID->1156896528] + CellLabel->"Out[1]="] }, Open ]] }, Open ]], @@ -301,9 +283,7 @@ Cell[TextData[{ ButtonNote->"PaVeReduce"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PaVe", - CellID->1153293303] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -311,7 +291,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"PaVe", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -320,25 +300,25 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - 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Joining plist and mlist gives the same \ -conventions as for A0, B0, C0, D0. Automatic simlifications are performed for \ -the coefficient functions of two-point integrals and for the scalar \ -integrals.", "synonyms" -> {}, "title" -> "PaVe", "titlemodifier" -> "", - "windowtitle" -> "PaVe", "type" -> "Symbol", "uri" -> + "PaVe[i, j, ..., {p10, p12, ...}, {m1^2, mw^2, ...}] denotes the \ +invariant (and scalar) Passarino-Veltman integrals, i.e. the coefficient \ +functions of the tensor integral decomposition. Joining plist and mlist gives \ +the same conventions as for A0, B0, C0, D0. Automatic simlifications are \ +performed for the coefficient functions of two-point integrals and for the \ +scalar integrals.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "PaVe", + "titlemodifier" -> "", "windowtitle" -> "PaVe", "type" -> "Symbol", "uri" -> "FeynCalc/ref/PaVe"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -346,8 +326,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -356,81 +337,54 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$118229], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/PaVeOrder", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$207213], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/PaVeOrder", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["PaVeOrder", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["PaVeOrder", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -120,7 +152,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1268026566], + CellID->795923657], Cell[CellGroupData[{ @@ -130,7 +162,12 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->629516765], + CellID->2100172249], + +Cell[BoxData[ + RowBox[{"ClearAll", "[", + RowBox[{"t", ",", "s"}], "]"}]], "Input", + CellLabel->"In[1]:="], Cell[CellGroupData[{ @@ -146,7 +183,7 @@ Cell[BoxData[ RowBox[{"me2", ",", "me2", ",", "0", ",", "0"}], "}"}]}]}], "]"}]], "Input", CellTags->"PaVeOrder", - CellLabel->"In[1]:=", + CellLabel->"In[2]:=", CellID->641538627], Cell[BoxData[ @@ -160,12 +197,11 @@ Cell[BoxData[ "me2", ",", "0", ",", "0", ",", "me2"}], ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - ImageSize->{305, 15}, + ImageSize->{311, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"PaVeOrder", - CellLabel->"Out[1]=", - CellID->1082848295] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -182,7 +218,7 @@ Cell[BoxData[ RowBox[{"me2", ",", "me2", ",", "0", ",", "0"}], "}"}]}]}], "]"}]], "Input", CellTags->"PaVeOrder", - CellLabel->"In[2]:=", + CellLabel->"In[3]:=", CellID->490694983], Cell[BoxData[ @@ -196,12 +232,11 @@ Cell[BoxData[ "me2", ",", "0", ",", "0", ",", "me2"}], ")"}], TraditionalForm], HoldForm], TraditionalForm]], "Output", - ImageSize->{305, 15}, + ImageSize->{311, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"PaVeOrder", - CellLabel->"Out[2]=", - CellID->1266309668] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -226,7 +261,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"f", ",", "e"}], "}"}]}], "}"}]}]}], "]"}]], "Input", CellTags->"PaVeOrder", - CellLabel->"In[3]:=", + CellLabel->"In[4]:=", CellID->1444685309], Cell[BoxData[ @@ -254,12 +289,11 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{318, 35}, + ImageSize->{322, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"PaVeOrder", - CellLabel->"Out[3]=", - CellID->1493961476] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -289,9 +323,7 @@ Cell[TextData[{ ButtonNote->"PaVeReduce"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PaVeOrder", - CellID->776510000] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -299,7 +331,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"PaVeOrder", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -308,10 +340,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 27.077538}", + "built" -> "{2020, 1, 5, 19, 0, 40.432063}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -321,11 +353,11 @@ TaggingRules->{ way. 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The lists may contain only a subsequence of the \ -D0-variables.", "synonyms" -> {}, "title" -> "PaVeOrder", "titlemodifier" -> - "", "windowtitle" -> "PaVeOrder", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/PaVeOrder"}, "SearchTextTranslated" -> ""}, +D0-variables.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "PaVeOrder", + "titlemodifier" -> "", "windowtitle" -> "PaVeOrder", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/PaVeOrder"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -333,8 +365,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -343,89 +376,78 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3793, 107, 388, 15, 31, "PrimaryExamplesSection", + Cell[4788, 139, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1268026566]}, + CellID->795923657]}, "PaVeOrder"->{ - Cell[4426, 136, 430, 13, 45, "Input", + Cell[5531, 173, 430, 13, 45, "Input", CellTags->"PaVeOrder", CellID->641538627], - Cell[4859, 151, 472, 16, 36, "Output", - CellTags->"PaVeOrder", - CellID->1082848295], - Cell[5368, 172, 430, 13, 45, "Input", + Cell[5964, 188, 451, 15, 37, "Output", + CellTags->"PaVeOrder"], + Cell[6452, 208, 430, 13, 45, "Input", CellTags->"PaVeOrder", CellID->490694983], - Cell[5801, 187, 472, 16, 36, "Output", - CellTags->"PaVeOrder", - CellID->1266309668], - Cell[6310, 208, 724, 21, 62, "Input", + Cell[6885, 223, 451, 15, 37, "Output", + CellTags->"PaVeOrder"], + Cell[7373, 243, 724, 21, 62, "Input", CellTags->"PaVeOrder", CellID->1444685309], - Cell[7037, 231, 855, 30, 56, "Output", - CellTags->"PaVeOrder", - CellID->1493961476], - Cell[8260, 284, 234, 9, 31, "Text", - 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CellTags->"PaVeOrder", - CellID->776510000] +Cell[9302, 318, 193, 7, 70, "SeeAlso"] }, Open ]], -Cell[8509, 296, 23, 0, 42, "FooterCell"] +Cell[9510, 328, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/PaVeOrderList.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/PaVeOrderList.nb index 36b829001..bca2ff681 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/PaVeOrderList.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/PaVeOrderList.nb @@ -3,69 +3,95 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6678, 208] -NotebookOptionsPosition[ 4383, 141] -NotebookOutlinePosition[ 6411, 197] -CellTagsIndexPosition[ 6336, 192] +NotebookDataLength[ 7640, 231] +NotebookOptionsPosition[ 5565, 174] +NotebookOutlinePosition[ 7431, 223] +CellTagsIndexPosition[ 7388, 220] WindowTitle->PaVeOrderList WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/PaVeOrderList\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/PaVeOrderList"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"PaVeOrder\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PaVeOrder"], "\<\"PaVeReduce\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PaVeReduce"], "\<\"PaVe\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/PaVe"], "\<\"D0\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/D0"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/PaVeOrderList\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/PaVeOrderList"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ PaVeOrderList.html"], StandardForm]], "Input", TextClipboardType -> - 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CellID->1224892054], +Cell[TextData[{ + Cell["PaVeOrderList", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +143,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["PaVeOrder", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/PaVeOrder", @@ -132,9 +167,7 @@ Cell[TextData[{ ButtonNote->"D0"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PaVeOrderList", - CellID->1960294739] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -151,10 +184,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - 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S*U*1D0)**3*(-(D*1D0) + 3D0))\"\>"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, @@ -825,22 +1148,23 @@ ME2, ME2, T, S, \"\>"}, Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]], TraditionalForm]], "Output", - ImageSize->{594, 321}, + ImageSize->{461, 1272}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"PaVeReduce", - CellLabel->"Out[11]//TableForm=", - CellID->273826743] + CellLabel->"Out[9]//TableForm=", + CellID->2020509582] }, Open ]], Cell[BoxData[ RowBox[{ - RowBox[{"DeleteFile", "/@", - RowBox[{"FileNames", "[", "\"\\"", "]"}]}], ";", - RowBox[{"Clear", "[", - RowBox[{"d122", ",", "se"}], "]"}], ";"}]], "Input", + RowBox[{ + RowBox[{"DeleteFile", "/@", + RowBox[{"FileNames", "[", "\"\\"", "]"}]}], ";", + RowBox[{"Clear", "[", + RowBox[{"d122", ",", "se"}], "]"}], ";"}], " "}]], "Input", CellTags->"PaVeReduce", - CellLabel->"In[12]:=", + CellLabel->"In[10]:=", CellID->793776799] }, Open ]], @@ -876,9 +1200,8 @@ Cell[TextData[{ ButtonNote->"PaVeOrder"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PaVeReduce", - CellID->1234185302] +}], "SeeAlso", + CellID->939950363] }, Open ]], Cell[" ", "FooterCell"] @@ -895,22 +1218,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2015, 11, 6, 23, 4, 29.112410}", + "built" -> "{2020, 1, 5, 19, 0, 41.675133}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "PaVeReduce[expr] reduces all Passarino-Veltman integrals (i.e. all \ -PaVe's) in expr down to scalar A0, B0, C0 and D0.", "synonyms" -> {}, "title" -> - "PaVeReduce", "titlemodifier" -> "", "windowtitle" -> "PaVeReduce", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/PaVeReduce"}, - "SearchTextTranslated" -> ""}, +PaVe's) in expr down to scalar A0, B0, C0 and D0.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "PaVeReduce", "titlemodifier" -> "", + "windowtitle" -> "PaVeReduce", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/PaVeReduce"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.2 for Linux x86 (64-bit) (July 6, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -919,7 +1242,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.2 for Linux x86 (64-bit) (July 6, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -927,230 +1250,173 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> + "None", "summary" -> + "PaVeUVPart[expr] replaces all occuring Passarino-Veltman functions by \ +their explicit values, where only the UV divergent part is preserved, while \ +possible IR divergences and the finite part are discarded. The function uses \ +the algorithm from \"Sulyok, G., A closed expression for the UV-divergent \ +parts of one-loop tensor integrals in dimensional regularization, Phys. Part. \ +Nuclei Lett. (2017) 14:631, arXiv:hep-ph/0609282 ", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "PaVeUVPart", "titlemodifier" -> "", + "windowtitle" -> "PaVeUVPart", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/PaVeUVPart"}, "SearchTextTranslated" -> ""}, +CellContext->"Global`", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> "Global`"], + Cell[ + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", + StyleDefinitions -> "Default.nb"] +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{ + "PrimaryExamplesSection"->{ + Cell[6479, 194, 387, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->887622295]} + } +*) +(*CellTagsIndex +CellTagsIndex->{ + {"PrimaryExamplesSection", 14092, 462} + } +*) +(*NotebookFileOutline +Notebook[{ +Cell[582, 21, 3093, 75, 53, "AnchorBarGrid", + CellID->1], +Cell[3678, 98, 287, 11, 45, "ObjectNameGrid"], +Cell[CellGroupData[{ +Cell[3990, 113, 791, 17, 170, "Usage", + CellID->982511436], +Cell[CellGroupData[{ +Cell[4806, 134, 739, 24, 31, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1956058901], +Cell[5548, 160, 31, 0, 70, "SectionHeaderSpacer"], +Cell[CellGroupData[{ +Cell[5604, 164, 113, 3, 70, "Input", + CellID->617667665], +Cell[5720, 169, 698, 18, 56, "Output", + CellID->717628530] +}, Open ]] +}, Closed]] +}, Open ]], +Cell[CellGroupData[{ +Cell[6479, 194, 387, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->887622295], +Cell[CellGroupData[{ +Cell[6891, 213, 195, 6, 26, "ExampleSection", + CellID->852270963], +Cell[CellGroupData[{ +Cell[7111, 223, 160, 5, 27, "Input", + CellID->1445277710], +Cell[7274, 230, 303, 11, 59, "Output", + CellID->384429231] +}, Open ]], +Cell[CellGroupData[{ +Cell[7614, 246, 311, 10, 33, "Input", + CellID->1518685822], +Cell[7928, 258, 341, 12, 55, "Output", + CellID->319680291] +}, Open ]], +Cell[CellGroupData[{ +Cell[8306, 275, 414, 12, 45, "Input", + CellID->759345267], +Cell[8723, 289, 406, 12, 42, "Output", + CellID->812213864], +Cell[9132, 303, 305, 11, 59, "Output", + CellID->1946544093] +}, Open ]], +Cell[CellGroupData[{ +Cell[9474, 319, 531, 14, 62, "Input", + CellID->1054433755], +Cell[10008, 335, 485, 14, 42, "Output", + CellID->792114270], +Cell[10496, 351, 628, 21, 62, "Output", + CellID->146736684] +}, Open ]] +}, Open ]], +Cell[11151, 376, 31, 0, 29, "SectionFooterSpacer"] +}, Open ]], +Cell[CellGroupData[{ +Cell[11219, 381, 270, 12, 31, "SeeAlsoSection", + CellID->1255426704], +Cell[11492, 395, 340, 13, 56, "SeeAlso"] +}, Open ]], +Cell[11847, 411, 23, 0, 41, "FooterCell"] +} +] +*) + +(* End of internal cache information *) + diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Pair.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Pair.nb index bf4fbfce3..3eec0e99f 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Pair.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Pair.nb @@ -3,69 +3,98 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 21595, 832] -NotebookOptionsPosition[ 14317, 581] -NotebookOutlinePosition[ 18784, 717] -CellTagsIndexPosition[ 18676, 711] +NotebookDataLength[ 22852, 853] +NotebookOptionsPosition[ 15912, 623] +NotebookOutlinePosition[ 20072, 745] +CellTagsIndexPosition[ 19964, 739] WindowTitle->Pair WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - 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ImageSize->{69, 20}, + ImageSize->{81, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Pair", - CellLabel->"Out[10]=", - CellID->1562380290] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -484,17 +541,16 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "q", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}]], "Input", CellTags->"Pair", - CellLabel->"In[11]:=", + CellLabel->"In[12]:=", CellID->1586756083], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Pair", - CellLabel->"Out[11]=", - CellID->824407583] + CellLabel->"Out[12]="] }, Open ]] }, Open ]], @@ -518,12 +574,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["FourVector", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], - FontFamily->"Verdana"], - ", ", StyleBox[ButtonBox["FV", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/FV", @@ -536,12 +586,6 @@ Cell[TextData[{ ButtonNote->"FVD"], FontFamily->"Verdana"], ", ", - 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"ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 15.768597}", + "built" -> "{2020, 1, 5, 19, 0, 23.098671}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -605,11 +647,11 @@ representation: x and y may have heads LorentzIndex or Momentum. If both x \ and y have head LorentzIndex, the metric tensor is understood. If x and y \ have head Momentum, a scalar product is meant. If one of x and y has head \ LorentzIndex and the other Momentum, a Lorentz vector p^\\[Mu] is \ -understood.", "synonyms" -> {}, "title" -> "Pair", "titlemodifier" -> "", - "windowtitle" -> "Pair", "type" -> "Symbol", "uri" -> +understood.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "Pair", + "titlemodifier" -> "", "windowtitle" -> "Pair", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Pair"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -617,8 +659,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -627,213 +670,191 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["PartialDRelations", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +146,9 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->660817011], + CellID->903885071], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -115,13 +156,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->670359256], - -Cell[CellGroupData[{ - -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"PartialDRelations", - CellID->56378705], + CellID->1255266426], Cell[CellGroupData[{ @@ -157,12 +192,11 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - 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SubsuperscriptBox[ - FormBox["C", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["C", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}], ".", SubscriptBox[ FormBox["B", TraditionalForm], FormBox["\[Mu]", TraditionalForm]]}]}], TraditionalForm]], "Output", - ImageSize->{133, 19}, + ImageSize->{198, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"PartialDRelations", - CellLabel->"Out[2]=", - CellID->42444932] + CellLabel->"Out[2]="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] -}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -246,39 +283,38 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[RawData["\<\ Cell[TextData[{ - ButtonBox[\"FCPartialD\", - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 17.229256}", + "built" -> "{2020, 1, 5, 19, 0, 24.270162}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "PartialDRelations is an option for ExpandPartialD. It is a list of rules \ -applied by ExpandPartialD at the end.", "synonyms" -> {}, "title" -> - "PartialDRelations", "titlemodifier" -> "", "windowtitle" -> +applied by ExpandPartialD at the end.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "PartialDRelations", "titlemodifier" -> "", "windowtitle" -> "PartialDRelations", "type" -> "Symbol", "uri" -> "FeynCalc/ref/PartialDRelations"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -318,8 +354,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -328,81 +365,65 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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PartialFourVector[exp, FV[p, mu], FV[p,nu], ...] gives the multiple \ +derivative." }]]} }]], "Usage", GridBoxOptions->{ @@ -112,7 +144,9 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1396902996], + CellID->1514889249], + +Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", @@ -120,13 +154,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->308511971], - -Cell[CellGroupData[{ - -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"PartialFourVector", - CellID->1758819018], + CellID->29019256], Cell[CellGroupData[{ @@ -136,9 +164,9 @@ Cell[BoxData[ RowBox[{"a", " ", SuperscriptBox["\[ExponentialE]", SuperscriptBox[ - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", "\[Nu]"}], "]"}], "2"]]}], ",", - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "]"}]], "Input", CellTags->"PartialFourVector", CellLabel->"In[1]:=", @@ -154,30 +182,25 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm], "2"]], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{77, 24}, + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + ImageSize->{86, 22}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"PartialFourVector", - CellLabel->"Out[1]=", - CellID->1052815023] + CellLabel->"Out[1]="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] -}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -197,12 +220,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - StyleBox[ButtonBox["FourVector", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], - FontFamily->"Verdana"], - ", ", StyleBox[ButtonBox["Pair", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/Pair", @@ -215,9 +232,7 @@ Cell[TextData[{ ButtonNote->"Contract"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PartialFourVector", - CellID->156343692] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -225,7 +240,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"PartialFourVector", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -234,23 +249,23 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 18.718563}", + "built" -> "{2020, 1, 5, 19, 0, 25.291809}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "PartialFourVector[exp, FourVector[p, mu]] calculates the partial \ -derivative of exp w.r.t. p(mu). PartialFourVector[exp, FourVector[p, mu], \ -FourVector[p,nu], ...] gives the multiple derivative.", "synonyms" -> {}, +derivative of exp w.r.t. p(mu). PartialFourVector[exp, FV[p, mu], FV[p,nu], \ +...] gives the multiple derivative.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "PartialFourVector", "titlemodifier" -> "", "windowtitle" -> "PartialFourVector", "type" -> "Symbol", "uri" -> "FeynCalc/ref/PartialFourVector"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -258,8 +273,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -268,67 +284,53 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$116521], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$201988], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/PartialIntegrate", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,20 @@ PartialIntegrate.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["PartialIntegrate", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["PartialIntegrate", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -96,36 +109,33 @@ exp/ap the factor that is to be differentiated." 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With this notation transversality of polarization vectors is provided, \ +i.e. , Pair[ Momentum[k], Momentum[ Polarization[k, I] ] ] yields 0. \ +Polarization[k,-I] denotes the complex conjugate polarization. Polarization \ +is also an option of various functions related to the operator product \ +expansion. 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 31.541132}", + "built" -> "{2020, 1, 5, 19, 0, 46.412929}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -371,19 +395,19 @@ TaggingRules->{ "None", "summary" -> "Polarization[k] is the head of a polarization momentum with (incoming) \ momentum k. A slashed polarization vector (e1(k) slash) has to be entered as \ -DiracSlash[Polarization[k]]. The internal representation for a polarization \ -vector e1 corresponding to a boson with four momentum k is: \ -Momentum[Polarization[k, I ] ]. With this notation transversality of \ -polarization vectors is provided, i.e. , Pair[Momentum[k], \ -Momentum[Polarization[k, I] ] ] yields 0. Polarization[k,-I] denotes the \ -complex conjugate polarization. Polarization is also an option of various \ -functions related to the operator product expansion. The setting 0 denotes \ -the unpolarized and 1 the polarized case.", "synonyms" -> {}, "title" -> - "Polarization", "titlemodifier" -> "", "windowtitle" -> "Polarization", - "type" -> "Symbol", "uri" -> "FeynCalc/ref/Polarization"}, - "SearchTextTranslated" -> ""}, +GS[Polarization[k]]. The internal representation for a polarization vector e1 \ +corresponding to a boson with four momentum k is: Momentum[Polarization[k, I \ +] ]. With this notation transversality of polarization vectors is provided, \ +i.e. , Pair[Momentum[k], Momentum[Polarization[k, I] ] ] yields 0. \ +Polarization[k,-I] denotes the complex conjugate polarization. Polarization \ +is also an option of various functions related to the operator product \ +expansion. The setting 0 denotes the unpolarized and 1 the polarized case.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "Polarization", + "titlemodifier" -> "", "windowtitle" -> "Polarization", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/Polarization"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -391,8 +415,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -401,145 +426,125 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["PositiveInteger", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +144,7 @@ Cell[TextData[{ ButtonNote->"DataType"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PositiveInteger", - CellID->1743918349] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,21 +161,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 37.408968}", + "built" -> "{2020, 1, 5, 19, 0, 49.846879}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "PositiveInteger is a data type. 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DataType[OPEm, PositiveInteger] \ -gives True.", "synonyms" -> {}, "title" -> "PositiveInteger", "titlemodifier" -> - "", "windowtitle" -> "PositiveInteger", "type" -> "Symbol", "uri" -> +gives True.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "PositiveInteger", "titlemodifier" -> "", "windowtitle" -> + "PositiveInteger", "type" -> "Symbol", "uri" -> "FeynCalc/ref/PositiveInteger"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -154,41 +185,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "PositiveInteger"->{ - Cell[3605, 107, 235, 9, 70, "Text", - CellTags->"PositiveInteger", - CellID->1743918349]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"PositiveInteger", 5681, 164} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[587, 21, 2274, 52, 70, "AnchorBarGrid", +Cell[587, 21, 3031, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2864, 75, 58, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2925, 78, 382, 11, 70, "Usage", +Cell[3621, 97, 292, 11, 70, "ObjectNameGrid"], +Cell[3916, 110, 382, 11, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3332, 93, 270, 12, 70, "SeeAlsoSection", +Cell[4323, 125, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3605, 107, 235, 9, 70, "Text", - CellTags->"PositiveInteger", - CellID->1743918349] +Cell[4596, 139, 187, 7, 70, "SeeAlso"] }, Open ]], -Cell[3855, 119, 23, 0, 70, "FooterCell"] +Cell[4798, 149, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/PositiveNumber.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/PositiveNumber.nb index 4500b0879..63034d2c3 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/PositiveNumber.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/PositiveNumber.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6153, 188] -NotebookOptionsPosition[ 3888, 122] -NotebookOutlinePosition[ 5886, 177] -CellTagsIndexPosition[ 5810, 172] +NotebookDataLength[ 6878, 209] +NotebookOptionsPosition[ 4832, 152] +NotebookOutlinePosition[ 6671, 201] +CellTagsIndexPosition[ 6628, 198] WindowTitle->PositiveNumber WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/PositiveNumber\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/PositiveNumber"]}, Visible -> False]]; 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E.g. DataType[Epsilon, PositiveNumber] = \ -True (by default). ", "synonyms" -> {}, "title" -> "PositiveNumber", - "titlemodifier" -> "", "windowtitle" -> "PositiveNumber", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/PositiveNumber"}}, +True (by default). ", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "PositiveNumber", "titlemodifier" -> "", "windowtitle" -> + "PositiveNumber", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/PositiveNumber"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -155,41 +186,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "PositiveNumber"->{ - Cell[3612, 108, 234, 9, 70, "Text", - CellTags->"PositiveNumber", - CellID->1422262610]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/PostFortranFile\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/PostFortranFile"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"Write2\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Write2"], "\<\"PreFortranFile\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/PreFortranFile"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/PostFortranFile\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/PostFortranFile"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ PostFortranFile.html"], StandardForm]], "Input", TextClipboardType -> - 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CellID->1224892054], +Cell[TextData[{ + Cell["PostFortranFile", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -120,9 +153,7 @@ Cell[TextData[{ ButtonNote->"PreFortranFile"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PostFortranFile", - CellID->1559653274] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -139,10 +170,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 39.983924}", + "built" -> "{2020, 1, 5, 19, 0, 51.753223}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -150,11 +181,12 @@ TaggingRules->{ "None", "summary" -> "PostFortranFile is an option for Write2 which may be set to a file name \ (or a list of file names) or a string, which will be put at the end of the \ -generated Fortran file.", "synonyms" -> {}, "title" -> "PostFortranFile", - "titlemodifier" -> "", "windowtitle" -> "PostFortranFile", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/PostFortranFile"}}, +generated Fortran file.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "PostFortranFile", "titlemodifier" -> "", "windowtitle" -> + "PostFortranFile", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/PostFortranFile"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -163,41 +195,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["Power2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -110,7 +142,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->2002944619], + CellID->1439015721], Cell[CellGroupData[{ @@ -120,7 +152,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1141506699], + CellID->1049005295], Cell[CellGroupData[{ @@ -137,12 +169,11 @@ Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{"-", "a"}], ")"}], "b"], TraditionalForm]], "Output", - ImageSize->{44, 19}, + ImageSize->{48, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Power2", - CellLabel->"Out[1]=", - CellID->1555519313] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -164,12 +195,11 @@ Cell[BoxData[ FormBox[ SuperscriptBox["a", "b"], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{63, 19}, + ImageSize->{69, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Power2", - CellLabel->"Out[2]=", - CellID->1786215167] + CellLabel->"Out[2]="] }, Open ]] }, Open ]], @@ -199,9 +229,7 @@ Cell[TextData[{ ButtonNote->"PowerFactor"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Power2", - CellID->1979787947] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -209,7 +237,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, WindowTitle->"Power2", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -218,10 +246,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 41.179587}", + "built" -> "{2020, 1, 5, 19, 0, 52.693298}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -229,11 +257,11 @@ TaggingRules->{ "None", "summary" -> "Power2[x, y] represents x^y. Sometimes Power2 is more useful than the \ Mathematica Power. Power2[-a,b] simplifies to (-1)^b Power2[a,b] (if no \ -Epsilon is in b ...).", "synonyms" -> {}, "title" -> "Power2", - "titlemodifier" -> "", "windowtitle" -> "Power2", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/Power2"}, "SearchTextTranslated" -> ""}, +Epsilon is in b ...).", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "Power2", "titlemodifier" -> "", "windowtitle" -> "Power2", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/Power2"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -242,7 +270,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -251,75 +279,65 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellTags->"PowerSimplify", - CellID->219988964] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -370,7 +397,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"PowerSimplify", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -379,10 +406,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 44.262033}", + "built" -> "{2020, 1, 5, 19, 0, 55.190344}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -393,11 +420,12 @@ n (x - y) n; thus assuming that the exponent is an integer (even if it is \ symbolic). 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FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -415,103 +444,89 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[6200, 203, 387, 15, 31, "PrimaryExamplesSection", + Cell[7269, 236, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->192981915]}, + CellID->1388239057]}, "PowerSimplify"->{ - Cell[6832, 232, 252, 9, 27, "Input", + Cell[7902, 265, 252, 9, 27, "Input", CellTags->"PowerSimplify", CellID->1178513781], - Cell[7087, 243, 215, 7, 36, "Output", - CellTags->"PowerSimplify", - CellID->1102382447], - Cell[7339, 255, 257, 9, 27, "Input", + Cell[8157, 276, 194, 6, 35, "Output", + CellTags->"PowerSimplify"], + Cell[8388, 287, 257, 9, 27, "Input", CellTags->"PowerSimplify", CellID->1283744805], - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/PreFortranFile\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/PreFortranFile"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"Write2\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Write2"], "\<\"PostFortranFile\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/PostFortranFile"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/PreFortranFile\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/PreFortranFile"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ PreFortranFile.html"], StandardForm]], "Input", TextClipboardType -> - 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CellID->1224892054], +Cell[TextData[{ + Cell["PreFortranFile", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -120,9 +153,7 @@ Cell[TextData[{ ButtonNote->"PostFortranFile"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"PreFortranFile", - CellID->659690590] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -139,10 +170,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 46.975244}", + "built" -> "{2020, 1, 5, 19, 0, 57.423750}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -150,11 +181,12 @@ TaggingRules->{ "None", "summary" -> "PreFortranFile is an option for Write2 which may be set to a file name \ (or a list of file names) or a string, which will be put at the beginning of \ -the generated Fortran file.", "synonyms" -> {}, "title" -> "PreFortranFile", - "titlemodifier" -> "", "windowtitle" -> "PreFortranFile", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/PreFortranFile"}}, +the generated Fortran file.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "PreFortranFile", "titlemodifier" -> "", "windowtitle" -> + "PreFortranFile", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/PreFortranFile"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -163,41 +195,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "PreFortranFile"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["Prefactor", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -121,9 +154,7 @@ Cell[TextData[{ ButtonNote->"OneLoopSum"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Prefactor", - CellID->1510913655] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -140,10 +171,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 45.804534}", + "built" -> "{2020, 1, 5, 19, 0, 56.437828}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -152,11 +183,11 @@ TaggingRules->{ "Prefactor is an option for OneLoop and OneLoopSum. 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What is meant is 1/(q^2-m^2). \ +PropagatorDenominator must appear inside FeynAmpDenominator, it is not a \ +standalone object.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "PropagatorDenominator", "titlemodifier" -> "", "windowtitle" -> + "PropagatorDenominator", "type" -> "Symbol", "uri" -> "FeynCalc/ref/PropagatorDenominator"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -387,8 +306,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) 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+ TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$216083], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/QP", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["QP", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["QP", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -106,14 +117,15 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], +Cell[RawData["\<\ Cell[TextData[{ - StyleBox[ButtonBox["QuarkPropagator", - BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/QuarkPropagator", - ButtonNote->"QuarkPropagator"], - FontFamily->"Verdana"], - "." -}], "Text", + ButtonBox[\"QuarkPropagator\", + BaseStyle->\"Link\", + ButtonData:>\"paclet:FeynCalc/ref/QuarkPropagator\", + ButtonNote->\"QuarkPropagator\"], + \".\" +}], \"SeeAlso\"]\ +\>"], "Text", CellTags->"QP", CellID->218226034] }, Open ]], @@ -132,10 +144,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 53.608891}", + "built" -> "{2020, 1, 5, 19, 1, 2.558030}", "history" -> {"9.0", "", "", ""}, "context" -> 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QP[p] is the massless quark \ propagator. 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CellID->1224892054], +Cell[TextData[{ + Cell["QuantumField", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,7 +147,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1441027904], + CellID->1519740058], Cell[CellGroupData[{ @@ -122,11 +157,9 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->71990275], + CellID->1271161724], -Cell["This denotes a scalar field.", "Text", - CellTags->"QuantumField", - CellID->173552947], +Cell["This denotes a scalar field.", "Notes"], Cell[CellGroupData[{ @@ -138,12 +171,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["S", TraditionalForm]], "Output", - ImageSize->{13, 15}, + ImageSize->{16, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuantumField", - CellLabel->"Out[1]=", - CellID->2038740597] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -157,12 +189,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ OverscriptBox["\[Psi]", "_"], TraditionalForm]], "Output", - ImageSize->{17, 15}, + ImageSize->{16, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuantumField", - CellLabel->"Out[2]=", - CellID->2083488651] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -175,17 +206,14 @@ Cell[BoxData[ Cell[BoxData[ FormBox["\[Psi]", TraditionalForm]], "Output", - ImageSize->{16, 15}, + ImageSize->{15, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuantumField", - CellLabel->"Out[3]=", - CellID->1186167697] + CellLabel->"Out[3]="] }, Open ]], -Cell["This is a field with a Lorentz index.", "Text", - CellTags->"QuantumField", - CellID->1204193660], +Cell["This is a field with a Lorentz index.", "Notes"], Cell[CellGroupData[{ @@ -204,17 +232,14 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{22, 18}, + ImageSize->{24, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuantumField", - CellLabel->"Out[4]=", - CellID->188307989] + CellLabel->"Out[4]="] }, Open ]], -Cell["Color indices should be put after the Lorentz ones.", "Text", - CellTags->"QuantumField", - CellID->1363299018], +Cell["Color indices should be put after the Lorentz ones.", "Notes"], Cell[CellGroupData[{ @@ -240,12 +265,11 @@ Cell[BoxData[ FormBox["a", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{24, 19}, + ImageSize->{29, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuantumField", - CellLabel->"Out[5]=", - CellID->568800193] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -261,12 +285,11 @@ Cell[BoxData[ RowBox[{"GaugeField", ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}]], "Output", - ImageSize->{438, 15}, + ImageSize->{441, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuantumField", - CellLabel->"Out[6]//StandardForm=", - CellID->232650919] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[TextData[{ @@ -281,9 +304,7 @@ Cell[TextData[{ RowBox[{ SubsuperscriptBox["A", "\[Mu]", "a"], "."}]}], TraditionalForm]]], " " -}], "Text", - CellTags->"QuantumField", - CellID->508873038], +}], "Notes"], Cell[CellGroupData[{ @@ -309,20 +330,17 @@ Cell[BoxData[ FormBox["a", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{24, 17}, + ImageSize->{29, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuantumField", - CellLabel->"Out[7]=", - CellID->1323752020] + CellLabel->"Out[7]="] }, Open ]], Cell["\<\ - The first list of indices is usually interpreted as type LorentzIndex, \ -except for OPEDelta, which gets converted to type Momentum. \ -\>", "Text", - CellTags->"QuantumField", - CellID->708047350], +The first list of indices is usually interpreted as type LorentzIndex, except \ +for OPEDelta, which gets converted to type Momentum. \ +\>", "Notes"], Cell[CellGroupData[{ @@ -341,17 +359,14 @@ Cell[BoxData[ RowBox[{"A", ",", RowBox[{"Momentum", "[", "OPEDelta", "]"}], ",", RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}]], "Output", - 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CellLabel->"Out[12]=", - CellID->2017233085] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -505,12 +524,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", - ImageSize->{33, 15}, + ImageSize->{31, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuantumField", - CellLabel->"Out[13]=", - CellID->1933229370] + CellLabel->"Out[13]="] }, Open ]] }, Open ]], @@ -552,17 +570,15 @@ Cell[TextData[{ ButtonNote->"ExpandPartialD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"QuantumField", - CellID->231016079] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"QuantumField", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -571,10 +587,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 23, 54.860059}", + "built" -> "{2020, 1, 5, 19, 1, 3.544006}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -584,11 +600,12 @@ TaggingRules->{ QuantumField[par, ftype, {lorind}, {sunind}] denotes a quantum field of type \ ftype with (possible) Lorentz-indices lorind and SU(N) indices sunind. 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ImageSize->{419, 35}, + ImageSize->{393, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"QuarkPropagator", - CellLabel->"Out[1]=", - CellID->759410596] + CellLabel->"Out[50]="] +}, Open ]] +}, Closed]] }, Open ]], Cell[CellGroupData[{ +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(2)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->708793879], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(2)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->438324506], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"QuarkPropagator", "[", RowBox[{"p", ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkPropagator", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1589814930], Cell[BoxData[ @@ -168,15 +250,22 @@ Cell[BoxData[ FormBox["p", TraditionalForm], TraditionalForm]}]}], - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"]], TraditionalForm]], "Output", - ImageSize->{47, 47}, + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False]], TraditionalForm]], "Output", + ImageSize->{49, 39}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuarkPropagator", - CellLabel->"Out[2]=", - CellID->1709152205] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -188,7 +277,7 @@ Cell[BoxData[ RowBox[{"p", ",", "m"}], "}"}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkPropagator", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1965811029], Cell[BoxData[ @@ -202,17 +291,89 @@ Cell[BoxData[ FormBox["p", TraditionalForm], TraditionalForm]}]}], ")"}]}], - RowBox[{ - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"], "-", - SuperscriptBox["m", "2"]}]], TraditionalForm]], "Output", - ImageSize->{88, 47}, + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]], "-", $CellContext`m^2], + Editable->False]], TraditionalForm]], "Output", + ImageSize->{92, 39}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"QuarkPropagator", - CellLabel->"Out[3]=", - CellID->545226998] + CellLabel->"Out[2]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"QP", "[", + RowBox[{"{", + RowBox[{"p", ",", "m"}], "}"}], "]"}]], "Input", + CellLabel->"In[1]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SubscriptBox["\[CapitalPi]", "q"], "(", + FormBox["p", + TraditionalForm], ")"}], TraditionalForm]], "Output", + ImageSize->{51, 18}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[1]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Explicit", "[", "%", "]"}]], "Input", + CellLabel->"In[2]:="], + +Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"(", + RowBox[{"m", "+", + RowBox[{"\[Gamma]", "\[CenterDot]", + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]}]}], ")"}]}], + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]], "-", $CellContext`m^2], + Editable->False]], TraditionalForm]], "Output", + ImageSize->{92, 39}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[2]="] +}, Open ]] }, Open ]] }, Open ]], @@ -248,9 +409,7 @@ Cell[TextData[{ ButtonNote->"QuarkGluonVertex"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"QuarkPropagator", - CellID->704256164] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -258,7 +417,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"QuarkPropagator", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -267,22 +426,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 0.622220}", + "built" -> "{2020, 1, 5, 19, 1, 13.015421}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "QuarkPropagator[p] is the massless quark propagator. \ -QuarkPropagator[{p,m}] or gives the quark propagator with mass m.", - "synonyms" -> {}, "title" -> "QuarkPropagator", "titlemodifier" -> "", + "QuarkPropagator[p] is the massless quark propagator. QuarkPropagator[{p, \ +m}] gives the quark propagator with mass m.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "QuarkPropagator", "titlemodifier" -> "", "windowtitle" -> "QuarkPropagator", "type" -> "Symbol", "uri" -> "FeynCalc/ref/QuarkPropagator"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -290,8 +449,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -300,89 +460,90 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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"", "windowtitle" -> "RHI", "type" -> "Symbol", "uri" -> +{al,be,ga,de,ep}].", "synonyms" -> {}, "tabletags" -> {}, "title" -> "RHI", + "titlemodifier" -> "", "windowtitle" -> "RHI", "type" -> "Symbol", "uri" -> "FeynCalc/ref/RHI"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -216,62 +208,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "PrimaryExamplesSection"->{ - Cell[4137, 111, 379, 15, 70, "PrimaryExamplesSection", - CellTags->"PrimaryExamplesSection", - 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CellID->1224892054], +Cell[TextData[{ + Cell["RHI", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,44 +140,6 @@ RHI[any, {a,b,c,d,e}, {al,be,ga,de,ep}]; \nRHI[{0,0,0,0,0},{a,b,c,d,e}, \ Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", - WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->1], - -Cell[CellGroupData[{ - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->1], - -Cell[BoxData[""], "Input", - CellTags->"RHI2FC", - CellLabel->"In[1]:=", - CellID->729912401] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["", "SectionFooterSpacer"], - Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -167,9 +161,7 @@ Cell[TextData[{ ButtonNote->"RHI2FC"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"RHI2FC", - CellID->2129471313] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -186,10 +178,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 6.067246}", + "built" -> "{2020, 1, 5, 19, 1, 17.156224}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -202,11 +194,11 @@ p.k1, y: p.k2, z: k1.k2. a: dl.k1, b: dl.k2, c: dl.(p-k1), d: dl.(p-k2), e: \ dl.(k1-k2), f: dl.(p+k1-k2), g: dl.(p-k1-k2) RHI[any___,{a,b,c,d,e,0,0}, \ {al,be,ga,de,ep}] simplifies to RHI[any, {a,b,c,d,e}, {al,be,ga,de,ep}]; \ RHI[{0,0,0,0,0},{a,b,c,d,e}, {al,be,ga,de,ep}] simplifies to RHI[{a,b,c,d,e}, \ -{al,be,ga,de,ep}].", "synonyms" -> {}, "title" -> "RHI", "titlemodifier" -> - "", "windowtitle" -> "RHI", "type" -> "Symbol", "uri" -> +{al,be,ga,de,ep}].", "synonyms" -> {}, "tabletags" -> {}, "title" -> "RHI", + "titlemodifier" -> "", "windowtitle" -> "RHI", "type" -> "Symbol", "uri" -> "FeynCalc/ref/RHI"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -215,62 +207,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "PrimaryExamplesSection"->{ - Cell[4114, 110, 379, 15, 70, "PrimaryExamplesSection", - CellTags->"PrimaryExamplesSection", - 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CellID->1224892054], +Cell[TextData[{ + Cell["RHM", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -92,44 +124,6 @@ Cell[BoxData[GridBox[{ Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", - WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->1], - -Cell[CellGroupData[{ - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->1], - 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"synonyms" -> {}, "title" -> "RHM", "titlemodifier" -> "", "windowtitle" -> - "RHM", "type" -> "Symbol", "uri" -> "FeynCalc/ref/RHM"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "RHM", "titlemodifier" -> + "", "windowtitle" -> "RHM", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/RHM"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -191,62 +184,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "PrimaryExamplesSection"->{ - Cell[3260, 94, 379, 15, 70, "PrimaryExamplesSection", - 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CellID->1224892054], +Cell[TextData[{ + Cell["RHO", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -94,44 +126,6 @@ suppressed. 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The Lorentz indices are \ suppressed. The explicit expressions may be recovered by RHO[i, mu, nu, p].", - "synonyms" -> {}, "title" -> "RHO", "titlemodifier" -> "", "windowtitle" -> - "RHO", "type" -> "Symbol", "uri" -> "FeynCalc/ref/RHO"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "RHO", "titlemodifier" -> + "", "windowtitle" -> "RHO", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/RHO"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -196,62 +189,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "PrimaryExamplesSection"->{ - Cell[3446, 96, 379, 15, 70, "PrimaryExamplesSection", - CellTags->"PrimaryExamplesSection", - CellID->1]}, - "RHO"->{ - Cell[4040, 123, 87, 3, 70, "Input", - CellTags->"RHO", - CellID->868607428], - Cell[4483, 148, 208, 9, 70, "Text", - CellTags->"RHO", - CellID->2131383850]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"PrimaryExamplesSection", 6633, 206}, - {"RHO", 6754, 210} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[575, 21, 2238, 52, 70, "AnchorBarGrid", +Cell[575, 21, 2971, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2816, 75, 46, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2865, 78, 556, 14, 70, "Usage", +Cell[3549, 97, 280, 11, 70, "ObjectNameGrid"], +Cell[3832, 110, 556, 14, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3446, 96, 379, 15, 70, "PrimaryExamplesSection", - CellTags->"PrimaryExamplesSection", - CellID->1], -Cell[CellGroupData[{ -Cell[3850, 115, 187, 6, 70, "ExampleSection", - CellID->1], -Cell[4040, 123, 87, 3, 70, "Input", - CellTags->"RHO", - CellID->868607428] -}, Open ]] -}, Open ]], -Cell[CellGroupData[{ -Cell[4176, 132, 31, 0, 70, "SectionFooterSpacer"], -Cell[4210, 134, 270, 12, 70, "SeeAlsoSection", +Cell[4413, 128, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[4483, 148, 208, 9, 70, "Text", - CellTags->"RHO", - CellID->2131383850] +Cell[4686, 142, 172, 7, 70, "SeeAlso"] }, Open ]], -Cell[4706, 160, 23, 0, 70, "FooterCell"] +Cell[4873, 152, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/RHP.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/RHP.nb index c36d24d08..a04d7ccc0 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/RHP.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/RHP.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 7732, 253] -NotebookOptionsPosition[ 4799, 164] -NotebookOutlinePosition[ 7120, 229] -CellTagsIndexPosition[ 7015, 223] +NotebookDataLength[ 7102, 214] +NotebookOptionsPosition[ 4966, 156] +NotebookOutlinePosition[ 6895, 206] +CellTagsIndexPosition[ 6852, 203] WindowTitle->RHP WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/RHP\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/RHP"]}, Visible -> False]]; 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/RHP.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$223645], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/RHP", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["RHP", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["RHP", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -96,44 +128,6 @@ nu. 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See the thesis of Roelof Hamberg (but correcting a \ -misprint).", "synonyms" -> {}, "title" -> "RHP", "titlemodifier" -> "", - "windowtitle" -> "RHP", "type" -> "Symbol", "uri" -> +misprint).", "synonyms" -> {}, "tabletags" -> {}, "title" -> "RHP", + "titlemodifier" -> "", "windowtitle" -> "RHP", "type" -> "Symbol", "uri" -> "FeynCalc/ref/RHP"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -199,62 +191,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["ReduceToScalars", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -119,9 +152,7 @@ Cell[TextData[{ ButtonNote->"OneLoopSum"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"ReduceToScalars", - CellID->1934839663] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -138,10 +169,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 3.456228}", + "built" -> "{2020, 1, 5, 19, 1, 15.154057}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -149,11 +180,12 @@ TaggingRules->{ "None", "summary" -> "ReduceToScalars is an option for OneLoop and OneLoopSum that specifies \ whether the result will be reduced to scalar A0, B0, C0 and D0 scalar \ -integrals.", "synonyms" -> {}, "title" -> "ReduceToScalars", "titlemodifier" -> - 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CellID->1224892054], +Cell[TextData[{ + Cell["Rename", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -113,9 +145,7 @@ Cell[TextData[{ ButtonNote->"Contract"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Rename", - CellID->345735960] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -132,21 +162,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 4.788383}", + "built" -> "{2020, 1, 5, 19, 1, 16.155323}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "Rename is an option for Contract. 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CellID->1224892054], +Cell[TextData[{ + Cell["RightPartialD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -111,7 +147,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1428598870], + CellID->1777068154], Cell[CellGroupData[{ @@ -121,7 +157,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->709509502], + CellID->2097032936], Cell[CellGroupData[{ @@ -139,12 +175,11 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{24, 27}, + ImageSize->{23, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"RightPartialD", - CellLabel->"Out[1]=", - CellID->1461309897] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -173,12 +208,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{47, 27}, + ImageSize->{50, 24}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"RightPartialD", - CellLabel->"Out[2]=", - CellID->1675009373] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -192,24 +226,24 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Mu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], TraditionalForm]], "Output", - ImageSize->{40, 19}, + TraditionalForm]], ")"}], TraditionalForm]], "Output", + ImageSize->{59, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"RightPartialD", - CellLabel->"Out[3]=", - CellID->528358345] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -226,12 +260,11 @@ Cell[BoxData[ RowBox[{"FCPartialD", "[", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}], ",", "A", ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]], "Output", - ImageSize->{496, 15}, + ImageSize->{500, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"RightPartialD", - CellLabel->"Out[4]//StandardForm=", - CellID->1851835493] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -247,12 +280,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"RightPartialD", "[", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}]], "Output", - ImageSize->{247, 15}, + ImageSize->{250, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"RightPartialD", - CellLabel->"Out[5]//StandardForm=", - CellID->1374997587] + CellLabel->"Out[5]//StandardForm="] }, Open ]] }, Open ]], @@ -275,29 +307,26 @@ Cell[TextData[{ WholeCellGroupOpener->True, CellID->1255426704], -Cell[RawData["\<\ Cell[TextData[{ - ButtonBox[\"ExpandPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/ExpandPartialD\", - ButtonNote->\"ExpandPartialD\"], - \", \", - ButtonBox[\"FCPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/PartialD\", - ButtonNote->\"FCPartialD\"], - \", \", - ButtonBox[\"LeftPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/LeftPartialD\", - ButtonNote->\"LeftPartialD\"], - \".\" -}], \"Text\", - CellTags->\"RightPartialD\", - CellID->1409903491]\ -\>"], "Text", - CellTags->"RightPartialD", - CellID->1409903491] + StyleBox[ButtonBox["ExpandPartialD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/ExpandPartialD", + ButtonNote->"ExpandPartialD"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["FCPartialD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/PartialD", + ButtonNote->"FCPartialD"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["LeftPartialD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/LeftPartialD", + ButtonNote->"LeftPartialD"], + FontFamily->"Verdana"], + "." +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -314,21 +343,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 12.499631}", + "built" -> "{2020, 1, 5, 19, 1, 22.076186}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "RightPartialD[mu] denotes \\[PartialD]\\[Mu], acting to the right.", - "synonyms" -> {}, "title" -> "RightPartialD", "titlemodifier" -> "", - "windowtitle" -> "RightPartialD", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/RightPartialD"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "RightPartialD", + "titlemodifier" -> "", "windowtitle" -> "RightPartialD", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/RightPartialD"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -337,7 +367,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -346,117 +376,101 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3425, 98, 388, 15, 31, "PrimaryExamplesSection", + Cell[4626, 134, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1428598870]}, + CellID->1777068154]}, "RightPartialD"->{ - Cell[4058, 127, 140, 4, 27, "Input", + Cell[5260, 163, 140, 4, 27, "Input", CellTags->"RightPartialD", CellID->27121698], - Cell[4201, 133, 357, 13, 48, "Output", - CellTags->"RightPartialD", - CellID->1461309897], - Cell[4595, 151, 273, 8, 27, "Input", + Cell[5403, 169, 336, 12, 45, "Output", + CellTags->"RightPartialD"], + Cell[5776, 186, 273, 8, 27, "Input", CellTags->"RightPartialD", CellID->1087611627], - Cell[4871, 161, 485, 19, 48, "Output", - CellTags->"RightPartialD", - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/RussianTrick\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/RussianTrick"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FourDivergence\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FourDivergence"], "\<\"FourLaplacian\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/FourLaplacian"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/RussianTrick\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/RussianTrick"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ RussianTrick.html"], StandardForm]], "Input", TextClipboardType -> - 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CellID->1224892054], +Cell[TextData[{ + Cell["RussianTrick", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -84,11 +120,10 @@ Cell[BoxData[GridBox[{ RowBox[{"{", RowBox[{"q1", ",", "q2", ",", "p"}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "(=RussianTrick[exp,p,p,{q1,q2,p}]) does the integration by parts where \ -p is the external momentum. RussianTrick[exp, k,l, {q1,q2,p}] \ -(=RussianTrick[exp,k,l]) does integration by parts where l is the momentum to \ -be differentiated.\n\nThe result is an expression which is vanishing." + " \[LineSeparator](=RussianTrick[exp,p,p,{q1,q2,p}]) does the \ +integration by parts where p is the external momentum. RussianTrick[exp, k,l, \ +{q1,q2,p}] (=RussianTrick[exp,k,l]) does integration by parts where l is the \ +momentum to be differentiated." }]]} }]], "Usage", GridBoxOptions->{ @@ -99,6 +134,41 @@ be differentiated.\n\nThe result is an expression which is vanishing." 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SD[i,j] is transformed into \ + " \[LineSeparator]denotes the SU(N) Kronecker delta with color indices i \ +and j in the adjoint represnetation. 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SD[i,j] is transformed into \ + "SD[i, j] denotes the SU(N) Kronecker delta with color indices i and j in \ +the adjoint represnetation. 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NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/SMP.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$239523], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/SMP", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,18 +95,28 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["SMP", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SMP", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ - RowBox[{"SMP", "[", "par", "]"}]], "InlineFormula"], - " \[LineSeparator]displays a symbol for the model parameter par. Typical \ -parameters are masses, coupling constants, mixing angles etc. Parameters that \ -are complex, like CKM matrix element, have an I as an additional parameter, \ -i.e. SMP[\\\"V_ud\\\",I] and SMP[\\\"V_ud\\\",-I]. SMP[] shows the list of \ -available parameters.\"" + RowBox[{"SMP", "[", "\"\\"", "]"}]], "InlineFormula"], + " \[LineSeparator]displays a symbol for the model parameter ", + Cell[BoxData["\"\\""], "InlineFormula"], + "." }]]} }]], "Usage", GridBoxOptions->{ @@ -95,6 +127,64 @@ available parameters.\"" Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->398927661], + +Cell["", "SectionHeaderSpacer"], + +Cell["\<\ +Typical parameters are masses, coupling constants, mixing angles etc. \ +\>", "Notes", + CellID->1067943069], + +Cell[TextData[{ + "Parameters that are complex, like CKM matrix element, have an ", + Cell[BoxData["I"], "InlineFormula"], + " as an additional argument, i.e. ", + Cell[BoxData[ + RowBox[{"SMP", "[", + RowBox[{"\"\\"", ",", "I"}], "]"}]], "InlineFormula"], + " and ", + Cell[BoxData[ + RowBox[{"SMP", "[", + RowBox[{"\"\\"", ",", + RowBox[{"-", "I"}]}], "]"}]], "InlineFormula"], + ". 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The option StringReplace can be used to \ +specify string replacement rules that will take care of characters (e.g. ^ or \ +_) that cannot appear in valid expressions. 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symbols \ +using ToExpression[\"sth\"]. The option StringReplace can be used to specify \ +string replacement rules that will take care of characters (e.g. ^or _) that \ +cannot appear in valid expressions. SMPToSymbol is useful when exporting \ +FeynCalc expressions to other tools, e.g. FORM.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "SMPToSymbol", "titlemodifier" -> "", + "windowtitle" -> "SMPToSymbol", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/SMPToSymbol"}, "SearchTextTranslated" -> ""}, +CellContext->"Global`", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->Notebook[{ + Cell[ + StyleData[ + StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], + Cell[ + StyleData["Input"], CellContext -> "Global`"], + Cell[ + StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", + StyleDefinitions -> "Default.nb"] +] +(* End of Notebook Content *) + +(* Internal cache information *) +(*CellTagsOutline +CellTagsIndex->{ + "PrimaryExamplesSection"->{ + Cell[6062, 188, 387, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->348954702]} + } +*) +(*CellTagsIndex +CellTagsIndex->{ + {"PrimaryExamplesSection", 10514, 347} + } +*) +(*NotebookFileOutline +Notebook[{ +Cell[583, 21, 3005, 74, 53, "AnchorBarGrid", + CellID->1], +Cell[3591, 97, 288, 11, 45, "ObjectNameGrid"], +Cell[CellGroupData[{ +Cell[3904, 112, 678, 15, 135, "Usage", + CellID->982511436], +Cell[CellGroupData[{ +Cell[4607, 131, 739, 24, 31, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1882068752], +Cell[5349, 157, 31, 0, 70, "SectionHeaderSpacer"], +Cell[CellGroupData[{ +Cell[5405, 161, 114, 3, 70, "Input", + CellID->1067943069], +Cell[5522, 166, 479, 15, 37, "Output", + CellID->602000371] +}, Open ]] +}, Closed]] +}, Open ]], +Cell[CellGroupData[{ +Cell[6062, 188, 387, 15, 31, "PrimaryExamplesSection", + CellTags->"PrimaryExamplesSection", + CellID->348954702], +Cell[CellGroupData[{ +Cell[6474, 207, 195, 6, 26, "ExampleSection", + CellID->646201416], +Cell[CellGroupData[{ +Cell[6694, 217, 185, 6, 29, "Input", + CellID->512390421], +Cell[6882, 225, 409, 16, 40, "Output", + CellID->320685510] +}, Open ]], +Cell[CellGroupData[{ +Cell[7328, 246, 108, 3, 27, "Input", + CellID->1934684273], +Cell[7439, 251, 402, 16, 39, "Output", + CellID->924611777] +}, Open ]] +}, Open ]], +Cell[7868, 271, 31, 0, 29, "SectionFooterSpacer"] +}, Open ]], +Cell[CellGroupData[{ +Cell[7936, 276, 270, 12, 31, "SeeAlsoSection", + CellID->1255426704], +Cell[8209, 290, 178, 5, 56, "SeeAlso", + CellID->1062507596] +}, Open ]], +Cell[8402, 298, 23, 0, 41, "FooterCell"] +} +] +*) + +(* End of internal cache information *) + diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SMVertex.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SMVertex.nb index 649558191..a5d8e38f5 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SMVertex.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SMVertex.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 11672, 395] -NotebookOptionsPosition[ 8336, 295] -NotebookOutlinePosition[ 10949, 366] -CellTagsIndexPosition[ 10837, 360] +NotebookDataLength[ 14554, 513] +NotebookOptionsPosition[ 10890, 401] +NotebookOutlinePosition[ 13197, 465] +CellTagsIndexPosition[ 13085, 459] WindowTitle->SMVertex WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/SMVertex\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/SMVertex"]}, Visible -> False]]; 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/SMVertex.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$139547], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/SMVertex", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; 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All momenta are flowing into \ -the vertex. SMVertex[\"HHH\", ___] give the three-higgs coupling. " + Cell[BoxData["SMVertex"], "InlineFormula"], + " \[LineSeparator]is a library of SM vertices. Currently it implements \ +only few vertices and is not really useful." }]]} }]], "Usage", GridBoxOptions->{ @@ -97,6 +125,57 @@ the vertex. SMVertex[\"HHH\", ___] give the three-higgs coupling. 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FormBox["\[Mu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["k", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "+", + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], "+", RowBox[{ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 57.855545}", + "built" -> "{2020, 1, 5, 19, 2, 2.767169}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "SMVertex[\"AWW\", p, mu, q, nu, k, rho] gives the photon-W-W vertex \ -(p,mu correspond to the photon, q,nu to the (incoming) W+ and k,rho to the \ -(incoming) W-. All momenta are flowing into the vertex. SMVertex[\"HHH\", \ -___] give the three-higgs coupling. ", "synonyms" -> {}, "title" -> - "SMVertex", "titlemodifier" -> "", "windowtitle" -> "SMVertex", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/SMVertex"}, "SearchTextTranslated" -> ""}, + "SMVertex is a library of SM vertices. Currently it implements only few \ +vertices and is not really useful.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "SMVertex", "titlemodifier" -> "", "windowtitle" -> "SMVertex", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/SMVertex"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -329,8 +434,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -339,64 +445,76 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 5.032287}", + "built" -> "{2020, 1, 5, 19, 2, 8.029871}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -282,11 +315,11 @@ TaggingRules->{ "None", "summary" -> "SO[q] is a four-dimensional scalar product of OPEDelta with q. It is \ transformed into Pair[Momentum[q], Momentum[OPEDelta] by FCI.", - "synonyms" -> {}, "title" -> "SO", "titlemodifier" -> "", "windowtitle" -> - "SO", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SO"}, - "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "SO", "titlemodifier" -> + "", "windowtitle" -> "SO", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/SO"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -295,7 +328,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -304,89 +337,77 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1608750131] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -168,12 +204,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{77, 17}, + ImageSize->{84, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SOD", - CellLabel->"Out[2]=", - CellID->1010314656] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -198,8 +233,7 @@ Cell[BoxData[ ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SOD", - CellLabel->"Out[3]//StandardForm=", - CellID->1393449003] + CellLabel->"Out[3]//StandardForm="] }, Open ]] }, Open ]], @@ -247,9 +281,7 @@ Cell[TextData[{ ButtonNote->"SOD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SOD", - CellID->1925156465] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -266,10 +298,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 0.515545}", + "built" -> "{2020, 1, 5, 19, 2, 4.666565}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -277,11 +309,11 @@ TaggingRules->{ "None", "summary" -> "SOD[q] is a D-dimensional scalar product of OPEDelta with q. 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CellID->1224892054], +Cell[TextData[{ + Cell["SP", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -115,7 +150,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1611303645], + CellID->1487555505], Cell[CellGroupData[{ @@ -125,7 +160,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->259486820], + CellID->1513609754], Cell[CellGroupData[{ @@ -164,12 +199,11 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{68, 20}, + ImageSize->{81, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SP", - CellLabel->"Out[1]=", - CellID->1148967332] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -190,13 +224,15 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -205,23 +241,24 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - RowBox[{"2", " ", + FormBox[ + RowBox[{ + RowBox[{"2", " ", + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"]}], "+", OverscriptBox[ - FormBox["p", - TraditionalForm], "_"]}], "+", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{133, 17}, + ImageSize->{151, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SP", - CellLabel->"Out[2]=", - CellID->53518921] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -267,12 +304,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm], "2"]}], TraditionalForm]], "Output", - ImageSize->{123, 20}, + ImageSize->{142, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SP", - CellLabel->"Out[3]=", - CellID->21872907] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -316,12 +352,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm], "2"]}], TraditionalForm]], "Output", - ImageSize->{136, 21}, + ImageSize->{154, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SP", - CellLabel->"Out[4]=", - CellID->988669305] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -337,12 +372,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"SP", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", - ImageSize->{68, 15}, + ImageSize->{70, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SP", - CellLabel->"Out[5]//StandardForm=", - CellID->591158186] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -362,12 +396,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"Momentum", "[", "a", "]"}], ",", RowBox[{"Momentum", "[", "b", "]"}]}], "]"}]], "Output", - ImageSize->{250, 15}, + ImageSize->{251, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SP", - CellLabel->"Out[6]//StandardForm=", - CellID->504879117] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -386,12 +419,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"SP", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", - ImageSize->{68, 15}, + ImageSize->{70, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SP", - CellLabel->"Out[7]//StandardForm=", - CellID->1698640474] + CellLabel->"Out[7]//StandardForm="] }, Open ]] }, Open ]], @@ -433,9 +465,7 @@ Cell[TextData[{ ButtonNote->"ScalarProduct"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SP", - CellID->468161499] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -443,7 +473,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 0}}, WindowTitle->"SP", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -452,10 +482,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 21.910512}", + "built" -> "{2020, 1, 5, 19, 2, 30.332486}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -463,11 +493,11 @@ TaggingRules->{ "None", "summary" -> "SP[a, b] denotes a four-dimensional scalar product. SP[a, b] is \ transformed into ScalarProduct[a, b] by FeynCalcInternal. SP[p] is the same \ -as SP[p, p] (= p^2).", "synonyms" -> {}, "title" -> "SP", "titlemodifier" -> - "", "windowtitle" -> "SP", "type" -> "Symbol", "uri" -> +as SP[p, p] (= p^2).", "synonyms" -> {}, "tabletags" -> {}, "title" -> "SP", + "titlemodifier" -> "", "windowtitle" -> "SP", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SP"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -476,7 +506,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -485,145 +515,125 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3546, 102, 388, 15, 31, "PrimaryExamplesSection", + Cell[4742, 137, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1611303645]}, + CellID->1487555505]}, "SP"->{ - Cell[4179, 131, 202, 7, 27, "Input", + Cell[5376, 166, 202, 7, 27, "Input", CellTags->"SP", CellID->1327327216], - Cell[4384, 140, 724, 31, 41, "Output", - CellTags->"SP", - CellID->1148967332], - Cell[5145, 176, 206, 8, 27, "Input", + Cell[5581, 175, 703, 30, 39, "Output", + CellTags->"SP"], + Cell[6321, 210, 206, 8, 27, "Input", CellTags->"SP", CellID->903181536], - Cell[5354, 186, 878, 37, 38, "Output", - CellTags->"SP", - CellID->53518921], - Cell[6269, 228, 252, 9, 27, "Input", + Cell[6530, 220, 946, 40, 37, "Output", + CellTags->"SP"], + Cell[7513, 265, 252, 9, 27, "Input", CellTags->"SP", CellID->1760867040], - Cell[6524, 239, 835, 35, 41, "Output", - CellTags->"SP", - CellID->21872907], - Cell[7396, 279, 186, 6, 27, "Input", + Cell[7768, 276, 816, 34, 39, "Output", + CellTags->"SP"], + Cell[8621, 315, 186, 6, 27, "Input", CellTags->"SP", CellID->1518821322], - Cell[7585, 287, 883, 36, 42, "Output", - CellTags->"SP", - CellID->988669305], - Cell[8505, 328, 175, 6, 27, "Input", + Cell[8810, 323, 863, 35, 39, "Output", + CellTags->"SP"], + Cell[9710, 363, 175, 6, 27, "Input", CellTags->"SP", CellID->1767436480], - Cell[8683, 336, 240, 8, 49, "Output", - CellTags->"SP", - CellID->591158186], - Cell[8960, 349, 205, 8, 27, "Input", + Cell[9888, 371, 220, 7, 51, "Output", + CellTags->"SP"], + Cell[10145, 383, 205, 8, 27, "Input", CellTags->"SP", CellID->736982087], - Cell[9168, 359, 315, 10, 49, "Output", - CellTags->"SP", - CellID->504879117], - Cell[9520, 374, 234, 9, 27, "Input", + Cell[10353, 393, 295, 9, 51, "Output", + CellTags->"SP"], + Cell[10685, 407, 234, 9, 70, "Input", CellTags->"SP", CellID->355867518], - Cell[9757, 385, 241, 8, 49, "Output", - CellTags->"SP", - CellID->1698640474], - Cell[10366, 416, 575, 21, 32, "Text", - CellTags->"SP", - CellID->468161499]} + Cell[10922, 418, 220, 7, 51, "Output", + CellTags->"SP"]} } *) (*CellTagsIndex CellTagsIndex->{ - 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{Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/SPC\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/SPC"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/SPC.html"], - StandardForm]], "Input", TextClipboardType -> "PlainText"]}, - Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$141594], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/SPC", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"ScalarProductCancel\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/ScalarProductCancel"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/SPC\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/SPC"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/SPC.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$243038], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/SPC", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["SPC", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SPC", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +144,7 @@ Cell[TextData[{ ButtonNote->"ScalarProductCancel"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SPC", - CellID->777067132] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,19 +161,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 6.525758}", + "built" -> "{2020, 1, 5, 19, 2, 9.173056}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "SPC is an abbreviation for ScalarProductCancel.", - "synonyms" -> {}, "title" -> "SPC", "titlemodifier" -> "", "windowtitle" -> - "SPC", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SPC"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "SPC", "titlemodifier" -> + "", "windowtitle" -> "SPC", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/SPC"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -152,41 +183,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "SPC"->{ - Cell[3512, 107, 255, 9, 70, "Text", - CellTags->"SPC", - CellID->777067132]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"SPC", 5507, 162} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[575, 21, 2238, 52, 70, "AnchorBarGrid", +Cell[575, 21, 3004, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2816, 75, 46, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2865, 78, 349, 11, 70, "Usage", +Cell[3582, 97, 280, 11, 70, "ObjectNameGrid"], +Cell[3865, 110, 349, 11, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3239, 93, 270, 12, 70, "SeeAlsoSection", +Cell[4239, 125, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3512, 107, 255, 9, 70, "Text", - CellTags->"SPC", - CellID->777067132] +Cell[4512, 139, 220, 7, 70, "SeeAlso"] }, Open ]], -Cell[3782, 119, 23, 0, 70, "FooterCell"] +Cell[4747, 149, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SPD.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SPD.nb index bc15ece41..f9bc7f9e7 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SPD.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SPD.nb @@ -3,69 +3,95 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 16991, 655] -NotebookOptionsPosition[ 11365, 461] -NotebookOutlinePosition[ 14929, 570] -CellTagsIndexPosition[ 14822, 564] +NotebookDataLength[ 17708, 664] +NotebookOptionsPosition[ 12505, 491] +NotebookOutlinePosition[ 15853, 590] +CellTagsIndexPosition[ 15746, 584] WindowTitle->SPD WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/SPD\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/SPD"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/SPD.html"], - StandardForm]], "Input", TextClipboardType -> "PlainText"]}, - Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$141947], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/SPD", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"PD\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/PD"], "\<\"Calc\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Calc"], "\<\"ExpandScalarProduct\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/ExpandScalarProduct"], "\<\"ScalarProduct\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/ScalarProduct"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/SPD\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/SPD"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/SPD.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$243489], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/SPD", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +99,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["SPD", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SPD", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -116,7 +152,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1090459362], + CellID->802463375], Cell[CellGroupData[{ @@ -126,7 +162,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->972663145], + CellID->1325491493], Cell[CellGroupData[{ @@ -162,12 +198,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], "2"], TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{65, 20}, + ImageSize->{75, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SPD", - CellLabel->"Out[1]=", - CellID->1537579140] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -188,11 +223,13 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - FormBox["p", - TraditionalForm], "-", - FormBox["q", - TraditionalForm]}], + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -201,21 +238,22 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - RowBox[{"2", " ", - FormBox["p", - TraditionalForm]}], "+", - FormBox["q", - TraditionalForm]}], + FormBox[ + RowBox[{ + RowBox[{"2", " ", + FormBox["p", + TraditionalForm]}], "+", + FormBox["q", + TraditionalForm]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{129, 17}, + ImageSize->{143, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SPD", - CellLabel->"Out[2]=", - CellID->1810693243] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -257,12 +295,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], TraditionalForm], "2"]}], TraditionalForm]], "Output", - ImageSize->{119, 20}, + ImageSize->{134, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SPD", - CellLabel->"Out[3]=", - CellID->533108024] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -302,12 +339,11 @@ Cell[BoxData[ FormBox["q", TraditionalForm], TraditionalForm], "2"]}], TraditionalForm]], "Output", - ImageSize->{131, 20}, + ImageSize->{146, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SPD", - CellLabel->"Out[4]=", - CellID->33170286] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -323,12 +359,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"SPD", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", - ImageSize->{76, 15}, + ImageSize->{78, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SPD", - CellLabel->"Out[5]//StandardForm=", - CellID->1457236269] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -350,12 +385,11 @@ Cell[BoxData[ RowBox[{"a", ",", "D"}], "]"}], ",", RowBox[{"Momentum", "[", RowBox[{"b", ",", "D"}], "]"}]}], "]"}]], "Output", - ImageSize->{296, 15}, + ImageSize->{297, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SPD", - CellLabel->"Out[6]//StandardForm=", - CellID->716068529] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -374,12 +408,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"SPD", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", - ImageSize->{76, 15}, + ImageSize->{78, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SPD", - CellLabel->"Out[7]//StandardForm=", - CellID->966232396] + CellLabel->"Out[7]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -399,12 +432,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"SPD", "[", RowBox[{"p", ",", "q"}], "]"}]], "Output", - ImageSize->{77, 15}, + ImageSize->{78, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SPD", - CellLabel->"Out[8]//StandardForm=", - CellID->1514523545] + CellLabel->"Out[8]//StandardForm="] }, Open ]] }, Open ]], @@ -452,17 +484,15 @@ Cell[TextData[{ ButtonNote->"ScalarProduct"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SPD", - CellID->1031641673] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"SPD", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -471,10 +501,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 7.745116}", + "built" -> "{2020, 1, 5, 19, 2, 10.302587}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -482,11 +512,11 @@ TaggingRules->{ "None", "summary" -> "SPD[a, b] denotes a D-dimensional scalar product. SPD[a, b] is \ transformed into ScalarProduct[a, b,Dimension->D] by FeynCalcInternal. SPD[p] \ -is the same as SPD[p,p] (= p^2).", "synonyms" -> {}, "title" -> "SPD", - "titlemodifier" -> "", "windowtitle" -> "SPD", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SPD"}, "SearchTextTranslated" -> ""}, +is the same as SPD[p,p] (= p^2).", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "SPD", "titlemodifier" -> "", "windowtitle" -> "SPD", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/SPD"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -494,8 +524,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -504,159 +535,137 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/SPL.html"], - StandardForm]], "Input", TextClipboardType -> "PlainText"]}, - Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$144735], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/SPL", - ".html"]], None}]}]}, 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StripOnInput->False], {"\<\"FeynCalc/ref/SPL\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/SPL"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/SPL.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$250257], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/SPL", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["SPL", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SPL", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +144,7 @@ Cell[TextData[{ ButtonNote->"SimplifyPolyLog"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SPL", - CellID->899844592] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,19 +161,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 20.564425}", + "built" -> "{2020, 1, 5, 19, 2, 29.202269}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "SPL is an abbreviation for SimplifyPolyLog.", - "synonyms" -> {}, "title" -> "SPL", "titlemodifier" -> "", "windowtitle" -> - "SPL", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SPL"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "SPL", "titlemodifier" -> + "", "windowtitle" -> "SPL", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/SPL"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -152,41 +183,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "SPL"->{ - Cell[3508, 107, 243, 9, 70, "Text", - CellTags->"SPL", - CellID->899844592]} 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a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUND.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUND.nb @@ -3,69 +3,94 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 19267, 743] -NotebookOptionsPosition[ 12835, 517] -NotebookOutlinePosition[ 16720, 639] -CellTagsIndexPosition[ 16612, 633] +NotebookDataLength[ 19316, 727] +NotebookOptionsPosition[ 13614, 533] +NotebookOutlinePosition[ 17097, 639] +CellTagsIndexPosition[ 16989, 633] WindowTitle->SUND WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", 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-249,12 +281,11 @@ Cell[BoxData[ TraditionalForm], FormBox["c", TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{42, 19}, + ImageSize->{49, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUND", - CellLabel->"Out[3]=", - CellID->1988918016] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -276,12 +307,11 @@ Cell[BoxData[ TraditionalForm], FormBox["b", TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{43, 19}, + ImageSize->{50, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUND", - CellLabel->"Out[4]=", - CellID->1040614065] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -305,12 +335,11 @@ Cell[BoxData[ RowBox[{"4", "-", SubsuperscriptBox["C", "A", "2"]}], ")"}], " ", SubscriptBox["C", "F"]}], TraditionalForm]], "Output", - ImageSize->{104, 21}, + ImageSize->{113, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUND", - CellLabel->"Out[5]=", 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"]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Input", CellTags->"SUNDelta", CellLabel->"In[1]:=", CellID->582133429], @@ -136,30 +176,69 @@ Cell[BoxData[ FormBox[ SuperscriptBox["\[Delta]", RowBox[{ - FormBox["a", + FormBox[ + FormBox["a", + TraditionalForm], TraditionalForm], - FormBox["b", + FormBox[ + FormBox["b", + TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{33, 19}, + ImageSize->{35, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNDelta", - CellLabel->"Out[1]=", - CellID->718384624] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Trick", "[", " ", + RowBox[{ + RowBox[{"SUNDelta", "[", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], + RowBox[{"SUNDelta", "[", + RowBox[{ + RowBox[{"SUNIndex", "[", "b", "]"}], ",", + RowBox[{"SUNIndex", "[", "c", "]"}]}], "]"}]}]], "Input", + CellLabel->"In[2]:="], + 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TraditionalForm]], "Output", - ImageSize->{32, 15}, + ImageSize->{34, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"SUNDelta", - CellLabel->"Out[2]=", - CellID->1779629564] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -189,7 +266,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Input", CellTags->"SUNDelta", - CellLabel->"In[3]:=", + CellLabel->"In[4]:=", CellID->2091383946], Cell[BoxData[ @@ -204,12 +281,11 @@ Cell[BoxData[ FormBox["b", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{33, 19}, + ImageSize->{35, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNDelta", - CellLabel->"Out[3]=", - CellID->791346519] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -217,45 +293,24 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], "//", "StandardForm"}]], "Input", - CellTags->"SUNDelta", - CellLabel->"In[4]:=", - CellID->2066302871], - -Cell[BoxData[ - RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}]], "Output", - ImageSize->{117, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"SUNDelta", - CellLabel->"Out[4]//StandardForm=", - CellID->1680727312] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], "//", "FCI"}], "//", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"SUNDelta", CellLabel->"In[5]:=", - CellID->76062746], + CellID->2066302871], Cell[BoxData[ RowBox[{"SUNDelta", "[", RowBox[{ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Output", - ImageSize->{277, 15}, + ImageSize->{280, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNDelta", - CellLabel->"Out[5]//StandardForm=", - CellID->1303706973] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -265,8 +320,10 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", - "StandardForm"}]], "Input", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], "//", "FCI"}], "//", + "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"SUNDelta", CellLabel->"In[6]:=", CellID->1106151471], @@ -274,12 +331,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"SD", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", - ImageSize->{68, 15}, + ImageSize->{70, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNDelta", - CellLabel->"Out[6]//StandardForm=", - CellID->1065622125] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -299,21 +355,19 @@ Cell[BoxData[ RowBox[{ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Output", - ImageSize->{277, 15}, + ImageSize->{280, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNDelta", - CellLabel->"Out[7]//StandardForm=", - CellID->708863202] + CellLabel->"Out[7]//StandardForm="] }, Open ]], Cell["\<\ -Symbolic arguments to SUNDelta are transformed into the data type SUNIndex \ -and integer arguments are transformed to ExplicitSUNIndex. The difference is \ -that SUNSimplify will only sum over symbolic indices.\ -\>", "Text", - CellTags->"SUNDelta", - CellID->1535277851], +The arguments of SUNDelta may also represent explicit integer indices via the \ +head ExplictiSUNIndex. The difference is that SUNSimplify will only sum over \ +symbolic indices.\ +\>", "Notes", + CellID->879136127], Cell[CellGroupData[{ @@ -321,11 +375,18 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "2"}], "]"}], + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"ExplicitSUNIndex", "[", "2", "]"}]}], "]"}], RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], RowBox[{"SUNDelta", "[", - RowBox[{"c", ",", "2"}], "]"}]}], "//", "SUNSimplify"}]], "Input", + RowBox[{ + RowBox[{"SUNIndex", "[", "c", "]"}], ",", + RowBox[{"ExplicitSUNIndex", "[", "2", "]"}]}], "]"}]}], "//", + "SUNSimplify"}]], "Input", CellTags->"SUNDelta", CellLabel->"In[8]:=", CellID->69005829], @@ -353,12 +414,11 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", - ImageSize->{62, 19}, + ImageSize->{64, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNDelta", - CellLabel->"Out[8]=", - CellID->1797928550] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -379,12 +439,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"ExplicitSUNIndex", "[", "2", "]"}], ",", RowBox[{"SUNIndex", "[", "c", "]"}]}], "]"}]}]], "Output", - ImageSize->{349, 33}, + ImageSize->{352, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNDelta", - CellLabel->"Out[9]//StandardForm=", - CellID->391311139] + CellLabel->"Out[9]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -392,7 +451,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ - RowBox[{"SUNDelta", "[", + RowBox[{"SD", "[", RowBox[{"1", ",", "2"}], "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SUNDelta", @@ -404,12 +463,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"ExplicitSUNIndex", "[", "1", "]"}], ",", RowBox[{"ExplicitSUNIndex", "[", "2", "]"}]}], "]"}]], "Output", - ImageSize->{405, 15}, + ImageSize->{406, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNDelta", - CellLabel->"Out[10]//StandardForm=", - CellID->432360453] + CellLabel->"Out[10]//StandardForm="] }, Open ]] }, Open ]], @@ -433,7 +491,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["ExplicitSUNIndex", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/ExplicitSUNIndex", @@ -470,17 +527,15 @@ Cell[TextData[{ ButtonNote->"Trick"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SUNDelta", - CellID->1124087961] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"SUNDelta", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -489,21 +544,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 32.603743}", + "built" -> "{2020, 1, 5, 19, 2, 42.435654}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "SUNDelta[a, b] is the Kronecker-delta for SU(N) with color indices a and \ -b.", "synonyms" -> {}, "title" -> "SUNDelta", "titlemodifier" -> "", - "windowtitle" -> "SUNDelta", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SUNDelta"}, "SearchTextTranslated" -> ""}, +b in the adjoint representation.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "SUNDelta", "titlemodifier" -> "", "windowtitle" -> "SUNDelta", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/SUNDelta"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -511,8 +567,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - 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It wraps \ +the head ", + ButtonBox["SUNIndex", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SUNIndex", + ButtonNote->"SUNIndex"], + " around its arguments." }]]} }]], "Usage", GridBoxOptions->{ GridBoxBackground->{ - "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, + "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {None, {None}}, "RowsIndexed" -> {}}}, - CellID->982511436], + CellID->455417684], + +Cell[CellGroupData[{ + +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->1517005805], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->238416033], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SUNDelta", "[", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], "^", "2"}]], "Input", + CellLabel->"In[1]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + RowBox[{"(", + SuperscriptBox["\[Delta]", + RowBox[{ + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]}]], ")"}], "2"], TraditionalForm]], "Output", + ImageSize->{55, 22}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[1]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNDeltaContract", "[", "%", "]"}]], "Input", + CellLabel->"In[2]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["N", "2"], "-", "1"}], TraditionalForm]], "Output", + ImageSize->{50, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[2]="] +}, Open ]] +}, Open ]], + +Cell["", "SectionFooterSpacer"] +}, Open ]], Cell[CellGroupData[{ @@ -125,17 +267,15 @@ Cell[TextData[{ ButtonNote->"SUNIndex"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SUNDeltaContract", - CellID->332681775] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{0, Automatic}, {Automatic, 0}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"SUNDeltaContract", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -144,24 +284,25 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 31.349483}", + "built" -> "{2020, 1, 5, 19, 2, 41.292880}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "SUNDeltaContract[expr] substitues for all SUNDelta in expr \ -SUNDeltaContract, contracts the SUN(N) indices and resubstitutes SUNDelta. \ -SUNDeltaContract[i, j] is the Kronecker-delta for SU(N) with contraction \ -properties. SUNDeltaContract wraps also the head SUNIndex around its \ -arguments.", "synonyms" -> {}, "title" -> "SUNDeltaContract", "titlemodifier" -> - "", "windowtitle" -> "SUNDeltaContract", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SUNDeltaContract"}}, + "SUNDeltaContract[exp] substitues for all SUNDelta in exp \ +SUNDeltaContract, contracts the adjoint SU (N) indices and resubstitutes \ +SUNDelta. SUNDeltaContract[i, j] is the Kronecker-delta for SU (N) in the \ +adjoint representation with contraction properties. It wraps the head \ +SUNIndex around its arguments.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "SUNDeltaContract", "titlemodifier" -> "", "windowtitle" -> + "SUNDeltaContract", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/SUNDeltaContract"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -169,8 +310,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -178,35 +320,51 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1766434801], Cell[BoxData[ @@ -180,20 +252,19 @@ Cell[BoxData[ TraditionalForm], FormBox["c", TraditionalForm]}]]}]}], TraditionalForm]], "Output", - ImageSize->{119, 19}, + ImageSize->{137, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNF", - CellLabel->"Out[2]=", - CellID->1741928660] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Calc", "[", "t1", "]"}]], "Input", + RowBox[{"Calc", "[", "%", "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->139383085], Cell[BoxData[ @@ -229,20 +300,19 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]}]]}]}], TraditionalForm]], "Output", - ImageSize->{119, 19}, + ImageSize->{137, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNF", - CellLabel->"Out[3]=", - CellID->1893375491] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - 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CellLabel->"In[9]:=", + CellLabel->"In[8]:=", CellID->963311023], Cell[BoxData[ @@ -508,12 +568,11 @@ Cell[BoxData[ TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{263, 25}, + ImageSize->{289, 22}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNF", - CellLabel->"Out[9]=", - CellID->215339899] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -524,18 +583,17 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "StandardForm"}]], "Input",\ CellTags->"SUNF", - CellLabel->"In[10]:=", + CellLabel->"In[9]:=", CellID->1003312113], Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Output", - ImageSize->{106, 15}, + ImageSize->{109, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNF", - CellLabel->"Out[10]//StandardForm=", - CellID->792790909] + CellLabel->"Out[9]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -547,7 +605,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SUNF", - CellLabel->"In[11]:=", + CellLabel->"In[10]:=", CellID->2081826967], Cell[BoxData[ @@ -556,12 +614,11 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}], ",", RowBox[{"SUNIndex", "[", "c", "]"}]}], "]"}]], "Output", - ImageSize->{346, 15}, + ImageSize->{352, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNF", - CellLabel->"Out[11]//StandardForm=", - CellID->1149570291] + CellLabel->"Out[10]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -574,18 +631,17 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"SUNF", - CellLabel->"In[12]:=", + CellLabel->"In[11]:=", CellID->1938677300], Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Output", - ImageSize->{106, 15}, + ImageSize->{109, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNF", - CellLabel->"Out[12]//StandardForm=", - CellID->1462891621] + CellLabel->"Out[11]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -594,7 +650,7 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"b", ",", "a", ",", "c"}], "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[13]:=", + CellLabel->"In[12]:=", CellID->334638901], Cell[BoxData[ @@ -607,12 +663,11 @@ Cell[BoxData[ TraditionalForm], FormBox["c", TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{42, 19}, + ImageSize->{48, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNF", - CellLabel->"Out[13]=", - CellID->532100486] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -622,7 +677,7 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"b", ",", "a", ",", "c"}], "]"}], "//", "FCI"}]], "Input", CellTags->"SUNF", - CellLabel->"In[14]:=", + CellLabel->"In[13]:=", CellID->1328454294], Cell[BoxData[ @@ -642,12 +697,11 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", - ImageSize->{52, 19}, + ImageSize->{59, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNF", - 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If \ +the argument is an integer, SUNIndex[a] turns into ExplicitSUNIndex[a]." }]]} }]], "Usage", GridBoxOptions->{ @@ -109,7 +143,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->2042176178], + CellID->205043259], Cell[CellGroupData[{ @@ -119,7 +153,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1593002537], + CellID->36840381], Cell[CellGroupData[{ @@ -131,12 +165,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["i", TraditionalForm]], "Output", - ImageSize->{9, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNIndex", - CellLabel->"Out[1]=", - CellID->969035127] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -153,8 +186,35 @@ Cell[BoxData[ ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNIndex", - CellLabel->"Out[2]//StandardForm=", - CellID->675650496] + CellLabel->"Out[2]//StandardForm="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNIndex", "[", "2", "]"}]], "Input", + CellLabel->"In[3]:="], + +Cell[BoxData[ + FormBox["2", TraditionalForm]], "Output", + ImageSize->{13, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[3]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "StandardForm"}]], "Input", + CellLabel->"In[4]:="], + +Cell[BoxData[ + RowBox[{"ExplicitSUNIndex", "[", "2", "]"}]], "Output", + ImageSize->{158, 15}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -166,7 +226,7 @@ Cell[BoxData[ RowBox[{"i", ",", "j"}], "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SUNIndex", - CellLabel->"In[3]:=", + CellLabel->"In[5]:=", CellID->874008605], Cell[BoxData[ @@ -174,12 +234,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"SUNIndex", "[", "i", "]"}], ",", RowBox[{"SUNIndex", "[", "j", "]"}]}], "]"}]], "Output", - ImageSize->{276, 15}, + ImageSize->{277, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNIndex", - CellLabel->"Out[3]//StandardForm=", - CellID->46597874] + CellLabel->"Out[5]//StandardForm="] }, Open ]] }, Open ]], @@ -203,7 +262,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["ExplicitSUNIndex", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/ExplicitSUNIndex", @@ -222,9 +280,7 @@ Cell[TextData[{ ButtonNote->"SUNF"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SUNIndex", - CellID->341377518] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -241,20 +297,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 39.102384}", + "built" -> "{2020, 1, 5, 19, 2, 53.205007}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> - "None", "summary" -> "SUNIndex is the head of SU(N) indices.", - "synonyms" -> {}, "title" -> "SUNIndex", "titlemodifier" -> "", - "windowtitle" -> "SUNIndex", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SUNIndex"}, "SearchTextTranslated" -> ""}, + "None", "summary" -> + "SUNIndex[a] is an SU(N) index in the adjoint representation. If the \ +argument is an integer, SUNIndex[a] turns into ExplicitSUNIndex[a].", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "SUNIndex", + "titlemodifier" -> "", "windowtitle" -> "SUNIndex", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/SUNIndex"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -263,7 +321,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -272,89 +330,85 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3302, 96, 388, 15, 31, "PrimaryExamplesSection", + Cell[4553, 130, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - 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If set to False, no \ -automatic renaming of dummy indices is done.", "synonyms" -> {}, "title" -> - "SUNIndexRename", "titlemodifier" -> "", "windowtitle" -> - "SUNIndexRename", "type" -> "Symbol", "uri" -> +automatic renaming of dummy indices is done.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "SUNIndexRename", "titlemodifier" -> "", + "windowtitle" -> "SUNIndexRename", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SUNIndexRename"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -162,41 +194,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "SUNIndexRename"->{ - Cell[3629, 108, 402, 15, 70, "Text", - CellTags->"SUNIndexRename", - CellID->1033928155]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"SUNIndexRename", 5900, 172} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[586, 21, 2270, 52, 70, "AnchorBarGrid", +Cell[586, 21, 3127, 76, 70, "AnchorBarGrid", CellID->1], -Cell[2859, 75, 57, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2919, 78, 412, 12, 70, "Usage", +Cell[3716, 99, 291, 11, 70, "ObjectNameGrid"], +Cell[4010, 112, 412, 12, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3356, 94, 270, 12, 70, "SeeAlsoSection", +Cell[4447, 128, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3629, 108, 402, 15, 70, "Text", - CellTags->"SUNIndexRename", - CellID->1033928155] +Cell[4720, 142, 355, 13, 70, "SeeAlso"] }, Open ]], -Cell[4046, 126, 23, 0, 70, "FooterCell"] +Cell[5090, 158, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUNN.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUNN.nb index 5185d4265..171292b2b 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUNN.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUNN.nb @@ -3,69 +3,97 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 8857, 303] -NotebookOptionsPosition[ 5810, 208] -NotebookOutlinePosition[ 8113, 274] -CellTagsIndexPosition[ 8007, 268] +NotebookDataLength[ 9998, 331] +NotebookOptionsPosition[ 7081, 243] +NotebookOutlinePosition[ 9322, 306] +CellTagsIndexPosition[ 9216, 300] WindowTitle->SUNN WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/SUNN\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/SUNN"]}, Visible -> False]]; 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/SUNN.\ +html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$259630], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/SUNN", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +101,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["SUNN", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SUNN", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -110,7 +148,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->399101034], + CellID->933193033], Cell[CellGroupData[{ @@ -120,7 +158,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->308163258], + CellID->394912443], Cell[CellGroupData[{ @@ -140,12 +178,11 @@ Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["N", "2"], "-", "1"}], TraditionalForm]], "Output", - ImageSize->{49, 18}, + ImageSize->{50, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNN", - CellLabel->"Out[1]=", - CellID->94438752] + CellLabel->"Out[1]="] }, Open ]] }, Open ]], @@ -199,9 +236,7 @@ Cell[TextData[{ ButtonNote->"CF"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SUNN", - CellID->1642067263] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -209,7 +244,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"SUNN", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -218,21 +253,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 41.927557}", + "built" -> "{2020, 1, 5, 19, 2, 55.647684}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "SUNN denotes the number of colors. Trick[SUNDelta[a, a]] yields (SUNN^2 \ --1).", "synonyms" -> {}, "title" -> "SUNN", "titlemodifier" -> "", - "windowtitle" -> "SUNN", "type" -> "Symbol", "uri" -> +-1).", "synonyms" -> {}, "tabletags" -> {}, "title" -> "SUNN", + "titlemodifier" -> "", "windowtitle" -> "SUNN", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SUNN"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -240,8 +275,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -250,61 +286,53 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3354, 97, 387, 15, 31, "PrimaryExamplesSection", + Cell[4681, 135, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->399101034]}, + CellID->933193033]}, "SUNN"->{ - Cell[3986, 126, 335, 10, 27, "Input", + Cell[5313, 164, 335, 10, 27, "Input", CellTags->"SUNN", CellID->1968246895], - Cell[4324, 138, 252, 9, 39, "Output", - CellTags->"SUNN", - CellID->94438752], - Cell[4944, 170, 824, 33, 32, "Text", - CellTags->"SUNN", - CellID->1642067263]} + Cell[5651, 176, 233, 8, 37, "Output", + CellTags->"SUNN"]} } *) (*CellTagsIndex CellTagsIndex->{ - {"PrimaryExamplesSection", 7601, 251}, - {"SUNN", 7731, 255} + {"PrimaryExamplesSection", 8914, 287}, + {"SUNN", 9045, 291} } *) (*NotebookFileOutline Notebook[{ -Cell[576, 21, 2229, 52, 51, "AnchorBarGrid", +Cell[576, 21, 3322, 80, 53, "AnchorBarGrid", CellID->1], -Cell[2808, 75, 47, 1, 42, "ObjectName", - CellID->1224892054], -Cell[2858, 78, 471, 15, 85, "Usage", +Cell[3901, 103, 281, 11, 45, "ObjectNameGrid"], +Cell[4185, 116, 471, 15, 87, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3354, 97, 387, 15, 31, "PrimaryExamplesSection", +Cell[4681, 135, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->399101034], + CellID->933193033], Cell[CellGroupData[{ -Cell[3766, 116, 195, 6, 25, "ExampleSection", - CellID->308163258], +Cell[5093, 154, 195, 6, 26, "ExampleSection", + CellID->394912443], Cell[CellGroupData[{ -Cell[3986, 126, 335, 10, 27, "Input", +Cell[5313, 164, 335, 10, 27, "Input", CellTags->"SUNN", CellID->1968246895], -Cell[4324, 138, 252, 9, 39, "Output", - CellTags->"SUNN", - CellID->94438752] +Cell[5651, 176, 233, 8, 37, "Output", + CellTags->"SUNN"] }, Open ]] }, Open ]], -Cell[4603, 151, 31, 0, 29, "SectionFooterSpacer"] +Cell[5911, 188, 31, 0, 29, "SectionFooterSpacer"] }, Open ]], Cell[CellGroupData[{ -Cell[4671, 156, 270, 12, 31, "SeeAlsoSection", +Cell[5979, 193, 270, 12, 31, "SeeAlsoSection", CellID->1255426704], -Cell[4944, 170, 824, 33, 32, "Text", - CellTags->"SUNN", - CellID->1642067263] +Cell[6252, 207, 787, 31, 56, "SeeAlso"] }, Open ]], -Cell[5783, 206, 23, 0, 42, "FooterCell"] +Cell[7054, 241, 23, 0, 41, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUNNToCACF.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUNNToCACF.nb index c8790c1ad..17f62da39 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUNNToCACF.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SUNNToCACF.nb @@ -3,69 +3,98 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 9259, 308] -NotebookOptionsPosition[ 6053, 212] -NotebookOutlinePosition[ 8494, 279] -CellTagsIndexPosition[ 8382, 273] +NotebookDataLength[ 10474, 337] +NotebookOptionsPosition[ 7411, 248] +NotebookOutlinePosition[ 9783, 312] +CellTagsIndexPosition[ 9671, 306] WindowTitle->SUNNToCACF WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/SUNNToCACF\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/SUNNToCACF"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/SUNNToCACF.\ -html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$149941], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/SUNNToCACF", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"CalcColorFactor\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/CalcColorFactor"], "\<\"SUNSimplify\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SUNSimplify"], "\<\"Trick\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/Trick"], "\<\"SUNN\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SUNN"], "\<\"CA\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CA"], "\<\"CF\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/CF"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/SUNNToCACF\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/SUNNToCACF"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ +SUNNToCACF.html"], StandardForm]], "Input", TextClipboardType -> + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$260072], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/SUNNToCACF", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +102,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["SUNNToCACF", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SUNNToCACF", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +146,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->2135442738], + CellID->1706728932], Cell[CellGroupData[{ @@ -117,7 +156,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1201189711], + CellID->1367742659], Cell[CellGroupData[{ @@ -138,12 +177,11 @@ Cell[BoxData[ RowBox[{"2", " ", SubscriptBox["C", "A"], " ", SubscriptBox["C", "F"]}], TraditionalForm]], "Output", - ImageSize->{57, 15}, + ImageSize->{65, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNNToCACF", - CellLabel->"Out[1]=", - CellID->573481763] + CellLabel->"Out[1]="] }, Open ]] }, Open ]], @@ -203,9 +241,7 @@ Cell[TextData[{ ButtonNote->"CF"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SUNNToCACF", - CellID->124208571] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -213,7 +249,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"SUNNToCACF", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -222,10 +258,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 43.402920}", + "built" -> "{2020, 1, 5, 19, 2, 56.662835}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -233,11 +269,11 @@ TaggingRules->{ "None", "summary" -> "SUNNToCACF is an option of SUNSimplify and CalcColorFactor. If set to \ True, the Casimir operator eigenvalues CA (=N) and CF (=(N^2-1)/(2 N)) are \ -introduced.", "synonyms" -> {}, "title" -> "SUNNToCACF", "titlemodifier" -> - "", "windowtitle" -> "SUNNToCACF", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SUNNToCACF"}, "SearchTextTranslated" -> ""}, +introduced.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "SUNNToCACF", + "titlemodifier" -> "", "windowtitle" -> "SUNNToCACF", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/SUNNToCACF"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -245,8 +281,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 29}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -255,61 +292,53 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3379, 94, 388, 15, 31, "PrimaryExamplesSection", + Cell[4799, 133, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->2135442738]}, + CellID->1706728932]}, "SUNNToCACF"->{ - Cell[4013, 123, 340, 10, 27, "Input", + Cell[5433, 162, 340, 10, 27, "Input", CellTags->"SUNNToCACF", CellID->1879564079], - Cell[4356, 135, 290, 10, 36, "Output", - CellTags->"SUNNToCACF", - CellID->573481763], - Cell[5014, 168, 997, 39, 32, "Text", - CellTags->"SUNNToCACF", - CellID->124208571]} + Cell[5776, 174, 270, 9, 37, "Output", + CellTags->"SUNNToCACF"]} } *) (*CellTagsIndex CellTagsIndex->{ - {"PrimaryExamplesSection", 7950, 256}, - {"SUNNToCACF", 8087, 260} + {"PrimaryExamplesSection", 9350, 293}, + {"SUNNToCACF", 9488, 297} } *) (*NotebookFileOutline Notebook[{ -Cell[582, 21, 2253, 52, 51, "AnchorBarGrid", +Cell[582, 21, 3439, 81, 53, "AnchorBarGrid", CellID->1], -Cell[2838, 75, 53, 1, 42, "ObjectName", - CellID->1224892054], -Cell[2894, 78, 460, 12, 99, "Usage", +Cell[4024, 104, 287, 11, 45, "ObjectNameGrid"], +Cell[4314, 117, 460, 12, 102, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3379, 94, 388, 15, 31, "PrimaryExamplesSection", +Cell[4799, 133, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - 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CellID->1224892054], +Cell[TextData[{ + Cell["SUNSimplify", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ - Cell[BoxData["SUNSimplify"], "InlineFormula"], - " \[LineSeparator]", - "simplifies products of SUNT (and complex conjugated) matrices. 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Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->70223274], + CellGroupingRules->{"SectionGrouping", 50}, + CellID->2137365557], -Cell[CellGroupData[{ - 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RowBox[{"t1", "=", - RowBox[{ - RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], " ", - RowBox[{"SUNDelta", "[", - RowBox[{"b", ",", "c"}], "]"}]}]}]], "Input", + RowBox[{ + RowBox[{"SUNDelta", "[", + RowBox[{"a", ",", "b"}], "]"}], " ", + RowBox[{"SUNDelta", "[", + RowBox[{"b", ",", "c"}], "]"}]}]], "Input", CellTags->"SUNSimplify", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1698138274], Cell[BoxData[ @@ -178,20 +240,19 @@ Cell[BoxData[ TraditionalForm], FormBox["c", TraditionalForm]}]]}], TraditionalForm]], "Output", - ImageSize->{64, 19}, + ImageSize->{69, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNSimplify", - CellLabel->"Out[2]=", - CellID->1129385138] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SUNSimplify", "[", "t1", "]"}]], "Input", + RowBox[{"SUNSimplify", "[", "%", "]"}]], "Input", CellTags->"SUNSimplify", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1520473065], Cell[BoxData[ @@ -206,23 +267,27 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - ImageSize->{32, 15}, + ImageSize->{34, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNSimplify", - CellLabel->"Out[3]=", - CellID->1288692360] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", "=", - RowBox[{ - RowBox[{"SUNT", "[", "a", "]"}], ".", - RowBox[{"SUNT", "[", "a", "]"}]}]}]], "Input", + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SUNT", "[", "a", "]"}], ".", + RowBox[{"SUNT", "[", "a", "]"}]}]], "Input", CellTags->"SUNSimplify", - CellLabel->"In[4]:=", + CellLabel->"In[1]:=", CellID->1992995975], Cell[BoxData[ @@ -234,42 +299,41 @@ Cell[BoxData[ SuperscriptBox["T", FormBox["a", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{48, 15}, + ImageSize->{55, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNSimplify", - CellLabel->"Out[4]=", - CellID->1292635919] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SUNSimplify", "[", "t2", "]"}]], "Input", + RowBox[{"SUNSimplify", "[", "%", "]"}]], "Input", CellTags->"SUNSimplify", - CellLabel->"In[5]:=", + CellLabel->"In[2]:=", CellID->1767152339], Cell[BoxData[ FormBox[ SubscriptBox["C", "F"], TraditionalForm]], "Output", - ImageSize->{24, 15}, + ImageSize->{26, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNSimplify", - CellLabel->"Out[5]=", - CellID->2143185906] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SUNSimplify", "[", - RowBox[{"t2", ",", + RowBox[{ + RowBox[{ + RowBox[{"SUNT", "[", "a", "]"}], ".", + RowBox[{"SUNT", "[", "a", "]"}]}], ",", RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}]], "Input", - CellTags->"SUNSimplify", - CellLabel->"In[6]:=", - CellID->671897568], + CellLabel->"In[3]:="], Cell[BoxData[ FormBox[ @@ -277,25 +341,29 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["N", "2"], "-", "1"}], RowBox[{"2", " ", "N"}]], TraditionalForm]], "Output", - 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CellID->1224892054], +Cell[TextData[{ + Cell["SUNT", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ RowBox[{"SUNT", "[", "a", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the SU(", + " \[LineSeparator]is the SU(", StyleBox["N", FontSlant->"Italic"], ") ", Cell[BoxData[ FormBox[ - SubscriptBox["T", "a"], TraditionalForm]]], - " generator in the fundamental representation." + SuperscriptBox["T", "a"], TraditionalForm]]], + " generator in the fundamental representation. The fundamental indices \ +are implicit." }]]} }]], "Usage", GridBoxOptions->{ @@ -114,7 +153,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->683323705], + CellID->6159029], Cell[CellGroupData[{ @@ -124,7 +163,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1568727464], + CellID->1899326785], Cell[CellGroupData[{ @@ -139,12 +178,11 @@ Cell[BoxData[ SuperscriptBox["T", FormBox["a", TraditionalForm]], TraditionalForm]], "Output", - ImageSize->{24, 15}, + ImageSize->{27, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[1]=", - CellID->1672661577] + CellLabel->"Out[1]="] }, Open ]], Cell[TextData[{ @@ -153,9 +191,7 @@ Cell[TextData[{ FormBox[ SubscriptBox["T", "a"], TraditionalForm]]], " is a noncommutative object, products have to separated by a dot (.)." -}], "Text", - CellTags->"SUNT", - CellID->1160812067], +}], "Notes"], Cell[CellGroupData[{ @@ -180,12 +216,11 @@ Cell[BoxData[ SuperscriptBox["T", FormBox["c", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{71, 19}, + ImageSize->{84, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[2]=", - CellID->818227996] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -201,31 +236,22 @@ Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["T", - FormBox[ - FormBox["a", - TraditionalForm], + FormBox["a", TraditionalForm]], ".", SuperscriptBox["T", - FormBox[ - FormBox["b", - TraditionalForm], + FormBox["b", TraditionalForm]], ".", SuperscriptBox["T", - FormBox[ - FormBox["c", - TraditionalForm], + FormBox["c", TraditionalForm]], ".", SuperscriptBox["T", - FormBox[ - FormBox["d", - TraditionalForm], + FormBox["d", TraditionalForm]]}], TraditionalForm]], "Output", - ImageSize->{95, 19}, + ImageSize->{114, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[3]=", - CellID->583778930] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -250,12 +276,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], RowBox[{"2", " ", "N"}]]}], TraditionalForm]], "Output", - ImageSize->{45, 46}, + ImageSize->{46, 39}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[4]=", - CellID->471863997] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -271,12 +296,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ SubsuperscriptBox["C", "F", "2"], TraditionalForm]], "Output", - ImageSize->{24, 20}, + ImageSize->{26, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[5]=", - CellID->1224364730] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -304,12 +328,11 @@ Cell[BoxData[ SubscriptBox["C", "A"], "-", RowBox[{"2", " ", SubscriptBox["C", "F"]}]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{130, 41}, + ImageSize->{144, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[6]=", - CellID->207267640] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -334,12 +357,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], RowBox[{"2", " ", "N"}]]}], TraditionalForm]], "Output", - ImageSize->{45, 46}, + ImageSize->{46, 39}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[7]=", - CellID->1434438138] + CellLabel->"Out[7]="] }, Open ]], Cell[TextData[{ @@ -356,9 +378,7 @@ Cell[TextData[{ RowBox[{"1", "/", "2"}], " ", RowBox[{ SubscriptBox["\[Delta]", "ab"], "."}]}]}], TraditionalForm]]] -}], "Text", - CellTags->"SUNT", - CellID->871639479], +}], "Notes"], Cell[CellGroupData[{ @@ -383,12 +403,11 @@ Cell[BoxData[ FormBox["b", TraditionalForm], TraditionalForm]}]], "2"], TraditionalForm]], "Output", - ImageSize->{38, 46}, + ImageSize->{39, 39}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[8]=", - CellID->1733460108] + CellLabel->"Out[8]="] }, Open ]], Cell[TextData[{ @@ -397,9 +416,7 @@ Cell[TextData[{ FormBox[ SubscriptBox["T", "f"], TraditionalForm]]], ", you need to include a factor 2Tf inside the trace." -}], "Text", - CellTags->"SUNT", - CellID->2043701440], +}], "Notes"], Cell[CellGroupData[{ @@ -426,12 +443,11 @@ Cell[BoxData[ FormBox["b", TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", - ImageSize->{53, 22}, + ImageSize->{57, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[9]=", - CellID->1858177206] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -452,12 +468,11 @@ Cell[BoxData[ RowBox[{ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]}]], "Output", - ImageSize->{295, 39}, + ImageSize->{297, 33}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - CellLabel->"Out[10]//StandardForm=", - CellID->1917924836] + CellLabel->"Out[10]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -474,12 +489,11 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"SUNT", "[", RowBox[{"SUNIndex", "[", "a", "]"}], "]"}]], "Output", - ImageSize->{142, 15}, + ImageSize->{144, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SUNT", - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$130635], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$225430], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/ScalarGluonVertex", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,20 @@ ScalarGluonVertex.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["ScalarGluonVertex", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["ScalarGluonVertex", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -84,20 +97,106 @@ Cell[BoxData[GridBox[{ RowBox[{"{", "p", "}"}], ",", " ", RowBox[{"{", "q", "}"}], ",", " ", RowBox[{"{", - RowBox[{"mu", ",", "a"}], "}"}]}], "]"}]], "InlineFormula"], - " \n\tor ScalarGluonVertex[ p, q, mu, a ] yields the \ -scalar-scalar-gluon vertex (p and q are incoming momenta). \ -ScalarGluonVertex[{mu,a}, {nu,b}] yields the scalar-scalar-gluon-gluon vertex \ -(p and q are incoming momenta).\n\tThe dimension and the name of the \ -coupling constant are determined by the options Dimension and \ -CouplingConstant." + RowBox[{"\[Mu]", ",", "a"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]or ", + Cell[BoxData[ + RowBox[{"ScalarGluonVertex", "[", + RowBox[{"p", ",", " ", "q", ",", " ", "\[Mu]", ",", " ", "a"}], + "]"}]], "InlineFormula"], + " yields the scalar-scalar-gluon vertex, where ", + Cell[BoxData["p"], "InlineFormula"], + " and ", + Cell[BoxData["q"], "InlineFormula"], + " are incoming momenta." + }]]}, + {"", Cell[TextData[{ + Cell[BoxData[ + RowBox[{"ScalarGluonVertex", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"\[Mu]", ",", "a"}], "}"}], ",", + RowBox[{"{", + RowBox[{"\[Nu]", ",", "b"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]yields the scalar-scalar-gluon-gluon vertex, where ", + Cell[BoxData["p"], "InlineFormula"], + " and ", + Cell[BoxData["q"], "InlineFormula"], + " are incoming momenta. syntax." }]]} }]], "Usage", GridBoxOptions->{ GridBoxBackground->{ - "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, + "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {None, {None}}, "RowsIndexed" -> {}}}, - CellID->982511436], + CellID->2010081510], + +Cell[CellGroupData[{ + +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->2080976489], + +Cell["", "SectionHeaderSpacer"], + +Cell[TextData[{ + "The dimension and the name of the coupling constant are determined by the \ +options ", + ButtonBox["Dimension", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/Dimension", + ButtonNote->"Dimension"], + " and ", + ButtonBox["CouplingConstant", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/CouplingConstant", + ButtonNote->"CouplingConstant"], + ". " +}], "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "ScalarGluonVertex", "]"}]], "Input", + CellLabel->"In[55]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Gauge", "\[Rule]", "1"}]}], "}"}], TraditionalForm]], "Output", + ImageSize->{334, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[55]="] +}, Open ]] +}, Closed]] +}, Open ]], Cell[CellGroupData[{ @@ -116,7 +215,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1584676055], + CellID->2037554269], Cell[CellGroupData[{ @@ -126,31 +225,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1754245303], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "ScalarGluonVertex", "]"}]], "Input", - CellTags->"ScalarGluonVertex", - CellLabel->"In[1]:=", - CellID->1577288725], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"CouplingConstant", "\[Rule]", - SubscriptBox["g", "s"]}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"Gauge", "\[Rule]", "1"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{351, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"ScalarGluonVertex", - CellLabel->"Out[1]=", - CellID->1150833543] -}, Open ]], + CellID->1269130457], Cell[CellGroupData[{ @@ -160,9 +235,9 @@ Cell[BoxData[ RowBox[{"{", "p", "}"}], ",", " ", RowBox[{"{", "q", "}"}], ",", " ", RowBox[{"{", - RowBox[{"mu", ",", " ", "a"}], "}"}]}], "]"}]], "Input", + RowBox[{"\[Mu]", ",", " ", "a"}], "}"}]}], "]"}]], "Input", CellTags->"ScalarGluonVertex", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->581447761], Cell[BoxData[ @@ -174,31 +249,24 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], " ", SubscriptBox["g", "s"], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - FormBox["p", - TraditionalForm], "-", - FormBox["q", - TraditionalForm]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{122, 17}, + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + ImageSize->{123, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"ScalarGluonVertex", - CellLabel->"Out[2]=", - CellID->260312021] + CellLabel->"Out[1]="] }, Open ]] }, Open ]] }, Open ]], @@ -217,25 +285,25 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 16.807308}", + "built" -> "{2020, 1, 5, 19, 1, 25.264443}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "ScalarGluonVertex[{p}, {q}, {mu, a}] or ScalarGluonVertex[p, q, mu, a ] \ -yields the scalar-scalar-gluon vertex (p and q are incoming momenta). \ -ScalarGluonVertex[{mu,a}, {nu,b}] yields the scalar-scalar-gluon-gluon vertex \ -(p and q are incoming momenta). The dimension and the name of the coupling \ -constant are determined by the options Dimension and CouplingConstant.", - "synonyms" -> {}, "title" -> "ScalarGluonVertex", "titlemodifier" -> "", - "windowtitle" -> "ScalarGluonVertex", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/ScalarGluonVertex"}, "SearchTextTranslated" -> ""}, + "ScalarGluonVertex[{p}, {q}, {\\[Mu], a}] or ScalarGluonVertex[p, q, \ +\\[Mu], a] yields the scalar-scalar-gluon vertex, where p and q are incoming \ +momenta. ScalarGluonVertex[{\\[Mu], a}, {\\[Nu], b}] yields the \ +scalar-scalar-gluon-gluon vertex, where p and q are incoming momenta. \ +syntax.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "ScalarGluonVertex", + "titlemodifier" -> "", "windowtitle" -> "ScalarGluonVertex", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/ScalarGluonVertex"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -244,7 +312,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -253,64 +321,61 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellLabel->"Out[8]=", - CellID->1856511612] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -481,12 +562,11 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], "+", FractionBox["s", "2"]}], TraditionalForm]], "Output", - ImageSize->{180, 39}, + ImageSize->{208, 31}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"ScalarProduct", - CellLabel->"Out[9]=", - CellID->1175433176] + CellLabel->"Out[9]="] }, Open ]], Cell[BoxData[ @@ -516,7 +596,6 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", StyleBox[ButtonBox["Calc", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/Calc", @@ -559,9 +638,7 @@ Cell[TextData[{ ButtonNote->"SPD"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"ScalarProduct", - CellID->912859437] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -569,7 +646,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"ScalarProduct", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -578,27 +655,29 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 22.280347}", + "built" -> "{2020, 1, 5, 19, 1, 27.743003}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "ScalarProduct[p, q] is the input for scalar product. ScalarProduct[p] is \ -equivalent to ScalarProduct[p, p]. Expansion of sums of momenta in \ -ScalarProduct is done with ExpandScalarProduct. Scalar product may be set, \ -e.g., ScalarProduct[a, b] = m^2; but a and b must not contain sums. Note that \ -ScalarProduct[a, b] = m^2 actually sets also: Pair[Momentum[a, ___], \ -Momentum[b, ___]] = m^2. It is encouraged to always set ScalarProduct's \ -before any calculation. This improves the performance of FeynCalc .", - "synonyms" -> {}, "title" -> "ScalarProduct", "titlemodifier" -> "", - "windowtitle" -> "ScalarProduct", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/ScalarProduct"}, "SearchTextTranslated" -> ""}, + "ScalarProduct[p, q] is the input for the scalar product of two Lorentz \ +vectors p and q. ScalarProduct[p] is equivalent to ScalarProduct[p, p]. \ +Expansion of sums of momenta in ScalarProduct is done with \ +ExpandScalarProduct. Scalar products may be set, e.g. via ScalarProduct[a, b] \ += m^2; but a and b may not contain sums. Note that ScalarProduct[a, b] = m^2 \ +actually sets Lorentzian scalar products in different dimensions specified by \ +the value of the SetDimensions option. It is highly recommended to set \ +ScalarProduct's before any calculation. This improves the performance of \ +FeynCalc..", "synonyms" -> {}, "tabletags" -> {}, "title" -> "ScalarProduct", + "titlemodifier" -> "", "windowtitle" -> "ScalarProduct", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/ScalarProduct"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -606,8 +685,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -616,179 +696,167 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["SelectFree", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -82,10 +115,9 @@ Cell[BoxData[GridBox[{ RowBox[{"SelectFree", "[", RowBox[{"expr", ",", " ", "a", ",", " ", "b", ",", " ", "..."}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is equivalent to Select[expr, FreeQ2[#, {a,b, ...}]&], except the \ -special cases: SelectFree[a, b] returns a and SelectFree[a,a] returns 1 \ -(where a is not a product or a sum).\n\nSelectFree is equivalent to Select1." + " \[LineSeparator]is equivalent to Select[expr, FreeQ2[#, {a,b, ...}]&], \ +except the special cases: SelectFree[a, b] returns a and SelectFree[a,a] \ +returns 1 (where a is not a product or a sum)." }]]} }]], "Usage", GridBoxOptions->{ @@ -111,7 +143,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->620692154], + CellID->1387947054], Cell[CellGroupData[{ @@ -121,7 +153,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->840314898], + CellID->276496415], Cell[CellGroupData[{ @@ -137,12 +169,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{"b", "+", "d"}], TraditionalForm]], "Output", - ImageSize->{38, 15}, + ImageSize->{44, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectFree", - CellLabel->"Out[1]=", - CellID->818540084] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -157,12 +188,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["y", TraditionalForm]], "Output", - ImageSize->{13, 15}, + ImageSize->{16, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectFree", - CellLabel->"Out[2]=", - CellID->1323839729] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -181,12 +211,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{"2", " ", "z"}], TraditionalForm]], "Output", - ImageSize->{24, 15}, + ImageSize->{26, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectFree", - CellLabel->"Out[3]=", - CellID->912675516] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -200,12 +229,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["a", TraditionalForm]], "Output", - ImageSize->{13, 15}, + ImageSize->{14, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectFree", - CellLabel->"Out[4]=", - CellID->1001842240] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -219,12 +247,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{11, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectFree", - CellLabel->"Out[5]=", - CellID->1438478141] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -238,12 +265,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{11, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectFree", - CellLabel->"Out[6]=", - CellID->1251533165] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +284,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{11, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectFree", - CellLabel->"Out[7]=", - CellID->1673614830] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -299,9 +324,7 @@ Cell[TextData[{ ButtonNote->"SelectNotFree"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SelectFree", - CellID->1096848115] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -318,10 +341,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 30.896890}", + "built" -> "{2020, 1, 5, 19, 1, 33.327293}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -329,12 +352,12 @@ TaggingRules->{ "None", "summary" -> "SelectFree[expr, a, b, ...] is equivalent to Select[expr, FreeQ2[#, \ {a,b, ...}]&], except the special cases: SelectFree[a, b] returns a and \ -SelectFree[a,a] returns 1 (where a is not a product or a sum). SelectFree is \ -equivalent to Select1.", "synonyms" -> {}, "title" -> "SelectFree", +SelectFree[a,a] returns 1 (where a is not a product or a sum).", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "SelectFree", "titlemodifier" -> "", "windowtitle" -> "SelectFree", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SelectFree"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -342,8 +365,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -352,145 +376,125 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellTags->"SelectFree", - CellID->1096848115] +Cell[8571, 313, 355, 13, 56, "SeeAlso"] }, Open ]], -Cell[8093, 306, 23, 0, 42, "FooterCell"] +Cell[8941, 329, 23, 0, 41, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SelectGraphs.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SelectGraphs.nb index 5ad3f2ccf..8945ce266 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SelectGraphs.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SelectGraphs.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 6819, 197] -NotebookOptionsPosition[ 4222, 126] -NotebookOutlinePosition[ 6554, 186] -CellTagsIndexPosition[ 6480, 181] +NotebookDataLength[ 7553, 217] +NotebookOptionsPosition[ 5172, 156] +NotebookOutlinePosition[ 7346, 209] +CellTagsIndexPosition[ 7303, 206] WindowTitle->SelectGraphs WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/SelectGraphs\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/SelectGraphs"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"OneLoopSum\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/OneLoopSum"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/SelectGraphs\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/SelectGraphs"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ SelectGraphs.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$134073], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/SelectGraphs", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$228960], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/SelectGraphs", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ SelectGraphs.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["SelectGraphs", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SelectGraphs", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -117,9 +149,7 @@ Cell[TextData[{ ButtonNote->"OneLoopSum"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SelectGraphs", - CellID->1262985927] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -136,10 +166,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 32.391359}", + "built" -> "{2020, 1, 5, 19, 1, 34.410470}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -151,11 +181,11 @@ Possible settings are: SelectGraphs\\[RightArrow]{ i, j, ... } or \ SelectGraphs\\[RightArrow]{ a, {b, c}, ... } which indicates the graphs to be \ taken from the list provided to OneLoopSum. In the second setting the list \ {b, c} indicates that all amplitudes from b to c should be taken.", - "synonyms" -> {}, "title" -> "SelectGraphs", "titlemodifier" -> "", - "windowtitle" -> "SelectGraphs", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SelectGraphs"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "SelectGraphs", + "titlemodifier" -> "", "windowtitle" -> "SelectGraphs", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/SelectGraphs"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -164,41 +194,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "SelectGraphs"->{ - Cell[3942, 112, 238, 9, 70, "Text", - CellTags->"SelectGraphs", - CellID->1262985927]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"SelectGraphs", 6365, 174} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[584, 21, 2262, 52, 70, "AnchorBarGrid", +Cell[584, 21, 3023, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2849, 75, 55, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2907, 78, 737, 16, 70, "Usage", +Cell[3610, 97, 289, 11, 70, "ObjectNameGrid"], +Cell[3902, 110, 737, 16, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3669, 98, 270, 12, 70, "SeeAlsoSection", +Cell[4664, 130, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3942, 112, 238, 9, 70, "Text", - CellTags->"SelectGraphs", - CellID->1262985927] +Cell[4937, 144, 193, 7, 70, "SeeAlso"] }, Open ]], -Cell[4195, 124, 23, 0, 70, "FooterCell"] +Cell[5145, 154, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SelectNotFree.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SelectNotFree.nb index 56029d7b4..e1cb04bab 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/SelectNotFree.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/SelectNotFree.nb @@ -3,69 +3,92 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 14064, 494] -NotebookOptionsPosition[ 8308, 311] -NotebookOutlinePosition[ 12048, 417] -CellTagsIndexPosition[ 11931, 411] +NotebookDataLength[ 15584, 547] +NotebookOptionsPosition[ 10172, 376] +NotebookOutlinePosition[ 13484, 470] +CellTagsIndexPosition[ 13367, 464] WindowTitle->SelectNotFree WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/SelectNotFree\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/SelectNotFree"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FreeQ2\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FreeQ2"], "\<\"SelectFree\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/SelectFree"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/SelectNotFree\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/SelectNotFree"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ SelectNotFree.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$134418], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/SelectNotFree", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$229405], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/SelectNotFree", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,19 +96,31 @@ SelectNotFree.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["SelectNotFree", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SelectNotFree", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ RowBox[{"SelectNotFree", "[", RowBox[{"expr", ",", " ", "x"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "returns that part of expr which is not free of any occurance of x.\n\n\ -SelectNotFree[expr, a, b, ...] is equivalent to Select[expr, !FreeQ2[#, {a, \ -b, ...}]&], except the special cases: SelectNotFree[a, b] returns 1 and \ -SelectNotFree[a, a] returns a (where a is not a product or a sum)." + " \[LineSeparator]returns that part of ", + Cell[BoxData["expr"], "InlineFormula"], + " which is not free of any occurance of ", + Cell[BoxData["x"], "InlineFormula"], + "." }]]} }]], "Usage", GridBoxOptions->{ @@ -96,6 +131,45 @@ SelectNotFree[a, a] returns a (where a is not a product or a sum)." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->645962762], + +Cell["", "SectionHeaderSpacer"], + +Cell["\<\ +SelectNotFree[expr, a, b, ...] is equivalent to Select[expr, !FreeQ2[#, {a, \ +b, ...}]&], except the special cases: SelectNotFree[a, b] returns 1 and \ +SelectNotFree[a, a] returns a (where a is not a product or a sum).\ +\>", "Notes", + CellID->1067943069] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -111,7 +185,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->473327242], + CellID->1930666558], Cell[CellGroupData[{ @@ -121,7 +195,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1904091965], + CellID->654434760], Cell[CellGroupData[{ @@ -138,12 +212,11 @@ Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"f", "(", "a", ")"}], "+", "a"}], TraditionalForm]], "Output", - ImageSize->{59, 15}, + ImageSize->{63, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectNotFree", - CellLabel->"Out[1]=", - CellID->879726471] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -163,12 +236,11 @@ Cell[BoxData[ FormBox[ RowBox[{"x", " ", "y", " ", RowBox[{"f", "(", "x", ")"}]}], TraditionalForm]], "Output", - ImageSize->{59, 15}, + ImageSize->{67, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectNotFree", - CellLabel->"Out[2]=", - CellID->1461838958] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -182,12 +254,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{11, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectNotFree", - CellLabel->"Out[3]=", - CellID->1791356409] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -202,12 +273,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectNotFree", - CellLabel->"Out[4]=", - CellID->209254169] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -221,12 +291,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["a", TraditionalForm]], "Output", - ImageSize->{13, 15}, + ImageSize->{14, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectNotFree", - CellLabel->"Out[5]=", - CellID->412334803] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -240,12 +309,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", - ImageSize->{11, 15}, + ImageSize->{11, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectNotFree", - CellLabel->"Out[6]=", - CellID->1168169225] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -261,12 +329,11 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ RowBox[{"f", "(", "x", ")"}], TraditionalForm]], "Output", - ImageSize->{35, 15}, + ImageSize->{38, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectNotFree", - CellLabel->"Out[7]=", - CellID->2104713784] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -302,9 +369,7 @@ Cell[TextData[{ ButtonNote->"SelectFree"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SelectNotFree", - CellID->1049407209] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -312,7 +377,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"SelectNotFree", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -321,25 +386,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 33.853869}", + "built" -> "{2020, 1, 5, 19, 1, 35.406203}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "SelectNotFree[expr, x] returns that part of expr which is not free of \ -any occurance of x. 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$134757], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$229845], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/SelectSplit", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ SelectSplit.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["SelectSplit", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SelectSplit", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -110,7 +121,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1947745496], + CellID->1354756641], Cell[CellGroupData[{ @@ -120,7 +131,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1740210034], + CellID->221507416], Cell[CellGroupData[{ @@ -171,12 +182,11 @@ Cell[BoxData[ SuperscriptBox["d", "5"], ",", SuperscriptBox["e", "6"]}], "}"}]}], "}"}], TraditionalForm]], "Output",\ - ImageSize->{262, 21}, + ImageSize->{275, 22}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectSplit", - CellLabel->"Out[1]=", - CellID->559959953] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -220,12 +230,11 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"f", "+", "g"}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{255, 21}, + ImageSize->{270, 22}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SelectSplit", - CellLabel->"Out[2]=", - CellID->2002061756] + CellLabel->"Out[2]="] }, Open ]] }, Open ]] }, Open ]], @@ -244,10 +253,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 35.605973}", + "built" -> "{2020, 1, 5, 19, 1, 36.542062}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -256,11 +265,11 @@ TaggingRules->{ "SelectSplit[l, p] constructs list of mutually exclusive subsets from l \ in which every element li satisfies a criterium pj[li] with pj from p and \ appends the subset of remaining unmatched elements.", "synonyms" -> {}, - "title" -> "SelectSplit", "titlemodifier" -> "", "windowtitle" -> - "SelectSplit", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SelectSplit"}, - "SearchTextTranslated" -> ""}, + "tabletags" -> {}, "title" -> "SelectSplit", "titlemodifier" -> "", + "windowtitle" -> "SelectSplit", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/SelectSplit"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -269,7 +278,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -278,64 +287,59 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[3487, 97, 388, 15, 31, "PrimaryExamplesSection", + Cell[3749, 108, 388, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1947745496]}, + CellID->1354756641]}, "SelectSplit"->{ - Cell[4121, 126, 822, 27, 51, "Input", + Cell[4382, 137, 822, 27, 53, "Input", CellTags->"SelectSplit", CellID->1220131740], - Cell[4946, 155, 637, 23, 42, "Output", - CellTags->"SelectSplit", - CellID->559959953], - Cell[5620, 183, 669, 22, 51, "Input", + Cell[5207, 166, 617, 22, 43, "Output", + CellTags->"SelectSplit"], + Cell[5861, 193, 669, 22, 53, "Input", CellTags->"SelectSplit", CellID->292281216], - Cell[6292, 207, 601, 20, 42, "Output", - CellTags->"SelectSplit", - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$135091], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$230275], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/Series2", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Series2", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Series2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -97,39 +110,40 @@ e, n] is equivalent to Series2[f, {e, 0, n}]." 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ImageSize->{172, 45}, + ImageSize->{177, 38}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Series2", - CellLabel->"Out[5]=", - CellID->503684567] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -299,7 +339,7 @@ Cell[BoxData[ RowBox[{"FinalSubstitutions", "\[Rule]", RowBox[{"{", "}"}]}]}], "]"}], "//", "FullSimplify"}]], "Input", CellTags->"Series2", - CellLabel->"In[6]:=", + CellLabel->"In[5]:=", CellID->31680807], Cell[BoxData[ @@ -333,12 +373,11 @@ Cell[BoxData[ TagBox["\[DoubledGamma]", Function[{}, EulerGamma]], "2"], " ", "x"}], "+", FractionBox["6", "x"]}], ")"}]}], TraditionalForm]], "Output", - ImageSize->{443, 43}, + ImageSize->{454, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Series2", - CellLabel->"Out[6]=", - CellID->607384212] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -358,7 +397,7 @@ Cell[BoxData[ "}"}]}], "]"}], "//", "Normal"}], "//", "Expand"}], "//", "FullSimplify"}]], "Input", CellTags->"Series2", - 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CellLabel->"In[10]:=", + CellLabel->"In[9]:=", CellID->1986693903], Cell[BoxData[ @@ -539,12 +573,11 @@ Cell[BoxData[ RowBox[{"2", " ", TagBox["\[CurlyEpsilon]", TraditionalForm]}], "+", "1"}],"x"}, "Hypergeometric2F1"], TraditionalForm]], "Output", - ImageSize->{133, 15}, + ImageSize->{133, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Series2", - CellLabel->"Out[10]=", - CellID->444344105] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -553,7 +586,7 @@ Cell[BoxData[ RowBox[{"Series2", "[", RowBox[{"%", ",", "Epsilon", ",", "3"}], "]"}]], "Input", CellTags->"Series2", - CellLabel->"In[11]:=", + CellLabel->"In[10]:=", CellID->180283674], Cell[BoxData[ @@ -661,12 +694,11 @@ Cell[BoxData[ TraditionalForm], "3"], " ", TemplateBox[{"3"}, "Zeta"]}], "+", "1"}], TraditionalForm]], "Output", - ImageSize->{471, 136}, + ImageSize->{481, 122}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Series2", - CellLabel->"Out[11]=", - CellID->1006368312] + CellLabel->"Out[10]="] }, Open ]], Cell[TextData[{ @@ -679,9 +711,7 @@ Cell[TextData[{ SubscriptBox["F", "1"]}]}], TraditionalForm]]], " tabulated in Series2.m. The interested user can consult the source code \ (search for HYPERLIST)." -}], "Text", - CellTags->"Series2", - CellID->1023055054] +}], "Notes"] }, Open ]] }, Open ]], @@ -690,7 +720,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"Series2", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -699,10 +729,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 37.140927}", + "built" -> "{2020, 1, 5, 19, 1, 37.652259}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -712,11 +742,11 @@ TaggingRules->{ Gamma-bug in Mathematica versions smaller than 5.0) equivalent to Series, \ except that it applies Normal on the result and has an option \ FinalSubstitutions. Series2[f, e, n] is equivalent to Series2[f, {e, 0, n}].", - "synonyms" -> {}, "title" -> "Series2", "titlemodifier" -> "", - "windowtitle" -> "Series2", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/Series2"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "Series2", + "titlemodifier" -> "", "windowtitle" -> "Series2", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/Series2"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -725,7 +755,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -733,203 +763,178 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["Series3", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -93,32 +127,33 @@ fixed. 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CellTags->"SimplifyDeltaFunction", - CellID->2042613065] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -505,7 +525,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"SimplifyDeltaFunction", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -514,10 +534,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 43.543399}", + "built" -> "{2020, 1, 5, 19, 1, 46.629198}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -526,12 +546,12 @@ TaggingRules->{ "SimplifyDeltaFunction[exp, x] simplifies f[x]*DeltaFunction[1-x] \ toLimit[f[x],x->1] DeltaFunction[1-x] and applies a list of transformation \ rules for DeltaFunctionPrime[1-x]*x^(OPEm-1)*f[x] where x^(OPEm-1) is \ -suppressed in exp.", "synonyms" -> {}, "title" -> "SimplifyDeltaFunction", - 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}], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +99,18 @@ SmallVariable.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["SmallVariable", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SmallVariable", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -127,9 +163,7 @@ Cell[TextData[{ ButtonNote->"PropagatorDenominator"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SmallVariable", - CellID->172314915] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -146,10 +180,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 52.324126}", + "built" -> "{2020, 1, 5, 19, 1, 58.444344}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -158,11 +192,11 @@ TaggingRules->{ "SmallVariable[me] is the head of small (negligible) variables. This \ means any mass with this head can be neglected if it appears in a sum, but \ not as an argument of Passarino-Veltman (PaVe) functions or \ -PropagatorDenominator.", "synonyms" -> {}, "title" -> "SmallVariable", - "titlemodifier" -> "", "windowtitle" -> "SmallVariable", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/SmallVariable"}}, +PropagatorDenominator.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "SmallVariable", "titlemodifier" -> "", "windowtitle" -> "SmallVariable", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/SmallVariable"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -171,41 +205,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["SmallVariables", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -114,9 +146,7 @@ Cell[TextData[{ ButtonNote->"OneLoop"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SmallVariables", - CellID->922771173] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -133,10 +163,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 53.737963}", + "built" -> "{2020, 1, 5, 19, 1, 59.430370}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -144,11 +174,12 @@ TaggingRules->{ "None", "summary" -> "SmallVariables is an option for OneLoop. \"SmallVariables->{Melectron}\" \ i.e. will substitute \"SmallVariable[Melectron]\" for all Melectron's in the \ -calculation.", "synonyms" -> {}, "title" -> "SmallVariables", "titlemodifier" -> - 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BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", - "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 56.600918}", - "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", - "keywords" -> {}, "specialkeywords" -> {}, - "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> - "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> - "None", "summary" -> "Smu is ...", "synonyms" -> {}, "title" -> "Smu", - "titlemodifier" -> "", "windowtitle" -> "Smu", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/Smu"}}, -CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", -StyleDefinitions->Notebook[{ - Cell[ - StyleData[ - StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], - Cell[ - StyleData["Input"], CellContext -> "Global`"], - Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$139879], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$240837], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/Sn", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["Sn", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Sn", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -114,19 +125,19 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 24, 59.310534}", + "built" -> "{2020, 1, 5, 19, 2, 3.846771}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "Sn is \\[Pi] n/2/(2 \\[Pi]) n.", "synonyms" -> {}, - "title" -> "Sn", "titlemodifier" -> "", "windowtitle" -> "Sn", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/Sn"}}, + "tabletags" -> {}, "title" -> "Sn", "titlemodifier" -> "", "windowtitle" -> + "Sn", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Sn"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -135,7 +146,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -149,13 +160,12 @@ CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[574, 21, 2234, 52, 70, "AnchorBarGrid", +Cell[574, 21, 2262, 53, 70, "AnchorBarGrid", CellID->1], -Cell[2811, 75, 45, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2859, 78, 598, 22, 70, "Usage", +Cell[2839, 76, 279, 11, 70, "ObjectNameGrid"], +Cell[3121, 89, 598, 22, 70, "Usage", CellID->982511436], -Cell[3460, 102, 23, 0, 70, "FooterCell"] +Cell[3722, 113, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Solve2.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Solve2.nb index bf68c51c6..3fbe2fff5 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Solve2.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Solve2.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 13722, 486] -NotebookOptionsPosition[ 8735, 323] -NotebookOutlinePosition[ 12149, 422] -CellTagsIndexPosition[ 12039, 416] +NotebookDataLength[ 14532, 516] +NotebookOptionsPosition[ 9695, 361] +NotebookOutlinePosition[ 12893, 452] +CellTagsIndexPosition[ 12783, 446] WindowTitle->Solve2 WindowFrame->Normal*) @@ -59,12 +59,13 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$140570], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$241722], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/Solve2", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Solve2", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Solve2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -95,32 +108,33 @@ Solve." 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CellLabel->"Out[3]=", - CellID->1865369573] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -223,7 +264,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"y", "\[Rule]", "h"}], "}"}]}]}], "]"}]], "Input", CellTags->"Solve2", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->455409208], Cell[BoxData[ @@ -231,12 +272,11 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{"-", "h"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{68, 15}, + ImageSize->{69, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Solve2", - CellLabel->"Out[4]=", - CellID->1227314769] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -256,7 +296,7 @@ Cell[BoxData[ RowBox[{"x", ",", "y"}], "}"}], ",", RowBox[{"Factoring", "\[Rule]", "Expand"}]}], "]"}]], "Input", CellTags->"Solve2", - CellLabel->"In[5]:=", + CellLabel->"In[4]:=", CellID->881839558], Cell[BoxData[ @@ -269,12 +309,11 @@ Cell[BoxData[ FractionBox["w", "4"]}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"d", "+", "p"}]}]}], "}"}], TraditionalForm]], "Output", - 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Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 2.033976}", + "built" -> "{2020, 1, 5, 19, 2, 5.771678}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -346,11 +384,11 @@ TaggingRules->{ equations (and returns just a list) and accepts the options Factoring and \ FinalSubstitutions. Solve2 uses the \"high school algorithm\" and factors \ intermediate results. 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$140906], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$242154], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/Solve3", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Solve3", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Solve3", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -93,6 +106,63 @@ sometimes better than Solve for systems involving rational polyonomials." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1639737478], + +Cell["", "SectionHeaderSpacer"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Solve3", "]"}]], "Input", + CellTags->"Solve3", + CellLabel->"In[26]:=", + CellID->1333669928], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "False"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"ParallelMap", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + ImageSize->{508, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellTags->"Solve3", + CellLabel->"Out[26]="] +}, Open ]] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -108,7 +178,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1651359721], + CellID->999196841], Cell[CellGroupData[{ @@ -118,32 +188,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1038726886], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "Solve3", "]"}]], "Input", - CellTags->"Solve3", - CellLabel->"In[1]:=", - CellID->1333669928], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Factoring", "\[Rule]", "False"}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"ParallelMap", "\[Rule]", "False"}]}], "}"}], - TraditionalForm]], "Output", - ImageSize->{427, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Solve3", - CellLabel->"Out[1]=", - CellID->1579913582] -}, Open ]], + CellID->1198337696], Cell[CellGroupData[{ @@ -161,7 +206,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellTags->"Solve3", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1175774569], Cell[BoxData[ @@ -176,12 +221,11 @@ Cell[BoxData[ RowBox[{"2", " ", "b"}], "-", "w"}], ")"}]}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"d", "+", "p"}]}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{201, 41}, + ImageSize->{212, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Solve3", - CellLabel->"Out[2]=", - CellID->158619342] + CellLabel->"Out[1]="] }, Open ]] }, Open ]] }, Open ]], @@ -200,10 +244,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 3.529024}", + "built" -> "{2020, 1, 5, 19, 2, 6.944816}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -212,11 +256,11 @@ TaggingRules->{ "Solve3 is equivalent to Solve, except that it works only for linear \ equations (and returns just a list) and uses the \"high school algorithm\" \ and is sometimes better than Solve for systems involving rational \ -polyonomials.", "synonyms" -> {}, "title" -> "Solve3", "titlemodifier" -> "", - "windowtitle" -> "Solve3", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/Solve3"}, "SearchTextTranslated" -> ""}, +polyonomials.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "Solve3", + "titlemodifier" -> "", "windowtitle" -> "Solve3", "type" -> "Symbol", + "uri" -> "FeynCalc/ref/Solve3"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -225,7 +269,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -233,65 +277,68 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["SpinPolarizationSum", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -113,9 +145,7 @@ Cell[TextData[{ ButtonNote->"FermionSpinSum"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SpinPolarizationSum", - CellID->2085782463] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -132,18 +162,18 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 17.145632}", + "built" -> "{2019, 3, 29, 17, 53, 53.180042}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "SpinPolarizationSum is an option for FermionSpinSum. The set (pure) \ -function acts on the usual spin sum.", "synonyms" -> {}, "title" -> - "SpinPolarizationSum", "titlemodifier" -> "", "windowtitle" -> +function acts on the usual spin sum.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "SpinPolarizationSum", "titlemodifier" -> "", "windowtitle" -> "SpinPolarizationSum", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SpinPolarizationSum"}}, CellContext->"Global`", @@ -163,34 +193,24 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "SpinPolarizationSum"->{ - Cell[3655, 108, 257, 9, 70, "Text", - CellTags->"SpinPolarizationSum", - CellID->2085782463]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"SpinPolarizationSum", 5802, 166} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[591, 21, 2290, 52, 70, "AnchorBarGrid", +Cell[591, 21, 3059, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2884, 75, 62, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2949, 78, 408, 12, 70, "Usage", +Cell[3653, 97, 296, 11, 70, "ObjectNameGrid"], +Cell[3952, 110, 408, 12, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3382, 94, 270, 12, 70, "SeeAlsoSection", +Cell[4385, 126, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3655, 108, 257, 9, 70, "Text", - CellTags->"SpinPolarizationSum", - CellID->2085782463] +Cell[4658, 140, 205, 7, 70, "SeeAlso"] }, Open ]], -Cell[3927, 120, 23, 0, 70, "FooterCell"] +Cell[4878, 150, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Spinor.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Spinor.nb index f19823225..68ff1f44c 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Spinor.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Spinor.nb @@ -3,69 +3,101 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 18982, 695] -NotebookOptionsPosition[ 12288, 477] -NotebookOutlinePosition[ 16635, 601] -CellTagsIndexPosition[ 16525, 595] +NotebookDataLength[ 20282, 755] +NotebookOptionsPosition[ 14563, 567] +NotebookOutlinePosition[ 17787, 663] +CellTagsIndexPosition[ 17677, 657] WindowTitle->Spinor WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/Spinor\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/Spinor"]}, Visible -> False]]; 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/Spinor.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$142301], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/Spinor", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; 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SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$247537], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/SpinorU", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,17 +108,35 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["SpinorU", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SpinorU", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData[ RowBox[{"SpinorU", "[", - RowBox[{"p", ",", " ", "m", ",", " ", "optarg"}], "]"}]], - "InlineFormula"], - " \[LineSeparator]", - "denotes a u-spinor." + RowBox[{"p", ",", " ", "m"}], "]"}]], "InlineFormula"], + " \[LineSeparator]denotes a ", + Cell[BoxData[ + FormBox[ + RowBox[{"u", + RowBox[{"(", + RowBox[{"p", ",", "m"}], ")"}]}], TraditionalForm]], "InlineFormula"], + "-spinor that depends on the ", + Cell[BoxData["4"], "InlineFormula"], + "-dimensional momentum ", + Cell[BoxData["p"], "InlineFormula"], + ". " }]]} }]], "Usage", GridBoxOptions->{ @@ -109,7 +162,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1436075671], + CellID->322452496], Cell[CellGroupData[{ @@ -119,137 +172,133 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1237662649], + CellID->2037298074], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorU", "[", "p", "]"}]], "Input", + RowBox[{"SpinorU", "[", + RowBox[{"p", ",", "m"}], "]"}]], "Input", CellTags->"SpinorU", CellLabel->"In[1]:=", CellID->1066488732], Cell[BoxData[ FormBox[ - RowBox[{ - FormBox["\<\"u\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], + RowBox[{"u", "(", FormBox["p", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{45, 17}, + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}], TraditionalForm]], "Output", + ImageSize->{63, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SpinorU", - CellLabel->"Out[1]=", - CellID->1004842359] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorU", "[", - RowBox[{"p", ",", "m"}], "]"}]], "Input", - CellTags->"SpinorU", + RowBox[{ + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", CellLabel->"In[2]:=", - CellID->1219506664], + CellID->2060242592], Cell[BoxData[ - FormBox[ + RowBox[{"Spinor", "[", RowBox[{ - FormBox["\<\"u\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox["p", - TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], TraditionalForm]], "Output", - ImageSize->{69, 17}, + RowBox[{"Momentum", "[", "p", "]"}], ",", "m", ",", "1"}], "]"}]], "Output",\ + + ImageSize->{205, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"SpinorU", - CellLabel->"Out[2]=", - CellID->1525867517] + CellLabel->"Out[2]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - 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RowBox[{"Momentum", "[", "p", "]"}], ",", "m", ",", "1"}], "]"}]], "Output",\ + RowBox[{"Momentum", "[", "p", "]"}], ",", "0", ",", "1"}], "]"}]], "Output",\ - ImageSize->{206, 15}, + ImageSize->{203, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"SpinorU", - CellLabel->"Out[4]//StandardForm=", - CellID->1261590967] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"SpinorU", "[", - RowBox[{"p", ",", "m"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", - "StandardForm"}]], "Input", - CellTags->"SpinorU", + RowBox[{"GS", "[", "p", "]"}], ".", + RowBox[{"SpinorU", "[", "p", "]"}]}]], "Input", CellLabel->"In[5]:=", - CellID->1260012205], + CellID->19834725], Cell[BoxData[ - RowBox[{"Spinor", "[", + FormBox[ RowBox[{ - RowBox[{"Momentum", "[", "p", "]"}], ",", "m", ",", "1"}], "]"}]], "Output",\ + RowBox[{"(", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", + RowBox[{"u", "(", + FormBox["p", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", + ImageSize->{90, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[5]="] +}, Open ]], - ImageSize->{206, 15}, +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracEquation", "[", "%", "]"}]], "Input", + CellLabel->"In[6]:=", + CellID->1275256319], + +Cell[BoxData[ + FormBox["0", TraditionalForm]], "Output", + ImageSize->{13, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"SpinorU", - CellLabel->"Out[5]//StandardForm=", - CellID->220809349] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -296,10 +345,32 @@ Cell[TextData[{ ButtonData->"paclet:FeynCalc/ref/SpinorVBar", ButtonNote->"SpinorVBar"], FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["SpinorUBarD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SpinorUBarD", + ButtonNote->"SpinorUBarD"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["SpinorUD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SpinorUD", + ButtonNote->"SpinorUD"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["SpinorVD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SpinorVD", + ButtonNote->"SpinorVD"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["SpinorVBarD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SpinorVBarD", + ButtonNote->"SpinorVBarD"], + FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SpinorU", - CellID->844883429] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -307,7 +378,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"SpinorU", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -316,20 +387,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 12.449124}", + "built" -> "{2020, 1, 5, 19, 2, 21.608256}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> - "None", "summary" -> "SpinorU[p, m, optarg] denotes a u-spinor.", - "synonyms" -> {}, "title" -> "SpinorU", "titlemodifier" -> "", - "windowtitle" -> "SpinorU", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SpinorU"}, "SearchTextTranslated" -> ""}, + "None", "summary" -> + "SpinorU[p, m] denotes a u (p, m)-spinor that depends on the \ +4-dimensional momentum p. ", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "SpinorU", "titlemodifier" -> "", "windowtitle" -> "SpinorU", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/SpinorU"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -337,8 +410,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{418, Automatic}, {Automatic, -8}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -347,117 +421,85 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline 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ButtonData->"paclet:FeynCalc/ref/SpinorVBarD", + ButtonNote->"SpinorVBarD"], + FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SpinorUBar", - CellID->350873739] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"SpinorUBar", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -311,21 +390,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 10.940056}", + "built" -> "{2020, 1, 5, 19, 2, 19.156613}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "SpinorUBar[p, m] denotes a OverscriptBox[u, _]-spinor.", - "synonyms" -> {}, "title" -> "SpinorUBar", "titlemodifier" -> "", - "windowtitle" -> "SpinorUBar", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SpinorUBar"}, "SearchTextTranslated" -> ""}, + "SpinorUBar[p, m] denotes a OverscriptBox[u, _](p, m)-spinor that depends \ +on the 4-dimensional momentum p.", "synonyms" -> {}, "tabletags" -> {}, + "title" -> "SpinorUBar", "titlemodifier" -> "", "windowtitle" -> + "SpinorUBar", "type" -> "Symbol", "uri" -> "FeynCalc/ref/SpinorUBar"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 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CellTags->"SpinorV", - CellLabel->"Out[5]//StandardForm=", - CellID->1429391488] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -298,10 +346,33 @@ Cell[TextData[{ ButtonData->"paclet:FeynCalc/ref/SpinorVBar", ButtonNote->"SpinorVBar"], FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["SpinorUBarD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SpinorUBarD", + ButtonNote->"SpinorUBarD"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["SpinorUD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SpinorUD", + ButtonNote->"SpinorUD"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["SpinorVD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SpinorVD", + ButtonNote->"SpinorVD"], + FontFamily->"Verdana"], + ", ", + StyleBox[ButtonBox["SpinorVBarD", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/SpinorVBarD", + ButtonNote->"SpinorVBarD"], + FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SpinorV", - CellID->1898482478] +}], "SeeAlso", + CellID->694651819] }, Open ]], Cell[" ", "FooterCell"] @@ -318,20 +389,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 15.611388}", + "built" -> "{2020, 1, 5, 19, 2, 26.503755}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> - "None", "summary" -> "SpinorV[p, m, optarg] denotes a v-spinor.", - "synonyms" -> {}, "title" -> "SpinorV", "titlemodifier" -> "", - "windowtitle" -> "SpinorV", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/SpinorV"}, "SearchTextTranslated" -> ""}, + "None", "summary" -> + "SpinorV[p, m] denotes a v (p, m)-spinor that depends on the \ +4-dimensional momentum p. ", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "SpinorV", "titlemodifier" -> "", "windowtitle" -> "SpinorV", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/SpinorV"}, "SearchTextTranslated" -> + ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -339,8 +412,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -349,117 +423,86 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellLabel->"Out[7]=", - CellID->454708211] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -370,17 +396,15 @@ Cell[TextData[{ ButtonNote->"SumT"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SumP", - CellID->1699670739] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"SumP", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -389,21 +413,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - 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False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$146457], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/SumS", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"SumP\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SumP"], "\<\"SumT\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/SumT"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/SumS\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/SumS"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/SumS.\ +html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$253789], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/SumS", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +96,20 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["SumS", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SumS", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -147,6 +182,58 @@ n] is Sum[Sign[r]^k/k^Abs[r] Sign[s]^j/j^Abs[s], {k, 1, n}, {j, 1, k}] etc." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1742453114], + +Cell["", "SectionHeaderSpacer"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "SumS", "]"}]], "Input", + CellTags->"SumS", + CellLabel->"In[8]:=", + CellID->2012785240], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Reduce", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output",\ + + ImageSize->{108, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellTags->"SumS", + CellLabel->"Out[8]="] +}, Open ]] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -162,7 +249,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->997576810], + CellID->1952002760], Cell[CellGroupData[{ @@ -172,28 +259,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1729221158], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "SumS", "]"}]], "Input", - CellTags->"SumS", - CellLabel->"In[1]:=", - CellID->2012785240], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Reduce", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output",\ - - ImageSize->{118, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"SumS", - CellLabel->"Out[1]=", - CellID->35078957] -}, Open ]], + CellID->1416377860], Cell[CellGroupData[{ @@ -202,7 +268,7 @@ Cell[BoxData[ RowBox[{"1", ",", RowBox[{"m", "-", "1"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->632054675], Cell[BoxData[ @@ -212,12 +278,11 @@ Cell[BoxData[ FormBox[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{67, 15}, + ImageSize->{69, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[2]=", - CellID->1556413384] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -227,7 +292,7 @@ Cell[BoxData[ RowBox[{"2", ",", RowBox[{"m", "-", "1"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1183001998], Cell[BoxData[ @@ -237,12 +302,11 @@ Cell[BoxData[ FormBox[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{67, 15}, + ImageSize->{70, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[3]=", - CellID->1711872116] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -252,7 +316,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "1"}], ",", "m"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->601997566], Cell[BoxData[ @@ -262,12 +326,11 @@ Cell[BoxData[ RowBox[{"-", "1"}]], "(", FormBox["m", TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{53, 15}, + ImageSize->{54, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[4]=", - CellID->1598419711] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -277,7 +340,7 @@ Cell[BoxData[ RowBox[{"1", ",", "m", ",", RowBox[{"Reduce", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[5]:=", + CellLabel->"In[4]:=", CellID->1985675154], Cell[BoxData[ @@ -289,12 +352,11 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], "+", FractionBox["1", "m"]}], TraditionalForm]], "Output", - ImageSize->{101, 41}, + ImageSize->{104, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[5]=", - CellID->1232098786] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -305,7 +367,7 @@ Cell[BoxData[ RowBox[{"m", "+", "2"}], ",", RowBox[{"Reduce", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[6]:=", + CellLabel->"In[5]:=", CellID->723810100], Cell[BoxData[ @@ -320,12 +382,11 @@ Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", "2"}], ")"}], "3"]]}], TraditionalForm]], "Output", - ImageSize->{144, 46}, + ImageSize->{150, 40}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[6]=", - CellID->378956112] + CellLabel->"Out[5]="] }, Open ]], Cell[BoxData[ @@ -334,7 +395,7 @@ Cell[BoxData[ RowBox[{"SumS", ",", RowBox[{"Reduce", "\[Rule]", "True"}]}], "]"}], ";"}]], "Input", CellTags->"SumS", - CellLabel->"In[7]:=", + CellLabel->"In[6]:=", CellID->1121632488], Cell[CellGroupData[{ @@ -344,7 +405,7 @@ Cell[BoxData[ RowBox[{"3", ",", RowBox[{"m", "+", "2"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[8]:=", + CellLabel->"In[7]:=", CellID->663420944], Cell[BoxData[ @@ -365,12 +426,11 @@ Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", "2"}], ")"}], "3"]]}], TraditionalForm]], "Output", - ImageSize->{260, 46}, + ImageSize->{271, 40}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[8]=", - CellID->1687595925] + CellLabel->"Out[7]="] }, Open ]], Cell[BoxData[ @@ -379,7 +439,7 @@ Cell[BoxData[ RowBox[{"SumS", ",", RowBox[{"Reduce", "\[Rule]", "False"}]}], "]"}], ";"}]], "Input", CellTags->"SumS", - CellLabel->"In[9]:=", + CellLabel->"In[8]:=", CellID->1754340999], Cell[CellGroupData[{ @@ -388,18 +448,17 @@ Cell[BoxData[ RowBox[{"SumS", "[", RowBox[{"1", ",", "4"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[10]:=", + CellLabel->"In[9]:=", CellID->913193894], Cell[BoxData[ FormBox[ FractionBox["25", "12"], TraditionalForm]], "Output", - ImageSize->{24, 41}, + ImageSize->{23, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[10]=", - CellID->205548473] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -410,18 +469,17 @@ Cell[BoxData[ RowBox[{"i", "=", "1"}], "4"], RowBox[{"1", "/", "i"}]}]], "Input", CellTags->"SumS", - CellLabel->"In[11]:=", + CellLabel->"In[10]:=", CellID->1966406647], Cell[BoxData[ FormBox[ FractionBox["25", "12"], TraditionalForm]], "Output", - ImageSize->{24, 41}, + ImageSize->{23, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[11]=", - CellID->1412895147] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -431,7 +489,7 @@ Cell[BoxData[ RowBox[{"1", ",", "2", ",", RowBox[{"m", "-", "1"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[12]:=", + CellLabel->"In[11]:=", CellID->1336627111], Cell[BoxData[ @@ -441,12 +499,11 @@ Cell[BoxData[ FormBox[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", - ImageSize->{72, 15}, + ImageSize->{74, 17}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[12]=", - CellID->18182330] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -455,19 +512,18 @@ Cell[BoxData[ RowBox[{"SumS", "[", RowBox[{"1", ",", "1", ",", "1", ",", "11"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[13]:=", + CellLabel->"In[12]:=", CellID->796483207], Cell[BoxData[ FormBox[ FractionBox["31276937512951", "4260000729600"], TraditionalForm]], "Output",\ - ImageSize->{117, 41}, + ImageSize->{115, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[13]=", - CellID->2038617627] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -477,19 +533,18 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "1"}], ",", "4"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[14]:=", + CellLabel->"In[13]:=", CellID->324759887], Cell[BoxData[ FormBox[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", - ImageSize->{33, 41}, + ImageSize->{34, 34}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[14]=", - CellID->549106078] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -498,19 +553,18 @@ Cell[BoxData[ RowBox[{"SumT", "[", RowBox[{"1", ",", "4"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[15]:=", + CellLabel->"In[14]:=", CellID->857412373], Cell[BoxData[ FormBox[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", - ImageSize->{33, 41}, + ImageSize->{34, 34}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumS", - CellLabel->"Out[15]=", - CellID->1019405443] + CellLabel->"Out[14]="] }, Open ]] }, Open ]], @@ -546,9 +600,7 @@ Cell[TextData[{ ButtonNote->"SumT"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"SumS", - CellID->1388374666] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -556,7 +608,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"SumS", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -565,10 +617,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 28.165293}", + "built" -> "{2020, 1, 5, 19, 2, 38.554768}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -578,11 +630,11 @@ TaggingRules->{ SumS[1,1,m] is \\[Sum]_i = 1^mS1(i)/i. SumS[k,l,m] is \\[Sum]_i = 1^m\\ \ Sl(i)/i^k. 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CellLabel->"Out[7]=", - CellID->1069824481] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -327,12 +353,11 @@ Cell[BoxData[ FractionBox["38987958697055013360489864298703621429610152138683927", "10512121660702378405316004964483761080879190528000000"]}], TraditionalForm]], "Output", - ImageSize->{429, 41}, + ImageSize->{425, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumT", - CellLabel->"Out[8]=", - CellID->1350292495] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -348,12 +373,11 @@ Cell[BoxData[ FormBox[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", - ImageSize->{33, 41}, + ImageSize->{34, 34}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumT", - CellLabel->"Out[9]=", - CellID->1565575302] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -370,12 +394,11 @@ Cell[BoxData[ FormBox[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", - ImageSize->{33, 41}, + ImageSize->{34, 34}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumT", - CellLabel->"Out[10]=", - CellID->1734591901] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -404,12 +427,11 @@ Cell[BoxData[ TemplateBox[{RowBox[{"-", "1"}],"1","m"}, "LerchPhi"]}], "-", RowBox[{"log", "(", "2", ")"}]}], TraditionalForm]], "Output", - ImageSize->{199, 18}, + ImageSize->{202, 19}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumT", - CellLabel->"Out[11]=", - CellID->1972297222] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -426,12 +448,11 @@ Cell[BoxData[ RowBox[{"-", FractionBox["57561743656913", "21300003648000"]}], TraditionalForm]], "Output", - ImageSize->{127, 41}, + ImageSize->{127, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"SumT", - CellLabel->"Out[12]=", - CellID->1330421141] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -450,12 +471,11 @@ Cell[BoxData[ FractionBox["38987958697055013360489864298703621429610152138683927", "10512121660702378405316004964483761080879190528000000"]}], TraditionalForm]], "Output", - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$151346], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$262445], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/SymbolicSum2", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ SymbolicSum2.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["SymbolicSum2", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["SymbolicSum2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -106,10 +117,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 25, 49.879190}", + "built" -> "{2020, 1, 5, 19, 3, 2.864271}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -118,11 +129,11 @@ TaggingRules->{ "SymbolicSum2 is similar to SymbolicSum (Algegra`SymbolicSum`SymbolicSum \ was a function to do symbolic summation. 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"paclet:FeynCalc/ref/OneLoopSimplify"], "\<\"TIDL\"\>":> + Documentation`HelpLookup["paclet:FeynCalc/ref/TIDL"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/TID\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/TID"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + + "http://reference.wolfram.com/language/FeynCalc/ref/TID.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$268141], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/TID", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +98,20 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["TID", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["TID", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -93,76 +130,115 @@ with loop momentum q" Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->167494522], + CellGroupingRules->{"SectionGrouping", 50}, + CellID->957893331], -Cell[CellGroupData[{ - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->535579332], +Cell["", "SectionHeaderSpacer"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "TID", "]"}]], "Input", CellTags->"TID", - CellLabel->"In[1]:=", + CellLabel->"In[26]:=", CellID->1576573941], Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ - RowBox[{"ChangeDimension", "\[Rule]", "D"}], ",", + RowBox[{"ApartFF", "\[Rule]", "True"}], ",", + RowBox[{"Check", "\[Rule]", "True"}], ",", RowBox[{"Collecting", "\[Rule]", "True"}], ",", RowBox[{"Contract", "\[Rule]", "True"}], ",", RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"DimensionalReduction", "\[Rule]", "False"}], ",", RowBox[{"DiracSimplify", "\[Rule]", "True"}], ",", RowBox[{"DiracTrace", "\[Rule]", "True"}], ",", - RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", RowBox[{"EpsEvaluate", "\[Rule]", "True"}], ",", + RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCLoopRemoveNegativePropagatorPowers", "\[Rule]", "True"}], ",", + + RowBox[{"FCLoopMixedToCartesianAndTemporal", "\[Rule]", "True"}], ",", RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", - RowBox[{"FeynAmpDenominatorCombine", "\[Rule]", "True"}], ",", RowBox[{"FeynAmpDenominatorSimplify", "\[Rule]", "True"}], ",", + RowBox[{"Factoring", "\[Rule]", + RowBox[{"{", + RowBox[{"Factor2", ",", "5000"}], "}"}]}], ",", + RowBox[{"FeynAmpDenominatorCombine", "\[Rule]", "True"}], ",", RowBox[{"GenPaVe", "\[Rule]", "False"}], ",", + RowBox[{"Isolate", "\[Rule]", "False"}], ",", RowBox[{"PaVeAutoOrder", "\[Rule]", "True"}], ",", RowBox[{"PaVeAutoReduce", "\[Rule]", "True"}], ",", - RowBox[{"ApartFF", "\[Rule]", "True"}], ",", - RowBox[{"Isolate", "\[Rule]", "False"}], ",", + RowBox[{"PauliTrick", "\[Rule]", "True"}], ",", + RowBox[{"ToPaVe", "\[Rule]", "False"}], ",", RowBox[{"UsePaVeBasis", "\[Rule]", "False"}], ",", - RowBox[{"ToPaVe", "\[Rule]", "False"}]}], "}"}], + RowBox[{"TimeConstrained", "\[Rule]", "3"}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{518, 130}, + ImageSize->{471, 166}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"TID", - CellLabel->"Out[1]=", - CellID->1697860323] + CellLabel->"Out[26]="] +}, Open ]] +}, Closed]] }, Open ]], Cell[CellGroupData[{ +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "PrimaryExamplesSection", + WholeCellGroupOpener->True, + CellTags->"PrimaryExamplesSection", + CellID->1140297004], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Basic Examples", + "\[NonBreakingSpace]\[NonBreakingSpace]", + Cell["(1)", "ExampleCount"] +}], "ExampleSection", "ExampleSection", + WholeCellGroupOpener->True, + CellID->742260497], + +Cell[CellGroupData[{ + Cell[BoxData[{ RowBox[{ RowBox[{"FCClearScalarProducts", "[", "]"}], ";"}], "\[IndentingNewLine]", @@ -180,7 +256,7 @@ Cell[BoxData[{ RowBox[{"FVD", "[", RowBox[{"k", ",", "\[Mu]"}], "]"}]}], "//", "FCI"}]}]}], "Input", CellTags->"TID", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->1762979144], Cell[BoxData[ @@ -230,11 +306,11 @@ Cell[BoxData[ TraditionalForm], FormBox["2", TraditionalForm]]}], ")"}], "2"]}]], TraditionalForm]], "Output", - ImageSize->{206, 51}, + ImageSize->{218, 45}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"TID", - CellLabel->"Out[2]=", + CellLabel->"Out[1]=", CellID->618277373] }, Open ]], @@ -261,320 +337,261 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"TID", "[", RowBox[{"int", ",", "k"}], "]"}]], "Input", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->972857906], Cell[BoxData[ GraphicsBox[ TagBox[RasterBox[CompressedData[" -1:eJztnQlUFFf2/zOZ/2RycpyT5CCyKEiQfVFApIkgKiqKgv7ixsFf1MTkp5HE -+bkHNTFxA0xOohgSklEHo6MT1yTCT0xQIC5EcEEQUDCgssjedLc0NL0U/25k -kO6uqq5X/aq7Gu7nnJlDkL733fuWfvXqVn1fW/a/c5c//9xzz617Uf1/c9/+ 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CellID->1224892054], +Cell[TextData[{ + Cell["TIDL", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -109,9 +141,7 @@ Cell[TextData[StyleBox[ButtonBox["TID", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/TID", ButtonNote->"TID"], - FontFamily->"Verdana"]], "Text", - CellTags->"TIDL", - CellID->627317385] + FontFamily->"Verdana"]], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -128,20 +158,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, 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StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "TIDL"->{ - Cell[3509, 107, 193, 6, 70, "Text", - CellTags->"TIDL", - CellID->627317385]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"TIDL", 5457, 160} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[576, 21, 2229, 52, 70, "AnchorBarGrid", +Cell[576, 21, 2975, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2808, 75, 47, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2858, 78, 353, 11, 70, "Usage", +Cell[3554, 97, 281, 11, 70, "ObjectNameGrid"], +Cell[3838, 110, 353, 11, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3236, 93, 270, 12, 70, "SeeAlsoSection", +Cell[4216, 125, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3509, 107, 193, 6, 70, "Text", - CellTags->"TIDL", - CellID->627317385] +Cell[4489, 139, 157, 4, 70, "SeeAlso"] }, Open ]], -Cell[3717, 116, 23, 0, 70, "FooterCell"] +Cell[4661, 146, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/TLI.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/TLI.nb index 4b407bf71..237170618 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/TLI.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/TLI.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 9404, 297] -NotebookOptionsPosition[ 5856, 195] -NotebookOutlinePosition[ 8657, 268] -CellTagsIndexPosition[ 8552, 262] +NotebookDataLength[ 10144, 316] +NotebookOptionsPosition[ 6945, 226] +NotebookOutlinePosition[ 9517, 292] +CellTagsIndexPosition[ 9452, 287] WindowTitle->TLI WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/TLI\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/TLI"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/TLI.html"], - StandardForm]], "Input", TextClipboardType -> "PlainText"]}, - Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$156164], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/TLI", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"TLI2FC\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/TLI2FC"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/TLI\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/TLI"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/TLI.html"]\ +, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$270787], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/TLI", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,20 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["TLI", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["TLI", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -108,32 +142,33 @@ TLI[{a,b,c,d,e}, {al,be,ga,de,ep}]." Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->1532521566], + CellGroupingRules->{"SectionGrouping", 50}, + CellID->2113120269], -Cell[CellGroupData[{ - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->2094721579], +Cell["", "SectionHeaderSpacer"], Cell[CellGroupData[{ @@ -151,16 +186,14 @@ Cell[BoxData[ RowBox[{"Momentum", "\[Rule]", RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{292, 15}, + ImageSize->{273, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"TLI", CellLabel->"Out[1]=", CellID->1974374076] }, Open ]] -}, Open ]], - -Cell["", "SectionFooterSpacer"] +}, Closed]] }, Open ]], Cell[CellGroupData[{ @@ -186,9 +219,7 @@ Cell[TextData[{ ButtonNote->"TLI2FC"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"TLI", - CellID->1589173280] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -205,10 +236,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 9.721614}", + "built" -> "{2020, 1, 5, 19, 3, 22.896311}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -222,11 +253,11 @@ dl.(p-k2), e: dl.(k1-k2). TLI[{mu1, ...}, {nu1, \ mu1 belongs to k1 and nu1 to k2. TLI[any___,{a,b,c,d,e,0,0}, \ {al,be,ga,de,ep}] simplifies to TLI[any, {a,b,c,d,e}, {al,be,ga,de,ep}]. \ TLI[{0,0,0,0,0},{a,b,c,d,e}, {al,be,ga,de,ep}] simplifies to TLI[{a,b,c,d,e}, \ -{al,be,ga,de,ep}].", "synonyms" -> {}, "title" -> "TLI", "titlemodifier" -> - "", "windowtitle" -> "TLI", "type" -> "Symbol", "uri" -> +{al,be,ga,de,ep}].", "synonyms" -> {}, "tabletags" -> {}, "title" -> "TLI", + "titlemodifier" -> "", "windowtitle" -> "TLI", "type" -> "Symbol", "uri" -> "FeynCalc/ref/TLI"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -234,8 +265,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -243,62 +275,49 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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CellTags->"PrimaryExamplesSection", - CellID->1532521566], +Cell[3860, 112, 1200, 28, 197, "Usage", + CellID->982511436], Cell[CellGroupData[{ -Cell[4503, 129, 196, 6, 25, "ExampleSection", - CellID->2094721579], +Cell[5085, 144, 739, 24, 31, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->2113120269], +Cell[5827, 170, 31, 0, 70, "SectionHeaderSpacer"], Cell[CellGroupData[{ -Cell[4724, 139, 124, 4, 27, "Input", +Cell[5883, 174, 124, 4, 70, "Input", CellTags->"TLI", CellID->1958640232], -Cell[4851, 145, 378, 13, 36, "Output", +Cell[6010, 180, 378, 13, 37, "Output", CellTags->"TLI", CellID->1974374076] }, Open ]] -}, Open ]], -Cell[5256, 162, 31, 0, 29, "SectionFooterSpacer"] +}, Closed]] }, Open ]], Cell[CellGroupData[{ -Cell[5324, 167, 270, 12, 31, "SeeAlsoSection", +Cell[6449, 200, 270, 12, 31, "SeeAlsoSection", CellID->1255426704], -Cell[5597, 181, 217, 9, 31, "Text", - CellTags->"TLI", - CellID->1589173280] +Cell[6722, 214, 181, 7, 56, "SeeAlso"] }, Open ]], -Cell[5829, 193, 23, 0, 42, "FooterCell"] +Cell[6918, 224, 23, 0, 41, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/TLI2.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/TLI2.nb index 7eac7d31c..bef2d5df2 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/TLI2.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/TLI2.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 5909, 186] -NotebookOptionsPosition[ 3764, 121] -NotebookOutlinePosition[ 5653, 175] -CellTagsIndexPosition[ 5587, 170] +NotebookDataLength[ 6677, 207] +NotebookOptionsPosition[ 4708, 151] +NotebookOutlinePosition[ 6470, 199] +CellTagsIndexPosition[ 6427, 196] WindowTitle->TLI2 WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/TLI2\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/TLI2"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/TLI2.html"]\ -, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$155135], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/TLI2", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"TLI\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/TLI"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/TLI2\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/TLI2"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/TLI2.\ +html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$269461], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/TLI2", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["TLI2", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["TLI2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +144,7 @@ Cell[TextData[{ ButtonNote->"TLI"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"TLI2", - CellID->573712863] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,20 +161,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 5.449964}", + "built" -> "{2020, 1, 5, 19, 3, 19.878359}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "TLI2 is like TLI, but without any functional properties.", - "synonyms" -> {}, "title" -> "TLI2", "titlemodifier" -> "", "windowtitle" -> - "TLI2", "type" -> "Symbol", "uri" -> "FeynCalc/ref/TLI2"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "TLI2", "titlemodifier" -> + "", "windowtitle" -> "TLI2", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/TLI2"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -153,41 +184,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "TLI2"->{ - Cell[3514, 107, 208, 9, 70, "Text", - 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CellID->1224892054], +Cell[TextData[{ + Cell["TLI2FC", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -92,39 +127,40 @@ Cell[BoxData[GridBox[{ Cell[CellGroupData[{ -Cell[TextData[{ - Cell[BoxData[ - InterpretationBox[ - StyleBox[ - GraphicsBox[{}, - BaselinePosition->Baseline, - ImageSize->{6, 0}], - CacheGraphics->False], - Spacer[6]]]], - "Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "PrimaryExamplesSection", +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", WholeCellGroupOpener->True, - CellTags->"PrimaryExamplesSection", - CellID->2131826391], + CellGroupingRules->{"SectionGrouping", 50}, + CellID->720851657], -Cell[CellGroupData[{ - -Cell[TextData[{ - "Basic Examples", - "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] -}], "ExampleSection", "ExampleSection", - WholeCellGroupOpener->True, - CellID->541322616], +Cell["", "SectionHeaderSpacer"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Options", "[", "TLI2FC", "]"}]], "Input", CellTags->"TLI2FC", - CellLabel->"In[1]:=", + CellLabel->"In[5]:=", CellID->972870614], Cell[BoxData[ @@ -140,21 +176,13 @@ Cell[BoxData[ RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], ",", RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}], "}"}]}]}], "}"}], TraditionalForm]], "Output", - ImageSize->{338, 35}, + ImageSize->{326, 35}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"TLI2FC", - CellLabel->"Out[1]=", - CellID->1369959726] -}, Open ]], - -Cell[BoxData[""], "Input", - CellTags->"TLI2FC", - CellLabel->"In[2]:=", - CellID->1527451776] -}, Open ]], - -Cell["", "SectionFooterSpacer"] + CellLabel->"Out[5]="] +}, Open ]] +}, Closed]] }, Open ]], Cell[CellGroupData[{ @@ -179,16 +207,14 @@ Cell[TextData[{ ButtonData->"paclet:FeynCalc/ref/TLI", ButtonNote->"TLI"], FontFamily->"Verdana"], - ". ", + ", ", StyleBox[ButtonBox["FC2TLI", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/FC2TLI", ButtonNote->"FC2TLI"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"TLI2FC", - CellID->708615958] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -196,7 +222,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"TLI2FC", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -205,21 +231,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - 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CellID->12061026] -}, Open ]], - -Cell["", "SectionFooterSpacer"] + CellLabel->"Out[6]="] +}, Open ]] +}, Closed]] }, Open ]], Cell[CellGroupData[{ @@ -184,17 +211,15 @@ Cell[TextData[{ ButtonNote->"TLI"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"TLIFP", - CellID->1633359984] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"TLIFP", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -203,21 +228,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - 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Depending on the setting of \ the option SUNTrace also a trace over SU(N) objects is performed. The \ Mathematica build-in function Tr is overloaded to call TR if any of \ -DiracGamma, DiracSlash, GA, GAD, GS or GSD are in the expression. Tr[list] \ -finds the trace of the matrix or tensor list. Tr[list, f] finds a generalized \ -trace, combining terms with f instead of Plus. Tr[list, f, n] goes down to \ -level n in list. Tr[expression ] calculates the DiracTrace, i.e., \ -TR[expression ] if any of DiracGamma, DiracSlash, GA, GAD, GS or GSD is \ -present in expression.", "synonyms" -> {}, "title" -> "TR", "titlemodifier" -> +DiracGamma, GA, GAD, GS or GSD are in the expression. Tr[list] finds the \ +trace of the matrix or tensor list. Tr[list, f] finds a generalized trace, \ +combining terms with f instead of Plus. Tr[list, f, n] goes down to level n \ +in list. Tr[expression ] calculates the DiracTrace, i.e., TR[expression ] if \ +any of DiracGamma, GA, GAD, GS or GSD is present in expression.", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "TR", "titlemodifier" -> "", "windowtitle" -> "TR", "type" -> "Symbol", "uri" -> "FeynCalc/ref/TR"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -1293,7 +917,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -1302,457 +926,271 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["Tdec", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -97,9 +133,9 @@ Cell[BoxData[GridBox[{ RowBox[{"{", RowBox[{"p1", ",", " ", "p2", ",", " ", "..."}], "}"}]}], "]"}]}]], "InlineFormula"], - " \[LineSeparator]", - "or Tdec[exp, {{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}] calculates the \ -tensorial decomposition formulas. The more common ones are saved in TIDL." + " \[LineSeparator]or Tdec[exp, {{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}] \ +calculates the tensorial decomposition formulas for Lorentzian integrals. The \ +more common ones are saved in TIDL." }]]} }]], "Usage", GridBoxOptions->{ @@ -110,39 +146,40 @@ tensorial decomposition formulas. The more common ones are saved in TIDL." 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ButtonNote->"FromTFI"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"ToTFI", - CellID->1170025384] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -412,10 +551,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 16.122002}", + "built" -> "{2020, 1, 5, 19, 3, 35.242673}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -424,11 +563,12 @@ TaggingRules->{ "ToTFI[expr, q1, q2, p] translates FeynCalc 2-loop self energy type \ integrals into the TFI notation, which can be used as input for the function \ TarcerRecurse from the TARCER package. 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CellID->1224892054], +Cell[TextData[{ + Cell["Tr2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -95,32 +135,33 @@ trace." 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"PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$158189], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/TraceDimension", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$276479], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/TraceDimension", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ TraceDimension.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["TraceDimension", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["TraceDimension", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -112,9 +144,7 @@ Cell[TextData[{ ButtonNote->"FeynCalc2FORM"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"TraceDimension", - CellID->623790716] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -131,21 +161,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 19.225708}", + "built" -> "{2020, 1, 5, 19, 3, 37.416275}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "TraceDimension is an option for FeynCalc2FORM. If set to 4: trace, if \ -set to n: tracen.", "synonyms" -> {}, "title" -> "TraceDimension", - "titlemodifier" -> "", "windowtitle" -> "TraceDimension", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/TraceDimension"}}, +set to n: tracen.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "TraceDimension", "titlemodifier" -> "", "windowtitle" -> + "TraceDimension", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/TraceDimension"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -154,41 +185,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "TraceDimension"->{ - Cell[3606, 107, 248, 9, 70, "Text", - CellTags->"TraceDimension", - CellID->623790716]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"TraceDimension", 5697, 164} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[586, 21, 2270, 52, 70, "AnchorBarGrid", +Cell[586, 21, 3037, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2859, 75, 57, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2919, 78, 389, 11, 70, "Usage", +Cell[3626, 97, 291, 11, 70, "ObjectNameGrid"], +Cell[3920, 110, 389, 11, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3333, 93, 270, 12, 70, "SeeAlsoSection", +Cell[4334, 125, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3606, 107, 248, 9, 70, "Text", - CellTags->"TraceDimension", - CellID->623790716] +Cell[4607, 139, 202, 7, 70, "SeeAlso"] }, Open ]], -Cell[3869, 119, 23, 0, 70, "FooterCell"] +Cell[4824, 149, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/TraceOfOne.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/TraceOfOne.nb index 8f232e427..f2d36c0ef 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/TraceOfOne.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/TraceOfOne.nb @@ -3,69 +3,93 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 9324, 315] -NotebookOptionsPosition[ 5804, 206] -NotebookOutlinePosition[ 8362, 278] -CellTagsIndexPosition[ 8250, 272] +NotebookDataLength[ 10213, 348] +NotebookOptionsPosition[ 7161, 257] +NotebookOutlinePosition[ 9269, 314] +CellTagsIndexPosition[ 9185, 309] WindowTitle->TraceOfOne WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - 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CellID->1224892054], +Cell[TextData[{ + Cell["TraceOfOne", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -107,7 +141,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->728832718], + CellID->2002840320], Cell[CellGroupData[{ @@ -117,50 +151,70 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->741598411], + CellID->1104752518], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracTrace", "[", "1", "]"}]], "Input", + CellLabel->"In[1]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox["1", + TraditionalForm], ")"}], TraditionalForm]], "Output", + ImageSize->{34, 16}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[1]="] +}, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"TR", "[", + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[2]:="], + +Cell[BoxData[ + FormBox["4", TraditionalForm]], "Output", + ImageSize->{13, 14}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[2]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracTrace", "[", RowBox[{"1", ",", - RowBox[{"SUNTrace", "\[Rule]", "False"}], ",", - RowBox[{"SUNNToCACF", "\[Rule]", "True"}], ",", RowBox[{"TraceOfOne", "\[Rule]", "tr1"}]}], "]"}]], "Input", - CellTags->"TraceOfOne", - CellLabel->"In[1]:=", - CellID->223402463], + CellLabel->"In[3]:="], Cell[BoxData[ - FormBox["tr1", TraditionalForm]], "Output", - ImageSize->{22, 15}, + FormBox[ + RowBox[{"tr", "(", + FormBox["1", + TraditionalForm], ")"}], TraditionalForm]], "Output", + ImageSize->{34, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"TraceOfOne", - CellLabel->"Out[1]=", - CellID->2044201134] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"TR", "[", - RowBox[{"1", ",", - RowBox[{"SUNTrace", "\[Rule]", "True"}], ",", - RowBox[{"SUNNToCACF", "\[Rule]", "True"}], ",", - RowBox[{"TraceOfOne", "\[Rule]", "tr2"}]}], "]"}]], "Input", - CellTags->"TraceOfOne", - CellLabel->"In[2]:=", - CellID->1954279511], + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[4]:="], Cell[BoxData[ - FormBox["tr2", TraditionalForm]], "Output", - ImageSize->{22, 15}, + FormBox["tr1", TraditionalForm]], "Output", + ImageSize->{20, 14}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"TraceOfOne", - CellLabel->"Out[2]=", - CellID->803728852] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -184,11 +238,10 @@ Cell[TextData[{ CellID->1255426704], Cell[TextData[{ - "See also: ", - StyleBox[ButtonBox["TR", + StyleBox[ButtonBox["DiracSimplify", BaseStyle->"Link", - ButtonData->"paclet:FeynCalc/ref/TR", - ButtonNote->"Tr"], + ButtonData->"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], FontFamily->"Verdana"], ", ", StyleBox[ButtonBox["DiracTrace", @@ -197,9 +250,7 @@ Cell[TextData[{ ButtonNote->"DiracTrace"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"TraceOfOne", - CellID->622050208] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -207,7 +258,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"TraceOfOne", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -216,21 +267,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 20.459944}", + "built" -> "{2020, 1, 5, 19, 3, 38.370305}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "TraceOfOne is an option for Tr and DiracTrace. Its setting determines \ -the value of the unit trace.", "synonyms" -> {}, "title" -> "TraceOfOne", - "titlemodifier" -> "", "windowtitle" -> "TraceOfOne", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/TraceOfOne"}, "SearchTextTranslated" -> ""}, +the value of the unit trace.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "TraceOfOne", "titlemodifier" -> "", "windowtitle" -> "TraceOfOne", + "type" -> "Symbol", "uri" -> "FeynCalc/ref/TraceOfOne"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -238,8 +290,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -248,75 +301,55 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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CellLabel->"Out[4]=", - CellID->272166616] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -381,16 +395,15 @@ Cell[BoxData[ RowBox[{ RowBox[{"GA", "[", "d", "]"}], ".", RowBox[{"GA", "[", "e", "]"}]}]}]], "Output", - ImageSize->{137, 15}, + ImageSize->{142, 15}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Trick", - CellLabel->"Out[5]//StandardForm=", - CellID->1559426683] + CellLabel->"Out[5]//StandardForm="] +}, Open ]] }, Open ]], Cell["", "SectionFooterSpacer"] -}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -440,17 +453,15 @@ Cell[TextData[{ ButtonNote->"DiracTrick"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Trick", - CellID->633331234] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] }, Saveable->False, ScreenStyleEnvironment->"Working", -WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{808, 911}, +WindowMargins->{{268, Automatic}, {Automatic, 20}}, WindowTitle->"Trick", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -459,10 +470,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 25.273573}", + "built" -> "{2020, 1, 5, 19, 3, 41.642366}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -470,11 +481,11 @@ TaggingRules->{ "None", "summary" -> "Trick[exp] performs several basic simplifications without expansion. \ Trick[exp] uses Contract, DotSimplify and SUNDeltaContract.", - "synonyms" -> {}, "title" -> "Trick", "titlemodifier" -> "", - "windowtitle" -> "Trick", "type" -> "Symbol", "uri" -> + "synonyms" -> {}, "tabletags" -> {}, "title" -> "Trick", "titlemodifier" -> + "", "windowtitle" -> "Trick", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Trick"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -482,8 +493,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - 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CellID->1224892054], +Cell[TextData[{ + Cell["TrickIntegrate", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -151,7 +183,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1642198825], + CellID->415536027], Cell[CellGroupData[{ @@ -161,7 +193,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->667432360], + CellID->854168379], Cell[CellGroupData[{ @@ -197,12 +229,11 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"t", ",", "0", ",", "1"}], "}"}]}], "]"}], TraditionalForm]], "Output", - ImageSize->{286, 21}, + ImageSize->{284, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"TrickIntegrate", - CellLabel->"Out[1]=", - CellID->308907212] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -235,12 +266,11 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"t", ",", "0", ",", "1"}], "}"}]}], "]"}], TraditionalForm]], "Output", - ImageSize->{252, 21}, + ImageSize->{249, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"TrickIntegrate", - CellLabel->"Out[2]=", - CellID->1473267114] + CellLabel->"Out[2]="] }, Open ]] }, Open ]], @@ -270,9 +300,7 @@ Cell[TextData[{ ButtonNote->"Epsilon"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"TrickIntegrate", - CellID->1095920169] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -280,7 +308,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{278, Automatic}, {Automatic, 28}}, WindowTitle->"TrickIntegrate", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> @@ -289,10 +317,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 22.012411}", + "built" -> "{2020, 1, 5, 19, 3, 39.483603}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -303,12 +331,12 @@ trick for the definite integral of ((1 - t) a Epsilon - 1 g[t]) from 0 to 1, \ yielding g[1]/a/Epsilon + Hold[Integrate][(1 - t) a Epsilon - 1 \ (g[t]-g[1]),{t,0,1}]. TrickIntegrate[t a Epsilon - 1 g[t], t] gives g[0]/(a \ Epsilon)+ Hold[Integrate][t a Epsilon - 1 (g[t]-g[0]),{t,0,1}], provided g[1] \ -and g[0] exist.", "synonyms" -> {}, "title" -> "TrickIntegrate", - "titlemodifier" -> "", "windowtitle" -> "TrickIntegrate", "type" -> - "Symbol", "uri" -> "FeynCalc/ref/TrickIntegrate"}, "SearchTextTranslated" -> - ""}, +and g[0] exist.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "TrickIntegrate", "titlemodifier" -> "", "windowtitle" -> + "TrickIntegrate", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/TrickIntegrate"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -317,7 +345,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -326,75 +354,65 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[4750, 138, 388, 15, 31, "PrimaryExamplesSection", + Cell[5739, 170, 387, 15, 31, "PrimaryExamplesSection", CellTags->"PrimaryExamplesSection", - CellID->1642198825]}, + CellID->415536027]}, "TrickIntegrate"->{ - Cell[5383, 167, 382, 13, 27, "Input", + Cell[6371, 199, 382, 13, 27, "Input", CellTags->"TrickIntegrate", CellID->1216797415], - Cell[5768, 182, 622, 22, 42, "Output", - CellTags->"TrickIntegrate", - CellID->308907212], - Cell[6427, 209, 328, 11, 27, "Input", + Cell[6756, 214, 602, 21, 42, "Output", + CellTags->"TrickIntegrate"], + Cell[7395, 240, 328, 11, 27, "Input", CellTags->"TrickIntegrate", CellID->256517011], - Cell[6758, 222, 568, 20, 42, "Output", - CellTags->"TrickIntegrate", - CellID->1473267114], - Cell[7694, 265, 231, 9, 32, "Text", - CellTags->"TrickIntegrate", - CellID->1095920169]} + Cell[7726, 253, 547, 19, 42, "Output", + CellTags->"TrickIntegrate"]} } *) (*CellTagsIndex CellTagsIndex->{ - {"PrimaryExamplesSection", 10111, 327}, - {"TrickIntegrate", 10253, 331} + {"PrimaryExamplesSection", 10998, 355}, + {"TrickIntegrate", 11139, 359} } *) (*NotebookFileOutline Notebook[{ -Cell[586, 21, 2270, 52, 51, "AnchorBarGrid", +Cell[586, 21, 3025, 74, 53, "AnchorBarGrid", CellID->1], -Cell[2859, 75, 57, 1, 42, "ObjectName", - 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TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$159202], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$277792], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/TrickMandelstam", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ TrickMandelstam.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["TrickMandelstam", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["TrickMandelstam", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -88,9 +99,8 @@ Cell[BoxData[GridBox[{ RowBox[{"m2", "^", "2"}], "+", RowBox[{"m3", "^", "2"}], "+", RowBox[{"m4", "^", "2"}]}]}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "simplifies all sums in expr so that one of the \nMandelstam variables \ -s, t or u is eliminated by the relation ", + " \[LineSeparator]simplifies all sums in expr so that one of the \ +Mandelstam variables s, t or u is eliminated by the relation ", StyleBox["s", FontSlant->"Italic"], " + ", @@ -144,7 +154,7 @@ Cell[TextData[{ }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->2111662586], + CellID->668257312], Cell[CellGroupData[{ @@ -154,7 +164,7 @@ Cell[TextData[{ Cell["(1)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->556438600], + CellID->1120472139], Cell[CellGroupData[{ @@ -187,12 +197,11 @@ Cell[BoxData[ RowBox[{"u", "-", SubsuperscriptBox["M", "W", "2"]}], ")"}]}], TraditionalForm]], "Output",\ - ImageSize->{101, 21}, + ImageSize->{107, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"TrickMandelstam", - CellLabel->"Out[1]=", - CellID->1660674587] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -224,12 +233,11 @@ Cell[BoxData[ SuperscriptBox["M", "4"]}], "-", SuperscriptBox["s", "2"], "-", "st", "-", "su"}], TraditionalForm]], "Output", - ImageSize->{127, 18}, + ImageSize->{131, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"TrickMandelstam", - CellLabel->"Out[2]=", - CellID->26761965] + CellLabel->"Out[2]="] }, Open ]] }, Open ]] }, Open ]], @@ -248,10 +256,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 23.720203}", + "built" -> "{2020, 1, 5, 19, 3, 40.529219}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -261,11 +269,12 @@ TaggingRules->{ all sums in expr so that one of the Mandelstam variables s, t or u is \ eliminated by the relation s + t + u = m_1^2 + m_2^2+ m_3^2+ m_4^2 . The \ trick is that the resulting sum has the most short number of terms.", - "synonyms" -> {}, "title" -> "TrickMandelstam", "titlemodifier" -> "", - "windowtitle" -> "TrickMandelstam", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/TrickMandelstam"}, "SearchTextTranslated" -> ""}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "TrickMandelstam", + "titlemodifier" -> "", "windowtitle" -> "TrickMandelstam", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/TrickMandelstam"}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -273,8 +282,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -283,64 +293,59 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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The setting of the option Polarization \ (unpolarized: 0; polarized: 1) determines whether the unpolarized or \ -polarized operator is returned", "synonyms" -> {}, "title" -> +polarized operator is returned", "synonyms" -> {}, "tabletags" -> {}, "title" -> "Twist2QuarkOperator", "titlemodifier" -> "", "windowtitle" -> "Twist2QuarkOperator", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Twist2QuarkOperator"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -179,41 +209,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "Twist2QuarkOperator"->{ - Cell[4500, 120, 272, 9, 70, "Text", - CellTags->"Twist2QuarkOperator", - CellID->1216439856]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"Twist2QuarkOperator", 7478, 189} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[591, 21, 2290, 52, 70, "AnchorBarGrid", +Cell[591, 21, 3069, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2884, 75, 62, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2949, 78, 1253, 24, 70, "Usage", +Cell[3663, 97, 296, 11, 70, "ObjectNameGrid"], +Cell[3962, 110, 1253, 24, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[4227, 106, 270, 12, 70, "SeeAlsoSection", +Cell[5240, 138, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[4500, 120, 272, 9, 70, "Text", - CellTags->"Twist2QuarkOperator", - CellID->1216439856] +Cell[5513, 152, 220, 7, 70, "SeeAlso"] }, Open ]], -Cell[4787, 132, 23, 0, 70, "FooterCell"] +Cell[5748, 162, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Twist3QuarkOperator.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Twist3QuarkOperator.nb index 9e88db0df..60956e7e5 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Twist3QuarkOperator.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Twist3QuarkOperator.nb @@ -3,69 +3,93 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 11526, 360] -NotebookOptionsPosition[ 7250, 242] -NotebookOutlinePosition[ 10515, 323] -CellTagsIndexPosition[ 10394, 317] +NotebookDataLength[ 13425, 423] +NotebookOptionsPosition[ 9125, 306] +NotebookOutlinePosition[ 12291, 383] +CellTagsIndexPosition[ 12168, 377] WindowTitle->Twist3QuarkOperator WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/Twist3QuarkOperator\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/Twist3QuarkOperator"]}, Visible -> False]]; 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The setting of the option \ Polarization (unpolarized: 0; polarized: 1) determines whether the \ -uppolarized or polarized operator is returned.", "synonyms" -> {}, "title" -> - "Twist3QuarkOperator", "titlemodifier" -> "", "windowtitle" -> - "Twist3QuarkOperator", "type" -> "Symbol", "uri" -> +uppolarized or polarized operator is returned.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "Twist3QuarkOperator", "titlemodifier" -> + "", "windowtitle" -> "Twist3QuarkOperator", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Twist3QuarkOperator"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -283,8 +347,9 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["Input"], CellContext -> "Global`"], Cell[ - StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + StyleData["Output"], CellContext -> "Global`"]}, + WindowMargins -> {{428, Automatic}, {Automatic, 60}}, Visible -> False, + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -292,76 +357,74 @@ StyleDefinitions->Notebook[{ (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ - 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Cell["FeynCalc/ref/Uncontract"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ +Uncontract.html"], StandardForm]], "Input", TextClipboardType -> + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$282616], + "http://reference.wolfram.com/system-modeler/", + 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CellID->1224892054], +Cell[TextData[{ + Cell["Vectors", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -113,9 +145,7 @@ Cell[TextData[{ ButtonNote->"FORM2FeynCalc"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"Vectors", - CellID->1205329040] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -132,10 +162,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 45.778003}", + "built" -> "{2020, 1, 5, 19, 3, 58.351530}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -143,11 +173,11 @@ TaggingRules->{ "None", "summary" -> "Vectors is an option for FORM2FeynCalc. Its default setting is \ Automatic. It may be set to a list, if the FORM-file does not contain a \ -V(ectors) statement.", "synonyms" -> {}, "title" -> "Vectors", - "titlemodifier" -> "", "windowtitle" -> "Vectors", "type" -> "Symbol", - "uri" -> "FeynCalc/ref/Vectors"}}, +V(ectors) statement.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "Vectors", "titlemodifier" -> "", "windowtitle" -> "Vectors", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/Vectors"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -156,41 +186,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "Vectors"->{ - Cell[3633, 108, 242, 9, 70, "Text", - CellTags->"Vectors", - CellID->1205329040]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"Vectors", 5753, 166} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[579, 21, 2241, 52, 70, "AnchorBarGrid", +Cell[579, 21, 3008, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2823, 75, 50, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2876, 78, 459, 12, 70, "Usage", +Cell[3590, 97, 284, 11, 70, "ObjectNameGrid"], +Cell[3877, 110, 459, 12, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3360, 94, 270, 12, 70, "SeeAlsoSection", +Cell[4361, 126, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3633, 108, 242, 9, 70, "Text", - CellTags->"Vectors", - CellID->1205329040] +Cell[4634, 140, 202, 7, 70, "SeeAlso"] }, Open ]], -Cell[3890, 120, 23, 0, 70, "FooterCell"] +Cell[4851, 150, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/West.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/West.nb index 0287d89c4..8cdff8aba 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/West.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/West.nb @@ -3,69 +3,91 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 5911, 155] -NotebookOptionsPosition[ 3686, 99] -NotebookOutlinePosition[ 5833, 151] -CellTagsIndexPosition[ 5790, 148] +NotebookDataLength[ 8835, 277] +NotebookOptionsPosition[ 6502, 211] +NotebookOutlinePosition[ 8306, 259] +CellTagsIndexPosition[ 8263, 256] WindowTitle->West WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/West\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/West"]}, Visible -> False]]; 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/West.\ +html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$285237], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], "FeynCalc/ref/West", + ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,20 +95,28 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["West", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["West", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ Cell[BoxData["West"], "InlineFormula"], - " \[LineSeparator]West is an option for DiracTrace, TR and other \ -functions that deal with traces of Dirac matrices. It applies only to the \ -computation of D-dimensional chiral traces (i.e. those that involve one ", - Cell[BoxData[ - SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], - ") in the Breitenlohner-Maison-t'Hooft-Veltman (BMHV) scheme. If set to \ -True, such traces will be computed according to formula (A.5) from Comp. \ -Phys. Comm 77 (1993) 286-298, which is also known as West's formula." + " \[LineSeparator]is an option for ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + " and several other functions that deal with traces of Dirac matrices." }]]} }]], "Usage", GridBoxOptions->{ @@ -95,6 +125,88 @@ Phys. Comm 77 (1993) 286-298, which is also known as West's formula." "RowsIndexed" -> {}}}, CellID->982511436], +Cell[CellGroupData[{ + +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], + +Cell["", "SectionHeaderSpacer"], + +Cell[TextData[{ + "The option applies only to the computation of ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional traces with an odd number of ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " in the Breitenlohner-Maison-t'Hooft-Veltman (BMHV) scheme." +}], "Notes"], + +Cell[TextData[{ + "With ", + Cell[BoxData[ + RowBox[{"West", "->", "True"}]], "InlineFormula"], + " (default setting), such traces are computed according to formula (A.5) \ +from Comp. Phys. Comm 77 (1993) 286-298, which is also known as West's \ +formula. " +}], "Notes"], + +Cell[TextData[{ + "For more details, see the documentation for ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + "." +}], "Notes", + CellID->1067943069] +}, Closed]], + +Cell[CellGroupData[{ + +Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "See Also" +}], "SeeAlsoSection", + WholeCellGroupOpener->True, + CellID->1255426704], + +Cell[TextData[StyleBox[ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + FontFamily->"Verdana"]], "SeeAlso"] +}, Open ]], + Cell[" ", "FooterCell"] }, Saveable->False, @@ -109,25 +221,21 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 47.252367}", + "built" -> "{2020, 1, 5, 19, 3, 59.302288}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> - "West West is an option for DiracTrace, TR and other functions that deal \ -with traces of Dirac matrices. It applies only to the computation of \ -D-dimensional chiral traces (i.e. those that involve one \\[Gamma]^5) in the \ -Breitenlohner-Maison-t'Hooft-Veltman (BMHV) scheme. If set to True, such \ -traces will be computed according to formula (A.5) from Comp. Phys. Comm 77 \ -(1993) 286-298, which is also known as West's formula.", "synonyms" -> {}, - "title" -> "West", "titlemodifier" -> "", "windowtitle" -> "West", "type" -> + "West is an option for DiracTrace and several other functions that deal \ +with traces of Dirac matrices.", "synonyms" -> {}, "tabletags" -> {}, "title" -> + "West", "titlemodifier" -> "", "windowtitle" -> "West", "type" -> "Symbol", "uri" -> "FeynCalc/ref/West"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -136,7 +244,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -150,13 +258,27 @@ CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[576, 21, 2229, 52, 70, "AnchorBarGrid", +Cell[576, 21, 2990, 74, 70, "AnchorBarGrid", CellID->1], -Cell[2808, 75, 47, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2858, 78, 798, 17, 70, "Usage", +Cell[3569, 97, 281, 11, 70, "ObjectNameGrid"], +Cell[3853, 110, 532, 15, 70, "Usage", CellID->982511436], -Cell[3659, 97, 23, 0, 70, "FooterCell"] +Cell[CellGroupData[{ +Cell[4410, 129, 730, 24, 70, "NotesSection", + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1], +Cell[5143, 155, 31, 0, 70, "SectionHeaderSpacer"], +Cell[5177, 157, 296, 7, 70, "Notes"], +Cell[5476, 166, 267, 7, 70, "Notes"], +Cell[5746, 175, 226, 8, 70, "Notes", + CellID->1067943069] +}, Closed]], +Cell[CellGroupData[{ +Cell[6009, 188, 270, 12, 70, "SeeAlsoSection", + CellID->1255426704], +Cell[6282, 202, 178, 4, 70, "SeeAlso"] +}, Open ]], +Cell[6475, 209, 23, 0, 70, "FooterCell"] } ] *) diff --git a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Write2.nb b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Write2.nb index 8ec4e3143..2a2642cfd 100644 --- a/FeynCalc/DocOutput/English/ReferencePages/Symbols/Write2.nb +++ b/FeynCalc/DocOutput/English/ReferencePages/Symbols/Write2.nb @@ -3,69 +3,92 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 10.3' *) +(* CreatedBy='Mathematica 10.4' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 24443, 861] -NotebookOptionsPosition[ 16738, 598] -NotebookOutlinePosition[ 21405, 741] -CellTagsIndexPosition[ 21295, 735] +NotebookDataLength[ 23681, 821] +NotebookOptionsPosition[ 17789, 630] +NotebookOutlinePosition[ 21122, 728] +CellTagsIndexPosition[ 21012, 722] WindowTitle->Write2 WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[GridBox[{ - {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[ - ActionMenuBox[ - FrameBox[ - InterpretationBox[Cell[TextData[{ - "URL", - StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", - StripOnInput->False] - }]], - TextCell[ - Row[{"URL", - Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], - StripOnInput->False], {"\<\"FeynCalc/ref/Write2\"\>":> - None, "\<\"Copy Wolfram Documentation Center URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell["FeynCalc/ref/Write2"]}, Visible -> False]]; 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/Write2.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$164701], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], "FeynCalc/ref/Write2", - ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$285699], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/Write2", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +96,20 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["Write2", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["Write2", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], + +Cell[CellGroupData[{ Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -84,10 +119,12 @@ Cell[BoxData[GridBox[{ RowBox[{"val1", " ", "=", " ", "expr1"}], ",", " ", RowBox[{"val2", " ", "=", " ", "expr2"}], ",", " ", "..."}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "writes the settings val1 = expr1, val2 = expr2 in sequence followed by \ -a newline, to the specified output file. Setting the option FormatType of \ -Write2 to FortranForm results in FORTRAN syntax output." + " \[LineSeparator]writes the settings ", + Cell[BoxData[ + RowBox[{ + RowBox[{"val1", " ", "=", " ", "expr1"}], ",", " ", + RowBox[{"val2", " ", "=", " ", "expr2"}]}]], "InlineFormula"], + " in sequence followed by a newline, to the specified output file." }]]} }]], "Usage", GridBoxOptions->{ @@ -98,6 +135,81 @@ Write2 to FortranForm results in FORTRAN syntax output." Cell[CellGroupData[{ +Cell[TextData[Cell[BoxData[ + ButtonBox[Cell[TextData[{ + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{6, 0}], + CacheGraphics->False], + Spacer[6]]]], + "Details" + }], "NotesFrameText"], + Appearance->{Automatic, None}, + BaseStyle->None, + ButtonFunction:>(FrontEndExecute[{ + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], All, ButtonCell], + FrontEndToken["OpenCloseGroup"], + FrontEnd`SelectionMove[ + FrontEnd`SelectedNotebook[], After, CellContents]}]& ), + Evaluator->None, + Method->"Preemptive"]]]], "NotesSection", + WholeCellGroupOpener->True, + CellGroupingRules->{"SectionGrouping", 50}, + CellID->1529498728], + +Cell["", "SectionHeaderSpacer"], + +Cell[TextData[{ + "Setting the option ", + Cell[BoxData["FormatType"], "InlineFormula"], + " of ", + ButtonBox["Write2", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/Write2", + ButtonNote->"Write2"], + " to ", + Cell[BoxData["FortranForm"], "InlineFormula"], + " results in Fortran syntax output." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Write2", "]"}]], "Input", + CellLabel->"In[150]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"D0Convention", "\[Rule]", "0"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"FormatType", "\[Rule]", "InputForm"}], ",", + RowBox[{"FortranFormatDoublePrecision", "\[Rule]", "True"}], ",", + RowBox[{"PageWidth", "\[Rule]", "62"}], ",", + RowBox[{"PostFortranFile", "\[Rule]", + RowBox[{"{", "\<\"\"\>", "}"}]}], ",", + RowBox[{"PreFortranFile", "\[Rule]", + RowBox[{"{", "\<\"\"\>", "}"}]}], ",", + RowBox[{"Precision", "\[Rule]", "15"}], ",", + RowBox[{"StringReplace", "\[Rule]", + RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", + ImageSize->{499, 53}, + ImageMargins->{{0, 0}, {0, 0}}, + ImageRegion->{{0, 1}, {0, 1}}, + CellLabel->"Out[150]="] +}, Open ]] +}, Closed]] +}, Open ]], + +Cell[CellGroupData[{ + Cell[TextData[{ Cell[BoxData[ InterpretationBox[ @@ -109,21 +221,21 @@ Cell[TextData[{ Spacer[6]]]], "Examples", "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] + Cell["(2)", "ExampleCount"] }], "PrimaryExamplesSection", WholeCellGroupOpener->True, CellTags->"PrimaryExamplesSection", - CellID->1897199636], + CellID->866533242], Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", "\[NonBreakingSpace]\[NonBreakingSpace]", - Cell["(1)", "ExampleCount"] + Cell["(2)", "ExampleCount"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, - CellID->1995411025], + CellID->115796692], Cell[CellGroupData[{ @@ -141,62 +253,18 @@ Cell[BoxData[ ShowStringCharacters->True, NumberMarks->True], FullForm], TraditionalForm]], "Output", - ImageSize->{27, 15}, - ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Write2", - CellLabel->"Out[1]//FullForm=", - CellID->296766764] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "Write2", "]"}]], "Input", - CellTags->"Write2", - CellLabel->"In[2]:=", - CellID->2021664467], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - 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ImageMargins->{{0, 0}, {0, 0}}, - ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Write2", - CellLabel->"Out[3]=", - CellID->930779746] -}, Open ]], + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], Cell[CellGroupData[{ @@ -215,7 +283,7 @@ Cell[BoxData[ RowBox[{"a", "-", "b"}], ")"}], "2"]}], ")"}], "2"], ",", "a", ",", "Factor"}], "]"}]}]], "Input", CellTags->"Write2", - CellLabel->"In[4]:=", + CellLabel->"In[1]:=", CellID->568187661], Cell[BoxData[ @@ -246,14 +314,15 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], "2"]}], TraditionalForm]], "Output", - ImageSize->{495, 21}, + ImageSize->{537, 21}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Write2", - CellLabel->"Out[4]=", - CellID->1801200835] + CellLabel->"Out[1]="] }, Open ]], +Cell["This writes the assignment r=t to a file.", "Notes"], + Cell[BoxData[ RowBox[{ RowBox[{"tempfilename", "=", @@ -261,25 +330,17 @@ Cell[BoxData[ RowBox[{"ToString", "[", "$SessionID", "]"}], "<>", "\"\<.s\>\""}]}], ";"}]], "Input", CellTags->"Write2", - CellLabel->"In[5]:=", + CellLabel->"In[2]:=", CellID->158339237], -Cell["This writes the assignment r=t to a file.", "Text", - CellTags->"Write2", - CellID->956230713], - Cell[BoxData[ RowBox[{ RowBox[{"Write2", "[", RowBox[{"tempfilename", ",", RowBox[{"r", "=", "t"}]}], "]"}], ";"}]], "Input", - CellTags->"Write2", - CellLabel->"In[6]:=", - CellID->1599031587], + CellLabel->"In[3]:="], -Cell["This shows the contents of the file.", "Text", - CellTags->"Write2", - CellID->304283335], +Cell["This shows the contents of the file.", "Notes"], Cell[CellGroupData[{ @@ -293,17 +354,14 @@ Cell[BoxData[ RowBox[{"$OperatingSystem", "===", "\"\\""}], ",", "\"\<:\>\"", ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], ",", "String"}], "]"}], "]"}]], "Input", - CellTags->"Write2", - CellLabel->"In[7]:=", - CellID->1505586368], + CellLabel->"In[4]:="], Cell[BoxData[ FormBox[ TagBox[ TagBox[GridBox[{ - {"\<\"r = ( 4*a^4 - 8*a^3*(b + c) - 4*a*(b + c)*(b^2 + c^2) + (b^2 + \ -c^2)^2 + \"\>"}, - {"\<\" 8*a^2*(b^2 + b*c + c^2)\"\>"}, + {"\<\"r = ( 4*a^4 - 8*a^3*(b + c) - 4*a*(b + c)*(b^2 + c^2) + \"\>"}, + {"\<\" (b^2 + c^2)^2 + 8*a^2*(b^2 + b*c + c^2)\"\>"}, {"\<\" );\"\>"} }, GridBoxAlignment->{ @@ -319,12 +377,10 @@ c^2)^2 + \"\>"}, Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]], TraditionalForm]], "Output", - ImageSize->{497, 51}, + ImageSize->{399, 50}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, - CellTags->"Write2", - CellLabel->"Out[7]//TableForm=", - CellID->432817826] + CellLabel->"Out[4]//TableForm="] }, Open ]], Cell[BoxData[ @@ -334,9 +390,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"$OperatingSystem", "===", "\"\\""}], ",", "\"\<:\>\"", ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], "]"}]], "Input", - CellTags->"Write2", - CellLabel->"In[8]:=", - CellID->62208628], + CellLabel->"In[5]:="], Cell[CellGroupData[{ @@ -347,7 +401,7 @@ Cell[BoxData[ RowBox[{"t", ",", "a", ",", RowBox[{"IsolateNames", "\[Rule]", "w"}]}], "]"}]}]}]], "Input", CellTags->"Write2", - CellLabel->"In[9]:=", + CellLabel->"In[6]:=", CellID->170691261], Cell[BoxData[ @@ -358,30 +412,29 @@ Cell[BoxData[ RowBox[{"8", " ", SuperscriptBox["a", "3"], " ", TagBox[ - RowBox[{"w", "(", "1423", ")"}], + RowBox[{"w", "(", "24", ")"}], HoldForm]}], "+", RowBox[{"8", " ", SuperscriptBox["a", "2"], " ", TagBox[ - RowBox[{"w", "(", "1425", ")"}], + RowBox[{"w", "(", "26", ")"}], HoldForm]}], "-", RowBox[{"4", " ", "a", " ", TagBox[ - RowBox[{"w", "(", "1423", ")"}], + RowBox[{"w", "(", "24", ")"}], HoldForm], " ", TagBox[ - RowBox[{"w", "(", "1424", ")"}], + RowBox[{"w", "(", "25", ")"}], HoldForm]}], "+", SuperscriptBox[ TagBox[ - RowBox[{"w", "(", "1424", ")"}], + RowBox[{"w", "(", "25", ")"}], HoldForm], "2"], "+", "x"}], TraditionalForm]], "Output", - ImageSize->{475, 18}, + ImageSize->{433, 18}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Write2", - CellLabel->"Out[9]=", - CellID->1764933631] + CellLabel->"Out[6]="] }, Open ]], Cell[BoxData[ @@ -390,7 +443,7 @@ Cell[BoxData[ RowBox[{"tempfilename", ",", RowBox[{"r", "=", "t2"}]}], "]"}], ";"}]], "Input", CellTags->"Write2", - CellLabel->"In[10]:=", + CellLabel->"In[7]:=", CellID->2074608494], Cell[CellGroupData[{ @@ -406,23 +459,23 @@ Cell[BoxData[ ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], ",", "String"}], "]"}], "]"}]], "Input", CellTags->"Write2", - CellLabel->"In[11]:=", + CellLabel->"In[8]:=", CellID->1647925835], Cell[BoxData[ FormBox[ TagBox[ TagBox[GridBox[{ - {"\<\"w[1423] = (b + c\"\>"}, + {"\<\"w[24] = (b + c\"\>"}, {"\<\" );\"\>"}, - {"\<\"w[1424] = (b^2 + c^2\"\>"}, + {"\<\"w[25] = (b^2 + c^2\"\>"}, {"\<\" );\"\>"}, - {"\<\"w[1425] = (b^2 + b*c + c^2\"\>"}, + {"\<\"w[26] = (b^2 + b*c + c^2\"\>"}, {"\<\" );\"\>"}, - {"\<\"r = ( 4*a^4 + x - 8*a^3*HoldForm[w[1423]] - \ -4*a*HoldForm[w[1423]]*\"\>"}, - {"\<\" HoldForm[w[1424]] + HoldForm[w[1424]]^2 + \ -8*a^2*HoldForm[w[1425]]\"\>"}, + {"\<\"r = ( 4*a^4 + x - 8*a^3*HoldForm[w[24]] - \ +4*a*HoldForm[w[24]]*\"\>"}, + {"\<\" HoldForm[w[25]] + HoldForm[w[25]]^2 + \ +8*a^2*HoldForm[w[26]]\"\>"}, {"\<\" );\"\>"} }, GridBoxAlignment->{ @@ -438,12 +491,11 @@ Cell[BoxData[ Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]], TraditionalForm]], "Output", - ImageSize->{496, 159}, + ImageSize->{451, 155}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->"Write2", - CellLabel->"Out[11]//TableForm=", - CellID->342974912] + CellLabel->"Out[8]//TableForm="] }, Open ]], Cell[BoxData[ @@ -454,16 +506,14 @@ Cell[BoxData[ RowBox[{"$OperatingSystem", "===", "\"\\""}], ",", "\"\<:\>\"", ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], "]"}]], "Input", CellTags->"Write2", - CellLabel->"In[12]:=", + CellLabel->"In[9]:=", CellID->1908725708], -Cell["\<\ -This is how to write out the expression t2 in Fortran format.\ -\>", "Text", - CellTags->"Write2", - CellID->422363964], - -Cell[CellGroupData[{ +Cell[TextData[{ + "This is how to write out the expression ", + Cell[BoxData["t2"], "InlineFormula"], + " in Fortran format." +}], "Notes"], Cell[BoxData[ RowBox[{ @@ -473,24 +523,9 @@ Cell[BoxData[ RowBox[{"FormatType", "\[Rule]", "FortranForm"}]}], "]"}], ";"}]], "Input",\ CellTags->"Write2", - CellLabel->"In[13]:=", + CellLabel->"In[10]:=", CellID->1416932507], -Cell[BoxData[ - FormBox[ - InterpretationBox[ - RowBox[{"\<\"FORTRAN generation WARNING!\\n\\t\\t\\t\\t\\tLine encountered \ -with more than 72 characters. Check line \"\>", "\[InvisibleSpace]", "3", - "\[InvisibleSpace]", "\<\" and \"\>", "\[InvisibleSpace]", "4"}], - SequenceForm[ - "FORTRAN generation WARNING!\n\t\t\t\t\tLine encountered with more than 72 \ -characters. 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Setting the option FormatType of Write2 to FortranForm results \ -in FORTRAN syntax output.", "synonyms" -> {}, "title" -> "Write2", +output file.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "Write2", "titlemodifier" -> "", "windowtitle" -> "Write2", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Write2"}, "SearchTextTranslated" -> ""}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -633,7 +664,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -642,227 +673,156 @@ StyleDefinitions->Notebook[{ (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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False]]; SelectionMove[ - DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$165049], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/WriteOut", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + False]]; SelectionMove[ + DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$286147], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/WriteOut", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +95,18 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> "RowsIndexed" -> {}}}, CellID->1], -Cell["WriteOut", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["WriteOut", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -114,9 +146,7 @@ Cell[TextData[{ ButtonNote->"OneLoop"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"WriteOut", - CellID->917997182] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -133,10 +163,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 50.394654}", + "built" -> "{2020, 1, 5, 19, 4, 1.458060}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -144,11 +174,11 @@ TaggingRules->{ "None", "summary" -> "WriteOut is an option for OneLoop. 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+ SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$286591], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/WriteOutPaVe", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +98,18 @@ WriteOutPaVe.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["WriteOutPaVe", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["WriteOutPaVe", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -126,9 +161,7 @@ Cell[TextData[{ ButtonNote->"OneLoopSum"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"WriteOutPaVe", - CellID->806653014] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -145,10 +178,10 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 51.741736}", + "built" -> "{2020, 1, 5, 19, 4, 2.547367}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -157,11 +190,11 @@ TaggingRules->{ "WriteOutPaVe is an option for PaVeReduce and OneLoopSum. If set to a \ string, the results of all Passarino-Veltman PaVe's are stored in files with \ names generated from this string and the arguments of PaVe.", - "synonyms" -> {}, "title" -> "WriteOutPaVe", "titlemodifier" -> "", - "windowtitle" -> "WriteOutPaVe", "type" -> "Symbol", "uri" -> - "FeynCalc/ref/WriteOutPaVe"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "WriteOutPaVe", + "titlemodifier" -> "", "windowtitle" -> "WriteOutPaVe", "type" -> + "Symbol", "uri" -> "FeynCalc/ref/WriteOutPaVe"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -170,41 +203,31 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline -CellTagsIndex->{ - "WriteOutPaVe"->{ - Cell[3716, 109, 549, 21, 70, "Text", - CellTags->"WriteOutPaVe", - CellID->806653014]} - } +CellTagsIndex->{} *) (*CellTagsIndex -CellTagsIndex->{ - {"WriteOutPaVe", 6223, 180} - } +CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[584, 21, 2262, 52, 70, "AnchorBarGrid", +Cell[584, 21, 3199, 77, 70, "AnchorBarGrid", CellID->1], -Cell[2849, 75, 55, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2907, 78, 511, 13, 70, "Usage", +Cell[3786, 100, 289, 11, 70, "ObjectNameGrid"], +Cell[4078, 113, 511, 13, 70, "Usage", CellID->982511436], Cell[CellGroupData[{ -Cell[3443, 95, 270, 12, 70, "SeeAlsoSection", +Cell[4614, 130, 270, 12, 70, "SeeAlsoSection", CellID->1255426704], -Cell[3716, 109, 549, 21, 70, "Text", - CellTags->"WriteOutPaVe", - CellID->806653014] +Cell[4887, 144, 505, 19, 70, "SeeAlso"] 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-59,12 +59,13 @@ Cell[BoxData[GridBox[{ URL[ StringJoin[ If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$165746], + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$287040], "http://reference.wolfram.com/system-modeler/", "http://reference.wolfram.com/language/"], "FeynCalc/ref/XYT", ".html"]], None}]}]}, Appearance->None, - MenuAppearance->Automatic]], + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], LineSpacing->{1.4, 0}]], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { @@ -73,8 +74,18 @@ Cell[BoxData[GridBox[{ "RowsIndexed" -> {}}}, CellID->1], -Cell["XYT", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["XYT", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -111,19 +122,20 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 53.051387}", + "built" -> "{2020, 1, 5, 19, 4, 3.645517}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> "None", "summary" -> "XYT[exp, x, y] transforms (x y) m away ...", - "synonyms" -> {}, "title" -> "XYT", "titlemodifier" -> "", "windowtitle" -> - "XYT", "type" -> "Symbol", "uri" -> "FeynCalc/ref/XYT"}}, + "synonyms" -> {}, "tabletags" -> {}, "title" -> "XYT", "titlemodifier" -> + "", "windowtitle" -> "XYT", "type" -> "Symbol", "uri" -> + "FeynCalc/ref/XYT"}}, CellContext->"Global`", -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -132,7 +144,7 @@ StyleDefinitions->Notebook[{ StyleData["Input"], CellContext -> "Global`"], Cell[ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, - FrontEndVersion -> "10.3 for Linux x86 (64-bit) (December 10, 2015)", + FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) @@ -146,13 +158,12 @@ CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ -Cell[575, 21, 2238, 52, 70, "AnchorBarGrid", +Cell[575, 21, 2266, 53, 70, "AnchorBarGrid", CellID->1], -Cell[2816, 75, 46, 1, 70, "ObjectName", - CellID->1224892054], -Cell[2865, 78, 559, 19, 70, "Usage", +Cell[2844, 76, 280, 11, 70, 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NotebookClose[DocumentationSearch`Private`nb$]; Null], - Delimiter, "\<\"Copy web URL\"\>":> - Module[{DocumentationSearch`Private`nb$}, - DocumentationSearch`Private`nb$ = NotebookPut[ - Notebook[{ - Cell[ - BoxData[ - MakeBoxes[ - Hyperlink[ - "http://reference.wolfram.com/language/FeynCalc/ref/\ + {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{ + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "See Also", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"See Also", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynRule\"\>":>Documentation`HelpLookup[ + "paclet:FeynCalc/ref/FeynRule"], "\<\"Twist2GluonOperator\"\>":> + Documentation`HelpLookup[ + "paclet:FeynCalc/ref/Twist2GluonOperator"], "\<\"Twist2QuarkOperator\"\ +\>":>Documentation`HelpLookup["paclet:FeynCalc/ref/Twist2QuarkOperator"]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"SeeAlso"]], + LineSpacing->{1.4, 0}], + "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ +\[ThickSpace]", + Cell[BoxData[ + ActionMenuBox[ + FrameBox[ + InterpretationBox[Cell[TextData[{ + "URL", + StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow", + StripOnInput->False] + }]], + TextCell[ + Row[{"URL", + Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]], + StripOnInput->False], {"\<\"FeynCalc/ref/ZeroMomentumInsertion\"\>":> + None, "\<\"Copy Wolfram Documentation Center URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell["FeynCalc/ref/ZeroMomentumInsertion"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; Null], + Delimiter, "\<\"Copy web URL\"\>":> + Module[{DocumentationSearch`Private`nb$}, + DocumentationSearch`Private`nb$ = NotebookPut[ + Notebook[{ + Cell[ + BoxData[ + MakeBoxes[ + Hyperlink[ + "http://reference.wolfram.com/language/FeynCalc/ref/\ ZeroMomentumInsertion.html"], StandardForm]], "Input", TextClipboardType -> - "PlainText"]}, Visible -> False]]; - SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; - FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; - NotebookClose[DocumentationSearch`Private`nb$]; - Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ - NotebookLocate[{ - URL[ - StringJoin[ - If[ - TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$166091], - "http://reference.wolfram.com/system-modeler/", - "http://reference.wolfram.com/language/"], - "FeynCalc/ref/ZeroMomentumInsertion", ".html"]], None}]}]}, - Appearance->None, - MenuAppearance->Automatic]], - LineSpacing->{1.4, 0}]], "AnchorBar"]} + "PlainText"]}, Visible -> False]]; + SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; + FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; + NotebookClose[DocumentationSearch`Private`nb$]; + Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{ + NotebookLocate[{ + URL[ + StringJoin[ + If[ + TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$287479], + "http://reference.wolfram.com/system-modeler/", + "http://reference.wolfram.com/language/"], + "FeynCalc/ref/ZeroMomentumInsertion", ".html"]], None}]}]}, + Appearance->None, + MenuAppearance->Automatic, + MenuStyle->"URLMenu"]], + LineSpacing->{1.4, 0}] + }], "AnchorBar"]} }]], "AnchorBarGrid", GridBoxOptions->{GridBoxItemSize->{"Columns" -> { Scaled[0.65], { @@ -73,8 +98,18 @@ ZeroMomentumInsertion.html"], StandardForm]], "Input", TextClipboardType -> "RowsIndexed" -> {}}}, CellID->1], -Cell["ZeroMomentumInsertion", "ObjectName", - CellID->1224892054], +Cell[TextData[{ + Cell["ZeroMomentumInsertion", "ObjectName"], + Cell[BoxData[ + InterpretationBox[ + StyleBox[ + GraphicsBox[{}, + BaselinePosition->Baseline, + ImageSize->{8, 0}], + CacheGraphics->False], + Spacer[8]]]], + Cell[BoxData[""], "ObjectNameTranslation"] +}], "ObjectNameGrid"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -124,9 +159,7 @@ Cell[TextData[{ ButtonNote->"Twist2QuarkOperator"], FontFamily->"Verdana"], "." -}], "Text", - CellTags->"ZeroMomentumInsertion", - CellID->237936766] +}], "SeeAlso"] }, Open ]], Cell[" ", "FooterCell"] @@ -143,21 +176,22 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "HasOptions" -> False, "ExampleCounter" -> 1, - "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> None, "RootCaptions" -> "", + Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> + None, "RootCaptions" -> "", "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 26, 54.477094}", + "built" -> "{2020, 1, 5, 19, 4, 4.479317}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" 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Automatic], Selectable -> False], DefaultBaseStyle -> + "ImageGraphics", ImageSizeRaw -> {8, 8}, PlotRange -> {{0, 8}, {0, 8}}, + ImageSize -> {8, 9}]}, "GrayLinkWithIcon", BaseStyle->{"TutorialJumpBoxLink"}], ""} }]], "TutorialJumpBox"], @@ -473,7 +483,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["\<\"/media/Data/Projects/Physics/FeynCalc/FeynCalc/Examples\"\>", TraditionalForm]], "Output", - ImageSize->{397, 15}, + ImageSize->{367, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellLabel->"Out[24]=", @@ -557,7 +567,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["\<\"/home/vs/.Mathematica/Applications\"\>", TraditionalForm]], "Output", - ImageSize->{247, 15}, + ImageSize->{226, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellLabel->"Out[26]=", @@ -641,47 +651,12 @@ The directory \"FeynCalc\" contains various files and subdirectories \ belonging to third-party packages which are not necessary to run 'standard' \ FeynCalc calculations and which do not use the autoloading conventions of \ FeynCalc. These packages are not initialized by default when starting \ -FeynCalc. Loading them can be switched on and off by setting appropiate \ +FeynCalc. Loading them can be switched on and off by setting appropriate \ variables to False or True before loading FeynCalc.\ \>", "Text", CellTags->"About Extras", CellID->953459903], -Cell[BoxData[ - FormBox[ - StyleBox[ - FrameBox[ - StyleBox[GridBox[{ - { - StyleBox["$LoadTARCER", - FontFamily->"Courier"], - RowBox[{ - "Specifies", " ", "if", " ", "TARCER", " ", "should", " ", "be", " ", - "loaded", " ", "by", " ", "FeynCalc"}]}, - { - StyleBox["$LoadPhi", - FontFamily->"Courier"], - RowBox[{ - "Specifies", " ", "if", " ", "PHI", " ", "should", " ", "be", " ", - "loaded", " ", "by", " ", "FeynCalc"}]}, - { - StyleBox["$LoadFeynArts", - FontFamily->"Courier"], - RowBox[{ - "Specifies", " ", "if", " ", "FeynArts", " ", "should", " ", "be", - " ", "loaded", " ", "by", " ", "FeynCalc"}]} - }, - GridBoxAlignment->{ - "Columns" -> {Right, {Left}}, "ColumnsIndexed" -> {}, - "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}], - GridBoxOptions->{ - GridBoxDividers->{ - "Columns" -> {{False}}, "ColumnsIndexed" -> {}, "Rows" -> {{False}}, - "RowsIndexed" -> {}}}]], "2ColumnBox"], TraditionalForm]], "Text", - Background->None, - CellTags->"About Extras", - CellID->2108182812], - Cell[CellGroupData[{ Cell["TARCER", "Subsection", @@ -710,7 +685,8 @@ TARCER is distributed with FeynCalc. To have FeynCalc load TARCER, evaluate\ Cell[BoxData[ RowBox[{ - RowBox[{"$LoadTARCER", "=", "True"}], ";"}]], "Input", + RowBox[{"$LoadAddOns", "=", + RowBox[{"{", "\"\\"", "}"}]}], ";"}]], "Input", CellTags->"tarcer", CellID->843778896], @@ -851,7 +827,7 @@ Cell[BoxData["$FeynArtsDirectory"], "Input", Cell[BoxData[ FormBox["\<\"/media/Data/Projects/Physics/FeynCalc/FeynCalc/FeynArts\"\>", TraditionalForm]], "Output", - ImageSize->{393, 15}, + ImageSize->{364, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellLabel->"Out[13]=", @@ -868,7 +844,8 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{ - RowBox[{"$LoadFeynArts", "=", "True"}], ";"}]], "Input", + RowBox[{"$LoadAddOns", "=", + RowBox[{"{", "\"\\"", "}"}]}], ";"}]], "Input", CellLabel->"In[16]:=", CellID->342627804], @@ -883,7 +860,8 @@ appear. Hit OK. Wait until the patching process finishes. Then restart ", Cell[BoxData[ RowBox[{ - RowBox[{"$LoadFeynArts", "=", "True"}], ";"}]], "Input", + RowBox[{"$LoadAddOns", "=", + RowBox[{"{", "\"\\"", "}"}]}], ";"}]], "Input", CellLabel->"In[18]:=", CellID->1900750623], @@ -917,7 +895,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["\<\"/media/Data/Projects/Physics/FeynCalc/FeynCalc/Examples\"\>", TraditionalForm]], "Output", - ImageSize->{397, 15}, + ImageSize->{367, 16}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, CellLabel->"Out[24]=", @@ -931,7 +909,7 @@ Cell[" ", "FooterCell"] Saveable->False, ScreenStyleEnvironment->"Working", WindowSize->{725, 750}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, WindowTitle->"Short introduction", TaggingRules->{ "ModificationHighlight" -> False, "ColorType" -> "TutorialColor", @@ -940,10 +918,9 @@ TaggingRules->{ ButtonBox[ "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> - Left], "ExampleCounter" -> 1, "ExamplePageLinks" -> {}, "NeedPlatMsgIn" -> - None, "RootCaptions" -> "", - "Metadata" -> { - "built" -> "{2016, 8, 21, 21, 27, 29.193972}", + Left], "ExampleCounter" -> 1, "NeedPlatMsgIn" -> None, "RootCaptions" -> + "", "Metadata" -> { + "built" -> "{2020, 1, 5, 19, 4, 31.052818}", "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> @@ -961,11 +938,12 @@ code. Some functions for input of objects like p^\[Mu],\[Gamma]^\[Nu],g^\[Mu] \ \[Nu], \[CurlyEpsilon]^\[Mu] \[Nu] \[Rho] \[Sigma], etc. (abbreviations in \ parentheses) are: GA (Dirac matrix), GS (Dirac slash), FV (4-vector), LC \ (Levi-Civita tensor), MT (metric tensor), Spinor, SUNDelta, SUNFDelta, SUNF, \ -SP (scalar product)", "synonyms" -> {}, "title" -> "Short introduction", - "titlemodifier" -> "", "windowtitle" -> "Short introduction", "type" -> - "Tutorial", "uri" -> "FeynCalc/tutorial/Intro"}, "SearchTextTranslated" -> - ""}, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +SP (scalar product)", "synonyms" -> {}, "tabletags" -> + DocumentationBuild`Make`Private`tabletaggingrules$298733, "title" -> + "Short introduction", "titlemodifier" -> "", "windowtitle" -> + "Short introduction", "type" -> "Tutorial", "uri" -> + "FeynCalc/tutorial/Intro"}, "SearchTextTranslated" -> ""}, +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->Notebook[{ Cell[ StyleData[ @@ -983,7 +961,7 @@ StyleDefinitions->Notebook[{ Cell[ StyleData["TutorialRelatedLinksSection"], CellGroupingRules -> {"SectionGrouping", 30}]}, Visible -> False, - 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CellTags->"$AL", - CellID->1837478580] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -394,12 +392,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$Abbreviations.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$Abbreviations.nb index 8be7833bd..10aa6025f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$Abbreviations.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$Abbreviations.nb @@ -187,9 +187,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/WriteOutPaVe", ButtonNote->"WriteOutPaVe"], "." -}], "Text", - CellTags->"$Abbreviations", - CellID->1391380109] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -275,12 +273,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$BreitMaison.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$BreitMaison.nb index 1cab8e27f..baebdfd49 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$BreitMaison.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$BreitMaison.nb @@ -117,14 +117,10 @@ Cell["$BreitMaison", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["$BreitMaison"], "InlineFormula"], - " \[LineSeparator]", - "The Breitenlohner-Maison ", - Cell[BoxData[ - FormBox[ - SubscriptBox["\[Gamma]", "5"], TraditionalForm]]], - " scheme is currently not supported by the Dirac algebra functions.Use \ -Tracer if you need it (PHI supplies the functions FCToTracer and \ -TracerToFC)." + " \[LineSeparator]is a legacy switch for the \ +Breitenlohner-Maison-t'Hooft-Veltman scheme. Use FCSetDiracGammaScheme to \ +specify a scheme for handling Dirac matrices in dimensional regularization \ +and FCGetDiracGammaScheme to check the current setting." }], "Usage", CellID->982511436], @@ -165,24 +161,17 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["Tr", + ButtonBox["FCSetDiracGammaScheme", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Tr", - ButtonNote->"Tr"], + ButtonData:>"paclet:FeynCalc/ref/FCSetDiracGammaScheme", + ButtonNote->"FCSetDiracGammaScheme"], ", ", - ButtonBox["$Larin", + ButtonBox["FCGetDiracGammaScheme", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/$Larin", - ButtonNote->"$Larin"], - ", ", - ButtonBox["West", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/West", - ButtonNote->"West"], + ButtonData:>"paclet:FeynCalc/ref/FCGetDiracGammaScheme", + ButtonNote->"FCGetDiracGammaScheme"], "." -}], "Text", - CellTags->"$BreitMaison", - CellID->1928344928] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -268,12 +257,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 741}, -WindowMargins->{{Automatic, 961}, {84, Automatic}}, +WindowMargins->{{934, Automatic}, {20, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$Covariant.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$Covariant.nb deleted file mode 100644 index f2fabb3ef..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$Covariant.nb +++ /dev/null @@ -1,257 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/$Covariant", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - 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CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["$Covariant", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["$Covariant"], "InlineFormula"], - " \[LineSeparator]", - "the boolean setting of $Covariant determines whether Lorentz indices are \ -displayed as lower indices (True) or as upper ones (False)." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - 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$Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCMemoryAvailable.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCMemoryAvailable.nb new file mode 100644 index 000000000..4fe4f3c30 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCMemoryAvailable.nb @@ -0,0 +1,282 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.0", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/$FCMemoryAvailable", "Categorization", + CellLabel->"URI"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["$FCMemoryAvailable", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData["$FCMemoryAvailable"], "InlineFormula"], + " \[LineSeparator]", + "is a global variable which is set to an integer ", + StyleBox["n", + FontSlant->"Italic"], + ", where ", + StyleBox["n", + FontSlant->"Italic"], + " is the available amount of main memory in MB. The default is 128. It \ +should be increased if possible. The higher $FCMemoryAvailable can be, the \ +more intermediate steps do not have to be repeated by FeynCalc." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData["$FCMemoryAvailable"], "Input", + CellTags->"$FCMemoryAvailable", + CellLabel->"In[53]:=", + CellID->695439641], + +Cell[BoxData[ + FormBox["4096", TraditionalForm]], "Output", + CellTags->"$FCMemoryAvailable", + CellLabel->"Out[53]="] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, +Visible->True, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCS.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCS.nb index 993b5edfe..210ec75e1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCS.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCS.nb @@ -280,12 +280,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCShowIEta.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCShowIEta.nb new file mode 100644 index 000000000..a1ff7ef1d --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCShowIEta.nb @@ -0,0 +1,345 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/$FCShowIEta", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["$FCShowIEta", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData["$FCShowIEta"], "InlineFormula"], + " \[LineSeparator]The boolean setting of $FCShowIEta detrmines whether I \ +\[Eta] should be displayed in the typesetting of GFAD and \ +GenericPropagatorDenominator objects or not. This setting affects only the \ +TraditionalForm typesetting and has absolutely no influence on the internal \ +handling of propagator denominators in FeynCalc." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData["$FCShowIEta"], "Input", + CellLabel->"In[330]:=", + CellID->710731682], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[330]=", + CellID->2143783398] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SFAD", "[", + RowBox[{"{", + RowBox[{"p", ",", + RowBox[{"m", "^", "2"}]}], "}"}], "]"}]], "Input", + CellLabel->"In[331]:=", + CellID->1378639796], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[331]=", + CellID->427014609] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"$FCShowIEta", "=", "False"}]], "Input", + CellLabel->"In[332]:=", + CellID->462213996], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + CellLabel->"Out[332]=", + CellID->1909211131] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SFAD", "[", + RowBox[{"{", + RowBox[{"p", ",", + RowBox[{"m", "^", "2"}]}], "}"}], "]"}]], "Input", + CellLabel->"In[333]:=", + CellID->2000350143], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[333]=", + CellID->92097782] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"$FCShowIEta", "=", "True"}]], "Input", + CellLabel->"In[334]:=", + CellID->942085505], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[334]=", + CellID->1291376477] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{480, Automatic}, {Automatic, 55}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCT.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCT.nb index 665adf838..9c51240fe 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCT.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCT.nb @@ -187,10 +187,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"$FCT", - CellID->1394179374], - Cell[BoxData[ RowBox[{ RowBox[{"$FCT", " ", "=", " ", "True"}], ";"}]], "Input", @@ -335,12 +331,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCTraditionalFormOutput.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCTraditionalFormOutput.nb new file mode 100644 index 000000000..bd4e10185 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FCTraditionalFormOutput.nb @@ -0,0 +1,272 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/$FCTraditionalFormOutput", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["$FCTraditionalFormOutput", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData["$FCTraditionalFormOutput"], "InlineFormula"], + " \[LineSeparator]The boolean setting of $FCTraditionalFormOutput determines \ +which output format type should be used in the notebook front end when \ +FeynCalc is loaded. If set to True, FeynCalc will activate the \ +TraditionalForm output. Otherwise, the StandardForm output (Mathematica's \ +default) will be used. This setting only changes the output format of the \ +current notebook, i.e. it is not persistent and will not modify the global \ +options of Mathematica. If unsure, it is recommended to set \ +$FCTraditionalFormOutput to True, so that you can benefit from the nice \ +FeynCalc typesetting for various QFT quantities." +}], "Usage", + CellID->982511436], + +Cell[CellGroupData[{ + +Cell[BoxData["$FCTraditionalFormOutput"], "Input", + CellLabel->"In[13]:=", + CellID->1499223899], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + CellLabel->"Out[13]=", + CellID->825857747] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{244, Automatic}, {Automatic, 106}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FeynCalcStuff.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FeynCalcStuff.nb deleted file mode 100644 index d315553f6..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FeynCalcStuff.nb +++ /dev/null @@ -1,256 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/$FeynCalcStuff", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["$FeynCalcStuff", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["$FeynCalcStuff"], "InlineFormula"], - " \[LineSeparator]", - "is the list of availabe stuff in FeynCalc." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell["XXXX", "SeeAlso", - CellID->929782353] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FeynCalcVersion.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FeynCalcVersion.nb index bb48a003f..44396269d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FeynCalcVersion.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FeynCalcVersion.nb @@ -186,22 +186,17 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"$FeynCalcVersion", - CellID->1483320671], - Cell[CellGroupData[{ Cell[BoxData["$FeynCalcVersion"], "Input", CellTags->"$FeynCalcVersion", - CellLabel->"In[1]:=", + CellLabel->"In[188]:=", CellID->806604709], Cell[BoxData[ - FormBox["\<\"9.0.0\"\>", TraditionalForm]], "Output", + FormBox["\<\"9.3.0\"\>", TraditionalForm]], "Output", CellTags->"$FeynCalcVersion", - CellLabel->"Out[1]=", - CellID->1396918294] + CellLabel->"Out[188]="] }, Open ]] }, Open ]], @@ -266,12 +261,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FortranContinuationCharacter.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FortranContinuationCharacter.nb index 6ed68cdbf..a173ef389 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$FortranContinuationCharacter.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$FortranContinuationCharacter.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Write2", ButtonNote->"Write2"], "." -}], "Text", - CellTags->"$FortranContinuationCharacter", - CellID->1130623945] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -193,10 +191,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"$FortranContinuationCharacter", - CellID->1942758352], - Cell[CellGroupData[{ Cell[BoxData["$FortranContinuationCharacter"], "Input", @@ -273,12 +267,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$Gauge.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$Gauge.nb index 7d95245b5..299c07e53 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$Gauge.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$Gauge.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Gauge", ButtonNote->"Gauge"], "." -}], "Text", - CellTags->"$Gauge", - CellID->1591453554] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$Larin.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$Larin.nb index 7fa5e8ffb..29c58176d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$Larin.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$Larin.nb @@ -117,35 +117,11 @@ Cell["$Larin", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["$Larin"], "InlineFormula"], - " \[LineSeparator]", - "If set to True, the Larin-Gorishny-Atkyampo-DelBurgo-scheme for ", - Cell[BoxData[ - FormBox[ - SubscriptBox["\[Gamma]", "5"], TraditionalForm]]], - " in ", - StyleBox["D", - FontSlant->"Italic"], - "-dimensions is used, i.e. before evaluating traces (but after moving ", - Cell[BoxData[ - FormBox[ - SubscriptBox["\[Gamma]", "5"], TraditionalForm]]], - " anticommuting in all dimensions to the right of the Dirac string) a \ -product gamma[mu].gamma5 is substituted to -I/6 Eps[mu,al,be,si] \ -gamma[al,be,si], where all indices live in ", - StyleBox["D", - FontSlant->"Italic"], - "-dimensions now. Especially the Levic-Civita tensor is taken to be ", - StyleBox["D", - FontSlant->"Italic"], - "-dimensional, i.e., contraction of two Eps's results in ", - StyleBox["D", - FontSlant->"Italic"], - "'s. This has (FOR ONE AXIAL-VECTOR-CURRENT ONLY, it is not so clear if this \ -scheme also works for more than one fermion line involving ", - Cell[BoxData[ - FormBox[ - SubscriptBox["\[Gamma]", "5"], TraditionalForm]]], - ") the same effect as the Breitenlohner-Maison-'t Hooft-Veltman scheme." + " \[LineSeparator] is a legacy switch for the \ +Larin-Gorishny-Atkyampo-DelBurgo scheme. The modern way is to use \ +FCSetDiracGammaScheme to specify a scheme for handling Dirac matrices in \ +dimensional regularization and FCGetDiracGammaScheme to check the current \ +setting." }], "Usage", CellID->982511436], @@ -185,29 +161,18 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[RawData["\<\ Cell[TextData[{ - ButtonBox[\"Tr\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/Tr\", - ButtonNote->\"Tr\"], - \", \", - ButtonBox[\"$BreitMaison\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/$BreitMaison\", - ButtonNote->\"$BreitMaison\"], - \", \", - ButtonBox[\"West\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/West\", - ButtonNote->\"West\"], - \".\" -}], \"Text\", - CellTags->\"$Larin\", - CellID->181403197]\ -\>"], "Text", - CellTags->"$Larin", - CellID->181403197] + ButtonBox["FCSetDiracGammaScheme", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FCSetDiracGammaScheme", + ButtonNote->"FCSetDiracGammaScheme"], + ", ", + ButtonBox["FCGetDiracGammaScheme", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FCGetDiracGammaScheme", + ButtonNote->"FCGetDiracGammaScheme"], + "." +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -219,8 +184,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -234,25 +197,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"$Larin", - CellID->1690224764], - -Cell[CellGroupData[{ - -Cell[BoxData["$Larin"], "Input", - CellTags->"$Larin", - CellLabel->"In[1]:=", - CellID->1245299015], - -Cell[BoxData[ - FormBox["True", TraditionalForm]], "Output", - CellTags->"$Larin", - CellLabel->"Out[1]=", - CellID->1660409352] -}, Open ]] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -314,12 +258,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 741}, -WindowMargins->{{Automatic, 943}, {Automatic, 79}}, +WindowMargins->{{905, Automatic}, {Automatic, 106}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$LeviCivitaSign.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$LeviCivitaSign.nb index 9a4e69d34..1dec2b2f0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$LeviCivitaSign.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$LeviCivitaSign.nb @@ -1,22 +1,3 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 10.3' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 13682, 554] -NotebookOptionsPosition[ 9031, 387] -NotebookOutlinePosition[ 9644, 411] -CellTagsIndexPosition[ 9566, 406] -WindowFrame->Normal*) - -(* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ "New in: ", @@ -138,15 +119,13 @@ Cell[TextData[{ Cell[BoxData["$LeviCivitaSign"], "InlineFormula"], " \[LineSeparator]is a global variable that determines the sign in the \ result of a Dirac trace of four gamma matrices and gamma5. $LeviCivitaSign \ -is by default set to -1 which corresponds to the convention \ -Tr[LeviCivita[a,b,c,d,5]] = -4*I*Eps[a,b,c,d]. Setting $LeviCivitaSign=-I \ -will switch to the FORM-convention." +is by default set to -1 which corresponds to the convention Tr[LC[a,b,c,d,5]] \ += -4*I*Eps[a,b,c,d]. Setting $LeviCivitaSign=-I will switch to the \ +FORM-convention." }], "Usage", - CellChangeTimes->{{3.677083863597835*^9, 3.677083881575591*^9}}, CellID->982511436], Cell["XXXX", "Notes", - CellChangeTimes->{{3.677083896911336*^9, 3.6770839265668697`*^9}}, CellID->1067943069] }, Open ]], @@ -213,15 +192,12 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData["$LeviCivitaSign"], "Input", - CellChangeTimes->{{3.677083940452142*^9, 3.6770839418053417`*^9}}, CellLabel->"In[4]:=", CellID->1712420789], Cell[BoxData[ FormBox[ RowBox[{"-", "1"}], TraditionalForm]], "Output", - CellChangeTimes->{3.677083942268503*^9, 3.677084042541326*^9, - 3.677084190399844*^9}, CellLabel->"Out[4]=", CellID->2017735240] }, Open ]], @@ -233,8 +209,6 @@ Cell[BoxData[ RowBox[{"GA", "[", RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "5"}], "]"}], "]"}]], "Input", - CellChangeTimes->{{3.677083949336968*^9, 3.677083986550789*^9}, { - 3.6770843934493504`*^9, 3.6770844011427383`*^9}}, CellLabel->"In[21]:=", CellID->722943498], @@ -260,14 +234,11 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", - CellChangeTimes->{{3.677084393967458*^9, 3.677084401925448*^9}}, CellLabel->"Out[21]=", CellID->24019145] }, Open ]], Cell["This sets the same convention as in FORM", "Notes", - CellChangeTimes->{{3.677083896911336*^9, 3.6770839265668697`*^9}, { - 3.677084159749695*^9, 3.67708416680619*^9}}, CellID->1734027625], Cell[CellGroupData[{ @@ -280,8 +251,6 @@ Cell[BoxData[{ RowBox[{"GA", "[", RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "5"}], "]"}], "]"}]}], "Input", - CellChangeTimes->{{3.677084138294552*^9, 3.677084148526932*^9}, - 3.677084408798975*^9}, CellLabel->"In[22]:=", CellID->1075951969], @@ -306,21 +275,17 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", - CellChangeTimes->{3.677084410012164*^9}, CellLabel->"Out[23]=", CellID->1430392236] }, Open ]], Cell["Back to the standard value", "Notes", - CellChangeTimes->{{3.677083896911336*^9, 3.6770839265668697`*^9}, { - 3.677084159749695*^9, 3.6770841814135723`*^9}}, CellID->223764811], Cell[BoxData[ RowBox[{ RowBox[{"$LeviCivitaSign", "=", RowBox[{"-", "1"}]}], ";"}]], "Input", - 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The value must be set before loading \ +FeynCalc. The default value is False." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{883, Automatic}, {Automatic, 241}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$LorentzIndices.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$LorentzIndices.nb deleted file mode 100644 index 07f53f813..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$LorentzIndices.nb +++ /dev/null @@ -1,454 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/$LorentzIndices", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["$LorentzIndices", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["$LorentzIndices"], "InlineFormula"], - " \[LineSeparator]", - "is a global variable. 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Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell["Examples", "Subsubsection", - CellTags->"$LorentzIndices", - CellID->1537148561], - -Cell[BoxData[ - RowBox[{ - RowBox[{"$LorentzIndices", "=", "True"}], ";"}]], "Input", - CellTags->"$LorentzIndices", - CellLabel->"In[1]:=", - CellID->1716323912], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{"MetricTensor", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", - RowBox[{"Dimension", "\[Rule]", "n"}]}], "]"}], - RowBox[{"DiracMatrix", "[", - RowBox[{"\[Alpha]", ",", - RowBox[{"Dimension", "\[Rule]", "n"}]}], "]"}]}]], "Input", - CellTags->"$LorentzIndices", - CellLabel->"In[2]:=", - CellID->1846109645], - -Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["\[Gamma]", - FormBox[ - SubscriptBox[ - FormBox["\[Alpha]", - TraditionalForm], - FormBox["n", - TraditionalForm]], - TraditionalForm]], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - SubscriptBox[ - FormBox["\[Alpha]", - TraditionalForm], - FormBox["n", - TraditionalForm]], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - SubscriptBox[ - FormBox["\[Beta]", - TraditionalForm], - FormBox["n", - TraditionalForm]], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"$LorentzIndices", - CellLabel->"Out[2]=", - CellID->988227023] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"%", "//", "StandardForm"}]], "Input", - CellTags->"$LorentzIndices", - CellLabel->"In[3]:=", - CellID->1902297841], - -Cell[BoxData[ - RowBox[{ - RowBox[{"DiracGamma", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Alpha]", ",", "n"}], "]"}], ",", "n"}], "]"}], " ", - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Alpha]", ",", "n"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Beta]", ",", "n"}], "]"}]}], "]"}]}]], "Output", - CellTags->"$LorentzIndices", - CellLabel->"Out[3]//StandardForm=", - CellID->2067378900] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{"MTD", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], " ", - RowBox[{"FVD", "[", - RowBox[{"p", ",", "\[Beta]"}], "]"}], - RowBox[{"GAD", "[", "\[Mu]", "]"}]}], "//", "FCI"}]], "Input", - CellTags->"$LorentzIndices", - CellLabel->"In[4]:=", - CellID->1893710771], - -Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["\[Gamma]", - FormBox[ - SubscriptBox[ - FormBox["\[Mu]", - TraditionalForm], - FormBox["D", - TraditionalForm]], - TraditionalForm]], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - SubscriptBox[ - FormBox["\[Beta]", - TraditionalForm], - FormBox["D", - TraditionalForm]], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - SubscriptBox[ - FormBox["\[Alpha]", - TraditionalForm], - FormBox["D", - TraditionalForm]], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - SubscriptBox[ - FormBox["\[Beta]", - TraditionalForm], - FormBox["D", - TraditionalForm]], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"$LorentzIndices", - CellLabel->"Out[4]=", - CellID->1671614812] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"%", "//", "StandardForm"}]], "Input", - CellTags->"$LorentzIndices", - CellLabel->"In[5]:=", - CellID->1327558227], - -Cell[BoxData[ - RowBox[{ - RowBox[{"DiracGamma", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", "D"}], "]"}], " ", - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Alpha]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Beta]", ",", "D"}], "]"}]}], "]"}], " ", - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Beta]", ",", "D"}], "]"}], ",", - RowBox[{"Momentum", "[", - RowBox[{"p", ",", "D"}], "]"}]}], "]"}]}]], "Output", - CellTags->"$LorentzIndices", - CellLabel->"Out[5]//StandardForm=", - CellID->1816548467] -}, Open ]], - -Cell[BoxData[ - RowBox[{ - RowBox[{"$LorentzIndices", "=", "False"}], ";"}]], "Input", - CellTags->"$LorentzIndices", - CellLabel->"In[6]:=", - CellID->326767008] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; 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Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$MIntegrate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$MIntegrate.nb index 3bf445721..2089c83b2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$MIntegrate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$MIntegrate.nb @@ -167,9 +167,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPEIntegrateDelta", ButtonNote->"OPEIntegrateDelta"], "." -}], "Text", - CellTags->"$MIntegrate", - CellID->193164279] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -196,10 +194,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"$MIntegrate", - CellID->896374065], - Cell[CellGroupData[{ Cell[BoxData["$MIntegrate"], "Input", @@ -213,19 +207,7 @@ Cell[BoxData[ CellTags->"$MIntegrate", CellLabel->"Out[1]=", CellID->1034422222] -}, Open ]], - -Cell[TextData[{ - "See also: ", - " ", - ButtonBox["OPEIntegrateDelta", - BaseStyle->"AddOnsLink", - ButtonData:>"OPEIntegrateDelta", - ButtonNote->"OPEIntegrateDelta"], - "." -}], "Text", - CellTags->"$MIntegrate", - CellID->404160805] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -289,12 +271,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$MU.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$MU.nb index f2983e189..a9f860f04 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$MU.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$MU.nb @@ -176,9 +176,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", ButtonNote->"DiracSimplify"], "." -}], "Text", - CellTags->"$MU", - CellID->58635825] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -205,10 +203,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"$MU", - CellID->1771415745], - Cell[CellGroupData[{ Cell[BoxData["$MU"], "Input", @@ -221,29 +215,7 @@ Cell[BoxData[ CellTags->"$MU", CellLabel->"Out[1]=", CellID->418655578] -}, Open ]], - -Cell[TextData[{ - "See also: ", - " ", - ButtonBox["Chisholm", - BaseStyle->"AddOnsLink", - ButtonData:>"Chisholm", - ButtonNote->"Chisholm"], - ", ", - ButtonBox["Contract", - BaseStyle->"AddOnsLink", - ButtonData:>"Contract", - ButtonNote->"Contract"], - ", ", - ButtonBox["DiracSimplify", - BaseStyle->"AddOnsLink", - ButtonData:>"DiracSimplify", - ButtonNote->"DiracSimplify"], - "." -}], "Text", - CellTags->"$MU", - CellID->265635386] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -307,12 +279,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$MemoryAvailable.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$MemoryAvailable.nb deleted file mode 100644 index c8eb29e4c..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$MemoryAvailable.nb +++ /dev/null @@ -1,285 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/$MemoryAvailable", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["$MemoryAvailable", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["$MemoryAvailable"], "InlineFormula"], - " \[LineSeparator]", - "is a global variable which is set to an integer ", - StyleBox["n", - FontSlant->"Italic"], - ", where ", - StyleBox["n", - FontSlant->"Italic"], - " is the available amount of main memory in MB. The default is 128. It \ -should be increased if possible. The higher $MemoryAvailable can be, the more \ -intermediate steps do not have to be repeated by FeynCalc." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell["XXXX", "SeeAlso", - CellID->929782353] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell["Examples", "Subsubsection", - CellTags->"$MemoryAvailable", - CellID->343639326], - -Cell[CellGroupData[{ - -Cell[BoxData["$MemoryAvailable"], "Input", - CellTags->"$MemoryAvailable", - CellLabel->"In[1]:=", - CellID->695439641], - -Cell[BoxData[ - FormBox["4096", TraditionalForm]], "Output", - CellTags->"$MemoryAvailable", - CellLabel->"Out[1]=", - CellID->1467745985] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$NonComm.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$NonComm.nb index 1f1981882..d0fc2af2b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$NonComm.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$NonComm.nb @@ -117,8 +117,7 @@ Cell["$NonComm", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["$NonComm"], "InlineFormula"], - " \[LineSeparator]", - "contains a list of all non-commutative heads present." + " \[LineSeparator]contains a list of all noncommutative heads present." }], "Usage", CellID->982511436], @@ -169,9 +168,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/NonCommutative", ButtonNote->"NonCommutative"], "." -}], "Text", - CellTags->"$NonComm", - CellID->1040108898] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -198,39 +195,37 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"$NonComm", - CellID->2045411989], - Cell[CellGroupData[{ Cell[BoxData["$NonComm"], "Input", CellTags->"$NonComm", - CellLabel->"In[1]:=", + CellLabel->"In[189]:=", CellID->1876740578], Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ - "ChiralityProjector", ",", "DiracGamma", ",", "DiracGammaT", ",", - "DiracMatrix", ",", "DiracSigma", ",", "DiracSlash", ",", "DiracSpinor", - ",", "GA", ",", + "ChiralityProjector", ",", "DiracGamma", ",", "DiracMatrix", ",", + "DiracSigma", ",", "DiracSlash", ",", "Spinor", ",", "GA", ",", SuperscriptBox[ OverscriptBox["\[Gamma]", "_"], FormBox["5", TraditionalForm]], ",", "GAD", ",", "GAE", ",", "GS", ",", "GSD", ",", "GSE", ",", "LeftPartialD", ",", "LeftRightPartialD", ",", - "LeftRightPartialD2", ",", "FCPartialD", ",", "PauliSigma", ",", + "LeftRightPartialD2", ",", "FCPartialD", ",", "OPESum", ",", "QuantumField", ",", "RightPartialD", ",", "Spinor", ",", "SpinorU", ",", - "SpinorUBar", ",", "SpinorV", ",", "SpinorVBar", ",", "SUNT", ",", "C", - ",", "CovariantD", ",", "OPESum", ",", "FieldStrength", ",", - "QuarkGluonVertex", ",", "QuarkPropagator", ",", "Twist2AlienOperator", - ",", "Twist2CounterOperator", ",", "Twist2QuarkOperator"}], "}"}], + "SpinorUBar", ",", "SpinorV", ",", "SpinorVBar", ",", "SUNT", ",", + "PauliSigma", ",", "PauliXi", ",", "PauliEta", ",", "TGA", ",", "CGA", + ",", "CGAD", ",", "CGAE", ",", "CGS", ",", "CGSD", ",", "CGSE", ",", "SI", + ",", "SID", ",", "SIE", ",", "CSI", ",", "CSID", ",", "CSIE", ",", + "FeynCalc`Package`dotsimpHold", ",", "FCChargeConjugateTransposed", ",", + "CovariantD", ",", "FieldStrength", ",", "QuarkGluonVertex", ",", + "QuarkPropagator", ",", "Twist2AlienOperator", ",", + "Twist2CounterOperator", ",", "Twist2QuarkOperator"}], "}"}], TraditionalForm]], "Output", CellTags->"$NonComm", - CellLabel->"Out[1]=", - CellID->1539262372] + CellLabel->"Out[189]="] }, Open ]] }, Open ]], @@ -295,12 +290,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$PairBrackets.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$PairBrackets.nb deleted file mode 100644 index 75adcefbf..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$PairBrackets.nb +++ /dev/null @@ -1,420 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - 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$Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$RenameFeynCalcObjects.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$RenameFeynCalcObjects.nb new file mode 100644 index 000000000..f2db7be2d --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$RenameFeynCalcObjects.nb @@ -0,0 +1,281 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/$RenameFeynCalcObjects", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["$RenameFeynCalcObjects", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"$RenameFeynCalcObjects", "[", "]"}]], "InlineFormula"], + " \[LineSeparator]specifies a List of replacement rules that allow to rename \ +FeynCalc objects on the run to avoid conflicts with other package before \ +FeynCalc is loaded (monkey patching). The value of $RenameFeynCalcObjects \ +must be specified before loading FeynCalc" +}], "Usage", + CellID->982511436], + +Cell["\<\ +The following code (when executed on a fresh kernel with the last two lines \ +uncommented) allows to load FeynCalc and Roman Lee's LiteRed on the same \ +kernel without shadowing issues\ +\>", "Notes", + CellID->379603153], + +Cell[BoxData[{ + RowBox[{ + RowBox[{ + RowBox[{"$RenameFeynCalcObjects", "=", + RowBox[{"{", + RowBox[{ + RowBox[{"\"\\"", "\[Rule]", "\"\\""}], + ",", + RowBox[{"\"\\"", "\[Rule]", "\"\\""}], ",", + RowBox[{"\"\\"", "\[Rule]", "\"\\""}]}], "}"}]}], + ";"}], "\[IndentingNewLine]", + RowBox[{"(*", + RowBox[{"<<", "FeynCalc`"}], "*)"}]}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"(*", + RowBox[{"<<", "LiteRed`"}], "*)"}]}]}], "Input", + CellID->1698473390] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{653, Automatic}, {Automatic, 240}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$SpinorMinimal.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$SpinorMinimal.nb deleted file mode 100644 index c9d2c23a4..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$SpinorMinimal.nb +++ /dev/null @@ -1,265 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/$SpinorMinimal", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["$SpinorMinimal", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["$SpinorMinimal"], "InlineFormula"], - " \[LineSeparator]", - "is a global switch for an additional simplification attempt in \ -DiracSimplify for more than one Spinor-line. The default is False, since \ -otherwise it costs too much time." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - ButtonBox["DiracSimplify", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], - "." -}], "Text", - CellTags->"$SpinorMinimal", - CellID->329467642] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/$VeryVerbose.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/$VeryVerbose.nb index 00565e528..0308bc808 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/$VeryVerbose.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/$VeryVerbose.nb @@ -187,10 +187,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"$VeryVerbose", - CellID->61376549], - Cell[CellGroupData[{ Cell[BoxData["$VeryVerbose"], "Input", @@ -405,12 +401,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/A0.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/A0.nb index 12f5010ff..b28f1518f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/A0.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/A0.nb @@ -185,9 +185,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PaVe", ButtonNote->"PaVe"], "." -}], "Text", - CellTags->"A0", - CellID->70965860] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -242,9 +240,7 @@ Cell[TextData[{ FormBox[ SubscriptBox["B", "0"], TraditionalForm]]], "." -}], "Text", - CellTags->"A0", - CellID->1026580483], +}], "Notes"], Cell[CellGroupData[{ @@ -325,9 +321,7 @@ Cell[TextData[{ RowBox[{ SubscriptBox["A", "0"], "(", "0", ")"}], TraditionalForm]]], " is set to 0." -}], "Text", - CellTags->"A0", - CellID->1221823578], +}], "Notes"], Cell[CellGroupData[{ @@ -423,12 +417,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 62}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/A0ToB0.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/A0ToB0.nb index 8e5d494d2..94eabf54b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/A0ToB0.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/A0ToB0.nb @@ -208,9 +208,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PaVe", ButtonNote->"PaVe"], "." -}], "Text", - CellTags->"A0ToB0", - CellID->1722982066] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -237,10 +235,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"A0ToB0", - CellID->2064085766], - Cell[CellGroupData[{ Cell[BoxData[ @@ -257,39 +251,7 @@ Cell[BoxData[ CellTags->"A0ToB0", CellLabel->"Out[1]=", CellID->1727801355] -}, Open ]], - -Cell[TextData[{ - "See also: ", - " ", - ButtonBox["A0", - BaseStyle->"AddOnsLink", - ButtonData:>"A0", - ButtonNote->"A0"], - ", ", - ButtonBox["B0", - BaseStyle->"AddOnsLink", - ButtonData:>"B0", - ButtonNote->"B0"], - ", ", - ButtonBox["C0", - BaseStyle->"AddOnsLink", - ButtonData:>"C0", - ButtonNote->"C0"], - ", ", - ButtonBox["D0", - BaseStyle->"AddOnsLink", - ButtonData:>"D0", - ButtonNote->"D0"], - ", ", - ButtonBox["PaVe", - BaseStyle->"AddOnsLink", - ButtonData:>"PaVe", - ButtonNote->"PaVe"], - "." -}], "Text", - CellTags->"A0ToB0", - CellID->1120307520] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -353,12 +315,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Abbreviation.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Abbreviation.nb index 965c7c71f..793f1759e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Abbreviation.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Abbreviation.nb @@ -202,9 +202,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/QuarkPropagator", ButtonNote->"QuarkPropagator"], "." -}], "Text", - CellTags->"Abbreviation", - CellID->1098399815] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -327,12 +325,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, 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"UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Amputate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Amputate.nb index eff3acab0..2bf2e8f75 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Amputate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Amputate.nb @@ -125,8 +125,26 @@ also p.q1 and p.q2; Pair\[Rule]All amputates all except OPEDelta." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Amputate", "]"}]], "Input", + CellTags->"Amputate", + CellLabel->"In[194]:=", + CellID->1884550851], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Pair", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"Unique", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"Amputate", + CellLabel->"Out[194]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -167,29 +185,27 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracGamma", ButtonNote->"DiracGamma"], ", ", - ButtonBox["DiracMatrix", + ButtonBox["GA", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData:>"paclet:FeynCalc/ref/GA", + ButtonNote->"GA"], ", ", ButtonBox["DiracSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", ButtonNote->"DiracSimplify"], ", ", - ButtonBox["DiracSlash", + ButtonBox["GS", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], + ButtonData:>"paclet:FeynCalc/ref/GS", + ButtonNote->"GS"], ", ", ButtonBox["DiracTrick", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracTrick", ButtonNote->"DiracTrick"], "." -}], "Text", - CellTags->"Amputate", - CellID->1266124166] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,58 +234,39 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Amputate", "]"}]], "Input", - CellTags->"Amputate", - CellLabel->"In[1]:=", - CellID->1884550851], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"Pair", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"Unique", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"Amputate", - CellLabel->"Out[1]=", - CellID->697719830] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{ - RowBox[{"DiracSlash", "[", "p", "]"}], ".", - RowBox[{"DiracSlash", "[", "q", "]"}]}]], "Input", + RowBox[{"GS", "[", "p", "]"}], ".", + RowBox[{"GS", "[", "q", "]"}]}]], "Input", CellTags->"Amputate", - CellLabel->"In[2]:=", + CellLabel->"In[27]:=", CellID->479729855], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"(", - RowBox[{ - OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm]}], ")"}], ".", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", RowBox[{"(", - RowBox[{ - OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"Amputate", - CellLabel->"Out[2]=", - CellID->1732499360] + CellLabel->"Out[27]="] }, Open ]], Cell[CellGroupData[{ @@ -278,27 +275,23 @@ Cell[BoxData[ RowBox[{"Amputate", "[", RowBox[{"%", ",", "q"}], "]"}]], "Input", CellTags->"Amputate", - CellLabel->"In[3]:=", + CellLabel->"In[28]:=", CellID->1612122659], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["q", - TraditionalForm], - TraditionalForm], + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], + FormBox[ FormBox[ - FormBox[ - FormBox[ - RowBox[{"$AL$2188", "\[InvisibleApplication]", - RowBox[{"(", "1", ")"}]}], - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", + RowBox[{"$AL$41318", "\[InvisibleApplication]", + RowBox[{"(", "1", ")"}]}], + TraditionalForm], + TraditionalForm]], " ", RowBox[{ RowBox[{"(", RowBox[{ @@ -311,13 +304,12 @@ Cell[BoxData[ SuperscriptBox["\[Gamma]", FormBox[ FormBox[ - RowBox[{"$AL$2188", "\[InvisibleApplication]", + RowBox[{"$AL$41318", "\[InvisibleApplication]", RowBox[{"(", "1", ")"}]}], TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Amputate", - CellLabel->"Out[3]=", - CellID->42958207] + CellLabel->"Out[28]="] }, Open ]] }, Open ]], @@ -382,12 +374,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{714, Automatic}, {Automatic, 143}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/AnomalousDimension.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/AnomalousDimension.nb index 0e3ba0c13..b55039bf8 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/AnomalousDimension.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/AnomalousDimension.nb @@ -123,8 +123,25 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "AnomalousDimension", "]"}]], "Input", + CellTags->"AnomalousDimension", + CellLabel->"In[1]:=", + CellID->1953214619], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Polarization", "\[Rule]", "1"}], ",", + RowBox[{"Simplify", "\[Rule]", "FullSimplify"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"AnomalousDimension", + CellLabel->"Out[1]=", + CellID->1686866166] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -176,9 +193,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SumT", ButtonNote->"SumT"], "." -}], "Text", - CellTags->"AnomalousDimension", - CellID->1774979938] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -205,29 +220,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "AnomalousDimension", "]"}]], "Input", - CellTags->"AnomalousDimension", - CellLabel->"In[1]:=", - CellID->1953214619], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Polarization", "\[Rule]", "1"}], ",", - RowBox[{"Simplify", "\[Rule]", "FullSimplify"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"AnomalousDimension", - CellLabel->"Out[1]=", - CellID->1686866166] -}, Open ]], - -Cell["Polarized case:", "Text", - CellTags->"AnomalousDimension", - CellID->2007063734], +Cell["Polarized case:", "Notes"], Cell[CellGroupData[{ @@ -236,7 +229,7 @@ Cell[BoxData[ RowBox[{"AnomalousDimension", ",", RowBox[{"Polarization", "\[Rule]", "1"}]}], "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[2]:=", + CellLabel->"In[196]:=", CellID->1676073016], Cell[BoxData[ @@ -247,8 +240,7 @@ Cell[BoxData[ RowBox[{"Simplify", "\[Rule]", "FullSimplify"}]}], "}"}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[2]=", - CellID->455353582] + CellLabel->"Out[196]="] }, Open ]], Cell[TextData[{ @@ -259,16 +251,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "0", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->1291876789], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gnsqq0", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[3]:=", + CellLabel->"In[197]:=", CellID->146201031], Cell[BoxData[ @@ -288,8 +278,7 @@ Cell[BoxData[ RowBox[{"m", "+", "1"}]], "-", "6"}], ")"}]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[3]=", - CellID->615808229] + CellLabel->"Out[197]="] }, Open ]], Cell[TextData[{ @@ -300,16 +289,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "0", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->1792202903], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gsqg0", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[4]:=", + CellLabel->"In[198]:=", CellID->1170655896], Cell[BoxData[ @@ -322,8 +309,7 @@ Cell[BoxData[ RowBox[{"m", "+", "1"}]]}], ")"}], " ", SubscriptBox["T", "f"]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[4]=", - CellID->2056489351] + CellLabel->"Out[198]="] }, Open ]], Cell[TextData[{ @@ -334,16 +320,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "0", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->1242785256], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gsgq0", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[5]:=", + CellLabel->"In[199]:=", CellID->1302484886], Cell[BoxData[ @@ -356,8 +340,7 @@ Cell[BoxData[ FractionBox["8", "m"]}], ")"}], " ", SubscriptBox["C", "F"]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[5]=", - CellID->339795493] + CellLabel->"Out[199]="] }, Open ]], Cell[TextData[{ @@ -368,16 +351,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "0", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->102826276], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gsgg0", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[6]:=", + CellLabel->"In[200]:=", CellID->255541888], Cell[BoxData[ @@ -401,8 +382,7 @@ Cell[BoxData[ RowBox[{"8", " ", SubscriptBox["T", "f"]}], "3"]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[6]=", - CellID->724940306] + CellLabel->"Out[200]="] }, Open ]], Cell[TextData[{ @@ -413,16 +393,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "0", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->1117022044], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gpsqq1", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[7]:=", + CellLabel->"In[201]:=", CellID->1738556670], Cell[BoxData[ @@ -448,8 +426,7 @@ Cell[BoxData[ SubscriptBox["C", "F"], " ", SubscriptBox["T", "f"]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[7]=", - CellID->297175504] + CellLabel->"Out[201]="] }, Open ]], Cell[TextData[{ @@ -460,16 +437,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "1", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->1509439590], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gnsqq1", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[8]:=", + CellLabel->"In[202]:=", CellID->1025475425], Cell[BoxData[ @@ -690,8 +665,7 @@ Cell[BoxData[ RowBox[{"m", "+", "1"}], ")"}], "2"]}]], "-", FractionBox["2", "3"]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[8]=", - CellID->1707320400] + CellLabel->"Out[202]="] }, Open ]], Cell[TextData[{ @@ -702,16 +676,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "1", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->26937910], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gsqg1", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[9]:=", + CellLabel->"In[204]:=", CellID->1790656955], Cell[BoxData[ @@ -854,8 +826,7 @@ Cell[BoxData[ RowBox[{"m", "+", "1"}], ")"}], "3"]]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[9]=", - CellID->578210880] + CellLabel->"Out[204]="] }, Open ]], Cell[TextData[{ @@ -866,16 +837,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "1", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->1644657872], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gsgq1", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[10]:=", + CellLabel->"In[205]:=", CellID->1820360375], Cell[BoxData[ @@ -1090,8 +1059,7 @@ Cell[BoxData[ RowBox[{"m", "+", "1"}], ")"}], "3"]]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[10]=", - CellID->1694165204] + CellLabel->"Out[205]="] }, Open ]], Cell[TextData[{ @@ -1102,16 +1070,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "1", ")"}], " "}]], TraditionalForm]]], "polarized:" -}], "Text", - CellTags->"AnomalousDimension", - CellID->462099557], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "gsgg1", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[11]:=", + CellLabel->"In[206]:=", CellID->1613754345], Cell[BoxData[ @@ -1280,8 +1246,7 @@ Cell[BoxData[ SubscriptBox["C", "F"], " ", SubscriptBox["T", "f"]}]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[11]=", - CellID->1244918806] + CellLabel->"Out[206]="] }, Open ]], Cell[TextData[{ @@ -1292,16 +1257,14 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "1", ")"}], " "}]], TraditionalForm]]], "polarized (different representation):" -}], "Text", - CellTags->"AnomalousDimension", - CellID->721182810], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"AnomalousDimension", "[", "GSGG1", "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[12]:=", + CellLabel->"In[207]:=", CellID->889064365], Cell[BoxData[ @@ -1443,8 +1406,7 @@ Cell[BoxData[ RowBox[{"m", "+", "1"}], ")"}], "3"]}]]}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[12]=", - CellID->1840404969] + CellLabel->"Out[207]="] }, Open ]], Cell[TextData[{ @@ -1456,9 +1418,7 @@ Cell[TextData[{ RowBox[{ RowBox[{"(", "1", ")"}], " "}]], TraditionalForm]]], ":" -}], "Text", - CellTags->"AnomalousDimension", - CellID->1805318835], +}], "Notes"], Cell[CellGroupData[{ @@ -1471,7 +1431,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"ij", ",", "1", ",", "17", ",", "2"}], "}"}]}], "]"}]], "Input", CellTags->"AnomalousDimension", - CellLabel->"In[13]:=", + CellLabel->"In[208]:=", CellID->621534472], Cell[BoxData[ @@ -1481,8 +1441,7 @@ Cell[BoxData[ "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}], TraditionalForm]], "Output", CellTags->"AnomalousDimension", - CellLabel->"Out[13]=", - CellID->494342750] + CellLabel->"Out[208]="] }, Open ]] }, Open ]], @@ -1547,12 +1506,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{397, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Anti5.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Anti5.nb index 709e59942..adb7fa64d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Anti5.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Anti5.nb @@ -118,26 +118,45 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"Anti5", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "anticommutes all ", + " \[LineSeparator]anticommutes all ", Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], - "in exp to the right. Anti5[exp, n] anticommutes all ", + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " in exp to the right.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"Anti5", "[", + RowBox[{"exp", ",", "n"}], "]"}]], "InlineFormula"], + " \[LineSeparator]anticommutes all ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " ", + Cell[BoxData["n"], "InlineFormula"], + "-times to the right.\n", + Cell[" ", "ModInfo"], Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", - RowBox[{"5", " "}]], TraditionalForm]]], - "n times to the right. Anti5[exp, -n] anticommutes all ", + RowBox[{"Anti5", "[", + RowBox[{"exp", ",", + RowBox[{"-", "n"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]anticommutes all ", Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], - " n times to the left." + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " ", + Cell[BoxData["n"], "InlineFormula"], + "-times to the left." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Anti5", "]"}]], "Input", + CellLabel->"In[54]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", "}"}], TraditionalForm]], "Output", + CellLabel->"Out[54]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -188,9 +207,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracTrick", ButtonNote->"DiracTrick"], "." -}], "Text", - CellTags->"Anti5", - CellID->1283449801] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -221,19 +238,31 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"DiracMatrix", "[", + RowBox[{"GA", "[", RowBox[{"5", ",", "\[Mu]"}], "]"}], " "}]], "Input", CellTags->"Anti5", - CellLabel->"In[1]:=", + CellLabel->"In[42]:=", CellID->2080632323], Cell[BoxData[ FormBox[ - RowBox[{"DiracMatrix", "(", - RowBox[{"5", ",", "\[Mu]"}], ")"}], TraditionalForm]], "Output", + RowBox[{ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[1]=", - CellID->294517214] + CellLabel->"Out[42]="] }, Open ]], Cell[CellGroupData[{ @@ -241,7 +270,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Anti5", "[", "%", "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[2]:=", + CellLabel->"In[43]:=", CellID->1232582412], Cell[BoxData[ @@ -259,18 +288,23 @@ Cell[BoxData[ FormBox["5", TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[2]=", - CellID->1246682665] + CellLabel->"Out[43]="] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"Anti5", "[", RowBox[{"%", ",", RowBox[{"-", "1"}]}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[3]:=", + CellLabel->"In[44]:=", CellID->1609506190], Cell[BoxData[ @@ -287,30 +321,63 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[3]=", - CellID->741917191] + CellLabel->"Out[44]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracMatrix", "[", + RowBox[{"GA", "[", RowBox[{ "5", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[4]:=", + CellLabel->"In[45]:=", CellID->1286690073], Cell[BoxData[ FormBox[ - RowBox[{"DiracMatrix", "(", - RowBox[{ - "5", ",", "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], - ")"}], TraditionalForm]], "Output", + RowBox[{ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Gamma]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Delta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[4]=", - CellID->733245772] + CellLabel->"Out[45]="] }, Open ]], Cell[CellGroupData[{ @@ -319,7 +386,7 @@ Cell[BoxData[ RowBox[{"Anti5", "[", RowBox[{"%", ",", "2"}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[5]:=", + CellLabel->"In[46]:=", CellID->197831622], Cell[BoxData[ @@ -354,8 +421,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[5]=", - CellID->446711059] + CellLabel->"Out[46]="] }, Open ]], Cell[CellGroupData[{ @@ -364,7 +430,7 @@ Cell[BoxData[ RowBox[{"Anti5", "[", RowBox[{"%%", ",", "Infinity"}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[6]:=", + CellLabel->"In[47]:=", CellID->1010214576], Cell[BoxData[ @@ -399,8 +465,7 @@ Cell[BoxData[ FormBox["5", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[6]=", - CellID->1568263833] + CellLabel->"Out[47]="] }, Open ]], Cell[CellGroupData[{ @@ -410,7 +475,7 @@ Cell[BoxData[ RowBox[{"%", ",", RowBox[{"-", "Infinity"}]}], "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[7]:=", + CellLabel->"In[48]:=", CellID->1359760692], Cell[BoxData[ @@ -445,26 +510,29 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[7]=", - CellID->177899299] + CellLabel->"Out[48]="] +}, Open ]] }, Open ]], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + Cell[TextData[{ "In the naive ", Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], - "- scheme D-dimensional ", + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + "-scheme ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional ", + Cell[BoxData["\[Gamma]"], "InlineFormula"], + "-matrices anticommute with", Cell[BoxData[ - FormBox["\[Gamma]", TraditionalForm]]], - "-matrices anticommute with ", - Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], "." -}], "Text", - CellTags->"Anti5", - CellID->1633748802], +}], "Notes"], Cell[CellGroupData[{ @@ -472,7 +540,7 @@ Cell[BoxData[ RowBox[{"GA5", ".", RowBox[{"GAD", "[", "\[Mu]", "]"}]}]], "Input", CellTags->"Anti5", - CellLabel->"In[8]:=", + CellLabel->"In[49]:=", CellID->1799781971], Cell[BoxData[ @@ -490,8 +558,7 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[8]=", - CellID->1994871864] + CellLabel->"Out[49]="] }, Open ]], Cell[CellGroupData[{ @@ -499,7 +566,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Anti5", "[", "%", "]"}]], "Input", CellTags->"Anti5", - CellLabel->"In[9]:=", + CellLabel->"In[50]:=", CellID->42617734], Cell[BoxData[ @@ -516,8 +583,70 @@ Cell[BoxData[ FormBox["5", TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Anti5", - CellLabel->"Out[9]=", - CellID->1660721309] + CellLabel->"Out[50]="] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[TextData[{ + ButtonBox["Anti5", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Anti5", + ButtonNote->"Anti5"], + " also works in the t'Hooft-Veltman-Breitenlohner-Maison scheme" +}], "Notes"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}], ";"}]], "Input", + CellLabel->"In[62]:="], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Anti5", "[", + RowBox[{"GA5", ".", + RowBox[{"GAD", "[", "\[Mu]", "]"}]}], "]"}]], "Input", + CellLabel->"In[63]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"2", " ", + RowBox[{ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "^"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]]}]}], "-", + RowBox[{ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]]}]}], TraditionalForm]], "Output", + CellLabel->"Out[63]="] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}], ";"}]], "Input", + + CellLabel->"In[64]:="] }, Open ]] }, Open ]], @@ -581,13 +710,14 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{864, 877}, +WindowMargins->{{730, Automatic}, {-5, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/AntiCommutator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/AntiCommutator.nb index 914bbe7d7..b66b6af1b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/AntiCommutator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/AntiCommutator.nb @@ -117,10 +117,15 @@ Cell["AntiCommutator", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"AntiCommutator", "[", - RowBox[{"x", ",", " ", "y"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "= c defines the anti-commutator of the non commuting objects x and y." + RowBox[{ + RowBox[{"AntiCommutator", "[", + RowBox[{"x", ",", " ", "y"}], "]"}], "=", "c"}]], "InlineFormula"], + " \[LineSeparator]defines the anti-commutator of the non commuting objects \ +", + Cell[BoxData["x"], "InlineFormula"], + " and ", + Cell[BoxData["y"], "InlineFormula"], + "." }], "Usage", CellID->982511436], @@ -181,9 +186,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DotSimplify", ButtonNote->"DotSimplify"], "." -}], "Text", - CellTags->"AntiCommutator", - CellID->1793111208] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,15 +221,13 @@ Cell[TextData[{ StyleBox["b", FontFamily->"Courier"], " as noncommutative variables." -}], "Text", - CellTags->"AntiCommutator", - CellID->1525212065], +}], "Notes"], Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", RowBox[{"a", ",", "b"}], "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[1]:=", + CellLabel->"In[209]:=", CellID->756062925], Cell[CellGroupData[{ @@ -235,7 +236,7 @@ Cell[BoxData[ RowBox[{"AntiCommutator", "[", RowBox[{"a", ",", "b"}], "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[2]:=", + CellLabel->"In[210]:=", CellID->1726378547], Cell[BoxData[ @@ -254,8 +255,7 @@ Cell[BoxData[ FormBox["\<\"}\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"AntiCommutator", - CellLabel->"Out[2]=", - CellID->479481037] + CellLabel->"Out[210]="] }, Open ]], Cell[CellGroupData[{ @@ -263,7 +263,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CommutatorExplicit", "[", "%", "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[3]:=", + CellLabel->"In[211]:=", CellID->693384404], Cell[BoxData[ @@ -272,8 +272,7 @@ Cell[BoxData[ RowBox[{"a", ".", "b"}], "+", RowBox[{"b", ".", "a"}]}], TraditionalForm]], "Output", CellTags->"AntiCommutator", - CellLabel->"Out[3]=", - CellID->147684859] + CellLabel->"Out[211]="] }, Open ]], Cell[CellGroupData[{ @@ -286,7 +285,7 @@ Cell[BoxData[ RowBox[{"a", "-", RowBox[{"2", "b"}]}]}], " ", "]"}], "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[4]:=", + CellLabel->"In[212]:=", CellID->1495920503], Cell[BoxData[ @@ -305,8 +304,7 @@ Cell[BoxData[ RowBox[{"a", "-", RowBox[{"2", " ", "b"}]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"AntiCommutator", - CellLabel->"Out[4]=", - CellID->1027223948] + CellLabel->"Out[212]="] }, Open ]], Cell[CellGroupData[{ @@ -319,27 +317,21 @@ Cell[BoxData[ RowBox[{"a", "-", RowBox[{"2", "b"}]}]}], " ", "]"}], "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[5]:=", + CellLabel->"In[213]:=", CellID->871283752], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{"a", "-", - RowBox[{"2", " ", "b"}]}], ")"}], ".", - RowBox[{"(", - RowBox[{"a", "+", "b"}], ")"}]}], "+", - RowBox[{ - RowBox[{"(", - RowBox[{"a", "+", "b"}], ")"}], ".", - RowBox[{"(", - RowBox[{"a", "-", - RowBox[{"2", " ", "b"}]}], ")"}]}]}], TraditionalForm]], "Output", + RowBox[{"-", + RowBox[{"a", ".", "b"}]}], "-", + RowBox[{"b", ".", "a"}], "+", + RowBox[{"2", " ", + RowBox[{"a", ".", "a"}]}], "-", + RowBox[{"4", " ", + RowBox[{"b", ".", "b"}]}]}], TraditionalForm]], "Output", CellTags->"AntiCommutator", - CellLabel->"Out[5]=", - CellID->980600157] + CellLabel->"Out[213]="] }, Open ]], Cell[BoxData[ @@ -348,12 +340,10 @@ Cell[BoxData[ OverscriptBox["c", "~"], ",", OverscriptBox["d", "~"]}], "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[6]:=", + CellLabel->"In[214]:=", CellID->422937377], -Cell["Defining {c,d} = z results in replacements of c.d by z-d.c.", "Text", - CellTags->"AntiCommutator", - CellID->405748459], +Cell["Defining {c,d} = z results in replacements of c.d by z-d.c.", "Notes"], Cell[CellGroupData[{ @@ -362,14 +352,13 @@ Cell[BoxData[ RowBox[{"AntiCommutator", "[", RowBox[{"c", ",", "d"}], "]"}], " ", "=", " ", "z"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[7]:=", + CellLabel->"In[215]:=", CellID->1154888291], Cell[BoxData[ FormBox["z", TraditionalForm]], "Output", CellTags->"AntiCommutator", - CellLabel->"Out[7]=", - CellID->1400406202] + CellLabel->"Out[215]="] }, Open ]], Cell[CellGroupData[{ @@ -379,7 +368,7 @@ Cell[BoxData[ RowBox[{"d", " ", ".", " ", "c", " ", ".", " ", "d"}], " ", "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[8]:=", + CellLabel->"In[216]:=", CellID->400792382], Cell[BoxData[ @@ -388,8 +377,7 @@ Cell[BoxData[ RowBox[{"d", " ", "z"}], "-", RowBox[{"d", ".", "d", ".", "c"}]}], TraditionalForm]], "Output", CellTags->"AntiCommutator", - CellLabel->"Out[8]=", - CellID->1500489599] + CellLabel->"Out[216]="] }, Open ]], Cell[CellGroupData[{ @@ -402,15 +390,14 @@ Cell[BoxData[ OverscriptBox["c", "~"]}], "]"}], " ", "=", " ", OverscriptBox["z", "~"]}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[9]:=", + CellLabel->"In[217]:=", CellID->392638266], Cell[BoxData[ FormBox[ OverscriptBox["z", "~"], TraditionalForm]], "Output", CellTags->"AntiCommutator", - CellLabel->"Out[9]=", - CellID->225220528] + CellLabel->"Out[217]="] }, Open ]], Cell[CellGroupData[{ @@ -422,7 +409,7 @@ Cell[BoxData[ OverscriptBox["c", "~"], " ", ".", " ", OverscriptBox["d", "~"]}], " ", "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[10]:=", + CellLabel->"In[218]:=", CellID->598753128], Cell[BoxData[ @@ -436,8 +423,7 @@ Cell[BoxData[ OverscriptBox["d", "~"], ".", OverscriptBox["d", "~"]}]}], TraditionalForm]], "Output", CellTags->"AntiCommutator", - CellLabel->"Out[10]=", - CellID->1740531218] + CellLabel->"Out[218]="] }, Open ]], Cell[BoxData[ @@ -446,7 +432,7 @@ Cell[BoxData[ OverscriptBox["c", "~"], ",", OverscriptBox["d", "~"]}], "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[11]:=", + CellLabel->"In[219]:=", CellID->108727372], Cell[BoxData[ @@ -454,7 +440,7 @@ Cell[BoxData[ RowBox[{"AntiCommutator", "[", RowBox[{"c", ",", "d"}], "]"}], "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[12]:=", + CellLabel->"In[220]:=", CellID->873286670], Cell[BoxData[ @@ -464,7 +450,7 @@ Cell[BoxData[ OverscriptBox["d", "~"], ",", OverscriptBox["c", "~"]}], "]"}], "]"}]], "Input", CellTags->"AntiCommutator", - CellLabel->"In[13]:=", + CellLabel->"In[221]:=", CellID->702830390] }, Open ]], @@ -529,12 +515,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{593, Automatic}, {Automatic, 76}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/AntiQuarkField.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/AntiQuarkField.nb index c748fc902..dd2434c93 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/AntiQuarkField.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/AntiQuarkField.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/QuarkField", ButtonNote->"QuarkField"], "." -}], "Text", - CellTags->"AntiQuarkField", - CellID->1809382525] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,15 +201,14 @@ Cell[CellGroupData[{ Cell[BoxData["AntiQuarkField"], "Input", CellTags->"AntiQuarkField", - CellLabel->"In[1]:=", + CellLabel->"In[222]:=", CellID->820739788], Cell[BoxData[ FormBox[ OverscriptBox["\[Psi]", "_"], TraditionalForm]], "Output", CellTags->"AntiQuarkField", - CellLabel->"Out[1]=", - CellID->1958170632] + CellLabel->"Out[222]="] }, Open ]] }, Open ]], @@ -276,12 +273,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{256, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Apart1.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Apart1.nb index 0c3b7bec6..503b2c496 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Apart1.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Apart1.nb @@ -169,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Apart3", ButtonNote->"Apart3"], "." -}], "Text", - CellTags->"Apart1", - CellID->104867705] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{229, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Apart2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Apart2.nb index b2fc46fa6..6efde5a57 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Apart2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Apart2.nb @@ -124,8 +124,24 @@ Please use ApartFF instead." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Apart2", "]"}]], "Input", + CellTags->"Apart2", + CellLabel->"In[223]:=", + CellID->1571464480], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Factoring", "\[Rule]", "True"}], ",", + RowBox[{"ExcludeMasses", "\[Rule]", + RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", + CellTags->"Apart2", + CellLabel->"Out[223]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -176,9 +192,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/ApartFF", ButtonNote->"ApartFF"], "." -}], "Text", - CellTags->"Apart2", - CellID->1960323984] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -207,26 +221,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Apart2", "]"}]], "Input", - CellTags->"Apart2", - CellLabel->"In[1]:=", - CellID->1571464480], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Factoring", "\[Rule]", "True"}], ",", - RowBox[{"ExcludeMasses", "\[Rule]", - RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", - CellTags->"Apart2", - CellLabel->"Out[1]=", - CellID->1842118848] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"FAD", "[", RowBox[{ @@ -236,7 +230,7 @@ Cell[BoxData[ RowBox[{"q", ",", "M"}], "}"}], ",", RowBox[{"q", "-", "p"}]}], "]"}]], "Input", CellTags->"Apart2", - CellLabel->"In[2]:=", + CellLabel->"In[224]:=", CellID->1580962822], Cell[BoxData[ @@ -245,32 +239,57 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["q", "2"], "\[InvisibleSpace]", "\<\"-\"\>", + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", "\[InvisibleSpace]", - SuperscriptBox["m", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`q^2, "-", $CellContext`m^2, "]"], + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]], "-", $CellContext`m^2], Editable->False], ")"}], ".", RowBox[{"(", InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["q", "2"], "\[InvisibleSpace]", "\<\"-\"\>", + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", "\[InvisibleSpace]", - SuperscriptBox["M", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`q^2, "-", $CellContext`M^2, "]"], + SuperscriptBox["M", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]], "-", $CellContext`M^2], Editable->False], ")"}], ".", - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox[ - RowBox[{"(", - RowBox[{"q", "-", "p"}], ")"}], "2"], - "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", (-$CellContext`p + $CellContext`q)^2, "]"], - Editable->False], ")"}]}]], TraditionalForm]], "Output", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q", + TraditionalForm], "-", + FormBox["p", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[-$CellContext`p + $CellContext`q, D], + FeynCalc`Momentum[-$CellContext`p + $CellContext`q, D]]], + Editable->False]}]], TraditionalForm]], "Output", CellTags->"Apart2", - CellLabel->"Out[2]=", - CellID->1281611536] + CellLabel->"Out[224]="] }, Open ]], Cell[CellGroupData[{ @@ -278,49 +297,100 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Apart2", "[", "%", "]"}]], "Input", CellTags->"Apart2", - CellLabel->"In[3]:=", + CellLabel->"In[225]:=", CellID->867958772], Cell[BoxData[ FormBox[ FractionBox[ RowBox[{ - FractionBox["1", - RowBox[{ - RowBox[{"(", - RowBox[{ - SuperscriptBox[ - FormBox["q", - TraditionalForm], "2"], "-", - SuperscriptBox["m", "2"]}], ")"}], ".", - SuperscriptBox[ + FormBox[ + FractionBox["1", + RowBox[{ RowBox[{"(", - RowBox[{ - FormBox["q", - TraditionalForm], "-", - FormBox["p", - TraditionalForm]}], ")"}], "2"]}]], "-", - FractionBox["1", - RowBox[{ - RowBox[{"(", - RowBox[{ + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]], "-", $CellContext`m^2], + Editable->False], ")"}], ".", + InterpretationBox[ SuperscriptBox[ - 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CellTags->"Apart3", - CellID->13488114] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{131, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ApartFF.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ApartFF.nb index eaea1fa1a..949606d92 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ApartFF.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ApartFF.nb @@ -1,22 +1,3 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - 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CellID->982511436], Cell["XXXX", "Notes", - CellID->1067943069] + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "B0", "]"}]], "Input", + CellTags->"B0", + CellLabel->"In[1]:=", + CellID->1219933183], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"BReduce", "\[Rule]", "False"}], ",", + RowBox[{"B0Unique", "\[Rule]", "False"}], ",", + RowBox[{"B0Real", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"B0", + CellLabel->"Out[1]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -189,9 +209,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PaVe", ButtonNote->"PaVe"], "." -}], "Text", - CellTags->"B0", - CellID->1803724154] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -220,27 +238,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "B0", "]"}]], "Input", - CellTags->"B0", - CellLabel->"In[1]:=", - CellID->1219933183], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - 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SuperscriptBox["m", "2"]}], "]"}]], "Input", + SuperscriptBox["m", "2"], ",", + RowBox[{"B0Unique", "\[Rule]", "True"}], ",", + RowBox[{"B0Real", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"B0", - CellLabel->"In[4]:=", + CellLabel->"In[7]:=", CellID->510341898], Cell[BoxData[ @@ -311,8 +299,7 @@ Cell[BoxData[ HoldForm], TraditionalForm], "+", "1"}], TraditionalForm]], "Output", CellTags->"B0", - CellLabel->"Out[4]=", - CellID->170690020] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -321,9 +308,11 @@ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{ SuperscriptBox["m", "2"], ",", "0", ",", - SuperscriptBox["m", "2"]}], "]"}]], "Input", + SuperscriptBox["m", "2"], ",", + RowBox[{"B0Unique", "\[Rule]", "True"}], ",", + RowBox[{"B0Real", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"B0", - CellLabel->"In[5]:=", + CellLabel->"In[8]:=", CellID->1178094654], Cell[BoxData[ @@ -341,8 +330,7 @@ Cell[BoxData[ HoldForm], TraditionalForm], "+", "2"}], TraditionalForm]], "Output", CellTags->"B0", - CellLabel->"Out[5]=", - CellID->2121507054] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -353,7 +341,7 @@ Cell[BoxData[ RowBox[{"m", "^", "2"}], ",", RowBox[{"m", "^", "2"}]}], "]"}]], "Input", CellTags->"B0", - CellLabel->"In[6]:=", + CellLabel->"In[9]:=", CellID->828170126], Cell[BoxData[ @@ -368,8 +356,7 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"B0", - CellLabel->"Out[6]=", - CellID->271170246] + CellLabel->"Out[9]="] }, Open ]] }, Open ]], @@ -434,12 +421,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{525, Automatic}, {Automatic, 81}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/B00.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/B00.nb index 2e292795d..2abace2ba 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/B00.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/B00.nb @@ -131,8 +131,23 @@ arguments are scalars and have dimension mass^2." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - 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CellLabel->"Out[6]=", - CellID->1063864886] + CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ @@ -595,31 +521,44 @@ Cell[BoxData[ SuperscriptBox["m", "2"], ",", SuperscriptBox["m", "2"]}], "]"}]], "Input", CellTags->"B00", - CellLabel->"In[7]:=", + CellLabel->"In[20]:=", CellID->1823175928], Cell[BoxData[ FormBox[ RowBox[{ - FractionBox["1", "2"], " ", - SuperscriptBox["m", "2"], " ", - RowBox[{"(", - RowBox[{ - FormBox[ - TagBox[ - FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{"-", + FractionBox[ + RowBox[{ + SuperscriptBox["m", "2"], " ", + FormBox[ + TagBox[ + FormBox[ RowBox[{ - SuperscriptBox["M", "2"], ",", - SuperscriptBox["m", "2"], ",", - SuperscriptBox["m", "2"]}], ")"}], - TraditionalForm], - HoldForm], - TraditionalForm], "+", "1"}], ")"}]}], TraditionalForm]], "Output", + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{ + SuperscriptBox["M", "2"], ",", + SuperscriptBox["m", "2"], ",", + SuperscriptBox["m", "2"]}], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm]}], + RowBox[{"1", "-", "D"}]]}], "-", + FractionBox[ + FormBox[ + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"A\"\>", "\<\"0\"\>"], "(", + SuperscriptBox["m", "2"], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm], + RowBox[{"2", " ", + RowBox[{"(", + RowBox[{"1", "-", "D"}], ")"}]}]]}], TraditionalForm]], "Output", CellTags->"B00", - CellLabel->"Out[7]=", - CellID->524392254] + CellLabel->"Out[20]="] }, Open ]] }, Open ]], @@ -684,12 +623,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{Automatic, 552}, {Automatic, -35}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/B0Real.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/B0Real.nb index fbe4c5f4b..1fbd37d0a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/B0Real.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/B0Real.nb @@ -160,15 +160,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["B0", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/B0", ButtonNote->"B0"], "." -}], "Text", - CellTags->"B0Real", - CellID->1839543320] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -195,9 +192,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["By default the arguments are not assumed real.", "Text", - CellTags->"B0Real", - CellID->130288840], +Cell["By default the arguments are not assumed real.", "Notes"], Cell[CellGroupData[{ @@ -205,59 +200,33 @@ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{"s", ",", "0", ",", "s"}], "]"}]], "Input", CellTags->"B0Real", - CellLabel->"In[1]:=", + CellLabel->"In[21]:=", CellID->1048836421], Cell[BoxData[ FormBox[ - RowBox[{ + TagBox[ FormBox[ - TagBox[ - FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{"0", ",", "s", ",", "s"}], ")"}], - TraditionalForm], - HoldForm], - TraditionalForm], "+", "2"}], TraditionalForm]], "Output", + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{"s", ",", "0", ",", "s"}], ")"}], + TraditionalForm], + HoldForm], TraditionalForm]], "Output", CellTags->"B0Real", - CellLabel->"Out[1]=", - CellID->997660714] + CellLabel->"Out[21]="] }, Open ]], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"B0", "//", "Options"}]], "Input", - CellTags->"B0Real", - CellLabel->"In[2]:=", - CellID->168010706], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"BReduce", "\[Rule]", "False"}], ",", - RowBox[{"B0Unique", "\[Rule]", "True"}], ",", - RowBox[{"B0Real", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"B0Real", - CellLabel->"Out[2]=", - CellID->994724143] -}, Open ]], - -Cell["With B0Real\[Rule]True, transformation is done.", "Text", - CellTags->"B0Real", - CellID->617964813], +Cell["With B0Real\[Rule]True, transformation is done.", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{"s", ",", "0", ",", "s", ",", - RowBox[{"B0Real", "\[Rule]", "True"}]}], "]"}]], "Input", + RowBox[{"B0Real", "\[Rule]", "True"}], ",", + RowBox[{"B0Unique", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"B0Real", - CellLabel->"In[3]:=", + CellLabel->"In[26]:=", CellID->848873063], Cell[BoxData[ @@ -273,8 +242,7 @@ Cell[BoxData[ HoldForm], TraditionalForm], "+", "2"}], TraditionalForm]], "Output", CellTags->"B0Real", - CellLabel->"Out[3]=", - CellID->1655563844] + CellLabel->"Out[26]="] }, Open ]] }, Open ]], @@ -339,12 +307,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1430, Automatic}, {Automatic, 225}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/B0Unique.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/B0Unique.nb index fe1764c64..7f4db03d8 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/B0Unique.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/B0Unique.nb @@ -160,15 +160,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["B0", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/B0", ButtonNote->"B0"], "." -}], "Text", - CellTags->"B0Unique", - CellID->993329416] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -195,9 +192,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["By default transformation is done.", "Text", - CellTags->"B0Unique", - CellID->1633725722], +Cell["By default no transformation is done.", "Notes"], Cell[CellGroupData[{ @@ -205,73 +200,48 @@ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{"0", ",", "0", ",", "s"}], "]"}]], "Input", CellTags->"B0Unique", - CellLabel->"In[1]:=", + CellLabel->"In[28]:=", CellID->539333149], Cell[BoxData[ FormBox[ - RowBox[{ + TagBox[ FormBox[ - TagBox[ - FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{"0", ",", "s", ",", "s"}], ")"}], - TraditionalForm], - HoldForm], - TraditionalForm], "+", "1"}], TraditionalForm]], "Output", - CellTags->"B0Unique", - CellLabel->"Out[1]=", - CellID->2030362910] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "B0", "]"}]], "Input", - CellTags->"B0Unique", - CellLabel->"In[2]:=", - CellID->1904628151], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"BReduce", "\[Rule]", "False"}], ",", - RowBox[{"B0Unique", "\[Rule]", "True"}], ",", - RowBox[{"B0Real", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{"0", ",", "0", ",", "s"}], ")"}], + TraditionalForm], + HoldForm], TraditionalForm]], "Output", CellTags->"B0Unique", - CellLabel->"Out[2]=", - CellID->226407255] + CellLabel->"Out[28]="] }, Open ]], -Cell["With B0Real\[Rule]False, nothing happens.", "Text", - CellTags->"B0Unique", - CellID->1308469818], +Cell["With B0Real\[Rule]True following transformation is applied", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{"0", ",", "0", ",", "s", ",", - RowBox[{"B0Unique", "\[Rule]", "False"}]}], "]"}]], "Input", + RowBox[{"B0Unique", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"B0Unique", - CellLabel->"In[3]:=", + CellLabel->"In[30]:=", CellID->224258616], Cell[BoxData[ FormBox[ - TagBox[ + RowBox[{ FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{"0", ",", "0", ",", "s"}], ")"}], - TraditionalForm], - HoldForm], TraditionalForm]], "Output", + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{"0", ",", "s", ",", "s"}], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm], "+", "1"}], TraditionalForm]], "Output", CellTags->"B0Unique", - CellLabel->"Out[3]=", - CellID->1908481089] + CellLabel->"Out[30]="] }, Open ]] }, Open ]], @@ -336,12 +306,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{857, Automatic}, {Automatic, 183}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/B1.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/B1.nb index 5770822cf..dd3501fec 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/B1.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/B1.nb @@ -130,8 +130,22 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "B1", "]"}]], "Input", + CellTags->"B1", + CellLabel->"In[31]:=", + CellID->1893937597], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"BReduce", "\[Rule]", "True"}], "}"}], TraditionalForm]], "Output", + + CellTags->"B1", + CellLabel->"Out[31]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -192,9 +206,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PaVeReduce", ButtonNote->"PaVeReduce"], "." -}], "Text", - CellTags->"B1", - CellID->1961153968] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -223,108 +235,97 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "B1", "]"}]], "Input", - CellTags->"B1", - CellLabel->"In[1]:=", - CellID->1893937597], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"BReduce", "\[Rule]", "True"}], "}"}], TraditionalForm]], "Output", - - CellTags->"B1", - CellLabel->"Out[1]=", - CellID->1980658046] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"B1", "[", RowBox[{ - RowBox[{"SP", "[", "p", "]"}], ",", + RowBox[{"SPD", "[", "p", "]"}], ",", SuperscriptBox["m", "2"], ",", SuperscriptBox["M", "2"]}], "]"}]], "Input", CellTags->"B1", - CellLabel->"In[2]:=", + CellLabel->"In[71]:=", CellID->1808836307], Cell[BoxData[ FormBox[ RowBox[{ - FractionBox[ - RowBox[{ - RowBox[{"(", - RowBox[{ - SuperscriptBox["M", "2"], "-", - SuperscriptBox["m", "2"]}], ")"}], " ", - RowBox[{"(", - RowBox[{ - FormBox[ - TagBox[ - FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], "2"], - TraditionalForm], ",", - SuperscriptBox["m", "2"], ",", - SuperscriptBox["M", "2"]}], ")"}], - TraditionalForm], - HoldForm], - TraditionalForm], "-", - FormBox[ - TagBox[ - FormBox[ + RowBox[{"-", + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{ + SuperscriptBox["m", "2"], "-", + SuperscriptBox["M", "2"], "+", + FormBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + TraditionalForm]}], ")"}], " ", + FormBox[ + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{"0", ",", - SuperscriptBox["m", "2"], ",", - SuperscriptBox["M", "2"]}], ")"}], + FormBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + TraditionalForm], ",", + SuperscriptBox["m", "2"], ",", + SuperscriptBox["M", "2"]}], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm]}], + RowBox[{"2", " ", + FormBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], - HoldForm], - TraditionalForm]}], ")"}]}], + TraditionalForm], "2"], + TraditionalForm]}]]}], "+", + FractionBox[ + FormBox[ + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"A\"\>", "\<\"0\"\>"], "(", + SuperscriptBox["m", "2"], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm], RowBox[{"2", " ", FormBox[ SuperscriptBox[ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["p", + TraditionalForm], TraditionalForm], "2"], TraditionalForm]}]], "-", - RowBox[{ - FractionBox["1", "2"], " ", + FractionBox[ FormBox[ TagBox[ FormBox[ RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], "2"], - TraditionalForm], ",", - SuperscriptBox["m", "2"], ",", - SuperscriptBox["M", "2"]}], ")"}], + SubscriptBox["\<\"A\"\>", "\<\"0\"\>"], "(", + SuperscriptBox["M", "2"], ")"}], TraditionalForm], HoldForm], - TraditionalForm]}]}], TraditionalForm]], "Output", + TraditionalForm], + RowBox[{"2", " ", + FormBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"B1", - CellLabel->"Out[2]=", - CellID->1988092032] + CellLabel->"Out[71]="] }, Open ]], Cell[CellGroupData[{ @@ -332,44 +333,36 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"B1", "[", RowBox[{ - RowBox[{"SP", "[", "p", "]"}], ",", + RowBox[{"SPD", "[", "p", "]"}], ",", SuperscriptBox["m", "2"], ",", SuperscriptBox["M", "2"], ",", RowBox[{"BReduce", "\[Rule]", "False"}]}], "]"}]], "Input", CellTags->"B1", - 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CellLabel->"Out[8]=", - CellID->303443152] + CellLabel->"Out[84]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"B11", "[", + RowBox[{"0", ",", + SuperscriptBox["m", "2"], ",", + SuperscriptBox["m", "2"], ",", + RowBox[{"BReduce", "\[Rule]", "False"}]}], "]"}]], "Input", + CellLabel->"In[85]:="], + +Cell[BoxData[ + FormBox[ + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"11\"\>"], "(", + RowBox[{"0", ",", + SuperscriptBox["m", "2"], ",", + SuperscriptBox["m", "2"]}], ")"}], + TraditionalForm], + HoldForm], TraditionalForm]], "Output", + CellLabel->"Out[85]="] }, Open ]], Cell[CellGroupData[{ @@ -638,28 +621,77 @@ Cell[BoxData[ SuperscriptBox["m", "2"], ",", SuperscriptBox["m", "2"]}], "]"}]], "Input", CellTags->"B11", - CellLabel->"In[9]:=", + CellLabel->"In[86]:=", CellID->1335567043], Cell[BoxData[ FormBox[ RowBox[{ - FractionBox["1", "3"], " ", - FormBox[ - TagBox[ + FractionBox[ + RowBox[{ + SuperscriptBox["m", "2"], " ", FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{ - SuperscriptBox["M", "2"], ",", - SuperscriptBox["m", "2"], ",", - SuperscriptBox["m", "2"]}], ")"}], - TraditionalForm], - HoldForm], - TraditionalForm]}], TraditionalForm]], "Output", + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{ + SuperscriptBox["M", "2"], ",", + SuperscriptBox["m", "2"], ",", + SuperscriptBox["m", "2"]}], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm]}], + RowBox[{ + RowBox[{"(", + RowBox[{"1", "-", "D"}], ")"}], " ", + SuperscriptBox["M", "2"]}]], "+", + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"2", "-", "D"}], ")"}], " ", + FormBox[ + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"A\"\>", "\<\"0\"\>"], "(", + SuperscriptBox["m", "2"], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm]}], + RowBox[{"2", " ", + RowBox[{"(", + RowBox[{"1", "-", "D"}], ")"}], " ", + SuperscriptBox["M", "2"]}]]}], TraditionalForm]], "Output", CellTags->"B11", - CellLabel->"Out[9]=", - CellID->2037163640] + CellLabel->"Out[86]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"B11", "[", + RowBox[{ + RowBox[{"SmallVariable", "[", + SuperscriptBox["M", "2"], "]"}], ",", + SuperscriptBox["m", "2"], ",", + SuperscriptBox["m", "2"], ",", + RowBox[{"BReduce", "\[Rule]", "False"}]}], "]"}]], "Input", + CellLabel->"In[87]:="], + +Cell[BoxData[ + FormBox[ + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"B\"\>", "\<\"11\"\>"], "(", + RowBox[{ + SuperscriptBox["M", "2"], ",", + SuperscriptBox["m", "2"], ",", + SuperscriptBox["m", "2"]}], ")"}], + TraditionalForm], + HoldForm], TraditionalForm]], "Output", + CellLabel->"Out[87]="] }, Open ]] }, Open ]], @@ -724,12 +756,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1012, Automatic}, {Automatic, 165}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/BReduce.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/BReduce.nb index 2137ef8da..4beaa0bd3 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/BReduce.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/BReduce.nb @@ -185,9 +185,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/B11", ButtonNote->"B11"], "." -}], "Text", - CellTags->"BReduce", - CellID->1422133579] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -224,9 +222,7 @@ Cell[TextData[{ FormBox[ SubscriptBox["A", "0"], TraditionalForm]]], "." -}], "Text", - CellTags->"BReduce", - CellID->233833972], +}], "Notes"], Cell[CellGroupData[{ @@ -234,7 +230,7 @@ Cell[BoxData[ RowBox[{"B0", "[", RowBox[{"0", ",", "s", ",", "s"}], "]"}]], "Input", CellTags->"BReduce", - CellLabel->"In[1]:=", + CellLabel->"In[88]:=", CellID->768966684], Cell[BoxData[ @@ -247,13 +243,10 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"BReduce", - CellLabel->"Out[1]=", - CellID->1373932648] + CellLabel->"Out[88]="] }, Open ]], -Cell["With BReduce\[Rule]True, transformation is done.", "Text", - CellTags->"BReduce", - CellID->174829946], +Cell["With BReduce\[Rule]True, transformation is done.", "Notes"], Cell[CellGroupData[{ @@ -262,24 +255,27 @@ Cell[BoxData[ RowBox[{"0", ",", "s", ",", "s", ",", RowBox[{"BReduce", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"BReduce", - CellLabel->"In[2]:=", + CellLabel->"In[91]:=", CellID->876027895], Cell[BoxData[ FormBox[ - RowBox[{ + RowBox[{"-", FractionBox[ - FormBox[ - TagBox[ - FormBox[ - RowBox[{ - SubscriptBox["\<\"A\"\>", "\<\"0\"\>"], "(", "s", ")"}], - TraditionalForm], - HoldForm], - TraditionalForm], "s"], "-", "1"}], TraditionalForm]], "Output", + RowBox[{ + RowBox[{"(", + RowBox[{"2", "-", "D"}], ")"}], " ", + FormBox[ + TagBox[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"A\"\>", "\<\"0\"\>"], "(", "s", ")"}], + TraditionalForm], + HoldForm], + TraditionalForm]}], + RowBox[{"2", " ", "s"}]]}], TraditionalForm]], "Output", CellTags->"BReduce", - CellLabel->"Out[2]=", - CellID->460346687] + CellLabel->"Out[91]="] }, Open ]] }, Open ]], @@ -344,12 +340,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1028, Automatic}, {Automatic, 103}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/BackgroundGluonVertex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/BackgroundGluonVertex.nb index 909f8ad84..0cb006571 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/BackgroundGluonVertex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/BackgroundGluonVertex.nb @@ -125,27 +125,91 @@ Cell[TextData[{ RowBox[{"q", ",", "nu", ",", "b"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"k", ",", "la", ",", "c"}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "or BackgroundGluonVertex[ p,mu,a , q,nu,b , k,la,c ] yields the 3-gluon \ -vertex in the background field gauge, where the first set of arguments \ -corresponds to the external background field. BackgroundGluonVertex[{p,mu,a}, \ -{q,nu,b}, {k,la,c}, {s,si,d}] or BackgroundGluonVertex[{mu,a}, {nu,b}, \ -{la,c}, {si,d}] or BackgroundGluonVertex[p,mu,a , q,nu,b , k,la,c , s,si,d] \ -or BackgroundGluonVertex[ mu,a , nu,b , la,c , si,d ] yields the 4-gluon \ -vertex, with {p,mu,a} and {k,la,c} denoting the external background fields. \ -The gauge, dimension and the name of the coupling constant are determined by \ -the options Gauge, Dimension and CouplingConstant. The Feynman rules are \ -taken from L.Abbot ", + " \[LineSeparator]yields the 3-gluon vertex in the background field gauge, \ +where the first set of arguments corresponds to the external background \ +field.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"BackgroundGluonVertex", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "mu", ",", "a"}], "}"}], ",", + RowBox[{"{", + RowBox[{"q", ",", "nu", ",", "b"}], "}"}], ",", + RowBox[{"{", + RowBox[{"k", ",", "la", ",", "c"}], "}"}], ",", + RowBox[{"{", + RowBox[{"s", ",", "si", ",", "d"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]yields the 4-gluon vertex, with ", + Cell[BoxData[ + RowBox[{"{", + RowBox[{"p", ",", "mu", ",", "a"}], "}"}]], "InlineFormula"], + " and ", + Cell[BoxData[ + RowBox[{"{", + RowBox[{"k", ",", "la", ",", "c"}], "}"}]], "InlineFormula"], + " denoting the external background fields." +}], "Usage", + CellID->2010081510], + +Cell[TextData[{ + "The gauge, dimension and the name of the coupling constant are determined \ +by the options ", + ButtonBox["Gauge", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Gauge", + ButtonNote->"Gauge"], + ", ", + ButtonBox["Dimension", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Dimension", + ButtonNote->"Dimension"], + " and ", + ButtonBox["CouplingConstant", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CouplingConstant", + ButtonNote->"CouplingConstant"], + ". " +}], "Notes", + CellID->1067943069], + +Cell[TextData[{ + "The Feynman rules are taken from L.Abbot ", StyleBox["NPB ", FontWeight->"Bold"], - "185 (1981), 189-203; except that all momenta are incoming. Note that \ -Abbot's coupling constant convention is consistent with the default setting \ -of GluonVertex." -}], "Usage", - CellID->982511436], + "185 (1981), 189-203; except that all momenta are incoming. " +}], "Notes"], + +Cell[TextData[{ + "Note that Abbot's coupling constant convention is consistent with the \ +default setting of ", + ButtonBox["GluonVertex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/GluonVertex", + ButtonNote->"GluonVertex"], + "." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "BackgroundGluonVertex", "]"}]], "Input", + CellTags->"BackgroundGluonVertex", + CellLabel->"In[1]:=", + CellID->236798928], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Gauge", "\[Rule]", "1"}]}], "}"}], TraditionalForm]], "Output", + CellTags->"BackgroundGluonVertex", + CellLabel->"Out[1]=", + CellID->114339715] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -180,15 +244,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - 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RowBox[{"FCGV", "(", "\<\"u25\"\>", ")"}], + RowBox[{"FCGV", "(", "\<\"u27\"\>", ")"}], TraditionalForm], TraditionalForm]}]], " ", RowBox[{"(", RowBox[{ RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]]}], "-", RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "+", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]]}], "+", RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}]}], ")"}]}]}], ")"}]}], + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]]}]}], ")"}]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"BackgroundGluonVertex", - CellLabel->"Out[3]=", - CellID->949247376] + CellLabel->"Out[180]="] }, Open ]], Cell[CellGroupData[{ @@ -795,7 +699,7 @@ Cell[BoxData[ RowBox[{"k", ",", "\[Lambda]", ",", "c"}], "}"}], ",", RowBox[{"Gauge", "\[Rule]", "\[Alpha]"}]}], "]"}]], "Input", CellTags->"BackgroundGluonVertex", - CellLabel->"In[4]:=", + CellLabel->"In[182]:=", CellID->410624714], Cell[BoxData[ @@ -819,127 +723,86 @@ Cell[BoxData[ RowBox[{"(", RowBox[{ RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - RowBox[{"-", - FormBox[ - FractionBox[ - FormBox["k", - TraditionalForm], "\[Alpha]"], - TraditionalForm]}], "+", - FormBox["p", - TraditionalForm], "-", - FormBox["q", - TraditionalForm]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox["g", + RowBox[{ FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "+", - RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox[ + RowBox[{"(", + FormBox[ + RowBox[{ + RowBox[{"-", + FractionBox[ FormBox["k", - TraditionalForm], "-", - FormBox["p", - TraditionalForm], "+", - FormBox[ - FractionBox[ - FormBox["q", - TraditionalForm], "\[Alpha]"], - TraditionalForm]}], - TraditionalForm], - TraditionalForm], ")"}], + TraditionalForm], "\[Alpha]"]}], "+", + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm]]}], "+", + RowBox[{ + SuperscriptBox["g", + RowBox[{ FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "+", + TraditionalForm]}]], " ", + SuperscriptBox[ + RowBox[{"(", + FormBox[ + RowBox[{ + FormBox["k", + TraditionalForm], "-", + FormBox["p", + TraditionalForm], "+", + FractionBox[ + FormBox["q", + TraditionalForm], "\[Alpha]"]}], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]]}], "+", RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - FormBox["q", - TraditionalForm], "-", - FormBox["k", - TraditionalForm]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox["g", + RowBox[{ FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output", + TraditionalForm]}]], " ", + SuperscriptBox[ + RowBox[{"(", + FormBox[ + RowBox[{ + FormBox["q", + TraditionalForm], "-", + FormBox["k", + TraditionalForm]}], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"BackgroundGluonVertex", - CellLabel->"Out[4]=", - CellID->998908990] + CellLabel->"Out[182]="] }, Open ]], Cell[CellGroupData[{ @@ -957,7 +820,7 @@ Cell[BoxData[ RowBox[{"s", ",", "\[Sigma]", ",", "d"}], "}"}], ",", RowBox[{"Gauge", "\[Rule]", "\[Alpha]"}]}], "]"}]], "Input", CellTags->"BackgroundGluonVertex", - CellLabel->"In[5]:=", + CellLabel->"In[183]:=", CellID->1007521255], Cell[BoxData[ @@ -980,7 +843,7 @@ Cell[BoxData[ TraditionalForm], FormBox[ FormBox[ - RowBox[{"FCGV", "(", "\<\"u26\"\>", ")"}], + RowBox[{"FCGV", "(", "\<\"u28\"\>", ")"}], TraditionalForm], TraditionalForm]}]], " ", SuperscriptBox["f", @@ -995,7 +858,7 @@ Cell[BoxData[ TraditionalForm], FormBox[ FormBox[ - RowBox[{"FCGV", "(", "\<\"u26\"\>", ")"}], + RowBox[{"FCGV", "(", "\<\"u28\"\>", ")"}], TraditionalForm], TraditionalForm]}]], " ", RowBox[{"(", @@ -1003,104 +866,68 @@ Cell[BoxData[ RowBox[{"-", FractionBox[ RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "\[Alpha]"]}], "+", - RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ + SuperscriptBox["g", + RowBox[{ FormBox[ FormBox["\[Lambda]", TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ + TraditionalForm], FormBox[ FormBox["\[Nu]", TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", - RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ FormBox[ FormBox["\[Mu]", TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ + TraditionalForm], FormBox[ FormBox["\[Sigma]", TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}]}], ")"}]}], "+", + TraditionalForm]}]]}], "\[Alpha]"]}], "+", + RowBox[{ + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]]}], "-", + RowBox[{ + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["f", RowBox[{ @@ -1114,7 +941,7 @@ Cell[BoxData[ TraditionalForm], FormBox[ FormBox[ - RowBox[{"FCGV", "(", "\<\"u26\"\>", ")"}], + RowBox[{"FCGV", "(", "\<\"u28\"\>", ")"}], TraditionalForm], TraditionalForm]}]], " ", SuperscriptBox["f", @@ -1129,111 +956,75 @@ Cell[BoxData[ TraditionalForm], FormBox[ FormBox[ - RowBox[{"FCGV", "(", "\<\"u26\"\>", ")"}], + RowBox[{"FCGV", "(", "\<\"u28\"\>", ")"}], TraditionalForm], TraditionalForm]}]], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "\[Alpha]"], "-", - RowBox[{ - FormBox[ SuperscriptBox["g", RowBox[{ FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], + FormBox["\[Lambda]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], + FormBox["\[Sigma]", TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ + TraditionalForm]}]], " ", SuperscriptBox["g", RowBox[{ FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], + FormBox["\[Nu]", TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "+", + TraditionalForm]}]]}], "\[Alpha]"], "-", RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}]}], ")"}]}], "+", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]]}], "+", + RowBox[{ + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["f", RowBox[{ @@ -1247,7 +1038,7 @@ Cell[BoxData[ TraditionalForm], FormBox[ FormBox[ - RowBox[{"FCGV", "(", "\<\"u26\"\>", ")"}], + RowBox[{"FCGV", "(", "\<\"u28\"\>", ")"}], TraditionalForm], TraditionalForm]}]], " ", SuperscriptBox["f", @@ -1262,81 +1053,56 @@ Cell[BoxData[ TraditionalForm], FormBox[ FormBox[ - RowBox[{"FCGV", "(", "\<\"u26\"\>", ")"}], + RowBox[{"FCGV", "(", "\<\"u28\"\>", ")"}], TraditionalForm], TraditionalForm]}]], " ", RowBox[{"(", RowBox[{ RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]]}], "-", RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Lambda]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}]}], ")"}]}]}], ")"}]}], + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Lambda]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]]}]}], ")"}]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"BackgroundGluonVertex", - CellLabel->"Out[5]=", - CellID->686414429] + CellLabel->"Out[183]="] }, Open ]] }, Open ]], @@ -1401,12 +1167,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{924, Automatic}, {Automatic, 121}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Bracket.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Bracket.nb index 3b96a1ca0..20b5a26bd 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Bracket.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Bracket.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Convolute", ButtonNote->"Convolute"], "." -}], "Text", - CellTags->"Bracket", - CellID->442526235] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,13 +250,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{700, 773}, +WindowMargins->{{1532, Automatic}, {Automatic, 178}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/C0.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/C0.nb index bdc3a7c66..c8f3fd491 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/C0.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/C0.nb @@ -191,9 +191,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PaVeOrder", ButtonNote->"PaVeOrder"], "." -}], "Text", - CellTags->"C0", - CellID->1972879175] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -227,7 +225,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c", ",", " ", "m12", ",", "m22", ",", "m32"}], "]"}]], "Input", CellTags->"C0", - CellLabel->"In[1]:=", + CellLabel->"In[93]:=", CellID->929768353], Cell[BoxData[ @@ -241,8 +239,7 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"C0", - CellLabel->"Out[1]=", - CellID->370674132] + CellLabel->"Out[93]="] }, Open ]], Cell[CellGroupData[{ @@ -253,7 +250,7 @@ Cell[BoxData[ RowBox[{"b", ",", "a", ",", "c", ",", "m32", ",", "m22", ",", "m12"}], "]"}], "//", "PaVeOrder"}]], "Input", CellTags->"C0", - CellLabel->"In[2]:=", + CellLabel->"In[94]:=", CellID->281164286], Cell[BoxData[ @@ -267,8 +264,7 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"C0", - CellLabel->"Out[2]=", - CellID->240939187] + CellLabel->"Out[94]="] }, Open ]], Cell[CellGroupData[{ @@ -283,7 +279,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"c", ",", "a"}], "}"}]}]}], "]"}]], "Input", CellTags->"C0", - CellLabel->"In[3]:=", + CellLabel->"In[95]:=", CellID->2033659557], Cell[BoxData[ @@ -297,8 +293,7 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"C0", - CellLabel->"Out[3]=", - CellID->1857619476] + CellLabel->"Out[95]="] }, Open ]] }, Open ]], @@ -363,12 +358,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1018, Automatic}, {Automatic, 147}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CA.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CA.nb index cfb9e94af..ead5e188e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CA.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CA.nb @@ -175,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNSimplify", ButtonNote->"SUNSimplify"], "." -}], "Text", - CellTags->"CA", - CellID->831413788] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -208,15 +206,14 @@ Cell[CellGroupData[{ Cell[BoxData["CA"], "Input", CellTags->"CA", - CellLabel->"In[1]:=", + CellLabel->"In[96]:=", CellID->373196199], Cell[BoxData[ FormBox[ SubscriptBox["C", "A"], TraditionalForm]], "Output", CellTags->"CA", - CellLabel->"Out[1]=", - CellID->1618948920] + CellLabel->"Out[96]="] }, Open ]], Cell[CellGroupData[{ @@ -226,28 +223,26 @@ Cell[BoxData[ RowBox[{"CA", ",", RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}]], "Input", CellTags->"CA", - CellLabel->"In[2]:=", + CellLabel->"In[97]:=", CellID->686554202], Cell[BoxData[ FormBox["N", TraditionalForm]], "Output", CellTags->"CA", - CellLabel->"Out[2]=", - CellID->2112958244] + CellLabel->"Out[97]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["SUNN"], "Input", CellTags->"CA", - CellLabel->"In[3]:=", + CellLabel->"In[98]:=", CellID->1806839104], Cell[BoxData[ FormBox["N", TraditionalForm]], "Output", CellTags->"CA", - CellLabel->"Out[3]=", - CellID->981411080] + CellLabel->"Out[98]="] }, Open ]] }, Open ]], @@ -312,12 +307,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1108, Automatic}, {Automatic, 165}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CF.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CF.nb index 137eacbc7..fc3238b62 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CF.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CF.nb @@ -179,9 +179,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNSimplify", ButtonNote->"SUNSimplify"], "." -}], "Text", - CellTags->"CF", - CellID->856648073] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -212,15 +210,14 @@ Cell[CellGroupData[{ Cell[BoxData["CF"], "Input", CellTags->"CF", - CellLabel->"In[1]:=", + CellLabel->"In[99]:=", CellID->606616156], Cell[BoxData[ FormBox[ SubscriptBox["C", "F"], TraditionalForm]], "Output", CellTags->"CF", - CellLabel->"Out[1]=", - CellID->1771246704] + CellLabel->"Out[99]="] }, Open ]], Cell[CellGroupData[{ @@ -230,7 +227,7 @@ Cell[BoxData[ RowBox[{"CF", ",", " ", RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}]], "Input", CellTags->"CF", - CellLabel->"In[2]:=", + CellLabel->"In[100]:=", CellID->943993167], Cell[BoxData[ @@ -240,22 +237,20 @@ Cell[BoxData[ SuperscriptBox["N", "2"], "-", "1"}], RowBox[{"2", " ", "N"}]], TraditionalForm]], "Output", CellTags->"CF", - CellLabel->"Out[2]=", - CellID->1827752058] + CellLabel->"Out[100]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData["SUNN"], "Input", CellTags->"CF", - CellLabel->"In[3]:=", + CellLabel->"In[101]:=", CellID->721736691], Cell[BoxData[ FormBox["N", TraditionalForm]], "Output", CellTags->"CF", - CellLabel->"Out[3]=", - CellID->2104582203] + CellLabel->"Out[101]="] }, Open ]], Cell[CellGroupData[{ @@ -267,7 +262,7 @@ Cell[BoxData[ RowBox[{"SUNN", "^", "2"}], "-", "1"}], ",", " ", RowBox[{"SUNNToCACF", " ", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"CF", - CellLabel->"In[4]:=", + CellLabel->"In[102]:=", CellID->1669593560], Cell[BoxData[ @@ -276,8 +271,7 @@ Cell[BoxData[ SubscriptBox["C", "A"], " ", SubscriptBox["C", "F"]}], TraditionalForm]], "Output", CellTags->"CF", - CellLabel->"Out[4]=", - CellID->2114118582] + CellLabel->"Out[102]="] }, Open ]] }, Open ]], @@ -342,12 +336,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{779, Automatic}, {Automatic, 147}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CFAD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CFAD.nb new file mode 100644 index 000000000..33b62b1e1 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CFAD.nb @@ -0,0 +1,584 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/CFAD", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["CFAD", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"CFAD", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"q1", "+"}], "..."}], ",", + RowBox[{ + RowBox[{ + RowBox[{"p1", ".", "q2"}], "+"}], "..."}], ","}], "}"}], " ", + RowBox[{"{", + RowBox[{ + RowBox[{"m", "^", "2"}], ",", "s"}], "}"}]}], ",", "n"}], "}"}], ",", + "..."}], "]"}]], "InlineFormula"], + " \[LineSeparator]denotes a Cartesian propagator given by 1/[(q1+...)^2 + \ +p1.q2 ... + m^2 + sign*I*eta]^n, where q1^2 and p1.q2 are Cartesian sclar \ +products in D-1 dimensions. 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Calc[exp] is the same as \ -DotSimplify[DiracSimplify[Contract[DiracSimplify[Explicit[ \ -SUNSimplify[Trick[exp], Explicit\[Rule]False] ]]]]]." + " \[LineSeparator] performs several simplifications that involve Contract, \ +DiracSimplify SUNSimplify, DotSimplify, EpsEvaluate, ExpandScalarProduct, \ +PowerSimplify, Expand2 and Trick." }], "Usage", CellID->982511436], @@ -162,6 +161,11 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ + ButtonBox["Trick", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Trick", + ButtonNote->"Trick"], + ", ", ButtonBox["DiracSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", @@ -171,15 +175,8 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracTrick", ButtonNote->"DiracTrick"], - ", ", - ButtonBox["Trick", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Trick", - ButtonNote->"Trick"], "." -}], "Text", - CellTags->"Calc", - CellID->573489970] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -206,49 +203,54 @@ Cell[BoxData[ $Line = 0; 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Null]], "ExampleDelimiter"], + Cell[TextData[{ "This simplifies ", Cell[BoxData[ @@ -257,9 +259,7 @@ Cell[TextData[{ SubscriptBox["f", "abc"], " ", RowBox[{ SubscriptBox["f", "abe"], "."}]}], TraditionalForm]]] -}], "Text", - CellTags->"Calc", - CellID->1416000027], +}], "Notes"], Cell[CellGroupData[{ @@ -271,7 +271,7 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "b", ",", "e"}], "]"}]}], "]"}]], "Input", CellTags->"Calc", - CellLabel->"In[2]:=", + CellLabel->"In[118]:=", CellID->779661922], Cell[BoxData[ @@ -289,12 +289,18 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"Calc", - CellLabel->"Out[2]=", - CellID->1521159153] + CellLabel->"Out[118]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ RowBox[{"FV", "[", @@ -306,80 +312,65 @@ Cell[BoxData[ RowBox[{ RowBox[{"q", "-", "p"}], ",", "\[Nu]"}], "]"}]}]], "Input", CellTags->"Calc", - CellLabel->"In[3]:=", + CellLabel->"In[121]:=", CellID->281198835], Cell[BoxData[ FormBox[ RowBox[{ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm], " ", FormBox[ - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Nu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], TraditionalForm], " ", FormBox[ - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["r", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["r", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Calc", - CellLabel->"Out[3]=", - CellID->481463556] + CellLabel->"Out[121]="] }, Open ]], Cell[CellGroupData[{ @@ -387,7 +378,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Calc", "[", "%", "]"}]], "Input", CellTags->"Calc", - CellLabel->"In[4]:=", + CellLabel->"In[122]:=", CellID->1838519780], Cell[BoxData[ @@ -439,79 +430,59 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->"Calc", - CellLabel->"Out[4]=", - CellID->1244287531] + CellLabel->"Out[122]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"GluonVertex", "[", - RowBox[{"p", ",", "1", ",", "q", ",", "2", ",", - RowBox[{ - RowBox[{"-", "p"}], "-", "q"}], ",", "3"}], "]"}]], "Input", + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "li1"}], "}"}], ",", + RowBox[{"{", + RowBox[{"q", ",", "li2"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"-", "p"}], "-", "q"}], ",", "li3"}], "}"}]}], "]"}]], "Input", CellTags->"Calc", - CellLabel->"In[5]:=", + CellLabel->"In[127]:=", CellID->1589340964], Cell[BoxData[ FormBox[ RowBox[{ - SuperscriptBox["f", + SuperscriptBox["V", RowBox[{ - FormBox[ - FormBox["ci1", - TraditionalForm], + FormBox["li1", TraditionalForm], - FormBox[ - FormBox["ci2", - TraditionalForm], + FormBox["li2", TraditionalForm], - FormBox[ - FormBox["ci3", - TraditionalForm], - TraditionalForm]}]], " ", + FormBox["li3", + TraditionalForm]}]], "(", RowBox[{ - SuperscriptBox["V", + FormBox["p", + TraditionalForm], + FormBox["\<\", \"\>", + TraditionalForm], + FormBox["q", + TraditionalForm], + FormBox["\<\", \"\>", + TraditionalForm], + FormBox[ RowBox[{ - FormBox[ - FormBox["li1", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["li2", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["li3", - TraditionalForm], - TraditionalForm]}]], "(", - RowBox[{ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox["\<\", \"\>", - TraditionalForm], - FormBox[ - FormBox["q", - TraditionalForm], - TraditionalForm], - FormBox["\<\", \"\>", - TraditionalForm], - FormBox[ - FormBox[ - RowBox[{ - RowBox[{"-", - FormBox["p", - TraditionalForm]}], "-", - FormBox["q", - TraditionalForm]}], - TraditionalForm], - TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", + RowBox[{"-", "p"}], "-", "q"}], + TraditionalForm]}], ")"}], TraditionalForm]], "Output", CellTags->"Calc", - CellLabel->"Out[5]=", - CellID->706901544] + CellLabel->"Out[127]="] }, Open ]], Cell[CellGroupData[{ @@ -529,14 +500,14 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "p"}], "-", "q"}], ",", "li3"}], "]"}]}], "]"}]], "Input", CellTags->"Calc", - CellLabel->"In[6]:=", + CellLabel->"In[128]:=", CellID->1411490249], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"Calc", - CellLabel->"Out[6]=", - CellID->1029776951] + CellLabel->"Out[128]="] +}, Open ]] }, Open ]] }, Open ]], @@ -601,12 +572,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{Automatic, 328}, {Automatic, -35}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CalcColorFactor.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CalcColorFactor.nb index 272e626ed..cd853f753 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CalcColorFactor.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CalcColorFactor.nb @@ -117,19 +117,34 @@ Cell["CalcColorFactor", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"CalcColorFactor", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "calculates the color factor of expr. CalcColorFactor is useful for \ -application on FeynArts produced amplitudes. CalcColorFactor is just a macro \ -function for CalcColorFactor[x_] := \nIf[FreeQ2[FeynCalcInternal[x], \ -SUNIndex], x, \n SUNSimplify[SUNSimplify[ (If[ \ -!FreeQ[#1, DiracGamma], DiracTrick[#1], #1] & )[ SUNSimplify[x]], Explicit \ --> False], Explicit -> True]]." + RowBox[{"CalcColorFactor", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]calculates the color factor of ", + Cell[BoxData["exp"], "InlineFormula"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + ButtonBox["CalcColorFactor", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CalcColorFactor", + ButtonNote->"CalcColorFactor"], + " is useful for application on FeynArts produced amplitudes." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "CalcColorFactor", "]"}]], "Input", + CellLabel->"In[41]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"SUNNToCACF", "\[Rule]", "True"}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[41]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -164,15 +179,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - ButtonBox["SUNSimplify", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/SUNSimplify", - ButtonNote->"SUNSimplify"], - "." -}], "Text", - CellTags->"CalcColorFactor", - CellID->1899752684] +Cell[TextData[ButtonBox["SUNSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNSimplify", + ButtonNote->"SUNSimplify"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -199,10 +209,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"CalcColorFactor", - CellID->86935840], - Cell[CellGroupData[{ Cell[BoxData[ @@ -213,7 +219,7 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "b", ",", "d"}], "]"}]}], "]"}]], "Input", CellTags->"CalcColorFactor", - CellLabel->"In[1]:=", + CellLabel->"In[42]:=", CellID->1491586567], Cell[BoxData[ @@ -231,253 +237,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"CalcColorFactor", - CellLabel->"Out[1]=", - CellID->1436200004] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Amplitude", "[", "\"\\"", "]"}]], "Input", - CellTags->"CalcColorFactor", - CellLabel->"In[2]:=", - CellID->1818256691], - -Cell[BoxData[ - FormBox[ - RowBox[{"SUNDeltaContract", "(", - RowBox[{ - RowBox[{ - SubsuperscriptBox["\[CapitalPi]", - RowBox[{ - FormBox["ci1", - TraditionalForm], - FormBox["ci3", - TraditionalForm]}], - RowBox[{ - FormBox["li1", - TraditionalForm], - FormBox["li3", - TraditionalForm]}]], "(", - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm], ")"}], " ", - RowBox[{ - SubsuperscriptBox["\[CapitalPi]", - RowBox[{ - FormBox["ci9", - TraditionalForm], - FormBox["ci11", - TraditionalForm]}], - RowBox[{ - FormBox["li9", - TraditionalForm], - FormBox["li11", - TraditionalForm]}]], "(", - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm], ")"}], " ", - RowBox[{ - SubsuperscriptBox["Q", - FormBox["ci11", - TraditionalForm], - FormBox["li11", - 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TraditionalForm]]}]}], - TraditionalForm], ")"}]}], ")"}]}], ")"}], TraditionalForm]], "Output", - CellTags->"CalcColorFactor", - CellLabel->"Out[2]=", - CellID->1553911339] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"CalcColorFactor", "@", - RowBox[{"Explicit", "@", "%"}]}]], "Input", - CellTags->"CalcColorFactor", - CellLabel->"In[3]:=", - CellID->361683152], - -Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{"(", - RowBox[{"\[ImaginaryI]", " ", - SubscriptBox["C", "F"], " ", - SubscriptBox["T", "f"], " ", - SuperscriptBox[ - RowBox[{"(", - FractionBox["1", - SuperscriptBox[ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm], "2"]], ")"}], "2"], " ", - SubsuperscriptBox["g", "s", "4"], " ", - RowBox[{"(", - RowBox[{ - SubscriptBox["C", "A"], "-", - RowBox[{"2", " ", - SubscriptBox["C", "F"]}]}], ")"}], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["li1", - TraditionalForm], - TraditionalForm], - TraditionalForm], - 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FormBox[ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], - TraditionalForm]}], ")"}], ".", - SuperscriptBox["\[Gamma]", - FormBox[ - FormBox["li9", - TraditionalForm], - TraditionalForm]], ".", - RowBox[{"(", - RowBox[{"\[Gamma]", "\[CenterDot]", "(", - FormBox[ - FormBox[ - RowBox[{ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], "-", - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm]}], - TraditionalForm], - TraditionalForm], ")"}], ")"}], ".", - SuperscriptBox["\[Gamma]", - FormBox[ - FormBox["li3", - TraditionalForm], - TraditionalForm]]}], - TraditionalForm], ")"}]}], ")"}], "/", - RowBox[{"(", - RowBox[{ - SuperscriptBox[ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], "2"], " ", - SuperscriptBox[ - RowBox[{"(", - RowBox[{ - FormBox[ - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], - TraditionalForm], "-", - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm]}], ")"}], "2"], " ", - SuperscriptBox[ - RowBox[{"(", - RowBox[{ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm], "-", - FormBox[ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm]}], ")"}], "2"]}], ")"}]}], - TraditionalForm]], "Output", - CellTags->"CalcColorFactor", - CellLabel->"Out[3]=", - CellID->1233692379] + CellLabel->"Out[42]="] }, Open ]] }, Open ]], @@ -542,12 +302,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{591, Automatic}, {Automatic, 224}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CalculateCounterTerm.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CalculateCounterTerm.nb index ceb436dca..f2f19b3ca 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CalculateCounterTerm.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CalculateCounterTerm.nb @@ -124,8 +124,28 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +This is a rather special function designed for some specific OPE \ +calculations. Not a universal routine for daily use.\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "CalculateCounterTerm", "]"}]], "Input", + CellLabel->"In[240]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Chisholm", "\[Rule]", "False"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", + RowBox[{"D", "\[Rule]", "4"}], "}"}]}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[240]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -247,12 +267,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1270, Automatic}, {Automatic, 247}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CartesianIndex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CartesianIndex.nb new file mode 100644 index 000000000..7cbdfa41e --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CartesianIndex.nb @@ -0,0 +1,336 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/CartesianIndex", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["CartesianIndex", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData["CartesianIndex"], "InlineFormula"], + " \[LineSeparator]is the head of Cartesian indices. The internal \ +representation of a three-dimensional i is CartesianIndex[i]. For other than \ +three dimensions: CartesianIndex[i, Dimension]. CartesianIndex[i, 3] \ +simplifies to CartesianIndex[i]. 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CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/CartesianToLorentz", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], 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Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["CartesianToLorentz", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"CartesianToLorentz", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator] rewrites Cartesian tensors in form of Lorentz tensors \ +(when possible). Using options one can specify which types of tensors should \ +be converted." +}], "Usage", + CellID->982511436], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "CartesianToLorentz", "]"}]], "Input", + CellLabel->"In[372]:=", + CellID->60038220], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"CSP", "\[Rule]", "True"}], ",", + RowBox[{"CGS", "\[Rule]", "True"}], ",", + RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", + RowBox[{"DiracGammaExpand", "\[Rule]", "True"}], ",", + RowBox[{"DotSimplify", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[372]=", + CellID->762732505] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell[TextData[{ + ButtonBox["LorentzToCartesian", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/LorentzToCartesian", + ButtonNote->"LorentzToCartesian"], + "." +}], "SeeAlso", + CellID->119070656] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; 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Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{948, Automatic}, {Automatic, 156}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Cases2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Cases2.nb index 83d9e5a51..46f1cb40e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Cases2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Cases2.nb @@ -191,10 +191,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"Cases2", - CellID->645978510], - Cell[CellGroupData[{ Cell[BoxData[ @@ -207,7 +203,7 @@ Cell[BoxData[ RowBox[{"f", "[", RowBox[{"c", ",", "d"}], "]"}]}], ",", "f"}], "]"}]], "Input", CellTags->"Cases2", - CellLabel->"In[1]:=", + CellLabel->"In[284]:=", CellID->1924250367], Cell[BoxData[ @@ -219,8 +215,7 @@ Cell[BoxData[ RowBox[{"f", "(", RowBox[{"c", ",", "d"}], ")"}]}], "}"}], TraditionalForm]], "Output", CellTags->"Cases2", - CellLabel->"Out[1]=", - CellID->1245535704] + CellLabel->"Out[284]="] }, Open ]], Cell[CellGroupData[{ @@ -235,7 +230,7 @@ Cell[BoxData[ RowBox[{"y", "-", "z"}], "]"}]}], "+", RowBox[{"g", "[", "y", "]"}]}], ",", "Sin", ",", "g"}], "]"}]], "Input", CellTags->"Cases2", - CellLabel->"In[2]:=", + CellLabel->"In[285]:=", CellID->1264635109], Cell[BoxData[ @@ -247,8 +242,7 @@ Cell[BoxData[ RowBox[{"sin", "(", RowBox[{"y", "-", "z"}], ")"}]}], "}"}], TraditionalForm]], "Output", CellTags->"Cases2", - CellLabel->"Out[2]=", - CellID->1551461505] + CellLabel->"Out[285]="] }, Open ]], Cell[CellGroupData[{ @@ -267,7 +261,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"Sin", ",", "g"}], "}"}]}], "]"}]], "Input", CellTags->"Cases2", - CellLabel->"In[3]:=", + CellLabel->"In[286]:=", CellID->1159301950], Cell[BoxData[ @@ -281,8 +275,7 @@ Cell[BoxData[ RowBox[{"sin", "(", RowBox[{"y", "-", "z"}], ")"}]}], "}"}], TraditionalForm]], "Output", CellTags->"Cases2", - CellLabel->"Out[3]=", - CellID->1202203267] + CellLabel->"Out[286]="] }, Open ]], Cell[CellGroupData[{ @@ -292,12 +285,12 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ - RowBox[{"DiracSlash", "[", "p", "]"}], ".", - RowBox[{"DiracSlash", "[", "q", "]"}]}], "+", - RowBox[{"ScalarProduct", "[", + RowBox[{"GS", "[", "p", "]"}], ".", + RowBox[{"GS", "[", "q", "]"}]}], "+", + RowBox[{"SP", "[", RowBox[{"p", ",", "p"}], "]"}]}], ",", "Dot"}], "]"}]], "Input", CellTags->"Cases2", - CellLabel->"In[4]:=", + CellLabel->"In[288]:=", CellID->775837316], Cell[BoxData[ @@ -305,24 +298,27 @@ Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"(", - RowBox[{ - OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm]}], ")"}], ".", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", RowBox[{"(", - RowBox[{ - OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm]}], ")"}]}], "}"}], TraditionalForm]], "Output", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}]}], "}"}], TraditionalForm]], "Output", CellTags->"Cases2", - CellLabel->"Out[4]=", - CellID->896832184] + CellLabel->"Out[288]="] }, Open ]] }, Open ]], @@ -387,12 +383,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{773, Automatic}, {Automatic, 240}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ChangeDimension.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ChangeDimension.nb index a1e676134..ff40f1d28 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ChangeDimension.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ChangeDimension.nb @@ -182,9 +182,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Eps", ButtonNote->"Eps"], "." -}], "Text", - CellTags->"ChangeDimension", - CellID->1962733391] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -215,9 +213,7 @@ Cell["\<\ Remember that LorentzIndex[mu, 4] is simplified to LorentzIndex[mu] and \ Momentum[p, 4] to Momentum[p]. Thus the fullowing objects are defined in four \ dimensions.\ -\>", "Text", - CellTags->"ChangeDimension", - CellID->1522324479], +\>", "Notes"], Cell[CellGroupData[{ @@ -227,7 +223,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", " ", RowBox[{"Momentum", "[", "p", "]"}]}], "}"}]], "Input", CellTags->"ChangeDimension", - CellLabel->"In[1]:=", + CellLabel->"In[289]:=", CellID->1127631822], Cell[BoxData[ @@ -240,8 +236,7 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"]}], "}"}], TraditionalForm]], "Output", CellTags->"ChangeDimension", - CellLabel->"Out[1]=", - CellID->621481036] + CellLabel->"Out[289]="] }, Open ]], Cell[CellGroupData[{ @@ -250,7 +245,7 @@ Cell[BoxData[ RowBox[{"ChangeDimension", "[", RowBox[{"%", ",", " ", "D"}], "]"}]], "Input", CellTags->"ChangeDimension", - CellLabel->"In[2]:=", + CellLabel->"In[290]:=", CellID->2044492451], Cell[BoxData[ @@ -262,8 +257,7 @@ Cell[BoxData[ FormBox["p", TraditionalForm]}], "}"}], TraditionalForm]], "Output", CellTags->"ChangeDimension", - CellLabel->"Out[2]=", - CellID->1291415822] + CellLabel->"Out[290]="] }, Open ]], Cell[CellGroupData[{ @@ -271,7 +265,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"ChangeDimension", - CellLabel->"In[3]:=", + CellLabel->"In[291]:=", CellID->1689591331], Cell[BoxData[ @@ -282,15 +276,12 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "D"}], "]"}]}], "}"}]], "Output", CellTags->"ChangeDimension", - CellLabel->"Out[3]//StandardForm=", - CellID->2101335861] + CellLabel->"Out[291]//StandardForm="] }, Open ]], Cell["\<\ This changes all non-4-dimensional objects to 4-dimensional ones.\ -\>", "Text", - CellTags->"ChangeDimension", - CellID->906094166], +\>", "Notes"], Cell[CellGroupData[{ @@ -300,7 +291,7 @@ Cell[BoxData[ RowBox[{"%%", ",", " ", "4"}], "]"}], " ", "//", " ", "StandardForm"}]], "Input", CellTags->"ChangeDimension", - CellLabel->"In[4]:=", + CellLabel->"In[292]:=", CellID->898970803], Cell[BoxData[ @@ -309,13 +300,10 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "}"}]], "Output", CellTags->"ChangeDimension", - CellLabel->"Out[4]//StandardForm=", - CellID->2072157462] + CellLabel->"Out[292]//StandardForm="] }, Open ]], -Cell["Consider the following list of 4- and D-dimensional object.", "Text", - CellTags->"ChangeDimension", - CellID->169525226], +Cell["Consider the following list of 4- and D-dimensional object.", "Notes"], Cell[CellGroupData[{ @@ -334,7 +322,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], " ", RowBox[{"f", "[", "D", "]"}]}]}], "}"}]], "Input", CellTags->"ChangeDimension", - CellLabel->"In[5]:=", + CellLabel->"In[296]:=", CellID->931498160], Cell[BoxData[ @@ -360,23 +348,17 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], " ", FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]}], ",", RowBox[{ RowBox[{"f", "(", "D", ")"}], " ", @@ -396,35 +378,28 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], " ", FormBox[ - 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Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CheckDB.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CheckDB.nb index 2e897de01..fce9990e0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CheckDB.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CheckDB.nb @@ -119,26 +119,60 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"CheckDB", "[", RowBox[{"exp", ",", " ", "fil"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "saves [with Put] or retrieves [with Get] exp from a file fil. It checks if \ -the setting of the option Directory is a valid directory name and if fil is a \ -valid file name and does exist. If it does, Get[fil] is executed. If fil does \ -not exist, exp gets evaluated and saved to fil. Saving and evaluating can be \ -further controlled with the options ForceSave and NoSave. If the option Check \ -is set to False the return value is what is evaluated [see above]. If Check \ -is set to True the return value is True or False depending on whether the \ -evaluation of exp agrees with what is loaded from fil or fil does not exist. \ -Default value of Check : False.\nNOTICE : If fil ends with \".Gen\" or \".Mod\ -\", the setting of Directory is ignored and fil is saved in the \ -\"CouplingVectors\" subdirectory of \"Phi\". If fil ends with \".Fac\", the \ -setting of Directory is ignored and fil is saved in the \"Factors\" \ -subdirectory of \"Phi\". If fil is a file name with full path, the setting \ -of Directory is also ignored." + " \[LineSeparator]saves [with Put] or retrieves [with Get] exp from a file \ +fil. It checks if the setting of the option Directory is a valid directory \ +name and if fil is a valid file name and does exist. If it does, Get[fil] is \ +executed. If fil does not exist, exp gets evaluated and saved to fil. Saving \ +and evaluating can be further controlled with the options ForceSave and \ +NoSave. If the option Check is set to False the return value is what is \ +evaluated [see above]. If Check is set to True the return value is True or \ +False depending on whether the evaluation of exp agrees with what is loaded \ +from fil or fil does not exist. Default value of Check : False." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +If fil ends with \".Gen\" or \".Mod\", the setting of Directory is ignored \ +and fil is saved in the \"CouplingVectors\" subdirectory of \"Phi\". If fil \ +ends with \".Fac\", the setting of Directory is ignored and fil is saved in \ +the \"Factors\" subdirectory of \"Phi\". If fil is a file name with full \ +path, the setting of Directory is also ignored.\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "CheckDB", "]"}]], "Input", + CellLabel->"In[305]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Directory", "\[RuleDelayed]", + RowBox[{"ToFileName", "[", + RowBox[{ + RowBox[{"{", "$FeynCalcDirectory", "}"}], ",", "\<\"Database\"\>"}], + "]"}]}], ",", + RowBox[{"ForceSave", "\[Rule]", "False"}], ",", + RowBox[{"NoSave", "\[Rule]", "False"}], ",", + RowBox[{"Check", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[305]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Attributes", "[", "CheckDB", "]"}]], "Input", + CellLabel->"In[306]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", "HoldFirst", "}"}], TraditionalForm]], "Output", + CellLabel->"Out[306]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -201,58 +235,10 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"CheckDB", - CellID->647730640], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "CheckDB", "]"}]], "Input", - CellTags->"CheckDB", - CellLabel->"In[1]:=", - CellID->2004487562], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Directory", "\[RuleDelayed]", - RowBox[{"ToFileName", "[", - RowBox[{ - RowBox[{"{", "$FeynCalcDirectory", "}"}], ",", "\<\"Database\"\>"}], - "]"}]}], ",", - RowBox[{"ForceSave", "\[Rule]", "False"}], ",", - RowBox[{"NoSave", "\[Rule]", "False"}], ",", - RowBox[{"Check", "\[Rule]", "False"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"CheckDB", - CellLabel->"Out[1]=", - CellID->1735070400] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Attributes", "[", "CheckDB", "]"}]], "Input", - CellTags->"CheckDB", - CellLabel->"In[2]:=", - CellID->62116505], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", "HoldFirst", "}"}], TraditionalForm]], "Output", - CellTags->"CheckDB", - CellLabel->"Out[2]=", - CellID->393414258] -}, Open ]], - Cell["\<\ The first time the Table function is evaluated and the result saved into the \ test.s file.\ -\>", "Text", - CellTags->"CheckDB", - CellID->1632453918], +\>", "Notes"], Cell[CellGroupData[{ @@ -269,29 +255,25 @@ Cell[BoxData[ RowBox[{"i", ",", "2"}], "}"}]}], "]"}], ",", "\"\\""}], "]"}]], "Input", CellTags->"CheckDB", - CellLabel->"In[3]:=", + CellLabel->"In[307]:=", CellID->1433287094], Cell["test test ", "Print", CellTags->"CheckDB", - CellLabel->"During evaluation of In[3]:=", - CellID->670482458], + CellLabel->"During evaluation of In[307]:="], Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], TraditionalForm]], "Output", CellTags->"CheckDB", - CellLabel->"Out[3]=", - CellID->1976770700] + CellLabel->"Out[307]="] }, Open ]], Cell["\<\ Executing the same a second time will just load the result from test.s and \ not evaluate the Table function.\ -\>", "Text", - CellTags->"CheckDB", - CellID->342347170], +\>", "Notes"], Cell[CellGroupData[{ @@ -308,7 +290,7 @@ Cell[BoxData[ RowBox[{"i", ",", "2"}], "}"}]}], "]"}], ",", "\"\\""}], "]"}]], "Input", CellTags->"CheckDB", - CellLabel->"In[4]:=", + CellLabel->"In[308]:=", CellID->1024102984], Cell[BoxData[ @@ -316,13 +298,10 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], TraditionalForm]], "Output", CellTags->"CheckDB", - CellLabel->"Out[4]=", - CellID->129097795] + CellLabel->"Out[308]="] }, Open ]], -Cell["This shows the actual saved value of test.s.", "Text", - CellTags->"CheckDB", - CellID->277506706], +Cell["This shows the actual saved value of test.s.", "Notes"], Cell[CellGroupData[{ @@ -335,14 +314,13 @@ Cell[BoxData[ RowBox[{"Options", "[", "CheckDB", "]"}]}], ",", "\"\\""}], "]"}], ",", "\"\\""}], "]"}]], "Input", CellTags->"CheckDB", - CellLabel->"In[5]:=", + CellLabel->"In[309]:=", CellID->1578936180], Cell[BoxData[ FormBox["\<\"{1, 2}\"\>", TraditionalForm]], "Output", CellTags->"CheckDB", - CellLabel->"Out[5]=", - CellID->796644611] + CellLabel->"Out[309]="] }, Open ]], Cell[BoxData[ @@ -353,7 +331,7 @@ Cell[BoxData[ RowBox[{"Options", "[", "CheckDB", "]"}]}], ",", "\"\\""}], "]"}], "]"}]], "Input", CellTags->"CheckDB", - CellLabel->"In[6]:=", + CellLabel->"In[310]:=", CellID->1720430951] }, Open ]], @@ -418,12 +396,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{784, Automatic}, {Automatic, 51}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ChiralityProjector.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ChiralityProjector.nb index ee6fa7254..59cad4a43 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ChiralityProjector.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ChiralityProjector.nb @@ -140,7 +140,10 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +The shortcut ChiralityProjector is deprecated, please use GA[6] and GA[7] \ +instead!\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -177,24 +180,17 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["DiracGamma", + ButtonBox["GA", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracGamma", - ButtonNote->"DiracGamma"], - ", ", - ButtonBox["DiracMatrix", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData:>"paclet:FeynCalc/ref/GA", + ButtonNote->"GA"], ", ", ButtonBox["FCI", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FCI", ButtonNote->"FCI"], "." -}], "Text", - CellTags->"ChiralityProjector", - CellID->326424545] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -231,7 +227,7 @@ Cell[BoxData[ RowBox[{"ChiralityProjector", "[", RowBox[{"-", "1"}], "]"}]}], "}"}]], "Input", CellTags->"ChiralityProjector", - CellLabel->"In[2]:=", + CellLabel->"In[313]:=", CellID->336937517], Cell[BoxData[ @@ -247,18 +243,20 @@ Cell[BoxData[ FormBox["7", TraditionalForm]]}], "}"}], TraditionalForm]], "Output", CellTags->"ChiralityProjector", - CellLabel->"Out[2]=", - CellID->1252517379] + CellLabel->"Out[313]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracSimplify", "[", - RowBox[{"%", ",", - RowBox[{"DiracSubstitute67", "\[Rule]", "True"}]}], "]"}]], "Input", + RowBox[{ + RowBox[{ + RowBox[{"DiracSimplify", "[", + RowBox[{"#", ",", + RowBox[{"DiracSubstitute67", "\[Rule]", "True"}]}], "]"}], "&"}], "/@", + "%"}]], "Input", CellTags->"ChiralityProjector", - CellLabel->"In[3]:=", + CellLabel->"In[314]:=", CellID->2102778570], Cell[BoxData[ @@ -280,8 +278,70 @@ Cell[BoxData[ FormBox["5", TraditionalForm]], "2"]}]}], "}"}], TraditionalForm]], "Output", CellTags->"ChiralityProjector", - CellLabel->"Out[3]=", - CellID->1744568026] + CellLabel->"Out[314]="] +}, Open ]], + +Cell["\<\ +ChiralityProjector is scheduled for removal in the future versions of \ +FeynCalc. The safe alternative is to use GA[6] and GA[7].\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{"GA", "[", "6", "]"}], ",", + RowBox[{"GA", "[", "7", "]"}]}], "}"}]], "Input", + CellLabel->"In[319]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["6", + TraditionalForm]], + TraditionalForm], ",", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["7", + TraditionalForm]], + TraditionalForm]}], "}"}], TraditionalForm]], "Output", + CellLabel->"Out[319]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"GA", "[", "6", "]"}], "]"}], "===", + RowBox[{"ChiralityProjector", "[", + RowBox[{"+", "1"}], "]"}]}]], "Input", + CellLabel->"In[320]:="], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[320]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"GA", "[", "7", "]"}], "]"}], "===", + RowBox[{"ChiralityProjector", "[", + RowBox[{"-", "1"}], "]"}]}]], "Input", + CellLabel->"In[321]:="], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[321]="] }, Open ]] }, Open ]], @@ -345,10 +405,11 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{1221, 770}, +WindowMargins->{{Automatic, 303}, {116, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Chisholm.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Chisholm.nb index 6ff927b1c..dc7aa039b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Chisholm.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Chisholm.nb @@ -117,15 +117,38 @@ Cell["Chisholm", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"Chisholm", "[", "x", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "substitutes products of three Dirac matrices or slashes by the Chisholm \ -identity." + RowBox[{"Chisholm", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]substitutes products of three Dirac matrices or slashes by \ +the Chisholm identity." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Chisholm", "]"}]], "Input", + CellLabel->"In[55]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Contract", "\[Rule]", "True"}], ",", + RowBox[{"DiracSimplify", "\[Rule]", "True"}], ",", + RowBox[{"DotSimplify", "\[Rule]", "True"}], ",", + RowBox[{"FCDiracIsolate", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCJoinDOTs", "\[Rule]", "True"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Mode", "\[Rule]", "1"}], ",", + RowBox[{"DiracSigmaExplicit", "\[Rule]", "False"}], ",", + RowBox[{"NonCommutative", "\[Rule]", "True"}], ",", + RowBox[{"MaxIterations", "\[Rule]", "\[Infinity]"}], ",", + RowBox[{"InsideDiracTrace", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[55]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -160,20 +183,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - ButtonBox["EpsChisholm", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/EpsChisholm", - ButtonNote->"EpsChisholm"], - ", ", - ButtonBox["ChisholmSpinor", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/ChisholmSpinor", - ButtonNote->"ChisholmSpinor"], - "." -}], "Text", - CellTags->"Chisholm", - CellID->1402112447] +Cell[TextData[ButtonBox["EpsChisholm", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/EpsChisholm", + ButtonNote->"EpsChisholm"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,179 +216,51 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Chisholm", "[", - RowBox[{"GA", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Mu]", ",", "\[Nu]"}], "]"}], - "]"}]], "Input", + RowBox[{"GA", "[", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}]], "Input", CellTags->"Chisholm", - CellLabel->"In[1]:=", - CellID->1963239115], + CellLabel->"In[60]:=", + CellID->820852327], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{"-", - RowBox[{"\[ImaginaryI]", " ", - 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CellLabel->"Out[102]=", - CellID->444068994] + CellLabel->"Out[385]="] }, Open ]], Cell[CellGroupData[{ @@ -594,7 +583,7 @@ Cell[BoxData[ RowBox[{"%", " ", "/.", " ", RowBox[{"fun", "\[Rule]", "FactorTerms"}]}]], "Input", CellTags->"Collect2", - CellLabel->"In[103]:=", + CellLabel->"In[386]:=", CellID->1964581263], Cell[BoxData[ @@ -618,8 +607,7 @@ Cell[BoxData[ SuperscriptBox["c", "2"]}], "-", SuperscriptBox["c", "3"]}], TraditionalForm]], "Output", CellTags->"Collect2", - CellLabel->"Out[103]=", - CellID->1797163188] + CellLabel->"Out[386]="] }, Open ]], Cell[TextData[{ @@ -655,7 +643,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"i", ",", "1", ",", "200000"}], "}"}]}], "]"}], "*", "c"}]}]}], ";"}]], "Input", - CellLabel->"In[124]:=", + CellLabel->"In[387]:=", CellID->18062506], Cell[CellGroupData[{ @@ -669,28 +657,27 @@ Cell[BoxData[ RowBox[{"Factoring", "\[Rule]", "False"}], ",", RowBox[{"IsolateNames", "\[Rule]", "KK"}], ",", RowBox[{"Expanding", "\[Rule]", "False"}]}], "]"}], "]"}]], "Input", - CellLabel->"In[129]:=", + CellLabel->"In[388]:=", CellID->908574489], Cell[BoxData[ FormBox[ RowBox[{"{", - RowBox[{"2.427166`", ",", + RowBox[{"2.648394`", ",", RowBox[{ RowBox[{"a", " ", TagBox[ - RowBox[{"KK", "(", "1416", ")"}], + RowBox[{"KK", "(", "123", ")"}], HoldForm]}], "+", RowBox[{"b", " ", TagBox[ - RowBox[{"KK", "(", "1417", ")"}], + RowBox[{"KK", "(", "124", ")"}], HoldForm]}], "+", RowBox[{"c", " ", TagBox[ - RowBox[{"KK", "(", "1415", ")"}], + RowBox[{"KK", "(", "122", ")"}], HoldForm]}]}]}], "}"}], TraditionalForm]], "Output", - CellLabel->"Out[129]=", - CellID->428829446] + CellLabel->"Out[388]="] }, Open ]], Cell[CellGroupData[{ @@ -705,29 +692,32 @@ Cell[BoxData[ RowBox[{"IsolateNames", "\[Rule]", "KK"}], ",", RowBox[{"IsolateFast", "\[Rule]", "True"}], ",", RowBox[{"Expanding", "\[Rule]", "False"}]}], "]"}], "]"}]], "Input", - CellLabel->"In[130]:=", + CellLabel->"In[389]:=", CellID->1760353952], Cell[BoxData[ FormBox[ RowBox[{"{", - RowBox[{"1.824256`", ",", + RowBox[{"1.940384`", ",", RowBox[{ RowBox[{"a", " ", TagBox[ - RowBox[{"KK", "(", "1416", ")"}], + RowBox[{"KK", "(", "123", ")"}], HoldForm]}], "+", RowBox[{"b", " ", TagBox[ - RowBox[{"KK", "(", "1417", ")"}], + RowBox[{"KK", "(", "124", ")"}], HoldForm]}], "+", RowBox[{"c", " ", TagBox[ - RowBox[{"KK", "(", "1415", ")"}], + RowBox[{"KK", "(", "122", ")"}], HoldForm]}]}]}], "}"}], TraditionalForm]], "Output", - CellLabel->"Out[130]=", - CellID->1586544186] -}, Open ]] + CellLabel->"Out[389]="] +}, Open ]], + +Cell[BoxData[ + RowBox[{"ClearAll", "[", "exp", "]"}]], "Input", + CellLabel->"In[390]:="] }, Open ]], Cell[CellGroupData[{ @@ -791,9 +781,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 741}, -WindowMargins->{{Automatic, 1137}, {Automatic, 70}}, +WindowMargins->{{796, Automatic}, {Automatic, 131}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Collect3.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Collect3.nb index 4bd0c9524..4ce5a322a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Collect3.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Collect3.nb @@ -146,8 +146,24 @@ to the list of monomials mulitplied by their coefficients." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Collect3", "]"}]], "Input", + CellTags->"Collect3", + CellLabel->"In[391]:=", + CellID->1015372413], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Factoring", "\[Rule]", "False"}], ",", + RowBox[{"Head", "\[Rule]", "Plus"}]}], "}"}], TraditionalForm]], "Output", + + CellTags->"Collect3", + CellLabel->"Out[391]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -193,9 +209,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Isolate", ButtonNote->"Isolate"], "." -}], "Text", - CellTags->"Collect3", - CellID->877664095] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -224,26 +238,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Collect3", "]"}]], "Input", - CellTags->"Collect3", - CellLabel->"In[1]:=", - CellID->1015372413], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Factoring", "\[Rule]", "False"}], ",", - RowBox[{"Head", "\[Rule]", "Plus"}]}], "}"}], TraditionalForm]], "Output", - - CellTags->"Collect3", - CellLabel->"Out[1]=", - CellID->581070159] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"Collect3", "[", RowBox[{ @@ -262,7 +256,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "Input", CellTags->"Collect3", - CellLabel->"In[2]:=", + CellLabel->"In[392]:=", CellID->956954453], Cell[BoxData[ @@ -281,8 +275,7 @@ Cell[BoxData[ SuperscriptBox["b", "2"], " ", "c"}], "+", SuperscriptBox["b", "2"]}], TraditionalForm]], "Output", CellTags->"Collect3", - CellLabel->"Out[2]=", - CellID->1763015133] + CellLabel->"Out[392]="] }, Open ]], Cell[CellGroupData[{ @@ -296,7 +289,7 @@ Cell[BoxData[ RowBox[{"a", "-", "b", "-", "c", "-", "d"}], ")"}], "5"], "]"}], ",", RowBox[{"{", "a", "}"}]}], "]"}]], "Input", CellTags->"Collect3", - CellLabel->"In[3]:=", + CellLabel->"In[393]:=", CellID->860117715], Cell[BoxData[ @@ -435,8 +428,7 @@ Cell[BoxData[ SuperscriptBox["d", "4"]}], "-", SuperscriptBox["d", "5"]}], TraditionalForm]], "Output", CellTags->"Collect3", - CellLabel->"Out[3]=", - CellID->1558649070] + CellLabel->"Out[393]="] }, Open ]] }, Open ]], @@ -501,12 +493,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1098, Automatic}, {Automatic, 194}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Collecting.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Collecting.nb index 7fa6cab86..be0d4786a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Collecting.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Collecting.nb @@ -175,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/TID", ButtonNote->"TID"], "." -}], "Text", - CellTags->"Collecting", - CellID->782318945] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -263,12 +261,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{839, Automatic}, {Automatic, 93}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Combine.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Combine.nb index ddf9e542f..6399cb387 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Combine.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Combine.nb @@ -126,8 +126,22 @@ sums in the denominator." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Combine", "]"}]], "Input", + CellTags->"Combine", + CellLabel->"In[394]:=", + CellID->194899276], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Expanding", "\[Rule]", "False"}], "}"}], + TraditionalForm]], "Output", + CellTags->"Combine", + CellLabel->"Out[394]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -168,9 +182,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Factor2", ButtonNote->"Factor2"], "." -}], "Text", - CellTags->"Combine", - CellID->2027442052] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -199,24 +211,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Combine", "]"}]], "Input", - CellTags->"Combine", - CellLabel->"In[1]:=", - CellID->194899276], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Expanding", "\[Rule]", "False"}], "}"}], - TraditionalForm]], "Output", - CellTags->"Combine", - CellLabel->"Out[1]=", - CellID->1836728683] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"Combine", "[", RowBox[{ @@ -227,7 +221,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"c", "-", "d"}], ")"}]}], "e"], "+", "g"}], "]"}]], "Input", CellTags->"Combine", - CellLabel->"In[2]:=", + CellLabel->"In[395]:=", CellID->809742744], Cell[BoxData[ @@ -241,15 +235,12 @@ Cell[BoxData[ RowBox[{"c", "-", "d"}], ")"}]}], "+", RowBox[{"e", " ", "g"}]}], "e"], TraditionalForm]], "Output", CellTags->"Combine", - CellLabel->"Out[2]=", - CellID->1151883280] + CellLabel->"Out[395]="] }, Open ]], Cell["\<\ Here the result from Together where the numerator is automatically expanded.\ -\>", "Text", - CellTags->"Combine", - CellID->18145815], +\>", "Notes"], Cell[CellGroupData[{ @@ -263,7 +254,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"c", "-", "d"}], ")"}]}], "e"], "+", "g"}], "]"}]], "Input", CellTags->"Combine", - CellLabel->"In[3]:=", + CellLabel->"In[396]:=", CellID->990215666], Cell[BoxData[ @@ -276,16 +267,13 @@ Cell[BoxData[ RowBox[{"b", " ", "d"}], "+", RowBox[{"e", " ", "g"}]}], "e"], TraditionalForm]], "Output", CellTags->"Combine", - CellLabel->"Out[3]=", - CellID->1980431254] + CellLabel->"Out[396]="] }, Open ]], Cell["\<\ If the option Expanding is set to True, the result of Combine is the same as \ Together, but uses a slightly different algorithm.\ -\>", "Text", - CellTags->"Combine", - CellID->484864717], +\>", "Notes"], Cell[CellGroupData[{ @@ -301,7 +289,7 @@ Cell[BoxData[ RowBox[{"c", "-", "d"}], ")"}]}], "e"], "+", "g"}], ",", RowBox[{"Expanding", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Combine", - CellLabel->"In[4]:=", + CellLabel->"In[397]:=", CellID->758144630], Cell[BoxData[ @@ -314,8 +302,7 @@ Cell[BoxData[ RowBox[{"b", " ", "d"}], "+", RowBox[{"e", " ", "g"}]}], "e"], TraditionalForm]], "Output", CellTags->"Combine", - CellLabel->"Out[4]=", - CellID->1932335260] + CellLabel->"Out[397]="] }, Open ]] }, Open ]], @@ -380,12 +367,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{750, Automatic}, {Automatic, 101}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CombineGraphs.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CombineGraphs.nb index eecbc020a..18e8f4be6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CombineGraphs.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CombineGraphs.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoopSum", ButtonNote->"OneLoopSum"], "." -}], "Text", - CellTags->"CombineGraphs", - CellID->1987423164] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{934, Automatic}, {Automatic, 267}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Commutator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Commutator.nb index 05aaf7d76..3644da7fc 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Commutator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Commutator.nb @@ -117,10 +117,15 @@ Cell["Commutator", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"Commutator", "[", - RowBox[{"x", ",", " ", "y"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "= c defines the commutator between the (non-commuting) objects x and y. " + RowBox[{ + RowBox[{"Commutator", "[", + RowBox[{"x", ",", " ", "y"}], "]"}], "=", "c"}]], "InlineFormula"], + " \[LineSeparator]defines the commutator between the (non-commuting) objects \ +", + Cell[BoxData["x"], "InlineFormula"], + " and ", + Cell[BoxData["y"], "InlineFormula"], + ". " }], "Usage", CellID->982511436], @@ -181,9 +186,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DotSimplify", ButtonNote->"DotSimplify"], "." -}], "Text", - CellTags->"Commutator", - CellID->1856568879] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -214,7 +217,7 @@ Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}]], "Input", CellTags->"Commutator", - CellLabel->"In[1]:=", + CellLabel->"In[409]:=", CellID->2000059968], Cell[CellGroupData[{ @@ -223,7 +226,7 @@ Cell[BoxData[ RowBox[{"Commutator", "[", RowBox[{"a", ",", "b"}], "]"}]], "Input", CellTags->"Commutator", - CellLabel->"In[2]:=", + CellLabel->"In[410]:=", CellID->922767227], Cell[BoxData[ @@ -234,8 +237,7 @@ Cell[BoxData[ FormBox["b", TraditionalForm], "\[NoBreak]", "]"}], TraditionalForm]], "Output", CellTags->"Commutator", - CellLabel->"Out[2]=", - CellID->803506141] + CellLabel->"Out[410]="] }, Open ]], Cell[CellGroupData[{ @@ -243,7 +245,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CommutatorExplicit", "[", "%", "]"}]], "Input", CellTags->"Commutator", - CellLabel->"In[3]:=", + CellLabel->"In[411]:=", CellID->1899692439], Cell[BoxData[ @@ -252,8 +254,7 @@ Cell[BoxData[ RowBox[{"a", ".", "b"}], "-", RowBox[{"b", ".", "a"}]}], TraditionalForm]], "Output", CellTags->"Commutator", - CellLabel->"Out[3]=", - CellID->114625701] + CellLabel->"Out[411]="] }, Open ]], Cell[CellGroupData[{ @@ -266,37 +267,32 @@ Cell[BoxData[ RowBox[{"a", "+", "b"}], ",", RowBox[{"c", "+", "d"}]}], "]"}], "]"}], " "}]], "Input", CellTags->"Commutator", - CellLabel->"In[4]:=", + CellLabel->"In[412]:=", CellID->1084501087], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{"a", "+", "b"}], ")"}], ".", - RowBox[{"(", - RowBox[{"c", "+", "d"}], ")"}]}], "-", - RowBox[{ - RowBox[{"(", - RowBox[{"c", "+", "d"}], ")"}], ".", - RowBox[{"(", - RowBox[{"a", "+", "b"}], ")"}]}]}], TraditionalForm]], "Output", + RowBox[{"a", ".", "c"}], "-", + RowBox[{"c", ".", "a"}], "+", + RowBox[{"a", ".", "d"}], "-", + RowBox[{"d", ".", "a"}], "+", + RowBox[{"b", ".", "c"}], "-", + RowBox[{"c", ".", "b"}], "+", + RowBox[{"b", ".", "d"}], "-", + RowBox[{"d", ".", "b"}]}], TraditionalForm]], "Output", CellTags->"Commutator", - CellLabel->"Out[4]=", - CellID->1005990059] + CellLabel->"Out[412]="] }, Open ]], Cell[BoxData[ RowBox[{"UnDeclareNonCommutative", "[", RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}]], "Input", CellTags->"Commutator", - CellLabel->"In[5]:=", + CellLabel->"In[413]:=", CellID->1895253329], -Cell["Verify the Jacobi identity.", "Text", - CellTags->"Commutator", - CellID->1857726821], +Cell["Verify the Jacobi identity.", "Notes"], Cell[BoxData[ RowBox[{ @@ -304,7 +300,7 @@ Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", RowBox[{"x", ",", "y", ",", "z"}], "]"}], ";"}]], "Input", CellTags->"Commutator", - CellLabel->"In[6]:=", + CellLabel->"In[414]:=", CellID->1446605314], Cell[CellGroupData[{ @@ -324,7 +320,7 @@ Cell[BoxData[ RowBox[{"\[Chi]", "[", RowBox[{"x", ",", "y"}], "]"}]}], "]"}]}]], "Input", CellTags->"Commutator", - CellLabel->"In[7]:=", + CellLabel->"In[415]:=", CellID->698764152], Cell[BoxData[ @@ -361,8 +357,7 @@ Cell[BoxData[ TraditionalForm], "\[NoBreak]", "]"}], TraditionalForm], "\[NoBreak]", "]"}]}], TraditionalForm]], "Output", CellTags->"Commutator", - CellLabel->"Out[7]=", - CellID->1488542158] + CellLabel->"Out[415]="] }, Open ]], Cell[CellGroupData[{ @@ -370,27 +365,26 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DotSimplify", "[", "%", "]"}]], "Input", CellTags->"Commutator", - CellLabel->"In[8]:=", + CellLabel->"In[416]:=", CellID->1391154075], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"Commutator", - CellLabel->"Out[8]=", - CellID->502281549] + CellLabel->"Out[416]="] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", "\[Chi]", "]"}]], "Input", CellTags->"Commutator", - CellLabel->"In[9]:=", + CellLabel->"In[417]:=", CellID->1837954422], Cell[BoxData[ RowBox[{"UnDeclareNonCommutative", "[", RowBox[{"x", ",", "y", ",", "z"}], "]"}]], "Input", CellTags->"Commutator", - CellLabel->"In[10]:=", + CellLabel->"In[418]:=", CellID->2037252072] }, Open ]], @@ -455,12 +449,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{839, Automatic}, {Automatic, 183}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CommutatorExplicit.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CommutatorExplicit.nb index e3af4e378..3311d4a49 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CommutatorExplicit.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CommutatorExplicit.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DotSimplify", ButtonNote->"DotSimplify"], "." -}], "Text", - CellTags->"CommutatorExplicit", - CellID->763111899] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,7 +201,7 @@ Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}]], "Input", CellTags->"CommutatorExplicit", - CellLabel->"In[1]:=", + CellLabel->"In[419]:=", CellID->596826267], Cell[CellGroupData[{ @@ -212,7 +210,7 @@ Cell[BoxData[ RowBox[{"Commutator", "[", RowBox[{"a", ",", "b"}], "]"}]], "Input", CellTags->"CommutatorExplicit", - CellLabel->"In[2]:=", + CellLabel->"In[420]:=", CellID->1546400369], Cell[BoxData[ @@ -223,8 +221,7 @@ Cell[BoxData[ FormBox["b", TraditionalForm], "\[NoBreak]", "]"}], TraditionalForm]], "Output", CellTags->"CommutatorExplicit", - CellLabel->"Out[2]=", - CellID->1736741048] + CellLabel->"Out[420]="] }, Open ]], Cell[CellGroupData[{ @@ -232,7 +229,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CommutatorExplicit", "[", "%", "]"}]], "Input", CellTags->"CommutatorExplicit", - CellLabel->"In[3]:=", + CellLabel->"In[421]:=", CellID->1022077689], Cell[BoxData[ @@ -241,8 +238,7 @@ Cell[BoxData[ RowBox[{"a", ".", "b"}], "-", RowBox[{"b", ".", "a"}]}], TraditionalForm]], "Output", CellTags->"CommutatorExplicit", - CellLabel->"Out[3]=", - CellID->1538616356] + CellLabel->"Out[421]="] }, Open ]], Cell[CellGroupData[{ @@ -253,7 +249,7 @@ Cell[BoxData[ RowBox[{"a", "-", "c"}], ",", RowBox[{"b", "-", "d"}]}], "]"}]], "Input", CellTags->"CommutatorExplicit", - CellLabel->"In[4]:=", + CellLabel->"In[422]:=", CellID->1564234454], Cell[BoxData[ @@ -274,8 +270,7 @@ Cell[BoxData[ FormBox["\<\"}\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"CommutatorExplicit", - CellLabel->"Out[4]=", - CellID->945514452] + CellLabel->"Out[422]="] }, Open ]], Cell[CellGroupData[{ @@ -283,7 +278,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CommutatorExplicit", "[", "%", "]"}]], "Input", CellTags->"CommutatorExplicit", - CellLabel->"In[5]:=", + CellLabel->"In[423]:=", CellID->631256546], Cell[BoxData[ @@ -300,8 +295,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"a", "-", "c"}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"CommutatorExplicit", - CellLabel->"Out[5]=", - CellID->272209917] + CellLabel->"Out[423]="] }, Open ]], Cell[CellGroupData[{ @@ -311,7 +305,7 @@ Cell[BoxData[ RowBox[{"CommutatorExplicit", "[", "%%", "]"}], "//", "DotSimplify"}]], "Input", CellTags->"CommutatorExplicit", - CellLabel->"In[6]:=", + CellLabel->"In[424]:=", CellID->1843011592], Cell[BoxData[ @@ -326,15 +320,14 @@ Cell[BoxData[ RowBox[{"c", ".", "d"}], "+", RowBox[{"d", ".", "c"}]}], TraditionalForm]], "Output", CellTags->"CommutatorExplicit", - CellLabel->"Out[6]=", - CellID->1425635977] + CellLabel->"Out[424]="] }, Open ]], Cell[BoxData[ RowBox[{"UnDeclareNonCommutative", "[", RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}]], "Input", CellTags->"CommutatorExplicit", - CellLabel->"In[7]:=", + CellLabel->"In[425]:=", CellID->1614014702] }, Open ]], @@ -399,12 +392,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{971, Automatic}, {Automatic, 216}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Complement1.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Complement1.nb new file mode 100644 index 000000000..dfa173cdb --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Complement1.nb @@ -0,0 +1,304 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/Complement1", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Complement1", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"Complement1", "[", + RowBox[{"l1", ",", "l2"}], "]"}]], "InlineFormula"], + " \[LineSeparator]where l1 and l2 are lists returns a list of elements from \ +l1 not in l2. Multiple occurences of an element in l1 are kept and multiple \ +occurences of an element in l2 are dropped multiply if present in l1." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; 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Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 769}, +WindowMargins->{{949, Automatic}, {Automatic, 176}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CompleteSquare.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CompleteSquare.nb index f29f72d03..454b6b4a3 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CompleteSquare.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CompleteSquare.nb @@ -32,7 +32,7 @@ Cell["FeynCalc`", "Categorization", CellLabel->"Context", CellID->468444828], -Cell["FeynCalc/ref/Completes", "Categorization", +Cell["FeynCalc/ref/CompleteSquare", "Categorization", CellLabel->"URI"] }, Open ]], @@ -111,13 +111,13 @@ Cell["XXXX", "Details", Cell[CellGroupData[{ -Cell["Completes", "ObjectName", +Cell["CompleteSquare", "ObjectName", CellID->1224892054], Cell[TextData[{ Cell[" ", "ModInfo"], - Cell[BoxData["Completes"], "InlineFormula"], - " \[LineSeparator]", + Cell[BoxData["CompleteSquare"], "InlineFormula"], + " \[LineSeparator]completes ", "the square of a second order polynomial in the momentum x. CompleteSquare[a \ ", Cell[BoxData[ @@ -220,105 +220,92 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{ - RowBox[{"5", - RowBox[{"SP", "[", - RowBox[{ - RowBox[{ - RowBox[{"2", "p"}], "+", - RowBox[{"3", "r"}]}], ",", - RowBox[{"p", "+", "r"}]}], "]"}]}], "//", "FCI"}]}]], "Input", - CellLabel->"In[2]:=", + RowBox[{"5", + RowBox[{"SP", "[", + RowBox[{ + RowBox[{ + RowBox[{"2", "p"}], "+", + RowBox[{"3", "r"}]}], ",", + RowBox[{"p", "+", "r"}]}], "]"}]}]], "Input", + CellLabel->"In[433]:=", CellID->42990982], Cell[BoxData[ FormBox[ RowBox[{"5", " ", RowBox[{"(", - RowBox[{ - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["r", - TraditionalForm], "_"]}], - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox[ - RowBox[{ - RowBox[{"2", " ", - 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TraditionalForm]}], ")"}]}], "-", + TraditionalForm]}], "2"]}], "-", FractionBox[ RowBox[{"5", " ", SuperscriptBox[ @@ -328,8 +315,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"]}], "8"]}], TraditionalForm]], "Output", CellTags->"CompleteSquare", - CellLabel->"Out[3]=", - CellID->332224925] + CellLabel->"Out[434]="] }, Open ]], Cell[CellGroupData[{ @@ -337,26 +323,33 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ - RowBox[{"t1", "-", "t2"}], "//", "ScalarProductExpand"}], "//", + RowBox[{"%", "-", "%%"}], "//", "ScalarProductExpand"}], "//", "Expand"}]], "Input", CellTags->"CompleteSquare", - CellLabel->"In[4]:=", + CellLabel->"In[435]:=", CellID->1768514898], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"CompleteSquare", - CellLabel->"Out[4]=", - CellID->2142949469] + CellLabel->"Out[435]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CompleteSquare", "[", - RowBox[{"t1", ",", "p", ",", "q"}], "]"}]], "Input", + RowBox[{ + RowBox[{"5", + RowBox[{"SP", "[", + RowBox[{ + RowBox[{ + RowBox[{"2", "p"}], "+", + RowBox[{"3", "r"}]}], ",", + RowBox[{"p", "+", "r"}]}], "]"}]}], ",", "p", ",", "q"}], + "]"}]], "Input", CellTags->"CompleteSquare", - CellLabel->"In[5]:=", + CellLabel->"In[436]:=", CellID->1850431752], Cell[BoxData[ @@ -394,16 +387,8 @@ Cell[BoxData[ TraditionalForm], "_"]}], "4"]}]}]}], "}"}], TraditionalForm]], "Output", CellTags->"CompleteSquare", - CellLabel->"Out[5]=", - CellID->468779431] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2"}], "]"}]], "Input", - CellTags->"CompleteSquare", - CellLabel->"In[6]:=", - CellID->1021144564] + CellLabel->"Out[436]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -467,12 +452,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1045, Automatic}, {Automatic, 164}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ComplexConjugate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ComplexConjugate.nb index 8d1d7d601..0eace1513 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ComplexConjugate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ComplexConjugate.nb @@ -117,18 +117,43 @@ Cell["ComplexConjugate", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"ComplexConjugate", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "complex conjugates expr. It operates on fermion lines, i.e., products of \ -Spinor[..] .DiracMatrix[..] . Spinor[..], and changes all occuring \ -LorentzIndex[mu] into LorentzIndex[ComplexIndex[mu]]. For taking the spin sum \ -(i.e. constructing the traces) use FermionSpinSum. WARNING: In expr should be \ -NO explicit I's in denominators!" + RowBox[{"ComplexConjugate", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]returns the complex conjugate of ", + Cell[BoxData["exp"], "InlineFormula"], + ", where the input expression must be a proper matrix element. " }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +All Dirac matrices are assumed to be inside closed Dirac spinor chains. If \ +this is not the case, the result will be inconsistent. \ +\>", "Notes"], + +Cell[TextData[{ + "Denominators may not contain explicit ", + Cell[BoxData["I"], "InlineFormula"], + "'s!" +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "ComplexConjugate", "]"}]], "Input", + CellLabel->"In[184]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Conjugate", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"DotSimplify", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCRenameDummyIndices", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[184]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -164,24 +189,22 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["ComplexIndex", + ButtonBox["FCRenameDummyIndices", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/ComplexIndex", - 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CellTags->"ComplexConjugate", - CellLabel->"Out[9]=", - CellID->936868064] + FormBox[ + OverscriptBox[ + FormBox["p2", + TraditionalForm], "_"], + TraditionalForm]}]]}], TraditionalForm]], "Output", + CellLabel->"Out[202]="] }, Open ]], +Cell[TextData[{ + "This behavior can be disabled by setting the option ", + ButtonBox["FCRenameDummyIndices", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FCRenameDummyIndices", + ButtonNote->"FCRenameDummyIndices"], + " to ", + Cell[BoxData["False"], "InlineFormula"], + "." +}], "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ComplexConjugate", "[", "%", "]"}]], "Input", - CellTags->"ComplexConjugate", - CellLabel->"In[10]:=", - CellID->822445915], + RowBox[{"ComplexConjugate", "[", + RowBox[{ + RowBox[{ + RowBox[{"GA", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], + RowBox[{ + RowBox[{"LC", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "[", + RowBox[{"p1", ",", "p2"}], "]"}]}], ",", + RowBox[{"FCRenameDummyIndices", "\[Rule]", "False"}]}], "]"}]], "Input", + CellLabel->"In[203]:="], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{"(", + RowBox[{ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], " ", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ - FormBox["\<\"\[CurlyPhi]\"\>", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], TraditionalForm], - FormBox["\<\"(\"\>", + FormBox[ + FormBox["\[Nu]", + TraditionalForm], TraditionalForm], FormBox[ OverscriptBox[ FormBox["p1", TraditionalForm], "_"], TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], ")"}], ".", + FormBox[ + OverscriptBox[ + FormBox["p2", + TraditionalForm], "_"], + TraditionalForm]}]]}], TraditionalForm]], "Output", + CellLabel->"Out[203]="] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[TextData[{ + "If particular variables must be replaced with their conjugate values, use \ +the option ", + Cell[BoxData["Conjugate"], "InlineFormula"], + "." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"GA", "[", "\[Mu]", "]"}], ".", + RowBox[{"(", + RowBox[{ + RowBox[{"c1", " ", + RowBox[{"GA", "[", "6", "]"}]}], "+", + RowBox[{"c2", " ", + RowBox[{"GA", "[", "7", "]"}]}]}], ")"}], ".", + RowBox[{"GA", "[", "\[Nu]", "]"}]}]], "Input", + CellLabel->"In[207]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + RowBox[{"(", + RowBox[{ + RowBox[{"c1", " ", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["6", + TraditionalForm]], + TraditionalForm]}], "+", + RowBox[{"c2", " ", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["7", + TraditionalForm]], + TraditionalForm]}]}], ")"}], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm]}], TraditionalForm]], "Output", + CellLabel->"Out[207]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ComplexConjugate", "[", "%", "]"}]], "Input", + CellTags->"ComplexConjugate", + CellLabel->"In[208]:=", + CellID->1414819233], + +Cell[BoxData[ + FormBox[ + RowBox[{ SuperscriptBox[ OverscriptBox["\[Gamma]", "_"], FormBox[ - FormBox["\[Lambda]", + FormBox["\[Nu]", TraditionalForm], TraditionalForm]], ".", RowBox[{"(", RowBox[{ - FormBox["\<\"\[CurlyPhi]\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["k1", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", + RowBox[{"c1", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["7", + TraditionalForm]]}], "+", + RowBox[{"c2", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["6", + TraditionalForm]]}]}], ")"}], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"ComplexConjugate", - CellLabel->"Out[10]=", - CellID->1665250585] + CellLabel->"Out[208]="] }, Open ]], -Cell["\<\ -Notice that SpinorUBar and SpinorU are only input functions. Internally they \ -are converted to Spinor objects.\ -\>", "Text", - CellTags->"ComplexConjugate", - CellID->833839056] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ComplexConjugate", "[", + RowBox[{ + RowBox[{ + RowBox[{"GA", "[", "\[Mu]", "]"}], ".", + RowBox[{"(", + RowBox[{ + RowBox[{"c1", " ", + RowBox[{"GA", "[", "6", "]"}]}], "+", + RowBox[{"c2", " ", + RowBox[{"GA", "[", "7", "]"}]}]}], ")"}], ".", + RowBox[{"GA", "[", "\[Nu]", "]"}]}], ",", + RowBox[{"Conjugate", "\[Rule]", + RowBox[{"{", + RowBox[{"c1", ",", "c2"}], "}"}]}]}], "]"}]], "Input", + CellLabel->"In[209]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + RowBox[{ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["7", + TraditionalForm]], " ", + TemplateBox[{"c1"}, + "Conjugate"]}], "+", + RowBox[{ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["6", + TraditionalForm]], " ", + TemplateBox[{"c2"}, + "Conjugate"]}]}], ")"}], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[209]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "StandardForm"}]], "Input", + CellLabel->"In[210]:="], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DiracGamma", "[", + RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], "]"}], ".", + RowBox[{"(", + RowBox[{ + RowBox[{ + RowBox[{"Conjugate", "[", "c2", "]"}], " ", + RowBox[{"DiracGamma", "[", "6", "]"}]}], "+", + RowBox[{ + RowBox[{"Conjugate", "[", "c1", "]"}], " ", + RowBox[{"DiracGamma", "[", "7", "]"}]}]}], ")"}], ".", + RowBox[{"DiracGamma", "[", + RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}]}]], "Output", + CellLabel->"Out[210]//StandardForm="] +}, Open ]] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -636,13 +1359,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{1053, 777}, +WindowMargins->{{Automatic, 340}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Contract.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Contract.nb index fc52c7211..138c74a3d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Contract.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Contract.nb @@ -127,8 +127,29 @@ products of sums of metric tensors and 4-vectors. " }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Contract", "]"}]], "Input", + CellLabel->"In[438]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Collecting", "\[Rule]", "True"}], ",", + RowBox[{"Contract3", "\[Rule]", "True"}], ",", + RowBox[{"EpsContract", "\[Rule]", "True"}], ",", + RowBox[{"Expanding", "\[Rule]", "True"}], ",", + RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", + RowBox[{"Factoring", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"MomentumCombine", "\[Rule]", "True"}], ",", + RowBox[{"Rename", "\[Rule]", "False"}], ",", + RowBox[{"Schouten", "\[Rule]", "0"}]}], "}"}], TraditionalForm]], "Output", + CellLabel->"Out[438]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -169,6 +190,11 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Pair", ButtonNote->"Pair"], ", ", + ButtonBox["CartesianPair", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CartesianPair", + ButtonNote->"CartesianPair"], + ", ", ButtonBox["DiracSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", @@ -179,9 +205,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/MomentumCombine", ButtonNote->"MomentumCombine"], "." -}], "Text", - CellTags->"Contract", - CellID->1189900625] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -210,40 +234,14 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Contract", "]"}]], "Input", - CellTags->"Contract", - CellLabel->"In[1]:=", - CellID->269618302], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Collecting", "\[Rule]", "True"}], ",", - RowBox[{"Contract3", "\[Rule]", "True"}], ",", - RowBox[{"EpsContract", "\[Rule]", "True"}], ",", - RowBox[{"Expanding", "\[Rule]", "True"}], ",", - RowBox[{"Factoring", "\[Rule]", "False"}], ",", - RowBox[{"FeynCalcInternal", "\[Rule]", "True"}], ",", - RowBox[{"MomentumCombine", "\[Rule]", "True"}], ",", - RowBox[{"Rename", "\[Rule]", "False"}], ",", - RowBox[{"Schouten", "\[Rule]", "0"}]}], "}"}], TraditionalForm]], "Output", - CellTags->"Contract", - CellLabel->"Out[1]=", - CellID->833332161] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{ - RowBox[{"MetricTensor", "[", + RowBox[{"MT", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], " ", - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}]], "Input", CellTags->"Contract", - CellLabel->"In[2]:=", + CellLabel->"In[439]:=", CellID->2011968461], Cell[BoxData[ @@ -257,9 +255,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm], " ", @@ -268,21 +264,16 @@ Cell[BoxData[ OverscriptBox["g", "_"], RowBox[{ FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], + FormBox["\[Nu]", TraditionalForm], TraditionalForm]}]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Contract", - CellLabel->"Out[2]=", - CellID->2005708503] + CellLabel->"Out[439]="] }, Open ]], Cell[CellGroupData[{ @@ -290,7 +281,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Contract", "[", "%", "]"}]], "Input", CellTags->"Contract", - CellLabel->"In[3]:=", + CellLabel->"In[440]:=", CellID->26500400], Cell[BoxData[ @@ -302,36 +293,35 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], + FormBox["\[Nu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"Contract", - CellLabel->"Out[3]=", - CellID->246386443] + CellLabel->"Out[440]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}], - RowBox[{"DiracMatrix", "[", "\[Mu]", "]"}]}]], "Input", + RowBox[{"GA", "[", "\[Mu]", "]"}]}]], "Input", CellTags->"Contract", - CellLabel->"In[4]:=", + CellLabel->"In[441]:=", CellID->2005973076], Cell[BoxData[ FormBox[ RowBox[{ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], " ", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], " ", FormBox[ SuperscriptBox[ FormBox[ @@ -340,15 +330,12 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - 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FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Contract", - CellLabel->"Out[6]=", - CellID->165921051] + CellLabel->"Out[449]="] }, Open ]], -Cell["The default dimension for MetricTensor is 4.", "Text", - CellTags->"Contract", - CellID->1017368063], +Cell["The default dimension for a metric tensor is 4.", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Contract", "[", "%", "]"}]], "Input", CellTags->"Contract", - CellLabel->"In[7]:=", + CellLabel->"In[450]:=", CellID->1110085557], Cell[BoxData[ FormBox["4", TraditionalForm]], "Output", CellTags->"Contract", - CellLabel->"Out[7]=", - CellID->1413622880] + CellLabel->"Out[450]="] }, Open ]], Cell["\<\ -A short way to enter D-dimensional metric tensors is given by MTD. The \".\" \ -as multiplication operator is not necessary but just convenient for \ -typesetting.\ -\>", "Text", - CellTags->"Contract", - CellID->607767486], +A short way to enter D-dimensional metric tensors is given by MTD.\ +\>", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"MTD", "[", - RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], " ", ".", " ", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], " ", RowBox[{"MTD", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]}]], "Input", CellTags->"Contract", - CellLabel->"In[8]:=", + CellLabel->"In[451]:=", CellID->1404498417], Cell[BoxData[ FormBox[ - RowBox[{ - FormBox[ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], - TraditionalForm], ".", + SuperscriptBox[ FormBox[ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], - TraditionalForm]}], TraditionalForm]], "Output", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], + TraditionalForm], "2"], TraditionalForm]], "Output", CellTags->"Contract", - CellLabel->"Out[8]=", - CellID->1257189010] + CellLabel->"Out[451]="] }, Open ]], Cell[CellGroupData[{ @@ -492,82 +441,25 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Contract", "[", "%", "]"}]], "Input", CellTags->"Contract", - CellLabel->"In[9]:=", + CellLabel->"In[452]:=", CellID->587791315], Cell[BoxData[ FormBox["D", TraditionalForm]], "Output", CellTags->"Contract", - CellLabel->"Out[9]=", - CellID->1587031926] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{"MTD", "[", - 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RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}], " ", - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"q", ",", "\[Mu]"}], "]"}]}]], "Input", CellTags->"Contract", - CellLabel->"In[11]:=", + CellLabel->"In[453]:=", CellID->1721182838], Cell[BoxData[ @@ -581,9 +473,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm], " ", @@ -595,15 +485,12 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Contract", - CellLabel->"Out[11]=", - CellID->320652273] + CellLabel->"Out[453]="] }, Open ]], Cell[CellGroupData[{ @@ -611,7 +498,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Contract", "[", "%", " ", "]"}]], "Input", CellTags->"Contract", - 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FormBox["\[Beta]", - TraditionalForm], + StyleBox["i", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox[ + StyleBox["j", + StripOnInput->False, + FontWeight->Bold], TraditionalForm], TraditionalForm], FormBox[ FormBox[ - FormBox["\[Sigma]", - TraditionalForm], + StyleBox["l", + StripOnInput->False, + FontWeight->Bold], TraditionalForm], TraditionalForm]}]], TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"Contract", - CellLabel->"Out[20]=", - CellID->1474380358] + CellLabel->"Out[487]="] }, Open ]], +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "4"}]}], "]"}], ";"}]], "Input", - CellTags->"Contract", - CellLabel->"In[21]:=", - CellID->476845114] + RowBox[{"Contract", "[", "%", "]"}], "//", "Factor2"}]], "Input", + CellLabel->"In[489]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"2", "-", "D"}], ")"}], " ", + RowBox[{"(", + RowBox[{"3", "-", "D"}], ")"}], " ", + SuperscriptBox["\[Delta]", + RowBox[{ + FormBox[ + FormBox[ + StyleBox["k", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox[ + StyleBox["l", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm]}]]}], TraditionalForm]], "Output", + CellLabel->"Out[489]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -1175,12 +1769,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{824, Automatic}, {Automatic, 151}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Contract1.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Contract1.nb deleted file mode 100644 index c8b8de2a9..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Contract1.nb +++ /dev/null @@ -1,425 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/Contract1", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - 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Neither Upper and Upper nor \ -Lower and Lower indices are contracted." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - ButtonBox["LorentzIndex", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LorentzIndex", - ButtonNote->"LorentzIndex"], - ", ", - ButtonBox["Lower", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Lower", - ButtonNote->"Lower"], - ", ", - ButtonBox["Upper", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Upper", - ButtonNote->"Upper"], - "." -}], "Text", - CellTags->"Contract1", - CellID->758167385] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; 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Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; 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CellID->982511436], Cell["XXXX", "Notes", - CellID->1067943069] + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Convolute", "]"}]], "Input", + CellTags->"Convolute", + CellLabel->"In[490]:=", + CellID->846637972], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Bracket", "\[Rule]", + RowBox[{"{", + TagBox["\[CurlyEpsilon]", + TraditionalForm], "}"}]}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", + RowBox[{"PlusDistribution", "\[Rule]", "Identity"}], "}"}]}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"Convolute", + CellLabel->"Out[490]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -217,9 +241,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/ConvoluteTable", ButtonNote->"ConvoluteTable"], "." -}], "Text", - CellTags->"Convolute", - CellID->573828711] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -249,55 +271,35 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Options", "[", "Convolute", "]"}]], "Input", - CellTags->"Convolute", - CellLabel->"In[1]:=", - CellID->846637972], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Bracket", "\[Rule]", - RowBox[{"{", - TagBox["\[CurlyEpsilon]", - TraditionalForm], "}"}]}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", - RowBox[{"PlusDistribution", "\[Rule]", "Identity"}], "}"}]}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"Convolute", - CellLabel->"Out[1]=", - CellID->487844073] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Convolute", "[", - RowBox[{"1", ",", "1"}], "]"}]], "Input", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{"1", ",", "1"}], "]"}], "/.", + RowBox[{ + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[2]:=", + CellLabel->"In[492]:=", CellID->1183792130], Cell[BoxData[ FormBox[ RowBox[{"-", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], - TraditionalForm]], "Output", + RowBox[{"log", "(", "x", ")"}]}], TraditionalForm]], "Output", CellTags->"Convolute", - CellLabel->"Out[2]=", - CellID->2333332] + CellLabel->"Out[492]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", - RowBox[{"x", ",", "x"}], "]"}]], "Input", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{"x", ",", "x"}], "]"}], "/.", + RowBox[{ + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[3]:=", + CellLabel->"In[494]:=", CellID->566730399], Cell[BoxData[ @@ -305,139 +307,149 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", SuperscriptBox["x", "2"]}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], - TraditionalForm]], "Output", + RowBox[{"log", "(", "x", ")"}]}], TraditionalForm]], "Output", CellTags->"Convolute", - CellLabel->"Out[3]=", - CellID->866957207] + CellLabel->"Out[494]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", - RowBox[{"1", ",", "x"}], "]"}]], "Input", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{"1", ",", "x"}], "]"}], "/.", + RowBox[{ + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - 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FractionBox[ - RowBox[{"Log", "[", "x", "]"}], - RowBox[{"1", "-", "x"}]]}], "]"}]], "Input", + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[16]:=", + CellLabel->"In[507]:=", CellID->1164478774], Cell[BoxData[ @@ -630,49 +652,50 @@ Cell[BoxData[ RowBox[{"-", FractionBox[ RowBox[{ - RowBox[{"log", "(", "x", ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], + SuperscriptBox["log", "2"], "(", "x", ")"}], SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "2"]]}], TraditionalForm]], "Output", CellTags->"Convolute", - CellLabel->"Out[16]=", - CellID->1346944538] + CellLabel->"Out[507]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", - RowBox[{"1", ",", - RowBox[{"Log", "[", "x", "]"}]}], "]"}]], "Input", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{"1", ",", + RowBox[{"Log", "[", "x", "]"}]}], "]"}], "/.", + RowBox[{ + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - 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RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], - TraditionalForm]], "Output", + RowBox[{ + SuperscriptBox["log", "2"], "(", "x", ")"}]}], TraditionalForm]], "Output", CellTags->"Convolute", - CellLabel->"Out[24]=", - CellID->395731069] + CellLabel->"Out[515]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + FractionBox["1", + RowBox[{"1", "-", "x"}]], ",", + FractionBox[ + RowBox[{"Log", "[", + RowBox[{"1", "-", "x"}], "]"}], + RowBox[{"1", "-", "x"}]]}], "]"}], "/.", RowBox[{ - FractionBox["1", - RowBox[{"1", "-", "x"}]], ",", - FractionBox[ - RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}], - RowBox[{"1", "-", "x"}]]}], "]"}]], "Input", + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[25]:=", + CellLabel->"In[516]:=", CellID->379553048], Cell[BoxData[ @@ -859,29 +891,31 @@ Cell[BoxData[ RowBox[{ RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], + RowBox[{"log", "(", "x", ")"}]}], SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "1"}], ")"}], "2"]]}], TraditionalForm]], "Output", CellTags->"Convolute", - CellLabel->"Out[25]=", - CellID->1955426678] + CellLabel->"Out[516]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", - RowBox[{ - FractionBox[ + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + FractionBox[ + RowBox[{"Log", "[", + RowBox[{"1", "-", "x"}], "]"}], + RowBox[{"1", "-", "x"}]], ",", RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}], - RowBox[{"1", "-", "x"}]], ",", - RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}]}], "]"}]], "Input", + RowBox[{"1", "-", "x"}], "]"}]}], "]"}], "/.", + RowBox[{ + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"Convolute", - CellLabel->"In[26]:=", + CellLabel->"In[517]:=", CellID->1743318528], Cell[BoxData[ @@ -891,39 +925,10 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["log", "2"], "(", RowBox[{"1", "-", "x"}], ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], + RowBox[{"log", "(", "x", ")"}]}], RowBox[{"x", "-", "1"}]], TraditionalForm]], "Output", CellTags->"Convolute", - CellLabel->"Out[26]=", - CellID->2109333521] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"ConvoluteTable", "[", - RowBox[{ - FractionBox[ - RowBox[{"Log", "[", - RowBox[{"1", "-", "x"}], "]"}], - RowBox[{"1", "-", "x"}]], ",", "1"}], "]"}]], "Input", - CellTags->"Convolute", - CellLabel->"In[27]:=", - CellID->1987067231], - -Cell[BoxData[ - FormBox[ - RowBox[{"False", "[", - RowBox[{ - FractionBox[ - RowBox[{"log", "(", - RowBox[{"1", "-", "x"}], ")"}], - RowBox[{"1", "-", "x"}]], ",", "1"}], "]"}], TraditionalForm]], "Output", - - CellTags->"Convolute", - CellLabel->"Out[27]=", - CellID->1326268935] + CellLabel->"Out[517]="] }, Open ]] }, Open ]], @@ -988,12 +993,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{901, Automatic}, {Automatic, 158}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ConvoluteTable.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ConvoluteTable.nb index 55573608c..064f70592 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ConvoluteTable.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ConvoluteTable.nb @@ -124,8 +124,29 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Convolute", "]"}]], "Input", + CellTags->"ConvoluteTable", + CellLabel->"In[521]:=", + CellID->1127190721], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Bracket", "\[Rule]", + RowBox[{"{", + TagBox["\[CurlyEpsilon]", + TraditionalForm], "}"}]}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", + RowBox[{"PlusDistribution", "\[Rule]", "Identity"}], "}"}]}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"ConvoluteTable", + CellLabel->"Out[521]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -171,9 +192,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Convolute", ButtonNote->"Convolute"], "." -}], "Text", - CellTags->"ConvoluteTable", - CellID->538606169] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -202,47 +221,19 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Convolute", "]"}]], "Input", - CellTags->"ConvoluteTable", - CellLabel->"In[1]:=", - CellID->1127190721], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Bracket", "\[Rule]", - RowBox[{"{", - TagBox["\[CurlyEpsilon]", - TraditionalForm], "}"}]}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", - RowBox[{"PlusDistribution", "\[Rule]", "Identity"}], "}"}]}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"ConvoluteTable", - CellLabel->"Out[1]=", - CellID->1360987202] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"ConvoluteTable", "[", - RowBox[{"1", ",", "1"}], "]"}]], "Input", + RowBox[{"1", ",", "1", ",", "x"}], "]"}]], "Input", CellTags->"ConvoluteTable", - CellLabel->"In[2]:=", + CellLabel->"In[528]:=", CellID->1383961976], Cell[BoxData[ FormBox[ RowBox[{"-", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x45\"\>", ")"}], ")"}]}], - TraditionalForm]], "Output", + RowBox[{"log", "(", "x", ")"}]}], TraditionalForm]], "Output", CellTags->"ConvoluteTable", - CellLabel->"Out[2]=", - CellID->1197018632] + CellLabel->"Out[528]="] }, Open ]], Cell[CellGroupData[{ @@ -251,7 +242,7 @@ Cell[BoxData[ RowBox[{"ConvoluteTable", "[", RowBox[{"x", ",", "x"}], "]"}]], "Input", CellTags->"ConvoluteTable", - CellLabel->"In[3]:=", + CellLabel->"In[529]:=", CellID->783988219], Cell[BoxData[ @@ -259,26 +250,23 @@ Cell[BoxData[ RowBox[{"False", "[", RowBox[{"x", ",", "x"}], "]"}], TraditionalForm]], "Output", CellTags->"ConvoluteTable", - CellLabel->"Out[3]=", - CellID->289063823] + CellLabel->"Out[529]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ConvoluteTable", "[", - RowBox[{"1", ",", "x"}], "]"}]], "Input", + RowBox[{"1", ",", "x", ",", "x"}], "]"}]], "Input", CellTags->"ConvoluteTable", - CellLabel->"In[4]:=", + CellLabel->"In[531]:=", CellID->1430786364], Cell[BoxData[ FormBox[ - RowBox[{"False", "[", - RowBox[{"1", ",", "x"}], "]"}], TraditionalForm]], "Output", + RowBox[{"1", "-", "x"}], TraditionalForm]], "Output", CellTags->"ConvoluteTable", - CellLabel->"Out[4]=", - CellID->1781441936] + CellLabel->"Out[531]="] }, Open ]] }, Open ]], @@ -343,12 +331,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{831, Automatic}, {Automatic, 130}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CounterT.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CounterT.nb index fe51ee5ca..167bbaa36 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CounterT.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CounterT.nb @@ -175,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/QuarkPropagator", ButtonNote->"QuarkPropagator"], "." -}], "Text", - CellTags->"CounterT", - CellID->1128461713] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -212,7 +210,7 @@ Cell[BoxData[ RowBox[{"Explicit", "\[Rule]", "True"}], ",", RowBox[{"CounterTerm", "\[Rule]", " ", "All"}]}], "]"}]], "Input", CellTags->"CounterT", - CellLabel->"In[1]:=", + CellLabel->"In[520]:=", CellID->505594925], Cell[BoxData[ @@ -240,32 +238,24 @@ Cell[BoxData[ RowBox[{ FractionBox[ RowBox[{"10", " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "3"], "-", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]]}], "3"], "-", RowBox[{ FractionBox["10", "3"], " ", SuperscriptBox[ @@ -273,22 +263,16 @@ Cell[BoxData[ FormBox["p", TraditionalForm], TraditionalForm], "2"], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}]}], ")"}]}], + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]]}]}], ")"}]}], TagBox["\[CurlyEpsilon]", TraditionalForm]], "+", FractionBox[ @@ -315,86 +299,75 @@ Cell[BoxData[ FormBox["p", TraditionalForm], TraditionalForm], "2"], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]]}], "-", FractionBox[ RowBox[{"4", " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "3"]}], ")"}]}], + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]]}], "3"]}], ")"}]}], TagBox["\[CurlyEpsilon]", TraditionalForm]]}], ")"}]}], "-", - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SuperscriptBox["\[Delta]", - RowBox[{ - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["b", - TraditionalForm], - TraditionalForm]}]], " ", - FormBox[ + FormBox[ + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox["\[Delta]", + RowBox[{ + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]}]], " ", SuperscriptBox["g", RowBox[{ FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], + FormBox["\[Nu]", TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"]]}], TraditionalForm]], "Output", + TraditionalForm]}]]}], + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False]], + TraditionalForm]}], TraditionalForm]], "Output", CellTags->"CounterT", - CellLabel->"Out[1]=", - CellID->1579672535] + CellLabel->"Out[520]="] }, Open ]] }, Open ]], @@ -459,12 +432,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{988, Automatic}, {Automatic, 183}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CounterTerm.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CounterTerm.nb index 6fed90585..fa4661eb0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CounterTerm.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CounterTerm.nb @@ -124,8 +124,28 @@ Feynman rule functions QuarkGluonVertex, GluonPropagator, QuarkPropagator." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "CounterTerm", "]"}]], "Input", + CellLabel->"In[527]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Dimension", "\[Rule]", + RowBox[{ + TagBox["\[CurlyEpsilon]", + TraditionalForm], "+", "4"}]}], ",", + RowBox[{"Gauge", "\[Rule]", "1"}], ",", + RowBox[{"QuarkMass", "\[Rule]", + RowBox[{"FCGV", "(", "\<\"M\"\>", ")"}]}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[527]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -181,9 +201,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/QuarkPropagator", ButtonNote->"QuarkPropagator"], "." -}], "Text", - CellTags->"CounterTerm", - CellID->257706146] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -215,7 +233,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CounterTerm", "[", "Zm", "]"}]], "Input", CellTags->"CounterTerm", - CellLabel->"In[1]:=", + CellLabel->"In[526]:=", CellID->1995023941], Cell[BoxData[ @@ -270,8 +288,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm]}]], "+", "1"}], TraditionalForm]], "Output", CellTags->"CounterTerm", - CellLabel->"Out[1]=", - CellID->1407493113] + CellLabel->"Out[526]="] }, Open ]] }, Open ]], @@ -336,12 +353,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{739, Automatic}, {Automatic, 77}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CouplingConstant.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CouplingConstant.nb index dcf3ae8b5..082494aad 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CouplingConstant.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CouplingConstant.nb @@ -117,19 +117,20 @@ Cell["CouplingConstant", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["CouplingConstant"], "InlineFormula"], - " \[LineSeparator]", - "is an option for several Feynman rule functions and for CovariantD and \ -FieldStrength.\nIn the convention of the subpackage PHI, CouplingConstant is \ -also the head of coupling constants. CouplingConstant takes three extra \ -optional arguments, with head RenormalizationState, RenormalizationScheme and \ -ExpansionState respectively. E.g. CouplingConstant[QED[1]] is the unit \ -charge, CouplingConstant[ChPT2[4],1] is the first of the coupling constants \ -of the lagrangian ChPT2[4]. CouplingConstant[a_,b_,c___][i_] := \ -CouplingConstant[a,b,RenormalizationState[i],c]." + " \[LineSeparator]is an option for several Feynman rule functions and for \ +CovariantD and FieldStrength." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +In the convention of the subpackage PHI, CouplingConstant is also the head of \ +coupling constants. CouplingConstant takes three extra optional arguments, \ +with head RenormalizationState, RenormalizationScheme and ExpansionState \ +respectively. E.g. CouplingConstant[QED[1]] is the unit charge, \ +CouplingConstant[ChPT2[4],1] is the first of the coupling constants of the \ +lagrangian ChPT2[4]. CouplingConstant[a_,b_,c___][i_] := \ +CouplingConstant[a,b,RenormalizationState[i],c].\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -175,15 +176,8 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FieldStrength", ButtonNote->"FieldStrength"], - ", ", - ButtonBox["\"PHI - A Mathematica package for ChPT calculations\"", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/phi", - ButtonNote->"phi"], "." -}], "Text", - CellTags->"CouplingConstant", - CellID->1805142582] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -269,12 +263,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{630, Automatic}, {Automatic, 73}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CovariantD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CovariantD.nb index bdc3c8dd1..01d5bceea 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CovariantD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CovariantD.nb @@ -117,31 +117,136 @@ Cell["CovariantD", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"CovariantD", "[", "mu", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is a generic covariant derivative with Lorentz index mu. With the \ -option-setting Explicit \[Rule] True, an explicit expression for a fermionic \ -field is returned, depending on the setting on the other options.\n\ -CovariantD[x, mu] is a generic covariant derivative with respect to x^mu.\n\ -CovariantD[mu, a, b] is a covariant derivative for a bosonic field; acting on \ -QuantumField[f,{},{a,b}], where f is some field name and a and b are two \ -SU(N) indices. Again, with the option-setting Explicit \[Rule] True, an \ -explicit expression is returned, depending on the setting on the other \ -options.\nCovariantD[OPEDelta, a, b] is a short form for \ -CovariantD[mu,a,b]*FourVector[OPEDelta, mu]. CovariantD[{OPEDelta, a, b}, \ -{n}] yields the product of n operators, where n is an integer. \ -CovariantD[OPEDelta, a, b, {m, n}] gives the expanded form of \ -CovariantD[OPEDelta, a, b]^m up to order g^n for the gluon, where n is an \ -integer and g the coupling constant indicated by the setting of the option \ -CouplingConstant. CovariantD[OPEDelta, {m, n}] gives the expanded form of \ -CovariantD[OPEDelta]^m up to order g^n of the fermionic field.\n\n Possible \ -settings of PartialD are: LeftPartialD, LeftRigthPartialD, RightPartialD. 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TraditionalForm]], ")"}], - RowBox[{ - RowBox[{"-", "2"}], "-", "j", "+", "m"}]]}]}], - HoldForm], - TraditionalForm], ")"}]}], - HoldForm], - TraditionalForm]}], "+", + TraditionalForm], + FormBox[ + FormBox[ + SubscriptBox["c72", "1"], + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + RowBox[{"(", + SubscriptBox[ + OverscriptBox["\[PartialD]", "\[RightArrow]"], + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm]], ")"}], + RowBox[{ + RowBox[{"-", "i"}], "+", "j"}]], ".", + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox[ + SubscriptBox["c72", "2"], + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + RowBox[{"(", + SubscriptBox[ + OverscriptBox["\[PartialD]", "\[RightArrow]"], + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm]], ")"}], + RowBox[{ + RowBox[{"-", "2"}], "-", "j", "+", "m"}]]}]}]}], + HoldForm], + TraditionalForm], ")"}]}], + HoldForm], + TraditionalForm], ")"}]}], "+", SuperscriptBox[ RowBox[{"(", SubscriptBox[ @@ -1130,8 +1217,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], ")"}], "m"]}], TraditionalForm]], "Output", CellTags->"CovariantD", - CellLabel->"Out[14]=", - CellID->2021495246] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ @@ -1143,25 +1229,24 @@ Cell[BoxData[ RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"CovariantD", - CellLabel->"In[15]:=", + CellLabel->"In[16]:=", CellID->790160491], Cell[BoxData[ RowBox[{ - RowBox[{ - RowBox[{"-", "\[ImaginaryI]"}], " ", "Gstrong", " ", + RowBox[{"RightPartialD", "[", + RowBox[{"Momentum", "[", "OPEDelta", "]"}], "]"}], "-", + RowBox[{"\[ImaginaryI]", " ", RowBox[{ RowBox[{"SUNT", "[", - RowBox[{"SUNIndex", "[", "c91", "]"}], "]"}], ".", + RowBox[{"SUNIndex", "[", "c75", "]"}], "]"}], ".", RowBox[{"QuantumField", "[", RowBox[{"GaugeField", ",", RowBox[{"Momentum", "[", "OPEDelta", "]"}], ",", - RowBox[{"SUNIndex", "[", "c91", "]"}]}], "]"}]}]}], "+", - RowBox[{"RightPartialD", "[", - RowBox[{"Momentum", "[", "OPEDelta", "]"}], "]"}]}]], "Output", + RowBox[{"SUNIndex", "[", "c75", "]"}]}], "]"}]}], " ", + RowBox[{"SMP", "[", "\<\"g_s\"\>", "]"}]}]}]], "Output", CellTags->"CovariantD", - CellLabel->"Out[15]//StandardForm=", - CellID->1789369971] + CellLabel->"Out[16]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -1173,7 +1258,7 @@ Cell[BoxData[ RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"CovariantD", - CellLabel->"In[16]:=", + CellLabel->"In[17]:=", CellID->160329117], Cell[BoxData[ @@ -1183,16 +1268,17 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}], " ", RowBox[{"SUNDelta", "[", RowBox[{"a", ",", "b"}], "]"}]}], "-", - RowBox[{"Gstrong", " ", + RowBox[{ RowBox[{"QuantumField", "[", RowBox[{"GaugeField", ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", - RowBox[{"SUNIndex", "[", "c92", "]"}]}], "]"}], " ", + RowBox[{"SUNIndex", "[", "c76", "]"}]}], "]"}], " ", + RowBox[{"SMP", "[", "\<\"g_s\"\>", "]"}], " ", RowBox[{"SUNF", "[", - RowBox[{"a", ",", "b", ",", "c92"}], "]"}]}]}]], "Output", + RowBox[{"a", ",", "b", ",", "c76"}], "]"}]}]}]], "Output", CellTags->"CovariantD", - CellLabel->"Out[16]//StandardForm=", - CellID->772324772] + CellLabel->"Out[17]//StandardForm="] +}, Open ]] }, Open ]] }, Open ]], @@ -1256,13 +1342,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{1013, 770}, +WindowMargins->{{1100, Automatic}, {273, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CovariantFieldDerivative.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CovariantFieldDerivative.nb index 012724329..6085f0426 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CovariantFieldDerivative.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/CovariantFieldDerivative.nb @@ -121,13 +121,23 @@ Cell[TextData[{ RowBox[{ RowBox[{"f", "[", "x", "]"}], ",", "x", ",", RowBox[{"{", - RowBox[{"li1", ",", "li2", ",", "..."}], "}"}], ",", "opts"}], "]"}]], + RowBox[{"li1", ",", "li2", ",", "..."}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is a covariant derivative of f[x] with respect to space-time variables x \ -and with Lorentz indices li1, li2,... CovariantFieldDerivative has only \ -typesetting definitions by default. The user is must supply his/her own \ -definition of the actual function." + " \[LineSeparator]is a covariant derivative of ", + Cell[BoxData[ + RowBox[{"f", "[", "x", "]"}]], "InlineFormula"], + " with respect to space-time variables ", + Cell[BoxData["x"], "InlineFormula"], + " and with Lorentz indices ", + Cell[BoxData[ + RowBox[{"li1", ",", " ", "li2", ",", "..."}]], "InlineFormula"], + ". ", + ButtonBox["CovariantFieldDerivative", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CovariantFieldDerivative", + ButtonNote->"CovariantFieldDerivative"], + " has only typesetting definitions by default. The user is must supply \ +his/her own definition of the actual function." }], "Usage", CellID->982511436], @@ -183,9 +193,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FieldDerivative", ButtonNote->"FieldDerivative"], "." -}], "Text", - CellTags->"CovariantFieldDerivative", - CellID->1307362516] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -223,7 +231,7 @@ Cell[BoxData[ RowBox[{"{", "\[Mu]", "}"}]}], "]"}], "[", "x", "]"}], ",", "x", ",", RowBox[{"{", "\[Mu]", "}"}]}], "]"}]], "Input", CellTags->"CovariantFieldDerivative", - CellLabel->"In[1]:=", + CellLabel->"In[18]:=", CellID->2083449432], Cell[BoxData[ @@ -251,8 +259,7 @@ Cell[BoxData[ TraditionalForm, Editable->True], ")"}], TraditionalForm]], "Output", CellTags->"CovariantFieldDerivative", - CellLabel->"Out[1]=", - CellID->1282830456] + CellLabel->"Out[18]="] }, Open ]] }, Open ]], @@ -317,12 +324,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{560, Automatic}, {35, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/CrossProduct.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/CrossProduct.nb deleted file mode 100644 index d88285cd1..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/CrossProduct.nb +++ /dev/null @@ -1,319 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/CrossProduct", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], 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CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData[ - RowBox[{"CrossProduct", "[", - RowBox[{"a", ",", " ", "b"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "denotes the three-dimensional cross-product of the three-vectors a and b." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - ButtonBox["DotProduct", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DotProduct", - ButtonNote->"DotProduct"], - ", ", - ButtonBox["ThreeVector", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/ThreeVector", - ButtonNote->"ThreeVector"], - "." -}], "Text", - CellTags->"CrossProduct", - CellID->1152724432] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"CrossProduct", "[", - RowBox[{ - RowBox[{"ThreeVector", "[", "a", "]"}], ",", - RowBox[{"CrossProduct", "[", - RowBox[{ - 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InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git 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"]"}]], "Input", CellTags->"D0", - CellLabel->"In[2]:=", + CellLabel->"In[533]:=", CellID->493215523], Cell[BoxData[ @@ -291,8 +288,7 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"D0", - CellLabel->"Out[2]=", - CellID->1336389725] + CellLabel->"Out[533]="] }, Open ]], Cell[CellGroupData[{ @@ -300,7 +296,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PaVeOrder", "[", "%", "]"}]], "Input", CellTags->"D0", - CellLabel->"In[3]:=", + CellLabel->"In[534]:=", CellID->1818800785], Cell[BoxData[ @@ -318,8 +314,7 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"D0", - CellLabel->"Out[3]=", - CellID->871188946] + CellLabel->"Out[534]="] }, Open ]] }, Open ]], @@ -384,12 +379,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{948, Automatic}, {Automatic, 160}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, 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"i6"}], "]"}]}], "]"}]], "Input", + CellLabel->"In[12]:=", + CellID->427410435], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"(", + RowBox[{ + FormBox["\<\"\[CurlyPhi]\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox["\<\",\"\>", + TraditionalForm], + FormBox["m", + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], ")"}], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], "+", "m"}], ")"}], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + FormBox["\<\"\[CurlyPhi]\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + RowBox[{"-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[12]=", + CellID->1753713613] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{Automatic, 404}, {20, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DOT.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DOT.nb index 5ccf1d44e..f2b60a14f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DOT.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DOT.nb @@ -119,17 +119,20 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"DOT", "[", RowBox[{"a", ",", " ", "b", ",", " ", "..."}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the FeynCalc function for non-commutative multiplication. By default it \ -is set to the Mathematica Dot function. This can in principle be disabled by \ -setting DOT=. (or by commenting out \[OpenCurlyDoubleQuote]DOT = Dot;\ -\[CloseCurlyDoubleQuote] in the file \"FeynCalc.m\"), but then \ -non-commutative products should to be entered like DOT[ DiracMatrix[mu], m + \ -DiracSlash[p], DiracMatrix[mu] ] etc." + " \[LineSeparator]is the FeynCalc function for non-commutative \ +multiplication. By default it is set to the ", + StyleBox["Mathematica", + FontSlant->"Italic"], + " Dot function. " }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +This can in principle be disabled by setting DOT=. (or by commenting out \ +\[OpenCurlyDoubleQuote]DOT = Dot;\[CloseCurlyDoubleQuote] in the file \ +\"FCConfig.m\"), but then non-commutative products should to be entered like \ +DOT[ GA[mu], m + GS[p], GA[mu] ] etc.\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -166,15 +169,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["DotSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DotSimplify", ButtonNote->"DotSimplify"], "." -}], "Text", - CellTags->"DOT", - CellID->1131348229] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -260,12 +260,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{768, Automatic}, {Automatic, 114}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DataType.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DataType.nb index 773fbe62d..4774b4f15 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DataType.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DataType.nb @@ -117,14 +117,18 @@ Cell["DataType", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"DataType", "[", - RowBox[{"exp", ",", " ", "type"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "= True defines the object exp to have data-type type. DataType[exp1, exp2, \ -..., type] defines the objects exp1, exp2, ...to have data-type type. The \ -default setting is DataType[__, _] := False. To assign a certain data-type, \ -do, e.g., DataType[x, PositiveInteger] = True.\n\nCurrently used DataTypes: \ -", + RowBox[{ + RowBox[{"DataType", "[", + RowBox[{"exp", ",", " ", "type"}], "]"}], "=", "True"}]], "InlineFormula"], + " \[LineSeparator]defines the object exp to have data-type type. \ +DataType[exp1, exp2, ..., type] defines the objects exp1, exp2, ...to have \ +data-type type. The default setting is DataType[__, _] := False. To assign a \ +certain data-type, do, e.g., DataType[x, PositiveInteger] = True." +}], "Usage", + CellID->982511436], + +Cell[TextData[{ + "Currently used DataTypes: ", ButtonBox["NonCommutative", BaseStyle->"AddOnsLink", ButtonData:>"NonCommutative", @@ -150,11 +154,15 @@ do, e.g., DataType[x, PositiveInteger] = True.\n\nCurrently used DataTypes: \ ButtonData:>"FreeIndex", ButtonNote->"FreeIndex"], ", ", - ButtonBox["GrassmannParity\n\n", + ButtonBox["GrassmannParity", BaseStyle->"AddOnsLink", ButtonData:>"GrassmannParity", - ButtonNote->"GrassmannParity"], - "PHI adds the DataTypes: ", + ButtonNote->"GrassmannParity"] +}], "Notes", + CellID->1067943069], + +Cell[TextData[{ + "If loaded, PHI adds the DataTypes: ", ButtonBox["UMatrix", BaseStyle->"AddOnsLink", ButtonData:>"UMatrix", @@ -165,11 +173,7 @@ do, e.g., DataType[x, PositiveInteger] = True.\n\nCurrently used DataTypes: \ ButtonData:>"UScalar", ButtonNote->"UScalar"], "." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] +}], "Notes"] }, Open ]], Cell[CellGroupData[{ @@ -209,15 +213,8 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DeclareNonCommutative", ButtonNote->"DeclareNonCommutative"], - ", ", - ButtonBox["\"PHI - A Mathematica package for ChPT calculations\"", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/phi", - ButtonNote->"phi"], "." -}], "Text", - CellTags->"DataType", - CellID->1742681066] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -244,9 +241,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["NonCommutative is just a data-type.", "Text", - CellTags->"DataType", - CellID->1046565146], +Cell["NonCommutative is just a data-type.", "Notes"], Cell[BoxData[ RowBox[{ @@ -255,7 +250,7 @@ Cell[BoxData[ RowBox[{"f", ",", "g", ",", " ", "NonCommutative"}], "]"}], " ", "=", " ", "True"}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[1]:=", + CellLabel->"In[561]:=", CellID->1643430273], Cell[CellGroupData[{ @@ -268,7 +263,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"2", "a"}], ")"}], ".", "f"}]}]}]], "Input", CellTags->"DataType", - CellLabel->"In[2]:=", + CellLabel->"In[562]:=", CellID->370505351], Cell[BoxData[ @@ -279,14 +274,13 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"2", " ", "a"}], ")"}], ".", "f"}]}], TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[2]=", - CellID->353088944] + CellLabel->"Out[562]="] }, Open ]], Cell["\<\ Since \"f \"and \"g\" have DataType NonCommutative the function DotSimplify \ extracts only \"a\" out of the noncommutative product.\ -\>", "Text", +\>", "Notes", CellTags->"DataType", CellID->2142748174], @@ -295,7 +289,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DotSimplify", "[", "t", "]"}]], "Input", CellTags->"DataType", - CellLabel->"In[3]:=", + CellLabel->"In[563]:=", CellID->1089346644], Cell[BoxData[ @@ -305,8 +299,7 @@ Cell[BoxData[ RowBox[{"2", " ", "a", " ", RowBox[{"g", ".", "f"}]}]}], TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[3]=", - CellID->1728093744] + CellLabel->"Out[563]="] }, Open ]], Cell[BoxData[ @@ -318,7 +311,7 @@ Cell[BoxData[ RowBox[{"DataType", "[", RowBox[{"a", ",", "even"}], "]"}], "=", "True"}]}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[4]:=", + CellLabel->"In[564]:=", CellID->2121249133], Cell[BoxData[ @@ -335,7 +328,7 @@ Cell[BoxData[ RowBox[{"n", ",", "odd"}], "]"}]}], "\[RuleDelayed]", RowBox[{"-", "1"}]}]}]}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[5]:=", + CellLabel->"In[565]:=", CellID->1782213069], Cell[BoxData[ @@ -352,7 +345,7 @@ Cell[BoxData[ RowBox[{"n", ",", "even"}], "]"}]}], "\[RuleDelayed]", "1"}]}]}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[6]:=", + CellLabel->"In[566]:=", CellID->1543768294], Cell[CellGroupData[{ @@ -370,7 +363,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "^", "z"}]}]}]], "Input", CellTags->"DataType", - CellLabel->"In[7]:=", + CellLabel->"In[567]:=", CellID->1135363295], Cell[BoxData[ @@ -386,8 +379,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "z"]}], TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[7]=", - CellID->538518934] + CellLabel->"Out[567]="] }, Open ]], Cell[CellGroupData[{ @@ -395,7 +387,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ptest1", "[", "t", "]"}]], "Input", CellTags->"DataType", - CellLabel->"In[8]:=", + CellLabel->"In[568]:=", CellID->703322505], Cell[BoxData[ @@ -409,8 +401,7 @@ Cell[BoxData[ RowBox[{"-", "1"}], ")"}], "z"], "-", "1"}], TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[8]=", - CellID->1174286962] + CellLabel->"Out[568]="] }, Open ]], Cell[CellGroupData[{ @@ -418,7 +409,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ptest2", "[", "%", "]"}]], "Input", CellTags->"DataType", - CellLabel->"In[9]:=", + CellLabel->"In[569]:=", CellID->1711798640], Cell[BoxData[ @@ -427,8 +418,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "z"], TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[9]=", - CellID->1170774235] + CellLabel->"Out[569]="] }, Open ]], Cell[BoxData[ @@ -437,16 +427,16 @@ Cell[BoxData[ RowBox[{"ptest1", ",", "ptest2", ",", "t", ",", "a", ",", "m"}], "]"}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[10]:=", + CellLabel->"In[570]:=", CellID->1299043006], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"DataType", "[", - RowBox[{"m", ",", "ganzeZahl"}], "]"}], "=", "True"}], ";"}]], "Input", + RowBox[{"m", ",", "integer"}], "]"}], "=", "True"}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[11]:=", + CellLabel->"In[571]:=", CellID->585585082], Cell[BoxData[ @@ -461,10 +451,10 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "^", "p_"}], "/;", RowBox[{"DataType", "[", - RowBox[{"p", ",", "ganzeZahl"}], "]"}]}], "\[RuleDelayed]", "1"}], + RowBox[{"p", ",", "integer"}], "]"}]}], "\[RuleDelayed]", "1"}], "}"}]}]}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[12]:=", + CellLabel->"In[572]:=", CellID->846476868], Cell[CellGroupData[{ @@ -480,7 +470,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "^", "n"}], " ", "x"}]}]}]], "Input", CellTags->"DataType", - CellLabel->"In[13]:=", + CellLabel->"In[573]:=", CellID->1533391272], Cell[BoxData[ @@ -495,8 +485,7 @@ Cell[BoxData[ RowBox[{"-", "1"}], ")"}], "n"], " ", "x"}]}], TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[13]=", - CellID->41432149] + CellLabel->"Out[573]="] }, Open ]], Cell[CellGroupData[{ @@ -504,7 +493,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"f", "[", "test", "]"}]], "Input", CellTags->"DataType", - CellLabel->"In[14]:=", + CellLabel->"In[574]:=", CellID->1293981643], Cell[BoxData[ @@ -516,8 +505,7 @@ Cell[BoxData[ RowBox[{"-", "1"}], ")"}], "n"], " ", "x"}], "+", "1"}], TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[14]=", - CellID->1117139634] + CellLabel->"Out[574]="] }, Open ]], Cell[BoxData[ @@ -525,7 +513,7 @@ Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"f", ",", "test"}], "]"}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[15]:=", + CellLabel->"In[575]:=", CellID->943541195], Cell[BoxData[ @@ -535,7 +523,7 @@ Cell[BoxData[ RowBox[{"f", ",", "g", ",", " ", "NonCommutative"}], "]"}], " ", "=", " ", "False"}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[16]:=", + CellLabel->"In[576]:=", CellID->1739727758], Cell[BoxData[ @@ -547,14 +535,12 @@ Cell[BoxData[ RowBox[{"DataType", "[", RowBox[{"a", ",", "even"}], "]"}], "=", "False"}]}], ";"}]], "Input", CellTags->"DataType", - CellLabel->"In[17]:=", + CellLabel->"In[577]:=", CellID->1265503982], Cell["\<\ Certain FeynCalc objects have DataType PositiveInteger set to True.\ -\>", "Text", - CellTags->"DataType", - CellID->1789811013], +\>", "Notes"], Cell[CellGroupData[{ @@ -562,19 +548,16 @@ Cell[BoxData[ RowBox[{"DataType", "[", RowBox[{"OPEm", ",", "PositiveInteger"}], "]"}]], "Input", CellTags->"DataType", - CellLabel->"In[18]:=", + CellLabel->"In[578]:=", CellID->693329232], Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[18]=", - CellID->1327437721] + CellLabel->"Out[578]="] }, Open ]], -Cell["PowerSimplify uses the DataType information.", "Text", - CellTags->"DataType", - CellID->2130197226], +Cell["PowerSimplify uses the DataType information.", "Notes"], Cell[CellGroupData[{ @@ -586,14 +569,13 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"2", "OPEm"}], ")"}]}], "]"}]], "Input", CellTags->"DataType", - CellLabel->"In[19]:=", + CellLabel->"In[579]:=", CellID->1014422116], Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[19]=", - CellID->410693850] + CellLabel->"Out[579]="] }, Open ]], Cell[CellGroupData[{ @@ -605,7 +587,7 @@ Cell[BoxData[ RowBox[{"-", " ", RowBox[{"SO", "[", "q", "]"}]}], ")"}], "^", "OPEm"}], "]"}]], "Input", CellTags->"DataType", - CellLabel->"In[20]:=", + CellLabel->"In[580]:=", CellID->1682583494], Cell[BoxData[ @@ -635,8 +617,7 @@ Cell[BoxData[ RowBox[{"\[ImaginaryI]", " ", "\[Pi]", " ", "m"}]}]]}], TraditionalForm]], "Output", CellTags->"DataType", - CellLabel->"Out[20]=", - CellID->359212449] + CellLabel->"Out[580]="] }, Open ]] }, Open ]], @@ -701,12 +682,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{874, Automatic}, {Automatic, 54}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeclareFCTensor.nb 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+Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[BoxData[ + RowBox[{"ClearAll", "[", "myTens", "]"}]], "Input", + CellLabel->"In[582]:=", + CellID->1149397665], + +Cell[BoxData[ + RowBox[{"DeclareFCTensor", "[", "myTens", "]"}]], "Input", + CellLabel->"In[583]:=", + CellID->384608883], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ExpandScalarProduct", "[", + RowBox[{"myTens", "[", + RowBox[{"z", ",", + RowBox[{"Momentum", "[", + RowBox[{"a", "+", "b"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"c", "+", "d"}], "]"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[584]:=", + CellID->816959797], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"myTens", "(", + RowBox[{"z", ",", + OverscriptBox[ + FormBox["a", + TraditionalForm], "_"], ",", + OverscriptBox[ + FormBox["c", + TraditionalForm], "_"]}], ")"}], "+", + RowBox[{"myTens", "(", + RowBox[{"z", ",", + OverscriptBox[ + FormBox["a", + TraditionalForm], "_"], ",", + OverscriptBox[ + FormBox["d", + TraditionalForm], "_"]}], ")"}], "+", + RowBox[{"myTens", "(", + RowBox[{"z", ",", + OverscriptBox[ + FormBox["b", + TraditionalForm], "_"], ",", + OverscriptBox[ + FormBox["c", + TraditionalForm], "_"]}], ")"}], "+", + RowBox[{"myTens", "(", + RowBox[{"z", ",", + OverscriptBox[ + FormBox["b", + TraditionalForm], "_"], ",", + OverscriptBox[ + FormBox["d", + TraditionalForm], "_"]}], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[584]=", + CellID->919476301] +}, Open ]], + +Cell[BoxData[ + RowBox[{"UnDeclareFCTensor", "[", "myTens", "]"}]], "Input", + CellLabel->"In[585]:=", + CellID->2018380174] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{834, Automatic}, {Automatic, 99}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeclareNonCommutative.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DeclareNonCommutative.nb index afb164dfd..5e7730901 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeclareNonCommutative.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DeclareNonCommutative.nb @@ -172,9 +172,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/UnDeclareNonCommutative", ButtonNote->"UnDeclareNonCommutative"], "." -}], "Text", - CellTags->"DeclareNonCommutative", - CellID->716831943] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -210,9 +208,7 @@ Cell[BoxData[ Cell["\<\ As a side effect of DeclareNonCommutative x is declared to be of data type \ NonCommutative.\ -\>", "Text", - CellTags->"DeclareNonCommutative", - CellID->836055796], +\>", "Notes"], Cell[CellGroupData[{ @@ -220,21 +216,20 @@ Cell[BoxData[ RowBox[{"DataType", "[", RowBox[{"x", ",", "NonCommutative"}], "]"}]], "Input", CellTags->"DeclareNonCommutative", - CellLabel->"In[2]:=", + CellLabel->"In[587]:=", CellID->903276535], Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", CellTags->"DeclareNonCommutative", - CellLabel->"Out[2]=", - CellID->2100185008] + CellLabel->"Out[587]="] }, Open ]], Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", RowBox[{"y", ",", "z"}], "]"}]], "Input", CellTags->"DeclareNonCommutative", - CellLabel->"In[3]:=", + CellLabel->"In[588]:=", CellID->429692038], Cell[CellGroupData[{ @@ -244,7 +239,7 @@ Cell[BoxData[ RowBox[{"a", ",", "x", ",", "y", ",", "z", ",", "NonCommutative"}], "]"}]], "Input", CellTags->"DeclareNonCommutative", - CellLabel->"In[4]:=", + CellLabel->"In[589]:=", CellID->498899039], Cell[BoxData[ @@ -253,15 +248,14 @@ Cell[BoxData[ RowBox[{"False", ",", "True", ",", "True", ",", "True"}], "}"}], TraditionalForm]], "Output", CellTags->"DeclareNonCommutative", - CellLabel->"Out[4]=", - CellID->1479757554] + CellLabel->"Out[589]="] }, Open ]], Cell[BoxData[ RowBox[{"UnDeclareNonCommutative", "[", RowBox[{"x", ",", "y", ",", "z"}], "]"}]], "Input", CellTags->"DeclareNonCommutative", - CellLabel->"In[5]:=", + CellLabel->"In[590]:=", CellID->660830730], Cell[CellGroupData[{ @@ -271,7 +265,7 @@ Cell[BoxData[ RowBox[{"a", ",", "x", ",", "y", ",", "z", ",", "NonCommutative"}], "]"}]], "Input", CellTags->"DeclareNonCommutative", - CellLabel->"In[6]:=", + CellLabel->"In[591]:=", CellID->1927435284], Cell[BoxData[ @@ -280,8 +274,7 @@ Cell[BoxData[ RowBox[{"False", ",", "False", ",", "False", ",", "False"}], "}"}], TraditionalForm]], "Output", CellTags->"DeclareNonCommutative", - CellLabel->"Out[6]=", - CellID->1909095440] + CellLabel->"Out[591]="] }, Open ]] }, Open ]], @@ -346,12 +339,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{692, Automatic}, {Automatic, 218}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunction.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunction.nb index cccd9cac0..e281a7408 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunction.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunction.nb @@ -118,19 +118,21 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"DeltaFunction", "[", "x", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the Dirac delta-function ", + " \[LineSeparator]is the Dirac delta-function ", Cell[BoxData[ FormBox[ RowBox[{"\[Delta]", "(", "x", ")"}], TraditionalForm]]], - ".\nNOTICE: After version 4 of ", - StyleBox["Mathematica", - FontSlant->"Italic"], - " there is a built-in function, DiracDelta, with comparable properties." + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell[TextData[{ + StyleBox["Mathematica", + FontSlant->"Italic"], + " also provides a built-in function ", + Cell[BoxData["DiracDelta"], "InlineFormula"], + " with comparable properties." +}], "Notes", CellID->1067943069] }, Open ]], @@ -187,9 +189,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SimplifyDeltaFunction", ButtonNote->"SimplifyDeltaFunction"], "." -}], "Text", - CellTags->"DeltaFunction", - CellID->1180269291] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -222,7 +222,7 @@ Cell[BoxData[ RowBox[{"DeltaFunction", "[", RowBox[{"1", "-", "x"}], "]"}]], "Input", CellTags->"DeltaFunction", - CellLabel->"In[1]:=", + CellLabel->"In[592]:=", CellID->1276544329], Cell[BoxData[ @@ -232,8 +232,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"DeltaFunction", - CellLabel->"Out[1]=", - CellID->1935055166] + CellLabel->"Out[592]="] }, Open ]], Cell[CellGroupData[{ @@ -248,15 +247,14 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"DeltaFunction", - CellLabel->"In[2]:=", + CellLabel->"In[593]:=", CellID->656921459], Cell[BoxData[ FormBox[ RowBox[{"f", "(", "1", ")"}], TraditionalForm]], "Output", CellTags->"DeltaFunction", - CellLabel->"Out[2]=", - CellID->904672527] + CellLabel->"Out[593]="] }, Open ]], Cell[CellGroupData[{ @@ -270,15 +268,14 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"DeltaFunction", - CellLabel->"In[3]:=", + CellLabel->"In[594]:=", CellID->146135859], Cell[BoxData[ FormBox[ RowBox[{"f", "(", "0", ")"}], TraditionalForm]], "Output", CellTags->"DeltaFunction", - CellLabel->"Out[3]=", - CellID->694516034] + CellLabel->"Out[594]="] }, Open ]], Cell[CellGroupData[{ @@ -293,26 +290,29 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"DeltaFunction", - CellLabel->"In[4]:=", + CellLabel->"In[595]:=", CellID->77885451], Cell[BoxData[ FormBox[ RowBox[{"f", "(", "1", ")"}], TraditionalForm]], "Output", CellTags->"DeltaFunction", - CellLabel->"Out[4]=", - CellID->877420351] + CellLabel->"Out[595]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"Convolute", "[", + RowBox[{ + RowBox[{"DeltaFunction", "[", + RowBox[{"1", "-", "x"}], "]"}], ",", "x"}], "]"}], "/.", RowBox[{ - RowBox[{"DeltaFunction", "[", - RowBox[{"1", "-", "x"}], "]"}], ",", "x"}], "]"}]], "Input", + RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", + RowBox[{"ToExpression", "[", "z", "]"}]}]}]], "Input", CellTags->"DeltaFunction", - CellLabel->"In[5]:=", + CellLabel->"In[597]:=", CellID->2128349], Cell[BoxData[ @@ -323,12 +323,9 @@ Cell[BoxData[ FormBox[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}], " ", - RowBox[{"log", "(", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ")"}]}], - TraditionalForm]], "Output", + RowBox[{"log", "(", "x", ")"}]}], TraditionalForm]], "Output", CellTags->"DeltaFunction", - CellLabel->"Out[5]=", - CellID->984049833] + CellLabel->"Out[597]="] }, Open ]] }, Open ]], @@ -393,12 +390,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1080, Automatic}, {Automatic, 240}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunctionDoublePrime.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunctionDoublePrime.nb index 58d6cfa44..3b0e9d003 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunctionDoublePrime.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunctionDoublePrime.nb @@ -165,15 +165,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["DeltaFunctionPrime", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DeltaFunctionPrime", ButtonNote->"DeltaFunctionPrime"], "." -}], "Text", - CellTags->"DeltaFunctionDoublePrime", - CellID->1988601213] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -259,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{963, Automatic}, {Automatic, 140}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunctionPrime.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunctionPrime.nb index 6655b99cb..7d2fc97b0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunctionPrime.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DeltaFunctionPrime.nb @@ -165,7 +165,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["Convolute", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Convolute", @@ -191,9 +190,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SimplifyDeltaFunction", ButtonNote->"SimplifyDeltaFunction"], "." -}], "Text", - CellTags->"DeltaFunctionPrime", - CellID->1121609320] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -226,7 +223,7 @@ Cell[BoxData[ RowBox[{"DeltaFunctionPrime", "[", RowBox[{"1", "-", "x"}], "]"}]], "Input", CellTags->"DeltaFunctionPrime", - CellLabel->"In[1]:=", + CellLabel->"In[598]:=", CellID->677883424], Cell[BoxData[ @@ -237,8 +234,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"DeltaFunctionPrime", - CellLabel->"Out[1]=", - CellID->1329619670] + CellLabel->"Out[598]="] }, Open ]], Cell[CellGroupData[{ @@ -253,7 +249,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"DeltaFunctionPrime", - CellLabel->"In[2]:=", + CellLabel->"In[599]:=", CellID->666771914], Cell[BoxData[ @@ -262,8 +258,7 @@ Cell[BoxData[ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "(", "1", ")"}], TraditionalForm]], "Output", CellTags->"DeltaFunctionPrime", - CellLabel->"Out[2]=", - CellID->1211576646] + CellLabel->"Out[599]="] }, Open ]], Cell[CellGroupData[{ @@ -278,14 +273,13 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"DeltaFunctionPrime", - CellLabel->"In[3]:=", + CellLabel->"In[600]:=", CellID->1722060708], Cell[BoxData[ FormBox["2", TraditionalForm]], "Output", CellTags->"DeltaFunctionPrime", - CellLabel->"Out[3]=", - CellID->1114808117] + CellLabel->"Out[600]="] }, Open ]] }, Open ]], @@ -350,12 +344,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1011, Automatic}, {Automatic, 185}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DenominatorOrder.nb 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x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracBasis.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracBasis.nb index 31d7f0f8b..ee80d2070 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracBasis.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracBasis.nb @@ -118,14 +118,24 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"DiracBasis", "[", "any", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is a head which is wrapped around Dirac structures (and the 1) as a result \ -of the function DiracReduce. Eventually you want to substitute DiracBasis by \ -Identity (or set: DiracBasis[1] = S; DiracBasis[DiracMatrix[mu]] = P; etc.)." + " \[LineSeparator]is a head which is wrapped around Dirac structures (and \ +the 1) as a result of the function ", + ButtonBox["DiracReduce", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracReduce", + ButtonNote->"DiracReduce"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell[TextData[{ + "For more details, see the documentation for ", + ButtonBox["DiracReduce", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracReduce", + ButtonNote->"DiracReduce"], + "." +}], "Notes", CellID->1067943069] }, Open ]], @@ -161,16 +171,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - "See also: ", - ButtonBox["DiracReduce", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracReduce", - ButtonNote->"DiracReduce"], - "." -}], "Text", - CellTags->"DiracBasis", - CellID->1805198737] +Cell[TextData[ButtonBox["DiracReduce", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracReduce", + ButtonNote->"DiracReduce"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -256,12 +260,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1358, Automatic}, {Automatic, 247}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracCanonical.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracCanonical.nb deleted file mode 100644 index 3cb941bbe..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracCanonical.nb +++ /dev/null @@ -1,265 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/DiracCanonical", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["DiracCanonical", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["DiracCanonical"], "InlineFormula"], - " \[LineSeparator]", - "is an option for DiracSimplify. 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If that is needed, use \ -DiracSimplify." + " \[LineSeparator]applies the Dirac equation without expanding ", + Cell[BoxData["exp"], "InlineFormula"], + ". If expansions are necessary, use ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DiracEquation", "]"}]], "Input", + CellLabel->"In[129]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[129]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -160,15 +176,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - ButtonBox["DiracSimplify", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], - "." -}], "Text", - CellTags->"DiracEquation", - CellID->1088896111] +Cell[TextData[ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -199,18 +210,41 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"Spinor", "[", - RowBox[{ - RowBox[{"Momentum", "[", "p", "]"}], ",", "m", ",", "1"}], "]"}], ".", - RowBox[{"DiracGamma", "[", - RowBox[{"Momentum", "[", "p", "]"}], "]"}]}]], "Input", - CellTags->"DiracEquation", - CellLabel->"In[1]:=", - CellID->1948002457], + RowBox[{"GS", "[", "p", "]"}], ".", + RowBox[{"SpinorU", "[", + RowBox[{"p", ",", "m"}], "]"}]}]], "Input", + CellLabel->"In[125]:="], Cell[BoxData[ FormBox[ RowBox[{ + RowBox[{"(", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", + RowBox[{"u", "(", + FormBox["p", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[125]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracEquation", "[", "%", "]"}]], "Input", + CellLabel->"In[126]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"m", " ", RowBox[{"(", RowBox[{ FormBox["\<\"\[CurlyPhi]\"\>", @@ -227,31 +261,162 @@ Cell[BoxData[ FormBox["m", TraditionalForm], FormBox["\<\")\"\>", - TraditionalForm]}], ")"}], ".", + TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[126]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"GS", "[", "p", "]"}], ".", + RowBox[{"SpinorV", "[", + RowBox[{"p", ",", "m"}], "]"}]}]], "Input", + CellLabel->"In[123]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"(", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", + RowBox[{"v", "(", + FormBox["p", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[123]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracEquation", "[", "%", "]"}]], "Input", + CellLabel->"In[124]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{ - OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox["\<\"\[CurlyPhi]\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + RowBox[{"-", + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"]}], + TraditionalForm], + FormBox["\<\",\"\>", + TraditionalForm], + FormBox["m", + TraditionalForm], + FormBox["\<\")\"\>", TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", - CellTags->"DiracEquation", - CellLabel->"Out[1]=", - CellID->1390956545] + CellLabel->"Out[124]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SpinorUBar", "[", + RowBox[{"p", ",", "0"}], "]"}], ".", + RowBox[{"GS", "[", "p", "]"}]}]], "Input", + CellLabel->"In[121]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + OverscriptBox["u", "_"], "(", + FormBox["p", + TraditionalForm], ")"}], ".", + RowBox[{"(", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[121]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DiracEquation", "[", "%", "]"}]], "Input", - CellTags->"DiracEquation", - CellLabel->"In[2]:=", - CellID->831374241], + CellLabel->"In[122]:="], + +Cell[BoxData[ + FormBox["0", TraditionalForm]], "Output", + CellLabel->"Out[122]="] +}, Open ]], + +Cell[TextData[{ + ButtonBox["DiracEquation", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracEquation", + ButtonNote->"DiracEquation"], + " also works in ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensions" +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SpinorVBarD", "[", + RowBox[{"p", ",", "m"}], "]"}], ".", + RowBox[{"GSD", "[", "p", "]"}]}]], "Input", + CellLabel->"In[127]:="], Cell[BoxData[ FormBox[ - RowBox[{"m", " ", + RowBox[{ + FormBox[ + RowBox[{ + OverscriptBox["v", "_"], "(", + FormBox["p", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}], + TraditionalForm], ".", + RowBox[{"(", + FormBox[ + RowBox[{"\[Gamma]", "\[CenterDot]", + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]}], + TraditionalForm], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[127]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracEquation", "[", "%", "]"}]], "Input", + CellLabel->"In[128]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"-", "m"}], " ", RowBox[{"(", RowBox[{ FormBox["\<\"\[CurlyPhi]\"\>", @@ -259,9 +424,9 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - OverscriptBox[ + RowBox[{"-", FormBox["p", - TraditionalForm], "_"], + TraditionalForm]}], TraditionalForm], FormBox["\<\",\"\>", TraditionalForm], @@ -269,9 +434,7 @@ Cell[BoxData[ TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", - CellTags->"DiracEquation", - CellLabel->"Out[2]=", - CellID->1802781574] + CellLabel->"Out[128]="] }, Open ]] }, Open ]], @@ -335,13 +498,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{898, 897}, +WindowMargins->{{1083, Automatic}, {Automatic, 159}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGamma.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGamma.nb index d3fa5401e..49ae7d0fa 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGamma.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGamma.nb @@ -119,15 +119,23 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"x", ",", " ", "dim"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the head of all Dirac matrices and slashes (in the internal \ -representation). Use DiracMatrix (or GA, GAD) and DiracSlash (or GS, GSD) for \ -manual (short) input. DiracGamma[x, 4] simplifies to DiracGamma[x]. \ -DiracGamma[5] is ", + " \[LineSeparator]is the head of all Dirac matrices and slashes (in the \ +internal representation). Use GA, GAD, GS or GSD for manual (short) input." +}], "Usage", + CellID->982511436], + +Cell["DiracGamma[x, 4] simplifies to DiracGamma[x].", "Notes", + CellID->1067943069], + +Cell[TextData[{ + "DiracGamma[5] is ", Cell[BoxData[ FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], - ". DiracGamma[6] is ", + SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]] +}], "Notes"], + +Cell[TextData[{ + "DiracGamma[6] is ", Cell[BoxData[ FormBox[ RowBox[{ @@ -135,18 +143,18 @@ DiracGamma[5] is ", RowBox[{"1", "+", SuperscriptBox["\[Gamma]", "5"]}], ")"}], "/", "2."}], TraditionalForm]]], - " DiracGamma[7] is ", + " " +}], "Notes"], + +Cell[TextData[{ + "DiracGamma[7] is ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "-", SuperscriptBox["\[Gamma]", "5"]}], ")"}], "/", "2."}], TraditionalForm]]] -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] +}], "Notes"] }, Open ]], Cell[CellGroupData[{ @@ -187,29 +195,27 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracGammaExpand", ButtonNote->"DiracGammaExpand"], ", ", - ButtonBox["DiracMatrix", + ButtonBox["GA", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData:>"paclet:FeynCalc/ref/GA", + ButtonNote->"GA"], ", ", ButtonBox["DiracSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", ButtonNote->"DiracSimplify"], ", ", - ButtonBox["DiracSlash", + ButtonBox["GS", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], + ButtonData:>"paclet:FeynCalc/ref/GS", + ButtonNote->"GS"], ", ", ButtonBox["DiracTrick", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracTrick", ButtonNote->"DiracTrick"], "." -}], "Text", - CellTags->"DiracGamma", - CellID->1692507192] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -241,7 +247,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DiracGamma", "[", "5", "]"}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[1]:=", + CellLabel->"In[604]:=", CellID->1046278698], Cell[BoxData[ @@ -251,8 +257,7 @@ Cell[BoxData[ FormBox["5", TraditionalForm]], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[1]=", - CellID->842552946] + CellLabel->"Out[604]="] }, Open ]], Cell[CellGroupData[{ @@ -261,7 +266,7 @@ Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"LorentzIndex", "[", "\[Alpha]", "]"}], "]"}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[2]:=", + CellLabel->"In[605]:=", CellID->1161111346], Cell[BoxData[ @@ -273,8 +278,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[2]=", - CellID->1687472527] + CellLabel->"Out[605]="] }, Open ]], Cell[TextData[{ @@ -289,9 +293,7 @@ Cell[TextData[{ FormBox[ RowBox[{"\[Gamma]", "\[CenterDot]", "q"}], TraditionalForm]]], "." -}], "Text", - CellTags->"DiracGamma", - CellID->299092642], +}], "Notes"], Cell[CellGroupData[{ @@ -300,7 +302,7 @@ Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"Momentum", "[", "q", "]"}], "]"}], " "}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[3]:=", + CellLabel->"In[606]:=", CellID->1887452273], Cell[BoxData[ @@ -313,8 +315,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[3]=", - CellID->1138458552] + CellLabel->"Out[606]="] }, Open ]], Cell[CellGroupData[{ @@ -327,7 +328,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", "-", "q"}], "]"}], "]"}]}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[4]:=", + CellLabel->"In[607]:=", CellID->1345474698], Cell[BoxData[ @@ -356,8 +357,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], ")"}], ")"}]}], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[4]=", - CellID->1631372749] + CellLabel->"Out[607]="] }, Open ]], Cell[CellGroupData[{ @@ -369,7 +369,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"q", ",", "D"}], "]"}], ",", "D"}], "]"}], " "}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[5]:=", + CellLabel->"In[608]:=", CellID->38879465], Cell[BoxData[ @@ -380,20 +380,18 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[5]=", - CellID->567019698] + CellLabel->"Out[608]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a1", "=", - RowBox[{ - RowBox[{"GS", "[", - RowBox[{"p", "-", "q"}], "]"}], ".", - RowBox[{"GS", "[", "p", "]"}]}]}]], "Input", + RowBox[{ + RowBox[{"GS", "[", + RowBox[{"p", "-", "q"}], "]"}], ".", + RowBox[{"GS", "[", "p", "]"}]}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[6]:=", + CellLabel->"In[610]:=", CellID->294479801], Cell[BoxData[ @@ -426,17 +424,15 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[6]=", - CellID->445474776] + CellLabel->"Out[610]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a2", "=", - RowBox[{"DiracGammaExpand", "[", "a1", "]"}]}]], "Input", + RowBox[{"DiracGammaExpand", "[", "%", "]"}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[7]:=", + CellLabel->"In[611]:=", CellID->324312499], Cell[BoxData[ @@ -467,22 +463,20 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[7]=", - CellID->754251999] + CellLabel->"Out[611]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a3", "=", - RowBox[{ - RowBox[{"GAD", "[", "\[Mu]", "]"}], ".", - RowBox[{"GSD", "[", - RowBox[{"p", "-", "q"}], "]"}], ".", - RowBox[{"GSD", "[", "q", "]"}], ".", - RowBox[{"GAD", "[", "\[Mu]", "]"}]}]}]], "Input", + RowBox[{ + RowBox[{"GAD", "[", "\[Mu]", "]"}], ".", + RowBox[{"GSD", "[", + RowBox[{"p", "-", "q"}], "]"}], ".", + RowBox[{"GSD", "[", "q", "]"}], ".", + RowBox[{"GAD", "[", "\[Mu]", "]"}]}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[8]:=", + CellLabel->"In[612]:=", CellID->667969280], Cell[BoxData[ @@ -524,17 +518,15 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[8]=", - CellID->712838090] + CellLabel->"Out[612]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a4", "=", - RowBox[{"DiracTrick", "[", "a3", "]"}]}]], "Input", + RowBox[{"DiracTrick", "[", "%", "]"}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[9]:=", + CellLabel->"In[613]:=", CellID->1907296195], Cell[BoxData[ @@ -546,11 +538,13 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - FormBox["p", - TraditionalForm], "-", - FormBox["q", - TraditionalForm]}], + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -582,17 +576,15 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[9]=", - CellID->1654426864] + CellLabel->"Out[613]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a5", "=", - RowBox[{"DiracSimplify", "[", "a4", "]"}]}]], "Input", + RowBox[{"DiracSimplify", "[", "%%", "]"}]], "Input", CellTags->"DiracGamma", - CellLabel->"In[10]:=", + CellLabel->"In[614]:=", CellID->41068363], Cell[BoxData[ @@ -646,17 +638,144 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"DiracGamma", - CellLabel->"Out[10]=", - CellID->1950498776] + CellLabel->"Out[614]="] }, Open ]], +Cell["\<\ +DiracGamma may also carry Cartesian indices or appear contracted with \ +Cartesian momenta.\ +\>", "Notes"], + +Cell[CellGroupData[{ + Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"a1", ",", "a2", ",", "a3", ",", "a4", ",", "a5"}], "]"}]], "Input", - - CellTags->"DiracGamma", - CellLabel->"In[11]:=", - CellID->2054807508] + RowBox[{"DiracGamma", "[", + RowBox[{"CartesianIndex", "[", "i", "]"}], "]"}]], "Input", + CellLabel->"In[616]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + OverscriptBox[ + FormBox[ + StyleBox["\<\"\[Gamma]\"\>", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], + FormBox[ + FormBox[ + StyleBox["i", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[616]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracGamma", "[", + RowBox[{ + RowBox[{"CartesianIndex", "[", + RowBox[{"i", ",", + RowBox[{"D", "-", "1"}]}], "]"}], ",", "D"}], "]"}]], "Input", + CellLabel->"In[619]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + FormBox[ + StyleBox["\<\"\[Gamma]\"\>", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + FormBox[ + FormBox[ + StyleBox["i", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[619]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracGamma", "[", + RowBox[{"CartesianMomentum", "[", "p", "]"}], "]"}]], "Input", + CellLabel->"In[617]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox[ + StyleBox["\<\"\[Gamma]\"\>", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox[ + StyleBox["p", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], + TraditionalForm]}], TraditionalForm]], "Output", + CellLabel->"Out[617]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracGamma", "[", + RowBox[{ + RowBox[{"CartesianMomentum", "[", + RowBox[{"p", ",", + RowBox[{"D", "-", "1"}]}], "]"}], ",", "D"}], "]"}]], "Input", + CellLabel->"In[620]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + FormBox[ + StyleBox["\<\"\[Gamma]\"\>", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "\[CenterDot]", + FormBox[ + FormBox[ + StyleBox["p", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm]}], TraditionalForm]], "Output", + CellLabel->"Out[620]="] +}, Open ]], + +Cell["\<\ +Temporal indices are represented using ExplicitLorentzIndex[0]\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracGamma", "[", + RowBox[{"ExplicitLorentzIndex", "[", "0", "]"}], "]"}]], "Input", + CellLabel->"In[618]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["0", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[618]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -719,13 +838,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{700, 767}, +WindowMargins->{{911, Automatic}, {Automatic, 189}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGammaCombine.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGammaCombine.nb index 58a961c33..3b5dc93cc 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGammaCombine.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGammaCombine.nb @@ -118,13 +118,30 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"DiracGammaCombine", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is (nearly) the inverse operation to DiracGammaExpand." + " \[LineSeparator]is (nearly) the inverse operation to ", + ButtonBox["DiracGammaExpand", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracGammaExpand", + ButtonNote->"DiracGammaExpand"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DiracGammaCombine", "]"}]], "Input", + CellLabel->"In[130]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[130]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -170,29 +187,17 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracGammaExpand", ButtonNote->"DiracGammaExpand"], ", ", - ButtonBox["DiracMatrix", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], - ", ", ButtonBox["DiracSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", ButtonNote->"DiracSimplify"], ", ", - ButtonBox["DiracSlash", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], - ", ", ButtonBox["DiracTrick", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracTrick", ButtonNote->"DiracTrick"], "." -}], "Text", - CellTags->"DiracGammaCombine", - CellID->269406671] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -222,12 +227,41 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracGammaCombine", "[", + RowBox[{ + RowBox[{"GS", "[", "p", "]"}], " ", "+", " ", + RowBox[{"GS", "[", "q", "]"}]}]], "Input", + CellLabel->"In[134]:="], + +Cell[BoxData[ + FormBox[ RowBox[{ - RowBox[{"GS", "[", "p", "]"}], " ", "+", " ", - RowBox[{"GS", "[", "q", "]"}]}], "]"}]], "Input", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], "+", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm]}], TraditionalForm]], "Output", + CellLabel->"Out[134]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracGammaCombine", "[", "%", "]"}]], "Input", CellTags->"DiracGammaCombine", - 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CellLabel->"Out[3]=", - CellID->801597804] + CellLabel->"Out[138]="] }, Open ]], Cell[CellGroupData[{ @@ -307,18 +368,20 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"StandardForm", "[", "%", "]"}]], "Input", CellTags->"DiracGammaCombine", - CellLabel->"In[4]:=", + CellLabel->"In[139]:=", CellID->1011380579], Cell[BoxData[ RowBox[{"DiracGamma", "[", - RowBox[{"Momentum", "[", - RowBox[{ - RowBox[{"2", " ", "p"}], "-", - RowBox[{"2", " ", "q"}]}], "]"}], "]"}]], "Output", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{ + RowBox[{ + RowBox[{"2", " ", "p"}], "-", + RowBox[{"3", " ", "q"}]}], ",", "D"}], "]"}], ",", "D"}], + "]"}]], "Output", CellTags->"DiracGammaCombine", - CellLabel->"Out[4]//StandardForm=", - CellID->1276677678] + CellLabel->"Out[139]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -326,31 +389,27 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DiracGammaExpand", "[", "%%", "]"}]], "Input", CellTags->"DiracGammaCombine", - CellLabel->"In[5]:=", + CellLabel->"In[140]:=", CellID->365053477], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"2", " ", - RowBox[{ - OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + RowBox[{"\[Gamma]", "\[CenterDot]", FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["p", + TraditionalForm], TraditionalForm]}]}], "-", - RowBox[{"2", " ", - RowBox[{ - OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + RowBox[{"3", " ", + RowBox[{"\[Gamma]", "\[CenterDot]", FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], + FormBox["q", + TraditionalForm], TraditionalForm]}]}]}], TraditionalForm]], "Output", CellTags->"DiracGammaCombine", - CellLabel->"Out[5]=", - CellID->1799332421] + CellLabel->"Out[140]="] +}, Open ]] }, Open ]] }, Open ]], @@ -415,12 +474,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{Automatic, 731}, {Automatic, 269}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGammaExpand.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGammaExpand.nb index ced3d57d7..14bb10b32 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGammaExpand.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracGammaExpand.nb @@ -118,14 +118,50 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"DiracGammaExpand", "[", "exp", "]"}]], "InlineFormula"], - 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1c972cbc3..78954a67d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracMatrix.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracMatrix.nb @@ -163,8 +163,29 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +The shortcut DiracMatrix is deprecated, please use GA instead!\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DiracMatrix", "]"}]], "Input", + CellTags->"DiracMatrix", + CellLabel->"In[322]:=", + CellID->1215792887], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"DiracMatrix", + CellLabel->"Out[322]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -200,54 +221,17 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["DiracGammaExpand", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracGammaExpand", - ButtonNote->"DiracGammaExpand"], - ", ", - ButtonBox["DiracGamma", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracGamma", - ButtonNote->"DiracGamma"], - ", ", - ButtonBox["DiracSimplify", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], - ", ", - ButtonBox["DiracSlash", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], - ", ", - ButtonBox["DiracTrick", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracTrick", - ButtonNote->"DiracTrick"], - ", ", ButtonBox["GA", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GA", ButtonNote->"GA"], ", ", - ButtonBox["GAD", + ButtonBox["FCI", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/GAD", - ButtonNote->"GAD"], - ", ", - ButtonBox["GS", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/GS", - ButtonNote->"GS"], - ", ", - ButtonBox["GSD", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/GSD", - ButtonNote->"GSD"], + ButtonData:>"paclet:FeynCalc/ref/FCI", + ButtonNote->"FCI"], "." -}], "Text", - CellTags->"DiracMatrix", - CellID->703033103] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -276,30 +260,10 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "DiracMatrix", "]"}]], "Input", - CellTags->"DiracMatrix", - CellLabel->"In[1]:=", - CellID->1215792887], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "4"}], ",", - RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"DiracMatrix", - CellLabel->"Out[1]=", - CellID->462215683] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"DiracMatrix", "[", "\[Mu]", "]"}]], "Input", CellTags->"DiracMatrix", - CellLabel->"In[2]:=", + CellLabel->"In[323]:=", CellID->888527237], Cell[BoxData[ @@ -311,19 +275,15 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"DiracMatrix", - CellLabel->"Out[2]=", - CellID->1128455616] + CellLabel->"Out[323]="] }, Open ]], Cell[TextData[{ - "This is how to enter the non-commutative product of two ", - Cell[BoxData[ - FormBox["Null", TraditionalForm]]], - ". The ", + "This is how to enter the non-commutative product of two. The ", StyleBox["Mathematica", FontSlant->"Italic"], " Dot \".\" is used as non-commutative multiplication operator." -}], "Text", +}], "Notes", CellTags->"DiracMatrix", CellID->477550014], @@ -334,7 +294,7 @@ Cell[BoxData[ RowBox[{"DiracMatrix", "[", "\[Mu]", "]"}], ".", RowBox[{"DiracMatrix", "[", "\[Nu]", "]"}]}]], "Input", CellTags->"DiracMatrix", - CellLabel->"In[3]:=", + CellLabel->"In[324]:=", CellID->216003987], Cell[BoxData[ @@ -353,8 +313,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"DiracMatrix", - CellLabel->"Out[3]=", - CellID->527384282] + CellLabel->"Out[324]="] }, Open ]], Cell[CellGroupData[{ @@ -364,25 +323,26 @@ Cell[BoxData[ RowBox[{"DiracMatrix", "[", "\[Alpha]", "]"}], "//", "StandardForm"}]], "Input", CellTags->"DiracMatrix", - CellLabel->"In[4]:=", + CellLabel->"In[328]:=", CellID->1775640770], Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"LorentzIndex", "[", "\[Alpha]", "]"}], "]"}]], "Output", CellTags->"DiracMatrix", - CellLabel->"Out[4]//StandardForm=", - CellID->209169397] + CellLabel->"Out[328]//StandardForm="] }, Open ]], +Cell["\<\ +DiracMatrix is scheduled for removal in the future versions of FeynCalc. The \ +safe alternative is to use GA.\ +\>", "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"DiracMatrix", "[", "\[Mu]", "]"}], "//", "FCE"}]], "Input", - CellTags->"DiracMatrix", - CellLabel->"In[5]:=", - CellID->1489042033], + RowBox[{"GA", "[", "\[Mu]", "]"}]], "Input", + CellLabel->"In[337]:="], Cell[BoxData[ FormBox[ @@ -392,33 +352,14 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - CellTags->"DiracMatrix", - CellLabel->"Out[5]=", - CellID->1529249901] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"%", "//", "StandardForm"}]], "Input", - CellTags->"DiracMatrix", - CellLabel->"In[6]:=", - CellID->80209945], - -Cell[BoxData[ - RowBox[{"GA", "[", "\[Mu]", "]"}]], "Output", - CellTags->"DiracMatrix", - CellLabel->"Out[6]//StandardForm=", - CellID->1573455068] + CellLabel->"Out[337]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GAD", "[", "\[Mu]", "]"}]], "Input", - CellTags->"DiracMatrix", - CellLabel->"In[7]:=", - CellID->512840116], + CellLabel->"In[338]:="], Cell[BoxData[ FormBox[ @@ -427,118 +368,37 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", - CellTags->"DiracMatrix", - CellLabel->"Out[7]=", - CellID->999762340] + CellLabel->"Out[338]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"%", "//", "FCI"}], "//", "StandardForm"}]], "Input", - CellTags->"DiracMatrix", - CellLabel->"In[8]:=", - CellID->1503246496], + RowBox[{"FCI", "[", + RowBox[{"GA", "[", "\[Mu]", "]"}], "]"}], "===", + RowBox[{"DiracMatrix", "[", "\[Mu]", "]"}]}]], "Input", + CellLabel->"In[339]:="], Cell[BoxData[ - RowBox[{"DiracGamma", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", "D"}], "]"}]], "Output", - CellTags->"DiracMatrix", - CellLabel->"Out[8]//StandardForm=", - CellID->1842955890] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"GA", "[", - RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}]], "Input", - CellTags->"DiracMatrix", - CellLabel->"In[9]:=", - CellID->1134451921], - -Cell[BoxData[ - FormBox[ - RowBox[{ - FormBox[ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - TraditionalForm], ".", - FormBox[ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - TraditionalForm], ".", - FormBox[ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"DiracMatrix", - CellLabel->"Out[9]=", - CellID->625741566] + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[339]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"GA", "[", - RowBox[{"a", " ", ".", " ", "b"}], "]"}], "//", "FCI"}]], "Input", - CellTags->"DiracMatrix", - CellLabel->"In[10]:=", - CellID->241194804], + RowBox[{"FCI", "[", + RowBox[{"GAD", "[", "\[Mu]", "]"}], "]"}], "===", + RowBox[{"DiracMatrix", "[", + RowBox[{"\[Mu]", ",", + RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]}]], "Input", + CellLabel->"In[340]:="], Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["b", - TraditionalForm], - TraditionalForm]]}], TraditionalForm]], "Output", - CellTags->"DiracMatrix", - CellLabel->"Out[10]=", - CellID->1051855483] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"%", "//", "StandardForm"}]], "Input", - CellTags->"DiracMatrix", - CellLabel->"In[11]:=", - CellID->256970123], - -Cell[BoxData[ - RowBox[{ - RowBox[{"DiracGamma", "[", - RowBox[{"LorentzIndex", "[", "a", "]"}], "]"}], ".", - RowBox[{"DiracGamma", "[", - RowBox[{"LorentzIndex", "[", "b", "]"}], "]"}]}]], "Output", - CellTags->"DiracMatrix", - CellLabel->"Out[11]//StandardForm=", - CellID->94050778] + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[340]="] }, Open ]] }, Open ]], @@ -602,13 +462,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{905, 910}, +WindowMargins->{{Automatic, 1292}, {164, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracOrder.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracOrder.nb index aeaf36b9a..7a51ae183 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracOrder.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracOrder.nb @@ -117,16 +117,59 @@ Cell["DiracOrder", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"DiracOrder", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "orders the Dirac matrices in expr alphabetically. \ -DiracOrder[expr,orderlist] orders the Dirac matrices in expr according to \ -orderlist." + RowBox[{"DiracOrder", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]orders the Dirac matrices in ", + Cell[BoxData["exp"], "InlineFormula"], + " lexicographically.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"DiracOrder", "[", + RowBox[{"exp", ",", " ", "orderlist"}], "]"}]], "InlineFormula"], + " \[LineSeparator] orders the Dirac matrices in ", + Cell[BoxData["exp"], "InlineFormula"], + " according to ", + Cell[BoxData["orderlist"], "InlineFormula"], + "." }], "Usage", - CellID->982511436], + CellID->2090318364], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + "DiracOrder is also an option of ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + " and some other functions dealing with Dirac algebra. If set to True, the \ +function ", + ButtonBox["DiracOrder", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracOrder", + ButtonNote->"DiracOrder"], + " will be applied to the intermediate result to reorder the Dirac matrices \ +lexicographically." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DiracOrder", "]"}]], "Input", + CellLabel->"In[159]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"DiracTrick", "\[Rule]", "True"}], ",", + RowBox[{"DiracGammaCombine", "\[Rule]", "False"}], ",", + RowBox[{"FCDiracIsolate", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCJoinDOTs", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"MaxIterations", "\[Rule]", "\[Infinity]"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[159]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -172,9 +215,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracTrick", ButtonNote->"DiracTrick"], "." -}], "Text", - CellTags->"DiracOrder", - CellID->2147102830] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -204,11 +245,11 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", " ", "=", " ", + RowBox[{" ", RowBox[{"GA", "[", RowBox[{"\[Beta]", ",", "\[Alpha]"}], "]"}]}]], "Input", CellTags->"DiracOrder", - CellLabel->"In[1]:=", + CellLabel->"In[163]:=", CellID->1559113060], Cell[BoxData[ @@ -231,39 +272,32 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DiracOrder", - CellLabel->"Out[1]=", - CellID->1026687398] + CellLabel->"Out[163]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracOrder", "[", "t1", "]"}]], "Input", + RowBox[{"DiracOrder", "[", "%", "]"}]], "Input", CellTags->"DiracOrder", - CellLabel->"In[2]:=", + CellLabel->"In[164]:=", CellID->1074180519], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"2", " ", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]}]]}], "-", RowBox[{ SuperscriptBox[ OverscriptBox["\[Gamma]", "_"], @@ -278,22 +312,33 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"DiracOrder", - CellLabel->"Out[2]=", - CellID->1702463614] + CellLabel->"Out[164]="] }, Open ]], -Cell["This is a string of Dirac matrices in D dimensions. 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Null]], "ExampleDelimiter"], + +Cell[TextData[{ + "By default ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " is moved to the right." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"GA", "[", + RowBox[{"5", ",", "\[Mu]", ",", "\[Nu]"}], "]"}]], "Input", CellTags->"DiracOrder", - CellLabel->"In[5]:=", + CellLabel->"In[174]:=", CellID->2005079104], Cell[BoxData[ @@ -408,27 +467,15 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DiracOrder", - CellLabel->"Out[5]=", - CellID->2004576322] + CellLabel->"Out[174]="] }, Open ]], -Cell[TextData[{ - "By default ", - Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", - RowBox[{"5", " "}]], TraditionalForm]]], - "is moved to the right." -}], "Text", - CellTags->"DiracOrder", - CellID->2082752140], - Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracOrder", "[", "t3", "]"}]], "Input", + RowBox[{"DiracOrder", "[", "%", "]"}]], "Input", CellTags->"DiracOrder", - CellLabel->"In[6]:=", + CellLabel->"In[175]:=", CellID->1342940029], Cell[BoxData[ @@ -451,18 +498,16 @@ Cell[BoxData[ FormBox["5", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"DiracOrder", - CellLabel->"Out[6]=", - CellID->1359695729] + CellLabel->"Out[175]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t4", "=", - RowBox[{"GA", "[", - RowBox[{"6", ",", "\[Mu]", ",", "7"}], "]"}]}]], "Input", + RowBox[{"GA", "[", + RowBox[{"6", ",", "\[Mu]", ",", "7"}], "]"}]], "Input", CellTags->"DiracOrder", - CellLabel->"In[7]:=", + CellLabel->"In[176]:=", CellID->71636230], Cell[BoxData[ @@ -489,16 +534,15 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DiracOrder", - CellLabel->"Out[7]=", - CellID->729653201] + CellLabel->"Out[176]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracOrder", "[", "t4", "]"}]], "Input", + RowBox[{"DiracOrder", "[", "%", "]"}]], "Input", CellTags->"DiracOrder", - CellLabel->"In[8]:=", + CellLabel->"In[177]:=", CellID->332885129], Cell[BoxData[ @@ -515,18 +559,28 @@ Cell[BoxData[ FormBox["7", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"DiracOrder", - CellLabel->"Out[8]=", - CellID->534859922] + CellLabel->"Out[177]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t5", "=", - RowBox[{"GA", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Delta]"}], "]"}]}]], "Input", + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[TextData[{ + Cell[BoxData["orderlist"], "InlineFormula"], + " comes into play when we need an ordering that is not lexicographic" +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"GA", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Delta]"}], "]"}]], "Input", CellTags->"DiracOrder", - CellLabel->"In[9]:=", + CellLabel->"In[181]:=", CellID->1751727580], Cell[BoxData[ @@ -557,34 +611,50 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DiracOrder", - CellLabel->"Out[9]=", - CellID->70359997] + CellLabel->"Out[181]="] }, Open ]], -Cell[TextData[{ - "This orders the ", - Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["\[Gamma]", "\[Alpha]"], - SuperscriptBox["\[Gamma]", "\[Beta]"], - SuperscriptBox["\[Gamma]", "\[Delta]"]}], TraditionalForm]]], - " in reverse order." -}], "Text", - CellTags->"DiracOrder", - CellID->238119482], +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracOrder", "[", "%", "]"}]], "Input", + CellLabel->"In[183]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Delta]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[183]="] +}, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DiracOrder", "[", - RowBox[{"t5", ",", + RowBox[{ + RowBox[{"GA", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Delta]"}], "]"}], ",", RowBox[{"{", RowBox[{"\[Delta]", ",", "\[Beta]", ",", "\[Alpha]"}], "}"}]}], "]"}]], "Input", - CellTags->"DiracOrder", - CellLabel->"In[10]:=", - CellID->203704442], + CellLabel->"In[184]:="], Cell[BoxData[ FormBox[ @@ -616,23 +686,17 @@ Cell[BoxData[ FormBox["\[Delta]", TraditionalForm], TraditionalForm]], " ", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]}]]}], "-", RowBox[{"2", " ", SuperscriptBox[ OverscriptBox["\[Gamma]", "_"], @@ -640,23 +704,17 @@ Cell[BoxData[ FormBox["\[Beta]", TraditionalForm], TraditionalForm]], " ", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Delta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "+", + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Delta]", + TraditionalForm], + TraditionalForm]}]]}], "+", RowBox[{"2", " ", SuperscriptBox[ OverscriptBox["\[Gamma]", "_"], @@ -664,70 +722,114 @@ Cell[BoxData[ FormBox["\[Alpha]", TraditionalForm], TraditionalForm]], " ", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Delta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}]}], TraditionalForm]], "Output", - CellTags->"DiracOrder", - CellLabel->"Out[10]=", - CellID->586951928] + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Delta]", + TraditionalForm], + TraditionalForm]}]]}]}], TraditionalForm]], "Output", + CellLabel->"Out[184]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracOrder", "[", "%", "]"}]], "Input", - CellTags->"DiracOrder", - CellLabel->"In[11]:=", - CellID->1795976011], + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; 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Only antisymmetry is implemented." + " \[LineSeparator]stands for i/2*(a . b - b . a) in 4 dimensions. a and b \ +must have Head DiracGamma, GA or GS. Only antisymmetry is implemented." }], "Usage", CellID->982511436], @@ -167,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracSigmaExplicit", ButtonNote->"DiracSigmaExplicit"], "." -}], "Text", - CellTags->"DiracSigma", - CellID->94805766] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -199,13 +196,12 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{"DiracSigma", "[", - RowBox[{ - RowBox[{"GA", "[", "\[Alpha]", "]"}], ",", - RowBox[{"GA", "[", "\[Beta]", "]"}]}], "]"}]}]], "Input", + RowBox[{"DiracSigma", "[", + RowBox[{ + RowBox[{"GA", "[", "\[Alpha]", "]"}], ",", + RowBox[{"GA", "[", "\[Beta]", "]"}]}], "]"}]], "Input", CellTags->"DiracSigma", - CellLabel->"In[1]:=", + CellLabel->"In[639]:=", CellID->1797257280], Cell[BoxData[ @@ -217,16 +213,15 @@ Cell[BoxData[ FormBox["\[Beta]", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"DiracSigma", - CellLabel->"Out[1]=", - CellID->669982831] + CellLabel->"Out[639]="] }, 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"DiracSigmaExplicit", "]"}]], "Input", + CellLabel->"In[60]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[60]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -161,14 +179,18 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ + ButtonBox["DiracGamma", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracGamma", + ButtonNote->"DiracGamma"], + ", ", ButtonBox["DiracSigma", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracSigma", ButtonNote->"DiracSigma"], "." -}], "Text", - CellTags->"DiracSigmaExplicit", - CellID->1461748259] +}], "SeeAlso", + CellID->1822030255] }, Open ]], Cell[CellGroupData[{ @@ -203,7 +225,7 @@ Cell[BoxData[ RowBox[{"GA", "[", "\[Alpha]", "]"}], ",", RowBox[{"GA", "[", "\[Beta]", "]"}]}], "]"}]], "Input", CellTags->"DiracSigmaExplicit", - CellLabel->"In[1]:=", + CellLabel->"In[61]:=", CellID->535100858], Cell[BoxData[ @@ -215,8 +237,7 @@ Cell[BoxData[ FormBox["\[Beta]", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"DiracSigmaExplicit", - CellLabel->"Out[1]=", - CellID->1064329329] + CellLabel->"Out[61]="] }, Open ]], Cell[CellGroupData[{ @@ -224,7 +245,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DiracSigmaExplicit", "[", "%", "]"}]], "Input", CellTags->"DiracSigmaExplicit", - CellLabel->"In[2]:=", + CellLabel->"In[62]:=", CellID->280405798], Cell[BoxData[ @@ -260,8 +281,115 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"DiracSigmaExplicit", - CellLabel->"Out[2]=", - CellID->1384105478] + CellLabel->"Out[62]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"GSD", "[", "p", "]"}], 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TraditionalForm]], "Output", + CellLabel->"Out[64]="] +}, Open ]] }, Open ]] }, Open ]], @@ -326,12 +454,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1207, Automatic}, {Automatic, 137}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracSimpCombine.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracSimpCombine.nb deleted file mode 100644 index 7dd6cddf2..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracSimpCombine.nb +++ /dev/null @@ -1,265 +0,0 @@ -Notebook[{ 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Double Lorentz indices and four vectors are contracted. The Dirac \ -equation is applied. All DiracMatrix[5], DiracMatrix[6] and DiracMatrix[7] \ -are moved to the right. 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ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + " not to touch the Dirac traces." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSimplify", "[", + RowBox[{ + RowBox[{"DiracTrace", "[", + RowBox[{ + RowBox[{"(", + RowBox[{ + RowBox[{"-", + RowBox[{"GSD", "[", "q", "]"}]}], "+", + RowBox[{"SMP", "[", "\"\\"", "]"}]}], ")"}], ".", + RowBox[{"GAD", "[", "\[Nu]", "]"}], ".", + RowBox[{"(", + RowBox[{ + RowBox[{"GSD", "[", + RowBox[{"p", "-", "q"}], "]"}], "+", + RowBox[{"SMP", "[", "\"\\"", "]"}]}], ")"}], ".", + RowBox[{"GAD", "[", "\[Mu]", "]"}]}], "]"}], " ", ",", + RowBox[{"DiracTraceEvaluate", "\[Rule]", "False"}], ",", + RowBox[{"DiracTrace", "\[Rule]", "False"}]}], "]"}]], "Input", + CellLabel->"In[185]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox[ + RowBox[{ + RowBox[{"(", + RowBox[{ + SubscriptBox["m", "e"], "-", + RowBox[{"\[Gamma]", "\[CenterDot]", + FormBox[ + FormBox["q", + TraditionalForm], + 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For every other scheme, please recheck your input \ +expressions and ensure that all matrices, spinors and tensors are purely \ +D-dimensional. You might want to use FCGetDimensions[exp] to find the \ +offending terms and fix them by hand or ChangeDimension[exp,D] to convert the \ +whole expression to D-dimensions. If you explicitly intend to use the \ +t'Hooft-Veltman scheme, please activate it via FCSetDiracGammaScheme[\\\"BMHV\ +\\\"]. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \ +ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ +ButtonData:>\\\"paclet:FeynCalc/ref/DiracTrace\\\", ButtonNote -> \ +\\\"FeynCalc`DiracTrace::mixmsg\\\"]\\)\"\>"}], + TraditionalForm]], "Message", "MSG", + CellLabel->"During evaluation of In[187]:="], + +Cell[BoxData[ + FormBox["$Aborted", TraditionalForm]], "Output", + CellLabel->"Out[187]="] +}, Open ]], + +Cell[TextData[{ + "By default, FeynCalc uses the naive dimensional regularization (NDR) \ +scheme, where all Dirac matrices are taken to be ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional. Therefore, in NDR you may not have mixtures of Dirac matrices \ +living in ", + Cell[BoxData["D"], "InlineFormula"], + " and 4 dimensions. However, such expressions are possible in the \ +t'Hooft-Veltman-Breitenlohner-Maison (BMHV) scheme." +}], "Notes"], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}], ";"}]], "Input", + CellLabel->"In[188]:="], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSimplify", "[", + RowBox[{ + RowBox[{"GAD", "[", "\[Mu]", "]"}], ".", + RowBox[{"(", + RowBox[{ + RowBox[{"GA", "[", "p", "]"}], "+", "m"}], ")"}], ".", + RowBox[{"GAD", "[", "\[Mu]", "]"}]}], "]"}]], "Input", + CellLabel->"In[189]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"-", + RowBox[{"D", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]]}]}], "+", + RowBox[{"2", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]]}], "+", + RowBox[{"D", " ", "m"}]}], TraditionalForm]], "Output", + CellLabel->"Out[189]="] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}], ";"}]], "Input", + + CellLabel->"In[190]:="], + +Cell[TextData[{ + "The BMHV scheme is a special prescription for handling ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " in dimensional regularization. Do not activate this scheme mindlessly just \ +to get rid of errors from ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + "! If you are doing a calculation in NDR or a calculation that does not \ +involve ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + ", better make sure that your input expressions are correctly written to be ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional objects." +}], "Notes"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[TextData[{ + "Traces that contain an odd number of ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " or chirality projectors cannot be calculated unambigously in NDR. To \ +avoid inconsistencies, ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + " will refuse to evaluate such traces in NDR." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracTrace", "[", + RowBox[{ + RowBox[{"GAD", "[", + RowBox[{ + "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "\[Alpha]", + ",", "\[Beta]"}], "]"}], ".", + RowBox[{"GA", "[", "5", "]"}]}], "]"}]], "Input", + CellLabel->"In[191]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox[ + RowBox[{ + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], + TraditionalForm]}], + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellLabel->"Out[191]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[192]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox[ + RowBox[{ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]]}], + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellLabel->"Out[192]="] +}, Open ]], + +Cell["\<\ +Such traces can be consistently calculated in the BMHV scheme. 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FeynCalc merely carries out the \ +algebraic operations that you request, but it is still your task to ensure \ +that what you do makes sense." +}], "Notes"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell["\<\ +Since FeynCalc 9.3 it is also possible to simplify Dirac matrices with \ +Cartesian or temporal indices. 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x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracSlash.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracSlash.nb index 329bd45bb..4e81c247c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracSlash.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracSlash.nb @@ -118,26 +118,44 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"DiracSlash", "[", "p", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the contraction ", + " \[LineSeparator]is the contraction ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["p", "\[Mu]"], SubscriptBox["\[Gamma]", RowBox[{"\[Mu]", " "}]]}], TraditionalForm]]], - "(FourVector[p, ", + "(FV[p, ", Cell[BoxData[ FormBox["\[Mu]", TraditionalForm]]], - "] DiracMatrix[", + "] GA[", Cell[BoxData[ FormBox["\[Mu]", TraditionalForm]]], - "]). Products of those can be entered in the form DiracSlash[p1, p2, ...]." + "]). Products of those can be entered in the form GS[p1, p2, ...]." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +The shortcut DiracSlash is deprecated, please use GS instead!\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DiracSlash", "]"}]], "Input", + CellLabel->"In[83]:=", + CellID->1215792887], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[83]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -173,44 +191,17 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["DiracGammaExpand", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracGammaExpand", - ButtonNote->"DiracGammaExpand"], - ", ", - ButtonBox["DiracGamma", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracGamma", - ButtonNote->"DiracGamma"], - ", ", - ButtonBox["DiracMatrix", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], - ", ", - ButtonBox["DiracSimplify", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], - ", ", - ButtonBox["DiracTrick", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracTrick", - ButtonNote->"DiracTrick"], - ", ", ButtonBox["GS", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GS", ButtonNote->"GS"], ", ", - ButtonBox["GSD", + ButtonBox["FCI", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/GSD", - ButtonNote->"GSD"], + ButtonData:>"paclet:FeynCalc/ref/FCI", + ButtonNote->"FCI"], "." -}], "Text", - CellTags->"DiracSlash", - CellID->1970754340] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -237,26 +228,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "DiracSlash", "]"}]], "Input", - CellTags->"DiracSlash", - CellLabel->"In[1]:=", - CellID->1930775738], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "4"}], ",", - RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"DiracSlash", - CellLabel->"Out[1]=", - CellID->286229782] -}, Open ]], - Cell[TextData[{ "This is q-slash, i.e., ", Cell[BoxData[ @@ -265,16 +236,14 @@ Cell[TextData[{ SuperscriptBox["\[Gamma]", "\[Mu]"], RowBox[{ SubscriptBox["q", "\[Mu]"], "."}]}], TraditionalForm]]] -}], "Text", - CellTags->"DiracSlash", - CellID->754243775], +}], "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DiracSlash", "[", "q", "]"}]], "Input", CellTags->"DiracSlash", - CellLabel->"In[2]:=", + CellLabel->"In[333]:=", CellID->1250007007], Cell[BoxData[ @@ -287,8 +256,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DiracSlash", - CellLabel->"Out[2]=", - CellID->302151266] + CellLabel->"Out[333]="] }, Open ]], Cell[CellGroupData[{ @@ -298,7 +266,7 @@ Cell[BoxData[ RowBox[{"DiracSlash", "[", "p", "]"}], ".", RowBox[{"DiracSlash", "[", "q", "]"}]}]], "Input", CellTags->"DiracSlash", - CellLabel->"In[3]:=", + CellLabel->"In[334]:=", CellID->751525159], Cell[BoxData[ @@ -321,8 +289,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", CellTags->"DiracSlash", - CellLabel->"Out[3]=", - CellID->1980224843] + CellLabel->"Out[334]="] }, Open ]], Cell[CellGroupData[{ @@ -331,7 +298,7 @@ Cell[BoxData[ RowBox[{"DiracSlash", "[", RowBox[{"p", ",", "q"}], "]"}]], "Input", CellTags->"DiracSlash", - CellLabel->"In[4]:=", + CellLabel->"In[335]:=", CellID->1690251158], Cell[BoxData[ @@ -354,17 +321,19 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", CellTags->"DiracSlash", - CellLabel->"Out[4]=", - CellID->1504514628] + CellLabel->"Out[335]="] }, Open ]], +Cell["\<\ +DiracSlash is scheduled for removal in the future versions of FeynCalc. The \ +safe alternative is to use GS.\ +\>", "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GS", "[", "p", "]"}]], "Input", - CellTags->"DiracSlash", - CellLabel->"In[5]:=", - CellID->2044929662], + CellLabel->"In[341]:="], Cell[BoxData[ FormBox[ @@ -375,48 +344,53 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"DiracSlash", - CellLabel->"Out[5]=", - CellID->1319428342] + CellLabel->"Out[341]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"GSD", "[", "p", "]"}]], "Input", + CellLabel->"In[342]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"\[Gamma]", "\[CenterDot]", + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]}], TraditionalForm]], "Output", + CellLabel->"Out[342]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"DiracSlash", "[", "q", "]"}], "//", "StandardForm"}]], "Input", - CellTags->"DiracSlash", - CellLabel->"In[6]:=", - CellID->1554186442], + RowBox[{"FCI", "[", + RowBox[{"GS", "[", "p", "]"}], "]"}], "===", + RowBox[{"DiracSlash", "[", "p", "]"}]}]], "Input", + CellLabel->"In[345]:="], Cell[BoxData[ - RowBox[{"DiracGamma", "[", - RowBox[{"Momentum", "[", "q", "]"}], "]"}]], "Output", - CellTags->"DiracSlash", - CellLabel->"Out[6]//StandardForm=", - CellID->1796628764] + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[345]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"GSD", "[", "p", "]"}], "]"}], "===", RowBox[{"DiracSlash", "[", - RowBox[{"q", ",", - RowBox[{"Dimension", "\[Rule]", "n"}]}], "]"}], "//", - "StandardForm"}]], "Input", - CellTags->"DiracSlash", - CellLabel->"In[7]:=", - CellID->841649305], + RowBox[{"p", ",", + RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]}]], "Input", + CellLabel->"In[346]:="], Cell[BoxData[ - RowBox[{"DiracGamma", "[", - RowBox[{ - RowBox[{"Momentum", "[", - RowBox[{"q", ",", "n"}], "]"}], ",", "n"}], "]"}]], "Output", - CellTags->"DiracSlash", - CellLabel->"Out[7]//StandardForm=", - CellID->59747004] + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[346]="] }, Open ]] }, Open ]], @@ -452,7 +426,7 @@ Cell[BoxData[ InterpretationBox[Cell["XXXX", "ExampleSubsection"], $Line = 0; 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option for DiracSimplify. If set to True the chirality-projectors \ -DiracGamma[6] and DiracGamma[7] are substituted by their definitions." + Cell[BoxData[ + RowBox[{"DiracSubstitute67", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator] inserts the explicit definitions of the chirality \ +projectors ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "6"]], "InlineFormula"], + " and ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "7"]], "InlineFormula"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + " ", + ButtonBox["DiracSubstitute67", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSubstitute67", + ButtonNote->"DiracSubstitute67"], + " is also an option of various FeynCalc functions that handle Dirac \ +algebra." +}], "Notes", + CellID->1827982253], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DiracSubstitute67", "]"}]], "Input", + CellLabel->"In[40]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[40]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -160,20 +190,23 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", + ButtonBox["DiracSubstitute5", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSubstitute5", + ButtonNote->"DiracSubstitute5"], + ", ", ButtonBox["DiracGamma", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracGamma", ButtonNote->"DiracGamma"], ", ", - ButtonBox["DiracSimplify", + ButtonBox["ToDiracGamma67", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], + ButtonData:>"paclet:FeynCalc/ref/ToDiracGamma67", + ButtonNote->"ToDiracGamma67"], "." -}], "Text", - CellTags->"DiracSubstitute67", - CellID->966852186] +}], "SeeAlso", + CellID->655647701] }, Open ]], Cell[CellGroupData[{ @@ -185,6 +218,8 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], +Cell[CellGroupData[{ + Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -200,6 +235,260 @@ Cell[BoxData[ Cell[CellGroupData[{ +Cell[BoxData[ + RowBox[{"DiracGamma", "[", "6", "]"}]], "Input", + CellLabel->"In[45]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["6", + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[45]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSubstitute67", "[", "%", "]"}]], "Input", + CellLabel->"In[46]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + FractionBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], "2"], "+", + FractionBox["1", "2"]}], TraditionalForm]], "Output", + CellLabel->"Out[46]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; 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Whether the trace is evaluated depends on the \ -option DiracTraceEvaluate. Direct trace evaluation should be performed with \ -TR (or Tr). The argument expr may be a product of Dirac matrices or slashes \ -separated by the Mathematica Dot (.).\n\nFor comments regarding ", - Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], - "schemes see the notes for ", - ButtonBox["TR", - BaseStyle->"AddOnsLink", - ButtonData:>"TR", - ButtonNote->"TR"], - "." + RowBox[{"DiracTrace", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]is the head of Dirac traces. By default the trace is not \ +evaluated. The evaluation occurs only when the option ", + ButtonBox["DiracTraceEvaluate", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTraceEvaluate", + ButtonNote->"DiracTraceEvaluate"], + " is set to ", + Cell[BoxData["True"], "InlineFormula"], + ". It is recommended to use ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + ", which will automatically evaluate all Dirac traces in the input \ +expression." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DiracTrace", "]"}]], "Input", + CellLabel->"In[72]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Contract", "\[Rule]", "True"}], ",", + RowBox[{"DiracTraceEvaluate", "\[Rule]", "False"}], ",", + RowBox[{"EpsContract", "\[Rule]", "False"}], ",", + RowBox[{"Expand", "\[Rule]", "True"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "Automatic"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"Mandelstam", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"PairCollect", "\[Rule]", "False"}], ",", + RowBox[{"Sort", "\[Rule]", "True"}], ",", + RowBox[{"Schouten", "\[Rule]", "0"}], ",", + RowBox[{"TraceOfOne", "\[Rule]", "4"}], ",", + RowBox[{"West", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", + + CellLabel->"Out[72]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -172,14 +199,42 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - 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If set to False, DiracTrace remains \ -unevaluated." + " \[LineSeparator]is an option for ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + ", ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + " and some other functions. If set to ", + Cell[BoxData["False"], "InlineFormula"], + ", Dirac traces remain unevaluated." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell[TextData[{ + "For more details, see the documentation for ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + " and ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + "." +}], "Notes", CellID->1067943069] }, Open ]], @@ -160,20 +182,16 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", - ButtonBox["DiracTrace", + ButtonBox["DiracSimplify", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracTrace", - ButtonNote->"DiracTrace"], + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], ", ", - ButtonBox["TR", + ButtonBox["DiracTrace", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/TR", - ButtonNote->"TR"], - "." -}], "Text", - CellTags->"DiracTraceEvaluate", - CellID->1627432666] + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -259,12 +277,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1012, Automatic}, {Automatic, 276}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracTrick.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracTrick.nb index aca82866c..611bd8271 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracTrick.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DiracTrick.nb @@ -118,15 +118,63 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"DiracTrick", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "contracts gamma matrices with each other and performs several \ -simplifications, but no expansion, use Calc or DiracSimplify for \ -non-commutative expansion." + " \[LineSeparator]contracts Dirac matrices with each other and performs \ +several simplifications but no expansions." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + "There are not many cases when a user will need to call this function \ +directly. Use ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + " to achieve maximal simplification of Dirac matrix chains." +}], "Notes"], + +Cell[TextData[{ + "Regarding the treatment of ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " in ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional expressions or the evaluation of expressions with tensors \ +living in different dimensions, see the explanations on the help pages for ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + " and ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + "." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DiracTrick", "]"}]], "Input", + CellLabel->"In[19]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"DiracGammaCombine", "\[Rule]", "False"}], ",", + RowBox[{"Expanding", "\[Rule]", "False"}], ",", + RowBox[{"FCDiracIsolate", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCJoinDOTs", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"InsideDiracTrace", "\[Rule]", "False"}], ",", + RowBox[{"ToDiracGamma67", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[19]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -162,24 +210,42 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["Calc", + ButtonBox["Contract", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Contract", + ButtonNote->"Contract"], + ", ", + ButtonBox["DiracEquation", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Calc", - ButtonNote->"Calc"], + ButtonData:>"paclet:FeynCalc/ref/DiracEquation", + ButtonNote->"DiracEquation"], + ", ", + ButtonBox["DiracGamma", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracGamma", + ButtonNote->"DiracGamma"], ", ", ButtonBox["DiracGammaExpand", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracGammaExpand", - ButtonNote->"DiracGammaExpand"], + ButtonData:>"paclet:FeynCalc/ref/DiracGammaCombine", + ButtonNote->"DiracGammaCombine"], ", ", - ButtonBox["DiracSimplify", + ButtonBox["DiracTrick", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], + ButtonData:>"paclet:FeynCalc/ref/DiracTrick", + ButtonNote->"DiracTrick"], + ", ", + ButtonBox["SirlinSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SirlinSimplify", + ButtonNote->"SirlinSimplify"], + ", ", + ButtonBox["SpinorChainTrick", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorChainTrick", + ButtonNote->"SpinorChainTrick"], "." -}], "Text", - CellTags->"DiracTrick", - CellID->505712200] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -206,37 +272,28 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "DiracTrick", "]"}]], "Input", - CellTags->"DiracTrick", - CellLabel->"In[1]:=", - CellID->1322032984], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Expanding", "\[Rule]", "False"}], "}"}], - TraditionalForm]], "Output", - CellTags->"DiracTrick", - CellLabel->"Out[1]=", - CellID->781797726] -}, Open ]], - -Cell["This is a string of Dirac matrices in four dimensions. 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RowBox[{"DoPolarizationSums", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "sums over vector polarizations for expressions with a factor of the form\n\ -Pair[LorentzIndex[rho1_], Momentum[Polarization[p_, -I]]]*\n\ -Pair[LorentzIndex[rho2_], Momentum[Polarization[p_, I]]]." + RowBox[{"DoPolarizationSums", "[", + RowBox[{"exp", ",", "k", ",", "n"}], "]"}]], "InlineFormula"], + " \[LineSeparator]sums over physical (transverse) polarizations of an \ +external massless vector boson with momentum ", + Cell[BoxData["k"], "InlineFormula"], + ", where ", + Cell[BoxData["n"], "InlineFormula"], + " is an auxiliary 4-vector from the gauge-dependent polarization sum \ +formula.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"DoPolarizationSums", "[", + RowBox[{"exp", ",", "k", ",", "0"}], "]"}]], "InlineFormula"], + " \[LineSeparator]replaces the polarization sum of an external massless \ +vector boson with momentum ", + Cell[BoxData["k"], "InlineFormula"], + " by ", + Cell[BoxData[ + RowBox[{"-", + SuperscriptBox["g", "\[Mu]\[Nu]"]}]], "InlineFormula"], + ". This corresponds to the summation over all four polarizations, including \ +the unphysical ones.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"DoPolarizationSums", "[", + RowBox[{"exp", ",", "k"}], "]"}]], "InlineFormula"], + " \[LineSeparator]sums over the three polarizations of an external massive \ +vector boson with momentum ", + Cell[BoxData["k"], "InlineFormula"], + " and mass ", + Cell[BoxData[ + SuperscriptBox["k", "2"]], "InlineFormula"], + "." }], "Usage", - CellID->982511436], + CellID->2010081510], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DoPolarizationSums", "]"}]], "Input", + CellLabel->"In[39]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Contract", "\[Rule]", "True"}], ",", + RowBox[{"ExtraFactor", "\[Rule]", "1"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"GaugeTrickN", "\[Rule]", 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CellID->407288908], Cell[BoxData[ @@ -238,10 +253,15 @@ Cell[BoxData[ RowBox[{"c", " ", "e", " ", "z"}], "+", RowBox[{"c", " ", "f", " ", "z"}]}], TraditionalForm]], "Output", CellTags->"DotExpand", - CellLabel->"Out[1]=", - CellID->887725401] + CellLabel->"Out[131]="] }, Open ]], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + Cell[BoxData[ RowBox[{ RowBox[{"DeclareNonCommutative", "/@", @@ -249,7 +269,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "f"}], "}"}]}], ";"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[2]:=", + CellLabel->"In[132]:=", CellID->1021626920], Cell[CellGroupData[{ @@ -264,7 +284,7 @@ Cell[BoxData[ RowBox[{"c", " ", "z"}]}], ",", RowBox[{"d", "+", "e", "+", "f"}]}], "]"}], "]"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[3]:=", + CellLabel->"In[133]:=", CellID->587871772], Cell[BoxData[ @@ -289,8 +309,7 @@ Cell[BoxData[ RowBox[{"z", " ", RowBox[{"c", ".", "f"}]}]}], TraditionalForm]], "Output", CellTags->"DotExpand", - CellLabel->"Out[3]=", - CellID->70533327] + CellLabel->"Out[133]="] }, Open ]], Cell[BoxData[ @@ -300,8 +319,15 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "f"}], "}"}]}], ";"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[4]:=", - CellID->1926968700], + CellLabel->"In[134]:=", + CellID->1926968700] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], Cell[CellGroupData[{ @@ -315,7 +341,7 @@ Cell[BoxData[ RowBox[{"c", " ", "z"}]}], ",", RowBox[{"d", "+", "e", "+", "f"}]}], "]"}], "]"}]], "Input", CellTags->"DotExpand", - CellLabel->"In[5]:=", + CellLabel->"In[135]:=", CellID->1551070412], Cell[BoxData[ @@ -331,8 +357,8 @@ Cell[BoxData[ RowBox[{"c", " ", "e", " ", "z"}], "+", RowBox[{"c", " ", "f", " ", "z"}]}], TraditionalForm]], "Output", CellTags->"DotExpand", - CellLabel->"Out[5]=", - CellID->283503340] + CellLabel->"Out[135]="] +}, Open ]] }, Open ]] }, Open ]], @@ -397,12 +423,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{Automatic, 234}, {Automatic, 71}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DotPower.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DotPower.nb index b31ef722c..1470f7f5d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DotPower.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DotPower.nb @@ -160,15 +160,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["DotSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DotSimplify", ButtonNote->"DotSimplify"], "." -}], "Text", - CellTags->"DotPower", - CellID->1936501485] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,9 +254,11 @@ WindowSize->{700, 770}, WindowMargins->{{-10, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DotProduct.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DotProduct.nb deleted file mode 100644 index 0f789ea38..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DotProduct.nb +++ /dev/null @@ -1,305 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/DotProduct", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["DotProduct", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData[ - RowBox[{"DotProduct", "[", - RowBox[{"x", ",", " ", "y"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "denotes the three-dimensional dot-product. If x and y have Head List, \ -DotProduct[x, a] (where a is a vector) performs Sum[ x[[k]] a[[k]], {k, 0, \ -3}]." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - ButtonBox["CrossProduct", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/CrossProduct", - ButtonNote->"CrossProduct"], - ", ", - ButtonBox["ThreeVector", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/ThreeVector", - ButtonNote->"ThreeVector"], - "." -}], "Text", - CellTags->"DotProduct", - CellID->712758366] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"DotProduct", "[", - RowBox[{ - RowBox[{"ThreeVector", "[", "a", "]"}], ",", - RowBox[{"3", - RowBox[{"ThreeVector", "[", "b", "]"}]}]}], "]"}]], "Input", - CellTags->"DotProduct", - CellLabel->"In[1]:=", - CellID->1589628961], - -Cell[BoxData[ - FormBox[ - RowBox[{"3", " ", - RowBox[{"(", - RowBox[{ - FormBox[ - OverscriptBox["a", "\[RightVector]"], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - OverscriptBox["b", "\[RightVector]"], - TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", - CellTags->"DotProduct", - CellLabel->"Out[1]=", - CellID->114728018] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DotSimplify.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DotSimplify.nb index da83f52d8..5f4d8119a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DotSimplify.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DotSimplify.nb @@ -117,17 +117,69 @@ Cell["DotSimplify", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"DotSimplify", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "expands and reorders noncommutative terms in expr. Simplifying relations \ -may be specified by the option DotSimplifyRelations or by Commutator and \ -AntiCommutator definitions. Whether expr is expanded noncommutatively depends \ -on the option Expanding." + RowBox[{"DotSimplify", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]expands and reorders noncommutative terms in ", + Cell[BoxData["exp"], "InlineFormula"], + ". " }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + "Simplifying relations may be specified by the option ", + ButtonBox["DotSimplifyRelations", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DotSimplifyRelations", + ButtonNote->"DotSimplifyRelations"], + " or by ", + ButtonBox["Commutator", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Commutator", + ButtonNote->"Commutator"], + " and ", + ButtonBox["AntiCommutator", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/AntiCommutator", + ButtonNote->"AntiCommutator"], + " definitions. " +}], "Notes"], + +Cell[TextData[{ + "Whether ", + Cell[BoxData["exp"], "InlineFormula"], + " is expanded noncommutatively depends on the option ", + ButtonBox["Expanding", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Expanding", + ButtonNote->"Expanding"], + "." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "DotSimplify", "]"}]], "Input", + CellTags->"DotSimplify", + CellLabel->"In[136]:=", + CellID->1331874134], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FCJoinDOTs", "\[Rule]", "True"}], ",", + RowBox[{"Expanding", "\[Rule]", "True"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"DotSimplifyRelations", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"DotPower", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"MaxIterations", "\[Rule]", "100"}], ",", + RowBox[{"PreservePropagatorStructures", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"DotSimplify", + CellLabel->"Out[136]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -178,9 +230,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Calc", ButtonNote->"Calc"], "." -}], "Text", - CellTags->"DotSimplify", - CellID->574897097] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -210,41 +260,16 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Options", "[", "DotSimplify", "]"}]], "Input", - CellTags->"DotSimplify", - CellLabel->"In[1]:=", - CellID->1331874134], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", + RowBox[{ + RowBox[{"GA", "[", "\[Mu]", "]"}], ".", + RowBox[{"(", RowBox[{ - RowBox[{"Expanding", "\[Rule]", "True"}], ",", - RowBox[{"DotSimplifyRelations", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"DotPower", "\[Rule]", "False"}], ",", - RowBox[{"CommonTrace", "\[Rule]", "False"}], ",", - RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", + RowBox[{"2", " ", + RowBox[{"GS", "[", "p", "]"}]}], "-", + RowBox[{"GS", "[", "q", "]"}]}], ")"}], ".", + RowBox[{"GA", "[", "\[Nu]", "]"}]}]], "Input", CellTags->"DotSimplify", - CellLabel->"Out[1]=", - CellID->1021382404] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{ - RowBox[{"GA", "[", "\[Mu]", "]"}], ".", - RowBox[{"(", - RowBox[{ - RowBox[{"2", " ", - RowBox[{"GS", "[", "p", "]"}]}], "-", - RowBox[{"GS", "[", "q", "]"}]}], ")"}], ".", - RowBox[{"GA", "[", "\[Nu]", "]"}]}]}]], "Input", - CellTags->"DotSimplify", - CellLabel->"In[2]:=", + CellLabel->"In[137]:=", CellID->1782604794], Cell[BoxData[ @@ -288,16 +313,15 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[2]=", - CellID->97040369] + CellLabel->"Out[137]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DotSimplify", "[", "t1", "]"}]], "Input", + RowBox[{"DotSimplify", "[", "%", "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[3]:=", + CellLabel->"In[138]:=", CellID->1204340698], Cell[BoxData[ @@ -347,27 +371,31 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[3]=", - CellID->715244913] + CellLabel->"Out[138]="] }, Open ]], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[4]:=", + CellLabel->"In[139]:=", CellID->194491386], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", "=", - RowBox[{"a", ".", - RowBox[{"(", - RowBox[{"b", "-", - RowBox[{"z", " ", "c"}]}], ")"}], ".", "a"}]}]], "Input", + RowBox[{"a", ".", + RowBox[{"(", + RowBox[{"b", "-", + RowBox[{"z", " ", "c"}]}], ")"}], ".", "a"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[5]:=", + CellLabel->"In[140]:=", CellID->2117662767], Cell[BoxData[ @@ -377,16 +405,15 @@ Cell[BoxData[ RowBox[{"b", "-", RowBox[{"c", " ", "z"}]}], ")"}], ".", "a"}], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[5]=", - CellID->1736919809] + CellLabel->"Out[140]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DotSimplify", "[", "t2", "]"}]], "Input", + RowBox[{"DotSimplify", "[", "%", "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[6]:=", + CellLabel->"In[141]:=", CellID->1117578635], Cell[BoxData[ @@ -396,8 +423,7 @@ Cell[BoxData[ RowBox[{"z", " ", RowBox[{"a", ".", "c", ".", "a"}]}]}], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[6]=", - CellID->1099682282] + CellLabel->"Out[141]="] }, Open ]], Cell[CellGroupData[{ @@ -407,22 +433,25 @@ Cell[BoxData[ RowBox[{"Commutator", "[", RowBox[{"a", ",", "c"}], "]"}], "=", "1"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[7]:=", + CellLabel->"In[142]:=", CellID->1442809361], Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[7]=", - CellID->2070115949] + CellLabel->"Out[142]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DotSimplify", "[", "t2", "]"}]], "Input", + RowBox[{"DotSimplify", "[", + RowBox[{"a", ".", + RowBox[{"(", + RowBox[{"b", "-", + RowBox[{"z", " ", "c"}]}], ")"}], ".", "a"}], "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[8]:=", + CellLabel->"In[143]:=", CellID->1013643835], Cell[BoxData[ @@ -435,24 +464,27 @@ Cell[BoxData[ RowBox[{"c", ".", "a", ".", "a"}], "+", "a"}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[8]=", - CellID->1231130458] + CellLabel->"Out[143]="] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"Commutator", "[", - RowBox[{"a", ",", "c"}], "]"}], "=", "."}]], "Input", + RowBox[{"a", ",", "c"}], "]"}], "=."}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[9]:=", + CellLabel->"In[144]:=", CellID->1466952413], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DotSimplify", "[", "t2", "]"}]], "Input", + RowBox[{"DotSimplify", "[", + RowBox[{"a", ".", + RowBox[{"(", + RowBox[{"b", "-", + RowBox[{"z", " ", "c"}]}], ")"}], ".", "a"}], "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[10]:=", + CellLabel->"In[146]:=", CellID->1037294655], Cell[BoxData[ @@ -462,8 +494,7 @@ Cell[BoxData[ RowBox[{"z", " ", RowBox[{"a", ".", "c", ".", "a"}]}]}], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[10]=", - CellID->918347217] + CellLabel->"Out[146]="] }, Open ]], Cell[CellGroupData[{ @@ -473,22 +504,25 @@ Cell[BoxData[ RowBox[{"AntiCommutator", "[", RowBox[{"b", ",", "a"}], "]"}], "=", "c"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[11]:=", + CellLabel->"In[147]:=", CellID->579521038], Cell[BoxData[ FormBox["c", TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[11]=", - CellID->675731172] + CellLabel->"Out[147]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DotSimplify", "[", "t2", "]"}]], "Input", + RowBox[{"DotSimplify", "[", + RowBox[{"a", ".", + RowBox[{"(", + RowBox[{"b", "-", + RowBox[{"z", " ", "c"}]}], ")"}], ".", "a"}], "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[12]:=", + CellLabel->"In[148]:=", CellID->164431463], Cell[BoxData[ @@ -500,30 +534,33 @@ Cell[BoxData[ RowBox[{"a", ".", "c", ".", "a"}]}], "+", RowBox[{"a", ".", "c"}]}], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[12]=", - CellID->412911369] + CellLabel->"Out[148]="] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"AntiCommutator", "[", - RowBox[{"b", ",", "a"}], "]"}], "=", "."}]], "Input", + RowBox[{"b", ",", "a"}], "]"}], "=."}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[13]:=", + CellLabel->"In[149]:=", CellID->216404314], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DotSimplify", "[", - RowBox[{"t2", ",", + RowBox[{ + RowBox[{"a", ".", + RowBox[{"(", + RowBox[{"b", "-", + RowBox[{"z", " ", "c"}]}], ")"}], ".", "a"}], ",", RowBox[{"DotSimplifyRelations", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"a", ".", "c"}], "\[Rule]", RowBox[{"1", "/", "z"}]}], "}"}]}]}], "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[14]:=", + CellLabel->"In[152]:=", CellID->2011362420], Cell[BoxData[ @@ -532,14 +569,25 @@ Cell[BoxData[ RowBox[{"a", ".", "b", ".", "a"}], "-", "a"}], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[14]=", - CellID->1420474961] + CellLabel->"Out[152]="] }, Open ]], +Cell[BoxData[ + RowBox[{"UnDeclareNonCommutative", "[", + RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Input", + CellLabel->"In[153]:="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", "x", "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[15]:=", + CellLabel->"In[169]:=", CellID->1063178346], Cell[CellGroupData[{ @@ -547,16 +595,12 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DotSimplify", "[", RowBox[{"x", ".", "x", ".", "x"}], "]"}]], "Input", - CellTags->"DotSimplify", - CellLabel->"In[16]:=", - CellID->1173966576], + CellLabel->"In[170]:="], Cell[BoxData[ FormBox[ - SuperscriptBox["x", "3"], TraditionalForm]], "Output", - CellTags->"DotSimplify", - CellLabel->"Out[16]=", - CellID->629656626] + RowBox[{"x", ".", "x", ".", "x"}], TraditionalForm]], "Output", + CellLabel->"Out[170]="] }, Open ]], Cell[CellGroupData[{ @@ -565,25 +609,24 @@ Cell[BoxData[ RowBox[{"DotSimplify", "[", RowBox[{ RowBox[{"x", ".", "x", ".", "x"}], ",", - RowBox[{"DotPower", "\[Rule]", "False"}]}], "]"}]], "Input", + RowBox[{"DotPower", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[17]:=", - CellID->49078014], + CellLabel->"In[171]:=", + CellID->1173966576], Cell[BoxData[ FormBox[ SuperscriptBox["x", "3"], TraditionalForm]], "Output", CellTags->"DotSimplify", - CellLabel->"Out[17]=", - CellID->316863354] + CellLabel->"Out[171]="] }, Open ]], Cell[BoxData[ - RowBox[{"UnDeclareNonCommutative", "[", - RowBox[{"a", ",", "b", ",", "c", ",", "x"}], "]"}]], "Input", + RowBox[{"UnDeclareNonCommutative", "[", "x", "]"}]], "Input", CellTags->"DotSimplify", - CellLabel->"In[18]:=", + CellLabel->"In[172]:=", CellID->1813929769] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -647,12 +690,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{Automatic, 268}, {Automatic, -35}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DotSimplifyRelations.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DotSimplifyRelations.nb index e4c181319..3bf4f50a8 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DotSimplifyRelations.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DotSimplifyRelations.nb @@ -161,15 +161,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["DotSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DotSimplify", ButtonNote->"DotSimplify"], "." -}], "Text", - CellTags->"DotSimplifyRelations", - CellID->1069685300] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -255,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{817, Automatic}, {Automatic, 63}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DummyIndex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DummyIndex.nb index 531c943cb..73804d0e4 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/DummyIndex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DummyIndex.nb @@ -160,15 +160,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["CovariantD", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/CovariantD", ButtonNote->"CovariantD"], "." -}], "Text", - CellTags->"DummyIndex", - CellID->1154365207] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{818, Automatic}, {Automatic, 142}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/DummyIndexFreeQ.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/DummyIndexFreeQ.nb new file mode 100644 index 000000000..1a7e4e22e --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/DummyIndexFreeQ.nb @@ -0,0 +1,473 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/DummyIndexFreeQ", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["DummyIndexFreeQ", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"DummyIndexFreeQ", "[", + RowBox[{"exp", ",", + RowBox[{"{", + RowBox[{"head1", ",", "head2", ",", "..."}], "}"}]}], "]"}]], + "InlineFormula"], + " \[LineSeparator]returns True if the expression contains dummy indices with \ +heads head1, head2, ... and False otherwise. As always in FeynCalc, Einstein \ +summation convention is implicitly assumed. The function is optimized for \ +large expressions, i.e. it is not so good as a criterion in e.g. Select" +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell[TextData[{ + ButtonBox["FCRenameDummyIndices", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FCRenameDummyIndices", + ButtonNote->"FCRenameDummyIndices"], + ", ", + ButtonBox["Contract", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Contract", + ButtonNote->"Contract"], + ", ", + ButtonBox["FreeIndexFreeQ", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FreeIndexFreeQ", + ButtonNote->"FreeIndexFreeQ"], + "." +}], "SeeAlso", + CellID->1732330916] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCI", "[", + RowBox[{ + RowBox[{"FV", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}], " ", + RowBox[{"FV", "[", + RowBox[{"q", ",", "\[Nu]"}], "]"}]}], "]"}]], "Input", + CellLabel->"In[662]:=", + CellID->953326827], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[662]=", + CellID->1392220727] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DummyIndexFreeQ", "[", + RowBox[{"%", ",", + RowBox[{"{", "LorentzIndex", "}"}]}], "]"}]], "Input", + CellLabel->"In[663]:=", + CellID->1482247787], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[663]=", + CellID->600599141] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCI", "[", + RowBox[{ + RowBox[{"FV", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}], " ", + RowBox[{"FV", "[", + RowBox[{"q", ",", "\[Mu]"}], "]"}]}], "]"}]], "Input", + CellLabel->"In[664]:=", + CellID->950756213], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[664]=", + CellID->600641716] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DummyIndexFreeQ", "[", + RowBox[{"%", ",", + RowBox[{"{", "LorentzIndex", "}"}]}], "]"}]], "Input", + CellLabel->"In[665]:=", + CellID->1892034700], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + CellLabel->"Out[665]=", + CellID->494121601] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCI", "[", + RowBox[{"SUNT", "[", + RowBox[{"a", ",", "b"}], "]"}], "]"}]], "Input", + CellLabel->"In[670]:=", + CellID->1754662751], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["T", + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["T", + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[670]=", + CellID->1021516466] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DummyIndexFreeQ", "[", + RowBox[{"%", ",", + RowBox[{"{", "SUNIndex", "}"}]}], "]"}]], "Input", + CellLabel->"In[671]:=", + CellID->1812674747], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[671]=", + CellID->1193808511] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCI", "[", + RowBox[{"SUNT", "[", + RowBox[{"a", ",", "a"}], "]"}], "]"}]], "Input", + CellLabel->"In[672]:=", + CellID->785933249], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["T", + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["T", + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[672]=", + CellID->424951304] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DummyIndexFreeQ", "[", + RowBox[{"%", ",", + RowBox[{"{", "SUNIndex", "}"}]}], "]"}]], "Input", + CellLabel->"In[673]:=", + CellID->293653821], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + CellLabel->"Out[673]=", + CellID->424642719] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{620, Automatic}, {95, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Eps.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Eps.nb index c57b928f7..4c5750f7e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Eps.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Eps.nb @@ -167,6 +167,11 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ + ButtonBox["EpsContract", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/EpsContract", + ButtonNote->"EpsContract"], + ", ", ButtonBox["EpsEvaluate", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/EpsEvaluate", @@ -181,15 +186,8 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/LCD", ButtonNote->"LCD"], - ", ", - ButtonBox["LeviCivita", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LeviCivita", - ButtonNote->"LeviCivita"], "." -}], "Text", - CellTags->"Eps", - CellID->328152737] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,23 +216,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Eps", "]"}]], "Input", - CellTags->"Eps", - CellLabel->"In[4]:=", - CellID->1709394854], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Dimension", "\[Rule]", "4"}], "}"}], TraditionalForm]], "Output", - CellTags->"Eps", - CellLabel->"Out[4]=", - CellID->587042521] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"Eps", "[", RowBox[{ @@ -243,12 +224,13 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}]}], "]"}]], "Input", CellTags->"Eps", - CellLabel->"In[5]:=", + CellLabel->"In[674]:=", CellID->882253219], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -267,8 +249,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[5]=", - CellID->1273521224] + CellLabel->"Out[674]="] }, Open ]], Cell[CellGroupData[{ @@ -281,12 +262,13 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}]}], "]"}]], "Input", CellTags->"Eps", - CellLabel->"In[6]:=", + CellLabel->"In[675]:=", CellID->1187356604], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ OverscriptBox[ @@ -306,8 +288,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[6]=", - CellID->1062644924] + CellLabel->"Out[675]="] }, Open ]], Cell[CellGroupData[{ @@ -318,81 +299,71 @@ Cell[BoxData[ RowBox[{"b", ",", "a", ",", "c", ",", "d"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"Eps", - CellLabel->"In[7]:=", + CellLabel->"In[676]:=", CellID->2026742577], -Cell[BoxData[ - RowBox[{"-", - RowBox[{"Eps", "[", - RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}]}]], "Output", - CellTags->"Eps", - CellLabel->"Out[7]//StandardForm=", - CellID->1877955055] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"Eps", "[", - RowBox[{"0", ",", "1", ",", "2", ",", "3"}], "]"}]], "Input", + RowBox[{"b", ",", "a", ",", "c", ",", "d"}], "]"}]], "Output", CellTags->"Eps", - CellLabel->"In[8]:=", - CellID->1867659172], - -Cell[BoxData[ - FormBox["1", TraditionalForm]], "Output", - CellTags->"Eps", - CellLabel->"Out[8]=", - CellID->76823232] + CellLabel->"Out[676]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Eps", "[", - RowBox[{"1", ",", "0", ",", "2", ",", "3"}], "]"}]], "Input", + RowBox[{ + RowBox[{"ExplicitLorentzIndex", "[", "0", "]"}], ",", + RowBox[{"ExplicitLorentzIndex", "[", "1", "]"}], ",", + RowBox[{"ExplicitLorentzIndex", "[", "2", "]"}], ",", + RowBox[{"ExplicitLorentzIndex", "[", "3", "]"}]}], "]"}]], "Input", CellTags->"Eps", - CellLabel->"In[9]:=", - CellID->272160740], + CellLabel->"In[677]:=", + CellID->1867659172], Cell[BoxData[ FormBox[ - RowBox[{"-", "1"}], TraditionalForm]], "Output", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox["0", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["1", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["2", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["3", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[9]=", - CellID->94949868] + CellLabel->"Out[677]="] }, Open ]], -Cell[BoxData[ - RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "4"}]}], "]"}], ";"}]], "Input", - CellTags->"Eps", - CellLabel->"In[10]:=", - CellID->1590807400], - Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a1", " ", "=", - RowBox[{"Eps", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Sigma]", ",", "D"}], "]"}]}], "]"}]}]], "Input", + RowBox[{"Eps", "[", + RowBox[{ + RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}]}], "]"}]], "Input", CellTags->"Eps", - CellLabel->"In[11]:=", + CellLabel->"In[683]:=", CellID->49792760], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -411,57 +382,46 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[11]=", - CellID->766535201] + CellLabel->"Out[683]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Contract", "[", - RowBox[{"a1", " ", "a1"}], "]"}]], "Input", + RowBox[{"%", " ", "%"}], "]"}]], "Input", CellTags->"Eps", - CellLabel->"In[12]:=", + CellLabel->"In[684]:=", CellID->1112439860], Cell[BoxData[ FormBox[ RowBox[{"-", "24"}], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[12]=", - CellID->2017064115] + CellLabel->"Out[684]="] }, Open ]], -Cell[BoxData[ - RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], ";"}]], "Input", - CellTags->"Eps", - CellLabel->"In[13]:=", - CellID->578443879], - Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a2", " ", "=", - RowBox[{"Eps", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Sigma]", ",", "D"}], "]"}]}], "]"}]}]], "Input", - CellTags->"Eps", - CellLabel->"In[14]:=", + RowBox[{"Eps", "[", + RowBox[{ + RowBox[{"LorentzIndex", "[", + RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", + RowBox[{"LorentzIndex", "[", + RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", + RowBox[{"LorentzIndex", "[", + RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", + RowBox[{"LorentzIndex", "[", + RowBox[{"\[Sigma]", ",", "D"}], "]"}]}], "]"}]], "Input", + CellTags->"Eps", + CellLabel->"In[685]:=", CellID->864825422], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -480,8 +440,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[14]=", - CellID->721475866] + CellLabel->"Out[685]="] }, Open ]], Cell[CellGroupData[{ @@ -489,9 +448,9 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Contract", "[", - RowBox[{"a2", " ", "a2"}], "]"}], "//", "Factor2"}]], "Input", + RowBox[{"%", " ", "%"}], "]"}], "//", "Factor2"}]], "Input", CellTags->"Eps", - CellLabel->"In[15]:=", + CellLabel->"In[686]:=", CellID->225723746], Cell[BoxData[ @@ -504,27 +463,25 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"3", "-", "D"}], ")"}], " ", "D"}], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[15]=", - CellID->943115930] + CellLabel->"Out[686]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"g5", "=", + RowBox[{ RowBox[{ + RowBox[{"-", + FractionBox["\[ImaginaryI]", "24"]}], RowBox[{ - RowBox[{"-", - FractionBox["\[ImaginaryI]", "24"]}], - RowBox[{ - RowBox[{"LCD", "[", - RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Alpha]"}], "]"}], - ".", - RowBox[{"GAD", "[", - RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Alpha]"}], - "]"}]}]}], "//", "FCI"}]}]], "Input", - CellTags->"Eps", - CellLabel->"In[16]:=", + RowBox[{"LCD", "[", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Alpha]"}], "]"}], + ".", + RowBox[{"GAD", "[", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Alpha]"}], + "]"}]}]}], "//", "FCI"}]], "Input", + CellTags->"Eps", + CellLabel->"In[690]:=", CellID->1182317355], Cell[BoxData[ @@ -533,7 +490,8 @@ Cell[BoxData[ RowBox[{"-", FractionBox["1", "24"]}], " ", "\[ImaginaryI]", " ", RowBox[{ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -572,41 +530,39 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[16]=", - CellID->338258002] + CellLabel->"Out[690]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"g5p", "=", + RowBox[{ RowBox[{ + RowBox[{"-", + FractionBox["\[ImaginaryI]", "24"]}], " ", RowBox[{ - RowBox[{"-", - FractionBox["\[ImaginaryI]", "24"]}], " ", - RowBox[{ - RowBox[{"LCD", "[", - RowBox[{ - SuperscriptBox["\[Mu]", "\[Prime]", - MultilineFunction->None], ",", - SuperscriptBox["\[Nu]", "\[Prime]", - MultilineFunction->None], ",", - SuperscriptBox["\[Rho]", "\[Prime]", - MultilineFunction->None], ",", - SuperscriptBox["\[Alpha]", "\[Prime]", - MultilineFunction->None]}], "]"}], ".", - RowBox[{"GAD", "[", - RowBox[{ - SuperscriptBox["\[Mu]", "\[Prime]", - MultilineFunction->None], ",", - SuperscriptBox["\[Nu]", "\[Prime]", - MultilineFunction->None], ",", - SuperscriptBox["\[Rho]", "\[Prime]", - MultilineFunction->None], ",", - SuperscriptBox["\[Alpha]", "\[Prime]", - MultilineFunction->None]}], "]"}]}]}], "//", "FCI"}]}]], "Input", - CellTags->"Eps", - CellLabel->"In[17]:=", + RowBox[{"LCD", "[", + RowBox[{ + SuperscriptBox["\[Mu]", "\[Prime]", + MultilineFunction->None], ",", + SuperscriptBox["\[Nu]", "\[Prime]", + MultilineFunction->None], ",", + SuperscriptBox["\[Rho]", "\[Prime]", + MultilineFunction->None], ",", + SuperscriptBox["\[Alpha]", "\[Prime]", + MultilineFunction->None]}], "]"}], ".", + RowBox[{"GAD", "[", + RowBox[{ + SuperscriptBox["\[Mu]", "\[Prime]", + MultilineFunction->None], ",", + SuperscriptBox["\[Nu]", "\[Prime]", + MultilineFunction->None], ",", + SuperscriptBox["\[Rho]", "\[Prime]", + MultilineFunction->None], ",", + SuperscriptBox["\[Alpha]", "\[Prime]", + MultilineFunction->None]}], "]"}]}]}], "//", "FCI"}]], "Input", + CellTags->"Eps", + CellLabel->"In[691]:=", CellID->1736669356], Cell[BoxData[ @@ -615,7 +571,8 @@ Cell[BoxData[ RowBox[{"-", FractionBox["1", "24"]}], " ", "\[ImaginaryI]", " ", RowBox[{ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox[ @@ -670,20 +627,16 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[17]=", - CellID->1568766861] + CellLabel->"Out[691]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"g52", "=", - RowBox[{"Factor2", "[", - RowBox[{"Calc", "[", - RowBox[{"g5", ".", "g5p"}], "]"}], "]"}]}]], "Input", - CellTags->"Eps", - CellLabel->"In[18]:=", - CellID->1776301198], + RowBox[{ + RowBox[{"DiracSimplify", "[", + RowBox[{"%", ".", "%%"}], "]"}], "//", "Factor2"}]], "Input", + CellLabel->"In[692]:="], Cell[BoxData[ FormBox[ @@ -696,34 +649,23 @@ Cell[BoxData[ RowBox[{"2", "-", "D"}], ")"}], " ", RowBox[{"(", RowBox[{"3", "-", "D"}], ")"}], " ", "D"}], TraditionalForm]], "Output", - CellTags->"Eps", - CellLabel->"Out[18]=", - CellID->1865773591] + CellLabel->"Out[692]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"g52", "/.", + RowBox[{"%", "/.", RowBox[{"D", "\[Rule]", "4"}]}]], "Input", CellTags->"Eps", - CellLabel->"In[19]:=", + CellLabel->"In[693]:=", CellID->505384444], Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"Eps", - CellLabel->"Out[19]=", - CellID->82320275] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"a1", ",", "a2", ",", "g5", ",", "g5p", ",", "g52"}], - "]"}]], "Input", - CellTags->"Eps", - CellLabel->"In[20]:=", - CellID->1000155621] + CellLabel->"Out[693]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -787,9 +729,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1072, Automatic}, {Automatic, 181}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsChisholm.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsChisholm.nb index 52dc4f928..51ad08119 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsChisholm.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsChisholm.nb @@ -117,15 +117,30 @@ Cell["EpsChisholm", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"EpsChisholm", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "substitutes for a gamma matrix contracted with a Levi-Civita tensor (Eps) \ -the Chisholm identity." + RowBox[{"EpsChisholm", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]applies the Chisholm identiy to a Dirac matrix contracted \ +with a Levi-Civita tensor" }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "EpsChisholm", "]"}]], "Input", + CellLabel->"In[54]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"DiracTrick", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCJoinDOTs", "\[Rule]", "True"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[54]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -165,10 +180,18 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Chisholm", ButtonNote->"Chisholm"], - "." -}], "Text", - CellTags->"EpsChisholm", - CellID->2052423258] + ", ", + ButtonBox["Eps", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Eps", + ButtonNote->"Eps"], + ", ", + ButtonBox["DiracGamma", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracGamma", + ButtonNote->"DiracGamma"] +}], "SeeAlso", + CellID->655647701] }, Open ]], Cell[CellGroupData[{ @@ -198,13 +221,60 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Chisholm", "[", - RowBox[{"GA", "[", + RowBox[{ + RowBox[{"LC", "[", RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], - "]"}]], "Input", - CellTags->"EpsChisholm", - CellLabel->"In[1]:=", - CellID->1696563627], + RowBox[{"GA", "[", + RowBox[{"\[Sigma]", ",", "5"}], "]"}]}]], "Input", + CellLabel->"In[55]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], + TraditionalForm]}], " ", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]], + TraditionalForm]}], TraditionalForm]], "Output", + CellLabel->"Out[55]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"EpsChisholm", "[", "%", "]"}]], "Input", + CellLabel->"In[56]:="], Cell[BoxData[ FormBox[ @@ -215,173 +285,76 @@ Cell[BoxData[ SuperscriptBox[ OverscriptBox["\[Gamma]", "_"], FormBox[ - FormBox["$MU$6147", + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], ".", SuperscriptBox[ OverscriptBox["\[Gamma]", "_"], FormBox[ - FormBox["\[Sigma]", + FormBox["\[Nu]", TraditionalForm], TraditionalForm]], ".", SuperscriptBox[ OverscriptBox["\[Gamma]", "_"], - FormBox["5", - TraditionalForm]]}], " ", - SuperscriptBox["\[Epsilon]", - RowBox[{ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], FormBox[ FormBox["\[Rho]", TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["$MU$6147", - TraditionalForm], - TraditionalForm]}]]}]}], "+", - RowBox[{ - RowBox[{ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], + TraditionalForm]]}]}]}], "+", + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - FormBox["\[Rho]", + FormBox["\[Mu]", TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], + TraditionalForm], FormBox[ - FormBox["\[Sigma]", + FormBox["\[Nu]", TraditionalForm], - TraditionalForm]]}], " ", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", - RowBox[{ - RowBox[{ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], + TraditionalForm]}]]}], "-", + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - FormBox["\[Nu]", + FormBox["\[Mu]", TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], + TraditionalForm], FormBox[ - FormBox["\[Sigma]", + FormBox["\[Rho]", TraditionalForm], - TraditionalForm]]}], " ", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "+", - RowBox[{ - RowBox[{ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], + TraditionalForm]}]]}], "+", + RowBox[{"\[ImaginaryI]", " ", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - FormBox["\[Mu]", + FormBox["\[Nu]", TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], + TraditionalForm], FormBox[ - FormBox["\[Sigma]", + FormBox["\[Rho]", TraditionalForm], - TraditionalForm]]}], " ", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}]}], TraditionalForm]], "Output", - CellTags->"EpsChisholm", - CellLabel->"Out[1]=", - CellID->378756372] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"EpsChisholm", "[", "%", "]"}]], "Input", - CellTags->"EpsChisholm", - CellLabel->"In[2]:=", - CellID->1192722750], - -Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]]}], TraditionalForm]], "Output", - CellTags->"EpsChisholm", - CellLabel->"Out[2]=", - CellID->1298618997] + TraditionalForm]}]]}]}], TraditionalForm]], "Output", + CellLabel->"Out[56]="] }, Open ]] }, Open ]], @@ -446,12 +419,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1232, Automatic}, {Automatic, 192}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsContract.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsContract.nb index 9fbe33481..073917d89 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsContract.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsContract.nb @@ -116,11 +116,11 @@ Cell["EpsContract", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], - Cell[BoxData["EpsContract"], "InlineFormula"], - " \[LineSeparator]", - "is an option of Contract specifying whether Levi-Civita tensors Eps[...] \ -will be contracted, i.e., products of two Eps are replaced via the \ -determinant formula." + Cell[BoxData[ + RowBox[{"EpsContract", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]handles contractions of two Levi-Civita tensors. It is \ +also an option of Contract and other functions that specifies whether such \ +contractions should be done or not." }], "Usage", CellID->982511436], @@ -171,9 +171,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Contract", ButtonNote->"Contract"], "." -}], "Text", - CellTags->"EpsContract", - CellID->1380465394] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,24 +201,15 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a1", " ", "=", - RowBox[{"Eps", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Sigma]", ",", "D"}], "]"}]}], "]"}]}]], "Input", - CellTags->"EpsContract", - CellLabel->"In[1]:=", - CellID->1863867389], + RowBox[{"LCD", "[", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], + "]"}]], "Input", + CellLabel->"In[697]:="], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -238,9 +227,54 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", + CellLabel->"Out[697]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"EpsContract", "[", + RowBox[{"%", " ", "%"}], "]"}], "//", "Factor2"}]], "Input", + CellLabel->"In[698]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "-", "D"}], ")"}], " ", + RowBox[{"(", + RowBox[{"2", "-", "D"}], ")"}], " ", + RowBox[{"(", + RowBox[{"3", "-", "D"}], ")"}], " ", "D"}], TraditionalForm]], "Output", + CellLabel->"Out[698]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"Contract", "[", + RowBox[{"%", " ", "%"}], "]"}], "//", "Factor2"}]], "Input", + CellTags->"EpsContract", + CellLabel->"In[699]:=", + CellID->1929247061], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "-", "D"}], ")"}], "2"], " ", + SuperscriptBox[ + RowBox[{"(", + RowBox[{"2", "-", "D"}], ")"}], "2"], " ", + SuperscriptBox[ + RowBox[{"(", + RowBox[{"3", "-", "D"}], ")"}], "2"], " ", + SuperscriptBox["D", "2"]}], TraditionalForm]], "Output", CellTags->"EpsContract", - CellLabel->"Out[1]=", - CellID->1306724827] + CellLabel->"Out[699]="] }, Open ]], Cell[CellGroupData[{ @@ -248,17 +282,21 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Contract", "[", RowBox[{ - RowBox[{"a1", " ", "a1"}], ",", + RowBox[{ + RowBox[{"LCD", "[", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], + "^", "2"}], ",", RowBox[{"EpsContract", "\[Rule]", "False"}]}], "]"}]], "Input", CellTags->"EpsContract", - CellLabel->"In[2]:=", - CellID->1929247061], + CellLabel->"In[700]:=", + CellID->903937612], Cell[BoxData[ FormBox[ SuperscriptBox[ RowBox[{"(", - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -277,27 +315,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], ")"}], "2"], TraditionalForm]], "Output", CellTags->"EpsContract", - CellLabel->"Out[2]=", - CellID->1644037415] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Contract", "[", - RowBox[{ - RowBox[{"a1", " ", "a1"}], ",", - RowBox[{"EpsContract", "\[Rule]", "True"}]}], "]"}]], "Input", - CellTags->"EpsContract", - CellLabel->"In[3]:=", - CellID->903937612], - -Cell[BoxData[ - FormBox[ - RowBox[{"-", "24"}], TraditionalForm]], "Output", - CellTags->"EpsContract", - CellLabel->"Out[3]=", - CellID->848962305] + CellLabel->"Out[700]="] }, Open ]] }, Open ]], @@ -362,12 +380,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1548, Automatic}, {Automatic, 89}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsContractFreeQ.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsContractFreeQ.nb new file mode 100644 index 000000000..d4d0e8019 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsContractFreeQ.nb @@ -0,0 +1,390 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/EpsContractFreeQ", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["EpsContractFreeQ", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"EpsContractFreeQ", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]returns True if the expression contains epsilon tensors \ +that can be contracted with each other. The function is optimized for large \ +expressions, i.e. it is not so good as a criterion in e.g. Select" +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell[TextData[{ + ButtonBox["Contract", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Contract", + ButtonNote->"Contract"], + ", ", + ButtonBox["EpsContract", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/EpsContract", + ButtonNote->"EpsContract"], + "." +}], "SeeAlso", + CellID->14792505] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCI", "[", + RowBox[{"LC", "[", + RowBox[{"p1", ",", "p2", ",", "p3", ",", "p4"}], "]"}], "]"}]], "Input", + CellLabel->"In[701]:=", + CellID->194594739], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox["p1", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["p2", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["p3", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["p4", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", + CellLabel->"Out[701]=", + CellID->216300725] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"EpsContractFreeQ", "[", "%", "]"}]], "Input", + CellLabel->"In[702]:=", + CellID->1135797473], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[702]=", + CellID->900745743] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCI", "[", + RowBox[{ + RowBox[{"LC", "[", + RowBox[{"p1", ",", "p2", ",", "p3", ",", "mu"}], "]"}], " ", + RowBox[{"LC", "[", + RowBox[{"q1", ",", "q2", ",", "q3", ",", "q4"}], "]"}]}], "]"}]], "Input", + + CellLabel->"In[703]:=", + CellID->401856309], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox["p1", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["p2", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["p3", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox["q1", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["q2", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["q3", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["q4", + TraditionalForm], + TraditionalForm]}]]}], TraditionalForm]], "Output", + CellLabel->"Out[703]=", + CellID->172471305] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"EpsContractFreeQ", "[", "%", "]"}]], "Input", + CellLabel->"In[704]:=", + CellID->1103072881], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + CellLabel->"Out[704]=", + CellID->1920409101] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1300, Automatic}, {Automatic, 256}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsDiscard.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsDiscard.nb index 55d16e188..6d0228340 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsDiscard.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsDiscard.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynCalc2FORM", ButtonNote->"FeynCalc2FORM"], "." -}], "Text", - CellTags->"EpsDiscard", - CellID->1847314913] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{933, Automatic}, {Automatic, 132}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsEvaluate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsEvaluate.nb index 1d84457ec..e27971367 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsEvaluate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsEvaluate.nb @@ -118,14 +118,29 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"EpsEvaluate", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "applies total antisymmetry and linearity (w.r.t. Momentum's) to all \ -Levi-Civita tensors (Eps') in expr." + " \[LineSeparator]applies total antisymmetry and linearity (w.r.t. momenta) \ +to all Levi-Civita tensors (Eps') in expr." }], "Usage", CellID->982511436], Cell["XXXX", "Notes", - CellID->1067943069] + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "EpsEvaluate", "]"}]], "Input", + CellLabel->"In[705]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"Momentum", "\[Rule]", "All"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[705]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -171,19 +186,17 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Eps", ButtonNote->"Eps"], ", ", - ButtonBox["LeviCivita", + ButtonBox["LC", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LeviCivita", - ButtonNote->"LeviCivita"], + ButtonData:>"paclet:FeynCalc/ref/LC", + ButtonNote->"LC"], ", ", ButtonBox["Trick", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Trick", ButtonNote->"Trick"], "." -}], "Text", - CellTags->"EpsEvaluate", - CellID->1755604338] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -213,21 +226,24 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Trick", "[", - RowBox[{ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], - " ", - RowBox[{"FourVector", "[", - RowBox[{ - RowBox[{"p", "+", "q"}], ",", "\[Sigma]"}], "]"}]}], "]"}]], "Input", + RowBox[{ + RowBox[{"Contract", "[", + RowBox[{ + RowBox[{"LC", "[", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], + " ", + RowBox[{"FV", "[", + RowBox[{ + RowBox[{"p", "+", "q"}], ",", "\[Sigma]"}], "]"}]}], "]"}], "//", + "MomentumCombine"}]], "Input", CellTags->"EpsEvaluate", - CellLabel->"In[1]:=", + CellLabel->"In[710]:=", CellID->684764895], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -253,8 +269,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"EpsEvaluate", - CellLabel->"Out[1]=", - CellID->440945173] + CellLabel->"Out[710]="] }, Open ]], Cell[CellGroupData[{ @@ -262,13 +277,14 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"EpsEvaluate", "[", "%", "]"}]], "Input", CellTags->"EpsEvaluate", - CellLabel->"In[2]:=", + CellLabel->"In[711]:=", CellID->84932068], Cell[BoxData[ FormBox[ RowBox[{ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -287,7 +303,8 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm]}]], "+", - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -307,8 +324,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"EpsEvaluate", - CellLabel->"Out[2]=", - CellID->352429971] + CellLabel->"Out[711]="] }, Open ]], Cell[CellGroupData[{ @@ -316,34 +332,25 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"StandardForm", "[", "%", "]"}]], "Input", CellTags->"EpsEvaluate", - CellLabel->"In[3]:=", + CellLabel->"In[712]:=", CellID->1124825353], Cell[BoxData[ RowBox[{ RowBox[{"Eps", "[", RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", - RowBox[{"Momentum", "[", "p", "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "+", + RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", + RowBox[{"Momentum", "[", "p", "]"}]}], "]"}], "+", RowBox[{"Eps", "[", RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", - RowBox[{"Momentum", "[", "q", "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]}]], "Output", + RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", + RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]}]], "Output", CellTags->"EpsEvaluate", - CellLabel->"Out[3]//StandardForm=", - CellID->746268781] + CellLabel->"Out[712]//StandardForm="] }, Open ]] }, Open ]], @@ -408,12 +415,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1018, Automatic}, {Automatic, 161}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsUncontract.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsUncontract.nb deleted file mode 100644 index fb9c9ac90..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsUncontract.nb +++ /dev/null @@ -1,268 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/EpsUncontract", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["EpsUncontract", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["EpsUncontract"], "InlineFormula"], - " \[LineSeparator]", - "does Uncontract on scalar products involving Eps." -}], "Usage", - CellID->982511436], - -Cell["XXXX", 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"ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; 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Cell[CellGroupData[{ Cell[BoxData["Epsilon"], "Input", CellTags->"Epsilon", - CellLabel->"In[1]:=", + CellLabel->"In[713]:=", CellID->777209644], Cell[BoxData[ @@ -211,15 +209,12 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm], TraditionalForm]], "Output", CellTags->"Epsilon", - CellLabel->"Out[1]=", - CellID->750039629] + CellLabel->"Out[713]="] }, Open ]], Cell["\<\ Epsilon has no functional properties, but some upvalues are changed:\ -\>", "Text", - CellTags->"Epsilon", - CellID->568077555], +\>", "Notes"], Cell[CellGroupData[{ @@ -242,7 +237,7 @@ Cell[BoxData[ RowBox[{"Re", "[", "Epsilon", "]"}], " ", ">", " ", "0"}]}], "}"}]], "Input", CellTags->"Epsilon", - CellLabel->"In[2]:=", + CellLabel->"In[714]:=", CellID->2127471490], Cell[BoxData[ @@ -251,8 +246,7 @@ Cell[BoxData[ RowBox[{"True", ",", "True", ",", "True", ",", "True", ",", "True"}], "}"}], TraditionalForm]], "Output", CellTags->"Epsilon", - CellLabel->"Out[2]=", - CellID->1912563910] + CellLabel->"Out[714]="] }, Open ]] }, Open ]], @@ -317,12 +311,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1085, Automatic}, {Automatic, 123}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsilonIR.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsilonIR.nb new file mode 100644 index 000000000..6243aef05 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsilonIR.nb @@ -0,0 +1,283 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/EpsilonIR", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["EpsilonIR", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData["EpsilonIR"], "InlineFormula"], + " \[LineSeparator] denotes ", + Cell[BoxData[ + RowBox[{"(", + RowBox[{"D", "-", "4"}], ")"}]], "InlineFormula"], + ", where ", + Cell[BoxData["D"], "InlineFormula"], + " is the number of space-time dimensions." +}], "Usage", + CellID->982511436], + +Cell[TextData[{ + Cell[TextData[ButtonBox["EpsilonIR", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/EpsilonIR"]], "InlineFunctionSans"], + " stands for a small negative number that explicitly regulates only IR \ +divergences." +}], "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData["EpsilonIR"], "Input", + CellLabel->"In[29]:=", + CellID->303667908], + +Cell[BoxData[ + FormBox[ + SubscriptBox["\[CurlyEpsilon]", "IR"], TraditionalForm]], "Output", + CellLabel->"Out[29]=", + CellID->128112661] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{934, Automatic}, {108, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, 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PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsilonUV.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsilonUV.nb new file mode 100644 index 000000000..6b35b1b03 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/EpsilonUV.nb @@ -0,0 +1,283 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/EpsilonUV", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["EpsilonUV", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData["EpsilonUV"], "InlineFormula"], + " \[LineSeparator] denotes ", + Cell[BoxData[ + RowBox[{"(", + RowBox[{"D", "-", "4"}], ")"}]], "InlineFormula"], + ", where ", + Cell[BoxData["D"], "InlineFormula"], + " is the number of space-time dimensions." +}], "Usage", + CellID->982511436], + +Cell[TextData[{ + Cell[TextData[ButtonBox["EpsilonUV", + BaseStyle->"Link", + ButtonData->"paclet:FeynCalc/ref/EpsilonUV"]], "InlineFunctionSans"], + " stands for a small positive number that explicitly regulates only UV \ +divergences." +}], "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData["EpsilonUV"], "Input", + CellLabel->"In[28]:=", + CellID->303667908], + +Cell[BoxData[ + FormBox[ + SubscriptBox["\[CurlyEpsilon]", "UV"], TraditionalForm]], "Output", + CellLabel->"Out[28]=", + CellID->632677437] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], 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CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Expand2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Expand2.nb index 280065dd0..f3a7cd7e0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Expand2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Expand2.nb @@ -191,6 +191,91 @@ Cell[BoxData[ Cell[CellGroupData[{ +Cell[BoxData[ + RowBox[{"Expand2", "[", + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"x1", "+", "x2", "+", "x3"}], ")"}], + RowBox[{"(", + RowBox[{ + RowBox[{"2", "x1"}], "+", + RowBox[{"3", "x2"}]}], ")"}]}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{"y1", "+", "y2", "+", "y3"}], ")"}], + RowBox[{"(", + RowBox[{ + RowBox[{"2", "y1"}], "+", + RowBox[{"3", "y2"}]}], ")"}]}]}], "]"}]], "Input", + CellLabel->"In[717]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"2", " ", + SuperscriptBox["x1", "2"]}], "+", + RowBox[{"5", " ", "x1", " ", "x2"}], "+", + RowBox[{"2", " ", "x1", " ", "x3"}], 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RowBox[{ + RowBox[{"2", " ", "x1"}], "+", + RowBox[{"3", " ", "x2"}]}], ")"}], " ", + RowBox[{"(", + RowBox[{"x1", "+", "x2", "+", "x3"}], ")"}]}], "+", + RowBox[{"2", " ", + SuperscriptBox["y1", "2"]}], "+", + RowBox[{"5", " ", "y1", " ", "y2"}], "+", + RowBox[{"2", " ", "y1", " ", "y3"}], "+", + RowBox[{"3", " ", + SuperscriptBox["y2", "2"]}], "+", + RowBox[{"3", " ", "y2", " ", "y3"}]}], TraditionalForm]], "Output", + CellLabel->"Out[716]="] +}, Open ]], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"Expand2", "[", RowBox[{ @@ -212,7 +297,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x1", ",", "x2"}], "}"}]}], "]"}]], "Input", CellTags->"Expand2", - CellLabel->"In[1]:=", + CellLabel->"In[715]:=", CellID->1988123480], Cell[BoxData[ @@ -234,8 +319,7 @@ Cell[BoxData[ RowBox[{"y1", "+", "y2", "+", "y3"}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"Expand2", - CellLabel->"Out[1]=", - CellID->1449504113] + CellLabel->"Out[715]="] }, Open ]] }, Open ]], @@ -300,12 +384,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{791, Automatic}, {Automatic, 136}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExpandAll2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExpandAll2.nb new file mode 100644 index 000000000..30449166b --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExpandAll2.nb @@ -0,0 +1,336 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/ExpandAll2", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + 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CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["ExpandAll2", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"ExpandAll2", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]", + " is similar to ExpandAll, but much faster on simple structures." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell["Benchmark against the standard ExpandAll", "Notes", + CellID->29146736], + +Cell[BoxData[ + RowBox[{ + RowBox[{"exp", "=", + RowBox[{ + RowBox[{"Sum", "[", + RowBox[{ + RowBox[{"p", "[", "i", "]"}], ",", + RowBox[{"{", + RowBox[{"i", ",", "1", ",", "100"}], "}"}]}], "]"}], " ", + RowBox[{"Sum", "[", + RowBox[{ + RowBox[{"q", "[", "i", "]"}], ",", + RowBox[{"{", + RowBox[{"i", ",", "1", ",", 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CellLabel->"In[721]:=", + CellID->1580956926], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[721]=", + CellID->1145286211] +}, Open ]], + +Cell[BoxData[ + RowBox[{"ClearAll", "[", + RowBox[{"exp", ",", "res1", ",", "res2"}], "]"}]], "Input", + CellLabel->"In[722]:=", + CellID->132487496] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{998, Automatic}, 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", + Cell[BoxData["QuantumField"], "InlineFormula"], + "'s and partial differentiation operators in ", + Cell[BoxData["exp"], "InlineFormula"], + " and applies the Leibniz rule." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "ExpandPartialD", "]"}]], "Input", + CellLabel->"In[59]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"PartialDRelations", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"(", "FeynCalc`ExpandPartialD`Private`a___", ")"}], ".", + RowBox[{"\[PartialD]", "/", "\[PartialD]", + SuperscriptBox[ + FormBox["FeynCalc`ExpandPartialD`Private`x_", + TraditionalForm], + FormBox[ + FormBox["FeynCalc`ExpandPartialD`Private`i_", + TraditionalForm], + TraditionalForm]]}], ".", + RowBox[{"(", "FeynCalc`ExpandPartialD`Private`b___", ")"}]}], + "\[RuleDelayed]", + RowBox[{"DOT", "(", + RowBox[{"FeynCalc`ExpandPartialD`Private`a", ",", + RowBox[{ + SubscriptBox[ + TagBox[ + StyleBox["\<\"\[PartialD]\"\>", + FontSlant->"Italic"], + StyleForm[#, FontSlant -> "Italic"]& ], + TagBox[ + FormBox[ + FormBox["FeynCalc`ExpandPartialD`Private`i", + TraditionalForm], + TraditionalForm], + TraditionalForm, + Editable->True]], "(", + TagBox[ + FormBox[ + RowBox[{ + "FeynCalc`ExpandPartialD`Private`dot", "(", + "FeynCalc`ExpandPartialD`Private`b", ")"}], + TraditionalForm], + TraditionalForm, + Editable->True], ")"}]}], ")"}]}], "}"}]}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[59]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -161,7 +214,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["ExplicitPartialD", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/ExplicitPartialD", @@ -187,9 +239,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RightPartialD", ButtonNote->"RightPartialD"], "." -}], "Text", - CellTags->"ExpandPartialD", - CellID->233477946] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -228,7 +278,7 @@ Cell[BoxData[ RowBox[{"A", ",", RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}]}], "]"}]}]], "Input", CellTags->"ExpandPartialD", - CellLabel->"In[1]:=", + CellLabel->"In[60]:=", CellID->1663995859], Cell[BoxData[ @@ -251,8 +301,7 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"ExpandPartialD", - CellLabel->"Out[1]=", - CellID->1621713620] + CellLabel->"Out[60]="] }, Open ]], Cell[CellGroupData[{ @@ -260,7 +309,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandPartialD", "[", "%", "]"}]], "Input", CellTags->"ExpandPartialD", - CellLabel->"In[2]:=", + CellLabel->"In[61]:=", CellID->42906170], Cell[BoxData[ @@ -272,75 +321,51 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - 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"\[PartialD]"}], FormBox[ FormBox["\[CapitalDelta]", TraditionalForm], - TraditionalForm]], - TraditionalForm], - FormBox[ - SubscriptBox["\[PartialD]", + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], FormBox[ - FormBox["\[CapitalDelta]", + FormBox["\[Mu]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}]}], "-", - RowBox[{"2", " ", - RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], "\[Null]"]}]}]}], "+", - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{ - FormBox[ - SubscriptBox["\[PartialD]", + TraditionalForm]], ")"}], ")"}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[CapitalDelta]", TraditionalForm], - TraditionalForm]], - TraditionalForm], - FormBox[ - SubscriptBox["\[PartialD]", + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], FormBox[ - FormBox["\[CapitalDelta]", + FormBox["\[Rho]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], ".", + TraditionalForm]], ")"}], ")"}]}]}]}], "+", + RowBox[{ + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox["\[Mu]", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + FormBox[ + SubscriptBox["\[PartialD]", + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], + FormBox[ + SubscriptBox["\[PartialD]", + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm]}], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], ")"}]}], "+", + RowBox[{ + RowBox[{"(", + RowBox[{ + FormBox[ + SubscriptBox["\[PartialD]", + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], + FormBox[ + SubscriptBox["\[PartialD]", + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm]], + TraditionalForm]}], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ".", SubscriptBox[ FormBox["A", TraditionalForm], FormBox["\[Rho]", TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"ExpandPartialD", - CellLabel->"Out[7]=", - CellID->1958358113] + CellLabel->"Out[68]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"8", " ", RowBox[{ RowBox[{"LeftRightPartialD", "[", "OPEDelta", "]"}], "^", "3"}]}]], "Input", CellTags->"ExpandPartialD", - CellLabel->"In[8]:=", + CellLabel->"In[69]:=", CellID->302634492], Cell[BoxData[ @@ -586,8 +625,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], "3"]}], TraditionalForm]], "Output", CellTags->"ExpandPartialD", - CellLabel->"Out[8]=", - CellID->1536350589] + CellLabel->"Out[69]="] }, Open ]], Cell[CellGroupData[{ @@ -595,7 +633,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExplicitPartialD", "[", "%", "]"}]], "Input", CellTags->"ExpandPartialD", - CellLabel->"In[9]:=", + CellLabel->"In[70]:=", CellID->1446708912], Cell[BoxData[ @@ -616,8 +654,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], ")"}], "3"], TraditionalForm]], "Output", CellTags->"ExpandPartialD", - CellLabel->"Out[9]=", - CellID->1037199372] + CellLabel->"Out[70]="] }, Open ]], Cell[CellGroupData[{ @@ -625,7 +662,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandPartialD", "[", "%", "]"}]], "Input", CellTags->"ExpandPartialD", - CellLabel->"In[10]:=", + CellLabel->"In[71]:=", CellID->752224], Cell[BoxData[ @@ -711,45 +748,54 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"ExpandPartialD", - CellLabel->"Out[10]=", - CellID->1175162542] + CellLabel->"Out[71]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ - RowBox[{"LeviCivita", "[", + RowBox[{"LC", "[", RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Tau]"}], "]"}], " ", RowBox[{"RightPartialD", "[", RowBox[{"\[Alpha]", ",", "\[Mu]", ",", "\[Beta]", ",", "\[Nu]"}], "]"}]}]], "Input", CellTags->"ExpandPartialD", - CellLabel->"In[11]:=", + CellLabel->"In[72]:=", CellID->623620416], Cell[BoxData[ FormBox[ RowBox[{ - SuperscriptBox["\[Epsilon]", - RowBox[{ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Tau]", - TraditionalForm], - TraditionalForm]}]], " ", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Tau]", + TraditionalForm], + TraditionalForm]}]], + TraditionalForm], " ", RowBox[{ SubscriptBox[ OverscriptBox["\[PartialD]", "\[RightArrow]"], @@ -776,8 +822,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"ExpandPartialD", - CellLabel->"Out[11]=", - CellID->1270626] + CellLabel->"Out[72]="] }, Open ]], Cell[CellGroupData[{ @@ -785,14 +830,14 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandPartialD", "[", "%", "]"}]], "Input", CellTags->"ExpandPartialD", - CellLabel->"In[12]:=", + CellLabel->"In[73]:=", CellID->726282079], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"ExpandPartialD", - CellLabel->"Out[12]=", - CellID->1503936453] + CellLabel->"Out[73]="] +}, Open ]] }, Open ]] }, Open ]], @@ -857,12 +902,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{948, Automatic}, {Automatic, 190}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExpandScalarProduct.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExpandScalarProduct.nb index 8e8edf53d..63e038845 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExpandScalarProduct.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExpandScalarProduct.nb @@ -118,14 +118,32 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"ExpandScalarProduct", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "expands scalar products of sums of momenta in expr. ExpandScalarProduct \ -does not use Expand on expr.\nScalarProductExpand=ExpandScalarProduct." + " \[LineSeparator]expands scalar products of sums of momenta in expr. \ +ExpandScalarProduct does not use Expand on expr." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "ExpandScalarProduct", "]"}]], "Input", + CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, + CellLabel->"In[723]:=", + CellID->668026966], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"EpsEvaluate", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"Full", "\[Rule]", "True"}], ",", + RowBox[{"Momentum", "\[Rule]", "All"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, + CellLabel->"Out[723]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -176,9 +194,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/MomentumCombine", ButtonNote->"MomentumCombine"], "." -}], "Text", - CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellID->2118240248] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -205,30 +221,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellID->2116782470], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "ExpandScalarProduct", "]"}]], "Input", - CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[1]:=", - CellID->668026966], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"FeynCalcInternal", "\[Rule]", "True"}], ",", - RowBox[{"Momentum", "\[Rule]", - RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", - CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[1]=", - CellID->4871317] -}, Open ]], - Cell[CellGroupData[{ Cell[BoxData[ @@ -238,7 +230,7 @@ Cell[BoxData[ RowBox[{"p1", "+", "p2", "+", "p3"}], ",", RowBox[{"p4", "+", "p5", "+", "p6"}]}], "]"}]}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[2]:=", + CellLabel->"In[724]:=", CellID->1575091533], Cell[BoxData[ @@ -247,16 +239,18 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p1", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["p2", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["p3", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p1", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["p2", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["p3", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -265,22 +259,23 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p4", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["p5", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["p6", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p4", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["p5", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["p6", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[2]=", - CellID->831714443] + CellLabel->"Out[724]="] }, Open ]], Cell[CellGroupData[{ @@ -288,7 +283,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "ScalarProductExpand"}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[3]:=", + CellLabel->"In[725]:=", CellID->1729317327], Cell[BoxData[ @@ -412,8 +407,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[3]=", - CellID->1718079082] + CellLabel->"Out[725]="] }, Open ]], Cell[CellGroupData[{ @@ -423,7 +417,7 @@ Cell[BoxData[ RowBox[{"p", ",", RowBox[{"p", "-", "q"}]}], "]"}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[4]:=", + CellLabel->"In[726]:=", CellID->790525557], Cell[BoxData[ @@ -439,19 +433,20 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[4]=", - CellID->1472369643] + CellLabel->"Out[726]="] }, Open ]], Cell[CellGroupData[{ @@ -459,7 +454,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandScalarProduct", "[", "%", "]"}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[5]:=", + CellLabel->"In[727]:=", CellID->171112254], Cell[BoxData[ @@ -485,8 +480,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[5]=", - CellID->638310365] + CellLabel->"Out[727]="] }, Open ]], Cell[CellGroupData[{ @@ -496,35 +490,30 @@ Cell[BoxData[ RowBox[{ RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[6]:=", + CellLabel->"In[728]:=", CellID->1175495192], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm], TraditionalForm]], "Output", + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[6]=", - CellID->323139512] + CellLabel->"Out[728]="] }, Open ]], Cell[CellGroupData[{ @@ -532,55 +521,45 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandScalarProduct", "[", "%", "]"}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[7]:=", + CellLabel->"In[729]:=", CellID->2071711528], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], "-", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], "-", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[7]=", - CellID->1585657038] + CellLabel->"Out[729]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"SP", "[", - RowBox[{ - RowBox[{"p", "-", "q"}], ",", - RowBox[{"q", "-", "r"}]}], "]"}], "//", "FCI"}]], "Input", + RowBox[{"SPD", "[", + RowBox[{ + RowBox[{"p", "-", "q"}], ",", + RowBox[{"q", "-", "r"}]}], "]"}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[8]:=", + CellLabel->"In[732]:=", CellID->1361432400], Cell[BoxData[ @@ -589,13 +568,13 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ + FormBox[ + RowBox[{ FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ + TraditionalForm], "-", FormBox["q", - TraditionalForm], "_"]}], + TraditionalForm]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -604,28 +583,26 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ + FormBox[ + RowBox[{ FormBox["q", - TraditionalForm], "_"], "-", - OverscriptBox[ + TraditionalForm], "-", FormBox["r", - TraditionalForm], "_"]}], + TraditionalForm]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[8]=", - CellID->1532584134] + CellLabel->"Out[732]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"%", "/.", - RowBox[{"Pair", "\[Rule]", "ExpandScalarProduct"}]}]], "Input", + RowBox[{"ExpandScalarProduct", "[", "%", "]"}]], "Input", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"In[9]:=", + CellLabel->"In[733]:=", CellID->1825158757], Cell[BoxData[ @@ -633,52 +610,44 @@ Cell[BoxData[ RowBox[{ RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["p", + TraditionalForm], TraditionalForm], FormBox["\<\"\[CenterDot]\"\>", TraditionalForm], FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], + FormBox["q", + TraditionalForm], TraditionalForm]}], "-", RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["p", + TraditionalForm], TraditionalForm], FormBox["\<\"\[CenterDot]\"\>", TraditionalForm], FormBox[ - OverscriptBox[ - FormBox["r", - TraditionalForm], "_"], + FormBox["r", + TraditionalForm], TraditionalForm]}], "+", RowBox[{ FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], + FormBox["q", + TraditionalForm], TraditionalForm], FormBox["\<\"\[CenterDot]\"\>", TraditionalForm], FormBox[ - OverscriptBox[ - FormBox["r", - TraditionalForm], "_"], + FormBox["r", + TraditionalForm], TraditionalForm]}], "-", SuperscriptBox[ FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], + FormBox["q", + TraditionalForm], TraditionalForm], "2"]}], TraditionalForm]], "Output", CellTags->{"ExpandScalarProduct", "ScalarProductExpand"}, - CellLabel->"Out[9]=", - CellID->334851798] + CellLabel->"Out[733]="] }, Open ]] }, Open ]], @@ -743,12 +712,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1001, Automatic}, {Automatic, 151}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Expanding.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Expanding.nb index 0612d1692..2cfa1942b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Expanding.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Expanding.nb @@ -188,9 +188,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNSimplify", ButtonNote->"SUNSimplify"], "." -}], "Text", - CellTags->"Expanding", - CellID->1847648167] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -276,12 +274,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{928, Automatic}, {Automatic, 187}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Explicit.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Explicit.nb index 1f7a3906f..0ac97c07a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Explicit.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Explicit.nb @@ -174,9 +174,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Twist2GluonOperator", ButtonNote->"Twist2GluonOperator"], "." -}], "Text", - CellTags->"Explicit", - CellID->1892239370] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -211,7 +209,7 @@ Cell[BoxData[ "p", ",", "\[Mu]", ",", "a", ",", " ", "q", ",", "\[Nu]", ",", "b", ",", "r", ",", "\[Rho]", ",", "c"}], "]"}]], "Input", CellTags->"Explicit", - CellLabel->"In[2]:=", + CellLabel->"In[734]:=", CellID->672712555], Cell[BoxData[ @@ -264,8 +262,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", CellTags->"Explicit", - CellLabel->"Out[2]=", - CellID->1698625354] + CellLabel->"Out[734]="] }, Open ]], Cell[CellGroupData[{ @@ -273,7 +270,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Explicit", "[", "%", "]"}]], "Input", CellTags->"Explicit", - CellLabel->"In[3]:=", + CellLabel->"In[735]:=", CellID->1603275034], Cell[BoxData[ @@ -297,143 +294,100 @@ Cell[BoxData[ RowBox[{"(", RowBox[{ RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], " ", + RowBox[{"(", + RowBox[{ + SuperscriptBox[ FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["p", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], + FormBox["\[Rho]", TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - RowBox[{"(", - RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], "-", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["q", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], ")"}]}], "+", - RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ + TraditionalForm]], "-", + SuperscriptBox[ FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["q", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], + FormBox["\[Rho]", TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - RowBox[{"(", + TraditionalForm]]}], ")"}]}], "+", + RowBox[{ + SuperscriptBox["g", RowBox[{ FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["r", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], "-", + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], ")"}]}], "+", - RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]}]], " ", + RowBox[{"(", + RowBox[{ + SuperscriptBox[ FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], + FormBox["r", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], + FormBox["\[Nu]", TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - RowBox[{"(", + TraditionalForm]], "-", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]]}], ")"}]}], "+", + RowBox[{ + SuperscriptBox["g", RowBox[{ FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["q", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], "-", + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["r", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], ")"}]}]}], ")"}]}], TraditionalForm]], "Output", + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]}]], " ", + RowBox[{"(", + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], "-", + SuperscriptBox[ + FormBox[ + FormBox["r", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], ")"}]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"Explicit", - CellLabel->"Out[3]=", - CellID->1578200832] + CellLabel->"Out[735]="] }, Open ]], Cell[CellGroupData[{ @@ -443,7 +397,7 @@ Cell[BoxData[ RowBox[{"p", ",", "\[Mu]", ",", "a", ",", "\[Nu]", ",", "b"}], "]"}]], "Input", CellTags->"Explicit", - CellLabel->"In[4]:=", + CellLabel->"In[736]:=", CellID->221852196], Cell[BoxData[ @@ -484,8 +438,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], ")"}], ")"}]}], TraditionalForm]], "Output", CellTags->"Explicit", - CellLabel->"Out[4]=", - CellID->524953586] + CellLabel->"Out[736]="] }, Open ]], Cell[CellGroupData[{ @@ -493,7 +446,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Explicit", "[", "%", "]"}]], "Input", CellTags->"Explicit", - CellLabel->"In[5]:=", + CellLabel->"In[737]:=", CellID->441966106], Cell[BoxData[ @@ -536,22 +489,16 @@ Cell[BoxData[ RowBox[{"(", RowBox[{ RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], 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CellTags->"Explicit", - CellLabel->"In[6]:=", + CellLabel->"In[738]:=", CellID->3454152], Cell[BoxData[ @@ -698,8 +620,7 @@ Cell[BoxData[ FormBox["a", TraditionalForm]], TraditionalForm]], "Output", CellTags->"Explicit", - CellLabel->"Out[6]=", - CellID->342672291] + CellLabel->"Out[738]="] }, Open ]], Cell[CellGroupData[{ @@ -707,7 +628,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Explicit", "[", "%", "]"}]], "Input", CellTags->"Explicit", - CellLabel->"In[7]:=", + CellLabel->"In[739]:=", CellID->1217375686], Cell[BoxData[ @@ -717,17 +638,11 @@ Cell[BoxData[ SubscriptBox["g", "s"], " ", SuperscriptBox["f", RowBox[{ - FormBox[ - FormBox["a", - TraditionalForm], + FormBox["a", TraditionalForm], - FormBox[ - FormBox["b24", - TraditionalForm], + FormBox["b186", TraditionalForm], - FormBox[ - FormBox["c25", - TraditionalForm], + FormBox["c187", TraditionalForm]}]], " ", RowBox[{ SubsuperscriptBox[ @@ -738,7 +653,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["b24", + FormBox["b186", TraditionalForm], TraditionalForm]], ".", SubsuperscriptBox[ @@ -749,11 +664,12 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["c25", + FormBox["c187", TraditionalForm], TraditionalForm]]}]}], "+", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], @@ -768,9 +684,10 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], @@ -785,10 +702,9 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}]}], TraditionalForm]], "Output", + TraditionalForm]], ")"}]}], TraditionalForm]], "Output", CellTags->"Explicit", - CellLabel->"Out[7]=", - CellID->559853350] + CellLabel->"Out[739]="] }, Open ]] }, Open ]], @@ -853,12 +769,13 @@ Cell[BoxData[ }, 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CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/ExplicitDiracIndex", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + 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for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitLorentzIndex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitLorentzIndex.nb index b00dc9cda..83ef1ca95 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitLorentzIndex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitLorentzIndex.nb @@ -160,7 +160,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["LorentzIndex", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/LorentzIndex", @@ -171,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Pair", ButtonNote->"Pair"], "." -}], "Text", - CellTags->"ExplicitLorentzIndex", - CellID->617137688] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -208,7 +205,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "1", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]], "Input", CellTags->"ExplicitLorentzIndex", - CellLabel->"In[1]:=", + CellLabel->"In[740]:=", CellID->537373072], Cell[BoxData[ @@ -217,20 +214,15 @@ Cell[BoxData[ OverscriptBox["g", "_"], RowBox[{ FormBox[ - FormBox[ - FormBox["1", - TraditionalForm], + FormBox["1", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"ExplicitLorentzIndex", - CellLabel->"Out[1]=", - CellID->1531481784] + CellLabel->"Out[740]="] }, Open ]], Cell[CellGroupData[{ @@ -238,7 +230,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"ExplicitLorentzIndex", - CellLabel->"In[2]:=", + CellLabel->"In[741]:=", CellID->93969146], Cell[BoxData[ @@ -247,8 +239,7 @@ Cell[BoxData[ RowBox[{"ExplicitLorentzIndex", "[", "1", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]], "Output", CellTags->"ExplicitLorentzIndex", - CellLabel->"Out[2]//StandardForm=", - CellID->551395089] + CellLabel->"Out[741]//StandardForm="] }, Open ]] }, Open ]], @@ -313,12 +304,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{962, Automatic}, {Automatic, 210}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitPartialD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitPartialD.nb index 663b9af31..0017c3061 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitPartialD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitPartialD.nb @@ -118,9 +118,17 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"ExplicitPartialD", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "inserts in exp the definition for LeftRightPartialD[z] (and \ -LeftRightPartialD2[z])." + " \[LineSeparator]inserts the definitions for ", + ButtonBox["LeftRightPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/LeftRightPartialD", + ButtonNote->"LeftRightPartialD"], + " and ", + ButtonBox["LeftRightPartialD2", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/LeftRightPartialD2", + ButtonNote->"LeftRightPartialD2"], + "." }], "Usage", CellID->982511436], @@ -161,7 +169,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["ExpandPartialD", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/ExpandPartialD", @@ -177,9 +184,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/LeftRightPartialD2", ButtonNote->"LeftRightPartialD2"], "." -}], "Text", - CellTags->"ExplicitPartialD", - CellID->1172851554] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -209,10 +214,27 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ExplicitPartialD", "[", " ", - RowBox[{"LeftRightPartialD", "[", "\[Mu]", "]"}], " ", "]"}]], "Input", + RowBox[{" ", + RowBox[{"LeftRightPartialD", "[", "\[Mu]", "]"}], " "}]], "Input", + CellLabel->"In[85]:="], + +Cell[BoxData[ + FormBox[ + SubscriptBox[ + OverscriptBox["\[PartialD]", "\[LeftRightArrow]"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[85]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ExplicitPartialD", "[", "%", "]"}]], "Input", CellTags->"ExplicitPartialD", - CellLabel->"In[1]:=", + CellLabel->"In[86]:=", CellID->2001527654], Cell[BoxData[ @@ -234,18 +256,37 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], ")"}]}], TraditionalForm]], "Output", CellTags->"ExplicitPartialD", - CellLabel->"Out[1]=", - CellID->1715328697] + CellLabel->"Out[86]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ExplicitPartialD", "[", " ", - RowBox[{"LeftRightPartialD2", "[", "\[Mu]", "]"}], " ", "]"}]], "Input", - CellTags->"ExplicitPartialD", - CellLabel->"In[2]:=", - CellID->1875131375], + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"LeftRightPartialD2", "[", "\[Mu]", "]"}]], "Input", + CellLabel->"In[1]:="], + +Cell[BoxData[ + FormBox[ + SubscriptBox[ + OverscriptBox["\[PartialD]", "\[LeftRightArrow]"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[1]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ExplicitPartialD", "[", "%", "]"}]], "Input", + CellLabel->"In[2]:="], Cell[BoxData[ FormBox[ @@ -262,18 +303,40 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", - CellTags->"ExplicitPartialD", - CellLabel->"Out[2]=", - CellID->1071634399] + CellLabel->"Out[2]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ExplicitPartialD", "[", " ", - RowBox[{"LeftRightPartialD", "[", "OPEDelta", "]"}], " ", "]"}]], "Input", + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"LeftRightPartialD", "[", "OPEDelta", "]"}], " "}]], "Input", + CellLabel->"In[3]:="], + +Cell[BoxData[ + FormBox[ + SubscriptBox[ + OverscriptBox["\[PartialD]", "\[LeftRightArrow]"], + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[3]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ExplicitPartialD", "[", "%", "]"}]], "Input", CellTags->"ExplicitPartialD", - CellLabel->"In[3]:=", + CellLabel->"In[4]:=", CellID->1791671183], Cell[BoxData[ @@ -295,18 +358,24 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], ")"}]}], TraditionalForm]], "Output", CellTags->"ExplicitPartialD", - CellLabel->"Out[3]=", - CellID->490499430] + CellLabel->"Out[4]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"16", " ", RowBox[{ RowBox[{"LeftRightPartialD", "[", "OPEDelta", "]"}], "^", "4"}]}]], "Input", CellTags->"ExplicitPartialD", - CellLabel->"In[4]:=", + CellLabel->"In[5]:=", CellID->2120633580], Cell[BoxData[ @@ -319,8 +388,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], "4"]}], TraditionalForm]], "Output", CellTags->"ExplicitPartialD", - CellLabel->"Out[4]=", - CellID->962398275] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -328,7 +396,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExplicitPartialD", "[", "%", "]"}]], "Input", CellTags->"ExplicitPartialD", - CellLabel->"In[5]:=", + CellLabel->"In[6]:=", CellID->1962668305], Cell[BoxData[ @@ -349,8 +417,8 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], ")"}], "4"], TraditionalForm]], "Output", CellTags->"ExplicitPartialD", - CellLabel->"Out[5]=", - CellID->2132998296] + CellLabel->"Out[6]="] +}, Open ]] }, Open ]] }, Open ]], @@ -415,12 +483,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{886, Automatic}, {88, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitSUNFIndex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitSUNFIndex.nb new file mode 100644 index 000000000..888190809 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitSUNFIndex.nb @@ -0,0 +1,325 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/ExplicitSUNFIndex", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["ExplicitSUNFIndex", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"ExplicitSUNFIndex", "[", "ind", "]"}]], "InlineFormula"], + " \[LineSeparator]is a specific SU(N) index in the fundamental \ +representation, i.e. ind is an integer." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell[TextData[{ + ButtonBox["SUNIndex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNIndex", + ButtonNote->"SUNIndex"], + ", ", + ButtonBox["SUNFIndex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNFIndex", + ButtonNote->"SUNFIndex"], + "." +}], "SeeAlso", + CellID->40109896] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ExplicitSUNFIndex", "[", "1", "]"}]], "Input", + CellLabel->"In[742]:=", + CellID->266217332], + +Cell[BoxData[ + FormBox["1", TraditionalForm]], "Output", + CellLabel->"Out[742]=", + CellID->1167023739] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNTF", "[", + RowBox[{"a", ",", "1", ",", "2"}], "]"}]], "Input", + CellLabel->"In[743]:=", + CellID->389081568], + +Cell[BoxData[ + FormBox[ + SubsuperscriptBox["T", + RowBox[{ + FormBox["1", + TraditionalForm], + FormBox["2", + TraditionalForm]}], + FormBox["a", + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[743]=", + CellID->1718232289] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"%", "//", "FCI"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[744]:=", + CellID->1621387441], + +Cell[BoxData[ + RowBox[{"SUNTF", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"SUNIndex", "[", "a", "]"}], "}"}], ",", + RowBox[{"ExplicitSUNFIndex", "[", "1", "]"}], ",", + RowBox[{"ExplicitSUNFIndex", "[", "2", "]"}]}], "]"}]], "Output", + CellLabel->"Out[744]//StandardForm=", + CellID->2133851564] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1064, Automatic}, {Automatic, 154}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitSUNIndex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitSUNIndex.nb index afbf0c1e2..d986db134 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitSUNIndex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExplicitSUNIndex.nb @@ -118,11 +118,8 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"ExplicitSUNIndex", "[", "ind", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is a specific SU(", - StyleBox["N", - FontSlant->"Italic"], - ") index, i.e., ind is an integer." + " \[LineSeparator] is a specific SU(N) index in the adjoint representation, \ +i.e. ind is an integer." }], "Usage", CellID->982511436], @@ -163,7 +160,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["FCI", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FCI", @@ -184,9 +180,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNIndex", ButtonNote->"SUNIndex"], "." -}], "Text", - CellTags->"ExplicitSUNIndex", - CellID->1491985045] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,14 +212,13 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExplicitSUNIndex", "[", "1", "]"}]], "Input", CellTags->"ExplicitSUNIndex", - CellLabel->"In[1]:=", + CellLabel->"In[745]:=", CellID->902504379], Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"ExplicitSUNIndex", - CellLabel->"Out[1]=", - CellID->835416034] + CellLabel->"Out[745]="] }, Open ]] }, Open ]], @@ -290,12 +283,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1016, Automatic}, {Automatic, 117}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExtraFactor.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExtraFactor.nb index b1314e879..daa9d2cc4 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExtraFactor.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExtraFactor.nb @@ -160,15 +160,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["FermionSpinSum", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FermionSpinSum", ButtonNote->"FermionSpinSum"], "." -}], "Text", - CellTags->"ExtraFactor", - CellID->1492736097] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{854, Automatic}, {Automatic, 146}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExtraVariables.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExtraVariables.nb index 0e17baf57..69d72fe2b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ExtraVariables.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ExtraVariables.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoopSum", ButtonNote->"OneLoopSum"], "." -}], "Text", - CellTags->"ExtraVariables", - CellID->908293507] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1086, Automatic}, {Automatic, 156}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FAD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FAD.nb index 9fe1ea1e3..0d82617f5 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FAD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FAD.nb @@ -125,8 +125,18 @@ FeynCalc internal form is performed by FeynCalcInternal." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FAD", "]"}]], "Input", + CellLabel->"In[751]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Dimension", "\[Rule]", "D"}], "}"}], TraditionalForm]], "Output", + CellLabel->"Out[751]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -192,9 +202,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PropagatorDenominator", ButtonNote->"PropagatorDenominator"], "." -}], "Text", - CellTags->"FAD", - CellID->92528208] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -228,31 +236,47 @@ Cell[BoxData[ RowBox[{"q", ",", RowBox[{"p", "-", "q"}]}], "]"}]], "Input", CellTags->"FAD", - CellLabel->"In[1]:=", + CellLabel->"In[746]:=", CellID->1136569018], Cell[BoxData[ FormBox[ FractionBox["1", RowBox[{ - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["q", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`q^2, "]"], - Editable->False], ")"}], ".", - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox[ - RowBox[{"(", - RowBox[{"p", "-", "q"}], ")"}], "2"], - "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", ($CellContext`p - $CellContext`q)^2, "]"], - Editable->False], ")"}]}]], TraditionalForm]], "Output", + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D], + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D]]], + Editable->False]}]], TraditionalForm]], "Output", CellTags->"FAD", - CellLabel->"Out[1]=", - CellID->574537865] + CellLabel->"Out[746]="] }, Open ]], Cell[CellGroupData[{ @@ -264,56 +288,111 @@ Cell[BoxData[ RowBox[{ RowBox[{"p", "-", "q"}], ",", "m"}], "}"}]}], "]"}]], "Input", CellTags->"FAD", - CellLabel->"In[2]:=", + CellLabel->"In[747]:=", CellID->1430394635], Cell[BoxData[ FormBox[ FractionBox["1", RowBox[{ + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False], ".", RowBox[{"(", InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["p", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`p^2, "]"], - Editable->False], ")"}], ".", - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", + RowBox[{ SuperscriptBox[ - RowBox[{"(", - RowBox[{"p", "-", "q"}], ")"}], "2"], - "\[InvisibleSpace]", "\<\"-\"\>", "\[InvisibleSpace]", - SuperscriptBox["m", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], SequenceForm[ - "[", ($CellContext`p - $CellContext`q)^2, "-", $CellContext`m^2, "]"], + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D], + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D]], + "-", $CellContext`m^2], Editable->False], ")"}]}]], TraditionalForm]], "Output", CellTags->"FAD", - CellLabel->"Out[2]=", - CellID->1777754458] + CellLabel->"Out[747]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ + RowBox[{"FAD", "[", RowBox[{ - RowBox[{ - RowBox[{"FAD", "[", - RowBox[{"q", ",", - RowBox[{"p", "-", "q"}]}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", - "StandardForm"}]], "Input", - CellTags->"FAD", - CellLabel->"In[3]:=", - CellID->434953197], + RowBox[{"{", + RowBox[{"p", ",", "0", ",", "2"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"p", "-", "q"}], ",", "m", ",", "3"}], "}"}]}], "]"}]], "Input", + CellLabel->"In[748]:="], Cell[BoxData[ - RowBox[{"FAD", "[", - RowBox[{"q", ",", - RowBox[{"p", "-", "q"}]}], "]"}]], "Output", - CellTags->"FAD", - CellLabel->"Out[3]//StandardForm=", - CellID->1226815761] + FormBox[ + FractionBox["1", + RowBox[{ + SuperscriptBox[ + RowBox[{"(", + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False], ")"}], "2"], ".", + SuperscriptBox[ + RowBox[{"(", + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D], + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D]], + "-", $CellContext`m^2], + Editable->False], ")"}], "3"]}]], TraditionalForm]], "Output", + CellLabel->"Out[748]="] }, Open ]], Cell[CellGroupData[{ @@ -326,7 +405,7 @@ Cell[BoxData[ RowBox[{"p", "-", "q"}]}], "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"FAD", - CellLabel->"In[4]:=", + CellLabel->"In[749]:=", CellID->2024009960], Cell[BoxData[ @@ -344,8 +423,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"q", ",", "D"}], "]"}]}], ",", "0"}], "]"}]}], "]"}]], "Output", CellTags->"FAD", - CellLabel->"Out[4]//StandardForm=", - CellID->962460787] + CellLabel->"Out[749]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -357,28 +435,21 @@ Cell[BoxData[ RowBox[{"FAD", "[", "p", "]"}], " ", RowBox[{"FAD", "[", RowBox[{"p", "-", "q"}], "]"}]}], " ", "//", " ", - "FeynAmpDenominatorCombine"}], "//", "StandardForm"}]], "Input", + RowBox[{ + RowBox[{"FeynAmpDenominatorCombine", "[", + RowBox[{"#", ",", + RowBox[{"FCE", "\[Rule]", "True"}]}], "]"}], "&"}]}], "//", + "StandardForm"}]], "Input", CellTags->"FAD", - CellLabel->"In[5]:=", + CellLabel->"In[750]:=", CellID->844291899], Cell[BoxData[ - RowBox[{"FeynAmpDenominator", "[", - RowBox[{ - RowBox[{"PropagatorDenominator", "[", - RowBox[{ - RowBox[{"Momentum", "[", - RowBox[{"p", ",", "D"}], "]"}], ",", "0"}], "]"}], ",", - RowBox[{"PropagatorDenominator", "[", - RowBox[{ - RowBox[{ - RowBox[{"Momentum", "[", - RowBox[{"p", ",", "D"}], "]"}], "-", - RowBox[{"Momentum", "[", - RowBox[{"q", ",", "D"}], "]"}]}], ",", "0"}], "]"}]}], "]"}]], "Output", + RowBox[{"FAD", "[", + RowBox[{"p", ",", + RowBox[{"p", "-", "q"}]}], "]"}]], "Output", CellTags->"FAD", - CellLabel->"Out[5]//StandardForm=", - CellID->3238120] + CellLabel->"Out[750]//StandardForm="] }, Open ]] }, Open ]], @@ -443,12 +514,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{844, Automatic}, {Automatic, 122}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FAPatch.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FAPatch.nb new file mode 100644 index 000000000..4b030bc96 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FAPatch.nb @@ -0,0 +1,267 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/FAPatch", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["FAPatch", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"FAPatch", "[", "]"}]], "InlineFormula"], + " \[LineSeparator]is an auxiliary function that patches FeynArts to be \ +compatible with FeynCalc." +}], "Usage", + CellID->982511436], + +Cell[TextData[{ + "If an unpatched copy of FeynArts is present in ", + ButtonBox["$FeynArtsDirectory", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/$FeynArtsDirectory", + ButtonNote->"$FeynArtsDirectory"], + ", evaluating ", + Cell[BoxData[ + RowBox[{"FAPatch", "[", "]"}]], "InlineFormula"], + " will start the patching process." +}], "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{740, Automatic}, {267, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FC.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FC.nb index 336c6b73f..6777540fe 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FC.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FC.nb @@ -179,9 +179,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynCalcInternal", ButtonNote->"FeynCalcInternal"], "." -}], "Text", - CellTags->"FC", - CellID->121401811] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -210,7 +208,7 @@ Cell[BoxData[ Cell[BoxData["FI"], "Input", CellTags->"FC", - CellLabel->"In[1]:=", + CellLabel->"In[752]:=", CellID->907505833], Cell[CellGroupData[{ @@ -222,18 +220,17 @@ Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"Momentum", "[", "p", "]"}], "]"}]}], "}"}]], "Input", CellTags->"FC", - CellLabel->"In[2]:=", + CellLabel->"In[753]:=", CellID->2003442189], Cell["{DiracGamma[5], DiracGamma[Momentum[p]]}", "Output", CellTags->"FC", - CellLabel->"Out[2]=", - CellID->914835770] + CellLabel->"Out[753]="] }, Open ]], Cell[BoxData["FC"], "Input", CellTags->"FC", - CellLabel->"In[3]:=", + CellLabel->"In[754]:=", CellID->119415853], Cell[CellGroupData[{ @@ -245,7 +242,7 @@ Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"Momentum", "[", "p", "]"}], "]"}]}], "}"}]], "Input", CellTags->"FC", - CellLabel->"In[4]:=", + CellLabel->"In[755]:=", CellID->1977687896], Cell[BoxData[ @@ -264,8 +261,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]}], "}"}], TraditionalForm]], "Output", CellTags->"FC", - CellLabel->"Out[4]=", - CellID->832664174] + CellLabel->"Out[755]="] }, Open ]] }, Open ]], @@ -330,12 +326,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1267, Automatic}, {Automatic, 276}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FC2RHI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FC2RHI.nb index 6d6fe382e..58e89ec09 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FC2RHI.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FC2RHI.nb @@ -127,8 +127,24 @@ IncludePair governs the inclusion of scalar products p.k1, p.k2 and k1.k2 \ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FC2RHI", "]"}]], "Input", + CellTags->"FC2RHI", + CellLabel->"In[756]:=", + CellID->744239659], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"IncludePair", "\[Rule]", "True"}], ",", + RowBox[{"Do", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", + CellTags->"FC2RHI", + CellLabel->"Out[756]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -169,9 +185,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI", ButtonNote->"RHI"], "." -}], "Text", - CellTags->"FC2RHI", - CellID->2109849659] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -183,8 +197,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -200,27 +212,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "FC2RHI", "]"}]], "Input", - CellTags->"FC2RHI", - CellLabel->"In[1]:=", - CellID->744239659], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"IncludePair", "\[Rule]", "True"}], ",", - RowBox[{"Do", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", - CellTags->"FC2RHI", - CellLabel->"Out[1]=", - CellID->283717471] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -280,12 +271,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1132, Automatic}, {Automatic, 245}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FC2TLI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FC2TLI.nb index 9bccaa9b1..65571916d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FC2TLI.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FC2TLI.nb @@ -126,8 +126,24 @@ products p.k1, p.k2 and k1.k2 (setting True)." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FC2TLI", "]"}]], "Input", + CellTags->"FC2TLI", + CellLabel->"In[757]:=", + CellID->145553931], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"IncludePair", "\[Rule]", "True"}], ",", + RowBox[{"Do", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", + CellTags->"FC2TLI", + CellLabel->"Out[757]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -168,9 +184,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/TLI", ButtonNote->"TLI"], "." -}], "Text", - CellTags->"FC2TLI", - CellID->918556858] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -182,8 +196,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -199,27 +211,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "FC2TLI", "]"}]], "Input", - CellTags->"FC2TLI", - CellLabel->"In[1]:=", - CellID->145553931], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"IncludePair", "\[Rule]", "True"}], ",", - RowBox[{"Do", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", - CellTags->"FC2TLI", - CellLabel->"Out[1]=", - CellID->615300118] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -279,12 +270,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{975, Automatic}, {Automatic, 174}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FCAbbreviate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FCAbbreviate.nb new file mode 100644 index 000000000..5a6782390 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FCAbbreviate.nb @@ -0,0 +1,658 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/FCAbbreviate", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], 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FCDuplicateFreeQ[list,test] uses test to determine whether two \ +objects should be considered duplicates.FCDuplicateFreeQ returns the same \ +results as the standard DuplicateFreeQ. The only reason for introducing \ +FCDuplicateFreeQ is that DuplicateFreeQ is not available in Mathematica 8 and \ +9, which are still supported by FeynCalc." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + 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TraditionalForm]], "Output", + CellLabel->"Out[804]=", + CellID->2639087] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCDuplicateFreeQ", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"a", ",", "b"}], "}"}], ",", + RowBox[{"{", + RowBox[{"a", ",", "c"}], "}"}]}], "}"}], "]"}]], "Input", + CellLabel->"In[805]:=", + CellID->1576732881], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[805]=", + CellID->52773390] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FCDuplicateFreeQ", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"a", ",", "b"}], "}"}], ",", + RowBox[{"{", + RowBox[{"a", ",", "c"}], "}"}]}], "}"}], ",", + RowBox[{"Function", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"x", ",", "y"}], "}"}], ",", + RowBox[{ + RowBox[{"First", "[", "x", "]"}], "===", + RowBox[{"First", "[", "y", "]"}]}]}], "]"}]}], "]"}]], "Input", + CellLabel->"In[806]:=", + CellID->800569343], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + CellLabel->"Out[806]=", + CellID->1930688687] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1261, Automatic}, {Automatic, 234}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FCE.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FCE.nb index b55db14c4..99c7ab794 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FCE.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FCE.nb @@ -118,13 +118,12 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"FCE", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "translates exp from the internal FeynCalc representation to a short form.\n\ -FCE is equivalent to FeynCalcExternal." + " \[LineSeparator]translates exp from the internal FeynCalc representation \ +to a short form." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["FCE is equivalent to FeynCalcExternal.", "Notes", CellID->1067943069] }, Open ]], @@ -176,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynCalcInternal", ButtonNote->"FeynCalcInternal"], "." -}], "Text", - CellTags->"FCE", - CellID->141332597] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -215,7 +212,7 @@ Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"Momentum", "[", "p", "]"}], "]"}]}], "}"}], "]"}]], "Input", CellTags->"FCE", - CellLabel->"In[1]:=", + CellLabel->"In[807]:=", CellID->2084841201], Cell[BoxData[ @@ -238,8 +235,7 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm]}], "}"}], TraditionalForm]], "Output", CellTags->"FCE", - CellLabel->"Out[1]=", - CellID->32096658] + CellLabel->"Out[807]="] }, Open ]], Cell[CellGroupData[{ @@ -247,7 +243,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FCE", - CellLabel->"In[2]:=", + CellLabel->"In[808]:=", CellID->458931786], Cell[BoxData[ @@ -256,8 +252,7 @@ Cell[BoxData[ RowBox[{"GA", "[", "5", "]"}], ",", RowBox[{"GS", "[", "p", "]"}]}], "}"}]], "Output", CellTags->"FCE", - CellLabel->"Out[2]//StandardForm=", - CellID->1043906196] + CellLabel->"Out[808]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -275,7 +270,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Input", CellTags->"FCE", - CellLabel->"In[3]:=", + CellLabel->"In[809]:=", CellID->2115567934], Cell[BoxData[ @@ -322,43 +317,32 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ",", FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], - TraditionalForm], ",", - FormBox[ - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Alpha]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], - TraditionalForm]], - TraditionalForm], + TraditionalForm]}]], + TraditionalForm], ",", + FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]}], "}"}], TraditionalForm]], "Output", CellTags->"FCE", - CellLabel->"Out[3]=", - CellID->1056453085] + CellLabel->"Out[809]="] }, Open ]], Cell[CellGroupData[{ @@ -366,7 +350,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FCE", - CellLabel->"In[4]:=", + CellLabel->"In[810]:=", CellID->811786447], Cell[BoxData[ @@ -382,8 +366,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", CellTags->"FCE", - CellLabel->"Out[4]//StandardForm=", - CellID->2003071088] + CellLabel->"Out[810]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -391,7 +374,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "FCI"}]], "Input", CellTags->"FCE", - CellLabel->"In[5]:=", + CellLabel->"In[811]:=", CellID->1616474928], Cell[BoxData[ @@ -429,40 +412,29 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm]}], ",", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], ",", - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Alpha]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "}"}], TraditionalForm]], "Output", + TraditionalForm]}]], ",", + SuperscriptBox[ + FormBox[ 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"//", "StandardForm"}]], "Input", CellTags->"FCI", - CellLabel->"In[5]:=", + CellLabel->"In[15]:=", CellID->1427781639], Cell[BoxData[ @@ -468,8 +442,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", CellTags->"FCI", - CellLabel->"Out[5]//StandardForm=", - CellID->2132613884] + CellLabel->"Out[15]//StandardForm="] }, Open ]] }, Open ]], @@ -534,12 +507,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{822, Automatic}, {Automatic, 203}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git 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(December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FCIntegrate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FCIntegrate.nb index 36ce20a40..fb8a7c490 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FCIntegrate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FCIntegrate.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FCNIntegrate", ButtonNote->"FCNIntegrate"], "." -}], "Text", - CellTags->"FCIntegrate", - CellID->1030773877] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{783, Automatic}, {Automatic, 191}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", 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TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FCPartialD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FCPartialD.nb index e403787fb..5869f0909 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FCPartialD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FCPartialD.nb @@ -209,9 +209,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RightPartialD", ButtonNote->"RightPartialD"], "." -}], "Text", - CellTags->"PartialD", - CellID->1527820766] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -238,10 +236,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"PartialD", - 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This is mainly relevant to the treatment of the fifth Dirac \ +matrix ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula", + FormatType->"StandardForm"], + ", which is not well-defined in dimensional regularization." +}], "Usage", + CellChangeTimes->{{3.77037986103098*^9, 3.770379894569189*^9}}, + CellID->982511436], + +Cell["Following schemes are supported: ", "Notes", + CellChangeTimes->{3.770380074322131*^9}, + CellID->1067943069], + +Cell[TextData[{ + "\"NDR\" - This is the default value. In the naive dimensional \ +regularization (also known as conventional dimensional regularization or CDR) \ +", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + " is assumed to anticommute with all Dirac matrices in ", + Cell[BoxData["D"], "InlineFormula"], + " dimensions. Hence, every Dirac trace can be rewritten in such a way, that \ +it contains either just one or not a single ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + " matrix. The latter traces are obviously unambiguous. The traces with one \ +", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + " are not well-defined in this scheme. It usually depends on the physics of \ +the process, whether and how they can contribute to the final result. \ +Therefore, FeynCalc will keep such traces unevaluated, leaving it to the user \ +to decide how to treat them. " +}], "Notes", + CellChangeTimes->{{3.770380083504825*^9, 3.7703801022364388`*^9}, { + 3.77799323866269*^9, 3.7779933083436213`*^9}}, + CellID->190401776], + +Cell[TextData[{ + "Notice that traces with an odd number of the usual Dirac matrices and \ +one ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + ", that vanish in 4 dimensions, will be also put to zero in this scheme." +}], "Notes", + CellChangeTimes->{{3.770380083504825*^9, 3.7703801022364388`*^9}, { + 3.77799323866269*^9, 3.777993282985037*^9}}, + CellID->1784502655], + +Cell[TextData[{ + "\"NDR-Discard\" - This is a special version of the NDR scheme. The Dirac \ +algebra is\nevaluated in the same way as with \"NDR\", but the remaining \ +traces with one ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]]], + "\nare put to zero. This assumes that such traces do not contribute to the \ +final result,\nwhich is obviously true only for specific calculations." +}], "Notes", + CellChangeTimes->{{3.777993348100638*^9, 3.7779933703996763`*^9}}, + CellID->665441283], + +Cell[TextData[{ + "\"BMHV\" - The Breitenlohner-Maison extension of the t'Hooft-Veltman \ +scheme. This scheme introduces Dirac and Lorentz tensors living in ", + Cell[BoxData["4"], "InlineFormula"], + ", ", + Cell[BoxData["D"], "InlineFormula"], + " or ", + Cell[BoxData[ + RowBox[{"D", "-", "4"}]], "InlineFormula"], + " dimensions, while ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " is a purely ", + Cell[BoxData["4"], "InlineFormula"], + "-dimensional object. BMHV is algebraically consistent but often suffers \ +from nonconservation of currents in the final results. The conservation must \ +be then enfornced by introducing finite counter-terms. 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"See also: ", ButtonBox["FCAntiSymmetrize", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FCAntiSymmetrize", ButtonNote->"FCAntiSymmetrize"], "." -}], "Text", - CellTags->"FCSymmetrize", - CellID->714962705] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -209,7 +206,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "]"}]], "Input", CellTags->"Symmetrize", - CellLabel->"In[2]:=", + CellLabel->"In[111]:=", CellID->848650980], Cell[BoxData[ @@ -223,8 +220,7 @@ Cell[BoxData[ RowBox[{"f", "(", RowBox[{"b", ",", "a"}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"Symmetrize", - CellLabel->"Out[2]=", - CellID->371734059] + CellLabel->"Out[111]="] }, Open ]], Cell[CellGroupData[{ @@ -237,7 +233,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], "]"}]], "Input", CellTags->"Symmetrize", - CellLabel->"In[3]:=", + CellLabel->"In[112]:=", CellID->1287424961], Cell[BoxData[ @@ -260,8 +256,7 @@ Cell[BoxData[ RowBox[{"z", ",", "y", ",", "x"}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"Symmetrize", - 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{ + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell["\<\ +If we want to introduce constants c1 and c2, the naive way doesn't lead to \ +the desired result\ +\>", "Notes", + CellID->247520490], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SPD", "[", + RowBox[{ + RowBox[{ + RowBox[{"c1", " ", "p1"}], "+", + RowBox[{"c2", " ", "p2"}]}], ",", "q"}], "]"}], "//", + "ExpandScalarProduct"}]], "Input", + CellLabel->"In[136]:=", + CellID->1215664914], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + FormBox[ + FormBox[ + RowBox[{"c1", " ", "p1"}], + TraditionalForm], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm]}], "+", + RowBox[{ + FormBox[ + FormBox[ + RowBox[{"c2", " ", "p2"}], + TraditionalForm], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm]}]}], TraditionalForm]], "Output", + CellLabel->"Out[136]=", + CellID->63183590] +}, Open ]], + +Cell["\<\ +The solution is to declare c1 and c2 as FCVariable so that FeynCalc can \ +distinguish them from the 4-momenta\ +\>", "Notes", + CellID->1683370483], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{ + RowBox[{ + RowBox[{"DataType", "[", + RowBox[{"c1", ",", "FCVariable"}], "]"}], "=", "True"}], ";"}], "\n", + RowBox[{ + RowBox[{ + RowBox[{"DataType", "[", + RowBox[{"c2", ",", "FCVariable"}], "]"}], "=", "True"}], ";"}], "\n", + RowBox[{ + RowBox[{"SPD", "[", + RowBox[{ + RowBox[{ + RowBox[{"c1", " ", "p1"}], "+", + RowBox[{"c2", " ", "p2"}]}], ",", "q"}], "]"}], "//", + "ExpandScalarProduct"}]}], "Input", + CellLabel->"In[137]:=", + CellID->1946914218], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"c1", " ", + RowBox[{"(", + RowBox[{ + FormBox[ + FormBox["p1", + TraditionalForm], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm]}], ")"}]}], "+", + RowBox[{"c2", " ", + RowBox[{"(", + RowBox[{ + FormBox[ + FormBox["p2", + TraditionalForm], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm]}], ")"}]}]}], TraditionalForm]], "Output", + CellLabel->"Out[139]=", + CellID->425164179] +}, Open ]], + +Cell["This works also for propagator denominators and matrices", "Notes", + CellID->84688361], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{"FCI", "[", + RowBox[{"SFAD", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"q", "+", + RowBox[{"c1", " ", "p1"}]}], ",", "m"}], "}"}], "]"}], + "]"}], "\[IndentingNewLine]", + RowBox[{"%", "//", "StandardForm"}]}], "Input", + CellLabel->"In[140]:=", + CellID->228259200], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",RowBox[{ + SuperscriptBox[ + RowBox[{ + FormBox["\"(\"", TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + RowBox[{"c1", " ", + FormBox["p1", TraditionalForm]}], "+", + FormBox["q", TraditionalForm]}], TraditionalForm], + TraditionalForm], + FormBox["\")\"", TraditionalForm]}], 2]}],RowBox[{"-", "m"}], + "\"+\"",RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[140]=", + CellID->365749151], + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{ + RowBox[{"c1", " ", + RowBox[{"Momentum", "[", + RowBox[{"p1", ",", "D"}], "]"}]}], "+", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], ",", "0", ",", + RowBox[{"-", "m"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Output", + CellLabel->"Out[141]//StandardForm=", + CellID->1642692538] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{ + RowBox[{ + RowBox[{"GAD", "[", "\[Mu]", "]"}], ".", + RowBox[{"(", + RowBox[{ + RowBox[{"GSD", "[", + RowBox[{"c1", " ", "p"}], "]"}], "+", "m"}], ")"}], ".", + RowBox[{"GAD", "[", "\[Nu]", "]"}]}], "//", "FCI"}], "\[IndentingNewLine]", + RowBox[{"%", "//", "StandardForm"}]}], "Input", + CellLabel->"In[142]:=", + CellID->1015735328], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + RowBox[{"c1", " ", + RowBox[{"\[Gamma]", "\[CenterDot]", + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]}]}], "+", "m"}], ")"}], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[142]=", + CellID->2133407116], + +Cell[BoxData[ + RowBox[{ + RowBox[{"DiracGamma", "[", + RowBox[{ + 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TraditionalForm], "_"], + FormBox[ + FormBox[ + StyleBox["i", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{"c1", " ", + RowBox[{ + OverscriptBox[ + FormBox[ + StyleBox["\<\"\[Sigma]\"\>", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox[ + StyleBox["p", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], + TraditionalForm]}]}], ")"}], ".", + SuperscriptBox[ + OverscriptBox[ + FormBox[ + StyleBox["\<\"\[Sigma]\"\>", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], + FormBox[ + FormBox[ + StyleBox["j", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[144]=", + CellID->825817380], + +Cell[BoxData[ + RowBox[{ + RowBox[{"PauliSigma", "[", + RowBox[{"CartesianIndex", "[", "i", "]"}], "]"}], ".", + RowBox[{"(", + RowBox[{"c1", " ", + RowBox[{"PauliSigma", "[", + RowBox[{"CartesianMomentum", "[", "p", "]"}], "]"}]}], ")"}], ".", + RowBox[{"PauliSigma", "[", + RowBox[{"CartesianIndex", "[", "j", "]"}], "]"}]}]], "Output", + CellLabel->"Out[145]//StandardForm=", + CellID->19578284] +}, Open ]], + +Cell["To undo the declarations use", "Notes", + CellID->874852462], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{ + RowBox[{"DataType", "[", + RowBox[{"c1", ",", "FCVariable"}], "]"}], "=", + "False"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"DataType", "[", + RowBox[{"c2", ",", "FCVariable"}], "]"}], "=", "False"}]}], "Input", + CellLabel->"In[146]:=", + CellID->219796287], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + CellLabel->"Out[146]=", + CellID->1930979781], + +Cell[BoxData[ + FormBox["False", TraditionalForm]], "Output", + CellLabel->"Out[147]=", + CellID->1284707712] +}, Open ]], + +Cell[BoxData[""], "Input", + CellID->58122944] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{917, Automatic}, {242, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FDS.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FDS.nb index df787bdc1..15464274d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FDS.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FDS.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynAmpDenominatorSimplify", ButtonNote->"FeynAmpDenominatorSimplify"], "." -}], "Text", - CellTags->"FDS", - CellID->429222179] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{983, Automatic}, {Automatic, 164}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FI.nb index 9c5961270..dc2fbf438 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FI.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FI.nb @@ -180,9 +180,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynCalcInternal", ButtonNote->"FeynCalcInternal"], "." -}], "Text", - CellTags->"FI", - CellID->1056689858] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -268,12 +266,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{841, Automatic}, {Automatic, 257}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FORM.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FORM.nb index 75c117fee..68a12cc3b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FORM.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FORM.nb @@ -171,9 +171,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynCalc2FORM", ButtonNote->"FeynCalc2FORM"], "." -}], "Text", - CellTags->"FORM", - CellID->2094325907] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,13 +256,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{960, 989}, +WindowMargins->{{Automatic, -10}, {Automatic, -35}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FORM2FeynCalc.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FORM2FeynCalc.nb index 9d12add00..79bb21e4e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FORM2FeynCalc.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FORM2FeynCalc.nb @@ -117,19 +117,78 @@ Cell["FORM2FeynCalc", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"FORM2FeynCalc", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "translates the FORM expr into FeynCalc notation. FORM2FeynCalc[file] \ -translates the FORM expresssions in file into FeynCalcnotation. \ -FORM2FeynCalc[file, x1, x2, ...] reads in a file in FORM-format and \ -translates the assignments for the variables a, b, ... into FeynCalc syntax. \ -If the option Set is True, the variables x1, x2 are assigned to the right \ -hand sides defined in the FORM-file." + RowBox[{"FORM2FeynCalc", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]translates the FORM ", + Cell[BoxData["exp"], "InlineFormula"], + " into FeynCalc notation.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"FORM2FeynCalc", "[", "file", "]"}]], "InlineFormula"], + " \[LineSeparator] translates the FORM expresssions in ", + Cell[BoxData["file"], "InlineFormula"], + " into FeynCalc notation.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"FORM2FeynCalc", "[", + RowBox[{"file", ",", "x1", ",", "x2", ",", "..."}], "]"}]], + "InlineFormula"], + " \[LineSeparator]reads in a file in FORM-format and translates the \ +assignments for the variables ", + Cell[BoxData[ + RowBox[{"a", ",", " ", "b", ",", " ", "..."}]], "InlineFormula"], + " into FeynCalc syntax." }], "Usage", - CellID->982511436], + CellID->2010081510], + +Cell[TextData[{ + "If the option ", + Cell[BoxData["Set"], "InlineFormula"], + " is ", + Cell[BoxData["True"], "InlineFormula"], + ", the variables ", + Cell[BoxData["x1"], "InlineFormula"], + ", ", + Cell[BoxData["x2"], "InlineFormula"], + " are assigned to the right hand sides defined in the FORM-file." +}], "Notes"], + +Cell["\<\ +The capabilities of this function are very limited, so that you should not \ +expect it to easily handle large and compicated expressions.\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FORM2FeynCalc", "]"}]], "Input", + CellTags->"FORM2FeynCalc", + CellLabel->"In[136]:=", + CellID->1139385107], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"Dot", "\[Rule]", "Dot"}], ",", + RowBox[{"HoldForm", "\[Rule]", "True"}], ",", + RowBox[{"LorentzIndex", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"FCGV", "(", "\<\"mu\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"nu\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"al\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"be\"\>", ")"}]}], "}"}]}], ",", + RowBox[{"Set", "\[Rule]", "False"}], ",", + RowBox[{"Replace", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"Vectors", "\[Rule]", "Automatic"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"FORM2FeynCalc", + CellLabel->"Out[136]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -164,15 +223,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - ButtonBox["FeynCalc2FORM", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FeynCalc2FORM", - ButtonNote->"FeynCalc2FORM"], - "." -}], "Text", - CellTags->"FORM2FeynCalc", - CellID->1782635377] +Cell[TextData[ButtonBox["FeynCalc2FORM", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FeynCalc2FORM", + ButtonNote->"FeynCalc2FORM"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,44 +255,10 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "FORM2FeynCalc", "]"}]], "Input", - CellTags->"FORM2FeynCalc", - CellLabel->"In[1]:=", - CellID->1139385107], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "4"}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"Dot", "\[Rule]", "Dot"}], ",", - RowBox[{"HoldForm", "\[Rule]", "True"}], ",", - RowBox[{"LorentzIndex", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"FCGV", "(", "\<\"mu\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"nu\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"al\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"be\"\>", ")"}]}], "}"}]}], ",", - RowBox[{"Set", "\[Rule]", "False"}], ",", - RowBox[{"Replace", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"Vectors", "\[Rule]", "Automatic"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"FORM2FeynCalc", - CellLabel->"Out[1]=", - CellID->1509057543] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"FORM2FeynCalc", "[", "\"\\"", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[2]:=", + CellLabel->"In[137]:=", CellID->1971183578], Cell[BoxData[ @@ -263,8 +283,7 @@ Cell[BoxData[ RowBox[{"x", ".", SuperscriptBox["m", "2"]}]}]}], TraditionalForm]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[2]=", - CellID->437204044] + CellLabel->"Out[137]="] }, Open ]], Cell[CellGroupData[{ @@ -272,7 +291,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[3]:=", + CellLabel->"In[138]:=", CellID->1292875249], Cell[BoxData[ @@ -283,16 +302,19 @@ Cell[BoxData[ RowBox[{"SP", "[", RowBox[{"p", ",", "q"}], "]"}]}]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[3]//StandardForm=", - CellID->1525941930] + CellLabel->"Out[138]//StandardForm="] }, Open ]], +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + Cell["\<\ Functions are automatically converted right, but bracketed expressions need \ to be substituted explicitly.\ -\>", "Text", - CellTags->"FORM2FeynCalc", - CellID->1823304465], +\>", "Notes"], Cell[CellGroupData[{ @@ -304,7 +326,7 @@ Cell[BoxData[ RowBox[{"\"\<[li2(1-x)]\>\"", "\[Rule]", "\"\\""}], "}"}]}]}], "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[4]:=", + CellLabel->"In[139]:=", CellID->1620741920], Cell[BoxData[ @@ -316,8 +338,7 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["log", "2"], "(", "x", ")"}]}], TraditionalForm]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[4]=", - CellID->827693663] + CellLabel->"Out[139]="] }, Open ]], Cell[CellGroupData[{ @@ -325,7 +346,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[5]:=", + CellLabel->"In[140]:=", CellID->1897584456], Cell[BoxData[ @@ -337,8 +358,7 @@ Cell[BoxData[ RowBox[{"2", ",", RowBox[{"1", "-", "x"}]}], "]"}]}]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[5]//StandardForm=", - CellID->879638641] + CellLabel->"Out[140]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -347,7 +367,7 @@ Cell[BoxData[ RowBox[{"FORM2FeynCalc", "[", "\"\\"", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[6]:=", + CellLabel->"In[141]:=", CellID->1533060910], Cell[BoxData[ @@ -362,8 +382,7 @@ Cell[BoxData[ RowBox[{"Hold", "[", "1", "]"}], ".", "y"}], "+", "x"}], TraditionalForm]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[6]=", - CellID->1027470118] + CellLabel->"Out[141]="] }, Open ]], Cell[CellGroupData[{ @@ -371,7 +390,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ReleaseHold", "[", "%", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[7]:=", + CellLabel->"In[142]:=", CellID->1512515442], Cell[BoxData[ @@ -383,8 +402,7 @@ Cell[BoxData[ RowBox[{"m", "+", "1"}]], "+", "x", "+", RowBox[{"1", ".", "y"}]}], TraditionalForm]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[7]=", - CellID->1640354437] + CellLabel->"Out[142]="] }, Open ]], Cell[CellGroupData[{ @@ -393,37 +411,30 @@ Cell[BoxData[ RowBox[{"FORM2FeynCalc", "[", "\"\\"", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[8]:=", + CellLabel->"In[143]:=", CellID->2089442701], Cell[BoxData[ FormBox[ RowBox[{ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["nu", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["nu", + TraditionalForm], + TraditionalForm]}]], TraditionalForm], "+", RowBox[{ RowBox[{"p", "(", "mu", ")"}], ".", RowBox[{"q", "(", "nu", ")"}]}]}], TraditionalForm]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[8]=", - CellID->758219802] + CellLabel->"Out[143]="] }, Open ]], Cell[CellGroupData[{ @@ -431,7 +442,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[9]:=", + CellLabel->"In[144]:=", CellID->1054646204], Cell[BoxData[ @@ -442,8 +453,7 @@ Cell[BoxData[ RowBox[{"MT", "[", RowBox[{"mu", ",", "nu"}], "]"}]}]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[9]//StandardForm=", - CellID->11165984] + CellLabel->"Out[144]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -457,37 +467,30 @@ Cell[BoxData[ RowBox[{"mu", "\[Rule]", "\[Mu]"}], ",", RowBox[{"nu", "\[Rule]", "\[Nu]"}]}], "}"}]}]}], "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[10]:=", + CellLabel->"In[145]:=", CellID->1352382070], Cell[BoxData[ FormBox[ RowBox[{ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm], "+", RowBox[{ RowBox[{"p", "(", "\[Mu]", ")"}], ".", RowBox[{"q", "(", "\[Nu]", ")"}]}]}], TraditionalForm]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[10]=", - CellID->291792517] + CellLabel->"Out[145]="] }, Open ]], Cell[CellGroupData[{ @@ -497,7 +500,7 @@ Cell[BoxData[ "\"\\"", "]"}]], "Input", CellTags->"FORM2FeynCalc", - CellLabel->"In[11]:=", + CellLabel->"In[146]:=", CellID->476542838], Cell[BoxData[ @@ -526,8 +529,8 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ")"}], ".", "blam"}], TraditionalForm]], "Output", CellTags->"FORM2FeynCalc", - CellLabel->"Out[11]=", - CellID->276944378] + CellLabel->"Out[146]="] +}, Open ]] }, Open ]] }, Open ]], @@ -592,12 +595,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{870, Automatic}, {Automatic, 258}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FORMEpilog.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FORMEpilog.nb index 68b16c33b..06bc57838 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FORMEpilog.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FORMEpilog.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FORMProlog", ButtonNote->"FORMProlog"], "." -}], "Text", - CellTags->"FORMEpilog", - CellID->703276888] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FORMProlog.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FORMProlog.nb index 6cceaaedd..311ef6223 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FORMProlog.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FORMProlog.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FORMEpilog", ButtonNote->"FORMEpilog"], "." -}], "Text", - CellTags->"FORMProlog", - CellID->553964491] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{956, Automatic}, {Automatic, 59}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FRH.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FRH.nb index 3bf678b45..85c8982d6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FRH.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FRH.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Isolate", ButtonNote->"Isolate"], "." -}], "Text", - CellTags->"FRH", - CellID->1874942431] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,7 +201,7 @@ Cell[BoxData[ RowBox[{"Hold", "[", RowBox[{"2", "-", "2"}], "]"}]}], "]"}]], "Input", CellTags->"FRH", - CellLabel->"In[1]:=", + CellLabel->"In[150]:=", CellID->1505003969], Cell[BoxData[ @@ -215,8 +213,7 @@ Cell[BoxData[ RowBox[{"2", "-", "2"}], "]"}]}], "+", "1", "-", "1"}], "]"}], TraditionalForm]], "Output", CellTags->"FRH", - CellLabel->"Out[1]=", - CellID->1110463745] + CellLabel->"Out[150]="] }, Open ]], Cell[CellGroupData[{ @@ -224,14 +221,13 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FRH", "[", "%", "]"}]], "Input", CellTags->"FRH", - CellLabel->"In[2]:=", + CellLabel->"In[151]:=", CellID->1714875295], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"FRH", - CellLabel->"Out[2]=", - CellID->313757423] + CellLabel->"Out[151]="] }, Open ]], Cell[CellGroupData[{ @@ -244,9 +240,9 @@ Cell[BoxData[ RowBox[{ RowBox[{"x", "^", "3"}], "-", "x", "-", "1"}], "==", "0"}], "]"}], ",", "x", ",", - RowBox[{"IsolateNames", "\[Rule]", "hh"}]}], "]"}]], "Input", + RowBox[{"IsolateNames", "\[Rule]", "KK"}]}], "]"}]], "Input", CellTags->"FRH", - CellLabel->"In[3]:=", + CellLabel->"In[159]:=", CellID->971664034], Cell[BoxData[ @@ -256,45 +252,120 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", "\[Rule]", TagBox[ - RowBox[{"hh", "(", "670", ")"}], + RowBox[{"KK", "(", "510", ")"}], HoldForm]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", TagBox[ - RowBox[{"hh", "(", "673", ")"}], + RowBox[{"KK", "(", "513", ")"}], HoldForm]}], "}"}], ",", RowBox[{"{", RowBox[{"x", "\[Rule]", TagBox[ - RowBox[{"hh", "(", "674", ")"}], + RowBox[{"KK", "(", "514", ")"}], HoldForm]}], "}"}]}], "}"}], TraditionalForm]], "Output", CellTags->"FRH", - CellLabel->"Out[3]=", - CellID->529538815] + CellLabel->"Out[159]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"FRH", "[", - RowBox[{"hh", "[", "3", "]"}], "]"}]], "Input", + RowBox[{"FRH", "[", "%", "]"}]], "Input", CellTags->"FRH", - CellLabel->"In[4]:=", + CellLabel->"In[160]:=", CellID->866394763], Cell[BoxData[ FormBox[ - RowBox[{"hh", "(", "3", ")"}], TraditionalForm]], "Output", - CellTags->"FRH", - CellLabel->"Out[4]=", - CellID->166257414] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", "hh", "]"}]], "Input", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"x", "\[Rule]", + RowBox[{ + RowBox[{ + FractionBox["1", "3"], " ", + RadicalBox[ + RowBox[{ + FractionBox["27", "2"], "-", + FractionBox[ + RowBox[{"3", " ", + SqrtBox["69"]}], "2"]}], "3"]}], "+", + FractionBox[ + RadicalBox[ + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"(", + RowBox[{"9", "+", + SqrtBox["69"]}], ")"}]}], "3"], + SuperscriptBox["3", + RowBox[{"2", "/", "3"}]]]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", "\[Rule]", + RowBox[{ + RowBox[{"-", + RowBox[{ + FractionBox["1", "6"], " ", + RowBox[{"(", + RowBox[{"1", "+", + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}]}], ")"}], " ", + RadicalBox[ + RowBox[{ + FractionBox["27", "2"], "-", + FractionBox[ + RowBox[{"3", " ", + SqrtBox["69"]}], "2"]}], "3"]}]}], "-", + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "-", + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}]}], ")"}], " ", + RadicalBox[ + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"(", + RowBox[{"9", "+", + SqrtBox["69"]}], ")"}]}], "3"]}], + RowBox[{"2", " ", + SuperscriptBox["3", + RowBox[{"2", "/", "3"}]]}]]}]}], "}"}], ",", + RowBox[{"{", + RowBox[{"x", "\[Rule]", + RowBox[{ + RowBox[{"-", + RowBox[{ + FractionBox["1", "6"], " ", + RowBox[{"(", + RowBox[{"1", "-", + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}]}], ")"}], " ", + RadicalBox[ + RowBox[{ + FractionBox["27", "2"], "-", + FractionBox[ + RowBox[{"3", " ", + SqrtBox["69"]}], "2"]}], "3"]}]}], "-", + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "+", + RowBox[{"\[ImaginaryI]", " ", + SqrtBox["3"]}]}], ")"}], " ", + RadicalBox[ + RowBox[{ + FractionBox["1", "2"], " ", + RowBox[{"(", + RowBox[{"9", "+", + SqrtBox["69"]}], ")"}]}], "3"]}], + RowBox[{"2", " ", + SuperscriptBox["3", + RowBox[{"2", "/", "3"}]]}]]}]}], "}"}]}], "}"}], + TraditionalForm]], "Output", CellTags->"FRH", - CellLabel->"In[5]:=", - CellID->1669049321] + CellLabel->"Out[160]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -358,12 +429,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{979, Automatic}, {Automatic, 177}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FUNCTION.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FUNCTION.nb index baf9866fa..cd76a9156 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FUNCTION.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FUNCTION.nb @@ -167,9 +167,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Write2", ButtonNote->"Write2"], "." -}], "Text", - CellTags->"FUNCTION", - CellID->234059656] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -255,12 +253,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{851, Automatic}, {Automatic, 123}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FV.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FV.nb index 82c6fa06c..924b671b2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FV.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FV.nb @@ -180,19 +180,12 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FVD", ButtonNote->"FVD"], ", ", - ButtonBox["FourVector", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], - ", ", ButtonBox["Pair", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Pair", ButtonNote->"Pair"], "." -}], "Text", - CellTags->"FV", - CellID->449809030] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -225,28 +218,23 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Input", CellTags->"FV", - CellLabel->"In[1]:=", + CellLabel->"In[161]:=", CellID->1800701132], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], TraditionalForm]], "Output", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", CellTags->"FV", - CellLabel->"Out[1]=", - CellID->1773215925] + CellLabel->"Out[161]="] }, Open ]], Cell[CellGroupData[{ @@ -256,35 +244,30 @@ Cell[BoxData[ RowBox[{ RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}]], "Input", CellTags->"FV", - CellLabel->"In[2]:=", + CellLabel->"In[162]:=", CellID->1600944575], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm], TraditionalForm]], "Output", + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", CellTags->"FV", - CellLabel->"Out[2]=", - CellID->1009721662] + CellLabel->"Out[162]="] }, Open ]], Cell[CellGroupData[{ @@ -294,15 +277,14 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"FV", - CellLabel->"In[3]:=", + CellLabel->"In[163]:=", CellID->2031151174], Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Output", CellTags->"FV", - CellLabel->"Out[3]//StandardForm=", - CellID->732230663] + CellLabel->"Out[163]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -314,7 +296,7 @@ Cell[BoxData[ RowBox[{"p", ",", "\[Mu]"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"FV", - CellLabel->"In[4]:=", + CellLabel->"In[164]:=", CellID->1187758267], Cell[BoxData[ @@ -323,16 +305,11 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]], "Output", CellTags->"FV", - CellLabel->"Out[4]//StandardForm=", - CellID->1070070718] + CellLabel->"Out[164]//StandardForm="] }, Open ]], -Cell["\<\ -There is no special function to expand momenta in FV; ExpandScalarProduct \ -does the job.\ -\>", "Text", - CellTags->"FV", - CellID->1859479702], +Cell["ExpandScalarProduct is used to expand momenta in FV", "Notes", + CellID->97927264], Cell[CellGroupData[{ @@ -341,67 +318,33 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{ RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}], "]"}]], "Input", - CellTags->"FV", - CellLabel->"In[5]:=", - CellID->260687674], + CellLabel->"In[165]:=", + CellID->1140711302], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], "-", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"FV", - CellLabel->"Out[5]=", - CellID->1212809923] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"StandardForm", "[", "%", "]"}]], "Input", - CellTags->"FV", - CellLabel->"In[6]:=", - CellID->306111649], - -Cell[BoxData[ - RowBox[{ - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", - RowBox[{"Momentum", "[", "p", "]"}]}], "]"}], "-", - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", - RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]}]], "Output", - CellTags->"FV", - CellLabel->"Out[6]//StandardForm=", - CellID->1086258444] + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], "-", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", + CellLabel->"Out[165]="] }, Open ]] }, Open ]], @@ -466,12 +409,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{804, Automatic}, {Automatic, 65}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FVD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FVD.nb index b643d06fb..5916d9499 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FVD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FVD.nb @@ -182,19 +182,12 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FV", ButtonNote->"FV"], ", ", - ButtonBox["FourVector", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], - ", ", ButtonBox["Pair", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Pair", ButtonNote->"Pair"], "." -}], "Text", - CellTags->"FVD", - CellID->213085227] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -227,27 +220,22 @@ Cell[BoxData[ RowBox[{"FVD", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Input", CellTags->"FVD", - CellLabel->"In[1]:=", + CellLabel->"In[166]:=", CellID->1179313259], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], TraditionalForm]], "Output", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", CellTags->"FVD", - CellLabel->"Out[1]=", - CellID->523628619] + CellLabel->"Out[166]="] }, Open ]], Cell[CellGroupData[{ @@ -257,33 +245,28 @@ Cell[BoxData[ RowBox[{ RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}]], "Input", CellTags->"FVD", - CellLabel->"In[2]:=", + CellLabel->"In[167]:=", CellID->4229236], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - FormBox["p", - TraditionalForm], "-", - FormBox["q", - TraditionalForm]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], TraditionalForm], - TraditionalForm]], - TraditionalForm], TraditionalForm]], "Output", + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", CellTags->"FVD", - CellLabel->"Out[2]=", - CellID->1285947653] + CellLabel->"Out[167]="] }, Open ]], Cell[CellGroupData[{ @@ -293,15 +276,14 @@ Cell[BoxData[ RowBox[{"FVD", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"FVD", - CellLabel->"In[3]:=", + CellLabel->"In[168]:=", CellID->417689841], Cell[BoxData[ RowBox[{"FVD", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Output", CellTags->"FVD", - CellLabel->"Out[3]//StandardForm=", - CellID->1974189044] + CellLabel->"Out[168]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -313,7 +295,7 @@ Cell[BoxData[ RowBox[{"p", ",", "\[Mu]"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"FVD", - CellLabel->"In[4]:=", + CellLabel->"In[169]:=", CellID->387897032], Cell[BoxData[ @@ -324,13 +306,10 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "D"}], "]"}]}], "]"}]], "Output", CellTags->"FVD", - CellLabel->"Out[4]//StandardForm=", - CellID->2132317319] + CellLabel->"Out[169]//StandardForm="] }, Open ]], -Cell["There is no special function to expand momenta in FVD.", "Text", - CellTags->"FVD", - CellID->1109547966], +Cell["There is no special function to expand momenta in FVD.", "Notes"], Cell[CellGroupData[{ @@ -340,41 +319,32 @@ Cell[BoxData[ RowBox[{ RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}], "]"}]], "Input", CellTags->"FVD", - CellLabel->"In[5]:=", + CellLabel->"In[170]:=", CellID->117451470], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], "-", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["q", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], "-", + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"FVD", - CellLabel->"Out[5]=", - CellID->1622123785] + CellLabel->"Out[170]="] }, Open ]], Cell[CellGroupData[{ @@ -382,7 +352,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"StandardForm", "[", "%", "]"}]], "Input", CellTags->"FVD", - CellLabel->"In[6]:=", + CellLabel->"In[171]:=", CellID->1697636138], Cell[BoxData[ @@ -400,8 +370,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"q", ",", "D"}], "]"}]}], "]"}]}]], "Output", CellTags->"FVD", - CellLabel->"Out[6]//StandardForm=", - CellID->779988217] + CellLabel->"Out[171]//StandardForm="] }, 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+ CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/FVE", "Categorization", + CellLabel->"URI"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + 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ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FVE", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Input", + CellTags->"FVE", + CellLabel->"In[172]:=", + CellID->1179313259], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellTags->"FVE", + CellLabel->"Out[172]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FVE", "[", + RowBox[{ + RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}]], "Input", + CellTags->"FVE", + CellLabel->"In[173]:=", + CellID->4229236], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + RowBox[{"(", + FormBox[ + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"]}], + TraditionalForm], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellTags->"FVE", + CellLabel->"Out[173]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FVE", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}], "//", "StandardForm"}]], "Input", + CellTags->"FVE", + CellLabel->"In[174]:=", + CellID->417689841], + +Cell[BoxData[ + RowBox[{"FVE", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Output", + CellTags->"FVE", + CellLabel->"Out[174]//StandardForm="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"FVE", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}], "]"}], "//", + "StandardForm"}]], "Input", + CellTags->"FVD", + CellLabel->"In[175]:=", + CellID->387897032], + +Cell[BoxData[ + RowBox[{"Pair", "[", + RowBox[{ + 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RowBox[{ + RowBox[{"FVE", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}], + RowBox[{"FV", "[", + RowBox[{"q", ",", "\[Mu]"}], "]"}]}], "]"}]], "Input", + CellLabel->"In[178]:="], + +Cell[BoxData[ + FormBox["0", TraditionalForm]], "Output", + CellLabel->"Out[178]="] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Open ]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{983, Automatic}, {207, Automatic}}, +Visible->True, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Factor1.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Factor1.nb index dd7bc5008..1f1369cfd 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Factor1.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Factor1.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Factor2", ButtonNote->"Factor2"], "." -}], "Text", - CellTags->"Factor1", - CellID->73262209] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -198,14 +196,13 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{ - RowBox[{"(", - RowBox[{"a", "-", "x"}], ")"}], - RowBox[{"(", - RowBox[{"b", "-", "x"}], ")"}]}]}]], "Input", + RowBox[{ + RowBox[{"(", + RowBox[{"a", "-", "x"}], ")"}], + RowBox[{"(", + RowBox[{"b", "-", "x"}], ")"}]}]], "Input", CellTags->"Factor1", - CellLabel->"In[1]:=", + CellLabel->"In[185]:=", CellID->106113384], Cell[BoxData[ @@ -216,20 +213,18 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"b", "-", "x"}], ")"}]}], TraditionalForm]], "Output", CellTags->"Factor1", - CellLabel->"Out[1]=", - CellID->705307377] + CellLabel->"Out[185]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"Factor1", "[", "t1", "]"}], ",", " ", - RowBox[{"Factor", "[", "t1", "]"}]}], "}"}]}]], "Input", + RowBox[{"{", + RowBox[{ + RowBox[{"Factor1", "[", "%", "]"}], ",", " ", + RowBox[{"Factor", "[", "%", "]"}]}], "}"}]], "Input", CellTags->"Factor1", - CellLabel->"In[2]:=", + CellLabel->"In[186]:=", CellID->1501862951], Cell[BoxData[ @@ -248,22 +243,20 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"x", "-", "b"}], ")"}]}]}], "}"}], TraditionalForm]], "Output", CellTags->"Factor1", - CellLabel->"Out[2]=", - CellID->1528620346] + CellLabel->"Out[186]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t3", "=", - RowBox[{"Expand", "[", - RowBox[{ - RowBox[{"(", - RowBox[{"a", "-", "b"}], ")"}], - RowBox[{"(", - RowBox[{"a", "+", "b"}], ")"}]}], "]"}]}]], "Input", + RowBox[{"Expand", "[", + RowBox[{ + RowBox[{"(", + RowBox[{"a", "-", "b"}], ")"}], + RowBox[{"(", + RowBox[{"a", "+", "b"}], ")"}]}], "]"}]], "Input", CellTags->"Factor1", - CellLabel->"In[3]:=", + CellLabel->"In[187]:=", CellID->641613489], Cell[BoxData[ @@ -272,16 +265,15 @@ Cell[BoxData[ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], TraditionalForm]], "Output", CellTags->"Factor1", - CellLabel->"Out[3]=", - CellID->2030611853] + CellLabel->"Out[187]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Factor", "[", "t3", "]"}]], "Input", + RowBox[{"Factor", "[", "%", "]"}]], "Input", CellTags->"Factor1", - CellLabel->"In[4]:=", + CellLabel->"In[188]:=", CellID->916389340], Cell[BoxData[ @@ -292,16 +284,15 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}]}], TraditionalForm]], "Output", CellTags->"Factor1", - CellLabel->"Out[4]=", - CellID->865327707] + CellLabel->"Out[188]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Factor1", "[", "t3", "]"}]], "Input", + RowBox[{"Factor1", "[", "%%", "]"}]], "Input", CellTags->"Factor1", - CellLabel->"In[5]:=", + CellLabel->"In[189]:=", CellID->892191531], Cell[BoxData[ @@ -310,16 +301,8 @@ Cell[BoxData[ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], TraditionalForm]], "Output", CellTags->"Factor1", - CellLabel->"Out[5]=", - CellID->1139945824] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2", ",", "t3"}], "]"}]], "Input", - CellTags->"Factor1", - CellLabel->"In[6]:=", - CellID->1482315372] + CellLabel->"Out[189]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -383,12 +366,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{889, Automatic}, {Automatic, 262}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Factor2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Factor2.nb index 6ecb92401..b80c84ede 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Factor2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Factor2.nb @@ -128,7 +128,22 @@ will work faster than Factor2." CellID->982511436], Cell["XXXX", "Notes", - CellID->1067943069] + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Factor2", "]"}]], "Input", + CellLabel->"In[191]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FactorFull", "\[Rule]", "False"}], ",", + RowBox[{"Method", "\[Rule]", "3"}]}], "}"}], TraditionalForm]], "Output", + CellLabel->"Out[191]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -169,9 +184,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Collect2", ButtonNote->"Collect2"], "." -}], "Text", - CellTags->"Factor2", - CellID->1336134208] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,33 +214,13 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Options", "[", "Factor2", "]"}]], "Input", - CellTags->"Factor2", - CellLabel->"In[1]:=", - CellID->1016935483], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"FactorFull", "\[Rule]", "False"}], ",", - RowBox[{"Method", "\[Rule]", "3"}]}], "}"}], TraditionalForm]], "Output", + RowBox[{ + RowBox[{"(", + RowBox[{"a", "-", "x"}], ")"}], + RowBox[{"(", + RowBox[{"b", "-", "x"}], ")"}]}]], "Input", CellTags->"Factor2", - CellLabel->"Out[1]=", - CellID->607387604] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{ - RowBox[{"(", - RowBox[{"a", "-", "x"}], ")"}], - RowBox[{"(", - RowBox[{"b", "-", "x"}], ")"}]}]}]], "Input", - CellTags->"Factor2", - CellLabel->"In[2]:=", + CellLabel->"In[192]:=", CellID->1709627606], Cell[BoxData[ @@ -238,20 +231,18 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"b", "-", "x"}], ")"}]}], TraditionalForm]], "Output", CellTags->"Factor2", - CellLabel->"Out[2]=", - CellID->309712518] + CellLabel->"Out[192]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", "=", - RowBox[{"{", - RowBox[{ - RowBox[{"Factor2", "[", "t1", "]"}], ",", " ", - RowBox[{"Factor", "[", "t1", "]"}]}], "}"}]}]], "Input", + RowBox[{"{", + RowBox[{ + RowBox[{"Factor2", "[", "%", "]"}], ",", " ", + RowBox[{"Factor", "[", "%", "]"}]}], "}"}]], "Input", CellTags->"Factor2", - CellLabel->"In[3]:=", + CellLabel->"In[193]:=", CellID->1823984490], Cell[BoxData[ @@ -270,22 +261,20 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"x", "-", "b"}], ")"}]}]}], "}"}], TraditionalForm]], "Output", CellTags->"Factor2", - CellLabel->"Out[3]=", - CellID->136738799] + CellLabel->"Out[193]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t3", "=", - RowBox[{"Expand", "[", - RowBox[{ - RowBox[{"(", - RowBox[{"a", "-", "b"}], ")"}], - RowBox[{"(", - RowBox[{"a", "+", "b"}], ")"}]}], "]"}]}]], "Input", + RowBox[{"Expand", "[", + RowBox[{ + RowBox[{"(", + RowBox[{"a", "-", "b"}], ")"}], + RowBox[{"(", + RowBox[{"a", "+", "b"}], ")"}]}], "]"}]], "Input", CellTags->"Factor2", - CellLabel->"In[4]:=", + CellLabel->"In[194]:=", CellID->3094581], Cell[BoxData[ @@ -294,16 +283,15 @@ Cell[BoxData[ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], TraditionalForm]], "Output", CellTags->"Factor2", - CellLabel->"Out[4]=", - CellID->470899621] + CellLabel->"Out[194]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Factor", "[", "t3", "]"}]], "Input", + RowBox[{"Factor", "[", "%", "]"}]], "Input", CellTags->"Factor2", - CellLabel->"In[5]:=", + CellLabel->"In[195]:=", CellID->791609042], Cell[BoxData[ @@ -314,16 +302,15 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}]}], TraditionalForm]], "Output", CellTags->"Factor2", - CellLabel->"Out[5]=", - CellID->2074352994] + CellLabel->"Out[195]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Factor2", "[", "t3", "]"}]], "Input", + RowBox[{"Factor2", "[", "%%", "]"}]], "Input", CellTags->"Factor2", - CellLabel->"In[6]:=", + CellLabel->"In[196]:=", CellID->880415397], Cell[BoxData[ @@ -332,18 +319,17 @@ Cell[BoxData[ SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]}], TraditionalForm]], "Output", CellTags->"Factor2", - CellLabel->"Out[6]=", - CellID->611482702] + CellLabel->"Out[196]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Factor2", "[", - RowBox[{"t3", ",", + RowBox[{"%%%", ",", RowBox[{"FactorFull", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Factor2", - CellLabel->"In[7]:=", + CellLabel->"In[197]:=", CellID->17862753], Cell[BoxData[ @@ -354,16 +340,8 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}]}], TraditionalForm]], "Output", CellTags->"Factor2", - CellLabel->"Out[7]=", - CellID->1886805891] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2", ",", "t3"}], "]"}]], "Input", - CellTags->"Factor2", - CellLabel->"In[8]:=", - CellID->2010909365] + CellLabel->"Out[197]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -427,12 +405,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{996, Automatic}, {Automatic, 248}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FactorFull.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FactorFull.nb index 9c9f2d58e..bfc038820 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FactorFull.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FactorFull.nb @@ -184,9 +184,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Factor2", ButtonNote->"Factor2"], "." -}], "Text", - CellTags->"FactorFull", - CellID->1018782586] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -272,12 +270,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1210, Automatic}, {Automatic, 209}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Factoring.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Factoring.nb index 7089b68c3..505c43398 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Factoring.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Factoring.nb @@ -176,9 +176,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Tr", ButtonNote->"Tr"], "." -}], "Text", - CellTags->"Factoring", - CellID->1376974355] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -264,12 +262,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{990, Automatic}, {Automatic, 233}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Factorout.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Factorout.nb index 4b1553509..9d833e230 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Factorout.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Factorout.nb @@ -169,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPEIntegrate", ButtonNote->"OPEIntegrate"], "." -}], "Text", - CellTags->"Factorout", - CellID->885134333] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1242, Automatic}, {Automatic, 242}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FermionSpinSum.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FermionSpinSum.nb index bd6dec4bb..afacf966d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FermionSpinSum.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FermionSpinSum.nb @@ -117,14 +117,45 @@ Cell["FermionSpinSum", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"FermionSpinSum", "[", "x", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "constructs the Traces out of squared ampliudes." + RowBox[{"FermionSpinSum", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]converts products of closed spinor chains in ", + Cell[BoxData["exp"], "InlineFormula"], + " into Dirac traces. " }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["Both Dirac and Majorana particles are supported.", "Notes"], + +Cell[TextData[{ + "It is understood, that ", + Cell[BoxData["exp"], "InlineFormula"], + " represents a squared amplitude." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FermionSpinSum", "]"}]], "Input", + CellLabel->"In[9]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Collecting", "\[Rule]", "True"}], ",", + RowBox[{"DotSimplify", "\[Rule]", "True"}], ",", + RowBox[{"ExtraFactor", "\[Rule]", "1"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCTraceFactor", "\[Rule]", "True"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "Factor"}], ",", + RowBox[{"Head", "\[Rule]", "Identity"}], ",", + RowBox[{"Momentum", "\[Rule]", "All"}], ",", + RowBox[{"SpinorChainTranspose", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[9]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -174,15 +205,8 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracTrace", ButtonNote->"DiracTrace"], - ", ", - ButtonBox["Tr", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Tr", - ButtonNote->"Tr"], "." -}], "Text", - CellTags->"FermionSpinSum", - CellID->1427307746] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -209,46 +233,9 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "FermionSpinSum", "]"}]], "Input", - CellTags->"FermionSpinSum", - CellLabel->"In[2]:=", - CellID->1391906924], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Collecting", "\[Rule]", "True"}], ",", - RowBox[{"Factoring", "\[Rule]", "Factor"}], ",", - RowBox[{"ExtraFactor", "\[Rule]", "1"}], ",", - RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", - RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", - RowBox[{"DotSimplify", "\[Rule]", "True"}], ",", - RowBox[{"Momentum", "\[Rule]", "All"}], ",", - RowBox[{"SpinPolarizationSum", "\[Rule]", "Identity"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"FermionSpinSum", - CellLabel->"Out[2]=", - CellID->1112492862] -}, Open ]], - -Cell[TextData[{ - "Spinors of fermions of mass ", - StyleBox["m", - FontSlant->"Italic"], - " are normalized to have square 2 ", - StyleBox["m", - FontSlant->"Italic"], - " or -2 ", - StyleBox["m", - FontSlant->"Italic"], - "." -}], "Text", - CellTags->"FermionSpinSum", - CellID->1255696897], +Cell["\<\ +FeynCalc uses the customary relativistic normalization of the spinors.\ +\>", "Notes"], Cell[CellGroupData[{ @@ -261,7 +248,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Momentum", "[", "p", "]"}], ",", "m"}], "]"}]}]], "Input", CellTags->"FermionSpinSum", - CellLabel->"In[3]:=", + CellLabel->"In[10]:=", CellID->278938360], Cell[BoxData[ @@ -276,35 +263,24 @@ Cell[BoxData[ TraditionalForm], ",", FormBox["m", TraditionalForm], ")"}], ".", - RowBox[{"(", - RowBox[{ - FormBox["\<\"u\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", + RowBox[{"u", "(", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"FermionSpinSum", - CellLabel->"Out[3]=", - CellID->1523865852] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"%", "//", "FCI"}], "//", "FermionSpinSum"}]], "Input", + RowBox[{"FermionSpinSum", "[", "%", "]"}]], "Input", CellTags->"FermionSpinSum", - CellLabel->"In[4]:=", + CellLabel->"In[11]:=", CellID->505730343], Cell[BoxData[ @@ -321,25 +297,22 @@ Cell[BoxData[ TraditionalForm]}], "+", "m"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"FermionSpinSum", - CellLabel->"Out[4]=", - CellID->385708083] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"%", "/.", - RowBox[{"DiracTrace", "\[Rule]", "TR"}]}]], "Input", + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", CellTags->"FermionSpinSum", - CellLabel->"In[5]:=", + CellLabel->"In[12]:=", CellID->1201144341], Cell[BoxData[ FormBox[ RowBox[{"4", " ", "m"}], TraditionalForm]], "Output", CellTags->"FermionSpinSum", - CellLabel->"Out[5]=", - CellID->867661469] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -353,7 +326,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Momentum", "[", "p", "]"}], ",", "m"}], "]"}]}]], "Input", CellTags->"FermionSpinSum", - CellLabel->"In[6]:=", + CellLabel->"In[13]:=", CellID->1209998846], Cell[BoxData[ @@ -368,35 +341,24 @@ Cell[BoxData[ TraditionalForm], ",", FormBox["m", TraditionalForm], ")"}], ".", - RowBox[{"(", - RowBox[{ - FormBox["\<\"v\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", + RowBox[{"v", "(", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"FermionSpinSum", - CellLabel->"Out[6]=", - CellID->1761985113] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"%", "//", "FCI"}], "//", "FermionSpinSum"}]], "Input", + RowBox[{"FermionSpinSum", "[", "%", "]"}]], "Input", CellTags->"FermionSpinSum", - CellLabel->"In[7]:=", + CellLabel->"In[14]:=", CellID->723398437], Cell[BoxData[ @@ -413,17 +375,15 @@ Cell[BoxData[ TraditionalForm]}], "-", "m"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"FermionSpinSum", - CellLabel->"Out[7]=", - CellID->1462275463] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"%", "/.", - RowBox[{"DiracTrace", "\[Rule]", "TR"}]}]], "Input", + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", CellTags->"FermionSpinSum", - CellLabel->"In[8]:=", + CellLabel->"In[15]:=", CellID->680865455], Cell[BoxData[ @@ -431,160 +391,158 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "4"}], " ", "m"}], TraditionalForm]], "Output", CellTags->"FermionSpinSum", - CellLabel->"Out[8]=", - CellID->1782629402] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t", "=", - RowBox[{ - RowBox[{"Spinor", "[", - RowBox[{"k1", ",", "m"}], "]"}], ".", - RowBox[{"DiracSlash", "[", "p", "]"}], ".", - RowBox[{"GA", "[", "5", "]"}], ".", - RowBox[{"Spinor", "[", - RowBox[{"p1", ",", "m"}], "]"}]}]}]], "Input", + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SpinorUBar", "[", + RowBox[{"k1", ",", "m"}], "]"}], ".", + RowBox[{"GS", "[", "p", "]"}], ".", + RowBox[{"GA", "[", "5", "]"}], ".", + RowBox[{"SpinorU", "[", + RowBox[{"p1", ",", "m"}], "]"}]}]], "Input", CellTags->"FermionSpinSum", - CellLabel->"In[9]:=", + CellLabel->"In[16]:=", CellID->1094170176], Cell[BoxData[ FormBox[ RowBox[{ + RowBox[{ + OverscriptBox["u", "_"], "(", + FormBox["k1", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}], ".", RowBox[{"(", - 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TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", + RowBox[{"u", "(", + FormBox["p1", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"FermionSpinSum", - CellLabel->"Out[9]=", - CellID->690680779] + CellLabel->"Out[16]="] }, Open ]], -Cell["\<\ -Notice that SpinorUBar and SpinorU are only input functions. Internally they \ -are converted to Spinor objects.\ -\>", "Text", - CellTags->"FermionSpinSum", - CellID->306087100], - Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ct", "=", - RowBox[{"ComplexConjugate", "[", "t", "]"}]}]], "Input", - CellTags->"FermionSpinSum", - CellLabel->"In[10]:=", - CellID->1096475209], + RowBox[{"%", " ", + RowBox[{"ComplexConjugate", "[", "%", "]"}]}]], "Input", + CellLabel->"In[17]:="], Cell[BoxData[ FormBox[ - RowBox[{"-", + RowBox[{ RowBox[{ + RowBox[{ + OverscriptBox["u", "_"], "(", + FormBox["k1", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}], ".", RowBox[{"(", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], + TraditionalForm], ".", + RowBox[{"u", "(", + FormBox["p1", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}]}], " ", + RowBox[{"(", + RowBox[{"-", RowBox[{ - FormBox["\<\"\[CurlyPhi]\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["p1", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], ")"}], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox["5", - TraditionalForm]], ".", - RowBox[{"(", - RowBox[{ - OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm]}], ")"}], ".", - RowBox[{"(", - RowBox[{ - FormBox["\<\"\[CurlyPhi]\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["k1", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], ")"}]}]}], TraditionalForm]], "Output", - CellTags->"FermionSpinSum", - CellLabel->"Out[10]=", - CellID->1746604990] + RowBox[{"(", + RowBox[{ + FormBox["\<\"\[CurlyPhi]\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["p1", + TraditionalForm], "_"], + TraditionalForm], + FormBox["\<\",\"\>", + TraditionalForm], + FormBox["m", + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], ")"}], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], ")"}], ".", + RowBox[{"(", + RowBox[{ + FormBox["\<\"\[CurlyPhi]\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["k1", + TraditionalForm], "_"], + TraditionalForm], + FormBox["\<\",\"\>", + TraditionalForm], + FormBox["m", + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], ")"}]}]}], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[17]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"FermionSpinSum", "[", - RowBox[{"t", " ", "ct"}], "]"}]], "Input", - CellTags->"FermionSpinSum", - CellLabel->"In[11]:=", - CellID->2140871689], + RowBox[{"FermionSpinSum", "[", "%", "]"}]], "Input", + CellLabel->"In[18]:="], Cell[BoxData[ FormBox[ @@ -598,13 +556,9 @@ Cell[BoxData[ OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", FormBox[ OverscriptBox[ - FormBox["p1", + FormBox["k1", TraditionalForm], "_"], TraditionalForm]}], "+", "m"}], ")"}], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox["5", - TraditionalForm]], ".", RowBox[{"(", RowBox[{ OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", @@ -613,15 +567,23 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm]}], ")"}], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], ".", RowBox[{"(", RowBox[{ RowBox[{ OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", FormBox[ OverscriptBox[ - FormBox["k1", + FormBox["p1", TraditionalForm], "_"], TraditionalForm]}], "+", "m"}], ")"}], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["5", + TraditionalForm]], ".", RowBox[{"(", RowBox[{ OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", @@ -629,101 +591,82 @@ Cell[BoxData[ OverscriptBox[ FormBox["p", TraditionalForm], "_"], - TraditionalForm]}], ")"}], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox["5", - TraditionalForm]]}], + TraditionalForm]}], ")"}]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", - CellTags->"FermionSpinSum", - CellLabel->"Out[11]=", - CellID->1062780285] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"%", " ", "/.", - RowBox[{"DiracTrace", "\[Rule]", "TR"}]}]], "Input", - CellTags->"FermionSpinSum", - CellLabel->"In[12]:=", - CellID->1433763873], + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[19]:="], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{"-", "4"}], " ", - RowBox[{"(", - RowBox[{ - RowBox[{ - SuperscriptBox[ + RowBox[{"-", + RowBox[{"4", " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], "2"], " ", + RowBox[{"(", + RowBox[{ FormBox[ OverscriptBox[ - FormBox["p", + FormBox["k1", TraditionalForm], "_"], - TraditionalForm], "2"], " ", - RowBox[{"(", - RowBox[{ - FormBox[ - OverscriptBox[ - FormBox["k1", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["p1", - TraditionalForm], "_"], - TraditionalForm]}], ")"}]}], "-", - RowBox[{"2", " ", - RowBox[{"(", - RowBox[{ - FormBox[ - OverscriptBox[ - FormBox["k1", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm]}], ")"}], " ", - RowBox[{"(", - RowBox[{ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["p1", - TraditionalForm], "_"], - TraditionalForm]}], ")"}]}], "+", - RowBox[{ - SuperscriptBox["m", "2"], " ", - SuperscriptBox[ + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], FormBox[ OverscriptBox[ - FormBox["p", + FormBox["p1", TraditionalForm], "_"], - TraditionalForm], "2"]}]}], ")"}]}], TraditionalForm]], "Output", - CellTags->"FermionSpinSum", - CellLabel->"Out[12]=", - CellID->153933314] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"t", ",", " ", "ct"}], "]"}]], "Input", - CellTags->"FermionSpinSum", - CellLabel->"In[13]:=", - CellID->1557584860] + TraditionalForm]}], ")"}]}]}], "+", + RowBox[{"8", " ", + RowBox[{"(", + RowBox[{ + FormBox[ + OverscriptBox[ + FormBox["k1", + TraditionalForm], "_"], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], ")"}], " ", + RowBox[{"(", + RowBox[{ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["p1", + TraditionalForm], "_"], + TraditionalForm]}], ")"}]}], "-", + RowBox[{"4", " ", + SuperscriptBox["m", "2"], " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], "2"]}]}], TraditionalForm]], "Output", + CellLabel->"Out[19]="] +}, Open ]] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -786,10 +729,11 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 683}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{999, 906}, +WindowMargins->{{399, Automatic}, {Automatic, 168}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmp.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmp.nb index 170fc2180..44ee67d82 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmp.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmp.nb @@ -119,16 +119,16 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"FeynAmp", "[", RowBox[{"q", ",", " ", "amp"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the head of a Feynman amplitude, where amp denotes the analytical \ -expression for the amplitude and q is the integration variable. FeynAmp[q1, \ -q2, amp] denotes a two-loop amplitude.\n\nFeynAmp has no functional \ -properties and serves just as a head. There are however special typesetting \ -rules attached." + " \[LineSeparator]is the head of a Feynman amplitude, where amp denotes the \ +analytical expression for the amplitude and q is the integration variable. \ +FeynAmp[q1, q2, amp] denotes a two-loop amplitude." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +FeynAmp has no functional properties and serves just as a head. There are \ +however special typesetting rules attached.\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Amplitude", ButtonNote->"Amplitude"], "." -}], "Text", - CellTags->"FeynAmp", - CellID->1771618737] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -202,9 +200,7 @@ Cell[BoxData[ Cell["\<\ This is a 1-loop gluon self-energy amplitude (ignoring factors of (2 \[Pi])).\ \ -\>", "Text", - CellTags->"FeynAmp", - CellID->1803940715], +\>", "Notes"], Cell[CellGroupData[{ @@ -230,7 +226,7 @@ Cell[BoxData[ "q", ",", " ", "\[Beta]", ",", "e", ",", " ", "\[Sigma]", ",", "f"}], "]"}]}]}], "]"}]], "Input", CellTags->"FeynAmp", - CellLabel->"In[1]:=", + CellLabel->"In[13]:=", CellID->772375685], Cell[BoxData[ @@ -378,13 +374,10 @@ Cell[BoxData[ TraditionalForm], ")"}]}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"FeynAmp", - CellLabel->"Out[1]=", - CellID->1301141355] + CellLabel->"Out[13]="] }, Open ]], -Cell["This is a generic 2-loop amplitude.", "Text", - CellTags->"FeynAmp", - CellID->311938840], +Cell["This is a generic 2-loop amplitude.", "Notes"], Cell[CellGroupData[{ @@ -394,7 +387,7 @@ Cell[BoxData[ SubscriptBox["q", "1"], ",", SubscriptBox["q", "2"], ",", "anyexpression"}], "]"}]], "Input", CellTags->"FeynAmp", - CellLabel->"In[2]:=", + CellLabel->"In[15]:=", CellID->1547526680], Cell[BoxData[ @@ -405,8 +398,7 @@ Cell[BoxData[ SubscriptBox["q", "2"], ",", "anyexpression"}], ")"}], TraditionalForm]], "Output", CellTags->"FeynAmp", - CellLabel->"Out[2]=", - CellID->1833982253] + CellLabel->"Out[15]="] }, Open ]] }, Open ]], @@ -471,12 +463,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{908, Automatic}, {Automatic, 213}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpDenominator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpDenominator.nb index dd2bb4581..e477a4e33 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpDenominator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpDenominator.nb @@ -117,11 +117,11 @@ Cell["FeynAmpDenominator", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"FeynAmpDenominator", "["}]], "InlineFormula"], - " \[LineSeparator]", - "PropagatorDenominator[ ... ], PropagatorDenominator[ ... ], ...] is the \ -head of the denominators of the propagators, i.e., FeynAmpDenominator[x] is \ -the representation of 1/x ." + RowBox[{"FeynAmpDenominator", "[", "...", "]"}]], "InlineFormula"], + " represents the inverse denominators of the propagators, i.e. \ +FeynAmpDenominator[x] is 1/x. Different propagator denominators are \ +represented using special heads such as PropagatorDenominator, \ +StandardPropagatorDenominator, CartesianPropagatorDenominator etc." }], "Usage", CellID->982511436], @@ -167,14 +167,27 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FAD", ButtonNote->"FAD"], ", ", + ButtonBox["SFAD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SFAD", + ButtonNote->"SFAD"], + ", ", + ButtonBox["CFAD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CFAD", + ButtonNote->"CFAD"], + ", ", + ButtonBox["GFAD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/GFAD", + ButtonNote->"GFAD"], + ", ", ButtonBox["FeynAmpDenominatorSimplify", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FeynAmpDenominatorSimplify", ButtonNote->"FeynAmpDenominatorSimplify"], "." -}], "Text", - CellTags->"FeynAmpDenominator", - CellID->1703753966] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,25 +214,49 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], +Cell[TextData[{ + "The old way to represent standard Lorentzian propagators is to use \ +PropagatorDenominator. Here the sign of the mass term is fixed to be ", + Cell[BoxData[ + RowBox[{"-", "1"}]], "InlineFormula"], + " and no information on the ", + Cell[BoxData[ + RowBox[{"I", " ", "\[Eta]"}]], "InlineFormula"], + "- prescription is available. Furterhmore, this way it is not possible to \ +enter eikonal propagators" +}], "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FeynAmpDenominator", "[", RowBox[{"PropagatorDenominator", "[", - RowBox[{"p", ",", "m"}], "]"}], "]"}]], "Input", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "m"}], "]"}], "]"}]], "Input", CellTags->"FeynAmpDenominator", - CellLabel->"In[1]:=", + CellLabel->"In[16]:=", CellID->1348679348], Cell[BoxData[ FormBox[ FractionBox["1", - RowBox[{ - SuperscriptBox["p", "2"], "-", - SuperscriptBox["m", "2"]}]], TraditionalForm]], "Output", + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]], "-", $CellContext`m^2], + Editable->False]], TraditionalForm]], "Output", CellTags->"FeynAmpDenominator", - CellLabel->"Out[1]=", - CellID->1385454227] + CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ @@ -228,12 +265,17 @@ Cell[BoxData[ RowBox[{"FeynAmpDenominator", "[", RowBox[{ RowBox[{"PropagatorDenominator", "[", - RowBox[{"p", ",", "m"}], "]"}], ",", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "m"}], "]"}], ",", RowBox[{"PropagatorDenominator", "[", RowBox[{ - RowBox[{"p", "-", "q"}], ",", "m"}], "]"}]}], "]"}]], "Input", + RowBox[{"Momentum", "[", + RowBox[{ + RowBox[{"p", "-", "q"}], ",", "D"}], "]"}], ",", "m"}], "]"}]}], + "]"}]], "Input", CellTags->"FeynAmpDenominator", - CellLabel->"In[2]:=", + CellLabel->"In[17]:=", CellID->1096136338], Cell[BoxData[ @@ -241,74 +283,772 @@ Cell[BoxData[ FractionBox["1", RowBox[{ RowBox[{"(", - RowBox[{ - SuperscriptBox["p", "2"], "-", - SuperscriptBox["m", "2"]}], ")"}], ".", + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]], "-", $CellContext`m^2], + Editable->False], ")"}], ".", RowBox[{"(", - RowBox[{ - SuperscriptBox[ - RowBox[{"(", - RowBox[{"p", "-", "q"}], ")"}], "2"], "-", - SuperscriptBox["m", "2"]}], ")"}]}]], TraditionalForm]], "Output", + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D], + FeynCalc`Momentum[$CellContext`p - $CellContext`q, D]], + "-", $CellContext`m^2], + Editable->False], ")"}]}]], TraditionalForm]], "Output", CellTags->"FeynAmpDenominator", - CellLabel->"Out[2]=", - CellID->303237864] + CellLabel->"Out[17]="] }, Open ]], +Cell["\<\ +The shortcut to enter FeynAmpDenominators with PropagatorDenominators is FAD\ +\>", "Notes"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ - RowBox[{"t", "=", + RowBox[{ RowBox[{"FeynAmpDenominator", "[", RowBox[{"PropagatorDenominator", "[", - RowBox[{"p", ",", "m"}], "]"}], "]"}]}], ";"}]], "Input", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "m"}], "]"}], "]"}], "//", + "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"FeynAmpDenominator", - CellLabel->"In[3]:=", - CellID->1741601383], + CellLabel->"In[18]:=", + CellID->1592188506], + +Cell[BoxData[ + RowBox[{"FAD", "[", + RowBox[{"{", + RowBox[{"p", ",", "m"}], "}"}], "]"}]], "Output", + CellTags->"FeynAmpDenominator", + CellLabel->"Out[18]//StandardForm="] +}, Open ]], + +Cell["\<\ +Since version 9.3, a more flexible input is possible using \ +StandardPropagatorDenominator\ +\>", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"t", "//", "FCI"}], "]"}]], "Input", - CellTags->"FeynAmpDenominator", - CellLabel->"In[4]:=", - CellID->1540629635], + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[19]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[19]="] +}, Open ]], + +Cell["\<\ +The mass term can be anything, as long as it does not depend on the loop \ +momenta\ +\>", "Notes"], + +Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FeynAmpDenominator", "[", - RowBox[{"PropagatorDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", RowBox[{ RowBox[{"Momentum", "[", - RowBox[{"p", ",", "D"}], "]"}], ",", "m"}], "]"}], "]"}]], "Output", - CellTags->"FeynAmpDenominator", - CellLabel->"Out[4]//StandardForm=", - CellID->1126645796] + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[20]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"", + SuperscriptBox["m", "2"],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[20]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", "MM", ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[21]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"","MM", + "\"+\"",RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[21]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"SPD", "[", + RowBox[{"q", ",", "q"}], "]"}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[22]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"",FormBox[ + SuperscriptBox[ + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm], 2], TraditionalForm], + "\"+\"",RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[22]="] +}, Open ]], + +Cell[TextData[{ + "One can also change the sign of the ", + Cell[BoxData[ + RowBox[{"I", " ", "\[Eta]"}]], "InlineFormula"], + "- prescription, although currently no internal functions make use of it" +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{"-", "1"}]}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[23]:="], 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RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"], "3"]], TraditionalForm]], "Output", + CellLabel->"Out[24]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "2"}], ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[25]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"", + SuperscriptBox["m", "2"],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"], "2"], TraditionalForm]], "Output", + CellLabel->"Out[25]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{"n", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[26]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],"\"+\"", + SuperscriptBox["m", "2"],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"], + RowBox[{"-", "n"}]], TraditionalForm]], "Output", + CellLabel->"Out[26]="] +}, Open ]], + +Cell["Eikonal propagators are also supported", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}], ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + 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FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",RowBox[{ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[28]="] +}, Open ]], + +Cell[TextData[{ + "FeynCalc keeps trace of the signs of the scalar products in the eikonal \ +propagators. This is where the ", + Cell[BoxData[ + RowBox[{"I", " ", "\[Eta]"}]], "InlineFormula"], + "- prescription may come handy" +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"-", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}]}], ",", "0", ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[29]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"","\"-\"",RowBox[{ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[29]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}], ",", "0", ",", + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{"-", "1"}]}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[30]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",RowBox[{ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm]}],"\"-\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[30]="] }, Open ]], +Cell["\<\ +The shortcut to enter FeynAmpDenominators with StandardPropagatorDenominators \ +is SFAD\ +\>", "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"t", "//", "FCE"}], "]"}]], "Input", + RowBox[{ + RowBox[{ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}], "//", "FCE"}], "//", + "StandardForm"}]], "Input", CellTags->"FeynAmpDenominator", - CellLabel->"In[5]:=", - CellID->1592188506], + CellLabel->"In[31]:=", + CellID->484409356], Cell[BoxData[ - RowBox[{"FAD", "[", + RowBox[{"SFAD", "[", RowBox[{"{", - RowBox[{"p", ",", "m"}], "}"}], "]"}]], "Output", + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + SuperscriptBox["m", "2"], ",", "1"}], "}"}], ",", "1"}], "}"}], + "]"}]], "Output", CellTags->"FeynAmpDenominator", - CellLabel->"Out[5]//StandardForm=", - CellID->1536013774] + CellLabel->"Out[31]//StandardForm="] }, Open ]], +Cell["\<\ +Eikonal propagators are entered using the dot (\".\") as in noncommutative \ +products\ +\>", "Notes"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{ - RowBox[{"Clear", "[", "t", "]"}], ";"}]], "Input", - CellTags->"FeynAmpDenominator", - CellLabel->"In[6]:=", - CellID->1230382152] + RowBox[{ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}], ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}], "//", "FCE"}], "//", + "StandardForm"}]], "Input", + CellLabel->"In[32]:="], + +Cell[BoxData[ + RowBox[{"SFAD", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"0", ",", + RowBox[{"p", ".", "q"}]}], "}"}], ",", + RowBox[{"{", + RowBox[{ + SuperscriptBox["m", "2"], ",", "1"}], "}"}], ",", "1"}], "}"}], + "]"}]], "Output", + CellLabel->"Out[32]//StandardForm="] +}, Open ]], + +Cell["\<\ +The Cartesian version of StandardPropagatorDenominator is called \ +CartesianPropagatorDenominator. The syntax is almost the same as in \ +StandardPropagatorDenominator, except that the momenta and scalar products \ +must be Cartesian.\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"CartesianPropagatorDenominator", "[", + RowBox[{ + RowBox[{"CartesianMomentum", "[", + RowBox[{"p", ",", + RowBox[{"D", "-", "1"}]}], "]"}], ",", "0", ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{"-", "1"}]}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[142]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox[ + StyleBox["p", Bold, StripOnInput -> False], TraditionalForm], + TraditionalForm], 2],"\"+\"",SuperscriptBox["m", "2"],"\"-\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[142]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"CartesianPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"CartesianPair", "[", + RowBox[{ + RowBox[{"CartesianMomentum", "[", + RowBox[{"p", ",", + RowBox[{"D", "-", "1"}]}], "]"}], ",", + RowBox[{"CartesianMomentum", "[", + RowBox[{"q", ",", + RowBox[{"D", "-", "1"}]}], "]"}]}], "]"}], ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{"-", "1"}]}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[143]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",RowBox[{ + FormBox[ + FormBox[ + StyleBox["p", Bold, StripOnInput -> False], TraditionalForm], + TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox[ + StyleBox["q", Bold, StripOnInput -> False], TraditionalForm], + TraditionalForm]}],"\"+\"",SuperscriptBox["m", "2"],"\"-\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[143]="] +}, Open ]], + +Cell["\<\ +The shortcut to enter FeynAmpDenominators with \ +CartesianPropagatorDenominators is CFAD\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCE", "[", + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"CartesianPropagatorDenominator", "[", + RowBox[{ + RowBox[{"CartesianMomentum", "[", + RowBox[{"p", ",", + RowBox[{"D", "-", "1"}]}], "]"}], ",", "0", ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{"1", ",", + RowBox[{"-", "1"}]}], "}"}]}], "]"}], "]"}], "]"}], "//", + "StandardForm"}]], "Input", + CellLabel->"In[146]:="], + +Cell[BoxData[ + RowBox[{"CFAD", "[", + RowBox[{"{", + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "0"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + SuperscriptBox["m", "2"], ",", + RowBox[{"-", "1"}]}], "}"}], ",", "1"}], "}"}], "]"}]], "Output", + CellLabel->"Out[146]//StandardForm="] +}, Open ]], + +Cell["\<\ +To represent completely arbitrary propagators one can use \ +GenericPropagatorDenominator. However, one should keep in mind that the \ +number of operations using such propagators is very limited.\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"GenericPropagatorDenominator", "[", + RowBox[{"x", ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[148]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{ + "\"(\"","x","\"+\"",RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[148]="] +}, Open ]], + +Cell["\<\ +This is a nonlinear propagator that appears in the calculation of the QCD \ +Energy-Energy-Correlation function\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"GenericPropagatorDenominator", "[", + RowBox[{ + RowBox[{ + RowBox[{"2", " ", "z", " ", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p1", ",", 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-WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{1403, 1068}, +WindowMargins->{{782, Automatic}, {128, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpDenominatorCombine.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpDenominatorCombine.nb index c1f2add02..b61ef1601 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpDenominatorCombine.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpDenominatorCombine.nb @@ -166,9 +166,7 @@ Cell[TextData[{ 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PropagatorDenominator in a canonical way. \ -FeynAmpDenominatorSimplify[exp, q1] simplifies all FeynAmpDenominator's in \ -exp in a canonical way, including some translation of momenta. \ -FeynAmpDenominatorSimplify[exp, q1, q2] additionally removes integrals with \ -no mass scale.\n\nFDS can be used as an alias." + " \[LineSeparator]tries to simplify each PropagatorDenominator in a \ +canonical way. FeynAmpDenominatorSimplify[exp, q1] simplifies all \ +FeynAmpDenominator's in exp in a canonical way, including some translation of \ +momenta. FeynAmpDenominatorSimplify[exp, q1, q2] additionally removes \ +integrals with no mass scale." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["FDS can be used as an alias.", "Notes", CellID->1067943069] }, Open ]], @@ -164,14 +163,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["OneLoopSimplify", + ButtonBox["TID", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/OneLoopSimplify", - ButtonNote->"OneLoopSimplify"], + ButtonData:>"paclet:FeynCalc/ref/TID", + ButtonNote->"TID"], "." -}], "Text", - CellTags->"FeynAmpDenominatorSimplify", - CellID->1104174358] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -202,14 +199,13 @@ Cell[CellGroupData[{ Cell[BoxData["FDS"], "Input", CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"In[1]:=", + CellLabel->"In[52]:=", CellID->792645925], Cell[BoxData[ FormBox["FeynAmpDenominatorSimplify", TraditionalForm]], "Output", CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"Out[1]=", - CellID->1554505245] + CellLabel->"Out[52]="] }, Open ]], Cell[TextData[{ @@ -225,9 +221,7 @@ Cell[TextData[{ SuperscriptBox["k", RowBox[{"2", "m"}]]}]}]}], "=", " ", RowBox[{"0", " ", "."}]}], TraditionalForm]]] -}], "Text", - CellTags->"FeynAmpDenominatorSimplify", - CellID->652878159], +}], "Notes"], Cell[CellGroupData[{ @@ -239,14 +233,13 @@ Cell[BoxData[ RowBox[{"FAD", "[", RowBox[{"k", ",", "k"}], "]"}]}], ",", "k"}], "]"}]], "Input", CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"In[2]:=", + CellLabel->"In[53]:=", CellID->50583569], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"FeynAmpDenominatorSimplify", - CellLabel->"Out[2]=", - CellID->1407968210] + CellLabel->"Out[53]="] }, Open ]], Cell[TextData[{ @@ -266,9 +259,7 @@ Cell[TextData[{ SubscriptBox["p", "2"]}], ")"}], "2"]}], ")"}]}], TraditionalForm]]], " into a standard form." -}], "Text", - CellTags->"FeynAmpDenominatorSimplify", - CellID->2080676792], +}], "Notes"], Cell[CellGroupData[{ @@ -282,38 +273,62 @@ Cell[BoxData[ RowBox[{"k", "-", SubscriptBox["p", "2"]}]}], "]"}], ",", "k"}], "]"}]], "Input", CellTags->"FeynAmpDenominatorSimplify", - 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+ FeynCalc`Momentum[$CellContext`p, D] + + FeynCalc`Momentum[$CellContext`q1, D]]], + Editable->False], " ", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q2", + TraditionalForm], "-", + FormBox["p", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + + FeynCalc`Pair[-FeynCalc`Momentum[$CellContext`p, D] + + FeynCalc`Momentum[$CellContext`q2, D], - + FeynCalc`Momentum[$CellContext`p, D] + + FeynCalc`Momentum[$CellContext`q2, D]]], + Editable->False], " ", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q1", + TraditionalForm], "-", + FormBox["q2", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q1, D] - + FeynCalc`Momentum[$CellContext`q2, D], + FeynCalc`Momentum[$CellContext`q1, D] - + FeynCalc`Momentum[$CellContext`q2, D]]], + Editable->False]}]], + TraditionalForm], + TraditionalForm], + TraditionalForm], + TraditionalForm], TraditionalForm]], "Output", + CellLabel->"Out[80]="] }, Open ]], Cell[CellGroupData[{ @@ -312,9 +451,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"%", "//", "FCE"}], "//", "StandardForm"}]], "Input", - CellTags->"FeynAmpDenominatorSplit", - CellLabel->"In[4]:=", - CellID->1536194379], + CellLabel->"In[81]:="], Cell[BoxData[ RowBox[{ @@ -328,37 +465,59 @@ Cell[BoxData[ RowBox[{"FAD", "[", RowBox[{ RowBox[{"-", "p"}], "+", "q2"}], "]"}]}]], "Output", - CellTags->"FeynAmpDenominatorSplit", - CellLabel->"Out[4]//StandardForm=", - CellID->1693985591] + CellLabel->"Out[81]//StandardForm="] }, Open ]], Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{"FeynAmpDenominatorSplit", "[", - RowBox[{"t", ",", "q1"}], "]"}], "//", "FCE"}], "//", - "StandardForm"}]], "Input", - CellTags->"FeynAmpDenominatorSplit", - CellLabel->"In[5]:=", - CellID->1257504819], - Cell[BoxData[ RowBox[{"FeynAmpDenominatorSplit", "[", RowBox[{ RowBox[{"FAD", "[", RowBox[{"q1", ",", - RowBox[{ - RowBox[{"-", "p"}], "+", "q1"}], ",", + RowBox[{"q1", "-", "p"}], ",", RowBox[{"q1", "-", "q2"}], ",", "q2", ",", - RowBox[{ - RowBox[{"-", "p"}], "+", "q2"}]}], "]"}], ",", "q1"}], "]"}]], "Output", - + RowBox[{"q2", "-", "p"}]}], "]"}], ",", + RowBox[{"Momentum", "\[Rule]", + RowBox[{"{", "q1", "}"}]}]}], "]"}]], "Input", + CellTags->"FeynAmpDenominatorSplit", + CellLabel->"In[83]:=", + CellID->1257504819], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FAD", "[", + RowBox[{"q2", ",", + RowBox[{ + RowBox[{"-", "p"}], "+", "q2"}]}], "]"}], " ", + RowBox[{"FAD", "[", + RowBox[{"q1", ",", + RowBox[{ + RowBox[{"-", "p"}], "+", "q1"}], ",", + RowBox[{"q1", "-", "q2"}]}], "]"}]}]], "Output", CellTags->"FeynAmpDenominatorSplit", - CellLabel->"Out[5]//StandardForm=", - CellID->863883694] + CellLabel->"Out[83]//StandardForm="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"%", "//", "FCE"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[84]:="], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FAD", "[", + RowBox[{"q2", ",", + RowBox[{ + RowBox[{"-", "p"}], "+", "q2"}]}], "]"}], " ", + RowBox[{"FAD", "[", + RowBox[{"q1", ",", + RowBox[{ + RowBox[{"-", "p"}], "+", "q1"}], ",", + RowBox[{"q1", "-", "q2"}]}], "]"}]}]], "Output", + CellLabel->"Out[84]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -369,30 +528,20 @@ Cell[BoxData[ RowBox[{"FeynAmpDenominatorCombine", "[", "%", "]"}], "//", "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"FeynAmpDenominatorSplit", - CellLabel->"In[6]:=", + CellLabel->"In[85]:=", CellID->1174376888], Cell[BoxData[ - RowBox[{"FeynAmpDenominatorSplit", "[", - RowBox[{ - RowBox[{"FAD", "[", - RowBox[{"q2", ",", "q1", ",", - RowBox[{ - RowBox[{"-", "p"}], "+", "q2"}], ",", - RowBox[{"q1", "-", "q2"}], ",", - RowBox[{ - RowBox[{"-", "p"}], "+", "q1"}]}], "]"}], ",", "q1"}], "]"}]], "Output", - - CellTags->"FeynAmpDenominatorSplit", - CellLabel->"Out[6]//StandardForm=", - CellID->1033440679] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", "t", "]"}]], "Input", + RowBox[{"FAD", "[", + RowBox[{"q1", ",", "q2", ",", + RowBox[{"q1", "-", "q2"}], ",", + RowBox[{ + RowBox[{"-", "p"}], "+", "q1"}], ",", + RowBox[{ + RowBox[{"-", "p"}], "+", "q2"}]}], "]"}]], "Output", CellTags->"FeynAmpDenominatorSplit", - CellLabel->"In[7]:=", - CellID->616885004] + CellLabel->"Out[85]//StandardForm="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -456,12 +605,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1158, Automatic}, {Automatic, 191}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpList.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpList.nb index 76afec64c..aa212d279 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpList.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynAmpList.nb @@ -123,13 +123,13 @@ Cell[TextData[{ RowBox[{"FeynAmp", "[", "...", "]"}], ",", " ", RowBox[{"FeynAmp", "[", "...", "]"}], ",", " ", "..."}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is a head of a list of Feynman amplitudes.\nFeynAmpList has no functional \ -properties and serves just as a head." + " \[LineSeparator]is a head of a list of Feynman amplitudes." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +FeynAmpList has no functional properties and serves just as a head.\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -171,9 +171,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynAmp", ButtonNote->"FeynAmp"], "." -}], "Text", - CellTags->"FeynAmpList", - CellID->1636179239] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -259,12 +257,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1237, Automatic}, {Automatic, 231}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalc.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalc.nb index f3493a5f8..e47968ff6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalc.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalc.nb @@ -186,31 +186,24 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"FeynCalc", - CellID->1788950203], - Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "FeynCalc"}]], "Input", CellTags->"FeynCalc", - CellLabel->"In[1]:=", + CellLabel->"In[86]:=", CellID->1258876634], Cell[BoxData[ - StyleBox["\<\"For installation notes visit www.feyncalc.org\\n\\nFor a list \ -of availabe objects type $FeynCalcStuff, which contains a list of all \ -functions and options in StringForm. You can get on-line information by \ -?function, e.g. ?Contract.\\n\\nThere are several useful functions for short \ -input, type $FCS for a list of short commands. Then type, e.g., \ -?GA.\\n\\n\\nTo enable/disable start-up messages, put the \ + StyleBox["\<\"For installation notes visit www.feyncalc.github.io. You can \ +get on-line information by ?function, e.g. ?Contract.\\n\\nThere are several \ +useful functions for short input, type $FCS for a list of short commands. \ +Then type, e.g., ?GA.\\n\\n\\nTo enable/disable start-up messages, put the \ line\\n\\n$FeynCalcStartupMessages = \ True;\\n\\nor\\n\\n$FeynCalcStartupMessages = False;\\n\\ninto your \ \\\"init.m\\\" file or into your \\\"FCConfig.m\\\" file.\"\>", "MSG"]], "Print", "PrintUsage", - CellTags->{"FeynCalc", "Info-1d55ee43-67b8-4d8b-8c35-3f3a2bc368ed"}, - CellID->144621555] + CellTags->{"FeynCalc", "Info-d5d5947c-0e52-48a8-b6a9-37ad11b1e404"}] }, Open ]] }, Open ]], @@ -275,12 +268,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1056, Automatic}, {Automatic, 182}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalc2FORM.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalc2FORM.nb index c3dfa75a6..12fae1a33 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalc2FORM.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalc2FORM.nb @@ -117,16 +117,75 @@ Cell["FeynCalc2FORM", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"FeynCalc2FORM", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "displays expr in FORM syntax. FeynCalc2FORM[file, x] writes x in FORM \ -syntax to a file. FeynCalc2FORM[file, x==y] writes x=y to a file in FORM \ -syntax." + RowBox[{"FeynCalc2FORM", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]displays ", + Cell[BoxData["exp"], "InlineFormula"], + " in FORM syntax.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"FeynCalc2FORM", "[", + RowBox[{"file", ",", "x"}], "]"}]], "InlineFormula"], + " \[LineSeparator]writes ", + Cell[BoxData["x"], "InlineFormula"], + " in FORM syntax to a file.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"FeynCalc2FORM", "[", + RowBox[{"file", ",", + RowBox[{"x", "\[Equal]", "y"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]writes ", + Cell[BoxData[ + RowBox[{"x", "=", "y"}]], "InlineFormula"], + " to a file in FORM syntax." }], "Usage", - CellID->982511436], + CellID->2010081510], + +Cell["\<\ +The capabilities of this function are very limited, so that you should not \ +expect it to easily handle large and compicated expressions.\ +\>", "Notes"], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FeynCalc2FORM", "]"}]], "Input", + CellTags->"FeynCalc2FORM", + CellLabel->"In[135]:=", + CellID->1031702605], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"EpsDiscard", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"FORMAbbreviations", "\[Rule]", + RowBox[{"{", + RowBox[{"\<\"syFC\"\>", ",", "\<\"vFC\"\>"}], "}"}]}], ",", + RowBox[{"FORMEpilog", "\[Rule]", + RowBox[{"{", + RowBox[{"\<\"print;\"\>", ",", "\<\".end\"\>"}], "}"}]}], ",", + RowBox[{"FORMIdStatements", "\[Rule]", "True"}], ",", + RowBox[{"FORMProlog", "\[Rule]", "\<\"write statistics;\"\>"}], ",", + RowBox[{"Replace", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"\<\"\\\\[Alpha]\"\>", "\[Rule]", "\<\"al\"\>"}], ",", + RowBox[{"\<\"\\\\[Beta]\"\>", "\[Rule]", "\<\"be\"\>"}], ",", + RowBox[{"\<\"\\\\[Gamma]\"\>", "\[Rule]", "\<\"ga\"\>"}], ",", + RowBox[{"\<\"\\\\[Delta]\"\>", "\[Rule]", "\<\"de\"\>"}], ",", + RowBox[{"\<\"\\\\[Mu]\"\>", "\[Rule]", "\<\"mu\"\>"}], ",", + RowBox[{"\<\"\\\\[Nu]\"\>", "\[Rule]", "\<\"nu\"\>"}], ",", + RowBox[{"\<\"\\\\[Rho]\"\>", "\[Rule]", "\<\"ro\"\>"}], ",", + RowBox[{"\<\"\\\\[Sigma]\"\>", "\[Rule]", "\<\"si\"\>"}]}], "}"}]}], + ",", + RowBox[{"TraceDimension", "\[Rule]", "4"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"FeynCalc2FORM", + CellLabel->"Out[135]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -161,15 +220,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - ButtonBox["FORM2FeynCalc", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FORM2FeynCalc", - ButtonNote->"FORM2FeynCalc"], - "." -}], "Text", - CellTags->"FeynCalc2FORM", - CellID->610402838] +Cell[TextData[ButtonBox["FORM2FeynCalc", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FORM2FeynCalc", + ButtonNote->"FORM2FeynCalc"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -198,40 +252,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "FeynCalc2FORM", "]"}]], "Input", - CellTags->"FeynCalc2FORM", - CellLabel->"In[1]:=", - CellID->1031702605], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"EpsDiscard", "\[Rule]", "False"}], ",", - RowBox[{"FORMEpilog", "\[Rule]", "\<\"\"\>"}], ",", - RowBox[{"FORMProlog", "\[Rule]", "\<\"write statistics;\"\>"}], ",", - RowBox[{"Replace", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"\<\"\\\\[Alpha]\"\>", "\[Rule]", "\<\"al\"\>"}], ",", - RowBox[{"\<\"\\\\[Beta]\"\>", "\[Rule]", "\<\"be\"\>"}], ",", - RowBox[{"\<\"\\\\[Gamma]\"\>", "\[Rule]", "\<\"ga\"\>"}], ",", - RowBox[{"\<\"\\\\[Delta]\"\>", "\[Rule]", "\<\"de\"\>"}], ",", - RowBox[{"\<\"\\\\[Mu]\"\>", "\[Rule]", "\<\"mu\"\>"}], ",", - RowBox[{"\<\"\\\\[Nu]\"\>", "\[Rule]", "\<\"nu\"\>"}], ",", - RowBox[{"\<\"\\\\[Rho]\"\>", "\[Rule]", "\<\"ro\"\>"}], ",", - RowBox[{"\<\"\\\\[Sigma]\"\>", "\[Rule]", "\<\"si\"\>"}]}], "}"}]}], - ",", - RowBox[{"TraceDimension", "\[Rule]", "4"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"FeynCalc2FORM", - CellLabel->"Out[1]=", - CellID->490814627] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{ RowBox[{"MT", "[", @@ -241,7 +261,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"y", "^", "2"}], "/", "d"}]}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[2]:=", + CellLabel->"In[120]:=", CellID->1451127405], Cell[BoxData[ @@ -250,43 +270,32 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["y", "2"], " ", FormBox[ - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], " ", + FormBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Mu]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], + FormBox["\[Nu]", TraditionalForm], - TraditionalForm]], - TraditionalForm], - TraditionalForm], " ", - FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + TraditionalForm]}]], TraditionalForm]}], "d"], TraditionalForm]], "Output", CellTags->"FeynCalc2FORM", - CellLabel->"Out[2]=", - CellID->1238649149] + CellLabel->"Out[120]="] }, Open ]], Cell[CellGroupData[{ @@ -295,13 +304,12 @@ Cell[BoxData[ RowBox[{ RowBox[{"FeynCalc2FORM", "[", "%", "]"}], ";"}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[3]:=", + CellLabel->"In[121]:=", CellID->208321779], Cell["(y^2*d_(mu,nu)*p(ro))/d", "Print", CellTags->"FeynCalc2FORM", - CellLabel->"During evaluation of In[3]:=", - CellID->460002283] + CellLabel->"During evaluation of In[121]:="] }, Open ]], Cell[CellGroupData[{ @@ -312,12 +320,13 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Delta]", ",", "\[Rho]"}], "]"}]}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[4]:=", + CellLabel->"In[122]:=", CellID->14977898], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Alpha]", @@ -336,8 +345,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"FeynCalc2FORM", - CellLabel->"Out[4]=", - CellID->1443194788] + CellLabel->"Out[122]="] }, Open ]], Cell[CellGroupData[{ @@ -346,24 +354,29 @@ Cell[BoxData[ RowBox[{ RowBox[{"FeynCalc2FORM", "[", "%", "]"}], ";"}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[5]:=", + CellLabel->"In[123]:=", CellID->1598383483], -Cell["(-i_)*e_(al,be,de,ro,Dimension->4)", "Print", +Cell["(-i_)*e_(al,be,de,ro)", "Print", CellTags->"FeynCalc2FORM", - 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CellLabel->"Out[12]=", - CellID->1936643337] + CellLabel->"Out[129]="] }, Open ]], Cell[BoxData[ @@ -1267,7 +1083,7 @@ Cell[BoxData[ RowBox[{"\"\\"", ",", RowBox[{"L", " ", "==", "t"}]}], "]"}], ";"}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[13]:=", + CellLabel->"In[130]:=", CellID->404985950], Cell[CellGroupData[{ @@ -1283,7 +1099,7 @@ Cell[BoxData[ ",", "\"\<\>\""}], "]"}], "<>", "\"\\""}], ",", "String"}], "]"}], "]"}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[14]:=", + CellLabel->"In[131]:=", CellID->69651380], Cell[BoxData[ @@ -1294,18 +1110,18 @@ Cell[BoxData[ {"\<\"Vectors p,q;\"\>"}, {"\<\"write statistics;\"\>"}, {"\<\"Local L = ( \"\>"}, - {"\<\"4*(d_(mu,si)*d_(nu,ro)*q.p-d_(mu,ro)*d_(nu,si)*q.p+d_(mu,nu)*d_(\ -ro,si)*q.p+\"\>"}, - {"\<\"d_(ro,si)*p(nu)*q(mu)-d_(nu,si)*p(ro)*q(mu)+d_(nu,ro)*p(si)*q(mu)-\ -\"\>"}, - {"\<\"d_(ro,si)*p(mu)*q(nu)+d_(mu,si)*p(ro)*q(nu)-d_(mu,ro)*p(si)*q(nu)+\ -\"\>"}, - {"\<\"d_(nu,si)*p(mu)*q(ro)-d_(mu,si)*p(nu)*q(ro)+d_(mu,nu)*p(si)*q(ro)-\ -\"\>"}, - {"\<\"d_(nu,ro)*p(mu)*q(si)+d_(mu,ro)*p(nu)*q(si)-d_(mu,nu)*p(ro)*q(si))\ - ); \"\>"}, + {"\<\"4*d_(mu,si)*d_(nu,ro)*q.p-4*d_(mu,ro)*d_(nu,si)*q.p+4*d_(mu,nu)*d_\ +(ro,si)*q.p+\"\>"}, + {"\<\"4*d_(ro,si)*p(nu)*q(mu)-4*d_(nu,si)*p(ro)*q(mu)+4*d_(nu,ro)*p(si)*\ +q(mu)-\"\>"}, + {"\<\"4*d_(ro,si)*p(mu)*q(nu)+4*d_(mu,si)*p(ro)*q(nu)-4*d_(mu,ro)*p(si)*\ +q(nu)+\"\>"}, + {"\<\"4*d_(nu,si)*p(mu)*q(ro)-4*d_(mu,si)*p(nu)*q(ro)+4*d_(mu,nu)*p(si)*\ +q(ro)-\"\>"}, + {"\<\"4*d_(nu,ro)*p(mu)*q(si)+4*d_(mu,ro)*p(nu)*q(si)-4*d_(mu,nu)*p(ro)*\ +q(si) ); \"\>"}, {"\<\" \"\>"}, - {"\<\"Print; \"\>"}, + {"\<\"print;\"\>"}, {"\<\".end\"\>"} }, GridBoxAlignment->{ @@ -1322,8 +1138,7 @@ ro,si)*q.p+\"\>"}, Function[BoxForm`e$, TableForm[BoxForm`e$]]], TraditionalForm]], "Output", CellTags->"FeynCalc2FORM", - CellLabel->"Out[14]//TableForm=", - CellID->1446352458] + CellLabel->"Out[131]//TableForm="] }, Open ]], Cell[BoxData[ @@ -1336,15 +1151,16 @@ Cell[BoxData[ RowBox[{"DeleteFile", "[", "\"\\"", "]"}]}], "]"}], ";"}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[15]:=", + CellLabel->"In[132]:=", CellID->687280976], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", "t", "]"}], ";"}]], "Input", CellTags->"FeynCalc2FORM", - CellLabel->"In[16]:=", + CellLabel->"In[133]:=", CellID->261285927] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -1407,13 +1223,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{1083, 936}, +WindowMargins->{{921, Automatic}, {Automatic, 170}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcExternal.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcExternal.nb index 6311cd05b..8fe5cb986 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcExternal.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcExternal.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynCalcInternal", ButtonNote->"FeynCalcInternal"], "." -}], "Text", - CellTags->"FeynCalcExternal", - CellID->35172117] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,7 +199,7 @@ Cell[BoxData[ RowBox[{"FeynCalcExternal", "[", RowBox[{"DiracGamma", "[", "5", "]"}], "]"}]], "Input", CellTags->"FeynCalcExternal", - CellLabel->"In[1]:=", + CellLabel->"In[87]:=", CellID->642848596], Cell[BoxData[ @@ -211,8 +209,7 @@ Cell[BoxData[ FormBox["5", TraditionalForm]], TraditionalForm]], "Output", CellTags->"FeynCalcExternal", - CellLabel->"Out[1]=", - CellID->539530492] + CellLabel->"Out[87]="] }, Open ]], Cell[CellGroupData[{ @@ -220,14 +217,13 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FeynCalcExternal", - CellLabel->"In[2]:=", + CellLabel->"In[88]:=", CellID->546432132], Cell[BoxData[ RowBox[{"GA", "[", "5", "]"}]], "Output", CellTags->"FeynCalcExternal", - CellLabel->"Out[2]//StandardForm=", - CellID->2042610193] + CellLabel->"Out[88]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -245,7 +241,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Input", CellTags->"FeynCalcExternal", - CellLabel->"In[3]:=", + CellLabel->"In[89]:=", CellID->1924736613], Cell[BoxData[ @@ -292,43 +288,32 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ",", FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], - TraditionalForm], ",", - FormBox[ - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Alpha]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], - TraditionalForm]], - TraditionalForm], + TraditionalForm]}]], + TraditionalForm], ",", + FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]}], "}"}], TraditionalForm]], "Output", CellTags->"FeynCalcExternal", - CellLabel->"Out[3]=", - CellID->1438725943] + CellLabel->"Out[89]="] }, Open ]], Cell[CellGroupData[{ @@ -336,7 +321,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FeynCalcExternal", - CellLabel->"In[4]:=", + CellLabel->"In[90]:=", CellID->127506318], Cell[BoxData[ @@ -352,8 +337,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", CellTags->"FeynCalcExternal", - CellLabel->"Out[4]//StandardForm=", - CellID->689065963] + CellLabel->"Out[90]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -361,7 +345,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "FeynCalcInternal"}]], "Input", CellTags->"FeynCalcExternal", - CellLabel->"In[5]:=", + CellLabel->"In[91]:=", CellID->1535054786], Cell[BoxData[ @@ -399,40 +383,29 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm]}], ",", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], ",", - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Alpha]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "}"}], TraditionalForm]], "Output", + TraditionalForm]}]], ",", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], "}"}], TraditionalForm]], "Output", CellTags->"FeynCalcExternal", - CellLabel->"Out[5]=", - CellID->16755113] + CellLabel->"Out[91]="] }, Open ]], Cell[CellGroupData[{ @@ -440,7 +413,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FeynCalcExternal", - CellLabel->"In[6]:=", + CellLabel->"In[92]:=", CellID->1247696784], Cell[BoxData[ @@ -467,8 +440,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}], "}"}]], "Output", CellTags->"FeynCalcExternal", - CellLabel->"Out[6]//StandardForm=", - CellID->1797900650] + CellLabel->"Out[92]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -478,7 +450,7 @@ Cell[BoxData[ RowBox[{"FeynCalcExternal", "[", "%", "]"}], "//", "StandardForm"}]], "Input", CellTags->"FeynCalcExternal", - CellLabel->"In[7]:=", + CellLabel->"In[93]:=", CellID->2037530155], Cell[BoxData[ @@ -494,8 +466,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", CellTags->"FeynCalcExternal", - CellLabel->"Out[7]//StandardForm=", - CellID->1902701879] + CellLabel->"Out[93]//StandardForm="] }, Open ]] }, Open ]], @@ -560,12 +531,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{804, Automatic}, {Automatic, 137}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcForm.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcForm.nb index c4562c758..01f4eed3d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcForm.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcForm.nb @@ -182,9 +182,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynCalcInternal", ButtonNote->"FeynCalcInternal"], "." -}], "Text", - CellTags->"FeynCalcForm", - CellID->1584845220] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -211,9 +209,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["This is the normal notebook display:", "Text", - CellTags->"FeynCalcForm", - CellID->1383220456], +Cell["This is the normal notebook display:", "Notes"], Cell[CellGroupData[{ @@ -224,7 +220,7 @@ Cell[BoxData[ RowBox[{"SUNT", "[", "b", "]"}], ".", RowBox[{"SUNT", "[", "c", "]"}]}], "]"}]], "Input", CellTags->"FeynCalcForm", - CellLabel->"In[1]:=", + CellLabel->"In[94]:=", CellID->1625719649], Cell[BoxData[ @@ -255,34 +251,32 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"FeynCalcForm", - CellLabel->"Out[1]=", - CellID->2135875157] + CellLabel->"Out[94]="] }, Open ]], Cell["\<\ This is the shorthand (terminal) display (easy-to-read form):\ -\>", "Text", - CellTags->"FeynCalcForm", - CellID->981626969], +\>", "Notes"], Cell[BoxData[ RowBox[{ RowBox[{"$PrePrint", " ", "=", " ", "FeynCalcForm"}], ";"}]], "Input", CellTags->"FeynCalcForm", - CellLabel->"In[2]:=", + CellLabel->"In[95]:=", CellID->1192476093], Cell[BoxData[ RowBox[{ RowBox[{"SetOptions", "[", - RowBox[{"$FrontEnd", ",", + RowBox[{"$FrontEndSession", ",", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Options", "[", - RowBox[{"$FrontEnd", ",", "\"\\""}], - "]"}], "/.", + RowBox[{ + "$FrontEndSession", ",", "\"\\""}], "]"}], + "/.", RowBox[{ RowBox[{"(", RowBox[{"\"\\"", "\[Rule]", "_"}], ")"}], "\[Rule]", @@ -291,7 +285,7 @@ Cell[BoxData[ ")"}], "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "]"}], ";"}]], "Input", CellTags->"FeynCalcForm", - CellLabel->"In[3]:=", + CellLabel->"In[96]:=", CellID->204502333], Cell[CellGroupData[{ @@ -303,42 +297,43 @@ Cell[BoxData[ RowBox[{"SUNT", "[", "b", "]"}], ".", RowBox[{"SUNT", "[", "c", "]"}]}], "]"}]], "Input", CellTags->"FeynCalcForm", - CellLabel->"In[4]:=", + CellLabel->"In[97]:=", CellID->1641498185], Cell[OutputFormData["\<\ SUNTrace[SUNT[SUNIndex[a]] . SUNT[SUNIndex[b]] . SUNT[SUNIndex[c]]]\ \>", "\<\ -tr[T[a] T[b] T[c]]\ +SUNTrace[SUNT[SUNIndex[a]] . SUNT[SUNIndex[b]] . + + + SUNT[SUNIndex[c]]]\ \>"], "Output", CellTags->"FeynCalcForm", - CellLabel->"Out[4]=", - CellID->1930690446] + CellLabel->"Out[97]="] }, Open ]], -Cell["Reset to normal notebook display:", "Text", - CellTags->"FeynCalcForm", - CellID->1776666281], +Cell["Reset to normal notebook display:", "Notes"], Cell[BoxData[ RowBox[{ RowBox[{"$PrePrint", "=."}], ";"}]], "Input", CellTags->"FeynCalcForm", - CellLabel->"In[5]:=", + CellLabel->"In[98]:=", CellID->1847759077], Cell[BoxData[ RowBox[{ RowBox[{"SetOptions", "[", - RowBox[{"$FrontEnd", ",", + RowBox[{"$FrontEndSession", ",", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Options", "[", - RowBox[{"$FrontEnd", ",", "\"\\""}], - "]"}], "/.", + RowBox[{ + "$FrontEndSession", ",", "\"\\""}], "]"}], + "/.", RowBox[{ RowBox[{"(", RowBox[{"\"\\"", "\[Rule]", "_"}], ")"}], "\[Rule]", @@ -347,8 +342,48 @@ Cell[BoxData[ ")"}], "[", RowBox[{"[", "1", "]"}], "]"}], "]"}]}], "]"}], ";"}]], "Input", CellTags->"FeynCalcForm", - CellLabel->"In[6]:=", - CellID->803099917] + CellLabel->"In[99]:=", + CellID->803099917], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNTrace", "[", + RowBox[{ + RowBox[{"SUNT", "[", "a", "]"}], ".", + RowBox[{"SUNT", "[", "b", "]"}], ".", + RowBox[{"SUNT", "[", "c", "]"}]}], "]"}]], "Input", + CellLabel->"In[100]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + FormBox["\<\"tr\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + RowBox[{ + SuperscriptBox["T", + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["T", + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["T", + FormBox[ + FormBox["c", + TraditionalForm], + TraditionalForm]]}], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], TraditionalForm]], "Output", + CellLabel->"Out[100]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -412,12 +447,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{608, Automatic}, {Automatic, 62}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcInternal.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcInternal.nb index 43e882378..8f5330b1b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcInternal.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcInternal.nb @@ -176,9 +176,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FCE", ButtonNote->"FCE"], "." -}], "Text", - CellTags->"FeynCalcInternal", - CellID->1416834624] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -220,7 +218,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Input", CellTags->"FeynCalcInternal", - CellLabel->"In[1]:=", + CellLabel->"In[101]:=", CellID->1722777606], Cell[BoxData[ @@ -267,43 +265,32 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ",", FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], - TraditionalForm], ",", - FormBox[ - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Alpha]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], - TraditionalForm]], - TraditionalForm], + TraditionalForm]}]], + TraditionalForm], ",", + FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]}], "}"}], TraditionalForm]], "Output", CellTags->"FeynCalcInternal", - CellLabel->"Out[1]=", - CellID->1418441538] + CellLabel->"Out[101]="] }, Open ]], Cell[CellGroupData[{ @@ -311,7 +298,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FeynCalcInternal", - CellLabel->"In[2]:=", + CellLabel->"In[102]:=", CellID->1982442552], Cell[BoxData[ @@ -327,8 +314,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", CellTags->"FeynCalcInternal", - CellLabel->"Out[2]//StandardForm=", - CellID->603554670] + CellLabel->"Out[102]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -336,7 +322,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "FeynCalcInternal"}]], "Input", CellTags->"FeynCalcInternal", - CellLabel->"In[3]:=", + CellLabel->"In[103]:=", CellID->1465614164], Cell[BoxData[ @@ -374,40 +360,29 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"], TraditionalForm]}], ",", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], ",", - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], + FormBox["\[Alpha]", + TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "}"}], TraditionalForm]], "Output", + TraditionalForm]}]], ",", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], "}"}], TraditionalForm]], "Output", CellTags->"FeynCalcInternal", - CellLabel->"Out[3]=", - CellID->618861015] + CellLabel->"Out[103]="] }, Open ]], Cell[CellGroupData[{ @@ -415,7 +390,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FeynCalcInternal", - CellLabel->"In[4]:=", + CellLabel->"In[104]:=", CellID->1783117065], Cell[BoxData[ @@ -442,8 +417,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}], "}"}]], "Output", CellTags->"FeynCalcInternal", - CellLabel->"Out[4]//StandardForm=", - CellID->1678932419] + CellLabel->"Out[104]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -453,7 +427,7 @@ Cell[BoxData[ RowBox[{"FeynCalcExternal", "[", "%", "]"}], "//", "StandardForm"}]], "Input", CellTags->"FeynCalcInternal", - CellLabel->"In[5]:=", + CellLabel->"In[105]:=", CellID->53564155], Cell[BoxData[ @@ -469,8 +443,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "}"}]], "Output", CellTags->"FeynCalcInternal", - CellLabel->"Out[5]//StandardForm=", - CellID->44863235] + CellLabel->"Out[105]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -490,7 +463,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}]}], "}"}], "]"}]], "Input", CellTags->"FeynCalcInternal", - CellLabel->"In[6]:=", + CellLabel->"In[106]:=", CellID->1030775122], Cell[BoxData[ @@ -535,11 +508,22 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]}]], ",", - FractionBox["1", - SuperscriptBox[ - FormBox["q", - TraditionalForm], "2"]], ",", - SuperscriptBox["\[Epsilon]", + FormBox[ + FractionBox["1", + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q, D], + FeynCalc`Momentum[$CellContext`q, D]]], + Editable->False]], + TraditionalForm], ",", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -558,8 +542,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], "}"}], TraditionalForm]], "Output", CellTags->"FeynCalcInternal", - CellLabel->"Out[6]=", - CellID->164140775] + CellLabel->"Out[106]="] }, Open ]], Cell[CellGroupData[{ @@ -567,7 +550,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"FeynCalcInternal", - CellLabel->"In[7]:=", + CellLabel->"In[107]:=", CellID->438838711], Cell[BoxData[ @@ -597,11 +580,10 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", - RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "4"}]}], "]"}]}], "}"}]], "Output", + RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}]}], "]"}]}], + "}"}]], "Output", CellTags->"FeynCalcInternal", - CellLabel->"Out[7]//StandardForm=", - CellID->700854959] + CellLabel->"Out[107]//StandardForm="] }, Open ]] }, Open ]], @@ -666,12 +648,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{932, Automatic}, {Automatic, 77}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcToLaTeX.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcToLaTeX.nb index 6c56795f9..5fc498470 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcToLaTeX.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynCalcToLaTeX.nb @@ -117,15 +117,28 @@ Cell["FeynCalcToLaTeX", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"FeynCalcToLaTeX", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "generates LaTeX with line-breaking for expr. \nFeynCalcToLaTeX[expr, 500] \ -generates LaTeX for expr where 500 is the Window width setting for the \ -Mathematica frontend. Increasing its value will generate less line breaks." + RowBox[{"FeynCalcToLaTeX", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]generates LaTeX with line-breaking for ", + Cell[BoxData["exp"], "InlineFormula"], + ".\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"FeynCalcToLaTeX", "[", + RowBox[{"expr", ",", "500"}], "]"}]], "InlineFormula"], + " \[LineSeparator]generates LaTeX for ", + Cell[BoxData["exp"], "InlineFormula"], + " where 500 is the Window width setting for the Mathematica frontend. \ +Increasing its value will generate less line breaks." }], "Usage", - CellID->982511436], + CellID->2010081510], -Cell["XXXX", "Notes", +Cell[TextData[{ + "This function appears to be broken in the recent ", + StyleBox["Mathematica", + FontSlant->"Italic"], + " versions, most likely it will be rewritten from scratch in a future \ +version of FeynCalc." +}], "Notes", CellID->1067943069] }, Open ]], @@ -248,12 +261,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1213, Automatic}, {Automatic, 220}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynRule.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynRule.nb index 1b9e4aa07..e6a5ffea6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynRule.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynRule.nb @@ -120,16 +120,78 @@ Cell[TextData[{ RowBox[{"FeynRule", "[", RowBox[{"lag", ",", " ", RowBox[{"{", "fields", "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "derives the Feynman rule corresponding to the field configuration fields of \ -the lagrangian lag.\n\nFeynRule does not calculate propagator Feynman rules.\n\ -\nThe option ZeroMomentumInsertion can be used for twist-2 and higher twist \ -operators." + " \[LineSeparator]derives the Feynman rule corresponding to the field \ +configuration ", + Cell[BoxData["fields"], "InlineFormula"], + " of the lagrangian ", + Cell[BoxData["lag"], "InlineFormula"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + ButtonBox["FeynRule", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FeynRule", + ButtonNote->"FeynRule"], + " does not calculate propagator Feynman rules." +}], "Notes"], + +Cell[TextData[{ + "The option ", + ButtonBox["ZeroMomentumInsertion", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/ZeroMomentumInsertion", + ButtonNote->"ZeroMomentumInsertion"], + " can be used for twist-2 and higher twist operators." +}], "Notes"], + +Cell[TextData[{ + ButtonBox["FeynRule", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FeynRule", + ButtonNote->"FeynRule"], + " is not very versatile and was primarily developed for QCD calculations. It \ +is often more useful when dealing with bosonic fields than with fermions. If \ +you need a more powerful and universal solution for deriving Feynman rules, \ +have a look at the standalone ", + StyleBox["Mathematica", + FontSlant->"Italic"], + " Package ", + ButtonBox["FeynRules", + BaseStyle->"Hyperlink", + ButtonData->{ + URL["http://feynrules.irmp.ucl.ac.be/"], None}, + ButtonNote->"http://feynrules.irmp.ucl.ac.be/"], + " (not related to FeynCalc)." +}], "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FeynRule", "]"}]], "Input", + CellLabel->"In[31]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Anti5", "\[Rule]", + RowBox[{"-", "\[Infinity]"}]}], ",", + RowBox[{"Assumptions", "\[Rule]", "Automatic"}], ",", + RowBox[{"Contract", "\[Rule]", "False"}], ",", + RowBox[{"Factor1", "\[Rule]", "False"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"FCPartialD", "\[Rule]", "RightPartialD"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Schouten", "\[Rule]", "False"}], ",", + RowBox[{"ZeroMomentumInsertion", "\[Rule]", "True"}], ",", + RowBox[{"InitialFunction", "\[Rule]", "Identity"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[31]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -164,15 +226,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - 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CellTags->"FeynmanParameterNames", - CellID->29982595] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{801, Automatic}, {Automatic, 120}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynmanParametrize.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynmanParametrize.nb index fef510845..a3cc37aeb 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynmanParametrize.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynmanParametrize.nb @@ -125,8 +125,27 @@ integration momentum)." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - 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Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -288,12 +281,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1099, Automatic}, {Automatic, 117}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynmanReduce.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynmanReduce.nb index 584694690..c348ada35 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynmanReduce.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FeynmanReduce.nb @@ -132,8 +132,25 @@ terms and operate on the terms one by one." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FeynmanReduce", "]"}]], "Input", + CellTags->"FeynmanReduce", + CellLabel->"In[111]:=", + CellID->160646569], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Flatten", "\[Rule]", "True"}], ",", + RowBox[{"Expand", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"FeynmanReduce", + CellLabel->"Out[111]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -181,8 +198,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -198,28 +213,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "FeynmanReduce", "]"}]], "Input", - CellTags->"FeynmanReduce", - CellLabel->"In[1]:=", - CellID->160646569], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"Flatten", "\[Rule]", "True"}], ",", - RowBox[{"Expand", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"FeynmanReduce", - CellLabel->"Out[1]=", - CellID->968892063] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -279,12 +272,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1160, Automatic}, {Automatic, 178}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FieldDerivative.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FieldDerivative.nb index e8889aa14..59ecda1d3 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FieldDerivative.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FieldDerivative.nb @@ -121,19 +121,52 @@ Cell[TextData[{ RowBox[{ RowBox[{"f", "[", "x", "]"}], ",", "x", ",", "li1", ",", "li2", ",", "..."}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the derivative of f[x] with respect to space-time variables x and with \ -Lorentz indices li1, li2, ..., where li1, li2, ... have head LorentzIndex. \ -FieldDerivative[f[x],x,li1,li2,...] can be given as \ -FieldDerivative[f[x],x,{l1,l2,...}], where l1 is li1 without the head, ... \ -FieldDerivative is defined only for objects with head QuantumField[...]. If \ -the space-time derivative of other objects is wanted, the corresponding rule \ -must be specified." + " \[LineSeparator] is the derivative of f[x] with respect to space-time \ +variables x and with Lorentz indices li1, li2, ..., where li1, li2, ... have \ +head ", + ButtonBox["LorentzIndex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/LorentzIndex", + ButtonNote->"LorentzIndex"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + Cell[BoxData[ + RowBox[{"FieldDerivative", "[", + RowBox[{ + RowBox[{"f", "[", "x", "]"}], ",", "x", ",", "li1", ",", "li2", ",", + "..."}], "]"}]], "InlineFormula"], + " can be given as ", + Cell[BoxData[ + RowBox[{ + RowBox[{"FieldDerivative", "[", + RowBox[{ + RowBox[{"f", "[", "x", "]"}], ",", "x", ",", + RowBox[{"{", + RowBox[{"l1", ",", "l2", ",", "..."}], "}"}]}], "]"}], ","}]], + "InlineFormula"], + " where ", + Cell[BoxData["l1"], "InlineFormula"], + " is ", + Cell[BoxData["li1"], "InlineFormula"], + " without the head." +}], "Notes"], + +Cell[TextData[{ + ButtonBox["FieldDerivative", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FieldDerivative", + ButtonNote->"FieldDerivative"], + " is defined only for objects with head ", + ButtonBox["QuantumField", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/QuantumField", + ButtonNote->"QuantumField"], + ". If the space-time derivative of other objects is wanted, the \ +corresponding rule must be specified." +}], "Notes"] }, Open ]], Cell[CellGroupData[{ @@ -174,14 +207,12 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FCPartialD", ButtonNote->"FCPartialD"], ", ", - ButtonBox["ExpandPartialD", + ButtonBox["ExpandParitalD", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/ExpandPartialD", - ButtonNote->"ExpandPartialD"], + ButtonData:>"paclet:FeynCalc/ref/ExpandParitalD", + ButtonNote->"ExpandParitalD"], "." -}], "Text", - CellTags->"FieldDerivative", - CellID->1023535536] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -229,7 +260,7 @@ Cell[BoxData[ RowBox[{"D", ",", RowBox[{"{", "\[Sigma]", "}"}]}], "]"}], "[", "y", "]"}]}]], "Input", CellTags->"FieldDerivative", - CellLabel->"In[1]:=", + CellLabel->"In[193]:=", CellID->1922686463], Cell[BoxData[ @@ -260,8 +291,7 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm]], "(", "y", ")"}]}], TraditionalForm]], "Output", CellTags->"FieldDerivative", - CellLabel->"Out[1]=", - CellID->841917756] + CellLabel->"Out[193]="] }, Open ]], Cell[CellGroupData[{ @@ -272,7 +302,7 @@ Cell[BoxData[ RowBox[{"%", ",", "x", ",", RowBox[{"{", "\[Mu]", "}"}]}], "]"}], "//", "DotExpand"}]], "Input", CellTags->"FieldDerivative", - CellLabel->"In[2]:=", + CellLabel->"In[194]:=", CellID->626008050], Cell[BoxData[ @@ -294,18 +324,19 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["C", TraditionalForm], FormBox[ FormBox["\[Rho]", TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", + TraditionalForm]], ")"}], ")"}], "\[InvisibleApplication]", RowBox[{"(", "x", ")"}]}], ".", RowBox[{ SubscriptBox[ @@ -317,18 +348,19 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Mu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", + TraditionalForm]], ")"}], ")"}], "\[InvisibleApplication]", RowBox[{"(", "x", ")"}]}], ".", RowBox[{ SubscriptBox[ @@ -349,8 +381,7 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm]], "(", "y", ")"}]}]}], TraditionalForm]], "Output", CellTags->"FieldDerivative", - CellLabel->"Out[2]=", - CellID->1663127681] + CellLabel->"Out[194]="] }, Open ]], Cell[CellGroupData[{ @@ -358,10 +389,10 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"FieldDerivative", "[", - RowBox[{"%", ",", "y", ",", + RowBox[{"%%", ",", "y", ",", RowBox[{"{", "\[Nu]", "}"}]}], "]"}], "//", "DotExpand"}]], "Input", CellTags->"FieldDerivative", - CellLabel->"In[3]:=", + CellLabel->"In[195]:=", CellID->1996069937], Cell[BoxData[ @@ -380,106 +411,6 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Nu]", TraditionalForm]], "(", "y", ")"}], ".", - RowBox[{ - RowBox[{"(", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["C", - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", - RowBox[{"(", "x", ")"}]}], ".", - RowBox[{ - RowBox[{"(", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["D", - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", - RowBox[{"(", "y", ")"}]}]}], "+", - RowBox[{ - RowBox[{ - SubscriptBox[ - FormBox["A", - TraditionalForm], - FormBox["\[Mu]", - TraditionalForm]], "(", "x", ")"}], ".", - RowBox[{ - RowBox[{"(", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["B", - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", - RowBox[{"(", "y", ")"}]}], ".", - RowBox[{ - RowBox[{"(", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["C", - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", - RowBox[{"(", "x", ")"}]}], ".", - RowBox[{ - SubscriptBox[ - FormBox["D", - TraditionalForm], - FormBox["\[Sigma]", - TraditionalForm]], "(", "y", ")"}]}], "+", - RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", - RowBox[{"(", "x", ")"}]}], ".", - RowBox[{ - SubscriptBox[ - FormBox["B", - TraditionalForm], - FormBox["\[Nu]", - TraditionalForm]], "(", "y", ")"}], ".", RowBox[{ SubscriptBox[ FormBox["C", @@ -489,51 +420,43 @@ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["D", TraditionalForm], FormBox[ FormBox["\[Sigma]", TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", + TraditionalForm]], ")"}], ")"}], "\[InvisibleApplication]", RowBox[{"(", "y", ")"}]}]}], "+", RowBox[{ RowBox[{ - RowBox[{"(", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", - RowBox[{"(", "x", ")"}]}], ".", + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox["\[Mu]", + TraditionalForm]], "(", "x", ")"}], ".", RowBox[{ RowBox[{"(", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["B", TraditionalForm], FormBox[ FormBox["\[Nu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], ")"}], "\[InvisibleApplication]", + TraditionalForm]], ")"}], ")"}], "\[InvisibleApplication]", RowBox[{"(", "y", ")"}]}], ".", RowBox[{ SubscriptBox[ @@ -548,8 +471,7 @@ Cell[BoxData[ FormBox["\[Sigma]", TraditionalForm]], "(", "y", ")"}]}]}], TraditionalForm]], "Output", CellTags->"FieldDerivative", - CellLabel->"Out[3]=", - CellID->785636748] + CellLabel->"Out[195]="] }, Open ]] }, Open ]], @@ -614,12 +536,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1013, Automatic}, {Automatic, 163}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FieldStrength.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FieldStrength.nb index 916c96235..98eb795d7 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FieldStrength.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FieldStrength.nb @@ -120,47 +120,90 @@ Cell[TextData[{ RowBox[{"FieldStrength", "[", RowBox[{"\[Mu]", ",", " ", "\[Nu]", ",", " ", "a"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the field strength tensor ", + " \[LineSeparator]is the field strength tensor ", Cell[BoxData[ - FormBox[ + RowBox[{ RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", "\[Mu]"], - SubsuperscriptBox["A", "\[Nu]", "a"]}], "-", - RowBox[{ - SubscriptBox["\[PartialD]", "\[Nu]"], - SubsuperscriptBox["A", "\[Mu]", "a"]}], "+", - RowBox[{ - SubscriptBox["g", "s"], " ", - SubsuperscriptBox["A", "\[Mu]", "b1"], - SubsuperscriptBox["A", "\[Nu]", "c1"]}]}], TraditionalForm]]], + SubscriptBox["\[PartialD]", "\[Mu]"], + SubsuperscriptBox["A", "\[Nu]", "a"]}], " ", "-", " ", + RowBox[{ + SubscriptBox["\[PartialD]", "\[Nu]"], + SubsuperscriptBox["A", "\[Mu]", "a"]}], " ", "+", " ", + RowBox[{ + SubscriptBox["g", "s"], + SubsuperscriptBox["A", "\[Mu]", "b"], + SubsuperscriptBox["A", "\[Nu]", "c"], " ", + SuperscriptBox["f", "abc"]}]}]], "InlineFormula"], + ".\n", + Cell[" ", "ModInfo"], Cell[BoxData[ - FormBox[ - RowBox[{" ", - SuperscriptBox["f", - RowBox[{"a", " ", "b1", " ", "c1"}]]}], TraditionalForm]]], - ". FieldStrength[\[Mu], \[Nu]] is the field strength tensor ", + RowBox[{"FieldStrength", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "InlineFormula"], + " \[LineSeparator]is the field strength tensor ", Cell[BoxData[ FormBox[ - RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", "\[Mu]"], - SubsuperscriptBox["A", "\[Nu]", "\[Null]"]}], "-", - RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", "\[Nu]"], - SubsuperscriptBox["A", "\[Mu]", "\[Null]"]}], "."}]}], - TraditionalForm]]], - " The name of the field (A) and the coupling constant (g) can be set through \ -the options or by additional arguments. The first two indices are interpreted \ -as type LorentzIndex, except OPEDelta, which is converted to \ -Momentum[OPEDelta]." + RowBox[{Cell[TextData[Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{ + SubscriptBox["\[PartialD]", "\[Mu]"], + SubscriptBox["A", "\[Nu]"]}], "-", + RowBox[{ + SubscriptBox["\[PartialD]", "\[Nu]"], + SubscriptBox["A", "\[Mu]"]}]}], TraditionalForm]], "InlineFormula"]], + "InlineFormula"], "."}], TraditionalForm]]] }], "Usage", - CellID->982511436], + CellID->2010081510], + +Cell[TextData[{ + "The name of the field (", + Cell[BoxData["A"], "InlineFormula"], + ") and the coupling constant (", + Cell[BoxData["g"], "InlineFormula"], + ") can be set through the options or by additional arguments. " +}], "Notes"], + +Cell[TextData[{ + "The first two indices are interpreted as type ", + ButtonBox["LorentzIndex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/LorentzIndex", + ButtonNote->"LorentzIndex"], + ", except ", + ButtonBox["OPEDelta", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/OPEDelta", + ButtonNote->"OPEDelta"], + ", which is converted to ", + Cell[BoxData[ + RowBox[{"Momentum", "[", "OPEDelta", "]"}]], "InlineFormula"], + "." +}], "Notes"], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FieldStrength", "]"}]], "Input", + CellTags->"FieldStrength", + CellLabel->"In[196]:=", + CellID->1871937792], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Explicit", "\[Rule]", "False"}], ",", + RowBox[{"IndexPosition", "\[Rule]", + RowBox[{"{", + RowBox[{"0", ",", "0"}], "}"}]}], ",", + RowBox[{"Symbol", "\[Rule]", "\<\"F\"\>"}], ",", + RowBox[{"QuantumField", "\[Rule]", "A"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"FieldStrength", + CellLabel->"Out[196]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -195,15 +238,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - ButtonBox["QuantumField", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/QuantumField", - ButtonNote->"QuantumField"], - "." -}], "Text", - CellTags->"FieldStrength", - CellID->830418848] +Cell[TextData[ButtonBox["QuantumField", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/QuantumField", + ButtonNote->"QuantumField"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -232,37 +270,11 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "FieldStrength", "]"}]], "Input", - CellTags->"FieldStrength", - CellLabel->"In[1]:=", - CellID->1871937792], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"CouplingConstant", "\[Rule]", - SubscriptBox["g", "s"]}], ",", - RowBox[{"Explicit", "\[Rule]", "False"}], ",", - RowBox[{"IndexPosition", "\[Rule]", - RowBox[{"{", - RowBox[{"0", ",", "0"}], "}"}]}], ",", - RowBox[{"Symbol", "\[Rule]", "\<\"F\"\>"}], ",", - RowBox[{"QuantumField", "\[Rule]", "A"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"FieldStrength", - CellLabel->"Out[1]=", - CellID->1632479646] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"FieldStrength", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Input", CellTags->"FieldStrength", - CellLabel->"In[2]:=", + CellLabel->"In[197]:=", CellID->302696897], Cell[BoxData[ @@ -274,8 +286,7 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm]}], "\[Null]"], TraditionalForm]], "Output", CellTags->"FieldStrength", - CellLabel->"Out[2]=", - CellID->1654266361] + CellLabel->"Out[197]="] }, Open ]], Cell[CellGroupData[{ @@ -284,7 +295,7 @@ Cell[BoxData[ RowBox[{"FieldStrength", "[", RowBox[{"\[Mu]", ",", "\[Nu]", ",", "a"}], "]"}]], "Input", CellTags->"FieldStrength", - CellLabel->"In[3]:=", + CellLabel->"In[198]:=", CellID->1691553307], Cell[BoxData[ @@ -298,8 +309,7 @@ Cell[BoxData[ FormBox["a", TraditionalForm]], TraditionalForm]], "Output", CellTags->"FieldStrength", - CellLabel->"Out[3]=", - CellID->1099758759] + CellLabel->"Out[198]="] }, Open ]], Cell[CellGroupData[{ @@ -309,41 +319,42 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"FieldStrength", - CellLabel->"In[4]:=", + CellLabel->"In[199]:=", CellID->278939746], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Nu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Mu]", TraditionalForm], - TraditionalForm], "\[Null]"]}]}], TraditionalForm]], "Output", + TraditionalForm]], ")"}]}], TraditionalForm]], "Output", CellTags->"FieldStrength", - CellLabel->"Out[4]=", - CellID->1642105709] + CellLabel->"Out[199]="] }, Open ]], Cell[CellGroupData[{ @@ -353,7 +364,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "a", ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"FieldStrength", - CellLabel->"In[5]:=", + CellLabel->"In[200]:=", CellID->474892601], Cell[BoxData[ @@ -365,9 +376,9 @@ Cell[BoxData[ RowBox[{ FormBox["a", TraditionalForm], - FormBox["b663", + FormBox["b849", TraditionalForm], - FormBox["c664", + FormBox["c850", TraditionalForm]}]], " ", RowBox[{ SubsuperscriptBox[ @@ -378,7 +389,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["b663", + FormBox["b849", TraditionalForm], TraditionalForm]], ".", SubsuperscriptBox[ @@ -389,11 +400,12 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["c664", + FormBox["c850", TraditionalForm], TraditionalForm]]}]}], "+", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], @@ -408,9 +420,10 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], @@ -425,70 +438,9 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}]}], TraditionalForm]], "Output", + TraditionalForm]], ")"}]}], TraditionalForm]], "Output", CellTags->"FieldStrength", - CellLabel->"Out[5]=", - CellID->409660918] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"FieldStrength", "[", - RowBox[{"\[Mu]", ",", "\[Nu]", ",", - RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}], "]"}]], "Input", - CellTags->"FieldStrength", - CellLabel->"In[6]:=", - CellID->2102395759], - -Cell[BoxData[ - RowBox[{ - RowBox[{"QuantumField", "[", - RowBox[{ - RowBox[{"FCPartialD", "[", - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}], ",", "GaugeField", - ",", - RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}]}], "]"}], "-", - RowBox[{"QuantumField", "[", - RowBox[{ - RowBox[{"FCPartialD", "[", - RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], "]"}], ",", "GaugeField", - ",", - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]}]], "Output", - CellTags->"FieldStrength", - CellLabel->"Out[6]//StandardForm=", - CellID->66342321] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"FieldStrength", "[", - RowBox[{"\[Mu]", ",", "OPEDelta", ",", - RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}], "]"}]], "Input", - CellTags->"FieldStrength", - CellLabel->"In[7]:=", - CellID->481183730], - -Cell[BoxData[ - RowBox[{ - RowBox[{"QuantumField", "[", - RowBox[{ - RowBox[{"FCPartialD", "[", - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}], ",", "GaugeField", - ",", - RowBox[{"Momentum", "[", "OPEDelta", "]"}]}], "]"}], "-", - RowBox[{"QuantumField", "[", - RowBox[{ - RowBox[{"FCPartialD", "[", - RowBox[{"Momentum", "[", "OPEDelta", "]"}], "]"}], ",", "GaugeField", - ",", - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]}]], "Output", - CellTags->"FieldStrength", - CellLabel->"Out[7]//StandardForm=", - CellID->1631615995] + CellLabel->"Out[200]="] }, Open ]], Cell[CellGroupData[{ @@ -497,10 +449,11 @@ Cell[BoxData[ RowBox[{"FieldStrength", "[", RowBox[{"\[Mu]", ",", "\[Nu]", ",", "a", ",", RowBox[{"CouplingConstant", "\[Rule]", - RowBox[{"-", "Gstrong"}]}], ",", + RowBox[{"-", + RowBox[{"SMP", "[", "\"\\"", "]"}]}]}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"FieldStrength", - CellLabel->"In[8]:=", + CellLabel->"In[202]:=", CellID->1847448290], Cell[BoxData[ @@ -513,9 +466,9 @@ Cell[BoxData[ RowBox[{ FormBox["a", TraditionalForm], - FormBox["b665", + FormBox["b853", TraditionalForm], - FormBox["c666", + FormBox["c854", TraditionalForm]}]], " ", RowBox[{ SubsuperscriptBox[ @@ -526,7 +479,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["b665", + FormBox["b853", TraditionalForm], TraditionalForm]], ".", SubsuperscriptBox[ @@ -537,11 +490,12 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["c666", + FormBox["c854", TraditionalForm], TraditionalForm]]}]}]}], "+", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], @@ -556,9 +510,10 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], @@ -573,10 +528,9 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}]}], TraditionalForm]], "Output", + TraditionalForm]], ")"}]}], TraditionalForm]], "Output", CellTags->"FieldStrength", - CellLabel->"Out[8]=", - CellID->865013743] + CellLabel->"Out[202]="] }, Open ]] }, Open ]], @@ -640,13 +594,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{700, 769}, +WindowMargins->{{1113, Automatic}, {235, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FinalFunction.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FinalFunction.nb index 1c586bac2..087f8ed92 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FinalFunction.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FinalFunction.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoopSum", ButtonNote->"OneLoopSum"], "." -}], "Text", - CellTags->"FinalFunction", - CellID->1102033150] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1150, Automatic}, {Automatic, 185}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FinalSubstitutions.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FinalSubstitutions.nb index f8ea0e344..1207bc401 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FinalSubstitutions.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FinalSubstitutions.nb @@ -175,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Write2", ButtonNote->"Write2"], "." -}], "Text", - CellTags->"FinalSubstitutions", - CellID->1617701707] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -263,12 +261,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{915, Automatic}, {Automatic, 152}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FourDivergence.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FourDivergence.nb index 017594233..a1cac2988 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FourDivergence.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FourDivergence.nb @@ -119,16 +119,39 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"FourDivergence", "[", RowBox[{"exp", ",", " ", - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", " ", "mu"}], "]"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "calculates the partial derivative of exp w.r.t. p(mu). FourDivergence[exp, \ -FourVector[p, mu], FourVector[p,nu], ...]gives the multiple derivative." + " \[LineSeparator]calculates the partial derivative of exp w.r.t ", + Cell[BoxData[ + SuperscriptBox["p", "\[Mu]"]], "InlineFormula"], + ". FourDivergence[exp, FV[p, mu], FV[p,nu], ...] gives the multiple \ +derivative." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FourDivergence", "]"}]], "Input", + CellLabel->"In[298]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Abort", "\[Rule]", "True"}], ",", + RowBox[{"ApartFF", "\[Rule]", "False"}], ",", + RowBox[{"Contract", "\[Rule]", "True"}], ",", + RowBox[{"Collecting", "\[Rule]", "True"}], ",", + RowBox[{"EpsEvaluate", "\[Rule]", "True"}], ",", + RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", + RowBox[{"Factoring", "\[Rule]", "Factor"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[298]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -169,9 +192,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RussianTrick", ButtonNote->"RussianTrick"], "." -}], "Text", - CellTags->"FourDivergence", - CellID->1618281503] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,11 +222,10 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t", "=", - RowBox[{"ScalarProduct", "[", - RowBox[{"p", ",", "q"}], "]"}]}]], "Input", + RowBox[{"SP", "[", + RowBox[{"p", ",", "q"}], "]"}]], "Input", CellTags->"FourDivergence", - CellLabel->"In[1]:=", + CellLabel->"In[112]:=", CellID->1686706616], Cell[BoxData[ @@ -224,19 +244,18 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"FourDivergence", - CellLabel->"Out[1]=", - CellID->712819199] + CellLabel->"Out[112]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FourDivergence", "[", - RowBox[{"t", ",", - RowBox[{"FourVector", "[", + RowBox[{"%", ",", + RowBox[{"FV", "[", RowBox[{"q", ",", "\[Mu]"}], "]"}]}], "]"}]], "Input", CellTags->"FourDivergence", - CellLabel->"In[2]:=", + CellLabel->"In[113]:=", CellID->1594453358], Cell[BoxData[ @@ -248,25 +267,21 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"FourDivergence", - CellLabel->"Out[2]=", - CellID->1032930238] + CellLabel->"Out[113]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t", "=", - RowBox[{"ScalarProduct", "[", - RowBox[{ - RowBox[{"p", "-", "k"}], ",", "q"}], "]"}]}]], "Input", + RowBox[{"SP", "[", + RowBox[{ + RowBox[{"p", "-", "k"}], ",", "q"}], "]"}]], "Input", CellTags->"FourDivergence", - CellLabel->"In[3]:=", + CellLabel->"In[114]:=", CellID->1521326595], Cell[BoxData[ @@ -275,13 +290,15 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["k", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["k", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -293,49 +310,90 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"FourDivergence", - CellLabel->"Out[3]=", - CellID->2094801531] + CellLabel->"Out[114]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FourDivergence", "[", - RowBox[{"t", ",", - RowBox[{"FourVector", "[", - RowBox[{ - RowBox[{"k", "-", "p"}], ",", "\[Mu]"}], "]"}]}], "]"}]], "Input", + RowBox[{"%", ",", + RowBox[{"FV", "[", + RowBox[{"k", ",", "\[Mu]"}], "]"}]}], "]"}]], "Input", CellTags->"FourDivergence", - CellLabel->"In[4]:=", + CellLabel->"In[115]:=", CellID->822682822], Cell[BoxData[ FormBox[ RowBox[{"-", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"FourDivergence", - CellLabel->"Out[4]=", - CellID->1487482336] + CellLabel->"Out[115]="] }, Open ]], +Cell[CellGroupData[{ + Cell[BoxData[ - RowBox[{"Clear", "[", "t", "]"}]], "Input", - CellTags->"FourDivergence", - CellLabel->"In[5]:=", - CellID->1056090995] + RowBox[{"SFAD", "[", + RowBox[{"{", + RowBox[{"p", ",", + RowBox[{"m", "^", "2"}]}], "}"}], "]"}]], "Input", + CellLabel->"In[116]:="], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[116]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FourDivergence", "[", + RowBox[{"%", ",", + RowBox[{"FVD", "[", + RowBox[{"p", ",", "\[Nu]"}], "]"}]}], "]"}]], "Input", + CellLabel->"In[117]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"-", + FractionBox[ + RowBox[{"2", " ", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]]}], + SuperscriptBox[ + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"], "2"]]}], TraditionalForm]], "Output", + CellLabel->"Out[117]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -399,12 +457,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{872, Automatic}, {Automatic, 151}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FourLaplacian.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FourLaplacian.nb index 8b3c38936..485d87ba4 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FourLaplacian.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FourLaplacian.nb @@ -138,7 +138,20 @@ Cell[TextData[{ CellID->982511436], Cell["XXXX", "Notes", - CellID->1067943069] + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FourLaplacian", "]"}]], "Input", + CellLabel->"In[118]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Dimension", "\[Rule]", "D"}], "}"}], TraditionalForm]], "Output", + CellLabel->"Out[118]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -184,9 +197,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RussianTrick", ButtonNote->"RussianTrick"], "." -}], "Text", - CellTags->"FourLaplacian", - CellID->736385282] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -215,28 +226,11 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "FourLaplacian", "]"}]], "Input", - CellTags->"FourLaplacian", - CellLabel->"In[1]:=", - CellID->244662667], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Dimension", "\[Rule]", "D"}], "}"}], TraditionalForm]], "Output", - CellTags->"FourLaplacian", - CellLabel->"Out[1]=", - CellID->1107918748] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"SP", "[", RowBox[{"q", ",", "q"}], "]"}]], "Input", CellTags->"FourLaplacian", - CellLabel->"In[2]:=", + CellLabel->"In[119]:=", CellID->678691277], Cell[BoxData[ @@ -248,8 +242,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"], TraditionalForm]], "Output", CellTags->"FourLaplacian", - CellLabel->"Out[2]=", - CellID->614689358] + CellLabel->"Out[119]="] }, Open ]], Cell[CellGroupData[{ @@ -258,15 +251,14 @@ Cell[BoxData[ RowBox[{"FourLaplacian", "[", RowBox[{"%", ",", "q", ",", "q"}], "]"}]], "Input", CellTags->"FourLaplacian", - CellLabel->"In[3]:=", + CellLabel->"In[120]:=", CellID->1086572094], Cell[BoxData[ FormBox[ RowBox[{"2", " ", "D"}], TraditionalForm]], "Output", CellTags->"FourLaplacian", - CellLabel->"Out[3]=", - CellID->1928361141] + CellLabel->"Out[120]="] }, Open ]], Cell[CellGroupData[{ @@ -280,7 +272,7 @@ Cell[BoxData[ RowBox[{"q", ",", RowBox[{"q", "-", "p"}]}], "]"}]}], "//", "FCI"}]], "Input", CellTags->"FourLaplacian", - 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CellLabel->"Out[5]=", - CellID->290457260] + CellLabel->"Out[122]="] }, Open ]] }, Open ]], @@ -641,12 +801,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1177, Automatic}, {Automatic, 130}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FourVector.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FourVector.nb index 50e121efb..f6017e346 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FourVector.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FourVector.nb @@ -128,8 +128,26 @@ Dimension \[Rule] D." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +The shortcut FourVector is deprecated, please use FV instead!\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "FourVector", "]"}]], "Input", + CellLabel->"In[355]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[355]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -170,19 +188,12 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FV", ButtonNote->"FV"], ", ", - ButtonBox["FVD", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FVD", - ButtonNote->"FVD"], - ", ", - ButtonBox["Pair", + ButtonBox["FCI", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Pair", - ButtonNote->"Pair"], + ButtonData:>"paclet:FeynCalc/ref/FCI", + ButtonNote->"FCI"], "." -}], "Text", - CellTags->"FourVector", - CellID->570089667] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -215,7 +226,7 @@ Cell[BoxData[ RowBox[{"FourVector", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Input", CellTags->"FourVector", - CellLabel->"In[1]:=", + CellLabel->"In[347]:=", CellID->1607662272], Cell[BoxData[ @@ -227,14 +238,11 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"FourVector", - CellLabel->"Out[1]=", - CellID->1688325660] + CellLabel->"Out[347]="] }, Open ]], Cell[CellGroupData[{ @@ -244,7 +252,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}]], "Input", CellTags->"FourVector", - CellLabel->"In[2]:=", + CellLabel->"In[348]:=", CellID->1944995744], Cell[BoxData[ @@ -263,14 +271,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], ")"}], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"FourVector", - CellLabel->"Out[2]=", - CellID->1086738867] + CellLabel->"Out[348]="] }, Open ]], Cell[CellGroupData[{ @@ -280,7 +285,7 @@ Cell[BoxData[ RowBox[{"FourVector", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}], "]"}]], "Input", CellTags->"FourVector", - CellLabel->"In[3]:=", + CellLabel->"In[349]:=", CellID->1554251701], Cell[BoxData[ @@ -289,8 +294,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]], "Output", CellTags->"FourVector", - CellLabel->"Out[3]//StandardForm=", - CellID->1875964060] + CellLabel->"Out[349]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -301,7 +305,7 @@ Cell[BoxData[ RowBox[{"p", ",", "\[Mu]", ",", RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "]"}]], "Input", CellTags->"FourVector", - CellLabel->"In[4]:=", + CellLabel->"In[350]:=", CellID->438982417], Cell[BoxData[ @@ -312,81 +316,88 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "D"}], "]"}]}], "]"}]], "Output", CellTags->"FourVector", - CellLabel->"Out[4]//StandardForm=", - CellID->1059556719] + CellLabel->"Out[350]//StandardForm="] }, Open ]], +Cell["\<\ +FourVector is scheduled for removal in the future versions of FeynCalc. The \ +safe alternative is to use FV.\ +\>", "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"FCE", "[", - RowBox[{"FourVector", "[", - RowBox[{"p", ",", "\[Mu]"}], "]"}], "]"}], "]"}]], "Input", - CellTags->"FourVector", - CellLabel->"In[5]:=", - CellID->757794355], + RowBox[{"FV", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Input", + CellLabel->"In[351]:="], Cell[BoxData[ - RowBox[{"FV", "[", - RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Output", - CellTags->"FourVector", - CellLabel->"Out[5]//StandardForm=", - CellID->1053929233] + FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[351]="] }, Open ]], -Cell["\<\ -There is no special function to expand momenta in FourVector. Since \ -FourVector is turned into Pair internally ExpandScalarProduct may be used.\ -\>", "Text", - CellTags->"FourVector", - CellID->600723667], - Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"ExpandScalarProduct", "[", - RowBox[{"FourVector", "[", - RowBox[{ - RowBox[{"p", "-", "q"}], ",", "\[Mu]"}], "]"}], "]"}]], "Input", - CellTags->"FourVector", - CellLabel->"In[6]:=", - CellID->1761121824], + RowBox[{"FVD", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}]], "Input", + CellLabel->"In[352]:="], Cell[BoxData[ FormBox[ - RowBox[{ + SuperscriptBox[ FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], "-", + FormBox["p", + TraditionalForm], + TraditionalForm], FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - 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WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{911, Automatic}, {Automatic, 131}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/FunctionalD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/FunctionalD.nb index c3fd62acb..f504676fd 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/FunctionalD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/FunctionalD.nb @@ -118,25 +118,56 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"FunctionalD", "[", - RowBox[{"expr", ",", " ", + RowBox[{"exp", ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"QuantumField", "[", - RowBox[{"name", ",", " ", - RowBox[{"{", "mu", "}"}], ",", " ", - RowBox[{"{", "a", "}"}]}], "]"}], "[", "p", "]"}], ",", " ", "..."}], - "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "calculates the functional derivative of expr with respect to the field list \ -(with incoming momenta p etc.) and does the fourier transform. \ -FunctionalD[expr, {QuantumField[name, {mu},{a}], ...}] calculates the \ -functional derivative and does partial integration but omits the x-space \ -delta functions.\n\nFunctionalD is a low level function used in FeynRule." + RowBox[{"name", ",", + RowBox[{"LorentzIndex", "[", "mu", "]"}], ",", "...", ",", + RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}], "[", "p", "]"}], ",", + "..."}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]calculates the functional derivative of ", + Cell[BoxData["exp"], "InlineFormula"], + " with respect to the ", + ButtonBox["QuantumField", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/QuantumField", + ButtonNote->"QuantumField"], + " list (with incoming momenta ", + Cell[BoxData["p"], "InlineFormula"], + ", etc.) and does the Fourier transform.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"FunctionalD", "[", + RowBox[{"expr", ",", + RowBox[{"{", + RowBox[{ + RowBox[{"QuantumField", "[", + RowBox[{"name", ",", + RowBox[{"LorentzIndex", "[", "mu", "]"}], ",", + RowBox[{"...", " ", + RowBox[{"SUNIndex", "[", "a", "]"}]}]}], "]"}], ",", "..."}], + "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]calculates the functional derivative and does partial \ +integration but omits the ", + Cell[BoxData["x"], "InlineFormula"], + "-space delta functions." }], "Usage", - CellID->982511436], + CellID->2010081510], -Cell["XXXX", "Notes", +Cell[TextData[{ + ButtonBox["FunctionalD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FunctionalD", + ButtonNote->"FunctionalD"], + " is a low level function used in ", + ButtonBox["FeynRule", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FeynRule", + ButtonNote->"FeynRule"], + "." +}], "Notes", CellID->1067943069] }, Open ]], @@ -183,9 +214,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/QuantumField", ButtonNote->"QuantumField"], "." -}], "Text", - CellTags->"FunctionalD", - CellID->2077547280] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -215,25 +244,26 @@ Cell[BoxData[ Cell[TextData[{ "Instead of the usual ", Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{ - RowBox[{"\[Delta]\[Phi]", "(", "x", ")"}], "/", - RowBox[{"\[Delta]\[Phi]", "(", "y", ")"}]}], "=", + RowBox[{ + RowBox[{"\[Delta]\[Phi]", RowBox[{ - SuperscriptBox["\[Delta]", - RowBox[{"(", "D", ")"}]], "(", - RowBox[{"x", "-", "y"}], ")"}]}], TraditionalForm]]], - " the arguments and the \[Delta] function are omitted, i.e., for the program \ -for simplicity: ", + RowBox[{"(", "x", ")"}], "/", "\[Delta]\[Phi]"}], + RowBox[{"(", "y", ")"}]}], "=", + RowBox[{ + SuperscriptBox["\[Delta]", + RowBox[{"(", "D", ")"}]], + RowBox[{"(", + RowBox[{"x", "-", "y"}], ")"}]}]}]], "InlineFormula"], + " the arguments and the ", + Cell[BoxData["\[Delta]"], "InlineFormula"], + " function are omitted, i.e., for the program for simplicity: ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[Delta]\[Phi]", "/", "\[Delta]\[Phi]"}], "=", "1"}], - TraditionalForm]]] -}], "Text", - CellTags->"FunctionalD", - CellID->2064540691], + TraditionalForm]], "InlineFormula"], + "." +}], "Notes"], Cell[CellGroupData[{ @@ -243,14 +273,13 @@ Cell[BoxData[ RowBox[{"QuantumField", "[", "\[Phi]", "]"}], ",", RowBox[{"QuantumField", "[", "\[Phi]", "]"}]}], "]"}]], "Input", CellTags->"FunctionalD", - CellLabel->"In[1]:=", + CellLabel->"In[342]:=", CellID->622999086], Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"FunctionalD", - CellLabel->"Out[1]=", - CellID->149077150] + CellLabel->"Out[342]="] }, Open ]], Cell[CellGroupData[{ @@ -262,7 +291,7 @@ Cell[BoxData[ 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Bearing in mind that for FeynCalc we have to be \ + SubsuperscriptBox["A", "\[Sigma]", "g"]], "InlineFormula"], + " has to be set to zero. 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RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}]}]}], "-", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "-", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2381,23 +2369,6 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ -2408,7 +2379,26 @@ Cell[BoxData[ FormBox[ FormBox["d", TraditionalForm], - TraditionalForm]]}]}], "+", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "+", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2426,23 +2416,6 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ -2453,7 +2426,26 @@ Cell[BoxData[ FormBox[ FormBox["d", TraditionalForm], - TraditionalForm]]}]}], "-", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "-", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2471,23 +2463,6 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ -2498,7 +2473,26 @@ Cell[BoxData[ FormBox[ FormBox["e", TraditionalForm], - TraditionalForm]]}]}], "+", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "+", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2516,23 +2510,6 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]]}], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ -2543,7 +2520,26 @@ Cell[BoxData[ FormBox[ FormBox["e", TraditionalForm], - TraditionalForm]]}]}], "+", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "+", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2572,23 +2568,25 @@ Cell[BoxData[ FormBox["b", TraditionalForm], TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["c", - TraditionalForm], - TraditionalForm]]}]}]}], "+", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["c", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "+", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2606,23 +2604,6 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["b", - TraditionalForm], - TraditionalForm]]}], ".", SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ -2633,7 +2614,26 @@ Cell[BoxData[ FormBox[ FormBox["c", TraditionalForm], - TraditionalForm]]}]}], "-", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "-", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2655,30 +2655,32 @@ Cell[BoxData[ FormBox["A", TraditionalForm], FormBox[ - FormBox["\[Sigma]", + FormBox["\[Nu]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["b", + FormBox["c", TraditionalForm], TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["c", - TraditionalForm], - TraditionalForm]]}]}]}], "-", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "-", RowBox[{ FractionBox["1", "4"], " ", SuperscriptBox["f", @@ -2696,34 +2698,36 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - 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RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + SubsuperscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}], "+", RowBox[{ - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm]], " ", SuperscriptBox["f", RowBox[{ FormBox[ @@ -6161,7 +4952,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["b", + FormBox["c", TraditionalForm], TraditionalForm], FormBox[ @@ -6169,11 +4960,6 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], " ", RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]], SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ 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TraditionalForm], - FormBox[ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["g", - TraditionalForm], - TraditionalForm]]}], "+", - RowBox[{ - RowBox[{ - FormBox[ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - TraditionalForm], - FormBox[ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["g", - TraditionalForm], - TraditionalForm]]}], "-", - RowBox[{ - RowBox[{ - FormBox[ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], - TraditionalForm], - FormBox[ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["g", - TraditionalForm], - TraditionalForm]]}]}], TraditionalForm]], "Output", + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"FunctionalD", - CellLabel->"Out[32]=", - CellID->594909875] + CellLabel->"Out[387]="] }, Open ]], -Cell["quod erat demonstrandum.", "Text", - CellTags->"FunctionalD", - CellID->927805887], +Cell["As expected:", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"dif1", "//", "FCCanonicalizeDummyIndices"}]], "Input", + CellLabel->"In[390]:="], + +Cell[BoxData[ + FormBox["0", TraditionalForm]], "Output", + CellLabel->"Out[390]="] +}, Open ]], + +Cell["Finally, unset the commutator of the bosonic fields.", "Notes"], Cell[BoxData[ RowBox[{ - RowBox[{"Unset", "[", - RowBox[{"s", "[", "\[Phi]", "]"}], "]"}], ";", - RowBox[{"Unset", "[", - RowBox[{"S", "[", "A", "]"}], "]"}], ";", - RowBox[{"Clear", "[", - RowBox[{ - "Ag", ",", "F1", ",", "F2", ",", "t1", ",", "t2", ",", "t3", ",", "t4", - ",", "F", ",", "r1", ",", "r2", ",", "r3", ",", "r4", ",", "symfun", ",", - "twof", ",", "twofnew", ",", "w0", ",", "w1", ",", "w2", ",", "dif1", ",", - "dif2", ",", "dif3"}], "]"}]}]], "Input", - CellTags->"FunctionalD", - CellLabel->"In[33]:=", - CellID->1348622684] + RowBox[{ + RowBox[{"UnDeclareCommutator", "[", + RowBox[{ + RowBox[{"QuantumField", "[", + RowBox[{"aaa___FCPartialD", ",", "A", ",", "bbb__"}], "]"}], ",", + RowBox[{"QuantumField", "[", + RowBox[{"ccc___FCPartialD", ",", "A", ",", "ddd__"}], "]"}]}], "]"}], + "=", "0"}], ";"}]], "Input", + CellLabel->"In[391]:="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -6380,13 +5083,14 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, 2}}, +WindowSize->{1206, 1065}, +WindowMargins->{{686, Automatic}, {101, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GA.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GA.nb index a2675b5ea..a0b789272 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GA.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GA.nb @@ -117,13 +117,13 @@ Cell["GA", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"GA", "[", "mu", "]"}]], "InlineFormula"], + RowBox[{"GA", "[", "\[Mu]", "]"}]], "InlineFormula"], " \[LineSeparator]", "can be used as input for a 4-dimensional ", Cell[BoxData[ FormBox[ - SubscriptBox["\[Gamma]", - RowBox[{"\[Mu]", " "}]], TraditionalForm]]], + SubscriptBox[ + SuperscriptBox["\[Gamma]", "\[Mu]"], " "], TraditionalForm]]], "and is transformed into DiracGamma[LorentzIndex[", Cell[BoxData[ FormBox["\[Mu]", TraditionalForm]]], @@ -178,10 +178,10 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["DiracMatrix", + ButtonBox["DiracGamma", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData:>"paclet:FeynCalc/ref/DiracGamma", + ButtonNote->"DiracGamma"], ", ", ButtonBox["GAD", BaseStyle->"Link", @@ -193,9 +193,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GS", ButtonNote->"GS"], "." -}], "Text", - CellTags->"GA", - CellID->1423338362] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -227,7 +225,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GA", "[", "\[Mu]", "]"}]], "Input", CellTags->"GA", - CellLabel->"In[1]:=", + CellLabel->"In[136]:=", CellID->192317475], Cell[BoxData[ @@ -239,8 +237,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"GA", - CellLabel->"Out[1]=", - CellID->1620727253] + CellLabel->"Out[136]="] }, Open ]], Cell[CellGroupData[{ @@ -252,7 +249,7 @@ Cell[BoxData[ RowBox[{"GA", "[", RowBox[{"\[Nu]", ",", "\[Mu]"}], "]"}]}]], "Input", CellTags->"GA", - CellLabel->"In[2]:=", + CellLabel->"In[137]:=", CellID->950175955], Cell[BoxData[ @@ -293,8 +290,7 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->"GA", - CellLabel->"Out[2]=", - CellID->751580324] + CellLabel->"Out[137]="] }, Open ]], Cell[CellGroupData[{ @@ -304,15 +300,14 @@ Cell[BoxData[ RowBox[{"FCI", "[", RowBox[{"GA", "[", "\[Mu]", "]"}], "]"}], "]"}]], "Input", CellTags->"GA", - CellLabel->"In[3]:=", + CellLabel->"In[138]:=", CellID->872281918], Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}]], "Output", CellTags->"GA", - CellLabel->"Out[3]//StandardForm=", - CellID->1671355959] + CellLabel->"Out[138]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -322,7 +317,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}]], "Input", CellTags->"GA", - CellLabel->"In[4]:=", + CellLabel->"In[139]:=", CellID->1064432869], Cell[BoxData[ @@ -361,8 +356,7 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"GA", - CellLabel->"Out[4]=", - CellID->973003462] + CellLabel->"Out[139]="] }, Open ]], Cell[CellGroupData[{ @@ -373,7 +367,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], "]"}]], "Input", CellTags->"GA", - CellLabel->"In[5]:=", + CellLabel->"In[140]:=", CellID->1945449635], Cell[BoxData[ @@ -383,8 +377,7 @@ Cell[BoxData[ RowBox[{"GA", "[", "\[Rho]", "]"}], ".", RowBox[{"GA", "[", "\[Sigma]", "]"}]}]], "Output", CellTags->"GA", - CellLabel->"Out[5]//StandardForm=", - CellID->390738149] + CellLabel->"Out[140]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -397,7 +390,7 @@ Cell[BoxData[ RowBox[{"GS", "[", "p", "]"}], "+", "m"}], ")"}], ".", RowBox[{"GA", "[", "\[Beta]", "]"}]}]], "Input", CellTags->"GA", - CellLabel->"In[6]:=", + CellLabel->"In[141]:=", CellID->1527316325], Cell[BoxData[ @@ -431,8 +424,7 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"GA", - CellLabel->"Out[6]=", - CellID->1420363209] + CellLabel->"Out[141]="] }, Open ]] }, Open ]], @@ -497,12 +489,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1130, Automatic}, {Automatic, 161}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GA5.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GA5.nb index 92b83decf..587aded40 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GA5.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GA5.nb @@ -174,9 +174,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GS", ButtonNote->"GS"], "." -}], "Text", - CellTags->"GA5", - CellID->1140253619] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -207,7 +205,7 @@ Cell[CellGroupData[{ Cell[BoxData["GA5"], "Input", CellTags->"GA5", - CellLabel->"In[1]:=", + CellLabel->"In[142]:=", CellID->51140118], Cell[BoxData[ @@ -217,23 +215,21 @@ Cell[BoxData[ FormBox["5", TraditionalForm]], TraditionalForm]], "Output", CellTags->"GA5", - CellLabel->"Out[1]=", - CellID->26317546] + CellLabel->"Out[142]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"%", "//", "Tr"}]], "Input", + RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"GA5", - CellLabel->"In[2]:=", + CellLabel->"In[143]:=", CellID->306400430], Cell[BoxData[ - FormBox["0", TraditionalForm]], "Output", + RowBox[{"DiracGamma", "[", "5", "]"}]], "Output", CellTags->"GA5", - CellLabel->"Out[2]=", - CellID->223026079] + CellLabel->"Out[143]//StandardForm="] }, Open ]] }, Open ]], @@ -298,12 +294,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1249, Automatic}, {Automatic, 233}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GAD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GAD.nb index 2352b428d..78ceacefe 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GAD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GAD.nb @@ -117,13 +117,13 @@ Cell["GAD", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"GAD", "[", "mu", "]"}]], "InlineFormula"], + RowBox[{"GAD", "[", "\[Mu]", "]"}]], "InlineFormula"], " \[LineSeparator]", "can be used as input for a D-dimensional ", Cell[BoxData[ FormBox[ - SubscriptBox["\[Gamma]", - RowBox[{"\[Mu]", " "}]], TraditionalForm]]], + SubscriptBox[ + SuperscriptBox["\[Gamma]", "\[Mu]"], " "], TraditionalForm]]], "and is transformed into DiracGamma[LorentzIndex[", Cell[BoxData[ FormBox["\[Mu]", TraditionalForm]]], @@ -178,10 +178,10 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["DiracMatrix", + ButtonBox["DiracGamma", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracMatrix", - ButtonNote->"DiracMatrix"], + ButtonData:>"paclet:FeynCalc/ref/DiracGamma", + ButtonNote->"DiracGamma"], ", ", ButtonBox["GA", BaseStyle->"Link", @@ -193,9 +193,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GS", ButtonNote->"GS"], "." -}], "Text", - CellTags->"GAD", - CellID->127950767] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -227,7 +225,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GAD", "[", "\[Mu]", "]"}]], "Input", CellTags->"GAD", - CellLabel->"In[1]:=", + CellLabel->"In[144]:=", CellID->617064291], Cell[BoxData[ @@ -238,8 +236,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"GAD", - CellLabel->"Out[1]=", - CellID->1066808251] + CellLabel->"Out[144]="] }, Open ]], Cell[CellGroupData[{ @@ -251,7 +248,7 @@ Cell[BoxData[ RowBox[{"GAD", "[", RowBox[{"\[Nu]", ",", "\[Mu]"}], "]"}]}]], "Input", CellTags->"GAD", - CellLabel->"In[2]:=", + CellLabel->"In[145]:=", CellID->1166403079], Cell[BoxData[ @@ -288,8 +285,7 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->"GAD", - CellLabel->"Out[2]=", - CellID->1547742824] + CellLabel->"Out[145]="] }, Open ]], Cell[CellGroupData[{ @@ -299,7 +295,7 @@ Cell[BoxData[ RowBox[{"FCI", "[", RowBox[{"GAD", "[", "\[Mu]", "]"}], "]"}], "]"}]], "Input", CellTags->"GAD", - CellLabel->"In[3]:=", + CellLabel->"In[146]:=", CellID->1483888506], Cell[BoxData[ @@ -308,8 +304,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", "D"}], "]"}]], "Output", CellTags->"GAD", - CellLabel->"Out[3]//StandardForm=", - CellID->129946086] + CellLabel->"Out[146]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -319,7 +314,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}]], "Input", CellTags->"GAD", - CellLabel->"In[4]:=", + CellLabel->"In[147]:=", CellID->193869943], Cell[BoxData[ @@ -354,8 +349,7 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"GAD", - CellLabel->"Out[4]=", - CellID->1706461221] + CellLabel->"Out[147]="] }, Open ]], Cell[CellGroupData[{ @@ -366,7 +360,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], "]"}]], "Input", CellTags->"GAD", - CellLabel->"In[5]:=", + CellLabel->"In[148]:=", CellID->488289901], Cell[BoxData[ @@ -376,8 +370,7 @@ Cell[BoxData[ RowBox[{"GAD", "[", "\[Rho]", "]"}], ".", RowBox[{"GAD", "[", "\[Sigma]", "]"}]}]], "Output", CellTags->"GAD", - CellLabel->"Out[5]//StandardForm=", - CellID->20038506] + CellLabel->"Out[148]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -390,7 +383,7 @@ Cell[BoxData[ RowBox[{"GSD", "[", "p", "]"}], "+", "m"}], ")"}], ".", RowBox[{"GAD", "[", "\[Beta]", "]"}]}]], "Input", CellTags->"GAD", - CellLabel->"In[6]:=", + CellLabel->"In[149]:=", CellID->1528585205], Cell[BoxData[ @@ -420,8 +413,7 @@ Cell[BoxData[ TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"GAD", - CellLabel->"Out[6]=", - CellID->1687383827] + CellLabel->"Out[149]="] }, Open ]] }, Open ]], @@ -486,12 +478,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1103, Automatic}, {Automatic, 134}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GAE.nb 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For brevity one can also use shorter \ +forms such as GFAD[{x, n}, ...], GFAD[{x}, ...] or GFAD[x, ...]. If s is not \ +explicitly specified, then its value is determined by the option EtaSign, \ +which has the default value +1. If n is not explicitly specified, then the \ +default value 1 is assumed. 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+ CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1227, Automatic}, {Automatic, 272}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GGV.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GGV.nb index 34114deeb..a061884c1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GGV.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GGV.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GluonGhostVertex", ButtonNote->"GluonGhostVertex"], "." -}], "Text", - CellTags->"GGV", - CellID->535760603] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{929, Automatic}, {Automatic, 172}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GHP.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GHP.nb index 48d8104e7..a0fbac1e0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GHP.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GHP.nb @@ -182,9 +182,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GluonGhostVertex", ButtonNote->"GluonGhostVertex"], "." -}], "Text", - CellTags->"GHP", - CellID->269539325] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -217,7 +215,7 @@ Cell[BoxData[ RowBox[{"GHP", "[", RowBox[{"p", ",", "a", ",", "b"}], "]"}]], "Input", CellTags->"GHP", - CellLabel->"In[1]:=", + CellLabel->"In[166]:=", CellID->1087938540], Cell[BoxData[ @@ -232,8 +230,7 @@ Cell[BoxData[ FormBox["p", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"GHP", - CellLabel->"Out[1]=", - CellID->798549713] + CellLabel->"Out[166]="] }, Open ]], Cell[CellGroupData[{ @@ -242,27 +239,34 @@ Cell[BoxData[ RowBox[{ RowBox[{"GHP", "[", "p", "]"}], "//", "Explicit"}]], "Input", CellTags->"GHP", - CellLabel->"In[2]:=", + CellLabel->"In[167]:=", CellID->16593768], Cell[BoxData[ FormBox[ FractionBox["\[ImaginaryI]", - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"]], TraditionalForm]], "Output", + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False]], TraditionalForm]], "Output", CellTags->"GHP", - CellLabel->"Out[2]=", - CellID->1879723497] + CellLabel->"Out[167]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GHP", "[", - RowBox[{"p", ",", "1", ",", "2"}], "]"}]], "Input", + RowBox[{"p", ",", "c1", ",", "c2"}], "]"}]], "Input", CellTags->"GHP", - CellLabel->"In[3]:=", + CellLabel->"In[169]:=", CellID->1429235603], Cell[BoxData[ @@ -270,15 +274,14 @@ Cell[BoxData[ RowBox[{ SubscriptBox["\[CapitalPi]", RowBox[{ - FormBox["ci1", + FormBox["c1", TraditionalForm], - FormBox["ci2", + FormBox["c2", TraditionalForm]}]], "(", FormBox["p", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"GHP", - CellLabel->"Out[3]=", - CellID->1586595147] + CellLabel->"Out[169]="] }, Open ]], Cell[CellGroupData[{ @@ -289,20 +292,19 @@ Cell[BoxData[ RowBox[{ RowBox[{"GHP", "[", RowBox[{ - RowBox[{"-", "k"}], ",", "3", ",", "4"}], "]"}], "//", "Explicit"}], + RowBox[{"-", "k"}], ",", "c3", ",", "c4"}], "]"}], "//", "Explicit"}], "]"}], "]"}]], "Input", CellTags->"GHP", - CellLabel->"In[4]:=", + CellLabel->"In[171]:=", CellID->1957617706], Cell[BoxData[ RowBox[{"\[ImaginaryI]", " ", RowBox[{"FAD", "[", "k", "]"}], " ", RowBox[{"SD", "[", - RowBox[{"ci3", ",", "ci4"}], "]"}]}]], "Output", + RowBox[{"c3", ",", "c4"}], "]"}]}]], "Output", CellTags->"GHP", - CellLabel->"Out[4]//StandardForm=", - CellID->1550998879] + CellLabel->"Out[171]//StandardForm="] }, Open ]] }, Open ]], @@ -367,12 +369,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{783, Automatic}, {Automatic, 159}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GO.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GO.nb index 55f8e357f..76d72c5fc 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GO.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GO.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Twist2GluonOperator", ButtonNote->"Twist2GluonOperator"], "." -}], "Text", - CellTags->"GO", - CellID->1926074292] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{958, Automatic}, {Automatic, 224}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GP.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GP.nb index f3106eabd..4a8451fd0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GP.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GP.nb @@ -117,8 +117,7 @@ Cell["GP", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["GP"], "InlineFormula"], - " \[LineSeparator]", - "is equivalent to GluonPropagator." + " \[LineSeparator]is equivalent to GluonPropagator." }], "Usage", CellID->982511436], @@ -164,9 +163,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GluonPropagator", ButtonNote->"GluonPropagator"], "." -}], "Text", - CellTags->"GP", - CellID->444986205] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +249,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{924, Automatic}, {Automatic, 168}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GS.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GS.nb index 4fe413dd8..4fd8d0ee6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GS.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GS.nb @@ -180,11 +180,6 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracGamma", ButtonNote->"DiracGamma"], ", ", - ButtonBox["DiracSlash", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], - ", ", ButtonBox["GA", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GA", @@ -195,9 +190,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GAD", ButtonNote->"GAD"], "." -}], "Text", - CellTags->"GS", - CellID->1515784011] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -229,7 +222,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GS", "[", "p", "]"}]], "Input", CellTags->"GS", - CellLabel->"In[1]:=", + CellLabel->"In[172]:=", CellID->1176675883], Cell[BoxData[ @@ -242,8 +235,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"GS", - CellLabel->"Out[1]=", - CellID->682141754] + CellLabel->"Out[172]="] }, Open ]], Cell[CellGroupData[{ @@ -254,15 +246,14 @@ Cell[BoxData[ RowBox[{"GS", "[", "p", "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"GS", - CellLabel->"In[2]:=", + CellLabel->"In[173]:=", CellID->1027241244], Cell[BoxData[ RowBox[{"DiracGamma", "[", RowBox[{"Momentum", "[", "p", "]"}], "]"}]], "Output", CellTags->"GS", - CellLabel->"Out[2]//StandardForm=", - CellID->1007084382] + CellLabel->"Out[173]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -271,7 +262,7 @@ Cell[BoxData[ RowBox[{"GS", "[", RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}]], "Input", CellTags->"GS", - CellLabel->"In[3]:=", + CellLabel->"In[174]:=", CellID->1339265647], Cell[BoxData[ @@ -318,8 +309,7 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"GS", - CellLabel->"Out[3]=", - CellID->1827181467] + CellLabel->"Out[174]="] }, Open ]], Cell[CellGroupData[{ @@ -330,7 +320,7 @@ Cell[BoxData[ RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"GS", - CellLabel->"In[4]:=", + CellLabel->"In[175]:=", CellID->837744205], Cell[BoxData[ @@ -340,8 +330,7 @@ Cell[BoxData[ RowBox[{"GS", "[", "r", "]"}], ".", RowBox[{"GS", "[", "s", "]"}]}]], "Output", CellTags->"GS", - CellLabel->"Out[4]//StandardForm=", - CellID->451922065] + CellLabel->"Out[175]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -354,7 +343,7 @@ Cell[BoxData[ RowBox[{"GS", "[", "p", "]"}], "+", "m"}], ")"}], ".", RowBox[{"GS", "[", "q", "]"}]}]], "Input", CellTags->"GS", - CellLabel->"In[5]:=", + CellLabel->"In[176]:=", CellID->2143558790], Cell[BoxData[ @@ -392,8 +381,7 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"GS", - CellLabel->"Out[5]=", - CellID->373152039] + CellLabel->"Out[176]="] }, Open ]] }, Open ]], @@ -458,12 +446,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{960, Automatic}, {Automatic, 222}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GSD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GSD.nb index 7336eca09..eabf90029 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GSD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GSD.nb @@ -180,11 +180,6 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracGamma", ButtonNote->"DiracGamma"], ", ", - ButtonBox["DiracSlash", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSlash", - ButtonNote->"DiracSlash"], - ", ", ButtonBox["GA", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GA", @@ -195,9 +190,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GAD", ButtonNote->"GAD"], "." -}], "Text", - CellTags->"GSD", - CellID->1911106257] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -229,7 +222,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GSD", "[", "p", "]"}]], "Input", CellTags->"GSD", - CellLabel->"In[1]:=", + CellLabel->"In[177]:=", CellID->4519520], Cell[BoxData[ @@ -240,8 +233,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"GSD", - CellLabel->"Out[1]=", - CellID->69860572] + CellLabel->"Out[177]="] }, Open ]], Cell[CellGroupData[{ @@ -252,7 +244,7 @@ Cell[BoxData[ RowBox[{"GSD", "[", "p", "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"GSD", - CellLabel->"In[2]:=", + CellLabel->"In[178]:=", CellID->714510926], Cell[BoxData[ @@ -261,8 +253,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "D"}], "]"}], ",", "D"}], "]"}]], "Output", CellTags->"GSD", - CellLabel->"Out[2]//StandardForm=", - CellID->2038587686] + CellLabel->"Out[178]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -271,7 +262,7 @@ Cell[BoxData[ RowBox[{"GSD", "[", RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}]], "Input", CellTags->"GSD", - CellLabel->"In[3]:=", + CellLabel->"In[179]:=", CellID->1291429952], Cell[BoxData[ @@ -310,8 +301,7 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"GSD", - CellLabel->"Out[3]=", - CellID->136445387] + CellLabel->"Out[179]="] }, Open ]], Cell[CellGroupData[{ @@ -322,7 +312,7 @@ Cell[BoxData[ RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"GSD", - CellLabel->"In[4]:=", + CellLabel->"In[180]:=", CellID->1183068674], Cell[BoxData[ @@ -332,8 +322,7 @@ Cell[BoxData[ RowBox[{"GSD", "[", "r", "]"}], ".", RowBox[{"GSD", "[", "s", "]"}]}]], "Output", CellTags->"GSD", - CellLabel->"Out[4]//StandardForm=", - CellID->1638135688] + CellLabel->"Out[180]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -346,7 +335,7 @@ Cell[BoxData[ RowBox[{"GSD", "[", "p", "]"}], "+", "m"}], ")"}], ".", RowBox[{"GSD", "[", "q", "]"}]}]], "Input", CellTags->"GSD", - CellLabel->"In[5]:=", + CellLabel->"In[181]:=", CellID->957956427], Cell[BoxData[ @@ -378,8 +367,7 @@ Cell[BoxData[ TraditionalForm]}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"GSD", - CellLabel->"Out[5]=", - CellID->1243501677] + CellLabel->"Out[181]="] }, Open ]] }, Open ]], @@ -444,12 +432,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{812, Automatic}, {Automatic, 169}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GSE.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GSE.nb 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DiracTrick has encountered a fatal problem and \ +must abort the computation. The problem reads: \ +\[NoBreak]\\!\\(\\*FormBox[\\\"\\\\\\\"Incorrect combination of dimensions \ +and g^5 scheme!\\\\\\\"\\\", TraditionalForm]\\)\[NoBreak] \ +\\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ +ButtonFrame->None, ButtonData:>\\\"paclet:FeynCalc/ref/DiracTrick\\\", \ +ButtonNote -> \\\"FeynCalc`DiracTrick::failmsg\\\"]\\)\"\>"}], + TraditionalForm]], "Message", "MSG", + CellLabel->"During evaluation of In[58]:="], + +Cell[BoxData[ + FormBox["$Aborted", TraditionalForm]], "Output", + CellLabel->"Out[58]="] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}], ";"}]], "Input", + CellLabel->"In[59]:="], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSimplify", "[", + RowBox[{ + RowBox[{"GSE", "[", "q", "]"}], ".", + RowBox[{"GS", "[", "q", "]"}], ".", + RowBox[{"GSE", "[", "q", "]"}]}], "]"}]], "Input", + CellLabel->"In[60]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"], + TraditionalForm], "2"], " ", + RowBox[{"(", + RowBox[{"-", + RowBox[{"(", + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[60]="] +}, Open ]], + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCSetDiracGammaScheme", "[", "\"\\"", "]"}], ";"}]], "Input", + + CellLabel->"In[61]:="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1037, Automatic}, {-10, Automatic}}, +Visible->True, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GTI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GTI.nb index 556a2d174..d924dfd1c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GTI.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GTI.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI", ButtonNote->"RHI"], "." -}], "Text", - CellTags->"GTI", - CellID->1799992921] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1050, Automatic}, {Automatic, 192}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GV.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GV.nb index d5157e3fe..129fe43df 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GV.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GV.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GluonVertex", ButtonNote->"GluonVertex"], "." -}], "Text", - CellTags->"GV", - CellID->1677627688] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{940, Automatic}, {167, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma1.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma1.nb index 703792bb7..9f9bf0e90 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma1.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma1.nb @@ -172,9 +172,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Gamma3", ButtonNote->"Gamma3"], "." -}], "Text", - CellTags->"Gamma1", - CellID->257898662] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -260,12 +258,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{891, Automatic}, {Automatic, 270}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma2.nb index 9dd69971a..940561d59 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma2.nb @@ -172,9 +172,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Gamma3", ButtonNote->"Gamma3"], "." -}], "Text", - CellTags->"Gamma2", - CellID->1475330785] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -260,12 +258,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1095, Automatic}, {171, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma3.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma3.nb index 0fff2c421..0aa58315b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma3.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gamma3.nb @@ -173,9 +173,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Gamma2", ButtonNote->"Gamma2"], "." -}], "Text", - CellTags->"Gamma3", - CellID->1609021158] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -261,12 +259,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1206, Automatic}, {208, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GammaEpsilon.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GammaEpsilon.nb index f6016d54b..09efaee17 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GammaEpsilon.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GammaEpsilon.nb @@ -171,9 +171,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Series2", ButtonNote->"Series2"], "." -}], "Text", - CellTags->"GammaEpsilon", - CellID->1891061042] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,9 +201,7 @@ Cell[BoxData[ Cell["\<\ If the argument is of the form (1+a Epsilon) the result is not calculated but \ tabulated.\ -\>", "Text", - CellTags->"GammaEpsilon", - CellID->1418061835], +\>", "Notes"], Cell[CellGroupData[{ @@ -214,7 +210,7 @@ Cell[BoxData[ RowBox[{"1", "+", RowBox[{"a", " ", "Epsilon"}]}], "]"}]], "Input", CellTags->"GammaEpsilon", - CellLabel->"In[1]:=", + CellLabel->"In[192]:=", CellID->584681345], Cell[BoxData[ @@ -260,13 +256,12 @@ Cell[BoxData[ SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "2"]}], "+", - RowBox[{"C$23297", " ", + RowBox[{"C$44993", " ", SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "6"]}], "+", "1"}], TraditionalForm]], "Output", CellTags->"GammaEpsilon", - CellLabel->"Out[1]=", - CellID->1401166400] + CellLabel->"Out[192]="] }, Open ]], Cell[CellGroupData[{ @@ -276,13 +271,13 @@ Cell[BoxData[ RowBox[{"1", "-", RowBox[{"Epsilon", "/", "2"}]}], "]"}]], "Input", CellTags->"GammaEpsilon", - CellLabel->"In[2]:=", + CellLabel->"In[193]:=", CellID->862497870], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{"C$23317", " ", + RowBox[{"C$45019", " ", SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "6"]}], "+", @@ -320,26 +315,23 @@ Cell[BoxData[ TemplateBox[{"3"}, "Zeta"]}], "24"], "+", "1"}], TraditionalForm]], "Output", CellTags->"GammaEpsilon", - CellLabel->"Out[2]=", - CellID->924354653] + CellLabel->"Out[193]="] }, Open ]], -Cell["For other arguments the expansion is calculated.", "Text", - CellTags->"GammaEpsilon", - CellID->185068189], +Cell["For other arguments the expansion is calculated.", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GammaEpsilon", "[", "Epsilon", "]"}]], "Input", CellTags->"GammaEpsilon", - CellLabel->"In[3]:=", + CellLabel->"In[194]:=", CellID->910709306], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{"C$24452", " ", + RowBox[{"C$46162", " ", SuperscriptBox[ TagBox["\[CurlyEpsilon]", TraditionalForm], "6"]}], "+", @@ -411,8 +403,7 @@ Cell[BoxData[ TemplateBox[{"5"}, "Zeta"]}]}], ")"}]}], "1440"]}], TraditionalForm]], "Output", CellTags->"GammaEpsilon", - CellLabel->"Out[3]=", - CellID->208287808] + CellLabel->"Out[194]="] }, Open ]], Cell[CellGroupData[{ @@ -420,7 +411,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GammaEpsilon", "[", "x", "]"}]], "Input", CellTags->"GammaEpsilon", - CellLabel->"In[4]:=", + CellLabel->"In[195]:=", CellID->766916522], Cell[BoxData[ @@ -428,8 +419,7 @@ Cell[BoxData[ TemplateBox[{"x"}, "Gamma"], TraditionalForm]], "Output", CellTags->"GammaEpsilon", - CellLabel->"Out[4]=", - CellID->460537482] + CellLabel->"Out[195]="] }, Open ]] }, Open ]], @@ -494,12 +484,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{911, Automatic}, {Automatic, 248}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GammaExpand.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GammaExpand.nb index d97e31126..a6b0bf36e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GammaExpand.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GammaExpand.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GammaEpsilon", ButtonNote->"GammaEpsilon"], "." -}], "Text", - CellTags->"GammaExpand", - CellID->1346477755] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,7 +199,7 @@ Cell[BoxData[ RowBox[{"Gamma", "[", RowBox[{"2", " ", "+", " ", "Epsilon"}], "]"}], "]"}]], "Input", CellTags->"GammaExpand", - CellLabel->"In[1]:=", + CellLabel->"In[196]:=", CellID->53996644], Cell[BoxData[ @@ -215,8 +213,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm], "+", "1"}]}, "Gamma"]}], TraditionalForm]], "Output", CellTags->"GammaExpand", - CellLabel->"Out[1]=", - CellID->388026766] + CellLabel->"Out[196]="] }, Open ]], Cell[CellGroupData[{ @@ -227,7 +224,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "3"}], "+", "Epsilon"}], "]"}], "]"}]], "Input", CellTags->"GammaExpand", - CellLabel->"In[2]:=", + CellLabel->"In[197]:=", CellID->1712828018], Cell[BoxData[ @@ -252,8 +249,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"GammaExpand", - CellLabel->"Out[2]=", - CellID->842543076] + CellLabel->"Out[197]="] }, Open ]], Cell[CellGroupData[{ @@ -263,7 +259,7 @@ Cell[BoxData[ RowBox[{"Gamma", "[", RowBox[{"1", " ", "+", " ", "Epsilon"}], "]"}], "]"}]], "Input", CellTags->"GammaExpand", - CellLabel->"In[3]:=", + CellLabel->"In[198]:=", CellID->509676592], Cell[BoxData[ @@ -272,8 +268,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm], "+", "1"}]}, "Gamma"], TraditionalForm]], "Output", CellTags->"GammaExpand", - CellLabel->"Out[3]=", - CellID->861147229] + CellLabel->"Out[198]="] }, Open ]] }, Open ]], @@ -338,12 +333,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{959, Automatic}, {Automatic, 261}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gauge.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gauge.nb index 388740525..007a4acfb 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gauge.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gauge.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GluonProgagator", ButtonNote->"GluonProgagator"], "." -}], "Text", - CellTags->"Gauge", - CellID->1660814530] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{712, Automatic}, {Automatic, 231}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GaugeField.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GaugeField.nb index d497475f2..915ac963b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GaugeField.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GaugeField.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/QuantumField", ButtonNote->"QuantumField"], "." -}], "Text", - CellTags->"GaugeField", - CellID->1344551251] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,14 +201,13 @@ Cell[CellGroupData[{ Cell[BoxData["GaugeField"], "Input", CellTags->"GaugeField", - CellLabel->"In[1]:=", + CellLabel->"In[199]:=", CellID->1050712800], Cell[BoxData[ FormBox["A", TraditionalForm]], "Output", CellTags->"GaugeField", - CellLabel->"Out[1]=", - CellID->501755105] + CellLabel->"Out[199]="] }, Open ]], Cell[CellGroupData[{ @@ -221,7 +218,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}]], "Input", CellTags->"GaugeField", - CellLabel->"In[2]:=", + CellLabel->"In[200]:=", CellID->1376527682], Cell[BoxData[ @@ -238,8 +235,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"GaugeField", - CellLabel->"Out[2]=", - CellID->511347556] + CellLabel->"Out[200]="] }, Open ]] }, Open ]], @@ -304,12 +300,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{853, Automatic}, {Automatic, 235}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GaugeXi.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GaugeXi.nb index 96d32da33..8a8444de9 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GaugeXi.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GaugeXi.nb @@ -169,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GaugeField", ButtonNote->"GaugeField"], "." -}], "Text", - 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"Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/GenericPropagatorDenominator", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["GenericPropagatorDenominator", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"GenericPropagatorDenominator", "[", + RowBox[{"expr", ",", + RowBox[{"{", + RowBox[{"n", ",", "s"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator] is a generic factor of the denominator of a propagator. \ +Unlike PropagatorDenominator that is supposed to mean 1/(q^2-m^2), expr in \ +GenericPropagatorDenominator can be an arbitrary combination of Pair, \ +CartesianPair and TemporalPair objects. Using n one can specify the power of \ +the propagator, while s (+1 or -1) fixes the sign of I*eta. \ +GenericPropagatorDenominator is an internal object. To enter such propagators \ +in FeynCalc you should use GFAD" +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + 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RowBox[{"(", + RowBox[{ + FormBox[ + FormBox["p2", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["Q", TraditionalForm], TraditionalForm]}], ")"}]}], "-", + RowBox[{ + FormBox[ + FormBox["p1", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["p2", TraditionalForm], TraditionalForm]}]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[205]=", + CellID->430028496] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1189, Automatic}, {269, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GhostPropagator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GhostPropagator.nb index d8ffcbf8c..ed174fdb2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GhostPropagator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GhostPropagator.nb @@ -119,19 +119,47 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"GhostPropagator", "[", RowBox[{"p", ",", " ", "a", ",", " ", "b"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "gives the ghost propagator where \"a\" and \"b\" are the color indices. \ -GhostPropagator[p] omits the ", + " \[LineSeparator]gives the ghost propagator where ", + Cell[BoxData["a"], "InlineFormula"], + " and ", + Cell[BoxData["b"], "InlineFormula"], + " are the color indices.\n", + Cell[" ", "ModInfo"], Cell[BoxData[ - FormBox[ - RowBox[{ - SubscriptBox["\[Delta]", - RowBox[{"a", "\[NoBreak]", "b"}]], "."}], TraditionalForm]]] + RowBox[{"GhostPropagator", "[", "p", "]"}]], "InlineFormula"], + " \[LineSeparator]omits the ", + Cell[BoxData[ + SubscriptBox["\[Delta]", + RowBox[{"a", "\[NoBreak]", "b"}]]], "InlineFormula"], + "." }], "Usage", - CellID->982511436], + CellID->2010081510], + +Cell[TextData[{ + Cell[BoxData["GHP"], "InlineFormula"], + " can be used as an abbreviation of ", + ButtonBox["GhostPropagator", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/GhostPropagator", + ButtonNote->"GhostPropagator"], + "." +}], "Notes"], + +Cell[CellGroupData[{ -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[BoxData[ + RowBox[{"Options", "[", "GhostPropagator", "]"}]], "Input", + CellLabel->"In[408]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Explicit", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[408]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -167,24 +195,22 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["GHP", + ButtonBox["GluonPropagator", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/GHP", - ButtonNote->"GHP"], + ButtonData:>"paclet:FeynCalc/ref/GhostPropagator", + ButtonNote->"GhostPropagator"], ", ", - ButtonBox["GluonPropagator", + ButtonBox["QCDFeynmanRuleConvention", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/GluonPropagator", - ButtonNote->"GluonPropagator"], + ButtonData:>"paclet:FeynCalc/ref/QCDFeynmanRuleConvention", + ButtonNote->"QCDFeynmanRuleConvention"], ", ", ButtonBox["GluonGhostVertex", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GluonGhostVertex", ButtonNote->"GluonGhostVertex"], "." -}], "Text", - CellTags->"GhostPropagator", - CellID->495663945] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -232,19 +258,14 @@ Cell[BoxData[ FormBox["p", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"GhostPropagator", - CellLabel->"Out[1]=", - CellID->512151226] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"GhostPropagator", "[", - RowBox[{"p", ",", "a", ",", "b", ",", - RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", - CellTags->"GhostPropagator", - CellLabel->"In[2]:=", - CellID->736877273], + RowBox[{"Explicit", "[", "%", "]"}]], "Input", + CellLabel->"In[2]:="], Cell[BoxData[ FormBox[ @@ -260,18 +281,30 @@ Cell[BoxData[ FormBox["b", TraditionalForm], TraditionalForm]}]]}], - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"]], TraditionalForm]], "Output", - CellTags->"GhostPropagator", - CellLabel->"Out[2]=", - CellID->1880336114] + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False]], TraditionalForm]], "Output", + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"GhostPropagator", "[", "p", "]"}]], "Input", + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"GHP", "[", "p", "]"}]], "Input", CellTags->"GhostPropagator", CellLabel->"In[3]:=", CellID->357152074], @@ -283,64 +316,31 @@ Cell[BoxData[ FormBox["p", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"GhostPropagator", - CellLabel->"Out[3]=", - CellID->1092778903] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"GhostPropagator", "[", - RowBox[{"p", ",", "1", ",", "2"}], "]"}], "//", "Explicit"}]], "Input", - CellTags->"GhostPropagator", - CellLabel->"In[4]:=", - CellID->1361525951], + RowBox[{"Explicit", "[", "%", "]"}]], "Input", + CellLabel->"In[4]:="], Cell[BoxData[ FormBox[ - FractionBox[ - RowBox[{"\[ImaginaryI]", " ", - SuperscriptBox["\[Delta]", - RowBox[{ - FormBox[ - FormBox["ci1", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["ci2", - TraditionalForm], - TraditionalForm]}]]}], - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"]], TraditionalForm]], "Output", - CellTags->"GhostPropagator", - CellLabel->"Out[4]=", - CellID->190043121] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"GhostPropagator", "[", - RowBox[{ - RowBox[{"-", "k"}], ",", "3", ",", "4"}], "]"}], "//", "Explicit"}], "//", - " ", "FCE"}], "//", "StandardForm"}]], "Input", - CellTags->"GhostPropagator", - CellLabel->"In[5]:=", - CellID->160188204], - -Cell[BoxData[ - RowBox[{"\[ImaginaryI]", " ", - RowBox[{"FAD", "[", "k", "]"}], " ", - RowBox[{"SD", "[", - RowBox[{"ci3", ",", "ci4"}], "]"}]}]], "Output", - CellTags->"GhostPropagator", - CellLabel->"Out[5]//StandardForm=", - CellID->657761817] + FractionBox["\[ImaginaryI]", + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False]], TraditionalForm]], "Output", + CellLabel->"Out[4]="] +}, Open ]] }, Open ]] }, Open ]], @@ -405,12 +405,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1495, Automatic}, {Automatic, 243}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonField.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonField.nb index 777b68248..de10206dd 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonField.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonField.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GaugeField", ButtonNote->"GaugeField"], "." -}], "Text", - CellTags->"GluonField", - CellID->2115683038] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -197,14 +195,13 @@ Cell[CellGroupData[{ Cell[BoxData["GluonField"], "Input", CellTags->"GluonField", - CellLabel->"In[1]:=", + CellLabel->"In[206]:=", CellID->807080920], Cell[BoxData[ FormBox["A", TraditionalForm]], "Output", CellTags->"GluonField", - CellLabel->"Out[1]=", - CellID->1953309416] + CellLabel->"Out[206]="] }, Open ]], Cell[CellGroupData[{ @@ -215,7 +212,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}]], "Input", CellTags->"GluonField", - CellLabel->"In[2]:=", + CellLabel->"In[207]:=", CellID->1368218379], Cell[BoxData[ @@ -232,8 +229,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"GluonField", - CellLabel->"Out[2]=", - CellID->1231631318] + CellLabel->"Out[207]="] }, Open ]] }, Open ]], @@ -298,12 +294,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{780, Automatic}, {Automatic, 256}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonGhostVertex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonGhostVertex.nb index 64419dfeb..5a6ecb88e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonGhostVertex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonGhostVertex.nb @@ -125,17 +125,63 @@ Cell[TextData[{ RowBox[{"q", ",", "nu", ",", "b"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"k", ",", "rho", ",", "c"}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "or GluonGhostVertex[ p,mu,a , q,nu,b , k,rho,c ] yields the Gluon-Ghost \ -vertex. The first argument represents the gluon and the third argument the \ -outgoing ghost field (but incoming four-momentum). The dimension and the name \ -of the coupling constant are determined by the options Dimension and \ -CouplingConstant." + " \[LineSeparator]or ", + Cell[BoxData[ + RowBox[{"GluonGhostVertex", "[", " ", + RowBox[{ + "p", ",", "mu", ",", "a", " ", ",", " ", "q", ",", "nu", ",", "b", " ", + ",", " ", "k", ",", "rho", ",", "c"}], " ", "]"}]], "InlineFormula"], + " yields the Gluon-Ghost vertex. The first argument represents the gluon and \ +the third argument the outgoing ghost field (but incoming 4-momentum)." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + Cell[BoxData["GGV"], "InlineFormula"], + " can be used as an abbreviation of ", + ButtonBox["GluonGhostVertex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/GluonGhostVertex", + ButtonNote->"GluonGhostVertex"], + "." +}], "Notes"], + +Cell[TextData[{ + "The dimension and the name of the coupling constant are determined by the \ +options ", + ButtonBox["Dimension", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Dimension", + ButtonNote->"Dimension"], + " and ", + ButtonBox["CouplingConstant", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CouplingConstant", + ButtonNote->"CouplingConstant"], + ". " +}], "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "GluonGhostVertex", "]"}]], "Input", + CellTags->"GluonGhostVertex", + CellLabel->"In[5]:=", + CellID->607510152], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Explicit", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"GluonGhostVertex", + CellLabel->"Out[5]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -171,7 +217,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["GluonPropagator", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GluonPropagator", @@ -179,22 +224,25 @@ Cell[TextData[{ ", ", ButtonBox["GluonSelfEnergy", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/GluonSelfEnergy", + ButtonData:>"pa\.17clet:FeynCalc/ref/GluonSelfEnergy", ButtonNote->"GluonSelfEnergy"], ", ", - ButtonBox["GhostPropagator", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/GhostPropagator", - ButtonNote->"GhostPropagator"], - ", ", ButtonBox["GluonVertex", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GluonVertex", ButtonNote->"GluonVertex"], + ", ", + ButtonBox["QCDFeynmanRuleConvention", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/QCDFeynmanRuleConvention", + ButtonNote->"QCDFeynmanRuleConvention"], + ", ", + ButtonBox["GhostPropagator", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/GhostPropagator", + ButtonNote->"GhostPropagator"], "." -}], "Text", - CellTags->"GluonGhostVertex", - CellID->508730211] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -224,38 +272,17 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Options", "[", "GluonGhostVertex", "]"}]], "Input", - CellTags->"GluonGhostVertex", - CellLabel->"In[1]:=", - CellID->607510152], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", + RowBox[{ + RowBox[{"GluonGhostVertex", "[", RowBox[{ - 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CellLabel->"Out[2]=", - CellID->1673363298] + CellLabel->"Out[82]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"%", "//", "Explicit"}], "//", "StandardForm"}]], "Input", - CellTags->"GluonGhostVertex", - CellLabel->"In[3]:=", - CellID->566433445], - -Cell[BoxData[ - RowBox[{ - RowBox[{"-", "Gstrong"}], " ", - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"Momentum", "[", - RowBox[{"k", ",", "D"}], "]"}]}], "]"}], " ", - RowBox[{"SUNF", "[", - RowBox[{ - RowBox[{"SUNIndex", "[", "a", "]"}], ",", - RowBox[{"SUNIndex", "[", "b", "]"}], ",", - RowBox[{"SUNIndex", "[", "c", "]"}]}], "]"}]}]], "Output", - CellTags->"GluonGhostVertex", - CellLabel->"Out[3]//StandardForm=", - CellID->1977739800] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"GluonGhostVertex", "[", - RowBox[{"p", ",", "1", ",", "q", ",", "2", ",", "k", ",", "3"}], - "]"}]], "Input", - CellTags->"GluonGhostVertex", - 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RowBox[{"mu", ",", " ", "a"}], "}"}], ",", " ", + RowBox[{"\[Mu]", ",", " ", "a"}], "}"}], ",", " ", RowBox[{"{", - RowBox[{"nu", ",", " ", "b"}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "or GluonPropagator[p, mu, a , nu, b ] yields the gluon propagator. \ -GluonPropagator[p, {mu}, {nu}] or GluonPropagator[p, mu, nu] omits the \ -SUNDelta. The gauge and the dimension is determined by the option Gauge and \ -Dimension. The following settings of Gauge are possible: 1 for the Feynman \ -gauge; ", + RowBox[{"\[Nu]", ",", " ", "b"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]or ", Cell[BoxData[ - FormBox["\[Alpha]", TraditionalForm]]], - " for the general covariant gauge; {Momentum[n] ,1} for the axial gauge.\n\n\ -GP can be used as an abbreviation of GluonPropagator." + RowBox[{"GluonPropagator", "[", + RowBox[{ + "p", ",", " ", "\[Mu]", ",", " ", "a", ",", " ", "\[Nu]", ",", " ", "b"}], + "]"}]], "InlineFormula"], + " yields the gluon propagator.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"GluonPropagator", "[", + RowBox[{"p", ",", + RowBox[{"{", "\[Mu]", "}"}], ",", + RowBox[{"{", "\[Nu]", "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]or ", + Cell[BoxData[ + RowBox[{"GluonPropagator", "[", + RowBox[{"p", ",", " ", "\[Mu]", ",", " ", "\[Nu]"}], "]"}]], + "InlineFormula"], + " omits the ", + ButtonBox["SUNDelta", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNDelta", + ButtonNote->"SUNDelta"], + "." }], "Usage", - CellID->982511436], + CellID->2010081510], + +Cell[TextData[{ + Cell[BoxData["GP"], "InlineFormula"], + " can be used as an abbreviation of ", + ButtonBox["GluonPropagator", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/GluonPropagator", + ButtonNote->"GluonPropagator"], + "." +}], "Notes"], + +Cell[TextData[{ + "The gauge and the dimension are determined by the options ", + ButtonBox["Gauge", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Gauge", + ButtonNote->"Gauge"], + " and ", + ButtonBox["Dimension", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Dimension", + ButtonNote->"Dimension"], + ". " +}], "Notes", + CellID->1067943069], + +Cell[TextData[{ + "The following settings of Gauge are possible: ", + Cell[BoxData["1"], "InlineFormula"], + " for the Feynman gauge; ", + Cell[BoxData["\[Alpha]"], "InlineFormula"], + " for the general covariant gauge; ", + Cell[BoxData[ + RowBox[{"{", + RowBox[{ + RowBox[{"Momentum", "[", "n", "]"}], " ", ",", "1"}], "}"}]], + "InlineFormula"], + " for the axial gauge." +}], "Notes"], + +Cell[CellGroupData[{ -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[BoxData[ + RowBox[{"Options", "[", "GluonPropagator", "]"}]], "Input", + CellLabel->"In[392]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"CounterTerm", "\[Rule]", "False"}], ",", + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Explicit", "\[Rule]", "False"}], ",", + RowBox[{"Gauge", "\[Rule]", "1"}], ",", + RowBox[{"\[CapitalOmega]", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[392]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -183,6 +254,11 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GluonVertex", ButtonNote->"GluonVertex"], ", ", + ButtonBox["GhostVertex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/GhostVertex", + ButtonNote->"GhostVertex"], + ", ", ButtonBox["GhostPropagator", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GhostPropagator", @@ -193,9 +269,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GluonGhostVertex", ButtonNote->"GluonGhostVertex"], "." -}], "Text", - 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CellLabel->"Out[3]=", - CellID->722359513] + CellLabel->"Out[15]="] }, Open ]] }, Open ]], @@ -668,12 +586,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1091, Automatic}, {246, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonVertex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonVertex.nb index 81ec558fe..827039472 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonVertex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GluonVertex.nb @@ -125,21 +125,114 @@ Cell[TextData[{ RowBox[{"q", ",", "nu", ",", "b"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"k", ",", "la", ",", "c"}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "or GluonVertex[p,mu,a , q,nu,b , k,la,c ] yields the 3-gluon vertex. \ -GluonVertex[{p,mu}, {q,nu}, {k,la}] yields the 3-gluon vertex without color \ -structure and the coupling constant. GluonVertex[{p,mu,a}, {q,nu,b}, \ -{k,la,c}, {s,si,d}] or GluonVertex[{mu,a}, {nu,b}, {la,c}, {si,d}] or \ -GluonVertex[p,mu,a , q,nu,b , k,la,c , s,si,d] or GluonVertex[ mu,a , nu,b , \ -la,c , si,d ] yields the 4-gluon vertex. The dimension and the name of the \ -coupling constant are determined by the options Dimension and \ -CouplingConstant.\n\nNote: All momenta are flowing into the vertex.\n\nGV can \ -be used as an abbreviation of GluonVertex." + " \[LineSeparator]or ", + Cell[BoxData[ + RowBox[{"GluonVertex", "[", + RowBox[{ + "p", ",", " ", "mu", ",", " ", "a", ",", " ", "q", ",", " ", "nu", ",", + " ", "b", ",", " ", "k", ",", " ", "la", ",", " ", "c"}], "]"}]], + "InlineFormula"], + " yields the 3-gluon vertex. \n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"GluonVertex", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "mu"}], "}"}], ",", + RowBox[{"{", + RowBox[{"q", ",", "nu"}], "}"}], ",", + RowBox[{"{", + RowBox[{"k", ",", "la"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]yields the 3-gluon vertex without color structure and the \ +coupling constant.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"GluonVertex", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "mu", ",", "a"}], "}"}], ",", + RowBox[{"{", + RowBox[{"q", ",", "nu", ",", "b"}], "}"}], ",", + RowBox[{"{", + RowBox[{"k", ",", "la", ",", "c"}], "}"}], ",", + RowBox[{"{", + RowBox[{"s", ",", "si", ",", "d"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]or ", + Cell[BoxData[ + RowBox[{"GluonVertex", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"mu", ",", "a"}], "}"}], ",", " ", + RowBox[{"{", + RowBox[{"nu", ",", "b"}], "}"}], ",", " ", + RowBox[{"{", + RowBox[{"la", ",", "c"}], "}"}], ",", " ", + RowBox[{"{", + RowBox[{"si", ",", "d"}], "}"}]}], "]"}]], "InlineFormula"], + " or ", + Cell[BoxData[ + RowBox[{"GluonVertex", "[", + RowBox[{ + "p", ",", "mu", ",", "a", ",", " ", "q", ",", "nu", ",", "b", ",", " ", + "k", ",", "la", ",", "c", " ", ",", " ", "s", ",", "si", ",", "d"}], + "]"}]], "InlineFormula"], + " or ", + Cell[BoxData[ + RowBox[{"GluonVertex", "[", + RowBox[{ + "mu", ",", "a", ",", "nu", ",", "b", ",", "la", ",", "c", ",", " ", "si", + ",", "d"}], " ", "]"}]], "InlineFormula"], + " yields the 4-gluon vertex." }], "Usage", - CellID->982511436], + CellID->2010081510], + +Cell[TextData[{ + Cell[BoxData["GV"], "InlineFormula"], + " can be used as an abbreviation of ", + ButtonBox["GluonVertex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/GluonVertex", + ButtonNote->"GluonVertex"], + "." +}], "Notes"], + +Cell[TextData[{ + "The dimension and the name of the coupling constant are determined by the \ +options ", + ButtonBox["Dimension", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Dimension", + ButtonNote->"Dimension"], + " and ", + ButtonBox["CouplingConstant", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CouplingConstant", + ButtonNote->"CouplingConstant"], + ". 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FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["li1", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["li2", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["li3", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["li4", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]]}], "-", RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["li1", - 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FormBox["ci3", + FormBox["c", TraditionalForm], TraditionalForm], FormBox[ - FormBox["ci4", + FormBox["d", TraditionalForm], TraditionalForm], FormBox[ @@ -1439,75 +1194,50 @@ Cell[BoxData[ RowBox[{"(", RowBox[{ RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["li1", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["li3", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["li2", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["li4", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], "-", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]]}], "-", RowBox[{ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["li1", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["li4", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["li2", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["li3", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}]}], ")"}]}]}], ")"}]}], + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Sigma]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]}]]}]}], ")"}]}]}], ")"}]}], TraditionalForm]], "Output", - CellTags->"GluonVertex", - CellLabel->"Out[11]=", - CellID->1675322303] + CellLabel->"Out[27]="] +}, Open ]] }, Open ]] }, Open ]], @@ -1571,13 +1301,14 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{700, 745}, +WindowMargins->{{833, Automatic}, {Automatic, 277}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/GrassmannParity.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/GrassmannParity.nb index 323a4bf76..5649fa2cf 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/GrassmannParity.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/GrassmannParity.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DataType", ButtonNote->"DataType"], "." -}], "Text", - CellTags->"GrassmannParity", - CellID->1069561356] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{934, Automatic}, {Automatic, 279}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gstrong.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gstrong.nb index bee79716b..8df0bd700 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Gstrong.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Gstrong.nb @@ -117,12 +117,19 @@ Cell["Gstrong", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["Gstrong"], "InlineFormula"], - " \[LineSeparator]", - "denotes the strong coupling constant." + " \[LineSeparator] is a shortcut for ", + Cell[BoxData[ + RowBox[{"SMP", "[", "\"\\"", "]"}]], "InlineFormula"], + " which represents the strong coupling constant." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell[TextData[{ + "The shortcut Gstrong is deprecated, please use ", + Cell[BoxData[ + RowBox[{"SMP", "[", "\"\\"", "]"}]], "InlineFormula"], + " instead!" +}], "Notes", CellID->1067943069] }, Open ]], @@ -159,7 +166,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["CovariantD", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/CovariantD"], @@ -172,9 +178,7 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/GluonVertex"], "." -}], "Text", - CellTags->"Gstrong", - CellID->317682057] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,25 +205,29 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["\<\ -Gstrong has no functional properties. Only a typesetting rule is defined.\ -\>", "Text", - CellTags->"Gstrong", - CellID->1604993747], - Cell[CellGroupData[{ Cell[BoxData["Gstrong"], "Input", CellTags->"Gstrong", - CellLabel->"In[1]:=", + CellLabel->"In[124]:=", CellID->1539112275], Cell[BoxData[ FormBox[ SubscriptBox["g", "s"], TraditionalForm]], "Output", CellTags->"Gstrong", - CellLabel->"Out[1]=", - CellID->50548467] + CellLabel->"Out[124]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "StandardForm"}]], "Input", + CellLabel->"In[125]:="], + +Cell[BoxData[ + RowBox[{"SMP", "[", "\<\"g_s\"\>", "]"}]], "Output", + CellLabel->"Out[125]//StandardForm="] }, Open ]] }, Open ]], @@ -284,12 +292,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{644, Automatic}, {Automatic, 274}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Hill.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Hill.nb index 2abd7c2f8..b55bb055c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Hill.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Hill.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SimplifyPolyLog", ButtonNote->"SimplifyPolyLog"], "." -}], "Text", - CellTags->"Hill", - CellID->227965464] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,7 +199,7 @@ Cell[BoxData[ RowBox[{"Hill", "[", RowBox[{"a", ",", "b"}], "]"}]], "Input", CellTags->"Hill", - CellLabel->"In[1]:=", + CellLabel->"In[210]:=", CellID->921040788], Cell[BoxData[ @@ -277,8 +275,7 @@ Cell[BoxData[ FractionBox[ SuperscriptBox["\[Pi]", "2"], "6"]}], TraditionalForm]], "Output", CellTags->"Hill", - CellLabel->"Out[1]=", - CellID->263318949] + CellLabel->"Out[210]="] }, Open ]], Cell[CellGroupData[{ @@ -291,14 +288,13 @@ Cell[BoxData[ RowBox[{"b", "\[RuleDelayed]", " ", ".656"}]}], " ", "//", " ", "Chop"}]], "Input", CellTags->"Hill", - CellLabel->"In[2]:=", + CellLabel->"In[211]:=", CellID->814240014], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"Hill", - CellLabel->"Out[2]=", - CellID->1038506621] + CellLabel->"Out[211]="] }, Open ]], Cell[CellGroupData[{ @@ -312,7 +308,7 @@ Cell[BoxData[ RowBox[{"x", " ", "y"}]}], "]"}], "//", "PowerExpand"}], "//", "SimplifyPolyLog"}], "//", "Expand"}]], "Input", CellTags->"Hill", - CellLabel->"In[3]:=", + CellLabel->"In[212]:=", CellID->209270855], Cell[BoxData[ @@ -347,8 +343,7 @@ Cell[BoxData[ RowBox[{"1", "-", "y"}], ")"}], " ", RowBox[{"log", "(", "y", ")"}]}]}], TraditionalForm]], "Output", CellTags->"Hill", - CellLabel->"Out[3]=", - CellID->336046460] + CellLabel->"Out[212]="] }, Open ]], Cell[CellGroupData[{ @@ -362,14 +357,13 @@ Cell[BoxData[ RowBox[{"y", "\[Rule]", " ", ".6"}]}], "//", "N"}], "//", "Chop"}]], "Input", CellTags->"Hill", - CellLabel->"In[4]:=", + CellLabel->"In[213]:=", CellID->1494969413], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"Hill", - CellLabel->"Out[4]=", - CellID->1646571531] + CellLabel->"Out[213]="] }, Open ]] }, Open ]], @@ -434,12 +428,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{856, Automatic}, {Automatic, 261}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypExplicit.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypExplicit.nb index 80f6a595b..762c1da0e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypExplicit.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypExplicit.nb @@ -167,9 +167,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/HypergeometricIR", ButtonNote->"HypergeometricIR"], "." -}], "Text", - CellTags->"HypExplicit", - CellID->762625741] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -202,7 +200,7 @@ Cell[BoxData[ RowBox[{"Hypergeometric2F1", "[", RowBox[{"a", ",", "b", ",", "c", ",", "z"}], "]"}]], "Input", CellTags->"HypExplicit", - CellLabel->"In[1]:=", + CellLabel->"In[214]:=", CellID->713088732], Cell[BoxData[ @@ -210,8 +208,7 @@ Cell[BoxData[ TemplateBox[{"a","b","c","z"}, "Hypergeometric2F1"], TraditionalForm]], "Output", CellTags->"HypExplicit", - CellLabel->"Out[1]=", - CellID->2050064924] + CellLabel->"Out[214]="] }, Open ]], Cell[CellGroupData[{ @@ -220,7 +217,7 @@ Cell[BoxData[ RowBox[{"HypExplicit", "[", RowBox[{"%", ",", "\[Nu]"}], "]"}]], "Input", CellTags->"HypExplicit", - CellLabel->"In[2]:=", + CellLabel->"In[215]:=", CellID->335460950], Cell[BoxData[ @@ -244,8 +241,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "+", "\[Nu]"}]}, "Gamma"]}]], TraditionalForm]], "Output", CellTags->"HypExplicit", - CellLabel->"Out[2]=", - CellID->1212116493] + CellLabel->"Out[215]="] }, Open ]], Cell[CellGroupData[{ @@ -258,7 +254,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"d", ",", "e"}], "}"}], ",", "z"}], "]"}]], "Input", CellTags->"HypExplicit", - CellLabel->"In[3]:=", + CellLabel->"In[216]:=", CellID->1980165795], Cell[BoxData[ @@ -316,8 +312,7 @@ Cell[BoxData[ Selectable->False], HypergeometricPFQ], TraditionalForm]], "Output", CellTags->"HypExplicit", - CellLabel->"Out[3]=", - CellID->1891206830] + CellLabel->"Out[216]="] }, Open ]], Cell[CellGroupData[{ @@ -326,7 +321,7 @@ Cell[BoxData[ RowBox[{"HypExplicit", "[", RowBox[{"%", ",", "\[Nu]"}], "]"}]], "Input", CellTags->"HypExplicit", - CellLabel->"In[4]:=", + CellLabel->"In[217]:=", CellID->1855078663], Cell[BoxData[ @@ -358,8 +353,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"e", "+", "\[Nu]"}]}, "Gamma"]}]], TraditionalForm]], "Output", CellTags->"HypExplicit", - CellLabel->"Out[4]=", - CellID->1089581291] + CellLabel->"Out[217]="] }, Open ]] }, Open ]], @@ -424,12 +418,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{829, Automatic}, {Automatic, 157}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypInt.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypInt.nb index fdc47e894..496063282 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypInt.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypInt.nb @@ -195,7 +195,7 @@ Cell[BoxData[ RowBox[{"Hypergeometric2F1", "[", RowBox[{"a", ",", "b", ",", "c", ",", "z"}], "]"}]], "Input", CellTags->"HypInt", - CellLabel->"In[1]:=", + CellLabel->"In[218]:=", CellID->204607872], Cell[BoxData[ @@ -203,8 +203,7 @@ Cell[BoxData[ TemplateBox[{"a","b","c","z"}, "Hypergeometric2F1"], TraditionalForm]], "Output", CellTags->"HypInt", - CellLabel->"Out[1]=", - CellID->1455067917] + CellLabel->"Out[218]="] }, Open ]], Cell[CellGroupData[{ @@ -213,7 +212,7 @@ Cell[BoxData[ RowBox[{"HypInt", "[", RowBox[{"%", ",", "t"}], "]"}]], "Input", CellTags->"HypInt", - CellLabel->"In[2]:=", + CellLabel->"In[219]:=", CellID->1185900959], Cell[BoxData[ @@ -252,8 +251,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "-", "b"}]}, "Gamma"]}]], TraditionalForm]], "Output", CellTags->"HypInt", - CellLabel->"Out[2]=", - CellID->1838289676] + CellLabel->"Out[219]="] }, Open ]] }, Open ]], @@ -318,12 +316,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1065, Automatic}, {Automatic, 177}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricAC.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricAC.nb index 018dd52ec..96aa87f0a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricAC.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricAC.nb @@ -131,8 +131,21 @@ Functions & their Applications\" by N.N.Lebedev)." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "HypergeometricAC", "]"}]], "Input", + CellTags->"HypergeometricAC", + CellLabel->"In[220]:=", + CellID->860770759], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Collect2", "\[Rule]", "True"}], "}"}], TraditionalForm]], "Output", + CellTags->"HypergeometricAC", + CellLabel->"Out[220]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -188,9 +201,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/ToHypergeometric", ButtonNote->"ToHypergeometric"], "." -}], "Text", - CellTags->"HypergeometricAC", - CellID->329204732] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -217,26 +228,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "HypergeometricAC", "]"}]], "Input", - CellTags->"HypergeometricAC", - CellLabel->"In[1]:=", - CellID->860770759], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Collect2", "\[Rule]", "True"}], "}"}], TraditionalForm]], "Output", - CellTags->"HypergeometricAC", - CellLabel->"Out[1]=", - CellID->655565009] -}, Open ]], - -Cell["These are all transformation rules currently built in.", "Text", - CellTags->"HypergeometricAC", - CellID->1364071537], +Cell["These are all transformation rules currently built in.", "Notes"], Cell[CellGroupData[{ @@ -247,7 +239,7 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "z"}], "]"}], "]"}]], "Input", CellTags->"HypergeometricAC", - CellLabel->"In[2]:=", + CellLabel->"In[221]:=", CellID->1062959179], Cell[BoxData[ @@ -293,8 +285,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"\[Gamma]", "-", "\[Beta]"}]}, "Gamma"]}]]}], TraditionalForm]], "Output", CellTags->"HypergeometricAC", - CellLabel->"Out[2]=", - CellID->1804175924] + CellLabel->"Out[221]="] }, Open ]], Cell[CellGroupData[{ @@ -306,7 +297,7 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "z"}], "]"}], "]"}]], "Input", CellTags->"HypergeometricAC", - CellLabel->"In[3]:=", + CellLabel->"In[222]:=", CellID->1497393441], Cell[BoxData[ @@ -352,8 +343,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"\[Gamma]", "-", "\[Beta]"}]}, "Gamma"]}]]}], TraditionalForm]], "Output", CellTags->"HypergeometricAC", - CellLabel->"Out[3]=", - CellID->615954992] + CellLabel->"Out[222]="] }, Open ]], Cell[CellGroupData[{ @@ -365,7 +355,7 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "z"}], "]"}], "]"}]], "Input", CellTags->"HypergeometricAC", - CellLabel->"In[4]:=", + CellLabel->"In[223]:=", CellID->1365244505], Cell[BoxData[ @@ -412,8 +402,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"\[Gamma]", "-", "\[Beta]"}]}, "Gamma"]}]]}], TraditionalForm]], "Output", CellTags->"HypergeometricAC", - CellLabel->"Out[4]=", - CellID->291107136] + CellLabel->"Out[223]="] }, Open ]], Cell[CellGroupData[{ @@ -425,7 +414,7 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "z"}], "]"}], "]"}]], "Input", CellTags->"HypergeometricAC", - CellLabel->"In[5]:=", + CellLabel->"In[224]:=", CellID->411308116], Cell[BoxData[ @@ -452,35 +441,34 @@ Cell[BoxData[ "Gamma"], " ", TemplateBox[{RowBox[{"\[Gamma]", "-", "\[Beta]"}]}, "Gamma"]}]], "+", - FractionBox[ - RowBox[{ - TemplateBox[{"\[Gamma]"}, - "Gamma"], " ", - SuperscriptBox["z", - RowBox[{"\[Alpha]", "-", "\[Gamma]"}]], " ", - TemplateBox[{RowBox[{"\[Alpha]", "+", "\[Beta]", "-", "\[Gamma]"}]}, - "Gamma"], " ", - SuperscriptBox[ - RowBox[{"(", - RowBox[{"1", "-", "z"}], ")"}], + RowBox[{ + FractionBox["1", + RowBox[{ + TemplateBox[{"\[Alpha]"}, + "Gamma"], " ", + TemplateBox[{"\[Beta]"}, + "Gamma"]}]], + TemplateBox[{"\[Gamma]"}, + "Gamma"], " ", + SuperscriptBox["z", + RowBox[{"\[Alpha]", "-", "\[Gamma]"}]], " ", + TemplateBox[{RowBox[{"\[Alpha]", "+", "\[Beta]", "-", "\[Gamma]"}]}, + "Gamma"], " ", + SuperscriptBox[ + RowBox[{"(", + RowBox[{"1", "-", "z"}], ")"}], + RowBox[{ + RowBox[{"-", "\[Alpha]"}], "-", "\[Beta]", "+", "\[Gamma]"}]], " ", + TemplateBox[{ + RowBox[{"1", "-", "\[Alpha]"}],RowBox[{"\[Gamma]", "-", "\[Alpha]"}], RowBox[{ - RowBox[{"-", "\[Alpha]"}], "-", "\[Beta]", "+", "\[Gamma]"}]], " ", - TemplateBox[{ - RowBox[{"1", "-", "\[Alpha]"}],RowBox[{"\[Gamma]", "-", "\[Alpha]"}], - RowBox[{ - RowBox[{"-", "\[Alpha]"}], "-", "\[Beta]", "+", "\[Gamma]", "+", - "1"}],RowBox[{"-", - FractionBox[ - RowBox[{"1", "-", "z"}], "z"]}]}, - "Hypergeometric2F1"]}], - RowBox[{ - TemplateBox[{"\[Alpha]"}, - "Gamma"], " ", - TemplateBox[{"\[Beta]"}, - "Gamma"]}]]}], TraditionalForm]], "Output", + RowBox[{"-", "\[Alpha]"}], "-", "\[Beta]", "+", "\[Gamma]", "+", + "1"}],RowBox[{"-", + FractionBox[ + RowBox[{"1", "-", "z"}], "z"]}]}, + "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"HypergeometricAC", - CellLabel->"Out[5]=", - CellID->1895074645] + CellLabel->"Out[224]="] }, Open ]], Cell[CellGroupData[{ @@ -492,7 +480,7 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "z"}], "]"}], "]"}]], "Input", CellTags->"HypergeometricAC", - CellLabel->"In[6]:=", + CellLabel->"In[225]:=", CellID->436366778], Cell[BoxData[ @@ -508,8 +496,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}], TraditionalForm]], "Output", CellTags->"HypergeometricAC", - CellLabel->"Out[6]=", - CellID->789329283] + CellLabel->"Out[225]="] }, Open ]], Cell[CellGroupData[{ @@ -521,7 +508,7 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "z"}], "]"}], "]"}]], "Input", CellTags->"HypergeometricAC", - CellLabel->"In[7]:=", + CellLabel->"In[226]:=", CellID->417226545], Cell[BoxData[ @@ -537,8 +524,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}], TraditionalForm]], "Output", CellTags->"HypergeometricAC", - CellLabel->"Out[7]=", - CellID->1946106454] + CellLabel->"Out[226]="] }, Open ]] }, Open ]], @@ -603,12 +589,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{903, Automatic}, {Automatic, 90}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricIR.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricIR.nb index fcb3de3fc..6c487d0ca 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricIR.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricIR.nb @@ -126,8 +126,22 @@ option Integratedx \[Rule] False." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "HypergeometricIR", "]"}]], "Input", + CellTags->"HypergeometricIR", + CellLabel->"In[227]:=", + CellID->384078315], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Integratedx", "\[Rule]", "False"}], "}"}], + TraditionalForm]], "Output", + CellTags->"HypergeometricIR", + CellLabel->"Out[227]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -178,9 +192,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/ToHypergeometric", ButtonNote->"ToHypergeometric"], "." -}], "Text", - CellTags->"HypergeometricIR", - CellID->1403310516] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -209,24 +221,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "HypergeometricIR", "]"}]], "Input", - CellTags->"HypergeometricIR", - CellLabel->"In[1]:=", - CellID->384078315], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Integratedx", "\[Rule]", "False"}], "}"}], - TraditionalForm]], "Output", - CellTags->"HypergeometricIR", - CellLabel->"Out[1]=", - CellID->43106065] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"HypergeometricIR", "[", RowBox[{ @@ -234,7 +228,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c", ",", "z"}], "]"}], ",", "t"}], "]"}]], "Input", CellTags->"HypergeometricIR", - CellLabel->"In[2]:=", + CellLabel->"In[228]:=", CellID->1374832181], Cell[BoxData[ @@ -261,8 +255,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "-", "b"}]}, "Gamma"]}]], TraditionalForm]], "Output", CellTags->"HypergeometricIR", - CellLabel->"Out[2]=", - CellID->1433332384] + CellLabel->"Out[228]="] }, Open ]], Cell[CellGroupData[{ @@ -281,7 +274,7 @@ Cell[BoxData[ RowBox[{"t", " ", "z"}]}], ")"}], "^", "a"}]}], ",", "t"}], "]"}]], "Input", CellTags->"HypergeometricIR", - CellLabel->"In[3]:=", + CellLabel->"In[229]:=", CellID->907804769], Cell[BoxData[ @@ -299,8 +292,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"b", "+", "c", "+", "2"}]}, "Gamma"]], TraditionalForm]], "Output", CellTags->"HypergeometricIR", - CellLabel->"Out[3]=", - CellID->1119784034] + CellLabel->"Out[229]="] }, Open ]], Cell[CellGroupData[{ @@ -309,7 +301,7 @@ Cell[BoxData[ RowBox[{"HypergeometricIR", "[", RowBox[{"%", ",", "t"}], "]"}]], "Input", CellTags->"HypergeometricIR", - CellLabel->"In[4]:=", + CellLabel->"In[230]:=", CellID->1094444131], Cell[BoxData[ @@ -325,8 +317,7 @@ Cell[BoxData[ RowBox[{"t", " ", "z"}], "+", "1"}], ")"}], "a"]}], TraditionalForm]], "Output", CellTags->"HypergeometricIR", - CellLabel->"Out[4]=", - CellID->1637166476] + CellLabel->"Out[230]="] }, Open ]] }, Open ]], @@ -391,12 +382,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{987, Automatic}, {Automatic, 207}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricSE.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricSE.nb index 2feeff716..c910e7663 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricSE.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/HypergeometricSE.nb @@ -128,8 +128,22 @@ sum (the Sum is omitted and nu, running from 0 to ", }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "HypergeometricSE", "]"}]], "Input", + CellTags->"HypergeometricSE", + CellLabel->"In[231]:=", + CellID->1143734993], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Simplify", "\[Rule]", "FullSimplify"}], "}"}], + TraditionalForm]], "Output", + CellTags->"HypergeometricSE", + CellLabel->"Out[231]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -170,9 +184,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/HypergeometricIR", ButtonNote->"HypergeometricIR"], "." -}], "Text", - CellTags->"HypergeometricSE", - CellID->715881200] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,24 +213,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "HypergeometricSE", "]"}]], "Input", - CellTags->"HypergeometricSE", - CellLabel->"In[1]:=", - CellID->1143734993], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Simplify", "\[Rule]", "FullSimplify"}], "}"}], - TraditionalForm]], "Output", - CellTags->"HypergeometricSE", - CellLabel->"Out[1]=", - CellID->2099172215] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"HypergeometricSE", "[", RowBox[{ @@ -226,7 +220,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c", ",", "z"}], "]"}], ",", "\[Nu]"}], "]"}]], "Input", CellTags->"HypergeometricSE", - CellLabel->"In[2]:=", + CellLabel->"In[232]:=", CellID->388138933], Cell[BoxData[ @@ -250,8 +244,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "+", "\[Nu]"}]}, "Gamma"]}]], TraditionalForm]], "Output", CellTags->"HypergeometricSE", - CellLabel->"Out[2]=", - CellID->1318858464] + CellLabel->"Out[232]="] }, Open ]], Cell[CellGroupData[{ @@ -267,7 +260,7 @@ Cell[BoxData[ RowBox[{"d", ",", "e"}], "}"}], ",", "z"}], "]"}], ",", "\[Nu]"}], "]"}]], "Input", CellTags->"HypergeometricSE", - CellLabel->"In[3]:=", + CellLabel->"In[233]:=", CellID->998113844], Cell[BoxData[ @@ -299,8 +292,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"e", "+", "\[Nu]"}]}, "Gamma"]}]], TraditionalForm]], "Output", CellTags->"HypergeometricSE", - CellLabel->"Out[3]=", - CellID->1095324364] + CellLabel->"Out[233]="] }, Open ]] }, Open ]], @@ -365,12 +357,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{926, Automatic}, {Automatic, 189}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPD.nb index 81dce3817..15fe49989 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPD.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PropagatorDenominator", ButtonNote->"PropagatorDenominator"], "." -}], "Text", - CellTags->"IFPD", - CellID->14313583] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{959, Automatic}, {Automatic, 137}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPDOff.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPDOff.nb index ad4529001..7fc83910d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPDOff.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPDOff.nb @@ -173,9 +173,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/IFPDOn", ButtonNote->"IFPDOn"], "." -}], "Text", - CellTags->"IFPDOff", - CellID->1144166368] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -231,8 +229,7 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"IFPDOff", - CellLabel->"Out[1]=", - CellID->784861447] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -248,8 +245,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Momentum", "[", "p", "]"}], ",", "m"}], "]"}]], "Output", CellTags->"IFPDOff", - CellLabel->"Out[2]//StandardForm=", - CellID->690906879] + CellLabel->"Out[2]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -272,8 +268,7 @@ Cell[BoxData[ TraditionalForm], "2"], "-", SuperscriptBox["m", "2"]}], TraditionalForm]], "Output", CellTags->"IFPDOff", - CellLabel->"Out[3]=", - CellID->2145155528] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -293,8 +288,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}]], "Output", CellTags->"IFPDOff", - CellLabel->"Out[4]//StandardForm=", - CellID->128477436] + CellLabel->"Out[4]//StandardForm="] }, Open ]] }, Open ]], @@ -359,12 +353,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{573, Automatic}, {Automatic, 178}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPDOn.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPDOn.nb index 6983f478f..bd5bc50f6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPDOn.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IFPDOn.nb @@ -175,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/IFPDOff", ButtonNote->"IFPDOff"], "." -}], "Text", - CellTags->"IFPDOn", - CellID->168214064] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -263,12 +261,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{777, Automatic}, {Automatic, 86}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IncludePair.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IncludePair.nb index 97d79689a..723f99c12 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IncludePair.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IncludePair.nb @@ -175,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynAmpDenominatorSimplify", ButtonNote->"FeynAmpDenominatorSimplify"], "." -}], "Text", - CellTags->"IncludePair", - CellID->419229587] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -263,12 +261,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{965, Automatic}, {Automatic, 108}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IndexPosition.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IndexPosition.nb index bbc9a90dd..b8b5fefea 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IndexPosition.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IndexPosition.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FieldStrength", ButtonNote->"FieldStrength"], "." -}], "Text", - CellTags->"IndexPosition", - CellID->976822558] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{779, Automatic}, {Automatic, 93}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/InitialFunction.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/InitialFunction.nb index b77f1b6fe..d5b3425a0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/InitialFunction.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/InitialFunction.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynRule", ButtonNote->"FeynRule"], "." -}], "Text", - CellTags->"InitialFunction", - CellID->1858355403] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{785, Automatic}, {Automatic, 141}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/InitialSubstitutions.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/InitialSubstitutions.nb index 7aa625251..c5172bc32 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/InitialSubstitutions.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/InitialSubstitutions.nb @@ -175,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Write2", ButtonNote->"Write2"], "." -}], "Text", - CellTags->"InitialSubstitutions", - CellID->643150740] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -263,12 +261,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{640, Automatic}, {Automatic, 59}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/InsideDiracTrace.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/InsideDiracTrace.nb index 798999ce1..66f70f40d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/InsideDiracTrace.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/InsideDiracTrace.nb @@ -117,17 +117,27 @@ Cell["InsideDiracTrace", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["InsideDiracTrace"], "InlineFormula"], - " \[LineSeparator]", - "is and option of DiracSimplify. If set to True, DiracSimplify assumes to \ -operate inside a DiracTrace, i.e., products of an odd number of Dirac \ -matrices are discarded. Furthermore simple traces are calculated (but divided \ -by a factor 4, i.e. : DiracSimplify[DiracMatrix[a,b], \ -InsideDiracTrace\[Rule]True] yields ScalarProduct[a,b]) Traces involving \ -more than four DiracGamma's and DiracGamma[5] are not performed." + " \[LineSeparator]is an option of ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + " and some other functions dealing with Dirac algebra. If set to ", + Cell[BoxData["True"], "InlineFormula", + FormatType->"StandardForm"], + ", the function assumes to operate inside a Dirac trace, i.e., products of \ +an odd number of Dirac matrices are discarded." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell[TextData[{ + "For more details, see the documentation for ", + ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], + "." +}], "Notes", CellID->1067943069] }, Open ]], @@ -163,20 +173,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[TextData[{ - ButtonBox["DiracSimplify", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", - ButtonNote->"DiracSimplify"], - ", ", - ButtonBox["DiracTrace", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DiracTrace", - ButtonNote->"DiracTrace"], - "." -}], "Text", - CellTags->"InsideDiracTrace", - CellID->1537569404] +Cell[TextData[ButtonBox["DiracSimplify", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -262,12 +262,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1288, Automatic}, {Automatic, 229}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IntegralTable.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IntegralTable.nb index b60cde2a3..0a321dd0d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IntegralTable.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IntegralTable.nb @@ -176,9 +176,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynAmpDenominatorSimplify", ButtonNote->"FeynAmpDenominatorSimplify"], "." -}], "Text", - CellTags->"IntegralTable", - CellID->498155720] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -264,12 +262,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{731, Automatic}, {Automatic, 143}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate2.nb index 653c02002..ff2f5b1a2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate2.nb @@ -117,30 +117,31 @@ Cell["Integrate2", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["Integrate2"], "InlineFormula"], - " \[LineSeparator]", - "is like Integrate, but : Integrate2[a_Plus, b__] := Map[Integrate2[#, b]&, \ -a] ( more linear algebra and partial fraction decomposition is done) \ -Integrate2[f[x] DeltaFunction[x], x] \[Rule] f[0] Integrate2[f[x] \ -DeltaFunction[x0-x], x] \[Rule] f[x0]. Integrate2[f[x] DeltaFunction[a + b \ -x], x] \[Rule] Integrate[f[x] (1/Abs[b]) DeltaFunction[a/b + x], x], where \ -abs[b] \[Rule] b, if b is a Symbol, and if b = -c, then abs[-c] \[Rule] c, \ -i.e., the variable contained in b is supposed to be positive. ", + " \[LineSeparator]is like Integrate, but : Integrate2[a_Plus, b__] := \ +Map[Integrate2[#, b]&, a] ( more linear algebra and partial fraction \ +decomposition is done) Integrate2[f[x] DeltaFunction[x], x] \[Rule] f[0] \ +Integrate2[f[x] DeltaFunction[x0-x], x] \[Rule] f[x0]. Integrate2[f[x] \ +DeltaFunction[a + b x], x] \[Rule] Integrate[f[x] (1/Abs[b]) \ +DeltaFunction[a/b + x], x], where abs[b] \[Rule] b, if b is a Symbol, and if \ +b = -c, then abs[-c] \[Rule] c, i.e., the variable contained in b is supposed \ +to be positive. ", Cell[BoxData[ FormBox[ RowBox[{" ", SuperscriptBox["\[Pi]", "2"]}], TraditionalForm]]], " is replaced by 6 Zeta2. Integrate2[1/(1-y),{y,x,1}] is intepreted as \ distribution, i.e. as Integrate2[-1/(1-y)],{y, 0, x}] \[Rule] Log[1-y]. \ -Integrate2[1/(1-x),{x,0,1}] \[Rule] 0.\n\nNOTE: Since Integrate2 does do a \ -reordering and partial fraction decomposition before calling the integral \ -table of Integrate3 it will in general be slower compared to Integrate3 for \ -sums of integrals. I.e., if the integrand has already an expanded form and if \ -partial fraction decomposition is not necessary it is more effective to use \ -Integrate3." +Integrate2[1/(1-x),{x,0,1}] \[Rule] 0." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +Since Integrate2 does do a reordering and partial fraction decomposition \ +before calling the integral table of Integrate3 it will in general be slower \ +compared to Integrate3 for sums of integrals. I.e., if the integrand has \ +already an expanded form and if partial fraction decomposition is not \ +necessary it is more effective to use Integrate3.\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -207,9 +208,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SumT", ButtonNote->"SumT"], "." -}], "Text", - CellTags->"Integrate2", - CellID->1134437741] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,13 +252,13 @@ Cell[BoxData[ RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], "//", "Timing"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[1]:=", + CellLabel->"In[5]:=", CellID->524907050], Cell[BoxData[ FormBox[ RowBox[{"{", - RowBox[{"0.006734`", ",", + RowBox[{"0.028933`", ",", RowBox[{ TemplateBox[{"3"}, "Zeta"], "-", @@ -268,8 +267,7 @@ Cell[BoxData[ RowBox[{"\[Zeta]", "(", "2", ")"}], " ", RowBox[{"log", "(", "2", ")"}]}]}]}], "}"}], TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[1]=", - CellID->1871676459] + CellLabel->"Out[5]="] }, Open ]], Cell[TextData[{ @@ -277,9 +275,7 @@ Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], "'s Integrate." -}], "Text", - CellTags->"Integrate2", - CellID->1563728584], +}], "Notes"], Cell[CellGroupData[{ @@ -292,7 +288,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[2]:=", + CellLabel->"In[6]:=", CellID->546710902], Cell[BoxData[ @@ -302,8 +298,7 @@ Cell[BoxData[ RowBox[{"4", " ", RowBox[{"log", "(", "2", ")"}]}]}], TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[2]=", - CellID->1681597308] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -317,7 +312,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[3]:=", + CellLabel->"In[7]:=", CellID->89878903], Cell[BoxData[ @@ -332,8 +327,7 @@ Cell[BoxData[ RowBox[{"2", " ", RowBox[{"log", "(", "2", ")"}]}]}], TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[3]=", - CellID->133418904] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -349,7 +343,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[4]:=", + CellLabel->"In[8]:=", CellID->1742557754], Cell[BoxData[ @@ -372,8 +366,7 @@ Cell[BoxData[ RowBox[{"2", " ", RowBox[{"log", "(", "2", ")"}]}]}], TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[4]=", - CellID->1994437751] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -388,15 +381,14 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[5]:=", + CellLabel->"In[9]:=", CellID->1356840886], Cell[BoxData[ FormBox[ RowBox[{"f", "(", "1", ")"}], TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[5]=", - CellID->809684251] + CellLabel->"Out[9]="] }, Open ]], Cell[TextData[{ @@ -450,10 +442,7 @@ Cell[TextData[{ RowBox[{"log", "(", "\[Delta]", ")"}]}], "+", RowBox[{"log", "(", "1", ")"}]}], "\[Implies]", "0."}]}], " "}], TraditionalForm]]] -}], "Text", - ZeroWidthTimes->False, - CellTags->"Integrate2", - CellID->1657711161], +}], "Notes"], Cell[CellGroupData[{ @@ -466,14 +455,13 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[6]:=", + CellLabel->"In[10]:=", CellID->1084770727], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[6]=", - CellID->1845418056] + CellLabel->"Out[10]="] }, Open ]], Cell[TextData[{ @@ -499,9 +487,7 @@ the ", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}], " ", "."}]}], TraditionalForm]]] -}], "Text", - CellTags->"Integrate2", - CellID->1551126642], +}], "Notes"], Cell[CellGroupData[{ @@ -515,14 +501,13 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", 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TemplateBox[{"4",FractionBox["1", "2"]}, "PolyLog"]}], "-", - RowBox[{"945", " ", + RowBox[{"63", " ", TemplateBox[{"3"}, "Zeta"], " ", - RowBox[{"log", "(", "2", ")"}]}], "+", - RowBox[{"8", " ", - SuperscriptBox["\[Pi]", "4"]}], "-", - RowBox[{"30", " ", + RowBox[{"log", "(", "2", ")"}]}], "-", + RowBox[{"2", " ", RowBox[{ SuperscriptBox["log", "4"], "(", "2", ")"}]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[17]=", - CellID->1666831938] + CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ @@ -1177,35 +1192,37 @@ Cell[BoxData[ RowBox[{"%", " ", "/.", " ", RowBox[{"OPEm", "\[Rule]", "2"}]}]], "Input", CellTags->"Integrate2", - CellLabel->"In[18]:=", + CellLabel->"In[23]:=", CellID->1839623139], Cell[BoxData[ FormBox[ RowBox[{ - FractionBox["1", "360"], " ", + FractionBox["1", "24"], " ", RowBox[{"(", RowBox[{ - RowBox[{"720", " ", + RowBox[{"48", " ", RowBox[{"\[Zeta]", "(", "2", ")"}]}], "+", - RowBox[{"450", " ", + RowBox[{"48", " ", + 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@@ Cell[BoxData[ RowBox[{"log", "(", "2", ")"}]}], "45"], "-", FractionBox["6959", "10800"]}], TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[28]=", - CellID->396258688] + CellLabel->"Out[36]="] }, Open ]], Cell[CellGroupData[{ @@ -3132,14 +2104,13 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "@", "%"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[29]:=", + CellLabel->"In[37]:=", CellID->1795528063], Cell[BoxData[ FormBox["0.06419859938720329`", TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[29]=", - CellID->958489189] + CellLabel->"Out[37]="] }, Open ]], Cell[CellGroupData[{ @@ -3155,14 +2126,13 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[30]:=", + CellLabel->"In[38]:=", CellID->190638847], Cell[BoxData[ FormBox["0.06419859938720252`", TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[30]=", - CellID->1001542201] + CellLabel->"Out[38]="] }, Open ]], Cell[CellGroupData[{ @@ -3180,7 +2150,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate2", - CellLabel->"In[31]:=", + CellLabel->"In[39]:=", CellID->1701338238], Cell[BoxData[ @@ -3370,8 +2340,7 @@ Cell[BoxData[ SuperscriptBox["log", "2"], "(", "2", ")"}], "m"]}], TraditionalForm]], "Output", CellTags->"Integrate2", - CellLabel->"Out[31]=", - CellID->164627498] + CellLabel->"Out[39]="] }, Open ]] }, Open ]], @@ -3436,12 +2405,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{851, Automatic}, {Automatic, 104}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate3.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate3.nb index 85d59af5a..8097a481f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate3.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate3.nb @@ -167,9 +167,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Integrate2", ButtonNote->"Integrate2"], "." -}], "Text", - CellTags->"Integrate3", - CellID->622342761] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -207,7 +205,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate3", - CellLabel->"In[1]:=", + CellLabel->"In[47]:=", CellID->425224867], Cell[BoxData[ @@ -218,8 +216,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"m", "+", "1"}], ")"}], "2"]]}], TraditionalForm]], "Output", CellTags->"Integrate3", - CellLabel->"Out[1]=", - CellID->559999213] + CellLabel->"Out[47]="] }, Open ]], Cell[CellGroupData[{ @@ -237,7 +234,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate3", - CellLabel->"In[2]:=", + CellLabel->"In[48]:=", CellID->1726046539], Cell[BoxData[ @@ -245,17 +242,22 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"\[Zeta]", "(", "2", ")"}], " ", - RowBox[{"FeynCalc`Integrate3`Private`S", "(", - RowBox[{"1", ",", "m"}], ")"}]}], "-", - RowBox[{"FeynCalc`Integrate3`Private`S", "(", - RowBox[{"1", ",", "2", ",", "m"}], ")"}], "-", - RowBox[{"FeynCalc`Integrate3`Private`S", "(", - RowBox[{"2", ",", "1", ",", "m"}], ")"}], "+", + RowBox[{ + SubscriptBox["S", "1"], "(", + FormBox["m", + TraditionalForm], ")"}]}], "-", + RowBox[{ + SubscriptBox["S", "12"], "(", + FormBox["m", + TraditionalForm], ")"}], "-", + RowBox[{ + SubscriptBox["S", "21"], "(", + FormBox["m", + TraditionalForm], ")"}], "+", TemplateBox[{"3"}, "Zeta"]}], TraditionalForm]], "Output", CellTags->"Integrate3", - CellLabel->"Out[2]=", - CellID->279018012] + CellLabel->"Out[48]="] }, Open ]], Cell[CellGroupData[{ @@ -283,7 +285,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate3", - CellLabel->"In[3]:=", + CellLabel->"In[49]:=", CellID->1210488286], Cell[BoxData[ @@ -294,12 +296,18 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"\[Zeta]", "(", "2", ")"}], " ", - RowBox[{"FeynCalc`Integrate3`Private`S", "(", - RowBox[{"1", ",", "m"}], ")"}]}], "-", - RowBox[{"FeynCalc`Integrate3`Private`S", "(", - RowBox[{"1", ",", "2", ",", "m"}], ")"}], "-", - RowBox[{"FeynCalc`Integrate3`Private`S", "(", - RowBox[{"2", ",", "1", ",", "m"}], ")"}], "+", + RowBox[{ + SubscriptBox["S", "1"], "(", + FormBox["m", + TraditionalForm], ")"}]}], "-", + RowBox[{ + SubscriptBox["S", "12"], "(", + FormBox["m", + TraditionalForm], ")"}], "-", + RowBox[{ + SubscriptBox["S", "21"], "(", + FormBox["m", + TraditionalForm], ")"}], "+", TemplateBox[{"3"}, "Zeta"]}], ")"}]}], "+", RowBox[{"b", " ", @@ -353,8 +361,7 @@ Cell[BoxData[ RowBox[{"log", "(", "2", ")"}]}]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"Integrate3", - CellLabel->"Out[3]=", - CellID->243111463] + CellLabel->"Out[49]="] }, Open ]], Cell[CellGroupData[{ @@ -367,14 +374,13 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate3", - CellLabel->"In[4]:=", + CellLabel->"In[50]:=", CellID->757263318], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"Integrate3", - CellLabel->"Out[4]=", - CellID->1705014554] + CellLabel->"Out[50]="] }, Open ]], Cell[CellGroupData[{ @@ -389,7 +395,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate3", - CellLabel->"In[5]:=", + CellLabel->"In[51]:=", CellID->818446262], Cell[BoxData[ @@ -398,8 +404,7 @@ Cell[BoxData[ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "(", "1", ")"}], TraditionalForm]], "Output", CellTags->"Integrate3", - CellLabel->"Out[5]=", - CellID->929710671] + CellLabel->"Out[51]="] }, Open ]], Cell[CellGroupData[{ @@ -413,14 +418,13 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Integrate3", - CellLabel->"In[6]:=", + CellLabel->"In[52]:=", CellID->1567611943], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"Integrate3", - CellLabel->"Out[6]=", - CellID->64714700] + CellLabel->"Out[52]="] }, Open ]] }, Open ]], @@ -485,12 +489,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{502, Automatic}, {Automatic, 63}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate4.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate4.nb index 0dc19cee2..855813814 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate4.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate4.nb @@ -169,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Integrate5", ButtonNote->"Integrate5"], "." -}], "Text", - CellTags->"Integrate4", - CellID->356211384] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{792, Automatic}, {Automatic, 65}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate5.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate5.nb index 1044e83bd..73bfc769d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate5.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integrate5.nb @@ -169,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Integrate4", ButtonNote->"Integrate4"], "." -}], "Text", - CellTags->"Integrate5", - CellID->458183738] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{901, Automatic}, {Automatic, 51}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IntegrateByParts.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IntegrateByParts.nb index 3f7c669ff..bef9c53e1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IntegrateByParts.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IntegrateByParts.nb @@ -128,8 +128,21 @@ integral over t from 0 to 1." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "IntegrateByParts", "]"}]], "Input", + CellTags->"IntegrateByParts", + CellLabel->"In[89]:=", + CellID->1168038147], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Hold", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output", + CellTags->"IntegrateByParts", + CellLabel->"Out[89]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -192,73 +205,28 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "IntegrateByParts", "]"}]], "Input", - CellTags->"IntegrateByParts", - CellLabel->"In[1]:=", - CellID->1168038147], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Hold", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output", - CellTags->"IntegrateByParts", - CellLabel->"Out[1]=", - CellID->247717548] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ - RowBox[{"IntegrateByParts", "[", - RowBox[{ + RowBox[{"(*", + RowBox[{"IntegrateByParts", "[", RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "-", "t"}], ")"}], "^", + RowBox[{"(", + RowBox[{ + RowBox[{"a", " ", "Epsilon"}], "-", "1"}], ")"}]}], " ", + RowBox[{"g", "[", "t", "]"}]}], ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", "t"}], ")"}], "^", RowBox[{"(", RowBox[{ - RowBox[{"a", " ", "Epsilon"}], "-", "1"}], ")"}]}], " ", - RowBox[{"g", "[", "t", "]"}]}], ",", - RowBox[{ - RowBox[{"(", - RowBox[{"1", "-", "t"}], ")"}], "^", - RowBox[{"(", - RowBox[{ - RowBox[{"a", " ", "Epsilon"}], "-", "1"}], ")"}]}], ",", "t"}], - "]"}]], "Input", - CellTags->"IntegrateByParts", - CellLabel->"In[2]:=", - CellID->328713984], - -Cell[BoxData[ - FormBox[ - RowBox[{ - FractionBox[ - RowBox[{ - SuperscriptBox[ - RowBox[{"(", - RowBox[{"1", "-", "t"}], ")"}], - RowBox[{"a", " ", - TagBox["\[CurlyEpsilon]", - TraditionalForm]}]], " ", - RowBox[{ - SuperscriptBox["g", "\[Prime]", - MultilineFunction->None], "(", "t", ")"}]}], - RowBox[{"a", " ", - TagBox["\[CurlyEpsilon]", - TraditionalForm]}]], "+", - FractionBox[ - RowBox[{"g", "(", "0", ")"}], - RowBox[{"a", " ", - TagBox["\[CurlyEpsilon]", - TraditionalForm]}]]}], TraditionalForm]], "Output", + RowBox[{"a", " ", "Epsilon"}], "-", "1"}], ")"}]}], ",", "t"}], "]"}], + "*)"}]], "Input", CellTags->"IntegrateByParts", - CellLabel->"Out[2]=", - CellID->2082695933] -}, Open ]] + CellLabel->"In[91]:=", + CellID->328713984] }, Open ]], Cell[CellGroupData[{ @@ -321,13 +289,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{706, 776}, +WindowMargins->{{858, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integratedx.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integratedx.nb index 9a38b954b..c19a17f64 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Integratedx.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Integratedx.nb @@ -192,9 +192,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/TimedIntegrate", ButtonNote->"TimedIntegrate"], "." -}], "Text", - CellTags->"Integratedx", - CellID->2008789767] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -280,12 +278,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{680, Automatic}, {Automatic, 90}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IntermediateSubstitutions.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IntermediateSubstitutions.nb index 666737911..09b6cc1c7 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IntermediateSubstitutions.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IntermediateSubstitutions.nb @@ -117,9 +117,9 @@ Cell["IntermediateSubstitutions", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["IntermediateSubstitutions"], "InlineFormula"], - " \[LineSeparator]", - "is an option for OneLoop. All substitutions indicated hereby are done at an \ -intermediate stage of the calculation." + " \[LineSeparator]is an option of various FeynCalc functions. All \ +substitutions indicated hereby are done at an intermediate stage of the \ +calculation." }], "Usage", CellID->982511436], @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoop", ButtonNote->"OneLoop"], "." -}], "Text", - CellTags->"IntermediateSubstitutions", - CellID->294086386] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1185, Automatic}, {Automatic, 126}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/InverseMellin.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/InverseMellin.nb index a8d94ed69..d2ddc22a1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/InverseMellin.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/InverseMellin.nb @@ -197,9 +197,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SumT", ButtonNote->"SumT"], "." -}], "Text", - CellTags->"InverseMellin", - CellID->344948900] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -233,7 +231,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"1", "/", "OPEm"}], ",", "y"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[1]:=", + CellLabel->"In[53]:=", CellID->1487905241], Cell[BoxData[ @@ -241,8 +239,7 @@ Cell[BoxData[ SuperscriptBox["y", RowBox[{"m", "-", "1"}]], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[1]=", - CellID->883502595] + CellLabel->"Out[53]="] }, Open ]], Cell[CellGroupData[{ @@ -254,7 +251,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"OPEm", "+", "3"}], ")"}]}], ",", "y"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[2]:=", + CellLabel->"In[54]:=", CellID->1769575859], Cell[BoxData[ @@ -262,8 +259,7 @@ Cell[BoxData[ SuperscriptBox["y", RowBox[{"m", "+", "2"}]], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[2]=", - CellID->886851930] + CellLabel->"Out[54]="] }, Open ]], Cell[CellGroupData[{ @@ -272,7 +268,7 @@ Cell[BoxData[ RowBox[{"InverseMellin", "[", RowBox[{"1", ",", "y"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[3]:=", + CellLabel->"In[55]:=", CellID->795107064], Cell[BoxData[ @@ -285,8 +281,7 @@ Cell[BoxData[ RowBox[{"1", "-", "y"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[3]=", - CellID->933445894] + CellLabel->"Out[55]="] }, Open ]], Cell[CellGroupData[{ @@ -297,7 +292,7 @@ Cell[BoxData[ RowBox[{"1", "/", RowBox[{"OPEm", "^", "4"}]}], ",", "y"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[4]:=", + CellLabel->"In[56]:=", CellID->1138973234], Cell[BoxData[ @@ -310,8 +305,7 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["log", "3"], "(", "y", ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[4]=", - CellID->321524707] + CellLabel->"Out[56]="] }, Open ]], Cell[CellGroupData[{ @@ -322,7 +316,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"1", "/", "OPEm"}], "+", "1"}], ",", "y"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[5]:=", + CellLabel->"In[57]:=", CellID->634260831], Cell[BoxData[ @@ -338,8 +332,7 @@ Cell[BoxData[ SuperscriptBox["y", RowBox[{"m", "-", "1"}]]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[5]=", - CellID->306464887] + CellLabel->"Out[57]="] }, Open ]], Cell[CellGroupData[{ @@ -350,7 +343,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"1", "/", "i"}], "+", "1"}], ",", "y", ",", "i"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[6]:=", + CellLabel->"In[58]:=", CellID->323775439], Cell[BoxData[ @@ -366,15 +359,12 @@ Cell[BoxData[ SuperscriptBox["y", RowBox[{"i", "-", "1"}]]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[6]=", - CellID->908783993] + CellLabel->"Out[58]="] }, Open ]], Cell["\<\ The inverse operation to InverseMellin is done by Integrate2.\ -\>", "Text", - CellTags->"InverseMellin", - CellID->823482436], +\>", "Notes"], Cell[CellGroupData[{ @@ -387,22 +377,19 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"y", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[7]:=", + CellLabel->"In[59]:=", CellID->1105681850], Cell[BoxData[ FormBox[ FractionBox["1", "m"], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[7]=", - CellID->575593932] + CellLabel->"Out[59]="] }, Open ]], Cell["\<\ Below is a list of all built-in basic inverse Mellin transforms .\ -\>", "Text", - CellTags->"InverseMellin", - CellID->1975947579], +\>", "Notes"], Cell[BoxData[ RowBox[{ @@ -503,7 +490,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "1"}], "+", "OPEm"}]}], "]"}]}], "}"}]}], ";"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[8]:=", + CellLabel->"In[60]:=", CellID->988000997], Cell[BoxData[ @@ -513,7 +500,7 @@ Cell[BoxData[ RowBox[{"InverseMellin", "[", RowBox[{"z", ",", "y"}], "]"}]}]}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[9]:=", + CellLabel->"In[61]:=", CellID->478330132], Cell[CellGroupData[{ @@ -524,7 +511,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "3"}], ")"}]}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[10]:=", + CellLabel->"In[62]:=", CellID->1863843750], Cell[BoxData[ @@ -541,8 +528,7 @@ Cell[BoxData[ SuperscriptBox["log", "2"], "(", "y", ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[10]=", - CellID->808010767] + CellLabel->"Out[62]="] }, Open ]], Cell[CellGroupData[{ @@ -553,7 +539,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "2"}], ")"}]}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[11]:=", + CellLabel->"In[63]:=", CellID->1662530554], Cell[BoxData[ @@ -568,8 +554,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}]]}], " ", RowBox[{"log", "(", "y", ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[11]=", - CellID->1524372587] + CellLabel->"Out[63]="] }, Open ]], Cell[CellGroupData[{ @@ -579,7 +564,7 @@ Cell[BoxData[ RowBox[{"PolyGamma", "[", RowBox[{"0", ",", "OPEm"}], "]"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[12]:=", + CellLabel->"In[64]:=", CellID->1349819643], Cell[BoxData[ @@ -607,15 +592,9 @@ Cell[BoxData[ SuperscriptBox["y", RowBox[{"m", "-", "1"}]]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[12]=", - CellID->1429383971] + CellLabel->"Out[64]="] }, Open ]], -Cell[BoxData[" "], "Input", - CellTags->"InverseMellin", - CellLabel->"In[13]:=", - CellID->558376463], - Cell[CellGroupData[{ Cell[BoxData[ @@ -624,7 +603,7 @@ Cell[BoxData[ RowBox[{"1", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[14]:=", + CellLabel->"In[65]:=", CellID->209318413], Cell[BoxData[ @@ -647,8 +626,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}]]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[14]=", - CellID->412047871] + CellLabel->"Out[65]="] }, Open ]], Cell[CellGroupData[{ @@ -662,7 +640,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"OPEm", "-", "1"}], ")"}]}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[15]:=", + CellLabel->"In[66]:=", CellID->108977754], Cell[BoxData[ @@ -683,8 +661,7 @@ Cell[BoxData[ RowBox[{"log", "(", RowBox[{"1", "-", "y"}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[15]=", - CellID->416733591] + CellLabel->"Out[66]="] }, Open ]], Cell[CellGroupData[{ @@ -698,7 +675,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"OPEm", "+", "1"}], ")"}]}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[16]:=", + CellLabel->"In[67]:=", CellID->1588128285], Cell[BoxData[ @@ -725,8 +702,7 @@ Cell[BoxData[ SuperscriptBox["y", "m"], " ", RowBox[{"log", "(", "y", ")"}]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[16]=", - CellID->1157098436] + CellLabel->"Out[67]="] }, Open ]], Cell[CellGroupData[{ @@ -740,7 +716,7 @@ Cell[BoxData[ RowBox[{"-", "1"}], "+", "OPEm"}]}], "]"}], "/", RowBox[{"OPEm", "^", "2"}]}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[17]:=", + CellLabel->"In[68]:=", CellID->1038982726], Cell[BoxData[ @@ -768,8 +744,7 @@ Cell[BoxData[ SuperscriptBox["log", "2"], "(", "y", ")"}]}]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[17]=", - CellID->408982504] + CellLabel->"Out[68]="] }, Open ]], Cell[CellGroupData[{ @@ -783,7 +758,7 @@ Cell[BoxData[ RowBox[{"-", "1"}], "+", "OPEm"}]}], "]"}], "/", "OPEm"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[18]:=", + CellLabel->"In[69]:=", CellID->1975519554], Cell[BoxData[ @@ -806,8 +781,7 @@ Cell[BoxData[ RowBox[{"1", "-", "y"}], ")"}]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[18]=", - CellID->2023526209] + CellLabel->"Out[69]="] }, Open ]], Cell[CellGroupData[{ @@ -822,7 +796,7 @@ Cell[BoxData[ RowBox[{"-", "1"}], "+", "OPEm"}]}], "]"}], "^", "2"}], "/", "OPEm"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[19]:=", + CellLabel->"In[70]:=", CellID->1312317430], Cell[BoxData[ @@ -856,8 +830,7 @@ Cell[BoxData[ SuperscriptBox["log", "2"], "(", "y", ")"}], "2"]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[19]=", - CellID->1387073931] + CellLabel->"Out[70]="] }, Open ]], Cell[CellGroupData[{ @@ -868,7 +841,7 @@ Cell[BoxData[ RowBox[{"2", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[20]:=", + CellLabel->"In[71]:=", CellID->1086751012], Cell[BoxData[ @@ -896,8 +869,7 @@ Cell[BoxData[ RowBox[{"1", "-", "y"}]]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[20]=", - CellID->229974260] + CellLabel->"Out[71]="] }, Open ]], Cell[CellGroupData[{ @@ -909,7 +881,7 @@ Cell[BoxData[ RowBox[{"2", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "/", "OPEm"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[21]:=", + CellLabel->"In[72]:=", CellID->410476681], Cell[BoxData[ @@ -936,8 +908,7 @@ Cell[BoxData[ SuperscriptBox["log", "2"], "(", "y", ")"}]}]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[21]=", - CellID->1435522619] + CellLabel->"Out[72]="] }, Open ]], Cell[CellGroupData[{ @@ -948,7 +919,7 @@ Cell[BoxData[ RowBox[{"3", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[22]:=", + CellLabel->"In[73]:=", CellID->1961481381], Cell[BoxData[ @@ -980,8 +951,7 @@ Cell[BoxData[ RowBox[{"1", "-", "y"}], ")"}]}]]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[22]=", - CellID->1258335869] + CellLabel->"Out[73]="] }, Open ]], Cell[CellGroupData[{ @@ -992,7 +962,7 @@ Cell[BoxData[ RowBox[{"1", ",", "1", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[23]:=", + CellLabel->"In[74]:=", CellID->617286063], Cell[BoxData[ @@ -1015,8 +985,7 @@ Cell[BoxData[ RowBox[{"1", "-", "y"}]], ")"}], "+"]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[23]=", - CellID->1509334069] + CellLabel->"Out[74]="] }, Open ]], Cell[CellGroupData[{ @@ -1028,7 +997,7 @@ Cell[BoxData[ RowBox[{"1", ",", "2", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "]"}]}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[24]:=", + CellLabel->"In[75]:=", CellID->1098001734], Cell[BoxData[ @@ -1064,8 +1033,7 @@ Cell[BoxData[ TraditionalForm], ")"}]}]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[24]=", - CellID->1548339288] + CellLabel->"Out[75]="] }, Open ]], Cell[CellGroupData[{ @@ -1077,7 +1045,7 @@ Cell[BoxData[ RowBox[{"2", ",", "1", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "]"}]}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[25]:=", + CellLabel->"In[76]:=", CellID->1981996384], Cell[BoxData[ @@ -1113,8 +1081,7 @@ Cell[BoxData[ TraditionalForm], ")"}]}]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[25]=", - CellID->422280001] + CellLabel->"Out[76]="] }, Open ]], Cell[CellGroupData[{ @@ -1125,7 +1092,7 @@ Cell[BoxData[ RowBox[{"1", ",", "1", ",", "1", ",", RowBox[{"OPEm", "-", "1"}]}], "]"}], "]"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[26]:=", + CellLabel->"In[77]:=", CellID->371125491], Cell[BoxData[ @@ -1151,8 +1118,7 @@ Cell[BoxData[ RowBox[{"1", "-", "y"}]], ")"}], "+"]}], ")"}]}], TraditionalForm]], "Output", CellTags->"InverseMellin", - CellLabel->"Out[26]=", - CellID->1490949014] + CellLabel->"Out[77]="] }, Open ]], Cell[BoxData[ @@ -1160,7 +1126,7 @@ Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"im", ",", "list"}], "]"}], ";"}]], "Input", CellTags->"InverseMellin", - CellLabel->"In[27]:=", + CellLabel->"In[78]:=", CellID->941829466] }, Open ]], @@ -1225,12 +1191,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{717, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Isolate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Isolate.nb index 84964d5f1..dc3cf7dcc 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Isolate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Isolate.nb @@ -127,8 +127,28 @@ abbreviations may be specified with the option IsolateNames." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Isolate", "]"}]], "Input", + CellTags->"Isolate", + CellLabel->"In[79]:=", + CellID->2088060696], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"IsolateNames", "\[Rule]", "KK"}], ",", + RowBox[{"IsolatePrint", "\[Rule]", "False"}], ",", + RowBox[{"IsolateFast", "\[Rule]", "False"}], ",", + RowBox[{"IsolateSplit", "\[Rule]", "\[Infinity]"}], ",", + RowBox[{"IsolateTimes", "\[Rule]", "False"}], ",", + RowBox[{"IsolatePlus", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"Isolate", + CellLabel->"Out[79]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -193,45 +213,21 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Isolate", "]"}]], "Input", - CellTags->"Isolate", - CellLabel->"In[1]:=", - CellID->2088060696], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"IsolateNames", "\[Rule]", "KK"}], ",", - RowBox[{"IsolatePrint", "\[Rule]", "False"}], ",", - RowBox[{"IsolateSplit", "\[Rule]", "\[Infinity]"}], ",", - RowBox[{"IsolateTimes", "\[Rule]", "False"}], ",", - RowBox[{"IsolatePlus", "\[Rule]", "False"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"Isolate", - CellLabel->"Out[1]=", - CellID->2033547322] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"t0", "=", RowBox[{"Isolate", "[", RowBox[{"a", "+", "b"}], "]"}]}]], "Input", CellTags->"Isolate", - CellLabel->"In[2]:=", + CellLabel->"In[80]:=", CellID->1761911845], Cell[BoxData[ FormBox[ TagBox[ - RowBox[{"KK", "(", "682", ")"}], + RowBox[{"KK", "(", "24", ")"}], HoldForm], TraditionalForm]], "Output", CellTags->"Isolate", - CellLabel->"Out[2]=", - CellID->2009964510] + CellLabel->"Out[80]="] }, Open ]], Cell[CellGroupData[{ @@ -249,7 +245,7 @@ Cell[BoxData[ RowBox[{"c", "+", "d"}], ")"}], " ", "f"}], " ", "+", " ", "e"}], ",", "f"}], "]"}]}]], "Input", CellTags->"Isolate", - CellLabel->"In[3]:=", + CellLabel->"In[81]:=", CellID->1164516818], Cell[BoxData[ @@ -257,15 +253,14 @@ Cell[BoxData[ RowBox[{"e", "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "(", "682", ")"}], + RowBox[{"KK", "(", "24", ")"}], HoldForm]}], "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "(", "683", ")"}], + RowBox[{"KK", "(", "25", ")"}], HoldForm]}]}], TraditionalForm]], "Output", CellTags->"Isolate", - CellLabel->"Out[3]=", - CellID->416280036] + CellLabel->"Out[81]="] }, Open ]], Cell[CellGroupData[{ @@ -273,22 +268,21 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"StandardForm", "[", "t1", "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[4]:=", + CellLabel->"In[82]:=", CellID->810104736], Cell[BoxData[ RowBox[{"e", "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "[", "682", "]"}], + RowBox[{"KK", "[", "24", "]"}], HoldForm]}], "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "[", "683", "]"}], + RowBox[{"KK", "[", "25", "]"}], HoldForm]}]}]], "Output", CellTags->"Isolate", - CellLabel->"Out[4]//StandardForm=", - CellID->1069603345] + CellLabel->"Out[82]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -298,7 +292,7 @@ Cell[BoxData[ RowBox[{"t0", ",", " ", "t1", ",", " ", RowBox[{"ReleaseHold", "[", "t1", "]"}]}], "}"}]], "Input", CellTags->"Isolate", - CellLabel->"In[5]:=", + CellLabel->"In[83]:=", CellID->113729976], Cell[BoxData[ @@ -306,16 +300,16 @@ Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[ - RowBox[{"KK", "(", "682", ")"}], + RowBox[{"KK", "(", "24", ")"}], HoldForm], ",", RowBox[{"e", "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "(", "682", ")"}], + RowBox[{"KK", "(", "24", ")"}], HoldForm]}], "+", RowBox[{"f", " ", TagBox[ - RowBox[{"KK", "(", "683", ")"}], + RowBox[{"KK", "(", "25", ")"}], HoldForm]}]}], ",", RowBox[{ RowBox[{"f", " ", @@ -326,8 +320,7 @@ Cell[BoxData[ RowBox[{"c", "+", "d"}], ")"}]}], "+", "e"}]}], "}"}], TraditionalForm]], "Output", CellTags->"Isolate", - CellLabel->"Out[5]=", - CellID->743594287] + CellLabel->"Out[83]="] }, Open ]], Cell[CellGroupData[{ @@ -351,7 +344,7 @@ Cell[BoxData[ RowBox[{"a", ",", "d"}], "}"}], ",", RowBox[{"IsolateNames", "\[Rule]", "fF"}]}], "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[6]:=", + CellLabel->"In[84]:=", CellID->689489417], Cell[BoxData[ @@ -359,17 +352,16 @@ Cell[BoxData[ RowBox[{ RowBox[{ TagBox[ - RowBox[{"fF", "(", "685", ")"}], + RowBox[{"fF", "(", "27", ")"}], HoldForm], " ", RowBox[{"a", "(", "z", ")"}]}], "+", RowBox[{ TagBox[ - RowBox[{"fF", "(", "684", ")"}], + RowBox[{"fF", "(", "26", ")"}], HoldForm], " ", RowBox[{"d", "(", "z", ")"}]}]}], TraditionalForm]], "Output", CellTags->"Isolate", - CellLabel->"Out[6]=", - CellID->2124185985] + CellLabel->"Out[84]="] }, Open ]], Cell[CellGroupData[{ @@ -377,30 +369,29 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"??", "fF"}]], "Input", CellTags->"Isolate", - CellLabel->"In[7]:=", + CellLabel->"In[85]:=", CellID->1089652184], Cell[CellGroupData[{ Cell["Global`fF", "Print", "PrintUsage", - CellTags->{"Info-5c3dc742-bd47-47d4-be3e-c64284c792e1", "Isolate"}, - CellID->811343181], + CellTags->{"Info-e2b39ee4-0424-4b02-a1ac-880dc8e10ae5", "Isolate"}], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ { RowBox[{ - RowBox[{"fF", "[", "684", "]"}], "=", + RowBox[{"fF", "[", "26", "]"}], "=", RowBox[{"y", "+", "z"}]}]}, {" "}, { RowBox[{ - RowBox[{"fF", "[", "685", "]"}], "=", + RowBox[{"fF", "[", "27", "]"}], "=", RowBox[{"b", "+", RowBox[{"c", " ", RowBox[{"\<\"HoldForm\"\>", "[", - RowBox[{"fF", "[", "684", "]"}], "]"}]}]}]}]} + RowBox[{"fF", "[", "26", "]"}], "]"}]}]}]}]} }, BaselinePosition->{Baseline, {1, 1}}, GridBoxAlignment->{ @@ -416,8 +407,7 @@ Cell[BoxData[ "RowsIndexed" -> {}}], Definition[$CellContext`fF], Editable->False]], "Print", - CellTags->{"Info-5c3dc742-bd47-47d4-be3e-c64284c792e1", "Isolate"}, - CellID->1424099393] + CellTags->{"Info-e2b39ee4-0424-4b02-a1ac-880dc8e10ae5", "Isolate"}] }, Open ]] }, Open ]], @@ -430,46 +420,23 @@ Cell[BoxData[ RowBox[{"IsolateNames", "\[Rule]", "l"}], ",", RowBox[{"IsolateSplit", "\[Rule]", "15"}]}], "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[8]:=", + CellLabel->"In[86]:=", CellID->2019918870], Cell[BoxData[ FormBox[ TagBox[ - RowBox[{"l", "(", "687", ")"}], + RowBox[{"l", "(", "29", ")"}], HoldForm], TraditionalForm]], "Output", CellTags->"Isolate", - CellLabel->"Out[8]=", - CellID->1344566773] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"{", - RowBox[{ - RowBox[{"l", "[", "2", "]"}], ",", - RowBox[{"l", "[", "1", "]"}]}], "}"}]], "Input", - CellTags->"Isolate", - CellLabel->"In[9]:=", - CellID->727095247], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"l", "(", "2", ")"}], ",", - RowBox[{"l", "(", "1", ")"}]}], "}"}], TraditionalForm]], "Output", - CellTags->"Isolate", - CellLabel->"Out[9]=", - CellID->1999836335] + CellLabel->"Out[86]="] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"t0", ",", "t1", ",", "l", ",", "fF"}], "]"}]], "Input", CellTags->"Isolate", - CellLabel->"In[10]:=", + CellLabel->"In[88]:=", CellID->808271947] }, Open ]], @@ -534,12 +501,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{939, Automatic}, {Automatic, 133}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolateNames.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolateNames.nb index aacc27940..60b5aa3ad 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolateNames.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolateNames.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Collect2", ButtonNote->"Collect2"], "." -}], "Text", - CellTags->"IsolateNames", - CellID->641552758] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{736, Automatic}, {Automatic, 194}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolatePrint.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolatePrint.nb index 16395da89..cc5127986 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolatePrint.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolatePrint.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Isolate", ButtonNote->"Isolate"], "." -}], "Text", - CellTags->"IsolatePrint", - CellID->1589107046] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1101, Automatic}, {Automatic, 77}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolateSplit.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolateSplit.nb index 3e4f60d6c..b0fe30760 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolateSplit.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/IsolateSplit.nb @@ -168,9 +168,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Isolate", ButtonNote->"Isolate"], "." -}], "Text", - CellTags->"IsolateSplit", - CellID->1638104774] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -256,12 +254,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{874, Automatic}, {Automatic, 228}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/KD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/KD.nb new file mode 100644 index 000000000..9f2ed32ed --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/KD.nb @@ -0,0 +1,374 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/KD", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + 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-172,9 +172,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/IsolateNames", ButtonNote->"IsolateNames"], "." -}], "Text", - CellTags->"KK", - CellID->1553777100] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -260,12 +258,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1012, Automatic}, {Automatic, 140}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Kummer.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Kummer.nb index b73e2d678..7bdf5670b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Kummer.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Kummer.nb @@ -168,9 +168,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/HypergeometricAC", ButtonNote->"HypergeometricAC"], "." -}], "Text", - CellTags->"Kummer", - CellID->1248445733] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -225,8 +223,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "-", "a"}],RowBox[{"c", "-", "b"}],"c","z"}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[1]=", - CellID->780995976] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -258,8 +255,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[2]=", - CellID->334128730] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -291,8 +287,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[3]=", - CellID->1379521301] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -325,8 +320,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[4]=", - CellID->1681078809] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -362,8 +356,7 @@ Cell[BoxData[ RowBox[{"a", "+", "b", "-", "c", "+", "1"}],RowBox[{"1", "-", "z"}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[5]=", - CellID->583730114] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -395,8 +388,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[6]=", - CellID->282378053] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -434,8 +426,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[7]=", - CellID->593894309] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -467,8 +458,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[8]=", - CellID->658206917] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -506,8 +496,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[9]=", - CellID->884891760] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -550,8 +539,7 @@ Cell[BoxData[ "1", "z"]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[10]=", - CellID->1201929686] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -600,8 +588,7 @@ Cell[BoxData[ RowBox[{"a", "-", "b", "+", "1"}],FractionBox["1", "z"]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[11]=", - CellID->1407407771] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -643,8 +630,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[12]=", - CellID->171828604] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -694,8 +680,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[13]=", - CellID->1340266483] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -736,8 +721,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[14]=", - CellID->1878402139] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ @@ -787,8 +771,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[15]=", - CellID->1646537872] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ @@ -831,8 +814,7 @@ Cell[BoxData[ "1", "z"]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[16]=", - CellID->976219709] + CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ @@ -880,8 +862,7 @@ Cell[BoxData[ RowBox[{"-", "a"}], "+", "b", "+", "1"}],FractionBox["1", "z"]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[17]=", - CellID->922572585] + CellLabel->"Out[17]="] }, Open ]], Cell[CellGroupData[{ @@ -921,8 +902,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[18]=", - CellID->1393980026] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -972,8 +952,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[19]=", - CellID->1288498782] + CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ @@ -1013,8 +992,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[20]=", - CellID->2121590638] + CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ @@ -1061,8 +1039,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[21]=", - CellID->1992183596] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ @@ -1103,8 +1080,7 @@ Cell[BoxData[ "z"}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[22]=", - CellID->652936361] + CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ @@ -1135,8 +1111,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "-", "a"}],RowBox[{"c", "-", "b"}],"c","z"}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[23]=", - CellID->1706021647] + CellLabel->"Out[23]="] }, Open ]], Cell[CellGroupData[{ @@ -1178,8 +1153,7 @@ Cell[BoxData[ RowBox[{"z", "-", "1"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[24]=", - CellID->378032271] + CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ @@ -1210,8 +1184,7 @@ Cell[BoxData[ RowBox[{"z", "-", "1"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[25]=", - CellID->2057626251] + CellLabel->"Out[25]="] }, Open ]], Cell[CellGroupData[{ @@ -1253,8 +1226,7 @@ Cell[BoxData[ RowBox[{"z", "-", "1"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[26]=", - CellID->129109138] + CellLabel->"Out[26]="] }, Open ]], Cell[CellGroupData[{ @@ -1285,8 +1257,7 @@ Cell[BoxData[ RowBox[{"z", "-", "1"}]]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[27]=", - CellID->149180370] + CellLabel->"Out[27]="] }, Open ]], Cell[CellGroupData[{ @@ -1327,8 +1298,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[28]=", - CellID->1291617006] + CellLabel->"Out[28]="] }, Open ]], Cell[CellGroupData[{ @@ -1361,8 +1331,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[29]=", - CellID->467825582] + CellLabel->"Out[29]="] }, Open ]], Cell[CellGroupData[{ @@ -1406,8 +1375,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[30]=", - CellID->1418885380] + CellLabel->"Out[30]="] }, Open ]], Cell[CellGroupData[{ @@ -1441,8 +1409,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}]]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[31]=", - CellID->1820473911] + CellLabel->"Out[31]="] }, Open ]], Cell[CellGroupData[{ @@ -1484,8 +1451,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[32]=", - CellID->1271802490] + CellLabel->"Out[32]="] }, Open ]], Cell[CellGroupData[{ @@ -1517,8 +1483,7 @@ Cell[BoxData[ RowBox[{"1", "-", "z"}], "z"]}]}, "Hypergeometric2F1"]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[33]=", - CellID->1670296832] + CellLabel->"Out[33]="] }, Open ]], Cell[CellGroupData[{ @@ -1578,8 +1543,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "-", "b"}]}, "Gamma"]}]]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[34]=", - CellID->1552242027] + CellLabel->"Out[34]="] }, Open ]], Cell[CellGroupData[{ @@ -1642,8 +1606,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "-", "b"}]}, "Gamma"]}]]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[35]=", - CellID->449279839] + CellLabel->"Out[35]="] }, Open ]], Cell[CellGroupData[{ @@ -1706,8 +1669,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"c", "-", "b"}]}, "Gamma"]}]]}]}], TraditionalForm]], "Output", CellTags->"Kummer", - CellLabel->"Out[36]=", - CellID->1951010163] + CellLabel->"Out[36]="] }, Open ]] }, Open ]], @@ -1772,12 +1734,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{817, Automatic}, {Automatic, 147}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/LC.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/LC.nb index 3c4eda311..b93d70842 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/LC.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/LC.nb @@ -119,10 +119,21 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"LC", "[", RowBox[{"m", ",", "n", ",", "r", ",", "s"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "evaluates to 4-dimensional LeviCivita[m,n,r,s] by virtue of applying \ -FeynCalcInternal. LC[m,...][p, ...] evaluates to 4-dimensional \ -LeviCivita[m,...][p,...] applying FeynCalcInternal." + " \[LineSeparator]evaluates to 4-dimensional ", + Cell[BoxData[ + SuperscriptBox["\[Epsilon]", + RowBox[{"m", " ", "n", " ", "r", " ", "s"}]]], "InlineFormula"], + " by virtue of applying FeynCalcInternal. LC[m,...][p, ...] evaluates to \ +4-dimensional ", + Cell[BoxData[ + RowBox[{ + SuperscriptBox["\[Epsilon]", + RowBox[{ + RowBox[{ + RowBox[{"m", " ", ".."}], " ", "\[Mu]"}], " ", ".."}]], + SubscriptBox["p", + RowBox[{"\[Mu]", " ", ".."}]]}]], "InlineFormula"], + " applying FeynCalcInternal." }], "Usage", CellID->982511436], @@ -163,19 +174,17 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["LeviCivita", + ButtonBox["Eps", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LeviCivita", - ButtonNote->"LeviCivita"], + ButtonData:>"paclet:FeynCalc/ref/Eps", + ButtonNote->"Eps"], ", ", ButtonBox["LCD", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/LCD", ButtonNote->"LCD"], "." -}], "Text", - CellTags->"LC", - CellID->283409041] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -214,7 +223,8 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -233,8 +243,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LC", - CellLabel->"Out[1]=", - CellID->1184653612] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -247,7 +256,8 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -266,8 +276,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LC", - CellLabel->"Out[2]=", - CellID->513333789] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -286,8 +295,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Sigma]", "]"}]}], "]"}]], "Output", CellTags->"LC", - CellLabel->"Out[3]//StandardForm=", - CellID->979116929] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -303,7 +311,8 @@ Cell[BoxData[ Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -324,8 +333,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LC", - CellLabel->"Out[4]=", - CellID->1590586499] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -345,8 +353,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], ",", RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]], "Output", CellTags->"LC", - CellLabel->"Out[5]//StandardForm=", - CellID->1014807484] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -386,8 +393,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", CellTags->"LC", - CellLabel->"Out[6]=", - CellID->218829035] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -452,12 +458,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1124, Automatic}, {Automatic, 84}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/LCD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/LCD.nb index f3d5ca1bb..344c8647f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/LCD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/LCD.nb @@ -119,12 +119,21 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"LCD", "[", RowBox[{"m", ",", "n", ",", "r", ",", "s"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "evaluates to D-dimensional LeviCivita[m,n,r,s] by virtue of \ -FeynCalcInternal. LCD[m,...][p, ...] evaluates to D-dimensional \ -LeviCivita[m,...][p,...] applying FeynCalcInternal.\n\nYou need to do \ -SetOptions[Eps, Dimension\[Rule]D] before LCD can be used as D-dimensional \ -Levi-Civita input function." + " \[LineSeparator]evaluates to D-dimensional ", + Cell[BoxData[ + SuperscriptBox["\[Epsilon]", + RowBox[{"m", " ", "n", " ", "r", " ", "s"}]]], "InlineFormula"], + " by virtue of FeynCalcInternal. LCD[m,...][p, ...] evaluates to \ +D-dimensional ", + Cell[BoxData[ + RowBox[{ + SuperscriptBox["\[Epsilon]", + RowBox[{ + RowBox[{ + RowBox[{"m", " ", ".."}], " ", "\[Mu]"}], " ", ".."}]], + SubscriptBox["p", + RowBox[{"\[Mu]", " ", ".."}]]}]], "InlineFormula"], + " applying FeynCalcInternal." }], "Usage", CellID->982511436], @@ -165,19 +174,17 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["LeviCivita", + ButtonBox["Eps", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LeviCivita", - ButtonNote->"LeviCivita"], + ButtonData:>"paclet:FeynCalc/ref/Eps", + ButtonNote->"Eps"], ", ", ButtonBox["LC", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/LC", ButtonNote->"LC"], "." -}], "Text", - CellTags->"LCD", - CellID->552899823] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -204,15 +211,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[ - RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], ";"}]], "Input", - CellTags->"LCD", - CellLabel->"In[1]:=", - CellID->246917287], - Cell[CellGroupData[{ Cell[BoxData[ @@ -220,12 +218,13 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}]], "Input", CellTags->"LCD", - CellLabel->"In[2]:=", + CellLabel->"In[7]:=", CellID->163498575], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -244,51 +243,18 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LCD", - CellLabel->"Out[2]=", - CellID->1669873163] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"%", "//", "FCI"}]], "Input", + RowBox[{ + RowBox[{"%", "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"LCD", - CellLabel->"In[3]:=", + CellLabel->"In[8]:=", CellID->950730684], -Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Epsilon]", - RowBox[{ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Sigma]", - TraditionalForm], - TraditionalForm]}]], TraditionalForm]], "Output", - CellTags->"LCD", - CellLabel->"Out[3]=", - CellID->774559606] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"%", "//", "StandardForm"}]], "Input", - CellTags->"LCD", - CellLabel->"In[4]:=", - CellID->1738716456], - Cell[BoxData[ RowBox[{"Eps", "[", RowBox[{ @@ -299,11 +265,9 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", RowBox[{"\[Rho]", ",", "D"}], "]"}], ",", RowBox[{"LorentzIndex", "[", - RowBox[{"\[Sigma]", ",", "D"}], "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]], "Output", + RowBox[{"\[Sigma]", ",", "D"}], "]"}]}], "]"}]], "Output", CellTags->"LCD", - CellLabel->"Out[4]//StandardForm=", - CellID->1281931789] + CellLabel->"Out[8]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -314,12 +278,13 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "[", RowBox[{"p", ",", "q"}], "]"}]], "Input", CellTags->"LCD", - CellLabel->"In[5]:=", + CellLabel->"In[9]:=", CellID->1568724284], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -338,8 +303,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LCD", - CellLabel->"Out[5]=", - CellID->474988897] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -348,7 +312,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"%", "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"LCD", - CellLabel->"In[6]:=", + CellLabel->"In[10]:=", CellID->531209658], Cell[BoxData[ @@ -361,11 +325,9 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "D"}], "]"}], ",", RowBox[{"Momentum", "[", - RowBox[{"q", ",", "D"}], "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]], "Output", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}]], "Output", CellTags->"LCD", - CellLabel->"Out[6]//StandardForm=", - CellID->1647742492] + CellLabel->"Out[10]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -383,7 +345,7 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], "[", "q", "]"}]}], "]"}], "]"}]], "Input", CellTags->"LCD", - CellLabel->"In[7]:=", + CellLabel->"In[11]:=", CellID->173575058], Cell[BoxData[ @@ -408,27 +370,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", CellTags->"LCD", - CellLabel->"Out[7]=", - CellID->932361259] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "4"}]}], "]"}]], "Input", - CellTags->"LCD", - CellLabel->"In[8]:=", - CellID->1229900885], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Dimension", "\[Rule]", "4"}], "}"}], TraditionalForm]], "Output", - CellTags->"LCD", - CellLabel->"Out[8]=", - CellID->1904977628] + CellLabel->"Out[11]="] }, Open ]] }, Open ]], @@ -493,12 +435,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{729, Automatic}, {Automatic, 111}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Lagrangian.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Lagrangian.nb index 93bdbd023..45e07f51b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Lagrangian.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Lagrangian.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynRule", ButtonNote->"FeynRule"], "." -}], "Text", - CellTags->"Lagrangian", - CellID->1051170443] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -204,7 +202,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Lagrangian", "[", "\"\\"", "]"}]], "Input", CellTags->"Lagrangian", - CellLabel->"In[1]:=", + CellLabel->"In[12]:=", CellID->345064330], Cell[BoxData[ @@ -236,20 +234,17 @@ Cell[BoxData[ RowBox[{"FCGV", "(", "\<\"a\"\>", ")"}], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Lagrangian", - CellLabel->"Out[1]=", - CellID->2119348269] + CellLabel->"Out[12]="] }, Open ]], -Cell["Twist-2 operator product expansion operators", "Text", - CellTags->"Lagrangian", - CellID->1898296666], +Cell["Twist-2 operator product expansion operators", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Lagrangian", "[", "\"\\"", "]"}]], "Input", CellTags->"Lagrangian", - CellLabel->"In[2]:=", + CellLabel->"In[13]:=", CellID->1741218479], Cell[BoxData[ @@ -297,8 +292,7 @@ Cell[BoxData[ RowBox[{"FCGV", "(", "\<\"b\"\>", ")"}], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Lagrangian", - CellLabel->"Out[2]=", - CellID->105197133] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -306,7 +300,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Lagrangian", "[", "\"\\"", "]"}]], "Input", CellTags->"Lagrangian", - CellLabel->"In[3]:=", + CellLabel->"In[14]:=", CellID->1557246101], Cell[BoxData[ @@ -316,7 +310,8 @@ Cell[BoxData[ SuperscriptBox["\[ImaginaryI]", "m"], " ", RowBox[{ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox[ @@ -375,8 +370,7 @@ Cell[BoxData[ RowBox[{"FCGV", "(", "\<\"b\"\>", ")"}], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Lagrangian", - CellLabel->"Out[3]=", - CellID->658984245] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ @@ -384,7 +378,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Lagrangian", "[", "\"\\"", "]"}]], "Input", CellTags->"Lagrangian", - CellLabel->"In[4]:=", + CellLabel->"In[15]:=", CellID->249786913], Cell[BoxData[ @@ -410,8 +404,7 @@ Cell[BoxData[ FormBox["\[Psi]", TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->"Lagrangian", - CellLabel->"Out[4]=", - CellID->2085030261] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ @@ -419,7 +412,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Lagrangian", "[", "\"\\"", "]"}]], "Input", CellTags->"Lagrangian", - CellLabel->"In[5]:=", + CellLabel->"In[16]:=", CellID->1220998815], Cell[BoxData[ @@ -449,8 +442,7 @@ Cell[BoxData[ FormBox["\[Psi]", TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->"Lagrangian", - CellLabel->"Out[5]=", - CellID->1018219384] + CellLabel->"Out[16]="] }, Open ]] }, Open ]], @@ -515,12 +507,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{950, Automatic}, {Automatic, 60}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftPartialD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftPartialD.nb index bafe2c5c9..356134e37 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftPartialD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftPartialD.nb @@ -189,9 +189,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RightPartialD", ButtonNote->"RightPartialD"], "." -}], "Text", - CellTags->"LeftPartialD", - CellID->333878293] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,10 +216,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"LeftPartialD", - CellID->112576831], - Cell[CellGroupData[{ Cell[BoxData[ @@ -231,7 +225,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}], ".", RowBox[{"LeftPartialD", "[", "\[Nu]", "]"}]}]], "Input", CellTags->"LeftPartialD", - CellLabel->"In[1]:=", + CellLabel->"In[17]:=", CellID->1505949422], Cell[BoxData[ @@ -249,8 +243,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"LeftPartialD", - CellLabel->"Out[1]=", - CellID->830365091] + CellLabel->"Out[17]="] }, Open ]], Cell[CellGroupData[{ @@ -258,27 +251,27 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandPartialD", "[", "%", "]"}]], "Input", CellTags->"LeftPartialD", - CellLabel->"In[2]:=", + CellLabel->"In[18]:=", CellID->1429866239], Cell[BoxData[ FormBox[ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Nu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Mu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], TraditionalForm]], "Output", + TraditionalForm]], ")"}], TraditionalForm]], "Output", CellTags->"LeftPartialD", - CellLabel->"Out[2]=", - CellID->1758698798] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -286,7 +279,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"StandardForm", "[", "%", "]"}]], "Input", CellTags->"LeftPartialD", - CellLabel->"In[3]:=", + CellLabel->"In[19]:=", CellID->145865999], Cell[BoxData[ @@ -296,8 +289,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], "]"}], ",", "A", ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]], "Output", CellTags->"LeftPartialD", - CellLabel->"Out[3]//StandardForm=", - CellID->1222822570] + CellLabel->"Out[19]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -306,15 +298,14 @@ Cell[BoxData[ RowBox[{"StandardForm", "[", RowBox[{"LeftPartialD", "[", "\[Mu]", "]"}], "]"}]], "Input", CellTags->"LeftPartialD", - CellLabel->"In[4]:=", + CellLabel->"In[20]:=", CellID->1674572572], Cell[BoxData[ RowBox[{"LeftPartialD", "[", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}]], "Output", CellTags->"LeftPartialD", - CellLabel->"Out[4]//StandardForm=", - CellID->2010768027] + CellLabel->"Out[20]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -329,7 +320,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}]}], "]"}], ".", RowBox[{"LeftPartialD", "[", "\[Rho]", "]"}]}]], "Input", CellTags->"LeftPartialD", - CellLabel->"In[5]:=", + CellLabel->"In[21]:=", CellID->1935363723], Cell[BoxData[ @@ -352,8 +343,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"LeftPartialD", - CellLabel->"Out[5]=", - CellID->1721340260] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ @@ -361,7 +351,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandPartialD", "[", "%", "]"}]], "Input", CellTags->"LeftPartialD", - CellLabel->"In[6]:=", + CellLabel->"In[22]:=", CellID->1467469251], Cell[BoxData[ @@ -373,41 +363,44 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}]}], "+", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}], "+", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}], ".", SubscriptBox[ FormBox["A", TraditionalForm], FormBox["\[Nu]", TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"LeftPartialD", - CellLabel->"Out[6]=", - CellID->1229859500] + CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ @@ -415,7 +408,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"StandardForm", "[", "%", "]"}]], "Input", CellTags->"LeftPartialD", - CellLabel->"In[7]:=", + CellLabel->"In[23]:=", CellID->692947033], Cell[BoxData[ @@ -439,8 +432,7 @@ Cell[BoxData[ RowBox[{"A", ",", RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}]}], "]"}]}]}]], "Output", CellTags->"LeftPartialD", - CellLabel->"Out[7]//StandardForm=", - CellID->296675662] + CellLabel->"Out[23]//StandardForm="] }, Open ]] }, Open ]], @@ -505,12 +497,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{898, Automatic}, {Automatic, 110}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftRightPartialD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftRightPartialD.nb index af8caacd0..499ea1295 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftRightPartialD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftRightPartialD.nb @@ -178,7 +178,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["ExplicitPartialD", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/ExplicitPartialD", @@ -209,9 +208,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RightPartialD", ButtonNote->"RightPartialD"], "." -}], "Text", - CellTags->"LeftRightPartialD", - CellID->2130291841] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -243,7 +240,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"LeftRightPartialD", "[", "\[Mu]", "]"}]], "Input", CellTags->"LeftRightPartialD", - CellLabel->"In[1]:=", + CellLabel->"In[24]:=", CellID->538126232], Cell[BoxData[ @@ -255,8 +252,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"LeftRightPartialD", - CellLabel->"Out[1]=", - CellID->1132769852] + CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ @@ -264,7 +260,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExplicitPartialD", "[", "%", "]"}]], "Input", CellTags->"LeftRightPartialD", - CellLabel->"In[2]:=", + CellLabel->"In[25]:=", CellID->438418910], Cell[BoxData[ @@ -286,8 +282,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], ")"}]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD", - CellLabel->"Out[2]=", - CellID->215900493] + CellLabel->"Out[25]="] }, Open ]], Cell[CellGroupData[{ @@ -299,7 +294,7 @@ Cell[BoxData[ RowBox[{"A", ",", RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}]}], "]"}]}]], "Input", CellTags->"LeftRightPartialD", - CellLabel->"In[3]:=", + CellLabel->"In[26]:=", CellID->1906170176], Cell[BoxData[ @@ -317,8 +312,7 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD", - CellLabel->"Out[3]=", - CellID->1398421327] + CellLabel->"Out[26]="] }, Open ]], Cell[CellGroupData[{ @@ -326,7 +320,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandPartialD", "[", "%", "]"}]], "Input", CellTags->"LeftRightPartialD", - CellLabel->"In[4]:=", + CellLabel->"In[27]:=", CellID->521183313], Cell[BoxData[ @@ -336,18 +330,19 @@ Cell[BoxData[ RowBox[{"(", RowBox[{ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Nu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], "-", + TraditionalForm]], ")"}], "-", RowBox[{ SubscriptBox[ OverscriptBox["\[PartialD]", "\[LeftArrow]"], @@ -361,8 +356,7 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD", - CellLabel->"Out[4]=", - CellID->1245680526] + CellLabel->"Out[27]="] }, Open ]], Cell[CellGroupData[{ @@ -377,7 +371,7 @@ Cell[BoxData[ RowBox[{"A", ",", RowBox[{"LorentzIndex", "[", "\[Rho]", "]"}]}], "]"}]}]], "Input", CellTags->"LeftRightPartialD", - CellLabel->"In[5]:=", + CellLabel->"In[28]:=", CellID->146402203], Cell[BoxData[ @@ -400,8 +394,7 @@ Cell[BoxData[ FormBox["\[Rho]", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD", - CellLabel->"Out[5]=", - CellID->488945383] + CellLabel->"Out[28]="] }, Open ]], Cell[CellGroupData[{ @@ -409,7 +402,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandPartialD", "[", "%", "]"}]], "Input", CellTags->"LeftRightPartialD", - CellLabel->"In[6]:=", + CellLabel->"In[29]:=", CellID->1596263636], Cell[BoxData[ @@ -424,41 +417,44 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], "\[Null]"]}]}], "-", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}], "-", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}], ".", SubscriptBox[ FormBox["A", TraditionalForm], FormBox["\[Rho]", TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD", - CellLabel->"Out[6]=", - CellID->1968825715] + CellLabel->"Out[29]="] }, Open ]] }, Open ]], @@ -523,12 +519,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{949, Automatic}, {Automatic, 87}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftRightPartialD2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftRightPartialD2.nb index ea3f01586..8f00bbca9 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftRightPartialD2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/LeftRightPartialD2.nb @@ -203,9 +203,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RightPartialD", ButtonNote->"RightPartialD"], "." -}], "Text", - CellTags->"LeftRightPartialD2", - CellID->1097237675] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -249,8 +247,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"LeftRightPartialD2", - CellLabel->"Out[1]=", - CellID->1370534562] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -277,8 +274,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD2", - CellLabel->"Out[2]=", - CellID->1797023804] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -310,8 +306,7 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD2", - CellLabel->"Out[3]=", - CellID->334849476] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -326,18 +321,19 @@ Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Nu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], "+", + TraditionalForm]], ")"}], "+", RowBox[{ SubscriptBox[ OverscriptBox["\[PartialD]", "\[LeftArrow]"], @@ -351,8 +347,7 @@ Cell[BoxData[ FormBox["\[Nu]", TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD2", - CellLabel->"Out[4]=", - CellID->412944908] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -392,8 +387,7 @@ Cell[BoxData[ FormBox["\[Rho]", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD2", - CellLabel->"Out[5]=", - CellID->637341112] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -413,41 +407,44 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], "\[Null]"]}]}], "+", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}], "+", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["A", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}], ".", SubscriptBox[ FormBox["A", TraditionalForm], FormBox["\[Rho]", TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"LeftRightPartialD2", - CellLabel->"Out[6]=", - CellID->545682027] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -512,12 +509,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{962, Automatic}, {Automatic, 88}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/LeviCivita.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/LeviCivita.nb index a4a91e2f8..3aa8af4b9 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/LeviCivita.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/LeviCivita.nb @@ -147,8 +147,26 @@ LeviCivita is changed). LeviCivita[", }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +The shortcut LeviCivita is deprecated, please use LC instead!\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "LeviCivita", "]"}]], "Input", + CellLabel->"In[356]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[356]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -184,29 +202,17 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["Eps", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Eps", - ButtonNote->"Eps"], - ", ", - ButtonBox["Contract", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Contract", - ButtonNote->"Contract"], - ", ", ButtonBox["LC", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LC", - ButtonNote->"LC"], + ButtonData:>"paclet:FeynCalc/ref/FV", + ButtonNote->"FV"], ", ", - ButtonBox["LCD", + ButtonBox["FCI", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LCD", - ButtonNote->"LCD"], + ButtonData:>"paclet:FeynCalc/ref/FCI", + ButtonNote->"FCI"], "." -}], "Text", - CellTags->"LeviCivita", - CellID->236168083] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -235,37 +241,18 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "LeviCivita", "]"}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[1]:=", - CellID->2141079579], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"LeviCivita", - CellLabel->"Out[1]=", - CellID->1665927785] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"LeviCivita", "[", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], "]"}]], "Input", CellTags->"LeviCivita", - CellLabel->"In[2]:=", + CellLabel->"In[359]:=", CellID->970809287], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Alpha]", @@ -284,94 +271,118 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LeviCivita", - CellLabel->"Out[2]=", - CellID->1096309803] + CellLabel->"Out[359]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "[", - RowBox[{"OPEDelta", ",", "p"}], "]"}]], "Input", + RowBox[{"LeviCivita", "[", "]"}], "[", + RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}]], "Input", CellTags->"LeviCivita", - CellLabel->"In[3]:=", - CellID->972968542], + CellLabel->"In[360]:=", + CellID->1735126440], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox["\[Nu]", - TraditionalForm], + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], + OverscriptBox[ + FormBox["r", + TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox["p", - TraditionalForm], + OverscriptBox[ + FormBox["s", + TraditionalForm], "_"], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LeviCivita", - CellLabel->"Out[3]=", - CellID->657040186] + CellLabel->"Out[360]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"LeviCivita", "[", "]"}], "[", - RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[4]:=", - CellID->1735126440], + RowBox[{"LeviCivita", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "[", + RowBox[{"p", ",", "q"}], "]"}]], "Input", + CellLabel->"In[361]:="], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ - FormBox["p", + FormBox["\[Alpha]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["q", + FormBox["\[Beta]", TraditionalForm], TraditionalForm], FormBox[ - FormBox["r", - TraditionalForm], + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox["s", - TraditionalForm], + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], TraditionalForm]}]], TraditionalForm]], "Output", - CellTags->"LeviCivita", - CellLabel->"Out[4]=", - CellID->986206459] + CellLabel->"Out[361]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Beta]", ",", "\[Delta]"}], + RowBox[{"StandardForm", "[", "%", "]"}]], "Input", + CellLabel->"In[362]:="], + +Cell[BoxData[ + RowBox[{"Eps", "[", + RowBox[{ + RowBox[{"LorentzIndex", "[", "\[Alpha]", "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Beta]", "]"}], ",", + RowBox[{"Momentum", "[", "p", "]"}], ",", + RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]], "Output", + CellLabel->"Out[362]//StandardForm="] +}, Open ]], + +Cell["\<\ +LeviCivita is scheduled for removal in the future versions of FeynCalc. The \ +safe alternative is to use LC.\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"LC", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], "]"}]], "Input", CellTags->"LeviCivita", - CellLabel->"In[5]:=", - CellID->1409243674], + CellLabel->"In[84]:=", + CellID->2075117917], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Alpha]", @@ -382,7 +393,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["\[Beta]", + FormBox["\[Gamma]", TraditionalForm], TraditionalForm], FormBox[ @@ -390,188 +401,166 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LeviCivita", - CellLabel->"Out[5]=", - CellID->1898302846] + CellLabel->"Out[84]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "[", - RowBox[{"OPEDelta", ",", "p"}], "]"}], "//", "StandardForm"}]], "Input", + RowBox[{"LC", "[", "]"}], "[", + RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}]], "Input", CellTags->"LeviCivita", - CellLabel->"In[6]:=", - CellID->851260878], + CellLabel->"In[85]:=", + CellID->528234025], Cell[BoxData[ - RowBox[{"Eps", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Mu]", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Nu]", ",", "D"}], "]"}], ",", - RowBox[{"Momentum", "[", - RowBox[{"OPEDelta", ",", "D"}], "]"}], ",", - RowBox[{"Momentum", "[", - RowBox[{"p", ",", "D"}], "]"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]], "Output", + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["r", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["s", + TraditionalForm], "_"], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LeviCivita", - CellLabel->"Out[6]//StandardForm=", - CellID->2076139317] + CellLabel->"Out[85]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", " ", "=", " ", - RowBox[{ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Rho]"}], - "]"}], ".", - RowBox[{"LeviCivita", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Rho]"}], - "]"}]}], " "}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[7]:=", - CellID->1953796449], + RowBox[{ + RowBox[{"LC", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "[", + RowBox[{"p", ",", "q"}], "]"}]], "Input", + CellLabel->"In[86]:="], Cell[BoxData[ FormBox[ - RowBox[{ - SuperscriptBox["\[Epsilon]", - RowBox[{ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Gamma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm]}]], ".", - SuperscriptBox["\[Epsilon]", - RowBox[{ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Gamma]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm]}]]}], TraditionalForm]], "Output", - CellTags->"LeviCivita", - CellLabel->"Out[7]=", - CellID->1617820485] + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm]}]], TraditionalForm]], "Output", + CellLabel->"Out[86]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Contract", "[", "t1", "]"}]], "Input", + RowBox[{"LCD", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], + "]"}]], "Input", CellTags->"LeviCivita", - CellLabel->"In[8]:=", - CellID->1087595628], + CellLabel->"In[87]:=", + CellID->293666632], Cell[BoxData[ FormBox[ - RowBox[{ - RowBox[{"-", - SuperscriptBox["D", "4"]}], "+", - RowBox[{"6", " ", - SuperscriptBox["D", "3"]}], "-", - RowBox[{"11", " ", - SuperscriptBox["D", "2"]}], "+", - RowBox[{"6", " ", "D"}]}], TraditionalForm]], "Output", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Gamma]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Delta]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LeviCivita", - CellLabel->"Out[8]=", - CellID->168636471] + CellLabel->"Out[87]="] }, Open ]], -Cell[BoxData[ - RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"LeviCivita", ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], ";", - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], ";"}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[9]:=", - CellID->391796206], - Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"Contract", "[", " ", - RowBox[{ - RowBox[{"LeviCivita", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Rho]"}], - "]"}], ".", - RowBox[{"LeviCivita", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Rho]"}], - "]"}]}], "]"}], "//", "Factor2"}]], "Input", + RowBox[{"LCD", "[", "]"}], "[", + RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}]], "Input", CellTags->"LeviCivita", - CellLabel->"In[10]:=", - CellID->132983157], + CellLabel->"In[88]:=", + CellID->19954627], Cell[BoxData[ FormBox[ - RowBox[{ - RowBox[{"(", - RowBox[{"1", "-", "D"}], ")"}], " ", - RowBox[{"(", - RowBox[{"2", "-", "D"}], ")"}], " ", - RowBox[{"(", - RowBox[{"3", "-", "D"}], ")"}], " ", "D"}], TraditionalForm]], "Output", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], + RowBox[{ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["r", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["s", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"LeviCivita", - CellLabel->"Out[10]=", - CellID->1319312223] + CellLabel->"Out[88]="] }, Open ]], -Cell[BoxData[ - RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"LeviCivita", ",", - RowBox[{"Dimension", "\[Rule]", "4"}]}], "]"}], ";", - RowBox[{"SetOptions", "[", - RowBox[{"Eps", ",", - RowBox[{"Dimension", "\[Rule]", "4"}]}], "]"}], ";"}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[11]:=", - CellID->506638236], - Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"LC", "[", - RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], - "]"}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[12]:=", - CellID->1005970568], + RowBox[{ + RowBox[{"LCD", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "[", + RowBox[{"p", ",", "q"}], "]"}]], "Input", + CellLabel->"In[89]:="], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", ""], RowBox[{ FormBox[ FormBox["\[Alpha]", @@ -582,23 +571,52 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["\[Gamma]", + FormBox["p", TraditionalForm], TraditionalForm], FormBox[ - FormBox["\[Delta]", + FormBox["q", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - CellTags->"LeviCivita", - CellLabel->"Out[12]=", - CellID->1506614030] + CellLabel->"Out[89]="] }, Open ]], +Cell[CellGroupData[{ + Cell[BoxData[ - RowBox[{"Clear", "[", "t1", "]"}]], "Input", - CellTags->"LeviCivita", - CellLabel->"In[13]:=", - CellID->839583368] + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"LC", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], + "]"}], "]"}], "===", + RowBox[{"LeviCivita", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], + "]"}]}]], "Input", + CellLabel->"In[90]:="], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[90]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"LCD", "[", + RowBox[{"\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]"}], + "]"}], "]"}], "===", + RowBox[{"LeviCivita", "[", + RowBox[{ + "\[Alpha]", ",", "\[Beta]", ",", "\[Gamma]", ",", "\[Delta]", ",", + RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]}]], "Input", + CellLabel->"In[91]:="], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[91]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -661,13 +679,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{879, 770}, +WindowMargins->{{1278, Automatic}, {Automatic, 208}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Li2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Li2.nb index e09bbc277..746e5576b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Li2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Li2.nb @@ -159,15 +159,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["Li3", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Li3", ButtonNote->"Li3"], "." -}], "Text", - CellTags->"Li2", - CellID->75864768] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -199,7 +196,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Li2", "[", "x", "]"}]], "Input", CellTags->"Li2", - CellLabel->"In[1]:=", + CellLabel->"In[7]:=", CellID->870020060], Cell[BoxData[ @@ -207,8 +204,7 @@ Cell[BoxData[ TemplateBox[{"2","x"}, "PolyLog"], TraditionalForm]], "Output", CellTags->"Li2", - CellLabel->"Out[1]=", - CellID->118594315] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -216,7 +212,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Li2", "//", "StandardForm"}]], "Input", CellTags->"Li2", - CellLabel->"In[2]:=", + CellLabel->"In[8]:=", CellID->1201153887], Cell[BoxData[ @@ -224,8 +220,7 @@ Cell[BoxData[ RowBox[{"PolyLog", "[", RowBox[{"2", ",", "#1"}], "]"}], "&"}]], "Output", CellTags->"Li2", - CellLabel->"Out[2]//StandardForm=", - CellID->798709898] + CellLabel->"Out[8]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -239,7 +234,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], "]"}], "x"], RowBox[{"\[DifferentialD]", "x"}]}]}]}]], "Input", CellTags->"Li2", - CellLabel->"In[3]:=", + CellLabel->"In[9]:=", CellID->80483927], Cell[BoxData[ @@ -247,8 +242,7 @@ Cell[BoxData[ TemplateBox[{"2","x"}, "PolyLog"], TraditionalForm]], "Output", CellTags->"Li2", - CellLabel->"Out[3]=", - CellID->788521289] + CellLabel->"Out[9]="] }, Open ]] }, Open ]], @@ -313,12 +307,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1154, Automatic}, {Automatic, 189}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Li3.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Li3.nb index 8481fc08e..3e401902e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Li3.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Li3.nb @@ -159,15 +159,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["Li2", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Li2", ButtonNote->"Li2"], "." -}], "Text", - CellTags->"Li3", - CellID->1253879809] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -199,7 +196,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Li3", "[", "x", "]"}]], "Input", CellTags->"Li3", - CellLabel->"In[1]:=", + CellLabel->"In[10]:=", CellID->750513892], Cell[BoxData[ @@ -207,8 +204,7 @@ Cell[BoxData[ TemplateBox[{"3","x"}, "PolyLog"], TraditionalForm]], "Output", CellTags->"Li3", - CellLabel->"Out[1]=", - CellID->955211084] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -216,7 +212,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Li3", "//", "StandardForm"}]], "Input", CellTags->"Li3", - CellLabel->"In[2]:=", + CellLabel->"In[11]:=", CellID->1277219612], Cell[BoxData[ @@ -224,8 +220,7 @@ Cell[BoxData[ RowBox[{"PolyLog", "[", RowBox[{"3", ",", "#1"}], "]"}], "&"}]], "Output", CellTags->"Li3", - CellLabel->"Out[2]//StandardForm=", - CellID->1455650217] + CellLabel->"Out[11]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -235,7 +230,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Li3", "[", "x", "]"}], ",", "x"}], "]"}]], "Input", CellTags->"Li3", - CellLabel->"In[3]:=", + CellLabel->"In[12]:=", CellID->918353048], Cell[BoxData[ @@ -244,8 +239,7 @@ Cell[BoxData[ TemplateBox[{"2","x"}, "PolyLog"], "x"], TraditionalForm]], "Output", CellTags->"Li3", - CellLabel->"Out[3]=", - CellID->749318248] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -257,7 +251,7 @@ Cell[BoxData[ RowBox[{"Li2", "[", "x", "]"}], "x"], RowBox[{"\[DifferentialD]", "x"}]}]}]], "Input", CellTags->"Li3", - CellLabel->"In[4]:=", + CellLabel->"In[13]:=", CellID->85803135], Cell[BoxData[ @@ -265,8 +259,7 @@ Cell[BoxData[ TemplateBox[{"3","x"}, "PolyLog"], TraditionalForm]], "Output", CellTags->"Li3", - CellLabel->"Out[4]=", - CellID->460713684] + CellLabel->"Out[13]="] }, Open ]] }, Open ]], @@ -331,12 +324,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1042, Automatic}, {Automatic, 153}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Li4.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Li4.nb new file mode 100644 index 000000000..ecb0cb7b9 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Li4.nb @@ -0,0 +1,325 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + 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CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Li4", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData["Li4"], "InlineFormula"], + " \[LineSeparator]is an abbreviation for the weight 4 polylogarithm \ +function, i.e., Li4 = PolyLog[4, #]&." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", 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InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Loop.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Loop.nb index b9d992b3d..7fc7fdad4 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Loop.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Loop.nb @@ -246,12 +246,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, 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TraditionalForm], + TraditionalForm]}]], " ", + RowBox[{"(", + RowBox[{ + RowBox[{ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["0", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["nu", + TraditionalForm], + TraditionalForm]}]], " ", + RowBox[{"(", + RowBox[{"-", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox[ + StyleBox[ + RowBox[{"$MU", "\[InvisibleApplication]", + RowBox[{"(", "$31", ")"}]}], + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox[ + StyleBox["p", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox[ + StyleBox["q", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], + TraditionalForm]}]]}], ")"}]}], "-", + RowBox[{ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox[ + StyleBox[ + RowBox[{"$MU", "\[InvisibleApplication]", + RowBox[{"(", "$32", ")"}]}], + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["nu", + TraditionalForm], + TraditionalForm]}]], " ", + RowBox[{"(", + RowBox[{ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], + TraditionalForm], "0"], " ", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox[ + StyleBox[ + RowBox[{"$MU", "\[InvisibleApplication]", + RowBox[{"(", "$31", ")"}]}], + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox[ + StyleBox[ + RowBox[{"$MU", "\[InvisibleApplication]", + RowBox[{"(", "$32", ")"}]}], + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox[ + StyleBox["p", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], + TraditionalForm]}]]}], "-", + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + TraditionalForm], "0"], " ", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], + RowBox[{ + FormBox[ + FormBox[ + StyleBox[ + RowBox[{"$MU", "\[InvisibleApplication]", + RowBox[{"(", "$31", ")"}]}], + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox[ + StyleBox[ + RowBox[{"$MU", "\[InvisibleApplication]", + RowBox[{"(", "$32", ")"}]}], + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox[ + StyleBox["q", + StripOnInput->False, + FontWeight->Bold], + TraditionalForm], "_"], + TraditionalForm]}]]}]}], ")"}]}]}], ")"}]}]}], + TraditionalForm]], "Output", + CellLabel->"Out[4]=", + CellID->354058269] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1339, Automatic}, {Automatic, 121}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Lower.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Lower.nb deleted file mode 100644 index 709b8c95d..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Lower.nb +++ /dev/null @@ -1,273 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/Lower", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Lower", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["Lower"], "InlineFormula"], - " \[LineSeparator]", - "may be used inside LorentzIndex to indicate a covariant LorentzIndex." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - ButtonBox["LorentzIndex", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LorentzIndex", - ButtonNote->"LorentzIndex"], - ", ", - ButtonBox["Upper", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Upper", - ButtonNote->"Upper"], - ", ", - ButtonBox["Contract1", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Contract1", - ButtonNote->"Contract1"], - "." -}], "Text", - CellTags->"Lower", - CellID->381475007] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MLimit.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MLimit.nb index b7ccac5b0..7945a8fe5 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MLimit.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/MLimit.nb @@ -207,14 +207,13 @@ Cell[BoxData[ RowBox[{"x", "\[Rule]", "1"}], ",", RowBox[{"y", "\[Rule]", "0"}]}], "}"}]}], "]"}]], "Input", CellTags->"MLimit", - CellLabel->"In[1]:=", + CellLabel->"In[19]:=", CellID->1100919712], Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"MLimit", - CellLabel->"Out[1]=", - CellID->1414668006] + CellLabel->"Out[19]="] }, Open ]] }, Open ]], @@ -279,12 +278,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1032, Automatic}, {Automatic, 233}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MT.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MT.nb index da0938280..b19153e78 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MT.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/MT.nb @@ -176,11 +176,6 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FCI", ButtonNote->"FCI"], ", ", - ButtonBox["MetricTensor", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/MetricTensor", - ButtonNote->"MetricTensor"], - ", ", ButtonBox["MTD", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/MTD", @@ -191,9 +186,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/MTE", ButtonNote->"MTE"], "." -}], "Text", - CellTags->"MT", - CellID->897903284] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -226,31 +219,24 @@ Cell[BoxData[ RowBox[{"MT", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Input", CellTags->"MT", - CellLabel->"In[1]:=", + CellLabel->"In[21]:=", CellID->2071184026], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], TraditionalForm]], "Output", + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"MT", - CellLabel->"Out[1]=", - CellID->839261192] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ @@ -263,14 +249,13 @@ Cell[BoxData[ RowBox[{"MT", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]}], "]"}]], "Input", CellTags->"MT", - CellLabel->"In[2]:=", + CellLabel->"In[22]:=", CellID->828510540], Cell[BoxData[ FormBox["4", TraditionalForm]], "Output", CellTags->"MT", - CellLabel->"Out[2]=", - CellID->1733599790] + CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ @@ -280,15 +265,14 @@ Cell[BoxData[ RowBox[{"MT", "[", RowBox[{"a", ",", "b"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MT", - CellLabel->"In[3]:=", + CellLabel->"In[23]:=", CellID->493237874], Cell[BoxData[ RowBox[{"MT", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", CellTags->"MT", - CellLabel->"Out[3]//StandardForm=", - CellID->2108634469] + CellLabel->"Out[23]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -299,7 +283,7 @@ Cell[BoxData[ RowBox[{"MT", "[", RowBox[{"a", ",", "b"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MT", - CellLabel->"In[4]:=", + CellLabel->"In[24]:=", CellID->2090805972], Cell[BoxData[ @@ -308,8 +292,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "a", "]"}], ",", RowBox[{"LorentzIndex", "[", "b", "]"}]}], "]"}]], "Output", CellTags->"MT", - CellLabel->"Out[4]//StandardForm=", - CellID->1337434264] + CellLabel->"Out[24]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -322,15 +305,14 @@ Cell[BoxData[ RowBox[{"a", ",", "b"}], "]"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MT", - CellLabel->"In[5]:=", + CellLabel->"In[25]:=", CellID->921483723], Cell[BoxData[ RowBox[{"MT", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", CellTags->"MT", - CellLabel->"Out[5]//StandardForm=", - CellID->62630223] + CellLabel->"Out[25]//StandardForm="] }, Open ]] }, Open ]], @@ -395,9 +377,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 741}, -WindowMargins->{{2111, Automatic}, {Automatic, 106}}, +WindowMargins->{{Automatic, 409}, {248, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MTD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MTD.nb index 4d219843a..2a1c3490f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MTD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/MTD.nb @@ -160,44 +160,33 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[RawData["\<\ Cell[TextData[{ - ButtonBox[\"FeynCalcExternal\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/FeynCalcExternal\", - ButtonNote->\"FeynCalcExternal\"], - \", \", - ButtonBox[\"FCE\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/FCE\", - ButtonNote->\"FCE\"], - \", \", - ButtonBox[\"FCI\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/FCI\", - ButtonNote->\"FCI\"], - \", \", - ButtonBox[\"MetricTensor\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/MetricTensor\", - ButtonNote->\"MetricTensor\"], - \", \", - ButtonBox[\"MT\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/MT\", - ButtonNote->\"MT\"], - \", \", - ButtonBox[\"MTE\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/MTE\", - ButtonNote->\"MTE\"], - \".\" -}], \"Text\", - CellTags->\"MTD\", - CellID->310039993]\ -\>"], "Text", - CellTags->"MTD", - CellID->310039993] + ButtonBox["FeynCalcExternal", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FeynCalcExternal", + ButtonNote->"FeynCalcExternal"], + ", ", + ButtonBox["FCE", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FCE", + ButtonNote->"FCE"], + ", ", + ButtonBox["FCI", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/FCI", + ButtonNote->"FCI"], + ", ", + ButtonBox["MT", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/MT", + ButtonNote->"MT"], + ", ", + ButtonBox["MTE", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/MTE", + ButtonNote->"MTE"], + "." +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -230,30 +219,23 @@ Cell[BoxData[ RowBox[{"MTD", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Input", CellTags->"MTD", - CellLabel->"In[1]:=", + CellLabel->"In[26]:=", CellID->1680977301], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], TraditionalForm]], "Output", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"MTD", - CellLabel->"Out[1]=", - CellID->1640321247] + CellLabel->"Out[26]="] }, Open ]], Cell[CellGroupData[{ @@ -266,14 +248,13 @@ Cell[BoxData[ RowBox[{"MTD", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]}], "]"}]], "Input", CellTags->"MTD", - CellLabel->"In[2]:=", + CellLabel->"In[27]:=", CellID->2085004373], Cell[BoxData[ FormBox["D", TraditionalForm]], "Output", CellTags->"MTD", - CellLabel->"Out[2]=", - CellID->366701652] + CellLabel->"Out[27]="] }, Open ]], Cell[CellGroupData[{ @@ -284,15 +265,14 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MTD", - CellLabel->"In[3]:=", + CellLabel->"In[28]:=", CellID->964321899], Cell[BoxData[ RowBox[{"MTD", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Output", CellTags->"MTD", - CellLabel->"Out[3]//StandardForm=", - CellID->842419980] + CellLabel->"Out[28]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -304,7 +284,7 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MTD", - CellLabel->"In[4]:=", + CellLabel->"In[29]:=", CellID->1887554420], Cell[BoxData[ @@ -315,8 +295,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", RowBox[{"\[Beta]", ",", "D"}], "]"}]}], "]"}]], "Output", CellTags->"MTD", - CellLabel->"Out[4]//StandardForm=", - CellID->255141216] + CellLabel->"Out[29]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -329,15 +308,14 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MTD", - CellLabel->"In[5]:=", + CellLabel->"In[30]:=", CellID->623099946], Cell[BoxData[ RowBox[{"MTD", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Output", CellTags->"MTD", - CellLabel->"Out[5]//StandardForm=", - CellID->141115701] + CellLabel->"Out[30]//StandardForm="] }, Open ]] }, Open ]], @@ -402,9 +380,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 741}, -WindowMargins->{{2020, Automatic}, {Automatic, 99}}, +WindowMargins->{{Automatic, 518}, {Automatic, 199}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MTE.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MTE.nb index 1c30ea93d..747b9e506 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MTE.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/MTE.nb @@ -176,11 +176,6 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FCI", ButtonNote->"FCI"], ", ", - ButtonBox["MetricTensor", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/MetricTensor", - ButtonNote->"MetricTensor"], - ", ", ButtonBox["MT", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/MT", @@ -191,9 +186,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/MTD", ButtonNote->"MTD"], "." -}], "Text", - CellTags->"MTD", - CellID->310039993] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -226,31 +219,24 @@ Cell[BoxData[ RowBox[{"MTE", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Input", CellTags->"MTD", - CellLabel->"In[12]:=", + CellLabel->"In[31]:=", CellID->1680977301], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "^"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], TraditionalForm]], "Output", + SuperscriptBox[ + OverscriptBox["g", "^"], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"MTD", - CellLabel->"Out[12]=", - CellID->1958039632] + CellLabel->"Out[31]="] }, Open ]], Cell[CellGroupData[{ @@ -263,15 +249,14 @@ Cell[BoxData[ RowBox[{"MTE", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]}], "]"}]], "Input", CellTags->"MTD", - CellLabel->"In[13]:=", + CellLabel->"In[32]:=", CellID->2085004373], Cell[BoxData[ FormBox[ RowBox[{"D", "-", "4"}], TraditionalForm]], "Output", CellTags->"MTD", - CellLabel->"Out[13]=", - CellID->558766132] + CellLabel->"Out[32]="] }, Open ]], Cell[CellGroupData[{ @@ -283,13 +268,12 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], " ", RowBox[{"MT", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]}], "]"}]], "Input", - CellLabel->"In[14]:=", + CellLabel->"In[33]:=", CellID->1799001225], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", - CellLabel->"Out[14]=", - CellID->40801765] + CellLabel->"Out[33]="] }, Open ]], Cell[CellGroupData[{ @@ -301,14 +285,13 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], " ", RowBox[{"MTD", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]}], "]"}]], "Input", - CellLabel->"In[15]:=", + CellLabel->"In[34]:=", CellID->1071300852], Cell[BoxData[ FormBox[ RowBox[{"D", "-", "4"}], TraditionalForm]], "Output", - CellLabel->"Out[15]=", - CellID->509955041] + CellLabel->"Out[34]="] }, Open ]], Cell[CellGroupData[{ @@ -319,15 +302,14 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MTD", - CellLabel->"In[16]:=", + CellLabel->"In[35]:=", CellID->964321899], Cell[BoxData[ RowBox[{"MTE", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Output", CellTags->"MTD", - CellLabel->"Out[16]//StandardForm=", - CellID->1333611151] + CellLabel->"Out[35]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -336,31 +318,24 @@ Cell[BoxData[ RowBox[{"MTE", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Input", CellTags->"MTD", - CellLabel->"In[17]:=", + CellLabel->"In[36]:=", CellID->842419980], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "^"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], TraditionalForm]], "Output", + SuperscriptBox[ + OverscriptBox["g", "^"], + RowBox[{ + FormBox[ + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Beta]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"MTD", - CellLabel->"Out[17]=", - CellID->869554807] + CellLabel->"Out[36]="] }, Open ]], Cell[CellGroupData[{ @@ -372,7 +347,7 @@ Cell[BoxData[ RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MTD", - CellLabel->"In[18]:=", + CellLabel->"In[37]:=", CellID->1887554420], Cell[BoxData[ @@ -387,8 +362,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "4"}], "+", "D"}]}], "]"}]}], "]"}]], "Output", CellTags->"MTD", - CellLabel->"Out[18]//StandardForm=", - CellID->369801037] + CellLabel->"Out[37]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -401,15 +375,14 @@ Cell[BoxData[ RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MTD", - CellLabel->"In[19]:=", + CellLabel->"In[38]:=", CellID->623099946], Cell[BoxData[ RowBox[{"MTE", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Output", CellTags->"MTD", - CellLabel->"Out[19]//StandardForm=", - CellID->1143698797] + CellLabel->"Out[38]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -418,31 +391,24 @@ Cell[BoxData[ RowBox[{"MTE", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Input", CellTags->"MTD", - CellLabel->"In[20]:=", + CellLabel->"In[39]:=", CellID->141115701], Cell[BoxData[ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "^"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], TraditionalForm]], "Output", + SuperscriptBox[ + OverscriptBox["g", "^"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"MTD", - CellLabel->"Out[20]=", - CellID->1588832862] + CellLabel->"Out[39]="] }, Open ]] }, Open ]], @@ -507,9 +473,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 741}, -WindowMargins->{{1996, Automatic}, {Automatic, 89}}, +WindowMargins->{{Automatic, 456}, {Automatic, 218}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Mandelstam.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Mandelstam.nb index 1d2668d86..30446733c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Mandelstam.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Mandelstam.nb @@ -192,9 +192,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SetMandelstam", ButtonNote->"SetMandelstam"], "." -}], "Text", - CellTags->"Mandelstam", - CellID->817062959] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -280,12 +278,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{500, Automatic}, {Automatic, 102}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Map2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Map2.nb index d68f31a9c..742b105c5 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Map2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Map2.nb @@ -167,9 +167,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/NTerms", ButtonNote->"NTerms"], "." -}], "Text", - CellTags->"Map2", - CellID->435233862] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,7 +201,7 @@ Cell[BoxData[ RowBox[{"f", ",", RowBox[{"a", "-", "b"}]}], "]"}]], "Input", CellTags->"Map2", - CellLabel->"In[1]:=", + CellLabel->"In[40]:=", CellID->194230717], Cell[BoxData[ @@ -213,8 +211,7 @@ Cell[BoxData[ RowBox[{"f", "(", RowBox[{"-", "b"}], ")"}]}], TraditionalForm]], "Output", CellTags->"Map2", - CellLabel->"Out[1]=", - CellID->979511779] + CellLabel->"Out[40]="] }, Open ]], Cell[CellGroupData[{ @@ -223,15 +220,14 @@ Cell[BoxData[ RowBox[{"Map2", "[", RowBox[{"f", ",", "x"}], "]"}]], "Input", CellTags->"Map2", - CellLabel->"In[2]:=", + CellLabel->"In[41]:=", CellID->1407522381], Cell[BoxData[ FormBox[ RowBox[{"f", "(", "x", ")"}], TraditionalForm]], "Output", CellTags->"Map2", - CellLabel->"Out[2]=", - CellID->1491769424] + CellLabel->"Out[41]="] }, Open ]], Cell[CellGroupData[{ @@ -242,7 +238,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}]}], "]"}]], "Input", CellTags->"Map2", - CellLabel->"In[3]:=", + CellLabel->"In[42]:=", CellID->1867340703], Cell[BoxData[ @@ -252,8 +248,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "}"}], ")"}], TraditionalForm]], "Output", CellTags->"Map2", - CellLabel->"Out[3]=", - CellID->1614084211] + CellLabel->"Out[42]="] }, Open ]], Cell[CellGroupData[{ @@ -262,15 +257,14 @@ Cell[BoxData[ RowBox[{"Map2", "[", RowBox[{"f", ",", "1"}], "]"}]], "Input", CellTags->"Map2", - CellLabel->"In[4]:=", + CellLabel->"In[43]:=", CellID->722460655], Cell[BoxData[ FormBox[ RowBox[{"f", "(", "1", ")"}], TraditionalForm]], "Output", CellTags->"Map2", - CellLabel->"Out[4]=", - CellID->1998194589] + CellLabel->"Out[43]="] }, Open ]] }, Open ]], @@ -335,12 +329,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{489, Automatic}, {Automatic, 130}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MemSet.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MemSet.nb index 3c61c497a..cc9909dfc 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MemSet.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/MemSet.nb @@ -123,7 +123,7 @@ Cell[TextData[{ "InlineFormula"], " \[LineSeparator]", "is like f[x_] := f[x] = body, but dependend on the value of the setting of \ -MemoryAvailable \[Rule] memorycut (memorycut - MemoryInUse[]/", +FCMemoryAvailable \[Rule] memorycut (memorycut - MemoryInUse[]/", Cell[BoxData[ FormBox[ SuperscriptBox["10", "6"], TraditionalForm]]], @@ -168,14 +168,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["MemoryAvailable", + ButtonBox["FCMemoryAvailable", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/MemoryAvailable", - ButtonNote->"MemoryAvailable"], + ButtonData:>"paclet:FeynCalc/ref/FCMemoryAvailable", + ButtonNote->"FCMemoryAvailable"], "." -}], "Text", - CellTags->"MemSet", - CellID->295395423] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -261,12 +259,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{662, Automatic}, {Automatic, 93}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MemoryAvailable.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MemoryAvailable.nb deleted file mode 100644 index beb1d64ec..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MemoryAvailable.nb +++ /dev/null @@ -1,270 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/MemoryAvailable", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["MemoryAvailable", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["MemoryAvailable"], "InlineFormula"], - " \[LineSeparator]", - "is an option of MemSet. It can be set to an integer n, where n is the \ -available amount of main memory in Mega Byte. The default setting is \ -$MemoryAvailable." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - ButtonBox["MemSet", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/MemSet", - ButtonNote->"MemSet"], - ", ", - ButtonBox["$MemoryAvailable", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/$MemoryAvailable", - ButtonNote->"$MemoryAvailable"], - "." -}], "Text", - CellTags->"MemoryAvailable", - CellID->134961378] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MetricTensor.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MetricTensor.nb index e5bfc42a7..e86b6789a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MetricTensor.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/MetricTensor.nb @@ -124,8 +124,27 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +The shortcut MetricTensor is deprecated, please use MT instead!\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "MetricTensor", "]"}]], "Input", + CellLabel->"In[25]:=", + CellID->1215792887], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[25]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -161,16 +180,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["FeynCalcExternal", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FeynCalcExternal", - ButtonNote->"FeynCalcExternal"], - ", ", - ButtonBox["FCE", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FCE", - ButtonNote->"FCE"], - ", ", ButtonBox["FCI", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FCI", @@ -186,9 +195,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/MTD", ButtonNote->"MTD"], "." -}], "Text", - CellTags->"MetricTensor", - CellID->309904132] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -221,7 +228,7 @@ Cell[BoxData[ RowBox[{"MetricTensor", "[", RowBox[{"\[Alpha]", ",", "\[Beta]"}], "]"}]], "Input", CellTags->"MetricTensor", - CellLabel->"In[1]:=", + CellLabel->"In[651]:=", CellID->187143262], Cell[BoxData[ @@ -230,20 +237,15 @@ Cell[BoxData[ OverscriptBox["g", "_"], RowBox[{ FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], + FormBox["\[Alpha]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"MetricTensor", - CellLabel->"Out[1]=", - CellID->1323519245] + CellLabel->"Out[651]="] }, Open ]], Cell[CellGroupData[{ @@ -251,15 +253,11 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Contract", "[", RowBox[{"%", " ", "%"}], "]"}]], "Input", - CellTags->"MetricTensor", - CellLabel->"In[2]:=", - CellID->888467606], + CellLabel->"In[652]:="], Cell[BoxData[ FormBox["4", TraditionalForm]], "Output", - CellTags->"MetricTensor", - CellLabel->"Out[2]=", - CellID->116818789] + CellLabel->"Out[652]="] }, Open ]], Cell[CellGroupData[{ @@ -267,9 +265,9 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MetricTensor", "[", RowBox[{"\[Alpha]", ",", "\[Beta]", ",", - RowBox[{"Dimension", "\[Rule]", "n"}]}], "]"}]], "Input", + RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]], "Input", CellTags->"MetricTensor", - CellLabel->"In[3]:=", + CellLabel->"In[653]:=", CellID->524835668], Cell[BoxData[ @@ -277,20 +275,15 @@ Cell[BoxData[ SuperscriptBox["g", RowBox[{ FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], + FormBox["\[Alpha]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"MetricTensor", - CellLabel->"Out[3]=", - CellID->1803847759] + CellLabel->"Out[653]="] }, Open ]], Cell[CellGroupData[{ @@ -299,14 +292,13 @@ Cell[BoxData[ RowBox[{"Contract", "[", RowBox[{"%", " ", "%"}], "]"}]], "Input", CellTags->"MetricTensor", - CellLabel->"In[4]:=", + CellLabel->"In[654]:=", CellID->125271051], Cell[BoxData[ - FormBox["n", TraditionalForm]], "Output", + FormBox["D", TraditionalForm]], "Output", CellTags->"MetricTensor", - CellLabel->"Out[4]=", - CellID->1132028331] + CellLabel->"Out[654]="] }, Open ]], Cell[CellGroupData[{ @@ -316,7 +308,7 @@ Cell[BoxData[ RowBox[{"MetricTensor", "[", RowBox[{"a", ",", "b"}], "]"}], "]"}]], "Input", CellTags->"MetricTensor", - CellLabel->"In[5]:=", + CellLabel->"In[655]:=", CellID->1318549517], Cell[BoxData[ @@ -325,70 +317,90 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "a", "]"}], ",", RowBox[{"LorentzIndex", "[", "b", "]"}]}], "]"}]], "Output", CellTags->"MetricTensor", - CellLabel->"Out[5]//StandardForm=", - CellID->1708064740] + CellLabel->"Out[655]//StandardForm="] }, Open ]], +Cell["\<\ +MetricTensor is scheduled for removal in the future versions of FeynCalc. The \ +safe alternative is to use MT.\ +\>", "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"MetricTensor", "[", - RowBox[{"a", ",", "b", ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "]"}]], "Input", - CellTags->"MetricTensor", - CellLabel->"In[6]:=", - CellID->1544242781], + RowBox[{"MT", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Input", + CellLabel->"In[658]:="], Cell[BoxData[ - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"a", ",", "D"}], "]"}], ",", - RowBox[{"LorentzIndex", "[", - RowBox[{"b", ",", "D"}], "]"}]}], "]"}]], "Output", - CellTags->"MetricTensor", - CellLabel->"Out[6]//StandardForm=", - CellID->2135349923] + FormBox[ + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", + CellLabel->"Out[658]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"FCE", "[", - RowBox[{"MetricTensor", "[", - RowBox[{"a", ",", "b"}], "]"}], "]"}], "]"}]], "Input", - CellTags->"MetricTensor", - CellLabel->"In[7]:=", - CellID->912797684], + RowBox[{"MTD", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Input", + CellLabel->"In[659]:="], Cell[BoxData[ - RowBox[{"MT", "[", - RowBox[{"a", ",", "b"}], "]"}]], "Output", - CellTags->"MetricTensor", - CellLabel->"Out[7]//StandardForm=", - CellID->489293900] + FormBox[ + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", + CellLabel->"Out[659]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"FCE", "[", - RowBox[{"MetricTensor", "[", - RowBox[{"a", ",", "b", ",", - RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}], "]"}], "]"}]], "Input", - CellTags->"MetricTensor", - CellLabel->"In[8]:=", - CellID->1275057625], + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"MT", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "]"}], "===", + RowBox[{"MetricTensor", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]}]], "Input", + CellLabel->"In[660]:="], Cell[BoxData[ - RowBox[{"MTD", "[", - RowBox[{"a", ",", "b"}], "]"}]], "Output", - CellTags->"MetricTensor", - CellLabel->"Out[8]//StandardForm=", - CellID->1657208619] + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[660]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", + RowBox[{"MTD", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "]"}], "===", + RowBox[{"MetricTensor", "[", + RowBox[{"\[Mu]", ",", "\[Nu]", ",", + RowBox[{"Dimension", "\[Rule]", "D"}]}], "]"}]}]], "Input", + CellLabel->"In[661]:="], + +Cell[BoxData[ + FormBox["True", TraditionalForm]], "Output", + CellLabel->"Out[661]="] }, Open ]] }, Open ]], @@ -424,7 +436,7 @@ Cell[BoxData[ InterpretationBox[Cell["XXXX", "ExampleSubsection"], $Line = 0; Null]], "ExampleSubsection", CellID->1295379749] -}, Closed]], +}, Open ]], Cell[BoxData[ InterpretationBox[Cell["Applications", "ExampleSection"], @@ -452,13 +464,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{938, 1002}, +WindowMargins->{{851, Automatic}, {Automatic, 37}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Momentum.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Momentum.nb index a8b08ba58..000647a30 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Momentum.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Momentum.nb @@ -182,9 +182,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/MomentumExpand", ButtonNote->"MomentumExpand"], "." -}], "Text", - CellTags->"Momentum", - CellID->1626096776] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -211,16 +209,14 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["This is a four dimensional momentum.", "Text", - CellTags->"Momentum", - CellID->44749889], +Cell["This is a 4-dimensional momentum.", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}]], "Input", CellTags->"Momentum", - CellLabel->"In[1]:=", + CellLabel->"In[44]:=", CellID->600679238], Cell[BoxData[ @@ -229,16 +225,13 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm]], "Output", CellTags->"Momentum", - CellLabel->"Out[1]=", - CellID->798967831] + CellLabel->"Out[44]="] }, Open ]], Cell["\<\ As an optional second argument the dimension must be specified if it is \ different from 4.\ -\>", "Text", - CellTags->"Momentum", - CellID->799788808], +\>", "Notes"], Cell[CellGroupData[{ @@ -246,46 +239,39 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "D"}], "]"}]], "Input", CellTags->"Momentum", - CellLabel->"In[2]:=", + CellLabel->"In[45]:=", CellID->298033535], Cell[BoxData[ FormBox["p", TraditionalForm]], "Output", CellTags->"Momentum", - CellLabel->"Out[2]=", - CellID->1920158684] + CellLabel->"Out[45]="] }, Open ]], -Cell["The dimension index is supressed in the output.", "Text", - CellTags->"Momentum", - CellID->179507545], +Cell["The dimension index is supressed in the output.", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"Momentum", "[", - RowBox[{"p", ",", "d"}], "]"}], "//", "StandardForm"}]], "Input", + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "d"}], "]"}]], "Input", CellTags->"Momentum", - CellLabel->"In[3]:=", + CellLabel->"In[46]:=", CellID->22007276], Cell[BoxData[ - RowBox[{"Momentum", "[", - RowBox[{"p", ",", "d"}], "]"}]], "Output", + FormBox["p", TraditionalForm]], "Output", CellTags->"Momentum", - CellLabel->"Out[3]//StandardForm=", - CellID->60455233] + CellLabel->"Out[46]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a1", "=", - RowBox[{"Momentum", "[", - RowBox[{"-", "q"}], "]"}]}]], "Input", + RowBox[{"Momentum", "[", + RowBox[{"-", "q"}], "]"}]], "Input", CellTags->"Momentum", - CellLabel->"In[4]:=", + CellLabel->"In[47]:=", CellID->1076166182], Cell[BoxData[ @@ -295,37 +281,35 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"]}], TraditionalForm]], "Output", CellTags->"Momentum", - CellLabel->"Out[4]=", - CellID->1153531189] + CellLabel->"Out[47]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a1", "//", "StandardForm"}]], "Input", + RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"Momentum", - CellLabel->"In[5]:=", + CellLabel->"In[48]:=", CellID->1156784400], Cell[BoxData[ RowBox[{"-", RowBox[{"Momentum", "[", "q", "]"}]}]], "Output", CellTags->"Momentum", - CellLabel->"Out[5]//StandardForm=", - CellID->129102697] + CellLabel->"Out[48]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a2", " ", "=", " ", + RowBox[{" ", RowBox[{ RowBox[{"Momentum", "[", RowBox[{"p", "-", "q"}], "]"}], " ", "+", " ", RowBox[{"Momentum", "[", RowBox[{"2", "q"}], "]"}]}]}]], "Input", CellTags->"Momentum", - CellLabel->"In[6]:=", + CellLabel->"In[49]:=", CellID->1010535805], Cell[BoxData[ @@ -346,16 +330,15 @@ Cell[BoxData[ FormBox["q", TraditionalForm], "_"]}]}], TraditionalForm]], "Output", CellTags->"Momentum", - CellLabel->"Out[6]=", - CellID->1815470309] + CellLabel->"Out[49]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a2", "//", "StandardForm"}]], "Input", + RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"Momentum", - CellLabel->"In[7]:=", + CellLabel->"In[50]:=", CellID->856207433], Cell[BoxData[ @@ -365,17 +348,16 @@ Cell[BoxData[ RowBox[{"2", " ", RowBox[{"Momentum", "[", "q", "]"}]}]}]], "Output", CellTags->"Momentum", - CellLabel->"Out[7]//StandardForm=", - CellID->1334247030] + CellLabel->"Out[50]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"a2", "//", "MomentumExpand"}], "//", "StandardForm"}]], "Input", + RowBox[{"%%", "//", "MomentumExpand"}], "//", "StandardForm"}]], "Input", CellTags->"Momentum", - CellLabel->"In[8]:=", + CellLabel->"In[51]:=", CellID->265634009], Cell[BoxData[ @@ -383,25 +365,23 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], "+", RowBox[{"Momentum", "[", "q", "]"}]}]], "Output", CellTags->"Momentum", - CellLabel->"Out[8]//StandardForm=", - CellID->748631793] + CellLabel->"Out[51]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"a2", "//", "MomentumCombine"}], "//", "StandardForm"}]], "Input", + RowBox[{"%%%", "//", "MomentumCombine"}], "//", "StandardForm"}]], "Input", CellTags->"Momentum", - CellLabel->"In[9]:=", + CellLabel->"In[52]:=", CellID->168866988], Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", "+", "q"}], "]"}]], "Output", CellTags->"Momentum", - CellLabel->"Out[9]//StandardForm=", - CellID->2082587543] + CellLabel->"Out[52]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -413,23 +393,15 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], ",", "d"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"Momentum", - CellLabel->"In[10]:=", + CellLabel->"In[53]:=", CellID->1679956191], Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "d"}], "]"}]], "Output", CellTags->"Momentum", - CellLabel->"Out[10]//StandardForm=", - CellID->932042446] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"a1", ",", "a2"}], "]"}]], "Input", - CellTags->"Momentum", - CellLabel->"In[11]:=", - CellID->919568834] + CellLabel->"Out[53]//StandardForm="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -493,12 +465,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{667, Automatic}, {Automatic, 33}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumCombine.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumCombine.nb index 4e2c997cb..eebd158c2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumCombine.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumCombine.nb @@ -124,8 +124,27 @@ MomentumCombine combines also Pair`s." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "MomentumCombine", "]"}]], "Input", + CellTags->"MomentumCombine", + CellLabel->"In[2]:=", + CellID->1545747738], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"LeafCount", "\[Rule]", "1"}], ",", + RowBox[{"Pair", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", + + CellTags->"MomentumCombine", + CellLabel->"Out[2]=", + CellID->1656307801] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -161,7 +180,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["ExpandScalarProduct", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/ExpandScalarProduct", @@ -176,15 +194,8 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/MomentumExpand", ButtonNote->"MomentumExpand"], - ", ", - ButtonBox["MomentumCombine2", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/MomentumCombine2", - ButtonNote->"MomentumCombine2"], "." -}], "Text", - CellTags->"MomentumCombine", - CellID->2131461260] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -213,23 +224,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "MomentumCombine", "]"}]], "Input", - CellTags->"MomentumCombine", - CellLabel->"In[1]:=", - CellID->1545747738], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"LeafCount", "\[Rule]", "1"}], "}"}], TraditionalForm]], "Output", - CellTags->"MomentumCombine", - CellLabel->"Out[1]=", - CellID->1201680776] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{ RowBox[{ @@ -239,7 +233,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "q", "]"}]}]}], " ", "//", " ", "MomentumCombine"}], " ", "//", " ", "StandardForm"}]], "Input", CellTags->"MomentumCombine", - CellLabel->"In[2]:=", + CellLabel->"In[5]:=", CellID->607844623], Cell[BoxData[ @@ -247,71 +241,60 @@ Cell[BoxData[ RowBox[{"p", "-", RowBox[{"2", " ", "q"}]}], "]"}]], "Output", CellTags->"MomentumCombine", - CellLabel->"Out[2]//StandardForm=", - CellID->683220670] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{ + RowBox[{ + RowBox[{"FV", "[", + RowBox[{"p", ",", "\[Mu]"}], "]"}], " ", "+", " ", + RowBox[{"2", " ", RowBox[{"FV", "[", - RowBox[{"p", ",", "\[Mu]"}], "]"}], " ", "+", " ", - RowBox[{"2", " ", - RowBox[{"FV", "[", - RowBox[{"q", ",", "\[Mu]"}], "]"}]}], " "}]}]], "Input", + RowBox[{"q", ",", "\[Mu]"}], "]"}]}], " "}]], "Input", CellTags->"MomentumCombine", - CellLabel->"In[3]:=", + CellLabel->"In[14]:=", CellID->199069763], Cell[BoxData[ FormBox[ RowBox[{ FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], + TraditionalForm], "+", + RowBox[{"2", " ", FormBox[ SuperscriptBox[ FormBox[ OverscriptBox[ - FormBox["p", + FormBox["q", TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - TraditionalForm], - TraditionalForm], "+", - RowBox[{"2", " ", - FormBox[ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->"MomentumCombine", - CellLabel->"Out[3]=", - CellID->1701893288] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"MomentumCombine", "[", "t1", "]"}]], "Input", + RowBox[{"MomentumCombine", "[", "%", "]"}]], "Input", CellTags->"MomentumCombine", - CellLabel->"In[4]:=", + CellLabel->"In[15]:=", CellID->316549312], Cell[BoxData[ @@ -331,24 +314,19 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], ")"}], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"MomentumCombine", - CellLabel->"Out[4]=", - CellID->1410863957] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"MomentumCombine", "[", "t1", "]"}], "//", - "StandardForm"}]], "Input", + RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"MomentumCombine", - CellLabel->"In[5]:=", + CellLabel->"In[16]:=", CellID->1834428785], Cell[BoxData[ @@ -359,55 +337,43 @@ Cell[BoxData[ RowBox[{"p", "+", RowBox[{"2", " ", "q"}]}], "]"}]}], "]"}]], "Output", CellTags->"MomentumCombine", - CellLabel->"Out[5]//StandardForm=", - CellID->1690546936] + CellLabel->"Out[16]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"MomentumCombine", "[", "t1", "]"}], "//", - "ExpandScalarProduct"}]], "Input", + RowBox[{"%%", "//", "ExpandScalarProduct"}]], "Input", CellTags->"MomentumCombine", - CellLabel->"In[6]:=", + CellLabel->"In[17]:=", CellID->1175875424], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], "+", + RowBox[{"2", " ", SuperscriptBox[ FormBox[ OverscriptBox[ - FormBox["p", + FormBox["q", TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], - TraditionalForm]], - TraditionalForm], "+", - RowBox[{"2", " ", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}]}], TraditionalForm]], "Output", + TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"MomentumCombine", - CellLabel->"Out[6]=", - CellID->130248016] + CellLabel->"Out[17]="] }, Open ]], Cell[CellGroupData[{ @@ -415,7 +381,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"StandardForm", "[", "%", "]"}]], "Input", CellTags->"MomentumCombine", - CellLabel->"In[7]:=", + CellLabel->"In[18]:=", CellID->1928655829], Cell[BoxData[ @@ -430,15 +396,84 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]}]}]], "Output", CellTags->"MomentumCombine", - CellLabel->"Out[7]//StandardForm=", - CellID->547997503] + CellLabel->"Out[18]//StandardForm="] }, Open ]], +Cell[CellGroupData[{ + Cell[BoxData[ - RowBox[{"Clear", "[", "t1", "]"}]], "Input", - CellTags->"MomentumCombine", - CellLabel->"In[8]:=", - CellID->1041568760] + RowBox[{ + RowBox[{"3", " ", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", + RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}], "+", + RowBox[{"2", " ", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", + RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]}]}]], "Input", + CellLabel->"In[11]:=", + CellID->986758311], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"3", " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], "+", + RowBox[{"2", " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}]}], TraditionalForm]], "Output", + CellLabel->"Out[11]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"MomentumCombine", "[", "%", "]"}]], "Input", + CellLabel->"In[12]:=", + CellID->160099516], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + RowBox[{"(", + FormBox[ + FormBox[ + RowBox[{ + RowBox[{"3", " ", + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"]}], "+", + RowBox[{"2", " ", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}]}], + TraditionalForm], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[12]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -502,12 +537,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{Automatic, 514}, {113, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumCombine2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumCombine2.nb deleted file mode 100644 index b0518d397..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumCombine2.nb +++ /dev/null @@ -1,363 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/MomentumCombine2", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["MomentumCombine2", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData[ - RowBox[{"MomentumCombine2", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - " is the inverse operation to MomentumExpand and ExpandScalarProduct. \ -MomentumCombine2 combines also FourVectors." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - "See also: ", - ButtonBox["MomentumCombine", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/MomentumCombine", - ButtonNote->"MomentumCombine"], - ", ", - ButtonBox["MomentumExpand", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/MomentumExpand", - ButtonNote->"MomentumExpand"], - ", ", - ButtonBox["ExpandScalarProduct", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/ExpandScalarProduct", - ButtonNote->"ExpandScalarProduct"], - ", ", - ButtonBox["FourVector", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], - "." -}], "Text", - CellTags->"MomentumCombine2", - CellID->815593520] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{"3", " ", - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", - RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}], "+", - RowBox[{"2", " ", - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", - RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]}]}]], "Input", - CellTags->"MomentumCombine2", - CellLabel->"In[1]:=", - CellID->1495417826], - -Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{"3", " ", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "+", - RowBox[{"2", " ", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}]}], TraditionalForm]], "Output", - CellTags->"MomentumCombine2", - CellLabel->"Out[1]=", - CellID->625977405] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{"MomentumCombine2", "[", "%", "]"}], "//", - "StandardForm"}]], "Input", - CellTags->"MomentumCombine2", - CellLabel->"In[2]:=", - CellID->1280124853], - -Cell[BoxData[ - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", - RowBox[{"Momentum", "[", - RowBox[{ - RowBox[{"3", " ", "p"}], "+", - RowBox[{"2", " ", "q"}]}], "]"}]}], "]"}]], "Output", - CellTags->"MomentumCombine2", - CellLabel->"Out[2]//StandardForm=", - CellID->1646133388] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumExpand.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumExpand.nb index cfb0453f7..4821c16d1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumExpand.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/MomentumExpand.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/MomentumCombine", ButtonNote->"MomentumCombine"], "." -}], "Text", - CellTags->"MomentumExpand", - CellID->669888532] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -207,7 +205,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", "+", "q"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"MomentumExpand", - CellLabel->"In[1]:=", + CellLabel->"In[54]:=", CellID->2119019213], Cell[BoxData[ @@ -215,8 +213,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], "+", RowBox[{"Momentum", "[", "q", "]"}]}]], "Output", CellTags->"MomentumExpand", - CellLabel->"Out[1]//StandardForm=", - CellID->1133313171] + CellLabel->"Out[54]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -226,7 +223,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"p", "+", "q"}], ",", "r"}], "]"}]], "Input", CellTags->"MomentumExpand", - CellLabel->"In[2]:=", + CellLabel->"In[55]:=", CellID->840853851], Cell[BoxData[ @@ -235,13 +232,15 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -253,8 +252,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"MomentumExpand", - CellLabel->"Out[2]=", - CellID->27880999] + CellLabel->"Out[55]="] }, Open ]], Cell[CellGroupData[{ @@ -262,7 +260,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"MomentumExpand", - CellLabel->"In[3]:=", + CellLabel->"In[56]:=", CellID->422127778], Cell[BoxData[ @@ -272,8 +270,7 @@ Cell[BoxData[ RowBox[{"p", "+", "q"}], "]"}], ",", RowBox[{"Momentum", "[", "r", "]"}]}], "]"}]], "Output", CellTags->"MomentumExpand", - CellLabel->"Out[3]//StandardForm=", - CellID->581832414] + CellLabel->"Out[56]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -284,7 +281,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"p", "+", "q"}], ",", "r"}], "]"}], "]"}]], "Input", CellTags->"MomentumExpand", - CellLabel->"In[4]:=", + CellLabel->"In[57]:=", CellID->1994358378], Cell[BoxData[ @@ -293,13 +290,15 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -311,8 +310,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"MomentumExpand", - CellLabel->"Out[4]=", - CellID->872056569] + CellLabel->"Out[57]="] }, Open ]], Cell[CellGroupData[{ @@ -320,7 +318,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"MomentumExpand", - CellLabel->"In[5]:=", + CellLabel->"In[58]:=", CellID->1059717092], Cell[BoxData[ @@ -331,8 +329,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "q", "]"}]}], ",", RowBox[{"Momentum", "[", "r", "]"}]}], "]"}]], "Output", CellTags->"MomentumExpand", - CellLabel->"Out[5]//StandardForm=", - CellID->1334904373] + CellLabel->"Out[58]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -344,7 +341,7 @@ Cell[BoxData[ RowBox[{"p", "+", "q"}], ",", RowBox[{"r", "-", "p"}]}], "]"}], "]"}]], "Input", CellTags->"MomentumExpand", - CellLabel->"In[6]:=", + CellLabel->"In[59]:=", CellID->242711247], Cell[BoxData[ @@ -353,13 +350,15 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -368,19 +367,20 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["r", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["r", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"MomentumExpand", - CellLabel->"Out[6]=", - CellID->549274117] + CellLabel->"Out[59]="] }, Open ]], Cell[CellGroupData[{ @@ -388,7 +388,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"MomentumExpand", - CellLabel->"In[7]:=", + CellLabel->"In[60]:=", CellID->277317176], Cell[BoxData[ @@ -402,70 +402,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}]}], "+", RowBox[{"Momentum", "[", "r", "]"}]}]}], "]"}]], "Output", CellTags->"MomentumExpand", - CellLabel->"Out[7]//StandardForm=", - CellID->1535384153] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Calc", "[", "%", "]"}]], "Input", - CellTags->"MomentumExpand", - CellLabel->"In[8]:=", - CellID->924306475], - -Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{"-", - RowBox[{ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm]}]}], "+", - RowBox[{ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["r", - TraditionalForm], "_"], - TraditionalForm]}], "-", - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], "2"], "+", - RowBox[{ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - OverscriptBox[ - FormBox["r", - TraditionalForm], "_"], - TraditionalForm]}]}], TraditionalForm]], "Output", - CellTags->"MomentumExpand", - CellLabel->"Out[8]=", - CellID->857785691] + CellLabel->"Out[60]//StandardForm="] }, Open ]] }, Open ]], @@ -530,12 +467,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{407, Automatic}, {Automatic, 65}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git 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85c47ed24..41f48b1b5 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/NTerms.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/NTerms.nb @@ -200,8 +200,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["2", TraditionalForm]], "Output", CellTags->"NTerms", - CellLabel->"Out[1]=", - CellID->306409458] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -216,8 +215,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"NTerms", - CellLabel->"Out[2]=", - CellID->730102974] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -231,8 +229,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"NTerms", - CellLabel->"Out[3]=", - CellID->313925848] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -246,8 +243,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"NTerms", - CellLabel->"Out[4]=", - CellID->2111597694] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], 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ButtonNote->"DataType"], "." -}], "Text", - CellTags->"NegativeInteger", - CellID->1863453208] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{914, Automatic}, {Automatic, 66}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Nf.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Nf.nb index ef38539bf..a93501416 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Nf.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Nf.nb @@ -184,9 +184,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SplittingFunction", ButtonNote->"SplittingFunction"], "." -}], "Text", - CellTags->"Nf", - CellID->822571614] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -272,12 +270,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Nielsen.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Nielsen.nb index 92ace6c55..34cde1cb6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Nielsen.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Nielsen.nb @@ -124,8 +124,21 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Nielsen", "]"}]], "Input", + CellTags->"Nielsen", + CellLabel->"In[5]:=", + CellID->393617069], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"PolyLog", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output", + CellTags->"Nielsen", + CellLabel->"Out[5]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -166,9 +179,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SimplifyPolyLog", ButtonNote->"SimplifyPolyLog"], "." -}], "Text", - CellTags->"Nielsen", - CellID->1377301931] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -195,34 +206,13 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Examples", "Subsubsection", - CellTags->"Nielsen", - CellID->108447826], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "Nielsen", "]"}]], "Input", - CellTags->"Nielsen", - CellLabel->"In[1]:=", - CellID->393617069], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"PolyLog", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output", - CellTags->"Nielsen", - CellLabel->"Out[1]=", - CellID->61376182] -}, Open ]], - Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Nielsen", "[", RowBox[{"1", ",", "2", ",", "x"}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[2]:=", + CellLabel->"In[6]:=", CellID->1266057514], Cell[BoxData[ @@ -237,16 +227,13 @@ Cell[BoxData[ FormBox["x", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"Nielsen", - CellLabel->"Out[2]=", - CellID->1282400495] + CellLabel->"Out[6]="] }, Open ]], Cell["\<\ Numerical evaluation is done via N[Nielsen[n_,p_,x_]] := \ (-1)^(n+p-1)/(n-1)!/p! NIntegrate[Log[1-x t]^p Log[t]^(n-1)/t,{t,0,1}];\ -\>", "Text", - CellTags->"Nielsen", - CellID->826105795], +\>", "Notes"], Cell[CellGroupData[{ @@ -255,19 +242,16 @@ Cell[BoxData[ RowBox[{"Nielsen", "[", RowBox[{"1", ",", "2", ",", ".45"}], "]"}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[3]:=", + CellLabel->"In[7]:=", CellID->1539557957], Cell[BoxData[ FormBox["0.07287162612104658`", TraditionalForm]], "Output", CellTags->"Nielsen", - CellLabel->"Out[3]=", - CellID->233293253] + CellLabel->"Out[7]="] }, Open ]], -Cell["Some special values are built in.", "Text", - CellTags->"Nielsen", - CellID->76431912], +Cell["Some special values are built in.", "Notes"], Cell[CellGroupData[{ @@ -285,7 +269,7 @@ Cell[BoxData[ RowBox[{"Nielsen", "[", RowBox[{"1", ",", "2", ",", "1"}], "]"}]}], "}"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[4]:=", + CellLabel->"In[8]:=", CellID->1900952317], Cell[BoxData[ @@ -301,8 +285,7 @@ Cell[BoxData[ TemplateBox[{"3"}, "Zeta"]}], "}"}], TraditionalForm]], "Output", CellTags->"Nielsen", - CellLabel->"Out[4]=", - CellID->488179787] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -312,7 +295,7 @@ Cell[BoxData[ RowBox[{"1", ",", "2", ",", "x", ",", RowBox[{"PolyLog", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[5]:=", + CellLabel->"In[9]:=", CellID->1917228474], Cell[BoxData[ @@ -335,8 +318,7 @@ Cell[BoxData[ TemplateBox[{"3"}, "Zeta"]}], TraditionalForm]], "Output", CellTags->"Nielsen", - CellLabel->"Out[5]=", - CellID->552589005] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -346,7 +328,7 @@ Cell[BoxData[ RowBox[{"1", ",", "3", ",", "x", ",", RowBox[{"PolyLog", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[6]:=", + CellLabel->"In[10]:=", CellID->2065085174], Cell[BoxData[ @@ -376,8 +358,7 @@ Cell[BoxData[ FractionBox[ SuperscriptBox["\[Pi]", "4"], "90"]}], TraditionalForm]], "Output", CellTags->"Nielsen", - CellLabel->"Out[6]=", - CellID->944860275] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -387,7 +368,7 @@ Cell[BoxData[ RowBox[{"3", ",", "1", ",", "x", ",", RowBox[{"PolyLog", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"Nielsen", - CellLabel->"In[7]:=", + CellLabel->"In[11]:=", CellID->1212916567], Cell[BoxData[ @@ -395,8 +376,7 @@ Cell[BoxData[ TemplateBox[{"4","x"}, "PolyLog"], TraditionalForm]], "Output", CellTags->"Nielsen", - CellLabel->"Out[7]=", - CellID->1203520778] + CellLabel->"Out[11]="] }, Open ]] }, Open ]], @@ -461,12 +441,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{573, Automatic}, {Automatic, 64}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommFreeQ.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommFreeQ.nb index 1a135910f..cc513bc54 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommFreeQ.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommFreeQ.nb @@ -182,9 +182,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNTrace", ButtonNote->"SUNTrace"], "." -}], "Text", - CellTags->"NonCommFreeQ", - CellID->177809745] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -270,12 +268,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{771, Automatic}, {Automatic, 146}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommQ.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommQ.nb index c5ea7d798..a0e3bc4a0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommQ.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommQ.nb @@ -181,9 +181,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNTrace", ButtonNote->"SUNTrace"], "." -}], "Text", - CellTags->"NonCommQ", - CellID->303191409] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -269,12 +267,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{503, Automatic}, {Automatic, 65}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommutative.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommutative.nb index 11ee55a96..b5f83901d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommutative.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/NonCommutative.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DeclareNonCommutative", ButtonNote->"DeclareNonCommutative"], "." -}], "Text", - CellTags->"NonCommutative", - CellID->776574018] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/NumericQ1.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/NumericQ1.nb index 76a74000a..ba27c2403 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/NumericQ1.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/NumericQ1.nb @@ -199,14 +199,13 @@ Cell[BoxData[ RowBox[{"Log", "[", "b", "]"}], "+", SuperscriptBox["c", "2"]}], "]"}]], "Input", CellTags->"NumericQ1", - CellLabel->"In[1]:=", + CellLabel->"In[12]:=", CellID->294886798], Cell[BoxData[ FormBox["False", TraditionalForm]], "Output", CellTags->"NumericQ1", - CellLabel->"Out[1]=", - CellID->583048133] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -220,14 +219,13 @@ Cell[BoxData[ SuperscriptBox["c", "2"]}], ",", RowBox[{"{", "}"}]}], "]"}]], "Input", CellTags->"NumericQ1", - CellLabel->"In[2]:=", + CellLabel->"In[13]:=", CellID->792660906], Cell[BoxData[ FormBox["False", TraditionalForm]], "Output", CellTags->"NumericQ1", - CellLabel->"Out[2]=", - CellID->1595713370] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -242,14 +240,13 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}]}], "]"}]], "Input", CellTags->"NumericQ1", - CellLabel->"In[3]:=", + CellLabel->"In[14]:=", CellID->103103501], Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", CellTags->"NumericQ1", - CellLabel->"Out[3]=", - CellID->397430963] + CellLabel->"Out[14]="] }, Open ]] }, Open ]], @@ -314,12 +311,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{503, Automatic}, {Automatic, 81}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/NumericalFactor.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/NumericalFactor.nb index d69cd0d9c..327b2b1b3 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/NumericalFactor.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/NumericalFactor.nb @@ -246,12 +246,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE.nb index ff0299f7a..3a787f3ce 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE.nb @@ -117,13 +117,13 @@ Cell["OPE", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["OPE"], "InlineFormula"], - " \[LineSeparator]", - "is a convenience variable to separate OPE insertions.\nOPE is also an \ -option of several input functions like GluonPropagator." + " \[LineSeparator]is a convenience variable to separate OPE insertions." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +OPE is also an option of several input functions like GluonPropagator.\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPE1Loop", ButtonNote->"OPE1Loop"], "." -}], "Text", - CellTags->"OPE", - CellID->1798984343] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE1Loop.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE1Loop.nb index 8c00326aa..f8d41e93d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE1Loop.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE1Loop.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPESum", ButtonNote->"OPESum"], "." -}], "Text", - CellTags->"OPE1Loop", - CellID->1134342572] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,9 +255,11 @@ WindowSize->{700, 770}, WindowMargins->{{-10, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE2TID.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE2TID.nb index 4ab9323b6..3b47636d6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE2TID.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPE2TID.nb @@ -117,26 +117,34 @@ Cell["OPE2TID", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"OPE2TID", "[", - RowBox[{"exp", ",", " ", "k1", ",", " ", "k2", ",", " ", "p"}], "]"}], - ".", " ", "The"}], " ", "setting", " ", "of", " ", "the", " ", "option", - " ", "EpsContract", " ", "determines", " ", "the", " ", "dimension", - " ", "in", " ", "which", " ", "the", " ", "Levi"}], "-", - RowBox[{"Civita", " ", "tensors", " ", "are", " ", - RowBox[{"contracted", "."}]}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "Part[{\"OPE2TID[exp, k1, k2, p]. The setting of the option EpsContract \ -determines the dimension in which the Levi-Civita tensors are contracted.\"}, \ -2]" + RowBox[{"OPE2TID", "[", + RowBox[{"exp", ",", " ", "k1", ",", " ", "k2", ",", " ", "p"}], "]"}]], + "InlineFormula"], + "\n\tdoes a special tensor integral decomposition of exp." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "OPE2TID", "]"}]], "Input", + CellTags->"OPE2TID", + CellLabel->"In[1]:=", + CellID->1639885788], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Uncontract", "\[Rule]", "False"}], ",", + RowBox[{"Contract", "\[Rule]", "True"}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"EpsContract", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"OPE2TID", + CellLabel->"Out[1]=", + CellID->1228598425] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -177,9 +185,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPESum", ButtonNote->"OPESum"], "." -}], "Text", - CellTags->"OPE2TID", - CellID->2032594420] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -191,8 +197,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -208,29 +212,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "OPE2TID", "]"}]], "Input", - CellTags->"OPE2TID", - CellLabel->"In[1]:=", - CellID->1639885788], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Uncontract", "\[Rule]", "False"}], ",", - RowBox[{"Contract", "\[Rule]", "True"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"EpsContract", "\[Rule]", "False"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"OPE2TID", - CellLabel->"Out[1]=", - CellID->1228598425] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -290,12 +271,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEDelta.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEDelta.nb index 40c9d3f33..f88886bf1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEDelta.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEDelta.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Twist2QuarkOperator", ButtonNote->"Twist2QuarkOperator"], "." -}], "Text", - CellTags->"OPEDelta", - CellID->1239185621] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -197,10 +195,10 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"OPEDelta", ",", "\[Mu]"}], "]"}]], "Input", CellTags->"OPEDelta", - CellLabel->"In[1]:=", + CellLabel->"In[29]:=", CellID->82705691], Cell[BoxData[ @@ -211,14 +209,11 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"OPEDelta", - CellLabel->"Out[1]=", - CellID->568278769] + CellLabel->"Out[29]="] }, Open ]], Cell[CellGroupData[{ @@ -227,19 +222,13 @@ Cell[BoxData[ RowBox[{"Contract", "[", RowBox[{"%", " ", "%"}], "]"}]], "Input", CellTags->"OPEDelta", - CellLabel->"In[2]:=", + CellLabel->"In[30]:=", CellID->1662840966], Cell[BoxData[ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], "2"], TraditionalForm]], "Output", + FormBox["0", TraditionalForm]], "Output", CellTags->"OPEDelta", - CellLabel->"Out[2]=", - CellID->1005702488] + CellLabel->"Out[30]="] }, Open ]], Cell[CellGroupData[{ @@ -248,19 +237,13 @@ Cell[BoxData[ RowBox[{"SP", "[", RowBox[{"OPEDelta", ",", "OPEDelta"}], "]"}]], "Input", CellTags->"OPEDelta", - CellLabel->"In[3]:=", + CellLabel->"In[31]:=", CellID->766618795], Cell[BoxData[ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], "2"], TraditionalForm]], "Output", + FormBox["0", TraditionalForm]], "Output", CellTags->"OPEDelta", - CellLabel->"Out[3]=", - CellID->1002463011] + CellLabel->"Out[31]="] }, Open ]] }, Open ]], @@ -325,12 +308,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEInt.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEInt.nb index 0d562fbb1..a32d9c049 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEInt.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEInt.nb @@ -117,26 +117,10 @@ Cell["OPEInt", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"OPEInt", "[", - RowBox[{"expr", ",", " ", "q", ",", " ", "p", ",", " ", "x"}], "]"}], - ".", " ", "The"}], " ", "dimension", " ", "is", " ", "changed", " ", - "to", " ", "the", " ", "one", " ", "indicated", " ", "by", " ", "the", - " ", "option", " ", - RowBox[{"Dimension", ".", " ", "The"}], " ", "setting", " ", "of", " ", - "the", " ", "option", " ", "EpsContract", " ", "determines", " ", "the", - " ", "dimension", " ", "in", " ", "which", " ", "the", " ", "Levi"}], - "-", - RowBox[{"Civita", " ", "tensors", " ", "are", " ", - RowBox[{"contracted", "."}]}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "Part[{\"OPEInt[expr, q, p, x]. The dimension is changed to the one \ -indicated by the option Dimension. The setting of the option EpsContract \ -determines the dimension in which the Levi-Civita tensors are \ -contracted.\"}, 2]" + RowBox[{"OPEInt", "[", + RowBox[{"expr", ",", " ", "q", ",", " ", "p", ",", " ", "x"}], "]"}]], + "InlineFormula"], + " \[LineSeparator]calculates 1-loop OPE-type self energies." }], "Usage", CellID->982511436], @@ -182,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI", ButtonNote->"RHI"], "." -}], "Text", - CellTags->"OPEInt", - CellID->1872757445] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -196,8 +178,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -211,12 +191,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"OPEInt", - CellLabel->"In[1]:=", - CellID->1228083412] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -278,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{315, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEIntegrate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEIntegrate.nb index 83c1935f1..e6c8274a1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEIntegrate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEIntegrate.nb @@ -117,31 +117,38 @@ Cell["OPEIntegrate", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"OPEIntegrate", "[", - RowBox[{"expr", ",", " ", "q", ",", " ", "x"}], "]"}], ".", " ", - "The"}], " ", "dimension", " ", "is", " ", "changed", " ", "to", " ", - "the", " ", "one", " ", "indicated", " ", "by", " ", "the", " ", - "option", " ", - RowBox[{"Dimension", ".", " ", "The"}], " ", "setting", " ", "of", " ", - "the", " ", "option", " ", "EpsContract", " ", "determines", " ", "the", - " ", "dimension", " ", "in", " ", "which", " ", "the", " ", "Levi"}], - "-", - RowBox[{"Civita", " ", "tensors", " ", "are", " ", - RowBox[{"contracted", "."}]}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "Part[{\"OPEIntegrate[expr, q, x]. The dimension is changed to the one \ -indicated by the option Dimension. The setting of the option EpsContract \ -determines the dimension in which the Levi-Civita tensors are \ -contracted.\"}, 2]" + RowBox[{"OPEIntegrate", "[", + RowBox[{"expr", ",", " ", "q", ",", " ", "x"}], "]"}]], "InlineFormula"], + " \[LineSeparator]calculates a one-loop OPE-type integral." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "OPEIntegrate", "]"}]], "Input", + CellLabel->"In[18]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Divideout", "\[Rule]", "1"}], ",", + RowBox[{"EpsContract", "\[Rule]", "4"}], ",", + RowBox[{"EpsilonOrder", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "True"}], ",", + RowBox[{"Factorout", "\[Rule]", "1"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", + RowBox[{"D", "\[Rule]", + RowBox[{ + TagBox["\[CurlyEpsilon]", + TraditionalForm], "+", "4"}]}], "}"}]}], ",", + RowBox[{"OPEIntegrateDelta", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[18]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -182,9 +189,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI", ButtonNote->"RHI"], "." -}], "Text", - CellTags->"OPEIntegrate", - CellID->1317066831] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -196,8 +201,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -211,12 +214,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"OPEIntegrate", - CellLabel->"In[1]:=", - CellID->614498431] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -278,12 +275,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{890, Automatic}, {Automatic, 226}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEIntegrateDelta.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEIntegrateDelta.nb index 90405483f..3ffaa38bf 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEIntegrateDelta.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEIntegrateDelta.nb @@ -119,18 +119,18 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"OPEIntegrateDelta", "[", RowBox[{"expr", ",", " ", "x", ",", " ", "m"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "introduces the \[Delta](1-x) (DeltaFunction[1-x]). The ", + " \[LineSeparator]introduces the \[Delta](1-x) (DeltaFunction[1-x]). The ", StyleBox["Mathematica", FontSlant->"Italic"], " Integrate function is called and each integration (from 0 to 1) is \ -recorded for reference (and bug-checking) in the list $MIntegrate. \nNotice \ -that the dimension specified by the option should also be the dimension used \ -in expr. It is replaced in OPEIntegrateDelta by (4+Epsilon)." +recorded for reference (and bug-checking) in the list $MIntegrate." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +Notice that the dimension specified by the option should also be the \ +dimension used in expr. It is replaced in OPEIntegrateDelta by (4+Epsilon).\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -172,9 +172,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI", ButtonNote->"RHI"], "." -}], "Text", - CellTags->"OPEIntegrateDelta", - CellID->2121617043] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -186,8 +184,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -201,12 +197,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"OPEIntegrateDelta", - CellLabel->"In[1]:=", - CellID->1585063282] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -268,12 +258,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{568, Automatic}, {Automatic, 187}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESum.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESum.nb index 8b9c2d22a..c013b358e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESum.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESum.nb @@ -174,9 +174,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPESumSimplify", ButtonNote->"OPESumSimplify"], "." -}], "Text", - CellTags->"OPESum", - CellID->1162371524] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -206,21 +204,20 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{"OPESum", "[", + RowBox[{"OPESum", "[", + RowBox[{ RowBox[{ RowBox[{ - RowBox[{ - RowBox[{"SO", "[", "p", "]"}], "^", "OPEi"}], - RowBox[{ - RowBox[{"SO", "[", "k", "]"}], "^", - RowBox[{"(", - RowBox[{"OPEm", "-", "OPEi", "-", "3"}], ")"}]}]}], ",", - RowBox[{"{", - RowBox[{"OPEi", ",", "0", ",", - RowBox[{"OPEm", "-", "3"}]}], "}"}]}], "]"}]}]], "Input", + RowBox[{"SO", "[", "p", "]"}], "^", "OPEi"}], + RowBox[{ + RowBox[{"SO", "[", "k", "]"}], "^", + RowBox[{"(", + RowBox[{"OPEm", "-", "OPEi", "-", "3"}], ")"}]}]}], ",", + RowBox[{"{", + RowBox[{"OPEi", ",", "0", ",", + RowBox[{"OPEm", "-", "3"}]}], "}"}]}], "]"}]], "Input", CellTags->"OPESum", - CellLabel->"In[1]:=", + CellLabel->"In[19]:=", CellID->448625968], Cell[BoxData[ @@ -254,16 +251,15 @@ Cell[BoxData[ TraditionalForm]}], ")"}], "i"]}]}], HoldForm], TraditionalForm]], "Output", CellTags->"OPESum", - CellLabel->"Out[1]=", - CellID->1323502805] + CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"OPESumExplicit", "[", "t1", "]"}]], "Input", + RowBox[{"OPESumExplicit", "[", "%", "]"}]], "Input", CellTags->"OPESum", - CellLabel->"In[2]:=", + CellLabel->"In[20]:=", CellID->575960405], Cell[BoxData[ @@ -326,14 +322,13 @@ Cell[BoxData[ FormBox["p", TraditionalForm]}]}]]}], TraditionalForm]], "Output", CellTags->"OPESum", - CellLabel->"Out[2]=", - CellID->988725801] + CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", " ", "=", " ", + RowBox[{" ", RowBox[{"OPESum", "[", RowBox[{ RowBox[{ @@ -350,7 +345,7 @@ Cell[BoxData[ RowBox[{"j", ",", "0", ",", RowBox[{"m", "-", "4"}]}], "}"}]}], "]"}]}]], "Input", CellTags->"OPESum", - CellLabel->"In[3]:=", + CellLabel->"In[21]:=", CellID->934947616], Cell[BoxData[ @@ -380,16 +375,15 @@ Cell[BoxData[ RowBox[{"-", "j"}], "+", "m", "-", "4"}]]}], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"OPESum", - CellLabel->"Out[3]=", - CellID->1408007149] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"OPESumExplicit", "[", "t2", "]"}]], "Input", + RowBox[{"OPESumExplicit", "[", "%", "]"}]], "Input", CellTags->"OPESum", - CellLabel->"In[4]:=", + CellLabel->"In[22]:=", CellID->1712949576], Cell[BoxData[ @@ -458,17 +452,8 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"b", "-", "c"}], ")"}]}]]}], TraditionalForm]], "Output", CellTags->"OPESum", - CellLabel->"Out[4]=", - CellID->1163635134] -}, Open ]], - -Cell[BoxData[ - RowBox[{" ", - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2"}], "]"}]}]], "Input", - CellTags->"OPESum", - CellLabel->"In[5]:=", - CellID->790847648] + CellLabel->"Out[22]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -532,12 +517,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{315, Automatic}, {Automatic, 77}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESumExplicit.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESumExplicit.nb index 8f425d4ee..1752690f1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESumExplicit.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESumExplicit.nb @@ -123,8 +123,19 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "OPESumExplicit", "]"}]], "Input", + CellLabel->"In[28]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Assumptions", "\[Rule]", "True"}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[28]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -170,9 +181,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPESumSimplify", ButtonNote->"OPESumSimplify"], "." -}], "Text", - CellTags->"OPESumExplicit", - CellID->1999250698] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -202,19 +211,18 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{"OPESum", "[", + RowBox[{"OPESum", "[", + RowBox[{ RowBox[{ - RowBox[{ - RowBox[{"A", "^", "i"}], - RowBox[{"B", "^", - RowBox[{"(", - RowBox[{"m", "-", "i", "-", "3"}], ")"}]}]}], ",", - RowBox[{"{", - RowBox[{"i", ",", "0", ",", - RowBox[{"m", "-", "3"}]}], "}"}]}], "]"}]}]], "Input", + RowBox[{"A", "^", "i"}], + RowBox[{"B", "^", + RowBox[{"(", + RowBox[{"m", "-", "i", "-", "3"}], ")"}]}]}], ",", + RowBox[{"{", + RowBox[{"i", ",", "0", ",", + RowBox[{"m", "-", "3"}]}], "}"}]}], "]"}]], "Input", CellTags->"OPESumExplicit", - CellLabel->"In[1]:=", + CellLabel->"In[29]:=", CellID->448095633], Cell[BoxData[ @@ -232,16 +240,15 @@ Cell[BoxData[ RowBox[{"-", "3"}], "-", "i", "+", "m"}]]}]}], HoldForm], TraditionalForm]], "Output", CellTags->"OPESumExplicit", - CellLabel->"Out[1]=", - CellID->1524447392] + CellLabel->"Out[29]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"OPESumExplicit", "[", "t1", "]"}]], "Input", + RowBox[{"OPESumExplicit", "[", "%", "]"}]], "Input", CellTags->"OPESumExplicit", - CellLabel->"In[2]:=", + CellLabel->"In[30]:=", CellID->21429542], Cell[BoxData[ @@ -260,14 +267,13 @@ Cell[BoxData[ TraditionalForm], RowBox[{"A", "-", "B"}]]}], TraditionalForm]], "Output", CellTags->"OPESumExplicit", - CellLabel->"Out[2]=", - CellID->110967973] + CellLabel->"Out[30]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", " ", "=", " ", + RowBox[{" ", RowBox[{"OPESum", "[", RowBox[{ RowBox[{ @@ -284,7 +290,7 @@ Cell[BoxData[ RowBox[{"j", ",", "0", ",", RowBox[{"m", "-", "4"}]}], "}"}]}], "]"}]}]], "Input", CellTags->"OPESumExplicit", - CellLabel->"In[3]:=", + CellLabel->"In[32]:=", CellID->1082502911], Cell[BoxData[ @@ -314,16 +320,15 @@ Cell[BoxData[ RowBox[{"-", "j"}], "+", "m", "-", "4"}]]}], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"OPESumExplicit", - CellLabel->"Out[3]=", - CellID->643122567] + CellLabel->"Out[32]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"OPESumExplicit", "[", "t2", "]"}]], "Input", + RowBox[{"OPESumExplicit", "[", "%", "]"}]], "Input", CellTags->"OPESumExplicit", - CellLabel->"In[4]:=", + CellLabel->"In[33]:=", CellID->773320980], Cell[BoxData[ @@ -392,17 +397,8 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"b", "-", "c"}], ")"}]}]]}], TraditionalForm]], "Output", CellTags->"OPESumExplicit", - CellLabel->"Out[4]=", - CellID->1923019791] -}, Open ]], - -Cell[BoxData[ - RowBox[{ - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2"}], "]"}], ";"}]], "Input", - CellTags->"OPESumExplicit", - CellLabel->"In[5]:=", - CellID->363319919] + CellLabel->"Out[33]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -466,12 +462,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{769, Automatic}, {Automatic, 51}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESumSimplify.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESumSimplify.nb index d9adffe61..3eedd2764 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESumSimplify.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPESumSimplify.nb @@ -123,8 +123,19 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "OPESumSimplify", "]"}]], "Input", + CellLabel->"In[34]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Assumptions", "\[Rule]", "True"}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[34]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -170,9 +181,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPESumExplicit", ButtonNote->"OPESumExplicit"], "." -}], "Text", - CellTags->"OPESumSimplify", - CellID->189414120] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -484,12 +493,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{830, Automatic}, {Automatic, 154}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEi.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEi.nb index 1b4113e48..3c89908f8 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEi.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OPEi.nb @@ -191,14 +191,13 @@ Cell[CellGroupData[{ Cell[BoxData["OPEi"], "Input", CellTags->"OPEi", - CellLabel->"In[1]:=", + CellLabel->"In[35]:=", CellID->1513541744], Cell[BoxData[ FormBox["i", TraditionalForm]], "Output", CellTags->"OPEi", - CellLabel->"Out[1]=", - CellID->1058262689] + CellLabel->"Out[35]="] }, Open ]], Cell[CellGroupData[{ @@ -210,7 +209,7 @@ Cell[BoxData[ " ", "OPEn", ",", " ", "OPEo", ",", " ", "PositiveInteger"}], "]"}]], "Input", CellTags->"OPEi", - CellLabel->"In[2]:=", + CellLabel->"In[36]:=", CellID->1628297296], Cell[BoxData[ @@ -220,8 +219,7 @@ Cell[BoxData[ "True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True", ",", "True"}], "}"}], TraditionalForm]], "Output", CellTags->"OPEi", - CellLabel->"Out[2]=", - CellID->1847732928] + CellLabel->"Out[36]="] }, Open ]], Cell[CellGroupData[{ @@ -266,7 +264,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"2", "OPEo"}], ")"}]}]}], "}"}], "]"}]], "Input", CellTags->"OPEi", - CellLabel->"In[3]:=", + CellLabel->"In[37]:=", CellID->233448399], Cell[BoxData[ @@ -275,13 +273,10 @@ Cell[BoxData[ RowBox[{"1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1"}], "}"}], TraditionalForm]], "Output", CellTags->"OPEi", - CellLabel->"Out[3]=", - CellID->1115714619] + CellLabel->"Out[37]="] }, Open ]], -Cell["Re has been changed:", "Text", - CellTags->"OPEi", - CellID->920512070], +Cell["Re has been changed:", "Notes"], Cell[CellGroupData[{ @@ -302,7 +297,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Re", "[", "OPEi", "]"}], ">", "1"}]}], "}"}]], "Input", CellTags->"OPEi", - CellLabel->"In[4]:=", + CellLabel->"In[38]:=", CellID->631981450], Cell[BoxData[ @@ -324,8 +319,7 @@ Cell[BoxData[ RowBox[{"Re", "(", "i", ")"}], ">", "1"}]}], "}"}], TraditionalForm]], "Output", CellTags->"OPEi", - CellLabel->"Out[4]=", - CellID->1830261914] + CellLabel->"Out[38]="] }, Open ]], Cell[CellGroupData[{ @@ -349,7 +343,7 @@ Cell[BoxData[ RowBox[{"-", "OPEi"}], " ", "+", " ", "OPEm"}], "]"}], " ", ">", " ", "2"}]}], "}"}]], "Input", CellTags->"OPEi", - CellLabel->"In[5]:=", + CellLabel->"In[39]:=", CellID->1153963056], Cell[BoxData[ @@ -367,8 +361,7 @@ Cell[BoxData[ RowBox[{"m", "-", "i"}], ")"}], ">", "2"}]}], "}"}], TraditionalForm]], "Output", CellTags->"OPEi", - CellLabel->"Out[5]=", - CellID->480392578] + CellLabel->"Out[39]="] }, Open ]], Cell[CellGroupData[{ @@ -390,7 +383,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Re", "[", "OPEm", "]"}], ">", "1"}]}], "}"}]], "Input", CellTags->"OPEi", - CellLabel->"In[6]:=", + CellLabel->"In[40]:=", CellID->1255237485], Cell[BoxData[ @@ -412,8 +405,7 @@ Cell[BoxData[ RowBox[{"Re", "(", "m", ")"}], ">", "1"}]}], "}"}], TraditionalForm]], "Output", CellTags->"OPEi", - CellLabel->"Out[6]=", - CellID->718023073] + CellLabel->"Out[40]="] }, Open ]] }, Open ]], @@ -478,12 +470,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{718, Automatic}, {Automatic, 138}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OneLoop.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OneLoop.nb index 843f8a0b5..f8face7cc 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OneLoop.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OneLoop.nb @@ -119,49 +119,59 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"OneLoop", "[", RowBox[{"q", ",", " ", "amplitude"}], "]"}]], "InlineFormula"], - " \[LineSeparator]calculates the one-loop Feynman diagram amplitude (", - StyleBox["n", - FontSlant->"Italic"], - "-point, where ", - StyleBox["n", - FontSlant->"Italic"], - "\[LessEqual]4 and the highest tensor rank of the integration momenta (after \ -cancellation of scalar products) may be up to 3; unless OneLoopSimplify is \ -used).\n\nThe argument q denotes the integration variable, i.e., the loop \ -momentum. OneLoop[name, q, amplitude] has as first argument a name of the \ -amplitude. If the second argument has head FeynAmp then OneLoop[q, \ -FeynAmp[name, k, expr]] and OneLoop[FeynAmp[name, k, expr]] tranform to \ -OneLoop[name, k, expr].\n\nNOTICE: While OneLoop is restricted to 't Hooft \ -Feynman gauge, the function ", - ButtonBox["OneLoopSimplify", - BaseStyle->"AddOnsLink", - ButtonData:>"OneLoopSimplify", - ButtonNote->"OneLoopSimplify"], - " does not have this restriction (but is usually slower).\n\nWARNING: If you \ -encounter anomalies: The default setting of West is True, i.e., the way ", - Cell[BoxData[ - FormBox[ - RowBox[{" ", - RowBox[{"tr", "(", - RowBox[{ - SuperscriptBox["\[Gamma]", "\[Mu]"], - SuperscriptBox["\[Gamma]", "\[Nu]"], - SuperscriptBox["\[Gamma]", "\[Rho]"], - SuperscriptBox["\[Gamma]", "\[Sigma]"], - SuperscriptBox["\[Gamma]", "\[Tau]"], - SuperscriptBox["\[Gamma]", "\[Lambda]"], - SuperscriptBox["\[Gamma]", "5"]}], ")"}]}], TraditionalForm]]], - " is calculated in D dimensions has changed compared to the old FeynCalc \ -version. Please keep in mind that the issue of ", - Cell[BoxData[ - FormBox[ - SuperscriptBox["\[Gamma]", "5"], TraditionalForm]]], - "schemes is inherintly tricky." + " \[LineSeparator]calculates the one-loop Feynman diagram amplitude. The \ +argument q denotes the integration variable, i.e., the loop momentum. \ +OneLoop[name, q, amplitude] has as first argument a name of the amplitude. If \ +the second argument has head FeynAmp then OneLoop[q, FeynAmp[name, k, expr]] \ +and OneLoop[FeynAmp[name, k, expr]] tranform to OneLoop[name, k, expr]." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["OneLoop is deprecated, please use TID instead!", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "OneLoop", "]"}]], "Input", + CellTags->"OneLoop", + CellLabel->"In[41]:=", + CellID->183705859], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"FormatType", "\[Rule]", "InputForm"}], ",", + RowBox[{"InitialSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"IntermediateSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"IsolateNames", "\[Rule]", "False"}], ",", + RowBox[{"Mandelstam", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"NPointTo4Point", "\[Rule]", "True"}], ",", + RowBox[{"OneLoopSimplify", "\[Rule]", "False"}], ",", + RowBox[{"PaVeAutoOrder", "\[Rule]", "True"}], ",", + RowBox[{"PaVeAutoReduce", "\[Rule]", "True"}], ",", + RowBox[{"Prefactor", "\[Rule]", "1"}], ",", + RowBox[{"ReduceGamma", "\[Rule]", "False"}], ",", + RowBox[{"ReduceToScalars", "\[Rule]", "False"}], ",", + RowBox[{"SmallVariables", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"WriteOut", "\[Rule]", "False"}], ",", + RowBox[{"WriteOutPaVe", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"OneLoop", + CellLabel->"Out[41]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -212,10 +222,10 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/D0", ButtonNote->"D0"], ", ", - ButtonBox["OneLoopSimplify", + ButtonBox["TID", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/OneLoopSimplify", - ButtonNote->"OneLoopSimplify"], + ButtonData:>"paclet:FeynCalc/ref/TID", + ButtonNote->"TID"], ", ", ButtonBox["TID", BaseStyle->"Link", @@ -231,9 +241,7 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/$LimitTo4", ButtonNote->"$LimitTo4"] -}], "Text", - CellTags->"OneLoop", - CellID->1073109549] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -262,59 +270,16 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "OneLoop", "]"}]], "Input", - CellTags->"OneLoop", - CellLabel->"In[1]:=", - CellID->183705859], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"DenominatorOrder", "\[Rule]", "False"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"Factoring", "\[Rule]", "False"}], ",", - RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", - 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CellLabel->"Out[2]=", - CellID->155772215] + CellLabel->"Out[39]="] }, Open ]], Cell[CellGroupData[{ @@ -340,7 +313,7 @@ Cell[BoxData[ RowBox[{"OneLoop", "[", RowBox[{"q", ",", "%"}], "]"}]], "Input", CellTags->"OneLoop", - CellLabel->"In[3]:=", + CellLabel->"In[40]:=", CellID->1041679425], Cell[BoxData[ @@ -353,80 +326,39 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"OneLoop", - CellLabel->"Out[3]=", - CellID->987393919] + CellLabel->"Out[40]="] }, Open ]], -Cell[BoxData[ - RowBox[{ - RowBox[{"mf", "/:", - RowBox[{"MakeBoxes", "[", - RowBox[{"mf", ",", "TraditionalForm"}], "]"}], "=", - RowBox[{"InterpretationBox", "[", - RowBox[{ - RowBox[{"SubscriptBox", "[", - RowBox[{"\"\\"", ",", "\"\\""}], "]"}], ",", "mf"}], "]"}]}], - ";"}]], "Input", - CellTags->"OneLoop", - CellLabel->"In[4]:=", - CellID->1188939388], - -Cell[TextData[{ - "Remember that FAD[{q,mf},{q-k,mf}] is a fast possibility to enter ", - Cell[BoxData[ - FormBox[ - RowBox[{"1", "/", - 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CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "OneLoopSimplify", "]"}]], "Input", + CellTags->"OneLoopSimplify", + CellLabel->"In[15]:=", + CellID->408969695], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Collecting", "\[Rule]", "True"}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"DiracSimplify", "\[Rule]", "True"}], ",", + RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "Automatic"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"OPE1Loop", "\[Rule]", "False"}], ",", + RowBox[{"PowerSimplify", "\[Rule]", "True"}], ",", + RowBox[{"SUNNToCACF", "\[Rule]", "True"}], ",", + RowBox[{"SUNTrace", "\[Rule]", "False"}], ",", + RowBox[{"ToPaVe", "\[Rule]", "False"}], ",", + RowBox[{"UsePaVeBasis", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"OneLoopSimplify", + CellLabel->"Out[15]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -162,11 +192,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - 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FormBox["l", - TraditionalForm], - TraditionalForm], "2"], " ", - RowBox[{"(", - RowBox[{ - FormBox[ - SubscriptBox[ FormBox[ - FormBox["p", + SubscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox["2", + TraditionalForm]], + TraditionalForm]}], ")"}], " ", + RowBox[{"(", + RowBox[{ + FormBox[ + FormBox["l", TraditionalForm], TraditionalForm], - FormBox["1", - TraditionalForm]], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - SubscriptBox[ + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], FormBox[ - FormBox["p", - TraditionalForm], + SubscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox["1", + TraditionalForm]], + TraditionalForm]}], ")"}]}], "+", + RowBox[{"2", " ", + SuperscriptBox[ + FormBox[ + FormBox["l", + TraditionalForm], + TraditionalForm], "2"], " ", + RowBox[{"(", + RowBox[{ + FormBox[ + SubscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox["1", + TraditionalForm]], TraditionalForm], - FormBox["2", - TraditionalForm]], - TraditionalForm]}], ")"}]}]}], ")"}], "/", - RowBox[{"(", - RowBox[{"4", " ", + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + SubscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox["2", + TraditionalForm]], + TraditionalForm]}], ")"}]}]}], ")"}], "/", RowBox[{"(", - RowBox[{"D", "-", "1"}], ")"}], " ", - RowBox[{ - SuperscriptBox[ - FormBox["k", - TraditionalForm], "2"], ".", - SuperscriptBox[ + RowBox[{"4", " ", RowBox[{"(", - RowBox[{ - FormBox["k", - TraditionalForm], "-", - SubscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox["1", - TraditionalForm]], "+", - SubscriptBox[ + RowBox[{"1", "-", "D"}], ")"}], " ", + RowBox[{ + InterpretationBox[ + SuperscriptBox[ FormBox[ - FormBox["p", + FormBox["k", TraditionalForm], - TraditionalForm], - FormBox["2", - TraditionalForm]]}], ")"}], "2"]}]}], ")"}]}], - TraditionalForm]], "Output", + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`k, D], + FeynCalc`Momentum[$CellContext`k, D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["k", + TraditionalForm], "-", + SubscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox["1", + TraditionalForm]], "+", + SubscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox["2", + TraditionalForm]]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`k, D] - FeynCalc`Momentum[ + Subscript[$CellContext`p, 1], D] + FeynCalc`Momentum[ + Subscript[$CellContext`p, 2], D], + FeynCalc`Momentum[$CellContext`k, D] - FeynCalc`Momentum[ + Subscript[$CellContext`p, 1], D] + FeynCalc`Momentum[ + Subscript[$CellContext`p, 2], D]]], + Editable->False]}]}], ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"OneLoopSimplify", - CellLabel->"Out[8]=", - CellID->347723347] + CellLabel->"Out[24]="] }, Open ]] }, Open ]], @@ -2038,12 +2356,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{902, Automatic}, {Automatic, 266}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OneLoopSum.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OneLoopSum.nb index 04b5db5d2..adfe94d8c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OneLoopSum.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OneLoopSum.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoop", ButtonNote->"OneLoop"], "." -}], "Text", - CellTags->"OneLoopSum", - CellID->702509014] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{713, Automatic}, {Automatic, 141}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/OptionsSelect.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/OptionsSelect.nb index dcc42211b..b5eddab06 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/OptionsSelect.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/OptionsSelect.nb @@ -248,12 +248,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PD.nb index 5e946742e..cf218c350 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PD.nb @@ -169,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/IFPD", ButtonNote->"IFPD"], "." -}], "Text", - CellTags->"PD", - CellID->155972299] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVe.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVe.nb index 36e52291f..287087e44 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVe.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVe.nb @@ -118,13 +118,19 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"PaVe", "[", - RowBox[{"i", ",", "j", ",", "..."}]}]], "InlineFormula"], - " \[LineSeparator]", - "{p10,p12,...},{m1^2, mw^2, ...}] denotes the invariant (and scalar) \ -Passarino-Veltman integrals, i.e. the coefficient functions of the tensor \ -integral decomposition. Joining plist and mlist gives the same conventions as \ -for A0, B0, C0, D0. Automatic simlifications are performed for the \ -coefficient functions of two-point integrals and for the scalar integrals." + RowBox[{"i", ",", "j", ",", "...", ",", + RowBox[{"{", + RowBox[{"p10", ",", "p12", ",", "..."}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"m1", "^", "2"}], ",", + RowBox[{"mw", "^", "2"}], ",", "..."}], "}"}]}], "]"}]], + "InlineFormula"], + " \[LineSeparator]denotes the invariant (and scalar) Passarino-Veltman \ +integrals, i.e. the coefficient functions of the tensor integral \ +decomposition. Joining plist and mlist gives the same conventions as for A0, \ +B0, C0, D0. Automatic simlifications are performed for the coefficient \ +functions of two-point integrals and for the scalar integrals." }], "Usage", CellID->982511436], @@ -170,9 +176,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PaVeReduce", ButtonNote->"PaVeReduce"], "." -}], "Text", - CellTags->"PaVe", - CellID->1153293303] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -199,40 +203,11 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["Some of the PaVe's reduce to special cases.", "Text", - CellTags->"PaVe", - CellID->1877067255], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"PaVe", "[", - RowBox[{"0", ",", - RowBox[{"{", - RowBox[{"a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "f"}], "}"}], - ",", - RowBox[{"{", - RowBox[{"m1", ",", "m2", ",", "m3", ",", "m4"}], "}"}]}], "]"}]], "Input", - - CellTags->"PaVe", - CellLabel->"In[1]:=", - CellID->200539338], - -Cell[BoxData[ - FormBox[ - TagBox[ - FormBox[ - RowBox[{ - SubscriptBox["\<\"D\"\>", "\<\"0\"\>"], "(", - RowBox[{ - "a", ",", "b", ",", "c", ",", "d", ",", "e", ",", "f", ",", "m1", ",", - "m2", ",", "m3", ",", "m4"}], ")"}], - TraditionalForm], - HoldForm], TraditionalForm]], "Output", - CellTags->"PaVe", - CellLabel->"Out[1]=", - CellID->1799689194] -}, Open ]], +Cell[TextData[{ + "Some of the PaVe's reduce to special cases with ", + Cell[BoxData[ + RowBox[{"PaVeAutoReduce", "\[Rule]", "True"}]], "InlineFormula"] +}], "Notes"], Cell[CellGroupData[{ @@ -243,104 +218,80 @@ Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"m", "^", "2"}], ",", - RowBox[{"M", "^", "2"}]}], "}"}]}], "]"}]], "Input", + RowBox[{"M", "^", "2"}]}], "}"}], ",", + RowBox[{"PaVeAutoReduce", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"PaVe", - CellLabel->"In[2]:=", + CellLabel->"In[49]:=", CellID->378525516], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{ - FractionBox["1", "6"], " ", - RowBox[{"(", - RowBox[{ + FractionBox[ + RowBox[{ + RowBox[{"(", + RowBox[{ + SuperscriptBox["m", "2"], "-", + RowBox[{"2", " ", "m", " ", "M"}], "+", + SuperscriptBox["M", "2"], "-", "pp"}], ")"}], " ", + RowBox[{"(", RowBox[{ - RowBox[{"(", + SuperscriptBox["m", "2"], "+", + RowBox[{"2", " ", "m", " ", "M"}], "+", + SuperscriptBox["M", "2"], "-", "pp"}], ")"}], " ", + FormBox[ + TagBox[ + FormBox[ RowBox[{ - SuperscriptBox["m", "2"], "-", - SuperscriptBox["M", "2"], "+", "pp"}], ")"}], " ", - RowBox[{"(", + SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", + RowBox[{"pp", ",", + SuperscriptBox["m", "2"], ",", + SuperscriptBox["M", "2"]}], ")"}], + TraditionalForm], + HoldForm], + TraditionalForm]}], + RowBox[{"4", " ", + RowBox[{"(", + RowBox[{"1", "-", "D"}], ")"}], " ", "pp"}]], "-", + FractionBox[ + RowBox[{ + FormBox[ + TagBox[ + FormBox[ RowBox[{ - FractionBox[ - RowBox[{ - RowBox[{"(", - RowBox[{ - SuperscriptBox["M", "2"], "-", - SuperscriptBox["m", "2"]}], ")"}], " ", - RowBox[{"(", - RowBox[{ - FormBox[ - TagBox[ - FormBox[ - RowBox[{ - SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", - RowBox[{"pp", ",", - SuperscriptBox["m", "2"], ",", - SuperscriptBox["M", "2"]}], ")"}], - TraditionalForm], - HoldForm], - 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CellLabel->"Out[2]=", - CellID->1156896528] + CellLabel->"Out[49]="] }, Open ]] }, Open ]], @@ -405,12 +356,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{745, Automatic}, {Automatic, 217}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeOrder.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeOrder.nb index 17d04bfc1..80f735549 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeOrder.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeOrder.nb @@ -178,9 +178,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PaVeReduce", ButtonNote->"PaVeReduce"], "." -}], "Text", - CellTags->"PaVeOrder", - CellID->776510000] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -207,6 +205,11 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], +Cell[BoxData[ + RowBox[{"ClearAll", "[", + RowBox[{"t", ",", "s"}], "]"}]], "Input", + CellLabel->"In[53]:="], + Cell[CellGroupData[{ Cell[BoxData[ @@ -221,7 +224,7 @@ Cell[BoxData[ RowBox[{"me2", ",", "me2", ",", "0", ",", "0"}], "}"}]}]}], "]"}]], "Input", CellTags->"PaVeOrder", - CellLabel->"In[1]:=", + CellLabel->"In[54]:=", CellID->641538627], Cell[BoxData[ @@ -236,8 +239,7 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"PaVeOrder", - CellLabel->"Out[1]=", - CellID->1082848295] + CellLabel->"Out[54]="] }, Open ]], Cell[CellGroupData[{ @@ -254,7 +256,7 @@ Cell[BoxData[ RowBox[{"me2", ",", "me2", ",", "0", ",", "0"}], "}"}]}]}], "]"}]], "Input", CellTags->"PaVeOrder", - CellLabel->"In[2]:=", + CellLabel->"In[55]:=", CellID->490694983], Cell[BoxData[ @@ -269,8 +271,7 @@ Cell[BoxData[ TraditionalForm], HoldForm], TraditionalForm]], "Output", CellTags->"PaVeOrder", - CellLabel->"Out[2]=", - CellID->1266309668] + CellLabel->"Out[55]="] }, Open ]], Cell[CellGroupData[{ @@ -295,7 +296,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"f", ",", "e"}], "}"}]}], "}"}]}]}], "]"}]], "Input", CellTags->"PaVeOrder", - CellLabel->"In[3]:=", + CellLabel->"In[56]:=", CellID->1444685309], Cell[BoxData[ @@ -324,8 +325,7 @@ Cell[BoxData[ HoldForm], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"PaVeOrder", - CellLabel->"Out[3]=", - CellID->1493961476] + CellLabel->"Out[56]="] }, Open ]] }, Open ]], @@ -390,12 +390,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{830, Automatic}, {Automatic, 179}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeOrderList.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeOrderList.nb index dec7c0c38..e76029f23 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeOrderList.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeOrderList.nb @@ -160,7 +160,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - 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CellTags->"PaVeReduce"] + CellTags->"PaVeReduce", + CellLabel->"Out[68]//TableForm=", + CellID->2020509582] }, Open ]], Cell[BoxData[ RowBox[{ - RowBox[{"DeleteFile", "/@", - RowBox[{"FileNames", "[", "\"\\"", "]"}]}], ";", - RowBox[{"Clear", "[", - RowBox[{"d122", ",", "se"}], "]"}], ";"}]], "Input", + RowBox[{ + RowBox[{"DeleteFile", "/@", + RowBox[{"FileNames", "[", "\"\\"", "]"}]}], ";", + RowBox[{"Clear", "[", + RowBox[{"d122", ",", "se"}], "]"}], ";"}], " "}]], "Input", CellTags->"PaVeReduce", - CellID->793776799], + CellLabel->"In[69]:=", + CellID->793776799] +}, Open ]], + +Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", @@ -923,6 +1170,8 @@ Cell[BoxData[ $Line = 0; Null]], "ExampleSection", CellID->1020263627], +Cell[CellGroupData[{ + Cell[BoxData[ InterpretationBox[Cell["Options", "ExampleSection"], $Line = 0; Null]], "ExampleSection", @@ -936,7 +1185,8 @@ Cell[BoxData[ Cell[BoxData[ InterpretationBox[Cell["XXXX", "ExampleSubsection"], $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749], + CellID->1295379749] +}, Closed]], Cell[BoxData[ InterpretationBox[Cell["Applications", "ExampleSection"], @@ -964,14 +1214,13 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 741}, -WindowMargins->{{2104, Automatic}, {Automatic, 69}}, -Visible->True, +WindowSize->{700, 770}, +WindowMargins->{{1083, Automatic}, {Automatic, 178}}, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"11.0 for Linux x86 (64-bit) (September 21, 2016)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] - diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeUVPart.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeUVPart.nb new file mode 100644 index 000000000..edd8fabfa --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PaVeUVPart.nb @@ -0,0 +1,433 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/PaVeUVPart", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["PaVeUVPart", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"PaVeUVPart", "[", "expr", "]"}]], "InlineFormula"], + " \[LineSeparator]replaces all occuring Passarino-Veltman functions by their \ +explicit values, where only the UV divergent part is preserved, while \ +possible IR divergences and the finite part are discarded. \[LineSeparator]\ +\[LineSeparator]The function uses the algorithm from \"Sulyok, G., A closed \ +expression for the UV-divergent parts of one-loop tensor integrals in \ +dimensional regularization, Phys. Part. Nuclei Lett. (2017) 14:631, \ +arXiv:hep-ph/0609282 " +}], "Usage", + CellID->982511436], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "PaVeUVPart", "]"}]], "Input", + CellLabel->"In[52]:=", + CellID->617667665], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Factoring", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCLoopExtract", "\[Rule]", "True"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Prefactor", "\[Rule]", "1"}], ",", + RowBox[{"ToPaVe2", "\[Rule]", "True"}], ",", + RowBox[{"Together", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[52]=", + CellID->717628530] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell[TextData[{ + ButtonBox["PaVe", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/PaVe", + ButtonNote->"PaVe"], + ", ", + ButtonBox["PaVeReduce", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/PaVeReduce", + ButtonNote->"PaVeReduce"], + "." +}], "SeeAlso"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"PaVeUVPart", "[", + RowBox[{"A0", "[", + RowBox[{"m", "^", "2"}], "]"}], "]"}]], "Input", + CellLabel->"In[70]:=", + CellID->1445277710], + +Cell[BoxData[ + FormBox[ + RowBox[{"-", + FractionBox[ + RowBox[{"2", " ", + SuperscriptBox["m", "2"]}], + RowBox[{"D", "-", "4"}]]}], TraditionalForm]], "Output", + CellLabel->"Out[70]=", + CellID->384429231] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"PaVeUVPart", "[", + RowBox[{"x", "+", + RowBox[{"y", " ", + RowBox[{"B0", "[", + RowBox[{ + RowBox[{"SPD", "[", + RowBox[{"p", ",", "p"}], "]"}], ",", "0", ",", + SuperscriptBox["M", "2"]}], "]"}]}]}], "]"}]], "Input", + CellLabel->"In[71]:=", + CellID->1518685822], + +Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{ + RowBox[{"D", " ", "x"}], "-", + RowBox[{"4", " ", "x"}], "-", + RowBox[{"2", " ", "y"}]}], + RowBox[{"D", "-", "4"}]], TraditionalForm]], "Output", + CellLabel->"Out[71]=", + CellID->319680291] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{"PaVe", "[", + RowBox[{"0", ",", "0", ",", + RowBox[{"{", + RowBox[{"p10", ",", "p12", ",", "p20"}], "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"m1", "^", "2"}], ",", + RowBox[{"m2", "^", "2"}], ",", + RowBox[{"m3", "^", "2"}]}], "}"}]}], "]"}], "\[IndentingNewLine]", + RowBox[{"PaVeUVPart", "[", "%", "]"}]}], "Input", + CellLabel->"In[72]:=", + CellID->759345267], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"C\"\>", "\<\"00\"\>"], "(", + RowBox[{"p10", ",", "p12", ",", "p20", ",", + SuperscriptBox["m1", "2"], ",", + SuperscriptBox["m2", "2"], ",", + SuperscriptBox["m3", "2"]}], ")"}], TraditionalForm]], "Output", + CellLabel->"Out[72]=", + CellID->812213864], + +Cell[BoxData[ + FormBox[ + RowBox[{"-", + FractionBox["1", + RowBox[{"2", " ", + RowBox[{"(", + RowBox[{"D", "-", "4"}], ")"}]}]]}], TraditionalForm]], "Output", + CellLabel->"Out[73]=", + CellID->1946544093] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{"PaVe", "[", + RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", + RowBox[{"{", + RowBox[{"p10", ",", "p12", ",", "p23", ",", "0", ",", "p20", ",", "p13"}], + "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"m1", "^", "2"}], ",", + RowBox[{"m2", "^", "2"}], ",", + RowBox[{"m3", "^", "2"}], ",", + RowBox[{"m4", "^", "2"}]}], "}"}]}], "]"}], "\[IndentingNewLine]", + RowBox[{"PaVeUVPart", "[", "%", "]"}]}], "Input", + CellLabel->"In[74]:=", + CellID->1054433755], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SubscriptBox["\<\"D\"\>", "\<\"000000\"\>"], "(", + RowBox[{ + "p10", ",", "p12", ",", "p23", ",", "0", ",", "p20", ",", "p13", ",", + SuperscriptBox["m1", "2"], ",", + SuperscriptBox["m2", "2"], ",", + SuperscriptBox["m3", "2"], ",", + SuperscriptBox["m4", "2"]}], ")"}], TraditionalForm]], "Output", + CellLabel->"Out[74]=", + CellID->792114270], + +Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{ + RowBox[{"-", + RowBox[{"5", " ", + SuperscriptBox["m1", "2"]}]}], "-", + RowBox[{"5", " ", + SuperscriptBox["m2", "2"]}], "-", + RowBox[{"5", " ", + SuperscriptBox["m3", "2"]}], "-", + RowBox[{"5", " ", + SuperscriptBox["m4", "2"]}], "+", "p10", "+", "p12", "+", "p13", "+", + "p20", "+", "p23"}], + RowBox[{"480", " ", + RowBox[{"(", + RowBox[{"D", "-", "4"}], ")"}]}]], TraditionalForm]], "Output", + CellLabel->"Out[75]=", + CellID->146736684] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{722, Automatic}, {Automatic, 253}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Pair.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Pair.nb index c480dbf4d..2f493bd7d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Pair.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Pair.nb @@ -169,11 +169,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["FourVector", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], - ", ", ButtonBox["FV", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FV", @@ -184,11 +179,6 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FVD", ButtonNote->"FVD"], ", ", - ButtonBox["MetricTensor", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/MetricTensor", - ButtonNote->"MetricTensor"], - ", ", ButtonBox["MT", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/MT", @@ -214,9 +204,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SPD", ButtonNote->"SPD"], "." -}], "Text", - CellTags->"Pair", - CellID->1831653521] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -243,9 +231,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["This represents a four-dimensional metric tensor.", "Text", - CellTags->"Pair", - CellID->1660838641], +Cell["This represents a four-dimensional metric tensor", "Notes"], Cell[CellGroupData[{ @@ -264,25 +250,18 @@ Cell[BoxData[ OverscriptBox["g", "_"], RowBox[{ FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], + FormBox["\[Alpha]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[1]=", - CellID->1133543032] + CellLabel->"Out[1]="] }, Open ]], -Cell["This is a D-dimensional metric tensor.", "Text", - CellTags->"Pair", - CellID->1732482457], +Cell["This is a D-dimensional metric tensor", "Notes"], Cell[CellGroupData[{ @@ -302,22 +281,43 @@ Cell[BoxData[ SuperscriptBox["g", RowBox[{ FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], + FormBox["\[Alpha]", TraditionalForm], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Beta]", - TraditionalForm], + FormBox["\[Beta]", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[2]=", - CellID->395860998] + CellLabel->"Out[2]="] +}, Open ]], + +Cell["\<\ +If the Lorentz indices live in different dimensions, this gets resolved \ +according to the t'Hoft-Veltman-Breitenlohner-Maison prescription\ +\>", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"LorentzIndex", "[", + RowBox[{"\[Alpha]", ",", + RowBox[{"n", "-", "4"}]}], "]"}], ",", + RowBox[{"LorentzIndex", "[", "\[Beta]", "]"}]}], "]"}]], "Input", + CellTags->"Pair", + CellLabel->"In[3]:=", + CellID->1343625376], + +Cell[BoxData[ + FormBox["0", TraditionalForm]], "Output", + CellTags->"Pair", + CellLabel->"Out[3]="] }, Open ]], +Cell["A 4-dimensional Lorentz vector", "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ @@ -326,7 +326,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Alpha]", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]], "Input", CellTags->"Pair", - CellLabel->"In[3]:=", + CellLabel->"In[4]:=", CellID->958079821], Cell[BoxData[ @@ -338,16 +338,45 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Alpha]", - TraditionalForm], + FormBox["\[Alpha]", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellTags->"Pair", + CellLabel->"Out[4]="] +}, Open ]], + +Cell["A D-dimensional Lorentz vector", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"LorentzIndex", "[", + RowBox[{"\[Alpha]", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}]}], "]"}]], "Input", + CellTags->"Pair", + CellLabel->"In[5]:=", + CellID->106742008], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Alpha]", TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[3]=", - CellID->53465480] + CellLabel->"Out[5]="] }, Open ]], +Cell["4-dimensional scalar products of Lorentz vectors", "Notes"], + Cell[CellGroupData[{ Cell[BoxData[ @@ -356,7 +385,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "q", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]], "Input", CellTags->"Pair", - CellLabel->"In[4]:=", + CellLabel->"In[6]:=", CellID->1770091706], Cell[BoxData[ @@ -375,8 +404,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[4]=", - CellID->2098206398] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -387,7 +415,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]], "Input", CellTags->"Pair", - CellLabel->"In[5]:=", + CellLabel->"In[7]:=", CellID->227830423], Cell[BoxData[ @@ -399,8 +427,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[5]=", - CellID->212297594] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -412,7 +439,7 @@ Cell[BoxData[ RowBox[{"p", "-", "q"}], "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]], "Input", CellTags->"Pair", - CellLabel->"In[6]:=", + CellLabel->"In[8]:=", CellID->25203155], Cell[BoxData[ @@ -428,19 +455,20 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[6]=", - CellID->1189007863] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -452,7 +480,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}], "^", "2"}]], "Input", CellTags->"Pair", - CellLabel->"In[7]:=", + CellLabel->"In[9]:=", CellID->1431519685], Cell[BoxData[ @@ -464,8 +492,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "4"], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[7]=", - CellID->966009047] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -477,7 +504,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}], "^", "3"}]], "Input", CellTags->"Pair", - CellLabel->"In[8]:=", + CellLabel->"In[10]:=", CellID->721851127], Cell[BoxData[ @@ -489,30 +516,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "6"], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[8]=", - CellID->1932921647] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{"Pair", "[", - RowBox[{ - RowBox[{"LorentzIndex", "[", - RowBox[{"\[Alpha]", ",", - RowBox[{"n", "-", "4"}]}], "]"}], ",", - RowBox[{"LorentzIndex", "[", "\[Beta]", "]"}]}], "]"}], "//", - "Contract"}]], "Input", - CellTags->"Pair", - CellLabel->"In[9]:=", - CellID->1343625376], - -Cell[BoxData[ - FormBox["0", TraditionalForm]], "Output", - CellTags->"Pair", - CellLabel->"Out[9]=", - CellID->1776583038] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -525,7 +529,7 @@ Cell[BoxData[ RowBox[{"p", "-", "q"}], "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}], "]"}]], "Input", CellTags->"Pair", - CellLabel->"In[10]:=", + CellLabel->"In[11]:=", CellID->294431519], Cell[BoxData[ @@ -551,8 +555,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[10]=", - CellID->1562380290] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -569,14 +572,13 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "q", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]}]], "Input", CellTags->"Pair", - CellLabel->"In[11]:=", + CellLabel->"In[12]:=", CellID->1586756083], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"Pair", - CellLabel->"Out[11]=", - CellID->824407583] + CellLabel->"Out[12]="] }, Open ]] }, Open ]], @@ -641,12 +643,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{665, Automatic}, {Automatic, 76}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PairCollect.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PairCollect.nb index 29042395a..b804c2e6f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PairCollect.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PairCollect.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Pair", ButtonNote->"Pair"], "." -}], "Text", - CellTags->"PairCollect", - CellID->777103219] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{812, Automatic}, {Automatic, 86}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract.nb index 51cd3236b..08931dd56 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract.nb @@ -159,7 +159,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["Pair", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Pair", @@ -170,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Contract", ButtonNote->"Contract"], "." -}], "Text", - CellTags->"PairContract", - CellID->229888043] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{723, Automatic}, {Automatic, 65}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract2.nb index 77ee6ba3d..5a65dd695 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract2.nb @@ -159,7 +159,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["Pair", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Pair", @@ -175,9 +174,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PairContract", ButtonNote->"PairContract"], "." -}], "Text", - CellTags->"PairContract2", - CellID->1911268297] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -263,12 +260,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{570, Automatic}, {Automatic, 33}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract3.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract3.nb index 1a5a8f127..b37ddfb86 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract3.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PairContract3.nb @@ -159,7 +159,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["Pair", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Pair", @@ -175,9 +174,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PairContract", ButtonNote->"PairContract"], "." -}], "Text", - CellTags->"PairContract3", - CellID->1570776194] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -263,12 +260,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{725, Automatic}, {Automatic, 32}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialDRelations.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialDRelations.nb index 625850e6c..a55f1e1cb 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialDRelations.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialDRelations.nb @@ -159,39 +159,33 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[RawData["\<\ Cell[TextData[{ - ButtonBox[\"FCPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/PartialD\", - ButtonNote->\"FCPartialD\"], - \", \", - ButtonBox[\"ExpandPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/ExpandPartialD\", - ButtonNote->\"ExpandPartialD\"], - \", \", - ButtonBox[\"LeftPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/LeftPartialD\", - ButtonNote->\"LeftPartialD\"], - \", \", - ButtonBox[\"LeftRightPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/LeftRightPartialD\", - ButtonNote->\"LeftRightPartialD\"], - \", \", - ButtonBox[\"RightPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/RightPartialD\", - ButtonNote->\"RightPartialD\"], - \".\" -}], \"Text\", - CellTags->\"PartialDRelations\", - CellID->730120334]\ -\>"], "Text", - CellTags->"PartialDRelations", - CellID->730120334] + ButtonBox["FCPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/PartialD", + ButtonNote->"FCPartialD"], + ", ", + ButtonBox["ExpandPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/ExpandPartialD", + ButtonNote->"ExpandPartialD"], + ", ", + ButtonBox["LeftPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/LeftPartialD", + ButtonNote->"LeftPartialD"], + ", ", + ButtonBox["LeftRightPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/LeftRightPartialD", + ButtonNote->"LeftRightPartialD"], + ", ", + ButtonBox["RightPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/RightPartialD", + ButtonNote->"RightPartialD"], + "." +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,10 +212,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"PartialDRelations", - CellID->56378705], - Cell[CellGroupData[{ Cell[BoxData[ @@ -234,7 +224,7 @@ Cell[BoxData[ RowBox[{"{", "\[Mu]", "}"}]}], "]"}], ".", RowBox[{"LeftPartialD", "[", "\[Nu]", "]"}]}]], "Input", CellTags->"PartialDRelations", - CellLabel->"In[1]:=", + CellLabel->"In[13]:=", CellID->1264073129], Cell[BoxData[ @@ -257,8 +247,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"PartialDRelations", - CellLabel->"Out[1]=", - CellID->1055472864] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -270,7 +259,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"A", "\[Rule]", "C"}], "}"}]}]}], "]"}]], "Input", CellTags->"PartialDRelations", - CellLabel->"In[2]:=", + CellLabel->"In[14]:=", CellID->1340152745], Cell[BoxData[ @@ -282,41 +271,44 @@ Cell[BoxData[ TraditionalForm], FormBox["\[Mu]", TraditionalForm]], ".", - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["B", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}]}], "+", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["B", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}]}], "+", RowBox[{ - RowBox[{ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], - SubsuperscriptBox[ - FormBox["C", - TraditionalForm], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], "\[Null]"]}], ".", + RowBox[{"(", + RowBox[{ + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], + SubscriptBox[ + FormBox["C", + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ")"}], ")"}], ".", SubscriptBox[ FormBox["B", TraditionalForm], FormBox["\[Mu]", TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"PartialDRelations", - CellLabel->"Out[2]=", - CellID->42444932] + CellLabel->"Out[14]="] }, Open ]] }, Open ]], @@ -381,12 +373,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{852, Automatic}, {Automatic, 115}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialFourVector.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialFourVector.nb index 50c7766ee..6c9544047 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialFourVector.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialFourVector.nb @@ -121,10 +121,9 @@ Cell[TextData[{ RowBox[{"exp", ",", " ", RowBox[{"FourVector", "[", RowBox[{"p", ",", " ", "mu"}], "]"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - " calculates the partial derivative of exp w.r.t. p(mu). \ -PartialFourVector[exp, FourVector[p, mu], FourVector[p,nu], ...] gives the \ -multiple derivative." + " \[LineSeparator] calculates the partial derivative of exp w.r.t. p(mu). \ +PartialFourVector[exp, FV[p, mu], FV[p,nu], ...] gives the multiple \ +derivative." }], "Usage", CellID->982511436], @@ -165,11 +164,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["FourVector", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], - ", ", ButtonBox["Pair", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Pair", @@ -180,9 +174,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Contract", ButtonNote->"Contract"], "." -}], "Text", - CellTags->"PartialFourVector", - CellID->156343692] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -209,10 +201,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"PartialFourVector", - CellID->1758819018], - Cell[CellGroupData[{ Cell[BoxData[ @@ -221,12 +209,12 @@ Cell[BoxData[ RowBox[{"a", " ", SuperscriptBox["\[ExponentialE]", SuperscriptBox[ - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", "\[Nu]"}], "]"}], "2"]]}], ",", - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}]}], "]"}]], "Input", CellTags->"PartialFourVector", - CellLabel->"In[1]:=", + CellLabel->"In[17]:=", CellID->877301924], Cell[BoxData[ @@ -239,23 +227,18 @@ Cell[BoxData[ FormBox["p", TraditionalForm], "_"], TraditionalForm], "2"]], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"PartialFourVector", - CellLabel->"Out[1]=", - CellID->1052815023] + CellLabel->"Out[17]="] }, Open ]] }, Open ]], @@ -320,12 +303,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1004, Automatic}, {Automatic, 201}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialIntegrate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialIntegrate.nb index 4a337f578..e6ea96b3c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialIntegrate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PartialIntegrate.nb @@ -126,8 +126,23 @@ be differentiated." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "PartialIntegrate", "]"}]], "Input", + CellTags->"PartialIntegrate", + CellLabel->"In[1]:=", + CellID->1554098382], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Integrate", "\[Rule]", "Integrate"}], "}"}], + TraditionalForm]], "Output", + CellTags->"PartialIntegrate", + CellLabel->"Out[1]=", + CellID->1807152704] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -190,28 +205,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"PartialIntegrate", - CellID->1897608068], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "PartialIntegrate", "]"}]], "Input", - CellTags->"PartialIntegrate", - CellLabel->"In[1]:=", - CellID->1554098382], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Integrate", "\[Rule]", "Integrate"}], "}"}], - TraditionalForm]], "Output", - CellTags->"PartialIntegrate", - CellLabel->"Out[1]=", - CellID->1807152704] -}, Open ]], - Cell[CellGroupData[{ Cell[BoxData[ @@ -224,7 +217,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"PartialIntegrate", - CellLabel->"In[2]:=", + CellLabel->"In[18]:=", CellID->899216893], Cell[BoxData[ @@ -267,8 +260,7 @@ Cell[BoxData[ RowBox[{"\[DifferentialD]", "x"}]}]}], ")"}]}], RowBox[{"\[DifferentialD]", "x"}]}]}]}], TraditionalForm]], "Output", CellTags->"PartialIntegrate", - CellLabel->"Out[2]=", - CellID->1654017289] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -282,7 +274,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"3", "x"}], "+", "2"}], "]"}], ",", "x"}], "]"}]}]], "Input", CellTags->"PartialIntegrate", - CellLabel->"In[3]:=", + CellLabel->"In[19]:=", CellID->474075126], Cell[BoxData[ @@ -299,8 +291,7 @@ Cell[BoxData[ RowBox[{"3", " ", "x"}], "+", "2"}], ")"}], "-", "1"}], ")"}]}], TraditionalForm]], "Output", CellTags->"PartialIntegrate", - CellLabel->"Out[3]=", - CellID->1187465286] + CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ @@ -315,7 +306,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"3", "x"}], "+", "2"}], "]"}]], ",", "x"}], "]"}]}]], "Input", CellTags->"PartialIntegrate", - CellLabel->"In[4]:=", + CellLabel->"In[20]:=", CellID->1976852949], Cell[BoxData[ @@ -332,8 +323,7 @@ Cell[BoxData[ RowBox[{"3", " ", "x"}], "+", "2"}], ")"}]}]]}], TraditionalForm]], "Output", CellTags->"PartialIntegrate", - CellLabel->"Out[4]=", - CellID->347096584] + CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ @@ -352,7 +342,7 @@ Cell[BoxData[ RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], "//", "FullSimplify"}]], "Input", CellTags->"PartialIntegrate", - CellLabel->"In[5]:=", + CellLabel->"In[21]:=", CellID->2004778923], Cell[BoxData[ @@ -363,8 +353,7 @@ Cell[BoxData[ FractionBox["5", RowBox[{"log", "(", "125", ")"}]]}], TraditionalForm]], "Output", CellTags->"PartialIntegrate", - CellLabel->"Out[5]=", - CellID->1569708030] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ @@ -380,7 +369,7 @@ Cell[BoxData[ RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], "//", "Simplify"}]], "Input", CellTags->"PartialIntegrate", - CellLabel->"In[6]:=", + CellLabel->"In[22]:=", CellID->359240358], Cell[BoxData[ @@ -391,15 +380,14 @@ Cell[BoxData[ FractionBox["5", RowBox[{"log", "(", "125", ")"}]]}], TraditionalForm]], "Output", CellTags->"PartialIntegrate", - CellLabel->"Out[6]=", - CellID->1067599584] + CellLabel->"Out[22]="] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"f", ",", "g"}], "]"}]], "Input", CellTags->"PartialIntegrate", - CellLabel->"In[7]:=", + CellLabel->"In[23]:=", CellID->1553816606] }, Open ]], @@ -464,12 +452,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{566, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PartitHead.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PartitHead.nb index 4360b85d8..0e228c6f5 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PartitHead.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PartitHead.nb @@ -248,12 +248,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PauliEta.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PauliEta.nb new file mode 100644 index 000000000..57b992350 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PauliEta.nb @@ -0,0 +1,343 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + 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PauliSigma[1], PauliSigma[2], \ -PauliSigma[3] give the explicit Pauli matrices. PauliSigma[] yields \ -{PauliSigma[1], PauliSigma[2], PauliSigma[3]}." + Cell[BoxData[ + RowBox[{"PauliSigma", "[", + RowBox[{"x", ",", "dim"}], "]"}]], "InlineFormula"], + " \[LineSeparator]is the internal representation of a Pauli matrix with a \ +Lorentz or Cartesian index or a contraction of a Pauli matrix and a Lorentz \ +or Cartesian vector. 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RowBox[{"PauliXi", "[", "I", "]"}]], "Input", + CellLabel->"In[280]:=", + CellID->47983789], + +Cell[BoxData[ + FormBox["\[Xi]", TraditionalForm]], "Output", + CellLabel->"Out[280]=", + CellID->1490471658] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"PauliXi", "[", + RowBox[{"-", "I"}], "]"}]], "Input", + CellLabel->"In[281]:=", + CellID->556532228], + +Cell[BoxData[ + FormBox[ + SuperscriptBox["\[Xi]", "\[Dagger]"], TraditionalForm]], "Output", + CellLabel->"Out[281]=", + CellID->429638525] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"PauliXi", "[", + RowBox[{"-", "I"}], "]"}], ".", + RowBox[{"SIS", "[", "p", "]"}], ".", + RowBox[{"PauliEta", "[", "I", "]"}]}]], "Input", + CellLabel->"In[282]:=", + CellID->1261818576], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["\[Xi]", "\[Dagger]"], ".", + RowBox[{"(", + FormBox[ + RowBox[{ + OverscriptBox["\[Sigma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", "\[Eta]"}], TraditionalForm]], "Output", + CellLabel->"Out[282]=", + CellID->244546897] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "ComplexConjugate"}]], "Input", + CellLabel->"In[283]:=", + CellID->1643081713], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["\[Eta]", "\[Dagger]"], ".", + RowBox[{"(", + RowBox[{ + OverscriptBox["\[Sigma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], ")"}], ".", "\[Xi]"}], TraditionalForm]], "Output", + CellLabel->"Out[283]=", + CellID->1727681521] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1013, Automatic}, {Automatic, 135}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PlusDistribution.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PlusDistribution.nb index 1f6689348..e13bcf4de 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PlusDistribution.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PlusDistribution.nb @@ -168,9 +168,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Integrate2", ButtonNote->"Integrate2"], "." -}], "Text", - CellTags->"PlusDistribution", - CellID->773699831] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -215,8 +213,7 @@ Cell[BoxData[ FractionBox["1", RowBox[{"1", "-", "x"}]], ")"}], "+"], TraditionalForm]], "Output", CellTags->"PlusDistribution", - CellLabel->"Out[1]=", - CellID->793477050] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -241,8 +238,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], ")"}], RowBox[{"1", "-", "x"}]], ")"}], "+"], TraditionalForm]], "Output", CellTags->"PlusDistribution", - CellLabel->"Out[2]=", - CellID->311507260] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -263,8 +259,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"PlusDistribution", - CellLabel->"Out[3]=", - CellID->1505699793] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -287,8 +282,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"PlusDistribution", - CellLabel->"Out[4]=", - CellID->1574569015] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -312,8 +306,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"PlusDistribution", - CellLabel->"Out[5]=", - CellID->207625118] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -344,8 +337,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], ")"}], RowBox[{"1", "-", "x"}]], ")"}], "+"]}], TraditionalForm]], "Output", CellTags->"PlusDistribution", - CellLabel->"Out[6]=", - CellID->593139408] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -410,12 +402,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{734, Automatic}, {Automatic, 99}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Polarization.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Polarization.nb index 9bb033396..2c85894d8 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Polarization.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Polarization.nb @@ -118,17 +118,15 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"Polarization", "[", "k", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the head of a polarization momentum with (incoming) momentum k. A \ -slashed polarization vector (e1(k) slash) has to be entered as \ -DiracSlash[Polarization[k]]. The internal representation for a polarization \ -vector e1 corresponding to a boson with four momentum k is: Momentum[ \ -Polarization[ k, I ] ]. With this notation transversality of polarization \ -vectors is provided, i.e. , Pair[ Momentum[k], Momentum[ Polarization[k, I] ] \ -] yields 0. Polarization[k,-I] denotes the complex conjugate polarization. \ -Polarization is also an option of various functions related to the operator \ -product expansion. The setting 0 denotes the unpolarized and 1 the polarized \ -case." + " \[LineSeparator]is the head of a polarization momentum with (incoming) \ +momentum k. A slashed polarization vector (e1(k) slash) has to be entered as \ +GS[Polarization[k]]. The internal representation for a polarization vector e1 \ +corresponding to a boson with four momentum k is: Momentum[ Polarization[ k, \ +I ] ]. With this notation transversality of polarization vectors is provided, \ +i.e. , Pair[ Momentum[k], Momentum[ Polarization[k, I] ] ] yields 0. \ +Polarization[k,-I] denotes the complex conjugate polarization. Polarization \ +is also an option of various functions related to the operator product \ +expansion. The setting 0 denotes the unpolarized and 1 the polarized case." }], "Usage", CellID->982511436], @@ -184,9 +182,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DoPolarizationSums", ButtonNote->"DoPolarizationSums"], "." -}], "Text", - CellTags->"Polarization", - CellID->1965130928] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -226,8 +222,7 @@ Cell[BoxData[ RowBox[{"Polarization", "(", RowBox[{"k", ",", "\[ImaginaryI]"}], ")"}], TraditionalForm]], "Output", CellTags->"Polarization", - CellLabel->"Out[1]=", - CellID->503395489] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -243,8 +238,7 @@ Cell[BoxData[ RowBox[{"Polarization", "[", RowBox[{"k", ",", "\[ImaginaryI]"}], "]"}]], "Output", CellTags->"Polarization", - CellLabel->"Out[2]//StandardForm=", - CellID->1532058091] + CellLabel->"Out[2]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -263,8 +257,7 @@ Cell[BoxData[ RowBox[{"k", ",", RowBox[{"-", "\[ImaginaryI]"}]}], ")"}], TraditionalForm]], "Output", CellTags->"Polarization", - CellLabel->"Out[3]=", - CellID->1609141955] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -283,14 +276,13 @@ Cell[BoxData[ RowBox[{"k", ",", RowBox[{"-", "\[ImaginaryI]"}]}], "]"}]], "Output", CellTags->"Polarization", - CellLabel->"Out[4]//StandardForm=", - CellID->1652128522] + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"DiracSlash", "[", + RowBox[{"GS", "[", RowBox[{"Polarization", "[", "k", "]"}], "]"}]], "Input", CellTags->"Polarization", CellLabel->"In[5]:=", @@ -307,15 +299,14 @@ Cell[BoxData[ TraditionalForm], ")"}], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Polarization", - CellLabel->"Out[5]=", - CellID->665542938] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"DiracSlash", "[", + RowBox[{"GS", "[", RowBox[{"Polarization", "[", "k", "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"Polarization", @@ -323,13 +314,11 @@ Cell[BoxData[ CellID->710690441], Cell[BoxData[ - RowBox[{"DiracGamma", "[", - RowBox[{"Momentum", "[", - RowBox[{"Polarization", "[", - RowBox[{"k", ",", "\[ImaginaryI]"}], "]"}], "]"}], "]"}]], "Output", + RowBox[{"GS", "[", + RowBox[{"Polarization", "[", + RowBox[{"k", ",", "\[ImaginaryI]"}], "]"}], "]"}]], "Output", CellTags->"Polarization", - CellLabel->"Out[6]//StandardForm=", - CellID->1978838604] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -362,8 +351,7 @@ Cell[BoxData[ TraditionalForm], ")"}], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Polarization", - CellLabel->"Out[7]=", - CellID->149210740] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -428,12 +416,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{799, Automatic}, {Automatic, 134}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PolarizationSum.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PolarizationSum.nb index 88e99cca1..57d14d5ec 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PolarizationSum.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PolarizationSum.nb @@ -118,16 +118,96 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"PolarizationSum", "[", - RowBox[{"mu", ",", "nu", ",", " ", "..."}], " ", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "defines (as abbreviations) several polarization sums. The first two \ -arguments are the interpreted as Lorentz indices, all further ones are \ -momenta. PolarizationSum performs no calculations." + RowBox[{"\[Mu]", ",", "\[Nu]", ",", " ", "..."}], " ", "]"}]], + "InlineFormula"], + " \[LineSeparator]returns different polarization sums depending on its \ +arguments" }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + Cell[BoxData[ + RowBox[{"PolarizationSum", "[", + RowBox[{"\[Mu]", ",", " ", "\[Nu]"}], "]"}]], "InlineFormula"], + " or ", + Cell[BoxData[ + RowBox[{"PolarizationSum", "[", + RowBox[{"\[Mu]", ",", " ", "\[Nu]", ",", " ", "k", ",", " ", "0"}], "]"}]], + "InlineFormula"], + " gives ", + Cell[BoxData[ + RowBox[{"-", + SuperscriptBox["g", "\[Mu]\[Nu]"]}]], "InlineFormula"], + "." +}], "Notes", + CellID->1067943069], + +Cell[TextData[{ + Cell[BoxData[ + RowBox[{"PolarizationSum", "[", + RowBox[{"\[Mu]", ",", " ", "\[Nu]", ",", " ", "k"}], "]"}]], + "InlineFormula"], + " returns ", + Cell[BoxData[ + RowBox[{ + RowBox[{"-", + SuperscriptBox["g", "\[Mu]\[Nu]"]}], "+", + FractionBox[ + RowBox[{ + SuperscriptBox["k", "\[Mu]"], + SuperscriptBox["k", "\[Nu]"]}], + SuperscriptBox["k", "2"]]}]], "InlineFormula"], + "." +}], "Notes"], + +Cell[TextData[{ + Cell[BoxData[ + RowBox[{"PolarizationSum", "[", + RowBox[{"\[Mu]", ",", " ", "\[Nu]", ",", " ", "k", ",", " ", "n"}], "]"}]], + "InlineFormula"], + " yields ", + Cell[BoxData[ + RowBox[{ + RowBox[{"-", + SuperscriptBox["g", "\[Mu]\[Nu]"]}], "+", + FractionBox[ + RowBox[{ + RowBox[{ + SuperscriptBox["k", "\[Mu]"], + SuperscriptBox["n", "\[Nu]"]}], "+", + RowBox[{ + SuperscriptBox["k", "\[Nu]"], + SuperscriptBox["n", "\[Mu]"]}]}], + RowBox[{"k", "\[CenterDot]", "n"}]], "-", + FractionBox[ + RowBox[{ + SuperscriptBox["n", "2"], + SuperscriptBox["k", "\[Mu]"], + SuperscriptBox["k", "\[Nu]"]}], + SuperscriptBox[ + RowBox[{"(", + RowBox[{"k", "\[CenterDot]", "n"}], ")"}], "2"]]}]], "InlineFormula"], + "." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "PolarizationSum", "]"}]], "Input", + CellLabel->"In[28]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"VirtualBoson", "\[Rule]", "False"}], ",", + RowBox[{"Heads", "\[Rule]", + RowBox[{"{", + RowBox[{"LorentzIndex", ",", "LorentzIndex"}], "}"}]}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[28]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -163,14 +243,22 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["Polarization", + ButtonBox["Polariazation", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Polariazation", + ButtonNote->"Polariazation"], + ", ", + ButtonBox["DoPolariazationSums", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Polarization", - ButtonNote->"Polarization"], + ButtonData:>"paclet:FeynCalc/ref/DoPolariazationSums", + ButtonNote->"DoPolariazationSums"], + ", ", + ButtonBox["Uncontract", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Uncontract", + ButtonNote->"Uncontract"], "." -}], "Text", - CellTags->"PolarizationSum", - CellID->986230835] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -199,65 +287,44 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "PolarizationSum", "]"}]], "Input", - CellTags->"PolarizationSum", - CellLabel->"In[1]:=", - CellID->2045558864], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "4"}], ",", - RowBox[{"VirtualBoson", "\[Rule]", "False"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"PolarizationSum", - CellLabel->"Out[1]=", - CellID->993421841] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"PolarizationSum", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}]], "Input", CellTags->"PolarizationSum", - CellLabel->"In[2]:=", + CellLabel->"In[29]:=", CellID->1305140513], Cell[BoxData[ FormBox[ RowBox[{"-", - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm]}], TraditionalForm]], "Output", + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"PolarizationSum", - CellLabel->"Out[2]=", - CellID->430115432] + CellLabel->"Out[29]="] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; 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"See also: ", - ButtonBox["FourVector", + ButtonBox["FV", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FourVector", - ButtonNote->"FourVector"], + ButtonData:>"paclet:FeynCalc/ref/FV", + ButtonNote->"FV"], ", ", ButtonBox["Pair", BaseStyle->"Link", @@ -177,9 +176,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Polarization", ButtonNote->"Polarization"], "." -}], "Text", - CellTags->"PolarizationVector", - CellID->1661672347] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -212,7 +209,7 @@ Cell[BoxData[ RowBox[{"PolarizationVector", "[", RowBox[{"k", ",", "\[Mu]"}], "]"}]], "Input", CellTags->"PolarizationVector", - CellLabel->"In[2]:=", + CellLabel->"In[8]:=", CellID->1596092203], Cell[BoxData[ @@ -221,16 +218,13 @@ Cell[BoxData[ SuperscriptBox[ OverscriptBox["\[CurlyEpsilon]", "_"], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], "(", FormBox["k", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"PolarizationVector", - CellLabel->"Out[2]=", - CellID->1849918377] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -240,7 +234,7 @@ Cell[BoxData[ RowBox[{"PolarizationVector", "[", RowBox[{"k", ",", "\[Mu]"}], "]"}], "]"}]], "Input", CellTags->"PolarizationVector", - CellLabel->"In[3]:=", + CellLabel->"In[9]:=", CellID->597384549], Cell[BoxData[ @@ -250,16 +244,13 @@ Cell[BoxData[ SuperscriptBox[ OverscriptBox["\[CurlyEpsilon]", "_"], "*"], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], "(", FormBox["k", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"PolarizationVector", - CellLabel->"Out[3]=", - CellID->1945453536] + CellLabel->"Out[9]="] }, Open ]], Cell[TextData[{ @@ -270,9 +261,7 @@ Cell[TextData[{ SubscriptBox["\[CurlyEpsilon]", "\[Mu]"], "(", "k", ")"}], TraditionalForm]]], "is a special four-vector." -}], "Text", - CellTags->"PolarizationVector", - CellID->1108597225], +}], "Notes"], Cell[CellGroupData[{ @@ -281,7 +270,7 @@ Cell[BoxData[ RowBox[{"PolarizationVector", "[", RowBox[{"k", ",", "mu"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"PolarizationVector", - CellLabel->"In[4]:=", + CellLabel->"In[10]:=", CellID->1765549294], Cell[BoxData[ @@ -292,25 +281,22 @@ Cell[BoxData[ RowBox[{"Polarization", "[", RowBox[{"k", ",", "\[ImaginaryI]"}], "]"}], "]"}]}], "]"}]], "Output", CellTags->"PolarizationVector", - CellLabel->"Out[4]//StandardForm=", - CellID->152992573] + CellLabel->"Out[10]//StandardForm="] }, Open ]], -Cell["The transverality property is not automatic.", "Text", - CellTags->"PolarizationVector", - CellID->1023112491], +Cell["The transverality property is not automatic.", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a1", " ", "=", " ", + RowBox[{" ", RowBox[{ RowBox[{"PolarizationVector", "[", RowBox[{"k", ",", "\[Mu]"}], "]"}], " ", - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"k", ",", "\[Mu]"}], "]"}]}]}]], "Input", CellTags->"PolarizationVector", - CellLabel->"In[5]:=", + CellLabel->"In[12]:=", CellID->1218109993], Cell[BoxData[ @@ -324,36 +310,29 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm], " ", - FormBox[ - RowBox[{ - SuperscriptBox[ - OverscriptBox["\[CurlyEpsilon]", "_"], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], "(", - FormBox["k", - TraditionalForm], ")"}], - TraditionalForm]}], TraditionalForm]], "Output", + RowBox[{ + SuperscriptBox[ + OverscriptBox["\[CurlyEpsilon]", "_"], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], "(", + FormBox["k", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"PolarizationVector", - CellLabel->"Out[5]=", - CellID->1099894979] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Contract", "[", "a1", "]"}]], "Input", + RowBox[{"Contract", "[", "%", "]"}]], "Input", CellTags->"PolarizationVector", - CellLabel->"In[6]:=", + CellLabel->"In[13]:=", CellID->918402341], Cell[BoxData[ @@ -373,22 +352,21 @@ Cell[BoxData[ TraditionalForm], ")"}], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"PolarizationVector", - CellLabel->"Out[6]=", - CellID->1789359074] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"a2", " ", "=", " ", + RowBox[{" ", RowBox[{ RowBox[{"PolarizationVector", "[", RowBox[{"k", ",", "\[Mu]", ",", RowBox[{"Transversality", "\[Rule]", "True"}]}], "]"}], " ", - RowBox[{"FourVector", "[", + RowBox[{"FV", "[", RowBox[{"k", ",", "\[Mu]"}], "]"}]}]}]], "Input", CellTags->"PolarizationVector", - CellLabel->"In[9]:=", + CellLabel->"In[14]:=", CellID->113884671], Cell[BoxData[ @@ -402,171 +380,36 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], TraditionalForm]], TraditionalForm], " ", - FormBox[ - RowBox[{ - SuperscriptBox[ - OverscriptBox["\[CurlyEpsilon]", "_"], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], "(", - FormBox["k", - TraditionalForm], ")"}], - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"PolarizationVector", - CellLabel->"Out[9]=", - CellID->1008334660] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Contract", "[", "a2", "]"}]], "Input", - CellTags->"PolarizationVector", - CellLabel->"In[10]:=", - CellID->554867330], - -Cell[BoxData[ - FormBox["0", TraditionalForm]], "Output", - CellTags->"PolarizationVector", - CellLabel->"Out[10]=", - CellID->1890424275] -}, Open ]], - -Cell[TextData[{ - "Depending on the alphabetical ordering of the momenta, simplifcations are \ -done - e.g. \[LineSeparator]", - Cell[BoxData[ - FormBox[ RowBox[{ - RowBox[{ - RowBox[{"-", - SuperscriptBox[ - RowBox[{"(", - RowBox[{"k", "-", "p", "-", "k"}], ")"}], "\[Mu]"]}], - RowBox[{ - SubscriptBox["\[CurlyEpsilon]", "\[Mu]"], "(", - FormBox[ - RowBox[{"k", "-", "p"}], - TraditionalForm], ")"}]}], "=", - RowBox[{ - RowBox[{ - SuperscriptBox["k", "\[Mu]"], - RowBox[{ - SubscriptBox["\[CurlyEpsilon]", "\[Mu]"], "(", - FormBox[ - RowBox[{"k", "-", "p"}], - TraditionalForm], ")"}]}], "=", - 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TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], + FormBox["\[Mu]", TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - RowBox[{ - SuperscriptBox[ - OverscriptBox["\[CurlyEpsilon]", "_"], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], "(", - FormBox[ - RowBox[{"k", "-", "p"}], - TraditionalForm], ")"}], - TraditionalForm]}], TraditionalForm]], "Output", + TraditionalForm]], "(", + FormBox["k", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"PolarizationVector", - CellLabel->"Out[14]=", - CellID->2007724546] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Contract", "[", "a3", "]"}]], "Input", + RowBox[{"Contract", "[", "%", "]"}]], "Input", CellTags->"PolarizationVector", CellLabel->"In[15]:=", - CellID->1968835101], - -Cell[BoxData[ - FormBox[ - RowBox[{ - FormBox[ - OverscriptBox[ - FormBox["k", - TraditionalForm], "_"], - TraditionalForm], - FormBox["\<\"\[CenterDot]\"\>", - TraditionalForm], - FormBox[ - RowBox[{ - OverscriptBox["\[CurlyEpsilon]", "_"], "(", - FormBox[ - RowBox[{"k", "-", "p"}], - TraditionalForm], ")"}], - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"PolarizationVector", - CellLabel->"Out[15]=", - CellID->1932094598] -}, Open ]], + CellID->554867330], Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"a1", ",", "a2", ",", "a3"}], "]"}]], "Input", + FormBox["0", TraditionalForm]], "Output", CellTags->"PolarizationVector", - CellLabel->"In[16]:=", - CellID->88853703] + CellLabel->"Out[15]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -630,9 +473,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{634, Automatic}, {Automatic, 140}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PositiveInteger.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PositiveInteger.nb index 58ee07b8a..4a2112511 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PositiveInteger.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PositiveInteger.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DataType", ButtonNote->"DataType"], "." -}], "Text", - CellTags->"PositiveInteger", - CellID->1743918349] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PositiveNumber.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PositiveNumber.nb index 909e18db3..8d5d89576 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PositiveNumber.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PositiveNumber.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DataType", ButtonNote->"DataType"], "." -}], "Text", - CellTags->"PositiveNumber", - CellID->1422262610] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PostFortranFile.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PostFortranFile.nb index 14248e5e1..8929474a7 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PostFortranFile.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PostFortranFile.nb @@ -171,9 +171,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PreFortranFile", ButtonNote->"PreFortranFile"], "." -}], "Text", - CellTags->"PostFortranFile", - CellID->1559653274] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -259,12 +257,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Power2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Power2.nb index d8c4f5706..4b380456f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Power2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Power2.nb @@ -168,9 +168,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PowerFactor", ButtonNote->"PowerFactor"], "." -}], "Text", - CellTags->"Power2", - CellID->1979787947] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -204,7 +202,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "a"}], ",", "b"}], "]"}]], "Input", CellTags->"Power2", - CellLabel->"In[1]:=", + CellLabel->"In[16]:=", CellID->1628207625], Cell[BoxData[ @@ -213,8 +211,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "a"}], ")"}], "b"], TraditionalForm]], "Output", CellTags->"Power2", - CellLabel->"Out[1]=", - CellID->1555519313] + CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ @@ -224,7 +221,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "a"}], ",", "b"}], "]"}]], "Input", CellTags->"Power2", - CellLabel->"In[2]:=", + CellLabel->"In[17]:=", CellID->1450604516], Cell[BoxData[ @@ -237,8 +234,7 @@ Cell[BoxData[ SuperscriptBox["a", "b"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Power2", - CellLabel->"Out[2]=", - CellID->1786215167] + CellLabel->"Out[17]="] }, Open ]] }, Open ]], @@ -303,12 +299,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{594, Automatic}, {Automatic, 156}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PowerFactor.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PowerFactor.nb index cb2e41fca..3bd7d5bce 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PowerFactor.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PowerFactor.nb @@ -178,9 +178,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PowerSimplify", ButtonNote->"PowerSimplify"], "." -}], "Text", - CellTags->"PowerFactor", - CellID->2043225141] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -214,7 +212,7 @@ Cell[BoxData[ SuperscriptBox["x", "a"], SuperscriptBox["y", "a"]}]], "Input", CellTags->"PowerFactor", - CellLabel->"In[1]:=", + CellLabel->"In[5]:=", CellID->1163522766], Cell[BoxData[ @@ -223,8 +221,7 @@ Cell[BoxData[ SuperscriptBox["x", "a"], " ", SuperscriptBox["y", "a"]}], TraditionalForm]], "Output", CellTags->"PowerFactor", - CellLabel->"Out[1]=", - CellID->160369455] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -232,7 +229,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"PowerFactor", "[", "%", "]"}]], "Input", CellTags->"PowerFactor", - CellLabel->"In[2]:=", + CellLabel->"In[6]:=", CellID->485962359], Cell[BoxData[ @@ -241,8 +238,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"x", " ", "y"}], ")"}], "a"], TraditionalForm]], "Output", CellTags->"PowerFactor", - CellLabel->"Out[2]=", - CellID->783402888] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -307,12 +303,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{810, Automatic}, {Automatic, 139}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PowerSimplify.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PowerSimplify.nb index 19f066c08..db951bb1a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PowerSimplify.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PowerSimplify.nb @@ -279,9 +279,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPEi", ButtonNote->"OPEm"], "." -}], "Text", - CellTags->"PowerSimplify", - CellID->219988964] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -324,8 +322,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"PowerSimplify", - CellLabel->"Out[1]=", - CellID->1102382447] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -347,8 +344,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "m"], TraditionalForm]], "Output", CellTags->"PowerSimplify", - CellLabel->"Out[2]=", - CellID->1909539921] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -370,8 +366,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "m"], TraditionalForm]], "Output", CellTags->"PowerSimplify", - CellLabel->"Out[3]=", - CellID->2035038976] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -391,8 +386,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "m"], TraditionalForm]], "Output", CellTags->"PowerSimplify", - CellLabel->"Out[4]=", - CellID->952797373] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -457,12 +451,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{790, Automatic}, {Automatic, 117}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PreFortranFile.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PreFortranFile.nb index 530cc7b5a..7f2fe8858 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PreFortranFile.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PreFortranFile.nb @@ -171,9 +171,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PostFortranFile", ButtonNote->"PostFortranFile"], "." -}], "Text", - CellTags->"PreFortranFile", - CellID->659690590] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -259,12 +257,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{714, Automatic}, {Automatic, 177}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Prefactor.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Prefactor.nb index e1f2b1d8c..f5a3d8367 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Prefactor.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Prefactor.nb @@ -172,9 +172,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoopSum", ButtonNote->"OneLoopSum"], "." -}], "Text", - CellTags->"Prefactor", - CellID->1510913655] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -260,12 +258,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{532, Automatic}, {Automatic, 80}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PropagatorDenominator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PropagatorDenominator.nb index 346984dbb..91535c9f7 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PropagatorDenominator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/PropagatorDenominator.nb @@ -118,22 +118,13 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"PropagatorDenominator", "[", - RowBox[{"q", ",", " ", "m"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is a factor of the denominator of a propagator. If p is supposed to be \ -D-dimensional enter: PropagatorDenominator[Momentum[q, D], m]. What is meant \ -is ", - Cell[BoxData[ - FormBox[ - RowBox[{" ", - RowBox[{"1", "/", - RowBox[{"(", - RowBox[{"q", "^", "2"}]}]}]}], TraditionalForm]]], - " - ", - Cell[BoxData[ - FormBox[ - RowBox[{"m", "^", "2"}], TraditionalForm]]], - "). PropagatorDenominator[p] evaluates to PropagatorDenominator[p, 0]. " + RowBox[{ + RowBox[{"Momentum", "[", "q", "]"}], ",", " ", "m"}], "]"}]], + "InlineFormula"], + " \[LineSeparator] is a factor of the denominator of a propagator. If q is \ +supposed to be D-dimensional, use PropagatorDenominator[Momentum[q, D], m]. \ +What is meant is 1/(q^2-m^2). PropagatorDenominator must appear inside \ +FeynAmpDenominator, it is not a standalone object." }], "Usage", CellID->982511436], @@ -179,19 +170,12 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynAmpDenominator", ButtonNote->"FeynAmpDenominator"], ", ", - ButtonBox["PropagatorDenominatorExplicit", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/PropagatorDenominatorExplicit", - ButtonNote->"PropagatorDenominatorExplicit"], - ", ", - ButtonBox["IFPD", + ButtonBox["FeynAmpDenominatorExplicit", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/IFPD", - ButtonNote->"IFPD"], + ButtonData:>"paclet:FeynCalc/ref/FeynAmpDenominatorExplicit", + ButtonNote->"FeynAmpDenominatorExplicit"], "." -}], "Text", - CellTags->"PropagatorDenominator", - CellID->1480042296] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -222,151 +206,65 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", - RowBox[{"PropagatorDenominator", "[", - RowBox[{"p", ",", "m"}], "]"}]}]], "Input", + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"PropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", "p", "]"}], ",", "m"}], "]"}], "]"}]}]], "Input", CellTags->"PropagatorDenominator", - CellLabel->"In[1]:=", + CellLabel->"In[7]:=", CellID->158185315], Cell[BoxData[ FormBox[ FractionBox["1", - RowBox[{ - SuperscriptBox["p", "2"], "-", - SuperscriptBox["m", "2"]}]], TraditionalForm]], "Output", - CellTags->"PropagatorDenominator", - CellLabel->"Out[1]=", - CellID->442450206] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"PropagatorDenominator", "[", "p", "]"}]], "Input", - CellTags->"PropagatorDenominator", - CellLabel->"In[2]:=", - CellID->498222960], - -Cell[BoxData[ - FormBox[ - FractionBox["1", - SuperscriptBox["p", "2"]], TraditionalForm]], "Output", + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p], + FeynCalc`Momentum[$CellContext`p]], "-", $CellContext`m^2], + Editable->False]], TraditionalForm]], "Output", CellTags->"PropagatorDenominator", - CellLabel->"Out[2]=", - CellID->1576931809] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t1", "=", + RowBox[{"FeynAmpDenominator", "[", RowBox[{"PropagatorDenominator", "[", - RowBox[{"q", ",", "m"}], "]"}], " "}]], "Input", - CellTags->"PropagatorDenominator", - CellLabel->"In[3]:=", - CellID->1389901751], - -Cell[BoxData[ - FormBox[ - FractionBox["1", RowBox[{ - SuperscriptBox["q", "2"], "-", - SuperscriptBox["m", "2"]}]], TraditionalForm]], "Output", - CellTags->"PropagatorDenominator", - CellLabel->"Out[3]=", - CellID->298016951] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"FCI", "[", "t1", "]"}], "]"}]], "Input", - CellTags->"PropagatorDenominator", - CellLabel->"In[4]:=", - CellID->2126879083], - -Cell[BoxData[ - RowBox[{"PropagatorDenominator", "[", - RowBox[{ - RowBox[{"Momentum", "[", - RowBox[{"q", ",", "D"}], "]"}], ",", "m"}], "]"}]], "Output", - CellTags->"PropagatorDenominator", - CellLabel->"Out[4]//StandardForm=", - CellID->537265154] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"StandardForm", "[", - RowBox[{"ChangeDimension", "[", - RowBox[{"t1", ",", "D"}], "]"}], "]"}]], "Input", - CellTags->"PropagatorDenominator", - CellLabel->"In[5]:=", - CellID->678156808], - -Cell[BoxData[ - RowBox[{"PropagatorDenominator", "[", - RowBox[{ - RowBox[{"Momentum", "[", - RowBox[{"q", ",", "D"}], "]"}], ",", "m"}], "]"}]], "Output", - CellTags->"PropagatorDenominator", - CellLabel->"Out[5]//StandardForm=", - CellID->2020025200] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"PropagatorDenominatorExplicit", "[", "t1", "]"}]], "Input", - CellTags->"PropagatorDenominator", - CellLabel->"In[6]:=", - CellID->253071892], + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "m"}], "]"}], "]"}]], "Input", + CellLabel->"In[8]:="], Cell[BoxData[ FormBox[ FractionBox["1", - RowBox[{ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], "2"], "-", - SuperscriptBox["m", "2"]}]], TraditionalForm]], "Output", - CellTags->"PropagatorDenominator", - CellLabel->"Out[6]=", - CellID->1114450386] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"StandardForm", "[", "%", "]"}]], "Input", - CellTags->"PropagatorDenominator", - CellLabel->"In[7]:=", - CellID->1713457301], - -Cell[BoxData[ - FractionBox["1", - RowBox[{ - RowBox[{"-", - SuperscriptBox["m", "2"]}], "+", - RowBox[{"Pair", "[", + InterpretationBox[ RowBox[{ - RowBox[{"Momentum", "[", "q", "]"}], ",", - RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]}]]], "Output", - CellTags->"PropagatorDenominator", - CellLabel->"Out[7]//StandardForm=", - CellID->1426276777] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", "t1", "]"}]], "Input", - CellTags->"PropagatorDenominator", - CellLabel->"In[8]:=", - CellID->598061343] + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]], "-", $CellContext`m^2], + Editable->False]], TraditionalForm]], "Output", + CellLabel->"Out[8]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -429,13 +327,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{700, 868}, +WindowMargins->{{932, Automatic}, {Automatic, 155}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/PropagatorDenominatorExplicit.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/PropagatorDenominatorExplicit.nb deleted file mode 100644 index 997cbddd7..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/PropagatorDenominatorExplicit.nb +++ /dev/null @@ -1,404 +0,0 @@ -Notebook[{ -Cell[TextData[{ - 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ButtonNote->"Twist2QuarkOperator"], "." -}], "Text", - CellTags->"QO", - CellID->1788859244] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/QP.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/QP.nb index 1ed07ebad..8e8318ef4 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/QP.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/QP.nb @@ -159,13 +159,15 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], +Cell[RawData["\<\ Cell[TextData[{ - ButtonBox["QuarkPropagator", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/QuarkPropagator", - ButtonNote->"QuarkPropagator"], - "." -}], "Text", + ButtonBox[\"QuarkPropagator\", + BaseStyle->\"Link\", + ButtonData:>\"paclet:FeynCalc/ref/QuarkPropagator\", + ButtonNote->\"QuarkPropagator\"], + \".\" +}], \"SeeAlso\"]\ +\>"], "Text", CellTags->"QP", CellID->218226034] }, Open ]], @@ -253,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuantumField.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuantumField.nb index 219d67037..668892469 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuantumField.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuantumField.nb @@ -180,9 +180,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/ExpandPartialD", ButtonNote->"ExpandPartialD"], "." -}], "Text", - CellTags->"QuantumField", - CellID->231016079] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -209,23 +207,20 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["This denotes a scalar field.", "Text", - CellTags->"QuantumField", - CellID->173552947], +Cell["This denotes a scalar field.", "Notes"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"QuantumField", "[", "S", "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[17]:=", + CellLabel->"In[10]:=", CellID->1327076480], Cell[BoxData[ FormBox["S", TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[17]=", - CellID->2038740597] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -233,15 +228,14 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"QuantumField", "[", "AntiQuarkField", "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[18]:=", + CellLabel->"In[11]:=", CellID->1661786669], Cell[BoxData[ FormBox[ OverscriptBox["\[Psi]", "_"], TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[18]=", - CellID->2083488651] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -249,19 +243,16 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"QuantumField", "[", "QuarkField", "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[19]:=", + CellLabel->"In[12]:=", CellID->377089919], Cell[BoxData[ FormBox["\[Psi]", TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[19]=", - CellID->1186167697] + CellLabel->"Out[12]="] }, Open ]], -Cell["This is a field with a Lorentz index.", "Text", - CellTags->"QuantumField", - CellID->1204193660], +Cell["This is a field with a Lorentz index.", "Notes"], Cell[CellGroupData[{ @@ -270,7 +261,7 @@ Cell[BoxData[ RowBox[{"B", ",", RowBox[{"{", "\[Mu]", "}"}]}], "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[20]:=", + CellLabel->"In[13]:=", CellID->776002298], Cell[BoxData[ @@ -281,13 +272,10 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm]], TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[20]=", - CellID->188307989] + CellLabel->"Out[13]="] }, Open ]], -Cell["Color indices should be put after the Lorentz ones.", "Text", - CellTags->"QuantumField", - CellID->1363299018], +Cell["Color indices should be put after the Lorentz ones.", "Notes"], Cell[CellGroupData[{ @@ -297,7 +285,7 @@ Cell[BoxData[ RowBox[{"{", "\[Mu]", "}"}], ",", RowBox[{"{", "a", "}"}]}], "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[21]:=", + CellLabel->"In[14]:=", CellID->674687696], Cell[BoxData[ @@ -314,8 +302,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[21]=", - CellID->568800193] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ @@ -323,7 +310,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[22]:=", + CellLabel->"In[15]:=", CellID->1682950318], Cell[BoxData[ @@ -332,8 +319,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], ",", RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}]], "Output", CellTags->"QuantumField", - CellLabel->"Out[22]//StandardForm=", - CellID->232650919] + CellLabel->"Out[15]//StandardForm="] }, Open ]], Cell[TextData[{ @@ -348,9 +334,7 @@ Cell[TextData[{ RowBox[{ SubsuperscriptBox["A", "\[Mu]", "a"], "."}]}], TraditionalForm]]], " " -}], "Text", - CellTags->"QuantumField", - CellID->508873038], +}], "Notes"], Cell[CellGroupData[{ @@ -360,7 +344,7 @@ Cell[BoxData[ RowBox[{"{", "OPEDelta", "}"}], ",", RowBox[{"{", "a", "}"}]}], "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[23]:=", + CellLabel->"In[16]:=", CellID->503486981], Cell[BoxData[ @@ -377,16 +361,13 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[23]=", - CellID->1323752020] + CellLabel->"Out[16]="] }, Open ]], Cell["\<\ - The first list of indices is usually interpreted as type LorentzIndex, \ -except for OPEDelta, which gets converted to type Momentum. \ -\>", "Text", - CellTags->"QuantumField", - CellID->708047350], +The first list of indices is usually interpreted as type LorentzIndex, except \ +for OPEDelta, which gets converted to type Momentum. \ +\>", "Notes"], Cell[CellGroupData[{ @@ -397,7 +378,7 @@ Cell[BoxData[ RowBox[{"{", "OPEDelta", "}"}], ",", RowBox[{"{", "a", "}"}]}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[24]:=", + CellLabel->"In[17]:=", CellID->511543671], Cell[BoxData[ @@ -406,13 +387,10 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "OPEDelta", "]"}], ",", RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}]], "Output", CellTags->"QuantumField", - CellLabel->"Out[24]//StandardForm=", - CellID->517587533] + CellLabel->"Out[17]//StandardForm="] }, Open ]], -Cell["Derivatives of fields are denoted as follows.", "Text", - CellTags->"QuantumField", - CellID->162225984], +Cell["Derivatives of fields are denoted as follows.", "Notes"], Cell[CellGroupData[{ @@ -422,27 +400,27 @@ Cell[BoxData[ RowBox[{"FCPartialD", "[", "\[Mu]", "]"}], ",", "A", ",", RowBox[{"{", "\[Mu]", "}"}]}], "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[25]:=", + CellLabel->"In[18]:=", CellID->737122763], Cell[BoxData[ FormBox[ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Mu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], TraditionalForm]], "Output", + TraditionalForm]], ")"}], TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[25]=", - CellID->407944783] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -452,23 +430,22 @@ Cell[BoxData[ RowBox[{ RowBox[{"FCPartialD", "[", "OPEDelta", "]"}], ",", "S"}], "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[26]:=", + CellLabel->"In[19]:=", CellID->1485590656], Cell[BoxData[ FormBox[ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[CapitalDelta]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ - FormBox["S", - TraditionalForm], "\[Null]", "\[Null]"]}], TraditionalForm]], "Output", + FormBox["S", + TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[26]=", - CellID->57451832] + CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ @@ -480,19 +457,18 @@ Cell[BoxData[ RowBox[{"{", "OPEDelta", "}"}], ",", RowBox[{"{", "a", "}"}]}], "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[27]:=", + CellLabel->"In[20]:=", CellID->1178067453], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SubscriptBox["\[PartialD]", - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm]], - TraditionalForm], + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm]], SubsuperscriptBox[ FormBox["A", TraditionalForm], @@ -503,10 +479,9 @@ Cell[BoxData[ FormBox[ FormBox["a", TraditionalForm], - TraditionalForm]]}], TraditionalForm]], "Output", + TraditionalForm]], ")"}], TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[27]=", - CellID->1175747409] + CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ @@ -520,25 +495,32 @@ Cell[BoxData[ RowBox[{"{", "OPEDelta", "}"}], ",", RowBox[{"{", "a", "}"}]}], "]"}]], "Input", CellTags->"QuantumField", - CellLabel->"In[28]:=", + CellLabel->"In[21]:=", CellID->1296308546], Cell[BoxData[ FormBox[ - RowBox[{"QuantumField", "(", - RowBox[{ + SuperscriptBox[ + FormBox[ SubsuperscriptBox["\[PartialD]", FormBox[ FormBox["\[CapitalDelta]", TraditionalForm], - TraditionalForm], "m"], ",", "A", ",", - FormBox["\[CapitalDelta]", - TraditionalForm], ",", - FormBox["a", - TraditionalForm]}], ")"}], TraditionalForm]], "Output", + TraditionalForm], "m"], + TraditionalForm], + RowBox[{ + FormBox["A", + TraditionalForm], + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[28]=", - CellID->2017233085] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ @@ -549,14 +531,13 @@ Cell[BoxData[ RowBox[{"QuantumField", "[", "A", "]"}], "]"}], " ", "===", " ", RowBox[{"QuantumField", "[", "A", "]"}]}]], "Input", CellTags->"QuantumField", - CellLabel->"In[29]:=", + CellLabel->"In[22]:=", CellID->1498512634], Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", CellTags->"QuantumField", - CellLabel->"Out[29]=", - CellID->1933229370] + CellLabel->"Out[22]="] }, Open ]] }, Open ]], @@ -621,9 +602,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkField.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkField.nb index cf5fa2b91..0491cdf46 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkField.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkField.nb @@ -117,13 +117,14 @@ Cell["QuarkField", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["QuarkField"], "InlineFormula"], - " \[LineSeparator]", - "is the name of a fermionic field. QuarkField is just a name with no \ -functional properties. Only typesetting rules are attached." + " \[LineSeparator]is the name of a fermionic field." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +This is just a name with no functional properties. Only typesetting rules are \ +attached.\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -170,9 +171,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/QuantumField", ButtonNote->"QuantumField"], "." -}], "Text", - CellTags->"QuarkField", - CellID->1398753735] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,14 +202,13 @@ Cell[CellGroupData[{ Cell[BoxData["QuarkField"], "Input", CellTags->"QuarkField", - CellLabel->"In[1]:=", + CellLabel->"In[9]:=", CellID->1364163366], Cell[BoxData[ FormBox["\[Psi]", TraditionalForm]], "Output", CellTags->"QuarkField", - CellLabel->"Out[1]=", - CellID->753517076] + CellLabel->"Out[9]="] }, Open ]] }, Open ]], @@ -275,12 +273,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{376, Automatic}, {Automatic, 243}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkFieldChi.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkFieldChi.nb new file mode 100644 index 000000000..aedb3ef92 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkFieldChi.nb @@ -0,0 +1,372 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/QuarkFieldChi", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["QuarkFieldChi", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData["QuarkFieldChi"], "InlineFormula"], + " \[LineSeparator]is the name of a fermionic field." +}], "Usage", + CellID->982511436], + +Cell["\<\ +This is just a name with no functional properties. 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Only typesetting rules are \ +attached.\ +\>", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; 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Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{849, Automatic}, {219, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkGluonVertex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkGluonVertex.nb index 97e2dad34..771ce5c5e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkGluonVertex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkGluonVertex.nb @@ -118,14 +118,59 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"QuarkGluonVertex", "[", - RowBox[{"mu", ",", " ", "a"}], "]"}]], "InlineFormula"], + RowBox[{"\[Mu]", ",", " ", "a"}], "]"}]], "InlineFormula"], " \[LineSeparator]", "gives the Feynman rule for the quark-gluon vertex. " }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + Cell[BoxData["QGV"], "InlineFormula"], + " can be used as an abbreviation of ", + ButtonBox["QuarkGluonVertex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/QuarkGluonVertex", + ButtonNote->"QuarkGluonVertex"], + "." +}], "Notes", + CellID->1067943069], + +Cell[TextData[{ + "The dimension and the name of the coupling constant are determined by the \ +options ", + ButtonBox["Dimension", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Dimension", + ButtonNote->"Dimension"], + " and ", + ButtonBox["CouplingConstant", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CouplingConstant", + ButtonNote->"CouplingConstant"], + ". " +}], "Notes", + CellID->14058075], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "QuarkGluonVertex", "]"}]], "Input", + CellLabel->"In[38]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"CounterTerm", "\[Rule]", "False"}], ",", + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Explicit", "\[Rule]", "False"}], ",", + RowBox[{"\[CapitalOmega]", "\[Rule]", "False"}], ",", + RowBox[{"Polarization", "\[Rule]", "0"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[38]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -166,9 +211,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GluonVertex", ButtonNote->"GluonVertex"], "." -}], "Text", - CellTags->"QuarkGluonVertex", - CellID->507567203] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -198,37 +241,60 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Options", "[", "QuarkGluonVertex", "]"}]], "Input", + RowBox[{"QuarkGluonVertex", "[", + RowBox[{"\[Mu]", ",", "a", ",", + RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkGluonVertex", - CellLabel->"In[1]:=", - CellID->1162740224], + CellLabel->"In[39]:=", + CellID->158944719], Cell[BoxData[ FormBox[ - RowBox[{"{", + RowBox[{"\[ImaginaryI]", " ", + SubscriptBox["g", "s"], " ", RowBox[{ - RowBox[{"CounterTerm", "\[Rule]", "False"}], ",", - RowBox[{"CouplingConstant", "\[Rule]", - SubscriptBox["g", "s"]}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"Explicit", "\[Rule]", "False"}], ",", - RowBox[{"\[CapitalOmega]", "\[Rule]", "False"}], ",", - RowBox[{"Polarization", "\[Rule]", "0"}]}], "}"}], - TraditionalForm]], "Output", + SuperscriptBox["T", + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"QuarkGluonVertex", - CellLabel->"Out[1]=", - CellID->1237177013] + CellLabel->"Out[39]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"QuarkGluonVertex", "[", - RowBox[{"\[Mu]", ",", "a", ",", - RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", - CellTags->"QuarkGluonVertex", - CellLabel->"In[2]:=", - CellID->158944719], + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"QGV", "[", + RowBox[{"\[Mu]", ",", "a"}], "]"}]], "Input", + CellLabel->"In[43]:="], + +Cell[BoxData[ + FormBox[ + SubsuperscriptBox["Q", + FormBox["a", + TraditionalForm], + FormBox["\[Mu]", + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[43]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Explicit", "[", "%", "]"}]], "Input", + CellLabel->"In[44]:="], Cell[BoxData[ FormBox[ @@ -245,20 +311,25 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", - CellTags->"QuarkGluonVertex", - CellLabel->"Out[2]=", - CellID->1997015232] + CellLabel->"Out[44]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"QuarkGluonVertex", "[", RowBox[{"\[Mu]", ",", "a", ",", RowBox[{"CounterTerm", " ", "\[Rule]", "1"}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkGluonVertex", - CellLabel->"In[3]:=", + CellLabel->"In[45]:=", CellID->196044183], Cell[BoxData[ @@ -286,8 +357,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm]], TraditionalForm]], "Output", CellTags->"QuarkGluonVertex", - CellLabel->"Out[3]=", - CellID->1493367329] + CellLabel->"Out[45]="] }, Open ]], Cell[CellGroupData[{ @@ -298,7 +368,7 @@ Cell[BoxData[ RowBox[{"CounterTerm", " ", "\[Rule]", "2"}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkGluonVertex", - CellLabel->"In[4]:=", + CellLabel->"In[46]:=", CellID->1947570088], Cell[BoxData[ @@ -322,8 +392,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm]], TraditionalForm]], "Output", CellTags->"QuarkGluonVertex", - CellLabel->"Out[4]=", - CellID->559873087] + CellLabel->"Out[46]="] }, Open ]], Cell[CellGroupData[{ @@ -334,7 +403,7 @@ Cell[BoxData[ RowBox[{"CounterTerm", " ", "\[Rule]", "3"}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkGluonVertex", - CellLabel->"In[5]:=", + CellLabel->"In[47]:=", CellID->339282308], Cell[BoxData[ @@ -361,12 +430,18 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm]], TraditionalForm]], "Output", CellTags->"QuarkGluonVertex", - CellLabel->"Out[5]=", - CellID->1688386600] + CellLabel->"Out[47]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + Cell[BoxData[ RowBox[{"QuarkGluonVertex", "[", RowBox[{ @@ -377,26 +452,22 @@ Cell[BoxData[ RowBox[{"OPE", "\[Rule]", "True"}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkGluonVertex", - CellLabel->"In[6]:=", + CellLabel->"In[48]:=", CellID->2017937273], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[CapitalOmega]", " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", + SuperscriptBox[ + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], " ", SubscriptBox["g", "s"], " ", RowBox[{ RowBox[{"(", @@ -466,8 +537,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}]}], TraditionalForm]], "Output", CellTags->"QuarkGluonVertex", - CellLabel->"Out[6]=", - CellID->389181480] + CellLabel->"Out[48]="] }, Open ]], Cell[CellGroupData[{ @@ -482,7 +552,7 @@ Cell[BoxData[ RowBox[{"OPE", "\[Rule]", "False"}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkGluonVertex", - CellLabel->"In[7]:=", + CellLabel->"In[49]:=", CellID->729288779], Cell[BoxData[ @@ -501,8 +571,8 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"QuarkGluonVertex", - CellLabel->"Out[7]=", - CellID->1936603618] + CellLabel->"Out[49]="] +}, Open ]] }, Open ]] }, Open ]], @@ -567,12 +637,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{446, Automatic}, {Automatic, 104}}, +WindowMargins->{{Automatic, 478}, {-14, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkMass.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkMass.nb index 6a63261b4..7d70b3dd5 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkMass.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkMass.nb @@ -174,9 +174,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RTL", ButtonNote->"RTL"], "." -}], "Text", - CellTags->"QuarkMass", - CellID->966046819] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -262,12 +260,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{350, Automatic}, {Automatic, 38}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkPropagator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkPropagator.nb index 20eac13f7..5a33db535 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkPropagator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/QuarkPropagator.nb @@ -118,14 +118,50 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"QuarkPropagator", "[", "p", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the massless quark propagator. QuarkPropagator[{p,m}] or gives the quark \ -propagator with mass m." + " \[LineSeparator]is the massless quark propagator.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"QuarkPropagator", "[", + RowBox[{"{", + RowBox[{"p", ",", "m"}], "}"}], "]"}]], "InlineFormula"], + " \[LineSeparator]gives the quark propagator with mass ", + Cell[BoxData["m"], "InlineFormula"], + "." }], "Usage", - CellID->982511436], + CellID->2010081510], + +Cell[TextData[{ + Cell[BoxData["QP"], "InlineFormula"], + " can be used as an abbreviation of ", + ButtonBox["QuarkPropagator", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/QuarkPropagator", + ButtonNote->"QuarkPropagator"], + "." +}], "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "QuarkPropagator", "]"}]], "Input", + CellLabel->"In[50]:="], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"CounterTerm", "\[Rule]", "False"}], ",", + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Explicit", "\[Rule]", "False"}], ",", + RowBox[{"Loop", "\[Rule]", "0"}], ",", + RowBox[{"\[CapitalOmega]", "\[Rule]", "False"}], ",", + RowBox[{"Polarization", "\[Rule]", "0"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[50]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -171,9 +207,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/QuarkGluonVertex", ButtonNote->"QuarkGluonVertex"], "." -}], "Text", - CellTags->"QuarkPropagator", - CellID->704256164] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -202,38 +236,12 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "QuarkPropagator", "]"}]], "Input", - CellTags->"QuarkPropagator", - CellLabel->"In[2]:=", - CellID->1137505588], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"CounterTerm", "\[Rule]", "False"}], ",", - RowBox[{"CouplingConstant", "\[Rule]", - SubscriptBox["g", "s"]}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"Explicit", "\[Rule]", "False"}], ",", - RowBox[{"Loop", "\[Rule]", "0"}], ",", - RowBox[{"\[CapitalOmega]", "\[Rule]", "False"}], ",", - RowBox[{"Polarization", "\[Rule]", "0"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"QuarkPropagator", - CellLabel->"Out[2]=", - CellID->759410596] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"QuarkPropagator", "[", RowBox[{"p", ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkPropagator", - CellLabel->"In[5]:=", + CellLabel->"In[51]:=", CellID->1589814930], Cell[BoxData[ @@ -245,12 +253,19 @@ Cell[BoxData[ FormBox["p", TraditionalForm], TraditionalForm]}]}], - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"]], TraditionalForm]], "Output", + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]]], + Editable->False]], TraditionalForm]], "Output", CellTags->"QuarkPropagator", - CellLabel->"Out[5]=", - CellID->1709152205] + CellLabel->"Out[51]="] }, Open ]], Cell[CellGroupData[{ @@ -262,7 +277,7 @@ Cell[BoxData[ RowBox[{"p", ",", "m"}], "}"}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"QuarkPropagator", - CellLabel->"In[6]:=", + CellLabel->"In[52]:=", CellID->1965811029], Cell[BoxData[ @@ -276,14 +291,80 @@ Cell[BoxData[ FormBox["p", TraditionalForm], TraditionalForm]}]}], ")"}]}], - RowBox[{ - SuperscriptBox[ - FormBox["p", - TraditionalForm], "2"], "-", - SuperscriptBox["m", "2"]}]], TraditionalForm]], "Output", + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]], "-", $CellContext`m^2], + Editable->False]], TraditionalForm]], "Output", CellTags->"QuarkPropagator", - CellLabel->"Out[6]=", - CellID->545226998] + CellLabel->"Out[52]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"QP", "[", + RowBox[{"{", + RowBox[{"p", ",", "m"}], "}"}], "]"}]], "Input", + CellLabel->"In[53]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SubscriptBox["\[CapitalPi]", "q"], "(", + FormBox["p", + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellLabel->"Out[53]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Explicit", "[", "%", "]"}]], "Input", + CellLabel->"In[54]:="], + +Cell[BoxData[ + FormBox[ + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", + RowBox[{"(", + RowBox[{"m", "+", + RowBox[{"\[Gamma]", "\[CenterDot]", + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]}]}], ")"}]}], + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`p, D], + FeynCalc`Momentum[$CellContext`p, D]], "-", $CellContext`m^2], + Editable->False]], TraditionalForm]], "Output", + CellLabel->"Out[54]="] +}, Open ]] }, Open ]] }, Open ]], @@ -348,12 +429,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{896, Automatic}, {Automatic, 179}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHI.nb index df7f93699..5e72151c3 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHI.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHI.nb @@ -182,9 +182,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI2FC", ButtonNote->"RHI2FC"], "." -}], "Text", - CellTags->"RHI", - CellID->1234981081] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -196,8 +194,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -211,12 +207,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"RHI", - CellLabel->"In[1]:=", - CellID->1055475085] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -278,12 +268,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{659, Automatic}, {Automatic, 61}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHI2FC.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHI2FC.nb index 9079cf3ec..2d050ac41 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHI2FC.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHI2FC.nb @@ -181,9 +181,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI2FC", ButtonNote->"RHI2FC"], "." -}], "Text", - CellTags->"RHI2FC", - CellID->2129471313] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -195,8 +193,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -210,12 +206,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"RHI2FC", - CellLabel->"In[1]:=", - CellID->729912401] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -277,12 +267,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{799, Automatic}, {Automatic, 168}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHM.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHM.nb index 0aefb0221..afefb8d1b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHM.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHM.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI", ButtonNote->"RHI"], "." -}], "Text", - CellTags->"RHM", - CellID->1366061454] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -179,8 +177,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -194,12 +190,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"RHM", - CellLabel->"In[1]:=", - CellID->233473012] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -261,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{801, Automatic}, {Automatic, 180}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHO.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHO.nb index 30cacc54c..9c6635d43 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHO.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHO.nb @@ -167,9 +167,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHI", ButtonNote->"RHI"], "." -}], "Text", - CellTags->"RHO", - CellID->2131383850] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -181,8 +179,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -196,12 +192,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"RHO", - CellLabel->"In[1]:=", - CellID->868607428] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -263,12 +253,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{606, Automatic}, {Automatic, 162}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHP.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHP.nb index c79716355..bd78b9e14 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/RHP.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/RHP.nb @@ -169,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/RHO", ButtonNote->"RHO"], "." -}], "Text", - CellTags->"RHP", - CellID->1242736892] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -183,8 +181,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -198,12 +194,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"RHP", - CellLabel->"In[1]:=", - CellID->374441694] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -265,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{715, Automatic}, {Automatic, 61}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/RTL.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/RTL.nb index 414fc4f6a..4e709ac88 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/RTL.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/RTL.nb @@ -171,9 +171,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Epsilon", ButtonNote->"Epsilon"], "." -}], "Text", - CellTags->"RTL", - CellID->463893301] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -185,8 +183,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -200,12 +196,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"RTL", - CellLabel->"In[1]:=", - CellID->1882300186] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -267,12 +257,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{541, Automatic}, {Automatic, 133}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ReduceGamma.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ReduceGamma.nb index cd899d418..34af2f362 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ReduceGamma.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ReduceGamma.nb @@ -117,9 +117,8 @@ Cell["ReduceGamma", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["ReduceGamma"], "InlineFormula"], - " \[LineSeparator]", - "is an option of OneLoop. If set to True all DiracMatrix[6] and \ -DiracMatrix[7] (i.e. all ChiralityProjector) are reduced to Gamma5." + " \[LineSeparator]is an option of OneLoop. If set to True all GA[6] and \ +GA[7] (i.e. all chirality projectors) are reduced to Gamma5." }], "Usage", CellID->982511436], @@ -165,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoop", ButtonNote->"OneLoop"], "." -}], "Text", - CellTags->"ReduceGamma", - CellID->581277123] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{762, Automatic}, {Automatic, 98}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ReduceToScalars.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ReduceToScalars.nb index def37ba93..bdb5f12d2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ReduceToScalars.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ReduceToScalars.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoopSum", ButtonNote->"OneLoopSum"], "." -}], "Text", - CellTags->"ReduceToScalars", - CellID->1934839663] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{727, Automatic}, {Automatic, 212}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Rename.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Rename.nb index 2f2eed4d5..995ac0ba6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Rename.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Rename.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Contract", ButtonNote->"Contract"], "." -}], "Text", - CellTags->"Rename", - CellID->345735960] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{617, Automatic}, {Automatic, 142}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/RightPartialD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/RightPartialD.nb index 0862a5dce..6fc89d9a2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/RightPartialD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/RightPartialD.nb @@ -163,29 +163,23 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell[RawData["\<\ Cell[TextData[{ - ButtonBox[\"ExpandPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/ExpandPartialD\", - ButtonNote->\"ExpandPartialD\"], - \", \", - ButtonBox[\"FCPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/PartialD\", - ButtonNote->\"FCPartialD\"], - \", \", - ButtonBox[\"LeftPartialD\", - BaseStyle->\"Link\", - ButtonData:>\"paclet:FeynCalc/ref/LeftPartialD\", - ButtonNote->\"LeftPartialD\"], - \".\" -}], \"Text\", - CellTags->\"RightPartialD\", - CellID->1409903491]\ -\>"], "Text", - CellTags->"RightPartialD", - CellID->1409903491] + ButtonBox["ExpandPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/ExpandPartialD", + ButtonNote->"ExpandPartialD"], + ", ", + ButtonBox["FCPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/PartialD", + ButtonNote->"FCPartialD"], + ", ", + ButtonBox["LeftPartialD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/LeftPartialD", + ButtonNote->"LeftPartialD"], + "." +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -217,7 +211,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"RightPartialD", "[", "\[Mu]", "]"}]], "Input", CellTags->"RightPartialD", - CellLabel->"In[1]:=", + CellLabel->"In[23]:=", CellID->27121698], Cell[BoxData[ @@ -229,8 +223,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], TraditionalForm]], "Output", CellTags->"RightPartialD", - CellLabel->"Out[1]=", - CellID->1461309897] + CellLabel->"Out[23]="] }, Open ]], Cell[CellGroupData[{ @@ -242,7 +235,7 @@ Cell[BoxData[ RowBox[{"A", ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]}]], "Input", CellTags->"RightPartialD", - CellLabel->"In[2]:=", + CellLabel->"In[24]:=", CellID->1087611627], Cell[BoxData[ @@ -260,8 +253,7 @@ Cell[BoxData[ FormBox["\[Mu]", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"RightPartialD", - CellLabel->"Out[2]=", - CellID->1675009373] + CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ @@ -269,27 +261,27 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ExpandPartialD", "[", "%", "]"}]], "Input", CellTags->"RightPartialD", - CellLabel->"In[3]:=", + CellLabel->"In[25]:=", CellID->1776931750], Cell[BoxData[ FormBox[ RowBox[{ - SubscriptBox["\[PartialD]", + SubscriptBox[ + RowBox[{"(", "\[PartialD]"}], FormBox[ FormBox["\[Mu]", TraditionalForm], TraditionalForm]], - SubsuperscriptBox[ + SubscriptBox[ FormBox["A", TraditionalForm], FormBox[ FormBox["\[Mu]", TraditionalForm], - TraditionalForm], "\[Null]"]}], TraditionalForm]], "Output", + TraditionalForm]], ")"}], TraditionalForm]], "Output", CellTags->"RightPartialD", - CellLabel->"Out[3]=", - CellID->528358345] + CellLabel->"Out[25]="] }, Open ]], Cell[CellGroupData[{ @@ -297,7 +289,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"RightPartialD", - CellLabel->"In[4]:=", + CellLabel->"In[26]:=", CellID->887044202], Cell[BoxData[ @@ -307,8 +299,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}], ",", "A", ",", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}]}], "]"}]], "Output", CellTags->"RightPartialD", - CellLabel->"Out[4]//StandardForm=", - CellID->1851835493] + CellLabel->"Out[26]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -318,15 +309,14 @@ Cell[BoxData[ RowBox[{"RightPartialD", "[", "\[Mu]", "]"}], "//", "StandardForm"}]], "Input", CellTags->"RightPartialD", - CellLabel->"In[5]:=", + CellLabel->"In[27]:=", CellID->472956421], Cell[BoxData[ RowBox[{"RightPartialD", "[", RowBox[{"LorentzIndex", "[", "\[Mu]", "]"}], "]"}]], "Output", CellTags->"RightPartialD", - CellLabel->"Out[5]//StandardForm=", - CellID->1374997587] + CellLabel->"Out[27]//StandardForm="] }, Open ]] }, Open ]], @@ -391,12 +381,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{709, Automatic}, {Automatic, 51}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/RussianTrick.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/RussianTrick.nb index d13806f50..df0025758 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/RussianTrick.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/RussianTrick.nb @@ -121,15 +121,14 @@ Cell[TextData[{ RowBox[{"exp", ",", " ", "k", ",", " ", RowBox[{"{", RowBox[{"q1", ",", "q2", ",", "p"}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "(=RussianTrick[exp,p,p,{q1,q2,p}]) does the integration by parts where p is \ -the external momentum. RussianTrick[exp, k,l, {q1,q2,p}] \ + " \[LineSeparator](=RussianTrick[exp,p,p,{q1,q2,p}]) does the integration by \ +parts where p is the external momentum. RussianTrick[exp, k,l, {q1,q2,p}] \ (=RussianTrick[exp,k,l]) does integration by parts where l is the momentum to \ -be differentiated.\n\nThe result is an expression which is vanishing." +be differentiated." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["The result is an expression which is vanishing.", "Notes", CellID->1067943069] }, Open ]], @@ -176,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FourLaplacian", ButtonNote->"FourLaplacian"], "." -}], "Text", - CellTags->"RussianTrick", - CellID->1345403817] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -219,7 +216,7 @@ Cell[BoxData[ "1", ",", " ", "1", ",", " ", "1", ",", " ", "1", ",", " ", "1"}], "}"}]}], "]"}]}]], "Input", CellTags->"RussianTrick", - CellLabel->"In[1]:=", + CellLabel->"In[28]:=", CellID->202624512], Cell[BoxData[ @@ -243,8 +240,7 @@ Cell[BoxData[ FormBox["0", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"RussianTrick", - CellLabel->"Out[1]=", - CellID->2099872204] + CellLabel->"Out[28]="] }, Open ]], Cell[CellGroupData[{ @@ -252,7 +248,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"t", "//", "RHI2FC"}]], "Input", CellTags->"RussianTrick", - CellLabel->"In[2]:=", + CellLabel->"In[29]:=", CellID->195595910], Cell[BoxData[ @@ -279,44 +275,111 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], "2"], "/", RowBox[{ - SuperscriptBox[ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], "2"], ".", - SuperscriptBox[ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm], "2"], ".", - SuperscriptBox[ - RowBox[{"(", - RowBox[{ + InterpretationBox[ + SuperscriptBox[ + FormBox[ FormBox[ RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], "-", - FormBox[ - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], - TraditionalForm]}], ")"}], "2"], ".", - SuperscriptBox[ - RowBox[{"(", - RowBox[{ + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D], + FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + FormBox[ FormBox[ RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm], "-", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D], + FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], FormBox[ - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], - TraditionalForm]}], ")"}], "2"], ".", - SuperscriptBox[ - RowBox[{"(", + FormBox[ + RowBox[{ + FormBox[ + RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], + TraditionalForm], "-", + FormBox[ + RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[-FeynCalc`Momentum[ + FeynCalc`FCGV["p"], D] + FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D], -FeynCalc`Momentum[ + FeynCalc`FCGV["p"], D] + FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], FormBox[ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], "-", + FormBox[ + RowBox[{ + FormBox[ + RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], + TraditionalForm], "-", + FormBox[ + RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[-FeynCalc`Momentum[ + FeynCalc`FCGV["p"], D] + FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D], -FeynCalc`Momentum[ + FeynCalc`FCGV["p"], D] + FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm]}], ")"}], "2"]}]}], TraditionalForm]], "Output", + FormBox[ + RowBox[{ + FormBox[ + RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], + TraditionalForm], "-", + FormBox[ + RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D] - FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D], FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D] - FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D]]], + Editable->False]}]}], TraditionalForm]], "Output", CellTags->"RussianTrick", - CellLabel->"Out[2]=", - CellID->1909433347] + CellLabel->"Out[29]="] }, Open ]], Cell[CellGroupData[{ @@ -326,7 +389,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"%", "//", "RHI2FC"}], ",", "q2"}], "]"}]], "Input", CellTags->"RussianTrick", - CellLabel->"In[3]:=", + CellLabel->"In[30]:=", CellID->767131830], Cell[BoxData[ @@ -355,44 +418,111 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], "2"]}], ")"}], "/", RowBox[{ - SuperscriptBox[ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], "2"], ".", - SuperscriptBox[ - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm], "2"], ".", - SuperscriptBox[ - RowBox[{"(", - RowBox[{ + InterpretationBox[ + SuperscriptBox[ + FormBox[ FormBox[ RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], "-", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D], + FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + FormBox[ FormBox[ - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], - TraditionalForm]}], ")"}], "2"], ".", - SuperscriptBox[ - RowBox[{"(", + RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D], + FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], FormBox[ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], - TraditionalForm], "-", - FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm]}], ")"}], "2"], ".", - SuperscriptBox[ - RowBox[{"(", + FormBox[ + RowBox[{ + FormBox[ + RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], + TraditionalForm], "-", + FormBox[ + RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[-FeynCalc`Momentum[ + FeynCalc`FCGV["p"], D] + FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D], -FeynCalc`Momentum[ + FeynCalc`FCGV["p"], D] + FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], FormBox[ - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], - TraditionalForm], "-", + FormBox[ + RowBox[{ + FormBox[ + RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], + TraditionalForm], "-", + FormBox[ + RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D] - FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D], FeynCalc`Momentum[ + FeynCalc`FCGV["q1"], D] - FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], FormBox[ - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], - TraditionalForm]}], ")"}], "2"]}]}], TraditionalForm]], "Output", + FormBox[ + RowBox[{ + FormBox[ + RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], + TraditionalForm], "-", + FormBox[ + RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}], + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[-FeynCalc`Momentum[ + FeynCalc`FCGV["p"], D] + FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D], -FeynCalc`Momentum[ + FeynCalc`FCGV["p"], D] + FeynCalc`Momentum[ + FeynCalc`FCGV["q2"], D]]], + Editable->False]}]}], TraditionalForm]], "Output", CellTags->"RussianTrick", - CellLabel->"Out[3]=", - CellID->2087454288] + CellLabel->"Out[30]="] }, Open ]], Cell[CellGroupData[{ @@ -400,7 +530,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FC2RHI", "[", "%", "]"}]], "Input", CellTags->"RussianTrick", - CellLabel->"In[4]:=", + CellLabel->"In[31]:=", CellID->2066492260], Cell[BoxData[ @@ -427,8 +557,7 @@ Cell[BoxData[ TraditionalForm]}]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"RussianTrick", - CellLabel->"Out[4]=", - CellID->641619861] + CellLabel->"Out[31]="] }, Open ]], Cell[CellGroupData[{ @@ -437,7 +566,7 @@ Cell[BoxData[ RowBox[{"Solve2", "[", RowBox[{"%", ",", "t"}], "]"}]], "Input", CellTags->"RussianTrick", - CellLabel->"In[5]:=", + CellLabel->"In[32]:=", CellID->1029114011], Cell[BoxData[ @@ -465,14 +594,13 @@ Cell[BoxData[ TraditionalForm]}]], TraditionalForm], "\[Rule]", "0"}], "}"}], TraditionalForm]], "Output", CellTags->"RussianTrick", - CellLabel->"Out[5]=", - CellID->1453686089] + CellLabel->"Out[32]="] }, Open ]], Cell[BoxData[ RowBox[{"Clear", "[", "t", "]"}]], "Input", CellTags->"RussianTrick", - CellLabel->"In[6]:=", + CellLabel->"In[33]:=", CellID->659830929] }, Open ]], @@ -537,12 +665,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{965, Automatic}, {Automatic, 184}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SD.nb index 367403488..98ebe0c5d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SD.nb @@ -119,11 +119,8 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"SD", "[", RowBox[{"i", ",", " ", "j"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the (FeynCalc-external) Kronecker-delta for SU(", - StyleBox["N", - FontSlant->"Italic"], - ") with color indices i and j. SD[i,j] is transformed into \ + " \[LineSeparator]denotes the SU(N) Kronecker delta with color indices i and \ +j in the adjoint represnetation. SD[i,j] is transformed into \ SUNDelta[SUNIndex[i],SUNIndex[j]] by FeynCalcInternal." }], "Usage", CellID->982511436], @@ -170,9 +167,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNDelta", ButtonNote->"SUNDelta"], "." -}], "Text", - CellTags->"SD", - CellID->2009139529] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -205,7 +200,7 @@ Cell[BoxData[ RowBox[{"SD", "[", RowBox[{"a", ",", "b"}], "]"}]], "Input", CellTags->"SD", - CellLabel->"In[1]:=", + CellLabel->"In[34]:=", CellID->476174335], Cell[BoxData[ @@ -217,8 +212,7 @@ Cell[BoxData[ FormBox["b", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SD", - CellLabel->"Out[1]=", - CellID->181124899] + CellLabel->"Out[34]="] }, Open ]], Cell[CellGroupData[{ @@ -227,7 +221,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"%", "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SD", - CellLabel->"In[2]:=", + CellLabel->"In[35]:=", CellID->1096492812], Cell[BoxData[ @@ -236,8 +230,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Output", CellTags->"SD", - CellLabel->"Out[2]//StandardForm=", - CellID->2135323799] + CellLabel->"Out[35]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -246,15 +239,14 @@ Cell[BoxData[ RowBox[{ RowBox[{"%", "//", "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"SD", - CellLabel->"In[3]:=", + CellLabel->"In[36]:=", CellID->315527863], Cell[BoxData[ RowBox[{"SD", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", CellTags->"SD", - CellLabel->"Out[3]//StandardForm=", - CellID->850743885] + CellLabel->"Out[36]//StandardForm="] }, Open ]] }, Open ]], @@ -319,12 +311,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{876, Automatic}, {Automatic, 175}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SDF.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SDF.nb new file mode 100644 index 000000000..0f201f2fa --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SDF.nb @@ -0,0 +1,320 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/SDF", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["SDF", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"SDF", "[", + RowBox[{"i", ",", "j"}], "]"}]], "InlineFormula"], + " \[LineSeparator]denotes the SU(N) Kronecker delta with color indices i and \ +j in the fundamental represnetation. SDF[i,j] is transformed into \ +SUNFDelta[SUNFIndex[i],SUNFIndex[j]] by FeynCalcInternal." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; 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Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{840, Automatic}, {Automatic, 197}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SFAD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SFAD.nb new file mode 100644 index 000000000..19f6d8a27 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SFAD.nb @@ -0,0 +1,409 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/SFAD", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["SFAD", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"SFAD", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + RowBox[{"q1", "+"}], "..."}], ",", + RowBox[{ + RowBox[{ + RowBox[{"p1", ".", "q2"}], "+"}], "..."}], ","}], "}"}], " ", + RowBox[{"{", + RowBox[{ + RowBox[{"m", "^", "2"}], ",", "s"}], "}"}]}], ",", "n"}], "}"}], ",", + "..."}], "]"}]], "InlineFormula"], + " \[LineSeparator]denotes a Lorentzian propagator given by 1/[(q1+...)^2 + \ +p1.q2 ... + m^2 + sign*I*eta]^n, where q1^2 and p1.q2 are scalar products of \ +Lorentz vectors in D dimensions. For brevity one can also use shorter forms \ +such as SFAD[{q1+ ..., m^2}, ...], SFAD[{q1+ ..., m^2 , n}, ...], SFAD[{q1+ \ +..., {m^2, -1}}, ...], SFAD[q1,...] etc. If s is not explicitly specified, \ +then its value is determined by the option EtaSign, which has the default \ +value +1. If n is not explicitly specified, then the default value 1 is \ +assumed. 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Typical \ -parameters are masses, coupling constants, mixing angles etc. Parameters that \ -are complex, like CKM matrix element, have an I as an additional parameter, \ -i.e. SMP[\\\"V_ud\\\",I] and SMP[\\\"V_ud\\\",-I]. SMP[] shows the list of \ -available parameters.\"" + RowBox[{"SMP", "[", "\"\\"", "]"}]], "InlineFormula"], + " \[LineSeparator]displays a symbol for the model parameter ", + Cell[BoxData["\"\\""], "InlineFormula"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +Typical parameters are masses, coupling constants, mixing angles etc. \ +\>", "Notes", + CellID->1067943069], + +Cell[TextData[{ + "Parameters that are complex, like CKM matrix element, have an ", + Cell[BoxData["I"], "InlineFormula"], + " as an additional argument, i.e. ", + Cell[BoxData[ + RowBox[{"SMP", "[", + RowBox[{"\"\\"", ",", "I"}], "]"}]], "InlineFormula"], + " and ", + Cell[BoxData[ + RowBox[{"SMP", "[", + RowBox[{"\"\\"", ",", + RowBox[{"-", "I"}]}], "]"}]], "InlineFormula"], + ". 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The option StringReplace can be used to specify \ +string replacement rules that will take care of characters (e.g. ^ or _) that \ +cannot appear in valid expressions. SMPToSymbol is useful when exporting \ +FeynCalc expressions to other tools, e.g. FORM." +}], "Usage", + CellChangeTimes->{{3.779713092145335*^9, 3.779713111885613*^9}}, + CellID->982511436], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "SMPToSymbol", "]"}]], "Input", + CellChangeTimes->{{3.779713124558276*^9, 3.77971313274993*^9}}, + CellLabel->"In[1]:=", + CellID->1067943069], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"StringReplace", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"\<\"_\"\>", "\[Rule]", "\<\"\"\>"}], ",", + RowBox[{"\<\"^\"\>", "\[Rule]", "\<\"\"\>"}]}], "}"}]}], ",", + RowBox[{"Conjugate", "\[Rule]", "\<\"CC\"\>"}]}], "}"}], + TraditionalForm]], "Output", + CellChangeTimes->{3.779713159142048*^9}, + CellLabel->"Out[1]=", + CellID->602000371] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + 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@@ -116,20 +116,27 @@ Cell["SMVertex", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], - Cell[BoxData[ - RowBox[{"SMVertex", "[", - RowBox[{ - "\"\\"", ",", " ", "p", ",", "mu", ",", " ", "q", ",", "nu", ",", - " ", "k", ",", "rho"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "gives the photon-W-W vertex (p,mu correspond to the photon, q,nu to the \ -(incoming) W+ and k,rho to the (incoming) W-. All momenta are flowing into \ -the vertex. SMVertex[\"HHH\", ___] give the three-higgs coupling. " + Cell[BoxData["SMVertex"], "InlineFormula"], + " \[LineSeparator]is a library of SM vertices. Currently it implements only \ +few vertices and is not really useful." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "SMVertex", "]"}]], "Input", + CellLabel->"In[58]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"Explicit", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[58]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -164,8 +171,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell["XXXX", "SeeAlso", - CellID->929782353] +Cell[TextData[ButtonBox["SMP", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SMP", + ButtonNote->"SMP"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -192,25 +201,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "SMVertex", "]"}]], "Input", - CellTags->"SMVertex", - CellLabel->"In[1]:=", - CellID->537549751], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "4"}], ",", - RowBox[{"Explicit", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"SMVertex", - CellLabel->"Out[1]=", - CellID->1908910905] -}, Open ]], +Cell["This is the photon-W-W vertex (all momenta ingoing)", "Notes"], Cell[CellGroupData[{ @@ -220,135 +211,152 @@ Cell[BoxData[ "\"\\"", ",", "p", ",", "\[Mu]", ",", " ", "q", ",", "\[Nu]", ",", " ", "k", ",", "\[Rho]"}], "]"}]], "Input", CellTags->"SMVertex", - CellLabel->"In[2]:=", + CellLabel->"In[59]:=", CellID->1911879451], Cell[BoxData[ FormBox[ RowBox[{ - RowBox[{"-", "\[ImaginaryI]"}], " ", "e", " ", + RowBox[{"-", "\[ImaginaryI]"}], " ", "\<\"e\"\>", " ", RowBox[{"(", RowBox[{ RowBox[{ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["k", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Nu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["k", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "+", + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]]}], "+", RowBox[{ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Rho]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["k", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["k", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "+", + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], "+", RowBox[{ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Rho]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output", + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm]]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"SMVertex", - CellLabel->"Out[2]=", - CellID->60024772] + CellLabel->"Out[59]="] +}, Open ]], + +Cell["This is the HHH-coupling", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SMVertex", "[", "\"\\"", "]"}]], "Input", + CellLabel->"In[60]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"-", + FractionBox[ + RowBox[{"3", " ", "\[ImaginaryI]", " ", "\<\"e\"\>", " ", + SubsuperscriptBox["m", "H", "2"]}], + RowBox[{"2", " ", + SubscriptBox["m", "W"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"sin", "("}], + SubscriptBox["\[Theta]", "W"], ")"}], ")"}]}]]}], + TraditionalForm]], "Output", + CellLabel->"Out[60]="] +}, Open ]], + +Cell["This is the H-electron-coupling", "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SMVertex", "[", "\"\\"", "]"}]], "Input", + CellLabel->"In[61]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"-", + FractionBox[ + RowBox[{"\[ImaginaryI]", " ", "\<\"e\"\>", " ", + SubscriptBox["m", "e"]}], + RowBox[{"2", " ", + SubscriptBox["m", "W"], " ", + RowBox[{"(", + RowBox[{ + RowBox[{"sin", "("}], + SubscriptBox["\[Theta]", "W"], ")"}], ")"}]}]]}], + TraditionalForm]], "Output", + CellLabel->"Out[61]="] }, Open ]] }, Open ]], @@ -412,10 +420,11 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{235, Automatic}, {Automatic, 66}}, +WindowSize->{1005, 937}, +WindowMargins->{{1240, Automatic}, {Automatic, 106}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SO.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SO.nb index 45714da2f..96a5426ac 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SO.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SO.nb @@ -161,7 +161,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["FCI", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FCI", @@ -187,9 +186,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SOD", ButtonNote->"SOD"], "." -}], "Text", - CellTags->"SO", - CellID->747915813] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -221,7 +218,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SO", "[", "p", "]"}]], "Input", CellTags->"SO", - CellLabel->"In[1]:=", + CellLabel->"In[5]:=", CellID->549535977], Cell[BoxData[ @@ -234,8 +231,7 @@ Cell[BoxData[ FormBox["p", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SO", - CellLabel->"Out[1]=", - CellID->1525917797] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -244,7 +240,7 @@ Cell[BoxData[ RowBox[{"SO", "[", RowBox[{"p", "-", "q"}], "]"}]], "Input", CellTags->"SO", - CellLabel->"In[2]:=", + CellLabel->"In[6]:=", CellID->2038998491], Cell[BoxData[ @@ -262,8 +258,7 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SO", - CellLabel->"Out[2]=", - CellID->1173558036] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -274,7 +269,7 @@ Cell[BoxData[ RowBox[{"SO", "[", "p", "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SO", - CellLabel->"In[3]:=", + CellLabel->"In[7]:=", CellID->73131493], Cell[BoxData[ @@ -283,8 +278,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "OPEDelta", "]"}], ",", RowBox[{"Momentum", "[", "p", "]"}]}], "]"}]], "Output", CellTags->"SO", - CellLabel->"Out[3]//StandardForm=", - CellID->1244939750] + CellLabel->"Out[7]//StandardForm="] }, Open ]] }, Open ]], @@ -349,12 +343,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SOD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SOD.nb index c95cbc2a6..30a11a305 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SOD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SOD.nb @@ -181,9 +181,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SOD", ButtonNote->"SOD"], "." -}], "Text", - CellTags->"SOD", - CellID->1925156465] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -228,8 +226,7 @@ Cell[BoxData[ FormBox["p", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SOD", - CellLabel->"Out[1]=", - CellID->1608750131] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -256,8 +253,7 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SOD", - CellLabel->"Out[2]=", - CellID->1010314656] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -279,8 +275,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"p", ",", "D"}], "]"}]}], "]"}]], "Output", CellTags->"SOD", - CellLabel->"Out[3]//StandardForm=", - CellID->1393449003] + CellLabel->"Out[3]//StandardForm="] }, Open ]] }, Open ]], @@ -345,12 +340,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SP.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SP.nb index 82036b466..dcaf03ebd 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SP.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SP.nb @@ -183,9 +183,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/ScalarProduct", ButtonNote->"ScalarProduct"], "." -}], "Text", - CellTags->"SP", - CellID->468161499] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -250,8 +248,7 @@ Cell[BoxData[ TraditionalForm], "2"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SP", - CellLabel->"Out[1]=", - CellID->1148967332] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -272,13 +269,15 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -287,20 +286,21 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - RowBox[{"2", " ", + FormBox[ + RowBox[{ + RowBox[{"2", " ", + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"]}], "+", OverscriptBox[ - FormBox["p", - TraditionalForm], "_"]}], "+", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SP", - CellLabel->"Out[2]=", - CellID->53518921] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -347,8 +347,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"]}], TraditionalForm]], "Output", CellTags->"SP", - CellLabel->"Out[3]=", - CellID->21872907] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -393,8 +392,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"]}], TraditionalForm]], "Output", CellTags->"SP", - CellLabel->"Out[4]=", - CellID->988669305] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -411,8 +409,7 @@ Cell[BoxData[ RowBox[{"SP", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", CellTags->"SP", - CellLabel->"Out[5]//StandardForm=", - CellID->591158186] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -433,8 +430,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "a", "]"}], ",", RowBox[{"Momentum", "[", "b", "]"}]}], "]"}]], "Output", CellTags->"SP", - CellLabel->"Out[6]//StandardForm=", - CellID->504879117] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -454,8 +450,7 @@ Cell[BoxData[ RowBox[{"SP", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", CellTags->"SP", - CellLabel->"Out[7]//StandardForm=", - CellID->1698640474] + CellLabel->"Out[7]//StandardForm="] }, Open ]] }, Open ]], @@ -520,12 +515,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{570, Automatic}, {Automatic, 57}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SPC.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SPC.nb index b034bcbdf..8adea61f1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SPC.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SPC.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/ScalarProductCancel", ButtonNote->"ScalarProductCancel"], "." -}], "Text", - CellTags->"SPC", - CellID->777067132] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{619, Automatic}, {Automatic, 88}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SPD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SPD.nb index fec218c26..536dcb070 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SPD.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SPD.nb @@ -189,9 +189,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/ScalarProduct", ButtonNote->"ScalarProduct"], "." -}], "Text", - CellTags->"SPD", - CellID->1031641673] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,8 +251,7 @@ Cell[BoxData[ TraditionalForm], "2"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SPD", - CellLabel->"Out[1]=", - CellID->1537579140] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -275,11 +272,13 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - FormBox["p", - TraditionalForm], "-", - FormBox["q", - TraditionalForm]}], + FormBox[ + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm], @@ -288,18 +287,19 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - RowBox[{"2", " ", - FormBox["p", - TraditionalForm]}], "+", - FormBox["q", - TraditionalForm]}], + FormBox[ + RowBox[{ + RowBox[{"2", " ", + FormBox["p", + TraditionalForm]}], "+", + FormBox["q", + TraditionalForm]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SPD", - CellLabel->"Out[2]=", - CellID->1810693243] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -342,8 +342,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], "2"]}], TraditionalForm]], "Output", CellTags->"SPD", - CellLabel->"Out[3]=", - CellID->533108024] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -384,8 +383,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], "2"]}], TraditionalForm]], "Output", CellTags->"SPD", - CellLabel->"Out[4]=", - CellID->33170286] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -402,8 +400,7 @@ Cell[BoxData[ RowBox[{"SPD", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", CellTags->"SPD", - CellLabel->"Out[5]//StandardForm=", - CellID->1457236269] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -426,8 +423,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"b", ",", "D"}], "]"}]}], "]"}]], "Output", CellTags->"SPD", - CellLabel->"Out[6]//StandardForm=", - CellID->716068529] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -447,8 +443,7 @@ Cell[BoxData[ RowBox[{"SPD", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", CellTags->"SPD", - CellLabel->"Out[7]//StandardForm=", - CellID->966232396] + CellLabel->"Out[7]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -469,8 +464,7 @@ Cell[BoxData[ RowBox[{"SPD", "[", RowBox[{"p", ",", "q"}], "]"}]], "Output", CellTags->"SPD", - CellLabel->"Out[8]//StandardForm=", - CellID->1514523545] + CellLabel->"Out[8]//StandardForm="] }, Open ]] }, Open ]], @@ -535,12 +529,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{521, Automatic}, {Automatic, 44}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SPE.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SPE.nb new file mode 100644 index 000000000..491cd8cd9 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SPE.nb @@ -0,0 +1,563 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.0", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/SPE", "Categorization", + CellLabel->"URI"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["SPE", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"SPE", "[", + RowBox[{"a", ",", " ", "b"}], "]"}]], "InlineFormula"], + " \[LineSeparator]denotes a D-4-dimensional scalar product. SPE[a, b] is \ +transformed into Pair[Momentum[a, -4 + D], Momentum[b, -4 + D]] by \ +FeynCalcInternal. SPE[p] is the same as SPE[p,p] ", + Cell[BoxData[ + RowBox[{"(", + RowBox[{"=", + SuperscriptBox["p", "2"]}], ")"}]], "InlineFormula"] +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell[TextData[{ + ButtonBox["PD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/PD", + ButtonNote->"PD"], + ", ", + ButtonBox["Calc", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Calc", + ButtonNote->"Calc"], + ", ", + ButtonBox["ExpandScalarProduct", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/ExpandScalarProduct", + ButtonNote->"ExpandScalarProduct"], + ", ", + ButtonBox["ScalarProduct", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/ScalarProduct", + ButtonNote->"ScalarProduct"], + ", ", + ButtonBox["SPD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/ScalarProduct", + ButtonNote->"ScalarProduct"], + "." +}], "SeeAlso"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SPE", "[", + RowBox[{"p", ",", "q"}], "]"}], " ", "+", " ", + RowBox[{"SPE", "[", "q", "]"}]}]], "Input", + CellTags->"SPE", + CellLabel->"In[1]:=", + CellID->1779475118], + +Cell[BoxData[ + FormBox[ + RowBox[{ + FormBox[ + RowBox[{ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"], + TraditionalForm]}], + TraditionalForm], "+", + FormBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"], + TraditionalForm], "2"], + TraditionalForm]}], TraditionalForm]], "Output", + CellTags->"SPE", + CellLabel->"Out[1]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SPE", "[", + RowBox[{ + RowBox[{"p", "-", "q"}], ",", + RowBox[{"q", "+", + RowBox[{"2", "p"}]}]}], "]"}]], "Input", + CellTags->"SPE", + CellLabel->"In[2]:=", + CellID->437622958], + +Cell[BoxData[ + FormBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"], "-", + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + RowBox[{"2", " ", + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"]}], "+", + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], TraditionalForm]], "Output", + CellTags->"SPE", + CellLabel->"Out[2]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Calc", "[", " ", + RowBox[{"SPE", "[", + RowBox[{ + RowBox[{"p", "-", "q"}], ",", + RowBox[{"q", "+", + RowBox[{"2", "p"}]}]}], "]"}], " ", "]"}]], "Input", + CellTags->"SPE", + CellLabel->"In[3]:=", + CellID->1031117972], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"-", + RowBox[{ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"], + TraditionalForm]}]}], "+", + RowBox[{"2", " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"], + TraditionalForm], "2"]}], "-", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"], + TraditionalForm], "2"]}], TraditionalForm]], "Output", + CellTags->"SPE", + CellLabel->"Out[3]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ExpandScalarProduct", "[", + RowBox[{"SPE", "[", + RowBox[{"p", "-", "q"}], "]"}], "]"}]], "Input", + CellTags->"SPE", + CellLabel->"In[4]:=", + CellID->87993462], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"-", + RowBox[{"2", " ", + RowBox[{"(", + RowBox[{ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"], + TraditionalForm], + FormBox["\<\"\[CenterDot]\"\>", + TraditionalForm], + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"], + TraditionalForm]}], ")"}]}]}], "+", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "^"], + TraditionalForm], "2"], "+", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "^"], + TraditionalForm], "2"]}], TraditionalForm]], "Output", + CellTags->"SPE", + CellLabel->"Out[4]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SPE", "[", + RowBox[{"a", ",", "b"}], "]"}], "//", "StandardForm"}]], "Input", + CellTags->"SPE", + CellLabel->"In[5]:=", + CellID->2034315321], + +Cell[BoxData[ + RowBox[{"SPE", "[", + RowBox[{"a", ",", "b"}], "]"}]], "Output", + CellTags->"SPE", + CellLabel->"Out[5]//StandardForm="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"SPE", "[", + RowBox[{"a", ",", "b"}], "]"}], "//", "FCI"}], "//", + "StandardForm"}]], "Input", + CellTags->"SPE", + CellLabel->"In[6]:=", + CellID->1917897688], + +Cell[BoxData[ + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"a", ",", + RowBox[{ + RowBox[{"-", "4"}], "+", "D"}]}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"b", ",", + RowBox[{ + RowBox[{"-", "4"}], "+", "D"}]}], "]"}]}], "]"}]], "Output", + CellTags->"SPE", + CellLabel->"Out[6]//StandardForm="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"SPE", "[", + RowBox[{"a", ",", "b"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", + "StandardForm"}]], "Input", + CellTags->"SPE", + CellLabel->"In[7]:=", + CellID->980827421], + +Cell[BoxData[ + RowBox[{"SPE", "[", + RowBox[{"a", ",", "b"}], "]"}]], "Output", + CellTags->"SPE", + CellLabel->"Out[7]//StandardForm="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCE", "[", + RowBox[{"ChangeDimension", "[", + RowBox[{ + RowBox[{"SP", "[", + RowBox[{"p", ",", "q"}], "]"}], ",", " ", + RowBox[{"D", "-", "4"}]}], "]"}], "]"}], "//", "StandardForm"}]], "Input", + CellTags->"SPE", + CellLabel->"In[8]:=", + CellID->1873446419], + +Cell[BoxData[ + RowBox[{"SPE", "[", + RowBox[{"p", ",", "q"}], "]"}]], "Output", + CellTags->"SPE", + CellLabel->"Out[8]//StandardForm="] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Open ]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{773, Automatic}, {Automatic, 220}}, +Visible->True, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SPL.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SPL.nb index 15506e39d..f6557b5c7 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SPL.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SPL.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SimplifyPolyLog", ButtonNote->"SimplifyPolyLog"], "." -}], "Text", - CellTags->"SPL", - CellID->899844592] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{748, Automatic}, {Automatic, 69}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUND.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUND.nb index f37c0470f..0b1a2566f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUND.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUND.nb @@ -183,9 +183,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNSimplify", ButtonNote->"SUNSimplify"], "." -}], "Text", - CellTags->"SUND", - CellID->37121422] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,7 +216,7 @@ Cell[BoxData[ RowBox[{"SUND", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Input", CellTags->"SUND", - CellLabel->"In[1]:=", + CellLabel->"In[39]:=", CellID->1395182696], Cell[BoxData[ @@ -232,19 +230,17 @@ Cell[BoxData[ FormBox["c", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SUND", - CellLabel->"Out[1]=", - CellID->257225185] + CellLabel->"Out[39]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"tt", "=", - RowBox[{"SUND", "[", - RowBox[{"a", ",", "b", ",", "c", ",", - RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]}]], "Input", + RowBox[{"SUND", "[", + RowBox[{"a", ",", "b", ",", "c", ",", + RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SUND", - CellLabel->"In[2]:=", + CellLabel->"In[40]:=", CellID->1361287318], Cell[BoxData[ @@ -305,8 +301,7 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"SUND", - CellLabel->"Out[2]=", - CellID->229657836] + CellLabel->"Out[40]="] }, Open ]], Cell[CellGroupData[{ @@ -315,7 +310,7 @@ Cell[BoxData[ RowBox[{"SUND", "[", RowBox[{"c", ",", "a", ",", "b"}], "]"}]], "Input", CellTags->"SUND", - CellLabel->"In[3]:=", + CellLabel->"In[41]:=", CellID->875422809], Cell[BoxData[ @@ -329,8 +324,7 @@ Cell[BoxData[ FormBox["c", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SUND", - CellLabel->"Out[3]=", - CellID->1988918016] + CellLabel->"Out[41]="] }, Open ]], Cell[CellGroupData[{ @@ -339,7 +333,7 @@ Cell[BoxData[ RowBox[{"SUND", "[", RowBox[{"a", ",", "b", ",", "b"}], "]"}]], "Input", CellTags->"SUND", - CellLabel->"In[4]:=", + CellLabel->"In[42]:=", CellID->2104582579], Cell[BoxData[ @@ -353,8 +347,7 @@ Cell[BoxData[ FormBox["b", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SUND", - CellLabel->"Out[4]=", - CellID->1040614065] + CellLabel->"Out[42]="] }, Open ]], Cell[CellGroupData[{ @@ -367,7 +360,7 @@ Cell[BoxData[ RowBox[{"SUND", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]}], "]"}]], "Input", CellTags->"SUND", - CellLabel->"In[5]:=", + CellLabel->"In[43]:=", CellID->1572742744], Cell[BoxData[ @@ -379,8 +372,7 @@ Cell[BoxData[ SubsuperscriptBox["C", "A", "2"]}], ")"}], " ", SubscriptBox["C", "F"]}], TraditionalForm]], "Output", CellTags->"SUND", - CellLabel->"Out[5]=", - CellID->1608432966] + CellLabel->"Out[43]="] }, Open ]], Cell[CellGroupData[{ @@ -397,7 +389,7 @@ Cell[BoxData[ RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}], "//", "Factor2"}]], "Input", CellTags->"SUND", - CellLabel->"In[6]:=", + CellLabel->"In[44]:=", CellID->2028272220], Cell[BoxData[ @@ -411,8 +403,7 @@ Cell[BoxData[ RowBox[{"4", "-", SuperscriptBox["N", "2"]}], ")"}]}], "N"], TraditionalForm]], "Output", CellTags->"SUND", - CellLabel->"Out[6]=", - CellID->576134912] + CellLabel->"Out[44]="] }, Open ]], Cell[CellGroupData[{ @@ -429,7 +420,7 @@ Cell[BoxData[ RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}], "//", "Factor2"}]], "Input", CellTags->"SUND", - CellLabel->"In[7]:=", + CellLabel->"In[45]:=", CellID->1938547204], Cell[BoxData[ @@ -451,8 +442,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], "N"]}], TraditionalForm]], "Output", CellTags->"SUND", - CellLabel->"Out[7]=", - CellID->985891006] + CellLabel->"Out[45]="] }, Open ]], Cell[CellGroupData[{ @@ -463,15 +453,14 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"SUND", - CellLabel->"In[8]:=", + CellLabel->"In[46]:=", CellID->1197762042], Cell[BoxData[ RowBox[{"SUND", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Output", CellTags->"SUND", - CellLabel->"Out[8]//StandardForm=", - CellID->702924348] + CellLabel->"Out[46]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -483,7 +472,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SUND", - CellLabel->"In[9]:=", + CellLabel->"In[47]:=", CellID->1553275724], Cell[BoxData[ @@ -493,8 +482,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "b", "]"}], ",", RowBox[{"SUNIndex", "[", "c", "]"}]}], "]"}]], "Output", CellTags->"SUND", - CellLabel->"Out[9]//StandardForm=", - CellID->1657792981] + CellLabel->"Out[47]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -507,22 +495,15 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"SUND", - CellLabel->"In[10]:=", + CellLabel->"In[48]:=", CellID->1610675678], Cell[BoxData[ RowBox[{"SUND", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Output", CellTags->"SUND", - CellLabel->"Out[10]//StandardForm=", - CellID->1049412344] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", "tt", "]"}]], "Input", - CellTags->"SUND", - CellLabel->"In[11]:=", - CellID->619973322] + CellLabel->"Out[48]//StandardForm="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -586,12 +567,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{296, Automatic}, {Automatic, 38}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNDelta.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNDelta.nb index 8e315f0c1..1c041ba4d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNDelta.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNDelta.nb @@ -119,11 +119,8 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"SUNDelta", "[", RowBox[{"a", ",", " ", "b"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the Kronecker-delta for SU(", - StyleBox["N", - FontSlant->"Italic"], - ") with color indices a and b." + " \[LineSeparator] is the Kronecker-delta for SU(N) with color indices a and \ +b in the adjoint representation." }], "Usage", CellID->982511436], @@ -164,7 +161,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["ExplicitSUNIndex", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/ExplicitSUNIndex", @@ -195,9 +191,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Trick", ButtonNote->"Trick"], "." -}], "Text", - CellTags->"SUNDelta", - CellID->1124087961] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -228,7 +222,9 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}]], "Input", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Input", CellTags->"SUNDelta", CellLabel->"In[1]:=", CellID->582133429], @@ -237,27 +233,63 @@ Cell[BoxData[ FormBox[ SuperscriptBox["\[Delta]", RowBox[{ - FormBox["a", + FormBox[ + FormBox["a", + TraditionalForm], TraditionalForm], - FormBox["b", + FormBox[ + FormBox["b", + TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SUNDelta", - CellLabel->"Out[1]=", - CellID->718384624] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Trick", "[", " ", + RowBox[{ + RowBox[{"SUNDelta", "[", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], + RowBox[{"SUNDelta", "[", + RowBox[{ + RowBox[{"SUNIndex", "[", "b", "]"}], ",", + RowBox[{"SUNIndex", "[", "c", "]"}]}], "]"}]}]], "Input", + CellLabel->"In[2]:="], + +Cell[BoxData[ + FormBox[ RowBox[{ - RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], " ", - RowBox[{"SUNDelta", "[", - RowBox[{"b", ",", "c"}], "]"}]}], " ", "]"}]], "Input", - CellTags->"SUNDelta", - CellLabel->"In[2]:=", - CellID->223165993], + SuperscriptBox["\[Delta]", + RowBox[{ + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]}]], " ", + SuperscriptBox["\[Delta]", + RowBox[{ + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["c", + TraditionalForm], + TraditionalForm]}]]}], TraditionalForm]], "Output", + CellLabel->"Out[2]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[3]:="], Cell[BoxData[ FormBox[ @@ -271,9 +303,7 @@ Cell[BoxData[ FormBox["c", TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", - CellTags->"SUNDelta", - CellLabel->"Out[2]=", - CellID->1779629564] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -284,7 +314,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Input", CellTags->"SUNDelta", - CellLabel->"In[3]:=", + CellLabel->"In[4]:=", CellID->2091383946], Cell[BoxData[ @@ -300,8 +330,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SUNDelta", - CellLabel->"Out[3]=", - CellID->791346519] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -309,30 +338,13 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], "//", "StandardForm"}]], "Input", - CellTags->"SUNDelta", - CellLabel->"In[4]:=", - CellID->2066302871], - -Cell[BoxData[ - RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}]], "Output", - CellTags->"SUNDelta", - CellLabel->"Out[4]//StandardForm=", - CellID->1680727312] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{ - RowBox[{ - RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], "//", "FCI"}], "//", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"SUNDelta", CellLabel->"In[5]:=", - CellID->76062746], + CellID->2066302871], Cell[BoxData[ RowBox[{"SUNDelta", "[", @@ -340,8 +352,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Output", CellTags->"SUNDelta", - CellLabel->"Out[5]//StandardForm=", - CellID->1303706973] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -351,8 +362,10 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", - "StandardForm"}]], "Input", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], "//", "FCI"}], "//", + "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"SUNDelta", CellLabel->"In[6]:=", CellID->1106151471], @@ -361,8 +374,7 @@ Cell[BoxData[ RowBox[{"SD", "[", RowBox[{"a", ",", "b"}], "]"}]], "Output", CellTags->"SUNDelta", - CellLabel->"Out[6]//StandardForm=", - CellID->1065622125] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -383,17 +395,15 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "a", "]"}], ",", RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}]], "Output", CellTags->"SUNDelta", - CellLabel->"Out[7]//StandardForm=", - CellID->708863202] + CellLabel->"Out[7]//StandardForm="] }, Open ]], Cell["\<\ -Symbolic arguments to SUNDelta are transformed into the data type SUNIndex \ -and integer arguments are transformed to ExplicitSUNIndex. The difference is \ -that SUNSimplify will only sum over symbolic indices.\ -\>", "Text", - CellTags->"SUNDelta", - CellID->1535277851], +The arguments of SUNDelta may also represent explicit integer indices via the \ +head ExplictiSUNIndex. The difference is that SUNSimplify will only sum over \ +symbolic indices.\ +\>", "Notes", + CellID->879136127], Cell[CellGroupData[{ @@ -401,11 +411,18 @@ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "2"}], "]"}], + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"ExplicitSUNIndex", "[", "2", "]"}]}], "]"}], RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], RowBox[{"SUNDelta", "[", - RowBox[{"c", ",", "2"}], "]"}]}], "//", "SUNSimplify"}]], "Input", + RowBox[{ + RowBox[{"SUNIndex", "[", "c", "]"}], ",", + RowBox[{"ExplicitSUNIndex", "[", "2", "]"}]}], "]"}]}], "//", + "SUNSimplify"}]], "Input", CellTags->"SUNDelta", CellLabel->"In[8]:=", CellID->69005829], @@ -434,8 +451,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"SUNDelta", - CellLabel->"Out[8]=", - CellID->1797928550] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -457,8 +473,7 @@ Cell[BoxData[ RowBox[{"ExplicitSUNIndex", "[", "2", "]"}], ",", RowBox[{"SUNIndex", "[", "c", "]"}]}], "]"}]}]], "Output", CellTags->"SUNDelta", - CellLabel->"Out[9]//StandardForm=", - CellID->391311139] + CellLabel->"Out[9]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -466,7 +481,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ - RowBox[{"SUNDelta", "[", + RowBox[{"SD", "[", RowBox[{"1", ",", "2"}], "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SUNDelta", @@ -479,8 +494,7 @@ Cell[BoxData[ RowBox[{"ExplicitSUNIndex", "[", "1", "]"}], ",", RowBox[{"ExplicitSUNIndex", "[", "2", "]"}]}], "]"}]], "Output", CellTags->"SUNDelta", - CellLabel->"Out[10]//StandardForm=", - CellID->432360453] + CellLabel->"Out[10]//StandardForm="] }, Open ]] }, Open ]], @@ -545,12 +559,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{565, Automatic}, {Automatic, 112}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNDeltaContract.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNDeltaContract.nb index e3ac2ef0b..fab41affd 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNDeltaContract.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNDeltaContract.nb @@ -117,17 +117,46 @@ Cell["SUNDeltaContract", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ - RowBox[{"SUNDeltaContract", "[", "expr", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "substitues for all SUNDelta in expr SUNDeltaContract, contracts the SUN(N) \ -indices and resubstitutes SUNDelta. SUNDeltaContract[i, j] is the \ -Kronecker-delta for SU(", - StyleBox["N", - FontSlant->"Italic"], - ") with contraction properties. SUNDeltaContract wraps also the head \ -SUNIndex around its arguments." + RowBox[{"SUNDeltaContract", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]substitues for all ", + ButtonBox["SUNDelta", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNDelta", + ButtonNote->"SUNDelta"], + " in ", + Cell[BoxData["exp"], "InlineFormula"], + " ", + ButtonBox["SUNDeltaContract", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNDeltaContract", + ButtonNote->"SUNDeltaContract"], + ", contracts the adjoint ", + Cell[BoxData[ + RowBox[{"SU", + RowBox[{"(", "N", ")"}]}]], "InlineFormula"], + " indices and resubstitutes ", + ButtonBox["SUNDelta", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNDelta", + ButtonNote->"SUNDelta"], + ".\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"SUNDeltaContract", "[", + RowBox[{"i", ",", "j"}], "]"}]], "InlineFormula"], + " \[LineSeparator]is the Kronecker-delta for ", + Cell[BoxData[ + RowBox[{"SU", + RowBox[{"(", "N", ")"}]}]], "InlineFormula"], + " in the adjoint representation with contraction properties. It wraps the \ +head ", + ButtonBox["SUNIndex", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNIndex", + ButtonNote->"SUNIndex"], + " around its arguments." }], "Usage", - CellID->982511436], + CellID->455417684], Cell["XXXX", "Notes", CellID->1067943069] @@ -176,9 +205,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNIndex", ButtonNote->"SUNIndex"], "." -}], "Text", - CellTags->"SUNDeltaContract", - CellID->332681775] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -190,6 +217,8 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], +Cell[CellGroupData[{ + Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -205,6 +234,47 @@ Cell[BoxData[ Cell[CellGroupData[{ +Cell[BoxData[ + RowBox[{ + RowBox[{"SUNDelta", "[", + RowBox[{ + RowBox[{"SUNIndex", "[", "a", "]"}], ",", + RowBox[{"SUNIndex", "[", "b", "]"}]}], "]"}], "^", "2"}]], "Input", + CellLabel->"In[56]:="], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + RowBox[{"(", + SuperscriptBox["\[Delta]", + RowBox[{ + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm]}]], ")"}], "2"], TraditionalForm]], "Output", + CellLabel->"Out[56]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNDeltaContract", "[", "%", "]"}]], "Input", + CellLabel->"In[57]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{ + SuperscriptBox["N", "2"], "-", "1"}], TraditionalForm]], "Output", + CellLabel->"Out[57]="] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -263,13 +333,15 @@ Cell[BoxData[ CellID->589267740] }, Open ]] }, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowSize->{700, 740}, +WindowMargins->{{Automatic, 151}, {61, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNF.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNF.nb index bdd6adba1..9e4d5c7a2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNF.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNF.nb @@ -127,8 +127,22 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "SUNF", "]"}]], "Input", + CellTags->"SUNF", + CellLabel->"In[11]:=", + CellID->121887364], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Explicit", "\[Rule]", "False"}], "}"}], + TraditionalForm]], "Output", + CellTags->"SUNF", + CellLabel->"Out[11]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -194,9 +208,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Trick", ButtonNote->"Trick"], "." -}], "Text", - CellTags->"SUNF", - CellID->639373109] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -226,34 +238,15 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Options", "[", "SUNF", "]"}]], "Input", - CellTags->"SUNF", - CellLabel->"In[1]:=", - CellID->121887364], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Explicit", "\[Rule]", "False"}], "}"}], - TraditionalForm]], "Output", - CellTags->"SUNF", - CellLabel->"Out[1]=", - CellID->788322241] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"t1", "=", + RowBox[{ RowBox[{ - RowBox[{ - RowBox[{"SUNF", "[", - RowBox[{"a", ",", "b", ",", "c"}], "]"}], "x"}], "+", - RowBox[{ - RowBox[{"SUNF", "[", - RowBox[{"b", ",", "a", ",", "c"}], "]"}], "y"}]}]}]], "Input", + RowBox[{"SUNF", "[", + RowBox[{"a", ",", "b", ",", "c"}], "]"}], "x"}], "+", + RowBox[{ + RowBox[{"SUNF", "[", + RowBox[{"b", ",", "a", ",", "c"}], "]"}], "y"}]}]], "Input", CellTags->"SUNF", - CellLabel->"In[2]:=", + CellLabel->"In[13]:=", CellID->1766434801], Cell[BoxData[ @@ -278,16 +271,15 @@ Cell[BoxData[ FormBox["c", TraditionalForm]}]]}]}], TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[2]=", - CellID->1741928660] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Calc", "[", "t1", "]"}]], "Input", + RowBox[{"Calc", "[", "%", "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[3]:=", + CellLabel->"In[14]:=", CellID->139383085], Cell[BoxData[ @@ -324,16 +316,15 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}]}], TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[3]=", - CellID->1893375491] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SUNSimplify", "[", "t1", "]"}]], "Input", + RowBox[{"SUNSimplify", "[", "%%", "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[4]:=", + CellLabel->"In[15]:=", CellID->479451850], Cell[BoxData[ @@ -356,8 +347,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[4]=", - CellID->622570571] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ @@ -366,7 +356,7 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "a", ",", "b"}], "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[5]:=", + CellLabel->"In[15]:=", CellID->1757637776], Cell[BoxData[ @@ -380,8 +370,7 @@ Cell[BoxData[ FormBox["b", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[5]=", - CellID->752391067] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ @@ -391,28 +380,22 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "a", ",", "b"}], "]"}], "//", "Calc"}]], "Input", CellTags->"SUNF", - CellLabel->"In[6]:=", + CellLabel->"In[16]:=", CellID->169262538], Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[6]=", - CellID->1205699996] + CellLabel->"Out[16]="] }, Open ]], Cell[TextData[{ "This is a consequence of the usual choice for the normalization of the ", Cell[BoxData[ FormBox[ - RowBox[{ - SubscriptBox["T", "a"], " ", "generatorsin", " ", - RowBox[{ - RowBox[{"(", - RowBox[{"see", " ", "SUNT"}], ")"}], "."}]}], TraditionalForm]]] -}], "Text", - CellTags->"SUNF", - CellID->565916861], + SubscriptBox["T", "a"], TraditionalForm]]], + " generators." +}], "Notes"], Cell[CellGroupData[{ @@ -421,7 +404,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c", ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[7]:=", + CellLabel->"In[23]:=", CellID->2026232239], Cell[BoxData[ @@ -480,8 +463,7 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[7]=", - CellID->621120740] + CellLabel->"Out[23]="] }, Open ]], Cell[CellGroupData[{ @@ -494,7 +476,7 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "b", ",", "d"}], "]"}]}], "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[8]:=", + CellLabel->"In[24]:=", CellID->386944916], Cell[BoxData[ @@ -512,8 +494,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[8]=", - CellID->631419441] + CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ @@ -525,7 +506,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[9]:=", + CellLabel->"In[25]:=", CellID->963311023], Cell[BoxData[ @@ -585,8 +566,7 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[9]=", - CellID->215339899] + CellLabel->"Out[25]="] }, Open ]], Cell[CellGroupData[{ @@ -597,15 +577,14 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"SUNF", - CellLabel->"In[10]:=", + CellLabel->"In[26]:=", CellID->1003312113], Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Output", CellTags->"SUNF", - CellLabel->"Out[10]//StandardForm=", - CellID->792790909] + CellLabel->"Out[26]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -617,7 +596,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SUNF", - CellLabel->"In[11]:=", + CellLabel->"In[27]:=", CellID->2081826967], Cell[BoxData[ @@ -627,8 +606,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "b", "]"}], ",", RowBox[{"SUNIndex", "[", "c", "]"}]}], "]"}]], "Output", CellTags->"SUNF", - CellLabel->"Out[11]//StandardForm=", - CellID->1149570291] + CellLabel->"Out[27]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -641,15 +619,14 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "c"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"SUNF", - CellLabel->"In[12]:=", + CellLabel->"In[28]:=", CellID->1938677300], Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]], "Output", CellTags->"SUNF", - CellLabel->"Out[12]//StandardForm=", - CellID->1462891621] + CellLabel->"Out[28]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -658,7 +635,7 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"b", ",", "a", ",", "c"}], "]"}]], "Input", CellTags->"SUNF", - CellLabel->"In[13]:=", + CellLabel->"In[29]:=", CellID->334638901], Cell[BoxData[ @@ -672,8 +649,7 @@ Cell[BoxData[ FormBox["c", TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SUNF", - CellLabel->"Out[13]=", - CellID->532100486] + CellLabel->"Out[29]="] }, Open ]], Cell[CellGroupData[{ @@ -683,7 +659,7 @@ Cell[BoxData[ RowBox[{"SUNF", "[", RowBox[{"b", ",", "a", ",", "c"}], "]"}], "//", "FCI"}]], "Input", CellTags->"SUNF", - CellLabel->"In[14]:=", + CellLabel->"In[30]:=", CellID->1328454294], Cell[BoxData[ @@ -704,8 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Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; 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If \ +the argument is an integer, SUNFIndex[a] turns into ExplicitSUNFIndex[a]." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNFIndex", "[", "i", "]"}]], "Input", + CellTags->"SUNIndex", + CellLabel->"In[1]:=", + CellID->973923672], + +Cell[BoxData[ + FormBox["i", TraditionalForm]], "Output", + CellTags->"SUNIndex", + CellLabel->"Out[1]=", + CellID->769084224] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "StandardForm"}]], "Input", + CellTags->"SUNIndex", + CellLabel->"In[2]:=", + CellID->293124345], + +Cell[BoxData[ + RowBox[{"SUNFIndex", "[", "i", "]"}]], "Output", + CellTags->"SUNIndex", + CellLabel->"Out[2]//StandardForm=", + CellID->529449408] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNFIndex", "[", "2", "]"}]], "Input", + CellLabel->"In[3]:=", + CellID->1927371187], + +Cell[BoxData[ + FormBox["2", TraditionalForm]], "Output", + CellLabel->"Out[3]=", + CellID->819007020] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "StandardForm"}]], "Input", + CellLabel->"In[4]:=", + CellID->1807480238], + +Cell[BoxData[ + RowBox[{"ExplicitSUNFIndex", "[", "2", "]"}]], "Output", + CellLabel->"Out[4]//StandardForm=", + CellID->2061967096] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"SUNFDelta", "[", + RowBox[{"i", ",", "j"}], "]"}], "//", "FCI"}], "//", + "StandardForm"}]], "Input", + CellTags->"SUNIndex", + CellLabel->"In[5]:=", + CellID->874008605], + +Cell[BoxData[ + RowBox[{"SUNFDelta", "[", + RowBox[{ + RowBox[{"SUNFIndex", "[", "i", "]"}], ",", + RowBox[{"SUNFIndex", "[", "j", "]"}]}], "]"}]], "Output", + CellTags->"SUNIndex", + CellLabel->"Out[5]//StandardForm=", + CellID->127438419] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1410, Automatic}, {Automatic, 267}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNFJacobi.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNFJacobi.nb index 50807144f..31e4660ef 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNFJacobi.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNFJacobi.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNSimplify", ButtonNote->"SUNSimplify"], "." -}], "Text", - CellTags->"SUNFJacobi", - CellID->614882988] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -213,7 +211,7 @@ Cell[BoxData[ RowBox[{"#", ",", RowBox[{"SUNFJacobi", "\[Rule]", "False"}]}], "]"}], "&"}]}]], "Input", CellTags->"SUNFJacobi", - CellLabel->"In[1]:=", + CellLabel->"In[6]:=", CellID->167388740], Cell[BoxData[ @@ -248,8 +246,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"SUNFJacobi", - CellLabel->"Out[1]=", - CellID->311054380] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -266,7 +263,7 @@ Cell[BoxData[ RowBox[{"#", ",", RowBox[{"SUNFJacobi", "\[Rule]", "True"}]}], "]"}], "&"}]}]], "Input", CellTags->"SUNFJacobi", - CellLabel->"In[2]:=", + CellLabel->"In[7]:=", CellID->693485776], Cell[BoxData[ @@ -331,8 +328,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}]}], TraditionalForm]], "Output", CellTags->"SUNFJacobi", - CellLabel->"Out[2]=", - CellID->692961439] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -397,12 +393,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{627, Automatic}, {Automatic, 194}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNFSimplify.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNFSimplify.nb new file mode 100644 index 000000000..a0af337fb --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNFSimplify.nb @@ -0,0 +1,633 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", 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Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{417, Automatic}, {90, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNIndex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNIndex.nb index febbb0008..ecb962874 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNIndex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNIndex.nb @@ -116,12 +116,10 @@ Cell["SUNIndex", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], - Cell[BoxData["SUNIndex"], "InlineFormula"], - " \[LineSeparator]", - "is the head of SU(", - StyleBox["N", - FontSlant->"Italic"], - ") indices." + Cell[BoxData[ + RowBox[{"SUNIndex", "[", "a", "]"}]], "InlineFormula"], + " \[LineSeparator]is an SU(N) index in the adjoint representation. If the \ +argument is an integer, SUNIndex[a] turns into ExplicitSUNIndex[a]." }], "Usage", CellID->982511436], @@ -162,7 +160,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["ExplicitSUNIndex", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/ExplicitSUNIndex", @@ -178,9 +175,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNF", ButtonNote->"SUNF"], "." -}], "Text", - CellTags->"SUNIndex", - CellID->341377518] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,8 +213,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["i", TraditionalForm]], "Output", CellTags->"SUNIndex", - CellLabel->"Out[1]=", - CellID->969035127] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -233,8 +227,29 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"SUNIndex", "[", "i", "]"}]], "Output", CellTags->"SUNIndex", - CellLabel->"Out[2]//StandardForm=", - CellID->675650496] + CellLabel->"Out[2]//StandardForm="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SUNIndex", "[", "2", "]"}]], "Input", + CellLabel->"In[3]:="], + +Cell[BoxData[ + FormBox["2", TraditionalForm]], "Output", + CellLabel->"Out[3]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "StandardForm"}]], "Input", + CellLabel->"In[4]:="], + +Cell[BoxData[ + RowBox[{"ExplicitSUNIndex", "[", "2", "]"}]], "Output", + CellLabel->"Out[4]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -246,7 +261,7 @@ Cell[BoxData[ RowBox[{"i", ",", "j"}], "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", CellTags->"SUNIndex", - CellLabel->"In[3]:=", + CellLabel->"In[5]:=", CellID->874008605], Cell[BoxData[ @@ -255,8 +270,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "i", "]"}], ",", RowBox[{"SUNIndex", "[", "j", "]"}]}], "]"}]], "Output", CellTags->"SUNIndex", - CellLabel->"Out[3]//StandardForm=", - CellID->46597874] + CellLabel->"Out[5]//StandardForm="] }, Open ]] }, Open ]], @@ -321,12 +335,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{731, Automatic}, {Automatic, 155}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNIndexRename.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNIndexRename.nb index f394fd55f..10fb2d087 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNIndexRename.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNIndexRename.nb @@ -170,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNIndex", ButtonNote->"SUNIndex"], "." -}], "Text", - CellTags->"SUNIndexRename", - CellID->1033928155] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -258,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{704, Automatic}, {Automatic, 121}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNN.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNN.nb index 690c1045e..d55e89197 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNN.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNN.nb @@ -188,9 +188,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/CF", ButtonNote->"CF"], "." -}], "Text", - CellTags->"SUNN", - CellID->1642067263] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -228,7 +226,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}], ",", RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}]], "Input", CellTags->"SUNN", - CellLabel->"In[1]:=", + CellLabel->"In[6]:=", CellID->1968246895], Cell[BoxData[ @@ -236,8 +234,7 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["N", "2"], "-", "1"}], TraditionalForm]], "Output", CellTags->"SUNN", - CellLabel->"Out[1]=", - CellID->94438752] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -302,12 +299,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{524, Automatic}, {Automatic, 61}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNNToCACF.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNNToCACF.nb index bb8c3480a..37f800a4a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNNToCACF.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNNToCACF.nb @@ -190,9 +190,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/CF", ButtonNote->"CF"], "." -}], "Text", - CellTags->"SUNNToCACF", - CellID->124208571] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -230,7 +228,7 @@ Cell[BoxData[ RowBox[{"SUNIndex", "[", "a", "]"}]}], "]"}], ",", RowBox[{"SUNNToCACF", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SUNNToCACF", - CellLabel->"In[1]:=", + CellLabel->"In[7]:=", CellID->1879564079], Cell[BoxData[ @@ -239,8 +237,7 @@ Cell[BoxData[ SubscriptBox["C", "A"], " ", SubscriptBox["C", "F"]}], TraditionalForm]], "Output", CellTags->"SUNNToCACF", - CellLabel->"Out[1]=", - CellID->573481763] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -305,12 +302,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{862, Automatic}, {237, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNSimplify.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNSimplify.nb index d24fe4478..23d59814d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNSimplify.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SUNSimplify.nb @@ -116,18 +116,33 @@ Cell["SUNSimplify", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], - Cell[BoxData["SUNSimplify"], "InlineFormula"], - " \[LineSeparator]", - "simplifies products of SUNT (and complex conjugated) matrices. Basic \ -renaming of dummy indices is done. If the option SUNTrace is set to False, \ -then any SUNT-matrices are taken out of DiracTrace[...]; otherwise a \ -color-trace is taken (by SUNTrace) before taking the SUN-objects in front of \ -DiracTrace[...]." + Cell[BoxData[ + RowBox[{"SUNSimplify", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]simplifies products of SUNT and SUNTF matrices in the \ +expression." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "SUNSimplify", "]"}]], "Input", + CellLabel->"In[60]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Expanding", "\[Rule]", "False"}], ",", + RowBox[{"Explicit", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "False"}], ",", + RowBox[{"SUNIndexRename", "\[Rule]", "True"}], ",", + RowBox[{"SUNFJacobi", "\[Rule]", "False"}], ",", + RowBox[{"SUNNToCACF", "\[Rule]", "True"}], ",", + RowBox[{"SUNTrace", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[60]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -163,19 +178,32 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["Trick", + ButtonBox["SUNTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNTrace", + ButtonNote->"SUNTrace"], + ", ", + ButtonBox["SUNT", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNT", + ButtonNote->"SUNT"], + ", ", + ButtonBox["SUNTF", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Trick", - ButtonNote->"Trick"], + ButtonData:>"paclet:FeynCalc/ref/SUNTF", + ButtonNote->"SUNTF"], ", ", - ButtonBox["CalcColorFactor", + ButtonBox["SUNF", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/CalcColorFactor", - ButtonNote->"CalcColorFactor"], + ButtonData:>"paclet:FeynCalc/ref/SUNF", + ButtonNote->"SUNF"], + ", ", + ButtonBox["SUND", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUND", + ButtonNote->"SUND"], "." -}], "Text", - CellTags->"SUNSimplify", - CellID->1451213327] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -205,39 +233,13 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Options", "[", "SUNSimplify", "]"}]], "Input", - CellTags->"SUNSimplify", - CellLabel->"In[1]:=", - CellID->287772200], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Expanding", "\[Rule]", "False"}], ",", - RowBox[{"Explicit", "\[Rule]", "False"}], ",", - RowBox[{"Factoring", "\[Rule]", "False"}], ",", - RowBox[{"SUNIndexRename", "\[Rule]", "True"}], ",", - RowBox[{"SUNFJacobi", "\[Rule]", "False"}], ",", - RowBox[{"SUNNToCACF", "\[Rule]", "True"}], ",", - RowBox[{"SUNTrace", "\[Rule]", "False"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"SUNSimplify", - CellLabel->"Out[1]=", - CellID->291333912] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"t1", "=", - RowBox[{ - RowBox[{"SUNDelta", "[", - RowBox[{"a", ",", "b"}], "]"}], " ", - RowBox[{"SUNDelta", "[", - RowBox[{"b", ",", "c"}], "]"}]}]}]], "Input", + RowBox[{ + RowBox[{"SUNDelta", "[", + RowBox[{"a", ",", "b"}], "]"}], " ", + RowBox[{"SUNDelta", "[", + RowBox[{"b", ",", "c"}], "]"}]}]], "Input", CellTags->"SUNSimplify", - CellLabel->"In[2]:=", + CellLabel->"In[61]:=", CellID->1698138274], Cell[BoxData[ @@ -256,16 +258,15 @@ Cell[BoxData[ FormBox["c", TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"SUNSimplify", - CellLabel->"Out[2]=", - CellID->1129385138] + CellLabel->"Out[61]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SUNSimplify", "[", "t1", "]"}]], "Input", + RowBox[{"SUNSimplify", "[", "%", "]"}]], "Input", CellTags->"SUNSimplify", - CellLabel->"In[3]:=", + CellLabel->"In[62]:=", CellID->1520473065], Cell[BoxData[ @@ -281,19 +282,23 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"SUNSimplify", - CellLabel->"Out[3]=", - CellID->1288692360] + CellLabel->"Out[62]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", "=", - RowBox[{ - RowBox[{"SUNT", "[", "a", "]"}], ".", - RowBox[{"SUNT", "[", "a", "]"}]}]}]], "Input", + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"SUNT", "[", "a", "]"}], ".", + RowBox[{"SUNT", "[", "a", "]"}]}]], "Input", CellTags->"SUNSimplify", - CellLabel->"In[4]:=", + CellLabel->"In[63]:=", CellID->1992995975], Cell[BoxData[ @@ -306,35 +311,34 @@ Cell[BoxData[ FormBox["a", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"SUNSimplify", - CellLabel->"Out[4]=", - CellID->1292635919] + CellLabel->"Out[63]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SUNSimplify", "[", "t2", "]"}]], "Input", + RowBox[{"SUNSimplify", "[", "%", "]"}]], "Input", CellTags->"SUNSimplify", - CellLabel->"In[5]:=", + CellLabel->"In[64]:=", CellID->1767152339], Cell[BoxData[ FormBox[ SubscriptBox["C", "F"], TraditionalForm]], "Output", CellTags->"SUNSimplify", - CellLabel->"Out[5]=", - CellID->2143185906] + CellLabel->"Out[64]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SUNSimplify", "[", - RowBox[{"t2", ",", + RowBox[{ + RowBox[{ + RowBox[{"SUNT", "[", "a", "]"}], ".", + RowBox[{"SUNT", "[", "a", "]"}]}], ",", RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}]], "Input", - CellTags->"SUNSimplify", - CellLabel->"In[6]:=", - CellID->671897568], + CellLabel->"In[65]:="], Cell[BoxData[ FormBox[ @@ -342,22 +346,26 @@ Cell[BoxData[ RowBox[{ SuperscriptBox["N", "2"], "-", "1"}], RowBox[{"2", " ", "N"}]], TraditionalForm]], "Output", - 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" \[LineSeparator]", - "is the SU(", + " \[LineSeparator]is the SU(", StyleBox["N", FontSlant->"Italic"], ") ", Cell[BoxData[ FormBox[ - SubscriptBox["T", "a"], TraditionalForm]]], - " generator in the fundamental representation." + SuperscriptBox["T", "a"], TraditionalForm]]], + " generator in the fundamental representation. The fundamental indices are \ +implicit." }], "Usage", CellID->982511436], @@ -197,9 +197,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNSimplify", ButtonNote->"SUNSimplify"], "." -}], "Text", - CellTags->"SUNT", - CellID->1735213783] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -231,7 +229,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SUNT", "[", "a", "]"}]], "Input", CellTags->"SUNT", - CellLabel->"In[1]:=", + CellLabel->"In[17]:=", CellID->1010106474], Cell[BoxData[ @@ -240,8 +238,7 @@ Cell[BoxData[ FormBox["a", TraditionalForm]], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[1]=", - CellID->1672661577] + CellLabel->"Out[17]="] }, Open ]], Cell[TextData[{ @@ -250,9 +247,7 @@ Cell[TextData[{ FormBox[ SubscriptBox["T", "a"], TraditionalForm]]], " is a noncommutative object, products have to separated by a dot (.)." -}], "Text", - CellTags->"SUNT", - CellID->1160812067], +}], "Notes"], Cell[CellGroupData[{ @@ -262,7 +257,7 @@ Cell[BoxData[ RowBox[{"SUNT", "[", "b", "]"}], ".", " ", RowBox[{"SUNT", "[", "c", "]"}]}]], "Input", CellTags->"SUNT", - CellLabel->"In[2]:=", + CellLabel->"In[18]:=", CellID->892665531], Cell[BoxData[ @@ -278,8 +273,7 @@ Cell[BoxData[ FormBox["c", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[2]=", - CellID->818227996] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -288,35 +282,26 @@ Cell[BoxData[ RowBox[{"SUNT", "[", RowBox[{"a", ",", "b", ",", "c", ",", "d"}], "]"}]], "Input", CellTags->"SUNT", - CellLabel->"In[3]:=", + CellLabel->"In[19]:=", CellID->1074191459], Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["T", - FormBox[ - FormBox["a", - TraditionalForm], + FormBox["a", TraditionalForm]], ".", SuperscriptBox["T", - FormBox[ - FormBox["b", - TraditionalForm], + FormBox["b", TraditionalForm]], ".", SuperscriptBox["T", - FormBox[ - FormBox["c", - TraditionalForm], + FormBox["c", TraditionalForm]], ".", SuperscriptBox["T", - FormBox[ - FormBox["d", - TraditionalForm], + FormBox["d", TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[3]=", - CellID->583778930] + CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ @@ -328,7 +313,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "a"}], "]"}], ",", RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}]], "Input", CellTags->"SUNT", - CellLabel->"In[4]:=", + CellLabel->"In[20]:=", CellID->984008279], Cell[BoxData[ @@ -342,8 +327,7 @@ Cell[BoxData[ TraditionalForm]], RowBox[{"2", " ", "N"}]]}], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[4]=", - CellID->471863997] + CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ @@ -353,15 +337,14 @@ Cell[BoxData[ RowBox[{"SUNT", "[", RowBox[{"a", ",", "b", ",", "b", ",", "a"}], "]"}], "]"}]], "Input", CellTags->"SUNT", - CellLabel->"In[5]:=", + CellLabel->"In[21]:=", CellID->1204560137], Cell[BoxData[ FormBox[ SubsuperscriptBox["C", "F", "2"], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[5]=", - CellID->1224364730] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ @@ -371,7 +354,7 @@ Cell[BoxData[ RowBox[{"SUNT", "[", RowBox[{"a", ",", "b", ",", "a"}], "]"}], "]"}]], "Input", CellTags->"SUNT", - CellLabel->"In[6]:=", + CellLabel->"In[22]:=", CellID->979223472], Cell[BoxData[ @@ -390,8 +373,7 @@ Cell[BoxData[ RowBox[{"2", " ", SubscriptBox["C", "F"]}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[6]=", - CellID->207267640] + CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ @@ -403,7 +385,7 @@ Cell[BoxData[ RowBox[{"a", ",", "b", ",", "a"}], "]"}], ",", RowBox[{"SUNNToCACF", "\[Rule]", "False"}]}], "]"}]], "Input", CellTags->"SUNT", - CellLabel->"In[7]:=", + CellLabel->"In[23]:=", CellID->568398491], Cell[BoxData[ @@ -417,8 +399,7 @@ Cell[BoxData[ TraditionalForm]], RowBox[{"2", " ", "N"}]]}], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[7]=", - CellID->1434438138] + CellLabel->"Out[23]="] }, Open ]], Cell[TextData[{ @@ -435,9 +416,7 @@ Cell[TextData[{ RowBox[{"1", "/", "2"}], " ", RowBox[{ SubscriptBox["\[Delta]", "ab"], "."}]}]}], TraditionalForm]]] -}], "Text", - CellTags->"SUNT", - CellID->871639479], +}], "Notes"], Cell[CellGroupData[{ @@ -446,7 +425,7 @@ Cell[BoxData[ RowBox[{"SUNT", "[", RowBox[{"a", ",", "b"}], "]"}], "]"}]], "Input", CellTags->"SUNT", - CellLabel->"In[8]:=", + CellLabel->"In[24]:=", CellID->345164772], Cell[BoxData[ @@ -463,8 +442,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]], "2"], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[8]=", - CellID->1733460108] + CellLabel->"Out[24]="] }, Open ]], Cell[TextData[{ @@ -473,9 +451,7 @@ Cell[TextData[{ FormBox[ SubscriptBox["T", "f"], TraditionalForm]]], ", you need to include a factor 2Tf inside the trace." -}], "Text", - CellTags->"SUNT", - CellID->2043701440], +}], "Notes"], Cell[CellGroupData[{ @@ -485,7 +461,7 @@ Cell[BoxData[ RowBox[{"SUNT", "[", RowBox[{"a", ",", "b"}], "]"}]}], "]"}]], "Input", CellTags->"SUNT", - CellLabel->"In[9]:=", + CellLabel->"In[25]:=", CellID->92682768], Cell[BoxData[ @@ -503,8 +479,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"SUNT", - CellLabel->"Out[9]=", - CellID->1858177206] + CellLabel->"Out[25]="] }, Open ]], Cell[CellGroupData[{ @@ -515,7 +490,7 @@ Cell[BoxData[ RowBox[{"SUNT", "[", RowBox[{"a", ",", "b"}], "]"}], "]"}], "//", "StandardForm"}]], "Input", CellTags->"SUNT", - 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RowBox[{"SUNTrace", "[", "expr", "]"}]], "InlineFormula"], + RowBox[{"SUNTrace", "[", "exp", "]"}]], "InlineFormula"], " \[LineSeparator]", "calculates the color-trace." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "SUNTrace", "]"}]], "Input", + CellLabel->"In[98]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Explicit", "\[Rule]", "False"}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[98]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -160,19 +171,32 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - ButtonBox["SUNSimplify", + ButtonBox["SUNTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNTrace", + ButtonNote->"SUNTrace"], + ", ", + ButtonBox["SUNT", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNT", + ButtonNote->"SUNT"], + ", ", + ButtonBox["SUNTF", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SUNTF", + ButtonNote->"SUNTF"], + ", ", + ButtonBox["SUNF", BaseStyle->"Link", - 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FormBox["c1129", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e66\"\>", ")"}], TraditionalForm], FormBox[ FormBox["d", @@ -815,14 +860,15 @@ Cell[BoxData[ TraditionalForm]}]], " ", SuperscriptBox["d", RowBox[{ - FormBox["c1129", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e66\"\>", ")"}], TraditionalForm], FormBox[ FormBox["c", TraditionalForm], TraditionalForm], FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm]}]]}], "-", FractionBox[ @@ -840,7 +886,7 @@ Cell[BoxData[ SuperscriptBox["\[Delta]", RowBox[{ FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm], FormBox[ @@ -863,7 +909,7 @@ Cell[BoxData[ SuperscriptBox["\[Delta]", RowBox[{ FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm], FormBox[ @@ -880,7 +926,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm]}]], " ", SuperscriptBox["\[Delta]", @@ -906,7 +952,7 @@ Cell[BoxData[ FormBox["b", TraditionalForm], TraditionalForm], - FormBox["c1128", + FormBox["c65", TraditionalForm]}]], " ", RowBox[{"(", RowBox[{ @@ -922,14 +968,16 @@ Cell[BoxData[ FormBox["d", TraditionalForm], TraditionalForm], - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm]}]], " ", SuperscriptBox["d", RowBox[{ - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm], FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm], FormBox[ @@ -940,7 +988,8 @@ Cell[BoxData[ FractionBox["1", "8"], " ", "\[ImaginaryI]", " ", SuperscriptBox["d", RowBox[{ - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm], FormBox[ FormBox["c", @@ -953,23 +1002,25 @@ Cell[BoxData[ SuperscriptBox["f", RowBox[{ FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm], FormBox[ FormBox["e", TraditionalForm], TraditionalForm], - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm]}]]}], "-", RowBox[{ FractionBox["1", "8"], " ", SuperscriptBox["d", RowBox[{ - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm], FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm], FormBox[ @@ -978,7 +1029,8 @@ Cell[BoxData[ TraditionalForm]}]], " ", SuperscriptBox["d", RowBox[{ - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm], FormBox[ FormBox["c", @@ -992,7 +1044,8 @@ Cell[BoxData[ FractionBox["1", "8"], " ", SuperscriptBox["d", RowBox[{ - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm], FormBox[ FormBox["c", @@ -1004,10 +1057,11 @@ Cell[BoxData[ TraditionalForm]}]], " ", SuperscriptBox["d", RowBox[{ - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm], FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm], FormBox[ @@ -1018,7 +1072,8 @@ Cell[BoxData[ FractionBox["1", "8"], " ", SuperscriptBox["d", RowBox[{ - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm], FormBox[ FormBox["d", @@ -1030,14 +1085,15 @@ Cell[BoxData[ TraditionalForm]}]], " ", SuperscriptBox["d", RowBox[{ - FormBox["c1130", + FormBox[ + RowBox[{"FCGV", "(", "\<\"e67\"\>", ")"}], TraditionalForm], FormBox[ FormBox["c", TraditionalForm], TraditionalForm], FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm]}]]}], "-", FractionBox[ @@ -1055,7 +1111,7 @@ Cell[BoxData[ SuperscriptBox["\[Delta]", RowBox[{ FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm], FormBox[ @@ -1078,7 +1134,7 @@ Cell[BoxData[ SuperscriptBox["\[Delta]", RowBox[{ FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm], FormBox[ @@ -1095,7 +1151,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm], FormBox[ - FormBox["c1128", + FormBox["c65", TraditionalForm], TraditionalForm]}]], " ", SuperscriptBox["\[Delta]", @@ -1156,18 +1212,17 @@ Cell[BoxData[ TraditionalForm]}]]}]}], ")"}]}], RowBox[{"2", " ", "N"}]]}], TraditionalForm]], "Output", CellTags->"SUNTrace", - CellLabel->"Out[8]=", - CellID->357301374] + CellLabel->"Out[105]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"SUNSimplify", "[", - RowBox[{"t2", ",", + RowBox[{"%", ",", RowBox[{"Explicit", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SUNTrace", - CellLabel->"In[9]:=", + CellLabel->"In[106]:=", CellID->1337618063], Cell[BoxData[ @@ -1208,108 +1263,8 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"SUNTrace", - CellLabel->"Out[9]=", - CellID->2000562450] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"SUNSimplify", "[", - RowBox[{ - RowBox[{"SUNF", "[", - RowBox[{"a", ",", "b", ",", "c"}], "]"}], " ", - RowBox[{"SUND", "[", - RowBox[{"d", ",", "b", ",", "c"}], "]"}]}], "]"}]], "Input", - CellTags->"SUNTrace", - CellLabel->"In[10]:=", - CellID->1959336477], - -Cell[BoxData[ - FormBox["0", TraditionalForm]], "Output", - CellTags->"SUNTrace", - CellLabel->"Out[10]=", - CellID->164079513] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"SUNSimplify", "[", - RowBox[{ - RowBox[{"SUNF", "[", - RowBox[{"a", ",", "b", ",", "c"}], "]"}], " ", - RowBox[{"SUND", "[", - RowBox[{"a", ",", "b", ",", "d"}], "]"}]}], "]"}]], "Input", - CellTags->"SUNTrace", - CellLabel->"In[11]:=", - CellID->849009416], - -Cell[BoxData[ - FormBox["0", TraditionalForm]], "Output", - CellTags->"SUNTrace", - CellLabel->"Out[11]=", - CellID->657628575] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"SUNSimplify", "[", - RowBox[{ - RowBox[{"SUNF", "[", - RowBox[{"a", ",", "b", ",", "c"}], "]"}], " ", - RowBox[{"SUND", "[", - RowBox[{"a", ",", "d", ",", "c"}], "]"}]}], "]"}]], "Input", - CellTags->"SUNTrace", - CellLabel->"In[12]:=", - CellID->1231032711], - -Cell[BoxData[ - FormBox["0", TraditionalForm]], "Output", - CellTags->"SUNTrace", - CellLabel->"Out[12]=", - CellID->839284650] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"SUNSimplify", "[", - RowBox[{ - RowBox[{"SUND", "[", - RowBox[{"a", ",", "b", ",", "c"}], "]"}], " ", - RowBox[{"SUND", "[", - RowBox[{"d", ",", "b", ",", "c"}], "]"}]}], "]"}]], "Input", - CellTags->"SUNTrace", - CellLabel->"In[13]:=", - CellID->1107366946], - -Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{"-", - RowBox[{"(", - RowBox[{"4", "-", - SubsuperscriptBox["C", "A", "2"]}], ")"}]}], " ", - SuperscriptBox["\[Delta]", - RowBox[{ - FormBox[ - FormBox["a", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox["d", - TraditionalForm], - TraditionalForm]}]], " ", - RowBox[{"(", - RowBox[{ - SubscriptBox["C", "A"], "-", - RowBox[{"2", " ", - SubscriptBox["C", "F"]}]}], ")"}]}], TraditionalForm]], "Output", - CellTags->"SUNTrace", - CellLabel->"Out[13]=", - CellID->1291039632] + CellLabel->"Out[106]="] +}, Open ]] }, Open ]] }, Open ]], @@ -1374,12 +1329,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{326, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarGluonVertex.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarGluonVertex.nb index 997f83a76..0b1f79d57 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarGluonVertex.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarGluonVertex.nb @@ -122,17 +122,65 @@ Cell[TextData[{ RowBox[{"{", "p", "}"}], ",", " ", RowBox[{"{", "q", "}"}], ",", " ", RowBox[{"{", - RowBox[{"mu", ",", "a"}], "}"}]}], "]"}]], "InlineFormula"], - " \n\tor ScalarGluonVertex[ p, q, mu, a ] yields the scalar-scalar-gluon \ -vertex (p and q are incoming momenta). ScalarGluonVertex[{mu,a}, {nu,b}] \ -yields the scalar-scalar-gluon-gluon vertex (p and q are incoming momenta).\n\ -\tThe dimension and the name of the coupling constant are determined by the \ -options Dimension and CouplingConstant." + RowBox[{"\[Mu]", ",", "a"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]or ", + Cell[BoxData[ + RowBox[{"ScalarGluonVertex", "[", + RowBox[{"p", ",", " ", "q", ",", " ", "\[Mu]", ",", " ", "a"}], "]"}]], + "InlineFormula"], + " yields the scalar-scalar-gluon vertex, where ", + Cell[BoxData["p"], "InlineFormula"], + " and ", + Cell[BoxData["q"], "InlineFormula"], + " are incoming momenta.\n", + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"ScalarGluonVertex", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"\[Mu]", ",", "a"}], "}"}], ",", + RowBox[{"{", + RowBox[{"\[Nu]", ",", "b"}], "}"}]}], "]"}]], "InlineFormula"], + " \[LineSeparator]yields the scalar-scalar-gluon-gluon vertex, where ", + Cell[BoxData["p"], "InlineFormula"], + " and ", + Cell[BoxData["q"], "InlineFormula"], + " are incoming momenta. syntax." }], "Usage", - CellID->982511436], + CellID->2010081510], + +Cell[TextData[{ + "The dimension and the name of the coupling constant are determined by the \ +options ", + ButtonBox["Dimension", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Dimension", + ButtonNote->"Dimension"], + " and ", + ButtonBox["CouplingConstant", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/CouplingConstant", + ButtonNote->"CouplingConstant"], + ". " +}], "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "ScalarGluonVertex", "]"}]], "Input", + CellLabel->"In[55]:="], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"CouplingConstant", "\[Rule]", + SubscriptBox["g", "s"]}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"Gauge", "\[Rule]", "1"}]}], "}"}], TraditionalForm]], "Output", + CellLabel->"Out[55]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -197,36 +245,15 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "ScalarGluonVertex", "]"}]], "Input", - CellTags->"ScalarGluonVertex", - CellLabel->"In[1]:=", - CellID->1577288725], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"CouplingConstant", "\[Rule]", - SubscriptBox["g", "s"]}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"Gauge", "\[Rule]", "1"}]}], "}"}], TraditionalForm]], "Output", - CellTags->"ScalarGluonVertex", - CellLabel->"Out[1]=", - CellID->1150833543] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"ScalarGluonVertex", "[", RowBox[{ RowBox[{"{", "p", "}"}], ",", " ", RowBox[{"{", "q", "}"}], ",", " ", RowBox[{"{", - RowBox[{"mu", ",", " ", "a"}], "}"}]}], "]"}]], "Input", + RowBox[{"\[Mu]", ",", " ", "a"}], "}"}]}], "]"}]], "Input", CellTags->"ScalarGluonVertex", - CellLabel->"In[2]:=", + CellLabel->"In[57]:=", CellID->581447761], Cell[BoxData[ @@ -238,28 +265,21 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], " ", SubscriptBox["g", "s"], " ", - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - FormBox["p", - TraditionalForm], "-", - FormBox["q", - TraditionalForm]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", + RowBox[{ + FormBox["p", + TraditionalForm], "-", + FormBox["q", + TraditionalForm]}], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"ScalarGluonVertex", - CellLabel->"Out[2]=", - CellID->260312021] + CellLabel->"Out[57]="] }, Open ]] }, Open ]], @@ -324,12 +344,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{796, Automatic}, {Automatic, 216}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarProduct.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarProduct.nb index 1d859cdc1..65ce83868 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarProduct.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarProduct.nb @@ -119,31 +119,37 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"ScalarProduct", "[", RowBox[{"p", ",", " ", "q"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the input for scalar product. ScalarProduct[p] is equivalent to \ -ScalarProduct[p, p]. Expansion of sums of momenta in ScalarProduct is done \ -with ExpandScalarProduct. Scalar product may be set, e.g., ScalarProduct[a, \ -b] = ", - Cell[BoxData[ - FormBox[ - RowBox[{"m", "^", "2"}], TraditionalForm]]], - "; but a and b must not contain sums. Note that ScalarProduct[a, b] = ", - Cell[BoxData[ - FormBox[ - RowBox[{"m", "^", "2"}], TraditionalForm]]], - " actually sets also: Pair[Momentum[a, ___], Momentum[b, ___]] = ", - Cell[BoxData[ - FormBox[ - RowBox[{"m", "^", "2"}], TraditionalForm]]], - ". It is encouraged to always set ScalarProduct's ", + " \[LineSeparator] is the input for the scalar product of two Lorentz \ +vectors p and q. ScalarProduct[p] is equivalent to ScalarProduct[p, p]. \ +Expansion of sums of momenta in ScalarProduct is done with \ +ExpandScalarProduct. Scalar products may be set, e.g. via ScalarProduct[a, b] \ += m^2; but a and b may not contain sums. Note that ScalarProduct[a, b] = m^2 \ +actually sets Lorentzian scalar products in different dimensions specified by \ +the value of the SetDimensions option. It is highly recommended to set \ +ScalarProduct's ", StyleBox["before", FontWeight->"Bold"], - " any calculation. This improves the performance of FeynCalc ." + " any calculation. This improves the performance of FeynCalc.." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "ScalarProduct", "]"}]], "Input", + CellLabel->"In[312]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "4"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "True"}], ",", + RowBox[{"SetDimensions", "\[Rule]", + RowBox[{"{", + RowBox[{"4", ",", "D"}], "}"}]}]}], "}"}], TraditionalForm]], "Output", + CellLabel->"Out[312]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -179,7 +185,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["Calc", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Calc", @@ -215,9 +220,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SPD", ButtonNote->"SPD"], "." -}], "Text", - CellTags->"ScalarProduct", - CellID->912859437] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -269,8 +272,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[1]=", - CellID->785575855] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -299,19 +301,20 @@ Cell[BoxData[ FormBox["\<\"(\"\>", TraditionalForm], FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"]}], + FormBox[ + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"]}], + TraditionalForm], TraditionalForm], FormBox["\<\")\"\>", TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[2]=", - CellID->1751795401] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -332,8 +335,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"], TraditionalForm]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[3]=", - CellID->170285827] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -353,8 +355,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm], "2"], TraditionalForm]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[4]=", - CellID->794666024] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -373,8 +374,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", "p", "]"}], ",", RowBox[{"Momentum", "[", "q", "]"}]}], "]"}]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[5]//StandardForm=", - CellID->2085175923] + CellLabel->"Out[5]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -397,8 +397,7 @@ Cell[BoxData[ RowBox[{"Momentum", "[", RowBox[{"q", ",", "D"}], "]"}]}], "]"}]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[6]//StandardForm=", - CellID->1965353289] + CellLabel->"Out[6]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -418,8 +417,7 @@ Cell[BoxData[ FormBox[ FractionBox["s", "2"], TraditionalForm]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[7]=", - CellID->622238783] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -491,8 +489,7 @@ Cell[BoxData[ TraditionalForm]}], "+", FractionBox["s", "2"]}], TraditionalForm]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[8]=", - CellID->1856511612] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -564,8 +561,7 @@ Cell[BoxData[ TraditionalForm]}], "+", FractionBox["s", "2"]}], TraditionalForm]], "Output", CellTags->"ScalarProduct", - CellLabel->"Out[9]=", - CellID->1175433176] + CellLabel->"Out[9]="] }, Open ]], Cell[BoxData[ @@ -636,12 +632,13 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 684}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{779, Automatic}, {Automatic, 200}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarProductCancel.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarProductCancel.nb index 38a929c96..e1587c725 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarProductCancel.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ScalarProductCancel.nb @@ -126,8 +126,34 @@ simple cases." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +ScalarProductCancel is deprecated, please use the more powerful ApartFF \ +instead!\ +\>", "Notes", + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "ScalarProductCancel", "]"}]], "Input", + CellTags->"ScalarProductCancel", + CellLabel->"In[1]:=", + CellID->183152643], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"ChangeDimension", "\[Rule]", "D"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"FeynAmpDenominatorSimplify", "\[Rule]", "True"}], ",", + RowBox[{"FeynAmpDenominatorCombine", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"ScalarProductCancel", + CellLabel->"Out[1]=", + CellID->55006305] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -163,11 +189,10 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", - ButtonBox["Calc", + ButtonBox["ApartFF", BaseStyle->"Link", - 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It may be set to an \ -integer indicating the maximum number of terms onto which the function \ -Schouten will be applied ." + RowBox[{"Schouten", "[", "exp", "]"}]], "InlineFormula"], + " \[LineSeparator]attempts to automatically remove spurious terms in ", + Cell[BoxData["exp"], "InlineFormula"], + " by applying the Schouten identity." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + ButtonBox["Schouten", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Schouten", + ButtonNote->"Schouten"], + " applies the identity for 4-vectors on at most ", + Cell[BoxData["42"], "InlineFormula"], + " terms in a sum." +}], "Notes"], + +Cell[TextData[{ + "If it should operate on a larger expression you can give a second argument, \ +e.g. ", + Cell[BoxData[ + RowBox[{"Schouten", "[", + RowBox[{"expr", ",", "4711"}], "]"}]], "InlineFormula"], + " which will work on sums with less than ", + Cell[BoxData["4711"], "InlineFormula"], + " terms." +}], "Notes"], + +Cell[TextData[{ + ButtonBox["Schouten", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Schouten", + ButtonNote->"Schouten"], + " is also an option of ", + ButtonBox["Contract", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Contract", + ButtonNote->"Contract"], + " and ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + ". 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$Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectFree.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectFree.nb index aa8c742b1..41fe8d05d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectFree.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectFree.nb @@ -120,15 +120,11 @@ Cell[TextData[{ RowBox[{"SelectFree", "[", RowBox[{"expr", ",", " ", "a", ",", " ", "b", ",", " ", "..."}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is equivalent to Select[expr, FreeQ2[#, {a,b, ...}]&], except the special \ -cases: SelectFree[a, b] returns a and SelectFree[a,a] returns 1 (where a is \ -not a product or a sum).\n\nSelectFree is equivalent to Select1." + " \[LineSeparator]is equivalent to Select[expr, FreeQ2[#, {a,b, ...}]&], \ +except the special cases: SelectFree[a, b] returns a and SelectFree[a,a] \ +returns 1 (where a is not a product or a sum)." }], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] + CellID->982511436] }, Open ]], Cell[CellGroupData[{ @@ -174,9 +170,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SelectNotFree", ButtonNote->"SelectNotFree"], "." -}], "Text", - CellTags->"SelectFree", - CellID->1096848115] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -218,8 +212,7 @@ Cell[BoxData[ FormBox[ RowBox[{"b", "+", "d"}], TraditionalForm]], "Output", CellTags->"SelectFree", - CellLabel->"Out[1]=", - CellID->818540084] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -235,8 +228,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["y", TraditionalForm]], "Output", CellTags->"SelectFree", - CellLabel->"Out[2]=", - CellID->1323839729] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -256,8 +248,7 @@ Cell[BoxData[ FormBox[ RowBox[{"2", " ", "z"}], TraditionalForm]], "Output", CellTags->"SelectFree", - CellLabel->"Out[3]=", - CellID->912675516] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -272,8 +263,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["a", TraditionalForm]], "Output", CellTags->"SelectFree", - CellLabel->"Out[4]=", - CellID->1001842240] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -288,8 +278,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"SelectFree", - CellLabel->"Out[5]=", - CellID->1438478141] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -304,8 +293,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"SelectFree", - CellLabel->"Out[6]=", - CellID->1251533165] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -321,8 +309,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"SelectFree", - CellLabel->"Out[7]=", - CellID->1673614830] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -387,12 +374,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{924, Automatic}, {Automatic, 181}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectGraphs.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectGraphs.nb index 940cda047..51bf72c5e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectGraphs.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectGraphs.nb @@ -169,9 +169,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoopSum", ButtonNote->"OneLoopSum"], "." -}], "Text", - CellTags->"SelectGraphs", - CellID->1262985927] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,12 +255,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{786, Automatic}, {Automatic, 178}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectNotFree.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectNotFree.nb index 892fe7b30..4a132098f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectNotFree.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectNotFree.nb @@ -119,15 +119,19 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"SelectNotFree", "[", RowBox[{"expr", ",", " ", "x"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "returns that part of expr which is not free of any occurance of x.\n\n\ -SelectNotFree[expr, a, b, ...] is equivalent to Select[expr, !FreeQ2[#, {a, \ -b, ...}]&], except the special cases: SelectNotFree[a, b] returns 1 and \ -SelectNotFree[a, a] returns a (where a is not a product or a sum)." + " \[LineSeparator]returns that part of ", + Cell[BoxData["expr"], "InlineFormula"], + " which is not free of any occurance of ", + Cell[BoxData["x"], "InlineFormula"], + ".\n\n" }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell["\<\ +SelectNotFree[expr, a, b, ...] is equivalent to Select[expr, !FreeQ2[#, {a, \ +b, ...}]&], except the special cases: SelectNotFree[a, b] returns 1 and \ +SelectNotFree[a, a] returns a (where a is not a product or a sum).\ +\>", "Notes", CellID->1067943069] }, Open ]], @@ -174,9 +178,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SelectFree", ButtonNote->"SelectFree"], "." -}], "Text", - CellTags->"SelectNotFree", - CellID->1049407209] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -219,8 +221,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"f", "(", "a", ")"}], "+", "a"}], TraditionalForm]], "Output", CellTags->"SelectNotFree", - CellLabel->"Out[1]=", - CellID->879726471] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -241,8 +242,7 @@ Cell[BoxData[ RowBox[{"x", " ", "y", " ", RowBox[{"f", "(", "x", ")"}]}], TraditionalForm]], "Output", CellTags->"SelectNotFree", - CellLabel->"Out[2]=", - CellID->1461838958] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -257,8 +257,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"SelectNotFree", - CellLabel->"Out[3]=", - CellID->1791356409] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -274,8 +273,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"SelectNotFree", - CellLabel->"Out[4]=", - CellID->209254169] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -290,8 +288,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["a", TraditionalForm]], "Output", CellTags->"SelectNotFree", - CellLabel->"Out[5]=", - CellID->412334803] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -306,8 +303,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["1", TraditionalForm]], "Output", CellTags->"SelectNotFree", - CellLabel->"Out[6]=", - CellID->1168169225] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -324,8 +320,7 @@ Cell[BoxData[ FormBox[ RowBox[{"f", "(", "x", ")"}], TraditionalForm]], "Output", CellTags->"SelectNotFree", - CellLabel->"Out[7]=", - CellID->2104713784] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -390,12 +385,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{931, Automatic}, {Automatic, 263}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectSplit.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectSplit.nb index d11399f29..670629f9d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectSplit.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SelectSplit.nb @@ -240,8 +240,7 @@ Cell[BoxData[ SuperscriptBox["e", "6"]}], "}"}]}], "}"}], TraditionalForm]], "Output", CellTags->"SelectSplit", - CellLabel->"Out[1]=", - CellID->559959953] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -286,8 +285,7 @@ Cell[BoxData[ RowBox[{"f", "+", "g"}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], TraditionalForm]], "Output", CellTags->"SelectSplit", - CellLabel->"Out[2]=", - CellID->2002061756] + CellLabel->"Out[2]="] }, Open ]] }, Open ]], @@ -352,12 +350,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{870, Automatic}, {275, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Series2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Series2.nb index 7ea12b3c5..478a25633 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Series2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Series2.nb @@ -127,8 +127,30 @@ is equivalent to Series2[f, {e, 0, n}]." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Series2", "]"}]], "Input", + CellTags->"Series2", + CellLabel->"In[3]:=", + CellID->1435843837], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Collecting", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "True"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", + RowBox[{ + TagBox["\[DoubledGamma]", + Function[{}, EulerGamma]], "\[Rule]", "0"}], "}"}]}], ",", + RowBox[{"SimplifyPolyLog", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"Series2", + CellLabel->"Out[3]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -193,32 +215,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Series2", "]"}]], "Input", - CellTags->"Series2", - CellLabel->"In[1]:=", - CellID->1435843837], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Collecting", "\[Rule]", "False"}], ",", - RowBox[{"Factoring", "\[Rule]", "True"}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", - RowBox[{ - TagBox["\[DoubledGamma]", - Function[{}, EulerGamma]], "\[Rule]", "0"}], "}"}]}], ",", - RowBox[{"SimplifyPolyLog", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"Series2", - CellLabel->"Out[1]=", - CellID->1982660957] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"Series2", "[", RowBox[{ @@ -231,7 +227,7 @@ Cell[BoxData[ RowBox[{"\[Delta]", "/", "2"}], ")"}]}], ",", "\[Delta]", ",", "1"}], "]"}]], "Input", CellTags->"Series2", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->785606174], Cell[BoxData[ @@ -246,8 +242,7 @@ Cell[BoxData[ RowBox[{"log", "(", "x", ")"}]}], "+", "1"}], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[2]=", - CellID->78273571] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -257,7 +252,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Gamma", "[", "x", "]"}], ",", "x", ",", "1"}], "]"}]], "Input", CellTags->"Series2", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1445520007], Cell[BoxData[ @@ -268,8 +263,7 @@ Cell[BoxData[ RowBox[{"\[Zeta]", "(", "2", ")"}], " ", "x"}], "+", FractionBox["1", "x"]}], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[3]=", - CellID->1484488938] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -281,7 +275,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"Series2", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->1607149077], Cell[BoxData[ @@ -309,8 +303,7 @@ Cell[BoxData[ 1, -EulerGamma, Rational[1, 12] (6 EulerGamma^2 + Pi^2)}, -1, 2, 1], Editable->False], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[4]=", - CellID->406465977] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -320,7 +313,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Gamma", "[", "x", "]"}], ",", "x", ",", "2"}], "]"}]], "Input", CellTags->"Series2", - CellLabel->"In[5]:=", + CellLabel->"In[4]:=", CellID->113546639], Cell[BoxData[ @@ -337,8 +330,7 @@ Cell[BoxData[ RowBox[{"\[Zeta]", "(", "2", ")"}], " ", "x"}], "+", FractionBox["1", "x"]}], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[5]=", - CellID->503684567] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -351,7 +343,7 @@ Cell[BoxData[ RowBox[{"FinalSubstitutions", "\[Rule]", RowBox[{"{", "}"}]}]}], "]"}], "//", "FullSimplify"}]], "Input", CellTags->"Series2", - CellLabel->"In[6]:=", + CellLabel->"In[5]:=", CellID->31680807], Cell[BoxData[ @@ -386,8 +378,7 @@ Cell[BoxData[ Function[{}, EulerGamma]], "2"], " ", "x"}], "+", FractionBox["6", "x"]}], ")"}]}], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[6]=", - CellID->607384212] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -407,7 +398,7 @@ Cell[BoxData[ "}"}]}], "]"}], "//", "Normal"}], "//", "Expand"}], "//", "FullSimplify"}]], "Input", CellTags->"Series2", - CellLabel->"In[7]:=", + CellLabel->"In[6]:=", CellID->1418084636], Cell[BoxData[ @@ -443,15 +434,12 @@ Cell[BoxData[ Function[{}, EulerGamma]], "2"], " ", "x"}], "+", FractionBox["12", "x"]}], ")"}]}], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[7]=", - CellID->743143408] + CellLabel->"Out[6]="] }, Open ]], Cell["\<\ There is a table of expansions of special hypergeometric functions.\ -\>", "Text", - CellTags->"Series2", - CellID->659671376], +\>", "Notes"], Cell[CellGroupData[{ @@ -470,7 +458,7 @@ Cell[BoxData[ RowBox[{"OPEm", "+", "Epsilon"}]}], "}"}], ",", "1"}], "]"}], ",", "Epsilon", ",", "1"}], "]"}]], "Input", CellTags->"Series2", - CellLabel->"In[8]:=", + CellLabel->"In[7]:=", CellID->1447119838], Cell[BoxData[ @@ -497,8 +485,7 @@ Cell[BoxData[ TemplateBox[{"1","m"}, "PolyGamma2"]}], "2"], "+", "1"}], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[8]=", - CellID->1252077467] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -520,7 +507,7 @@ Cell[BoxData[ RowBox[{"Epsilon", " ", "+", " ", "OPEm"}]}], "}"}], ",", " ", "1"}], "]"}], ",", "Epsilon", ",", "1"}], "]"}]}]], "Input", CellTags->"Series2", - CellLabel->"In[9]:=", + CellLabel->"In[8]:=", CellID->1777911067], Cell[BoxData[ @@ -558,8 +545,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}]}]}], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[9]=", - CellID->859590251] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -570,7 +556,7 @@ Cell[BoxData[ RowBox[{"1", " ", "+", " ", RowBox[{"2", " ", "Epsilon"}]}], ",", "x"}], "]"}]], "Input", CellTags->"Series2", - CellLabel->"In[10]:=", + CellLabel->"In[9]:=", CellID->1986693903], Cell[BoxData[ @@ -580,8 +566,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm]}], "+", "1"}],"x"}, "Hypergeometric2F1"], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[10]=", - CellID->444344105] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -590,7 +575,7 @@ Cell[BoxData[ RowBox[{"Series2", "[", RowBox[{"%", ",", "Epsilon", ",", "3"}], "]"}]], "Input", CellTags->"Series2", - CellLabel->"In[11]:=", + CellLabel->"In[10]:=", CellID->180283674], Cell[BoxData[ @@ -699,8 +684,7 @@ Cell[BoxData[ TemplateBox[{"3"}, "Zeta"]}], "+", "1"}], TraditionalForm]], "Output", CellTags->"Series2", - CellLabel->"Out[11]=", - CellID->1006368312] + CellLabel->"Out[10]="] }, Open ]], Cell[TextData[{ @@ -713,9 +697,7 @@ Cell[TextData[{ SubscriptBox["F", "1"]}]}], TraditionalForm]]], " tabulated in Series2.m. The interested user can consult the source code \ (search for HYPERLIST)." -}], "Text", - CellTags->"Series2", - CellID->1023055054] +}], "Notes"] }, Open ]], Cell[CellGroupData[{ @@ -779,12 +761,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{645, Automatic}, {Automatic, 86}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Series3.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Series3.nb index 312ff5edf..899b839a8 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Series3.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Series3.nb @@ -124,8 +124,25 @@ fixed. Series3[f, e, n] is equivalent to Series3[f, {e, 0, n}]." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Series3", "]"}]], "Input", + CellTags->"Series3", + CellLabel->"In[1]:=", + CellID->457203194], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Factoring", "\[Rule]", "True"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", + CellTags->"Series3", + CellLabel->"Out[1]=", + CellID->2070948847] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -166,9 +183,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Series2", ButtonNote->"Series2"], "." -}], "Text", - CellTags->"Series3", - CellID->601286817] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -197,26 +212,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Series3", "]"}]], "Input", - CellTags->"Series3", - CellLabel->"In[1]:=", - CellID->457203194], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Factoring", "\[Rule]", "True"}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", - CellTags->"Series3", - CellLabel->"Out[1]=", - CellID->2070948847] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"Series3", "[", RowBox[{ @@ -229,7 +224,7 @@ Cell[BoxData[ RowBox[{"\[Delta]", "/", "2"}], ")"}]}], ",", "\[Delta]", ",", "1"}], "]"}]], "Input", CellTags->"Series3", - CellLabel->"In[2]:=", + CellLabel->"In[11]:=", CellID->1953540257], Cell[BoxData[ @@ -243,8 +238,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], ")"}], " ", "x"}], ")"}]}], "+", "1"}], TraditionalForm]], "Output", CellTags->"Series3", - CellLabel->"Out[2]=", - CellID->2052658342] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -256,7 +250,7 @@ Cell[BoxData[ RowBox[{"Gamma", "[", "x", "]"}], ",", "x", ",", "1"}], "]"}], "//", "FullSimplify"}]], "Input", CellTags->"Series3", - CellLabel->"In[3]:=", + CellLabel->"In[12]:=", CellID->1278931466], Cell[BoxData[ @@ -266,8 +260,7 @@ Cell[BoxData[ TagBox["\[DoubledGamma]", Function[{}, EulerGamma]], "+", "1"}], TraditionalForm]], "Output", CellTags->"Series3", - CellLabel->"Out[3]=", - CellID->654585164] + CellLabel->"Out[12]="] }, Open ]] }, Open ]], @@ -332,12 +325,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{694, Automatic}, {Automatic, 124}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SetMandelstam.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SetMandelstam.nb index 5f83deda3..05962858e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SetMandelstam.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SetMandelstam.nb @@ -118,21 +118,93 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"SetMandelstam", "[", + RowBox[{"s", ",", " ", "t", ",", " ", "u", ",", " ", + SubscriptBox["p", "1"], ",", " ", + SubscriptBox["p", "2"], ",", " ", + SubscriptBox["p", "3"], ",", " ", + SubscriptBox["p", "4"], ",", " ", + SubscriptBox["m", "1"], ",", " ", + SubscriptBox["m", "2"], ",", " ", + SubscriptBox["m", "3"], ",", " ", + SubscriptBox["m", "4"]}], "]"}]], "InlineFormula"], + " \[LineSeparator]defines the Mandelstam variables ", + Cell[BoxData[ + RowBox[{"s", "=", + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + SubscriptBox["p", "1"], "+", + SubscriptBox["p", "2"]}], ")"}], "2"]}]], "InlineFormula"], + ", ", + Cell[BoxData[ + RowBox[{"t", "=", + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + SubscriptBox["p", "1"], "+", + SubscriptBox["p", "3"]}], ")"}], "2"]}]], "InlineFormula"], + ", ", + Cell[BoxData[ + RowBox[{"u", "=", + SuperscriptBox[ + RowBox[{"(", + RowBox[{ + SubscriptBox["p", "1"], "+", + SubscriptBox["p", "4"]}], ")"}], "2"]}]], "InlineFormula"], + " and sets the momenta on-shell: ", + Cell[BoxData[ + RowBox[{ + SuperscriptBox[ + SubscriptBox["p", "1"], "2"], "=", + SuperscriptBox[ + SubscriptBox["m", "1"], "2"]}]], "InlineFormula"], + ", ", + Cell[BoxData[ + RowBox[{ + SuperscriptBox[ + SubscriptBox["p", "2"], "2"], "=", + SuperscriptBox[ + SubscriptBox["m", "2"], "2"]}]], "InlineFormula"], + ", ", + Cell[BoxData[ + RowBox[{ + SuperscriptBox[ + SubscriptBox["p", "3"], "2"], "=", + SuperscriptBox[ + SubscriptBox["m", "3"], "2"]}]], "InlineFormula"], + ", ", + Cell[BoxData[ + RowBox[{ + SuperscriptBox[ + SubscriptBox["p", "4"], "2"], "=", + SuperscriptBox[ + SubscriptBox["m", "4"], "2"]}]], "InlineFormula"], + ". 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+ CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{999, Automatic}, {Automatic, 238}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Simplify2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Simplify2.nb index f0a5c6716..16805d483 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Simplify2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Simplify2.nb @@ -173,8 +173,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -188,12 +186,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"Simplify2", - CellLabel->"In[1]:=", - CellID->1866023548] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -255,12 +247,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{770, Automatic}, {Automatic, 97}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyDeltaFunction.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyDeltaFunction.nb index 05a92da4b..1d9579a7b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyDeltaFunction.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyDeltaFunction.nb @@ -173,9 +173,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DeltaFunctionPrime", ButtonNote->"DeltaFunctionPrime"], "." -}], "Text", - CellTags->"SimplifyDeltaFunction", - CellID->2042613065] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -222,8 +220,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[1]=", - CellID->117200739] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -248,8 +245,7 @@ Cell[BoxData[ RowBox[{"x", "\[Rule]", "1"}]], "\[ThinSpace]", RowBox[{"g", "(", "x", ")"}]}], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[2]=", - CellID->226766481] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -273,8 +269,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[3]=", - CellID->1487082282] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -313,8 +308,7 @@ Cell[BoxData[ RowBox[{"x", "\[Rule]", "1"}]], "\[ThinSpace]", RowBox[{"g", "(", "x", ")"}]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[4]=", - CellID->1033550143] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -338,8 +332,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[5]=", - CellID->2058651279] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -358,8 +351,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[6]=", - CellID->214547923] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -386,8 +378,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[7]=", - CellID->102107043] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -407,8 +398,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[8]=", - CellID->1247820634] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -437,8 +427,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[9]=", - CellID->1462784843] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -453,8 +442,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["0", TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[10]=", - CellID->1037602810] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -481,8 +469,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[11]=", - CellID->1786873704] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -502,8 +489,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], TraditionalForm], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyDeltaFunction", - CellLabel->"Out[12]=", - CellID->1434858408] + CellLabel->"Out[12]="] }, Open ]] }, Open ]], @@ -568,12 +554,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{614, Automatic}, {Automatic, 65}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyGTI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyGTI.nb index e4c8af33e..70498fa9d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyGTI.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyGTI.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/GTI", ButtonNote->"GTI"], "." -}], "Text", - CellTags->"SimplifyGTI", - CellID->1783714031] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -178,8 +176,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -193,12 +189,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData[""], "Input", - CellTags->"SimplifyGTI", - CellLabel->"In[1]:=", - CellID->1050810759] -}, Open ]], - Cell[CellGroupData[{ Cell["More Examples", "ExtendedExamplesSection", @@ -260,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{770, Automatic}, {Automatic, 159}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyPolyLog.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyPolyLog.nb index aa5ba7377..fa610fcf6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyPolyLog.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SimplifyPolyLog.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Nielsen", ButtonNote->"Nielsen"], "." -}], "Text", - CellTags->"SimplifyPolyLog", - CellID->1770209649] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -235,8 +233,7 @@ Cell[BoxData[ RowBox[{"\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[{"log", "(", "x", ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[2]=", - CellID->2071359595] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -263,8 +260,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], ")"}], " ", RowBox[{"log", "(", "x", ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[3]=", - CellID->669626223] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -299,8 +295,7 @@ Cell[BoxData[ RowBox[{"log", "(", RowBox[{"x", "+", "1"}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[4]=", - CellID->1110979124] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -333,8 +328,7 @@ Cell[BoxData[ RowBox[{"1", "-", "x"}], ")"}], " ", RowBox[{"log", "(", "x", ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[5]=", - CellID->2004136203] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -373,8 +367,7 @@ Cell[BoxData[ RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[6]=", - CellID->746814688] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -411,8 +404,7 @@ Cell[BoxData[ RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[7]=", - CellID->965485175] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -460,8 +452,7 @@ Cell[BoxData[ SuperscriptBox["log", "3"], "(", RowBox[{"1", "-", "x"}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[8]=", - CellID->350232376] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -493,8 +484,7 @@ Cell[BoxData[ SuperscriptBox["log", "3"], "(", "x", ")"}], "6"]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[9]=", - CellID->1378986370] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -511,8 +501,7 @@ Cell[BoxData[ Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[10]=", - CellID->1264404285] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -562,8 +551,7 @@ Cell[BoxData[ TemplateBox[{"3"}, "Zeta"]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[11]=", - CellID->1217956432] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -630,8 +618,7 @@ Cell[BoxData[ RowBox[{"log", "(", RowBox[{"1", "-", "x"}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[12]=", - CellID->1165745994] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -693,8 +680,7 @@ Cell[BoxData[ TemplateBox[{"3"}, "Zeta"]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[13]=", - CellID->1811068047] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -813,8 +799,7 @@ Cell[BoxData[ SuperscriptBox["log", "2"], "(", RowBox[{"1", "-", "x"}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[14]=", - CellID->2000726501] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ @@ -840,8 +825,7 @@ Cell[BoxData[ RowBox[{"a", " ", "c"}], "+", "b"}], "c"], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[15]=", - CellID->352084172] + CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ @@ -862,8 +846,7 @@ Cell[BoxData[ RowBox[{"-", RowBox[{"log", "(", "x", ")"}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[16]=", - CellID->1162064393] + CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ @@ -889,8 +872,7 @@ Cell[BoxData[ RowBox[{"x", "+", "1"}], RowBox[{"1", "-", "x"}]]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[17]=", - CellID->1326650152] + CellLabel->"Out[17]="] }, Open ]], Cell[CellGroupData[{ @@ -915,8 +897,7 @@ Cell[BoxData[ SuperscriptBox["x", "2"], "+", "1"}]], "+", "x"}], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[18]=", - CellID->580053978] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -941,8 +922,7 @@ Cell[BoxData[ SuperscriptBox["x", "2"], "-", "1"}]], "+", "x"}], ")"}]}], TraditionalForm]], "Output", CellTags->"SimplifyPolyLog", - CellLabel->"Out[19]=", - CellID->654978590] + CellLabel->"Out[19]="] }, Open ]], Cell[BoxData[ @@ -1013,12 +993,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{873, Automatic}, {Automatic, 149}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SinorUBarD.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SinorUBarD.nb new file mode 100644 index 000000000..9fb727457 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SinorUBarD.nb @@ -0,0 +1,257 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + 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Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SmallEpsilon.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SmallEpsilon.nb index 5a9a20ad5..8c1d0cbbb 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SmallEpsilon.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SmallEpsilon.nb @@ -245,12 +245,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, 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WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{571, Automatic}, {Automatic, 89}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SmallVariables.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SmallVariables.nb index 695911658..1a6d2328b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SmallVariables.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SmallVariables.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoop", ButtonNote->"OneLoop"], "." -}], "Text", - CellTags->"SmallVariables", 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CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Sn.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Sn.nb index 46728056b..a1569607b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Sn.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Sn.nb @@ -256,12 +256,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Solve2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Solve2.nb index 8fa6805af..9f32c3689 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Solve2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Solve2.nb @@ -126,8 +126,25 @@ Solve." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Solve2", "]"}]], "Input", + CellTags->"Solve2", + CellLabel->"In[1]:=", + CellID->1980966786], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Factoring", "\[Rule]", "Factor2"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", + CellTags->"Solve2", + CellLabel->"Out[1]=", + CellID->549167872] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -192,26 +209,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Solve2", "]"}]], "Input", - CellTags->"Solve2", - CellLabel->"In[1]:=", - CellID->1980966786], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Factoring", "\[Rule]", "Factor2"}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", - CellTags->"Solve2", - CellLabel->"Out[1]=", - CellID->549167872] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"Solve2", "[", RowBox[{ @@ -226,7 +223,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellTags->"Solve2", - CellLabel->"In[2]:=", + CellLabel->"In[21]:=", CellID->1039333426], Cell[BoxData[ @@ -242,15 +239,12 @@ Cell[BoxData[ RowBox[{"y", "\[Rule]", RowBox[{"d", "+", "p"}]}]}], "}"}], TraditionalForm]], "Output", CellTags->"Solve2", - CellLabel->"Out[2]=", - CellID->1123970589] + CellLabel->"Out[21]="] }, Open ]], Cell["\<\ If no equation sign is given the polynomials are supposed to be 0.\ -\>", "Text", - CellTags->"Solve2", - CellID->599967125], +\>", "Notes"], Cell[CellGroupData[{ @@ -259,7 +253,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"x", "+", "y"}], ",", "x"}], "]"}]], "Input", CellTags->"Solve2", - CellLabel->"In[3]:=", + CellLabel->"In[22]:=", CellID->1138368341], Cell[BoxData[ @@ -268,8 +262,7 @@ Cell[BoxData[ RowBox[{"x", "\[Rule]", RowBox[{"-", "y"}]}], "}"}], TraditionalForm]], "Output", CellTags->"Solve2", - CellLabel->"Out[3]=", - CellID->1865369573] + CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ @@ -282,7 +275,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"y", "\[Rule]", "h"}], "}"}]}]}], "]"}]], "Input", CellTags->"Solve2", - CellLabel->"In[4]:=", + CellLabel->"In[23]:=", CellID->455409208], Cell[BoxData[ @@ -291,8 +284,7 @@ Cell[BoxData[ RowBox[{"x", "\[Rule]", RowBox[{"-", "h"}]}], "}"}], TraditionalForm]], "Output", CellTags->"Solve2", - CellLabel->"Out[4]=", - CellID->1227314769] + CellLabel->"Out[23]="] }, Open ]], Cell[CellGroupData[{ @@ -312,7 +304,7 @@ Cell[BoxData[ RowBox[{"x", ",", "y"}], "}"}], ",", RowBox[{"Factoring", "\[Rule]", "Expand"}]}], "]"}]], "Input", CellTags->"Solve2", - CellLabel->"In[5]:=", + CellLabel->"In[24]:=", CellID->881839558], Cell[BoxData[ @@ -326,8 +318,7 @@ Cell[BoxData[ RowBox[{"y", "\[Rule]", RowBox[{"d", "+", "p"}]}]}], "}"}], TraditionalForm]], "Output", CellTags->"Solve2", - CellLabel->"Out[5]=", - CellID->950466968] + CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ @@ -346,7 +337,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellTags->"Solve2", - CellLabel->"In[6]:=", + CellLabel->"In[25]:=", CellID->564833870], Cell[BoxData[ @@ -363,8 +354,7 @@ Cell[BoxData[ RowBox[{"y", "\[Rule]", RowBox[{"d", "+", "p"}]}]}], "}"}], "}"}], TraditionalForm]], "Output", CellTags->"Solve2", - CellLabel->"Out[6]=", - CellID->1055420746] + CellLabel->"Out[25]="] }, Open ]] }, Open ]], @@ -429,12 +419,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{720, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Solve3.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Solve3.nb index 34c07bdf1..75052a2b8 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Solve3.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Solve3.nb @@ -124,8 +124,27 @@ better than Solve for systems involving rational polyonomials." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Solve3", "]"}]], "Input", + CellTags->"Solve3", + CellLabel->"In[26]:=", + CellID->1333669928], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"Factoring", "\[Rule]", "False"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"ParallelMap", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"Solve3", + CellLabel->"Out[26]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -190,28 +209,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Solve3", "]"}]], "Input", - CellTags->"Solve3", - CellLabel->"In[1]:=", - CellID->1333669928], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Factoring", "\[Rule]", "False"}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"ParallelMap", "\[Rule]", "False"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"Solve3", - CellLabel->"Out[1]=", - CellID->1579913582] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"Solve3", "[", RowBox[{ @@ -226,7 +223,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], "]"}]], "Input", CellTags->"Solve3", - CellLabel->"In[2]:=", + CellLabel->"In[27]:=", CellID->1175774569], Cell[BoxData[ @@ -242,8 +239,7 @@ Cell[BoxData[ RowBox[{"y", "\[Rule]", RowBox[{"d", "+", "p"}]}]}], "}"}], TraditionalForm]], "Output", CellTags->"Solve3", - CellLabel->"Out[2]=", - CellID->158619342] + CellLabel->"Out[27]="] }, Open ]] }, Open ]], @@ -308,12 +304,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{889, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinPolarizationSum.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinPolarizationSum.nb deleted file mode 100644 index 6dea90dc6..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinPolarizationSum.nb +++ /dev/null @@ -1,264 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/SpinPolarizationSum", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - 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The set (pure) function acts on the usual \ -spin sum." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - ButtonBox["FermionSpinSum", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/FermionSpinSum", - ButtonNote->"FermionSpinSum"], - "." -}], "Text", - CellTags->"SpinPolarizationSum", - CellID->2085782463] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Spinor.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Spinor.nb index 6bda659ac..faf0a6c3f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Spinor.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Spinor.nb @@ -119,8 +119,12 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"Spinor", "[", RowBox[{"p", ",", " ", "m", ",", " ", "o"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the head of Dirac spinors. Which of the spinors ", + " \[LineSeparator]is the head of Dirac spinors. " +}], "Usage", + CellID->982511436], + +Cell[TextData[{ + "Which of the spinors ", StyleBox["u", FontSlant->"Italic"], ", ", @@ -130,21 +134,47 @@ Cell[TextData[{ Cell[BoxData[ FormBox[ OverscriptBox["u", "_"], TraditionalForm]]], - " ", - Cell[BoxData[ - FormBox[ - RowBox[{",", " "}], TraditionalForm]]], - "or ", + " or ", Cell[BoxData[ FormBox[ OverscriptBox["v", RowBox[{"_", " "}]], TraditionalForm]]], "is understood, depends on the sign of the momentum (p) argument and the \ -relative position of DiracSlash[p]: Spinor[sign p, mass] is that spinor which \ -yields: sign*mass*Spinor[p, mass] if the Dirac equation is applied (by \ -DiracEquation or DiracSimplify).\nThe optional argument o can be used for \ -additional degrees of freedom. If no optional argument o is supplied, a 1 is \ -subsituted in.\nSpinors of fermions of mass ", +relative position in the chain." +}], "Notes"], + +Cell[TextData[{ + "Spinor[Momentum[p],m] means \.7f", + Cell[BoxData[ + FormBox[ + OverscriptBox["u", "_"], TraditionalForm]]], + " if it stands at the beginning of the chain." +}], "Notes"], + +Cell[TextData[{ + "Spinor[Momentum[p],m] means \.7f", + Cell[BoxData[ + FormBox["u", TraditionalForm]]], + " if it stands at the end of the chain." +}], "Notes"], + +Cell[TextData[{ + "Spinor[-Momentum[p],m] means \.7f", + Cell[BoxData[ + FormBox[ + OverscriptBox["v", "_"], TraditionalForm]]], + " if it stands at the beginning of the chain." +}], "Notes"], + +Cell[TextData[{ + "Spinor[-Momentum[p],m] means \.7f", + Cell[BoxData[ + FormBox["v", TraditionalForm]]], + " if it stands at the end of the chain." +}], "Notes"], + +Cell[TextData[{ + "Spinors of fermions of mass ", StyleBox["m", FontSlant->"Italic"], " are normalized to have square ", @@ -167,11 +197,13 @@ subsituted in.\nSpinors of fermions of mass ", StyleBox["m", FontSlant->"Italic"], "." -}], "Usage", - CellID->982511436], +}], "Notes", + CellID->1067943069], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell["\<\ +The optional argument o can be used for additional degrees of freedom. If no \ +optional argument o is supplied, a 1 is subsituted in.\ +\>", "Notes"] }, Open ]], Cell[CellGroupData[{ @@ -237,9 +269,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SpinorVBar", ButtonNote->"SpinorVBar"], "." -}], "Text", - CellTags->"Spinor", - CellID->659330762] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -271,7 +301,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Spinor", "[", "p", "]"}]], "Input", CellTags->"Spinor", - CellLabel->"In[1]:=", + CellLabel->"In[28]:=", CellID->1573141935], Cell[BoxData[ @@ -289,8 +319,7 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Spinor", - CellLabel->"Out[1]=", - CellID->50146827] + CellLabel->"Out[28]="] }, Open ]], Cell[CellGroupData[{ @@ -299,7 +328,7 @@ Cell[BoxData[ RowBox[{"Spinor", "[", RowBox[{"p", ",", "m"}], "]"}]], "Input", CellTags->"Spinor", - CellLabel->"In[2]:=", + CellLabel->"In[29]:=", CellID->67205944], Cell[BoxData[ @@ -321,16 +350,13 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Spinor", - CellLabel->"Out[2]=", - CellID->1920456025] + CellLabel->"Out[29]="] }, Open ]], Cell["\<\ FeynCalc uses covariant normalization (as opposed to e.g. the normalization \ used in Bjorken&Drell).\ -\>", "Text", - CellTags->"Spinor", - CellID->815063905], +\>", "Notes"], Cell[CellGroupData[{ @@ -342,15 +368,14 @@ Cell[BoxData[ RowBox[{"Spinor", "[", RowBox[{"p", ",", "m"}], "]"}]}], "//", "DiracSimplify"}]], "Input", CellTags->"Spinor", - CellLabel->"In[3]:=", + CellLabel->"In[30]:=", CellID->540190510], Cell[BoxData[ FormBox[ RowBox[{"2", " ", "m"}], TraditionalForm]], "Output", CellTags->"Spinor", - CellLabel->"Out[3]=", - CellID->18406301] + CellLabel->"Out[30]="] }, Open ]], Cell[CellGroupData[{ @@ -361,9 +386,9 @@ Cell[BoxData[ RowBox[{"Spinor", "[", RowBox[{ RowBox[{"-", "p"}], ",", "m"}], "]"}], ".", - RowBox[{"DiracSlash", "[", "p", "]"}]}], "]"}]], "Input", + RowBox[{"GS", "[", "p", "]"}]}], "]"}]], "Input", CellTags->"Spinor", - CellLabel->"In[4]:=", + CellLabel->"In[26]:=", CellID->654515033], Cell[BoxData[ @@ -389,8 +414,7 @@ Cell[BoxData[ FormBox["\<\")\"\>", TraditionalForm]}], ")"}]}], TraditionalForm]], "Output", CellTags->"Spinor", - CellLabel->"Out[4]=", - CellID->1309692921] + CellLabel->"Out[26]="] }, Open ]], Cell[CellGroupData[{ @@ -399,7 +423,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"Spinor", "[", "p", "]"}], "//", "StandardForm"}]], "Input", CellTags->"Spinor", - CellLabel->"In[5]:=", + CellLabel->"In[32]:=", CellID->864077691], Cell[BoxData[ @@ -407,17 +431,9 @@ Cell[BoxData[ RowBox[{ RowBox[{"Momentum", "[", "p", "]"}], ",", "0", ",", "1"}], "]"}]], "Output", CellTags->"Spinor", - CellLabel->"Out[5]//StandardForm=", - CellID->1424658698] + CellLabel->"Out[32]//StandardForm="] }, Open ]], -Cell["\<\ -By convention, ChangeDimension does not operate on momenta in Spinor's (but \ -on e.g. DiracSlash[Momentum[p]]). \ -\>", "Text", - CellTags->"Spinor", - 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" }], "Usage", CellID->982511436], @@ -181,10 +189,28 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/SpinorVBar", ButtonNote->"SpinorVBar"], + ", ", + ButtonBox["SpinorUBarD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorUBarD", + ButtonNote->"SpinorUBarD"], + ", ", + ButtonBox["SpinorUD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorUD", + ButtonNote->"SpinorUD"], + ", ", + ButtonBox["SpinorVD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorVD", + ButtonNote->"SpinorVD"], + ", ", + ButtonBox["SpinorVBarD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorVBarD", + ButtonNote->"SpinorVBarD"], "." -}], "Text", - CellTags->"SpinorU", - CellID->844883429] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -214,115 +240,108 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorU", "[", "p", "]"}]], "Input", + RowBox[{"SpinorU", "[", + RowBox[{"p", ",", "m"}], "]"}]], "Input", CellTags->"SpinorU", - CellLabel->"In[1]:=", + CellLabel->"In[41]:=", CellID->1066488732], Cell[BoxData[ FormBox[ - RowBox[{ - FormBox["\<\"u\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], + RowBox[{"u", "(", FormBox["p", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], TraditionalForm]], "Output", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SpinorU", - CellLabel->"Out[1]=", - CellID->1004842359] + CellLabel->"Out[41]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorU", "[", - RowBox[{"p", ",", "m"}], "]"}]], "Input", - CellTags->"SpinorU", - CellLabel->"In[2]:=", - CellID->1219506664], + RowBox[{ + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[42]:=", + CellID->2060242592], Cell[BoxData[ - FormBox[ + RowBox[{"Spinor", "[", RowBox[{ - FormBox["\<\"u\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox["p", - TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"SpinorU", - CellLabel->"Out[2]=", - CellID->1525867517] + RowBox[{"Momentum", "[", "p", "]"}], ",", "m", ",", "1"}], "]"}]], "Output", + CellLabel->"Out[42]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"SpinorU", "[", - RowBox[{"p", ",", "m"}], "]"}], "//", "StandardForm"}]], "Input", + RowBox[{"SpinorU", "[", "p", "]"}]], "Input", CellTags->"SpinorU", - CellLabel->"In[3]:=", - CellID->1318814434], + CellLabel->"In[43]:=", + CellID->1219506664], Cell[BoxData[ - RowBox[{"SpinorU", "[", - RowBox[{"p", ",", "m"}], "]"}]], "Output", + FormBox[ + RowBox[{"u", "(", + FormBox["p", + TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SpinorU", - CellLabel->"Out[3]//StandardForm=", - CellID->409865214] + CellLabel->"Out[43]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{ - RowBox[{"SpinorU", "[", - RowBox[{"p", ",", "m"}], "]"}], "//", "FCI"}], "//", - "StandardForm"}]], "Input", - CellTags->"SpinorU", - CellLabel->"In[4]:=", - CellID->403119311], + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[44]:=", + CellID->1046277707], Cell[BoxData[ RowBox[{"Spinor", "[", RowBox[{ - RowBox[{"Momentum", "[", "p", "]"}], ",", "m", ",", "1"}], "]"}]], "Output", - CellTags->"SpinorU", - CellLabel->"Out[4]//StandardForm=", - CellID->1261590967] + RowBox[{"Momentum", "[", "p", "]"}], ",", "0", ",", "1"}], "]"}]], "Output", + CellLabel->"Out[44]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"SpinorU", "[", - RowBox[{"p", ",", "m"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", - "StandardForm"}]], "Input", - CellTags->"SpinorU", - CellLabel->"In[5]:=", - CellID->1260012205], + RowBox[{"GS", "[", "p", "]"}], ".", + RowBox[{"SpinorU", "[", "p", "]"}]}]], "Input", + CellLabel->"In[45]:=", + CellID->19834725], Cell[BoxData[ - RowBox[{"Spinor", "[", + FormBox[ RowBox[{ - RowBox[{"Momentum", "[", "p", "]"}], ",", "m", ",", "1"}], "]"}]], "Output", - CellTags->"SpinorU", - CellLabel->"Out[5]//StandardForm=", - CellID->220809349] + RowBox[{"(", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", + RowBox[{"u", "(", + FormBox["p", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[45]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracEquation", "[", "%", "]"}]], "Input", + CellLabel->"In[46]:=", + CellID->1275256319], + +Cell[BoxData[ + FormBox["0", TraditionalForm]], "Output", + CellLabel->"Out[46]="] }, Open ]] }, Open ]], @@ -387,12 +406,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{255, Automatic}, {68, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorUBar.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorUBar.nb index 10bfcb7f3..92a15fdfd 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorUBar.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorUBar.nb @@ -119,12 +119,17 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"SpinorUBar", "[", RowBox[{"p", ",", " ", "m"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "denotes a ", + " \[LineSeparator]denotes a ", Cell[BoxData[ FormBox[ - OverscriptBox["u", "_"], TraditionalForm]]], - "-spinor." + RowBox[{ + OverscriptBox["u", "_"], "(", + RowBox[{"p", ",", "m"}], ")"}], TraditionalForm]], "InlineFormula"], + "-spinor that depends on the ", + Cell[BoxData["4"], "InlineFormula"], + "-dimensional momentum ", + Cell[BoxData["p"], "InlineFormula"], + "." }], "Usage", CellID->982511436], @@ -184,10 +189,28 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/SpinorVBar", ButtonNote->"SpinorVBar"], + ", ", + ButtonBox["SpinorUBarD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorUBarD", + ButtonNote->"SpinorUBarD"], + ", ", + ButtonBox["SpinorUD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorUD", + ButtonNote->"SpinorUD"], + ", ", + ButtonBox["SpinorVD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorVD", + ButtonNote->"SpinorVD"], + ", ", + ButtonBox["SpinorVBarD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorVBarD", + ButtonNote->"SpinorVBarD"], "." -}], "Text", - CellTags->"SpinorUBar", - CellID->350873739] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -214,110 +237,114 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["One argument only assumes a massless spinor.", "Text", - CellTags->"SpinorUBar", - CellID->1710109400], - Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorUBar", "[", "p", "]"}]], "Input", - CellTags->"SpinorUBar", - CellLabel->"In[1]:=", - CellID->1755344465], + RowBox[{"SpinorUBar", "[", + RowBox[{"p", ",", "m"}], "]"}]], "Input", + CellTags->"SpinorU", + CellLabel->"In[68]:=", + CellID->1066488732], Cell[BoxData[ FormBox[ RowBox[{ OverscriptBox["u", "_"], "(", FormBox["p", + TraditionalForm], ",", + FormBox["m", TraditionalForm], ")"}], TraditionalForm]], "Output", - CellTags->"SpinorUBar", - CellLabel->"Out[1]=", - CellID->1842146552] + CellTags->"SpinorU", + CellLabel->"Out[68]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorUBar", "[", - RowBox[{"p", ",", "m"}], "]"}]], "Input", - CellTags->"SpinorUBar", - CellLabel->"In[2]:=", - CellID->427410867], + RowBox[{ + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[69]:=", + CellID->2060242592], + +Cell[BoxData[ + RowBox[{"Spinor", "[", + RowBox[{ + RowBox[{"Momentum", "[", "p", "]"}], ",", "m", ",", "1"}], "]"}]], "Output", + CellLabel->"Out[69]//StandardForm="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SpinorUBar", "[", "p", "]"}]], "Input", + CellTags->"SpinorU", + CellLabel->"In[70]:=", + CellID->1219506664], Cell[BoxData[ FormBox[ RowBox[{ OverscriptBox["u", "_"], "(", FormBox["p", - TraditionalForm], ",", - FormBox["m", TraditionalForm], ")"}], TraditionalForm]], "Output", - CellTags->"SpinorUBar", - CellLabel->"Out[2]=", - CellID->1886464450] + CellTags->"SpinorU", + CellLabel->"Out[70]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"SpinorUBar", "[", - 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CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["SpinorUD", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"SpinorUD", "[", + RowBox[{"p", ",", "m"}], "]"}]], "InlineFormula"], + " \[LineSeparator]denotes a ", + Cell[BoxData[ + FormBox[ + RowBox[{"u", + RowBox[{"(", + RowBox[{"p", ",", "m"}], ")"}]}], TraditionalForm]], "InlineFormula"], + "-spinor that depends on the ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional momentum ", + Cell[BoxData["p"], "InlineFormula"], + ". 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Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SpinorUD", "[", + RowBox[{"p", ",", "m"}], "]"}]], "Input", + CellTags->"SpinorU", + CellLabel->"In[33]:=", + CellID->1066488732], + +Cell[BoxData[ + FormBox[ + RowBox[{"u", "(", + FormBox["p", + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellTags->"SpinorU", + CellLabel->"Out[33]=", + CellID->658020456] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[34]:=", + CellID->2060242592], + +Cell[BoxData[ + RowBox[{"Spinor", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "m", ",", "1"}], "]"}]], "Output", + CellLabel->"Out[34]//StandardForm=", + CellID->1063623654] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SpinorUD", "[", "p", "]"}]], "Input", + CellTags->"SpinorU", + CellLabel->"In[35]:=", + CellID->1219506664], + +Cell[BoxData[ + FormBox[ + RowBox[{"u", "(", + FormBox["p", + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellTags->"SpinorU", + CellLabel->"Out[35]=", + CellID->882792700] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[36]:=", + CellID->1046277707], + +Cell[BoxData[ + RowBox[{"Spinor", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", "1"}], "]"}]], "Output", + CellLabel->"Out[36]//StandardForm=", + CellID->1065078839] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{"GSD", "[", "p", "]"}], ".", + RowBox[{"SpinorUD", "[", "p", "]"}]}]], "Input", + CellLabel->"In[39]:=", + CellID->19834725], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"(", + FormBox[ + RowBox[{"\[Gamma]", "\[CenterDot]", + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm]}], + TraditionalForm], ")"}], ".", + FormBox[ + RowBox[{"u", "(", + FormBox["p", + TraditionalForm], ")"}], + TraditionalForm]}], TraditionalForm]], "Output", + CellLabel->"Out[39]=", + CellID->100090183] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracEquation", "[", "%", "]"}]], "Input", + CellLabel->"In[40]:=", + CellID->1275256319], + +Cell[BoxData[ + FormBox["0", TraditionalForm]], "Output", + CellLabel->"Out[40]=", + CellID->633382777] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{350, Automatic}, {-10, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorV.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorV.nb index a917a1525..62c1a131b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorV.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorV.nb @@ -118,10 +118,17 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"SpinorV", "[", - RowBox[{"p", ",", " ", "m", ",", " ", "optarg"}], "]"}]], - "InlineFormula"], - " \[LineSeparator]", - "denotes a v-spinor." + RowBox[{"p", ",", " ", "m"}], "]"}]], "InlineFormula"], + " \[LineSeparator]denotes a ", + Cell[BoxData[ + RowBox[{"v", + RowBox[{"(", + RowBox[{"p", ",", "m"}], ")"}]}]], "InlineFormula"], + "-spinor that depends on the ", + Cell[BoxData["4"], "InlineFormula"], + "-dimensional momentum ", + Cell[BoxData["p"], "InlineFormula"], + ". " }], "Usage", CellID->982511436], @@ -181,10 +188,29 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/SpinorVBar", ButtonNote->"SpinorVBar"], + ", ", + ButtonBox["SpinorUBarD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorUBarD", + ButtonNote->"SpinorUBarD"], + ", ", + ButtonBox["SpinorUD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorUD", + ButtonNote->"SpinorUD"], + ", ", + ButtonBox["SpinorVD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorVD", + ButtonNote->"SpinorVD"], + ", ", + ButtonBox["SpinorVBarD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorVBarD", + ButtonNote->"SpinorVBarD"], "." -}], "Text", - CellTags->"SpinorV", - CellID->1898482478] +}], "SeeAlso", + CellID->694651819] }, Open ]], Cell[CellGroupData[{ @@ -214,119 +240,112 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorV", "[", "p", "]"}]], "Input", - CellTags->"SpinorV", - CellLabel->"In[1]:=", - CellID->1210511040], + RowBox[{"SpinorV", "[", + RowBox[{"p", ",", "m"}], "]"}]], "Input", + CellTags->"SpinorU", + CellLabel->"In[60]:=", + CellID->1066488732], Cell[BoxData[ FormBox[ - RowBox[{ - FormBox["\<\"v\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], + RowBox[{"v", "(", FormBox["p", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"SpinorV", - CellLabel->"Out[1]=", - CellID->663666949] + TraditionalForm], ",", + FormBox["m", + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellTags->"SpinorU", + CellLabel->"Out[60]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorV", "[", - RowBox[{"p", ",", "m"}], "]"}]], "Input", - CellTags->"SpinorV", - CellLabel->"In[2]:=", - CellID->495899740], + RowBox[{ + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[61]:=", + CellID->2060242592], Cell[BoxData[ - FormBox[ + RowBox[{"Spinor", "[", RowBox[{ - FormBox["\<\"v\"\>", - TraditionalForm], - FormBox["\<\"(\"\>", - TraditionalForm], - FormBox["p", - TraditionalForm], - FormBox["\<\",\"\>", - TraditionalForm], - FormBox["m", - TraditionalForm], - FormBox["\<\")\"\>", - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"SpinorV", - CellLabel->"Out[2]=", - CellID->526244319] + RowBox[{"-", + RowBox[{"Momentum", "[", "p", "]"}]}], ",", "m", ",", "1"}], + "]"}]], "Output", + CellLabel->"Out[61]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"SpinorV", "[", - RowBox[{"p", ",", "m"}], "]"}], "//", "StandardForm"}]], "Input", - CellTags->"SpinorV", - CellLabel->"In[3]:=", - CellID->54240099], + RowBox[{"SpinorV", "[", "p", "]"}]], "Input", + CellTags->"SpinorU", + CellLabel->"In[62]:=", + CellID->1219506664], Cell[BoxData[ - RowBox[{"SpinorV", "[", - RowBox[{"p", ",", "m"}], "]"}]], "Output", - CellTags->"SpinorV", - CellLabel->"Out[3]//StandardForm=", - CellID->1454860616] + FormBox[ + RowBox[{"v", "(", + FormBox["p", + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellTags->"SpinorU", + CellLabel->"Out[62]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{ - RowBox[{"SpinorV", "[", - RowBox[{"p", ",", "m"}], "]"}], "//", "FCI"}], "//", - "StandardForm"}]], "Input", - CellTags->"SpinorV", - CellLabel->"In[4]:=", - CellID->719384042], + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[63]:=", + CellID->1046277707], Cell[BoxData[ RowBox[{"Spinor", "[", RowBox[{ RowBox[{"-", - RowBox[{"Momentum", "[", "p", "]"}]}], ",", "m", ",", "1"}], + RowBox[{"Momentum", "[", "p", "]"}]}], ",", "0", ",", "1"}], "]"}]], "Output", - CellTags->"SpinorV", - CellLabel->"Out[4]//StandardForm=", - CellID->1229887592] + CellLabel->"Out[63]//StandardForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{ - RowBox[{ - RowBox[{"SpinorV", "[", - RowBox[{"p", ",", "m"}], "]"}], "//", "FCI"}], "//", "FCE"}], "//", - "StandardForm"}]], "Input", - CellTags->"SpinorV", - CellLabel->"In[5]:=", - CellID->943725638], + RowBox[{"GS", "[", "p", "]"}], ".", + RowBox[{"SpinorV", "[", "p", "]"}]}]], "Input", + CellLabel->"In[66]:=", + CellID->19834725], Cell[BoxData[ - RowBox[{"Spinor", "[", + FormBox[ RowBox[{ - RowBox[{"-", - RowBox[{"Momentum", "[", "p", "]"}]}], ",", "m", ",", "1"}], - "]"}]], "Output", - CellTags->"SpinorV", - CellLabel->"Out[5]//StandardForm=", - CellID->1429391488] + RowBox[{"(", + FormBox[ + RowBox[{ + OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm]}], + TraditionalForm], ")"}], ".", + RowBox[{"v", "(", + FormBox["p", + TraditionalForm], ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[66]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracEquation", "[", "%", "]"}]], "Input", + CellLabel->"In[67]:=", + CellID->1275256319], + +Cell[BoxData[ + FormBox["0", TraditionalForm]], "Output", + CellLabel->"Out[67]="] }, Open ]] }, Open ]], @@ -391,12 +410,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{152, Automatic}, {-10, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorVBar.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorVBar.nb index 413ebff5b..f27546136 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorVBar.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SpinorVBar.nb @@ -119,12 +119,17 @@ Cell[TextData[{ Cell[BoxData[ RowBox[{"SpinorVBar", "[", RowBox[{"p", ",", " ", "m"}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "denotes a ", + " \[LineSeparator]denotes a ", Cell[BoxData[ FormBox[ - OverscriptBox["v", "_"], TraditionalForm]]], - "(p,m)-spinor." + RowBox[{ + OverscriptBox["v", "_"], "(", + RowBox[{"p", ",", "m"}], ")"}], TraditionalForm]], "InlineFormula"], + "-spinor that depends on the ", + Cell[BoxData["4"], "InlineFormula"], + "-dimensional momentum ", + Cell[BoxData["p"], "InlineFormula"], + ". " }], "Usage", CellID->982511436], @@ -170,6 +175,11 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Spinor", ButtonNote->"Spinor"], ", ", + ButtonBox["SpinorUBar", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorUBar", + ButtonNote->"SpinorUBar"], + ", ", ButtonBox["SpinorU", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/SpinorU", @@ -180,14 +190,28 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SpinorV", ButtonNote->"SpinorV"], ", ", - ButtonBox["SpinorUBar", + ButtonBox["SpinorUBarD", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/SpinorUBar", - ButtonNote->"SpinorUBar"], + ButtonData:>"paclet:FeynCalc/ref/SpinorUBarD", + ButtonNote->"SpinorUBarD"], + ", ", + ButtonBox["SpinorUD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorUD", + ButtonNote->"SpinorUD"], + ", ", + ButtonBox["SpinorVD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorVD", + ButtonNote->"SpinorVD"], + ", ", + ButtonBox["SpinorVBarD", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/SpinorVBarD", + ButtonNote->"SpinorVBarD"], "." -}], "Text", - CellTags->"SpinorVBar", - CellID->1366275510] +}], "SeeAlso", + CellID->780468192] }, Open ]], Cell[CellGroupData[{ @@ -217,107 +241,115 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorVBar", "[", "p", "]"}]], "Input", - CellTags->"SpinorVBar", - CellLabel->"In[1]:=", - CellID->646348691], + RowBox[{"SpinorVBar", "[", + RowBox[{"p", ",", "m"}], "]"}]], "Input", + CellTags->"SpinorU", + CellLabel->"In[86]:=", + CellID->1066488732], Cell[BoxData[ FormBox[ RowBox[{ OverscriptBox["v", "_"], "(", FormBox["p", + TraditionalForm], ",", + FormBox["m", TraditionalForm], ")"}], TraditionalForm]], "Output", - CellTags->"SpinorVBar", - CellLabel->"Out[1]=", - CellID->1882446348] + CellTags->"SpinorU", + CellLabel->"Out[86]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"SpinorVBar", "[", - RowBox[{"p", ",", "m"}], "]"}]], "Input", - CellTags->"SpinorVBar", - CellLabel->"In[2]:=", - CellID->528224322], + RowBox[{ + RowBox[{"FCI", "[", "%", "]"}], "//", "StandardForm"}]], "Input", + CellLabel->"In[87]:=", + CellID->2060242592], Cell[BoxData[ - 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+ +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{1102, 858}, +WindowMargins->{{1197, Automatic}, {194, Automatic}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/StandardMatrixElement.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/StandardMatrixElement.nb index 316c6956b..5d946bd20 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/StandardMatrixElement.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/StandardMatrixElement.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoop", ButtonNote->"OneLoop"], "." -}], "Text", - CellTags->"StandardMatrixElement", - CellID->844790882] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/StandardPropagatorDenominator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/StandardPropagatorDenominator.nb new file mode 100644 index 000000000..1994cde76 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/StandardPropagatorDenominator.nb @@ -0,0 +1,343 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/StandardPropagatorDenominator", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["StandardPropagatorDenominator", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{ + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"q1", ",", "D"}], "]"}], "+"}], "..."}], ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"q1", ",", "D"}], "]"}], ",", + RowBox[{ + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p1", ",", "D"}], "]"}], "+"}], "..."}], ",", + RowBox[{"m", "^", "2"}], ",", + RowBox[{"{", + RowBox[{"n", ",", "s"}], "}"}]}], "]"}]}]}]], "InlineFormula"], + " \[LineSeparator]encodes a generic Lorentzian propagator denominator \ +1/[(q1+...)^2 + q1.p1 + ... + m^2 + s*I eta]^n. This allows to accomodate for \ +standard propagators of the type 1/(p^2-m^2) but also for propagators \ +encountered in manifestly Lorentz covariant effective field theories such as \ +HQET or SCET. StandardPropagatorDenominator is an internal object. To enter \ +such propagators in FeynCalc you should use SFAD." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", "0", ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[1]:=", + CellID->127407996], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",SuperscriptBox[ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], 2],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[1]=", + CellID->1047178842] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"FeynAmpDenominator", "[", + RowBox[{"StandardPropagatorDenominator", "[", + RowBox[{"0", ",", + RowBox[{"Pair", "[", + RowBox[{ + RowBox[{"Momentum", "[", + RowBox[{"p", ",", "D"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"q", ",", "D"}], "]"}]}], "]"}], ",", + RowBox[{"-", + RowBox[{"m", "^", "2"}]}], ",", + RowBox[{"{", + RowBox[{"1", ",", "1"}], "}"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[2]:=", + CellID->1886042593], + +Cell[BoxData[ + FormBox[ + FractionBox["1", + TemplateBox[{"\"(\"",RowBox[{ + FormBox[ + FormBox["p", TraditionalForm], TraditionalForm], + FormBox["\"\[CenterDot]\"", TraditionalForm], + FormBox[ + FormBox["q", TraditionalForm], TraditionalForm]}],RowBox[{"-", + SuperscriptBox["m", "2"]}],"\"+\"", + RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""}, + "RowDefault"]], TraditionalForm]], "Output", + CellLabel->"Out[2]=", + CellID->492218860] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1595, Automatic}, {Automatic, 231}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/StringChomp.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/StringChomp.nb new file mode 100644 index 000000000..a7dcff36c --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/StringChomp.nb @@ -0,0 +1,286 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/StringChomp", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["StringChomp", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"StringChomp", "[", "str", "]"}]], "InlineFormula"], + " \[LineSeparator] chops initial and final white space of the string ", + Cell[BoxData["str"], "InlineFormula"], + "." +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"StringChomp", "[", "\"\< abc \>\"", "]"}]], "Input", + CellLabel->"In[147]:=", + CellID->296966363], + +Cell[BoxData[ + FormBox["\<\"abc\"\>", TraditionalForm]], "Output", + CellLabel->"Out[147]=", + CellID->1659907677] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"%", "//", "InputForm"}]], "Input", + CellLabel->"In[148]:=", + CellID->1353126443], + +Cell["\"abc\"", "Output", + CellLabel->"Out[148]//InputForm=", + CellID->1988507982] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1184, Automatic}, {Automatic, 227}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SubLoop.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SubLoop.nb index bc41a1245..6bcd4692a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SubLoop.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SubLoop.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OPE1Loop", ButtonNote->"OPE1Loop"], "." -}], "Text", - CellTags->"SubLoop", - CellID->1624471809] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{866, Automatic}, {Automatic, 88}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SumP.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SumP.nb index 4f75168b5..49ecbf882 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SumP.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SumP.nb @@ -199,9 +199,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SumT", ButtonNote->"SumT"], "." -}], "Text", - CellTags->"SumP", - CellID->1699670739] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -246,8 +244,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], "\[NoBreak]", ")"}], TraditionalForm]], "Output", CellTags->"SumP", - CellLabel->"Out[1]=", - CellID->850869174] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -268,8 +265,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], "\[NoBreak]", ")"}], TraditionalForm]], "Output", CellTags->"SumP", - CellLabel->"Out[2]=", - CellID->1599542692] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -288,8 +284,7 @@ Cell[BoxData[ FormBox["m", TraditionalForm], "\[NoBreak]", ")"}], TraditionalForm]], "Output", CellTags->"SumP", - CellLabel->"Out[3]=", - CellID->440466816] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -305,8 +300,7 @@ Cell[BoxData[ FormBox[ FractionBox["25", "12"], TraditionalForm]], "Output", CellTags->"SumP", - CellLabel->"Out[4]=", - CellID->1429863848] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -330,8 +324,7 @@ Cell[BoxData[ FormBox[ FractionBox["25", "12"], TraditionalForm]], "Output", CellTags->"SumP", - CellLabel->"Out[5]=", - CellID->1088247533] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -375,8 +368,7 @@ Cell[BoxData[ FractionBox["n", "2"], TraditionalForm], ")"}]}]}], TraditionalForm]], "Output", CellTags->"SumP", - CellLabel->"Out[6]=", - CellID->703036669] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -392,8 +384,7 @@ Cell[BoxData[ FormBox[ FractionBox["25", "12"], TraditionalForm]], "Output", CellTags->"SumP", - CellLabel->"Out[7]=", - CellID->454708211] + CellLabel->"Out[7]="] }, Open ]] }, Open ]], @@ -458,12 +449,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SumS.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SumS.nb index 9295e11e9..71ae81077 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SumS.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SumS.nb @@ -178,8 +178,22 @@ Sum[Sign[r]^k/k^Abs[r] Sign[s]^j/j^Abs[s], {k, 1, n}, {j, 1, k}] etc." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "SumS", "]"}]], "Input", + CellTags->"SumS", + CellLabel->"In[8]:=", + CellID->2012785240], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Reduce", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output", + + CellTags->"SumS", + CellLabel->"Out[8]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -225,9 +239,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SumT", ButtonNote->"SumT"], "." -}], "Text", - CellTags->"SumS", - CellID->1388374666] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -256,30 +268,12 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "SumS", "]"}]], "Input", - CellTags->"SumS", - CellLabel->"In[1]:=", - CellID->2012785240], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Reduce", "\[Rule]", "False"}], "}"}], TraditionalForm]], "Output", - - CellTags->"SumS", - CellLabel->"Out[1]=", - CellID->35078957] -}, Open ]], - -Cell[CellGroupData[{ - Cell[BoxData[ RowBox[{"SumS", "[", RowBox[{"1", ",", RowBox[{"m", "-", "1"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[2]:=", + CellLabel->"In[1]:=", CellID->632054675], Cell[BoxData[ @@ -290,8 +284,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[2]=", - CellID->1556413384] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -301,7 +294,7 @@ Cell[BoxData[ RowBox[{"2", ",", RowBox[{"m", "-", "1"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[3]:=", + CellLabel->"In[2]:=", CellID->1183001998], Cell[BoxData[ @@ -312,8 +305,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[3]=", - CellID->1711872116] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -323,7 +315,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "1"}], ",", "m"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[4]:=", + CellLabel->"In[3]:=", CellID->601997566], Cell[BoxData[ @@ -334,8 +326,7 @@ Cell[BoxData[ FormBox["m", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[4]=", - CellID->1598419711] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -345,7 +336,7 @@ Cell[BoxData[ RowBox[{"1", ",", "m", ",", RowBox[{"Reduce", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[5]:=", + CellLabel->"In[4]:=", CellID->1985675154], Cell[BoxData[ @@ -358,8 +349,7 @@ Cell[BoxData[ TraditionalForm], ")"}], "+", FractionBox["1", "m"]}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[5]=", - CellID->1232098786] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -370,7 +360,7 @@ Cell[BoxData[ RowBox[{"m", "+", "2"}], ",", RowBox[{"Reduce", "\[Rule]", "True"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[6]:=", + CellLabel->"In[5]:=", CellID->723810100], Cell[BoxData[ @@ -386,8 +376,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"m", "+", "2"}], ")"}], "3"]]}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[6]=", - CellID->378956112] + CellLabel->"Out[5]="] }, Open ]], Cell[BoxData[ @@ -396,7 +385,7 @@ Cell[BoxData[ RowBox[{"SumS", ",", RowBox[{"Reduce", "\[Rule]", "True"}]}], "]"}], ";"}]], "Input", CellTags->"SumS", - CellLabel->"In[7]:=", + CellLabel->"In[6]:=", CellID->1121632488], Cell[CellGroupData[{ @@ -406,7 +395,7 @@ Cell[BoxData[ RowBox[{"3", ",", RowBox[{"m", "+", "2"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[8]:=", + CellLabel->"In[7]:=", CellID->663420944], Cell[BoxData[ @@ -428,8 +417,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"m", "+", "2"}], ")"}], "3"]]}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[8]=", - CellID->1687595925] + CellLabel->"Out[7]="] }, Open ]], Cell[BoxData[ @@ -438,7 +426,7 @@ Cell[BoxData[ RowBox[{"SumS", ",", RowBox[{"Reduce", "\[Rule]", "False"}]}], "]"}], ";"}]], "Input", CellTags->"SumS", - CellLabel->"In[9]:=", + CellLabel->"In[8]:=", CellID->1754340999], Cell[CellGroupData[{ @@ -447,15 +435,14 @@ Cell[BoxData[ RowBox[{"SumS", "[", RowBox[{"1", ",", "4"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[10]:=", + CellLabel->"In[9]:=", CellID->913193894], Cell[BoxData[ FormBox[ FractionBox["25", "12"], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[10]=", - CellID->205548473] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -466,15 +453,14 @@ Cell[BoxData[ RowBox[{"i", "=", "1"}], "4"], RowBox[{"1", "/", "i"}]}]], "Input", CellTags->"SumS", - CellLabel->"In[11]:=", + CellLabel->"In[10]:=", CellID->1966406647], Cell[BoxData[ FormBox[ FractionBox["25", "12"], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[11]=", - CellID->1412895147] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -484,7 +470,7 @@ Cell[BoxData[ RowBox[{"1", ",", "2", ",", RowBox[{"m", "-", "1"}]}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[12]:=", + CellLabel->"In[11]:=", CellID->1336627111], Cell[BoxData[ @@ -495,8 +481,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[12]=", - CellID->18182330] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -505,7 +490,7 @@ Cell[BoxData[ RowBox[{"SumS", "[", RowBox[{"1", ",", "1", ",", "1", ",", "11"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[13]:=", + CellLabel->"In[12]:=", CellID->796483207], Cell[BoxData[ @@ -513,8 +498,7 @@ Cell[BoxData[ FractionBox["31276937512951", "4260000729600"], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[13]=", - CellID->2038617627] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -524,7 +508,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"-", "1"}], ",", "4"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[14]:=", + CellLabel->"In[13]:=", CellID->324759887], Cell[BoxData[ @@ -532,8 +516,7 @@ Cell[BoxData[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[14]=", - CellID->549106078] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -542,7 +525,7 @@ Cell[BoxData[ RowBox[{"SumT", "[", RowBox[{"1", ",", "4"}], "]"}]], "Input", CellTags->"SumS", - CellLabel->"In[15]:=", + CellLabel->"In[14]:=", CellID->857412373], Cell[BoxData[ @@ -550,8 +533,7 @@ Cell[BoxData[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", CellTags->"SumS", - CellLabel->"Out[15]=", - CellID->1019405443] + CellLabel->"Out[14]="] }, Open ]] }, Open ]], @@ -616,12 +598,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{746, Automatic}, {Automatic, 155}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SumT.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SumT.nb index c562f7fcb..be17d4c51 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SumT.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SumT.nb @@ -183,9 +183,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SumS", ButtonNote->"SumS"], "." -}], "Text", - CellTags->"SumT", - CellID->183277524] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -231,8 +229,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[1]=", - CellID->405969020] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -254,8 +251,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[2]=", - CellID->7209567] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -275,8 +271,7 @@ Cell[BoxData[ FormBox["m", TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[3]=", - CellID->1837745290] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -303,8 +298,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "m"], "m"]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[4]=", - CellID->1964068780] + CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ @@ -321,8 +315,7 @@ Cell[BoxData[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[5]=", - CellID->627215383] + CellLabel->"Out[5]="] }, Open ]], Cell[CellGroupData[{ @@ -344,8 +337,7 @@ Cell[BoxData[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[6]=", - CellID->1602884528] + CellLabel->"Out[6]="] }, Open ]], Cell[CellGroupData[{ @@ -367,8 +359,7 @@ Cell[BoxData[ RowBox[{"m", "-", "1"}], TraditionalForm], ")"}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[7]=", - CellID->1069824481] + CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -387,8 +378,7 @@ Cell[BoxData[ "10512121660702378405316004964483761080879190528000000"]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[8]=", - CellID->1350292495] + CellLabel->"Out[8]="] }, Open ]], Cell[CellGroupData[{ @@ -405,8 +395,7 @@ Cell[BoxData[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[9]=", - CellID->1565575302] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -424,8 +413,7 @@ Cell[BoxData[ RowBox[{"-", FractionBox["7", "12"]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[10]=", - CellID->1734591901] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -455,8 +443,7 @@ Cell[BoxData[ "LerchPhi"]}], "-", RowBox[{"log", "(", "2", ")"}]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[11]=", - CellID->1972297222] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -474,8 +461,7 @@ Cell[BoxData[ FractionBox["57561743656913", "21300003648000"]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[12]=", - CellID->1330421141] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -495,8 +481,7 @@ Cell[BoxData[ "10512121660702378405316004964483761080879190528000000"]}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[13]=", - CellID->833938013] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -524,8 +509,7 @@ Cell[BoxData[ RowBox[{"-", FractionBox["155903", "216000"]}]}], "}"}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[14]=", - CellID->540691812] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ @@ -558,8 +542,7 @@ Cell[BoxData[ RowBox[{"-", FractionBox["155903", "216000"]}]}], "}"}], TraditionalForm]], "Output", CellTags->"SumT", - CellLabel->"Out[15]=", - CellID->1165392017] + CellLabel->"Out[15]="] }, Open ]] }, Open ]], @@ -624,12 +607,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{998, Automatic}, {Automatic, 96}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SymbolicSum2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SymbolicSum2.nb index 846a73811..426916e7d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SymbolicSum2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SymbolicSum2.nb @@ -247,12 +247,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/SymbolicSum3.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/SymbolicSum3.nb index 74c8d6b05..b4539fe79 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/SymbolicSum3.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/SymbolicSum3.nb @@ -247,12 +247,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TBox.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TBox.nb index 68135098d..76ba28948 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TBox.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TBox.nb @@ -249,12 +249,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, 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+ $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1569, Automatic}, {Automatic, 219}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TGA.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TGA.nb new file mode 100644 index 000000000..b40547174 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TGA.nb @@ -0,0 +1,315 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/TGA", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["TGA", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"TGA", "[", "]"}]], "InlineFormula"], + " \[LineSeparator] can be used as input for ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "0"]], "InlineFormula"], + " in 4 dimensions and is transformed into \ +DiracGamma[ExplicitLorentzIndex[0]] by FeynCalcInternal" +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"TGA", "[", "]"}]], "Input", + CellLabel->"In[214]:=", + CellID->119105896], + +Cell[BoxData[ + FormBox[ + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox[ + FormBox["0", + TraditionalForm], + TraditionalForm]], TraditionalForm]], "Output", + CellLabel->"Out[214]=", + CellID->89968456] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"TGA", "[", "]"}], "//", "FCI"}], "//", "StandardForm"}]], "Input", + + CellLabel->"In[215]:=", + CellID->1381819423], + +Cell[BoxData[ + RowBox[{"DiracGamma", "[", + RowBox[{"ExplicitLorentzIndex", "[", "0", "]"}], "]"}]], "Output", + CellLabel->"Out[215]//StandardForm=", + CellID->80537985] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{ + RowBox[{ + RowBox[{"TGA", "[", "]"}], ".", + RowBox[{"TGA", "[", "]"}]}], "//", "DiracSimplify"}]], "Input", + CellLabel->"In[216]:=", + CellID->858599894], + +Cell[BoxData[ + FormBox["1", TraditionalForm]], "Output", + CellLabel->"Out[216]=", + CellID->704259393] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1023, Automatic}, {Automatic, 260}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TID.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TID.nb index b4383834c..57c2a02bb 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TID.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TID.nb @@ -124,8 +124,50 @@ loop momentum q" }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "TID", "]"}]], "Input", + CellTags->"TID", + CellLabel->"In[26]:=", + CellID->1576573941], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"ApartFF", "\[Rule]", "True"}], ",", + RowBox[{"Check", "\[Rule]", "True"}], ",", + RowBox[{"Collecting", "\[Rule]", "True"}], ",", + RowBox[{"Contract", "\[Rule]", "True"}], ",", + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"DiracSimplify", "\[Rule]", "True"}], ",", + RowBox[{"DiracTrace", "\[Rule]", "True"}], ",", + RowBox[{"EpsEvaluate", "\[Rule]", "True"}], ",", + RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", + RowBox[{"FCLoopRemoveNegativePropagatorPowers", "\[Rule]", "True"}], ",", + + RowBox[{"FCLoopMixedToCartesianAndTemporal", "\[Rule]", "True"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"FeynAmpDenominatorSimplify", "\[Rule]", "True"}], ",", + RowBox[{"Factoring", "\[Rule]", + RowBox[{"{", + RowBox[{"Factor2", ",", "5000"}], "}"}]}], ",", + RowBox[{"FeynAmpDenominatorCombine", "\[Rule]", "True"}], ",", + RowBox[{"GenPaVe", "\[Rule]", "False"}], ",", + RowBox[{"Isolate", "\[Rule]", "False"}], ",", + RowBox[{"PaVeAutoOrder", "\[Rule]", "True"}], ",", + RowBox[{"PaVeAutoReduce", "\[Rule]", "True"}], ",", + RowBox[{"PauliTrick", "\[Rule]", "True"}], ",", + RowBox[{"ToPaVe", "\[Rule]", "False"}], ",", + RowBox[{"UsePaVeBasis", "\[Rule]", "False"}], ",", + RowBox[{"TimeConstrained", "\[Rule]", "3"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"TID", + CellLabel->"Out[26]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -171,9 +213,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/TIDL", ButtonNote->"TIDL"], "." -}], "Text", - CellTags->"TID", - CellID->930175642] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -202,44 +242,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "TID", "]"}]], "Input", - CellTags->"TID", - CellLabel->"In[12]:=", - CellID->1576573941], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"ChangeDimension", "\[Rule]", "D"}], ",", - RowBox[{"Collecting", "\[Rule]", "True"}], ",", - RowBox[{"Contract", "\[Rule]", "True"}], ",", - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"DimensionalReduction", "\[Rule]", "False"}], ",", - RowBox[{"DiracSimplify", "\[Rule]", "True"}], ",", - RowBox[{"DiracTrace", "\[Rule]", "True"}], ",", - RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", - RowBox[{"EpsEvaluate", "\[Rule]", "True"}], ",", - RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", - RowBox[{"FCVerbose", "\[Rule]", "False"}], 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Cell[BoxData[ - SubscriptBox["B", "0"]], "InlineFormula", - FormatType->"StandardForm"], + SubscriptBox["B", "0"]], "InlineFormula"], ", ", Cell[BoxData[ - SubscriptBox["C", "0"]], "InlineFormula", - FormatType->"StandardForm"], + SubscriptBox["C", "0"]], "InlineFormula"], ", ", Cell[BoxData[ - SubscriptBox["D", "0"]], "InlineFormula", - FormatType->"StandardForm"], + SubscriptBox["D", "0"]], "InlineFormula"], " etc. " }], "Notes", CellID->538152640], @@ -2505,9 +2503,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 684}, -WindowMargins->{{239, Automatic}, {Automatic, -8}}, +WindowMargins->{{683, Automatic}, {Automatic, 118}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TIDL.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TIDL.nb index 24d08a471..8d32539e9 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TIDL.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TIDL.nb @@ -161,9 +161,7 @@ Cell["See Also", "SeeAlsoSection", Cell[TextData[ButtonBox["TID", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/TID", - ButtonNote->"TID"]], "Text", - CellTags->"TIDL", - CellID->627317385] + ButtonNote->"TID"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -249,12 +247,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{803, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI.nb index d10102d54..660a20c49 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI.nb @@ -139,7 +139,28 @@ TLI[{a,b,c,d,e}, {al,be,ga,de,ep}]." CellID->982511436], Cell["XXXX", "Notes", - CellID->1067943069] + CellID->1067943069], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "TLI", "]"}]], "Input", + CellTags->"TLI", + CellLabel->"In[1]:=", + CellID->1958640232], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"EpsilonOrder", "\[Rule]", "0"}], ",", + RowBox[{"Momentum", "\[Rule]", + RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"TLI", + CellLabel->"Out[1]=", + CellID->1974374076] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -180,9 +201,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/TLI2FC", ButtonNote->"TLI2FC"], "." -}], "Text", - CellTags->"TLI", - CellID->1589173280] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -194,8 +213,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -211,28 +228,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "TLI", "]"}]], "Input", - CellTags->"TLI", - CellLabel->"In[1]:=", - CellID->1958640232], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"EpsilonOrder", "\[Rule]", "0"}], ",", - RowBox[{"Momentum", "\[Rule]", - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"TLI", - CellLabel->"Out[1]=", - CellID->1974374076] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -292,12 +287,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{804, Automatic}, {Automatic, 146}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI2.nb index 39af1fa80..f9466a4bb 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI2.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/TLI", ButtonNote->"TLI"], "." -}], "Text", - CellTags->"TLI2", - CellID->573712863] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{808, Automatic}, {Automatic, 171}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI2FC.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI2FC.nb index e50a04e28..d6b83762a 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI2FC.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLI2FC.nb @@ -123,8 +123,30 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "TLI2FC", "]"}]], "Input", + CellTags->"TLI2FC", + CellLabel->"In[5]:=", + CellID->972870614], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"Momentum", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}], "}"}]}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"TLI2FC", + CellLabel->"Out[5]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -164,15 +186,13 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/TLI", ButtonNote->"TLI"], - ". ", + ", ", ButtonBox["FC2TLI", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FC2TLI", ButtonNote->"FC2TLI"], "." -}], "Text", - CellTags->"TLI2FC", - CellID->708615958] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -184,8 +204,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -201,38 +219,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "TLI2FC", "]"}]], "Input", - CellTags->"TLI2FC", - CellLabel->"In[1]:=", - CellID->972870614], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "D"}], ",", - RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", - RowBox[{"Momentum", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"FCGV", "(", "\<\"q1\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"q2\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}], "}"}]}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"TLI2FC", - CellLabel->"Out[1]=", - CellID->1369959726] -}, Open ]], - -Cell[BoxData[""], "Input", - CellTags->"TLI2FC", - CellLabel->"In[2]:=", - CellID->1527451776] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -292,12 +278,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{704, Automatic}, {Automatic, 46}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLIFP.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLIFP.nb index 26ef21ae7..ff5c29c7b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLIFP.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLIFP.nb @@ -123,8 +123,33 @@ Cell[TextData[{ }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "TLIFP", "]"}]], "Input", + CellTags->"TLIFP", + CellLabel->"In[6]:=", + CellID->1039512168], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynmanParameterNames", "\[Rule]", + RowBox[{"{", + RowBox[{ + RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"t\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"u\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"s\"\>", ")"}], ",", + RowBox[{"FCGV", "(", "\<\"y\"\>", ")"}]}], "}"}]}], ",", + RowBox[{"GammaExpand", "\[Rule]", "True"}], ",", + RowBox[{"Momentum", "\[Rule]", + RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}], ",", + RowBox[{"Print", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", + CellTags->"TLIFP", + CellLabel->"Out[6]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -165,9 +190,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/TLI", ButtonNote->"TLI"], "." -}], "Text", - CellTags->"TLIFP", - CellID->1633359984] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -179,8 +202,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -196,41 +217,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "TLIFP", "]"}]], "Input", - CellTags->"TLIFP", - CellLabel->"In[1]:=", - CellID->1039512168], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"FeynmanParameterNames", "\[Rule]", - RowBox[{"{", - RowBox[{ - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"t\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"u\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"s\"\>", ")"}], ",", - RowBox[{"FCGV", "(", "\<\"y\"\>", ")"}]}], "}"}]}], ",", - RowBox[{"GammaExpand", "\[Rule]", "True"}], ",", - RowBox[{"Momentum", "\[Rule]", - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}], ",", - RowBox[{"Print", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", - CellTags->"TLIFP", - CellLabel->"Out[1]=", - CellID->266885943] -}, Open ]], - -Cell[BoxData[""], "Input", - CellTags->"TLIFP", - CellLabel->"In[2]:=", - CellID->12061026] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -290,12 +276,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{970, Automatic}, {Automatic, 90}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLIHYP.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLIHYP.nb index 875aaa1be..8efc5f90c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TLIHYP.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TLIHYP.nb @@ -124,8 +124,27 @@ possible." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "TLIHYP", "]"}]], "Input", + CellTags->"TLIHYP", + CellLabel->"In[1]:=", + CellID->1476708263], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"FeynmanParameterNames", "\[Rule]", + RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}]}], ",", + RowBox[{"Momentum", "\[Rule]", + RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"TLIHYP", + CellLabel->"Out[1]=", + CellID->1697792562] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -166,9 +185,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/TLI", ButtonNote->"TLI"], "." -}], "Text", - CellTags->"TLIHYP", - CellID->827493739] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -180,8 +197,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -197,29 +212,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "TLIHYP", "]"}]], "Input", - CellTags->"TLIHYP", - CellLabel->"In[1]:=", - CellID->1476708263], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"FeynmanParameterNames", "\[Rule]", - RowBox[{"FCGV", "(", "\<\"x\"\>", ")"}]}], ",", - RowBox[{"Momentum", "\[Rule]", - RowBox[{"FCGV", "(", "\<\"p\"\>", ")"}]}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"TLIHYP", - CellLabel->"Out[1]=", - CellID->1697792562] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -279,12 +271,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{805, Automatic}, {Automatic, 99}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TR.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TR.nb index 10e3b2fe1..8048d3a3f 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TR.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TR.nb @@ -118,25 +118,51 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"TR", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "calculates the Dirac trace of exp. Depending on the setting of the option \ -SUNTrace also a trace over SU(", + " \[LineSeparator]calculates the Dirac trace of exp. Depending on the \ +setting of the option SUNTrace also a trace over SU(", StyleBox["N", FontSlant->"Italic"], ") objects is performed. The ", StyleBox["Mathematica", FontSlant->"Italic"], - " build-in function Tr is overloaded to call TR if any of DiracGamma, \ -DiracSlash, GA, GAD, GS or GSD are in the expression.\nTr[list] finds the \ -trace of the matrix or tensor list. Tr[list, f] finds a generalized trace, \ -combining terms with f instead of Plus. Tr[list, f, n] goes down to level n \ -in list.\nTr[ expression ] calculates the DiracTrace, i.e., TR[ expression ] \ -if any of DiracGamma, DiracSlash, GA, GAD, GS or GSD is present in expression." + " build-in function Tr is overloaded to call TR if any of DiracGamma, GA, \ +GAD, GS or GSD are in the expression.\nTr[list] finds the trace of the matrix \ +or tensor list. Tr[list, f] finds a generalized trace, combining terms with f \ +instead of Plus. Tr[list, f, n] goes down to level n in list.\nTr[ expression \ +] calculates the DiracTrace, i.e., TR[ expression ] if any of DiracGamma, \ +GA, GAD, GS or GSD is present in expression." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "TR", "]"}]], "Input", + CellLabel->"In[14]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Contract", "\[Rule]", "True"}], ",", + RowBox[{"DiracTraceEvaluate", "\[Rule]", "True"}], ",", + RowBox[{"EpsContract", "\[Rule]", "True"}], ",", + RowBox[{"Explicit", "\[Rule]", "True"}], ",", + RowBox[{"Expand", "\[Rule]", "True"}], ",", + RowBox[{"Factoring", "\[Rule]", "Automatic"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "True"}], ",", + RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", + RowBox[{"Mandelstam", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"PairCollect", "\[Rule]", "False"}], ",", + RowBox[{"SUNNToCACF", "\[Rule]", "False"}], ",", + RowBox[{"SUNTrace", "\[Rule]", "False"}], ",", + RowBox[{"Schouten", "\[Rule]", "0"}], ",", + RowBox[{"TraceOfOne", "\[Rule]", "4"}], ",", + RowBox[{"West", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output", + + CellLabel->"Out[14]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -172,7 +198,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - 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" \[LineSeparator]", - "or Tdec[exp, {{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}] calculates the \ -tensorial decomposition formulas. The more common ones are saved in TIDL." + " \[LineSeparator]or Tdec[exp, {{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}] \ +calculates the tensorial decomposition formulas for Lorentzian integrals. 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CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ @@ -228,7 +225,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"TensorFunction", - CellLabel->"In[3]:=", + CellLabel->"In[8]:=", CellID->608128480], Cell[BoxData[ @@ -238,8 +235,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Tau]", "]"}]}], "]"}]], "Output", CellTags->"TensorFunction", - CellLabel->"Out[3]//StandardForm=", - CellID->2056952905] + CellLabel->"Out[8]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -250,7 +246,7 @@ Cell[BoxData[ RowBox[{"FV", "[", RowBox[{"p", ",", "\[Mu]"}], "]"}], " ", "%"}], "]"}]], "Input", CellTags->"TensorFunction", - CellLabel->"In[4]:=", + CellLabel->"In[9]:=", CellID->1580634540], Cell[BoxData[ @@ -265,8 +261,7 @@ Cell[BoxData[ FormBox["\[Tau]", TraditionalForm]}], ")"}], TraditionalForm]], "Output", CellTags->"TensorFunction", - CellLabel->"Out[4]=", - CellID->974516100] + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ @@ -274,7 +269,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"TensorFunction", - CellLabel->"In[5]:=", + CellLabel->"In[10]:=", CellID->1813534641], Cell[BoxData[ @@ -284,8 +279,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Nu]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Tau]", "]"}]}], "]"}]], "Output", CellTags->"TensorFunction", - CellLabel->"Out[5]//StandardForm=", - CellID->1570637008] + CellLabel->"Out[10]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -297,7 +291,7 @@ Cell[BoxData[ RowBox[{"f", ",", "\"\\""}], "}"}], ",", "\[Alpha]", ",", "\[Beta]"}], "]"}]], "Input", CellTags->"TensorFunction", - CellLabel->"In[6]:=", + CellLabel->"In[11]:=", CellID->1404961078], Cell[BoxData[ @@ -309,8 +303,7 @@ Cell[BoxData[ FormBox["\[Beta]", TraditionalForm]}], ")"}], TraditionalForm]], "Output", CellTags->"TensorFunction", - CellLabel->"Out[6]=", - CellID->1735854485] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -322,7 +315,7 @@ Cell[BoxData[ RowBox[{"f", ",", "\"\\""}], "}"}], ",", "\[Beta]", ",", "\[Alpha]"}], "]"}]], "Input", CellTags->"TensorFunction", - CellLabel->"In[7]:=", + CellLabel->"In[12]:=", CellID->65548372], Cell[BoxData[ @@ -334,8 +327,7 @@ Cell[BoxData[ FormBox["\[Beta]", TraditionalForm]}], ")"}], TraditionalForm]], "Output", CellTags->"TensorFunction", - CellLabel->"Out[7]=", - CellID->1376266618] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -343,7 +335,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"%", "//", "StandardForm"}]], "Input", CellTags->"TensorFunction", - CellLabel->"In[8]:=", + CellLabel->"In[13]:=", CellID->645212918], Cell[BoxData[ @@ -352,8 +344,7 @@ Cell[BoxData[ RowBox[{"LorentzIndex", "[", "\[Alpha]", "]"}], ",", RowBox[{"LorentzIndex", "[", "\[Beta]", "]"}]}], "]"}]], "Output", CellTags->"TensorFunction", - CellLabel->"Out[8]//StandardForm=", - CellID->1120370784] + 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Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{683, Automatic}, {Automatic, 238}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ThreeVector.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ThreeVector.nb deleted file mode 100644 index 88ab3fa0c..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ThreeVector.nb +++ /dev/null @@ -1,270 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/ThreeVector", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["ThreeVector", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData[ - RowBox[{"ThreeVector", "[", "p", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "is the three dimensional vector p." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - "See also: ", - ButtonBox["DotProduct", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/DotProduct", - ButtonNote->"DotProduct"], - ", ", - ButtonBox["CrossProduct", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/CrossProduct", - ButtonNote->"CrossProduct"], - "." -}], "Text", - CellTags->"ThreeVector", - CellID->930921791] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; 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Options of Integrate can be given and are passed on." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "TimedIntegrate", "]"}]], "Input", + CellTags->"TimedIntegrate", + CellLabel->"In[1]:=", + CellID->92169636], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Timing", "\[Rule]", "10"}], ",", + RowBox[{"Assumptions", "\[Rule]", + RowBox[{ + TagBox["\[CurlyEpsilon]", + TraditionalForm], ">", "0"}]}], ",", + RowBox[{"Integrate", "\[Rule]", "Integrate"}], ",", + RowBox[{"Expand", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"TimedIntegrate", + CellLabel->"Out[1]=", + CellID->1160941869] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -189,34 +211,7 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "TimedIntegrate", "]"}]], "Input", - 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CellID->430041707] + CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ @@ -333,9 +283,10 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}], "^", RowBox[{"(", - RowBox[{"Epsilon", "-", "2"}], ")"}]}], ",", "x"}], "]"}]], "Input", + RowBox[{"Epsilon", "-", "2"}], ")"}]}], ",", "x", ",", + RowBox[{"PlusDistribution", "\[Rule]", "Identity"}]}], "]"}]], "Input", CellTags->"ToDistribution", - CellLabel->"In[5]:=", + CellLabel->"In[11]:=", CellID->1034527004], Cell[BoxData[ @@ -388,8 +339,7 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"1", "-", "x"}], ")"}], "2"]]}], TraditionalForm]], "Output", CellTags->"ToDistribution", - CellLabel->"Out[5]=", - CellID->454332293] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -408,7 +358,7 @@ Cell[BoxData[ RowBox[{"GenerateConditions", "\[Rule]", "False"}]}], "]"}], ",", "Epsilon", ",", "3"}], "]"}]], "Input", CellTags->"ToDistribution", - CellLabel->"In[6]:=", + CellLabel->"In[12]:=", CellID->941654875], Cell[BoxData[ @@ -424,29 +374,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm], "-", "1"}], TraditionalForm]], "Output", CellTags->"ToDistribution", - CellLabel->"Out[6]=", - CellID->1061431105] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "@", "Integrate"}]], "Input", - CellTags->"ToDistribution", - CellLabel->"In[7]:=", - CellID->1737951035], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Assumptions", "\[RuleDelayed]", "$Assumptions"}], ",", - RowBox[{"GenerateConditions", "\[Rule]", "Automatic"}], ",", - RowBox[{"PrincipalValue", "\[Rule]", "False"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"ToDistribution", - CellLabel->"Out[7]=", - CellID->1658308803] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -464,7 +392,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input", CellTags->"ToDistribution", - CellLabel->"In[8]:=", + CellLabel->"In[14]:=", CellID->1539995997], Cell[BoxData[ @@ -480,8 +408,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm], "-", "1"}], TraditionalForm]], "Output", CellTags->"ToDistribution", - CellLabel->"Out[8]=", - CellID->2114127907] + CellLabel->"Out[14]="] }, Open ]] }, Open ]], @@ -546,12 +473,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{757, Automatic}, {Automatic, 101}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ToFI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ToFI.nb new file mode 100644 index 000000000..ab00b0204 --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ToFI.nb @@ -0,0 +1,261 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/ToFI", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + 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+ CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1313, Automatic}, {Automatic, 258}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ToHypergeometric.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ToHypergeometric.nb index 9ce340148..976cb0cd6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ToHypergeometric.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ToHypergeometric.nb @@ -195,9 +195,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/HypergeometricSE", ButtonNote->"HypergeometricSE"], "." -}], "Text", - CellTags->"ToHypergeometric", - CellID->811059910] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -257,8 +255,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"b", "+", "c", "+", "2"}]}, "Gamma"]], TraditionalForm]], "Output", CellTags->"ToHypergeometric", - CellLabel->"Out[1]=", - CellID->309474484] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -295,8 +292,7 @@ Cell[BoxData[ TemplateBox[{"c"}, "Gamma"]], TraditionalForm]], "Output", CellTags->"ToHypergeometric", - CellLabel->"Out[2]=", - CellID->730361964] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -334,8 +330,7 @@ Cell[BoxData[ TemplateBox[{RowBox[{"b", "+", "c", "+", "2"}]}, "Gamma"]], TraditionalForm]], "Output", CellTags->"ToHypergeometric", - CellLabel->"Out[3]=", - CellID->602855066] + CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ @@ -374,8 +369,7 @@ Cell[BoxData[ TemplateBox[{"c"}, "Gamma"]], TraditionalForm]], "Output", CellTags->"ToHypergeometric", - CellLabel->"Out[4]=", - CellID->1693879110] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -440,12 +434,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{694, Automatic}, {Automatic, 134}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ToLarin.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ToLarin.nb index b6cff8374..39bd8834c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ToLarin.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ToLarin.nb @@ -118,29 +118,40 @@ Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData[ RowBox[{"ToLarin", "[", "exp", "]"}]], "InlineFormula"], - " \[LineSeparator]", - "translates all ", + " \[LineSeparator] substitutes ", Cell[BoxData[ - FormBox[ - RowBox[{ - SuperscriptBox["\[Gamma]", "\[Mu]"], " ", - SuperscriptBox["\[Gamma]", "5"]}], TraditionalForm]]], - " in exp into ", + RowBox[{ + SuperscriptBox["\[Gamma]", "\[Mu]"], + SuperscriptBox["\[Gamma]", "5"]}]], "InlineFormula"], + " with ", Cell[BoxData[ - FormBox[ - RowBox[{ - RowBox[{ - RowBox[{"-", "\[ImaginaryI]"}], "/", "6"}], " ", - SuperscriptBox["\[CurlyEpsilon]", "\[Mu]\[Nu]\[Lambda]\[Sigma]"], - SuperscriptBox["\[Gamma]", "\[Nu]"], " ", - SuperscriptBox["\[Gamma]", "\[Lambda]"], " ", - RowBox[{ - SuperscriptBox["\[Gamma]", "\[Sigma]"], "."}]}], TraditionalForm]]] + RowBox[{ + RowBox[{"-", + FractionBox["I", "6"]}], + SuperscriptBox["\[Epsilon]", + RowBox[{"\[Mu]", " ", "\[Nu]", " ", "\[Lambda]", " ", "\[Sigma]"}]], + SuperscriptBox["\[Gamma]", "\[Nu]"], + SuperscriptBox["\[Gamma]", "\[Lambda]"], + SuperscriptBox["\[Gamma]", "\[Sigma]"]}]], "InlineFormula"], + "." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "ToLarin", "]"}]], "Input", + CellLabel->"In[60]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "D"}], ",", + RowBox[{"FeynCalcInternal", "\[Rule]", "False"}]}], "}"}], + TraditionalForm]], "Output", + CellLabel->"Out[60]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -180,10 +191,13 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Eps", ButtonNote->"Eps"], - "." -}], "Text", - CellTags->"ToLarin", - CellID->2133763221] + ", ", + ButtonBox["DiracGamma", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracGamma", + ButtonNote->"DiracGamma"] +}], "SeeAlso", + CellID->655647701] }, Open ]], Cell[CellGroupData[{ @@ -214,67 +228,92 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ - RowBox[{"DiracMatrix", "[", "\[Nu]", "]"}], ".", - RowBox[{"DiracMatrix", "[", "\[Mu]", "]"}], ".", - RowBox[{"DiracMatrix", "[", "5", "]"}]}]], "Input", + RowBox[{"GAD", "[", + RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], ".", + RowBox[{"GA", "[", "5", "]"}]}]], "Input", CellTags->"ToLarin", - CellLabel->"In[1]:=", + CellLabel->"In[58]:=", CellID->975355057], Cell[BoxData[ FormBox[ RowBox[{ - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Mu]", - 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SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["du28", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["du29", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["du30", + TraditionalForm], + TraditionalForm]]}], " ", SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm]], ".", - SuperscriptBox[ - OverscriptBox["\[Gamma]", "_"], - FormBox["5", - TraditionalForm]]}], TraditionalForm]], "Output", - CellTags->"ToLarin", - CellLabel->"Out[2]=", - CellID->758627970] + OverscriptBox["\[Epsilon]", ""], + RowBox[{ + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], + FormBox[ + 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TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + RowBox[{"-", + FormBox["ps", + TraditionalForm]}], + TraditionalForm], + FormBox["\<\",\"\>", + TraditionalForm], + FormBox[ + SubscriptBox["m", "s"], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], ")"}], ".", + SuperscriptBox["\[Gamma]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], ".", + SuperscriptBox[ + OverscriptBox["\[Gamma]", "_"], + FormBox["7", + TraditionalForm]], ".", + RowBox[{"(", + RowBox[{ + FormBox["\<\"\[CurlyPhi]\"\>", + TraditionalForm], + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox["pd", + TraditionalForm], + TraditionalForm], + FormBox["\<\",\"\>", + TraditionalForm], + FormBox[ + SubscriptBox["m", "d"], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], ")"}]}]}], + TraditionalForm], "\[RightDoubleBracketingBar]"}]}], + TraditionalForm]], "Output", + CellLabel->"Out[67]=", + CellID->1462221407] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{1367, Automatic}, {Automatic, 105}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ToTFI.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ToTFI.nb index 66346152d..4ea59acc4 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ToTFI.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ToTFI.nb @@ -165,15 +165,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["FromTFI", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/FromTFI", ButtonNote->"FromTFI"], "." -}], "Text", - CellTags->"ToTFI", - CellID->1170025384] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -220,53 +217,102 @@ Cell[BoxData[ FormBox[ FractionBox["1", RowBox[{ + InterpretationBox[ + SuperscriptBox[ + FormBox[ + FormBox["q1", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q1, D], + FeynCalc`Momentum[$CellContext`q1, D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q1", + TraditionalForm], "-", + FormBox["p", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[-$CellContext`p + $CellContext`q1, D], + FeynCalc`Momentum[-$CellContext`p + $CellContext`q1, D]]], + Editable->False], ".", RowBox[{"(", InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["q1", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`q1^2, "]"], - Editable->False], ")"}], ".", - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", + RowBox[{ SuperscriptBox[ - RowBox[{"(", - RowBox[{"q1", "-", "p"}], ")"}], "2"], - "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", (-$CellContext`p + $CellContext`q1)^2, "]"], - Editable->False], ")"}], ".", - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox["q2", "2"], "\[InvisibleSpace]", "\<\"-\"\>", + FormBox[ + FormBox["q2", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", "\[InvisibleSpace]", - SuperscriptBox["M", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", $CellContext`q2^2, "-", $CellContext`M^2, "]"], + SuperscriptBox["M", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q2, D], + FeynCalc`Momentum[$CellContext`q2, D]], "-", $CellContext`M^2], Editable->False], ")"}], ".", RowBox[{"(", InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", + RowBox[{ SuperscriptBox[ - RowBox[{"(", - RowBox[{"q2", "-", "p"}], ")"}], "2"], - "\[InvisibleSpace]", "\<\"-\"\>", "\[InvisibleSpace]", - SuperscriptBox["m", "2"], "\[InvisibleSpace]", "\<\"]\"\>"}], + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q2", + TraditionalForm], "-", + FormBox["p", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], SequenceForm[ - "[", (-$CellContext`p + $CellContext`q2)^2, "-", $CellContext`m^2, "]"], - + FeynCalc`Pair[ + FeynCalc`Momentum[-$CellContext`p + $CellContext`q2, D], + FeynCalc`Momentum[-$CellContext`p + $CellContext`q2, D]], + "-", $CellContext`m^2], Editable->False], ")"}], ".", - RowBox[{"(", - InterpretationBox[ - RowBox[{"\<\"[\"\>", "\[InvisibleSpace]", - SuperscriptBox[ - RowBox[{"(", - RowBox[{"q1", "-", "q2"}], ")"}], "2"], - "\[InvisibleSpace]", "\<\"]\"\>"}], - SequenceForm["[", ($CellContext`q1 - $CellContext`q2)^2, "]"], - Editable->False], ")"}]}]], TraditionalForm]], "Output", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q1", + TraditionalForm], "-", + FormBox["q2", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q1 - $CellContext`q2, D], + FeynCalc`Momentum[$CellContext`q1 - $CellContext`q2, D]]], + Editable->False]}]], TraditionalForm]], "Output", CellTags->"ToTFI", - CellLabel->"Out[1]=", - CellID->1537933132] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -308,8 +354,7 @@ Cell[BoxData[ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}]}], ")"}], TraditionalForm]], "Output", CellTags->"ToTFI", - CellLabel->"Out[2]=", - CellID->777497565] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -338,8 +383,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}]}], "]"}]], "Output", CellTags->"ToTFI", - CellLabel->"Out[3]//StandardForm=", - CellID->234884685] + CellLabel->"Out[3]//StandardForm="] }, Open ]], Cell[CellGroupData[{ @@ -391,42 +435,105 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}], ")"}]}], RowBox[{ - SuperscriptBox[ - FormBox["q1", - TraditionalForm], "2"], ".", - SuperscriptBox[ - RowBox[{"(", - RowBox[{ + InterpretationBox[ + SuperscriptBox[ + FormBox[ FormBox["q1", - TraditionalForm], "-", - FormBox["p", - TraditionalForm]}], ")"}], "2"], ".", + TraditionalForm], + TraditionalForm], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q1, D], + FeynCalc`Momentum[$CellContext`q1, D]]], + Editable->False], ".", + InterpretationBox[ + SuperscriptBox[ + RowBox[{ + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q1", + TraditionalForm], "-", + FormBox["p", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[-FeynCalc`Momentum[$CellContext`p, D] + + FeynCalc`Momentum[$CellContext`q1, D], - + FeynCalc`Momentum[$CellContext`p, D] + + FeynCalc`Momentum[$CellContext`q1, D]]], + Editable->False], ".", RowBox[{"(", - RowBox[{ - SuperscriptBox[ - FormBox["q2", - TraditionalForm], "2"], "-", - SuperscriptBox["M", "2"]}], ")"}], ".", + InterpretationBox[ + RowBox[{ + SuperscriptBox[ + FormBox[ + FormBox["q2", + TraditionalForm], + TraditionalForm], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["M", "2"]}], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q2, D], + FeynCalc`Momentum[$CellContext`q2, D]], "-", $CellContext`M^2], + Editable->False], ")"}], ".", RowBox[{"(", - RowBox[{ - SuperscriptBox[ - RowBox[{"(", + InterpretationBox[ + RowBox[{ + SuperscriptBox[ RowBox[{ - FormBox["q2", - TraditionalForm], "-", - FormBox["p", - TraditionalForm]}], ")"}], "2"], "-", - SuperscriptBox["m", "2"]}], ")"}], ".", - SuperscriptBox[ - RowBox[{"(", + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q2", + TraditionalForm], "-", + FormBox["p", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], "\[InvisibleSpace]", "\<\"-\"\>", + "\[InvisibleSpace]", + SuperscriptBox["m", "2"]}], + SequenceForm[ + FeynCalc`Pair[-FeynCalc`Momentum[$CellContext`p, D] + + FeynCalc`Momentum[$CellContext`q2, D], - + FeynCalc`Momentum[$CellContext`p, D] + + FeynCalc`Momentum[$CellContext`q2, D]], "-", $CellContext`m^2], + Editable->False], ")"}], ".", + InterpretationBox[ + SuperscriptBox[ RowBox[{ - FormBox["q1", - TraditionalForm], "-", - FormBox["q2", - TraditionalForm]}], ")"}], "2"]}]], TraditionalForm]], "Output", + FormBox["\<\"(\"\>", + TraditionalForm], + FormBox[ + FormBox[ + RowBox[{ + FormBox["q1", + TraditionalForm], "-", + FormBox["q2", + TraditionalForm]}], + TraditionalForm], + TraditionalForm], + FormBox["\<\")\"\>", + TraditionalForm]}], "2"], + SequenceForm[ + FeynCalc`Pair[ + FeynCalc`Momentum[$CellContext`q1, D] - + FeynCalc`Momentum[$CellContext`q2, D], + FeynCalc`Momentum[$CellContext`q1, D] - + FeynCalc`Momentum[$CellContext`q2, D]]], + Editable->False]}]], TraditionalForm]], "Output", CellTags->"ToTFI", - CellLabel->"Out[4]=", - CellID->544347485] + CellLabel->"Out[4]="] }, Open ]] }, Open ]], @@ -491,12 +598,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{642, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Tr2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Tr2.nb index 569fc0999..ea3e92421 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Tr2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Tr2.nb @@ -125,8 +125,23 @@ exp. If exp does not contain DiracTrace's, Tr2[exp] takes the Dirac trace." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Tr2", "]"}]], "Input", + CellTags->"Tr2", + CellLabel->"In[1]:=", + CellID->111461302], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{"Factoring", "\[Rule]", "False"}], "}"}], + TraditionalForm]], "Output", + CellTags->"Tr2", + CellLabel->"Out[1]=", + CellID->1087832967] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -162,7 +177,6 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["Tr", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/Tr", @@ -188,9 +202,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/SUNTrace", ButtonNote->"SUNTrace"], "." -}], "Text", - CellTags->"Tr2", - CellID->762070093] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -202,8 +214,6 @@ Cell["XXXX", "MoreAbout", CellID->1665078683] }, Open ]], -Cell[CellGroupData[{ - Cell[BoxData[ InterpretationBox[GridBox[{ { @@ -219,45 +229,6 @@ Cell[BoxData[ Cell[CellGroupData[{ -Cell[BoxData[ - RowBox[{"Options", "[", "Tr2", "]"}]], "Input", - CellTags->"Tr2", - CellLabel->"In[1]:=", - CellID->111461302], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{"Factoring", "\[Rule]", "False"}], "}"}], - TraditionalForm]], "Output", - CellTags->"Tr2", - CellLabel->"Out[1]=", - CellID->1087832967] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"TR", "[", - RowBox[{ - RowBox[{"a", " ", "Tf"}], ",", - RowBox[{"SUNTrace", "\[Rule]", "True"}]}], "]"}]], "Input", - CellTags->"Tr2", - CellLabel->"In[2]:=", - CellID->1913639318], - -Cell[BoxData[ - FormBox[ - RowBox[{"4", " ", "a", " ", - SubscriptBox["T", "f"]}], TraditionalForm]], "Output", - CellTags->"Tr2", - CellLabel->"Out[2]=", - CellID->1821071798] -}, Open ]] -}, Open ]], - -Cell[CellGroupData[{ - Cell["More Examples", "ExtendedExamplesSection", CellTags->"ExtendedExamples", CellID->1854448968], @@ -317,12 +288,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{1250, Automatic}, {268, Automatic}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TraceDimension.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TraceDimension.nb index abd1e59eb..66f71bf46 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TraceDimension.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TraceDimension.nb @@ -164,9 +164,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FeynCalc2FORM", ButtonNote->"FeynCalc2FORM"], "." -}], "Text", - CellTags->"TraceDimension", - CellID->623790716] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,12 +250,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{443, Automatic}, {Automatic, 80}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TraceOfOne.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TraceOfOne.nb index 72a38e615..1623ff19e 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TraceOfOne.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TraceOfOne.nb @@ -160,20 +160,17 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", - ButtonBox["TR", + ButtonBox["DiracSimplify", BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/TR", - ButtonNote->"Tr"], + ButtonData:>"paclet:FeynCalc/ref/DiracSimplify", + ButtonNote->"DiracSimplify"], ", ", ButtonBox["DiracTrace", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/DiracTrace", ButtonNote->"DiracTrace"], "." -}], "Text", - CellTags->"TraceOfOne", - CellID->622050208] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -203,39 +200,53 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"TR", "[", + RowBox[{"DiracTrace", "[", "1", "]"}]], "Input", + CellLabel->"In[7]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"tr", "(", + FormBox["1", + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellLabel->"Out[7]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[8]:="], + +Cell[BoxData[ + FormBox["4", TraditionalForm]], "Output", + CellLabel->"Out[8]="] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"DiracTrace", "[", RowBox[{"1", ",", - RowBox[{"SUNTrace", "\[Rule]", "False"}], ",", - RowBox[{"SUNNToCACF", "\[Rule]", "True"}], ",", RowBox[{"TraceOfOne", "\[Rule]", "tr1"}]}], "]"}]], "Input", - CellTags->"TraceOfOne", - CellLabel->"In[1]:=", - CellID->223402463], + CellLabel->"In[9]:="], Cell[BoxData[ - FormBox["tr1", TraditionalForm]], "Output", - CellTags->"TraceOfOne", - CellLabel->"Out[1]=", - CellID->2044201134] + FormBox[ + RowBox[{"tr", "(", + FormBox["1", + TraditionalForm], ")"}], TraditionalForm]], "Output", + CellLabel->"Out[9]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"TR", "[", - RowBox[{"1", ",", - RowBox[{"SUNTrace", "\[Rule]", "True"}], ",", - RowBox[{"SUNNToCACF", "\[Rule]", "True"}], ",", - RowBox[{"TraceOfOne", "\[Rule]", "tr2"}]}], "]"}]], "Input", - CellTags->"TraceOfOne", - CellLabel->"In[2]:=", - CellID->1954279511], + RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input", + CellLabel->"In[10]:="], Cell[BoxData[ - FormBox["tr2", TraditionalForm]], "Output", - CellTags->"TraceOfOne", - CellLabel->"Out[2]=", - CellID->803728852] + FormBox["tr1", TraditionalForm]], "Output", + CellLabel->"Out[10]="] }, Open ]] }, Open ]], @@ -300,12 +311,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{963, Automatic}, {Automatic, 180}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Trick.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Trick.nb index a11d86216..0aa5aa2e2 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Trick.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Trick.nb @@ -186,9 +186,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DiracTrick", ButtonNote->"DiracTrick"], "." -}], "Text", - CellTags->"Trick", - CellID->633331234] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -215,10 +213,6 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell[BoxData["Examples"], "Subsubsection", - CellTags->"Trick", - CellID->890627813], - Cell[TextData[{ "This calculates ", Cell[BoxData[ @@ -232,10 +226,7 @@ Cell[TextData[{ FormBox[ SubsuperscriptBox["g", "\[Nu]", "\[Nu]"], TraditionalForm]]], " in D dimensions." -}], "Text", - ZeroWidthTimes->True, - CellTags->"Trick", - CellID->1624506888], +}], "Notes"], Cell[CellGroupData[{ @@ -250,7 +241,7 @@ Cell[BoxData[ RowBox[{"MTD", "[", RowBox[{"\[Nu]", ",", "\[Nu]"}], "]"}]}], "}"}], "]"}]], "Input", CellTags->"Trick", - CellLabel->"In[1]:=", + CellLabel->"In[11]:=", CellID->1470455200], Cell[BoxData[ @@ -264,8 +255,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], ",", "D"}], "}"}], TraditionalForm]], "Output", CellTags->"Trick", - CellLabel->"Out[1]=", - CellID->472477170] + CellLabel->"Out[11]="] }, Open ]], Cell[CellGroupData[{ @@ -281,80 +271,65 @@ Cell[BoxData[ RowBox[{ RowBox[{"q", "-", "p"}], ",", "\[Nu]"}], "]"}]}]], "Input", CellTags->"Trick", - CellLabel->"In[2]:=", + CellLabel->"In[12]:=", CellID->1607408478], Cell[BoxData[ FormBox[ RowBox[{ FormBox[ - FormBox[ - SuperscriptBox[ - OverscriptBox["g", "_"], - RowBox[{ - FormBox[ - FormBox[ - FormBox["\[Mu]", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["\[Nu]", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], + SuperscriptBox[ + OverscriptBox["g", "_"], + RowBox[{ + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]}]], TraditionalForm], " ", FormBox[ - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], "-", - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Nu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], "-", + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm]], TraditionalForm], " ", FormBox[ - FormBox[ - SuperscriptBox[ - RowBox[{"(", - FormBox[ - FormBox[ - RowBox[{ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], "+", - OverscriptBox[ - FormBox["r", - TraditionalForm], "_"]}], - TraditionalForm], - TraditionalForm], ")"}], + SuperscriptBox[ + RowBox[{"(", FormBox[ FormBox[ - FormBox["\[Mu]", - TraditionalForm], + RowBox[{ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], "+", + OverscriptBox[ + FormBox["r", + TraditionalForm], "_"]}], TraditionalForm], - TraditionalForm]], - TraditionalForm], + TraditionalForm], ")"}], + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]], TraditionalForm]}], TraditionalForm]], "Output", CellTags->"Trick", - CellLabel->"Out[2]=", - CellID->379098985] + CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ @@ -362,7 +337,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Trick", "[", "%", "]"}]], "Input", CellTags->"Trick", - CellLabel->"In[3]:=", + CellLabel->"In[13]:=", CellID->1357228781], Cell[BoxData[ @@ -414,8 +389,7 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]}], TraditionalForm]], "Output", CellTags->"Trick", - CellLabel->"Out[3]=", - CellID->1886505726] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ @@ -426,7 +400,7 @@ Cell[BoxData[ RowBox[{"GA", "[", "d", "]"}], ".", RowBox[{"GA", "[", "e", "]"}]}], "]"}]], "Input", CellTags->"Trick", - CellLabel->"In[4]:=", + CellLabel->"In[14]:=", CellID->542077909], Cell[BoxData[ @@ -446,8 +420,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]]}]}], TraditionalForm]], "Output", CellTags->"Trick", - CellLabel->"Out[4]=", - CellID->272166616] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ @@ -456,7 +429,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"%", "//", "FCE"}], "//", "StandardForm"}]], "Input", CellTags->"Trick", - CellLabel->"In[5]:=", + CellLabel->"In[15]:=", CellID->1364919880], Cell[BoxData[ @@ -465,8 +438,7 @@ Cell[BoxData[ RowBox[{"GA", "[", "d", "]"}], ".", RowBox[{"GA", "[", "e", "]"}]}]}]], "Output", CellTags->"Trick", - CellLabel->"Out[5]//StandardForm=", - CellID->1559426683] + CellLabel->"Out[15]//StandardForm="] }, Open ]] }, Open ]], @@ -531,12 +503,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{759, Automatic}, {Automatic, 80}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TrickIntegrate.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TrickIntegrate.nb index a1dd65b13..f019de591 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TrickIntegrate.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TrickIntegrate.nb @@ -208,9 +208,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Epsilon", ButtonNote->"Epsilon"], "." -}], "Text", - CellTags->"TrickIntegrate", - CellID->1095920169] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -251,7 +249,7 @@ Cell[BoxData[ RowBox[{"a", " ", "Epsilon"}], "-", "1"}], ")"}]}], " ", RowBox[{"g", "[", "t", "]"}]}], ",", "t"}], "]"}]], "Input", CellTags->"TrickIntegrate", - CellLabel->"In[1]:=", + CellLabel->"In[16]:=", CellID->1216797415], Cell[BoxData[ @@ -272,8 +270,7 @@ Cell[BoxData[ RowBox[{"t", ",", "0", ",", "1"}], "}"}]}], "]"}], TraditionalForm]], "Output", CellTags->"TrickIntegrate", - CellLabel->"Out[1]=", - CellID->308907212] + CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ @@ -288,7 +285,7 @@ Cell[BoxData[ RowBox[{"a", " ", "Epsilon"}], "-", "1"}], ")"}]}], " ", RowBox[{"g", "[", "t", "]"}]}], ",", "t"}], "]"}]], "Input", CellTags->"TrickIntegrate", - CellLabel->"In[2]:=", + CellLabel->"In[17]:=", CellID->256517011], Cell[BoxData[ @@ -307,8 +304,7 @@ Cell[BoxData[ RowBox[{"t", ",", "0", ",", "1"}], "}"}]}], "]"}], TraditionalForm]], "Output", CellTags->"TrickIntegrate", - CellLabel->"Out[2]=", - CellID->1473267114] + CellLabel->"Out[17]="] }, Open ]] }, Open ]], @@ -373,12 +369,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{951, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TrickMandelstam.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TrickMandelstam.nb index 9e3a639a6..1cdf21897 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TrickMandelstam.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/TrickMandelstam.nb @@ -126,9 +126,8 @@ Cell[TextData[{ RowBox[{"m2", "^", "2"}], "+", RowBox[{"m3", "^", "2"}], "+", RowBox[{"m4", "^", "2"}]}]}], "}"}]}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "simplifies all sums in expr so that one of the \nMandelstam variables s, t \ -or u is eliminated by the relation ", + " \[LineSeparator]simplifies all sums in expr so that one of the Mandelstam \ +variables s, t or u is eliminated by the relation ", StyleBox["s", FontSlant->"Italic"], " + ", @@ -243,7 +242,7 @@ Cell[BoxData[ SubsuperscriptBox["M", "W", "2"]}]}], "}"}]}], "]"}], "//", "Factor2"}]], "Input", CellTags->"TrickMandelstam", - CellLabel->"In[1]:=", + CellLabel->"In[18]:=", CellID->576381697], Cell[BoxData[ @@ -255,8 +254,7 @@ Cell[BoxData[ SubsuperscriptBox["M", "W", "2"]}], ")"}]}], TraditionalForm]], "Output", CellTags->"TrickMandelstam", - CellLabel->"Out[1]=", - CellID->1660674587] + CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ @@ -278,7 +276,7 @@ Cell[BoxData[ RowBox[{"2", RowBox[{"M", "^", "2"}]}]}], "}"}]}], "]"}]], "Input", CellTags->"TrickMandelstam", - CellLabel->"In[2]:=", + CellLabel->"In[19]:=", CellID->2075024335], Cell[BoxData[ @@ -289,8 +287,7 @@ Cell[BoxData[ SuperscriptBox["s", "2"], "-", "st", "-", "su"}], TraditionalForm]], "Output", CellTags->"TrickMandelstam", - CellLabel->"Out[2]=", - CellID->26761965] + CellLabel->"Out[19]="] }, Open ]] }, Open ]], @@ -355,12 +352,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{775, Automatic}, {Automatic, 115}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2AlienOperator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2AlienOperator.nb index 2abe4d334..e0f593a8c 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2AlienOperator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2AlienOperator.nb @@ -234,8 +234,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm]], TraditionalForm]], "Output", CellTags->"Twist2AlienOperator", - CellLabel->"Out[1]=", - CellID->891789414] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -263,19 +262,15 @@ Cell[BoxData[ RowBox[{"(", RowBox[{"-", "1"}], ")"}], "m"], "+", "1"}], ")"}], " ", SubsuperscriptBox["g", "s", "3"], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", + SuperscriptBox[ + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm]], " ", SubscriptBox["S", "n"], " ", RowBox[{ SuperscriptBox["T", @@ -402,8 +397,7 @@ Cell[BoxData[ TraditionalForm]}], ")"}]}], ")"}], RowBox[{"m", "-", "2"}]]}]}], ")"}]}]}], TraditionalForm]], "Output", CellTags->"Twist2AlienOperator", - CellLabel->"Out[2]=", - CellID->589738199] + CellLabel->"Out[2]="] }, Open ]] }, Open ]], @@ -468,12 +462,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{646, Automatic}, {Automatic, 68}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2CounterOperator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2CounterOperator.nb index a5c3319fb..f03d110a4 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2CounterOperator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2CounterOperator.nb @@ -240,22 +240,16 @@ Cell[BoxData[ RowBox[{"m", "+", "2"}]], "-", FractionBox["8", RowBox[{"m", "-", "1"}]]}], ")"}], " ", - FormBox[ - SuperscriptBox["g", - RowBox[{ - FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["nu", - TraditionalForm], - TraditionalForm], - TraditionalForm]}]], - TraditionalForm], " ", + SuperscriptBox["g", + RowBox[{ + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["nu", + TraditionalForm], + TraditionalForm]}]], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ @@ -284,32 +278,24 @@ Cell[BoxData[ FormBox["p", TraditionalForm], TraditionalForm], "2"], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["nu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", + SuperscriptBox[ + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["nu", + TraditionalForm], + TraditionalForm]], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ @@ -352,63 +338,46 @@ Cell[BoxData[ RowBox[{"(", RowBox[{ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["nu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], "+", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["nu", + TraditionalForm], + TraditionalForm]]}], "+", RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["p", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["nu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}]}], ")"}]}]}], ")"}]}]}]}], + SuperscriptBox[ + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["nu", + TraditionalForm], + TraditionalForm]]}]}], ")"}]}]}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"Twist2CounterOperator", - CellLabel->"Out[1]=", - CellID->246528770] + CellLabel->"Out[1]="] }, Open ]], Cell[CellGroupData[{ @@ -461,8 +430,7 @@ Cell[BoxData[ TagBox["\[CurlyEpsilon]", TraditionalForm]], TraditionalForm]], "Output", CellTags->"Twist2CounterOperator", - CellLabel->"Out[2]=", - CellID->773930559] + CellLabel->"Out[2]="] }, Open ]], Cell[CellGroupData[{ @@ -503,19 +471,15 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]], " ", SubsuperscriptBox["g", "s", "3"], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - FormBox["\[CapitalDelta]", - TraditionalForm], - TraditionalForm], - FormBox[ - FormBox[ - FormBox["mu", - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", + SuperscriptBox[ + FormBox[ + FormBox["\[CapitalDelta]", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["mu", + TraditionalForm], + TraditionalForm]], " ", SubscriptBox["S", "n"], " ", RowBox[{"(", RowBox[{ @@ -608,8 +572,7 @@ Cell[BoxData[ TraditionalForm], TraditionalForm]}]}]]}], ")"}]}]}]}], TraditionalForm]], "Output", CellTags->"Twist2CounterOperator", - CellLabel->"Out[3]=", - CellID->1953247697] + CellLabel->"Out[3]="] }, Open ]] }, Open ]], @@ -674,12 +637,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{538, Automatic}, {Automatic, -8}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2GluonOperator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2GluonOperator.nb index 44df6bd8c..3b92abaa9 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2GluonOperator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2GluonOperator.nb @@ -181,9 +181,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Twist2QuarkOperator", ButtonNote->"Twist2QuarkOperator"], "." -}], "Text", - CellTags->"Twist2GluonOperator", - CellID->171220448] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -210,33 +208,81 @@ Cell[BoxData[ $Line = 0; Null]], "PrimaryExamplesSection", CellID->880084151], -Cell["The setting All for Explicit performs the sums.", "Text", - CellTags->"Twist2GluonOperator", - CellID->820989411], +Cell["The setting All for Explicit performs the sums.", "Notes"], + +Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{ - RowBox[{"SetOptions", "[", - RowBox[{"Twist2GluonOperator", ",", " ", - RowBox[{"Polarization", " ", "\[Rule]", " ", "1"}], ",", " ", - RowBox[{"Explicit", "\[Rule]", "All"}]}], "]"}], ";"}]], "Input", + RowBox[{"Twist2GluonOperator", "[", + RowBox[{ + RowBox[{"{", + RowBox[{"p", ",", "\[Mu]", ",", "a"}], "}"}], ",", + RowBox[{"{", + RowBox[{"q", ",", "\[Nu]", ",", "b"}], "}"}], ",", + RowBox[{"{", + RowBox[{"r", ",", "\[Rho]", ",", "c"}], "}"}], ",", " ", + RowBox[{"Polarization", " ", "\[Rule]", " ", "1"}], ",", " ", + RowBox[{"Explicit", "\[Rule]", "All"}]}], "]"}]], "Input", CellTags->"Twist2GluonOperator", - CellLabel->"In[1]:=", - CellID->1824993691], + CellLabel->"In[3]:=", + CellID->1893252067], Cell[BoxData[ - RowBox[{ - RowBox[{"Twist2GluonOperator", "[", - RowBox[{ - RowBox[{"{", - RowBox[{"p", ",", "\[Mu]", ",", "a"}], "}"}], ",", - RowBox[{"{", - RowBox[{"q", ",", "\[Nu]", ",", "b"}], "}"}], ",", - RowBox[{"{", - RowBox[{"r", ",", "\[Rho]", ",", "c"}], "}"}]}], "]"}], ";"}]], "Input", + FormBox[ + RowBox[{ + RowBox[{"(", + RowBox[{"1", "-", + FormBox[ + SuperscriptBox[ + RowBox[{"(", + RowBox[{"-", "1"}], ")"}], "m"], + TraditionalForm]}], ")"}], " ", + SubscriptBox["g", "s"], " ", + SuperscriptBox["f", + RowBox[{ + FormBox[ + FormBox["a", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["b", + TraditionalForm], + TraditionalForm], + FormBox[ + FormBox["c", + TraditionalForm], + TraditionalForm]}]], " ", + RowBox[{"(", + RowBox[{ + SubsuperscriptBox["O", + RowBox[{ + FormBox[ + FormBox["\[Nu]", + TraditionalForm], + TraditionalForm], "\[VeryThinSpace]", + FormBox[ + FormBox["\[Rho]", + TraditionalForm], + TraditionalForm], "\[VeryThinSpace]", + FormBox[ + FormBox["\[Mu]", + TraditionalForm], + TraditionalForm]}], "G3"], "(", + FormBox[ + FormBox["q", + TraditionalForm], + TraditionalForm], ",", + FormBox[ + FormBox["r", + TraditionalForm], + TraditionalForm], ",", + FormBox[ + FormBox["p", + TraditionalForm], + TraditionalForm], ")"}], ")"}]}], TraditionalForm]], "Output", CellTags->"Twist2GluonOperator", - CellLabel->"In[2]:=", - CellID->1893252067] + CellLabel->"Out[3]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -300,12 +346,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{713, Automatic}, {Automatic, 44}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2QuarkOperator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2QuarkOperator.nb index bc69c3dbf..5a7bd34d0 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2QuarkOperator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist2QuarkOperator.nb @@ -177,9 +177,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Twist2GluonOperator", ButtonNote->"Twist2GluonOperator"], "." -}], "Text", - CellTags->"Twist2QuarkOperator", - CellID->1216439856] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -265,12 +263,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{921, Automatic}, {Automatic, 126}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist3QuarkOperator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist3QuarkOperator.nb index 1c7f9c736..d5ea34d4b 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist3QuarkOperator.nb +++ 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+ CellLabel->"Out[5]="] }, Open ]] }, Open ]], @@ -336,12 +329,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{835, Automatic}, {Automatic, 121}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist4GluonOperator.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist4GluonOperator.nb index 3d02cabd2..025659aef 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist4GluonOperator.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Twist4GluonOperator.nb @@ -188,9 +188,7 @@ 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CellTags->"Twist4GluonOperator", - CellLabel->"Out[1]=", - CellID->198500674] + CellLabel->"Out[6]="] }, Open ]] }, Open ]], @@ -9403,12 +7960,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{762, Automatic}, {Automatic, 49}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/TwoLoopSimplify.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/TwoLoopSimplify.nb index 60c1325e8..bee5b2a97 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/TwoLoopSimplify.nb +++ 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RowBox[{"ClearAll", "[", "myTens", "]"}]], "Input", + CellLabel->"In[1]:=", + CellID->459227138], + +Cell[BoxData[ + RowBox[{"DeclareFCTensor", "[", "myTens", "]"}]], "Input", + CellLabel->"In[2]:=", + CellID->384608883], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"ExpandScalarProduct", "[", + RowBox[{"myTens", "[", + RowBox[{"z", ",", + RowBox[{"Momentum", "[", + RowBox[{"a", "+", "b"}], "]"}], ",", + RowBox[{"Momentum", "[", + RowBox[{"c", "+", "d"}], "]"}]}], "]"}], "]"}]], "Input", + CellLabel->"In[3]:=", + CellID->816959797], + +Cell[BoxData[ + FormBox[ + RowBox[{ + RowBox[{"myTens", "(", + RowBox[{"z", ",", + OverscriptBox[ + FormBox["a", + TraditionalForm], "_"], ",", + OverscriptBox[ + FormBox["c", + TraditionalForm], "_"]}], ")"}], "+", + RowBox[{"myTens", "(", + RowBox[{"z", ",", + OverscriptBox[ + FormBox["a", + TraditionalForm], "_"], ",", + OverscriptBox[ + FormBox["d", + TraditionalForm], "_"]}], ")"}], "+", + RowBox[{"myTens", "(", + RowBox[{"z", ",", + 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InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{923, Automatic}, {Automatic, 200}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/UnDeclareNonCommutative.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/UnDeclareNonCommutative.nb index 3b5ba8459..bf1c690a6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/UnDeclareNonCommutative.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/UnDeclareNonCommutative.nb @@ -172,9 +172,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/DeclareNonCommutative", ButtonNote->"DeclareNonCommutative"], "." -}], "Text", - CellTags->"UnDeclareNonCommutative", - CellID->349709371] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -204,38 +202,33 @@ Cell[BoxData[ Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", "x", "]"}]], "Input", CellTags->"UnDeclareNonCommutative", - CellLabel->"In[1]:=", + CellLabel->"In[5]:=", CellID->1470795437], Cell["\<\ As a side-effect of DeclareNonCommutative x is declared to be of DataType \ NonCommutative.\ -\>", "Text", - CellTags->"UnDeclareNonCommutative", - CellID->467320049], +\>", "Notes"], Cell[CellGroupData[{ Cell["DataType[x,NonCommutative]", "Input", CellTags->"UnDeclareNonCommutative", - CellLabel->"In[2]:=", + CellLabel->"In[6]:=", CellID->88675667], Cell[BoxData[ FormBox["True", TraditionalForm]], "Output", CellTags->"UnDeclareNonCommutative", - CellLabel->"Out[2]=", - CellID->415876422] + CellLabel->"Out[6]="] }, Open ]], -Cell["The inverse operation is UnDeclareNonCommutative.", "Text", - CellTags->"UnDeclareNonCommutative", - CellID->568029723], +Cell["The inverse operation is UnDeclareNonCommutative.", "Notes"], Cell[BoxData[ RowBox[{"UnDeclareNonCommutative", "[", "x", "]"}]], "Input", CellTags->"UnDeclareNonCommutative", - CellLabel->"In[3]:=", + CellLabel->"In[7]:=", CellID->669742468], Cell[CellGroupData[{ @@ -244,21 +237,20 @@ Cell[BoxData[ RowBox[{"DataType", "[", RowBox[{"x", ",", "NonCommutative"}], "]"}]], "Input", CellTags->"UnDeclareNonCommutative", - CellLabel->"In[4]:=", + CellLabel->"In[8]:=", CellID->294586102], Cell[BoxData[ FormBox["False", TraditionalForm]], "Output", CellTags->"UnDeclareNonCommutative", - CellLabel->"Out[4]=", - CellID->1002154582] + CellLabel->"Out[8]="] }, Open ]], Cell[BoxData[ RowBox[{"DeclareNonCommutative", "[", RowBox[{"y", ",", "z"}], "]"}]], "Input", CellTags->"UnDeclareNonCommutative", - CellLabel->"In[5]:=", + CellLabel->"In[9]:=", CellID->1907752862], Cell[CellGroupData[{ @@ -267,7 +259,7 @@ Cell[BoxData[ RowBox[{"DataType", "[", RowBox[{"y", ",", "z", ",", "NonCommutative"}], "]"}]], "Input", CellTags->"UnDeclareNonCommutative", - CellLabel->"In[6]:=", + CellLabel->"In[10]:=", CellID->1458539742], Cell[BoxData[ @@ -275,15 +267,14 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"True", ",", "True"}], "}"}], TraditionalForm]], "Output", CellTags->"UnDeclareNonCommutative", - CellLabel->"Out[6]=", - CellID->799895096] + CellLabel->"Out[10]="] }, Open ]], Cell[BoxData[ RowBox[{"UnDeclareNonCommutative", "[", RowBox[{"y", ",", "z"}], "]"}]], "Input", CellTags->"UnDeclareNonCommutative", - CellLabel->"In[7]:=", + CellLabel->"In[11]:=", CellID->1096625129], Cell[CellGroupData[{ @@ -292,7 +283,7 @@ Cell[BoxData[ RowBox[{"DataType", "[", RowBox[{"y", ",", "z", ",", "NonCommutative"}], "]"}]], "Input", CellTags->"UnDeclareNonCommutative", - CellLabel->"In[8]:=", + CellLabel->"In[12]:=", CellID->702684679], Cell[BoxData[ @@ -300,8 +291,7 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"False", ",", "False"}], "}"}], TraditionalForm]], "Output", CellTags->"UnDeclareNonCommutative", - CellLabel->"Out[8]=", - CellID->493928013] + CellLabel->"Out[12]="] }, Open ]] }, Open ]], @@ -366,12 +356,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{714, Automatic}, {Automatic, 82}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Uncontract.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Uncontract.nb index 0f232262c..3852b28ef 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Uncontract.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Uncontract.nb @@ -127,8 +127,28 @@ momenta except OPEDelta." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Uncontract", "]"}]], "Input", + CellTags->"Uncontract", + CellLabel->"In[1]:=", + CellID->1318320011], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"Dimension", "\[Rule]", "Automatic"}], ",", + RowBox[{"DimensionalReduction", "\[Rule]", "False"}], ",", + RowBox[{"Pair", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"Unique", "\[Rule]", "True"}]}], "}"}], + TraditionalForm]], "Output", + CellTags->"Uncontract", + CellLabel->"Out[1]=", + CellID->659553310] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -169,9 +189,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Contract", ButtonNote->"Contract"], "." -}], "Text", - CellTags->"Uncontract", - CellID->1158023183] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -201,41 +219,19 @@ Cell[BoxData[ Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Options", "[", "Uncontract", "]"}]], "Input", - CellTags->"Uncontract", - CellLabel->"In[1]:=", - CellID->1318320011], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"Dimension", "\[Rule]", "Automatic"}], ",", - RowBox[{"DimensionalReduction", "\[Rule]", "False"}], ",", - RowBox[{"Pair", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"Unique", "\[Rule]", "True"}]}], "}"}], - TraditionalForm]], "Output", - CellTags->"Uncontract", - CellLabel->"Out[1]=", - CellID->659553310] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"t1", " ", "=", " ", + RowBox[{" ", RowBox[{ - RowBox[{"LeviCivita", "[", + RowBox[{"LC", "[", RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "[", RowBox[{"p", ",", "q"}], "]"}]}]], "Input", CellTags->"Uncontract", - CellLabel->"In[2]:=", + CellLabel->"In[13]:=", CellID->851114003], Cell[BoxData[ FormBox[ - SuperscriptBox["\[Epsilon]", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -256,39 +252,35 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]], TraditionalForm]], "Output", CellTags->"Uncontract", - CellLabel->"Out[2]=", - CellID->1899728699] + CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Uncontract", "[", - RowBox[{"t1", ",", " ", "p"}], "]"}]], "Input", + RowBox[{"%", ",", " ", "p"}], "]"}]], "Input", CellTags->"Uncontract", - CellLabel->"In[3]:=", + CellLabel->"In[14]:=", CellID->1865320721], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ FormBox[ - FormBox[ - FormBox[ - RowBox[{"$AL$44995", "\[InvisibleApplication]", - RowBox[{"(", "1", ")"}]}], - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - SuperscriptBox["\[Epsilon]", + RowBox[{"$AL", "\[InvisibleApplication]", + RowBox[{"(", "$343", ")"}]}], + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + OverscriptBox["\[Epsilon]", "_"], RowBox[{ FormBox[ FormBox["\[Mu]", @@ -300,8 +292,8 @@ Cell[BoxData[ TraditionalForm], FormBox[ FormBox[ - RowBox[{"$AL$44995", "\[InvisibleApplication]", - RowBox[{"(", "1", ")"}]}], + RowBox[{"$AL", "\[InvisibleApplication]", + RowBox[{"(", "$343", ")"}]}], TraditionalForm], TraditionalForm], FormBox[ @@ -310,17 +302,15 @@ Cell[BoxData[ TraditionalForm], "_"], TraditionalForm]}]]}], TraditionalForm]], "Output", CellTags->"Uncontract", - CellLabel->"Out[3]=", - CellID->203669378] + CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"t2", "=", - RowBox[{"DiracSlash", "[", "p", "]"}]}]], "Input", + RowBox[{"GS", "[", "p", "]"}]], "Input", CellTags->"Uncontract", - CellLabel->"In[4]:=", + CellLabel->"In[15]:=", CellID->1250693732], 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TraditionalForm], "_"], - TraditionalForm], + RowBox[{"$AL", "\[InvisibleApplication]", + RowBox[{"(", "$349", ")"}]}], + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ FormBox[ - FormBox[ - FormBox[ - RowBox[{"$AL$45013", "\[InvisibleApplication]", - RowBox[{"(", "1", ")"}]}], - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", + RowBox[{"$AL", "\[InvisibleApplication]", + RowBox[{"(", "$349", ")"}]}], + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"Uncontract", - CellLabel->"Out[8]=", - CellID->7406466] + CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ @@ -547,91 +515,67 @@ Cell[BoxData[ RowBox[{"Uncontract", "[", RowBox[{ RowBox[{ - RowBox[{"ScalarProduct", "[", + RowBox[{"SP", "[", RowBox[{"p", ",", "q"}], "]"}], "^", "2"}], ",", "q", ",", RowBox[{"Pair", "\[Rule]", "All"}]}], "]"}]], "Input", CellTags->"Uncontract", - CellLabel->"In[9]:=", + CellLabel->"In[22]:=", CellID->1461988505], Cell[BoxData[ FormBox[ RowBox[{ - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox[ - RowBox[{"$AL$45017", "\[InvisibleApplication]", - RowBox[{"(", "1", ")"}]}], - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ - FormBox[ - OverscriptBox[ - FormBox["p", - TraditionalForm], "_"], - TraditionalForm], - FormBox[ - FormBox[ - FormBox[ - RowBox[{"$AL$45017", "\[InvisibleApplication]", - RowBox[{"(", "2", ")"}]}], - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], + RowBox[{"$AL", "\[InvisibleApplication]", + RowBox[{"(", "$350", ")"}]}], + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["p", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ FormBox[ - FormBox[ - FormBox[ - RowBox[{"$AL$45017", "\[InvisibleApplication]", - RowBox[{"(", "1", ")"}]}], - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm], " ", - FormBox[ - SuperscriptBox[ + RowBox[{"$AL", "\[InvisibleApplication]", + RowBox[{"(", "$351", ")"}]}], + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ FormBox[ - OverscriptBox[ - FormBox["q", - TraditionalForm], "_"], - TraditionalForm], + RowBox[{"$AL", "\[InvisibleApplication]", + RowBox[{"(", "$350", ")"}]}], + TraditionalForm], + TraditionalForm]], " ", + SuperscriptBox[ + FormBox[ + OverscriptBox[ + FormBox["q", + TraditionalForm], "_"], + TraditionalForm], + FormBox[ FormBox[ - FormBox[ - FormBox[ - RowBox[{"$AL$45017", "\[InvisibleApplication]", - RowBox[{"(", "2", ")"}]}], - TraditionalForm], - TraditionalForm], - TraditionalForm]], - TraditionalForm]}], TraditionalForm]], "Output", - CellTags->"Uncontract", - CellLabel->"Out[9]=", - CellID->1916509902] -}, Open ]], - -Cell[BoxData[ - RowBox[{"Clear", "[", - RowBox[{"t1", ",", "t2"}], "]"}]], "Input", + RowBox[{"$AL", "\[InvisibleApplication]", + RowBox[{"(", "$351", ")"}]}], + TraditionalForm], + TraditionalForm]]}], TraditionalForm]], "Output", CellTags->"Uncontract", - CellLabel->"In[10]:=", - CellID->1699220508] + CellLabel->"Out[22]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -695,12 +639,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{710, Automatic}, {Automatic, 127}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Upper.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Upper.nb deleted file mode 100644 index 0ec1b38a3..000000000 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Upper.nb +++ /dev/null @@ -1,273 +0,0 @@ -Notebook[{ -Cell[TextData[{ - "New in: ", - Cell["9.0", "HistoryData", - CellTags->"New"], - " | Modified in: ", - Cell[" ", "HistoryData", - CellTags->"Modified"], - " | Obsolete in: ", - Cell[" ", "HistoryData", - CellTags->"Obsolete"], - " | Excised in: ", - Cell[" ", "HistoryData", - CellTags->"Excised"] -}], "History", - CellID->1247902091], - -Cell[CellGroupData[{ - -Cell["Categorization", "CategorizationSection", - CellID->1122911449], - -Cell["Symbol", "Categorization", - CellLabel->"Entity Type", - CellID->686433507], - -Cell["FeynCalc", "Categorization", - CellLabel->"Paclet Name", - CellID->605800465], - -Cell["FeynCalc`", "Categorization", - CellLabel->"Context", - CellID->468444828], - -Cell["FeynCalc/ref/Upper", "Categorization", - CellLabel->"URI"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Keywords", "KeywordsSection", - CellID->477174294], - -Cell["XXXX", "Keywords", - CellID->1164421360] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Syntax Templates", "TemplatesSection", - CellID->1872225408], - -Cell[BoxData[""], "Template", - CellLabel->"Additional Function Template", - CellID->1562036412], - -Cell[BoxData[""], "Template", - CellLabel->"Arguments Pattern", - CellID->158391909], - -Cell[BoxData[""], "Template", - CellLabel->"Local Variables", - CellID->1360575930], - -Cell[BoxData[""], "Template", - CellLabel->"Color Equal Signs", - CellID->793782254] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Details", "DetailsSection", - CellID->307771771], - -Cell["XXXX", "Details", - CellLabel->"Lead", - CellID->670882175], - -Cell["XXXX", "Details", - CellLabel->"Developers", - CellID->350963985], - -Cell["XXXX", "Details", - CellLabel->"Authors", - CellID->8391405], - -Cell["XXXX", "Details", - CellLabel->"Feature Name", - CellID->3610269], - -Cell["XXXX", "Details", - CellLabel->"QA", - CellID->401364205], - -Cell["XXXX", "Details", - CellLabel->"DA", - CellID->350204745], - -Cell["XXXX", "Details", - CellLabel->"Docs", - CellID->732958810], - -Cell["XXXX", "Details", - CellLabel->"Features Page Notes", - CellID->222905350], - -Cell["XXXX", "Details", - CellLabel->"Comments", - CellID->240026365] -}, Closed]], - -Cell[CellGroupData[{ - -Cell["Upper", "ObjectName", - CellID->1224892054], - -Cell[TextData[{ - Cell[" ", "ModInfo"], - Cell[BoxData["Upper"], "InlineFormula"], - " \[LineSeparator]", - "may be used inside LorentzIndex to indicate an contravariant LorentzIndex." -}], "Usage", - CellID->982511436], - -Cell["XXXX", "Notes", - CellID->1067943069] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Tutorials", "TutorialsSection", - CellID->250839057], - -Cell["XXXX", "Tutorials", - CellID->341631938] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Demonstrations", "RelatedDemonstrationsSection", - CellID->1268215905], - -Cell["XXXX", "RelatedDemonstrations", - CellID->1129518860] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["Related Links", "RelatedLinksSection", - CellID->1584193535], - -Cell["XXXX", "RelatedLinks", - CellID->1038487239] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["See Also", "SeeAlsoSection", - CellID->1255426704], - -Cell[TextData[{ - ButtonBox["LorentzIndex", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/LorentzIndex", - ButtonNote->"LorentzIndex"], - ", ", - ButtonBox["Lower", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Lower", - ButtonNote->"Lower"], - ", ", - ButtonBox["Contract1", - BaseStyle->"Link", - ButtonData:>"paclet:FeynCalc/ref/Contract1", - ButtonNote->"Contract1"], - "." -}], "Text", - CellTags->"Upper", - CellID->1540043735] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["More About", "MoreAboutSection", - CellID->38303248], - -Cell["XXXX", "MoreAbout", - CellID->1665078683] -}, Open ]], - -Cell[BoxData[ - InterpretationBox[GridBox[{ - { - StyleBox["Examples", "PrimaryExamplesSection"], - ButtonBox[ - RowBox[{ - RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], - BaseStyle->"ExtendedExamplesLink", - ButtonData:>"ExtendedExamples"]} - }], - $Line = 0; Null]], "PrimaryExamplesSection", - CellID->880084151], - -Cell[CellGroupData[{ - -Cell["More Examples", "ExtendedExamplesSection", - CellTags->"ExtendedExamples", - CellID->1854448968], - -Cell[BoxData[ - InterpretationBox[Cell["Scope", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1293636265], - -Cell[BoxData[ - InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1020263627], - -Cell[CellGroupData[{ - -Cell[BoxData[ - InterpretationBox[Cell["Options", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2061341341], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1757724783], - -Cell[BoxData[ - InterpretationBox[Cell["XXXX", "ExampleSubsection"], - $Line = 0; Null]], "ExampleSubsection", - CellID->1295379749] -}, Closed]], - -Cell[BoxData[ - InterpretationBox[Cell["Applications", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->258228157], - -Cell[BoxData[ - InterpretationBox[Cell["Properties & Relations", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->2123667759], - -Cell[BoxData[ - InterpretationBox[Cell["Possible Issues", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1305812373], - -Cell[BoxData[ - InterpretationBox[Cell["Interactive Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->1653164318], - -Cell[BoxData[ - InterpretationBox[Cell["Neat Examples", "ExampleSection"], - $Line = 0; Null]], "ExampleSection", - CellID->589267740] -}, Open ]] -}, -WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, -Visible->True, -PrivateNotebookOptions->{"FileOutlineCache"->False}, -CellContext->"Global`", -TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", -StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", - CharacterEncoding -> "UTF-8"] -] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Vectors.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Vectors.nb index 040caed33..75ffc2127 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Vectors.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Vectors.nb @@ -165,9 +165,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/FORM2FeynCalc", ButtonNote->"FORM2FeynCalc"], "." -}], "Text", - CellTags->"Vectors", - CellID->1205329040] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -253,12 +251,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{759, Automatic}, {Automatic, 91}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/West.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/West.nb index d848ac123..f753621b6 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/West.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/West.nb @@ -117,19 +117,41 @@ Cell["West", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["West"], "InlineFormula"], - " \[LineSeparator]West is an option for DiracTrace, TR and other functions \ -that deal with traces of Dirac matrices. It applies only to the computation \ -of D-dimensional chiral traces (i.e. those that involve one ", - Cell[BoxData[ - SuperscriptBox["\[Gamma]", "5"]], "InlineFormula", - FormatType->"StandardForm"], - ") in the Breitenlohner-Maison-t'Hooft-Veltman (BMHV) scheme. If set to \ -True, such traces will be computed according to formula (A.5) from Comp. \ -Phys. Comm 77 (1993) 286-298, which is also known as West's formula." + " \[LineSeparator]is an option for ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + " and several other functions that deal with traces of Dirac matrices." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", +Cell[TextData[{ + "The option applies only to the computation of ", + Cell[BoxData["D"], "InlineFormula"], + "-dimensional traces with an odd number of ", + Cell[BoxData[ + SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"], + " in the Breitenlohner-Maison-t'Hooft-Veltman (BMHV) scheme." +}], "Notes"], + +Cell[TextData[{ + "With ", + Cell[BoxData[ + RowBox[{"West", "->", "True"}]], "InlineFormula"], + " (default setting), such traces are computed according to formula (A.5) \ +from Comp. Phys. Comm 77 (1993) 286-298, which is also known as West's \ +formula. " +}], "Notes"], + +Cell[TextData[{ + "For more details, see the documentation for ", + ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"], + "." +}], "Notes", CellID->1067943069] }, Open ]], @@ -165,8 +187,10 @@ Cell[CellGroupData[{ Cell["See Also", "SeeAlsoSection", CellID->1255426704], -Cell["XXXX", "SeeAlso", - CellID->929782353] +Cell[TextData[ButtonBox["DiracTrace", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/DiracTrace", + ButtonNote->"DiracTrace"]], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -252,9 +276,10 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 741}, -WindowMargins->{{Automatic, 919}, {32, Automatic}}, +WindowMargins->{{779, Automatic}, {Automatic, 221}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Write2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Write2.nb index b973be004..07f65321d 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Write2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Write2.nb @@ -122,15 +122,54 @@ Cell[TextData[{ RowBox[{"val1", " ", "=", " ", "expr1"}], ",", " ", RowBox[{"val2", " ", "=", " ", "expr2"}], ",", " ", "..."}], "]"}]], "InlineFormula"], - " \[LineSeparator]", - "writes the settings val1 = expr1, val2 = expr2 in sequence followed by a \ -newline, to the specified output file. Setting the option FormatType of \ -Write2 to FortranForm results in FORTRAN syntax output." + " \[LineSeparator]writes the settings ", + Cell[BoxData[ + RowBox[{ + RowBox[{"val1", " ", "=", " ", "expr1"}], ",", " ", + RowBox[{"val2", " ", "=", " ", "expr2"}]}]], "InlineFormula"], + " in sequence followed by a newline, to the specified output file." }], "Usage", CellID->982511436], -Cell["XXXX", "Notes", - CellID->1067943069] +Cell[TextData[{ + "Setting the option ", + Cell[BoxData["FormatType"], "InlineFormula"], + " of ", + ButtonBox["Write2", + BaseStyle->"Link", + ButtonData:>"paclet:FeynCalc/ref/Write2", + ButtonNote->"Write2"], + " to ", + Cell[BoxData["FortranForm"], "InlineFormula"], + " results in Fortran syntax output." +}], "Notes"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Options", "[", "Write2", "]"}]], "Input", + CellLabel->"In[150]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"{", + RowBox[{ + RowBox[{"D0Convention", "\[Rule]", "0"}], ",", + RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", + RowBox[{"FinalSubstitutions", "\[Rule]", + RowBox[{"{", "}"}]}], ",", + RowBox[{"FormatType", "\[Rule]", "InputForm"}], ",", + RowBox[{"FortranFormatDoublePrecision", "\[Rule]", "True"}], ",", + RowBox[{"PageWidth", "\[Rule]", "62"}], ",", + RowBox[{"PostFortranFile", "\[Rule]", + RowBox[{"{", "\<\"\"\>", "}"}]}], ",", + RowBox[{"PreFortranFile", "\[Rule]", + RowBox[{"{", "\<\"\"\>", "}"}]}], ",", + RowBox[{"Precision", "\[Rule]", "15"}], ",", + RowBox[{"StringReplace", "\[Rule]", + RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", + CellLabel->"Out[150]="] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -176,9 +215,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/PaVeReduce", ButtonNote->"PaVeReduce"], "." -}], "Text", - CellTags->"Write2", - CellID->1387459580] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -210,7 +247,7 @@ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FullForm", "[", "$FortranContinuationCharacter", "]"}]], "Input", CellTags->"Write2", - CellLabel->"In[1]:=", + CellLabel->"In[151]:=", CellID->1324211307], Cell[BoxData[ @@ -222,52 +259,14 @@ Cell[BoxData[ NumberMarks->True], FullForm], TraditionalForm]], "Output", CellTags->"Write2", - CellLabel->"Out[1]//FullForm=", - CellID->296766764] -}, Open ]], - -Cell[CellGroupData[{ - -Cell[BoxData[ - RowBox[{"Options", "[", "Write2", "]"}]], "Input", - CellTags->"Write2", - CellLabel->"In[2]:=", - CellID->2021664467], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", - RowBox[{ - RowBox[{"D0Convention", "\[Rule]", "0"}], ",", - RowBox[{"FinalSubstitutions", "\[Rule]", - RowBox[{"{", "}"}]}], ",", - RowBox[{"FormatType", "\[Rule]", "InputForm"}], ",", - RowBox[{"FortranFormatDoublePrecision", "\[Rule]", "True"}], ",", - RowBox[{"PageWidth", "\[Rule]", "62"}], ",", - RowBox[{"PostFortranFile", "\[Rule]", "\<\"\"\>"}], ",", - RowBox[{"PreFortranFile", "\[Rule]", "\<\"\"\>"}], ",", - RowBox[{"StringReplace", "\[Rule]", - RowBox[{"{", "}"}]}]}], "}"}], TraditionalForm]], "Output", - CellTags->"Write2", - CellLabel->"Out[2]=", - CellID->426630983] + CellLabel->"Out[151]//FullForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"Attributes", "[", "Write2", "]"}]], "Input", - CellTags->"Write2", - CellLabel->"In[3]:=", - CellID->653070552], - -Cell[BoxData[ - FormBox[ - RowBox[{"{", "HoldRest", "}"}], TraditionalForm]], "Output", - CellTags->"Write2", - CellLabel->"Out[3]=", - CellID->930779746] -}, Open ]], + InterpretationBox[Cell["\t", "ExampleDelimiter"], + $Line = 0; Null]], "ExampleDelimiter"], Cell[CellGroupData[{ @@ -286,7 +285,7 @@ Cell[BoxData[ RowBox[{"a", "-", "b"}], ")"}], "2"]}], ")"}], "2"], ",", "a", ",", "Factor"}], "]"}]}]], "Input", CellTags->"Write2", - CellLabel->"In[4]:=", + CellLabel->"In[152]:=", CellID->568187661], Cell[BoxData[ @@ -318,10 +317,11 @@ Cell[BoxData[ SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]}], ")"}], "2"]}], TraditionalForm]], "Output", CellTags->"Write2", - CellLabel->"Out[4]=", - CellID->1801200835] + CellLabel->"Out[152]="] }, Open ]], +Cell["This writes the assignment r=t to a file.", "Notes"], + Cell[BoxData[ RowBox[{ RowBox[{"tempfilename", "=", @@ -329,25 +329,17 @@ Cell[BoxData[ RowBox[{"ToString", "[", "$SessionID", "]"}], "<>", "\"\<.s\>\""}]}], ";"}]], "Input", CellTags->"Write2", - CellLabel->"In[5]:=", + CellLabel->"In[153]:=", CellID->158339237], -Cell["This writes the assignment r=t to a file.", "Text", - CellTags->"Write2", - CellID->956230713], - Cell[BoxData[ RowBox[{ RowBox[{"Write2", "[", RowBox[{"tempfilename", ",", RowBox[{"r", "=", "t"}]}], "]"}], ";"}]], "Input", - CellTags->"Write2", - CellLabel->"In[6]:=", - CellID->1599031587], + CellLabel->"In[154]:="], -Cell["This shows the contents of the file.", "Text", - CellTags->"Write2", - CellID->304283335], +Cell["This shows the contents of the file.", "Notes"], Cell[CellGroupData[{ @@ -361,17 +353,14 @@ Cell[BoxData[ RowBox[{"$OperatingSystem", "===", "\"\\""}], ",", "\"\<:\>\"", ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], ",", "String"}], "]"}], "]"}]], "Input", - CellTags->"Write2", - CellLabel->"In[7]:=", - CellID->1505586368], + CellLabel->"In[156]:="], Cell[BoxData[ FormBox[ TagBox[ TagBox[GridBox[{ - {"\<\"r = ( 4*a^4 - 8*a^3*(b + c) - 4*a*(b + c)*(b^2 + c^2) + (b^2 + \ -c^2)^2 + \"\>"}, - {"\<\" 8*a^2*(b^2 + b*c + c^2)\"\>"}, + {"\<\"r = ( 4*a^4 - 8*a^3*(b + c) - 4*a*(b + c)*(b^2 + c^2) + \"\>"}, + {"\<\" (b^2 + c^2)^2 + 8*a^2*(b^2 + b*c + c^2)\"\>"}, {"\<\" );\"\>"} }, GridBoxAlignment->{ @@ -387,9 +376,7 @@ c^2)^2 + \"\>"}, Column], Function[BoxForm`e$, TableForm[BoxForm`e$]]], TraditionalForm]], "Output", - CellTags->"Write2", - CellLabel->"Out[7]//TableForm=", - CellID->432817826] + CellLabel->"Out[156]//TableForm="] }, Open ]], Cell[BoxData[ @@ -399,9 +386,7 @@ Cell[BoxData[ RowBox[{ RowBox[{"$OperatingSystem", "===", "\"\\""}], ",", "\"\<:\>\"", ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], "]"}]], "Input", - CellTags->"Write2", - CellLabel->"In[8]:=", - CellID->62208628], + CellLabel->"In[157]:="], Cell[CellGroupData[{ @@ -412,7 +397,7 @@ Cell[BoxData[ RowBox[{"t", ",", "a", ",", RowBox[{"IsolateNames", "\[Rule]", "w"}]}], "]"}]}]}]], "Input", CellTags->"Write2", - CellLabel->"In[9]:=", + CellLabel->"In[158]:=", CellID->170691261], Cell[BoxData[ @@ -423,27 +408,26 @@ Cell[BoxData[ RowBox[{"8", " ", SuperscriptBox["a", "3"], " ", TagBox[ - RowBox[{"w", "(", "1423", ")"}], + RowBox[{"w", "(", "24", ")"}], HoldForm]}], "+", RowBox[{"8", " ", SuperscriptBox["a", "2"], " ", TagBox[ - RowBox[{"w", "(", "1425", ")"}], + RowBox[{"w", "(", "26", ")"}], HoldForm]}], "-", RowBox[{"4", " ", "a", " ", TagBox[ - RowBox[{"w", "(", "1423", ")"}], + RowBox[{"w", "(", "24", ")"}], HoldForm], " ", TagBox[ - RowBox[{"w", "(", "1424", ")"}], + RowBox[{"w", "(", "25", ")"}], HoldForm]}], "+", SuperscriptBox[ TagBox[ - RowBox[{"w", "(", "1424", ")"}], + RowBox[{"w", "(", "25", ")"}], HoldForm], "2"], "+", "x"}], TraditionalForm]], "Output", CellTags->"Write2", - CellLabel->"Out[9]=", - CellID->1764933631] + CellLabel->"Out[158]="] }, Open ]], Cell[BoxData[ @@ -452,7 +436,7 @@ Cell[BoxData[ RowBox[{"tempfilename", ",", RowBox[{"r", "=", "t2"}]}], "]"}], ";"}]], "Input", CellTags->"Write2", - CellLabel->"In[10]:=", + CellLabel->"In[159]:=", CellID->2074608494], Cell[CellGroupData[{ @@ -468,23 +452,23 @@ Cell[BoxData[ ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], ",", "String"}], "]"}], "]"}]], "Input", CellTags->"Write2", - CellLabel->"In[11]:=", + CellLabel->"In[160]:=", CellID->1647925835], Cell[BoxData[ FormBox[ TagBox[ TagBox[GridBox[{ - {"\<\"w[1423] = (b + c\"\>"}, + {"\<\"w[24] = (b + c\"\>"}, {"\<\" );\"\>"}, - {"\<\"w[1424] = (b^2 + c^2\"\>"}, + {"\<\"w[25] = (b^2 + c^2\"\>"}, {"\<\" );\"\>"}, - {"\<\"w[1425] = (b^2 + b*c + c^2\"\>"}, + {"\<\"w[26] = (b^2 + b*c + c^2\"\>"}, {"\<\" );\"\>"}, - {"\<\"r = ( 4*a^4 + x - 8*a^3*HoldForm[w[1423]] - \ -4*a*HoldForm[w[1423]]*\"\>"}, - {"\<\" HoldForm[w[1424]] + HoldForm[w[1424]]^2 + \ -8*a^2*HoldForm[w[1425]]\"\>"}, + {"\<\"r = ( 4*a^4 + x - 8*a^3*HoldForm[w[24]] - \ +4*a*HoldForm[w[24]]*\"\>"}, + {"\<\" HoldForm[w[25]] + HoldForm[w[25]]^2 + \ +8*a^2*HoldForm[w[26]]\"\>"}, {"\<\" );\"\>"} }, GridBoxAlignment->{ @@ -501,8 +485,7 @@ Cell[BoxData[ Function[BoxForm`e$, TableForm[BoxForm`e$]]], TraditionalForm]], "Output", CellTags->"Write2", - CellLabel->"Out[11]//TableForm=", - CellID->342974912] + CellLabel->"Out[160]//TableForm="] }, Open ]], Cell[BoxData[ @@ -513,16 +496,14 @@ Cell[BoxData[ RowBox[{"$OperatingSystem", "===", "\"\\""}], ",", "\"\<:\>\"", ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], "]"}]], "Input", CellTags->"Write2", - CellLabel->"In[12]:=", + CellLabel->"In[161]:=", CellID->1908725708], -Cell["\<\ -This is how to write out the expression t2 in Fortran format.\ -\>", "Text", - CellTags->"Write2", - CellID->422363964], - -Cell[CellGroupData[{ +Cell[TextData[{ + "This is how to write out the expression ", + Cell[BoxData["t2"], "InlineFormula"], + " in Fortran format." +}], "Notes"], Cell[BoxData[ RowBox[{ @@ -531,24 +512,9 @@ Cell[BoxData[ RowBox[{"r", "=", "t2"}], ",", RowBox[{"FormatType", "\[Rule]", "FortranForm"}]}], "]"}], ";"}]], "Input", CellTags->"Write2", - CellLabel->"In[13]:=", + CellLabel->"In[162]:=", CellID->1416932507], -Cell[BoxData[ - FormBox[ - InterpretationBox[ - RowBox[{"\<\"FORTRAN generation WARNING!\\n\\t\\t\\t\\t\\tLine encountered \ -with more than 72 characters. Check line \"\>", "\[InvisibleSpace]", "3", - "\[InvisibleSpace]", "\<\" and \"\>", "\[InvisibleSpace]", "4"}], - SequenceForm[ - "FORTRAN generation WARNING!\n\t\t\t\t\tLine encountered with more than 72 \ -characters. Check line ", 3, " and ", 4], - Editable->False], TraditionalForm]], "Print", - CellTags->"Write2", - CellLabel->"During evaluation of In[13]:=", - CellID->1570874226] -}, Open ]], - Cell[CellGroupData[{ Cell[BoxData[ @@ -562,20 +528,19 @@ Cell[BoxData[ ",", "\"\<\>\""}], "]"}], "<>", "tempfilename"}], ",", "String"}], "]"}], "]"}]], "Input", CellTags->"Write2", - CellLabel->"In[14]:=", + CellLabel->"In[164]:=", CellID->2122464458], Cell[BoxData[ FormBox[ TagBox[ TagBox[GridBox[{ - {"\<\" w(1423)= b + c\"\>"}, - {"\<\" w(1424)= b^2 + c^2\"\>"}, - {"\<\" w(1425)= b^2 + b*c + c^2\"\>"}, - {"\<\" r = 4.*a^4 + x - 8.*a^3*HoldForm[w[1423]] - \ -4.*a*HoldForm[w[1423]]*\"\>"}, - {"\<\" HoldForm[w[1424]] + HoldForm[w[1424]]^2 + \ -8.*a^2*HoldForm[w[1425]]\"\>"}, + {"\<\" w(24)= b + c\"\>"}, + {"\<\" w(25)= b**2 + c**2\"\>"}, + {"\<\" w(26)= b**2 + b*c + c**2\"\>"}, + {"\<\" r = x + a**4*4D0 - a**3*8D0*w(24) - a*4D0*w(24)*w(25) + \ +\"\>"}, + {"\<\" & w(25)**2 + a**2*8D0*w(26)\"\>"}, {"\<\" \"\>"} }, GridBoxAlignment->{ @@ -592,8 +557,7 @@ Cell[BoxData[ Function[BoxForm`e$, TableForm[BoxForm`e$]]], TraditionalForm]], "Output", CellTags->"Write2", - CellLabel->"Out[14]//TableForm=", - CellID->1300360264] + CellLabel->"Out[164]//TableForm="] }, Open ]], Cell[BoxData[ @@ -608,8 +572,9 @@ Cell[BoxData[ RowBox[{"w", ",", "t", ",", "t2", ",", "r", ",", "tempfilename"}], "]"}], ";"}]], "Input", CellTags->"Write2", - CellLabel->"In[15]:=", + CellLabel->"In[165]:=", CellID->1809491647] +}, Open ]] }, Open ]], Cell[CellGroupData[{ @@ -673,12 +638,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{949, Automatic}, {Automatic, 178}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/WriteOut.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/WriteOut.nb index 42ed1c08a..16642c948 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/WriteOut.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/WriteOut.nb @@ -166,9 +166,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoop", ButtonNote->"OneLoop"], "." -}], "Text", - CellTags->"WriteOut", - CellID->917997182] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -254,12 +252,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{510, Automatic}, {Automatic, 108}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/WriteOutPaVe.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/WriteOutPaVe.nb index 5612c363e..474c077e1 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/WriteOutPaVe.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/WriteOutPaVe.nb @@ -176,9 +176,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/OneLoopSum", ButtonNote->"OneLoopSum"], "." -}], "Text", - CellTags->"WriteOutPaVe", - CellID->806653014] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -264,12 +262,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{689, Automatic}, {Automatic, 83}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/XYT.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/XYT.nb index 7f0fe536c..673aa65a8 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/XYT.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/XYT.nb @@ -253,12 +253,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{0, Automatic}, {Automatic, 31}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/ZeroMomentumInsertion.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/ZeroMomentumInsertion.nb index 512734397..863c96582 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/ZeroMomentumInsertion.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/ZeroMomentumInsertion.nb @@ -174,9 +174,7 @@ Cell[TextData[{ ButtonData:>"paclet:FeynCalc/ref/Twist2QuarkOperator", ButtonNote->"Twist2QuarkOperator"], "." -}], "Text", - CellTags->"ZeroMomentumInsertion", - CellID->237936766] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -262,12 +260,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{669, Automatic}, {Automatic, 81}}, Visible->True, PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, CellContext->"Global`", TrackCellChangeTimes->False, -FrontEndVersion->"10.3 for Linux x86 (64-bit) (October 9, 2015)", +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", CharacterEncoding -> "UTF-8"] ] + diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Zeta10.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Zeta10.nb new file mode 100644 index 000000000..f92fa3acf --- /dev/null +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Zeta10.nb @@ -0,0 +1,316 @@ +Notebook[{ +Cell[TextData[{ + "New in: ", + Cell["9.3", "HistoryData", + CellTags->"New"], + " | Modified in: ", + Cell[" ", "HistoryData", + CellTags->"Modified"], + " | Obsolete in: ", + Cell[" ", "HistoryData", + CellTags->"Obsolete"], + " | Excised in: ", + Cell[" ", "HistoryData", + CellTags->"Excised"] +}], "History", + CellID->1247902091], + +Cell[CellGroupData[{ + +Cell["Categorization", "CategorizationSection", + CellID->1122911449], + +Cell["Symbol", "Categorization", + CellLabel->"Entity Type", + CellID->686433507], + +Cell["FeynCalc", "Categorization", + CellLabel->"Paclet Name", + CellID->605800465], + +Cell["FeynCalc`", "Categorization", + CellLabel->"Context", + CellID->468444828], + +Cell["FeynCalc/ref/Zeta10", "Categorization", + CellLabel->"URI"] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Keywords", "KeywordsSection", + CellID->477174294], + +Cell["XXXX", "Keywords", + CellID->1164421360] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Syntax Templates", "TemplatesSection", + CellID->1872225408], + +Cell[BoxData[""], "Template", + CellLabel->"Additional Function Template", + CellID->1562036412], + +Cell[BoxData[""], "Template", + CellLabel->"Arguments Pattern", + CellID->158391909], + +Cell[BoxData[""], "Template", + CellLabel->"Local Variables", + CellID->1360575930], + +Cell[BoxData[""], "Template", + CellLabel->"Color Equal Signs", + CellID->793782254] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Details", "DetailsSection", + CellID->307771771], + +Cell["XXXX", "Details", + CellLabel->"Lead", + CellID->670882175], + +Cell["XXXX", "Details", + CellLabel->"Developers", + CellID->350963985], + +Cell["XXXX", "Details", + CellLabel->"Authors", + CellID->8391405], + +Cell["XXXX", "Details", + CellLabel->"Feature Name", + CellID->3610269], + +Cell["XXXX", "Details", + CellLabel->"QA", + CellID->401364205], + +Cell["XXXX", "Details", + CellLabel->"DA", + CellID->350204745], + +Cell["XXXX", "Details", + CellLabel->"Docs", + CellID->732958810], + +Cell["XXXX", "Details", + CellLabel->"Features Page Notes", + CellID->222905350], + +Cell["XXXX", "Details", + CellLabel->"Comments", + CellID->240026365] +}, Closed]], + +Cell[CellGroupData[{ + +Cell["Zeta10", "ObjectName", + CellID->1224892054], + +Cell[TextData[{ + Cell[" ", "ModInfo"], + Cell[BoxData[ + RowBox[{"Zeta10", "[", "]"}]], "InlineFormula"], + " \[LineSeparator]denotes Zeta[10]" +}], "Usage", + CellID->982511436], + +Cell["XXXX", "Notes", + CellID->1067943069] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Tutorials", "TutorialsSection", + CellID->250839057], + +Cell["XXXX", "Tutorials", + CellID->341631938] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Demonstrations", "RelatedDemonstrationsSection", + CellID->1268215905], + +Cell["XXXX", "RelatedDemonstrations", + CellID->1129518860] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Related Links", "RelatedLinksSection", + CellID->1584193535], + +Cell["XXXX", "RelatedLinks", + CellID->1038487239] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["See Also", "SeeAlsoSection", + CellID->1255426704], + +Cell["XXXX", "SeeAlso", + CellID->929782353] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More About", "MoreAboutSection", + CellID->38303248], + +Cell["XXXX", "MoreAbout", + CellID->1665078683] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[GridBox[{ + { + StyleBox["Examples", "PrimaryExamplesSection"], + ButtonBox[ + RowBox[{ + RowBox[{"More", " ", "Examples"}], " ", "\[RightTriangle]"}], + BaseStyle->"ExtendedExamplesLink", + ButtonData:>"ExtendedExamples"]} + }], + $Line = 0; Null]], "PrimaryExamplesSection", + CellID->880084151], + +Cell[CellGroupData[{ + +Cell[BoxData["Zeta10"], "Input", + CellLabel->"In[195]:=", + CellID->200433303], + +Cell[BoxData[ + FormBox[ + RowBox[{"\[Zeta]", "(", "10", ")"}], TraditionalForm]], "Output", + CellLabel->"Out[195]=", + CellID->1818507146] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"N", "[", + RowBox[{"Zeta", "[", "10", "]"}], "]"}]], "Input", + CellLabel->"In[196]:=", + CellID->1700915442], + +Cell[BoxData[ + FormBox["1.000994575127818`", TraditionalForm]], "Output", + CellLabel->"Out[196]=", + CellID->1418962907] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SimplifyPolyLog", "[", + RowBox[{"Pi", "^", "10"}], "]"}]], "Input", + CellLabel->"In[197]:=", + CellID->1737149642], + +Cell[BoxData[ + FormBox[ + RowBox[{"93555", " ", + RowBox[{"\[Zeta]", "(", "10", ")"}]}], TraditionalForm]], "Output", + CellLabel->"Out[197]=", + CellID->1066570387] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Conjugate", "[", "Zeta10", "]"}]], "Input", + CellLabel->"In[206]:=", + CellID->598568302], + +Cell[BoxData[ + FormBox[ + RowBox[{"\[Zeta]", "(", "10", ")"}], TraditionalForm]], "Output", + CellLabel->"Out[206]=", + CellID->1293514538] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["More Examples", "ExtendedExamplesSection", + CellTags->"ExtendedExamples", + CellID->1854448968], + +Cell[BoxData[ + InterpretationBox[Cell["Scope", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1293636265], + +Cell[BoxData[ + InterpretationBox[Cell["Generalizations & Extensions", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1020263627], + +Cell[CellGroupData[{ + +Cell[BoxData[ + InterpretationBox[Cell["Options", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2061341341], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1757724783], + +Cell[BoxData[ + InterpretationBox[Cell["XXXX", "ExampleSubsection"], + $Line = 0; Null]], "ExampleSubsection", + CellID->1295379749] +}, Closed]], + +Cell[BoxData[ + InterpretationBox[Cell["Applications", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->258228157], + +Cell[BoxData[ + InterpretationBox[Cell["Properties & Relations", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->2123667759], + +Cell[BoxData[ + InterpretationBox[Cell["Possible Issues", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1305812373], + +Cell[BoxData[ + InterpretationBox[Cell["Interactive Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->1653164318], + +Cell[BoxData[ + InterpretationBox[Cell["Neat Examples", "ExampleSection"], + $Line = 0; Null]], "ExampleSection", + CellID->589267740] +}, Open ]] +}, +WindowSize->{700, 770}, +WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +PrivateNotebookOptions->{"FileOutlineCache"->False}, +CreateCellID->False, +CellContext->"Global`", +TrackCellChangeTimes->False, +FrontEndVersion->"10.3 for Linux x86 (64-bit) (December 10, 2015)", +StyleDefinitions->FrontEnd`FileName[{"Wolfram"}, "FunctionPageStyles.nb", + CharacterEncoding -> "UTF-8"] +] diff --git a/FeynCalc/DocSource/English/ReferencePages/Symbols/Zeta2.nb b/FeynCalc/DocSource/English/ReferencePages/Symbols/Zeta2.nb index bad2fe41b..757310129 100644 --- a/FeynCalc/DocSource/English/ReferencePages/Symbols/Zeta2.nb +++ b/FeynCalc/DocSource/English/ReferencePages/Symbols/Zeta2.nb @@ -117,8 +117,7 @@ Cell["Zeta2", "ObjectName", Cell[TextData[{ Cell[" ", "ModInfo"], Cell[BoxData["Zeta2"], "InlineFormula"], - " \[LineSeparator]", - "denotes Zeta[2]. N[Zeta[2]] evaluates to N[Zeta[2]]." + " \[LineSeparator]denotes Zeta[2]." }], "Usage", CellID->982511436], @@ -159,15 +158,12 @@ Cell["See Also", "SeeAlsoSection", CellID->1255426704], Cell[TextData[{ - "See also: ", ButtonBox["SimplifyPolyLog", BaseStyle->"Link", ButtonData:>"paclet:FeynCalc/ref/SimplifyPolyLog", ButtonNote->"SimplifyPolyLog"], "." -}], "Text", - CellTags->"Zeta2", - CellID->798811969] +}], "SeeAlso"] }, Open ]], Cell[CellGroupData[{ @@ -240,6 +236,18 @@ Cell[BoxData[ CellTags->"Zeta2", CellLabel->"Out[3]=", CellID->494970297] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Conjugate", "[", "Zeta2", "]"}]], "Input", + CellLabel->"In[202]:="], + +Cell[BoxData[ + FormBox[ + RowBox[{"\[Zeta]", "(", "2", ")"}], TraditionalForm]], "Output", + CellLabel->"Out[202]="] }, Open ]] }, Open ]], @@ -304,12 +312,14 @@ Cell[BoxData[ }, Open ]] }, WindowSize->{700, 770}, -WindowMargins->{{-10, Automatic}, {Automatic, -8}}, +WindowMargins->{{851, Automatic}, 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"Text", - CellChangeTimes->{{3.6643599620756283`*^9, 3.664359981894837*^9}}, CellID->1534169418], Cell[TextData[{ @@ -150,9 +129,6 @@ Cell[TextData[{ RowBox[{"etc", "."}]}], TraditionalForm]]], " (abbreviations in parentheses) are:" }], "Text", - CellChangeTimes->{{3.6643600683581676`*^9, 3.664360068649622*^9}, { - 3.664360103261983*^9, 3.6643601038697844`*^9}, {3.664360202389187*^9, - 3.664360241341753*^9}}, CellID->1157525339], Cell[TextData[{ @@ -197,8 +173,6 @@ Cell[TextData[{ ButtonData->"paclet:FeynCalc/ref/SP"], " (scalar product)" }], "Text", - CellChangeTimes->{{3.664360245994879*^9, 3.664360349068862*^9}, { - 3.664360541716607*^9, 3.664360657659786*^9}}, CellID->757206658], Cell["Some functions for manipulations are:", "Text", @@ -274,8 +248,6 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/ApartFF"] }], "Text", - CellChangeTimes->{{3.6643607339108057`*^9, 3.6643608053223352`*^9}, { - 3.6643609153756123`*^9, 3.664361026897187*^9}}, CellID->833014432], 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Some are very \ special ones (e.g. for tools for 2-loop QCD diagrams originating in twist-2 \ OPE), some are still experimental.\ \>", "Text", - CellChangeTimes->{3.66436201708527*^9, 3.664362049077449*^9, - 3.6643620934212017`*^9}, CellID->1833132382], Cell[TextData[{ @@ -377,8 +339,6 @@ Cell[TextData[{ BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/ToLarin"] }], "Text", - CellChangeTimes->{{3.664362246340498*^9, 3.6643622469502087`*^9}, - 3.664362278643958*^9}, CellTags->"intro", CellID->716203363], @@ -400,8 +360,6 @@ correcting a minor misprint in 14) of Appendix 7 from ", BaseStyle->"Link", ButtonData->"paclet:FeynCalc/ref/Integrate2"] }], "SmallText", - CellChangeTimes->{{3.664361204185831*^9, 3.664361208865102*^9}, { - 3.6643612396572037`*^9, 3.664361239657754*^9}}, CellTags->{"intro", "introfoot"}, CellID->721081683] }, Open ]], @@ -421,7 +379,6 @@ Cell[TextData[{ FontSlant->"Italic"], " installation tree, which is (evaluate the following command)" }], "Text", - CellChangeTimes->{{3.6643623788602753`*^9, 3.664362402803527*^9}}, CellID->846823627], Cell[CellGroupData[{ @@ -431,14 +388,12 @@ Cell[BoxData[ RowBox[{"{", RowBox[{"$UserBaseDirectory", ",", "\"\\""}], "}"}], "]"}]], "Input", - CellChangeTimes->{3.664362389555352*^9}, CellLabel->"In[26]:=", CellID->1006438652], Cell[BoxData[ FormBox["\<\"/home/vs/.Mathematica/Applications\"\>", TraditionalForm]], "Output", - CellChangeTimes->{3.664362404638443*^9}, CellLabel->"Out[26]=", CellID->205843633] }, Open ]] @@ -455,7 +410,6 @@ automatic loading of FeynCalc on every ", FontSlant->"Italic"], " startup." }], "Text", - CellChangeTimes->{{3.664362421043448*^9, 3.664362449877076*^9}}, CellID->469196418], Cell[TextData[{ @@ -472,7 +426,6 @@ objects. This can be done by clicking on the ", FontWeight->"Bold"], "." }], "Text", - CellChangeTimes->{{3.664362488980373*^9, 3.664362627786993*^9}}, CellID->434623157], Cell[CellGroupData[{ @@ -483,23 +436,19 @@ Cell[TextData[{ FontWeight->"Bold"], " and don't want to be bothered, just uncomment the line" }], "Text", - CellChangeTimes->{{3.664362632875*^9, 3.66436269723413*^9}}, CellID->13342743], Cell[BoxData[ RowBox[{"(*", RowBox[{ RowBox[{"$FCAdvice", " ", "=", " ", "True"}], ";"}], "*)"}]], "Input", - CellChangeTimes->{{3.6643627023263273`*^9, 3.6643627051861353`*^9}}, CellID->2016141554] }, Open ]], Cell["in FCConfig.m.", "Text", - CellChangeTimes->{{3.664362707633235*^9, 3.664362723977644*^9}}, CellID->491195527], Cell["", "Text", - CellChangeTimes->{{3.664362488980373*^9, 3.6643625214234743`*^9}}, CellID->351638376], Cell[TextData[{ @@ -515,8 +464,6 @@ Cell[TextData[{ FontWeight->"Bold"], ", or by evaluating" }], "Text", - CellChangeTimes->{{3.664362488980373*^9, 3.664362521421033*^9}, - 3.66436257333941*^9}, CellID->430968534] }, Open ]], @@ -532,55 +479,15 @@ The directory \"FeynCalc\" contains various files and subdirectories \ belonging to third-party packages which are not necessary to run 'standard' \ FeynCalc calculations and which do not use the autoloading conventions of \ FeynCalc. These packages are not initialized by default when starting \ -FeynCalc. Loading them can be switched on and off by setting appropiate \ +FeynCalc. 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Mertig and R. Scharf and published in ", ButtonNote->"http://arxiv.org/abs/hep-ph/9801383"], "." }], "Text", - CellChangeTimes->{{3.664362892153569*^9, 3.664362923521014*^9}, { - 3.664362962969199*^9, 3.664363016968184*^9}}, CellID->1972678903], Cell[CellGroupData[{ @@ -606,12 +511,12 @@ Cell[CellGroupData[{ Cell["\<\ TARCER is distributed with FeynCalc. 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-(* :Title: EWElectronMuonNeutrinoToMuonElectronNeutrinoTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the scattering cross section for an electron and - a muon neutrino going to a muon and an electro neutrino in - Electroweak theory at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the scattering cross section for an electron and -a muon neutrino going to a muon and an electro neutrino in Electroweak theory at tree level."]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< {Lorentz, UnitaryLorentz}]; - - -topElNuScattering = CreateTopologies[0, 2 -> 2]; -diagsElNuScatteringTree = InsertFields[topElNuScattering, {F[2, - {1}],F[1, {2}]} -> {F[1,{1}],F[2,{2}]}, InsertionLevel -> {Classes}, - Model -> {SM, UnitarySM},GenericModel->{Lorentz, UnitaryLorentz}]; -Paint[diagsElNuScatteringTree, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->False]; - - -(* ::Section:: *) -(*Obtain the amplitude*) - - -ampElNuScatteringTree=FCFAConvert[CreateFeynAmp[diagsElNuScatteringTree], -List->False,SMP->True,ChangeDimension->4, IncomingMomenta->{p,q1},OutgoingMomenta->{q2,k}, -FinalSubstitutions->{SMP["e"]->Sqrt[8/Sqrt[2] SMP["G_F"] SMP["m_W"]^2SMP["sin_W"]^2]}]//Contract - - -(* ::Section:: *) -(*Setup the kinematics*) - - -FCClearScalarProducts[]; -SetMandelstam[s,t,u,p,q1,-q2,-k,SMP["m_e"],0,0,SMP["m_mu"]]; - - -(* ::Section:: *) -(*Obtain squared amplitude for the unpolarized process*) - - -(* ::Text:: *) -(*There is no polarization averaging for neutrinos here, as right handed neutrinos do not interact*) - - -sqElNuScatteringTree=ampElNuScatteringTree FCRenameDummyIndices[ComplexConjugate[ampElNuScatteringTree]]// -FermionSpinSum[#,ExtraFactor->1/2]&//ReplaceAll[#, DiracTrace :> Tr]&//Contract//Factor2 - - -(* ::Text:: *) -(*In the following we neglect the momentum in the W-propagator as compared to the W-mass. This is a very good approximation at low energies, as then (k-q1)^2 <= m_mu^2 << m_W^2.*) - - -sqElNuScatteringTree2=(FCE[sqElNuScatteringTree]/.{k-q1->0})//PropagatorDenominatorExplicit//Factor2 - - -(* ::Section:: *) -(*Total cross-section*) - - -(* ::Text:: *) -(*The total cross-section *) - - -prefac=4Pi/(64 Pi^2 s) Sqrt[(s-SMP["m_mu"]^2)^2]/Sqrt[(s-SMP["m_e"]^2)^2] - - -crossSectionTotal=sqElNuScatteringTree2*prefac//PowerExpand - - -(* ::Section:: *) -(*Check with the literature*) - - -crossSectionTotalKnown=(SMP["G_F"]^2*(s - SMP["m_mu"]^2)^2)/(Pi*s); -Print["Check with Greiner and Mueller, Gauge Theory of Weak Interactions, Chapter 3:", - If[Simplify[crossSectionTotal-crossSectionTotalKnown]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/EW/EWHiggsToTwoFermionsTree.m b/FeynCalc/Examples/EW/EWHiggsToTwoFermionsTree.m deleted file mode 100644 index 664dee9a6..000000000 --- a/FeynCalc/Examples/EW/EWHiggsToTwoFermionsTree.m +++ /dev/null @@ -1,90 +0,0 @@ -(* ::Package:: *) - -(* :Title: EWHiggsToTwoFermionsTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the total decay rate for the decay - of a Higgs into 2 fermions in Electroweak Theory at tree level. *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the total decay rate for the decay of a Higgs into 2 fermions in Electroweak Theory at tree level."]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2], {S[1]} -> {F[2,{l}],-F[2,{l}]}, -InsertionLevel -> {Classes}]; -Paint[diagsHiggsToLeptonsTree,ColumnsXRows->{1,1},Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -diagsHiggsToQuarksTree = InsertFields[CreateTopologies[0,1 -> 2], {S[1]} -> {F[3,{l}],-F[3,{l}]}, -InsertionLevel -> {Classes}]; -Paint[diagsHiggsToQuarksTree,ColumnsXRows->{1,1},Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -FCClearScalarProducts[]; -SP[p1,p1]=SMP["m_l"]^2; -SP[k1,k1]=SMP["m_q"]^2; -SP[p2,p2]=SMP["m_l"]^2; -SP[k2,k2]=SMP["m_q"]^2; -SP[pH,pH]=SMP["m_H"]^2; -SP[p1,p2]=(SMP["m_H"]^2-2 SMP["m_l"]^2)/2; -SP[k1,k2]=(SMP["m_H"]^2-2 SMP["m_q"]^2)/2; - -ampdiagsHiggsToLeptonsTree=FCFAConvert[CreateFeynAmp[diagsHiggsToLeptonsTree],IncomingMomenta->{pH},OutgoingMomenta->{p1,p2},List->False,ChangeDimension->4, -DropSumOver->True,SMP->True,UndoChiralSplittings->True,FinalSubstitutions->{MLE[l]->SMP["m_l"]}]//Contract//DotSimplify - -ampdiagsHiggsToQuarksTree=FCFAConvert[CreateFeynAmp[diagsHiggsToQuarksTree],IncomingMomenta->{pH},OutgoingMomenta->{k1,k2},List->False,ChangeDimension->4, -DropSumOver->True,SMP->True,UndoChiralSplittings->True,FinalSubstitutions->{MQU[l]->SMP["m_q"]}]//Contract//DotSimplify - - -(* ::Section:: *) -(*Calculate the total decay rates*) - - -ampSqLeptons=ampdiagsHiggsToLeptonsTree*ComplexConjugate[ampdiagsHiggsToLeptonsTree]//FermionSpinSum//ReplaceAll[#,DiracTrace->Tr]&//Simplify -ampSqQuarks=ampdiagsHiggsToQuarksTree*ComplexConjugate[ampdiagsHiggsToQuarksTree]//FermionSpinSum//ReplaceAll[#,DiracTrace->Tr]&//SUNSimplify[#,SUNNToCACF->False]&//Simplify - - -$Assumptions={SMP["m_H"]>0,SMP["m_l"]>0}; -phaseSpacePrefactor[m_]:=1/(16 Pi SMP["m_H"])Sqrt[1-4 m^2 / SMP["m_H"]^2]; -decayRateTotalLeptonsTree=phaseSpacePrefactor[SMP["m_l"]] ampSqLeptons// -ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&//FullSimplify//Factor2 - -decayRateTotalQuarksTree=phaseSpacePrefactor[SMP["m_q"]]*ampSqQuarks// -ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&//FullSimplify//Factor2 - - -decayRateTotalLeptonsTreeKnown=(AlphaFS SMP["m_H"])/(8 SMP["sin_W"]^2)( SMP["m_l"]^2/SMP["m_W"]^2 (1- 4 SMP["m_l"]^2/SMP["m_H"]^2)^(3/2)); -decayRateTotalQuarksTreeKnown=SUNN(decayRateTotalLeptonsTreeKnown/.SMP["m_l"]->SMP["m_q"]); - -Print["Check with Peskin and Schroeder, Final Project III, part (a): ", - If[(Simplify[decayRateTotalLeptonsTree-decayRateTotalLeptonsTreeKnown]===0) && - (Simplify[decayRateTotalQuarksTree-decayRateTotalQuarksTreeKnown]===0), "CORRECT.", "!!! WRONG !!!"]]; - diff --git a/FeynCalc/Examples/EW/EWHiggsToWPlusWMinusTree.m b/FeynCalc/Examples/EW/EWHiggsToWPlusWMinusTree.m deleted file mode 100644 index 5ffaeadee..000000000 --- a/FeynCalc/Examples/EW/EWHiggsToWPlusWMinusTree.m +++ /dev/null @@ -1,78 +0,0 @@ -(* ::Package:: *) - -(* :Title: EWHiggsToWPlusWMinusTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the total decay rate for the decay - of a Higgs into W^+ W^- in Electroweak Theory at tree level. *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the total decay rate for the decay of a Higgs into W^+ W^- in Electroweak Theory at tree level."]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2], {S[1]} -> {-V[3],V[3]}, -InsertionLevel -> {Classes}]; -Paint[diagsHiggsToWPlusWMinusTree,ColumnsXRows->{1,1},Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -FCClearScalarProducts[]; -SP[k1,k1]=SMP["m_W"]^2; -SP[k2,k2]=SMP["m_W"]^2; -SP[pH,pH]=SMP["m_H"]^2; -SP[k1,k2]=(SMP["m_H"]^2-2 SMP["m_W"]^2)/2; - -ampHiggsToWPlusWMinusTree=FCFAConvert[CreateFeynAmp[diagsHiggsToWPlusWMinusTree],IncomingMomenta->{pH},OutgoingMomenta->{k1,k2},List->False,ChangeDimension->4, -DropSumOver->True,SMP->True,UndoChiralSplittings->True]//Contract//DotSimplify - - -(* ::Section:: *) -(*Calculate the total decay rate*) - - -ampSq=ampHiggsToWPlusWMinusTree*ComplexConjugate[ampHiggsToWPlusWMinusTree]//DoPolarizationSums[#,k1]&//DoPolarizationSums[#,k2]&//Simplify - - -$Assumptions={SMP["m_H"]>0,SMP["m_W"]>0}; -phaseSpacePrefactor[m_]:=1/(16 Pi SMP["m_H"])Sqrt[1-4 m^2 / SMP["m_H"]^2]; -decayRateTotalTree=phaseSpacePrefactor[SMP["m_W"]] ampSq// -ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&//FullSimplify - - -(decayRateTotalTree/.SMP["m_W"]^2-> h[SMP["m_W"]^2/SMP["m_H"]^2]SMP["m_H"]^2/. -SMP["m_W"]^4-> h[SMP["m_W"]^4/SMP["m_H"]^4]SMP["m_H"]^4)//FullSimplify//ReplaceAll[#,h->Identity]& - - -decayRateTotalTreeKnown= SMP["g_W"]^2/(64 Pi) SMP["m_H"]^3/SMP["m_W"]^2 Sqrt[1- 4 SMP["m_W"]^2/SMP["m_H"]^2](1- -4 SMP["m_W"]^2/SMP["m_H"]^2 + 12 SMP["m_W"]^4/SMP["m_H"]^4); -Print["Check with Gunion, Haber, Kane, Dawson, Higgs Hunter Guide, Eq 2.11: ", - If[Simplify[decayRateTotalTree- - (decayRateTotalTreeKnown//ReplaceAll[#,SMP["g_W"]-> SMP["e"]/SMP["sin_W"]]&//ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&)]===0, - "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/EW/EWHiggsToZZTree.m b/FeynCalc/Examples/EW/EWHiggsToZZTree.m deleted file mode 100644 index 1652acd09..000000000 --- a/FeynCalc/Examples/EW/EWHiggsToZZTree.m +++ /dev/null @@ -1,80 +0,0 @@ -(* ::Package:: *) - -(* :Title: EWHiggsToZZTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the total decay rate for the decay - of a Higgs into Z^0 Z^0 in Electroweak Theory at tree level. *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the total decay rate for the decay of a Higgs into Z^0 Z^0 in Electroweak Theory at tree level."]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2], {S[1]} -> {V[2],V[2]}, -InsertionLevel -> {Classes}]; -Paint[diagsHiggsToZZTree,ColumnsXRows->{1,1},Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -FCClearScalarProducts[]; -SP[k1,k1]=SMP["m_Z"]^2; -SP[k2,k2]=SMP["m_Z"]^2; -SP[pH,pH]=SMP["m_H"]^2; -SP[k1,k2]=(SMP["m_H"]^2-2 SMP["m_Z"]^2)/2; - -ampHiggsToZZTree=FCFAConvert[CreateFeynAmp[diagsHiggsToZZTree],IncomingMomenta->{pH},OutgoingMomenta->{k1,k2},List->False,ChangeDimension->4, -DropSumOver->True,SMP->True,UndoChiralSplittings->True]//Contract//DotSimplify - - -(* ::Section:: *) -(*Calculate the total decay rate*) - - -ampSq=ampHiggsToZZTree*ComplexConjugate[ampHiggsToZZTree]//DoPolarizationSums[#,k1]&//DoPolarizationSums[#,k2]&//Simplify - - -$Assumptions={SMP["m_H"]>0,SMP["m_W"]>0}; -symmetryFactor=1/2; -phaseSpacePrefactor[m_]:=1/(16 Pi SMP["m_H"])Sqrt[1-4 m^2 / SMP["m_H"]^2]; -decayRateTotalTree=symmetryFactor phaseSpacePrefactor[SMP["m_Z"]] ampSq// -ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&//FullSimplify - - -(decayRateTotalTree/.SMP["m_Z"]^2-> h[SMP["m_Z"]^2/SMP["m_H"]^2]SMP["m_H"]^2/. -SMP["m_Z"]^4-> h[SMP["m_Z"]^4/SMP["m_H"]^4]SMP["m_H"]^4)//FullSimplify//ReplaceAll[#,h->Identity]& - - -decayRateTotalTreeKnown= SMP["g_W"]^2/(128 Pi) SMP["m_H"]^3/SMP["m_W"]^2 Sqrt[1- 4 SMP["m_Z"]^2/SMP["m_H"]^2](1- -4 SMP["m_Z"]^2/SMP["m_H"]^2 + 12 SMP["m_Z"]^4/SMP["m_H"]^4); -Print["Check with Gunion, Haber, Kane, Dawson, Higgs Hunter Guide, Eq 2.10: ", - If[(Simplify[decayRateTotalTree- - (decayRateTotalTreeKnown//ReplaceAll[#,SMP["g_W"]-> SMP["e"]/SMP["sin_W"]]&//ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&)]// - ReplaceRepeated[#,SMP["cos_W"] -> SMP["m_W"]/SMP["m_Z"]]&)===0, - "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/EW/EWMuonDecayTree.m b/FeynCalc/Examples/EW/EWMuonDecayTree.m deleted file mode 100644 index c7a535d8e..000000000 --- a/FeynCalc/Examples/EW/EWMuonDecayTree.m +++ /dev/null @@ -1,160 +0,0 @@ -(* ::Package:: *) - -(* :Title: EWMuonDecayTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the total decay rate for muon going into an - electron, an electron anitnueutrino and a muon neutrino in - Electroweak Theory at tree level. *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the total decay rate for muon going into an electron, -an electron anitnueutrino and a muon neutrino in Electroweak Theory at tree level."]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< {Lorentz, UnitaryLorentz}]; - - -topMuonDecayTree = CreateTopologies[0, 1 -> 3]; -diagsMuonDecayTree = InsertFields[topMuonDecayTree, {F[2, {2}]} -> {F[2, - {1}],-F[1,{1}],F[1,{2}]}, InsertionLevel -> {Classes}, - Model -> {SM, UnitarySM},GenericModel->{Lorentz, UnitaryLorentz}]; -Paint[diagsMuonDecayTree, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->False]; - - -(* ::Section:: *) -(*Obtain the amplitude*) - - -ampMuonDecayTree=FCFAConvert[CreateFeynAmp[diagsMuonDecayTree,Truncated -> False],List->False,SMP->True,ChangeDimension->4, -IncomingMomenta->{p},OutgoingMomenta->{k,q1,q2}, -FinalSubstitutions->{SMP["e"]->Sqrt[8/Sqrt[2] SMP["G_F"] SMP["m_W"]^2SMP["sin_W"]^2]}]//Contract - - -(* ::Section:: *) -(*Setup the kinematics*) - - -FCClearScalarProducts[] -SP[k,k]=SMP["m_e"]^2; -SP[q1,q1]=0; -SP[q2,q2]=0; - - -(* ::Section:: *) -(*Obtain squared amplitude for the unpolarized process*) - - -(* ::Text:: *) -(*We average over the polarizations of the muon, hence the additional factor 1/2*) - - -sqAmpMuonDecayTree = ampMuonDecayTree ComplexConjugate[FCRenameDummyIndices[ampMuonDecayTree]]// -FermionSpinSum[#,ExtraFactor -> 1/2]&//ReplaceAll[#, DiracTrace :> Tr]&//Contract//Factor2 - - -(* ::Text:: *) -(*In the following we neglect the momentum in the W-propagator as compared to the W-mass. This is a very good approximation at low energies, as then (k+q1)^2 = (p-q2)^2 <= m_mu^2 << m_W^2.*) - - -sqAmpMuonDecayTree2=(FCE[sqAmpMuonDecayTree]/.{k+q1->0})//PropagatorDenominatorExplicit - - -(* ::Section:: *) -(*Total decay rate for the unpolarized process*) - - -(* ::Text:: *) -(*To compute the total decay rate, we follow the calculation done in Okun, "Leptons and Quarks", Chapter 3. The differential decay rate is given by*) -(**) -(*d \[CapitalGamma] = 1/(2M) d^3 k / ((2\[Pi])^3 2 k^0) d^3 q1 / ((2\[Pi])^3 2 q1^0) d^3 q2 / ((2\[Pi])^3 2 q2^0) (2\[Pi])^4 \[Delta]^4 (q-q1-q2) sqAmpMuonDecayTree2 with q = p-k*) - - -prefac=(2SMP["m_mu"] (2Pi)^5 8)^-1; -diffDecayRate = prefac d3q1/En[q1] d3q2/En[q2] d3k/En[k] delta4[q-q1-q2] sqAmpMuonDecayTree2 - - -(* ::Text:: *) -(*First we reduce the tensor integrals in q1 to q2 to scalar ones by using tensor decomposition*) - - -q1q2[mu_,nu_]:=ReplaceAll[Tdec[{{q1x,mu},{q2x,nu}},{q},List->False,Dimension->4], -{SP[q1x,q2x]->SP[q,q]/2, SP[q,q1x|q2x]->SP[q,q]/2}]; - - -q1q2[mu,nu]//Factor2 - - -diffDecayRate1=Uncontract[diffDecayRate,q1,q2,Pair->All] - - -diffDecayRate2=((diffDecayRate1//FCE)/. FV[q1,mu_]FV[q2,nu_]:>q1q2[mu,nu])//Contract//FCE - - -(* ::Text:: *) -(*Integrating over q1 and q2 (in the rest frame of the decaying muon) we get rid of the Dirac delta and simplify the integral*) - - -diffDecayRate3=diffDecayRate2/.{d3q2 delta4[q-q1-q2]-> delta[En[q]-2En[q1]]}/.{En[q2]->En[q1]}/. -{d3q1-> 4Pi dq10 En[q1]^2}/.{dq10 delta[En[q]-2En[q1]]->1/2} - - -(* ::Text:: *) -(*Then we use the kinematics of the process, to simplify things even further. Here we also use the fact that the mass of the *) -(*electron is very small as compared to its energy*) - - -diffDecayRate4=(diffDecayRate3//.{SP[q,p]->SMP["m_mu"]^2-SMP["m_mu"] En[k],SP[k,q]|SP[p,k]-> SMP["m_mu"] En[k], -SP[q,q]-> SMP["m_mu"]^2-2 SMP["m_mu"]En[k]})//Simplify - - -(* ::Text:: *) -(*Next we trade d3k for dOmega d k^0 (k^0)^2 and introduce Eps that is defined as 2 k^0/ m_mu*) - - -diffDecayRate5=(diffDecayRate4/.d3k-> dk0 En[k]^2 4Pi /. En[k]-> Eps SMP["m_mu"]/2/. -dk0-> dEps SMP["m_mu"]/2)//Factor2 - - -(* ::Text:: *) -(*Integrating over Eps we arrive to the final result*) - - -decayRateTotal=Integrate[diffDecayRate5/.dEps->1,{Eps,0,1}] - - -(* ::Section:: *) -(*Check with the literature*) - - -decayRateTotalKnown=(SMP["G_F"]^2*SMP["m_mu"]^5)/(192*Pi^3); -Print["Check with the Okun, Chapter 3.2:", - If[Simplify[decayRateTotal-decayRateTotalKnown]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/EW/EWNeutrinoDownQuarkToLeptonUpQuarkTree.m b/FeynCalc/Examples/EW/EWNeutrinoDownQuarkToLeptonUpQuarkTree.m deleted file mode 100644 index f0821f532..000000000 --- a/FeynCalc/Examples/EW/EWNeutrinoDownQuarkToLeptonUpQuarkTree.m +++ /dev/null @@ -1,128 +0,0 @@ -(* ::Package:: *) - -(* :Title: EWNeutrinoDownQuarkToLeptonUpQuarkTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the scattering cross section for a neutrino and - a down-type quark going to the corresponding lepton and up-type q - uark in Electroweak theory at tree level. *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the scattering cross section for a neutrino and -a down-type quark going to the corresponding lepton and up-type quark in Electroweak theory at tree level."]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< {Lorentz, UnitaryLorentz}]; - - -topQuarkNuScattering = CreateTopologies[0, 2 -> 2]; -diagsQuarkNuScatteringTree = InsertFields[topQuarkNuScattering, -{F[4,{1,1}],F[1,{2}]} -> {F[3,{1,1}],F[2,{2}]}, InsertionLevel -> {Classes}, -Model -> {SM, UnitarySM},GenericModel->{Lorentz, UnitaryLorentz}]; -Paint[diagsQuarkNuScatteringTree, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->False]; - - -(* ::Section:: *) -(*Obtain the amplitude*) - - -ampQuarkNuScatteringTree=FCFAConvert[CreateFeynAmp[diagsQuarkNuScatteringTree],DropSumOver->True, -List->False,SMP->True,ChangeDimension->4, IncomingMomenta->{pd,pn},OutgoingMomenta->{pu,pl}, -FinalSubstitutions->{SMP["e"]->Sqrt[8/Sqrt[2] SMP["G_F"] SMP["m_W"]^2SMP["sin_W"]^2], -CKM[1,1]->SMP[{"V_ud",I}]}]//Contract - - -(* ::Section:: *) -(*Setup the kinematics*) - - -FCClearScalarProducts[]; -SetMandelstam[s,t,u,pd,pn,-pu,-pl,SMP["m_d"],0,SMP["m_u"],SMP["m_l"]]; - - -(* ::Section:: *) -(*Obtain squared amplitude for the unpolarized process*) - - -(* ::Text:: *) -(*There is no polarization averaging for neutrinos here, as right handed neutrinos do not interact*) - - -sqAmpQuarkNuScatteringTree=ampQuarkNuScatteringTree FCRenameDummyIndices[ComplexConjugate[ampQuarkNuScatteringTree]]// -FermionSpinSum[#,ExtraFactor->1/2]&//ReplaceAll[#, DiracTrace :> Tr]&//Contract//Factor2 - - -(* ::Text:: *) -(*In the following we neglect the momentum in the W-propagator as compared to the W-mass. This is a very good approximation at low energies, as then (pl-pn)^2 <= m_l^2 << m_W^2.*) - - -sqAmpQuarkNuScatteringTree2=(FCE[sqAmpQuarkNuScatteringTree]/.{pl-pn->0})//PropagatorDenominatorExplicit//Factor2 - - -(* ::Section:: *) -(*Total cross-section*) - - -(* ::Text:: *) -(*The total cross-section *) - - -prefac=4Pi/(64 Pi^2 s) Sqrt[(s-SMP["m_l"]^2-SMP["m_u"]^2)^2-4 SMP["m_l"]^2 SMP["m_u"]^2]/Sqrt[(s-SMP["m_d"]^2)^2] - - -crossSectionTotal=sqAmpQuarkNuScatteringTree2*prefac//PowerExpand - - -(* ::Text:: *) -(*If the lepton is a muon, then the up quark mass can be neglected*) - - -crossSectionTotalMuon=PowerExpand[crossSectionTotal/.{SMP["m_u"]->0,SMP["m_l"]->SMP["m_mu"]}] - - -(* ::Section:: *) -(*Check with the literature*) - - -(* ::Text:: *) -(*The result for the muon and neglected up quark mass can be found in Grozin, "Using REDUCE in High Energy Physics", Chapter 5.3*) - - -crossSectionTotalMuonKnown=(SMP["G_F"]^2*(s - SMP["m_mu"]^2)^2*SMP["V_ud", -I]*SMP["V_ud", I])/(Pi*s); -Print["Check with Grozin, Chapter 5.3:", - If[Simplify[crossSectionTotalMuon-crossSectionTotalMuonKnown]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/EW/OneLoop/H-GG.m b/FeynCalc/Examples/EW/OneLoop/H-GG.m new file mode 100644 index 000000000..853a260f0 --- /dev/null +++ b/FeynCalc/Examples/EW/OneLoop/H-GG.m @@ -0,0 +1,171 @@ +(* ::Package:: *) + +(* :Title: H-GG *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: H -> Gl Gl, EW, total decay rate, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Higgs decaying into two gluons*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="H -> Gl Gl, EW, total decay rate, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2,ExcludeTopologies->WFCorrections], + {S[1]} -> {V[5],V[5]}, InsertionLevel ->{Particles},Model->"SMQCD", + ExcludeParticles->{F[3|4,{1|2}],F[4,{3}]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +amp[0]=FCFAConvert[CreateFeynAmp[diags,PreFactor->-1],IncomingMomenta->{pH}, + OutgoingMomenta->{k1,k2},LoopMomenta->{q},List->False,Contract->True, + TransversePolarizationVectors->{k1,k2}, ChangeDimension->D, + DropSumOver->True,SMP->True,UndoChiralSplittings->True]; + + +amp[1]=amp[0]//FCTraceFactor//SUNSimplify + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +ScalarProduct[k1,k1]=0; +ScalarProduct[k2,k2]=0; +ScalarProduct[pH,pH]=SMP["m_H"]^2; +ScalarProduct[k1,k2]=(SMP["m_H"]^2)/2; + + +(* ::Section:: *) +(*Evaluate the amplitudes*) + + +(* ::Text:: *) +(*Dirac trace and tensor decomposition*) + + +amp[2]=amp[1]//DiracSimplify//TID[#,q,ToPaVe->True]& + + +(* ::Text:: *) +(*The explicit values for the PaVe functions B0 and C0 can be obtained e.g. from H. Patel's Package-X. Here we just insert the known results.*) + + +loopInts={ + B0[SMP["m_H"]^2,SMP["m_t"]^2,SMP["m_t"]^2]-> + 1/(16*Epsilon*Pi^4) - (-2*SMP["m_H"] + + EulerGamma*SMP["m_H"] - Log[4*Pi]*SMP["m_H"] - + Log[ScaleMu^2/SMP["m_t"]^2]*SMP["m_H"] - + Log[(-SMP["m_H"]^2 + 2*SMP["m_t"]^2 + + SMP["m_H"]*Sqrt[SMP["m_H"]^2 - 4*SMP["m_t"]^2])/ + (2*SMP["m_t"]^2)]*Sqrt[SMP["m_H"]^2 - + 4*SMP["m_t"]^2])/(16*Pi^4*SMP["m_H"]), + C0[0,0,SMP["m_H"]^2,SMP["m_t"]^2,SMP["m_t"]^2,SMP["m_t"]^2]-> + Log[(-SMP["m_H"]^2 + 2*SMP["m_t"]^2 + + SMP["m_H"]*Sqrt[SMP["m_H"]^2 - 4*SMP["m_t"]^2])/ + (2*SMP["m_t"]^2)]^2/(32*Pi^4*SMP["m_H"]^2) +}; + + +$Assumptions={SMP["m_H"]>0,SMP["m_t"]>0}; +amp[3]=(amp[2]/.loopInts)//FCReplaceD[#,D->4-2Epsilon]&// + Series[#,{Epsilon,0,0}]&//Normal + + +(* ::Text:: *) +(*As expected, the result is finite (i.e. contains no 1/Epsilon poles), so that it is safe to switch back to 4 dimensions*) + + +amp[4]=amp[3]//ChangeDimension[#,4]& + + +(* ::Section:: *) +(*Square the amplitudes*) + + +ampSquared[0]=1/2(amp[4] (ComplexConjugate[amp[4]]))// + SUNSimplify[#,SUNNToCACF->False]&// + DoPolarizationSums[#,k1,k2]&//DoPolarizationSums[#,k2,k1]&// + Simplify + + +(* ::Section:: *) +(*Total decay rate*) + + +phaseSpacePrefactor[m_]:=1/(16 Pi SMP["m_H"])Sqrt[1-4 m^2 / SMP["m_H"]^2] + + +totalDecayRate=phaseSpacePrefactor[0] ampSquared[0]// +ReplaceAll[#,{SMP["e"]^2->4 Pi SMP["alpha_fs"], +SMP["g_s"]^4->16 Pi^2 SMP["alpha_s"]^2}]&//Simplify + + +ISq=totalDecayRate/( SMP["alpha_s"]^2/(9 Pi^2) SMP["m_H"]^2/SMP["m_W"]^2 * + SMP["alpha_fs"]SMP["m_H"]/(8 SMP["sin_W"]^2)) + + +(* ::Text:: *) +(*ISq corresponds to I(m_H^2/m_q^2) from Peskin and Schroeder, Final Project 3, part (c). It should go to 1 for m_q -> Infinity and to 0 for m_q -> 0*) + + +limit1=Limit[ISq,SMP["m_t"]->Infinity]/.SUNN->3 +limit2=Limit[ISq,SMP["m_t"]->0] + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = {1,0}; +FCCompareResults[{limit1,limit2}, +knownResults,Factoring->Simplify, +Text->{"\tCompare to Peskin and Schroeder,An Introduction to QFT, \ +Final Project III, part (c):", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/AnelEl-AnmuMu.m b/FeynCalc/Examples/EW/Tree/AnelEl-AnmuMu.m new file mode 100644 index 000000000..36436bfc9 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/AnelEl-AnmuMu.m @@ -0,0 +1,154 @@ +(* ::Package:: *) + +(* :Title: AnEl-AnmuMu *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Anel El -> Anmu Mu, EW, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Electron electron-antineutrino annihilation into a muon-antineutrino and a muon*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Anel El -> Anmu Mu, EW, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< {Lorentz, UnitaryLorentz}]; + + +diags = InsertFields[CreateTopologies[0, 2 -> 2], {-F[1, {1}], + F[2, {1}]} -> {-F[1,{2}],F[2,{2}]}, InsertionLevel -> {Classes}, + Model -> {SM, UnitarySM},GenericModel->{Lorentz, UnitaryLorentz}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,GaugeRules->{FAGaugeXi[W|Z]->Infinity}], +IncomingMomenta->{q1,pe}, OutgoingMomenta->{q2,pm},ChangeDimension->4,List->False, +SMP->True, Contract->True,DropSumOver->True, +FinalSubstitutions->{SMP["e"]->Sqrt[8/Sqrt[2]*SMP["G_F"]* +SMP["m_W"]^2SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, q1, pe, -q2, -pm, 0, SMP["m_e"], 0, SMP["m_mu"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*There is no polarization averaging for neutrinos here, as right handed neutrinos do not interact*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FermionSpinSum[#, ExtraFactor -> 1/2]&//DiracSimplify//Factor + + +(* ::Text:: *) +(*In the following we neglect the momentum in the W-propagator as compared to the W-mass. This is a very good approximation at low energies, as then (pm-q2)^2 <= m_mu^2 << m_W^2.*) + + +ampSquared[1]=ampSquared[0]//FCE//ReplaceAll[#,{pm+q2->0}]&// + FeynAmpDenominatorExplicit//Series[#,{SMP["m_W"],Infinity,0}]&//Normal + + +(* ::Section:: *) +(*Total cross section*) + + +(* ::Text:: *) +(*We need to carry out the angular integration, so let us specify the values of the temporal and spatial components of the 4-vectors*) + + +TC[q2]=(s-SMP["m_mu"]^2)/(2Sqrt[s]); +TC[pe]=(s+SMP["m_e"]^2)/(2Sqrt[s]); +CSP[pe]=(s-SMP["m_e"]^2)^2/(4s); +CSP[pm]=(s-SMP["m_mu"]^2)^2/(4s); +CSP[q2]=(s-SMP["m_mu"]^2)^2/(4s); + + +prefac=2Pi/(64 Pi^2 s) Sqrt[(s-SMP["m_mu"]^2)^2]/Sqrt[(s-SMP["m_e"]^2)^2] + + +integral=Integrate[Simplify[ampSquared[1]/.u-> SMP["m_e"]^2- + 2(TC[q2]TC[pe]-Sqrt[CSP[q2]]Sqrt[CSP[pe]]x)],{x,-1,1}] + + +(* ::Text:: *) +(*The total cross-section *) + + +crossSectionTotal=integral*prefac//PowerExpand//Factor2 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (SMP["G_F"]^2*(s - SMP["m_mu"]^2)^2)(s^2+(SMP["m_mu"]^2+SMP["m_e"]^2)/2 s+ + SMP["m_mu"]^2 SMP["m_e"]^2)/(3Pi s^3) +}; +FCCompareResults[{crossSectionTotal}, +knownResults, +Text->{"\tCompare to Grozin, \ +Using REDUCE in High Energy Physics, Chapter 5.3:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/AnelEl-QubarQd.m b/FeynCalc/Examples/EW/Tree/AnelEl-QubarQd.m new file mode 100644 index 000000000..e5fdf497c --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/AnelEl-QubarQd.m @@ -0,0 +1,154 @@ +(* ::Package:: *) + +(* :Title: AnelEl-QubarQd *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Anel El -> Qubar Qd, EW, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Electron electron-antineutrino annihilation into an antiup and a down*) +(*quark*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Anel El -> Qubar Qd, EW, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< {Lorentz, UnitaryLorentz}]; + + +diags = InsertFields[CreateTopologies[0, 2 -> 2], {-F[1, + {1}],F[2, {1}]} -> {-F[3,{1}],F[4,{1}]}, InsertionLevel -> {Classes}, + Model -> {SM, UnitarySM},GenericModel->{Lorentz, UnitaryLorentz}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,GaugeRules->{FAGaugeXi[W|Z]->Infinity}], +DropSumOver->True, IncomingMomenta->{q,pe}, OutgoingMomenta->{l1,l2}, +ChangeDimension->4,List->False, SMP->True, Contract->True, +FinalSubstitutions->{SMP["e"]->Sqrt[8/Sqrt[2]*SMP["G_F"]* +SMP["m_W"]^2SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, q, pe, -l1, -l2, 0, SMP["m_e"], SMP["m_u"], SMP["m_d"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*There is no polarization averaging for neutrinos here, as right handed neutrinos do not interact*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FermionSpinSum[#, ExtraFactor -> 1/2]&//DiracSimplify//Factor + + +(* ::Text:: *) +(*In the following we neglect the momentum in the W-propagator as compared to the W-mass. This is a very good approximation at low energies, as then (pm-q2)^2 <= m_mu^2 << m_W^2.*) + + +ampSquared[1]=ampSquared[0]//FCE//ReplaceAll[#,{l1+l2->0}]&// + FeynAmpDenominatorExplicit//Series[#,{SMP["m_W"],Infinity,0}]&//Normal + + +(* ::Section:: *) +(*Total cross-section*) + + +(* ::Text:: *) +(*We need to carry out the angular integration, so let us specify the values of the temporal and spatial components of the 4-vectors*) + + +TC[pe]=(s+SMP["m_e"]^2)/(2Sqrt[s]); +TC[l1]=(s+(SMP["m_u"]^2-SMP["m_d"]^2))/(2Sqrt[s]); +CSP[pe]=(s-SMP["m_e"]^2)^2/(4s); +CSP[l1]=((s-SMP["m_u"]^2-SMP["m_d"]^2)^2-4SMP["m_u"]^2 SMP["m_d"]^2)/(4s); + + +prefac=2Pi/(64 Pi^2 s) Sqrt[CSP[l1]]/Sqrt[CSP[pe]]; + + +integral=Collect2[ampSquared[1] /.u-> SMP["m_e"]^2+SMP["m_u"]^2-2(TC[l1]TC[pe]-Sqrt[CSP[l1]]Sqrt[CSP[pe]]x),x,IsolateNames->KK]// +Integrate[#,{x,-1,1}]&//FRH//SUNSimplify//Simplify + + +(* ::Text:: *) +(*The total cross-section *) + + +crossSectionTotal=integral*prefac//PowerExpand//Factor2 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (CA*SMP["G_F"]^2*Sqrt[(s - SMP["m_d"]^2 - 2*SMP["m_d"]*SMP["m_u"] - + SMP["m_u"]^2)*(s - SMP["m_d"]^2 + 2*SMP["m_d"]*SMP["m_u"] - SMP["m_u"]^2)]* +(2*s^3 - s^2*SMP["m_d"]^2 - s*SMP["m_d"]^4 + s^2*SMP["m_e"]^2 + +s*SMP["m_d"]^2*SMP["m_e"]^2 - 2*SMP["m_d"]^4*SMP["m_e"]^2 - +s^2*SMP["m_u"]^2 + 2*s*SMP["m_d"]^2*SMP["m_u"]^2 + +s*SMP["m_e"]^2*SMP["m_u"]^2 + 4*SMP["m_d"]^2*SMP["m_e"]^2*SMP["m_u"]^2 - +s*SMP["m_u"]^4 - 2*SMP["m_e"]^2*SMP["m_u"]^4)*SMP["V_ud", -I]* +SMP["V_ud", I])/(6*Pi*s^3) +}; +FCCompareResults[{crossSectionTotal}, +knownResults, +Text->{"\tCompare to the known result:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/AnelEl-WW.m b/FeynCalc/Examples/EW/Tree/AnelEl-WW.m new file mode 100644 index 000000000..4a6c7c17a --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/AnelEl-WW.m @@ -0,0 +1,203 @@ +(* ::Package:: *) + +(* :Title: AnEl-WW *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Anel El -> W W, EW, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Electron positron annihilation into W bosons*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Anel El -> W W, EW, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], -F[2, {1}]} -> + {V[3], -V[3]}, InsertionLevel -> {Classes}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->True, SMP->True, Contract->True,FinalSubstitutions->{SMP["e"]->Sqrt[4Pi SMP["alpha_fs"]], + SMP["m_Z"]->SMP["m_W"]/SMP["cos_W"]}]; + + +(* ::Text:: *) +(*Let us separately mark the Higgs contribution separately*) + + +amp[1] ={markHiggs amp[0][[1]],amp[0][[2]],amp[0][[3]], amp[0][[4]]}; + + +amp[2] = Total[amp[1]]//DiracSimplify; + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_e"], SMP["m_W"], SMP["m_W"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0]=(amp[2] (ComplexConjugate[amp[2]]))// + FeynAmpDenominatorExplicit//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//DoPolarizationSums[#,k1]&//DoPolarizationSums[#,k2]&// + TrickMandelstam[#,{s,t,u,2SMP["m_e"]^2+2SMP["m_W"]^2}]&; + + +ampSquaredFull[0]=(ampSquared[0]/.markHiggs->1/.u->2SMP["m_e"]^2+2SMP["m_W"]^2-s-t)// + Simplify; + + +ampSquaredFull[1]=Simplify[Numerator[ampSquaredFull[0]]/. + SMP["cos_W"]->Sqrt[1-SMP["sin_W"]^2]]/Denominator[ampSquaredFull[0]] + + +(* ::Text:: *) +(*The Higgs diagram is needed to cancel the divergence that goes like m_e*Sqrt[s] in the high energy limit.*) +(*If we neglect the electron mass, then this particular diagram does not contribute.*) + + +ampSquaredMassless[0]=(ampSquared[0]/.SMP["m_e"]->0/.u->2SMP["m_W"]^2-s-t)// + Simplify; + + +ampSquaredMassless[1]=Simplify[Numerator[ampSquaredMassless[0]]/. + SMP["cos_W"]->Sqrt[1-SMP["sin_W"]^2]]/Denominator[ampSquaredMassless[0]] + + +(* ::Section:: *) +(*Total cross section*) + + +prefac=1/(16 Pi s^2); +integral=prefac*Integrate[ampSquaredFull[1],t]; + + +logFreePart=SelectFree2[integral,Log]; +logPartRaw=SelectNotFree2[integral,Log]//Simplify; + + +tUpper=-1/2(s-2SMP["m_W"]^2-2SMP["m_e"]^2-Sqrt[(s-4 SMP["m_e"]^2)(s-4 SMP["m_W"]^2)]); +tLower=-1/2(s-2SMP["m_W"]^2-2SMP["m_e"]^2+Sqrt[(s-4 SMP["m_e"]^2)(s-4 SMP["m_W"]^2)]); + + +logPart=Numerator[logPartRaw]/(Denominator[logPartRaw]/.(-s SMP["cos_W"]^2+SMP["m_W"]^2)^2-> + (-s SMP["cos_W"]^2+SMP["m_W"]^2)(-s (1-SMP["sin_W"]^2)+SMP["m_W"]^2))//Simplify + + +xsectionPart1=((logFreePart/.{t->tUpper})-(logFreePart/.{t->tLower}))// + Simplify//PowerExpand//Simplify + + +xsectionPart2=logPart/.Log[t+a_:0]:>Log[(tUpper+a)/(tLower+a)]//Simplify + + +crossSectionTotal=(xsectionPart1+xsectionPart2) + + +(* ::Text:: *) +(*Neglecting the electron mass produces a much simpler formula for the total cross section*) + + +xsectionMasslessPart1=(xsectionPart1/.SMP["m_e"]->0)// + Collect2[#,SMP["sin_W"],Factoring->Factor2, + FCFactorOut->Pi*SMP["alpha_fs"]^2*Sqrt[s-4 SMP["m_W"]^2]/ + (96 s^2 Sqrt[s]*(-s SMP["cos_W"]^2+SMP["m_W"]^2)^2 SMP["sin_W"]^4)]& + + +xsectionMasslessPart2=(xsectionPart2/.SMP["m_e"]->0)// + Collect2[#,SMP["sin_W"],Factoring->Factor2, + FCFactorOut->Log[(s-2 SMP["m_W"]^2-Sqrt[s (s-4 SMP["m_W"]^2)])/(s-2 SMP["m_W"]^2+Sqrt[s (s-4 SMP["m_W"]^2)])]*Pi*SMP["alpha_fs"]^2/ + ((96*s^3*(-s SMP["cos_W"]^2+SMP["m_W"]^2) SMP["sin_W"]^4))]& + + +crossSectionTotalMassless=xsectionMasslessPart1+xsectionMasslessPart2 + + +(* ::Text:: *) +(*We can also plot the full cross-section (in pb) as a function of Sqrt[s] (in GeV)*) + + +crossSectionTotalPlot= + 3.89*10^8*crossSectionTotal/.{SMP["m_e"]->0.51*10^(-3),SMP["m_H"]->125.0,SMP["m_W"]->80.4,SMP["sin_W"]->Sqrt[0.231], + SMP["cos_W"]->Sqrt[1.0-0.231],SMP["alpha_fs"]->1/137,s->sqrtS^2}//Simplify + + +(* ::Text:: *) +(*The plot can be compared to the one in Physics at LEP2: Vol. 1 (Altarelli:1996gh), page 93, Fig. 2*) + + +If[ $FrontEnd =!= Null, + Plot[crossSectionTotalPlot,{sqrtS,162,205}] +] + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (Pi*Log[(-2 + s - Sqrt[(-4 + s)*s])/(-2 + s + Sqrt[(-4 + s)*s])]*SMP["alpha_fs"]^2*(24*s*(4 + s + s^2) - + 24*(4 + 10*s + 2*s^2 + s^3)*SMP["sin_W"]^2))/(96*s^3*(1 - s*SMP["cos_W"]^2)*SMP["sin_W"]^4) + +(Pi*Sqrt[-4 + s]*SMP["alpha_fs"]^2*(-3*s*(32 - 20*s + 21*s^2) + 16*(3 + 8*s)*(2 + s^2)*SMP["sin_W"]^2 - +4*(96 + 160*s + 8*s^2 + 15*s^3)*SMP["sin_W"]^4))/(96*s^(5/2)*(1 - s*SMP["cos_W"]^2)^2*SMP["sin_W"]^4) +}; +FCCompareResults[{crossSectionTotalMassless/.SMP["m_W"]->1}, +knownResults, +Text->{"\tCompare to Grozin, \ +Using REDUCE in High Energy Physics, Chapter 5.4:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/EW/Tree/AnelEl-ZZ.m b/FeynCalc/Examples/EW/Tree/AnelEl-ZZ.m new file mode 100644 index 000000000..72f7d0a07 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/AnelEl-ZZ.m @@ -0,0 +1,197 @@ +(* ::Package:: *) + +(* :Title: AnEl-ZZ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Anel El -> Z Z, EW, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Electron positron annihilation into Z bosons*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Anel El -> Z Z, EW, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], -F[2, {1}]} -> + {V[2], V[2]}, InsertionLevel -> {Classes}]; + +Paint[diags, ColumnsXRows -> {3, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k1,k2}, List->True, SMP->True, + Contract->True, FinalSubstitutions->{SMP["e"]->Sqrt[4Pi SMP["alpha_fs"]], + SMP["m_W"]->SMP["m_Z"] SMP["cos_W"]}]; + + +(* ::Text:: *) +(*Let us separately mark the Higgs contribution separately*) + + +amp[1] ={markHiggs amp[0][[1]],amp[0][[2]],amp[0][[3]]}; + + +amp[2] = Total[amp[1]]//DiracSimplify; + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_e"], SMP["m_Z"], SMP["m_Z"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We need to multiply by 1/2 to account for two identical particles in the final state*) + + +ampSquared[0]=1/2*(amp[2] (ComplexConjugate[amp[2]]))// + FeynAmpDenominatorExplicit//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//DoPolarizationSums[#,k1]&//DoPolarizationSums[#,k2]&// + TrickMandelstam[#,{s,t,u,2SMP["m_e"]^2+2SMP["m_Z"]^2}]&; + + +ampSquaredFull[0]=(ampSquared[0]/.markHiggs->1/.u->2SMP["m_e"]^2+2SMP["m_Z"]^2-s-t)// + Simplify; + + +ampSquaredFull[1]=Simplify[Numerator[ampSquaredFull[0]]/. + SMP["cos_W"]->Sqrt[1-SMP["sin_W"]^2]]/Denominator[ampSquaredFull[0]] + + +(* ::Text:: *) +(*If we neglect the electron mass, then the Higgs diagram does not contribute.*) + + +ampSquaredMassless[0]=(ampSquared[0]/.SMP["m_e"]->0/.u->2SMP["m_Z"]^2-s-t)// + Simplify + + +ampSquaredMassless[1]=Simplify[Numerator[ampSquaredMassless[0]]/. + SMP["cos_W"]->Sqrt[1-SMP["sin_W"]^2]]/Denominator[ampSquaredMassless[0]] + + +(* ::Section:: *) +(*Total cross section*) + + +prefac=1/(16 Pi s^2); +integral=prefac*Integrate[ampSquaredFull[1],t]; + + +logFreePart=SelectFree2[integral,Log]; +logPart=SelectNotFree2[integral,Log]//Simplify; + + +tUpper=-1/2(s-2SMP["m_Z"]^2-2SMP["m_e"]^2-Sqrt[(s-4 SMP["m_e"]^2)(s-4 SMP["m_Z"]^2)]); +tLower=-1/2(s-2SMP["m_Z"]^2-2SMP["m_e"]^2+Sqrt[(s-4 SMP["m_e"]^2)(s-4 SMP["m_Z"]^2)]); + + +xsectionPart1=((logFreePart/.{t->tUpper})-(logFreePart/.{t->tLower}))// + Simplify + + +xsectionPart2=logPart/.Log[t+a_:0]:> Log[(tUpper+a)/(tLower+a)]//Simplify + + +crossSectionTotal=(xsectionPart1+xsectionPart2) + + +(* ::Text:: *) +(*Neglecting the electron mass produces a much simpler formula for the total cross section*) + + +xsectionMasslessPart1=(xsectionPart1/.SMP["m_e"]->0)//Simplify + + +xsectionMasslessPart2=(xsectionPart2/.SMP["m_e"]->0)//Simplify + + +crossSectionTotalMassless=xsectionMasslessPart1+xsectionMasslessPart2 + + +(* ::Text:: *) +(*We can also plot the full cross-section (in pb) as a function of Sqrt[s] (in GeV)*) + + +crossSectionTotalPlot= + 3.89*10^8*crossSectionTotal/.{SMP["m_e"]->0.51*10^(-3),SMP["m_H"]->125.0,SMP["m_Z"]->91.2,SMP["sin_W"]->Sqrt[0.231], + SMP["cos_W"]->Sqrt[1.0-0.231],SMP["alpha_fs"]->1/137,s->sqrtS^2}//Simplify + + +(* ::Text:: *) +(*The plot can be compared to the one in arXiv:hep-ex/9911003, Fig. 8*) + + +If[ $FrontEnd =!= Null, + Plot[crossSectionTotalPlot,{sqrtS,183,200}] +] + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + -(Pi*(4*(-2 + s)*Sqrt[(-4 + s)*s] + + (4 + s^2)*Log[(-2 + s - Sqrt[(-4 + s)*s])/(-2 + s + Sqrt[(-4 + s)*s])] - + (4 + s^2)*Log[(-2 + s + Sqrt[(-4 + s)*s])/(-2 + s - Sqrt[(-4 + s)*s])])* +SMP["alpha_fs"]^2*(1 - 8*SMP["sin_W"]^2 + 24*SMP["sin_W"]^4 - 32*SMP["sin_W"]^6 + + 32*SMP["sin_W"]^8))/(32*(-2 + s)*s^2*SMP["cos_W"]^4*SMP["sin_W"]^4) +}; +FCCompareResults[{crossSectionTotalMassless/.SMP["m_Z"]->1}, +knownResults, +Text->{"\tCompare to the known result: ", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/EW/Tree/ElNmu-MuNel.m b/FeynCalc/Examples/EW/Tree/ElNmu-MuNel.m new file mode 100644 index 000000000..d366326fc --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/ElNmu-MuNel.m @@ -0,0 +1,136 @@ +(* ::Package:: *) + +(* :Title: ElNmu-MuNuel *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Nmu -> Mu Nuel, EW, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Electron muon-neutrino annihilation into a muon and an electron-neutrino*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Nmu -> Mu Nuel, EW, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< {Lorentz, UnitaryLorentz}]; + + +diags = InsertFields[CreateTopologies[0, 2 -> 2], + {F[2,{1}],F[1, {2}]} -> {F[1,{1}],F[2,{2}]}, InsertionLevel -> {Classes}, + Model -> {SM, UnitarySM},GenericModel->{Lorentz, UnitaryLorentz}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,GaugeRules->{FAGaugeXi[W|Z]->Infinity}], +IncomingMomenta->{p,q1}, OutgoingMomenta->{q2,k},ChangeDimension->4,List->False, +SMP->True, Contract->True,DropSumOver->True, +FinalSubstitutions->{SMP["e"]->Sqrt[8/Sqrt[2]*SMP["G_F"]* +SMP["m_W"]^2SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p, q1, -q2, -k, SMP["m_e"], 0, 0, SMP["m_mu"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*There is no polarization averaging for neutrinos here, as right handed neutrinos do not interact*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FermionSpinSum[#, ExtraFactor -> 1/2]&//DiracSimplify//Factor + + +(* ::Text:: *) +(*In the following we neglect the momentum in the W-propagator as compared to the W-mass. This is a very good approximation at low energies, as then (k-q1)^2 <= m_mu^2 << m_W^2.*) + + +ampSquared[1]=ampSquared[0]//FCE//ReplaceAll[#,{k-q1->0}]&// + FeynAmpDenominatorExplicit//Series[#,{SMP["m_W"],Infinity,0}]&//Normal + + +(* ::Section:: *) +(*Total cross section*) + + +(* ::Text:: *) +(*The total cross-section *) + + +prefac=4Pi/(64 Pi^2 s) Sqrt[(s-SMP["m_mu"]^2)^2]/Sqrt[(s-SMP["m_e"]^2)^2] + + +crossSectionTotal=prefac*ampSquared[1]//PowerExpand + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (SMP["G_F"]^2*(s - SMP["m_mu"]^2)^2)/(Pi*s) +}; +FCCompareResults[{crossSectionTotal}, +knownResults, +Text->{"\tCompare to Greiner and Mueller, \ +Gauge Theory of Weak Interactions, Chapter 3:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/H-FFbar.m b/FeynCalc/Examples/EW/Tree/H-FFbar.m new file mode 100644 index 000000000..5ca99cd08 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/H-FFbar.m @@ -0,0 +1,142 @@ +(* ::Package:: *) + +(* :Title: H-FFbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: H -> F Fbar, EW, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Higgs decaying into a fermion-antifermion pair*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="H -> F Fbar, EW, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {S[1]} -> + {F[2,{l}],-F[2,{l}]}, InsertionLevel -> {Classes}]; + +Paint[diagsLeptons, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +diagsQuarks = InsertFields[CreateTopologies[0,1 -> 2], {S[1]} -> + {F[3,{l}],-F[3,{l}]}, InsertionLevel -> {Classes}]; + +Paint[diagsQuarks, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +ampLeptons[0]=FCFAConvert[CreateFeynAmp[diagsLeptons],IncomingMomenta->{pH}, + OutgoingMomenta->{p1,p2},List->False,ChangeDimension->4, + DropSumOver->True,SMP->True,Contract->True,UndoChiralSplittings->True, + FinalSubstitutions->{MLE[l]->SMP["m_l"]}] + + +ampQuarks[0]=FCFAConvert[CreateFeynAmp[diagsQuarks],IncomingMomenta->{pH}, + OutgoingMomenta->{k1,k2},List->False,ChangeDimension->4, + DropSumOver->True,SMP->True,Contract->True,UndoChiralSplittings->True, + FinalSubstitutions->{MQU[l]->SMP["m_q"]}] + + +ampLeptons[1]=ampLeptons[0]//DiracSimplify + + +ampQuarks[1]=ampQuarks[0]//DiracSimplify + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SP[p1,p1]=SMP["m_l"]^2; +SP[k1,k1]=SMP["m_q"]^2; +SP[p2,p2]=SMP["m_l"]^2; +SP[k2,k2]=SMP["m_q"]^2; +SP[pH,pH]=SMP["m_H"]^2; +SP[p1,p2]=(SMP["m_H"]^2-2 SMP["m_l"]^2)/2; +SP[k1,k2]=(SMP["m_H"]^2-2 SMP["m_q"]^2)/2; + + +(* ::Section:: *) +(*Square the amplitudes*) + + +ampLeptonsSquared[0]=ampLeptons[1]*ComplexConjugate[ampLeptons[1]]// + FermionSpinSum//DiracSimplify//Simplify + + +ampQuarksSquared[0]=ampQuarks[1]*ComplexConjugate[ampQuarks[1]]// + FermionSpinSum//DiracSimplify//SUNSimplify + + +(* ::Section:: *) +(*Total decay rates*) + + +$Assumptions={SMP["m_H"]>0,SMP["m_l"]>0}; +phaseSpacePrefactor[m_]:=1/(16 Pi SMP["m_H"])Sqrt[1-4 m^2 / SMP["m_H"]^2]; + + +totalDecayRateLeptons=phaseSpacePrefactor[SMP["m_l"]]ampLeptonsSquared[0]// +ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&//Simplify + + +totalDecayRateQuarks=phaseSpacePrefactor[SMP["m_q"]]ampQuarksSquared[0]// +ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&//Simplify + + +(AlphaFS SMP["m_H"])/(8 SMP["sin_W"]^2)( SMP["m_l"]^2/SMP["m_W"]^2* + (1- 4 SMP["m_l"]^2/SMP["m_H"]^2)^(3/2))-totalDecayRateLeptons//Factor + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (AlphaFS SMP["m_H"])/(8 SMP["sin_W"]^2)( SMP["m_l"]^2/SMP["m_W"]^2* + (1- 4 SMP["m_l"]^2/SMP["m_H"]^2)^(3/2)), + (CA*SMP["alpha_fs"]*SMP["m_H"]*SMP["m_q"]^2* +(1 - (4*SMP["m_q"]^2)/SMP["m_H"]^2)^(3/2))/(8*SMP["m_W"]^2*SMP["sin_W"]^2) +}; +FCCompareResults[{totalDecayRateLeptons,totalDecayRateQuarks}, +knownResults,Factoring->Simplify, +Text->{"\tCompare to Peskin and Schroeder,An Introduction to QFT, \ +Final Project III, part (a):", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/EW/Tree/H-WW.m b/FeynCalc/Examples/EW/Tree/H-WW.m new file mode 100644 index 000000000..39467db32 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/H-WW.m @@ -0,0 +1,116 @@ +(* ::Package:: *) + +(* :Title: H-WW *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: H -> W W, EW, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Higgs decaying into a W boson pair*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="H -> W W, EW, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {S[1]} -> {-V[3],V[3]}, + InsertionLevel -> {Classes}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +amp[0]=FCFAConvert[CreateFeynAmp[diags],IncomingMomenta->{pH}, + OutgoingMomenta->{k1,k2},List->False,ChangeDimension->4, + DropSumOver->True,SMP->True,Contract->True,UndoChiralSplittings->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SP[k1,k1]=SMP["m_W"]^2; +SP[k2,k2]=SMP["m_W"]^2; +SP[pH,pH]=SMP["m_H"]^2; +SP[k1,k2]=(SMP["m_H"]^2-2 SMP["m_W"]^2)/2; + + +(* ::Section:: *) +(*Square the amplitudes*) + + +ampSquared[0]=(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//DoPolarizationSums[#,k1]&// + DoPolarizationSums[#,k2]&//Simplify + + +(* ::Section:: *) +(*Total decay rate*) + + +$Assumptions={SMP["m_H"]>0,SMP["m_W"]>0}; +phaseSpacePrefactor[m_]:=1/(16 Pi SMP["m_H"])Sqrt[1-4 m^2 / SMP["m_H"]^2]; + + +totalDecayRate=phaseSpacePrefactor[SMP["m_W"]] ampSquared[0]// +ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&//Simplify + + +(* ::Text:: *) +(*Rewrite the result in a nicer way*) + + +(totalDecayRate/.SMP["m_W"]^2-> h[SMP["m_W"]^2/SMP["m_H"]^2]SMP["m_H"]^2/. +SMP["m_W"]^4-> h[SMP["m_W"]^4/SMP["m_H"]^4]SMP["m_H"]^4)//FullSimplify// +ReplaceAll[#,h->Identity]& + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + SMP["g_W"]^2/(64 Pi) SMP["m_H"]^3/SMP["m_W"]^2 Sqrt[1- 4 SMP["m_W"]^2/ + SMP["m_H"]^2](1-4 SMP["m_W"]^2/SMP["m_H"]^2 + 12 SMP["m_W"]^4/SMP["m_H"]^4)}// + ReplaceAll[#,SMP["g_W"]-> SMP["e"]/SMP["sin_W"]]&// + ReplaceAll[#,SMP["e"]^2->4 Pi SMP["alpha_fs"]]&; +FCCompareResults[{totalDecayRate}, +knownResults,Factoring->Simplify, +Text->{"\tCompare to Gunion, Haber, Kane and Dawson, \ +Higgs Hunter Guide, Eq 2.11:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/EW/Tree/H-ZZ.m b/FeynCalc/Examples/EW/Tree/H-ZZ.m new file mode 100644 index 000000000..62cc9c417 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/H-ZZ.m @@ -0,0 +1,115 @@ +(* ::Package:: *) + +(* :Title: H-ZZ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: H -> Z Z, EW, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Higgs decaying into a Z boson pair*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="H -> Z Z, EW, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {S[1]} -> {V[2],V[2]}, + InsertionLevel -> {Classes}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +amp[0]=FCFAConvert[CreateFeynAmp[diags],IncomingMomenta->{pH}, + OutgoingMomenta->{k1,k2},List->False,ChangeDimension->4, + DropSumOver->True,SMP->True,Contract->True,UndoChiralSplittings->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SP[k1,k1]=SMP["m_Z"]^2; +SP[k2,k2]=SMP["m_Z"]^2; +SP[pH,pH]=SMP["m_H"]^2; +SP[k1,k2]=(SMP["m_H"]^2-2 SMP["m_Z"]^2)/2; + + +(* ::Section:: *) +(*Square the amplitudes*) + + +ampSquared[0]=1/2(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//DoPolarizationSums[#,k1]&// + DoPolarizationSums[#,k2]&//Simplify + + +(* ::Section:: *) +(*Total decay rates*) + + +$Assumptions={SMP["m_H"]>0,SMP["m_Z"]>0}; +phaseSpacePrefactor[m_]:=1/(16 Pi SMP["m_H"])Sqrt[1-4 m^2 / SMP["m_H"]^2]; + + +totalDecayRate=phaseSpacePrefactor[SMP["m_Z"]] ampSquared[0]// +ReplaceRepeated[#,{SMP["e"]^2->4 Pi SMP["alpha_fs"], 1/SMP["m_Z"]^4-> + SMP["cos_W"]^4/SMP["m_W"]^4}]&//Simplify + + +(* ::Text:: *) +(*Rewrite the result in a nicer way*) + + +(totalDecayRate/.SMP["m_Z"]^2-> h[SMP["m_Z"]^2/SMP["m_H"]^2]SMP["m_H"]^2/. +SMP["m_Z"]^4-> h[SMP["m_Z"]^4/SMP["m_H"]^4]SMP["m_H"]^4)//FullSimplify//ReplaceAll[#,h->Identity]& + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (SMP["alpha_fs"]*SMP["m_H"]^3*Sqrt[1 - (4*SMP["m_Z"]^2)/SMP["m_H"]^2]* +(1 - (4*SMP["m_Z"]^2)/SMP["m_H"]^2 + (12*SMP["m_Z"]^4)/SMP["m_H"]^4))/ +(32*SMP["m_W"]^2*SMP["sin_W"]^2)}; +FCCompareResults[{totalDecayRate}, +knownResults,Factoring->Simplify, +Text->{"\tCompare to Gunion, Haber, Kane and Dawson, \ +Higgs Hunter Guide, Eq 2.10:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/EW/Tree/Mu-ElAnelNmu.m b/FeynCalc/Examples/EW/Tree/Mu-ElAnelNmu.m new file mode 100644 index 000000000..777c0ebb6 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/Mu-ElAnelNmu.m @@ -0,0 +1,188 @@ +(* ::Package:: *) + +(* :Title: Mu-ElAnelNmu *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Mu -> El Anel Nmu, EW, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Muon decaying into an electron, electron-antineutrino and a muon-neutrino*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Mu -> El Anel Nmu, EW, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< {Lorentz, UnitaryLorentz}]; + + +diags = InsertFields[CreateTopologies[0, 1 -> 3], + {F[2, {2}]} -> {F[2, {1}],-F[1,{1}],F[1,{2}]}, InsertionLevel -> {Classes}, + Model -> {SM, UnitarySM},GenericModel->{Lorentz, UnitaryLorentz}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,GaugeRules->{FAGaugeXi[W|Z]->Infinity}], +IncomingMomenta->{p}, OutgoingMomenta->{k,q1,q2},ChangeDimension->4,List->False, +SMP->True, Contract->True,DropSumOver->True, +FinalSubstitutions->{SMP["e"]->Sqrt[8/Sqrt[2]*SMP["G_F"]* +SMP["m_W"]^2SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[] +SP[k,k]=SMP["m_e"]^2; +SP[q1,q1]=0; +SP[q2,q2]=0; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We average over the polarizations of the muon, hence the additional factor 1/2*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FermionSpinSum[#, ExtraFactor -> 1/2]&//DiracSimplify//Factor + + +(* ::Text:: *) +(*In the following we neglect the momentum in the W-propagator as compared to the W-mass. This is a very good approximation at low energies, as then (k+q1)^2 <= m_mu^2 << m_W^2.*) + + +ampSquared[1]=ampSquared[0]//FCE//ReplaceAll[#,{k+q1->0}]&// + FeynAmpDenominatorExplicit//Series[#,{SMP["m_W"],Infinity,0}]&//Normal + + +(* ::Section:: *) +(*Total decay rate*) + + +(* ::Text:: *) +(*To compute the total decay rate, we follow the calculation done in Okun, Leptons and Quarks, Chapter 3. The differential decay rate is given by*) +(**) +(*d \[CapitalGamma] = 1/(2M) d^3 k / ((2\[Pi])^3 2 k^0) d^3 q1 / ((2\[Pi])^3 2 q1^0) d^3 q2 / ((2\[Pi])^3 2 q2^0) (2\[Pi])^4 \[Delta]^4 (q-q1-q2) sqAmpMuonDecayTree2 with q = p-k*) + + +prefac=(2SMP["m_mu"] (2Pi)^5 8)^-1; +diffDecayRate = prefac d3q1/En[q1] d3q2/En[q2] d3k/En[k] delta4[q-q1-q2]* + ampSquared[1] + + +(* ::Text:: *) +(*First we reduce the tensor integrals in q1 to q2 to scalar ones by using tensor decomposition*) + + +q1q2[mu_,nu_]:=ReplaceAll[Tdec[{{q1x,mu},{q2x,nu}},{q},List->False,Dimension->4], +{SP[q1x,q2x]->SP[q,q]/2, SP[q,q1x|q2x]->SP[q,q]/2}]; + + +q1q2[mu,nu]//Factor2 + + +diffDecayRate1=Uncontract[diffDecayRate,q1,q2,Pair->All] + + +diffDecayRate2=((diffDecayRate1//FCE)/. FV[q1,mu_]FV[q2,nu_]:>q1q2[mu,nu])// + Contract//FCE + + +(* ::Text:: *) +(*Integrating over q1 and q2 (in the rest frame of the decaying muon) we get rid of the Dirac delta and simplify the integral*) + + +diffDecayRate3=diffDecayRate2/.{d3q2 delta4[q-q1-q2]-> delta[En[q]-2En[q1]]}/.{En[q2]->En[q1]}/. +{d3q1-> 4Pi dq10 En[q1]^2}/.{dq10 delta[En[q]-2En[q1]]->1/2} + + +(* ::Text:: *) +(*Then we use the kinematics of the process, to simplify things even further. Here we also use the fact that the mass of the electron is very small as compared to its energy*) + + +diffDecayRate4=(diffDecayRate3//.{SP[q,p]->SMP["m_mu"]^2-SMP["m_mu"] En[k],SP[k,q]|SP[p,k]-> SMP["m_mu"] En[k], +SP[q,q]-> SMP["m_mu"]^2-2 SMP["m_mu"]En[k]})//Simplify + + +(* ::Text:: *) +(*Next we trade d3k for dOmega d k^0 (k^0)^2 and introduce Eps that is defined as 2 k^0/ m_mu*) + + +diffDecayRate5=(diffDecayRate4/.d3k-> dk0 En[k]^2 4Pi /. En[k]-> Eps SMP["m_mu"]/2/. +dk0-> dEps SMP["m_mu"]/2)//Factor2 + + +(* ::Text:: *) +(*Integrating over Eps we arrive to the final result*) + + +decayRateTotal=Integrate[diffDecayRate5/.dEps->1,{Eps,0,1}] + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (SMP["G_F"]^2*SMP["m_mu"]^5)/(192*Pi^3) +}; +FCCompareResults[{decayRateTotal}, +knownResults, +Text->{"\tCompare to Okun, Leptons and Quarks, \ +Chapter 3.2:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/NleQdt-LeQut.m b/FeynCalc/Examples/EW/Tree/NleQdt-LeQut.m new file mode 100644 index 000000000..a65aab839 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/NleQdt-LeQut.m @@ -0,0 +1,157 @@ +(* ::Package:: *) + +(* :Title: NleQdt-LeQut *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Nle Qdt -> Le Qut, EW, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Neutrino down-type quark annihilation into a lepton and an up-type quark*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Nle Qdt -> Le Qut, EW, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< {Lorentz, UnitaryLorentz}]; + + +diags = InsertFields[CreateTopologies[0, 2 -> 2], +{F[4,{1,1}],F[1,{2}]} -> {F[3,{1,1}],F[2,{2}]}, InsertionLevel -> {Classes}, +Model -> {SM, UnitarySM},GenericModel->{Lorentz, UnitaryLorentz}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,GaugeRules->{FAGaugeXi[W|Z]->Infinity}], +IncomingMomenta->{pd,pn}, OutgoingMomenta->{pu,pl},ChangeDimension->4, +List->False, SMP->True, Contract->True,DropSumOver->True, +FinalSubstitutions->{SMP["e"]->Sqrt[8/Sqrt[2]*SMP["G_F"]* +SMP["m_W"]^2SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, pd, pn, -pu, -pl, SMP["m_d"], 0, SMP["m_u"], SMP["m_l"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*There is no polarization averaging for neutrinos here, as right handed neutrinos do not interact*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FermionSpinSum[#, ExtraFactor -> 1/2]&//DiracSimplify//Factor + + +(* ::Text:: *) +(*In the following we neglect the momentum in the W-propagator as compared to the W-mass. This is a very good approximation at low energies, as then (pl-pn)^2 <= m_mu^2 << m_W^2.*) + + +ampSquared[1]=ampSquared[0]//FCE//ReplaceAll[#,{pl-pn->0}]&// + FeynAmpDenominatorExplicit//Series[#,{SMP["m_W"],Infinity,0}]&//Normal + + +(* ::Section:: *) +(*Total cross section*) + + +(* ::Text:: *) +(*The total cross-section *) + + +prefac=4Pi/(64 Pi^2 s) Sqrt[(s-SMP["m_l"]^2-SMP["m_u"]^2)^2-4 SMP["m_l"]^2 * + SMP["m_u"]^2]/Sqrt[(s-SMP["m_d"]^2)^2] + + +crossSectionTotal=prefac*ampSquared[1]//PowerExpand + + +(* ::Text:: *) +(*If the lepton is a muon, then the up quark mass can be neglected*) + + +crossSectionTotalMuon=PowerExpand[crossSectionTotal/.{SMP["m_u"]->0, + SMP["m_l"]->SMP["m_mu"]}] + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults + + +knownResults = { + (SMP["G_F"]^2*(s - SMP["m_mu"]^2)^2*SMP["V_ud", -I]*SMP["V_ud", I])/(Pi*s) +}; +FCCompareResults[{crossSectionTotalMuon}, +knownResults, +Text->{"\tCompare to Grozin, \ +Using REDUCE in High Energy Physics, Chapter 5.3:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/QQbar-ZZ.m b/FeynCalc/Examples/EW/Tree/QQbar-ZZ.m new file mode 100644 index 000000000..420f2a2db --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/QQbar-ZZ.m @@ -0,0 +1,118 @@ +(* ::Package:: *) + +(* :Title: QQbar-ZZ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Qbar -> Z Z, EW, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark antiquark annihilation into Z bosons*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q Qbar -> Z Z, EW, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], + -F[3, {1}]} -> {V[2], V[2]}, InsertionLevel -> {Particles}, + ExcludeParticles->{S[_]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*For simplicity let us neglect the masses of the quarks*) + + +amp[0] = 9/4 SMP["e_Q"]^2 FCFAConvert[CreateFeynAmp[diags], + IncomingMomenta->{p1,p2}, OutgoingMomenta->{k1,k2}, ChangeDimension->4, + List->False, SMP->True, Contract->True, DropSumOver->True, + TransversePolarizationVectors->{k1,k2}, FinalSubstitutions->{SMP["m_u"]->0}]; + + +amp[1] = amp[0]//DiracSimplify + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2 ,0, 0, SMP["m_Z"], SMP["m_Z"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We average over the spins and the colors of the quarks, hence the additional factor 1/3^2 1/2^2. Since the final state particles are indistinguishable, we add an extra 1/2.*) + + +ampSquared[0]=(1/3^2)(1/2)(amp[1] (ComplexConjugate[amp[1]]))// + FeynAmpDenominatorExplicit//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//DoPolarizationSums[#,k1]&//DoPolarizationSums[#,k2]&// + SUNSimplify[#,SUNNToCACF->False]&//TrickMandelstam[#,{s,t,u,2 SMP["m_Z"]^2}]& + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + 2 SMP["e"]^4 SUNN /72((-SMP["e_Q"]SMP["sin_W"]/SMP["cos_W"])^4+ + ( 3/2 SMP["e_Q"] 1/(2 SMP["sin_W"] SMP["cos_W"] )- + SMP["e_Q"]SMP["sin_W"]/SMP["cos_W"])^4)*((2(t/u+u/t-SMP["m_Z"]^4(1/t^2+1/u^2))+ + 8 SMP["m_Z"]^2 s/(t u))) +}; +FCCompareResults[{ampSquared[0]}, +knownResults, +Factoring->Function[x,TrickMandelstam[x,{s,t,u,2 SMP["m_Z"]^2}]], +Text->{"\tCompare to J. Ohnemus and J. Owens, \ +Phys. Rev. D43, 3626-3639, 1991, Eq. 4:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/EW/Tree/Qt-QbW.m b/FeynCalc/Examples/EW/Tree/Qt-QbW.m new file mode 100644 index 000000000..be222c07a --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/Qt-QbW.m @@ -0,0 +1,133 @@ +(* ::Package:: *) + +(* :Title: Qt-QbW *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Qt -> Qb W, EW, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Top quark decaying into a quark and a W boson*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Qt -> Qb W, EW, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], +{F[3,{3}]} -> {F[4,{3}],-V[3]}, InsertionLevel -> {Particles}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p}, + OutgoingMomenta->{k1,k2},ChangeDimension->4,List->False, SMP->True, + Contract->True,DropSumOver->True, FinalSubstitutions-> + {SMP["e"]->Sqrt[8/Sqrt[2]SMP["G_F"] SMP["m_W"]^2SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[] +SP[p]=SMP["m_t"]^2; +SP[k1]=SMP["m_b"]^2; +SP[k2]=SMP["m_W"]^2; +SP[k1,k2]=Simplify[(SP[p]-SP[k1]-SP[k2])/2]; +SP[p,k1]=Simplify[ExpandScalarProduct[SP[k1+k2,k1]]]; +SP[p,k2]=Simplify[ExpandScalarProduct[SP[k1+k2,k2]]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We average over the polarizations of the top quark, hence the additional factor 1/2*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))//SUNSimplify// + FermionSpinSum[#, ExtraFactor -> 1/2]&//DiracSimplify// + DoPolarizationSums[#,k2]&//Simplify + + +(* ::Section:: *) +(*Total decay rate*) + + +phaseSpacePrefactor[m1_,m2_,M_]:=1/(16 Pi M)Sqrt[1-(m1+m2)^2/M^2]* + Sqrt[1-(m1-m2)^2/M^2]; + + +totalDecayRate=phaseSpacePrefactor[SMP["m_b"],SMP["m_W"],SMP["m_t"]]* + ampSquared[0]//Simplify//ReplaceAll[#,Sqrt[x_]Sqrt[y_]:> + Sqrt[ExpandAll[x y]]]& + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + SMP["m_t"]^3(CA*SMP["G_F"]*Sqrt[((SMP["m_b"] - SMP["m_t"] - + SMP["m_W"])*(SMP["m_b"] + SMP["m_t"] - SMP["m_W"])*(SMP["m_b"] - + SMP["m_t"] + SMP["m_W"])*(SMP["m_b"] + SMP["m_t"] + SMP["m_W"]))/ + SMP["m_t"]^4]*((1-SMP["m_b"]^2/SMP["m_t"]^2)^2+ SMP["m_W"]^2/ + SMP["m_t"]^2(1+SMP["m_b"]^2/SMP["m_t"]^2)-2SMP["m_W"]^4/SMP["m_t"]^4 + )*SMP["V_tb", -I]*SMP["V_tb", I])/(8*Sqrt[2]*Pi) +}; +FCCompareResults[{totalDecayRate}, +knownResults, +Text->{"\tCompare to Grozin, \ +Using REDUCE in High Energy Physics, Chapter 5.2:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/EW/Tree/QuQdbar-AelNel.m b/FeynCalc/Examples/EW/Tree/QuQdbar-AelNel.m new file mode 100644 index 000000000..c074ea021 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/QuQdbar-AelNel.m @@ -0,0 +1,124 @@ +(* ::Package:: *) + +(* :Title: QuQdbar-AelNel *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Qu Qdbar -> Ael Nel, EW, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Up quark antidown quark annihilation into a positron and an electron neutrino*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Qu Qdbar -> Ael Nel, EW, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< {Lorentz, UnitaryLorentz}]; + + +diags = InsertFields[CreateTopologies[0, 2 -> 2], + {F[3, {1}],-F[4, {1}]} -> {-F[2, {1}],F[1,{1}]}, + InsertionLevel -> {Particles}, Model -> {SM, UnitarySM}, + GenericModel->{Lorentz, UnitaryLorentz}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,GaugeRules->{FAGaugeXi[W|Z]->Infinity}], +IncomingMomenta->{p1,p2}, OutgoingMomenta->{k1,k2},ChangeDimension->4,List->False, +SMP->True, Contract->True, DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[] +SetMandelstam[s, t, u, p1, p2, -k1, -k2 , 0, 0, 0, 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We average over the spins and the colors of the quarks, hence the additional factor 1/3^2 1/2^2.*) + + +ampSquared[0] = 1/3^2*(amp[0] (ComplexConjugate[amp[0]]))// + FermionSpinSum[#, ExtraFactor -> 1/2^2]&//DiracSimplify// + FeynAmpDenominatorExplicit//SUNSimplify[#,SUNNToCACF->False]&// + ReplaceAll[#,SUNN->3]& + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (t^2*SMP["e"]^4*SMP["V_ud", -I]*SMP["V_ud", I])/ + (12*(s - SMP["m_W"]^2)^2*SMP["sin_W"]^4) +}; +FCCompareResults[{ampSquared[0]}, +knownResults, +Text->{"\tCompare to CompHEP:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/QutbarQdt-NelAnel.m b/FeynCalc/Examples/EW/Tree/QutbarQdt-NelAnel.m new file mode 100644 index 000000000..515eb80ba --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/QutbarQdt-NelAnel.m @@ -0,0 +1,123 @@ +(* ::Package:: *) + +(* :Title: QutbarQdt-NelAnel *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Qutbar Qdt -> Nel Anel, EW, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Antiup quark down quark annihilation into an electron and an antielectron-neutrino*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Qutbar Qdt -> Nel Anel, EW, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< {Lorentz, UnitaryLorentz}]; + + +diags = InsertFields[CreateTopologies[0, 2 -> 2], + {-F[3, {1}],F[4, {1}]} -> {F[2, {1}],-F[1,{1}]}, + InsertionLevel -> {Particles}, Model -> {SM, UnitarySM}, + GenericModel->{Lorentz, UnitaryLorentz}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,GaugeRules->{FAGaugeXi[W|Z]->Infinity}], +IncomingMomenta->{p2,p1}, OutgoingMomenta->{k1,k2},ChangeDimension->4,List->False, +SMP->True, Contract->True, DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[] +SetMandelstam[s, t, u, p1, p2, -k1, -k2 , 0, 0, 0, 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We average over the spins and the colors of the quarks, hence the additional factor 1/3^2 1/2^2.*) + + +ampSquared[0] = 1/3^2*(amp[0] (ComplexConjugate[amp[0]]))// + FermionSpinSum[#, ExtraFactor -> 1/2^2]&//DiracSimplify// + FeynAmpDenominatorExplicit//SUNSimplify[#,SUNNToCACF->False]&// + ReplaceAll[#,SUNN->3]& + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (u^2*SMP["e"]^4*SMP["V_ud", -I]*SMP["V_ud", I])/(12*(s - SMP["m_W"]^2)^2*SMP["sin_W"]^4) +}; +FCCompareResults[{ampSquared[0]}, +knownResults, +Text->{"\tCompare to CompHEP:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/W-ElAnel.m b/FeynCalc/Examples/EW/Tree/W-ElAnel.m new file mode 100644 index 000000000..b1cbd1fce --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/W-ElAnel.m @@ -0,0 +1,122 @@ +(* ::Package:: *) + +(* :Title: W-ElAnel *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: W -> El Anel, EW, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*W decaying into an electron and an electron-antineutrino*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="W -> El Anel, EW, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], + {V[3]} -> {F[2,{1}],-F[1,{1}]}, InsertionLevel -> {Particles}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p}, + OutgoingMomenta->{k1,k2},ChangeDimension->4,List->False, SMP->True, + Contract->True,DropSumOver->True, FinalSubstitutions-> + {SMP["e"]->Sqrt[8/Sqrt[2]SMP["G_F"] SMP["m_W"]^2SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[] +SP[p]=SMP["m_W"]^2; +SP[k1]=SMP["m_e"]^2; +SP[k2]=0; +SP[k1,k2]=(SMP["m_W"]^2-SMP["m_e"]^2)/2; +SP[p,k1]=(SMP["m_W"]^2+SMP["m_e"]^2)/2; +SP[p,k2]=(SMP["m_W"]^2-SMP["m_e"]^2)/2; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We average over the polarizations of the W-boson, hence the additional factor 1/3*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))//SUNSimplify// + FermionSpinSum//DiracSimplify// + DoPolarizationSums[#,p,ExtraFactor -> 1/3]&//Simplify + + +(* ::Section:: *) +(*Total decay rate*) + + +phaseSpacePrefactor[m1_,m2_,M_]:=1/(16 Pi M)Sqrt[1-(m1+m2)^2/M^2]* + Sqrt[1-(m1-m2)^2/M^2]; + + +totalDecayRate=phaseSpacePrefactor[SMP["m_e"],0,SMP["m_W"]]* + ampSquared[0]//Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (SMP["G_F"](SMP["m_e"] - SMP["m_W"])^2(SMP["m_e"] + + SMP["m_W"])^2(SMP["m_e"]^2 + 2*SMP["m_W"]^2))/ + (12*Sqrt[2]*Pi*SMP["m_W"]^3) +}; +FCCompareResults[{totalDecayRate}, +knownResults, +Text->{"\tCompare to Grozin, \ +Using REDUCE in High Energy Physics, Chapter 5.2:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/EW/Tree/W-QiQjbar.m b/FeynCalc/Examples/EW/Tree/W-QiQjbar.m new file mode 100644 index 000000000..5b2a067a1 --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/W-QiQjbar.m @@ -0,0 +1,134 @@ +(* ::Package:: *) + +(* :Title: W-QiQjbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: W -> Qi Qjbar, EW, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*W decaying into a quark and an antiquark of different flavors*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="W -> Qi Qjbar, EW, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], + {V[3]} -> {-F[3,{1}],F[4,{1}]}, InsertionLevel -> {Particles}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p}, + OutgoingMomenta->{k1,k2},ChangeDimension->4,List->False, SMP->True, + Contract->True,DropSumOver->True, FinalSubstitutions-> + {SMP["e"]->Sqrt[8/Sqrt[2]SMP["G_F"] SMP["m_W"]^2SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[] +SP[p]=SMP["m_W"]^2; +SP[k1]=SMP["m_u"]^2; +SP[k2]=SMP["m_d"]^2; +SP[k1,k2]=(SMP["m_W"]^2-SMP["m_u"]^2-SMP["m_d"]^2)/2; +SP[p,k1]=Simplify[ExpandScalarProduct[SP[k1+k2,k1]]]; +SP[p,k2]=Simplify[ExpandScalarProduct[SP[k1+k2,k2]]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We average over the polarizations of the W-boson, hence the additional factor 1/3.*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))//SUNSimplify// + FermionSpinSum//DiracSimplify// + DoPolarizationSums[#,p,ExtraFactor -> 1/3]&//Simplify + + +(* ::Section:: *) +(*Total decay rate*) + + +phaseSpacePrefactor[m1_,m2_,M_]:=1/(16 Pi M)Sqrt[1-(m1+m2)^2/M^2]* + Sqrt[1-(m1-m2)^2/M^2]; + + +totalDecayRate=phaseSpacePrefactor[SMP["m_u"], SMP["m_d"], SMP["m_W"]]* + ampSquared[0]//Simplify// + ReplaceAll[#,Sqrt[x_]Sqrt[y_]:>Sqrt[ExpandAll[x y]]]&//Factor2 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + SMP["m_W"]^3(CA*SMP["G_F"]*Sqrt[((SMP["m_d"] - SMP["m_u"] - SMP["m_W"])*(SMP["m_d"] + SMP["m_u"] - SMP["m_W"])* + (SMP["m_d"] - SMP["m_u"] + SMP["m_W"])*(SMP["m_d"] + SMP["m_u"] + SMP["m_W"]))/SMP["m_W"]^4]* +(1-(SMP["m_u"]^2+SMP["m_d"]^2)/(2SMP["m_W"]^2)-(SMP["m_u"]^2-SMP["m_d"]^2)^2/(2 SMP["m_W"]^4))*SMP["V_ud", -I]*SMP["V_ud", I])/ +(6*Sqrt[2]*Pi) +}; +FCCompareResults[{totalDecayRate}, +knownResults, +Text->{"\tCompare to Grozin, \ +Using REDUCE in High Energy Physics, Chapter 5.2:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/EW/Tree/Z-FFbar.m b/FeynCalc/Examples/EW/Tree/Z-FFbar.m new file mode 100644 index 000000000..47b4fc96b --- /dev/null +++ b/FeynCalc/Examples/EW/Tree/Z-FFbar.m @@ -0,0 +1,218 @@ +(* ::Package:: *) + +(* :Title: Z-FFbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Z -> F Fbar, EW, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Z boson decaying into a fermion-antifermion pair*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Z -> F Fbar, EW, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], + {V[2]} -> {F[1,{l}],-F[1,{l}]}, InsertionLevel -> {Classes}]; + +Paint[diagsLeptonsMassless, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +diagsLeptonsMassive = InsertFields[CreateTopologies[0,1 -> 2], + {V[2]} -> {F[2,{l}],-F[2,{l}]}, InsertionLevel -> {Classes}]; + +Paint[diagsLeptonsMassive, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +diagsUpQuarks = InsertFields[CreateTopologies[0,1 -> 2], + {V[2]} -> {F[3,{l}],-F[3,{l}]}, InsertionLevel -> {Classes}]; + +Paint[diagsUpQuarks, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +diagsDownQuarks = InsertFields[CreateTopologies[0,1 -> 2], + {V[2]} -> {F[4,{l}],-F[4,{l}]}, InsertionLevel -> {Classes}]; + +Paint[diagsDownQuarks, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +ampLeptonsMassless[0]=FCFAConvert[CreateFeynAmp[diagsLeptonsMassless],IncomingMomenta->{p}, + OutgoingMomenta->{l1,l2},List->False,ChangeDimension->4, + DropSumOver->True,SMP->True,Contract->True, + FinalSubstitutions->{MLE[l]->SMP["m_l"], SMP["e"]->Sqrt[8/Sqrt[2]* + SMP["G_F"] SMP["m_Z"]^2 SMP["cos_W"]^2 SMP["sin_W"]^2]}] + + +ampLeptonsMassive[0]=FCFAConvert[CreateFeynAmp[diagsLeptonsMassive],IncomingMomenta->{p}, + OutgoingMomenta->{p1,p2},List->False,ChangeDimension->4, + DropSumOver->True,SMP->True,Contract->True, + FinalSubstitutions->{MLE[l]->SMP["m_l"], SMP["e"]->Sqrt[8/Sqrt[2]* + SMP["G_F"] SMP["m_Z"]^2 SMP["cos_W"]^2 SMP["sin_W"]^2]}] + + +ampUpQuarks[0]=FCFAConvert[CreateFeynAmp[diagsUpQuarks],IncomingMomenta->{p}, + OutgoingMomenta->{k1,k2},List->False,ChangeDimension->4, + DropSumOver->True,SMP->True,Contract->True, + FinalSubstitutions->{MQU[l]->SMP["m_q"], SMP["e"]->Sqrt[8/Sqrt[2]* + SMP["G_F"] SMP["m_Z"]^2 SMP["cos_W"]^2 SMP["sin_W"]^2]}] + + +ampDownQuarks[0]=FCFAConvert[CreateFeynAmp[diagsDownQuarks],IncomingMomenta->{p}, + OutgoingMomenta->{k1,k2},List->False,ChangeDimension->4, + DropSumOver->True,SMP->True,Contract->True, + FinalSubstitutions->{MQD[l]->SMP["m_q"], SMP["e"]->Sqrt[8/Sqrt[2]* + SMP["G_F"] SMP["m_Z"]^2 SMP["cos_W"]^2 SMP["sin_W"]^2]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[] +SP[p]=SMP["m_Z"]^2; +SP[k1]=SMP["m_q"]^2; +SP[k2]=SMP["m_q"]^2; + +SP[p1]=SMP["m_l"]^2; +SP[p2]=SMP["m_l"]^2; + +SP[l1]=0; +SP[l2]=0; + +SP[k1,k2]=Simplify[(SP[p]-SP[k1]-SP[k2])/2]; +SP[p,k1]=Simplify[ExpandScalarProduct[SP[k1+k2,k1]]]; +SP[p,k2]=Simplify[ExpandScalarProduct[SP[k1+k2,k2]]]; + +SP[p1,p2]=Simplify[(SP[p]-SP[p1]-SP[p2])/2]; +SP[p,p1]=Simplify[ExpandScalarProduct[SP[p1+p2,p1]]]; +SP[p,p2]=Simplify[ExpandScalarProduct[SP[p1+p2,p2]]]; + +SP[l1,l2]=Simplify[(SP[p]-SP[l1]-SP[l2])/2]; +SP[p,l1]=Simplify[ExpandScalarProduct[SP[l1+l2,l1]]]; +SP[p,l2]=Simplify[ExpandScalarProduct[SP[l1+l2,l2]]]; + + +(* ::Section:: *) +(*Square the amplitudes*) + + +(* ::Text:: *) +(*We average over the polarizations of the W-boson, hence the additional factor 1/3*) + + +ampSquaredLeptonsMassless[0] = + (ampLeptonsMassless[0] (ComplexConjugate[ampLeptonsMassless[0]]))// + FermionSpinSum//DiracSimplify// + DoPolarizationSums[#,p,ExtraFactor -> 1/3]&//Simplify + + +ampSquaredLeptonsMassive[0] = + (ampLeptonsMassive[0] (ComplexConjugate[ampLeptonsMassive[0]]))// + FermionSpinSum//DiracSimplify// + DoPolarizationSums[#,p,ExtraFactor -> 1/3]&//Simplify + + +ampSquaredUpQuarks[0] = + (ampUpQuarks[0] (ComplexConjugate[ampUpQuarks[0]]))// + FermionSpinSum//DiracSimplify//SUNSimplify// + DoPolarizationSums[#,p,ExtraFactor -> 1/3]&//Simplify + + +ampSquaredDownQuarks[0] = + (ampDownQuarks[0] (ComplexConjugate[ampDownQuarks[0]]))// + FermionSpinSum//DiracSimplify//SUNSimplify// + DoPolarizationSums[#,p,ExtraFactor -> 1/3]&//Simplify + + +(* ::Section:: *) +(*Total decay rates*) + + +phaseSpacePrefactor[m1_,m2_,M_]:=1/(16 Pi M)Sqrt[1-(m1+m2)^2/M^2]* + Sqrt[1-(m1-m2)^2/M^2]; + + +totalDecayRateLeptonsMassless=phaseSpacePrefactor[0,0,SMP["m_Z"]]* + ampSquaredLeptonsMassless[0]//Simplify + + +totalDecayRateLeptonsMassive=phaseSpacePrefactor[SMP["m_l"],SMP["m_l"],SMP["m_Z"]]* + ampSquaredLeptonsMassive[0]//Simplify + + +totalDecayRateUpQuarks=phaseSpacePrefactor[SMP["m_q"],SMP["m_q"],SMP["m_Z"]]* + ampSquaredUpQuarks[0]//Simplify + + +totalDecayRateDownQuarks=phaseSpacePrefactor[SMP["m_q"],SMP["m_q"],SMP["m_Z"]]* + ampSquaredDownQuarks[0]//Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +tmp=(SMP["G_F"]*Sqrt[1 - (4*mf^2)/SMP["m_Z"]^2]*SMP["m_Z"]^3* + (cv^2(1+2mf^2/SMP["m_Z"]^2)+ca^2(1-4mf^2/SMP["m_Z"]^2)))/(6*Pi Sqrt[2]); +knownResults = { + tmp/.{cv|ca->1/2,mf->0}, + tmp/.{cv->-1/2+2SMP["sin_W"]^2,ca->-1/2,mf->SMP["m_l"]}, + CA tmp/.{cv->1/2-4/3SMP["sin_W"]^2,ca->1/2,mf->SMP["m_q"]}, + CA tmp/.{cv->-1/2+2/3SMP["sin_W"]^2,ca->-1/2,mf->SMP["m_q"]} +}; +FCCompareResults[{ + totalDecayRateLeptonsMassless, + totalDecayRateLeptonsMassive, + totalDecayRateUpQuarks, + totalDecayRateDownQuarks}, +knownResults, +Text->{"\tCompare to Grozin, \ +Using REDUCE in High Energy Physics, Chapter 5.2:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/FeynRules/EulerHeisenberg/EulerHeisenberg.fr b/FeynCalc/Examples/FeynRules/EulerHeisenberg/EulerHeisenberg.fr new file mode 100644 index 000000000..dc7994dd8 --- /dev/null +++ b/FeynCalc/Examples/FeynRules/EulerHeisenberg/EulerHeisenberg.fr @@ -0,0 +1,40 @@ +M$ModelName = "Euler-Heisenberg Lagrangian"; + +$FeymanGauge=True; + +M$Information = { + Authors -> {"V. Shtabovenko"}, + Institutions -> {"Technische Universität München"}, + Emails -> {"v.shtabovenko@tum.de"}, + Date -> "March 2, 2017" +}; + +M$Parameters = { + EL == {ParameterType -> Internal}, + ME == {ParameterType -> External}, + c1 == {ParameterType -> External}, + c2 == {ParameterType -> External} +}; + +M$GaugeGroups = { + U1 == { + Abelian -> True, + CouplingConstant -> EL, + GaugeBoson -> A, + Charge -> Q + } +}; + +M$ClassesDescription = { + + V[1] == { + ClassName -> A, + SelfConjugate -> True, + Mass -> 0, + PropagatorLabel -> "\\gamma", + PropagatorType -> W, + PropagatorArrow -> None + } +}; + +LEH = -1/4 FS[A, imu, inu] FS[A, imu, inu] + (c1/ME^4) (FS[A, imu1, inu1] FS[A, imu1, inu1] FS[A, imu2, inu2] FS[A, imu2, inu2]) + (c2/ME^4) FS[A, imu, inu] FS[A, inu, isi] FS[A, isi, irho] FS[A, irho, imu]; diff --git a/FeynCalc/Examples/FeynRules/EulerHeisenberg/GenerateModelEulerHeisenberg.m b/FeynCalc/Examples/FeynRules/EulerHeisenberg/GenerateModelEulerHeisenberg.m new file mode 100644 index 000000000..5b785d60c --- /dev/null +++ b/FeynCalc/Examples/FeynRules/EulerHeisenberg/GenerateModelEulerHeisenberg.m @@ -0,0 +1,47 @@ +(* ::Package:: *) + +(* :Title: GenerateModelEulerHeisenberg *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Generates FeynArts model for the Euler-Heisenberg Lagrangian *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Section:: *) +(*Euler-Heisenberg Lagrangian model for FeynArts*) + + +(* ::Subsection:: *) +(*Load FeynRules*) + + +FR$Parallel=False; +$FeynRulesPath=SetDirectory[$UserBaseDirectory<>"/Applications/FeynRules"]; +<"EulerHeisenberg",CouplingRename->False]; + + + diff --git a/FeynCalc/Examples/FeynRules/EulerHeisenberg/ValidateModelEulerHeisenberg.m b/FeynCalc/Examples/FeynRules/EulerHeisenberg/ValidateModelEulerHeisenberg.m new file mode 100644 index 000000000..83bf7280c --- /dev/null +++ b/FeynCalc/Examples/FeynRules/EulerHeisenberg/ValidateModelEulerHeisenberg.m @@ -0,0 +1,87 @@ +(* ::Package:: *) + +(* :Title: ValidateModelEulerHeisenberg *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Validates FeynArts model for the Euler-Heisenberg Lagrangian *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Section:: *) +(*Load FeynCalc and FeynArts*) + + +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print["Validation of the FeynArts model for the Euler-Heisenberg Lagrangian"]; +]; +If[$Notebooks === False, $FeynCalcStartupMessages = False]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Check vertices*) + + +diag=InsertFields[CreateTopologies[0,2 -> 2],{V[1],V[1]} -> {V[1],V[1]}, +InsertionLevel -> {Classes},Model -> FileNameJoin[{"EulerHeisenberg","EulerHeisenberg"}], +GenericModel->FileNameJoin[{"EulerHeisenberg","EulerHeisenberg"}]]; + + +amp=FCFAConvert[CreateFeynAmp[diag, Truncated -> True,PreFactor->1], +IncomingMomenta->{p1,p2},OutgoingMomenta->{p2,p3},UndoChiralSplittings->True, +DropSumOver->True, List->False,SMP->True]; + + +c1Part=1/SMP["m_e"]^4 32 I c1 (FV[p1,Lor2] FV[p2,Lor1] FV[p2,Lor4] FV[p3,Lor3]- +FV[p2,Lor4] FV[p3,Lor3] MT[Lor1,Lor2] SP[p1,p2]-FV[p2,Lor4] FV[p3,Lor2] MT[Lor1,Lor3] SP[p1,p2]- +FV[p2,Lor2] FV[p2,Lor3] MT[Lor1,Lor4] SP[p1,p3]+MT[Lor1,Lor4] MT[Lor2,Lor3] SP[p1,p3] SP[p2,p2]+ +FV[p1,Lor4] FV[p3,Lor1] (FV[p2,Lor2] FV[p2,Lor3]-MT[Lor2,Lor3] SP[p2,p2])- +FV[p1,Lor2] FV[p2,Lor1] MT[Lor3,Lor4] SP[p2,p3]+MT[Lor1,Lor3] MT[Lor2,Lor4] SP[p1,p2] SP[p2,p3]+ +MT[Lor1,Lor2] MT[Lor3,Lor4] SP[p1,p2] SP[p2,p3]+FV[p1,Lor3] FV[p2,Lor1] (FV[p2,Lor4] FV[p3,Lor2]-MT[Lor2,Lor4] SP[p2,p3])); + + +c2Part=1/SMP["m_e"]^4 8 I c2 (-FV[p2,Lor4] FV[p3,Lor3] MT[Lor1,Lor2] SP[p1,p2]- +FV[p2,Lor4] FV[p3,Lor2] MT[Lor1,Lor3] SP[p1,p2]-FV[p2,Lor3] FV[p3,Lor2] MT[Lor1,Lor4] SP[p1,p2]- +FV[p2,Lor2] FV[p3,Lor3] MT[Lor1,Lor4] SP[p1,p2]-FV[p2,Lor3] FV[p2,Lor4] MT[Lor1,Lor2] SP[p1,p3]- +FV[p2,Lor2] FV[p2,Lor4] MT[Lor1,Lor3] SP[p1,p3]-FV[p1,Lor4] FV[p3,Lor3] MT[Lor1,Lor2] SP[p2,p2]- +FV[p1,Lor4] FV[p3,Lor2] MT[Lor1,Lor3] SP[p2,p2]+FV[p1,Lor3] FV[p3,Lor2] MT[Lor1,Lor4] SP[p2,p2]+ +FV[p1,Lor2] FV[p3,Lor3] MT[Lor1,Lor4] SP[p2,p2]+MT[Lor1,Lor3] MT[Lor2,Lor4] SP[p1,p3] SP[p2,p2]+ +MT[Lor1,Lor2] MT[Lor3,Lor4] SP[p1,p3] SP[p2,p2]+FV[p3,Lor1] (-2 FV[p2,Lor4] MT[Lor2,Lor3] SP[p1,p2] ++FV[p2,Lor3] MT[Lor2,Lor4] SP[p1,p2]+FV[p2,Lor2] (FV[p1,Lor3] FV[p2,Lor4]+MT[Lor3,Lor4] SP[p1,p2])- +FV[p1,Lor3] MT[Lor2,Lor4] SP[p2,p2]+FV[p1,Lor2] (FV[p2,Lor3] FV[p2,Lor4]-MT[Lor3,Lor4] SP[p2,p2]))+ +FV[p1,Lor4] FV[p2,Lor3] MT[Lor1,Lor2] SP[p2,p3]+FV[p1,Lor4] FV[p2,Lor2] MT[Lor1,Lor3] SP[p2,p3]- +FV[p1,Lor3] FV[p2,Lor2] MT[Lor1,Lor4] SP[p2,p3]-FV[p1,Lor2] FV[p2,Lor3] MT[Lor1,Lor4] SP[p2,p3]+ +2 MT[Lor1,Lor4] MT[Lor2,Lor3] SP[p1,p2] SP[p2,p3]+MT[Lor1,Lor3] MT[Lor2,Lor4] SP[p1,p2] SP[p2,p3]+ +MT[Lor1,Lor2] MT[Lor3,Lor4] SP[p1,p2] SP[p2,p3]+FV[p2,Lor1] ((FV[p1,Lor4] FV[p2,Lor3]+ +FV[p1,Lor3] FV[p2,Lor4]) FV[p3,Lor2]+FV[p1,Lor2] FV[p2,Lor4] FV[p3,Lor3]+ +2 FV[p2,Lor4] MT[Lor2,Lor3] SP[p1,p3]-FV[p2,Lor3] MT[Lor2,Lor4] SP[p1,p3]+ +FV[p2,Lor2] (FV[p1,Lor4] FV[p3,Lor3]-MT[Lor3,Lor4] SP[p1,p3])-2 FV[p1,Lor4] MT[Lor2,Lor3] SP[p2,p3]- +FV[p1,Lor3] MT[Lor2,Lor4] SP[p2,p3]-FV[p1,Lor2] MT[Lor3,Lor4] SP[p2,p3])); + + +(* ::Subsection:: *) +(*Check*) + + +Print["Check vertices in the Euler-Heisenberg Lagrangian model: ", + If[{Simplify[FCE[SelectNotFree2[amp,c1]]-c1Part],Simplify[FCE[SelectNotFree2[amp,c2]]-c2Part]}===Table[0,2], "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/FeynRules/Phi3/GenerateModelPhi3.m b/FeynCalc/Examples/FeynRules/Phi3/GenerateModelPhi3.m new file mode 100644 index 000000000..9ec13e507 --- /dev/null +++ b/FeynCalc/Examples/FeynRules/Phi3/GenerateModelPhi3.m @@ -0,0 +1,45 @@ +(* ::Package:: *) + +(* :Title: GenerateModelPhi3 *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Generates FeynArts model for the scalar phi^3 theory *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Section:: *) +(*phi^3 model for FeynArts*) + + +(* ::Subsection:: *) +(*Load FeynRules*) + + +FR$Parallel=False; +$FeynRulesPath=SetDirectory[$UserBaseDirectory<>"/Applications/FeynRules"]; +<"Phi3",CouplingRename->False]; diff --git a/FeynCalc/Examples/FeynRules/Phi3/Phi3.fr b/FeynCalc/Examples/FeynRules/Phi3/Phi3.fr new file mode 100644 index 000000000..608fc4ba5 --- /dev/null +++ b/FeynCalc/Examples/FeynRules/Phi3/Phi3.fr @@ -0,0 +1,30 @@ +M$ModelName = "Phi3"; + +M$Information = { + Authors -> {"V. Shtabovenko"}, + Institutions -> {"Technische Universität München"}, + Emails -> {"v.shtabovenko@tum.de"}, + Date -> "September 1, 2016" +}; + +M$Parameters = +Join[{g == {ParameterType -> + Internal}}, (# == {ParameterType -> External}) & /@ {Zm, Zphi, Zg}] + +M$ClassesDescription = { + + S[1] == { + ClassName -> phi, + ParticleName -> "\[Phi]", + PropagatorLabel -> "\[Phi]", + SelfConjugate -> True, + Mass -> Mphi + } + +}; + +LPhi3 = LPhi3R + LPhi3CT; + +LPhi3R = 1/2 del[phi, mu] del[phi, mu] - 1/2 Mphi^2*phi^2 - 1/(3!) g*phi^3; + +LPhi3CT = 1/2 FR$CT (Zphi-1) del[phi, mu] del[phi, mu] - 1/2 FR$CT Mphi^2 (Zm Zphi-1)*phi^2 - 1/(3!) FR$CT (Zg Zphi^(3/2)-1)*g*phi^3; diff --git a/FeynCalc/Examples/FeynRules/Phi34/GenerateModelPhi34.m b/FeynCalc/Examples/FeynRules/Phi34/GenerateModelPhi34.m new file mode 100644 index 000000000..b89d46e0d --- /dev/null +++ b/FeynCalc/Examples/FeynRules/Phi34/GenerateModelPhi34.m @@ -0,0 +1,55 @@ +(* ::Package:: *) + +(* :Title: GenerateModelPhi34 *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Generates FeynArts model for the scalar theory + with phi^3 and phi^4 interactions *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Section:: *) +(*phi^3+phi^4 model for FeynArts*) + + +(* ::Subsection:: *) +(*Load FeynRules*) + + +FR$Parallel=False; +$FeynRulesPath=SetDirectory[$UserBaseDirectory<>"/Applications/FeynRules"]; +<"Phi34",CouplingRename->False]; + + + + + + + + + diff --git a/FeynCalc/Examples/FeynRules/Phi34/Phi34.fr b/FeynCalc/Examples/FeynRules/Phi34/Phi34.fr new file mode 100644 index 000000000..b136b60b1 --- /dev/null +++ b/FeynCalc/Examples/FeynRules/Phi34/Phi34.fr @@ -0,0 +1,27 @@ +M$ModelName = "Phi34"; + +M$Information = { + Authors -> {"V. Shtabovenko"}, + Institutions -> {"Technische Universität München"}, + Emails -> {"v.shtabovenko@tum.de"}, + Date -> "September 1, 2016" +}; + +M$Parameters = +Join[{g3 == {ParameterType -> + Internal}}, {g4 == {ParameterType -> + Internal}}] + +M$ClassesDescription = { + + S[1] == { + ClassName -> phi, + ParticleName -> "\[Phi]", + PropagatorLabel -> "\[Phi]", + SelfConjugate -> True, + Mass -> Mphi + } + +}; + +LPhi34 = 1/2 del[phi, mu] del[phi, mu] - 1/2 Mphi^2*phi^2 - 1/(3!) g3*phi^3 - 1/(4!) g4*phi^4; diff --git a/FeynCalc/Examples/FeynRules/Phi4/GenerateModelPhi4.m b/FeynCalc/Examples/FeynRules/Phi4/GenerateModelPhi4.m new file mode 100644 index 000000000..7c4c4e8eb --- /dev/null +++ b/FeynCalc/Examples/FeynRules/Phi4/GenerateModelPhi4.m @@ -0,0 +1,51 @@ +(* ::Package:: *) + +(* :Title: GenerateModelPhi4 *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Generates FeynArts model for the scalar phi^4 theory *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Section:: *) +(*phi^4 model for FeynArts*) + + +(* ::Subsection:: *) +(*Load FeynRules*) + + +FR$Parallel=False; +$FeynRulesPath=SetDirectory[$UserBaseDirectory<>"/Applications/FeynRules"]; +<"Phi4",CouplingRename->False]; + + + + + + diff --git a/FeynCalc/Examples/FeynRules/Phi4/Phi4.fr b/FeynCalc/Examples/FeynRules/Phi4/Phi4.fr new file mode 100644 index 000000000..a3325679d --- /dev/null +++ b/FeynCalc/Examples/FeynRules/Phi4/Phi4.fr @@ -0,0 +1,29 @@ +M$ModelName = "Phi4"; + +M$Information = { + Authors -> {"V. Shtabovenko"}, + Institutions -> {"Technische Universität München"}, + Emails -> {"v.shtabovenko@tum.de"}, + Date -> "September 1, 2016" +}; + +M$Parameters = +Join[{g == {ParameterType -> + Internal}}, (# == {ParameterType -> External}) & /@ {Zm, Zphi, Zg}] + +M$ClassesDescription = { + + S[1] == { + ClassName -> phi, + ParticleName -> "\[Phi]", + PropagatorLabel -> "\[Phi]", + SelfConjugate -> True, + Mass -> Mphi + } + +}; + +LPhi4 = LPhi4R + LPhi4CT; + +LPhi4R = 1/2 del[phi, mu] del[phi, mu] - 1/2 Mphi^2*phi^2 - 1/(4!) g*phi^4; +LPhi4CT = 1/2 FR$CT (Zphi-1) del[phi, mu] del[phi, mu] - 1/2 Mphi^2 FR$CT (Zm Zphi-1)*phi^2 - 1/(4!) FR$CT (Zg Zphi^2-1)*g*phi^4; diff --git a/FeynCalc/Examples/FeynRules/QCD/GenerateModelQCD.m b/FeynCalc/Examples/FeynRules/QCD/GenerateModelQCD.m new file mode 100644 index 000000000..79a11fea1 --- /dev/null +++ b/FeynCalc/Examples/FeynRules/QCD/GenerateModelQCD.m @@ -0,0 +1,47 @@ +(* ::Package:: *) + +(* :Title: GenerateModelQCD *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Generates FeynArts model for QCD *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Section:: *) +(*QCD model for FeynArts*) + + +(* ::Subsection:: *) +(*Load FeynRules*) + + +FR$Parallel=False; +$FeynRulesPath=SetDirectory[$UserBaseDirectory<>"/Applications/FeynRules"]; +<"QCD",CouplingRename->False]; + + +input=FileNameJoin[{$UserBaseDirectory,"Applications","FeynCalc","FeynArts","Models","QCD","QCD.gen"}]; +tmp = Import[input, "Text"] <> "\n"; +res=StringJoin[{tmp,"GaugeXi[V[5,___]]=GaugeXi[\"G\"]; \n GaugeXi[U[5,___]]=GaugeXi[\"G\"]; \n"}]; +Export[input, res, "Text"]; diff --git a/FeynCalc/Examples/FeynRules/QCD/QCD.fr b/FeynCalc/Examples/FeynRules/QCD/QCD.fr new file mode 100644 index 000000000..af849b5d1 --- /dev/null +++ b/FeynCalc/Examples/FeynRules/QCD/QCD.fr @@ -0,0 +1,137 @@ +M$ModelName = "QCD"; + +FeynmanGauge=False; + +M$Information = { +Authors -> {"V. Shtabovenko"}, +Institutions -> {"Technische Universität München"}, +Emails -> {"v.shtabovenko@tum.de"}, +Date -> "July 15, 2017" +}; + +IndexRange[Index[Gluon ]] = NoUnfold[Range[8]]; +IndexRange[Index[Colour ]] = NoUnfold[Range[3]]; +IndexRange[Index[Generation]] = Range[3]; + +IndexStyle[Gluon, a]; +IndexStyle[Colour, m]; +IndexStyle[Generation, f]; + +GaugeXi[V[5]] = GaugeXi["G"]; +GaugeXi[U[5]] = GaugeXi["G"]; + +M$Parameters = +Join[{gs == {ParameterType -> + Internal}}, (# == {ParameterType -> External}) & /@ {Zm, ZA, + Zpsi, Zxi, Zg, Zu}] + +M$GaugeGroups = { +SU3C == { + Abelian -> False, + CouplingConstant -> gs, + GaugeBoson -> G, + StructureConstant -> f, + Representations -> {T,Colour}, + SymmetricTensor -> dSUN +} + +}; + + + +M$ClassesDescription = { +(* +F[2] == { + ClassName -> l, + ClassMembers -> {ele, mu, ta}, + SelfConjugate -> False, + Indices -> {Index[Generation]}, + FlavorIndex -> Generation, + Mass -> {Mlep, {ME,5.11*^-4}, {MM,0.10566}, {ML,1.777}}, + Width -> 0, + QuantumNumbers -> {Q -> 1, LeptonNumber -> 1}, + PropagatorLabel -> {"l", "e", "mu", "ta"}, + PropagatorType -> Straight, + PropagatorArrow -> Forward +}, +*) +V[5] == { + ClassName -> G, + SelfConjugate -> True, + Indices -> {Index[Gluon]}, + Mass -> 0, + PropagatorLabel -> "g", + PropagatorType -> C, + PropagatorArrow -> None +}, + +U[5] == { + ClassName -> ghG, + SelfConjugate -> False, + Indices -> {Index[Gluon]}, + Ghost -> G, + QuantumNumbers ->{GhostNumber -> 1}, + Mass -> 0, + PropagatorLabel -> "uG", + PropagatorType -> GhostDash, + PropagatorArrow -> Forward +}, + +F[3] == { + ClassName -> uq, + ClassMembers -> {u, c, t}, + Indices -> {Index[Generation], Index[Colour]}, + FlavorIndex -> Generation, + SelfConjugate -> False, + Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}}, + Width -> 0, + PropagatorLabel -> {"uq", "u", "c", "t"}, + PropagatorType -> Straight, + PropagatorArrow -> Forward +}, +F[4] == { + ClassName -> dq, + ClassMembers -> {d, s, b}, + Indices -> {Index[Generation], Index[Colour]}, + FlavorIndex -> Generation, + SelfConjugate -> False, + Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}}, + Width -> 0, + PropagatorLabel -> {"dq", "d", "s", "b"}, + PropagatorType -> Straight, + PropagatorArrow -> Forward +} +}; + +LQCD = LQCDR + LQCDCT; + +LQCDR = ( +(* Pure gauge part of LQCD; Signs of gs adjusted to match the FeynArts' convention; + Actually, here the sign should be opposite, but then for some reason FeynRules + would generate a wrong 3-gluon vertex *) +- 1/4 (del[G[mu,aa],nu] - del[G[nu,aa],mu] +gs f[aa,bb,cc] G[mu,bb] G[nu,cc])* + (del[G[mu,aa],nu] - del[G[nu,aa],mu] +gs f[aa,dd,ee] G[mu,dd] G[nu,ee]) +(* Fermionic part of LQCD; Signs of gs adjusted to match FeynArts' convention *) + + uqbar.Ga[mu].(I del[uq,mu] - gs T[aa].G[mu,aa].uq) + + dqbar.Ga[mu].(I del[dq,mu] - gs T[aa].G[mu,aa].dq) + - Mu[fi] uqbar[s,fi,nn].uq[s,fi,nn] - Md[fi] dqbar[s,fi,nn].dq[s,fi,nn] +(* Ghost part of LQCD; Signs of gs adjusted to match the FeynArts' convention *) + - ghGbar[ii].del[del[ghG[ii],mu],mu] + - gs f[aa,cc,bb] G[mu,cc] del[ghGbar[aa],mu].ghG[bb] +); + + +LQCDCT = FR$CT ( + + (Zpsi-1) I (uqbar.Ga[imu].del[uq,imu] + dqbar.Ga[imu].del[dq,imu]) + - (Zpsi Zm -1) (Mu[fi] uqbar[s,fi,nn].uq[s,fi,nn] + Md[fi] dqbar[s,fi,nn].dq[s,fi,nn]) + (* Sign of gs adjusted to match the FeynArts' convention *) + + (Zpsi Sqrt[ZA] Zg - 1) (-gs) (uqbar.T[aa].Ga[imu].uq + dqbar.T[aa].Ga[imu].dq) G[imu,aa] + -1/4 (ZA-1) (del[G[mu,aa],nu] - del[G[nu,aa],mu])(del[G[mu,aa],nu] - del[G[nu,aa],mu]) + -1/(2 GaugeXi[V[5]])(ZA/Zxi-1) del[G[imu,aa],imu] del[G[inu,aa],inu] + (* Sign of gs adjusted to match the FeynArts' convention *) + - (Zg ZA^(3/2) -1) (-gs) del[G[nu,aa],mu] f[aa,bb,cc] G[mu,bb] G[nu,cc] + -1/4 (Zg^2 ZA^2 - 1) gs^2 f[aa,bb,cc] G[mu,bb] G[nu,cc] f[aa,dd,ee] G[mu,dd] G[nu,ee] + - (Zu-1) ghGbar[ii].del[del[ghG[ii],mu],mu] + (* Sign of gs adjusted to match the FeynArts' convention *) + - (Zg Sqrt[ZA] Zu -1) (-gs) f[aa,bb,cc] del[ghGbar[aa],mu].ghG[bb] G[mu,cc] + ); diff --git a/FeynCalc/Examples/FeynRules/QCD/ValidateModelQCD.m b/FeynCalc/Examples/FeynRules/QCD/ValidateModelQCD.m new file mode 100644 index 000000000..2337d59c7 --- /dev/null +++ b/FeynCalc/Examples/FeynRules/QCD/ValidateModelQCD.m @@ -0,0 +1,106 @@ +(* ::Package:: *) + +(* :Title: ValidateModelQCD *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Validates FeynArts model for QCD *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Section:: *) +(*Load FeynCalc and FeynArts*) + + +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print["Validation of the FeynArts model for QCD."]; +]; +If[$Notebooks === False, $FeynCalcStartupMessages = False]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Compare vertices to FeynArts*) + + +top1To2 = CreateTopologies[0,1 -> 2]; +top2To2 = CreateTopologies[0,2 -> 2]; + + +compFu1To2[x_]:=FCFAConvert[CreateFeynAmp[x, Truncated -> True,PreFactor->1], +IncomingMomenta->{p1},OutgoingMomenta->{p2,p3},UndoChiralSplittings->True, +DropSumOver->True,List->False,SMP->True]//Contract; + + +compFu2To2[x_]:=FCFAConvert[CreateFeynAmp[x, Truncated -> True,PreFactor->1], +IncomingMomenta->{p1,p2},OutgoingMomenta->{p3,p4},UndoChiralSplittings->True, +DropSumOver->True,List->False,SMP->True]//Contract; + + +diagsFR[top_,in_,out_]:=InsertFields[top, in ->out, +InsertionLevel -> {Classes},Model -> FileNameJoin[{"QCD","QCD"}], +GenericModel->FileNameJoin[{"QCD","QCD"}]]; + + +diagsFA[top_,in_,out_]:=InsertFields[top, in ->out, +InsertionLevel -> {Classes}, Model -> "SMQCD", GenericModel->Lorentz]; + + +(* ::Subsection:: *) +(*QQG-coupling*) + + +particles={{F[3, {1}]},{F[3, {1}],V[5]}}; +diff1=compFu1To2[diagsFR[top1To2,Sequence@@particles]]-compFu1To2[diagsFA[top1To2,Sequence@@particles]] + + +(* ::Subsection:: *) +(*GhGhG-coupling*) + + +particles={{U[5]},{U[5],V[5]}}; +diff2=compFu1To2[diagsFR[top1To2,Sequence@@particles]]-compFu1To2[diagsFA[top1To2,Sequence@@particles]] + + +(* ::Subsection:: *) +(*GGG-coupling*) + + +particles={{V[5]},{V[5],V[5]}}; +diff3=ExpandScalarProduct[compFu1To2[diagsFR[top1To2,Sequence@@particles]]-compFu1To2[diagsFA[top1To2,Sequence@@particles]]]//Simplify + + +(* ::Subsection:: *) +(*GGGG-coupling*) + + +particles={{V[5],V[5]},{V[5],V[5]}}; +diff4=ExpandScalarProduct[compFu2To2[DiagramExtract[diagsFR[top2To2,Sequence@@particles],1]]- +compFu2To2[DiagramExtract[diagsFA[top2To2,Sequence@@particles],1]]]//FCCanonicalizeDummyIndices//Simplify + + +(* ::Subsection:: *) +(*Check*) + + +Print["Check signs in the QCD model: ", + If[{diff1,diff2,diff3,diff4}===Table[0,4], "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/FeynRules/QCDBGF/GenerateModelQCDBGF.m b/FeynCalc/Examples/FeynRules/QCDBGF/GenerateModelQCDBGF.m index c8ad05785..69c2f42cb 100644 --- a/FeynCalc/Examples/FeynRules/QCDBGF/GenerateModelQCDBGF.m +++ b/FeynCalc/Examples/FeynRules/QCDBGF/GenerateModelQCDBGF.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Generates FeynArts model for QCD in background field diff --git a/FeynCalc/Examples/FeynRules/QCDBGF/PureYMSelfEnergyInQCDBGFAtOneLoop.m b/FeynCalc/Examples/FeynRules/QCDBGF/PureYMSelfEnergyInQCDBGFAtOneLoop.m deleted file mode 100644 index 24e3d9a76..000000000 --- a/FeynCalc/Examples/FeynRules/QCDBGF/PureYMSelfEnergyInQCDBGFAtOneLoop.m +++ /dev/null @@ -1,74 +0,0 @@ -(* ::Package:: *) - -(* :Title: PureYMSelfEnergyInQCDBGFAtOneLoop *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the self-energy diagrams in pure Yang Mills using -background field formalism at one loop. *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the self-energy diagrams in pure Yang Mills using -background field formalism at one loop."]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -<True]; - - -(* ::Section:: *) -(*Generate Feynman diagrams*) - - -topsYMSE=CreateTopologies[1, 1 -> 1,ExcludeTopologies -> {Tadpoles}]; -diagsYMSE=InsertFields[topsYMSE, {V[50,{a}]} -> {V[50,{b}]},InsertionLevel -> {Classes}, -Model -> FileNameJoin[{"QCDBGF","QCDBGF"}],GenericModel->FileNameJoin[{"QCDBGF","QCDBGF"}], -ExcludeParticles->{F[_]}]; -Paint[DiagramExtract[diagsYMSE,{3,4}], ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None, -ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampYMSE1=FCFAConvert[CreateFeynAmp[DiagramExtract[diagsYMSE,{3,4}], Truncated -> True,PreFactor->1], -IncomingMomenta->{k},OutgoingMomenta->{k},LoopMomenta->{l},UndoChiralSplittings->True, -DropSumOver->True,List->True,SMP->True,ChangeDimension->D] - - -ampYMSE2=TID[#,l,ToPaVe->True]&/@SUNSimplify/@Contract/@ampYMSE1 - - -ampYMSE3=Factor2/@Normal/@(Series[#,{EpsilonUV,0,0}]&/@FCReplaceD[#, -D->4-2EpsilonUV]&/@(ampYMSE2/.B0[FCI[SPD[k]],0,0]->1/(16*EpsilonUV*Pi^4))) - - -(* ::Section:: *) -(*Check with the literature*) - - -resAbbott={ -I CA SMP["g_s"]^2 SUNDelta[a,b]/(4Pi)^2(1/(3 EpsilonUV))(MTD[Lor1,Lor2]SPD[k]-FVD[k,Lor1]FVD[k,Lor2]), -I CA SMP["g_s"]^2 SUNDelta[a,b]/(4Pi)^2(10/(3 EpsilonUV))(MTD[Lor1,Lor2]SPD[k]-FVD[k,Lor1]FVD[k,Lor2]) -}; - - -Print["Check with Abbott, Nucl. Phys. B 185 (1981) 189-203, Eqs 5.11-5.12: ", - If[Simplify[ampYMSE3-FCI[resAbbott]]==={0,0}, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/FeynRules/QCDBGF/QCDBGF.fr b/FeynCalc/Examples/FeynRules/QCDBGF/QCDBGF.fr index c4289a23f..9a566a471 100644 --- a/FeynCalc/Examples/FeynRules/QCDBGF/QCDBGF.fr +++ b/FeynCalc/Examples/FeynRules/QCDBGF/QCDBGF.fr @@ -1,24 +1,24 @@ M$ModelName = "QCD in the background field formalism"; M$Information = { - Authors -> {"V. Shtabovenko"}, - Version -> "1.0.0", - Date -> "09. 10. 2014", - Institutions -> {"Technische Universitaet Muenchen"}, - URLs -> "https://github.com/FeynCalc" + Authors -> {"V. Shtabovenko"}, + Version -> "1.0.0", + Date -> "09. 10. 2014", + Institutions -> {"Technische Universitaet Muenchen"}, + URLs -> "https://github.com/FeynCalc" }; FeynmanGauge = False; M$GaugeGroups = { - SU3C == { - Abelian -> False, - CouplingConstant -> gs, - GaugeBoson -> G, - StructureConstant -> f, - Representations -> {T,Colour}, - SymmetricTensor -> dSUN - } +SU3C == { + Abelian -> False, + CouplingConstant -> gs, + GaugeBoson -> G, + StructureConstant -> f, + Representations -> {T,Colour}, + SymmetricTensor -> dSUN +} }; IndexRange[Index[Gluon ]] = NoUnfold[Range[8]]; @@ -32,70 +32,70 @@ IndexStyle[Generation, f]; M$ClassesDescription = { - V[5] == { - ClassName -> G, - SelfConjugate -> True, - Indices -> {Index[Gluon]}, - Mass -> 0, - ParticleName -> "g", - PropagatorLabel -> "g", - PropagatorType -> C, - PropagatorArrow -> None - }, - - U[5] == { - ClassName -> ghG, - SelfConjugate -> False, - Indices -> {Index[Gluon]}, - Ghost -> G, - QuantumNumbers ->{GhostNumber -> 1}, - Mass -> 0, - Width -> 0, - PropagatorLabel -> ComposedChar["u", "g"], - PropagatorType -> GhostDash, - PropagatorArrow -> Forward - }, - - V[50] == { - ClassName -> B, - SelfConjugate -> True, - Indices -> {Index[Gluon]}, - Mass -> 0, - ParticleName -> "A", - PropagatorType -> C, - InsertOnly -> {Internal, External}, - PropagatorArrow -> None - }, - - F[3] == { - ClassName -> uq, - ClassMembers -> {u, c, t}, - Indices -> {Index[Generation], Index[Colour]}, - FlavorIndex -> Generation, - SelfConjugate -> False, - Mass -> {MQU, {MU, 0.00255}, {MC, 1.27}, {MT, 172}}, - QuantumNumbers -> {Q -> 2/3}, - PropagatorLabel -> {ComposedChar["u", Index[Generation]], "u", "c", "t"}, - PropagatorType -> Straight, - PropagatorArrow -> Forward, - ParticleName -> {"u", "c", "t" }, - AntiParticleName -> {"u~", "c~", "t~"} - }, - - F[4] == { - ClassName -> dq, - ClassMembers -> {d, s, b}, - Indices -> {Index[Generation], Index[Colour]}, - FlavorIndex -> Generation, - SelfConjugate -> False, - Mass -> {MQD, {MD, 0.00504}, {MS, 0.101}, {MB, 4.7}}, - QuantumNumbers -> {Q -> -1/3}, - PropagatorLabel -> {ComposedChar["d", Index[Generation]], "d", "s", "b"}, - PropagatorType -> Straight, - PropagatorArrow -> Forward, - ParticleName -> {"d", "s", "b" }, - AntiParticleName -> {"d~", "s~", "b~"} - } +V[5] == { + ClassName -> G, + SelfConjugate -> True, + Indices -> {Index[Gluon]}, + Mass -> 0, + ParticleName -> "g", + PropagatorLabel -> "g", + PropagatorType -> C, + PropagatorArrow -> None +}, + +U[5] == { + ClassName -> ghG, + SelfConjugate -> False, + Indices -> {Index[Gluon]}, + Ghost -> G, + QuantumNumbers ->{GhostNumber -> 1}, + Mass -> 0, + Width -> 0, + PropagatorLabel -> ComposedChar["u", "g"], + PropagatorType -> GhostDash, + PropagatorArrow -> Forward +}, + +V[50] == { + ClassName -> B, + SelfConjugate -> True, + Indices -> {Index[Gluon]}, + Mass -> 0, + ParticleName -> "A", + PropagatorType -> C, + InsertOnly -> {Internal, External}, + PropagatorArrow -> None +}, + +F[3] == { + ClassName -> uq, + ClassMembers -> {u, c, t}, + Indices -> {Index[Generation], Index[Colour]}, + FlavorIndex -> Generation, + SelfConjugate -> False, + Mass -> {MQU, {MU, 0.00255}, {MC, 1.27}, {MT, 172}}, + QuantumNumbers -> {Q -> 2/3}, + PropagatorLabel -> {ComposedChar["u", Index[Generation]], "u", "c", "t"}, + PropagatorType -> Straight, + PropagatorArrow -> Forward, + ParticleName -> {"u", "c", "t" }, + AntiParticleName -> {"u~", "c~", "t~"} +}, + +F[4] == { + ClassName -> dq, + ClassMembers -> {d, s, b}, + Indices -> {Index[Generation], Index[Colour]}, + FlavorIndex -> Generation, + SelfConjugate -> False, + Mass -> {MQD, {MD, 0.00504}, {MS, 0.101}, {MB, 4.7}}, + QuantumNumbers -> {Q -> -1/3}, + PropagatorLabel -> {ComposedChar["d", Index[Generation]], "d", "s", "b"}, + PropagatorType -> Straight, + PropagatorArrow -> Forward, + ParticleName -> {"d", "s", "b" }, + AntiParticleName -> {"d~", "s~", "b~"} +} }; GaugeXi[V[5]] = GaugeXi[G]; @@ -104,36 +104,36 @@ GaugeXi[V[50]] = GaugeXi[G]; M$Parameters = { - aS == { - ParameterType -> External, - Value -> 0.1184 - }, +aS == { + ParameterType -> External, + Value -> 0.1184 +}, - gs == { - ParameterType -> Internal, - Value -> Sqrt[4 Pi aS] - } +gs == { + ParameterType -> Internal, + Value -> Sqrt[4 Pi aS] +} }; LQCD := Block[{mu,nu,al,aa,bb,cc,dd,ee}, - (* Pure gauge part of LQCD; Signs of gs adjusted to match FeynArts' convention; - Actually, here the sign should be opposite, but then for some reason FeynRules - would generate a wrong 3-gluon vertex *) - - 1/4 (del[G[mu,aa]+B[mu,aa],nu] - del[G[nu,aa]+B[nu,aa],mu] +gs f[aa,bb,cc] (G[mu,bb]+B[mu,bb]) (G[nu,cc]+B[nu,cc]))* - (del[G[mu,aa]+B[mu,aa],nu] - del[G[nu,aa]+B[nu,aa],mu] +gs f[aa,dd,ee] (G[mu,dd]+B[mu,dd]) (G[nu,ee]+B[nu,ee])) - (* Fermionic part of LQCD; Signs of gs adjusted to match FeynArts' convention *) - + dqbar.Ga[mu].(I del[dq,mu] - gs T[aa].(G[mu,aa] + B[mu,aa]).dq) - + uqbar.Ga[mu].(I del[uq,mu] - gs T[aa].(G[mu,aa] + B[mu,aa]).uq) - - MQU dqbar.dq - - MQD dqbar.dq - (* L_FP from Abbott 1980, Eq. 3.2; Signs of gs adjusted to match FeynArts' convention *) - - 1/(2 GaugeXi[G]) (del[G[mu,aa], mu]-del[B[mu,aa], mu] - gs f[aa,bb,cc] B[mu,bb] G[mu,cc])* - (del[G[nu,aa], nu]-del[B[nu,aa], nu] - gs f[aa,dd,ee] B[nu,dd] G[nu,ee]) - (* L_GHOST from Abbott 1980, Eq. 4.2; Signs of gs adjusted to match FeynArts' convention *) - - ghGbar.del[del[ghG,mu],mu] - - gs f[aa,cc,bb] (G[mu,cc]+B[mu,cc]) del[ghGbar[aa],mu].ghG[bb] - + gs f[aa,cc,bb] B[mu,cc] ghGbar[aa].del[ghG[bb],mu] - - gs^2 f[aa,cc,ee] f[dd,bb,ee] B[mu,cc] (G[mu,dd]+B[mu,dd]) ghGbar[aa].ghG[bb] + (* Pure gauge part of LQCD; Signs of gs adjusted to match FeynArts' convention; + Actually, here the sign should be opposite, but then for some reason FeynRules + would generate a wrong 3-gluon vertex *) +- 1/4 (del[G[mu,aa]+B[mu,aa],nu] - del[G[nu,aa]+B[nu,aa],mu] +gs f[aa,bb,cc] (G[mu,bb]+B[mu,bb]) (G[nu,cc]+B[nu,cc]))* + (del[G[mu,aa]+B[mu,aa],nu] - del[G[nu,aa]+B[nu,aa],mu] +gs f[aa,dd,ee] (G[mu,dd]+B[mu,dd]) (G[nu,ee]+B[nu,ee])) + (* Fermionic part of LQCD; Signs of gs adjusted to match FeynArts' convention *) + + dqbar.Ga[mu].(I del[dq,mu] - gs T[aa].(G[mu,aa] + B[mu,aa]).dq) + + uqbar.Ga[mu].(I del[uq,mu] - gs T[aa].(G[mu,aa] + B[mu,aa]).uq) + - MQU dqbar.dq + - MQD dqbar.dq + (* L_FP from Abbott 1980, Eq. 3.2; Signs of gs adjusted to match FeynArts' convention *) + - 1/(2 GaugeXi[G]) (del[G[mu,aa], mu]-del[B[mu,aa], mu] - gs f[aa,bb,cc] B[mu,bb] G[mu,cc])* + (del[G[nu,aa], nu]-del[B[nu,aa], nu] - gs f[aa,dd,ee] B[nu,dd] G[nu,ee]) + (* L_GHOST from Abbott 1980, Eq. 4.2; Signs of gs adjusted to match FeynArts' convention *) + - ghGbar.del[del[ghG,mu],mu] + - gs f[aa,cc,bb] (G[mu,cc]+B[mu,cc]) del[ghGbar[aa],mu].ghG[bb] + + gs f[aa,cc,bb] B[mu,cc] ghGbar[aa].del[ghG[bb],mu] + - gs^2 f[aa,cc,ee] f[dd,bb,ee] B[mu,cc] (G[mu,dd]+B[mu,dd]) ghGbar[aa].ghG[bb] ]; diff --git a/FeynCalc/Examples/FeynRules/QCDBGF/ValidateModelQCDBGF.m b/FeynCalc/Examples/FeynRules/QCDBGF/ValidateModelQCDBGF.m index a90113612..3be738e42 100644 --- a/FeynCalc/Examples/FeynRules/QCDBGF/ValidateModelQCDBGF.m +++ b/FeynCalc/Examples/FeynRules/QCDBGF/ValidateModelQCDBGF.m @@ -4,12 +4,12 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) -(* :Summary: Validates FeynArts model for QCD in background field +(* :Summary: Validates FeynArts model for QCD in background field formalism *) (* ------------------------------------------------------------------------ *) @@ -25,10 +25,12 @@ Print["Validation of the FeynArts model for QCD in background field formalism"]; ]; If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; +$LoadAddOns={"FeynArts"}; < 2]; -compFu1To2[x_]:=FCFAConvert[FCPrepareFAAmp[CreateFeynAmp[x, Truncated -> True,PreFactor->1]], +compFu1To2[x_]:=FCFAConvert[CreateFeynAmp[x, Truncated -> True,PreFactor->1], IncomingMomenta->{p1},OutgoingMomenta->{p2,p3},UndoChiralSplittings->True, DropSumOver->True,List->False,SMP->True]//Contract; -compFu2To2[x_]:=FCFAConvert[FCPrepareFAAmp[CreateFeynAmp[x, Truncated -> True,PreFactor->1]], +compFu2To2[x_]:=FCFAConvert[CreateFeynAmp[x, Truncated -> True,PreFactor->1], IncomingMomenta->{p1,p2},OutgoingMomenta->{p3,p4},UndoChiralSplittings->True, DropSumOver->True,List->False,SMP->True]//Contract; @@ -112,8 +114,8 @@ ggbDiag=InsertFields[top1To2, {V[50,{a}]} ->{V[5,{b}],V[5,{c}]}, InsertionLevel -> {Classes},Model -> FileNameJoin[{"QCDBGF","QCDBGF"}], GenericModel->FileNameJoin[{"QCDBGF","QCDBGF"}]]; -ggbAbbott=-(((FV[q, nu] + FV[-p + r, nu]*GaugeXi[G])*MT[la, mu]*SMP["g_s"]*SUNF[a, b, c])/GaugeXi[G]) + FV[-q + r, mu]*MT[la, nu]*SMP["g_s"]*SUNF[a, b, c] + - ((FV[r, la] + FV[-p + q, la]*GaugeXi[G])*MT[mu, nu]*SMP["g_s"]*SUNF[a, b, c])/GaugeXi[G]; +ggbAbbott=-(((FV[q, nu] + FV[-p + r, nu]*GaugeXi[G])*MT[la, mu]*SMP["g_s"]*SUNF[a, b, c])/GaugeXi[G]) + FV[-q + r, mu]*MT[la, nu]*SMP["g_s"]*SUNF[a, b, c] + +((FV[r, la] + FV[-p + q, la]*GaugeXi[G])*MT[mu, nu]*SMP["g_s"]*SUNF[a, b, c])/GaugeXi[G]; ggbVertexFR=FCFAConvert[CreateFeynAmp[ggbDiag, Truncated -> True,PreFactor->-1,GaugeRules->{}], IncomingMomenta->{-p},OutgoingMomenta->{q,r},UndoChiralSplittings->True, DropSumOver->True,List->False,SMP->True,LorentzIndexNames->{mu,nu,la}]//FCE//Collect2[#,MT,Factoring->FullSimplify]&//MomentumCombine @@ -129,7 +131,7 @@ GenericModel->FileNameJoin[{"QCDBGF","QCDBGF"}]]; ghghbFR=FCFAConvert[CreateFeynAmp[ghghbDiag, Truncated -> True,PreFactor->-1,GaugeRules->{}], IncomingMomenta->{-p},OutgoingMomenta->{-q,r},UndoChiralSplittings->True, -DropSumOver->True,List->False,SMP->True,LorentzIndexNames->{mu,nu,la}]//FCE//FCI//MomentumCombine2 +DropSumOver->True,List->False,SMP->True,LorentzIndexNames->{mu,nu,la}]//FCE//FCI//MomentumCombine ghghbAbbott=FV[p + q, mu]*SMP["g_s"]*SUNF[a, b, c]; diff7=FCI[(ghghbAbbott-ghghbFR)] @@ -141,14 +143,14 @@ ggbbDiag=InsertFields[top2To2, {V[50,{a}],V[5,{d}]} ->{V[5,{b}],V[50,{c}]}, InsertionLevel -> {Classes},Model -> FileNameJoin[{"QCDBGF","QCDBGF"}], GenericModel->FileNameJoin[{"QCDBGF","QCDBGF"}]]; -ggbbAbbott=((-I)*(MT[la, rho]*MT[mu, nu] + GaugeXi[G]*(-(MT[la, nu]*MT[mu, rho]) + MT[la, mu]*MT[nu, rho]))*SMP["g_s"]^2*SUNF[a, d, x]*SUNF[b, c, x])/GaugeXi[G] + - I*(-(MT[la, rho]*MT[mu, nu]) + MT[la, nu]*MT[mu, rho])*SMP["g_s"]^2*SUNF[a, c, x]*SUNF[b, d, x] + - (I*(MT[la, nu]*MT[mu, rho] + GaugeXi[G]*(-(MT[la, rho]*MT[mu, nu]) + MT[la, mu]*MT[nu, rho]))*SMP["g_s"]^2*SUNF[a, b, x]*SUNF[c, d, x])/GaugeXi[G]; +ggbbAbbott=((-I)*(MT[la, rho]*MT[mu, nu] + GaugeXi[G]*(-(MT[la, nu]*MT[mu, rho]) + MT[la, mu]*MT[nu, rho]))*SMP["g_s"]^2*SUNF[a, d, x]*SUNF[b, c, x])/GaugeXi[G] + +I*(-(MT[la, rho]*MT[mu, nu]) + MT[la, nu]*MT[mu, rho])*SMP["g_s"]^2*SUNF[a, c, x]*SUNF[b, d, x] + +(I*(MT[la, nu]*MT[mu, rho] + GaugeXi[G]*(-(MT[la, rho]*MT[mu, nu]) + MT[la, mu]*MT[nu, rho]))*SMP["g_s"]^2*SUNF[a, b, x]*SUNF[c, d, x])/GaugeXi[G]; ggbbVertexFR=FCFAConvert[CreateFeynAmp[DiagramExtract[ggbbDiag,{1}], Truncated -> True,PreFactor->-1,GaugeRules->{}], IncomingMomenta->{-p},OutgoingMomenta->{q,r},UndoChiralSplittings->True, DropSumOver->True,List->False,SMP->True,LorentzIndexNames->{mu,nu,rho,la}]//FCE//FCCanonicalizeDummyIndices[#,SUNIndexNames->{x}]&// Collect2[#,SUNF,Factoring->FullSimplify]& -diff8=FCI[(ggbbAbbott-ggbbVertexFR)] +diff8=FCI[(ggbbAbbott-ggbbVertexFR)]//FCCanonicalizeDummyIndices (* ::Subsection:: *) diff --git a/FeynCalc/Examples/FeynRules/QED/GenerateModelQED.m b/FeynCalc/Examples/FeynRules/QED/GenerateModelQED.m index de669605a..fa73b5ae3 100644 --- a/FeynCalc/Examples/FeynRules/QED/GenerateModelQED.m +++ b/FeynCalc/Examples/FeynRules/QED/GenerateModelQED.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Generates FeynArts model for QED *) diff --git a/FeynCalc/Examples/FeynRules/QED/QED.fr b/FeynCalc/Examples/FeynRules/QED/QED.fr index 5e14e50a8..9603ecc9a 100644 --- a/FeynCalc/Examples/FeynRules/QED/QED.fr +++ b/FeynCalc/Examples/FeynRules/QED/QED.fr @@ -1,59 +1,60 @@ M$ModelName = "QED"; -$FeymanGauge=False; +FeynmanGauge=False; M$Information = { - Authors -> {"V. Shtabovenko"}, - Institutions -> {"Technische Universität München"}, - Emails -> {"v.shtabovenko@tum.de"}, - Date -> "November 2, 2016" + Authors -> {"V. Shtabovenko"}, + Institutions -> {"Technische Universität München"}, + Emails -> {"v.shtabovenko@tum.de"}, + Date -> "November 2, 2016" }; IndexRange[Index[Generation]] = Range[3]; IndexStyle[Generation, f]; M$Parameters = - Join[{EL == {ParameterType -> - Internal}}, (# == {ParameterType -> External}) & /@ {Zm, ZA, - Zpsi, Zxi, Ze}] +Join[{EL == {ParameterType -> + Internal}}, (# == {ParameterType -> External}) & /@ {Zm, ZA, + Zpsi, Zxi, Zg}] M$GaugeGroups = { - U1 == { - Abelian -> True, - CouplingConstant -> EL, - GaugeBoson -> A, - Charge -> Q - } + U1 == { + Abelian -> True, + CouplingConstant -> EL, + GaugeBoson -> A, + Charge -> Q + } }; M$ClassesDescription = { - F[2] == { - ClassName -> l, - ClassMembers -> {ele, mu, ta}, - SelfConjugate -> False, - Indices -> {Index[Generation]}, - FlavorIndex -> Generation, - Mass -> {Mlep, {ME,5.11*^-4}, {MM,0.10566}, {ML,1.777}}, - Width -> 0, - QuantumNumbers -> {Q -> 1, LeptonNumber -> 1}, - PropagatorLabel -> {"l", "e", "mu", "ta"}, - PropagatorType -> Straight, - PropagatorArrow -> Forward - }, - - V[1] == { - ClassName -> A, - SelfConjugate -> True, - Mass -> 0, - PropagatorLabel -> "\\gamma", - PropagatorType -> W, - PropagatorArrow -> None - } +F[2] == { + ClassName -> l, + ClassMembers -> {ele, mu, ta}, + SelfConjugate -> False, + Indices -> {Index[Generation]}, + FlavorIndex -> Generation, + Mass -> {Mlep, {ME,5.11*^-4}, {MM,0.10566}, {ML,1.777}}, + Width -> 0, + QuantumNumbers -> {Q -> 1, LeptonNumber -> 1}, + PropagatorLabel -> {"l", "e", "mu", "ta"}, + PropagatorType -> Straight, + PropagatorArrow -> Forward +}, + +V[1] == { + ClassName -> A, + SelfConjugate -> True, + Mass -> 0, + PropagatorLabel -> "\\gamma", + PropagatorType -> W, + PropagatorArrow -> None +} }; + LQED = LQEDR + LQEDCT; LQEDR = -1/4 FS[A, imu, inu] FS[A, imu, inu] + I lbar.Ga[imu].DC[l, imu]- Mlep[fi] lbar[s,fi].l[s,fi]; LQEDCT = FR$CT (-(ZA -1) 1/4 FS[A, imu, inu] FS[A, imu, inu] - -1/(2GaugeXi[V[1]])(ZA/Zxi-1) del[A[imu],imu] del[A[inu],inu] - + (Zpsi-1) I lbar.Ga[imu].del[l,imu] - (Zpsi Zm -1) Mlep[fi] lbar[s,fi].l[s,fi] - + (Zpsi Sqrt[ZA] Ze - 1) EL lbar.Ga[imu].l A[imu]); + -1/(2GaugeXi[V[1]])(ZA/Zxi-1) del[A[imu],imu] del[A[inu],inu] + + (Zpsi-1) I lbar.Ga[imu].del[l,imu] - (Zpsi Zm -1) Mlep[fi] lbar[s,fi].l[s,fi] + + (Zpsi Sqrt[ZA] Ze - 1) EL lbar.Ga[imu].l A[imu]); diff --git a/FeynCalc/Examples/FeynRules/QED/ValidateModelQED.m b/FeynCalc/Examples/FeynRules/QED/ValidateModelQED.m index c0221b8b4..3d4dd0aef 100644 --- a/FeynCalc/Examples/FeynRules/QED/ValidateModelQED.m +++ b/FeynCalc/Examples/FeynRules/QED/ValidateModelQED.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Validates FeynArts model for QED *) @@ -24,10 +24,12 @@ Print["Validation of the FeynArts model for QED"]; ]; If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; +$LoadAddOns={"FeynArts"}; < 2]; -compFu1To2[x_]:=FCFAConvert[FCPrepareFAAmp[CreateFeynAmp[x, Truncated -> True,PreFactor->1]], +compFu1To2[x_]:=FCFAConvert[CreateFeynAmp[x, Truncated -> True,PreFactor->1], IncomingMomenta->{p1},OutgoingMomenta->{p2,p3},UndoChiralSplittings->True, DropSumOver->True,List->False,SMP->True]//Contract; diff --git a/FeynCalc/Examples/MSSM/Tree/MnelEl-MnelEl.m b/FeynCalc/Examples/MSSM/Tree/MnelEl-MnelEl.m new file mode 100644 index 000000000..db841a1a4 --- /dev/null +++ b/FeynCalc/Examples/MSSM/Tree/MnelEl-MnelEl.m @@ -0,0 +1,177 @@ +(* ::Package:: *) + +(* :Title: MnelEl-MnelEl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Mnel El -> Mnel El, MSSM, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Neutralino-electron scattering*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Mnel El -> Mnel El, MSSM, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[11, {1}], + F[2, {1}]} -> {F[11,{1}],F[2,{1}]}, InsertionLevel -> {Classes}, + Model -> MSSM, ExcludeParticles -> {S[1], S[2], S[3], S[4], V[_]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},ChangeDimension->4,List->False, SMP->True, + DropSumOver->True]//.{ + USf[args1__][args2__]:> + USf[args2,args1],Index[Sfermion, 5]:>Sfe5, + Conjugate[ZNeu[a__]]:>ZNeuC[a], + Conjugate[USf[a_,b_,c_,d_]]:>USfC[a,b,c,d]} + + +Cases2[amp[0],USf] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, MNeu[1], SMP["m_e"], MNeu[1], SMP["m_e"]]; + + +(* ::Section:: *) +(*Evaluate the amplitude*) + + +amp[1]=DiracSimplify[amp[0]]; + + +ampCC[1]=ComplexConjugate[amp[1],Conjugate->{ZNeuC,ZNeu,USf,USfC}]//.{ + Conjugate[USf][a_,b_,c_,d_]:>USfC[a,b,c,d], + Conjugate[ZNeu][a__]:>ZNeuC[a], + Conjugate[ZNeuC][a__]:>ZNeu[a], + Conjugate[USfC][a_,b_,c_,d_]:>USf[a,b,c,d], + Sfe5->Sfe5c}; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*To avoid having too many terms, we isolate everything that is not required to calculate the spin sums*) + + +amp[2]=Collect2[amp[1],Spinor,LorentzIndex,IsolateNames->KK]; +ampCC[2]=Collect2[ampCC[1],Spinor,LorentzIndex,IsolateNames->KK]; + + +ampSquared[0] = (amp[2] ampCC[2])//FermionSpinSum//DiracSimplify; + + +(* ::Text:: *) +(*For simplicity, we neglect the masses of the external particles.*) + + +ampSquared[1]=ampSquared[0]//FRH//PropagatorDenominatorExplicit// + ReplaceAll[#,{MNeu[1]->0,SMP["m_e"]->0}]&//Factor2// + TrickMandelstam[#,{s,t,u,0}]&; + + +(* ::Text:: *) +(*As we will show below, the pieces that contain a Levi-Civita tensor can be discarded, so we ignore*) +(*them in the final result*) + + +ampSquared[2]=SelectFree2[ampSquared[1],Eps]//Simplify + + +(* ::Text:: *) +(*The explicit dependence on the Levi-Civita tensor vanishes once we exploit the unitarity of the*) +(*sfermion mixing matrix USf*) + + +discarded=SelectNotFree2[ampSquared[1],Eps]//Simplify + + +Sum[discarded,{Sfe5,1,2},{Sfe5c,1,2}]//Simplify//ReplaceRepeated[#, +{USf[1,1,re__]USfC[1,2,re__]:>-USf[2,1,re]USfC[2,2,re], +USf[1,2,re__]USfC[1,1,re__]:>-USf[2,2,re]USfC[2,1,re] +}]&//Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + -(SMP["e"]^4*(SMP["sin_W"]^4*(USf[Sfe5, 1, 2, 1]*((s*u*(2*s*u + t*MSf[Sfe5c, 2, 1]^2) + MSf[Sfe5, 2, 1]^2*(s*t*u + (s^2 + u^2)*MSf[Sfe5c, 2, 1]^2))*USf[Sfe5c, 1, 2, 1]*USfC[Sfe5, 1, 2, 1] + + 4*(2*s*u + t*MSf[Sfe5, 2, 1]^2)*(2*s*u + t*MSf[Sfe5c, 2, 1]^2)*USf[Sfe5c, 2, 2, 1]*USfC[Sfe5, 2, 2, 1])*USfC[Sfe5c, 1, 2, 1] + + 4*USf[Sfe5, 2, 2, 1]*((2*s*u + t*MSf[Sfe5, 2, 1]^2)*(2*s*u + t*MSf[Sfe5c, 2, 1]^2)*USf[Sfe5c, 1, 2, 1]*USfC[Sfe5, 1, 2, 1] + + 4*(s*u*(2*s*u + t*MSf[Sfe5c, 2, 1]^2) + MSf[Sfe5, 2, 1]^2*(s*t*u + (s^2 + u^2)*MSf[Sfe5c, 2, 1]^2))*USf[Sfe5c, 2, 2, 1]*USfC[Sfe5, 2, 2, 1])*USfC[Sfe5c, 2, 2, 1])*ZNeu[1, 1]^2* + ZNeuC[1, 1]^2 + (s*u*(2*s*u + t*MSf[Sfe5c, 2, 1]^2) + MSf[Sfe5, 2, 1]^2*(s*t*u + (s^2 + u^2)*MSf[Sfe5c, 2, 1]^2))*SMP["cos_W"]^4*USf[Sfe5, 1, 2, 1]*USf[Sfe5c, 1, 2, 1]*USfC[Sfe5, 1, 2, 1]* + USfC[Sfe5c, 1, 2, 1]*ZNeu[1, 2]^2*ZNeuC[1, 2]^2 + 2*SMP["cos_W"]*SMP["sin_W"]^3* + (USf[Sfe5, 1, 2, 1]*((s*u*(2*s*u + t*MSf[Sfe5c, 2, 1]^2) + MSf[Sfe5, 2, 1]^2*(s*t*u + (s^2 + u^2)*MSf[Sfe5c, 2, 1]^2))*USf[Sfe5c, 1, 2, 1]*USfC[Sfe5, 1, 2, 1] + + 2*(2*s*u + t*MSf[Sfe5, 2, 1]^2)*(2*s*u + t*MSf[Sfe5c, 2, 1]^2)*USf[Sfe5c, 2, 2, 1]*USfC[Sfe5, 2, 2, 1])*USfC[Sfe5c, 1, 2, 1] + + 2*(2*s*u + t*MSf[Sfe5, 2, 1]^2)*(2*s*u + t*MSf[Sfe5c, 2, 1]^2)*USf[Sfe5, 2, 2, 1]*USf[Sfe5c, 1, 2, 1]*USfC[Sfe5, 1, 2, 1]*USfC[Sfe5c, 2, 2, 1])*ZNeu[1, 1]*ZNeuC[1, 1]* + (ZNeu[1, 2]*ZNeuC[1, 1] + ZNeu[1, 1]*ZNeuC[1, 2]) + 2*(s*u*(2*s*u + t*MSf[Sfe5c, 2, 1]^2) + MSf[Sfe5, 2, 1]^2*(s*t*u + (s^2 + u^2)*MSf[Sfe5c, 2, 1]^2))*SMP["cos_W"]^3*SMP["sin_W"]* + USf[Sfe5, 1, 2, 1]*USf[Sfe5c, 1, 2, 1]*USfC[Sfe5, 1, 2, 1]*USfC[Sfe5c, 1, 2, 1]*ZNeu[1, 2]*ZNeuC[1, 2]*(ZNeu[1, 2]*ZNeuC[1, 1] + ZNeu[1, 1]*ZNeuC[1, 2]) + + SMP["cos_W"]^2*SMP["sin_W"]^2*(4*(2*s*u + t*MSf[Sfe5, 2, 1]^2)*(2*s*u + t*MSf[Sfe5c, 2, 1]^2)*USf[Sfe5, 2, 2, 1]*USf[Sfe5c, 1, 2, 1]*USfC[Sfe5, 1, 2, 1]*USfC[Sfe5c, 2, 2, 1]*ZNeu[1, 1]* + ZNeu[1, 2]*ZNeuC[1, 1]*ZNeuC[1, 2] + USf[Sfe5, 1, 2, 1]*USfC[Sfe5c, 1, 2, 1]*(4*(2*s*u + t*MSf[Sfe5, 2, 1]^2)*(2*s*u + t*MSf[Sfe5c, 2, 1]^2)*USf[Sfe5c, 2, 2, 1]*USfC[Sfe5, 2, 2, 1]* + ZNeu[1, 1]*ZNeu[1, 2]*ZNeuC[1, 1]*ZNeuC[1, 2] + (s*u*(2*s*u + t*MSf[Sfe5c, 2, 1]^2) + MSf[Sfe5, 2, 1]^2*(s*t*u + (s^2 + u^2)*MSf[Sfe5c, 2, 1]^2))*USf[Sfe5c, 1, 2, 1]*USfC[Sfe5, 1, 2, 1]* + (ZNeu[1, 2]^2*ZNeuC[1, 1]^2 + 4*ZNeu[1, 1]*ZNeu[1, 2]*ZNeuC[1, 1]*ZNeuC[1, 2] + ZNeu[1, 1]^2*ZNeuC[1, 2]^2)))))/ + (4*(s - MSf[Sfe5, 2, 1]^2)*(-u + MSf[Sfe5, 2, 1]^2)*(s - MSf[Sfe5c, 2, 1]^2)*(u - MSf[Sfe5c, 2, 1]^2)*SMP["cos_W"]^4*SMP["sin_W"]^4) +}; +FCCompareResults[{ampSquared[2]}, +knownResults, +Text->{"\tCompare to FormCalc:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/Tdec/GrossNeveuMultiloopTID.m b/FeynCalc/Examples/Misc/GrossNeveuMultiloopTID.m similarity index 96% rename from FeynCalc/Examples/Tdec/GrossNeveuMultiloopTID.m rename to FeynCalc/Examples/Misc/GrossNeveuMultiloopTID.m index 8f0d6fb96..ca56c04be 100644 --- a/FeynCalc/Examples/Tdec/GrossNeveuMultiloopTID.m +++ b/FeynCalc/Examples/Misc/GrossNeveuMultiloopTID.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Computation of tensor decompositions for multi-loop integrals diff --git a/FeynCalc/Examples/Misc/Integrate2.m b/FeynCalc/Examples/Misc/Integrate2.m index 60c977385..70735c640 100644 --- a/FeynCalc/Examples/Misc/Integrate2.m +++ b/FeynCalc/Examples/Misc/Integrate2.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Computation of the moments of \\hat{A}_qq^NS,PHYS from diff --git a/FeynCalc/Examples/TID/VerifyTIDLFourLoop.m b/FeynCalc/Examples/Misc/VerifyTIDLFourLoop.m similarity index 86% rename from FeynCalc/Examples/TID/VerifyTIDLFourLoop.m rename to FeynCalc/Examples/Misc/VerifyTIDLFourLoop.m index 8e86662e6..db6317920 100644 --- a/FeynCalc/Examples/TID/VerifyTIDLFourLoop.m +++ b/FeynCalc/Examples/Misc/VerifyTIDLFourLoop.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Verify 4-loop tensor decomposition formulas stored in TIDL diff --git a/FeynCalc/Examples/TID/VerifyTIDLOneLoop.m b/FeynCalc/Examples/Misc/VerifyTIDLOneLoop.m similarity index 96% rename from FeynCalc/Examples/TID/VerifyTIDLOneLoop.m rename to FeynCalc/Examples/Misc/VerifyTIDLOneLoop.m index d83ff4156..56ed8ab63 100644 --- a/FeynCalc/Examples/TID/VerifyTIDLOneLoop.m +++ b/FeynCalc/Examples/Misc/VerifyTIDLOneLoop.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Verify 1-loop tensor decomposition formulas stored in TIDL diff --git a/FeynCalc/Examples/TID/VerifyTIDLThreeLoop.m b/FeynCalc/Examples/Misc/VerifyTIDLThreeLoop.m similarity index 88% rename from FeynCalc/Examples/TID/VerifyTIDLThreeLoop.m rename to FeynCalc/Examples/Misc/VerifyTIDLThreeLoop.m index c595f4d56..19c56dba2 100644 --- a/FeynCalc/Examples/TID/VerifyTIDLThreeLoop.m +++ b/FeynCalc/Examples/Misc/VerifyTIDLThreeLoop.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Verify 3-loop tensor decomposition formulas stored in TIDL diff --git a/FeynCalc/Examples/TID/VerifyTIDLTwoLoop.m b/FeynCalc/Examples/Misc/VerifyTIDLTwoLoop.m similarity index 94% rename from FeynCalc/Examples/TID/VerifyTIDLTwoLoop.m rename to FeynCalc/Examples/Misc/VerifyTIDLTwoLoop.m index b040c45e3..fddb4942e 100644 --- a/FeynCalc/Examples/TID/VerifyTIDLTwoLoop.m +++ b/FeynCalc/Examples/Misc/VerifyTIDLTwoLoop.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Verify 2-loop tensor decomposition formulas stored in TIDL diff --git a/FeynCalc/Examples/Misc/paulisigmas.m b/FeynCalc/Examples/Misc/paulisigmas.m deleted file mode 100644 index b46861411..000000000 --- a/FeynCalc/Examples/Misc/paulisigmas.m +++ /dev/null @@ -1,14 +0,0 @@ -$LoadTARCER=$LoadPhi=False; -< - {s[i_].s[j_] :> (k=Unique["k"]; KroneckerDelta[i, j] + I Eps[i,j,k] s[k])}] - ] - ) //. (KroneckerDelta[x_, y_] f_ :> (f/.x->y) /; !FreeQ[f, x]) /. - ( x_ s[ij_] :> ( (x /. ij :> k0) s[k0] ) /; !FreeQ[x,ij]) - )&; - -ssimp[ s[i1].s[i2].s[i3].s[i4].s[i5] ] - diff --git a/FeynCalc/Examples/Misc/solve3.m b/FeynCalc/Examples/Misc/solve3.m index 60eb3bd67..134eb3244 100644 --- a/FeynCalc/Examples/Misc/solve3.m +++ b/FeynCalc/Examples/Misc/solve3.m @@ -1,5 +1,4 @@ - timingstart = AbsoluteTime[]; -$LoadTARCER=$LoadPhi=False; +timingstart = AbsoluteTime[]; <True]; + + +(* ::Section:: *) +(*Generate Feynman diagrams*) + + +params={InsertionLevel->{Particles},Model -> FileNameJoin[{"Phi3","Phi3"}], +GenericModel -> FileNameJoin[{"Phi3","Phi3"}]}; +top[i_,j_]:=CreateTopologies[1, i -> j,ExcludeTopologies->Tadpoles]; +topCT[i_,j_]:=CreateCTTopologies[1, i ->j]; +topVertex[i_,j_]:=CreateTopologies[1, i ->j, + ExcludeTopologies->{WFCorrections}]; +topVertexCT[i_,j_]:=CreateCTTopologies[1, i ->j, + ExcludeTopologies->{WFCorrectionCTs}]; + +{diagPhi3SE,diagPhi3SECT} = InsertFields[#, {S[1]} -> {S[1]}, +Sequence@@params]&/@{top[1,1],topCT[1,1]}; +{diagVertex,diagVertexCT} = InsertFields[#, {S[1]}->{S[1],S[1]}, +Sequence@@params]&/@{topVertex[1,2],topVertexCT[1,2]}; + + +diag1[0]=diagPhi3SE[[0]][Sequence@@diagPhi3SE, + Sequence@@diagPhi3SECT]; +diag2[0]=diagVertex[[0]][Sequence@@diagVertex, + Sequence@@diagVertexCT]; + + +Paint[diag1[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diag2[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +(* ::Text:: *) +(*Self-energy including the counter-term*) + + +amp1[0] = FCFAConvert[CreateFeynAmp[diag1[0],Truncated->True, + GaugeRules->{},PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu}, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{Zm->SMP["Z_m"], Zphi->SMP["Z_phi"], + GaugeXi[S[1]]->1,Mphi->m}] + + +(* ::Text:: *) +(*Quartic vertex including the counter-term*) + + +amp2[0] = FCFAConvert[CreateFeynAmp[diag2[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p1}, OutgoingMomenta->{p2,p3}, + LorentzIndexNames->{mu}, LoopMomenta->{l}, + UndoChiralSplittings->True, ChangeDimension->D, + List->False, SMP->True,FinalSubstitutions->{Zg->SMP["Z_g"], + Zphi->SMP["Z_phi"], GaugeXi[S[1]]->1,Mphi->m}] + + +(* ::Section:: *) +(*Calculate the amplitudes*) + + +(* ::Subsection:: *) +(*Self-energy*) + + +amp1[1] = amp1[0]//ReplaceAll[#,{SMP["Z_phi"]->1+alpha SMP["d_phi"], +SMP["Z_m"]->1+alpha SMP["d_m"]}]&//Series[#,{alpha,0,1}]&// +Normal//ReplaceAll[#,alpha->1]& + + +(* ::Text:: *) +(*Express the self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +amp1[2]=ToPaVe[amp1[1],l] + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +amp1Div[0]=PaVeUVPart[amp1[2],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +FCHideEpsilon//SelectNotFree2[#,{SMP["Delta"],SMP["d_m"], +SMP["d_phi"]}]&//Simplify + + +(* ::Text:: *) +(*Equating the result to zero and solving for d_phi and d_m we obtain the renormalization constants in the minimal subtraction schemes.*) + + +sol[1]=Solve[SelectNotFree2[amp1Div[0], p]==0, + SMP["d_phi"]]//Flatten//Simplify; +sol[2]=Solve[(SelectFree2[amp1Div[0], p]==0)/.sol[1], + SMP["d_m"]]//Flatten//Simplify; +solMS1=Join[sol[1],sol[2]]/.{ + SMP["d_phi"]->SMP["d_phi^MS"], + SMP["d_m"]->SMP["d_m^MS"],SMP["Delta"]->1/Epsilon +} +solMSbar1=Join[sol[1],sol[2]]/.{ + SMP["d_phi"]->SMP["d_phi^MSbar"], + SMP["d_m"]->SMP["d_m^MSbar"] +} + + +(* ::Subsection:: *) +(*Cubic vertex*) + + +amp2[1] = amp2[0]//ReplaceRepeated[#,{SMP["Z_g"]->1+alpha SMP["d_g"], +SMP["Z_phi"]->1+alpha SMP["d_phi"]}]&// +Series[#,{alpha,0,1}]&//Normal//ReplaceAll[#,alpha->1]& + + +(* ::Text:: *) +(*Express the cubic vertex in tems of the Passarino-Veltman coefficient functions.*) + + +amp2[2]=ToPaVe[amp2[1],l] + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +amp2Div[0]=PaVeUVPart[amp2[2],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +FCHideEpsilon//SelectNotFree2[#,{SMP["Delta"],SMP["d_g"],SMP["d_phi"]}]&//Simplify + + +sol[3]=Solve[(amp2Div[0]==0)/.sol[1], + SMP["d_g"]]//Flatten//Simplify; +solMS2=sol[3]/.{ + SMP["d_g"]->SMP["d_g^MS"], + SMP["Delta"]->1/Epsilon +} +solMSbar2=sol[3]/.{ + SMP["d_g"]->SMP["d_g^MSbar"] +} + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = { + SMP["d_phi^MS"] -> 0, + SMP["d_m^MS"] -> (g^2*1/Epsilon)/(32*Pi^2 m^2), + SMP["d_g^MS"] -> 0, + + SMP["d_phi^MSbar"] -> 0, + SMP["d_m^MSbar"] -> (g^2*SMP["Delta"])/(32*Pi^2 m^2), + SMP["d_g^MSbar"] -> 0 + }; +FCCompareResults[Join[solMS1,solMS2,solMSbar1,solMSbar2],knownResult, +Text->{"\tCompare to Cheng and Li, Gauge theory of elementary particle \ +physics, Problems and Solutions, Eq. 2.120:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/Phi4/OneLoop/PhiPhi-PhiPhi.m b/FeynCalc/Examples/Phi4/OneLoop/PhiPhi-PhiPhi.m new file mode 100644 index 000000000..3d8a56611 --- /dev/null +++ b/FeynCalc/Examples/Phi4/OneLoop/PhiPhi-PhiPhi.m @@ -0,0 +1,166 @@ +(* ::Package:: *) + +(* :Title: PhiPhi-PhiPhi *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Phi Phi -> Phi Phi, Phi^4, asymptotic limit, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Phi Phi scattering at 1-loop*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +(* ::Text:: *) +(*This example uses a custom Phi^4 model created with FeynRules. Please evaluate the file*) +(*FeynCalc/Examples/FeynRules/Phi4/GenerateModelPhi4.m before running it for the first time.*) + + +description="Phi Phi -> Phi Phi, Phi^4, asymptotic limit, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Generate Feynman diagrams*) + + +(* ::Text:: *) +(*Nicer typesetting*) + + +MakeBoxes[p1,TraditionalForm]:="\!\(\*SubscriptBox[\(p\), \(1\)]\)"; +MakeBoxes[p2,TraditionalForm]:="\!\(\*SubscriptBox[\(p\), \(2\)]\)"; +MakeBoxes[k1,TraditionalForm]:="\!\(\*SubscriptBox[\(k\), \(1\)]\)"; +MakeBoxes[k2,TraditionalForm]:="\!\(\*SubscriptBox[\(k\), \(2\)]\)"; + + +diags = InsertFields[CreateTopologies[1, 2 -> 2, + ExcludeTopologies->{WFCorrections}], + {S[1],S[1]}-> {S[1],S[1]}, InsertionLevel -> {Classes}, + Model -> FileNameJoin[{"Phi4","Phi4"}]]; +Paint[diags, ColumnsXRows -> {3, 1}, Numbering -> None,SheetHeader->None, +ImageSize->{512,256}]; + + +diagsCT = InsertFields[CreateCTTopologies[1, 2 -> 2, + ExcludeTopologies->{WFCorrectionCTs}], {S[1],S[1]}-> {S[1],S[1]}, + InsertionLevel -> {Classes}, Model -> FileNameJoin[{"Phi4","Phi4"}]]; +Paint[diagsCT, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->None, +ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,PreFactor->1], + IncomingMomenta->{p1,p2}, OutgoingMomenta->{k1,k2}, + LoopMomenta->{q},ChangeDimension->D,List->False, + FinalSubstitutions->{Mphi->m}] + + +ampCT[0] = FCFAConvert[CreateFeynAmp[diagsCT,PreFactor->1], + IncomingMomenta->{p1,p2}, OutgoingMomenta->{k1,k2}, + LoopMomenta->{q},ChangeDimension->D,List->False, + FinalSubstitutions->{Mphi->m,Zg->1+SMP["d_g^MSbar"]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +(* ::Text:: *) +(*For simplicity, let us consider the massless case*) + + +FCClearScalarProducts[] +SetMandelstam[s, t, u, p1, p2, -k1, -k2, 0, 0, 0, 0]; + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +amp[1]=amp[0]//ReplaceAll[#,m->0]&//ToPaVe[#,q]& + + +(* ::Text:: *) +(*The explicit value of the integral can be obtained from Package-X via the FeynHelpers add-on.*) + + +loopInt={ +B0[s_,0,0]:>-(-2 + Log[4*Pi] - + Log[(-4*Pi*ScaleMu^2)/s])/(16*Pi^4) + SMP["Delta"]/(16*Pi^4) +}; + + +amp[2]=(amp[1]/.loopInt)//Simplify + + +ampFull[0]=Expand[(amp[2]+ampCT[0])/. + SMP["d_g^MSbar"] ->(3*g^2*SMP["Delta"])/(32*Pi^2)] + + +FCCompareResults[FreeQ[ampFull,SMP["Delta"]],True, +Text->{"\tThe UV divergence is cancelled by the counter-term:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; + + +(* ::Text:: *) +(*Now let us look at the asymptotic limit where s goes to infinity and t is fixed*) + + +ampFullAsy[0]=Series[ampFull[0]/.u->-s-t,{s,Infinity,0}]//Normal + + +(* ::Text:: *) +(*The leading order behavior is governed by the log of s*) + + +ampFullAsy[1]=ampFullAsy[0]//PowerExpand//SelectNotFree2[#,s]& + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = ((-I/16)*g^2*Log[s])/Pi^2; +FCCompareResults[ampFullAsy[1],knownResult, +Text->{"\tCompare to Peskin and Schroeder, An Introduction to QFT, \ +Ex 10.4:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/Phi4/OneLoop/Renormalization.m b/FeynCalc/Examples/Phi4/OneLoop/Renormalization.m new file mode 100644 index 000000000..6580d8f13 --- /dev/null +++ b/FeynCalc/Examples/Phi4/OneLoop/Renormalization.m @@ -0,0 +1,229 @@ +(* ::Package:: *) + +(* :Title: Renormalization *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Renormalization, phi^4, MS and MSbar, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*1-loop phi^4 renormalization in the minimal subtraction schemes*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +(* ::Text:: *) +(*This example uses a custom phi^4 model created with FeynRules. Please evaluate the file*) +(*FeynCalc/Examples/FeynRules/Phi4/GenerateModelPhi4.m before running it for the first time.*) + + +description="Renormalization, phi^4, MS and MSbar, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Generate Feynman diagrams*) + + +params={InsertionLevel->{Particles},Model -> FileNameJoin[{"Phi4","Phi4"}], +GenericModel -> FileNameJoin[{"Phi4","Phi4"}]}; +top[i_,j_]:=CreateTopologies[1, i -> j]; +topCT[i_,j_]:=CreateCTTopologies[1, i ->j]; +topVertex[i_,j_]:=CreateTopologies[1, i ->j, + ExcludeTopologies->{WFCorrections}]; +topVertexCT[i_,j_]:=CreateCTTopologies[1, i ->j, + ExcludeTopologies->{WFCorrectionCTs}]; + +{diagPhi4SE,diagPhi4SECT} = InsertFields[#, {S[1]} -> {S[1]}, +Sequence@@params]&/@{top[1,1],topCT[1,1]}; +{diagVertex,diagVertexCT} = InsertFields[#, {S[1],S[1]}->{S[1],S[1]}, +Sequence@@params]&/@{topVertex[2,2],topVertexCT[2,2]}; + + +diag1[0]=diagPhi4SE[[0]][Sequence@@diagPhi4SE, + Sequence@@diagPhi4SECT]; +diag2[0]=diagVertex[[0]][Sequence@@diagVertex, + Sequence@@diagVertexCT]; + + +Paint[diag1[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diag2[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +(* ::Text:: *) +(*Self-energy including the counter-term*) + + +amp1[0] = FCFAConvert[CreateFeynAmp[diag1[0],Truncated->True, + GaugeRules->{},PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu}, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{Zm->SMP["Z_m"], Zphi->SMP["Z_phi"], + GaugeXi[S[1]]->1,Mphi->m}] + + +(* ::Text:: *) +(*Quartic vertex including the counter-term*) + + +amp2[0] = FCFAConvert[CreateFeynAmp[diag2[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p1,p2}, OutgoingMomenta->{p3,p4}, + LorentzIndexNames->{mu}, LoopMomenta->{l}, + UndoChiralSplittings->True, ChangeDimension->D, + List->False, SMP->True,FinalSubstitutions->{Zg->SMP["Z_g"], + Zphi->SMP["Z_phi"], GaugeXi[S[1]]->1,Mphi->m}] + + +(* ::Section:: *) +(*Calculate the amplitudes*) + + +(* ::Subsection:: *) +(*Self-energy*) + + +amp1[1] = amp1[0]//ReplaceAll[#,{SMP["Z_phi"]->1+alpha SMP["d_phi"], +SMP["Z_m"]->1+alpha SMP["d_m"]}]&//Series[#,{alpha,0,1}]&// +Normal//ReplaceAll[#,alpha->1]& + + +(* ::Text:: *) +(*Express the self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +amp1[2]=ToPaVe[amp1[1],l] + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +amp1Div[0]=PaVeUVPart[amp1[2],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +FCHideEpsilon//SelectNotFree2[#,{SMP["Delta"],SMP["d_m"], +SMP["d_phi"]}]&//Simplify + + +(* ::Text:: *) +(*Equating the result to zero and solving for d_phi and d_m we obtain the renormalization constants in the minimal subtraction schemes.*) + + +sol[1]=Solve[SelectNotFree2[amp1Div[0], p]==0, + SMP["d_phi"]]//Flatten//Simplify; +sol[2]=Solve[(SelectFree2[amp1Div[0], p]==0)/.sol[1], + SMP["d_m"]]//Flatten//Simplify; +solMS1=Join[sol[1],sol[2]]/.{ + SMP["d_phi"]->SMP["d_phi^MS"], + SMP["d_m"]->SMP["d_m^MS"],SMP["Delta"]->1/Epsilon +} +solMSbar1=Join[sol[1],sol[2]]/.{ + SMP["d_phi"]->SMP["d_phi^MSbar"], + SMP["d_m"]->SMP["d_m^MSbar"] +} + + +(* ::Subsection:: *) +(*Quartic vertex*) + + +amp2[1] = amp2[0]//ReplaceRepeated[#,{SMP["Z_g"]->1+alpha SMP["d_g"], +SMP["Z_phi"]->1+alpha SMP["d_phi"]}]&// +Series[#,{alpha,0,1}]&//Normal//ReplaceAll[#,alpha->1]& + + +(* ::Text:: *) +(*Express the quartic vertex in tems of the Passarino-Veltman coefficient functions.*) + + +amp2[2]=ToPaVe[amp2[1],l] + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +amp2Div[0]=PaVeUVPart[amp2[2],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +FCHideEpsilon//SelectNotFree2[#,{SMP["Delta"],SMP["d_g"],SMP["d_phi"]}]&//Simplify + + +sol[3]=Solve[(amp2Div[0]==0)/.sol[1], + SMP["d_g"]]//Flatten//Simplify; +solMS2=sol[3]/.{ + SMP["d_g"]->SMP["d_g^MS"], + SMP["Delta"]->1/Epsilon +} +solMSbar2=sol[3]/.{ + SMP["d_g"]->SMP["d_g^MSbar"] +} + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = { + SMP["d_phi^MS"] -> 0, + SMP["d_m^MS"] -> (g*1/Epsilon)/(32*Pi^2), + SMP["d_g^MS"] -> (3*g*1/Epsilon)/(32*Pi^2), + + SMP["d_phi^MSbar"] -> 0, + SMP["d_m^MSbar"] -> (g*SMP["Delta"])/(32*Pi^2), + SMP["d_g^MSbar"] -> (3*g*SMP["Delta"])/(32*Pi^2) + }; +FCCompareResults[Join[solMS1,solMS2,solMSbar1,solMSbar2],knownResult, +Text->{"\tCompare to Bailin and Love, Introduction to Gauge Field Theory, \ +Eqs. 7.73-7.74 and Eqs. 7.76-7.77:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/OneLoop/Gh-Gh.m b/FeynCalc/Examples/QCD/OneLoop/Gh-Gh.m new file mode 100644 index 000000000..f666021e8 --- /dev/null +++ b/FeynCalc/Examples/QCD/OneLoop/Gh-Gh.m @@ -0,0 +1,111 @@ +(* ::Package:: *) + +(* :Title: Gh-Gh *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Gh -> Gh, QCD, only UV divergences, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*QCD ghost self-energy*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Gh -> Gh, QCD, only UV divergences, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 1, ExcludeTopologies->{Tadpoles}], + {U[5]} -> {U[5]}, InsertionLevel -> {Particles}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {1,1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags, Truncated -> True, GaugeRules->{}, + PreFactor->1], IncomingMomenta->{p}, OutgoingMomenta->{p},LoopMomenta->{q}, + UndoChiralSplittings->True, ChangeDimension->D, List->False, SMP->True, + DropSumOver->True, Contract->True] + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +amp[1]=amp[0]//SUNSimplify//TID[#,q,ToPaVe->True]& + + +(* ::Text:: *) +(*The UV divergence of the amplitude can be obtained via PaVeUVPart.*) +(*Here we also need to reintroduce the implicit 1/(2Pi)^D prefactor.*) +(*Hint: If you need the full result for the amplitude, use PaXEvaluate from FeynHelpers.*) + + +ampDiv[0]=PaVeUVPart[amp[1],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +SelectNotFree2[#,Epsilon]&//Simplify + + +(* ::Text:: *) +(*The self-energy amplitude is usually defined as (p^2 delta^ab Pi(p^2)*) + + +pi[0]= FCI[ampDiv[0]/(I SUNDelta[SUNIndex[Glu1], SUNIndex[Glu2]]*SPD[p,p])]//Cancel + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = -SMP["g_s"]^2/(4Pi)^2 CA (3-GaugeXi[g])/4*1/Epsilon; +FCCompareResults[pi[0],knownResult, +Text->{"\tCompare to Muta, Foundations of QCD, \ +Eq. 2.5.136:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/OneLoop/GhGl-Gh.m b/FeynCalc/Examples/QCD/OneLoop/GhGl-Gh.m new file mode 100644 index 000000000..fd6110218 --- /dev/null +++ b/FeynCalc/Examples/QCD/OneLoop/GhGl-Gh.m @@ -0,0 +1,194 @@ +(* ::Package:: *) + +(* :Title: GhGl-Gh *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: GhGl - Gh, QCD, only UV divergences, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*QCD ghost-gluon vertex at 1-loop*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +(* ::Text:: *) +(*This example uses a custom QCD model created with FeynRules. Please evaluate the file*) +(*FeynCalc/Examples/FeynRules/QCD/GenerateModelQCD.m before running it for the first time.*) + + +description="GhGl - Gh, QCD, only UV divergences, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Generate Feynman diagrams*) + + +(* ::Text:: *) +(*Nicer typesetting*) + + +MakeBoxes[mu,TraditionalForm]:="\[Mu]"; +MakeBoxes[nu,TraditionalForm]:="\[Nu]"; +MakeBoxes[rho,TraditionalForm]:="\[Rho]"; + + +template = insertFields[createTopologies[1, 1 -> 2, + ExcludeTopologies -> {Tadpoles,WFCorrections, + WFCorrectionCTs,SelfEnergies}], {U[5]} -> + {V[5],U[5]}, InsertionLevel -> {Particles}, + Model -> FileNameJoin[{"QCD","QCD"}], + GenericModel -> FileNameJoin[{"QCD","QCD"}]]; + + +diags=template/.createTopologies->CreateTopologies/. + insertFields->InsertFields; +diagsCT=template/.createTopologies->CreateCTTopologies/. + insertFields->InsertFields; + + +Paint[diags, ColumnsXRows -> {2,1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diagsCT, ColumnsXRows -> {2,1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit. We keep the full gauge dependence.*) + + +amp1[0] = FCFAConvert[CreateFeynAmp[DiagramExtract[diags,{1,2}], + Truncated->True, GaugeRules->{},PreFactor->1], + IncomingMomenta->{p1}, OutgoingMomenta->{p2,p3}, + LorentzIndexNames->{mu,nu,rho}, DropSumOver->True, + SUNIndexNames->{a,b,c}, LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{SMP["m_u"]->SMP["m_q"]}] + + +(* ::Text:: *) +(*Counter-term*) + + +amp2[0] = FCFAConvert[CreateFeynAmp[diagsCT, + Truncated->True, GaugeRules->{},PreFactor->1], + IncomingMomenta->{p1}, OutgoingMomenta->{p2,p3}, + LorentzIndexNames->{mu,nu,rho}, SUNIndexNames->{a,b,c}, + DropSumOver->True, LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{SMP["m_u"]->SMP["m_q"], + ZA->SMP["Z_A"],Zg->SMP["Z_g"],Zu->SMP["Z_u"]}] + + +(* ::Section:: *) +(*Calculate the amplitudes*) + + +(* ::Subsection:: *) +(*Ghost-gluon vertex*) + + +AbsoluteTiming[amp1[1]=TID[(FCE[amp1[0]]/.{-p2-p3->-p1}),l, + UsePaVeBasis->True,ToPaVe->True];] + + +amp1Div[0]=amp1[1]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]&; + + +amp1Div[1]=amp1Div[0]//SUNSimplify[#,Explicit->True]&//ReplaceAll[#, + SUNTrace[x__]:>SUNTrace[x,Explicit->True]]&// + FCReplaceD[#,D->4-2 Epsilon]&//Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SelectNotFree2[#,SMP["Delta"]]&//FCE// + Collect2[#,MTD,Factoring->Function[x,MomentumCombine[Factor[x]]]]& + + +(* ::Subsection:: *) +(*Counter-term*) + + +amp2[1]=amp2[0]//ReplaceAll[#,{SMP["Z_A"]->1+alpha SMP["d_A"], + SMP["Z_u"]->1+alpha SMP["d_u"], + SMP["Z_g"]->1+alpha SMP["d_g"]}]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&//ExpandScalarProduct//FCE// + Collect2[#,MTD,GaugeXi,Factoring->Function[x,MomentumCombine[Factor[x]]]]& + + +(* ::Text:: *) +(*Check the cancellation of the UV divergences in the MSbar scheme. The renormalization constants*) +(*are obtained from another example calculation, "Renormalization.m"*) + + +renormalizationConstants = { + SMP["d_A"]->SMP["alpha_s"]/(4Pi) SMP["Delta"] (1/2 CA(13/3-GaugeXi["G"])-2/3 Nf), + SMP["d_g"]->((-11*CA*SMP["alpha_s"])/(24 Pi)SMP["Delta"] + (Nf*SMP["alpha_s"])/(12*Pi)SMP["Delta"]), + SMP["d_u"]->SMP["alpha_s"]/(4Pi) CA SMP["Delta"] (3-GaugeXi["G"])/4 +}/.SMP["alpha_s"]->SMP["g_s"]^2/(4Pi); + + +uvDiv[0]=ExpandScalarProduct[amp1Div[1]+ amp2[1]]//Simplify + + +uvDiv[1]=(uvDiv[0]/.renormalizationConstants)//Simplify + + +FCCompareResults[uvDiv[1],0, +Text->{"\tThe UV divergence of the ghost-gluon vertex at 1-loop is cancelled by \ +the counter-term :", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = + -I(-I SMP["g_s"] FVD[p3,mu]SUNF[a,b,c]( SMP["g_s"]^2/(4Pi)^2 CA* + GaugeXi["G"]/2 SMP["Delta"])); +FCCompareResults[amp1Div[1],knownResult, +Text->{"\tCompare to Muta, Foundations of QCD, \ +Eq. 2.5.142:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/OneLoop/Gl-Gl-BackgroundFieldGauge.m b/FeynCalc/Examples/QCD/OneLoop/Gl-Gl-BackgroundFieldGauge.m new file mode 100644 index 000000000..42300e64b --- /dev/null +++ b/FeynCalc/Examples/QCD/OneLoop/Gl-Gl-BackgroundFieldGauge.m @@ -0,0 +1,112 @@ +(* ::Package:: *) + +(* :Title: Gl-Gl-BackgroundFieldGauge *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Gl -> Gl, YM+BGF, only UV divergences, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Pure Yang-Mills 1-loop gluon self-energy in the background field formalism*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Gl -> Gl, YM+BGF, only UV divergences, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 1,ExcludeTopologies -> {Tadpoles}], + {V[50,{a}]} -> {V[50,{b}]},InsertionLevel -> {Classes}, + Model -> FileNameJoin[{"QCDBGF","QCDBGF"}], + GenericModel->FileNameJoin[{"QCDBGF","QCDBGF"}], + ExcludeParticles->{F[_]}]; + +Paint[diags, ColumnsXRows -> {2,2}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,512}]; + + +(* ::Section:: *) +(*Obtain corresponding amplitudes*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags, Truncated -> True, GaugeRules->{}, + PreFactor->1], IncomingMomenta->{p}, OutgoingMomenta->{p},LoopMomenta->{l}, + LorentzIndexNames->{mu,nu}, UndoChiralSplittings->True, + ChangeDimension->D, List->True, SMP->True, DropSumOver->True, + FinalSubstitutions->{SMP["m_u"]->SMP["m_q"], + GaugeXi[V[5, {_}]]:>GaugeXi[G]}]; + + +amp[1]=DiracSimplify/@amp[0]; + + +amp[2]=SUNSimplify[TID[#,l,ToPaVe->True]]&/@amp[1]; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude.*) + + +ampDiv[0]=PaVeUVPart[#,Prefactor->1/(2Pi)^D]&/@amp[2] + + +ampDiv[1]=FCReplaceD[ampDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,-1}]&//Normal//Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = { + 0, + 0, + I CA SMP["g_s"]^2 SUNDelta[a,b]/(4Pi)^2(1/(3 Epsilon))* + (MTD[mu,nu]SPD[p]-FVD[p,mu]FVD[p,nu]), + I CA SMP["g_s"]^2 SUNDelta[a,b]/(4Pi)^2(10/(3 Epsilon))* + (MTD[mu,nu]SPD[p]-FVD[p,mu]FVD[p,nu]) +}//FCI; +FCCompareResults[ampDiv[1]/.GaugeXi[G]->1,knownResult, +Text->{"\tCompare to Abbott, \ +Nucl. Phys. B 185 (1981) 189-203, Eqs 5.11-5.12:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/OneLoop/Gl-Gl.m b/FeynCalc/Examples/QCD/OneLoop/Gl-Gl.m new file mode 100644 index 000000000..2c9779c08 --- /dev/null +++ b/FeynCalc/Examples/QCD/OneLoop/Gl-Gl.m @@ -0,0 +1,198 @@ +(* ::Package:: *) + +(* :Title: Gl-Gl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Gl -> Gl, QCD, only UV divergences, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*QCD vacuum polarization*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Gl -> Gl, QCD, only UV divergences, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 1, ExcludeTopologies->{Tadpoles}], + {V[5]} -> {V[5]}, InsertionLevel -> {Particles}, Model -> "SMQCD", + ExcludeParticles->{S[_],V[2|3],F[4],F[3,{2|3}]}]; + +Paint[diags, ColumnsXRows -> {2,2}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,512}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags, Truncated -> True, GaugeRules->{}, + PreFactor->1], IncomingMomenta->{p}, OutgoingMomenta->{p},LoopMomenta->{q}, + LorentzIndexNames->{mu,nu}, UndoChiralSplittings->True, + ChangeDimension->D, List->True, SMP->True, DropSumOver->True, + Contract->True,FinalSubstitutions->{SMP["m_u"]->SMP["m_q"]}] + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +(* ::Subsection:: *) +(*The gluon tadpole *) + + +(* ::Text:: *) +(*This contribution is zero in dimensional regularization, because the loop integrals have no scale (and they are not log divergent)*) + + +amp1[0] = TID[amp[0][[1]], q, ToPaVe->True] + + +FCCompareResults[amp1[0],0, +Text->{"\tThe gluon tadpole vanishes:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; + + +(* ::Subsection:: *) +(*The quark loop*) + + +amp2[0] = amp[0][[2]]//SUNSimplify//TID[#, q, ToPaVe->True]& + + +(* ::Text:: *) +(*The contribution of the quark loop alone is gauge invariant.*) + + +tmp=Contract[FVD[p,mu]FVD[p,nu] amp2[0]]//Factor +FCCompareResults[tmp,0, +Text->{"\tThe quark loop contribution is gauge invariant:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; + + +(* ::Subsection:: *) +(*The ghost loop*) + + +amp3[0] = amp[0][[3]]//SUNSimplify//TID[#, q, ToPaVe->True]& + + +(* ::Text:: *) +(*The contribution of the gluon loop alone is not gauge invariant.*) + + +tmp1=Contract[FVD[p,mu]FVD[p,nu] amp3[0]]//Factor + + +(* ::Subsection:: *) +(*The gluon loop*) + + +amp4[0] = amp[0][[4]]//SUNSimplify//TID[#, q, ToPaVe->True]& + + +(* ::Text:: *) +(*The contribution of the gluon loop alone is not gauge invariant. Notice, however, that the sum*) +(*of the ghost and gluon contributions is gauge invariant!*) + + +tmp2=Contract[FVD[p,mu]FVD[p,nu] amp4[0]]//Factor + + +FCCompareResults[tmp1+tmp2,0, +Text->{"\tThe sum of the ghost and gluon loop contributions is gauge invariant:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; + + +(* ::Subsection:: *) +(*Putting everything together*) + + +(* ::Text:: *) +(*When adding all the contributions together, we multiply the quark contribution by N_f to account for the 6 quark flavors that actually run in that loop. We ignore the fact that different flavors have different masses, since the divergent piece of the gluon self-energy will not depend on the quark mass.*) + + +amp[1]=Nf amp2[0]+amp3[0]+amp4[0] + + +(* ::Text:: *) +(*The UV divergence of the amplitude can be obtained via PaVeUVPart.*) +(*Here we also need to reintroduce the implicit 1/(2Pi)^D prefactor.*) +(*Hint: If you need the full result for the amplitude, use PaXEvaluate from FeynHelpers.*) + + +ampDiv[0]=PaVeUVPart[amp[1],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +SelectNotFree2[#,Epsilon]&//Simplify + + +(* ::Text:: *) +(*The self-energy amplitude is usually defined as (p^2 g^{mu nu} - p^mu p^nu) i Pi(p^2)*) + + +pi[0]= FCI[ampDiv[0]/(I SUNDelta[SUNIndex[Glu1], SUNIndex[Glu2]]* + (SPD[p,p]MTD[mu,nu]-FVD[p,mu]FVD[p,nu]))]//Cancel + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = -(SMP["g_s"]^2/(4Pi)^2)*(4/3*(1/2)*Nf- +(1/2)CA(13/3-GaugeXi[g]))*1/Epsilon; +FCCompareResults[pi[0],knownResult, +Text->{"\tCompare to Muta, Foundations of QCD, \ +Eqs 2.5.131-2.5.132:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/OneLoop/Gl-GlGl.m b/FeynCalc/Examples/QCD/OneLoop/Gl-GlGl.m new file mode 100644 index 000000000..0040e08ab --- /dev/null +++ b/FeynCalc/Examples/QCD/OneLoop/Gl-GlGl.m @@ -0,0 +1,302 @@ +(* ::Package:: *) + +(* :Title: Gl-GlGl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Gl - Gl Gl, QCD, only UV divergences, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*QCD 3-gluon vertex at 1-loop*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +(* ::Text:: *) +(*This example uses a custom QCD model created with FeynRules. Please evaluate the file*) +(*FeynCalc/Examples/FeynRules/QCD/GenerateModelQCD.m before running it for the first time.*) + + +description="Gl - Gl Gl, QCD, only UV divergences, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Generate Feynman diagrams*) + + +(* ::Text:: *) +(*Nicer typesetting*) + + +MakeBoxes[mu,TraditionalForm]:="\[Mu]"; +MakeBoxes[nu,TraditionalForm]:="\[Nu]"; +MakeBoxes[rho,TraditionalForm]:="\[Rho]"; + + +template = insertFields[createTopologies[1, 1 -> 2, + ExcludeTopologies -> {Tadpoles,WFCorrections, + WFCorrectionCTs,SelfEnergies}], {V[5]} -> + {V[5],V[5]}, InsertionLevel -> {Particles}, + Model -> FileNameJoin[{"QCD","QCD"}], + GenericModel -> FileNameJoin[{"QCD","QCD"}], + ExcludeParticles->{F[3|4,{2|3}],F[4,{1}]}]; + + +diags=template/.createTopologies->CreateTopologies/. + insertFields->InsertFields; +diagsCT=template/.createTopologies->CreateCTTopologies/. + insertFields->InsertFields; + + +Paint[diags, ColumnsXRows -> {3,1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diagsCT, ColumnsXRows -> {3,1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit. We keep the full gauge dependence. To simplify comparisons*) +(*to the literature, we make all momenta incoming.*) + + +(* ::Text:: *) +(*Quark contribution. Notice that we multiply the amplitude by Nf to account for the number*) +(*of quark flavours in the loop.*) + + +amp1[0] = FCFAConvert[CreateFeynAmp[DiagramExtract[diags,{1,2}], + Truncated->True, GaugeRules->{},PreFactor->1], + IncomingMomenta->{p1}, OutgoingMomenta->{p2,p3}, + LorentzIndexNames->{mu,nu,rho}, DropSumOver->True, + SUNIndexNames->{a,b,c}, LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True,Prefactor->Nf, + FinalSubstitutions->{SMP["m_u"]->SMP["m_q"],p2->-p2,p3->-p3}] + + +(* ::Text:: *) +(*Ghost contribution*) + + +amp2[0] = FCFAConvert[CreateFeynAmp[DiagramExtract[diags,{3,4}], + Truncated->True, GaugeRules->{},PreFactor->1], + IncomingMomenta->{p1}, OutgoingMomenta->{p2,p3}, + LorentzIndexNames->{mu,nu,rho}, SUNIndexNames->{a,b,c}, + DropSumOver->True, LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{SMP["m_u"]->SMP["m_q"],p2->-p2,p3->-p3}] + + +(* ::Text:: *) +(*Gluon contribution*) + + +amp3[0] = FCFAConvert[CreateFeynAmp[DiagramExtract[diags,{5,6,7,8}], + Truncated->True, GaugeRules->{},PreFactor->1], + IncomingMomenta->{p1}, OutgoingMomenta->{p2,p3}, + LorentzIndexNames->{mu,nu,rho}, SUNIndexNames->{a,b,c}, + DropSumOver->True, LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{SMP["m_u"]->SMP["m_q"],p2->-p2,p3->-p3}]; + + +(* ::Text:: *) +(*Counter-term*) + + +amp4[0] = FCFAConvert[CreateFeynAmp[diagsCT, + Truncated->True, GaugeRules->{},PreFactor->1], + IncomingMomenta->{p1}, OutgoingMomenta->{p2,p3}, + LorentzIndexNames->{mu,nu,rho}, SUNIndexNames->{a,b,c}, + DropSumOver->True, LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{SMP["m_u"]->SMP["m_q"],p2->-p2,p3->-p3, + ZA->SMP["Z_A"],Zg->SMP["Z_g"]}] + + +(* ::Section:: *) +(*Calculate the amplitudes*) + + +(* ::Subsection:: *) +(*Quark contribution*) + + +AbsoluteTiming[amp1[1]=TID[FCE[amp1[0]]/.{p2+p3->-p1,-p2-p3->p1},l, + UsePaVeBasis->True,ToPaVe->True];] + + +amp1Div[0]=amp1[1]//PaVeUVPart[#,Prefactor->1/(2Pi)^D,FCLoopExtract->False]&; + + +amp1Div[1]=amp1Div[0]//SUNSimplify[#,Explicit->True]&//ReplaceAll[#, + SUNTrace[x__]:>SUNTrace[x,Explicit->True]]&// + FCReplaceD[#,D->4-2 Epsilon]&//Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SelectNotFree2[#,SMP["Delta"]]&//FCE// + Collect2[#,MTD,Factoring->Function[x,MomentumCombine[Factor[x]]]]& + + +(* ::Text:: *) +(*In the calculation p3 was eliminated via the 4-momentum conservation p1+p2+p3=0. *) +(*Now we need to reintroduce it*) + + +amp1Div[2]=amp1Div[1]/. {2p1+p2->p1-p3,p1+2p2->p2-p3} + + +(* ::Subsection:: *) +(*Ghost contribution*) + + +AbsoluteTiming[amp2[1]=TID[FCE[amp2[0]]/.{p2+p3->-p1,-p2-p3->p1},l, + UsePaVeBasis->True,ToPaVe->True];] + + +amp2Div[0]=amp2[1]//PaVeUVPart[#,Prefactor->1/(2Pi)^D,FCLoopExtract->False]&; + + +amp2Div[1]=amp2Div[0]//SUNSimplify[#,Explicit->True]&//ReplaceAll[#, + SUNTrace[x__]:>SUNTrace[x,Explicit->True]]&// + FCReplaceD[#,D->4-2 Epsilon]&//Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SelectNotFree2[#,SMP["Delta"]]&//FCE// + Collect2[#,MTD,Factoring->Function[x,MomentumCombine[Factor[x]]]]& + + +(* ::Text:: *) +(*In the calculation p3 was eliminated via the 4-momentum conservation p1+p2+p3=0. *) +(*Now we need to reintroduce it*) + + +amp2Div[2]=amp2Div[1]/. {2p1+p2->p1-p3,p1+2p2->p2-p3} + + +(* ::Subsection:: *) +(*Gluon contribution*) + + +(* ::Text:: *) +(*This calculation requires about 70 seconds on a modern laptop*) + + +AbsoluteTiming[amp3[1]=TID[FCE[amp3[0]]/.{p2+p3->-p1,-p2-p3->p1},l, + UsePaVeBasis->True,ExpandScalarProduct->False,ToPaVe->True];] + + +amp3Div[0]=amp3[1]//PaVeUVPart[#,Prefactor->1/(2Pi)^D,FCLoopExtract->False]&; + + +amp3Div[1]=amp3Div[0]//SUNSimplify//FCReplaceD[#,D->4-2 Epsilon]&// + Series[#,{Epsilon,0,0}]&//Normal//FCHideEpsilon// + SelectNotFree2[#,SMP["Delta"]]&//FCE// + Collect2[#,MTD,Factoring->Function[x,MomentumCombine[Factor[x]]]]& + + +amp3Div[2]=(((amp3Div[1]/.{p3->-p1-p2})//ExpandScalarProduct//FCE// + Collect2[#,MTD,GaugeXi,Factoring->Function[x,MomentumCombine[Factor[x]]]]&)/. + 2p1+p2->p1-p3/.p1+2p2->p2-p3/. 22p1+11p2 -> 11p1-11p3/. + -22p2-11p1 -> -11p2+11p3)//ExpandScalarProduct//FCE// + Collect2[#,MTD,Factoring->Function[x,MomentumCombine[Factor[x]]]]& + + +(* ::Subsection:: *) +(*Counter-term*) + + +amp4[1]=amp4[0]//ReplaceAll[#,{SMP["Z_A"]->1+alpha SMP["d_A"], + SMP["Z_g"]->1+alpha SMP["d_g"]}]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&//ExpandScalarProduct//FCE// + Collect2[#,MTD,GaugeXi,Factoring->Function[x,MomentumCombine[Factor[x]]]]& + + +(* ::Text:: *) +(*Check the cancellation of the UV divergences in the MSbar scheme. The renormalization constants*) +(*are obtained from another example calculation, "Renormalization.m"*) + + +renormalizationConstants = { + SMP["d_A"]->SMP["alpha_s"]/(4Pi) SMP["Delta"] (1/2 CA(13/3-GaugeXi["G"])-2/3 Nf), + SMP["d_g"]->((-11*CA*SMP["alpha_s"])/(24 Pi)SMP["Delta"] + (Nf*SMP["alpha_s"])/(12*Pi)SMP["Delta"]) +}/.SMP["alpha_s"]->SMP["g_s"]^2/(4Pi); + + +uvDiv[0]=ExpandScalarProduct[amp1Div[2]+amp2Div[2]+amp3Div[2]+amp4[1]]//FCE// +Collect2[#,MTD,Factoring->Function[x,MomentumCombine[Factor[x]]]]& + + +uvDiv[1]=(uvDiv[0]/.renormalizationConstants)//Simplify + + +FCCompareResults[uvDiv[1],0, +Text->{"\tThe UV divergence of the 3-gluon vertex at 1-loop is cancelled by \ +the counter-term :", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; + + +(* ::Section:: *) +(*Check the final results*) + + +VertexLorentzStruct[{p_,q_,k_},{mu_,nu_,si_},{a_,b_,c_}]:= +-I SUNF[a,b,c](MTD[mu,nu]FVD[p-q,si]+MTD[nu,si]FVD[q-k,mu]+MTD[si,mu]FVD[k-p,nu]); + + +knownResult = { + (I SMP["g_s"]) Nf SMP["g_s"]^2/(4Pi)^2*(-2/3)SMP["Delta"]* + VertexLorentzStruct[{p1,p2,p3},{mu,nu,rho},{a,b,c}], + + + (I SMP["g_s"]) SMP["g_s"]^2/(4Pi)^2 CA/8 (1/3)SMP["Delta"]* + VertexLorentzStruct[{p1,p2,p3},{mu,nu,rho},{a,b,c}], + + + (I SMP["g_s"]) SMP["g_s"]^2/(4Pi)^2 CA/8 SMP["Delta"]*( + -4-9GaugeXi["G"]+15+3GaugeXi["G"])* + VertexLorentzStruct[{p1,p2,p3},{mu,nu,rho},{a,b,c}] +}//FCI; +FCCompareResults[{amp1Div[2],amp2Div[2],amp3Div[2]}, knownResult, + Text->{"\tCompare to Pascual and Tarrach, QCD: Renormalization \ +for the Practitioner, Eq III.46:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/OneLoop/Q-Q.m b/FeynCalc/Examples/QCD/OneLoop/Q-Q.m new file mode 100644 index 000000000..6d880dc8a --- /dev/null +++ b/FeynCalc/Examples/QCD/OneLoop/Q-Q.m @@ -0,0 +1,122 @@ +(* ::Package:: *) + +(* :Title: Q-Q *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q -> Q, QCD, only UV divergences, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*QCD quark self-energy*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q -> Q, QCD, only UV divergences, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 1, + ExcludeTopologies->Tadpoles], {F[3,{1}]} -> + {F[3,{1}]}, InsertionLevel -> {Particles}, Model -> "SMQCD", + ExcludeParticles->{S[_],V[1|2|3]}]; + +Paint[diags, ColumnsXRows -> {1, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit. We keep the full gauge dependence.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags, Truncated -> True, + PreFactor->1, GaugeRules->{}], IncomingMomenta->{p}, + OutgoingMomenta->{p},LoopMomenta->{q}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, DropSumOver->True, + Contract->True,FinalSubstitutions->{SMP["m_u"]->SMP["m_q"]}] + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +amp[1] = amp[0]//SUNSimplify//TID[#, q, ToPaVe->True]& + + +(* ::Text:: *) +(*The UV divergence of the amplitude can be obtained via PaVeUVPart.*) +(*Here we also need to reintroduce the implicit 1/(2Pi)^D prefactor.*) +(*Hint: If you need the full result for the amplitude, use PaXEvaluate from FeynHelpers.*) + + +ampDiv[0] = PaVeUVPart[amp[1],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +SelectNotFree2[#,Epsilon]&//Simplify + + +(* ::Text:: *) +(*The self-energy amplitude is usually defined as -i Sigma(p^2)*) + + +sigma[0] = I ampDiv[0] + + +sigmaFeynmanGauge[0] = sigma[0]/.GaugeXi[g]->1 + + +(* ::Section:: *) +(*Check the final results*) + + +(* ::Text:: *) +(*Notice that the result in the book must be multiplied by (-1) due to the way how self-energy is defined there (c.f. Eq. 2.4.4 and Eq. 2.4.6).*) + + +knownResult =-(-SMP["g_s"]^2/(4Pi)^2 CF*(3+GaugeXi[g])(1/Epsilon)*SMP["m_q"]+ + GSD[p]*SMP["g_s"]^2/(4Pi)^2*CF*GaugeXi[g]*(1/Epsilon))SDF[Col1,Col2]; +FCCompareResults[sigma[0],knownResult, +Text->{"\tCompare to Muto, Foundations of QCD, \ +Eq 10.41:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/OneLoop/Renormalization.m b/FeynCalc/Examples/QCD/OneLoop/Renormalization.m new file mode 100644 index 000000000..df4abb12b --- /dev/null +++ b/FeynCalc/Examples/QCD/OneLoop/Renormalization.m @@ -0,0 +1,403 @@ +(* ::Package:: *) + +(* :Title: Renormalization *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Renormalization, QCD, MS and MSbar, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*1-loop QCD renormalization in the minimal subtraction schemes*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +(* ::Text:: *) +(*This example uses a custom QCD model created with FeynRules. Please evaluate the file*) +(*FeynCalc/Examples/FeynRules/QCD/GenerateModelQCD.m before running it for the first time.*) + + +description="Renormalization, QCD, MS and MSbar, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Generate Feynman diagrams*) + + +(* ::Text:: *) +(*Nicer typesetting*) + + +MakeBoxes[mu,TraditionalForm]:="\[Mu]"; +MakeBoxes[nu,TraditionalForm]:="\[Nu]"; +MakeBoxes[rho,TraditionalForm]:="\[Rho]"; +MakeBoxes[si,TraditionalForm]:="\[Sigma]"; + + +params={InsertionLevel->{Particles},Model -> FileNameJoin[{"QCD","QCD"}], +GenericModel -> FileNameJoin[{"QCD","QCD"}],ExcludeParticles->{F[3|4,{2|3}],F[4,{1}]}}; +top[i_,j_]:=CreateTopologies[1, i -> j, + ExcludeTopologies -> {Tadpoles,WFCorrections,WFCorrectionCTs}]; +topTriangle[i_,j_]:=CreateTopologies[1, i -> j, + ExcludeTopologies -> {Tadpoles,WFCorrections,WFCorrectionCTs,SelfEnergies}]; + +topCT[i_,j_]:=CreateCTTopologies[1, i ->j, + ExcludeTopologies ->{Tadpoles,WFCorrections,WFCorrectionCTs}]; +topTriangleCT[i_,j_]:=CreateCTTopologies[1, i -> j, + ExcludeTopologies -> {Tadpoles,WFCorrections,WFCorrectionCTs,SelfEnergyCTs}]; + +{diagQuarkSE,diagQuarkSECT} = InsertFields[#, {F[3,{1}]} -> {F[3,{1}]}, + Sequence@@params]&/@{top[1,1],topCT[1,1]}; + +{diagGluonSE,diagGluonSECT} = InsertFields[#, {V[5]} -> {V[5]}, + Sequence@@params]&/@{top[1,1],topCT[1,1]}; + +{diagGhostSE,diagGhostSECT} = InsertFields[#, {U[5]} -> {U[5]}, + Sequence@@params]&/@{top[1,1],topCT[1,1]}; + +{diagQuarkGluonVertex,diagQuarkGluonVertexCT} = InsertFields[#, + {F[3,{1}],V[5]}->{F[3,{1}]}, Sequence@@params]&/@{topTriangle[2,1],topTriangleCT[2,1]}; + + +diag1[0]=diagQuarkSE[[0]][Sequence@@diagQuarkSE, + Sequence@@diagQuarkSECT]; +diag2[0]=diagGluonSE[[0]][Sequence@@diagGluonSE, + Sequence@@diagGluonSECT]; +diag3[0]=diagGhostSE[[0]][Sequence@@diagGhostSE, + Sequence@@diagGhostSECT]; +diag4[0]=diagQuarkGluonVertex[[0]][Sequence@@diagQuarkGluonVertex, + Sequence@@diagQuarkGluonVertexCT]; + + +Paint[diag1[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diag2[0], ColumnsXRows -> {4, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,128}]; + + +Paint[diag3[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diag4[0], ColumnsXRows -> {3, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +(* ::Text:: *) +(*Quark self-energy including the counter-term*) + + +ampQuarkSE[0] = FCFAConvert[CreateFeynAmp[diag1[0],Truncated->True, + GaugeRules->{},PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu,nu}, DropSumOver->True, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{Zm->SMP["Z_m"], Zpsi->SMP["Z_psi"], + SMP["m_u"]->SMP["m_q"]}] + + +(* ::Text:: *) +(*Gluon self-energy including the counter-term*) + + +ampGluonSE[0] = FCFAConvert[CreateFeynAmp[diag2[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu,nu,rho,si}, DropSumOver->True, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->True, SMP->True, + FinalSubstitutions->{ZA->SMP["Z_A"], Zxi->SMP["Z_xi"], + SMP["m_u"]->SMP["m_q"]}] + + +(* ::Text:: *) +(*Ghost self-energy including the counter-term*) + + +ampGhostSE[0] = FCFAConvert[CreateFeynAmp[diag3[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu,nu}, DropSumOver->True, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{Zu->SMP["Z_u"]}] + + +(* ::Text:: *) +(*Quark-gluon vertex including the counter-term*) + + +ampQGlVertex[0] = FCFAConvert[CreateFeynAmp[diag4[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p1,k}, OutgoingMomenta->{p2}, + LorentzIndexNames->{mu,nu,rho}, DropSumOver->True, LoopMomenta->{l}, + UndoChiralSplittings->True, ChangeDimension->D, + List->False, SMP->True, FinalSubstitutions-> + {ZA->SMP["Z_A"], Zg->SMP["Z_g"], Zpsi->SMP["Z_psi"], + SMP["m_u"]->SMP["m_q"]}] + + +(* ::Section:: *) +(*Calculate the amplitudes*) + + +(* ::Subsection:: *) +(*Quark self-energy*) + + +(* ::Text:: *) +(*Tensor reduction allows us to express the quark self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +ampQuarkSE[1]=ampQuarkSE[0]//SUNSimplify//DiracSimplify// + TID[#,l,UsePaVeBasis->True,ToPaVe->True]&; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude.*) + + +ampQuarkSEDiv[0]=ampQuarkSE[1]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]&; + + +ampQuarkSEDiv[1]=FCReplaceD[ampQuarkSEDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,0}]&//Normal//FCHideEpsilon//Simplify + + +ampQuarkSEDiv[2]=ampQuarkSEDiv[1]//ReplaceRepeated[#,{ + SMP["Z_m"]->1+alpha SMP["d_m"], + SMP["Z_psi"]->1+alpha SMP["d_psi"]}]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&//SelectNotFree2[#,SMP["Delta"],SMP["d_m"], + SMP["d_psi"]]& + + +ampQuarkSEDiv[3]=ampQuarkSEDiv[2]//SUNSimplify// + Collect2[#,DiracGamma,Factoring->Simplify]& + + +sol[1]=Solve[SelectNotFree2[ampQuarkSEDiv[3], DiracGamma]==0,SMP["d_psi"]]// + Flatten//ReplaceAll[#,Rule[a_,b_]:>Rule[a,SUNSimplify[b]]]&// + ReplaceAll[#,SMP["g_s"]^2->4Pi SMP["alpha_s"]]&; + +sol[2]=Solve[(SelectFree2[ampQuarkSEDiv[3], DiracGamma]==0)/.sol[1],SMP["d_m"]]// + Flatten//ReplaceAll[#,Rule[a_,b_]:>Rule[a,SUNSimplify[b]]]&// + ReplaceAll[#,SMP["g_s"]^2->4Pi SMP["alpha_s"]]&; + +solMS1=Join[sol[1],sol[2]]/.{ + SMP["d_psi"]->SMP["d_psi^MS"], + SMP["d_m"]->SMP["d_m^MS"],SMP["Delta"]->1/Epsilon +} +solMSbar1=Join[sol[1],sol[2]]/.{ + SMP["d_psi"]->SMP["d_psi^MSbar"], + SMP["d_m"]->SMP["d_m^MSbar"] +} + + +(* ::Subsection:: *) +(*Gluon self-energy*) + + +(* ::Text:: *) +(*Tensor reduction allows us to express the gluon self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +ampGluonSE[1]=(ampGluonSE[0][[1]]+Nf ampGluonSE[0][[2]]+ + Total[ampGluonSE[0][[3;;]]])//SUNSimplify//DiracSimplify; + + +ampGluonSE[2]=TID[ampGluonSE[1],l,UsePaVeBasis->True,ToPaVe->True]; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +ampGluonSEDiv[0]=ampGluonSE[2]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]& + + +ampGluonSEDiv[1]=FCReplaceD[ampGluonSEDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SUNSimplify; + + +ampGluonSEDiv[2]=ampGluonSEDiv[1]//ReplaceRepeated[#,{ + SMP["Z_A"]->1+alpha SMP["d_A"], + SMP["Z_xi"]->1+alpha SMP["d_A"]}]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&//SelectNotFree2[#,SMP["Delta"],SMP["d_A"], + SMP["d_xi"]]& + + +sol[3]=Solve[ampGluonSEDiv[2]==0,SMP["d_A"]]//Flatten// + ReplaceAll[#,SMP["g_s"]^2->4Pi SMP["alpha_s"]]&//Simplify +solMS2=sol[3]/.{SMP["d_A"]->SMP["d_A^MS"],SMP["Delta"]->1/Epsilon} +solMSbar2=sol[3]/.{SMP["d_A"]->SMP["d_A^MSbar"]} + + +(* ::Subsection:: *) +(*Ghost self-energy*) + + +(* ::Text:: *) +(*Tensor reduction allows us to express the ghost self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +ampGhostSE[1]=ampGhostSE[0]//SUNSimplify//DiracSimplify; + + +ampGhostSE[2]=TID[ampGhostSE[1],l,UsePaVeBasis->True,ToPaVe->True]; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +ampGhostSEDiv[0]=ampGhostSE[2]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]& + + +ampGhostSEDiv[1]=FCReplaceD[ampGhostSEDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SUNSimplify + + +ampGhostSEDiv[2]=ampGhostSEDiv[1]//ReplaceRepeated[#,{ + SMP["Z_u"]->1+alpha SMP["d_u"]}]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&// + SelectNotFree2[#,SMP["Delta"],SMP["d_u"]]&//Simplify + + +sol[4]=Solve[ampGhostSEDiv[2]==0,SMP["d_u"]]//Flatten// + ReplaceAll[#,SMP["g_s"]^2->4Pi SMP["alpha_s"]]&//Simplify +solMS3=sol[4]/.{SMP["d_u"]->SMP["d_u^MS"],SMP["Delta"]->1/Epsilon} +solMSbar3=sol[4]/.{SMP["d_u"]->SMP["d_u^MSbar"]} + + +(* ::Subsection:: *) +(*Quark-gluon vertex*) + + +(* ::Text:: *) +(*Tensor reduction allows us to express the quark-gluon vertex in tems of the Passarino-Veltman coefficient functions.*) + + +ampQGlVertex[1]=ampQGlVertex[0]//SUNSimplify//DiracSimplify; + + +ampQGlVertex[2]=TID[ampQGlVertex[1],l,UsePaVeBasis->True,ToPaVe->True]; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +ampQGlVertexDiv[0]=ampQGlVertex[2]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]& + + +ampQGlVertexDiv[1]=FCReplaceD[ampQGlVertexDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SUNSimplify; + + +ampQGlVertexDiv[2]=ampQGlVertexDiv[1]//ReplaceRepeated[#,{ + SMP["Z_g"]->1+alpha SMP["d_g"], + SMP["Z_A"]->1+alpha SMP["d_A"], + SMP["Z_psi"]->1+alpha SMP["d_psi"] + }]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&// + SelectNotFree2[#,SMP["Delta"],SMP["d_g"],SMP["d_A"],SMP["d_psi"]]&//Simplify + + +ampQGlVertexDiv[3]=ampQGlVertexDiv[2]//SUNSimplify[#,Explicit->True]&// + ReplaceAll[#,SUNTrace[x__]:>SUNTrace[x,Explicit->True]]&// + Collect2[#,Epsilon,SUNIndex]& + + +ampQGlVertexDiv[4]=ampQGlVertexDiv[3]// + ReplaceAll[#,suntf[xx_,_SUNFIndex,_SUNFIndex]:>SUNT@@xx]&// + ReplaceAll[#,SUNTF->suntf]&//ReplaceAll[#, + suntf[xx_,_SUNFIndex,_SUNFIndex]:>SUNT@@xx]&// + SUNSimplify//Collect2[#,SMP]& + + +ampQGlVertexDiv[5]=(ampQGlVertexDiv[4]/.{ + SMP["d_A"]->SMP["d_A^MS"], + SMP["d_psi"]->SMP["d_psi^MS"], + SMP["d_g"]->SMP["d_g"], + SMP["Delta"]->1/Epsilon +}/.solMS1/.solMS2)//ReplaceAll[#,SMP["g_s"]^3->4Pi SMP["alpha_s"]SMP["g_s"]]&// +Collect2[#,Epsilon]&//SUNSimplify + + +sol[5]=Solve[ampQGlVertexDiv[5]==0,SMP["d_g"]]//Flatten//Simplify +solMS4=sol[5]/.{SMP["d_g"]->SMP["d_g^MS"]} +solMSbar4=sol[5]/.{SMP["d_g"]->SMP["d_g^MSbar"],1/Epsilon->SMP["Delta"]} + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = { + SMP["d_psi^MS"]->-SMP["alpha_s"]/(4Pi) 1/Epsilon CF GaugeXi["G"], + SMP["d_m^MS"]->-SMP["alpha_s"]/(4Pi) 1/Epsilon 3 CF, + SMP["d_psi^MSbar"]->-SMP["alpha_s"]/(4Pi) SMP["Delta"] CF GaugeXi["G"], + SMP["d_m^MSbar"]->-SMP["alpha_s"]/(4Pi) SMP["Delta"] 3 CF, + SMP["d_A^MS"]->SMP["alpha_s"]/(4Pi) 1/Epsilon (1/2 CA(13/3-GaugeXi["G"])-2/3 Nf), + SMP["d_A^MSbar"]->SMP["alpha_s"]/(4Pi) SMP["Delta"] (1/2 CA(13/3-GaugeXi["G"])-2/3 Nf), + SMP["d_u^MS"]->SMP["alpha_s"]/(4Pi) CA/Epsilon (3-GaugeXi["G"])/4, + SMP["d_u^MSbar"]->SMP["alpha_s"]/(4Pi) CA SMP["Delta"] (3-GaugeXi["G"])/4, + SMP["d_g^MS"]->((-11*CA*SMP["alpha_s"])/(24*Epsilon*Pi) + (Nf*SMP["alpha_s"])/(12*Epsilon*Pi)), + SMP["d_g^MSbar"]->((-11*CA*SMP["alpha_s"])/(24 Pi)SMP["Delta"] + (Nf*SMP["alpha_s"])/(12*Pi)SMP["Delta"]) +}//Factor2; +FCCompareResults[Join[solMS1,solMSbar1,solMS2,solMSbar2,solMS3,solMSbar3,solMS4,solMSbar4]//Factor2,knownResult, +Text->{"\tCompare to Muta, Foundations of QCD, \ +Eqs 2.5.131-2.5.147:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/OneLoop/RenormalizationMassless.m b/FeynCalc/Examples/QCD/OneLoop/RenormalizationMassless.m new file mode 100644 index 000000000..ae4dd2de9 --- /dev/null +++ b/FeynCalc/Examples/QCD/OneLoop/RenormalizationMassless.m @@ -0,0 +1,395 @@ +(* ::Package:: *) + +(* :Title: Renormalization *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Renormalization, massless QCD, MS and MSbar, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*1-loop massless QCD renormalization in the minimal subtraction schemes*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +(* ::Text:: *) +(*This example uses a custom QCD model created with FeynRules. Please evaluate the file*) +(*FeynCalc/Examples/FeynRules/QCD/GenerateModelQCD.m before running it for the first time.*) + + +description="Renormalization, massless QCD, MS and MSbar, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Generate Feynman diagrams*) + + +(* ::Text:: *) +(*Nicer typesetting*) + + +MakeBoxes[mu,TraditionalForm]:="\[Mu]"; +MakeBoxes[nu,TraditionalForm]:="\[Nu]"; +MakeBoxes[rho,TraditionalForm]:="\[Rho]"; +MakeBoxes[si,TraditionalForm]:="\[Sigma]"; + + +params={InsertionLevel->{Particles},Model -> FileNameJoin[{"QCD","QCD"}], +GenericModel -> FileNameJoin[{"QCD","QCD"}],ExcludeParticles->{F[3|4,{2|3}],F[4,{1}]}}; +top[i_,j_]:=CreateTopologies[1, i -> j, + ExcludeTopologies -> {Tadpoles,WFCorrections,WFCorrectionCTs}]; +topTriangle[i_,j_]:=CreateTopologies[1, i -> j, + ExcludeTopologies -> {Tadpoles,WFCorrections,WFCorrectionCTs,SelfEnergies}]; + +topCT[i_,j_]:=CreateCTTopologies[1, i ->j, + ExcludeTopologies ->{Tadpoles,WFCorrections,WFCorrectionCTs}]; +topTriangleCT[i_,j_]:=CreateCTTopologies[1, i -> j, + ExcludeTopologies -> {Tadpoles,WFCorrections,WFCorrectionCTs,SelfEnergyCTs}]; + +{diagQuarkSE,diagQuarkSECT} = InsertFields[#, {F[3,{1}]} -> {F[3,{1}]}, + Sequence@@params]&/@{top[1,1],topCT[1,1]}; + +{diagGluonSE,diagGluonSECT} = InsertFields[#, {V[5]} -> {V[5]}, + Sequence@@params]&/@{top[1,1],topCT[1,1]}; + +{diagGhostSE,diagGhostSECT} = InsertFields[#, {U[5]} -> {U[5]}, + Sequence@@params]&/@{top[1,1],topCT[1,1]}; + +{diagQuarkGluonVertex,diagQuarkGluonVertexCT} = InsertFields[#, + {F[3,{1}],V[5]}->{F[3,{1}]}, Sequence@@params]&/@{topTriangle[2,1],topTriangleCT[2,1]}; + + +diag1[0]=diagQuarkSE[[0]][Sequence@@diagQuarkSE, + Sequence@@diagQuarkSECT]; +diag2[0]=diagGluonSE[[0]][Sequence@@diagGluonSE, + Sequence@@diagGluonSECT]; +diag3[0]=diagGhostSE[[0]][Sequence@@diagGhostSE, + Sequence@@diagGhostSECT]; +diag4[0]=diagQuarkGluonVertex[[0]][Sequence@@diagQuarkGluonVertex, + Sequence@@diagQuarkGluonVertexCT]; + + +Paint[diag1[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diag2[0], ColumnsXRows -> {4, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,128}]; + + +Paint[diag3[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diag4[0], ColumnsXRows -> {3, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +(* ::Text:: *) +(*Quark self-energy including the counter-term*) + + +ampQuarkSE[0] = FCFAConvert[CreateFeynAmp[diag1[0],Truncated->True, + GaugeRules->{},PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu,nu}, DropSumOver->True, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{Zm->SMP["Z_m"], Zpsi->SMP["Z_psi"], + SMP["m_u"]->0}] + + +(* ::Text:: *) +(*Gluon self-energy including the counter-term*) + + +ampGluonSE[0] = FCFAConvert[CreateFeynAmp[diag2[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu,nu,rho,si}, DropSumOver->True, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->True, SMP->True, + FinalSubstitutions->{ZA->SMP["Z_A"], Zxi->SMP["Z_xi"], + SMP["m_u"]->0}] + + +(* ::Text:: *) +(*Ghost self-energy including the counter-term*) + + +ampGhostSE[0] = FCFAConvert[CreateFeynAmp[diag3[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu,nu}, DropSumOver->True, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{Zu->SMP["Z_u"]}] + + +(* ::Text:: *) +(*Quark-gluon vertex including the counter-term*) + + +ampQGlVertex[0] = FCFAConvert[CreateFeynAmp[diag4[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p1,k}, OutgoingMomenta->{p2}, + LorentzIndexNames->{mu,nu,rho}, DropSumOver->True, LoopMomenta->{l}, + UndoChiralSplittings->True, ChangeDimension->D, + List->False, SMP->True, FinalSubstitutions-> + {ZA->SMP["Z_A"], Zg->SMP["Z_g"], Zpsi->SMP["Z_psi"], + SMP["m_u"]->0}] + + +(* ::Section:: *) +(*Calculate the amplitudes*) + + +(* ::Subsection:: *) +(*Quark self-energy*) + + +(* ::Text:: *) +(*Tensor reduction allows us to express the quark self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +ampQuarkSE[1]=ampQuarkSE[0]//SUNSimplify//DiracSimplify// + TID[#,l,UsePaVeBasis->True,ToPaVe->True]&; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude.*) + + +ampQuarkSEDiv[0]=ampQuarkSE[1]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]&; + + +ampQuarkSEDiv[1]=FCReplaceD[ampQuarkSEDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,0}]&//Normal//FCHideEpsilon//Simplify + + +ampQuarkSEDiv[2]=ampQuarkSEDiv[1]//ReplaceRepeated[#,{ + SMP["Z_m"]->1+alpha SMP["d_m"], + SMP["Z_psi"]->1+alpha SMP["d_psi"]}]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&//SelectNotFree2[#,SMP["Delta"],SMP["d_m"], + SMP["d_psi"]]& + + +ampQuarkSEDiv[3]=ampQuarkSEDiv[2]//SUNSimplify// + Collect2[#,DiracGamma,Factoring->Simplify]& + + +sol[1]=Solve[ampQuarkSEDiv[3]==0,SMP["d_psi"]]// + Flatten//ReplaceAll[#,Rule[a_,b_]:>Rule[a,SUNSimplify[b]]]&// + ReplaceAll[#,SMP["g_s"]^2->4Pi SMP["alpha_s"]]&; + +solMS1=sol[1]/.{ + SMP["d_psi"]->SMP["d_psi^MS"],SMP["Delta"]->1/Epsilon +} +solMSbar1=sol[1]/.{ + SMP["d_psi"]->SMP["d_psi^MSbar"] +} + + +(* ::Subsection:: *) +(*Gluon self-energy*) + + +(* ::Text:: *) +(*Tensor reduction allows us to express the gluon self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +ampGluonSE[1]=(ampGluonSE[0][[1]]+Nf ampGluonSE[0][[2]]+ + Total[ampGluonSE[0][[3;;]]])//SUNSimplify//DiracSimplify; + + +ampGluonSE[2]=TID[ampGluonSE[1],l,UsePaVeBasis->True,ToPaVe->True]; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +ampGluonSEDiv[0]=ampGluonSE[2]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]& + + +ampGluonSEDiv[1]=FCReplaceD[ampGluonSEDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SUNSimplify; + + +ampGluonSEDiv[2]=ampGluonSEDiv[1]//ReplaceRepeated[#,{ + SMP["Z_A"]->1+alpha SMP["d_A"], + SMP["Z_xi"]->1+alpha SMP["d_A"]}]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&//SelectNotFree2[#,SMP["Delta"],SMP["d_A"], + SMP["d_xi"]]& + + +sol[3]=Solve[ampGluonSEDiv[2]==0,SMP["d_A"]]//Flatten// + ReplaceAll[#,SMP["g_s"]^2->4Pi SMP["alpha_s"]]&//Simplify +solMS2=sol[3]/.{SMP["d_A"]->SMP["d_A^MS"],SMP["Delta"]->1/Epsilon} +solMSbar2=sol[3]/.{SMP["d_A"]->SMP["d_A^MSbar"]} + + +(* ::Subsection:: *) +(*Ghost self-energy*) + + +(* ::Text:: *) +(*Tensor reduction allows us to express the ghost self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +ampGhostSE[1]=ampGhostSE[0]//SUNSimplify//DiracSimplify; + + +ampGhostSE[2]=TID[ampGhostSE[1],l,UsePaVeBasis->True,ToPaVe->True]; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +ampGhostSEDiv[0]=ampGhostSE[2]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]& + + +ampGhostSEDiv[1]=FCReplaceD[ampGhostSEDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SUNSimplify + + +ampGhostSEDiv[2]=ampGhostSEDiv[1]//ReplaceRepeated[#,{ + SMP["Z_u"]->1+alpha SMP["d_u"]}]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&// + SelectNotFree2[#,SMP["Delta"],SMP["d_u"]]&//Simplify + + +sol[4]=Solve[ampGhostSEDiv[2]==0,SMP["d_u"]]//Flatten// + ReplaceAll[#,SMP["g_s"]^2->4Pi SMP["alpha_s"]]&//Simplify +solMS3=sol[4]/.{SMP["d_u"]->SMP["d_u^MS"],SMP["Delta"]->1/Epsilon} +solMSbar3=sol[4]/.{SMP["d_u"]->SMP["d_u^MSbar"]} + + +(* ::Subsection:: *) +(*Quark-gluon vertex*) + + +(* ::Text:: *) +(*Tensor reduction allows us to express the quark-gluon vertex in tems of the Passarino-Veltman coefficient functions.*) + + +ampQGlVertex[1]=ampQGlVertex[0]//SUNSimplify//DiracSimplify; + + +ampQGlVertex[2]=TID[ampQGlVertex[1],l,UsePaVeBasis->True,ToPaVe->True]; + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +ampQGlVertexDiv[0]=ampQGlVertex[2]//PaVeUVPart[#,Prefactor->1/(2Pi)^D]& + + +ampQGlVertexDiv[1]=FCReplaceD[ampQGlVertexDiv[0],D->4-2Epsilon]// + Series[#,{Epsilon,0,0}]&// + Normal//FCHideEpsilon//SUNSimplify; + + +ampQGlVertexDiv[2]=ampQGlVertexDiv[1]//ReplaceRepeated[#,{ + SMP["Z_g"]->1+alpha SMP["d_g"], + SMP["Z_A"]->1+alpha SMP["d_A"], + SMP["Z_psi"]->1+alpha SMP["d_psi"] + }]&//Series[#,{alpha,0,1}]&// + Normal//ReplaceAll[#,alpha->1]&// + SelectNotFree2[#,SMP["Delta"],SMP["d_g"],SMP["d_A"],SMP["d_psi"]]&//Simplify + + +ampQGlVertexDiv[3]=ampQGlVertexDiv[2]//SUNSimplify[#,Explicit->True]&// + ReplaceAll[#,SUNTrace[x__]:>SUNTrace[x,Explicit->True]]&// + Collect2[#,Epsilon,SUNIndex]& + + +ampQGlVertexDiv[4]=ampQGlVertexDiv[3]// + ReplaceAll[#,suntf[xx_,_SUNFIndex,_SUNFIndex]:>SUNT@@xx]&// + ReplaceAll[#,SUNTF->suntf]&//ReplaceAll[#, + suntf[xx_,_SUNFIndex,_SUNFIndex]:>SUNT@@xx]&// + SUNSimplify//Collect2[#,SMP]& + + +ampQGlVertexDiv[5]=(ampQGlVertexDiv[4]/.{ + SMP["d_A"]->SMP["d_A^MS"], + SMP["d_psi"]->SMP["d_psi^MS"], + SMP["d_g"]->SMP["d_g"], + SMP["Delta"]->1/Epsilon +}/.solMS1/.solMS2)//ReplaceAll[#,SMP["g_s"]^3->4Pi SMP["alpha_s"]SMP["g_s"]]&// +Collect2[#,Epsilon]&//SUNSimplify + + +sol[5]=Solve[ampQGlVertexDiv[5]==0,SMP["d_g"]]//Flatten//Simplify +solMS4=sol[5]/.{SMP["d_g"]->SMP["d_g^MS"]} +solMSbar4=sol[5]/.{SMP["d_g"]->SMP["d_g^MSbar"],1/Epsilon->SMP["Delta"]} + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = { + SMP["d_psi^MS"]->-SMP["alpha_s"]/(4Pi) 1/Epsilon CF GaugeXi["G"], + SMP["d_psi^MSbar"]->-SMP["alpha_s"]/(4Pi) SMP["Delta"] CF GaugeXi["G"], + SMP["d_A^MS"]->SMP["alpha_s"]/(4Pi) 1/Epsilon (1/2 CA(13/3-GaugeXi["G"])-2/3 Nf), + SMP["d_A^MSbar"]->SMP["alpha_s"]/(4Pi) SMP["Delta"] (1/2 CA(13/3-GaugeXi["G"])-2/3 Nf), + SMP["d_u^MS"]->SMP["alpha_s"]/(4Pi) CA/Epsilon (3-GaugeXi["G"])/4, + SMP["d_u^MSbar"]->SMP["alpha_s"]/(4Pi) CA SMP["Delta"] (3-GaugeXi["G"])/4, + SMP["d_g^MS"]->((-11*CA*SMP["alpha_s"])/(24*Epsilon*Pi) + (Nf*SMP["alpha_s"])/(12*Epsilon*Pi)), + SMP["d_g^MSbar"]->((-11*CA*SMP["alpha_s"])/(24 Pi)SMP["Delta"] + (Nf*SMP["alpha_s"])/(12*Pi)SMP["Delta"]) +}//Factor2; +FCCompareResults[Join[solMS1,solMSbar1,solMS2,solMSbar2,solMS3,solMSbar3,solMS4,solMSbar4]//Factor2,knownResult, +Text->{"\tCompare to Muta, Foundations of QCD, \ +Eqs 2.5.131-2.5.147:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/QCDGGToGGTree.m b/FeynCalc/Examples/QCD/QCDGGToGGTree.m deleted file mode 100644 index c87b6d409..000000000 --- a/FeynCalc/Examples/QCD/QCDGGToGGTree.m +++ /dev/null @@ -1,91 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDGGToGGTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - g g -> g g scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the g g -> g g scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsGGToGG = InsertFields[topGGToGG, {V[5],V[5]}-> {V[5],V[5]}, - InsertionLevel -> {Classes}, - Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsGGToGG, ColumnsXRows -> {2, 2}, Numbering -> None,SheetHeader->None,ImageSize->{512,512}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampGGToGG = FCFAConvert[CreateFeynAmp[diagsGGToGG,Truncated -> False],IncomingMomenta->{k1,k2}, -OutgoingMomenta->{k3,k4},TransversePolarizationVectors->{k1,k2,k3,k4},DropSumOver->True, -ChangeDimension->4,SMP->True]//Contract//SUNFSimplify[#, Explicit->True,SUNNToCACF->False]&; - - -(* The calculation becomes easier if energy momentum conservation is applied *) -SetMandelstam[s, t, u, k1, k2, -k3, -k4, 0, 0, 0, 0]; -ampGGToGG1=ampGGToGG//PropagatorDenominatorExplicit//ReplaceAll[#, - Momentum[k1]->Momentum[k3+k4-k2]]&//ExpandScalarProduct//ReplaceAll[#,Momentum[k2]->Momentum[k3+ - k4-k1]]&//ExpandScalarProduct//ReplaceAll[#,Momentum[k3]->Momentum[k1+k2- - k4]]&//ExpandScalarProduct//ExpandScalarProduct//ReplaceAll[#,Momentum[k4]->Momentum[k1+k2- - k3]]&//ExpandScalarProduct//Simplify; -ampGGToGGCC1=ampGGToGG1//ComplexConjugate//FCRenameDummyIndices; - - -(* ::Section:: *) -(*Unpolarized process g g -> g g *) - - -polsums[x_,vec_,aux_,spinfac_]:=x//Collect2[#,Pair[_,Momentum[Polarization[vec,__]]]]&//Isolate[#, - {Polarization[vec,__]}]&//DoPolarizationSums[#,vec,aux,ExtraFactor->spinfac]&//FixedPoint[ReleaseHold,#]& - - -ClearAll[re]; -Table[Print[" calculating color factors in products of the amplitudes ", i, " and ", j," (CC), time = ", -Timing[re[i,j]=(ampGGToGG1[[i]]ampGGToGGCC1[[j]]//SUNSimplify[#,Explicit->True,SUNNToCACF->False]&)][[1]]];re[i,j],{i,4},{j,i}]; - - -ClearAll[pre]; -Table[Print[" calculating product of the amplitudes ", i, " and ", j," (CC), time = ", Timing[pre[i,j]=re[i,j]//polsums[#,k1,k2, -1/2]&//polsums[#,k2,k1,1/2]&//polsums[#,k3,k4,1]&//polsums[#,k4,k3,1]&//Simplify][[1]]];pre[i,j],{i,4},{j,i}]; - - -fpre[i_,j_]:=pre[i,j]/;(i>=j); -fpre[i_,j_]:=ComplexConjugate[pre[j,i]]/;(i3})//Simplify - - -masslesssqAmpGGToGG=TrickMandelstam[sqAmpGGToGG,{s,t,u,0}] - - -masslesssqAmpGGToGGEllis=(9/2)SMP["g_s"]^4 (3 - t u/s^2 - s u/t^2 - s t/u^2); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[TrickMandelstam[Simplify[masslesssqAmpGGToGGEllis-masslesssqAmpGGToGG],{s,t,u,0}]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDGGToQiQBariTree.m b/FeynCalc/Examples/QCD/QCDGGToQiQBariTree.m deleted file mode 100644 index fe40462ac..000000000 --- a/FeynCalc/Examples/QCD/QCDGGToQiQBariTree.m +++ /dev/null @@ -1,70 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDGGToQiQBariTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - g g -> q_i qbar_i scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the g g -> q_i qbar_i scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsGGToQiQBari = InsertFields[topGGToQiQBari, {V[5],V[5]}-> {F[3, {1}], - -F[3, {1}]}, InsertionLevel -> {Classes}, - Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsGGToQiQBari, ColumnsXRows -> {3, 1}, Numbering -> None,SheetHeader->None,ImageSize->{768,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampGGToQiQBari = FCFAConvert[CreateFeynAmp[diagsGGToQiQBari,Truncated -> False],IncomingMomenta->{k1,k2}, -OutgoingMomenta->{p1,p2},UndoChiralSplittings->True,TransversePolarizationVectors->{k1,k2}, -DropSumOver->True,ChangeDimension->4,SMP->True] - - -(* ::Section:: *) -(*Unpolarized process g g -> q_i qbar_i*) - - -SetMandelstam[s, t, u, k1, k2, -p1, -p2, 0, 0, SMP["m_u"], SMP["m_u"]]; -sqAmpGGToQiQBari =(1/8^2)(Total[ampGGToQiQBari] Total[(ComplexConjugate[ampGGToQiQBari]// - FCRenameDummyIndices)])//PropagatorDenominatorExplicit//SUNSimplify[#,Explicit->True, - SUNNToCACF->False]&//FermionSpinSum//Contract//ReplaceAll[#,{DiracTrace->Tr, - SUNN->3}]&//DoPolarizationSums[#,k1,k2,ExtraFactor->1/2]&//DoPolarizationSums[#,k2, - k1,ExtraFactor->1/2]&//Simplify - - -masslesssqAmpGGToQiQBari = TrickMandelstam[(sqAmpGGToQiQBari /. {SMP["m_u"] -> 0})//Simplify,{s,t,u,0}] - - -masslesssqAmpGGToQiQBariEllis=(1/6)SMP["g_s"]^4 (t^2+u^2)/(t u)-(3/8)SMP["g_s"]^4 (t^2+u^2)/(s^2); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[TrickMandelstam[Simplify[masslesssqAmpGGToQiQBariEllis-masslesssqAmpGGToQiQBari],{s,t,u,0}]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDGQiToGQi.m b/FeynCalc/Examples/QCD/QCDGQiToGQi.m deleted file mode 100644 index 23affe3da..000000000 --- a/FeynCalc/Examples/QCD/QCDGQiToGQi.m +++ /dev/null @@ -1,68 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDGQiToQGiTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - g q_i -> g q_i scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the g q_i -> g q_i scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsGQiToQGi = InsertFields[topGQiToQGi, {F[3, {1}],V[5]}-> {F[3, - {1}],V[5]}, InsertionLevel -> {Classes}, - Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsGQiToQGi, ColumnsXRows -> {3, 1}, Numbering -> None, SheetHeader->None,ImageSize->{768,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampGQiToQGi = FCFAConvert[CreateFeynAmp[diagsGQiToQGi,Truncated -> False],IncomingMomenta->{p1,k1},OutgoingMomenta->{p2,k2}, -DropSumOver->True,ChangeDimension->4,UndoChiralSplittings->True,List->False,TransversePolarizationVectors->{k1,k2},SMP->True]; - - -(* ::Section:: *) -(*Unpolarized process g q_i -> g q_i *) - - -SetMandelstam[s, t, u, p1, k1, -p2, -k2, SMP["m_u"], 0, SMP["m_u"], 0]; -sqAmpGQiToQGi =(1/(3*8))(ampGQiToQGi (ComplexConjugate[ampGQiToQGi]// - FCRenameDummyIndices))//PropagatorDenominatorExplicit//SUNSimplify[#,Explicit->True, - SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor->1/2]&//Contract//ReplaceAll[#,{DiracTrace->Tr, - SUNN->3}]&//DoPolarizationSums[#,k1,k2,ExtraFactor->1/2]&//DoPolarizationSums[#,k2,k1]&//Simplify - - -masslesssqAmpGQiToQGi = TrickMandelstam[(sqAmpGQiToQGi /. {SMP["m_u"] -> 0})//Simplify,{s,t,u,0}] - - -masslesssqAmpGQiToQGiEllis=-(4/9)SMP["g_s"]^4 (s^2+u^2)/(s u)+SMP["g_s"]^4 (u^2+s^2)/(t^2); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[TrickMandelstam[Simplify[masslesssqAmpGQiToQGiEllis-masslesssqAmpGQiToQGi],{s,t,u,0}]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDGammaStarGToQiQBari.m b/FeynCalc/Examples/QCD/QCDGammaStarGToQiQBari.m deleted file mode 100644 index cd6f507bf..000000000 --- a/FeynCalc/Examples/QCD/QCDGammaStarGToQiQBari.m +++ /dev/null @@ -1,88 +0,0 @@ -(* ::Package:: *) - -(* :Title: masslessAmpGammaStarGToQiQBari *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - g + gamma^* -> q_i qbar_i subprocess in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the g + gamma^* -> q_i qbar_i subprocess in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsGammaStarGToQiQBari = InsertFields[topGammaStarGToQiQBari,{V[1],V[5]}->{F[3, {1}], -F[3, {1}]}, - InsertionLevel -> {Classes}, Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsGammaStarGToQiQBari, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None,ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -(* Note that here we set only the polarization vector of the gluon to be transverse. -Since the photon is virtual, it can have unphysical polarizations as well.*) - - -ampGammaStarGToQiQBari=FCFAConvert[CreateFeynAmp[diagsGammaStarGToQiQBari,Truncated -> False],IncomingMomenta->{kGamma,kG}, -OutgoingMomenta->{p1,p2},UndoChiralSplittings->True,TransversePolarizationVectors->{kG},DropSumOver->True,List->False,SMP->True]//Contract - - -(* ::Section:: *) -(*Unpolarized process g + gamma^* -> q_i qbar_i*) - - -SetMandelstam[s, t, u, kGamma, kG, -p1, -p2, qQ, 0, SMP["m_u"], SMP["m_u"]]; - - -(* The final result depends on the electric charge of the quarks. Since we generated the diagrams for up and anti-up, we divide -the amplitude by 2/3 and multiply it by EQ to have explicit quark charge dependence *) - - -ampGammaStarGToQiQBari2 = ampGammaStarGToQiQBari/(2/3)*EQ; - - -(* Now come the usual steps, but with some special features. We don't average over the polarizations of the virtual photon, -and we use the gauge trick for the sum over its polarizations. Of course, in this case the sum goes over all 4 unphysical -polarizations, not just 2. Apart from that, we have the normal averaging over the 8 colors and 2 polarizations of the real -gluon. For the polarization sum of the gluon we use the quark momentum as the auxiliary vector *) - - -ampGammaStarGToQiQBari3=ampGammaStarGToQiQBari2*(ComplexConjugate[ampGammaStarGToQiQBari2]//FCRenameDummyIndices)// -PropagatorDenominatorExplicit//FermionSpinSum//ReplaceAll[#,{DiracTrace->Tr}]&//DoPolarizationSums[#,kG,p1,ExtraFactor->1/(2*8)]&// -DoPolarizationSums[#,kGamma,0,VirtualBoson->True,GaugeTrickN->4]&//SUNSimplify[#,SUNNToCACF->False]&; - - -ampGammaStarGToQiQBari4=(ampGammaStarGToQiQBari3/.{SMP["m_u"]->0,SUNN->3})//Simplify - - -masslessAmpGammaStarGToQiQBari=(TrickMandelstam[ampGammaStarGToQiQBari4,{s,t,u,qQ^2}]/.qQ->I Q)//Simplify - - -masslessAmpGammaStarGToQiQBariField= SMP["e"]^2 EQ^2 SMP["g_s"]^2 2 (u/t+t/u + 2 Q^2(u+t+Q^2)/(t u)); -Print["Check with R. Field, Eq 4.3.20: ", - If[Simplify[masslessAmpGammaStarGToQiQBariField-masslessAmpGammaStarGToQiQBari]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDGhostSelfEnergyTwoLoops.m b/FeynCalc/Examples/QCD/QCDGhostSelfEnergyTwoLoops.m deleted file mode 100644 index a84eaeeaa..000000000 --- a/FeynCalc/Examples/QCD/QCDGhostSelfEnergyTwoLoops.m +++ /dev/null @@ -1,216 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDGhostSelfEnergyTwoLoops *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the ghost self-energy in QCD at 2-loops *) - -(* ------------------------------------------------------------------------ *) - - -(* ::Section:: *) -(*The 2-loop ghost self-energy in QCD*) - - -(* ::Subsection:: *) -(*Load FeynCalc, FeynArts and Tarcer*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the ghost self-energy in QCD at 2-loops"]; -]; -$LoadFeynArts = $LoadTARCER = True; -< 1,ExcludeTopologies -> {Tadpoles}]; -diags=InsertFields[tops, {U[5]} -> {U[5]},InsertionLevel -> {Classes}, GenericModel -> "Lorentz",Model -> "SMQCD"]; -Paint[diags,SheetHeader -> False, Numbering -> None,ImageSize->{512,512}]; - - -(* ::Subsection:: *) -(*Calculating the bare 2-loop off-shell ghost selfenergy diagrams*) - - -(* ::Text:: *) -(*The computation is performed with massless quarks. Furthermore, we choose to abbreviate square of the ingoing (and outgoing) momentum p by pp.*) - - -ScalarProduct[p,p]=pp; - - -(* ::Text:: *) -(*Now we obtain the corresponding amplitudes. The prefactor 1/(2Pi)^(2D) for the loop integrals is understood. Notice that we ignore the first diagram (zero in DR) and the the fifth diagram, since*) -(*its contribution is identical to that of the fourth diagram.*) - - -amps=FCFAConvert[CreateFeynAmp[DiagramExtract[diags,{2,3,4,6,7,8,9}],Truncated -> True,GaugeRules->{},PreFactor->-I], -IncomingMomenta->{p},OutgoingMomenta->{p},LoopMomenta->{q1,q2},UndoChiralSplittings->True,DropSumOver->True, -ChangeDimension->D,SMP->True]/.{MQU[Index[Generation, 3]]->0,GaugeXi[_]->GaugeXi}/.GaugeXi->1-GaugeXi; - - -(* ::Text:: *) -(*We simplify the color and Dirac algebra, do some partial fractioning and convert the integrals to the TRACER notation. To do this we define the following helper function*) - - -RepRuleCancelQP={ -x_. Power[Pair[Momentum[q_,dim_:4],Momentum[q_,dim_:4]],n_] * -FeynAmpDenominator[a___,PD[Momentum[q_,dim_:4],0],b___]:>x Power[Pair[Momentum[q,dim],Momentum[q,dim]],n-1] FeynAmpDenominator[a,b], - -x_. Pair[Momentum[q_,dim_:4],Momentum[q_,dim_:4]] * -FeynAmpDenominator[a___,PD[Momentum[q_,dim_:4],0],b___]:>x FeynAmpDenominator[a,b], - -x_. Pair[Momentum[p_,dim_:4],Momentum[q_,dim_:4]] * -FeynAmpDenominator[a___,PD[Momentum[q_,dim_:4]-Momentum[p_,dim_:4],0],b___]:> --(1/2)x FeynAmpDenominator[a,b] -+(1/2)x Pair[Momentum[p,dim],Momentum[p,dim]]FeynAmpDenominator[a,PD[Momentum[q,dim]-Momentum[p,dim],0],b] -+(1/2)x Pair[Momentum[q,dim],Momentum[q,dim]]FeynAmpDenominator[a,PD[Momentum[q,dim]-Momentum[p,dim],0],b], - -x_. Power[Pair[Momentum[p_,dim_:4],Momentum[q_,dim_:4]],n_] * -FeynAmpDenominator[a___,PD[Momentum[q_,dim_:4]-Momentum[p_,dim_:4],0],b___]:> --(1/2)x Power[Pair[Momentum[p,dim],Momentum[q,dim]],n-1] FeynAmpDenominator[a,b] -+(1/2)x Power[Pair[Momentum[p,dim],Momentum[q,dim]],n-1] Pair[Momentum[p,dim],Momentum[p,dim]]FeynAmpDenominator[a,PD[Momentum[q,dim]-Momentum[p,dim],0],b] -+(1/2)x Power[Pair[Momentum[p,dim],Momentum[q,dim]],n-1] Pair[Momentum[q,dim],Momentum[q,dim]]FeynAmpDenominator[a,PD[Momentum[q,dim]-Momentum[p,dim],0],b] -}; -ClearAll[diagCompute]; -diagCompute[ex_]:= -ex//SUNSimplify[#,Explicit->True,SUNTrace->True]&// -ReplaceAll[#,DiracTrace[x__]:>DiracTrace[x,DiracTraceEvaluate->True]]&// -Contract//FCLoopIsolate[#,{q1,q2},Head->loopHead]&//ReplaceRepeated[#,RepRuleCancelQP]&// -ReplaceAll[#,loopHead->Identity]&//ToTFI[#,q1,q2,p]&; - - -(* ::Text:: *) -(*and apply it to every single amplitude.*) - - -tmp=AbsoluteTiming[diagCompute/@amps]; -Print["Needed ",AccountingForm[tmp[[1]],3]," s for the algebraic simplifications"]; -res=tmp[[2]]; - - -allints = Cases2[res, TFI]; -allints // Length - - -(* ::Text:: *) -(*There are 272 integrals to be done for the ghost self energy. There are several possibilities how to proceed. One possibility is to calculate the integrals one by one and save them to a file in the Database directory. This can be conveniently done using the CheckDB function. If the file "IntegralsQCDTwoLoopGhostSelfEnergy.db" does not exist the first argument of CheckDB is evaluated, otherwise the list is loaded and assigned to inttable. A laptop with one i5-560m CPU running Mathematica 10 on Fedora 22 needs about 15 seconds to generate the file.*) - - -Timing[inttable = - CheckDB[Dispatch[ - Thread[allints -> - Table[WriteString["stdout", "."]; - TarcerRecurse[allints[[i]]], {i, Length[allints]}]]], - "IntegralsQCDTwoLoopGhostSelfEnergy.db"];] - - -(* ::Text:: *) -(*Now we need to insert the calculated integrals and rewrite the whole expression into a nicer form. Note that the Tarcer two loop integrals are defined to have only 1/(Pi)^D in the measure. Therefore, we will need to multiply the full result by 1/(4Pi)^D, since we did not include the prefactor (1/(2Pi)^D)^2 in the very beginning.*) - - -Timing[result = - PropagatorDenominatorExplicit[FCI[(Collect2[#, {TAI, TBI, TJI}, Factoring -> Factor2] & /@ (res /. - inttable))]];] - - -(* ::Text:: *) -(*Here is the full result.*) - - -result=result//.SMP["g_s"]:>gs - - -(* ::Text:: *) -(*Now let us compare our result with the literature. This computation can be found in A.I. Davydychev, P .Osland, O.V. Tarasov, Phys. Rev. D 58, 036007 (1998). The preprint is available at arXiv:hep-ph/9801380.*) -(**) -(*The general expression for the ghost self-energy (two-point function) is given by Eq. 2.15. What we computed is -delta^{a1 a2} p^2 G^{(2)}(p^2) (c.f. Eq. 6.5). The authors write G^{(2)}(p^2) as G^{(2,q)}(p^2) + G^{(2,\[Xi])(red)}(p^2) + G^{(2,\[Xi])(irred)}(p^2) (c.f. Eq 2.6), where G^{(2,q)}(p^2) is the contribution of the quark loops (both one-particle irreducible and one-particle reducible), G^{(2,\[Xi])(irred)}(p^2) is the one particle irreducible contribution of the gluon and ghost loops and G^{(2,\[Xi])(red)}(p^2) is the one particle reducible one.*) -(**) -(*The quark loop contribution is given by the third diagram*) - - -G2q=result[[3]] - - -(* ::Text:: *) -(*This should give us the same as Eq 6.13, with T = Nf Tf (c.f. Eq. 4.6) and eta = ( Gamma[D/2-1]^2 Gamma[3-D/2] ) / Gamma[D-3]. Remember that we must remove - delta^{ab} p^2 from our G2q and multiply it by (1/(4Pi)^D).*) - - -G2qEval= -1/(4Pi)^D TarcerExpand[G2q, D -> 4 - 2 Epsilon, 0]// -ReplaceRepeated[#,{pp SUNDelta[a_,b_]->1,CA^2->2T*CA}]& - - -(* ::Text:: *) -(*Our result contains SEpsilon[4 - 2*Epsilon] which is an abbreviation for Exp[-Epsilon*EulerGamma]. Since eta is given by Exp[- Epsilon*EulerGamma] (1- 1/12 Pi^2 Epsilon^2 + ...) (c.f. Eq 4.7), it it clear that SEpsilon[4 - 2*Epsilon]^2 comes from there. To bring our result into the suitable form, we therefore must divide the term in the brackets by (1- 1/12 Pi^2 Epsilon^2)^2 or (1- Zeta2/2 Epsilon^2)^2 and again expand it in Epsilon. After that we can replace SEpsilon[4 - 2*Epsilon]^2 by eta^2.*) - - -G2qFinal=G2qEval//ReplaceAll[#,Dot[a_,b_]:>Dot[a, Normal[Series[b/(1 - Zeta2/2 Epsilon^2)^2,{Epsilon,0,0}]]]]&// -ReplaceAll[#,{SEpsilon[4 - 2*Epsilon]^2->eta^2,gs->SMP["g_s"]}]& - - -G2qFinalPaper = (((CA*eta^2*SMP["g_s"]^4*T)/(-pp)^(2*Epsilon))(-53/8 - 1/(2*Epsilon^2) - 7/(4*Epsilon))/(4*Pi)^D); -Print["Check with Davydychev, Osland and Tarasov, hep-ph/9801380, Eq 6.13: ", - If[Simplify[((G2qFinal/.{Dot->Times})-G2qFinalPaper)]===0, "CORRECT.", "!!! WRONG !!!"]]; - - -(* ::Text:: *) -(*Now let us repeat the same game for G^{(2,\[Xi])(red)}(p^2) which is given by Eq. 6.14. The reducible part comes from the diagram 7, hence*) - - -G2xiRed=result[[7]]; -G2xiRedEval= -1/(4Pi)^D TarcerExpand[G2xiRed, D -> 4 - 2 Epsilon, 0]// -ReplaceRepeated[#,{pp SUNDelta[a_,b_]->1}]&; -G2xiRedFinal=G2xiRedEval//ReplaceAll[#,Dot[a_,b_]:>Dot[a, Normal[Series[b/(1 - Zeta2/2 Epsilon^2)^2,{Epsilon,0,0}]]]]&// -ReplaceAll[#,{SEpsilon[4 - 2*Epsilon]^2->eta^2,gs->SMP["g_s"]}]& - - -G2xiRedPaper=(((CA^2*eta^2*SMP["g_s"]^4)/(-pp)^(2*Epsilon)) *( 3 + (1 + GaugeXi/2)/Epsilon + GaugeXi + - (4 + 4*GaugeXi + GaugeXi^2)/(16*Epsilon^2))/(4*Pi)^D); -Print["Check with Davydychev, Osland and Tarasov, hep-ph/9801380, Eq 6.14: ", - If[Simplify[((G2xiRedFinal/.{Dot->Times})-G2xiRedPaper)]===0, "CORRECT.", "!!! WRONG !!!"]]; - - -(* ::Text:: *) -(*Finally, we still need to verify G^{(2,\[Xi])(irred)}(p^2), the irreducible contribution of the gluon and ghost loops given by the remaining diagrams and shown in Eq 6.12*) - - -G2xiIrred=Collect2[Plus@@Join[result[[1;;2]],result[[4;;6]]], {TBI, TJI}]; -G2xiIrredEval= -1/(4Pi)^D TarcerExpand[G2xiIrred, D -> 4 - 2 Epsilon, 0]// -ReplaceRepeated[#,{pp SUNDelta[a_,b_]->1,Nf*Tf->T}]&; -G2xiIrredFinal=G2xiIrredEval//ReplaceAll[#,Dot[a_,b_]:>Dot[a,Collect[b,{SEpsilon[_],(-pp)^(-2Epsilon)}]]]&// -ReplaceAll[#,Dot[a_, SEpsilon[x_]^2 (-pp)^(-2Epsilon) b_]:>Dot[SEpsilon[x]^2 (-pp)^(-2Epsilon) a,b]]&// -ReplaceAll[#,Dot[a_,b_]:>Dot[a, Normal[Series[b/(1 - Zeta2/2 Epsilon^2)^2,{Epsilon,0,0}]]]]&// -ReplaceAll[#,{SEpsilon[4 - 2*Epsilon]^2->eta^2,gs->SMP["g_s"]}]& - - -G2xiIrredPaper=(((CA^2*eta^2*SMP["g_s"]^4)/(-pp)^(2*Epsilon)) ( 1/Epsilon(67/16 - (9*GaugeXi)/32) + - (1 + (3*GaugeXi)/16 - (3*GaugeXi^2)/32)/Epsilon^2 + 503/32 +(-73*GaugeXi)/64 + -(3*GaugeXi^2)/8 - (3*Zeta[3])/4 - (3*GaugeXi^2*Zeta[3])/16)/(4*Pi)^D); -Print["Check with Davydychev, Osland and Tarasov, hep-ph/9801380, Eq 6.12: ", - If[Simplify[((G2xiIrredFinal/.{Dot->Times})-G2xiIrredPaper)]===0, "CORRECT.", "!!! WRONG !!!"]]; - - -(* ::Text:: *) -(*Last but not least, let us verify the full contribution of the gluon and ghost loops which is given by Eq. 6.15*) - - -G2xFinal=(G2xiIrredFinal+G2xiRedFinal)//ReplaceAll[#,f_ Dot[a_,b_]+ f_ Dot[a_,c_]:>f Dot[a,Collect[Simplify[b+c],{1/Epsilon}]]]& - - -G2xPaper=(((CA^2*eta^2*SMP["g_s"]^4)/(-pp)^(2*Epsilon)) * ((83/16 + 7/32*GaugeXi)/Epsilon + - (5/4 + 7/16*GaugeXi - 1/32 GaugeXi^2)/Epsilon^2 + 599/32 - 3/4 Zeta[3] - 9/64 GaugeXi + 3/8 GaugeXi^2 - 3/16 GaugeXi^2 Zeta[3] )/ - (4*Pi)^D); -Print["Check with Davydychev, Osland and Tarasov, hep-ph/9801380, Eq 6.15: ", - If[Simplify[((G2xFinal/.{Dot->Times})-G2xPaper)]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDGluonSelfEnergyOneLoop.m b/FeynCalc/Examples/QCD/QCDGluonSelfEnergyOneLoop.m deleted file mode 100644 index fd8cca84a..000000000 --- a/FeynCalc/Examples/QCD/QCDGluonSelfEnergyOneLoop.m +++ /dev/null @@ -1,184 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDGluonSelfEnergyOneLoop *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the gluon self-energy in QCD at one loop *) - -(* ------------------------------------------------------------------------ *) - - -(* ::Section:: *) -(*The 1-loop gluon self-energy in QCD*) - - -(* ::Subsection:: *) -(*Load FeynCalc, FeynArts and Tarcer*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the 1-loop gluon self-energy in QCD"]; -]; -$LoadFeynArts = $LoadTARCER = True; -< 1 ,ExcludeTopologies->{Tadpoles}], - {V[5]} -> {V[5]}, InsertionLevel -> {Classes}, GenericModel -> "Lorentz",Model->"SMQCD", - ExcludeParticles->{S[1],S[2],S[3],V[2],V[3],U[1],U[2],U[3],F[4],U[4]}], ColumnsXRows -> {4, 1}, - SheetHeader -> False, Numbering -> None,SheetHeader->None,ImageSize->{512,128}]; - - -(* ::Text:: *) -(*Notice that we choose the prefactor to be 1/(2^D)*(Pi)^(D/2). This is because the 1/Pi^(D/2) piece of the general prefactor 1/(2Pi)^D goes into the definition of the loop integrals using Tarcer's notation.*) - - -amps =FCFAConvert[CreateFeynAmp[diags, Truncated -> True, GaugeRules->{},PreFactor->1/((2^D)*(Pi)^(D/2))], -IncomingMomenta->{p},OutgoingMomenta->{p},LoopMomenta->{q},DropSumOver->True,ChangeDimension->D,UndoChiralSplittings->True, -TransversePolarizationVectors->{k1,k2},SMP->True]/. {MQU[Index[Generation, 3]]->MQ,GaugeXi[_]->GaugeXi}; - - -(* ::Subsection:: *) -(*The gluon tadpole loop*) - - -ampGluonLoop = amps[[1]]//ChangeDimension[#,D]&//SUNSimplify[#,Explicit->True]&//Contract//Simplify - - -(* ::Text:: *) -(*The above expression is zero in dimensional regularization, because the loop integrals have no scale*) - - -ampGluonLoopEval=ampGluonLoop//ToTFI[#,q,p]& - - -(* ::Text:: *) -(*We can compare this result to Eq. A.9 in Foundations of QCD by T. Muto. Notice that the result in the book must be multiplied by (-1) due to the way how self-energy is defined there (c.f. Eq. 2.4.4 and Eq. 2.4.6).*) - - -Print["Check with Muta, Eq. A.9: ", - If[ampGluonLoopEval===0, "CORRECT.", "!!! WRONG !!!"]]; - - -(* ::Subsection:: *) -(*The quark loop*) - - -ampQuarkLoopEval = amps[[2]]//ChangeDimension[#,D]&//ReplaceAll[#,DiracTrace->Tr]&// - SUNSimplify[#,Explicit->True]&//ReplaceAll[#,SUNTr->SUNTrace]&//TID[#,q]&// - Simplify//ToTFI[#,q,p]&//Simplify - - -(* ::Text:: *) -(*The contribution of the quark loop alone is gauge invariant.*) - - -Contract[FVD[p,Lor1]FVD[p,Lor2]ampQuarkLoopEval] - - -(* ::Subsection:: *) -(*The ghost loop*) - - -ampGhostLoopEval = amps[[3]]//ChangeDimension[#,D]&//SUNSimplify[#,Explicit->True]&// - ExpandScalarProduct//TID[#,q]&//Simplify//ToTFI[#,q,p]&//Simplify - - -(* ::Text:: *) -(*The contribution of the ghost loop alone is not gauge invariant.*) - - -Contract[FVD[p,Lor1]FVD[p,Lor2]ampGhostLoopEval]//Simplify - - -(* ::Subsection:: *) -(*The gluon loop*) - - -ampGluonLoop = amps[[4]]//ChangeDimension[#,D]&//SUNSimplify[#,Explicit->True]&// - Contract//TID[#,q]&//ToTFI[#,q,p]&//Simplify - - -ampGluonLoopEval=((ampGluonLoop/.{GaugeXi->-OneMinusGaugeXi+1})//Expand// - Collect[#,OneMinusGaugeXi,Simplify]&)/.{OneMinusGaugeXi->(1-GaugeXi)} - - -(* ::Text:: *) -(*The contribution of the gluon loop alone is not gauge invariant.*) - - -Contract[FVD[p,Lor1]FVD[p,Lor2]ampGluonLoopEval]//Simplify - - -(* ::Subsection:: *) -(*Putting everything together*) - - -ampGluonGhostEval=Simplify[ampGluonLoopEval+ampGhostLoopEval] - - -(* ::Text:: *) -(*The sum of the gluon and ghost loop contributions in clearly gauge invariant!*) - - -Contract[FVD[p,Lor1]FVD[p,Lor2]ampGluonGhostEval]//Simplify - - -(* ::Text:: *) -(*When adding all the contributions together, we multiply the quark contribution by Nf to account for the 6 quark flavours that actually run in that loop. We ignore the fact that different flavours have different masses, since the divergent piece of the gluon self-energy will not depend on the quark mass.*) - - -ampTotal=(ampGluonGhostEval+Nf*ampQuarkLoopEval)//TarcerRecurse - - -(* ::Text:: *) -(*Since we are interested only in the divergent piece of the self-energy function, we do not have to compute full loop integrals. It is sufficient to substitute just the divergent pieces. The one loop integrals in Tarcer's notation are related to the scalar Passarino-Veltman integrals via a prefactor. For example, TAI[D, 0, {{1, M}}] = (I*(Pi)^(2-D/2) (2Pi)^(D-4)) A0[M^2]. The same goes also for B0.The divergent pieces of A0 and B0 integrals can be easily found in the literature, for example in A.Denner and S. Dittmayer, Reduction of one-loop tensor 5-point integrals, Nucl.Phys.B658:175-202,2003. The preprint is available at arXiv:hep-ph/0212259. According to the Appendix C, we have A0[M^2]= -2M^2 /(D-4) and B0[p^2, M^2, 0] = -2/(D-4).*) -(*Multiplying these results with (I*(Pi)^(2-D/2) (2Pi)^(D-4)) and keeping only terms proportional to 1/Epsilon we obtain*) - - -prefactor=(I*(Pi)^(2-D/2) (2Pi)^(D-4)); -ampsSing=(ampTotal/.{TBI[___]:>(-2)/(D-4)*prefactor,TAI[___]:>-2 MQ^2/(D-4)*prefactor})//FCI// - ReplaceAll[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal//SelectNotFree[#,Epsilon]& - - -(* ::Text:: *) -(*Finally, since self-energy function is usually defined as I*Pi = Amplitude, to obtain Sigma we need to multiply our result by -I . This gives*) - - -gluonSelfEnergy=-I*ampsSing - - -(* ::Text:: *) -(*We can compare this result to Eq. 2.5.131 and Eq. 2.5.132 in Foundations of QCD by T. Muto. *) - - -gaugePrefactor=(Pair[LorentzIndex[Lor1], Momentum[p]]*Pair[LorentzIndex[Lor2], Momentum[p]] - Pair[LorentzIndex[Lor1], LorentzIndex[Lor2]]* - Pair[Momentum[p], Momentum[p]]); -gluonSelfEnergyMuta=(SMP["g_s"]^2/(4Pi)^2)*(4/3*(1/2)*Nf-(1/2)CA(13/3-GaugeXi))*1/Epsilon* -gaugePrefactor*SUNDelta[SUNIndex[Glu1], SUNIndex[Glu2]]; -Print["Check with Muta, Eq 2.5.131 and Eq. 2.5.132: ", - If[Simplify[gluonSelfEnergy-gluonSelfEnergyMuta]===0, "CORRECT.", "!!! WRONG !!!"]]; - - -(* ::Text:: *) -(*Another cross-check is to compare to Eq. 16.71 in Peskin and Schroeder, where the authors sum up the gluon and ghost contributions in Feynman gauge. All we need to do is just set the gauge parameter GaugeXi to 1 and remove the quark contribution. The latter is easy to do, since the quark contribution is the only piece proportional to Nf.*) - - -ampsSingGluonQuarkFeynmanGauge=Simplify[ampsSing/.{GaugeXi->1,Nf->0}] - - -ampsSingFeynmanGaugePeskin=I*(-gaugePrefactor)*(-SMP["g_s"]^2/(4Pi)^2*(-5/3)*CA*(1/Epsilon))*SUNDelta[SUNIndex[Glu1], SUNIndex[Glu2]]; -Print["Check with Peskin and Schroeder, Eq 16.71: ", - If[Simplify[ampsSingGluonQuarkFeynmanGauge-ampsSingFeynmanGaugePeskin]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQiGammaStarToQiGTree.m b/FeynCalc/Examples/QCD/QCDQiGammaStarToQiGTree.m deleted file mode 100644 index 1982f49e9..000000000 --- a/FeynCalc/Examples/QCD/QCDQiGammaStarToQiGTree.m +++ /dev/null @@ -1,88 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDQiGammaStarToQiGTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - q_i + gamma^* -> q_i g subprocess in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the q_i + gamma^* -> q_i g subprocess in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsQiGammaStarToQiG = InsertFields[topQiGammaStarToQiG,{F[3, {1}],V[1]}->{V[5],F[3, {1}]}, - InsertionLevel -> {Classes}, Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsQiGammaStarToQiG, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None,ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -(* Note that here we set only the polarization vector of the gluon to be transverse. -Since the photon is virtual, it can have unphysical polarizations as well.*) - - -ampQiGammaStarToQiG =FCFAConvert[CreateFeynAmp[diagsQiGammaStarToQiG,Truncated -> False],IncomingMomenta->{p1,kGamma}, -OutgoingMomenta->{kG,p2},UndoChiralSplittings->True,TransversePolarizationVectors->{kG},DropSumOver->True,List->False,SMP->True]//Contract - - -(* ::Section:: *) -(*Unpolarized process q_i + gamma^* -> q_i g*) - - -SetMandelstam[s, t, u, p1,kGamma, -kG,-p2, SMP["m_u"], qQ,0,SMP["m_u"]]; - - -(* The final result depends on the electric charge of the quarks. Since we generated the diagrams for up and anti-up, we divide -the amplitude by 2/3 and multiply it by EQ to have explicit quark charge dependence *) - - -ampQiGammaStarToQiG2 = ampQiGammaStarToQiG/(2/3)*EQ - - -(* Now come the usual steps, but with some special features. We don't average over the polarizations of the virtual photon, -and we use the gauge trick for the sum over its polarizations. Of course, in this case the sum goes over all 4 unphysical -polarizations, not just 2. Apart from that, we have the normal averaging over the 3 colors and 2 polarizations of the incoming quark. -For the polarization sum of the gluon we use the quark momentum as the auxiliary vector *) - - -ampQiGammaStarToQiG3=ampQiGammaStarToQiG2*(ComplexConjugate[ampQiGammaStarToQiG2]//FCRenameDummyIndices)// -PropagatorDenominatorExplicit//FermionSpinSum[#,ExtraFactor->1/(2*3)]&//ReplaceAll[#,{DiracTrace->Tr}]&//DoPolarizationSums[#,kG,p1]&// -DoPolarizationSums[#,kGamma,0,VirtualBoson->True,GaugeTrickN->4]&//SUNSimplify[#,SUNNToCACF->False]&; - - -ampQiGammaStarToQiG4=(ampQiGammaStarToQiG3/.{SMP["m_u"]->0,SUNN->3})//Simplify - - -masslessAmpQiGammaStarToQiG=(TrickMandelstam[ampQiGammaStarToQiG4,{s,t,u,qQ^2}]/.u->qQ^2-s-t/.qQ->I Q)//Simplify - - -masslessAmpQiGammaStarToQiGField= (16/3) SMP["e"]^2 EQ^2 SMP["g_s"]^2 (-t/s-s/t - 2 Q^2(s+t+Q^2)/(t s)); -Print["Check with R. Field, Eq 4.3.10: ", - If[Simplify[masslessAmpQiGammaStarToQiGField-masslessAmpQiGammaStarToQiG]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQiQBariToGGTree.m b/FeynCalc/Examples/QCD/QCDQiQBariToGGTree.m deleted file mode 100644 index e00adbea2..000000000 --- a/FeynCalc/Examples/QCD/QCDQiQBariToGGTree.m +++ /dev/null @@ -1,68 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDQiQBariToGGTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - q_i qbar_i -> g g scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the q_i qbar_i -> g g scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsQiQBariToGG = InsertFields[topQiQBariToGG, {F[3, {1}], -F[3, {1}]} -> {V[5],V[5]}, - InsertionLevel -> {Classes}, Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsQiQBariToGG, ColumnsXRows -> {3, 1}, Numbering -> None,SheetHeader->None,ImageSize->{768,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampQiQBariToGG =FCFAConvert[CreateFeynAmp[diagsQiQBariToGG,Truncated -> False],IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2}, -DropSumOver->True,ChangeDimension->4,UndoChiralSplittings->True,List->False,TransversePolarizationVectors->{k1,k2},SMP->True]; - - -(* ::Section:: *) -(*Unpolarized process q_i qbar_i -> g g *) - - -SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], 0, 0]; -sqAmpQiQBariToGG =(1/3^2)(ampQiQBariToGG* - (ComplexConjugate[ampQiQBariToGG]//FCRenameDummyIndices))//PropagatorDenominatorExplicit// - SUNSimplify[#,Explicit->True,SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// - Contract//ReplaceAll[#,{DiracTrace->Tr,SUNN->3}]&//DoPolarizationSums[#,k1,k2]&// - DoPolarizationSums[#,k2,k1]&//Simplify - - -masslesssqAmpQiQBariToGG = TrickMandelstam[(sqAmpQiQBariToGG /. {SMP["m_u"] -> 0})//Simplify,{s,t,u,0}] - - -masslesssqAmpQiQBariToGGEllis=(32/27)SMP["g_s"]^4 (t^2+u^2)/(t u)-(8/3)SMP["g_s"]^4 (t^2+u^2)/(s^2); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[TrickMandelstam[Simplify[masslesssqAmpQiQBariToGGEllis-masslesssqAmpQiQBariToGG],{s,t,u,0}]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQiQBariToGammaStarGTree.m b/FeynCalc/Examples/QCD/QCDQiQBariToGammaStarGTree.m deleted file mode 100644 index 8b1787193..000000000 --- a/FeynCalc/Examples/QCD/QCDQiQBariToGammaStarGTree.m +++ /dev/null @@ -1,89 +0,0 @@ -(* ::Package:: *) - -(* :Title: QiQBariToGammaStarGTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - q_i + qbar_i -> gamma^* + g subprocess in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the q_i + qbar_i -> gamma^* + g subprocess in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsQiQBariToGammaStarGTree = InsertFields[topQiQBariToGammaStarGTree,{F[3, {1}],-F[3, {1}]}->{V[1],V[5]}, - InsertionLevel -> {Classes}, Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsQiQBariToGammaStarGTree, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None, -ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -(* Note that here we set only the polarization vector of the gluon to be transverse. -Since the photon is virtual, it can have unphysical polarizations as well.*) - - -ampQiQBariToGammaStarGTree =ampGammaStarGToQiQBari=FCFAConvert[CreateFeynAmp[diagsQiQBariToGammaStarGTree,Truncated -> False],IncomingMomenta->{p1,p2}, -OutgoingMomenta->{kGamma,kG},UndoChiralSplittings->True,TransversePolarizationVectors->{kG},DropSumOver->True,List->False,SMP->True]//Contract - - -(* ::Section:: *) -(*Unpolarized process q_i + qbar_i -> gamma^* + g*) - - -SetMandelstam[s, t, u, p1,p2,-kGamma, -kG, SMP["m_u"], SMP["m_u"], M,0]; - - -(* The final result depends on the electric charge of the quarks. Since we generated the diagrams for up and anti-up, we divide -the amplitude by 2/3 and multiply it by EQ to have explicit quark charge dependence *) - - -ampQiQBariToGammaStarGTree2 = ampQiQBariToGammaStarGTree/(2/3)*EQ - - -(* Now come the usual steps, but with some special features. We don't average over the polarizations of the virtual photon, -and we use the gauge trick for the sum over its polarizations. Of course, in this case the sum goes over all 4 unphysical -polarizations, not just 2. Apart from that, we have the normal averaging over the 3 colors and 2 polarizations of the incoming quark and -antiquark. For the polarization sum of the gluon we use the photon momentum as the auxiliary vector *) - - -ampQiQBariToGammaStarGTree3=ampQiQBariToGammaStarGTree2*(ComplexConjugate[ampQiQBariToGammaStarGTree2]//FCRenameDummyIndices)// -PropagatorDenominatorExplicit//FermionSpinSum[#,ExtraFactor->1/(2*3)^2]&//ReplaceAll[#,{DiracTrace->Tr}]&//DoPolarizationSums[#,kG,kGamma]&// -DoPolarizationSums[#,kGamma,0,VirtualBoson->True,GaugeTrickN->4]&//SUNSimplify[#,SUNNToCACF->False]&; - - -ampQiQBariToGammaStarGTree4=(ampQiQBariToGammaStarGTree3/.{SMP["m_u"]->0,SUNN->3})//Simplify - - -masslessAmpQiQBariToGammaStarGTree=(TrickMandelstam[ampQiQBariToGammaStarGTree4,{s,t,u,M^2}])//Simplify - - -masslessAmpQiQBariToGammaStarGTreeField= (8/9) SMP["e"]^2 EQ^2 SMP["g_s"]^2 (u/t+t/u + 2 M^2(-t-u+M^2)/(t u)); -Print["Check with R. Field, Eq 5.2.3: ", - If[Simplify[masslessAmpQiQBariToGammaStarGTreeField-masslessAmpQiQBariToGammaStarGTree]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQiQBariToQiQBariTree.m b/FeynCalc/Examples/QCD/QCDQiQBariToQiQBariTree.m deleted file mode 100644 index 9b1cbe348..000000000 --- a/FeynCalc/Examples/QCD/QCDQiQBariToQiQBariTree.m +++ /dev/null @@ -1,68 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDQiQBariToQiQBariTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - q_i qbar_i -> q_i qbar_i scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the q_i qbar_i -> q_i qbar_i scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsQiQBariToQiQBari = InsertFields[topQiQBariToQiQBari, {F[3, {1}], - -F[3, {1}]} -> {F[3, {1}], -F[3, {1}]}, InsertionLevel -> {Classes}, - Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsQiQBariToQiQBari, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None,ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampQiQBariToQiQBari=FCFAConvert[CreateFeynAmp[diagsQiQBariToQiQBari,Truncated -> False],IncomingMomenta->{p1,p2},OutgoingMomenta->{p3,p4}, -DropSumOver->True,ChangeDimension->4,UndoChiralSplittings->True,List->False,SMP->True]; - - -(* ::Section:: *) -(*Unpolarized process q_i qbar_i -> q_i qbar_i *) - - -SetMandelstam[s, t, u, p1, p2, -p3, -p4, SMP["m_u"], SMP["m_u"], SMP["m_u"], SMP["m_u"]]; -sqAmpQiQBariToQiQBari =(1/3^2)* - (ampQiQBariToQiQBari (ComplexConjugate[ampQiQBariToQiQBari]//FCRenameDummyIndices))// - PropagatorDenominatorExplicit//Contract//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// - SUNSimplify[#,Explicit->True,SUNNToCACF->False]&//ReplaceAll[#,{DiracTrace->Tr,SUNN->3}]&//Contract//Simplify - - -masslesssqAmpQiQBariToQiQBari = (sqAmpQiQBariToQiQBari /. {SMP["m_u"] -> 0})//Simplify - - -masslesssqAmpQiQBariToQiQBariEllis=((4/9)SMP["g_s"]^4 ((s^2+u^2)/t^2+(t^2+u^2)/s^2)-(8/27)SMP["g_s"]^4 u^2/(s t)); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[Simplify[(masslesssqAmpQiQBariToQiQBariEllis-masslesssqAmpQiQBariToQiQBari)]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQiQBariToQjQBarjTree.m b/FeynCalc/Examples/QCD/QCDQiQBariToQjQBarjTree.m deleted file mode 100644 index 58de2e33c..000000000 --- a/FeynCalc/Examples/QCD/QCDQiQBariToQjQBarjTree.m +++ /dev/null @@ -1,67 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDQiQBariToQjQBarjTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - q_i qbar_i -> q_j qbar_j scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the q_i qbar_i -> q_j qbar_j scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts=True; -< 2]; -diagsQiQBariToQjQBarj = InsertFields[topQiQBariToQjQBarj, {F[3, {1}], -F[3, {1}]} -> {F[3, {2}], - -F[3, {2}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsQiQBariToQjQBarj, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampQiQBariToQjQBarj=FCFAConvert[CreateFeynAmp[diagsQiQBariToQjQBarj,Truncated -> False],IncomingMomenta->{p1,p2},OutgoingMomenta->{p3,p4}, -DropSumOver->True,ChangeDimension->4,UndoChiralSplittings->True,List->False,SMP->True]; - - -(* ::Section:: *) -(*Unpolarized process q_i qbar_i -> q_j qbar_j *) - - -SetMandelstam[s, t, u, p1, p2, -p3, -p4, SMP["m_u"], SMP["m_u"], SMP["m_c"], SMP["m_c"]]; -sqAmpQiQBariToQjQBarj =(1/3^2)*(ampQiQBariToQjQBarj (ComplexConjugate[ampQiQBariToQjQBarj]// - FCRenameDummyIndices))//PropagatorDenominatorExplicit//Contract//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// - ReplaceAll[#,{DiracTrace->Tr,SUNN->3}]&//Contract//Simplify//SUNSimplify[#,Explicit->True, - SUNNToCACF->False]&//ReplaceAll[#,{SUNN->3}]& - - -masslesssqAmpQiQBariToQjQBarj = (sqAmpQiQBariToQjQBarj /. {SMP["m_u"] -> 0,SMP["m_c"]->0})//Simplify - - -masslesssqAmpQiQBariToQjQBarjEllis=((4/9)SMP["g_s"]^4 (t^2+u^2)/s^2); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[(masslesssqAmpQiQBariToQjQBarjEllis-masslesssqAmpQiQBariToQjQBarj)===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQiQBarjToQiQBarjTree.m b/FeynCalc/Examples/QCD/QCDQiQBarjToQiQBarjTree.m deleted file mode 100644 index 11053d25a..000000000 --- a/FeynCalc/Examples/QCD/QCDQiQBarjToQiQBarjTree.m +++ /dev/null @@ -1,67 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDQiQBarjToQiQBarjTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - q_i qbar_j -> q_i qbar_j scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the q_i qbar_j -> q_i qbar_j scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts=True; -< 2]; -diagsQiQBarjToQiQBarj = InsertFields[topQiQBarjToQiQBarj, {F[3, {1}], -F[3, {2}]} -> {F[3, {1}], - -F[3, {2}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsQiQBarjToQiQBarj, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampQiQBarjToQiQBarj = FCFAConvert[CreateFeynAmp[diagsQiQBarjToQiQBarj,Truncated -> False],IncomingMomenta->{p1,p2},OutgoingMomenta->{p3,p4}, -DropSumOver->True,ChangeDimension->4,UndoChiralSplittings->True,List->False,SMP->True]; - - -(* ::Section:: *) -(*Unpolarized process q_i qbar_j -> q_i qbar_j *) - - -SetMandelstam[s, t, u, p1, p2, -p3, -p4, SMP["m_u"], SMP["m_c"], SMP["m_u"], SMP["m_c"]]; -sqAmpQiQBarjToQiQBarj =(1/3^2)*(ampQiQBarjToQiQBarj (ComplexConjugate[ampQiQBarjToQiQBarj]// - FCRenameDummyIndices))//PropagatorDenominatorExplicit//Contract// - FermionSpinSum[#, ExtraFactor -> 1/2^2]&//ReplaceAll[#,{DiracTrace->Tr,SUNN->3}]&//Contract//SUNSimplify[#, - Explicit->True,SUNNToCACF->False]&//ReplaceAll[#,{SUNN->3}]&//Simplify - - -masslesssqAmpQiQBarjToQiQBarj = (sqAmpQiQBarjToQiQBarj /. {SMP["m_u"] -> 0,SMP["m_c"]->0})//Simplify - - -masslesssqAmpQiQBarjToQiQBarjEllis=((4/9)SMP["g_s"]^4 (s^2+u^2)/t^2); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[(masslesssqAmpQiQBarjToQiQBarjEllis-masslesssqAmpQiQBarjToQiQBarj)===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQiQiToQiQiTree.m b/FeynCalc/Examples/QCD/QCDQiQiToQiQiTree.m deleted file mode 100644 index 238abd265..000000000 --- a/FeynCalc/Examples/QCD/QCDQiQiToQiQiTree.m +++ /dev/null @@ -1,68 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDQiQiToQiQiTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - q_i q_j -> q_i q_j scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the q_i q_i -> q_i q_i scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts=True; -< 2]; -diagsQiQiToQiQi = InsertFields[topQiQiToQiQi, {F[3, {1}], F[3, {1}]} -> {F[ - 3, {1}], F[3, {1}]}, InsertionLevel -> {Classes}, - Model -> "SMQCD", ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsQiQiToQiQi, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None,ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampQiQiToQiQi=FCFAConvert[CreateFeynAmp[diagsQiQiToQiQi,Truncated -> False],IncomingMomenta->{p1,p2},OutgoingMomenta->{p3,p4}, -DropSumOver->True,ChangeDimension->4,UndoChiralSplittings->True,List->False,SMP->True]; - - -(* ::Section:: *) -(*Unpolarized process q_i q_i -> q_i q_i *) - - -SetMandelstam[s, t, u, p1, p2, -p3, -p4, SMP["m_u"], SMP["m_u"], SMP["m_u"], SMP["m_u"]]; -sqAmpQiQiToQiQi =(1/3^2)*(ampQiQiToQiQi (ComplexConjugate[ampQiQiToQiQi]//FCRenameDummyIndices))// - PropagatorDenominatorExplicit//Contract//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// - SUNSimplify[#,Explicit->True,SUNNToCACF->False]&// - ReplaceAll[#,{DiracTrace->Tr,SUNN->3}]&//Contract//Simplify - - -masslesssqAmpQiQiToQiQi = (sqAmpQiQiToQiQi /. {SMP["m_u"] -> 0})//Simplify - - -masslesssqAmpQiQiToQiQiEllis=((4/9)SMP["g_s"]^4 ((s^2+u^2)/t^2+(s^2+t^2)/u^2)-(8/27)SMP["g_s"]^4 s^2/(t u)); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[Simplify[(masslesssqAmpQiQiToQiQiEllis-masslesssqAmpQiQiToQiQi)]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQiQjToQiQjTree.m b/FeynCalc/Examples/QCD/QCDQiQjToQiQjTree.m deleted file mode 100644 index 21b8feb2b..000000000 --- a/FeynCalc/Examples/QCD/QCDQiQjToQiQjTree.m +++ /dev/null @@ -1,68 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDQiQjToQiQjTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for the - q_i q_j -> q_i q_j scattering in QCD at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for the q_i q_j -> q_i q_j scattering in QCD at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts=True; -< 2]; -diagsQiQjToQiQj = InsertFields[topQiQjToQiQj, {F[3, {1}], F[3, {2}]} -> {F[3, {1}], - F[3, {2}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", - ExcludeParticles -> {S[1], S[2], V[1],V[2]}]; -Paint[diagsQiQjToQiQj, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampQiQjToQiQj=FCFAConvert[CreateFeynAmp[diagsQiQjToQiQj,Truncated -> False],IncomingMomenta->{p1,p2},OutgoingMomenta->{p3,p4}, -DropSumOver->True,ChangeDimension->4,UndoChiralSplittings->True,List->False,SMP->True]; - - -(* ::Section:: *) -(*Unpolarized process q_i q_j -> q_i q_j *) - - -SetMandelstam[s, t, u, p1, p2, -p3, -p4, SMP["m_u"], SMP["m_c"], SMP["m_u"], SMP["m_c"]]; -sqAmpQiQjToQiQj =(1/3^2)*(ampQiQjToQiQj (ComplexConjugate[ampQiQjToQiQj]// - FCRenameDummyIndices))//PropagatorDenominatorExplicit//Contract// - FermionSpinSum[#, ExtraFactor -> 1/2^2]&//SUNSimplify[#,Explicit->True,SUNNToCACF->False]&// - ReplaceAll[#,{DiracTrace->Tr,SUNN->3}]&//Contract//Simplify - - -masslesssqAmpQiQjToQiQj = (sqAmpQiQjToQiQj /. {SMP["m_u"] -> 0,SMP["m_c"]->0})//Simplify - - -masslesssqAmpQiQjToQiQjEllis=((4/9)SMP["g_s"]^4 (s^2+u^2)/t^2); -Print["Check with Ellis, Stirling and Weber, Table 7.1: ", - If[(masslesssqAmpQiQjToQiQjEllis-masslesssqAmpQiQjToQiQj)===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/QCDQuarkSelfEnergyOneLoop.m b/FeynCalc/Examples/QCD/QCDQuarkSelfEnergyOneLoop.m deleted file mode 100644 index 7f7539540..000000000 --- a/FeynCalc/Examples/QCD/QCDQuarkSelfEnergyOneLoop.m +++ /dev/null @@ -1,93 +0,0 @@ -(* ::Package:: *) - -(* :Title: QCDQuarkSelfEnergyOneLoop *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the quark self-energy in QCD at 1-loop *) - -(* ------------------------------------------------------------------------ *) - - -(* ::Section:: *) -(*The quark self-energy in QCD at 1-loop *) - - -(* ::Subsection:: *) -(*Load FeynCalc, FeynArts and Tarcer*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the quark self-energy in QCD at 1-loop"]; -]; -$LoadFeynArts = $LoadTARCER = True; -< 1, - ExcludeTopologies -> {Tadpoles}], {F[3,{1}]} -> {F[3,{1}]}, - InsertionLevel -> {Classes}, GenericModel -> "Lorentz", - Model -> "SMQCD",ExcludeParticles->{S[1],S[2],S[3],V[1],V[2],V[3]}], ColumnsXRows -> {1, 1}, - SheetHeader -> False,SheetHeader->None,Numbering -> None,ImageSize->{256,256}]; - - -(* ::Text:: *) -(*Notice that we choose the prefactor to be 1/(2^D)*(Pi)^(D/2). This is because the 1/Pi^(D/2) piece of the general prefactor 1/(2Pi)^D goes into the definition of the loop integrals using Tarcer's notation. Furthermore, we do not fix the gauge but let the gauge parameter GaugeXi take arbitrary values.*) - - -amps=FCFAConvert[CreateFeynAmp[diags, Truncated -> True,GaugeRules->{},PreFactor->1/((2^D)*(Pi)^(D/2))],IncomingMomenta->{p}, -OutgoingMomenta->{p},LoopMomenta->{q},DropSumOver->True,UndoChiralSplittings->True,ChangeDimension->D,List->False,SMP->True]/.{SMP["m_u"]->M,GaugeXi[g]->GaugeXi} - - -ampsEval=amps//Contract//SUNSimplify//TID[#,q]&//ToTFI[#,q,p]&//TarcerRecurse//FCI - - -(* ::Text:: *) -(*Since we are interested only in the divergent piece of the self-energy function, we do not have to compute full loop integrals. It is sufficient to substitute just the divergent pieces. The one loop integrals in Tarcer's notation are related to the scalar Passarino-Veltman integrals via a prefactor. For example, TAI[D, 0, {{1, M}}] = (I*(Pi)^(2-D/2) (2Pi)^(D-4)) A0[M^2]. The same goes also for B0.The divergent pieces of A0 and B0 integrals can be easily found in the literature, for example in A.Denner and S. Dittmayer, Reduction of one-loop tensor 5-point integrals, Nucl.Phys.B658:175-202,2003. The preprint is available at arXiv:hep-ph/0212259. According to the Appendix C, we have A0[M^2]= -2M^2 /(D-4) and B0[p^2, M^2, 0] = -2/(D-4).*) -(*Multiplying these results with (I*(Pi)^(2-D/2) (2Pi)^(D-4)) and keeping only terms proportional to 1/Epsilon we obtain*) - - -prefactor=(I*(Pi)^(2-D/2) (2Pi)^(D-4)); -ampsSing=(ampsEval/.{TBI[x___]:>(-2)/(D-4)*prefactor,TAI[x___]:>-2 M^2/(D-4)*prefactor})// -ReplaceAll[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal//SelectNotFree[#,Epsilon]&//Factor2 - - -(* ::Text:: *) -(*Finally, since self-energy function is usually defined as -I*Sigma = Amplitude, to obtain Sigma we need to multiply our result by I . This gives*) - - -quarSelfEnergy=I*ampsSing//Collect[#,M,Simplify]& - - -(* ::Text:: *) -(*We can compare this result to Eq. 2.5.138 in Foundations of QCD by T. Muto. Notice that the result in the book must be multiplied by (-1) due to the way how self-energy is defined there (c.f. Eq. 2.4.4 and Eq. 2.4.6).*) - - -quarSelfEnergyMuta=-(-SMP["g_s"]^2/(4Pi)^2 CF*(3+GaugeXi)(1/Epsilon)*M+GS[p]*SMP["g_s"]^2/(4Pi)^2* - CF*GaugeXi*(1/Epsilon))SDF[Col1,Col2]//FCI; -Print["Check with Muta, Eq 2.5.138: ", - If[Simplify[quarSelfEnergy-FCI[quarSelfEnergyMuta]]===0, "CORRECT.", "!!! WRONG !!!"]]; - - -(* ::Text:: *) -(*Another cross-check is to compare to Eq. 16.76 in Peskin and Schroeder, where the authors compute the self-energy diagram for massless quarks in Feynman gauge. All we need to do is just set the quarks mass M to zero and the gauge parameter GaugeXi to 1.*) - - -ampsSingMassless=(ampsEval/.{M->0,TBI[x___]:>(-2)/(D-4)*prefactor,GaugeXi->1})// -ReplaceAll[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal//SelectNotFree[#,Epsilon]& - - -ampsSingMasslessPeskin=I*SMP["g_s"]^2/(4Pi)^2*GS[p]*CF*(1/Epsilon)SDF[Col1,Col2]//FCI; -Print["Check with Peskin and Schroeder, Eq 16.76: ", - If[Simplify[ampsSingMassless-FCI[ampsSingMasslessPeskin]]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QCD/Tree/ElAel-QQbar.m b/FeynCalc/Examples/QCD/Tree/ElAel-QQbar.m new file mode 100644 index 000000000..37fac351c --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/ElAel-QQbar.m @@ -0,0 +1,202 @@ +(* ::Package:: *) + +(* :Title: ElAel-QQbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Ael -> Q Qbar, QCD, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark production in electron-positron annihilation*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Ael -> Q Qbar, QCD, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], -F[2, {1}]} -> + {F[3, {1}], -F[3, {1}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True, + Prefactor->3/2 SMP["e_Q"],FinalSubstitutions->{SMP["m_u"]->SMP["m_q"]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"]^2, SMP["m_e"]^2, + SMP["m_q"]^2, SMP["m_q"]^2]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify// + TrickMandelstam[#,{s,t,u,2SMP["m_q"]^2+2SMP["m_e"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_q"|"m_e"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Total cross-section*) + + +(* ::Text:: *) +(*The differential cross-section d sigma/ d Omega is given by*) + + +prefac1=1/(64 Pi^2 s); + + +integral1=(Factor[ampSquaredMasslessSUNN3[0]/.{t->-s/2(1-Cos[Th]),u->-s/2(1+Cos[Th]), +SMP["e"]^4->(4 Pi SMP["alpha_fs"])^2}]) + + +diffXSection1= prefac1 integral1 + + +(* ::Text:: *) +(*The differential cross-section d sigma/ d t d phi is given by*) + + +prefac2=1/(128 Pi^2 s) + + +integral2=Simplify[ampSquaredMasslessSUNN3[0]/(s/4) /.{u-> -s-t, +SMP["e"]^4->(4 Pi SMP["alpha_fs"])^2}] + + +diffXSection2=prefac2 integral2 + + +(* ::Text:: *) +(*The total cross-section. We see that integrating both expressions gives the same result*) + + +2 Pi Integrate[diffXSection1 Sin[Th],{Th,0,Pi}] + + +crossSectionTotal=2 Pi Integrate[diffXSection2,{t,-s,0}] + + +(* ::Text:: *) +(*Notice that up to the overall factor color factor 3 and the quark electric charge squared this result is identical to the total cross-section for the muon production in electron-positron annihilation.*) + + +crossSectionTotalQED=4*Pi*SMP["alpha_fs"]^2/3/s + + +(* ::Text:: *) +(*Taking the ratio of the two gives us the famous R-ration prediction of the parton mode, where the summation over the quark flavors in front of the charge squared is understood*) + + +crossSectionTotal/crossSectionTotalQED + + +quarkCharges={ eq[u|c|t]->2/3,eq[d|s|b]->-1/3}; + + +(* ::Text:: *) +(*Depending on the available center of mass energy, we may not be able to produce all the existing*) +(*quark flavors. Below 3 GeV (roughly twice the mass of the charm quark) we have only up, down and strange quarks and the R-ratio is given by*) + + +Sum[3 eq[i]^2,{i,{u,d,s}}]/.quarkCharges + + +(* ::Text:: *) +(*At higher energies but below 9 GeV (roughly twice the mass of the bottom quark) we also have the *) +(*contribution from the charm quark*) + + +Sum[3 eq[i]^2,{i,{u,d,s,c}}]/.quarkCharges + + +(* ::Text:: *) +(*At even higher energies the bottom quark must also be taken into account*) + + +Sum[3 eq[i]^2,{i,{u,d,s,c,b}}]/.quarkCharges + + +(* ::Text:: *) +(*At some point we finally reach sufficiently high energies to produce the top quark*) + + +Sum[3 eq[i]^2,{i,{u,d,s,c,b,t}}]/.quarkCharges + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (6*(t^2 + u^2)*SMP["e"]^4*SMP["e_Q"]^2)/(s^2), + (4*Pi*SMP["alpha_fs"]^2*SMP["e_Q"]^2)/s +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0],crossSectionTotal}, +knownResults, +Text->{"\tCompare to CalcHEP and to Field, \ +Applications of Perturbative QCD, Eq. 2.1.15:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/Ga-QQbar.m b/FeynCalc/Examples/QCD/Tree/Ga-QQbar.m new file mode 100644 index 000000000..e5112a9bf --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/Ga-QQbar.m @@ -0,0 +1,142 @@ +(* ::Package:: *) + +(* :Title: Ga-QQbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Ga^* -> Q Qbar, QCD, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark production from the decay of a virtual photon*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Ga^* -> Q Qbar, QCD, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {V[1]} -> + {F[3, {1}], -F[3, {1}]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True, + Prefactor->3/2 SMP["e_Q"],FinalSubstitutions->{SMP["m_u"]->SMP["m_q"]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SP[k1]=SMP["m_q"]^2; +SP[k2]=SMP["m_q"]^2; +SP[k1,k2]= (QQ - SP[k1] - SP[k2])/2; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum//DoPolarizationSums[#,p,0, + VirtualBoson->True]&//DiracSimplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_q"] -> 0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Total decay rate*) + + +(* ::Text:: *) +(*The differential decay rate d Gamma/ d Omega is given by*) + + +prefac=ExpandScalarProduct[1/(64 Pi^2) 1/Sqrt[(SP[k1+k2])]] + + +diffDecayRate=prefac ampSquaredMasslessSUNN3[0]/. +SMP["e"]^2->(4 Pi SMP["alpha_fs"]) + + +(* ::Text:: *) +(*The total decay-rate*) + + +decayRateTotal=4 Pi diffDecayRate + + +(* ::Text:: *) +(*Notice that up to the overall color factor 3 and the quark electric charge squared this result is identical to the total decay rate of a virtual photon into a muon-antimuon pair*) + + +decayRateTotalQED= SMP["alpha_fs"] Sqrt[QQ] + + +(* ::Text:: *) +(*Taking the ration of the two gives us the famous R-ration prediction of the parton mode, where the summation over the quark flavors in front of the charge squared is understood*) + + +decayRateTotal/decayRateTotalQED + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + 3 SMP["alpha_fs"] SMP["e_Q"]^2 Sqrt[QQ] +}; +FCCompareResults[{decayRateTotal},knownResults, +Text->{"\tCompare to Field, \ +Applications of Perturbative QCD, Eq. 2.1.30", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/Ga-QQbarGl.m b/FeynCalc/Examples/QCD/Tree/Ga-QQbarGl.m new file mode 100644 index 000000000..d0c32ff7f --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/Ga-QQbarGl.m @@ -0,0 +1,180 @@ +(* ::Package:: *) + +(* :Title: Ga-QQbarGl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Ga^* -> Q Qbar Gl, QCD, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark production with a real gluon emission from the decay of a virtual photon*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Ga^* -> Q Qbar Gl, QCD, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 3], {V[1]} -> + {F[3, {1}], -F[3, {1}], V[5]}, InsertionLevel -> {Classes}, + Model -> "SMQCD"]; +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p}, + OutgoingMomenta->{k1,k2,k3},UndoChiralSplittings->True, + ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True, + Prefactor->3/2 SMP["e_Q"],FinalSubstitutions->{SMP["m_u"]->SMP["m_q"]}] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SP[k1]=SMP["m_q"]^2; +SP[k2]=SMP["m_q"]^2; +SP[k3]=0; +SP[k1,k2]=QQ/2(1-x3); +SP[k1,k3]=QQ/2(1-x2); +SP[k2,k3]=QQ/2(1-x1); + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] =(amp[0] (ComplexConjugate[amp[0]]))//SUNSimplify// + DoPolarizationSums[#,p,0, + VirtualBoson->True]&//DoPolarizationSums[#,k3,0, + VirtualBoson->True]&//FermionSpinSum// + DiracSimplify//FeynAmpDenominatorExplicit//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_q"] -> 0, +x3->2-x1-x2,SMP["e"]^2->(4 Pi SMP["alpha_fs"]),SMP["g_s"]^2->(4 Pi SMP["alpha_s"])}]&// +Simplify//SUNSimplify[#,SUNNToCACF->False]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Total decay rate*) + + +pref= QQ/(128 Pi^3 ) 1/(2 Sqrt[QQ]) + + +normBorn = 3 SMP["alpha_fs"] SMP["e_Q"]^2 Sqrt[QQ] + + +(* ::Text:: *) +(*Differential cross-section normalized w.r.t to the Born cross-section 1/sigma_0 d sigma / (d x1 d x2)*) + + +normDiffCrossSection=ampSquaredMasslessSUNN3[0] pref/normBorn + + +(* ::Text:: *) +(*This integral is divergent for x1->1 and x2->1. The source of these divergences are infrared (when the gluon energy*) +(*approaches 0) and collinear (when the gluon and quark become collinear) singularities.*) + + +If[ $FrontEnd =!= Null, + Plot3D[(normDiffCrossSection/.SMP["alpha_s"]->1),{x1,0,1},{x2,0,1}] +] + + +(* ::Text:: *) +(*Introducing a regulator beta=m^2/Q^2 to enforce that the Mandelstam variables s and t are always larger than m^2 gives*) + + +normDiffCrossSection + + +tmpIntegral=Integrate[normDiffCrossSection,{x2,1-x1,1-beta}, + Assumptions->{beta0,x1>=0,x1<=1}] + + +(*integralReg=Integrate[tmpIntegral,{x1,beta,1-beta},Assumptions->{beta>0}]*) +integralReg=ConditionalExpression[ +((5 - 10*beta - 4*(3 + (-4 + beta)*beta + (2*I)*Pi)*ArcTanh[1 - 2*beta] + + 2*Log[1 - beta]*Log[(1 - beta)/beta^2] + 2*Log[beta]^2 + + 4*PolyLog[2, (1 - beta)^(-1)] - 4*PolyLog[2, beta^(-1)])* +SMP["alpha_s"])/(3*Pi), beta < 1/2] + + +(* ::Text:: *) +(*Expanding around beta=0 we obtain*) + + +integralRegExpanded=Series[Simplify[Normal[integralReg]],{beta,0,0}, + Assumptions->beta>0]//Normal + + +(* ::Text:: *) +(*Factoring out the Born cross-section we arrive to*) + + +integralRegExpandedFinal=Collect2[integralRegExpanded,Log,Pi,FCFactorOut->2/(3 Pi)SMP["alpha_s"]] + + +(* ::Text:: *) +(*To get rid of the singularities we must also include the virtual contributions to the cross-section!*) + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (2*(x1^2 + x2^2)*SMP["alpha_s"])/(3*Pi*(-1 + x1)*(-1 + x2)) +}; +FCCompareResults[{normDiffCrossSection},knownResults, +Text->{"\tCompare to Field, \ +Applications of Perturbative QCD, Eq. 2.3.32", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/GaGl-QQbar.m b/FeynCalc/Examples/QCD/Tree/GaGl-QQbar.m new file mode 100644 index 000000000..401c771de --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/GaGl-QQbar.m @@ -0,0 +1,114 @@ +(* ::Package:: *) + +(* :Title: GaGl-QQbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Ga Gl -> Q Qbar, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Virtual photon-gluon scattering to a quark-antiquark pair*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Ga Gl -> Q Qbar, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {V[1],V[5]}-> + {F[3, {1}], -F[3, {1}]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{p2}, List->False, SMP->True, + Contract->True,DropSumOver->True, Prefactor->3/2 SMP["e_Q"]] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, qQ, 0, SMP["m_u"], SMP["m_u"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*Now come the usual steps, but with some special features. We do not average over the polarizations of the virtual photon, but use the gauge trick for the sum over its polarizations. In this case the sum goes over all 4 unphysical polarizations, not just 2.*) + + +ampSquared[0] = 1/(SUNN^2-1)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2]&// + DiracSimplify//DoPolarizationSums[#,p1,0, + VirtualBoson->True,GaugeTrickN->4]&//DoPolarizationSums[#,p2,k1]&// + TrickMandelstam[#,{s,t,u, 2SMP["m_u"]^2+qQ^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,qQ^2}]& + + +ampSquaredMasslessSUNN3[0] = + Simplify[ampSquaredMassless[0]/.SUNN->3/.qQ->I Q] + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + SMP["e"]^2 SMP["e_Q"]^2 SMP["g_s"]^2 2 (u/t+t/u + 2 Q^2(u+t+Q^2)/(t u)) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCheck with R. Field, Applications of Perturbative QCD, Eq 4.3.20:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/GlGl-GlGl.m b/FeynCalc/Examples/QCD/Tree/GlGl-GlGl.m new file mode 100644 index 000000000..ecd825330 --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/GlGl-GlGl.m @@ -0,0 +1,136 @@ +(* ::Package:: *) + +(* :Title: GlGl-GlGl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Gl Gl -> Gl Gl, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Gluon-gluon to gluon-gluon scattering*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Gl Gl -> Gl Gl, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {V[5], V[5]} -> + {V[5], V[5]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{k1,k2}, + OutgoingMomenta->{k3,k4},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k1,k2,k3,k4}, List->True, SMP->True, + Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, k1, k2, -k3, -k4, 0, 0, 0, 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/((SUNN^2-1)^2)(amp[1] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&; + + +polsums[x_,vec_,aux_,spinfac_]:=x//Collect2[#,Pair[_, +Momentum[Polarization[vec,__]]]]&//Isolate[#,{Polarization[vec,__]}]&// +DoPolarizationSums[#,vec,aux,ExtraFactor->spinfac]&//FixedPoint[ReleaseHold,#]& + + +ClearAll[re]; +Table[Print[" calculating color factors in products of the amplitudes ", i, +" and ", j," (CC), time = ", +Timing[re[i,j]=(amp[0][[i]]ComplexConjugate[amp[0]][[j]]// +FeynAmpDenominatorExplicit// +SUNSimplify[#,Explicit->True,SUNNToCACF->False]&)][[1]]];re[i,j],{i,4},{j,i}]; + + +ClearAll[pre]; +Table[Print[" calculating product of the amplitudes ", i, " and ", j, +" (CC), time = ", Timing[pre[i,j]=re[i,j]//polsums[#,k1,k2, +1/2]&//polsums[#,k2,k1,1/2]&//polsums[#,k3,k4,1]&// +polsums[#,k4,k3,1]&//Simplify][[1]]];pre[i,j],{i,4},{j,i}]; + + +fpre[i_,j_]:=pre[i,j]/;(i>=j); +fpre[i_,j_]:=ComplexConjugate[pre[j,i]]/;(i3 + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (9/2)SMP["g_s"]^4 (3 - t u/s^2 - s u/t^2 - s t/u^2) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:","CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/GlGl-QQbar.m b/FeynCalc/Examples/QCD/Tree/GlGl-QQbar.m new file mode 100644 index 000000000..63e40a0fb --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/GlGl-QQbar.m @@ -0,0 +1,111 @@ +(* ::Package:: *) + +(* :Title: GlGl-QQbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Gl Gl -> Q Qbar, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark pair production from gluon-gluon annihilation*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Gl Gl -> Q Qbar, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {V[5], V[5]}-> + {F[3, {1}], -F[3, {1}]}, InsertionLevel -> {Classes}, + Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{p1,p2}, List->False, SMP->True, + Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, 0, 0, SMP["m_u"]^2, SMP["m_u"]^2]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/((SUNN^2-1)^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum// + DiracSimplify//DoPolarizationSums[#,p1,p2, + ExtraFactor -> 1/2]&//DoPolarizationSums[#,p2,p1,ExtraFactor -> 1/2]&// + TrickMandelstam[#,{s,t,u,2 SMP["m_u"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (1/6)SMP["g_s"]^4 (t^2+u^2)/(t u)-(3/8)SMP["g_s"]^4 (t^2+u^2)/(s^2) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:","CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/MuAmu-QQbar.m b/FeynCalc/Examples/QCD/Tree/MuAmu-QQbar.m new file mode 100644 index 000000000..0a08a7c10 --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/MuAmu-QQbar.m @@ -0,0 +1,131 @@ +(* ::Package:: *) + +(* :Title: MuAmu-QQbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Mu Amu -> Q Qbar, QCD, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark production in muon-antimuon annihilation*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Mu Amu -> Q Qbar, QCD, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {2}], -F[2, {2}]} -> + {F[3, {1}], -F[3, {1}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True, + Prefactor->3/2 SMP["e_Q"]] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_mu"]^2, SMP["m_mu"]^2, + SMP["m_u"]^2, SMP["m_u"]^2]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify// + TrickMandelstam[#,{s,t,u,2SMP["m_u"]^2+2SMP["m_mu"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"|"m_mu"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Total cross-section*) + + +integral=Integrate[Simplify[ampSquaredMasslessSUNN3[0]/(s/4) /. +u-> -s-t],{t,-s,0}]/.SMP["e"]^4->(4 Pi SMP["alpha_fs"])^2 + + +prefac=2Pi/(128 Pi^2 s) + + +(* ::Text:: *) +(*The total cross-section *) + + +crossSectionTotal=integral*prefac//PowerExpand//Factor2 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (6*(t^2 + u^2)*SMP["e"]^4*SMP["e_Q"]^2)/(s^2), + (4*Pi*SMP["alpha_fs"]^2*SMP["e_Q"]^2)/s +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0],crossSectionTotal}, +knownResults, +Text->{"\tCompare to CalcHEP and to Field, \ +Applications of Perturbative QCD, Eq. 2.1.15", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QGa-GlQ.m b/FeynCalc/Examples/QCD/Tree/QGa-GlQ.m new file mode 100644 index 000000000..9170e51fd --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QGa-GlQ.m @@ -0,0 +1,114 @@ +(* ::Package:: *) + +(* :Title: QGa-GlQ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Ga -> Gl Q, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-virtual photon scattering to a gluon and a quark*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q Ga -> Gl Q, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], V[1]} -> + {V[5], F[3, {1}]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k1}, List->False, SMP->True, + Contract->True,DropSumOver->True, Prefactor->3/2 SMP["e_Q"]] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], qQ, 0, SMP["m_u"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*Now come the usual steps, but with some special features. We do not average over the polarizations of the virtual photon, but use the gauge trick for the sum over its polarizations. In this case the sum goes over all 4 unphysical polarizations, not just 2.*) + + +ampSquared[0] = 1/(SUNN)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2]&// + DiracSimplify//DoPolarizationSums[#,p2,0, + VirtualBoson->True,GaugeTrickN->4]&//DoPolarizationSums[#,k1,p2]&// + TrickMandelstam[#,{s,t,u, 2SMP["m_u"]^2+qQ^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,qQ^2}]& + + +ampSquaredMasslessSUNN3[0] = + Simplify[ampSquaredMassless[0]/.SUNN->3/.u->qQ^2-s-t/.qQ->I Q] + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (16/3) SMP["e"]^2 SMP["e_Q"]^2 SMP["g_s"]^2 (-t/s-s/t - 2 Q^2(s+t+Q^2)/(t s)) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCheck with R. Field, Applications of Perturbative QCD, Eq 4.3.10:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QGl-QGl.m b/FeynCalc/Examples/QCD/Tree/QGl-QGl.m new file mode 100644 index 000000000..e00ea37a4 --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QGl-QGl.m @@ -0,0 +1,111 @@ +(* ::Package:: *) + +(* :Title: QGl-QGl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Gl -> Q Gl, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-gluon scattering*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q Gl -> Q Gl, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}],V[5]}-> + {F[3, {1}],V[5]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {2, 2}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,512}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,k1}, + OutgoingMomenta->{p2,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k1,k2}, List->False, SMP->True, + Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, k1, -p2, -k2, SMP["m_u"], 0, SMP["m_u"], 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN (SUNN^2-1))(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2]&// + DiracSimplify//DoPolarizationSums[#,k1,k2, + ExtraFactor->1/2]&//DoPolarizationSums[#,k2,k1]&// + TrickMandelstam[#,{s,t,u,2SMP["m_u"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + Simplify + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + -(4/9)SMP["g_s"]^4 (s^2+u^2)/(s u)+SMP["g_s"]^4 (u^2+s^2)/(t^2) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QQbar-ElAel.m b/FeynCalc/Examples/QCD/Tree/QQbar-ElAel.m new file mode 100644 index 000000000..941411f8c --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QQbar-ElAel.m @@ -0,0 +1,130 @@ +(* ::Package:: *) + +(* :Title: QQbar-ElAel *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Qbar -> El Ael, QCD, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark annihilation into an electron-positron pair*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q Qbar -> El Ael, QCD, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], -F[3, {1}]} -> + {F[2, {1}], -F[2, {1}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True, + Prefactor->3/2 SMP["e_Q"]] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], + SMP["m_e"], SMP["m_e"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//TrickMandelstam[#,{s,t,u,2SMP["m_u"]^2+2SMP["m_e"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"|"m_e"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Total cross-section*) + + +integral=Integrate[Simplify[ampSquaredMasslessSUNN3[0]/(s/4) /. +u-> -s-t],{t,-s,0}]/.SMP["e"]^4->(4 Pi SMP["alpha_fs"])^2 + + +prefac=2Pi/(128 Pi^2 s) + + +(* ::Text:: *) +(*The total cross-section *) + + +crossSectionTotal=integral*prefac//PowerExpand//Factor2 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (2*(t^2 + u^2)*SMP["e"]^4*SMP["e_Q"]^2)/(3*s^2), + (4*Pi*SMP["alpha_fs"]^2*SMP["e_Q"]^2)/(9*s) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0],crossSectionTotal}, +knownResults, +Text->{"\tCompare to CalcHEP and to Field, \ +Applications of Perturbative QCD, Eq. 5.1.17:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QQbar-GaGa.m b/FeynCalc/Examples/QCD/Tree/QQbar-GaGa.m new file mode 100644 index 000000000..a57bc6f3c --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QQbar-GaGa.m @@ -0,0 +1,114 @@ +(* ::Package:: *) + +(* :Title: QQbar-GaGa *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Qbar -> Ga Ga, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark pair annihilation into photons*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q Qbar -> Ga Ga, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], -F[3, {1}]} -> + {V[1], V[1]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k1,k2}, List->False, SMP->True, + Contract->True,DropSumOver->True, Prefactor->9/4 SMP["e_Q"]^2] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], 0, 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*We average over the spins and the colors of the quarks, hence the additional factor 1/N^2*1/2^2. *) +(*Since the final state particles are indistinguishable, we add an extra 1/2*) + + +ampSquared[0] = 1/2*1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//DoPolarizationSums[#,k1,k2]&// + DoPolarizationSums[#,k2,k1]&//TrickMandelstam[#,{s,t,u,2 SMP["m_u"]^2}]&// + Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + ((t^2 + u^2)*SMP["e"]^4*SMP["e_Q"]^4)/(3*t*u) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to CalcHEP:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QQbar-GaGl.m b/FeynCalc/Examples/QCD/Tree/QQbar-GaGl.m new file mode 100644 index 000000000..7b38137c1 --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QQbar-GaGl.m @@ -0,0 +1,113 @@ +(* ::Package:: *) + +(* :Title: QQbar-GaGl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Qbar -> Ga Gl, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark pair annihilation into a virtual photon and a gluon*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q Qbar -> Ga Gl, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], -F[3, {1}]} -> + {V[1], V[5]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k2}, List->False, SMP->True, + Contract->True,DropSumOver->True, Prefactor->3/2 SMP["e_Q"]] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], M, 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +(* ::Text:: *) +(*Now come the usual steps, but with some special features. We do not average over the polarizations of the virtual photon but use the gauge trick for the sum over its polarizations. In this case the sum goes over all 4 unphysical polarizations, not just 2.*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//DoPolarizationSums[#,k1,0,VirtualBoson->True,GaugeTrickN->4]&// + DoPolarizationSums[#,k2,k1]&//TrickMandelstam[#,{s,t,u,2 SMP["m_u"]^2+M^2}]&// + Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,M^2}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (8/9) SMP["e"]^2 SMP["e_Q"]^2 SMP["g_s"]^2 (u/t+t/u + 2 M^2(-t-u+M^2)/(t u)) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCheck with R. Field, Applications of Perturbative QCD, Eq 5.2.3:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QQbar-GlGl.m b/FeynCalc/Examples/QCD/Tree/QQbar-GlGl.m new file mode 100644 index 000000000..bdde03f7a --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QQbar-GlGl.m @@ -0,0 +1,110 @@ +(* ::Package:: *) + +(* :Title: QQbar-GlGl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Qbar -> Gl Gl, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark pair annihilation into gluons*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q Qbar -> Gl Gl, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], -F[3, {1}]} -> + {V[5], V[5]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k1,k2}, List->False, SMP->True, + Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], 0, 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//DoPolarizationSums[#,k1,k2]&// + DoPolarizationSums[#,k2,k1]&//TrickMandelstam[#,{s,t,u,2 SMP["m_u"]^2}]&// + Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (32/27)SMP["g_s"]^4 (t^2+u^2)/(t u)-(8/3)SMP["g_s"]^4 (t^2+u^2)/(s^2) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:","CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QQbar-MuAmu.m b/FeynCalc/Examples/QCD/Tree/QQbar-MuAmu.m new file mode 100644 index 000000000..6e5e52a9e --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QQbar-MuAmu.m @@ -0,0 +1,131 @@ +(* ::Package:: *) + +(* :Title: QQbar-MuAmu *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Qbar -> Mu Amu, QCD, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark annihilation into a muon-antimuon pair*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Q Qbar -> Mu Amu, QCD, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], -F[3, {1}]} -> + {F[2, {2}], -F[2, {2}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True, + Prefactor->3/2 SMP["e_Q"]] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], + SMP["m_mu"], SMP["m_mu"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//TrickMandelstam[#,{s,t,u,2SMP["m_u"]^2+2SMP["m_mu"]^2}]&// + Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"|"m_mu"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Total cross-section*) + + +integral=Integrate[Simplify[ampSquaredMasslessSUNN3[0]/(s/4) /. +u-> -s-t],{t,-s,0}]/.SMP["e"]^4->(4 Pi SMP["alpha_fs"])^2 + + +prefac=2Pi/(128 Pi^2 s) + + +(* ::Text:: *) +(*The total cross-section *) + + +crossSectionTotal=integral*prefac//PowerExpand//Factor2 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (2*(t^2 + u^2)*SMP["e"]^4*SMP["e_Q"]^2)/(3*s^2), + (4*Pi*SMP["alpha_fs"]^2*SMP["e_Q"]^2)/(9*s) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0],crossSectionTotal}, +knownResults, +Text->{"\tCompare to CalcHEP and to Field, \ +Applications of Perturbative QCD, Eq. 5.1.17:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QiQi-QiQi.m b/FeynCalc/Examples/QCD/Tree/QiQi-QiQi.m new file mode 100644 index 000000000..da8c237d9 --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QiQi-QiQi.m @@ -0,0 +1,110 @@ +(* ::Package:: *) + +(* :Title: QiQi-QiQi *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Qi Qi -> Qi Qi, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-quark scattering (same flavors)*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Qi Qi -> Qi Qi, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], F[3, {1}]} -> + {F[3, {1}], F[3, {1}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[1|2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], + SMP["m_u"], SMP["m_u"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//TrickMandelstam[#,{s,t,u,4 SMP["m_u"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + ((4/9)SMP["g_s"]^4 ((s^2+u^2)/t^2+(s^2+t^2)/u^2)-(8/27)SMP["g_s"]^4 s^2/(t u)) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QiQibar-QiQibar.m b/FeynCalc/Examples/QCD/Tree/QiQibar-QiQibar.m new file mode 100644 index 000000000..51f0ef0df --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QiQibar-QiQibar.m @@ -0,0 +1,110 @@ +(* ::Package:: *) + +(* :Title: QiQibar-QiQibar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Qi Qjbar -> Qi Qjbar, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark scattering (same flavors)*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Qi Qibar -> Qi Qibar, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], -F[3, {1}]} -> + {F[3, {1}], -F[3, {1}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[1|2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], + SMP["m_u"], SMP["m_u"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//TrickMandelstam[#,{s,t,u,4SMP["m_u"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + ((4/9)SMP["g_s"]^4 ((s^2+u^2)/t^2+(t^2+u^2)/s^2)-(8/27)SMP["g_s"]^4 u^2/(s t)) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QiQibar-QjQjbar.m b/FeynCalc/Examples/QCD/Tree/QiQibar-QjQjbar.m new file mode 100644 index 000000000..b32a00045 --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QiQibar-QjQjbar.m @@ -0,0 +1,110 @@ +(* ::Package:: *) + +(* :Title: QiQibar-QjQjbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Qi Qjbar -> Qi Qjbar, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark scattering (same flavors)*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Qi Qibar -> Qj Qjbar, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], -F[3, {1}]} -> + {F[3, {2}], -F[3, {2}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[1|2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_u"], + SMP["m_c"], SMP["m_c"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//TrickMandelstam[#,{s,t,u,2SMP["m_u"]^2+2SMP["m_c"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"|"m_c"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + ((4/9)SMP["g_s"]^4 (t^2+u^2)/s^2) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QiQj-QiQj.m b/FeynCalc/Examples/QCD/Tree/QiQj-QiQj.m new file mode 100644 index 000000000..77aea7d30 --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QiQj-QiQj.m @@ -0,0 +1,110 @@ +(* ::Package:: *) + +(* :Title: QiQj-QiQj *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Qi Qj -> Qi Qj, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-quark scattering (different flavors)*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Qi Qj -> Qi Qj, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], F[3, {2}]} -> + {F[3, {1}], F[3, {2}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[1|2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_c"], + SMP["m_u"], SMP["m_c"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//TrickMandelstam[#,{s,t,u,2SMP["m_u"]^2+2SMP["m_c"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"|"m_c"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + ((4/9)SMP["g_s"]^4 (s^2+u^2)/t^2) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/Tree/QiQjbar-QiQjbar.m b/FeynCalc/Examples/QCD/Tree/QiQjbar-QiQjbar.m new file mode 100644 index 000000000..d77ceab57 --- /dev/null +++ b/FeynCalc/Examples/QCD/Tree/QiQjbar-QiQjbar.m @@ -0,0 +1,110 @@ +(* ::Package:: *) + +(* :Title: QiQjbar-QiQjbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Qi Qjbar -> Qi Qjbar, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Quark-antiquark scattering (different flavors)*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Qi Qjbar -> Qi Qjbar, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[3, {1}], -F[3, {2}]} -> + {F[3, {1}], -F[3, {2}]}, InsertionLevel -> {Classes}, Model -> "SMQCD", + ExcludeParticles -> {S[_],V[1|2]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True,DropSumOver->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_u"], SMP["m_c"], + SMP["m_u"], SMP["m_c"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = 1/(SUNN^2)(amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//SUNSimplify[#,Explicit->True, + SUNNToCACF->False]&//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//TrickMandelstam[#,{s,t,u,2SMP["m_u"]^2+2SMP["m_c"]^2}]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_u"|"m_c"] -> 0}]&// + TrickMandelstam[#,{s,t,u,0}]& + + +ampSquaredMasslessSUNN3[0] = ampSquaredMassless[0]/.SUNN->3 + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + ((4/9)SMP["g_s"]^4 (s^2+u^2)/t^2) +}; +FCCompareResults[{ampSquaredMasslessSUNN3[0]},{knownResults}, +Text->{"\tCompare to Ellis, Stirling and Weber, QCD and Collider Physics, \ +Table 7.1:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring-> +Function[x,Simplify[TrickMandelstam[x,{s,t,u,0}]]]] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QCD/TwoLoops/Gh-Gh.m b/FeynCalc/Examples/QCD/TwoLoops/Gh-Gh.m new file mode 100644 index 000000000..8b501e483 --- /dev/null +++ b/FeynCalc/Examples/QCD/TwoLoops/Gh-Gh.m @@ -0,0 +1,242 @@ +(* ::Package:: *) + +(* :Title: Gh-Gh *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Gh -> Gh, massless QCD, 2-loops *) + +(* ------------------------------------------------------------------------ *) + + +(* ::Title:: *) +(*QCD ghost self-energy*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Gh -> Gh, massless QCD, 2-loops"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"TARCER", "FeynArts"}; +< 1,ExcludeTopologies -> {Tadpoles}], + {U[5]} -> {U[5]}, InsertionLevel -> {Classes}, Model -> "SMQCD"]; + +Paint[diags, ColumnsXRows -> {4,1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{768,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The prefactor 1/(2Pi)^(2D) for the loop integrals is understood. Notice that we ignore the first diagram (zero in DR) and the fifth diagram, since its contribution is identical to that of the fourth diagram.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[DiagramExtract[diags,{2,3,4,6,7,8,9}], Truncated -> True, GaugeRules->{}, + PreFactor->-I], IncomingMomenta->{p}, OutgoingMomenta->{p},LoopMomenta->{q1,q2}, + UndoChiralSplittings->True, ChangeDimension->D, List->True, SMP->True, + DropSumOver->True,FinalSubstitutions->{MQU[Index[Generation, 3]]->0,GaugeXi[_]->1-GaugeXi}]; + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +ScalarProduct[p,p]=pp; + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +amp[1]=FCTraceFactor/@amp[0]; + + +(* ::Text:: *) +(*We simplify the color and Dirac algebra, do some partial fractioning and convert the integrals to the TRACER notation. To do this we define the following helper function*) + + +RepRuleCancelQP={ +x_. Power[Pair[Momentum[q_,dim_:4],Momentum[q_,dim_:4]],n_] * +FeynAmpDenominator[a___,PD[Momentum[q_,dim_:4],0],b___]:>x Power[Pair[Momentum[q,dim],Momentum[q,dim]],n-1] FeynAmpDenominator[a,b], + +x_. Pair[Momentum[q_,dim_:4],Momentum[q_,dim_:4]] * +FeynAmpDenominator[a___,PD[Momentum[q_,dim_:4],0],b___]:>x FeynAmpDenominator[a,b], + +x_. Pair[Momentum[p_,dim_:4],Momentum[q_,dim_:4]] * +FeynAmpDenominator[a___,PD[Momentum[q_,dim_:4]-Momentum[p_,dim_:4],0],b___]:> +-(1/2)x FeynAmpDenominator[a,b] ++(1/2)x Pair[Momentum[p,dim],Momentum[p,dim]]FeynAmpDenominator[a,PD[Momentum[q,dim]-Momentum[p,dim],0],b] ++(1/2)x Pair[Momentum[q,dim],Momentum[q,dim]]FeynAmpDenominator[a,PD[Momentum[q,dim]-Momentum[p,dim],0],b], + +x_. Power[Pair[Momentum[p_,dim_:4],Momentum[q_,dim_:4]],n_] * +FeynAmpDenominator[a___,PD[Momentum[q_,dim_:4]-Momentum[p_,dim_:4],0],b___]:> +-(1/2)x Power[Pair[Momentum[p,dim],Momentum[q,dim]],n-1] FeynAmpDenominator[a,b] ++(1/2)x Power[Pair[Momentum[p,dim],Momentum[q,dim]],n-1] Pair[Momentum[p,dim],Momentum[p,dim]]FeynAmpDenominator[a,PD[Momentum[q,dim]-Momentum[p,dim],0],b] ++(1/2)x Power[Pair[Momentum[p,dim],Momentum[q,dim]],n-1] Pair[Momentum[q,dim],Momentum[q,dim]]FeynAmpDenominator[a,PD[Momentum[q,dim]-Momentum[p,dim],0],b] +}; +ClearAll[diagCompute]; +diagCompute[ex_]:= +ex//SUNSimplify[#,Explicit->True,SUNTrace->True]&// +ReplaceAll[#,DiracTrace[x__]:>DiracTrace[x,DiracTraceEvaluate->True]]&// +Contract//FCLoopIsolate[#,{q1,q2},Head->loopHead]&//ReplaceRepeated[#,RepRuleCancelQP]&// +ReplaceAll[#,loopHead->Identity]&//ToTFI[#,q1,q2,p]&; + + +(* ::Text:: *) +(*and apply it to every single amplitude.*) + + +AbsoluteTiming[amp[2]=diagCompute/@amp[1];] + + +allints = Cases2[amp[2], TFI]; +allints // Length + + +(* ::Text:: *) +(*There are 271 integrals to be done for the ghost self energy. There are several possibilities how to proceed. One possibility is to calculate the integrals one by one and save them to a file in the Database directory. This can be conveniently done using the CheckDB function. If the file "IntegralsQCDTwoLoopGhostSelfEnergy.db" does not exist the first argument of CheckDB is evaluated, otherwise the list is loaded and assigned to inttable.*) + + +Timing[inttable = + CheckDB[Dispatch[ + Thread[allints -> + Table[WriteString["stdout", "."]; + TarcerRecurse[allints[[i]]], {i, Length[allints]}]]], + "IntegralsQCDTwoLoopGhostSelfEnergy.db"];] + + +(* ::Text:: *) +(*Now we need to insert the calculated integrals and rewrite the whole expression into a nicer form. Note that the Tarcer two loop integrals are defined to have only 1/(Pi)^D in the measure. Therefore, we will need to multiply the full result by 1/(4Pi)^D, since we did not include the prefactor (1/(2Pi)^D)^2 in the very beginning.*) + + +Timing[amp[3] = + FeynAmpDenominatorExplicit[FCI[(Collect2[#, {TAI, TBI, TJI}, Factoring -> Factor2] & /@ + (amp[2] /. inttable))]];] + + +(* ::Text:: *) +(*The final result*) + + +resFinal=amp[3]//.SMP["g_s"]:>gs + + +(* ::Section:: *) +(*Check the final results*) + + +(* ::Text:: *) +(*Now let us compare our result with the literature. This computation can be found in A.I. Davydychev, P .Osland, O.V. Tarasov, Phys. Rev. D 58, 036007 (1998). The preprint is available at arXiv:hep-ph/9801380.*) +(**) +(*The general expression for the ghost self-energy (two-point function) is given by Eq. 2.15. What we computed is -delta^{a1 a2} p^2 G^{(2)}(p^2) (c.f. Eq. 6.5). The authors write G^{(2)}(p^2) as G^{(2,q)}(p^2) + G^{(2,\[Xi])(red)}(p^2) + G^{(2,\[Xi])(irred)}(p^2) (c.f. Eq 2.6), where G^{(2,q)}(p^2) is the contribution of the quark loops (both one-particle irreducible and one-particle reducible), G^{(2,\[Xi])(irred)}(p^2) is the one particle irreducible contribution of the gluon and ghost loops and G^{(2,\[Xi])(red)}(p^2) is the one particle reducible one.*) +(**) +(*The quark loop contribution is given by the third diagram*) + + +G2q=resFinal[[3]] + + +(* ::Text:: *) +(*This should give us the same as Eq 6.13, with T = Nf Tf (c.f. Eq. 4.6) and eta = ( Gamma[D/2-1]^2 Gamma[3-D/2] ) / Gamma[D-3]. Remember that we must remove - delta^{ab} p^2 from our G2q and multiply it by (1/(4Pi)^D).*) + + +G2qEval= (-1/(4Pi)^D TarcerExpand[G2q, D -> 4 - 2 Epsilon, 0])/. + pp SUNDelta[a_,b_]->1/.CA->2T*CA + + +(* ::Text:: *) +(*Our result contains SEpsilon[4 - 2*Epsilon] which is an abbreviation for Exp[-Epsilon*EulerGamma]. Since eta is given by Exp[- Epsilon*EulerGamma] (1- 1/12 Pi^2 Epsilon^2 + ...) (c.f. Eq 4.7), it is clear that SEpsilon[4 - 2*Epsilon]^2 comes from there. To bring our result into the suitable form, we therefore must divide the term in the brackets by (1- 1/12 Pi^2 Epsilon^2)^2 or (1- Zeta2/2 Epsilon^2)^2 and again expand it in Epsilon. After that we can replace SEpsilon[4 - 2*Epsilon]^2 by eta^2.*) + + +G2qFinal=G2qEval//ReplaceAll[#,Dot[a_,b_]:>Dot[a, Normal[Series[b/(1 - Zeta2/2 Epsilon^2)^2,{Epsilon,0,0}]]]]&// +ReplaceAll[#,{SEpsilon[4 - 2*Epsilon]^2->eta^2,gs->SMP["g_s"]}]& + + +G2qFinalPaper=(((CA*eta^2*SMP["g_s"]^4*T)/(-pp)^(2*Epsilon))* + (-53/8 - 1/(2*Epsilon^2) - 7/(4*Epsilon))/(4*Pi)^D); + + +(* ::Text:: *) +(*Repeat the same for G^{(2,\[Xi])(red)}(p^2) which is given by Eq. 6.14. The reducible part comes from the diagram 7, hence*) + + +G2xiRed=resFinal[[7]]; +G2xiRedEval= -1/(4Pi)^D TarcerExpand[G2xiRed, D -> 4 - 2 Epsilon, 0]// +ReplaceRepeated[#,{pp SUNDelta[a_,b_]->1}]&; +G2xiRedFinal=G2xiRedEval//ReplaceAll[#,Dot[a_,b_]:>Dot[a, Normal[Series[b/(1 - Zeta2/2 Epsilon^2)^2,{Epsilon,0,0}]]]]&// +ReplaceAll[#,{SEpsilon[4 - 2*Epsilon]^2->eta^2,gs->SMP["g_s"]}]& + + +G2xiRedPaper=(((CA^2*eta^2*SMP["g_s"]^4)/(-pp)^(2*Epsilon)) *( 3 + (1 + GaugeXi/2)/Epsilon + GaugeXi + + (4 + 4*GaugeXi + GaugeXi^2)/(16*Epsilon^2))/(4*Pi)^D); + + +(* ::Text:: *) +(*Finally, we still need to verify G^{(2,\[Xi])(irred)}(p^2), the irreducible contribution of the gluon and ghost loops given by the remaining diagrams and shown in Eq 6.12*) + + +G2xiIrred=Collect2[Plus@@Join[resFinal[[1;;2]],resFinal[[4;;6]]], {TBI, TJI}]; +G2xiIrredEval= -1/(4Pi)^D TarcerExpand[G2xiIrred, D -> 4 - 2 Epsilon, 0]// +ReplaceRepeated[#,{pp SUNDelta[a_,b_]->1,Nf*Tf->T}]&; +G2xiIrredFinal=G2xiIrredEval//ReplaceAll[#,Dot[a_,b_]:>Dot[a,Collect[b,{SEpsilon[_],(-pp)^(-2Epsilon)}]]]&// +ReplaceAll[#,Dot[a_, SEpsilon[x_]^2 (-pp)^(-2Epsilon) b_]:>Dot[SEpsilon[x]^2 (-pp)^(-2Epsilon) a,b]]&// +ReplaceAll[#,Dot[a_,b_]:>Dot[a, Normal[Series[b/(1 - Zeta2/2 Epsilon^2)^2,{Epsilon,0,0}]]]]&// +ReplaceAll[#,{SEpsilon[4 - 2*Epsilon]^2->eta^2,gs->SMP["g_s"]}]& + + +G2xiIrredPaper=(((CA^2*eta^2*SMP["g_s"]^4)/(-pp)^(2*Epsilon)) ( 1/Epsilon(67/16 - (9*GaugeXi)/32) + + (1 + (3*GaugeXi)/16 - (3*GaugeXi^2)/32)/Epsilon^2 + 503/32 +(-73*GaugeXi)/64 + +(3*GaugeXi^2)/8 - (3*Zeta[3])/4 - (3*GaugeXi^2*Zeta[3])/16)/(4*Pi)^D); + + +(* ::Text:: *) +(*Last but not least, let us verify the full contribution of the gluon and ghost loops which is given by Eq. 6.15*) + + +G2xFinal=(G2xiIrredFinal+G2xiRedFinal)//ReplaceAll[#,f_ Dot[a_,b_]+ f_ Dot[a_,c_]:>f Dot[a,Collect[Simplify[b+c],{1/Epsilon}]]]& + + +G2xPaper=(((CA^2*eta^2*SMP["g_s"]^4)/(-pp)^(2*Epsilon)) * ((83/16 + 7/32*GaugeXi)/Epsilon + + (5/4 + 7/16*GaugeXi - 1/32 GaugeXi^2)/Epsilon^2 + 599/32 - 3/4 Zeta[3] - 9/64 GaugeXi + 3/8 GaugeXi^2 - 3/16 GaugeXi^2 Zeta[3] )/ + (4*Pi)^D); + + +knownResult = {G2qFinalPaper,G2xiRedPaper,G2xiIrredPaper,G2xPaper}; +FCCompareResults[({G2qFinal,G2xiRedFinal,G2xiIrredFinal,G2xFinal}/.{Dot->Times}),knownResult, +Text->{"\tCompare to Davydychev, Osland and Tarasov, hep-ph/9801380, \ +Eqs. 6.12-6.15:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic},Factoring->Simplify]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/QED/OneLoop/El-El.m b/FeynCalc/Examples/QED/OneLoop/El-El.m new file mode 100644 index 000000000..3ff67b7de --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/El-El.m @@ -0,0 +1,126 @@ +(* ::Package:: *) + +(* :Title: El-El *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El -> El, QED, only UV divergences, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*QED electron self-energy*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El -> El, QED, only UV divergences, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 1, + ExcludeTopologies->Tadpoles], {F[2,{1}]} -> + {F[2,{1}]}, InsertionLevel -> {Particles}, + ExcludeParticles->{S[_],V[2|3],(S|U)[_],F[3|4],F[2,{2|3}]}]; + +Paint[diags, ColumnsXRows -> {1, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit. We keep the full gauge dependence.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags, Truncated -> True, + PreFactor->1, GaugeRules->{}], IncomingMomenta->{p}, + OutgoingMomenta->{p},LoopMomenta->{q}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, Contract->True] + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +amp[1] = TID[amp[0], q, ToPaVe->True] + + +(* ::Text:: *) +(*The UV divergence of the amplitude can be obtained via PaVeUVPart.*) +(*Here we also need to reintroduce the implicit 1/(2Pi)^D prefactor.*) +(*Hint: If you need the full result for the amplitude, use PaXEvaluate from FeynHelpers.*) + + +ampDiv[0] = PaVeUVPart[amp[1],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +SelectNotFree2[#,Epsilon]&//Simplify + + +(* ::Text:: *) +(*The self-energy amplitude is usually defined as -i Sigma(p^2)*) + + +sigma[0] = I ampDiv[0] + + +sigmaFeynmanGauge[0] = sigma[0]/.GaugeXi[A]->1 + + +(* ::Section:: *) +(*Check the final results*) + + +(* ::Text:: *) +(*Keep in mind that Peskin and Schroeder use D = 4-Epsilon,*) +(*while we did the calculation with D = 4-2Epsilon.*) + + +knownResult = SMP["e"]^2/(4Pi)^(D/2) Gamma[2-D/2]/ + ((1-x) SMP["m_e"]^2+ x ScaleMu^2 - x(1-x) SPD[p,p])^(2-D/2)* + ((4-Epsilon)SMP["m_e"]-(2-Epsilon)x GSD[p])// + FCReplaceD[#,D->4-Epsilon]&//Series[#,{Epsilon,0,0}]&// + Normal//SelectNotFree2[#,Epsilon]&//Integrate[#,{x,0,1}]&// + ReplaceAll[#,1/Epsilon->1/(2Epsilon)]&; +FCCompareResults[sigmaFeynmanGauge[0],knownResult, +Text->{"\tCompare to Peskin and Schroeder, An Introduction to QFT, \ +Eq 10.41:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/OneLoop/El-GaEl.m b/FeynCalc/Examples/QED/OneLoop/El-GaEl.m new file mode 100644 index 000000000..ec80f5eeb --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/El-GaEl.m @@ -0,0 +1,157 @@ +(* ::Package:: *) + +(* :Title: El-GaEl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El -> Ga El, QED, form factor, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Electron's g-2 in QED*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El -> Ga El, QED, F2(0) form factor, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2, + ExcludeTopologies->{Tadpoles, WFCorrections}], {F[2,{1}]} -> + {V[1],F[2,{1}]}, InsertionLevel -> {Particles}, + ExcludeParticles->{S[_],V[2|3],(S|U)[_],F[3|4],F[2,{2|3}]}]; + +Paint[diags, ColumnsXRows -> {1, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit. We need to replace e with -e to be compatible*) +(*with the convnention D^mu = d^mu + ie A^mu*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,PreFactor->1], + IncomingMomenta->{p1}, OutgoingMomenta->{k,p2}, + LorentzIndexNames->{mu}, + LoopMomenta->{q}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions-> {SMP["e"]->-SMP["e"]}]/. + k->p1-p2/.q->q+p1 + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +ME=SMP["m_e"]; +ScalarProduct[p1,p1]=ME^2; +ScalarProduct[p2,p2]=ME^2; +ScalarProduct[k,k]=0; +ScalarProduct[p1,p2]=ME^2; + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +(* ::Text:: *) +(*Amputate the polarization vector.*) + + +amp[1] = amp[0]//ReplaceAll[#, + Pair[Momentum[Polarization[___],___],___]:>1]&// + Contract//ReplaceAll[#, SMP["e"]^3-> 4 Pi SMP["e"] SMP["alpha_fs"]]& + + +amp[2] = TID[amp[1], q, ToPaVe->True]//DiracSimplify// + Collect2[#,Spinor]& + + +(* ::Text:: *) +(*To extract F2 (0) we need to look only at the piece proportional to (p1+p2)^mu. Thus we can drop the g^mu -piece*) + + +amp[3] = amp[2]//ReplaceAll[#,FCI[GAD[mu]]:>0]&//DotSimplify + + +(* ::Text:: *) +(*The explicit values for the PaVe functions C1, C11 and C12 can be obtained e.g. from H. Patel's Package-X. Here we just insert the known results.*) + + +amp[4] = amp[3]/.{ + PaVe[1,{ME^2,0,ME^2},{0,ME^2,ME^2},OptionsPattern[]]-> + 1/(32Pi^4 ME^2), + PaVe[1,1,{ME^2,0,ME^2},{0,ME^2,ME^2},OptionsPattern[]]-> + -(1/(96Pi^4 ME^2)), + PaVe[1,2,{ME^2,0,ME^2},{0,ME^2,ME^2},OptionsPattern[]]-> + -(1/(192Pi^4 ME^2)) +} + + +(* ::Text:: *) +(*As expected, F2 (0) is free of any divergences. So we can safely do the limit D ->4*) + + +amp[5] = amp[4]//ChangeDimension[#,4]&//ReplaceAll[#,D->4]& + + +(* ::Text:: *) +(*We obtained $\frac{i e}{2 m_e} (p_1+p_2)^\mu F_2 (0) \bar{u}(p_2) u(p_1)$.*) +(*Dividing by the numerical prefactor and substituting $e^2 = 4\pi^2 \alpha$ yields F2(0)*) + + +f2[0]=(amp[5]/((I SMP["e"])/(2 ME)))// + ReplaceAll [#,{Spinor[__].Spinor[__]:>1, + FCI[FV[p1,_]+FV[p2,_]]:>1}]& + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = AlphaFS/(2Pi); +FCCompareResults[f2[0],knownResult, +Text->{"\tCompare to J. Schwinger, Phys. Rev. 73, \ +416-417, 1948:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/OneLoop/ElAel-ElAel.m b/FeynCalc/Examples/QED/OneLoop/ElAel-ElAel.m new file mode 100644 index 000000000..5de161929 --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/ElAel-ElAel.m @@ -0,0 +1,342 @@ +(* ::Package:: *) + +(* :Title: ElAel-ElAel *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Ael -> El Ael, QED, Born-virtual, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Bhabha scattering*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Ael -> El Ael, QED, Born-virtual, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2, + ExcludeTopologies->{Tadpoles,WFCorrections}], {F[2, {1}], -F[2, {1}]} -> + {F[2,{1}], -F[2, {1}]}, InsertionLevel -> {Particles}, + Restrictions->QEDOnly,ExcludeParticles->{F[1|3|4,_],F[2,{3}]}]; +Paint[diagsTree, ColumnsXRows -> {6, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{1024,256}]; + + +diagsLoop=InsertFields[CreateTopologies[1, 2 -> 2, + ExcludeTopologies->{Tadpoles,WFCorrections}], {F[2, {1}], -F[2, {1}]} -> + {F[2,{1}], -F[2, {1}]}, InsertionLevel -> {Particles}, + Restrictions->QEDOnly,ExcludeParticles->{F[1|3|4,_],F[2,{3}]}]; +Paint[DiagramExtract[diagsLoop,1..8,9,11], ColumnsXRows -> {4, 3}, Numbering -> Simple, + SheetHeader->None,ImageSize->{1024,480}]; + + +diagsLoopCT=InsertFields[CreateCTTopologies[1, 2 -> 2,ExcludeTopologies->{Tadpoles,WFCorrectionCTs}], + {F[2, {1}], -F[2, {1}]} ->{F[2,{1}], -F[2, {1}]}, InsertionLevel -> {Particles}, + Restrictions->QEDOnly,ExcludeParticles->{F[1|3|4,_],F[2,{3}]}]; + +Paint[diagsLoopCT, ColumnsXRows -> {4, 3}, Numbering -> Simple, + SheetHeader->None,ImageSize->{1024,480}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +ampLoopCT[0]=FCFAConvert[CreateFeynAmp[diagsLoopCT,Truncated -> False,PreFactor->1]//. +{(h:dZfL1|dZfR1)[z__]:>dZf1[z],Conjugate[(h:dZfL1|dZfR1)[z__]]:>dZf1[z],dZZA1->0}, +IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2},LoopMomenta->{l},ChangeDimension->D, +DropSumOver->True,UndoChiralSplittings->True,SMP->True, +FinalSubstitutions->{SMP["m_e"]->0,SMP["m_mu"]->0}]; + + +ampLoop[0]=FCFAConvert[CreateFeynAmp[DiagramExtract[diagsLoop,1..8,9,11], + Truncated -> False,PreFactor->1],IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2}, + LoopMomenta->{q},ChangeDimension->D,DropSumOver->True,UndoChiralSplittings->True, + SMP->True,FinalSubstitutions->{SMP["m_e"]->0,SMP["m_mu"]->0}]; + + +ampTree[0]=FCFAConvert[CreateFeynAmp[diagsTree,Truncated -> False,PreFactor->1], + IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2}, + ChangeDimension->D,DropSumOver->True,UndoChiralSplittings->True, + SMP->True, FinalSubstitutions->{SMP["m_e"]->0,SMP["m_mu"]->0}]; + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, 0, 0, 0, 0]; + + +(* ::Section:: *) +(*Evaluate the amplitudes*) + + +$KeepLogDivergentScalelessIntegrals=True; + + +ampLoop[1]= + (FCTraceFactor/@DotSimplify[#,Expanding->False]&/@Join[ampLoop[0][[1;;8]],Nf ampLoop[0][[9;;9]],Nf ampLoop[0][[10;;10]]]); + + +ampTree[1]= + (FCTraceFactor/@DotSimplify[#,Expanding->False]&/@ampTree[0]); + + +ampLoopCT[1]= + (FCTraceFactor/@DotSimplify[#,Expanding->False]&/@ampLoopCT[0]); + + +evalFuSimple[ex_]:=ex//Contract//DiracSimplify//TID[#,q,ToPaVe->True]&// + DiracSimplify//Contract//ReplaceAll[#,(h:A0|B0|C0|D0)[x__]:> + TrickMandelstam[h[x],{s,t,u,0}]]&// + FeynAmpDenominatorExplicit//Collect2[#,{A0,B0,C0,D0}, + Factoring->Function[x,Factor2[TrickMandelstam[x,{s,t,u,0}]]]]&; + + +(*about 100 seconds*) +AbsoluteTiming[ampLoop[2]=evalFuSimple/@ampLoop[1];] + + +ampTree[2]=(Total[ampTree[1]]//Contract//DiracSimplify)//FeynAmpDenominatorExplicit// + FCCanonicalizeDummyIndices[#,LorentzIndexNames->{mu}]& + + +(* ::Text:: *) +(*Obtain the Born-virtual interference term*) + + +(*about 10 seconds*) +AbsoluteTiming[bornVirtualUnrenormalized[0]= + Collect2[Total[ampLoop[2]],Spinor,LorentzIndex,IsolateNames->KK] * + ComplexConjugate[ampTree[2]]// + FermionSpinSum[#,ExtraFactor->1/2^2]&//DiracSimplify// + FRH//TrickMandelstam[#,{s,t,u,0}]&//Collect2[#,B0,C0,D0]&;] + + +(* ::Text:: *) +(*The explicit expressions for the PaVe functions can be obtained e.g. using Package-X / PaXEvaluate*) + + +PaVeEvalRules={ +B0[0, 0, 0] -> -1/(16*EpsilonIR*Pi^4) + 1/(16*EpsilonUV*Pi^4), +B0[s_, 0, 0]:> 1/(16*EpsilonUV*Pi^4) - (-2 + EulerGamma - Log[4*Pi] - Log[-(ScaleMu^2/s)])/ + (16*Pi^4), +C0[0, s_, 0, 0, 0, 0] :> C0[0, 0, s, 0, 0, 0], +C0[0, 0, s_, 0, 0, 0] :> 1/(16*EpsilonIR^2*Pi^4*s) - + (EulerGamma - Log[4*Pi] - Log[-(ScaleMu^2/s)])/(16*EpsilonIR*Pi^4*s) - + (-6*EulerGamma^2 + Pi^2 + 12*EulerGamma*Log[4*Pi] - 6*Log[4*Pi]^2 + + 12*EulerGamma*Log[-(ScaleMu^2/s)] - 12*Log[4*Pi]*Log[-(ScaleMu^2/s)] - + 6*Log[-(ScaleMu^2/s)]^2)/(192*Pi^4*s), +D0[0, 0, 0, 0, s_, t_, 0, 0, 0, 0] :> 1/(4*EpsilonIR^2*Pi^4*s*t) - + (2*EulerGamma - 2*Log[4*Pi] - Log[-(ScaleMu^2/s)] - Log[-(ScaleMu^2/t)])/ + (8*EpsilonIR*Pi^4*s*t) - (-3*EulerGamma^2 + 2*Pi^2 + 6*EulerGamma*Log[4*Pi] - + 3*Log[4*Pi]^2 + 3*EulerGamma*Log[-(ScaleMu^2/s)] - 3*Log[4*Pi]*Log[-(ScaleMu^2/s)] + + 3*EulerGamma*Log[-(ScaleMu^2/t)] - 3*Log[4*Pi]*Log[-(ScaleMu^2/t)] - + 3*Log[-(ScaleMu^2/s)]*Log[-(ScaleMu^2/t)])/(24*Pi^4*s*t) +}; + + +bornVirtualUnrenormalized[1]=bornVirtualUnrenormalized[0]//.PaVeEvalRules; + + +(* ::Text:: *) +(*Put together the counter-term contribution and the residue pole contribution*) + + +MSbarRC={ + SMP["dZ_psi"]->- SMP["e"]^2/(16Pi^2) 1/EpsilonUV, + SMP["dZ_A"]-> - Nf SMP["e"]^2/(12Pi^2) 1/EpsilonUV +}; + + +RuleRS={ + dZe1-> - 1/2 SMP["dZ_A"], + dZAA1->SMP["dZ_A"], + (dZf1|dZf2)[__]-> SMP["dZ_psi"] +}; + + +legResidueContrib= 1 + SMP["e"]^2/(4 Pi)*1/(4 Pi) 1/EpsilonIR; + + +aux0=(Total[ampLoopCT[1]]/.RuleRS/.MSbarRC)//FeynAmpDenominatorExplicit//Contract// + DiracSimplify//FCCanonicalizeDummyIndices[#,LorentzIndexNames->{mu}]&; + + +ctContribS=SelectNotFree2[aux0,s]/SelectNotFree2[ampTree[2],s]//Simplify; +ctContribT=SelectNotFree2[aux0,t]/SelectNotFree2[ampTree[2],t]//Simplify; + + +fullCTAndResidue[0]=SelectNotFree[ampTree[2],s](ctContribS+(4*1/2)(legResidueContrib-1))+ + SelectNotFree[ampTree[2],t](ctContribT+(4*1/2)(legResidueContrib-1)) + + +(* ::Text:: *) +(*Now get the interference of the counter term and residue contribution with the Born amplitude*) + + +bornCTAndResidue[0]= fullCTAndResidue[0] ComplexConjugate[ampTree[2]]// +FermionSpinSum[#,ExtraFactor->1/2^2]&//DiracSimplify//Simplify// + TrickMandelstam[#,{s,t,u,0}]& + + +(* ::Text:: *) +(*For convenience, let us pull out an overall prefactor to get rid of ScaleMu, EulerGamma and some Pi's*) + + +aux1=FCSplit[bornCTAndResidue[0],{EpsilonUV}]// + ReplaceAll[#,{EpsilonIR->1/SMP["Delta_IR"],EpsilonUV->1/SMP["Delta_UV"]}]&; +bornCTAndResidue[1]=(FCReplaceD[1/Exp[EpsilonIR(Log[4Pi]-EulerGamma)] aux1[[1]],D->4-2EpsilonIR]+ + FCReplaceD[1/Exp[EpsilonUV(Log[4Pi]-EulerGamma)] aux1[[2]],D->4-2EpsilonUV])// + FCShowEpsilon//Series[#,{EpsilonUV,0,0}]&// + Normal//Series[#,{EpsilonIR,0,0}]&//Normal//Collect2[#,EpsilonUV,EpsilonIR]& + + +aux2=FCSplit[bornVirtualUnrenormalized[1],{EpsilonUV}]; +bornVirtualUnrenormalized[2]=FCReplaceD[1/ScaleMu^(2EpsilonIR)* + 1/Exp[EpsilonIR(Log[4Pi]-EulerGamma)] aux2[[1]], + D->4-2EpsilonIR]+FCReplaceD[1/ScaleMu^(2EpsilonUV)* + 1/Exp[EpsilonUV(Log[4Pi]-EulerGamma)] aux2[[2]],D->4-2EpsilonUV]// + Collect2[#,EpsilonUV,EpsilonIR]&//Normal//Series[#,{EpsilonUV,0,0}]&// + Normal//Series[#,{EpsilonIR,0,0}]&//Normal// + ReplaceAll[#,Log[-ScaleMu^2/(h:s|t|u)]:>2 Log[ScaleMu]-Log[-h]]&// + TrickMandelstam[#,{s,t,u,0}]&//Collect2[#,EpsilonUV,EpsilonIR]&; + + +(* ::Text:: *) +(*Finally, we obtain the UV-finite but IR-divergent Born-virtual interference term*) + + +bornVirtualRenormalized[0]=(bornVirtualUnrenormalized[2]+bornCTAndResidue[1])// + TrickMandelstam[#,{s,t,u,0}]&//Collect2[#,EpsilonUV,EpsilonIR]& + + +(* ::Text:: *) +(*We can compare our O(eps^0) result to Eq. 2.32 in arXiv:hep-ph/0010075*) + + +ClearAll[LitA,LitATilde,auxBox6,Box6Eval,TriEval]; +Li4=PolyLog[4,#1]&; +ruleLit={LitV->Log[-s/u],LitW->Log[-t/u],v->s/u,w->t/u}; + + +LitA= ( +4*GaugeXi*(1-2 Epsilon)*u/s^2((2-3*Epsilon)u^2-6*Epsilon*t*u+3(2-Epsilon)t^2)*Box6[s,t] + +-4 GaugeXi/(1-2 Epsilon)*t/s^2*((4-12*Epsilon+7*Epsilon^2)t^2- +6*Epsilon*(1-2*Epsilon)*t*u+(4-10*Epsilon+5*Epsilon^2)*u^2)*Tri[t] + +-8/((1-2*Epsilon)(3-2*Epsilon))*1/s*(2Epsilon(1-Epsilon)*t*((1-Epsilon)*t-Epsilon*u)*Nf- +Epsilon(3-2*Epsilon)*(2-Epsilon+2*Epsilon^2)*t*u+ +(1-Epsilon)(3-2*Epsilon)(2-(1-GaugeXi)*Epsilon+2 Epsilon^2)t^2)*Tri[s]); + + +LitATilde= ( + 8(1-2Epsilon)u/(s t)((1-4 Epsilon+Epsilon^2)t^2- + 2 Epsilon(2-Epsilon)t*u+(1-Epsilon)^2 u^2)Box6[s,t] + ++ 8(1-2Epsilon)1/s(Epsilon(2-3Epsilon-Epsilon^2)t^2+ +2Epsilon(1-3Epsilon-Epsilon^2)t*u-(2-2Epsilon+3Epsilon^2+Epsilon^3)u^2)Box6[s,u] + +- 8(1-Epsilon)/((1-2*Epsilon)(3-2*Epsilon))*1/t(2Epsilon*(1-Epsilon)(u^2+Epsilon s t)Nf +-(3-2Epsilon)(2Epsilon(1+Epsilon^2)t^2+Epsilon(3+2Epsilon^2)t*u- + 2(1-Epsilon+Epsilon^2)u^2))Tri[s] + ++ 8/(1-2*Epsilon)*1/s(Epsilon(2-5Epsilon+2Epsilon^2-Epsilon^3)t^2+ + Epsilon(1-3Epsilon+Epsilon^2-Epsilon^3)t*u- + (1-Epsilon)(2-3Epsilon-Epsilon^2)u^2) Tri[t] + +- 8/(1-2*Epsilon)*u/(s t)(Epsilon(2-4Epsilon+Epsilon^2-Epsilon^3)t^2+ + Epsilon(2-3Epsilon-Epsilon^3)t*u-(1-Epsilon)(2-4Epsilon-Epsilon^2)u^2)Tri[u]); + + +auxBox6=(1/2((LitV-LitW)^2+Pi^2)+2*Epsilon*(Li3[-v]-LitV Li2[-v]-1/3 LitV^3-Pi^2/2 LitV) +-2 Epsilon^2 (Li4[-v]+LitW Li3[-v]-1/2 LitV^2 Li2[-v]-1/8 LitV^4- +1/6 LitV^3 LitW + 1/4*LitV^2*LitW^2- Pi^2/4 LitV^2-Pi^2/3 LitV LitW - 2 Zeta4)); + +Box6Eval[s,t]=u^(-1-Epsilon)/(2(1-2*Epsilon))(1- Pi^2/12 Epsilon^2)( +auxBox6 + (auxBox6/.{LitW->LitV,LitV->LitW,v->w,w->v})); + +Box6Eval[s,u]=Box6Eval[s,t]/.ruleLit/.{t->u,u->t}; + +TriEval[s_]:=-(-s)^(-1-Epsilon)/Epsilon^2 (1-Pi^2/12 Epsilon^2- + 7/3 Zeta[3] Epsilon^3-47/16 Zeta4 Epsilon^4) + + +reLitAux=(( 2/3 Nf/Epsilon*8((t^2+u^2)/s^2-Epsilon) + ++((LitA/.{Tri->TriEval,Box6->Box6Eval}/.ruleLit)+ + (LitA/.{Tri->TriEval,Box6->Box6Eval}/. +{GaugeXi->-GaugeXi}/. ruleLit/.{t->u,u->t}))/.GaugeXi->1)+ + ++2/3 Nf/Epsilon*8*(1-Epsilon)((u^2)/(s t)+Epsilon) + ++((LitATilde/.{Tri->TriEval,Box6->Box6Eval}/.ruleLit))); + + +(* ::Text:: *) +(*knownResult is the 1-loop result. Notice that is also an implicit overall prefactor prefLit from Eq. 2.8*) + + +prefLit=32 Pi^2/SMP["e"]^6; + + +knownResult=(reLitAux+(reLitAux/.{s->t,t->s})); + + +diff=Series[knownResult- +prefLit(bornVirtualRenormalized[0]/.EpsilonIR->Epsilon),{Epsilon,0,0}]//Normal// +TrickMandelstam[#,{s,t,u,0}]&//PowerExpand//SimplifyPolyLog//TrickMandelstam[#,{s,t,u,0}]& + + +(* ::Section:: *) +(*Check the final results*) + + +FCCompareResults[0,diff, +Text->{"\tCompare to arXiv:hep-ph/0010075:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/QED/OneLoop/ElAel-MuAmu.m b/FeynCalc/Examples/QED/OneLoop/ElAel-MuAmu.m new file mode 100644 index 000000000..4fa808234 --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/ElAel-MuAmu.m @@ -0,0 +1,314 @@ +(* ::Package:: *) + +(* :Title: ElAel-MuAmu *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Ael -> Mu Amu, QED, Born-virtual, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Muon production*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Ael -> Mu Amu, QED, Born-virtual, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2, + ExcludeTopologies->{Tadpoles,WFCorrections}], {F[2, {1}], -F[2, {1}]} -> + {F[2,{2}], -F[2, {2}]}, InsertionLevel -> {Particles}, + Restrictions->QEDOnly,ExcludeParticles->{F[1|3|4,_],F[2,{3}]}]; +Paint[diagsTree, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{1024,256}]; + + +diagsLoop=InsertFields[CreateTopologies[1, 2 -> 2, + ExcludeTopologies->{Tadpoles,WFCorrections}], {F[2, {1}], -F[2, {1}]} -> + {F[2,{2}], -F[2, {2}]}, InsertionLevel -> {Particles}, + Restrictions->QEDOnly,ExcludeParticles->{F[1|3|4,_],F[2,{3}]}]; +Paint[DiagramExtract[diagsLoop,1..5], ColumnsXRows -> {5, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{1024,196}]; + + +diagsLoopCT=InsertFields[CreateCTTopologies[1, 2 -> 2,ExcludeTopologies->{Tadpoles,WFCorrectionCTs}], + {F[2, {1}], -F[2, {1}]} ->{F[2,{2}], -F[2, {2}]}, InsertionLevel -> {Particles}, + Restrictions->QEDOnly,ExcludeParticles->{F[1|3|4,_],F[2,{3}]}]; + +Paint[diagsLoopCT, ColumnsXRows -> {3, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{1024,196}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +ampLoopCT[0]=FCFAConvert[CreateFeynAmp[diagsLoopCT,Truncated -> False,PreFactor->1]//. +{(h:dZfL1|dZfR1)[z__]:>dZf1[z],Conjugate[(h:dZfL1|dZfR1)[z__]]:>dZf1[z],dZZA1->0}, +IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2},LoopMomenta->{l},ChangeDimension->D, +DropSumOver->True,UndoChiralSplittings->True,SMP->True, +FinalSubstitutions->{SMP["m_e"]->0,SMP["m_mu"]->0}]; + + +ampLoop[0]=FCFAConvert[CreateFeynAmp[DiagramExtract[diagsLoop,1..5], + Truncated -> False,PreFactor->1],IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2}, + LoopMomenta->{q},ChangeDimension->D,DropSumOver->True,UndoChiralSplittings->True, + SMP->True,FinalSubstitutions->{SMP["m_e"]->0,SMP["m_mu"]->0}]; + + +ampTree[0]=FCFAConvert[CreateFeynAmp[diagsTree,Truncated -> False,PreFactor->1], + IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2}, + ChangeDimension->D,DropSumOver->True,UndoChiralSplittings->True, + SMP->True, FinalSubstitutions->{SMP["m_e"]->0,SMP["m_mu"]->0}]; + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, 0, 0, 0, 0]; + + +(* ::Section:: *) +(*Evaluate the amplitudes*) + + +$KeepLogDivergentScalelessIntegrals=True; + + +ampLoop[1]= + (FCTraceFactor/@DotSimplify[#,Expanding->False]&/@Join[ampLoop[0][[1;;4]],Nf ampLoop[0][[5;;5]]]); + + +ampTree[1]= + (FCTraceFactor/@DotSimplify[#,Expanding->False]&/@ampTree[0]); + + +ampLoopCT[1]= + (FCTraceFactor/@DotSimplify[#,Expanding->False]&/@ampLoopCT[0]); + + +evalFuSimple[ex_]:=ex//Contract//DiracSimplify//TID[#,q,ToPaVe->True]&// + DiracSimplify//Contract//ReplaceAll[#,(h:A0|B0|C0|D0)[x__]:> + TrickMandelstam[h[x],{s,t,u,0}]]&// + FeynAmpDenominatorExplicit//Collect2[#,{A0,B0,C0,D0}, + Factoring->Function[x,Factor2[TrickMandelstam[x,{s,t,u,0}]]]]&; + + +(*about 50 seconds*) +AbsoluteTiming[ampLoop[2]=evalFuSimple/@ampLoop[1];] + + +ampTree[2]=(Total[ampTree[1]]//Contract//DiracSimplify)//FeynAmpDenominatorExplicit// + FCCanonicalizeDummyIndices[#,LorentzIndexNames->{mu}]& + + +(* ::Text:: *) +(*Obtain the Born-virtual interference term*) + + +(*about 3 seconds*) +AbsoluteTiming[bornVirtualUnrenormalized[0]= + Collect2[Total[ampLoop[2]],Spinor,LorentzIndex,IsolateNames->KK] * + ComplexConjugate[ampTree[2]]// + FermionSpinSum[#,ExtraFactor->1/2^2]&//DiracSimplify// + FRH//TrickMandelstam[#,{s,t,u,0}]&//Collect2[#,B0,C0,D0]&;] + + +(* ::Text:: *) +(*The explicit expressions for the PaVe functions can be obtained e.g. using Package-X / PaXEvaluate*) + + +PaVeEvalRules={ +B0[0, 0, 0] -> -1/(16*EpsilonIR*Pi^4) + 1/(16*EpsilonUV*Pi^4), +B0[s_, 0, 0]:> 1/(16*EpsilonUV*Pi^4) - (-2 + EulerGamma - Log[4*Pi] - Log[-(ScaleMu^2/s)])/ + (16*Pi^4), +C0[0, s_, 0, 0, 0, 0] :> C0[0, 0, s, 0, 0, 0], +C0[0, 0, s_, 0, 0, 0] :> 1/(16*EpsilonIR^2*Pi^4*s) - + (EulerGamma - Log[4*Pi] - Log[-(ScaleMu^2/s)])/(16*EpsilonIR*Pi^4*s) - + (-6*EulerGamma^2 + Pi^2 + 12*EulerGamma*Log[4*Pi] - 6*Log[4*Pi]^2 + + 12*EulerGamma*Log[-(ScaleMu^2/s)] - 12*Log[4*Pi]*Log[-(ScaleMu^2/s)] - + 6*Log[-(ScaleMu^2/s)]^2)/(192*Pi^4*s), +D0[0, 0, 0, 0, s_, t_, 0, 0, 0, 0] :> 1/(4*EpsilonIR^2*Pi^4*s*t) - + (2*EulerGamma - 2*Log[4*Pi] - Log[-(ScaleMu^2/s)] - Log[-(ScaleMu^2/t)])/ + (8*EpsilonIR*Pi^4*s*t) - (-3*EulerGamma^2 + 2*Pi^2 + 6*EulerGamma*Log[4*Pi] - + 3*Log[4*Pi]^2 + 3*EulerGamma*Log[-(ScaleMu^2/s)] - 3*Log[4*Pi]*Log[-(ScaleMu^2/s)] + + 3*EulerGamma*Log[-(ScaleMu^2/t)] - 3*Log[4*Pi]*Log[-(ScaleMu^2/t)] - + 3*Log[-(ScaleMu^2/s)]*Log[-(ScaleMu^2/t)])/(24*Pi^4*s*t) +}; + + +bornVirtualUnrenormalized[1]=bornVirtualUnrenormalized[0]//.PaVeEvalRules; + + +(* ::Text:: *) +(*Put together the counter-term contribution and the residue pole contribution*) + + +MSbarRC={ + SMP["dZ_psi"]->- SMP["e"]^2/(16Pi^2) 1/EpsilonUV, + SMP["dZ_A"]-> - Nf SMP["e"]^2/(12Pi^2) 1/EpsilonUV +}; + + +RuleRS={ + dZe1-> - 1/2 SMP["dZ_A"], + dZAA1->SMP["dZ_A"], + (dZf1|dZf2)[__]-> SMP["dZ_psi"] +}; + + +legResidueContrib= 1 + SMP["e"]^2/(4 Pi)*1/(4 Pi) 1/EpsilonIR; + + +aux0=(Total[ampLoopCT[1]]/.RuleRS/.MSbarRC)//FeynAmpDenominatorExplicit//Contract// + DiracSimplify//FCCanonicalizeDummyIndices[#,LorentzIndexNames->{mu}]&; + + +ctContrib=(aux0/ampTree[2])//Simplify; + + +fullCTAndResidue[0]=(ctContrib+(4*1/2)(legResidueContrib-1))ampTree[2] + + +(* ::Text:: *) +(*Now get the interference of the counter term and residue contribution with the Born amplitude*) + + +bornCTAndResidue[0]= fullCTAndResidue[0] ComplexConjugate[ampTree[2]]// +FermionSpinSum[#,ExtraFactor->1/2^2]&//DiracSimplify//Simplify// + TrickMandelstam[#,{s,t,u,0}]& + + +(* ::Text:: *) +(*For convenience, let us pull out an overall prefactor to get rid of ScaleMu, EulerGamma and some Pi's*) + + +aux1=FCSplit[bornCTAndResidue[0],{EpsilonUV}]// + ReplaceAll[#,{EpsilonIR->1/SMP["Delta_IR"],EpsilonUV->1/SMP["Delta_UV"]}]&; +bornCTAndResidue[1]=(FCReplaceD[1/Exp[EpsilonIR(Log[4Pi]-EulerGamma)] aux1[[1]],D->4-2EpsilonIR]+ + FCReplaceD[1/Exp[EpsilonUV(Log[4Pi]-EulerGamma)] aux1[[2]],D->4-2EpsilonUV])// + FCShowEpsilon//Series[#,{EpsilonUV,0,0}]&// + Normal//Series[#,{EpsilonIR,0,0}]&//Normal//Collect2[#,EpsilonUV,EpsilonIR]& + + +aux2=FCSplit[bornVirtualUnrenormalized[1],{EpsilonUV}]; +bornVirtualUnrenormalized[2]=FCReplaceD[1/ScaleMu^(2EpsilonIR)* + 1/Exp[EpsilonIR(Log[4Pi]-EulerGamma)] aux2[[1]], + D->4-2EpsilonIR]+FCReplaceD[1/ScaleMu^(2EpsilonUV)* + 1/Exp[EpsilonUV(Log[4Pi]-EulerGamma)] aux2[[2]],D->4-2EpsilonUV]// + Collect2[#,EpsilonUV,EpsilonIR]&//Normal//Series[#,{EpsilonUV,0,0}]&// + Normal//Series[#,{EpsilonIR,0,0}]&//Normal// + ReplaceAll[#,Log[-ScaleMu^2/(h:s|t|u)]:>2 Log[ScaleMu]-Log[-h]]&// + TrickMandelstam[#,{s,t,u,0}]&//Collect2[#,EpsilonUV,EpsilonIR]&; + + +(* ::Text:: *) +(*Finally, we obtain the UV-finite but IR-divergent Born-virtual interference term*) + + +bornVirtualRenormalized[0]=(bornVirtualUnrenormalized[2]+bornCTAndResidue[1])// + TrickMandelstam[#,{s,t,u,0}]&//Collect2[#,EpsilonUV,EpsilonIR]& + + +(* ::Text:: *) +(*We can compare our O(eps^0) result to Eq. 2.22 in arXiv:hep-ph/0010075*) + + +ClearAll[LitA,LitATilde,auxBox6,Box6Eval,TriEval]; +Li4=PolyLog[4,#1]&; +ruleLit={LitV->Log[-s/u],LitW->Log[-t/u],v->s/u,w->t/u}; + + +LitA= ( +4*GaugeXi*(1-2 Epsilon)*u/s^2((2-3*Epsilon)u^2-6*Epsilon*t*u+3(2-Epsilon)t^2)*Box6[s,t] + +-4 GaugeXi/(1-2 Epsilon)*t/s^2*((4-12*Epsilon+7*Epsilon^2)t^2- +6*Epsilon*(1-2*Epsilon)*t*u+(4-10*Epsilon+5*Epsilon^2)*u^2)*Tri[t] + +-8/((1-2*Epsilon)(3-2*Epsilon))*1/s*(2Epsilon(1-Epsilon)*t*((1-Epsilon)*t-Epsilon*u)*Nf- +Epsilon(3-2*Epsilon)*(2-Epsilon+2*Epsilon^2)*t*u+ +(1-Epsilon)(3-2*Epsilon)(2-(1-GaugeXi)*Epsilon+2 Epsilon^2)t^2)*Tri[s]); + + +auxBox6=(1/2((LitV-LitW)^2+Pi^2)+2*Epsilon*(Li3[-v]-LitV Li2[-v]-1/3 LitV^3-Pi^2/2 LitV) +-2 Epsilon^2 (Li4[-v]+LitW Li3[-v]-1/2 LitV^2 Li2[-v]-1/8 LitV^4- +1/6 LitV^3 LitW + 1/4*LitV^2*LitW^2- Pi^2/4 LitV^2-Pi^2/3 LitV LitW - 2 Zeta4)); + +Box6Eval[s,t]=u^(-1-Epsilon)/(2(1-2*Epsilon))(1- Pi^2/12 Epsilon^2)( +auxBox6 + (auxBox6/.{LitW->LitV,LitV->LitW,v->w,w->v})); + +Box6Eval[s,u]=Box6Eval[s,t]/.ruleLit/.{t->u,u->t}; + +TriEval[s_]:=-(-s)^(-1-Epsilon)/Epsilon^2 (1-Pi^2/12 Epsilon^2- + 7/3 Zeta[3] Epsilon^3-47/16 Zeta4 Epsilon^4) + + +knownResult=(( 2/3 Nf/Epsilon*8((t^2+u^2)/s^2-Epsilon) + ++((LitA/.{Tri->TriEval,Box6->Box6Eval}/.ruleLit)+ + (LitA/.{Tri->TriEval,Box6->Box6Eval}/. +{GaugeXi->-GaugeXi}/. ruleLit/.{t->u,u->t}))/.GaugeXi->1)); + + +(* ::Text:: *) +(*knownResult is the 1-loop result. Notice that is also an implicit overall prefactor prefLit from Eq. 2.8*) + + +prefLit=32 Pi^2/SMP["e"]^6; + + +diff=Series[knownResult- +prefLit(bornVirtualRenormalized[0]/.EpsilonIR->Epsilon),{Epsilon,0,0}]//Normal// +TrickMandelstam[#,{s,t,u,0}]&//PowerExpand//SimplifyPolyLog//TrickMandelstam[#,{s,t,u,0}]& + + +(* ::Section:: *) +(*Check the final results*) + + +FCCompareResults[0,diff, +Text->{"\tCompare to arXiv:hep-ph/0010075:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/QED/OneLoop/Ga-Ga.m b/FeynCalc/Examples/QED/OneLoop/Ga-Ga.m new file mode 100644 index 000000000..3b0c7040e --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/Ga-Ga.m @@ -0,0 +1,141 @@ +(* ::Package:: *) + +(* :Title: Ga-Ga *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Ga -> Ga, QED, only UV divergences, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*QED vacuum polarization*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Ga -> Ga, QED, only UV divergences, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 1], {V[1]} -> + {V[1]}, InsertionLevel -> {Particles}, + ExcludeParticles->{S[_],V[2|3],(S|U)[_],F[3|4],F[2,{2|3}]}]; + +Paint[diags, ColumnsXRows -> {1, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags, Truncated -> True, PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p},LoopMomenta->{q}, + LorentzIndexNames->{mu,nu}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + Contract->True] + + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +amp[1] = TID[amp[0], q, ToPaVe->True] + + +(* ::Text:: *) +(*Check the gauge invariance*) + + +tmp=Contract[FVD[p,mu]FVD[p,nu] amp[1]]//Factor +FCCompareResults[tmp,0, +Text->{"\tThe photon self-energy is gauge invariant:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; + + +(* ::Text:: *) +(*The UV divergence of the amplitude can be obtained via PaVeUVPart.*) +(*Here we also need to reintroduce the implicit 1/(2Pi)^D prefactor.*) +(*Hint: If you need the full result for the amplitude, use PaXEvaluate from FeynHelpers.*) + + +ampDiv[0]=PaVeUVPart[amp[1],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +SelectNotFree2[#,Epsilon]&//Simplify + + +(* ::Text:: *) +(*The self-energy amplitude is usually defined as (p^2 g^{mu nu} - p^mu p^nu) i Pi(p^2)*) + + +pi[0]= FCI[ampDiv[0]/(I(SPD[p,p]MTD[mu,nu]-FVD[p,mu]FVD[p,nu]))]//Cancel + + +(* ::Section:: *) +(*Check the final results*) + + +(* ::Text:: *) +(*Keep in mind that Peskin and Schroeder use D = 4-Epsilon,*) +(*while we did the calculation with D = 4-2Epsilon.*) + + +knownResult = -SMP["e"]^2/(4Pi)^(D/2) Gamma[2-D/2]/ + (SMP["m_e"]^2- x(1-x)SPD[p,p])^(2-D/2)*(8x(1-x))// + FCReplaceD[#,D->4-Epsilon]&//Series[#,{Epsilon,0,0}]&// + Normal//SelectNotFree2[#,Epsilon]&//Integrate[#,{x,0,1}]&// + ReplaceAll[#,1/Epsilon->1/(2Epsilon)]&; +FCCompareResults[pi[0],knownResult, +Text->{"\tCompare to Peskin and Schroeder, An Introduction to QFT, \ +Eq 10.44:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/OneLoop/Ga-GaGa.m b/FeynCalc/Examples/QED/OneLoop/Ga-GaGa.m new file mode 100644 index 000000000..f92007e7c --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/Ga-GaGa.m @@ -0,0 +1,98 @@ +(* ::Package:: *) + +(* :Title: Ga-GaGa *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Ga -> Ga Ga, QED, amplitude, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*3-photon interaction in QED*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Ga -> Ga Ga, QED, amplitude, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], + {V[1]} -> {V[1],V[1]}, InsertionLevel -> {Particles}, + ExcludeParticles->{S[_],V[_],U[_],F[3|4],F[2,{2|3}]}]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,PreFactor->1, + Truncated->True], IncomingMomenta->{k1}, + OutgoingMomenta->{k2, k3}, LoopMomenta->{q}, + LorentzIndexNames->{mu,nu,rho}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True] + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +(* ::Text:: *) +(*We obtain two triangle diagrams. The sum vanishes because the contribution of the first diagram cancels the contribution of the second diagram.*) + + +amp[1] = amp[0]//FCTraceFactor + + +(* ::Section:: *) +(*Check the final results*) + + +FCCompareResults[amp[1],0, +Text->{"\tVerify Furry's theorem for 3-photons at 1-loop:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/OneLoop/Ga-GaGaGaGa.m b/FeynCalc/Examples/QED/OneLoop/Ga-GaGaGaGa.m new file mode 100644 index 000000000..a6a7b96b3 --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/Ga-GaGaGaGa.m @@ -0,0 +1,106 @@ +(* ::Package:: *) + +(* :Title: Ga-GaGa *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Ga -> Ga Ga Ga Ga, QED, amplitude, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*5-photon interaction in QED*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Ga -> Ga Ga Ga Ga, QED, amplitude, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 4], + {V[1]} -> {V[1],V[1],V[1],V[1]}, InsertionLevel -> {Particles}, + ExcludeParticles->{S[_],V[_],U[_],F[3|4],F[2,{2|3}]}]; + +Paint[diags, ColumnsXRows -> {4, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,PreFactor->1, + Truncated->True], IncomingMomenta->{k1}, + OutgoingMomenta->{k2, k3, k4, k5}, LoopMomenta->{q}, + LorentzIndexNames->{mu,nu,rho}, UndoChiralSplittings->True, + ChangeDimension->D, List->True, SMP->True] + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +(* ::Text:: *) +(*We obtain 24 diagrams. The sum vanishes because the contribution of each odd diagram is exactly cancelled by the contribution of the next even diagram, i.e. A1+A2=0, A3+A4=0 and so on*) + + +amp[1] = amp[0]//FCTraceFactor; + + +amp[2]=Total/@Partition[amp[1],2,2,1,{}] + + +amp[3]=Total[amp[2]] + + +(* ::Section:: *) +(*Check the final results*) + + +FCCompareResults[amp[3],0, +Text->{"\tVerify Furry's theorem for 5-photons at 1-loop:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/OneLoop/Ga.m b/FeynCalc/Examples/QED/OneLoop/Ga.m new file mode 100644 index 000000000..7a4e0af08 --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/Ga.m @@ -0,0 +1,101 @@ +(* ::Package:: *) + +(* :Title: Ga *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Ga, QED, amplitude, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Photon tadpole in QED*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Ga, QED, amplitude, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 0], + {V[1]} -> {}, InsertionLevel -> {Particles}, + ExcludeParticles->{S[_],V[_],U[_],F[3|4],F[2,{2|3}]}]; + +Paint[diags, ColumnsXRows -> {1, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit.*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags,PreFactor->1, + Truncated->True], IncomingMomenta->{k}, + LorentzIndexNames->{mu}, LoopMomenta->{q}, + UndoChiralSplittings->True, ChangeDimension->D, + List->False, SMP->True] + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +(* ::Text:: *) +(*Having performed the Dirac algebra we clearly see that this diagram must *) +(*vanish because the loop integral is antisymmetric under q^mu -> - q^mu.*) + + +amp[1] = DiracSimplify[amp[0]] + + +(* ::Text:: *) +(*TID can recognize this and we obtain zero*) + + +amp[2] = TID[amp[1], q] + + +(* ::Section:: *) +(*Check the final results*) + + +FCCompareResults[amp[2],0, +Text->{"\tVerify Furry's theorem for 1-photon at 1-loop:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/OneLoop/PiToGaGa.m b/FeynCalc/Examples/QED/OneLoop/PiToGaGa.m new file mode 100644 index 000000000..c1d7024e1 --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/PiToGaGa.m @@ -0,0 +1,130 @@ +(* ::Package:: *) + +(* :Title: PiToGaGa *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Pi -> Ga Ga, QED, axial current, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Adler-Bell-Jackiw anomaly in QED*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Pi -> Ga Ga, QED, axial current, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +<p,p->k,la->nu,nu->la} + + +(* ::Section:: *) +(*Calculate the amplitude*) + + +(* ::Text:: *) +(*Contracting both amplitudes with I*(k+p)^mu we can check the non-conservation of the axial current.*) + + +amp[0] = Contract[I*FVD[k+p,mu](amp1[0]+amp2[0])] + + +(* ::Text:: *) +(*For this calculation it is crucial to use a correct scheme for gamma^5. As in the book, we use the *) +(*Breitenlohner-Maison-t'Hooft-Veltman prescription.*) + + +FCSetDiracGammaScheme["BMHV"]; +amp[1] = TID[amp[0] ,l, ToPaVe->True] + + +FCClearScalarProducts[]; +Momentum[k,D|D-4]=Momentum[k]; +Momentum[p,D|D-4]=Momentum[p]; + + +(* ::Text:: *) +(*The explicit values for the PaVe functions B0 and C0 can be obtained e.g. from H. Patel's Package-X. *) +(*Here we just insert the known results. The C0 function is finite here, so because of the prefactor (D-4) it *) +(*gives no contribution in the D->4 limit.*) + + +amp[2]=Collect2[amp[1],{B0,C0}]//. { + B0[FCI@SP[p_,p_],0,0]:> + 1/(16 Epsilon \[Pi]^4)-(-2+EulerGamma)/(16 \[Pi]^4)+ + Log[-((4 \[Pi] ScaleMu^2)/Pair[Momentum[p],Momentum[p]])]/(16 \[Pi]^4), + B0[FCI[SP[p,p]+2SP[p,k]+SP[k,k]],0,0]:> + B0[FCI[SP[k+p,k+p]],0,0], + (D-4)ExpandScalarProduct[C0[SP[k],SP[p],SP[k+p],0,0,0]]->0 +} + + +(* ::Text:: *) +(*Now we insert the explicit values, convert the external momenta to 4 dimensions and expand in Epsilon*) + + +amp[3] = amp[2]//FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal + + +(* ::Text:: *) +(*The result should be twice Eq. 19.59 in Peskin and Schroeder*) + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = 2(SMP["e"]^2/(4 Pi^2)LC[al,la,be,nu]FV[k,al]FV[p,be])//Contract; +FCCompareResults[amp[3],knownResult, +Text->{"\tCompare to Peskin and Schroeder, An Introduction to QFT, \ +Eq 19.59:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/OneLoop/Renormalization.m b/FeynCalc/Examples/QED/OneLoop/Renormalization.m new file mode 100644 index 000000000..4a3af517e --- /dev/null +++ b/FeynCalc/Examples/QED/OneLoop/Renormalization.m @@ -0,0 +1,301 @@ +(* ::Package:: *) + +(* :Title: Renormalization *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Renormalization, QED, MS and MSbar, 1-loop *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*1-loop QED renormalization in the minimal subtraction schemes*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +(* ::Text:: *) +(*This example uses a custom QED model created with FeynRules. Please evaluate the file*) +(*FeynCalc/Examples/FeynRules/QED/GenerateModelQED.m before running it for the first time.*) + + +description="Renormalization, QED, MS and MSbar, 1-loop"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +<True]; + + +(* ::Section:: *) +(*Generate Feynman diagrams*) + + +(* ::Text:: *) +(*Nicer typesetting*) + + +MakeBoxes[mu,TraditionalForm]:="\[Mu]"; +MakeBoxes[nu,TraditionalForm]:="\[Nu]"; + + +params={InsertionLevel->{Particles},Model -> FileNameJoin[{"QED","QED"}], +GenericModel -> FileNameJoin[{"QED","QED"}],ExcludeParticles->{F[2,{2|3}]}}; +top[i_,j_]:=CreateTopologies[1, i -> j, +ExcludeTopologies -> {Tadpoles,WFCorrections,WFCorrectionCTs}]; +topCT[i_,j_]:=CreateCTTopologies[1, i ->j, +ExcludeTopologies ->{Tadpoles,WFCorrections,WFCorrectionCTs}]; + +{diagElectronSE,diagElectronSECT} = InsertFields[#, {F[2,{1}]} -> {F[2,{1}]}, +Sequence@@params]&/@{top[1,1],topCT[1,1]}; +{diagPhotonSE,diagPhotonSECT} = InsertFields[#, {V[1]} -> {V[1]}, +Sequence@@params]&/@{top[1,1],topCT[1,1]}; +{diagVertex,diagVertexCT} = InsertFields[#, {F[2,{1}],V[1]}->{F[2,{1}]}, +Sequence@@params]&/@{top[2,1],topCT[2,1]}; + + +diag1[0]=diagElectronSE[[0]][diagElectronSE[[1]],diagElectronSECT[[1]]]; +diag2[0]=diagPhotonSE[[0]][diagPhotonSE[[1]],diagPhotonSECT[[1]]]; +diag3[0]=diagVertex[[0]][diagVertex[[1]],diagVertexCT[[1]]]; + + +Paint[diag1[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diag2[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +Paint[diag3[0], ColumnsXRows -> {2, 1},SheetHeader->None, +Numbering -> Simple, ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitudes*) + + +(* ::Text:: *) +(*The 1/(2Pi)^D prefactor is implicit. We need to replace e with -e to be compatible*) +(*with the convention D^mu = d^mu + ie A^mu*) + + +(* ::Text:: *) +(*Electron self-energy including the counter-term*) + + +amp1[0] = FCFAConvert[CreateFeynAmp[diag1[0],Truncated->True, + GaugeRules->{},PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu}, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{Zm->SMP["Z_m"], Zpsi->SMP["Z_psi"], + SMP["e"]->Sqrt[4Pi SMP["alpha_fs"]],GaugeXi[V[1]]->GaugeXi}, + Contract->True] + + +(* ::Text:: *) +(*Photon self-energy including the counter-term*) + + +amp2[0] = FCFAConvert[CreateFeynAmp[diag2[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p}, OutgoingMomenta->{p}, + LorentzIndexNames->{mu,nu}, + LoopMomenta->{l}, UndoChiralSplittings->True, + ChangeDimension->D, List->False, SMP->True, + FinalSubstitutions->{ZA->SMP["Z_A"], Zxi->SMP["Z_xi"], + SMP["e"]->Sqrt[4Pi SMP["alpha_fs"]],GaugeXi[V[1]]->GaugeXi}, + Contract->True]//FCTraceFactor + + +(* ::Text:: *) +(*Electron-photon vertex including the counter-term*) + + +amp3[0] = FCFAConvert[CreateFeynAmp[diag3[0],Truncated->True, + GaugeRules->{}, PreFactor->1], + IncomingMomenta->{p1,k}, OutgoingMomenta->{p2}, + LorentzIndexNames->{mu}, LoopMomenta->{l}, + UndoChiralSplittings->True, ChangeDimension->D, + List->False, SMP->True, FinalSubstitutions-> + {ZA->SMP["Z_A"], Ze->SMP["Z_e"], Zpsi->SMP["Z_psi"], + SMP["e"]^3->4Pi SMP["alpha_fs"] SMP["e"],GaugeXi[V[1]]->GaugeXi}, + Contract->True]/.SMP["e"]->-SMP["e"] + + +(* ::Section:: *) +(*Calculate the amplitudes*) + + +(* ::Subsection:: *) +(*Electron self-energy*) + + +amp1[1] = amp1[0]//ReplaceAll[#,{SMP["Z_psi"]->1+alpha SMP["d_psi"], +SMP["Z_m"]->1+alpha SMP["d_m"]}]&//Series[#,{alpha,0,1}]&// +Normal//ReplaceAll[#,alpha->1]& + + +(* ::Text:: *) +(*Tensor reduction allows us to express the electron self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +amp1[2]=TID[amp1[1],l,ToPaVe->True] + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +amp1Div[0]=PaVeUVPart[amp1[2],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +FCHideEpsilon//SelectNotFree2[#,{SMP["Delta"],SMP["d_m"], +SMP["d_psi"]}]&//Simplify + + +(* ::Text:: *) +(*Equating the result to zero and solving for d_psi and d_m we obtain the renormalization constants in *) +(*the minimal subtraction schemes.*) + + +sol[1]=Solve[SelectNotFree2[amp1Div[0], DiracGamma]==0, + SMP["d_psi"]]//Flatten//Simplify; +sol[2]=Solve[(SelectFree2[amp1Div[0], DiracGamma]==0)/.sol[1], + SMP["d_m"]]//Flatten//Simplify; +solMS1=Join[sol[1],sol[2]]/.{ + SMP["d_psi"]->SMP["d_psi^MS"], + SMP["d_m"]->SMP["d_m^MS"],SMP["Delta"]->1/Epsilon +} +solMSbar1=Join[sol[1],sol[2]]/.{ + SMP["d_psi"]->SMP["d_psi^MSbar"], + SMP["d_m"]->SMP["d_m^MSbar"] +} + + +(* ::Subsection:: *) +(*Photon self-energy*) + + +amp2[1] = amp2[0]//ReplaceRepeated[#,{SMP["Z_xi"]->SMP["Z_A"], +SMP["Z_A"]->1+alpha SMP["d_A"]}]&//Series[#,{alpha,0,1}]&// +Normal//ReplaceAll[#,alpha->1]& + + +(* ::Text:: *) +(*Tensor reduction allows us to express the electron self-energy in tems of the Passarino-Veltman coefficient functions.*) + + +amp2[2]=TID[amp2[1],l,ToPaVe->True] + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +amp2Div[0]=PaVeUVPart[amp2[2],Prefactor->1/(2Pi)^D]// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +FCHideEpsilon//SelectNotFree2[#,{SMP["Delta"],SMP["d_A"]}]&//Simplify + + +(* ::Text:: *) +(*Equating this to zero and solving for d_A we obtain the wave-function renormalization constant for the photon in the minimal subtraction schemes.*) + + +sol[3]=Solve[amp2Div[0]==0,SMP["d_A"]]//Flatten; +solMS2=sol[3]/.{SMP["d_A"]->SMP["d_A^MS"],SMP["Delta"]->1/Epsilon} +solMSbar2=sol[3]/.{SMP["d_A"]->SMP["d_A^MSbar"]} + + +(* ::Subsection:: *) +(*Electron-photon vertex*) + + +amp3[1] = amp3[0]//ReplaceRepeated[#,{SMP["Z_psi"]->1+alpha SMP["d_psi"], +SMP["Z_A"]->1+alpha SMP["d_A"],SMP["Z_e"]->1+alpha SMP["d_e"]}]&// +Series[#,{alpha,0,1}]&//Normal//ReplaceAll[#,alpha->1]& + + +(* ::Text:: *) +(*The result of the tensor reduction is quite large, since we keep the full gauge dependence and do not specify the kinematics*) + + +amp3[2]=TID[amp3[1],l,ToPaVe->True,UsePaVeBasis->True] + + +(* ::Text:: *) +(*Discard all the finite pieces of the 1-loop amplitude*) + + +amp3Div[0]=PaVeUVPart[amp3[2],Prefactor->1/(2Pi)^D]//DiracSimplify// +FCReplaceD[#,D->4-2Epsilon]&//Series[#,{Epsilon,0,0}]&//Normal// +FCHideEpsilon//SelectNotFree2[#,{SMP["Delta"],SMP["d_A"], +SMP["d_e"],SMP["d_psi"]}]&//Simplify + + +ward[0]=Simplify[amp3Div[0]/(-FCI [I SMP["e"] GAD[mu]])==0] + + +wardMS[0]=Simplify[ward[0]/.Epsilon->1/SMP["Delta"]/. + {SMP["d_psi"]->SMP["d_psi^MSbar"]}/.solMSbar1] +wardMSbar[0]=Simplify[ward[0]/.{SMP["d_psi"]->SMP["d_psi^MSbar"]}/. + solMSbar1] + + +knownResults={SMP["d_A"] + 2*SMP["d_e"] == 0, + SMP["d_A"] + 2*SMP["d_e"] == 0}; +FCCompareResults[{wardMS[0],wardMSbar[0]},knownResults, +Text->{"\tVerify Ward's identity:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = { + SMP["d_psi^MS"] -> -(GaugeXi*SMP["alpha_fs"])/(4*Epsilon*Pi), + SMP["d_m^MS"] -> (-3*SMP["alpha_fs"])/(4*Epsilon*Pi), + SMP["d_A^MS"] -> -SMP["alpha_fs"]/(3*Epsilon*Pi), + SMP["d_psi^MSbar"] -> -(GaugeXi*SMP["alpha_fs"]*SMP["Delta"])/(4*Pi), + SMP["d_m^MSbar"] -> (-3*SMP["alpha_fs"]*SMP["Delta"])/(4*Pi), + SMP["d_A^MSbar"] -> -(SMP["alpha_fs"]*SMP["Delta"])/(3*Pi) + }; +FCCompareResults[Join[solMS1,solMS2,solMSbar1,solMSbar2],knownResult, +Text->{"\tCheck the final result:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; + + + diff --git a/FeynCalc/Examples/QED/QEDABJAxialAnomaly.m b/FeynCalc/Examples/QED/QEDABJAxialAnomaly.m deleted file mode 100644 index 6d1ab3ce0..000000000 --- a/FeynCalc/Examples/QED/QEDABJAxialAnomaly.m +++ /dev/null @@ -1,97 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDABJAxialAnomaly *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the Adler-Bell-Jackiw anomaly in QED *) - -(* ------------------------------------------------------------------------ *) - - -(* ::Section:: *) -(*Adler-Bell-Jackiw anomaly in QED*) - - -(* ::Subsection:: *) -(*Load FeynCalc*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the Adler-Bell-Jackiw anomaly in QED"]; -]; -<< FeynCalc` - - -(* ::Subsection:: *) -(*Compute the diagrams*) - - -(* ::Text:: *) -(*According to Peskin and Schroeder (Ch 19.2), the amplitude for the first triangle diagram reads*) - - -amp1=((-1)(-I SMP["e"])^2 DiracTrace[GAD[mu].GA[5].QuarkPropagator[l-k].GAD[la].QuarkPropagator[l].GAD[nu].QuarkPropagator[l+p]])// -Explicit - - -(* ::Text:: *) -(*And the second one follows from the first by interchanging k with p and la with nu*) - - -amp2=amp1/.{k->p,p->k,la->nu,nu->la} - - -(* ::Text:: *) -(*Contracting both amplitudes with I*(k+p)^mu we can check the non-conservation of the axial current.*) - - -ampDotted=Contract[I*FVD[k+p,mu](amp1+amp2)] - - -(* ::Text:: *) -(*For this calculation it is crucial to use a correct scheme for gamma^5. As in the book, we use the Breitenlohner-Maison-t'Hooft-Veltman*) -(*prescription.*) - - -$BreitMaison=True; -ampDotted2=ampDotted/.DiracTrace->Tr - - -(* ::Text:: *) -(*Now comes the tensor decomposition. Notice that although in the BMHV scheme the external momenta live in 4 dimensions, we do the computation with D-dimensional external momenta. This is fine, since at the end we can send them to 4 dimensions to obtain the physical result.*) - - -ampDotted3=TID[ampDotted2,l]//ToPaVe[#,l]&//EpsEvaluate - - -(* ::Text:: *) -(*The explicit values for the PaVe functions B0 and C0 can be obtained e.g. from H. Patel's Package-X. Here we just insert the known results. The *) -(*C0 function is finite here, so because of the prefactor (D-4) it gives no contribution in the D->4 limit.*) - - -loopInts={B0[FCI@SPD[p_,p_],0,0]:>1/(16 Epsilon \[Pi]^4)-(-2+EulerGamma)/(16 \[Pi]^4)+Log[-((4 \[Pi] ScaleMu^2)/Pair[Momentum[p,D],Momentum[p,D]])]/(16 \[Pi]^4), -B0[FCI[SPD[p,p]+2SPD[p,k]+SPD[k,k]],0,0]:>B0[FCI[SPD[k+p,k+p]],0,0], -(D-4)ExpandScalarProduct[C0[SPD[k],SPD[p],SPD[k+p],0,0,0]]->0} - - -(* ::Text:: *) -(*Now we insert the explicit values, convert the external momenta to 4 dimensions and expand in Epsilon*) - - -abjRes=Series[ChangeDimension[(ampDotted3//.loopInts),4]/.D->4-2Epsilon,{Epsilon,0,0}]//Normal - - -(* ::Text:: *) -(*The result should be twice Eq. 19.59 in Peskin and Schroeder*) - - -abjPeskin = SMP["e"]^2/(4 Pi^2)LC[al,la,be,nu]FV[k,al]FV[p,be]//Contract//FCI; -Print["Check with Peskin and Schroeder, Eq 19.59: ", If[(abjRes-2*abjPeskin)===0, - "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QED/QEDBhabhaScatteringTree.m b/FeynCalc/Examples/QED/QEDBhabhaScatteringTree.m deleted file mode 100644 index 5036dbb34..000000000 --- a/FeynCalc/Examples/QED/QEDBhabhaScatteringTree.m +++ /dev/null @@ -1,68 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDBhabhaScatteringTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for Bhabha - scattering in QED at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for Bhabha scattering in QED at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsBhabha = InsertFields[topBhabha, {F[2, {1}], -F[2, {1}]} -> - {F[ 2, {1}], -F[2, {1}]}, InsertionLevel -> {Classes}, - Model -> "SM", ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsBhabha, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None,ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampBhabha=FCFAConvert[CreateFeynAmp[diagsBhabha, Truncated -> False], -IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4,List->False, SMP->True] - - -(* ::Section:: *) -(*Unpolarized process e^- e^+ -> e^- e^+ *) - - -SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_e"], SMP["m_e"], SMP["m_e"]]; -sqAmpBhabha = - (ampBhabha (ComplexConjugate[ampBhabha]//FCRenameDummyIndices))//PropagatorDenominatorExplicit// - Contract//FermionSpinSum[#, ExtraFactor -> 1/2^2] & //ReplaceAll[#, DiracTrace :> Tr]&//Contract//Simplify - - -masslessSqAmpBhabha = (sqAmpBhabha /. {SMP["m_e"] -> 0})//Simplify - - -masslessSqAmpBhabhaLiterature = -(2 SMP["e"]^4 (s^2+u^2)/t^2 + 4 SMP["e"]^4 u^2/(s t) + 2 SMP["e"]^4 (t^2+u^2)/s^2); -Print["Check with the known result: ", - If[Simplify[(masslessSqAmpBhabhaLiterature-masslessSqAmpBhabha)]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QED/QEDComptonScatteringTree.m b/FeynCalc/Examples/QED/QEDComptonScatteringTree.m deleted file mode 100644 index ae2d9eda1..000000000 --- a/FeynCalc/Examples/QED/QEDComptonScatteringTree.m +++ /dev/null @@ -1,70 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDComptonScatteringTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for Compton - scattering in QED at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for Compton scattering in QED at tree level"]; -]; -$LoadFeynArts= True; -< 2]; -diagsCompton = InsertFields[topCompton, {F[2, {1}], V[1]} -> - {F[2, {1}], V[1]}, InsertionLevel -> {Classes}, - Model -> "SM", ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsCompton, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None, -ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampCompton=FCFAConvert[CreateFeynAmp[diagsCompton, Truncated -> False], -IncomingMomenta->{p1,k1},OutgoingMomenta->{p2,k2},TransversePolarizationVectors->{k1,k2}, -UndoChiralSplittings->True,ChangeDimension->4,List->False, SMP->True] - - -(* ::Section:: *) -(*Unpolarized process e^- gamma -> e^- gamma *) - - -SetMandelstam[s, t, u, p1, k1, -p2, -k2, SMP["m_e"], 0, SMP["m_e"], 0]; -sqAmpCompton = (ampCompton (ComplexConjugate[ampCompton]//FCRenameDummyIndices))// - PropagatorDenominatorExplicit//Expand//DoPolarizationSums[#,k1,0,ExtraFactor -> - 1/2]&//DoPolarizationSums[#,k2,0]&//Contract//FermionSpinSum[#, ExtraFactor -> 1/2]&// - ReplaceAll[#, DiracTrace :> Tr] & // Contract//Simplify//TrickMandelstam[#,{s,t,u,2SMP["m_e"]^2}]&//Simplify - - -sqAmpComptonPeskin = (2SMP["e"]^4(SP[p1,k2]/SP[p1,k1]+SP[p1,k1]/SP[p1,k2]+ - 2SMP["m_e"]^2 (1/SP[p1,k1]-1/SP[p1,k2])+SMP["m_e"]^4 (1/SP[p1,k1]-1/SP[p1,k2])^2))//FCI//Simplify; -Print["Check with Peskin and Schroeder, Eq 5.87: ", If[(sqAmpComptonPeskin-sqAmpCompton)===0, - "CORRECT.", "!!! WRONG !!!"]]; - - -masslessSqAmpCompton = (sqAmpCompton /. {SMP["m_e"] -> 0})//Simplify diff --git a/FeynCalc/Examples/QED/QEDElectronGMinusTwoOneLoop.m b/FeynCalc/Examples/QED/QEDElectronGMinusTwoOneLoop.m deleted file mode 100644 index 447b81e99..000000000 --- a/FeynCalc/Examples/QED/QEDElectronGMinusTwoOneLoop.m +++ /dev/null @@ -1,111 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDElectronGMinusTwoOneLoop *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the electron's g-2 in QED at 1-loop *) - -(* ------------------------------------------------------------------------ *) - - -(* ::Section:: *) -(*Electron's g-2 in QED*) - - -(* ::Subsection:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the electron's g-2 in QED at 1-loop"]; -]; -$LoadFeynArts=True; -<< FeynCalc` -$FAVerbose=0; - - -(* ::Subsection:: *) -(*Generate Feynman diagrams*) - - -topVertex = CreateTopologies[1, 1 -> 2,ExcludeTopologies -> {Tadpoles,WFCorrections}]; -diagsVertex = InsertFields[topVertex, {F[2, {1}]} -> - {V[1],F[2, {1}]},InsertionLevel -> {Classes},ExcludeParticles -> {S[1], S[2],S[3],V[3], V[2]}]; -Paint[diagsVertex, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -ampVertex=FCFAConvert[CreateFeynAmp[diagsVertex,Truncated -> False,PreFactor->-1],IncomingMomenta->{p1}, -OutgoingMomenta->{k,p2},LoopMomenta->{q},UndoChiralSplittings->True,SMP->True,ChangeDimension->D, -List->False,FinalSubstitutions->{SMP["m_e"]->ME}]/.k->p1-p2/.q->q+p1 - - -(* ::Subsection:: *) -(*Set up the kinematics*) - - -FCClearScalarProducts[]; -ScalarProduct[p1,p1]=ME^2; -ScalarProduct[p2,p2]=ME^2; -ScalarProduct[k,k]=0; -ScalarProduct[p1,p2]=ME^2; - - -(* ::Subsection:: *) -(*Compute the diagrams*) - - -ampVertex1=ampVertex//ReplaceAll[#,Pair[Momentum[Polarization[___],___],___]:>1]&//Contract - - -(* ::Text:: *) -(*Now we simplify the Dirac algebra and reduce our tensor loop integrals into scalar ones.*) - - -ampVertex2=OneLoopSimplify[ampVertex1,q]//Collect2[#,Spinor]& - - -(* ::Text:: *) -(*Remember that to extract F2 (0) we need to look only at the piece proportional to (p1+p2)^mu. So let us drop the g^mu -piece*) - - -ampVertex3=ampVertex2//ReplaceAll[#,FCI[GAD[Lor1]]:>0]&//DotSimplify - - -(* ::Text:: *) -(*The explicit values for the PaVe functions C1, C11 and C12 can be obtained e.g. from H. Patel's Package-X. Here we just insert the known results.*) - - -ampVertex4=ampVertex3/.{PaVe[1,{ME^2,0,ME^2},{0,ME^2,ME^2},OptionsPattern[]]->1/(32Pi^4 ME^2), -PaVe[1,1,{ME^2,0,ME^2},{0,ME^2,ME^2},OptionsPattern[]]->-(1/(96Pi^4 ME^2)), -PaVe[1,2,{ME^2,0,ME^2},{0,ME^2,ME^2},OptionsPattern[]]->-(1/(192Pi^4 ME^2))} - - -(* ::Text:: *) -(*As expected, F2 (0) is free of any divergences. So we can safely do the limit D ->4*) - - -ampVertex5=ampVertex4//ChangeDimension[#,4]&//ReplaceAll[#,D->4]& - - -(* ::Text:: *) -(*What we obtained so far is nothing else than $\frac{i e}{2 m_e} (p_1+p_2)^\mu F_2 (0) \bar{u}(p_2) u(p_1)$*) -(*Dividing by the numerical prefactor and substituting $e^2 = 4\pi^2 \alpha$ yields*) - - -res=(ampVertex5/((I SMP["e"])/(2 ME)))//ReplaceAll [#,{SMP["e"]^2->AlphaFS 4\[Pi],Spinor[__].Spinor[__]:>1,FCI[FV[p1,_]+FV[p2,_]]:>1}]& - - -(* ::Text:: *) -(*The result should agree with the known value for F2(0)*) - - -resLit = AlphaFS/(2Pi); -Print["Check with the known result: ", If[(res-resLit)===0, - "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QED/QEDElectronMuonScatteringTree.m b/FeynCalc/Examples/QED/QEDElectronMuonScatteringTree.m deleted file mode 100644 index 21e62d95a..000000000 --- a/FeynCalc/Examples/QED/QEDElectronMuonScatteringTree.m +++ /dev/null @@ -1,80 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDElectronMuonScatteringTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for electron - muon scattering in QED at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for electron muon scattering in QED at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsElMuScat = InsertFields[topElMuScat, {F[2, {1}], F[2, {2}]} -> - {F[2, {1}], F[2, {2}]}, InsertionLevel -> {Classes}, - Model -> "SM", ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsElMuScat, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampElMuScat = FCFAConvert[CreateFeynAmp[diagsElMuScat, Truncated -> False], -IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2},UndoChiralSplittings->True, -ChangeDimension->4,List->False,SMP->True] - - -(* ::Section:: *) -(*Unpolarized process e^- mu^- -> e^- mu^-*) - - -SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_mu"], SMP["m_e"], SMP["m_mu"]]; -sqAmpElMuScat = (ampElMuScat (ComplexConjugate[ampElMuScat]//FCRenameDummyIndices))// - PropagatorDenominatorExplicit//Contract//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// - ReplaceAll[#, DiracTrace :> Tr]&//Contract//Simplify - - - -masslessElectronsSqAmpElMuScat = (sqAmpElMuScat /. {SMP["m_e"] -> 0})//Simplify - - -masslessElectronsSqAmpElMuScatPeskin= (8SMP["e"]^4 (SP[p1,k2]SP[p2,k1]+SP[p1,p2]SP[k1,k2]- - SMP["m_mu"]^2 SP[p1,k1]))/(SP[k1-p1])^2// ReplaceAll[#,SMP["m_e"]->0]&//FCI//ExpandScalarProduct//Simplify; -Print["Check with Peskin and Schroeder, Eq 5.61: ", - If[(masslessElectronsSqAmpElMuScatPeskin-masslessElectronsSqAmpElMuScat)===0, - "CORRECT.", "!!! WRONG !!!"]]; - - -masslessElectronsMuonsSqAmpElMuScat = (masslessElectronsSqAmpElMuScat /. {SMP["m_mu"] -> 0})//Simplify - - -mmasslessElectronsMuonsSqAmpElMuScatPeskin=((8SMP["e"]^4/t^2)((s/2)^2+(u/2)^2))//Simplify; -Print["Check with Peskin and Schroeder, Eq 5.71: ", - If[(mmasslessElectronsMuonsSqAmpElMuScatPeskin-masslessElectronsMuonsSqAmpElMuScat)===0, - "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QED/QEDMoellerScatteringTree.m b/FeynCalc/Examples/QED/QEDMoellerScatteringTree.m deleted file mode 100644 index a8879cef9..000000000 --- a/FeynCalc/Examples/QED/QEDMoellerScatteringTree.m +++ /dev/null @@ -1,69 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDMoellerScatteringTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for Moeller - scattering in QED at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for Moeller scattering in QED at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts= True; -< 2]; -diagsMoeller = InsertFields[topMoeller, {F[2, {1}], F[2, {1}]} -> {F[ - 2, {1}], F[2, {1}]}, InsertionLevel -> {Classes}, Model -> "SM", - ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsMoeller, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None,ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampMoeller=FCFAConvert[CreateFeynAmp[diagsMoeller, Truncated -> False], -IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4,List->False,SMP->True] - - -(* ::Section:: *) -(*Unpolarized process e^- e^- -> e^- e^- *) - - -SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_e"], SMP["m_e"], SMP["m_e"]]; -sqAmpMoeller = - (ampMoeller (ComplexConjugate[ampMoeller]//FCRenameDummyIndices))// - PropagatorDenominatorExplicit//Contract//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// - ReplaceAll[#, DiracTrace :> Tr] & // Contract//Simplify - - -masslessSqAmpMoeller = (sqAmpMoeller /. {SMP["m_e"] -> 0})//Simplify - - -masslessSqAmpMoellerLiterature = -2 SMP["e"]^4 (s^2/t^2+ u^2/t^2 + s^2/u^2 + t^2/u^2 ) + 4 SMP["e"]^4 s^2/(t u); -Print["Check with the known result: ", - If[Simplify[(masslessSqAmpMoellerLiterature-masslessSqAmpMoeller)]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QED/QEDMuonProductionTree.m b/FeynCalc/Examples/QED/QEDMuonProductionTree.m deleted file mode 100644 index 2f0c562ca..000000000 --- a/FeynCalc/Examples/QED/QEDMuonProductionTree.m +++ /dev/null @@ -1,100 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDMuonProductionTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for muon - production in QED at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for muon production in QED at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts=True; -< 2]; -diagsMuonProd = - InsertFields[topMuonProd, {F[2, {1}], -F[2, {1}]} -> {F[2, - {2}], -F[2, {2}]}, InsertionLevel -> {Classes}, Model -> "SM", - ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsMuonProd, ColumnsXRows -> {1, 1}, Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampMuonProd = FCFAConvert[CreateFeynAmp[diagsMuonProd, Truncated -> False], -IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4,List->False,SMP->True]; - - -(* ::Section:: *) -(*Unpolarized process e^- e^+ -> mu^- mu^+ *) - - -$ProcessID - - -SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_e"], SMP["m_mu"], SMP["m_mu"]]; -sqAmpMuonProd = (ampMuonProd (ComplexConjugate[ampMuonProd]//FCRenameDummyIndices))// - PropagatorDenominatorExplicit//Contract//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// - ReplaceAll[#, DiracTrace :> Tr] &//Contract//Simplify - - -masslessElectronsSqAmpMuonProd = (sqAmpMuonProd /. {SMP["m_e"] -> 0})//Simplify - - -masslessElectronsMuonsSqAmpMuonProdPeskin = (8SMP["e"]^4 (SP[p1,k1]SP[p2,k2]+SP[p1,k2]SP[p2,k1]+SMP["m_mu"]^2 SP[p1,p2]))/(SP[p1+p2])^2// - ReplaceAll[#,SMP["m_e"]->0]&//ExpandScalarProduct//Simplify; -Print["Check with Peskin and Schroeder, Eq 5.10: ", - If[(masslessElectronsMuonsSqAmpMuonProdPeskin-masslessElectronsSqAmpMuonProd)===0, - "CORRECT.", "!!! WRONG !!!"]]; - - -masslessElectronsMuonsSqAmpMuonProd = (masslessElectronsSqAmpMuonProd /. {SMP["m_mu"] -> 0})//Simplify - - -masslessElectronsMuonsSqAmpMuonProdPeskinMandelstam=((8SMP["e"]^4/s^2)((t/2)^2+(u/2)^2))//Simplify; -Print["Check with Peskin and Schroeder, Eq 5.70: ", - If[(masslessElectronsMuonsSqAmpMuonProdPeskinMandelstam-masslessElectronsMuonsSqAmpMuonProd)===0, "CORRECT.", "!!! WRONG !!!"]]; - - -(* ::Section:: *) -(*Polarized process e_R^- e_L^+ -> mu_R^- mu_L^+ *) - - -ampMuonProdElRPosLMuRAntiMuL=ampMuonProd/.{Spinor[-Momentum[k2],SMP["m_mu"],1]->GA[6].Spinor[-Momentum[k2],SMP["m_mu"],1], - Spinor[Momentum[p1],SMP["m_e"],1]->GA[6].Spinor[Momentum[p1],SMP["m_e"],1]} - - -sqAmpMuonProdElRPosLMuRAntiMuL = (((ampMuonProdElRPosLMuRAntiMuL (ComplexConjugate[ampMuonProdElRPosLMuRAntiMuL]// - FCRenameDummyIndices))//PropagatorDenominatorExplicit//Contract//FermionSpinSum// - ReplaceAll[#, DiracTrace :> Tr] &//Contract)/.{SMP["m_e"]->0,SMP["m_mu"]->0})//Simplify - - -sqAmpMuonProdElRPosLMuRAntiMuLPeskin=(16SMP["e"]^4 (SP[p1,k2]SP[p2,k1]))/(SP[p1+p2])^2// - ReplaceAll[#,{SMP["m_e"]->0,SMP["m_mu"]->0}]&//FCI//ExpandScalarProduct//Simplify; -Print["Check with Peskin and Schroeder, Eq 5.21: ", - If[(sqAmpMuonProdElRPosLMuRAntiMuLPeskin-sqAmpMuonProdElRPosLMuRAntiMuL)===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QED/QEDOnePhotonTadpoleOneLoop.m b/FeynCalc/Examples/QED/QEDOnePhotonTadpoleOneLoop.m deleted file mode 100644 index e6d9ea8d1..000000000 --- a/FeynCalc/Examples/QED/QEDOnePhotonTadpoleOneLoop.m +++ /dev/null @@ -1,68 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDOnePhotonTadpoleOneLoop *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the 1-photon tadpole diagram in QED at 1-loop *) - -(* ------------------------------------------------------------------------ *) - - -(* ::Section:: *) -(*The 1-photon tadpole in QED*) - - -(* ::Subsection:: *) -(*Load FeynCalc, FeynArts and Tarcer*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the 1-photon tadpole diagram in QED at 1-loop"]; -]; -$LoadFeynArts=True; -<< FeynCalc` -$FAVerbose=0; - - -(* ::Subsection:: *) -(*Generate Feynman diagrams*) - - -Paint[diags = InsertFields[CreateTopologies[1, 1 -> 0 ], {V[1]} -> {}, - InsertionLevel -> {Particles}, GenericModel -> "Lorentz", - ExcludeParticles->{S[1],S[2],S[3],V[2],V[3],F[3],F[4], - U[1],U[2],U[3],U[4],F[2,{2}],F[2,{3}]}], ColumnsXRows -> {1, 1}, - SheetHeader -> False, Numbering -> None,SheetHeader->None,ImageSize->{256,256}]; - - -(* ::Text:: *) -(*Notice that we choose the prefactor to be 1/(2^D)*(Pi)^(D/2). This is because the 1/Pi^(D/2) piece of the general prefactor 1/(2Pi)^D goes into the definition of the loop integrals using Tarcer's notation.*) - - -amps = FCFAConvert[CreateFeynAmp[diags, Truncated -> True,GaugeRules->{},PreFactor->1/((2^D)*(Pi)^(D/2))], -IncomingMomenta->{k},LoopMomenta->{q},UndoChiralSplittings->True,ChangeDimension->D,List->False,SMP->True]; - - -(* ::Text:: *) -(*We obtain three tadpole diagrams. Having performed the Dirac algebra we clearly see that these diagrams must vanish because the loop integrals are antisymmetric under q^mu -> - q^mu.*) - - -ampsEval=(ChangeDimension[amps,D]//Contract//DiracSimplify)/.{DiracTrace->Tr} - - -(* ::Text:: *) -(*FeynCalc's tensor integral decomposition function TID can recognize that.*) - - -onePhotonTadpoleFinal = ampsEval//TID[#,q]& - - -Print["The 1-photon tadpole diagrams in QED vanish: ", - If[Simplify[onePhotonTadpoleFinal]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QED/QEDPairAnnihilationTree.m b/FeynCalc/Examples/QED/QEDPairAnnihilationTree.m deleted file mode 100644 index c39c90754..000000000 --- a/FeynCalc/Examples/QED/QEDPairAnnihilationTree.m +++ /dev/null @@ -1,70 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDPairAnnihilationTree *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the matrix element squared for electron - postiron annihilation into two photons in QED at tree level *) - -(* ------------------------------------------------------------------------ *) - - - -(* ::Section:: *) -(*Load FeynCalc and FeynArts*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the matrix element squared for electron postiron annihilation into two photons in QED at tree level"]; -]; -If[$Notebooks === False, $FeynCalcStartupMessages = False]; -$LoadFeynArts=True; -< 2]; -diagsPairAnnihilation = InsertFields[topPairAnnihilation, {F[2, {1}], - -F[2, {1}]} -> {V[1], V[1]}, InsertionLevel -> {Classes}, - Model -> "SM", ExcludeParticles -> {S[1], S[2], V[2]}]; -Paint[diagsPairAnnihilation, ColumnsXRows -> {2, 1}, Numbering -> None,SheetHeader->None,ImageSize->{512,256}]; - - -(* ::Section:: *) -(*Obtain corresponding amplitudes*) - - -ampPairAnnihilation=FCFAConvert[CreateFeynAmp[diagsPairAnnihilation, Truncated -> False], -IncomingMomenta->{p1,p2},OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4,List->False,SMP->True] - - -(* ::Section:: *) -(*Unpolarized process e^+ e^- -> 2 gamma *) - - -SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_e"], 0, 0]; -sqAmpPairAnnihilation = (ampPairAnnihilation (ComplexConjugate[ampPairAnnihilation]// - FCRenameDummyIndices))//PropagatorDenominatorExplicit//Expand//DoPolarizationSums[#,k1, - 0]&//DoPolarizationSums[#,k2,0]&//Contract//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// - ReplaceAll[#, DiracTrace -> Tr] & // Contract//Simplify//TrickMandelstam[#, - {s,t,u,2SMP["m_e"]^2}]&//Simplify - - -sqAmpPairAnnihilationPeskin = (2SMP["e"]^4(SP[p1,k2]/SP[p1,k1]+SP[p1,k1]/SP[p1,k2]+ - 2SMP["m_e"]^2 (1/SP[p1,k1]+1/SP[p1,k2])-SMP["m_e"]^4 (1/SP[p1,k1]+1/SP[p1,k2])^2))//FCI//Simplify; -Print["Check with Peskin and Schroeder, Eq 5.105: ", - If[(sqAmpPairAnnihilationPeskin-sqAmpPairAnnihilation)===0, "CORRECT.", "!!! WRONG !!!"]]; - - -sqMasslessAmpPairAnnihilation=sqAmpPairAnnihilation//ReplaceAll[#,SMP["m_e"]->0]& diff --git a/FeynCalc/Examples/QED/QEDThreePhotonDiagramsOneLoop.m b/FeynCalc/Examples/QED/QEDThreePhotonDiagramsOneLoop.m deleted file mode 100644 index 08da62e44..000000000 --- a/FeynCalc/Examples/QED/QEDThreePhotonDiagramsOneLoop.m +++ /dev/null @@ -1,62 +0,0 @@ -(* ::Package:: *) - -(* :Title: QEDThreePhotonDiagramsOneLoop *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Computation of the 3-photon diagrams in QED at 1-loop *) - -(* ------------------------------------------------------------------------ *) - - -(* ::Section:: *) -(*The 3-photon diagrams in QED at 1-loop*) - - -(* ::Subsection:: *) -(*Load FeynCalc, FeynArts and Tarcer*) - - -If[ $FrontEnd === Null, - $FeynCalcStartupMessages = False; - Print["Computation of the 3-photon diagrams in QED at 1-loop"]; -]; -$LoadFeynArts=True; -<< FeynCalc` -$FAVerbose=0; - - -(* ::Subsection:: *) -(*Generate Feynman diagrams*) - - -Paint[diags = InsertFields[CreateTopologies[1, 1 -> 2 ], {V[1]} -> {V[1],V[1]}, - InsertionLevel -> {Particles}, GenericModel -> "Lorentz", - Model->"SMQCD",ExcludeParticles->{S[1],S[2],S[3],V[2],V[3],F[3],F[4], - U[1],U[2],U[3],U[4],F[2,{2}],F[2,{3}]}], ColumnsXRows -> {2, 1}, - SheetHeader -> False, Numbering -> None,ImageSize->{512,256}]; - - -(* ::Text:: *) -(*Notice that we choose the prefactor to be 1/(2^D)*(Pi)^(D/2). This is because the 1/Pi^(D/2) piece of the general prefactor 1/(2Pi)^D goes into the definition of the loop integrals using Tarcer's notation.*) - - -amps = FCFAConvert[CreateFeynAmp[diags, Truncated -> True,GaugeRules->{},PreFactor->1/((2^D)*(Pi)^(D/2))], -IncomingMomenta->{k1},OutgoingMomenta->{k2,k3},LoopMomenta->{q},UndoChiralSplittings->True,ChangeDimension->D,List->False,SMP->True]; - - -(* ::Text:: *) -(*We obtain two triangle diagrams. The sum vanishes because the second diagram is the negative*) -(*of the first one.*) - - -threePhotonFinal=Simplify[(amps/.{DiracTrace->Tr})] - - -Print["The 3-photon diagrams in QED vanish: ", - If[Simplify[threePhotonFinal]===0, "CORRECT.", "!!! WRONG !!!"]]; diff --git a/FeynCalc/Examples/QED/Tree/ElAel-ElAel.m b/FeynCalc/Examples/QED/Tree/ElAel-ElAel.m new file mode 100644 index 000000000..b845e180f --- /dev/null +++ b/FeynCalc/Examples/QED/Tree/ElAel-ElAel.m @@ -0,0 +1,103 @@ +(* ::Package:: *) + +(* :Title: ElAel-ElAel *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Ael -> El Ael, QED, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Bhabha scattering*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Ael -> El Ael, QED, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], -F[2, {1}]} -> + {F[ 2, {1}], -F[2, {1}]}, InsertionLevel -> {Classes}, + Restrictions->QEDOnly]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, + SMP["m_e"], SMP["m_e"], SMP["m_e"], SMP["m_e"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_e"] -> 0}]&// + Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = (2 SMP["e"]^4 (s^2+u^2)/t^2 + +4 SMP["e"]^4 u^2/(s t) + 2 SMP["e"]^4 (t^2+u^2)/s^2); +FCCompareResults[ampSquaredMassless[0],knownResult, +Text->{"\tCheck the final result:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/Tree/ElAel-GaGa.m b/FeynCalc/Examples/QED/Tree/ElAel-GaGa.m new file mode 100644 index 000000000..690d5425e --- /dev/null +++ b/FeynCalc/Examples/QED/Tree/ElAel-GaGa.m @@ -0,0 +1,104 @@ +(* ::Package:: *) + +(* :Title: ElAel-GaGa *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Ael -> Ga Ga, QED, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Pair annihilation*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Ael -> Ga Ga, QED, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], -F[2, {1}]} -> + {V[1], V[1]}, InsertionLevel -> {Classes}, + Restrictions->QEDOnly]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k1,k2}, List->False, SMP->True, + Contract->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_e"], 0, 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit// + DoPolarizationSums[#,k1,0]&//DoPolarizationSums[#,k2,0]&// + FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify// + TrickMandelstam[#,{s,t,u,2SMP["m_e"]^2}]&//Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = (2SMP["e"]^4(SP[p1,k2]/SP[p1,k1]+SP[p1,k1]/SP[p1,k2]+ + 2SMP["m_e"]^2 (1/SP[p1,k1]+1/SP[p1,k2])- + SMP["m_e"]^4 (1/SP[p1,k1]+1/SP[p1,k2])^2)); +FCCompareResults[ampSquared[0],knownResult, +Text->{"\tCompare to Peskin and Schroeder, An Introduction to QFT, \ +Eq 5.105:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/Tree/ElAel-MuAmu.m b/FeynCalc/Examples/QED/Tree/ElAel-MuAmu.m new file mode 100644 index 000000000..7e5be1906 --- /dev/null +++ b/FeynCalc/Examples/QED/Tree/ElAel-MuAmu.m @@ -0,0 +1,182 @@ +(* ::Package:: *) + +(* :Title: ElAel-MuAmu *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Ael -> Mu Amu, QED, total cross section, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Muon production*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Ael -> Mu Amu, QED, total cross section, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], -F[2, {1}]} -> + {F[2,{2}], -F[2, {2}]}, InsertionLevel -> {Classes}, + Restrictions->QEDOnly]; + +Paint[diags, ColumnsXRows -> {1, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True] + + +(* ::Text:: *) +(*Polarized production: the particles are right-handed, while the antiparticles are left-handed*) + + +ampPolarized[0] = amp[0]/.{ + Spinor[-Momentum[k2], r__]:> + GA[6].Spinor[-Momentum[k2],r], + Spinor[Momentum[k1], r__]:> + Spinor[Momentum[k1], r].GA[7], + Spinor[Momentum[p1],r__]:> + GA[6].Spinor[Momentum[p1],r], + Spinor[-Momentum[p2],r__]:> + Spinor[Momentum[p2],r].GA[7] +} + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, SMP["m_e"], SMP["m_e"], + SMP["m_mu"], SMP["m_mu"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//Simplify + + +ampSquaredPolarized[0] = + (ampPolarized[0] (ComplexConjugate[ampPolarized[0]]))// + FeynAmpDenominatorExplicit//FermionSpinSum//DiracSimplify//Simplify + + +ampSquaredMassless1[0] = ampSquared[0]//ReplaceAll[#,{ + SMP["m_e"] -> 0}]& + + +ampSquaredMassless2[0] = ampSquared[0]//ReplaceAll[#,{ + SMP["m_e"] -> 0,SMP["m_mu"] -> 0}]&//Simplify + + +ampSquaredPolarizedMassless[0] = ampSquaredPolarized[0]//ReplaceAll[#,{ + SMP["m_e"] -> 0,SMP["m_mu"] -> 0}]&//Simplify + + +(* ::Section:: *) +(*Total cross-section*) + + +(* ::Text:: *) +(*The differential cross-section d sigma/ d Omega is given by*) + + +prefac1=1/(64 Pi^2 s); + + +integral1=(Factor[ampSquaredMassless2[0]/.{t->-s/2(1-Cos[Th]),u->-s/2(1+Cos[Th]), +SMP["e"]^4->(4 Pi SMP["alpha_fs"])^2}]) + + +diffXSection1= prefac1 integral1 + + +(* ::Text:: *) +(*The differential cross-section d sigma/ d t d phi is given by*) + + +prefac2=1/(128 Pi^2 s) + + +integral2=Simplify[ampSquaredMassless2[0]/(s/4) /. + {u-> -s-t,SMP["e"]^4->(4 Pi SMP["alpha_fs"])^2}] + + +diffXSection2=prefac2 integral2 + + +(* ::Text:: *) +(*The total cross-section. We see that integrating both expressions gives the same result*) + + +2 Pi Integrate[diffXSection1 Sin[Th],{Th,0,Pi}] + + +crossSectionTotal=2 Pi Integrate[diffXSection2,{t,-s,0}] + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (8SMP["e"]^4 (SP[p1,k1]SP[p2,k2]+SP[p1,k2]SP[p2,k1]+ + SMP["m_mu"]^2 SP[p1,p2]))/(SP[p1+p2])^2//ExpandScalarProduct// + ReplaceAll[#,SMP["m_e"]->0]&, + (16SMP["e"]^4 (SP[p1,k2]SP[p2,k1]))/(SP[p1+p2])^2, + ((8SMP["e"]^4/s^2)((t/2)^2+(u/2)^2)),(4*Pi*SMP["alpha_fs"]^2)/(3*s) +}; +FCCompareResults[{ampSquaredMassless1[0],ampSquaredPolarized[0], +ampSquaredMassless2[0],crossSectionTotal},knownResults, +Text->{"\tCompare to Peskin and Schroeder, An Introduction to QFT, \ +Eqs 5.10, 5.21, 5.70 and to Field, \ +Applications of Perturbative QCD, Eq. 2.1.14", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/Tree/ElEl-ElEl.m b/FeynCalc/Examples/QED/Tree/ElEl-ElEl.m new file mode 100644 index 000000000..54f73124a --- /dev/null +++ b/FeynCalc/Examples/QED/Tree/ElEl-ElEl.m @@ -0,0 +1,104 @@ +(* ::Package:: *) + +(* :Title: ElEll-ElEl *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El El -> El El, QED, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Moeller scattering*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El El -> El El, QED, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], F[2, {1}]} -> + {F[2, {1}], F[2, {1}]}, InsertionLevel -> {Classes}, + Restrictions->QEDOnly]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, + SMP["m_e"], SMP["m_e"], SMP["m_e"], SMP["m_e"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit// + FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_e"] -> 0}]&// + Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = 2 SMP["e"]^4 (s^2/t^2+ u^2/t^2+s^2/u^2+t^2/u^2)+ + 4 SMP["e"]^4 s^2/(t u); +FCCompareResults[ampSquaredMassless[0],knownResult, +Text->{"\tCheck the final result:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/Tree/ElGa-ElGa.m b/FeynCalc/Examples/QED/Tree/ElGa-ElGa.m new file mode 100644 index 000000000..9c564bcfd --- /dev/null +++ b/FeynCalc/Examples/QED/Tree/ElGa-ElGa.m @@ -0,0 +1,103 @@ +(* ::Package:: *) + +(* :Title: ElGa-ElGa *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Ga -> El Ga, QED, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Compton scattering*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Ga -> El Ga, QED, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], V[1]} -> + {F[2, {1}], V[1]}, InsertionLevel -> {Classes}, + Restrictions->QEDOnly]; + +Paint[diags, ColumnsXRows -> {2, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{512,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,k1}, + OutgoingMomenta->{p2,k2},UndoChiralSplittings->True,ChangeDimension->4, + TransversePolarizationVectors->{k1,k2}, List->False, SMP->True, + Contract->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, k1, -p2, -k2, SMP["m_e"], 0, SMP["m_e"], 0]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit// + DoPolarizationSums[#,k1,0]&//DoPolarizationSums[#,k2,0]&// + FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//TrickMandelstam[#,{s,t,u,2SMP["m_e"]^2}]&//Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +knownResult = (2SMP["e"]^4(SP[p1,k2]/SP[p1,k1]+ + SP[p1,k1]/SP[p1,k2]+ 2SMP["m_e"]^2 (1/SP[p1,k1]-1/SP[p1,k2])+ + SMP["m_e"]^4 (1/SP[p1,k1]-1/SP[p1,k2])^2)); +FCCompareResults[ampSquared[0],knownResult, +Text->{"\tCompare to Peskin and Schroeder, An Introduction to QFT, \ +Eq 5.87:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/Tree/ElMu-ElMu.m b/FeynCalc/Examples/QED/Tree/ElMu-ElMu.m new file mode 100644 index 000000000..d5ff5cd78 --- /dev/null +++ b/FeynCalc/Examples/QED/Tree/ElMu-ElMu.m @@ -0,0 +1,112 @@ +(* ::Package:: *) + +(* :Title: ElMu-ElMu *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: El Mu -> El Mu, QED, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Electron-muon scattering*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="El Mu -> El Mu, QED, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {F[2, {1}], F[2, {2}]} -> + {F[ 2, {1}], F[2, {2}]}, InsertionLevel -> {Classes}, + Restrictions->QEDOnly]; + +Paint[diags, ColumnsXRows -> {1, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p1,p2}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SetMandelstam[s, t, u, p1, p2, -k1, -k2, + SMP["m_e"], SMP["m_mu"], SMP["m_e"], SMP["m_mu"]]; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//FermionSpinSum[#, ExtraFactor -> 1/2^2]&// + DiracSimplify//Simplify + + +ampSquaredMassless1[0] = ampSquared[0]//ReplaceAll[#,{SMP["m_e"] -> 0}]&// + Simplify + + +ampSquaredMassless2[0] = ampSquared[0]//ReplaceAll[#,{ + SMP["m_e"] -> 0,SMP["m_mu"] -> 0}]&//Simplify + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + (8SMP["e"]^4 (SP[p1,k2]SP[p2,k1]+SP[p1,p2]SP[k1,k2]- + SMP["m_mu"]^2 SP[p1,k1]))/(SP[k1-p1])^2//ExpandScalarProduct// + ReplaceAll[#,SMP["m_e"]->0]&, + ((8SMP["e"]^4/t^2)((s/2)^2+(u/2)^2)) +}; +FCCompareResults[{ampSquaredMassless1[0],ampSquaredMassless2[0]},knownResults, +Text->{"\tCompare to Peskin and Schroeder, An Introduction to QFT, \ +Eqs 5.61 and 5.71:", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}] +Print["\tCPU Time used: ", Round[N[TimeUsed[],3],0.001], " s."]; diff --git a/FeynCalc/Examples/QED/Tree/Ga-MuAmu.m b/FeynCalc/Examples/QED/Tree/Ga-MuAmu.m new file mode 100644 index 000000000..b98112e4d --- /dev/null +++ b/FeynCalc/Examples/QED/Tree/Ga-MuAmu.m @@ -0,0 +1,128 @@ +(* ::Package:: *) + +(* :Title: Ga-MuAmu *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Ga^* -> Mu Amu, QED, total decay rate, tree *) + +(* ------------------------------------------------------------------------ *) + + + +(* ::Title:: *) +(*Muon production from the decay of a*) +(*virtual photon*) + + +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + + +description="Ga^* -> Mu Amu, QED, total decay rate, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; +If[ $Notebooks === False, + $FeynCalcStartupMessages = False +]; +$LoadAddOns={"FeynArts"}; +< 2], {V[1]} -> + {F[2,{2}], -F[2, {2}]}, InsertionLevel -> {Classes}, + Restrictions->QEDOnly]; + +Paint[diags, ColumnsXRows -> {1, 1}, Numbering -> Simple, + SheetHeader->None,ImageSize->{256,256}]; + + +(* ::Section:: *) +(*Obtain the amplitude*) + + +amp[0] = FCFAConvert[CreateFeynAmp[diags], IncomingMomenta->{p}, + OutgoingMomenta->{k1,k2},UndoChiralSplittings->True,ChangeDimension->4, + List->False, SMP->True, Contract->True] + + +(* ::Section:: *) +(*Fix the kinematics*) + + +FCClearScalarProducts[]; +SP[k1]=SMP["m_mu"]^2; +SP[k2]=SMP["m_mu"]^2; +SP[k1,k2]= (QQ - SP[k1] - SP[k2])/2; + + +(* ::Section:: *) +(*Square the amplitude*) + + +ampSquared[0] = (amp[0] (ComplexConjugate[amp[0]]))// + FeynAmpDenominatorExplicit//FermionSpinSum//DiracSimplify// + DoPolarizationSums[#,p,0,VirtualBoson->True]&//Simplify + + +ampSquaredMassless[0] = ampSquared[0]//ReplaceAll[#,{ + SMP["m_mu"] -> 0}]& + + +(* ::Section:: *) +(*Total decay rate*) + + +(* ::Text:: *) +(*The differential decay rate d Gamma/ d Omega is given by*) + + +prefac=ExpandScalarProduct[1/(64 Pi^2) 1/Sqrt[(SP[k1+k2])]] + + +diffDecayRate=prefac ampSquaredMassless[0]/. +SMP["e"]^2->(4 Pi SMP["alpha_fs"]) + + +(* ::Text:: *) +(*The total decay-rate*) + + +decayRateTotal=4 Pi diffDecayRate + + +(* ::Section:: *) +(*Check the final results*) + + +knownResults = { + SMP["alpha_fs"] Sqrt[QQ] +}; +FCCompareResults[{decayRateTotal},knownResults, +Text->{"\tCompare to Field, \ +Applications of Perturbative QCD, Eq. 2.1.29", +"CORRECT.","WRONG!"}, Interrupt->{Hold[Quit[1]],Automatic}]; +Print["\tCPU Time used: ", Round[N[TimeUsed[],4],0.001], " s."]; diff --git a/FeynCalc/Examples/README.md b/FeynCalc/Examples/README.md new file mode 100644 index 000000000..3b27ad11d --- /dev/null +++ b/FeynCalc/Examples/README.md @@ -0,0 +1,285 @@ +# Examples + +This directory contains examples of interesting calculations from textbooks and papers that can be reproduced using +_FeynCalc_. + +# Available examples + +## Phi^3 + +### 1-loop level + +* Renormalization + +## Phi^4 + +### 1-loop level + +* Phi Phi -> Phi Phi +* Renormalization + +### 1-loop level + +## QED + +### Tree level + +* El Ael -> El Ael +* El Ael-> Ga Ga +* El Ael-> Mu Amu +* El El-> El El +* El Ga-> El Ga +* El Mu-> El Mu +* Ga -> Mu Amu + + +### 1-loop level + +* El -> El +* El -> Ga El +* Ga +* Ga -> Ga +* Ga -> Ga Ga +* Ga -> Ga Ga Ga Ga +* Pi -> GaGa +* Renormalization in the MS and MSbar schemes + +## QCD + +### Tree level + +* El Ael -> Q Qbar +* Ga Gl -> Q Qbar +* Ga -> Q Qbar +* Ga -> Q Qbar Gl +* Gl Gl -> Gl Gl +* Gl Gl -> Q Qbar +* Mu Amu -> Q Qbar +* Q Ga -> Gl Q +* Q Gl -> Q Gl +* Qi Qibar -> Qi Qibar +* Qi Qibar -> Qj Qjbar +* Qi Qi -> Qi Qi +* Qi Qjbar -> Qi Qjbar +* Qi Qj -> Qi Qj +* Q Qbar -> El Ael +* Q Qbar -> Ga Ga +* Q Qbar -> Ga Gl +* Q Qbar -> Gl Gl +* Q Qbar -> Mu Amu + + +### 1-loop level + +* Gh -> Gh +* Gh Gl -> Gh +* Gl -> Gl +* Gl -> Gl in the background field gauge +* Gl -> Gl Gl +* Q -> Q +* Renormalization +* Renormalization Massless + +### 2-loop level + +* Gh -> Gh + +## EW + +### Tree level + +* Anel El -> Anmu Mu +* Anel El -> Qubar Qd +* Anel El -> W W +* Anel El -> Z Z +* El Nmu -> Mu Nel +* H -> F Fbar +* H -> W W +* H -> Z Z +* Mu -> El Anel Nmu +* NleQdt -> Le Qut +* QQbar -> Z Z +* Qt -> Qb W +* Qu Qdbar -> Ael Nel +* Qutbar Qdt -> Nel Anel +* W -> El Anel +* W -> Qi Qjbar +* Z -> F Fbar + +### 1-loop level + +* H -> Gl Gl + +# Directory structure + +## Main directories + +* `QCD` - calculations in Quantum Chromodynamics (including electroweak corrections to QCD processes and Effective Field Theories of QCD) +* `EW` - calculations in Electroweak Theory (including QCD corrections to EW processes and Effective Field Theories of EW interactions) +* `QED` - calculation in Quantum Electrodynamics (including Effective Field Theories of QED) +* `FeynRules` - New _FeynRules_ models for _FeynArts_ (to generate the models and use them with _FeynArts_ you must have the [FeynRules](http://feynrules.irmp.ucl.ac.be/) package installed) +* `Misc` - miscellaneous examples that do not fit into other categories (including showcases for single _FeynCalc_ functions) + +## Subdirectories + +* `Tree` - calculations at tree level +* `OneLoop` - calculations at 1-loop level +* `TwoLoop` - calculations at 2-loop level + +# Filename structure + +Each particle interaction process is named according to the following scheme + +## Gauge bosons + +* `Ga` - photon +* `Gl` - gluon +* `W` - W boson +* `Z` - Z boson +* `H` - Higgs boson + +## Fermions (except for leptons) + +* `F`, `Fbar` - fermion, antifermion + +## Leptons + +* `Le`, `Ale` - lepton, antilepton +* `Nle`, `Anle` - lepton neutrino, lepton antineutrino + +* `El`, `Mu`, `Tau` - electron, muon, tau +* `Ael`, `Amu`, `Atau` - positron, antimuon, antitau + +* `Nel`, `Nmu`, `Ntau`- electron neutrino, muon neutrino, tau neutrino +* `Anel`, `Anmu`, `Antau`- electron antineutrino, muon antineutrino, tau antineutrino + +## Quarks +* `Q`, `Qbar` - quark, antiquark +* `Qi`, `Qibar` - `i`-flavor quark, `i`-flavor antiquark +* `Qj`, `Qjbar` - `j`-flavor quark, `j`-flavor antiquark +* `Qh`, `Qhbar` - heavy quark, heavy antiquark +* `Ql`, `Qlbar` - light quark, light antiquark + +* `Qut`, `Qutbar` - up-type quark, up-type antiquark +* `Qdt`, `Qdtbar` - down-type quark, down-type antiquark + +* `Qu`, `Qd`, `Qc` - up quark, down quark, charm quark +* `Qs`, `Qt`, `Qb` - strange quark, top quark, bottom quark + +* `Qubar`, `Qdbar`, `Qcbar` - up antiquark, down antiquark, charm antiquark +* `Qsbar`, `Qtbar`, `Qbbar` - strange antiquark, top antiquark, bottom antiquark + +## Auxiliary fields + +* `Gh` - ghost +* `Bga` - background photon field +* `Bgl` - background gluon field +* `Bgw` - background W field +* `Bgz` - background Z field + +# Example file structure + +Each calculation script is usually organized according to the following template + +## Boilerplate + +``` +(* :Title: QQbar-QQbar *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Q Qbar -> Q Qbar, QCD, matrix element squared, tree *) + +(* ------------------------------------------------------------------------ *) +``` + +## Title +``` +(* ::Title:: *) +(*Quark-antiquark scattering in QCD*) +``` + +## Sections + +``` +(* ::Section:: *) +(*Load FeynCalc and the necessary add-ons or other packages*) + +description="Q Qbar -> Q Qbar, QCD, matrix element squared, tree"; +If[ $FrontEnd === Null, + $FeynCalcStartupMessages = False; + Print[description]; +]; 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-(* End of internal cache information *) diff --git a/FeynCalc/ExportImport/FCAbbreviate.m b/FeynCalc/ExportImport/FCAbbreviate.m index 41594bc33..2e5dc025b 100755 --- a/FeynCalc/ExportImport/FCAbbreviate.m +++ b/FeynCalc/ExportImport/FCAbbreviate.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Introduces abbreviations for scalar products of external @@ -20,11 +20,11 @@ (* ------------------------------------------------------------------------ *) FCAbbreviate::usage = -"FCAbbreviate[expr, {q1,q2,...},{p1,p2,...}] introduces abbreivations for \ +"FCAbbreviate[exp, {q1,q2,...},{p1,p2,...}] introduces abbreivations for \ scalar products of external momenta, SMP-objects and other variables that are \ present in the expression. Functions (LeafCount > 1) are not supported. The \ -main purpose is to simplift export of FeynCalc expressions to other software \ -tools that might not be provide the richness of Mathematica's syntax. The \ +main purpose is to simplify the export of FeynCalc expressions to other software \ +tools that might not provide the richness of Mathematica's syntax. The \ result is returned as a list of replacement rules for scalar products, SMPs \ and all other variables present."; @@ -59,11 +59,16 @@ If [OptionValue[FCVerbose]===False, abbVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], abbVerbose=OptionValue[FCVerbose] ]; ]; + If[ !FreeQ2[expr, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + FCPrint[1, "FCAbbreviate: Entering. ", FCDoControl->abbVerbose]; FCPrint[1, "FCAbbreviate: Entering with", expr, FCDoControl->abbVerbose]; @@ -76,7 +81,7 @@ First[Cases[OptionValue[Names], Rule[Variables, x_String] :> x]]; head = OptionValue[Head]; - ex = FCE[PropagatorDenominatorExplicit[expr]]; + ex = FCE[FeynAmpDenominatorExplicit[expr]]; (*List of all possible scalar products of external momenta *) allSPs = Union[Flatten[Outer[spd, extmoms, extmoms]]]; diff --git a/FeynCalc/ExportImport/FORM2FeynCalc.m b/FeynCalc/ExportImport/FORM2FeynCalc.m index 39016440a..a402b2122 100755 --- a/FeynCalc/ExportImport/FORM2FeynCalc.m +++ b/FeynCalc/ExportImport/FORM2FeynCalc.m @@ -56,6 +56,7 @@ "Li2" -> "(PolyLog[2,#]&)", "li2" -> "(PolyLog[2,#]&)", "Li3" -> "(PolyLog[3,#]&)", + "Li4" -> "(PolyLog[4,#]&)", "li3" -> "(PolyLog[3,#]&)", "S12(1 - y)" -> "Nielsen[1,2,1-y]", "[d_(1-x)]" -> "DeltaFunction[1-x]", @@ -93,12 +94,17 @@ FORM2FeynCalc[fi, False, ru]; -FORM2FeynCalc[fi_, exprs___, lastexpr_ /; Head[lastexpr] =!= Rule, - ru___Rule] := - Block[ {file, dim, ff, ffj, hh, dott, parsit, rr, vectors, indices, - stringrules, vv, rv, nof, holdform , dotrule, holdplus, - myDot,myfile - }, +FORM2FeynCalc[fi_, exprs___, lastexpr_ /; Head[lastexpr] =!= Rule, ru___Rule] := + Block[{ file, dim, ff, ffj, hh, dott, parsit, rr, vectors, indices, + stringrules, vv, rv, nof, holdform , dotrule, holdplus, + myDot,myfile, set, vecs, vecsubs, rli}, + + + If[ !FreeQ2[{fi,exprs}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + Map[Unset, Hold[exprs, lastexpr]]; dim = Dimension /. {ru}/. Options[FORM2FeynCalc]; holdform = HoldForm /. {ru}/. Options[FORM2FeynCalc]; @@ -150,7 +156,7 @@ "0"<>#, # ]&[ToString[a]]; - vecsubs = Table[vecs[[ij]]->toexp["C"<>count[ij]],{ij,Length[vecs]}]; + vecsubs = Table[vecs[[r]]->toexp["C"<>count[r]],{r,Length[vecs]}]; (* XXX *) diff --git a/FeynCalc/ExportImport/FeynCalc2FORM.m b/FeynCalc/ExportImport/FeynCalc2FORM.m index 075617c3a..b826231c3 100755 --- a/FeynCalc/ExportImport/FeynCalc2FORM.m +++ b/FeynCalc/ExportImport/FeynCalc2FORM.m @@ -1,15 +1,24 @@ +(* ::Package:: *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Title: FeynCalc2FORM*) +(* :Title: FeynCalc2FORM *) -(* :Author: Rolf Mertig *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* ------------------------------------------------------------------------ *) -(* :History: File created on 16 March '99 at 9:43 *) -(* ------------------------------------------------------------------------ *) +(* :Summary: Converts FeynCalc expressions to FORM *) (* ------------------------------------------------------------------------ *) +EpsDiscard::usage= +"EpsDiscard is an option for FeynCalc2FORM. \ +If set to True all Levi-Civita tensors are replaced by 0 after contraction."; + FeynCalc2FORM::usage = "FeynCalc2FORM[expr] displays expr in FORM syntax. \n FeynCalc2FORM[file, x] writes x in FORM syntax to a file. \n @@ -23,10 +32,25 @@ "FORMProlog is an option for FeynCalc2FORM. It may be set \ to a string which is put after the type declarations of the FORM-file."; +FORMIdStatements::usage = +"FORMIdStatements is an option for FeynCalc2FORM. It may be set \ +to a string which is put after the local expression of the FORM-file. \ +When set to True, FeynCalc will try to generate the statements \ +automatically from the known values of scalar products."; + TraceDimension::usage = "TraceDimension is an option for FeynCalc2FORM. \ If set to 4: trace, if set to n: tracen."; +FeynCalc2FORM::failmsg = "Error! FeynCalc2FORM has encountered a fatal problem and must \ +abort the evaluation. The problem reads: `1`"; + +FORMAbbreviations::usage = +"FORMAbbreviations is an option for FeynCalc2FORM. It specifies how special symbols \ +will be abbreviated in the resulting FORM file. + +"; + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -34,39 +58,72 @@ Begin["`FeynCalc2FORM`Private`"] +fc2fVerbose::usage=""; + (* for taking traces *) -Options[FeynCalc2FORM] = {EpsDiscard -> False, -FORMEpilog -> "", FORMProlog -> "write statistics;", -Replace -> {"\\[Alpha]"-> "al", "\\[Beta]"->"be", -"\\[Gamma]" -> "ga", "\\[Delta]" -> "de", -"\\[Mu]" -> "mu", "\\[Nu]" -> "nu", "\\[Rho]" -> "ro", -"\\[Sigma]" -> "si" - }, -TraceDimension -> 4 }; - -FeynCalc2FORM[ file_:"tFc2F", xy_, ru___Rule] := +Options[FeynCalc2FORM] = { + EpsDiscard -> False, + FCVerbose -> False, + FinalSubstitutions -> {}, + FORMAbbreviations -> {"syFC","vFC"}, + FORMEpilog -> {"print;",".end"}, + FORMIdStatements -> True, + FORMProlog -> "write statistics;", + Replace -> { + "\\[Alpha]"-> "al", "\\[Beta]"->"be", + "\\[Gamma]" -> "ga", "\\[Delta]" -> "de", + "\\[Mu]" -> "mu", "\\[Nu]" -> "nu", "\\[Rho]" -> "ro", + "\\[Sigma]" -> "si"}, + TraceDimension -> 4 +}; + +FeynCalc2FORM[ file_:"tFc2F", xy_, OptionsPattern[]] := Block[ {holdy, lors, lors4, lorsn, lordim, other, noatomic, newx ,x,y, - srules, srule2, temp}, + srules, srule2, temp, downp, index4list, indexnlist, momentumlist, addmom, + newsymlist, idlist, lm2form, dpi, polvecs, form2fc, newxstr, ij, new, nidlist, + formpro, n2form, nosyml, form2l, jjj, formepi,optFinalSubstitutions, + optFORMIdStatements}, + + If[ !FreeQ2[{xy}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + + If [OptionValue[FCVerbose]===False, + fc2fVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fc2fVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "FeynCalc2FORM: Entering.", FCDoControl->fc2fVerbose]; + FCPrint[3, "FeynCalc2FORM: Entering with:", xy, FCDoControl->fc2fVerbose]; + If[ Head[xy] === Equal, x = xy[[1]]; y = xy[[2]], x = False; y = xy ]; - srules = Replace /. {ru} /. Options[FeynCalc2FORM]; - srule2 = Table[StringJoin@@Rest[Drop[ - Characters[ToString[InputForm[srules[[i,1]] ]]],-1]] -> - srules[[i,2]],{i,Length[srules]} - ]; + + srules = OptionValue[Replace]; + optFinalSubstitutions = OptionValue[FinalSubstitutions]; + optFORMIdStatements = OptionValue[FORMIdStatements]; + + srule2 = Table[ StringJoin@@Rest[Drop[Characters[ToString[InputForm[srules[[i,1]] ]]],-1]] -> srules[[i,2]], {i,Length[srules]}]; + srules = Join[srules,srule2]; + holdy = Hold@@ {(FeynCalcInternal[y]//DiracGammaExpand//MomentumExpand) /. - Pair -> ExpandScalarProduct /. + z_Pair -> ExpandScalarProduct[z] /. {Pair[a_,b_]^2 :> (Pair[a,b] . Pair[a,b]) /; !FreeQ[{a,b}, LorentzIndex] } }; - If[ (TraceDimension /. {ru} /. Options[FeynCalc2FORM]) === 4, + + If[ OptionValue[TraceDimension], + If[ !FreeQ[holdy, LorentzIndex[_,_]], holdy = holdy /. LorentzIndex[a,_] :> LorentzIndex[a] ]; @@ -78,12 +135,15 @@ ]; ]; + + (* get the list of LorentzIndex *) lors = Cases2[holdy, LorentzIndex]; lors = Union[lors] /. LorentzIndex[a_] :> a; lors4 = SelectFree[lors, LorentzIndex]; lorsn = SelectNotFree[lors, LorentzIndex]; lordim = Union[lorsn /. LorentzIndex[_, di_] :> di]; + If[ Length[lordim] === 1, lordim = lordim[[1]], If[ Length[lordim] >1, @@ -91,47 +151,56 @@ lordim = 4 ] ]; + + + lors = lors /. LorentzIndex[a_, _] :> a; lorsn = lorsn /. LorentzIndex[a_, _] :> a; (* get the list of Momentum*) - moms = Cases2[holdy, Momentum]; (* a may be a sum *) - momentumlist = Union[Flatten[moms /. Momentum[a_,___] :> Variables[a]]]; + momentumlist = Union[Flatten[Cases2[{holdy,$ScalarProducts}, Momentum] /. Momentum[a_,___] :> Variables[a]]]; - (* get all other atomic variables *) (* see p. 725 *) - other = SelectFree[Union[Cases[holdy, _Symbol, -1]], - Join[lors, momentumlist] - ]; - noatomic = Union[Flatten[Map[Variables, - Cases[holdy/.DOT->Times,h_ /; - (!MemberQ[{LorentzIndex,Momentum,DiracGamma,Eps, - DiracTrace,Pair,Symbol}, Head[y]] - ),Infinity]]]]; - noatomic = Select[noatomic, - (!MemberQ[{LorentzIndex,Momentum,DiracGamma,Eps, - DiracTrace,Symbol,Pair}, - Head[#]])& - ]; - - (* replace the non-Symbol arguments of LorentzIndex and - Momentum by Symbols *) + + + noatomic = + Union[Flatten[ + Map[Variables, Cases[holdy/.DOT->Times, h_ /;(!MemberQ[{LorentzIndex,Momentum,DiracGamma,Eps, DiracTrace,Pair, Symbol}, Head[y]]),Infinity]]] + ]; + + FCPrint[2, "FeynCalc2FORM: preliminary noatomic:", noatomic, FCDoControl->fc2fVerbose]; + + noatomic = Select[noatomic, (!MemberQ[{LorentzIndex,Momentum,DiracGamma,Eps, DiracTrace,Symbol,Pair, Polarization, String}, Head[#]])&]; + + FCPrint[2, "FeynCalc2FORM: final noatomic:", noatomic, FCDoControl->fc2fVerbose]; + + (* replace the non-Symbol arguments of LorentzIndex and Momentum by Symbols *) nosyml = Select[Join[momentumlist, lors], Head[#] =!= Symbol &]; - lm2form = Table[ nosyml[[i]] -> - ToExpression[ StringJoin[ "vFC", ToString[i] ] ], - {i, Length[nosyml]} - ]; + lm2form = Table[ nosyml[[i]] -> ToExpression[ StringJoin[ OptionValue[FORMAbbreviations][[2]], ToString[i] ] ], {i, Length[nosyml]}]; + FCPrint[2, "FeynCalc2FORM: Replacement table for the non-Symbol arguments of LorentzIndex and Momentum:", lm2form, FCDoControl->fc2fVerbose]; + + (* get all other atomic variables *) (* see p. 725 *) + + other = SelectFree[Union[Cases[holdy/.lm2form, _Symbol, -1]], Join[lors, momentumlist,(lm2form /. Rule[_, b_] :> b)]]; + other = Union[other,SelectFree[Union[Cases[FCI[((SP @@ #) & /@ $ScalarProducts)]/.lm2form, _Symbol, -1]], Join[lors, momentumlist,(lm2form /. Rule[_, b_] :> b)]]]; + + + FCPrint[2, "FeynCalc2FORM: other:", other, FCDoControl->fc2fVerbose]; (* for the reverse substitutions *) form2l = Map[Reverse, lm2form]; + FCPrint[2, "FeynCalc2FORM: form2l :", form2l, FCDoControl->fc2fVerbose]; + index4list = lors4 /. lm2form; indexnlist = lorsn /. lm2form; momentumlist = momentumlist /. lm2form; eps2f[a__] := - -I Global`eE[a] /. Momentum[aa_,___] :> - aa /. LorentzIndex[bb_,___]:>bb; + -I Global`eE[a] /. Momentum[aa_,___] :> aa /. LorentzIndex[bb_,___]:>bb; + pair2f[LorentzIndex[a_,___], LorentzIndex[b_,___]] := Global`dD[a/.lm2form, b/.lm2form]; + $tracecount = 0; + diracg[5] := Global`gA5[$tracecount]; diracg[6] := @@ -141,6 +210,7 @@ diracg[_[ls_]] := Global`gA[$tracecount, ls]; + (* assume that momenta are Symbols *) pair2f[LorentzIndex[a_Symbol,___], Momentum[b_, ___]] := b[a/.lm2form]; @@ -148,74 +218,107 @@ b.a; (* construct the list of substitutions for all noatomics *) - n2form = Table[ noatomic[[i]] -> - ToExpression[ StringJoin[ "syFC", ToString[i] ] ], - {i, Length[noatomic]} - ]; + n2form = Table[ noatomic[[i]] -> ToExpression[ StringJoin[ OptionValue[FORMAbbreviations][[1]], ToString[i] ] ], {i, Length[noatomic]}]; + FCPrint[2, "FeynCalc2FORM: n2form :", n2form, FCDoControl->fc2fVerbose]; + + form2fc = Join[form2l, Map[Reverse, n2form]]; + + FCPrint[2, "FeynCalc2FORM: form2fc :", form2fc, FCDoControl->fc2fVerbose]; + newsymlist = noatomic /. n2form; + FCPrint[2, "FeynCalc2FORM: preliminary newsymlist:", newsymlist, FCDoControl->fc2fVerbose]; + newsymlist = Join[other, newsymlist]; - If[ !FreeQ[holdy, Complex], + + (* ??? + If[ !FreeQ[holdy/.lm2form, Complex], AppendTo[newsymlist, I] - ]; + ];*) + + FCPrint[2, "FeynCalc2FORM: final newsymlist:", newsymlist, FCDoControl->fc2fVerbose]; + + + dirtr[a_] := - ($tracecount++; + ( + $tracecount++; a /. diracgamma -> diracg - ); + ); + new = ( (holdy /. lm2form /. Pair -> pair2f /. Eps -> eps2f /. DiracGamma -> diracgamma /. DOT->NonCommutativeMultiply /. DiracTrace -> dirtr /. diracgamma -> diracg )[[1]] ) //.n2form; + temp = OpenWrite[$TemporaryPrefix<>"teEmpf", FormatType -> InputForm]; Write[temp, new]; - newx = ReadList[ - (*If[$OperatingSystem === "MacOS", $PathnameSeparator,""]*) - $TemporaryPrefix <> "teEmpf", String - ]; + newx = ReadList[$TemporaryPrefix <> "teEmpf", String]; Close[temp]; DeleteFile[$TemporaryPrefix <> "teEmpf" ]; - (*Mac fix 18/9-2000, F.Orellana. Ditto for FileType below*) If[ FileType[file] === File, DeleteFile[file] ]; - newx = StringReplace[StringReplace[newx,srules], - {"\""->"", "dD"->"d_", "["->"(", "\\"->"", - "]" -> ")", " " -> "", "I" -> "i_", - "gA5" -> "g5_", - "gA6" -> "g6_", - "gA7" -> "g7_", - "gA"->"g_", - "eE"->"e_", - " . "->".", - "$"->"_", - "**" -> "*" - } - ]; + + newx = + StringReplace[StringReplace[newx,srules], { + "\""->"", + "dD"->"d_", + "["->"(", "\\"->"", + "]" -> ")", + " " -> "", + "I" -> "i_", + "gA5" -> "g5_", + "gA6" -> "g6_", + "gA7" -> "g7_", + "gA"->"g_", + "eE"->"e_", + " . "->".", + "$"->"_", + "**" -> "*", + "Sqrt" -> "sqrt_" + } + ]; (* construct the id - statements *) - downp = Select[DownValues[Pair]/.Momentum[a_,___]:>Momentum[a], - FreeQ2[#, {Blank, Pattern}]&]; - idlist = {}; - For[i = 1, i<=Length[downp], i++, - dpi = {downp[[i, 1,1,1,1]], downp[[i,1,1,2,1]]}; - If[ FreeQ[dpi, Plus], - AppendTo[idlist, Append[dpi, downp[[i, 2]]]] - ] - ]; - idlist = idlist /. lm2form; + downp = Select[DownValues[Pair]/.Momentum[a_,___]:>Momentum[a], FreeQ2[#, {Blank, Pattern}]&]; + + If[ FreeQ[holdy,OPEDelta], + downp = SelectFree[downp,OPEDelta]; + idlist = Map[Join[#, {SP @@ #}] &, SelectFree[$ScalarProducts, Plus, OPEDelta, ExplicitLorentzIndex[0], TemporalMomentum, CartesianIndex, CartesianMomentum] /. Momentum[z_, ___] :> z], + + idlist = Map[Join[#, {SP @@ #}] &, SelectFree[$ScalarProducts, Plus, ExplicitLorentzIndex[0], TemporalMomentum, CartesianIndex, CartesianMomentum] /. Momentum[z_, ___] :> z] + ]; + + + + + + FCPrint[2, "FeynCalc2FORM: Preliminary list of id statements:", idlist, FCDoControl->fc2fVerbose]; + + idlist = idlist /. lm2form /. n2form; + + FCPrint[2, "FeynCalc2FORM: List of id statements after applying lm2form: ", idlist, FCDoControl->fc2fVerbose]; + If[ !FreeQ[momentumlist/.form2fc, Polarization], polvecs = SelectNotFree[momentumlist/.form2fc, Polarization]; nidlist = Table[{polvecs[[j]], polvecs[[j,1]],0},{j,Length[polvecs]}]; nidlist = nidlist /. lm2form; idlist = Join[idlist, nidlist]; + FCPrint[3, "FeynCalc2FORM: List of id statements after adding polarization vectors:", idlist, FCDoControl->fc2fVerbose] ]; + + (* there might be additional momenta *) - addmom = Cases[Cases2[downp, Momentum], _Symbol, -1]; + addmom = Cases[SelectFree[Cases2[$ScalarProducts, Momentum], Polarization], _Symbol, -1]; momentumlist = Union[momentumlist, addmom]; + + (* Final symbols *) + OpenWrite[file, FormatType -> InputForm]; If[ Length[newsymlist] > 0, WriteString[file, "Symbols "]; @@ -227,33 +330,52 @@ ]; WriteString[file, Last[newsymlist], ";\n"]; ]; + + (* Final indices *) + index4list = Map[StringReplace[ToString[#],srules]&,index4list]; indexnlist = Map[StringReplace[ToString[#],srules]&,indexnlist]; + + + If[ Length[index4list] > 0 && x =!= False, WriteString[file, "Indices "]; + For[ij = 1, ij < Length[index4list], ij++, - WriteString[file, index4list[[ij]],","]; + WriteString[file, index4list[[ij]],","]; ]; + WriteString[file, Last[index4list], ";\n"]; ]; + If[ Length[indexnlist] > 0 && x =!= False, WriteString[file, "Indices "]; + For[ij = 1, ij < Length[indexnlist], ij++, WriteString[file, indexnlist[[ij]],"=",lordim,","]; ]; + WriteString[file, Last[indexnlist], "=",lordim," ;\n"]; ]; + + (* Final vectors *) + If[ Length[momentumlist] > 0 && x =!= False, WriteString[file, "Vectors "]; + For[ij = 1, ij < Length[momentumlist], ij++, - WriteString[file, momentumlist[[ij]]]; - If[ ij < Length[momentumlist], + WriteString[file, momentumlist[[ij]]]; + If[ ij < Length[momentumlist], WriteString[file, ","] - ]; - ]; + ]; + ]; + WriteString[file, Last[momentumlist], ";\n"]; ]; - formpro = FORMProlog/. {ru} /. Options[FeynCalc2FORM]; + + (* Final prolog *) + + formpro = OptionValue[FORMProlog]; If[ formpro =!= "" && x =!= False, If[ Head[formpro] =!= List, formpro = Flatten[{formpro}] @@ -264,6 +386,9 @@ ]; Write[file]; ]; + + (* Final local expresisons *) + If[ x=!= False, WriteString[file, "Local ",x , " = ( \n"]; ]; @@ -277,68 +402,103 @@ WriteString[file, "\n"]; ] ]; + If[ x===False && file === "tFc2F", - (*Print[newx[[jjj]]]*) WriteString["stdout", newx[[jjj]],"\n"] ] - ]; + ]; + If[ x=!= False, WriteString[file, " ); \n \n"]; ]; + (* Final trace statements *) + (* in case there are traces *) If[ $tracecount > 0 && x =!= False, For[i = 1, i <= $tracecount, i++, - If[ (TraceDimension /. {ru} /. Options[FeynCalc2FORM]) === 4, + If[ OptionValue[TraceDimension] === 4, WriteString[file, "trace4,"<>ToString[i]<>";\n"], WriteString[file, "tracen,"<>ToString[i]<>";\n"] ]; ]; WriteString[file, "contract 0;\n\n"] ]; - If[ (EpsDiscard /. {ru} /. Options[FeynCalc2FORM]) && - x =!= False, + + If[ OptionValue[EpsDiscard] && x =!= False, WriteString[file, - "if ( count(e_,1) > 0 );\n", - " discard;\n", - "endif;\n\n" ] + "if ( count(e_,1) > 0 );\n", + " discard;\n", + "endif;\n\n" + ] ]; - If[ Length[idlist] > 0 && x =!= False, - Write[file]; - For[ij = 1, ij <= Length[idlist], ij++, - (* - If[Head[Expand[idlist[[ij, 3]]]] =!= Plus, - *) - WriteString[file, "id ",idlist[[ij, 1]],".",idlist[[ij, 2]], - " = ", idlist[[ij, 3]]//InputForm, "; \n" - ]; -(* - ]; -*) - ]; - Write[file]; + + (* Final id statements *) + + Which[ + optFORMIdStatements===True, + If[ Length[idlist] > 0 && x =!= False, + Write[file]; + For[ij = 1, ij <= Length[idlist], ij++, + WriteString[file, "id ",idlist[[ij, 1]],".",idlist[[ij, 2]], " = ", idlist[[ij, 3]]//InputForm, "; \n"]; + ]; + Write[file]; + ], + optFORMIdStatements===False, + Null, + + MatchQ[optFORMIdStatements,_String|_List], + If[ optFORMIdStatements =!= "" && x=!= False, + If[ Head[optFORMIdStatements] =!= List, + optFORMIdStatements = Flatten[{optFORMIdStatements}] + ]; + + Write[file]; + For[ij = 1, ij <= Length[optFORMIdStatements], ij++, + WriteString[file, optFORMIdStatements[[ij]],"\n"]; + ]; + + Write[file]; + ], + True, + Message[FeynCalc2FORM::failmsg,"Unsupported value of FORMIdStatements"]; + Abort[] ]; - formepi = FORMEpilog /. {ru} /. Options[FeynCalc2FORM]; + + + (* Final epilog *) + + formepi = OptionValue[FORMEpilog]; + If[ formepi =!= "" && x=!= False, If[ Head[formepi] =!= List, formepi = Flatten[{formepi}] ]; + Write[file]; For[ij = 1, ij <= Length[formepi], ij++, WriteString[file, formepi[[ij]],"\n"]; ]; + Write[file]; ]; + +(* This goes into FORMEpilog! If[ x=!= False, WriteString[file, "Print; \n"]; - WriteString[file, ".end"]; + WriteString[file, ".end"] ]; +*) + Close[file]; If[ file === "tFc2F", If[ FileType["tFc2F"]===File, DeleteFile["tFc2F"] ] ]; + + + form2fc ]; diff --git a/FeynCalc/ExportImport/FeynCalcToLaTeX.m b/FeynCalc/ExportImport/FeynCalcToLaTeX.m index 3faeee05e..d1182fdda 100644 --- a/FeynCalc/ExportImport/FeynCalcToLaTeX.m +++ b/FeynCalc/ExportImport/FeynCalcToLaTeX.m @@ -25,17 +25,23 @@ F2L = FeynCalcToLaTeX; FeynCalcToLaTeX[expr_, width_:500] := + ( + If[ !FreeQ2[expr, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + If[ !$Notebooks, Needs["JLink`"]; JLink`InstallJava[]; JLink`UseFrontEnd[f2tex[expr, width]], f2tex[expr,width] - ]; + ]); (* this is of course heuristics; should change to java.util.regexp or so ... *) f2tex[expr_, width_:500] := - Module[ {r, n, w,y,z}, + Module[ {r, n, w,y,z, tt}, r = Cell[BoxData[FormBox[(MakeBoxes[#1, TraditionalForm] & )[expr], TraditionalForm]], "Output"]; n = NotebookPut[Notebook[{r}, WindowSize -> {width, Inherited}, diff --git a/FeynCalc/ExportImport/SMPToSymbol.m b/FeynCalc/ExportImport/SMPToSymbol.m new file mode 100755 index 000000000..d8b972d66 --- /dev/null +++ b/FeynCalc/ExportImport/SMPToSymbol.m @@ -0,0 +1,90 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: SMPToSymbol *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Introduces abbreviations for scalar products of external + momenta, SMPs and other variables which appear in the + expression. Functions are not allowed. Mainly meant to be + used for export of FeynCalc expressions when interfacing + with other tools. *) + +(* ------------------------------------------------------------------------ *) + +SMPToSymbol::usage = +"SMPToSymbol[exp] converts objects of type SMP[\"sth\"] in exp to symbols using +ToExpression[\"sth\"]. The option StringReplace can be used to specify string +replacement rules that will take care of characters (e.g. ^ or _) that +cannot appear in valid expressions. SMPToSymbol is useful when exporting FeynCalc +expressions to other tools, e.g. FORM."; + +SMPToSymbol::failmsg = "Error! SMPToSymbol has encountered a fatal problem and must \ +abort the computation. The problem reads: `1`"; + +(* ------------------------------------------------------------------------ *) + +Begin["`SMPToSymbol`"] +End[] + +Begin["`SMPToSymbol`Private`"] + +Options[SMPToSymbol] = { + StringReplace-> {"_"->"", "^"->""}, + Conjugate -> "CC" +}; + +SMPToSymbol[expr_, OptionsPattern[]] := + Block[{res, allSMPs, symbols, optConjugate, optStringReplace, rule}, + + optConjugate = OptionValue[Conjugate]; + optStringReplace = OptionValue[StringReplace]; + allSMPs = Cases2[expr, SMP]; + + If[ allSMPs==={}, + Return[expr] + ]; + + symbols = allSMPs /. { + SMP[s_String]->s, + SMP[{s_String, Complex[0,1]}]->s, + SMP[{s_String, Complex[0,-1]}]:>s<>optConjugate + }; + + If[ !MatchQ[symbols,{_String..}], + Message[SMPToSymbol::failmsg, "Failed to extract strings out of all SMPs."]; + Abort[] + ]; + + symbols = StringReplace[symbols,optStringReplace]; + + If[ !MatchQ[SyntaxQ/@symbols,{True..}], + Message[SMPToSymbol::failmsg, "The final strings do not represent valid Mathematica expressions."]; + Abort[] + ]; + + symbols = ToExpression/@symbols; + + If[ !MatchQ[Head/@symbols,{Symbol..}], + Message[SMPToSymbol::failmsg, "The resulting expressions are not simple symbols."]; + Abort[] + ]; + + rule = Thread[Rule[allSMPs,symbols]]; + + + res = expr /. Dispatch[rule]; + + + res + ]; + +FCPrint[1,"SMPToSymbol.m loaded."]; +End[] diff --git a/FeynCalc/ExportImport/Write2.m b/FeynCalc/ExportImport/Write2.m index bb1cf21e5..fb6a3c990 100644 --- a/FeynCalc/ExportImport/Write2.m +++ b/FeynCalc/ExportImport/Write2.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2018 Rolf Mertig - Copyright (C) 1997-2018 Frederik Orellana - Copyright (C) 2014-2018 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Writes expressions to files *) @@ -61,6 +61,7 @@ w2Verbose::usage=""; finsubst::usage=""; pagewidth::usage=""; +optFormatType::usage=""; Options[Write2] = { D0Convention -> 0, @@ -95,7 +96,7 @@ If[ OptionValue[FCVerbose]===False, w2Verbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], w2Verbose=OptionValue[FCVerbose] ]; ]; @@ -410,7 +411,7 @@ Block[ {kk, qq}, FCPrint[2,"Write2: vhf: Entering with ", n y]; kk = y[[1, 0]]; - (Table[ HoldForm @@ {qq[ii]}, {ii, y[[1,1]]} ] /. qq -> kk)/.finsubst + (Table[ HoldForm @@ {qq[i]}, {i, y[[1,1]]} ] /. qq -> kk)/.finsubst ] /; NumberQ[n]; vhf[y_] := @@ -446,7 +447,7 @@ pww[x_, rat_Rational] := (Power[x,N[rat]]/. xxx_Real/; optFFDP :> fhead[xxx]); pww[x_, he_] := - ((x^he)/. xxx_Real/; optFFDP :> fhead[xxx]) /; Head[he]=!=Rational; + ((x^he)/. z_Real/; optFFDP :> fhead[z]) /; Head[he]=!=Rational; fhead[x_]:= x/; Head[x]=!=Real && FreeQ2[{x},{Pattern,Blank}]; diff --git a/FeynCalc/FCMain.m b/FeynCalc/FCMain.m new file mode 100644 index 000000000..81acaf5aa --- /dev/null +++ b/FeynCalc/FCMain.m @@ -0,0 +1,553 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCMain *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Global FeynCalc functions and objects. *) + +(* ------------------------------------------------------------------------ *) + +$Abbreviations::usage = +"$Abbreviations is a list of string substitution rules used when \ +generating names for storing intermediate results. \ +It is used by OneLoop and PaVeReduce.\ +The elements of the list should be of the form \"name\" -> \"abbreviation\"."; + +$AL::usage = +"$AL is the head of dummy indices which may be introduced by \ +Uncontract."; + +$Containers::usage = +"$FieldContainers is a set of heads over which FieldDerivative should \ +distribute, in the following sense: Let c be a member of $Containers. Then \ +FieldDerivative[c[f, g, h][x], x, {mu}] -> \ +c[FieldDerivative[f[x], x, {mu}], FieldDerivative[f[x], x, {mu}], \ +FieldDerivative[f[x], x, {mu}]]."; + +$DisableMemSet::usage= +"The boolean setting of $DisableMemSet allows to disable \ +memoizaion that is activated via MemSet. This can be \ +useful for debugging purposes"; + +DOT::usage = +"DOT[a, b, ...] is the FeynCalc function for non-commutative \ +multiplication. By default it is set to the Mathematica Dot \ +functions. By setting \n +DOT=. \n +this can be disabled. \ +Note that then non-commutative products should to be entered \ +like DOT[ GA[mu], m + GS[p], GA[mu] ], \ +etc."; + +$DistributiveFunctions::usage = +"$DistributiveFunctions is a set of functions over which FieldDerivative \ +should be distributed."; + +$FAPatch::usage = +"$FAPatch switches on and off checking for \ +an unpatched FeynArts installation on FeynCalc startup. Default value : True."; + +FC::usage = +"FC changes the output format to FeynCalcForm. \ +To change to InputForm use FI."; + +$FCCheckContext::usage = +"If set to True, FeynCalc will try to detect unwanted leakage of internal \ +objects into the Global or FeynCalc contexts. The default value is False, \ +however $FCCheckContext will be automatically enabled in the development +version."; + +$FCCloudTraditionalForm::usage= +"$FCCloudTraditionalForm determines whether the cell output will be done \ +in TraditionalForm when FeynCalc is run in Wolfram Cloud. This is done by setting \ +$Post=TraditionalForm. The default value of $FCCloudTraditionalForm is True." + +$FCTraditionalFormOutput::usage= +"The boolean setting of $FCTraditionalFormOutput determines which \ +output format type should be used in the notebook front end when \ +FeynCalc is loaded. If set to True, FeynCalc will activate the \ +TraditionalForm output. Otherwise, the StandardForm output \ +(Mathematica's default) will be used. This setting only changes \ +the output format of the current notebook, i.e. it is not persistent \ +and will not modify the global options of Mathematica. If unsure, it +is recommended to set $FCTraditionalFormOutput to True, so that you \ +can benefit from the nice FeynCalc typesetting for various QFT quantities."; + +$FeynCalcStartupMessages::usage= +"$FeynCalcStartupMessages specifies whether some additional information about \ +FeynCalc should be displayed when the package is loaded. Its value must be set \ +before loading FeynCalc. The default value is True."; + +$FeynCalcDevelopmentVersion::usage = +"The boolean setting of $FeynCalcDevelopmentVersion determines whether \ +the current version is a development or a stable version."; + +$FCTensorList::usage = +"$FCTensorList contains a list of all tensor heads present."; + +$FCShowIEta::usage = +"The boolean setting of $FCShowIEta detrmines whether I \[Eta] should \ +be displayed in the typesetting of GFAD and GenericPropagatorDenominator \ +objects or not. This setting affects only the TraditionalForm typesetting \ +and has absolutely no influence on the internal handling of propagator \ +denominators in FeynCalc."; + +FCSetMetricSignature::usage = +"FCSetMetricSignature sets the signature of the Minkowski metric used when \ +working with Cartesian objects, like CartesianPair, CartesianIndex, CartesianMomentum etc. \ +The default choice is (1,-1,-1,-1) which corresponds to \ +FCSetMetricSignature[{1,-1}]"; + +FCGetMetricSignature::usage = +"FCGetMetricSignature[] returns the signature of the Minkowski metric used when \ +working with Cartesian objects, like CartesianPair, CartesianIndex, CartesianMomentum etc. \ +{1,-1} corresponds to (1,-1,-1,-1) and {-1,1} means (-1, 1, 1, 1)"; + +FCPrint::usage = +"FCPrint[level, x] outputs Print[x] if the value of $VeryVerbose \ +is larger than level."; + +$FCS::usage = "$FCS is a list of functions with a short name. \ +E.g. GA[nu] can be used instead of DiracGamma[nu]."; + +FeynCalc::usage = +"For installation notes visit www.feyncalc.github.io. You can get \ +on-line information by ?function, e.g. ?Contract.\n +There are several useful functions for short input, type $FCS for a list of \ +short commands. Then type, e.g., ?GA.\n\n +To enable/disable start-up messages, put the line\n +$FeynCalcStartupMessages = True;\n +or\n +$FeynCalcStartupMessages = False;\n +into your \"init.m\" file or into your \"FCConfig.m\" file." + +$FeynCalcVersion::usage = +"$FeynCalcVersion is a string that represents the version of FeynCalc."; + +FI::usage = +"FI changes the output format to InputForm. \ +This is useful to see the internal representation of FeynCalc \ +objects. To change back to FeynCalcForm use FC."; + +$KeepLogDivergentScalelessIntegrals::usage = +"$KeepLogDivergentScalelessIntegrals is an experimental global option that forces \ +FeynCalc not to set 1-loop integrals of type 1/q^4 to zero. This is useful \ +when one has to explicitly distinguish between IR- and UV-divergences in \ +dimensional regularization. Notice that OneLoop is not guaranteed to respect this \ +option."; + +$LeviCivitaSign::usage = +"$LeviCivitaSign is a global variable that determines \ +the sign in the result of a Dirac trace of four gamma matrices \ +and gamma5. $LeviCivitaSign is by default set to -1 which corresponds \ +to the convention Tr[GA[a,b,c,d,5]] = -4*I*Eps[a,b,c,d]. \ +Setting $LeviCivitaSign=-I will switch to the FORM-convention. \n + +In terms of explicit components, $LeviCivitaSign=1 corresponds to setting \ +eps^{0123} = 1 (as in Peskin and Schroeder), while choosing $LeviCivitaSign=-1 \ +gives us the convention of Bjorken and Drell with eps^{0123} = -1. Two other \ +possible choices are $LeviCivitaSign=-I to have eps^{0123} = I as in FORM and \ +$LeviCivitaSign=I which would give eps^{0123} = -I."; + +$LimitTo4::usage = +"$LimitTo4 is a global variable that determines whether \ +UV-divergent Passarino-Veltman functions are simplified by \ +taking the limit D-4 -> 0. A general UV-finite \ +Passarino-Veltman function can be written as \ +PaVe = a/(D-4) + b + O(Epsilon), with a being the prefactor \ +of the pole and b being the finite part. Therefore, products \ +of such functions with coefficients that are rational functions \ +of D ( f(D) = f(4) + f'(4) (D-4) + O(Epsilon^2) ) can be simplified \ +to f(D) PaVe = f(4) PaVe + a f'(4) + O(Epsilon), whenever such \ +products appear in the reduction. This relation is correct only if \ +the Passarino-Veltman functions have no IR divergences, or if such \ +divergences are regulated without using dimensional regularization. +For this reason, even when $LimitTo4 is set to True, the simplifications \ +are applied only to A and B functions. Although B functions can exhibit an \ +IR divegence, such integrals are zero in dimensional regularization, so no \ +mixing of Epsilons from IR and UV can occur. The default value of \ +$LimitTo4 is True."; + +$LimitTo4IRUnsafe::usage = +"$LimitTo4IRUnsafe is a global variable that determines whether \ +the simplifications described in $LimitTo4 are applied also to \ +C and D Passarino-Veltman functions. In this case it is assumed \ +that such functions are either IR finite, or the IR divergences \ +are regulated without using dimensional regularization \ +(i.e. by introducing fictitious masses). Otherwise the results \ +will be inconsistent. If this option is activated, it is the task \ +of the user to ensure that IR divergences are properly regulated, \ +such that no mixing of Epsilons from IR and UV can occur. The default \ +value of $$LimitTo4IRUnsafe is False."; + +$LoadAddOns::usage = +"$LoadAddOns specifies which addons should be loaded with FeynCalc. \ +E.g. $LoadAddOns={\"FeynHelpers\"}. The value must be set before \ +loading FeynCalc. The default value is False."; + +$FCMemoryAvailable::usage = +"$FCMemoryAvailable is a global variable which is set to an integer \ +n, where n is the available amount of main memory in MB. \ +The default is 4096. It should be increased if possible. \ +The higher $FCMemoryAvailable can be, the more intermediate \ +steps do not have to be repeated by FeynCalc."; + +$MU::usage = +"$MU is the head of dummy indices which may be introduced by \ +Chisholm, Contract, DiracSimplify, FermionSpinSum and various \ +QCD functions. By default it is unset, but can be set to anything."; + +$Multiplications::usage = +"$Multiplications is a set functions which should be treated as \ +(commutative or non-commutative) multiplications by FieldDerivative."; + +$NonComm::usage = +"$NonComm contains a list of all non-commutative heads present."; + +$ScalarProducts::usage = +"$ScalarProducts contains a list of all vector pairs for which a \ +scalar product value has been defined."; + +$OPEWard::usage = +"$OPEWard is experimental."; + +$RenameFeynCalcObjects::usage = +"$RenameFeynCalcObjects specifies a List of replacement rules that \ +allow to rename FeynCalc objects on the run to avoid conflicts with \ +other package before FeynCalc is loaded (monkey patching). The value \ +of $RenameFeynCalcObjects must be specified before loading FeynCalc."; + +TBox::usage = +"TBox[a, b, ...] produces a RowBox[{a,b, ...}] where \ +a,b, ... are boxed in TraditionalForm."; + +UseWriteString::usage = +"UseWriteString is an option for FCPrint. If set to True, \ +the expression is printed via WriteString instead of Print."; + +$VeryVerbose::usage = +"$VeryVerbose is a global variable with default setting 0. \ +If set to 1, 2, ..., less and more intermediate comments and informations \ +are displayed during calculations."; + +$FCAdvice::usage = +"If $FCAdvice is set to True, FeynCalc will display some \ +advices on optimal Mathematica configuration for using FeynCalc." + +WriteStringOutput::usage = +"UseWriteStringOutput an option for FCPrint. It specifies, to which \ +stream WriteString should output the expression"; + +FeynCalc::faerror = +"FeynArts not found or damaged. Please download the FeynArts \ +tarball from www.feynarts.de, unpack it to `1` and restart FeynCalc."; + +FeynCalc::phierror = +"PHI failed to load. Please try resintalling FeynCalc."; + +FeynCalc::tfadvice = +"You are not using TraditionalForm as the default format type of new \ +output cells. Without TraditionalForm FeynCalc cannot use built-in \ +typeseting rules that make various objects like Lorentz vectors or \ +Dirac matrices look nicer. To change the format type go to \ +Edit->Preferences->Evaluation."; + +FeynCalc::nrfail = +"This function is not yet ready to work with new non-covariant objects \ +in FeynCalc."; + +FeynCalc::context = +"FeynCalc has detected strange objects in the Global or FeynCalc contexts."; + +FCDoControl::usage = +"FCDoControl is an option for FCPrint that specifies which variable \ +is used to control the debugging output of FCPrint. The default value \ +is $VeryVerbose."; + +FCSetDiracGammaScheme::usage = +"FCSetDiracGammaScheme[\"scheme\"] allows you to specify how Dirac matrices \ +will be handled in D dimensions. This is mainly relevant to \ +the treatment of the fifth Dirac matrix g^5, which is not well-defined \ +in dimensional regularization. Following schemes are supported: \ + +\"NDR\" - This is the default value. In the naive dimensional regularization \ +(also known as conventional dimensional regularization or CDR) g^5 is assumed \ +to anticommute with all Dirac matrices in D dimensions. Hence, every Dirac trace \ +can be rewritten in such a way, that it contains either just one or not a single g^5 \ +matrix. The latter traces are obviously unambiguous. The traces with one g^5 are \ +not well-defined in this scheme. It usually depends on the physics of the process, \ +whether and how they can contribute to the final result. Therefore, FeynCalc will \ +keep such traces unevaluated, leaving it to the user to decide how to treat them. \ +Notice that traces with an odd number of the usual Dirac matrices and one g^5, \ +that vanish in 4 dimensions, will be also put to zero in this scheme.\n + +\"NDR-Discard\" - This is a special version of the NDR scheme. The Dirac algebra is \ +evaluated in the same way as with \"NDR\", but the remaining traces with one g^5 \ +are put to zero. This assumes that such traces do not contribute to the final result, \ +which is obviously true only for specific calculations.\n + +\"BMHV\" - The Breitenlohner-Maison extension of the t'Hooft-Veltman scheme. This \ +scheme introduces Dirac and Lorentz tensors living in 4, D or D-4 dimensions, while \ +g^5 is a purely 4-dimensional object. BMHV is algebraically consistent but often \ +suffers from nonconservation of currents in the final results. The conservation must \ +be then enfornced by introducing finite counter-terms. The counter-terms are to be \ +supplied by the user, since FeynCalc does not do this automatically.\n + +\"Larin\" - Special prescription developed by Larin, also known as the \ +Larin-Gorishny-Atkyampo-DelBurgo scheme. Essentially, it is a shortcut \ +(mostly used in QCD) for obtaining the same results as in BMHV but without \ +the necessity to deal with tensors from different dimensions. That is, before evaluating traces \ +(but after moving gamma5 anticommuting in D-dimensions to the \ +right of the Dirac string inside a trace) a product gamma[mu].gamma5 is \ +substituted to -I/6 Eps[mu,al,be,si] gamma[al,be,si], \ +where all indices live in D-dimensions now. \ +The Levi-Civita tensor is taken to be \ +D-dimensional, i.e., contraction of two Eps's results in D's. \ +This scheme is often used for performance reasons and is assumed \ +to give the same results as the \ +Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme. However, gamma5 is \ +not anticommuting inside closed fermion loops and it is not so clear \ +if this scheme works for more than one fermion line involving gamma5. \ +When in doubt, it might be better to use BMHV instead."; + +FCGetDiracGammaScheme::usage = +"FCGetDiracGammaScheme[] shows the currently used scheme for handling Dirac \ +matrices in D dimensions."; + +FCSetPauliSigmaScheme::usage = +"FCSetPauliSigmaScheme[\"scheme\"] allows you to specify how Pauli matrices \ +will be handled in D-1 dimensions. This is mainly related to \ +the commutator of two Pauli matrices, which involves a Levi-Civita \ +tensor. The latter is not a well-defined quantity in D-1 dimensions. \ +Following schemes are supported: \ + +\"None\" - This is the default value. The anticommutator relation is not \ +applied to D-1 dimensional Pauli matrices. + +\"Naive\" - Naively apply the commutator relation in D-1-dimensions, i.e. \ +CSID[i,j]-CSID[i,j] = 2 i CLCD[i,j,k] SID[k]. The Levi-Civita tensor lives \ +in D-1-dimensions, so that a contraction of two such tensors which have all \ +indices in common yields (D-3) (D-2) (D-1)." + +FCGetPauliSigmaScheme::usage = +"FCGetPauliSigmaScheme[] shows the currently used scheme for handling Pauli +matrices in D-1 dimensions."; + +FCEnableTraditionalFormOutput::usage = +"FCEnableTraditionalFormOutput[] sets the output format of the current \ +FrontEnd to TraditionalForm. The setting is not persistent, such that \ +it does not influence any subequent Mathematica FrontEnd sessions."; + +FCDisableTraditionalFormOutput::usage = +"FCDisableTraditionalFormOutput[] sets the output format of the current \ +FrontEnd to StandardForm. The setting is not persistent, such that \ +it does not influence any subequent Mathematica FrontEnd sessions."; + +FeynCalc::failmsg = +"Error! FeynCalc has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) +Begin["`Package`"] + +End[] + +Begin["`Private`"] + +$Abbreviations = { + ", "->"", + "^"->"", + "{"->"", + "/" -> "", + "Subscript"->"su", + "SmallVariable"->"sma", + "}"->"", + "["->"", + "]"->"", + "*" -> "", + " " -> "" , + "\n" -> "", + "\r" -> "" +}; + + +$Containers = {}; +$DisableMemSet = False; +$DistributiveFunctions = {Conjugate, Transpose}; +$FCShowIEta = True; +$FCS = { + "CDr", + "FAD", + "FC", + "FCE", + "FCI", + "FDr", + "FI", + "FV", + "FVD", + "FVE", + "GA", + "GA5", + "GAD", + "GAE", + "GGV", + "GP", + "GS", + "GSD", + "GSE", + "LC", + "LCD", + "MT", + "MTD", + "MTE", + "QGV", + "QO", + "SD", + "SDF", + "SOD", + "SP", + "SPC", + "SPD", + "SPE", + "SPL" +}; + +$KeepLogDivergentScalelessIntegrals = False; +$LeviCivitaSign = -1; +$LimitTo4 = False; +$LimitTo4IRUnsafe = False; +$FCMemoryAvailable = Floor[$SystemMemory/10^6/4]; +$Multiplications = {Times, DOT}; +$OPEWard = False; + +(* Mathematica versions 8 and 9 do not have the $SystemMemory variable, + so for them we set the available memory for memoization to 4 GiB*) +If[ !MatchQ[OptionValue[FCMemoryAvailable],_Integer?Positive], + $FCMemoryAvailable=4096 +]; + +If[ !ValueQ[$VeryVerbose], + $VeryVerbose = 0 +]; + +If[ !ValueQ[$NonComm], + $NonComm = {} +]; + +If[ !ValueQ[$FCTensorList], + $FCTensorList = {} +]; + +If[ !ValueQ[$ScalarProducts], + $ScalarProducts = {} +]; + +DOT = Dot; + +(* DOT moved into main context. 32/2-2003. F.Orellana. + The reason for this is the following: In order to use + DOT instead of Dot consistenly everywhere, we need to be + able to do e.g. f[DOT[a_,b_]]:=g[a,b]. Because DOT is immediately + set to something else (Dot), this works only if DOT is in + $ContextPath at the moment this definition is evaluated. + In the context of the packages, $ContextPath is typically + {"System`", "FeynCalc`"}. + *) + +SetAttributes[FCPrint, HoldRest]; + +Options[FCPrint] = { + FCDoControl :> $VeryVerbose, + UseWriteString -> False, + WriteStringOutput ->"stdout" +} + + +FeynCalc`Package`MetricT = 1; +FeynCalc`Package`MetricS = -1; +FeynCalc`Package`PauliSigmaScheme = "None"; +FeynCalc`Package`DiracGammaScheme = "NDR"; + +FCEnableTraditionalFormOutput[]:= + (CurrentValue[$FrontEndSession, {CommonDefaultFormatTypes, "Output"}] = TraditionalForm;); + +FCDisableTraditionalFormOutput[]:= + (CurrentValue[$FrontEndSession, {CommonDefaultFormatTypes, "Output"}] = StandardForm; ); + + +FCSetDiracGammaScheme[s_String]:= + If[ MatchQ[s,"NDR"|"NDR-Drop"|"BMHV"|"Larin"], + FeynCalc`Package`DiracGammaScheme = s, + Message[FeynCalc::failmsg, "Unknown scheme for Dirac matrices in D dimensions."]; + Abort[] + ]; + +FCGetDiracGammaScheme[]:= + FeynCalc`Package`DiracGammaScheme; + +FCSetPauliSigmaScheme[s_String]:= + If[ MatchQ[s,"None"|"Naive"], + FeynCalc`Package`PauliSigmaScheme = s, + Message[FeynCalc::failmsg, "Unknown scheme for Pauli matrices in D-1 dimensions."]; + Abort[] + ]; + +FCGetPauliSigmaScheme[]:= + FeynCalc`Package`PauliSigmaScheme; + +FCSetMetricSignature[{t_Integer,s_Integer}]:= + ( + If[ {s^2,t^2}=!={1,1}, + Message[FeynCalc::failmsg, "The square of each diagonal element of the metric tensor must be unity."]; + Abort[] + ]; + FeynCalc`Package`MetricT = t; + FeynCalc`Package`MetricS = s; + ); + + +FCGetMetricSignature[]:= + {FeynCalc`Package`MetricT,FeynCalc`Package`MetricS}; + + +FCPrint[level_, fcprintx__ /;!OptionQ[{fcprintx}] , OptionsPattern[]] := + Block[{flowcontrol=OptionValue[FCDoControl]}, + If[ flowcontrol >= level, + If[ OptionValue[UseWriteString], + WriteString[OptionValue[WriteStringOutput],fcprintx], + Print[fcprintx] + ] + ] + ]; + +FI := + (Format[LineBreak[_]] := + ""; + $PrePrint = InputForm;); +FC := + (Format[LineBreak[_]] := + "\n"; + (If[ !$Notebooks, + $PrePrint = FeynCalc`FeynCalcForm, + Unset[$PrePrint] + ]);); + +TBox[] = + "\[Null]"; +TBox[a_] := + ToBoxes[a, TraditionalForm]; +TBox[a_,b__] := + RowBox @ Map[(ToBoxes @@ {#, TraditionalForm})&, {a, b}]; + + +FCPrint[1,"FCMain loaded."]; +End[] + diff --git a/FeynCalc/FeynCalc.m b/FeynCalc/FeynCalc.m index 8d98e60ba..3eddccf04 100644 --- a/FeynCalc/FeynCalc.m +++ b/FeynCalc/FeynCalc.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: FeynCalc is a Mathematica package for symbolic evaluation @@ -19,365 +19,123 @@ If[ MemberQ[$Packages,"FeynCalc`"], - Print["FeynCalc is already loaded! To reload it, please restart the kernel."]; + Print[Style["FeynCalc is already loaded! If you are trying to reload FeynCalc or load \ +FeynArts, TARCER, PHI, FeynHelpers or any other add-on, please restart the kernel.","Text", Red, Bold]]; Abort[] ]; If[ ($VersionNumber < 8.0), - Print["You need at least Mathematica 8.0 to run FeynCalc. Quitting the Mathematica kernel."]; + Print[Style["You need at least Mathematica 8.0 to run FeynCalc. Evaluation aborted.",Red, Bold]]; Abort[] ]; (* Find out where FeynCalc is installed *) -If[ !ValueQ[FeynCalc`$FeynCalcDirectory], - FeynCalc`$FeynCalcDirectory = - DirectoryName[$InputFileName] +If[ !ValueQ[Global`$FeynCalcDirectory], + (* By default FeynCalc is assumed to be located in the directory that contains FeynCalc.m *) + FeynCalc`$FeynCalcDirectory = DirectoryName[$InputFileName], + FeynCalc`$FeynCalcDirectory = Global`$FeynCalcDirectory ]; +Remove[Global`$FeynCalcDirectory]; If[ FileNames["*",{FeynCalc`$FeynCalcDirectory}] === {}, - Print["Could not find a FeynCalc installation. Quitting the Mathematica kernel."]; + Print[Style["Could not find a FeynCalc installation. Evaluation aborted.",Red,Bold]]; Clear[FeynCalc`$FeynCalcDirectory]; Abort[]; ]; (* Set the version number *) -FeynCalc`$FeynCalcVersion = "9.2.0"; +FeynCalc`$FeynCalcVersion = "9.3.0"; -(* Set defaults here, not in the config file *) If[ !ValueQ[Global`$FeynCalcStartupMessages], - Global`$FeynCalcStartupMessages = True + FeynCalc`$FeynCalcStartupMessages = True, + FeynCalc`$FeynCalcStartupMessages = Global`$FeynCalcStartupMessages ]; +Remove[Global`$FeynCalcStartupMessages]; -If[ !ValueQ[Global`$LoadTARCER], - Global`$LoadTARCER = False +If[ !ValueQ[Global`$LoadAddOns], + FeynCalc`$LoadAddOns = {}, + FeynCalc`$LoadAddOns = Global`$LoadAddOns ]; +Remove[Global`$LoadAddOns]; -If[ !ValueQ[Global`$LoadPhi], - Global`$LoadPhi = False +If[ ValueQ[Global`$LoadTARCER], + (*Print[Style["$LoadTARCER is deprecated since FeynCalc 9.3, please use $LoadAddOns={\"TARCER\"} instead!",Red, Bold]];*) + FeynCalc`$LoadAddOns = Join[FeynCalc`$LoadAddOns,{"TARCER"}] ]; +Remove[Global`$LoadTARCER] -If[ !ValueQ[Global`$LoadFeynArts], - Global`$LoadFeynArts = False +If[ ValueQ[Global`$LoadPhi], + (*Print[Style["$LoadPhi is deprecated since FeynCalc 9.3, please use $LoadAddOns={\"FeynArts\"} instead!",Red, Bold]];*) + FeynCalc`$LoadAddOns = Join[FeynCalc`$LoadAddOns,{"PHI"}] ]; +Remove[Global`$LoadPhi]; -If[ !ValueQ[FeynCalc`$FAPatch], - FeynCalc`$FAPatch = True +If[ ValueQ[Global`$LoadFeynArts], + (*Print[Style["$LoadFeynArts is deprecated since FeynCalc 9.3, please use $LoadAddOns={\"FeynArts\"} instead!",Red, Bold]];*) + FeynCalc`$LoadAddOns = Join[FeynCalc`$LoadAddOns,{"FeynArtsLoader"}] ]; +Remove[Global`$LoadFeynArts]; -If[ !ValueQ[FeynCalc`$FCAdvice], - FeynCalc`$FCAdvice = True +If[ !ValueQ[Global`$FAPatch], + FeynCalc`$FAPatch = True, + FeynCalc`$FAPatch = Global`$FAPatch ]; +Remove[Global`$FAPatch] -If[ !ValueQ[Global`$LoadAddOns], - Global`$LoadAddOns = {} +If[ !ValueQ[Global`$FCAdvice], + FeynCalc`$FCAdvice = True, + FeynCalc`$FCAdvice = Global`$FCAdvice ]; +Remove[Global`$FCAdvice] -If[ !ValueQ[Global`$FCCloudTraditionalForm], - FeynCalc`$FCCloudTraditionalForm = True; - Remove[Global`$FCCloudTraditionalForm], - FeynCalc`$FCCloudTraditionalForm = Global`$FCCloudTraditionalForm; - Remove[Global`$FCCloudTraditionalForm] -]; -If[ !ValueQ[FeynCalc`$FeynArtsDirectory], - FeynCalc`$FeynArtsDirectory = FileNameJoin[{FeynCalc`$FeynCalcDirectory, "FeynArts"}] +If[ !ValueQ[Global`$RenameFeynCalcObjects], + FeynCalc`$RenameFeynCalcObjects = {}, + FeynCalc`$RenameFeynCalcObjects = Global`$RenameFeynCalcObjects ]; +Remove[Global`$RenameFeynCalcObjects]; -(* Load configuration file *) -If[ FileExistsQ[FileNameJoin[{FeynCalc`$FeynCalcDirectory,"FCConfig.m"}]], - Get[FileNameJoin[{FeynCalc`$FeynCalcDirectory,"FCConfig.m"}]] +If[ !ValueQ[Global`$FCCloudTraditionalForm], + FeynCalc`$FCCloudTraditionalForm = True, + FeynCalc`$FCCloudTraditionalForm = Global`$FCCloudTraditionalForm ]; +Remove[Global`$FCCloudTraditionalForm]; If[ !ValueQ[Global`$FCTraditionalFormOutput], FeynCalc`$FCTraditionalFormOutput = False, FeynCalc`$FCTraditionalFormOutput = Global`$FCTraditionalFormOutput ]; -Remove[Global`$FCTraditionalFormOutput] +Remove[Global`$FCTraditionalFormOutput]; + +If[ !ValueQ[FeynCalc`$FeynArtsDirectory], + FeynCalc`$FeynArtsDirectory = FileNameJoin[{FeynCalc`$FeynCalcDirectory, "FeynArts"}] +]; -If[ Global`$FeynCalcStartupMessages=!=False, +If[ FeynCalc`$FeynCalcStartupMessages=!=False, PrintTemporary[Style["Loading FeynCalc from "<> FeynCalc`$FeynCalcDirectory, "Text"]] ]; +If[ TrueQ[FileExistsQ[FileNameJoin[{FeynCalc`$FeynCalcDirectory, ".testing"}]]], + FeynCalc`$FeynCalcDevelopmentVersion = True, + FeynCalc`$FeynCalcDevelopmentVersion = False +]; -BeginPackage["FeynCalc`"]; - -$Abbreviations::usage = -"$Abbreviations is a list of string substitution rules used when \ -generating names for storing intermediate results. \ -It is used by OneLoop and PaVeReduce.\ -The elements of the list should be of the form \"name\" -> \"abbreviation\"."; - -$AchmedRoss::usage = -"experimental"; +If[ !ValueQ[Global`$FCCheckContext], + If[ TrueQ[FeynCalc`$FeynCalcDevelopmentVersion], + FeynCalc`$FCCheckContext = True, + FeynCalc`$FCCheckContext = False + ], + FeynCalc`$FCCheckContext = Global`$FCCheckContext +]; +Remove[Global`$FCCheckContext]; -$AL::usage = -"$AL is the head of dummy indices which may be introduced by \ -Uncontract."; -$BreitMaison::usage = -"The Breitenlohner-Maison gamma5 scheme is currently not supported by \ -the Dirac algebra functions. Use Tracer if you need it."; -(* - "The setting of $BreitMaison determines whether the Breitenlohner- - Maison scheme is applied. If $BreitMaison=True, the so-called - naive gamma5 prescription is used, i.e. gamma5 anticommutes in - all dimensions. The default is False. The setting should - be chosen in the file FeynCalc.m BEFORE loading the package. - Reversion during a session is not possible."; -*) +Global`globalContextBeforeLoadingFC = Names["Global`*"]; -$Containers::usage = -"$FieldContainers is a set of heads over which FieldDerivative should -distribute, in the following sense: Let c be a member of $Containers. Then -FieldDerivative[c[f, g, h][x], x, {mu}] -> -c[FieldDerivative[f[x], x, {mu}], FieldDerivative[f[x], x, {mu}], -FieldDerivative[f[x], x, {mu}]]."; - -$Covariant::usage = -"The boolean setting of $Covariant determines whether \ -lorentz indices are displayed as lower indices (True) or as \ -upper ones (False)."; - -$DisableMemSet::usage= -"The boolean setting of $DisableMemSet allows to disable \ -memoizaion that is activated via MemSet. This can be \ -useful for debugging purposes"; - -DOT::usage = -"DOT[a, b, ...] is the FeynCalc function for non-commutative \ -multiplication. By default it is set to the Mathematica Dot \ -functions. By setting \n -DOT=. \n -this can be disabled. \ -Note that then non-commutative products should to be entered \ -like DOT[ DiracMatrix[mu], m + DiracSlash[p], DiracMatrix[mu] ], \ -etc."; - -$DistributiveFunctions::usage = -"$DistributiveFunctions is a set of functions over which FieldDerivative -should be distributed."; - -$FAPatch::usage = -"$FAPatch switches on and off checking for \ -an unpatched FeynArts installation on FeynCalc startup. Default value : True."; - -FC::usage = -"FC changes the output format to FeynCalcForm. \ -To change to InputForm use FI."; - -$FCCheckProgress::usage = -"If set to True, some selected functions will display a progress monitor -during their evaluation. While this can be useful for long computations, -on short expressions the progress bars make evaluating slightly slower. -By default $FCCheckProgress is set to False."; - -$FCCloudTraditionalForm::usage= -"$FCCloudTraditionalFormetermines whether the the cell output will be done \ -in TraditionalForm when FeynCalc is run in Wolfram Cloud. This is done by setting -$Post=TraditionalForm. The default value of $FCCloudTraditionalForm is True." - -$FCTensorList::usage = -"$FCTensorList contains a list of all tensor heads present."; - -FCPrint::usage = -"FCPrint[level, x] outputs Print[x] if the value of $VeryVerbose -is larger than level."; - -$FCS::usage = "$FCS is a list of functions with a short name. \ -E.g. GA[nu] can be used instead of DiracGamma[nu]."; - -FeynCalc::usage = -"For installation notes visit www.feyncalc.org\n -For a list of availabe objects type $FeynCalcStuff, \ -which contains a list of all functions and options in StringForm. \ -You can get on-line information by ?function, e.g. ?Contract.\n -There are several useful functions for short input, type $FCS for a list of \ -short commands. Then type, e.g., ?GA.\n\n -To enable/disable start-up messages, put the line\n -$FeynCalcStartupMessages = True;\n -or\n -$FeynCalcStartupMessages = False;\n -into your \"init.m\" file or into your \"FCConfig.m\" file." - -$FeynCalcStuff::usage = -"$FeynCalcStuff is the list of availabe stuff in FeynCalc."; - -$FeynCalcVersion::usage = -"$FeynCalcVersion is a string that represents the version of FeynCalc."; - -FI::usage = -"FI changes the output format to InputForm. \ -This is useful to see the internal representation of FeynCalc \ -objects. To change back to FeynCalcForm use FC."; - -$Gauge::usage = -"$Gauge(= 1/xi) is a constant specifying the gauge fixing parameter of QED \ -in Lorentz gauge. The usual choice is Feynman gauge, $Gauge=1. \ -Notice that $Gauge is used by some functions, the option Gauge by others."; - -GenerateTarcerMX::usage = -"GenerateTarcerMX creates the *.mx file for TARCER. This is necessary to use -TARCER and has to be done only once. The evaluation usually takes a -couple of minutes." - -$KeepLogDivergentScalelessIntegrals::usage = -"$KeepLogDivergentScalelessIntegrals is an experimental global option that forces \ -FeynCalc not to set 1-loop integrals of type 1/q^4 to zero. This is useful \ -when one has to explicitly distinguish between IR- and UV-divergences in \ -dimensional regularization. Notice that OneLoop is not guaranteed to respect this \ -option."; - -$IndexPrefix::usage = -"$IndexPrefix is a list of prefixes for default Lorentz and color indices -used by GluonPropagator and similar functions."; - -$Larin::usage = -"If set to True, the Larin-Gorishny-Atkyampo-DelBurgo-scheme for \ -gamma5 in D-dimensions is used, i.e. before evaluating traces \ -(but after moving gamma5 anticommuting in D-dimensions to the \ -right of the Dirac string inside a trace) a product gamma[mu].gamma5 is \ -substituted to -I/6 Eps[mu,al,be,si] gamma[al,be,si], \ -where all indices live in D-dimensions now. \ -The Levi-Civita tensor is taken to be \ -D-dimensional, i.e., contraction of two Eps's results in D's. \ -This scheme is often used for performance reasons and is assumed \ -to give the same results as the \ -Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme. However, gamma5 is \ -not anticommuting inside closed fermion loops and it is not so clear -if this scheme works for more than one fermion line involving gamma5. \ -When in doubt, it might be better to use BMHV instead."; - -$LeviCivitaSign::usage = -"$LeviCivitaSign is a global variable that determines \ -the sign in the result of a Dirac trace of four gamma matrices \ -and gamma5. $LeviCivitaSign is by default set to -1 which corresponds \ -to the convention Tr[LeviCivita[a,b,c,d,5]] = -4*I*Eps[a,b,c,d]. \ -Setting $LeviCivitaSign=-I will switch to the FORM-convention."; - -$LimitTo4::usage = -"$LimitTo4 is a global variable that determines whether \ -UV-divergent Passarino-Veltman functions are simplified by \ -taking the limit D-4 -> 0. A general UV-finite \ -Passarino-Veltman function can be written as \ -PaVe = a/(D-4) + b + O(Epsilon), with a being the prefactor \ -of the pole and b being the finite part. Therefore, products \ -of such functions with coefficients that are rational functions \ -of D ( f(D) = f(4) + f'(4) (D-4) + O(Epsilon^2) ) can be simplified \ -to f(D) PaVe = f(4) PaVe + a f'(4) + O(Epsilon), whenever such \ -products appear in the reduction. This relation is correct only if -the Passarino-Veltman functions have no IR divergences, or if such \ -divergences are regulated without using dimensional regularization. -For this reason, even when $LimitTo4 is set to True, the simplifications \ -are applied only to A and B functions. Although B functions can exhibit an \ -IR divegence, such integrals are zero in dimensional regularization, so no \ -mixing of Epsilons from IR and UV can occur. The default value of \ -$LimitTo4 is True."; - -$LimitTo4IRUnsafe::usage = -"$LimitTo4IRUnsafe is a global variable that determines whether \ -the simplifications described in $LimitTo4 are applied also to \ -C and D Passarino-Veltman functions. In this case it is assumed \ -that such functions are either IR finite, or the IR divergences \ -are regulated without using dimensional regularization \ -(i.e. by introducing fictitious masses). Otherwise the results \ -will be inconsistent. If this option is activated, it is the task \ -of the user to ensure that IR divergences are properly regulated, \ -such that no mixing of Epsilons from IR and UV can occur. The default \ -value of $$LimitTo4IRUnsafe is False."; - -$LorentzIndices::usage = -"$LorentzIndices is a global variable. If set to True the dimension \ -of LorentzIndex is displayed as an index."; - -MakeFeynCalcPrivateContext::usage = -"MakeFeynCalcPrivateContext[val] constructs -FeynCalc`Private`val."; - -$MemoryAvailable::usage = -"$MemoryAvailable is a global variable which is set to an integer \ -n, where n is the available amount of main memory in MB. \ -The default is 4096. It should be increased if possible. \ -The higher $MemoryAvailable can be, the more intermediate \ -steps do not have to be repeated by FeynCalc."; - -$MU::usage = -"$MU is the head of dummy indices which may be introduced by \ -Chisholm, Contract, DiracSimplify, FermionSpinSum and various \ -QCD functions. By default it is unset, but can be set to anything."; - -$Multiplications::usage = -"$Multiplications is a set functions which should be treated as -(commutative or non-commutative) multiplications by FieldDerivative."; - -$NonComm::usage = -"$NonComm contains a list of all non-commutative heads present."; - -$ScalarProducts::usage = -"$ScalarProducts contains a list of all vector pairs for which a \ -scalar product value has been defined."; - -$OPEWard::usage = -"$OPEWard is experimental."; - -OptionsSelect::usage = -"OptionsSelect[function,opts] returns the option settings of opts \ -accepted by function. When an option occurs several times in opts, the first \ -setting is selected"; - -TBox::usage = -"TBox[a, b, ...] produces a RowBox[{a,b, ...}] where \ -a,b, ... are boxed in TraditionalForm."; - -UseWriteString::usage = -"UseWriteString is an option for FCPrint. If set to True, -the expression is printed via WriteString instead of Print."; - -$VeryVerbose::usage = -"$VeryVerbose is a global variable with default setting 0. \ -If set to 1, 2, ..., less and more intermediate comments and informations \ -are displayed during calculations."; - -$FCAdvice::usage = -"If $FCAdvice is set to True, FeynCalc will display some -advices on optimal Mathematica configuration for using FeynCalc." - -WriteStringOutput::usage = -"UseWriteStringOutput an option for FCPrint. It specifies, to which -stream WriteString should output the expression"; - -FeynCalc::faerror = -"FeynArts not found or damaged. Please download the FeynArts \ -tarball from www.feynarts.de, unpack it to `1` and restart FeynCalc."; - -FeynCalc::taerror = -"TARCER*.mx file not found or damaged. Please evaluate the command \ -GenerateTarcerMX to create it."; - -FeynCalc::phierror = -"PHI failed to load. Please try resintalling FeynCalc."; - -FeynCalc::tfadvice = -"You are not using TraditionalForm as the default format type of new \ -output cells. Without TraditionalForm FeynCalc cannot use built-in \ -typeseting rules that make various objects like Lorentz vectors or \ -Dirac matrices look nicer. To change the format type go to \ -Edit->Preferences->Evaluation."; - -FCMonitor::usage = -"FCMonitor is a simple function that activates Monitor if there -is a notebook interface available and disables it otherwise."; - -FCMonitorStub::usage = -"FCMonitorStub is a stub for Monitor when the notebook interface -is not available"; - -FCDoControl::usage = -"FCDoControl is an option for FCPrint that specifies which variable -is used to control the debugging output of FCPrint. The default value -is $VeryVerbose."; +BeginPackage["FeynCalc`"]; FCDeclareHeader::usage = "FCDeclareHeader is an internal FeynCalc function to declare @@ -407,155 +165,20 @@ to f(D) PaVe = f(4) PaVe + a f'(4) + O(Epsilon), whenever such \ Begin["`Private`"] -TarcerDialogText = "TARCER*.mx file not found or damaged. Creating a new \ -file can take couple of minutes, but this has to be done only once. \ -After the new file is generated you need to restart FeynCalc. Should \ -we generate new TARCER*.mx now?" - -$AchmedRoss = False; - -$Abbreviations = { - ", "->"", - "^"->"", - "{"->"", - "/" -> "", - "Subscript"->"su", - "SmallVariable"->"sma", - "}"->"", - "["->"", - "]"->"", - "*" -> "", - " " -> "" , - "\n" -> "", - "\r" -> "" -}; - -$BreitMaison = False; -$Containers = {}; -$Covariant = False; -$DisableMemSet = False; -$DistributiveFunctions = {Conjugate, Transpose}; -$FCCheckProgress = False; - -$FCS = { - "CDr", - "FAD", - "FC", - "FCE", - "FCI", - "FDr", - "FI", - "FV", - "FVD", - "FVE", - "GA", - "GA5", - "GAD", - "GAE", - "GGV", - "GP", - "GS", - "GSD", - "GSE", - "LC", - "LCD", - "MT", - "MTD", - "MTE", - "QGV", - "QO", - "SD", - "SDF", - "SOD", - "SP", - "SPC", - "SPD", - "SPE", - "SPL" -}; - -$IndexPrefix = {"li","ci"}; -$KeepLogDivergentScalelessIntegrals = False; -$Larin = False; -$LeviCivitaSign = -1; -$LimitTo4 = False; -$LimitTo4IRUnsafe = False; -$LorentzIndices = False; -$MemoryAvailable = 4096; -$Multiplications = {Times, DOT}; -$OPEWard = False; - -If[ !ValueQ[$VeryVerbose], - $VeryVerbose = 0 -]; - -If[ !ValueQ[$NonComm], - $NonComm = {} -]; - -If[ !ValueQ[$FCTensorList], - $FCTensorList = {} -]; - -If[ !ValueQ[$ScalarProducts], - $ScalarProducts = {} -]; - - -$Gauge/: - MakeBoxes[$Gauge,TraditionalForm]:= - MakeBoxes[StyleForm["\[Lambda]",FontSlant->"Italic"]]; - -GenerateTarcerMX := - If[ Get@ToFileName[{$FeynCalcDirectory, "Tarcer"}, "TARCER.m"]=!= $Failed, - Print["Succesfully created ", Last@FileNames["*.mx", FileNameJoin[{$FeynCalcDirectory, "Tarcer"}]]] - ] - -DOT = Dot; - -(* DOT moved into main context. 32/2-2003. F.Orellana. - The reason for this is the following: In order to use - DOT instead of Dot consistenly everywhere, we need to be - able to do e.g. f[DOT[a_,b_]]:=g[a,b]. Because DOT is immediately - set to something else (Dot), this works only if DOT is in - $ContextPath at the moment this definition is evaluated. - In the context of the packages, $ContextPath is typically - {"System`", "FeynCalc`"}. - *) - -FCEnableTraditionalFormOutput[]:= - (CurrentValue[$FrontEndSession, {CommonDefaultFormatTypes, "Output"}] = TraditionalForm;); - -FCDisableTraditionalFormOutput[]:= - (CurrentValue[$FrontEndSession, {CommonDefaultFormatTypes, "Output"}] = StandardForm; ); - -SetAttributes[FCPrint, HoldRest]; - -Options[FCPrint] = { - FCDoControl :> $VeryVerbose, - UseWriteString -> False, - WriteStringOutput ->"stdout" -} - -FCPrint[level_, fcprintx__ /;!OptionQ[{fcprintx}] , OptionsPattern[]] := - Block[{flowcontrol=OptionValue[FCDoControl]}, - If[ flowcontrol >= level, - If[ OptionValue[UseWriteString], - WriteString[OptionValue[WriteStringOutput],fcprintx], - Print[fcprintx] - ] - ] - ]; - -FCMonitor:= - If[$Notebooks && $FCCheckProgress, Monitor, FCMonitorStub]; +FCDeclareHeader[file_, type_String:"file"] := + Module[ {strm, einput, moreLines = True}, -FCMonitorStub[x_,__]:= - x; + Switch[ + type, + "file", + strm = OpenRead[file], + "string", + strm = StringToStream[file], + _, + Print["FeynCalc: FCDeclareHeader: Unknown input type. Evaluation aborted"]; + Abort[]; + ]; -FCDeclareHeader[file_] := - Module[ {strm, einput, moreLines = True}, - strm = OpenRead[file]; If[ Head[strm] =!= InputStream, Return[$Failed] ]; @@ -567,132 +190,99 @@ set to something else (Dot), this works only if DOT is in moreLines = False ] ]; - Close[file] + Close[strm] ]; +End[] -FI := - (Format[LineBreak[_]] := - ""; - $PrePrint = InputForm;); -FC := - (Format[LineBreak[_]] := - "\n"; - (If[ !$Notebooks, - $PrePrint = FeynCalc`FeynCalcForm, - Unset[$PrePrint] - ]);); - -TBox[] = - "\[Null]"; -TBox[a_] := - ToBoxes[a, TraditionalForm]; -TBox[a_,b__] := - RowBox @ Map[(ToBoxes @@ {#, TraditionalForm})&, {a, b}]; - -l[w_Integer] := - l[w] = - Block[ {pre}, - If[ !MatchQ[pre = $IndexPrefix,{_String,_String}], - pre = {ToString[Unique["l"]], ToString[Unique["c"]]} - ]; - ToExpression[pre[[1]]<>ToString[w]] - ]; - -c[w_Integer] := - c[w] = - Block[ {pre}, - If[ !MatchQ[pre = $IndexPrefix,{_String,_String}], - pre = {ToString[Unique["l"]], ToString[Unique["c"]]} - ]; - ToExpression[pre[[2]]<>ToString[w]] - ]; - -(*TODO: Get rid of OptionsSelect everywhere. Use FilterRules[opts, Options[function]] instead *) -OptionsSelect[function_, opts___] := - Select[(Cases[{opts}, _Rule|_RuleDelayed, Infinity] //. - {{a___, b_ -> c_, d___, b_ -> e_, f___} -> {a, b -> c, d, f}, - {a___, b_ :> c_, d___, b_ :> e_, f___} -> {a, b :> c, d, f}}), - (!FreeQ[#, (Options[function] /. - {((a_ -> b_) | (a_ :> b_)) -> ((a -> _) | (a :> _))} /. - List -> Alternatives)])&]; - -MakeFeynCalcPrivateContext[x_String] := - MakeFeynCalcPrivateContext[x] = ToExpression["FeynCalc`Private`"<>x]; - -End[]; +(* Load the configuration file *) +If[ FileExistsQ[FileNameJoin[{FeynCalc`$FeynCalcDirectory,"FCConfig.m"}]], + Get[FileNameJoin[{FeynCalc`$FeynCalcDirectory,"FCConfig.m"}]] +]; (* need to do this first, otherwise $NonComm and $FCTensorList do not get built correctly *) boostrappingList = Join[ - Map[ToFileName[{$FeynCalcDirectory,"Shared"},#]&, {"SharedTools.m", "DataType.m"}], - Map[ToFileName[{$FeynCalcDirectory,"NonCommAlgebra"},#]&, {"NonCommutative.m"}], - Map[ToFileName[{$FeynCalcDirectory,"Lorentz"},#]&, {"DeclareFCTensor.m"}] + Map[FileNameJoin[{$FeynCalcDirectory,"Shared",#}]&, {"SharedTools.m", "DataType.m"}], + Map[FileNameJoin[{$FeynCalcDirectory,"NonCommAlgebra",#}]&, {"NonCommutative.m"}], + Map[FileNameJoin[{$FeynCalcDirectory,"Lorentz",#}]&, {"DeclareFCTensor.m"}] ]; -listShared = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"Shared"}]]; -listNonCommAlgebra = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"NonCommAlgebra"}]]; -listLorentz = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"Lorentz"}]]; -listDirac = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"Dirac"}]]; -listSUN = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"SUN"}]]; -listLoopIntegrals = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"LoopIntegrals"}]]; -listFeynman = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"Feynman"}]]; -listQCD = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"QCD"}]]; -listTables = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"Tables"}]]; -listExportImport = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"ExportImport"}]]; -listMisc = FileNames[{"*.m"},ToFileName[{$FeynCalcDirectory,"Misc"}]]; +mainList = {FileNameJoin[{$FeynCalcDirectory, "FCMain.m"}]}; + +allList = { + Select[FileNames[{"*.m"}, FileNameJoin[{$FeynCalcDirectory, "Shared"}]], StringFreeQ[#, "LegacyObjects"] &], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"NonCommAlgebra"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"Lorentz"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"Dirac"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"Pauli"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"SUN"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"LoopIntegrals"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"Feynman"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"QCD"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"Tables"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"ExportImport"}]], + FileNames[{"*.m"},FileNameJoin[{$FeynCalcDirectory,"Misc"}]], + {FileNameJoin[{$FeynCalcDirectory, "Shared", "LegacyObjects.m"}]} +}; + +fcSelfPatch[file_String]:= + Block[{originalCode,repList}, + + repList = Map[{ + Rule[RegularExpression["\\b" <> First[#] <> "\\b"], Last[#]], + Rule[RegularExpression["\\_" <> First[#] <> "\\b"], "_" <> Last[#]], + Rule[RegularExpression[First[#] <> "\\_\\b"], Last[#] <> "_"]} &, $RenameFeynCalcObjects] // Flatten; + originalCode = Import[file, "Text"]; + StringReplace[originalCode, repList, MetaCharacters -> Automatic] + ]; AppendTo[$ContextPath, "FeynCalc`Package`"]; -FCDeclareHeader/@listShared; -FCDeclareHeader/@listNonCommAlgebra; -FCDeclareHeader/@listLorentz; -FCDeclareHeader/@listDirac; -FCDeclareHeader/@listSUN; -FCDeclareHeader/@listLoopIntegrals; -FCDeclareHeader/@listFeynman; -FCDeclareHeader/@listQCD; -FCDeclareHeader/@listTables; -FCDeclareHeader/@listExportImport; -FCDeclareHeader/@listMisc; - -Get/@boostrappingList; -Get/@listShared; -Get/@listNonCommAlgebra; -Get/@listLorentz; -Get/@listDirac; -Get/@listSUN; -Get/@listLoopIntegrals; -Get/@listFeynman; -Get/@listQCD; -Get/@listTables; -Get/@listExportImport; -Get/@listMisc; +patchedMain =(fcSelfPatch/@mainList); +patchedBoostrap =(fcSelfPatch/@boostrappingList) +patchedList = Map[Function[argList, fcSelfPatch /@ argList], allList]; + +FCDeclareHeader[#,"string"]&/@(patchedMain); +ToExpression/@patchedMain; + +Map[Function[argList, FCDeclareHeader[#,"string"]& /@ argList], patchedList]; + +ToExpression/@patchedBoostrap; +Map[Function[argList, ToExpression /@ argList], patchedList]; EndPackage[]; +Remove["FeynCalc`boostrappingList"]; +Remove["FeynCalc`allList"]; +Remove["FeynCalc`mainList"]; +Remove["FeynCalc`argList"]; +Remove["FeynCalc`fcSelfPatch"]; +Remove["FeynCalc`patched*"]; +Remove["FeynCalc`originalCode"]; +Remove["FeynCalc`repList"]; +Remove["FeynCalc`file"]; + (* If necessary, swtich the output format of the current frontend to TraditionalForm *) If[ $FCTraditionalFormOutput, CurrentValue[$FrontEndSession, {CommonDefaultFormatTypes, "Output"}] = TraditionalForm ]; -(* From Mathematica 4.0 onwards there is "Tr" functions; - Overload Tr to use TR -*) +(* From Mathematica 4.0 onwards there is "Tr" functions; Overload Tr to use TR *) Unprotect[Tr]; Tr[Pattern[FeynCalc`Private`trarg,BlankSequence[]]] := - TR[FeynCalc`Private`trarg] /; !FreeQ[{FeynCalc`Private`trarg}, DiracGamma | DiracMatrix | DiracSlash | GA | GAD | GAE | GS | GSD | GSE | Pair]; + TR[FeynCalc`Private`trarg] /; !FreeQ[{FeynCalc`Private`trarg}, FeynCalc`Package`TrFeynCalcObjects]; Tr::usage = "FeynCalc extension: Tr[list] finds the trace of the matrix or tensor list. Tr[list, f] finds a generalized trace, combining terms with f instead of Plus. Tr[list, f, n] goes down to level n in list. \n Tr[ expression ] calculates the DiracTrace, i.e., TR[ expression ], if any of DiracGamma, -DiracSlash, GA, GAD, GAE, GS, GSD or GAE are present in expression."; +GA, GAD, GAE, GS, GSD or GAE are present in expression."; Tr/:Options[Tr]:=Options[TR]; Protect[Tr]; -If[ !$Notebooks && Global`$FeynCalcStartupMessages, +If[ !$Notebooks && $FeynCalcStartupMessages, $PrePrint = FeynCalcForm; WriteString["stdout", "$PrePrint is set to FeynCalcForm. Use FI and FC to change the display format.\n"], @@ -704,9 +294,12 @@ set to something else (Dot), this works only if DOT is in (* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) (* Print FeynCalc's startup message *) -If[ Global`$FeynCalcStartupMessages =!= False, - Print[ Style["FeynCalc ", "Text", Bold], Style[$FeynCalcVersion <> ". For help, use the ", - "Text"], +If[ $FeynCalcStartupMessages =!= False, + Print[ Style["FeynCalc ", "Text", Bold], + If[ TrueQ[$FeynCalcDevelopmentVersion], + Style[$FeynCalcVersion <> " (development version). For help, use the ", "Text"], + Style[$FeynCalcVersion <> " (stable version). For help, use the ", "Text"] + ], Style[DisplayForm@ButtonBox["documentation center", BaseStyle->"Link", ButtonData :> "paclet:FeynCalc/", ButtonNote -> "paclet:FeynCalc/"], "Text"], Style[", check out the ", "Text"], @@ -715,132 +308,90 @@ set to something else (Dot), this works only if DOT is in Style[" or write to the ", "Text"], Style[DisplayForm@ButtonBox["mailing list.",ButtonData :> {URL["http://www.feyncalc.org/forum/"], None},BaseStyle -> "Hyperlink", ButtonNote -> "http://www.feyncalc.org/forum/"],"Text"]]; + Print[ Style["To save your and our time, please check our ","Text"], Style[DisplayForm@ButtonBox["FAQ",ButtonData :> {URL["https://github.com/FeynCalc/feyncalc/wiki/FAQ"], None},BaseStyle -> "Hyperlink", + ButtonNote -> "https://github.com/FeynCalc/feyncalc/wiki"],"Text"] , Style[" for answers to some common FeynCalc questions.","Text"] ]; Print[ Style["See also the supplied ","Text"], Style[DisplayForm@ButtonBox["examples.", BaseStyle -> "Hyperlink", ButtonFunction :> SystemOpen[FileNameJoin[{$FeynCalcDirectory, "Examples"}]], Evaluator -> Automatic, Method -> "Preemptive"], "Text"], Style[" If you use FeynCalc in your research, please cite","Text"]]; - Print [Style[" \[Bullet] V. Shtabovenko, R. Mertig and F. Orellana, Comput. Phys. Commun., 207C, 432-444, 2016, arXiv:1601.01167","Text"]]; + + + Print [Style[" \[Bullet] V. Shtabovenko, R. Mertig and F. Orellana, P3H-20-002, TTP19-020, TUM-EFT 130/19, arXiv:2001.xxxxx","Text"]]; + Print [Style[" \[Bullet] V. Shtabovenko, R. Mertig and F. Orellana, Comput. Phys. Commun., 207, 432-444, 2016, arXiv:1601.01167","Text"]]; Print [Style[" \[Bullet] R. Mertig, M. B\[ODoubleDot]hm, and A. Denner, Comput. Phys. Commun., 64, 345-359, 1991.","Text"]] ]; -(* Load PHI... *) -If[ $LoadPhi, - If[ $FeynCalcStartupMessages, - PrintTemporary[Style["Loading PHI from " <> FileNameJoin[{$FeynCalcDirectory, "Phi"}], "Text"]]; - ]; - If[Get[FileNameJoin[{$FeynCalcDirectory, "Phi","Phi.m"}]] =!=$Failed, - If[ Global`$FeynCalcStartupMessages, - Print[ Style["PHI ", "Text", Bold], - Style[Phi`$PhiVersion <>", for examples visit ", - "Text"], - Style[DisplayForm@ButtonBox["www.feyncalc.org/phi.", ButtonData :> {URL["http://www.feyncalc.org/phi/"], None}, - BaseStyle -> "Hyperlink", ButtonNote -> "http://www.feyncalc.org/phi/"],"Text"] - ] - ], - Message[FeynCalc::phierror] - ]; -]; +(* Some addons might need to add new stuff to the $ContextPath. While inside the + FeynCalc` path they obviously cannot do this by themselves. However, via + FeynCalc`Private`AddToTheContextPath they can ask FeynCalc to do this for + them. +*) +FeynCalc`Private`AddToTheContextPath={}; -(* Load FeynArts... *) -If[ $LoadFeynArts, - If[ $FeynCalcStartupMessages, - PrintTemporary[Style["Loading FeynArts from " <> $FeynArtsDirectory, "Text"]]; - ]; - Block[ {FeynCalc`Private`loadfa, FeynCalc`Private`fafiles, FeynCalc`Private`strm, FeynCalc`Private`patch=True, FeynCalc`Private`str}, - If[ $FAPatch, - (* Check if FeynArts needs to be patched *) - If[(FeynCalc`Private`fafiles = FileNames["FeynArts.m", $FeynArtsDirectory])=!={}, - FeynCalc`Private`strm = OpenRead[First[FeynCalc`Private`fafiles]]; - If[ Head[FeynCalc`Private`strm] =!= InputStream, - Message[General::noopen, First[FeynCalc`Private`fafiles]]; - Abort[] - ]; - While[ ToString[FeynCalc`Private`str] != "EndOfFile", - FeynCalc`Private`str = Read[FeynCalc`Private`strm, String]; - If[ StringMatchQ[ToString[FeynCalc`Private`str], "*patched for use with FeynCalc*", IgnoreCase -> True], - FeynCalc`Private`patch = False - ] - ]; - Close[First[FeynCalc`Private`fafiles]], - Message[General::noopen, FileNameJoin[{$FeynArtsDirectory, "FeynArts.m"}]]; - Message[FeynCalc::faerror, $FeynArtsDirectory]; - FeynCalc`Private`patch = False - ]; - (* Apply the patch *) - If[ FeynCalc`Private`patch, - FAPatch[] - ] - ]; - FeynCalc`Private`loadfa=Block[ {Print= System`Print},Get[FileNameJoin[{$FeynArtsDirectory, "FeynArts.m"}]]]; - If[FeynCalc`Private`loadfa =!=$Failed, - (* If everything went fine *) - If[ Global`$FeynCalcStartupMessages, - Print[ Style["FeynArts ", "Text", Bold], - Style[StringReplace[ToString[FeynArts`$FeynArtsVersion],"FeynArts "->""] <>" patched for use with FeynCalc, for documentation use the ", - "Text"], - Style[DisplayForm@ButtonBox["manual", BaseStyle -> "Hyperlink", ButtonFunction :> - SystemOpen[First@FileNames[{"*.pdf", "*.PDF"}, FileNameJoin[{$FeynArtsDirectory, "manual"}]]], - Evaluator -> Automatic, Method -> "Preemptive"], "Text"], - Style[" or visit ", "Text"], - Style[DisplayForm@ButtonBox["www.feynarts.de.", ButtonData :> {URL["http://www.feynarts.de/"], None}, - BaseStyle -> "Hyperlink", ButtonNote -> "www.feynarts.de/"],"Text"] - ] - ], - (* If FeynArts didn't load *) - Message[FeynCalc::faerror, $FeynArtsDirectory]; - ]; - ]; +FeynCalc`Private`AddToTheWhiteListedContextAdditions={}; + +BeginPackage["FeynCalc`"]; +If[ $LoadAddOns=!={}, + $LoadAddOns = $LoadAddOns /. {"FeynArts" -> "FeynArtsLoader"}; + FCDeclareHeader/@Map[ToFileName[{$FeynCalcDirectory, "AddOns",#},#<>".m"] &, $LoadAddOns]; + Get/@Map[ToFileName[{$FeynCalcDirectory, "AddOns",#},#<>".m"] &, $LoadAddOns] ]; +EndPackage[]; + +If[ FeynCalc`Private`AddToTheContextPath=!={} && ListQ[FeynCalc`Private`AddToTheContextPath], + $ContextPath = Join[FeynCalc`Private`AddToTheContextPath,$ContextPath] +] + +If[ $FCCheckContext, + + Global`globalContextAfterLoadingFC = Names["Global`*"]; + + Global`fcContextLowerCase = Select[Names["FeynCalc`*"], LowerCaseQ[StringTake[#, 1]] &]; -(* Load TARCER... *) -If[ $LoadTARCER, - If[ $FeynCalcStartupMessages, - PrintTemporary[Style["Loading TARCER from " <> FileNameJoin[{$FeynCalcDirectory, "Tarcer"}], "Text"]] + If[$RenameFeynCalcObjects=!={}, + Global`fcContextLowerCase = Complement[Global`fcContextLowerCase, Last /@ $RenameFeynCalcObjects] ]; - Block[{FeynCalc`Private`tarcerfilenames}, - FeynCalc`Private`tarcerfilenames = - FileNames["tarcer"<> StringReplace[$System,{"-"->"","Microsoft"->"","("->"",")"->""," "->""}] <>"*.mx", - ToFileName[{FeynCalc`$FeynCalcDirectory,"Tarcer"}],IgnoreCase->True]; - If[ FeynCalc`Private`tarcerfilenames=!={}, - (* If the .mx file of TARCER is found, load it now. *) - If[ Get[Last[FeynCalc`Private`tarcerfilenames]]=!=$Failed, - If[ $FeynCalcStartupMessages, - Print[ Style["TARCER ", "Text", Bold], - Style[Tarcer`$TarcerVersion <> - ", for description see the preprint hep-ph/9801383 at ", "Text"], - Style[DisplayForm@ButtonBox["arxiv.org.", ButtonData :> - {URL["http://arxiv.org/abs/hep-ph/9801383"], None}, - BaseStyle -> {"Hyperlink"}, ButtonNote -> "http://arxiv.org/abs/hep-ph/9801383"],"Text"] - ] - ], - Message[FeynCalc::taerror]; - If [$Notebooks, - If[ ChoiceDialog[FeynCalc`Private`TarcerDialogText], - GenerateTarcerMX - ] - ] - ], - Message[FeynCalc::taerror]; - If [$Notebooks, - If[ ChoiceDialog[FeynCalc`Private`TarcerDialogText], - GenerateTarcerMX - ] - ] + + Global`whiteListedContextAdditions = { + "Colour", "CT", "cto", "d", "dD", "eE", "FAChiralityProjector", + "FADiracMatrix", "FADiracSlash", "FADiracSpinor", "FADiracTrace", + "FAFourVector", "FAGS", "FAMetricTensor", "FAPolarizationVector", + "FAScalarProduct", "FASUNF", "FASUNT", "ff", "gA", "gA5", "gA6", + "gA7", "globalContextAfterLoadingFC", "Gluon", "GraphName","dSUN", + "Lorentz", "M", "pp", "TJI111e", "$INTC", "$Special", "$SpecialTLI", + "fcContextLowerCase", "newObjectsInTheContext", "MajoranaSpinor", + "newObjectsInTheGlobalContext", "whiteListedContextAdditions", "GetFlip", + "Dirac" + }; + + Global`whiteListedContextAdditions = Join[Global`whiteListedContextAdditions,FeynCalc`Private`AddToTheWhiteListedContextAdditions]; + + Global`newObjectsInTheGlobalContext = Complement[Global`globalContextAfterLoadingFC, Global`globalContextBeforeLoadingFC]// + Complement[#,Global`whiteListedContextAdditions]&; + + If[ (Global`fcContextLowerCase=!={} || Global`newObjectsInTheGlobalContext=!={}) && FreeQ[FeynCalc`$LoadAddOns,{"PHI"}], + Message[FeynCalc::context]; + If[ Global`fcContextLowerCase=!={}, + Print["New lowercase objects in the FeynCalc context: ", Global`fcContextLowerCase] ]; + If[ Global`newObjectsInTheGlobalContext=!={}, + Print["New lowercase objects in the Global context: ", Global`newObjectsInTheGlobalContext] + ] ]; - (* This seems to be needed for MMA8 *) - If[FreeQ[$ContextPath,"Tarcer`"],PrependTo[$ContextPath,"Tarcer`"]]; -]; -BeginPackage["FeynCalc`"]; -If[ Global`$LoadAddOns=!={}, - FCDeclareHeader/@Map[ToFileName[{$FeynCalcDirectory, "AddOns",#},#<>".m"] &, Global`$LoadAddOns]; - Get/@Map[ToFileName[{$FeynCalcDirectory, "AddOns",#},#<>".m"] &, Global`$LoadAddOns] -]; -EndPackage[]; + Remove["Global`fcContextLowerCase"]; + Remove["Global`newObjectsInTheGlobalContext"]; + Remove["Global`whiteListedContextAdditions"]; + Remove["Global`globalContextBeforeLoadingFC"]; + Remove["Global`globalContextAfterLoadingFC"]; + +] + + + If[ $CloudEvaluation && $FCCloudTraditionalForm, diff --git a/FeynCalc/Feynman/BackgroundGluonVertex.m b/FeynCalc/Feynman/BackgroundGluonVertex.m index 54c6242e4..216cc0bf4 100755 --- a/FeynCalc/Feynman/BackgroundGluonVertex.m +++ b/FeynCalc/Feynman/BackgroundGluonVertex.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Gluon vertex in the background field gauge *) @@ -47,11 +47,6 @@ Gauge -> 1 }; -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - -BackgroundGluonVertex[x___, i_Integer, y___] := - BackgroundGluonVertex[x, l[i], c[i], y]; - (* 3 - vertex *) BackgroundGluonVertex[x1_,x2_,x3_,x4_,x5_,x6_,x7_,x8_, x9_, opts:OptionsPattern[]] := BackgroundGluonVertex[{x1,x2,x3}, {x4,x5,x6}, {x7,x8,x9} , opts] /; diff --git a/FeynCalc/Feynman/ChargeConjugationMatrix.m b/FeynCalc/Feynman/ChargeConjugationMatrix.m deleted file mode 100755 index e85c5c4b5..000000000 --- a/FeynCalc/Feynman/ChargeConjugationMatrix.m +++ /dev/null @@ -1,39 +0,0 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: ChargeConjugationMatrix *) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 22 June '97 at 22:58 *) -(* ------------------------------------------------------------------------ *) - -(* :Summary: ChargeConjugationMatrix is an experimental - implementation of C *) - -(* ------------------------------------------------------------------------ *) -ChargeConjugationMatrix::usage = -"ChargeConjugationMatrix denotes the charge conjugation matrix C."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`ChargeConjugationMatrix`Private`"] - -If[ FreeQ[$NonComm, ChargeConjugationMatrix] && Head[$NonComm] === List, - AppendTo[$NonComm, ChargeConjugationMatrix] -]; - -ChargeConjugationMatrix /: (ChargeConjugationMatrix^n_Integer?EvenQ /; n>0) := -I^n; - -ChargeConjugationMatrix /: (ChargeConjugationMatrix^n_Integer?OddQ /; n>2) := -ChargeConjugationMatrix (I^(n-1)); - -ChargeConjugationMatrix /: -MakeBoxes[ChargeConjugationMatrix, TraditionalForm] := "C"; - -FCPrint[1,"ChargeConjugationMatrix.m loaded."]; -End[] diff --git a/FeynCalc/Feynman/ChargeConjugationMatrixInv.m b/FeynCalc/Feynman/ChargeConjugationMatrixInv.m deleted file mode 100755 index 49d8d5a48..000000000 --- a/FeynCalc/Feynman/ChargeConjugationMatrixInv.m +++ /dev/null @@ -1,34 +0,0 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: ChargeConjugationMatrixInv *) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 22 June '97 at 22:58 *) -(* ------------------------------------------------------------------------ *) - -(* ------------------------------------------------------------------------ *) - -ChargeConjugationMatrixInv::usage = -"ChargeConjugationMatrixInv is the inverse of ChargeConjugationMatrix. \ -It is substituted immediately by -ChargeConjugationMatrix."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`ChargeConjugationMatrixInv`Private`"] - - -ChargeConjugationMatrixInv = - -ChargeConjugationMatrix; - -(* -If[FreeQ[$NonComm, ChargeConjugationMatrixInv] && Head[$NonComm]===List, - AppendTo[$NonComm, ChargeConjugationMatrixInv]]; -*) - -FCPrint[1,"ChargeConjugationMatrixInv.m loaded."]; -End[] diff --git a/FeynCalc/Feynman/ComplexConjugate.m b/FeynCalc/Feynman/ComplexConjugate.m index 0cd2b403b..c387f9f5c 100755 --- a/FeynCalc/Feynman/ComplexConjugate.m +++ b/FeynCalc/Feynman/ComplexConjugate.m @@ -1,166 +1,366 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) +(* ::Package:: *) -(* :Title: ComplexConjugate *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Author: Rolf Mertig *) +(* :Title: ComplexConjugate *) -(* ------------------------------------------------------------------------ *) -(* :History: File created on 21 February '99 at 2:00 *) -(* ------------------------------------------------------------------------ *) - -(* :Summary: construct the complex conjugate amplitude, - introducing complex conjugated indices automatically +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) -(* :Comments: ComplexConjugate does NOT work if complex - quantities are in denominators!!!!!!!!!!!!!!! -*) +(* :Summary: Construct the complex conjugate amplitude *) (* ------------------------------------------------------------------------ *) ComplexConjugate::usage = -"ComplexConjugate[expr] complex conjugates expr. It operates on \ -Fermion-lines, i.e., products of Spinor[..] .DiracMatrix[..] . Spinor[..]. \ -For taking the spin sum (i.e. constructing the traces) use FermionSpinSum. \n \n -WARNING: In expr should be NO explicit I in denominators!"; +"ComplexConjugate[exp] returns the complex conjugate of exp, where the input \ +expression must be a proper matrix element. In particular, all Dirac \ +matrices are assumed to be inside closed Dirac spinor chains. If this is not \ +the case, the result will be inconsistent. Futhermore, denominators may not contain \ +explicit I's!"; -(* ------------------------------------------------------------------------ *) +ComplexConjugate::failmsg = +"Error! ComplexConjugate has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; + +ComplexConjugate::warnmsg = +"Warning! `1`"; Begin["`Package`"] End[] Begin["`ComplexConjugate`Private`"] -dotlin[x_] := - DotSimplify[x, Expanding -> False]; -(* -HoldPattern[ rev[yz__ /; FreeQ2[{yz}, {SUNT}] ] ]:= +ccjVerbose::usage=""; +holdDOT::usage=""; +holdDOTReversed::usage=""; + + +(* for large expressions it is better to not use DotSimplify *) +Options[ComplexConjugate] = { + Conjugate -> {}, + DotSimplify -> True, + FCE -> False, + FCI -> False, + FCRenameDummyIndices -> True, + FCVerbose -> False +}; + +(*TODO Check denominators using FCExtractDenominatorFactors*) + +ComplexConjugate[expr_List, opts:OptionsPattern[]]:= + ComplexConjugate[#,opts]&/@expr; + +ComplexConjugate[expr_/;Head[expr]=!=List, OptionsPattern[]]:= + Block[{ ex,res,optConjugate, ruleConjugate, ru, time, + prefList, diracList, sunList, pauliList, + prefHead, pauliHead, sunHead, diracHead, + prefListEval, diracListEval, sunListEval, pauliListEval, + repRule, ccRules}, + + optConjugate = OptionValue[Conjugate]; + + If [OptionValue[FCVerbose]===False, + ccjVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + ccjVerbose=OptionValue[FCVerbose] + ]; + ]; + + + FCPrint[1,"ComplexConjugate: Entering.", FCDoControl->ccjVerbose]; + FCPrint[3,"ComplexConjugate: Entering with: ", expr, FCDoControl->ccjVerbose]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + time = AbsoluteTime[]; + FCPrint[1,"ComplexConjugate: Applying FCMatrixIsolate.", FCDoControl->ccjVerbose]; + ex = FCMatrixIsolate[ex,FCI->True, FCColorIsolate->{sunHead}, FCDiracIsolate->{diracHead, + {FCI->True, DiracChain->True, Expanding->False, FCJoinDOTs->False, DiracSigmaExplicit->True, DiracGammaCombine->False}}, + FCPauliIsolate->{pauliHead}, Head->prefHead]; + FCPrint[1,"ComplexConjugate: Done applying FCMatrixIsolate, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->ccjVerbose]; + FCPrint[3,"ComplexConjugate: After FCMatrixIsolate: ", ex, FCDoControl->ccjVerbose]; + + (* + If the matrix structure of the expression is too convoluted, we need to redo the isolation after applying + DotSimplify (this time with Expanding set to True) + *) + time = AbsoluteTime[]; + FCPrint[1,"ComplexConjugate: Applying additional isolations.", FCDoControl->ccjVerbose]; + ex = ex /. { + diracHead[z_]/; !FreeQ2[z,Join[FeynCalc`Package`PauliHeadsList,FeynCalc`Package`SUNHeadsList]] :> + FCMatrixIsolate[DotSimplify[z,FCI->True],FCI->True, FCColorIsolate->{sunHead}, FCDiracIsolate->{diracHead, + {FCI->True, DiracChain->True, Expanding->False, FCJoinDOTs->False, DiracSigmaExplicit->True, DiracGammaCombine->False}}, + FCPauliIsolate->{pauliHead}, Head->prefHead] + } /. { + pauliHead[z_]/; !FreeQ2[z,Join[FeynCalc`Package`DiracHeadsList,FeynCalc`Package`SUNHeadsList,{FCChargeConjugateTransposed}]] :> + FCMatrixIsolate[DotSimplify[z,FCI->True],FCI->True, FCColorIsolate->{sunHead}, FCDiracIsolate->{diracHead, + {FCI->True, DiracChain->True, Expanding->False, FCJoinDOTs->False, DiracSigmaExplicit->True, DiracGammaCombine->False}}, + FCPauliIsolate->{pauliHead}, Head->prefHead] + } /. { + sunHead[z_]/; !FreeQ2[z,Join[FeynCalc`Package`DiracHeadsList,FeynCalc`Package`PauliHeadsList]] :> + FCMatrixIsolate[DotSimplify[z,FCI->True],FCI->True, FCColorIsolate->{sunHead}, FCDiracIsolate->{diracHead, + {FCI->True, DiracChain->True, Expanding->False, FCJoinDOTs->False, DiracSigmaExplicit->True, DiracGammaCombine->False}}, + FCPauliIsolate->{pauliHead}, Head->prefHead] + } /. { + prefHead[z_]/; !FreeQ2[z,Join[FeynCalc`Package`DiracHeadsList,FeynCalc`Package`PauliHeadsList,FeynCalc`Package`SUNHeadsList,{DOT}]] :> + FCMatrixIsolate[DotSimplify[z,FCI->True],FCI->True, FCColorIsolate->{sunHead}, FCDiracIsolate->{diracHead, + {FCI->True, DiracChain->True, Expanding->False, FCJoinDOTs->False, DiracSigmaExplicit->True, DiracGammaCombine->False}}, + FCPauliIsolate->{pauliHead}, Head->prefHead] + }; + FCPrint[1,"ComplexConjugate: Done applying additional isolations, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->ccjVerbose]; + FCPrint[3,"ComplexConjugate: After additional isolations: ", ex, FCDoControl->ccjVerbose]; + + prefList = Cases2[ex,prefHead]; + diracList = Cases2[ex,diracHead]; + pauliList = Cases2[ex,pauliHead]; + sunList = Cases2[ex,sunHead]; + + (*Some checks*) + If[ !FreeQ2[prefList,Join[FeynCalc`Package`DiracHeadsList,FeynCalc`Package`PauliHeadsList,FeynCalc`Package`SUNHeadsList,{DOT}]], + Message[ComplexConjugate::warnmsg, "The list of prefactors contains Dirac, Pauli or SU(N) symbols. Their correct complex conjugation is not guaranteed."] + ]; + + If[ !FreeQ2[diracList,Join[FeynCalc`Package`PauliHeadsList,FeynCalc`Package`SUNHeadsList]], + Message[ComplexConjugate::warnmsg, "The list of Dirac chains contains Pauli or SU(N) symbols. Their correct complex conjugation is not guaranteed."] + ]; + + If[ !FreeQ2[pauliList,Join[FeynCalc`Package`DiracHeadsList,FeynCalc`Package`SUNHeadsList,{FCChargeConjugateTransposed}]], + Message[ComplexConjugate::warnmsg, "The list of Pauli chains contains Dirac or SU(N) symbols. Their correct complex conjugation is not guaranteed."] + ]; + + If[ !FreeQ2[sunList,Join[FeynCalc`Package`DiracHeadsList,FeynCalc`Package`PauliHeadsList]], + Message[ComplexConjugate::warnmsg, "The list of SU(N) chains contains Dirac or Pauli symbols. Their correct complex conjugation is not guaranteed."] + ]; + + diracListEval = (diracChainCC /@ (diracList /. DOT->holdDOT /. diracHead -> Identity)) /. {holdDOTReversed-> DOT, diracGammaHold->DiracGamma}; + + FCPrint[3,"ComplexConjugate: After diracChainCC: ", diracListEval, FCDoControl->ccjVerbose]; + + pauliListEval = (pauliChainCC /@ (pauliList /. DOT->holdDOT /. pauliHead -> Identity)) /. holdDOTReversed-> DOT; + + FCPrint[3,"ComplexConjugate: After pauliChainCC: ", pauliListEval, FCDoControl->ccjVerbose]; + + sunListEval = (sunChainCC /@ (sunList /. DOT->holdDOT /. sunHead -> Identity)) /. holdDOTReversed-> DOT; + + FCPrint[3,"ComplexConjugate: After sunChainCC: ", sunListEval, FCDoControl->ccjVerbose]; + + prefListEval = prefCC /@ (prefList /. prefHead -> Identity); + + FCPrint[3,"ComplexConjugate: After prefCC: ", prefListEval, FCDoControl->ccjVerbose]; + + If[ OptionValue[DotSimplify], + time = AbsoluteTime[]; + FCPrint[1,"ComplexConjugate: Applying DotSimplify.", FCDoControl->ccjVerbose]; + diracListEval = DotSimplify[#,FCI->True, Expanding->False]&/@diracListEval; + pauliListEval = DotSimplify[#,FCI->True, Expanding->False]&/@pauliListEval; + sunListEval = DotSimplify[#,FCI->True, Expanding->False]&/@sunListEval; + FCPrint[1,"ComplexConjugate: Done applying DotSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->ccjVerbose]; + FCPrint[3,"ComplexConjugate: Dirac list after DotSimplify: ", diracListEval, FCDoControl->ccjVerbose]; + FCPrint[3,"ComplexConjugate: Pauli list after DotSimplify: ", pauliListEval, FCDoControl->ccjVerbose]; + FCPrint[3,"ComplexConjugate: SU(N) list after DotSimplify: ", sunListEval, FCDoControl->ccjVerbose]; + ]; + + + + repRule = Join[ + Thread[Rule[diracList,diracListEval]], + Thread[Rule[pauliList,pauliListEval]], + Thread[Rule[sunList,sunListEval]], + Thread[Rule[prefList,prefListEval]] + ]; + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[FCRenameDummyIndices], + time = AbsoluteTime[]; + FCPrint[1,"ComplexConjugate: Renaming dummy indices in the final result.", FCDoControl->ccjVerbose]; + res = FCRenameDummyIndices[res, FCI->True]; + FCPrint[1,"ComplexConjugate: Done renaming dummy indices in the final result, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->ccjVerbose]; + FCPrint[3,"ComplexConjugate: After FCRenameDummyIndices: ", ex, FCDoControl->ccjVerbose] + ]; + + If[ optConjugate=!={} && Head[optConjugate]===List, + + ccRules = Union[Cases[optConjugate, (Rule | RuleDelayed)[_, _]]]; + optConjugate = Complement[optConjugate, ccRules]; + ruleConjugate= Thread[ru[optConjugate,Conjugate/@optConjugate]]/. ru->Rule; + res = res /. Join[ruleConjugate,ccRules] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + + +(* safe for memoization, as we merely reverse the ordering of the elements in a list *) +reverseDOT[x__]:= + MemSet[reverseDOT[x], + holdDOTReversed@@Reverse[{x}] + ]; + +(* safe for memoization, as we merely reverse the ordering of the elements in a list *) +reverseSUNTF[{a__},b_,c_]:= + MemSet[reverseSUNTF[{a},b,c], + SUNTF[Reverse[{a}], c, b] + ]; + +rev[yz__] := + (DOT @@ (Reverse[FRH[{ yz }]])) /; Length[Position[{yz}, Spinor]] < 3; + + +genericEval[x_]:= + x; + +diracChainCC[ex1_DiracChain ex2_]:= + diracChainCC[ex1] diracChainCC[ex2]; -*) (* -HoldPattern[ rev[yz__] ]:= + Even a standalone Dirac matrix is assumed to be part + of a closed chain *) -rev[yz__] := +diracChainCC[DiracGamma[arg_,dim___]]:= + DiracGamma[arg,dim]/;!MemberQ[{5,6,7},arg]; + +diracChainCC[DiracGamma[5]]:= + -DiracGamma[5]; + +diracChainCC[DiracGamma[6]]:= + DiracGamma[7]; + +diracChainCC[DiracGamma[7]]:= + DiracGamma[6]; + +diracChainCC[Spinor[arg__]]:= + Spinor[arg]; + +diracChainCC[ex_/;MemberQ[{holdDOT,FCCCT},Head[ex]]]:= + Block[{ res=ex, diracGammaHold}, + + If[ !FreeQ[res, Eps], + res = res /. a_Eps :> Conjugate[$LeviCivitaSign]/$LeviCivitaSign a + ]; + + If[ !FreeQ[res, FCChargeConjugateTransposed], + res = res /. FCChargeConjugateTransposed[z_, opts:OptionsPattern[]] :> + (z /. DiracGamma[a__] :> - diracGammaHold[a] /. holdDOT -> holdDOTReversed) + ]; + + res = res /. {DiracGamma[5]-> -diracGammaHold[5], DiracGamma[6]-> diracGammaHold[7], + DiracGamma[7]-> diracGammaHold[6]} /. DiracGamma[a__] :> diracGammaHold[a] /. holdDOT -> reverseDOT; + + (* CAREFUL: Complex[a_, b_] -> Complex[a, -b] is only true if no complex + variables are in denominators!!!!, (which is the case in HEP, unless you + have width in the propagators ...) *) + res = res /. Complex[a_, b_] :> Complex[a, -b]; + + res + + ]/; FreeQ[ex,DiracChain]; + +diracChainCC[DiracChain[a_, i_, j_]]:= + DiracChain[(diracChainCC[a]/.diracGammaHold->DiracGamma/. holdDOTReversed->DOT),j,i]; + +diracChainCC[DiracChain[a_Spinor, i_]]:= + DiracChain[a,i]; + +diracChainCC[DiracChain[i_, a_Spinor]]:= + DiracChain[i,a]; + + + + (* -Isolate[ +pauliChainCC[ex1_PauliChain ex2_]:= + pauliChainCC[ex1] pauliChainCC[ex2]; *) - (DOT @@ (Reverse[FRH[{ yz }]]/. - (*Changed 28/2-2001 by F.Orellana, because of bug report by T.Rashba*)(* - DiracGamma[5]->(-DiracGamma[5])/. - {DiracGamma[6] :> DiracGamma[7], - DiracGamma[7]:>DiracGamma[6]}/.*) - {ChargeConjugationMatrix :> (-ChargeConjugationMatrix), ChargeConjugationMatrixInv -> (-ChargeConjugationMatrixInv)} - )(*, IsolateNames->c$CC, IsolateSplit->Infinity - ]*) - ) /; Length[Position[{yz}, Spinor]] < 3; - -c$CCfrh /: HoldForm[c$CCfrh[ii_]] := c$CC[ii]; - -(*cLIndex[x_, dime___] := LorentzIndex[ComplexIndex[x], dime]; -cSIndex[x_] := SUNIndex[ComplexIndex[x]];*) - -conpa[x__] := - conpa[x] = Pair[x] - -(* ComplexConjugatedef *) -(*sunfcomp[a___] := SUNF @@ ({a}/.ComplexIndex -> Identity); -sundeltacomp[a___] := SUNDelta @@ ({a}/.ComplexIndex -> Identity);*) -(*Added SumOver stuff. F.Orellana. 20/8-2002*) -(*Dropped again 19/1-2003. Let's try and keep some hierarchy: - FeynCalc -> PHI -> FeynArts. Dropped this whole business and ComplexIndex also; - it is not maintainable (say you want another real function - you don't want to - have to to type it in here in this file...)*) -(*sumovercomp[a___] := FeynArts`SumOver @@ ({a}/.ComplexIndex -> Identity); -ugencomp[a__] := Phi`Objects`UGenerator @@ ({a}/.ComplexIndex -> Identity);*) (* -nenenen -sundcomp[a___] := SUND @@ ({a}/.ComplexIndex -> Identity); + Even a standalone Pauli matrix is assumed to be part + of a closed chain *) +pauliChainCC[PauliSigma[arg__]]:= + PauliSigma[arg]; -(* for large expressions it is better to not use DotSimplify *) -Options[ComplexConjugate] = {DotSimplify -> True}; - -ComplexConjugate[b_HoldForm,___?OptionQ] := - b /; FreeQ2[FeynCalcInternal[FRH[b]], - {DOT,LorentzIndex,SUNIndex,SUNTF,Complex}]; - -ComplexConjugate[x_ /; (Head[x] =!= HoldForm), opts___?OptionQ] := - compcon[FeynCalcInternal[x]/.SUNTrace->suntrac, opts - ] /. (*SUNF -> sunfcomp /.*) - (*FeynArts`SumOver -> sumovercomp /. - Phi`Objects`UGenerator -> ugencomp /.*) - SUNDelta -> SUNDeltaContract /. - (*SUNDeltaContract -> sundeltacomp/.*) - compcon -> compcon2 /. compcon2 -> - ComplexConjugate /. suntrac-> - SUNTrace; - -compcon2[x_/;!FreeQ[x, HoldForm], opts___?OptionQ] := - compcon[FRH[x], opts]; -compcon[x_^n_?(Element[#,Reals]===True)&, opts___?OptionQ] := - compcon[x,opts]^n; -compcon[x_Plus, opts___?OptionQ] := - compcon[#,opts]& /@ x; -compcon[x_Times, opts___?OptionQ] := - compcon[#,opts]& /@ x; - - -compcon[b_HoldForm, ___?OptionQ] := - b /; - FreeQ2[FRH[b], {DOT,LorentzIndex,SUNIndex,SUNTF,Complex}]; -compcon[x_ /; (Head[x] =!= Plus) && (Head[x] =!= Times), opts___?OptionQ] := - If[ FreeQ[x, DOT | Complex | DiracGamma | SUNTF], - x, - Block[ {nx = x,oone, suntrac, dotsim}, - dotsim = DotSimplify /. {opts} /. Options[ComplexConjugate]; - If[ !FreeQ[nx, SUNF], - nx = Expand[nx, SUNF] - ]; - If[ !FreeQ[nx,SUNT], - If[ dotsim, - nx = dotlin[nx] - ] - ]; -(* this is wrong if nx had Head List ... (change 02/99) - nx = (DOT[oone, nx] /. DOT -> rev /. rev -> DOT); +pauliChainCC[PauliXi[Complex[0,arg_]]]:= + PauliXi[Complex[0,-arg]]; +pauliChainCC[PauliEta[Complex[0,arg_]]]:= + PauliEta[Complex[0,-arg]]; -*) - If[ !FreeQ[nx, SUNTF], - nx = nx /.{SUNTF[{a__},b_,c_]:> SUNTF[Reverse[{a}], c, b] } - ]; +pauliChainCC[ex_holdDOT]:= + Block[{ res=ex, pauliSigmaHold}, - If[ !FreeQ[nx, Eps], - nx = nx /. Eps[a__] :> Conjugate[$LeviCivitaSign]/$LeviCivitaSign Eps[a] - ]; + If[ !FreeQ[res, Eps], + res= res /. a_Eps :> Conjugate[$LeviCivitaSign]/$LeviCivitaSign a + ]; - nx = nx /. DiracGamma[a__]:> - DOT[oone, DiracGamma[a]](*Added 28/2-2001 by F.Orellana - see above*)/; - FreeQ[{5,6,7},Evaluate[{a}[[1]]]]/. - DiracGamma[5]->(-DiracGamma[5])/. - {DiracGamma[6] :> DiracGamma[7], - DiracGamma[7]:>DiracGamma[6]}(**)/. - DOT -> rev /. rev -> DOT /. oone -> 1; -(* -I think this Isolate-optimization is outdated and causes too much overhead, RM, 14.10.2003 + res = res /. holdDOT -> reverseDOT; + + (* CAREFUL: Complex[a_, b_] -> Complex[a, -b] is only true if no complex + variables are in denominators!!!!, (which is the case in HEP, unless you + have width in the propagators ...) *) + res = res /. Complex[a_, b_] :> Complex[a, -b]; + + res + + ]; + +sunChainCC[ex:Except[_Plus | _Times]]:= + Block[{ res=ex}, + + If[ !FreeQ[res, SUNTF], + res = res /. SUNTF -> reverseSUNTF + ]; + + If[ !FreeQ[res, holdDOT], + res = res /. holdDOT -> reverseDOT + ]; + + res = res /. Complex[a_, b_] :> Complex[a, -b]; + + res + + ]; + +sunChainCC[ex_Plus]:= + sunChainCC/@ex; + +sunChainCC[ex_Times]:= + sunChainCC/@ex; + + +prefCC[ex:Except[_Plus | _Times]]:= + Block[{ res=ex, pauliSigmaHold}, + + If[ !FreeQ[res, Eps], + res= res /. a_Eps :> Conjugate[$LeviCivitaSign]/$LeviCivitaSign a + ]; + + (* CAREFUL: Complex[a_, b_] -> Complex[a, -b] is only true if no complex + variables are in denominators!!!!, (which is the case in HEP, unless you + have width in the propagators ...) *) + res = res /. Complex[a_, b_] :> Complex[a, -b]; + + res + + ]; + +prefCC[ex_Plus]:= + prefCC/@ex; + +prefCC[ex_Times]:= + prefCC/@ex; - nx = nx //. c$CC -> c$CCfrh /. oone -> 1; -*) - nx = nx /. - (*LorentzIndex -> cLIndex /. - SUNIndex -> cSIndex /.*) - Complex[a_, b_] -> Complex[a, -b]; - If[ dotsim, - nx = dotlin[nx] - ]; - nx - ] - ] /; FreeQ[x, HoldForm]; -(* CAREFUL: Complex[a_, b_] -> Complex[a, -b] is only true if no complex - variables are in denominators!!!!, (which is the case in HEP, unless you - have width in the propagators ...) -*) FCPrint[1,"ComplexConjugate.m loaded."]; End[] diff --git a/FeynCalc/Feynman/CovariantD.m b/FeynCalc/Feynman/CovariantD.m index 95c857bbd..e4de42f0c 100755 --- a/FeynCalc/Feynman/CovariantD.m +++ b/FeynCalc/Feynman/CovariantD.m @@ -14,23 +14,15 @@ CovariantD::usage = "CovariantD[mu] is a generic covariant derivative with \ -Lorentz index mu. With the option-setting Explicit -> True, \ -an explicit expression for a fermionic field is returned, \ -depending on the setting on the other options. - -CovariantD[x, mu] is a generic covariant derivative with respect to x^mu. \ - -CovariantD[mu, a, b] is a covariant derivative for a bosonic field; \ -acting on QuantumField[f,{},{a,b}], where f is some field name and \ -a and b are two SU(N) indices. - -Again, with the option-setting Explicit -> True, an explicit expression \ -is returned, depending on the setting on the other options. - -CovariantD[OPEDelta, a, b] is a short form for CovariantD[mu,a,b]*FourVector[OPEDelta, mu]. \ - -CovariantD[{OPEDelta, a, b}, {n}] yields the product of n operators, where n is an integer. \ - +Lorentz index mu. \n +CovariantD[x, mu] is a generic covariant derivative with respect to x^mu. \n +CovariantD[mu, a, b] is a covariant derivative for a bosonic field that \ +acts on QuantumField[f,{},{a,b}], where f is some field name and \ +a and b are two SU(N) indices in the adjoint representation. \n +To obtain the explicit expression for a particular covariant derivatine, the \ +option Explicit must be set to True. \n +CovariantD[OPEDelta, a, b] is a short form for CovariantD[mu,a,b]*FV[OPEDelta, mu]. \n +CovariantD[{OPEDelta, a, b}, {n}] yields the product of n operators, where n is an integer. \n CovariantD[OPEDelta, a, b, {m, n}] gives the expanded form of CovariantD[OPEDelta, a, b]^m \ up to order g^n for the gluon, where n is an integer and g the coupling constant indicated \ by the setting of the option CouplingConstant. CovariantD[OPEDelta, {m, n}] gives the expanded \ @@ -173,10 +165,10 @@ a and b are two SU(N) indices. {m_ /; (Head[m] =!= Integer), n_Integer}, ru___Rule ] := Block[ {geen}, - (Sum[geen[jj, m, a, + (Sum[geen[j, m, a, QuantumField /. {ru} /. Options[CovariantD], CouplingConstant /. {ru} /. Options[CovariantD] - ], {jj, 0, n} + ], {j, 0, n} ] /. geen -> gen[Join[{ru}, Options[CovariantD]]] ) ]; diff --git a/FeynCalc/Feynman/CovariantFieldDerivative.m b/FeynCalc/Feynman/CovariantFieldDerivative.m index 94e439bbf..4e2bc6e68 100644 --- a/FeynCalc/Feynman/CovariantFieldDerivative.m +++ b/FeynCalc/Feynman/CovariantFieldDerivative.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Gauge covariant field derivative *) @@ -16,7 +16,7 @@ (* ------------------------------------------------------------------------ *) CovariantFieldDerivative::usage = -"CovariantFieldDerivative[f[x],x,{li1,li2,...},opts] is a covariant \ +"CovariantFieldDerivative[f[x],x,{li1,li2,...}] is a covariant \ derivative of f[x] with respect to space-time variables x and with Lorentz \ indices li1, li2,... CovariantFieldDerivative has only typesetting \ definitions by default. The user is must supply his/her own \ diff --git a/FeynCalc/Feynman/DoPolarizationSums.m b/FeynCalc/Feynman/DoPolarizationSums.m index 1d6a1985e..d72d1fdf4 100644 --- a/FeynCalc/Feynman/DoPolarizationSums.m +++ b/FeynCalc/Feynman/DoPolarizationSums.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Compute polarization sums of vector bosons *) @@ -15,21 +15,14 @@ DoPolarizationSums::usage = "DoPolarizationSums[exp,k,n] sums over physical (transverse) \ -polarizations of external massless vector bosons with momentum k. \ -Here, n is an auxiliary four vector that goes into the gauge-dependent \ -polarization sum to ensure that we are summing only over physical polarizations. - -DoPolarizationSums[exp,k,0] replaces the polarization sum of external massless vector \ -bosons with momentum k by -g(mu,nu). This corresponds to summing over all four \ -physical and unphysical polarizations. - -DoPolarizationSums[exp,k] sums over polarizations \ -of external massive vector bosons with momentum k and mass k^2. -"; - -PolarizationUncontract::usage = -"PolarizationUncontract[exp,k] does Uncontract -on scalar products involving polarization vectors that depend on k."; +polarizations of an external massless vector boson with momentum k, \ +where n is an auxiliary 4-vector from the gauge-dependent \ +polarization sum formula.\n +DoPolarizationSums[exp,k,0] replaces the polarization sum of an external massless vector \ +boson with momentum k by - MT[mu,nu]. This corresponds to the summation over all four \ +polarizations, including the unphysical ones. \n +DoPolarizationSums[exp,k] sums over the three polarizations \ +of an external massive vector boson with momentum k and mass SP[k,k]."; GaugeTrickN::usage = "GaugeTrickN is an option for DoPolarizationSums. It specifies the number \ @@ -39,6 +32,10 @@ external states are virtual photons, then GaugeTrickN should be set to 4. " +DoPolarizationSums::failmsg = +"Error! DoPolarizationSums has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -46,92 +43,92 @@ Begin["`DoPolarizationSums`Private`"] - -DoPolarizationSums::"noresolv" = - "Could not resolve polarization structure of `1`. Evaluation aborted!"; - Options[DoPolarizationSums] = { Contract -> True, ExtraFactor -> 1, + FCE -> False, + FCI -> False, GaugeTrickN -> 2, + Head -> Identity, VirtualBoson -> False }; +DoPolarizationSums[expr_, vectors:Except[_?OptionQ].., OptionsPattern[]] := + Block[ {polInd1,polInd2,res,ex ,tmp,dim,kk,polList,freePart,polPart,head1=Null,head2=Null}, + kk = {vectors}[[1]]; -Options[doPolarizationSum] = { - Contract -> True, - VirtualBoson -> False, - GaugeTrickN -> 2 -}; + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + polInd1 = $MU[Unique[]]; + polInd2 = $MU[Unique[]]; + + polList = SelectNotFree[SelectNotFree[Sort[DeleteDuplicates[Cases[ex,_Momentum | _CartesianMomentum,Infinity]]],Polarization],kk]; + + If[ polList=!={}, + + If[ !MatchQ[polList, { + (CartesianMomentum|Momentum)[Polarization[kk,Complex[0,1], ___Rule],di___], + (CartesianMomentum|Momentum)[Polarization[kk,Complex[0,-1], ___Rule],di___]} | { + (CartesianMomentum|Momentum)[Polarization[kk,Complex[0,-1], ___Rule],di___], + (CartesianMomentum|Momentum)[Polarization[kk,Complex[0,1], ___Rule],di___]}], + Print[StandardForm[polList]]; + Message[DoPolarizationSums::failmsg,"Polarization vector do not seem to appear in a proper way in the expression."]; + Abort[] + ]; + + dim = FCGetDimensions[polList,ChangeDimension->True]//First; + + tmp = ex/.{ + Momentum[Polarization[kk,Complex[0,1], ___Rule],dim] :> (head1=LorentzIndex; LorentzIndex[polInd1,dim]), + CartesianMomentum[Polarization[kk,Complex[0,1], ___Rule],dim-1] :> (head1=CartesianIndex; CartesianIndex[polInd1,dim-1]), + + Momentum[Polarization[kk,Complex[0,-1], ___Rule],dim] :> (head2=LorentzIndex; LorentzIndex[polInd2,dim]), + CartesianMomentum[Polarization[kk,Complex[0,-1], ___Rule],dim-1] :> (head2=CartesianIndex; CartesianIndex[polInd2,dim-1]) + }; + + {freePart, polPart} = FCSplit[tmp,{polInd1,polInd2}], + + (* No polarization vectors in the expression *) + freePart = ex; + polPart = 0; + ]; -(* This is done for performance reasons. Instead of uncontracting every terms that involves k (what Uncontract would -by default), we uncontract only contractions with polarization vectors. *) -PolarizationUncontract[expr_, k_, opts:OptionsPattern[]] := - Block[ {temp,polvecmom1,polvecmom2,op1,op2, tmp}, - - (*TODO Caching! *) - tmp = Collect2[ExpandScalarProduct[expr,Momentum->{k},EpsEvaluate->True],k,Factoring->False]; - tmp = tmp/.{ - Polarization[k,Complex[0,1],op___Rule]:> (op1 = op; polvecmom1), - Polarization[k,Complex[0,-1],op___Rule]:> (op2 = op; polvecmom2) - }; - temp = Uncontract[tmp,polvecmom1,polvecmom2,FilterRules[Join[{opts},{Pair->All}], Options[Uncontract]]]; - temp /.{polvecmom1 :> Polarization[k, Complex[0,1],op1],polvecmom2 :> Polarization[k, Complex[0,-1],op2]} - ]; - -(* Polarization sums for massless vector bosons. *) -doPolarizationSum[expr_,k_, n:Except[_?OptionQ], opts:OptionsPattern[]] := - Block[ {temp,viBo}, - viBo = OptionValue[VirtualBoson]; - Which[ - Count[expr, Polarization[k,__], Infinity, Heads -> True] === 0, - If[ k=!=0 && n=!=0, - 2 expr, - OptionValue[GaugeTrickN] expr - ], - Count[expr, Polarization[k,__], Infinity, Heads -> True] // EvenQ, - temp = (expr /. Pair[LorentzIndex[rho1_, dim_:4], - Momentum[Polarization[k, -I, OptionsPattern[]], dim_:4]] Pair[ - LorentzIndex[rho2_, dim_:4], - Momentum[Polarization[k, I, OptionsPattern[]], dim_:4]] :> - PolarizationSum[rho1,rho2,k,n, Dimension->dim, VirtualBoson-> viBo]); - If[ OptionValue[Contract], - Contract[temp], - temp - ], - True, - Message[DoPolarizationSums::"noresolv", InputForm[expr]]; - ] - ]/; (k=!=0 && n=!=0) || (k=!=0 && n===0); -(* Polarization sums for massive vector bosons with mass k^2. *) -doPolarizationSum[expr_,k:Except[_?OptionQ], OptionsPattern[]] := - Block[ {temp}, Which[ - Count[expr, Polarization[k,__], Infinity, Heads -> True] === 0, - 3 expr, - Count[expr, Polarization[k,__], Infinity, Heads -> True] // EvenQ, - temp = (expr //. Pair[LorentzIndex[rho1_, dim_:4], - Momentum[Polarization[k, -I, OptionsPattern[]], dim_:4]] Pair[ - LorentzIndex[rho2_, dim_:4], - Momentum[Polarization[k, I, OptionsPattern[]], dim_:4]] :> - PolarizationSum[rho1,rho2,k, Dimension->dim]); - If[ OptionValue[Contract], - Contract[temp], - temp + Length[{vectors}] === 1 && kk=!=0, + If[ polPart=!=0, + polPart = OptionValue[Head][PolarizationSum[polInd1,polInd2,kk, Dimension->dim, Heads->{head1,head2}]] polPart + ]; + freePart = 3 freePart, + + Length[{vectors}] === 2 && kk=!=0, + If[ polPart=!=0, + polPart = OptionValue[Head][PolarizationSum[polInd1,polInd2,kk, {vectors}[[2]], Dimension->dim, VirtualBoson-> OptionValue[VirtualBoson], Heads->{head1,head2}]] polPart; + ]; + If[{vectors}[[2]]=!=0, + freePart = 2 freePart, + freePart = OptionValue[GaugeTrickN] freePart ], True, - Message[DoPolarizationSums::"noresolv", InputForm[expr]]; - ] - ]/; k=!=0; -DoPolarizationSums[expr_, vectors:Except[_?OptionQ].., opts:OptionsPattern[]] := - Block[ {exp1, exp2,polvecmom1,polvecmom2,res}, - exp1 = PolarizationUncontract[FCI[expr],{vectors}[[1]],opts]; - If[ Head[exp1] === Plus, - exp2 = List @@ exp1, - exp2 = {exp1} + Message[DoPolarizationSums::failmsg,"Unknown polarization sum"]; + Abort[] ]; - OptionValue[ExtraFactor]*Total[Map[doPolarizationSum[#,vectors,FilterRules[{opts},Options[doPolarizationSum]]]&,exp2]] + + If[ OptionValue[Contract], + polPart = Contract[polPart,FCI->True] + ]; + + res = OptionValue[ExtraFactor] freePart + OptionValue[ExtraFactor] polPart; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]/; Length[{vectors}] === 1 || Length[{vectors}] === 2; FCPrint[1,"DoPolarizationSums.m loaded."]; diff --git a/FeynCalc/Feynman/ExpandPartialD.m b/FeynCalc/Feynman/ExpandPartialD.m index 3fa404c0d..1839c8e61 100755 --- a/FeynCalc/Feynman/ExpandPartialD.m +++ b/FeynCalc/Feynman/ExpandPartialD.m @@ -1,21 +1,25 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) +(* ::Package:: *) -(* :Title: ExpandPartialD *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Author: Rolf Mertig *) +(* :Title: ExpandPartialD *) -(* ------------------------------------------------------------------------ *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* :Summary: Leibniz Rule on products of QuantumField *) +(* :Summary: Leibniz Rule on products of QuantumField *) (* ------------------------------------------------------------------------ *) ExpandPartialD::usage = -"ExpandPartialD[exp] expands DOT products of QuantumField's in exp \ -using the Leibniz rule." +"ExpandPartialD[exp] expands noncommutative products of QuantumField's and partial \ +differentiation operators in exp and applies the Leibniz rule." -(* Added 22/2-2003 in order to use FieldDerivative in a - flexible way. F.Orellana *) +(* Added 22/2-2003 in order to use FieldDerivative in a flexible way. F.Orellana *) PartialDRelations::usage = "PartialDRelations is an option for ExpandPartialD. It is a list of rules \ applied by ExpandPartialD at the end." @@ -27,211 +31,157 @@ Begin["`ExpandPartialD`Private`"] -(* ******************************************************************** *) +epdVerbose::usage=""; +optPartialDRelations::usage=""; +opk::usage=""; + +quanfDot = DOT; +epskillDot = DOT; -With[ {lor = LorentzIndex, dot = DOT, fd = FieldDerivative}, - Options[ExpandPartialD] = - (*Expensive, I'm afraid... F.Orellana*) - {PartialDRelations -> {dot[a___, FCPartialD[x_,lor[mu_]], b___] :> - dot[a, fd[dot[b], x, lor[mu]]]}} -]; +Options[ExpandPartialD] = { + FCI -> False, + FCVerbose -> False, + PartialDRelations -> {DOT[a___, FCPartialD[x_,LorentzIndex[i_]], b___] :> DOT[a, FieldDerivative[dot[b], x, LorentzIndex[i]]]} +} (* Expand one multiplication at a time. F.Orellana *) -ExpandPartialD[x_, opts___Rule] := - Fold[ExpandPartialD1[#1, #2, opts]&, x, - Complement[$Multiplications, {Times}]]; +ExpandPartialD[expr_, OptionsPattern[]] := + Block[{res, ex}, + + If [OptionValue[FCVerbose]===False, + epdVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + epdVerbose=OptionValue[FCVerbose] + ]; + ]; -(* -ExpandPartialD1[x_] := Expand[FixedPoint[qfe, FCI[x], 7], QuantumField]; -*) + optPartialDRelations = OptionValue[PartialDRelations]; -(* moet dat ???? *) -DeclareNonCommutative[OPESum]; + FCPrint[1, "ExpandPartialD: Entering.", FCDoControl->epdVerbose]; -$OPEKCOUNT = 0; + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; -sunsi[xx_] := - If[ FreeQ[xx, SUNIndex], - xx, - xx /. SUNDelta -> SUNDeltaContract /. - SUNDeltaContract -> SUNDelta - ]; -(* suggested by Peter Cho; ADDED 03/16/1998 *) -epskill[exp_ /; FreeQ[exp, Eps]] := - exp; -epskill[exp_Plus] := - Map[epskill, exp]; + If[ !FreeQ2[x, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; -epskill[any_ /; FreeQ2[any,{RightPartialD, LeftPartialD}]] := - any; + res = Fold[internalExpand[#1, #2]&, ex, Complement[$Multiplications, {Times}]]; -(* careful, ..., LeftPartialD and RightPartialD are operators, - thus here is no need to look at QuantumField's -*) -epskill[prod_Times] := - ( (prod /. (*DOT*)(fcdot/.Options[epskill]) -> mydot) //. { - (Eps[a___, LorentzIndex[mu_,___],b___, - LorentzIndex[nu_, ___], c___ - ] * mydot[pa1___, (LeftPartialD | RightPartialD)[LorentzIndex[mu_,___]], - pa2___, - (LeftPartialD | RightPartialD)[LorentzIndex[nu_,___]], - pa3___] - ) :> 0, - (Eps[a___, LorentzIndex[mu_,___],b___, - LorentzIndex[nu_, ___], c___ - ] * mydot[pa1___, (LeftPartialD | RightPartialD)[LorentzIndex[nu_,___]], - pa2___, - (LeftPartialD | RightPartialD)[LorentzIndex[mu_,___]], - pa3___] - ) :> 0, - (* however, here (03/21/98) one has to be careful ... *) - (*BUGFIXED ?*) - ( - ( Eps[a___, LorentzIndex[mu_,___], b___, - LorentzIndex[nu_,___], c___ ] | - Eps[a___, LorentzIndex[nu_,___], b___, - LorentzIndex[mu_,___], c___ ] - ) * - ( - SUND[de1___SUNIndex, SUNIndex[s1_], de2___SUNIndex, - SUNIndex[s2_], de3___SUNIndex ] | - SUND[de1___SUNIndex, SUNIndex[s2_], de2___SUNIndex, - SUNIndex[s1_], de3___SUNIndex ] - ) * - mydot[pa1___, QuantumField[___FCPartialD, - FCPartialD[LorentzIndex[mu_,___]], - ___FCPartialD, - fieldname_, LorentzIndex[_,___], - SUNIndex[s1_] - ], - pa2___, - QuantumField[___FCPartialD, - FCPartialD[LorentzIndex[nu_,___]], - ___FCPartialD, - fieldname_, LorentzIndex[_,___], - SUNIndex[s2_] - ], - pa3___] - ) :> 0 , + FCPrint[1, "ExpandPartialD: Leaving.", FCDoControl->epdVerbose]; - ( - (Eps[a___, LorentzIndex[nu_,___], b___, - LorentzIndex[mu_, ___],c___ - ] | - Eps[a___, LorentzIndex[mu_,___], b___, - LorentzIndex[nu_, ___],c___ - ] - ) * QuantumField[___FCPartialD, - FCPartialD[LorentzIndex[mu_,___]], - ___FCPartialD, - FCPartialD[LorentzIndex[nu_,___]], - ___FCPartialD, - name_ /; (Head[name]=!=FCPartialD) && - (Head[name]=!=LorentzIndex), - LorentzIndex[_,___], colormaybe___ - ] - ) :> 0 /; Length[{colormaybe}]<2 - , - ( - (ep : ( - Eps[a___, LorentzIndex[nu_,___], b___, - LorentzIndex[mu_, ___],c___ - ] | - Eps[a___, LorentzIndex[mu_,___], b___, - LorentzIndex[nu_, ___],c___ - ] - ) - ) * QuantumField[p1___FCPartialD, FCPartialD[LorentzIndex[mu_,di___]], - p2___FCPartialD, - name_ /; (Head[name] =!= FCPartialD) && - (Head[name] =!= LorentzIndex), - LorentzIndex[nu_,de___], rest___ - ] - ) :> (EpsEvaluate[ep/.{mu:>nu, nu:>mu}] QuantumField[ - p1,FCPartialD[LorentzIndex[nu,de]], p2, name, - LorentzIndex[mu, di],rest] - ) /; !OrderedQ[{mu,nu}] - , - ( - (ep : ( - Eps[a___, LorentzIndex[nu_,___], b___, - LorentzIndex[mu_, ___],c___ - ] | - Eps[a___, LorentzIndex[mu_,___], b___, - LorentzIndex[nu_, ___],c___ - ] - ) - ) * mydot[quf1___, - QuantumField[p1___FCPartialD, - FCPartialD[LorentzIndex[mu_,de___]], - p2___FCPartialD, - name_ /; (Head[name] =!= FCPartialD) && - (Head[name] =!= LorentzIndex), - LorentzIndex[nu_,di___], rest___ - ], - quf2___] - ) :> (EpsEvaluate[ep/.{mu:>nu, nu:>mu}] mydot[quf1, - QuantumField[p1,FCPartialD[LorentzIndex[nu, di]], p2, name, - LorentzIndex[mu,de], rest], quf2] - ) /; !OrderedQ[{mu, nu}] - } /. mydot->(*DOT*)(fcdot/.Options[epskill]) - ) /; !FreeQ2[prod, {Eps,LeftPartialD,RightPartialD} - ] && $EpsRules===True; -$EpsRules = True; - -ExpandPartialD1[x_Plus, dot_, opts___Rule] := - Map[ExpandPartialD1[#,dot,opts]&,x]; - -(*Hack to allow other multiplications. F.Orellana. 24/2-2003*) -Options[quanf] = {fcdot->DOT}; -Options[epskill] = {fcdot->DOT}; - -ExpandPartialD1[x_, dot_, opts___Rule] := + res + + ]; +internalExpand[x_Plus, dot_] := + Map[internalExpand[#,dot]&,x]; + +internalExpand[x_, dot_] := Block[{res}, If[ FreeQ2[x, {FCPartialD, LeftPartialD, RightPartialD, LeftRightPartialD, FieldStrength, QuantumField}], Return[x] ]; - FCPrint[3,"ExpandPartialD: ExpandPartialD1: Entering with ", x]; - - SetOptions[quanf, fcdot->dot]; - SetOptions[epskill, fcdot->dot]; + FCPrint[3,"ExpandPartialD: internalExpand: Entering with ", x, FCDoControl->epdVerbose]; - res = Expand[Expand[FixedPoint[qfe[dot,#]&,FCI[x],3],SUNIndex] // sunsi, Eps]; + (* This allows for other multiplications than just DOT. *) + quanfDot = dot; + epskillDot = dot; - FCPrint[3,"ExpandPartialD: ExpandPartialD1: After qfe ", res]; + res = FixedPoint[qfe[dot,#]&,x,3]; + FCPrint[3,"ExpandPartialD: internalExpand: After qfe ", res, FCDoControl->epdVerbose]; - res = epskill[res] /. epskill -> Identity; + If[!FreeQ[res,SUNIndex], + res = Expand[res,SUNIndex] /. SUNDelta -> SUNDeltaContract /. SUNDeltaContract -> SUNDelta + ]; - FCPrint[3,"ExpandPartialD: ExpandPartialD1: After epskill ", res]; + If[!FreeQ[res,Eps], + FCPrint[1,"ExpandPartialD: Applying epskill.", FCDoControl->epdVerbose]; + res = epskill[Expand[res,Eps]] /. epskill -> Identity; + FCPrint[3,"ExpandPartialD: internalExpand: After epskill: ", res, FCDoControl->epdVerbose]; + ]; - (*Allow for other products through setting - of PartialDRelations. This will of course - manipulate these products only by applying - PartialDRelations. Still... - F.Orellana, 22/2-2003.*) - res = res //. (PartialDRelations/.{opts}/.Options[ExpandPartialD]); + (*Allow for other products through setting of PartialDRelations. This will of course + manipulate these products only by applying PartialDRelations. Still... F.Orellana, 22/2-2003.*) + res = res //. optPartialDRelations; - FCPrint[3,"ExpandPartialD: ExpandPartialD1: Leaving with ", res]; + FCPrint[3,"ExpandPartialD: internalExpand: Leaving with ", res, FCDoControl->epdVerbose]; res ] /; Head[x] =!= Plus; +$OPEKCOUNT = 0; + +(* suggested by Peter Cho; ADDED 03/16/1998 *) +epskill[exp_ /; FreeQ[exp, Eps]] := + exp; + +epskill[exp_Plus] := + Map[epskill, exp]; + +epskill[any_ /; FreeQ2[any,{RightPartialD, LeftPartialD}]] := + any; + +(* careful, ..., LeftPartialD and RightPartialD are operators, + thus here is no need to look at QuantumField's *) +epskill[prod_Times] := + ( (prod /. epskillDot -> mydot) //. { + + (Eps[a___, LorentzIndex[mu_,___],b___, LorentzIndex[nu_, ___], c___] * + mydot[pa1___, (LeftPartialD | RightPartialD)[LorentzIndex[mu_,___]], pa2___, + (LeftPartialD | RightPartialD)[LorentzIndex[nu_,___]], pa3___]) :> 0, + + (Eps[a___, LorentzIndex[mu_,___],b___, LorentzIndex[nu_, ___], c___] * + mydot[pa1___, (LeftPartialD | RightPartialD)[LorentzIndex[nu_,___]], pa2___, + (LeftPartialD | RightPartialD)[LorentzIndex[mu_,___]], pa3___]) :> 0, + (* however, here (03/21/98) one has to be careful ... *) + (*BUGFIXED ?*) + + ((Eps[a___, LorentzIndex[mu_,___], b___, LorentzIndex[nu_,___], c___ ] | + Eps[a___, LorentzIndex[nu_,___], b___, LorentzIndex[mu_,___], c___ ]) * + (SUND[de1___SUNIndex, SUNIndex[s1_], de2___SUNIndex, SUNIndex[s2_], de3___SUNIndex ] | + SUND[de1___SUNIndex, SUNIndex[s2_], de2___SUNIndex, SUNIndex[s1_], de3___SUNIndex ]) * + mydot[pa1___, QuantumField[___FCPartialD, FCPartialD[LorentzIndex[mu_,___]], ___FCPartialD, + fieldname_, LorentzIndex[_,___], SUNIndex[s1_]], pa2___, QuantumField[___FCPartialD, + FCPartialD[LorentzIndex[nu_,___]], ___FCPartialD, fieldname_, LorentzIndex[_,___], SUNIndex[s2_]], pa3___] + ) :> 0 , + + ((Eps[a___, LorentzIndex[nu_,___], b___, LorentzIndex[mu_, ___],c___] | + Eps[a___, LorentzIndex[mu_,___], b___, LorentzIndex[nu_, ___],c___]) * QuantumField[___FCPartialD, + FCPartialD[LorentzIndex[mu_,___]], ___FCPartialD, FCPartialD[LorentzIndex[nu_,___]], ___FCPartialD, + name_ /; (Head[name]=!=FCPartialD) && (Head[name]=!=LorentzIndex), LorentzIndex[_,___], l___] + ) :> 0 /; Length[{l}]<2, + + ((e : (Eps[a___, LorentzIndex[n_,___], b___, LorentzIndex[m_, ___],c___] | + Eps[a___, LorentzIndex[m_,___], b___, LorentzIndex[n_, ___],c___]) + ) * QuantumField[p___FCPartialD, FCPartialD[LorentzIndex[m_,d___]], q___FCPartialD, + t_ /; (Head[t] =!= FCPartialD) && (Head[t] =!= LorentzIndex), LorentzIndex[nu_,s___], r___] + ) :> + (EpsEvaluate[e /. {m:>n, n:>m}, FCI->True] QuantumField[p,FCPartialD[LorentzIndex[n,s]], q, t, + LorentzIndex[m, d],r]) /; !OrderedQ[{m,n}], + + ((e : (Eps[a___, LorentzIndex[n_,___], b___, LorentzIndex[m_, ___],c___] | + Eps[a___, LorentzIndex[m_,___], b___, LorentzIndex[n_, ___],c___])) * + mydot[quf1___, QuantumField[p___FCPartialD, FCPartialD[LorentzIndex[m_,s___]], q___FCPartialD, + t_ /; (Head[t] =!= FCPartialD) && (Head[t] =!= LorentzIndex), LorentzIndex[nu_,d___], r___], x___] + ) :> (EpsEvaluate[e/.{m:>n, n:>m}, FCI->True] mydot[x, QuantumField[p,FCPartialD[LorentzIndex[n, d]], q, t, + LorentzIndex[m,s], r], x] + ) /; !OrderedQ[{m, n}] + + } /. mydot-> epskillDot) /; !FreeQ2[prod, {Eps,LeftPartialD,RightPartialD}]; + + +(* Ignore CovariantD[x, LorentzIndex[mu]] - it will be caught by PartialDRelations*) fcovcheck[y_] := - If[ True, - y /. FieldStrength[ab__] :> - FieldStrength[ab, Explicit -> True]/. - (*Small change (condition) 26/2-2003. F.Orellana. - Ignore CovariantD[x, LorentzIndex[mu]] - it will be - caught by PartialDRelations*) - CovariantD[ab__] :> CovariantD[ab, Explicit -> True] /; - Length[{ab}] =!= 2 || Or@@((Head[#]===List)&/@{ab}), - y - ]; + y /. FieldStrength[ab__] :> FieldStrength[ab, Explicit -> True]/. CovariantD[ab__] :> CovariantD[ab, Explicit -> True] /; + Length[{ab}] =!= 2 || Or@@((Head[#]===List)&/@{ab}); opesumplus2[y_,b__] := If[ Head[y]===Plus, @@ -242,7 +192,6 @@ opesumplus2[Expand[a],b]; qfe[dot_, x_] := - MemSet[qfe[dot,x], DotSimplify[ (*The replacement below commented out by F.Orellana, 12/3/2005. It breaks the procedure of applying the expansion to all @@ -254,16 +203,13 @@ LeftPartialD[Momentum[OPEDelta]^mm], RightPartialD[Momentum[OPEDelta]]^ (mm_ (*/; Head[mm]=!=Integer*)):> RightPartialD[Momentum[OPEDelta]^mm] - } ] /. dot -> qf1 /. qf1 -> qf2 /. qf2 -> qf1 /. - qf1 -> qf3 /. - qf3 -> qf5 /. qf5 -> dot /. QuantumField -> - quanf /. quanf -> QuantumField /. OPESum -> - opesumplus - ] - ]; + }, FCI->True] /. dot -> qf1 /. qf1 -> qf2 /. qf2 -> qf1 /. qf1 -> qf3 /. qf3 -> qf5 /. qf5 -> dot /. QuantumField -> + quanf /. quanf -> QuantumField /. OPESum -> opesumplus, FCI->True]; + (* linearity *) qf1[1,b___] := qf1[b]; + qf1[a__, OPESum[b_, c__], d___] := OPESum[qf1[a, b, d], c]; @@ -285,26 +231,19 @@ (* move all DiracGamma, etc. to the left *) qf2[a___, b_, n_, c___] := - qf2[a, n, b, c] /; - (!NonCommFreeQ[n]) && - FreeQ2[n, {Pattern, FCPartialD, LeftPartialD, RightPartialD, - QuantumField, Blank, qf1, qf2} ] && - ((Head[b] === FCPartialD) || (Head[b] === QuantumField) || - (Head[b] === LeftPartialD) || (Head[b] === RightPartialD)); + qf2[a, n, b, c] /; (!NonCommFreeQ[n]) && FreeQ2[n, {Pattern, FCPartialD, LeftPartialD, RightPartialD, QuantumField, Blank, qf1, qf2} ] && + ((Head[b] === FCPartialD) || (Head[b] === QuantumField) || (Head[b] === LeftPartialD) || (Head[b] === RightPartialD)); qf3[f1_qf3] := f1; -qf3[a___, FCPartialD[Momentum[OPEDelta]^m_], - FCPartialD[Momentum[OPEDelta]^n_], b___ - ] := + +qf3[a___, FCPartialD[Momentum[OPEDelta]^m_], FCPartialD[Momentum[OPEDelta]^n_], b___] := qf3[a, FCPartialD[Momentum[OPEDelta]^(m+n)], b]; -qf3[a___, LeftPartialD[Momentum[OPEDelta]^m_], - LeftPartialD[Momentum[OPEDelta]^n_], b___ - ] := + +qf3[a___, LeftPartialD[Momentum[OPEDelta]^m_], LeftPartialD[Momentum[OPEDelta]^n_], b___] := qf3[a, LeftPartialD[Momentum[OPEDelta]^(m+n)], b]; -qf3[a___, RightPartialD[Momentum[OPEDelta]^m_], - RightPartialD[Momentum[OPEDelta]^n_], b___ - ] := + +qf3[a___, RightPartialD[Momentum[OPEDelta]^m_], RightPartialD[Momentum[OPEDelta]^n_], b___] := qf3[a, RightPartialD[Momentum[OPEDelta]^(m+n)], b]; (* Keine Experimente!!!! (...) *) @@ -320,133 +259,80 @@ qf5[a___, QuantumField[f1__], LeftPartialD[mu_], b___] := (qf5st[a, quanf[FCPartialD[mu], f1], b] /. quanf -> QuantumField /. - qf5st -> qf5) /; FreeQ2[{a}, {FCPartialD, QuantumField, LeftPartialD, - RightPartialD}]; + qf5st -> qf5) /; FreeQ2[{a}, {FCPartialD, QuantumField, LeftPartialD, RightPartialD}]; -qf5[a___, QuantumField[f2__], - QuantumField[f1__], LeftPartialD[mu_], b___ - ] := +qf5[a___, QuantumField[f2__], QuantumField[f1__], LeftPartialD[mu_], b___] := ((qf5st[a, quanf[f2], quanf[FCPartialD[mu], f1], b] + qf5st[a, quanf[f2], LeftPartialD[mu], quanf[f1], b] ) /. quanf -> QuantumField /. qf5st -> qf5 ) /; ((Head[mu] === LorentzIndex) || (Head[mu] === Momentum)); -qf5[a___, RightPartialD[mu_], QuantumField[f1__], - QuantumField[f2__], b___] := +qf5[a___, RightPartialD[mu_], QuantumField[f1__], QuantumField[f2__], b___] := ((qf5st[a, quanf[FCPartialD[mu], f1], quanf[f2], b] + qf5st[a, quanf[f1], RightPartialD[mu], quanf[f2], b] - ) /. quanf -> QuantumField /. qf5st -> qf5 + ) /. quanf -> QuantumField /. qf5st -> qf5 ) /; ((Head[mu] === LorentzIndex) || (Head[mu] === Momentum)); -qf5st[a___, RightPartialD[Momentum[OPEDelta]^m_], - RightPartialD[Momentum[OPEDelta]^n_], b___ - ] := +qf5st[a___, RightPartialD[Momentum[OPEDelta]^m_], RightPartialD[Momentum[OPEDelta]^n_], b___] := qf5st[a, RightPartialD[Momentum[OPEDelta]^(m+n)], b]; -qf5st[a___, LeftPartialD[Momentum[OPEDelta]^m_], - LeftPartialD[Momentum[OPEDelta]^n_], b___ - ] := +qf5st[a___, LeftPartialD[Momentum[OPEDelta]^m_], LeftPartialD[Momentum[OPEDelta]^n_], b___] := qf5st[a, LeftPartialD[Momentum[OPEDelta]^(m+n)], b]; -qf5st[a___, FCPartialD[Momentum[OPEDelta]^m_], - FCPartialD[Momentum[OPEDelta]^n_], b___ - ] := +qf5st[a___, FCPartialD[Momentum[OPEDelta]^m_], FCPartialD[Momentum[OPEDelta]^n_], b___] := qf5st[a, FCPartialD[Momentum[OPEDelta]^(m+n)], b]; (* start from the right*) (* who wants to do this in FORM or Maple ??? *) -qf5[c_/;Head[c] =!= LeftPartialD, b___, QuantumField[f1__], - LeftPartialD[Momentum[OPEDelta]^m_], a___ - ] := - ( (opk = OPEk[$OPEKCOUNT++]; - OPESum[Binomial[m, opk] * - qf5st[c, b, - LeftPartialD[Momentum[OPEDelta]^(m-opk)], - quanf[FCPartialD[Momentum[OPEDelta]^opk], f1], - a - ], - {opk, 0, m} - ] +qf5[c_/;Head[c] =!= LeftPartialD, b___, QuantumField[f1__], LeftPartialD[Momentum[OPEDelta]^m_], a___] := + ( + (opk = OPEk[$OPEKCOUNT++]; + OPESum[Binomial[m, opk] qf5st[c, b, LeftPartialD[Momentum[OPEDelta]^(m-opk)], quanf[FCPartialD[Momentum[OPEDelta]^opk], f1], a], {opk, 0, m}] )/. quanf -> QuantumField /. qf5st -> qf5 - )(* /; FreeQ[{a}, PartialD]*); - -(* start from the left *) (* who wants to do this in FORM or Maple ??? *) - -qf5[a___,RightPartialD[Momentum[OPEDelta]^m_], - QuantumField[f1__], b___,c_/;FreeQ[{FCPartialD,RightPartialD},Head[c]] - ] := - ( (opk = OPEk[$OPEKCOUNT++]; - OPESum[Binomial[m, opk] * - qf5st[a, quanf[FCPartialD[Momentum[OPEDelta]^opk], f1], - RightPartialD[Momentum[OPEDelta]^(m-opk)], b, c - ], - {opk, 0, m} - ] + ); + +(* start from the left *) + +qf5[a___,RightPartialD[Momentum[OPEDelta]^m_], QuantumField[f1__], b___,c_/;FreeQ[{FCPartialD,RightPartialD},Head[c]]] := + ( + (opk = OPEk[$OPEKCOUNT++]; + OPESum[Binomial[m, opk] qf5st[a, quanf[FCPartialD[Momentum[OPEDelta]^opk], f1], + RightPartialD[Momentum[OPEDelta]^(m-opk)], b, c], {opk, 0, m} ] )/. quanf -> QuantumField /. qf5st -> qf5 - (* CHANGE 06/94 *) - )(* /; FreeQ[{a}, PartialD]*); + ); quanf[quanf[a__], b___, c_ /; Head[c] =!= FCPartialD] := - ((*DOT*)(fcdot/.Options[quanf])[quanf[a], qf5[b,c]]); + quanfDot[quanf[a], qf5[b,c]]; -quanf[f1___, FCPartialD[Momentum[OPEDelta]^m_], - FCPartialD[Momentum[OPEDelta]], - f2___ - ] := +quanf[f1___, FCPartialD[Momentum[OPEDelta]^m_], FCPartialD[Momentum[OPEDelta]], f2___] := quanf[f1, FCPartialD[Momentum[OPEDelta]^(m+1)], f2]; -quanf[f1___, LeftPartialD[Momentum[OPEDelta]^m_], - LeftPartialD[Momentum[OPEDelta]], - f2___ - ] := +quanf[f1___, LeftPartialD[Momentum[OPEDelta]^m_], LeftPartialD[Momentum[OPEDelta]], f2___] := quanf[f1, LeftPartialD[Momentum[OPEDelta]^(m+1)], f2]; -quanf[f1___, RightPartialD[Momentum[OPEDelta]^m_], - RightPartialD[Momentum[OPEDelta]], - f2___ - ] := +quanf[f1___, RightPartialD[Momentum[OPEDelta]^m_], RightPartialD[Momentum[OPEDelta]], f2___] := quanf[f1, RightPartialD[Momentum[OPEDelta]^(m+1)], f2]; -quanf[f1___, FCPartialD[Momentum[OPEDelta]], - FCPartialD[Momentum[OPEDelta]^m_], - f2___ - ] := +quanf[f1___, FCPartialD[Momentum[OPEDelta]], FCPartialD[Momentum[OPEDelta]^m_], f2___] := quanf[f1, FCPartialD[Momentum[OPEDelta]^(m+1)], f2]; -quanf[f1___, RightPartialD[Momentum[OPEDelta]], - RightPartialD[Momentum[OPEDelta]^m_], - f2___ - ] := +quanf[f1___, RightPartialD[Momentum[OPEDelta]], RightPartialD[Momentum[OPEDelta]^m_], f2___] := quanf[f1, RightPartialD[Momentum[OPEDelta]^(m+1)], f2]; -quanf[f1___, LeftPartialD[Momentum[OPEDelta]], - LeftPartialD[Momentum[OPEDelta]^m_], - f2___ - ] := +quanf[f1___, LeftPartialD[Momentum[OPEDelta]], LeftPartialD[Momentum[OPEDelta]^m_], f2___] := quanf[f1, LeftPartialD[Momentum[OPEDelta]^(m+1)], f2]; -quanf[f1___, FCPartialD[Momentum[OPEDelta]^m_], - FCPartialD[Momentum[OPEDelta]^n_], - f2___ - ] := +quanf[f1___, FCPartialD[Momentum[OPEDelta]^m_], FCPartialD[Momentum[OPEDelta]^n_], f2___] := quanf[f1, FCPartialD[Momentum[OPEDelta]^(m+n)], f2]; -quanf[f1___, LeftPartialD[Momentum[OPEDelta]^m_], - LeftPartialD[Momentum[OPEDelta]^n_], - f2___ - ] := +quanf[f1___, LeftPartialD[Momentum[OPEDelta]^m_], LeftPartialD[Momentum[OPEDelta]^n_], f2___] := quanf[f1, LeftPartialD[Momentum[OPEDelta]^(m+n)], f2]; -quanf[f1___, RightPartialD[Momentum[OPEDelta]^m_], - RightPartialD[Momentum[OPEDelta]^n_], - f2___ - ] := +quanf[f1___, RightPartialD[Momentum[OPEDelta]^m_], RightPartialD[Momentum[OPEDelta]^n_], f2___] := quanf[f1, RightPartialD[Momentum[OPEDelta]^(m+n)], f2]; (* new 03/98 commutativity in partial derivatives *) -quanf[par1_FCPartialD, parr__FCPartialD, - fname_/;Head[fname]=!=FCPartialD, rest___] := - (((quanf[##, fname, rest])&)@@Sort[{par1,parr}]) /; - !OrderedQ[{par1,parr}] +quanf[par1_FCPartialD, parr__FCPartialD, fname_/;Head[fname]=!=FCPartialD, rest___] := + (((quanf[##, fname, rest])&)@@Sort[{par1,parr}]) /; !OrderedQ[{par1,parr}] FCPrint[1,"ExpandPartialD.m loaded."]; End[] diff --git a/FeynCalc/Feynman/ExplicitPartialD.m b/FeynCalc/Feynman/ExplicitPartialD.m index cc6c6868d..4546796b8 100755 --- a/FeynCalc/Feynman/ExplicitPartialD.m +++ b/FeynCalc/Feynman/ExplicitPartialD.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Partial derivative *) @@ -16,8 +16,8 @@ (* ------------------------------------------------------------------------ *) ExplicitPartialD::usage = -"ExplicitPartialD[exp] inserts in exp the definition for \ -LeftRightPartialD[z] (and LeftRightPartialD2[z])."; +"ExplicitPartialD[exp] inserts the definitions for \ +LeftRightPartialD[z] and LeftRightPartialD2[z]."; Begin["`Package`"] End[] diff --git a/FeynCalc/Feynman/FAPatch.m b/FeynCalc/Feynman/FAPatch.m index 9473b5460..10e14f1ab 100644 --- a/FeynCalc/Feynman/FAPatch.m +++ b/FeynCalc/Feynman/FAPatch.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Patch for FeynArts *) @@ -16,15 +16,20 @@ (* ------------------------------------------------------------------------ *) FAPatch::usage = -"If an unpatched copy of FeynArts is present in $FeynArtsDirectory, \ -evaluating FAPatch causes the files making up FeynArts to be modified in \ -order for FeynArts to be compatible with FeynCalc."; +"FAPatch[] is an auxiliary function that patches FeynArts to be compatible \ +with FeynCalc. If an unpatched copy of FeynArts is present in $FeynArtsDirectory, \ +evaluating FAPatch[] will start the patching process."; PatchModelsOnly::usage = "PatchModelsOnly is an Option of FAPatch. When set to True, FAPatch will patch \ only the model files in the Models directory of the FeynArts installation. This \ is useful when you have added new custom models, e.g. generated by FeynRules."; +FAModelsDirectory::usage = +"FAModelsDirectory is an Option of FAPatch. It points to the directory \ +that contains FeynArts models. The default value is ``Models'' inside \ +$FeynArtsDirectory."; + FCFilePatch::usage = "FCFilePatch[input,output, rp] replaces the patterns given by rp in the file input \ and writes the modified version to output. rp should be a list of the form \ @@ -46,11 +51,14 @@ Begin["`FAPatch`Private`"] +nmodels::usage=""; + FCFilePatch[input_String, output_String, replacements_List] := Block[{tmp, res}, tmp = Import[input, "Text"] <> "\n"; If[ !StringMatchQ[tmp, "*Patched for use with FeynCalc*", IgnoreCase -> True], + nmodels++; res = StringReplace[tmp, replacements, MetaCharacters -> Automatic]; res = StringJoin[{"(* Patched for use with FeynCalc *)\n",res}], res = tmp @@ -62,48 +70,53 @@ Options[FAPatch] = { - PatchModelsOnly -> False, - Replace -> { - "FourVector" -> "FAFourVector", - "DiracSpinor" -> "FADiracSpinor", - "DiracSlash" -> "FADiracSlash", - "DiracMatrix" -> "FADiracMatrix", - "DiracTrace" -> "FADiracTrace", - "MetricTensor" -> "FAMetricTensor", - "ScalarProduct" -> "FAScalarProduct", - "ChiralityProjector" -> "FAChiralityProjector", - "GS" -> "FAGS", - "SUNT" -> "FASUNT", - "SUNF" -> "FASUNF", - "LeviCivita" -> "FALeviCivita", - "Loop" -> "FALoop", - "NonCommutative" -> "FANonCommutative", - "PolarizationVector" -> "FAPolarizationVector", - "FeynAmp" -> "FAFeynAmp", - "PropagatorDenominator" -> "FAPropagatorDenominator", - "GaugeXi" -> "FAGaugeXi", - "FeynAmpDenominator" -> "FAFeynAmpDenominator", - "FeynAmpList" -> "FAFeynAmpList", - "ME" -> "FCGV[\"ME\"]", - "MM" -> "FCGV[\"MM\"]", - "ML" -> "FCGV[\"ML\"]", - "MU" -> "FCGV[\"MU\"]", - "MD" -> "FCGV[\"MD\"]", - "MC" -> "FCGV[\"MC\"]", - "MS" -> "FCGV[\"MS\"]", - "MT" -> "FCGV[\"MT\"]", - "MB" -> "FCGV[\"MB\"]", - "MH" -> "FCGV[\"MH\"]", - "MZ" -> "FCGV[\"MZ\"]", - "MW" -> "FCGV[\"MW\"]", - "EL" -> "FCGV[\"EL\"]", - "CW" -> "FCGV[\"CW\"]", - "SW" -> "FCGV[\"SW\"]" + Quiet -> False, + PatchModelsOnly -> False, + FAModelsDirectory :> FileNameJoin[{$FeynArtsDirectory, "Models"}], + Replace -> { + "FourVector" -> "FAFourVector", + "DiracSpinor" -> "FADiracSpinor", + "DiracSlash" -> "FADiracSlash", + "DiracMatrix" -> "FADiracMatrix", + "DiracTrace" -> "FADiracTrace", + "MetricTensor" -> "FAMetricTensor", + "ScalarProduct" -> "FAScalarProduct", + "ChiralityProjector" -> "FAChiralityProjector", + "GS" -> "FAGS", + "SI" -> "FASI", + "SUNT" -> "FASUNT", + "SUNF" -> "FASUNF", + "LeviCivita" -> "FALeviCivita", + "Loop" -> "FALoop", + "NonCommutative" -> "FANonCommutative", + "PolarizationVector" -> "FAPolarizationVector", + "FeynAmp" -> "FAFeynAmp", + "PropagatorDenominator" -> "FAPropagatorDenominator", + "GaugeXi" -> "FAGaugeXi", + "FeynAmpDenominator" -> "FAFeynAmpDenominator", + "FeynAmpList" -> "FAFeynAmpList", + "ME" -> "FCGV[\"ME\"]", + "MM" -> "FCGV[\"MM\"]", + "ML" -> "FCGV[\"ML\"]", + "MU" -> "FCGV[\"MU\"]", + "MD" -> "FCGV[\"MD\"]", + "MC" -> "FCGV[\"MC\"]", + "MS" -> "FCGV[\"MS\"]", + "MT" -> "FCGV[\"MT\"]", + "MB" -> "FCGV[\"MB\"]", + "MH" -> "FCGV[\"MH\"]", + "MZ" -> "FCGV[\"MZ\"]", + "MW" -> "FCGV[\"MW\"]", + "EL" -> "FCGV[\"EL\"]", + "CW" -> "FCGV[\"CW\"]", + "SW" -> "FCGV[\"SW\"]" } }; FAPatch[OptionsPattern[]] := - Block[{repList, feynartsFile, allfiles,filenames}, + Block[{ repList, feynartsFile, allfiles, filenames, optFAModelsDirectory}, + + optFAModelsDirectory = OptionValue[FAModelsDirectory]; repList = Map[{ Rule[RegularExpression["\\b" <> First[#] <> "\\b"], Last[#]], @@ -118,7 +131,7 @@ If[ FileNames["FeynArts.m", $FeynArtsDirectory] === {} || FileNames["*", FileNameJoin[{$FeynArtsDirectory, "FeynArts"}]] === {} || - FileNames["*", FileNameJoin[{$FeynArtsDirectory, "Models"}]] === {}, + FileNames["*", optFAModelsDirectory] === {}, Message[FAPatch::incomplete]; Abort[] ]; @@ -143,10 +156,10 @@ If[ !OptionValue[PatchModelsOnly], filenames = Flatten[{ FileNames[{"*.m"}, FileNameJoin[{$FeynArtsDirectory}]], - FileNames[{"*.mod", "*.gen"}, FileNameJoin[{$FeynArtsDirectory, "Models"}], Infinity], + FileNames[{"*.mod", "*.gen"}, optFAModelsDirectory, Infinity], FileNames[{"*.m", "*.m-ok"}, FileNameJoin[{$FeynArtsDirectory, "FeynArts"}]]} ], - filenames = FileNames[{"*.mod", "*.gen"}, FileNameJoin[{$FeynArtsDirectory, "Models"}], Infinity] + filenames = FileNames[{"*.mod", "*.gen"}, optFAModelsDirectory, Infinity] ]; @@ -155,24 +168,29 @@ If[FileNameTake[FileInformation[#, "AbsoluteFileName"]] === FileNameTake[#], #, Unevaluated@Sequence[]] &, filenames ]; - - If[ !OptionValue[PatchModelsOnly], + nmodels=0; + If[ !OptionValue[PatchModelsOnly] || OptionValue[Quiet], If[ ChoiceDialog["An installation of FeynArts has been found in \"" <> $FeynArtsDirectory <> "\". This program will now patch FeynArts to allow interoperation with FeynCalc. Continue?", WindowTitle->"Patch Feynarts"], (* The actual patching *) - WriteString["stdout","Patching FeynArts..."]; + FCPrint[0, "Patching FeynArts... ", UseWriteString -> True]; Map[FCFilePatch[#, #, repList] &, allfiles]; - WriteString["stdout"," done!\n"], - WriteString["stdout","Patching aborted, no files were changed.\n"]; + FCPrint[0, "done!\n", UseWriteString -> True], + + FCPrint[0, "Patching aborted, no files were changed.\n", UseWriteString -> True]; Return[] ], - WriteString["stdout","Patching FeynArts models..."]; + Map[FCFilePatch[#, #, repList] &, allfiles]; - WriteString["stdout"," done!\n"] - ] + If[ nmodels=!=0, + FCPrint[0, "Patched " <> ToString[nmodels] <> " FeynArts models.\n", UseWriteString -> True]; + ] + + ]; + nmodels=0; ]; diff --git a/FeynCalc/Feynman/FCFAConvert.m b/FeynCalc/Feynman/FCFAConvert.m index bbd636056..c8ba6e110 100644 --- a/FeynCalc/Feynman/FCFAConvert.m +++ b/FeynCalc/Feynman/FCFAConvert.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: FCFAConvert converts a FeynArts amplitude to FeynCalc *) @@ -58,34 +58,41 @@ Begin["`FCFAConvert`Private`"] Options[FCFAConvert] = { - ChangeDimension -> False, - DropSumOver -> False, - FinalSubstitutions->{}, - IncomingMomenta->{}, - List -> True, - LoopMomenta->{}, - LorentzIndexNames->{}, - OutgoingMomenta->{}, - SMP -> False, - SUNFIndexNames->{}, - SUNIndexNames->{}, - TransversePolarizationVectors->{}, - UndoChiralSplittings -> False + ChangeDimension -> False, + Contract -> False, + DropSumOver -> False, + FCFADiracChainJoin -> True, + FeynAmpDenominatorCombine -> True, + FinalSubstitutions -> {}, + IncomingMomenta -> {}, + List -> True, + LoopMomenta -> {}, + LorentzIndexNames -> {}, + OutgoingMomenta -> {}, + Prefactor -> 1, + SMP -> False, + SUNFIndexNames -> {}, + SUNIndexNames -> {}, + TransversePolarizationVectors -> {}, + UndoChiralSplittings -> False }; -FCFAConvert[(FeynArts`FAFeynAmpList|FeynAmpList)[__][diags__], OptionsPattern[]] := +FCFAConvert[(FeynArts`FAFeynAmpList|FeynAmpList)[__][diags___], OptionsPattern[]] := Block[ { diagsConverted,repRuleMomenta,repRuleLorentzIndices, repRulePolVectors,inMoms,outMoms,liNames,polVecs,loopMoms,dim, - sunNames, sunfNames, repRuleSUNIndices, repRuleSUNFIndices}, + sunNames, sunfNames, repRuleSUNIndices, repRuleSUNFIndices, + prefactor}, + + inMoms = OptionValue[IncomingMomenta]; + outMoms = OptionValue[OutgoingMomenta]; + loopMoms = OptionValue[LoopMomenta]; + liNames = OptionValue[LorentzIndexNames]; + sunNames = OptionValue[SUNIndexNames]; + sunfNames = OptionValue[SUNFIndexNames]; + polVecs = OptionValue[TransversePolarizationVectors]; + dim = OptionValue[ChangeDimension]; + prefactor = OptionValue[Prefactor]; - inMoms = OptionValue[IncomingMomenta]; - outMoms = OptionValue[OutgoingMomenta]; - loopMoms = OptionValue[LoopMomenta]; - liNames = OptionValue[LorentzIndexNames]; - sunNames = OptionValue[SUNIndexNames]; - sunfNames = OptionValue[SUNFIndexNames]; - polVecs = OptionValue[TransversePolarizationVectors]; - dim = OptionValue[ChangeDimension]; repRuleMomenta={}; repRuleLorentzIndices={}; @@ -95,7 +102,10 @@ diagsConverted= Map[#[[3]]&,{diags}]; - diagsConverted = FCPrepareFAAmp[diagsConverted,UndoChiralSplittings->OptionValue[UndoChiralSplittings],SMP->OptionValue[SMP]]; + diagsConverted = FCPrepareFAAmp[diagsConverted,UndoChiralSplittings->OptionValue[UndoChiralSplittings],SMP->OptionValue[SMP], + FeynAmpDenominatorCombine->OptionValue[FeynAmpDenominatorCombine]]; + + diagsConverted = prefactor diagsConverted; If[ OptionValue[DropSumOver], diagsConverted = diagsConverted/.FeynArts`SumOver[___]:> 1 @@ -132,6 +142,10 @@ diagsConverted= ChangeDimension[diagsConverted,dim] ]; + If[ TrueQ[OptionValue[Contract]], + diagsConverted = Contract[#,FCI->True]&/@diagsConverted + ]; + If[ !OptionValue[List], diagsConverted = Total[diagsConverted] ]; @@ -140,6 +154,10 @@ diagsConverted = diagsConverted /. OptionValue[FinalSubstitutions] ]; + If[ !FreeQ[diagsConverted,DiracIndex] && OptionValue[FCFADiracChainJoin], + diagsConverted = FCFADiracChainJoin[diagsConverted,FCI->True] + ]; + Return[diagsConverted] ]; diff --git a/FeynCalc/Feynman/FCFADiracChainJoin.m b/FeynCalc/Feynman/FCFADiracChainJoin.m new file mode 100644 index 000000000..c8fd52a27 --- /dev/null +++ b/FeynCalc/Feynman/FCFADiracChainJoin.m @@ -0,0 +1,206 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCFADiracChainJoin *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Rebuilds Dirac chains for 4-fermion operators *) + +(* ------------------------------------------------------------------------ *) + +FCFADiracChainJoin::usage = +"FCFADiracChainJoin[exp] processes the output of FeynArts (after FCFAConvert) \ +with explicit Dirac indices and joins matrices and spinors into closed chains. \ +This is necessary e.g. for models with 4-fermion operators, where FeynArts \ +cannot determine the correct relative signs. When two matrices have a common \ +index but the positions do not match, as in A_ij B_ik, it is assumed that \ +we can take the charge conjugate transposed of either matrix to obtain, e.g. \ +(C A^T C^-1)_ji B_ik or (C B^T C^-1)_ki A_ij."; + +FCFADiracChainJoin::failmsg = +"Error! FCFADiracChainJoin has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +FCFADiracChainJoin::indexsum = +"Cannot process input expressions with unresolved FeynArts index sums. If this error appears when running FCFAConvert, \ +please set the option FCFADiracChainJoin to False and check the output with uncontracted Dirac indices to identify the \ +unresolved IndexSum objects." + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCFADiracChainJoin`Private`"] + +dchjVerbose::usage=""; +ordering::usage=""; +optHead::usage=""; +optFirst::usage=""; + + + +Options[FCFADiracChainJoin] = { + FCE -> False, + FCI -> False, + FCVerbose -> False, + First -> {}, + Head -> Identity +}; + +FCFADiracChainJoin[expr_, OptionsPattern[]] := + Block[{ ex, tmp, res, diracObjects, diracObjectsEval, null1, null2, + dsHead, time, repRule}, + + optHead = OptionValue[Head]; + optFirst = FCI[OptionValue[First]]; + + If[ Head[optFirst]=!=List, + Message[FCFADiracChainJoin::failmsg,"The value of the option First must be a list."]; + Abort[] + ]; + + If [OptionValue[FCVerbose]===False, + dchjVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + dchjVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "FCFADiracChainJoin. Entering.", FCDoControl->dchjVerbose]; + FCPrint[3, "FCFADiracChainJoin: Entering with ", expr, FCDoControl->dchjVerbose]; + + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ2[ex,{DiracChain,DiracIndexDelta}], + Return[ex] + ]; + + If[ OptionValue[FCVerbose]===False, + dchjVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + dchjVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "FCFADiracChainJoin: Isolating Dirac chains.", FCDoControl->dchjVerbose]; + time=AbsoluteTime[]; + + tmp = FCDiracIsolate[ex,FCI->True,Head->dsHead, DotSimplify->False, DiracGammaCombine->False, FCJoinDOTs-> False, + DiracSigmaExplicit->False, LorentzIndex->False, Spinor->False, DiracGamma->False, DiracChain->True, + Factoring -> False]; + diracObjects = Cases[tmp+null1+null2, dsHead[_], Infinity]//Sort//DeleteDuplicates; + + FCPrint[1, "FCFADiracChainJoin: Done isolating spinor chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dchjVerbose]; + FCPrint[3, "FCFADiracChainJoin: After FCDiracIsolate ", tmp, FCDoControl->dchjVerbose]; + + + + FCPrint[3,"FCFADiracChainJoin: diracObjects: ", diracObjects , FCDoControl->dchjVerbose]; + + If[ !FreeQ[diracObjects,FeynArts`IndexSum], + Message[FCFADiracChainJoin::indexsum]; + Abort[] + ]; + + + FCPrint[1, "FCFADiracChainJoin: Joining Dirac chains.", FCDoControl->dchjVerbose]; + time=AbsoluteTime[]; + diracObjectsEval = Map[(diracChainEvalM[#])&, (diracObjects/.dsHead->Identity)]; + + FCPrint[3, "FCFADiracChainJoin: After diracChainEvalM:", diracObjectsEval, FCDoControl->dchjVerbose]; + + diracObjectsEval = diracObjectsEval /. diracChainEvalM -> diracChainEvalS /. diracChainEvalS -> diracChainEvalSign; + + FCPrint[1, "FCFADiracChainJoin: Done simplifying Dirac chains, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dchjVerbose]; + FCPrint[3, "FCFADiracChainJoin: diracObjectsEval: ", diracObjectsEval, FCDoControl->dchjVerbose]; + + If[ !FreeQ2[diracObjectsEval,{diracChainEvalSign,FCChargeConjugateTransposed,DiracChain,DiracIndex}], + Message[FCFADiracChainJoin::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ]; + + FCPrint[1, "FCFADiracChainJoin: Inserting Dirac objects back.", FCDoControl->dchjVerbose]; + time=AbsoluteTime[]; + repRule = MapThread[Rule[#1,#2]&,{diracObjects,diracObjectsEval}]; + FCPrint[3,"FCFADiracChainJoin: repRule: ",repRule , FCDoControl->dchjVerbose]; + res = ( tmp/. Dispatch[repRule]); + FCPrint[1, "FCFADiracChainJoin: Done inserting Dirac objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dchjVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "FCFADiracChainJoin: Leaving.", FCDoControl->dchjVerbose]; + FCPrint[3, "FCFADiracChainJoin: Leaving with ", res, FCDoControl->dchjVerbose]; + + + + res + +]; + +(* A_*i* d_ij *) +diracChainEvalM[rest_. DiracChain[a__,i_DiracIndex,b___] DiracIndexDelta[i_DiracIndex,j_DiracIndex]]:= + diracChainEvalM[rest DiracChain[a,j,b]]; + +(* A_ij B_jk -> (A.B)_ik *) +diracChainEvalM[rest_. DiracChain[chain1_,a_DiracIndex,i_DiracIndex] DiracChain[chain2_,i_DiracIndex,b_DiracIndex]]:= + diracChainEvalM[rest DiracChain[DOT[chain1,chain2],a,b]]/; a=!=i && b=!=i; + +(* A_ai B_bi -> (A. C B^T C^-1)_ab *) +diracChainEvalM[rest_. DiracChain[chain1_,a_DiracIndex,i_DiracIndex] DiracChain[chain2_,b_DiracIndex,i_DiracIndex]]:= + diracChainEvalM[rest DiracChain[DOT[chain1,FCCCT[chain2, Explicit->True, FCDiracIsolate->False, FCI->True]],a,b]]/; a=!=i && b=!=i; + +(* A_ia B_ib -> (C A^T C^-1)_ab *) +diracChainEvalM[rest_. DiracChain[chain1_,i_DiracIndex,a_DiracIndex] DiracChain[chain2_,i_DiracIndex,b_DiracIndex]]:= + diracChainEvalM[rest DiracChain[DOT[FCCCT[chain1, Explicit->True, FCDiracIsolate->False, FCI->True],chain2],a,b]]/; a=!=i && b=!=i; + +(* A_ii -> Tr(A) *) +diracChainEvalM[rest_. DiracChain[chain_/;chain=!=1,i_DiracIndex,i_DiracIndex]]:= + DiracTrace[chain] diracChainEvalM[rest]; + +diracChainEvalM[rest_. DiracChain[1,i_DiracIndex,i_DiracIndex]]:= + DiracTrace[1] diracChainEvalM[rest]; + +(* d_ii -> Tr(1) *) +diracChainEvalM[rest_. DiracIndexDelta[i_DiracIndex,i_DiracIndex]]:= + DiracTrace[1] diracChainEvalM[rest]; + +(* d_ij d_jk -> d_ik *) +diracChainEvalM[rest_. DiracIndexDelta[i_DiracIndex,j_DiracIndex] DiracIndexDelta[j_DiracIndex,k_DiracIndex]]:= + diracChainEvalM[rest DiracIndexDelta[i,k]]; + +(* d_ij^2 -> Tr(1) *) +diracChainEvalM[rest_. DiracIndexDelta[i_DiracIndex, j_DiracIndex]^2]:= + DiracTrace[1] diracChainEvalM[rest]/; i=!=j; + +(* u_i v_j A_ij -> ubar.A.v or vbar.A.u *) +diracChainEvalS[rest_. DiracChain[S: Spinor[_. m1_Momentum, ___], a_DiracIndex] DiracChain[z_, a_DiracIndex, b_DiracIndex] DiracChain[Spinor[s_. m2_Momentum, r___], b_DiracIndex]]:= + diracChainEvalS[rest ordering[First[m1],First[m2]]] DOT[S, z, Spinor[-s m2, r]]/; optFirst==={} || MemberQ[optFirst, S]; + +(* u_i v_j A_ij -> ubar.A.v or vbar.A.u *) +diracChainEvalS[rest_. DiracChain[S: Spinor[_. m1_Momentum, ___], a_DiracIndex] DiracChain[z_, a_DiracIndex, b_DiracIndex] DiracChain[Spinor[s_. m2_Momentum, r___], b_DiracIndex]]:= + diracChainEvalS[rest ordering[First[m2],First[m1]]] FCCCT[DOT[S, z, Spinor[-s m2, r]], Explicit->True, FCDiracIsolate->False, FCI->True]/; MemberQ[optFirst, Spinor[s m2, r]]; + +diracChainEvalS[rest_. ordering[a__] ordering[b__]]:= + diracChainEvalS[rest ordering[a,b]]; + +(*fixes the relative sign checking the orderings of the external fermions. This +essentially reproduces the corresponding code in FormCalc. *) +diracChainEvalSign[ordering[a__]]:= + optHead[Signature[{a}] (-1)^(Length[{a}]/2)]; + +FCPrint[1,"FCFADiracChainJoin.m loaded"]; +End[] diff --git a/FeynCalc/Feynman/FCPrepareFAAmp.m b/FeynCalc/Feynman/FCPrepareFAAmp.m index 603958cb1..e8844505c 100644 --- a/FeynCalc/Feynman/FCPrepareFAAmp.m +++ b/FeynCalc/Feynman/FCPrepareFAAmp.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: FCPrepareFAAmp converts a FeynArts amplitude to FeynCalc *) @@ -32,13 +32,19 @@ Begin["`FCPrepareFAAmp`Private`"] +tmp::usage=""; + Options[FCPrepareFAAmp] = { - SMP -> False, - UndoChiralSplittings -> False + FeynAmpDenominatorCombine -> True, + SMP -> False, + UndoChiralSplittings -> False }; FCPrepareFAAmp[expr_, OptionsPattern[]] := - Block[ {replist0,replist1,replist2,replist3,repListSMP,tempvar,temp}, + Block[{ replist0,replist1,replist2,replist3,repListSMP,tempvar,temp,holdDOT, + optFeynAmpDenominatorCombine}, + + optFeynAmpDenominatorCombine = OptionValue[FeynAmpDenominatorCombine]; repListSMP = { FCGV["EL"] -> SMP["e"], @@ -55,18 +61,29 @@ FCGV["MB"] -> SMP["m_b"], FCGV["MH"] -> SMP["m_H"], FCGV["MW"] -> SMP["m_W"], - FCGV["MZ"] -> SMP["m_Z"] + FCGV["MZ"] -> SMP["m_Z"], + HoldPattern[FeynArts`CKM[1,1]] -> SMP["V_ud",I], + HoldPattern[FeynArts`CKM[1,2]] -> SMP["V_us",I], + HoldPattern[FeynArts`CKM[1,3]] -> SMP["V_ub",I], + HoldPattern[FeynArts`CKM[2,1]] -> SMP["V_cd",I], + HoldPattern[FeynArts`CKM[2,2]] -> SMP["V_cs",I], + HoldPattern[FeynArts`CKM[2,3]] -> SMP["V_cb",I], + HoldPattern[FeynArts`CKM[3,1]] -> SMP["V_td",I], + HoldPattern[FeynArts`CKM[3,2]] -> SMP["V_ts",I], + HoldPattern[FeynArts`CKM[3,3]] -> SMP["V_tb",I] }; - replist0 = {NonCommutative[x__] :> FeynArts`FANonCommutative[x] - - }; + replist0 = { + NonCommutative[x__] :> FeynArts`FANonCommutative[x], + FeynArts`IndexSum[x_, {ind_, _, _}] /; Length[Cases[x, ind, Infinity, Heads -> True]] == 2 && FreeQ[x,FeynArts`IndexSum] :> (tmp = Unique["Ind"] ; x /. ind -> tmp) + }; replist1 = {FeynArts`Index[Global`Lorentz, x_] :> LorentzIndex[ToExpression["Lor" <> ToString[x]]], FeynArts`Index[Global`Gluon, x_] :> SUNIndex[ToExpression["Glu" <> ToString[x]]], FeynArts`Index[Global`Colour, x_] :> SUNFIndex[ToExpression["Col" <> ToString[x]]], + FeynArts`Index[Global`Dirac, x_] :> DiracIndex[ToExpression["Dir" <> ToString[x]]], FeynArts`FourMomentum[FeynArts`Incoming,x_] :> ToExpression["InMom" <> ToString[x]], FeynArts`FourMomentum[FeynArts`Outgoing,x_] :> ToExpression["OutMom" <> ToString[x]], FeynArts`FourMomentum[FeynArts`Internal,x_] :> ToExpression["LoopMom" <> ToString[x]] @@ -75,7 +92,7 @@ Conjugate[Global`FAPolarizationVector][_, x_, y_] :> Pair[LorentzIndex[y],Momentum[Polarization[x,-I]]], Global`FAChiralityProjector[-1] :> DiracGamma[7], Global`FAChiralityProjector[1] :> DiracGamma[6], - Global`FADiracMatrix :> DiracGamma, + Global`FADiracMatrix[x_] :> DiracGamma[LorentzIndex[x]], Global`FAScalarProduct[x_,y_] :> Pair[Momentum[x],Momentum[y]], Global`FADiracSlash[x_] :> DiracGamma[Momentum[x]], Global`FADiracSpinor :> Spinor, @@ -92,33 +109,79 @@ Global`FASUNF[a_,b_,c_] :> SUNF[a,b,c], Global`dSUN[a_,b_,c_] :> SUND[a,b,c], Global`FASUNT :> SUNTF, - FeynArts`IndexDelta[a_SUNFIndex, b_SUNFIndex]:> SUNFDelta[a,b], - FeynArts`IndexDelta[a_SUNIndex, b_SUNIndex]:> SUNDelta[a,b], + FeynArts`IndexDelta[a: (_SUNFIndex| _ExplicitSUNFIndex), b:(_SUNFIndex| _ExplicitSUNFIndex)]:> SUNFDelta[a,b], + FeynArts`IndexDelta[a: (_SUNIndex| _ExplicitSUNIndex), b:(_SUNIndex| _ExplicitSUNIndex)]:> SUNDelta[a,b], FeynArts`FAFeynAmp :> FeynAmp, - FeynArts`FAFeynAmpDenominator[x__] :> (FeynAmpDenominator@@({x}/. z_Momentum:>z[[1]]/. { + FeynArts`FAFeynAmpDenominator[x__] :> ( + FeynAmpDenominator@@({x}/. z_Momentum:>z[[1]]/. { FeynArts`FAPropagatorDenominator[a_,b_] :> PropagatorDenominator[Momentum[a],b], FeynArts`FAPropagatorDenominator[a_,b_,n_Integer] :> Sequence@@Table[PropagatorDenominator[Momentum[a],b],{j,1,n}] - } - )), + })), FeynArts`FAGaugeXi :> GaugeXi, FeynArts`FANonCommutative :> DOT, - FeynArts`FermionChain :> DOT, - FeynArts`MatrixTrace :> DiracTrace + Global`MajoranaSpinor :> Spinor }]; replist3 = { + FeynArts`FermionChain :> DOT, + FeynArts`DiracObject[a__][i_DiracIndex] :> DiracChain[DOT[a],i], + FeynArts`DiracObject[a__][i_DiracIndex, j_DiracIndex] :> DiracChain[DOT[a],i,j], + FeynArts`MatrixTrace :> DiracTrace, FeynArts`FAPropagatorDenominator[x_,y_] :> FeynAmpDenominator[PropagatorDenominator[Momentum[(x/. z_Momentum:>z[[1]])],y]], - FeynArts`FAPropagatorDenominator[x_,y_,n_Integer] :> FeynAmpDenominator@@Table[PropagatorDenominator[Momentum[(x/. z_Momentum:>z[[1]])],y],{j,1,n}] + FeynArts`FAPropagatorDenominator[x_,y_,n_Integer]/;optFeynAmpDenominatorCombine :> + FeynAmpDenominator@@Table[PropagatorDenominator[Momentum[(x/. z_Momentum:>z[[1]])],y],{j,1,n}], + FeynArts`FAPropagatorDenominator[x_,y_,n_Integer]/;!optFeynAmpDenominatorCombine :> + Product[FeynAmpDenominator[PropagatorDenominator[Momentum[(x/. z_Momentum:>z[[1]])],y]] ,{j,1,n}] }; - temp = expr //. replist0 //. replist1 //. replist2 //. replist3; + temp = FCReplaceRepeated[expr, replist0, replist1, replist2, replist3]; If[ OptionValue[SMP], temp = temp /.repListSMP ]; If[ OptionValue[UndoChiralSplittings], - temp = temp//.{(a1__ DiracGamma[x_].DiracGamma[6] a2__ + a1__ DiracGamma[x_].DiracGamma[7] a2__) :> a1 DiracGamma[x] a2, - (a1__ DiracGamma[6] a2__ + a1__ DiracGamma[7] a2__) :> a1 a2} + temp = temp//.{ + + (*Single chains*) + + (* g^mu P_R + g^mu R_L -> g^mu *) + (a1__ DiracGamma[x_].DiracGamma[6] a2__ + a1__ DiracGamma[x_].DiracGamma[7] a2__) :> + a1 DiracGamma[x] a2, + + (* (g^mu P_R)_ij + (g^mu R_L_ij -> (g^mu)_ij *) + (a_. DiracChain[(c_. DiracGamma[x_]).DiracGamma[6], i_DiracIndex, j_DiracIndex] + a_. DiracChain[(c_. DiracGamma[x_]).DiracGamma[7], i_DiracIndex, j_DiracIndex] ) :> + a DiracChain[c DiracGamma[x], i, j], + (a1__ DiracGamma[6] a2__ + a1__ DiracGamma[7] a2__) :> a1 a2, + + (* (P_R)_ij + (R_L)_ij -> (1)_ij *) + (a_. DiracChain[DiracGamma[6], i_DiracIndex, j_DiracIndex] + a_. DiracChain[DiracGamma[7], i_DiracIndex, j_DiracIndex]) :> + a DiracChain[1, i, j], + + (*Double chains*) + (* (g^mu P_x)_ij (g^mu P_R)_kl + (g^nu P_x)_ij (g^nu P_L)_kl -> (g^mu P_x)_ij (g^mu)_kl *) + (a_. DiracChain[DiracGamma[x1_LorentzIndex].DiracGamma[(h:7|6)], i_DiracIndex, j_DiracIndex] * + DiracChain[DiracGamma[x1_LorentzIndex].DiracGamma[6], k_DiracIndex, l_DiracIndex] + + a_. DiracChain[DiracGamma[x2_LorentzIndex].DiracGamma[(h:7|6)], i_DiracIndex, j_DiracIndex] * + DiracChain[DiracGamma[x2_LorentzIndex].DiracGamma[7], k_DiracIndex, l_DiracIndex] ) :> + a DiracChain[DiracGamma[x1].DiracGamma[h], i, j] DiracChain[DiracGamma[x1], k, l], + + (* (g^mu)_ij (g^mu P_R)_kl + (g^nu)_ij (g^nu P_L)_kl -> (g^mu)_ij (g^mu)_kl *) + (a_. DiracChain[DiracGamma[x1_LorentzIndex], i_DiracIndex, j_DiracIndex] * + DiracChain[DiracGamma[x1_LorentzIndex].DiracGamma[6], k_DiracIndex, l_DiracIndex] + + + a_. DiracChain[DiracGamma[x2_LorentzIndex], i_DiracIndex, j_DiracIndex] * + DiracChain[DiracGamma[x2_LorentzIndex].DiracGamma[7], k_DiracIndex, l_DiracIndex] ) :> + a DiracChain[DiracGamma[x1], i, j] DiracChain[DiracGamma[x1], k, l] + + + } /. DOT -> holdDOT /. { + a_. holdDOT[-DiracGamma[x_], DiracGamma[6]] + a_. holdDOT[-DiracGamma[x_], DiracGamma[7]] :> -a DiracGamma[x], + + a_. DiracChain[holdDOT[-DiracGamma[x_], DiracGamma[6]], i_DiracIndex, j_DiracIndex] + a_. DiracChain[holdDOT[-DiracGamma[x_], DiracGamma[7]], i_DiracIndex, j_DiracIndex] :> + -a DiracChain[DiracGamma[x], i, j] + + }/. holdDOT -> DOT ]; + temp ]; diff --git a/FeynCalc/Feynman/FermionSpinSum.m b/FeynCalc/Feynman/FermionSpinSum.m index 07ec82841..893c5c158 100755 --- a/FeynCalc/Feynman/FermionSpinSum.m +++ b/FeynCalc/Feynman/FermionSpinSum.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Do the trace-formation (i.e. fermionic spin-sums) *) @@ -17,11 +17,13 @@ FermionSpinSum::usage = -"FermionSpinSum[x] constructs Traces out of squared ampliudes in x."; +"FermionSpinSum[exp] converts products of closed spinor chains in exp into +Dirac traces. Both Dirac and Majorana particles are supported. It is understood, +that exp represents a squared amplitude."; -DiracSimplify::spinorsleft = -"Error! After applying FermionSpinSum to all spinor chains the output -still contains spinors. Evaluation aborted."; +FermionSpinSum::spinorsleft = +"Error! After applying FermionSpinSum to all spinor chains the output \ +still contains spinors."; (* ------------------------------------------------------------------------ *) @@ -34,27 +36,33 @@ Options[FermionSpinSum] = { Collecting -> True, - Factoring -> Factor, + DotSimplify -> True, ExtraFactor -> 1, + FCE -> False, FCI -> False, + FCTraceFactor -> True, FCVerbose -> False, - DotSimplify -> True, + Factoring -> Factor, + Head -> Identity, Momentum -> All, - SpinPolarizationSum -> Identity + SpinorChainTranspose -> True }; FermionSpinSum[expr_List, opts:OptionsPattern[]]:= Map[FermionSpinSum[#, opts]&, expr]; FermionSpinSum[expr_, OptionsPattern[]] := - Block[ {spinPolarizationSum,extraFactor,moms, ex, spChain, ssIso, time}, + Block[ {spinPolarizationSum,extraFactor,moms, ex, spChain, ssIso, time, + optSpinorChainTranspose, optSpinPolarizationSum}, - extraFactor = OptionValue[ExtraFactor]; - moms = OptionValue[Momentum]; + extraFactor = OptionValue[ExtraFactor]; + moms = OptionValue[Momentum]; + optSpinorChainTranspose = OptionValue[SpinorChainTranspose]; + optSpinPolarizationSum = OptionValue[Head]; If [OptionValue[FCVerbose]===False, fssVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], fssVerbose=OptionValue[FCVerbose] ]; ]; @@ -76,48 +84,84 @@ FCPrint[1,"FermionSpinSum: collecting done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->fssVerbose]; FCPrint[3, "FermionSpinSum: After collecting terms w.r.t spinors: ",ex, FCDoControl->fssVerbose]; - - (* Applying spin sum formula *) - time=AbsoluteTime[]; - FCPrint[1, "FermionSpinSum: Applying spin sum formula.", FCDoControl->fssVerbose]; + FCPrint[1, "FermionSpinSum: Applying the spin sum formula.", FCDoControl->fssVerbose]; ex = ex //. { - (* Product of two spinor chains, all momenta *) - spChain[DOT[Spinor[s1_. Momentum[pe1_,dim_:4], mass1_, ___], dots1___, Spinor[s2_. Momentum[pe2_,dim_:4], mass2_, ___]]] * - spChain[DOT[Spinor[s2_. Momentum[pe2_,dim_:4], mass2_, ___], dots2___, Spinor[s1_. Momentum[pe1_,dim_:4], mass1_, ___]]]/; - FreeQ[{dots1,dots2},Spinor] && (moms===All || (MemberQ[moms,pe1] && MemberQ[moms,pe2] )) :> - DiracTrace[DOT[spinPolarizationSum[(DiracGamma[Momentum[pe1,dim],dim] + s1 mass1)], dots1, - spinPolarizationSum[(DiracGamma[Momentum[pe2,dim],dim] + s2 mass2)], dots2]], - - spChain[DOT[Spinor[s1_. Momentum[pe1_,dim_:4], mass1_, ___], dots1___, Spinor[s2_. Momentum[pe2_,dim_:4], mass2_, arg2___]]] * - spChain[DOT[Spinor[s3_. Momentum[pe3_,dim_:4], mass3_, arg3___], dots2___, Spinor[s1_. Momentum[pe1_,dim_:4], mass1_, ___]]]/; - FreeQ[{dots1,dots2},Spinor] && (moms===All || MemberQ[moms,pe1]) :> - spChain[DOT[Spinor[s3 Momentum[pe3,dim], mass3, arg3], dots2, - spinPolarizationSum[(DiracGamma[Momentum[pe1,dim],dim] + s1 mass1)], dots1, - Spinor[s2 Momentum[pe2,dim], mass2, arg2]]], + (* Product of two spinor chains, Dirac spinors *) + spChain[DOT[Spinor[s_. Momentum[p_,d_:4], Y_, ___], a___, Spinor[t_. Momentum[q_,d_:4], Z_, ___]]] * + spChain[DOT[Spinor[t_. Momentum[q_,d_:4], Z_, ___], b___, Spinor[s_. Momentum[p_,d_:4], Y_, ___]]]/; + FreeQ[{a,b},Spinor] && (moms===All || (MemberQ[moms,p] && MemberQ[moms,q] )) :> + DiracTrace[DOT[spinPolarizationSum[(DiracGamma[Momentum[p,d],d] + s Y)], a, + spinPolarizationSum[(DiracGamma[Momentum[q,d],d] + t Z)], b]], + + spChain[DOT[Spinor[s_. Momentum[p_,d_:4], m_, ___], a___, Spinor[t_. Momentum[q_,d_:4], Y_, W___]]] * + spChain[DOT[Spinor[u_. Momentum[r_,d_:4], Z_, X___], b___, Spinor[s_. Momentum[p_,d_:4], m_, ___]]]/; + FreeQ[{a,b},Spinor] && (moms===All || MemberQ[moms,p]) :> + spChain[DOT[Spinor[u Momentum[r,d], Z, X], b, + spinPolarizationSum[(DiracGamma[Momentum[p,d],d] + s m)], a, + Spinor[t Momentum[q,d], Y, W]]], + + (* Product of two spinor chains, Majorana spinors, ubar(p).X vbar(p).Y. + The -1 in front of spChain comes from switching the spinors after having transposed the second chain *) + spChain[DOT[Spinor[s_. Momentum[p_,d_:4], m_,___], a___, Spinor[t_. Momentum[q_,d_:4], Y___]]] * + spChain[DOT[Spinor[u_. Momentum[p_,d_:4], m_,___], b___, Spinor[v_. Momentum[r_,d_:4], Z___]]]/; + FreeQ[{a,b},Spinor] && (optSpinorChainTranspose && moms===All || (MemberQ[moms,p] && (-u===s) )) :> + -1*spChain[DOT[Spinor[- v Momentum[r,d], Z], + If[ TrueQ[{b}==={}], + Unevaluated[Sequence[]], + FCChargeConjugateTransposed[DOT[b],FCI->True,DotSimplify->False,Explicit->True] + ], + spinPolarizationSum[(DiracGamma[Momentum[p,d],d] + s m)], a, Spinor[t Momentum[q,d], Y]]], + + (* Product of two spinor chains, Majorana spinors, X.u(p) Y.v(p). + The -1 in front of spChain comes from switching the spinors after having transposed the second chain *) + spChain[DOT[Spinor[s_. Momentum[p_,d_:4], Y___], a___, Spinor[t_. Momentum[q_,d_:4], m_,___]]] * + spChain[DOT[Spinor[u_. Momentum[r_,d_:4], Z___], b___, Spinor[v_. Momentum[q_,d_:4], m_, ___]]]/; + FreeQ[{a,b},Spinor] && (optSpinorChainTranspose && moms===All || (MemberQ[moms,q] && (-v===t) )) :> + -1*spChain[DOT[Spinor[s Momentum[p,d], Y], a , + spinPolarizationSum[(DiracGamma[Momentum[q,d],d] + t m)], + If[ TrueQ[{b}==={}], + Unevaluated[Sequence[]], + FCChargeConjugateTransposed[DOT[b],FCI->True,DotSimplify->False,Explicit->True] + ], Spinor[-u Momentum[r,d], Z]]], (* A spinor chain with one spin sum inside *) - spChain[DOT[Spinor[s_. Momentum[pe_,dim_:4], mass_, ___], dots___, Spinor[s_. Momentum[pe_,dim_:4], mass_, ___]]] /; - FreeQ[{dots},Spinor] && (moms===All || MemberQ[moms,pe]) :> - DiracTrace[DOT[spinPolarizationSum[(DiracGamma[Momentum[pe,dim],dim] + s mass)], dots]] + spChain[DOT[Spinor[s_. Momentum[p_,d_:4], mass_, ___], x___, Spinor[s_. Momentum[p_,d_:4], m_, ___]]] /; + FreeQ[{x},Spinor] && (moms===All || MemberQ[moms,p]) :> + DiracTrace[DOT[spinPolarizationSum[(DiracGamma[Momentum[p,d],d] + s m)], x]] }; - FCPrint[1,"FermionSpinSum: applying spin sum formula done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->fssVerbose]; - FCPrint[3,"FermionSpinSum: After applying spin sum formula: ", ex, FCDoControl->fssVerbose]; + FCPrint[1,"FermionSpinSum: Applying the spin sum formula done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->fssVerbose]; + FCPrint[3,"FermionSpinSum: After applying the spin sum formula: ", ex, FCDoControl->fssVerbose]; + + If[ !FreeQ[ex,FCChargeConjugateTransposed], + ex = ex /. FCChargeConjugateTransposed[spinPolarizationSum[x_],r___]:> + spinPolarizationSum[FCChargeConjugateTransposed[x,Explicit->True,r]] + ]; If[ OptionValue[DotSimplify], time=AbsoluteTime[]; FCPrint[1, "FermionSpinSum: Applying DotSimplify.", FCDoControl->fssVerbose]; - ex = ex /. spinPolarizationSum[x_]:> spinPolarizationSum[DotSimplify[x,Expanding->False]]; - FCPrint[1,"FermionSpinSum: applying spin sum formula done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->fssVerbose]; - FCPrint[3,"FermionSpinSum: After applying spin sum formula: ", ex, FCDoControl->fssVerbose]; + ex = ex /. spinPolarizationSum[x_]:> spinPolarizationSum[DotSimplify[x,Expanding->False,FCI->True]]; + FCPrint[1,"FermionSpinSum: Applying DotSimplify done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->fssVerbose]; + FCPrint[3,"FermionSpinSum: After DotSimplify: ", ex, FCDoControl->fssVerbose]; ]; - ex = ex /. spinPolarizationSum -> OptionValue[SpinPolarizationSum]; + If[ optSpinPolarizationSum===Identity && OptionValue[FCTraceFactor], + time=AbsoluteTime[]; + FCPrint[1, "FermionSpinSum: Applying FCTraceFactor.", FCDoControl->fssVerbose]; + ex = ex /. DiracTrace[x_]/;!FreeQ[x,spinPolarizationSum] :> FCTraceFactor[DiracTrace[(x/.spinPolarizationSum->Identity)],FCI->True]; + FCPrint[1,"FermionSpinSum: Applying FCTraceFactor done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->fssVerbose]; + FCPrint[3,"FermionSpinSum: After FCTraceFactor: ", ex, FCDoControl->fssVerbose]; + ]; + + If[ !FreeQ[ex,spinPolarizationSum], + ex = ex /. spinPolarizationSum -> optSpinPolarizationSum; + ]; If[ moms===All && !FreeQ[ex,spChain], - Message[DiracSimplify::spinorsleft]; + Message[FermionSpinSum::spinorsleft]; ]; ex = ex /. spChain -> Identity; @@ -134,6 +178,10 @@ ex = ex extraFactor; + If[ OptionValue[FCE], + ex = FCE[ex] + ]; + ex ]/; Head[expr]=!=List; diff --git a/FeynCalc/Feynman/FeynRule.m b/FeynCalc/Feynman/FeynRule.m index 69df41a93..dead8d4d2 100755 --- a/FeynCalc/Feynman/FeynRule.m +++ b/FeynCalc/Feynman/FeynRule.m @@ -32,6 +32,11 @@ assumptions::usage=""; frVerbose::usage=""; +schouten::usage=""; +opes::usage=""; +localSUND::usage=""; +localSUNF::usage=""; +sdummy::usage=""; (* Functions that are applied to the expression first. Added 3/8-2000 by Frederik Orellana to allow interoperability with Phi: @@ -57,8 +62,8 @@ ]; frex[nl_] := - frex[nl] = Block[ {nla = DotSimplify[nl],sdum, flag, ff, fm,ff1, cli,tem, - nlafirst, newlorlist, lorindlist, sunindlist, newsunlist}, + frex[nl] = Block[ {nla = DotSimplify[nl],sdum, flag, ff, fm,ff1, ff2, cli,tem, + nlafirst, newlorlist, lorindlist, sunindlist, newsunlist, uniquelist}, FCPrint[1, "FeynRule: frex: Entering with ", nla, FCDoControl->frVerbose]; @@ -95,26 +100,26 @@ (* select those which occur an even number of times *) newlorlist = {}; newsunlist = {}; - For[iij = 1, iij <= Length[lorindlist], iij++, - If[ EvenQ[Length[Position[nlafirst, lorindlist[[iij]]]]], - AppendTo[newlorlist, lorindlist[[iij]]] + For[r = 1, r <= Length[lorindlist], r++, + If[ EvenQ[Length[Position[nlafirst, lorindlist[[r]]]]], + AppendTo[newlorlist, lorindlist[[r]]] ]; ]; - For[iij = 1, iij <= Length[sunindlist], iij++, - If[ EvenQ[Length[Position[nlafirst, sunindlist[[iij]]]]], - AppendTo[newsunlist, sunindlist[[iij]]] + For[r = 1, r <= Length[sunindlist], r++, + If[ EvenQ[Length[Position[nlafirst, sunindlist[[r]]]]], + AppendTo[newsunlist, sunindlist[[r]]] ] ]; FCPrint[1, "FeynRule: frex: newlorlist ", newlorlist, FCDoControl->frVerbose]; FCPrint[1, "FeynRule: frex: newsunlist ", newsunlist, FCDoControl->frVerbose]; - uniquelist = Join[Table[newlorlist[[ij]] -> - (newlorlist[[ij]]/.LorentzIndex -> lorunique), - {ij, Length[newlorlist]} + uniquelist = Join[Table[newlorlist[[i]] -> + (newlorlist[[i]]/.LorentzIndex -> lorunique), + {i, Length[newlorlist]} ], - Table[newsunlist[[jj]] -> - (newsunlist[[jj]]/.SUNIndex -> sununique), - {jj, Length[newsunlist]} + Table[newsunlist[[j]] -> + (newsunlist[[j]]/.SUNIndex -> sununique), + {j, Length[newsunlist]} ] ]; FCPrint[1, "FeynRule: frex: uniquelist = ", uniquelist, FCDoControl->frVerbose]; @@ -273,8 +278,8 @@ w_/;(Variables[w] === Variables[{i,n}])] ) :> (((-1)^n (-1)^(i+em) pow[a, v + n - 2 i]* pow[b, w - n + 2 i] - ) /. (-1)^(xa_ + 2 xb_) :> ((-1)^xa /; - MemberQ[{OPEi,OPEj,OPEk,OPEl,OPEm},xb] + ) /. (-1)^(y_ + 2 z_) :> ((-1)^y /; + MemberQ[{OPEi,OPEj,OPEk,OPEl,OPEm},z] ) ) /; (!OrderedQ[{a,b}]) && ((pow === Power) || (pow === Power2)) && @@ -291,7 +296,7 @@ sutr[pli_List][x_, {i_, 0, j_}, b__] := MemSet[sutr[pli][x,{i,0,j}, b], Block[ {xx = x, te}, - te = If[ FreeQ[x, (-1)^(_. i + em_.)], + te = If[ FreeQ[x, (-1)^(_. i + _.)], enmomcon[x, pli], x ]; @@ -305,7 +310,7 @@ sutr[pli_List][x_, {i_, 0, j_}] := MemSet[sutr[pli][x,{i,0,j}], Block[ {xx = x, te}, - te = If[ FreeQ[x, (-1)^(_. i + em_.)], + te = If[ FreeQ[x, (-1)^(_. i + _.)], enmomcon3[x, pli], x ]; @@ -399,22 +404,31 @@ FeynRule[lag_, fii_List, ru___Rule] := If[ Length[lag] === 0, - Print["well well ", lag, " does not look like a lagrangian"], + Print[lag, " does not look like a lagrangian"], Block[ {(*InitialFunction stuff added by F.Orellana 3/8-2000*) - initf = InitialFunction /. {ru} /. Options[FeynRule], - nlag = ExpandAll[fcis[initf[lag]]], temp1, temp, + initf, nlag, temp1, temp, fili = fii, lfili, qli,specope, groupindices, result,fields,tfields,plist, - vert,sdummy, getsu,gsu,subs, + vert, getsu,gsu,subs, qfi, qqq, oldnoncomm, onepm, onemm, - plho,schouten,opsumb,opsumb2, + plho,opsumb,opsumb2, $binindices, indd, oplei,anti5, leib,coup,cdp,cedepe,opexbin, - zeromomentum,partiald,fcVerbose + zeromomentum,partiald,fcVerbose, + sumBinomial, puref, nres, nee }, + initf = InitialFunction /. {ru} /. Options[FeynRule]; + nlag = ExpandAll[fcis[initf[lag]]]; + + If[ !FreeQ2[{lag,fii}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + + FCPrint[1, "FeynRule: Entering with ", lag, FCDoControl->frVerbose]; nlag = nlag /. SUND -> localSUND /. SUNF -> localSUNF; @@ -452,7 +466,7 @@ leib[y_] := y /. OPESum -> oplei /. oplei -> OPESum; fields = Map[ ( QuantumField[___, #, - Pattern @@ {Unique[dm], ___}][___])&, #[[0, 1]]& /@ fili]; + Pattern @@ {Unique["dm"], ___}][___])&, #[[0, 1]]& /@ fili]; If[ !FreeQ[nlag, Sum], nlag = nlag /. Sum -> OPESum ]; @@ -570,10 +584,10 @@ UnDeclareNonCommutative[groupindices]; If[ Head[vert] === Plus, result = 0; - For[iij = 1, iij <= Length[vert], iij++, - FCPrint[2, "iij of FunctionalD = ", iij, " out of ", Length[vert], FCDoControl->frVerbose]; + For[j = 1, j <= Length[vert], j++, + FCPrint[2, "iij of FunctionalD = ", j, " out of ", Length[vert], FCDoControl->frVerbose]; result = result + - DotSimplify[FunctionalD[vert[[iij]], fili], + DotSimplify[FunctionalD[vert[[j]], fili], Expanding -> False ] /. (a_ /; (a =!= (-1)))^ (w_ /; (Head[w] =!= Integer)) :> Power2[a, w]; @@ -583,7 +597,7 @@ (w_ /; (Head[w] =!= Integer)) :> Power2[a, w]; ]; FCPrint[1, "FeynRule: After functional differentiation ", result, FCDoControl->frVerbose]; - qli[a__,el__LorentzIndex, ___][_] := + qli[__,el__LorentzIndex, ___][_] := {el}; lfili = Flatten[fili /. QuantumField -> qli]; result = Expand2[result/.SUNDelta->SUNDeltaContract/.SUNDeltaContract->SUNDelta]; @@ -600,10 +614,9 @@ FCPrint[1, "FeynRule: After dirdot ", result, FCDoControl->frVerbose]; ]; - alllor = Union[Cases[result, LorentzIndex[__], Infinity]]; FCPrint[1, "FeynRule: After Cases ", result, FCDoControl->frVerbose]; - If[ alllor =!= Sort[lfili], + If[ Union[Cases[result, LorentzIndex[__], Infinity]] =!= Sort[lfili], If[ (Contract /. Options[FeynRule]) === True, result = result// Contract; FCPrint[1, "FeynRule: After another contraction ", result, FCDoControl->frVerbose]; @@ -656,9 +669,9 @@ opexbin[a_, b_] := Factor2[PowerSimplify[SymbolicSum[a,b],Assumptions->assumptions ] ] /; !FreeQ[a,Binomial]; - For[ib = 1, ib <= Length[$binindices], ib++, - FCPrint[1, "ib = ", ib, " out of ", Length[$binindices], FCDoControl->frVerbose]; - indd = $binindices[[ib]]; + For[r = 1, r <= Length[$binindices], r++, + FCPrint[1, "r = ", r, " out of ", Length[$binindices], FCDoControl->frVerbose]; + indd = $binindices[[r]]; If[ !FreeQ[result, sumBinomial], Clear[opsumb, opsumb2]; opsumb[xx_Plus] := @@ -702,9 +715,9 @@ If[ Head[result] =!= Plus, result = opesback[result, fii], nres = 0; - For[ij = 1, ij<=Length[result], ij++, - FCPrint[1, "ij = ", ij, FCDoControl->frVerbose]; - nee = opesback[result[[ij]], fii]; + For[r = 1, r<=Length[result], r++, + FCPrint[1, "r = ", r, FCDoControl->frVerbose]; + nee = opesback[result[[r]], fii]; nres = nres + nee; ]; result = nres; @@ -825,11 +838,11 @@ resu = Map[fop, resu]; ]; If[ legs<5, - resu = Factor2[resu /. Complex[0,be_]->(be iI) + resu = Factor2[resu /. Complex[0,be_]->(be y) ] /. {(onepm (-1)^OPEm) :> onepm } /. {(onemm (-1)^OPEm) :> (-onemm)} /. - {iI^(2 a_) :> (-1)^a} /. - { iI :> I, (*Plus :> pluc, *) + {y^(2 a_) :> (-1)^a} /. + { y :> I, (*Plus :> pluc, *) onepm :> ((1+(-1)^OPEm)/2), onemm :> ((1-(-1)^OPEm)/2) }, @@ -863,7 +876,7 @@ resu = Factor2[resu] ]; ]; - If[ !FreeQ[resu, _Complex^em_], + If[ !FreeQ[resu, _Complex^_], resu = PowerSimplify[resu,Assumptions->assumptions] ]; resu @@ -875,16 +888,16 @@ ] := 1/exp; InvertFermion[n_. DiracGamma[Momentum[pe_]] + m_.] := - -I (n DiracSlash[pe] - m)/(n^2 ScalarProduct[pe, pe] - m^2); + -I (n GS[pe] - m)/(n^2 ScalarProduct[pe, pe] - m^2); InvertBoson[exp_, k_, m_, n_] := Block[{geteq, la}, geteq[x_ ] := ({#[[1]]==0, #[[2]]==0}& @ Collect2[Contract[x], lor]) /. Pair[___, lor[__], ___] -> 1; -(A MetricTensor[m, n] + B FourVector[k, m] FourVector[k, n]) /. - Solve[geteq[exp (A MetricTensor[m, la] + - B FourVector[k, m] FourVector[k, la]) - - MetricTensor[la, n]], {A, B}][[1]] +(A MT[m, n] + B FV[k, m] FV[k, n]) /. + Solve[geteq[exp (A MT[m, la] + + B FV[k, m] FV[k, la]) - + MT[la, n]], {A, B}][[1]] ]; *) diff --git a/FeynCalc/Feynman/FieldDerivative.m b/FeynCalc/Feynman/FieldDerivative.m index 49090439a..881cd23c9 100644 --- a/FeynCalc/Feynman/FieldDerivative.m +++ b/FeynCalc/Feynman/FieldDerivative.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Field derivative *) @@ -19,9 +19,8 @@ "FieldDerivative[f[x],x,li1,li2,...] is the derivative of f[x] with \ respect to space-time variables x and with Lorentz indices li1, li2, ..., \ where li1, li2, ... have head LorentzIndex. \n - FieldDerivative[f[x],x,li1,li2,...] can be given as \ -FieldDerivative[f[x],x,{l1,l2,...}], where l1 is li1 without the head, ... \ +FieldDerivative[f[x],x,{l1,l2,...}], where l1 is li1 without the head. \n NOTICE: FieldDerivative is defined only for objects with head QuantumField[...]. \ If the space-time derivative of other objects is wanted, the corresponding \ rule must be specified."; @@ -94,9 +93,9 @@ (* Recursive definition of multiple derivatives: *) FieldDerivative[aa_, x_, loris__LorentzIndex, lori1_LorentzIndex] := (newfunc[1] = FieldDerivative[aa, x, lori1]; - Do[newfunc[rep + 1] = - FieldDerivative[newfunc[rep], x, ##]& @@ - Take[{loris}, {-rep}], {rep, 1, Length[{loris}]}]; + Do[newfunc[r + 1] = + FieldDerivative[newfunc[r], x, ##]& @@ + Take[{loris}, {-r}], {r, 1, Length[{loris}]}]; newfunc[Length[{loris}] + 1]); FieldDerivative /: diff --git a/FeynCalc/Feynman/FieldStrength.m b/FeynCalc/Feynman/FieldStrength.m index 5c34d9876..c8d098628 100644 --- a/FeynCalc/Feynman/FieldStrength.m +++ b/FeynCalc/Feynman/FieldStrength.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Field strength tensor *) @@ -18,10 +18,9 @@ FieldStrength::usage = "FieldStrength[mu,nu,a] is the field strength tensor \ F_{mu nu}^a = partial_mu A_nu^a - partial_nu A_mu^a + \ -g f^{abc} A_mu^b A_nu^c. \ - +g f^{abc} A_mu^b A_nu^c. \n FieldStrength[mu,nu] is the field strength tensor \ -F_{mu nu}^a = partial_mu A_nu^a - partial_nu A_mu. \ +F_{mu nu}^a = partial_mu A_nu^a - partial_nu A_mu. \n The name of the field (A) and the coupling constant (g) \ can be set through the options or by additional arguments: \ FieldStrength[mu,nu,a, A, g] or, specifying the dummy \ diff --git a/FeynCalc/Feynman/FunctionalD.m b/FeynCalc/Feynman/FunctionalD.m index 4d2572aa3..a7700b679 100755 --- a/FeynCalc/Feynman/FunctionalD.m +++ b/FeynCalc/Feynman/FunctionalD.m @@ -15,11 +15,9 @@ (* ------------------------------------------------------------------------ *) FunctionalD::usage = -"FunctionalD[expr, -{QuantumField[name, LorentzIndex[mu], ..., SUNIndex[a]][p], ...}] calculates \ -the functional derivative of expr with respect to the QuantumField list (with \ -incoming momenta p, etc.) and does the fourier transform. \ -\n +"FunctionalD[exp, {QuantumField[name, LorentzIndex[mu], ..., SUNIndex[a]][p], ...}] \ +calculates the functional derivative of exp with respect to the QuantumField list \ +(with incoming momenta p, etc.) and does the Fourier transform.\n FunctionalD[expr, {QuantumField[name, LorentzIndex[mu], ... \ SUNIndex[a]], ...}] calculates the functional derivative and does \ partial integration but omits the x-space delta functions."; diff --git a/FeynCalc/Feynman/GhostPropagator.m b/FeynCalc/Feynman/GhostPropagator.m index ac34dfe6a..170568cae 100755 --- a/FeynCalc/Feynman/GhostPropagator.m +++ b/FeynCalc/Feynman/GhostPropagator.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Ghost propagator *) @@ -35,13 +35,12 @@ Explicit -> False }; -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - -GhostPropagator[x___, i_Integer, y___] := - GhostPropagator[x, c[i], y]; - -GhostPropagator[p_, OptionsPattern[]] := - (I FeynAmpDenominator[PropagatorDenominator[p, 0]]) /;OptionValue[Explicit]; +GhostPropagator[pi_, OptionsPattern[]] := + Block[ {p, glp}, + p = Momentum[pi, OptionValue[Dimension]]; + glp = I FeynAmpDenominator[PropagatorDenominator[p, 0]]; + QCDFeynmanRuleConvention[GhostPropagator] glp + ] /; OptionValue[Explicit]; GhostPropagator[pi_, ai_, bi_, OptionsPattern[]] := Block[ {p, a, b, glp}, @@ -49,7 +48,7 @@ a = SUNIndex[ai]; b = SUNIndex[bi]; glp = I FeynAmpDenominator[PropagatorDenominator[p, 0]] SUNDelta[a, b]; - glp + QCDFeynmanRuleConvention[GhostPropagator] glp ] /; OptionValue[Explicit]; GhostPropagator /: diff --git a/FeynCalc/Feynman/GluonGhostVertex.m b/FeynCalc/Feynman/GluonGhostVertex.m index 8429b1d25..a034f47ea 100755 --- a/FeynCalc/Feynman/GluonGhostVertex.m +++ b/FeynCalc/Feynman/GluonGhostVertex.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Gluon ghost vertex *) @@ -21,9 +21,11 @@ GluonGhostVertex::usage = "GluonGhostVertex[{p,mu,a}, {q,nu,b}, {k,rho,c}] or \ -GluonGhostVertex[ p,mu,a , q,nu,b , k,rho,c ] yields" <> ToString[ -Hyperlink[Style["\[RightSkeleton]", "SR"], "paclet:FeynCalc/ref/GluonGhostVertex"], -StandardForm] +GluonGhostVertex[ p,mu,a , q,nu,b , k,rho,c ] yields the gluon-ghost-vertex. \ +The first argument represents the gluon and the third argument the outgoing \ +ghost field (but incoming 4-momentum). \n +The dimension and the name of the coupling constant are determined by the \ +options Dimension and CouplingConstant." (* ------------------------------------------------------------------------ *) @@ -38,16 +40,10 @@ Explicit -> False }; -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - - GluonGhostVertex[{_, ai_}, {bi_}, {ki_, ci_}, opt:OptionsPattern[]] := GluonGhostVertex[{FCGV["x"], FCGV["y"], ai}, {FCGV["z"],FCGV["h"],bi}, {ki,FCGV["l"],ci}, opt] /; OptionValue[Explicit]; -GluonGhostVertex[x___, i_Integer, y___] := - GluonGhostVertex[x, l[i], c[i], y]; - GGV = GluonGhostVertex; GluonGhostVertex[a_,b_,c_, d_,e_,f_, g_,h_,i_, opt:OptionsPattern[]] := diff --git a/FeynCalc/Feynman/GluonPropagator.m b/FeynCalc/Feynman/GluonPropagator.m index 6c6d5d1b7..7ba9b69fe 100755 --- a/FeynCalc/Feynman/GluonPropagator.m +++ b/FeynCalc/Feynman/GluonPropagator.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Gluon propagator *) @@ -20,11 +20,10 @@ GluonPropagator::usage = "GluonPropagator[p, {mu, a}, {nu, b}] or GluonPropagator[p, mu, a , nu, b ] \ -yields the gluon propagator. - +yields the gluon propagator. \n GluonPropagator[p, {mu}, {nu}] or GluonPropagator[p, mu, nu] omits the SUNDelta. \ Using {p,M} instead of p as the first argument gives the Gluon a mass. \ -The gauge and the dimension is determined by the option Gauge and Dimension. \ +The gauge and the dimension are determined by the options Gauge and Dimension. \ The following settings of Gauge are possible: \ 1 : the Feynman gauge; \ alpha : the general covariant gauge; \ @@ -47,11 +46,6 @@ GP = GluonPropagator; Abbreviation[GluonPropagator] = HoldForm[GP]; -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - -GluonPropagator[x___, i_Integer, y___] := - GluonPropagator[x, l[i], c[i], y]/;2 1000] /. LorentzIndex -> lorf /. lorf -> LorentzIndex; lorf[y_lorf,___] := @@ -65,9 +59,6 @@ momf[y_momf,___] := y; -GluonVertex[x___, i_Integer, y___] := - GluonVertex[x, l[i], c[i], y]; - (* 3 - vertex *) GluonVertex[x1_,x2_,x3_,x4_,x5_,x6_,x7_,x8_, x9_, y___Rule] := GluonVertex[{x1,x2,x3}, {x4,x5,x6}, {x7,x8,x9} , y] /; @@ -132,7 +123,7 @@ GluonVertex /: MakeBoxes[GluonVertex[{_,mu1_},{_,mu2_},{_,mu3_},{_,mu4_}], TraditionalForm] := - SuperscriptBox["W",TBox[mu1,mu2,mu3,mu4]]; + SuperscriptBox["V",TBox[mu1,mu2,mu3,mu4]]; GluonVertex /: MakeBoxes[GluonVertex[{p1_,mu1_, a_},{p2_,mu2_,b_},{p3_,mu3_,c_},{p4_,mu4_,d_}], TraditionalForm] := diff --git a/FeynCalc/Feynman/PolarizationSum.m b/FeynCalc/Feynman/PolarizationSum.m index f85258f40..57cd50d25 100755 --- a/FeynCalc/Feynman/PolarizationSum.m +++ b/FeynCalc/Feynman/PolarizationSum.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Polarization sums for massive and massless vector @@ -21,12 +21,11 @@ PolarizationSum::usage = -"PolarizationSum[ mu,nu, ... ] defines (as abbreviations) different polarization sums. \ -PolarizationSum[mu, nu] = -g(mu nu); \ -PolarizationSum[mu, nu, k] = -g(mu nu) + k(mu) k(nu)/k^2; \ -PolarizationSum[mu, nu, k, n] = polarization sum for spin 1 fields; \ -(n = external momentum). \ -PolarizationSum[mu, nu, k, 0] is equivalent to -g(mu nu)"; +"PolarizationSum[mu,nu, ... ] returns different polarization sums depending on \ +its arguments. \n +PolarizationSum[mu, nu] or PolarizationSum[mu, nu, k, 0] gives -g(mu nu); \n +PolarizationSum[mu, nu, k] returns -g(mu nu) + k(mu) k(nu)/k^2; \n +PolarizationSum[mu, nu, k, n] yields the general polarization sum for spin 1 fields;"; PolarizationSum::notmassless= "Warning! You are inserting a polarization sum for massless vector bosons, \ @@ -44,6 +43,10 @@ the auxiliary vector `1`. However, the scalar product between the momentum of the \ external boson `2` and `1` is zero, which shouldn't be the case." +PolarizationSum::failmsg = +"Error! PolarizationSum has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -53,34 +56,60 @@ Options[PolarizationSum] = { Dimension -> 4, - VirtualBoson -> False + VirtualBoson -> False, + Heads -> {LorentzIndex, LorentzIndex} }; +indSelect[type_, name_, dim_]:= + Switch[type, + LorentzIndex, + LorentzIndex[name,dim], + CartesianIndex, + CartesianIndex[name,dim-1], + ExplicitLorentzIndex[0], + ExplicitLorentzIndex[0], + _, + Message[PolarizationSum::failmsg,"Unknown head."]; + Abort[] + ]; + + (* Polarization sum for massless vector bosons with gauge terms omitted, e.g. for photons in QED. *) PolarizationSum[mu_,nu_, OptionsPattern[]] := - -Pair[LorentzIndex[mu,OptionValue[Dimension]],LorentzIndex[nu,OptionValue[Dimension]]]; + -Pair[indSelect[OptionValue[Heads][[1]], mu , OptionValue[Dimension]], + indSelect[OptionValue[Heads][[2]], nu , OptionValue[Dimension]]]; (* Same as above. Putting the auxiliary vector n^mu to zero essentially omits the gauge terms. *) PolarizationSum[mu_,nu_, k_, 0, OptionsPattern[]] := - (If[ScalarProduct[k,k]=!=0 && !OptionValue[VirtualBoson], - Message[PolarizationSum::notmassless, k] + Block[{dim = OptionValue[Dimension]}, + + If[ Pair[Momentum[k,dim],Momentum[k,dim]]=!=0 && !OptionValue[VirtualBoson], + Message[PolarizationSum::notmassless, k] ]; - -Pair[LorentzIndex[mu,OptionValue[Dimension]],LorentzIndex[nu,OptionValue[Dimension]]])/; k=!=0; + + -Pair[indSelect[OptionValue[Heads][[1]], mu , OptionValue[Dimension]], + indSelect[OptionValue[Heads][[1]], nu , OptionValue[Dimension]]] + + ]/; k=!=0; (* Polarization sum for massive vector bosons, e.g. W's and Z's in the Electroweak Theory. Note that the particle mass enters as k^2, where k is the four-momentum of the boson. *) PolarizationSum[mu_,nu_, k_, OptionsPattern[]] := - Block[ {dim = OptionValue[Dimension]}, - If[ScalarProduct[k,k]===0, + Block[ {dim = OptionValue[Dimension],ind1, ind2}, + + If[ Pair[Momentum[k,dim],Momentum[k,dim]]===0 && !OptionValue[VirtualBoson], Message[PolarizationSum::notmassive, k] ]; - -Pair[LorentzIndex[mu,dim],LorentzIndex[nu,dim]] + - (Pair[Momentum[k,dim],LorentzIndex[mu,dim]] * - Pair[Momentum[k,dim],LorentzIndex[nu,dim]])/ - Factor2[ExpandScalarProduct[Momentum[k,dim],Momentum[k,dim]]] + + ind1 = indSelect[OptionValue[Heads][[1]], mu , dim]; + ind2 = indSelect[OptionValue[Heads][[2]], nu , dim]; + + -Pair[ind1,ind2] + + (Pair[Momentum[k,dim],ind1] Pair[Momentum[k,dim],ind2])/ + Factor2[ExpandScalarProduct[Pair[Momentum[k,dim],Momentum[k,dim]]],FCI->True] ]/; k=!=0; (* Polarization sum for massless vector bosons with gauge terms included, @@ -89,21 +118,24 @@ these two conditions by itself, i.e. the user must ensure that they are satisfied. *) PolarizationSum[mu_,nu_, k_, n_, OptionsPattern[]] := - Block[ {dim = OptionValue[Dimension]}, - If[ScalarProduct[k,k]=!=0, + Block[ {dim = OptionValue[Dimension],ind1,ind2}, + If[ Pair[Momentum[k,dim],Momentum[k,dim]]=!=0 && !OptionValue[VirtualBoson], Message[PolarizationSum::notmassless, k] ]; - If[ScalarProduct[n,k]===0, + If[ Pair[Momentum[n,dim],Momentum[k,dim]]===0, Message[PolarizationSum::auxerror,n, k] ]; - (-Pair[LorentzIndex[mu,dim],LorentzIndex[nu,dim]] - - (Pair[Momentum[k,dim],LorentzIndex[mu,dim]] * - Pair[Momentum[k,dim],LorentzIndex[nu,dim]] * - Factor2[ExpandScalarProduct[Momentum[n,dim],Momentum[n,dim]]])/ - Factor2[ExpandScalarProduct[Momentum[k,dim],Momentum[n,dim]]^2] + - (Pair[Momentum[n,dim],LorentzIndex[mu,dim]] Pair[Momentum[k,dim],LorentzIndex[nu,dim]] + - Pair[Momentum[k,dim],LorentzIndex[mu,dim]] Pair[Momentum[n,dim],LorentzIndex[nu,dim]])/ - Factor2[ExpandScalarProduct[Momentum[k,dim],Momentum[n,dim]]])//Collect2[#,Pair]& + ind1 = indSelect[OptionValue[Heads][[1]], mu , dim]; + ind2 = indSelect[OptionValue[Heads][[2]], nu , dim]; + + + (-Pair[ind1,ind2] - + (Pair[Momentum[k,dim],ind1] Pair[Momentum[k,dim],ind2] * + Factor2[ExpandScalarProduct[Pair[Momentum[n,dim],Momentum[n,dim]],FCI->True]])/ + Factor2[ExpandScalarProduct[Pair[Momentum[k,dim],Momentum[n,dim]],FCI->True]^2] + + (Pair[Momentum[n,dim],ind1] Pair[Momentum[k,dim],ind2] + + Pair[Momentum[k,dim],ind1] Pair[Momentum[n,dim],ind2])/ + Factor2[ExpandScalarProduct[Pair[Momentum[k,dim],Momentum[n,dim]],FCI->True]])//Collect2[#,Pair]& ]/; k=!=0 && n=!=0; FCPrint[1,"PolarizationSum.m loaded."]; diff --git a/FeynCalc/Feynman/QCDFeynmanRuleConvention.m b/FeynCalc/Feynman/QCDFeynmanRuleConvention.m index effd75074..ec9744bfa 100755 --- a/FeynCalc/Feynman/QCDFeynmanRuleConvention.m +++ b/FeynCalc/Feynman/QCDFeynmanRuleConvention.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Feynman rule convention for QCD *) @@ -16,9 +16,12 @@ (* ------------------------------------------------------------------------ *) QCDFeynmanRuleConvention::usage = -"QCDFeynmanRuleConvention[GluonPropagator], \ -QCDFeynmanRuleConvention[GluonGhostVertex], etc. can be set to \ -different values. The default is the Itzykson-Zuber convention. "; +"fixes the sign convention in the QCD Feynman rules for the ghost propagator and the \ +ghost-gluon vertex. This is done by setting the value of QCDFeynmanRuleConvention[GhostPropagator] \ +and QCDFeynmanRuleConvention[GluonGhostVertex]. The default values are 1 for \ +both, which corresponds to the convention used in most books. Setting them to -1 \ +enforces the convention that can be found e.g. in the book \"Applications of Perturbative \ +QCD\" by R. Field."; (* ------------------------------------------------------------------------ *) @@ -27,7 +30,8 @@ Begin["`QCDFeynmanRuleConvention`Private`"] -QCDFeynmanRuleConvention[_] = 1; +QCDFeynmanRuleConvention[GhostPropagator] = 1; +QCDFeynmanRuleConvention[GluonGhostVertex] = 1; FCPrint[1,"QCDFeynmanRuleConvention.m loaded"]; End[] diff --git a/FeynCalc/Feynman/QuarkGluonVertex.m b/FeynCalc/Feynman/QuarkGluonVertex.m index e0038214e..4532c47c0 100755 --- a/FeynCalc/Feynman/QuarkGluonVertex.m +++ b/FeynCalc/Feynman/QuarkGluonVertex.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Quark gluon vertex *) @@ -45,11 +45,6 @@ QGV = QuarkGluonVertex; -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - -QuarkGluonVertex[x___, i_Integer, y___] := - QuarkGluonVertex[x, l[i], c[i], y]; - QuarkGluonVertex[x1_,x2_,x3_,x4_,x5_,x6_,x7_,x8_, x9_, y:OptionsPattern[]] := QuarkGluonVertex[{x1,x2,x3}, {x4,x5,x6}, {x7,x8,x9} , y] /; FreeQ[Union[Map[Head, {x1,x2,x3,x4,x5,x6,x7,x8,x9}]], Integer|Rule]; diff --git a/FeynCalc/Feynman/QuarkPropagator.m b/FeynCalc/Feynman/QuarkPropagator.m index c35f55a9f..68d30b9c9 100755 --- a/FeynCalc/Feynman/QuarkPropagator.m +++ b/FeynCalc/Feynman/QuarkPropagator.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Quark propagator *) diff --git a/FeynCalc/Feynman/SMP.m b/FeynCalc/Feynman/SMP.m index c7e082b13..d9931993d 100755 --- a/FeynCalc/Feynman/SMP.m +++ b/FeynCalc/Feynman/SMP.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Some model parameters *) @@ -17,24 +17,32 @@ SMP::usage= "SMP[\"par\"] displays a symbol for the model parameter par. \ Typical parameters are masses, coupling constants, mixing angles etc. \ -Parameters that are complex, like CKM matrix element, have an I as an additional parameter, +Parameters that are complex, like CKM matrix element, have an I as an additional argument, i.e. SMP[\"V_ud\",I] and SMP[\"V_ud\",-I]. \n -SMP[] shows the list of available parameters."; +SMP[] shows the list of all available parameters."; Gstrong::usage = "Gstrong is a shortcut for SMP[\"g_s\"]."; AlphaStrong::usage = -"AlphaStrong is a shortcut for SMP[\"alpha_s\"]."; +"AlphaStrong is a shortcut for SMP[\"alpha_s\"] which represents the strong coupling \ +constant."; AlphaFS::usage = -"AlphaFS is a shortcut for SMP[\"alpha_fs\"]."; +"AlphaFS is a shortcut for SMP[\"alpha_fs\"] which represents the fine-structure \ +constant."; Begin["`Package`"] End[] Begin["`SMP`Private`"] +(* Number of flavors *) + +SMP /: + MakeBoxes[SMP["N_F"], TraditionalForm] := + SubscriptBox["N", "F"]; + (* Particle masses *) SMP /: @@ -114,10 +122,18 @@ MakeBoxes[SMP["g_s"], TraditionalForm] := SubscriptBox["g", "s"]; +SMP /: + MakeBoxes[SMP["g"], TraditionalForm] := + ToBoxes["g"]; + SMP /: MakeBoxes[SMP["e"], TraditionalForm] := ToBoxes["e"]; +SMP /: + MakeBoxes[SMP["e_Q"], TraditionalForm] := + SubscriptBox["e", "Q"]; + SMP /: MakeBoxes[SMP["Q_u"], TraditionalForm] := SubscriptBox["Q", "u"]; @@ -244,6 +260,30 @@ MakeBoxes[SMP["V_tb", c_Complex], TraditionalForm] /; c === Complex[0, -1] := SubsuperscriptBox["V", "tb", "*"]; +SMP /: + MakeBoxes[SMP["s_12"], TraditionalForm] := + SubscriptBox["s", "12"]; + +SMP /: + MakeBoxes[SMP["s_13"], TraditionalForm] := + SubscriptBox["s", "13"]; + +SMP /: + MakeBoxes[SMP["s_23"], TraditionalForm] := + SubscriptBox["s", "23"]; + +SMP /: + MakeBoxes[SMP["c_12"], TraditionalForm] := + SubscriptBox["c", "12"]; + +SMP /: + MakeBoxes[SMP["c_13"], TraditionalForm] := + SubscriptBox["c", "13"]; + +SMP /: + MakeBoxes[SMP["c_23"], TraditionalForm] := + SubscriptBox["c", "23"]; + (* Generic renormalization constants *) SMP /: MakeBoxes[SMP["d_psi"], TraditionalForm] := SubscriptBox["\[Delta]","\[Psi]"]; @@ -257,12 +297,18 @@ SMP /: MakeBoxes[SMP["d_e"], TraditionalForm] := SubscriptBox["\[Delta]","e"]; +SMP /: MakeBoxes[SMP["d_g"], TraditionalForm] := + SubscriptBox["\[Delta]","g"]; + SMP /: MakeBoxes[SMP["d_u"], TraditionalForm] := SubscriptBox["\[Delta]","u"]; SMP /: MakeBoxes[SMP["d_xi"], TraditionalForm] := SubscriptBox["\[Delta]","\[Xi]"]; +SMP /: MakeBoxes[SMP["d_phi"], TraditionalForm] := + SubscriptBox["\[Delta]","\[Phi]"]; + SMP /: MakeBoxes[SMP["Z_psi"], TraditionalForm] := SubscriptBox["Z", "\[Psi]"]; @@ -281,6 +327,12 @@ SMP /: MakeBoxes[SMP["Z_e"], TraditionalForm] := SubscriptBox["Z", "e"]; +SMP /: MakeBoxes[SMP["Z_g"], TraditionalForm] := + SubscriptBox["Z", "g"]; + +SMP /: MakeBoxes[SMP["Z_phi"], TraditionalForm] := + SubscriptBox["Z", "\[Phi]"]; + SMP /: MakeBoxes[SMP["dZ_psi"], TraditionalForm] := SubscriptBox["\[Delta]Z", "\[Psi]"]; @@ -293,12 +345,18 @@ SMP /: MakeBoxes[SMP["dZ_e"], TraditionalForm] := SubscriptBox["\[Delta]Z", "e"]; +SMP /: MakeBoxes[SMP["dZ_g"], TraditionalForm] := + SubscriptBox["\[Delta]Z", "g"]; + SMP /: MakeBoxes[SMP["dZ_u"], TraditionalForm] := SubscriptBox["\[Delta]Z", "u"]; SMP /: MakeBoxes[SMP["dZ_xi"], TraditionalForm] := SubscriptBox["\[Delta]Z", "\[Xi]"]; +SMP /: MakeBoxes[SMP["dZ_phi"], TraditionalForm] := + SubscriptBox["\[Delta]Z", "\[Phi]"]; + (* MS renormalization constants *) SMP /: MakeBoxes[SMP["d_psi^MS"], TraditionalForm] := @@ -313,12 +371,18 @@ SMP /: MakeBoxes[SMP["d_e^MS"], TraditionalForm] := SubsuperscriptBox["\[Delta]","e", "MS"]; +SMP /: MakeBoxes[SMP["d_g^MS"], TraditionalForm] := + SubsuperscriptBox["\[Delta]","g", "MS"]; + SMP /: MakeBoxes[SMP["d_u^MS"], TraditionalForm] := SubsuperscriptBox["\[Delta]","u", "MS"]; SMP /: MakeBoxes[SMP["d_xi^MS"], TraditionalForm] := SubsuperscriptBox["\[Delta]","\[Xi]", "MS"]; +SMP /: MakeBoxes[SMP["d_phi^MS"], TraditionalForm] := + SubsuperscriptBox["\[Delta]","\[Phi]", "MS"]; + SMP /: MakeBoxes[SMP["Z_psi^MS"], TraditionalForm] := SubsuperscriptBox["Z", "\[Psi]", "MS"]; @@ -337,6 +401,12 @@ SMP /: MakeBoxes[SMP["Z_e^MS"], TraditionalForm] := SubsuperscriptBox["Z", "e", "MS"]; +SMP /: MakeBoxes[SMP["Z_g^MS"], TraditionalForm] := + SubsuperscriptBox["Z", "g", "MS"]; + + SMP /: MakeBoxes[SMP["Z_phi^MS"], TraditionalForm] := + SubsuperscriptBox["Z", "\[Phi]", "MS"]; + SMP /: MakeBoxes[SMP["dZ_psi^MS"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "\[Psi]", "MS"]; @@ -349,12 +419,18 @@ SMP /: MakeBoxes[SMP["dZ_e^MS"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "e","MS"]; +SMP /: MakeBoxes[SMP["dZ_g^MS"], TraditionalForm] := + SubsuperscriptBox["\[Delta]Z", "g","MS"]; + SMP /: MakeBoxes[SMP["dZ_u^MS"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "u","MS"]; SMP /: MakeBoxes[SMP["dZ_xi^MS"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "\[Xi]","MS"]; +SMP /: MakeBoxes[SMP["dZ_phi^MS"], TraditionalForm] := + SubsuperscriptBox["\[Delta]Z", "\[Phi]","MS"]; + (* MSbar renormalization constants *) SMP /: MakeBoxes[SMP["d_psi^MSbar"], TraditionalForm] := @@ -372,12 +448,18 @@ SMP /: MakeBoxes[SMP["d_e^MSbar"], TraditionalForm] := SubsuperscriptBox["\[Delta]","e", OverscriptBox["MS", "\[LongDash]"]]; +SMP /: MakeBoxes[SMP["d_g^MSbar"], TraditionalForm] := + SubsuperscriptBox["\[Delta]","g", OverscriptBox["MS", "\[LongDash]"]]; + SMP /: MakeBoxes[SMP["d_u^MSbar"], TraditionalForm] := SubsuperscriptBox["\[Delta]","u", OverscriptBox["MS", "\[LongDash]"]]; SMP /: MakeBoxes[SMP["d_xi^MSbar"], TraditionalForm] := SubsuperscriptBox["\[Delta]","\[Xi]", OverscriptBox["MS", "\[LongDash]"]]; +SMP /: MakeBoxes[SMP["d_phi^MSbar"], TraditionalForm] := + SubsuperscriptBox["\[Delta]","\[Phi]", OverscriptBox["MS", "\[LongDash]"]]; + SMP /: MakeBoxes[SMP["Z_psi^MSbar"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "\[Psi]", OverscriptBox["MS", "\[LongDash]"]]; @@ -396,6 +478,12 @@ SMP /: MakeBoxes[SMP["Z_e^MSbar"], TraditionalForm] := SubsuperscriptBox["Z", "e", OverscriptBox["MS", "\[LongDash]"]]; +SMP /: MakeBoxes[SMP["Z_g^MSbar"], TraditionalForm] := + SubsuperscriptBox["Z", "g", OverscriptBox["MS", "\[LongDash]"]]; + +SMP /: MakeBoxes[SMP["Z_phi^MSbar"], TraditionalForm] := + SubsuperscriptBox["Z", "\[Phi]", OverscriptBox["MS", "\[LongDash]"]]; + SMP /: MakeBoxes[SMP["dZ_psi^MSbar"], TraditionalForm] := SubsuperscriptBox["Z", "\[Psi]", OverscriptBox["MS", "\[LongDash]"]]; @@ -408,12 +496,18 @@ SMP /: MakeBoxes[SMP["dZ_e^MSbar"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "e",OverscriptBox["MS", "\[LongDash]"]]; +SMP /: MakeBoxes[SMP["dZ_g^MSbar"], TraditionalForm] := + SubsuperscriptBox["\[Delta]Z", "g",OverscriptBox["MS", "\[LongDash]"]]; + SMP /: MakeBoxes[SMP["dZ_u^MSbar"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "u",OverscriptBox["MS", "\[LongDash]"]]; SMP /: MakeBoxes[SMP["dZ_xi^MSbar"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "\[Xi]",OverscriptBox["MS", "\[LongDash]"]]; +SMP /: MakeBoxes[SMP["dZ_phi^MSbar"], TraditionalForm] := + SubsuperscriptBox["\[Delta]Z", "\[Phi]",OverscriptBox["MS", "\[LongDash]"]]; + (* OS renormalization constants *) SMP /: MakeBoxes[SMP["d_psi^OS"], TraditionalForm] := @@ -428,12 +522,18 @@ SMP /: MakeBoxes[SMP["d_e^OS"], TraditionalForm] := SubsuperscriptBox["\[Delta]","e", "OS"]; +SMP /: MakeBoxes[SMP["d_g^OS"], TraditionalForm] := + SubsuperscriptBox["\[Delta]","g", "OS"]; + SMP /: MakeBoxes[SMP["d_u^OS"], TraditionalForm] := SubsuperscriptBox["\[Delta]","u", "OS"]; SMP /: MakeBoxes[SMP["d_xi^OS"], TraditionalForm] := SubsuperscriptBox["\[Delta]","\[Xi]", "OS"]; +SMP /: MakeBoxes[SMP["d_phi^OS"], TraditionalForm] := + SubsuperscriptBox["\[Delta]","\[Phi]", "OS"]; + SMP /: MakeBoxes[SMP["Z_psi^OS"], TraditionalForm] := SubsuperscriptBox["Z", "\[Psi]", "OS"]; @@ -452,6 +552,12 @@ SMP /: MakeBoxes[SMP["Z_e^OS"], TraditionalForm] := SubsuperscriptBox["Z", "e", "OS"]; +SMP /: MakeBoxes[SMP["Z_g^OS"], TraditionalForm] := + SubsuperscriptBox["Z", "g", "OS"]; + +SMP /: MakeBoxes[SMP["Z_phi^OS"], TraditionalForm] := + SubsuperscriptBox["Z", "\[Phi]", "OS"]; + SMP /: MakeBoxes[SMP["dZ_psi^OS"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "\[Psi]", "OS"]; @@ -464,12 +570,18 @@ SMP /: MakeBoxes[SMP["dZ_e^OS"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "e","OS"]; +SMP /: MakeBoxes[SMP["dZ_g^OS"], TraditionalForm] := + SubsuperscriptBox["\[Delta]Z", "g","OS"]; + SMP /: MakeBoxes[SMP["dZ_u^OS"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "u","OS"]; SMP /: MakeBoxes[SMP["dZ_xi^OS"], TraditionalForm] := SubsuperscriptBox["\[Delta]Z", "\[Xi]","OS"]; +SMP /: MakeBoxes[SMP["dZ_phi^OS"], TraditionalForm] := + SubsuperscriptBox["\[Delta]Z", "\[Phi]","OS"]; + (* Epsilon related stuff *) SMP /: MakeBoxes[SMP["Delta"], TraditionalForm] := @@ -487,32 +599,33 @@ SMP[]= Block[{li}, li={ + "N_F", "m_e","m_mu","m_tau", "m_u","m_d","m_c", "m_s","m_t","m_b", "m_H","m_W","m_Z", "m_q","m_Q","m_qu","m_qd", "m_l","m_pi", - "g_s","e","Q_u","Q_d", + "g", "g_s","e","e_Q","Q_u","Q_d", "G_F","g_W","g'_W", "cos_W","sin_W","theta_W", "cos_C","sin_C","theta_C", "alpha_fs","alpha_s", - "d_psi", "d_A", "d_m", "d_u", "d_xi", "d_e", - "Z_psi", "Z_A", "Z_m", "Z_u", "Z_xi", "Z_e", - "dZ_psi", "dZ_A", "dZ_m", "dZ_u", "dZ_xi", "dZ_e", + "d_psi", "d_phi", "d_A", "d_m", "d_u", "d_xi", "d_e", "d_g", + "Z_psi", "Z_phi", "Z_A", "Z_m", "Z_u", "Z_xi", "Z_e", "Z_g", + "dZ_psi", "dZ_phi", "dZ_A", "dZ_m", "dZ_u", "dZ_xi", "dZ_e", "dZ_g", - "d_psi^MS", "d_A^MS", "d_m^MS", "d_u^MS", "d_xi^MS", "d_e^MS", - "Z_psi^MS", "Z_A^MS", "Z_m^MS", "Z_u^MS", "Z_xi^MS", "Z_e^MS", - "dZ_psi^MS", "dZ_A^MS", "dZ_m^MS", "dZ_u^MS", "dZ_xi^MS", "dZ_e^MS", + "d_psi^MS", "d_phi^MS", "d_A^MS", "d_m^MS", "d_u^MS", "d_xi^MS", "d_e^MS", "d_g^MS", + "Z_psi^MS", "Z_phi^MS", "Z_A^MS", "Z_m^MS", "Z_u^MS", "Z_xi^MS", "Z_e^MS", "Z_g^MS", + "dZ_psi^MS", "dZ_phi^MS", "dZ_A^MS", "dZ_m^MS", "dZ_u^MS", "dZ_xi^MS", "dZ_e^MS", "dZ_g^MS", - "d_psi^MSbar", "d_A^MSbar", "d_m^MSbar", "d_u^MSbar", "d_xi^MSbar", "d_e^MSbar", - "Z_psi^MSbar", "Z_A^MSbar", "Z_m^MSbar", "Z_u^MSbar", "Z_xi^MSbar", "Z_e^MSbar", - "dZ_psi^MSbar", "dZ_A^MSbar", "dZ_m^MSbar", "dZ_u^MSbar", "dZ_xi^MSbar", "dZ_e^MSbar", + "d_psi^MSbar", "d_phi^MSbar", "d_A^MSbar", "d_m^MSbar", "d_u^MSbar", "d_xi^MSbar", "d_e^MSbar", "d_g^MSbar", + "Z_psi^MSbar", "Z_phi^MSbar", "Z_A^MSbar", "Z_m^MSbar", "Z_u^MSbar", "Z_xi^MSbar", "Z_e^MSbar", "Z_g^MSbar", + "dZ_psi^MSbar", "dZ_phi^MSbar", "dZ_A^MSbar", "dZ_m^MSbar", "dZ_u^MSbar", "dZ_xi^MSbar", "dZ_e^MSbar", "dZ_g^MSbar", - "d_psi^OS", "d_A^OS", "d_m^OS", "d_u^OS", "d_xi^OS", "d_e^OS", - "Z_psi^OS", "Z_A^OS", "Z_m^OS", "Z_u^OS", "Z_xi^OS", "Z_e^OS", - "dZ_psi^OS", "dZ_A^OS", "dZ_m^OS", "dZ_u^OS", "dZ_xi^OS", "dZ_e^OS", + "d_psi^OS", "d_phi^OS", "d_A^OS", "d_m^OS", "d_u^OS", "d_xi^OS", "d_e^OS", "d_g^OS", + "Z_psi^OS", "Z_phi^OS", "Z_A^OS", "Z_m^OS", "Z_u^OS", "Z_xi^OS", "Z_e^OS", "Z_g^OS", + "dZ_psi^OS", "dZ_phi^OS", "dZ_A^OS", "dZ_m^OS", "dZ_u^OS", "dZ_xi^OS", "dZ_e^OS", "dZ_g^OS", {"V_ud",I},{"V_ud",-I}, {"V_us",I},{"V_us",-I}, @@ -522,11 +635,18 @@ {"V_cb",I},{"V_cb",-I}, {"V_td",I},{"V_td",-I}, {"V_ts",I},{"V_ts",-I}, - {"V_tb",I},{"V_tb",-I} + {"V_tb",I},{"V_tb",-I}, + "s_12", "s_13", "s_23", + "c_12", "c_13", "c_23" }; {SMP /@ li, li} // Transpose ]; +SMP /: + Conjugate[SMP[a_, Complex[0,1]]] := SMP[{a, -I}]; + +SMP /: + Conjugate[SMP[a_, Complex[0,-1]]] := SMP[{a, I}]; SMP[{x__}]:= SMP[x]; @@ -540,7 +660,7 @@ AlphaFS:= SMP["alpha_fs"]; -SetAttributes[SMP, Protected] +SetAttributes[SMP, Protected]; FCPrint[1,"SMP.m loaded."]; End[] diff --git a/FeynCalc/Feynman/SMVertex.m b/FeynCalc/Feynman/SMVertex.m index f01c08ed0..5c04a5c90 100755 --- a/FeynCalc/Feynman/SMVertex.m +++ b/FeynCalc/Feynman/SMVertex.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Some Standard model vertices *) @@ -16,10 +16,8 @@ (* ------------------------------------------------------------------------ *) SMVertex::usage = -"SMVertex[\"AWW\", p,mu, q,nu, k,rho] gives the photon-W-W vertex \ -(p,mu correspond to the photon, q,nu to the (incoming) W+ and k,rho \ -to the (incoming) W-. All momenta are flowing into the vertex. \n -SMVertex[\"HHH\", ___] give the three-higgs coupling."; +"is a library of SM vertices. Currently it implements only few vertices and \ +is not really useful."; (* ------------------------------------------------------------------------ *) @@ -45,9 +43,9 @@ to the (incoming) W-. All momenta are flowing into the vertex. \n SMVertex["AWW", mom1_, li1_, mom2_, li2_, mom3_, li3_, OptionsPattern[]] := Block[ {dim, res}, res = ChangeDimension[ - -I*SMP["e"]*( MetricTensor[li1, li2] * FourVector[(mom2 -mom1 ),li3]+ - MetricTensor[li2, li3] * FourVector[(mom3 -mom2 ),li1]+ - MetricTensor[li3, li1] * FourVector[(mom1 -mom3 ),li2]), OptionValue[Dimension]]; + -I*SMP["e"]*( MT[li1, li2] * FV[(mom2 -mom1 ),li3]+ + MT[li2, li3] * FV[(mom3 -mom2 ),li1]+ + MT[li3, li1] * FV[(mom1 -mom3 ),li2]), OptionValue[Dimension]]; res ]/; OptionValue[Explicit]; diff --git a/FeynCalc/Feynman/ScalarGluonVertex.m b/FeynCalc/Feynman/ScalarGluonVertex.m index d0800227f..6ba8c4b43 100755 --- a/FeynCalc/Feynman/ScalarGluonVertex.m +++ b/FeynCalc/Feynman/ScalarGluonVertex.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Scalar gluon vertex *) @@ -17,11 +17,9 @@ ScalarGluonVertex::usage = "ScalarGluonVertex[{p}, {q}, {mu,a}] or ScalarGluonVertex[ p, q, mu, a ] yields \ -the scalar-scalar-gluon vertex (p and q are incoming momenta). - -ScalarGluonVertex[{mu,a}, {nu,b}] yields the scalar-scalar-gluon-gluon vertex \ -(p and q are incoming momenta). - +the scalar-scalar-gluon vertex, where p and q are incoming momenta. \n +ScalarGluonVertex[{mu,a}, {nu,b}] yields the scalar-scalar-gluon-gluon vertex, \ +where p and q are incoming momenta.\n The dimension and the name of the coupling constant are determined by the \ options Dimension and CouplingConstant."; @@ -38,11 +36,6 @@ Gauge -> 1 }; -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - -ScalarGluonVertex[x___, i_Integer, y___] := - ScalarGluonVertex[x, l[i], c[i], y]; - (* 3 - vertex *) ScalarGluonVertex[x1_,x2_,x3_,x4_, opts:OptionsPattern[]] := ScalarGluonVertex[{x1}, {x2}, {x3,x4}, opts] /; diff --git a/FeynCalc/Feynman/SquareAmplitude.m b/FeynCalc/Feynman/SquareAmplitude.m index d4816e2da..7067055df 100644 --- a/FeynCalc/Feynman/SquareAmplitude.m +++ b/FeynCalc/Feynman/SquareAmplitude.m @@ -1,29 +1,28 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) +(* ::Package:: *) -(* :Title: SquareAmplitude *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Author: Rolf Mertig *) +(* :Title: SquareAmplitude *) -(* ------------------------------------------------------------------------ *) -(* :History: File created on 21 December '98 at 0:52 *) -(* ------------------------------------------------------------------------ *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* :Summary: square amplitudes *) +(* :Summary: Squares the amplitude *) (* ------------------------------------------------------------------------ *) -EnergyMomentumConservation::usage = -"EnergyMomentumConservation is an option of SquareAmplitude (experimental)."; SquareAmplitude::usage = -"SquareAmplitude[amp] squares the amplitude amp. EXPERIMENTAL!!! \ -Don't rely on it."; - -SpinSumExternalMomentum::usage = -"SpinSumExternalMomentum is an option of SquareAmplitude (experimental)."; +"SquareAmplitude[m1,m2] multiplies the amplitudes from the list m1 with their +complex conjugate from the list m2 to obtain the list of products m1_i*m2_j."; -SelectedGraphs::usage = -"SelectedGraphs is an option of SquareAmplitude (experimental)."; +SquareAmplitude::failmsg = +"Error! SquareAmplitude has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" (* ------------------------------------------------------------------------ *) @@ -32,1024 +31,93 @@ Begin["`SquareAmplitude`Private`"] -(* ************************************************************* *) -duM = Unique[System`C]; -gamcount[x_] := - Length[Position[x, DiracGamma]]; - -specsir[a_] := - Block[ {tem, nosp}, - nosp = Select[a, FreeQ[#, Spinor]&]/.$MU-> duM; - tem = (a/nosp)/.$MU-> duM; - If[ !FreeQ[tem, duM[2]], - tem = Contract[DiracOrder[tem, - {duM[1], Momentum[_], duM[2]} - ]//DiracSimplify] - ]; - If[ Length[Position[tem, Spinor]] > 2, - FCPrint[2,"entering specsir2 with ",tem//FeynCalcForm]; - tem = specsir2[tem]; - FCPrint[2,"exiting specsir2 with", tem//FeynCalcForm]; - ]; - Expand[tem nosp] - ]; -ChisholmSave[x_] := - MemSet[ChisholmSave[x], Chisholm[x]]; -EpsChisholmSave[x_] := - MemSet[EpsChisholmSave[x], EpsChisholm[x]]; -specsir2[x_] := - specsir2[x] = - Block[ {ste, ste1, ste2,ste1r,ste2r,duMy}, - ste = x /. $MU -> duMy; - (* there are two possibilities ... *) - ste1r = {DOT[Spinor[pe1__] , g1__ , Spinor[pe2__]] * - DOT[Spinor[pe3__] , g2__ , Spinor[pe4__]] * - DOT[Spinor[pe5__] , g3__ , Spinor[pe6__]] :> - (Expand[DiracSimplify[ - DiracOrder[DiracSimplify[Contract[DOT[Spinor[pe1] , g1 , Spinor[pe2]] * - EpsChisholmSave[ DOT[Spinor[pe3] , g2 , Spinor[pe4]] * - ChisholmSave[DOT[Spinor[pe5] , g3 , Spinor[pe6]]] - ] ] ], {$MU[1], Momentum[_], $MU[2]} ] - ]] /. $MU -> duMy - )/; - (Length[{g1}] < 3) && (Length[{g2}] < 3) && (Length[{g3}] > 2) - }; - ste2r = {DOT[Spinor[pe1__] , g1__ , Spinor[pe2__]] * - DOT[Spinor[pe3__] , g2__ , Spinor[pe4__]] * - DOT[Spinor[pe5__] , g3__ , Spinor[pe6__]] :> - (Expand[DiracSimplify[ - DiracOrder[DiracSimplify[ - Contract[DOT[Spinor[pe3] , g2 , Spinor[pe4]] * - EpsChisholm[ DOT[Spinor[pe1] , g1 , Spinor[pe2]] * - Chisholm[DOT[Spinor[pe5] , g3 , Spinor[pe6]]] - ] ] ],{$MU[1], Momentum[_], $MU[2]} ] - ]] /. $MU -> duMy - )/; - (Length[{g1}] < 3) && (Length[{g2}] < 3) && (Length[{g3}] > 2) - }; - ste1 = ste/.ste1r; - If[ (!FreeQ[ste1, DOT[DiracMatrix[duMy[_]],DiracGamma[Momentum[_]], - DiracMatrix[duMy[_]]] - ]) && (ste1=!= ste), - ste1 = ste1 /. ste2r /. ste1r - ]; - If[ (ste1 =!= 0) && - (!FreeQ[ste1, DOT[DiracMatrix[duMy[_]],DiracGamma[Momentum[_]], - DiracMatrix[duMy[_]]] - ]), - ste2 = ste /. ste2r; - If[ (!FreeQ[ste2, DOT[DiracMatrix[duMy[_]],DiracGamma[Momentum[_]], - DiracMatrix[duMy[_]]] - ]) && (ste2=!= ste), - ste2 = ste2 /. ste1r /. ste2r - ], - ste2 = ste1 - ]; - If[ ste1 =!= 0, - ste1 = DiracSimplify[DiracOrder[DiracSimplify[ste1]]]//Expand; - ste2 = DiracSimplify[DiracOrder[DiracSimplify[ste2]]]//Expand; - If[ !FreeQ[ste1, DOT[DiracMatrix[duMy[_]],DiracGamma[Momentum[_]], - DiracMatrix[duMy[_]]]], - ste1 = First[Sort[Select[{ste1, ste2}, FreeQ[#,RuleDelayed]&], - (LeafCount[{##}[[1]]] < LeafCount[{##}[[2]]] )& ] ] - ]; - ]; - ste1 - ]; -(* end of specsir2 *) - -(* **************************************************************** *) -(* SquareAmplitudedef *) -(* **************************************************************** *) -(* careful: this function is still under development!!! *) - -(* ----------------------------------------------------------------- *) -susa[xxx_] := - susa[xxx] = SUNSimplify[xxx, Factoring->True]; -(* /. SUNTrace -> ST; *) -susm[nuLL] := - 0; -susm[xx_Plus] := - Map[susm, xx]; -susm[xx_ /; FreeQ[xx,SUNIndex]] := - xx; -susm[xx_ /;( (Head[xx] =!= Plus) && (!FreeQ[xx, SUNIndex])) - ] := - Expand[ - Select[xx, FreeQ[#1, SUNIndex] & ]* - susa[Select[xx, !FreeQ[#1, SUNIndex] & ]] (*, SUNIndex*)]; +sqaVerbose::usage=""; Options[SquareAmplitude] = { - Dimension -> 4, - EnergyMomentumConservation -> {}, - EpsDiscard -> False, - ExtraFactor -> 1, - Collecting -> False, - Factoring -> False, - FinalSubstitutions -> {}, - InitialSubstitutions -> {}, - IntermediateSubstitutions -> {}, - IsolateNames -> KK, -(* IsolateSplit -> 4711 I,*) - Mandelstam -> {FCGV["s"], FCGV["t"]}, - SelectedGraphs -> All, - SpinPolarizationSum -> 1, - SpinSumExternalMomentum -> Automatic, - WriteOut -> False - }; + FCE -> False, + FCI -> False, + FCVerbose -> False, + Indexed -> False, + List -> True, + Real -> False +}; -(* the FeynArts convention is to put the Process -> {} rule - as the last argument in FeynAmpList -*) -SquareAmplitude[ FeynAmpList[he___, - process_Rule][amps__], - opts___Rule] := - Block[ {sli = {}, amp = FeynCalcInternal[{amps}], proctype, dim, nam, - colorpart = 1,pluiso,gluON,den1,numfaN,enmomsubst, - enmomback,inisubst,pli, - mand,factoring,exmom,exm, es,te, sel, scalP, - p1,p2,k1,k2,k3,k4,m12,m22,m32,m42,m52,m62, - finsubst,proc,extrafact}, - dim = Dimension /. {opts} /. Options[SquareAmplitude]; - mand = Mandelstam /. {opts} /. Options[SquareAmplitude]; - inisubst = FeynCalcInternal[InitialSubstitutions /. {opts} /. Options[SquareAmplitude]]; - collecting = Collecting /. {opts} /. Options[SquareAmplitude]; - factoring = Factoring /. {opts} /. Options[SquareAmplitude]; - finsubst = FeynCalcInternal[FinalSubstitutions /. {opts} /. Options[SquareAmplitude]]; - isolhead = IsolateNames /. {opts} /. Options[SquareAmplitude]; - exmom = SpinSumExternalMomentum /. {opts} /. Options[SquareAmplitude]; - extrafact = ExtraFactor /. {opts} /. Options[SquareAmplitude]; - extrafact = FeynCalcInternal[extrafact]; - {es, te} = {mand[[1]], mand[[2]]}; - If[ Length[mand === 3], - uu = mand[[3]] - ]; - amp = amp /. SUNDelta -> SUNDeltaContract /. - SUNDeltaContract -> SUNDelta; - sel = SelectedGraphs /. {opts} /. Options[SquareAmplitude]; - If[ sel === All, - sli = amp, - For[jj = 1, jj <= Length[amp], jj++, - If[ MemberQ[sel, jj], - AppendTo[sli, amp[[jj]]] - ] ] - ]; - plsI[xx__] := - Isolate[Plus[xx], {DiracGamma, Spinor, LorentzIndex, SUNIndex}, - IsolateNames -> isolhead, IsolateSplit->555I]; +diagmarkIdentity[_,_]:= + 1; - (* *********************************** *) - {es, te} = {mand[[1]], mand[[2]]}; - If[ Length[mand===3], - uu = mand[[3]] - ]; - proc = Last[process]; - proctype = Map[Length, proc]; - Which[ - proctype === (2 -> 1), - proc = proc[[1]] -> Join[proc[[2]], {{0,0,0}, {0,0,0}, {0,0,0}}], - proctype === (1 -> 2), - proc = Join[proc[[1]], {{0,0,0}}] -> - Join[proc[[2]], {{0,0,0}, {0,0,0}, {0,0,0}}], - proctype === (2 -> 2), - proc = proc[[1]] -> Join[proc[[2]], {{0,0,0}, {0,0,0}}], - proctype === (2 ->3), - proc = proc[[1]] -> Join[proc[[2]], {{0,0,0}}] - ]; - p1m1 = {proc[[1, 1, 2]], proc[[1, 1, 3]]^2}; - p2m2 = {proc[[1, 2, 2]], proc[[1, 2, 3]]^2}; - k1m3 = {proc[[2, 1, 2]], proc[[2, 1, 3]]^2}; - k2m4 = {proc[[2, 2, 2]], proc[[2, 2, 3]]^2}; - k3m5 = {proc[[2, 3, 2]], proc[[2, 3, 3]]^2}; - k4m6 = {proc[[2, 4, 2]], proc[[2, 4, 3]]^2}; - fields = { proc[[1,1,1]], proc[[1,2,1]], - proc[[2,1,1]], proc[[2,2,1]], proc[[2,3,1]], proc[[2,4,1]] - }; +SquareAmplitude[m1_List, m2_List/;!OptionQ[m2], OptionsPattern[]] := + Block[ {ex, mList, mccList, diagmark, optIndexed, tmp, res}, - (* - (* this has to be thought over again ... *) - extrafact = extrafact ( NF^0 (*( (Length[Position[fields, tmp`F[I]]] + - Length[Position[fields, tmp`F[-I]]])/2 - )*) - ); - *) - extrafact = ExpandScalarProduct[extrafact]//Expand; - {p1, p2, k1, k2, k3, k4} = #[[1]]& /@ {p1m1, p2m2, k1m3, k2m4, k3m5, k4m6}; - {m12, m22, m32, m42, m52, m62} = #[[2]]& /@ - {p1m1, p2m2, k1m3, k2m4, k3m5, k4m6}; - If[ MemberQ[{1 -> 2, 2 -> 1, 2 -> 2}, proctype], - enmomsubst = k1 -> p1+p2-k2-k3-k4; - enmomback = {p1+p2-k2-k3-k4->k1, - Momentum[p1]+Momentum[p2]-Momentum[k2]- - Momentum[k3]-Momentum[k4] -> Momentum[k1], - -Momentum[p1]-Momentum[p2]+Momentum[k2]+ - Momentum[k3]+Momentum[k4] -> (-Momentum[k1]) - }, - enmomsubst = {}; - enmomback = {}; - ]; + optIndexed = OptionValue[Indexed]; - (* Oh je *) - pair2 = FeynCalc`Contract`Private`pair2; - scalP[a_, b_, c_] := - If[ dim =!= 4, - Apply[ Set, {ScalarProduct[a,b, Dimension -> dim], c//Expand}]; - Apply[ Set, {ScalarProduct[a,b, Dimension -> 4], c//Expand} ]; - Apply[ Set, {pair2[Momentum[a, dim], Momentum[b, dim]], c//Expand} ]; - Apply[ Set, {pair2[Momentum[a ], Momentum[b ]], c//Expand} ], - Apply[ Set, {ScalarProduct[a,b, Dimension -> 4], c//Expand} ]; - Apply[ Set, {pair2[Momentum[a], Momentum[b]], c//Expand}]; - ]; - sCP[a_] := - ScalarProduct[a, a, Dimension -> dim]; - sCP[a_,b_] := - ScalarProduct[a, b, Dimension -> dim]; - If[ Head[Pair[Momentum[p1], Momentum[p1]]] === Pair, - If[ proctype === (1 -> 2), - scalP[p1, p1, m12]; - scalP[k1, k1, m32]; - scalP[k2, k2, m42]; - scalP[k1, k2, 1/2 (sCP[p1] - sCP[k1] - sCP[k2])]; - scalP[p1, k1, 1/2 (sCP[p1] - sCP[k2] + sCP[k1])]; - scalP[p1, k2, 1/2 (sCP[p1] - sCP[k1] + sCP[k2])]; - ]; - If[ proctype === (2 -> 1), - scalP[p1,p1, m12]; - scalP[p2,p2, m22]; - scalP[k1,k1, m32]; - scalP[p1,p2, 1/2 (sCP[k1] - sCP[p1] - sCP[p2])]; - scalP[p1,k1,-1/2 (sCP[p2] - sCP[p1] - sCP[k1])]; - scalP[p2,k1,-1/2 (sCP[p1] - sCP[p2] - sCP[k1])]; - ]; - uUu = Expand[m12 + m22 + m32 + m42 - es - te]; - If[ proctype === (2 -> 2), - scalP[p1, p1, m12]; - scalP[p1, p2, - m12/2 - m22/2 + es/2]; - scalP[p1, k1, m12/2 + m32/2 - te/2]; - scalP[p1, k2, m12/2 + m42/2 - uUu/2]; - scalP[p2, p2, m22]; - scalP[p2, k1, m22/2 + m32/2 - uUu/2]; - scalP[p2, k2, m22/2 + m42/2 - te/2]; - scalP[k1, k1, m32]; - scalP[k1, k2, -m32/2 - m42/2 + es/2]; - scalP[k2, k2, m42]; - ]; - If[ proctype === (2 ->3), - scalP[p1, p1, m12]; - scalP[p2, p2, m22]; - scalP[k1, k1, m32]; - scalP[k2, k2, m42]; - scalP[k3, k3, m52]; - scalP[p1, p2, tmp`P[p1, p2]/2 - m12/2 - m22/2]; - scalP[p1, k1,-tmp`P[p1,-k1]/2 + m12/2 + m32/2]; - scalP[p1, k2,-tmp`P[p1,-k2]/2 + m12/2 + m42/2]; - scalP[p1, k3,-tmp`P[p1,-k3]/2 + m12/2 + m52/2]; - scalP[p2, k1,-tmp`P[p2,-k1]/2 + m22/2 + m32/2]; - scalP[p2, k2,-tmp`P[p2,-k2]/2 + m22/2 + m42/2]; - scalP[p2, k3,-tmp`P[p2,-k3]/2 + m22/2 + m52/2]; - scalP[k1, k2, tmp`P[k1, k2]/2 - m32/2 - m42/2]; - scalP[k1, k3, tmp`P[k1, k3]/2 - m32/2 - m52/2]; - scalP[k2, k3, tmp`P[k2, k3]/2 - m42/2 - m52/2]; - ]; + If[ m1==={} || m2==={}, + Message[SquareAmplitude::failmsg, "The lists of amplitudes cannot be empty."]; + Abort[] ]; - (* - If[(k3 =!= 0) && (k4 =!= 0), - SetMandelstam[tmp`P, {p1, p2, -k1, -k2, -k3, -k4}, - {p1m1[[2]], p2m2[[2]], k1m3[[2]], - k2m4[[2]], k3m5[[2]], k4m6[[2]]} - ] - ]; - *) - (* *********************************** *) + (*If[ Length[m1]=!=Length[m2], + Message[SquareAmplitude::failmsg, "The lists of amplitudes have different lengths."]; + Abort[] + ];*) - (* sum the amplitudes *) - amp = Sum[ propdenexp[Last[sli[[i]]], - {p1,p2,-k1,-k2,-k3,-k4}], {i,1, Length[sli]} - ] /. inisubst; - amp0 = amp; - If[ dim =!= 4, - amp = ChangeDimension[amp, dim]; - extrafact = ChangeDimension[extrafact, dim]; + If[ optIndexed=!=False && (optIndexed===True || Head[optIndexed]=!=Symbol), + Message[SquareAmplitude::failmsg, "The value of the option Indexed must be either False or a function name."]; + Abort[] ]; - (*tmp`am = amp;*) - FCPrint[2,"amp = ",amp]; - FCPrint[1,"extrafact = ",extrafact]; - If[ !FreeQ[amp, DiracGamma], - amp = DiracSimplify[amp /. enmomsubst /. - Pair -> pPpPpP, Expanding -> False - ] /. enmomback /. pPpPpP->Pair, - amp = ExpandScalarProduct[Contract[amp/.enmomsubst]] /. enmomback - ]; - FCPrint[1,"checK"]; - sund[xxxx_] := - 1; - sund[glu_, xxxx_] := - SUNDeltaContract[glu, SUNIndex[xxxx]]; - gluON[] = Sequence[]; - mU = Unique[System`C]; - sU = Unique[System`C]; - gL = Unique[System`C]; -(* -mU = Unique[mUUn]; sU = Unique[sUUu]; gL = Unique[glLLu]; -*) - gluON[_SUNIndex] = gL; - FCPrint[1,"Length of amp = " , Length[amp]]; - (* a list of rules for substituting indices for the polarization momenta *) - momtolor = - {Momentum[Polarization[p1, _, glui___SUNIndex], ___] :> - (LorentzIndex[mU[1, gluON[glui]],dim] sund[glui, sU[1]]), - Momentum[Polarization[p2, _, glui___SUNIndex], ___] :> - (LorentzIndex[mU[2, gluON[glui]],dim] sund[glui, sU[2]]), - Momentum[Polarization[k1, _, glui___SUNIndex], ___] :> - (LorentzIndex[mU[3, gluON[glui]],dim] sund[glui, sU[3]]), - Momentum[Polarization[k2, _, glui___SUNIndex], ___] :> - (LorentzIndex[mU[4, gluON[glui]],dim] sund[glui, sU[4]]), - Momentum[Polarization[k3, _, glui___SUNIndex], ___] :> - (LorentzIndex[mU[5, gluON[glui]],dim] sund[glui, sU[5]]), - Momentum[Polarization[k4, _, glui___SUNIndex], ___] :> - (LorentzIndex[mU[6, gluON[glui]],dim] sund[glui, sU[6]]) - }; - pairdel[ c___, n_ b_LorentzIndex, d___] := - pairdel[c,n b, d] = n pairdel[c,b, d]; - dirdel[n_ b_LorentzIndex, d___] := - dirdel[n b, d] = n DiracGamma[b, d]; - If[ !FreeQ[amp, SUNIndex], - (* collecting w.r.t. to SUNIndex *) - FCPrint[1,"collecting w.r.t. SUNIndex"]; - If[ $FeynContract === True, - pair2PAIR[a_, b_] := - If[ FreeQ[{a,b}, SUNIndex], - tmp`PAIR[a,b], - Pair[a, b] - ]; - FCPrint[1,"substing PAIR"]; - amp = amp /. Pair -> pair2PAIR; - amp00 = amp; - FCPrint[1,"substing PAIR done"]; - amp = tmp`CCollect[amp, {Pair, SUNF, SUNT, SUNDelta}]; - FCPrint[1,"back from CCollect"]; - amp = amp /. tmp`PAIR -> Pair, - amp = Collect2[amp, SUNIndex,Factoring -> False]; - ]; - amp11 = amp; - FCPrint[1,"SUNSimplifying"]; - amp = SUNSimplify[amp, Explicit -> False]; - If[ !FreeQ[amp,SUNF], - amp = SUNSimplify[amp, Explicit -> True] - ]; - If[ !FreeQ[amp, SUNTrace], - amp = Collect2[amp, SUNTrace] - ]; - ]; - oldamp = amp; - amp = amp /. momtolor; - If[ !FreeQ[amp, SUNIndex], - FCPrint[2,"pairdel"]; - amp = amp/. Pair -> pairdel /. pairdel->Pair/. - DiracGamma->dirdel/.dirdel->DiracGamma; - amp = ChangeDimension[amp, dim]; - FCPrint[2,"contracting"]; - amp = Contract[ amp/.enmomsubst, Expanding -> False ]; - amp = ExpandScalarProduct[amp] /. enmomback; - (* - amp = ChangeDimension[amp, dim]; - *) - FCPrint[1,"collecting w.r.t. SUNIndex"]; - If[ $FeynContract === True, - FCPrint[1,"substing PAIR( 2 )"]; - amp = amp /. Pair -> pair2PAIR; - FCPrint[1,"substing PAIR( 2 ) done"]; - amp00 = amp; - amp = tmp`CCollect[amp, {Pair, SUNF, SUNT, SUNDelta}]; - FCPrint[1,"back from CCollect"]; - amp = amp /. tmp`PAIR -> Pair, - amp = Collect2[amp, SUNIndex,Factoring -> False]; - ]; - amp22 = amp; - amppp = amp; - If[ Head[amp] === Times, - colorpart = Select[amp, !FreeQ[#, SUNIndex]&]; - amp = Select[amp, FreeQ[#, SUNIndex]&], - colorpart = 1; - iii = 0; - (* - amp = Map[#/.Plus-> plUUU&, amp + nuLL1 + nuLL2]; - amp = Sum[(Print[iii++];susa[amp[[ij]]]), {ij, Length[amp]}]; - amp = Expand[amp /. nuLL1 -> 0 /. nuLL2->0,SUNIndex] /. plUUU -> Plus; - *) - ]; - If[ !FreeQ[colorpart, SUNIndex], - FCPrint[2,"colorpart = ",colorpart] + If [OptionValue[FCVerbose]===False, + sqaVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + sqaVerbose=OptionValue[FCVerbose] ]; ]; - amp44 = amp; - FCPrint[2,"Length of amp44 = ",Length[amp44]]; - FCPrint[2,"leafcount of amp44 = ",LeafCount[amp44]]; - If[ Head[amp44] === Plus, - namp = 0; - lamp44 = Length[amp44]; - For[ia = 1, ia <= lamp44, ia++, - FCPrint[2,"contracting amp44[[",ia,"]] out of ", lamp44]; - namp = namp + ExpandScalarProduct[Contract[amp44[[ia]]]]; - ]; - amp = namp, - amp = Contract[amp]//ExpandScalarProduct; - ]; - amp45 = amp; - FCPrint[2,"Length of amp45 = ",Length[amp45]]; - nuLL = Unique[System`C]; - (* - nuLL = Unique[nuLlllllL]; - *) - collect4[x_ /; (Head[x] =!= Plus), _] := - x; - collect4[su_Plus, a_Symbol] := - Block[ {suntr, ll, j = 0, vp, new = 0,cc, - temp = su}, - FCPrint[1,"this cridder is ", Length[temp], " terms long"]; - While[ (ll = Length[temp]) > 0, - j++; - FCPrint[2,"j = ",j, " length of temp = ",ll]; - If[ Head[temp] === Plus, - part1 = First[temp], - part1 = temp - ]; - vp = Select[part1 DUM, !FreeQ[#, a]&]; - FCPrint[2,"vp = ", vp//FeynCalcForm]; - cc = Coefficient[temp, vp]; - new = new + vp cc; - temp = temp - ((#vp& /@ (cc + nuLL))/.nuLL->0) - ]; - new - ]; - If[ $FeynContract === True, - FCPrint[1,"substing PAIR( 3 )"]; - amp = amp /. Pair -> pair2PAIR; - FCPrint[1,"substing PAIR( 3 ) done"]; - amp00 = amp; - amp = tmp`CCollect[amp, {Pair, SUNF, SUNT, SUNDelta}]; - FCPrint[1,"back from CCollect"]; - amp = amp /. tmp`PAIR -> Pair, - amp = Collect2[amp, SUNIndex,Factoring -> False]; - ]; - amp55 = amp; - (* CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC *) - (* construct the tensor from the polarization sums *) - (* CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC *) - pli = {p1, p2, k1, k2, k3, k4}; - pli2 = ExpandScalarProduct[ScalarProduct[#, #]]& /@ pli; - prod = extrafact; - exm = {0,0,0,0,0,0}; - If[ exmom =!= Automatic, - If[ Head[exmom] === List, - exm = exmom - ]; - If[ (Head[exmom] === Symbol) || (exmom === 0), - exm = {exmom, exmom,exmom,exmom,exmom,exmom} - ]; + If[ OptionValue[FCI], + {mList, mccList} = {m1, m2}, + {mList, mccList} = FCI[{m1, m2}] ]; - (* - mom4set[xp_Symbol] := Apply[SetDelayed, {Momentum[xp,___], Momentum[xp]}]; - *) - mom4set[xp_Symbol] := - Apply[Set, {Momentum[xp,___], Momentum[xp]}]; - Map[mom4set, exm]; - FCPrint[2,"exm = ",exm]; - FCPrint[2,"fields = ", fields]; - For[ij = 1, ij < 7, ij++, - If[ pli =!= 0, - (* check for photon *) - (*Dropped ComplexIndex. This should be adjusted accordingly. F.Orellana, 20/2-2003*) - If[ (fields[[ij]] === tmp`V[1]) && !FreeQ[amp, mU[ij]], - prod = prod (- MetricTensor[mU[ij], ComplexIndex[mU[ij]], - Dimension -> dim]) - ]; - (* check for gluon*) - If[ (fields[[ij]] === tmp`G[1]) && !FreeQ[amp, mU[ij,gL]], - If[ exmom === Automatic, - Which[ - proctype === (2->3), - exm = {pli[[2]], pli[[1]], pli[[5]], pli[[3]], pli[[4]]}, - proctype === (2->2), - exm = {pli[[2]], pli[[1]], pli[[4]], pli[[3]]}, - proctype === (2->1), - exm = {pli[[3]], pli[[1]], pli[[2]]}, - proctype === (1->2), - exm = {pli[[3]], pli[[1]], pli[[2]]} - ]; - ]; - prod = prod PolarizationSum[mU[ij, gL], ComplexIndex[mU[ij, gL]], - pli[[ij]], exm[[ij]], Dimension -> dim]; - ]; - (* check for massive Vectorbosons *) - If[ MatchQ[fields[[ij]], - tmp`V[iii_ /; iii=!=1]] && !FreeQ[amp, mU[ij]], - prod = prod PolarizationSum[mU[ij], ComplexIndex[mU[ij]], - pli[[ij]], Dimension -> dim] - ]; - (* check for ghosts *) - If[ MatchQ[fields[[ij]], tmp`U[_]], - Print["GHOSTCHECK"]; - prod = I prod - ]; - ]; - ]; - FCPrint[1,"polarization sums = ", prod//FeynCalcForm]; - If[ dim =!= 4, - prod = prod/.{Pair[LorentzIndex[a_], LorentzIndex[b_]]:> - Pair[LorentzIndex[a, dim], LorentzIndex[b, dim]], - Pair[LorentzIndex[a_], Momentum[b_]]:> - Pair[LorentzIndex[a, dim], Momentum[b, dim]], - Pair[Momentum[a_], Momentum[b_]]:> - Pair[Momentum[a, dim], Momentum[b,dim]], - DiracGamma[LorentzIndex[a_]] :> - DiracGamma[LorentzIndex[a,dim],dim], - DiracGamma[Momentum[a_]] :> - DiracGamma[Momentum[a, dim], dim] - }; - ]; - amp = Contract[ amp, Expanding -> False ]; - (* - pluli[x__] := Collect2[ Plus[x], LorentzIndex , Factoring -> False ]; - *) - pluli[x__] := - Collect2[ Plus[x], LorentzIndex , Factoring -> True ]; - amp66 = amp; - FCPrint[1,Length[amp66]]; - frhdot[xx__] := - FRH[DOT[xx]]; - amp = ((# /. Plus -> plsI&) /@ amp)/.DOT -> frhdot /. - PropagatorDenominator[aa__]:> FRH[PropagatorDenominator[aa]]; - FCPrint[1,"leafcount = ",LeafCount[amp]]; - FCPrint[1,"combining"]; - amp1 = Combine[amp]; - FCPrint[1,"combining done "]; - den1 = Denominator[amp1]; - FCPrint[2,"denominator = ",den1//FRH]; - FCPrint[3,"LeafCount = ",LeafCount[amp1]]; - colorfactor = susa[colorpart ComplexConjugate[colorpart]]; - If[ colorfactor =!= 1, - FCPrint[1,"the global colorfactor of the squared amplitudes is ",colorfactor]; - ]; - nam = Numerator[amp1]; - If[ LeafCount[nam] < 1000, - nam = Factor1[nam] - ]; - numfaN = NumericalFactor[nam]; - FCPrint[1,"numfaN = " , numfaN]; - nam = nam/numfaN; - den1 = den1/numfaN; - (* - If[FreeQ2[nam, {SUNIndex, DiracGamma}], - nam = pluli[nam](*, - nam = Map[#/.Plus->pluli&, nam]; *) - ]; - *) + FCPrint[3, "SquareAmplitude: Entering.", FCDoControl->sqaVerbose]; + FCPrint[3, "SquareAmplitude: Entering with m1: ", mList, FCDoControl->sqaVerbose]; + FCPrint[3, "SquareAmplitude: Entering with m2: ", mccList, FCDoControl->sqaVerbose]; - (* - tmp`$ZWISCHEN = True; - If[tmp`$ZWISCHEN === True, nam >> "nam.s"; - den1 >> "den1.s"; prod >>"prod.s" ]; - *) - prod = Collect2[prod, LorentzIndex]; - amp = SquareAmplitude[nam, ExtraFactor -> (prod colorfactor), - IsolateNames -> isolhead, - Mandelstam -> {}, Factoring -> False, - IntermediateSubstitutions -> enmomsubst, - FinalSubstitutions -> enmomback, - EnergyMomentumConservation -> - {-p1,-p2,k1,k2,k3,k4 } - ]; - (* ++++++++++++++++++++++++++++++++++ *) - FCPrint[1,"collecing "]; - amp = amp /. enmomsubst; - amp77 = amp; - $CheckCollect = False; - If[ $CheckCollect === True, - amp = Collect2[ amp, isolhead ]/.Plus -> plsI; + If[ TrueQ[optIndexed===False], + diagmark = diagmarkIdentity, + diagmark = optIndexed ]; - amp = amp / den1 ComplexConjugate[1/den1]; - If[ collecting === True, - amp = Collect2[ amp, isolhead ] - ]; - If[ (proctype === (2->1) ) || (proctype === (1->2) ), - factoring = True - ]; - If[ factoring =!= True, - pluisol[xx__] := - Isolate[Plus[xx], - IsolateNames -> isolhead, IsolateSplit->888]; - amp = Isolate[amp /. Plus -> pluisol, IsolateNames -> isolhead, - IsolateSplit -> 888], - amp = amp /. finsubst; - amp = Collect2[ amp, isolhead ]//FRH//Factor2; - amp = amp /. finsubst; - amp = Factor2[amp]; - If[ (proctype === (2->2)) && (Length[mand] === 4), - amp = TrickMandelstam[amp, mand] - ]; - ]; - amp - ]; - -(* XFX *) -SquareAmplitude[ exp_ /; FreeQ[exp, FeynAmp], ops___Rule ] := - Block[ {ts,sps,amp2,cts,plu3,neamp,intermed,amp, - amps1, amps2,pamp,lis, saveminamp, file,finsubst2, isolhead2, - nwres, mand2, extrafact2,factoring2,epsAway,myfile}, - ts = FeynCalcInternal[exp] /. SUNDelta -> SUNDeltaContract /. - SUNDeltaContract ->SUNDelta; - enmo = EnergyMomentumConservation /. {ops} /. Options[SquareAmplitude]; - intermed = FeynCalcInternal[IntermediateSubstitutions /. {ops} /. - Options[SquareAmplitude]]; - isolhead2 = IsolateNames /. {ops} /. Options[SquareAmplitude]; - saveminamp = WriteOut /. {ops} /. Options[SquareAmplitude]; - extrafact2 = FeynCalcInternal[ExtraFactor /. {ops} /. Options[SquareAmplitude]]; - factoring2 = Factoring /. {ops} /. Options[SquareAmplitude]; - finsubst2 = FeynCalcInternal[FinalSubstitutions /. {ops} /. - Options[SquareAmplitude]]; - epsAway = EpsDiscard /. {ops} /. Options[SquareAmplitude]; + If[ OptionValue[Real], - (*Mac fix, 18/9-2000, F.Orellana. Ditto for FileType's below*) - If[ StringQ[saveminamp], - myfile = FileType[saveminamp]; - Which[myfile === File, - file = {saveminamp};, - myfile === None, - file = {};, - True, - Print["There was a problem:\n",saveminamp," is inaccessible"]; - Return[] - ], - file = {} + (* If the matrix element is purely real. *) + tmp = Table[ If[ i===j, + mList[[i]] mccList[[j]] diagmark[i,j], + 2 mList[[i]]mccList[[j]]diagmark[i,j] + ], + {i,1,Length[mList]},{j,i} + ], + (* If the matrix element contains both real and imaginary parts. *) + tmp = Table[ mList[[i]] mccList[[j]] diagmark[i,j], {i,1,Length[mList]},{j,1,Length[mList]}] ]; - (*If[StringQ[saveminamp], file = FileNames @@ {saveminamp}, file = {}];*) - plu3[y__] := - Isolate[Plus[y], - {DiracGamma, LorentzIndex,Spinor,Eps,SUNIndex}, - IsolateNames -> isolhead2, - IsolateSplit -> 444I]; - etl[x__] := - plu3[x] /; FreeQ[{x}, Eps]; - nuLL1 = Unique[System`C]; - nuLL2 = Unique[System`C]; -(* -nuLL1 = Unique[cCU]; nuLL2 = Unique[cCU]; -*) - etl[y__] := - Block[ {ee}, - ee = PartitHead[Plus[y], Eps]; - (Collect2[ee[[2]]+nuLL1 + nuLL2, Eps,Factoring->False - ] /. nuLL1 -> 0 /. nuLL2 -> 0(*/.Plus->plu2*)) + - (ee[[1]]/.Plus->plu3) - (* -(Factor2[ee[[1]], FactorTime->242]/.Plus->plu3) -*) - ] /; !FreeQ[{y}, Eps]; - (* ++++++++++++++++++++++++++++++++++++ *) - FCPrint[2,"enmo = ", enmo]; - If[ file =!= {}, - FCPrint[2,"loading previous result ", file]; - (Get @@ {saveminamp}); - ts = tmp`$TSAMP; - lis = Length[ts]; - nuLlLL = Unique[System`C];(* - nuLlLL = Unique[cCUn]; - *) - (* - FCPrint[2,"colling2insquareamplitudeagain"]; - ts = ((#/.Plus->etl)& /@ (ts + nuLlLL)) /. nuLlLL->0 - *) - , - ts = propdenexp[ts, enmo]; - FCPrint[2,"diracsimplifyinginsquareamplitude"]; - ts = DiracSimplify[ts]; - ots = ts; - FCPrint[2,LeafCount[ots]]; - If[ Head[ts] === Plus, - FCPrint[2,"colling2insquareamplitude"]; - ts = Collect2[ts, {Spinor,SUNIndex}, Factoring -> False]; - ots2 = ts; - (* - ts = Collect2[ts, {Spinor,SUNIndex}, Factoring -> True]; - *) - ]; - (* ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss *) - spmin[xxxx_, enmomcon_List] := - Block[ {xx = xxxx, - enms = (Map[Momentum, enmomcon]//ExpandScalarProduct), smmin,sol, sba, - check, res = 0, simP}, - If[ Length[enmomcon] === 0, - res = xxxx, - sol[pe_,___] := - Solve[(Plus@@enms)==0, - PowerExpand[Sqrt[pe^2]]][[1,1]]; - sba[pe_,___] := - {Reverse[sol[pe]], Map[-#&,Reverse[sol[pe]]]}; - check[pe_, __, a_List] := - !FreeQ[a, Last[sol[pe][[2]]]/ - NumericalFactor[Last[sol[pe][[2]]]]]; - smmin[Spinor[pe1__], a___, Spinor[pe2__]] := - smmin[Spinor[pe1] . a . Spinor[pe2]] = - If[ FreeQ[{a}, Momentum], - Spinor[pe1] . a . Spinor[pe2], - If[ check[pe1, {a}], - DiracSimplify[(Spinor[pe1]/.sol[pe1]) . a . Spinor[pe2]] /. sba[pe1], - If[ check[pe2, {a}], - DiracSimplify[Spinor[pe1] . a . (Spinor[pe2]/.sol[pe2])]/.sba[pe2], - Spinor[pe1] . a . Spinor[pe2] - ], - Spinor[pe1] . a . Spinor[pe2] - ] - ]; - specsu[x_] := - specsu2[Expand[x, Spinor]]; - specsu2[x_Plus] := - Map[specsu2, x]; - simP[xy_] := (*simP[xy]=*) - specsu[ - FixedPoint[Expand[DiracSimplify[ - Contract[#(* /.DOT->smmin /. smmin -> DOT*)]]]&, xy, 7] - ] /. specsu2 -> specsir; - xx = DiracSimplify[xx]; - xx = Collect2[xx, Spinor, Factoring->False]; - xx = Collect2[specsu[xx]/.specsu2 -> specsir, Spinor,Factoring->False]; - If[ Head[xx] =!= Plus, - res = simP[xx], - For[iji = 1, iji <= Length[xx], iji++, - FCPrint[2,"iji = ",iji, " out of ", Length[xx]]; - res = res + (nP = simP[xx[[iji]]]); - FCPrint[2,"nP = ",nP//FeynCalcForm]; - ]; - ]; - ]; - res - ]; - (* sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss *) - If[ (!FreeQ[ts, Spinor]) && (enmo=!= {}), - FCPrint[2,"minimizing SME's"]; - ts = spmin[ts, enmo]; - FCPrint[2,"colling2insquareamplitudeagain"]; - ts = (Collect2[ts, {Spinor, SUNIndex} ] + nuLlLL) /. nuLlLL->0; - ]; - FCPrint[1,"ts//Length = ",ts//Length]; - ts = ((#/.Plus->etl)& /@ (ts + nuLlLL)) /. nuLlLL->0; - If[ StringQ[saveminamp], - Write2 @@ {saveminamp, tmp`$TSAMP == FRH[ts]} - ]; - ]; - (* ++++++++++++++++++++++++ *) - If[ ValueQ[tmp`ENM], - enmLI = tmp`ENM, - enmLI = {} - ]; - (* - epsi[x_] := x /. Eps -> epsimP; - epsimP[x__] := EpsEvaluate[Eps @@ ({x} /. enmLI)]; - *) - extrafact2 = Collect2[ extrafact2 , LorentzIndex]; - (* for the non-fermionic case *) - contractP[a_,b_] := - Block[ {tem, tem1, tem2}, - FCPrint[2,"entering contractP"]; - tem = Contract2[a, b, Collecting -> False]; - FCPrint[2,"exiting contractP"]; - tem - ]; - ijj = 1; - (* - mulL[a_,a_]:=1; - mulL[a_,b_]:=2; - *) - mulL[__] := - 1; - neamp = 0; - FCPrint[2,"ts[[1]] = ", ts[[1]]//FeynCalcForm]; + FCPrint[3, "SquareAmplitude: Amplitude squared: ", tmp, FCDoControl->sqaVerbose]; - (* Select w.r.t. to the structure of the amplitude *) - If[ !FreeQ[ts, Spinor], - cts = ComplexConjugate[ts//FRH] /. Plus -> plu3; - cts = ((#/.Plus->etl)& /@ (cts + nuLlLL)) /. nuLlLL->0; - FCPrint[2,"length of cts = ", cts//Length]; - If[ Head[ts] =!= Plus, - neamp = FermionSpinSum[susm[ts cts], - ExtraFactor -> extrafact2] /. enmLI, - (* somehow very very weird ... *) - For[i = 1, i<=Length[ts], i++, - (* - For[j = i, j <= Length[ts], j++, - (* ] *) - *) - For[j = 1, j <= Length[ts], j++, - FCPrint[2,"i = ",i, " j = ",j, " out of ",Length[ts]]; - calc = mulL[i, j] (FermionSpinSum[susm[ts[[i]] cts[[j]]], - ExtraFactor -> extrafact2] /. enmLI); - If[ (epsAway===True) && ((Length[Position[calc, DiracGamma[5]]] + - Length[Position[calc, DiracGamma[6]]] + - Length[Position[calc, DiracGamma[7]]] - )) === 1, - calc = calc /. DOT -> dOOt; - calc = calc /. x:dOOt[DiracGamma[__]..] :> - (DOT[x] /. DiracGamma[7] -> (1/2) /. - DiracGamma[6] -> (1/2) /. - DiracGamma[5] -> 0 - ); - calc = DiracSimplify[calc, Expanding -> False]; - ]; - If[ calc===0&&lis>2, - FCPrint[2,"this one vanishes ..."], - FCPrint[2,"LeafCount newtrace = ", LeafCount[calc]]; - neamp = neamp + calc; - FCPrint[2,"Length of neamp = ",Length[neamp]]; - ]; - ] - ] - ], - pluIS[xx__] := - If[ FreeQ[{xx}, SUNIndex], - pluIS2[xx], - Plus[xx] - ]; - (* - ts = FRH[ts] /. Plus -> pluIS; - *) - ts = FRH[ts]; - cts = ComplexConjugate[ts] /. Plus -> plu3; - If[ Head[ts] === Plus, - samp = susm[Expand[susa[ts cts /. Plus -> pluIS] ]], - samp = susm[susa[ts cts/. Plus -> pluIS ]] - ]; - samp = samp /. pluIS2 -> Plus; - (* WWW *) - If[ Head[samp] === Times, - sampfa = Select[samp, FreeQ[#, LorentzIndex]&]; - FCPrint[2,"sampfa = ",sampfa]; - newsamp = samp/sampfa, - sampfa = 1; - newsamp = samp - ]; - FCPrint[2,"sampfa = ",sampfa]; - FCPrint[2,"extrafact2 = ",extrafact2]; - (* FCPrint[2," newsamp = ",newsamp]; *) - ti = Timing[ - If[ Head[newsamp]===Plus, - samp = {}; - For[iis = 1, iis<=Length[newsamp], iis++, - FCPrint[2,"contract samp ", iis," out of ",Length[newsamp]]; - nsamp = contractP[newsamp[[iis]], extrafact2]; - (* - nsamp = Contract3[newsamp[[iis]] extrafact2]; - *) - AppendTo[samp, nsamp]; - ]; - samp = Apply[Plus, samp], - samp = contractP[newsamp, extrafact2]; - (* - samp = Contract3[newsamp extrafact2]; -*) + res = Flatten[tmp]; - ]; - FCPrint[2,"Length of samp = ",samp//Length]; - ]; - FCPrint[1, "checccckkkkkk ", TimeUsed[]]; - neamp = samp sampfa; - FCPrint[1,"time needed for polarization sums = ", - ti[[1]]//FeynCalcForm]; - FCPrint[1," collecting now "]; - ]; - FCPrint[2,"after expanding the length of the amplitude is ", - Length[neamp + neuladsg]-1]; - If[ FreeQ[neamp, DiracTrace], - amps2 = neamp, -(* -If[Head[neamp] === Times, - pamp = Select[neamp, !FreeQ2[#, {DiracGamma,Complex}]&]; - amps2 = neamp / pamp, - pamp = neamp; amps2 = 1 - ]; -*) - SetOptions[DiracTrace, PairCollect -> True]; - SetOptions[TR, PairCollect -> True]; - mom4[xyx_,___] := - Momentum[xyx]; - lastsimp[yyy_] := - Block[ {rel, mul = 1, yy = yyy}, - If[ Head[yy] === Times, - mul = Select[yy, FreeQ2[#,{Eps, LorentzIndex}]&]; - yy = yy/mul - ]; - rel = Contract[yy/.intermed, - EpsContract -> True]; - If[ !FreeQ[rel,Pair], - rel = rel /. Momentum -> mom4; - tmp`REL = rel; - rel = ExpandScalarProduct[rel]; - ]; - FCPrint[2,"beforefactor3"]; - If[ LeafCount[rel]<9200, - rel = Factor2[rel] - ]; - FCPrint[2,"afterfactor3"]; - If[ epsAway===True, - rel = rel /. Eps[__]->0 - ]; - If[ rel ===0, - FCPrint[2,"TRS00000000"], - rel = rel mul; - If[ FreeQ[rel, Eps], - rel = rel/.Plus->plu3, - rel = rel /. Plus-> etl - ]; - ]; - If[ rel =!= 0, - FCPrint[2,"TRESULT = ", rel//FeynCalcForm] - ]; - rel - ]; - TRS[xyz__] := - MemSet[TRS[xyz] , TR[xyz]]; - epsimp[x__] := - If[ !FreeQ[{x},Eps], - Schouten[Plus[x], 4444], - Plus[x] - ]; - If[ !FreeQ[ neamp, DiracGamma], - If[ Head[neamp]=!=Plus, - nwres = { SUNSimplify[neamp/.DiracTrace->TRS]}, - nwres = {}; - For[ij = 1, ij <= Length[neamp], ij++, FCPrint[2,"ij = ",ij, - " out of ", Length[neamp](*, - "|| length of nwres = ",Length[nwres]*)]; - AppendTo[nwres, (ww = lastsimp[neamp[[ij]] /. DiracTrace -> TRS])]; - ], - nwres = {SUNSimplify[neamp/.DiracTrace->TRS]} - ]; - ]; - FCPrint[2,"changing list to sum"]; - amps2 = (Plus@@nwres); + If[ !OptionValue[List], + res = Total[res] ]; - (*tmp`AMPS2=amps2;*) - If[ factoring2 === True, - amps2 = Factor2[ExpandScalarProduct[ - (amps2//FRH) /. intermed] /. Momentum -> mom4], - amps2 = Expand[ExpandScalarProduct[ - (amps2//FRH) /. intermed] /. Momentum -> mom4] - ]; - amps2 = ExpandScalarProduct[amps2/.intermed] /. finsubst2; - If[ Length[mand2] ===4, - amps2 = TrickMandelstam[amps2, mand2] + If[ OptionValue[FCE], + res = FCE[res] ]; - amps2 - ]; - -(* ********************************************************************** *) - - -propdenex[a_, m_] := - propdenex[a, m] = 1/Factor2[ - FixedPoint[ExpandScalarProduct, ScalarProduct[a, a] - m^2] ]; - -HoldPattern[propdp[su_][a_, m_]] := - propdenex[a,m] /; Length[su] <= 2; -propdp[su_][a_, m_] := - Block[ {na = ExpandScalarProduct[ - If[ FreeQ[a,Momentum], - Momentum[a], - a - ]], i, vn, tte = {na}}, - vn = Variables[na]; - tte = Join[tte, - Table[ Expand[na /. (Solve[ su==0, vn[[i]] ][[1]])], {i, Length[vn]}] - ]; - tte = Sort[Union[tte], nsortQ][[1]]; - propdenex[tte, m] - ] /; Length[su] > 2; + FCPrint[1, "SquareAmplitude: Leaving.", FCDoControl->sqaVerbose]; -fdpsave[x__] := - fdpsave2 @@ ({x}/.PropagatorDenominator->pdsave); + res -propdenexp[x_ /;FreeQ[x,PropagatorDenominator],___] := - x; -propdenexp[x_] := - PropagatorDenominatorExplicit[x]; -propdenexp[x_, {}] := - propdenexp[x]; -propdenexp[x_, {en__}] := - x /. - FeynAmpDenominator -> fdpsave /. - PropagatorDenominator -> propdp[Plus@@ExpandScalarProduct[Momentum/@{en}] - ] /. pdsave -> PropagatorDenominator/. - fdpsave2 -> FeynAmpDenominator; + ] FCPrint[1,"SquareAmplitude.m loaded."]; End[] diff --git a/FeynCalc/Feynman/ToStandardMatrixElement.m b/FeynCalc/Feynman/ToStandardMatrixElement.m new file mode 100755 index 000000000..b7a583731 --- /dev/null +++ b/FeynCalc/Feynman/ToStandardMatrixElement.m @@ -0,0 +1,166 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: ToStandardMatrixElement *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: *) + +(* ------------------------------------------------------------------------ *) + +ToStandardMatrixElement::usage = +"ToStandardMatrixElement[exp] wraps Dirac structures, color structures and \ +polarization vectors with the head StandardMatrixElement. \ +The idea of having standard matrix elements stems from A. Denner's \ +\"Techniques for the calculation of electroweak radiative corrections \ +at the one-loop level and results for W-physics at LEP200\", \ +cf. arXiv:0709.1075."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`ToStandardMatrixElement`Private`"] + +tsmeVerbose::usage=""; + +Options[ToStandardMatrixElement] = { + CartesianIndex -> False, + CartesianIndexNames -> {}, + ChangeDimension -> False, + DiracOrder -> True, + DiracSimplify -> True, + DiracEquation -> True, + DiracSubstitute5 -> True, + DiracSubstitute67 -> False, + ExceptHeads -> {}, + FCColorIsolate -> True, + FCDiracIsolate -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> {Factor, 5000}, + LorentzIndex -> False, + LorentzIndexNames -> {}, + Polarization -> True, + SirlinSimplify -> False, + Spinor -> False, + SpinorChainChiralSplit -> True, + SpinorChainTrick -> True, + TimeConstrained -> 3 +} + +standmat/: + standmat[x_] standmat[y_] := + standmat[x y]; + +ToStandardMatrixElement[expr_List, opts:OptionsPattern[]]:= + ToStandardMatrixElement[#, opts]&/@expr; + +ToStandardMatrixElement[expr_/;Head[expr]=!=List, OptionsPattern[]]:= + Block[{ex,res,time, chead, dhead, holdDOT, optTimeConstrained}, + + + If [OptionValue[FCVerbose]===False, + tsmeVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + tsmeVerbose=OptionValue[FCVerbose] + ]; + ]; + + optTimeConstrained = OptionValue[TimeConstrained]; + + FCPrint[1,"ToStandardMatrixElement: Entering.", FCDoControl->tsmeVerbose]; + FCPrint[3,"ToStandardMatrixElement: Entering with: ", expr, FCDoControl->tsmeVerbose]; + + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + + If[ OptionValue[DiracSimplify], + time=AbsoluteTime[]; + FCPrint[1, "ToStandardMatrixElement: Applying DiracSimplify.", FCDoControl->tsmeVerbose]; + ex = DiracSimplify[ex, FCI->True, DiracOrder->OptionValue[DiracOrder], DiracSubstitute67->OptionValue[DiracSubstitute67], + DiracSubstitute5->OptionValue[DiracSubstitute5], SpinorChainTrick->OptionValue[SpinorChainTrick], SirlinSimplify->OptionValue[SirlinSimplify], + DiracEquation->OptionValue[DiracEquation], LorentzIndexNames-> OptionValue[LorentzIndexNames], + CartesianIndexNames-> OptionValue[CartesianIndexNames]]; + FCPrint[1, "ToStandardMatrixElement: DiracSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tsmeVerbose]; + FCPrint[3, "ToStandardMatrixElement: After DiracSimplify: ", ex, FCDoControl->tsmeVerbose] + ]; + + + + If[ OptionValue[SpinorChainChiralSplit], + time=AbsoluteTime[]; + FCPrint[1, "ToStandardMatrixElement: Applying SpinorChainChiralSplit.", FCDoControl->tsmeVerbose]; + ex = SpinorChainChiralSplit[ex, FCI->True, Factoring->False, DiracSubstitute5->OptionValue[DiracSubstitute5]]; + FCPrint[1, "ToStandardMatrixElement: SpinorChainChiralSplit done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tsmeVerbose]; + FCPrint[3, "ToStandardMatrixElement: After SpinorChainChiralSplit: ", ex, FCDoControl->tsmeVerbose] + ]; + + + If[ OptionValue[FCDiracIsolate], + time=AbsoluteTime[]; + FCPrint[1, "ToStandardMatrixElement: Applying FCDiracIsolate.", FCDoControl->tsmeVerbose]; + ex = FCDiracIsolate[ex, Polarization->OptionValue[Polarization], FCI->True, Head->dhead, Collecting->False, ExceptHeads -> OptionValue[ExceptHeads], + LorentzIndex -> OptionValue[LorentzIndex], CartesianIndex -> OptionValue[CartesianIndex]]; + FCPrint[1, "ToStandardMatrixElement: FCDiracIsolate done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tsmeVerbose]; + FCPrint[3, "ToStandardMatrixElement: After FCDiracIsolate: ", ex, FCDoControl->tsmeVerbose] + ]; + + If[ OptionValue[Spinor], + ex = ex /. dhead[x_]/; FreeQ[x,Spinor] :> x + ]; + + + + If[ OptionValue[FCColorIsolate], + time=AbsoluteTime[]; + FCPrint[1, "ToStandardMatrixElement: Applying FCColorIsolate.", FCDoControl->tsmeVerbose]; + ex = FCColorIsolate[ex, FCI->True, Head-> chead, Collecting->False, ExceptHeads -> OptionValue[ExceptHeads]]; + FCPrint[1, "ToStandardMatrixElement: FCColorIsolate done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tsmeVerbose]; + FCPrint[3, "ToStandardMatrixElement: After FCColorIsolate: ", ex, FCDoControl->tsmeVerbose]; + ]; + + time=AbsoluteTime[]; + FCPrint[1, "ToStandardMatrixElement: Applying Collect2.", FCDoControl->tsmeVerbose]; + ex = Collect2[ex,dhead,chead, Factoring->OptionValue[Factoring],TimeConstrained->optTimeConstrained]; + FCPrint[1, "ToStandardMatrixElement: Collect2 done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tsmeVerbose]; + FCPrint[3, "ToStandardMatrixElement: After Collect2: ", ex, FCDoControl->tsmeVerbose]; + + ex = ex //. chead|dhead->standmat /. standmat -> StandardMatrixElement; + + If[ OptionValue[ChangeDimension]=!=False, + FCPrint[1, "ToStandardMatrixElement: Applying ChangeDimension.", FCDoControl->tsmeVerbose]; + ex = ChangeDimension[ex,OptionValue[ChangeDimension],FCI->True]; + FCPrint[3, "ToStandardMatrixElement: After ChangeDimension: ", ex, FCDoControl->tsmeVerbose]; + ]; + + + res = ex; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + + FCPrint[1,"ToStandardMatrixElement: Leaving.", FCDoControl->tsmeVerbose]; + FCPrint[3,"ToStandardMatrixElement: Leaving with: ", res, FCDoControl->tsmeVerbose]; + + res + + ]; + +FCPrint[1,"ToStandardMatrixElement.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/Apart.m b/FeynCalc/LoopIntegrals/Apart.m index 0a8b1eea6..73857cf79 100755 --- a/FeynCalc/LoopIntegrals/Apart.m +++ b/FeynCalc/LoopIntegrals/Apart.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Collection of different partial fractioning routines *) @@ -65,14 +65,22 @@ (* FeynAmpDenominator is an internal option to make ApartFF behave like SPC, i.e. block partial fractioning on loop integrals that don't contain scalar products *) Options[ApartFF] = { - Collecting -> True, - DropScaleless -> True, - ExpandScalarProduct -> True, - FCI -> False, - FCVerbose -> False, - FDS -> True, - FeynAmpDenominator -> True, - FeynAmpDenominatorCombine -> True + Collecting -> True, + DropScaleless -> True, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False, + FCProgressBar -> False, + FCVerbose -> False, + FDS -> True, + Factoring -> {Factor, 5000}, + FeynAmpDenominator -> True, + FeynAmpDenominatorCombine -> True, + MaxIterations -> Infinity, + Numerator -> True, + SetDimensions -> {3, 4, D-1, D}, + TemporalMomentum -> False, + TimeConstrained -> 3 }; Apart2[y_, OptionsPattern[]] := @@ -101,11 +109,14 @@ ApartFF[int_, lmoms_List , OptionsPattern[]]:= Block[{ exp,tmp,loopHead,null1,null2,res,rest, - loopInts,intsUnique,solsList,repRule}, + loopInts,intsUnique,solsList,repRule, time, + optCollecting, tcRepList}, + + optCollecting = OptionValue[Collecting]; If [OptionValue[FCVerbose]===False, affVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], affVerbose=OptionValue[FCVerbose] ]; ]; @@ -119,49 +130,110 @@ exp = FeynAmpDenominatorCombine[exp] ]; + FCPrint[1, "ApartFF: Entering.", FCDoControl->affVerbose]; FCPrint[3, "ApartFF: Entering with ", exp, FCDoControl->affVerbose]; FCPrint[3, "ApartFF: Loop momenta are ", lmoms, FCDoControl->affVerbose]; + + (* + By default we will not do partial fractioning w.r.t the temporal loop momenta, since those + are not regularized in DR. + *) + tcRepList = {}; + If[ !OptionValue[TemporalMomentum] && !FreeQ[exp,TemporalMomentum], + tcRepList = Map[Rule[TemporalMomentum[#], TemporalMomentum[Unique["fctm"]]] &, lmoms]; + exp = exp /. Dispatch[tcRepList] + ]; + + (* Split loop integrals from the rest *) - tmp = FCLoopSplit[exp,lmoms]; + tmp = FCLoopSplit[exp,lmoms, Collecting->False]; + + time=AbsoluteTime[]; + FCPrint[1, "ApartFF: Applying FCLoopRemoveNegativePropagatorPowers.", FCDoControl->affVerbose]; + tmp = FCLoopRemoveNegativePropagatorPowers[tmp,FCI->True,FCLoopPropagatorPowersCombine -> False]; + FCPrint[1, "ApartFF: Done applying FCLoopRemoveNegativePropagatorPowers, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->affVerbose]; + FCPrint[3, "ApartFF: After FCLoopRemoveNegativePropagatorPowers: ", tmp, FCDoControl->affVerbose]; + + time=AbsoluteTime[]; + FCPrint[1, "ApartFF: Extracting unique loop integrals.", FCDoControl->affVerbose]; If[ OptionValue[FeynAmpDenominator], rest = tmp[[1]]; - loopInts = FCLoopIsolate[Plus@@tmp[[2;;4]], lmoms, FCI->True, Head->loopHead, DropScaleless->True, PaVe->False], + loopInts = FCLoopIsolate[Plus@@tmp[[2;;4]], lmoms, FCI->True, Head->loopHead, DropScaleless->True, PaVe->False, Numerator->OptionValue[Numerator]], rest = tmp[[1]]+tmp[[2]]; - loopInts = FCLoopIsolate[Plus@@tmp[[3;;4]], lmoms, FCI->True, Head->loopHead, DropScaleless->True, PaVe->False] + loopInts = FCLoopIsolate[Plus@@tmp[[3;;4]], lmoms, FCI->True, Head->loopHead, DropScaleless->True, PaVe->False, Numerator->OptionValue[Numerator]] ]; + + (* Split loop integrals from the rest *) intsUnique = (Cases[loopInts+null1+null2,loopHead[___],Infinity]/.null1|null2->0)//Union; + FCPrint[1, "ApartFF: Done extracting unique loop integrals, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->affVerbose]; + FCPrint[1,"ApartFF: Number of the unique integrals: ", Length[intsUnique], FCDoControl->affVerbose]; FCPrint[3,"ApartFF: List of the unique integrals: ", intsUnique, FCDoControl->affVerbose]; + time=AbsoluteTime[]; + + FCPrint[1, "ApartFF: Applying FCApart.", FCDoControl->affVerbose]; (* Apply FCApart to each of the unique loop integrals *) - solsList = Map[FCApart[#,lmoms,FCI->True,FDS->OptionValue[FDS],DropScaleless->OptionValue[DropScaleless]]&,(intsUnique/.loopHead->Identity)]; + solsList = MapIndexed[ (If[ OptionValue[FCProgressBar], + FCProgressBar["ApartFF: Processing integral ",First[#2],Length[intsUnique]] + ]; + FCApart[#1,lmoms,FCI->True,FDS->OptionValue[FDS],DropScaleless->OptionValue[DropScaleless], + MaxIterations->OptionValue[MaxIterations],SetDimensions->OptionValue[SetDimensions]])&,(intsUnique/.loopHead->Identity)]; + + FCPrint[1, "ApartFF: Done applying FCApart, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->affVerbose]; + FCPrint[3, "ApartFF: After FCApart: ", solsList, FCDoControl->affVerbose]; If[Length[solsList]=!=Length[intsUnique], Message[ApartFF::failmsg,"ApartFF can't create the solution list."]; Abort[] ]; - repRule = MapIndexed[(Rule[#1, First[solsList[[#2]]]]) &, intsUnique]; - + repRule = Thread[Rule[intsUnique, solsList]]; FCPrint[3, "ApartFF: Replacement rule ", repRule, FCDoControl->affVerbose]; (* Substitute simplified integrals back into the original expression *) + + time=AbsoluteTime[]; + FCPrint[1, "ApartFF: Inserting simplified integrals back into the original expression.", FCDoControl->affVerbose]; res = FeynAmpDenominatorCombine[rest + (loopInts/.repRule)]; + FCPrint[1, "ApartFF: Done inserting simplified integrals, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->affVerbose]; + + + If[ tcRepList=!={}, + res = res /. Dispatch[Reverse/@tcRepList] + ]; If [OptionValue[ExpandScalarProduct], - res = ExpandScalarProduct[res] + time=AbsoluteTime[]; + FCPrint[1, "ApartFF: Applying ExpandScalarProduct.", FCDoControl->affVerbose]; + res = ExpandScalarProduct[res, FCI->True]; + FCPrint[1, "ApartFF: Done applying ExpandScalarProduct, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->affVerbose] ]; - If[ OptionValue[Collecting], - res = Collect2[res,FeynAmpDenominator] + If[ optCollecting=!=False, + time=AbsoluteTime[]; + FCPrint[1, "ApartFF: Applying Collect2.", FCDoControl->affVerbose]; + + If[ TrueQ[optCollecting===True], + res = Collect2[res,FeynAmpDenominator, Factoring->OptionValue[Factoring], TimeConstrained->OptionValue[TimeConstrained]], + res = Collect2[res,optCollecting, Factoring->OptionValue[Factoring], TimeConstrained->OptionValue[TimeConstrained]] + ]; + + FCPrint[1, "ApartFF: Done applying Collect2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->affVerbose] ]; + FCPrint[1, "ApartFF: Leaving.", FCDoControl->affVerbose]; FCPrint[3, "ApartFF: Leaving with ", res, FCDoControl->affVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + res ] diff --git a/FeynCalc/LoopIntegrals/CTdec.m b/FeynCalc/LoopIntegrals/CTdec.m new file mode 100644 index 000000000..1fc00f51c --- /dev/null +++ b/FeynCalc/LoopIntegrals/CTdec.m @@ -0,0 +1,159 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: CTdec *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Computes tensor decompositions for Cartesian multiloop + integrals using projection methods *) + +(* ------------------------------------------------------------------------ *) + +CTdec::usage = "CTdec[{{qi, a}, {qj, b}, ...}, {p1, p2, ...}] or \ +CTdec[exp, {{qi, a}, {qj, b}, ...}, {p1, p2, ...}] \ +calculates the tensorial decomposition formulas for Cartesian integrals. \ +The more common ones are saved in TIDL."; + +CTdec::failmsg = +"Error! TID has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] + +End[] + +Begin["`CTdec`Private`"] + +ctdecVerbose::usage=""; + +Options[CTdec] = { + BasisOnly -> False, + Dimension -> D-1, + FCVerbose -> False, + Factoring -> {Factor2, Factor}, + FeynCalcExternal -> True, + List -> True, + UseParallelization -> True, + UseTIDL -> True +}; + + +CTdec[exp_:1, li : {{_, _} ..}, ppli_List/;FreeQ[ppli,OptionQ], OptionsPattern[]] := + Block[ {resTdec, tmp, tmpPair, time, rules, dimD, optDimension, heads, + headsEval, ruleHeads, optBasisOnly, res, optFactoring, momHead}, + + optDimension = OptionValue[Dimension]; + optBasisOnly = OptionValue[BasisOnly]; + optFactoring = OptionValue[Factoring]; + + If [OptionValue[FCVerbose]===False, + ctdecVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + ctdecVerbose=OptionValue[FCVerbose] + ] + ]; + + FCPrint[1, "CTdec: Entering with ", exp, li, ppli, "" , FCDoControl->ctdecVerbose]; + + (* + We implement CTdec as a frontend for Tdec. The construction of the basis for + Cartesian integrals proceeds exactly in the same way as for Minkowskian integrals, + so there is no need to reinvent the wheel. The only thing one has to check in advance + are possible vanishing Gram determinants. + *) + + (* Abort decomposition if there are vanishing Gram determinants, unless + we have a 1-point function or were requested just to provide the tensor basis *) + If[!optBasisOnly && ppli=!={}, + FCPrint[1, "CTdec: Checking Gram determinant...", FCDoControl->ctdecVerbose]; + If[ FCGramDeterminant[ppli,Dimension->optDimension,Head -> {CartesianPair, CartesianMomentum}]===0, + FCPrint[1, "CTdec: Tensor decomposition is not possible due to vanishing Gram determinants", FCDoControl->ctdecVerbose]; + tmp=Apply[Times, Map[CartesianPair[CartesianMomentum[#[[1]],optDimension], CartesianIndex[#[[2]],optDimension]]&, li]]; + rules={}; + + If[ exp =!= 1, + tmp = Contract[exp tmp, EpsContract -> False] + ]; + + If[ TrueQ[OptionValue[List]], + res = {rules, tmp}, + res = tmp + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + Return[res], + FCPrint[1, "CTdec: The Gram determinant is non-vanishing.", FCDoControl->ctdecVerbose]; + ]; + ]; + + time = AbsolutTime[]; + FCPrint[1, "CTdec: Calling Tdec.", FCDoControl->ctdecVerbose]; + resTdec = Tdec[exp,li,ppli, BasisOnly->optBasisOnly, Dimension->dimD, Factoring->OptionValue[Factoring], + List->True, FCE->False, UseParallelization->OptionValue[UseParallelization], UseTIDL-> OptionValue[UseTIDL], + Head -> momHead]; + FCPrint[1, "CTdec: Done calling Tdec, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->ctdecVerbose]; + + resTdec = resTdec /. Pair -> tmpPair //. {Momentum-> CartesianMomentum, LorentzIndex -> CartesianIndex, dimD -> optDimension} /. + tmpPair -> CartesianPair /. momHead -> Identity; + + If[ !FreeQ2[resTdec,{Pair,LorentzIndex,Momentum}], + Message[CTdec::failmsg, "Failed to convert the output of Tdec to Cartesian objects"] + ]; + + If[ optBasisOnly, + res = resTdec /. FCGV["PaVe"] -> FCGV["CartesianPaVe"]; + If[ exp =!= 1, + res = Contract[exp res, EpsContract -> False] + ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + Return[res] + ]; + + {rules, tmp} = resTdec; + + If[ Head[rules]===List && Length[rules]>0, + heads = Cases2[tmp, CartesianMomentum, CartesianIndex]; + headsEval = Map[(#/. rules)&, heads]; + ruleHeads = Thread[Rule[heads,headsEval]]; + tmp = tmp /. ruleHeads; + ]; + + If[ exp =!= 1, + tmp = Contract[exp tmp, EpsContract -> False] + ]; + + If[ TrueQ[OptionValue[List]], + res = {rules, tmp}, + If[ Head[rules]===List && Length[rules]>0, + res = tmp /. rules, + res = tmp + ] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "CTdec: Leaving.", FCDoControl->ctdecVerbose]; + FCPrint[3, "CTdec: Leaving with: ", res, FCDoControl->ctdecVerbose]; + + res + + ]; + +FCPrint[1, "CTdec.m loaded.", FCDoControl->ctdecVerbose]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCApart.m b/FeynCalc/LoopIntegrals/FCApart.m index c37544af5..e29551e6c 100755 --- a/FeynCalc/LoopIntegrals/FCApart.m +++ b/FeynCalc/LoopIntegrals/FCApart.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Partial fractioning for loop integrals with linearly @@ -47,24 +47,27 @@ counter::usage=""; Options[FCApart] = { - Check -> True, - Collecting -> True, - DropScaleless -> True, + Check -> True, + Collecting -> True, + DropScaleless -> True, ExpandScalarProduct -> True, - FCI -> False, - FCVerbose -> False, - FDS -> True, - MaxIterations -> Infinity, - SetDimensions-> {4,D} + FCE -> False, + FCI -> False, + FCVerbose -> False, + FDS -> True, + Factoring -> {Factor, 5000}, + MaxIterations -> Infinity, + SetDimensions -> {3,4,D, D-1}, + TimeConstrained -> 3 }; FCApart[expr_, lmoms_List, OptionsPattern[]] := Block[{ex,vectorSet,res,check, scalarTerm, vectorTerm=1, pref=1, tmp, - scaleless1=0,scaleless2=0}, + scaleless1=0,scaleless2=0,time, optFactoring, optTimeConstrained}, If [OptionValue[FCVerbose]===False, fcaVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], fcaVerbose=OptionValue[FCVerbose] ]; ]; @@ -74,7 +77,9 @@ ex = expr ]; - counter = OptionValue[MaxIterations]; + counter = OptionValue[MaxIterations]; + optFactoring = OptionValue[Factoring]; + optTimeConstrained = OptionValue[TimeConstrained]; FCPrint[3,"FCApart: Entering with ", ex, FCDoControl->fcaVerbose]; @@ -85,25 +90,51 @@ ]; If[ OptionValue[ExpandScalarProduct], - ex = ExpandScalarProduct[ex] + ex = ExpandScalarProduct[ex, FCI->True] + ]; + + + + + + (* + We need to cancel things like p.q/(p.q+i Eta) before invoking FCLoopBasis functions! + *) + If[!FreeQ2[ex, {StandardPropagatorDenominator, CartesianPropagatorDenominator}], + ex = cancelSP[ex]; + ex = ex /. fadHold[r___, (h: StandardPropagatorDenominator|CartesianPropagatorDenominator)[a__, {n_, s_}], t___]/;n<0 :> + fadHold[r,t] FeynAmpDenominatorExplicit[FeynAmpDenominator[h[a, {n, s}]],FCI->True, ExpandScalarProduct->OptionValue[ExpandScalarProduct]]; + ex = ex /. fadHold[] -> 1 /. fadHold-> FeynAmpDenominator; + FCPrint[3,"FCApart: After the initial cancelling of scalar products ", ex, FCDoControl->fcaVerbose] + ]; + + (* To bring the propagators into a proper form. + However, this might also mess up the signs of the + propagators in the already fixed topology, so if FDS is set to False, + this simplification should not be done as well! *) + If[ OptionValue[FDS], + ex = ex /. FeynAmpDenominator -> FeynCalc`Package`feynsimp[lmoms] ]; - (* To bring the propagators into a proper form *) - ex = ex /. FeynAmpDenominator -> feynsimp[lmoms]; If [ FreeQ2[ex,lmoms], FCPrint[3,"FCApart: The intermediate expression contains no loop integrals ", ex, FCDoControl->fcaVerbose]; + + If[ OptionValue[FCE], + ex = FCE[ex] + ]; + Return[ex]; ]; (* Partial fractioning should work also for loop integrals that contain loop momenta with uncontracted indices, or loop momenta contracted with Epsilon tensors and Dirac gammas *) - If[ !FreeQ2[ex,{LorentzIndex,Eps,DiracGamma}], - scalarTerm = SelectFree[ex, LorentzIndex,Eps,DiracGamma]; - vectorTerm = SelectNotFree[ex, LorentzIndex,Eps,DiracGamma]; + If[ !FreeQ2[ex,{LorentzIndex,CartesianIndex,Eps,DiracGamma}], + scalarTerm = SelectFree[ex, LorentzIndex,CartesianIndex,Eps,DiracGamma]; + vectorTerm = SelectNotFree[ex, LorentzIndex,CartesianIndex,Eps,DiracGamma]; - If[ scalarTerm*vectorTerm =!= ex || !FreeQ[scalarTerm,LorentzIndex], + If[ scalarTerm*vectorTerm =!= ex || !FreeQ2[scalarTerm,{LorentzIndex,CartesianIndex}], Message[FCApart::error, ex]; Abort[] ], @@ -115,6 +146,12 @@ (* If the integral can't be partial fractioned any further, then we have nothing to do here *) If[ !FCLoopBasisOverdeterminedQ[scalarTerm,lmoms, SetDimensions->OptionValue[SetDimensions], FCI->True], + FCPrint[3,"FCApart: No furher partial fractioning is possible in ", ex, FCDoControl->fcaVerbose]; + + If[ OptionValue[FCE], + ex = FCE[ex] + ]; + Return[ex]; ]; @@ -133,19 +170,26 @@ (* Otherwise, we need to first obtain the list of polynomials that appear in the integral plus their vector representation. *) - vectorSet= FCLoopBasisExtract[scalarTerm, lmoms, OptionValue[SetDimensions]]; + + + + + vectorSet= FCLoopBasisExtract[scalarTerm, lmoms, SetDimensions->OptionValue[SetDimensions]]; (* All the partial fractioning is done by pfrac *) + time=AbsoluteTime[]; + FCPrint[1,"FCApart: Doing the actual partial fractioning via pfrac", FCDoControl->fcaVerbose]; res = pref*vectorTerm*pfrac[vectorSet]; + FCPrint[1, "FCApart: Done applying pfrac, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcaVerbose]; (*pfrac can appear in the final result if MaxIterations is not Infinity *) - res = res/.pfrac -> pfracOut; + res = res/. (pfracRaw|pfrac) -> pfracOut /. pfracOut[u_List, {}] :> pfracOut[u]; (* propagators with zero exponents are unity *) res = res /. pfracOut[{_, _, {}, _}]->1 /. pfracOut[{_, _, {0..}, _}]->1; If [OptionValue[Collecting], - res = Collect2[res,pfracOut] + res = Collect2[res,pfracOut, Factoring->optFactoring, TimeConstrained->optTimeConstrained] ]; FCPrint[3,"FCApart: Preliminary result ", res, FCDoControl->fcaVerbose]; @@ -153,8 +197,10 @@ (* The output is converted back into the standard FeynCalc notation *) res = res/. pfracOut[{_,_,x_,y_}]:> FeynAmpDenominatorCombine[Times@@MapIndexed[Power[y[[First[#2]]],Abs[#1]]&,x]]; + res = FCLoopRemoveNegativePropagatorPowers[res,FCI->True,FCLoopPropagatorPowersCombine -> False]; + If [OptionValue[Collecting], - res = Collect2[res, Join[{FeynAmpDenominator},lmoms]] + res = Collect2[res, Join[{FeynAmpDenominator},lmoms], Factoring->optFactoring, TimeConstrained->optTimeConstrained] ]; FCPrint[3,"FCApart: Preliminary result converted back to FeynCalc notation ", res, FCDoControl->fcaVerbose]; @@ -163,7 +209,7 @@ (* Check that the sum of the resulting integrals brought to the commond denominator is identical to the original integral *) If [OptionValue[Check], - If[ check=Together[PropagatorDenominatorExplicit[ex] - Together[PropagatorDenominatorExplicit[res]]]; check=!=0, + If[ check=Together[FeynAmpDenominatorExplicit[ex] - Together[FeynAmpDenominatorExplicit[res]]]; check=!=0, Message[FCApart::checkfail,ToString[ex,InputForm]]; FCPrint[0, StandardForm[check]]; Abort[] @@ -173,7 +219,7 @@ If [OptionValue[FDS], res = FDS[res, Sequence@@lmoms]; If [OptionValue[Collecting], - res = Collect2[res, Join[{FeynAmpDenominator},lmoms]] + res = Collect2[res, Join[{FeynAmpDenominator},lmoms], Factoring->optFactoring, TimeConstrained->optTimeConstrained] ] ]; @@ -193,24 +239,35 @@ ]; If [OptionValue[Collecting], - res = Collect2[res, Join[{FeynAmpDenominator},lmoms]] + res = Collect2[res, Join[{FeynAmpDenominator},lmoms], Factoring->optFactoring, TimeConstrained->optTimeConstrained] ]; - - FCPrint[3,"FCApart: Leaving with ", res,FCDoControl->fcaVerbose]; + If[ OptionValue[FCE], + res = FCE[res] + ]; Return[res] ]/; (lmoms=!={}) && !FreeQ2[expr,lmoms]; pfrac[inputVectorSet_List]:= - Block[{ vectorSet,removalList,f,v,ca,M,expCounts,spIndices, - spPosition,spExponent,spfCoeff,spType,res,iterList, dummy, eiPos,tmpNS,tmp}, + FCUseCache[pfracRaw,{inputVectorSet},{}]/; counter===Infinity; - counter--; - FCPrint[3,"FCApart: pfrac: Counter is ", counter, FCDoControl->fcaVerbose]; +(* If MaxIterations is not set to Infinity, then most likely some debugging + is ongoing. In this case we do not want to do any caching of pfrac! *) +pfrac[inputVectorSet_List]:= + ( + counter--; + FCPrint[3,"FCApart: pfrac: Counter is ", counter, FCDoControl->fcaVerbose]; + pfracRaw[inputVectorSet] + )/; counter>0 && counter=!=Infinity; + +pfracRaw[inputVectorSet_List, OptionsPattern[]]:= + Block[{ vectorSet,removalList,f,v,ca,M,expCounts,spIndices, + spPosition,spExponent,spfCoeff,spType,res,iterList, dummy, eiPos,tmpNS,tmp, + hRule, vectorSet12, nlCoeffs}, (* We need to determine f_i and f from Eq. 10 in arXiv:1204.2314. This can be done by computing the nullspace basis of the matrix M @@ -241,7 +298,11 @@ ]; (* Now we compute M and check linear independence of the propagators and scalar products*) - ca = Normal[CoefficientArrays@@(vectorSet[[1;;2]])]; + nlCoeffs=Select[vectorSet[[2]], !MemberQ[{Pair, CartesianPair, TemporalPair}, Head[#]] &]; + hRule = Map[Rule[#, Unique["caVar"]] &, nlCoeffs]; + vectorSet12 = {vectorSet[[1]] //. hRule, Join[Complement[vectorSet[[2]],nlCoeffs],Last/@hRule]}; + + ca = Normal[CoefficientArrays@@(vectorSet12)]; M = Transpose[ca[[2]]]; tmpNS = Sort[NullSpace[M]]; @@ -297,8 +358,10 @@ res = pfrac[{Delete[vectorSet[[1]],{spPosition}],vectorSet[[2]],Delete[expCounts,{spPosition}],Delete[vectorSet[[4]],{spPosition}]}]; (* Here we reinsert the factored out scalar product *) FCPrint[3,"FCApart: pfrac: Output after treating the vanishing coefficient f_i", res," ",FCDoControl->fcaVerbose]; - res = res/.(h:pfrac|pfracOut)[{b1_,b2_,b3_,b4_}]:>h[{Join[b1,{spType}],b2,Join[b3,{spExponent}], - Join[b4,{spType}]}]; + res = res/.{ + pfracOut[{a_,b_,c_,d_}]:>pfracOut[{Join[a,{spType}],b,Join[c,{spExponent}], Join[d,{spType}]}], + (pfracRaw|pfrac)[{a_,b_,c_,d_}]:>pfrac[{Join[a,{spType}],b,Join[c,{spExponent}], Join[d,{spType}]}] + }; Return[res], FCPrint[3,"FCApart: pfrac: The coefficient of ", spType, " is not zero",FCDoControl->fcaVerbose]; @@ -353,8 +416,25 @@ ]; FCPrint[3,"FCApart: pfrac: Leaving pfrac with", res,FCDoControl->fcaVerbose]; + res -]/; counter=!=0; +]; + +cancelSP[ex_]:= + ex /. FeynAmpDenominator -> fadHold //. Dispatch[{ + + b_Pair fadHold[r1___, StandardPropagatorDenominator[0, b_Pair, 0_, {n_, s_}],r2___] :> + fadHold[r1, StandardPropagatorDenominator[0, b, 0, {n - 1, s}], r2], + + Power[b_Pair,m_] fadHold[r1___, StandardPropagatorDenominator[0, b_Pair, 0, {n_, s_}],r2___] :> + fadHold[r1, StandardPropagatorDenominator[0, b, 0, {n - m, s}], r2], + + b_CartesianPair fadHold[r1___, CartesianPropagatorDenominator[0, b_CartesianPair, 0, {n_, s_}],r2___] :> + fadHold[r1, CartesianPropagatorDenominator[0, b, 0, {n - 1, s}], r2], + + Power[b_CartesianPair,m_] fadHold[r1___, CartesianPropagatorDenominator[0, b_CartesianPair, 0, {n_, s_}],r2___] :> + fadHold[r1, CartesianPropagatorDenominator[0, b, 0, {n - m, s}], r2] + }] /. fadHold[r1___, (StandardPropagatorDenominator|CartesianPropagatorDenominator)[__, {0, _}], r2___] :> fadHold[r1,r2]; FCPrint[1,"FCApart.m loaded."]; diff --git a/FeynCalc/LoopIntegrals/FCGram.m b/FeynCalc/LoopIntegrals/FCGram.m new file mode 100644 index 000000000..71cadf48b --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCGram.m @@ -0,0 +1,94 @@ +(* ::Package:: *) + + + +(* :Title: FCGram *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Gram matrix and Gram determinant *) + +(* ------------------------------------------------------------------------ *) + +FCGramMatrix::usage = +"FCGramMatrix[{p1,p2,...}] creates Gram matrix from the given list of momenta."; + +FCGramDeterminant::usage = +"FCGramDeterminant[{p1,p2,...}] computes the determinant of the Gram matrix created \ +from the given list of momenta."; + +FCGram::failmsg = "Error! FCGram has encountered a fatal problem and \ +must abort the computation. The problem reads: `1`"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCGram`Private`"] + +nptfpVerbose=Null; + +Options[FCGramMatrix] = { + Dimension -> D, + FCE -> False, + Head -> {Pair, Momentum}, + Prefactor -> 2 +}; + +Options[FCGramDeterminant] = { + Dimension -> D, + ExpandScalarProduct -> True, + FCE -> False, + Head -> {Pair, Momentum}, + Prefactor -> 2 +}; + +FCGramMatrix[moms_List,OptionsPattern[]]:= + Block[{mat,len, dim, res, pairHead,momHead}, + len = Length[moms]; + dim = OptionValue[Dimension]; + pairHead = OptionValue[Head][[1]]; + momHead = OptionValue[Head][[2]]; + + mat = Table[pairHead[momHead[moms[[i]],dim], momHead[moms[[j]],dim]], {i, 1, len}, {j, 1, len}]; + + If[ !MatrixQ[mat], + Message[FCGram::failmsg, "The created Gram matrix is incorrect."]; + Abort[] + ]; + + res = OptionValue[Prefactor] mat; + + If[ OptionValue[FCE], + res = FCE[res]; + ]; + + res + + + ]/; moms=!={}; + +FCGramDeterminant[moms_List,OptionsPattern[]]:= + Block[{mat,det}, + mat = FCGramMatrix[moms,Dimension->OptionValue[Dimension],Prefactor->OptionValue[Prefactor], Head->OptionValue[Head]]; + det = Det[mat]; + + If[OptionValue[ExpandScalarProduct], + det = ExpandScalarProduct[det] + ]; + + If[ OptionValue[FCE], + det = FCE[det]; + ]; + + det + ]; + +FCPrint[1,"FCGram.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCHideShowEpsilon.m b/FeynCalc/LoopIntegrals/FCHideShowEpsilon.m index 92d622270..20a2478fa 100755 --- a/FeynCalc/LoopIntegrals/FCHideShowEpsilon.m +++ b/FeynCalc/LoopIntegrals/FCHideShowEpsilon.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Substitutes 1/Epsilon - EulerGamma + Log[4Pi] with @@ -22,7 +22,7 @@ FCShowEpsilon::usage = "FCShowEpsilon[expr] substitutes SMP[\"Delta\"] with 1/Epsilon - \ -EulerGamma + Log[4Pi] with"; +EulerGamma + Log[4Pi]"; FCHideEpsilon::failmsg = "Error! FCHideEpsilon has encountered a fatal problem and must abort the computation. \ @@ -40,20 +40,23 @@ Begin["`FCHideShowEpsilon`Private`"] Options[FCHideEpsilon] = { - Factoring -> Factor, - Collecting -> True, - D -> 4 - 2 Epsilon + Collecting -> True, + D -> 4 - 2 Epsilon, + Factoring -> Factor, + Subtract -> EulerGamma - Log[4Pi] }; Options[FCShowEpsilon] = { - D -> 4 - 2 Epsilon + D -> 4 - 2 Epsilon, + Subtract -> EulerGamma - Log[4Pi] }; FCHideEpsilon[expr_, OptionsPattern[]] := - Block[{tmp,wrap,factoring,pref, dVal}, + Block[{tmp,wrap,factoring,pref, dVal, subtract}, factoring = OptionValue[Factoring]; dVal = OptionValue[D]; + subtract = OptionValue[Subtract]; tmp = Collect2[expr,{Epsilon,EpsilonUV,EpsilonIR},Factoring->factoring]; @@ -74,9 +77,9 @@ 1/EpsilonIR -> wrap[pref/EpsilonIR]/pref }; - tmp = tmp /. { wrap[pref/Epsilon] -> SMP["Delta"] + EulerGamma - Log[4Pi], - wrap[pref/EpsilonUV] -> SMP["Delta_UV"] + EulerGamma - Log[4Pi], - wrap[pref/EpsilonIR] -> SMP["Delta_IR"] + EulerGamma - Log[4Pi] + tmp = tmp /. { wrap[pref/Epsilon] -> SMP["Delta"] + subtract, + wrap[pref/EpsilonUV] -> SMP["Delta_UV"] + subtract, + wrap[pref/EpsilonIR] -> SMP["Delta_IR"] + subtract }; If[ OptionValue[Collecting], @@ -88,9 +91,10 @@ ]; FCShowEpsilon[expr_, OptionsPattern[]] := - Block[{tmp,pref, dVal}, + Block[{tmp,pref, dVal, subtract}, dVal = OptionValue[D]; + subtract = OptionValue[Subtract]; Which[ dVal === 4 - 2 Epsilon, @@ -102,9 +106,9 @@ Abort[] ]; - tmp = expr/. { SMP["Delta"] -> pref/Epsilon - EulerGamma + Log[4Pi], - SMP["Delta_UV"] -> pref/EpsilonUV - EulerGamma + Log[4Pi], - SMP["Delta_IR"] -> pref/EpsilonIR - EulerGamma + Log[4Pi] + tmp = expr/. { SMP["Delta"] -> pref/Epsilon - subtract, + SMP["Delta_UV"] -> pref/EpsilonUV - subtract, + SMP["Delta_IR"] -> pref/EpsilonIR - subtract }; tmp diff --git a/FeynCalc/LoopIntegrals/FCLoopBasis.m b/FeynCalc/LoopIntegrals/FCLoopBasis.m index 5f91de0d6..210dcda90 100755 --- a/FeynCalc/LoopIntegrals/FCLoopBasis.m +++ b/FeynCalc/LoopIntegrals/FCLoopBasis.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Information about the propagators of the given multi-loop @@ -32,6 +32,36 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), integrals with tools that do Integration-By-Parts (IBP) reduction (e.g. FIRE). \ Furthermore, int must not contain propagators that are linearly dependent."; +FCLoopBasisSplit::usage = +"FCLoopBasisSplit[int, {q1,q2,...}] checks if the given loop integral factorizes \ +and if so splits it into independent integrals."; + +FCLoopBasisGetSize::usage = +"FCLoopBasisGetSize[n1,n2] returns the number of linearly independent propagators \ +for a topology that contains n1 loop momenta and n2 external momenta."; + +FCLoopBasisPropagatorsToTopology::usage = +"FCLoopBasisPropagatorsToTopology[{pr1, pr2, ...}] takes the list \ +of Pairs and FeynAmpDenominators pr1, p2, ... and converts it into a \ +list of propagators that can be used to describe a topology."; + +FCLoopBasisCreateScalarProducts::usage= +"FCLoopBasisCreateScalarProducts[{q1, q2, ...},{p1, p2,...},{d1, d2, ...}, head] generates \ +a list of all loop-momentum dependent scalar products made out of the loop momenta q1, q2, ... and \ +external momenta p1, p2, ... in the space-time dimensions d1, d2, .... The argument head can \ +be Pair to generate Lorentzian scalar products or CartesianPair to generate Cartesian scalar \ +products."; + +FCLoopBasisExtract::usage= +"FCLoopBasisExtract[int, {q1,q2,...}] is an auxiliary function that extract the scalar products \ +that form the basis of the loop integral in int. It needs to know the loop momenta on which the integral \ +depends and the dimensions of the momenta that may occur in the integral."; + +FCLoopBasisIntegralToPropagators::usage= +"FCLoopBasisIntegralToPropagators[int, {q1,q2,...}] is an auxiliary function that converts the loop integral int that \ +depends on the loop momenta q1, q2, ... to a list of propagators and scalar products. All propagators and \ +scalar products that do not depend on the loop momenta are discarded, unless the Rest option is set to True."; + FCLoopBasis::unknownmoms = "Error! Loop integral `1` depends on momenta that were not specified or it doesn't depend on \ some of the specified momenta. Evaluation aborted."; @@ -42,149 +72,710 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), FCLoopBasisFindCompletion::fail= "FCLoopBasisFindCompletion failed to determine propagators that are required to complete basis of `1`. \ -Evaluation aborted." +Evaluation aborted."; FCLoopBasisFindCompletion::notcomplete= "The propagators determined by FCLoopBasisFindCompletion for `1` do not lead to a complete basis! \ -Evaluation aborted." +Evaluation aborted."; FCLoopBasisFindCompletion::basisoverdet= "The integral `1` contains linearly dependent propagators. You need to rewrite it as a sum of integrals \ -with linearly independent propagators before you can proceed with the completion of the propagator basis." +with linearly independent propagators before you can proceed with the completion of the propagator basis."; -FCLoopBasisExtract::usage= -"FCLoopBasisExtract[int, {q1,q2,...},{4,D}] is an auxiliary function that extract the scalar products \ -that form the basis of the loop integral in int. It needs to know the loop momenta on which the integral \ -depends and the dimensions of the momenta that may occur in the integral."; +FCLoopBasisIntegralToPropagators::failmsg = +"Error! FCLoopBasisIntegralToPropagators has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; + +FCLoopBasisCreateScalarProducts::failmsg = +"Error! FCLoopBasisCreateScalarProducts encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; -FCLoopBasisExtract::nodims= -"Error! FCLoopBasisExtract is unable to build up a list of possible scalar products, because the supplied \ -dimensions are not present in the given expression. Evaluation aborted." +FCLoopBasisPropagatorsToTopology::failmsg = +"Error! FCLoopBasisPropagatorsToTopology encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; + +FCLoopBasisExtract::failmsg = +"Error! FCLoopBasisExtract has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; FCLoopBasisFindCompletion::failmsg = "Error! FCLoopBasisFindCompletion has encountered a fatal problem and must abort the computation. \ -The problem reads: `1`" +The problem reads: `1`"; + +FCLoopBasisOverdeterminedQ::failmsg = +"Error! FCLoopBasisOverdeterminedQ has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; FCLoopBasisIncompleteQ::failmsg = "Error! FCLoopBasisIncompleteQ has encountered a fatal problem and must abort the computation. \ -The problem reads: `1`" +The problem reads: `1`"; Begin["`Package`"] End[] Begin["`FCLoopBasis`Private`"] +pow::usage=""; null::usage=""; +lintegral::usage=""; +fclbeVerbose::usage=""; +optEtaSign::usage=""; +itpVerbose::usage=""; +spd::usage=""; + +SetAttributes[spd,Orderless]; + +Options[FCLoopBasisExtract] = { + FCI -> False, + FCE -> False, + FCVerbose -> False, + FCTopology -> False, + SetDimensions -> {3, 4, D, D-1} +}; Options[FCLoopBasisIncompleteQ] = { - FCI -> False, - FCVerbose -> False, - SetDimensions-> {4,D} + FCI -> False, + FCVerbose -> False, + FCTopology -> False, + SetDimensions -> {3, 4, D, D-1} }; Options[FCLoopBasisOverdeterminedQ] = { - FCI -> False, - FCVerbose -> False, - SetDimensions-> {4,D} + FCI -> False, + FCVerbose -> False, + SetDimensions -> {3, 4, D, D-1} }; Options[FCLoopBasisFindCompletion] = { - FCI -> False, - FCVerbose -> False, - Method -> ScalarProduct, - SetDimensions-> {4,D} + Abort -> False, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Check -> True, + Method -> ScalarProduct, + SetDimensions -> {3, 4, D, D-1} }; -FCLoopBasisExtract[sps_. fad_FeynAmpDenominator, loopmoms_List, dims_List]:= - Block[{one, two, coeffs, spd, lmoms,allmoms, extmoms, sprods, props, basisElements, - basisElementsOrig, availableDims}, - SetAttributes[spd,Orderless]; +Options[FCLoopBasisSplit] = { + FCE -> False, + FeynAmpDenominatorCombine -> True, + Head -> FCGV["LoopInt"], + List -> True +}; + +Options[FCLoopBasisCreateScalarProducts] = { + FCE -> False +}; + +Options[FCLoopBasisIntegralToPropagators] = { + CartesianPair -> False, + EtaSign -> {1,-1,1}, + ExpandScalarProduct -> False, + FCE -> False, + FCI -> False, + FCVerbose -> False, + MomentumCombine -> False, + Negative -> False, + Pair -> False, + Rest -> False, + Sort -> True, + Tally -> False, + TemporalPair -> False, + ToSFAD -> True +} + +Options[FCLoopBasisPropagatorsToTopology] = { + DeleteDuplicates -> True, + ExpandScalarProduct -> False, + FCE -> False, + FCI -> False, + MomentumCombine -> False +}; + +FCLoopBasisGetSize[lmoms_Integer?Positive,emoms_Integer?NonNegative,extra_Integer:0]:= + lmoms*(lmoms + 1)/2 + lmoms*emoms + extra; + +rulePropagatorPowers = { + CartesianPropagatorDenominator[arg__, {i_, s_}]/; Abs[i]=!=1 && i=!=0 :> + CartesianPropagatorDenominator[arg, {Sign[i], s}], + + StandardPropagatorDenominator[arg__, {i_, s_}]/; Abs[i]=!=1 && i=!=0 :> + StandardPropagatorDenominator[arg, {Sign[i], s}], + + GenericPropagatorDenominator[arg_, {i_, s_}]/; Abs[i]=!=1 && i=!=0 :> + GenericPropagatorDenominator[arg, {Sign[i], s}] +}; + +rulePropagatorPowersToOne = { + CartesianPropagatorDenominator[arg__, {i_, s_}]/; i=!=1 :> + CartesianPropagatorDenominator[arg, {1, s}], + + StandardPropagatorDenominator[arg__, {i_, s_}]/; i=!=1 :> + StandardPropagatorDenominator[arg, {1, s}], + + GenericPropagatorDenominator[arg_, {i_, s_}]/; i=!=1 :> + GenericPropagatorDenominator[arg, {1, s}] +}; + +(* FADs *) +auxIntegralToPropagators[Power[exp_FeynAmpDenominator, n_Integer?Positive], lmoms_List]:= + ConstantArray[SelectNotFree[FeynAmpDenominatorSplit[exp, FCI->True, MomentumExpand->False, List->True],lmoms], n]/; Length[List@@exp]>1; + +auxIntegralToPropagators[Power[exp_FeynAmpDenominator, n_Integer?Positive], _]:= + ConstantArray[{exp}, n]/; Length[List@@exp]===1; + +auxIntegralToPropagators[exp_FeynAmpDenominator, lmoms_List]:= + SelectNotFree[FeynAmpDenominatorSplit[exp, FCI->True, MomentumExpand->False, List->True],lmoms]/; Length[List@@exp]>1 && Head[exp]=!=Power; + +auxIntegralToPropagators[exp_FeynAmpDenominator, _]:= + {exp}/; Length[List@@exp]===1; + + +(* SPDs *) +auxIntegralToPropagators[pref0_. Power[pref_. exp_Pair, n_Integer?Positive], lmoms_]:= + ConstantArray[FeynAmpDenominator[StandardPropagatorDenominator[0, pow[pref0,1/n] pref exp, 0, {-1, optEtaSign[[1]]}]], n]/; FreeQ2[{pref,pref0},lmoms]; + +auxIntegralToPropagators[pref_. exp_Pair, lmoms_]:= + FeynAmpDenominator[StandardPropagatorDenominator[0, pref exp, 0, {-1, optEtaSign[[1]]}]]/; FreeQ2[pref,lmoms]; - (* List of all the momenta that appear inside the integral *) - allmoms=Union[Cases[sps*fad,Momentum[x_,_:4]:>x,Infinity]]; - extmoms = Complement[allmoms,loopmoms]; - lmoms = Intersection[loopmoms,Complement[allmoms,extmoms]]; +(* CSPDs *) +auxIntegralToPropagators[pref0_. Power[pref_. exp_CartesianPair, n_Integer?Positive], lmoms_]:= + ConstantArray[FeynAmpDenominator[CartesianPropagatorDenominator[0, pow[pref0,1/n] pref exp, 0, {-1, optEtaSign[[2]]}]], n]/; FreeQ2[{pref,pref0},lmoms]; +auxIntegralToPropagators[pref_. exp_CartesianPair, lmoms_]:= + FeynAmpDenominator[CartesianPropagatorDenominator[0, pref exp, 0, {-1, optEtaSign[[2]]}]]/; FreeQ2[pref,lmoms]; - (* Collect all scalar products in the numerator that depend on the \ - loop momenta *) - sprods = (List @@ (sps*one*two)) //ReplaceAll[#, one | two -> Unevaluated[Sequence[]]] &; +(* This one should catch all nonstandard propagators. *) +auxIntegralToPropagators2[pref0_. Power[exp_, n_Integer?Positive], lmoms_]:= + ConstantArray[FeynAmpDenominator[GenericPropagatorDenominator[exp, {-1, optEtaSign[[3]]}]], n]/; !FreeQ2[exp,lmoms] && FreeQ2[pref0,lmoms]; - (* Pick out only those SPs that depend on loop momenta *) - sprods = Select[sprods,!FreeQ2[#,lmoms]&]; +auxIntegralToPropagators2[exp_, lmoms_]:= + FeynAmpDenominator[GenericPropagatorDenominator[exp, {-1, optEtaSign[[3]]}]]/; !FreeQ2[exp,lmoms] && Head[exp]=!=Power; - sprods = sprods /. Power[x_,y_]/; y>1:> Sequence@@Table[x,{i,1,y}]; - (*TODO Need to check that there are no scalar products with negative powers!!!*) - (* Collect all the propagator denominators *) - props = fad/.FeynAmpDenominator[x__]:> FeynAmpDenominator/@{x}; - If[ sprods=!={}, - sprods = Transpose[Tally[sprods]], - sprods = {{},{}} + +FCLoopBasisIntegralToPropagators[expr_, lmoms_List, OptionsPattern[]]:= + Block[{exp, tmp, res, dummy, expAsList, rest}, + + If [OptionValue[FCVerbose]===False, + itpVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + itpVerbose=OptionValue[FCVerbose] + ]; ]; - props = Transpose[Tally[props]]; - (*(* Make propagators have negative exponents*) - props[[2]] = -props[[2]];*) - (* Make scalar products have negative exponents*) - sprods[[2]] = -sprods[[2]]; + If[ Length[lmoms]<1, + Message[FCLoopBasisIntegralToPropagators::failmsg,"The list of the loop momenta cannot be empty."]; + Abort[] + ]; - basisElementsOrig = {Join[sprods[[1]],props[[1]]],Join[sprods[[2]],props[[2]]]}; + If[!OptionValue[FCI], + exp = FCI[expr], + exp = expr + ]; + FCPrint[1,"FCLoopBasisIntegralToPropagators: Entering.", FCDoControl->itpVerbose]; + FCPrint[3,"FCLoopBasisIntegralToPropagators: Entering with ", exp, FCDoControl->itpVerbose]; - basisElements = basisElementsOrig/. - FeynAmpDenominator[PD[x__]]:> 1/(PropagatorDenominatorExplicit[PD[x]]); + If[ !MemberQ[{Power, Times,FeynAmpDenominator,Pair,CartesianPair,TemporalPair,List},Head[exp]] || FreeQ2[exp,lmoms], + Message[FCLoopBasisIntegralToPropagators::failmsg,"The input expression does not seem to be a valid loop integral."]; + Abort[] + ]; - availableDims = Intersection[Union[Cases[basisElements, Momentum[_, dim_: 4] :> dim, Infinity]],dims]; + optEtaSign = OptionValue[EtaSign]; - If [availableDims==={}, - Message[FCLoopBasisExtract::nodims]; + If[ Head[exp]===List, + expAsList = exp, + expAsList = List@@(dummy*exp) + ]; + + If[ Head[expAsList]=!=List, + Message[FCLoopBasisIntegralToPropagators::failmsg, "Failed to convert the input expression to a list."]; Abort[] ]; - (* all possible scalar products of loop momenta among themselves \ - and with external momenta *) - coeffs = - Union[Join[Flatten[Outer[spd, lmoms, extmoms]], - Flatten[Outer[spd, lmoms, lmoms]]]]; - coeffs = Union[Flatten[coeffs/.spd[a_,b_]:>(Pair[Momentum[a,#],Momentum[b,#]]&/@availableDims)]]; + If[ OptionValue[ToSFAD] && !FreeQ[expAsList,PropagatorDenominator], + expAsList = ToSFAD[expAsList] + ]; + If[ OptionValue[MomentumCombine], + expAsList = If[ FreeQ[#,FeynAmpDenominator], + MomentumCombine[#,FCI->True], + #]&/@expAsList + ]; - (* Now we have all the polynomials that appear in the loop integral. - We also save their exponents as the second element of this list*) + FCPrint[3,"FCLoopBasisIntegralToPropagators: Expression as list: ", expAsList, FCDoControl->itpVerbose]; + tmp = Select[expAsList,(MemberQ[{FeynAmpDenominator, Pair, CartesianPair, TemporalPair, Power, Times, Plus},Head[#]] && !FreeQ2[#,lmoms])&]; - (* Finally, convert all these polynomials into vectors ... *) - {basisElements[[1]], coeffs, basisElements[[2]], basisElementsOrig[[1]]} + rest = Complement[expAsList,tmp] /. dummy -> Unevaluated[Sequence[]]; + + If[ Head[tmp]=!=List || Head[rest]=!=List, + Message[FCLoopBasisIntegralToPropagators::failmsg, "Failed to extract the loop structure of the input expression."]; + Abort[] + ]; + + + If[ rest==={}, + rest = 1, + rest = Times@@rest + ]; + + FCPrint[3,"FCLoopBasisIntegralToPropagators: tmp: ", tmp, FCDoControl->itpVerbose]; + FCPrint[3,"FCLoopBasisIntegralToPropagators: rest: ", rest, FCDoControl->itpVerbose]; + + If[ !FreeQ2[rest,lmoms] || !FreeQ2[tmp,{LorentzIndex,CartesianIndex}], + Message[FCLoopBasisIntegralToPropagators::failmsg,"The input expression does not seem to be a valid scalar loop integral."]; + Abort[] + ]; + tmp = tmp /. { + (h : StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[a__, {n_Integer, s_}]/; + Abs[n]=!=1 :> Sequence@@ConstantArray[h[a, {Sign[n],s}], Abs[n]] + }; + + tmp = auxIntegralToPropagators[#,lmoms]&/@tmp; + + + (* + This tricky construction is needed to handle integrals with scalar products like + (-a.q - b.q - c.q)^n which, upon applying MomentumCombine, yield -(q.(a+b+c))^3. + We want to write this as 1/[-(q.(a+b+c))]^3 instead of -1/[(q.(a+b+c))]^3, since + otherwise Rest->None will return errors. + *) + tmp = tmp /. auxIntegralToPropagators -> auxIntegralToPropagators2 /. + pow[a_Integer?Negative, b_]/; MatchQ[1/b, _Integer?Positive] :> - Power[-a,1/b] /. + pow -> Power; + + If[ !FreeQ2[tmp,{auxIntegralToPropagators,auxIntegralToPropagators2}], + Message[FCLoopBasisIntegralToPropagators::failmsg, "Failed to extract the propagators."]; + Abort[] + ]; + + + If[ OptionValue[Tally], + res = Tally[Flatten[tmp]]; + (* TODO Need the possibility to have a custom sort function *) + (*TODO For the future one might add a better sorting *) + If[OptionValue[Sort], + res = Sort[res,(#1[[1]]>#2[[1]])&] + ]; + + (* This extra check should catch things like SFAD[{{0, p1.q}, {0, 1}, -1}] SFAD[{{0, p1.q}, {0, 1}, 2}]. *) + If[ Length[First[Transpose[res]]]=!=Length[Union[First[Transpose[res]]/. Dispatch[rulePropagatorPowersToOne]]], + Message[FCLoopBasisIntegralToPropagators::failmsg,"The loop integral contains uncancelled scalar products."]; + Abort[] + ], + + res = DeleteDuplicates[Flatten[tmp]/.Dispatch[rulePropagatorPowers]]; + + If[OptionValue[Sort], + res = Sort[res] + ]; + + + (* This extra check should catch things like SFAD[{{0, p1.q}, {0, 1}, -1}] SFAD[{{0, p1.q}, {0, 1}, 2}]. *) + If[ Length[res]=!=Length[Union[res/. Dispatch[rulePropagatorPowersToOne]]], + Message[FCLoopBasisIntegralToPropagators::failmsg,"The loop integral contains uncancelled scalar products."]; + Abort[] + ] + ]; + + (* + When Negative is set to True, the powers of numerators are counted as negative. + *) + + If[ OptionValue[Negative], + res = res /. { + {FeynAmpDenominator[(h : StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[a__, {n_Integer, s_}]], + pow_} /; (n < 0 && pow > 0) :> + {FeynAmpDenominator[h[a, {n, s}]], -pow} + } + ]; + + (* If we do not want the scalar products to be represent as FADs, we can undo it here. *) + If[ OptionValue[Pair], + res = res /. FeynAmpDenominator[StandardPropagatorDenominator[0, sp_, 0, {-1, _}]] :> sp + + ]; + + If[ OptionValue[CartesianPair], + res = res /. FeynAmpDenominator[CartesianPropagatorDenominator[0, sp_, 0, {-1, _}]] :> sp + + ]; + + If[ OptionValue[TemporalPair], + res = res /. FeynAmpDenominator[GenericPropagatorDenominator[sp_, {-1, _}]] :> sp + ]; + + + (* + The loop integral may be multiplied with other non-loop terms. The option + rest specifies what should be done with those. When set to False, the non-loop + terms are simply dropped. When set to True, the non-loop term will be returned as + the second list element. When set to False, it will be dropped. The setting None + specifies that by definition there should be no non-loop terms, so that when rest + is not equal 1, it will generate an error. + *) + Switch[ + OptionValue[Rest], + True, + res = {res,rest}, + False, + Null, + None, + If[ rest=!=1, + Message[FCLoopBasisIntegralToPropagators::failmsg,"The input expression may not contain non-loop terms!"]; + Abort[] + ], + _, + Message[FCLoopBasisIntegralToPropagators::failmsg,"Unknown value of the option Rest."]; + Abort[] + ]; + + If[ OptionValue[ExpandScalarProduct], + res = ExpandScalarProduct[res,FCI->True] + ]; + + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1,"FCLoopBasisIntegralToPropagators: Leaving.", FCDoControl->itpVerbose]; + FCPrint[3,"FCLoopBasisIntegralToPropagators: Leaving with ", res, FCDoControl->itpVerbose]; + + res + ]; + + + +FCLoopBasisCreateScalarProducts[lmoms_List, extmoms_List, dims_List, head_Symbol, OptionsPattern[]] := + Block[{tmp, res, dummyDim, repRule}, + + If[ Length[lmoms] === 0, + Message[FCLoopBasisCreateScalarProducts::failmsg, "The list of loop momenta may not be empty."]; + Abort[] + ]; + + If[ Length[dims] === 0, + Message[FCLoopBasisCreateScalarProducts::failmsg, "The list of the dimensions may not be empty."]; + Abort[] + ]; + + tmp = Join[{#, #} & /@ lmoms, Subsets[lmoms, {2}], Flatten[Thread[List[extmoms, #]] & /@ lmoms, 1]]; + + If[ Length[tmp] =!=FCLoopBasisGetSize[Length[lmoms], Length[extmoms]], + Message[FCLoopBasisCreateScalarProducts::failmsg, "The number of the obtained scalar products is incorrect."]; + Abort[] + ]; + + If[ !MatchQ[tmp, {{_, _} ..}], + Message[FCLoopBasisCreateScalarProducts::failmsg,"The list of the obtained scalar products is incorrect."]; + Print[tmp]; + Abort[] + ]; + + Which[ + head === Pair, + res = Map[Pair[Momentum[#[[1]], dummyDim], Momentum[#[[2]], dummyDim ]] &, tmp], + head === CartesianPair, + res = Map[CartesianPair[CartesianMomentum[#[[1]], dummyDim], CartesianMomentum[#[[2]], dummyDim ]] &, tmp], + True, + Message[FCLoopBasisCreateScalarProducts::failmsg, "Unknown scalar product head."]; + Abort[] + ]; + + repRule = List /@ Thread[Rule[dummyDim, dims]]; + res = Flatten[res /. repRule]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + + + +FCLoopBasisPropagatorsToTopology[props_List /; props =!= {}, +OptionsPattern[]] := + Block[{expr, tmp, res}, + + If[! OptionValue[FCI], + expr = FCI[props], + expr = props + ]; + + If[ OptionValue[MomentumCombine], + expr = MomentumCombine[expr, FCI -> True] + ]; + + tmp = expr /. { + FeynAmpDenominator[a_PropagatorDenominator] :> + 1/FeynAmpDenominator[a], + FeynAmpDenominator[(h : StandardPropagatorDenominator | CartesianPropagatorDenominator | GenericPropagatorDenominator)[a__, {n_Integer, s_}]] /; + n > 0 :> FeynAmpDenominator[h[a, {-n, s}]] + }; + + res = FeynAmpDenominatorExplicit[#, FCI -> True, ExpandScalarProduct -> False] & /@ tmp; + + If[ OptionValue[ExpandScalarProduct], + res = ExpandScalarProduct[res, FCI -> True] + ]; + + + If[ OptionValue[DeleteDuplicates], + If[ DeleteDuplicates[res]=!=res, + Print[res]; + Message[FCLoopBasisPropagatorsToTopology::failmsg, "The list of propagators contains dupicates."]; + Abort[] + ] + ]; + + If[ !FreeQ2[Denominator/@res,{Pair,CartesianPair,TemporalPair}], + Message[FCLoopBasisPropagatorsToTopology::failmsg, "Inverse scalar products should be entered via FeynAmpDenominators."]; + Abort[] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; +res ]; + +FCLoopBasisExtract[exp_, loopmoms_List, OptionsPattern[]]:= + Block[{ expr, coeffs, lmoms,allmoms, extmoms, basisElements, + availableDims, dims, res, useToSFAD, integralBasis, integralBasisT, + coeffsPair, coeffsCartesianPair, coeffsTemporalPair, + lorentzianDims, cartesianDims, null1, null2, aux}, + + If [OptionValue[FCVerbose]===False, + fclbeVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fclbeVerbose=OptionValue[FCVerbose] + ]; + ]; + + dims = OptionValue[SetDimensions]; + + If[ dims==={}, + Message[FCLoopBasisExtract::failmsg,"The list of dimensions cannot be empty."]; + Abort[] + ]; + + If[ loopmoms==={}, + Message[FCLoopBasisExtract::failmsg,"The list of loop momenta cannot be empty."]; + Abort[] + ]; + + If[ !OptionValue[FCI], + expr = FCI[exp], + expr = exp + ]; + + + FCPrint[1,"FCLoopBasisExtract: Entering.", FCDoControl->fclbeVerbose]; + FCPrint[3,"FCLoopBasisExtract: Entering with: ", expr, FCDoControl->fclbeVerbose]; + FCPrint[3,"FCLoopBasisExtract: Loop momenta: ", loopmoms, FCDoControl->fclbeVerbose]; + + If[ !FCLoopNonIntegerPropagatorPowersFreeQ[expr], + Message[FCLoopBasisExtract::failmsg, "Integrals with noninteger propagator powers are not supported."]; + Abort[] + ]; + + useToSFAD = !FreeQ[expr, StandardPropagatorDenominator]; + + integralBasis = FCLoopBasisIntegralToPropagators[expr, loopmoms, FCI->True, Rest->None, Negative->True, Tally->True, + Pair->True,CartesianPair->True, ToSFAD->useToSFAD, MomentumCombine -> True, ExpandScalarProduct->True, + Sort->False + ]; + + FCPrint[3,"FCLoopBasisExtract: Integral basis from FCLoopBasisIntegralToPropagators: ", integralBasis, FCDoControl->fclbeVerbose]; + + integralBasis = Join[SelectNotFree[integralBasis,Pair,CartesianPair],SelectFree[integralBasis,Pair,CartesianPair]]; + + FCPrint[3,"FCLoopBasisExtract: Reshuffled integral basis: ", integralBasis, FCDoControl->fclbeVerbose]; + + integralBasisT = Transpose[integralBasis]; + + (* List of all momenta that appear inside the integral *) + allmoms=Cases[MomentumExpand[integralBasis], (Momentum|CartesianMomentum|TemporalMomentum)[x_,___]:>x,Infinity]//Sort//DeleteDuplicates; + + (* All momenta that are not listed as loop momenta will be treated as external momenta. *) + extmoms = Complement[allmoms,loopmoms]; + + (* + Normally, if the integral does not depend on some of the loop momenta specified by the user, + we will not include these momenta to the basis. However, if we are dealing with a subtopology + of a given topology, the full dependence must be taken into account. This is achieved by setting + the option FCTopology to True. + *) + If[ OptionValue[FCTopology], + lmoms = loopmoms, + lmoms = Intersection[loopmoms,Complement[allmoms,extmoms]] + ]; + + basisElements = FCLoopBasisPropagatorsToTopology[integralBasisT[[1]],FCI->True,ExpandScalarProduct->True, DeleteDuplicates->False]; + + FCPrint[3,"FCLoopBasisExtract: Basis elements from FCLoopBasisPropagatorsToTopology: ", basisElements, FCDoControl->fclbeVerbose]; + + availableDims = Intersection[FCGetDimensions[basisElements],dims]; + + If[ availableDims==={}, + Message[FCLoopBasisExtract::failmsg,"The supplied dimensions are not present in the given expression."]; + Abort[] + ]; + + lorentzianDims=Cases[availableDims, 4 | _Symbol]; + If[ lorentzianDims=!={}, + coeffsPair = Sort[FCLoopBasisCreateScalarProducts[lmoms,extmoms,lorentzianDims,Pair]], + coeffsPair = {} + ]; + + cartesianDims=Cases[availableDims, 3 | _Symbol - 1]; + If[ cartesianDims=!={}, + coeffsCartesianPair = Sort[FCLoopBasisCreateScalarProducts[lmoms,extmoms,cartesianDims,CartesianPair]], + coeffsCartesianPair = {} + ]; + + coeffsTemporalPair = Sort[TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[#]]&/@lmoms]; + coeffs = {}; + + If[ !FreeQ[expr,Momentum], + coeffs = Join[coeffs,coeffsPair] + ]; + + If[ !FreeQ[expr,CartesianMomentum], + coeffs = Join[coeffs,coeffsCartesianPair] + ]; + + If[ !FreeQ[expr,TemporalMomentum], + coeffs = Join[coeffs,coeffsTemporalPair] + ]; + + (* Experimental: Sort of support propagators that are not linear in the loop momentum dependent + scalar poducts. We can count every f(sp(l1,x)) as a separate coefficient. This is not optimal, + but should mostly work. *) + aux = Flatten[List @@ (ExpandAll[#] + null1 + null2) & /@ basisElements /. null1 | null2 :> Unevaluated[Sequence[]]]; + aux = Union[Map[SelectNotFree[#, lmoms] &, aux] //. {r___, 1, s___} :> {r, s}]; + coeffs = Join[coeffs, Complement[aux,coeffs]]; + + FCPrint[3,"FCLoopBasisExtract: Loop momentum dependent coefficients: ", coeffs, FCDoControl->fclbeVerbose]; + + FCPrint[1,"FCLoopBasisExtract: Leaving.", FCDoControl->fclbeVerbose]; + + res = {basisElements, coeffs, integralBasisT[[2]], integralBasisT[[1]]}; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + +]; + + +loopSplitFu[done_List, remaining_, lmoms_, subsets_] := + Block[{splitting,tmp}, + splitting = + Catch[ + Map[( + tmp = {SelectNotFree[remaining, #], #, SelectFree[remaining, #]}; + If[ TrueQ[tmp[[1]] =!= 1 && FreeQ2[tmp[[1]], Complement[lmoms, #]]], + Throw[tmp], + Null + ] + ) &, subsets] + ]; + If[ TrueQ[Last[splitting]===1], + Join[done, {lintegral[splitting[[1]], splitting[[2]]]}], + loopSplitFu[Join[done, {lintegral[splitting[[1]], splitting[[2]]]}], splitting[[3]], lmoms, subsets] + ] + + ]/; remaining =!= 1; + +loopSplitFu[done_List, 1, _, _] := + done; + +FCLoopBasisSplit[sps_. fad_FeynAmpDenominator, lmoms_List, OptionsPattern[]] := + Block[{ex, rest, res, loopMomenta}, + ex = FeynAmpDenominatorSplit[sps fad, FCI->True]; + loopMomenta=Select[lmoms,!FreeQ[ex,#]&]; + If[ loopMomenta==={}, + Return[OptionValue[Head][sps fad,0]] + ]; + {ex, rest} = {SelectNotFree[ex,loopMomenta], SelectFree[ex,loopMomenta]}; + + res = loopSplitFu[{},ex, lmoms, Rest[Subsets[lmoms]]]; + + If[ rest=!=1, + res = Join[res,{lintegral[rest,0]}] + ]; + + If [OptionValue[FeynAmpDenominatorCombine], + res = res/. lintegral[x_,y_] :> lintegral[FeynAmpDenominatorCombine[x,FCI->True],y] + ]; + + res = res /. lintegral -> OptionValue[Head]; + + + + If[ !OptionValue[List], + res = Times@@res + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + FCLoopBasisIncompleteQ[expr_, lmoms_List, OptionsPattern[]] := - Block[ {ex, vecs, ca, res, fclbVerbose, rank, len}, + Block[ {ex, vecs, ca, res, fclbVerbose, rank, len, dims}, If [OptionValue[FCVerbose]===False, fclbVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], fclbVerbose=OptionValue[FCVerbose] ]; ]; + If[ FreeQ2[expr,lmoms], + Message[FCLoopBasisIncompleteQ::failmsg, "The input expression does not depend on the given loop momenta."]; + Abort[] + ]; + If[ !OptionValue[FCI], ex = FCI[expr], ex = expr ]; + If[ Head[ex]===FCTopology, + ex = Times@@(ex[[2]]) + ]; + If[ !MatchQ[ex, _. _FeynAmpDenominator], Message[FCLoopBasis::fail,ToString[ex,InputForm],lmoms]; Abort[] ]; + If[ TrueQ[cartesianIntegralQ[ex]], + (*Cartesian integral *) + dims = Cases[OptionValue[SetDimensions], 3 | _Symbol - 1], + (*Lorentzian integral *) + dims = Cases[OptionValue[SetDimensions], 4 | _Symbol ] + ]; + FCPrint[3,"FCLoopBasisIncompleteQ: Entering with: ", ex, FCDoControl->fclbVerbose]; FCPrint[3,"FCLoopBasisIncompleteQ: Loop momenta: ", lmoms, FCDoControl->fclbVerbose]; - vecs= FCLoopBasisExtract[ex, lmoms, OptionValue[SetDimensions]]; + vecs= FCLoopBasisExtract[ex, lmoms, SetDimensions->dims, FCTopology->OptionValue[FCTopology]]; FCPrint[3,"FCLoopBasisIncompleteQ: Output of extractBasisVectors: ", vecs, FCDoControl->fclbVerbose]; @@ -208,20 +799,30 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), ]; FCLoopBasisOverdeterminedQ[expr_, lmoms_List, OptionsPattern[]] := - Block[ {ex, vecs, ca, res, fclbVerbose}, + Block[{ ex, vecs, ca, res, fclbVerbose, dims, lmomSP, + check, hRule, vecs12New, nlCoeffs}, If [OptionValue[FCVerbose]===False, fclbVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], fclbVerbose=OptionValue[FCVerbose] ]; ]; + If[ FreeQ2[expr,lmoms], + Message[FCLoopBasisOverdeterminedQ::failmsg, "The input expression does not depend on the given loop momenta."]; + Abort[] + ]; + If[ !OptionValue[FCI], ex = FCI[expr], ex = expr ]; + If[ Head[ex]===FCTopology, + ex = Times@@(ex[[2]]) + ]; + If[ !MatchQ[ex, _. _FeynAmpDenominator], Message[FCLoopBasis::fail,ToString[ex,InputForm]]; Abort[] @@ -230,45 +831,87 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), FCPrint[3,"FCLoopBasisOverdeterminedQ: Entering with: ", ex, FCDoControl->fclbVerbose]; FCPrint[3,"FCLoopBasisOverdeterminedQ: Loop momenta: ", lmoms, FCDoControl->fclbVerbose]; - vecs= FCLoopBasisExtract[ex, lmoms, OptionValue[SetDimensions]]; + vecs= FCLoopBasisExtract[ex, lmoms, SetDimensions->OptionValue[SetDimensions]]; FCPrint[3,"FCLoopBasisOverdeterminedQ: Output of extractBasisVectors: ", vecs, FCDoControl->fclbVerbose]; (* Finally, convert all these polynomials into vectors ... *) - ca = Normal[CoefficientArrays@@(vecs[[1;;2]])]; + + (* This is to make cases like Sqrt[CSPD[k]] work, otherwise CoefficientArrays would fail here.*) + + nlCoeffs=Select[vecs[[2]], !MemberQ[{Pair, CartesianPair, TemporalPair}, Head[#]] &]; + hRule = Map[Rule[#, Unique["caVar"]] &, nlCoeffs]; + vecs12New = {vecs[[1]] //. hRule, Join[Complement[vecs[[2]],nlCoeffs],Last/@hRule]}; + ca = Normal[CoefficientArrays@@vecs12New]; FCPrint[3,"FCLoopBasisOverdeterminedQ: Output of CoefficientArrays: ", ca, FCDoControl->fclbVerbose]; (* ... and check if some of those vectors are linearly dependent *) res = (NullSpace[Transpose[Last[ca]]] =!= {}); + res ]; FCLoopBasisFindCompletion[expr_, lmoms_List, OptionsPattern[]] := Block[ {ex, vecs, ca, res, fclbVerbose,extraVectors, extraProps={}, method, - missingSPs, oldRank, newRank, len,prs={},null}, + missingSPs, oldRank, newRank, len,prs={},null, isCartesian, dims, originalPrs={}, + posList, extraProps2,time, matrix, time0, optAbort, throwRes}, + + time0 = AbsoluteTime[]; If [OptionValue[FCVerbose]===False, fclbVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], fclbVerbose=OptionValue[FCVerbose] ]; ]; + If[ Length[lmoms]<1, + Message[FCLoopBasisFindCompletion::failmsg, "The number of loop momenta must be larger or equal than one."]; + Abort[] + ]; + + If[ FreeQ2[expr,lmoms], + Message[FCLoopBasisFindCompletion::failmsg, "The input expression does not depend on the given loop momenta."]; + Abort[] + ]; + method = OptionValue[Method]; + optAbort = OptionValue[Abort]; If[ Head[method]===List && method=!={}, - FCPrint[1,"FCLoopBasisFindCompletion: Using user-supplied propagators to complete the basis.", - FCDoControl->fclbVerbose]; + FCPrint[1,"FCLoopBasisFindCompletion: Using user-supplied propagators to complete the basis.", FCDoControl->fclbVerbose]; + + + FCPrint[1,"FCLoopBasisFindCompletion: Verifying and rewriting the user-supplied propagators.", FCDoControl->fclbVerbose]; + time=AbsoluteTime[]; + prs = ExpandScalarProduct[FCI[method],Momentum->lmoms]; + + originalPrs = {method,prs}; + FCPrint[3,"FCLoopBasisFindCompletion: prs: ", prs, FCDoControl->fclbVerbose]; - If[ Union[Flatten[propCheck/@prs]]=!={True}, - Message[FCLoopBasisFindCompletion::failmsg,"User-supplied propagators are not in a proper form."]; + + + (* If the heads of the user-supplied scalar products are all known, we can bypass the more complicated check *) + If[ !FCSubsetQ[{FeynAmpDenominator,Pair,CartesianPair}, DeleteDuplicates[Sort[Head/@prs]]], + + If[ Union[Flatten[propCheck/@prs]]=!={True}, + Message[FCLoopBasisFindCompletion::failmsg,"User-supplied propagators are not in a proper form."]; + Abort[] + ]; + ]; + + + If[ Length[prs] =!= Length[DeleteDuplicates[Sort[prs]]], + Message[FCLoopBasisFindCompletion::failmsg,"The list of the user-supplied propagators may not contain duplicates."]; Abort[] ]; - method=ScalarProduct; + method=ScalarProduct; + FCPrint[1,"FCLoopBasisFindCompletion: Done verifying and rewriting the user-supplied propagators, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fclbVerbose]; + ]; If[ !OptionValue[FCI], @@ -276,23 +919,44 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), ex = expr ]; - If[ !MatchQ[ex, _. _FeynAmpDenominator], + FCPrint[1,"FCLoopBasisFindCompletion: Doing some additional checks.", FCDoControl->fclbVerbose]; + time=AbsoluteTime[]; + + If[ !MatchQ[ex, n_. _FeynAmpDenominator/;FreeQ[n, FeynAmpDenominator]], Message[FCLoopBasis::fail,ToString[ex,InputForm]]; Abort[] ]; - vecs= FCLoopBasisExtract[ex, lmoms, OptionValue[SetDimensions]]; + If[ TrueQ[cartesianIntegralQ[ex]], + (*Cartesian integral *) + dims = Cases[OptionValue[SetDimensions], 3 | _Symbol - 1], + (*Lorentzian integral *) + dims = Cases[OptionValue[SetDimensions], 4 | _Symbol ] + ]; + + FCPrint[1,"FCLoopBasisFindCompletion: Additional checks done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fclbVerbose]; + + FCPrint[1,"FCLoopBasisFindCompletion: Applying FCLoopBasisExtract and converting to vectors.", FCDoControl->fclbVerbose]; + time=AbsoluteTime[]; + + vecs= FCLoopBasisExtract[ex, lmoms, SetDimensions->dims]; + + + FCPrint[3,"FCLoopBasisFindCompletion: Output of extractBasisVectors: ", vecs, FCDoControl->fclbVerbose]; (* Finally, convert all these polynomials into vectors ... *) ca = Normal[CoefficientArrays@@(vecs[[1;;2]])]; + matrix = Transpose[Last[ca]]; FCPrint[3,"FCLoopBasisFindCompletion: Output of CoefficientArrays: ", ca, FCDoControl->fclbVerbose]; len = Length[vecs[[2]]]; - oldRank = MatrixRank[Transpose[Last[ca]]]; + oldRank = MatrixRank[matrix]; + + FCPrint[1,"FCLoopBasisFindCompletion: Done applying FCLoopBasisExtract and converting to vectors, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fclbVerbose]; (* If the basis is overcomplete, stop here *) - If[ NullSpace[Transpose[Last[ca]]] =!= {}, + If[ NullSpace[matrix] =!= {}, Message[FCLoopBasisFindCompletion::basisoverdet, ToString[ex,InputForm]]; Abort[] ]; @@ -302,8 +966,12 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), Return[{{ex},{1}}]; ]; + + FCPrint[1,"FCLoopBasisFindCompletion: Finding a completion of the basis.", FCDoControl->fclbVerbose]; + time=AbsoluteTime[]; + (* There are different possibilities to complete the basis *) - Catch[ + throwRes = Catch[ Which[ (* The main idea is quite simple: We compute the nullspace and contract each of the null space vectors with the list of the loop momentum dependent scalar products. This is quite fast, but the extra propagators @@ -342,7 +1010,12 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), (* Otherwise, decide if this scalar products increases the matrix rank*) If[ newRank>oldRank, oldRank = newRank; - extraProps = Append[extraProps, #] + extraProps = Append[extraProps, #], + (* If the option Abort is set to True, stop the loop once we encounter a user-supplied propagator that cannot be + used to complete the basis *) + If[ optAbort, + Throw[0] + ]; ] ])&, If[prs==={},vecs[[2]],prs] @@ -353,23 +1026,57 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), ]; ]; - (* Check that with those propagators the basis is now complete *) - If [getRank[{Join[vecs[[1]], fdsInvert[extraProps]],vecs[[2]]}] =!= len, - Message[FCLoopBasisFindCompletion::notcomplete, ToString[ex,InputForm]]; - Abort[] + FCPrint[1,"FCLoopBasisFindCompletion: Done finding a completion of the basis, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fclbVerbose]; + + If[ TrueQ[throwRes===0], + + extraProps = {}, + + (* Check that with those propagators the basis is now complete. We can also disable this check, which is + useful when we want to augment the topology step by step by succesively adding new propagators. *) + If[ OptionValue[Check], + If [getRank[{Join[vecs[[1]], fdsInvert[extraProps]],vecs[[2]]}] =!= len, + Message[FCLoopBasisFindCompletion::notcomplete, ToString[ex,InputForm]]; + Abort[] + ] + ]; + + If[ originalPrs=!={} && !OptionValue[ExpandScalarProduct], + posList = Position[originalPrs[[2]], #] & /@ extraProps; + + If[ !MatchQ[posList, {{{_Integer}}...}], + Message[FCLoopBasisFindCompletion::failmsg,"Something went wrong when determining the positions of custom propagators."]; + ]; + posList = posList /. {{i_Integer}} :> {i}; + + extraProps2= Extract[originalPrs[[1]], posList]; + + If[ Length[extraProps]=!=Length[extraProps2], + Message[FCLoopBasisFindCompletion::failmsg,"Something went wrong when selecting custom propagators."]; + ]; + extraProps = extraProps2; + + ] ]; res = {ex, extraProps}; + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1,"FCLoopBasisFindCompletion: Leaving, toal timing: ", N[AbsoluteTime[] - time0, 4], FCDoControl->fclbVerbose]; + res ]; fdsInvert[x_]:= - (x/.f_FeynAmpDenominator:> 1/PropagatorDenominatorExplicit[f]); + (x/.f_FeynAmpDenominator:> 1/FeynAmpDenominatorExplicit[f, FCI->True]); propCheck[x_]:= - MatchQ[#, ((c_. FeynAmpDenominator[__])/;FreeQ[c, Pair])|((c_. Pair[__])/;FreeQ[c, Pair])|(c_/;FreeQ[c, Pair])]&/@(List@@(Expand2[x, Pair]+null) /. + MatchQ[#, ((c_. FeynAmpDenominator[__])/;FreeQ2[c, {Pair, CartesianPair}])|((c_. (Pair|CartesianPair)[__])/; + FreeQ2[c, {Pair, CartesianPair}])|(c_/;FreeQ2[c, {Pair, CartesianPair}])]&/@(List@@(Expand2[x, {Pair, CartesianPair}]+null) /. null -> Unevaluated[Sequence[]]); (* Compute rank of the propagator matrix. Safe for memoization *) @@ -378,5 +1085,24 @@ included in the loop integral int (that depends on the loop momenta q1,q2,...), MatrixRank[Transpose[Last[Normal[CoefficientArrays@@x]]]] ]; + +cartesianIntegralQ[ex_]:= + Which[ + !FreeQ[ex,PropagatorDenominator] && !FreeQ[ex,StanardPropagatorDenominator], + Message[FCLoopBasisExtract::failmsg,"Integrals that contain both FADs and SFADs are not supported."]; + Abort[], + (*Lorentzian integral *) + !FreeQ[ex,Momentum] && FreeQ[ex,CartesianMomentum], + Return[False], + (*Cartesian integral *) + FreeQ[ex,Momentum] && !FreeQ[ex,CartesianMomentum], + Return[True], + !FreeQ[ex,Momentum] && !FreeQ[ex,CartesianMomentum], + (*Mixed integral*) + Message[FCLoopBasisExtract::failmsg,"Integrals that simultaneously depend on Lorentz and Cartesian vectors are not supported."]; + Abort[] + ]; + + FCPrint[1,"FCLoopBasis.m loaded."]; End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopCanonicalize.m b/FeynCalc/LoopIntegrals/FCLoopCanonicalize.m index 48b9217dc..d1a9649f3 100755 --- a/FeynCalc/LoopIntegrals/FCLoopCanonicalize.m +++ b/FeynCalc/LoopIntegrals/FCLoopCanonicalize.m @@ -6,16 +6,16 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Canonicalizes indices of 1-loop integrals *) (* ------------------------------------------------------------------------ *) -FCLoopCanonicalize::usage = "FCLoopCanonicalize[expr,q,loopHead] is an auxiliary \ +FCLoopCanonicalize::usage = "FCLoopCanonicalize[exp,q,loopHead] is an auxiliary \ internal function that canonicalizes indices of 1-loop integrals \ with loop momentum q that are wrapped inside loopHead. The output is given as a \ list of four entries, from which the last one contains a list of all the unique \ @@ -24,14 +24,9 @@ integrals should be inserted into FCLoopSolutionList to obtain the final \ replacement list that will be applied to the original expression." -FCLoopCanonicalize::fail = -"Error! FCLoopCanonicalize failed to canonicalize loop integrals in `1`!"; - -FCLoopCanonicalize::notunique = -"Error! The random index generated by FCLoopCanonicalize already appears in the expression!"; - -FCLoopCanonicalize::nonloop = -"Error! The expression `1` contains non-loop terms wrapped with the head `2`!"; +FCLoopCanonicalize::failmsg = +"Error! FCLoopCanonicalize has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" Begin["`Package`"] End[] @@ -44,32 +39,52 @@ }; FCLoopCanonicalize[expr_, q_, head_, OptionsPattern[]] := - Block[ {ex, loopList, repIndexList, reversedRepIndexList, - canIndexList, uniqueCanIndexList, null1, null2, seed,res, loopIntHeads}, - seed = ToString[Unique["li"]]; + Block[{ ex, loopList, repIndexList, reversedRepIndexList, + canIndexList, uniqueCanIndexList, null1, null2, seed, + res, loopIntHeads}, + loopIntHeads = OptionValue[PaVeIntegralHeads]; + seed = ToString[Unique["cli"]]; (*This is the list of all the loop integrals in the expression.*) If[ OptionValue[FCI], ex = expr, ex = FCI[expr] ]; + + loopList = Union[Cases[ex + null1 + null2, head[_] , Infinity]]; + If[ !FreeQ[ex,seed], - Message[FCLoopCanonicalize::notunique]; + Message[FCLoopCanonicalize::failmsg,"The generated dummy indices are not unique."]; Abort[] ]; - loopList = Union[Cases[ex + null1 + null2, head[_] , Infinity]]; + If[ Cases[loopList, head[x_]/;FreeQ2[x,Join[{q},loopIntHeads]] , Infinity]=!={}, - Message[FCLoopCanonicalize::nonloop, expr, head]; + Message[FCLoopCanonicalize::failmsg, "The input expression incorrect contains nonloop terms."]; Abort[] ]; - (* Here we collect the tensor indices of each integral from the - previous list *) + + + (* Here we collect the tensor indices of each integral from the previous list *) repIndexList = - ((MapIndexed[Rule[#1,LorentzIndex[FCGV[(seed <> ToString[Identity @@ #2])], (#1/.LorentzIndex[_,dim_:4]:>dim)]] &, Cases[#, - Pair[x_, LorentzIndex[y__]] /; ! FreeQ[x, q] :> - LorentzIndex[y], Infinity] // Union] // Flatten) & /@ - loopList); + Which[ + !FreeQ[#,LorentzIndex] && FreeQ[#,CartesianIndex], + + ((MapIndexed[Rule[#1,LorentzIndex[FCGV[(seed <> ToString[Identity @@ #2])], (#1/.LorentzIndex[_,dim_:4]:>dim)]] &, + Cases[#, Pair[x_, LorentzIndex[y__]] /; ! FreeQ[x, q] :> LorentzIndex[y], Infinity] // Union] // Flatten)), + + FreeQ[#,LorentzIndex] && !FreeQ[#,CartesianIndex], + (MapIndexed[Rule[#1,CartesianIndex[FCGV[(seed <> ToString[Identity @@ #2])], (#1/.CartesianIndex[_,dim_:3]:>dim)]] &, Cases[#, + CartesianPair[x_, CartesianIndex[y__]] /; ! FreeQ[x, q] :> + CartesianIndex[y], Infinity] // Union] // Flatten), + + FreeQ[#,LorentzIndex] && FreeQ[#,CartesianIndex], + {}, + _, + Message[FCLoopCanonicalize::failmsg, "Unknown integral type."]; + Abort[] + ] & /@loopList; + (* This is the list of all the loop tensor integrals with canonicalized indices. *) canIndexList = (MapIndexed[(#1 /. First[repIndexList[[#2]]]) &, @@ -83,10 +98,7 @@ (* Final cross-check to ensure that we didn't mess anything up *) res = {loopList, reversedRepIndexList, canIndexList, uniqueCanIndexList}; If [(ex/. head->Identity) =!= (ex/.FCLoopSolutionList[res, (res[[4]]/. head->Identity)]), - Message[FCLoopCanonicalize::fail,expr]; - Print[(ex/. head->Identity)]; - Print[(ex/.FCLoopSolutionList[res, (res[[4]]/. head->Identity)])]; - Print[FCLoopSolutionList[res, (res[[4]]/. head->Identity)]]; + Message[FCLoopCanonicalize::failexp,"Failed to canonicalize loop integrals in the input expression."]; Abort[] ]; diff --git a/FeynCalc/LoopIntegrals/FCLoopEikonalPropagatorFreeQ.m b/FeynCalc/LoopIntegrals/FCLoopEikonalPropagatorFreeQ.m new file mode 100755 index 000000000..5fb35a777 --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCLoopEikonalPropagatorFreeQ.m @@ -0,0 +1,64 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCLoopEikonalPropagatorFreeQ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Returns False if the integral contains eikonal propagators *) + +(* ------------------------------------------------------------------------ *) + +FCLoopEikonalPropagatorFreeQ::usage = +"FCLoopEikonalPropagatorFreeQ[exp] checks if the integral is free of eikonal propagators \ +1/[p.q+x]. If the option First is set to False, propagators that have both a quadratic and \ +linear piece, e.g. 1/[(q-p)^2+q.r+x] will also count as eikonal propagators. The option Momentum can be \ +used to check for the presence of eikonal propagators only with respect to particular \ +momenta. The check is performed only for StandardPropagatorDenominator and \ +CartesianPropagatorDenominator."; + +FCLoopEikonalPropagatorFreeQ::failmsg = +"FCLoopEikonalPropagatorFreeQ has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +Begin["`Package`"] +End[] + +Begin["`FCLoopEikonalPropagatorFreeQ`Private`"] + +Options[FCLoopEikonalPropagatorFreeQ] = { + First -> True, + Momentum -> All +}; + + +FCLoopEikonalPropagatorFreeQ[sps_. fad_FeynAmpDenominator, OptionsPattern[]]:= + Block[{fadList,res, eikProps, optMomentum, optFirst}, + + optMomentum = OptionValue[Momentum]; + optFirst = OptionValue[First]; + + fadList = Sort[List@@fad]; + If[ optMomentum=!=All && !MatchQ[optMomentum,{__}], + Message[FCLoopEikonalPropagatorFreeQ::failmsg,"Incorrect value of the option Momentum"]; + Abort[] + ]; + + If[ optMomentum===All, + eikProps = Cases[fadList, (StandardPropagatorDenominator|CartesianPropagatorDenominator)[w_/;(w===0 && optFirst) || !optFirst, + x_/;x=!=0,_,_]:> True,Infinity], + eikProps = Cases[fadList, (StandardPropagatorDenominator|CartesianPropagatorDenominator)[w_/;(w===0 && optFirst) || !optFirst, + x_/;x=!=0 && !FreeQ2[{x},optMomentum],_,_]:> True,Infinity] + ]; + + eikProps==={} + ]/;FreeQ[sps,FeynAmpDenominator] + +FCPrint[1,"FCLoopEikonalPropagatorFreeQ.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopExtract.m b/FeynCalc/LoopIntegrals/FCLoopExtract.m index f04b18f3f..e5b3445dd 100755 --- a/FeynCalc/LoopIntegrals/FCLoopExtract.m +++ b/FeynCalc/LoopIntegrals/FCLoopExtract.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Extracts unique multiloop integrals from the given expression *) @@ -16,7 +16,7 @@ (* ------------------------------------------------------------------------ *) FCLoopExtract::usage = -"FCLoopExtract[expr,{q1,q2,...},loopHead] exctracts loop integrals \ +"FCLoopExtract[expr,{q1,q2,...},loopHead] extracts loop integrals \ that depend on q1,q2,... from the given expression " <> ToString[ Hyperlink[Style["\[RightSkeleton]", "SR"], "paclet:FeynCalc/ref/FCLoopExtract"], StandardForm] @@ -30,14 +30,26 @@ Begin["`FCLoopExtract`Private`"] Options[FCLoopExtract] = { - DropScaleless -> False, - FCI -> False, - FCLoopIBPReducableQ -> False, - FCLoopSplit -> {2,3,4}, - Factoring -> Factor, - FeynAmpDenominatorCombine -> True, - MultiLoop -> False, - PaVe -> True + CFAD -> True, + Collecting -> True, + DropScaleless -> False, + ExpandScalarProduct -> False, + Factoring -> {Factor2, 5000}, + FAD -> True, + Full -> False, + FCI -> False, + FCE -> False, + FCLoopIBPReducableQ -> False, + FCLoopSplit -> {2,3,4}, + FCLoopBasisSplit -> False, + Factoring -> Factor, + FeynAmpDenominatorCombine -> True, + GFAD -> True, + MultiLoop -> False, + Numerator -> True, + PaVe -> True, + SFAD -> True, + TimeConstrained -> 3 }; FCLoopExtract[ex_, lmoms_, loopHead_, OptionsPattern[]] := @@ -45,7 +57,7 @@ (*This is the list of all the loop integrals in the expression.*) If[ !OptionValue[FCI], - exp = FeynCalcInternal[ex], + exp = FCI[ex], exp = ex ]; @@ -54,7 +66,7 @@ ]; (* Split loop integrals from the rest *) - tmp = FCLoopSplit[exp,lmoms, FCI->True]; + tmp = FCLoopSplit[exp,lmoms, FCI->True, Collecting->False]; rel = Sort[OptionValue[FCLoopSplit]]; irrel = Complement[{1,2,3,4},rel]; @@ -65,16 +77,34 @@ rest = Plus@@tmp[[irrel]]; loopInts = FCLoopIsolate[Plus@@tmp[[rel]], lmoms, FCI->True, Head->loopHead, + FAD -> OptionValue[FAD], + CFAD -> OptionValue[CFAD], + SFAD -> OptionValue[SFAD], + Collecting -> OptionValue[Collecting], DropScaleless-> OptionValue[DropScaleless], MultiLoop-> OptionValue[MultiLoop], PaVe-> OptionValue[PaVe], - ExpandScalarProduct -> False, + Numerator-> OptionValue[Numerator], + ExpandScalarProduct -> OptionValue[ExpandScalarProduct], + Full -> OptionValue[Full], Factoring->OptionValue[Factoring], - FCLoopIBPReducableQ->OptionValue[FCLoopIBPReducableQ]]; + FCLoopIBPReducableQ->OptionValue[FCLoopIBPReducableQ], + GFAD -> OptionValue[GFAD], + Factoring -> OptionValue[Factoring], + TimeConstrained -> OptionValue[TimeConstrained] + ]; + + If[ OptionValue[FCLoopBasisSplit], + loopInts = loopInts/.loopHead[zz_] :> FCLoopBasisSplit[zz,lmoms,List->False,Head->loopHead] /. loopHead[zz_,0]:>loopHead[zz] + ]; - (* Extract unique loop integrals *) + (* Extract the unique loop integrals *) intsUnique = (Cases[loopInts+null1+null2,loopHead[__],Infinity]/.null1|null2->0)//Union; + If[ OptionValue[FCE], + {rest,loopInts,intsUnique} = FCE[{rest,loopInts,intsUnique}] + ]; + {rest,loopInts,intsUnique} ] diff --git a/FeynCalc/LoopIntegrals/FCLoopIBPReducableQ.m b/FeynCalc/LoopIntegrals/FCLoopIBPReducableQ.m index 936ae69d1..6743ca786 100755 --- a/FeynCalc/LoopIntegrals/FCLoopIBPReducableQ.m +++ b/FeynCalc/LoopIntegrals/FCLoopIBPReducableQ.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Returns True if the integral contains propagators raised to @@ -17,8 +17,8 @@ (* ------------------------------------------------------------------------ *) FCLoopIBPReducableQ::usage = -"FCLoopBasisIncompleteQ[int] checks if the integral contains propagators raised to -integer powers"; +"FCLoopIBPReducableQ[int] checks if the integral contains propagators raised to +integer powers."; FCLoopIBPReducableQ::failmsg = "ErroFCLoopIBPReducableQ has encountered a fatal problem and must abort the computation. \ @@ -32,9 +32,13 @@ (* Safe for memoization *) FCLoopIBPReducableQ[sps_. fad_FeynAmpDenominator]:= MemSet[FCLoopIBPReducableQ[sps fad], - Block[{fadList,res}, + Block[{fadList,res, propPowers}, + fadList = Sort[List@@fad]; - res = (fadList=!=Union[fadList] || MatchQ[sps, _. Power[Pair[__], _]]); + + propPowers = Union[Flatten[{1,Cases[List@@fad, (StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[__,{n_,_}]:>n, Infinity]}]]; + + res = (fadList=!=Union[fadList] || MatchQ[sps, _. Power[(Pair|CartesianPair)[__], _]] || MatchQ[propPowers,{1,__}]); res ] ]; diff --git a/FeynCalc/LoopIntegrals/FCLoopIsolate.m b/FeynCalc/LoopIntegrals/FCLoopIsolate.m index 948aa1951..4fac68244 100755 --- a/FeynCalc/LoopIntegrals/FCLoopIsolate.m +++ b/FeynCalc/LoopIntegrals/FCLoopIsolate.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Isolates loop integrals *) @@ -42,34 +42,58 @@ Begin["`FCLoopIsolate`Private`"] +fcliVerbose::usage=""; + Options[FCLoopIsolate] = { - ExceptHeads -> {}, - ExpandScalarProduct -> False, - Head -> FCGV["LoopInt"], - ClearHeads -> {FCGV["LoopInt"]}, - Collecting -> True, - DotSimplify -> True, - DiracGammaExpand -> True, - DropScaleless -> False, - Expanding -> True, + CFAD -> True, + ClearHeads -> {FCGV["LoopInt"]}, + Collecting -> True, + DiracGammaExpand -> True, + DotSimplify -> True, + DropScaleless -> False, + ExceptHeads -> {}, + ExpandScalarProduct -> False, + Expanding -> True, + FAD -> True, + FCE -> False, + FCI -> False, + FCLoopIBPReducableQ -> False, + FCVerbose -> False, + Factoring -> {Factor2, 5000}, FeynAmpDenominatorSplit -> True, - Factoring -> Factor, - FCLoopIBPReducableQ -> False, - Isolate -> False, - IsolateNames -> KK, - FCI -> False, - PaVeIntegralHeads -> FeynCalc`Package`PaVeHeadsList, - MultiLoop -> False, - PaVe->True + Full -> True, + GFAD -> True, + Head -> FCGV["LoopInt"], + Isolate -> False, + IsolateNames -> KK, + MultiLoop -> False, + Numerator -> True, + PaVe -> True, + PaVeIntegralHeads -> FeynCalc`Package`PaVeHeadsList, + SFAD -> True, + TimeConstrained -> 3 }; fullDep[z_,lmoms_]:= - (Union[Cases[ExpandScalarProduct[z,FCI->True], Momentum[x_, ___]/;!FreeQ2[x, lmoms] :> x, Infinity]] === Sort[lmoms]); + (Union[Cases[ExpandScalarProduct[z,FCI->True], (CartesianMomentum|Momentum)[x_, ___]/;!FreeQ2[x, lmoms] :> x, Infinity]] === Sort[lmoms]); FCLoopIsolate[expr_, lmoms0_List /; FreeQ[lmoms0, OptionQ], OptionsPattern[]] := - Block[ {res, null1, null2, ex,lmoms,tmp, loopIntHeads}, + Block[{ res, null1, null2, ex,lmoms,tmp, loopIntHeads, time, optExceptHeads, optHead, + dummy1, dummy2}, loopIntHeads = OptionValue[PaVeIntegralHeads]; + optExceptHeads = OptionValue[ExceptHeads]; + optHead = OptionValue[Head]; + + If [OptionValue[FCVerbose]===False, + fcliVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fcliVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1,"FCLoopIsolate: Entering.", FCDoControl->fcliVerbose]; + FCPrint[3,"FCLoopIsolate: Entering with: ", expr, FCDoControl->fcliVerbose]; If[ MatchQ[lmoms0,{{___}}], Message[FCLoopIsolate::fail, ex]; @@ -81,10 +105,13 @@ lmoms = lmoms0 ]; + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying FCI and ClearHeads.", FCDoControl->fcliVerbose]; If[OptionValue[FCI], ex = expr/. (Map[Rule[#, Identity] &, OptionValue[ClearHeads]]), ex = FCI[expr]/. (Map[Rule[#, Identity] &, OptionValue[ClearHeads]]) ]; + FCPrint[1, "FCLoopIsolate: Done applying FCI and ClearHeads, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose]; If[ lmoms==={}, (*Nothing to do!*) @@ -92,70 +119,162 @@ ]; If[ OptionValue[Expanding], + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying Expand2.", FCDoControl->fcliVerbose]; ex = Expand2[ex, lmoms]; + FCPrint[1, "FCLoopIsolate: Done applying Expand2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] ]; (* Here we pull loop momenta out of Dirac slashes *) If[ OptionValue[ExpandScalarProduct], + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying ExpandScalarProduct.", FCDoControl->fcliVerbose]; tmp = FCSplit[ex, lmoms, Expanding->OptionValue[Expanding]]; - ex = tmp[[1]]+ ExpandScalarProduct[tmp[[2]],Momentum->lmoms] + ex = tmp[[1]]+ ExpandScalarProduct[tmp[[2]],Momentum->lmoms,Full->OptionValue[Full]]; + FCPrint[1, "FCLoopIsolate: Done applying ExpandScalarProduct, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] ]; (* Here we pull loop momenta out of Dirac slashes *) If[ OptionValue[DiracGammaExpand] && !FreeQ[ex,DiracGamma], + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying DiracGammaExpand.", FCDoControl->fcliVerbose]; tmp = FCSplit[ex, lmoms, Expanding->OptionValue[Expanding]]; - ex = tmp[[1]]+ tmp[[2]]/. DiracGamma[x_,dim_:4]/;!FreeQ2[x,lmoms] :> DiracGammaExpand[DiracGamma[x,dim]] + ex = tmp[[1]]+ tmp[[2]]/. DiracGamma[x_,dim_:4]/;!FreeQ2[x,lmoms] :> DiracGammaExpand[DiracGamma[x,dim]]; + FCPrint[1, "FCLoopIsolate: Done applying DiracGammaExpand, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] ]; (* and out of the DOTs *) If[ OptionValue[DotSimplify] && !FreeQ[ex,DOT], + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying DotSimplify.", FCDoControl->fcliVerbose]; tmp = FCSplit[ex, lmoms, Expanding->OptionValue[Expanding]]; - ex = tmp[[1]]+ DotSimplify[tmp[[2]]] + ex = tmp[[1]]+ DotSimplify[tmp[[2]]]; + FCPrint[1, "FCLoopIsolate: Done applying DotSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] ]; If[ OptionValue[Collecting], - ex = Collect2[ex,lmoms,Factoring->OptionValue[Factoring]]; + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying Collect2.", FCDoControl->fcliVerbose]; + + If[ TrueQ[OptionValue[Numerator]], + ex = Collect2[ex,lmoms,Factoring->OptionValue[Factoring], TimeConstrained->OptionValue[TimeConstrained]], + (*If we care only about the denominators, we can speed up this step*) + ex = Collect2[ex,FeynAmpDenominator,Factoring->OptionValue[Factoring], TimeConstrained->OptionValue[TimeConstrained]] + ]; + + + FCPrint[1, "FCLoopIsolate: Done applying Collect2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] ]; If[ OptionValue[FeynAmpDenominatorSplit] && !FreeQ[ex,FeynAmpDenominator], - ex = FeynAmpDenominatorSplit[ex,Momentum->lmoms] + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying FeynAmpDenominatorSplit.", FCDoControl->fcliVerbose]; + ex = FeynAmpDenominatorSplit[ex,Momentum->lmoms]; + FCPrint[1, "FCLoopIsolate: Done applying FeynAmpDenominatorSplit, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] ]; - res = (Map[(SelectFree[#, lmoms]* - OptionValue[Head][SelectNotFree[#, lmoms]]) &, - ex + null1 + null2] /. {null1 | null2 -> 0} /. - OptionValue[Head][1] -> 1); - res = res /. {OptionValue[Head][x_] /; !FreeQ2[x, OptionValue[ExceptHeads]] :> x}; - If[ Together[(res /. OptionValue[Head] -> Identity)-ex] =!= 0, + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Splitting products of loop and non-loop terms.", FCDoControl->fcliVerbose]; + res = (Map[(SelectFree[#, lmoms] optHead[SelectNotFree[#, lmoms]]) &, ex + null1 + null2] /. {null1 | null2 -> 0} /. optHead[1] -> 1); + FCPrint[1, "FCLoopIsolate: Done splitting products of loop and non-loop terms, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose]; + + + If[ optExceptHeads=!={}, + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying the option ExceptHeads.", FCDoControl->fcliVerbose]; + res = res /. {optHead[x_] /; !FreeQ2[x, optExceptHeads] :> x}; + FCPrint[1, "FCLoopIsolate: Done applying the option ExceptHeads, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] + ]; + + + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Checking the intermediate result.", FCDoControl->fcliVerbose]; + If[ Together[(res /. optHead -> Identity)-ex] =!= 0, Message[FCLoopIsolate::fail, ex]; Abort[] ]; + FCPrint[1, "FCLoopIsolate: Done checking the intermediate result, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose]; If[ OptionValue[DropScaleless], - res = res /. OptionValue[Head][z__]/; FreeQ2[z,Join[{FeynAmpDenominator},loopIntHeads]] :> 0; + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Removing scaleless integrals.", FCDoControl->fcliVerbose]; + res = res /. optHead[z__]/; FreeQ2[z,Join[{FeynAmpDenominator},loopIntHeads]] :> 0; + FCPrint[1, "FCLoopIsolate: Done removing scaleless integrals, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose]; ]; If[ OptionValue[Isolate], - res = Isolate[res,OptionValue[Head],IsolateNames->OptionValue[IsolateNames]]/. - OptionValue[Head][x_] :> OptionValue[Head][FRH[x]] + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying Isolate.", FCDoControl->fcliVerbose]; + res = Isolate[res,optHead,IsolateNames->OptionValue[IsolateNames]]/. optHead[x_] :> optHead[FRH[x]]; + FCPrint[1, "FCLoopIsolate: Done applying isolate, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose]; ]; - If [ !FreeQ[res/. OptionValue[Head][__] :> 1, lmoms] & , + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Checking the intermediate result.", FCDoControl->fcliVerbose]; + If [ !FreeQ[res/. optHead[__] :> 1, lmoms] & , Message[FCLoopIsolate::fail, ex]; Abort[] ]; + FCPrint[1, "FCLoopIsolate: Done checking the intermediate result, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose]; + + If [ !OptionValue[Numerator], + + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying the option Numerator.", FCDoControl->fcliVerbose]; + res = res /. optHead[z_] :> optHead[SelectNotFree[z dummy1 dummy2,FeynAmpDenominator]]*SelectFree[z dummy1 dummy2,FeynAmpDenominator] /. dummy1|dummy2->1; + FCPrint[1, "FCLoopIsolate: Done applying the option Numerator, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] + ]; If [ OptionValue[MultiLoop], - res = res /. OptionValue[Head][z__]/; !fullDep[z,lmoms0] :> z; + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying the option MultiLoop.", FCDoControl->fcliVerbose]; + res = res /. optHead[z__]/; !fullDep[z,lmoms0] :> z; + FCPrint[1, "FCLoopIsolate: Done applying the option MultiLoop, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] + ]; + + If [ !OptionValue[SFAD] && !FreeQ[res,StandardPropagatorDenominator], + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying the option SFAD.", FCDoControl->fcliVerbose]; + res = res /. optHead[z__]/; !FreeQ[{z}, StandardPropagatorDenominator] :> z; + FCPrint[1, "FCLoopIsolate: Done applying the option SFAD, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] + ]; + + If [ !OptionValue[CFAD] && !FreeQ[res,CartesianPropagatorDenominator], + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying the option CFAD.", FCDoControl->fcliVerbose]; + res = res /. optHead[z__]/; !FreeQ[{z}, CartesianPropagatorDenominator] :> z; + FCPrint[1, "FCLoopIsolate: Done applying the option CFAD, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] ]; - (* Keep only integrals that are IBP-reducable *) + If [ !OptionValue[GFAD] && !FreeQ[res,GenericPropagatorDenominator], + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying the option GFAD.", FCDoControl->fcliVerbose]; + res = res /. optHead[z__]/; !FreeQ[{z}, GenericPropagatorDenominator] :> z; + FCPrint[1, "FCLoopIsolate: Done applying the option GFAD, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] + ]; + + If [ !OptionValue[FAD] && !FreeQ[res,PropagatorDenominator], + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying the option FAD.", FCDoControl->fcliVerbose]; + res = res /. optHead[z__]/; !FreeQ[{z}, PropagatorDenominator] :> z; + FCPrint[1, "FCLoopIsolate: Done applying the option FAD, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] + ]; + + (* Keep only integrals that are IBP-reducible *) If [ OptionValue[FCLoopIBPReducableQ], - res = res /. OptionValue[Head][z__]/; !FCLoopIBPReducableQ[z] :> z; + time = AbsoluteTime[]; + FCPrint[1,"FCLoopIsolate: Applying the option FCLoopIBPReducableQ.", FCDoControl->fcliVerbose]; + res = res /. optHead[z__]/; !FCLoopIBPReducableQ[z] :> z; + FCPrint[1, "FCLoopIsolate: Done applying the option FCLoopIBPReducableQ, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcliVerbose] ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + FCPrint[1,"FCLoopIsolate: Leaving.", FCDoControl->fcliVerbose]; + FCPrint[3,"FCLoopIsolate: Leaving with: ", res, FCDoControl->fcliVerbose]; res diff --git a/FeynCalc/LoopIntegrals/FCLoopMixedIntegralQ.m b/FeynCalc/LoopIntegrals/FCLoopMixedIntegralQ.m new file mode 100755 index 000000000..c3d60b15b --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCLoopMixedIntegralQ.m @@ -0,0 +1,61 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCLoopMixedIntegralQ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Returns True if the integral depends both on Lorentzian and + Cartesian quantities *) + +(* ------------------------------------------------------------------------ *) + +FCLoopMixedIntegralQ::usage = +"FCLoopMixedIntegralQ[exp] returns True if the integral contains both Lorentz +and Cartesian indices and momenta."; + +FCLoopMixedIntegralQ::failmsg = +"FCLoopMixedIntegralQ has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +Begin["`Package`"] +End[] + +Begin["`FCLoopMixedIntegralQ`Private`"] + +FCLoopMixedIntegralQ[sps_. fad_FeynAmpDenominator]:= + Block[{heads,res}, + + heads = Cases[sps fad, (h:LorentzIndex|CartesianIndex|ExplicitLorentzIndex|Momentum|CartesianMomentum|TemporalMomentum)[__]:>h,Infinity]//Union; + + Which[ + heads==={}, + res=False, + + (FreeQ2[heads,{LorentzIndex,Momentum,ExplicitLorentzIndex,TemporalMomentum}] && !FreeQ2[heads,{CartesianIndex,CartesianMomentum}]) || + (FreeQ2[heads,{LorentzIndex,Momentum,CartesianIndex,CartesianMomentum}] && !FreeQ2[heads,{ExplicitLorentzIndex,TemporalMomentum}]) || + (FreeQ2[heads,{ExplicitLorentzIndex,TemporalMomentum,CartesianIndex,CartesianMomentum}] && !FreeQ2[heads,{LorentzIndex,Momentum}]), + res=False, + + (!FreeQ2[heads,{LorentzIndex,Momentum}] && !FreeQ2[heads,{CartesianIndex,CartesianMomentum}]) || + (!FreeQ2[heads,{LorentzIndex,Momentum}] && !FreeQ2[heads,{ExplicitLorentzIndex,TemporalMomentum}]) || + (!FreeQ2[heads,{CartesianIndex,CartesianMomentum}] && !FreeQ2[heads,{ExplicitLorentzIndex,TemporalMomentum}]) || + (!FreeQ2[heads,{LorentzIndex,Momentum}] && !FreeQ2[heads,{ExplicitLorentzIndex,TemporalMomentum}] && !FreeQ2[heads,{CartesianIndex,CartesianMomentum}]), + res=True, + + True, + Message[FCLoopMixedIntegralQ::failmsg,"Unknown combination of heads."]; + Abort[] + ]; + + res + ]/;FreeQ[sps,FeynAmpDenominator] + +FCPrint[1,"FCLoopMixedIntegralQ.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.m b/FeynCalc/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.m new file mode 100755 index 000000000..0a3516b3f --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.m @@ -0,0 +1,117 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCLoopMixedToCartesianAndTemporal *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Converts mixed integrals to Cartesian and temporal + integrals *) + +(* ------------------------------------------------------------------------ *) + +FCLoopMixedToCartesianAndTemporal::usage = +"FCLoopMixedToCartesianAndTemporal[int, {q1, q2, ...}] attempts to convert loop \ +integrals that contain both Lorentz and Cartesian or temporal indices/momenta to pure \ +temporal and Cartesian indices."; + +FCLoopMixedToCartesianAndTemporal::failmsg = +"FCLoopMixedToCartesianAndTemporal has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +Begin["`Package`"] +End[] + +Begin["`FCLoopMixedToCartesianAndTemporal`Private`"] + +loopMomenta::usage=""; +prefactor::usage=""; + +Options[FCLoopMixedToCartesianAndTemporal] = { + FCE -> False, + Uncontract -> False +}; + +FCLoopMixedToCartesianAndTemporal[sps_. fad_FeynAmpDenominator, lmoms_List/;lmoms=!={}, OptionsPattern[]]:= + Block[{fadConverted, spsConverted, res}, + + If[ FreeQ2[sps fad,{Momentum,LorentzIndex,Pair}] || FreeQ2[sps fad,lmoms], + (* Nothing to do *) + Return[sps fad] + ]; + + loopMomenta=lmoms; + + prefactor=1; + + If[!FreeQ[fad,PropagatorDenominator], + fadConverted = ToSFAD[fad], + fadConverted = fad + ]; + + spsConverted = LorentzToCartesian[sps,FCI->True]; + + If[ OptionValue[Uncontract], + spsConverted = Uncontract[spsConverted, Sequence@@lmoms, Pair -> All, CartesianPair->All] + ]; + + fadConverted = MomentumCombine[fadConverted,FCI->True] /. StandardPropagatorDenominator-> SFADToCFAD/. + SFADToCFAD -> StandardPropagatorDenominator; + + res = prefactor*spsConverted*fadConverted; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]/;FreeQ[sps,FeynAmpDenominator] + + + +SFADToCFAD[x_, y_, mm_, {n_,s_}]:= + Block[{tp,sp,cfadSlot1,cfadSlot2,relSign,tmp}, + {sp,tp} = FCSplit[LorentzToCartesian[Pair[x,x],ExpandScalarProduct->False,FCI->False],{ExplicitLorentzIndex[0]}]; + + Which[ + MatchQ[sp, CartesianPair[a_CartesianMomentum,a_CartesianMomentum]], + cfadSlot1 = First[sp]; + relSign = 1, + MatchQ[sp, -CartesianPair[a_CartesianMomentum,a_CartesianMomentum]], + cfadSlot1 = First[-sp]; + relSign = -1, + sp===0, + cfadSlot1 = 0; + relSign = -1, + True, + Return[StandardPropagatorDenominator[x,y,mm,{n,s}]] + ]; + + If[ FreeQ2[y,loopMomenta], + tp = tp + y; + cfadSlot2 = 0, + + tmp = FCSplit[LorentzToCartesian[y,ExpandScalarProduct->False,FCI->False],{ExplicitLorentzIndex[0]}]; + tp = tp + tmp[[2]]; + cfadSlot2 = tmp[[1]] + ]; + + prefactor=prefactor*(relSign^n); + + CartesianPropagatorDenominator[cfadSlot1, cfadSlot2/relSign, tp/relSign+mm/relSign,{n,s/relSign}] + ]/;!FreeQ2[x,loopMomenta] || !FreeQ2[y,loopMomenta]; + + + + + + +FCPrint[1,"FCLoopMixedToCartesianAndTemporal.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopNonIntegerPropagatorPowersFreeQ.m b/FeynCalc/LoopIntegrals/FCLoopNonIntegerPropagatorPowersFreeQ.m new file mode 100755 index 000000000..eb31f7c21 --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCLoopNonIntegerPropagatorPowersFreeQ.m @@ -0,0 +1,36 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCLoopNonIntegerPropagatorPowersFreeQ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Returns True if the integral contains no noninteger + propagator powers *) + +(* ------------------------------------------------------------------------ *) + +FCLoopNonIntegerPropagatorPowersFreeQ::usage = +"FCLoopNonIntegerPropagatorPowersFreeQ[int] checks if the integral contains propagators raised to \ +noninteger (i.e. fractional or symbolic) powers."; + +Begin["`Package`"] +End[] + +Begin["`FCLoopNonIntegerPropagatorPowersFreeQ`Private`"] + + +FCLoopNonIntegerPropagatorPowersFreeQ[sps_. fad_FeynAmpDenominator]:= + Block[{props}, + props = Cases[fad, (StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatoDenominator)[__,{n_/;Head[n]=!=Integer,_}],Infinity]; + props==={} + ]/;FreeQ[sps,FeynAmpDenominator] + +FCPrint[1,"FCLoopNonIntegerPropagatorPowersFreeQ.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopPropagatorPowersCombine.m b/FeynCalc/LoopIntegrals/FCLoopPropagatorPowersCombine.m new file mode 100644 index 000000000..20fbac43c --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCLoopPropagatorPowersCombine.m @@ -0,0 +1,80 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCLoopPropagatorPowersCombine *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Combines propagator powers . *) + +(* ------------------------------------------------------------------------ *) + +FCLoopPropagatorPowersCombine::usage = +"FCLoopPropagatorPowersCombine[exp] combines the same propagators in a \ +FeynAmpDenominator to one propagator raised to an integer power."; + +FCLoopPropagatorPowersCombine::failmsg = +"FCLoopPropagatorPowersCombine has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCLoopPropagatorPowersCombine`Private`"] + +Options[FCLoopPropagatorPowersCombine] = { + FCE -> False, + FCI -> False +}; + +FCLoopPropagatorPowersCombine[expr_, OptionsPattern[]] := + Block[{ex, res, fadsList, fadsListEval, repRule, fad}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[FreeQ2[ex, {StandardPropagatorDenominator, CartesianPropagatorDenominator, GenericPropagatorDenominator}], + Return[ex] + ]; + + fadsList = Cases2[ex, FeynAmpDenominator]; + + fadsListEval = fadsList /. FeynAmpDenominator -> FeynCalc`Package`fdsor /. FeynAmpDenominator -> fad /. { + fad[a___, + (h:StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[x__, {n1_Integer,s_}], + (h:StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[x__, {n2_Integer,s_}], + b___] :> + fad[a,h[x,{n1+n2,s}],b] + } /. (StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[__, {0,_}] :> Unevaluated[Sequence[]] /. + fad[] -> 1 /. fad -> FeynAmpDenominator; + + repRule = Thread[Rule[fadsList,fadsListEval]]; + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + + ]; + + + + + + +FCPrint[1,"FCLoopPropagatorPowersCombine.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopPropagatorPowersExpand.m b/FeynCalc/LoopIntegrals/FCLoopPropagatorPowersExpand.m new file mode 100644 index 000000000..b11f5331a --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCLoopPropagatorPowersExpand.m @@ -0,0 +1,76 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCLoopPropagatorPowersExpand *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Expands propagator powers . *) + +(* ------------------------------------------------------------------------ *) + +FCLoopPropagatorPowersExpand::usage = +"FCLoopPropagatorPowersExpand[exp] rewrites propagators raised to integer \ +powers as products."; + +FCLoopPropagatorPowersExpand::failmsg = +"FCLoopPropagatorPowersExpand has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCLoopPropagatorPowersExpand`Private`"] + +Options[FCLoopPropagatorPowersExpand] = { + FCE -> False, + FCI -> False +}; + +FCLoopPropagatorPowersExpand[expr_, OptionsPattern[]] := + Block[{ex, res, fadsList, fadsListEval, repRule}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[FreeQ2[ex, {StandardPropagatorDenominator, CartesianPropagatorDenominator, GenericPropagatorDenominator}], + Return[ex] + ]; + + fadsList = Cases2[ex, FeynAmpDenominator]; + + fadsListEval = fadsList /. { + (h:StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[x__, {n_Integer,s_}]/;Abs[n]>1 :> + Sequence@@ConstantArray[h[x,{1,s}],n] + }; + + repRule = Thread[Rule[fadsList,fadsListEval]]; + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + + ]; + + + + + + +FCPrint[1,"FCLoopPropagatorPowersExpand.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopRemoveNegativePropagatorPowers.m b/FeynCalc/LoopIntegrals/FCLoopRemoveNegativePropagatorPowers.m new file mode 100644 index 000000000..9fccbc0b0 --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCLoopRemoveNegativePropagatorPowers.m @@ -0,0 +1,82 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCLoopRemoveNegativePropagatorPowers *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Expands propagator powers . *) + +(* ------------------------------------------------------------------------ *) + +FCLoopRemoveNegativePropagatorPowers::usage = +"FCLoopRemoveNegativePropagatorPowers[exp] rewrites propagators raised to integer \ +powers as products."; + +FCLoopRemoveNegativePropagatorPowers::failmsg = +"FCLoopRemoveNegativePropagatorPowers has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCLoopRemoveNegativePropagatorPowers`Private`"] + +Options[FCLoopRemoveNegativePropagatorPowers] = { + FCE -> False, + FCI -> False, + FCLoopPropagatorPowersCombine -> True +}; + +FCLoopRemoveNegativePropagatorPowers[expr_, OptionsPattern[]] := + Block[{ex, res, fadsList, fadsListEval, repRule, fad}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ OptionValue[FCLoopPropagatorPowersCombine], + ex = FCLoopPropagatorPowersCombine[ex,FCI->True] + ]; + + If[FreeQ2[ex, {StandardPropagatorDenominator, CartesianPropagatorDenominator, GenericPropagatorDenominator}], + Return[ex] + ]; + + fadsList = Cases2[ex, FeynAmpDenominator]; + + fadsListEval = fadsList /. FeynAmpDenominator -> fad /. { + fad[a___, + (h:StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[x__, {n_Integer,s_}], b___]/; n<0 :> + FeynAmpDenominatorExplicit[FeynAmpDenominator[h[x,{n,s}]],FCI->True] fad[a,b] + } /. fad[] -> 1 /. fad -> FeynAmpDenominator; + + repRule = Thread[Rule[fadsList,fadsListEval]]; + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + + ]; + + + + + + +FCPrint[1,"FCLoopRemoveNegativePropagatorPowers.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopSamePropagatorHeadsQ.m b/FeynCalc/LoopIntegrals/FCLoopSamePropagatorHeadsQ.m new file mode 100755 index 000000000..15a4d0d5a --- /dev/null +++ b/FeynCalc/LoopIntegrals/FCLoopSamePropagatorHeadsQ.m @@ -0,0 +1,47 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCLoopSamePropagatorHeadsQ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Returns True if the FeynAmpDenominator contains propagator + denominators of the same type. *) + +(* ------------------------------------------------------------------------ *) + +FCLoopSamePropagatorHeadsQ::usage = +"FCLoopSamePropagatorHeadsQ[exp] returns True if the FeynAmpDenominator of exp \ +contains only propagator denominators of the same type (e.g. only \ +StandardPropagatorDenominator or only CartesianPropagatorDenominator)."; + +FCLoopSamePropagatorHeadsQ::failmsg = +"FCLoopSamePropagatorHeadsQ has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +Begin["`Package`"] +End[] + +Begin["`FCLoopSamePropagatorHeadsQ`Private`"] + +FCLoopSamePropagatorHeadsQ[sps_. fad_FeynAmpDenominator]:= + Block[{heads}, + + heads = Cases[sps fad, (h:PropagatorDenominator|StandardPropagatorDenominator|CartesianPropagatorDenominator|GenericPropagatorDenominator)[__]:>h,Infinity]// + Union; + If[ heads==={}, + Message[FCLoopSamePropagatorHeadsQ::failmsg,"The integral contains unknown propagator denominators."]; + ]; + + (Length[heads] === 1) + + ]/;FreeQ[sps,FeynAmpDenominator] + +FCPrint[1,"FCLoopSamePropagatorHeadsQ.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FCLoopSolutionList.m b/FeynCalc/LoopIntegrals/FCLoopSolutionList.m index d5ec1f432..9ff9c04a7 100755 --- a/FeynCalc/LoopIntegrals/FCLoopSolutionList.m +++ b/FeynCalc/LoopIntegrals/FCLoopSolutionList.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Creates subsitution lists of type Integral-> @@ -23,14 +23,9 @@ simplified integrals solsList to create the substitution list of type \ \"Integral\" -> \"simplified Integral\"." -FCLoopSolutionList::fail= -"FCLoopSolutionList failed to create a list of solutions out of the given \ -integrals"; - -FCLoopSolutionList::indexmissmatch= -"FCLoopSolutionList found that the Lorentz indices in the list of solutions \ -are different from those in the list of unique integrals. `1` doesn't match `2` and -`3` is not zero!"; +FCLoopSolutionList::failmsg = +"Error! FCLoopSolutionList has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" Begin["`Package`"] @@ -49,36 +44,32 @@ (* Small cross-check *) If[ Length[uniqueCanIndexList]=!=Length[solsList] || Length[canIndexList]=!=Length[reversedRepIndexList], - Message[FCLoopSolutionList::fail]; - Print["1"]; + Message[FCLoopSolutionList::failmsg, "The input is inconsistent."]; Abort[] ]; - (* Also check that the solutions have the same Lorentz indices - as the integrals for which they will be substituted *) - Inner[If[ ((z1=Union@Sort@Cases[#1, LorentzIndex[_, _ : 4], Infinity])=!= - (z2=Union@Sort@Cases[#2, LorentzIndex[_, _ : 4], Infinity])) && !MatchQ[z3=#2,0 | _[0] ], - Message[FCLoopSolutionList::indexmissmatch,z1,z2,z3]; - Abort[] - ]&,uniqueCanIndexList,solsList]; - - (* This is the replacement list Integral -> Solution for the integrals - with canonicalized indices *) + + + Inner[If[((z1=Union@Sort@Cases[#1, (CartesianIndex|LorentzIndex)[_, ___], Infinity])=!= + (z2=Union@Sort@Cases[#2, (CartesianIndex|LorentzIndex)[_, ___], Infinity])) && !MatchQ[z3=#2,0 | _[0] ], + Message[FCLoopSolutionList::failmsg,"The indices in the solutions list are different from those in the unique integrals list."]; + Abort[]]&,uniqueCanIndexList,solsList]; + + (* This is the replacement list Integral -> Solution for the integrals with canonicalized indices. *) repSolList = MapIndexed[(Rule[#1, First[solsList[[#2]]]]) &, uniqueCanIndexList]; - (* This is the more general replacement list for integrals with - indices that are not canonicalized*) + + (* This is the more general replacement list for integrals with indices that are not canonicalized *) reducedLoopList = MapIndexed[((#1 /.First[(reversedRepIndexList[[#2]])])) &, (canIndexList /.repSolList)]; - (*This is the final replacement list Original integral -> Reduced integral*) + + (* This is the final replacement list Original integral -> Reduced integral *) finalRepList = MapIndexed[(Rule[#1, First[reducedLoopList[[#2]]]]) &, loopList]; - (* Check also that the final replacement list contains no - canonicalized indices *) - If[ !FreeQ2[finalRepList, - Union[Cases[canIndexList, LorentzIndex[_, _ : 4], Infinity]]], - Message[FCLoopSolutionList::fail]; - Print["3"]; + (* Check also that the final replacement list contains no canonicalized indices *) + If[ !FreeQ2[finalRepList, Union[Cases[canIndexList, LorentzIndex[_, _ : 4], Infinity]]] || + !FreeQ2[finalRepList, Union[Cases[canIndexList, CartesianIndex[_, _ : 3], Infinity]]], + Message[FCLoopSolutionList::failmsg,"Failed to create a list of solutions out of the given integrals."]; Abort[] ]; diff --git a/FeynCalc/LoopIntegrals/FCLoopSplit.m b/FeynCalc/LoopIntegrals/FCLoopSplit.m index 45e94aced..68edae1c0 100755 --- a/FeynCalc/LoopIntegrals/FCLoopSplit.m +++ b/FeynCalc/LoopIntegrals/FCLoopSplit.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Splits the expression into pieces with different @@ -17,7 +17,7 @@ (* ------------------------------------------------------------------------ *) FCLoopSplit::usage = -"FCLoopSplit[expr,{q1,q2,...}] separates expr \ +"FCLoopSplit[exp,{q1,q2,...}] separates exp \ into following four pieces: \n 1) terms that are free of loop integrals \ 2) terms with scalar loop integrals \ @@ -25,9 +25,9 @@ are contracted \ 4) terms with tensor loop integrals, where at least some \ loop momenta have free indices \ -The result is returned as a list with the 4 above elements"; +The result is returned as a list with the 4 above elements."; -FCLoopSplit::fail = +FCLoopSplit::failmsg = "Splitting the expression `1` into loop and non-loop pieces failed!"; Begin["`Package`"] @@ -36,23 +36,25 @@ Begin["`FCLoopSplit`Private`"] Options[FCLoopSplit] = { - Collecting -> True, - DotSimplify -> True, - DiracGammaExpand -> True, - Expanding -> True, - FCI -> False, - PaVeIntegralHeads -> FeynCalc`Package`PaVeHeadsList + Collecting -> True, + DiracGammaExpand -> True, + DotSimplify -> True, + Expanding -> True, + FCE -> False, + FCI -> False, + Factoring -> Factor2, + PaVeIntegralHeads -> FeynCalc`Package`PaVeHeadsList }; FCLoopSplit[expr_, lmoms_List /; FreeQ[lmoms, OptionQ], OptionsPattern[]] := Block[{ null1, null2, ex, loopFree, loopScalar, loopTensorQP, loopTensorFreeInd,oldLoopFree,oldLoopScalar, - addToLoopScalar,tmp,loopIntHeads}, + addToLoopScalar,tmp,loopIntHeads, res}, loopIntHeads = OptionValue[PaVeIntegralHeads]; If[ MatchQ[lmoms,{{___}}], - Message[FCLoopSplit::fail, ex]; + Message[FCLoopSplit::failmsg, ex]; Abort[] ]; @@ -77,15 +79,19 @@ ]; If[ OptionValue[Collecting], - ex = Collect2[ex,lmoms]; + ex = Collect2[ex,Join[lmoms,loopIntHeads],Factoring->OptionValue[Factoring]]; ]; + loopFree = Select[ex+ null1+ null2, FreeQ2[#,Join[lmoms,loopIntHeads]]&]/. {null1|null2 -> 0}; + loopScalar = Select[ex+ null1+ null2, - (!FreeQ2[#,Join[lmoms,loopIntHeads]] && FreeQ2[# /. FeynAmpDenominator[__] :> 1, lmoms]) &]/. {null1|null2 -> 0}; + (!FreeQ2[#,Join[lmoms,loopIntHeads]] && FreeQ2[# /. FeynAmpDenominator[__] :> Unique[], lmoms]) &]/. {null1|null2 -> 0}; + loopTensorQP = Select[ex-loopScalar+ null1+ null2, - (!FreeQ2[#,lmoms] && FreeQ2[# /. {FeynAmpDenominator[__] :> 1, - Pair[Momentum[a_,_:4],Momentum[b_,_:4]]/;!FreeQ2[{a,b},lmoms] :> 1}, lmoms]) &]/. {null1|null2 -> 0}; + (!FreeQ2[#,lmoms] && FreeQ2[# /. {FeynAmpDenominator[__] :> Unique[], + (Pair|CartesianPair|TemporalPair)[(CartesianMomentum|TemporalMomentum|Momentum)[a_,___],(CartesianMomentum|ExplicitLorentzIndex|Momentum)[b_,___]]/;!FreeQ2[{a,b},lmoms] :> Unique[]}, lmoms]) &]/. {null1|null2 -> 0}; + loopTensorFreeInd = ex - loopFree - loopScalar - loopTensorQP; If[ OptionValue[Collecting], @@ -101,20 +107,27 @@ {loopFree,addToLoopScalar} = FCSplit[loopFree,loopIntHeads]; loopScalar = loopScalar + addToLoopScalar; If[ Together[(loopScalar+loopFree)-(oldLoopFree+oldLoopScalar)]=!=0, - Message[FCLoopSplit::fail, ex]; + Message[FCLoopSplit::failmsg, ex]; Abort[] ]; (*Check that different pieces are what they should be *) If[!FreeQ2[loopFree,{lmoms}] || !FreeQ2[loopScalar/. FeynAmpDenominator[__] :> Unique[],{lmoms}] || - !FreeQ2[loopTensorQP/.Pair[Momentum[a_,_:4],Momentum[b_,_:4]]/;!FreeQ2[{a,b},lmoms] :> 0,{lmoms}] || - !FreeQ2[loopTensorFreeInd/.Pair[Momentum[a_,_:4],LorentzIndex[_,_:4]]/;!FreeQ2[a,lmoms] :> 0,{lmoms}] || + !FreeQ2[loopTensorQP/.(Pair|CartesianPair|TemporalPair)[(CartesianMomentum|Momentum|TemporalMomentum)[a_,___],(CartesianMomentum|Momentum|ExplicitLorentzIndex)[b_,___]]/;!FreeQ2[{a,b},lmoms] :> Unique[],{lmoms}] || + !FreeQ2[loopTensorFreeInd/.(Pair|CartesianPair)[(Momentum|CartesianMomentum)[a_,___],(LorentzIndex|CartesianIndex)[_,___]]/;!FreeQ2[a,lmoms] :> Unique[],{lmoms}] || Together[loopFree+loopScalar+loopTensorQP+loopTensorFreeInd - ex]=!=0, - Message[FCLoopSplit::fail, ex]; + Message[FCLoopSplit::failmsg, ex]; Abort[] ]; - {loopFree,loopScalar,loopTensorQP,loopTensorFreeInd} + + res = {loopFree,loopScalar,loopTensorQP,loopTensorFreeInd}; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res ]; FCPrint[1,"FCLoopSplit.m loaded."]; diff --git a/FeynCalc/LoopIntegrals/FCMultiLoopTID.m b/FeynCalc/LoopIntegrals/FCMultiLoopTID.m index 16a9656aa..80c67806c 100644 --- a/FeynCalc/LoopIntegrals/FCMultiLoopTID.m +++ b/FeynCalc/LoopIntegrals/FCMultiLoopTID.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Tensor reduction of multi-loop integrals *) @@ -32,6 +32,10 @@ 1-loop tensor decompositions. For that you should use TID. The input expression \ will not be processed further."; +FCMultiLoopTID::gramzero = +"Warning! One of the multi-loop tensor integrals contains vanishing Gram determinants. \ +FCMultiLoopTID cannot handle such cases properly."; + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -45,25 +49,31 @@ mltidVerbose::usage=""; Options[FCMultiLoopTID] = { - Dimension -> D, - Collecting -> True, - Contract -> True, - DiracSimplify -> True, + ApartFF -> True, + Collecting -> True, + Contract -> True, + Dimension -> D, + DiracSimplify -> True, ExpandScalarProduct -> True, - FCI -> False, - FCE -> False, - FCVerbose -> False, - FDS -> True, - ApartFF -> True + Factoring -> {Factor2, 5000}, + FCE -> False, + FCI -> False, + FCVerbose -> False, + FDS -> True, + TimeConstrained -> 3 }; FCMultiLoopTID[expr_ , qs_List/; FreeQ[qs, OptionQ], OptionsPattern[]] := - Block[ { n, ex, rest,loopInts,intsUnique, repRule,ruleUncontract,solsList, - null1, null2, res, tmpli}, + Block[{ n, ex, rest, loopInts, intsUnique, repRule, solsList, + null1, null2, res, tmpli, time, mltidIsolate, optFactoring, + optTimeConstrained}, + + optFactoring = OptionValue[Factoring]; + optTimeConstrained = OptionValue[TimeConstrained]; If [OptionValue[FCVerbose]===False, mltidVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], mltidVerbose=OptionValue[FCVerbose] ]; ]; @@ -78,72 +88,123 @@ ex = FCI[expr] ]; + FCPrint[1,"FCMultiLoopTID: Entering. ", FCDoControl->mltidVerbose]; FCPrint[3,"FCMultiLoopTID: Entering FCMultiLoopTID with: ", ex, FCDoControl->mltidVerbose]; n = OptionValue[Dimension]; - ruleUncontract = { - DiracGamma[Momentum[x_, dim_:4], dim_:4] /;!FreeQ2[x, qs] :> - (tmpli=Unique[]; Pair[Momentum[x,dim],LorentzIndex[tmpli,dim]] DiracGamma[LorentzIndex[tmpli,dim],dim]), - Eps[a___,Momentum[x_, dim_:4], b___] /;!FreeQ2[x, qs] :> - (tmpli=Unique[]; Pair[Momentum[x,dim],LorentzIndex[tmpli,dim]] Eps[a, LorentzIndex[tmpli,dim], b]) - }; - If[ FreeQ2[ex,qs], Return[ex] ]; - If[ OptionValue[Contract] && !FreeQ[ex,LorentzIndex], - ex = Contract[ex, FCI->True] + If[ OptionValue[Contract] && !FreeQ2[ex, {LorentzIndex, CartesianIndex}], + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying Contract.", FCDoControl->mltidVerbose]; + ex = Contract[ex, FCI->True]; + FCPrint[1, "FCMultiLoopTID: Done applying Contract, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose] ]; - If[ !FreeQ2[Union[FCGetDimensions[ex/.DiracGamma[5|6|7]:>null1]],{4,-4}] && !$BreitMaison, + If[ !FreeQ2[Union[FCGetDimensions[ex/.{DiracGamma[5|6|7]:>null1,TemporalPair[__]->Unique[]}, ChangeDimension->True]],{4,-4}] && (FeynCalc`Package`DiracGammaScheme =!= "BMHV"), Message[FCMultiLoopTID::failmsg,"Your input contains a mixture of 4- and D-dimensional quantities. This is in general not allowed in dimensional regularization, unless you are using the Breitenlohner-Maison-t'Hooft-Veltman scheme."]; Abort[] ]; If[ OptionValue[DiracSimplify] && !FreeQ2[ex,{DiracGamma,DiracSigma,Spinor}], + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying DiracSimplify.", FCDoControl->mltidVerbose]; ex = DiracSimplify[ex, FCI->True]; - FCPrint[3,"FCMultiLoopTID: After DiracSimplify: ", ex, FCDoControl->mltidVerbose] + FCPrint[3,"FCMultiLoopTID: After DiracSimplify: ", ex, FCDoControl->mltidVerbose]; + FCPrint[1, "FCMultiLoopTID: Done applying DiracSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose] ]; + + If[ OptionValue[ApartFF], + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying ApartFF.", FCDoControl->mltidVerbose]; ex = ApartFF[ex,qs,FCI->True,FDS->OptionValue[FDS]]; - FCPrint[3,"FCMultiLoopTID: After first ApartFF: ", ex, FCDoControl->mltidVerbose] + FCPrint[3,"FCMultiLoopTID: After first ApartFF: ", ex, FCDoControl->mltidVerbose]; + FCPrint[1, "FCMultiLoopTID: Done applying ApartFF, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose] ]; + ex = Collect2[ex, qs, Factoring -> optFactoring, TimeConstrained -> optTimeConstrained, IsolateNames -> mltidIsolate] /. + (h: Pair|FeynAmpDenominator)[x__] /; !FreeQ[{x}, q] :> FRH[h[x], IsolateNames->mltidIsolate]; + (* Single out relevant loop momenta *) + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Expanding w.r.t the relevant loop momenta.", FCDoControl->mltidVerbose]; ex = ex//DiracGammaExpand[#,Momentum->qs, FCI->True]&//ExpandScalarProduct[#,Momentum->qs,EpsEvaluate->True, FCI->True]&; + If[ !FreeQ[ex,DiracChain], + ex = DiracChainExpand[ex,FCI->True,Momentum->qs] + ]; + + FCPrint[1, "FCMultiLoopTID: Done expanding w.r.t the relevant loop momenta, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose]; + FCPrint[3, "FCMultiLoopTID: After the expansion: ", ex, FCDoControl->mltidVerbose]; + (* The Dirac matrices and epsilon tensors could also be 4-dimensional. Then we need to first uncontract and then convert the loop momenta to D dimensions *) - ex = ex//.ruleUncontract; + + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Uncontracting Lorentz indices.", FCDoControl->mltidVerbose]; - If[ $BreitMaison && !FreeQ[ex,LorentzIndex], + ex = Uncontract[ex, Sequence@@qs, Pair -> {Polarization}, CartesianPair-> {Polarization}, FCI->True]; + If[ !FreeQ[ex,DiracTrace], + FCPrint[1, "FCMultiLoopTID: Applying FCTraceExpand.", FCDoControl->mltidVerbose]; + time=AbsoluteTime[]; + ex = ex /. DiracTrace[x__]/;!FreeQ2[x, qs] :> FCTraceExpand[DiracTrace[x],FCI->True]; + FCPrint[1, "FCMultiLoopTID: Done applying FCTraceExpand timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose]; + FCPrint[3, "FCMultiLoopTID: After FCTraceExpand: ", ex , FCDoControl->mltidVerbose]; + ]; + + + If[ !FreeQ[ex,DiracChain], + ex = DiracChainFactor[ex,FCI->True] + ]; + + FCPrint[1, "FCMultiLoopTID: Done uncontracting Lorentz indices, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose]; + FCPrint[3, "FCMultiLoopTID: After Uncontract: ", ex, FCDoControl->mltidVerbose]; + + If[ (FeynCalc`Package`DiracGammaScheme === "BMHV") && !FreeQ[ex,LorentzIndex], + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Handling 4 and D-4 dimensional loop momenta.", FCDoControl->mltidVerbose]; ex = ex /. { Pair[Momentum[q_,n-4],LorentzIndex[i_,n-4]]/; MemberQ[qs,q]:> (tmpli=Unique[]; Pair[Momentum[q,n],LorentzIndex[tmpli,n]] Pair[LorentzIndex[tmpli,n-4],LorentzIndex[i,n-4]]), Pair[Momentum[q_],LorentzIndex[i_]]/; MemberQ[qs,q] :> - (tmpli=Unique[]; Pair[Momentum[q,n],LorentzIndex[tmpli,n]] Pair[LorentzIndex[tmpli],LorentzIndex[i]]) + (tmpli=Unique[]; Pair[Momentum[q,n],LorentzIndex[tmpli,n]] Pair[LorentzIndex[tmpli],LorentzIndex[i]]), + + CartesianPair[CartesianMomentum[q,n-4],CartesianIndex[i_,n-4]]:> + (tmpli=Unique[]; CartesianPair[CartesianMomentum[q,n-1],CartesianIndex[tmpli,n-1]] CartesianPair[CartesianIndex[tmpli,n-4],CartesianIndex[i,n-4]]), + CartesianPair[CartesianMomentum[q],CartesianIndex[i_]]:> + (tmpli=Unique[]; CartesianPair[CartesianMomentum[q,n-1],CartesianIndex[tmpli,n-1]] CartesianPair[CartesianIndex[tmpli],CartesianIndex[i]]) }; - If[ !FreeQ2[ex, {Pair[Momentum[q_/;MemberQ[qs,q], n-4],LorentzIndex[_,n-4]],Pair[Momentum[q_/;MemberQ[qs,q]],LorentzIndex[_]]}], + If[ !FreeQ2[ex, {Pair[Momentum[q,n-4],LorentzIndex[_,n-4]],Pair[Momentum[q],LorentzIndex[_]], + CartesianPair[CartesianMomentum[q,n-4],CartesianIndex[_,n-4]],CartesianPair[CartesianMomentum[q],CartesianIndex[_]]}], Message[FCMultiLoopTID::failmsg,"Failed to eliminate 4 and D-4 dimensional loop momenta."]; Abort[] ]; FCPrint[2,"FCMultiLoopTID: Tensor parts after handling 4 and D-4 dimensional loop momenta: ", ex, FCDoControl->mltidVerbose]; + FCPrint[1, "FCMultiLoopTID: Done handling 4 and D-4 dimensional loop momenta, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose]; ]; - FCPrint[3,"FCMultiLoopTID: After Uncontract: ", ex, FCDoControl->mltidVerbose]; - {rest,loopInts,intsUnique} = FCLoopExtract[ex, qs,loopHead, - FCLoopSplit -> {4}, MultiLoop->False,FCI->True,PaVe->False]; + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying FCLoopExtract.", FCDoControl->mltidVerbose]; - FCPrint[3,"FCMultiLoopTID: List of the unique integrals: ", intsUnique, FCDoControl->mltidVerbose]; + {rest,loopInts,intsUnique} = FCLoopExtract[ex, qs,loopHead, FCLoopSplit -> {4}, MultiLoop->False,FCI->True,PaVe->False, + Factoring -> optFactoring, TimeConstrained -> optTimeConstrained]; + FCPrint[1, "FCMultiLoopTID: Done applying FCLoopExtract, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose]; + FCPrint[2,"FCMultiLoopTID: List of the unique integrals: ", intsUnique, FCDoControl->mltidVerbose]; (* Apply tidSingleIntegral to each of the unique loop integrals *) + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying tidSingleIntegral.", FCDoControl->mltidVerbose]; solsList = Map[tidSingleIntegral[#,qs,n]&,(intsUnique/.loopHead->Identity)]; + FCPrint[1, "FCMultiLoopTID: Done applying tidSingleIntegral, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose]; + FCPrint[3,"FCMultiLoopTID: List of the simplified integrals: ", solsList, FCDoControl->mltidVerbose]; If[!FreeQ[solsList,tidSingleIntegral], Message[FCMultiLoopTID::failmsg, @@ -151,31 +212,57 @@ Abort[] ]; - repRule = MapThread[Rule[#1,#2]&,{intsUnique,solsList}]; + If[ OptionValue[ApartFF]===True || OptionValue[ApartFF]===Last, + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying ApartFF to each of the unique integrals.", FCDoControl->mltidVerbose]; + solsList = ApartFF[#,qs,FCI->True,FDS->OptionValue[FDS]]&/@solsList; + FCPrint[3,"FCMultiLoopTID: After last ApartFF: ", solsList, FCDoControl->mltidVerbose]; + FCPrint[1, "FCMultiLoopTID: Done applying ApartFF, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose] + ]; + + If[ OptionValue[FDS], + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying FDS to each of the unique integrals.", FCDoControl->mltidVerbose]; + solsList = FDS[#,Sequence@@qs,FCI->True]&/@solsList; + FCPrint[3,"FCMultiLoopTID: After last FDS: ", solsList, FCDoControl->mltidVerbose]; + FCPrint[1, "FCMultiLoopTID: Done applying FDS, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose] + ]; + + repRule = Thread[Rule[intsUnique,solsList]]; FCPrint[3,"FCMultiLoopTID: Replacement rule: ", repRule, FCDoControl->mltidVerbose]; - res = rest + (loopInts/.repRule); + res = rest + (loopInts/. Dispatch[repRule]); FCPrint[3,"FCMultiLoopTID: Prelmininary result: ", res, FCDoControl->mltidVerbose]; - If[ OptionValue[ApartFF], - res = ApartFF[res,qs,FCI->True,FDS->OptionValue[FDS]]; - FCPrint[3,"FCMultiLoopTID: After last ApartFF: ", res, FCDoControl->mltidVerbose] - ]; - If [OptionValue[ExpandScalarProduct], + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying ExpandScalarProduct.", FCDoControl->mltidVerbose]; res = ExpandScalarProduct[res, FCI->True]; - FCPrint[3,"FCMultiLoopTID: After ExpandScalarProduct: ", res, FCDoControl->mltidVerbose] + FCPrint[3,"FCMultiLoopTID: After ExpandScalarProduct: ", res, FCDoControl->mltidVerbose]; + FCPrint[1, "FCMultiLoopTID: Done applying ExpandScalarProduct, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose] ]; If[ OptionValue[Contract], + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying Contract.", FCDoControl->mltidVerbose]; res = Contract[res, FCI->True]; - FCPrint[3,"FCMultiLoopTID: After Contract: ", res, FCDoControl->mltidVerbose] + FCPrint[3,"FCMultiLoopTID: After Contract: ", res, FCDoControl->mltidVerbose]; + FCPrint[1, "FCMultiLoopTID: Done applying Contract, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose] ]; + res = FRH[res,IsolateNames->mltidIsolate]; + If[ OptionValue[Collecting], + time=AbsoluteTime[]; + FCPrint[1, "FCMultiLoopTID: Applying Collect2.", FCDoControl->mltidVerbose]; res = Collect2[res,FeynAmpDenominator,Sequence@@qs]; - FCPrint[3,"FCMultiLoopTID: After Collect2: ", res, FCDoControl->mltidVerbose] + FCPrint[3,"FCMultiLoopTID: After Collect2: ", res, FCDoControl->mltidVerbose]; + FCPrint[1, "FCMultiLoopTID: Done applying Collect2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->mltidVerbose] + ]; + + If[ OptionValue[FCE], + res = FCE[res] ]; If[ OptionValue[FCE], @@ -186,8 +273,18 @@ res ]; -tidSingleIntegral[int_, qs_ , n_] := - Block[{ ex=int,res,allmoms,extmoms,lmoms,lis,rest,umoms,gramZero=False,null1,null2 + +tidSingleIntegral[int_, qs_List , n_] := + Block[{num,den,tmp}, + {num, den} = FCProductSplit[int, {FeynAmpDenominator}]; + tmp= FCProductSplit[num, {ExplicitLorentzIndex[0]}]; + tmp[[2]] tidSingleIntegral[tmp[[1]] den,qs,n] + ]/; !FreeQ[int /. _FeynAmpDenominator -> Unique[],ExplicitLorentzIndex[0]]; + + +tidSingleIntegral[int_, qs_List , n_] := + Block[{ ex=int,res,allmoms,extmoms,lmoms,lis,rest,umoms,gramZero=False, + null1,null2, cis, umomsHead, tdecHead, tdecDim }, FCPrint[2,"FCMultiLoopTID: tidSingleIntegral: Entering with ", ex, FCDoControl->mltidVerbose]; @@ -198,7 +295,11 @@ ]; (* List of all the momenta that appear inside the integral *) - allmoms=Union[Cases[int+null1+null2,Momentum[x_,_:4]:>x,Infinity]]; + allmoms=Union[Cases[int+null1+null2, (Momentum|CartesianMomentum)[x_,___]:>x,Infinity]]; + + (* Polarization vectors cannot appear in denominators, so we remove them from the list *) + allmoms = SelectFree[allmoms,Polarization]; + extmoms = Sort[Complement[allmoms,qs]]; lmoms = Sort[Intersection[qs,Complement[allmoms,extmoms]]]; @@ -206,47 +307,91 @@ FCPrint[3,"FCMultiLoopTID: tidSingleIntegral: External momenta: ", extmoms, FCDoControl->mltidVerbose]; lis = SelectNotFree[int*null1*null2, LorentzIndex]/.null1|null2->1; - rest = SelectFree[int*null1*null2, LorentzIndex]/.null1|null2->1; + cis = SelectNotFree[int*null1*null2, CartesianIndex]/.null1|null2->1; + rest = SelectFree[int*null1*null2, CartesianIndex, LorentzIndex]/.null1|null2->1; + + FCPrint[3,"FCMultiLoopTID: tidSingleIntegral: Lorentz indices: ", lis, FCDoControl->mltidVerbose]; + FCPrint[3,"FCMultiLoopTID: tidSingleIntegral: Cartesian indices: ", cis, FCDoControl->mltidVerbose]; + FCPrint[3,"FCMultiLoopTID: tidSingleIntegral: Rest: ", rest, FCDoControl->mltidVerbose]; + + Which[ + lis=!=1 && cis===1, + tdecHead=Tdec; + tdecDim=n; + FCPrint[3,"FCMultiLoopTID: tidSingleIntegral: Lorentz branch.", FCDoControl->mltidVerbose]; + (* Some cross-checks *) + If[ lis rest=!=int || !MatchQ[lis,HoldPattern[Times[Pair[Momentum[_, ___], LorentzIndex[_, ___]] ..]] | Pair[Momentum[_, ___], LorentzIndex[_, ___]] ], + Message[FCMultiLoopTID::failmsg,"tidSingleIntegral failed to extract the loop momenta with free Lorentz indices"]; + Abort[]; + ]; + + (* Create list of loop momenta and their Lorentz indices as used in Tdec *) + umoms = Sort[Cases[lis+null1+null2,Pair[Momentum[x_,n],LorentzIndex[i_,n]]:>{x,i},Infinity]]; + (* Check the Gram determinant *) + If[ extmoms=!={}, + FCPrint[2, "FCMultiLoopTID: tidSingleIntegral: Checking Gram determinant...", FCDoControl->mltidVerbose]; + If[ FCGramDeterminant[extmoms, Head -> {Pair, Momentum}, Dimension -> D]===0, + FCPrint[1, "FCMultiLoopTID: tidSingleIntegral: Zero Gram determinant detected!", FCDoControl->mltidVerbose]; + gramZero=True + ] + ], + lis===1 && cis=!=1, + tdecHead=CTdec; + tdecDim=n-1; + FCPrint[3,"FCMultiLoopTID: tidSingleIntegral: Cartesian branch.", FCDoControl->mltidVerbose]; + (* Some cross-checks *) + If[cis rest=!=int || !MatchQ[cis,HoldPattern[Times[CartesianPair[CartesianMomentum[_, ___], CartesianIndex[_, ___]] ..]] | CartesianPair[CartesianMomentum[_, ___], + CartesianIndex[_, ___]] ], + (*Print[{lis,rest,int}]; + Print[!MatchQ[lis,HoldPattern[Times[Pair[Momentum[_, _ : 4], LorentzIndex[_, _ : 4]] ..]] | Pair[Momentum[_, _ : 4], LorentzIndex[_, _ : 4]] ]]; + Print[Union[Cases[lis,Momentum[q_,_:4]:>q,Infinity]]]; + Print[lmoms]; + Print[Union[Cases[lis,Momentum[q_,_:4]:>q,Infinity]]=!=lmoms];*) + Message[FCMultiLoopTID::failmsg,"tidSingleIntegral failed to extract the loop momenta with free Lorentz indices"]; + Abort[]; + ]; + + (* Create list of loop momenta and their Lorentz indices as used in Tdec *) + umoms = Sort[Cases[cis+null1+null2,CartesianPair[CartesianMomentum[x_,n-1],CartesianIndex[i_,n-1]]:>{x,i},Infinity]]; + (* Check the Gram determinant *) + If[ extmoms=!={}, + FCPrint[2, "FCMultiLoopTID: tidSingleIntegral: Checking Gram determinant...", FCDoControl->mltidVerbose]; + If[ FCGramDeterminant[extmoms, Head -> {CartesianPair, CartesianMomentum}, Dimension -> D - 1]===0, + FCPrint[1, "FCMultiLoopTID: tidSingleIntegral: Zero Gram determinant detected!", FCDoControl->mltidVerbose]; + gramZero=True + ] + ], + + (*Nothing to do*) + lis===1 && cis===1, + Return[int], + + True, + Message[FCMultiLoopTID::failmsg, "Tensor reduction of integrals with mixed Lorentz and Cartesian indices is currently not supported."]; + Abort[] - (* Some cross-checks *) - If[lis rest=!=int || !MatchQ[lis,HoldPattern[Times[Pair[Momentum[_, _ : 4], LorentzIndex[_, _ : 4]] ..]] | Pair[Momentum[_, _ : 4], LorentzIndex[_, _ : 4]] ], - Print[{lis,rest,int}]; - Print[!MatchQ[lis,HoldPattern[Times[Pair[Momentum[_, _ : 4], LorentzIndex[_, _ : 4]] ..]] | Pair[Momentum[_, _ : 4], LorentzIndex[_, _ : 4]] ]]; - Print[Union[Cases[lis,Momentum[q_,_:4]:>q,Infinity]]]; - Print[lmoms]; - Print[Union[Cases[lis,Momentum[q_,_:4]:>q,Infinity]]=!=lmoms]; - Message[FCMultiLoopTID::failmsg,"tidSingleIntegral failed to extract the loop momenta with free Lorentz indices"]; - Abort[]; ]; - (* Create list of loop momenta and their Lorentz indices as used in Tdec *) - umoms = Sort[Cases[lis+null1+null2,Pair[Momentum[x_,n],LorentzIndex[li_,n]]:>{x,li},Infinity]]; - - (* Check the Gram determinant *) - If[ extmoms=!={}, - FCPrint[2, "FCMultiLoopTID: tidSingleIntegral: Checking Gram determinant...", FCDoControl->mltidVerbose]; - If[ExpandScalarProduct[Det[extmoms//Table[2 ScalarProduct[#[[i]], #[[j]],Dimension->D], {i, 1, Length[#]}, {j, 1, Length[#]}] &]]===0, - FCPrint[1, "FCMultiLoopTID: tidSingleIntegral: Zero Gram determinant detected!", FCDoControl->mltidVerbose]; - gramZero=True - ] - ]; FCPrint[3,"FCMultiLoopTID: tidSingleIntegral: Input for Tdec: ", {umoms,extmoms}, " ", FCDoControl->mltidVerbose]; - (* If the Gram deterimnant vanishes, all we can do here is to rewrite the integral in terms of some coefficient functions. From these GCF ("generalized coefficient functions") the user can in principle reconstruct the original integral and thus compute them outside of FeynCalc *) If[ gramZero, - res = Tdec[umoms,extmoms,List->False,FeynCalc`Package`BasisOnly -> True]/. - FCGV["GCF"][x__,li_,pli_]:>FCGV["GCF"][x,Map[{ToString[#[[1]]],#[[2]]}&,li],pli,ToString[FCE@int,InputForm]], - res = Tdec[umoms,extmoms,List->False]*rest; + If[ Length[qs]===1, + res = TID[int,First[qs],FCI->True], + Message[FCMultiLoopTID::gramzero]; + res = tdecHead[umoms,extmoms,List->False,FeynCalc`Package`BasisOnly -> True,Dimension->tdecDim]/. + FCGV["GCF"][x__,i_,p_]:>FCGV["GCF"][x,Map[{ToString[#[[1]]],#[[2]]}&,i],p,ToString[FCE@int,InputForm]] + ], + res = tdecHead[umoms,extmoms,List->False,Dimension->tdecDim]*rest; ]; (*TODO For large expression Isolate would be useful here *) FCPrint[2,"FCMultiLoopTID: tidSingleIntegral: Leaving with ", res, FCDoControl->mltidVerbose]; res - ]; + ]/; FreeQ[int /. _FeynAmpDenominator -> Unique[],ExplicitLorentzIndex[0]]; FCPrint[1,"FCMultiLoopTID.m loaded."]; End[] diff --git a/FeynCalc/LoopIntegrals/FCReplaceD.m b/FeynCalc/LoopIntegrals/FCReplaceD.m index 1f4ffbb1f..61cb0755d 100755 --- a/FeynCalc/LoopIntegrals/FCReplaceD.m +++ b/FeynCalc/LoopIntegrals/FCReplaceD.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Replaces D by the given expression (e.g. 4-2*Epsilon) @@ -31,34 +31,30 @@ FCReplaceD::repfail= "Error! Failed to replace all occurences of `1` with `2`. Evaluation aborted."; -FCReplaceD::error=" -Error! Something went wrong while partial fractioning the loop integral `1` by FCReplaceD. \ -Evaluation aborted"; - (* ------------------------------------------------------------------------ *) Begin["`Package`"] End[] -fcrdVerbose::usage=""; - Begin["`FCReplaceD`Private`"] +fcrdVerbose::usage=""; + Options[FCReplaceD] = { - FCI -> False, - FCVerbose -> False + FCE -> False, + FCI -> False, + FCVerbose -> False }; -FCReplaceD[expr_, replacement_Rule, OptionsPattern[]] := +FCReplaceD[expr_, Rule[dim_Symbol, x_], OptionsPattern[]] := Block[{ex,vectorSet,res,check, scalarTerm, vectorTerm=1, pref=1, tmp, - scaleless1=0,scaleless2=0,ruleProtect,holddim,dim,diga}, + scaleless1=0,scaleless2=0,ruleProtect,holddim,diga, pasi}, - dim=First[replacement]; FCPrint[1,"FCReplaceD: dim: " ,dim, FCDoControl->fcrdVerbose]; If [OptionValue[FCVerbose]===False, fcrdVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], fcrdVerbose=OptionValue[FCVerbose] ]; ]; @@ -68,40 +64,48 @@ ex = expr ]; - tmp = ex /. DiracGamma -> diga; - tmp = tmp //. diga[a_,di_] :> diga[holddim[a,ToString[di,InputForm]]]; + tmp = ex /. DiracGamma -> diga /. PauliSigma -> pasi; + tmp = tmp //. { diga[a_,di_] :> diga[holddim[a,ToString[di,InputForm]]], + pasi[a_,di_] :> pasi[holddim[a,ToString[di,InputForm]]]}; FCPrint[1,"FCReplaceD: tmp: " ,tmp, FCDoControl->fcrdVerbose]; - tmp = tmp //. (h:LorentzIndex|ExplicitLorentzIndex|Momentum)[a_,di_] :> h[holddim[a,ToString[di,InputForm]]]; + tmp = tmp //. (h:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[a_,di_] :> h[holddim[a,ToString[di,InputForm]]]; FCPrint[1,"FCReplaceD: tmp: " ,tmp, FCDoControl->fcrdVerbose]; - If[ !FreeQ[Cases2[tmp,{ExplicitLorentzIndex,LorentzIndex,Momentum,DiracGamma}],dim], + If[ !FreeQ[Cases2[tmp,{ExplicitLorentzIndex,LorentzIndex,Momentum,CartesianIndex,CartesianMomentum,DiracGamma,PauliSigma}],dim], Message[FCReplaceD::checkfail]; Abort[] ]; - tmp = tmp //. replacement; + tmp = tmp //. {dim -> x}; If[ !FreeQ[tmp,dim], - Message[FCReplaceD::repfail,dim,Last[replacement]]; + Message[FCReplaceD::repfail,dim,x]; Abort[] ]; - res = tmp //. (h:LorentzIndex|ExplicitLorentzIndex|Momentum)[holddim[a_,str_String]]:> h[a,ToExpression[str]]; - res = res /. (h:LorentzIndex|ExplicitLorentzIndex|Momentum)[a_]/;Head[a]=!=holddim :> h[a]; + res = tmp //. (h:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[holddim[a_,str_String]]:> h[a,ToExpression[str]]; + res = res /. (h:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[a_]/;Head[a]=!=holddim :> h[a]; res = res /. diga[holddim[a_,str_String]] :> DiracGamma[a,ToExpression[str]]; res = res /. diga[a_]/;Head[a]=!=holddim :> DiracGamma[a]; - If[ !FreeQ2[res,{holddim,diga}], + res = res /. pasi[holddim[a_,str_String]] :> PauliSigma[a,ToExpression[str]]; + res = res /. pasi[a_]/;Head[a]=!=holddim :> PauliSigma[a]; + + If[ !FreeQ2[res,{holddim,diga,pasi}], Message[FCReplaceD::resfail]; Abort[] ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + res ]; diff --git a/FeynCalc/LoopIntegrals/FeynAmpDenominatorCombine.m b/FeynCalc/LoopIntegrals/FeynAmpDenominatorCombine.m index 45151c512..7f8e8401d 100644 --- a/FeynCalc/LoopIntegrals/FeynAmpDenominatorCombine.m +++ b/FeynCalc/LoopIntegrals/FeynAmpDenominatorCombine.m @@ -20,19 +20,23 @@ (* ------------------------------------------------------------------------ *) Begin["`Package`"] + +fdsor; + End[] Begin["`FeynAmpDenominatorCombine`Private`"] feyncomb[] = 1; + feyncomb /: feyncomb[a__] feyncomb[b__] := feyncomb[a, b]; feyncomb /: feyncomb[a__]^n_Integer?Positive := - feyncomb @@ Flatten[Table[{a}, {ii, n}]]; + feyncomb @@ Flatten[Table[{a}, {n}]]; lev[PropagatorDenominator[a_, 0], PropagatorDenominator[b_, 0]] := If[ Length[Variables[a]] < Length[Variables[b]], @@ -40,18 +44,63 @@ False ]; +lev[CartesianPropagatorDenominator[a1_, a2_, _, _], CartesianPropagatorDenominator[b1_, b2_, _, _]] := + If[ Length[Variables[{a1,a2}]] < Length[Variables[{b1,b2}]], + True, + If[ Length[Variables[{a1,a2}]] === Length[Variables[{b1,b2}]], + OrderedQ[{{a1,a2},{b1,b2}}], + False + ] + ]; + +lev[StandardPropagatorDenominator[a1_, a2_, _, _], StandardPropagatorDenominator[b1_, b2_, _, _]] := + If[ Length[Variables[{a1,a2}]] < Length[Variables[{b1,b2}]], + True, + If[ Length[Variables[{a1,a2}]] === Length[Variables[{b1,b2}]], + OrderedQ[{{a1,a2},{b1,b2}}], + False + ] + ]; + fdsor[a__] := Apply[FeynAmpDenominator, Sort[MomentumExpand[{a}], lev]]; -mfci[y_] := - If[ FreeQ[y, FeynAmpDenominator], - FeynCalcInternal[y], - y - ]; +Options[FeynAmpDenominatorCombine] = { + FCE -> False, + FCI -> False, + Momentum -> All +}; + +FeynAmpDenominatorCombine[expr_, OptionsPattern[]] := + Block[{ex,res, optMomentum}, -FeynAmpDenominatorCombine[x_] := - Expand2[x//mfci, FeynAmpDenominator] /. - FeynAmpDenominator -> feyncomb /. feyncomb -> fdsor; + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + optMomentum = OptionValue[Momentum]; + + If[FreeQ[ex,FeynAmpDenominator], + Return[ex] + ]; + + res = Expand2[ex, FeynAmpDenominator]; + + + If[ optMomentum=!=All && Head[optMomentum]===List, + res = res /. FeynAmpDenominator[x__]/;!FreeQ2[{x},OptMomentum] :> feyncomb[x] /. feyncomb -> fdsor, + res = res /. FeynAmpDenominator -> feyncomb /. feyncomb -> fdsor + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + + ]; FCPrint[1,"FeynAmpDenominatorCombine.m loaded."]; End[] diff --git a/FeynCalc/LoopIntegrals/FeynAmpDenominatorExplicit.m b/FeynCalc/LoopIntegrals/FeynAmpDenominatorExplicit.m new file mode 100644 index 000000000..44bef234a --- /dev/null +++ b/FeynCalc/LoopIntegrals/FeynAmpDenominatorExplicit.m @@ -0,0 +1,144 @@ +(* ::Package:: *) + + + +(* :Title: FeynAmpDenominatorExplicit *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Rewrite FADs into SPDs *) + +(* ------------------------------------------------------------------------ *) + +FeynAmpDenominatorExplicit::usage = +"FeynAmpDenominatorExplicit[exp] changes each occurence of \ +PropagatorDenominator[a,b] in exp into 1/(ScalarProduct[a,a]-b^2) and \ +replaces FeynAmpDenominator by Times."; + +FeynAmpDenominatorExplicit::failmsg = +"Error! FeynAmpDenominatorExplicit encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +PropagatorDenominatorExplicit::usage= +"PropagatorDenominatorExplicit is equivalent to FeynAmpDenominatorExplicit"; + +(* ------------------------------------------------------------------------ *) + + + +Begin["`Package`"] +End[] + +Begin["`FeynAmpDenominatorExplicit`Private`"] + +PropagatorDenominatorExplicit = FeynAmpDenominatorExplicit; + +Options[FeynAmpDenominatorExplicit] = { + Denominator -> False, + Dimension -> False, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False, + Head -> Identity, + Mandelstam -> {}, + MomentumCombine -> False, + SmallVariable -> False +}; + +id[x_, ___]:= + x; + +FeynAmpDenominatorExplicit[expr_, OptionsPattern[]] := + Block[{ex, dim, res, head1, head2, mandel, ruleNormal, ruleMandelstam, fad, esp, mc}, + + If[ OptionValue[ExpandScalarProduct], + esp=ExpandScalarProduct, + esp=id + ]; + + If[ OptionValue[MomentumCombine], + mc=MomentumCombine, + mc=id + ]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex,FeynAmpDenominator], + Return[ex] + ]; + + ex = ex /. FeynAmpDenominator -> fad; + + dim = OptionValue[Dimension]; + mandel = OptionValue[Mandelstam]; + + ruleNormal = { + + PropagatorDenominator[a_ ,b_] :> + (1/Expand[esp[mc[Pair[a, a]],FCI->True] - b^2]), + (*TODO Do not ignore I*eta!*) + GenericPropagatorDenominator[pr_ ,{n_, _}] :> + (1/Expand[esp[mc[pr],FCI->True]])^n, + + CartesianPropagatorDenominator[ex1_, ex2_, m2_ ,{n_, _}] :> + (1/Expand[esp[mc[CartesianPair[ex1,ex1]+ ex2 + m2],FCI->True]])^n, + + StandardPropagatorDenominator[ex1_, ex2_, m2_ ,{n_, _}] :> + (1/Expand[esp[mc[Pair[ex1,ex1]+ ex2 + m2],FCI->True]])^n + }; + + ruleMandelstam = { + PropagatorDenominator[a_ ,b_] :> + (1/TrickMandelstam[esp[mc[Pair[a, a]],FCI->True] - b^2, mandel]), + + GenericPropagatorDenominator[pr_ , {n_, _}] :> + (1/TrickMandelstam[esp[mc[pr],FCI->True],mandel])^n + }; + + If[ mandel==={}, + res = ex //. ruleNormal, + res = ex //. ruleMandelstam + ]; + + If[ OptionValue[SmallVariable], + res = res /. fad[c___]:> (fad[c]/.SmallVariable[_]:>0) + ]; + + If[ dim===False, + res = res /. fad[c___] :> head1[Times[c]], + res = res /. fad[c___] :> head1[ChangeDimension[Times[c],dim]] + ]; + + If[ TrueQ[OptionValue[Denominator]], + res = res /. head1[x_] /; Numerator[x] === 1 :> 1/head2[Denominator[x]]; + If[ !FreeQ[res,head1], + Message[FeynAmpDenominatorExplicit::failmsg, "The numerator is not unity!"]; + Abort[] + ]; + res = res /. head2->OptionValue[Head], + res = res /. head1->OptionValue[Head] + ]; + + If[ !FreeQ2[res,{fad,FeynAmpDenominator,head1,head2}], + Message[FeynAmpDenominatorExplicit::failmsg, "Something went wrong while writing out the denominators."]; + Abort[] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + +FCPrint[1,"FeynAmpDenominatorExplicit.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/FeynAmpDenominatorSimplify.m b/FeynCalc/LoopIntegrals/FeynAmpDenominatorSimplify.m index ae64997a4..005173709 100644 --- a/FeynCalc/LoopIntegrals/FeynAmpDenominatorSimplify.m +++ b/FeynCalc/LoopIntegrals/FeynAmpDenominatorSimplify.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Simplifies loop integrals by doing shifts and detects @@ -45,170 +45,488 @@ lenso feynsimp +feynord End[] Begin["`FeynAmpDenominatorSimplify`Private`"] fdsVerbose::usage=""; +loopHead::usage=""; +cLoopHead::usage=""; +sLoopHead::usage=""; +null1::usage=""; +null2::usage=""; FDS = FeynAmpDenominatorSimplify; Options[FeynAmpDenominatorSimplify] = { - ApartFF -> True, - Collecting -> True, - ExpandScalarProduct -> True, - FCI -> False, - FeynAmpDenominatorCombine -> True, - FCVerbose -> False, - FC2RHI -> False, - IntegralTable -> {}, - IncludePair -> False, - DetectLoopTopologies -> True + ApartFF -> False, + Collecting -> True, + DetectLoopTopologies -> True, + ExpandScalarProduct -> True, + FC2RHI -> False, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> Factor, + FeynAmpDenominatorCombine -> True, + IncludePair -> False, + IntegralTable -> {}, + Rename -> True }; SetAttributes[FeynAmpDenominatorSimplify, Listable]; -(* For the case that there is nothing to do *) -FeynAmpDenominatorSimplify[a_ /; FreeQ[a, PD], ___,OptionsPattern[]] := - a /; FreeQ[a, FAD]; - -(* Simple wrappers *) -FeynAmpDenominatorSimplify[exp_,Momentum[q1_, _:4],opts:OptionsPattern[]] := - FeynAmpDenominatorSimplify[exp, q1,opts]; - -FeynAmpDenominatorSimplify[exp_,Momentum[q1_, _:4], Momentum[q2_, _:4],opts:OptionsPattern[]] := - FeynAmpDenominatorSimplify[exp, q1, q2,opts]; - -(* Without knowing what the loop momenta are, FDS can just try to sort propagators - and pull out the overall minus signs, but nothing more *) -FeynAmpDenominatorSimplify[exp_, OptionsPattern[]] := - exp /. PD -> procan /. procan -> - PD /. FeynAmpDenominator -> feyncan; - -procan[a_, m_] := - Block[ {tt , one}, - tt = Factor2[one MomentumExpand[a]]; - If[ NumericalFactor[tt] === -1, - PD[-tt/.one->1, m], - PD[tt/.one->1, m] - ] - ]; - -(* Handling general multiloop integrals with more than 2 loop momenta *) -FeynAmpDenominatorSimplify[exp_, qmore__, - q1_/;Head[q1] =!= Rule, q2_ /;Head[q2] =!= Rule,opts:OptionsPattern[]] := - FeynAmpDenominatorSimplify[exp /. FeynAmpDenominator -> feynsimp[{q2}], qmore, q1,opts]; - -(* FDS for 1-loop integrals *) -FeynAmpDenominatorSimplify[ex_, q1_/;Head[q1]=!=Momentum, OptionsPattern[]] := - Block[ {exp,rest,loopInts,intsUnique,null1,null2,solsList,res,repRule}, +FeynAmpDenominatorSimplify[expr_, qs___/;FreeQ[{qs},Momentum], opt:OptionsPattern[]] := + Block[ {ex,rest,loopInts,intsUnique, solsList,res,repRule,time, topoCheckUnique, + topoCheck, multiLoopHead, solsList2, intsTops, intsTops2, optCollecting, power, fadList, + fadListEval, fadHold, intsUniqueClassified}, If [OptionValue[FCVerbose]===False, fdsVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], fdsVerbose=OptionValue[FCVerbose] ]; ]; - If[ !FreeQ2[$ScalarProducts, {q1}], + If[ !FreeQ2[$ScalarProducts, {qs}], Message[FDS::failmsg, "Some loop momenta have scalar product rules attached to them. Evaluation aborted!"]; Abort[] ]; - FCPrint[1,"FDS: Entering 1-loop FDS with: ", ex, FCDoControl->fdsVerbose]; + optCollecting = OptionValue[Collecting]; + + If[ !OptionValue[FCI], + ex = FeynCalcInternal[expr], + ex = expr + ]; + + FCPrint[1,"FDS: Entering FDS. ", FCDoControl->fdsVerbose]; + FCPrint[3,"FDS: Entering with: ", ex, FCDoControl->fdsVerbose]; + + If[ FreeQ[ex,FeynAmpDenominator], + FCPrint[1,"FDS: Nothing to do.", FCDoControl->fdsVerbose]; + Return[ex] + ]; + + ex = ex /. Power[FeynAmpDenominator[a__], b_ ] :> power[fadHold[a],b]; + + fadList = Cases2[ex+null1+null2,FeynAmpDenominator,power]; + + fadListEval = fadList /. {power[fadHold[a__],n_] /; n>1 :> FeynAmpDenominator[Sequence@@(Table[a,{i,1,n}])]} /. + power -> Power /. fadHold -> FeynAmpDenominator; + + If[ !FreeQ[fadListEval, PD], + fadListEval = fadListEval /. PD -> procan /. procan -> PD + ]; + + If[ !FreeQ[fadListEval, StandardPropagatorDenominator], + fadListEval = fadListEval /. StandardPropagatorDenominator -> procanSFAD /. procanSFAD -> StandardPropagatorDenominator + ]; + + If[ !FreeQ[fadListEval, CartesianPropagatorDenominator], + fadListEval = fadListEval /. CartesianPropagatorDenominator -> procanCFAD /. procanCFAD -> CartesianPropagatorDenominator + ]; + + FCPrint[3,"FDS: After fixing the signs of squared momenta in the propagators: ", fadListEval, FCDoControl->fdsVerbose]; + + If[ Length[{qs}]===0, + FCPrint[1,"FDS: No loop momenta were given.", FCDoControl->fdsVerbose]; + fadListEval = fadListEval /. FeynAmpDenominator -> feyncan; + repRule = Thread[Rule[fadList,fadListEval]]; + Return[ex /. Dispatch[repRule]] + ]; + + repRule = Thread[Rule[fadList,fadListEval]]; + ex = ex /. Dispatch[repRule]; + + FCPrint[3,"FDS: New ex: ", ex, FCDoControl->fdsVerbose]; (* Extract unique loop integrals *) - {rest,loopInts,intsUnique} = FCLoopExtract[ex, {q1},loopHead, DropScaleless->True,FCI->OptionValue[FCI], PaVe->False]; + FCPrint[1,"FDS: Extracting unique loop integrals. ", FCDoControl->fdsVerbose]; + time=AbsoluteTime[]; + + (*TODO Need to speed this up for cases where there is only one single FAD! *) + (*TODO Drop scaleless for 1-loop??? *) + (* Here we can exploit the possible factorization in a multiloop integral *) + {rest,loopInts,intsUnique} = FCLoopExtract[ex, {qs},loopHead, FCI->True, PaVe->False, FCLoopBasisSplit->True, + ExpandScalarProduct->True, Full->False, GFAD->False, CFAD->True, SFAD->True]; + + FCPrint[1, "FDS: Done extracting unique loop integrals, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdsVerbose]; + FCPrint[1, "FDS: Number of the unique integrals: ", Length[intsUnique], FCDoControl->fdsVerbose]; FCPrint[3, "FDS: List of unique integrals ", intsUnique, FCDoControl->fdsVerbose]; - (* Apply fdsOneLoop to each of the unique loop integrals *) - solsList = Map[fdsOneLoop[#,q1]&,(intsUnique/.loopHead->Identity)]; + (* All the mixed integrals will be ignored *) + intsUniqueClassified = integralClassify/@intsUnique; + + FCPrint[3, "FDS: List of the unique integrals after their classification ", intsUniqueClassified, FCDoControl->fdsVerbose]; + + loopInts = loopInts /. Thread[Rule[intsUnique,intsUniqueClassified]]; + intsUnique = intsUniqueClassified; + + FCPrint[1,"FDS: Simplifying the unique integrals. ", FCDoControl->fdsVerbose]; + time=AbsoluteTime[]; + solsList = intsUnique /. { + (loopHead|sLoopHead|cLoopHead)[z_,{l_}] :> fdsOneLoop[z,l], + loopHead[z_,{l1_,l2_}] :> multiLoopHead[oldFeynAmpDenominatorSimplify[z,l1,l2,opt]], + loopHead[z_,{l1_,l2_, l3__}] :> multiLoopHead[fdsMultiLoop[z,l1,l2,l3]], + sLoopHead[z_,{_,__}] :> z, + cLoopHead[z_,{_,__}] :> z + }; + + solsList = (FeynAmpDenominatorCombine[#]/. FeynAmpDenominator -> feynord[{qs}])&/@solsList; + + FCPrint[1, "FDS:Done simpifying the unique loop integrals, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdsVerbose]; + FCPrint[3, "FDS: List of the simplified integrals ", solsList, FCDoControl->fdsVerbose]; If[!FreeQ[solsList,fdsOneLoop], Message[FDS::failmsg,"fdsOneLoop couldn't be applied to some of the unique integrals."]; Abort[] ]; - repRule = MapThread[Rule[#1,#2]&,{intsUnique,solsList}]; + (* Tailored simplifications for speical 2-loop topologies *) + If[ OptionValue[DetectLoopTopologies] && !FreeQ[solsList,multiLoopHead] && FreeQ2[solsList,{StandardPropagatorDenominator,CartesianPropagatorDenominator}] , + FCPrint[3, "FDS: Simplifying special topologies.", FCDoControl->fdsVerbose]; + + + (* Isolate single loop integrals in every solution *) + solsList = solsList /. + {multiLoopHead[x__]:> Map[topoCheck,Expand2[x,FeynAmpDenominator]+null1+null2]}/. topoCheck[null1|null2] -> 0; + + topoCheckUnique = Cases[solsList,topoCheck[x__],Infinity]//Sort//DeleteDuplicates; + FCPrint[3, "FDS: Unique terms ", topoCheckUnique, FCDoControl->fdsVerbose]; + + + intsTops=getTopology[#,{qs}]&/@(topoCheckUnique/.topoCheck->Identity); + FCPrint[3, "FDS: Topologies ", intsTops, FCDoControl->fdsVerbose]; + + intsTops2 = checkTopology/@intsTops; + FCPrint[3, "FDS: Checked topologies ", intsTops2, FCDoControl->fdsVerbose]; + + If[ intsTops2=!={}, + solsList2 = MapIndexed[ + (* Here one could add more topologies if needed *) + Which[ #1==="2-loop-self-energy", + (fds2LoopsSE[(First[topoCheckUnique[[#2]]]/.topoCheck->Identity),qs,(Total[intsTops[[#2]]])[[3]][[1]]]/. FeynAmpDenominator -> feyncan), + #1==="generic", + (First[topoCheckUnique[[#2]]]/. topoCheck->Identity), + True, + Message[FDS::failmsg,"Unknown 2-loop topology!"]; + Abort[] + + ]&,intsTops2], + solsList2= {} + ]; + + solsList = solsList /. Thread[Rule[topoCheckUnique,solsList2]], + + (* Otherwise just remove the multiLoopHead heads *) + solsList = solsList/.multiLoopHead->Identity + ]; + + repRule = Thread[Rule[intsUnique,solsList]]; FCPrint[3, "FDS: Replacement rule: ", repRule, FCDoControl->fdsVerbose]; (* Substitute the simplified integrals back into the original expression *) res = rest + (loopInts/.repRule); + (* + Some integrals might be identical up to a renaming of the loop momenta, e.g. + 1/[(q1^2-m1^2)(q2^2-m2^2)] and 1/[(q2^2-m1^2)(q1^2-m2^2)]. In the following + we check all possible exchanges of the loop momentum variables and sort them + canonically. + *) + + If[ OptionValue[Rename] && Length[{qs}]>=2, + + time=AbsoluteTime[]; + FCPrint[1, "FDS: fdsMultiLoop: Checking symmetries under renamings of the loop momenta.", FCDoControl->fdsVerbose]; + + (* The option FeynAmpDenominatorCombine effectively decides whether the detected factorization of a loop integral + will be preserved (FeynAmpDenominatorCombine->False) or broken (FeynAmpDenominatorCombine->True) *) + {rest,loopInts,intsUnique} = FCLoopExtract[res, {qs},loopHead, FCI->True, PaVe->False, FCLoopBasisSplit->False, + ExpandScalarProduct->True, Full->False, FeynAmpDenominatorCombine->OptionValue[FeynAmpDenominatorCombine]]; + + solsList = intsUnique /. loopHead[x_]:> renameLoopMomenta[x,{qs}]; + repRule = Thread[Rule[intsUnique,solsList]]; + + res = rest + (loopInts/.repRule); + FCPrint[1, "FDS: Done checking symmetries under renamings of the loop momenta, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdsVerbose]; + FCPrint[3, "FDS: fdsMultiLoop: After the renaming of the loop momenta: ", res, FCDoControl->fdsVerbose] + ]; + + (*TODO: DO NOT EXPAND IN THE LOOP MOMENTA!!!! *) If [OptionValue[ExpandScalarProduct], - res = ExpandScalarProduct[res] + FCPrint[1,"FDS: Applying ExpandScalarProduct. ", FCDoControl->fdsVerbose]; + time=AbsoluteTime[]; + res = ExpandScalarProduct[res, FCI->True]; + FCPrint[1, "FDS: Done applying ExpandScalarProduct, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdsVerbose]; + FCPrint[3, "FDS: After ExpandScalarProduct: ", res, FCDoControl->fdsVerbose] + ]; + + If[ optCollecting=!=False, + FCPrint[1,"FDS: Applying Collect2. ", FCDoControl->fdsVerbose]; + time=AbsoluteTime[]; + + + If[ TrueQ[optCollecting===True], + res = Collect2[res,FeynAmpDenominator, Factoring->OptionValue[Factoring]], + res = Collect2[res,optCollecting, Factoring->OptionValue[Factoring]] + ]; + + FCPrint[1, "FDS: Done applying Collect2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdsVerbose]; + FCPrint[3, "FDS: After Collect2: ", res, FCDoControl->fdsVerbose] ]; - If[ OptionValue[Collecting], - res = Collect2[res,FeynAmpDenominator] + If[ OptionValue[FCE], + res = FCE[res] ]; FCPrint[3, "FDS: Leaving with: ", res, FCDoControl->fdsVerbose]; res ]; + + +renameLoopMomenta[int_,qs_List]:= + Block[{ permutations,listOfRenamings,equivalentInts, + lmoms,nLoops,rule,res}, + + lmoms = Select[qs,!FreeQ[int,#]&]; + nLoops = Length[lmoms]; + + permutations = Permute[lmoms, PermutationGroup[Cycles[{#}]&/@Subsets[Range[nLoops], {2, nLoops}]]]; + + If[ permutations==={{}}, + Return[int] + ]; + + listOfRenamings=Sort[Thread[rule[Table[lmoms, {i,1,Length[permutations]}], permutations]] /.rule[x_List,y_List] :> Thread[rule[x,y]] /. + rule[a_, a_] :> Unevaluated[Sequence[]]] /. rule -> Rule; + + equivalentInts = Map[(int/. # /. FeynAmpDenominator -> feynsimp[lmoms] /. FeynAmpDenominator -> feynord[lmoms])&, listOfRenamings]; + + res = equivalentInts//Sort//First; + + res + ]; + +procan[a_, m_] := + Block[{tt, one, numfac}, + tt = Factor2[one MomentumExpand[a]]; + numfac = NumericalFactor[tt]; + If[TrueQ[numfac < 0 && MatchQ[numfac, _Rational | _Integer]], + PD[Expand[-tt /. one -> 1], m], + PD[Expand[tt /. one -> 1], m] + ] + ]; + + +procanSFAD[0, rest__]:= + StandardPropagatorDenominator[0, rest]; + +procanCFAD[0, rest__]:= + CartesianPropagatorDenominator[0, rest]; + + +procanSFAD[a_, rest__] := + Block[{tt, one, numfac}, + tt = Factor2[one MomentumExpand[a]]; + numfac = NumericalFactor[tt]; + If[TrueQ[numfac < 0 && MatchQ[numfac, _Rational | _Integer]], + StandardPropagatorDenominator[Expand[-tt /. one -> 1], rest], + StandardPropagatorDenominator[Expand[tt /. one -> 1], rest] + ] + ]/; a=!=0; + +procanCFAD[a_, rest__] := + Block[{tt, one, numfac}, + tt = Factor2[one MomentumExpand[a]]; + numfac = NumericalFactor[tt]; + If[TrueQ[numfac < 0 && MatchQ[numfac, _Rational | _Integer]], + CartesianPropagatorDenominator[Expand[-tt /. one -> 1], rest], + CartesianPropagatorDenominator[Expand[tt /. one -> 1], rest] + ] + ]/; a=!=0; + + + + fdsOneLoop[loopInt : (_. FeynAmpDenominator[props__]), q_]:= - Block[{tmp,res,tmpNew,solsList,repRule}, + Block[{tmp,res,tmpNew,solsList,repRule,sps,fad}, - (* The input of fdsOneLoop is guaranteed to contain - only a signle 1-loop integral. This makes many things simpler. *) + (* + The input of fdsOneLoop is guaranteed to contain + only a signle 1-loop integral. This makes many things simpler. + *) FCPrint[3, "FDS: fdsOneLoop: Entering with: ", loopInt, FCDoControl->fdsVerbose]; - (* Order the propagators such, that the massless propagator with the smalles + (* + Order the propagators such, that the massless propagator with the smallest number of the external momenta goes first. This is not the standard ordering, - but it is useful as the first step to bring the integral into canonical form *) + but it is useful as the first step to bring the integral into canonical form + *) tmp = loopInt /. FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord2[{q}]; FCPrint[3, "FDS: fdsOneLoop: After first ordering of the propagators: ", tmp, FCDoControl->fdsVerbose]; (* Integrals that are antisymmetric under q->-q are removed *) - tmp = removeAnitsymmetricIntegrals[tmp,q]; + tmp = removeAnitsymmetricIntegrals[tmp,{q}, {q}]; + + If[ tmp===0, + Return[0] + ]; + FCPrint[3, "FDS: fdsOneLoop: After removing antisymmetric integrals: ", tmp, FCDoControl->fdsVerbose]; - (* Special trick for same mass propagators to avoid terms like 1/[q^2-m^2] [(q-p)^2-m^2]^3 instead of - 1/[q^2-m^2]^3 [(q-p)^2-m^2] *) - tmp = tmp/. {a_. FeynAmpDenominator[(ch1: PD[Momentum[q,dim_:4],m_]..),(ch2: PD[Momentum[q,dim_:4]+ pe_,m_]..),rest___]/; - FreeQ[pe,q] && pe=!=0 && Length[{ch1}] < Length[{ch2}] && m=!=0 :> - ((a FeynAmpDenominator[ch1,ch2,rest])/. q :> - q - (pe/.Momentum->extractm))} /. - FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]] /. - FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord[{q}]; + (* + Special trick for same mass propagators to avoid terms like 1/[q^2-m^2] [(q-p)^2-m^2]^3 instead of + 1/[q^2-m^2]^3 [(q-p)^2-m^2] + *) + If[ !FreeQ[tmp,PropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[(v: PD[Momentum[q, dim___],m_]..),(w: PD[Momentum[q, dim___]+ pe_,m_]..), r___]/; + FreeQ[pe,q] && pe=!=0 && Length[{v}] < Length[{w}] && m=!=0 :> + ((a FeynAmpDenominator[v,w,r])/. q :> - q - (pe/.Momentum->extractm))} /. + FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]] /. + FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord[{q}] + ]; + + If[ !FreeQ[tmp,StandardPropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[(v: StandardPropagatorDenominator[Momentum[q,dim___],0,m_,s_]..), + (w: StandardPropagatorDenominator[Momentum[q,dim___]+ pe_,0,m_, s_]..), r___]/; + FreeQ[pe,q] && pe=!=0 && Length[{v}] < Length[{w}] && m=!=0 :> + ((a FeynAmpDenominator[v,w,r])/. q :> - q - (pe/.Momentum->extractm))} /. + FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]] /. + FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord[{q}] + ]; + + If[ !FreeQ[tmp,CartesianPropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[(v: CartesianPropagatorDenominator[CartesianMomentum[q,dim___],0,m_,s_]..), + (w: CartesianPropagatorDenominator[CartesianMomentum[q,dim___]+ pe_,0,m_, s_]..),r___]/; + FreeQ[pe,q] && pe=!=0 && Length[{v}] < Length[{w}] && m=!=0 :> + ((a FeynAmpDenominator[v,w,r])/. q :> - q - (pe/.CartesianMomentum->extractm))} /. + FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]]/. FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord[{q}] + ]; FCPrint[3, "FDS: fdsOneLoop: After using special trick for same mass propagators: ", tmp, FCDoControl->fdsVerbose]; - (* Special trick for massless propagators to avoid terms like 1/q^2 [(q-p)^2]^3 instead of - 1/[q^2]^3 [(q-p)^2] *) - tmp = tmp/. {a_. FeynAmpDenominator[(ch1: PD[Momentum[q,dim_:4],0]..),(ch2: PD[Momentum[q,dim_:4]+ pe_,0]..),rest___]/; - FreeQ[pe,q] && pe=!=0 && Length[{ch1}] < Length[{ch2}] :> - ((a FeynAmpDenominator[ch1,ch2,rest])/. q :> - q - (pe/.Momentum->extractm))} /. + (* + Special trick for massless propagators to avoid terms like 1/q^2 [(q-p)^2]^3 instead of + 1/[q^2]^3 [(q-p)^2] + *) + If[ !FreeQ[tmp,PropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[(v: PD[Momentum[q,dim___],0]..),(w: PD[Momentum[q,dim___]+ pe_,0]..), r___]/; + FreeQ[pe,q] && pe=!=0 && Length[{v}] < Length[{w}] :> + ((a FeynAmpDenominator[v,w,r])/. q :> - q - (pe/.Momentum->extractm))} /. + FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]] /. + FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord2[{q}] + ]; + + If[ !FreeQ[tmp,StandardPropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[(v: StandardPropagatorDenominator[Momentum[q,dim___],0,0,s_]..), + (w: StandardPropagatorDenominator[Momentum[q,dim___]+ pe_,0,0,s_]..),r___]/; + FreeQ[pe,q] && pe=!=0 && Length[{v}] < Length[{w}] :> + ((a FeynAmpDenominator[v,w,r])/. q :> - q - (pe/.Momentum->extractm))} /. FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]] /. - FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord2[{q}]; + FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord2[{q}] + ]; + + If[ !FreeQ[tmp,CartesianPropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[(v: CartesianPropagatorDenominator[CartesianMomentum[q,dim___],0,0,s_]..), + (w: CartesianPropagatorDenominator[CartesianMomentum[q,dim___]+ pe_,0,0,s_]..), r___]/; + FreeQ[pe,q] && pe=!=0 && Length[{v}] < Length[{w}] :> + ((a FeynAmpDenominator[v,w,r])/. q :> - q - (pe/.CartesianMomentum->extractm))} /. + FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]] /. + FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord2[{q}] + ]; FCPrint[3, "FDS: fdsOneLoop: After using special trick for massless propagators: ", tmp, FCDoControl->fdsVerbose]; (* Perform a shift to make the very first propagator free of external momenta *) - tmp = tmp/. {a_. FeynAmpDenominator[PD[Momentum[q,dim_:4]+pe_, m_],rest___]/; FreeQ[pe,q] :> - ((a FeynAmpDenominator[PD[Momentum[q,dim]+pe, m],rest])/. q :> q - (pe/.Momentum->extractm))} /. + If[ !FreeQ[tmp, PropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[PD[Momentum[q, d___]+pe_, m_],r___]/; FreeQ[pe,q] :> + ((a FeynAmpDenominator[PD[Momentum[q, d]+pe, m], r])/. q :> q - (pe/.Momentum->extractm))} /. FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]]; + ]; + + If[ !FreeQ[tmp, StandardPropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, d___]+pe_,x_, m_, s_],r___]/; FreeQ[pe,q] :> + ((a FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, d]+pe, x, m, s], r])/. q :> q - (pe/.Momentum->extractm))} /. + FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]]; + ]; + + If[ !FreeQ[tmp, CartesianPropagatorDenominator], + tmp = tmp/. {a_. FeynAmpDenominator[CartesianPropagatorDenominator[CartesianMomentum[q, d___]+pe_,x_, m_, s_], r___]/; FreeQ[pe,q] :> + ((a FeynAmpDenominator[CartesianPropagatorDenominator[CartesianMomentum[q, d]+pe, x, m, s], r])/. q :> q - (pe/.CartesianMomentum->extractm))} /. + FeynAmpDenominator[a__]:>MomentumExpand[FeynAmpDenominator[a]]; + ]; + + If[ tmp===0, + Return[0] + ]; + + (* Prior to removing scaleless integrals we want to ensure that the loop integral is of a particular form *) + If[ !MatchQ[tmp, (a_. b_FeynAmpDenominator)/;FreeQ[a,FeynAmpDenominator]], + Message[FeynAmpDenominatorSimplify::failmsg, "The loop integral is not in the expected form."]; + Abort[] + ]; FCPrint[3, "FDS: fdsOneLoop: After shifting the very first propagator: ", tmp, FCDoControl->fdsVerbose]; - (* Remove massless tadpoles (vanish in DR) *) - If[!$KeepLogDivergentScalelessIntegrals, - tmp = tmp /. {_. FeynAmpDenominator[PD[Momentum[q,_:4], 0]..] :> 0}, - If[ (tmp/. FeynAmpDenominator[___]->1)===1, - tmp = tmp /. {_. FeynAmpDenominator[l:PD[Momentum[q,_:4], 0]..]/;Length[{l}]=!=2 :> 0} + {sps,fad} = FCProductSplit[tmp,{FeynAmpDenominator}]; + + (* If FAD has no dependence on the loop momentum, the integral is clearly scaleless *) + If[ FreeQ[fad,q], + Return[0] + ]; + + + (* + An integral that contains only Cartesian eikonal propagators vanishes by symmetry q->-q, while + massless Cartesian tadpoles vanish in DR. This is true also for mixed integrals. + *) + fad = fad /. { + FeynAmpDenominator[x : CartesianPropagatorDenominator[0, _, _, {_, _}] ..] /; !FreeQ[{x}, CartesianMomentum[q, __]] -> 0, + FeynAmpDenominator[CartesianPropagatorDenominator[CartesianMomentum[q, ___], 0, 0, _]..] -> 0 + }; + + (* + It is not safe to remove certain scaleless integrals (like 1/q^2) if the integral depends both on + Lorentzian and Cartesian quantities. + *) + If[ FCLoopMixedIntegralQ[sps*fad]===False, + + (* An integral that contains only Lorentzian eikonal propagators vanishes by symmetry q->-q *) + fad = fad /. {FeynAmpDenominator[x : StandardPropagatorDenominator[0, _, _, {_, _}] ..] /; !FreeQ[{x}, Momentum[q, __]] -> 0}; + + (* Remove massless Lorentzian tadpoles (vanish in DR) *) + If[!$KeepLogDivergentScalelessIntegrals, + fad = fad /. { + FeynAmpDenominator[PD[Momentum[q,___], 0]..] -> 0, + FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q,___], 0, 0 ,_]..] -> 0 + }, + If[ sps===1, + fad = fad /. { + FeynAmpDenominator[l:PD[Momentum[q,___], 0]..]/;Length[{l}]=!=2 -> 0, + FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q,___], 0, 0 , {1,_}]..]/;Length[{l}]=!=2 :> 0 + } + ] ] ]; + tmp = sps*fad; + FCPrint[3, "FDS: fdsOneLoop: After removing massless tadpoles: ", tmp, FCDoControl->fdsVerbose]; - (* If the integral topology is more complicated than a massive tadpole, then - we possibly need to do some shifts *) - If[ Length[Union[{props}]]>1, + (* + If the integral topology is more complicated than a massive tadpole, then + we possibly need to do some shifts. + *) + If[ Length[Union[{props}]]>1 && FCLoopEikonalPropagatorFreeQ[tmp], FCPrint[3, "FDS: fdsOneLoop: The integral is at least a bubble: ", tmp, FCDoControl->fdsVerbose]; tmp=fdsOneLoopsGeneric[tmp,q] ]; @@ -220,19 +538,23 @@ res = tmp ]; FCPrint[3, "FDS: fdsOneLoop: res: ", res, FCDoControl->fdsVerbose]; - (* After the shifts our single integral usually turns into a sum of - integrals with different numerators. Some of them might vanish by symmetry *) - - res = Expand2[ExpandScalarProduct[res,Momentum->{q},EpsEvaluate->True],q]; + (* + After the shifts our single integral usually turns into a sum of + integrals with different numerators. Some of them might vanish by symmetry + *) + res = Expand2[ExpandScalarProduct[res,Momentum->{q},EpsEvaluate->True, Full->False, FCI->True],q]; FCPrint[3, "FDS: fdsOneLoop: res: ", res, FCDoControl->fdsVerbose]; - tmpNew = FCLoopExtract[res, {q},loopHead, DropScaleless->True,FCI->True, PaVe->False]; + tmpNew = FCLoopExtract[res, {q},loopHead, DropScaleless->True,FCI->True, PaVe->False, + ExpandScalarProduct->True, Full->False, FCI->True ]; FCPrint[3, "FDS: fdsOneLoop: tmpNew: ", tmpNew, FCDoControl->fdsVerbose]; - solsList = Map[removeAnitsymmetricIntegrals[#,q]&,(tmpNew[[3]]/.loopHead->Identity)]; + solsList = Map[removeAnitsymmetricIntegrals[#,{q}, {q}]&,(tmpNew[[3]]/.loopHead->Identity)]; FCPrint[3, "FDS: fdsOneLoop: solsList: ", solsList, FCDoControl->fdsVerbose]; - repRule = MapThread[Rule[#1,#2]&,{tmpNew[[3]],solsList}]; + + repRule = Thread[Rule[tmpNew[[3]],solsList]]; + FCPrint[3, "FDS: fdsOneLoop: repRule: ", repRule, FCDoControl->fdsVerbose]; res = tmpNew[[1]] + (tmpNew[[2]]/.repRule); @@ -251,13 +573,17 @@ to bring each integral to the "canonical" form. Pure heuristics, since without knowing the precise topology, there is no way to guess the true canonical form of the given integral. *) fdsOneLoopsGeneric[expr : (_. FeynAmpDenominator[props__]), q_] := - Block[ {prs, prs2, canonicalProps,shiftList,res,null1,null2}, + Block[ {prs, prs2, canonicalProps,shiftList,res}, FCPrint[3, "FDS: fdsOneLoopsGeneric: Entering with ", expr, FCDoControl->fdsVerbose]; (* Convert the integral to a more suitable form, i.e. 1/[q^2-m1^2][(q+p)^2-m2^2] becomes {q,q+p} *) - prs = Expand/@({props} /. PropagatorDenominator[z_, _ : 0] :> (z /. Momentum[a_, _ : 4] :> a)); + prs = Expand/@({props} /. { + PropagatorDenominator[z_, _ : 0] :> (z /. Momentum[a_, _ : 4] :> a), + StandardPropagatorDenominator[z_, _ ,_ ,_] :> (z /. Momentum[a_, _ : 4] :> a), + CartesianPropagatorDenominator[z_, _ ,_ ,_] :> (z /. CartesianMomentum[a_, _ : 3] :> a) + }); (* List of possible canonical propagators *) canonicalProps = createOneLoopCanonicalPropsList[prs,q,True]; @@ -368,11 +694,13 @@ checkOneLoopProp[x, canonicalProps]= MatchQ[x, Alternatives @@ canonicalProps]; -(* Generate some posssible canonical propagators out of the given +(* + Generate some posssible canonical propagators out of the given list of all momenta and their prefactors. This is of course pure heuristics, since a priori we don't know how the momenta realy flow through the diagram... - Safe for memoization. *) + Safe for memoization. +*) createOneLoopCanonicalPropsList[prs_,q_,ext_]:= createOneLoopCanonicalPropsList[prs,q,ext]= Block[{moms,extra,fu,res}, @@ -443,7 +771,7 @@ Map[Solve[(xx /. q -> dummyP) == #, dummyP] &, canonicalProps] /. dummyP -> q ]; -(* Sorts the list of possible shifts according the the given criteria *) +(* Sorts the list of possible shifts according to the given criteria *) sortWeightedShifts[{x1_,a1_,b1_,x2_},{y1_,a2_,b2_,y2_}]:= sortWeightedShifts[{x1,a1,b1,x2},{y1,a2,b2,y2}]= Which[ @@ -463,21 +791,26 @@ ]; -(* Checks if the integral vanishes by symmetry. Memoization should be done via - FCUseCache *) -removeAnitsymmetricIntegrals[int_,q_]:= - If[ Expand[(MomentumExpand[EpsEvaluate[int/.q->-q]] /. - FeynAmpDenominator -> feynsimp[{q}] /. FeynAmpDenominator -> feynord[{q}])+int]===0, +(* Checks if the integral vanishes by symmetry (multiloop version). + Memoization should be done via FCUseCache *) +removeAnitsymmetricIntegrals[int_, qmin_List, qs_List]:= + If[ TrueQ[Expand[(MomentumExpand[EpsEvaluate[int/.Thread[Rule[qmin, -qmin]] ,FCI->True]] /. + FeynAmpDenominator -> feynsimp[qs] /. FeynAmpDenominator -> feynord2[qs])+int]===0], 0, int - ]; + ]/; int=!=0; -(* Sort propagators in a FeynAmpDenominator. +removeAnitsymmetricIntegrals[0,{__}, {__}]:= + 0; + +(* + Sort propagators in a FeynAmpDenominator. Propagators with the smallest number of momenta go first. If the number of momenta is the same, do the lexicographic ordering of the momenta. If the momenta are the same, do the lexicographic ordering of the masses. - Safe for memoization. + Safe for memoization. The second slots of SFADs and CFADs are not an issue, + as no momentum expansions are involved. *) lenso[PD[x_, m1_], PD[y_, m2_]]:= lenso[PD[x, m1], PD[y, m2]]= @@ -494,13 +827,33 @@ Abort[] ]; +lenso[ (h1:StandardPropagatorDenominator|CartesianPropagatorDenominator)[x1_, x2_, m1_, s1_], + (h2:StandardPropagatorDenominator|CartesianPropagatorDenominator)[y1_, y2_, m2_, s2_]]:= + lenso[ h1[x1, x2, m1, s1], h2[y1, y2, m2, s2]]= + Which[ + h1===StandardPropagatorDenominator && h2===CartesianPropagatorDenominator, + True, + h1===CartesianPropagatorDenominator && h2===StandardPropagatorDenominator, + False, + NTerms[x1+x2] =!= NTerms[y1+y2], + NTerms[x1+x2] < NTerms[y1+y2], + NTerms[x1+x2] === NTerms[y1+y2], + If[ x1+x2=!=y1+y2, + OrderedQ[{x1+x2,y1+y2}], + OrderedQ[{m1,m2}] + ], + True, + Message[FDS::failmsg,"Can't sort the list of propagators."]; + Abort[] + ]; -(* Special sorting for fdsOneLoopGeneral. The massless propagator with the - smallest number of external momenta is put first. - Safe for memoization. +(* + Special sorting for fdsOneLoopGeneral. The massless propagator with the + smallest number of external momenta is put first. Safe for memoization. + The second slots of SFADs and CFADs are not an issue, as no momentum + expansions are involved. *) - lenso2[PD[x_, m1_], PD[y_, m2_]]:= lenso2[PD[x, m1], PD[y, m2]]= Which[ @@ -524,178 +877,166 @@ Abort[] ]; -(* Sort the propagators into some canonical order. Safe for memoization *) -feynord[a__PD] := +lenso2[ (h1:StandardPropagatorDenominator|CartesianPropagatorDenominator)[x1_, x2_, m1_, s1_], + (h2:StandardPropagatorDenominator|CartesianPropagatorDenominator)[y1_, y2_, m2_, s2_]]:= + lenso2[ h1[x1, x2, m1, s1], h2[y1, y2, m2, s2]]= + Which[ + h1===StandardPropagatorDenominator && h2===CartesianPropagatorDenominator, + True, + h1===CartesianPropagatorDenominator && h2===StandardPropagatorDenominator, + False, + m1=!=0 && m2=!=0, + OrderedQ[{m1,m2}], + m1===0 && m2=!=0, + True, + m1=!=0 && m2===0, + False, + m1===0 && m2===0, + If[ NTerms[x1+x2] < NTerms[y1+y2], + True, + If[ NTerms[x1+x2] === NTerms[y1+y2], + OrderedQ[{x1+x2,y1+y2}], + False + ], + False + ], + True, + Message[FDS::failmsg,"Can't sort the list of propagators."]; + Abort[] + ]; + +(* + Sort the propagators into some canonical order. Safe for memoization. + The second slots of SFADs and CFADs are not an issue, as no momentum + expansions are involved. +*) +feynord[a__] := MemSet[feynord[a], FeynAmpDenominator @@ Sort[{a}, lenso] - ]; + ]/;!FreeQ2[{a},{PropagatorDenominator,StandardPropagatorDenominator,CartesianPropagatorDenominator}]; feynord[qs_List][a__] := MemSet[feynord[qs][a], FeynAmpDenominator @@ Join[Sort[SelectNotFree[{a}, Sequence@@qs], lenso], Sort[SelectFree[{a}, Sequence@@qs], lenso]] - ]; + ]/;!FreeQ2[{a},{PropagatorDenominator,StandardPropagatorDenominator,CartesianPropagatorDenominator}]; feynord2[qs_List][a__] := MemSet[feynord2[qs][a], FeynAmpDenominator @@ Join[Sort[SelectNotFree[{a}, Sequence@@qs], lenso2], Sort[SelectFree[{a}, Sequence@@qs], lenso2]] - ]; - + ]/;!FreeQ2[{a},{PropagatorDenominator,StandardPropagatorDenominator,CartesianPropagatorDenominator}]; (* Replaces 1/[(-q+x)^2-m^2] by 1/[(q-x)^2-m^2] (multiloop version). Safe for memoization despite MomentumExpand, since it is applied only inside FeynAmpDenominator, where feynsimpthere are no Pair's *) + +feynsimpAux[q_,pe_,di_,lmoms_,head_]:= + q===First[Sort[Intersection[Cases[-head[q,di] + pe + null1 + null2, head[qq_, ___] :> qq,Infinity], lmoms]]] + feynsimp[lmoms_List][a__PD] := MemSet[feynsimp[lmoms][a], - FeynAmpDenominator@@(Expand[MomentumExpand[{a}]] //. - PD[-Momentum[q_,di_:4] + pe_:0, m_]/; MemberQ[lmoms,q] && FreeQ2[pe,lmoms] :> PD[Momentum[q,di] - pe, m]) + Block[{pd}, + FeynAmpDenominator@@(Expand[MomentumExpand[{a}]] //. { + PD[-Momentum[q_,di_:4] + pe_:0, m_]/; MemberQ[lmoms,q] && FreeQ2[pe,lmoms] :> pd[Momentum[q,di] - pe, m], + PD[-Momentum[q_,di_:4] + pe_:0, m_]/; MemberQ[lmoms,q] && feynsimpAux[q, pe, di,lmoms, Momentum] :> + pd[Momentum[q,di] - pe, m] + } /. pd -> PD) + ] ]; +(* If there are not only PropagatorDenominators inside FeynAmpDenominator, then + the memoization is not safe anymore! *) +feynsimp[lmoms_List][a__ /; !MatchQ[{a},{__PD}](* && FreeQ[{a},GenericPropagatorDenominator]*)] := + Block[{pd, stpd, cpd}, + FeynAmpDenominator@@(Expand[MomentumExpand[{a}]] //. { -(* FDS for 2-loop integrals *) -FeynAmpDenominatorSimplify[ex_, q1_, q2_/;Head[q2]=!=Rule, opt:OptionsPattern[]] := - Block[ {exp, res, null1, null2, fclsOutput, intsRest, intsFDS, intsFDS2, intsFDS3, intsFDS4, - fds2Loops,fds1LoopQ1,fds1LoopQ2, intsFDSUnique, intsTops, intsTops2, - intsFDSUniqueFromSols, intsFDSUniqueFromSols2, intsFDSUniqueNested, solsListNested, - repRuleNested, fds2LoopsNested, - solsList, repRule - }, - - If [OptionValue[FCVerbose]===False, - fdsVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], - fdsVerbose=OptionValue[FCVerbose] - ]; - ]; - - If[ !FreeQ2[$ScalarProducts, {q1,q2}], - Message[FDS::failmsg, "Some loop momenta have scalar product rules attached to them. Evaluation aborted!"]; - Abort[] - ]; - - FCPrint[1,"FDS: Entering 2-loop FDS with", ex, FCDoControl->fdsVerbose]; - - If[ !OptionValue[FCI], - exp = FeynCalcInternal[ex], - exp = ex - ]; - - If [ OptionValue[FeynAmpDenominatorCombine], - exp = FeynAmpDenominatorCombine[exp] - ]; - - - (* Let us first extract all the scalar loop integrals *) - fclsOutput = FCLoopSplit[ex,{q1,q2},FCI->False]; - intsRest = fclsOutput[[1]]; - intsFDS = fclsOutput[[2]]+fclsOutput[[3]]+fclsOutput[[4]]; - - FCPrint[3, "FDS: Terms to be ignored ", intsRest, FCDoControl->fdsVerbose]; - FCPrint[3, "FDS: Possibly relevant terms ", intsFDS, FCDoControl->fdsVerbose]; + PD[-Momentum[q_,di_:4] + pe_:0, m_]/; MemberQ[lmoms,q] && FreeQ2[pe,lmoms] && scetPropagatorFreeQ[{a}, q] :> + pd[Momentum[q,di] - pe, m], - (* Nothing to do *) - If[ intsFDS === 0, - Return[ex] - ]; - - (* Split FADs to extract only loop momenta dependent pieces *) - intsFDS = FeynAmpDenominatorSplit[intsFDS,Momentum->{q1,q2}]; - - (* Let us now isolate all the 2-loop and 1-loop integrals that depend on q1,q2 *) - intsFDS2 = FCLoopIsolate[intsFDS, {q1,q2}, FCI->True, MultiLoop->True, Head->fds2Loops]; - intsFDS3 = FCLoopIsolate[intsFDS2, {q1}, FCI->True, MultiLoop->True, Head->fds1LoopQ1, ExceptHeads->{fds2Loops}]; - intsFDS4 = FCLoopIsolate[intsFDS3, {q2}, FCI->True, MultiLoop->True, Head->fds1LoopQ2, ExceptHeads->{fds2Loops}]; - (* Put the FADs back together *) - intsFDS4 = intsFDS4/. (h:fds2Loops|fds1LoopQ1|fds1LoopQ2)[x__]:> h[FeynAmpDenominatorCombine[x]]; + PD[-Momentum[q_,di_:4] + pe_:0, m_]/; MemberQ[lmoms,q] && feynsimpAux[q, pe, di,lmoms, Momentum] + && scetPropagatorFreeQ[{a}, q] :> + pd[Momentum[q,di] - pe, m], - FCPrint[3, "FDS: Isolated terms ", intsFDS4, FCDoControl->fdsVerbose]; + StandardPropagatorDenominator[-Momentum[q_,di_:4] + pe_:0, x1_, x2_, x3_]/; MemberQ[lmoms,q] && FreeQ2[pe,lmoms] && scetPropagatorFreeQ[{a}, q] :> + stpd[Momentum[q,di] - pe, (x1 /. q -> - q) , x2, x3], - (* Extract all the unique integrals *) - intsFDSUnique = Cases[intsFDS4+null1+null2,(fds2Loops|fds1LoopQ1|fds1LoopQ2)[x__],Infinity]//Union; - FCPrint[3, "FDS: Unique terms ", intsFDSUnique, FCDoControl->fdsVerbose]; + StandardPropagatorDenominator[-Momentum[q_,di_:4] + pe_:0, x1_, x2_, x3_]/; MemberQ[lmoms,q] && feynsimpAux[q, pe, di,lmoms, Momentum] && scetPropagatorFreeQ[{a}, q] :> + stpd[Momentum[q,di] - pe, (x1 /. q -> - q) , x2, x3], - (* Apply standard simplifications *) - solsList = MapIndexed[ - Which [ Head[#]===fds2Loops, - fds2Loops[oldFeynAmpDenominatorSimplify[(#/. fds2Loops->Identity),q1,q2,opt]], - Head[#]===fds1LoopQ1, - FeynAmpDenominatorSimplify[(#/. fds1LoopQ1->Identity),q1,opt], - Head[#]===fds1LoopQ2, - FeynAmpDenominatorSimplify[(#/. fds1LoopQ2->Identity),q2,opt], - True, - Message[FDS::failmsg,"Unknown integral type!"]; - ]&,intsFDSUnique]; + CartesianPropagatorDenominator[-CartesianMomentum[q_,di_:3] + pe_:0, x1_, x2_, x3_]/; MemberQ[lmoms,q] && FreeQ2[pe,lmoms] && scetPropagatorFreeQ[{a}, q] :> + cpd[CartesianMomentum[q,di] - pe, (x1 /. q -> - q) , x2, x3], + CartesianPropagatorDenominator[-CartesianMomentum[q_,di_:3] + pe_:0, x1_, x2_, x3_]/; MemberQ[lmoms,q] && feynsimpAux[q, pe, di,lmoms, CartesianMomentum] && scetPropagatorFreeQ[{a}, q] :> + cpd[CartesianMomentum[q,di] - pe, (x1 /. q -> - q) , x2, x3] - (* Tailored simplifications for speical 2-loop topologies *) - If[ OptionValue[DetectLoopTopologies], - FCPrint[3, "FDS: Simplifying special topologies.", FCDoControl->fdsVerbose]; - + } /. {pd -> PD, stpd -> StandardPropagatorDenominator, cpd -> CartesianPropagatorDenominator}) + ]; - (* Isolate single loop integrals in every solution *) - intsFDSUniqueFromSols2 = solsList/. - {fds2Loops[x__]:> Map[fds2LoopsNested,Expand2[x,FeynAmpDenominator]+null1+null2]}/. - fds2LoopsNested[null1|null2] -> 0; +(* + Check for the presence of the propagators like 1/(p.q+I eta) where the shift q-> -q + would yields 1/(p.q+I eta) ==== 1/(-p.q+I eta) =!= -1/(p.q+I eta) +*) +scetPropagatorFreeQ[{a__}, l_]:= + (Cases[{a}, (StandardPropagatorDenominator|CartesianPropagatorDenominator)[0, x_ /; ! FreeQ[x, l], _, _], Infinity] === {}) - (* Extract unique nested integrals *) - intsFDSUniqueNested = Cases[intsFDSUniqueFromSols2,fds2LoopsNested[x__],Infinity]//Union; - FCPrint[3, "FDS: Unique terms ", intsFDSUniqueNested, FCDoControl->fdsVerbose]; +fdsMultiLoop[loopInt : (_. FeynAmpDenominator[props__]), qs__]:= + Block[{ tmp,res,tmpNew,solsList,repRule}, + (* The input of fdsMultiLoop is guaranteed to contain + only a single loop integral. This makes many things simpler. *) - intsTops=getTopology[#,{q1,q2}]&/@(intsFDSUniqueNested/.fds2LoopsNested->Identity); - FCPrint[3, "FDS: Topologies ", intsTops, FCDoControl->fdsVerbose]; + tmp = loopInt; - intsTops2 = checkTopology/@intsTops; - FCPrint[3, "FDS: Checked topologies ", intsTops2, FCDoControl->fdsVerbose]; + FCPrint[3, "FDS: fdsMultiLoop: Entering with: ", tmp, FCDoControl->fdsVerbose]; - solsListNested = MapIndexed[ - (* Here one could add more topologies if needed *) - Which[ #1==="2-loop-self-energy", - (fds2LoopsSE[(First[intsFDSUniqueNested[[#2]]]/.fds2LoopsNested->Identity),q1,q2,(Total[intsTops[[#2]]])[[3]][[1]]]/. FeynAmpDenominator -> feyncan), - #1==="generic", - (First[intsFDSUniqueNested[[#2]]]/. fds2LoopsNested->Identity), - True, - Message[FDS::failmsg,"Unknown 2-loop topology!"]; - Abort[] + (* Order the propagators such, that the massless propagator with the smallest + number of the external momenta goes first. This is not the standard ordering, + but it is useful as the first step to bring the integral into canonical form *) + tmp = tmp /. FeynAmpDenominator -> feynsimp[{qs}] /. FeynAmpDenominator -> feynord2[{qs}]; + FCPrint[3, "FDS: fdsMultiLoop: After first ordering of the propagators: ", tmp, FCDoControl->fdsVerbose]; - ]&,intsTops2]; + (* Integrals that are antisymmetric under qi->-qi are removed *) + tmp = Fold[removeAnitsymmetricIntegrals[#1, #2, {qs}] &, tmp, Subsets[{qs}]]; - If[Length[intsFDSUniqueNested]=!=Length[solsListNested] || !FreeQ2[solsListNested,{fds2Loops,fds1LoopQ1,fds1LoopQ2,fds2LoopsNested}], - Message[FDS::failmsg,"FDS can't create the solution list."]; - Abort[] - ]; - repRuleNested = MapIndexed[(Rule[#1, First[solsListNested[[#2]]]]) &, intsFDSUniqueNested]; + FCPrint[3, "FDS: fdsMultiLoop: After removing antisymmetric integrals: ", tmp, FCDoControl->fdsVerbose]; - solsList = intsFDSUniqueFromSols2/.repRuleNested, - (* Otherwise just remove the fds2Loops heads *) - solsList = solsList/.fds2Loops->Identity + If[ tmp===0, + Return[0], + res = tmp ]; + (* + FCPrint[3, "FDS: fdsMultiLoop: res: ", res, FCDoControl->fdsVerbose]; + (* After the shifts our single integral usually turns into a sum of + integrals with different numerators. Some of them might vanish by symmetry *) + res = Expand2[ExpandScalarProduct[res,Momentum->{qs},EpsEvaluate->True],qs]; + FCPrint[3, "FDS: fdsMultiLoop: res: ", res, FCDoControl->fdsVerbose]; - If[Length[solsList]=!=Length[intsFDSUnique] || !FreeQ2[solsList,{fds2Loops,fds1LoopQ1,fds1LoopQ2,fds2LoopsNested}], - Message[FDS::failmsg,"FDS can't create the solution list."]; - Abort[] - ]; - (* Final replacement rule *) - repRule = MapIndexed[(Rule[#1, First[solsList[[#2]]]]) &, intsFDSUnique]; + tmpNew = FCLoopExtract[res, {q},loopHead, DropScaleless->True,FCI->True, PaVe->False]; + FCPrint[3, "FDS: fdsOneLoop: tmpNew: ", tmpNew, FCDoControl->fdsVerbose]; - res = intsRest + (intsFDS4/.repRule); + solsList = Map[removeAnitsymmetricIntegrals[#,q]&,(tmpNew[[3]]/.loopHead->Identity)]; + FCPrint[3, "FDS: fdsOneLoop: solsList: ", solsList, FCDoControl->fdsVerbose]; - If[ !FreeQ2[res,{fds2Loops,fds1LoopQ1,fds1LoopQ2}], - Message[FDS::failmsg,"Some subroutines in FDS didn't work properly."]; - Abort[] - ]; + repRule = Thread[Rule[tmpNew[[3]],solsList]]; + FCPrint[3, "FDS: fdsOneLoop: repRule: ", repRule, FCDoControl->fdsVerbose]; - FCPrint[1,"FDS: Leaving 2-loop FDS with", res, FCDoControl->fdsVerbose]; - res - ]; + res = tmpNew[[1]] + (tmpNew[[2]]/.repRule); + FCPrint[3, "FDS: fdsOneLoop: res: ", res, FCDoControl->fdsVerbose]; + *) + (* Finally, order all the propagators canonically *) + res = res /. FeynAmpDenominator :> feynord[{qs}]; + FCPrint[3, "FDS: fdsMultiLoop: Final ordering: ", res, FCDoControl->fdsVerbose]; + FCPrint[3, "FDS: fdsMultiLoop: Leaving with: ", res, FCDoControl->fdsVerbose]; + res + ]/; !FreeQ2[{props},{qs}]; oldFeynAmpDenominatorSimplify[ex_, q1_, q2_/;Head[q2]=!=Rule, opt:OptionsPattern[]] := Block[ {exp=ex, ot, pot,topi, topi2, bas, basic,res,pru,oneONE,fadalll,fadallq1q2,amucheck}, @@ -719,8 +1060,7 @@ (* to improve speed *) zexp /. FeynAmpDenominator -> amucheck[zq1,zq2] /. amucheck -> nopcheck, (* normal procedure *) - translat[ zexp /. FeynAmpDenominator -> amucheck[zq1,zq2] /. - amucheck -> nopcheck, zq1, zq2] /. + translat[ zexp /. FeynAmpDenominator -> amucheck[zq1,zq2] /. amucheck -> nopcheck, zq1, zq2] /. FeynAmpDenominator -> feynsimp[{zq1}] /. FeynAmpDenominator -> feynsimp[{zq2}] /. FeynAmpDenominator -> feynord ] /. { @@ -728,17 +1068,18 @@ FeynAmpDenominator[pr1___, PD[_. + Momentum[zq1,_:4], _], pr2___ ] :> 0 /; FreeQ[{pr1, pr2}, zq1] }; - amucheck[k1_, k2_][PD[aa_. Momentum[k1_,dii___] + bb_. ,0].., b___] := - 0 /; FreeQ[{b}, k1]; + (*Seems that for some reason we are not allowed to touch those named blanks*) + amucheck[k1_, _][PD[_. Momentum[k1_,___] + bb_. ,0].., b___] := + 0 /; FreeQ[{b}, k1] && bb=!=0; - amucheck[k1_, k2_][b___,PD[aa_. Momentum[k1_,dii___] + bb_. ,0]..] := - 0 /; FreeQ[{b}, k1]; + amucheck[k1_, _][b___,PD[_. Momentum[k1_,___] + bb_. ,0]..] := + 0 /; FreeQ[{b}, k1] && bb=!=0; - amucheck[k1_, k2_][b___,PD[aa_. Momentum[k2_,dii___] + bb_. ,0]..] := - 0 /; FreeQ[{b}, k2]; + amucheck[_, k2_][b___,PD[_. Momentum[k2_,___] + bb_. ,0]..] := + 0 /; FreeQ[{b}, k2] && bb=!=0; - amucheck[k1_, k2_][PD[aa_. Momentum[k2_,dii___] + bb_. ,0].., b___] := - 0 /; FreeQ[{b}, k2]; + amucheck[_, k2_][PD[_. Momentum[k2_,___] + bb_. ,0].., b___] := + 0 /; FreeQ[{b}, k2] && bb=!=0; pe[qu1_,qu2_, prop_] := Block[ {pet = SelectFree[Cases2[prop//MomentumExpand,Momentum]/. @@ -821,7 +1162,7 @@ exp = topi[exp] /. topi -> topi2 /. topi2[a_] :> FCIntegral[a//FeynCalcExternal]; exp = exp /. ot /. ot /. pot /. pot /. FCIntegral[b_] :> - FeynCalcInternal[b]; + FCI[b]; ]; FCPrint[3,"FDS: oldFeynAmpDenominatorSimplify: Before fadall", exp, "", FCDoControl->fdsVerbose]; @@ -829,8 +1170,7 @@ If[ Head[exp] =!= Plus, If[ OptionValue[Options[FDS],{opt},FC2RHI], (* This is OPE related stuff with FC2RHI *) - res = FC2RHI[FixedPoint[fadalll[#, q1, q2]&, Expand2[exp, q1], 7] /. pru, q1, q2, - IncludePair -> (IncludePair /. {opt} /. Options[FDS])], + res = FC2RHI[FixedPoint[fadalll[#, q1, q2]&, Expand2[exp, q1], 7] /. pru, q1, q2, IncludePair -> (IncludePair /. {opt} /. Options[FDS])], (* This is the usual routine *) res = FixedPoint[fadalll[#, q1, q2]&, Expand2[exp, q1], 7] /. pru ], @@ -876,11 +1216,11 @@ fds2LoopsSE[expr_,q1_,q2_,p_]:= (MomentumExpand[FixedPoint[fds2LoopsSE2[#,q1,q2,p]&,expr,5]]/. { - PropagatorDenominator[-Momentum[q1,dim_:4], m_]:>PropagatorDenominator[Momentum[q1,dim], m], - PropagatorDenominator[-Momentum[q2,dim_:4], m_]:>PropagatorDenominator[Momentum[q2,dim], m], - PropagatorDenominator[Momentum[p, dim1_:4]-Momentum[q1, dim2_:4], m_]:>PropagatorDenominator[Momentum[q1, dim2]-Momentum[p, dim1],m], - PropagatorDenominator[Momentum[p, dim1_:4]-Momentum[q2, dim2_:4], m_]:>PropagatorDenominator[Momentum[q2, dim2]-Momentum[p, dim1],m], - PropagatorDenominator[Momentum[q2, dim1_:4]-Momentum[q1, dim2_:4], m_]:>PropagatorDenominator[Momentum[q1, dim2]-Momentum[q2, dim1],m] + PropagatorDenominator[-Momentum[q1,d_:4], m_]:>PropagatorDenominator[Momentum[q1,d], m], + PropagatorDenominator[-Momentum[q2,d_:4], m_]:>PropagatorDenominator[Momentum[q2,d], m], + PropagatorDenominator[Momentum[p, d_:4]-Momentum[q1, e_:4], m_]:>PropagatorDenominator[Momentum[q1, e]-Momentum[p, d],m], + PropagatorDenominator[Momentum[p, d_:4]-Momentum[q2, e_:4], m_]:>PropagatorDenominator[Momentum[q2, e]-Momentum[p, d],m], + PropagatorDenominator[Momentum[q2, d_:4]-Momentum[q1, e_:4], m_]:>PropagatorDenominator[Momentum[q1, e]-Momentum[q2, d],m] })/;!FreeQ[expr,q1] && !FreeQ[expr,q2]; (* special iterative algorithm tailored for 2-loop self-energy integrals that determines the correct shifts @@ -1153,7 +1493,7 @@ re = ExpandScalarProduct[prmomex[a /. {RuleDelayed @@ ( {x, y} /. Momentum -> extractm), RuleDelayed @@ ( {w, z} /. Momentum -> extractm)}], - FeynCalcInternal -> False]; + FCI -> True]; ]; ]; re @@ -1171,7 +1511,7 @@ If[ checkfd[tem] === False, re = a, re = ExpandScalarProduct[prmomex[a /. (Rule @@ ( {x, y} /. Momentum -> extractm ))], - FeynCalcInternal -> False] + FCI -> True] ]; ]; re @@ -1199,7 +1539,7 @@ Pair[Momentum[OPEDelta, di], Momentum[pi, di]] - Pair[Momentum[OPEDelta, di], Momentum[pe, di]] + Pair[Momentum[OPEDelta, di], Momentum[q1, di]]), w] - ) /. q1->(-q1+pe-pi),FeynCalcInternal -> False]; + ) /. q1->(-q1+pe-pi),FCI -> True]; tt = PowerSimplify[tt]; If[ FreeQ[tt, (pow_ /; (pow === Power2 || pow === Power))[(a_Plus),v_ /; Head[v] =!= Integer]], @@ -1221,7 +1561,7 @@ tt = ExpandScalarProduct[(fa powe[( -Pair[Momentum[OPEDelta, di], Momentum[pe, di]] + Pair[Momentum[OPEDelta, di], Momentum[q1, di]]), w] - ) /. q1->(-q1+pe),FeynCalcInternal -> False]; + ) /. q1->(-q1+pe),FCI -> True]; If[ FreeQ[tt, (pow_ /; (pow === Power2 || pow === Power))[(a_Plus),v_] ], If[ !FreeQ[tt,Eps], @@ -1241,7 +1581,7 @@ tt = ExpandScalarProduct[(fa powe[( Pair[Momentum[OPEDelta, di], Momentum[pe, di]] - Pair[Momentum[OPEDelta, di], Momentum[q1, di]]), w] - ) /. q1->(-q1+pe),FeynCalcInternal -> False]; + ) /. q1->(-q1+pe),FCI -> True]; If[ FreeQ[tt, (pow_ /; (pow === Power2 || pow === Power))[(a_Plus),v_] ], If[ !FreeQ[tt,Eps], @@ -1498,6 +1838,25 @@ (FCPrint[1,"in translat" , x, "|", q1, "|" ,q2]; Expand2[x, FeynAmpDenominator] + nuLlL1 + nuLlL2)] /. {nuLlL1:>0, nuLlL2:>0} ]]; +integralClassify[loopHead[x_,y_]]:= + MemSet[integralClassify[loopHead[x,y]], + Which[ + FreeQ2[x,{StandardPropagatorDenominator,CartesianPropagatorDenominator,GenericPropagatorDenominator}] && + !FreeQ2[x,{PropagatorDenominator}], + (* FAD *) + loopHead[x,y], + FreeQ2[x,{PropagatorDenominator,CartesianPropagatorDenominator,GenericPropagatorDenominator}] && + !FreeQ2[x,{StandardPropagatorDenominator}], + (* SFAD *) + sLoopHead[x,y], + FreeQ2[x,{PropagatorDenominator,StadndardPropagatorDenominator,GenericPropagatorDenominator}] && + !FreeQ2[x,{CartesianPropagatorDenominator}], + (* CFAD *) + cLoopHead[x,y], + True, + x + ]]; + FCPrint[1,"FeynAmpDenominatorSimplify.m loaded."]; End[] diff --git a/FeynCalc/LoopIntegrals/FeynAmpDenominatorSplit.m b/FeynCalc/LoopIntegrals/FeynAmpDenominatorSplit.m index d35f02258..6894cb81f 100644 --- a/FeynCalc/LoopIntegrals/FeynAmpDenominatorSplit.m +++ b/FeynCalc/LoopIntegrals/FeynAmpDenominatorSplit.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Splits FeynAmpDenominators into multiple parts *) @@ -29,28 +29,45 @@ Begin["`FeynAmpDenominatorSplit`Private`"] -Options[FeynAmpDenominatorSplit]={ - FCI -> False, - FCE -> False, - Momentum -> All +Options[FeynAmpDenominatorSplit] = { + FCE -> False, + FCI -> False, + List -> False, + Momentum -> All, + MomentumExpand -> True }; FeynAmpDenominatorSplit[expr_, OptionsPattern[]] := - Block[{res,momList,fad}, + Block[{res,momList,fad,head, allFads, allFadsEval,repRule}, If[ !OptionValue[FCI], res = FCI[expr], res = expr ]; + If[ TrueQ[OptionValue[List]], + head = List, + head = Times + ]; momList = OptionValue[Momentum]; + allFads = Cases2[res,FeynAmpDenominator]; + allFadsEval = allFads; + + + If[ OptionValue[MomentumExpand], + allFadsEval = MomentumExpand/@allFadsEval + ]; + If[ momList=!=All && Head[momList]===List, - res = res /. FeynAmpDenominator[props__] :> fad[SelectFree[{props},Sequence@@momList]]* - fad[SelectNotFree[{props},Sequence@@momList]] /. fad[{}]:>1 /. fad[{pr__}]:>FeynAmpDenominator[pr], - res = res /. FeynAmpDenominator[a__] :> Times@@Map[FeynAmpDenominator, {a}] + allFadsEval = allFadsEval /. FeynAmpDenominator[props__] :> head[fad[SelectFree[{props},Sequence@@momList]], + fad[SelectNotFree[{props},Sequence@@momList]]] /. fad[{}]:>1 /. fad[{pr__}]:>FeynAmpDenominator[pr], + allFadsEval = allFadsEval /. FeynAmpDenominator[a__] :> head@@Map[FeynAmpDenominator, {a}] ]; + repRule = Thread[Rule[allFads,allFadsEval]]; + res = res/. Dispatch[repRule]; + If [OptionValue[FCE], res=FCE[res] ]; diff --git a/FeynCalc/LoopIntegrals/FeynmanDoIntegrals.m b/FeynCalc/LoopIntegrals/FeynmanDoIntegrals.m index 68caac0cd..494a816c1 100644 --- a/FeynCalc/LoopIntegrals/FeynmanDoIntegrals.m +++ b/FeynCalc/LoopIntegrals/FeynmanDoIntegrals.m @@ -39,11 +39,17 @@ options of the integration functions specified (FCIntegrate and FCNIntegrate) \ Begin["`FeynmanDoIntegrals`Private`"] -Options[FeynmanDoIntegrals] = {NIntegrate -> False, Dimension -> D, - EpsilonOrder -> {-2,0}, FCIntegrate -> TimedIntegrate, - Simplify -> True, Expand -> True, Series -> True, - FCNIntegrate -> (DOT[Sequence @@ ((Integratedx@@#1)& ) /@ {##2}, #1]&) - (*((0*#1) &)*)(*TimedIntegrate[##, Timing -> 10, Integrate -> NIntegrate]*)}; +Options[FeynmanDoIntegrals] = { + Dimension -> D, + EpsilonOrder -> {-2,0}, + Expand -> True, + FCIntegrate -> TimedIntegrate, + FCNIntegrate -> (DOT[Sequence @@ ((Integratedx@@#1)& ) /@ {##2}, #1]&), + NIntegrate -> False, + Series -> True, + Simplify -> True + (*((0*#1) &)*)(*TimedIntegrate[##, Timing -> 10, Integrate -> NIntegrate]*) +}; FeynmanDoIntegrals::"integrate" = "There is a problem checking for \ integrability. Please check that your input is correct. Aborting."; @@ -114,7 +120,7 @@ options of the integration functions specified (FCIntegrate and FCNIntegrate) \ FeynmanDoIntegrals[DOT[ints0:(Integratedx[_, _, _]..), (exp_?((FreeQ[#, Integratedx])&))], moms0_List:dum, vars0_List:dum, opts___Rule] := - Block[ {tc,tcc,tmpcol,a,ress}, + Block[ {tc,tcc,tmpcol,ress}, (*Check for DeltaFunctions and try to factor them out*) If[ FreeQ[exp, DeltaFunction[_]] =!= False, @@ -162,7 +168,11 @@ options of the integration functions specified (FCIntegrate and FCNIntegrate) \ expred, varsdrop, newvars, delcol, ChVars, x1, x2, res, intopts, nintopts, fci, fcin*) DD = Dimension /. Flatten[{opts}] /. Options[FeynmanDoIntegrals], - epsorders = EpsilonOrder /. Flatten[{opts}] /. Options[FeynmanDoIntegrals]}, + epsorders = EpsilonOrder /. Flatten[{opts}] /. Options[FeynmanDoIntegrals], + serie,fci,fcin,intopts,nintopts,exp,serie0,serie1,serie2,tmpres,transfac, + ruls,kk,varsdrop,epsorder,vars,varlims0,varlims,varlimsout,varp, newvars, + expred, delcol,serie4,serie5, del, res,moms, cou, serie3, seri, tmp, tRule + }, varsdrop = {}; (*Options to pass to Integrate and NIntegrate*) @@ -229,8 +239,8 @@ options of the integration functions specified (FCIntegrate and FCNIntegrate) \ varsdrop = Union[varsdrop, {newvars[[-1]]}]; (*Jacobian. This should be Abs[Det[...]], but with out choice of ChVars, the determinant is always positive*) - transfac = transfac*Det[Table[D[(ChVars @@ RotateRight[newvars])[[ii]], newvars[[jj]]], - {ii, Length[newvars]}, {jj,Length[newvars]}]] //. + transfac = transfac*Det[Table[D[(ChVars @@ RotateRight[newvars])[[i]], newvars[[j]]], + {i, Length[newvars]}, {j,Length[newvars]}]] //. newvars[[-1]] -> Plus@@delcol[[1]]; (*Integration limits*) varlims = If[ MatchQ[#[[1]],Alternatives@@newvars], @@ -270,6 +280,7 @@ options of the integration functions specified (FCIntegrate and FCNIntegrate) \ (*If so chosen, expand without blowing up too much:*) If[ (Expand /. Flatten[{opts}] /. Options[FeynmanDoIntegrals]), ruls = {}; + tRule = {z_^(b_)/;!FreeQ2[b, {DD,Epsilon}] :> z^(b /. {DD -> 4, Epsilon -> 0})}; FCPrint[2,"Starting expansion of expression size: ", LeafCount[exp]]; serie = Expand[dumf*transfac*(expred) /. Log[(a_?(!FreeQ[#, kk]&))*(b_?(FreeQ[#, kk]&))] :> @@ -280,8 +291,7 @@ options of the integration functions specified (FCIntegrate and FCNIntegrate) \ Itzykson&Zuber calculation*) a_?( (!NumberQ[#] && NumericQ1[#, Union[vars,{(*Epsilon*)}]] && PolynomialQ[(Denominator[#]* Numerator[#])& [ - Factor[# /. r_^(b_?((!FreeQ[#, DD|Epsilon])& )) :> - r^(b /. {DD -> 4, Epsilon -> 0})]], + Factor[# /. tRule]], vars]) & ) :> (sym = Unique["r"]; ruls = Append[ruls, sym -> a]; sym))] /. ruls; diff --git a/FeynCalc/LoopIntegrals/FeynmanParametrize1.m b/FeynCalc/LoopIntegrals/FeynmanParametrize1.m index 2a1a32ef1..711bea9c3 100644 --- a/FeynCalc/LoopIntegrals/FeynmanParametrize1.m +++ b/FeynCalc/LoopIntegrals/FeynmanParametrize1.m @@ -29,6 +29,9 @@ Begin["`FeynmanParametrize1`Private`"] +endrule::usage=""; +squarerule::usage=""; + Options[FeynmanParametrize1] = { FeynmanParameterNames -> {FCGV["a"], FCGV["b"], FCGV["c"], FCGV["d"], FCGV["e"]}, Method -> Denominator, @@ -39,7 +42,7 @@ FeynmanParametrize1::"noint" = "Could not integrate out `1` in `2`. Got `3`."; -fpar[{par__}][k_][f:FeynAmpDenominator[PropagatorDenominator[_,___]..], opts___Rule] := +fpar[{par__}][(*k*)_][f:FeynAmpDenominator[PropagatorDenominator[_,___]..], (*opts*)___Rule] := Block[ {i, n = Length[f], dum, pars = dum@@{par}}, pars = ReplacePart[pars,0,n]; (n-1)! * Dot[(DOT@@Table[Integratedx[pars[[i]],0,pars[[i-1]]],{i,n-1}]), @@ -52,7 +55,7 @@ epar[{par__}][k_][ (rest___)(f:FeynAmpDenominator[PropagatorDenominator[_,___]..]), opts___Rule] := - Block[ {i, n = Length[f], pars = {par}, res, y, ee, rr, cc, exp, + Block[ {i, n = Length[f], pars = {par}, res, y, cc, exp, mom, res1, rest1, dum, k2coeff, p}, (* Exponential factors already there *) @@ -100,7 +103,9 @@ FeynmanParametrize1[exp_,q_,opt___Rule] := Block[ {(*dim,dims,rul,aa,aaa,ee,qfacs,noqfacs,qq,res,par,dum, - efpar,rr,t,cc,ef,co,y,lis,sil,liss,re,wrap,b,qfac,noqfac,ints,res1,dd*)}, + efpar,rr,t,cc,ef,co,y,lis,sil,liss,re,wrap,b,qfac,noqfac,ints,res1,dd*) + dims,dim,rul,efpar,qfac,noqfac,qq,par,res,res1,len,len1, + qfacs,noqfacs,ef,wrap, dum, rebug, co, undebug, lis, sil, cc, lis1}, endrule = {}; qq = q/.Momentum[aaa_,___]:>aaa; par = FeynmanParameterNames/.{opt}/.Options[FeynmanParametrize1]; @@ -176,7 +181,7 @@ (* No integration *) ef = efpar[par][qq][FeynCalcInternal[qfacs],opt], (* Integration *) - ef = efpar[par][qq][FeynCalcInternal[qfacs*Times@@Cases[{rr},E^(ee_?(!FreeQ[#,qq]&))]],opt] + ef = efpar[par][qq][FeynCalcInternal[qfacs*Times@@Cases[{rr},E^(_?(!FreeQ[#,qq]&))]],opt] ]* (* wrap is just so we can later absorb into the DOT[Integratedx...] stuff *) @@ -194,13 +199,13 @@ (*The integration momentum y*) y = endrule[[1]]; (* Get the coefficient on y^2 in the exponential *) - co = -Coefficient[(ef/._*DOT[dd_,dd1__]:>DOT[dd,dd1])[[-1]]/.E^(ee_)->ee,Pair[y,y]]; + co = -Coefficient[(ef/._*DOT[dd_,dd1__]:>DOT[dd,dd1])[[-1]]/.E^(e_)->e,Pair[y,y]]; (* Do the y-integrals *) FCPrint[1,"Expanding and replacing tensor terms with integrated terms, using integration momentum ", endrule[[2]], " and coefficient ", co]; (rebug = Replace[ (undebug = Uncontract[Expand[ExpandProductExpand[ - Times@@Replace[{rr}, E^(ee_?(!FreeQ[#,qq]&)) -> 1 , 1] /. + Times@@Replace[{rr}, E^(_?(!FreeQ[#,qq]&)) -> 1 , 1] /. squarerule]], y[[1]], Pair -> All]), dum | dum * ( tt : ( _?(FreeQ[#, y]&))) | diff --git a/FeynCalc/LoopIntegrals/FeynmanReduce.m b/FeynCalc/LoopIntegrals/FeynmanReduce.m index 59926134a..e9519c74d 100644 --- a/FeynCalc/LoopIntegrals/FeynmanReduce.m +++ b/FeynCalc/LoopIntegrals/FeynmanReduce.m @@ -29,13 +29,16 @@ Begin["`Private`"] +dum::usage=""; +de::usage=""; + Options[FeynmanReduce] = {Dimension->D,Flatten->True,Expand->True}; FeynmanReduce[exp_Plus,params_List:dum,opts___Rule] := FeynmanReduce[#,params,opts]&/@exp; FeynmanReduce[exp_Times,params_List:dum,opts___Rule] := Times@@(FeynmanReduce[#,params,opts]& /@ - (de = Select[ List@@exp,MatchQ[#,DOT[ints:(Integratedx[_,_,_]..), + (de = Select[ List@@exp,MatchQ[#,DOT[(*ints:*)(Integratedx[_,_,_]..), r_?(FreeQ[#,Integratedx]&)]]& ])) * Times@@Complement[List@@exp,de]; FeynmanReduce[DOT[ints:(Integratedx[_,_,_]..), @@ -48,9 +51,9 @@ FeynmanReduce[exp_,params_List:dum,opts___Rule] := - Block[ {ps,ex,ints,cprul,al,pp,PP,cpp,cPP, + Block[ {ps,ex,cprul,al,cpp,cPP, go,a,intss,dumf,dumff,dim,dr,ss,ppex,PPex,sym, - p,ruls,r,rr,rrr,l,min,inc,un}, + ruls,rr,rrr,l,min,inc,un}, go = False; dim = Dimension/.Flatten[{opts}]/.Options[FeynmanReduce]; dr = r_^(b_?(!FreeQ[#,dim]&)):>r^(b/.dim->4); diff --git a/FeynCalc/LoopIntegrals/Hill.m b/FeynCalc/LoopIntegrals/Hill.m deleted file mode 100755 index 8b7f1b888..000000000 --- a/FeynCalc/LoopIntegrals/Hill.m +++ /dev/null @@ -1,31 +0,0 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: Hill*) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 22 June '97 at 22:59 *) -(* ------------------------------------------------------------------------ *) - -(* ------------------------------------------------------------------------ *) - - -Hill::usage = "Hill[x,y] gives the Hill identity with arguments x and y. \ -The returned object is 0."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`Hill`Private`"] - -Hill[x_, y_] := - PolyLog[2,x] - PolyLog[2,y] + PolyLog[2,Factor2[y/x]] + PolyLog[2, Factor2[(1-x)/(1-y)]] - - PolyLog[2, Factor2[y/x (1-x)/(1-y)]] - Pi^2/6 + Log[x] (Log[Factor2[1-x]] - Log[Factor2[1-y]]) + - Log[Factor2[(1-x)/(1-y)]] ( Log[Factor2[(x-y)/(1-y)]]-Log[x]- Log[Factor2[(x-y)/x]] + Log[Factor2[1-y]]) - - Log[Factor2[y/x (1-x)/(1-y)]] (Log[Factor2[(x-y)/(x (1-y))]] - Log[Factor2[(x-y)/x]] + Log[Factor2[1-y]]) - -FCPrint[1,"Hill.m loaded."]; -End[] diff --git a/FeynCalc/LoopIntegrals/Hypergeometric.m b/FeynCalc/LoopIntegrals/Hypergeometric.m index df928e91e..4fc355b30 100755 --- a/FeynCalc/LoopIntegrals/Hypergeometric.m +++ b/FeynCalc/LoopIntegrals/Hypergeometric.m @@ -61,11 +61,13 @@ by their definition in terms of a sum (the Sum is omitted and \ Begin["`Hypergeometric`Private`"] +tohyp::usage=""; + Options[HypergeometricAC] = {Collect2 -> True}; HypergeometricAC[n_Integer][exp_, opt___Rule] := Block[ {g = Gamma, A1, A2, B1, B2, f21 = Hypergeometric2F1, - res, colopt, vars}, + res, colopt, vars, hyp}, colopt = Collect2 /. {opt} /. Options[HypergeometricAC]; A1[a_,b_,c_] := g[c] g[c-a-b]/g[c-a]/g[c-b]; diff --git a/FeynCalc/LoopIntegrals/IFPDOff.m b/FeynCalc/LoopIntegrals/IFPDOff.m index 4006a84b1..153fb66bf 100644 --- a/FeynCalc/LoopIntegrals/IFPDOff.m +++ b/FeynCalc/LoopIntegrals/IFPDOff.m @@ -78,6 +78,13 @@ If[ FreeQ[exp, IFPD], exp, Block[ {int,qq,sub,t1,t2,t3,t4}, + + If[ !FreeQ2[{exp}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + + int = Apply[Hold, {exp}]; qq = {qu} /. Momentum[a_,___] :> a; t2 = Cases2[int, IFPD]; @@ -90,7 +97,7 @@ int = int /. sub; int = Operate[# /. Hold -> Identity&, int]; int = int /. FEP[a_, b_]^n_Integer?Negative :> - (ExpandScalarProduct[a, a] - b^2)^(-n); + (ExpandScalarProduct[Pair[a, a]] - b^2)^(-n); int = int /. {FEP :> FP, IFPD :> ifex}; int ] diff --git a/FeynCalc/LoopIntegrals/IFPDOn.m b/FeynCalc/LoopIntegrals/IFPDOn.m index 5e858f801..7774bb528 100644 --- a/FeynCalc/LoopIntegrals/IFPDOn.m +++ b/FeynCalc/LoopIntegrals/IFPDOn.m @@ -31,6 +31,11 @@ to the IFPD one (Inverse Feynman Propagator Denominator). I.e., \ Block[ {int,qq,sub,t0,t1,t2,t3,t4,MyHold,feynsub,ifnu, condition,pa,unsameq, checkm, checkp, thr,t0r,bb}, + If[ !FreeQ2[{exp}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + int = FeynAmpDenominatorSplit[exp]; t0 = Cases2[int, FeynAmpDenominator]; FCPrint[3,"t0: ",t0]; @@ -68,7 +73,7 @@ to the IFPD one (Inverse Feynman Propagator Denominator). I.e., \ (* calculate a canonical q.p as a side effect*) t3 = ifp[t3, qq]; FCPrint[3,"IFPDOn: t3 after ifp ", t3]; - sub = Table[(Pair @@ t3[[ij,1]]) -> t3[[ij,2]],{ij,Length[t3]}]; + sub = Table[(Pair @@ t3[[r,1]]) -> t3[[r,2]],{r,Length[t3]}]; int = int /. feynsub /. sub; int /. MyHold -> Identity ] diff --git a/FeynCalc/LoopIntegrals/NPointTo4Point.m b/FeynCalc/LoopIntegrals/NPointTo4Point.m new file mode 100644 index 000000000..e8ebb3576 --- /dev/null +++ b/FeynCalc/LoopIntegrals/NPointTo4Point.m @@ -0,0 +1,163 @@ +(* ::Package:: *) + + + +(* :Title: NPointTo4Point *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Reduction of IR finite scalar 5-point functions to + scalar 4-point functions according to arXiv:0709.1075 *) + +(* ------------------------------------------------------------------------ *) + +NPointTo4Point::usage = +"NPointTo4Point[expr, q] reduces scalar IR finite 5-point functions to scalar 4-point \ +functions according to Eq. 4.52 in arXiv:0709.1075."; + +NPointTo4Point::failmsg = "Error! NPointTo4Point has encountered a fatal problem and \ +must abort the computation. The problem reads: `1`"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`NPointTo4Point`Private`"] + +nptfpVerbose::usage=""; +isoName::usage=""; +dim::usage=""; + +Options[NPointTo4Point] = { + Dimension -> D, + FCE -> False, + FCVerbose -> False, + Factoring -> Factor2, + IsolateNames -> False, + List -> False +}; + +SetAttributes[matrixElement, Orderless]; + +smn[_] := + 0; + +smdaemon[x_] := + x /. SmallVariable -> smn; + +(* single Y_ij*) +matrixElement[{pi_, mi_}, {pj_, mj_}] := + Expand[smdaemon[mi^2 + mj^2 - ExpandScalarProduct[Pair[Momentum[pi - pj, dim],Momentum[pi - pj, dim]]]]]; + +getDet[mli_List,pli_List,sps_,fad_, termHold_, detFunc_, factFunc_, OptionsPattern[]]:= + Block[{pl = Prepend[pli, 0], n = Length[mli], Y, augmY, prefac}, + + (* create a list of the columns of eq. (4.54) *) + Y = Table[matrixElement[{pl[[i]], mli[[i]]}, {pl[[j]], mli[[j]]}], {j,1,n}, {i,1,n}]; + + If[ !SymmetricMatrixQ[Y], + Message[NPointTo4Point::failmsg, "Y-matrix is not symmetric."]; + Abort[] + ]; + + (* Y-matrix augmented with a row of (1,1,1,1,1) *) + augmY = Map[Prepend[#, 1] &, Y]; + + FCPrint[3,"NPointTo4Point: getDet: Y-matrix: ", Y, FCDoControl->nptfpVerbose]; + FCPrint[3,"NPointTo4Point: getDet: augmented Y-matrix: ", augmY, FCDoControl->nptfpVerbose]; + + (* Computing T_0^5 according to Eq. 4.52, working through the first row. *) + prefac = 1/termHold[detFunc[Y]]; + {prefac, sps Sum[(-1)^i termHold[factFunc[detFunc[Drop[augmY, None, {i+1,i+1}]]]] Drop[fad, {i, i}], {i, 1, Length[fad]}]} + ]; + +subdethold[x_] := + Isolate[x, IsolateNames -> isoName]; + +NPointTo4Point[expr_Plus,q_,opts:OptionsPattern[]]:= + Map[NPointTo4Point[#,q,opts]&,expr]; + +NPointTo4Point[pref_. fad_FeynAmpDenominator,qu_, OptionsPattern[]]:= + Block[{pp, res, tim,pl,ml, termHold,tmp, factoring}, + + + If[ !FreeQ2[{pref fad}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + + If[ OptionValue[FCVerbose]===False, + nptfpVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + nptfpVerbose=OptionValue[FCVerbose] + ]; + ]; + + If[ Length[List@@fad]=!=5 || !FreeQ[pref,qu], + Return[pref fad] + ]; + + FCPrint[0,"NPointTo4Point: The reduction of the scalar 5-point function ", fad ,"is valid only if \ +all the IR divergences were explicitly regularized with fictitious masses!", FCDoControl->nptfpVerbose]; + + isoName = OptionValue[IsolateNames]; + dim = OptionValue[Dimension]; + + If[ OptionValue[Factoring]===False, + factoring->Identity, + factoring = OptionValue[Factoring] + ]; + + If[ isoName===False, + termHold = Identity, + termHold = subdethold; + ]; + + FCPrint[3,"NPointTo4Point: Entering with: ", pref fad, FCDoControl->nptfpVerbose]; + + pp[a_, (*b*)_] := Expand[(a /. m_Momentum :> m[[1]]) - qu]; + + pl = Rest[fad /. FeynAmpDenominator->List /. PropagatorDenominator -> pp]; + + If[ FCGramDeterminant[pl]===0, + FCPrint[1,"NPointTo4Point: Zero Gram determinant encountered. Returning unevaluated result.", FCDoControl->nptfpVerbose]; + Return[pref fad] + ]; + + FCPrint[3,"NPointTo4Point: pl: ", pl, FCDoControl->nptfpVerbose]; + + ml = fad /. FeynAmpDenominator->List /. pd_PropagatorDenominator :> pd[[2]]; + FCPrint[3,"NPointTo4Point: ml: ", ml, FCDoControl->nptfpVerbose]; + + (*Extract the determinant*) + tmp = FCUseCache[getDet,{ml,pl,pref,fad, termHold, Det, factoring}]; + + If[ OptionValue[List], + res = tmp, + res = tmp[[1]] tmp[[2]] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[3,"NPointTo4Point: res: ", res, FCDoControl->nptfpVerbose]; + + res + + ]; + +NPointTo4Point[pref_. fad_FeynAmpDenominator,_, OptionsPattern[]]:= + (pref fad)/; Length[List@@fad]<5; + +NPointTo4Point[expr_,_, OptionsPattern[]]:= + expr/; FreeQ[expr,FeynAmpDenominator]; + +FCPrint[1,"NPointTo4Point.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/OneLoop.m b/FeynCalc/LoopIntegrals/OneLoop.m index d94428935..106f0d1ca 100644 --- a/FeynCalc/LoopIntegrals/OneLoop.m +++ b/FeynCalc/LoopIntegrals/OneLoop.m @@ -13,10 +13,6 @@ CombineGraphs::usage = "CombineGraphs is an option for OneLoopSum."; -DenominatorOrder::usage = -"DenominatorOrder is an option for OneLoop, if set to True the \ -PropagatorDenominator will be ordered in a standard way."; - FinalFunction::usage = "FinalFunction is an option for OneLoopSum."; ExtraVariables::usage = @@ -59,7 +55,7 @@ ReduceGamma::usage = "ReduceGamma is an option of OneLoop. If set to True all \ -DiracMatrix[6] and DiracMatrix[7] (i.e. all ChiralityProjector) \ +GA[6] and GA[7] (i.e. all chirality projectors) \ are reduced to Gamma5."; ReduceToScalars::usage = @@ -73,9 +69,6 @@ substitute \"SmallVariable[Melectron]\" \ for all Melectron's in the calculation."; -StandardMatrixElement::usage = -"StandardMatrixElement[ ... ] is the head for matrix element abbreviations."; - SetStandardMatrixElements::usage = "SetStandardMatrixElements[{sm1 -> abb1}, {sm2 -> abb2}, ...]. Set abbreviations \ abb1, abb2, ... for matrix elements sm1, sm2, ... \\ \ @@ -96,76 +89,19 @@ Begin["`OneLoop`Private`"] oneloopVerbose::usage=""; - -StandardMatrixElement /: -MakeBoxes[StandardMatrixElement[x_], TraditionalForm - ] := -RowBox[{"\[LeftDoubleBracketingBar]",TBox[x],"\[RightDoubleBracketingBar]"}]; - -StandardMatrixElement[0] := - 0; - - If[ StandardMatrixElement =!= Identity, - StandardMatrixElement[x_Plus] := - Map[StandardMatrixElement,x] - ]; - -(* ********************************************************************* *) -(* oneloop10 *) -(* ********************************************************************* *) - coneins[ x_ ] := - MemSet[coneins[x], - x/.Pair -> PairContract/. PairContract -> Pair]; - dotlin[x_] := - DotSimplify[x, Expanding -> False]; - -(* contractlidef *) - contractli[x_] := - Contract[ x, Expanding->True, Factoring->False, - EpsContract->False - ] // Expand; - conall[ x_ ] := - Contract[ x, (*conalldef*) - Expanding->True, EpsContract->True, Factoring->False - ] // Expand; - -(* -collin[ expr_, varh_, expa_]:= Collect[expr,Cases2[expr,varh]]; -*) - -collin[ expr_, varh_, expa_] := - Block[ {nx,se,i,co,new, null,res,frex,totvarh}, - new = 0; - nx = expr; - If[ expa =!= True, - frex[yy__] := - Plus[yy]/;!FreeQ2[{yy}, varh]; - nx = nx/.Plus -> frex - ]; - nx = Expand[nx]; - totvarh = Select[ Variables[ nx ], (!FreeQ2[#,varh])&]; - If[ (Length[nx] < 2142) && (LeafCount[nx]< 10^6), - res = Collect[ nx, totvarh ], - For[ i = 1, i <= Length[totvarh], i++, - co = Coefficient[ nx, totvarh[[i]] ]; - nx = nx - Expand[ co totvarh[[i]] ]; - new = new + totvarh[[i]] co ]; - res = nx + new - ]; - If[ expa =!= True, - res = res/.frex -> Plus - ]; - res - ]; - - - spinorchainevaluate[x_] := - Expand[DiracOrder[DiracSimplify[x]],q]; -(* - spinorchainevaluate[x_]:=DiracOrder[ - Expand[Contract[ SpinorChainEvaluate[x] ], DiracGamma],{q} - ]; -*) +breakdown::usage=""; +paveautoorder::usage=""; +paveautoreduce::usage=""; +reducegamma67::usage=""; +writeOutPaVee::usage=""; +born::usage=""; +scaling::usage=""; +writeOutPaVe::usage=""; +fFC::usage=""; +fFCT::usage=""; + +spinorchainevaluate[x_] := + Expand[DiracOrder[DiracSimplify[x]],q]; (* ********************************************************************* *) (* oneloop11 *) @@ -173,63 +109,56 @@ Options[OneLoop] = { - DenominatorOrder -> False, - Dimension -> D, - FinalSubstitutions -> {}, - Factoring -> False, - FCVerbose -> False, - FormatType -> InputForm, - InitialSubstitutions -> {}, - IntermediateSubstitutions -> {}, - IsolateNames -> False, - Mandelstam -> {}, - OneLoopSimplify -> False, - PaVeAutoOrder -> True, - PaVeAutoReduce -> True, - Prefactor -> 1, - ReduceGamma -> False, - ReduceToScalars -> False, - SmallVariables -> {}, - WriteOut -> False, - WriteOutPaVe -> False, - Sum -> True - }; + Dimension -> D, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> False, + FinalSubstitutions -> {}, + FormatType -> InputForm, + InitialSubstitutions -> {}, + IntermediateSubstitutions -> {}, + IsolateNames -> False, + Mandelstam -> {}, + NPointTo4Point -> True, + OneLoopSimplify -> False, + PaVeAutoOrder -> True, + PaVeAutoReduce -> True, + Prefactor -> 1, + ReduceGamma -> False, + ReduceToScalars -> False, + SmallVariables -> {}, + WriteOut -> False, + WriteOutPaVe -> False +}; (* setting WriteOut to "" retrieves also previously calculated results *) (* OneLoopdef *) (*New Jan 1999*) -OneLoop[FeynAmp[name_, k_, expr_], opts___] := +OneLoop[FeynAmp[name_, k_, expr_], opts:OptionsPattern[]] := OneLoop[name, k, expr, opts]; -OneLoop[_, FeynAmp[name_, k_, expr_], opts___] := +OneLoop[_, FeynAmp[name_, k_, expr_], opts:OptionsPattern[]] := OneLoop[name, k, expr, opts]; OneLoop[qq_,amp_] := OneLoop[False, qq,amp]/; qq=!=False; OneLoop[qq_,amp_, opts:OptionsPattern[]] := - OneLoop[False, qq,amp,opts]/; - qq=!=False; - -OneLoop[grname_,q_,integ_,opts:OptionsPattern[]] := - Block[ {oneamp = FeynCalcInternal[integ],iv,onemandel, - denf, denorder, denprop, isolatehead,tric, - var2,smallv,finsubst,fact,qpcancel,pvabbrev, - writeout,prop,dnq,dfsor,dfsorb, denomOrder,dfli, - vcid,intcan,de, oneoptga67,vin3, sqB,usual,tostandmat, - vint4,ret,vret,fmas,vva,smalist,isol,i, $higherpoint, - pvlist, pva,pvar,arglist,npref, nfact, nre,formattype,pLu, - prode, - collpav,simpit,prefactor,in3p, in3q, resin3q,newprefactor, - newnewprefactor, - newret, facto,ret2,defs,dim,breakdown,options, name = grname,DDim, - newoneamp,ip,lenneu, lenneu2, neuamp,paone,paone2,oneselect,fsub, - intermedsubst,writeoutrecover = False, oldfile, ftemp, - writeoutpav, uvpart,to4dim, oneampresult, null1, null2, - oneloopVerbose,nonLoopTerms,loopTerms, oneloopsimplify,inisubs, - reducegamma67,oneopt,tim,smav, smdaemon, smalldirac - }, + OneLoop[False, qq,amp,opts]/; qq=!=False; + +OneLoop[grname_,q_, expr_, OptionsPattern[]] := + Block[ {oneamp, iv,onemandel, denf, denprop, + isolateNames,tric, smallv,finalSubstitutions,writeOut, tostandmat, vva,isol,i, + $higherpoint, pva,pvar,arglist,npref, formatType, prode, + collpav,prefactor, newprefactor, newnewprefactor, + defs, dim, name = grname, newoneamp,ip,lenneu, parf, newamp, + lenneu2, neuamp,paone,paone2,oneselect,fsub, intermediateSubstitutions, + writeOutPaVe, oneampresult, null1, null2, oneloopVerbose, + nonLoopTerms=0,loopTerms=0, oneloopSimplify,initialSubstitutions, + tim,smav, smdaemon, smalldirac,startTime=AbsoluteTime[], namp, bB00, bB11,bB1, + oneampsave, voneampsma}, If [!FreeQ[$ScalarProducts, q], Message[OneLoop::failmsg, "The loop momentum " <> ToString[q,InputForm] <> " has scalar product rules attached to it."]; @@ -242,825 +171,389 @@ Abort[] ]; - If[ $BreitMaison || $Larin, - Message[OneLoop::failmsg, "OneLoop cannot be used for computations in the BMHV or Larin schemes. Use TID instead."]; + If[ !FreeQ2[{expr}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; Abort[] ]; - options = {opts}; - (* for FA2.0 *) - If[ Length[options] > 0, - If[ MatchQ[options[[1]] ,(a_List -> b_List)], - FA2Info = options[[1]]; - options = Rest[options] - ] + onemandel = OptionValue[Mandelstam]; + dim = OptionValue[Dimension]; + formatType = OptionValue[FormatType]; + isolateNames = OptionValue[IsolateNames]; + oneloopSimplify = OptionValue[OneLoopSimplify]; + prefactor = OptionValue[Prefactor]; + smallv = Flatten[{OptionValue[SmallVariables]}]; + initialSubstitutions = OptionValue[InitialSubstitutions]; + finalSubstitutions = OptionValue[FinalSubstitutions]; + intermediateSubstitutions = OptionValue[IntermediateSubstitutions]; + writeOutPaVe = OptionValue[WriteOutPaVe]; + reducegamma67 = OptionValue[ReduceGamma]; + writeOut = OptionValue[WriteOut]; + paveautoorder = OptionValue[PaVeAutoOrder]; + paveautoreduce = OptionValue[PaVeAutoReduce]; + breakdown = OptionValue[ReduceToScalars]; + + $higherpoint = False; + + If[ OptionValue[FCI], + oneamp = expr, + oneamp = FCI[expr] ]; - ( oneopt = Join[ options,Options[OneLoop] ]; - onemandel = Mandelstam/.oneopt; - denorder = DenominatorOrder/.oneopt; - dim = Dimension/.oneopt; - If[ dim===True, - dim = D - ]; - formattype = FormatType/.oneopt; - isolatehead = IsolateNames/.oneopt; - oneloopsimplify = OneLoopSimplify/.oneopt; - prefactor = Prefactor/.oneopt; - qpcancel = True; - smallv = Flatten[{ SmallVariables/.oneopt }]; - inisubs = InitialSubstitutions/.oneopt; - finsubst = FinalSubstitutions/.oneopt; - intermedsubst = IntermediateSubstitutions/.oneopt; - fact = Factoring/.oneopt; - writeoutpav = WriteOutPaVe /. oneopt; - uvpart = False; - reducegamma67 = ReduceGamma/.oneopt; - writeout = WriteOut/.oneopt; - - paveautoorder = PaVeAutoOrder /. oneopt; - paveautoreduce = PaVeAutoReduce /. oneopt; - If[ writeout === True || writeout === " ", - writeout = ""; - writeoutrecover = False - ]; - If[ writeout === True || writeout === "", - writeoutrecover = True - ]; - breakdown = ReduceToScalars/.oneopt; - If[ (breakdown===True) && ($LimitTo4 === False), - SetOptions[PaVeReduce, Dimension -> dim] - ]; - ); - If[ uvpart === True, - breakdown = True; - $LimitTo4 = True; - SetOptions[PaVeReduce, Dimension -> True]; - dim = 4 + + If[ !FreeQ2[Union[FCGetDimensions[oneamp/.DiracGamma[5|6|7]:>null1]],{4,-4}] && (FeynCalc`Package`DiracGammaScheme =!= "BMHV"), + Message[OneLoop::failmsg,"Your input contains a mixture of 4- and D-dimensional quantities. This is in general not allowed in dimensional regularization, unless you are using the Breitenlohner-Maison-t'Hooft-Veltman scheme."]; + Abort[] ]; - If[ (breakdown===True) && ( (writeoutpav===False) || (writeoutpav===True) ), - writeoutpav = "" + + If[ (breakdown===True) && ( (writeOutPaVe===False) || (writeOutPaVe===True) ), + writeOutPaVe = "" ]; If [OptionValue[FCVerbose]===False, oneloopVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], oneloopVerbose=OptionValue[FCVerbose] ]; ]; - tim = Timing[ - If[ StringQ[ name ] && StringQ[writeout], - name = StringJoin[writeout, name] + If[ !StringQ[name] && name=!=False, + Message[OneLoop::failmsg, "If you want the result to be saved to a file, the first argument of OneLoop must be a string."]; + Abort[] ]; + + If[ !StringQ[writeOut] && writeOut=!=False && writeOut=!=True, + Message[OneLoop::failmsg, "The value of the option WriteOut must be True, False or a path."]; + Abort[] + ]; + + If[ (writeOut===True || StringQ[writeOut]) && StringQ[name], + If[StringQ[writeOut], + name = FileNameJoin[{writeOut,name}] + ]; + Which[ + formatType === InputForm, + name = StringJoin[name, ".m"], + formatType === FortranForm, + name = StringJoin[name, ".for"], + True, + Message[OneLoop::failmsg, "Unsupported FormatType."]; + Abort[] + ] + ]; + + (* + TODO: Adjust the manual regarding GraphName If[ Head[name]===GraphName, name = StringJoin @@ (ToString/@{First[name], Last[name]}), If[ (name=!=False) && (Head[name]=!=String), name = ToString[name] ] ]; - If[ Head[name]===String, - Which[ formattype === InputForm, name = StringJoin[name, ".m"], - formattype === FortranForm, name = StringJoin[name, ".for"], - formattype === MacsymaForm, name = StringJoin[name, ".mac"], - formattype === MapleForm, name = StringJoin[name, ".map"] - ] - ]; + + + TODO: ??? If[ StringQ[name], (*Mac fix, 18/9-2000, F.Orellana. Ditto for FileType's below*) - oldfile = FileType[name]; - If[ oldfile === File, + If[ FileType[name] === File, FCPrint[1, "oldfile =", name, FCDoControl->oneloopVerbose]; - ftemp = ( Get[name] ); - If[ ValueQ[OneLoopResult[grname]] && FreeQ[ftemp, FeynAmpDenominator], + If[ ValueQ[OneLoopResult[grname]] && FreeQ[Get[name], FeynAmpDenominator], oneamp = OneLoopResult[grname] ]; ] ]; - oneamp = ChangeDimension[FeynCalcInternal[oneamp],dim]; + *) (* in case oneamp has no FeynAmpDenominator: write oneamp out *) If[ FreeQ2[ oneamp , {FeynAmpDenominator,FAD}], oneampresult = oneamp, - (* ********************************************************************* *) - (* oneloop12 *) - (* ********************************************************************* *) + (* ********************************************************************* *) + (* oneloop12 *) + (* ********************************************************************* *) - (* * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * *) - (* Starting the game: *) - (* * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * *) - - (*epschisholmdef*) - epschisholm[x_] := - x/;FreeQ[x, Eps] || FreeQ[x, DiracGamma]; - epschisholm[x_Plus] := - Map[epschisholm,x]; - epschisholm[x_] := - If[ reducegamma67, - EpsChisholm[x], - EpsChisholm[x]/.DiracGamma[5] -> (DiracGamma[6]-DiracGamma[7]) - ] /; Head[x]=!=Plus; - If[ FreeQ[oneamp, DOT[Spinor[p1__] , a__ , Spinor[p2__] * - Spinor[p3__] , b__ , Spinor[p4__]] - ], - FeynCalc`DiracSimplify`Private`$sirlin = False - ]; - FCPrint[3, "FeynCalc`DiracSimplify`Private`$sirlin = ", FeynCalc`DiracSimplify`Private`$sirlin, FCDoControl->oneloopVerbose]; - (* smallv *) - smav = Table[smallv[[iv]]->SmallVariable[ smallv[[iv]] ], - {iv,1,Length[smallv]} ]; - (* do the initial substitutions *) - oneamp = ( oneamp/.smav )/.inisubs; - (* neglect any small variable in the numerators of the fermion propagators *) - smalldirac /: smalldirac[_] + DiracGamma[a__]:= - DiracGamma[a]; - - (* and in the spinors *) - smalldirac /: Spinor[ pe_, smalldirac[_], op___]:= - Spinor[pe,0,op]; - - oneamp = oneamp /. SmallVariable -> smalldirac /. - smalldirac -> SmallVariable; - (* put heads on the momenta in the denominators *) - denf[x_,y_] := - denprop[Momentum[x],y]/;FreeQ[x,Momentum]; - denf[x_,y_] := - denprop[x,y]/;!FreeQ[x,Momentum]; - (* if a propagator has no integration momentum *) - denprop[a_, b_] := - (1/TrickMandelstam[(Pair[a,a]//ExpandScalarProduct) - - b^2, onemandel] /. SmallVariable[_]->0)/; FreeQ[a, q]; - (* ********************************************************************* *) - (* oneloop13 *) - (* ********************************************************************* *) + (* * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * *) + (* Starting the game: *) + (* * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * *) - (* ONEAMPCHANGE: denominators *) - If[ Cases[x, DOT[Spinor[a_,_,_] , (___) , Spinor[b_,_,_] * - Spinor[c_,_,_] , (___) , Spinor[d_,_,_] - ] - ] =!= {}, - $fourfermion = True - ]; + FCPrint[1, "OneLoop: Applying initial substitutions.", FCDoControl->oneloopVerbose]; + oneamp = oneamp/.initialSubstitutions; + FCPrint[1, "OneLoop: Done applying initial substitutions.", FCDoControl->oneloopVerbose]; - oneamp = FeynAmpDenominatorSplit[oneamp//Trick//FeynAmpDenominatorCombine, Momentum->{q}]; - oneamp = oneamp /. FeynAmpDenominator[xyz__] :> PropagatorDenominatorExplicit[FeynAmpDenominator[xyz]] /;FreeQ[{xyz}, q]; - oneamp = oneamp/.PropagatorDenominator -> denf /. - denprop -> PropagatorDenominator; + FCPrint[1, "OneLoop: Handling SmallVariable objects.", FCDoControl->oneloopVerbose]; + smav = Table[smallv[[iv]]->SmallVariable[ smallv[[iv]] ], {iv,1,Length[smallv]} ]; + (* do the initial substitutions *) + oneamp = oneamp/.smav; - If[ oneloopsimplify=== True, - oneamp = OneLoopSimplify[oneamp, q, Dimension -> dim] - ]; - FCPrint[2, "length of oneamp = ", Length[oneamp], FCDoControl->oneloopVerbose]; - oneamp = FDS[oneamp,q]; - oneamp = FDS[Expand[ApartFF[oneamp,{q}], FeynAmpDenominator],q,FCI->True,ApartFF->False]; + (* TODO FCNeglectSmallVariable *) + (* neglect any small variable in the numerators of the fermion propagators *) + smalldirac /: + smalldirac[_] + DiracGamma[a__]:= + DiracGamma[a]; - (* reduce N-point to 4-point, still temporary *) - SetAttributes[ Y, Orderless ]; - smn[a_] := - 0; - smdaemon[x_] := - x/.SmallVariable->smn; - Y[{pi_, mi_}, {pj_, mj_}] := - Expand[smdaemon[ mi^2 + mj^2 -ScalarProduct[pi - pj, pi - pj]//ExpandScalarProduct]]; + (* and in the spinors *) + smalldirac /: + Spinor[ e_, smalldirac[_], o___]:= + Spinor[e,0,o]; + oneamp = oneamp /. SmallVariable -> smalldirac /. smalldirac -> SmallVariable; - (* pli is the list of momenta (without q), being one less than mli *) + FCPrint[1, "OneLoop: Done handling SmallVariable objects.", FCDoControl->oneloopVerbose]; - (* ********************************************************************* *) - (* oneloop14 *) - (* ********************************************************************* *) - (* Reducing N-=point to 4 point *) - (* ********************************************************************* *) - gr454[mli_List, pli_List] := - gr454[mli, pli] = - Block[ {pl = Prepend[pli, 0], n = Length[mli]}, - (* create a list of the columns of eq. (4.54) *) - columnli = Prepend[ Table[ Y[{pl[[i]], mli[[i]]}, {pl[[j]], mli[[j]]}], - {j,1,n}, {i,1,n}], - Array[#^0&, n] - ]; - columnli - ]; - (*define this such that sgr[{...},{...}, -1 ] is the Y_{ij} determinant *) - sgr[mli_, pli_, i_] := - sgr[mli, pli, i] = - Factor2[Drop[gr454[mli, pli], {i+2,i+2}]//Det]; - redamp[x_Plus,qu_] := - redamp[#,qu]&/@x; - redamp[x_,qu_] := - Block[ {pl, ml, fm, pp,res = x}, - fd = PartitHead[x, FeynAmpDenominator]; - If[ Length[fd[[2]]] > 4 && FreeQ[(x/.FeynAmpDenominator[___]:>1),qu], - fm[pe_,___] := - pe; - pp[a_, b_] := - Expand[(a/.Momentum->fm) - qu]; - mm[a_, b_] := - b; - pl = List @@ (fd[[2]]/.PropagatorDenominator->pp ); - pl = Rest[pl]; - ml = List @@ (fd[[2]]/.PropagatorDenominator->mm); -(*Extract the determinant *) - res = {1/sgr[ml, pl, -1] , - Sum[ (-1)^(j+1) subdethold[sgr[ml,pl, j] - ] fd[[1]] * - Drop[fd[[2]], {j+1,j+1}], - {j, 0, Length[fd[[2]]]-1} - ] - } - ]; - res - ] /; Head[x] =!= Plus; - subdethold[x_Plus] := - x/;Length[x] < 4; - subdethold[x_] := - ReleaseHold[Isolate[x, IsolateSplit->Infinity, - IsolateNames->SUB - ] /. SUB -> SUBDET - ]; - $higherpoint = False; - fdhigh[xx__] := - If[ Length[Union[{xx}]] < 5, + FCPrint[1, "OneLoop: Applying Trick.", FCDoControl->oneloopVerbose]; + oneamp = Trick[oneamp]; + FCPrint[1, "OneLoop: Done applying Trick.", FCDoControl->oneloopVerbose]; + + FCPrint[1, "OneLoop: Applying FeynAmpDenominatorCombine.", FCDoControl->oneloopVerbose]; + oneamp = FeynAmpDenominatorCombine[oneamp]; + FCPrint[1, "OneLoop: Done applying FeynAmpDenominatorCombine.", FCDoControl->oneloopVerbose]; + + FCPrint[1, "OneLoop: Simplyfing non-loop propagators.", FCDoControl->oneloopVerbose]; + oneamp = FeynAmpDenominatorSplit[oneamp, Momentum->{q}]; + oneamp = oneamp /. FeynAmpDenominator[x__]/;FreeQ[{x}, q] :> FeynAmpDenominatorExplicit[FeynAmpDenominator[x], + Mandelstam->onemandel,SmallVariable->True]; + FCPrint[1, "OneLoop: Done simplyfing non-loop propagators.", FCDoControl->oneloopVerbose]; + + If[ oneloopSimplify, + FCPrint[1, "OneLoop: Applying OneLoopSimplify.", FCDoControl->oneloopVerbose]; + oneamp = OneLoopSimplify[oneamp, q, Dimension -> dim]; + FCPrint[1, "OneLoop: Done applying OneLoopSimplify.", FCDoControl->oneloopVerbose]; + ]; + + FCPrint[1, "OneLoop: Applying FDS.", FCDoControl->oneloopVerbose]; + oneamp = FDS[oneamp,q]; + oneamp = FDS[Expand[ApartFF[oneamp,{q}], FeynAmpDenominator],q,FCI->True,ApartFF->False]; + FCPrint[1, "OneLoop: Done applying FDS.", FCDoControl->oneloopVerbose]; + + fdhigh[x__] := + If[ Length[Union[{x}]] < 5, 0, - FeynAmpDenominator[xx] + FeynAmpDenominator[x] ]; - If[ !FreeQ[oneamp /. FeynAmpDenominator -> fdhigh, FeynAmpDenominator], + + If[ !FreeQ[oneamp /. FeynAmpDenominator -> fdhigh, FeynAmpDenominator] && OptionValue[NPointTo4Point], $higherpoint = True; - namp = redamp[ oneamp,q ]; - If[ Head[namp]===List, - prefactor = prefactor namp[[1]]; - oneamp = namp[[2]], - oneamp = namp - ] + namp = NPointTo4Point[ oneamp,q, List->True, Dimension -> 4, IsolateNames->SUB]/. SUB -> SUBDET; + prefactor = prefactor namp[[1]]; + oneamp = namp[[2]] ]; - - - (* Put here the i pi^2 from the integrals *) + (* Put here the i pi^2 from the integrals *) newprefactor = prefactor I Pi^2; - (* ONEAMPCHANGE: extract coupling constants *) + (* ONEAMPCHANGE: extract coupling constants *) If[ Head[oneamp] === Times, - oneselect = Select[oneamp, - FreeQ2[#, {Pair, PropagatorDenominator,Eps, - dim, - Momentum,LorentzIndex, SUNF, - SUNDelta, SUNT, - DiracGamma, Spinor} - ]& - ]; + oneselect = Select[oneamp, FreeQ2[#, {Pair, PD,Eps, dim, Momentum,LorentzIndex, SUNF, SUNDelta, SUNT, DiracGamma, Spinor}]&]; oneamp = oneamp/oneselect; newprefactor = Factor2[ newprefactor oneselect ]; ]; - If[ (!FreeQ[ newprefactor, dim ]) || (!FreeQ[newprefactor, LorentzIndex]) - || (!FreeQ[newprefactor, DiracGamma]), - newnewprefactor = Select[newprefactor, - !FreeQ2[#, {dim, LorentzIndex, DiracGamma}]&]; + + If[ (!FreeQ[ newprefactor, dim ]) || (!FreeQ[newprefactor, LorentzIndex]) || (!FreeQ[newprefactor, DiracGamma]), + newnewprefactor = Select[newprefactor, !FreeQ2[#, {dim, LorentzIndex, DiracGamma}]&]; If[ !FreeQ[newnewprefactor, DiracGamma], oneamp = DOT[newnewprefactor , oneamp], oneamp = oneamp newnewprefactor ]; - newprefactor = smalld[newprefactor / newnewprefactor + nUUUl - ]/. nUUUl -> 0; + newprefactor = smalld[newprefactor / newnewprefactor + null1]/. null1 -> 0; If[ newprefactor === 0, oneamp = 0 ]; ]; - (* ********************************************************************* *) - (* oneloop15 *) - (* ********************************************************************* *) - - - (* change the dimension , to4dimdef*) - to4dim[x_] := - x/.{Momentum[v_,_]:>Momentum[v], - LorentzIndex[w_,_]:>LorentzIndex[w]}; - oneamp0 = oneamp; - - FCPrint[2, "check", FCDoControl->oneloopVerbose]; - (* ONEAMPCHANGE: make dimensions right *) - If[ dim===4, - oneamp = SUNSimplify[to4dim[ oneamp ], Explicit -> False], - oneamp = oneamp + null; - newone = SUNSimplify[ ChangeDimension[oneamp, dim], - Explicit -> False ]; - oneamp = newone/.null -> 0 - ]; - FCPrint[3, " oneamp = ", oneamp, FCDoControl->oneloopVerbose]; - If[ (!FreeQ[oneamp, SUNF]) || (!FreeQ[oneamp, SUNDelta]) || - (!FreeQ[oneamp, SUNT]), + FCPrint[1, "OneLoop: Applying SUNSimplify.", FCDoControl->oneloopVerbose]; + oneamp = SUNSimplify[oneamp, Explicit -> False]; + If[ !FreeQ2[oneamp,{SUNF,SUNDelta,SUNT}], oneamp = oneamp /. SUNF -> sUNF /. SUNDelta -> sUNDelta; - AppendTo[finsubst, {sUNF -> SUNF, sUNDelta -> SUNDelta}]; + AppendTo[finalSubstitutions, {sUNF -> SUNF, sUNDelta -> SUNDelta}] ]; + FCPrint[1, "OneLoop: Done applying SUNSimplify.", FCDoControl->oneloopVerbose]; - (* ********************************************************************* *) - (* oneloop16 *) - (* ********************************************************************* *) + (* bringing the denominator in a canonical form *) + FCPrint[1, "OneLoop: Applying FDS again to have the propagagators ordered canonically.", FCDoControl->oneloopVerbose]; + oneamp = FDS[oneamp,q,FCI->True,ApartFF->False]; + FCPrint[1, "OneLoop: Done applying FDS again.", FCDoControl->oneloopVerbose]; - (* for propagators without the integration variable q *) - dnq[a___,PropagatorDenominator[pe_,ma_],b___] := - ExpandScalarProduct[ - (1/Factor2[ smalld[TrickMandelstam[ ExpandScalarProduct[Pair[pe,pe]]-ma^2, - onemandel ]//Expand] ] ) dnq[a,b] ] /; FreeQ[pe,q]; - prode[a_,b_] := - PropagatorDenominator[a//MomentumExpand,b] /; !FreeQ[a,q]; - prode[ppe_,mm_] := - ExpandScalarProduct[ - (1/Factor2[ smalld[TrickMandelstam[ - ExpandScalarProduct[Pair[ppe,ppe]]-mm^2, - onemandel ]//Expand] ] ) ] /; FreeQ[ppe,q]; - - (* ONEAMPCHANGE: extract denominators without q's *) - oneamp = oneamp/.FeynAmpDenominator->dnq/.dnq->FeynAmpDenominator/. - PropagatorDenominator->prode; - dfsor[ve_,ma_] := - defs[ma][ve]//MomentumExpand; - dfsorb[a_][b_] := - PropagatorDenominator[b,a]; - (* denomOrder orders the PropagatorDenominator , denomOrderdef *) - (* the eventually necessary translation of q is done with intcan. *) - denomOrder[ a__ ] := - Block[ { dfli = {a},ru }, -(* this is checked always *) - ru = {PropagatorDenominator[c_. Momentum[ce_. q ,di___],ma0_]:> - PropagatorDenominator[Sqrt[c^2] Momentum[Sqrt[ce^2] q,di],ma0], - PropagatorDenominator[x_+be_ Momentum[q,di___],mA_] :> - PropagatorDenominator[Expand[-x+Momentum[q,di] ],mA]/;(be===-1) - }; - dfli = dfli//.ru; - If[ !MatchQ[ First[dfli], PropagatorDenominator[Momentum[q,___],_] ], - denorder = True - ]; - If[ denorder === True, - dfli = Sort[ dfli/.PropagatorDenominator->dfsor ]/.defs->dfsorb; - (* For boxes: bring a evtl. 0 at position 3 *) - If[ Length[ dfli ] === 4, - dfli = RotateRight[dfli,2] - ] - ]; - If[ Length[dfli]===3 && denorder === True, - dfli = dfli/.{den1_, PropagatorDenominator[pe2_,ma1_], - PropagatorDenominator[pe3_,ma2_]}:> - {den1, PropagatorDenominator[pe3,ma2], - PropagatorDenominator[pe2,ma1]}/; - Length[ pe2 ] > Length[ pe3 ] - ]; - If[ denorder === True, - dfli = dfli/.{den1_,PropagatorDenominator[pe2_,ma2_],den3_, - PropagatorDenominator[pe3_,ma2_]}:> - {den1, PropagatorDenominator[pe3,ma2],den3, - PropagatorDenominator[pe2,ma2]}/; - Length[pe2]>Length[pe3]; - FCPrint[3, "after denomOrdering : ", dfli, FCDoControl->oneloopVerbose]; - ]; - FeynAmpDenominator@@dfli - ](* endBlock *); - (* ********************************************************************* *) - (* oneloop17 *) - (* ********************************************************************* *) - vcid[pe_,___] := - pe; - (* for translating the integration variable q in the first propagator *) - (* intcandef *) - intcan[x_] := - x/;FreeQ[x,q]; - intcan[x_Plus] := - intcan/@x; - intcan[ a_ b_ ] := - a intcan[b]/; FreeQ[a,q]; - intcan[x_Times] := - (SelectFree[x, q] intcan[SelectNotFree[x,q]]) /; - SelectFree[x, q] =!= 1; - intcan[any_. FeynAmpDenominator[ - PropagatorDenominator[p_ + Momentum[q,dim], m1_],dfrest___ ] - ] := - denomExpand[ ( any FeynAmpDenominator[ - PropagatorDenominator[ p + Momentum[q,dim],m1], dfrest] - )/.q->( q - (p/.Momentum->vcid) ) - ]; - (* bringing the denominator in a canonical form *) - - (* ONEAMPCHANGE : fixing all denominators , evtl. ordering *) - oneamp = denomExpand[ oneamp ]; - oneamp = denomExpand[ oneamp ]/.FeynAmpDenominator->denomOrder; - oneamp = (intcan[oneamp//MomentumExpand]//MomentumExpand)/. - intcan->Identity; - oneamp = Map[ (Numerator[#]/Factor2[Denominator[#]])&, oneamp + null ]; - oneamp = oneamp/.null->0; - FCPrint[3, "oneamp after ordering = ", oneamp, FCDoControl->oneloopVerbose]; - - (* ONEAMPCHANGE : bringing all denominator in standard order *) - consum[x_] := - conall[x]/;Head[x]=!=Plus; (* consumdef *) - consum[x_Plus] := - Block[ {nx = 0,i}, - For[i = 1, i<=Length[x], i++, - FCPrint[2, "contracting # ", i, " out of ", Length[x], FCDoControl->oneloopVerbose]; - nx = nx + conall[x[[i]]] - ]; - nx - ]; - (* consum2def *) - consum2[x_] := - smalld[ExpandScalarProduct[conall[x]]]/;Head[x]=!=Plus; - consum2[x_Plus] := - Block[ {nx = 0}, - For[i = 1, i<=Length[x], i++, - FCPrint[2, "contracting # ", i, " out of ", Length[x], FCDoControl->oneloopVerbose]; - nx = nx + (Expand[ - ExpandScalarProduct[conall[x[[i]]]]]//smalld) - ]; - nx - ]; - (* ********************************************************************* *) - (* oneloop18 *) - (* ********************************************************************* *) + + + FCPrint[1, "OneLoop: Applying Contract.", FCDoControl->oneloopVerbose]; oneamp = Contract[ oneamp, Expanding -> False]; - oneampc = oneamp; + FCPrint[1, "OneLoop: Done applying Contract.", FCDoControl->oneloopVerbose]; + + + FCPrint[1, "OneLoop: Applying DiracSimplify.", FCDoControl->oneloopVerbose]; oneamp = DiracSimplify[oneamp, Expanding -> False]; - oneampd = oneamp; - FCPrint[2, "OneLoop: before collin ", oneamp, FCDoControl->oneloopVerbose]; - oneamp = collin[ consum[oneamp]//smalld, FeynAmpDenominator, False ]; - (* ONEAMPCHANGE : contracting Lorentz indices and expanding *) - (* now a canonized form is achieved *) - (* and all Lorentzindices which are not part of a DiracGamma contracted *) - If[ !FreeQ[oneamp,DiracGamma], - FCPrint[1, "Simplification of Dirac structures", FCDoControl->oneloopVerbose] - ]; - If[ !FreeQ[oneamp,DiracTrace], - FCPrint[1, "and calculation of Traces", FCDoControl->oneloopVerbose] - ]; + FCPrint[1, "OneLoop: Done applying DiracSimplify.", FCDoControl->oneloopVerbose]; + + + + FCPrint[1, "OneLoop: Applying Contract and collecting terms.", FCDoControl->oneloopVerbose]; + oneamp = Collect2[Expand[Contract[oneamp, Expanding->True, EpsContract->True, Factoring->False]]//smalld, FeynAmpDenominator, Factoring->Factor]; + FCPrint[1, "OneLoop: Done applying Contract and collecting terms.", FCDoControl->oneloopVerbose]; - (* ONEAMPCHANGE : contracting Lorentz indices and trace calculation *) - (*oneampe = oneamp;*) + (* ONEAMPCHANGE : contracting Lorentz indices and expanding *) + (* now a canonized form is achieved *) + (* and all Lorentzindices which are not part of a DiracGamma contracted *) + + + (* ONEAMPCHANGE : contracting Lorentz indices and trace calculation *) + (*oneampe = oneamp;*) If[ !FreeQ[oneamp, DiracTrace], - neuamp = 0; - oneamp = collin[ oneamp, DiracTrace, False]; - If[ Head[oneamp] =!= Plus, - oneamp = Expand[oneamp /. DiracTrace->TR], - For[i = 1, i<=Length[oneamp], i++, - FCPrint[1, "calculating trace # ", i, " out of ", Length[oneamp], FCDoControl->oneloopVerbose]; - timi = Timing[ - neuamp = neuamp + Expand[ oneamp[[i]]/.DiracTrace->TR] - ][[1]]; - FCPrint[1, "time needed = ", timi, FCDoControl->oneloopVerbose]; - ]; - oneampf = oneamp; - oneamp = Collect2[neuamp, FeynAmpDenominator, Factoring -> False] - ] + (*neuamp = 0;*) + FCPrint[1, "OneLoop: Calculating Dirac traces.", FCDoControl->oneloopVerbose]; + oneamp = Collect2[ oneamp, DiracTrace, Factoring->False]; + oneamp = oneamp /. DiracTrace[t_]:>DiracTrace[t,DiracTraceEvaluate->True]; + oneamp = Collect2[ oneamp, FeynAmpDenominator, Factoring -> False]; + FCPrint[1, "OneLoop: Done calculating Dirac traces.", FCDoControl->oneloopVerbose] ]; - (*oneampzero = oneamp;*) - (* ONEAMPCHANGE : bringing gamma5, gamma6 and gamma7 into standard - way according to the setting of the option ReduceGamma - *) - If[ !reducegamma67, - oneamp = oneamp /. - {DOT[ Spinor[p1__],(a___),Spinor[p2__]] :> - (DOT[Spinor[p1],a,DiracGamma[6],Spinor[p2]] + DOT[Spinor[p1],a,DiracGamma[7],Spinor[p2]])}; - ]; + If[ reducegamma67, - oneamp = oneamp /. DiracGamma[6] -> (1/2 + DiracGamma[5]/2)/. DiracGamma[7] -> (1/2 - DiracGamma[5]/2) + FCPrint[1, "OneLoop: Inserting explicit chiral projectors.", FCDoControl->oneloopVerbose]; + oneamp = oneamp /. DiracGamma[6] -> (1/2 + DiracGamma[5]/2)/. DiracGamma[7] -> (1/2 - DiracGamma[5]/2); + FCPrint[1, "OneLoop: Done inserting explicit chiral projectors.", FCDoControl->oneloopVerbose] ]; - (* ********************************************************************* *) - (* oneloop19 *) - (* ********************************************************************* *) - FCPrint[1, "contraction, etc. ", FCDoControl->oneloopVerbose]; - diracorder[x_] := - x /; FreeQ[ x, DiracGamma ]; - diracorder[x_] := - Collect2[DiracOrder[x(*, {q}*)], DOT,Factoring->False - ] /; Head[x]=!=Plus; - diracorder[x_Plus] := - Collect2[ Map[DiracOrder[#(*, {q}*)]&, x], DOT, - Factoring->False]; - $Test = True; - paex[x_,y_] := - If[ !FreeQ[{x,y}, Eps], - ExpandScalarProduct[Pair[x,y]], - Pair[x,y] - ]; - epsit[x_] := - If[ $Test === True, - epschisholm[Collect2[x/.Pair->paex, {Eps,Spinor}, - Factoring -> False ]], - x - ]; - simpit[x_ /; FreeQ[x, DiracGamma]] := - (FCPrint[3, "checkkkk", FCDoControl->oneloopVerbose]; - consum2[x]); - simpit[x_] := - (FCPrint[3, "OneLoop: simpit", FCDoControl->oneloopVerbose]; - diracorder[ Collect2[ consum2[x]//epsit, DOT, - Factoring->False - ] // DiracSimplify]) /; !FreeQ[x, DiracGamma]; - - (* we want to keep the distinction in different graphs *) - (* ONEAMPCHANGE *) - (*oneamp1 = oneamp; *) + + FCPrint[1, "oneamp = ", oneamp, FCDoControl->oneloopVerbose]; - neuamp = 0; - If[ Head[oneamp] === Plus, - lenneu = Length[oneamp], - lenneu = 1 + + + neuamp = Contract[oneamp, Expanding->True, EpsContract->True, Factoring->False]; + neuamp = ExpandScalarProduct[neuamp, FCI->True]//Expand//smalld; + neuamp = EpsChisholm[neuamp,FCI->True]; + If[ !reducegamma67, + neuamp = neuamp /.DiracGamma[5] -> (DiracGamma[6]-DiracGamma[7]) ]; - For[ ip = 1, ip <= lenneu, ip++, - FCPrint[2, "working with part # ", ip, " out of ", lenneu, FCDoControl->oneloopVerbose]; - If[ lenneu > 1, - parf = PartitHead[oneamp[[ip]], FeynAmpDenominator]//smalld, - parf = PartitHead[oneamp, FeynAmpDenominator]//smalld - ]; - neuamp = neuamp + ((Expand[ If[parf[[2]]=!=0,parf[[2]],1] simpit[parf[[1]]] - ]) //smalld) - ]; + + neuamp = DiracOrder[neuamp, FCI->True]; + neuamp = neuamp//smalld; + + + FCPrint[2, "Length of neuamp = ", Length[neuamp], FCDoControl->oneloopVerbose]; If[ FreeQ[neuamp, DOT], oneamp = neuamp, oneamp = Collect2[neuamp, DOT, Factoring->False]; ]; - oneamp2 = oneamp; - FCPrint[3, "oneamp2 = ", oneamp2, FCDoControl->oneloopVerbose]; - -(* ONEAMPCHANGE *) - If[ intermedsubst =!= {}, - oneamp = oneamp /. intermedsubst /. intermedsubst; - neuamp = 0; - If[ Head[oneamp] === Plus, - lenneu = Length[oneamp], - lenneu = 1 + + If[ intermediateSubstitutions =!= {}, + (*??*) + oneamp = oneamp /. intermediateSubstitutions /. intermediateSubstitutions; + neuamp = Contract[oneamp, Expanding->True, EpsContract->True, Factoring->False]; + neuamp = ExpandScalarProduct[neuamp, FCI->True]//Expand//smalld; + neuamp = EpsChisholm[neuamp,FCI->True]; + If[ !reducegamma67, + neuamp = neuamp /.DiracGamma[5] -> (DiracGamma[6]-DiracGamma[7]) ]; - For[ iip = 1, iip <= lenneu, iip++, - FCPrint[2, "working with (substituted) part # ", iip, " out of ", lenneu, FCDoControl->oneloopVerbose]; - If[ lenneu > 1, - parf = PartitHead[oneamp[[iip]], FeynAmpDenominator], - parf = PartitHead[oneamp, FeynAmpDenominator] - ]; - neuamp = neuamp + ((Expand[ parf[[2]] simpit[parf[[1]]] - ]) //smalld) - ]; + (*neuamp = DiracSimplify[neuamp, FCI->True];*) + neuamp = DiracOrder[neuamp, FCI->True]; + neuamp = neuamp//smalld ]; + oneamp = neuamp; - FCPrint[2, "check1", FCDoControl->oneloopVerbose]; FCPrint[3, "neuamp = ", neuamp, FCDoControl->oneloopVerbose]; - (* Zwischenspiel... *) - smadot[] = 1; - standard /: standard[a_] standard[b_] := standard[a b]; - smadot[x___] := - standard[ dotlin[DOT[x]]/.dim->4 ] /. - standard -> StandardMatrixElement; - If[ StandardMatrixElement =!= Identity, - StandardMatrixElement[x_Plus] := - Map[StandardMatrixElement,x] - ]; - (* ********************************************************************* *) - (* oneloop20 *) - (* ********************************************************************* *) - - (* tostandmatdef *) - tostandmat[xy_] := - Block[ {te, standa}, - standa[a__] := - dotlin[DOT[a]] /; - !FreeQ2[{a}, {DOT,Pair,Spinor}]; - standa[a_,b__] := - StandardMatrixElement[a,b]/; - FreeQ2[a, {DOT,Pair,Spinor}]; - te = tempstandmat[Expand[xy]]//Expand; - If[ !FreeQ[te, DiracGamma[6]], - te = te/.StandardMatrixElement -> standa/. - standa -> spinorsandpairs/. - spinorsandpairs->smadot/. - DiracGamma[6] -> - (1/2 + DiracGamma[5]/2); - te = spinorchainevaluate[te]//Expand; - te = tempstandmat[te]//Expand - ]; - If[ !FreeQ[te, DiracGamma[7]], - te = te/.StandardMatrixElement -> standa/. - standa -> spinorsandpairs/. - spinorsandpairs->smadot/. - DiracGamma[7] -> - (1/2 - DiracGamma[5]/2); - te = DiracSimplify[te]//DiracOrder//Expand; - te = tempstandmat[te//Contract]//Expand - ]; - te = te /.DOT->spinorsandpairs/. - spinorsandpairs->smadot; - te - ] /; reducegamma67 === True; - tostandmat[xy_] := - Block[ {te, standa, pluh, pluh2}, - standa[xx_] := - xx/;!FreeQ2[xx, - {DOT,Pair,Polarization}]; - standa[a_,b__] := - StandardMatrixElement[a,b]; - pluh[x__] := - Plus[x] /; !FreeQ2[{x}, - {Spinor,GellMannMatrix, SUNIndex, - Polarization,Pair}]; - te = xy /. Plus -> pluh /. pluh->pluh2; - te = tempstandmat[Expand[te]]//Expand; - te = te /. pluh2 -> Plus; - te = te/.StandardMatrixElement -> standa/. - DiracGamma[5] -> - (DiracGamma[6] - DiracGamma[7]); - te = te//dotlin; - (* 1 = gamma6 + gamma7 *) - If[ !FreeQ[te, Spinor], - te = te //. { - DOT[ - Spinor[p1__],(a___),Spinor[p2__] ]:> - (DOT[Spinor[p1],a,DiracGamma[6],Spinor[p2]] + - DOT[Spinor[p1],a,DiracGamma[7],Spinor[p2]] - ) /; FreeQ2[{a}, {DiracGamma[6], - DiracGamma[7]} ] - }; - te = Expand[DiracSimplify[te]//DiracOrder, - Spinor]//Contract; - te = Expand[ te, Pair ] - ]; - te = tempstandmat[te]; - te = te /.DOT->spinorsandpairs/. - spinorsandpairs->smadot; - te - ] /; reducegamma67 =!= True; - - (* ********************************************************************* *) - (* oneloop21 *) - (* ********************************************************************* *) + (* ********************************************************************* *) + (* oneloop21 *) + (* ********************************************************************* *) - (* ONEAMPCHANGE : spinor stuff and matrixelements *) + (* ONEAMPCHANGE : spinor stuff and matrixelements *) FCPrint[2, " Dirac-Algebra again", FCDoControl->oneloopVerbose]; FCPrint[2, "before spinorch: oneamp = ", oneamp//Length, FCDoControl->oneloopVerbose]; - (* - oneamp = conall[spinorchainevaluate[oneamp//smalld ]]// - ExpandScalarProduct; - *) - If[ Head[oneamp]===Plus, - FCPrint[2, "substituting", FCDoControl->oneloopVerbose]; - If[ Length[oneamp]<10, - oneamp = oneamp/.{DiracGamma[Momentum[pe_,di_Symbol],di_Symbol]:> - DiracGamma[Momentum[pe]]/;FreeQ[pe,q] }; - oneamp = conall[oneamp//smalld ]// ExpandScalarProduct, - newamp = 0; - For[ij = 1, ij <= Length[oneamp], ij++, - If[ IntegerQ[ij/100], - FCPrint[2, "ij = ", ij, FCDoControl->oneloopVerbose] - ]; - temp = (oneamp[[ij]]/. - {DiracGamma[Momentum[pe_,di_Symbol],di_Symbol]:> - DiracGamma[Momentum[pe]]/;FreeQ[pe,q] }); - temp = conall[temp//smalld] // ExpandScalarProduct; - newamp = newamp + Expand[temp, q] - ]; - oneamp = newamp - ]; - ]; - (* - oneamp = Collect2[oneamp/.subdethold->Identity, q, Factoring-> False]; - *) + + oneamp = Contract[oneamp//smalld, FCI->True, Expanding->True, EpsContract->True, Factoring->False]; + oneamp = ExpandScalarProduct[oneamp,FCI->True]; + FCPrint[2, "collect w.r.t. ", q, FCDoControl->oneloopVerbose]; oneamp = Collect2[oneamp, q, Factoring -> False]; FCPrint[2, "oneamp ", oneamp, FCDoControl->oneloopVerbose]; - (* ********************************************************************* *) - (* oneloop22 *) - (* ********************************************************************* *) + (* ********************************************************************* *) + (* oneloop22 *) + (* ********************************************************************* *) - If[ (oneamp =!= 0), + If[ oneamp =!= 0, (*This is a good point to isolate possible non-loop terms in the input expression *) oneamp=Collect2[oneamp,q]; - nonLoopTerms = Select[oneamp+ null1+ null2, FreeQ[#, q]&]/. {null1|null2 -> 0}; - loopTerms = Select[oneamp+ null1+ null2, !FreeQ[#, q]&]/. {null1|null2 -> 0}; - If[loopTerms+nonLoopTerms=!=oneamp, - FCPrint[1,"Splitting the expression " <> ToString[oneamp,InputForm] <> - "into loop and non-loop pieces in OneLoop failed."]; - Abort[] - ]; + {nonLoopTerms,loopTerms} = FCSplit[oneamp,{q}]; oneamp=loopTerms; - (* ONEAMPCHANGE : cancelling q p 's *) - If[ qpcancel === True, - FCPrint[1, "cancelling qp's", FCDoControl->oneloopVerbose]; - qpcanc[b_,qu_] := - Select[null1 + null2 + - Collect2[ApartFF[b,{qu}]//smalld, qu], - !FreeQ[#,FeynAmpDenominator]&]; - oneamp = qpcanc[qpcanc[oneamp, q],q]; - FCPrint[1, "OneLoop: cancelling qp's done, oneamp= ",oneamp, FCDoControl->oneloopVerbose]; - If[ !FreeQ[oneamp,Pair[Momentum[q,_:4],Momentum[q,_:4]]], - FCPrint[0,"Something went wrong in the cancelling of scalar products. Evaluation aborted!"]; - Abort[] - ]; + (* ONEAMPCHANGE : cancelling q p 's *) + FCPrint[1, "cancelling qp's", FCDoControl->oneloopVerbose]; + qpcanc[b_,h_] := + Select[null1 + null2 + Collect2[ApartFF[b,{h}]//smalld, h], !FreeQ[#,FeynAmpDenominator]&]; + + oneamp = qpcanc[qpcanc[oneamp, q],q]; + FCPrint[1, "OneLoop: cancelling qp's done, oneamp= ",oneamp, FCDoControl->oneloopVerbose]; + If[ !FreeQ[oneamp,Pair[Momentum[q,_:4],Momentum[q,_:4]]], + FCPrint[0,"Something went wrong in the cancelling of scalar products. Evaluation aborted!"]; + Abort[] ]; - (* order the denominators again *) - If[ denorder === True, - oneamp = denomExpand[ oneamp ]/.FeynAmpDenominator->denomOrder - ]; - oneamp = (intcan[oneamp//MomentumExpand]//ExpandScalarProduct)/. - intcan->Identity, - (*oneamp = 0*) - nonLoopTerms=0; - loopTerms=0; + + + FCPrint[1, "OneLoop: Applying FDS again to have the propagagators ordered canonically.", FCDoControl->oneloopVerbose]; + oneamp = FDS[oneamp,q,FCI->True,ApartFF->False]; + FCPrint[1, "OneLoop: Done applying FDS again.", FCDoControl->oneloopVerbose] ]; - (*oneamp1 = oneamp;*) + + FCPrint[1, "simplifying again in ", oneamp, FCDoControl->oneloopVerbose]; + If[ !FreeQ[oneamp, Spinor], - oneamp = Map[spinorchainevaluate, oneamp + nUUl]/.nUUl->0; - oneamp = Expand[ ExpandScalarProduct[ oneamp ], q] + oneamp = DiracOrder[DiracSimplify[oneamp,FCI->True],FCI->True]; + oneamp = Expand2[ExpandScalarProduct[oneamp, FCI->True], q] ]; + FCPrint[1, "collecting w.r.t.", q, " ", Length[oneamp], " terms", FCDoControl->oneloopVerbose]; - oneamp = FixedPoint[ ReleaseHold, smalld[oneamp] ]; - timecoll = $FactorTime; - $FactorTime = 360; - tim = Timing[ - - If[ $ToughStuff =!=True, - oneamp = Collect2[ oneamp, q ], - oneamp = Collect2[ oneamp, q, Factoring -> False]; - ]; - oneamp2 = oneamp; - If[ Head[oneamp] === Plus, - newoneamp = 0; - lenneu2 = Length[oneamp]; - If[ dim=!=4, - qdi = {q,dim}, - qdi = {q} - ]; - For[ii = 1, ii<=lenneu2, ii++, - FCPrint[2, "isolating; ii = ", ii, " out of ", lenneu2, FCDoControl->oneloopVerbose]; - newoneamp = newoneamp + Isolate[oneamp[[ii]], qdi, - IsolateNames ->fFC, - IsolateSplit->Infinity] - ]; - oneamp = newoneamp - ]; - ]; - $FactorTime = timecoll; - FCPrint[1, "time for collect2 and isolate : ", tim[[1]]//FeynCalcForm, FCDoControl->oneloopVerbose]; + oneamp = FixedPoint[ReleaseHold, smalld[oneamp]]; + oneamp = Collect2[oneamp, q]; + oneamp = Isolate[oneamp, {q,dim}, IsolateNames ->fFC, IsolateSplit->Infinity]; + + FCPrint[1, "isolated and collected, before tensorintegraldecomposition:/n - length of isolated graph = ", Length[oneamp], FCDoControl->oneloopVerbose]; + length of isolated graph = ", Length[oneamp], FCDoControl->oneloopVerbose]; FCPrint[1, "memory in use = ", MemoryInUse[], FCDoControl->oneloopVerbose]; FCPrint[3, "oneamp = ", oneamp, FCDoControl->oneloopVerbose]; - (* ONEAMPCHANGE : tensorintegraldecomposition *) - (* relax this here. RM 20110622 *) - (* - If[!FreeQ2[oneamp, {Pair[x_,y_Plus] , DiracGamma[x_Plus,___]}], - *) - FCPrint[1, "cheCK", FCDoControl->oneloopVerbose]; - oneamp = DiracSimplify[oneamp]//ExpandScalarProduct; - (* - ]; - *) - (* bug (found by Christian Bauer, 07/97) - fixed here for objects like eps[al,nu,si,p-q] (can occur - after canonicalization of denominators; need then to expand the eps; - this is done with EpsEvaluate) - *) + oneamp = DiracSimplify[oneamp,FCI->True]//ExpandScalarProduct[#,FCI->True]&; + If[ !FreeQ[oneamp, Eps], oneamp = Collect2[EpsEvaluate[oneamp],q], -(* add this here for safety, since otherwise tensint might now work correctly. RM 20110622*) + (* add this here for safety, since otherwise tensint might now work correctly. RM 20110622*) oneamp = Collect2[oneamp,q] ]; - (*XXX*) - sirlinsave = FeynCalc`DiracSimplify`Private`$sirlin; - FeynCalc`DiracSimplify`Private`$sirlin = False; + (*XXX*) + FCPrint[1, "q = ", q, FCDoControl->oneloopVerbose]; - oneamp = tensint[ oneamp,dim,q,{Mandelstam->onemandel} ]; + + (* TODO: here tensint will be replaced by TID *) + oneamp = tensint[ oneamp,dim,q, onemandel]; oneamp = oneamp /.{B1 :> bB1, B00 :> bB00, B11 :> bB11}; oneamp = oneamp//smalld; oneamp = oneamp /.{bB1 :> B1, bB00 :> B00, bB11 :> B11}; - FeynCalc`DiracSimplify`Private`$sirlin = sirlinsave; + oneamp = FixedPoint[ReleaseHold, oneamp]; FCPrint[1, "after tensint ", FCDoControl->oneloopVerbose]; FCPrint[3, "after tensint : oneamp = ", oneamp, FCDoControl->oneloopVerbose]; If[ !FreeQ[oneamp, Spinor], oneamp = Collect2[oneamp, Spinor, Factoring -> False], If[ !FreeQ[oneamp, Pair], - oneamp = Collect2[oneamp, {Pair, Polarization}, - Factoring -> False], + oneamp = Collect2[oneamp, {Pair, Polarization}, Factoring -> False], oneamp = Expand[oneamp] ] ]; - (* StandardMatrixElement[ Spinor[] ... ] -> Spinor[] ... *) + (* StandardMatrixElement[ Spinor[] ... ] -> Spinor[] ... *) standback[x_] := x /; !FreeQ[ x, Spinor ]; - oneamp = oneamp /. StandardMatrixElement -> standback /. - standback -> StandardMatrixElement; + oneamp = oneamp /. StandardMatrixElement -> standback /. standback -> StandardMatrixElement; oneampsave = oneamp; FCPrint[3, "oneampsave = ", oneampsave, FCDoControl->oneloopVerbose]; @@ -1069,198 +562,156 @@ (* ********************************************************************* *) FCPrint[1, "after collecting ", FCDoControl->oneloopVerbose]; - (* ONEAMPCHaNGE : spinor stuff and matrixelements *) + (* ONEAMPCHaNGE : spinor stuff and matrixelements *) If[ (!FreeQ[ oneamp,Spinor ]), If[ Length[oneamp]>42, - oneamp = Isolate[ oneamp, {Spinor, DiracGamma, Pair}, - IsolateNames-> fFCT, - IsolateSplit -> Infinity]; + oneamp = Isolate[ oneamp, {Spinor, DiracGamma, Pair}, IsolateNames-> fFCT, IsolateSplit -> Infinity]; ]; FCPrint[1, "length of oneamp now: ", Length[oneamp], FCDoControl->oneloopVerbose]; - If[ (reducegamma67 === True) || - (!FreeQ[oneamp, - DOT[Spinor[p1__] , a___ , Spinor[p2__]] * - DOT[Spinor[p3__] , b___ , Spinor[p4__]] - ]), - oneamp = oneamp/. DiracGamma[7]->(1/2 - DiracGamma[5]/2)/. - DiracGamma[6]->(1/2 + DiracGamma[5]/2); + + If[ (reducegamma67 === True) || (!FreeQ[oneamp, DOT[Spinor[p1__] , a___ , Spinor[p2__]] DOT[Spinor[p3__] , b___ , Spinor[p4__]]]), + oneamp = oneamp/. DiracGamma[7]->(1/2 - DiracGamma[5]/2)/. DiracGamma[6]->(1/2 + DiracGamma[5]/2); ]; - oneamp = Expand[DiracSimplify[oneamp],DOT]//DiracOrder// - ExpandScalarProduct; + + oneamp = Expand[DiracSimplify[oneamp],DOT]//DiracOrder//ExpandScalarProduct; oneamp = DiracSimplify[oneamp]; - If[ (reducegamma67 =!= True) && - (!FreeQ[oneamp, - DOT[Spinor[p1__] , a___ , Spinor[p2__]] * - DOT[Spinor[p3__] , b___ , Spinor[p4__]] - ]), - oneamp = oneamp /. - {DOT[ Spinor[p1__],(a___),Spinor[p2__]] :> - (DOT[Spinor[p1],a,DiracGamma[6],Spinor[p2]] + - DOT[Spinor[p1],a,DiracGamma[7],Spinor[p2]] - ) - }; + + If[ (reducegamma67 =!= True) && (!FreeQ[oneamp, DOT[Spinor[p1__] , a___ , Spinor[p2__]] DOT[Spinor[p3__] , b___ , Spinor[p4__]]]), + oneamp = oneamp /. {DOT[ Spinor[p__],(a___),Spinor[r__]] :> + (DOT[Spinor[p],a,DiracGamma[6],Spinor[r]] + DOT[Spinor[p],a,DiracGamma[7],Spinor[r]])}; oneamp = DiracSimplify[oneamp] ]; + If[ $higherpoint===False, oneamp = FixedPoint[ReleaseHold, oneamp] ]; FCPrint[1, "after spinorchainevaluate", FCDoControl->oneloopVerbose] ]; + oneamp = oneamp /.{B1 :> bB1, B00 :> bB00, B11 :> bB11}; oneamp = oneamp//smalld; oneamp = oneamp /.{bB1 :> B1, bB00 :> B00, bB11 :> B11}; - (* If something changed, we have to order again *) + (* If something changed, we have to order again *) If[ oneamp =!= oneampsave, If[ !FreeQ[oneamp, Spinor], oneamp = Collect2[oneamp, Spinor, Factoring -> False], If[ !FreeQ[oneamp, Pair], - oneamp = Collect2[oneamp, {Pair, Polarization}, - Factoring -> False], + oneamp = Collect2[oneamp, {Pair, Polarization}, Factoring -> False], oneamp = Expand[oneamp] ] ] ]; + FCPrint[1, "after Collecting ", FCDoControl->oneloopVerbose]; - standmatd[xxx__] := - StandardMatrixElement[dotdotlin[xxx]]; - standmatd[] = 1; - (* this may take a lot of time ... *) - If[ (StandardMatrixElement =!= Identity), - If[ !FreeQ2[ oneamp, {DOT, DiracGamma, Polarization, - SUNF, SUNDelta, SUNT - } ] && FreeQ[ oneamp, Spinor ], - If[ Head[oneamp]===Plus, - oneamp = Sum[ (oneamp[[iii]] spip[])/. - spip -> spinorsandpairs /. - spinorsandpairs -> standmatd, - {iii,1,Length[oneamp]}], - oneamp = Expand[oneamp spip[], Polarization]/. - spip->spinorsandpairs /. spinorsandpairs -> - standmatd - ] - ] - ]; - If[ (StandardMatrixElement =!= Identity) && - (!FreeQ2[oneamp, {Spinor, Polarization, SUNIndex}]), - FCPrint[1, "before tostandmat", FCDoControl->oneloopVerbose]; - If[ Head[oneamp] === Plus, - paone = Select[oneamp, !FreeQ2[#, - {Spinor, Polarization, SUNIndex}]&]; - paone = {oneamp - paone, paone}, - paone = {0, oneamp} - ]; - paone2 = Isolate[Collect2[paone[[2]], {Spinor,Polarization,SUNIndex}, - Factoring -> False], - {Spinor,Polarization,SUNIndex}, - IsolateNames -> tempFC, - IsolateSplit->Infinity]; - oneamp = FixedPoint[ReleaseHold, tostandmat[paone2] ] + paone[[1]]; - FCPrint[1, "after tostandmat", FCDoControl->oneloopVerbose]; - FCPrint[3, "after tostandmat : oneamp = ", oneamp, FCDoControl->oneloopVerbose]; + + If[ (StandardMatrixElement =!= Identity) && !FreeQ2[oneamp,Join[FeynCalc`Package`DiracHeadsList,FeynCalc`Package`SUNHeadsList,{Polarization}]] && !FreeQ[oneamp,Spinor], + oneamp = ToStandardMatrixElement[oneamp, FCI->True, DiracSubstitute67->reducegamma67, Spinor->True] ]; - (* ********************************************************************* *) - (* oneloop25 *) - (* ********************************************************************* *) - (* ONEAMPCHANGE : spinor stuff and matrixelements *) + (* ********************************************************************* *) + (* oneloop25 *) + (* ********************************************************************* *) + + (* ONEAMPCHANGE : spinor stuff and matrixelements *) If[ !FreeQ[oneamp, StandardMatrixElement], FCPrint[1, "collecting w.r.t. standard matrixelements ", FCDoControl->oneloopVerbose]; - oneamp = collin[oneamp/.inisubs, StandardMatrixElement, True - ]; + oneamp = Collect2[oneamp/.initialSubstitutions, StandardMatrixElement, Factoring->Factor]; FCPrint[1, "collecting done", FCDoControl->oneloopVerbose]; ]; - (* ONEAMPCHANGE : inserting the subdeterminants again *) + (* ONEAMPCHANGE : inserting the subdeterminants again *) + If[ !FreeQ[ oneamp, SUBDET ], - oneamp = oneamp /. SUBDET -> SUB; + oneamp = FRH[oneamp /. SUBDET -> SUB, IsolateNames->SUB]; FCPrint[1, "subdeterminants reinserted", FCDoControl->oneloopVerbose] ]; + tric[y_Plus] := tric /@ y; tric[x_] := TrickMandelstam[x, onemandel]/;Length[onemandel]>0; tric[x_] := x/;onemandel==={}; - fma[xx_] := - True/;Head[xx]===StandardMatrixElement; - vva[xx_] := - True/;!FreeQ[{xx},PaVe]; + + vva[x_] := + True/;!FreeQ[{x},PaVe]; If[ LeafCount[oneamp]<1000, voneampsma = Variables[oneamp]/.SmallVariable->Identity; - smalist = Select[ voneampsma, fma ]; - pvlist = Select[ voneampsma, vva ]//Union; - arglist = Union[pvlist/.PaVe->pvar], + arglist = Union[Union[Select[voneampsma, vva]]/.PaVe->pvar], arglist = {} ]; + collpav[x_Symbol] := x; + collpav[a_StandardMatrixElement b_] := a collpav[b]; + collpav[x_] := - tric[ Collect2[x,{A0,B0,B1,B00,B11,C0,D0,PaVe}, - Factoring -> True] ]; - (* ********************************************************************* *) - (* oneloop26 *) - (* ********************************************************************* *) + tric[ Collect2[x,{A0,B0,B1,B00,B11,C0,D0,PaVe}, Factoring -> True] ]; - (* substituting the final substitutions *) - fsub[x_, su_] := + (* ********************************************************************* *) + (* oneloop26 *) + (* ********************************************************************* *) + + (* substituting the final substitutions *) + fsub[x_, s_] := Block[ {nx = x,ij}, - For[ij = 1, ij<=Length[su], ij++, - nx = nx/.su[[ij]] + For[ij = 1, ij<=Length[s], ij++, + nx = nx/.s[[ij]] ]; nx ]; - oneamp = fsub[ oneamp, finsubst ]; + + oneamp = fsub[oneamp, finalSubstitutions]; + If[ !FreeQ[oneamp, SUNIndex], oneamp = SUNSimplify[oneamp, Explicit -> True]; ]; - (* getting a common factor *) - oneamp = oneamp + nUl1 + nUl2; - If[ fact===True, + (* getting a common factor *) + oneamp = oneamp + null1 + null2; + If[ OptionValue[Factoring]===True, factor3[x_] := Factor2[x, FactorFull -> False]; + npref[0] = 0; npref[w_ v_] := - (factor3[w]/.Plus->pluS) npref[v]/; - FreeQ2[w,{A0, B0,B1, C0, D0, B00, B11, PaVe}]; - oneamp = factor3[(npref /@ Map[factor3,oneamp ])/.nUl1->0/.nUl2->0 - ]/.pluS->Plus/.npref->collpav, - oneamp = Map[collpav, oneamp] /. nUl1 ->0 /.nUl2 -> 0; + (factor3[w]/.Plus->pluS) npref[v]/; FreeQ2[w,{A0, B0,B1, C0, D0, B00, B11, PaVe}]; + oneamp = factor3[(npref /@ Map[factor3,oneamp ])/.null1|null2->0]/.pluS->Plus/.npref->collpav, + + oneamp = Map[collpav, oneamp] /.null1|null2->0; ]; - (* Isolating *) - If[ isolatehead=!=False, + (* Isolating *) + If[ isolateNames=!=False, isol[x_] := - Isolate[x,IsolateNames->isolatehead]; - sh[he_][x__] := - isol[he[x]]; - scaliso = {A0->sh[A0], B0->sh[B0], B1->sh[b1], B00->sh[B00], - B11->sh[B11], C0->sh[C0], D0->sh[D0]}; + Isolate[x,IsolateNames->isolateNames]; + sh[h_][x__] := + isol[h[x]]; + (*scaliso = {A0->sh[A0], B0->sh[B0], B1->sh[b1], B00->sh[B00], B11->sh[B11], C0->sh[C0], D0->sh[D0]};*) isoplu[x__] := isol[Plus[x]]; - oneamp = isol[ oneamp/.D0->sh[D0]/.C0->sh[C0]/. - B11->sh[B11]/.B00->sh[B00]/.B1->sh[b1]/. - B0->sh[B0]/.A0->sh[A0]/.Plus->isoplu/. - isoplu->Plus ]; + oneamp = isol[ oneamp/.D0->sh[D0]/.C0->sh[C0]/. B11->sh[B11]/.B00->sh[B00]/.B1->sh[B1]/. B0->sh[B0]/.A0->sh[A0]/.Plus->isoplu/. isoplu->Plus]; isol[x_] := x ]; - (* putting everything together again, including the prefactor *) + (* putting everything together again, including the prefactor *) + If[ FreeQ[oneamp, q], oneamp = ChangeDimension[oneamp, 4], - newprefactor = newprefactor/I/Pi + newprefactor = newprefactor/I/Pi; ]; + oneampresult = oneamp; - oneampresult = fsub[newprefactor, finsubst] oneampresult; + oneampresult = FRH[(fsub[newprefactor, finalSubstitutions]/.SUBDET->SUB),IsolateNames->SUB] oneampresult; (* Here we add back the non-loop terms *) oneampresult = nonLoopTerms + oneampresult; FCPrint[3, "oneampresult = ", oneampresult, FCDoControl->oneloopVerbose]; - If[ isolatehead=!=False, + If[ isolateNames=!=False, oneampresult = isol[oneampresult] ]; ](* end of If FreeQ oneamp, FeynAmpDenomiantor, FAD *) ; @@ -1270,103 +721,87 @@ (* ********************************************************************* *) (* writing the result in a file specified by grname *) - If[ (writeout=!=False )&& StringQ[ name ] && - (!ValueQ[OneLoopResult[grname]]), - If[ formattype===FortranForm, - wri[ name, Hold[grname = oneampresult], - FormatType -> FortranForm - ]/.wri -> Write2, - wri[ name, Hold[OneLoopResult[ grname ] = oneampresult], - FormatType->formattype]/.wri -> Write2; - If[ Length[FA2Info] > 0, - wri[ name, Hold[OneLoopInfo[ grname ] = FA2Info], - FormatType->InputForm]/.wri -> Write2; - ]; + If[ (writeOut=!=False) && StringQ[name] && (!ValueQ[OneLoopResult[grname]]), + If[ formatType===FortranForm, + wri[ name, Hold[grname = oneampresult], FormatType -> FortranForm]/.wri -> Write2, + + wri[ name, Hold[OneLoopResult[ grname ] = oneampresult], FormatType->formatType]/.wri -> Write2; ] ]; - If[ (!ValueQ[ OneLoopResult[ grname ]]) && (grname=!=False), + + If[ (!ValueQ[OneLoopResult[grname]]) && (grname=!=False), set[ OneLoopResult[grname], oneampresult ]/.set->Set ]; - If[ (!ValueQ[ OneLoopInfo[ grname ]]) && (grname=!=False), - set[ OneLoopInfo[grname], FA2Info]/.set->Set + + If[ (!ValueQ[OneLoopInfo[grname]]) && (grname=!=False), + set[ OneLoopInfo[grname], {}]/.set->Set ]; - (* ********************************************************************* *) - (* oneloop28 *) - (* ********************************************************************* *) + (* ********************************************************************* *) + (* oneloop28 *) + (* ********************************************************************* *) + + (* --------------------------------------------------------------------- *) + (* some cosmetics for print1 *) + (* --------------------------------------------------------------------- *) + (* only if no abbreviations are introduced: print eventually *) + (* for printing purposes abbreviations are useful,but *) + (* this may actually under certain circumstances be incorrect! *) + (* Though the result returned by OneLoop is of course correct *) + If[ isolateNames===False, - (* --------------------------------------------------------------------- *) - (* some cosmetics for print1 *) - (* --------------------------------------------------------------------- *) - (* only if no abbreviations are introduced: print eventually *) - (* for printing purposes abbreviations are useful,but *) - (* this may actually under certain circumstances be incorrect! *) - (* Though the result returned by OneLoop is of course correct *) - If[ isolatehead===False, PaVeAbbreviate[x_] := x/.PaVe->paVeabbrevi/.paVeabbrevi->PaVe; paVeabbrevi[x__,{y__},{m1_,m2_,m3_}, OptionsPattern[]] := ToExpression[ StringJoin@@Prepend[Map[ToString,{x}],"C"] ]; + paVeabbrevi[x__,{y__},{m1_,m2_,m3_,m4_}, OptionsPattern[]] := ToExpression[ StringJoin@@Prepend[Map[ToString,{x}],"D"] ]; - pva[xxx_] := - xxx//PaVeAbbreviate; - pvar[xx__,li1_{},li2_List, OptionsPattern[]] := - "As"[li2[[1]]]/;Length[li2]===1; - pvar[xx__,li1_List,li2_List, OptionsPattern[]] := - "Bs"@@Flatten[{li1,li2}]/;Length[li2]===2; - pvar[xx__,li1_List,li2_List, OptionsPattern[]] := - "Cs"@@Flatten[{li1,li2}]/;Length[li2]===3; - pvar[xx__,li1_List,li2_List, OptionsPattern[]] := - "Ds"@@Flatten[{li1,li2}]/;Length[li2]===4; + + pva[z_] := + z//PaVeAbbreviate; + + pvar[xx__,l_{},m_List, OptionsPattern[]] := + "As"[m[[1]]]/;Length[m]===1; + + pvar[xx__,l_List,li2_List, OptionsPattern[]] := + "Bs"@@Flatten[{l,m}]/;Length[m]===2; + + pvar[xx__,l_List,li2_List, OptionsPattern[]] := + "Cs"@@Flatten[{l,m}]/;Length[m]===3; + + pvar[xx__,l_List,li2_List, OptionsPattern[]] := + "Ds"@@Flatten[{l,m}]/;Length[m]===4; + FCPrint[2, " ", FCDoControl->oneloopVerbose]; FCPrint[2, " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *", FCDoControl->oneloopVerbose]; FCPrint[2, " ", FCDoControl->oneloopVerbose]; If[ grname=!=False, - FCPrint[1, " The result for ", grname, " is ", oneampresult//LeafCount, " leafcount long " - (* - Shallow[ oneampresult,{6, 20} ] - *), FCDoControl->oneloopVerbose]; + FCPrint[1, " The result for ", grname, " is ", oneampresult//LeafCount, " leafcount long ", FCDoControl->oneloopVerbose]; FCPrint[3, LeafCount[oneampresult], FCDoControl->oneloopVerbose]; ]; - If[ Length[ arglist ]>0 && !breakdown===True, + If[ Length[ arglist ]>0 && !breakdown, FCPrint[2, "Arguments: ", arglist//Union, FCDoControl->oneloopVerbose] ]; FCPrint[2, " ", FCDoControl->oneloopVerbose]; FCPrint[2, " * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *", FCDoControl->oneloopVerbose]; FCPrint[2, " ", FCDoControl->oneloopVerbose]; - ](* endIf IsolateNames *); + ]; (* ----------------------------------------------------------------- *) - ]; (* end Timing *) - If[ grname=!=False, - FCPrint[1, "CPU - time for ", grname, ": ", tim[[1]]//FeynCalcForm, FCDoControl->oneloopVerbose], - FCPrint[1, "CPU - time : ", tim[[1]]//FeynCalcForm, FCDoControl->oneloopVerbose] - ]; - oneampresult /. - - (*New 31/7-2002. Support for FeynArts 3.0 SumOver. F.Orellana*) - If[ (Sum /. Flatten[{opts}] /. Options[OneLoop]) === False, - FeynArts`SumOver[___] -> 1, - {} - ] //. - If[ (Sum /. Flatten[{opts}] /. Options[OneLoop]) === Explicit, - Times[f__, FeynArts`SumOver[i_, r_, ___]] :> - (If[ Head[r] =!= List, - FCPrint[2, "Summing ", i, " from 1 to ", r, FCDoControl->oneloopVerbose]; - rr = Range[1, r], - FCPrint[2, "Summing ", i, " over ", r, FCDoControl->oneloopVerbose]; - rr = r - ]; - Plus @@ ((Times[f] /. i -> #)& /@ rr)), - {} - ] - ] /; FreeQ[q,Rule] && FreeQ[q,Plus]; -(* ******************************************************************* *) + FCPrint[1,"OneLoop: All done, timing: ", N[AbsoluteTime[] - startTime, 4], FCDoControl->oneloopVerbose]; + + If[ OptionValue[FCE], + oneampresult = FCE[oneampresult] + ]; + + oneampresult + ] /; FreeQ[q,Rule] && FreeQ[q,Plus]; + (* ********************************************************************* *) (* oneloop30 *) @@ -1376,52 +811,40 @@ (* OneLoopSumdef *) Options[OneLoopSum] = { -(* -multiply with the Born diagrams - Born -> 1, -*) - CombineGraphs -> {}, - Dimension -> True, - ExtraVariables -> {}, - FinalFunction ->Identity, - FinalSubstitutions -> {}, - FormatType -> InputForm, - InitialSubstitutions -> {}, - IntermediateSubstitutions -> {}, - IsolateNames -> KK, -(* - KeepOnly -> False, -*) - Mandelstam -> {}, - Prefactor -> 1, - ReduceToScalars -> True, -(* - Scaling -> {}, -*) - SelectGraphs -> All, - WriteOutPaVe -> False - }; -(* -KeepOnly::usage= -"KeepOnly is an option of OneLoop. -It may be set to B0, C0, D0 keeping only the corresponding -coefficients. The default setting is False. If KeepOnly is set -to {} then the part of the amplitude which is not coefficient -of B0, C0, D0 is kept."; - -*) + CombineGraphs -> {}, + Dimension -> True, + ExtraVariables -> {}, + FinalFunction ->Identity, + FinalSubstitutions -> {}, + FormatType -> InputForm, + InitialSubstitutions -> {}, + IntermediateSubstitutions -> {}, + IsolateNames -> KK, + Mandelstam -> {}, + Prefactor -> 1, + ReduceToScalars -> True, + SelectGraphs -> All, + WriteOutPaVe -> False +}; OneLoopSum[ex_, ops___] := - Block[ {mand,reduce,na,i,exx,nsres,sres, - len0,len,jj, vars, varpave,isolatehead,alreadysummed, - filename, formattype,selectgraphs,combinegraphs,pres, - aa0,bb0,cc0,dd0,ddb0,finfunc,inisuB,extravars, - acdc, lnw, nres, j, nvd, set, npi3, newpa, simp,nplin, - mandelspec,sumcol,colll,prefactor,feynli,dims,fsub,keeponly, - d0multiply, c0multiply, d0scalIsolate,c0scalIsolate,vsm, - intermedsub,isol2,combinelist,np,nnp,npavopt,iiv,lres,mmsu,iim, - feynAmpden1, feynAmpden2,masss1, masss2, fim,checklabel }, + Block[ {mand,reduce,na, exx,nsres,sres, + len0,len, vars, varpave,isolateNames,alreadysummed, + filename, formatType,selectgraphs,combinegraphs,pres, + aa0,bb0,cc0,dd0,ddb0,bb1, bb00, bb11, finfunc,inisuB,extravars, + acdc, lnw, nres, nvd, set, npi3, newpa, simp,nplin, + mandelspec,sumcol,colll,prefactor,feynli,dims,fsub,keeponly, + d0multiply, c0multiply, d0scalIsolate,c0scalIsolate,vsm, + intermedsub,isol2,combinelist,np,nnp,npavopt,iiv,lres,mmsu,iim, + feynAmpden1, feynAmpden2,masss1, masss2, fim,checklabel,finalSubstitutions, lnp, + opsli, tim,amps,nex,ncombine, specrule, sumli, raTio, mansu, db0multiply, lenpa}, exx = ex; + + If[ !FreeQ2[{exx}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + sres = 0; SetOptions[DiracTrace, DiracTraceEvaluate -> False ]; exx = FixedPoint[ ReleaseHold, exx ]; @@ -1433,14 +856,14 @@ born = 1; combinegraphs = CombineGraphs/.opsli; extravars = ExtraVariables/.opsli; - isolatehead = IsolateNames/.opsli; - If[ isolatehead === True, - isolatehead = IsolateNames/.Options[Isolate] + isolateNames = IsolateNames/.opsli; + If[ isolateNames === True, + isolateNames = IsolateNames/.Options[Isolate] ]; dims = Dimension /.opsli; - finalsubst = FinalSubstitutions/.opsli; + finalSubstitutions = FinalSubstitutions/.opsli; finfunc = FinalFunction/.opsli; - formattype = FormatType/.opsli; + formatType = FormatType/.opsli; inisuB = InitialSubstitutions /. opsli; intermedsub = IntermediateSubstitutions /. opsli; (* @@ -1454,7 +877,7 @@ scaling = Scaling /. opsli; *) scaling = {}; - writeoutpave = WriteOutPaVe/.opsli; + writeOutPaVee = WriteOutPaVe/.opsli; If[ intermedsub =!= {}, SetOptions[ OneLoop, IntermediateSubstitutions -> intermedsub ] ]; @@ -1499,10 +922,10 @@ combinegraphs = Map[ Sort, combinegraphs ]; If[ combinegraphs =!= False, ncombine = {}; - For[ ii = 1, ii <= Length[combinegraphs], ii++, - If[ Length[ Intersection[selectgraphs, combinegraphs[[ii]]] ] > 0, + For[ r = 1, r <= Length[combinegraphs], r++, + If[ Length[ Intersection[selectgraphs, combinegraphs[[r]]] ] > 0, AppendTo[ncombine, - Intersection[selectgraphs,combinegraphs[[ii]]]] + Intersection[selectgraphs,combinegraphs[[r]]]] ] ]; combinegraphs = ncombine; combinelist = Flatten[combinegraphs]; @@ -1523,23 +946,23 @@ Block[ {nam,lq = First[exli][[2]]}, nam = GraphName[exli[[1,1,1]], ToExpression[ StringJoin@@ Map[ ToString, - Table[First[ exli[[numli[[jj]]]]]// - Last, {jj,Length[numli]} ] + Table[First[ exli[[numli[[r]]]]]// + Last, {r,Length[numli]} ] ] ] ]; - amps = Sum[ exli[[numli[[ij]]]]//Last, {ij,Length[numli]} ]; + amps = Sum[ exli[[numli[[i]]]]//Last, {i,Length[numli]} ]; FeynAmp[nam,lq,amps] ]; nex = {}; alreadysummed = {}; - For[ ii = 1, ii <= len0, ii++, - If[ MemberQ[selectgraphs, ii] && FreeQ[alreadysummed,ii], - If[ !FreeQ[combinelist, ii], - sumli = sumit[exx, Select[combinegraphs, !FreeQ[#,ii]&][[1]]]; + For[ r = 1, r <= len0, r++, + If[ MemberQ[selectgraphs, r] && FreeQ[alreadysummed,r], + If[ !FreeQ[combinelist, r], + sumli = sumit[exx, Select[combinegraphs, !FreeQ[#,r]&][[1]]]; AppendTo[nex, sumli]; AppendTo[alreadysummed, - Select[combinegraphs, !FreeQ[#,ii]&][[1]]], - AppendTo[nex, exx[[ii]]]; - AppendTo[alreadysummed, ii] + Select[combinegraphs, !FreeQ[#,r]&][[1]]], + AppendTo[nex, exx[[r]]]; + AppendTo[alreadysummed, r] ] ] ]; @@ -1702,11 +1125,10 @@ If[ vsm=!={}, FCPrint[1, "collect with respect to StandardMatrixElement", FCDoControl->oneloopVerbose]; nsres = 0; - For[ij = 1, ij<=Length[vsm], ij++, - FCPrint[1, "ij = ", ij, " out of ", Length[vsm], FCDoControl->oneloopVerbose]; - dif = D[ sres, vsm[[ij]] ]; - nsres = nsres + collp[ dif ] vsm[[ij]]; - sres = sres /. vsm[[ij]] -> 0 + For[i = 1, i<=Length[vsm], i++, + FCPrint[1, "i = ", i, " out of ", Length[vsm], FCDoControl->oneloopVerbose]; + nsres = nsres + collp[ D[ sres, vsm[[i]] ] ] vsm[[i]]; + sres = sres /. vsm[[i]] -> 0 ]; sres = nsres + sres; FCPrint[1, "collecting done", FCDoControl->oneloopVerbose], @@ -1747,14 +1169,14 @@ varpave = FixedPoint[ ReleaseHold, varpave ]; lenpa = Length[varpave]; pavit[xXX_PaVe, dir_, prev_:False] := - Block[ {nx, file, temp, set,xxxa,abbs}, + Block[ {nx, file, temp, xxxa,abbs}, paV[xy__, p_List, m_List] := PaVe[xy,C,p,C,m, PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce]; - xxx = paV@@xXX; + (*xxx = paV@@xXX;*) (*Changed 18/9-2000, F.Orellana*) abbs = DownValues[Abbreviation] /. Abbreviation -> Identity /. HoldPattern -> Identity; - nx = StringReplace[ ToString[InputForm[xxx/.abbs], PageWidth -> 222], + nx = StringReplace[ ToString[InputForm[paV@@xXX/.abbs], PageWidth -> 222], $Abbreviations ]; (**) @@ -1780,12 +1202,11 @@ If[ (file === None) && (keeponly === False), tim = Timing[ If[ prev === False, - temp = PaVeReduce[xXX, Dimension -> dims, - (*Added 19/9-2000. F.Orellana*)WriteOutPaVe->dir(**)]//paveorder, + temp = PaVeReduce[xXX, Dimension -> dims, WriteOutPaVe->dir]//paveorder, temp = paveorder[prev] ]; ][[1]]; - FCPrint[1, "Time needed = ", tim//FeynCalcForm, FCDoControl->oneloopVerbose]; + FCPrint[1, "Time needed = ", tim, FCDoControl->oneloopVerbose]; OpenWrite @@ {nx}; WriteString @@ {nx, "( "}; Write @@ {nx, temp}; @@ -1798,16 +1219,14 @@ For[ j = 1,j<=lenpa,j++, FCPrint[1, "working with # ", j, " out of ", lenpa, FCDoControl->oneloopVerbose]; FCPrint[1, "calculating ", InputForm[ varpave[[j]] ], FCDoControl->oneloopVerbose]; - If[ writeoutpave===True, - writeoutpave = "" + If[ writeOutPaVee===True, + writeOutPaVee = "" ]; - If[ !StringQ[writeoutpave], - tii = Timing[ - nvd = PaVeReduce[ varpave[[j]], IsolateNames ->False, - Dimension -> dims - ] // paveorder + If[ !StringQ[writeOutPaVee], + t = Timing[ + nvd = PaVeReduce[ varpave[[j]], IsolateNames ->False, Dimension -> dims] // paveorder ]; - FCPrint[1, tii[[1]], " needed", FCDoControl->oneloopVerbose] + FCPrint[1, t[[1]], " needed", FCDoControl->oneloopVerbose] ]; (* ********************************************************************* *) @@ -1815,7 +1234,7 @@ (* ********************************************************************* *) SQR[xxx_] := PowerExpand[Sqrt[xxx]]; - If[ StringQ[writeoutpave], + If[ StringQ[writeOutPaVee], (* Check if the difference w.r.t. the previous PaVe is only in the mass arguments. *) nvd = False; @@ -1835,7 +1254,7 @@ {iim, Length[Last[varpave[[j]]]]} ]; If[ (varpave[[j-1]] /. mmsu) === varpave[[j]], - nvd = pavit[varpave[[j]], writeoutpave, + nvd = pavit[varpave[[j]], writeOutPaVee, (varpave[[j-1]]/.PaVe->pavesave ) /. mmsu ]; @@ -1843,7 +1262,7 @@ ] ]; If[ nvd === False, - nvd = pavit[varpave[[j]], writeoutpave] + nvd = pavit[varpave[[j]], writeOutPaVee] ] ]; set[ varpave[[j]]/.PaVe->pavesave ,nvd ]/.set->Set @@ -1858,7 +1277,7 @@ isol2[isol2[a_]] := isol2[a]; acdc = Join[extravars,{A0,B0,B1,B00,B11,DB0,C0,D0,PaVe}]; - acdc = Union[acdc, acdc /. finalsubst]; + acdc = Union[acdc, acdc /. finalSubstitutions]; FCPrint[1, "acdc = ", acdc, FCDoControl->oneloopVerbose]; (* partdef *) part[a_Times] := @@ -1909,32 +1328,31 @@ If[ FreeQ[sres, StandardMatrixElement], lnw = 1 ]; - For[jj = 1, jj<=lnw, jj++, + For[v = 1, v<=lnw, v++, If[ lnw === 1, If[ FreeQ[sres, StandardMatrixElement], newpa = {sres, 1}, newpa = PartitHead[ Expand[sres, StandardMatrixElement], StandardMatrixElement ] ], - newpa = PartitHead[ sres[[jj]],StandardMatrixElement ] + newpa = PartitHead[ sres[[v]],StandardMatrixElement ] ]; - FCPrint[1, " # ", jj, " out of ", lnw, " ", newpa[[2]], FCDoControl->oneloopVerbose]; + FCPrint[1, " # ", v, " out of ", lnw, " ", newpa[[2]], FCDoControl->oneloopVerbose]; (* Collect wrt. all the scalar integrals *) FCPrint[1, "Shallow ", Shallow[newpa[[1]]], FCDoControl->oneloopVerbose]; np = newpa[[1]]; FCPrint[1, "leafcount of np = ", LeafCount[np], FCDoControl->oneloopVerbose]; If[ Global`$Special === True, - oldnp = np; np = Collect2[np, acdc, Factoring -> False]; ]; - tinp = Timing[ + (*tinp = Timing[*) np = Collect2[ np, acdc, Factoring -> True]; nnp = paveorder[np]; If[ np =!= nnp, np = Collect2[nnp, acdc, Factoring -> True]; ]; - ]; - FCPrint[1, "timing for collecting = ", tinp[[1]], FCDoControl->oneloopVerbose]; + (*];*) + (*FCPrint[1, "timing for collecting = ", tinp[[1]], FCDoControl->oneloopVerbose];*) zero[__] := 0; (* combine the terms without PaVe's *) @@ -1948,9 +1366,8 @@ nplin = nplin/.B11->zero; nplin = nplin/.PaVe->zero; If[ extravars =!= {}, - For[iext = 1, iext <= Length[extravars], iext++, - nplin = nplin /. extravars[[iext]] -> 0 - ] + For[i = 1, i <= Length[extravars], i++, + nplin = nplin /. extravars[[i]] -> 0] ]; If[ nplin === 0, FCPrint[1, "nplin = 0", FCDoControl->oneloopVerbose], @@ -1975,10 +1392,10 @@ FCPrint[1, "combining coefficients of B0, C0, ...", FCDoControl->oneloopVerbose]; (* This ist the loop of A0B0C0D0 *) (* putting it now over a common denominator *) - For[i3 = 1, i3<=lnp, i3++, - FCPrint[1, "i3 = ", i3, " out of ", lnp, " - LeafCount = ", LeafCount[np[[i3]]], FCDoControl->oneloopVerbose]; - npi3 = finfunc @@ {part[ np[[i3]] + For[r = 1, r<=lnp, r++, + FCPrint[1, "i3 = ", r, " out of ", lnp, " + LeafCount = ", LeafCount[np[[r]]], FCDoControl->oneloopVerbose]; + npi3 = finfunc @@ {part[ np[[r]] ]/.part->simp}; If[ born =!= 1, npi3 = part[npi3 born]/.part->simp; @@ -2002,19 +1419,19 @@ (* oneloop35 *) (* ********************************************************************* *) fsub[x_] := - Block[ {nx = x,su,ij}, - su = finalsubst; - For[ij = 1, ij<=Length[su], ij++, - nx = nx/.su[[ij]] + Block[ {nx = x,su}, + su = finalSubstitutions; + For[r = 1, r<=Length[su], r++, + nx = nx/.su[[r]] ]; nx ]; mand = fsub[mand]; nres = fsub[ FixedPoint[tog, prefactor, 5] nres]; - check = nres; + {aa0, bb0, bb1, bb00, bb11, ddb0, cc0, dd0} = {A0, B0, B1, B00, B11, DB0, C0, D0} // fsub; - If[ isolatehead=!=False, + If[ isolateNames=!=False, FCPrint[1, "isolating now ", FCDoControl->oneloopVerbose]; plupp0[x__] := Plus[x] /; !FreeQ[{x},plupp0]; @@ -2025,16 +1442,16 @@ If[ Length[mand]===4, isolmand[x_] := Isolate[x, {mand[[1]],mand[[2]],mand[[3]]}, - IsolateNames->isolatehead], + IsolateNames->isolateNames], isolmand[x_] := - Isolate[x,IsolateNames->isolatehead ] + Isolate[x,IsolateNames->isolateNames ] ]; isolate0[x_] := - Isolate[x, IsolateNames->isolatehead ]; + Isolate[x, IsolateNames->isolateNames ]; isc[x_][y__] := isol1[x][(TrickMandelstam[fsub[x[y]]/.dd0->D0,mand ]//paveorder)/. - D0 -> dd0, IsolateNames->isolatehead]; + D0 -> dd0, IsolateNames->isolateNames]; If[ Length[mand]===4, isol1[_][x_, y_] := Isolate[x, y] /; FreeQ2[x, Take[mand, 3]] @@ -2072,7 +1489,7 @@ (* oneloop36 *) (* ********************************************************************* *) - (* If isolatehead .. *) + (* If isolateNames .. *) (*Only if the option Factoring of OneLoop is True, factor also here *) If[ (Factoring/.Options[OneLoop]) === True, specrule = {(a_Symbol - b_Symbol) (a_Symbol+b_Symbol)->(a^2-b^2)}; @@ -2091,7 +1508,7 @@ dbb0 -> isc2[ddb0] /. aa0 -> isc2[aa0]/. PaVe -> isc2[PaVe]; nres = nres/.isol2 -> isol22; - nres = Map[factor3, nres + nuLL]/.specrule; + nres = Map[factor3, nres + nuLL]/. specrule; colp[x__] := Map[TrickMandelstam[#,mand]&, Collect2[Plus[x], {aa0,bb0,bb00,bb11,bb1,ddb0, @@ -2120,17 +1537,25 @@ (* ******************************************************************* *) - (*smallddef *) -small2/: small2[x_]^n_ := small2[x^2] /; n > 0; -small2/: small2[_] a_ :=0; -small3/: small3[_] + a_ :=a; +(*smallddef *) +small2/: + small2[x_]^n_ := + small2[x^2] /; n > 0; +small2/: + small2[_] _ := + 0; + +small3/: + small3[_] + a_ := + a; + small4[x_^m_] := SmallVariable[x]^m; - smalld[x_] := - x/;FreeQ[x,SmallVariable]; - smalld[x_] := - x/.SmallVariable->small2/.small2->small3/. - small3->small4/.small4->SmallVariable; + +smalld[x_] := + x/;FreeQ[x,SmallVariable]; +smalld[x_] := + x/.SmallVariable->small2/.small2->small3/. small3->small4/.small4->SmallVariable; (* ******************************************************************* *) (* ********************************************************************* *) @@ -2138,69 +1563,65 @@ (* ********************************************************************* *) (*spinorsandpairsdef*) - dotdotlin[x___] := - dotlin[DOT[x]]; +dotdotlin[x___] := + DotSimplify[DOT[x],Expanding->False]; (*tempstandmatdef*) - standma[x_] := - dotdotlin[x]/;!FreeQ2[x, {Polarization, DOT}]; - tempstandmat[x_] := - Block[ {ttt}, - ttt = x; - If[ StandardMatrixElement =!= Identity, - If[ FreeQ[ttt, Spinor] && - !FreeQ2[ttt,{SUNF,SUNDelta, SUNT, Pair}], - If[ LeafCount[ttt]>500, - FCPrint[2, "expanding in tempstandmat", FCDoControl->oneloopVerbose] - ]; - ttt = Expand[ttt spinorsandpairs[]]; - If[ LeafCount[ttt]>500, - FCPrint[2, "expanding in tempstandmat done", FCDoControl->oneloopVerbose] - ]; - ttt = ttt /. spinorsandpairs -> dotsp +standma[x_] := + dotdotlin[x]/;!FreeQ2[x, {Polarization, DOT}]; + +tempstandmat[x_] := + Block[ {ttt}, + ttt = x; + If[ StandardMatrixElement =!= Identity, + If[ FreeQ[ttt, Spinor] && !FreeQ2[ttt,{SUNF,SUNDelta, SUNT, Pair}], + If[ LeafCount[ttt]>500, + FCPrint[2, "expanding in tempstandmat", FCDoControl->oneloopVerbose] ]; - If[ (Length[DownValues[spinorsandpairs]]>1) || - ValueQ[StandardMatrixElement], - ttt = x/.DOT->spinorsandpairs/. - spinorsandpairs->StandardMatrixElement/. - StandardMatrixElement->standma/.standma-> - StandardMatrixElement; + ttt = Expand[ttt spinorsandpairs[]]; + If[ LeafCount[ttt]>500, + FCPrint[2, "expanding in tempstandmat done", FCDoControl->oneloopVerbose] ]; - (* - If[$fourfermion =!= True, - If[FreeQ[ttt, Polarization] && !FreeQ[ttt,Spinor], - ttt = SpecificPolarization[ttt] - ] - ]; -*) - ]; - ttt + ttt = ttt /. spinorsandpairs -> dotsp + ]; + If[ (Length[DownValues[spinorsandpairs]]>1) || ValueQ[StandardMatrixElement], + ttt = x/.DOT->spinorsandpairs/. spinorsandpairs->StandardMatrixElement/. StandardMatrixElement->standma/.standma-> StandardMatrixElement; + ]; + ]; + ttt + ]; + +spinorsandpairs[a_,b__] := + dotdotlin[a,b]//spinorsandpairs; - spinorsandpairs[a_,b__] := - dotdotlin[a,b]//spinorsandpairs; - dotsp[] = 1; - dotsp[x_] := - x; +dotsp[] = + 1; +dotsp[x_] := + x; - spinorsandpairs/: - spinorsandpairs[x___] Pair[ Momentum[a__], Momentum[b__]]^n_. := - spinorsandpairs[dotsp[x] Pair[Momentum[a],Momentum[b]]^n]/; !FreeQ[{a,b},Polarization]; +spinorsandpairs/: + spinorsandpairs[x___] Pair[ Momentum[a__], Momentum[b__]]^n_. := + spinorsandpairs[dotsp[x] Pair[Momentum[a],Momentum[b]]^n]/; !FreeQ[{a,b},Polarization]; - spinorsandpairs/: spinorsandpairs[x___] Eps[w__] := - spinorsandpairs[dotsp[x] Eps[w]]/; !FreeQ[{w}, Polarization]; +spinorsandpairs/: spinorsandpairs[x___] Eps[w__] := + spinorsandpairs[dotsp[x] Eps[w]]/; !FreeQ[{w}, Polarization]; - spinorsandpairs/: - spinorsandpairs[x___] a_SUNT:= spinorsandpairs[dotsp[x], a]; +spinorsandpairs/: + spinorsandpairs[x___] a_SUNT:= + spinorsandpairs[dotsp[x], a]; - spinorsandpairs/: - spinorsandpairs[x___] a_SUNF:= spinorsandpairs[dotsp[x] a]; +spinorsandpairs/: + spinorsandpairs[x___] a_SUNF:= + spinorsandpairs[dotsp[x] a]; - spinorsandpairs/: - spinorsandpairs[x___] a_SUNDelta:= spinorsandpairs[dotsp[x] a]; +spinorsandpairs/: + spinorsandpairs[x___] a_SUNDelta:= + spinorsandpairs[dotsp[x] a]; - spinorsandpairs/: spinorsandpairs[x___] spinorsandpairs[y___] := +spinorsandpairs/: + spinorsandpairs[x___] spinorsandpairs[y___] := spinorsandpairs[dotsp[x] dotsp[y]]; (* ********************************************************************* *) @@ -2211,51 +1632,47 @@ (* Tensorintegraldecomposition *) (* *************************************************************** *) -denomExpand[y__] := - y/.FeynAmpDenominator->denexp; (*denomExpanddef*) -denexp[z__] := - Expand //@ MomentumExpand[ FeynAmpDenominator[z] ]; (* *************************************************************** *) (* suind substitutes for qu dummy indices for the tensor integral *) (* decomposition, the first argument of suind is a sumand *) (* *************************************************************** *) (* Hier das RICHTIGE suind ::: *) - suind[ y_,qu_,dim_,md_] := - Block[ {i,res = y, posli, - currentposli}, (*suinddef*) - posli = Position[y,Momentum[qu,___] ]; - If[ posli=!={}, - For[i = 1, i <= Length[posli],i++, - currentposli = Position[res, Momentum[qu,___] ]; - res = ReplacePart[res, LorentzIndex[md[i],dim], - currentposli[[1]] ] - ] - ]; - res +suind[ y_,qu_,dim_,md_] := + Block[ {i,res = y, posli, currentposli}, + posli = Position[y,Momentum[qu,___] ]; + If[ posli=!={}, + For[i = 1, i <= Length[posli],i++, + currentposli = Position[res, Momentum[qu,___] ]; + res = ReplacePart[res, LorentzIndex[md[i],dim],currentposli[[1]]] + ] ]; + res + ]; (* *************************************************************** *) (* for the divergent parts "epsilon - substitution" *) (* *************************************************************** *) - epst[x__] := - If[ uvpart === True, - 0, - epst2[x] - ]; - epst2[gr_,x_,4,resid_] := - to4dim[ gr ]; (*epstdef*) - epst2[gr_,x_,d_Symbol,_] := - to4dim[ gr ]/;FreeQ[x,d]; - epst2[gr_,x_,d_Symbol,resid_] := - Block[ {epstresul,epstin,epseps,epx}, - epx = to4dim[x]; - epstin = Expand[(epx/.d->(4-epseps))-(epx/.d->4) - ]//spinorchainevaluate; - epstresul = to4dim[gr + Normal[ Series[epstin,{epseps,0,1}] - ]/.epseps->resid ]//Expand; - epstresul - ]; + +to4dim[x_] := + x/.{Momentum[v_,_]:>Momentum[v], LorentzIndex[w_,_]:>LorentzIndex[w]}; + +epst[x__] := + epst2[x]; + +epst2[gr_,(*x*)_,4,(*resid*)_] := + to4dim[ gr ]; + +epst2[gr_,x_,d_Symbol,_] := + to4dim[ gr ]/;FreeQ[x,d]; + +epst2[gr_,x_,d_Symbol,resid_] := + Block[ {epstresul,epstin,epseps,epx}, + epx = to4dim[x]; + epstin = Expand[(epx/.d->(4-epseps))-(epx/.d->4)]//spinorchainevaluate; + epstresul = to4dim[gr + Normal[ Series[epstin,{epseps,0,1}]]/.epseps->resid ]//Expand; + epstresul + ]; (* ********************************************************************* *) (* oneloop39 *) @@ -2264,164 +1681,169 @@ (* *************************************************************** *) (* A useful evaluation function ( for tensint ) *) (* *************************************************************** *) - to4d2[x_] := - x /; $LimitTo4 =!= True; - to4d2[x_] := - (x/.{Momentum[fope_,_]:>Momentum[fope]/;FreeQ[fope,q], - LorentzIndex[muu_,_] :> LorentzIndex[muu]} - ) /; $LimitTo4 === True; - dirsim[a_ b_] := - a dirsim[b] /; FreeQ2[a, {Spinor,DiracGamma}]; +to4d2[x_] := + x /; $LimitTo4 =!= True; +to4d2[x_] := + (x/.{Momentum[f_,_]:>Momentum[f]/;FreeQ[f,q], LorentzIndex[u_,_] :> LorentzIndex[u]}) /; $LimitTo4 === True; + +dirsim[a_ b_] := + a dirsim[b] /; FreeQ2[a, {Spinor,DiracGamma}]; + SetAttributes[eval,Listable]; (*evaldef*) - eval[evy_] := - MemSet[ eval[evy], - Block[ {evalte,nul1,nul2,ie,neval,nt}, - FCPrint[3, "OneLoop: eval: Entering with ", evy ,FCDoControl->oneloopVerbose]; - evalte = to4d2[ evy/.NonCommutativeMultiply->Times ]; - If[ !FreeQ[ evalte, LorentzIndex ], - evalte = contractli[ evalte ]; - ]; - evalte = FixedPoint[ReleaseHold,evalte]//to4d2; - evalte = Expand[ dotlin[ evalte ]//ExpandScalarProduct, DOT ]; - If[ (Length[evalte]>5) && !FreeQ[evalte, DOT], - evalte = Collect2[ evalte, DOT, Factoring -> False] +eval[evy_] := + MemSet[ eval[evy], + Block[ {evalte,nul1,nul2,ie,neval,nt}, + FCPrint[3, "OneLoop: eval: Entering with ", evy ,FCDoControl->oneloopVerbose]; + evalte = to4d2[ evy/.NonCommutativeMultiply->Times ]; + If[ !FreeQ[ evalte, LorentzIndex ], + evalte = Contract[evalte, Expanding->True, Factoring->False, EpsContract->False] // Expand; + ]; + evalte = FixedPoint[ReleaseHold,evalte]//to4d2; + + evalte = Expand[ DotSimplify[ evalte, Expanding->False ]//ExpandScalarProduct, DOT ]; + If[ (Length[evalte]>5) && !FreeQ[evalte, DOT], + evalte = Collect2[ evalte, DOT, Factoring -> False] + ]; + + If[ !FreeQ[ evalte, DiracGamma], + evalte = Map[ dirsim, evalte + nul1 ]/. dirsim->DiracSimplify/.nul1 -> 0; + + If[ LeafCount[evalte]>100, + evalte = Collect2[evalte,DOT, Factoring -> False]; ]; - If[ !FreeQ[ evalte, DiracGamma], - evalte = Map[ dirsim, evalte + nul1 ]/. - dirsim->DiracSimplify/.nul1 -> 0; - If[ LeafCount[evalte]>100, - evalte = Collect2[evalte,DOT, Factoring -> False]; + evalte = evalte + nul1 + nul2; + neval = 0; + For[ie = 1, ie<=Length[evalte], ie++, + If[ Length[evalte[[ie]]]>0, + FCPrint[3, "ie = ", ie, " out of ", Length[evalte], FCDoControl->oneloopVerbose] ]; - evalte = evalte + nul1 + nul2; - neval = 0; - For[ie = 1, ie<=Length[evalte], ie++, - If[ Length[evalte[[ie]]]>0, - FCPrint[3, "ie = ", ie, " out of ", Length[evalte], FCDoControl->oneloopVerbose] - ]; - nt = Contract[DiracOrder[evalte[[ie]]] - ]//ExpandScalarProduct; - nt = DiracSimplify[nt]//DiracOrder; - nt = Expand[nt, DOT]; - FCPrint[3, "length of nt = ", nt//Length, FCDoControl->oneloopVerbose]; - neval = neval + nt - ]; - evalte = neval/.nul1->0/.nul2->0; + nt = Contract[DiracOrder[evalte[[ie]]]]//ExpandScalarProduct; + nt = DiracSimplify[nt]//DiracOrder; + nt = Expand[nt, DOT]; + FCPrint[3, "length of nt = ", nt//Length, FCDoControl->oneloopVerbose]; + neval = neval + nt ]; - If[ !FreeQ[evalte, Eps], - evalte = evalte//EpsEvaluate//epschisholm; - (* The default is that Eps's will be contracted away!*) - evalte = Expand[ conall[ evalte ]//ExpandScalarProduct]; - evalte = epschisholm[ evalte ]//DiracSimplify//DiracOrder; - evalte = Contract[ evalte ]; - evalte = Expand[ evalte//ExpandScalarProduct ] - ]; - evalte = tempstandmat[ evalte ]; - evalte = Expand[evalte]; - FCPrint[3, "OneLoop: eval: Leaving with ", evalte ,FCDoControl->oneloopVerbose]; - evalte - ]]; + evalte = neval/.nul1->0/.nul2->0; + ]; + + If[ !FreeQ[evalte, Eps], + evalte = evalte//EpsEvaluate//EpsChisholm[#,FCI->True]&; + (* The default is that Eps's will be contracted away!*) + evalte = Expand[ Contract[evalte, Expanding->True, EpsContract->True, Factoring->False] // Expand//ExpandScalarProduct]; + evalte = EpsChisholm[evalte,FCI->True]//DiracSimplify//DiracOrder; + evalte = Contract[evalte]; + evalte = Expand[evalte//ExpandScalarProduct ] + ]; + evalte = tempstandmat[ evalte ]; + evalte = Expand[evalte]; + FCPrint[3, "OneLoop: eval: Leaving with ", evalte ,FCDoControl->oneloopVerbose]; + evalte + ]]; (* ********************************************************************* *) (* ********************************************************************* *) (* oneloop40 *) (* ********************************************************************* *) (*tensintdef*) -tensint[x_,dim_,q_,options___] := (*tensint[x,dim,q,options]=*) - Block[ {(*tensj,tensi,tensic,*)tensg = 0,(*mandel,*)tensx = x(*,tensdnp,tensdnp1,*) +tensint[x_,dim_,q_, mandel_List] := (*tensint[x,dim,q,options]=*) + Block[ {(*tensj,tensi,tensic,*)tensg = 0,(*mandel,*)tensx = x, + tenslnt,tensdnp, tensdnp1, tenslep, tensldn, mud, tdenlen + (*,tensdnp,tensdnp1,*) (*tenslnt,tensldn,tensqmax,tenslep,tensdnqq,tensdnqqb,*) (*tensqc,tensjq*)(*,tensfq,ltx*) + }, tensg = Catch[ - FCPrint[2, "OneLoop: tensint: entering with ", tensx ,FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tensint: entering ", q, " dimension ", dim, " ", x//FeynCalcForm, FCDoControl->oneloopVerbose]; - (* diracSimplify must have been used previously *) - mandel = Mandelstam /.Join[ options,Options[ tensint ] ]; - (* tensor integral decomposition *) - (*ltx = nterms[tensx];*) - If[ Head[tensx]===Plus, - tenslnt = Length[tensx], - tenslnt = 1 - ]; - - (* The tensj - loop runs over all different loop integrals *) - Clear[tensqc]; - For[ tensj = 1, tensj <= tenslnt, tensj++, - FCPrint[1, "OneLoop: tensint: tensorintegral # ", tensj, " / ", tenslnt, FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tensint: tensorintegral ", If[ tenslnt===1, tensx, tensx[[tensj]]], FCDoControl->oneloopVerbose]; - tensqc[tensj][any_] := - 0; - (* splitting into q^i_1 ... q^i_j and FeynAmpDenominator for each term *) - If[ tenslnt===1, - tensdnp = PartitHead[ tensx,FeynAmpDenominator ], - tensdnp = PartitHead[ tensx[[tensj]],FeynAmpDenominator ] - ]; - FCPrint[3,"OneLoop: tensint: tensdnp1 ",tensdnp, FCDoControl->oneloopVerbose]; - (* Collect according to the number of q's *) - tensdnp1 = Collect2[ tensdnp[[1]],q, Factoring -> False]; + FCPrint[2, "OneLoop: tensint: entering with ", tensx, FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tensint: entering ", q, " dimension ", dim, " ", x, FCDoControl->oneloopVerbose]; + (* diracSimplify must have been used previously *) + + (* tensor integral decomposition *) + (*ltx = nterms[tensx];*) + If[ Head[tensx]===Plus, + tenslnt = Length[tensx], + tenslnt = 1 + ]; + + (* The j - loop runs over all different loop integrals *) + Clear[tensqc]; + For[ j = 1, j <= tenslnt, j++, + FCPrint[1, "OneLoop: tensint: tensorintegral # ", j, " / ", tenslnt, FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tensint: tensorintegral ", If[ tenslnt===1, tensx, tensx[[j]]], FCDoControl->oneloopVerbose]; + tensqc[j][_] := + 0; + (* splitting into q^i_1 ... q^i_j and FeynAmpDenominator for each term *) + If[ tenslnt===1, + tensdnp = PartitHead[ tensx,FeynAmpDenominator ], + tensdnp = PartitHead[ tensx[[j]],FeynAmpDenominator ] + ]; + FCPrint[3,"OneLoop: tensint: tensdnp1 ",tensdnp, FCDoControl->oneloopVerbose]; + (* Collect according to the number of q's *) + tensdnp1 = Collect2[ tensdnp[[1]],q, Factoring -> False]; - FCPrint[3,"OneLoop: tensint: tensdnp1 ",tensdnp1, FCDoControl->oneloopVerbose]; + FCPrint[3,"OneLoop: tensint: tensdnp1 ",tensdnp1, FCDoControl->oneloopVerbose]; - (*This for dealing with things like (q.x)^n *) - pairpow/: pairpow[a___,Momentum[q,di___],b___]^n_Integer?Positive := - (pairpow[a,Momentum[q,di],b]^(n-1))**pairpow[a,Momentum[q,di],b]; + (*This for dealing with things like (q.x)^n *) + pairpow/: pairpow[a___,Momentum[q,di___],b___]^n_Integer?Positive := + (pairpow[a,Momentum[q,di],b]^(n-1))**pairpow[a,Momentum[q,di],b]; - tensdnp1 = tensdnp1/.Pair->pairpow/.pairpow->Pair; + tensdnp1 = tensdnp1/.Pair->pairpow/.pairpow->Pair; - FCPrint[3,"OneLoop: tensint: tensdnp1 after pairpow ",tensdnp1, FCDoControl->oneloopVerbose]; - FCPrint[1, "OneLoop: tensint: Checking rank of ", tensdnp1, FCDoControl->oneloopVerbose]; - If[ Head[tensdnp1]===Plus, - tensldn = Length[tensdnp1], - tensldn = 1 - ]; - FCPrint[3, "OneLoop: tensint: tensldn: ", tensldn, FCDoControl->oneloopVerbose]; - tensqmax[tensj] = 0; - FCPrint[3, "OneLoop: tensint: Entering 1st nested loop", FCDoControl->oneloopVerbose]; - For[ tensic = 1, tensic <= tensldn, tensic++, - If[ tensldn===1, - (*one term in the numerator *) - - (* Determines the tensor rank *) - tenslep = Length[Position[tensdnp1,q ] ]; - (* BREAK EVENTUALLY *) - If[ tenslep>3, - Print["FYI: Tensor integrals of rank higher than 3 encountered; Please use the option CancelQP -> True or OneLoopSimplify->True or use another program."]; - Throw[x] - ]; - FCPrint[3, "OneLoop: tensint: tensdnp1 ", tensdnp1, FCDoControl->oneloopVerbose]; - tensqc[tensj][tenslep] += suind[ tensdnp1,q,dim,mud ], - (*more terms in the numerator *) - (* Determines the tensor rank *) - tenslep = Length[ Position[tensdnp1[[tensic]],q ] ]; - tensqc[tensj][tenslep] += suind[tensdnp1[[tensic]],q,dim,mud] + FCPrint[3,"OneLoop: tensint: tensdnp1 after pairpow ",tensdnp1, FCDoControl->oneloopVerbose]; + FCPrint[1, "OneLoop: tensint: Checking rank of ", tensdnp1, FCDoControl->oneloopVerbose]; + If[ Head[tensdnp1]===Plus, + tensldn = Length[tensdnp1], + tensldn = 1 ]; - FCPrint[3, "OneLoop: tensqc[tensj][tenslep]: ", tensqc[tensj][tenslep], FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tensint: tensldn: ", tensldn, FCDoControl->oneloopVerbose]; + tensqmax[j] = 0; + FCPrint[3, "OneLoop: tensint: Entering 1st nested loop", FCDoControl->oneloopVerbose]; + For[ i = 1, i <= tensldn, i++, + If[ tensldn===1, + (*one term in the numerator *) + + (* Determines the tensor rank *) + tenslep = Length[Position[tensdnp1,q ] ]; + (* BREAK EVENTUALLY *) + If[ tenslep>3, + Print["FYI: Tensor integrals of rank higher than 3 encountered; Please use the option CancelQP -> True or OneLoopSimplify->True or use another program."]; + Throw[x] + ]; + FCPrint[3, "OneLoop: tensint: tensdnp1 ", tensdnp1, FCDoControl->oneloopVerbose]; + tensqc[j][tenslep] += suind[ tensdnp1,q,dim,mud ], + (*more terms in the numerator *) + (* Determines the tensor rank *) + tenslep = Length[ Position[tensdnp1[[i]],q ] ]; + tensqc[j][tenslep] += suind[tensdnp1[[i]],q,dim,mud] + ]; + FCPrint[3, "OneLoop: tensqc[j][tenslep]: ", tensqc[j][tenslep], FCDoControl->oneloopVerbose]; - If[ tenslep > tensqmax[tensj], - tensqmax[tensj] = tenslep - ] - ]; - FCPrint[3, "OneLoop: tensint: 1st nested loop done", FCDoControl->oneloopVerbose]; - - FCPrint[3, "OneLoop: tensint: tensdnp1 ", tensdnp1, FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tensint: tensqmax[tensj] ", tensqmax[tensj], FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tensint: tensg before the nested loop ", tensg, FCDoControl->oneloopVerbose]; - - - - FCPrint[3, "OneLoop: tensint: Entering 2nd nested loop", FCDoControl->oneloopVerbose]; - For[ tensjq = 0, tensjq <= tensqmax[tensj], tensjq++, - tdenlen = Length[ tensdnp[[2]] ]; - FCPrint[2, "OneLoop: tensint: Tensorintegral (N = ", tdenlen, ") : # of q's = ", tensjq, " decomposing ", Length[tensqc[tensj][tensjq]], " term(s)", FCDoControl->oneloopVerbose]; - (* tdec is the function that is actually doing the decomposition !*) - FCPrint[3, "OneLoop: tensint: tensqc[tensj][tensjq] ", tensqc[tensj][tensjq], "", FCDoControl->oneloopVerbose]; - tensg += tdec[ tensqc[tensj][tensjq], tensdnp[[2]],q, - tensjq,dim,mud,mandel - ]/.NonCommutativeMultiply->Times - ];(*tensjq - loop*) - FCPrint[3, "OneLoop: tensint: 2nd nested loop done", FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tensint: tensg after the 2nd nested loop ", tensg, FCDoControl->oneloopVerbose]; - ]; - tensg = Expand[tensg] + If[ tenslep > tensqmax[j], + tensqmax[j] = tenslep + ] + ]; + FCPrint[3, "OneLoop: tensint: 1st nested loop done", FCDoControl->oneloopVerbose]; + + FCPrint[3, "OneLoop: tensint: tensdnp1 ", tensdnp1, FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tensint: tensqmax[j] ", tensqmax[j], FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tensint: tensg before the nested loop ", tensg, FCDoControl->oneloopVerbose]; + + + + FCPrint[3, "OneLoop: tensint: Entering 2nd nested loop", FCDoControl->oneloopVerbose]; + For[ s = 0, s <= tensqmax[j], s++, + tdenlen = Length[ tensdnp[[2]] ]; + FCPrint[2, "OneLoop: tensint: Tensorintegral (N = ", tdenlen, ") : # of q's = ", s, " decomposing ", Length[tensqc[j][s]], " term(s)", FCDoControl->oneloopVerbose]; + (* tdec is the function that is actually doing the decomposition !*) + FCPrint[3, "OneLoop: tensint: tensqc[j][s] ", tensqc[j][s], "", FCDoControl->oneloopVerbose]; + tensg += tdec[ tensqc[j][s], tensdnp[[2]],q, + s,dim,mud,mandel + ]/.NonCommutativeMultiply->Times + ];(*s - loop*) + FCPrint[3, "OneLoop: tensint: 2nd nested loop done", FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tensint: tensg after the 2nd nested loop ", tensg, FCDoControl->oneloopVerbose]; + ]; + tensg = Expand[tensg] ]; FCPrint[2, "OneLoop: tensint: Leaving with tensg= ", tensg, FCDoControl->oneloopVerbose]; @@ -2435,61 +1857,48 @@ (* *************************************************************** *) (* tensor integrals; "qn" denotes the number of "q's" *) (* *************************************************************** *) -pavremember[x__] := - MemSet[pavremember[x], PaVeReduce[x]]; - tdec[0,___] := (*tdecdef*) - 0; +tdec[0,___] := (*tdecdef*) + 0; - tdec[ expr_,props_,Q_,qn_ ,di_,mudu_,mand_] := (*tdecdef*) - MemSet[ tdec[ expr,props,Q,qn,di,mudu,mand], - Block[ {spl0, mande,tensps = {},tdecnew,tdec0j,tdectij, - tensdf2,tensdf1, pav0, - tdecex = expr/.Pair-> PairContract, +tdec[ expr_,props_,Q_,qn_ ,di_,mudu_,mand_] := (*tdecdef*) + MemSet[ tdec[ expr,props,Q,qn,di,mudu,mand], + Block[{ spl0, mande,tensps = {},tdecnew,tdec0j,tdectij, + tensdf2,tensdf1, pav0, tdecex = expr/.Pair-> PairContract, tdi,tdecti,tdectj,tdectk,tdectl,tdectm,tdecr = 0, - tdecpl,tdecml,tdeclpl, - rul,spl,add - }, - FCPrint[3, "entering tdec with expr = ", expr//FeynCalcForm, FCDoControl->oneloopVerbose]; - FCPrint[3, "props = ", props, FCDoControl->oneloopVerbose]; - FCPrint[3, "Q = ", Q, FCDoControl->oneloopVerbose]; - (* number of vectors in the numerator *) - FCPrint[3, "qn = ", qn, FCDoControl->oneloopVerbose]; - FCPrint[3, "di = ", di, FCDoControl->oneloopVerbose]; - FCPrint[3, "mudu = ", mudu, FCDoControl->oneloopVerbose]; - FCPrint[3, "mand = ", mand, FCDoControl->oneloopVerbose]; - tensdf2[_,b_] := - b; - tensdf1[a_,_] := - Expand[ to4dim[ - MomentumExpand[a-Momentum[Q]]] - ]; + tdecpl,tdecml,tdeclpl, rul,spl,add, tmppair, conall }, + FCPrint[3, "entering tdec with expr = ", expr, FCDoControl->oneloopVerbose]; + FCPrint[3, "props = ", props, FCDoControl->oneloopVerbose]; + FCPrint[3, "Q = ", Q, FCDoControl->oneloopVerbose]; + (* number of vectors in the numerator *) + FCPrint[3, "qn = ", qn, FCDoControl->oneloopVerbose]; + FCPrint[3, "di = ", di, FCDoControl->oneloopVerbose]; + FCPrint[3, "mudu = ", mudu, FCDoControl->oneloopVerbose]; + FCPrint[3, "mand = ", mand, FCDoControl->oneloopVerbose]; + tensdf2[_,b_] := + b; + tensdf1[a_,_] := + Expand[ to4dim[MomentumExpand[a-Momentum[Q]]]]; + + conall[ x_ ] := + Contract[x, Expanding->True, EpsContract->True, Factoring->False] // Expand; + If[ tdecex===0, tdecr = 0, (* Here it goes *) (* define add *) - add[gra_,pva_,exp_] := + add[g_,pva_,x_] := Block[ {addre, pv = pva}, - FCPrint[3, "OneLoop: tdec: add: gra: ", gra, FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tdec: add: gra: ", g, FCDoControl->oneloopVerbose]; FCPrint[3, "OneLoop: tdec: add: pv: ", pv, FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tdec: add: exp: ", exp, FCDoControl->oneloopVerbose]; - If[ breakdown === True, - pv = pavremember[pv, WriteOutPaVe -> writeoutpav ]; - If[ uvpart === True, - pv = pv /. C0[__] -> 0 /. D0[__]->0 /. B0[__]-> UVDELTA; - If[ FreeQ2[pv, {B1,B00,B11}], - FCPrint[2, "pv = ", pv//FeynCalcForm, FCDoControl->oneloopVerbose]; - pv = Factor2[D[ pv, UVDELTA]], - FCPrint[2, "pv = ", pv//FeynCalcForm, FCDoControl->oneloopVerbose]; - Print["problems with uvcheck in OneLoop!!!", Dialog[]] - ]; - FCPrint[2, "uvcheck ", pv//FeynCalcForm, FCDoControl->oneloopVerbose]; - ]; + FCPrint[3, "OneLoop: tdec: add: exp: ", x, FCDoControl->oneloopVerbose]; + If[ breakdown, + pv = PaVeReduce[pv, WriteOutPaVe -> writeOutPaVe, Dimension->di] ]; If[ $LimitTo4 === True, - addre = gra + (Expand[ExpandScalarProduct[ pv to4dim[ exp/.di->4 ]]]), - addre = gra + (Expand[ExpandScalarProduct[ pv exp]]) + addre = g + (Expand[ExpandScalarProduct[ pv to4dim[ x/.di->4 ]]]), + addre = g + (Expand[ExpandScalarProduct[ pv x]]) ]; addre ]; @@ -2497,14 +1906,12 @@ (* calculate the List of scalar products needed as arguments *) (* get the list of p's from the propagators, ignoring the first propagator *) - tdecpl = Drop[ Expand[ props//MomentumExpand]/. - PropagatorDenominator->tensdf1/. - FeynAmpDenominator->List,1 ]//DiracGammaCombine; + tdecpl = Drop[ Expand[ props//MomentumExpand] /. FeynAmpDenominator->List /. PD->tensdf1,1 ]//DiracGammaCombine[#,FCI->True]&; tdecpl = Expand[tdecpl]; FCPrint[2, "tdecpl = ", tdecpl, FCDoControl->oneloopVerbose]; (* get the list of m's from the propagators *) - tdecml = props/.PropagatorDenominator->tensdf2/. FeynAmpDenominator->List; + tdecml = props/. FeynAmpDenominator->List /.PD->tensdf2; FCPrint[3, "tdecml = ", tdecml, FCDoControl->oneloopVerbose]; tdecml = #^2& /@ tdecml; FCPrint[3, "tdecml = ", tdecml, FCDoControl->oneloopVerbose]; @@ -2521,183 +1928,174 @@ ]; (* calculation of (N (N-1)/2) scalar pipj - arguments *) - spl0[a_,b_,man_] := - (TrickMandelstam@@Prepend[{man},Expand[Pair[a-b,a-b]]//ExpandScalarProduct])//smalld; + spl0[a_,b_,m_] := + (TrickMandelstam@@Prepend[{m},Expand[Pair[a-b,a-b]]//ExpandScalarProduct])//smalld; - spl[aa__] := - spl0[aa,mand]//ExpandAll; + spl[a__] := + spl0[a,mand]//ExpandAll; FCPrint[3, "OneLoop: tdec: covnerting FADs to PaVe functions.", FCDoControl->oneloopVerbose]; - tensps = ExpandScalarProduct[FeynCalc`Package`momentumRoutingDenner[tdecpl,spl[#,0]&]]; + tensps = ExpandScalarProduct[FeynCalc`Package`momentumRoutingDenner[tdecpl,tmppair]]; + tensps = tensps /. tmppair[a__] :> spl[a,0]; - FCPrint[3, "OneLoop: tdec: tensps ", tensps," ", FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tdec: tdecr ", tdecr, FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tdec: tdecex ", tdecex, FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tdec: tensps ", tensps," ", FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tdec: tdecr ", tdecr, FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tdec: tdecex ", tdecex, FCDoControl->oneloopVerbose]; - (* scalar integrals *) - If[ qn==0, + (* scalar integrals *) + If[ qn==0, - (* new prefactor *) - tdecnew = eval[ tdecex ]; + (* new prefactor *) + tdecnew = eval[ tdecex ]; - If[ $LimitTo4 === True, - Which[ - tdeclpl == 0, - (* e A0 = 2m^2 *) - tdecr = epst[ tdecr,tdecnew,tdi, 2 tdecml[[1]] ], - tdeclpl == 1, - (* e B0 = 2 *) - tdecr = epst[ tdecr,tdecnew,tdi, 2 ]; - ] - ]; - - FCPrint[3, "OneLoop: tdec: tdecenew ", tdecnew, FCDoControl->oneloopVerbose]; - - (* if the option DenominatorOrder is True, then order here again *) - If[ denomOrder === True, - pav0 = PaVeOrder[PaVe[0,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce]], - pav0 = PaVe[0,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce] - ]; + If[ $LimitTo4 === True, + Which[ + tdeclpl == 0, + (* e A0 = 2m^2 *) + tdecr = epst[ tdecr,tdecnew,tdi, 2 tdecml[[1]] ], + tdeclpl == 1, + (* e B0 = 2 *) + tdecr = epst[ tdecr,tdecnew,tdi, 2 ]; + ] + ]; - FCPrint[3, "OneLoop: tdec: pav0: ", pav0, FCDoControl->oneloopVerbose]; - (* Reduction of PaVe functions into simpler ones... *) - tdecr = add[ tdecr, pav0, tdecnew ]; - FCPrint[3, "OneLoop: tdec: qn==0, tdecr=", tdecr, FCDoControl->oneloopVerbose] - ]; + FCPrint[3, "OneLoop: tdec: tdecenew ", tdecnew, FCDoControl->oneloopVerbose]; - (* q^mu (...) *) - If[ qn==1, - (* new prefactor *) - tdecnew = Table[ eval[ tdecex/.LorentzIndex[mudu[1],___]-> tdecpl[[tdecti]] ], {tdecti,1,tdeclpl}]; + pav0 = PaVeOrder[PaVe[0,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce]]; - FCPrint[3, "OneLoop: tdec: qn==1, tdecnew=", tdecnew, FCDoControl->oneloopVerbose]; - If[ ($LimitTo4 === True) && (tdeclpl === 1), (* e B1 = -1 *) - tdecr = epst[ tdecr,tdecnew[[1]], tdi,-1 ] + FCPrint[3, "OneLoop: tdec: pav0: ", pav0, FCDoControl->oneloopVerbose]; + (* Reduction of PaVe functions into simpler ones... *) + tdecr = add[ tdecr, pav0, tdecnew ]; + FCPrint[3, "OneLoop: tdec: qn==0, tdecr=", tdecr, FCDoControl->oneloopVerbose] ]; - FCPrint[3, "OneLoop: tdec: qn==1, tdecr=", tdecr, FCDoControl->oneloopVerbose]; - For[ tdectj = 1,tdectj<=tdeclpl,tdectj++, - tdecr = add[ tdecr, PaVe[tdectj,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce], - tdecnew[[tdectj]] - ] ]; - FCPrint[3, "OneLoop: tdec: qn==1, tdecr=", tdecr, FCDoControl->oneloopVerbose] - ]; - (* q^mu q^nu (...) *) - If[ qn==2, - tdecnew = eval[ tdecex/.LorentzIndex[mudu[1],dime___] :> LorentzIndex[mudu[2],dime]]; - FCPrint[3, "OneLoop: tdec: qn==2, tdecnew=", tdecnew, FCDoControl->oneloopVerbose]; - - If[ $LimitTo4 === True, - Which[ - tdeclpl == 0, (* e A00 = m^4/2 *) - tdecr = epst[ tdecr,tdecnew,tdi, - tdecml[[1]]^2/2 - ], - tdeclpl == 1, (* e B00 *) - tdecr = epst[ tdecr,tdecnew,tdi, - (-1/3 spl[tdecpl[[1]],0] + - tdecml[[1]] + - tdecml[[2]] )/2 - ] , - tdeclpl == 2, (* e C00 = 1/2 *) - tdecr = epst[ tdecr, tdecnew, tdi, 1/2 ] - ] + (* q^mu (...) *) + If[ qn==1, + (* new prefactor *) + tdecnew = Table[eval[ tdecex/.LorentzIndex[mudu[1],___]-> tdecpl[[tdecti]] ], {tdecti,1,tdeclpl}]; + + FCPrint[3, "OneLoop: tdec: qn==1, tdecnew=", tdecnew, FCDoControl->oneloopVerbose]; + If[ ($LimitTo4 === True) && (tdeclpl === 1), (* e B1 = -1 *) + tdecr = epst[ tdecr,tdecnew[[1]], tdi,-1 ] + ]; + FCPrint[3, "OneLoop: tdec: qn==1, tdecr=", tdecr, FCDoControl->oneloopVerbose]; + For[ tdectj = 1,tdectj<=tdeclpl,tdectj++, + tdecr = add[ tdecr, PaVe[tdectj,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce], tdecnew[[tdectj]]] + ]; + FCPrint[3, "OneLoop: tdec: qn==1, tdecr=", tdecr, FCDoControl->oneloopVerbose] ]; - FCPrint[3, "OneLoop: tdec: qn==2, tdecr=", tdecr, FCDoControl->oneloopVerbose]; - tdecr = add[ tdecr, PaVe[0,0,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce], tdecnew ]; - FCPrint[3, "OneLoop: tdec: qn==2, tdecr=", tdecr, FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tdec: qn==2, tdecex=", tdecex, FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tdec: qn==2, tdeclpl=", tdeclpl, FCDoControl->oneloopVerbose]; - tdecnew = Table[{Sort[{tdecti,tdectj}], - tdecex/.LorentzIndex[mudu[1],___]->tdecpl[[tdecti]]/. - LorentzIndex[mudu[2],___]->tdecpl[[tdectj]] - },{tdectj,1,tdeclpl},{tdecti,1,tdeclpl} - ]; + (* q^mu q^nu (...) *) + If[ qn==2, + tdecnew = eval[ tdecex/.LorentzIndex[mudu[1],d___] :> LorentzIndex[mudu[2],d]]; + FCPrint[3, "OneLoop: tdec: qn==2, tdecnew=", tdecnew, FCDoControl->oneloopVerbose]; - FCPrint[3, "OneLoop: tdec: qn==2, tdecnew=", FullForm[tdecnew], FCDoControl->oneloopVerbose]; - tdecnew = eval[ Flatten[ tdecnew,1 ] ]; - FCPrint[3, "OneLoop: tdec: qn==2, tdecnew=", tdecnew, FCDoControl->oneloopVerbose]; - If[ ($LimitTo4 === True) && (tdeclpl == 1), (* e B11 = 2/3 *) - tdecr = epst[ tdecr,tdecnew[[1,2]],tdi, 2/3 ] - ]; - For[ tdectj = 1,tdectj<=Length[tdecnew],tdectj++, - tdecr = add[ tdecr, - PaVe@@Join[tdecnew[[tdectj,1]],{tensps},{tdecml},{PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce}], - tdecnew[[tdectj,2]] - ]; If[ $LimitTo4 === True, - tdecr = tdecr /.tdi->4 + Which[ + tdeclpl == 0, + (* e A00 = m^4/2 *) + tdecr = epst[tdecr,tdecnew,tdi, tdecml[[1]]^2/2], + tdeclpl == 1, + (* e B00 *) + tdecr = epst[ tdecr,tdecnew,tdi, (-1/3 spl[tdecpl[[1]],0] + tdecml[[1]] + tdecml[[2]] )/2] , + tdeclpl == 2, + (* e C00 = 1/2 *) + tdecr = epst[ tdecr, tdecnew, tdi, 1/2 ] + ] ]; + + FCPrint[3, "OneLoop: tdec: qn==2, tdecr=", tdecr, FCDoControl->oneloopVerbose]; + tdecr = add[ tdecr, PaVe[0,0,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce], tdecnew ]; + FCPrint[3, "OneLoop: tdec: qn==2, tdecr=", tdecr, FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tdec: qn==2, tdecex=", tdecex, FCDoControl->oneloopVerbose]; + FCPrint[3, "OneLoop: tdec: qn==2, tdeclpl=", tdeclpl, FCDoControl->oneloopVerbose]; + tdecnew = Table[{Sort[{tdecti,tdectj}], + tdecex/.LorentzIndex[mudu[1],___]->tdecpl[[tdecti]]/. LorentzIndex[mudu[2],___]->tdecpl[[tdectj]]},{tdectj,1,tdeclpl},{tdecti,1,tdeclpl} ]; - FCPrint[3, "OneLoop: tdec: qn==2, tdecr=", tdecr, FCDoControl->oneloopVerbose] - ]; + FCPrint[3, "OneLoop: tdec: qn==2, tdecnew=", FullForm[tdecnew], FCDoControl->oneloopVerbose]; + tdecnew = eval[Flatten[tdecnew,1]]; - (* q^mu q^nu q^rho (...) *) + FCPrint[3, "OneLoop: tdec: qn==2, tdecnew=", tdecnew, FCDoControl->oneloopVerbose]; + If[ ($LimitTo4 === True) && (tdeclpl == 1), (* e B11 = 2/3 *) + tdecr = epst[ tdecr,tdecnew[[1,2]],tdi, 2/3 ] + ]; + + For[ tdectj = 1,tdectj<=Length[tdecnew],tdectj++, + tdecr = add[ tdecr, PaVe@@Join[tdecnew[[tdectj,1]],{tensps},{tdecml},{PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce}], tdecnew[[tdectj,2]]]; + If[ $LimitTo4 === True, + tdecr = tdecr /.tdi->4 + ]; + ]; + + FCPrint[3, "OneLoop: tdec: qn==2, tdecr=", tdecr, FCDoControl->oneloopVerbose] + ]; + + + (* q^mu q^nu q^rho (...) *) If[ qn == 3, (* The 00i - terms *) tdecnew = {}; For[ tdectij = 1, tdectij <= tdeclpl, tdectij++, tdecnew = Append[ tdecnew, eval[ - conall[ tdecex/.NonCommutativeMultiply->Times/. - {LorentzIndex[mudu[1],dime___]-> - LorentzIndex[mudu[2],dime], - LorentzIndex[mudu[3],___]->tdecpl[[tdectij]]}] - + conall[ tdecex/.NonCommutativeMultiply->Times/. - {LorentzIndex[mudu[2],dime___]-> - LorentzIndex[mudu[3],dime], - LorentzIndex[mudu[1],___]->tdecpl[[tdectij]]}] - + conall[ tdecex/.NonCommutativeMultiply->Times/. - {LorentzIndex[mudu[1],dime___]-> - LorentzIndex[mudu[3],dime], - LorentzIndex[mudu[2],___]->tdecpl[[tdectij]]}] - ] - ] - ]; + conall[ tdecex/.NonCommutativeMultiply->Times/. + {LorentzIndex[mudu[1],d___]-> LorentzIndex[mudu[2],d], + LorentzIndex[mudu[3],___]->tdecpl[[tdectij]]}] + + conall[ tdecex/.NonCommutativeMultiply->Times/. + {LorentzIndex[mudu[2],d___]-> LorentzIndex[mudu[3],d], + LorentzIndex[mudu[1],___]->tdecpl[[tdectij]]}] + + conall[ tdecex/.NonCommutativeMultiply->Times/. + {LorentzIndex[mudu[1],d___]-> LorentzIndex[mudu[3],d], + LorentzIndex[mudu[2],___]->tdecpl[[tdectij]]}]]] + ]; + If[ ($LimitTo4 === True) && (tdeclpl==2), (* C001 = -1/6 *) tdecr = epst[ tdecr,tdecnew[[1]], tdi,-1/6 ]; tdecr = epst[ tdecr,tdecnew[[2]], tdi,-1/6 ] ]; + For[ tdec0j = 1, tdec0j <= tdeclpl, tdec0j++, - tdecr = add[ tdecr, PaVe[0,0,tdec0j,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce], - tdecnew[[tdec0j]] ] - ]; + tdecr = add[tdecr,PaVe[0,0,tdec0j,tensps,tdecml,PaVeAutoOrder->paveautoorder,PaVeAutoReduce->paveautoreduce], tdecnew[[tdec0j]]] + ]; + For[ tdecti = 1, tdecti <= tdeclpl, tdecti++, For[ tdectj = 1, tdectj <= tdeclpl, tdectj++, For[ tdectk = 1, tdectk <= tdeclpl, tdectk++, tdecr = add[ tdecr, - PaVe@@Join[Sort[{tdecti,tdectj,tdectk}], - {tensps},{tdecml} - ], + PaVe@@Join[Sort[{tdecti,tdectj,tdectk}],{tensps},{tdecml}], (eval[ tdecex/.LorentzIndex[mudu[1],___]-> tdecpl[[tdecti]]/. LorentzIndex[mudu[2],___]-> tdecpl[[tdectj]]/. LorentzIndex[mudu[3],___]-> - tdecpl[[tdectk]] - ] - ) - ]; + tdecpl[[tdectk]]])]; If[ $LimitTo4 === True, tdecr = tdecr/.tdi->4 ] - ] ] ]; - FCPrint[3, "OneLoop: tdec: qn==3, tdecr=", tdecr, FCDoControl->oneloopVerbose] + ] + ] + ]; + FCPrint[3, "OneLoop: tdec: qn==3, tdecr=", tdecr, FCDoControl->oneloopVerbose] ]; + If[ qn>3, tdecr = expr ]; + tdecr = Expand[tdecr]; - (* end if tdecex == 0 *) ]; + (* end if tdecex == 0 *) + ]; + FCPrint[3, "exiting tdec with ", tdecr, FCDoControl->oneloopVerbose]; If[ !FreeQ[tdecr, Null], Print["Null encountered in tdec; entering DIALOG"]; Dialog[{expr,props,Q,qn ,di,mudu,mand}] ]; tdecr - ]]/; expr =!= 0; + + ] + ]/; expr =!= 0; (* ************************************************************** *) @@ -2705,92 +2103,67 @@ (* oneloop42 *) (* ********************************************************************* *) -(* ---------------------------------------------------------------- *) -(* ---------------------------------------------------------------- *) - nterms[x_Plus] := - Length[x]; (*ntermsdef *) - nterms[x_] := - Block[ {ntermslex = Expand[x]}, - If[ Head[ntermslex]===Plus, - ntermslex = Length[ntermslex], - If[ x===0, - ntermslex = 0, - ntermslex = 1 - ] - ]; - ntermslex - ]; -(* ------------------------------------------------------------ *) -(* ********************************************************************* *) -(* ********************************************************************* *) -(* ********************************************************************* *) -(* oneloop43 *) -(* ********************************************************************* *) - - - dndummy[x__] := - dummy FeynAmpDenominator[x]; - vcid[x_,___] := - x; - - -(* ********************************************************************* *) -(* oneloop44 *) -(* ********************************************************************* *) - (* SetStandardMatrixElementdef *) -Options[SetStandardMatrixElements] = {WriteOut -> False}; +Options[SetStandardMatrixElements] = { + WriteOut -> False +}; + SetStandardMatrixElements[rx_List,en_:{}, op___Rule] := Block[ {links = {},nmat,mat,ix,i,ii,j,sup,newli = {}, ops, enm, - savmem,neweq,mati,set,isos,isolspc,nullll,x,x2,sumand, - mati1, set2, filename, temp}, + savmem,neweq,mati,set,isos,isolspc,nullll,x,x2,sumand, + mati1, set2, filename, temp, file, dummy}, ops = {op}; enm = en; + If[ {ops}==={} || (!FreeQ[enm, WriteOut]), ops = en; enm = {} ]; + filename = WriteOut /. ops /. Options[SetStandardMatrixElements]; + If[ StringQ[filename], file = FileType[filename] ]; + If[ ValueQ[file] && (file === File), temp = Get[filename]; temp = Select[temp, !FreeQ[#,Spinor]&] ]; + If[ Length[temp]>0, temp/.Literal->Identity/.RuleDelayed->Set; FCPrint[2, "loading old matrixelementdefinitions from ", filename, FCDoControl->oneloopVerbose]; FCPrint[3, "lold matrixelementdefinitions: ", temp, FCDoControl->oneloopVerbose], - savmem = $MemoryAvailable; - $MemoryAvailable = 0; + savmem = $FCMemoryAvailable; + $FCMemoryAvailable = 0; x = {}; For[ix = 1, ix <= Length[rx], ix ++, If[ FreeQ[rx[[ix,1]], Plus], - x = Prepend[x,{rx[[ix,1]], - StandardMatrixElement@@Flatten[{rx[[ix,2]]}] - } ], - x = Append[x, {rx[[ix,1]], - StandardMatrixElement@@Flatten[{rx[[ix,2]]}] - } ] + x = Prepend[x,{rx[[ix,1]], StandardMatrixElement@@Flatten[{rx[[ix,2]]}]}], + x = Append[x, {rx[[ix,1]], StandardMatrixElement@@Flatten[{rx[[ix,2]]}]}] ] ]; + x = Flatten[x, 1]; - If[ Cases[x, DOT[Spinor[a_,_,_] , (___) , Spinor[b_,_,_]] * - DOT[Spinor[c_,_,_] , (___) , Spinor[d_,_,_]] - ] =!= {}, + + If[ Cases[x, DOT[Spinor[a_,_,_] , (___) , Spinor[b_,_,_]] DOT[Spinor[c_,_,_] , (___) , Spinor[d_,_,_]]] =!= {}, x = x /. DiracGamma[6] -> (1/2 + 1/2 DiracGamma[5]); x = x /. DiracGamma[7] -> (1/2 - 1/2 DiracGamma[5]) ]; + FCPrint[2, Length[x], FCDoControl->oneloopVerbose]; FCPrint[2, "enm = ", enm, FCDoControl->oneloopVerbose]; FCPrint[2, "ops= ", ops, FCDoControl->oneloopVerbose]; + If[ enm==={}, mat = DiracSimplify[ x ]//Expand//DiracOrder//Contract, mat = DiracSimplify[ x/.enm ]//Expand//DiracOrder//Contract ]; + nmat = Expand[ ExpandScalarProduct[mat] ]//smalld; nmat = nmat /. DOT -> spinorsandpairs; + isos[b_spinorsandpairs] := b; isos[a_?NumberQ] := @@ -2798,92 +2171,76 @@ isos[a_ b_spinorsandpairs] := b isos[a]; isolspc[xx_] := - Map[ isos, - collin[ xx, spinorsandpairs, True] + nullll - ]/.nullll->0; - mat = Table[ {isolspc[ nmat[[2 ii - 1]] ], - nmat[[2 ii]]},{ii,1,Length[nmat]/2} - ]; - pat[x_,_] := - x; - (* Need this for pattern in the SME's, e.g., 4-fermion processes *) + Map[isos, Collect2[ xx, spinorsandpairs, Factoring->Factor] + nullll]/.nullll->0; + + mat = Table[ {isolspc[ nmat[[2 ii - 1]] ], nmat[[2 ii]]},{ii,1,Length[nmat]/2}]; + + pat[u_,_] := + u; + + (* Need this for pattern in the SME's, e.g., 4-fermion processes *) set2[a_, b_] := Set @@ {a, b/.Pattern->pat}; + For[ i = 1, i<=Length[mat],i++, - FCPrint[2, "i = ", i, " out of ", Length[mat], FCDoControl->oneloopVerbose]; - mat = Expand[ (mat//ExpandScalarProduct)/.spinorsandpairs->DOT ]; - mat = mat /. DOT -> spinorsandpairs; - mati1 = Expand[isolspc[mat[[i,1]]]]; - For[j = 1,j<=nterms[mati1],j++, - If[ nterms[mati1] === 1, - sumand = mati1, - sumand = mati1[[j]] - ]; - FCPrint[2, "sumand = ", sumand, FCDoControl->oneloopVerbose]; - If[ !(FreeQ[sumand,spinorsandpairs]), - sup = PartitHead[ sumand,spinorsandpairs]//Expand; - If[ (!MemberQ[ links,sup[[2]]/.spinorsandpairs->DOT/. - Pair -> bier ]) && - Head[ sup[[2]] ] === spinorsandpairs, - FCPrint[2, "o.k1", FCDoControl->oneloopVerbose]; - links = Append[ links, sup[[2]]/.spinorsandpairs->DOT/. - Pair -> bier - ]//Expand; - neweq = set[ sup[[2]], Together/@(collin[ - Expand[ - ((mat[[i,2]]-mati1+sumand )/sup[[1]] - )/.isos->Identity - ],spinorsandpairs ,True - ] - ) - ]; - (* Avoid things like a=a *) - If[ (neweq[[1]] - neweq[[2]]) =!= 0, - FCPrint[2, "setting", FCDoControl->oneloopVerbose]; - newli = Append[ newli,neweq/.set->set2 ]//Expand; - j = nterms[mati1]+1 - ]; + FCPrint[2, "i = ", i, " out of ", Length[mat], FCDoControl->oneloopVerbose]; + mat = Expand[ (mat//ExpandScalarProduct)/.spinorsandpairs->DOT ]; + mat = mat /. DOT -> spinorsandpairs; + mati1 = Expand[isolspc[mat[[i,1]]]]; + For[j = 1, j<=NTerms[mati1], j++, + If[ NTerms[mati1] === 1, + sumand = mati1, + sumand = mati1[[j]] + ]; + FCPrint[2, "sumand = ", sumand, FCDoControl->oneloopVerbose]; + If[ !(FreeQ[sumand,spinorsandpairs]), + sup = PartitHead[ sumand,spinorsandpairs]//Expand; + If[ (!MemberQ[ links,sup[[2]]/.spinorsandpairs->DOT/. Pair -> dummy]) && Head[ sup[[2]] ] === spinorsandpairs, + FCPrint[2, "o.k.", FCDoControl->oneloopVerbose]; + links = Append[links, sup[[2]]/.spinorsandpairs->DOT/. Pair -> dummy]//Expand; + neweq = set[sup[[2]], Together/@(Collect2[Expand[((mat[[i,2]]-mati1+sumand )/sup[[1]])/.isos->Identity],spinorsandpairs, Factoring->Factor])]; + (* Avoid things like a=a *) + If[ (neweq[[1]] - neweq[[2]]) =!= 0, + FCPrint[2, "setting", FCDoControl->oneloopVerbose]; + newli = Append[ newli,neweq/.set->set2 ]//Expand; + j = NTerms[mati1]+1 + ]; + ] ] ] - ] - ](* i - loop *); - FCPrint[2, "Solving the system of linear equations for standard - matrix elements", FCDoControl->oneloopVerbose]; + ](* i - loop *); - (* - (* This takes care of the fact that 1 = Gamma6 + Gamma7 *) - If[ (!FreeQ[ rx, DiracGamma[6] ]) || (!FreeQ[ rx, DiracGamma[7] ]), - SetStandardMatrixElements[ - rx/.DiracGamma[6]->(1/2 + DiracGamma[5]/2)/. - DiracGamma[7]->(1/2 - DiracGamma[5]/2), enm] - ]; - *) - $MemoryAvailable = savmem; + FCPrint[2, "Solving the system of linear equations for standard matrix elements", FCDoControl->oneloopVerbose]; + + $FCMemoryAvailable = savmem; If[ StringQ[filename], Put @@ {DownValues[spinorsandpairs], filename} ] ]; newli ]; -(* ------------------------------------------------------------ *) GetOneLoopResult[x_, li_List] := Block[ {name, list,new, lenli}, name = ToString[x]; list = Table[StringJoin[name, "N",li[[i]]//ToString, ".m"], {i, Length[li]}]; + none[__,y_] := ToExpression[ StringJoin[ Rest[ Characters[ToString[y]] ] ]]; + new = 0; lenli = Length[li]; + For[j = 1, j <= lenli, j++, FCPrint[1, "loading # ", j, " out of ", lenli, FCDoControl->oneloopVerbose]; Get[list[[j]]]; - ]; + ]; + For[j = 1, j <= lenli, j++, FCPrint[1, "summing # ", j, " out of ", lenli, FCDoControl->oneloopVerbose]; - new = new + Expand[ DownValues[OneLoopResult][[j,2]], - StandardMatrixElement ]; - ]; + new = new + Expand[DownValues[OneLoopResult][[j,2]], StandardMatrixElement]; + ]; + new ]; diff --git a/FeynCalc/LoopIntegrals/OneLoopSimplify.m b/FeynCalc/LoopIntegrals/OneLoopSimplify.m index c1af17089..f1ea07551 100644 --- a/FeynCalc/LoopIntegrals/OneLoopSimplify.m +++ b/FeynCalc/LoopIntegrals/OneLoopSimplify.m @@ -1,14 +1,17 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) +(* ::Package:: *) -(* :Title: OneLoopSimplify *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Author: Rolf Mertig *) +(* :Title: OneLoopSimpify *) -(* ------------------------------------------------------------------------ *) -(* :History: File created on 19 January '99 at 1:11 *) -(* ------------------------------------------------------------------------ *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* :Summary: OneLoopSimplify *) +(* :Summary: Simplification of 1-loop integrals *) (* ------------------------------------------------------------------------ *) @@ -38,259 +41,205 @@ Begin["`OneLoopSimplify`Private`"] -Options[OneLoopSimplify] = {Collecting -> False, - Dimension -> D, - DimensionalReduction -> False, - DiracSimplify -> True, - FinalSubstitutions -> {}, - IntegralTable -> {}, - OPE1Loop -> False, - ApartFF -> True, - SUNNToCACF -> True, - SUNTrace -> False - }; - - -OneLoopSimplify[qu_ /; Head[qu]=== Symbol, amp_ /;Head[amp]=!=Symbol, - opt___Rule] := - OneLoopSimplify[amp,qu,opt] /; - !FreeQ[amp,qu]; - -OneLoopSimplify[FeynAmp[_, qu_Symbol, expr_], ___, opts___Rule] := - OneLoopSimplify[ expr, qu, opts]; - -OneLoopSimplify[amp_, qu_, opt___Rule] := - If[ FreeQ[amp, qu], - Message[OneLoopSimplify::nivar, qu]; - amp, - Block[ {q, dim, sunntocacf, t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, spc, - substis, pae, dimred,lt6, lnt6,dirsimplify, nt6,dirsimp, - ope1loop, integraltable,time}, - - - If [!FreeQ[$ScalarProducts, q], - Message[OneLoopSimplify::failmsg, "The loop momentum " <> ToString[qu,InputForm] <> " has scalar product rules attached to it."]; - Abort[] - ]; - - If[ $KeepLogDivergentScalelessIntegrals, - Message[OneLoopSimplify::failmsg, "OneLoopSimplify does not support the option $KeepLogDivergentScalelessIntegrals!."]; - Abort[] - ]; - - - q = qu; - dim = Dimension /. {opt} /. Options[OneLoopSimplify]; - dirsimplify = DiracSimplify/. {opt} /. Options[OneLoopSimplify]; - dimred = DimensionalReduction /. {opt} /. Options[OneLoopSimplify]; - sunntocacf = SUNNToCACF /. {opt} /. Options[OneLoopSimplify]; - suntrace = SUNTrace /. {opt} /. Options[OneLoopSimplify]; - ope1loop = OPE1Loop /. {opt} /. Options[OneLoopSimplify]; - substis = FinalSubstitutions /. {opt} /. Options[OneLoopSimplify]; - spc = ApartFF /. {opt} /. Options[OneLoopSimplify]; - integraltable = IntegralTable /. {opt} /. Options[OneLoopSimplify]; - FCPrint[2,"Using dimension ",dim]; - If[ dimred =!= True, - t1 = Trick[ChangeDimension[FeynCalcInternal[amp], dim]], - t1 = Trick[FeynCalcInternal[amp]] - ]; - If[ dimred =!= True, - substis = ChangeDimension[substis, dim] - ]; - (*t1 = Collect2[Isolate[t1,q,IsolateNames->loopisolate],FeynAmpDenominator[__]];*) - time = AbsoluteTime[]; - t1 = FeynAmpDenominatorCombine[t1//Explicit]; - FCPrint[2,"FeynAmpDenominatorCombine done. t1 = ",t1]; - t1 = FeynAmpDenominatorSimplify[Collect2[t1,q,Factoring->False], q, - IntegralTable -> integraltable]; - (*t1 = FRH[t1,IsolateNames->loopisolate];*) - (*If[!FreeQ[t1,loopisolate], - Print["Something went wrong: ", t1]; - Abort[]; - ];*) - FCPrint[1,"OneLoopSimplify: Time spent on FeynAmpDenominatorSimplify: ", N[AbsoluteTime[] - time, 4]]; - FCPrint[2,"OneLoopSimplify: FeynAmpDenominatorCombine done. t1 = ",t1]; - (*t1 = Isolate[t1,{SUNIndex,SUNFIndex},IsolateNames->loopisolate]/. DOT->holdDOT/. holdDOT[x__]/; - !FreeQ2[x,{SUNIndex,SUNFIndex}]:>DOT[FRH[x,IsolateNames->loopisolate]]/. holdDOT->DOT;*) - FCPrint[2,"OneLoopSimplify: Doing SUNSimplify on ",t1]; - time = AbsoluteTime[]; - If[ !FreeQ2[t1, {SUNIndex,SUNFIndex}], - t2 = SUNSimplify[t1, SUNNToCACF -> sunntocacf, - SUNTrace -> suntrace, - Explicit -> False], - t2 = t1 - ]; - (*t2 = FRH[t2,IsolateNames->loopisolate];*) - FCPrint[1,"OneLoopSimplify: Time spent on SUNSimplify: ", N[AbsoluteTime[] - time, 4]]; - FCPrint[1,"OneLoopSimplify: After SUNSimplify: ", t2]; - If[ !FreeQ[t2, DiracGamma], - t2 = DiracTrick[t2]; - t2 = t2 /. DiracTrace -> TR - ]; - FCPrint[1,"OneLoopSimplify: After DiracTrick and DiracTrace: ", t2]; - If[ FreeQ2[t2, {DiracGamma, Eps}], - t3 = Contract3[t2], - t3 = Contract[t2] - ]; - FCPrint[1,"OneLoopSimplify: After contractions: ", t3]; - (*t3 = Isolate[Collect2[DiracGammaExpand[t3],DiracGamma[__]],{DiracGamma},IsolateNames->loopisolate]/. - DOT->holdDOT/. holdDOT[x__]/; - !FreeQ2[x,{DiracGamma}]:>DOT[FRH[x,IsolateNames->loopisolate]]/. holdDOT->DOT;*) - time = AbsoluteTime[]; - If[ (!FreeQ[t3, DiracGamma]) && (dirsimplify === True), - FCPrint[1,"OneLoopSimplify: Applying DiracSimplify on ", t3]; - t3 = DiracSimplify[Collect2[t3, DiracGamma, Factoring -> False]]; - t3 = t3 /. DiracTrace -> TR - ]; - If[ (!FreeQ[t3, DiracGamma]) && (dirsimplify === True), - FCPrint[1,"DiracOrdering ", t3]; - t3 = Collect2[t3, DiracGamma, Factoring->False]; - If[ Head[t3] =!= Plus, - t3 = DiracSimplify[DiracOrder[t3]], - t3 = Map[DiracSimplify[DiracOrder[#]]&, t3] - ]; - FCPrint[1,"DiracOrdering done: ", t3]; - ]; - (*t3 = FRH[t3,IsolateNames->loopisolate];*) - FCPrint[1,"OneLoopSimplify: Time spent on Dirac algebra: ", N[AbsoluteTime[] - time, 4]]; - FCPrint[1,"OneLoopSimplify: After doing Dirac algebra: ", t3]; - - t3= (*Isolate[*)Collect2[ ExpandScalarProduct[t3], {FeynAmpDenominator, q, OPEDelta}](*, - {q, OPEDelta, FeynAmpDenominator},IsolateNames->loopisolate]*); - time = AbsoluteTime[]; - If[ (Collecting /. {opt} /. Options[OneLoopSimplify]) === True, - t4 = Collect2[ExpandScalarProduct[t3], q, Factoring->Factor], - t4 = ExpandScalarProduct[t3] - ]; - FCPrint[1,"t4=", t4]; - If[ spc =!= True, - t5 = t4, - t5 = ApartFF[t4, {q}]; - If[ !FreeQ[t5, DiracGamma], - dirsimp[z__] := - dirsimp[z] = If[ !FreeQ[{z}, DiracGamma], - DiracSimplify[DOT[z]], - DOT[z] - ]; - t5 = t5 /. DOT -> dirsimp - ] - ]; - - (* Need to reisolate things here *) - (*t5 = FRH[t5,IsolateNames->loopisolate];*) - t5 = Collect2[ ExpandScalarProduct[t5], {FeynAmpDenominator, q, OPEDelta}]; +olsVerbose::usage=""; + +Options[OneLoopSimplify] = { + Collecting -> True, + Dimension -> D, + DiracSimplify -> True, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> Automatic, + FinalSubstitutions -> {}, + OPE1Loop -> False, + PowerSimplify -> True, + SUNNToCACF -> True, + SUNTrace -> False, + ToPaVe -> False, + UsePaVeBasis -> False +}; + +(*Do we really need to support this syntax???*) +OneLoopSimplify[qu_ /; Head[qu]=== Symbol, amp_ /;Head[amp]=!=Symbol, opt:OptionsPattern[]] := + OneLoopSimplify[amp,qu,opt] /; !FreeQ[amp,qu]; + +OneLoopSimplify[FeynAmp[_, qu_Symbol, expr_], ___, opt:OptionsPattern[]] := + OneLoopSimplify[expr, qu, opt]; + +OneLoopSimplify[expr_, qu_, OptionsPattern[]] := + Block[ {amp, q, dim, sunntocacf, substis,optDiracSimplify, + ope1loop, time, optCollecting, suntrace,tmp, optFactoring, res}, + + If [!FreeQ[$ScalarProducts, q], + Message[OneLoopSimplify::failmsg, "The loop momentum " <> ToString[qu,InputForm] <> " has scalar product rules attached to it."]; + Abort[] + ]; + + If[ $KeepLogDivergentScalelessIntegrals && OptionValue[OPE1Loop], + Message[OneLoopSimplify::failmsg, "OneLoopSimplify does not support the option $KeepLogDivergentScalelessIntegrals withe OPE1Loop set to true."]; + Abort[] + ]; + + If[ !FreeQ2[{expr}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + + If [OptionValue[FCVerbose]===False, + olsVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + olsVerbose=OptionValue[FCVerbose] + ]; + ]; + + If[ FreeQ[expr, qu], + Print[expr]; + Print[qu]; + Message[OneLoopSimplify::nivar, qu]; + Return[expr] + ]; + + (* Notice that here we apply ChangeDimension only to the isolated tensor integrals, + not to the whole expression! If the dimension of the whole expression must be changed, + then this should be explicitly done by the user! *) + + q = qu; + dim = OptionValue[Dimension]; + optDiracSimplify = OptionValue[DiracSimplify]; + sunntocacf = OptionValue[SUNNToCACF]; + suntrace = OptionValue[SUNTrace]; + ope1loop = OptionValue[OPE1Loop]; + substis = OptionValue[FinalSubstitutions]; + optCollecting = OptionValue[Collecting]; + + + If[ OptionValue[Factoring] === Automatic, + optFactoring = + Function[x, If[ LeafCount[x] < 5000, + Factor2[x], + x + ] + ], + optFactoring = OptionValue[Factoring] + ]; + + + + FCPrint[1,"OneLoopSimplify: Entering.", FCDoControl->olsVerbose]; + FCPrint[3,"OneLoopSimplify: Entering with: ", expr, FCDoControl->olsVerbose]; + + If[ OptionValue[FCI], + amp = expr, + amp = FCI[expr] + ]; + + + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying Contract.", FCDoControl->olsVerbose]; + tmp = Contract[amp, EpsContract -> False, Expanding -> False, FCI -> True]; + FCPrint[1, "OneLoopSimplify: Contract done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After Contract: ", tmp, FCDoControl->olsVerbose]; + + If[ !FreeQ2[tmp, FeynCalc`Package`SUNHeadsList], + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying SUNSimplify.", FCDoControl->olsVerbose]; + tmp = SUNSimplify[tmp, SUNNToCACF -> sunntocacf, SUNTrace -> suntrace, Explicit -> False]; + FCPrint[1, "OneLoopSimplify: SUNSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After SUNSimplify: ", tmp, FCDoControl->olsVerbose] + ]; + + If[ !FreeQ2[tmp, FeynCalc`Package`DiracHeadsList] && optDiracSimplify, + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying DiracSimplify.", FCDoControl->olsVerbose]; + tmp = DiracSimplify[tmp, FCI->True]; + FCPrint[1, "OneLoopSimplify: DiracSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After DiracSimplify: ", tmp, FCDoControl->olsVerbose] + ]; + + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying Contract.", FCDoControl->olsVerbose]; + tmp = Contract[tmp, EpsContract -> False, Expanding -> False, FCI -> True]; + FCPrint[1, "OneLoopSimplify: Contract done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After Contract: ", tmp, FCDoControl->olsVerbose]; + + + + If[ (!FreeQ[tmp, OPEDelta]) && ope1loop, + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying OPE1Loop.", FCDoControl->olsVerbose]; + tmp = OPE1Loop[q, tmp, SUNNToCACF -> sunntocacf, Explicit -> False]; + FCPrint[1, "OneLoopSimplify: OPE1Loop done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After OPE1Loop: ", tmp, FCDoControl->olsVerbose] + ]; + + + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying TID.", FCDoControl->olsVerbose]; + tmp = TID[tmp, q, Dimension -> dim, FCI->True, DiracSimplify -> optDiracSimplify, ToPaVe->OptionValue[ToPaVe], UsePaVeBasis->OptionValue[UsePaVeBasis]]; + FCPrint[1, "OneLoopSimplify: TID done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After TID: ", tmp, FCDoControl->olsVerbose]; + + + + tmp = tmp /. substis; + + + If[ !FreeQ2[tmp, FeynCalc`Package`DiracHeadsList] && optDiracSimplify, + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying DiracSimplify.", FCDoControl->olsVerbose]; + tmp = DiracSimplify[tmp, FCI->True]; + FCPrint[1, "OneLoopSimplify: DiracSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After DiracSimplify: ", tmp, FCDoControl->olsVerbose] + ]; + + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying Contract.", FCDoControl->olsVerbose]; + tmp = Contract[tmp, EpsContract -> False, Expanding -> False, FCI -> True]; + FCPrint[1, "OneLoopSimplify: Contract done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After Contract: ", tmp, FCDoControl->olsVerbose]; - t5 = Collect2[t5, q, Factoring->Factor]; - FCPrint[1,"t5=", t5]; - FCPrint[1,"\n\n after cancelling scalar products \n\n", t5]; + If[ OptionValue[ExpandScalarProduct], + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying ExpandScalarProduct.", FCDoControl->olsVerbose]; + tmp = ExpandScalarProduct[tmp, FCI -> True]; + FCPrint[1, "OneLoopSimplify: ExpandScalarProduct done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After ExpandScalarProduct: ", tmp, FCDoControl->olsVerbose]; + ]; + If[ OptionValue[PowerSimplify], + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying PowerSimplify.", FCDoControl->olsVerbose]; + tmp = PowerSimplify[tmp]; + FCPrint[1, "OneLoopSimplify: PowerSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After PowerSimplify: ", tmp, FCDoControl->olsVerbose]; + ]; - If[ (!FreeQ[t5, OPEDelta]) && (ope1loop === True), - t5 = Collect2[ OPE1Loop[q, t5, SUNNToCACF -> sunntocacf, - Explicit -> False - ] /. dummyhead->Identity, q, - Factoring->Factor - ] - ]; - (* XXX *) - t6 = t5; - FCPrint[1,"OneLoopSimplify: Time spent on cancelling scalar products: ", N[AbsoluteTime[] - time, 4]]; - time = AbsoluteTime[]; - - - FCPrint[2,"doing TID on",t6]; - t6 = TID[t6, q, - DimensionalReduction -> dimred, - FeynAmpDenominatorSimplify -> True, - (*Added 7/8-2000, F.Orellana*) - Dimension -> dim, - ChangeDimension -> dim]; - - If[!FreeQ[t6/.FeynAmpDenominator[___]:>1,q], - Message[OneLoopSimplify::numerators]; - Abort[] - ]; - FCPrint[1,"TID returned: ",t6]; - If[ !FreeQ[t6,FeynAmpDenominator], - t6 = Expand2[t6+null1+null2,FeynAmpDenominator] - ]; - FCPrint[1,"doing TID done ", t6]; - t6 = t6 /. substis /. {null1 :> 0, null2 :> 0}; - - - - (*t6 = FRH[t6,IsolateNames->loopisolate];*) - FCPrint[1,"OneLoopSimplify: Time spent on tensor reduction: ", N[AbsoluteTime[] - time, 4]]; - - - - If[ !FreeQ[t6,DiracGamma], - (*t6 = FRH[t6,IsolateNames->loopisolate]; - t6 = Isolate[Collect2[DiracGammaExpand[t6],DiracGamma[__]],{DiracGamma},IsolateNames->loopisolate]/. - DOT->holdDOT/. holdDOT[x__]/; !FreeQ2[x,{DiracGamma}]:>DOT[FRH[x,IsolateNames->loopisolate]]/. - holdDOT->DOT;*) - t6 = Collect2[DiracGammaExpand[t6],DiracGamma[__]]; - time = AbsoluteTime[]; - FCPrint[1,"collecing after FRH in TID",t6]; - t6 = Collect2[t6, DiracGamma, Factoring -> False]; - FCPrint[1,"collecing after FRH in TID done",t6]; - If[ Head[t6] === Plus, - t6 = Map[ExpandScalarProduct[DiracOrder[DiracSimplify[#]]]&, - t6]; - t6 = Collect2[t6, q]; - t6 = ApartFF[t6, {q}] - ]; - FCPrint[1,"OneLoopSimplify: Time spent on Dirac algebra: ", N[AbsoluteTime[] - time, 4]]; - (*t6 = FRH[t6,IsolateNames->loopisolate];*) - ]; + time=AbsoluteTime[]; + FCPrint[1, "OneLoopSimplify: Applying FeynAmpDenominatorSimplify.", FCDoControl->olsVerbose]; + tmp = FDS[tmp, q, FCI -> True]; + FCPrint[1, "OneLoopSimplify: FeynAmpDenominatorSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->olsVerbose]; + FCPrint[3, "OneLoopSimplify: After FeynAmpDenominatorSimplify: ", tmp, FCDoControl->olsVerbose]; + If[ OptionValue[Collecting], + tmp = Collect2[tmp, Join[{qu},FeynCalc`Package`PaVeHeadsList], Expanding->False, Factoring->optFactoring] + ]; - (* Need to reisolate things here *) - (*s6 = FRH[t6,IsolateNames->loopisolate];*) + res = tmp; - t6= Collect2[ ExpandScalarProduct[t6], {FeynAmpDenominator, q, OPEDelta}]; + If [OptionValue[FCE], + res = FCE[res] + ]; - (*t6= Isolate[Collect2[ ExpandScalarProduct[t6], {FeynAmpDenominator, q, OPEDelta}], - {q, OPEDelta},IsolateNames->loopisolate];*) - time = AbsoluteTime[]; - If[ dimred =!= True, - t6 = PowerSimplify[ChangeDimension[t6,dim]/.substis], - t6 = PowerSimplify[t6]/.substis - ]; - FCPrint[1,"OneLoopSimplify: Time spent on PowerSimplify: ", N[AbsoluteTime[] - time, 4]]; - - time = AbsoluteTime[]; - t6 = Expand2[t6,q]; - If[ Head[t6] =!= Plus, - t6 = FeynAmpDenominatorSimplify[t6, q, IntegralTable -> integraltable], - fdisav[za_] := - fdisav[za] = FeynAmpDenominatorSimplify[za,q, - IntegralTable -> integraltable]; - t6 = Sum[SelectFree[t6[[i]],q] fdisav[fdisav[SelectNotFree[t6[[i]],q]]], - {i,Length[t6]}]; - ]; - - FCPrint[1,"OneLoopSimplify: Time spent on FeynAmpDenominatorSimplify: ", N[AbsoluteTime[] - time, 4]]; - - t7 = PowerSimplify[Collect2[t6, qu, Expanding->False, - Factoring -> False]/.substis - ]; - pae[a_,b_] := - MemSet[pae[a,b], ExpandScalarProduct[a,b]]; - (*t7=FRH[t7,IsolateNames->loopisolate];*) - If[!FreeQ[t7/.FeynAmpDenominator[___]:>1,q], - Message[OneLoopSimplify::numerators] - ]; - t7 = t7 /. Pair -> pae /. Power2->Power; - If[ LeafCount[t7]<1000, - t7 = Collect2[t7, qu, Expanding->False], - t7 = Collect2[t7,qu,Factoring->False,Expanding->False]; - ]; - t7 - ] + FCPrint[1,"OneLoopSimplify: Leaving.", FCDoControl->olsVerbose]; + FCPrint[3,"OneLoopSimplify: Leaving with: ", res, FCDoControl->olsVerbose]; + + res ]; + FCPrint[1,"OneLoopSimplify.m loaded."]; End[] diff --git a/FeynCalc/LoopIntegrals/PaVe.m b/FeynCalc/LoopIntegrals/PaVe.m index 6ac952d5a..c693c48b2 100644 --- a/FeynCalc/LoopIntegrals/PaVe.m +++ b/FeynCalc/LoopIntegrals/PaVe.m @@ -13,7 +13,7 @@ (* ------------------------------------------------------------------------ *) GenPaVe::usage = -"PaVe[ i,j,..., {{0,m0},{Momentum[p1],m1},{Momentum[p2],m2},...} denotes the invariant \ +"GenPaVe[i,j,..., {{0,m0},{Momentum[p1],m1},{Momentum[p2],m2},...] denotes the invariant \ (and scalar) Passarino-Veltman integrals, i.e. the coefficient functions of \ the tensor integral decomposition. In contrast to PaVe which uses the LoopTools \ convention, masses and external momenta in GenPaVe are written in the same order as \ diff --git a/FeynCalc/LoopIntegrals/PaVeIntegrals.m b/FeynCalc/LoopIntegrals/PaVeIntegrals.m index 23666b82b..b76e386e4 100644 --- a/FeynCalc/LoopIntegrals/PaVeIntegrals.m +++ b/FeynCalc/LoopIntegrals/PaVeIntegrals.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Definitions of Passarino Veltman integrals and their @@ -99,12 +99,31 @@ coefficient function of g(mu nu). All arguments are scalars and have \ ClearAttributes[B1, ReadProtectecd]; ClearAttributes[B11, ReadProtectecd]; -Options[A0] = {A0ToB0 -> False}; -Options[B0] = {BReduce -> False, B0Unique -> False, B0Real -> False }; -Options[B00] = {BReduce->True}; -Options[B1] = {BReduce->True}; -Options[B11] = {BReduce->True}; -Options[DB1] = {BReduce->True}; +Options[A0] = { + A0ToB0 -> False +}; + +Options[B0] = { + B0Real -> False, + B0Unique -> False, + BReduce -> False +}; + +Options[B00] = { + BReduce -> True +}; + +Options[B1] = { + BReduce -> True +}; + +Options[B11] = { + BReduce -> True +}; + +Options[DB1] = { + BReduce -> True +}; smanull[_] := 0; @@ -112,8 +131,6 @@ coefficient function of g(mu nu). All arguments are scalars and have \ Block[ {nx = Factor2[x]/.SmallVariable->smanull}, Factor2[Numerator[nx]]/ Factor2[Denominator[nx]] ]; -pcheck[zz__] := - FreeQ2[{zz},{Blank,BlankSequence,BlankNullSequence,Pattern}]; A0[0,OptionsPattern[]]:= 0; @@ -123,7 +140,7 @@ coefficient function of g(mu nu). All arguments are scalars and have \ A0[mm_,OptionsPattern[]] := PaVeReduce[PaVe[0,{},{mm}],PaVeAutoReduce->True,A0ToB0->True]/; OptionValue[A0ToB0] && - !( BReduce/.Options[B0]) && pcheck[mm] && FreeQ[{mm},{SmallVariable}]; + !( BReduce/.Options[B0]) && FCPatternFreeQ[{mm},{SmallVariable}]; A0 /: MakeBoxes[A0[m_, OptionsPattern[]] ,TraditionalForm] := @@ -168,7 +185,7 @@ coefficient function of g(mu nu). All arguments are scalars and have \ (* further B0 reduction *) B0[pp_,mm1_,mm2_,OptionsPattern[]] := - PaVeReduce[PaVe[0,{pp},{mm1,mm2}],BReduce->True,PaVeAutoReduce->True]/; OptionValue[BReduce] && pcheck[pp,mm1,mm2] && + PaVeReduce[PaVe[0,{pp},{mm1,mm2}],BReduce->True,PaVeAutoReduce->True]/; OptionValue[BReduce] && FCPatternFreeQ[{pp,mm1,mm2}] && (pp/.SmallVariable[_]->0)===0; B0 /: @@ -179,10 +196,10 @@ coefficient function of g(mu nu). All arguments are scalars and have \ 0/; !$KeepLogDivergentScalelessIntegrals; B00[pp_,mm1_,mm2_, OptionsPattern[]] := - b00[pp,mm1,mm2] /; $LimitTo4 && OptionValue[BReduce] && pcheck[pp,mm1,mm2] && !MatchQ[{pp,mm1,mm2},{0,0,0}]; + b00[pp,mm1,mm2] /; $LimitTo4 && OptionValue[BReduce] && FCPatternFreeQ[{pp,mm1,mm2}] && !MatchQ[{pp,mm1,mm2},{0,0,0}]; B00[pp_,mm1_,mm2_, OptionsPattern[]] := - PaVeReduce[PaVe[0,0,{pp},{mm1,mm2}],PaVeAutoReduce->True] /; !$LimitTo4 && OptionValue[BReduce] && pcheck[pp,mm1,mm2]; + PaVeReduce[PaVe[0,0,{pp},{mm1,mm2}],PaVeAutoReduce->True] /; !$LimitTo4 && OptionValue[BReduce] && FCPatternFreeQ[{pp,mm1,mm2}]; b00[0, SmallVariable[mm_], SmallVariable[mm_]] := 0; @@ -205,7 +222,7 @@ coefficient function of g(mu nu). All arguments are scalars and have \ ToBoxes[HoldForm[PaVe[0,0,{p10},{m02,m12}]],TraditionalForm]; B1[pp_,mm1_,mm2_, OptionsPattern[]] := - b1[pp,mm1,mm2] /; $LimitTo4 && OptionValue[BReduce] && pcheck[pp,mm1,mm2] && !MatchQ[{pp,mm1,mm2},{0,0,0}]; + b1[pp,mm1,mm2] /; $LimitTo4 && OptionValue[BReduce] && FCPatternFreeQ[{pp,mm1,mm2}] && !MatchQ[{pp,mm1,mm2},{0,0,0}]; B1[0,0,0, OptionsPattern[]] := 0/; !$KeepLogDivergentScalelessIntegrals; @@ -213,7 +230,7 @@ coefficient function of g(mu nu). All arguments are scalars and have \ (* General case for $LimitTo4=False; The case with zero momentum and different masses is exluded *) B1[pp_,mm1_,mm2_, OptionsPattern[]] := PaVeReduce[PaVe[1,{pp},{mm1,mm2}],PaVeAutoReduce->True] /; - !$LimitTo4 && OptionValue[BReduce] && pcheck[pp,mm1,mm2] && !(pp===0 && (mm1=!=mm2)); + !$LimitTo4 && OptionValue[BReduce] && FCPatternFreeQ[{pp,mm1,mm2}] && !(pp===0 && (mm1=!=mm2)); (* Special cases, valid for $LimitTo4=True; *) @@ -265,12 +282,12 @@ coefficient function of g(mu nu). All arguments are scalars and have \ 0/; !$KeepLogDivergentScalelessIntegrals; B11[pp_,mm1_,mm2_, OptionsPattern[]] := - b11[pp,mm1,mm2] /; $LimitTo4 && OptionValue[BReduce] && pcheck[pp,mm1,mm2] && !MatchQ[{pp,mm1,mm2},{0,0,0}]; + b11[pp,mm1,mm2] /; $LimitTo4 && OptionValue[BReduce] && FCPatternFreeQ[{pp,mm1,mm2}] && !MatchQ[{pp,mm1,mm2},{0,0,0}]; (* General case for $LimitTo4=True; The case with zero momentum and different masses is exluded *) B11[pp_,mm1_,mm2_, OptionsPattern[]] := PaVeReduce[PaVe[1,1,{pp},{mm1,mm2}],PaVeAutoReduce->True] /; - !$LimitTo4 && OptionValue[BReduce] && pcheck[pp,mm1,mm2] && !(pp===0 && (mm1=!=mm2)); + !$LimitTo4 && OptionValue[BReduce] && FCPatternFreeQ[{pp,mm1,mm2}] && !(pp===0 && (mm1=!=mm2)); (* Special cases, valid for $LimitTo4=True; *) b11[ 0,mm1_,mm1_ ] := diff --git a/FeynCalc/LoopIntegrals/PaVeOrder.m b/FeynCalc/LoopIntegrals/PaVeOrder.m index 8dc9b0948..a96a0f64f 100644 --- a/FeynCalc/LoopIntegrals/PaVeOrder.m +++ b/FeynCalc/LoopIntegrals/PaVeOrder.m @@ -25,13 +25,16 @@ Begin["`PaVeOrder`Private`"] -Options[PaVeOrder] = {PaVeOrderList -> {}}; +Options[PaVeOrder] = { + PaVeOrderList -> {} +}; (* smallLL is intermediately introduced for SmallVariable *) (* PaVeOrderdef *) PaVeOrder[expr_,opt___Rule] := Block[ {new, dordering, opli, cordering, be0, be1, aa0, be11, be00, dordering0,j,nulL }, + opli = PaVeOrderList/.{opt}/. Options[PaVeOrder]; If[ opli === False, new = expr, @@ -84,9 +87,9 @@ ]; ]; varg = Variables[arg]; - For[iv = 1,iv<=Length[varg],iv++, - If[ (!FreeQ[six, varg[[iv]]^2]) && FreeQ[arg,varg[[iv]]^2], - arg = arg/.varg[[iv]]->(varg[[iv]]^2) + For[r = 1,r<=Length[varg],r++, + If[ (!FreeQ[six, varg[[r]]^2]) && FreeQ[arg,varg[[r]]^2], + arg = arg/.varg[[r]]->(varg[[r]]^2) ]; ]; puref = func[Apply[or,(stringmatchq[slot[1], #]& /@ tomatch[arg]) @@ -130,9 +133,9 @@ ]; ]; varg = Variables[arg]; - For[iv = 1,iv<=Length[varg],iv++, - If[ (!FreeQ[ten, varg[[iv]]^2]) && FreeQ[arg,varg[[iv]]^2], - arg = arg/.varg[[iv]]->(varg[[iv]]^2) + For[r = 1,r<=Length[varg],r++, + If[ (!FreeQ[ten, varg[[r]]^2]) && FreeQ[arg,varg[[r]]^2], + arg = arg/.varg[[r]]->(varg[[r]]^2) ]; ]; puref = func[Apply[or,(stringmatchq[slot[1], #]& /@ tomatch[arg]) diff --git a/FeynCalc/LoopIntegrals/PaVeReduce.m b/FeynCalc/LoopIntegrals/PaVeReduce.m index 050130217..bbbed2373 100644 --- a/FeynCalc/LoopIntegrals/PaVeReduce.m +++ b/FeynCalc/LoopIntegrals/PaVeReduce.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Reduction of Passarino-Veltman coefficient functions into @@ -28,32 +28,36 @@ pvrVerbose::usage=""; breduce::usage=""; a0tob0::usage=""; - -Options[ PaVeReduce ] = { - A0ToB0->False, - BReduce -> False, - Collecting -> True, - Dimension -> True, - FCVerbose -> False, - Factoring -> Factor2, - IsolateNames->False, - Mandelstam->{}, - PaVeAutoReduce -> False, - PaVeOrderList -> {}, - WriteOutPaVe -> False +maxIterations::usage=""; + +Options[PaVeReduce ] = { + A0ToB0 -> False, + BReduce -> False, + Collecting -> True, + Dimension -> True, + FCE -> True, + FCVerbose -> False, + Factoring -> Factor2, + IsolateNames -> False, + Mandelstam -> {}, + MaxIterations -> Infinity, + PaVeAutoReduce -> False, + PaVeOrderList -> {}, + WriteOutPaVe -> False }; PaVeReduce[x_, opts:OptionsPattern[]] := Block[ {op, wriout, nnx = x, res, time}, - op=Join[FilterRules[Options[PaVeReduce], Except[{opts}]], {opts}]; - wriout = OptionValue[WriteOutPaVe]; - breduce = OptionValue[BReduce]; - a0tob0 = OptionValue[A0ToB0]; + op = Join[FilterRules[Options[PaVeReduce], Except[{opts}]], {opts}]; + wriout = OptionValue[WriteOutPaVe]; + breduce = OptionValue[BReduce]; + a0tob0 = OptionValue[A0ToB0]; + maxIterations = OptionValue[MaxIterations]; If [OptionValue[FCVerbose]===False, pvrVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], pvrVerbose=OptionValue[FCVerbose] ]; ]; @@ -94,9 +98,15 @@ FCPrint[3,"PaVeReduce: After Collect2: ", res, FCDoControl->pvrVerbose] ]; - FCPrint[3,"PaVeReduce: Leaving.", res, FCDoControl->pvrVerbose]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[3,"PaVeReduce: Leaving.", FCDoControl->pvrVerbose]; FCPrint[3,"PaVeReduce: Leaving with: ", res, FCDoControl->pvrVerbose]; + + res ]; @@ -113,12 +123,6 @@ PaVeBr[i__, p_List, m_List, OptionsPattern[]] := tT[Length[m]][i][Join[p, m]]; -breakdown[x_] := - If[ FreeQ[x,PaVe], - x, - FixedPoint[(#/.T->tT)&,x/.PaVe->PaVeBr] - ]; - drop[] = {}; (* i.e. no index is an empty list *) drop[x__] := @@ -629,11 +633,11 @@ If the option Dimension is set to some explicit variable (d for instance), nn = Length[nw], nn = 1 ]; - For[ij = 1, ij<=nn, ij++, - FCPrint[2,"breaking down # ", ij, " / ", nn]; + For[i = 1, i<=nn, i++, + FCPrint[2,"breaking down # ", i, " / ", nn]; If[ nn===1, pre = PartitHead[nw,StandardMatrixElement], - pre = PartitHead[nw[[ij]],StandardMatrixElement] + pre = PartitHead[nw[[i]],StandardMatrixElement] ]; re = re + pre[[2]] pavereduce[ pre[[1]], opts] ]; @@ -677,21 +681,21 @@ If the option Dimension is set to some explicit variable (d for instance), isolateP[x__] := Isolate[x, IsolateNames -> isok]; - tri[xx_ yy_] := - tri[xx] tri[yy]; + tri[x_ y_] := + tri[x] tri[y]; - tri[any_ xx_] := - ( any tri[xx] )/;FreeQ[any,Plus] || Head[any]===PaVe; + tri[a_ x_] := + ( a tri[x] )/;FreeQ[a,Plus] || Head[a]===PaVe; - tri[any_ ] := - any /;FreeQ[any,Plus] || Head[any]===PaVe; + tri[a_ ] := + a /;FreeQ[a,Plus] || Head[a]===PaVe; mand = mand /. SmallVariable->Identity; If[ mand==={}, If[ ($LimitTo4 === False ) && (Head[brex] === PaVe), tvarS = Variables[ Join @@ Take[(brex /. - PaVe[args1__, args_List, OptionsPattern[]] :> PaVe[args1, args]), -2] ]; + PaVe[x__, y_List, OptionsPattern[]] :> PaVe[x, y]), -2] ]; trick[z_] := Collect2[z, tvarS], trick[z_] := @@ -712,25 +716,28 @@ If the option Dimension is set to some explicit variable (d for instance), backpd[a_] := D0[a]; - backpd[a_,b_,c_,d_,e_,f_,m1_,m2_,m3_,m4_] := - PaVeOrder[ D0[a,b,c,d,e,f,m1,m2,m3,m4], PaVeOrderList -> paveorderli]; + backpd[a_,b_,c_,d_,e_,f_, v_,w_,x_,y_] := + PaVeOrder[ D0[a,b,c,d,e,f,v,w,x,y], PaVeOrderList -> paveorderli]; - pluep[yy__] := - Plus[yy]/;!FreeQ2[{yy}, {$epsilon,A0,B0,B1,B00,B11}]; + pluep[y__] := + Plus[y]/;!FreeQ2[{y}, {$epsilon,A0,B0,B1,B00,B11}]; FCPrint[3,"PaVeReduce: pavereduce: Staring reduction.", FCDoControl->pvrVerbose]; breakx = breakx/.msu; (* Currently, the reduction is not implemented for pentagons and other higher point function *) breakx = breakx /. { - PaVe[i_,j___, moms_List, ml_List, ops:OptionsPattern[]]/; - MatchQ[{i,j}, {Integer___}] && Length[moms]>6 :> - paveProtect[i,j, moms, ml, ops] + PaVe[i_,j___, m_List, l_List, o:OptionsPattern[]]/; + MatchQ[{i,j}, {Integer___}] && Length[m]>6 :> + paveProtect[i,j, m, l, o] }; breakx = ToPaVe2[breakx]; - t = breakdown[breakx]; + If[ FreeQ[breakx,PaVe], + t = breakx, + t = FixedPoint[(#/.T->tT)&,breakx/.PaVe->PaVeBr, maxIterations] + ]; FCPrint[3,"PaVeReduce: pavereduce: First stage done: ", t, FCDoControl->pvrVerbose]; @@ -739,11 +746,11 @@ If the option Dimension is set to some explicit variable (d for instance), FCPrint[3,"PaVeReduce: pavereduce: Second stage done: ", t, FCDoControl->pvrVerbose]; If[ !FreeQ[t, HoldForm], - t = FRH[t] + t = FRH[t, IsolateNames -> isok] ]; - If[ !FreeQ[t,tT], - t = t//. tT[n_Integer][inds__][{a__}] :> PaVe[inds,Drop[{a},-n],Take[{a},-n]] + If[ !FreeQ2[t,{T,tT}], + t = t//. (T|tT)[n_Integer][i__][{a__}] :> PaVe[i,Drop[{a},-n],Take[{a},-n]] ]; t = Expand2[t,Join[PaVeHeadsList,{$epsilon}]]; @@ -775,8 +782,8 @@ If the option Dimension is set to some explicit variable (d for instance), cofun2[y_] := y/;FreeQ[y,Plus]; - cofun2[yy_] := - trick[yy]; + cofun2[y_] := + trick[y]; If[ isok=!=False && Head[result]=!=PaVe, diff --git a/FeynCalc/LoopIntegrals/PaVeUVPart.m b/FeynCalc/LoopIntegrals/PaVeUVPart.m new file mode 100755 index 000000000..39b6326e2 --- /dev/null +++ b/FeynCalc/LoopIntegrals/PaVeUVPart.m @@ -0,0 +1,245 @@ +(* ::Package:: *) + + + +(* :Title: PaVeUVPart *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Extracts UV divergent parts of Passarino-Veltman + coefficient functions *) + +(* ------------------------------------------------------------------------ *) + + +PaVeUVPart::usage = +"PaVeUVPart[expr] replaces all occuring Passarino-Veltman functions by \ +their explicit values, where only the UV divergent part is \ +preserved, while possible IR divergences and the finite part are \ +discarded. \n + +The function uses the algorithm from \"Sulyok, G., A closed \ +expression for the UV-divergent parts +of one-loop tensor integrals in dimensional regularization, Phys. \ +Part. Nuclei Lett. (2017) 14:631, arXiv:hep-ph/0609282\" "; + +PaVeUVPart::failmsg = +"Error! PaVeUVPart has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`PaVeUVPart`Private`"] + +MM::usage=""; +PP::usage=""; +pvuvVerbose::usage=""; +dim::usage=""; +factoring::usage=""; +uvp::usage=""; +prefactor::usage=""; + +Options[PaVeUVPart] = { + Dimension -> D, + FCE -> False, + FCI -> False, + FCLoopExtract -> True, + FCVerbose -> False, + Factoring -> True, + Prefactor -> 1, + ToPaVe2 -> True, + Together -> True +}; + +PaVeUVPart[expr_, OptionsPattern[]] := + Block[{ex,repList,res, dummy, rest,loopInts,intsUnique, intsUniqueEval, paVeInt, repRule}, + + dim = OptionValue[Dimension]; + factoring = OptionValue[Factoring]; + prefactor = OptionValue[Prefactor]; + + Switch[ factoring, + False, + factoring = Identity, + True, + factoring = Factor2, + _, + True + ]; + + If [OptionValue[FCVerbose]===False, + pvuvVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + pvuvVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "PaVeUVPart: Entering.", FCDoControl->pvuvVerbose]; + FCPrint[3, "PaVeUVPart: Entering with: ", expr, FCDoControl->pvuvVerbose]; + + If[ FreeQ2[expr,FeynCalc`Package`PaVeHeadsList], + Return[expr] + ]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + + If[ OptionValue[FCLoopExtract], + + (* Normal mode *) + FCPrint[1, "PaVeUVPart: Normal mode.", FCDoControl->pvuvVerbose]; + {rest,loopInts,intsUnique} = FCLoopExtract[ex,{dummy},paVeInt,PaVe->True, FCI->True]; + FCPrint[3, "PaVeUVPart: List of the unique integrals: ", intsUnique, FCDoControl->pvuvVerbose]; + + If[ OptionValue[ToPaVe2], + intsUniqueEval = ToPaVe2/@((intsUnique/.paVeInt->Identity)); + FCPrint[3, "PaVeUVPart: List of the unique integrals after ToPaVe2: ", intsUniqueEval, FCDoControl->pvuvVerbose], + + intsUniqueEval = ((intsUnique/.paVeInt->Identity)); + ]; + + intsUniqueEval = intsUniqueEval /. convRule /. uvp->uvpEval; + FCPrint[3, "PaVeUVPart: List of the evaluated PaVe functions ", intsUniqueEval, FCDoControl->pvuvVerbose]; + + repRule = Thread[Rule[intsUnique,intsUniqueEval]]; + FCPrint[3, "PaVeUVPart: Replacement rule ", repRule, FCDoControl->pvuvVerbose]; + + res = rest + (loopInts /. repRule), + + (* Fast mode *) + FCPrint[1, "PaVeUVPart: Fast mode.", FCDoControl->pvuvVerbose]; + + If[ OptionValue[ToPaVe2], + ex = ToPaVe2[ex] + ]; + + res = ex /. convRule /. uvp->uvpEval + ]; + + If[ OptionValue[Together], + res = Together[res] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[3, "PaVeUVPart: Leaving.", FCDoControl->pvuvVerbose]; + FCPrint[3, "PaVeUVPart: Leaving with: ", res, FCDoControl->pvuvVerbose]; + + res + + ]; + + +convRule = { + PaVe[inds__?NumberQ, moms_List, masses_List, OptionsPattern[]] :> + uvp[UVPartT[Length[masses]][inds], Thread[Rule[momentumRoutingDenner2[Length[masses] - 1], moms]], + Thread[Rule[Table[MM[i], {i, 0, Length[masses] - 1}], masses]]] +}; + +uvpEval[exp_, ru1_, ru2_] := + prefactor/(dim - 4) factoring[exp /. ru1 /. ru2] + + +SetAttributes[PP, Orderless]; + +momentumRoutingDenner2[nn_] := + MemSet[momentumRoutingDenner2[nn], + Block[{firstLines, lastLine, kmax = (nn + 1)/2, res}, + firstLines = Transpose[Table[(PP[k + l, l]), {l, 0, 2 kmax - 1}, {k, 1, kmax - 1}]]; + lastLine = Table[(PP[kmax + l, l]), {l, 0, kmax - 1}]; + res = Join[Flatten[firstLines], lastLine] //. { + PP[2 kmax, y_] :> PP[0, y], PP[x_, y_] /; x > 2 kmax :> PP[x - 2 kmax, y], PP[0] -> 0}; + + res = Replace[res, 0 -> Unevaluated@Sequence[], 1]; + + If[ Length[res] =!= ((kmax - 1)*2 kmax + kmax), + Message[PaVeUVPart::failmsg, "Wrong number of the kinematic invariants!"]; + Abort[] + ]; + res + ] + ] /; OddQ[nn]; + + +momentumRoutingDenner2[nn_] := + MemSet[momentumRoutingDenner2[nn], + Block[{firstLines, lastLine, kmax = nn/2, res, p}, + res = Transpose[Table[(PP[k + l, l]), {l, 0, 2 kmax}, {k, 1, kmax}]]; + + res = Flatten[res //. { + PP[2 kmax + 1, y_] :> PP[0, y], PP[x_, y_] /; (x > 2 kmax + 1) :> PP[x - 2 kmax - 1, y], PP[0] -> 0}]; + + res = Replace[res, 0 -> Unevaluated@Sequence[], 1]; + + If[ Length[res] =!= (kmax*(2 kmax + 1)), + Message[PaVeUVPart::failmsg, "Wrong number of the kinematic invariants!"]; + Abort[] + ]; + res + ] + ] /; EvenQ[nn]; + +(* This is a slightly modified version of G. Sulyok's original UVPartT from the Mathematica notebook shipped with arXiv:hep-ph/0609282 *) + +UVPartT[1][k___] := + MemSet[UVPartT[1][k], + -(MM[0]^(1 + Quotient[Count[{k}, 0],2])/(2^(Quotient[Count[{k}, 0],2] - 1) (Quotient[Count[{k}, 0],2] + 1)!)) + ]; + +UVPartT[N_Integer?Positive /; N >= 2][k___] := + MemSet[UVPartT[N][k], + Block[{indexanzahl, a, indexlist={}, ii, jj, nom, denom, res, range, tensIndCountNoZero, tensIndCountZero, + pref, indexNumber, llow, lup, ll, tmp}, + + indexNumber = N/2 (N + 1); + tensIndCountNoZero = Count[{k}, Except[0]]; + tensIndCountZero = Count[{k}, 0]; + + tmp = Table[ll[ii], {ii, 1, indexNumber - 1}]; + llow = Join[{(Quotient[tensIndCountZero, 2] - N + 2)}, tmp]; + lup = Join[tmp, {0}]; + + With[{zzz = Sequence @@ Delete[{lup[[#]], 0, llow[[#]]} & /@ Range[indexNumber], {-1}]}, + Do[indexlist = Insert[indexlist, llow - lup, 1], zzz]]; + + a[PN_] := + Join[PP[#, 0] & /@ Range[PN - 1], Flatten[Table[(PP[ii, 0] + PP[jj, 0] - PP[ii, jj]), {jj, 1, PN - 1}, {ii, jj + 1, PN - 1}]], + -(PP[#, 0] - MM[#] + MM[0]) & /@ Range[PN - 1], {MM[0]}]; + + range = Range[Length[indexlist]]; + + nom = (Product[ + (Sum[indexlist[[#, (i/2) (2 N - 3 - i) + j]], {i, 1, j - 1}] + + Sum[indexlist[[#, (j/2) (2 N - 1 - j) + i]], {i, 1, N - 1 - j}] + + 2 indexlist[[#, j]] + indexlist[[#, (N/2) (N - 1) + j]] + Count[{k}, j])!, {j, 1, N - 1}] &) /@ range; + + denom = ( + (2 Sum[indexlist[[#, i]], {i, 1, (N/2) (N - 1)}] + + Sum[indexlist[[#, i]], {i, (N/2) (N - 1) + 1, (N/2) (N + 1) - 1}] + + (N - 1) + tensIndCountNoZero)! & + ) /@ range; + + pref = (-1)^(1 + tensIndCountNoZero)/(2^(Quotient[tensIndCountZero, 2] - 1) (Quotient[tensIndCountZero, 2] - N + 2)!); + + res = pref Plus @@ ((Multinomial[Sequence @@ indexlist[[#]]] & /@ range) ((Times @@ (a[N]^indexlist[[#]])) & /@ range) nom/denom); + + res + ] + ]; + + +FCPrint[1,"PaVeUVPart.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/PartialIntegrate.m b/FeynCalc/LoopIntegrals/PartialIntegrate.m index eea18526a..133910297 100644 --- a/FeynCalc/LoopIntegrals/PartialIntegrate.m +++ b/FeynCalc/LoopIntegrals/PartialIntegrate.m @@ -22,6 +22,8 @@ Begin["`PartialIntegrate`Private`"] +integrate::usage=""; + (*Options[PartialIntegrate] = {Hold -> False};*) Options[PartialIntegrate] = {Integrate -> Integrate}; diff --git a/FeynCalc/LoopIntegrals/PropagatorDenominatorExplicit.m b/FeynCalc/LoopIntegrals/PropagatorDenominatorExplicit.m deleted file mode 100644 index dac41f588..000000000 --- a/FeynCalc/LoopIntegrals/PropagatorDenominatorExplicit.m +++ /dev/null @@ -1,68 +0,0 @@ -(* ::Package:: *) - - - -(* :Title: PropagatorDenominatorExplicit *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Rewrite FADs into SPDs *) - -(* ------------------------------------------------------------------------ *) - -PropagatorDenominatorExplicit::usage = -"PropagatorDenominatorExplicit[exp] changes each occurence of \ -PropagatorDenominator[a,b] in exp into 1/(ScalarProduct[a,a]-b^2) and \ -replaces FeynAmpDenominator by Times."; - -PDEHead::usage = -"PDEHead is an option of PropagatorDenominatorExplicit. It allows \ -to wrap propagators into a specified head after applying \ -PropagatorDenominatorExpliciti. The default value is Identity."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`PropagatorDenominatorExplicit`Private`"] - -Options[PropagatorDenominatorExplicit] = { - FCI -> False, - Dimension -> False, - PDEHead->Identity -} - -PropagatorDenominatorExplicit[expr_, OptionsPattern[]] := - Block[{ex, dim, res, head}, - - If[ OptionValue[FCI], - ex = expr, - ex = FCI[expr] - ]; - - dim = OptionValue[Dimension]; - head = OptionValue[PDEHead]; - - res = ex //. { - PropagatorDenominator[a_ /; !FreeQ[a, Momentum] ,b_] :> - (1/Expand[ExpandScalarProduct[Pair[a, a]] - b^2]), - - PropagatorDenominator[a_ /; FreeQ[a, Momentum] ,b_] :> - (1/Expand[ExpandScalarProduct[Pair[Momentum[a], Momentum[a]]] - b^2]) - }; - - If[dim===False, - res = res /. FeynAmpDenominator[c___] :> head[Times[c]], - res = res /. FeynAmpDenominator[c___] :> head[ChangeDimension[Times[c],dim]] - ]; - res - ]; - -FCPrint[1,"PropagatorDenominatorExplicit.m loaded."]; -End[] diff --git a/FeynCalc/LoopIntegrals/RussianTrick.m b/FeynCalc/LoopIntegrals/RussianTrick.m index cd219c3bf..20a5198a8 100755 --- a/FeynCalc/LoopIntegrals/RussianTrick.m +++ b/FeynCalc/LoopIntegrals/RussianTrick.m @@ -23,7 +23,10 @@ Begin["`RussianTrick`Private`"] -Options[RussianTrick] = {Dimension -> D, FC2TLI -> False}; +Options[RussianTrick] = { + Dimension -> D, + FC2TLI -> False +}; RussianTrick[exp_,k_, opt___Rule] := RussianTrick[exp,k,k,{FCGV["q1"], FCGV["q2"], FCGV["p"]},opt]; @@ -32,11 +35,17 @@ RussianTrick[exp,k,pe,{FCGV["q1"], FCGV["q2"], FCGV["p"]},opt]; RussianTrick[ex_, p_,k_, {q1_, q2_, pe_}, opt___Rule] := - Block[ {fv, t1, t2, t3, dime, exp,mu, dim}, + Block[ {t1, t2, t3, dime, exp,mu, dim}, + + If[ !FreeQ2[{ex}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + exp = FCI[ex]; dim = Dimension /. {opt} /. Options[RussianTrick]; - fv = ExpandScalarProduct[FourVector[##, Dimension -> dim]]&; - t1 = FourDivergence[exp fv[p,mu], fv[k, mu]]; + t1 = FourDivergence[exp ExpandScalarProduct[Pair[Momentum[p,dim],LorentzIndex[mu,dim]]], + ExpandScalarProduct[Pair[Momentum[k,dim],LorentzIndex[mu,dim]]]]; t2 = ApartFF[t1, {q1, q2}]; t2 = Collect2[FeynAmpDenominatorSimplify[t2, q1,q2], q1,q2]; If[ Head[t2] === Plus, diff --git a/FeynCalc/LoopIntegrals/ScalarProductCancel.m b/FeynCalc/LoopIntegrals/ScalarProductCancel.m index d8821bda2..cc3a563fd 100755 --- a/FeynCalc/LoopIntegrals/ScalarProductCancel.m +++ b/FeynCalc/LoopIntegrals/ScalarProductCancel.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Cancels loop-momentum dependent scalar products in the @@ -40,11 +40,11 @@ SPC = ScalarProductCancel; Options[ScalarProductCancel] = { - ChangeDimension -> D, - FCI -> False, - FCVerbose -> False, - FDS -> True, - FeynAmpDenominatorCombine -> True + ChangeDimension -> D, + FCI -> False, + FCVerbose -> False, + FDS -> True, + FeynAmpDenominatorCombine -> True }; SetAttributes[ScalarProductCancel, Listable]; @@ -66,9 +66,15 @@ ScalarProductCancel[int_, qs___, qlast_ , OptionsPattern[]]:= Block[{exp,rank,tmp,tmpHead,null1,null2,res, maxRank}, + + If[ !FreeQ2[{int}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + If [OptionValue[FCVerbose]===False, spcVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], spcVerbose=OptionValue[FCVerbose] ]; ]; @@ -365,7 +371,7 @@ that differ only in the mass are equivalent for our purposes, we set all masses to zero, to avoid duplicates. Furthermore, we ignore all the propagators that do not depend on any of the loop momenta from the qs List *) - props = Union[Cases[ex, PropagatorDenominator[moms_, _]/;!FreeQ2[moms,qs] :> (Expand[moms] /. Momentum[x_, _ : 4] :> x),Infinity]]; + props = Union[Cases[ex, PropagatorDenominator[m_, _]/;!FreeQ2[m,qs] :> (Expand[m] /. Momentum[x_, _ : 4] :> x),Infinity]]; (* List of all the unique propagators that depend on the loop momentum and are written such that they match the propagators in props. Note that here we account diff --git a/FeynCalc/LoopIntegrals/TFIOrder.m b/FeynCalc/LoopIntegrals/TFIOrder.m index 7756e6568..014bd634e 100644 --- a/FeynCalc/LoopIntegrals/TFIOrder.m +++ b/FeynCalc/LoopIntegrals/TFIOrder.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Orders the arguments of some TFI functions in a @@ -17,7 +17,7 @@ (* ------------------------------------------------------------------------ *) TFIOrder::usage = -"TFIOrder[expr] orders the arguments of some TFI functions in a \ +"TFIOrder[exp] orders the arguments of some TFI functions in exp in a \ standard way."; @@ -32,6 +32,12 @@ TFIOrder[expr_, OptionsPattern[]] := Block[{res,repRule}, + + If[ !FreeQ2[{expr}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + repRule= { (*Symmetry under the interchang q1 <-> q2*) Tarcer`TFI[d_, p_, {{1, m1_}, {1, m2_}, {1, m3_}, {1, m4_}, {1, m5_}}] /; ! OrderedQ[{m1, m2}] :> diff --git a/FeynCalc/LoopIntegrals/TID.m b/FeynCalc/LoopIntegrals/TID.m index 4f1e5b254..b90e3d9d9 100644 --- a/FeynCalc/LoopIntegrals/TID.m +++ b/FeynCalc/LoopIntegrals/TID.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Tensor reduction of 1-loop integrals *) @@ -41,57 +41,84 @@ Begin["`TID`Private`"] -(* This is just for the Workbench to know - that these internal functions are not typos *) tidVerbose::usage=""; tidPaVe::usage=""; tidIsolate::usage=""; genpave::usage=""; paveao::usage=""; pavear::usage=""; +ffdp::usage=""; +qQQ::usage=""; +optTimeConstrained::usage=""; procanonical[l_][y_,m_] := PropagatorDenominator[y /. (-Momentum[l,di___] + a_.) :> (Momentum[l,di] - a), m]; +procanonical[l_][y_, 0 ,m_, s_] := + CartesianPropagatorDenominator[y /. + (-CartesianMomentum[l,di___] + a_.) :> + (CartesianMomentum[l,di] - a), 0, m, s]; + +procanonical[_][y_, x_/;x=!=0, m_, s_] := + CartesianPropagatorDenominator[y, x, m, s]; + +procanonical[l_][y_, 0 ,m_, s_] := + StandardPropagatorDenominator[y /. + (-Momentum[l,di___] + a_.) :> + (Momentum[l,di] - a), 0, m, s]; + +procanonical[_][y_, x_/;x=!=0, m_, s_] := + StandardPropagatorDenominator[y, x, m, s]; + Options[TID] = { - ChangeDimension -> D, - Collecting -> True, - Contract -> True, - Dimension -> D, - DimensionalReduction -> False, - DiracSimplify -> True, - DiracTrace -> True, - ExpandScalarProduct -> True, - EpsEvaluate ->True, - FCI -> False, - FCVerbose -> False, - FeynAmpDenominatorCombine -> True, - FDS -> True, - GenPaVe->False, - PaVeAutoOrder -> True, - PaVeAutoReduce -> True, - ApartFF -> True, - Isolate -> False, - UsePaVeBasis -> False, - ToPaVe->False + ApartFF -> True, + Check -> True, + Collecting -> True, + Contract -> True, + Dimension -> D, + DiracSimplify -> True, + DiracTrace -> True, + EpsEvaluate -> True, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False, + FCLoopMixedToCartesianAndTemporal -> True, + FCLoopRemoveNegativePropagatorPowers -> True, + FCVerbose -> False, + FDS -> True, + Factoring -> {Factor2, 5000}, + FeynAmpDenominatorCombine -> True, + GenPaVe -> False, + Isolate -> False, + PaVeAutoOrder -> True, + PaVeAutoReduce -> True, + PauliSimplify -> True, + TimeConstrained -> 3, + ToPaVe -> False, + UsePaVeBasis -> False }; + +TID[am_ , {q_}, opts:OptionsPattern[]] := + TID[am, q, opts] + TID[am_ , q_, OptionsPattern[]] := Block[ {n, t0, t1, t3, t4, t5, t6, null1, null2, qrule, - res,nres,irrelevant = 0, - contractlabel, diditlabel, famp,chd,fds,tid, tidinternal, - dimred, (*limitto4=$LimitTo4,*)iter,sp,tp, - - loopIntegral, wrapped,loopList,repIndexList,canIndexList,uniqueCanIndexList, - solsList, repSolList, reversedRepIndexList,reducedLoopList, - finalRepList,isoContract,tmp,tempIsolate,loopListOrig, tmpli + res,nres,irrelevant = 0, contractlabel, fds, iter,sp,tp, + loopIntegral, wrapped,loopList,repIndexList,canIndexList,uniqueCanIndexList, + solsList, repSolList, reversedRepIndexList,reducedLoopList, + finalRepList,isoContract,tmp,tempIsolate,loopListOrig, tmpli, time, time0, fclcOutput, + optExpandScalarProduct, noTID, fadCollect }, + optExpandScalarProduct = OptionValue[ExpandScalarProduct]; + optTimeConstrained = OptionValue[TimeConstrained]; + If [OptionValue[FCVerbose]===False, tidVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], tidVerbose=OptionValue[FCVerbose] ]; ]; @@ -102,7 +129,8 @@ Abort[] ]; - FCPrint[1,"TID: Entering TID with: ", am, FCDoControl->tidVerbose]; + FCPrint[1,"TID: Entering TID.", FCDoControl->tidVerbose]; + FCPrint[3,"TID: Entering with: ", am, FCDoControl->tidVerbose]; If[ OptionValue[FCI], t0 = am, @@ -110,160 +138,193 @@ ]; - - dimred = OptionValue[DimensionalReduction]; + (* Notice that here we apply ChangeDimension only to the isolated tensor integrals, + not to the whole expression! If the dimension of the whole expression must be changed, + then this should be explicitly done by the user! *) n = OptionValue[Dimension]; contractlabel = OptionValue[Contract]; fds = OptionValue[FDS]; - chd = OptionValue[ChangeDimension]; paveao = OptionValue[PaVeAutoOrder]; pavear = OptionValue[PaVeAutoReduce]; genpave = OptionValue[GenPaVe]; - - - - If[ t0 === 0, - Return[0] + If[ FreeQ[t0,q], + Return[t0] ]; - (*If[ dimred =!= True, - FCMonitor[ - t0 = ChangeDimension[t0, chd]; - (*$LimitTo4=False;*) - Grid[{{"Applying ChangeDimension", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ] - ];*) - - (* - t5 = t5 /. {LorentzIndex[aa_, en_Symbol] :> LorentzIndex[aa], - Momentum[b_, en_Symbol] :> Momentum[b] - }; - *) - (* Contract is necessary here to simplify things like FV[q,i]^2 *) - If[ contractlabel && !FreeQ[t0,LorentzIndex], - t0 = Contract[t0]; + If[ contractlabel && !FreeQ2[t0,{LorentzIndex,CartesianIndex}], + FCPrint[1, "TID: Applying Contract.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = Contract[t0, FCI->True, ExpandScalarProduct->optExpandScalarProduct]; + FCPrint[1, "TID: Done applying Contract, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "After Contract: ", t0 , FCDoControl->tidVerbose] ]; (* The input expression can be potentially very large, so it's better to take some measures here. Non-commutative products are not isolated! *) - FCMonitor[ - t0 = Isolate[Collect2[t0,{q,FeynAmpDenominator}],{q,FeynAmpDenominator,Dot}, - IsolateNames->tempIsolate]/.Dot[x___]:>FRH[Dot[x],IsolateNames->tempIsolate]; - Grid[{{"Isolating loop integrals in the input expression", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ]; + FCPrint[1, "TID: Applying Collect2.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + + t0 = Collect2[t0,{q,FeynAmpDenominator}, TimeConstrained->optTimeConstrained]; + FCPrint[1, "TID: Done applying Collect2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After Collect2: ", t0 , FCDoControl->tidVerbose]; + + FCPrint[1, "TID: Applying Isolate.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = Isolate[t0,{q,FeynAmpDenominator,Dot}, IsolateNames->tempIsolate]/.Dot[x___]:>FRH[Dot[x],IsolateNames->tempIsolate]; + FCPrint[1, "TID: Done applying Isolate, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After Isolate: ", t0 , FCDoControl->tidVerbose]; - If[ !FreeQ2[Union[FCGetDimensions[t0/.DiracGamma[5|6|7]:>null1]],{4,-4}] && !$BreitMaison, + If[ !FreeQ2[Union[FCGetDimensions[t0, FreeQ->{DiracGamma[5|6|7], TemporalPair[__]}, ChangeDimension->True]],{4,-4}] && (FeynCalc`Package`DiracGammaScheme =!= "BMHV"), Message[TID::failmsg,"Your input contains a mixture of 4- and D-dimensional quantities. This is in general not allowed in dimensional regularization, unless you are using the Breitenlohner-Maison-t'Hooft-Veltman scheme."]; Abort[] ]; - FCPrint[2,"TID: After Isolate: ", t0, FCDoControl->tidVerbose]; - If[ OptionValue[FeynAmpDenominatorCombine], - FCMonitor[ - t0 = fspec[FeynAmpDenominatorCombine[t0], q]; - Grid[{{"Applying FeynAmpDenominatorCombine", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ] + FCPrint[1, "TID: Applying FeynAmpDenominatorCombine.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = FeynAmpDenominatorCombine[t0, FCI->True, Momentum->{q}]; + FCPrint[1, "TID: Done applying FeynAmpDenominatorCombine, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After FeynAmpDenominatorCombine: ", t0 , FCDoControl->tidVerbose] ]; - If[ fds, - FCMonitor[ - t0 = FeynAmpDenominatorSimplify[t0, q]; - Grid[{{"Simplifying denominators and doing partial fractioning", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ] - + If[ OptionValue[FCLoopRemoveNegativePropagatorPowers], + FCPrint[1,"TID: Applying FCLoopRemoveNegativePropagatorPowers.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = FCLoopRemoveNegativePropagatorPowers[t0, FCI->True]; + FCPrint[1, "TID: Done applying FCLoopRemoveNegativePropagatorPowers, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After FCLoopRemoveNegativePropagatorPowers: ", t0 , FCDoControl->tidVerbose] ]; - t0 = FDS[t0,q]; - - FCPrint[2,"TID: After FDS: ", t0, FCDoControl->tidVerbose]; + FCPrint[1, "TID: Applying FRH.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; t0 = FRH[t0,IsolateNames->tempIsolate]; + FCPrint[1, "TID: Done applying FRH, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After FRH: ", t0 , FCDoControl->tidVerbose]; - FCPrint[2,"TID: Before DiracSimplify: ", t0, FCDoControl->tidVerbose]; If[ OptionValue[DiracSimplify] && !FreeQ2[t0,{DiracGamma,DiracSigma,Spinor}], - FCMonitor[t0 = DiracSimplify[t0], - Grid[{{"Simplifying the Dirac structure of the input expression", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ] + FCPrint[1, "TID: Applying DiracSimplify.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = DiracSimplify[t0,FCI->True, DiracTraceEvaluate->OptionValue[DiracTrace], Expand2->False]; + FCPrint[1, "TID: Done applying DiracSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After DiracSimplify: ", t0 , FCDoControl->tidVerbose] ]; - FCPrint[2,"TID: Before DiracTrace: ", t0, FCDoControl->tidVerbose]; + If[ OptionValue[PauliSimplify] && !FreeQ2[t0,{PauliSigma}], + FCPrint[1, "TID: Applying PauliTrick.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = PauliSimplify[t0,FCI->True, Expand2->False]; + FCPrint[1, "TID: Done applying PauliSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After PauliSimplify: ", t0 , FCDoControl->tidVerbose] + ]; - If[ OptionValue[DiracTrace] && !FreeQ[t0,DiracTrace], - t0 = t0 /. DiracTrace[x__]/; !FreeQ[{x},q]:>DiracTrace[x,DiracTraceEvaluate->True] + + If[ fds, + FCPrint[1, "TID: Applying FDS.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = FeynAmpDenominatorSimplify[t0, q, FCI->True, Collecting->False]; + (* The fact that we need to apply FDS twice here, tells a lot about the quality of FDS. *) + t0 = FeynAmpDenominatorSimplify[t0, q, FCI->True, Collecting->False]; + FCPrint[1, "TID: Done applying FDS, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3," TID: After FDS: ", t0 , FCDoControl->tidVerbose] ]; - FCPrint[2,"TID: Before first ApartFF: ", t0, FCDoControl->tidVerbose]; If[ OptionValue[ApartFF], - t0 = ApartFF[t0,{q},FCI->True]; - ]; - FCPrint[2,"TID: After first ApartFF: ", t0, FCDoControl->tidVerbose]; - (* - If[ !FreeQ2[t0,DiracGamma], - t0 = DiracGammaExpand[t0]; - FCPrint[2,"TID: After expanding Dirac slashes: ", t0, FCDoControl->tidVerbose] + FCPrint[1, "TID: Applying ApartFF.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = ApartFF[t0,{q},FCI->True, Collecting->{q}, SetDimensions->{4,n,3,n-1}]; + FCPrint[1, "TID: Done applying ApartFF, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After ApartFF: ", t0 , FCDoControl->tidVerbose] ]; - *) - (* Single out loop momenta *) - t0 = ExpandScalarProduct[t0,Momentum->{q}]; + (* Single out the loop momenta *) + FCPrint[1, "TID: Applying ExpandScalarProduct.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t0 = ExpandScalarProduct[t0,Momentum->{q}, FCI->True, Full->False]; + FCPrint[1, "TID: Done applying ExpandScalarProduct, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After ExpandScalarProduct: ", t0 , FCDoControl->tidVerbose]; - (* Uncontract first *) - FCMonitor[t1 = Uncontract[t0, q, Pair -> All, DimensionalReduction -> dimred(*, - Dimension -> n*)] /. PropagatorDenominator -> procanonical[q];, - Grid[{{"Uncontracting loop momenta", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ]; + FCPrint[1,"TID: Applying Uncontract.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t1 = Uncontract[t0, q, Pair -> All, CartesianPair->All, FCI->True] /. PropagatorDenominator -> procanonical[q]; + FCPrint[1, "TID: Done applying Uncontract, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3," TID: After Uncontract: ", t1 , FCDoControl->tidVerbose]; + + If[ !FreeQ[t1,DiracTrace], + FCPrint[1, "TID: Applying FCTraceExpand.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + t1 = t1 /. DiracTrace[x__]/;!FreeQ[x, q] :> FCTraceExpand[DiracTrace[x],FCI->True]; + FCPrint[1, "TID: Done applying FCTraceExpand timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After FCTraceExpand: ", t1 , FCDoControl->tidVerbose]; + ]; - FCMonitor[ - (* Check if user disabled DiracSimplify but the given - Dirac Structure is not suitable for the reduction *) - If[ !FreeQ[t1/. {Pair[Momentum[q, dim_: 4], LorentzIndex[_, dim_: 4]] :> Unique[], - FeynAmpDenominator[___]:>Unique[]}, q], - Message[TID::failmsg, "Ucontracting loop momenta in " <> ToString[t1,InputForm] <> - "failed."]; - Abort[] - ]; - tmp = FCLoopSplit[t1,{q},FCI->True]; - irrelevant = tmp[[1]]+tmp[[2]]+tmp[[3]]; - tp = tmp[[4]]; - (* tp can still contain scaleless integrals like q^2, q.p etc. - We need to get rid of them here *) - t1 = removeScaleless[tp,q], - Grid[{{"Splitting into tensor and scalar parts", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] + (* Check if user disabled DiracSimplify but the given + Dirac Structure is not suitable for the reduction *) + If[ !FreeQ[t1/. { + Pair[Momentum[q, dim___], LorentzIndex[_, dim___]] :> Unique[], + CartesianPair[CartesianMomentum[q, dim___], CartesianIndex[_, dim___]] :> Unique[], + FeynAmpDenominator[___]:>Unique[], + TemporalMomentum[q]:> Unique + }, q], + Message[TID::failmsg, "Uncontracting loop momenta in " <> ToString[t1,InputForm] <> + "failed."]; + Abort[] ]; - FCPrint[2,"TID: Tensor parts of the original expression: ", t1, FCDoControl->tidVerbose]; - FCPrint[2,"TID: Scalar and non-loop parts of the original expression: ", irrelevant, FCDoControl->tidVerbose]; + FCPrint[1,"TID: Sorting loop integrals.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + + tmp = FCLoopSplit[t1/. TemporalMomentum[q] -> TemporalMomentum[q0],{q},FCI->True, Factoring->Factor]/. + TemporalMomentum[q0] -> TemporalMomentum[q]; + irrelevant = tmp[[1]]+tmp[[2]]+tmp[[3]]; + tp = tmp[[4]]; + (* tp can still contain scaleless integrals like q^2, q.p etc. + We need to get rid of them here *) + t1 = removeScaleless[tp,q]; + + FCPrint[1, "TID: Done sorting loop integrals, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + + FCPrint[3,"TID: Tensor parts of the original expression: ", t1, FCDoControl->tidVerbose]; + FCPrint[3,"TID: Scalar and non-loop parts of the original expression: ", irrelevant, FCDoControl->tidVerbose]; + + If[ OptionValue[ToPaVe], + FCPrint[1, "TID: Applying ToPaVe to the scalar part of the input expression.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + irrelevant = ToPaVe[irrelevant,q, FCI->True]; + FCPrint[1, "TID: Done applying ToPaVe, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After ToPaVe: ", res , FCDoControl->tidVerbose] + ]; (* Here comes the trick to handle uncontracted loop momenta in 4 or D-4 dimensions. This is needed only in the BMHV scheme *) - If[ $BreitMaison && !FreeQ[t1,LorentzIndex], - t1 = t1 /. { + If[ (FeynCalc`Package`DiracGammaScheme === "BMHV") && !FreeQ2[t1,{LorentzIndex,CartesianIndex}], + time=AbsoluteTime[]; + FCPrint[1, "TID: Handling 4 and D-4 dimensional loop momenta.", FCDoControl->tidVerbose]; + t1 = t1 //. { Pair[Momentum[q,n-4],LorentzIndex[i_,n-4]]:> (tmpli=Unique[]; Pair[Momentum[q,n],LorentzIndex[tmpli,n]] Pair[LorentzIndex[tmpli,n-4],LorentzIndex[i,n-4]]), Pair[Momentum[q],LorentzIndex[i_]]:> - (tmpli=Unique[]; Pair[Momentum[q,n],LorentzIndex[tmpli,n]] Pair[LorentzIndex[tmpli],LorentzIndex[i]]) + (tmpli=Unique[]; Pair[Momentum[q,n],LorentzIndex[tmpli,n]] Pair[LorentzIndex[tmpli],LorentzIndex[i]]), + CartesianPair[CartesianMomentum[q,n-4],CartesianIndex[i_,n-4]]:> + (tmpli=Unique[]; CartesianPair[CartesianMomentum[q,n-1],CartesianIndex[tmpli,n-1]] CartesianPair[CartesianIndex[tmpli,n-4],CartesianIndex[i,n-4]]), + CartesianPair[CartesianMomentum[q],CartesianIndex[i_]]:> + (tmpli=Unique[]; CartesianPair[CartesianMomentum[q,n-1],CartesianIndex[tmpli,n-1]] CartesianPair[CartesianIndex[tmpli],CartesianIndex[i]]) }; - If[ !FreeQ2[t1, {Pair[Momentum[q,n-4],LorentzIndex[_,n-4]],Pair[Momentum[q],LorentzIndex[_]]}], + If[ !FreeQ2[t1, {Pair[Momentum[q,n-4],LorentzIndex[_,n-4]],Pair[Momentum[q],LorentzIndex[_]], + CartesianPair[CartesianMomentum[q,n-4],CartesianIndex[_,n-4]],CartesianPair[CartesianMomentum[q],CartesianIndex[_]]}], Message[TID::failmsg,"Failed to eliminate 4 and D-4 dimensional loop momenta."]; Abort[] ]; - FCPrint[2,"TID: Tensor parts after handling 4 and D-4 dimensional loop momenta: ", t1, FCDoControl->tidVerbose]; + FCPrint[1, "TID: Done handling 4 and D-4 dimensional loop momenta, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3,"TID: Tensor parts after handling 4 and D-4 dimensional loop momenta: ", t1, FCDoControl->tidVerbose] ]; If[t1===0, @@ -271,200 +332,284 @@ res = 0, (* otherwise we need to reduce it to scalar integrals *) - FCMonitor[ - t1 = Collect2[t1,{q,FeynAmpDenominator}]; - (* wrap all loop-momentum dependent pieces in loopIntegral *) - wrapped = FCLoopIsolate[t1,{q},Head->loopIntegral]; + time0=AbsoluteTime[]; + FCPrint[1, "TID: Starting reduction of tensor integrals.", FCDoControl->tidVerbose]; + - (* This is the list of all the tensor loop integrals in the expression. *) - loopListOrig=Union[Cases[{wrapped},_. loopIntegral[x_]:>x,Infinity]]; - FCPrint[3,"TID: loopList: ", loopList, FCDoControl->tidVerbose]; - (* Before applying ChangeDimension, check again, that there are no 4-vectors that - are not D-dimensional *) - If[ FCGetDimensions[Union[Cases[loopListOrig, _LorentzIndex, Infinity]]]=!={n}, - Message[TID::failmsg,"The tensor part still contains 4 or D-4 dimensional loop momenta."]; + (* wrap all loop-momentum dependent pieces in loopIntegral *) + + FCPrint[1, "TID: Applying FCLoopIsolate.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + wrapped = FCLoopIsolate[t1,{q},Head->loopIntegral, FCI->True]; + FCPrint[1, "TID: Done applying FCLoopIsolate, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + + If[ OptionValue[FCLoopMixedToCartesianAndTemporal] && !FreeQ2[{wrapped,irrelevant},{CartesianMomentum,TemporalMomentum}], + + FCPrint[1, "TID: Applying FCLoopMixedToCartesianAndTemporal, timing: ", FCDoControl->tidVerbose]; + wrapped = wrapped /. loopIntegral[y_]/;FCLoopMixedIntegralQ[y] :> + FCLoopIsolate[FCLoopMixedToCartesianAndTemporal[y,{q}, Uncontract->True] /. TemporalPair[x__]/;!FreeQ[{x},q] :> MomentumExpand[TemporalPair[x]] + /. TemporalMomentum[q] -> TemporalMomentum[q0] //. { + ExplicitLorentzIndex[0] :> holdExplicitLorentzIndex[0], + TemporalMomentum[x_]/;FreeQ[x,q] :> holdTemporalMomentum[x], + TemporalPair[x__]/;FreeQ[{x},q] :> holdTemporalPair[x] + },{q},Head->loopIntegral, FCI->True]; + + FCPrint[1, "TID: Done applying FCLoopMixedToCartesianAndTemporal, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + + irrelevant = FCLoopIsolate[irrelevant,{q},Head->loopIntegral, FCI->True] /. + loopIntegral[y_]/;FCLoopMixedIntegralQ[y] :> FCLoopMixedToCartesianAndTemporal[y,{q}] /. loopIntegral-> Identity + ]; + + + (* remove all kinds of integrals that cannot or should not be handled by TID *) + wrapped = wrapped /. { + loopIntegral[y_]/; (FCLoopMixedIntegralQ[y] || !FCLoopEikonalPropagatorFreeQ[y,First->False] || !FCLoopSamePropagatorHeadsQ[y]) :> noTID y, + (*This one is for cases like TC[k] FVD[k,mu] FAD[k,k+p]*) + loopIntegral[y_FeynAmpDenominator] :> noTID y + }; + + FCPrint[3, "TID: After FCLoopIsolate: ", wrapped , FCDoControl->tidVerbose]; + If[ !FreeQ[wrapped,loopIntegral], + (* The 4th element in fclcOutput is our list of unique tensor integrals that need to be reduced. *) + FCPrint[1,"TID: Applying FCLoopCanonicalize.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + fclcOutput = FCLoopCanonicalize[wrapped, q, loopIntegral,FCI->True]; + FCPrint[1, "TID: Done applying FCLoopCanonicalize, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After FCLoopCanonicalize: ", fclcOutput , FCDoControl->tidVerbose]; + + + uniqueCanIndexList = fclcOutput[[4]] /. loopIntegral->Identity; + + + (* Check that there are no 4-vectors that are not D-dimensional *) + If[ !FreeQ[uniqueCanIndexList,LorentzIndex], + If[ FCGetDimensions[Union[Cases[uniqueCanIndexList, _LorentzIndex, Infinity]]]=!={n}, + Message[TID::failmsg,"The tensor part still contains 4 or D-4 dimensional loop momenta."]; + Abort[] + ]; + ]; + + (* Check that there are no 3-vectors that are not D-1-dimensional *) + If[ !FreeQ[uniqueCanIndexList,CartesianIndex], + If[ FCGetDimensions[Union[Cases[uniqueCanIndexList, _CartesianIndex, Infinity]]]=!={n-1}, + Message[TID::failmsg,"The tensor part still contains 3 or D-4 dimensional loop momenta."]; + Abort[] + ]; + ]; + + (* Here we reduce the unique tensor integrals to scalar integrals *) + + FCPrint[1,"TID: Reducing ", Length[uniqueCanIndexList], " unique 1-loop tensor integrals.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + solsList= tidSingleIntegral[#, q , n, OptionValue[UsePaVeBasis]]&/@uniqueCanIndexList; + + FCPrint[1, "TID: Done reducing unique 1-loop tensor integrals, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After the reduction: ", solsList , FCDoControl->tidVerbose]; + + FCPrint[1, "TID: Done reducing tensor integrals, timing: ", N[AbsoluteTime[] - time0, 4], FCDoControl->tidVerbose]; + + (* Make sure that the reduction worked out correctly *) + If[ !FreeQ2[FRH[solsList]/. FeynAmpDenominator[__] :> Unique[], {q,tidSingleIntegral,tidReduce,tidConvert}], + Message[TID::failmsg, "Running tidSingleIntegral failed to achieve full tensor reduction of the unique integrals in", solsList]; Abort[] ]; - loopList = ChangeDimension[#, chd]&/@loopListOrig; - FCPrint[3,"TID: loopList after ChangeDimension: ", loopList, FCDoControl->tidVerbose]; + If[ OptionValue[ApartFF], + FCPrint[1, "TID: Applying ApartFF to the list of the reduced integrals.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + solsList = ApartFF[#,{q},FCI->True, SetDimensions->{4,n,3,n-1}]&/@solsList; + FCPrint[1, "TID: Done applying ApartFF, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After ApartFF: ", solsList , FCDoControl->tidVerbose] + ]; - (* Here we collect the tensor indices of each integral from the - previous list *) - repIndexList=((MapIndexed[Rule[#1,LorentzIndex[ToExpression[("i"<>ToString[Identity@@#2])],n]]&,Cases[#,LorentzIndex[__], - Infinity]//Union]//Flatten)&/@loopList); - (* This is the list of all the loop tensor integrals with canonicalized indices. *) - canIndexList=(MapIndexed[(#1/.First[repIndexList[[#2]]])&,loopList]); + If[ OptionValue[ToPaVe], + FCPrint[1, "TID: Applying ToPaVe to the list of the reduced integrals.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + solsList = ToPaVe[(#/.tidPaVe->Identity),q, FCI->True]&/@solsList; + FCPrint[1, "TID: Done applying ToPaVe, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After ToPaVe: ", res , FCDoControl->tidVerbose] + ]; - (* Finally we obtain the (usually much smaller) list of all the unique tensor integrals. Only those - need to be reduced. *) - uniqueCanIndexList=canIndexList//DeleteDuplicates, - (* Get rid of scalar integrals inside our list of unique integrals *) - (*uniqueCanIndexList = Select[uniqueCanIndexList, ! FreeQ[# /. FeynAmpDenominator[__] :> Unique[], q] &];*) - Grid[{{"Identifying unique integrals in the tensor part", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ]; + FCPrint[1, "TID: Creating the final list of replacements.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; - (* Here we reduce the unique tensor integrals to scalar integrals *) - FCPrint[1,"TID: List of the unique integrals to be tensor reduced ", uniqueCanIndexList, FCDoControl->tidVerbose]; - FCMonitor[ - solsList=MapIndexed[(iter=Total[#2]; tidSingleIntegral[#1, q , n, dimred, OptionValue[UsePaVeBasis]])&,uniqueCanIndexList]; - iter=Length[uniqueCanIndexList]+1, - Grid[{{"Reducing unique tensor integrals", - ProgressIndicator[iter, {1, Length[uniqueCanIndexList]+1}]}}] - ]; - FCPrint[1,"TID: List of the reduced integrals ", solsList, FCDoControl->tidVerbose]; - (* Make sure that the reduction worked out correctly *) - If[ !FreeQ2[FRH[solsList]/. FeynAmpDenominator[__] :> Unique[], {q,tidSingleIntegral,tidReduce,tidConvert}], - Message[TID::failmsg, "Running tidSingleIntegral failed to achieve full tensor reduction of the unique integrals in", solsList]; - Abort[] - ]; + finalRepList = FCLoopSolutionList[fclcOutput,solsList]; + + FCPrint[3, "TID: Final list of replacements: ", finalRepList, FCDoControl->tidVerbose]; + FCPrint[3, "TID: To be applied on: ", wrapped, FCDoControl->tidVerbose]; - FCMonitor[ - (* This is the replacement list Integral->Solution *) - repSolList = MapIndexed[(Rule[loopIntegral[#1], First[solsList[[#2]]]]) &, uniqueCanIndexList]; - (* This is the replacement list Canonicalized Lorentz index -> Original Lorentz index *) - reversedRepIndexList = Map[(Reverse /@ #) &, repIndexList]; - (* This is the list of the reduced original integrals *) - canIndexList = loopIntegral/@canIndexList; - reducedLoopList = MapIndexed[((#1 /. First[(reversedRepIndexList[[#2]])])) &, (canIndexList /.repSolList)]; - (* This is the final replacement list Original integral -> Reduced integral *) - finalRepList = MapIndexed[(Rule[loopIntegral[#1], First[reducedLoopList[[#2]]]]) &, loopListOrig]//Dispatch, - Grid[{{"Preparing the list of final subsitutions", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ]; - FCMonitor[ - FCPrint[1,"TID: Final list of replacements: ", finalRepList, FCDoControl->tidVerbose]; - FCPrint[1,"TID: To be applied on: ", wrapped, FCDoControl->tidVerbose]; (* And this is the final result *) res = wrapped/.finalRepList/.tidPaVe->Identity, - Grid[{{"Substituting the reductions of the tensor part", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ]; - FCMonitor[ - (* Make sure that the reduction worked out correctly *) - If[ !FreeQ2[FRH[solsList]/. FeynAmpDenominator[__] :> Unique[], {q,tidSingleIntegral,tidReduce,tidConvert}], - Message[TID::failmsg, "Running 2 tidSingleIntegral failed to achieve full tensor reduction of the unique integrals in", solsList]; - Abort[] + + res = wrapped/.tidPaVe->Identity ]; - (* Check again that the parts of the final result contain only scalar intnegrals *) - If[ (!FreeQ[FRH[res]/. FeynAmpDenominator[__] :> Unique[], q]) || (!FreeQ[irrelevant/. FeynAmpDenominator[__] :> Unique[], q]), - Message[TID::failmsg, "tidSingleIntegral 3 failed to achieve full tensor reduction in", res+irrelevant]; - Abort[] - ], - Grid[{{"Checking the reduction", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] + + FCPrint[1, "TID: Done creating the final list of replacements, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + + If[ OptionValue[Check], + FCPrint[1, "TID: Doing some cross-checks.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + + If[ (!FreeQ[FRH[res] /. noTID -> 0 /. FeynAmpDenominator[__] :> Unique[], q]) || (!FreeQ[irrelevant/. { + FeynAmpDenominator[__] :> Unique[], TemporalMomentum[q] :> Unique[] }, q]), + Message[TID::failmsg, "tidSingleIntegral failed to achieve a full tensor reduction in", res+irrelevant]; + Abort[] + ]; + FCPrint[1, "TID: Cross-checks done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose] ]; - (* We hat to uncontract some Lorentz indices at the beginning, so we should better contract them + (* We had to uncontract some Lorentz indices at the beginning, so we should better contract them again at the end *) - If[ contractlabel && !FreeQ[res,LorentzIndex], - FCMonitor[ - res= Isolate[res,LorentzIndex,IsolateNames->isoContract]// - ReplaceAll[#,LorentzIndex[pp__]/;!FreeQ[{pp},HoldForm]:>FRH[LorentzIndex[pp]]]&// - Contract//ReplaceAll[#,Pair[pp__]/;!FreeQ[{pp},HoldForm]:>FRH[Pair[pp]]]&; - - If [OptionValue[ExpandScalarProduct], - res = ExpandScalarProduct[res] + + + + If[ contractlabel && !FreeQ2[res,{LorentzIndex,CartesianIndex}], + + FCPrint[1, "TID: Applying Isolate.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + res= Isolate[res,{LorentzIndex,CartesianIndex,holdExplicitLorentzIndex},IsolateNames->isoContract]// + ReplaceAll[#,LorentzIndex[z__]/;!FreeQ[{z},HoldForm]:>FRH[LorentzIndex[z]]]&// + ReplaceAll[#,CartesianIndex[z__]/;!FreeQ[{z},HoldForm]:>FRH[CartesianIndex[z]]]&; + FCPrint[1, "TID: Done applying Isolate, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After Isolate: ", res , FCDoControl->tidVerbose]; + + FCPrint[1, "TID: Applying Contract.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + res = Contract[res,FCI->True, ExpandScalarProduct->optExpandScalarProduct]// + ReplaceAll[#,Pair[z__]/;!FreeQ[{z},HoldForm]:>FRH[Pair[z]]]&// + ReplaceAll[#,CartesianPair[z__]/;!FreeQ[{z},HoldForm]:>FRH[CartesianPair[z]]]&; + FCPrint[1, "TID: Done applying Contract, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After Contract: ", res , FCDoControl->tidVerbose]; + + If[ optExpandScalarProduct, + FCPrint[1, "TID: Applying ExpandScalarProduct.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + res = ExpandScalarProduct[res,FCI->True]; + FCPrint[1, "TID: Done applying ExpandScalarProduct, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After ExpandScalarProduct: ", res , FCDoControl->tidVerbose] ]; - res = res//FRH[#,IsolateNames->isoContract]&, - Grid[{{"Contracting Lorentz indices in the final expression", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ] - ]; - (* Check again that the parts of the final result contain only scalar intnegrals *) - If[ !FreeQ[FRH[res]/. FeynAmpDenominator[__] :> Unique[], q] || !FreeQ[irrelevant/. FeynAmpDenominator[__] :> Unique[], q], - Message[TID::failmsg, "tidSingleIntegral failed to achieve full tensor reduction in", res+irrelevant]; - Abort[] + + res = res//FRH[#,IsolateNames->isoContract]& ]; - (* Check that the isolated prefactors are free of loop-momenta and Lorentz indices*) - If[ !FreeQ2[Cases[res+irrelevant, HoldForm[__], Infinity]//DeleteDuplicates// - FRH[#,IsolateNames->tidIsolate]&,{q,LorentzIndex}], - Message[TID::failmsg, "Isolated prefactors of" <>ToString[res,InputForm] <> " contain loop momenta or isolated Lorentz indices."]; - Abort[] - ] - ]; + If[ OptionValue[Check], - (* The final result is a sum of the reduced tensor part and the original scalar part *) - res = res+irrelevant; + FCPrint[1, "TID: Doing some cross-checks.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; - If[ OptionValue[FeynAmpDenominatorCombine] && - !FreeQ2[res, (FeynAmpDenominator[xxx__]^_.) *(FeynAmpDenominator[yyy__]^_.)], - res = FeynAmpDenominatorCombine[res] - ]; + (* Check again that the parts of the final result contain only scalar intnegrals *) - If[ fds, - FCMonitor[ - res = FeynAmpDenominatorSimplify[res, q], - Grid[{{"Applying FDS to the final result", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] + If[ !FreeQ[FRH[res]/. noTID -> 0 /. FeynAmpDenominator[__] :> Unique[], q] || (!FreeQ[irrelevant/. { + FeynAmpDenominator[__] :> Unique[], TemporalMomentum[q] :> Unique[] }, q]), + Message[TID::failmsg, "tidSingleIntegral failed to achieve full tensor reduction in", res+irrelevant]; + Abort[] + ]; + + + (* Check that the isolated prefactors are free of loop-momenta and Lorentz indices*) + If[ !FreeQ2[Cases[res+irrelevant, HoldForm[__], Infinity]//DeleteDuplicates// + FRH[#,IsolateNames->tidIsolate]&,{q,LorentzIndex,CartesianIndex}], + Message[TID::failmsg, "Isolated prefactors of" <>ToString[res,InputForm] <> " contain loop momenta or isolated Lorentz indices."]; + Abort[] + ]; + FCPrint[1, "TID: Cross-checks done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose] ] - ]; + ]; + (* The final result is a sum of the reduced tensor part and the original scalar part *) + res = (res+irrelevant)/. noTID->1; - If [OptionValue[ToPaVe], - res = ToPaVe[res,q] + If[ OptionValue[FeynAmpDenominatorCombine] && !FreeQ2[res, (FeynAmpDenominator[x__]^_.) *(FeynAmpDenominator[y__]^_.)], + FCPrint[1, "TID: Applying FeynAmpDenominatorCombine.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + res = FeynAmpDenominatorCombine[res, FCI->True, Momentum->{q}]; + FCPrint[1, "TID: Done applying FeynAmpDenominatorCombine, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After FeynAmpDenominatorCombine: ", res , FCDoControl->tidVerbose] ]; (* Since the large prefactors are isolated, collecting w.r.t to the scalar loop integrals should not be too expensive. *) If[ OptionValue[Collecting], - FCMonitor[ - res= Collect2[res,Join[{FeynAmpDenominator},PaVeHeadsList],Factoring->Factor2], - Grid[{{"Collecting w.r.t the scalar loop integrals", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ] + FCPrint[1, "TID: Applying Collect2.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + fadCollect = Cases[res, FeynAmpDenominator[x__]/;!FreeQ2[{x},q], Infinity]; + res= Collect2[res,Join[Join[fadCollect,{q0}],PaVeHeadsList],Factoring->OptionValue[Factoring],TimeConstrained->optTimeConstrained]; + FCPrint[1, "TID: Done applying Collect2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After Collect2: ", res , FCDoControl->tidVerbose] + ]; (* The result with isolated prefactors is naturally more compact, but unless the user wants it explicitly, we will return him the full result with everything written out *) If[ OptionValue[Isolate]===False, - res = FRH[res, IsolateNames->tidIsolate], - FCMonitor[ + FCPrint[1, "TID: Removing abbreviations.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + res = FRH[res, IsolateNames->tidIsolate]; + FCPrint[1, "TID: Done removing abbreviations, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose], Which[ OptionValue[Isolate]===All, - res = Isolate[res,{q,FeynAmpDenominator}, IsolateNames->tidIsolate]/. + FCPrint[1,"TID: Improving abbreviations.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + res = Isolate[res,Join[{q,FeynAmpDenominator},FeynCalc`Package`PaVeHeadsList], IsolateNames->tidIsolate]/. { FeynAmpDenominator[x__]/;!FreeQ[{x},q] :> FRH[FeynAmpDenominator[x], IsolateNames->tidIsolate], + PaVe[x__] :> FRH[PaVe[x], IsolateNames->tidIsolate] + }; + FCPrint[1, "TID: Done improving abbreviations, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose], True, - res = Isolate[res,{q,FeynAmpDenominator,LorentzIndex}, IsolateNames->tidIsolate] - ], - Grid[{{"Isolating non-loop prefactors in the final result", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ] - ]; - If[ dimred, - res = res /. Momentum[aa_,n] :> Momentum[aa] + res = Isolate[res,{q,FeynAmpDenominator,LorentzIndex,CartesianIndex,holdExplicitLorentzIndex, + holdTemporalMomentum,holdTemporalPair}, IsolateNames->tidIsolate] + ] ]; - If [OptionValue[ExpandScalarProduct], - FCMonitor[ - res = ExpandScalarProduct[res], - Grid[{{"Expanding scalar products in the final result", - ProgressIndicator[Dynamic[Clock[Infinity]], Indeterminate]}}] - ] + res = res //. {holdExplicitLorentzIndex->ExplicitLorentzIndex, holdTemporalMomentum->TemporalMomentum,holdTemporalPair->TemporalPair, q0->q}; + + + If[ optExpandScalarProduct, + FCPrint[1, "TID: Applying ExpandScalarProduct.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + res = ExpandScalarProduct[res, FCI->True]; + FCPrint[1, "TID: Done applying ExpandScalarProduct, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After ExpandScalarProduct: ", res , FCDoControl->tidVerbose] + ]; - If [OptionValue[EpsEvaluate], - res = EpsEvaluate[res] + If [OptionValue[EpsEvaluate] && !FreeQ[res,Eps], + FCPrint[1, "TID: Applying EpsEvaluate.", FCDoControl->tidVerbose]; + time=AbsoluteTime[]; + res = EpsEvaluate[res, FCI->True]; + FCPrint[1, "TID: Done applying EpsEvaluate, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[3, "TID: After EpsEvaluate: ", res , FCDoControl->tidVerbose] ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; - (*$LimitTo4=limitto4;*) res - ]; + ]/; Head[q]=!=List; -tidSingleIntegral[int_, q_ , n_, dimred_, pavebasis_] := +tidSingleIntegral[int_, q_ , n_, pavebasis_] := Block[{ ex=int,res,rank, iList1, uList1, iList2, uList2, null, loopIntegral, nwr, sList1, sList2, rList2, rList1}, - FCPrint[1,"TID: tidSingleIntegral: Entering with ", ex, FCDoControl->tidVerbose]; + FCPrint[3, "TID: tidSingleIntegral: Entering with ", ex, FCDoControl->tidVerbose]; + + + ex = FCLoopPropagatorPowersExpand[ex,FCI->True]; - rank = ex/. (x : Pair[Momentum[q, n], LorentzIndex[_, n]] ..) FeynAmpDenominator[__] :> Length[{x}]; + Which[ + FreeQ[ex, CartesianIndex] && !FreeQ[ex,LorentzIndex], + rank = ex/. (x : Pair[Momentum[q, n], LorentzIndex[_, n]] ..) FeynAmpDenominator[__] :> Length[{x}], + FreeQ[ex, LorentzIndex] && !FreeQ[ex, CartesianIndex], + rank = ex/. (x : CartesianPair[CartesianMomentum[q, n-1], CartesianIndex[_, n-1]] ..) FeynAmpDenominator[__] :> Length[{x}], + True, + Message[TID::failmsg, "tidSingleIntegral failed to determine the integral type. "]; + Abort[] + ]; FCPrint[2, "TID: tidSingleIntegral: We are dealing with a rank ", rank, " integral.", FCDoControl->tidVerbose]; If [ !MatchQ[rank, _Integer?Positive], @@ -474,6 +619,7 @@ (* Note that if the integral contains vanishing Gram determinants, tidReduce will return the result in terms of PaVe integrals and then there is not much left to do here *) + ex=tidReduce[tidConvert[ex,q],q,n,pavebasis]; (* This wraps loop-momentum dependent pieces in the output of tidReduce into @@ -482,7 +628,7 @@ of fishing them out from huge prefactors. Note that we need some special care to protect the PaVe functions if they appear in the final result *) iList1 = (Map[SelectFree[#, {q,tidPaVe}] loopIntegral[SelectNotFree[#, {q,tidPaVe}]] &, - Expand2[ex, LorentzIndex] + null] /. null -> 0); + Expand2[ex, {LorentzIndex, CartesianIndex}] + null] /. null -> 0); (* Create a list of unique loopIntegrate pieces from the previous list *) uList1 = iList1 //Union[Cases[{#}, _. loopIntegral[x_] :> x, Infinity]] & // @@ -491,7 +637,7 @@ (* Now we expand the loopIntegrate pieces in q thus breaking them into sums of scalar and tensor integrals *) iList2 = ((Map[SelectFree[#, {q,tidPaVe}] loopIntegral[SelectNotFree[#, {q,tidPaVe}]] &, # + - null] /.null -> 0) & /@ (Collect2[#, {q, FeynAmpDenominator}] & /@uList1)); + null] /.null -> 0) & /@ (Collect2[#, {q, FeynAmpDenominator}, TimeConstrained->optTimeConstrained] & /@uList1)); (* Again, create a list of unique loopIntegrate pieces from the previous list. This list contains all the unique integrals from the original tensor integral that need @@ -500,49 +646,57 @@ uList2 = iList2 // Union[Cases[{#}, _. loopIntegral[x_]/;(FreeQ[x,tidPaVe] && !FreeQ[x/.FeynAmpDenominator[__]:>1,q]) :> x, Infinity]] & //DeleteDuplicates; - FCPrint[2,"TID: tidSingleIntegral: List of unique integrals ", uList2, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidSingleIntegral: List of unique integrals ", uList2, FCDoControl->tidVerbose]; (* Reduce all the integrals from uList2 into scalar integrals*) - nwr[exp_]:= (NestWhile[tidFullReduce[#,q,rank,n,dimred,pavebasis]&, exp, + nwr[e_]:= (NestWhile[tidFullReduce[#,q,n,pavebasis]&, e, ! FreeQ[# /. FeynAmpDenominator[__] :> Unique[], q] &, 1, rank+2]); sList2 = nwr/@uList2; - sList2 = Collect2[#,{q,FeynAmpDenominator}]&/@sList2; + sList2 = Collect2[#,{q,FeynAmpDenominator}, TimeConstrained->optTimeConstrained]&/@sList2; (* Here we drop all the scaleless integrals, unless something scaleless is wrapped in tidPaVe, which means that it comes from the PaVe functions*) - FCPrint[2,"TID: tidSingleIntegral: List of solutions before dropping non-loop terms ", sList2, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidSingleIntegral: List of solutions before dropping non-loop terms ", sList2, FCDoControl->tidVerbose]; sList2 = removeNonloop[#,q]&/@sList2; - FCPrint[2,"TID: tidSingleIntegral: List of solutions after dropping non-loop terms ", sList2, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidSingleIntegral: List of solutions after dropping non-loop terms ", sList2, FCDoControl->tidVerbose]; If[ !FreeQ[sList2/. FeynAmpDenominator[__] :> Unique[], q], Message[TID::failmsg, "tidSingleIntegral failed to achieve full tensor reduction in " <> ToString[sList2,InputForm]]; Abort[] ]; - FCPrint[2,"TID: tidSingleIntegral: uList1 ", uList1, FCDoControl->tidVerbose]; - FCPrint[2,"TID: tidSingleIntegral: uList2 ", uList2, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidSingleIntegral: uList1 ", uList1, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidSingleIntegral: uList2 ", uList2, FCDoControl->tidVerbose]; rList2 = MapIndexed[(Rule[loopIntegral[#1], First[sList2[[#2]]]]) &,uList2]; rList1 = MapIndexed[(Rule[loopIntegral[#1], First[(iList2 /. rList2)[[#2]]]]) &, uList1]; - res = Isolate[iList1 /. rList1 /. loopIntegral[z_tidPaVe]:>z, {LorentzIndex,q,FeynAmpDenominator,tidPaVe}, IsolateNames->tidIsolate]; + res = Isolate[iList1 /. rList1 /. loopIntegral[z_tidPaVe]:>z, {LorentzIndex,CartesianIndex, + q,FeynAmpDenominator,tidPaVe,holdExplicitLorentzIndex,holdTemporalMomentum,holdTemporalPair,q0}, IsolateNames->tidIsolate]; + + res = res /. { + FeynAmpDenominator[x__]/;!FreeQ[{x},q] :> FRH[FeynAmpDenominator[x]], + (h:CartesianIndex|CartesianMomentum)[x_,d_]:> h[x,FRH[d]] + }; + If[ (!FreeQ[res, loopIntegral]), Message[TID::failmsg, "tidSingleIntegral failed to achieve full tensor reduction in " <> ToString[sList2,InputForm]]; Abort[] ]; - FCPrint[2,"TID: tidSingleIntegral: Final result is ", res, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidSingleIntegral: Final result is ", res, FCDoControl->tidVerbose]; res - ]/; Head[int]=!=Plus && MatchQ[int,(FeynAmpDenominator[y__] /; ! FreeQ[{y}, q]) Times[ - Pair[Momentum[q, _ : 4], LorentzIndex[_, _ : 4]] ..]]; + ]/; Head[int]=!=Plus && (MatchQ[int,(FeynAmpDenominator[y__] /; ! FreeQ[{y}, q]) Times[ + Pair[Momentum[q, ___], LorentzIndex[_, ___]] ..]] || MatchQ[int,(FeynAmpDenominator[y__] /; ! FreeQ[{y}, q]) Times[ + CartesianPair[CartesianMomentum[q, ___], CartesianIndex[_, ___]] ..]]); -tidFullReduce[expr_,q_,rank_,n_, dimred_,pavebasis_]:= +tidFullReduce[expr_,q_,n_, pavebasis_]:= Block[{ ex=expr, sp, tp, tpSP, tpTP, res, time,uList,sList,rList, null1, null2, null3, null4, null, loopIntegral, tempIso,tpScaleless}, - FCPrint[2,"TID: tidFullReduce: Entering with ", ex, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Entering with ", ex, FCDoControl->tidVerbose]; If [FreeQ[ex /. FeynAmpDenominator[__] :> Unique[], q], Message[TID::failmsg, "Entered tidFullReduce with a purely scalar integral " <> ToString[ex,InputForm]]; @@ -561,26 +715,23 @@ "into tensor and scalar pieces in tidFullReduce failed."]; Abort[] ]; - FCPrint[2,"TID: tidFullReduce: Tensor parts tp", tp, FCDoControl->tidVerbose]; - FCPrint[2,"TID: tidFullReduce: Scalar parts sp", sp, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Tensor parts tp", tp, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Scalar parts sp", sp, FCDoControl->tidVerbose]; (* List of unique integrals in the tensor part *) tp = FCLoopIsolate[tp,{q},Head->loopIntegral,FCI->True]; uList = (Cases[tp+null1+null2,loopIntegral[__],Infinity]/.null1|null2->Unevaluated@Sequence[])//Union; - (*uList = (Map[SelectFree[#, {q}] loopIntegral[SelectNotFree[#, {q}]] &, - tp + null1+null2] /. null1|null2 -> 0) // Union[Cases[{#}, loopIntegral[x_], Infinity]]&// - DeleteDuplicates;*) - FCPrint[2,"TID: tidFullReduce: Entering FCApart with ", (uList/.loopIntegral->Identity), FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Entering FCApart with ", (uList/.loopIntegral->Identity), FCDoControl->tidVerbose]; (* Try to cancel all the scalar products in the denominators. This shouldn't require more than rank+1 iterations. However, it is not always possible to cancel all the scalar products without doing additional reductions *) time=AbsoluteTime[]; - sList = Map[ApartFF[(#/.loopIntegral->Identity),{q},FCI->True,FeynAmpDenominatorCombine->False]&,uList]; + sList = Map[ApartFF[(#/.loopIntegral->Identity),{q},FCI->True,FeynAmpDenominatorCombine->False, SetDimensions->{3,4,n,n-1}]&,uList]; - FCPrint[2,"TID: tidFullReduce: List of unique integrals after cancelling scalar products ", sList, + FCPrint[2, "TID: tidFullReduce: List of unique integrals after cancelling scalar products ", sList, FCDoControl->tidVerbose]; (* Replacement list "Unique integral" -> "Simplified integral" *) @@ -589,12 +740,12 @@ (* Substitute simplified integrals back into the tensor part *) tp = tp/.rList; - FCPrint[2,"TID: tidFullReduce: FCApart time: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; - FCPrint[2,"TID: tidFullReduce: After FCApart: ", tp, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: FCApart time: ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: After FCApart: ", tp, FCDoControl->tidVerbose]; (* After FCApart our original tensor part contains both tensor and scalar pieces. Separate them again *) time=AbsoluteTime[]; - tp = Collect2[tp,{q,FeynAmpDenominator}] + null3 + null4; + tp = Collect2[tp,{q,FeynAmpDenominator}, TimeConstrained->optTimeConstrained] + null3 + null4; tpSP = Select[tp, FreeQ[# /. FeynAmpDenominator[__] :> Unique[], q] &]; tpTP = Select[tp, ! FreeQ[# /. FeynAmpDenominator[__] :> Unique[], q] &]; If[tpSP + tpTP =!= tp || !FreeQ[tpTP,tidPaVe], @@ -602,10 +753,10 @@ "into tensor and scalar pieces in tidFullReduce failed."]; Abort[] ]; - FCPrint[2,"TID: tidFullReduce: Time to sort w.r.t to the loop momentum after FCApart ", + FCPrint[2, "TID: tidFullReduce: Time to sort w.r.t to the loop momentum after FCApart ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; - FCPrint[2,"TID: tidFullReduce: Tensor piece ", tpTP, FCDoControl->tidVerbose]; - FCPrint[2,"TID: tidFullReduce: Scalar piece ", tpSP, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Tensor piece ", tpTP, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Scalar piece ", tpSP, FCDoControl->tidVerbose]; (* Here we get rid of all the non-loop terms in the results, except for tidPaVe *) tpTP = removeNonloop[tpTP, q]; @@ -618,18 +769,16 @@ products can't be cancelled by FCApart. To get rid of those we need to perform another tensor decomposition on those integrals *) If[tpTP=!=0, - FCPrint[2,"TID: tidFullReduce: Looks like we need another tensor reduction for ", tpTP, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Looks like we need another tensor reduction for ", tpTP, FCDoControl->tidVerbose]; time=AbsoluteTime[]; tpTP = FCLoopIsolate[tpTP,{q},Head->loopIntegral,FCI->True]; (* Doing the brute force tensor reduction of the whole new tensor part might take a lot of time. Instead, we identify only unique integrals, reduce them separately and substitute the results into the original expression. *) uList = (Cases[tpTP+null1+null2,loopIntegral[__],Infinity]/.null1|null2->Unevaluated@Sequence[])//Union; - (* uList = (Map[SelectFree[#, {q}] loopIntegral[SelectNotFree[#, {q}]] &, - tpTP + null] /. null -> 0)// Union[Cases[{#}, loopIntegral[x_], Infinity]]& // DeleteDuplicates;*) (* Uncontract is done with the same options as in the beginning of TID *) - sList = (Uncontract[(#/.loopIntegral->Identity), q, Pair -> All, DimensionalReduction -> dimred(*, Dimension -> n*)]&)/@uList; + sList = (Uncontract[(#/.loopIntegral->Identity), q, Pair -> All, CartesianPair->All]&)/@uList; sList = SelectFree[#,{q}] tidReduce[tidConvert[SelectNotFree[#,{q}],q],q,n,pavebasis]&/@sList; rList = MapIndexed[(Rule[#1, First[sList[[#2]]]]) &, uList]; tpTP = tpTP/.rList; @@ -639,32 +788,32 @@ " in tidFullReduce failed."]; Abort[] ]; - FCPrint[2,"TID: tidFullReduce: Time to perform another tensor reduction ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; - FCPrint[2,"TID: tidFullReduce: Tensor part after another tensor reduction ", tpTP, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Time to perform another tensor reduction ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Tensor part after another tensor reduction ", tpTP, FCDoControl->tidVerbose]; (* To perform the tensor reduction on unique integrals in the tensor part we had to uncontract all the loop momenta. Now we contract existing dummy Lorentz indices *) time=AbsoluteTime[]; - tpTP = Isolate[tpTP,LorentzIndex,IsolateNames->tempIso]; - tpTP = Contract[tpTP]; + tpTP = Isolate[tpTP,{LorentzIndex,CartesianIndex,holdExplicitLorentzIndex,holdTemporalMomentum,holdTemporalPair,q0},IsolateNames->tempIso]; + tpTP = Contract[tpTP, FCI->True]; tpTP = FRH[tpTP,IsolateNames->tempIso]; - FCPrint[2,"TID: tidFullReduce: Time to contract Lorentz indices after another tensor reduction ", + FCPrint[2,"TID: tidFullReduce: Time to contract the indices after another tensor reduction ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; FCPrint[2,"TID: tidFullReduce: Tensor piece after contracting Lorentz indices ", tpTP, FCDoControl->tidVerbose]; - If [!FreeQ[tpTP,LorentzIndex], - Message[TID::failmsg, "Contracting Lorentz indices in " <> ToString[tpTP] <> + If [!FreeQ2[tpTP,{LorentzIndex,CartesianIndex}], + Message[TID::failmsg, "Contracting indices in " <> ToString[tpTP] <> " in tidFullReduce failed."]; Abort[] ] ]; (* The final step is to isolate all the prefactors that don't depend on the loop momentum in the full result *) time=AbsoluteTime[]; - res = Isolate[Collect2[(sp + tpSP + tpTP), {q,FeynAmpDenominator,tidPaVe}]//. - {null1 | null2 | null3 | null4 -> 0}, {q, FeynAmpDenominator,tidPaVe}, IsolateNames->tidIsolate] /. Pair[x__] /; - !FreeQ[{x}, q] :> FRH[Pair[x], IsolateNames->tidIsolate]; - FCPrint[2,"TID: tidFullReduce: Time to sort the final result of this iteration ", N[AbsoluteTime[] - time, 4], + res = Isolate[Collect2[(sp + tpSP + tpTP), {q,FeynAmpDenominator,tidPaVe, q0}, TimeConstrained->optTimeConstrained]//. + {null1 | null2 | null3 | null4 -> 0}, {q, FeynAmpDenominator,tidPaVe, q0}, IsolateNames->tidIsolate] /. + (h: Pair|CartesianPair|FeynAmpDenominator)[x__] /; !FreeQ[{x}, q] :> FRH[h[x], IsolateNames->tidIsolate]; + FCPrint[2, "TID: tidFullReduce: Time to sort the final result of this iteration ", N[AbsoluteTime[] - time, 4], FCDoControl->tidVerbose]; - FCPrint[2,"TID: tidFullReduce: Result of this iteration ", res, FCDoControl->tidVerbose]; - FCPrint[2,"TID: tidFullReduce: --------------------------------------------------------", FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: Result of this iteration ", res, FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidFullReduce: --------------------------------------------------------", FCDoControl->tidVerbose]; res ]/; Head[expr]=!=tidPaVe; @@ -683,7 +832,7 @@ <> ToString[expr] <> " in TID failed."]; Abort[] ]; - FCPrint[3,"TID: removeScaleless: Dropping scaleless integrals ",scaleless]; + FCPrint[3, "TID: removeScaleless: Dropping scaleless integrals ",scaleless]; (expr-scaleless)/. {null1|null2 -> 0} ]/; Head[expr]=!=List; @@ -700,7 +849,7 @@ <> ToString[expr, InputForm] <> " in TID failed."]; Abort[] ]; - FCPrint[3,"TID: removeNonloop: Dropping scaleless integrals ", nonloop]; + FCPrint[3, "TID: removeNonloop: Dropping scaleless integrals ", nonloop]; (expr-nonloop)/. {null1|null2 -> 0} ]/; Head[expr]=!=List; @@ -708,65 +857,125 @@ tidConvert[expr_, q_]:= Block[{ex=expr,qQQprepare,getfdp,res,temp}, - FCPrint[2,"TID: tidConvert: Entering with ", expr]; + FCPrint[2, "TID: tidConvert: Entering with ", expr]; getfdp[w__] := - (ffdp@@(First/@(MomentumCombine[{w}] /. q->0)) /. Momentum[a_,_:4] :> a)/; - FreeQ[{w}, PropagatorDenominator[_ Momentum[q, ___] + _., _]]; + (ffdp@@(First/@(MomentumCombine[{w},FCI->True,FV->False,SP->False] /. q->0)) /. Momentum[a_,___] :> a)/; + FreeQ[{w}, (PropagatorDenominator|StandardPropagatorDenominator)[_ Momentum[q, ___] + _., __]]; (* get the momenta on which the integral depends *) - qQQprepare[FeynAmpDenominator[any__] f_ /; (!FreeQ[f, Momentum[q,___]])] := - (FeynAmpDenominator[any] qQQ[getfdp[any] f]) /; FreeQ[f, OPEDelta]; + qQQprepare[FeynAmpDenominator[a__] f_ /; (!FreeQ[f, Momentum[q,___]])] := + (FeynAmpDenominator[a] qQQ[getfdp[a] f]) /; FreeQ[f, OPEDelta]; + + qQQprepare[FeynAmpDenominator[a__] f_ /; (!FreeQ[f, Momentum[q,___]])] := + (FeynAmpDenominator[a] SelectNotFree[SelectNotFree[f,q],OPEDelta]* + qQQ[Append[getfdp[a],OPEDelta] f/SelectNotFree[SelectNotFree[f,q],OPEDelta]])/; + !FreeQ[SelectNotFree[f,q], OPEDelta] && (getfdp[a]=!=1); (* avoid tadpoles *) - qQQprepare[FeynAmpDenominator[any__] f_ /; (!FreeQ[f, Momentum[q,___]])] := - (FeynAmpDenominator[any] SelectNotFree[SelectNotFree[f,q],OPEDelta]* - qQQ[Append[getfdp[any],OPEDelta] f/SelectNotFree[SelectNotFree[f,q],OPEDelta]])/; - !FreeQ[SelectNotFree[f,q], OPEDelta] && (getfdp[any]=!=1); (* avoid tadpoles *) temp = qQQprepare[ex]; res = temp/. ffdp[0,r___]:>ffdp[r]; + If[ !FreeQ[res,qQQprepare] || FreeQ[res,qQQ] || !MatchQ[temp, _ qQQ[ffdp[0,___] _ ]], Message[TID::failmsg, "tidConvert failed to prepare the integral " <> ToString[res]]; Abort[] ]; + FCPrint[4, "TID: tidConvert: Leaving with ", res]; + res + ]/; Head[expr]=!=Plus && MatchQ[expr,(FeynAmpDenominator[(x : (PropagatorDenominator|StandardPropagatorDenominator)[__] ..)] /; + !FreeQ[{x}, q]) Times[Pair[Momentum[q, ___], LorentzIndex[_, ___]] ..]]; + +tidConvert[expr_, q_]:= + Block[{ex=expr,qQQprepare,getfdp,res,temp}, + FCPrint[2, "TID: tidConvert: Entering with ", expr]; + getfdp[w__] := + (ffdp@@(First/@(MomentumCombine[{w},FCI->True,FV->False,SP->False] /. q->0)) /. CartesianMomentum[a_,___] :> a)/; + FreeQ[{w}, CartesianPropagatorDenominator[_ CartesianMomentum[q, ___] + _., __]]; + + (* get the momenta on which the integral depends *) + qQQprepare[FeynAmpDenominator[a__] f_ /; (!FreeQ[f, CartesianMomentum[q,___]])] := + (FeynAmpDenominator[a] qQQ[getfdp[a] f]); + + temp = qQQprepare[ex]; + res = temp/. ffdp[0,r___]:>ffdp[r]; + + If[ !FreeQ[res,qQQprepare] || FreeQ[res,qQQ] || FreeQ[res,ffdp] || !MatchQ[temp, _ qQQ[ffdp[0,___] _ ]], + Message[TID::failmsg, "tidConvert failed to prepare the integral " <> ToString[res]]; + Abort[] + ]; res - ]/; Head[expr]=!=Plus && MatchQ[expr,(FeynAmpDenominator[x__] /; ! FreeQ[{x}, q]) Times[ - Pair[Momentum[q, _ : 4], LorentzIndex[_, _ : 4]] ..]]; + ]/; Head[expr]=!=Plus && FreeQ[expr,OPEDelta] && MatchQ[expr,(FeynAmpDenominator[(x : CartesianPropagatorDenominator[__] ..)]/; + !FreeQ[{x}, q]) Times[CartesianPair[CartesianMomentum[q, ___], CartesianIndex[_, ___]] ..]]; (* Integrals that have no FeynAmpDenominator correspond to the scaleless integrals and are zero in DR *) tidConvert[expr_, q_]:= - (FCPrint[2,"TID: tidConvert: Dropping the scaleless integral ", - expr, FCDoControl->tidVerbose]; 0)/; Head[expr]=!=Plus && - MatchQ[expr,Pair[Momentum[q, _ : 4], LorentzIndex[_, _ : 4]] | - HoldPattern[Times[Pair[Momentum[q, _ : 4], LorentzIndex[_, _ : 4]] ..]]]; + ( + FCPrint[2, "TID: tidConvert: Dropping the scaleless integral ", expr, FCDoControl->tidVerbose]; + 0 + )/; Head[expr]=!=Plus && MatchQ[expr,Pair[Momentum[q, ___], LorentzIndex[_, ___]] | + HoldPattern[Times[Pair[Momentum[q, ___], LorentzIndex[_, ___]] ..]]]; + +tidConvert[expr_, q_]:= + ( + FCPrint[2, "TID: tidConvert: Dropping the scaleless integral ", expr, FCDoControl->tidVerbose]; + 0 + )/; Head[expr]=!=Plus && MatchQ[expr,CartesianPair[CartesianMomentum[q, ___], CartesianIndex[_, ___]] | + HoldPattern[Times[CartesianPair[CartesianMomentum[q, ___], CartesianIndex[_, ___]] ..]]]; tidReduce[0,_,_,_]:= 0; tidReduce[int_,q_,n_,pavebasis_]:= -Block[{massless=False,masses,nPoint,tdeclist,pavePrepare,time,qrule, - vanishingGramDet=False,gramMatrix,res}, - If[pavebasis, - vanishingGramDet=True - ]; - If[MatchQ[int, _ FeynAmpDenominator[PropagatorDenominator[_, 0] ..]], +Block[{massless=False,masses,nPoint,time,qrule, + vanishingGramDet=False,gramMatrix,res,momList,cartesianIntegral}, + + + FCPrint[4, "TID: tidReduce: entering with: ", int, FCDoControl->tidVerbose]; + + Which[ + !FreeQ[int, PropagatorDenominator] && FreeQ[int, StandardPropagatorDenominator], + If[MatchQ[int, _ FeynAmpDenominator[PropagatorDenominator[_, 0] ..]], massless=True; + ]; + masses=Cases[int, PropagatorDenominator[_, x_] :> x^2, Infinity]; + cartesianIntegral=False, + + FreeQ[int, PropagatorDenominator] && !FreeQ[int, StandardPropagatorDenominator], + If[MatchQ[int, _ FeynAmpDenominator[StandardPropagatorDenominator[_, _, 0, _] ..]], + massless=True; + ]; + masses=Cases[int, StandardPropagatorDenominator[_,_, x_, _] :> -x, Infinity]; + cartesianIntegral=False, + + !FreeQ[int, CartesianPropagatorDenominator] && FreeQ2[int, {PropagatorDenominator,StandardPropagatorDenominator}], + If[MatchQ[int, _ FeynAmpDenominator[CartesianPropagatorDenominator[_, _, 0, _] ..]], + massless=True; + ]; + masses=Cases[int, CartesianPropagatorDenominator[_,_, x_, _] :> -x, Infinity]; + cartesianIntegral=True, + + True, + Message[TID::failmsg, "tidReduce failed to determine the integral type. "]; + Abort[] + ]; + + If[pavebasis && !cartesianIntegral, + vanishingGramDet=True ]; - masses=Cases[int, PropagatorDenominator[_, x_] :> x^2, Infinity]; If [ (massless && !MatchQ[masses,{0..}]) || Head[masses=!=List], - Message[TID::failmsg, "tidReduce failed to extract the mass - dependence of the integral " <> ToString[int, InputForm]]; + Message[TID::failmsg, "tidReduce failed to extract the mass dependence of the integral " <> ToString[int, InputForm]]; Abort[] ]; - nPoint = int/. _ FeynAmpDenominator[props__]:>Length[{props}]; + nPoint = int/. _ FeynAmpDenominator[p__]:>Length[{p}]; + If [ !MatchQ[nPoint, _Integer?Positive], Message[TID::failmsg, "tidReduce failed to extract the number of propagators in the integral " <> ToString[int, InputForm]]; Abort[] ]; - FCPrint[2,"TID: tidReduce: we are dealing with a ", nPoint, "-point function" FCDoControl->tidVerbose]; + FCPrint[2, "TID: tidReduce: we are dealing with a ", nPoint, "-point function", FCDoControl->tidVerbose]; If[Length[masses]=!=nPoint, @@ -777,112 +986,108 @@ (* If the integral doesn't depend on any external momenta, then there is no point to check the Gram determinant *) - If[(int/. _ qQQ[_ ffdp[xx___]]:>List@@fdp[xx])=!={}, - gramMatrix = (int/. _ qQQ[_ ffdp[xx___]]:>List@@fdp[xx])// - Table[2 ScalarProduct[#[[i]], #[[j]],Dimension->n], {i, 1, Length[#]}, {j, 1, Length[#]}] &; - If[!MatrixQ[gramMatrix] || !FreeQ2[gramMatrix,{FeynAmpDenominator,PropagatorDenominator}], - Message[TID::failmsg, "tidReduce failed to write down the Gram matrix of the integral" <> - ToString[int, InputForm]]; - Abort[] - ]; - If[ExpandScalarProduct[Det[gramMatrix]]===0, - vanishingGramDet = True - ] - ]; + momList = int/. _ qQQ[_ ffdp[x___]]:> List@@fdp[x]; - tdeclist[{vecs__}, {moms___}] := - {{vecs} /. {Pair[LorentzIndex[aa_, nn_], Momentum[bb_, nn_]] :> {bb, aa}}, {moms}}; - - pavePrepare[ex_,np_Integer?Positive,{moms___},{ms___}]:= - (FCPrint[3,"TID: pavePrepare: entering with ", {ex, np, {moms},{ms}}, FCDoControl->tidVerbose]; - ex/.FCGV["PaVe"][{nums__}]:> (I Pi^2)PaVe[nums, - ExpandScalarProduct[FeynCalc`Package`momentumRoutingDenner[{moms},ScalarProduct[#,#,Dimension->n]&]], - {ms}, PaVeAutoOrder->paveao, PaVeAutoReduce->pavear])/; - (Length[{moms}]+1)===Length[{ms}] && Length[{ms}]===np && !genpave; + If[ !cartesianIntegral, + FCPrint[4, "TID: tidReduce: Lorentzian integral!", FCDoControl->tidVerbose]; + (* Lorentzian integrals *) + If[momList=!={}, + If[ FCGramDeterminant[momList,Dimension->n] === 0, + vanishingGramDet = True + ]; + ]; + qrule = { + (* General reduction for integrals with non-vanishing Gram determinants *) + qQQ[ffdp[m___] (v : Pair[LorentzIndex[_, nn_], Momentum[_, nn_]] ..)]/; !vanishingGramDet :> + (Tdec[(Sequence @@ tdeclistLorentzian[{v}, List@@fdp[m]]), Dimension -> n, List -> False, FCE->False]), - pavePrepare[ex_,np_Integer?Positive,{moms___},{ms___}]:= - (FCPrint[3,"TID: pavePrepare: entering with ", {ex, np, {moms},{ms}}, FCDoControl->tidVerbose]; - ex/.FCGV["PaVe"][{nums__}]:>(I Pi^2)GenPaVe[{nums}, Thread[List[Flatten[-{0, moms}, 1], (PowerExpand/@Sqrt/@{ms})]]])/; - (Length[{moms}]+1)===Length[{ms}] && Length[{ms}]===np && genpave; + (* Reduction formulas up to 4-point functions for vanishing Gram determinants *) + qQQ[ffdp[m___] (v : Pair[LorentzIndex[_, nn_], Momentum[_, nn_]] ..)]* + FeynAmpDenominator[__]/; + vanishingGramDet :> + (FCPrint[3,"Trying to handle vanishing Gram determinants in", int, FCDoControl->tidVerbose]; + Tdec[(Sequence @@ tdeclistLorentzian[{v}, {m}]), Dimension -> n, BasisOnly -> True, + FeynCalcExternal->False]/.FCGV["PaVe"][x_]:>tidPaVe[pavePrepare[FCGV["PaVe"][x],nPoint,{m},masses, n]]) + }, + FCPrint[4, "TID: tidReduce: Cartesian integral!", FCDoControl->tidVerbose]; + (* Cartesian integrals *) + If[momList=!={}, + If[ FCGramDeterminant[momList,Dimension->n-1,Head->{CartesianPair,CartesianMomentum}] === 0, + vanishingGramDet = True; + Message[TID::failmsg, "Reduction of Cartesian integrals with vanishing Gram determinants is currently not supported."]; + Abort[] + ]; + ]; qrule = { (* General reduction for integrals with non-vanishing Gram determinants *) - qQQ[ffdp[moms___] (vecs : Pair[LorentzIndex[_, nn_], Momentum[_, nn_]] ..)]/; - !vanishingGramDet :> - (Tdec[(Sequence @@ tdeclist[{vecs}, List@@fdp[moms]]), Dimension -> n, List -> False, FCE->False]), + qQQ[ffdp[m___] (v : CartesianPair[CartesianIndex[_, nn_], CartesianMomentum[_, nn_]] ..)]/; !vanishingGramDet :> + (CTdec[(Sequence @@ tdeclistCartesian[{v}, List@@fdp[m]]), Dimension -> n-1, List -> False, FCE->False])(*, + (* Reduction formulas up to 4-point functions for vanishing Gram determinants *) - qQQ[ffdp[moms___] (vecs : Pair[LorentzIndex[_, nn_], Momentum[_, nn_]] ..)]* + qQQ[ffdp[m___] (v : Pair[LorentzIndex[_, nn_], Momentum[_, nn_]] ..)]* FeynAmpDenominator[__]/; vanishingGramDet :> - (FCPrint[1,"Trying to handle vanishing Gram determinants in", int, FCDoControl->tidVerbose]; - Tdec[(Sequence @@ tdeclist[{vecs}, {moms}]), Dimension -> n, BasisOnly -> True, - FeynCalcExternal->False]/.FCGV["PaVe"][xx_]:>tidPaVe[pavePrepare[FCGV["PaVe"][xx],nPoint,{moms},masses]]) - }; + (FCPrint[3,"Trying to handle vanishing Gram determinants in", int, FCDoControl->tidVerbose]; + Tdec[(Sequence @@ tdeclistLorentzian[{v}, {m}]), Dimension -> n, BasisOnly -> True, + FeynCalcExternal->False]/.FCGV["PaVe"][x_]:>tidPaVe[pavePrepare[FCGV["PaVe"][x],nPoint,{m},masses]])*) + } + + ]; + res = int /. qrule; + If[ !FreeQ[res,pavePrepare], Message[TID::failmsg, "tidReduce failed to convert the" <> ToString[res,InputForm] <> "to Passarino-Veltman coefficient functions."]; Abort[] ]; - If[ !FreeQ2[res,{qQQ,Pair[Momentum[q, _ : 4], LorentzIndex[_, _ : 4]]}], + + If[ !FreeQ2[res,{qQQ,Pair[Momentum[q, ___], LorentzIndex[__]], qQQ,CartesianPair[CartesianMomentum[q, ___], CartesianIndex[__]]}], Message[TID::failmsg, "tidReduce failed to reduce the integral " <> ToString[int,InputForm]]; Abort[] ]; FCPrint[3,"TID: tidReduce: leaving with ", res, FCDoControl->tidVerbose]; res ]/; Head[int]=!=Plus && int=!=0 && - MatchQ[int,(FeynAmpDenominator[y__] /; ! FreeQ[{y}, q])qQQ[(Pair[Momentum[q, _ : 4], LorentzIndex[_, _ : 4]] ..) _ffdp]]; + (MatchQ[int,(FeynAmpDenominator[y__] /; ! FreeQ[{y}, q])qQQ[(Pair[Momentum[q, ___], LorentzIndex[__]] ..) _ffdp]] || + MatchQ[int,(FeynAmpDenominator[y__] /; ! FreeQ[{y}, q])qQQ[(CartesianPair[CartesianMomentum[q, ___], CartesianIndex[__]] ..) _ffdp]]); -scsav[a_Momentum,b_Momentum] := - scsav[a,b] = ExpandScalarProduct[a,b]//Expand; -fdp[a___,0,b___] := - fdp[a,b]; -(* if there are same momenta but different masses *) -fdp[a___, b_, b_, c___] := - fdp[a,b,c]; (* CCC *) -(* some speciality for on-shell stuff *) -(* in dim. reg. *) -fspec[y_,_] := - y; -(* -fspec[y_,k_] := y /. FeynAmpDenominator :> fadd[k] /. fadd[k] :> - FeynAmpDenominator; -*) -fadd[k_][PropagatorDenominator[Momentum[k_, D], 0], - PropagatorDenominator[Momentum[k_, D] - Momentum[p_, D], 0] - ] := - 0 /; Pair[Momentum[p, D], Momentum[p, D]] === 0; -fadd[k_][PropagatorDenominator[Momentum[k_, D], 0], - PropagatorDenominator[Momentum[k_, D] + Momentum[p_, D], 0] - ] := - 0 /; Pair[Momentum[p,D], Momentum[p,D]] === 0; -(* -somehow this does not work, even though it should - -fspec[y_,k_] := - y //. {FeynAmpDenominator[PropagatorDenominator[Momentum[k, D], 0], - PropagatorDenominator[Momentum[k, D] - - Momentum[p_, D], 0] - ] :> 0 /; - (Pair[Momentum[p,D], Momentum[p,D]] === 0 - }; +tdeclistLorentzian[{vecs__}, {moms___}] := + {{vecs} /. {Pair[LorentzIndex[a_, nn_], Momentum[b_, nn_]] :> {b, a}}, {moms}}; -fspec[y_,k_] := - y//. {FeynAmpDenominator[PropagatorDenominator[Momentum[k, D], 0], - PropagatorDenominator[Momentum[k, D] + - Momentum[p_, D], 0] - ] :> 0 /; - Pair[Momentum[p, D], Momentum[p, D]] === 0 - }; +tdeclistCartesian[{vecs__}, {moms___}] := + {{vecs} /. {CartesianPair[CartesianIndex[a_, nn_], CartesianMomentum[b_, nn_]] :> {b, a}}, {moms}}; + + +pavePrepare[ex_,np_Integer?Positive,{moms___},{ms___}, dim_]:= + ( + FCPrint[3, "TID: pavePrepare: entering with ", {ex, np, {moms},{ms}}, FCDoControl->tidVerbose]; + ex/. FCGV["PaVe"][{n__}]:> + (I Pi^2)PaVe[n,ExpandScalarProduct[FeynCalc`Package`momentumRoutingDenner[{moms},ScalarProduct[#,#,Dimension->dim]&]], + {ms}, PaVeAutoOrder->paveao, PaVeAutoReduce->pavear] + )/; (Length[{moms}]+1)===Length[{ms}] && Length[{ms}]===np && !genpave; + +pavePrepare[ex_,np_Integer?Positive,{moms___},{ms___}, _]:= + ( + FCPrint[3, "TID: pavePrepare: entering with ", {ex, np, {moms},{ms}}, FCDoControl->tidVerbose]; + ex/.FCGV["PaVe"][{n__}]:>(I Pi^2)GenPaVe[{n}, Thread[List[Flatten[-{0, moms}, 1], (PowerExpand/@Sqrt/@{ms})]]] + )/; (Length[{moms}]+1)===Length[{ms}] && Length[{ms}]===np && genpave; + + +fdp[a___,0,b___] := + fdp[a,b]; +(* if there are same momenta but different masses *) +fdp[a___, b_, b_, c___] := + fdp[a,b,c]; (* CCC *) -*) FCPrint[1,"TID.m loaded."]; End[] diff --git a/FeynCalc/LoopIntegrals/TIDL.m b/FeynCalc/LoopIntegrals/TIDL.m index 5ad9b3cb1..f50f4131d 100644 --- a/FeynCalc/LoopIntegrals/TIDL.m +++ b/FeynCalc/LoopIntegrals/TIDL.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. -Copyright (C) 1990-2016 Rolf Mertig -Copyright (C) 1997-2016 Frederik Orellana -Copyright (C) 2014-2016 Vladyslav Shtabovenko +Copyright (C) 1990-2018 Rolf Mertig +Copyright (C) 1997-2018 Frederik Orellana +Copyright (C) 2014-2018 Vladyslav Shtabovenko *) (* :Summary: Library of tensor integral decomposition formulas. @@ -32,6 +32,9 @@ Begin["`TIDL`Private`"] +encli::usage=""; +tidl::usage=""; + Options[TIDL] = { Dimension -> D }; @@ -60,23 +63,30 @@ (*To add new (long) formulas the following compression mechanism is quite effective: -exp = Tdec[{{q, i1}, {q, i2}, {q, i3}, {q, i4}, {q, i5}, {q, i6}, {q, - i7}, {q, i8}}, {}, UseTIDL -> False, List -> False]; -exp2 = Collect2[exp, {q, FVD, MTD}]; -exp2 = Map[Isolate[#, HoldForm, IsolateNames -> ISO] &, -exp2 // ChangeDimension[#, 4] & // FCE // - ReplaceAll[#, D -> n] &]; -exp2 = Collect2[exp2, {q, HoldForm}] // FRH -z1 = Map[Isolate[#, HoldForm, IsolateNames -> ISO] &, +extmoms = {p1, p2} +tList = {{q1, mu}, {q1, nu}, {q2, rho}}; +exp = Tdec[tList, extmoms, UseTIDL -> False, List -> False]; +lmoms = Union[First /@ tList]; + +exp2 = Collect2[FCE[exp], Join[{lmoms}, {FVD, MTD}]]; +exp3 = Map[Isolate[#, HoldForm, IsolateNames -> ISO] &, exp2 // ChangeDimension[#, 4] & // FCE // ReplaceAll[#, D -> n] &]; -li = Cases[List@z1, HoldForm[ISO[__]], Infinity] // Union; +exp4 = Collect2[exp3, Join[{MT, FV, HoldForm}]] // FRH; +z1raw = Map[ +Isolate[#, HoldForm, IsolateNames -> ISO, IsolateTimes -> False] &, + exp4 // ChangeDimension[#, 4] & // FCE // ReplaceAll[#, D -> n] &]; +li = Cases[List@z1raw, HoldForm[ISO[__]], Infinity] // Union; +If[! FreeQ[FCI[li // FRH], LorentzIndex], +Print["Inconsistencies detected!"]; +Abort[] +] reru = MapIndexed[ Rule[#1, ToExpression[("s" <> ToString[Identity @@ #2])]] &, li] // Flatten; -z2 = Map[ReplaceAll[#, HoldForm[a_] :> Rule[HoldForm[a], a]] &, li]; -z1 = z1 /. reru; -z2 = z2 /. reru; +z2raw = Map[ReplaceAll[#, HoldForm[a_] :> Rule[HoldForm[a], a]] &, li]; +z1 = z1raw /. reru; +z2 = z2raw /. reru; reru2 = MapIndexed[ Rule[#1, ToExpression[("t" <> ToString[Identity @@ #2])]] &, Cases[z1, SP[_, _], Infinity] // Union] // Flatten; @@ -97,17 +107,30 @@ Cases[z2, MT[_, _], Infinity] // Union] // Flatten; reru2 = Join[reru2, reru3, reru4]; reru21 = Join[reru21, reru31, reru41]; -Put[{Collect2[z1 /. reru /. reru2, l], z2 /. reru21 /. reru2, -Map[Reverse, Join[reru21, reru2]]}, "formula.m"]; -bli = Union@Flatten[{(Join[reru, reru2, reru3, reru4, reru21, reru31, - reru41] /. {Rule[_, a_] :> a}), encli}] - - -Then edit formula.m and remove all spaces. Use following skeleton for Block - -Block[{bli}, -encli="formula.m"; -scpexp[encli,n] +finExp = (z1 /. reru /. reru2); +finRu1 = z2 /. reru21 /. reru2; +finRu2 = Map[Reverse, Join[reru21, reru2]]; +If[Collect2[ + FCE[(finExp //. finRu1 //. finRu2)] - + FCE[(ChangeDimension[exp2, 4] /. D -> n)], FV, MT] =!= 0, +Print["Formula incosistent!"]; +Abort[] +]; +Put[{finExp, finRu1, finRu2}, "formula.m"]; +bli = Union@ +Flatten[{(Join[reru, reru2, reru3, reru4, reru21, reru31, + reru41] /. {Rule[_, a_] :> a}), encli}]; +tmp = Import["formula.m", "Text"] ; +Export["formula.m", +"Block[" <> ToString[bli, InputForm] <> ",\n" <> +"encli=" <> +StringReplace[tmp, " " -> ""] <> ";\n" <> +"scpexp[encli,n]]", +"Text"]; + + +Then put the block from formula.m to the corresponding file in +FeynCalc/Tables/TIDL *) (* Load precomputed tensor integral decompositions from FeynCalc/Tables/TIDL *) diff --git a/FeynCalc/LoopIntegrals/TarcerToFC.m b/FeynCalc/LoopIntegrals/TarcerToFC.m index 229447801..b54bfe801 100644 --- a/FeynCalc/LoopIntegrals/TarcerToFC.m +++ b/FeynCalc/LoopIntegrals/TarcerToFC.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Conversion of TARCER integrals to FeynCalc ones *) @@ -20,7 +20,9 @@ in Tarcer-notation to the FeynCalc notation. \ See TFI for details on the convention. \ As in case of ToTFI, the 1/Pi^D and 1/Pi^D/2 prefactors are implicit, i.e. \ -TarcerToFC doesn't add them."; +TarcerToFC doesn't add them. \n +To recover momenta from scalar products use the option ScalarProduct e.g. as \ +in TarcerToFC[TBI[D, pp^2, {{1, 0}, {1, 0}}], {q1, q2}, ScalarProduct -> {{pp^2, p1}}]"; TarcerToFC::failmsg = "Error! TarcerToFC has encountered a fatal problem and \ must abort the computation. The problem reads: `1`"; @@ -32,31 +34,50 @@ Begin["`TarcerToFC`Private`"] -(* Care about TVi and TJi later *) +Options[TarcerToFC] = { + FCE -> False, + FCI -> False, + ScalarProduct -> {} +}; -Options[TarcerToFC] = {}; +TarcerToFC[expr_List, {q1_, q2_}, opts:OptionsPattern[]]:= + TarcerToFC[#, {q1, q2}, opts]&/expr; -momconv[0]:= - 0; +TarcerToFC[expr_/;Head[expr]=!=List, {q1_, q2_}, OptionsPattern[]] := + Block[{ ex, res, rules, tarcerHeads, tarcerInts, tarcerIntsConverted, + ruConv, dimsPresent, optScalarProduct, momConvRules, momconv}, -momconv[p_^2]:= - MemSet[momconv[p^2],p]; + tarcerHeads = {Tarcer`TFI,Tarcer`TVI,Tarcer`TJI,Tarcer`TBI,Tarcer`TAI}; + optScalarProduct = OptionValue[ScalarProduct]; -momconv[Pair[Momentum[p_,d_:4],Momentum[p_,d_:4]]]:= - MemSet[momconv[Pair[Momentum[p,d],Momentum[p,d]]],p]; + momConvRules = { + momconv[0]->0, + momconv[Pair[Momentum[p_,d___],Momentum[p_,d___]]] -> p + }; -momconv[SP[p_,p_]]:= - MemSet[momconv[SP[p,p]],p] + If[!MatchQ[optScalarProduct,{}|{{_,_}..}], + Message[TarcerToFC::failmsg,"The option ScalarProduct must be of the form {{m2,p1},{pp,p2},...}"]; + Abort[] + ]; -momconv[SPD[p_,p_]]:= - MemSet[momconv[SPD[p,p]],p] + If[ optScalarProduct=!={}, + momConvRules = Join[momConvRules,Map[Rule[momconv[#[[1]]], #[[2]]] &, optScalarProduct]] + ]; -momconv[pp_Symbol]:= - MemSet[momconv[pp],Sqrt[pp]]; + If[ !FCDuplicateFreeQ[First/@momConvRules], + Message[TarcerToFC::failmsg,"The rules given via the ScalarProduct option must be unambiguous."]; + Abort[] + ]; + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; -TarcerToFC[exp_, {q1_, q2_}, OptionsPattern[]] := - Block[ {out, rules}, + (* Nothing to do *) + If[ FreeQ2[ex,tarcerHeads], + ex + ]; If[ !FreeQ2[$ScalarProducts, {q1,q2}], Message[TarcerToFC::failmsg, "Some loop momenta have scalar product rules attached to them. Evaluation aborted!"]; @@ -65,7 +86,7 @@ rules = { - Tarcer`TFI[d_Symbol, pp_, {u_,v_,r_,s_,t_}, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_},{nu4_,m4_},{nu5_,m5_}}] :> + Tarcer`TFI[d_, pp_, {u_,v_,r_,s_,t_}, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_},{nu4_,m4_},{nu5_,m5_}}] :> Pair[Momentum[q1,d],Momentum[q1,d]]^u* Pair[Momentum[q2,d],Momentum[q2,d]]^v* Pair[Momentum[momconv[pp],d],Momentum[q1,d]]^r* @@ -73,29 +94,54 @@ Pair[Momentum[q1,d],Momentum[q2,d]]^t* FCI[FAD[{q1,m1,nu1},{q2,m2,nu2},{q1-momconv[pp],m3,nu3},{q2-momconv[pp],m4,nu4},{q1-q2,m5,nu5},Dimension->d]], - Tarcer`TFI[d_Symbol, pp_, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_},{nu4_,m4_},{nu5_,m5_}}] :> + + Tarcer`TFI[d_, pp_, dp_, {a_,b_}, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_},{nu4_,m4_},{nu5_,m5_}}] :> + Pair[Momentum[dp,d],Momentum[q1,d]]^a* + Pair[Momentum[dp,d],Momentum[q2,d]]^b* + Identity[FAD[{q1,m1,nu1},{q2,m2,nu2},{q1-momconv[pp],m3,nu3},{q2-momconv[pp],m4,nu4},{q1-q2,m5,nu5},Dimension->d]], + + Tarcer`TFI[d_, pp_, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_},{nu4_,m4_},{nu5_,m5_}}] :> FCI[FAD[{q1,m1,nu1},{q2,m2,nu2},{q1-momconv[pp],m3,nu3},{q2-momconv[pp],m4,nu4},{q1-q2,m5,nu5},Dimension->d]], - Tarcer`TFI[d_Symbol, pp_, {nu1_,nu2_,nu3_,nu4_,nu5_}] :> + Tarcer`TFI[d_, pp_, {nu1_,nu2_,nu3_,nu4_,nu5_}] :> FCI[FAD[{q1,0,nu1},{q2,0,nu2},{q1-momconv[pp],0,nu3},{q2-momconv[pp],0,nu4},{q1-q2,0,nu5},Dimension->d]], - Tarcer`TVI[d_Symbol, pp_, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_},{nu4_,m4_}}] :> + Tarcer`TVI[d_, pp_, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_},{nu4_,m4_}}] :> FCI[FAD[{q1-q2,m1,nu1},{q2,m2,nu2},{q1-momconv[pp],m3,nu3},{q2-momconv[pp],m4,nu4},Dimension->d]], - Tarcer`TJI[d_Symbol, pp_, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_}}] :> + Tarcer`TJI[d_, pp_, {{nu1_,m1_},{nu2_,m2_},{nu3_,m3_}}] :> FCI[FAD[{q1,m1,nu1},{q1-q2,m2,nu2},{q2-momconv[pp],m3,nu3},Dimension->d]], - Tarcer`TBI[d_Symbol, pp_, {{nu1_,m1_},{nu2_,m2_}}] :> + Tarcer`TBI[d_, pp_, {{nu1_,m1_},{nu2_,m2_}}] :> FCI[FAD[{q1,m1,nu1},{q1-momconv[pp],m2,nu2},Dimension->d]], - Tarcer`TAI[d_Symbol, 0, {{nu1_,m1_}}] :> + Tarcer`TAI[d_, 0, {{nu1_,m1_}}] :> FCI[FAD[{q1,m1,nu1},Dimension->d]] }; - out = exp /. Dispatch[rules]; - out + tarcerInts = Cases2[ex,tarcerHeads]; + + dimsPresent = Union[First/@tarcerInts]; + + tarcerIntsConverted = tarcerInts/. Dispatch[rules] /. momConvRules; + ruConv = Thread[Rule[tarcerInts,tarcerIntsConverted]]; + + (* + If the p.p was replaced by a mass squared, we obviously cannot recover the original momentum. + It is up to the user to do that. Th + *) + + ruConv = SelectFree[ruConv,momconv]; + + res = ex /. Dispatch[ruConv]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res ]; FCPrint[1,"TarcerToFC.m loaded."]; diff --git a/FeynCalc/LoopIntegrals/Tdec.m b/FeynCalc/LoopIntegrals/Tdec.m index 3b790e16c..12bf6cad7 100644 --- a/FeynCalc/LoopIntegrals/Tdec.m +++ b/FeynCalc/LoopIntegrals/Tdec.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Computes tensor decompositions for multiloop integrals @@ -19,7 +19,7 @@ Tdec::usage = "Tdec[{q,mu}, {p}]; \ Tdec[{{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}] or \ Tdec[exp, {{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}] \ -calculates the tensorial decomposition formulas. \ +calculates the tensorial decomposition formulas for Lorentzian integrals. \ The more common ones are saved in TIDL."; UseParallelization::usage = @@ -75,14 +75,15 @@ symmMT::usage=""; Options[Tdec] = { - BasisOnly -> False, - Dimension -> D, - FCVerbose -> False, - Factoring -> Factor2, - FeynCalcExternal -> True, - List -> True, - UseParallelization -> True, - UseTIDL -> True + BasisOnly -> False, + Dimension -> D, + FCVerbose -> False, + Factoring -> {Factor2, Factor}, + FCE -> True, + Head -> Identity, + List -> True, + UseParallelization -> True, + UseTIDL -> True }; SetAttributes[symmMT,Orderless]; @@ -242,7 +243,7 @@ index lists (via Tuples) is much simpler, as compared to the metric (* Here one has to be careful; We can exchange the indices according to the symmetries, - but we are not allowed to change the overall oredering. Consider for example + but we are not allowed to change the overall ordering. Consider for example {{1,0,0},{nu,mu,rho},{nu,rho}} {{1,0,0},{rho,mu,nu},{nu,rho}} The ordering {1,0,0} is fixed by the tensor structure, i.e. we cannot @@ -323,7 +324,7 @@ index lists (via Tuples) is much simpler, as compared to the metric Tdec[exp_:1, li : {{_, _} ..}, ppli_List/;FreeQ[ppli,OptionQ], OptionsPattern[]] := Block[ {tt, factor, dim, proli, nccli, ccli, pli, eqli, neqli, nttt,listlabel, fce, - veqli, seqli, scqli, solu,ii,ex,ce,xy, + veqli, seqli, scqli, solu,ii,ex,ce,xy, optHead, extMom,basisonly,multiLoop=False,lis,mlis,basis,multiLoopSyms={}}, dim = OptionValue[Dimension]; @@ -331,10 +332,11 @@ index lists (via Tuples) is much simpler, as compared to the metric fce = OptionValue[FeynCalcExternal]; factor = OptionValue[Factoring]; basisonly = OptionValue[BasisOnly]; + optHead = OptionValue[Head]; If [OptionValue[FCVerbose]===False, tdecVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], tdecVerbose=OptionValue[FCVerbose] ] ]; @@ -374,7 +376,7 @@ index lists (via Tuples) is much simpler, as compared to the metric we have a 1-point function or were requested just to provide the tensor basis *) If[!basisonly && ppli=!={}, FCPrint[1, "Tdec: Checking Gram determinant...", FCDoControl->tdecVerbose]; - If[ExpandScalarProduct[Det[ppli//Table[2 ScalarProduct[#[[i]], #[[j]],Dimension->dim], {i, 1, Length[#]}, {j, 1, Length[#]}] &]]===0, + If[ FCGramDeterminant[ppli,Dimension->dim]===0, FCPrint[1, "Tensor decomposition with Tdec is not possible due to vanishing Gram determinants", FCDoControl->tdecVerbose]; tt=Apply[Times, Map[Pair[Momentum[#[[1]],dim], LorentzIndex[#[[2]],dim]]&, li]]; seqli={}; @@ -412,8 +414,8 @@ index lists (via Tuples) is much simpler, as compared to the metric If[ basisonly, If[multiLoop, (* for multiloop coefficient functions some more infos can be useful *) - Return[(basis/.extMom->Identity/.CC[xx__]:> FCGV["GCF"][xx,li,ppli])], - Return[(basis/.extMom->Identity/.CC[xx__]:> FCGV["PaVe"][xx])] + Return[(basis/.extMom->optHead/.CC[xx__]:> FCGV["GCF"][xx,li,ppli])], + Return[(basis/.extMom->optHead/.CC[xx__]:> FCGV["PaVe"][xx])] ] ]; FCPrint[1, "Tdec: symmetrized tensor basis ",basis, FCDoControl->tdecVerbose]; @@ -505,8 +507,8 @@ with the original tensor equations to get a system of linear (scalar) equations FCPrint[1, "Tdec: after solu substitution ", N[MemoryInUse[]/10^6,3], " MB ; time used ", TimeUsed[]//FeynCalcForm, FCDoControl->tdecVerbose]; FCPrint[2, "Tdec: tt: ", tt, FCDoControl->tdecVerbose]; FCPrint[2, "Tdec: seqli: ", seqli, FCDoControl->tdecVerbose]; - tt = tt/.extMom->Identity; - seqli = seqli/.extMom->Identity; + tt = tt/.extMom->optHead; + seqli = seqli/.extMom->optHead; If[ fce, tt = FeynCalcExternal[tt]; seqli = FeynCalcExternal[seqli]; diff --git a/FeynCalc/LoopIntegrals/ToPaVe.m b/FeynCalc/LoopIntegrals/ToPaVe.m index 5f008d0ae..41adcf4b0 100755 --- a/FeynCalc/LoopIntegrals/ToPaVe.m +++ b/FeynCalc/LoopIntegrals/ToPaVe.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Converts scalar 1-loop integrals to Passarino Veltman @@ -17,8 +17,8 @@ (* ------------------------------------------------------------------------ *) -ToPaVe::usage = "ToPaVe[expr,q] converts all the scalar 1-loop integrals that \ -depend on the momentum q to scalar Passarino Veltman functions +ToPaVe::usage = "ToPaVe[exp,q] converts all scalar 1-loop integrals in exp that \ +depend on the momentum q to scalar Passarino Veltman functions \ A0, B0, C0, D0 etc."; OtherLoopMomenta::usage = "OtherLoopMomenta is an option of ToPaVe. It takes \ @@ -39,48 +39,71 @@ momentumRoutingDenner; + Begin["`ToPaVe`Private`"] +optPaVeOrder::usage=""; genpave::usage=""; Options[ToPaVe] = { - GenPaVe->False, - OtherLoopMomenta -> {}, - PaVeAutoOrder -> True, - PaVeAutoReduce -> True + FCE -> False, + FCI -> False, + GenPaVe -> False, + OtherLoopMomenta -> {}, + PaVeAutoOrder -> True, + PaVeAutoReduce -> True, + PaVeOrder -> True }; ToPaVe[expr_, q_, OptionsPattern[]] := - Block[{ex,loopInt,irrel,rel,repList,res}, - + Block[{ ex, loopInt, irrel, rel, repList, res, loopList, + optOtherLoopMomenta, loopListEval}, If [!FreeQ[$ScalarProducts, q], - Message[ToPaVe::failmsg, "The loop momentum " <> ToString[q,InputForm] <> - " has scalar product rules attached to it."]; + Message[ToPaVe::failmsg, "The loop momentum " <> ToString[q,InputForm] <> " has scalar product rules attached to it."]; Abort[] ]; - genpave = OptionValue[GenPaVe]; + genpave = OptionValue[GenPaVe]; + optPaVeOrder = OptionValue[PaVeOrder]; + optOtherLoopMomenta = OptionValue[OtherLoopMomenta]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; - ex = FCLoopSplit[expr,{q}]; + ex = FCLoopSplit[ex,{q}, FCI->True]; irrel = ex[[1]]+ex[[3]]+ex[[4]]; rel = ex[[2]]; - rel = FCLoopIsolate[rel,{q},Head->loopInt]; + rel = FCLoopIsolate[rel,{q},Head->loopInt, FCI->True, GFAD->False, CFAD->False, SFAD->True]; + + loopList = Cases2[rel,loopInt]; + + loopListEval = FCLoopPropagatorPowersExpand[#,FCI->True]&/@(loopList/.loopInt->Identity); + + loopListEval = Map[ + If[ FreeQ2[#,optOtherLoopMomenta], + toPaVe[#,q,OptionValue[PaVeAutoOrder],OptionValue[PaVeAutoReduce]], + # + ]&,loopListEval]; - repList = - Union[Cases[{rel}, loopInt[x_] :> Rule[loopInt[x], - If[ FreeQ2[x,OptionValue[OtherLoopMomenta]], - toPaVe[x,q,OptionValue[PaVeAutoOrder],OptionValue[PaVeAutoReduce]], - x - ] - ], Infinity]]; - res = (rel/.repList) + irrel; + (* Not all SFADs can be converted to PaVe functions! *) + loopListEval = loopListEval /. toPaVe[z_,_,_,_]/;!FreeQ[z,StandardPropagatorDenominator] :> z; + + repList = Thread[Rule[loopList,loopListEval]]; + + res = (rel/. Dispatch[repList]) + irrel; If[ !FreeQ[res,toPaVe], Message[ToPaVe::failmsg,"Not all 1-loop scalar integrals could be converted to PaVe functions. Please apply FDS to the input and try again."]; Abort[] ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + res ]; @@ -91,7 +114,7 @@ momentumRoutingDenner[moms_List, fu_] := MemSet[momentumRoutingDenner[moms, fu], Block[{firstLines, lastLine, kmax = (Length[moms] + 1)/2, res, p, repRule}, - repRule = MapThread[Rule[#1, #2] &, {Table[p[i], {i, 1, 2 kmax - 1}], moms}]; + repRule = Thread[Rule[Table[p[i], {i, 1, 2 kmax - 1}], moms]]; firstLines = Transpose[Table[(p[k + l] - p[l])//fu, {l, 0, 2 kmax - 1}, {k, 1, kmax - 1}]]; lastLine = Table[(p[kmax + l] - p[l])//fu, {l, 0, kmax - 1}]; res = Join[Flatten[firstLines], lastLine] //. {p[2 kmax] -> p[0], p[x_] /; x > 2 kmax :> p[x - 2 kmax], p[0] -> 0}; @@ -99,21 +122,21 @@ Message[ToPaVe::failmsg, "Wrong number of the kinematic invariants!"]; Abort[] ]; - (res /. repRule) + (res /. Dispatch[repRule]) ] ]/; OddQ[(Length[moms])] momentumRoutingDenner[moms_List, fu_] := MemSet[momentumRoutingDenner[moms, fu], Block[{firstLines, lastLine, kmax = (Length[moms])/2, res, p, repRule}, - repRule = MapThread[Rule[#1, #2] &, {Table[p[i], {i, 1, 2 kmax}], moms}]; + repRule = Thread[Rule[Table[p[i], {i, 1, 2 kmax}], moms]]; res = Transpose[Table[(p[k + l] - p[l])//fu, {l, 0, 2 kmax}, {k, 1, kmax}]]; res = Flatten[res //. {p[2 kmax + 1] -> p[0], p[x_] /; (x > 2 kmax + 1) :> p[x - 2 kmax - 1], p[0] -> 0}]; If[Length[res] =!= (kmax*(2 kmax + 1)), Message[ToPaVe::failmsg, "Wrong number of the kinematic invariants!"]; Abort[] ]; - (res /. repRule) + (res /. Dispatch[repRule]) ] ]/; EvenQ[(Length[moms])] @@ -132,8 +155,34 @@ Message[ToPaVe::failmsg, "toPave: Wrong number of the kinematic invariants!"]; Abort[] ]; - res = I Pi^2 PaVeOrder[ PaVe[0, ExpandScalarProduct[(momentumRoutingDenner[tmp[[1]],pair[#,#]&]/.pair->Pair)], - Power[#, 2] & /@ Join[{m1},tmp[[2]]], PaVeAutoOrder->paveao, PaVeAutoReduce->pavear]]; + res = I Pi^2 PaVe[0, ExpandScalarProduct[(momentumRoutingDenner[tmp[[1]],pair[#,#]&]/.pair->Pair)], + Power[#, 2] & /@ Join[{m1},tmp[[2]]], PaVeAutoOrder->paveao, PaVeAutoReduce->pavear]; + + If[ optPaVeOrder, + res = PaVeOrder[res] + ]; + + res + ]/;!genpave; + +toPaVe[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q_, dim_], 0, mm1_, {1,1}], + re:StandardPropagatorDenominator[Momentum[q_, dim_] + _ : 0, 0, _, {1,1}] ...],q_,paveao_,pavear_]:= + Block[{tmp,res,pair}, + If[ {re} === {}, + tmp = {{},{}}, + tmp = Transpose[Cases[{re}, StandardPropagatorDenominator[Momentum[q, dim] + x_: 0,0, m_: 0, {1,1}] :> {x, -m}]]; + ]; + If[ Length[tmp[[1]]]=!=Length[{re}] || Length[tmp[[2]]]=!=Length[{re}], + Message[ToPaVe::failmsg, "toPave: Wrong number of the kinematic invariants!"]; + Abort[] + ]; + res = I Pi^2 PaVe[0, ExpandScalarProduct[(momentumRoutingDenner[tmp[[1]],pair[#,#]&]/.pair->Pair)], + Join[{-mm1},tmp[[2]]], PaVeAutoOrder->paveao, PaVeAutoReduce->pavear]; + + If[ optPaVeOrder, + res = PaVeOrder[res] + ]; + res ]/;!genpave; diff --git a/FeynCalc/LoopIntegrals/ToPaVe2.m b/FeynCalc/LoopIntegrals/ToPaVe2.m index 942945afc..6944c6b34 100755 --- a/FeynCalc/LoopIntegrals/ToPaVe2.m +++ b/FeynCalc/LoopIntegrals/ToPaVe2.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Converts scalar direct Passarino Veltman to PaVe functions *) @@ -30,8 +30,14 @@ Options[ToPaVe2] = { }; -ToPaVe2[expr_, OptionsPattern[]] := +ToPaVe2[expr_PaVe, OptionsPattern[]]:= + expr; + +ToPaVe2[expr_/;Head[expr]=!=PaVe, OptionsPattern[]] := Block[{ex}, + + + If[ !OptionValue[PaVe, PaVeAutoReduce], ex =expr /. { A0[m_, OptionsPattern[]] :> PaVe[0,{},{m}], diff --git a/FeynCalc/LoopIntegrals/ToSFAD.m b/FeynCalc/LoopIntegrals/ToSFAD.m new file mode 100755 index 000000000..e589e862e --- /dev/null +++ b/FeynCalc/LoopIntegrals/ToSFAD.m @@ -0,0 +1,88 @@ +(* ::Package:: *) + + + +(* :Title: ToSFAD *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Converts FADs and PropagatorDenominators to + SFADs and StandardPropagatorDenominators *) + +(* ------------------------------------------------------------------------ *) + + +ToSFAD::usage = "ToSFAD[exp] converts all propagator denominators written \ +as FAD or FeynAmpDenmoninator[...,PropagatorDenominator[...],...] to SFAD \ +or FeynAmpDenmoninator[...,StandardPropagatorDenominator[...],...] respectively."; + +ToSFAD::failmsg = +"Error! ToSFAD has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`ToSFAD`Private`"] + +optEtaSign::usage=""; + +Options[ToSFAD] = { + EtaSign -> 1 +}; + +fadArgToSfadArg[x_/;Head[x]=!=List]:= + {{x, 0}, {0, optEtaSign}, 1} + +fadArgToSfadArg[{x_, y_}]:= + {{x, 0}, {y^2, optEtaSign}, 1} + +fadArgToSfadArg[{x_, y_, n_}]:= + {{x, 0}, {y^2, optEtaSign}, n} + +ToSFAD[expr_, OptionsPattern[]] := + Block[{res,fads,pds,fadsConverted,pdsConverted,rulePds,ruleFads,ruleFinal}, + + If[ FreeQ2[{expr}, {FAD, PropagatorDenominator}], + (* Nothing to do. *) + Return[expr] + ]; + + optEtaSign = OptionValue[EtaSign]; + + fads = Cases2[expr, FAD]; + pds = Cases2[expr, PropagatorDenominator]; + + fadsConverted = fads /. { + FAD[a__, opt:OptionsPattern[]] :> SFAD@@(Join[fadArgToSfadArg/@{a},{opt}]) + }; + + pdsConverted = pds /. { + PropagatorDenominator[a_,b_] :> StandardPropagatorDenominator[a,0,b^2,{1, optEtaSign}] + }; + + ruleFads = Thread[Rule[fads,fadsConverted]]; + rulePds = Thread[Rule[pds,pdsConverted]]; + + ruleFinal = Dispatch[Join[ruleFads,rulePds]]; + + res = expr /.ruleFinal; + + If[ !FreeQ2[{res}, {FAD, PropagatorDenominator}], + Message[ToSFAD::failmsg,"Failed to eliminate all the occurences of FADs or PDs."] + ]; + + res + + ]; + + +FCPrint[1,"ToSFAD.m loaded."]; +End[] diff --git a/FeynCalc/LoopIntegrals/ToTFI.m b/FeynCalc/LoopIntegrals/ToTFI.m index a6d7be27d..ac0ae0317 100644 --- a/FeynCalc/LoopIntegrals/ToTFI.m +++ b/FeynCalc/LoopIntegrals/ToTFI.m @@ -27,14 +27,32 @@ Begin["`ToTFI`Private`"] toTFIVerbose::usage=""; +qq::usage=""; +mM::usage=""; + +c1::usage=""; +c2::usage=""; +c3::usage=""; +c4::usage=""; +c5::usage=""; +c6::usage=""; +dq1::usage=""; +dq2::usage=""; +pq1::usage=""; +pq2::usage=""; +q1q1::usage=""; +q1q2::usage=""; +q2q2::usage=""; Options[ToTFI] = { - Dimension -> D, - FCVerbose->False, - Method -> Automatic, - FDS -> True, - Collecting -> True, - ApartFF -> False + ApartFF -> False, + Collecting -> True, + Dimension -> D, + FCVerbose -> False, + FDS -> True, + FCI -> False, + Method -> Automatic, + TID -> False }; @@ -49,37 +67,98 @@ ToTFI[a_/;Head[a]=!=Plus,{q_},{p_},opts:OptionsPattern[]] := ToTFI[a,q,p,opts]/; !OptionQ[{p}]; -ToTFI[a_/;Head[a]=!=Plus,q_/;Head[q]=!=List,p_/;Head[p]=!=List,opts:OptionsPattern[]] := - (ToExpression["TFIRecurse"][ - FCE[ToTFI[FDS[FCI[Expand[FAD[{qq, mM}] Expand[ApartFF[a, {q}], q]]],q], q, qq, p, opts]]/. - ToExpression["TFI"]:>ToExpression["TFR"]] /. ToExpression["TAI"][_, 0, {{1, mM}}] :> 1 - ) /; MemberQ[$ContextPath, "Tarcer`"] && !OptionQ[p]; +ToTFI[expr_/;Head[expr]=!=Plus,q_/;Head[q]=!=List,p_/;Head[p]=!=List,opts:OptionsPattern[]] := + Block[{ex, tmp, res}, + + If [OptionValue[FCVerbose]===False, + toTFIVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + toTFIVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[3, "ToTFI (1-loop): Entering with ", expr, FCDoControl->toTFIVerbose]; + + If[OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ OptionValue[TID], + FCPrint[1, "ToTFI (1-loop): Applying TID.", FCDoControl->toTFIVerbose]; + ex = TID[ex,q, FCI->True]; + FCPrint[3, "ToTFI (1-loop): After TID: ", ex, FCDoControl->toTFIVerbose], + + + FCPrint[1, "ToTFI (1-loop): Applying ApartFF.", FCDoControl->toTFIVerbose]; + ex = ApartFF[ex, {q}, FCI->True]; + FCPrint[3, "ToTFI (1-loop): After ApartFF: ", ex, FCDoControl->toTFIVerbose] + ]; + + tmp = Expand[FDS[FeynAmpDenominator[PropagatorDenominator[Momentum[qq, D], mM]] ex, q, qq],q]; + FCPrint[3, "ToTFI (1-loop): Fake 2-loop integral: ", tmp, FCDoControl->toTFIVerbose]; + + tmp = ToTFI[tmp,q, qq, p, FCI->True, opts] /. Tarcer`TFI -> Tarcer`TFR; + FCPrint[3, "ToTFI (1-loop): After ToTFI: ", tmp, FCDoControl->toTFIVerbose]; + + tmp = Tarcer`TFIRecurse[tmp]; + FCPrint[3, "ToTFI (1-loop): After TFIRecurse: ", tmp, FCDoControl->toTFIVerbose]; + + res = tmp /. { + Tarcer`TAI[_, 0, {{1, mM}}] :> 1, + Tarcer`TAI[_, {{1, mM}}] :> 1 + }; + + FCPrint[3, "ToTFI (1-loop): After removing fake tadpoles: ", res, FCDoControl->toTFIVerbose]; + + If[ !FreeQ2[res,{mM,qq}], + Message[ToTFI::failmsg, "Failed to perform reduction of 1-loop scalar integrals. Try to rerun ToTFI with TID->True"]; + Abort[] + ]; + + FCPrint[3, "ToTFI (1-loop): Leaving. ", FCDoControl->toTFIVerbose]; + FCPrint[3, "ToTFI (1-loop): Leaving with: ", res, FCDoControl->toTFIVerbose]; + + res + + + ] /; MemberQ[$ContextPath, "Tarcer`"] && !OptionQ[p]; (* 2-loops *) ToTFI[expr_, {q1_,q2_},{p_},opts:OptionsPattern[]] := ToTFI[expr, q1,q2,p,opts]/; !OptionQ[{p}]; ToTFI[expr_, q1_/;Head[q1]=!=List,q2_/;Head[q2]=!=List,p_/;Head[p]=!=List,opts:OptionsPattern[]] := - Block[{int,fclsOutput,intsTFI,intsRest,intsTFI2,intsTFI3,intsTFIUnique,tmp, + Block[{ex, int,fclsOutput,intsTFI,intsRest,intsTFI2,intsTFI3,intsTFIUnique,tmp, solsList,tfiLoopIntegral,repRule,null1,null2,res, tfi1LoopQ1,tfi1LoopQ2}, - FCPrint[3, "ToTFI: Entering with ", expr, FCDoControl->toTFIVerbose]; + If[ !FreeQ2[{expr}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; If [OptionValue[FCVerbose]===False, toTFIVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], toTFIVerbose=OptionValue[FCVerbose] ]; ]; + FCPrint[3, "ToTFI: Entering with ", expr, FCDoControl->toTFIVerbose]; + + If[OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + If[ !FreeQ2[$ScalarProducts, {q1,q2}], Message[ToTFI::failmsg, "Some loop momenta have scalar product rules attached to them. Evaluation aborted!"]; Abort[] ]; (* Let us first extract all the scalar loop integrals *) - fclsOutput = FCLoopSplit[expr,{q1,q2}]; + fclsOutput = FCLoopSplit[ex,{q1,q2}, FCI->True]; intsRest = fclsOutput[[1]]+fclsOutput[[4]]; intsTFI = fclsOutput[[2]]+fclsOutput[[3]]; @@ -88,7 +167,7 @@ (* Nothing to do *) If[ intsTFI === 0, - Return[expr] + Return[ex] ]; intsTFI = FeynAmpDenominatorSplit[intsTFI,Momentum->{q1,q2}]; @@ -117,7 +196,7 @@ (* Quick and dirty way to get rid of the 1-loop integrals here *) - intsTFI3 = intsTFI3/.{tfi1LoopQ1[xy_]:>ToTFI[xy,q1,p],tfi1LoopQ2[xy_]:>ToTFI[xy,q2,p]}; + intsTFI3 = intsTFI3/.{tfi1LoopQ1[j_]:>ToTFI[j,q1,p,opts],tfi1LoopQ2[j_]:>ToTFI[j,q2,p,opts]}; (* Now we extract all the unique loop integrals *) intsTFIUnique = (Cases[intsTFI3+null1+null2,tfiLoopIntegral[___],Infinity]/.null1|null2->0)//Union; @@ -168,7 +247,10 @@ saveToTFI[z_/;Head[z]=!=Plus, q1_, q2_, p_, opts:OptionsPattern[]] := saveToTFI[z, q1,q2,p,opts] = Catch[ - Module[ {dim, met, pp, deltap, t0, t1,t2,t3, dummyterm, result, pairs,tmp}, + Module[{ dim, met, pp, deltap, t0, + t1,t2,t3, dummyterm, result, pairs, dummytag, + n1, n2, s1, s2, s3, s4 ,s5, a1, a2, n3, n4, n5 + }, dim = Dimension /. {opts} /. Options[ToTFI]; met = Method /. {opts} /. Options[ToTFI]; pp = FeynCalcExternal[Pair[Momentum[p,dim],Momentum[p,dim]]]; @@ -235,8 +317,8 @@ r ] ]; - t1 = t0 /. PropagatorDenominator -> prtoci /. - {FeynAmpDenominator[a__] :> Apply[Times, {a}] , + t1 = t0 /. FeynAmpDenominator[a__] :> Apply[Times, {a}] /. PropagatorDenominator -> prtoci /. + { Pair[Momentum[OPEDelta,___], Momentum[q1, ___]] :> dq1, Pair[Momentum[OPEDelta,___], Momentum[q2, ___]] :> dq2, Pair[Momentum[p,___], Momentum[q1, ___]] :> pq1, @@ -297,7 +379,7 @@ ] ] ]; - FeynCalcExternal[result] + FCE[result] ]]; FCPrint[1,"ToTFI.m loaded."]; diff --git a/FeynCalc/LoopIntegrals/TrickIntegrate.m b/FeynCalc/LoopIntegrals/TrickIntegrate.m index 75e639186..52f9c7d18 100644 --- a/FeynCalc/LoopIntegrals/TrickIntegrate.m +++ b/FeynCalc/LoopIntegrals/TrickIntegrate.m @@ -30,7 +30,9 @@ trick for the definite integral of ((1-t)^(a Epsilon -1) g[t]) \ Begin["`TrickIntegrate`Private`"] -Options[TrickIntegrate] = {Hold -> True}; +Options[TrickIntegrate] = { + Hold -> True +}; hopt[vau_,op___Rule][z_] := If[ !TrueQ[Hold /. {op} /. Options[TrickIntegrate]], @@ -44,10 +46,7 @@ trick for the definite integral of ((1-t)^(a Epsilon -1) g[t]) \ (* if there is nothing to substract, then : *) TrickIntegrate[w_/;Head[w]=!=Plus, v_, opt___] := (hopt[v,opt][SelectFree[w, v](Hold[Integrate]@@ {SelectNotFree[w,v], {v,0,1}})] - ) //. holdLimit->limit /; - (!MatchQ[w,(1-v)^(a_. Epsilon-1) ex_.] && - !MatchQ[w, v^(a_. Epsilon-1) ex_.] - ); + ) //. holdLimit->limit /; (!MatchQ[w,(1-v)^(a_. Epsilon-1) _.] && !MatchQ[w, v^(a_. Epsilon-1) _.]); (* this is just linearity *) TrickIntegrate[exp_. y^a_. (1-y)^b_ (1-x_ y_)^g_, y_, opt___Rule] := @@ -109,7 +108,7 @@ trick for the definite integral of ((1-t)^(a Epsilon -1) g[t]) \ v = 0 then: return the input *) res = If[ (lim === Indeterminate) (*|| (!FreeQ[tt, Log[v]])*) || - (MatchQ[lim, _. (1-v)^(bb_. Epsilon-1)]), + (MatchQ[lim, _. (1-v)^(_. Epsilon-1)]), tt pre (v)^(a Epsilon-1), (*special PowerExpand by hand ... *) lim = lim /. {((z_Symbol) (1-r_Symbol))^eps_ :> z^eps (1-r)^eps, diff --git a/FeynCalc/LoopIntegrals/TwoLoopSimplify.m b/FeynCalc/LoopIntegrals/TwoLoopSimplify.m index ef383cc87..0ac53eee1 100644 --- a/FeynCalc/LoopIntegrals/TwoLoopSimplify.m +++ b/FeynCalc/LoopIntegrals/TwoLoopSimplify.m @@ -24,9 +24,11 @@ Begin["`TwoLoopSimplify`Private`"] -Options[TwoLoopSimplify] = -{Dimension -> D, FeynCalcExternal -> True, IntegralTable -> {}, -ToLarin->True +Options[TwoLoopSimplify] = { + Dimension -> D, + FCE -> True, + IntegralTable -> {}, + ToLarin -> True }; TwoLoopSimplify[exp_, opt___Rule] := @@ -34,11 +36,17 @@ TwoLoopSimplify[exp_, {q1_, q2_}, opt___Rule] := Block[ {dirsuntrace, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, - t13, t14, - lt7, lt10, lt12, + t13, t14, t15, t16, tolarin, + lt7, lt10, lt12, null1, null2, dim, colg, two, twlist, twsublist, con, nan,tem, ht7, ht10, ht11, ht12, table, pe, op2, decomposelist }, + + If[ !FreeQ2[{exp}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + table = IntegralTable /. {opt} /. Options[TwoLoopSimplify]; tolarin = ToLarin /. {opt} /. Options[TwoLoopSimplify]; If[ (table =!= {}) && Head[table] === List, @@ -123,9 +131,9 @@ ]; twlist = Cases2[t6, Twist2GluonOperator]; twsublist = {}; - For[ii = 1, ii<=Length[twlist], ii++,WriteString["stdout",ii," "]; - AppendTo[twsublist, twlist[[ii]] -> - (twlist[[ii]] /. Twist2GluonOperator -> two) + For[r = 1, r<=Length[twlist], r++,WriteString["stdout",r," "]; + AppendTo[twsublist, twlist[[r]] -> + (twlist[[r]] /. Twist2GluonOperator -> two) ] ]; t6 = t6 /.Dispatch[twsublist]; @@ -142,8 +150,8 @@ nan = 0; lt7 = Length[t7]; ht7 = Hold@@{t7}; - For[jj = 1, jj <= lt7, jj++, Print["exp ",jj," (",lt7,") "]; - nan = nan + (DiracSimplify[con[Expand2[ht7[[1,jj]], + For[r = 1, r <= lt7, r++, Print["exp ",r," (",lt7,") "]; + nan = nan + (DiracSimplify[con[Expand2[ht7[[1,r]], {LorentzIndex,q1,q2} ]] /. DiracTrace -> Tr2]); ]; @@ -198,14 +206,13 @@ t12 = t11, tem = 0; ht11 = Hold@@{t11}; - len = Length[t11]; Do[ - WriteString["stdout",jj," "]; - tem = tem + Expand[ht11[[1,jj]]]; - If[ IntegerQ[jj/100], + WriteString["stdout",r," "]; + tem = tem + Expand[ht11[[1,r]]]; + If[ IntegerQ[r/100], Print["len = ",Length[tem]] ] - , {jj, len} + , {r, Length[t11]} ]; t12 = Collect2[tem,{q1,q2}, Expanding -> False]; ]; @@ -214,10 +221,10 @@ t13 = 0; lt12 = Length[t12]; ht12 = Hold@@{t12}; - Do[ WriteString["stdout",ik," "]; - t13 = t13 + Isolate[ht12[[1,ik]],{q1,q2}, IsolateSplit->Infinity] + Do[ WriteString["stdout",r," "]; + t13 = t13 + Isolate[ht12[[1,r]],{q1,q2}, IsolateSplit->Infinity] , - {ik, lt12} + {r, lt12} ]; ]; t14 = Expand2[t13] /. Pair -> PairContract /. PairContract -> Pair /. diff --git a/FeynCalc/LoopIntegrals/UVPart.m b/FeynCalc/LoopIntegrals/UVPart.m deleted file mode 100644 index f3233ac9d..000000000 --- a/FeynCalc/LoopIntegrals/UVPart.m +++ /dev/null @@ -1,79 +0,0 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: UVPart *) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 22 June '97 at 23:01 *) -(* ------------------------------------------------------------------------ *) - -(* ------------------------------------------------------------------------ *) - -UVPart::usage = -"UVPart[exp, q] discards ultraviolet finite integrals (q = integration momentum)."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`UVPart`Private`"] - -UVPart[0,_] := - 0; - -UVPart[exp_Plus, q_] := - Map[UVPart[#, q]&, exp]; - -UVPart[exp_,q_] := - Block[ {neglect, qcheck}, - neglect[ FeynAmpDenominator[PD[Momentum[q,___],0]..]] := - 0; - - neglect[ FeynAmpDenominator[PD[Momentum[q,___],0]..] (_. + - _. Pair[Momentum[q,___], Momentum[OPEDelta,___]])^_.] := - 0; - - neglect[ FeynAmpDenominator[_PD, _PD, __PD]] := - 0; - - qcheck[w_] := - If[ !FreeQ[w, DiracGamma], - False, - (* check if all occurences of q are q.OPDElta's *) - Block[ {w1, w2, qQ}, - Catch[ - w1 = SelectNotFree[Cases2[w, Pair], q]; - If[ !MatchQ[w1, {Pair[Momentum[q,___], Momentum[OPEDelta,___]]..}], - Throw[False], - w2 = Table[w1[[i]] -> (w1[[i]]/.q->qQ),{i,Length[w1]}]; - If[ FreeQ[w/.w2,q], - Throw[True], - Throw[False] - ] - ] - ] - ] - ]; - - neglect[ (_. + _. Pair[Momentum[q,___], Momentum[OPEDelta,___]])^_. * - FeynAmpDenominator[_PD, _PD, __PD]] := - 0; - - neglect[ (a_ /; qcheck[a]) * - FeynAmpDenominator[_PD, _PD, __PD]] := - 0; - - neglect[ (a_ /; qcheck[a]) * (b_ /; qcheck[b]) * - FeynAmpDenominator[_PD, _PD, __PD]] := - 0; - - If[ Head[exp] =!= Times, - exp, - SelectFree[exp,q] (neglect[SelectNotFree[exp,q]]/.neglect->Identity) - ] - ]; - -FCPrint[1,"UVPart.m loaded."]; -End[] diff --git a/FeynCalc/Lorentz/Amputate.m b/FeynCalc/Lorentz/Amputate.m index d4535b060..1546aee7a 100755 --- a/FeynCalc/Lorentz/Amputate.m +++ b/FeynCalc/Lorentz/Amputate.m @@ -37,8 +37,7 @@ Map[Amputate[#,q]&, x]; (* change September 2003 by Rolf Mertig, -otherwise Amputate[Pair[Momentum[k1, D], Momentum[q2, D]], q1, q2, Pair -> k1] would not work -*) +otherwise Amputate[Pair[Momentum[k1, D], Momentum[q2, D]], q1, q2, Pair -> k1] would not work *) Amputate[x_, OptionsPattern[]] := x; @@ -47,20 +46,32 @@ Amputate[ex_, qi:Except[_?OptionQ], opt:OptionsPattern[]] := Block[ {q,exp,eeps,nex,li,li1,li2,dim,par,dummy,inc,a$AL, TIMES}, + + + If[ !FreeQ2[{ex}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + exp = FeynCalcInternal[ex]; dim = Dimension /. {opt} /. Options[Amputate]; + If[ Head[qi]===Momentum, q = First[qi], q = qi ]; + par = Flatten[{Pair /. {opt} /. Options[Amputate]}]; + If[ (Unique /. {opt} /. Options[Amputate]) === True, a$AL = Unique[$AL], a$AL = $AL ]; + If[ par===All, par = SelectFree[Map[First, SelectFree[Cases2[exp, Momentum], OPEDelta]],q] ]; + If[ (par === {} && FreeQ2[exp, {Eps, DiracGamma}]) || (Head[dummy exp] =!= Times), exp, nex = exp; @@ -74,6 +85,7 @@ nex = nex //. {eeps[a___,Momentum[q,___],b___] :> (li = LorentzIndex[a$AL[inc = inc+1],dim]; Pair[Momentum[q,dim], li] eeps[a,li,b])} /. eeps -> Eps /. TIMES -> Times; ]; + If[ par=!={} && Length[par]>0 && Head[par]===List, nex = nex /. Pair[aa__/;!FreeQ2[{aa}, par]]^n_Integer?Positive :> Apply[times, Table[Pair[aa], {j,n}]]; @@ -84,9 +96,12 @@ Pair[Momentum[q, dim], li1] Pair[Momentum[q, dim], li2] *Pair[li1, li2]); par = SelectFree[par, q]; ]; - nex = nex //.{Pair[Momentum[q,___], Momentum[pe_,___]] :> (li = LorentzIndex[a$AL[inc = inc+1],dim]; - Pair[Momentum[q,dim], li] Pair[Momentum[pe,dim],li])/;MemberQ[par,pe]} /. times -> Times; + nex = nex //.{ + Pair[Momentum[q,___], Momentum[pe_,___]] :> (li = LorentzIndex[a$AL[inc = inc+1],dim]; + Pair[Momentum[q,dim], li] Pair[Momentum[pe,dim],li])/;MemberQ[par,pe] + } /. times -> Times; ]; + If[ !FreeQ[nex, DiracGamma], nex = nex /. DiracGamma -> dirg; nex = nex //. dirg[Momentum[q,___],___] :> diff --git a/FeynCalc/Lorentz/CartesianToLorentz.m b/FeynCalc/Lorentz/CartesianToLorentz.m new file mode 100755 index 000000000..cae38c1d1 --- /dev/null +++ b/FeynCalc/Lorentz/CartesianToLorentz.m @@ -0,0 +1,126 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: CartesianToLorentz *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Converts selected Cartesian tensors into Lorentz tensors. *) + +(* ------------------------------------------------------------------------ *) + + +CartesianToLorentz::usage= +"CartesianToLorentz[exp] rewrites Cartesian tensors in form of Lorentz tensors \ +(when possible). Using options one can specify which types of tensors \ +should be converted."; + +CartesianToLorentz::fail= +"Error! CartesianToLorentz has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`CartesianToLorentz`Private`"] + +Options[CartesianToLorentz] = { + CGS -> True, + CSP -> True, + DiracGammaExpand -> True, + DotSimplify -> True, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False +}; + +CartesianToLorentz[expr_, OptionsPattern[]]:= + Block[{ex, heads, tmp, res, uniqList,null1,null2, uniqListEval, repRule}, + + heads = {}; + + If[ OptionValue[CSP], + heads = Join[heads,{CartesianPair}] + ]; + + If[ OptionValue[CGS], + heads = Join[heads,{DiracGamma}] + ]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + If[ heads==={}, + Return[ex] + ]; + + uniqList = Cases[ex+null1+null2,Alternatives@@(Blank/@heads),Infinity]//DeleteDuplicates//Sort; + + uniqListEval = uniqList; + + If[ OptionValue[ExpandScalarProduct], + uniqListEval = ExpandScalarProduct[#,FCI->True]&/@uniqListEval; + ]; + + If[ OptionValue[DiracGammaExpand], + uniqListEval = DiracGammaExpand[uniqListEval,FCI->True]; + ]; + + If[ OptionValue[CSP], + uniqListEval = uniqListEval /. CartesianPair -> cspToSp /. cspToSp -> CartesianPair + ]; + + If[ OptionValue[CGS], + uniqListEval = uniqListEval /. DiracGamma -> cdiracSlashToDiracSlash /. cdiracSlashToDiracSlash -> DiracGamma + ]; + + repRule = Thread[Rule[uniqList, uniqListEval]]; + + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[DotSimplify], + res = DotSimplify[res,FCI->True] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + +cspToSp[CartesianMomentum[a_], CartesianMomentum[b_]]:= + FeynCalc`Package`MetricS (Pair[Momentum[a],Momentum[b]] - + FeynCalc`Package`MetricT TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[a]] TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[b]]); + +cspToSp[CartesianMomentum[a_, dim_Symbol-1], CartesianMomentum[b_, dim_Symbol-1]]:= + FeynCalc`Package`MetricS (Pair[Momentum[a,dim],Momentum[b,dim]] - + FeynCalc`Package`MetricT TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[a]] TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[b]]); + +cspToSp[CartesianMomentum[a_, dim_Symbol-4], CartesianMomentum[b_, dim_Symbol-4]]:= + FeynCalc`Package`MetricS Pair[Momentum[a,dim-4],Momentum[b,dim-4]]; + +cdiracSlashToDiracSlash[CartesianMomentum[p_]]:= + FeynCalc`Package`MetricS (DiracGamma[Momentum[p]] - + FeynCalc`Package`MetricT TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[p]] DiracGamma[ExplicitLorentzIndex[0]]); + +cdiracSlashToDiracSlash[CartesianMomentum[p_, dim_Symbol-1], dim_Symbol]:= + FeynCalc`Package`MetricS (DiracGamma[Momentum[p,dim],dim] - + FeynCalc`Package`MetricT TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[p]] DiracGamma[ExplicitLorentzIndex[0]]); + +cdiracSlashToDiracSlash[CartesianMomentum[p_, dim_Symbol-4], dim_Symbol-4]:= + FeynCalc`Package`MetricS DiracGamma[Momentum[p,dim-4],dim-4]; + +FCPrint[1,"CartesianToLorentz.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/ChangeDimension.m b/FeynCalc/Lorentz/ChangeDimension.m index c39bf2b06..21381f51f 100755 --- a/FeynCalc/Lorentz/ChangeDimension.m +++ b/FeynCalc/Lorentz/ChangeDimension.m @@ -1,22 +1,29 @@ +(* ::Package:: *) + (* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Title: ChangeDimension *) +(* :Title: ChangeDimension *) -(* :Author: Rolf Mertig *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* ------------------------------------------------------------------------ *) -(* :History: File created on 22 June '97 at 22:58 *) -(* ------------------------------------------------------------------------ *) - -(* :Summary: change dimension from 4 to D or back *) +(* :Summary: Change dimension of Lorentz and Cartesian tensors *) (* ------------------------------------------------------------------------ *) ChangeDimension::usage= -"ChangeDimension[exp, dim] changes all LorentzIndex and Momenta in \ +"ChangeDimension[exp, dim] changes all LorentzIndex and Momentum objects in \ exp to dimension dim (and thus also Dirac slashes and Dirac matrices \ -in FeynCalcInternal-representation)."; +in FeynCalcInternal-representation). CartesianIndex and CartesianMomentum objects become \ +changed to dimension dim-1."; +ChangeDimension::failmsg = +"Error! ChangeDimension has encountered a fatal problem and must abort \ +the computation. The problem reads: `1`" (* ------------------------------------------------------------------------ *) @@ -25,32 +32,61 @@ exp to dimension dim (and thus also Dirac slashes and Dirac matrices \ Begin["`ChangeDimension`Private`"] -ChangeDimension[x_, diim_] := +Options[ChangeDimension] ={ + FCI -> False, + FCE -> False +}; + +ChangeDimension[ex_, dim_, OptionsPattern[]] := Block[ - {xx = FeynCalcInternal[x], dirGG, dirGAMM, pAiR, ld , md,spi4,eps,eps2}, - If[ diim === 4, - xx = xx /. {LorentzIndex[a_,___] :> LorentzIndex[a] , - Momentum[b_,___] :> Momentum[b], - DiracGamma[c_,___] :> DiracGamma[c], Eps[a__,Dimension->D]:>Eps[a]}, - ld[a_,___] := - LorentzIndex[a, diim]; - md[a_,___] := - Momentum[a, diim]; - (*spi4[a_, b__] := - Spinor[a /. Momentum[bbb_, ___] -> Momentum[bbb], b]*); - dirGG[aa_,___] := - dirGAMM[aa, diim]/; !MatchQ[aa,5|6|7]; - dirGG[(aa: 5|6|7)] := - dirGAMM[aa]; - eps[a__, OptionsPattern[]]:= - eps2[a, Dimension->diim]; - xx = xx /. Pair -> pAiR /. DiracGamma -> dirGAMM /. Eps -> eps; - xx = xx /. {Momentum :> md, LorentzIndex -> ld} /. - {md :> Momentum, ld :> LorentzIndex} ; - xx = xx /. dirGAMM -> dirGG/. dirGAMM -> DiracGamma /. pAiR -> Pair /. eps2->Eps; - (*xx = xx /. Spinor -> spi4*); + { expr, res, tmp, lorentzDim, cartesianDim, + holdPair, holdDiracChain, holdDiracGamma, holdCartesianPair, holdEps, holdPauliSigma}, + + If[ OptionValue[FCI], + expr = ex, + expr = FCI[ex] + ]; + + Switch[ dim, + 4, + lorentzDim = 4; + cartesianDim = 3, + _Symbol, + lorentzDim = dim; + cartesianDim = dim-1, + _Symbol -4, + lorentzDim = dim; + cartesianDim = dim, + _, + Message[ChangeDimension::failmsg, "Unsupported choice of dimension!"]; + Abort[] + ]; + + tmp = expr /. DiracChain -> holdDiracChain /. DiracGamma -> holdDiracGamma /. PauliSigma -> holdPauliSigma /. Pair-> holdPair /. CartesianPair->holdCartesianPair /. Eps -> holdEps; + + tmp = tmp /. holdDiracGamma[(z: 5|6|7)] :> DiracGamma[z]; + + tmp = tmp /. { + LorentzIndex[z_,___] :> LorentzIndex[z,lorentzDim], + CartesianIndex[z_,___] :> CartesianIndex[z,cartesianDim], + Momentum[z_,___] :> Momentum[z,lorentzDim], + CartesianMomentum[z_,___] :> CartesianMomentum[z,cartesianDim] + }; + + tmp = tmp /. { + holdDiracGamma[z_,___] :> holdDiracGamma[z,lorentzDim], + holdPauliSigma[z_,___] :> holdPauliSigma[z,cartesianDim] + }; + + res = tmp /. holdDiracGamma -> DiracGamma /. holdPauliSigma -> PauliSigma /. holdPair -> Pair /. holdCartesianPair -> CartesianPair /. holdEps -> Eps /. holdDiracChain -> DiracChain; + + + If[ OptionValue[FCE], + res = FCE[res] ]; - xx + + res + ]; FCPrint[1,"ChangeDimension.m loaded"]; diff --git a/FeynCalc/Lorentz/CompleteSquare.m b/FeynCalc/Lorentz/CompleteSquare.m index 66744e3dc..92d7cc277 100644 --- a/FeynCalc/Lorentz/CompleteSquare.m +++ b/FeynCalc/Lorentz/CompleteSquare.m @@ -24,35 +24,36 @@ CompleteSquare[e_, x_ ,y_:Null] := Module[ {a, b, c, xx, ex, exp, dims, dim, rul, pa}, - (* Make sure all momenta have the same dimension *) - dims = Union[Cases[e, (Dimension->_)|(Momentum[_,_]),Infinity]]; - If[ dims =!= {}, - dims = Union[(#[[2]])& /@ dims] + If[ !FreeQ2[{e,x,y}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] ]; + + (* Make sure all momenta have the same dimension *) + dims = FCGetDimensions[e]; + Which[ - Length[dims] == 0, - dim = Sequence[]; - xx = Momentum[x]; - ex = e;, - Length[dims] == 1, - dim = dims[[1]]; - xx = Momentum[x,dim]; - ex = e;, - True, - dim = dims[[1]]; - xx = Momentum[x, dim]; - rul = ((Rule@@#)& /@ Transpose[ - {dims, Table[dim,{Length[dims]}]}]); - ex = e //. rul; + Length[dims] == 1, + dim = dims[[1]]; + xx = Momentum[x,dim]; + ex = e, + True, + dim = dims[[1]]; + xx = Momentum[x, dim]; + rul = ((Rule@@#)& /@ Transpose[{dims, Table[dim,{Length[dims]}]}]); + ex = e //. rul; ]; - exp = Expand[ExpandScalarProduct[Contract[ex]]]/. - {Pair[pp:Momentum[x,___],p:Momentum[_?(FreeQ[#,x]&),___]]:>p*pp, - Pair[p:Momentum[_?(FreeQ[#,x]&),___],pp:Momentum[x,___]]:>p*pp}; + + exp = Expand[ExpandScalarProduct[Contract[ex]]]/. { + Pair[pp:Momentum[x,___],p:Momentum[_?(FreeQ[#,x]&),___]]:>p pp, + Pair[p:Momentum[_?(FreeQ[#,x]&),___],pp:Momentum[x,___]]:>p pp + }; + pa = Pair[xx,xx]; a = Coefficient[exp, pa, 1]; - If[ Length[CoefficientList[exp,x]]>3|| - Length[CoefficientList[exp,pa]]>2||a===0, + If[ Length[CoefficientList[exp,x]]>3 || Length[CoefficientList[exp,pa]]>2||a===0, exp, + b = Coefficient[exp, xx, 1 ]; c = Coefficient[Coefficient[exp, xx, 0 ], pa, 0 ]; If[ y===Null, diff --git a/FeynCalc/Lorentz/Contract.m b/FeynCalc/Lorentz/Contract.m index 9196568e9..623d2795e 100755 --- a/FeynCalc/Lorentz/Contract.m +++ b/FeynCalc/Lorentz/Contract.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Contraction routines for Lorentz algebra *) @@ -30,9 +30,6 @@ exp2 should be the product (or expanded sum) of the polarization \ polarization vectors by the corresponding sum. This usually improves \ performance."; -Contract2::usage = -"Contract2[expr] (still experimental)."; - Contract3::usage = "Contract3[expr] (still experimental)."; @@ -49,21 +46,17 @@ exp2 should be the product (or expanded sum) of the polarization \ Begin["`Package`"] FCFastContract; +contract2; End[] Begin["`Contract`Private`"] cnVerbose::usage=""; - -fci[x_] := - If[ (FeynCalcInternal /. Options[Contract]) === True, - FeynCalcInternal[x], - x - ]; +optExpandScalarProduct::usage=""; FCFastContract[x_,OptionsPattern[]]:= - x /. Pair -> PairContract /. PairContract -> Pair; + x /. Pair -> PairContract /. PairContract -> Pair /. CartesianPair -> CartesianPairContract /. CartesianPairContract -> CartesianPair; Contract3[x_Plus, opts:OptionsPattern[]] := @@ -72,69 +65,131 @@ exp2 should be the product (or expanded sum) of the polarization \ Contract3[x_ /; (Head[x] =!= Times) && Head[x] =!= Plus,opts:OptionsPattern[]] := Contract[x, Contract3->False,opts]; -Contract3[x_Times, opts:OptionsPattern[]] := - If[ !FreeQ[x, DiracGamma | Eps], - Contract[x, Contract3 -> False,opts], - If[ FreeQ[fci[x], LorentzIndex], - fci[x], - Block[ {nx = x, nonli, lipa, nec = 0, ic,epli}, - nx = Contract[x , Expanding -> False, Contract3->False, opts]; - If[ Head[nx] =!= Times, - nec = Contract[nx, Contract3->False], - nonli = Select[nx, FreeQ[#, LorentzIndex]&]; - lipa = Select[nx,!FreeQ[#, LorentzIndex]&]; - If[ Head[lipa] =!= Times, - If[ Head[lipa] === Plus, - nec = Contract3[lipa (*epli*),opts], - nec = Contract[lipa (*epli*), Contract3->False,opts] - ], - If[ Length[lipa] < 2, - nec = Contract[lipa (*epli*), Contract3->False, opts], - nec = lipa[[1]](*epli*); - For[ic = 2, ic <= Length[lipa], ic++, - FCPrint[2,"ic = ", ic, " out of ",Length[lipa]]; - If[ LeafCount[nec] < LeafCount[lipa[[ic]]] || - If[ True, - !FreeQ[lipa[[ic]], Twist2GluonOperator], - False - ], - nec = Contract[lipa[[ic]], nec, Contract3->False,opts], - nec = Contract[nec, lipa[[ic]], Contract3->False,opts] - ]; - FCPrint[2,"expand scalar products"]; - nec = ExpandScalarProduct[nec]; - - FCPrint[2,"expand scalar products done"]; - - If[ !FreeQ[nec, LorentzIndex], - FCPrint[2,"expanding LorentzIndex now"]; - tim = TimeUsed[]; - nec = Expand[nec, LorentzIndex]; - FCPrint[2,"expanding LorentzIndex DONE ", - TimeUsed[] - tim]; - ]; - ]; - ]; - ]; - nec = nec nonli; +Contract3[expr_Times, opts:OptionsPattern[]] := + Block[{ex, nonli, lipa, nec = 0, ic,epli, time, res, time2}, + + + If[ !OptionValue[Contract,{opts},FCI], + ex = FCI[expr], + ex = expr + ]; + + + FCPrint[1,"Contract: Contract3: Entering.", FCDoControl->cnVerbose]; + FCPrint[3,"Contract: Contract3: Entering with:", expr, FCDoControl->cnVerbose]; + + If[ !FreeQ2[ex, {DiracGamma,DiracChain,Eps}], + FCPrint[1,"Contract: Contract3: Expression contains DiracGamma or Eps. Passing to Contract.", FCDoControl->cnVerbose]; + Return[Contract[ex, FCI->True, Contract3 -> False,opts]] + ]; + + If[ FreeQ[ex, LorentzIndex], + FCPrint[1,"Contract: Contract3: Expression is free of Lorentz indices. Leaving.", FCDoControl->cnVerbose]; + Return[ex] + ]; + + time=AbsoluteTime[]; + FCPrint[1,"Contract: Contract3: Applying Contract without expansions.", FCDoControl->cnVerbose]; + ex = Contract[ex, FCI->True, Expanding -> False, Contract3->False, opts]; + FCPrint[1,"Contract: Contract3: Contract done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + + If[ Head[ex] =!= Times, + FCPrint[1,"Contract: Contract3: Expression is not in the factorized form. Passing to Contract.", FCDoControl->cnVerbose]; + Return[Contract[ex, FCI->True, Contract3->False]] + ]; + + + time=AbsoluteTime[]; + FCPrint[1,"Contract: Contract3: Splitting into parts free and not free of Lorentz indices.", FCDoControl->cnVerbose]; + nonli = Select[ex, FreeQ[#, LorentzIndex]&]; + lipa = Select[ex,!FreeQ[#, LorentzIndex]&]; + + If[ Factor[nonli lipa - ex]=!=0, + Message[Contract::fail, "Splitting of the factorized expression in Contract3 failed."]; + FCPrint[0,{nonli,lipa,ex}]; + Abort[] + ]; + FCPrint[1,"Contract: Contract3: Splitting done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + + FCPrint[3,"Contract: Contract3: Part free of Lorentz indices:", nonli, FCDoControl->cnVerbose]; + FCPrint[3,"Contract: Contract3: Part with Lorentz indices:", lipa, FCDoControl->cnVerbose]; + + + + If[ Head[lipa] =!= Times, + FCPrint[1,"Contract: Contract3: Part with Lorentz indices is not factorized!", FCDoControl->cnVerbose]; + If[ Head[lipa] === Plus, + FCPrint[1,"Contract: Contract3: Part with Lorentz indices is a sum. Applying Contract3 again.", FCDoControl->cnVerbose]; + nec = Contract3[lipa, opts], + FCPrint[1,"Contract: Contract3: Part with Lorentz indices is not a sum. Passing to Contract.", FCDoControl->cnVerbose]; + nec = Contract[lipa, FCI->True, Contract3->False,opts] + ]; + + res = nec nonli; + FCPrint[1,"Contract: Contract3: Leaving.", FCDoControl->cnVerbose]; + FCPrint[3,"Contract: Contract3: Leaving with:",res, FCDoControl->cnVerbose]; + Return[res] + ]; + + + If[ Length[lipa] < 2, + time2=AbsoluteTime[]; + FCPrint[1,"Contract: Contract3: Applying Contract.", FCDoControl->cnVerbose]; + nec = Contract[lipa, FCI->True, Contract3->False, opts]; + FCPrint[1,"Contract: Contract3: Contract done. Timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->cnVerbose], + + + + (* The expression is of the form A1*A2*A3*...*An, where each factor contains Lorentz indices.*) + time2=AbsoluteTime[]; + FCPrint[1,"Contract: Contract3: Applying contractProduct.", FCDoControl->cnVerbose]; + + nec = lipa[[1]]; + (* nec = A1 *) + For[ic = 2, ic <= Length[lipa], ic++, + FCPrint[1,"ic = ", ic, " out of ",Length[lipa]]; + (*Print[{lipa[[ic]],nec}];*) + (* if A1 is simpler than Ai, *) + If[ LeafCount[nec] < LeafCount[lipa[[ic]]] || !FreeQ[lipa[[ic]], Twist2GluonOperator], + nec = contractProduct[lipa[[ic]], nec, Contract3->False,opts], + nec = contractProduct[nec, lipa[[ic]], Contract3->False,opts] ]; - nec - ] - ] + + + If[ optExpandScalarProduct, + FCPrint[2,"expand scalar products"]; + nec = ExpandScalarProduct[nec,FCI->False]; + FCPrint[2,"expand scalar products done"] + ]; + + If[ !FreeQ[nec, LorentzIndex], + FCPrint[2,"expanding LorentzIndex now"]; + time = TimeUsed[]; + nec = Expand[nec, LorentzIndex]; + FCPrint[2,"expanding LorentzIndex DONE ", + TimeUsed[] - time]; + ]; + ]; + FCPrint[1,"Contract: Contract3: contractProduct done. Timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->cnVerbose] + ]; + + nec = nec nonli; + + nec ]; (* #################################################################### *) -Options[Contract2] = { +Options[contract2] = { Collecting -> False }; (* bb is assumed to be collected w.r.t. to LorentzIndex !!! *) -Contract2[a_, bb_, ops___Rule] := +contract2[a_, bb_, ops___Rule] := Block[ {sel, ct, rc, lco, lct, lastct, nop, b = bb, col, conT}, - col = Collecting /. {ops} /. Options[Contract2]; + col = Collecting /. {ops} /. Options[contract2]; If[ Head[a] =!= Times, - rc = Contract[a, b], + rc = contractProduct[a, b], lco[x_,y_] := If[ Length[x]>Length[y], True, @@ -145,18 +200,18 @@ exp2 should be the product (or expanded sum) of the polarization \ nop = Select[ct, FreeQ[#, Plus]&]; ct = ct/nop; If[ Head[ct] =!= Times, - rc = sel Contract[ct nop, b], + rc = sel contractProduct[ct nop, b], ct = Sort[List @@ ct, lco]; If[ nop =!= 1, - lastct = contract21[b, nop, ops], + lastct = contractLongShort[b, nop, ops], lastct = b nop ]; lct = Length[ct]; If[ lct === 1, - rc = sel contractLColl[ct[[1]], lastct] + rc = sel contractLongLong[ct[[1]], lastct] ]; If[ lct > 1, - rc = sel Contract[Times @@ Take[ct, lct-1], + rc = sel contractProduct[Times @@ Take[ct, lct-1], ct[[lct]], lastct ] ]; ]; @@ -166,13 +221,13 @@ exp2 should be the product (or expanded sum) of the polarization \ rc = Contract[rc, Expanding -> False]; ]; If[ !FreeQ[rc, LorentzIndex], - FCPrint[1,"contracting agagin at the end of Contract2 "]; + FCPrint[1,"contracting agagin at the end of contract2."]; rc = Contract[rc] ]; rc ]; -Contract2[a_] := +contract2[a_] := Block[ {sel, ct, rc, lco, lct, lastct, nop}, If[ Head[a] =!= Times, rc = Contract[a], @@ -189,22 +244,21 @@ exp2 should be the product (or expanded sum) of the polarization \ rc = sel Contract[ct nop], ct = Sort[List @@ ct, lco]; If[ nop =!= 1, - lastct = contract21[Last[ct], nop], + lastct = contractLongShort[Last[ct], nop], lastct = Last[ct] nop; ]; lct = Length[ct]; If[ lct === 2, - rc = sel contractLColl[ct[[1]], lastct] + rc = sel contractLongLong[ct[[1]], lastct] ]; If[ lct > 2, - rc = sel Contract[Times @@ Take[ct, lct-2], - ct[[lct-1]], lastct ] + rc = sel contractProduct[Times @@ Take[ct, lct-2], ct[[lct-1]], lastct] ]; ]; ]; FCPrint[2,"lct = ",lct]; If[ !FreeQ[rc, LorentzIndex], - FCPrint[1,"contracting agagin at the end of Contract2 "]; + FCPrint[1,"contracting agagin at the end of contract2 "]; rc = Contract[rc] ]; rc @@ -230,24 +284,26 @@ exp2 should be the product (or expanded sum) of the polarization \ Options[Contract] = { - Collecting -> True, - Contract3 -> True, - EpsContract -> True, - Expanding -> True, - Factoring -> False, - FCI -> True, - FCVerbose -> False, - MomentumCombine -> True, - Rename -> False, - Schouten -> 0 + Collecting -> True, + Contract3 -> True, + EpsContract -> True, + Expanding -> True, + ExpandScalarProduct -> True, + Factoring -> False, + FCE -> False, + FCI -> False, + FCVerbose -> False, + MomentumCombine -> True, + Rename -> False, + Schouten -> 0 }; Contract[l_List, opts:OptionsPattern[]] := Contract[#,opts]&/@l; (* Main entry point *) -Contract[y_, z:OptionsPattern[]] := - Block[{ex=fci[y],tmp,rest1=0,rest2=0,rest3=0,noDummy=0,nodot, +Contract[expr_, z:OptionsPattern[]] := + Block[{ex, tmp, rest1=0,rest2=0,rest3=0,noDummy=0,nodot, null1,null2,freeIndList,freeHead,tmpFin,res,expandOpt, epsContractOpt,renameOpt,schoutenOpt,times,tmpList,time,tmpCheck}, @@ -255,29 +311,33 @@ exp2 should be the product (or expanded sum) of the polarization \ epsContractOpt = OptionValue[EpsContract]; renameOpt = OptionValue[Rename]; schoutenOpt = OptionValue[Schouten]; + optExpandScalarProduct = OptionValue[ExpandScalarProduct]; If [OptionValue[FCVerbose]===False, cnVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], cnVerbose=OptionValue[FCVerbose] ]; ]; - If[expandOpt, - ex = Expand2[ex,LorentzIndex] + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr ]; + (* At first we try to achieve maximal simplification without doing expansions *) + FCPrint[1, "Contract: Entering main contract", FCDoControl->cnVerbose]; FCPrint[3, "Contract: Entering with", ex, FCDoControl->cnVerbose]; - If[ FreeQ2[ex, {LorentzIndex,Eps}], + If[ FreeQ2[ex, {CartesianIndex, LorentzIndex, Eps}], Return[ex] ]; time=AbsoluteTime[]; FCPrint[1,"Contract: Separating terms that contain Lorentz indices from those that don't.", FCDoControl->cnVerbose]; (* First splitting: Terms that do not need any contractions are not processed further *) - {rest1,tmp} = FCSplit[ex, {LorentzIndex,Eps},Expanding->False]; + {rest1,tmp} = FCSplit[ex, {CartesianIndex, LorentzIndex, Eps},Expanding->False]; (* TODO isolate terms without LorentzIndex and Eps*) FCPrint[1,"Contract: Splitting done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; @@ -285,13 +345,21 @@ exp2 should be the product (or expanded sum) of the polarization \ FCPrint[3, "Contract: Other terms: ", rest1, FCDoControl->cnVerbose]; If[!FreeQ[tmp,PairContract], - FCPrint[1,"Contract: Replacing PairContract with Contract.", FCDoControl->cnVerbose]; + FCPrint[1,"Contract: Replacing PairContract with Pair.", FCDoControl->cnVerbose]; + rest1 = rest1 /. PairContract -> Pair; tmp = tmp /. PairContract -> Pair; ]; + If[!FreeQ[tmp,CartesianPairContract], + FCPrint[1,"Contract: Replacing CartesianPairContract with CartesianPair.", FCDoControl->cnVerbose]; + rest1 = rest1 /. CartesianPairContract -> CartesianPair; + tmp = tmp /. CartesianPairContract -> CartesianPair; + ]; + time=AbsoluteTime[]; FCPrint[1,"Contract: Separating terms that contain Lorentz indices with a FreeIndex DataType", FCDoControl->cnVerbose]; - freeIndList = Cases[tmp+null1+null2,LorentzIndex[ind_,_:4]/; DataType[ind,FreeIndex]:> {ind,freeHead[ind]},Infinity]//Union; + freeIndList = Cases[res, _LorentzIndex, Infinity] // DeleteDuplicates // Sort // + Cases[#, LorentzIndex[i_, ___] /; DataType[i, FreeIndex] :> {i, freeHead[i]}, Infinity] & // DeleteDuplicates // Sort; If[ freeIndList=!={}, FCPrint[3, "Contract: List of indices that should not be summed over", freeIndList, FCDoControl->cnVerbose]; tmp/. Map[(Rule @@ #) &, freeIndList]; @@ -299,38 +367,35 @@ exp2 should be the product (or expanded sum) of the polarization \ ]; FCPrint[1,"Contract: Splitting done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; - FCPrint[3, "Contract: Terms that contain Lorentz indices with a FreeIndex DataType: ", tmp, FCDoControl->cnVerbose]; - FCPrint[3, "Contract: Other terms: ", rest2, FCDoControl->cnVerbose]; - - (* Assuming that numer of terms Upper and Lower is rather small*) - time=AbsoluteTime[]; - FCPrint[1,"Contract: Separating terms that contain Lorentz indices with Upper or Lower", FCDoControl->cnVerbose]; - If[ !FreeQ2[tmp, {Upper,Lower}], - {tmp,rest3} = FCSplit[tmp, {Upper,Lower},Expanding->False]; - FCPrint[3, "Contract: Terms that contain Upper or Lower: ", rest3, FCDoControl->cnVerbose]; - FCPrint[3, "Contract: Other terms: ", tmp, FCDoControl->cnVerbose]; - If[rest3=!=0, - rest3 = Contract1[rest3] - ] - ]; - FCPrint[1,"Contract: Splitting done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; - FCPrint[3, "Contract: Terms that contain Lorentz indices with Upper or Lower: ", tmp, FCDoControl->cnVerbose]; - FCPrint[3, "Contract: Other terms: ", rest3, FCDoControl->cnVerbose]; + FCPrint[3, "Contract: Terms that contain Lorentz indices with a FreeIndex DataType: ", rest2, FCDoControl->cnVerbose]; + FCPrint[3, "Contract: Other terms: ", tmp, FCDoControl->cnVerbose]; (* Now we determine terms that contain dummy indices *) (* TODO Fish out the eps terms beforehand!!! *) time=AbsoluteTime[]; FCPrint[1,"Contract: Separating terms that contain dummy Lorentz indices", FCDoControl->cnVerbose]; tmpCheck = tmp; - tmp = tmp /. Power[a_, b_Integer?Positive] /; !FreeQ[a, LorentzIndex] :> Apply[times, Table[a, {i, b}]]; - tmpList = Apply[List,tmp+null1+null2]; + If[ !FreeQ[tmp,Power], + tmp = tmp /. Power[a_, b_Integer?Positive] /; !FreeQ2[a, {CartesianIndex, LorentzIndex}] :> Apply[times, Table[a, {i, b}]]; + ]; + + If[ !DummyIndexFreeQ[tmp,{CartesianIndex,LorentzIndex}], - tmp = Select[tmpList, hasDummyIndices]; - noDummy = Complement[tmpList,tmp]; + tmpList = Apply[List,tmp+null1+null2]; + tmp = Select[tmpList, hasDummyIndices]; + noDummy = Complement[tmpList,tmp]; - (*noDummy contains epsilon tensors like LC[a,b,c,d]LC[e,f,g,h]*) - tmp = Total[tmp]/.times->Times/.null1|null2->0; - noDummy = Total[noDummy]/.times->Times/.null1|null2->0; + (*noDummy contains epsilon tensors like LC[a,b,c,d]LC[e,f,g,h]*) + tmp = Total[tmp]/.times->Times/.null1|null2->0; + noDummy = Total[noDummy]/.times->Times/.null1|null2->0, + + If[ !FreeQ[tmp,times], + tmp = tmp /.times->Times; + ]; + + noDummy = tmp; + tmp = 0 + ]; (* check that we didn't loose any terms *) If[tmp+noDummy =!=tmpCheck, @@ -370,71 +435,122 @@ exp2 should be the product (or expanded sum) of the polarization \ If[ OptionValue[MomentumCombine] && LeafCount[tmp] < 1000, time=AbsoluteTime[]; FCPrint[1,"Contract: Applying MometumCombine.", FCDoControl->cnVerbose]; - tmp = MomentumCombine[tmp]; + tmp = MomentumCombine[tmp, FCI->True]; FCPrint[1,"Contract: MometumCombine done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; ]; FCPrint[3, "Contract: After MometumCombine: ", tmp, FCDoControl->cnVerbose]; time=AbsoluteTime[]; - FCPrint[1,"Contract: Applying contracT.", FCDoControl->cnVerbose]; - tmpFin = contracT[tmp,z]; - FCPrint[1,"Contract: contracT done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + (* + Now we should choose the best strategy to evaluate the expression in tmp. + Essentially, it can be a sum, a product or a standalone term. If it is a sum + we evaluate it term by term. The evaluation function is also applicable to + products or standalone terms. + *) + + If[ !FreeQ[tmp,LorentzIndex], + FCPrint[1,"Contract: Applying mainContract.", FCDoControl->cnVerbose]; + Which[ Head[tmp]===Plus, + tmp = mainContract[#,z]&/@tmp, + + Head[tmp]===Times, + tmp = mainContract[tmp,z], + + True, + tmp = mainContract[tmp,z] + ]; + FCPrint[1,"Contract: mainContract done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + FCPrint[3, "Contract: After mainContract: ", tmp, FCDoControl->cnVerbose] + ]; + + If[ !FreeQ[tmp,CartesianIndex], + FCPrint[1,"Contract: Applying cartesianContract.", FCDoControl->cnVerbose]; + Which[ Head[tmp]===Plus, + tmpFin = cartesianContract[#,z]&/@tmp, - FCPrint[3, "Contract: After contracT: ", tmpFin, FCDoControl->cnVerbose]; + Head[tmp]===Times, + tmpFin = cartesianContract[tmp,z], + + True, + tmpFin = cartesianContract[tmp,z] + ]; + FCPrint[1,"Contract: mainContract done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + FCPrint[3, "Contract: After mainContract: ", tmpFin, FCDoControl->cnVerbose], + + tmpFin = tmp + ]; (* Here we are done *) If[ expandOpt, time=AbsoluteTime[]; - FCPrint[1,"Contract: Expanding w.r.t Lorentz indices.", FCDoControl->cnVerbose]; + FCPrint[1,"Contract: Expanding w.r.t Lorentz and Cartesian indices.", FCDoControl->cnVerbose]; If[!FreeQ[tmpFin, LorentzIndex], - tmpFin = Expand[tmpFin,LorentzIndex] + tmpFin = Expand[tmpFin, CartesianIndex] + ]; + If[!FreeQ[tmpFin, CartesianIndex], + tmpFin = Expand[tmpFin, CartesianIndex] ]; If[!FreeQ[noDummy, LorentzIndex], - noDummy = Expand[noDummy,LorentzIndex] + noDummy = Expand[noDummy, LorentzIndex] + ]; + If[!FreeQ[noDummy, CartesianIndex], + noDummy = Expand[noDummy, CartesianIndex] ]; + FCPrint[1,"Contract: Expansion done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; ]; - - If[ !FreeQ[tmpFin, Eps] && renameOpt, + If[ !FreeQ[tmpFin, Eps], time=AbsoluteTime[]; - FCPrint[1,"Contract: Renaming dummy indices in epsilon tensors.", FCDoControl->cnVerbose]; - tmpFin = doubleindex[Expand[ tmpFin//EpsEvaluate, Eps]]; - FCPrint[1,"Contract: Renaming done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + FCPrint[1,"Contract: Applying EpsEvaluate.", FCDoControl->cnVerbose]; + If[ !FreeQ[tmpFin, Eps], + tmpFin = EpsEvaluate[tmpFin,FCI->True]; + ]; + + If[ renameOpt, + time=AbsoluteTime[]; + FCPrint[1,"Contract: Renaming dummy indices in epsilon tensors.", FCDoControl->cnVerbose]; + tmpFin = doubleindex[Expand2[ EpsEvaluate[tmpFin,FCI->True], Eps]]; + FCPrint[1,"Contract: Renaming done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + ] ]; + If[ epsContractOpt, time=AbsoluteTime[]; FCPrint[1,"Contract: Contracting epsilon tensors.", FCDoControl->cnVerbose]; - If[ !FreeQ[tmpFin, Eps], - tmpFin = FCLoopIsolate[EpsEvaluate[tmpFin],{Eps},Head->tmpHead,PaVe->False,FCI->True, - ExpandScalarProduct->False,DiracGammaExpand->False,DotSimplify->False,FeynAmpDenominatorSplit->False, - Factoring->False]/. tmpHead-> epsCleverCon - + If[ !EpsContractFreeQ[tmpFin], + tmpFin = EpsContract[tmpFin,FCI->True] ]; - If[ !FreeQ[noDummy, Eps], - noDummy = FCLoopIsolate[EpsEvaluate[noDummy],{Eps},Head->tmpHead,PaVe->False,FCI->True, - ExpandScalarProduct->False,DiracGammaExpand->False,DotSimplify->False,FeynAmpDenominatorSplit->False, - Factoring->False]/. tmpHead-> epsCleverCon + If[ !EpsContractFreeQ[noDummy], + noDummy = EpsContract[noDummy,FCI->True] ]; FCPrint[1,"Contract: Epsilon contractions done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; ]; If[ expandOpt, time=AbsoluteTime[]; - FCPrint[1,"Contract: Expanding in Lorentz indices.", FCDoControl->cnVerbose]; + FCPrint[1,"Contract: Expanding in Lorentz and Cartesian indices.", FCDoControl->cnVerbose]; If[ !FreeQ[tmpFin, LorentzIndex], tmpFin = Expand[tmpFin, LorentzIndex] ]; + If[!FreeQ[tmpFin, CartesianIndex], + tmpFin = Expand[tmpFin, CartesianIndex] + ]; + If[ !FreeQ[noDummy, LorentzIndex], noDummy = Expand[noDummy,LorentzIndex] ]; + If[!FreeQ[noDummy, CartesianIndex], + noDummy = Expand[noDummy, CartesianIndex] + ]; + FCPrint[1,"Contract: Expansions done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; If[ epsContractOpt, @@ -456,19 +572,31 @@ exp2 should be the product (or expanded sum) of the polarization \ time=AbsoluteTime[]; FCPrint[1,"Contract: Applying EpsEvaluate.", FCDoControl->cnVerbose]; If[ !FreeQ[tmpFin, Eps], - tmpFin = tmpFin//EpsEvaluate; + tmpFin = EpsEvaluate[tmpFin,FCI->True]; ]; If[ !FreeQ[noDummy, Eps], - noDummy = noDummy//EpsEvaluate; + noDummy = EpsEvaluate[noDummy,FCI->True]; ]; FCPrint[1,"Contract: EpsEvaluate done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; ]; - time=AbsoluteTime[]; - FCPrint[1,"Contract: Applying PairContract.", FCDoControl->cnVerbose]; - tmpFin = tmpFin /. Pair->PairContract3 /. PairContract3 -> PairContract /.PairContract->Pair; - FCPrint[1,"Contract: PairContract done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + If[ !FreeQ[tmpFin,Pair] && !DummyIndexFreeQ[tmpFin,{LorentzIndex,CartesianIndex}], + time=AbsoluteTime[]; + FCPrint[1,"Contract: Applying PairContract.", FCDoControl->cnVerbose]; + If[ TrueQ[optExpandScalarProduct], + tmpFin = tmpFin /. Pair->PairContract3 /. PairContract3 -> PairContract /.PairContract->Pair, + tmpFin = tmpFin /. Pair->FeynCalc`Package`pairContract3NoExpand /. FeynCalc`Package`pairContract3NoExpand -> PairContract /.PairContract->Pair; + ]; + FCPrint[1,"Contract: PairContract done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose] + ]; + + If[ !FreeQ[tmpFin,CartesianPair] && !DummyIndexFreeQ[tmpFin,{LorentzIndex,CartesianIndex}], + time=AbsoluteTime[]; + FCPrint[1,"Contract: Applying CartesianPairContract.", FCDoControl->cnVerbose]; + tmpFin = tmpFin /. CartesianPair-> CartesianPairContract /. CartesianPairContract -> CartesianPair; + FCPrint[1,"Contract: CartesianPairContract done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + ]; (*Here we can unite the two*) tmpFin = tmpFin + noDummy; @@ -498,77 +626,69 @@ exp2 should be the product (or expanded sum) of the polarization \ FCPrint[1,"Contract: Factoring done: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose] ]; - FCPrint[1, "Contract: Leaving. ", FCDoControl->cnVerbose]; - FCPrint[1, "Contract: Leaving with :", res, FCDoControl->cnVerbose]; - res - ]/; Head[y]=!=List; - -Contract[a_, b_ /;Head[b] =!= Rule, c_ /; Head[c] =!= Rule, ops:OptionsPattern[]] := - Block[ {lc, new = 0, i}, - - If [OptionValue[FCVerbose]===False, - cnVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], - cnVerbose=OptionValue[FCVerbose] - ]; + If[ OptionValue[FCE], + res = FCE[res] ]; - FCPrint[2, "Contract: Before calling another Contract ", FCDoControl->cnVerbose]; + FCPrint[1, "Contract: Leaving. ", FCDoControl->cnVerbose]; + FCPrint[3, "Contract: Leaving with :", res, FCDoControl->cnVerbose]; + res + ]/; Head[expr]=!=List; - lc = Contract[b, c, ops]; - FCPrint[2, "Contract: Before calling another Contract ", FCDoControl->cnVerbose]; - new = Contract[lc, a, ops]; +(* Contract[A1==An] *) +Contract[Equal[a_, b_], opts:OptionsPattern[]] := + Contract[a, FCI->True, opts] == Contract[b, FCI->True, opts]; - FCPrint[2, "Contract: Leaving ", FCDoControl->cnVerbose]; - new - ]; +(* Contract[A1,A2,A3] *) +contractProduct[a_, b: Except[_Rule], c: Except[_Rule], ops:OptionsPattern[]] := + contractProduct[contractProduct[b, c, ops], a, ops]; -Contract[x_, y_ /; Head[y]=!=Rule, c:OptionsPattern[]] := - (Contract[fci[x], c] y) /; FreeQ2[fci[y], {LorentzIndex,Eps}]; +contractProduct[x_, y_ /; Head[y]=!=Rule, opts:OptionsPattern[]] := + (y Contract[x, FCI->True, opts]) /; FreeQ2[y, {LorentzIndex,Eps}]; -Contract[x_, y_Times, opts:OptionsPattern[]] := - Block[ {a = fci[x], b = fci[y], bb}, +(* Contract[A1,A2*...*An] +contractLongShort is for contracting products of products, +contractLongLong is for contacting products of sums! + *) +contractProduct[a_, b_Times, opts:OptionsPattern[]] := + Block[ {bb}, If[ MatchQ[b, Apply[HoldPattern, {Times__Pair}]], - contract21[ a, b ,opts], + contractLongShort[ a, b ,opts], If[ MatchQ[b, HoldPattern[Times__Pair]], - contract21[ a, b ,opts], + contractLongShort[ a, b ,opts], bb = Collect3[b, Pair, Factoring-> False]; If[ Head[bb] === Plus, - contractLColl[a, bb], - contract21[a, bb, opts] + contractLongLong[a, bb], + contractLongShort[a, bb, opts] ] ] ] ]; +contractProduct[a_, b: Except[_Times | _Plus | _Rule], opts:OptionsPattern[]] := + Contract[a b, FCI->True, opts]; -Contract[a_, b_ /; ((Head[b]=!=Times) && (Head[b] =!= Plus) && (Head[b] =!= Rule)), c:OptionsPattern[]] := - Contract[ a b, c ]; - -Contract[a_, b_Plus, OptionsPattern[]] := - If[ OptionValue[Collecting] === True, - contractLColl[fci[a], +(* Contract[X,A1+...+An] *) +contractProduct[a_, b_Plus, opts:OptionsPattern[]] := + If[ OptionValue[Contract,{opts},Collecting], + contractLongLong[a, If[ FreeQ[List@@b, Plus], - fci[b], - Collect2[fci[b], LorentzIndex] + b, + Collect2[b, LorentzIndex] ] - ], - contractLColl[fci[a], fci[b]] + ], + contractLongLong[a, b] ]; - -Contract[Equal[a_, b_], ops___Rule] := - Contract[a,ops] == Contract[b, ops]; - hasDummyIndices[expr_] := - (Cases[expr, LorentzIndex[ind_, ___] :> ind, Infinity,Heads->True]//Tally//Transpose//Last//Max//Greater[#, 1]&) /; - !FreeQ[{expr}, LorentzIndex]; + (Cases[expr, (LorentzIndex|CartesianIndex)[i_, ___] :> i, Infinity,Heads->True]//Tally//Transpose//Last//Max//Greater[#, 1]&) /; + !FreeQ2[{expr}, {LorentzIndex,CartesianIndex}]; hasDummyIndices[expr_] := False/; - FreeQ[{expr},LorentzIndex]; + FreeQ2[{expr}, {LorentzIndex,CartesianIndex}]; -contracT[x_,opts:OptionsPattern[]] := +mainContract[x : Except[_Plus], opts:OptionsPattern[]] := Block[ { contractres = x, contractexpandopt, es, time, contract3, schout, contractfactoring }, @@ -577,80 +697,126 @@ exp2 should be the product (or expanded sum) of the polarization \ contractfactoring = OptionValue[Contract,{opts},Factoring]; contract3 = OptionValue[Contract,{opts},Contract3]; - FCPrint[1, "Contract: contracT: Entering", FCDoControl->cnVerbose]; - FCPrint[3, "Contract: contracT: Entering with ",x, FCDoControl->cnVerbose]; + FCPrint[1, "Contract: mainContract: Entering", FCDoControl->cnVerbose]; + FCPrint[3, "Contract: mainContract: Entering with ",x, FCDoControl->cnVerbose]; + (* NEW: September 16th 2003: adding Contract3 directly here ... *) - If[ contract3 && contractexpandopt, + If[ contract3, If[ MemberQ[{Plus, Times}, Head[contractres]], time=AbsoluteTime[]; - FCPrint[1, "Contract: contracT: Applying Contract3.", FCDoControl->cnVerbose]; - contractres = Contract3[contractres,opts]; - FCPrint[1,"Contract: contracT: Contract3 done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; - FCPrint[3,"Contract: contracT: After Contract3: ", contractres , FCDoControl->cnVerbose] + FCPrint[1, "Contract: mainContract: Applying Contract3.", FCDoControl->cnVerbose]; + contractres = Contract3[contractres,FCI->True,opts]; + FCPrint[1,"Contract: mainContract: Contract3 done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + FCPrint[3,"Contract: mainContract: After Contract3: ", contractres , FCDoControl->cnVerbose] ] ]; - time=AbsoluteTime[]; - FCPrint[1, "Contract: contracT: Applying PairContract.", FCDoControl->cnVerbose]; - contractres = contractres /. Pair -> PairContract3 /. PairContract3 -> PairContract/. - PairContract -> sceins /. sceins -> Pair; - FCPrint[1,"Contract: contracT: PairContract done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; - FCPrint[3,"Contract: contracT: After PairContract: ", contractres , FCDoControl->cnVerbose]; + + If[ !DummyIndexFreeQ[contractres,{LorentzIndex,CartesianIndex}], + time=AbsoluteTime[]; + FCPrint[1, "Contract: mainContract: Applying PairContract.", FCDoControl->cnVerbose]; + + If[ TrueQ[optExpandScalarProduct], + contractres = contractres /. Pair -> PairContract3 /. PairContract3 -> PairContract/. + PairContract -> sceins /. sceins -> Pair, + contractres = contractres /. Pair -> FeynCalc`Package`pairContract3NoExpand /. FeynCalc`Package`pairContract3NoExpand -> PairContract/. + PairContract -> sceins /. sceins -> Pair + ]; + + FCPrint[1,"Contract: mainContract: PairContract done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + FCPrint[3,"Contract: mainContract: After PairContract: ", contractres , FCDoControl->cnVerbose] + ]; (* optimization *) If[ Head[contractres === Plus] && Length[contractres > 47], If[ !FreeQ[contractres, Eps], time=AbsoluteTime[]; - FCPrint[1, "Contract: contracT: Applying optimization.", FCDoControl->cnVerbose]; + FCPrint[1, "Contract: mainContract: Applying optimization.", FCDoControl->cnVerbose]; es = { Pair[LorentzIndex[a_, D], b_] Eps[c___,LorentzIndex[a_],d___] :> Eps[c,b,d], Pair[LorentzIndex[a_, D], b_] Eps[c___,LorentzIndex[a_, D],d___] :> Eps[c,b,d] }; contractres = contractres //. es; - FCPrint[1,"Contract: contracT: Optimization done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; - FCPrint[3,"Contract: contracT: After optimization: ", contractres , FCDoControl->cnVerbose] + FCPrint[1,"Contract: mainContract: Optimization done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + FCPrint[3,"Contract: mainContract: After optimization: ", contractres , FCDoControl->cnVerbose] ] ]; + + time=AbsoluteTime[]; + FCPrint[1, "Contract: mainContract: Applying another optimization.", FCDoControl->cnVerbose]; + If[ contractexpandopt && !contract3 && !FreeQ[contractres, LorentzIndex], (* NEW October 2003, this speeds things up in general*) contractres = Expand[Expand[contractres, LorentzIndex] //. simplerules]; contractres = contractres /. {((yy_Plus) /;!FreeQ[yy, LorentzIndex])^2 :> - ((Contract @@ {yy/.PairContract->Pair, yy/.PairContract->Pair,opts} + ((contractProduct @@ {yy/.PairContract->Pair, yy/.PairContract->Pair,opts} ) /. Pair -> PairContract /. PairContract -> Pair) }; ]; + FCPrint[1,"Contract: mainContract: Anotzher optimization done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; contractres ]; -(* contractLColldef *) -contractLColl[a_, b_ /; Head[b] =!= Plus] := + +cartesianContract[x : Except[_Plus], opts:OptionsPattern[]] := + Block[ { contractres = x, contractexpandopt, time}, + + contractexpandopt = OptionValue[Contract,{opts},Expanding]; + + FCPrint[1, "Contract: cartesianContract: Entering", FCDoControl->cnVerbose]; + FCPrint[3, "Contract: cartesianContract: Entering with ",x, FCDoControl->cnVerbose]; + + If[ contractexpandopt, + contractres = Expand2[contractres,CartesianIndex] + ]; + + time=AbsoluteTime[]; + FCPrint[1, "Contract: cartesianContract: Applying PairContract.", FCDoControl->cnVerbose]; + contractres = contractres /. Pair -> PairContract /. CartesianPair -> CartesianPairContract /. PairContract->Pair /. CartesianPairContract->CartesianPair; + FCPrint[1,"Contract: cartesianContract: PairContract done. Timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cnVerbose]; + FCPrint[3,"Contract: cartesianContract: After PairContract: ", contractres , FCDoControl->cnVerbose]; + + + FCPrint[1,"Contract: cartesianContract: Leaving.", FCDoControl->cnVerbose]; + FCPrint[3,"Contract: cartesianContract: Leaving with: ", contractres , FCDoControl->cnVerbose]; + + contractres + ]; + +(* contractLongLongdef *) +(* b must be collected w.r.t LorentzIndex, + covers cases for + X*Pair[...] and X*Y, where X can be a sum or not and + Y is not a sum *) +contractLongLong[a_, b_ /; Head[b] =!= Plus] := If[ Head[b] === Pair, - contract21[a, b], + contractLongShort[a, b], If[ Head[a] === Plus, - contractLColl[b, a], - Contract[a b] + contractLongLong[b, a], + Contract[a b, FCI->True] ] ]; -contractLColl[lon_, shor_Plus] := - Block[ {neew = {}, long = lon, - short = shor, tet}, +(* b must be collected w.r.t LorentzIndex, + covers X*(A1+...+An) *) +contractLongLong[lon_, shor_Plus] := + Block[ {neew = {}, long = lon, short = shor, tet, ij}, FCPrint[1,"Long contraction ", Length[long], " * ", Length[short], " \n ",UseWriteString->True]; For[ij = 1, ij <= Length[short], ij++, FCPrint[3,"stdout"," | ", ij, " XXX | ",UseWriteString->True]; ; - FCPrint[1, "before contract21 "]; - tet = contract21[long, short[[ij]] ]; - FCPrint[1, "after contract21 "]; + FCPrint[1, "before contractLongShort "]; + tet = contractLongShort[long, short[[ij]] ]; + FCPrint[1, "after contractLongShort "]; If[ !FreeQ[tet, LorentzIndex], tet = tet /. Pair->pairsave /. pair2 -> Pair ]; If[ !FreeQ[tet, LorentzIndex], - FCPrint[1,"expanding in contractLColl ",UseWriteString->True]; + FCPrint[1,"expanding in contractLongLong ",UseWriteString->True]; tet = Expand[Expand[tet] /. Pair->pairsave /. pair2 -> Pair]; (* tet = Expand2[tet, LorentzIndex] /. Pair->pairsave /. pair2 -> Pair; @@ -660,13 +826,15 @@ exp2 should be the product (or expanded sum) of the polarization \ neew = Join[neew, Apply[List, tet]], AppendTo[neew, tet] ]; - ]; + ]; + FCPrint[2,"applying plus to neew "]; neew = Apply[Plus, neew]; - FCPrint[2,"exiting contractLColl"]; + FCPrint[2,"exiting contractLongLong"]; neew ]; + (* local easy contraction rules *) (* paird *) SetAttributes[{pairsave, pair2,fdi}, Orderless]; @@ -691,21 +859,22 @@ exp2 should be the product (or expanded sum) of the polarization \ pairsave[a_, b_] := pairsave[a, b] = - If[ FreeQ[{a,b},LorentzIndex], - ExpandScalarProduct[a,b], + If[ FreeQ[{a,b},LorentzIndex] && optExpandScalarProduct, + ExpandScalarProduct[Pair[a,b],FCI->True], pair2[a, b] ]; pair2[LorentzIndex[a_, di1___], LorentzIndex[a_, di2___]] := fdi[di1, di2]; pair2/: pair2[LorentzIndex[a_, dim1___], LorentzIndex[b_, dim2___]]^2 := - fdi[dim1, dim2]; + fdi[dim1, dim2]/; a=!=b; -pair2/: pair2[LorentzIndex[a_,de1___], Momentum[b_, de2___]]^2 := +pair2/: pair2[LorentzIndex[_,de1___], Momentum[b_, de2___]]^2 := Pair[Momentum[b, fdi[de1,de2]], Momentum[b,fdi[de1,de2]]]; -pair2/: pair2[LorentzIndex[al_,di___], z_] pair2[LorentzIndex[al_,di2___], - w_] := pair2[z, w]; +pair2/: pair2[LorentzIndex[al_,___], z_] pair2[LorentzIndex[al_,___], w_] := + pair2[z, w]; + (* ???????? BLOEDSINN; PairContract does it (*NEW*) pair2/: pair2[LorentzIndex[al_,di___], z_] Twist2GluonOperator[ww__] := @@ -713,7 +882,7 @@ exp2 should be the product (or expanded sum) of the polarization \ !FreeQ[{ww}, LorentzIndex[al,di]]; *) -(* contract21 can still have products in the first argument *) +(* contractLongShort can still have products in the first argument *) (* by construction the second argument will always be either a product or just Pair[ , ] *) @@ -740,13 +909,22 @@ exp2 should be the product (or expanded sum) of the polarization \ nxx ]; -contract21[z_, yy_ /; ((Head[yy] =!= Pair) && Head[yy] =!= Times), opts:OptionsPattern[]] := - Contract[z yy, opts]; +(* If y is a single object that is not a Pair (e.g. Dot) *) +contractLongShort[x_, y: Except[_Times | _Pair], opts:OptionsPattern[]] := + Contract[x y, FCI->True, opts]; + +(* If x is a single object that is not a Pair (e.g. Dot) *) +contractLongShort[x: Except[_Times | _Plus], y_, opts:OptionsPattern[]] := + Contract[x y, FCI->True, Expanding -> False, opts]; + +(* If x is a product *) +contractLongShort[x_Times, y_, opts:OptionsPattern[]] := + ( (x/#) contit[#, y, opts] )&[Select[x, !FreeQ[#, LorentzIndex]&] ]; -contract21[xx_Plus, yy_, opts:OptionsPattern[]] := - contract22[xx, yy /. Pair -> pairsave, opts] /. - contra4 -> contra3a /. contra3a -> contra3b /. - Pair -> pairsave /. contra3b -> contra3c /. pair2 -> Pair; +(* If x is a sum *) +contractLongShort[x_Plus, y_, opts:OptionsPattern[]] := + contract22[x, y /. Pair -> pairsave, opts] /. + contra4 -> contra3a /. contra3a -> contra3b /. Pair -> pairsave /. contra3b -> contra3c /. pair2 -> Pair; list2[x_] := If[ Head[x] === Times, @@ -764,75 +942,27 @@ exp2 should be the product (or expanded sum) of the polarization \ contract22[xx_, yy_Times, opts:OptionsPattern[]] := ( (yy/#) contra4[xx, list2[#], opts] )&[Select[yy, !FreeQ[#, LorentzIndex]&]]; -contract21[xx_ /;(Head[xx] =!= Plus) && (Head[xx] =!= Times), yy_, opts:OptionsPattern[]] := - Contract[xx yy,Expanding -> False, opts]; - -contract21[xxx_Times, yyy_, opts:OptionsPattern[]] := - ( (xxx/#) contit[#, yyy, opts] )&[Select[xxx, !FreeQ[#, LorentzIndex]&] ]; - contit[xx_ , yy_, opts:OptionsPattern[]] := If[ FreeQ[xx, LorentzIndex], - xx Contract[yy,opts], + xx Contract[yy, FCI->True, opts], If[ Head[xx] =!= Times, - Contract[xx yy,opts], + Contract[xx yy, FCI->True, opts], If[ Length[xx] =!= 2, - Contract[xx yy,opts], + Contract[xx yy, FCI->True, opts], If[ (Head[xx[[1]]] === Plus) && (Head[xx[[2]]] === Plus), - iCcount = 1; FCPrint[2,"contracting a product of a ",Length[xx[[1]]], " term sum by a", Length[xx[[2]]], " term sum"]; (* that's the common situation !! *) - Apply[ Plus, Flatten[Table[ (xx[[1, ii]] xx[[2, jj]] yy) /. - Pair -> pairsave /. pair2 -> Pair, {ii,1,Length[xx[[1]]]}, - {jj,1,Length[xx[[2]]]}]]], - Contract[xx yy,opts] + Apply[ Plus, Flatten[Table[ (xx[[1, i]] xx[[2, j]] yy) /. + Pair -> pairsave /. pair2 -> Pair, {i,1,Length[xx[[1]]]}, + {j,1,Length[xx[[2]]]}]]], + Contract[xx yy, FCI->True, opts] ] ] ] ]; - -(* #################################################################### *) - -(* contractlidef *) -contractli[x_] := - MemSet[contractli[x],x] /; FreeQ[x//Hold,LorentzIndex]; - -contractli[x_] := - Contract[ x, Expanding->True, Factoring->False, EpsContract->False]; - -conall[ x_ ] := - Contract[ x, Expanding->True, EpsContract->True, Factoring->False]; - -epsCleverCon[expr_]:= - expr //. Power[Eps[a__],n_] :> epsHold[epscon[a]^n] //. - Eps[a__] Eps[b__]/; Length[Intersection[{a},{b}]]===3 :> epsHold[epscon[a]epscon[b]] //. - Eps[a__] Eps[b__]/; Length[Intersection[{a},{b}]]===2 :> epsHold[epscon[a]epscon[b]] //. - Eps[a__] Eps[b__]/; Length[Intersection[{a},{b}]]===1 :> epsHold[epscon[a]epscon[b]] /. - Eps -> epscon /. epscon -> Eps /. epsHold->Identity; - -epscon/: epscon[a1_,a2_,a3_,a4_,OptionsPattern[Eps]]^2 := - ((( - ($LeviCivitaSign)^2 Det[{{PairContract[a1,a1],PairContract[a1,a2],PairContract[a1,a3],PairContract[a1,a4]}, - {PairContract[a2,a1],PairContract[a2,a2],PairContract[a2,a3],PairContract[a2,a4]}, - {PairContract[a3,a1],PairContract[a3,a2],PairContract[a3,a3],PairContract[a3,a4]}, - {PairContract[a4,a1],PairContract[a4,a2],PairContract[a4,a3],PairContract[a4,a4]}}]//Expand)/.PairContract->Pair )); - - -epscon/: epscon[a1_,a2_,a3_,a4_,opts:OptionsPattern[Eps]]^n_Integer?Positive := - ((hold[epscon[a1,a2,a3,a4,opts]^2]*epscon[a1,a2,a3,a4,opts]^(n-2))/. - hold->Identity )/; n>=3 && FreeQ[{a1,a2,a3,a4},LorentzIndex]; - -epscon/: epscon[a1_,a2_,a3_,a4_,OptionsPattern[Eps]]^n_Integer?Positive := - (Message[Contract::fail,"Epsilon tensor to a power higher than two with \ -uncontracted Lorentz indices violates Einsein summation convention!"]; Abort[])/; n>=3 && !FreeQ[{a1,a2,a3,a4},LorentzIndex]; - -epscon/: epscon[a1_,a2_,a3_,a4_,OptionsPattern[Eps]] epscon[b1_,b2_,b3_,b4_,OptionsPattern[Eps]] := - ( - ($LeviCivitaSign)^2 Det[{{PairContract[a1,b1],PairContract[a1,b2],PairContract[a1,b3],PairContract[a1,b4]}, - {PairContract[a2,b1],PairContract[a2,b2],PairContract[a2,b3],PairContract[a2,b4]}, - {PairContract[a3,b1],PairContract[a3,b2],PairContract[a3,b3],PairContract[a3,b4]}, - {PairContract[a4,b1],PairContract[a4,b2],PairContract[a4,b3],PairContract[a4,b4]}}]//Expand)/.PairContract->Pair; - sceins[0,_] := 0; sceins[a_LorentzIndex b_, c_] := @@ -840,67 +970,56 @@ exp2 should be the product (or expanded sum) of the polarization \ sceins[a_Momentum b_, c_] := b sceins[a, c]; - -dim[] = 4; -dim[d_] := - d; - -(* do this immediately, Oct. 2003 *) simplerules = { - Pair[LorentzIndex[a_, di___], b_] Pair[LorentzIndex[a_, di___], c_] :> Pair[b, c], - Pair[LorentzIndex[x_, di___], LorentzIndex[x_, di___]] :> dim[di], - Pair[LorentzIndex[x_, di___], y_]^2 :> Pair[y, y] + Pair[LorentzIndex[a_, dim_:4], b_] Pair[LorentzIndex[a_, dim_:4], c_] :> Pair[b, c], + Pair[LorentzIndex[x_, dim_:4], LorentzIndex[x_, dim_:4]] :> dim, + Pair[LorentzIndex[_, _:4], y_]^2 :> Pair[y, y] }; +(* #################################################################### *) + ident3[a_,_] := a; -(* #################################################################### *) - - (* decide whether the (first) appearance of inds in expr is ordered *) - (*ordqdef*) - ordq[expr_,inds_List] := - Block[ {pos, min}, - pos = Position[expr, #]& /@ inds; - pos = pos /. {} -> Sequence[]; - If[ Length[pos]>0, - pos = Map[First,pos] - ]; - min = Min[Length/@pos]; - pos = Map[Take[#,min]&, pos]; - OrderedQ[pos] +(* decide whether the (first) appearance of inds in expr is ordered *) +(*ordqdef*) +ordq[expr_,inds_List] := + Block[ {pos, min}, + pos = Position[expr, #]& /@ inds; + pos = pos /. {} -> Sequence[]; + If[ Length[pos]>0, + pos = Map[First,pos] ]; + min = Min[Length/@pos]; + pos = Map[Take[#,min]&, pos]; + OrderedQ[pos] + ]; + + +eps2rules = {Eps[LorentzIndex[_,dia___], b_Momentum, c_Momentum, d_Momentum]^2 :> + Eps[LorentzIndex[$MU[1], dia], b, c, d]^2, + + Eps[LorentzIndex[a_,dia___], LorentzIndex[b_,dia___], c_Momentum, d_Momentum]^2/; a=!=b :> + Eps[LorentzIndex[$MU[1], dia], LorentzIndex[$MU[2],dia], c, d]^2, + Eps[LorentzIndex[a_,dia___], LorentzIndex[b_,dia___], LorentzIndex[c_,dia___], d_Momentum]^2/; a=!=b && b=!=c :> + Eps[LorentzIndex[$MU[1], dia], LorentzIndex[$MU[2],dia], LorentzIndex[$MU[3], dia], d]^2, -eps2rules = {Eps[LorentzIndex[a_,dia___], b_Momentum, - c_Momentum, d_Momentum, opts:OptionsPattern[]]^2 :> - Eps[LorentzIndex[$MU[1], dia], b, c, d, opts]^2, - Eps[LorentzIndex[a_,dia___], LorentzIndex[b_,dia___], - c_Momentum, d_Momentum, opts:OptionsPattern[]]^2 :> - Eps[LorentzIndex[$MU[1], dia], LorentzIndex[$MU[2],dia], - c, d, opts]^2, - Eps[LorentzIndex[a_,dia___], LorentzIndex[b_,dia___], - LorentzIndex[c_,dia___], d_Momentum, opts:OptionsPattern[]]^2 :> - Eps[LorentzIndex[$MU[1], dia], LorentzIndex[$MU[2],dia], - LorentzIndex[$MU[3], dia], d, opts]^2, - Eps[LorentzIndex[a_,dia___], LorentzIndex[b_,dia___], - LorentzIndex[c_,dia___], LorentzIndex[d_,dia___], opts:OptionsPattern[]]^2 :> - Eps[LorentzIndex[$MU[1], dia], LorentzIndex[$MU[2],dia], - LorentzIndex[$MU[3], dia], LorentzIndex[$MU[4], dia], opts - ]^2 - }; - - (* doubleindexdef *) - (* For canonizing dummy indices between Eps and other functions *) + Eps[LorentzIndex[a_,dia___], LorentzIndex[b_,dia___], LorentzIndex[c_,dia___], LorentzIndex[d_,dia___]]^2/; a=!=b && b=!=c && c=!=d :> + Eps[LorentzIndex[$MU[1], dia], LorentzIndex[$MU[2],dia], LorentzIndex[$MU[3], dia], LorentzIndex[$MU[4], dia]]^2 +}; + +(* doubleindexdef *) +(* For canonizing dummy indices between Eps and other functions *) doubleindex[0] = 0; doubleindex[x_] := Block[ {xy = x, suli = {}, muUU}, - For[ijj = 1, ijj < 7, ijj ++, - If[ EvenQ[Length[Position[x, $MU[ijj]]]] && !FreeQ[x, $MU[ijj]], - AppendTo[suli, RuleDelayed @@ {$MU[ijj], muUU[ijj]}] + For[i = 1, i < 7, i ++, + If[ EvenQ[Length[Position[x, $MU[i]]]] && !FreeQ[x, $MU[i]], + AppendTo[suli, RuleDelayed @@ {$MU[i], muUU[i]}] ]; ]; If[ Length[suli] > 0, @@ -908,18 +1027,11 @@ exp2 should be the product (or expanded sum) of the polarization \ xy = xy /. suli ]; xy = doubleindex0[x]; -(* - If[!FreeQ[x, Eps] && !FreeQ[x, $MU], - doubleindex0[doubleindex0[x]], - doubleindex0[x] - ]; -*) + If[ xy === 0, FCPrint[1,"doubleindexTROUBLE???????????? "]; Print["entering with", x]; ]; -(* -*) xy ]; @@ -930,13 +1042,10 @@ exp2 should be the product (or expanded sum) of the polarization \ If[ Head[x] === Plus, Map[doubleindex, x], double2[y_] := - double3a[y /. {Eps :> eepp} , 1 - ] /. double3a -> double3; + double3a[y /. {Eps :> eepp} , 1] /. double3a -> double3; double3a[y_, i_] := - double3a[y, i+1] /; - Length[Position[y, $MU[i]]] > 0; - double2[x] /. eepp -> Eps /. - double3 -> ident3/. eepp -> Eps + double3a[y, i+1] /; Length[Position[y, $MU[i]]] > 0; + double2[x] /. eepp -> Eps /. double3 -> ident3/. eepp -> Eps ] ] /. eps2rules ]; @@ -958,15 +1067,11 @@ exp2 should be the product (or expanded sum) of the polarization \ LorentzIndex[a, BlankNullSequence[]]; double3[ m_. eepp[a1___, LorentzIndex[be_, di___], a2___], j_ ] := - (m/.be->$MU[j]) Eps[a1,LorentzIndex[$MU[j],di],a2]/; - (!FreeQ[m, LorentzIndex[be, ___]]) && - FreeQ2[m, Select[{a1,a2}, Head[#]===LorentzIndex&] /. LorentzIndex -> lorhipa]; + (m/.be->$MU[j]) Eps[a1,LorentzIndex[$MU[j],di],a2]/; (!FreeQ[m, LorentzIndex[be, ___]]) && FreeQ2[m, Select[{a1,a2}, Head[#]===LorentzIndex&] /. LorentzIndex -> lorhipa]; double3[ m_. eepp[a1___, LorentzIndex[mu1_, di1___], a2___, LorentzIndex[mu2_, di2___],a3___], j_ ] := ((m/.mu1->$MU[j]/.mu2->$MU[j+1]) Eps[a1,LorentzIndex[$MU[j],di1],a2, LorentzIndex[$MU[j+1],di2],a3])/; - ( FreeQ2[{m,a1,a2,a3}, {$MU[j], $MU[j+1]}] && - (!FreeQ[m, LorentzIndex[mu1, ___]]) && - (!FreeQ[m, LorentzIndex[mu2, ___]]) && + (FreeQ2[{m,a1,a2,a3}, {$MU[j], $MU[j+1]}] && (!FreeQ[m, LorentzIndex[mu1, ___]]) && (!FreeQ[m, LorentzIndex[mu2, ___]]) && (FreeQ2[m, Select[{a1,a2,a3}, Head[#]===LorentzIndex&]/. LorentzIndex -> lorhipa]) && ordq[m, {mu1,mu2}]); double3[ m_. eepp[a1___, LorentzIndex[mu1_, di1___], a2___, LorentzIndex[mu2_, di2___],a3___], j_ ] := @@ -976,13 +1081,9 @@ exp2 should be the product (or expanded sum) of the polarization \ (!FreeQ[m, LorentzIndex[mu2, ___]]) && (FreeQ2[m, Select[{a1,a2,a3}, Head[#]===LorentzIndex&]/. LorentzIndex -> lorhipa]) && ordq[m, {mu2,mu1}]); -double3[ m_. eepp[a1___, LorentzIndex[mu1_, di1___], a2___, LorentzIndex[mu2_, di2___], a3___, - LorentzIndex[mu3_, di3___], a4___ ], j_ ] := +double3[ m_. eepp[a1___, LorentzIndex[mu1_, di1___], a2___, LorentzIndex[mu2_, di2___], a3___, LorentzIndex[mu3_, di3___], a4___ ], j_ ] := Block[ {dte,a,b,c}, - dte = ( (m/.mu1->$MU[j]/.mu2->$MU[j+1]/.mu3->$MU[j+2]) * - Eps[a1,LorentzIndex[$MU[j],di1], a2, - LorentzIndex[$MU[j+1],di2],a3, - LorentzIndex[$MU[j+2],di3], a4]); + dte = ( (m/.mu1->$MU[j]/.mu2->$MU[j+1]/.mu3->$MU[j+2]) Eps[a1,LorentzIndex[$MU[j],di1], a2, LorentzIndex[$MU[j+1],di2],a3, LorentzIndex[$MU[j+2],di3], a4]); a = $MU[j]; b = $MU[j+1]; c = $MU[j+2]; @@ -1005,60 +1106,64 @@ exp2 should be the product (or expanded sum) of the polarization \ !FreeQ2[m, LorentzIndex[mu3,___]] ) && FreeQ2[m, Select[{a1,a2,a3,a4}, Head[#]===LorentzIndex&]/. LorentzIndex -> lorhipa]; -double3[ m_. eepp[LorentzIndex[mu1_,di1___],LorentzIndex[mu2_,di2___], - LorentzIndex[mu3_,di3___],LorentzIndex[mu4_,di4___]], _ ] := +double3[ m_. eepp[LorentzIndex[mu1_,di1___],LorentzIndex[mu2_,di2___], LorentzIndex[mu3_,di3___],LorentzIndex[mu4_,di4___]], _ ] := Block[ {dte,a,b,c,d}, - dte = (m/.mu1->$MU[1]/.mu2->$MU[2]/.mu3->$MU[3]/.mu4->$MU[4]) * - Eps[LorentzIndex[$MU[1],di1], LorentzIndex[$MU[2],di2], - LorentzIndex[$MU[3],di3], LorentzIndex[$MU[4],di4]]; + dte = (m/.mu1->$MU[1]/.mu2->$MU[2]/.mu3->$MU[3]/.mu4->$MU[4]) Eps[LorentzIndex[$MU[1],di1], LorentzIndex[$MU[2],di2], LorentzIndex[$MU[3],di3], LorentzIndex[$MU[4],di4]]; a = $MU[1]; b = $MU[2]; c = $MU[3]; d = $MU[4]; Which[ - ordq[m, {mu1, mu2, mu3, mu4}], ReplaceAll[dte, - {a -> a, b -> b, c -> c, d -> d}], - ordq[m, {mu1, mu2, mu4, mu3}], - ReplaceAll[dte, {a -> a, b -> b, c -> d, d -> c}], - ordq[m, {mu1, mu3, mu2, mu4}], ReplaceAll[dte, - {a -> a, b -> c, c -> b, d -> d}], ordq[m, {mu1, mu3, mu4, mu2}], - ReplaceAll[dte, {a -> a, b -> c, c -> d, d -> b}], - ordq[m, {mu1, mu4, mu2, mu3}], ReplaceAll[dte, - {a -> a, b -> d, c -> b, d -> c}], ordq[m, {mu1, mu4, mu3, mu2}], - ReplaceAll[dte, {a -> a, b -> d, c -> c, d -> b}], - ordq[m, {mu2, mu1, mu3, mu4}], ReplaceAll[dte, - {a -> b, b -> a, c -> c, d -> d}], ordq[m, {mu2, mu1, mu4, mu3}], - ReplaceAll[dte, {a -> b, b -> a, c -> d, d -> c}], - ordq[m, {mu2, mu3, mu1, mu4}], ReplaceAll[dte, - {a -> b, b -> c, c -> a, d -> d}], ordq[m, {mu2, mu3, mu4, mu1}], - ReplaceAll[dte, {a -> b, b -> c, c -> d, d -> a}], - ordq[m, {mu2, mu4, mu1, mu3}], ReplaceAll[dte, - {a -> b, b -> d, c -> a, d -> c}], ordq[m, {mu2, mu4, mu3, mu1}], - ReplaceAll[dte, {a -> b, b -> d, c -> c, d -> a}], - ordq[m, {mu3, mu1, mu2, mu4}], ReplaceAll[dte, - {a -> c, b -> a, c -> b, d -> d}], ordq[m, {mu3, mu1, mu4, mu2}], - ReplaceAll[dte, {a -> c, b -> a, c -> d, d -> b}], - ordq[m, {mu3, mu2, mu1, mu4}], ReplaceAll[dte, - {a -> c, b -> b, c -> a, d -> d}], ordq[m, {mu3, mu2, mu4, mu1}], - ReplaceAll[dte, {a -> c, b -> b, c -> d, d -> a}], - ordq[m, {mu3, mu4, mu1, mu2}], ReplaceAll[dte, - {a -> c, b -> d, c -> a, d -> b}], ordq[m, {mu3, mu4, mu2, mu1}], - ReplaceAll[dte, {a -> c, b -> d, c -> b, d -> a}], - ordq[m, {mu4, mu1, mu2, mu3}], ReplaceAll[dte, - {a -> d, b -> a, c -> b, d -> c}], ordq[m, {mu4, mu1, mu3, mu2}], - ReplaceAll[dte, {a -> d, b -> a, c -> c, d -> b}], - ordq[m, {mu4, mu2, mu1, mu3}], ReplaceAll[dte, - {a -> d, b -> b, c -> a, d -> c}], ordq[m, {mu4, mu2, mu3, mu1}], - ReplaceAll[dte, {a -> d, b -> b, c -> c, d -> a}], - ordq[m, {mu4, mu3, mu1, mu2}], ReplaceAll[dte, - {a -> d, b -> c, c -> a, d -> b}], ordq[m, {mu4, mu3, mu2, mu1}], - ReplaceAll[dte, {a -> d, b -> c, c -> b, d -> a}] + ordq[m, {mu1, mu2, mu3, mu4}], + ReplaceAll[dte, {a -> a, b -> b, c -> c, d -> d}], + ordq[m, {mu1, mu2, mu4, mu3}], + ReplaceAll[dte, {a -> a, b -> b, c -> d, d -> c}], + ordq[m, {mu1, mu3, mu2, mu4}], + ReplaceAll[dte, {a -> a, b -> c, c -> b, d -> d}], + ordq[m, {mu1, mu3, mu4, mu2}], + ReplaceAll[dte, {a -> a, b -> c, c -> d, d -> b}], + ordq[m, {mu1, mu4, mu2, mu3}], + ReplaceAll[dte, {a -> a, b -> d, c -> b, d -> c}], + ordq[m, {mu1, mu4, mu3, mu2}], + ReplaceAll[dte, {a -> a, b -> d, c -> c, d -> b}], + ordq[m, {mu2, mu1, mu3, mu4}], + ReplaceAll[dte, {a -> b, b -> a, c -> c, d -> d}], + ordq[m, {mu2, mu1, mu4, mu3}], + ReplaceAll[dte, {a -> b, b -> a, c -> d, d -> c}], + ordq[m, {mu2, mu3, mu1, mu4}], + ReplaceAll[dte, {a -> b, b -> c, c -> a, d -> d}], + ordq[m, {mu2, mu3, mu4, mu1}], + ReplaceAll[dte, {a -> b, b -> c, c -> d, d -> a}], + ordq[m, {mu2, mu4, mu1, mu3}], + ReplaceAll[dte, {a -> b, b -> d, c -> a, d -> c}], + ordq[m, {mu2, mu4, mu3, mu1}], + ReplaceAll[dte, {a -> b, b -> d, c -> c, d -> a}], + ordq[m, {mu3, mu1, mu2, mu4}], + ReplaceAll[dte, {a -> c, b -> a, c -> b, d -> d}], + ordq[m, {mu3, mu1, mu4, mu2}], + ReplaceAll[dte, {a -> c, b -> a, c -> d, d -> b}], + ordq[m, {mu3, mu2, mu1, mu4}], + ReplaceAll[dte, {a -> c, b -> b, c -> a, d -> d}], + ordq[m, {mu3, mu2, mu4, mu1}], + ReplaceAll[dte, {a -> c, b -> b, c -> d, d -> a}], + ordq[m, {mu3, mu4, mu1, mu2}], + ReplaceAll[dte, {a -> c, b -> d, c -> a, d -> b}], + ordq[m, {mu3, mu4, mu2, mu1}], + ReplaceAll[dte, {a -> c, b -> d, c -> b, d -> a}], + ordq[m, {mu4, mu1, mu2, mu3}], + ReplaceAll[dte, {a -> d, b -> a, c -> b, d -> c}], + ordq[m, {mu4, mu1, mu3, mu2}], + ReplaceAll[dte, {a -> d, b -> a, c -> c, d -> b}], + ordq[m, {mu4, mu2, mu1, mu3}], + ReplaceAll[dte, {a -> d, b -> b, c -> a, d -> c}], + ordq[m, {mu4, mu2, mu3, mu1}], + ReplaceAll[dte, {a -> d, b -> b, c -> c, d -> a}], + ordq[m, {mu4, mu3, mu1, mu2}], + ReplaceAll[dte, {a -> d, b -> c, c -> a, d -> b}], + ordq[m, {mu4, mu3, mu2, mu1}], + ReplaceAll[dte, {a -> d, b -> c, c -> b, d -> a}] ] - ] /; (!FreeQ2[m, LorentzIndex[mu1,___]] && - !FreeQ2[m, LorentzIndex[mu2,___]] && - !FreeQ2[m, LorentzIndex[mu3,___]] && - !FreeQ2[m, LorentzIndex[mu4,___]] - ) && FreeQ2[m, {$MU[1], $MU[2], $MU[3], $MU[4]}]; + ] /; (!FreeQ2[m, LorentzIndex[mu1,___]] && !FreeQ2[m, LorentzIndex[mu2,___]] && !FreeQ2[m, LorentzIndex[mu3,___]] && !FreeQ2[m, LorentzIndex[mu4,___]]) && FreeQ2[m, {$MU[1], $MU[2], $MU[3], $MU[4]}]; FCPrint[1,"Contract.m loaded."]; End[] diff --git a/FeynCalc/Lorentz/Contract1.m b/FeynCalc/Lorentz/Contract1.m deleted file mode 100755 index 96e115e7c..000000000 --- a/FeynCalc/Lorentz/Contract1.m +++ /dev/null @@ -1,118 +0,0 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: Contract1*) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 6 March '98 at 15:35 *) -(* ------------------------------------------------------------------------ *) - -(* ------------------------------------------------------------------------ *) - - -Contract1::usage = -"Contract1[exp] contracts Upper and Lower indices."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`Contract1`Private`"] - -SetAttributes[Contract1, HoldAll]; -SetAttributes[ct, HoldAll]; -SetAttributes[cot, HoldRest]; - -ct[a_] := - a; - -ct[a__] := - cot[Evaluate[SelectNotFree[{a}, Upper]], - Evaluate[SelectFree[{a}, Upper]] - ]; - -SetAttributes[TTimes, HoldAll]; -SetAttributes[ttimes, HoldAll]; - -cot[{},{z___}] := - TTimes[z]; -cot[{z___},{}] := - TTimes[z]; - -cot[{a_, b___}, {z___}] := - cot[{b},{a, z}] /; Head[a]=!=Pair; -(* -cot[{a_, b___}, {z___}] := a cot[{b},{z}] /; FreeQ[a,Lower]; -*) - -cot[{Pair[LorentzIndex[Upper[l1_],di1___], - LorentzIndex[Upper[l2_],di2___] - ], y___}, {z___} - ] := - If[ !FreeQ[{y,z}, LorentzIndex[Lower[l1],di1]], - cot@@({{y},{z}}/.LorentzIndex[Lower[l1],di1]-> - LorentzIndex[Upper[l2],di2] - ), - If[ !FreeQ[{y,z}, LorentzIndex[Lower[l2],di2]], - cot@@({{y},{z}}/.LorentzIndex[Lower[l2],di2]-> - LorentzIndex[Upper[l1],di1] - ), - cot@@{{y}, {Pair[LorentzIndex[Upper[l1],di1], - LorentzIndex[Upper[l2],di2] - ] ,z - } - } - ] - ]; - -cot[{Pair[LorentzIndex[Upper[l_],di___], b_/;FreeQ[b,Upper] - ], y___}, {z___}] := - If[ !FreeQ[{y,z}, LorentzIndex[Lower[l],di]], - cot@@({{y},{z}}/.LorentzIndex[Lower[l],di]->b), - cot[{y},{Pair[LorentzIndex[Upper[l],di],b], z}] - ]; - -cot[{Pair[b_ /;FreeQ[b,Upper], - LorentzIndex[Upper[l_],di___]], y___}, {z___}] := - If[ !FreeQ[{y,z}, LorentzIndex[Lower[l],di]], - cot@@({{y},{z}}/.LorentzIndex[Lower[l],di]->b), - cot@@{{y},{Pair[LorentzIndex[Upper[l],di],b], z}} - ]; - - -ttimes[{a___},{b___}] := - TTimes[a, b]; -SetAttributes[con,HoldAll]; -SetAttributes[Contract1,HoldAll]; - -(* -Contract1[exp_] := FixedPoint[con, exp, 1000]; -*) -Contract1[exp_] := - con[exp]; - -fdim[] = 4; -fdim[x_] := - x; - -con[exp_] := (*con[exp] =*) - Block[ {temp}, - If[ FreeQ[exp, Upper], - temp = exp, - temp = exp /. Times -> ct /. cot -> ttimes; - If[ !FreeQ[exp, Plus], - temp = Expand2[exp, Upper] /. Dispatch[{TTimes :> ct, Times -> ct}], - temp = exp /. Dispatch[{TTimes :> ct, Times -> ct}] - ] - ]; - If[ !FreeQ[temp,Lower], - temp = temp /. Pair[LorentzIndex[Lower[ll_],di___], - LorentzIndex[Upper[ll_],di___]] :> fdim[di]; - ]; - temp/.TTimes->Times - ]; - -FCPrint[1,"Contract1.m loaded."]; -End[] diff --git a/FeynCalc/Lorentz/CrossProduct.m b/FeynCalc/Lorentz/CrossProduct.m deleted file mode 100755 index 53bb79504..000000000 --- a/FeynCalc/Lorentz/CrossProduct.m +++ /dev/null @@ -1,40 +0,0 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: CrossProduct *) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 16 December '98 at 16:48 *) -(* ------------------------------------------------------------------------ *) - -(* ------------------------------------------------------------------------ *) - -CrossProduct::usage= -"CrossProduct[a, b] denotes the three-dimensional cross-product."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`CrossProduct`Private`"] - -(* antisymmetry *) -CrossProduct[b_, a_] := - CrossProduct[a, b] /; !OrderedQ[{b,a}]; - -(* linearity *) -CrossProduct[a_Plus, b_] := Map[CrossProduct[#, b]&, a]; -CrossProduct[(n_/;NumberQ[n]) a_, b_] := n CrossProduct[a, b]; - -CrossProduct[a_ThreeVector, CrossProduct[b_, c_]] := -DotProduct[a, c] b - DotProduct[a, b] c; - -CrossProduct[CrossProduct[b_, c_], a_ThreeVector] := --(DotProduct[a, c] b - DotProduct[a, b] c); - -CrossProduct /: MakeBoxes[CrossProduct[a_,b_], TraditionalForm] := -TBox[a,"\[Cross]",b]; - -FCPrint[1,"CrossProduct.m loaded."]; -End[] diff --git a/FeynCalc/Lorentz/DeclareFCTensor.m b/FeynCalc/Lorentz/DeclareFCTensor.m index b124b9a27..f2ff9fd08 100755 --- a/FeynCalc/Lorentz/DeclareFCTensor.m +++ b/FeynCalc/Lorentz/DeclareFCTensor.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Specify that given heads should be treated as tensor objects *) diff --git a/FeynCalc/Lorentz/DotProduct.m b/FeynCalc/Lorentz/DotProduct.m deleted file mode 100755 index aa4904b51..000000000 --- a/FeynCalc/Lorentz/DotProduct.m +++ /dev/null @@ -1,57 +0,0 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: DotProduct *) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 16 December '98 at 16:48 *) -(* ------------------------------------------------------------------------ *) - -(* ------------------------------------------------------------------------ *) - -DotProduct::usage= -"DotProduct[x, y] denotes the three-dimensional dot-product. \ -If x and y have Head List, DotProduct[x, a] (where a is a vector) \ -performs Sum[ x[[k]] a[[k]], {k, 0, 3}]."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`DotProduct`Private`"] - - -DotProduct[ThreeVector[b_], ThreeVector[a_]] := -DotProduct[ThreeVector[a], ThreeVector[b]] /; - !OrderedQ[{b,a}]; - -DotProduct[x_List, {a1_ /; Head[a1] =!= List, - a2_ /; Head[a2] =!= List, - a3_ /; Head[a3] =!= List} - ] := x[[1]] a1 + x[[2]] a2 + x[[3]] a3; - -(* linearity *) -DotProduct[a_Plus, b_] := Map[DotProduct[#, b]&, a]; -DotProduct[b_, a_Plus] := Map[DotProduct[b, #]&, a]; -DotProduct[(n_/;NumberQ[n]) a_, b_] := n DotProduct[a, b]; -DotProduct[b_, (n_/;NumberQ[n]) a_] := n DotProduct[b, a]; -DotProduct[(n_DotProduct) a_, b_] := n DotProduct[a, b]; -DotProduct[b_, (n_DotProduct) a_] := n DotProduct[b, a]; - -(* CrossProduct orders already its arguments *) -DotProduct[c_ThreeVector, CrossProduct[a_, b_]] := -DotProduct[a, CrossProduct[b, c]] /; OrderedQ[{a,b,c}]; - -DotProduct[CrossProduct[a_, b_], c_ThreeVector] := -DotProduct[c, CrossProduct[a, b]]; - -DotProduct[b_ThreeVector, CrossProduct[c_, a_]] := -DotProduct[a, CrossProduct[b, c]] /; OrderedQ[{a,b,c}]; - -DotProduct /: MakeBoxes[DotProduct[a_,b_], TraditionalForm] := -TBox[a,"\[CenterDot]",b]; - -FCPrint[1,"DotProduct.m loaded."]; -End[] diff --git a/FeynCalc/Lorentz/DummyIndexFreeQ.m b/FeynCalc/Lorentz/DummyIndexFreeQ.m new file mode 100755 index 000000000..f95d0ab5c --- /dev/null +++ b/FeynCalc/Lorentz/DummyIndexFreeQ.m @@ -0,0 +1,88 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: DummyIndexFreeQ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Checks if the expression contains dummy indices *) + +(* ------------------------------------------------------------------------ *) + + + +DummyIndexFreeQ::usage = +"DummyIndexFreeQ[exp, {head1, head2, ...}] returns True if the expression \ +contains dummy indices with heads head1, head2, ... and False otherwise. \ +As always in FeynCalc, Einstein summation convention is implicitly assumed. \ +The function is optimized for large expressions, i.e. it is not so good as \ +a criterion in e.g. Select"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`DummyIndexFreeQ`Private`"] + +DummyIndexFreeQ[expr_, heads_List] := + True/; FreeQ2[expr,heads]; + +DummyIndexFreeQ[expr_, heads_List] := + Block[{fullLiList, freeLiList, ex, times, i, sel, sel2}, + + + FCPrint[1, "DummyIndexFreeQ: Entering."]; + FCPrint[3, "DummyIndexFreeQ: Entering with: ", expr]; + + If[ Head[expr]===Times, + ex = SelectNotFree[expr, heads], + ex = expr + ]; + + ex = ExpandAll2[ex]; + + If[Head[ex]===Plus, + ex=First[ex] + ]; + + If[ !FreeQ[ex, Power], + ex = ex /. Power[a_, b_Integer?Positive] /; !FreeQ2[a, heads] :> + Apply[times, Table[a, {i, b}]]; + ]; + + FCPrint[3, "DummyIndexFreeQ: Final ex: ", ex]; + + sel = Blank/@heads; + If[ Length[heads]===1, + sel = Identity@@(Blank/@heads); + sel2 = Identity@@heads, + + sel = Alternatives@@(Blank/@heads); + sel2 = Alternatives@@heads + ]; + + FCPrint[1, "DummyIndexFreeQ: sel: ", sel]; + + freeLiList = Cases[ex, sel, Infinity]// + ReplaceAll[#, (sel2)[z_, ___] :> z] & // Tally // Cases[#, {z_, 1} :> z] &; + + FCPrint[3, "DummyIndexFreeQ: freeLiList: ", freeLiList]; + + fullLiList = Cases[expr, sel, Infinity] // DeleteDuplicates // Sort; + FCPrint[3, "DummyIndexFreeQ: fullLiList: ", fullLiList]; + + fullLiList = fullLiList // ReplaceAll[#, (sel2)[z_, ___] :> z] & // DeleteDuplicates // Sort; + FCPrint[3, "DummyIndexFreeQ: fullLiList: ", fullLiList]; + + (Complement[fullLiList, freeLiList] === {}) + ]/; !FreeQ2[expr,heads]; + +FCPrint[1,"DummyIndexFreeQ.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/EpsContract.m b/FeynCalc/Lorentz/EpsContract.m new file mode 100755 index 000000000..ba946b4a0 --- /dev/null +++ b/FeynCalc/Lorentz/EpsContract.m @@ -0,0 +1,144 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: EpsContract *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Contractions of two Eps tensors. *) + +(* ------------------------------------------------------------------------ *) + + +EpsContract::usage= +"EpsContract[exp] handles contractions of two Levi-Civita \ +tensors. It is also an option of Contract and other functions that specifies \ +whether such contractions should be done or not."; + +EpsContract::failmsg= +"Error! EpsContract has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`EpsContract`Private`"] + +Options[EpsContract] = { + Collecting -> True, + FCE -> False, + FCI -> False, + Factoring -> False +}; + +EpsContract[expr_, OptionsPattern[]]:= + Block[{ex, tmp, res, epsList, epsListEval,repRule, epsHead,null1,null2,epsIsolate}, + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + If[ FreeQ[ex,Eps], + Return[ex] + ]; + + If[ OptionValue[Collecting], + ex = Collect2[ex,Eps,Factoring->OptionValue[Factoring],IsolateNames->epsIsolate] + ]; + + If[ Head[ex]===Plus, + res = Map[(SelectFree[#, Eps] epsHead[SelectNotFree[#, Eps]]) &, ex], + res = SelectFree[ex, Eps] epsHead[SelectNotFree[ex, Eps]] + + ]; + + If[ Together[(res /. epsHead -> Identity)-ex] =!= 0, + Message[EpsContract::failmsg, "Failed to isolate epsilon tensors"]; + Abort[] + ]; + + epsList = Cases[res+null1+null2, _epsHead, Infinity]//Sort//DeleteDuplicates; + + epsListEval = epsCleverCon/@(epsList/. epsHead->Identity); + + repRule = Thread[Rule[epsList, epsListEval]]; + + res = FRH[res/. Dispatch[repRule],IsolateNames->epsIsolate]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + + ]; + +(* + epsCleverCon first applies the determinant formula to those tensors, + that have the largest number of common indices. This helps to avoid + spurious terms due to the Schouten identity. C.f. the explanation of + Jos Vermaseren: https://github.com/vermaseren/form/issues/65 +*) +epsCleverCon[expr_]:= + expr //. Power[Eps[a__],n_] :> epsHold[epscon[a]^n] //. + Eps[a__] Eps[b__]/; Length[Intersection[{a},{b}]]===3 :> epsHold[epscon[a]epscon[b]] //. + Eps[a__] Eps[b__]/; Length[Intersection[{a},{b}]]===2 :> epsHold[epscon[a]epscon[b]] //. + Eps[a__] Eps[b__]/; Length[Intersection[{a},{b}]]===1 :> epsHold[epscon[a]epscon[b]] /. + Eps -> epscon /. epscon -> Eps /. epsHold->Identity; + +epscon/: + epscon[a1_,a2_,a3_,a4_]^2 := + (( - ($LeviCivitaSign)^2 Det[{ + {PairContract[a1,a1],PairContract[a1,a2],PairContract[a1,a3],PairContract[a1,a4]}, + {PairContract[a2,a1],PairContract[a2,a2],PairContract[a2,a3],PairContract[a2,a4]}, + {PairContract[a3,a1],PairContract[a3,a2],PairContract[a3,a3],PairContract[a3,a4]}, + {PairContract[a4,a1],PairContract[a4,a2],PairContract[a4,a3],PairContract[a4,a4]} + }])/.PairContract->Pair)/; Complement[DeleteDuplicates[Head/@{a1,a2,a3,a4}], {LorentzIndex, Momentum, ExplicitLorentzIndex}]==={}; + +epscon/: + epscon[a1_,a2_,a3_]^2 := + ((( ($LeviCivitaSign)^2 Det[{ + {CartesianPairContract[a1,a1],CartesianPairContract[a1,a2],CartesianPairContract[a1,a3]}, + {CartesianPairContract[a2,a1],CartesianPairContract[a2,a2],CartesianPairContract[a2,a3]}, + {CartesianPairContract[a3,a1],CartesianPairContract[a3,a2],CartesianPairContract[a3,a3]} + }]//Expand)/.CartesianPairContract->CartesianPair ))/; Complement[DeleteDuplicates[Head/@{a1,a2,a3}], {CartesianIndex, CartesianMomentum}]==={}; + + + +epscon/: + epscon[a1_,a2_,a3_,a4_]^n_Integer?Positive := + ((hold[epscon[a1,a2,a3,a4]^2] epscon[a1,a2,a3,a4]^(n-2))/. hold->Identity )/; n>=3 && DeleteDuplicates[Head/@{a1,a2,a3,a4}]==={Momentum}; + +epscon/: + epscon[a1_,a2_,a3_,a4_]^n_Integer?Positive := + (Message[EpsContract::failmsg,"Epsilon tensor to a power higher than two with uncontracted Lorentz indices violates Einsein summation convention!"]; Abort[])/; n>=3 && !FreeQ[{a1,a2,a3,a4},LorentzIndex]; + +epscon/: + epscon[a1_,a2_,a3_,a4_] epscon[b1_,b2_,b3_,b4_] := + (( - ($LeviCivitaSign)^2 Det[{{PairContract[a1,b1],PairContract[a1,b2],PairContract[a1,b3],PairContract[a1,b4]}, + {PairContract[a2,b1],PairContract[a2,b2],PairContract[a2,b3],PairContract[a2,b4]}, + {PairContract[a3,b1],PairContract[a3,b2],PairContract[a3,b3],PairContract[a3,b4]}, + {PairContract[a4,b1],PairContract[a4,b2],PairContract[a4,b3],PairContract[a4,b4]}}]//Expand)/.PairContract->Pair)/; + Complement[DeleteDuplicates[Head/@{a1,a2,a3,a4,b1,b2,b3,b4}], {LorentzIndex, Momentum, ExplicitLorentzIndex}]==={}; + +epscon/: + epscon[a1_,a2_,a3_] epscon[b1_,b2_,b3_] := + (( ($LeviCivitaSign)^2 Det[{{CartesianPairContract[a1,b1],CartesianPairContract[a1,b2],CartesianPairContract[a1,b3]}, + {CartesianPairContract[a2,b1],CartesianPairContract[a2,b2],CartesianPairContract[a2,b3]}, + {CartesianPairContract[a3,b1],CartesianPairContract[a3,b2],CartesianPairContract[a3,b3]}}]//Expand)/.CartesianPairContract->CartesianPair)/; + Complement[DeleteDuplicates[Head/@{a1,a2,a3,b1,b2,b3}], {CartesianIndex, CartesianMomentum}]==={}; + + + +FCPrint[1,"EpsContract.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/EpsContractFreeQ.m b/FeynCalc/Lorentz/EpsContractFreeQ.m new file mode 100755 index 000000000..ea0c03b7a --- /dev/null +++ b/FeynCalc/Lorentz/EpsContractFreeQ.m @@ -0,0 +1,59 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: EpsContractFreeQ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Checks if the expression contains contractalbe epsilon tensors *) + +(* ------------------------------------------------------------------------ *) + + + +EpsContractFreeQ::usage = +"EpsContractFreeQ[exp] returns True if the expression \ +contains epsilon tensors that can be contracted with each other. \ +The function is optimized for large expressions, i.e. it is not so \ +good as a criterion in e.g. Select"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`EpsContractFreeQ`Private`"] + +EpsContractFreeQ[expr_] := + True/; FreeQ[expr, Eps]; + +EpsContractFreeQ[expr_] := + Block[{tmp, head, ex, times, i}, + + If[ Head[expr]===Times, + ex = SelectNotFree[expr, Eps], + ex = expr + ]; + + If[ !FreeQ[ex, Power], + ex = ex /. Power[a_, b_Integer?Positive] /; ! FreeQ[a, Eps] :> Apply[times, Table[a, {i, b}]]; + ]; + ex = ExpandAll2[ex]; + + If[Head[ex] === Plus, + tmp = Map[head @@ Cases[#, _Eps , Infinity] &, List @@ ex], + tmp = Cases[ex, _Eps , Infinity] + ]; + tmp = tmp /. head[] | head[_] :> Unevaluated@Sequence[]; + tmp === {} + + ] /;!FreeQ[expr, Eps]; + +FCPrint[1,"EpsContractFreeQ.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/EpsEvaluate.m b/FeynCalc/Lorentz/EpsEvaluate.m index ca78f7980..17baf1cbf 100644 --- a/FeynCalc/Lorentz/EpsEvaluate.m +++ b/FeynCalc/Lorentz/EpsEvaluate.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Simplification of epsilon tensors *) @@ -19,8 +19,9 @@ "EpsEvaluate[expr] applies total antisymmetry and \ linearity (w.r.t. Momentum's) to all Levi-Civita tensors (Eps's) in expr ."; -EpsEvaluate::fail = -"Something went while simplifying epsilon tensors. Evaluation aborted! " +EpsEvaluate::failmsg = +"Error! EpsEvaluate has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; (* ------------------------------------------------------------------------ *) @@ -30,28 +31,29 @@ Begin["`EpsEvaluate`Private`"] Options[EpsEvaluate] = { - FCI -> False, - Momentum -> All - }; + FCE -> False, + FCI -> False, + Momentum -> All +}; EpsEvaluate[expr_, OptionsPattern[]]:= - Block[{x,momList,uniqList,rud,repRule,null1,null2}, + Block[{ex, momList, uniqList, rud, repRule, null1, null2, res}, momList = OptionValue[Momentum]; If[ !OptionValue[FCI], - x = FCI[expr], - x = expr + ex = FCI[expr], + ex = expr ]; (* Nothing to do... *) - If[ FreeQ[x,Eps], - Return[x] + If[ FreeQ[ex,Eps], + Return[ex] ]; (* List of all the unique Epsilon tensors *) - uniqList = Cases[x+null1+null2,Eps[__],Infinity]//Union; + uniqList = Cases[ex+null1+null2,_Eps,Infinity]//DeleteDuplicates//Sort; (* If the user specified to perform expansion only for some special momenta, let's do it *) @@ -61,33 +63,44 @@ (* List of the expanded epsilons *) - repRule = Thread[rud[uniqList, uniqList/.Eps->epsEval]] /. rud->RuleDelayed; + repRule = Thread[rud[uniqList, uniqList/.Eps->epsEval]]; + repRule = repRule /. rud[a_, a_] :> Unevaluated@Sequence[] /. rud->RuleDelayed; (* Simple cross check *) - If[ !FreeQ2[repRule,{epsEval,epsEvalLinearity,epsEvalAntiSym}], - Message[EpsEvaluate::fail]; + If[ !FreeQ2[repRule,{epsEval,epsEvalLinearity,epsEvalAntiSymm}], + Message[EpsEvaluate::failmsg, "Some expressions could not be evaluated."]; Abort[] ]; - x/.Dispatch[repRule] + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res ]; -epsEval[a_,b_,c_,d_, opts:OptionsPattern[Eps]] := - (Expand/@(Distribute[DOT[a,b,c,d]//MomentumExpand]))/. - DOT->epsEvalLinearity/.epsEvalLinearity->epsEvalAntiSymm/.epsEvalAntiSymm[z__]:>Eps[z,opts] +epsEval[a_,b_,c__] := + (Expand/@(Distribute[DOT[a,b,c]//MomentumExpand]))/. + DOT->epsEvalLinearity/.epsEvalLinearity->epsEvalAntiSymm/.epsEvalAntiSymm -> epsEvalAntiSymm2 /. epsEvalAntiSymm2 -> Eps -epsEvalLinearity[a___,b_ (c : (LorentzIndex | ExplicitLorentzIndex | Momentum)[_,_: 4]),d___] := +epsEvalLinearity[a___,b_ (c : (LorentzIndex | ExplicitLorentzIndex | Momentum | CartesianIndex | CartesianMomentum | TemporalMomentum)[__]),d___] := b epsEvalLinearity[a,c,d]; epsEvalLinearity[___,0,___] := 0; epsEvalAntiSymm[x__] := - 0/; Signature[{x}]===0 && Length[{x}]===4; + 0/; Signature[{x}]===0 && MemberQ[{3,4},Length[{x}]]; epsEvalAntiSymm[x__] := - Signature[{x}] epsEvalAntiSymm@@Sort[{x}] /; !OrderedQ[{x}] && Length[{x}]===4; + Signature[{x}] epsEvalAntiSymm@@Sort[{x}] /; !OrderedQ[{x}] && MemberQ[{3,4},Length[{x}]]; + +epsEvalAntiSymm2[x___, ExplicitLorentzIndex[0], y__] := + (-1)^Length[{y}]*epsEvalAntiSymm2[x,y,ExplicitLorentzIndex[0]]; FCPrint[1,"EpsEvaluate.m loaded."]; End[] diff --git a/FeynCalc/Lorentz/ExpandScalarProduct.m b/FeynCalc/Lorentz/ExpandScalarProduct.m index 1185b445f..68d827df2 100644 --- a/FeynCalc/Lorentz/ExpandScalarProduct.m +++ b/FeynCalc/Lorentz/ExpandScalarProduct.m @@ -1,7 +1,17 @@ -(* ------------------------------------------------------------------------ *) -(* ------------------------------------------------------------------------ *) +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: ExpandScalarProduct *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* :Summary: ExpandScalarProduct expands scalar products *) +(* :Summary: Expansion of scalar products and vectors *) (* ------------------------------------------------------------------------ *) @@ -22,54 +32,83 @@ Begin["`ExpandScalarProduct`Private`"] ScalarProductExpand = ExpandScalarProduct; -tmpHead; +tmpHead::usage=""; +objects::usage=""; Options[ExpandScalarProduct] = { EpsEvaluate -> False, - FCI -> True, - Momentum -> All + FCE -> False, + FCI -> False, + Full -> True, + Momentum -> All }; -ExpandScalarProduct[x_, OptionsPattern[]] := - Block[ {nx = x, pali,moms}, +ExpandScalarProduct[expr_, OptionsPattern[]] := + Block[ {ex, pairList, pairListExpanded, moms, protect, momentum, relevant, null1, null2}, moms = OptionValue[Momentum]; - If[ OptionValue[FCI], - nx = FCI[nx] + If[ moms=!=All && Head[moms]=!=List, + moms = {moms} ]; + objects = Join[$FCTensorList,{TemporalPair}]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + (* This is to speed up things when dealing with tirival scalar products *) - If[ MatchQ[nx, Pair[Momentum[_, ___], Momentum[_, ___]]] && FreeQ[nx,Plus], - Return[nx] + If[ MatchQ[ex, Pair[Momentum[_, ___], Momentum[_, ___]] | CartesianPair[CartesianMomentum[_, ___], CartesianMomentum[_, ___]]] && FreeQ[ex,Plus], + Return[ex] ]; - If[ FreeQ2[nx,$FCTensorList], - Return[nx] + + If[ FreeQ2[ex,objects], + Return[ex] + ]; + + + relevant = Cases[ex + null1 + null2, (Alternatives @@ objects)[a_, b___] /; !FreeQ[{a, b}, Plus], Infinity]; + + If[relevant==={}, + Return[ex], + relevant = relevant//Sort//DeleteDuplicates ]; If [moms===All, - pali = Select[Cases2[nx, $FCTensorList], !FreeQ2[#, TensorArgsList]&], - pali = Select[Cases2[nx, $FCTensorList], (!FreeQ2[#, TensorArgsList] && !FreeQ2[#, moms])&] + pairList = Select[Cases2[relevant, objects], !FreeQ2[#, TensorArgsList]&]; + pairListExpanded = pairList, + pairList = Select[Cases2[relevant, objects], (!FreeQ2[#, TensorArgsList] && !FreeQ2[#, moms])&]; + If[ TrueQ[!OptionValue[Full]], + pairListExpanded = pairList //. { + Momentum[c_. mom_ + rest_: 0, dim___] /; MemberQ[moms, mom] :> momentum[c mom + protect[rest], dim], + Momentum[rest_, dim___] /; FreeQ[rest, moms] :> momentum[protect[rest], dim] + } /. momentum -> Momentum, + pairListExpanded = pairList + ] ]; - If[ pali =!= {}, - nx = nx /. Dispatch[Thread[pali -> pairexpand[pali]]] + If[ pairList =!= {}, + pairListExpanded = (pairexpand/@pairListExpanded) /. protect -> Identity; + ex = ex /. Dispatch[Thread[Rule[pairList,pairListExpanded]]] ]; - If[ OptionValue[EpsEvaluate], - nx = EpsEvaluate[nx,FCI->True,Momentum->OptionValue[Momentum]] + If[ OptionValue[EpsEvaluate] && !FreeQ[ex,Eps], + ex = EpsEvaluate[ex,FCI->True,Momentum->OptionValue[Momentum]] ]; - nx - ]; + If[ OptionValue[FCE], + ex = FCE[ex] + ]; -(* TODO this is a legacy syntax that one should get rid of! *) -ExpandScalarProduct[x_, y:Except[_?OptionQ], OptionsPattern[]] := - scevdoit[Pair,x, y]; + ex + ]; pairexpand[x_] := - x /. (head : (Alternatives @@ $FCTensorList))[arg__]/; head=!=Eps :>scevdoit[head,arg] ; + x /. (head : (Alternatives @@ objects))[arg__]/; head=!=Eps :>scevdoit[head,arg] ; scevdoit[head_,arg__] := Distribute[tmpHead@@(Expand[MomentumExpand/@{arg}])]/.tmpHead->head; diff --git a/FeynCalc/Lorentz/FCCanonicalizeDummyIndices.m b/FeynCalc/Lorentz/FCCanonicalizeDummyIndices.m index 9ebf44ef0..20424a599 100644 --- a/FeynCalc/Lorentz/FCCanonicalizeDummyIndices.m +++ b/FeynCalc/Lorentz/FCCanonicalizeDummyIndices.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Canonicalizes dummy Lorentz indices *) @@ -46,19 +46,23 @@ canodummyVerbose::usage=""; Options[FCCanonicalizeDummyIndices] = { - FCI -> False, - LorentzIndexNames -> {}, - SUNIndexNames -> {}, - SUNFIndexNames -> {}, - CustomIndexNames -> {}, - Momentum -> All, - NotMomentum -> {}, - Head -> {LorentzIndex,SUNIndex,SUNFIndex}, - FCVerbose-> False, - DotSimplify -> True, - FCTraceExpand -> True, - FCVerbose -> False, - Function -> Function[{x, seed}, FCGV[(ToString[seed] <> ToString[Identity @@ x])]] + CartesianIndexNames -> {}, + CustomIndexNames -> {}, + DiracChainExpand -> True, + DiracIndexNames -> {}, + DotSimplify -> True, + FCE -> False, + FCI -> False, + FCTraceExpand -> True, + FCVerbose -> False, + FCVerbose -> False, + Function -> Function[{x, seed}, FCGV[(ToString[seed] <> ToString[Identity @@ x])]], + Head -> {LorentzIndex,CartesianIndex,SUNIndex,SUNFIndex, DiracIndex}, + LorentzIndexNames -> {}, + Momentum -> All, + NotMomentum -> {}, + SUNFIndexNames -> {}, + SUNIndexNames -> {} }; makeRepIndexList[mIndexHead_,mWrappinHead_,mSeed_,mFunc_,mFinalList_,mUniqueExp_]:= @@ -73,23 +77,23 @@ dummyHeads = Cases2[totalRepLis,wrapHead]; If[ Length[dummyNames]True] + ]; + If[ OptionValue[DotSimplify], - ex = DotSimplify[ex,FCI->False] + ex = DotSimplify[ex,FCI->True] ]; + If[ OptionValue[DiracChainExpand], + ex = DiracChainExpand[ex,FCI->True] + ]; tmp = Expand2[ex, indhead]; {rest0,tmp} = FCSplit[tmp,indhead]; - If[ OptionValue[FCTraceExpand], - tmp = FCTraceExpand[tmp,FCI->True] + + + If[ !FreeQ[tmp,Power], + tmp = tmp /. Power[z_, n_Integer?Positive]/;!FreeQ2[z, indhead] :> Apply[times, Table[z, {Abs[n]}]]^Sign[n] ]; - indexList = - Map[Tally, Map[Cases[#, (Alternatives@@indhead)[ind_, ___]/;(Head[ind]=!=Upper && - Head[ind]=!=Lower), - Infinity]&,Apply[List, tmp+null1+null2]]]// Flatten[#, 1] & // Union; + dimensions = FCGetDimensions[tmp,FCI->True]; + FCPrint[3,"FCCanonicalizeDummyIndices: dimensions: ", dimensions, FCDoControl->canodummyVerbose]; - FCPrint[2,"FCCanonicalizeDummyIndices: List of indices and their multiplicities: ", indexList, - FCDoControl->canodummyVerbose]; + indexList = Map[ + ReplaceAll[Cases[#, (Alternatives@@indhead)[_, ___], Infinity],(h:(Alternatives@@indhead))[ind_, ___]:>h[ind]]&, + Apply[List, tmp+null1+null2]]; + + FCPrint[3,"FCCanonicalizeDummyIndices: Preliminary indexList: ", indexList, FCDoControl->canodummyVerbose]; + + indexList = Tally/@(indexList); + + FCPrint[3,"FCCanonicalizeDummyIndices: Preliminary indexList after Tally: ", indexList, FCDoControl->canodummyVerbose]; + + indexList = indexList// Flatten[#, 1] & // Union; + + FCPrint[2,"FCCanonicalizeDummyIndices: List of indices and their multiplicities: ", indexList, FCDoControl->canodummyVerbose]; If[ Select[indexList, ((#[[2]]) > 2) &]=!={}, Message[FCCanonicalizeDummyIndices::failmsg,"The input expression contains dummy indices that @@ -154,6 +178,15 @@ ]; finalList = Cases[indexList, {ind_, 2} -> ind ]; + finalList = finalList /. {(h:LorentzIndex|CartesianIndex)[x_] :> Map[h[x,#]&,dimensions]}; + finalList = Flatten[finalList]; + + FCPrint[3,"FCCanonicalizeDummyIndices: finalList: ", finalList, FCDoControl->canodummyVerbose]; + + If[ finalList==={}, + FCPrint[1,"FCCanonicalizeDummyIndices: No dummy indices to canonicalize, returning the original expression.", FCDoControl->canodummyVerbose]; + Return[exUnexpanded]; + ]; tmp = FCLoopIsolate[tmp,finalList,Head->isoHead,Factoring->False,DotSimplify->OptionValue[DotSimplify]]; @@ -166,30 +199,80 @@ FCPrint[2,"FCCanonicalizeDummyIndices: Unique expressions: ", uniqueExpressions, FCDoControl->canodummyVerbose]; - If[ (Head[moms]=!=All && Head[moms]===List) || notmoms=!={}, - (* only for particular momenta *) - indexExtract = Map[Cases[#, _[a___, LorentzIndex[y__],b___]/;!FreeQ2[{a,b},moms] && FreeQ2[{a,b},notmoms] && MemberQ[finalList,LorentzIndex[y]]:> LorentzIndex[y], Infinity]&, uniqueExpressions], - (* for all momenta *) - indexExtract = Map[Cases[#, LorentzIndex[y__]/; MemberQ[finalList,LorentzIndex[y]], Infinity]&, uniqueExpressions] - ]; + (* Lorentz indices *) + If[ !FreeQ[indhead,LorentzIndex], + If[ (Head[moms]=!=All && Head[moms]===List) || notmoms=!={}, + (* only for particular momenta *) + indexExtract = Map[Cases[#, _[a___, LorentzIndex[y__],b___]/;!FreeQ2[{a,b},moms] && FreeQ2[{a,b},notmoms] && MemberQ[finalList,LorentzIndex[y]]:> LorentzIndex[y], Infinity]&, uniqueExpressions], + (* for all momenta *) + indexExtract = Map[Cases[#, LorentzIndex[y__]/; MemberQ[finalList,LorentzIndex[y]], Infinity]&, uniqueExpressions] + ]; - indexExtract = DeleteDuplicates/@indexExtract; + indexExtract = DeleteDuplicates/@indexExtract; - FCPrint[2,"FCCanonicalizeDummyIndices: Set of dummy Lorentz indices: ", indexExtract, FCDoControl->canodummyVerbose]; + FCPrint[2,"FCCanonicalizeDummyIndices: Set of dummy Lorentz indices: ", indexExtract, FCDoControl->canodummyVerbose]; - If[ !MatchQ[indexExtract, {{___LorentzIndex} ...}], - Message[FCCanonicalizeDummyIndices::failmsg, - "Failed to properly extract dummy Lorentz indices."]; - FCPrint[1,"FCCanonicalizDummyIndices: Entering with: ", indexExtract, FCDoControl->canodummyVerbose]; - Abort[] + If[ !MatchQ[indexExtract, {{___LorentzIndex} ...}], + Message[FCCanonicalizeDummyIndices::failmsg, + "Failed to properly extract dummy Lorentz indices."]; + FCPrint[1,"FCCanonicalizDummyIndices: Entering with: ", indexExtract, FCDoControl->canodummyVerbose]; + Abort[] + ]; + + repIndexListLor = Map[Function[x, MapIndexed[Rule[#1, LorentzIndex[lihead@fu[#2, seedLor]]] &,x]][#] &, + DeleteDuplicates/@(indexExtract/. (LorentzIndex[aa_,_]:> LorentzIndex[aa])) + ]; + + FCPrint[2,"FCCanonicalizeDummyIndices: repIndexListLor: ", repIndexListLor, FCDoControl->canodummyVerbose]; + + repIndexListLor = repIndexListLor/. Rule -> rule /. + {rule[LorentzIndex[x_],LorentzIndex[y_]]:> Map[rule[LorentzIndex[x,#],LorentzIndex[y,#]]&,dimensions]} /. rule -> Rule; + + repIndexListLor = DeleteDuplicates/@(Flatten/@repIndexListLor); + + FCPrint[2,"FCCanonicalizeDummyIndices: repIndexListLor: ", repIndexListLor, FCDoControl->canodummyVerbose], + + repIndexListLor=Sequence[]; ]; - repIndexListLor = Map[Function[x, MapIndexed[Rule[#1, LorentzIndex[lihead@fu[#2, seedLor], - (#1 /.LorentzIndex[_, dim_: 4] :> dim)]] &,x]][#] &, indexExtract]; + (* Cartesian indices *) + If[ !FreeQ[indhead,CartesianIndex], + If[ (Head[moms]=!=All && Head[moms]===List) || notmoms=!={}, + (* only for particular momenta *) + indexExtract = Map[Cases[#, _[a___, CartesianIndex[y__],b___]/;!FreeQ2[{a,b},moms] && FreeQ2[{a,b},notmoms] && MemberQ[finalList,CartesianIndex[y]]:> CartesianIndex[y], Infinity]&, uniqueExpressions], + (* for all momenta *) + indexExtract = Map[Cases[#, CartesianIndex[y__]/; MemberQ[finalList,CartesianIndex[y]], Infinity]&, uniqueExpressions] + ]; + + indexExtract = DeleteDuplicates/@indexExtract; + + FCPrint[2,"FCCanonicalizeDummyIndices: Set of dummy Cartesian indices: ", indexExtract, FCDoControl->canodummyVerbose]; + + If[ !MatchQ[indexExtract, {{___CartesianIndex} ...}], + Message[FCCanonicalizeDummyIndices::failmsg, + "Failed to properly extract dummy Cartesian indices."]; + FCPrint[1,"FCCanonicalizDummyIndices: Entering with: ", indexExtract, FCDoControl->canodummyVerbose]; + Abort[] + ]; + + repIndexListCar = Map[Function[x, MapIndexed[Rule[#1, CartesianIndex[cihead@fu[#2, seedCar]]] &,x]][#] &, + DeleteDuplicates/@(indexExtract/. (CartesianIndex[aa_,_]:> CartesianIndex[aa]))]; + + repIndexListCar = repIndexListCar/. Rule -> rule /. + {rule[CartesianIndex[x_],CartesianIndex[y_]]:> Map[rule[CartesianIndex[x,#],CartesianIndex[y,#]]&,dimensions]} /. rule -> Rule; - FCPrint[2,"FCCanonicalizeDummyIndices: repIndexListLor: ", repIndexListLor, FCDoControl->canodummyVerbose]; + repIndexListCar = DeleteDuplicates/@(Flatten/@repIndexListCar); - otherHeads = Complement[Union[indhead],{LorentzIndex,SUNIndex,SUNFIndex}]; + + + FCPrint[2,"FCCanonicalizeDummyIndices: repIndexListCar: ", repIndexListCar, FCDoControl->canodummyVerbose], + repIndexListCar = Sequence[] + + ]; + + (* Rest *) + + otherHeads = Complement[Union[indhead],{LorentzIndex,CartesianIndex,SUNIndex,SUNFIndex,DiracIndex}]; FCPrint[1,"FCCanonicalizeDummyIndices: Custom index heads present: ", otherHeads, FCDoControl->canodummyVerbose]; If[otherHeads =!={}, @@ -199,10 +282,13 @@ FCDoControl->canodummyVerbose]; ]; - repIndexListTotal = {repIndexListLor, + repIndexListTotal = {repIndexListLor,repIndexListCar, makeRepIndexList[SUNIndex,sunhead,Unique["sun"],fu,finalList,uniqueExpressions], - makeRepIndexList[SUNFIndex,sunfhead,Unique["sunf"],fu,finalList,uniqueExpressions] + makeRepIndexList[SUNFIndex,sunfhead,Unique["sunf"],fu,finalList,uniqueExpressions], + makeRepIndexList[DiracIndex,dihead,Unique["di"],fu,finalList,uniqueExpressions] }; + + If [ repIndexListsCustom =!={}, repIndexListTotal = Join[repIndexListTotal,repIndexListsCustom]; ]; @@ -213,7 +299,13 @@ (* Renaming of dummy indices according to the supplied list *) - cList = {{OptionValue[LorentzIndexNames],lihead},{OptionValue[SUNIndexNames],sunhead},{OptionValue[SUNFIndexNames],sunfhead}}; + cList = { + {OptionValue[LorentzIndexNames],lihead}, + {OptionValue[CartesianIndexNames],cihead}, + {OptionValue[SUNIndexNames],sunhead}, + {OptionValue[SUNFIndexNames],sunfhead}, + {OptionValue[DiracIndexNames],dihead} + }; If[ OptionValue[CustomIndexNames]=!={}, cList = Join[cList,Map[{Last[#], ToExpression[ToString[First[#]]<>"head"]}&,OptionValue[CustomIndexNames]]]; ]; @@ -240,11 +332,15 @@ canIndexList = (MapIndexed[(#1 /. First[repIndexListTotal[[#2]]]) &, uniqueExpressions]); FCPrint[3,"FCCanonicalizeDummyIndices: canIndexList: ", canIndexList, FCDoControl->canodummyVerbose]; - finalRepList = MapThread[Rule[#1, #2] &, {uniqueExpressions, canIndexList}]; + finalRepList = Thread[Rule[uniqueExpressions, canIndexList]]; FCPrint[3,"FCCanonicalizeDummyIndices: canIndexList: ", finalRepList, FCDoControl->canodummyVerbose]; - res = (rest0+tmp) /.finalRepList /. isoHead|lihead|sunhead|sunfhead->Identity; + res = (rest0+tmp) /.finalRepList /. isoHead|lihead|cihead|sunhead|sunfhead|dihead->Identity /. times -> Times; + + If[OptionValue[FCE], + res = FCE[res] + ]; res ] diff --git a/FeynCalc/Lorentz/FCClearScalarProducts.m b/FeynCalc/Lorentz/FCClearScalarProducts.m index 56385d7ff..153752255 100755 --- a/FeynCalc/Lorentz/FCClearScalarProducts.m +++ b/FeynCalc/Lorentz/FCClearScalarProducts.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Clears definitions of scalar products *) @@ -36,12 +36,24 @@ FCClearScalarProducts[OptionsPattern[]] := ( - DownValues[Pair] = initialPairDownValues; - DownValues[ScalarProduct] = initialScalarProductDownValues; - UpValues[ScalarProduct] = initialScalarProductUpValues; - DownValues[SP] = initialSPDownValues; - DownValues[SPD] = initialSPDDownValues; - $ScalarProducts = initialScalarProducts; + DownValues[Pair] = FeynCalc`Package`initialPairDownValues; + DownValues[CartesianPair] = FeynCalc`Package`initialCartesianPairDownValues; + DownValues[TemporalPair] = FeynCalc`Package`initialTemporalPairDownValues; + DownValues[ScalarProduct] = FeynCalc`Package`initialScalarProductDownValues; + UpValues[ScalarProduct] = FeynCalc`Package`initialScalarProductUpValues; + DownValues[CartesianScalarProduct] = FeynCalc`Package`initialCartesianScalarProductDownValues; + UpValues[CartesianScalarProduct] = FeynCalc`Package`initialCartesianScalarProductUpValues; + DownValues[SP] = FeynCalc`Package`initialSPDownValues; + DownValues[SPD] = FeynCalc`Package`initialSPDDownValues; + DownValues[SPE] = FeynCalc`Package`initialSPEDownValues; + DownValues[CSP] = FeynCalc`Package`initialCSPDownValues; + DownValues[CSPD] = FeynCalc`Package`initialCSPDDownValues; + DownValues[CSPE] = FeynCalc`Package`initialCSPEDownValues; + DownValues[TC] = FeynCalc`Package`initialTCDownValues; + DownValues[Momentum] = FeynCalc`Package`initialMomentumDownValues; + DownValues[TemporalMomentum] = FeynCalc`Package`initialTemporalMomentumDownValues; + DownValues[CartesianMomentum] = FeynCalc`Package`initialCartesianMomentumDownValues; + $ScalarProducts = FeynCalc`Package`initialScalarProducts; ); FCPrint[1,"FCClearScalarProducts.m loaded"]; diff --git a/FeynCalc/Lorentz/FCGetDimensions.m b/FeynCalc/Lorentz/FCGetDimensions.m index 454686f9b..dadff480f 100755 --- a/FeynCalc/Lorentz/FCGetDimensions.m +++ b/FeynCalc/Lorentz/FCGetDimensions.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Extracts dimensions of 4-momenta and Dirac matrices *) @@ -22,26 +22,58 @@ if one want to be sure that all quantities inside a particular expression are purely 4-dimensional or purely D-dimensional."; +FCGetDimensions::failmsg = +"Error! FCGetDimensions has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + Begin["`Package`"] End[] Begin["`FCGetDimensions`Private`"] Options[FCGetDimensions] = { - FCI -> False + ChangeDimension -> False, + FCI -> False, + FreeQ -> {}, + "DiracGamma[5]" -> True }; FCGetDimensions[expr_, OptionsPattern[]]:= - Block[{ex, res, null1,null2}, + Block[{ex, res, null1,null2,head, optFreeQ}, + + optFreeQ = OptionValue[FreeQ]; + If[ Head[optFreeQ]=!=List, + Message[FCGetDimensions::failmsg, "The value of the FreeQ option must be a list."]; + ]; If[ !OptionValue[FCI], ex = FCI[expr], ex = expr ]; + If[ optFreeQ=!={}, + ex = ex/. Dispatch[Rule[#, Unique["fcgd"]] & /@ optFreeQ]; + + If[ !FreeQ2[ex,optFreeQ], + Message[FCGetDimensions::failmsg, "Failed to mask the specified objects."]; + Abort[] + ] + ]; + + res = Cases[ex+null1+null2, _Momentum | _DiracGamma | _PauliSigma | _LorentzIndex | + _ExplicitLorentzIndex | _CartesianIndex | _CartesianMomentum | _TemporalMomentum, Infinity]//DeleteDuplicates//Sort; + res = res /. (Momentum|TemporalMomentum|DiracGamma|LorentzIndex|ExplicitLorentzIndex)[_, dim_:4]:> dim; + res = res /. (CartesianIndex|CartesianMomentum)[_, dim_:3]:> head[dim]; + res = res /. PauliSigma[_, dim_:3]:> dim; + + (* Sometimes we do not need to distinguish between dimensions of Lorentz and Cartesian objects. + For example, a 3-dimensional Cartesian vector can be regarded as a part of a 4-dimensional Lorentz vector *) + If[OptionValue[ChangeDimension], + res = res /.{head[3]->head[4],head[s_Symbol-1]:>s} + ]; + + res = (res /. head -> Identity)//DeleteDuplicates//Sort; - res = Union[Cases[ex+null1+null2, - (Momentum|DiracGamma|DiracGammaT|LorentzIndex|ExplicitLorentzIndex)[_, dim_: 4] :> dim, Infinity]]; res ]; diff --git a/FeynCalc/Lorentz/FCPermuteMomentaRules.m b/FeynCalc/Lorentz/FCPermuteMomentaRules.m new file mode 100755 index 000000000..5abf8bd10 --- /dev/null +++ b/FeynCalc/Lorentz/FCPermuteMomentaRules.m @@ -0,0 +1,79 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCPermuteMomentaRules *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Generates all possible permutations of the given momenta *) + +(* ------------------------------------------------------------------------ *) + + + +FCPermuteMomentaRules::usage = +"FCPermuteMomentaRules[{p1, p2, ...}] returns a set of rules that contain +all possible permutations of the momenta p1, p2, ... . This can be useful when +working with amplitudes that exhibit a symmetry in some or all of the final +state momenta or when trying to find mappings between loop integrals from +different topologies."; + +FCPermuteMomentaRules::failmsg = +"Error! FCPermuteMomentaRules has encountered a fatal problem and must abort the computation. \n +The problem reads: `1`"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCPermuteMomentaRules`Private`"] + +FCPermuteMomentaRules[ex_ /; Head[ex] =!= List] := + ( + Message[FCPermuteMomentaRules::failmsg, "The input expression is not a list."]; + Abort[] + ); + +FCPermuteMomentaRules[{}] := + {{}}; + +FCPermuteMomentaRules[{_}] := + {{}}; + +FCPermuteMomentaRules[lmoms_List] := + Block[{ permutations, len, rule, res}, + + If[! FCDuplicateFreeQ[lmoms], + Message[FCPermuteMomentaRules::failmsg, "The list of the momenta contains duplicates."]; + Abort[] + ]; + len = Length[lmoms]; + + permutations = Permute[lmoms, PermutationGroup[Cycles[{#}] & /@ Subsets[Range[len], {2, len}]]]; + + If[ !MatchQ[permutations, {{_, __} ..}], + Message[FCPermuteMomentaRules::failmsg, "The obtained list of permutations is incorrect."]; + Abort[] + ]; + + res = Thread[rule[ConstantArray[lmoms, Length[permutations]], permutations]]; + res = res /. rule[x_List, y_List] :> Thread[rule[x, y]] /. rule[a_, a_] :> Unevaluated[Sequence[]] /. rule -> Rule; + res = SortBy[res, Length]; + + If[ !MatchQ[res, {{}, {_Rule ..} ..}], + Message[FCPermuteMomentaRules::failmsg, "The obtained list of rules is incorrect."]; + Abort[] + ]; + + res + ]; + +FCPrint[1,"FCPermuteMomentaRules.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/FCRenameDummyIndices.m b/FeynCalc/Lorentz/FCRenameDummyIndices.m index da00601f4..47d473852 100644 --- a/FeynCalc/Lorentz/FCRenameDummyIndices.m +++ b/FeynCalc/Lorentz/FCRenameDummyIndices.m @@ -4,22 +4,24 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) -(* :Summary: Rename dummy Lorentz and SU(N) indices *) +(* :Summary: Rename dummy Lorentz, Cartesian, SU(N) and Dirac indices *) (* ------------------------------------------------------------------------ *) FCRenameDummyIndices::usage = " -FCRenameDummyIndices[expr] identifies all dummy Lorentz and SU(N) indices \ -and changes their names pairwise to random symbols. This can be useful if \ -you have an expression that contains dummy indices and want to compute the \ -square of it. For example, the square of GA[a, l, a] equals 16. However, \ -if you forget to rename the dummy indices and compute GA[a, l, a, a, l, a] \ -instead of GA[a, l, a, b, l, b], you will get 64."; +FCRenameDummyIndices[expr] identifies all dummy indices with heads given in \ +the value of the option Head and changes their names pairwise to random symbols. \ +This is particularly important when squaring amplitudes, since otherwise the result +will be inconsistent."; + +FCRenameDummyIndices::failmsg = +"Error! FCRenameDummyIndices has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" (* ------------------------------------------------------------------------ *) @@ -27,32 +29,113 @@ End[] Begin["`FCRenameDummyIndices`Private`"] +rdiVerbose::usage=""; + +Options[FCRenameDummyIndices] = { + DotSimplify -> True, + Expanding -> True, + FCE -> False, + FCI -> False, + Head -> { + LorentzIndex, + CartesianIndex, + SUNIndex, + SUNFIndex, + DiracIndex + }, + FCVerbose -> False + +}; + +FCRenameDummyIndices[expr_List, opts:OptionsPattern[]] := + Map[FCRenameDummyIndices[#,opts] &, expr]; + +FCRenameDummyIndices[expr_, OptionsPattern[]] := + Block[{ indexList = {}, replacementList, exprFCI, ex, res, heads, + patt, optExpanding, time}, + + If [OptionValue[FCVerbose]===False, + rdiVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + rdiVerbose=OptionValue[FCVerbose] + ]; + ]; + + heads = OptionValue[Head]; + optExpanding = OptionValue[Expanding]; + + If[ !OptionValue[FCI], + exprFCI = FCI[expr], + exprFCI = expr + ]; + + FCPrint[1,"FCRenameDummyIndices: Entering.", FCDoControl->rdiVerbose]; + FCPrint[3,"FCRenameDummyIndices: Entering with ", exprFCI, FCDoControl->rdiVerbose]; + + If[ DummyIndexFreeQ[exprFCI, heads], + FCPrint[1,"FCRenameDummyIndices: No relevant dummy indices found, leaving.", FCDoControl->rdiVerbose]; + Return[exprFCI] + ]; + + ex = exprFCI; + + If[ OptionValue[DotSimplify], + time=AbsoluteTime[]; + FCPrint[1, "FCRenameDummyIndices: Applying DotSimplify.", FCDoControl->rdiVerbose]; + exprFCI = DotSimplify[exprFCI, FCI->True, Expanding->optExpanding]; + FCPrint[1, "FCRenameDummyIndices: DotSimplify done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->rdiVerbose]; + FCPrint[3, "FCRenameDummyIndices: After FCColorIsolate: ", exprFCI, FCDoControl->rdiVerbose]; + + ]; + + If[ optExpanding, + time=AbsoluteTime[]; + FCPrint[1, "FCRenameDummyIndices: Applying Expand.", FCDoControl->rdiVerbose]; + exprFCI = Expand[exprFCI]; + FCPrint[1, "FCRenameDummyIndices: Expand done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->rdiVerbose]; + FCPrint[3, "FCRenameDummyIndices: After Expand: ", exprFCI, FCDoControl->rdiVerbose]; + ]; + + + If[ Head[heads]=!=List || heads==={}, + Message[FCRenameDummyIndices::failmsg, "You did not specify which index heads should be renamed."]; + Abort[] + ]; + + If[ Length[heads]>1, + patt = Alternatives@@heads, + patt = Identity@@heads + ]; -FCRenameDummyIndices[expr_List] := - Map[FCRenameDummyIndices[#] &, expr]; -FCRenameDummyIndices[expr_] := - Block[ {indexList = {}, replacementList, exprFCI}, - exprFCI = expr // FCI // DotSimplify // Expand; If[ Head[exprFCI]===Plus, indexList = - Map[Tally, Map[Cases[#, (LorentzIndex | SUNIndex | SUNFIndex)[ind_, ___]/;(Head[ind]=!=Upper && - Head[ind]=!=Lower) :> ind, - Infinity]&,Apply[List, exprFCI]]]// Flatten[#, 1] & // Union;, + Map[Tally, Map[Cases[#, (patt)[ind_, ___] :> ind, Infinity]&,Apply[List, exprFCI]]]// Flatten[#, 1] & // Union, indexList = - Cases[exprFCI, (LorentzIndex | SUNIndex | SUNFIndex)[ind_,___]/;(Head[ind]=!=Upper && - Head[ind]=!=Lower) :> ind, - Infinity] // Tally; + Cases[exprFCI, (patt)[ind_,___] :> ind, Infinity] // Tally; ]; - FCPrint[1,"List of indices to be randomized: ", StandardForm[indexList]]; + + FCPrint[1,"FCRenameDummyIndices: List of indices to be randomized: ", StandardForm[indexList], FCDoControl->rdiVerbose]; + If[ Select[indexList, ((#[[2]]) > 2) &]=!={}, - FCPrint[0,"Warning! The expression ", exprFCI, " violates Einstein notation!"]; - FCPrint[0,"Following indices appear more than twice: ", Select[indexList, ((#[[2]]) > 2) &]]; + Message[FCRenameDummyIndices::failmsg, "The input expression violates Einstein summation. Some dummy indices appear more than twice."]; + Abort[] + ]; + + replacementList = Map[Rule[(h: patt)[#[[1]],di___], h[$AL[Unique[]],di]] &, Cases[indexList, {_, 2}]]; + + FCPrint[2,"FCRenameDummyIndices: List of replacement rules: ", replacementList]; + + res = ex //. replacementList; + + If[ OptionValue[FCE], + res = FCE[res] ]; - replacementList = Map[Rule[#[[1]], $AL[Unique[]]] &, Cases[indexList, {_, 2}]]; - FCPrint[2,"List of replacement rules: ", replacementList]; - result = FCI[expr] //. replacementList; - result + + FCPrint[1,"FCRenameDummyIndices: Leaving.", FCDoControl->rdiVerbose]; + FCPrint[3,"FCRenameDummyIndices: Leaving with ", res, FCDoControl->rdiVerbose]; + + res ] FCPrint[1,"FCRenameDummyIndices.m loaded."]; diff --git a/FeynCalc/Lorentz/FCReplaceMomenta.m b/FeynCalc/Lorentz/FCReplaceMomenta.m new file mode 100755 index 000000000..27f376c55 --- /dev/null +++ b/FeynCalc/Lorentz/FCReplaceMomenta.m @@ -0,0 +1,188 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCReplaceMomenta *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Replaces the given momenta with other momenta *) + +(* ------------------------------------------------------------------------ *) + +FCReplaceMomenta::usage = +"FCReplaceMomenta[exp,rule] replaces the given momentum according to the \ +specified replacement rules. Various options can be used to customize the replacement \ +procedure."; + +FCReplaceMomenta::repfail= +"Error! Failed to replace all occurences of `1` with `2`. Evaluation aborted."; + +FCReplaceMomenta::failmsg = +"Error! FCReplaceMomenta has encountered a fatal problem and must abort \ +the computation. The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCReplaceMomenta`Private`"] + +fcrmVerbose::usage=""; + +Options[FCReplaceMomenta] = { + Dimensions -> All, + EpsEvaluate -> False, + ExpandScalarProduct -> False, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Head -> { (*All is also possible*) + DiracGamma,PauliSigma,CartesianPair, + TemporalPair,Pair,Eps,FeynAmpDenominator + }, + MomentumExpand -> True, + Polarization -> False, + Replace -> { + Momentum, CartesianMomentum, TemporalMomentum + }, + SelectFree -> {}, + Variables -> {} +}; + +FCReplaceMomenta[expr_, replacementRules_List/;replacementRules=!={}, OptionsPattern[]] := + Block[{ ex,res, relevantMomenta,relevantObjects,sel, relevantMomentumHeads, + objectHeads, momentumHeads,dims, rule, pat, finalRepRule, intermediateRepRule, + relevantObjectsEval, variableRule, vars, null1, null2, selectFree, tmp, maskedObjects, + ruleMask + }, + + If [OptionValue[FCVerbose]===False, + fcrmVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fcrmVerbose=OptionValue[FCVerbose] + ]; + ]; + + + objectHeads = OptionValue[Head]; + momentumHeads = OptionValue[Replace]; + dims = OptionValue[Dimensions]; + vars = OptionValue[Variables]; + selectFree = OptionValue[SelectFree]; + + maskedObjects = {}; + + FCPrint[1,"FCReplaceMomenta: Entering.", FCDoControl->fcrmVerbose]; + FCPrint[3,"FCReplaceMomenta: Entering with ", expr, FCDoControl->fcrmVerbose]; + + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + (*we also want something like p1->x*p2 to work!*) + + If[ !MathcQ[replacementRules,{Rule___}], + Message[FCReplaceMomenta::failmsg, "The momentum replacement rules are incorrect."]; + Abort[] + + ]; + + relevantMomenta = First/@replacementRules; + + (* First we extract all the relevant objects that contain the momenta we want to replace*) + If[objectHeads=!=All, + + sel = Blank/@objectHeads; + If[ Length[objectHeads]===1, + sel = Identity@@(Blank/@objectHeads), + sel = Alternatives@@(Blank/@objectHeads) + ]; + + relevantObjects = Cases[ex+null1+null2, sel, Infinity]//Sort//DeleteDuplicates; + + If[ selectFree=!={} && Head[selectFree]===List, + tmp = SelectFree[relevantObjects,Sequence@@selectFree]; + maskedObjects = Complement[relevantObjects,tmp]; + relevantObjects = tmp; + FCPrint[2,"FCReplaceMomenta: Filtered objects according to the SelectFree option: ", relevantObjects, FCDoControl->fcrmVerbose] + ]; + + relevantObjects = SelectNotFree[relevantObjects,relevantMomenta], + + + + + relevantObjects = Cases[ex+null1+null2, h_[x__]/;!FreeQ2[{x}, relevantMomenta], Infinity]//Sort//DeleteDuplicates + + ]; + + If[ OptionValue[MomentumExpand], + relevantObjectsEval = MomentumExpand/@relevantObjects, + relevantObjectsEval = relevantObjects + ]; + + (* Then we generate the replacement rules*) + + If[ Length[momentumHeads]===1, + sel = First[momentumHeads], + sel = Alternatives@@(momentumHeads) + ]; + + + + + If[ dims===All, + intermediateRepRule = Map[Rule[(h:sel)[#[[1]],di___], h[#[[2]],di]]&, replacementRules], + intermediateRepRule = Map[Rule[(h:sel)[#[[1]],di_:4]/;MemberQ[dims,di], h[#[[2]],di]]&, replacementRules] + ]; + + If[ OptionValue[Polarization], + intermediateRepRule = Join[intermediateRepRule, Map[Rule[Polarization[#[[1]],di___], Polarization[#[[2]],di]]&, replacementRules]] + ]; + + + FCPrint[3,"FCReplaceMomenta: Intermediate repalcement rule:.", intermediateRepRule, FCDoControl->fcrmVerbose]; + + relevantObjectsEval = relevantObjectsEval /. Dispatch[intermediateRepRule]; + + + relevantObjectsEval = (MomentumExpand/@relevantObjectsEval) //. (h:sel)[x_ y_, dm___]/; MemberQ[vars,x] :> x h[y, dm] ; + + finalRepRule = Thread[Rule[relevantObjects,relevantObjectsEval]]; + + FCPrint[3,"FCReplaceMomenta: Final repalcement rule:.", finalRepRule, FCDoControl->fcrmVerbose]; + + If[ TrueQ[maskedObjects=!={}], + (* We do not want any replacements inside the heads that were previously filtered out! *) + ruleMask = Thread[Rule[maskedObjects, Table[Unique["fcReplaceMomentaMask"], {i, 1, Length[maskedObjects]}]]]; + res = ex /. ruleMask /. finalRepRule /. Reverse /@ ruleMask, + + res = ex /. finalRepRule + ]; + + If [OptionValue[EpsEvaluate], + res = EpsEvaluate[res,FCI->True] + ]; + + If [OptionValue[ExpandScalarProduct], + res = ExpandScalarProduct[res,FCI->True] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + +FCPrint[1,"FCReplaceMomenta.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/FCRerouteMomenta.m b/FeynCalc/Lorentz/FCRerouteMomenta.m new file mode 100755 index 000000000..5a9eb8946 --- /dev/null +++ b/FeynCalc/Lorentz/FCRerouteMomenta.m @@ -0,0 +1,239 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCRerouteMomenta *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Changes the routing of the momenta by exploiting + 4-momentum conservation *) + +(* ------------------------------------------------------------------------ *) + +FCRerouteMomenta::usage = +"FCRerouteMomenta[exp,{p1,p2,...},{k1,k2,...}] changes the routing of the \ +momenta by exploiting the 4-momentum conservation law p1+p2+... = k1+k2+... \ +The main aim of this function is to simplify the input expression by replacing \ +simple linear combinations of the external momenta with shorter expressions. \ +For example, in a process p1+p2 -> k1+k2+k3, the combination k1+k2-p2 can be \ +replaced with the shorter expression p1-k3. The replacements are applied using \ +the FeynCalcExternal form of the expression. Ideally, this function should be \ +used directly on the output of a diagram generator such as FeynArts or QGRAF."; + +FCRerouteMomenta::failmsg = +"Error! FCRerouteMomenta has encountered a fatal problem and must abort the computation. \n +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCRerouteMomenta`Private`"] + + +pickMomenta::usage=""; +list::usage=""; +fcrmVerbose::usage=""; + + +Options[FCRerouteMomenta] = { + Check -> True, + DiracGammaCombine -> False, + Eliminate -> {}, + Expand -> ExpandAll, + FCE -> False, + FCVerbose -> False, + InitialSubstitutions -> {}, + MaxIterations -> Infinity, + MomentumCombine -> False, + Replace -> { + FAD, SFAD, CFAD, GFAD, + GS, GSD, GSE, + FV, FVD, FVE, + CV, CVD, CVE, + SP, SPD, SPE, + CSP, CSPD, CSPE, TC + } +}; + +FCRerouteMomenta[expr_, in_List/; in=!={}, out_List /; (out =!= {} && ! OptionQ[out]), OptionsPattern[]] := + Block[{ ex, lin = Length[in], lout = Length[out], rule = {}, longest, shortest, lenl, lens, + lentot, nums, selections = {}, selections2, objects, objectsEval, ruleFinal, + res, optEliminate, optInitialSubstitutions, lastRule}, + + optEliminate = OptionValue[Eliminate]; + optInitialSubstitutions = OptionValue[InitialSubstitutions]; + + If [OptionValue[FCVerbose]===False, + fcrmVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fcrmVerbose=OptionValue[FCVerbose] + ]; + ]; + + ex = FCI[expr]; + + FCPrint[1,"FCRerouteMomenta: Entering.", FCDoControl->fcrmVerbose]; + FCPrint[3,"FCRerouteMomenta: Entering with ", expr, FCDoControl->fcrmVerbose]; + + If[ OptionValue[DiracGammaCombine] && !FreeQ[ex,DiracGamma], + FCPrint[1,"FCRerouteMomenta: Applying DiracGammaCombine.", FCDoControl->fcrmVerbose]; + ex = DiracGammaCombine[ex,FCI->True] + ]; + + If[ OptionValue[MomentumCombine] && !FreeQ2[ex,{Pair,CartesianPair,TemporalPair}], + FCPrint[1,"FCRerouteMomenta: Applying MomentumCombine.", FCDoControl->fcrmVerbose]; + ex = MomentumCombine[ex,FCI->True] + ]; + + ex = FCE[ex]; + + If[! MatchQ[{in, out}, {{__Symbol}, {__Symbol}}], + Print["error. incorrect input"]; + Abort[] + ]; + + (*We need to know which list contains the largest number of momenta *) + If[TrueQ[Length[in] > Length[out]], + {longest, shortest} = {in, out}; + {lenl, lens} = {Length[longest], Length[shortest]}, + + {longest, shortest} = {out, in}; + {lenl, lens} = {Length[longest], Length[shortest]} + ]; + lentot = lenl + lens; + + (* In the following we assume that the momentum conservation equation is of the form + Total[longest]=Total[shortest], i.e. the largest number of the momenta is on the lhs *) + + (*Determine the maximum number of momenta on the lhs of a rule*) + nums = Table[lentot - i, {i, 0, Quotient[lentot, 2]}]; + + (* If the total number of the momenta is an even number, e.g. + 2->2 or 1->3, then a rule with an equal number of momenta on both sides + is apriori not useful! + However, it may be useful if we want to eliminate some momenta in favor + of other momenta! *) + + If[TrueQ[EvenQ[lenl + lens]] && optEliminate==={}, + nums = Most[nums] + ]; + + (* Generate all possible replacements by picking a given number of + the momenta on the lhs and subtracting from it some momenta from the rhs. + + In any case the number of the momenta on the lhs of the + replacement rule is larger than the number on the rhs. *) + selections = Flatten[pickMomenta[#, longest, shortest] & /@ nums] /. list[] -> Unevaluated[Sequence[]] /. list -> List; + + (* We can also generate replacement rules by just omiting a given number of + the momenta on the lhs of the 4-momentum conservation equation *) + + nums = Range[Quotient[lentot, 2] + 1, lenl - 1]; + If[ TrueQ[nums =!= {}], + selections2 = Flatten[Map[Subsets[longest, {#}] &, nums] /. List[a___Symbol] :> list[a]], + selections2 = {} + ]; + + selections = Join[selections, selections2]; + + (* If the numbers of the incoming and outgoing momenta are different, we can also use the + replacement rule lhs->rhs. If the numbers are the same, we should not use this rule, unless + we want to eliminate some momenta! + *) + If[ lenl =!= lens, + selections = Join[selections, {longest}], + If[ optEliminate=!={}, + Which[ + FreeQ2[longest,optEliminate] && !FreeQ2[shortest,optEliminate], + selections = Join[selections, {shortest}], + !FreeQ2[longest,optEliminate] && FreeQ2[shortest,optEliminate], + selections = Join[selections, {longest}], + True, + Null + ] + ] + ]; + + (* Obtain the final set of the replacement rules *) + rule = Map[Rule[Total[#], Total[#] - Total[longest] + Total[shortest]] &, selections]; + + (* Check that each replacement rule is correct, i.e. it does not violate the + 4-momentum conservation *) + If[ OptionValue[Check], + If [DeleteDuplicates[Map[(#[[1]]-#[[2]]-Total[longest]+Total[shortest])&, rule]]=!={0}, + Message[FCRerouteMomenta::failmsg,"Some of the automatically generated rules violate the 4-momentum conservation."]; + Abort[] + ] + ]; + + (* Duplicate each replacement rule by considering a case where the + overall sign is opposite *) + + rule = Join[rule, Expand[rule /. Rule[a_, b_] :> Rule[-a, -b]]]; + + (* If some momenta where previously eliminated, we must ensure that they will not be + reintroduced by some of the replacement rules! *) + If[ optEliminate=!={}, + rule = Select[rule, FreeQ2[#[[2]], optEliminate] &] + ]; + + lastRule = Select[rule, (NTerms[#[[1]]]===NTerms[#[[2]]])&]; + rule = Complement[rule,lastRule]; + + + FCPrint[1,"FCRerouteMomenta: Final set of replacement rules: " ,rule, FCDoControl->fcrmVerbose]; + + (* Now we extract all the FeynCalc objects, to which the replacement rules are applicable *) + objects = Cases2[ex, OptionValue[Replace]]; + + FCPrint[3,"FCRerouteMomenta: List of suitable objects: " ,objects, FCDoControl->fcrmVerbose]; + + If[ TrueQ[optInitialSubstitutions=!={}], + objectsEval = objects/. optInitialSubstitutions, + objectsEval = objects + ]; + + objectsEval = FixedPoint[ReplaceAll[OptionValue[Expand]/@(#),rule]&, objectsEval,OptionValue[MaxIterations]]; + FCPrint[3,"FCRerouteMomenta: List of suitable objects after applying the replacements: " ,objects, FCDoControl->fcrmVerbose]; + + (* If we want to eliminate particular momenta, we may also make use of replacement rules + that do not change the total number of the momenta. Such rules are available only if the + total number of the momenta is even. Obviously, such rules must be applied only at the very + end, since otherwise we might miss more useful rules or run into an infinite recursion + + *) + + objectsEval = objectsEval /. lastRule; + + + ruleFinal = Thread[Rule[objects, objectsEval]]; + FCPrint[3,"FCRerouteMomenta: The resulting replacement rule: ", ruleFinal, FCDoControl->fcrmVerbose]; + + + res = ex /. ruleFinal; + If[ !OptionValue[FCE], + res = FCI[res] + ]; + + FCPrint[1,"FCRerouteMomenta: Leaving.", FCDoControl->fcrmVerbose]; + FCPrint[3,"FCRerouteMomenta: Leaving with ", expr, FCDoControl->fcrmVerbose]; + + res + + +]; + +pickMomenta[num_, l_, s_] := + Flatten[Table[Outer[Union, Subsets[l, {num - i}], Subsets[-s, {i}], 1], {i, 1, num - 1}] /. List[a___Symbol, -1 b_Symbol, c___] :> list[a, -b, c]]; + + +FCPrint[1,"FCRerouteMomenta.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/FCSchoutenBruteForce.m b/FeynCalc/Lorentz/FCSchoutenBruteForce.m new file mode 100644 index 000000000..149eafcda --- /dev/null +++ b/FeynCalc/Lorentz/FCSchoutenBruteForce.m @@ -0,0 +1,260 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCSchoutenBruteForce *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Applies Schouten identity in 4 dimensions multiple times *) + +(* ------------------------------------------------------------------------ *) + + +FCSchoutenBruteForce::usage = +"FCSchoutenBruteForce[exp,{},{}] can be used to show that certain terms are zero \ +by repeatedly Schouten identity in a brute force way. The algorithm tries to \ +find replacements which follow from the Schouten identity and make the length \ +of the given expression shorter. It is not guaranteed to terminate and in \ +general can often get stucked. Still, with some luck it is often possible \ +to show that certain terms vanish by a sequence of transformations that would \ +be otherwise very difficult to find."; + +Begin["`Package`"] +End[] + +Begin["`FCSchoutenBruteForce`Private`"] + +fcsbVerbose::usage=""; + +Options[FCSchoutenBruteForce] = { + Collecting -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> Factor2, + Information -> True, + List -> False, + Rule -> True, + Schouten -> False, + SchoutenAllowNegativeGain -> False, + SchoutenAllowZeroGain -> False, + Take -> 1 +}; + +checkSchouten[x_, repRule_]:= +Block[{lenBefore,lenAfter}, + lenBefore = NTerms[x]; + lenAfter = NTerms[Expand[x /. Pair[a__]^z_ :> Pair[a] pow[Pair,z-1] /. repRule[[1]] :> repRule[[2]]] /. pow -> Power ]; + lenBefore-lenAfter +]; + +FCSchoutenBruteForce[expr_, epsvars_List, vars_List/;(!OptionQ[vars] || vars==={}), OptionsPattern[]] := + Block[{ + ex, res, sublists, combos, maxRed = 5, cs, gain=0,list,tmp=0,epsInds,moms, + repRule, join, optSchoutenAllowZeroGain, optSchoutenAllowNegativeGain, optRule, optTake, + resSchouten1, resSchouten2, resSchouten, lengthOriginal, lengthResSchouten, time, condition, resLength, + finalRule}, + + + If[ OptionValue[FCVerbose]===False, + fcsbVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fcsbVerbose=OptionValue[FCVerbose] + ]; + ]; + + optSchoutenAllowZeroGain = OptionValue[SchoutenAllowZeroGain]; + optSchoutenAllowNegativeGain = OptionValue[SchoutenAllowNegativeGain]; + optRule = OptionValue[Rule]; + optTake = OptionValue[Take]; + + + FCPrint[1, "FCSchoutenBruteForce: Entering.", FCDoControl->fcsbVerbose]; + FCPrint[3, "FCSchoutenBruteForce: Entering with ", ex, FCDoControl->fcsbVerbose]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex,Eps], + Return[ex] + ]; + + ex = Expand2[EpsEvaluate[ex,FCI->True]]; + lengthOriginal = NTerms[ex]; + + If[ OptionValue[Schouten], + + FCPrint[1, "FCSchoutenBruteForce: Applying Schouten.", FCDoControl->fcsbVerbose]; + + resSchouten1=Schouten[ex,Infinity]; + resSchouten2=Schouten[ex]; + + If[ TrueQ[NTerms[resSchouten1]fcsbVerbose]; + ex = resSchouten, + FCPrint[1, "FCSchoutenBruteForce: Applying Schouten did not make the expression shorter:", lengthOriginal-lengthResSchouten, FCDoControl->fcsbVerbose] + ] + ]; + + If[ epsvars==={}, + FCPrint[1, "FCSchoutenBruteForce: No arguments of Eps specified, extracting all possible arguments.", FCDoControl->fcsbVerbose]; + epsInds = Cases[ex,Eps[x__]:>{x},Infinity]//Union, + epsInds = {epsvars} + ]; + + If[ vars==={}, + FCPrint[1, "FCSchoutenBruteForce: No arguments of scalar products specified, extracting all possible arguments.", FCDoControl->fcsbVerbose]; + moms = Cases2[ex,{Momentum,LorentzIndex}], + moms = vars + ]; + + FCPrint[1, "FCSchoutenBruteForce: There are ", Length[epsInds], " possible Eps arguments." FCDoControl->fcsbVerbose]; + FCPrint[1, "FCSchoutenBruteForce: There are ", Length[moms], " possible scalar product arguments." FCDoControl->fcsbVerbose]; + FCPrint[3, "FCSchoutenBruteForce: moms:", moms, FCDoControl->fcsbVerbose]; + FCPrint[3, "FCSchoutenBruteForce: vars:", vars, FCDoControl->fcsbVerbose]; + + sublists = Subsets[moms, {2}]; + sublists = Join[sublists,Map[{#,#}&,moms]]; + sublists = Sort/@sublists; + sublists = Union[sublists]; + + join[x_] := + Map[Join[#, x] &, epsInds]; + + sublists = Flatten[join /@ sublists, 1]; + + FCPrint[1, "FCSchoutenBruteForce: There are ", Length[sublists], " possible replacements to check." FCDoControl->fcsbVerbose]; + + FCPrint[1, "FCSchoutenBruteForce: Preparing the list of possible replacements.", FCDoControl->fcsbVerbose]; + time = AbsoluteTime[]; + + combos = { + +Eps[#[[1]], #[[2]], #[[3]], #[[4]]] Pair[#[[5]], #[[6]]], + -Eps[#[[2]], #[[3]], #[[4]], #[[5]]] Pair[#[[1]], #[[6]]] + -Eps[#[[3]], #[[4]], #[[5]], #[[1]]] Pair[#[[2]], #[[6]]] + -Eps[#[[4]], #[[5]], #[[1]], #[[2]]] Pair[#[[3]], #[[6]]] + -Eps[#[[5]], #[[1]], #[[2]], #[[3]]] Pair[#[[4]], #[[6]]] + }&/@ sublists; + + + combos = {EpsEvaluate[#[[1]],FCI->True],EpsEvaluate[#[[2]],FCI->True]}&/@ combos; + + combos = + If[ MatchQ[#[[1]], -1 * _Eps _Pair], + {Expand2[-1*#[[1]]],Expand2[-1*#[[2]]]}, + {#[[1]],#[[2]]} + ]& /@ combos; + + combos = Union[combos] /. {0,_} -> Unevaluated[Sequence[]] /. + {a_,a_} -> Unevaluated[Sequence[]] /. {a_,_}/;FreeQ[ex,a] :> Unevaluated[Sequence[]]; + + FCPrint[1, "FCSchoutenBruteForce: Done Preparing the list of possible replacements, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->fcsbVerbose]; + FCPrint[3, "FCSchoutenBruteForce: List of possible replacements: ", combos, FCDoControl->fcsbVerbose]; + + + FCPrint[1, "FCSchoutenBruteForce: Checking replacements.", FCDoControl->fcsbVerbose]; + time = AbsoluteTime[]; + + + list = Catch[ + Map[(cs = checkSchouten[ex,#]; + If[cs < maxRed, {cs, #}, Throw[{cs, #}]]) &, combos] + ]; + + If[MatchQ[list,{_Integer,{_,_}}], + list={list}; + ]; + + list = Sort[list, (#1[[1]] > #2[[1]]) &]; + + FCPrint[1, "FCSchoutenBruteForce: Done checking replacements, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->fcsbVerbose]; + FCPrint[3, "FCSchoutenBruteForce: List of possible replacements: ", list, FCDoControl->fcsbVerbose]; + + repRule = {{},{}}; + gain=0; + + If[ Length[list]=!=0, + + Which[ + optSchoutenAllowZeroGain && optSchoutenAllowNegativeGain, + condition = True, + optSchoutenAllowZeroGain && !optSchoutenAllowNegativeGain, + condition = (list[[optTake]])[[1]]>=0, + True, + condition = (list[[optTake]])[[1]]>0 + ]; + + If[ condition, + repRule = (list[[optTake]])[[2]]; + gain = (list[[optTake]])[[1]]; + ] + + ]; + + res = ex /. repRule[[1]] :> repRule[[2]]; + + finalRule = RuleDelayed@@repRule; + + resLength=Length[Expand2[res]]; + + If[ OptionValue[Information], + Which[ + gain>0, + If [optRule, + FCPrint[0, "FCSchoutenBruteForce: The following rule was applied: ", finalRule, " ", FCDoControl->fcsbVerbose]; + ]; + FCPrint[0, "FCSchoutenBruteForce: The numbers of terms in the expression decreased by: ", gain, FCDoControl->fcsbVerbose]; + FCPrint[0, "FCSchoutenBruteForce: Current length of the expression: ", resLength, FCDoControl->fcsbVerbose], + gain===0 && (repRule =!= {{},{}}), + If [optRule, + FCPrint[0, "FCSchoutenBruteForce: The following rule was applied: ", finalRule, " ", FCDoControl->fcsbVerbose]; + ]; + FCPrint[0, "FCSchoutenBruteForce: The numbers of terms remained unchanged.", FCDoControl->fcsbVerbose]; + FCPrint[0, "FCSchoutenBruteForce: Current length of the expression: ", resLength, FCDoControl->fcsbVerbose], + gain<0 && (repRule =!= {{},{}}), + If [optRule, + FCPrint[0, "FCSchoutenBruteForce: The following rule was applied: ", finalRule, " ", FCDoControl->fcsbVerbose]; + ]; + FCPrint[0, "FCSchoutenBruteForce: The number of terms increased by: ", gain, FCDoControl->fcsbVerbose]; + FCPrint[0, "FCSchoutenBruteForce: Current length of the expression: ", resLength, FCDoControl->fcsbVerbose], + repRule === {{},{}}, + FCPrint[0, "FCSchoutenBruteForce: No suitable replacement rules were found.", FCDoControl->fcsbVerbose] + ]; + ]; + + If[ OptionValue[Collecting], + res = Collect2[res,Eps,Pair,Factoring->OptionValue[Factoring]] + ]; + + If[ OptionValue[List], + res = {res,finalRule} + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "FCSchoutenBruteForce: Leaving.", FCDoControl->fcsbVerbose]; + FCPrint[3, "FCSchoutenBruteForce: Leaving with: ", res, FCDoControl->fcsbVerbose]; + + res +]; + + +FCPrint[1,"FCSchoutenBruteForce loaded."]; +End[] diff --git a/FeynCalc/Lorentz/FourDivergence.m b/FeynCalc/Lorentz/FourDivergence.m index 91d74e92e..bcbbf47b1 100755 --- a/FeynCalc/Lorentz/FourDivergence.m +++ b/FeynCalc/Lorentz/FourDivergence.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Compute partial derivatives w.r.t to the given 4-vector(s) *) @@ -16,8 +16,8 @@ (* ------------------------------------------------------------------------ *) FourDivergence::usage = -"FourDivergence[exp, FourVector[p, mu]] calculates the partial derivative of exp w.r.t. p(mu). \ -FourDivergence[exp, FourVector[p, mu], FourVector[p,nu], ...] gives the multiple derivative."; +"FourDivergence[exp, FV[p, mu]] calculates the partial derivative of exp w.r.t. p^mu. \ +FourDivergence[exp, FV[p, mu], FV[p,nu], ...] gives the multiple derivative."; PartialFourVector::usage= "PartialFourVector is equivalent to FourDivergence"; @@ -32,6 +32,23 @@ "The structure `1` w.r.t which you are trying to differentiate is too complicated \ to ensure the correct result. Evaluation aborted!" +FourDivergence::failmsg = +"Error! FourDivergence has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +FourDivergence::warn = +"Warning! The input expression also depends on `1` in dimensions other than `2`. \ +The derivative of a vector in one dimension w.r.t the same vector in a different \ +dimension is zero by convention. Please check that this is indeed intended. You \ +can deactivate this message for the current session by evaluating \ +Off[FourDivergence::warn]."; + +FourDivergence::warnCartesian = +"Warning! The input expression also depends on the 3-momentum `1`. The derivatives of \ +such quantities w.r.t the corresponding 4-vector are zero. Please check that \ +this is indeed intended. You can deactivate this message for the current session by \ +evaluating Off[ThreeDivergence::warnCartesian]."; + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -39,56 +56,118 @@ Begin["`FourDivergence`Private`"] +fdVerbose::usage=""; + PartialFourVector = FourDivergence; Options[FourDivergence] = { - FCI -> False, - Contract -> True, - EpsEvaluate -> True, - ExpandScalarProduct -> True + Abort -> True, + ApartFF -> False, + Collecting -> True, + Contract -> True, + EpsEvaluate -> True, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> Factor }; -FourDivergence[x_, fv:Except[_?OptionQ].., OptionsPattern[]] := - Block[{ nx,ve,tliflag = False, +FourDivergence[expr_, fv:Except[_?OptionQ].., OptionsPattern[]] := + Block[{ex, ve, tliflag = False, time, args, hold}, + + If [OptionValue[FCVerbose]===False, + fdVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fdVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "FourDivergence: Entering.", FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: Entering with: ", expr, FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: Differentiating w.r.t ", {fv}, FCDoControl->fdVerbose]; - uList,sList,repRule,null1,null2, deriv}, If [!OptionValue[FCI], - {nx,ve} = {FCI[x],FCI[{fv}]}, - {nx,ve} = {x,{fv}} + {ex,ve} = {FCI[expr],FCI[{fv}]}, + {ex,ve} = {expr,{fv}} ]; + args = Cases[{ve}, z_Momentum :> First[z], Infinity] // Sort // DeleteDuplicates; + (* QCD-related stuff *) - If[ !FreeQ[nx, TLI], - nx = TLI2FC[nx]; + If[ !FreeQ[ex, TLI], + ex = TLI2FC[ex]; tliflag = True ]; - nx = fourDerivative[nx,Sequence@@ve]; + FCPrint[1, "FourDivergence: Applying fourDerivative ", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = fourDerivative[ex,Sequence@@ve]; + FCPrint[1, "FourDivergence: fourDerivative done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: After fourDerivative ", ex, FCDoControl->fdVerbose]; (* Put FADs back together *) - If[ !FreeQ[nx, FeynAmpDenominator], - nx = FeynAmpDenominatorCombine[nx] + If[ !FreeQ[ex, FeynAmpDenominator], + FCPrint[1, "FourDivergence: Applying FeynAmpDenominatorCombine.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = FeynAmpDenominatorCombine[ex, FCI->True]; + FCPrint[1, "FourDivergence: FeynAmpDenominatorCombine done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: After FeynAmpDenominatorCombine: ", ex, FCDoControl->fdVerbose] ]; (* QCD-related stuff *) - If[ tliflag && FreeQ[nx, LorentzIndex], - nx = FC2TLI[nx, (Momentum/.Options[TLI2FC])[[1]], (Momentum/.Options[TLI2FC])[[2]]] + If[ tliflag && FreeQ[ex, LorentzIndex], + ex = FC2TLI[ex, (Momentum/.Options[TLI2FC])[[1]], (Momentum/.Options[TLI2FC])[[2]]] ]; If[ OptionValue[Contract], - nx = Contract[nx] + FCPrint[1, "FourDivergence: Applying Contract.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = Contract[ex, FCI->True]; + FCPrint[1, "FourDivergence: Contract done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: After Contract: ", ex, FCDoControl->fdVerbose] ]; If[ OptionValue[ExpandScalarProduct], - nx = ExpandScalarProduct[nx] + FCPrint[1, "FourDivergence: Applying ExpandScalarProduct.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = ExpandScalarProduct[ex, FCI->True, EpsEvaluate->OptionValue[EpsEvaluate]]; + FCPrint[1, "FourDivergence: ExpandScalarProduct done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: After ExpandScalarProduct: ", ex, FCDoControl->fdVerbose] ]; - If[ OptionValue[EpsEvaluate], - nx = EpsEvaluate[nx] + If[ OptionValue[ApartFF], + FCPrint[1, "FourDivergence: Applying ApartFF.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = ApartFF[ex, args, FCI->True, FDS->False, DropScaleless->False]; + FCPrint[1, "FourDivergence: ApartFF done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: After ApartFF: ", ex, FCDoControl->fdVerbose] ]; - nx + If[ OptionValue[Collecting], + FCPrint[1, "FourDivergence: Applying Collect2.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + If[ !FreeQ[ex,FeynAmpDenominator], + ex = Collect2[ex, FeynAmpDenominator, Factoring->hold]; + ex = ex /. hold[]->1 /. z_hold:> Collect2[First[z],args,Factoring->OptionValue[Factoring]], + + ex = Collect2[ex, args, Factoring->OptionValue[Factoring]] + ]; + + FCPrint[1, "FourDivergence: Collect2 done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: After Collect2: ", ex, FCDoControl->fdVerbose] + ]; + + If[ OptionValue[FCE], + ex = FCE[ex] + ]; + + FCPrint[3, "FourDivergence: Leaving.", FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: Leaving with: ", ex, FCDoControl->fdVerbose]; + + + ex ]; @@ -97,64 +176,75 @@ fourDerivative[fourDerivative[x, a], b]; fourDerivative[x_, ve_]:= - Block[{ nx = x,p ,mu,linCombHide={},linCombShow={}, - uList,sList,repRule, deriv,null1,null2,un}, - (* check the we are differentiating w.r.t a vector *) - If [!MatchQ[ve,Pair[_. Momentum[_,_:4]+ _:0,_:4]], - Message[FourDivergence::notvec, ve]; + Block[{ nx = x,p, p0, mu, dList, dListEval, repRuleFinal, deriv, + null1,null2,un, fadHead, fadList, fadListEval, + repRule1, repRule2={}, res}, + + FCPrint[3, "FourDivergence: fourDerivative: Entering with: ", x, FCDoControl->fdVerbose]; + + (* check that we are differentiating w.r.t a vector *) + If[ !MatchQ[ve,Pair[Momentum[_Symbol,___],_LorentzIndex]], + Message[FourDivergence::failmsg, ToString[ve,InputForm] <> " is not a Lorentz vector."]; Abort[] ]; + p = ve/.Pair[z_Momentum,_] :> z; + mu = ve/.Pair[z_LorentzIndex,_] :> z; + p0 = First[p]; - p = ve/.Pair[z: (_. Momentum[_,_:4]+ _:0),_] :> z; - mu = ve/.Pair[z_LorentzIndex,_] :> z; + FCPrint[3, "FourDivergence: fourDerivative: p and mu: ", {p,mu}, FCDoControl->fdVerbose]; If [p===ve || mu===ve || Head[mu]=!=LorentzIndex || FreeQ[p,Momentum], Message[FourDivergence::extfail, ve]; Abort[] ]; - (* If we are differentiating w.r.t to a linear combination four-vectors, e.g. - (p+q+l)^mu, then we can easily miss terms. The only way this - can work out, is when the linear combination is present in the - expression precisely in the same form as it is in ve. - Otherise, we should better abort the evaluation to avoid - returning a wrong result - *) - If[ !MatchQ[p,Momentum[m_/;FreeQ2[m,{Plus,Times}],_:4]], - un=Unique[]; - linCombHide = {Rule[p,un],Rule[MomentumCombine[MomentumExpand[-p]],-un]}; - linCombShow = Reverse/@linCombHide; - - If[ FreeQ2[nx/.linCombHide, Variables[p/.Momentum[a_,_:4]:>a]], - nx = nx/.linCombHide; - p = p/.linCombHide, - Message[FourDivergence::toocompl,ve]; - Abort[] - ]; - - ]; - - (* Expand slashes, scalar products and epsilon tensor that contain momenta w.r.t to which we want to differentiate *) + (* Expand slashes, scalar products and epsilon tensors that contain momenta w.r.t to which we want to differentiate *) If[ !FreeQ[nx, DiracGamma], - nx = DiracGammaExpand[nx, Momentum->{p/.Momentum[a_,_:4]:> a}, FCI->True]; + nx = DiracGammaExpand[nx, Momentum -> {p0}, FCI->True]; + FCPrint[3, "FourDivergence: fourDerivative: After DiracGammaExpand: ", nx, FCDoControl->fdVerbose]; ]; - If[ !FreeQ[nx, Eps], - nx = EpsEvaluate[nx, Momentum->{p/.Momentum[a_,_:4]:> a}, FCI->True]; + + nx = ExpandScalarProduct[nx, Momentum -> {p0}, EpsEvaluate->True, FCI->True]; + FCPrint[3, "FourDivergence: fourDerivative: After ExpandScalarProduct: ", nx, FCDoControl->fdVerbose]; + + If[ !FreeQ[nx,CartesianMomentum[p0,___]], + Message[FourDivergence::warnCartesian, ToString[p0,InputForm]]; ]; - nx = ExpandScalarProduct[nx, Momentum->{p/.Momentum[a_,_:4]:> a}, FCI->True]; + (* Differentation of FADs is very easy to mess up, so we need to be careful here. + Essentially, we have d/dx 1/f(g(x)) = -1/[f(g(x))]^2 * f'(g(x))* g'(x), where f(x)=x, i.e. + the sole purpose of f(x) is that we can recover FADs after the differentiation, c.f. + D[1/f[g[x]], x] /. f -> Identity *) If[ !FreeQ[nx, FeynAmpDenominator], - nx = FeynAmpDenominatorSplit[nx] + (* FeynAmpDenominatorSplit is necessary here. Without it, the results are still correct, + but they become too complicated. *) + nx = FeynAmpDenominatorSplit[nx,FCI->True]; + fadList = Cases[nx + null1 + null2, zzz_FeynAmpDenominator /; ! FreeQ[zzz, p], Infinity]; + fadListEval = FeynAmpDenominatorExplicit[#,FCI->True,Head->fadHead,Denominator->True]&/@fadList; + repRule1 = Thread[Rule[fadList,fadListEval]]; + repRule2 = (Reverse /@ repRule1) /. Rule[a_, b_] :> Rule[1/a, 1/b]; + + FCPrint[3, "FourDivergence: fourDerivative: repRule1: ", repRule1, FCDoControl->fdVerbose]; + FCPrint[3, "FourDivergence: fourDerivative: repRule2: ", repRule1, FCDoControl->fdVerbose]; + + nx = nx /. repRule1; + + FCPrint[3, "FourDivergence: fourDerivative: After applying repRule1: ", nx, FCDoControl->fdVerbose]; + ]; - (* This is the main part *) + If[ Cases[(nx/. p-> Unique[]) + null1 + null2, Momentum[p0,___], Infinity]=!={}, + Message[FourDivergence::warn,ToString[p0], ToString[p/.Momentum[_,dim_:4]:>dim]] + ]; + (* This is the main part *) nx = D[nx, p] /. Derivative -> deriv; - uList = Cases[nx+null1+null2,deriv[a___][b___][c___],Infinity]//Union; -(*FourDivergence[FCI[GSD[q]], FVD[q, mu]] // StandardForm*) - sList = uList /. (deriv[__][FeynAmpDenominator][__]) :> 1 /. { - deriv[1,0][PD][pe_,b_] :> (-2 Pair[pe,mu] FeynAmpDenominator[PD[pe, b], PD[pe, b]]), + FCPrint[3, "FourDivergence: fourDerivative: After D: ", nx, FCDoControl->fdVerbose]; + + dList = Cases[nx+null1+null2,deriv[___][___][___],Infinity]//Sort//DeleteDuplicates; + + dListEval = dList /. (deriv[__][fadHead][__]) :> 1 /. { deriv[1, 0][Pair][p, a_] :> Pair[a, mu] , deriv[0, 1][Pair][a_, p] :> Pair[a, mu] , deriv[1,0][DiracGamma][p,dim_] :> DiracGamma[mu,dim] , @@ -162,13 +252,22 @@ deriv[1,0,0,0][Eps][p,c__] :> Eps[mu,c] , deriv[0,1,0,0][Eps][a_,p,c__] :> Eps[a,mu,c] , deriv[0,0,1,0][Eps][a__,p,c_] :> Eps[a,mu,c] , - deriv[0,0,0,1][Eps][c__,p] :> Eps[c,mu]} /. deriv -> Derivative; + deriv[0,0,0,1][Eps][c__,p] :> Eps[c,mu] + } /. deriv -> Derivative; + + repRuleFinal = Thread[Rule[dList,dListEval]]; + FCPrint[3, "FourDivergence: fourDerivative: Final replacement list: ", repRuleFinal, FCDoControl->fdVerbose]; - repRule = MapIndexed[(Rule[#1, First[sList[[#2]]]]) &, uList]; + res = nx /. Dispatch[repRuleFinal] /. Dispatch[repRule2]; - nx = nx/.Dispatch[repRule]/.Dispatch[linCombShow]; + If[ !FreeQ2[res,{Derivative,deriv,fadHead}], + Message[FourDivergence::failmsg, "The output contains unevaluated derivatives."]; + If[ TrueQ[OptionValue[Abort]], + Abort[] + ] + ]; - nx + res ]; FCPrint[1,"FourDivergence.m loaded."]; diff --git a/FeynCalc/Lorentz/FourLaplacian.m b/FeynCalc/Lorentz/FourLaplacian.m index 48fea5e64..f820b090a 100755 --- a/FeynCalc/Lorentz/FourLaplacian.m +++ b/FeynCalc/Lorentz/FourLaplacian.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Laplace operator *) @@ -23,6 +23,8 @@ Begin["`FourLaplacian`Private`"] +xxx::usage=""; + Options[FourLaplacian] = { Dimension -> D }; diff --git a/FeynCalc/Lorentz/FreeIndexFreeQ.m b/FeynCalc/Lorentz/FreeIndexFreeQ.m new file mode 100755 index 000000000..d7537df14 --- /dev/null +++ b/FeynCalc/Lorentz/FreeIndexFreeQ.m @@ -0,0 +1,81 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FreeIndexFreeQ *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Checks if the expression contains dummy indices *) + +(* ------------------------------------------------------------------------ *) + + + +FreeIndexFreeQ::usage = +"FreeIndexFreeQ[exp, {head1, head2, ...}] returns True if the expression \ +contains uncontracted indices with heads head1, head2, ... and False otherwise. \ +As always in FeynCalc, Einstein summation convention is implicitly assumed. \ +The function is optimized for large expressions, i.e. it is not so good as \ +a criterion in e.g. Select."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FreeIndexFreeQ`Private`"] + +FreeIndexFreeQ[expr_, heads_List] := + True/; FreeQ2[expr,heads]; + +FreeIndexFreeQ[expr_, heads_List] := + Block[{fullLiList, freeLiList, ex, times, i, sel, sel2}, + + + FCPrint[1, "FreeIndexFreeQ: Entering."]; + FCPrint[3, "FreeIndexFreeQ: Entering with: ", expr]; + + If[ Head[expr]===Times, + ex = SelectNotFree[expr, heads], + ex = expr + ]; + + ex = ExpandAll2[ex]; + + If[Head[ex]===Plus, + ex=First[ex] + ]; + + If[ !FreeQ[ex, Power], + ex = ex /. Power[a_, b_Integer?Positive] /; !FreeQ2[a, heads] :> + Apply[times, Table[a, {i, b}]]; + ]; + + FCPrint[3, "FreeIndexFreeQ: Final ex: ", ex]; + + sel = Blank/@heads; + If[ Length[heads]===1, + sel = Identity@@(Blank/@heads); + sel2 = Identity@@heads, + + sel = Alternatives@@(Blank/@heads); + sel2 = Alternatives@@heads + ]; + + FCPrint[1, "FreeIndexFreeQ: sel: ", sel]; + + freeLiList = Cases[ex, sel, Infinity]// + ReplaceAll[#, (sel2)[z_, ___] :> z] & // Tally // Cases[#, {z_, 1} :> z] &; + + (freeLiList==={}) + + ]/; !FreeQ2[expr,heads]; + +FCPrint[1,"FreeIndexFreeQ.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/LorentzToCartesian.m b/FeynCalc/Lorentz/LorentzToCartesian.m new file mode 100755 index 000000000..825692049 --- /dev/null +++ b/FeynCalc/Lorentz/LorentzToCartesian.m @@ -0,0 +1,280 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: LorentzToCartesian *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Converts selected Lorentz tensors into Cartesian tensors. *) + +(* ------------------------------------------------------------------------ *) + + +LorentzToCartesian::usage= +"LorentzToCartesian[exp] rewrites Lorentz tensors in form of Cartesian tensors \ +(when possible). Using options one can specify which types of tensors \ +should be converted."; + +LorentzToCartesian::fail= +"Error! LorentzToCartesian has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`LorentzToCartesian`Private`"] + +tmpci::usage=""; +lorIndex::usage=""; + +Options[LorentzToCartesian] = { + DiracGammaExpand -> True, + DotSimplify -> True, + EpsEvaluate -> True, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False, + FCTensor -> True, + FV -> True, + GA -> True, + GS -> True, + LC -> True, + LorentzIndex -> True, + PauliSigmaExpand -> True, + SI -> True, + SIS -> True, + SP -> True +}; + +LorentzToCartesian[expr_, OptionsPattern[]]:= + Block[{ex, heads, tmp, tensorList, res, uniqList,null1,null2, uniqListEval, repRule, times,dotTimes}, + + heads = {}; + + tensorList = Complement[$FCTensorList, {CartesianPair, Pair, Eps}]; + + lorIndex = OptionValue[LorentzIndex]; + + + If[ OptionValue[SP] || OptionValue[FV], + heads = Join[heads,{Pair}] + ]; + + If[ OptionValue[LC], + heads = Join[heads,{Eps}] + ]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + uniqList = Cases[ex+null1+null2,Alternatives@@(Blank/@heads),Infinity]//DeleteDuplicates//Sort; + + uniqListEval = uniqList; + + If[ OptionValue[ExpandScalarProduct], + uniqListEval = ExpandScalarProduct[#,FCI->True]&/@uniqListEval; + ]; + + If[ OptionValue[SP], + uniqListEval = uniqListEval /. Pair -> spToCsp /. spToCsp -> Pair + ]; + + If[ OptionValue[FV], + uniqListEval = uniqListEval /. Pair -> fvToCv /. fvToCv -> Pair + ]; + + If[ OptionValue[LC], + uniqListEval = uniqListEval /. Eps -> ltensorToCTensor /. ltensorToCTensor -> Eps; + If[ OptionValue[EpsEvaluate], + uniqListEval = EpsEvaluate[uniqListEval,FCI->True] + ]; + ]; + + repRule = Thread[Rule[uniqList, uniqListEval]]; + + ex = ex /. Dispatch[repRule]; + + (* For DiracGammas and other tensors we cannot avoid introducing dummy indices. So if these objects appear in powers, we need + to make sure that we do not break Einstein summation. *) + If[ OptionValue[DiracGammaExpand], + ex = DiracGammaExpand[ex,FCI->True]; + ]; + + If[ OptionValue[PauliSigmaExpand], + ex = PauliSigmaExpand[ex,FCI->True]; + ]; + + If[ (OptionValue[GA] || OptionValue[GS]) && !FreeQ[ex,Power], + ex = ex /. Power[z_, n_Integer?Positive]/;!FreeQ[z, DiracGamma] :> Apply[dotTimes, Table[z, {Abs[n]}]]^Sign[n] + ]; + + If[ (OptionValue[SI] || OptionValue[SIS]) && !FreeQ[ex,Power], + ex = ex /. Power[z_, n_Integer?Positive]/;!FreeQ[z, PauliSigma] :> Apply[dotTimes, Table[z, {Abs[n]}]]^Sign[n] + ]; + + If[ (OptionValue[FCTensor]) && !FreeQ[ex,Power], + ex = ex /. Power[z_, n_Integer?Positive]/;!FreeQ2[z, tensorList] :> Apply[times, Table[z, {Abs[n]}]]^Sign[n] + ]; + + + If[ OptionValue[GA], + ex = ex /. DiracGamma -> diracGammaToCDiracGamma /. diracGammaToCDiracGamma -> DiracGamma + ]; + + If[ OptionValue[GS], + ex = ex /. DiracGamma -> diracSlashToCDiracSlash /. diracSlashToCDiracSlash -> DiracGamma + ]; + + If[ OptionValue[SI], + ex = ex /. PauliSigma -> pauliSigmaToCPauliSigma /. pauliSigmaToCPauliSigma -> PauliSigma + ]; + + If[ OptionValue[SIS], + ex = ex /. PauliSigma -> pauliSlashToCPauliSlash /. pauliSlashToCPauliSlash -> PauliSigma + ]; + + If[ OptionValue[FCTensor], + Scan[(ex = ex /. # -> ltensorToCTensor /. ltensorToCTensor -> #)&, tensorList] + ]; + + res = ex/. times->Times /. dotTimes->DOT; + + If[ OptionValue[DotSimplify], + res = DotSimplify[res,FCI->True] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + +spToCsp[Momentum[a_], Momentum[b_]]:= + FeynCalc`Package`MetricT TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[a]] TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[b]] + + FeynCalc`Package`MetricS CartesianPair[CartesianMomentum[a],CartesianMomentum[b]]; + +spToCsp[Momentum[a_, dim_Symbol], Momentum[b_, dim_Symbol]]:= + FeynCalc`Package`MetricT TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[a]] TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[b]] + + FeynCalc`Package`MetricS CartesianPair[CartesianMomentum[a,dim-1],CartesianMomentum[b,dim-1]]; + +spToCsp[Momentum[a_, dim_Symbol-4], Momentum[b_, dim_Symbol-4]]:= + FeynCalc`Package`MetricS CartesianPair[CartesianMomentum[a,dim-4],CartesianMomentum[b,dim-4]]; + +fvToCv[LorentzIndex[a_], Momentum[b_]]:= + FeynCalc`Package`MetricT Pair[LorentzIndex[a], ExplicitLorentzIndex[0]] Pair[ExplicitLorentzIndex[0], Momentum[b]] + + FeynCalc`Package`MetricS Pair[LorentzIndex[a],CartesianMomentum[b]]; + +fvToCv[LorentzIndex[a_, dim_Symbol], Momentum[b_, dim_Symbol]]:= + FeynCalc`Package`MetricT Pair[LorentzIndex[a], ExplicitLorentzIndex[0]] Pair[ExplicitLorentzIndex[0], Momentum[b]] + + FeynCalc`Package`MetricS Pair[LorentzIndex[a,dim],CartesianMomentum[b,dim-1]]; + +fvToCv[LorentzIndex[a_, dim_Symbol-4], Momentum[b_, dim_Symbol-4]]:= + FeynCalc`Package`MetricS Pair[LorentzIndex[a,dim-4],CartesianMomentum[b,dim-4]]; + +ltensorToCTensor[a___, LorentzIndex[b_], c___]:= + ( + tmpci = CartesianIndex[$MU[Unique[]]]; + FeynCalc`Package`MetricT ltensorToCTensor[a,ExplicitLorentzIndex[0],c] Pair[ExplicitLorentzIndex[0], LorentzIndex[b]] + + FeynCalc`Package`MetricS Pair[LorentzIndex[b],tmpci] ltensorToCTensor[a,tmpci,c] + )/; lorIndex + +ltensorToCTensor[a___, LorentzIndex[b_, dim_Symbol], c___]:= + ( + tmpci = CartesianIndex[$MU[Unique[]],dim-1]; + FeynCalc`Package`MetricT ltensorToCTensor[a,ExplicitLorentzIndex[0],c] Pair[ExplicitLorentzIndex[0], LorentzIndex[b,dim]] + + FeynCalc`Package`MetricS Pair[LorentzIndex[b,dim],tmpci] ltensorToCTensor[a,tmpci,c] + )/; lorIndex + +ltensorToCTensor[a___, Momentum[b_], c___]:= + FeynCalc`Package`MetricT ltensorToCTensor[a,ExplicitLorentzIndex[0],c] Pair[ExplicitLorentzIndex[0], Momentum[b]] + + FeynCalc`Package`MetricS ltensorToCTensor[a,CartesianMomentum[b],c]; + +ltensorToCTensor[a___, Momentum[b_, dim_Symbol], c___]:= + FeynCalc`Package`MetricT ltensorToCTensor[a,ExplicitLorentzIndex[0],c] Pair[ExplicitLorentzIndex[0], Momentum[b]] + + FeynCalc`Package`MetricS ltensorToCTensor[a,CartesianMomentum[b,dim-1],c]; + + +diracGammaToCDiracGamma[LorentzIndex[a_]]:= + ( + tmpci= CartesianIndex[$MU[Unique[]]]; + FeynCalc`Package`MetricT Pair[LorentzIndex[a], ExplicitLorentzIndex[0]] DiracGamma[ExplicitLorentzIndex[0]] + + FeynCalc`Package`MetricS Pair[LorentzIndex[a], tmpci] DiracGamma[tmpci] + ); + +diracGammaToCDiracGamma[LorentzIndex[a_, dim_Symbol], dim_Symbol]:= + ( + tmpci= CartesianIndex[$MU[Unique[]],dim-1]; + FeynCalc`Package`MetricT Pair[LorentzIndex[a], ExplicitLorentzIndex[0]] DiracGamma[ExplicitLorentzIndex[0]] + + FeynCalc`Package`MetricS Pair[LorentzIndex[a,dim], tmpci] DiracGamma[tmpci,dim] + ); + +diracGammaToCDiracGamma[LorentzIndex[a_, dim_Symbol-4], dim_Symbol-4]:= + ( + tmpci= CartesianIndex[$MU[Unique[]],dim-4]; + FeynCalc`Package`MetricS Pair[LorentzIndex[a,dim-4], tmpci] DiracGamma[tmpci,dim-4] + ); + +diracSlashToCDiracSlash[Momentum[p_]]:= + FeynCalc`Package`MetricT DiracGamma[ExplicitLorentzIndex[0]] Pair[ExplicitLorentzIndex[0], Momentum[p]] + + FeynCalc`Package`MetricS DiracGamma[CartesianMomentum[p]]; + +diracSlashToCDiracSlash[Momentum[p_, dim_Symbol], dim_Symbol]:= + FeynCalc`Package`MetricT DiracGamma[ExplicitLorentzIndex[0]] Pair[ExplicitLorentzIndex[0], Momentum[p]] + + FeynCalc`Package`MetricS DiracGamma[CartesianMomentum[p,dim-1],dim]; + +diracSlashToCDiracSlash[Momentum[p_, dim_Symbol-4], dim_Symbol-4]:= + FeynCalc`Package`MetricS DiracGamma[CartesianMomentum[p,dim-4],dim-4]; + + +pauliSigmaToCPauliSigma[LorentzIndex[a_]]:= + ( + tmpci= CartesianIndex[$MU[Unique[]]]; + FeynCalc`Package`MetricT Pair[LorentzIndex[a], ExplicitLorentzIndex[0]] + + FeynCalc`Package`MetricS Pair[LorentzIndex[a], tmpci] PauliSigma[tmpci] + ); + +pauliSigmaToCPauliSigma[LorentzIndex[a_, dim_Symbol], dim_Symbol-1]:= + ( + tmpci= CartesianIndex[$MU[Unique[]],dim-1]; + FeynCalc`Package`MetricT Pair[LorentzIndex[a], ExplicitLorentzIndex[0]] + + FeynCalc`Package`MetricS Pair[LorentzIndex[a,dim], tmpci] PauliSigma[tmpci,dim-1] + ); + +pauliSigmaToCPauliSigma[LorentzIndex[a_, dim_Symbol-4], dim_Symbol-4]:= + ( + tmpci= CartesianIndex[$MU[Unique[]],dim-4]; + FeynCalc`Package`MetricS Pair[LorentzIndex[a,dim], tmpci] PauliSigma[tmpci,dim-4] + ); + +pauliSlashToCPauliSlash[Momentum[a_]]:= + FeynCalc`Package`MetricT TemporalPair[TemporalMomentum[a], ExplicitLorentzIndex[0]] + + FeynCalc`Package`MetricS PauliSigma[CartesianMomentum[a]]; + +pauliSlashToCPauliSlash[Momentum[a_, dim_Symbol], dim_Symbol-1]:= + FeynCalc`Package`MetricT TemporalPair[TemporalMomentum[a], ExplicitLorentzIndex[0]] + + FeynCalc`Package`MetricS PauliSigma[CartesianMomentum[a,dim-1],dim-1]; + +pauliSlashToCPauliSlash[Momentum[a_, dim_Symbol-4], dim_Symbol-4]:= + FeynCalc`Package`MetricS PauliSigma[CartesianMomentum[a,dim-4],dim-4]; + + +powerExpand[ex_, head_, times_]:= + ex /. Power[Pattern[z,Blank[head]], n_Integer?Positive] :> + Apply[times, Table[z, {Abs[n]}]]^Sign[n]/; !FreeQ[ex,Power]; + +powerExpand[ex_, _, _, _]:= + ex/; FreeQ[ex,Power]; + +FCPrint[1,"LorentzToCartesian.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/MomentumCombine.m b/FeynCalc/Lorentz/MomentumCombine.m index 233a71934..8781858ec 100644 --- a/FeynCalc/Lorentz/MomentumCombine.m +++ b/FeynCalc/Lorentz/MomentumCombine.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: MomentumCombine *) @@ -16,12 +16,8 @@ (* ------------------------------------------------------------------------ *) MomentumCombine::usage = -"MomentumCombine[expr] combines momenta and Pairs with the same LorentzIndexentz \ -indices and momenta."; - -MomentumCombine2::usage = -"MomentumCombine2[expr] is the inverse operation to MomentumExpand and \ -ExpandScalarProduct. MomentumCombine2 combines also FourVectors."; +"MomentumCombine[expr] combines momenta and Pair and Eps tensors with the same \ +LorentzIndexentz indices and momenta."; (* ------------------------------------------------------------------------ *) @@ -30,59 +26,123 @@ Begin["`MomentumCombine`Private`"]; +rulesMain = { + (n3_. Momentum[x_, dim_:4] + n4_. Momentum[y_, dim_:4]):> + (Momentum[ Expand[n3 x + n4 y],dim]/; (NumberQ[n3] && NumberQ[n4])), -MomentumCombine2[expr_] := - expr /. Plus-> plm; - -plm[xX__] := - If[ Length[{xX}] > 10, - Plus[xX], - Plus[xX] //. { - (n3_. Momentum[x_,di___] + n4_. Momentum[y_,di___] - ):> - (Momentum[ Expand[n3 x + n4 y],di]/;(NumberQ[n3]&&NumberQ[n4])), - (n3_. Pair[a_LorentzIndex, Momentum[x_,di___]] + - n4_. Pair[a_LorentzIndex, Momentum[y_,di___]] - ):> (Pair[a, Momentum[ Expand[n3 x + n4 y],di] - ]/;(NumberQ[n3] && NumberQ[n4]) - ) - , - (n3_ Pair[a_LorentzIndex, Momentum[x_,di___]] + - n3_ Pair[a_LorentzIndex, Momentum[y_,di___]] - ):> (n3 Pair[a, Momentum[Expand[x+y], di]]/;(!NumberQ[n3]) - ), - (n3_. Pair[a_LorentzIndex, Momentum[x_,di___]] + - n4_. Pair[a_LorentzIndex, Momentum[y_,di___]] - ):> (Pair[a, Expand[MomentumExpand[ - n3 Momentum[Expand[x], di] + n4 Momentum[Expand[y],di] - ] ] - ]/;(!NumberQ[n3] || NumberQ[n4]) && - FreeQ2[{n3, n4}, {Pair, Momentum, LorentzIndex}] - ) - } - ]; + (n3_. TemporalMomentum[x_] + n4_. TemporalMomentum[y_]):> + (TemporalMomentum[ Expand[n3 x + n4 y]]/; (NumberQ[n3] && NumberQ[n4])), + + (n3_. CartesianMomentum[x_, dim_:3] + n4_. CartesianMomentum[y_, dim_:3]):> + (CartesianMomentum[ Expand[n3 x + n4 y],dim]/; (NumberQ[n3] && NumberQ[n4])) +}; + +rulesSP = { + (n3_. Pair[a_Momentum, Momentum[x_, dim_:4]] + n4_. Pair[a_Momentum, Momentum[y_, dim_:4]]):> + Pair[a, Momentum[Expand[n3 x + n4 y],dim]]/;(NumberQ[n3] && NumberQ[n4] && n3=!=n4), + + (n3_. Pair[a_Momentum, Momentum[x_, dim_:4]] + n3_. Pair[a_Momentum, Momentum[y_, dim_:4]]):> + n3 Pair[a, Momentum[Expand[x + y],dim]], + + (n3_. Pair[a_Momentum, Momentum[x_, dim_:4]] - n3_. Pair[a_Momentum, Momentum[y_, dim_:4]]):> + n3 Pair[a, Momentum[Expand[x - y],dim]], + + (n3_. CartesianPair[a_CartesianMomentum, CartesianMomentum[x_, dim_:3]] + n4_. CartesianPair[a_CartesianMomentum, CartesianMomentum[y_, dim_:3]]):> + CartesianPair[a, CartesianMomentum[Expand[n3 x + n4 y],dim]]/;(NumberQ[n3] && NumberQ[n4] && n3=!=n4), + + (n3_. CartesianPair[a_CartesianMomentum, CartesianMomentum[x_, dim_:3]] + n3_. CartesianPair[a_CartesianMomentum, CartesianMomentum[y_, dim_:3]]):> + n3 CartesianPair[a, CartesianMomentum[Expand[x + y],dim]], + + (n3_. CartesianPair[a_CartesianMomentum, CartesianMomentum[x_, dim_:3]] - n3_. CartesianPair[a_CartesianMomentum, CartesianMomentum[y_, dim_:3]]):> + n3 CartesianPair[a, CartesianMomentum[Expand[x - y],dim]] +} + +rulesFV = { + (n3_. Pair[a_LorentzIndex, Momentum[x_, dim_:4]] + n4_. Pair[a_LorentzIndex, Momentum[y_, dim_:4]]):> + Pair[a, Momentum[ Expand[n3 x + n4 y],dim]]/; (NumberQ[n3] && NumberQ[n4] && n3=!=n4), + + (n3_. Pair[a_LorentzIndex, Momentum[x_, dim_:4]] + n3_. Pair[a_LorentzIndex, Momentum[y_, dim_:4]]):> + n3 Pair[a, Momentum[Expand[x+y], dim]], + + (n3_. Pair[a_LorentzIndex, Momentum[x_, dim_:4]] - n3_. Pair[a_LorentzIndex, Momentum[y_, dim_:4]]):> + n3 Pair[a, Momentum[Expand[x-y], dim]], + + (n3_. CartesianPair[a_CartesianIndex, CartesianMomentum[x_, dim_:3]] + n4_. CartesianPair[a_CartesianIndex, CartesianMomentum[y_, dim_:3]]):> + CartesianPair[a, CartesianMomentum[ Expand[n3 x + n4 y],dim]]/; (NumberQ[n3] && NumberQ[n4] && n3=!=n4), + + (n3_. CartesianPair[a_CartesianIndex, CartesianMomentum[x_, dim_:3]] + n3_. CartesianPair[a_CartesianIndex, CartesianMomentum[y_, dim_:3]]):> + n3 CartesianPair[a, CartesianMomentum[Expand[x+y], dim]], + + (n3_. CartesianPair[a_CartesianIndex, CartesianMomentum[x_, dim_:3]] - n3_. CartesianPair[a_CartesianIndex, CartesianMomentum[y_, dim_:3]]):> + n3 CartesianPair[a, CartesianMomentum[Expand[x-y], dim]], + + (n3_. TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[x_]] + n4_. TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[y_]]):> + TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[ Expand[n3 x + n4 y]]]/; (NumberQ[n3] && NumberQ[n4] && n3=!=n4), -Options[MomentumCombine] = {LeafCount -> 1}; + (n3_. TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[x_]] + n3_. TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[y_]]):> + n3 TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[Expand[x+y]]], + + (n3_. TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[x_]] - n3_. TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[y_]]):> + n3 TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[Expand[x-y]]] + +(* + (n3_. Pair[a_LorentzIndex, Momentum[x_,dim_:4]] + n4_. Pair[a_LorentzIndex, Momentum[y_,dim_:4]]):> + Pair[a, Expand[MomentumExpand[n3 Momentum[x, dim] + n4 Momentum[y,dim]]]]/; + (!NumberQ[n3] || !NumberQ[n4]) && FreeQ2[{n3,n4},{LorentzIndex,Momentum,Pair}]*) +}; + +rulesLC = { + (n3_. Eps[a___, (h:CartesianMomentum|Momentum)[x_, dim___], b___] + n4_. Eps[a___, (h:CartesianMomentum|Momentum)[y_, dim___], b___]):> + Eps[a, h[ Expand[n3 x + n4 y],dim], b]/; (NumberQ[n3] && NumberQ[n4] && n3=!=n4), + + (n3_. Eps[a___, (h:CartesianMomentum|Momentum)[x_, dim___], b___] + n3_. Eps[a___, (h:CartesianMomentum|Momentum)[y_, dim___], b___]):> + n3 Eps[a, h[ Expand[x + y],dim], b], + + (n3_. Eps[a___, (h:CartesianMomentum|Momentum)[x_, dim___], b___] - n3_. Eps[a___, (h:CartesianMomentum|Momentum)[y_, dim___], b___]):> + n3 Eps[a, h[ Expand[x - y],dim], b] + +}; + +Options[MomentumCombine] = { + FCE -> False, + FCI -> False, + FV -> True, + LC -> True, + LeafCount -> 1, + SP -> True +}; MomentumCombine[expr_, OptionsPattern[]] := - If[ LeafCount[expr] < OptionValue[LeafCount], - expr, - If[ FreeQ[expr, Momentum], - FeynCalcInternal[expr], - expr - ] //. { - - (n3_. Momentum[x_,di___] + n4_. Momentum[y_,di___]):> - (Momentum[ Expand[n3 x + n4 y],di]/;(NumberQ[n3] && NumberQ[n4])), - - (n3_. Pair[a_LorentzIndex, Momentum[x_,di___]] + n4_. Pair[a_LorentzIndex, Momentum[y_,di___]]):> - (Pair[a, Momentum[ Expand[n3 x + n4 y],di] - ]/;(NumberQ[n3] && NumberQ[n4])), - - (n3_. Pair[a_Momentum, Momentum[x_,di___]] + n4_. Pair[a_Momentum, Momentum[y_,di___]]):> - (Pair[a, Momentum[ Expand[n3 x + n4 y],di] - ]/;(NumberQ[n3] && NumberQ[n4])) - } + Block[{ex,res,rules=rulesMain}, + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + If[ OptionValue[FV], + rules = Join[rules,rulesFV] + ]; + + If[ OptionValue[SP], + rules = Join[rules,rulesSP] + ]; + + If[ OptionValue[LC], + rules = Join[rules,rulesLC] + ]; + + If[ LeafCount[ex] < OptionValue[LeafCount], + Return[ex] + ]; + + res = ex //. Dispatch[rules]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res ]; FCPrint["MomentumCombine.m loaded"]; diff --git a/FeynCalc/Lorentz/MomentumExpand.m b/FeynCalc/Lorentz/MomentumExpand.m index f67b44f49..d7420b168 100644 --- a/FeynCalc/Lorentz/MomentumExpand.m +++ b/FeynCalc/Lorentz/MomentumExpand.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2018 Rolf Mertig + Copyright (C) 1997-2018 Frederik Orellana + Copyright (C) 2014-2018 Vladyslav Shtabovenko *) (* :Summary: Expands momenta *) @@ -25,6 +25,7 @@ End[] Begin["`MomentumExpand`Private`"]; +pair::usage=""; fourvecevlin[n_?NumberQ z_, dim_:4] := n Momentum[z, dim]; @@ -36,8 +37,31 @@ hold[dim]]] /. hold->Identity) ]; +threevecevlin[n_?NumberQ z_, dim_:3] := + n CartesianMomentum[z, dim]; + +threevecev[y_,dim_:3] := + threevecev[y,dim] = + Block[ {hold}, + (Distribute[threevecevlin[ Expand[y, CartesianMomentum], + hold[dim]]] /. hold->Identity) + ]; + +zerovecevlin[n_?NumberQ z_] := + n TemporalMomentum[z]; + +zerovecev[y_] := + zerovecev[y] = + Distribute[zerovecevlin[Expand[y, TemporalMomentum]]]; + + + MomentumExpand[expr_] := - expr /.Spinor -> spinor /. Momentum -> fourvecev /. fourvecevlin -> Momentum /. spinor ->Spinor; + expr /. Spinor -> spinor /. FeynAmpDenominator -> fad /. PropagatorDenominator -> pd /. Pair-> pair /. CartesianPair-> cpair /. TemporalPair-> tpair /. + Momentum -> fourvecev /. fourvecevlin -> Momentum /. + CartesianMomentum -> threevecev /. threevecevlin -> CartesianMomentum /. + TemporalMomentum -> zerovecev /. zerovecevlin -> TemporalMomentum /. + pair -> Pair /. cpair -> CartesianPair /. tpair -> TemporalPair /. spinor ->Spinor /. pd -> PropagatorDenominator /. fad -> FeynAmpDenominator; FCPrint[1,"MomentumExpand.m loaded."]; End[] diff --git a/FeynCalc/Lorentz/PairContract.m b/FeynCalc/Lorentz/PairContract.m index 8ee9f670b..faf1fe30c 100644 --- a/FeynCalc/Lorentz/PairContract.m +++ b/FeynCalc/Lorentz/PairContract.m @@ -8,167 +8,210 @@ PairContract::usage = "PairContract is like Pair, but with (local) contraction properties."; -PairContract2::usage = -"PairContract2 is like Pair, but with local contraction properties \ -among PairContract2's."; +CartesianPairContract::usage = +"CartesianPairContract is like CartesianPair, but with (local) contraction properties."; PairContract3::usage = "PairContract3 is like Pair, but with local contraction properties \ among PairContract3's."; +PairContract::failmsg = +"Error! PairContract has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + (* ------------------------------------------------------------------------ *) Begin["`Package`"] + +(*pairContract3NoExpand is like PairContract3, but without ExpandScalarProduct *) +pairContract3NoExpand; + End[] Begin["`PairContract`Private`"] +SetAttributes[CartesianPairContract,Orderless]; + + +CartesianPairContract[CartesianIndex[i_],CartesianIndex[i_]]:= + 3; + +CartesianPairContract[CartesianIndex[i_],CartesianIndex[i_, _Symbol-4]]:= + 0; + +CartesianPairContract[CartesianIndex[i_],CartesianIndex[i_, _Symbol-1]]:= + 3; + +CartesianPairContract[CartesianIndex[i_, dim_],CartesianIndex[i_, dim_]]:= + dim; + +CartesianPairContract[CartesianIndex[i_, dim_Symbol-1],CartesianIndex[i_, dim_Symbol-4]]:= + dim-4; + +CartesianPairContract/: + CartesianPairContract[_CartesianIndex,x_]^2 := + CartesianPairContract[x,x]; + +CartesianPairContract /: + CartesianPairContract[a_, b_LorentzIndex]^(n_ /; n > 2) := + ( + Message[PairContract::failmsg, "The expression " <> ToString[CartesianPair[a, b]^n, InputForm] <> " violates Lorentz covariance!"]; + Abort[] + ) /; a =!= b; + +CartesianPairContract/: + CartesianPairContract[i_CartesianIndex,x_] f_[a__]:= + (f[a]/. CartesianIndex[First[i],___] -> x)/; !FreeQ[f[a], CartesianIndex[First[i],___]]; + +CartesianPairContract/: + CartesianPairContract[CartesianIndex[i_,___],j_CartesianIndex] (h:Pair|PairContract)[CartesianIndex[i_,___], l_LorentzIndex]:= + h[j,l]; + + SetAttributes[PairContract3,Orderless]; -PairContract3[LorentzIndex[z_,di___], LorentzIndex[z_,di___]] := - If[ {di}==={}, - 4, - di - ]; +PairContract3[LorentzIndex[z_], LorentzIndex[z_]] := + 4; + +PairContract3[LorentzIndex[z_,dim_], LorentzIndex[z_,dim_]] := + dim; -PairContract3[Momentum[a__], Momentum[b__]] := - ExpandScalarProduct[Pair[Momentum[a], Momentum[b]],FCI->False]; +PairContract3[(h1:Momentum|CartesianMomentum)[a__], (h2:Momentum|CartesianMomentum)[b__]] := + ExpandScalarProduct[Pair[h1[a], h2[b]],FCI->True]; PairContract3 /: - PairContract3[LorentzIndex[__],LorentzIndex[x__]]^2 := - PairContract3[LorentzIndex[x],LorentzIndex[x]]; + PairContract3[_LorentzIndex,x_LorentzIndex]^2 := + PairContract3[x,x]; PairContract3 /: - PairContract3[LorentzIndex[__],x_]^2 := - ExpandScalarProduct[x,x]; + PairContract3[_LorentzIndex,(h:Momentum|CartesianMomentum)[x__]]^2 := + ExpandScalarProduct[Pair[h[x],h[x]],FCI->True]; +PairContract3 /: + PairContract3[a_, b_LorentzIndex]^(n_ /; n > 2) := + ( + Message[PairContract::failmsg, "The expression " <> ToString[Pair[a, b]^n, InputForm] <> " violates Lorentz covariance!"]; + Abort[] + ) /; a =!= b; PairContract3/: PairContract3[LorentzIndex[z__],x_] PairContract3[LorentzIndex[z__],y_] := If[ FreeQ[{x,y}, LorentzIndex], - ExpandScalarProduct[x,y], + ExpandScalarProduct[Pair[x,y],FCI->True], PairContract3[x,y] ]; -SetAttributes[PairContract2,Orderless]; -(* -PairContract2[Momentum[a__], Momentum[b__] ] := -Pair[Momentum[a], Momentum[b]]; -*) -Clear[PairContract2]; -PairContract2/: -PairContract2[LorentzIndex[z_],x_] * -PairContract2[LorentzIndex[z_],y_] := -If[ FreeQ[{x,y},LorentzIndex], - Pair[x,y], - PairContract2[x,y] -]; +SetAttributes[pairContract3NoExpand,Orderless]; + + +pairContract3NoExpand[LorentzIndex[z_], LorentzIndex[z_]] := + 4; + +pairContract3NoExpand[LorentzIndex[z_,dim_], LorentzIndex[z_,dim_]] := + dim; + + +pairContract3NoExpand[Momentum[a__], Momentum[b__]] := + Pair[Momentum[a], Momentum[b]]; +pairContract3NoExpand /: + pairContract3NoExpand[_LorentzIndex, x_LorentzIndex]^2 := + pairContract3NoExpand[x,x]; +pairContract3NoExpand /: + pairContract3NoExpand[_LorentzIndex,(h:Momentum|CartesianMomentum)[x__]]^2 := + Pair[h[x],h[x]]; + + +pairContract3NoExpand/: + pairContract3NoExpand[LorentzIndex[z__],x_] pairContract3NoExpand[LorentzIndex[z__],y_] := + If[ FreeQ[{x,y}, LorentzIndex], + Pair[x,y], + pairContract3NoExpand[x,y] + ]; + +pairContract3NoExpand /: + pairContract3NoExpand[a_, b_LorentzIndex]^(n_ /; n > 2) := + ( + Message[PairContract::failmsg, "The expression " <> ToString[Pair[a, b]^n, InputForm] <> " violates Lorentz covariance!"]; + Abort[] + ) /; a =!= b; + +SetAttributes@@{{PairContract,sceins,sce,sczwei} ,Orderless}; (* this option is only to be set by SetOptions ... *) Options[PairContract] = {Factoring -> False}; -SetAttributes@@{{PairContract,sceins,scev,sce,scevdoit,sczwei} ,Orderless}; - -scev[x_,y_] := - MemSet[ scev[x,y], scevdoit[x,y] ]; -scev[x_,y_] := - scevdoit[x,y]; -scevdoit[x_,y_] := - Distribute[ sceins@@ - ( Expand[ MomentumExpand/@{x,y} ] ) - ]/.sceins->sczwei/.sczwei->PairContract/.PairContract->Pair; PairContract[0,_]:= 0; -PairContract[ LorentzIndex[a_,di___], epsmu_ LorentzIndex[mu_, dimen___] ] := - ( epsmu /. LorentzIndex[mu,dimen]->LorentzIndex[a,di] ) /; - (!FreeQ2[epsmu, {Eps, LorentzIndex[mu, dimen]}]); -(*TODO: polarization->Polarization, but only after adding the support for the - Transversality option!*) -PairContract[ Momentum[x_,___],Momentum[polarization[x_,___]]] := - 0; -PairContract[ Momentum[x_,___],Momentum[polarization[_?NumberQ x_,___]]] := - 0; -PairContract[Momentum[pi_,___],Momentum[polarization[x_Plus, ki___]]] := - scev[Momentum[x+pi], Momentum[polarization[x, ki]]]/; - ( pi + Last[x] )===0; -PairContract[Momentum[pi_,___],Momentum[polarization[x_Plus, ki___]]] := - scev[Momentum[pi-x], Momentum[polarization[x, ki]]]/; - ( pi - Last[x] )===0; - PairContract[ LorentzIndex[x_], LorentzIndex[x_] ] := 4; -(*new ...*) + PairContract[ LorentzIndex[x_], LorentzIndex[x_,_Symbol] ] := 4; PairContract[ LorentzIndex[x_,di_], LorentzIndex[x_,di_] ] := di; -PairContract /: HoldPattern[PairContract[lor_[_,___],x_]]^2 := - (PairContract[x,x]) /; lor === LorentzIndex; -(* CHANGE 09/94 *) -PairContract[Momentum[x_,___],Momentum[polarization[x_, ___],___]] := - 0; -PairContract[Momentum[x_,___],Momentum[polarization[_?NumberQ x_, ___],___] - ] := +PairContract[ CartesianIndex[x_], CartesianIndex[x_] ] := + 3 FeynCalc`Package`MetricS; + +PairContract[ CartesianIndex[x_], CartesianIndex[x_, _Symbol-1] ] := + 3 FeynCalc`Package`MetricS; + +PairContract[ CartesianIndex[x_], CartesianIndex[x_, _Symbol-4] ] := 0; -PairContract[Momentum[pi_,___],Momentum[polarization[x_Plus, ki___], dii___] - ] := - contract[expandscalarproduct[Pair[ - Momentum[x+pi, dii], Momentum[polarization[x, ki], dii]]] - ] /; ( pi + Last[x] ) === 0; -PairContract[Momentum[pi_,___],Momentum[polarization[x_Plus, ki___], dii___] - ] := - contract[expandscalarproduct[Pair[ - Momentum[pi-x,dii], Momentum[polarization[x, ki],dii]]] - ] /; ( pi - Last[x] ) === 0; -(* by convention ... *) -PairContract[Momentum[polarization[x_,__],___], - Momentum[polarization[x_,__],___] ] := - -1; -(* CHANGE 09/94 *) - -(* -PairContract/: PairContract[LorentzIndex[z_,___],x_] * - PairContract[LorentzIndex[z_,___],y_] := - PairContract[x,y]; -*) + +PairContract[ CartesianIndex[x_, di_], CartesianIndex[x_, di_] ] := + di FeynCalc`Package`MetricS; + +PairContract[ CartesianIndex[x_, di_Symbol-1], CartesianIndex[x_, di_Symbol-4] ] := + (di-4) FeynCalc`Package`MetricS; + +PairContract /: + PairContract[_LorentzIndex,x_]^2 := + PairContract[x,x]; + +PairContract /: + PairContract[a_, b_LorentzIndex]^(n_ /; n > 2) := + ( + Message[PairContract::failmsg, "The expression " <> ToString[Pair[a, b]^n, InputForm] <> " violates Lorentz covariance!"]; + Abort[] + ) /; a =!= b; PairContract/: PairContract[LorentzIndex[z_,___],x_] f_[a__] := -(f[a]/.LorentzIndex[z,___]->x)/; -(!FreeQ[f[a],LorentzIndex[z,___]]); + (f[a]/.LorentzIndex[z,___]->x)/; (!FreeQ[f[a],LorentzIndex[z,___]]); -PairContract[Momentum[a_Symbol,b_Symbol]] := - Pair[Momentum[a],Momentum[b]]; +PairContract/: + DOT[A___, HoldPattern[PairContract[lor_[z_,___],x_]], B___, m_. f_[a__], c___ ] := + DOT[A,B,(m f[a]/.LorentzIndex[z,___]->x),c]/; ((!FreeQ[f[a], LorentzIndex[z,___]]) && (lor === LorentzIndex)); PairContract/: - DOT[A___, HoldPattern[PairContract[lor_[z_,___],x_]], B___, - m_. f_[a__], c___ ] := -DOT[A,B,(m f[a]/.LorentzIndex[z,___]->x),c]/; - ((!FreeQ[f[a], LorentzIndex[z,___]]) && (lor === LorentzIndex)); - -PairContract/: DOT[A___, m_. f_[a__], B___, - HoldPattern[PairContract[lor_[z_,___],x_]], c___ ] := -DOT[A.(m f[a]/.LorentzIndex[z,___]->x),B,c]/; - ((!FreeQ[f[a]//Hold,LorentzIndex[z,___]]) && (lor === LorentzIndex)); + DOT[A___, m_. f_[a__], B___, HoldPattern[PairContract[lor_[z_,___],x_]], c___ ] := + DOT[A.(m f[a]/.LorentzIndex[z,___]->x),B,c]/; ((!FreeQ[f[a]//Hold,LorentzIndex[z,___]]) && (lor === LorentzIndex)); + (* **************************************************************** *) (* definitions for dimension = D-4 *) (* **************************************************************** *) PairContract[ _[_,_Symbol-4],_[_] ] := 0; + PairContract[ v_[x_,di_Symbol-4],w_[y_,di_Symbol] ] := - PairContract[v[x,di-4],w[y,di-4] ]; + PairContract[v[x,di-4],w[y,di-4] ]/; FreeQ2[{x,y},{CartesianIndex,CartesianMomentum,ExplicitLorentzIndex[0],TemporalMomentum}]; + PairContract[ w_[y_,_Symbol],v_[x_] ] := - PairContract[ v[x], w[y] ]; + PairContract[ v[x], w[y] ]/; FreeQ2[{x,y},{CartesianIndex,CartesianMomentum,ExplicitLorentzIndex[0],TemporalMomentum}]; + PairContract[ v_[x_], w_[y_,_Symbol] ] := - PairContract[ v[x], w[y] ]; + PairContract[ v[x], w[y] ]/; FreeQ2[{x,y},{CartesianIndex,CartesianMomentum,ExplicitLorentzIndex[0],TemporalMomentum}]; + + + sceins[0,_] := - 0; (*sceinsdef*) + 0; sceins[a_LorentzIndex b_, c_] := b sceins[a, c]; sceins[a_Momentum b_, c_] := @@ -179,25 +222,21 @@ sczwei[v[x, di-4], w[y, di-4]]; sczwei[ w_[y_,_Symbol],v_[x_] ] := sczwei[ v[x],w[y] ]; + sce[x_,y_] := - MemSet[sce[x, y], (*scedef*) - If[ (Factoring /. Options[PairContract]) === True, - Factor2[ - Distribute[sceins@@( Expand[ MomentumExpand/@{x,y} ]) - ]/.sceins->sczwei/.sczwei->Pair - ], - Distribute[sceins@@( Expand[ MomentumExpand/@{x,y} ]) - ]/.sceins->sczwei/.sczwei->Pair - ] ]; + If[ (Factoring /. Options[PairContract]) === True, + Factor2[Distribute[sceins@@( Expand[ MomentumExpand/@{x,y} ])]/.sceins->sczwei/.sczwei->Pair], + Distribute[sceins@@( Expand[ MomentumExpand/@{x,y} ]) ]/.sceins->sczwei/.sczwei->Pair + ]; + PairContract[x_,y_] := - MemSet[ PairContract[x,y], - Block[ {sCOt = sce[x,y]}, - If[ FreeQ[ sCOt, Pair ] || - (Head[sCOt]=!=Plus), - sCOt, - Pair[x,y] - ] - ] ]/;FreeQ[{x,y},LorentzIndex]; + Block[ {sCOt = sce[x,y]}, + If[ FreeQ[ sCOt, Pair ] || (Head[sCOt]=!=Plus), + sCOt, + Pair[x,y] + ] + ]/;FreeQ2[{x,y},{LorentzIndex,CartesianIndex}]; + FCPrint[1,"PairContract.m loaded."]; End[] diff --git a/FeynCalc/Lorentz/ScalarProduct.m b/FeynCalc/Lorentz/ScalarProduct.m index b54341c70..6425f86ec 100644 --- a/FeynCalc/Lorentz/ScalarProduct.m +++ b/FeynCalc/Lorentz/ScalarProduct.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Scalar products *) @@ -16,23 +16,30 @@ (* ------------------------------------------------------------------------ *) ScalarProduct::usage = -"ScalarProduct[p, q] is the input for scalar product. \ -ScalarProduct[p] is equivalent to ScalarProduct[p, p]. \ -Expansion of sums of momenta in ScalarProduct is done with \ -ExpandScalarProduct. Scalar products may be set, e.g. \ +"ScalarProduct[p, q] is the input for the scalar product of two \ +Lorentz vectors p and q. ScalarProduct[p] is equivalent to \ +ScalarProduct[p, p]. Expansion of sums of momenta in ScalarProduct is +done with ExpandScalarProduct. Scalar products may be set, e.g. via \ ScalarProduct[a, b] = m^2; but a and b may not contain sums. \ -Note that ScalarProduct[a, b] = m^2 actually sets also: \ -Pair[Momentum[a, ___], Momentum[b, ___]] = m^2 and \ -SPD[a,b] = m^2 and SP[a,b]=m^2. \ -It is enouraged to always set ScalarProduct's BEFORE any \ -calculation. This improves the performance of FeynCalc ."; - -SetDimensions::usage = -"SetDimensions is an option for ScalarProduct. It determines \ -for which dimensions the scalar products will be set when ScalarProduct \ -is used with the equality sign, e.g in ScalarProduct[a, b] = m^2. By default, the \ -scalar products are set for 4 and D dimensions. By changing this option \ -the user can add other dimensions or delete the exising ones."; +Note that ScalarProduct[a, b] = m^2 actually sets Lorentzian scalar products \ +in different dimensions specified by the value of the SetDimensions option. \ +It is highly recommended to set ScalarProduct's BEFORE any \ +calculation. This improves the performance of FeynCalc."; + +CartesianScalarProduct::usage = +"CartesianScalarProduct[p, q] is the input for the scalar product of two \ +Cartesian vectors p and q. CartesianScalarProduct[p] is equivalent to \ +CartesianScalarProduct[p, p]. Expansion of sums of momenta in CartesianScalarProduct is +done with ExpandScalarProduct. Scalar products may be set, e.g. via \ +ScalarProduct[a, b] = m^2; but a and b may not contain sums. \ +Note that ScalarProduct[a, b] = m^2 actually sets Cartesian scalar products \ +in different dimensions specified by the value of the SetDimensions option. \ +It is highly recommended to set ScalarProduct's BEFORE any \ +calculation. This improves the performance of FeynCalc."; + +SetTemporalComponent::usage = +"SetTemporalComponent[p, val] sets the value of the temporal +component of a 4-vector p, TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[p]] to val."; ScalarProduct::emptydim = "If you want to set scalar products via ScalarProduct[a, b] = m^2, you must \ @@ -42,21 +49,37 @@ ScalarProduct::fail = "Something went wrong while setting scalar products! Evaluation aborted." +CartesianScalarProduct::emptydim = +"If you want to set scalar products via CartesianScalarProduct[a, b] = m^2, you must \ +specify at least one dimension via the option SetDimensions->{dims...}! Evaluation \ +aborted." + +CartesianScalarProduct::fail = +"Something went wrong while setting scalar products! Evaluation aborted." + (* ------------------------------------------------------------------------ *) Begin["`Package`"] initialScalarProductDownValues; initialScalarProductUpValues; +initialCartesianScalarProductDownValues; +initialCartesianScalarProductUpValues; End[] Begin["`ScalarProduct`Private`"] Options[ScalarProduct] = { - Dimension->4, - FCI -> True, - SetDimensions -> {4,D} + Dimension -> 4, + FCI -> True, + SetDimensions -> {4,D} +}; + +Options[CartesianScalarProduct] = { + Dimension -> 3, + FCI -> True, + SetDimensions -> {3,D-1} }; ScalarProduct /: @@ -73,6 +96,22 @@ Pair[Momentum[a, OptionValue[Dimension]], Momentum[b, OptionValue[Dimension]]]/; FreeQ[{a,b}, Momentum] && OptionValue[FCI]; + +CartesianScalarProduct /: + MakeBoxes[CartesianScalarProduct[a_, b_, opts:OptionsPattern[]], TraditionalForm]:= + ToBoxes[FCI[CartesianScalarProduct[a,b,opts]],TraditionalForm]/; !OptionValue[CartesianScalarProduct,{opts},FCI]; + +CartesianScalarProduct[a_, b_, opts:OptionsPattern[]] := + CartesianScalarProduct[b, a, opts]/;!OrderedQ[{a, b}]; + +CartesianScalarProduct[x_, opts:OptionsPattern[]] := + CartesianScalarProduct[x, x, opts]; + +CartesianScalarProduct[a_,b_, OptionsPattern[]] := + CartesianPair[CartesianMomentum[a, OptionValue[Dimension]], CartesianMomentum[b, OptionValue[Dimension]]]/; + FreeQ[{a,b}, CartesianMomentum] && OptionValue[FCI]; + + ScalarProduct/: Set[ScalarProduct[araw_,braw_,c:OptionsPattern[]] , z_]:= Block[ {downv, pair, ruleClearSP,ruleClearPair, a,b, @@ -94,7 +133,7 @@ ]; spList = Flatten[Map[(Flatten[Outer[HoldPattern[sp[#1,#2,dummy[Dimension,slot]]]&, - Sequence@@tuples]]/.slot->Slot[1])&,dims]/.dummy->Rule]/.sp[xxx__,Dimension->4]->sp[xxx]/.sp->ScalarProduct; + Sequence@@tuples]]/.slot->Slot[1])&,dims]/.dummy->Rule]/.sp[j__,Dimension->4]->sp[j]/.sp->ScalarProduct; pairList = Flatten[Map[(Flatten[Outer[hp[pair[Momentum[#1, slot], Momentum[#2, slot]]] &, Sequence@@tuples]]/.slot->Slot[1])&,dims]] /. hp->HoldPattern; @@ -113,7 +152,7 @@ (* Rules for removing previous DownValues *) ruleClearSP = DeleteDuplicates[Flatten[Map[(Flatten[Outer[dummy[HoldPattern[sp[#1, #2, Rule[Dimension, slot]]], pair[#1, #2, Rule[Dimension, slot]]] &, Sequence@@tuples]] /. slot -> Slot[1]) &, dims] /. - pair -> ScalarProduct /. dummy -> RuleDelayed /.sp[xxx__,Dimension->4]->sp[xxx]/.sp->ScalarProduct]]; + pair -> ScalarProduct /. dummy -> RuleDelayed /.sp[j__,Dimension->4]->sp[j]/.sp->ScalarProduct]]; ruleClearPair = DeleteDuplicates[Flatten[Map[(Flatten[Outer[dummy[hp[pr[Momentum[#1, slot], Momentum[#2, slot]]], pair[#1, #2, Rule[Dimension, slot]]] &, Sequence@@tuples]] /. slot -> Slot[1]) &, dims] /. @@ -198,17 +237,237 @@ ]; (* Last but not least, add the set scalar product to our list*) - FCPrint[1,"ScalarProduct: Adding vectors the the list of set scalar products"]; + FCPrint[1,"ScalarProduct: Adding vectors to the list of set scalar products"]; entry= Sort[{Momentum[araw],Momentum[braw]}]; If[ !MemberQ[$ScalarProducts,entry], AppendTo[$ScalarProducts,entry] ]; setval - ]/; araw=!=0 && braw=!=0 && FreeQ2[{araw,braw},{Pattern,Blank,BlankSequence,BlankNullSequence}]; + ]/; araw=!=0 && braw=!=0 && FCPatternFreeQ[{araw,braw}]; + + +CartesianScalarProduct/: + Set[CartesianScalarProduct[araw_,braw_,c:OptionsPattern[]] , z_]:= + Block[ {downv, cpair, ruleClearCSP,ruleClearCartesianPair, a,b, + ruleClearFCECSP,ruleClearFCECSPD,ruleClearFCECSPE, + cspList, cpairList, fceList, valsListOrig, valsList, + slot,dims,setval,dummy, tuples, hp, cpr, csp, entry, + ruleClearCartesianMomentum, cmomList}, + + dims = OptionValue[CartesianScalarProduct,{c},SetDimensions]; + {a,b} = Sort[{araw,braw}]; + tuples = { {(a/NumericalFactor[a]), Expand[(a/NumericalFactor[a])], Expand[-(a/NumericalFactor[a])]}, + {(b/NumericalFactor[b]), Expand[(b/NumericalFactor[b])], Expand[-(b/NumericalFactor[b])]}}; + valsListOrig = {setval, setval, -setval, setval,setval, -setval, -setval, -setval, setval}; + + setval = z/(NumericalFactor[a]*NumericalFactor[b]); + + If[dims==={}, + Message[CartesianScalarProduct::emptydim]; + Abort[] + ]; + + cspList = Flatten[Map[(Flatten[Outer[HoldPattern[csp[#1,#2,dummy[Dimension,slot]]]&, + Sequence@@tuples]]/.slot->Slot[1])&,dims]/.dummy->Rule]/.csp[j__,Dimension->3]:>csp[j]/.csp->CartesianScalarProduct; + + cpairList = Flatten[Map[(Flatten[Outer[hp[cpair[CartesianMomentum[#1, slot], CartesianMomentum[#2, slot]]] &, + Sequence@@tuples]]/.slot->Slot[1])&,dims]] /. hp->HoldPattern; + + fceList = Flatten[Outer[HoldPattern[cpair[#1, #2]] &, Sequence@@tuples]]; + + cmomList = DeleteDuplicates[Flatten[Map[Map[dummy[hp[cm[#, slot]], 0] &, tuples[[1]]] /. slot -> Slot[1] &, dims]]] /. + cm[x_,3]:> cm[x] /. hp->HoldPattern; + + + + valsList = Flatten[Table[valsListOrig, {i, 1,Length[dims]}]]; + + If[Length[cspList]=!=Length[cpairList] || Length[cspList]=!=Length[valsList], + Message[CartesianScalarProduct::fail]; + Abort[] + ]; + + (* Rules for removing previous DownValues *) + ruleClearCSP = DeleteDuplicates[Flatten[Map[(Flatten[Outer[dummy[HoldPattern[csp[#1, #2, Rule[Dimension, slot]]], + cpair[#1, #2, Rule[Dimension, slot]]] &, Sequence@@tuples]] /. slot -> Slot[1]) &, dims] /. + cpair -> CartesianScalarProduct /. dummy -> RuleDelayed /.csp[j__,Dimension->3]:>csp[j]/.csp->CartesianScalarProduct]]; + + ruleClearCartesianPair = DeleteDuplicates[Flatten[Map[(Flatten[Outer[dummy[hp[cpr[CartesianMomentum[#1, slot], CartesianMomentum[#2, slot]]], + cpair[#1, #2, Rule[Dimension, slot]]] &, Sequence@@tuples]] /. slot -> Slot[1]) &, dims] /. + cpair -> CartesianScalarProduct /. dummy -> RuleDelayed]] /. hp->HoldPattern /. cpr->CartesianPair; + + (*For a^2 = 0 we need to set CartesianMomentum[a]=0 as well! *) + + If[setval===0 && a===b, + ruleClearCartesianMomentum = DeleteDuplicates[ + Flatten[Map[(Flatten[Outer[dummy[hp[cm[#1, slot]], CartesianMomentum + [#1, slot]] &, Sequence @@ tuples]] /. slot -> Slot[1]) &, dims] /. + cpair -> CartesianScalarProduct /. dummy -> RuleDelayed]]/. cm[x_,3]:> cm[x] /. hp -> HoldPattern /. cm -> CartesianMomentum; + ]; + + ruleClearFCECSP = DeleteDuplicates[Flatten[Outer[dummy[HoldPattern[CSP[#1,#2]], + cpair[#1, #2, Rule[Dimension, 3]]] &, Sequence@@tuples] /. slot -> Slot[1] /. + cpair -> CartesianScalarProduct /. dummy -> RuleDelayed]]; + + ruleClearFCECSPD = DeleteDuplicates[Flatten[Outer[dummy[HoldPattern[CSPD[#1,#2]], + cpair[#1, #2, Rule[Dimension, D-1]]] &, Sequence@@tuples] /. slot -> Slot[1] /. + cpair -> CartesianScalarProduct /. dummy -> RuleDelayed]]; + + ruleClearFCECSPE = DeleteDuplicates[Flatten[Outer[dummy[HoldPattern[CSPE[#1,#2]], + cpair[#1, #2, Rule[Dimension, D-4]]] &, Sequence@@tuples] /. slot -> Slot[1] /. + cpair -> CartesianScalarProduct /. dummy -> RuleDelayed]]; + + (* Check if CartesianScalarProduct's have already been set to something. If yes, + remove existing value. Notice that say (p-q)^2 and (q-p)^2 are the same but + treated as different by Mathematica, so that we need to account for these cases *) + If[ (cspList/.HoldPattern->Identity/.CartesianPair->cpair) =!= cpairList/.HoldPattern->Identity, + + FCPrint[1,"CartesianScalarProduct: Removing old values for ", CartesianScalarProduct[a,b,c], " and it variations "]; + (* for CartesianScalarProduct *) + downv = DownValues[CartesianScalarProduct]; + downv = Complement[downv,ruleClearCSP]; + DownValues[CartesianScalarProduct] = downv; + + (* for CartesianPair *) + downv = DownValues[CartesianPair]; + downv = Complement[downv,ruleClearCartesianPair]; + DownValues[CartesianPair] = downv; + + (* for CSP *) + If[ !FreeQ[dims,3], + downv = DownValues[CSP]; + downv = Complement[downv,ruleClearFCECSP]; + DownValues[CSP] = downv + ]; + + (* for CSPD *) + If[ !FreeQ[dims,D-1], + downv = DownValues[CSPD]; + downv = Complement[downv,ruleClearFCECSPD]; + DownValues[CSPD] = downv; + ]; + + (* for CSPE *) + downv = DownValues[CSPE]; + If[ !FreeQ[dims,D-4], + downv = Complement[downv,ruleClearFCECSPE]; + DownValues[CSPE] = downv; + ]; + + (* for CartesianMomentum *) + + (*For a^2 = 0 we need to set CartesianMomentum[a]=0 as well! *) + If[setval===0 && a===b, + downv = DownValues[CartesianMomentum]; + downv = Complement[downv,ruleClearCartesianMomentum]; + DownValues[CartesianMomentum] = downv; + ]; + + FCPrint[3,"CartesianScalarProduct: Downvalues for CartesianScalarProduct after removal ", DownValues[CartesianScalarProduct]]; + FCPrint[3,"CartesianScalarProduct: Downvalues for CartesianPair after removal ", DownValues[CartesianPair]]; + FCPrint[3,"CartesianScalarProduct: Downvalues for CSP after removal ", DownValues[CSP]]; + FCPrint[3,"CartesianScalarProduct: Downvalues for CSPD after removal ", DownValues[CSPD]]; + FCPrint[3,"CartesianScalarProduct: Downvalues for CSPE after removal ", DownValues[CSPE]]; + ]; + + + FCPrint[1,"CartesianScalarProduct: Setting DownValues for CartesianScalarProduct"]; + DownValues[CartesianScalarProduct]=Join[DeleteDuplicates[Thread[dummy[cspList,valsList]]]/.dummy->RuleDelayed,DownValues[CartesianScalarProduct]]; + + FCPrint[1,"CartesianScalarProduct: Setting DownValues for CartesianPair"]; + DownValues[CartesianPair]=Join[DeleteDuplicates[Thread[dummy[cpairList/.cpair->CartesianPair,valsList]]]/.dummy->RuleDelayed,DownValues[CartesianPair]]; + + FCPrint[1,"CartesianScalarProduct: Setting DownValues for CSPD"]; + If[ MemberQ[dims,D-1], + DownValues[CSPD]=Join[DeleteDuplicates[Thread[dummy[fceList/.cpair->CSPD,valsListOrig]]]/.dummy->RuleDelayed,DownValues[CSPD]] + ]; + + FCPrint[1,"CartesianScalarProduct: Setting DownValues for CSPE"]; + If[ MemberQ[dims,D-4], + DownValues[CSPE]=Join[DeleteDuplicates[Thread[dummy[fceList/.cpair->CSPE,valsListOrig]]]/.dummy->RuleDelayed,DownValues[CSPE]] + ]; + + FCPrint[1,"CartesianScalarProduct: Setting DownValues for CSP"]; + If[ MemberQ[dims,3], + DownValues[CSP]=Join[DeleteDuplicates[Thread[dummy[fceList/.cpair->CSP,valsListOrig]]]/.dummy->RuleDelayed,DownValues[CSP]] + ]; + + If[ setval===0 && a===b, + FCPrint[1,"CartesianScalarProduct: Setting DownValues for CartesianMomentum"]; + DownValues[CartesianMomentum]=Join[cmomList/.cm->CartesianMomentum/.dummy->RuleDelayed,DownValues[CartesianMomentum]]; + ]; + + (* Last but not least, add the set scalar product to our list*) + FCPrint[1,"CartesianScalarProduct: Adding vectors to the list of set scalar products"]; + entry= Sort[{CartesianMomentum[araw],CartesianMomentum[braw]}]; + If[ !MemberQ[$ScalarProducts,entry], + AppendTo[$ScalarProducts,entry] + ]; + + setval + ]/; araw=!=0 && braw=!=0 && FCPatternFreeQ[{araw,braw}]; + + +SetTemporalComponent[araw_, z_, OptionsPattern[]]:= + Block[ {downv, a, ruleClearTV, ruleClearTemporalPair, + tPairList, fceList, valsListOrig, valsList, + setval,dummy, tuples}, + + a = araw; + tuples = { (a/NumericalFactor[a]), Expand[(a/NumericalFactor[a])], Expand[-(a/NumericalFactor[a])] }; + valsListOrig = {setval, setval, -setval}; + + setval = z/(NumericalFactor[a]); + tPairList = Flatten[Map[HoldPattern[TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[#]]] &,tuples]]; + fceList = Flatten[Map[HoldPattern[TC[#]] &,tuples]]; + valsList = valsListOrig; + + (* Rules for removing previous DownValues *) + ruleClearTV = Thread[dummy[fceList, fceList/.HoldPattern->Identity]]/.dummy->RuleDelayed; + ruleClearTemporalPair = Thread[dummy[tPairList, tPairList/.HoldPattern->Identity]]/.dummy->RuleDelayed; + + (* Check if temporal componeents have already been set to something. If yes, + remove existing value. *) + If[ Head[TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[a]]]=!=TemporalPair, + + FCPrint[1,"SetTemporalComponent: Removing old values for and its variations"]; + + (* for TemporalPair *) + downv = DownValues[TemporalPair]; + downv = Complement[downv,ruleClearTemporalPair]; + DownValues[TemporalPair] = downv; + + (* for TC *) + + downv = DownValues[TC]; + downv = Complement[downv,ruleClearTV]; + DownValues[TC] = downv; + + FCPrint[3,"SetTemporalComponent: Downvalues for TemporalPair after removal ", DownValues[TemporalPair]]; + FCPrint[3,"SetTemporalComponent: Downvalues for TC after removal ", DownValues[TC]]; + ]; + + FCPrint[1,"SetTemporalComponent: Setting DownValues for TemporalPair"]; + DownValues[TemporalPair] = Join[Thread[dummy[tPairList, valsList]]/.dummy->RuleDelayed,DownValues[TemporalPair]]; + + FCPrint[1,"SetTemporalComponent: Setting DownValues for TC"]; + DownValues[TC] = Join[Thread[dummy[fceList, valsList]]/.dummy->RuleDelayed,DownValues[TC]]; + + (* Last but not least, add the set scalar product to our list*) + FCPrint[1,"SetTemporalComponent: Adding TemporalMomentum to the list of set scalar products"]; + + If[ !MemberQ[$ScalarProducts,{TemporalMomentum[a]}], + AppendTo[$ScalarProducts,{TemporalMomentum[a]}] + ]; + ]/; araw=!=0 && FCPatternFreeQ[{araw}]; + +initialScalarProductDownValues = DownValues[ScalarProduct]; +initialScalarProductUpValues = UpValues[ScalarProduct]; +initialCartesianScalarProductDownValues = DownValues[CartesianScalarProduct]; +initialCartesianScalarProductUpValues = UpValues[CartesianScalarProduct]; -initialScalarProductDownValues = DownValues[ScalarProduct]; -initialScalarProductUpValues = UpValues[ScalarProduct]; +Protect[SetTemporalComponent]; FCPrint[1,"ScalarProduct.m loaded."]; End[] diff --git a/FeynCalc/Lorentz/Schouten.m b/FeynCalc/Lorentz/Schouten.m new file mode 100755 index 000000000..a29e27455 --- /dev/null +++ b/FeynCalc/Lorentz/Schouten.m @@ -0,0 +1,159 @@ + + +(* :Title: Schouten *) + +(* :Author: Rolf Mertig *) + +(* ------------------------------------------------------------------------ *) +(* :History: File created on 22 June '97 at 23:00 *) +(* ------------------------------------------------------------------------ *) + +(* :Summary: Option and Function *) + +(* ------------------------------------------------------------------------ *) + +Schouten::usage = +"Schouten[exp] attempts to automatically remove spurious terms in exp by applying \ +the Schouten identity. \n +Schouten applies the identity for 4-vectors on at most \ +42 terms in a sum. If it should operate on a larger expression you \ +can give a second argument, e.g.: Schouten[expr, 4711] which will work \ +on sums with less than 4711 terms.\n +Schouten is also an option of Contract and \ +DiracTrace. It may be set to an integer \ +indicating the maximum number of terms onto which the \ +function Schouten will be applied ."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`Schouten`Private`"] + +Schouten[y_, 0] := + y; +Schouten[y_, oparg_:42] := + ( + If[ !FreeQ2[{y}, FeynCalc`Package`NRStuff], + Message[FeynCalc::nrfail]; + Abort[] + ]; + + FixedPoint[schouten[#, oparg]&, FeynCalcInternal[y], 14] + ); + +liget[_. Eps[x1_[y1_], x2_[y2_], x3_[y3_], x4_[y4_]] Pair[x5_[y5_], x6_[y6_]]] := + {x1[y1],x2[y2],x3[y3],x4[y4],x5[y5],x6[y6]}; + +lisch[{a1_,a2_,a3_,a4_,a5_,a6_}] := + Pair[a5,a6] Eps[a1,a2,a3,a4]; + + +epc[a_, b_] := + If[ Length[Position[PartitHead[a, Eps][[2]], LorentzIndex]] False]; + If[ Head[tem]===Plus, + Length[tem], + 1 + ] + ]; + +schouten[x_,opar_:42] := + Block[ {i=0,nx,temp0,temp,lind,ltemp,ntemp, + schou,sor, all,result,numberofli, optarg = opar, + temp1, nxf = 1}, + + nx = EpsEvaluate[ExpandScalarProduct[x]//Expand]//Expand; + (* Split the sum into two parts *) + result = nx; + + (* eps x1 + eps x2 + ... + rest, then split the eps part from the rest! *) + all = PartitHead[nx, Eps]; + + If[ !(Head[all[[2]]]===Plus), + Return[result nxf] + ]; + + temp0 = PartitHead[all[[2]], Pair]; + + temp = temp0[[2]]; + + (*let us assume that optarg is always an Integer! *) + (* then dummIlabel is always false! *) + + If[ !((Head[temp]===Plus) && Length[temp] > 1 && (Length[temp] < optarg)), + Return[result nxf] + ]; + + ltemp = Length[temp]; + + (*pick up the first term of temp and count the number of Lorentz indices in that term*) + temp1 = temp[[1]]; + numberofli = Length[Position[temp1, LorentzIndex]]; + (* it is interesting that the number of indices in the very first term influences the whole algorithm!*) + + temp = + Catch[ + (*so we look at each term in the expression temp *) + While[i < Length[temp], i++; + + (*if the term contains no Eps or Pair, do nothing. *) + If[ !FreeQ2[temp[[i]],{Eps,Pair}], + + (* + extracts indices or momenta of the current term eps[i1,i2,i3,i4] pair[i5,i6] + Notice that if there are several eps' and pairs', the choice becomes sort of random + + *) + lind = liget[temp[[i]]]; + + (* Strange, can lind return something different than 6??*) + If[ Length[lind]===6, + (* create a list of 5 possible arrangements of terms of Schouten ident. *) + + schou = lisch /@ Map[Append[#, Last[lind]]&,NestList[RotateLeft,Take[lind,5],4]]; + + (*special sorting, w.r.t the position of the Lorentz indices in eps *) + sor = Sort[ schou, epc ]//Reverse; + (*rotate one position to the left if temp does not contain the first element of sor *) + Do[ + If[ FreeQ[temp, sor[[1]]], + sor = RotateLeft[sor] + ], + {6} + ]; + + If[ !FreeQ[temp, sor[[1]]], + (*for the case that temp does contain an element of sort, apply the identity*) + ntemp = Expand[EpsEvaluate[temp/.sor[[1]]-> (-Plus@@Rest[sor])]]; + (* or all LorentzIndices are inside all Eps's *) + (* if the number of terms containing eps is smaller than the original length, or the number o + of the Lorentz indices remains unchanged, take this identity(?).*) + If[ (epsnterms[ntemp] < ltemp) || + (Union[Length[Position[#, LorentzIndex]]& /@ Select[Variables[ntemp], Head[#]===Eps&]] === {numberofli}), + Throw[temp = ntemp] + ] + ] + ] + ] + ]; + temp + ]; + + result = all[[1]] + temp0[[1]] + temp; + result nxf + ]; + +FCPrint[1,"Schouten.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/SetMandelstam.m b/FeynCalc/Lorentz/SetMandelstam.m index f0fffb4bb..b8f1a5348 100755 --- a/FeynCalc/Lorentz/SetMandelstam.m +++ b/FeynCalc/Lorentz/SetMandelstam.m @@ -1,12 +1,17 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) +(* ::Package:: *) -(* :Title: SetMandelstam *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Author: Rolf Mertig *) +(* :Title: SetMandelstam *) -(* ------------------------------------------------------------------------ *) +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* :Summary: define kinematical invariants *) +(* :Summary: Defines of kinematical invariants *) (* ------------------------------------------------------------------------ *) @@ -28,65 +33,71 @@ Begin["`SetMandelstam`Private`"] -Options[SetMandelstam] = {Dimension -> {4, D}}; +Options[SetMandelstam] = { + Dimension -> {4, D} +}; (*sma*) -small2/: small2[x_]^n_ := small2[x^2] /; n > 0; -small2/: small2[_] _ :=0; -small3/: small3[_] + a_ :=a; +small2/: small2[x_]^n_ := + small2[x^2] /; n > 0; + +small2/: small2[_] _ := + 0; + +small3/: small3[_] + a_ := + a; + small4[x_^m_] := SmallVariable[x]^m; - sma[x_] := - x/;FreeQ[x,SmallVariable]; - sma[x_] := - x/.SmallVariable->small2/.small2->small3/. - small3->small4/.small4->SmallVariable; + +sma[x_] := + x/;FreeQ[x,SmallVariable]; + +sma[x_] := + x/.SmallVariable->small2/.small2->small3/. small3->small4/.small4->SmallVariable; setit[a_,b_,___] := set[a,sma[(b//Expand)]]/.set->Set; -(* SetMandelstamdef *) -SetMandelstam[s_,t_,u_, { {p1_, m12_}, {p2_, m22_} } -> - { {p3_, m32_}, {p4_, m42_} }] := - SetMandelstam[s,t,u, p1, p2, -p3, -p4, Sqrt[m12], Sqrt[m22], - Sqrt[m32], Sqrt[m42]]; -SetMandelstam[s_,t_,u_,p1_,p2_,p3_,p4_,m1_,m2_,m3_,m4_,opt___Rule] := - Block[ {settemp,oldmem,setvars,sol,pp1, pp2, pp3, pp4, dims, $MemoryAvailable = 0}, - dims = Flatten[{Dimension /. {opt} /. Options[SetMandelstam]}]; + + +SetMandelstam[s_,t_,u_, { {p1_, m12_}, {p2_, m22_} } -> { {p3_, m32_}, {p4_, m42_} }] := + SetMandelstam[s,t,u, p1, p2, -p3, -p4, Sqrt[m12], Sqrt[m22], Sqrt[m32], Sqrt[m42]]; + +SetMandelstam[s_,t_,u_,p1_,p2_,p3_,p4_,m1_,m2_,m3_,m4_, OptionsPattern[]] := + Block[ {settemp,setvars,sol, dims}, + + dims = OptionValue[Dimension]; + If[ Head[dims] =!= List, dims = { dims } ]; - (* note that p1, p2, p3, p4 may have have a minus - sign *) - {pp1, pp2, pp3, pp4} = #/NumericalFactor[#] & /@ {p1, p2, p3, p4}; - scd[a_,b_, 4] := - ScalarProduct[a,b]; - scd[a_,b_, d_] := - ScalarProduct[a,b,Dimension->d]; + settemp = Union[Flatten[Join[Table[{ - scd[p1,p1,dims[[i]]] == m1^2, - scd[p2,p2,dims[[i]]] == m2^2, - scd[p3,p3,dims[[i]]] == m3^2, - scd[p4,p4,dims[[i]]] == m4^2, - scd[p1,p2,dims[[i]]] == sma[1/2 s - 1/2 m1^2 - 1/2 m2^2], - scd[p1,p3,dims[[i]]] == sma[1/2 t - 1/2 m1^2 - 1/2 m3^2], - scd[p1,p4,dims[[i]]] == sma[1/2 u - 1/2 m1^2 - 1/2 m4^2], - scd[p2,p3,dims[[i]]] == sma[1/2 u - 1/2 m2^2 - 1/2 m3^2], - scd[p2,p4,dims[[i]]] == sma[1/2 t - 1/2 m2^2 - 1/2 m4^2], - scd[p3,p4,dims[[i]]] == sma[1/2 s - 1/2 m3^2 - 1/2 m4^2] + ScalarProduct[p1,p1,Dimension->dims[[i]]] == m1^2, + ScalarProduct[p2,p2,Dimension->dims[[i]]] == m2^2, + ScalarProduct[p3,p3,Dimension->dims[[i]]] == m3^2, + ScalarProduct[p4,p4,Dimension->dims[[i]]] == m4^2, + ScalarProduct[p1,p2,Dimension->dims[[i]]] == sma[1/2 s - 1/2 m1^2 - 1/2 m2^2], + ScalarProduct[p1,p3,Dimension->dims[[i]]] == sma[1/2 t - 1/2 m1^2 - 1/2 m3^2], + ScalarProduct[p1,p4,Dimension->dims[[i]]] == sma[1/2 u - 1/2 m1^2 - 1/2 m4^2], + ScalarProduct[p2,p3,Dimension->dims[[i]]] == sma[1/2 u - 1/2 m2^2 - 1/2 m3^2], + ScalarProduct[p2,p4,Dimension->dims[[i]]] == sma[1/2 t - 1/2 m2^2 - 1/2 m4^2], + ScalarProduct[p3,p4,Dimension->dims[[i]]] == sma[1/2 s - 1/2 m3^2 - 1/2 m4^2] }, {i, Length[dims]} ]]]]; + If[ FreeQ2[{p1,p2,p3,p4}, {Plus,Times}], - settemp = Union[settemp, FeynCalcExternal[settemp]]; + settemp = Union[settemp, FCE[settemp]]; sol = settemp /. Equal ->setit, - (* else *) - settemp = settemp//FeynCalcInternal; - settemp = settemp//ExpandScalarProduct; - settemp = settemp//Expand; - settemp = Union[settemp, FeynCalcExternal[settemp]]; + + settemp = ExpandScalarProduct[settemp]//Expand; + settemp = Union[settemp, FCE[settemp]]; + (* want also for 4 or D dimensions to set SP[p,p] = ... etc. *) setvars = Cases2[settemp, {Pair, SP, SPD}]; If[ Complement[Head/@setvars,{Pair, SP, SPD}] === {}, - sol = Solve[ settemp,setvars ]/.Rule->setit + sol = Solve[settemp, setvars]/.Rule->setit ]; ]; sol @@ -99,51 +110,52 @@ scalarproduct[a_, b_] := FeynCalcInternal[ScalarProduct[a,b]]//ExpandScalarProduct; -SetMandelstam[x_, pl_List, ml_List, opt___?OptionQ] := - Block[ {settemp,oldmem,setvars,sol,n = Length[ml], psu,pkl,sq2,eqq,ppl,dims}, - oldmem = $MemoryAvailable; - $MemoryAvailable = 0; - dims = Flatten[{Dimension /. {opt} /. Options[SetMandelstam]}]; +SetMandelstam[x_, pl_List, ml_List, OptionsPattern[]] := + Block[ {settemp, setvars, sol, n = Length[ml], psu, pkl, sq2, eqq, + dims, var, npk, nsol, j1, j2, enm}, + + dims = OptionValue[Dimension]; + If[ Head[dims] =!= List, dims = { dims } ]; - ppl = #/NumericalFactor[#] & /@ pl; -(* - Table[ setdel[ Momentum[ppl[[ij]], _Symbol], Momentum[ppl[[ij]]] ], - {ij, Length[ppl]} ] /. setdel -> SetDelayed; -*) - settemp = Join[ Table[scalarproduct[pl[[i]], pl[[i]]] == ml[[i]]^2, {i,1,n}], - Table[scalarproduct[pl[[j]], pl[[j+1]]] == sma[1/2 x[j,j+1] - 1/2 ml[[j]]^2 - 1/2 ml[[j+1]]^2], {j,1,n-1}], - {scalarproduct[ pl[[1]],pl[[n]] ] == sma[1/2 x[1,n] - 1/2 ml[[1]]^2 - 1/2 ml[[n]]^2]}]//ExpandScalarProduct//Expand; + + settemp = Join[ + Table[scalarproduct[pl[[i]], pl[[i]]] == ml[[i]]^2, {i,1,n}], + Table[scalarproduct[pl[[j]], pl[[j+1]]] == sma[1/2 x[j,j+1] - 1/2 ml[[j]]^2 - 1/2 ml[[j+1]]^2], {j,1,n-1}], + {scalarproduct[ pl[[1]],pl[[n]] ] == sma[1/2 x[1,n] - 1/2 ml[[1]]^2 - 1/2 ml[[n]]^2]}]//ExpandScalarProduct//Expand; setvars = Cases[settemp, _Pair, -1]; settemp = Union[Join@@(Map[ChangeDimension[settemp, #]&, dims])]; - - settemp = Union[Join[settemp, FeynCalcExternal[settemp]]]; + settemp = Union[Join[settemp, FCE[settemp]]]; setvars = Union[Join@@Map[ChangeDimension[setvars, #]&, dims]]; - setvars = Union[Join[setvars, FeynCalcExternal[setvars]]]; - sol = Solve[ settemp,setvars ]/.Rule->setit; + setvars = Union[Join[setvars, FCE[setvars]]]; + + sol = Solve[settemp,setvars ]/.Rule->setit; + sq2[y_] := scalarproduct[y, y]//ExpandScalarProduct//Expand; + pkl = {}; - For[ k = 1, k<=n, k++, - For[ l = k+1, l<= n, l++, - npk = scalarproduct[ pl[[k]], pl[[l]] ]//ExpandScalarProduct; - If[ (Head[npk] === Pair) || (Head[-npk]=== Pair), - AppendTo[pkl,{pl[[k]], pl[[l]]}] - ] - ] + For[ k = 1, k<=n, k++, + For[ l = k+1, l<= n, l++, + npk = scalarproduct[ pl[[k]], pl[[l]] ]//ExpandScalarProduct; + If[ (Head[npk] === Pair) || (Head[-npk]=== Pair), + AppendTo[pkl,{pl[[k]], pl[[l]]}] + ] + ] ]; psu = Plus@@pl; + enm[a_] := Expand[- Apply[Plus, Drop[pl,{a,a}]]]; Do[ eqq = {sq2[psu] == 0}; - eqq = Join[ eqq, Table[ sq2[pl[[ii]] + pl[[n]]] - sq2[enm[ii] + pl[[n]]] ==0 , {ii, 2,n-3}] + eqq = Join[ eqq, Table[ sq2[pl[[l]] + pl[[n]]] - sq2[enm[l] + pl[[n]]] ==0 , {l, 2,n-3}] ]; For[ j1 = 1, j10, eqq = Union[Join@@Map[ChangeDimension[eqq, #]&, dims]]; - eqq = Union[Join[eqq, FeynCalcExternal[eqq]]]; + eqq = Union[Join[eqq, FCE[eqq]]]; var = Union[Join@@Map[ChangeDimension[var, #]&, dims]]; - var = Union[Join[var, FeynCalcExternal[var]]]; + var = Union[Join[var, FCE[var]]]; ]; If[ Length[var] > 0, @@ -168,8 +181,8 @@ nsol = nsol /. Rule -> setit ] , {2}]; - $MemoryAvailable = oldmem; - MapAll[ Expand, Append[sol, nsol]//Flatten ] + + MapAll[Expand, Append[sol, nsol]//Flatten ] ]; FCPrint[1,"SetMandelstam.m loaded."]; diff --git a/FeynCalc/Lorentz/TensorFunction.m b/FeynCalc/Lorentz/TensorFunction.m index a196bec08..37e8c32f5 100755 --- a/FeynCalc/Lorentz/TensorFunction.m +++ b/FeynCalc/Lorentz/TensorFunction.m @@ -28,12 +28,13 @@ Begin["`TensorFunction`Private`"] -Options[TensorFunction] = {Dimension -> 4}; +Options[TensorFunction] = { + Dimension -> 4 +}; TensorFunction[ef_, munu___,last_/;Head[last]=!=Rule, OptionsPattern[]] := - Block[ {f, dim, at="", patt}, + Block[ {f, dim, at=""}, dim = OptionValue[Dimension]; - patt = {Pattern,Sequence,BlankSequence,BlankNullSequence}; If[ Head[ef] === List && Length[ef] === 2, f = First[ef]; @@ -49,9 +50,9 @@ SetAttributes@@{tf, Orderless}, at === "A", Evaluate[tf[a__]] := - Condition[Signature[{a}] Apply[tf, Sort[{a}]],!OrderedQ[{a}] && FreeQ2[{a},patt]]; + Condition[Signature[{a}] Apply[tf, Sort[{a}]],!OrderedQ[{a}] && FCPatternFreeQ[{a}]]; Evaluate[tf[a__]] := - Condition[0,Signature[{a}]===0 && FreeQ2[{a},patt]], + Condition[0,Signature[{a}]===0 && FCPatternFreeQ[{a}]], True, Message[TensorFunction::usym,at]; Abort[] @@ -60,7 +61,7 @@ (* Any tensor function contracted with a null vector is zero *) Evaluate[tf[a___,0,b___]] := - Condition[0,FreeQ2[{a,b},patt]]; + Condition[0,FCPatternFreeQ[{a,b}]]; tf@@(Map[LorentzIndex[#, dim]&, {munu,last}]) ] diff --git a/FeynCalc/Lorentz/ThreeDivergence.m b/FeynCalc/Lorentz/ThreeDivergence.m new file mode 100755 index 000000000..af299d18b --- /dev/null +++ b/FeynCalc/Lorentz/ThreeDivergence.m @@ -0,0 +1,262 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: ThreeDivergence *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Compute partial derivatives w.r.t to the given 3-vector(s) *) + +(* ------------------------------------------------------------------------ *) + +ThreeDivergence::usage = +"ThreeDivergence[exp, CV[p, i]] calculates the partial derivative of exp w.r.t. p^i. \ +ThreeDivergence[exp, CV[p, i], CV[p,i], ...] gives the multiple derivative."; + +ThreeDivergence::notvec= +"`1` is not a Lorentz vector. Evaluation aborted!" + +ThreeDivergence::extfail= +"Failed to extract the name of the Lorentz vector from `1`. Evaluation aborted!" + +ThreeDivergence::toocompl= +"The structure `1` w.r.t which you are trying to differentiate is too complicated \ +to ensure the correct result. Evaluation aborted!" + +ThreeDivergence::failmsg = +"Error! ThreeDivergence has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +ThreeDivergence::warn = +"Warning! The input expression also depends on `1` in dimensions other than `2`. \ +The derivative of a vector in one dimension w.r.t the same vector in a different \ +dimension is zero by convention. Please check that this is indeed intended. You \ +can deactivate this message for the current session by evaluating \ +Off[ThreeDivergence::warn]."; + +ThreeDivergence::warnLorentz = +"Warning! The input expression also depends on the 4-momentum `1`. The derivatives of \ +such quantities w.r.t the corresponding 3-vector are zero. Please check that \ +this is indeed intended. You can deactivate this message for the current session by \ +evaluating Off[ThreeDivergence::warnLorentz]."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`ThreeDivergence`Private`"] + +fdVerbose::usage=""; + +Options[ThreeDivergence] = { + Abort -> True, + ApartFF -> False, + Collecting -> True, + Contract -> True, + EpsEvaluate -> True, + ExpandScalarProduct -> True, + FCE -> False, + FCI -> False, + FCVerbose -> False, + Factoring -> Factor +}; + +ThreeDivergence[expr_, cv:Except[_?OptionQ].., OptionsPattern[]] := + Block[{ex, ve, tliflag = False, time, args, hold}, + + If [OptionValue[FCVerbose]===False, + fdVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fdVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "ThreeDivergence: Entering.", FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: Entering with: ", expr, FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: Differentiating w.r.t ", {cv}, FCDoControl->fdVerbose]; + + + If [!OptionValue[FCI], + {ex,ve} = {FCI[expr],FCI[{cv}]}, + {ex,ve} = {expr,{cv}} + ]; + + args = Cases[{ve}, z_CartesianMomentum :> First[z], Infinity] // Sort // DeleteDuplicates; + + FCPrint[1, "ThreeDivergence: Applying threeDerivative ", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = threeDerivative[ex,Sequence@@ve]; + FCPrint[1, "ThreeDivergence: threeDerivative done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: After threeDerivative ", ex, FCDoControl->fdVerbose]; + + (* Put FADs back together *) + If[ !FreeQ[ex, FeynAmpDenominator], + FCPrint[1, "ThreeDivergence: Applying FeynAmpDenominatorCombine.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = FeynAmpDenominatorCombine[ex, FCI->True]; + FCPrint[1, "ThreeDivergence: FeynAmpDenominatorCombine done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: After FeynAmpDenominatorCombine: ", ex, FCDoControl->fdVerbose] + ]; + + If[ OptionValue[Contract], + FCPrint[1, "ThreeDivergence: Applying Contract.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = Contract[ex, FCI->True]; + FCPrint[1, "ThreeDivergence: Contract done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: After Contract: ", ex, FCDoControl->fdVerbose] + ]; + + If[ OptionValue[ExpandScalarProduct], + FCPrint[1, "ThreeDivergence: Applying ExpandScalarProduct.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = ExpandScalarProduct[ex, FCI->True, EpsEvaluate->OptionValue[EpsEvaluate]]; + FCPrint[1, "ThreeDivergence: ExpandScalarProduct done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: After ExpandScalarProduct: ", ex, FCDoControl->fdVerbose] + ]; + + If[ OptionValue[ApartFF], + FCPrint[1, "ThreeDivergence: Applying ApartFF.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + ex = ApartFF[ex, args, FCI->True, FDS->False, DropScaleless->False]; + FCPrint[1, "ThreeDivergence: ApartFF done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: After ApartFF: ", ex, FCDoControl->fdVerbose] + ]; + + If[ OptionValue[Collecting], + FCPrint[1, "ThreeDivergence: Applying Collect2.", FCDoControl->fdVerbose]; + time=AbsoluteTime[]; + If[ !FreeQ[ex,FeynAmpDenominator], + ex = Collect2[ex, FeynAmpDenominator, Factoring->hold]; + ex = ex /. hold[]->1 /. z_hold:> Collect2[First[z],args,Factoring->OptionValue[Factoring]], + + ex = Collect2[ex, args, Factoring->OptionValue[Factoring]] + ]; + + FCPrint[1, "ThreeDivergence: Collect2 done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: After Collect2: ", ex, FCDoControl->fdVerbose] + ]; + + If[ OptionValue[FCE], + ex = FCE[ex] + ]; + + FCPrint[3, "ThreeDivergence: Leaving.", FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: Leaving with: ", ex, FCDoControl->fdVerbose]; + + + ex + ]; + + +(* For multiple derivatives *) +threeDerivative[x_, a_, b__] := + threeDerivative[threeDerivative[x, a], b]; + +threeDerivative[x_, ve_]:= + Block[{ nx = x,p, p0, mu, dList, dListEval, repRuleFinal, deriv, + null1,null2,un, fadHead, fadList, fadListEval, + repRule1, repRule2={}, res}, + + FCPrint[3, "ThreeDivergence: threeDerivative: Entering with: ", x, FCDoControl->fdVerbose]; + + (* check that we are differentiating w.r.t a vector *) + If[ !MatchQ[ve,CartesianPair[CartesianMomentum[_Symbol,___],_CartesianIndex]], + Message[ThreeDivergence::failmsg, ToString[ve,InputForm] <> " is not a Cartesian vector."]; + Abort[] + ]; + + p = ve/.CartesianPair[z_CartesianMomentum,_] :> z; + mu = ve/.CartesianPair[z_CartesianIndex,_] :> z; + p0 = First[p]; + + FCPrint[3, "ThreeDivergence: threeDerivative: p and mu: ", {p,mu}, FCDoControl->fdVerbose]; + + If [p===ve || mu===ve || Head[mu]=!=CartesianIndex || FreeQ[p,CartesianMomentum], + Message[ThreeDivergence::failmsg, "Failed to extract the name of the Lorentz vector from " <> + ToString[ve,InputForm] <> ". Evaluation aborted!"]; + Abort[] + ]; + + (* Expand slashes, scalar products and epsilon tensors that contain momenta w.r.t to which we want to differentiate *) + If[ !FreeQ[nx, DiracGamma], + nx = DiracGammaExpand[nx, Momentum -> {p0}, FCI->True]; + FCPrint[3, "ThreeDivergence: threeDerivative: After DiracGammaExpand: ", nx, FCDoControl->fdVerbose]; + ]; + + nx = ExpandScalarProduct[nx, Momentum -> {p0}, EpsEvaluate->True, FCI->True]; + FCPrint[3, "ThreeDivergence: threeDerivative: After ExpandScalarProduct: ", nx, FCDoControl->fdVerbose]; + + If[ !FreeQ[nx,Momentum[p0,___]], + Message[ThreeDivergence::warnLorentz, ToString[p0,InputForm]]; + ]; + + (* Differentation of FADs is very easy to mess up, so we need to be careful here. + Essentially, we have d/dx 1/f(g(x)) = -1/[f(g(x))]^2 * f'(g(x))* g'(x), where f(x)=x, i.e. + the sole purpose of f(x) is that we can recover FADs after the differentiation, c.f. + D[1/f[g[x]], x] /. f -> Identity *) + If[ !FreeQ[nx, FeynAmpDenominator], + (* FeynAmpDenominatorSplit is necessary here. Without it, the results are still correct, + but they become too complicated. *) + nx = FeynAmpDenominatorSplit[nx,FCI->True]; + fadList = Cases[nx + null1 + null2, zzz_FeynAmpDenominator /; ! FreeQ[zzz, p], Infinity]; + fadListEval = FeynAmpDenominatorExplicit[#,FCI->True,Head->fadHead,Denominator->True]&/@fadList; + repRule1 = Thread[Rule[fadList,fadListEval]]; + repRule2 = (Reverse /@ repRule1) /. Rule[a_, b_] :> Rule[1/a, 1/b]; + + FCPrint[3, "ThreeDivergence: threeDerivative: repRule1: ", repRule1, FCDoControl->fdVerbose]; + FCPrint[3, "ThreeDivergence: threeDerivative: repRule2: ", repRule1, FCDoControl->fdVerbose]; + + nx = nx /. repRule1; + + FCPrint[3, "ThreeDivergence: threeDerivative: After applying repRule1: ", nx, FCDoControl->fdVerbose]; + + ]; + + If[ Cases[(nx/. p-> Unique[]) + null1 + null2, CartesianMomentum[p0,___], Infinity]=!={}, + Message[ThreeDivergence::warn,ToString[p0], ToString[p/.CartesianMomentum[_,dim_:3]:>dim]] + ]; + + (* This is the main part *) + nx = D[nx, p] /. Derivative -> deriv; + FCPrint[3, "ThreeDivergence: threeDerivative: After D: ", nx, FCDoControl->fdVerbose]; + + dList = Cases[nx+null1+null2,deriv[___][___][___],Infinity]//Sort//DeleteDuplicates; + + dListEval = dList /. (deriv[__][fadHead][__]) :> 1 /. { + deriv[1, 0][CartesianPair][p, a_] :> CartesianPair[a, mu] , + deriv[0, 1][CartesianPair][a_, p] :> CartesianPair[a, mu] , + deriv[1,0][DiracGamma][p,dim_] :> DiracGamma[mu,dim] , + deriv[1][DiracGamma][p] :> DiracGamma[mu] , + deriv[1,0,0,0][Eps][p,c__] :> Eps[mu,c] , + deriv[0,1,0,0][Eps][a_,p,c__] :> Eps[a,mu,c] , + deriv[0,0,1,0][Eps][a__,p,c_] :> Eps[a,mu,c] , + deriv[0,0,0,1][Eps][c__,p] :> Eps[c,mu], + deriv[1,0,0][Eps][p,c__] :> Eps[mu,c] , + deriv[0,1,0][Eps][a_,p,c__] :> Eps[a,mu,c] , + deriv[0,0,1][Eps][a__,p,c_] :> Eps[a,mu,c] + } /. deriv -> Derivative; + + repRuleFinal = Thread[Rule[dList,dListEval]]; + FCPrint[3, "ThreeDivergence: threeDerivative: Final replacement list: ", repRuleFinal, FCDoControl->fdVerbose]; + + res = nx /. Dispatch[repRuleFinal] /. Dispatch[repRule2]; + + If[ !FreeQ2[res,{Derivative,deriv,fadHead}], + Message[ThreeDivergence::failmsg, "The output contains unevaluated derivatives."]; + If[ TrueQ[OptionValue[Abort]], + Abort[] + ] + ]; + + res + ]; + +FCPrint[1,"ThreeDivergence.m loaded."]; +End[] diff --git a/FeynCalc/Lorentz/ThreeVector.m b/FeynCalc/Lorentz/ThreeVector.m deleted file mode 100755 index e74332141..000000000 --- a/FeynCalc/Lorentz/ThreeVector.m +++ /dev/null @@ -1,31 +0,0 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: ThreeVector *) - -(* :Author: Rolf Mertig *) - -(* ------------------------------------------------------------------------ *) -(* :History: File created on 16 December '98 at 17:11 *) -(* ------------------------------------------------------------------------ *) - -(* :Summary: ThreeVector *) - -(* ------------------------------------------------------------------------ *) - -ThreeVector::usage = -"ThreeVector[p] is the three dimensional vector p."; - -(* ------------------------------------------------------------------------ *) - -Begin["`Package`"] -End[] - -Begin["`ThreeVector`Private`"] - - -ThreeVector /: MakeBoxes[ThreeVector[p_], TraditionalForm] := -(* RM: changed Global`OverVector to OverVector 20100119 *) -MakeBoxes[OverVector[p], TraditionalForm]; - -FCPrint[1,"ThreeVector.m loaded."]; -End[] diff --git a/FeynCalc/Lorentz/TrickMandelstam.m b/FeynCalc/Lorentz/TrickMandelstam.m index dcb06a8a8..78f2289f8 100755 --- a/FeynCalc/Lorentz/TrickMandelstam.m +++ b/FeynCalc/Lorentz/TrickMandelstam.m @@ -28,111 +28,121 @@ Begin["`TrickMandelstam`Private`"] -(*factor3def*) -factor3[x_] :=(*factor3[x]=*) +factor3[x_] := Factor2[x, FactorFull -> False]; -(*ntermsdef*) - nterms[x_Plus] := - Length[x]; - nterms[x_] := - Block[ {ntermslex = Expand[x]}, - If[ Head[ntermslex]===Plus, - ntermslex = Length[ntermslex], - If[ x===0, - ntermslex = 0, - ntermslex = 1 - ] - ]; - ntermslex + +nterms[x_Plus] := + Length[x]; + +nterms[x_] := + Block[ {ntermslex = Expand[x]}, + If[ Head[ntermslex]===Plus, + ntermslex = Length[ntermslex], + If[ x===0, + ntermslex = 0, + ntermslex = 1 + ] ]; -(*nsortQdef*) - nsortQ[x_,y_] := - True/;nterms[x]<=nterms[y]; - nsortQ[x_,y_] := - False/;nterms[x]>nterms[y]; + ntermslex + ]; + +nsortQ[x_,y_] := + True/;nterms[x]<=nterms[y]; + +nsortQ[x_,y_] := + False/;nterms[x]>nterms[y]; TrickMandelstam[y_, {}] := y; + TrickMandelstam[ y_, __ ] := factor3[y] /; FreeQ[y,Plus]; + TrickMandelstam[x_,es_,te_,uu_, mas_] := TrickMandelstam[x, {es,te,uu,mas}]; + TrickMandelstam[x_List,y__] := Map[TrickMandelstam[#,y]&, x]; + TrickMandelstam[a_ , {es_, te_, uu_, mm_}] := Block[ {tres}, + tres = trickmandelstam[a//factor3, {es,te,uu,mm}]; If[ LeafCount[tres]<2000, tres = Cancel[tres] ]; + tres//factor3 ]; trickmandelstam[yy_Times, ar_List] := Map[TrickMandelstam[#, ar]&, yy]; + trickmandelstam[yy_Power, ar_List] := TrickMandelstam[yy[[1]], ar]^yy[[2]]; + trickmandelstam[y_, args_List] := Block[ {nulLl}, trickmandelstam[nulLl+y,args]/.nulLl->0 - ] /; (Head[y]=!=Times) && - (Head[y]=!=Power) && (Head[y]=!=Plus); - - drickstu[exp_,{},___] := - exp; - drickstu[exp_,{s_,t_,u_,_},___] := - exp /; !FreeQ[{s,t,u},Plus]; - - short1[x_Plus,es_,te_,uu_,ma_] := - (Sort[{x, Expand[ x/.te->(ma-es-uu) ], - Expand[ x/.uu->(ma-te-es) ] - },nsortQ]//First ); - short1[a_ b_,c__] := - short1[a,c] short1[b,c]; - short1[a_^n_,c__] := - short1[a,c]^n; - - short1[x_,__] := - x/;(Head[x]=!=Plus) && (Head[x]=!=Times) && - (Head[x]=!=Power); + ] /; (Head[y]=!=Times) && (Head[y]=!=Power) && (Head[y]=!=Plus); + +drickstu[exp_,{},___] := + exp; + +drickstu[exp_,{s_,t_,u_,_},___] := + exp /; !FreeQ[{s,t,u},Plus]; + +short1[x_Plus,es_,te_,uu_,ma_] := + (Sort[{x, Expand[ x/.te->(ma-es-uu) ], Expand[x/.uu->(ma-te-es)]},nsortQ]//First ); + +short1[a_ b_,c__] := + short1[a,c] short1[b,c]; + +short1[a_^n_,c__] := + short1[a,c]^n; + +short1[x_,__] := + x/;(Head[x]=!=Plus) && (Head[x]=!=Times) && (Head[x]=!=Power); + trickmandelstam[x_Plus,man_List] := Block[ {tricktemp,merk,nx = x,plusch, plusch0}, - merk[y_] := - MemSet[ merk[y],drickstu[y,man] ]; + plusch0[z__] := Plus[z] /; !FreeQ[{z},plusch0]; - (* This is for arguments of D0, etc. ... *) + + (* This is for arguments of D0, etc. ... *) plusch[z__] := - drickstu[Plus[z],man]/; - (Length[{z}]===(Length[Plus@@man]-1))&& FreeQ[{z},Plus]; + drickstu[Plus[z],man]/; (Length[{z}]===(Length[Plus@@man]-1))&& FreeQ[{z},Plus]; + plusch[z__] := - (factor3 /@ Collect2[ Plus[z], Take[man, 3] ] ) /; - Length[{z}]=!=(Length[Plus@@man]-1); - tricktemp = merk[ nx ]; - (tricktemp/.Plus->plusch0/.plusch0->plusch /. - plusch->Plus) + (factor3 /@ Collect2[ Plus[z], Take[man, 3] ] ) /; Length[{z}]=!=(Length[Plus@@man]-1); + + tricktemp = drickstu[nx,man]; + + (tricktemp/.Plus->plusch0/.plusch0->plusch /. plusch->Plus) ]/;(Length[man]===4 || man==={}) && Head[x]=!=Times; - drickback[x_,__] := - x; - drickstu[ x_Plus,{s_,t_,u_,m_} ] := - Block[ {result,tristemp,eM,otherv,nuLL,trickman}, -(* Check if an overall factorization is possible *) - tristemp = factor3[ x/.s->(m-t-u) ]; - If[ Head[tristemp]=!=Plus, - result = TrickMandelstam[tristemp,{s,t,u,m}], - otherv = Complement[ Variables[tristemp], Variables[s+t+u+m] ]; -(* The simplifications cannot occur outside certain coefficients *) - If[ otherv =!= {}, - result = factor3/@ (Collect2[eM tristemp, Append[otherv,eM]] - ); - result = Map[short1[#,s,t,u,m]&,result+nuLL]/.nuLL->0/.eM->1; - result = Map[factor3, result], - result = short1[tristemp, s,t,u,m] - ] - ]; - result + +drickback[x_,__] := + x; + +drickstu[ x_Plus,{s_,t_,u_,m_} ] := + Block[ {result,tristemp,eM,otherv,nuLL,trickman}, + (* Check if an overall factorization is possible *) + tristemp = factor3[ x/.s->(m-t-u) ]; + If[ Head[tristemp]=!=Plus, + result = TrickMandelstam[tristemp,{s,t,u,m}], + otherv = Complement[ Variables[tristemp], Variables[s+t+u+m] ]; + (* The simplifications cannot occur outside certain coefficients *) + If[ otherv =!= {}, + result = factor3/@ (Collect2[eM tristemp, Append[otherv,eM]]); + result = Map[short1[#,s,t,u,m]&,result+nuLL]/.nuLL->0/.eM->1; + result = Map[factor3, result], + result = short1[tristemp, s,t,u,m] + ] ]; + result + ]; FCPrint[1,"TrickMandelstam.m loaded."]; End[] diff --git a/FeynCalc/Lorentz/Uncontract.m b/FeynCalc/Lorentz/Uncontract.m index 64ef36877..21d90f9e4 100755 --- a/FeynCalc/Lorentz/Uncontract.m +++ b/FeynCalc/Lorentz/Uncontract.m @@ -6,12 +6,12 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) -(* :Summary: Uncontracts Lorentz tensors *) +(* :Summary: Uncontracts Lorentz and Cartesian tensors *) (* ------------------------------------------------------------------------ *) @@ -20,6 +20,10 @@ also p.q1 and p.q2; Pair -> All uncontracts all except \ OPEDelta. Dimension -> Automatic leaves dimensions unchanged."; +Uncontract::failmsg = +"Error! Uncontract has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -27,112 +31,451 @@ Begin["`Uncontract`Private`"] +ucVerbose::usage=""; +dim::usage=""; +nPower::usage=""; +sPower::usage=""; + Options[Uncontract] = { - Dimension -> Automatic, - DimensionalReduction -> False, - Pair -> {}, - Unique -> True + CartesianMomentum -> True, + CartesianPair -> {}, + Dimension -> Automatic, + DiracChainExpand -> True, + DiracGamma -> True, + DotSimplify -> True, + Eps -> True, + FCE -> False, + FCI -> False, + FCTensor -> All, + FCVerbose -> False, + Momentum -> True, + Pair -> {}, + PauliSigma -> True, + Polarization -> True, + Square -> True }; -Uncontract[x_Plus, q__] := - Map[Uncontract[#,q]&, x]; - Uncontract[x_List, q__] := Map[Uncontract[#,q]&, x]; -Uncontract[x_, q1__, q2:Except[_?OptionQ], opt:OptionsPattern[]] := - Uncontract[Uncontract[x,q2,opt],q1, opt]; +Uncontract[x_, q1__, q2:Except[_?OptionQ], opts:OptionsPattern[]] := + Uncontract[Uncontract[x,q2,opts],q1, opts]; + +Uncontract[ex_, All, opts:OptionsPattern[]] := + Block[{exp,moms,null1,null2,res}, + + If [OptionValue[FCVerbose]===False, + ucVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + ucVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "Uncontract: Entering Uncontract for all momenta.", FCDoControl->ucVerbose]; + + If[ OptionValue[FCI], + exp = ex, + exp = FCI[ex] + ]; + moms = Cases[(exp + null1+null2)/. _FeynAmpDenominator :> Unique[], (Momentum | CartesianMomentum)[z_, ___] :> z, Infinity] // DeleteDuplicates // Sort; + FCPrint[1, "Uncontract: List of momenta:", moms , FCDoControl->ucVerbose]; + + If[ moms=!={}, + res = Uncontract[exp, Sequence@@moms, FCI->True ,opts], + res = exp + ]; + + FCPrint[1, "Uncontract: Leaving Uncontract for all momenta.", FCDoControl->ucVerbose]; + + res + + ]; + Uncontract[ex_, q:Except[_?OptionQ], OptionsPattern[]] := - Block[{ exp,eeps,nex,li,li1,li2,dim,par,dummy,inc, - a$AL,dr, lidr,seq,dimSelect,times}, + Block[{ exp,li, li2, pairs, cpairs, times,null1,null2, + allObjects, selectedObjects,dotTimes, + momAllow, cmomAllow, + epsRules={}, digaRules={}, sigmaRules={}, pairRules={}, cpairRules={}, + repRuleObjects = {}, res, uniqueHead, qRule, + tensorList, tensorRules = {}, + alternativesTensorList, tensoruncontract, fctensor, qMark, tmp + }, + + If [OptionValue[FCVerbose]===False, + ucVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + ucVerbose=OptionValue[FCVerbose] + ]; + ]; - par = OptionValue[Pair]; + FCPrint[1, "Uncontract: Entering Uncontract", FCDoControl->ucVerbose]; + FCPrint[3, "Uncontract: Entering with, ", ex , FCDoControl->ucVerbose]; + FCPrint[3, "Uncontract: q: ", q , FCDoControl->ucVerbose]; + + pairs = OptionValue[Pair]; + cpairs = OptionValue[CartesianPair]; dim = OptionValue[Dimension]; + fctensor = OptionValue[FCTensor]; + + momAllow = OptionValue[Momentum]; + cmomAllow = OptionValue[CartesianMomentum]; + Which[ fctensor===All, + tensoruncontract=True; + tensorList = Complement[$FCTensorList, {CartesianPair, Pair, Eps}], + Head[fctensor]===List && fctensor=!={}, + tensoruncontract=True; + tensorList = fctensor, + True, + tensoruncontract = False; + tensorList = {} + ]; - lidr[z_] := - If[ OptionValue[DimensionalReduction], - z/.{LorentzIndex[aa_,_]:>LorentzIndex[aa]/. Momentum[bb_,_] :> Momentum[bb]}, - z - ]; - dimSelect[z_]:= - If[ dim===Automatic, - seq[z], - dim - ]; - exp = FeynCalcInternal[ex]; + If[ Length[tensorList] > 1, + alternativesTensorList = Alternatives@@(Blank/@tensorList), + If[ tensorList==={}, + alternativesTensorList = Null, + alternativesTensorList = Blank[(Identity@@tensorList)] + ] + ]; + + + qRule = q :> qMark[q]; + + + If[ momAllow, + + pairRules = Join[pairRules, {Pair[Momentum[g_,d_:4], Momentum[p_, e_:4]]/;!FreeQ[g,qMark] && FreeQ[p,qMark] :> + ( li = LorentzIndex[$AL[Unique[]],dimSelectLorentz[d]]; + Pair[Momentum[g, dimSelectLorentz[d]],li] Pair[li, Momentum[p,dimSelectLorentz[e]] ]), + + Pair[Momentum[g_,d_:4], Momentum[p_, d_:4]]/;!FreeQ[g,qMark] && !FreeQ[p,qMark] :> + ( li = LorentzIndex[$AL[Unique[]],dimSelectLorentz[d]]; + li2 = LorentzIndex[$AL[Unique[]],dimSelectLorentz[d]]; + Pair[li, li2] Pair[Momentum[g, dimSelectLorentz[d]],li] Pair[li2, Momentum[p,dimSelectLorentz[d]]]) + + }]; + + epsRules = Join[epsRules, + {Eps[a___, Momentum[g_,d_:4] ,b___]/;!FreeQ[g,qMark] :> + ( li = LorentzIndex[$AL[Unique[]],dimSelectLorentz[d]]; + Pair[Momentum[g, dimSelectLorentz[d]],li] Eps[a,li,b]) + }]; + + digaRules = Join[digaRules, + {DiracGamma[Momentum[g_,d_:4],d_:4]/;!FreeQ[g,qMark] :> + ( li = LorentzIndex[$AL[Unique[]],dimSelectLorentz[d]]; + Pair[Momentum[g, dimSelectLorentz[d]],li] DiracGamma[li,dimSelectLorentz[d]]) + }]; + + sigmaRules = Join[sigmaRules, + {PauliSigma[Momentum[g_,d_:4],e_:3]/;!FreeQ[g,qMark] :> + ( li = LorentzIndex[$AL[Unique[]],dimSelectLorentz[d]]; + Pair[Momentum[g, dimSelectLorentz[d]],li] PauliSigma[li,dimSelectCartesian[e]]) + }]; + + tensorRules = Join[tensorRules, + {(h_/;MemberQ[tensorList,h])[a___, Momentum[g_,d_:4] ,b___]/;!FreeQ[g,qMark] :> + ( li = LorentzIndex[$AL[Unique[]],dimSelectLorentz[d]]; + Pair[Momentum[g, dimSelectLorentz[d]],li] h[a,li,b]) + }]; + + ]; + + If[ cmomAllow, + + pairRules = Join[pairRules, {Pair[CartesianMomentum[g_,d_:3], LorentzIndex[p_, e_:4]]/;!FreeQ[g,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d]]; + CartesianPair[CartesianMomentum[g, dimSelectCartesian[d]],li] Pair[li, LorentzIndex[p,dimSelectLorentz[e]] ]) + }]; + + + cpairRules = Join[cpairRules, {CartesianPair[CartesianMomentum[g_,d_:3], CartesianMomentum[p_, d_:3]]/;!FreeQ[g,qMark] && FreeQ[p,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d]]; + CartesianPair[CartesianMomentum[g, dimSelectCartesian[d]],li] CartesianPair[li, CartesianMomentum[p,dimSelectCartesian[d]] ]), + + CartesianPair[CartesianMomentum[g_,d_:3], CartesianMomentum[p_, d_:3]]/;!FreeQ[g,qMark] && !FreeQ[p,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d]]; + li2 = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d]]; + CartesianPair[li,li2] CartesianPair[CartesianMomentum[g, dimSelectCartesian[d]],li] CartesianPair[li2, CartesianMomentum[p,dimSelectCartesian[d]] ]) + }]; + + epsRules = Join[epsRules,{Eps[a___, CartesianMomentum[g_,d_:3] ,b___]/;!FreeQ[g,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d]]; + CartesianPair[CartesianMomentum[g, dimSelectCartesian[d]],li]Eps[a,li,b]) + }]; + digaRules = Join[digaRules, + {DiracGamma[CartesianMomentum[g_]]/;!FreeQ[g,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[3]]; + CartesianPair[CartesianMomentum[g, dimSelectCartesian[3]],li] DiracGamma[li,dimSelectLorentz[4]]), + + + DiracGamma[CartesianMomentum[g_,d_Symbol-1],d_Symbol]/;!FreeQ[g,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d-1]]; + CartesianPair[CartesianMomentum[g, dimSelectCartesian[d-1]],li] DiracGamma[li,dimSelectLorentz[d]]), + + DiracGamma[CartesianMomentum[g_,d_Symbol-4],d_Symbol-4]/;!FreeQ[g,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d-4]]; + CartesianPair[CartesianMomentum[g, dimSelectCartesian[d-4]],li] DiracGamma[li,dimSelectLorentz[d-4]]) + }]; + + sigmaRules = Join[sigmaRules, {PauliSigma[CartesianMomentum[g_,d_:3],d_:3]/;!FreeQ[g,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d]]; + CartesianPair[CartesianMomentum[g, dimSelectCartesian[d]],li] PauliSigma[li, dimSelectCartesian[d]]) + }]; + + tensorRules = Join[tensorRules,{(h_/;MemberQ[tensorList,h])[a___, CartesianMomentum[g_,d_:3] ,b___]/;!FreeQ[g,qMark] :> + ( li = CartesianIndex[$AL[Unique[]],dimSelectCartesian[d]]; + CartesianPair[CartesianMomentum[g, dimSelectCartesian[d]],li]h[a,li,b]) + }]; + + + ]; + + If[ OptionValue[FCI], + exp = ex, + exp = FCI[ex] + ]; + + FCPrint[1, "Uncontract: Applying Expand2 and ExpandScalarProduct", FCDoControl->ucVerbose]; exp = Expand2[ExpandScalarProduct[exp,Momentum->{q}],q]; + FCPrint[1, "Uncontract: Done applying Expand2 and ExpandScalarProduct", FCDoControl->ucVerbose]; + FCPrint[3, "Uncontract: After Expand2 and ExpandScalarProduct: ", exp, FCDoControl->ucVerbose]; + + (* Select suitable Pairs *) + If[pairs=!={}, + FCPrint[1, "Uncontract: Uncontracting Pair objects.", FCDoControl->ucVerbose]; + (* now all q's are marked with qMark *) + exp = powerExpand[exp, q, Pair, times]; + + If[ !FreeQ2[exp,{nPower,sPower}], + Message[Uncontract::failmsg,"Cannot uncontract negative or symbolic powers of expressions."]; + Abort[] + ]; - If[ OptionValue[Unique] === True, - a$AL = Unique[$AL], - a$AL = $AL + allObjects = Cases[(exp + null1 + null2)/. _FeynAmpDenominator :> Unique[], _Pair, Infinity]//DeleteDuplicates//Sort; + Which[ pairs===All, + selectedObjects = allObjects, + Head[pairs]===List, + selectedObjects = SelectNotFree[SelectNotFree[allObjects, q], pairs], + True, + Message[Uncontract::failmsg,"Unknown Pair input"]; + Abort[] + ]; + selectedObjects = SelectFree[selectedObjects, OPEDelta]; + If[ !OptionValue[Polarization], + selectedObjects = SelectFree[selectedObjects, Polarization]; + ]; + (* do not uncontract momenta squared *) + If[ !OptionValue[Square], + selectedObjects = selectedObjects /. Pair[zx_, zy_]/; !FreeQ[zx,q] && !FreeQ[zy,q] :> Unevaluated[Sequence[]] + ]; + repRuleObjects = Thread[Rule[selectedObjects,(selectedObjects/.qRule)]]; + FCPrint[3, "Uncontract: List pairs objects that should be uncontracted: ", repRuleObjects, FCDoControl->ucVerbose]; + exp = exp /. repRuleObjects; + (* now qMark marks only Pairs that should be uncontracted *) + FCPrint[3, "Uncontract: Replacement rule for Pairs: ", pairRules , FCDoControl->ucVerbose]; + exp = exp //. pairRules /. qMark -> Identity; + FCPrint[3, "Uncontract: After applying the replacement rule for Pairs: ", exp , FCDoControl->ucVerbose] ]; - If[ par===All, - par = Map[First, SelectFree[Cases2[exp, Momentum], OPEDelta]] + (* Select suitable CartesianPairs *) + If[cpairs=!={}, + FCPrint[1, "Uncontract: Uncontracting CartesianPair objects.", FCDoControl->ucVerbose]; + exp = powerExpand[exp, q, CartesianPair, times]; + + If[ !FreeQ2[exp,{nPower,sPower}], + Message[Uncontract::failmsg,"Cannot uncontract negative or symbolic powers of expressions."]; + Abort[] + ]; + + allObjects = Cases[(exp + null1 + null2)/. _FeynAmpDenominator :> Unique[], _CartesianPair, Infinity]//DeleteDuplicates//Sort; + Which[ cpairs===All, + selectedObjects = allObjects, + Head[cpairs]===List, + selectedObjects = SelectNotFree[SelectNotFree[allObjects, q], cpairs], + True, + Message[Uncontract::failmsg,"Unknown CartesianPair input"]; + Abort[] + ]; + selectedObjects = SelectFree[selectedObjects, OPEDelta]; + If[ !OptionValue[Polarization], + selectedObjects = SelectFree[selectedObjects, Polarization]; + ]; + If[ !OptionValue[Square], + (* do not uncontract momenta squared *) + selectedObjects = selectedObjects /. CartesianPair[zx_, zy_]/; !FreeQ[zx,q] && !FreeQ[zy,q] :> Unevaluated[Sequence[]] + ]; + repRuleObjects = Thread[Rule[selectedObjects,(selectedObjects/.qRule)]]; + FCPrint[3, "Uncontract: List pairs objects that should be uncontracted: ", repRuleObjects, FCDoControl->ucVerbose]; + exp = exp /. repRuleObjects; + (* now qMark marks only CartesianPairs that should be uncontracted *) + FCPrint[3, "Uncontract: Replacement rule for CartesianPairs: ", cpairRules , FCDoControl->ucVerbose]; + exp = exp //. cpairRules /. qMark -> Identity; + FCPrint[3, "Uncontract: After applying the replacement rule for CartesianPairs: ", exp , FCDoControl->ucVerbose] ]; - If[ (par === {} && FreeQ2[exp, {Eps, DiracGamma}]) || (Head[dummy exp] =!= Times), - exp, + (* Select suitable DiracGammas *) + If[ !FreeQ[exp,DiracGamma] && OptionValue[DiracGamma], + FCPrint[1, "Uncontract: Uncontracting DiracGamma objects.", FCDoControl->ucVerbose]; + exp = powerExpand[exp, q, DiracGamma, dotTimes] /. qRule; - nex = exp; - If[ FreeQ[nex, a$AL], - inc = 0, - inc = (Max @@ Map[First, Cases2[nex, a$AL]]); + If[ !FreeQ2[exp,{nPower,sPower}], + Message[Uncontract::failmsg,"Cannot uncontract negative or symbolic powers of expressions."]; + Abort[] ]; + tmp = (exp + null1 + null2) /. _FeynAmpDenominator :> Unique[]; + allObjects = Cases[tmp /. _DiracChain :> Unique[], _DiracGamma, Infinity]//DeleteDuplicates//Sort; - If[ !FreeQ[nex,Eps], - nex = nex /. Eps -> eeps; - nex = nex /. eeps[aa__]^n_Integer?Positive :> - Apply[times, Table[eeps[aa], {j,Abs[n]}]]^Sign[n]; + If[ !FreeQ[exp,DiracChain], + allObjects = Join[allObjects, Cases[tmp, DiracChain[_,_,_], Infinity]//DeleteDuplicates//Sort]; + ]; - nex = nex //. {eeps[a___,Momentum[(c: q | Polarization[q,__]),d_:4],b___] :> - (li = LorentzIndex[a$AL[inc = inc+1], dimSelect[d]]; - Pair[Momentum[c, dimSelect[d]], li] eeps[a,lidr[li],b])} /. eeps -> Eps /. times -> Times; + selectedObjects = SelectNotFree[allObjects, q]; + If[ !OptionValue[Polarization], + selectedObjects = SelectFree[selectedObjects, Polarization]; ]; - If[ !FreeQ[nex, DiracGamma], - (* The momentum that we want to uncontract might be inside a slash like GS[a+b+c]! *) - nex = nex /. DiracGamma[xxx_, dd_:4]/;!FreeQ2[xxx,{q}] :> DiracGammaExpand[DiracGamma[xxx,dd]]; - nex = nex /. DiracGamma -> dirg; + repRuleObjects = Thread[Rule[selectedObjects,(DiracGammaExpand[selectedObjects,FCI->True,Momentum->{q}]/.qRule)]]; + FCPrint[3, "Uncontract: List DiracGamma objects that should be uncontracted: ", repRuleObjects, FCDoControl->ucVerbose]; + exp = exp /. repRuleObjects; + (* now qMark marks only DiracGammas that should be uncontracted *) + FCPrint[3, "Uncontract: Replacement rule for DiracGamma: ", digaRules , FCDoControl->ucVerbose]; + exp = exp //. digaRules /. qMark -> Identity; + FCPrint[3, "Uncontract: After applying the replacement rule for DiracGamma: ", exp , FCDoControl->ucVerbose] + ]; - nex = nex //. dirg[Momentum[(c: q | Polarization[q,__]),d_:4],___] :> - (li = LorentzIndex[a$AL[inc = inc+1],dimSelect[d]]; - Pair[Momentum[c,dimSelect[d]], li] dirg[lidr[li],dimSelect[d]]) /. dirg -> DiracGamma; + (* Select suitable PaulSigmas *) + If[ !FreeQ[exp,PauliSigma] && OptionValue[PauliSigma], + FCPrint[1, "Uncontract: Uncontracting PauliSigma objects.", FCDoControl->ucVerbose]; + exp = powerExpand[exp, q, PauliSigma, dotTimes] /. qRule; - nex = DotSimplify[nex,Expanding -> False]; + If[ !FreeQ2[exp,{nPower,sPower}], + Message[Uncontract::failmsg,"Cannot uncontract negative or symbolic powers of expressions."]; + Abort[] ]; - If[ par=!={} && Length[par]>0 && Head[par]===List, - (*Uncontract denominators also. Change by F.Orellana. 3/11-2002*) - (*Reverted, RM 06/22-2011 *) + allObjects = Cases[(exp + null1 + null2)/. _FeynAmpDenominator :> Unique[], _PauliSigma, Infinity]//DeleteDuplicates//Sort; + selectedObjects = SelectNotFree[allObjects, q]; + If[ !OptionValue[Polarization], + selectedObjects = SelectFree[selectedObjects, Polarization]; + ]; + repRuleObjects = Thread[Rule[selectedObjects,(PauliSigmaExpand[selectedObjects,FCI->True,Momentum->{q}]/.qRule)]]; + FCPrint[3, "Uncontract: List PauliSigma objects that should be uncontracted: ", repRuleObjects, FCDoControl->ucVerbose]; + exp = exp /. repRuleObjects; + (* now qMark marks only PauliSigmas that should be uncontracted *) + FCPrint[3, "Uncontract: Replacement rule for PauliSigma: ", sigmaRules , FCDoControl->ucVerbose]; + exp = exp //. sigmaRules /. qMark -> Identity; + FCPrint[3, "Uncontract: After applying the replacement rule for PauliSigma: ", exp , FCDoControl->ucVerbose] + ]; - nex = nex /. tf_[aa__/;!FreeQ2[{aa}, par]]^n_Integer?Positive/; (MemberQ[$FCTensorList,tf] && tf=!=Eps) :> - Apply[times, Table[tf[aa], {j,Abs[n]}]]^Sign[n]; + (* Select suitable Eps tensors *) + If[ !FreeQ[exp,Eps] && OptionValue[Eps], + FCPrint[1, "Uncontract: Uncontracting Eps objects.", FCDoControl->ucVerbose]; + exp = EpsEvaluate[exp,FCI->True,Momentum->{q}]; + exp = powerExpand[exp, q, Eps, times] /. qRule; - If[ MemberQ[par, q], - nex = nex //. Pair[Momentum[(c1: q | Polarization[q,__]),d_:4], Momentum[(c2: q | Polarization[q,__]),d_:4]] :> - (li1 = LorentzIndex[a$AL[inc = inc+1], dimSelect[d]]; - li2 = LorentzIndex[a$AL[inc = inc+1], dimSelect[d]]; - Pair[Momentum[c1, dimSelect[d]], li1] Pair[Momentum[c2, dimSelect[d]], li2] Pair[li1, li2]); - par = SelectFree[par, q]; - ]; - nex = nex //.{Pair[Momentum[(c: q | Polarization[q,__]),d_:4], Momentum[pe_,___]] :> - (li = LorentzIndex[a$AL[inc = inc+1],dimSelect[d]]; - Pair[Momentum[c,dimSelect[d]], li] Pair[Momentum[pe,dimSelect[d]],lidr[li]])/;MemberQ[par,pe]} ; + If[ !FreeQ2[exp,{nPower,sPower}], + Message[Uncontract::failmsg,"Cannot uncontract negative or symbolic powers of expressions."]; + Abort[] + ]; - (* Uncontract tensor functions *) - If[ !FreeQ[nex, (tf_/;MemberQ[$FCTensorList,tf] && tf=!=Pair && tf=!=Eps)[___,Momentum[(q | Polarization[q,__]),___],___]], - nex = nex //. { (tf_/; MemberQ[$FCTensorList,tf] && tf=!=Pair && tf=!=Eps)[a___,Momentum[(c: q | Polarization[q,__]),d_:4],b___] :> - (li = LorentzIndex[a$AL[inc = inc+1],dimSelect[d]]; - tf[a, li, b] Pair[Momentum[c,dimSelect[d]],lidr[li]])} - ]; + allObjects = Cases[(exp + null1 + null2)/. _FeynAmpDenominator :> Unique[], _Eps, Infinity]//DeleteDuplicates//Sort; + selectedObjects = SelectNotFree[allObjects, q]; + If[ !OptionValue[Polarization], + selectedObjects = SelectFree[selectedObjects, Polarization]; + ]; + repRuleObjects = Thread[Rule[selectedObjects,(selectedObjects/.qRule)]]; + FCPrint[3, "Uncontract: List Eps objects that should be uncontracted: ", repRuleObjects, FCDoControl->ucVerbose]; + exp = exp /. repRuleObjects; + (* now qMark marks only Eps tensors that should be uncontracted *) + FCPrint[3, "Uncontract: Replacement rule for Eps tensors: ", epsRules , FCDoControl->ucVerbose]; + exp = exp //. epsRules /. qMark -> Identity; + FCPrint[3, "Uncontract: After applying the replacement rule for Eps tensors: ", exp , FCDoControl->ucVerbose] + ]; + (* Select possibly remaining tensors *) + If[ !FreeQ2[exp,tensorList] && tensoruncontract, + FCPrint[1, "Uncontract: Uncontracting tensors: ", tensorList , FCDoControl->ucVerbose]; + exp = Fold[powerExpand[#1, q, #2, times] &, exp, tensorList] /. qRule; + + If[ !FreeQ2[exp,{nPower,sPower}], + Message[Uncontract::failmsg,"Cannot uncontract negative or symbolic powers of expressions."]; + Abort[] + ]; + + allObjects = Cases[(exp + null1 + null2)/. _FeynAmpDenominator :> Unique[], alternativesTensorList , Infinity]//DeleteDuplicates//Sort; + selectedObjects = SelectNotFree[allObjects, q]; + If[ !OptionValue[Polarization], + selectedObjects = SelectFree[selectedObjects, Polarization]; ]; - nex/. times -> Times/.dummy->1/.seq:>Sequence + + repRuleObjects = Thread[Rule[selectedObjects,(selectedObjects/.qRule)]]; + FCPrint[3, "Uncontract: List of other tensors that should be uncontracted: ", repRuleObjects, FCDoControl->ucVerbose]; + exp = exp /. repRuleObjects; + (* now qMark marks only Eps tensors that should be uncontracted *) + FCPrint[3, "Uncontract: Replacement rule for other tensors: ", tensorRules , FCDoControl->ucVerbose]; + exp = exp //. tensorRules /. qMark -> Identity; + FCPrint[3, "Uncontract: After applying the replacement rule for other tensors: ", exp , FCDoControl->ucVerbose] + ]; + res = exp /. times -> Times /. dotTimes -> DOT; + + If[ OptionValue[DiracChainExpand] && !FreeQ[res,DiracChain], + res = DiracChainExpand[res,FCI->True,Momentum->{q}] + ]; + + FCPrint[1, "Uncontract: Intermediate result: " ,res, FCDoControl->ucVerbose]; + + If[ OptionValue[DotSimplify] && !FreeQ2[res,{DiracGamma,PauliSigma}], + res = DotSimplify[res,Expanding -> False, FCI->True]; + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]/; q=!=All; + +powerExpand[ex_, q_, head_, times_]:= + ( + ex /. { + Power[Pattern[z,Blank[head]], n_Integer?Positive]/;!FreeQ[z,q] :> + Apply[times, Table[z, {Abs[n]}]]^Sign[n], + Power[Pattern[z,Blank[head]], n_Integer?Negative]/;!FreeQ[z,q] :> + nPower[z,n], + Power[Pattern[z,Blank[head]], n_Symbol]/;!FreeQ[z,q] :> + sPower[z,n] + } + )/; !FreeQ[ex,Power]; + +powerExpand[ex_, _, _, _]:= + ex/; FreeQ[ex,Power]; + +dimSelectCartesian[z_]:= + If[ dim===Automatic, + z, + Switch[ + dim, + 4, + 3, + _Symbol, + dim - 1, + _Symbol - 4, + dim, + _, + Message[Uncontract::failmsg, "Unsupported dimension!"]; + Abort[] ] ]; +dimSelectLorentz[z_]:= + If[ dim===Automatic, + z, + dim + ]; + FCPrint[1,"Uncontract.m loaded."]; End[] diff --git a/FeynCalc/NonCommAlgebra/Calc.m b/FeynCalc/NonCommAlgebra/Calc.m index 55d453d87..44c7b8386 100755 --- a/FeynCalc/NonCommAlgebra/Calc.m +++ b/FeynCalc/NonCommAlgebra/Calc.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: A lot of simplifications in one command *) @@ -34,6 +34,7 @@ Calc[expr_, OptionsPattern[]] := Block[{calc,assumpts,usePowerExpand}, + assumpts = OptionValue[Assumptions]; usePowerExpand = OptionValue[PowerExpand]; calc[exp_]:= diff --git a/FeynCalc/NonCommAlgebra/DotExpand.m b/FeynCalc/NonCommAlgebra/DotExpand.m index 583352787..07789cf52 100644 --- a/FeynCalc/NonCommAlgebra/DotExpand.m +++ b/FeynCalc/NonCommAlgebra/DotExpand.m @@ -14,7 +14,7 @@ DotExpand::usage = -"DotExpand[expr] expands DOT products in expr."; +"DotExpand[exp] expands dot products in exp."; (* ------------------------------------------------------------------------ *) diff --git a/FeynCalc/NonCommAlgebra/DotSimplify.m b/FeynCalc/NonCommAlgebra/DotSimplify.m index 0e625b91b..2c42cae20 100755 --- a/FeynCalc/NonCommAlgebra/DotSimplify.m +++ b/FeynCalc/NonCommAlgebra/DotSimplify.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Simplifies non-commututative products *) @@ -16,7 +16,7 @@ (* ------------------------------------------------------------------------ *) DotSimplify::usage = -"DotSimplify[expr] expands and reorders noncommutative terms in expr. \ +"DotSimplify[expr] expands and reorders noncommutative terms in expr. \n Simplifying relations may be specified by the option \ DotSimplifyRelations or by Commutator and AntiCommutator definitions. \ Whether expr is expanded noncommutatively depends @@ -42,6 +42,10 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ chains of Dirac matrices will not be expanded."; +DotSimplify::failmsg = +"Error! DotSimplify has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -67,59 +71,78 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ Abort[]); Options[DotSimplify] = { - Expanding -> True, - FCVerbose -> False, - DotSimplifyRelations -> {}, - DotPower -> False, (*True*)(*CHANGE 26/9-2002. To have this work: FermionSpinSum[ComplexConjugate[Spinor[p,m].Spinor[p,m]]]. - F.Orellana*) - FeynCalcInternal -> True, - PreservePropagatorStructures -> False + DotPower -> False, (*True*)(*CHANGE 26/9-2002. To have this work: FermionSpinSum[ComplexConjugate[Spinor[p,m].Spinor[p,m]]]. F.Orellana*) + DotSimplifyRelations -> {}, + Expanding -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCVerbose -> False, + MaxIterations -> 100, + PreservePropagatorStructures -> False }; -DotSimplify[xxx_, OptionsPattern[]] := +DotSimplify[expr_, OptionsPattern[]] := Block[ {pid, ne, dlin,dlin0, x, DOTcomm, cru, aru, commm, acommm, acom, cdoot, sdoot,simpf, actorules, cotorules, acomall, comall, simrel,tic, dodot,holdDOT - ,vars,xxX,yyY,condition,sameQ,orderedQ,hold, xx, sunTrace, - holdDOTColor, holdDOTDirac, nvar + ,vars,xxX,yyY,condition,sameQ,orderedQ,hold, ex, sunTrace, tmpDOT, + holdDOTColor, holdDOTDirac, holdDOTPauli, holdDOTRest1, holdDOTRest2, holdDOTRest3, + nvar, time, time0, maxIterations, dlin1, momList, momListEval, momRule }, If [OptionValue[FCVerbose]===False, dsVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], dsVerbose=OptionValue[FCVerbose] ]; ]; simrel = OptionValue[DotSimplifyRelations]; + maxIterations = OptionValue[MaxIterations]; FCPrint[1, "DotSimplify: Entering.", FCDoControl->dsVerbose]; - If[ FreeQ[xxx,DOT] && NonCommFreeQ[xxx], - Return[xxx] + If[ FreeQ[expr,DOT] && NonCommFreeQ[expr], + Return[expr] ]; - (* Here a different convention for FCI is used, False means that FCI is needed*) - If[ OptionValue[FCI] =!= True, - xx = xxx, - xx = FCI[xxx]; + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] ]; FCPrint[3, "DotSimplify: Entering with", FCDoControl->dsVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "DotSimplify: Applying FactorTerms to the arguments of momenta.", FCDoControl->dsVerbose]; + If[ !FreeQ[ex, Momentum], + momList = Cases2[ex, Momentum]; + momListEval = momList /. Momentum[a_, dim___] :> Momentum[FactorTerms[a], dim]; + momRule = Thread[Rule[momList,momListEval]]; + ex = ex /. Dispatch[momRule] + ]; + If[ !FreeQ[ex, CartesianMomentum], + momList = Cases2[ex, CartesianMomentum]; + momListEval = momList /. CartesianMomentum[a_, dim___] :> CartesianMomentum[FactorTerms[a], dim]; + momRule = Thread[Rule[momList,momListEval]]; + ex = ex /. Dispatch[momRule] + ]; - (* this speeds things up, however, I'd really like to get rid of it ..., RM*) - momf[xX_] := - momf[xX] = Momentum[FactorTerms[xX]]; - - xx = xx /. Momentum[p_] :> momf[p] /. simrel; - + If[ !FreeQ[ex, TemporalMomentum], + momList = Cases2[ex, TemporalMomentum]; + momListEval = momList /. TemporalMomentum[a_, dim___] :> TemporalMomentum[FactorTerms[a], dim]; + momRule = Thread[Rule[momList,momListEval]]; + ex = ex /. Dispatch[momRule] + ]; + FCPrint[1, "DotSimplify: Done applying FactorTerms, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + time0=AbsoluteTime[]; FCPrint[1, "DotSimplify: Entering the main loop.", FCDoControl->dsVerbose]; x = Catch[ - + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Applying DotSimplifyRelations.", FCDoControl->dsVerbose]; If[ simrel =!= {}, (* If there are any supplied DotSimplifyRelations relations, we need to apply them*) @@ -133,38 +156,27 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ sru[aa :> bb]; simrel = Map[sru, simrel]; ]; + FCPrint[1, "DotSimplify: Done applying DotSimplifyRelations, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3, "DotSimplify: After DotSimplifyRelations: ", ex, FCDoControl->dsVerbose]; + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Writing out commutators and anticommutators.", FCDoControl->dsVerbose]; (*If the expression contains commutators or anticommutators, write them out explicitly, i.e. [a,b] -> ab-ba etc.*) - If[ (!FreeQ[xx, Commutator]) || (!FreeQ[xx, AntiCommutator]), - x = CommutatorExplicit[xx], - x = xx - ]; - - (* CHANGE 07/26/94 *) - - (*If the expression contains SU(N) matrices, put Dot on hold*) - If[ !FreeQ[x, SUNT], - FCPrint[1, "DotSimplify: Putting Dot on hold.", FCDoControl->dsVerbose]; - SetAttributes[TimesDot, HoldAll]; - TimesDot[a__] := - If[ FreeQ[{a}, SUNT], - Times[a], - DOT[a] - ]; - x = x /. Times -> TimesDot; - FCPrint[1, "DotSimplify: After Putting Dot on hold: ", x, FCDoControl->dsVerbose] + If[ (!FreeQ[ex, Commutator]) || (!FreeQ[ex, AntiCommutator]), + x = CommutatorExplicit[ex], + x = ex ]; + FCPrint[1, "DotSimplify: Done writing out commutators and anticommutators, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; - + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Writing out non-commutative objects explicitly.", FCDoControl->dsVerbose]; (*If the expression contains powers of non-commutative objects, write them out explicitly, i.e. a.(b^4).c -> a.b.b.b.b.c *) (* maybe this is somewhat slow; use FORM then ... *) If[ !FreeQ[x, (a_/;NonCommQ[a])^n_Integer?Positive], x = x /. {(a_/;NonCommQ[a])^n_Integer?Positive :> DOT @@ Table[a, {n}]}; ]; - - FCPrint[3, "DotSimplify: After writing out non-commutuative objects ",x, FCDoControl->dsVerbose]; + FCPrint[1, "DotSimplify: Done writing out non-commutative objects explicitly, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3, "DotSimplify: After writing out non-commutuative objects: ",x, FCDoControl->dsVerbose]; (* check special case *) @@ -173,27 +185,29 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ If this is so, and there no commutators or anticommuators inside, expand the expression and return it *) + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Working out user-defined non-commutative objects.", FCDoControl->dsVerbose]; If[ simrel === {}, - vars = Union[Variables[Cases[xx - //. DOT[a___, n_?NumberQ o1_. + o2_:0, b___] :> DOT[a, o1 nvar[n]+o2, b], _, Infinity] ]]; + vars = Union[Variables[Cases[Cases2[ex,DOT] //. DOT[a___, n_?NumberQ o1_. + o2_:0, b___] :> DOT[a, o1 nvar[n]+o2, b], _, Infinity] ]]; If[ Union[Map[DataType[#, NonCommutative]&, vars]] === {True}, If[ FreeQ2[{DownValues[Commutator], DownValues[AntiCommutator]},vars], - (* that means : just expansion, no acomms, comms *) - x = Distribute[x /. DOT -> doot] //. - doot[a___, n_?NumberQ b_, c___] :> (n doot[a, b, c]); + (* that means : just expansion, no acomms, comms *) + x = Distribute[x /. DOT -> doot] //. doot[a___, n_?NumberQ b_, c___] :> (n doot[a, b, c]); Throw[x /. doot -> dootpow] ] ] ]; + FCPrint[1, "DotSimplify: Done working out user-defined non-commutative objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; - FCPrint[3, "DotSimplify: After checking simrel", x, FCDoControl->dsVerbose]; + FCPrint[3, "DotSimplify: After checking simrel: ", x, FCDoControl->dsVerbose]; If[ OptionValue[PreservePropagatorStructures], + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Preserving propagator structures.", FCDoControl->dsVerbose]; x = x /. SUNTrace ->sunTrace //. DOT->holdDOT //. holdDOT[a___, ee_. (c_ + d_DiracGamma), b___] /;FreeQ2[{c},{DiracGamma,holdDOT}] :> holdDOT[a, ee dotsimpHold[c + d], b] //. holdDOT->DOT /. sunTrace -> SUNTrace; + FCPrint[3, "DotSimplify: Done preserving propagator structures, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; FCPrint[3, "DotSimplify: After preserving propagator structures: ", x, FCDoControl->dsVerbose]; ]; @@ -233,23 +247,23 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ cotorules[{}] = {}; cotorules[a__List] := - (cotorules[a] = + ( + cotorules[a] = Select[Map[cru, a /. (h:LeftPartialD|RightPartialD|FCPartialD|LeftRightPartialD|LeftRightPartialD2) -> hold[h] /. Commutator -> commm /. HoldPattern :> Identity /. RuleDelayed -> List ], FreeQ[#, cru]&] - - - )/; - a=!={}; + )/; a=!={}; actorules[{}] = {}; actorules[a__List] := - (actorules[a] = Select[Map[aru, a /. (h:LeftPartialD|RightPartialD|FCPartialD|LeftRightPartialD|LeftRightPartialD2) -> hold[h] - /. AntiCommutator -> acommm /. HoldPattern :> Identity /. RuleDelayed -> List], FreeQ[#, aru]&])/; - a=!={}; + ( + actorules[a] = Select[Map[aru, a /. (h:LeftPartialD|RightPartialD|FCPartialD|LeftRightPartialD|LeftRightPartialD2) -> hold[h] + /. AntiCommutator -> acommm /. HoldPattern :> Identity /. RuleDelayed -> List], FreeQ[#, aru]&] + )/; a=!={}; comall[ yy__ ] := yy //. (Flatten[cotorules[DownValues@@{Commutator}]] //. hold[h_]:> h); + acomall[ yy__ ] := yy //. (Flatten[actorules[DownValues@@{AntiCommutator}]] //. hold[h_]:> h); @@ -259,14 +273,14 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ *) Off[Rule::rhs]; - + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Working out commutators and anti-commutators.", FCDoControl->dsVerbose]; If[ simrel === {}, DOTcomm[xy__] := - FixedPoint[acomall, FixedPoint[comall, DOT[xy], 242], 242], + FixedPoint[acomall, FixedPoint[comall, DOT[xy], maxIterations], maxIterations], DOTcomm[xy__] := - FixedPoint[acomall, FixedPoint[comall, DOT[xy]//.simrel, 242] //. simrel, 242] //. simrel + FixedPoint[acomall, FixedPoint[comall, DOT[xy]//.simrel, maxIterations] //. simrel, maxIterations] //. simrel ]; (* Expand sums, if needed *) @@ -274,12 +288,20 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ dlin0[a___] := (Distribute[dlin[a]] //. dlin[h___, n_Integer c_, b___] :> (n dlin[h, c, b])); ]; - + FCPrint[1, "DotSimplify: Done working out commutators and anti-commutators, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; FCPrint[3, "DotSimplify: After working out commutators and anti-commutators:", x, FCDoControl->dsVerbose]; + If[ OptionValue[FCJoinDOTs] && !OptionValue[Expanding], + time=AbsoluteTime[]; + FCPrint[1, "DotSimplify: Joining DOTs.", FCDoControl->dsVerbose]; + x = x/.DOT-> holdDOT //. {holdDOT[a___, b1_, c___] + holdDOT[a___, b2_, c___] :> holdDOT[a, b1 + b2, c]}; + x = x /. holdDOT->DOT; + FCPrint[1, "DotSimplify: Done joining DOTs, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3, "DotSimplify: After joining DOTs: ", x, FCDoControl->dsVerbose] + ]; - - FCPrint[1, "DotSimplify: Non-commutative expansion. Time used:", TimeUsed[], FCDoControl->dsVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "DotSimplify: Doing non-commutative expansions.", FCDoControl->dsVerbose]; dlin[] = 1; dlin1[{ok___}, b_/;DataType[b, NonCommutative], c___] := @@ -291,62 +313,105 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ dlin1[{ok___},b_, c___] := If[ NonCommFreeQ[b] === True && FreeQ[b, dlin1], b dlin1[{ok}, c], + If[ Head[b] === Times, If[ Select[b, NonCommFreeQ[#]&] =!= 1, - Select[b, NonCommFreeQ[#]&]* - dlin1[{ok, Select[b, - !NonCommFreeQ[#]&]}, c], - dlin1[{ok},b[[1]]] * - dlin1[{},Rest[b],c] + Select[b, NonCommFreeQ[#]&] dlin1[{ok, Select[b, !NonCommFreeQ[#]&]}, c], + (*The head is Times, and there are only noncommutative objects inside *) + (*dlin1[{ok},b[[1]]] dlin1[{},Rest[b],c]*) + (* If there is a Times between noncommutative objects with the same head, there clearly must be + something wrong; TODO: head2 instead of Head to map all relevant Dirac heads to the same name. *) + If[ Intersection[(Head/@Cases2[b[[1]],$NonComm]),(Head/@Cases2[Rest[b],$NonComm])]=!={}, + Message[DotSimplify::failmsg,"Detected commutative multiplication of noncommutative objects."]; + Abort[] + ]; + + dlin1[{ok},b[[1]],Rest[b],c] ], dlin1[{ok,b},c] ] ]; + (* Evaluate all the commutators and anticommutators*) x = x/. SUNTrace -> sunTrace; - If[ FreeQ[Attributes @@ {DOT}, Flat], - x = FixedPoint[(# /. DOT -> dlin0/. dlin0 -> dlin //. - dlin[a__] :> dlin1[{}, a] //. dlin1[{ookk___}] :> DOT[ookk] //. - DOT[aa___, DOT[b__], c___] :> DOT[aa, b, c] /. DOT -> DOTcomm)&, x, 123] /. dlin -> DOT, - - simpf[y_] := - MemSet[simpf[y], - (y /. DOT -> dlin0 /. dlin0 -> dlin //. dlin[a__] :> dlin1[{}, a] //. - dlin1[{ookk___}] :> DOT[ookk] /. DOT -> DOTcomm) /. dlin -> DOT]; - x = FixedPoint[simpf, x, 123]; + + (* Sort out some trivial DOTs right away *) + x = x /. DOT -> tmpDOT /. tmpDOT[a__]/; FreeQ[{a},tmpDOT] && MatchQ[{a},{__DiracGamma}] :> holdDOT[a] /. tmpDOT->DOT; + FCPrint[3, "DotSimplify: After sorting out trivial DOTs: ", x, FCDoControl->dsVerbose]; + + simpf[y_] := + (y /. DOT -> dlin0 /. dlin0 -> dlin //. dlin[a__] :> dlin1[{}, a] //. dlin1[{a___}] :> DOT[a] /. DOT -> DOTcomm) /. dlin -> DOT; + x = FixedPoint[simpf, x, maxIterations]; + + FCPrint[4, "DotSimplify: After simpf:", x, FCDoControl->dsVerbose]; + + If[ !FreeQ[x, DiracChain], + time=AbsoluteTime[]; + FCPrint[1, "DotSimplify: Applying DiracChainFactor.", FCDoControl->dsVerbose]; + x = DiracChainFactor[x, FCI->True]; + FCPrint[1, "DotSimplify: DiracChainFactor done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3, "DotSimplify: After DiracChainFactor: ", x, FCDoControl->dsVerbose] ]; - x = x/. sunTrace -> SUNTrace; + + x = x/. sunTrace -> SUNTrace /. holdDOT -> DOT; + + FCPrint[1, "DotSimplify: Non-commutative expansions done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; FCPrint[3, "DotSimplify: After doing non-commutative expansion:", x, FCDoControl->dsVerbose]; x ]; + FCPrint[1, "DotSimplify: Leaving the main loop, timing: ", N[AbsoluteTime[] - time0, 4], FCDoControl->dsVerbose]; FCPrint[2, "DotSimplify: After catch", x, FCDoControl->dsVerbose]; (*Pull out nested SU(N) and Dirac traces*) If[ !FreeQ2[x, {SUNTrace,DiracTrace}], + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Pulling out nested SU(N) and Dirac traces. ", FCDoControl->dsVerbose]; x = x //. { DOT[a___,(b: DiracTrace | SUNTrace)[arg__],c___] :> (b[arg] DOT[a,c]) , - (tr1: DiracTrace|SUNTrace)[(tr2 : DiracTrace|SUNTrace)[arg__] a_] :> tr2[arg] tr1[a] + (tr1: DiracTrace|SUNTrace)[(tr2 : DiracTrace|SUNTrace)[arg__] a_] :> tr2[arg] tr1[a], + + (tr1: DiracTrace|SUNTrace)[a_. b_/;!FreeQ2[b,{DiracTrace,SUNTrace}]]/; + NonCommFreeQ[b/.(DiracTrace|SUNTrace)[___]:>1] :> b tr1[a] + }; + + FCPrint[1, "DotSimplify: Done pulling out nested SU(N) and Dirac traces, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; FCPrint[3, "DotSimplify: After pulling out nested SU(N) and Dirac traces.", x, FCDoControl->dsVerbose]; ]; - (* Dirac and SU(N) matrices commute with each other, so they need to be properly separated*) - If[ !FreeQ[x, SUNT], + (* Dirac, Pauli and SU(N) matrices commute with each other, so they need to be properly separated*) + If[ !FreeQ2[x, {SUNT,PauliSigma,PauliEta,PauliXi}], + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Pulling out SU(N) matrices", FCDoControl->dsVerbose]; x = x /. DOT->holdDOT; - x = x //. holdDOT[zzz__] :> (holdDOTColor@@Select[{zzz}, (Head[#] === SUNT) &])(holdDOTDirac@@Select[{zzz}, (Head[#] =!= SUNT) &]); - (* SUNT's in a DiracTrace are pulled out but NOT summed over *) - x = x //. DiracTrace[f_ g_holdDOTColor ] :> g DiracTrace[f]/. (holdDOTColor|holdDOTDirac)[] -> 1 /. holdDOTColor|holdDOTDirac -> DOT; - FCPrint[3, "DotSimplify: After pulling out SU(N) matrices: ", x, FCDoControl->dsVerbose] + (* Notice that here we are checking heads, so this will not break a possibly complicated nested structure *) + + x = x //. holdDOT[zzz__] :> (holdDOTColor@@Select[{zzz}, (Head[#] === SUNT) &])(holdDOTRest1@@Select[{zzz}, (Head[#] =!= SUNT) &]); + FCPrint[1, "DotSimplify: Pulling out Dirac matrices", FCDoControl->dsVerbose]; + + x = x //. holdDOTRest1[zzz__] :> (holdDOTDirac@@Select[{zzz}, !FreeQ2[{#},{DiracGamma,Spinor}]& ])* + (holdDOTRest2@@Select[{zzz}, FreeQ2[{#},{DiracGamma,Spinor}]& ]); + FCPrint[1, "DotSimplify: Pulling out Pauli matrices", FCDoControl->dsVerbose]; + + x = x //. holdDOTRest2[zzz__] :> (holdDOTPauli@@Select[{zzz}, !FreeQ2[{#},{PauliSigma,PauliEta,PauliXi}]& ])* + (holdDOTRest3@@Select[{zzz}, FreeQ2[{#},{PauliSigma,PauliEta,PauliXi}]&]); + + (* SUNT's and PauliSigma's in a DiracTrace are pulled out but NOT summed over *) + x = x //. DiracTrace[f_ g :(_holdDOTColor | _holdDOTPauli ) ] :> g DiracTrace[f]/. + (holdDOTColor|holdDOTDirac|holdDOTPauli|holdDOTRest1|holdDOTRest2|holdDOTRest3)[] -> 1 /. + holdDOTColor|holdDOTDirac|holdDOTPauli|holdDOTRest1|holdDOTRest2|holdDOTRest3 -> DOT; + FCPrint[1, "DotSimplify: Done pulling out all matrices, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; + FCPrint[3, "DotSimplify: After pulling out all matrices: ", x, FCDoControl->dsVerbose] ]; (* if the expression contains a QuantumField, factor it out*) If[ !FreeQ[x, QuantumField], + time=AbsoluteTime[]; FCPrint[1, "DotSimplify: Factoring out QuantumField's", FCDoControl->dsVerbose]; x = x /. DOT->dodot //. {dodot[a___,b_/;Head[b] =!= SUNT, c__SUNT,d___] :> dodot[a,c,b,d]} /. dodot->DOT; x = x /. DOT[a__SUNT, b__QuantumField] :> (DOT[a]*DOT[b]); + FCPrint[1, "DotSimplify: Done factoring out QuantumField's, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->dsVerbose]; FCPrint[3, "DotSimplify: After factoring out QuantumFields", x, FCDoControl->dsVerbose] ]; @@ -365,11 +430,16 @@ numerators of fermionic propagators like (GS[p]+m) that appear in \ FCPrint[1, "DotSimplify: Leaving.", FCDoControl->dsVerbose]; FCPrint[3, "DotSimplify: Leaving with: ", x, FCDoControl->dsVerbose]; + + If[ OptionValue[FCE], + x = FCE[x] + ]; + x ]; dootpow[a__] := - If[ FreeQ2[{a}, {DiracGamma,SUNT}], + If[ FreeQ2[{a}, {DiracGamma,SUNT,Spinor}], Apply[DOT, (#[[1]]^Length[#])& /@ Split[{a}]], DOT[a] ]; diff --git a/FeynCalc/NonCommAlgebra/FCMatrixIsolate.m b/FeynCalc/NonCommAlgebra/FCMatrixIsolate.m new file mode 100755 index 000000000..ce0af4e7a --- /dev/null +++ b/FeynCalc/NonCommAlgebra/FCMatrixIsolate.m @@ -0,0 +1,170 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCMatrixIsolate *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Isolates matrix objects *) + +(* ------------------------------------------------------------------------ *) + +FCMatrixIsolate::usage = +"FCMatrixIsolate[exp] wraps the occurring Dirac, Pauli and color objects into heads \ +specified by the user."; + +FCMatrixIsolate::failmsg = +"Error! FCMatrixIsolate has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; + +Begin["`Package`"] +End[] + +Begin["`FCMatrixIsolate`Private`"] +relevantPart::usage=""; + +diracHead::usage=""; +pauliHead::usage=""; +sunHead::usage=""; + +optsDirac::usage=""; +optsPauli::usage=""; +optsSUN::usage=""; + +fcmiVerbose::usage=""; + +Options[FCMatrixIsolate] = { + Collecting -> True, + FCColorIsolate -> {FCGV["ColorObject"], {FCI->True, Expanding->False}}, + FCDiracIsolate -> {FCGV["DiracObject"], {FCI->True, DiracChain->True, Expanding->False, FCJoinDOTs->False}}, + FCE -> False, + FCI -> False, + FCPauliIsolate -> {FCGV["PauliObject"], {FCI->True, Expanding->False, FCJoinDOTs->False}}, + FCVerbose -> False, + Factoring -> Factor, + Head -> Identity, + Ordering -> {FCDiracIsolate,FCColorIsolate,FCPauliIsolate}, + TimeConstrained -> 3 +}; + +FCMatrixIsolate[expr_List, opts:OptionsPattern[]]:= + FCMatrixIsolate[#, opts]&/@expr + +FCMatrixIsolate[expr_/;Head[expr]=!=List, OptionsPattern[]] := + Block[{ res, ex, optHead, optOrdering, time, + optFCDiracIsolate, optFCPauliIsolate, optFCColorIsolate + }, + + optHead = OptionValue[Head]; + optOrdering = OptionValue[Ordering]; + optFCDiracIsolate = OptionValue[FCDiracIsolate]; + optFCPauliIsolate = OptionValue[FCPauliIsolate]; + optFCColorIsolate = OptionValue[FCColorIsolate]; + + If [OptionValue[FCVerbose]===False, + fcmiVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fcmiVerbose=OptionValue[FCVerbose] + ]; + ]; + + If[ !MatchQ[optOrdering,{__}] || !FCSubsetQ[{FCDiracIsolate,FCColorIsolate,FCPauliIsolate},Union[optOrdering]], + Message[FCMatrixIsolate::failmsg, "The value of the Ordering option is incorrect."]; + Abort[] + ]; + + If[ Head[optFCDiracIsolate]=!=List || Head[optFCPauliIsolate]=!=List || Head[optFCColorIsolate]=!=List, + Message[FCMatrixIsolate::failmsg, "The option values of the isolating function must be given as lists."]; + Abort[] + ]; + + If[OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + FCPrint[1,"FCMatrixIsolate: Entering.", FCDoControl->fcmiVerbose]; + FCPrint[3,"FCMatrixIsolate: Entering with: ", expr, FCDoControl->fcmiVerbose]; + + + diracHead = optFCDiracIsolate[[1]]; + pauliHead = optFCPauliIsolate[[1]]; + sunHead = optFCColorIsolate[[1]]; + + + If[ Length[optFCDiracIsolate]===1, + optsDirac = FilterRules[Options[FCMatrixIsolate], FCDiracIsolate][[1]][[2]][[2]], + optsDirac = FilterRules[optFCDiracIsolate[[2]], Except[Head]] + ]; + + If[ Length[optFCPauliIsolate]===1, + optsPauli = FilterRules[Options[FCMatrixIsolate], FCPauliIsolate][[1]][[2]][[2]], + optsPauli = FilterRules[optFCPauliIsolate[[2]], Except[Head]] + ]; + + If[ Length[optFCColorIsolate]===1, + optsSUN = FilterRules[Options[FCMatrixIsolate], FCColorIsolate][[1]][[2]][[2]], + optsSUN = FilterRules[optFCColorIsolate[[2]], Except[Head]] + ]; + + FCPrint[1,"FCMatrixIsolate: Ordering of isolations:", optOrdering, FCDoControl->fcmiVerbose]; + optOrdering = optOrdering /. {FCDiracIsolate -> isolateDirac, FCPauliIsolate -> isolatePauli, FCColorIsolate -> isolateSUN}; + + ex = relevantPart[ex]; + + time=AbsoluteTime[]; + FCPrint[1, "FCMatrixIsolate: Applying isolating functions.", FCDoControl->fcmiVerbose]; + ex = Fold[#2[#1] &, ex, optOrdering]; + FCPrint[1, "FCMatrixIsolate: Done applying isolating functions, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcmiVerbose]; + FCPrint[3, "FCMatrixIsolate: After applying isolating functions:", ex, FCDoControl->fcmiVerbose]; + + res = ex /. relevantPart-> OptionValue[Head]; + + If[ OptionValue[Collecting], + ex = Collect2[ex,{diracHead,pauliHead,sunHead},Factoring->OptionValue[Factoring],TimeConstrained->OptionValue[TimeConstrained]]; + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + ]; + +isolateDirac[x_]:= + isolateMatrices[x, {FCDiracIsolate, FeynCalc`Package`DiracHeadsList, {diracHead,relevantPart}, optsDirac}]; + +isolatePauli[x_]:= + isolateMatrices[x, {FCPauliIsolate, FeynCalc`Package`PauliHeadsList, {pauliHead,relevantPart}, optsPauli}]; + +isolateSUN[x_]:= + isolateMatrices[x, {FCColorIsolate, FeynCalc`Package`SUNHeadsList, {sunHead,relevantPart}, optsSUN}]; + +isolateMatrices[x_, {fu_, checkHeads_List, isoHeads_, opts_}]:= + Block[{obj, objEval, repRule, time}, + obj = Cases2[x, relevantPart]; + FCPrint[1, "FCMatrixIsolate: isolateMatrices: Entering ", fu, FCDoControl->fcmiVerbose]; + FCPrint[3, "FCMatrixIsolate: isolateMatrices: Entering with", x, FCDoControl->fcmiVerbose]; + If[ FreeQ2[obj, checkHeads], + Return[x] + ]; + + time= AbsoluteTime[]; + FCPrint[1, "FCMatrixIsolate: isolateMatrices: Applying ", fu, FCDoControl->fcmiVerbose]; + objEval = fu[#, Join[opts, {Head->isoHeads}]]&/@ (obj/.relevantPart->Identity); + FCPrint[1, "FCMatrixIsolate: isolateMatrices: Done applying "<>ToString[fu,InputForm]<>", timing: ", + N[AbsoluteTime[] - time, 4], FCDoControl->fcmiVerbose]; + repRule = Thread[Rule[obj,objEval]]; + + (x /. Dispatch[repRule]) + +]; + +FCPrint[1,"FCMatrixIsolate.m loaded."]; +End[] diff --git a/FeynCalc/NonCommAlgebra/FCTraceExpand.m b/FeynCalc/NonCommAlgebra/FCTraceExpand.m index d269253d2..4522e2f33 100644 --- a/FeynCalc/NonCommAlgebra/FCTraceExpand.m +++ b/FeynCalc/NonCommAlgebra/FCTraceExpand.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Expands traces using linearity *) @@ -16,7 +16,7 @@ (* ------------------------------------------------------------------------ *) FCTraceExpand::usage = -"FCTraceExpand[expr] expands traces of Dirac and SU(N) matrices \ +"FCTraceExpand[expr] expands traces of Dirac and SU(N) matrices \ using linearity of the trace. The traces themselves are not \ evaluated."; @@ -32,15 +32,16 @@ fctreVerbose::usage=""; Options[FCTraceExpand] = { - DiracGammaExpand -> True, - DiracTrace -> True, - DotSimplify -> True, - FCI -> False, - FCTraceFactor -> True, - FCVerbose -> False, - Momentum -> All, - PreservePropagatorStructures -> False, - SUNTrace -> True + DiracGammaExpand -> True, + DiracTrace -> True, + DotSimplify -> True, + FCE -> False, + FCI -> False, + FCTraceFactor -> True, + FCVerbose -> False, + Momentum -> All, + PreservePropagatorStructures -> False, + SUNTrace -> True }; FCTraceExpand[expr_, OptionsPattern[]] := @@ -52,7 +53,7 @@ If [OptionValue[FCVerbose]===False, fctreVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], fctreVerbose=OptionValue[FCVerbose] ]; ]; @@ -61,7 +62,7 @@ ex = expr, ex = FCI[expr] ]; - + (*TODO: Add fast mode*) FCPrint[1, "FCTraceExpand: Entering.", FCDoControl->fctreVerbose]; FCPrint[3, "FCTraceExpand: Entering with", ex, FCDoControl->fctreVerbose]; @@ -95,17 +96,21 @@ FCPrint[1, "FCTraceExpand: Done expanding Dirac traces: ", diracTraces2, FCDoControl->fctreVerbose]; If [OptionValue[DiracGammaExpand], - diracTraces2 = DiracGammaExpand/@diracTraces2 + FCPrint[1, "FCTraceExpand: Applying DiracGammaExpand to the Dirac traces", FCDoControl->fctreVerbose]; + diracTraces2 = DiracGammaExpand[#,FCI->True]&/@diracTraces2; + FCPrint[3, "FCTraceExpand: After applying DiracGammaExpand ", diracTraces2, FCDoControl->fctreVerbose] ]; If[ OptionValue[FCTraceFactor], - FCPrint[1, "FCTraceExpand: Applying FCTraceFactor ", FCDoControl->fctreVerbose]; + FCPrint[1, "FCTraceExpand: Applying FCTraceFactor to the Dirac traces", FCDoControl->fctreVerbose]; diracTraces2 = FCTraceFactor/@diracTraces2; FCPrint[3, "FCTraceExpand: After applying FCTraceFactor ", diracTraces2, FCDoControl->fctreVerbose] ]; If[ diracTraces =!= {}, - ex = ex /. Dispatch[Thread[diracTraces -> traceexpand[diracTraces2]]] + FCPrint[1, "FCTraceExpand: Expanding Dirac traces.", FCDoControl->fctreVerbose]; + ex = ex /. Dispatch[Thread[diracTraces -> traceexpand[diracTraces2]]]; + FCPrint[3, "FCTraceExpand: After the expansion of Dirac traces: ", ex, FCDoControl->fctreVerbose] ]; ]; @@ -119,6 +124,12 @@ res = ex; + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "FCTraceExpand: Leaving.", FCDoControl->fctreVerbose]; + FCPrint[3, "FCTraceExpand: Leaving with ", res, FCDoControl->fctreVerbose]; res @@ -129,13 +140,13 @@ expandDirac[x_] := If [dotSimp, - Distribute[DiracTrace@(Expand[DotSimplify[x,PreservePropagatorStructures->propPres]])], + Distribute[DiracTrace@(Expand[DotSimplify[x,PreservePropagatorStructures->propPres,FCI->True]])], Distribute[DiracTrace@(Expand[x])] ] expandColor[x_] := If [dotSimp, - Distribute[SUNTrace@(Expand[DotSimplify[x,PreservePropagatorStructures->propPres]])], + Distribute[SUNTrace@(Expand[DotSimplify[x,PreservePropagatorStructures->propPres,FCI->True]])], Distribute[SUNTrace@(Expand[x])] ] diff --git a/FeynCalc/NonCommAlgebra/FCTraceFactor.m b/FeynCalc/NonCommAlgebra/FCTraceFactor.m index 3b6db31ef..b993c44ca 100644 --- a/FeynCalc/NonCommAlgebra/FCTraceFactor.m +++ b/FeynCalc/NonCommAlgebra/FCTraceFactor.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Factors traces using linearity *) @@ -28,7 +28,8 @@ Begin["`FCTraceFactor`Private`"] Options[FCTraceFactor] = { - FCI -> False + FCI -> False, + FCE -> False }; FCTraceFactor[expr_, OptionsPattern[]] := @@ -51,6 +52,10 @@ res = ex /. Dispatch[Thread[diracTraces -> tracefactor[diracTraces]]] ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + res ]; diff --git a/FeynCalc/NonCommAlgebra/NonCommutative.m b/FeynCalc/NonCommAlgebra/NonCommutative.m index 390504448..7402fbb69 100644 --- a/FeynCalc/NonCommAlgebra/NonCommutative.m +++ b/FeynCalc/NonCommAlgebra/NonCommutative.m @@ -1,7 +1,15 @@ -(* ------------------------------------------------------------------------ *) -(* ------------------------------------------------------------------------ *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: NonCommutative *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) -(* :Summary: test for non-commutativity *) +(* :Summary: Tests for non-commutativity *) (* ------------------------------------------------------------------------ *) @@ -47,6 +55,14 @@ Settings of AntiCommutator (e.g.AntiCommutator[a,b]=c) \ noncommutative, i.e., DataType[a,b, ..., NonCommutative] = False \ is performed."; +UnDeclareAntiCommutator::usage = +"UnDeclareAntiCommutator[a, b] undeclares the value assigned to the +anticommutator of a and b."; + +UnDeclareCommutator::usage = +"UnDeclareCommutator[a, b] undeclares the value assigned to the +commutator of a and b."; + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -108,23 +124,49 @@ Settings of AntiCommutator (e.g.AntiCommutator[a,b]=c) \ UnDeclareNonCommutative[b__] := (Map[Set[DataType[#, NonCommutative], False]&, Flatten[{b}]]; Null); +UnDeclareCommutator[a_, b_] := + Block[{exp, comm, dw}, + exp = HoldPattern[comm[a, b]] /. comm -> Commutator; + dw = SelectFree[DownValues[Commutator], exp]; + DownValues[Commutator] = dw; + ]; + +UnDeclareAntiCommutator[a_, b_] := + Block[{exp, acomm, dw}, + exp = HoldPattern[acomm[a, b]] /. acomm -> AntiCommutator; + dw = SelectFree[DownValues[AntiCommutator], exp]; + DownValues[AntiCommutator] = dw; + ]; + (* Have traces treated as commutating objects. F.Orellana, 11/9-2002. *) -excludeTraces = a : (DiracTrace | SUNTrace)[__] :> + +excludeTraces = {_DiracTrace :> Unique["DiracTrace"], _SUNTrace :> Unique["SUNTrace"]}; +(* +a : (DiracTrace | SUNTrace)[__] :> (a /. (Rule[#, ToString[#]] & /@{DiracTrace, SUNTrace, Sequence @@ $NonComm})); +*) NonCommFreeQ[_?NumberQ] := True; -NonCommFreeQ[x_] := - MemSet[NonCommFreeQ[x], FreeQ2[x /. excludeTraces, $NonComm]]; -(*Comment: Because of this MemSet, NonCommFreeQ is updated when setting a new - DataType[x,NonCommutative]=True or DataType[x,NonCommutative]=False. - Rolf implemented it this way to gain speed I suppose. F.Orellana*) +NonCommFreeQ[x_] := + MemSet[NonCommFreeQ[x], + If[ !FreeQ2[x,{DiracTrace,SUNTrace}], + FreeQ2[x /. excludeTraces, $NonComm], + FreeQ2[x, $NonComm] + ] + ]; NonCommQ[_?NumberQ] := False; + NonCommQ[x_] := - MemSet[NonCommQ[x], !FreeQ2[x /. excludeTraces, $NonComm]]; + MemSet[NonCommQ[x], + If[ !FreeQ2[x,{DiracTrace,SUNTrace}], + !FreeQ2[x /. excludeTraces, $NonComm], + !FreeQ2[x, $NonComm] + ] + ]; FCPrint[1,"NonCommutative loaded"]; End[] diff --git a/FeynCalc/NonCommAlgebra/TR.m b/FeynCalc/NonCommAlgebra/TR.m index 4025b00d8..b8a5af83a 100644 --- a/FeynCalc/NonCommAlgebra/TR.m +++ b/FeynCalc/NonCommAlgebra/TR.m @@ -24,68 +24,70 @@ the option SUNTrace also a trace over SU(N) objects is performed. \ trVerbose::usage=""; -Options[ TR ] = { - Contract -> 400000, - DiracTraceEvaluate -> True, - EpsContract -> True, - Explicit -> True, - Expand -> True, - Factoring -> Automatic, +Options[TR] = { + Contract -> True, + DiracTraceEvaluate -> True, + EpsContract -> True, + Expand -> True, + Explicit -> True, + FCE -> False, FCVerbose -> True, - FeynCalcExternal -> False, - Mandelstam -> {}, + Factoring -> Automatic, + Mandelstam -> {}, PairCollect -> False, SUNNToCACF -> False, - SUNTrace -> False, - Schouten -> 0, - TraceOfOne -> 4, + SUNTrace -> False, + Schouten -> 0, + TraceOfOne -> 4, West -> True }; -TR[x_, rul:OptionsPattern[]] := - Block[{tt=FeynCalcInternal[x], doot, diractr, dit, fcex, diractrev, sunntocacf, +TR[expr_, rul:OptionsPattern[]] := + Block[{ex, doot, diractr, dit, fcex, diractrev, sunntocacf, diracTraceOpts,sunTraceOpts,trOpts}, If [OptionValue[FCVerbose]===False, trVerbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], trVerbose=OptionValue[FCVerbose] ]; ]; - FCPrint[1,"TR: Entering with: ", tt, FCDoControl->trVerbose]; + FCPrint[1,"TR: Entering with: ", expr, FCDoControl->trVerbose]; - diractrev = OptionValue[DiracTraceEvaluate]; - sunntocacf = OptionValue[SUNNToCACF]; - trOpts = Flatten[Join[{rul}, FilterRules[Options[TR], Except[{rul}]]]]; - diracTraceOpts = Flatten[FilterRules[Options[trOpts], Options[DiracTrace]]]; - sunTraceOpts = Flatten[FilterRules[Options[trOpts], Options[SUNTrace]]]; + ex=FeynCalcInternal[expr]; - If[!FreeQ[x,CF|CA], + diractrev = OptionValue[DiracTraceEvaluate]; + sunntocacf = OptionValue[SUNNToCACF]; + trOpts = Flatten[Join[{rul}, FilterRules[Options[TR], Except[{rul}]]]]; + diracTraceOpts = Flatten[FilterRules[Options[trOpts], Options[DiracTrace]]]; + sunTraceOpts = Flatten[FilterRules[Options[trOpts], Options[SUNTrace]]]; + + If[!FreeQ2[ex, {CF,CA}], sunntocacf = True ]; If[OptionValue[Explicit], - tt = Explicit[tt] + ex = Explicit[ex] ]; - If[OptionValue[SUNTrace] && !FreeQ2[tt, {SUNIndex,ExplicitSUNIndex}], + If[OptionValue[SUNTrace] && !FreeQ2[ex, {SUNIndex,ExplicitSUNIndex}], FCPrint[1,"TR: Computing the SU(N) trace.", FCDoControl->trVerbose]; - tt = DiracTrace[tt,diracTraceOpts]; - tt = SUNSimplify[tt, SUNNToCACF -> sunntocacf, SUNTrace -> True, Explicit -> False]; - tt = tt /. (DiracTraceEvaluate -> False) :> (DiracTraceEvaluate -> diractrev) // + ex = DiracTrace[ex,diracTraceOpts]; + ex = SUNSimplify[ex, SUNNToCACF -> sunntocacf, SUNTrace -> True, Explicit -> False]; + ex = ex /. (DiracTraceEvaluate -> False) :> (DiracTraceEvaluate -> diractrev) // SUNSimplify[#, SUNTrace -> False, SUNNToCACF -> sunntocacf, Explicit -> False]&, - If[FreeQ[tt, SUNIndex|ExplicitSUNIndex], - tt = DiracTrace[tt, diracTraceOpts]; + If[FreeQ[ex, SUNIndex|ExplicitSUNIndex], + ex = DiracTrace[ex, diracTraceOpts]; If[ OptionValue[SUNTrace], - tt = SUNSimplify[tt, SUNTrace -> True, SUNNToCACF -> sunntocacf, Explicit -> False] + ex = SUNSimplify[ex, SUNTrace -> True, SUNNToCACF -> sunntocacf, Explicit -> False] ]; - tt = tt /. (DiracTraceEvaluate -> False) :> (DiracTraceEvaluate -> diractrev) // + ex = ex /. (DiracTraceEvaluate -> False) :> (DiracTraceEvaluate -> diractrev) // SUNSimplify[#, SUNTrace -> False, SUNNToCACF -> sunntocacf, Explicit -> False]&, - (*!FreeQ[tt, SUNIndex|ExplicitSUNIndex] -> !SUNTrace*) - tt = DiracTrace[Trick[tt]// SUNSimplify[#, SUNNToCACF -> sunntocacf, + (*!FreeQ[ex, SUNIndex|ExplicitSUNIndex] -> !SUNTrace*) + ex = DiracTrace[Trick[ex]// SUNSimplify[#, SUNNToCACF -> sunntocacf, SUNTrace -> OptionValue[SUNTrace], Explicit -> OptionValue[Explicit]]&, diracTraceOpts] ] ]; @@ -94,14 +96,14 @@ the option SUNTrace also a trace over SU(N) objects is performed. \ FCPrint[4,"TR: Options for Dirac trace: ", {diracTraceOpts}, FCDoControl->trVerbose]; diractr[y__] := (DiracTrace @@ Join[{y}, diracTraceOpts]); - tt = tt /. DiracTrace -> diractr; + ex = ex /. DiracTrace -> diractr; - If[ OptionValue[FeynCalcExternal], - tt = FeynCalcExternal[tt] + If[ OptionValue[FCE], + ex = FCE[ex] ]; - FCPrint[1,"TR: Leaving with: ",tt, FCDoControl->trVerbose]; - tt + FCPrint[1,"TR: Leaving with: ", ex, FCDoControl->trVerbose]; + ex ]; FCPrint[1,"TR.m loaded"]; diff --git a/FeynCalc/NonCommAlgebra/Tr2.m b/FeynCalc/NonCommAlgebra/Tr2.m index 0cdd6d004..6e73c76e6 100644 --- a/FeynCalc/NonCommAlgebra/Tr2.m +++ b/FeynCalc/NonCommAlgebra/Tr2.m @@ -26,7 +26,9 @@ Begin["`Tr2`Private`"] -Options[ Tr2 ] = {Factoring -> False}; +Options[Tr2] = { + Factoring -> False +}; dirtr[x_, OptionsPattern[]] := @@ -64,12 +66,13 @@ trdifficult[y_, ops___Rule] := If[MatchQ[y, _. DOT[(a__) /; FreeQ2[{a}, {DiracGamma[5],DiracGamma[6], DiracGamma[7]}], DiracGamma[5]]], treasy[Expand[ExpandScalarProduct[Contract[DiracOrder[Collect2[DiracSimplify[y, InsideDiracTrace -> True], - DOT, Factoring -> False]],EpsEvaluate->False]],DiracGamma],ops], - treasy[Expand[ExpandScalarProduct[Contract[DiracOrder[y],EpsEvaluate->False]], DiracGamma], ops] + DOT, Factoring -> False]],EpsContract->False]],DiracGamma],ops], + treasy[Expand[ExpandScalarProduct[Contract[DiracOrder[y],EpsContract->False]], DiracGamma], ops] ] /. treasy -> DiracTrace /. DiracTrace -> trup /. trup -> DiracTrace /. DiracTrace -> trap; Tr2[x_] := Block[{tt=FCI[x]}, + If[FreeQ[tt, DiracTrace], tt = DiracTrace[tt] ]; diff --git a/FeynCalc/NonCommAlgebra/Trick.m b/FeynCalc/NonCommAlgebra/Trick.m index 468020d50..da82b5b82 100644 --- a/FeynCalc/NonCommAlgebra/Trick.m +++ b/FeynCalc/NonCommAlgebra/Trick.m @@ -16,13 +16,14 @@ Begin["`Trick`Private`"]; Trick[x_] := - Block[{tt, paulisigsimp, sigident,doot,cov,palr}, + Block[{tt, sigident,doot,cov}, + SetAttributes[cov,HoldFirst]; cov[y_] := y /. CovariantD[a__] :> CovariantD[a, Explicit -> True]; - SetAttributes[palr,HoldFirst]; + tt = DotSimplify[FeynCalcInternal[x]//cov(*//palr*), Expanding -> False] /. SUNDelta -> SUNDeltaContract /. SUNDeltaContract -> SUNDelta; - If[!FreeQ[tt, LorentzIndex], + If[!FreeQ2[tt, {LorentzIndex,CartesianIndex}], tt = Contract[tt, EpsContract -> False, Expanding -> False] ]; If[!FreeQ[tt, SUNT], @@ -33,11 +34,7 @@ tt = tt /. ( SUNF[a_,b_,c_] SUNF[d_,e_,f_] :> SUNSimplify[SUNF[a,b,c] SUNF[d,e,f]] ) /. SUNDelta->SUNDeltaContract /. SUNDeltaContract->SUNDelta ]; - paulisigsimp[y_] := FixedPoint[sigident, y, 1442]; - sigident[z_] := DotSimplify[(z /. DOT -> doot //. {doot[w1___, DotProduct[PauliSigma, a_], - DotProduct[PauliSigma, b_], w2___] :> (doot[w1, DotProduct[a, b], w2] + I doot[w1, DotProduct[PauliSigma, - CrossProduct[a, b]], w2])} /. doot -> DOT), Expanding -> False]; - tt = paulisigsimp[tt]; + tt = FeynAmpDenominatorCombine[tt]; tt ]; diff --git a/FeynCalc/PacletInfo.m b/FeynCalc/PacletInfo.m index 8764c7c55..69b2a8c09 100644 --- a/FeynCalc/PacletInfo.m +++ b/FeynCalc/PacletInfo.m @@ -4,7 +4,7 @@ Paclet[ Name -> "FeynCalc", - Version -> "9.2.0", + Version -> "9.3.0", MathematicaVersion -> "8+", Description -> "FeynCalc is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics.", Creator -> "Rolf Mertig, Frederik Orellana, Vladyslav Shtabovenko", diff --git a/FeynCalc/Pauli/FCPauliIsolate.m b/FeynCalc/Pauli/FCPauliIsolate.m new file mode 100755 index 000000000..2c22a9ae6 --- /dev/null +++ b/FeynCalc/Pauli/FCPauliIsolate.m @@ -0,0 +1,234 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCPauliIsolate *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Isolates chains of Pauli matrices *) + +(* ------------------------------------------------------------------------ *) + +FCPauliIsolate::usage = +"FCPauliIsolate[exp] wraps chains of Pauli matrices into heads specified \ +by the user " <> ToString[ +Hyperlink[Style["\[RightSkeleton]", "SR"], "paclet:FeynCalc/ref/FCPauliIsolate"], +StandardForm]; + +FCPauliIsolate::fail = +"FCPauliIsolate failed to isolate Pauli structures in `1`!"; + +Begin["`Package`"] +End[] + +Begin["`FCPauliIsolate`Private`"] + +Options[FCPauliIsolate] = { + CartesianIndex -> False, + ClearHeads -> {FCGV["PauliChain"]}, + Collecting -> True, + DotSimplify -> True, + ExceptHeads -> {}, + Expanding -> True, + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCVerbose -> False, + Factoring -> Factor, + Head -> FCGV["PauliChain"], + Isolate -> False, + IsolateFast -> False, + IsolateNames -> KK, + LorentzIndex -> False, + PauliEta -> True, + PauliSigma -> True, + PauliSigmaCombine -> True, + PauliXi -> True, + Polarization -> False, + Split -> True, + TimeConstrained -> 3 +}; + +makeSelectionList[expr_,heads_List]:= + MemSet[makeSelectionList[expr,heads], + Join[heads,Intersection[Cases[SelectFree[expr, heads], l: (_LorentzIndex| _CartesianIndex) :> l[[1]] ,Infinity], + Cases[SelectNotFree[expr, heads], l: (_LorentzIndex| _CartesianIndex) :> l[[1]] ,Infinity]]] +]; + +FCPauliIsolate[expr_List, opts:OptionsPattern[]]:= + FCPauliIsolate[#, opts]&/@expr; + +FCPauliIsolate[expr_/;Head[expr]=!=List, OptionsPattern[]] := + Block[{ res, null1, null2, ex,tmp, head, selectionList, lorHead, + tmpHead,tmpHead2, time, fcpiVerbose, headsList, + optTimeConstrained, optHead, headR}, + + If [OptionValue[FCVerbose]===False, + fcpiVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + fcpiVerbose=OptionValue[FCVerbose] + ]; + ]; + + optTimeConstrained = OptionValue[TimeConstrained]; + headsList = PauliHeadsList; + + If[ OptionValue[Polarization], + headsList = Join[headsList,{Polarization}]; + ]; + + If[ OptionValue[LorentzIndex]===All, + headsList = Join[headsList,{LorentzIndex}]; + ]; + + If[ OptionValue[CartesianIndex]===All, + headsList = Join[headsList,{CartesianIndex}]; + ]; + + optHead = OptionValue[Head]; + + If[MatchQ[optHead,{_,_}], + {head, headR} = optHead, + + head = optHead; + headR = Identity + ]; + + + If[OptionValue[FCI], + ex = expr/. (Map[Rule[#, Identity] &, OptionValue[ClearHeads]]), + ex = FCI[expr]/. (Map[Rule[#, Identity] &, OptionValue[ClearHeads]]) + ]; + + FCPrint[3, "FCPauliIsolate: Entering with: ", ex, FCDoControl->fcpiVerbose]; + + If[ FreeQ2[ex,headsList], + Return[restHead[ex] /. restHead -> headR] + ]; + + If[ OptionValue[PauliSigmaCombine], + time=AbsoluteTime[]; + FCPrint[1, "FCPauliIsolate: Applying PauliSigmaCombine.", FCDoControl->fcpiVerbose]; + ex = PauliSigmaCombine[ex, FCI->True]; + FCPrint[1, "FCPauliIsolate: Done applying PauliSigmaCombine, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcpiVerbose]; + FCPrint[3, "FCPauliIsolate: After PauliSigmaCombine: ", ex, FCDoControl->fcpiVerbose] + ]; + + If[ OptionValue[Expanding], + time=AbsoluteTime[]; + FCPrint[1, "FCPauliIsolate: Applying Expand2.", FCDoControl->fcpiVerbose]; + ex = Expand2[ex, headsList]; + FCPrint[1, "FCPauliIsolate: Done applying Expand2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcpiVerbose]; + FCPrint[3, "FCPauliIsolate: After Expand2: ", ex, FCDoControl->fcpiVerbose] + ]; + + If[ OptionValue[DotSimplify] && !FreeQ[ex,DOT], + time=AbsoluteTime[]; + FCPrint[1, "FCPauliIsolate: Applying DotSimplify.", FCDoControl->fcpiVerbose]; + tmp = FCSplit[ex, headsList, Expanding->OptionValue[Expanding]]; + ex = tmp[[1]]+ DotSimplify[tmp[[2]],Expanding->False,FCI->True, FCJoinDOTs->OptionValue[FCJoinDOTs]]; + FCPrint[1, "FCPauliIsolate: Done applying DotSimplify, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcpiVerbose]; + FCPrint[3, "FCPauliIsolate: After DotSimplify: ", ex, FCDoControl->fcpiVerbose] + ]; + + If[ OptionValue[Collecting], + time=AbsoluteTime[]; + FCPrint[1, "FCPauliIsolate: Applying Collect2.", FCDoControl->fcpiVerbose]; + ex = Collect2[ex,headsList,Factoring->OptionValue[Factoring],TimeConstrained->optTimeConstrained]; + FCPrint[1, "FCPauliIsolate: Done applying Collect2, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcpiVerbose] + ]; + + + + time=AbsoluteTime[]; + FCPrint[1, "FCPauliIsolate: Handling Lorentz and Cartesian indices.", FCDoControl->fcpiVerbose]; + If[ OptionValue[LorentzIndex]===True || OptionValue[CartesianIndex]===True, + res = (Map[(selectionList=makeSelectionList[#,headsList]; restHead[SelectFree[#, selectionList]] head[SelectNotFree[#, selectionList]])&, + ex + null1 + null2] /. {null1 | null2 -> 0} /. head[1] -> 1), + + res = (Map[(restHead[SelectFree[#, headsList]] head[SelectNotFree[#, headsList]]) &, + ex + null1 + null2] /. {null1 | null2 -> 0} /. head[1] -> 1) + ]; + FCPrint[1, "FCPauliIsolate: Done handling Lorentz and Cartesian indices, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcpiVerbose]; + + res = res /. {head[x_] /; !FreeQ2[x, OptionValue[ExceptHeads]] :> x}; + + If[ Together[(res /. restHead|head|tmpHead|lorHead|tmpHead2 -> Identity)-ex] =!= 0, + Message[FCPauliIsolate::fail, ex]; + Abort[] + ]; + + If[ OptionValue[Split], + time=AbsoluteTime[]; + FCPrint[1, "FCPauliIsolate: Doing splittings.", FCDoControl->fcpiVerbose]; + res = res /. DOT->holdDOT //. {head[a_holdDOT b_holdDOT c_.] :> head[a]head[b c], + head[holdDOT[r1___,(a: _PauliEta | _PauliXi),b___,(c: _PauliEta | _PauliXi), (d: _PauliEta | _PauliXi), e___, (f: _PauliEta | _PauliXi), r2___]]/;FreeQ2[{r1,b,e,r2}, {PauliEta,PauliXi}] :> + head[holdDOT[a,b,c]] head[holdDOT[d,e,f]] head[holdDOT[r1,r2]] }/. holdDOT[] ->1 /. holdDOT -> DOT; + FCPrint[1, "FCPauliIsolate: Splittings done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcpiVerbose] + ]; + + time=AbsoluteTime[]; + FCPrint[1, "FCPauliIsolate: Removing unneeded isolations.", FCDoControl->fcpiVerbose]; + (* Here we unisolate objects that are not needed *) + + If[ !OptionValue[PauliSigma], + res = res //. head[x_PauliSigma y_.] :> x head[y] //. + head[DOT[x__] y_.]/; FreeQ[{x},Spinor] && !FreeQ[{x},PauliSigma] :> DOT[x] head[y]; + ]; + + If[ !OptionValue[PauliXi], + res = res //. head[DOT[x__] y_.]/; !FreeQ[{x},PauliXi] :> DOT[x] head[y]; + ]; + + If[ !OptionValue[PauliEta], + res = res //. head[DOT[x__] y_.]/; !FreeQ[{x},PauliEta] :> DOT[x] head[y]; + ]; + + res = res //. head[x_]/; FreeQ2[x,headsList] :> x; + + FCPrint[1, "FCPauliIsolate: Done removing unneeded isolations, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcpiVerbose]; + + If[ OptionValue[Isolate], + time=AbsoluteTime[]; + FCPrint[1, "FCPauliIsolate: Applying Isolate.", FCDoControl->fcpiVerbose]; + res = res/. restHead[x_]:> Isolate[x,IsolateNames->OptionValue[IsolateNames],IsolateFast->OptionValue[IsolateFast]], + res = res /. restHead[0]->0 /. restHead -> headR; + FCPrint[1, "FCPauliIsolate: Done applying Isolate, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->fcpiVerbose]; + ]; + + tmp = headsList; + + If[ OptionValue[LorentzIndex]===True, + tmp = Join[tmp,{LorentzIndex}] + ]; + + If[ OptionValue[CartesianIndex]===True, + tmp = Join[tmp,{CartesianIndex}] + ]; + + (* If LorentzIndex/CartesianIndex is set to true, this check guarantees that all Lorentz/Cartesian tensors are inside head *) + If [ !FreeQ2[res/. head[__] :> 1, tmp] & || !FreeQ[res,head[]], + Message[FCPauliIsolate::fail, ex]; + Abort[] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + FCPrint[1, "FCPauliIsolate: Leaving.", FCDoControl->fcpiVerbose]; + + res + ]; + +restHead[0]= + 0; + +FCPrint[1,"FCPauliIsolate.m loaded."]; +End[] diff --git a/FeynCalc/Pauli/PauliOrder.m b/FeynCalc/Pauli/PauliOrder.m new file mode 100644 index 000000000..def8836c8 --- /dev/null +++ b/FeynCalc/Pauli/PauliOrder.m @@ -0,0 +1,203 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: PauliOrder *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Lexicographic ordering of Pauli matrices *) + +(* ------------------------------------------------------------------------ *) + +PauliOrder::usage = +"PauliOrder[exp] orders the Pauli matrices in expr alphabetically. \ +PauliOrder[exp, orderlist] orders the Pauli matrices in expr according \ +to orderlist."; + +PauliOrder::failmsg = +"Error! PauliOrder has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`PauliOrder`Private`"]; + +pauliReduce::usage=""; +poVerbose::usage=""; +holdDOT::usage=""; +tmp::usage=""; + +Options[PauliOrder] = { + FCE -> False, + FCI -> False, + FCJoinDOTs -> True, + FCPauliIsolate -> True, + FCVerbose -> False, + MaxIterations -> Infinity, + PauliReduce -> False, + PauliSigmaCombine -> False, + PauliTrick -> True +}; + +PauliOrder[expr_, (opts:OptionsPattern[])/;opts=!={}] := + PauliOrder[expr, {}, opts]; + +PauliOrder[expr_, orderList_List/; (!OptionQ[orderList] || orderList==={}), OptionsPattern[]]:= + Block[{ex,res,dsHead,dsPart,freePart,null1,null2,pauliObjects,tmp, maxIterations, pauliObjectsEval, repRule,time}, + + maxIterations = OptionValue[MaxIterations]; + + pauliReduce = OptionValue[PauliReduce]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ2[ex,PauliHeadsList], + Return[ex] + ]; + + If[ OptionValue[FCVerbose]===False, + poVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + poVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "PauliOrder. Entering.", FCDoControl->poVerbose]; + FCPrint[3, "PauliOrder: Entering with ", ex, FCDoControl->poVerbose]; + + If[ OptionValue[FCPauliIsolate], + (* This is the normal mode which works well both for large and small expressions *) + FCPrint[1, "PauliOrder: Normal mode.", FCDoControl->poVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "PauliOrder: Extracting Pauli objects.", FCDoControl->poVerbose]; + ex = FCPauliIsolate[ex,FCI->True,Head->dsHead, DotSimplify->True, PauliSigmaCombine->OptionValue[PauliSigmaCombine], + FCJoinDOTs->OptionValue[FCJoinDOTs]]; + + + {freePart,dsPart} = FCSplit[ex,{dsHead}]; + FCPrint[3,"PauliOrder: dsPart: ",dsPart , FCDoControl->poVerbose]; + FCPrint[3,"PauliOrder: freePart: ",freePart , FCDoControl->poVerbose]; + + pauliObjects = Cases[dsPart+null1+null2, dsHead[_], Infinity]//DeleteDuplicates//Sort; + FCPrint[1, "PauliOrder: Done extracting Pauli objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->poVerbose]; + + time=AbsoluteTime[]; + If[orderList=!={}, + FCPrint[1, "PauliOrder: Ordering according to: ", orderList, FCDoControl->poVerbose]; + pauliObjectsEval = Map[pauliOrderCustom[#,orderList]&, (pauliObjects/. DOT -> holdDOT/.dsHead->Identity)]; + FCPrint[1, "PauliOrder: Ordering done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->poVerbose], + + FCPrint[1, "PauliOrder. Using lexicographic ordering.", FCDoControl->poVerbose]; + pauliObjectsEval = Map[pauliOrderLex[#,maxIterations]&, (pauliObjects/. DOT -> holdDOT/.dsHead->Identity)]; + FCPrint[1, "PauliOrder: Ordering done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->poVerbose] + ]; + + time=AbsoluteTime[]; + FCPrint[1, "PauliOrder: Inserting Pauli objects back.", FCDoControl->poVerbose]; + + pauliObjectsEval = pauliObjectsEval /. holdDOT[]->1 /.holdDOT->DOT /. CartesianPairContract -> CartesianPair; + If[ !FreeQ[pauliObjectsEval,Pair], + pauliObjectsEval = pauliObjectsEval/. Pair->PairContract /. PairContract->Pair + ]; + + repRule = Thread[Rule[pauliObjects,pauliObjectsEval]]; + FCPrint[3,"PauliOrder: repRule: ",repRule , FCDoControl->poVerbose]; + tmp = freePart + (dsPart /. Dispatch[repRule]); + FCPrint[1, "PauliOrder: Done inserting Pauli objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->poVerbose]; + FCPrint[3,"PauliOrder: Intermediate result: ", tmp, FCDoControl->poVerbose], + + (* This is the fast mode for standalone Pauli chains *) + FCPrint[1, "PauliOrder: Fast mode.", FCDoControl->poVerbose]; + time=AbsoluteTime[]; + tmp = ex /. DOT -> holdDOT; + + If[orderList=!={}, + FCPrint[1, "PauliOrder: Ordering according to: ", orderList, FCDoControl->poVerbose]; + tmp = pauliOrderCustom[tmp, orderList]; + FCPrint[1, "PauliOrder: Ordering done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->poVerbose], + + FCPrint[1, "PauliOrder. Using lexicographic ordering.", FCDoControl->poVerbose]; + tmp = pauliOrderLex[tmp, maxIterations]; + FCPrint[1, "PauliOrder: Ordering done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->poVerbose] + + ]; + tmp = tmp/. holdDOT[]->1 /.holdDOT->DOT /. CartesianPairContract->CartesianPair; + If[ !FreeQ[pauliObjectsEval,Pair], + pauliObjectsEval = pauliObjectsEval/. Pair->PairContract /. PairContract->Pair + ]; + + ]; + + + res = tmp; + + If[ OptionValue[PauliTrick], + time=AbsoluteTime[]; + FCPrint[1, "PauliOrder: Applying PauliTrick.", FCDoControl->poVerbose]; + res = PauliTrick[res, FCI->True, PauliReduce->pauliReduce]; + FCPrint[1, "PauliOrder: Done applying PauliTrick,timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->poVerbose] + ]; + + FCPrint[1, "PauliOrder: Leaving.", FCDoControl->poVerbose]; + FCPrint[3, "PauliOrder: Leaving with ", res, FCDoControl->poVerbose]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + +pauliOrderLex[x_, maxIterations_]:= + FixedPoint[(# /. { + holdDOT[a___,PauliSigma[(h1:CartesianIndex|CartesianMomentum)[ar1__], dim1_:3],PauliSigma[(h2:CartesianIndex|CartesianMomentum)[ar2__], dim2_:3],b___]/; + !OrderedQ[{h1[First[{ar1}],dim1],h2[First[{ar2}],dim2]}] && h1[First[{ar1}],dim1]=!=h2[First[{ar2}],dim2] :> + -holdDOT[a, PauliSigma[h2[ar2],dim2], PauliSigma[h1[ar1],dim1] ,b] + + 2 CartesianPairContract[h1[ar1],h2[ar2]] holdDOT[a,b], + + holdDOT[a___,PauliSigma[(h:CartesianIndex|CartesianMomentum|ExplicitLorentzIndex)[ar___], dim_:3], + PauliSigma[(h:CartesianIndex|CartesianMomentum|ExplicitLorentzIndex)[ar___], dim_:3],b___] :> + holdDOT[a,b] PauliTrick[DOT[PauliSigma[h[ar],dim].PauliSigma[h[ar],dim]],FCI->True,FCPauliIsolate->False, PauliReduce->pauliReduce] + + + })&, x, maxIterations] + +customOrdering[x_, currentElement_]:= + x //. { + holdDOT[a___,PauliSigma[(h1:CartesianIndex|CartesianMomentum)[ar1__], dim1_:3],PauliSigma[(h2:CartesianIndex|CartesianMomentum)[ar2__], dim2_:3],b___]/; + !FreeQ[h2[First[{ar2}],dim2],currentElement] && h1[First[{ar1}],dim1]=!=h2[First[{ar2}],dim2] :> + -holdDOT[a, PauliSigma[h2[ar2],dim2], PauliSigma[h1[ar1],dim1] ,b] + + 2 CartesianPairContract[h1[ar1],h2[ar2]] holdDOT[a,b], + + holdDOT[a___,PauliSigma[(h:CartesianIndex|CartesianMomentum|ExplicitLorentzIndex)[ar___], dim_:3], + PauliSigma[(h:CartesianIndex|CartesianMomentum|ExplicitLorentzIndex)[ar___], dim_:3],b___] :> + holdDOT[a,b] PauliTrick[DOT[PauliSigma[h[ar],dim].PauliSigma[h[ar],dim]],FCI->True,FCPauliIsolate->False, PauliReduce->pauliReduce] +}; + + + +pauliOrderCustom[x_, orderList_List]:= + ( + tmp=x; + Scan[(tmp = customOrdering[tmp,#])&, Reverse[orderList]]; + tmp + ); + + + + +FCPrint[1,"PauliOrder.m loaded."]; +End[] diff --git a/FeynCalc/Pauli/PauliSigmaCombine.m b/FeynCalc/Pauli/PauliSigmaCombine.m new file mode 100644 index 000000000..5f2e8c230 --- /dev/null +++ b/FeynCalc/Pauli/PauliSigmaCombine.m @@ -0,0 +1,79 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: PauliSigmaCombine *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: The inverse of PauliSigmaExpand *) + +(* ------------------------------------------------------------------------ *) + +PauliSigmaCombine::usage = +"PauliSigmaCombine[exp] is (nearly) the inverse operation to PauliSigmaExpand."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`PauliSigmaCombine`Private`"] + +pscVerbose::usage=""; + +Options[PauliSigmaCombine] = { + FCI -> False, + FCE -> False +}; + +PauliSigmaCombine[expr_, OptionsPattern[]] := + Block[{ ex, tmp, res, holdDOT, freePart, diracPart, holdPlus, pauliList, pauliListEval, repRule, + null1, null2}, + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ[ex, PauliSigma], + Return[ex] + ]; + + ex = (ex/. Plus -> holdPlus); + pauliList = (Cases[ex+null1+null2,holdPlus[z__]/; !FreeQ[{z},PauliSigma], Infinity])//DeleteDuplicates//Sort; + + pauliListEval = pauliList /. p_holdPlus :> holdPlus@@Sort[List@@p] //. { + holdPlus[a___, n1_. PauliSigma[CartesianMomentum[x_,dim_:3],dim_:3], n2_. PauliSigma[CartesianMomentum[y_, dim_:3], dim_:3], b___]/;(NumberQ[n1] && NumberQ[n2]) :> + holdPlus[a, PauliSigma[CartesianMomentum[n1 x + n2 y, dim], dim], b], + holdPlus[a___, n1_. PauliSigma[CartesianMomentum[x_,dim_:3],dim_:3], n2_. PauliSigma[CartesianMomentum[x_, dim_:3], dim_:3], b___]/;(NumberQ[n1] && NumberQ[n2]) :> + holdPlus[a, (n1+n2)PauliSigma[CartesianMomentum[x, dim], dim], b], + + holdPlus[a___, n1_. PauliSigma[Momentum[x_,dim1_:4],dim2_:3], n2_. PauliSigma[Momentum[y_, dim1_:4], dim2_:3], b___]/;(NumberQ[n1] && NumberQ[n2]) :> + holdPlus[a, PauliSigma[Momentum[n1 x + n2 y, dim1], dim2], b], + + holdPlus[a___, n1_. PauliSigma[Momentum[x_,dim1_:4],dim2_:3], n2_. PauliSigma[Momentum[x_, dim1_:4], dim2_:3], b___]/;(NumberQ[n1] && NumberQ[n2]) :> + holdPlus[a, (n1+n2)PauliSigma[Momentum[x, dim1], dim2], b] + + + } /. holdPlus -> Plus; + + repRule = Thread[Rule[pauliList,pauliListEval]]; + + res = ex /. Dispatch[repRule] /. holdPlus -> Plus; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + +FCPrint[1,"PauliSigmaCombine.m loaded"]; +End[] diff --git a/FeynCalc/Pauli/PauliSigmaExpand.m b/FeynCalc/Pauli/PauliSigmaExpand.m new file mode 100644 index 000000000..bf43f8989 --- /dev/null +++ b/FeynCalc/Pauli/PauliSigmaExpand.m @@ -0,0 +1,89 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: PauliSigmaExpand *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Expands Pauli sigmas contracted with Cartesian vectors *) + +(* ------------------------------------------------------------------------ *) + +PauliSigmaExpand::usage = +"PauliSigmaExpand[exp] expands all PauliSigma[Momentum[a+b+..]] in \ +exp into (PauliSigma[Momentum[a]] + PauliSigma[Momentum[b]] + ...)."; + +PauliSigmaExpand::fail = +"Something went while expanding momenta contracted with Pauli matrices. +Evaluation aborted! " + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`PauliSigmaExpand`Private`"] + +Options[PauliSigmaExpand] = { + FCE -> False, + FCI -> False, + Momentum -> All +}; + +PauliSigmaExpand[expr_, OptionsPattern[]] := + Block[{ex, null1, null2, uniqList, solsList, repRule, momList, rud, res}, + + momList = OptionValue[Momentum]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + + (* Nothing to do... *) + If[ FreeQ[ex,PauliSigma], + Return[ex] + ]; + + (* List of all the unique Feynman slashes *) + uniqList = Cases[ex+null1+null2, PauliSigma[arg_ /; ! FreeQ2[{arg}, {Momentum,CartesianMomentum}],___], Infinity]//DeleteDuplicates//Sort; + + (* If the user specified to perform expansion only for some + special slashed momenta, let's do it *) + If[ momList=!=All && Head[momList]===List, + uniqList = Select[uniqList, !FreeQ2[#, momList]&] + ]; + + (* Final replacement rule *) + repRule = Thread[rud[uniqList, uniqList/. PauliSigma -> psev /. psevlin -> PauliSigma]] /. rud -> RuleDelayed; + + (* Simple cross check *) + If[ !FreeQ2[repRule,{psev,psevlin}], + Message[PauliSigmaExpand::fail]; + Abort[] + ]; + + res = ex /. Dispatch[repRule]; + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + res + + ]; + +psev[x_,di_:3] := + psevlin[Expand[MomentumExpand[x], Momentum], di]; + +psevlin[x_Plus, di_:3] := + Map[psevlin[#, di]&, x]; + +FCPrint[1,"PauliSigmaExpand.m loaded."]; +End[] diff --git a/FeynCalc/Pauli/PauliSimplify.m b/FeynCalc/Pauli/PauliSimplify.m new file mode 100755 index 000000000..3dbfed831 --- /dev/null +++ b/FeynCalc/Pauli/PauliSimplify.m @@ -0,0 +1,351 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: PauliSimplify *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Like PauliTrick, but including non-commutative expansions + and simplifications of spinor chains *) + +(* ------------------------------------------------------------------------ *) + +PauliSimplify::usage = +"PauliSimplify[exp] simplifies products of Pauli matrices \ +and expands non-commutative products. \ +Double indices and vectors are contracted. \ +The order of the Pauli matrices is not changed."; + +PauliSimplify::failmsg = +"Error! PauliSimplify encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`PauliSimplify`Private`"] + +psVerbose::usage=""; +(*optInsidePauliTrace::usage="";*) +optExpanding::usage=""; +optExpandScalarProduct::usage=""; +optPauliSigmaCombine::usage=""; +optPauliOrder::usage=""; +optFactoring::usage=""; +optEpsContract::usage=""; +optContract::usage=""; +optPauliReduce::usage=""; + +Options[PauliSimplify] = { + (*InsidePauliTrace -> False,*) + (*PauliTrace -> True,*) + Contract -> True, + EpsContract -> True, + Expand2 -> True, + ExpandScalarProduct -> True, + Expanding -> True, + FCCheckSyntax -> False, + FCE -> False, + FCI -> False, + FCPauliIsolate -> True, + FCVerbose -> False, + Factoring -> False, + PauliOrder -> False, + PauliReduce -> True, + PauliSigmaCombine -> False + (*PauliTraceEvaluate -> True,*) +}; + +PauliSimplify[expr_, OptionsPattern[]] := + Block[{ex,res,time, null1, null2, holdDOT, freePart=0, psPart, pauliObjects, + pauliObjectsEval, repRule, tmp, tmpHead}, + + If [OptionValue[FCVerbose]===False, + psVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + psVerbose=OptionValue[FCVerbose] + ]; + ]; + + optContract = OptionValue[Contract]; + optPauliSigmaCombine = OptionValue[PauliSigmaCombine]; + optPauliOrder = OptionValue[PauliOrder]; + optEpsContract = OptionValue[EpsContract]; + optExpandScalarProduct = OptionValue[ExpandScalarProduct]; + optExpanding = OptionValue[Expanding]; + optPauliReduce = OptionValue[PauliReduce]; + (*optInsidePauliTrace = OptionValue[InsidePauliTrace];*) + + + If[ OptionValue[Factoring] === Automatic, + optFactoring = + Function[x, If[ LeafCount[x] < 5000, + Factor[x], + x + ] + ], + optFactoring = OptionValue[Factoring] + ]; + + FCPrint[1, "PauliSimplify: Entering.", FCDoControl->psVerbose]; + FCPrint[3, "PauliSimplify: Entering with ", expr, FCDoControl->psVerbose]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ OptionValue[FCCheckSyntax], + time=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: Checking the syntax", FCDoControl->psVerbose]; + FCCheckSyntax[ex,FCI->True]; + FCPrint[1, "PauliSimplify: Checking the syntax done", FCDoControl->psVerbose]; + FCPrint[1,"PauliSimplify: Done checking the syntax, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->psVerbose] + ]; + + If[ FreeQ2[ex,PauliHeadsList], + Return[ex] + ]; + + (* Here we separately simplify each chain of Pauli matrices *) + If[ OptionValue[FCPauliIsolate], + (* This is the standard mode for calling PauliSimplify *) + FCPrint[1,"PauliSimplify: Normal mode.", FCDoControl->psVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: Extracting Pauli objects.", FCDoControl->psVerbose]; + (* First of all we need to extract all the Pauli structures in the input. *) + ex = FCPauliIsolate[ex,FCI->True,Head->psHead, DotSimplify->True, PauliSigmaCombine->OptionValue[PauliSigmaCombine], + LorentzIndex->True, CartesianIndex->True]; + + (* + If[ !FreeQ[ex,PauliTrace] && !OptionValue[PauliTrace], + ex = ex /. psHead[zz_]/; !FreeQ[zz,PauliTrace] :> zz + ]; + *) + + {freePart,psPart} = FCSplit[ex,{psHead}]; + FCPrint[3,"PauliSimplify: psPart: ",psPart , FCDoControl->psVerbose]; + FCPrint[3,"PauliSimplify: freePart: ",freePart , FCDoControl->psVerbose]; + FCPrint[1, "PauliSimplify: Done extracting Pauli objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->psVerbose]; + + pauliObjects = Cases[psPart+null1+null2, psHead[_], Infinity]//Sort//DeleteDuplicates; + pauliObjectsEval = pauliObjects; + FCPrint[3,"PauliSimplify: pauliObjects: ", pauliObjects , FCDoControl->psVerbose]; + + (* + If[ OptionValue[PauliTraceEvaluate], + time=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: Calculating Pauli traces.", FCDoControl->psVerbose]; + pauliObjectsEval = pauliObjectsEval /. PauliTrace[zz_, opts:OptionsPattern[]] :> PauliTrace[zz, + PauliTraceEvaluate->True, Expand-> optExpandScalarProduct, opts]; + FCPrint[1, "PauliSimplify: Done calculating Pauli traces, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->psVerbose]; + FCPrint[3,"PauliSimplify: pauliObjects after calcuating Pauli traces: ", pauliObjects , FCDoControl->psVerbose] + + ]; + *) + + time=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: Applying pauliSimplifyEval", FCDoControl->psVerbose]; + + pauliObjectsEval = FeynCalc`Package`pauliTrickEvalFastFromPauliSimplifyList[(pauliObjectsEval/.psHead->Identity), + {False,False(*optInsidePauliTrace,optPauliOrder*)}]; + + pauliObjectsEval = pauliSimplifyEval/@pauliObjectsEval; + + FCPrint[3,"PauliSimplify: After pauliSimplifyEval: ", pauliObjectsEval, FCDoControl->psVerbose]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->psVerbose]; + + If[ !FreeQ2[pauliObjectsEval,{FeynCalc`Package`pauliTrickEvalFastFromPauliSimplifyList,pauliSimplifyEval,holdDOT}], + Message[PauliSimplify::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ]; + + FCPrint[1, "PauliSimplify: Inserting Pauli objects back.", FCDoControl->psVerbose]; + time=AbsoluteTime[]; + repRule = Thread[Rule[pauliObjects,pauliObjectsEval]]; + FCPrint[3,"PauliSimplify: repRule: ",repRule , FCDoControl->psVerbose]; + tmp = (psPart /. Dispatch[repRule]); + FCPrint[1, "PauliSimplify: Done inserting Pauli objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->psVerbose], + + (* This is a fast mode for input that is already isolated, e.g. for calling PauliSimplify/@exprList + from internal functions *) + FCPrint[1,"PauliSimplify: Fast mode.", FCDoControl->psVerbose]; + + tmp = FeynCalc`Package`pauliTrickEvalFastFromPauliSimplifySingle[ex, {tmpHead,False,False(* optInsidePauliTrace,optPauliOrder*)}]; + + (* It might happen that after pauliTrickEvalFast there are no Pauli matrices left.*) + + FCPrint[3,"PauliSimplify: After pauliTrickEvalFast: ", tmp , FCDoControl->psVerbose]; + + If[ !FreeQ2[tmp,{PauliHeadsList,tmpHead}], + tmp = tmp /. tmpHead -> pauliSimplifyEval + ]; + + If[ !FreeQ2[tmp,{FeynCalc`Package`pauliTrickEvalFastFromPauliSimplifySingle,pauliSimplifyEval,holdDOT}], + Message[PauliSimplify::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ] + ]; + + FCPrint[3, "PauliSimplify: Intermediate result: ", tmp, FCDoControl->psVerbose]; + + res = freePart + tmp; + + If[ optExpanding && OptionValue[Expand2], + time=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: Expanding the result.", FCDoControl->psVerbose]; + res = Expand2[res]; + FCPrint[1,"PauliSimplify: Expanding done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->psVerbose]; + FCPrint[3, "PauliSimplify: After expanding: ", res, FCDoControl->psVerbose] + ]; + + + If[ OptionValue[FCE], + res = FCE[res] + ]; + + (*res = ex;*) + FCPrint[1,"PauliSimplify: Leaving.", FCDoControl->psVerbose]; + FCPrint[3,"PauliSimplify: Leaving with ", res, FCDoControl->psVerbose]; + res + ]; + +pauliSimplifyEval[expr_]:= + Block[{tmp=expr, time, time2, res}, + + (* General algorithm of pauliSimplifyEval: + + 1) Apply PauliTrick to the unexpanded expression + 2) Expand the expression using DotSimplify and apply PauliTrick again + 3) If there are uncontracted indices, contract them + 4) If needed, expand scalar products + + 5) If needed, order the remaining Pauli matrices canonically + 6) If needed, factor the result + + *) + + + + FCPrint[1, "PauliSimplify: pauliSimplifyEval: Entering", FCDoControl->psVerbose]; + FCPrint[3, "PauliSimplify: pauliSimplifyEval: Entering with: ", tmp, FCDoControl->psVerbose]; + + + + (* First application of PauliTrick, no expansions so far *) + If[ !FreeQ[tmp, PauliSigma], + time=AbsoluteTime[]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Applying PauliTrick.", FCDoControl->psVerbose]; + tmp = PauliTrick[tmp, FCI -> True, (*InsidePauliTrace-> optInsidePauliTrace,*) FCPauliIsolate->False, PauliReduce->optPauliReduce]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: PauliTrick done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->psVerbose]; + FCPrint[3,"PauliSimplify: pauliSimplifyEval: After PauliTrick: ", tmp, FCDoControl->psVerbose] + ]; + + (* Expansion of Pauli slashes *) + If[ !optPauliSigmaCombine && !FreeQ[tmp, PauliSigma], + tmp = PauliSigmaExpand[tmp,FCI->True]; + ]; + + + If[ optExpanding && !FreeQ[tmp, PauliSigma], + time2=AbsoluteTime[]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Applying Dotsimplify.", FCDoControl->psVerbose]; + tmp = DotSimplify[tmp, FCI->True, Expanding -> True, FCJoinDOTs->False]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Dotsimplify done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->psVerbose]; + FCPrint[3,"PauliSimplify: pauliSimplifyEval: After Dotsimplify: ", tmp, FCDoControl->psVerbose]; + ]; + + If[ !FreeQ[tmp, PauliSigma], + + If[ optContract=!=False && !DummyIndexFreeQ[tmp,{LorentzIndex,CartesianIndex}], + time2=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: pauliSimplifyEval: Applying Contract.", FCDoControl->psVerbose]; + tmp = Contract[tmp, Expanding->True, EpsContract-> False, Factoring->False]; + FCPrint[1, "PauliSimplify: pauliSimplifyEval: Contract done, timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->psVerbose]; + FCPrint[3, "PauliSimplify: pauliSimplifyEval: After Contract: ", tmp, FCDoControl->psVerbose]; + + time2=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: pauliSimplifyEval: Applying EpsContract.", FCDoControl->psVerbose]; + If[ optEpsContract, + tmp = EpsContract[tmp,FCI->True] + ]; + FCPrint[1, "PauliSimplify: pauliSimplifyEval: EpsContract done, timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->psVerbose]; + FCPrint[3, "PauliSimplify: pauliSimplifyEval: After EpsContract: ", tmp, FCDoControl->psVerbose]; + + + ]; + + time2=AbsoluteTime[]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Applying PauliTrick.", FCDoControl->psVerbose]; + tmp = PauliTrick[tmp, FCI -> True, (*InsidePauliTrace-> optInsidePauliTrace,*) FCJoinDOTs->False, PauliReduce->optPauliReduce]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: PauliTrick done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->psVerbose]; + FCPrint[3,"PauliSimplify: pauliSimplifyEval: After PauliTrick: ", tmp, FCDoControl->psVerbose]; + ]; + + (* Doing index contractions *) + If[ optContract=!=False && !DummyIndexFreeQ[tmp,{LorentzIndex,CartesianIndex}], + time2=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: pauliSimplifyEval: Applying Contract.", FCDoControl->psVerbose]; + tmp = Contract[tmp, EpsContract-> False]; + FCPrint[1, "PauliSimplify: pauliSimplifyEval: Contract done, timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->psVerbose]; + + time2=AbsoluteTime[]; + FCPrint[1, "PauliSimplify: pauliSimplifyEval: Applying EpsContract.", FCDoControl->psVerbose]; + If[ optEpsContract, + tmp = EpsContract[tmp,FCI->True] + ]; + FCPrint[1, "PauliSimplify: pauliSimplifyEval: EpsContract done, timing: ", N[AbsoluteTime[] - time2, 4] , FCDoControl->psVerbose]; + FCPrint[3, "PauliSimplify: pauliSimplifyEval: After EpsContract: ", tmp, FCDoControl->psVerbose]; + ]; + + (* Expansion of the scalar products. *) + If[ optExpandScalarProduct && !FreeQ[tmp,Momentum], + time2=AbsoluteTime[]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Expanding scalar products", FCDoControl->psVerbose]; + tmp = ExpandScalarProduct[tmp,FCI->False]; + FCPrint[1,"PauliSimplify:pauliSimplifyEvale: Done expanding the result, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->psVerbose] + ]; + + (* Canonical ordering of the Pauli matrices. *) + If[ optPauliOrder, + time2=AbsoluteTime[]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Applying PauliOrder.", FCDoControl->psVerbose]; + tmp = PauliOrder[tmp, FCI->True, FCJoinDOTs->OptionValue[Expanding]]; + FCPrint[1,"PauliSimplify:pauliSimplifyEvale: Done applying PauliOrder, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->psVerbose] + ]; + + If[ optExpanding && (!optPauliSigmaCombine), + time2=AbsoluteTime[]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Applying Dotsimplify.", FCDoControl->psVerbose]; + tmp = DotSimplify[tmp, FCI->True, Expanding -> True]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Dotsimplify done, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->psVerbose]; + FCPrint[3,"PauliSimplify: pauliSimplifyEval: After Dotsimplify: ", tmp, FCDoControl->psVerbose]; + ]; + + (* Factoring *) + If[ optFactoring=!=False, + time2=AbsoluteTime[]; + FCPrint[1,"PauliSimplify: pauliSimplifyEval: Factoring the result.", FCDoControl->psVerbose]; + tmp = optFactoring[tmp]; + FCPrint[1,"PauliSimplify:pauliSimplifyEvale: Done factoring, timing: ", N[AbsoluteTime[] - time2, 4], FCDoControl->psVerbose] + ]; + + res = tmp; + + FCPrint[3,"PauliSimplify: pauliSimplifyEval: Leaving with: ", res, FCDoControl->psVerbose]; + + res + + + ]; + +FCPrint[1,"PauliSimplify.m loaded."]; +End[] diff --git a/FeynCalc/Pauli/PauliTrick.m b/FeynCalc/Pauli/PauliTrick.m new file mode 100755 index 000000000..5276261be --- /dev/null +++ b/FeynCalc/Pauli/PauliTrick.m @@ -0,0 +1,384 @@ +(* ::Package:: *) + + + +(* :Title: PauliTrick *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Contraction and simplification rules for Pauli matrices *) + +(* ------------------------------------------------------------------------ *) + +PauliTrick::usage = +"PauliTrick[exp] contracts sigma matrices with each other and \ +performs several simplifications (no expansion, use PauliSimplify for this)."; + +PauliTrick::failmsg = +"Error! PauliTrick has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + + + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] + +pauliTrickEvalFastFromPauliSimplifyList + +End[] + +Begin["`PauliTrick`Private`"] + +paTrVerbose::usage=""; +pauliReduce::usage=""; +optJoin::usage=""; +pasi::usage=""; +tmpli::usage=""; + +Options[PauliTrick] = { + Expanding -> False, + FCE -> False, + FCI -> False, + FCJoinDOTs -> False, + FCPauliIsolate -> True, + FCVerbose -> False, + PauliSigmaCombine -> False, + PauliReduce -> True +}; + +pauliTrickEvalFastFromPauliSimplifyList[pauliObjects_List, {(*optInsidePauliTrace*)_, (*optPauliOrder*)_}]:= + Block[{(*tmp1,tmp2,*) res}, + (*tmp1 = insideDiracTrace; + tmp2 = diracOrder; + insideDiracTrace = optInsidePauliTrace; + pauliOrder = optPauliOrder;*) + res = (pauliTrickEvalFast/@pauliObjects) /. pauliTrickEvalFast->Identity; + (*insidePauliTrace = tmp1; + diracOrder = tmp2;*) + res + ]; + + +pauliTrickEvalFastFromPauliSimplifySingle[pauliObject_, {tmpHead_, (*optInsidePauliTrace*)_, (*optPauliOrder*)_}]:= + Block[{(*tmp1,tmp2,*) res}, + (*tmp1 = insideDiracTrace; + tmp2 = diracOrder; + insideDiracTrace = optInsidePauliTrace; + diracOrder = optPauliOrder;*) + res = pauliTrickEvalFast[pauliObject] /. pauliTrickEvalFast->tmpHead; + (*insideDiracTrace = tmp1; + diracOrder = tmp2;*) + res + ]; + +PauliTrick[expr_,OptionsPattern[]] := + Block[{ res, tmp, ex, null1, null2, holdDOT, freePart, paPart, pauliObjects, + pauliObjectsEval, repRule, time, paHead}, + + (* Algorithm of PauliTrick: + + x) Isolate all Pauli objects and handle them separately. Of course there is an extra option + to skip this if the input is already a single object (e.g. when PauliTrick is called by + PauliTrace or PauliSimplify) Then apply the evaluating function to each of the objects, + create replacement rules (standard) and substitute the results back. + + x) The inner working of the evaluating function: + xx) Check the dimension of the chain, could be purely 4-dim, purely D-dim or mixed (BMHV). + Also check that BMHV was indeed activated if mixed dimensions appear + + xx) Then we do all the simplifications. + *) + + optJoin = OptionValue[FCJoinDOTs]; + pauliReduce = OptionValue[PauliReduce]; + + If [OptionValue[FCVerbose]===False, + paTrVerbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + paTrVerbose=OptionValue[FCVerbose] + ]; + ]; + + FCPrint[1, "PauliTrick. Entering.", FCDoControl->paTrVerbose]; + FCPrint[3, "PauliTrick: Entering with ", expr, FCDoControl->paTrVerbose]; + + If[ OptionValue[FCI], + ex = expr, + ex = FCI[expr] + ]; + + If[ FreeQ2[ex,PauliHeadsList], + Return[ex] + ]; + + + + If[ OptionValue[FCPauliIsolate], + (* This is the standard mode for calling PauliTrick *) + FCPrint[1,"PauliTrick: Normal mode.", FCDoControl->paTrVerbose]; + time=AbsoluteTime[]; + FCPrint[1, "PauliTrick: Extracting Pauli objects.", FCDoControl->paTrVerbose]; + (* First of all we need to extract all the Pauli structures in the input. *) + ex = FCPauliIsolate[ex,FCI->True,Head->paHead, DotSimplify->True, PauliSigmaCombine->OptionValue[PauliSigmaCombine],LorentzIndex->True, + FCJoinDOTs -> optJoin]; + + {freePart,paPart} = FCSplit[ex,{paHead}]; + FCPrint[3,"PauliTrick: paPart: ",paPart , FCDoControl->paTrVerbose]; + FCPrint[3,"PauliTrick: freePart: ",freePart , FCDoControl->paTrVerbose]; + FCPrint[1, "PauliTrick: Done extracting Pauli objects, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->paTrVerbose]; + + pauliObjects = Cases[paPart+null1+null2, paHead[_], Infinity]//Union; + FCPrint[3,"PauliTrick: pauliObjects: ",pauliObjects , FCDoControl->paTrVerbose]; + + time=AbsoluteTime[]; + FCPrint[1, "PauliTrick: Applying PauliTrickEval", FCDoControl->paTrVerbose]; + + pauliObjectsEval = Map[(pauliTrickEvalFast[#]/. pauliTrickEvalFast->PauliTrickEval)&, (pauliObjects/.paHead->Identity)]; + FCPrint[3,"PauliTrick: After PauliTrickEval: ", pauliObjectsEval, FCDoControl->paTrVerbose]; + FCPrint[1,"PauliTrick: PauliTrickEval done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->paTrVerbose]; + + If[ !FreeQ2[pauliObjectsEval,{pauliTrickEvalFast,PauliTrickEval,holdDOT}], + Message[PauliTrick::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ]; + FCPrint[1, "PauliTrick: Inserting Pauli objects back.", FCDoControl->paTrVerbose]; + time=AbsoluteTime[]; + repRule = Thread[Rule[pauliObjects,pauliObjectsEval]]; + FCPrint[3,"PauliTrick: repRule: ",repRule , FCDoControl->paTrVerbose]; + res = freePart + (paPart/. Dispatch[repRule]); + FCPrint[1, "PauliTrick: Done inserting Pauli objects back, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->paTrVerbose], + + FCPrint[1,"PauliTrick: Fast mode.", FCDoControl->paTrVerbose]; + (* This is a fast mode for input that is already isolated, e.g. for calling PauliTrick/@exprList + from internal functions *) + res = pauliTrickEvalFast[ex]; + + (* It might happen that after pauliTrickEvalFast there are no Pauli matrices left.*) + + FCPrint[3,"PauliTrick: After pauliTrickEvalFast: ", res , FCDoControl->paTrVerbose]; + + If[ !FreeQ2[res,{PauliHeadsList,pauliTrickEvalFast}], + res = res /. pauliTrickEvalFast->PauliTrickEval + ]; + + If[ !FreeQ2[res,{pauliTrickEvalFast,PauliTrickEval,holdDOT}], + Message[PauliTrick::failmsg,"Evaluation of isolated objects failed."]; + Abort[] + ] + ]; + + + If[ OptionValue[Expanding], + time=AbsoluteTime[]; + FCPrint[1, "PauliTrick: Expanding the result.", FCDoControl->paTrVerbose]; + res = Expand[res]; + FCPrint[1,"PauliTrick: Expanding done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->paTrVerbose]; + FCPrint[3, "PauliTrick: After expanding: ", res, FCDoControl->paTrVerbose] + ]; + + If[ OptionValue[FCE], + res = FCE[res] + + ]; + + FCPrint[1, "PauliTrick. Leaving.", FCDoControl->paTrVerbose]; + FCPrint[3, "PauliTrick: Leaving with ", res, FCDoControl->paTrVerbose]; + + res + ]; + +(* Here we can quickly handle trivial contractions of short expressions *) + +pauliTrickEvalFast[ex:PauliSigma[__]]:= + ex; + +pauliTrickEvalFast[DOT[b___,PauliSigma[l_LorentzIndex, dim_:3], PauliSigma[l_LorentzIndex, dim_:3], d___]] := + (FeynCalc`Package`MetricT + FeynCalc`Package`MetricS dim) pauliTrickEvalFast[DOT[ b,d ]]/;!MatchQ[dim,_Symbol-4]; + +pauliTrickEvalFast[DOT[b___,PauliSigma[l_LorentzIndex, dim_Symbol-4], PauliSigma[l_LorentzIndex, dim_Symbol-4], d___]] := + FeynCalc`Package`MetricS (dim-4) pauliTrickEvalFast[DOT[ b,d ]]; + +pauliTrickEvalFast[DOT[b___,PauliSigma[l_CartesianIndex, dim_:3], PauliSigma[l_CartesianIndex, dim_:3], d___]] := + dim pauliTrickEvalFast[DOT[ b,d ]]; + +pauliTrickEvalFast[DOT[b___,PauliSigma[c_Momentum, dim___], PauliSigma[c_Momentum, dim___], d___ ]] := + FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] pauliTrickEvalFast[DOT[b,d]]; + +pauliTrickEvalFast[DOT[b___,PauliSigma[c_CartesianMomentum, dim___], PauliSigma[c_CartesianMomentum, dim___], d___ ]] := + FCUseCache[ExpandScalarProduct,{CartesianPair[c,c]},{}] pauliTrickEvalFast[DOT[b,d]]; + + + +pauliTrickEvalFast[DOT[]]:= + 1; + +PauliTrickEval[ex_/;Head[ex]=!=PauliSigma]:= + Block[{res=ex, holdDOT, time, dim, noncommPresent,null1,null2,paHead}, + + FCPrint[1, "PauliTrick: PauliTrickEval: Entering.", FCDoControl->paTrVerbose]; + FCPrint[3, "PauliTrick: PauliTrickEval: Entering with", ex , FCDoControl->paTrVerbose]; + + res = res/. DOT -> holdDOT; + + If[ !FreeQ[res,Pair], + res = Expand2[res,Pair]/. Pair->PairContract /. PairContract->Pair; + ]; + + If[ !FreeQ[res,CartesianPair], + res = Expand2[res,CartesianPair]/. CartesianPair->CartesianPairContract /. CartesianPairContract->CartesianPair; + ]; + + + If[ FreeQ2[res,PauliHeadsList], + Return[res] + ]; + + dim = FCGetDimensions[res]; + + + noncommPresent = !NonCommFreeQ[res/.PauliSigma->pasi]; + FCPrint[3, "PauliTrick: PauliTrickEval: unknown non-commutative objects present:", noncommPresent, FCDoControl->paTrVerbose]; + + FCPrint[3, "PauliTrick: PauliTrickEval: Dimensions:", dim, FCDoControl->paTrVerbose]; + + + FCPrint[1, "PauliTrick: PauliTrickEval: Doing simplifications.", FCDoControl->paTrVerbose]; + Which[ + (* Purely 4- or 3-dimensional *) + MatchQ[dim,{}|{3}|{4}|{3,4}], + FCPrint[1, "PauliTrick: PauliTrickEval: Purely 4-dim.", FCDoControl->paTrVerbose]; + res = res /. holdDOT -> pauli4Dim /. pauli4Dim -> holdDOT; + FCPrint[3, "PauliTrick: PauliTrickEval: After pauli4Dim: ", res, FCDoControl->paTrVerbose], + (* Purely D-dimensional *) + MatchQ[dim,{_Symbol-1}|{_Symbol}|{_Symbol,_Symbol-1}|{_Symbol-1,_Symbol}], + FCPrint[1, "PauliTrick: PauliTrickEval: Purely D-dim.", FCDoControl->paTrVerbose]; + res = res /. holdDOT -> pauliDDim /. pauliDDim -> holdDOT; + FCPrint[3, "PauliTrick: PauliTrickEval: After pauliDDim: ", res, FCDoControl->paTrVerbose], + (* Anything else is most likely an error *) + True, + Message[PauliTrick::failmsg,"Unsupported combination of dimensions!"]; + Abort[] + ]; + FCPrint[1, "PauliTrick: PauliTrickEval: Done with simplifications.", FCDoControl->paTrVerbose]; + + res = res /. holdDOT -> DOT; + + FCPrint[1, "PauliTrick: PauliTrickEval: Leaving.", FCDoControl->paTrVerbose]; + FCPrint[3, "PauliTrick: PauliTrickEval: Leaving with ", res, FCDoControl->paTrVerbose]; + res + ]; + + +(* ------------------------------------------------------------------------ *) + + +pauli4Dim[]:= + 1; + +(*TODO More relations for Lorentz indices.*) +(* (si^mu p^mu) (si^nu p^nu) *) +pauli4Dim[b___, PauliSigma[c_Momentum], PauliSigma[c_Momentum], d___ ] := + FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] pauli4Dim[b,d]; + +(* si^mu si_mu *) +pauli4Dim[b___,PauliSigma[l_LorentzIndex], PauliSigma[l_LorentzIndex], d___] := + (FeynCalc`Package`MetricT + 3 FeynCalc`Package`MetricS) pauli4Dim[b, d]; + +(* si^i si^i *) +pauli4Dim[b___, PauliSigma[l_CartesianIndex], PauliSigma[l_CartesianIndex], d___] := + 3 pauli4Dim[b,d]; + +(* (si^i p^i) (si^i p^i) *) +pauli4Dim[b___, PauliSigma[c_CartesianMomentum], PauliSigma[c_CartesianMomentum], d___ ] := + FCUseCache[ExpandScalarProduct,{CartesianPair[c,c]},{}] pauli4Dim[b,d]; + +(* si^i si^j ... s^i / si.p si^j ... s.p *) +pauli4Dim[b___,PauliSigma[(c1: _CartesianMomentum | _CartesianIndex)], PauliSigma[(c2: _CartesianMomentum | _CartesianIndex)], d___ ]/;c1=!=c2 := + ( + tmpli= CartesianIndex[$MU[Unique[]]]; + ((FCUseCache[ExpandScalarProduct,{CartesianPair[c1,c2]},{}] pauli4Dim[b,d] + I Eps[c1,c2,tmpli] pauli4Dim[b,PauliSigma[tmpli],d])/. + CartesianPair->CartesianPairContract /. CartesianPairContract->CartesianPair) + )/; pauliReduce; + + +(* si^i .... si^i *) +pauli4Dim[b___, PauliSigma[c1_CartesianIndex], ch:PauliSigma[(_CartesianMomentum | _CartesianIndex )]..., PauliSigma[c1_CartesianIndex], d___ ] := + Block[ {iVar, len = Length[{ch}]}, + (-1)^len pauli4Dim[b,ch,d] + 2 Sum[(-1)^(iVar+1) pauli4Dim@@Join[{b},Drop[{ch},{iVar, iVar}],{ch}[[iVar;;iVar]],{d}], {iVar, 1,len-1}] + ]/; (Length[{ch}]>0) /; !pauliReduce; + + +(* si.p .... si.p *) +pauli4Dim[b___, PauliSigma[c1_CartesianMomentum], ch:PauliSigma[(_CartesianMomentum | _CartesianIndex )]..., PauliSigma[c1_CartesianMomentum], d___ ] := + Block[ {iVar, len = Length[{ch}]}, + (-1)^len pauli4Dim[b,ch,d] FCUseCache[ExpandScalarProduct,{CartesianPair[c1,c1]},{}] + + 2 Sum[(-1)^(iVar+1) FCUseCache[FCFastContract,{CartesianPair[c1,{ch}[[iVar,1]]] pauli4Dim@@Join[{b},Drop[{ch},{iVar, iVar}],{PauliSigma[c1],d}]},{}], {iVar, 1,len}] + ]/; (Length[{ch}]>0) /; !pauliReduce; + + +(* ------------------------------------------------------------------------ *) + + +pauliDDim[]:= + 1; + + +(*TODO More relations for Lorentz indices.*) +(* si^mu si_mu *) +pauliDDim[b___,PauliSigma[l_LorentzIndex, dim_-1], PauliSigma[l_LorentzIndex, dim_-1], d___] := + (FeynCalc`Package`MetricT + (dim-1) FeynCalc`Package`MetricS) pauliDDim[b, d]; + +(* (si^mu p^mu) (si^nu p^nu) *) +pauliDDim[b___,PauliSigma[c_Momentum, dim_-1], PauliSigma[c_Momentum, dim_-1], d___ ] := + FCUseCache[ExpandScalarProduct,{Pair[c,c]},{}] pauliDDim[b,d]; + +(* si^i si^i *) +pauliDDim[b___,PauliSigma[l_CartesianIndex, dim_-1], PauliSigma[l_CartesianIndex, dim_-1], d___] := + (dim-1) pauliDDim[b,d]; + +(* (si^i p^i) (si^i p^i) *) +pauliDDim[b___,PauliSigma[c_CartesianMomentum, dim_-1], PauliSigma[c_CartesianMomentum, dim_-1], d___ ] := + FCUseCache[ExpandScalarProduct,{CartesianPair[c,c]},{}] pauliDDim[b,d]; + +(* si^i si^j *) +pauliDDim[b___,PauliSigma[(c1: _CartesianMomentum | _CartesianIndex),dim_-1], PauliSigma[(c2: _CartesianMomentum | _CartesianIndex),dim_-1], d___ ]/;c1=!=c2 := + ( + tmpli= CartesianIndex[$MU[Unique[]],dim-1]; + FCUseCache[ExpandScalarProduct,{CartesianPair[c1,c2]},{}] pauliDDim[b,d] + I Eps[c1,c2,tmpli] pauliDDim[b,PauliSigma[tmpli,dim-1],d] + )/; pauliReduce && FeynCalc`Package`PauliSigmaScheme==="Naive"; + + +(* si^i .... si^i *) +pauliDDim[b___, PauliSigma[c1_CartesianIndex, dim_-1], ch:PauliSigma[(_CartesianMomentum | _CartesianIndex ) ,dim_-1]..., PauliSigma[c1_CartesianIndex,dim_-1], d___ ] := + Block[ {iVar, len = Length[{ch}]}, + (-1)^len (dim-3) pauliDDim[b,ch,d] + 2 Sum[(-1)^(iVar+1) pauliDDim@@Join[{b},Drop[{ch},{iVar, iVar}],{ch}[[iVar;;iVar]],{d}], {iVar, 1,len-1}] + ]/; (Length[{ch}]>0) /; !pauliReduce || (pauliReduce && FeynCalc`Package`PauliSigmaScheme=!="Naive"); + + +(* si.p .... si.p *) +pauliDDim[b___, PauliSigma[c1_CartesianMomentum, dim_-1], ch:PauliSigma[(_CartesianMomentum | _CartesianIndex ), dim_-1]..., PauliSigma[c1_CartesianMomentum, dim_-1], d___ ] := + Block[ {iVar, len = Length[{ch}]}, + (-1)^len pauliDDim[b,ch,d] FCUseCache[ExpandScalarProduct,{CartesianPair[c1,c1]},{}] + + 2 Sum[(-1)^(iVar+1) FCUseCache[FCFastContract,{CartesianPair[c1,{ch}[[iVar,1]]] pauliDDim@@Join[{b},Drop[{ch},{iVar, iVar}],{PauliSigma[c1, dim -1],d}]},{}], {iVar, 1,len}] + ]/; (Length[{ch}]>0) /; !pauliReduce || (pauliReduce && FeynCalc`Package`PauliSigmaScheme=!="Naive"); + + +(* +(* si^i si^j ... s^i / si.p si^j ... s.p *) +pauliDDim[b___, PauliSigma[(c1: _CartesianMomentum | _CartesianIndex),dim_-1], + PauliSigma[(c2: _CartesianMomentum | _CartesianIndex),dim_-1], + ch:PauliSigma[(CartesianMomentum | CartesianIndex )[_, dim_-1],dim_-1]..., + PauliSigma[(c1: _CartesianMomentum | _CartesianIndex),dim_-1], d___ ]/;c1=!=c2 := + ( + -pauliDDim[b, PauliSigma[c2,dim-1], PauliSigma[c1,dim-1], ch, PauliSigma[c1,dim-1], d] + + 2 FCUseCache[ExpandScalarProduct,{CartesianPair[c1,c2]},{}] pauliDDim[b, ch, PauliSigma[c1,dim-1], d] + )/; FeynCalc`Package`PauliSigmaScheme=!="Naive"; +*) +FCPrint[1,"PauliTrick.m loaded."]; +End[] diff --git a/FeynCalc/Phi/Channels.m b/FeynCalc/Phi/Channels.m deleted file mode 100644 index a5be7763c..000000000 --- a/FeynCalc/Phi/Channels.m +++ /dev/null @@ -1,1890 +0,0 @@ -(* Wolfram Language package *) - -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: Channels (Phi) *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Utilities for kinematics, isospin, etc *) - -(* ------------------------------------------------------------------------ *) - -MassArguments::usage = -"MassArguments is an option for AmplitudeProjection relevant when \ -OnMassShell is set to True, specifying the optional extra arguments supplied \ -to ParticleMass. Default value : {RenormalizationState[0]}."; - -FieldProjection::usage = -"FieldProjection[IsoVector[QuantumField[Particle[p]]],opts] returns the \ -field specified by the option Channel as a linear combination of the \ -isospin components of QuantumField[Particle[p]]."; - -AmplitudeProjection::usage = -"AmplitudeProjection[amp,opts], where amp[i1,i2,...] is a function of the \ -isospin indices i1, i2, ... of the external particles, returns the amplitude \ -of the channel specified by the option Channel. AmplitudeProjection uses the \ -rules specified in $IsoSpinProjectionRules. NOTICE: For the particles under \ -consideration, PHI must know their anti-particles. That is, e.g. \ -ChargeConjugate[PionPlus] is PionMinus."; - - -$IsoSpinProjectionRules::usage = -"$IsoSpinProjectionRules is a set of rules used by FieldProjection and \ -AmplitudeProjection to project out in channels. Changing the default setting \ -of this quantity should be done with care. Notice that the setting of \ -$IsoSpinProjectionRules is related to the values of \ -WriteOutUmatrices[UGeneratorMatrix[i,opts]], where i is an integer. The \ -default set of rules is not very large, but more rules in the same syntax may \ -easily be added."; - -$SUNCompletenessRules::usage = -"$SUNCompletenessRules is an environment \ -variable used by SUNReduce to (hopefully) simplify expressions involving products of \ -traces of products of generator matrices (UMatrix[UGenerator[SUNIndex[j]]]) \ -with other matrices."; - -Channel::usage = -"Channel is an option of FieldProjection and AmplitudeProjection, \ -specifying which channel the field or amplitude should be projected out in. \ -For FieldProjection, the possible settings are listed in $Particles. For \ -AmplitudeProjection, the possible settings are \ -{{p1,p2,...}->{pp1,pp2,...},{i,...}}, where p1,.. and pp1,... are generic \ -particles from $Particles like Pion etc. and i is the isospin, or simply \ -{{p1,p2,...}->{pp1,pp2,...}}, where p1,.. and pp1,... now have to be \ -iso-eigenstates like PionPlus etc.. Default value : PionPlus for \ -FieldProjection and {{Pion,Pion}->{Pion,Pion},{2}} for AmplitudeProjection."; - -USum::usage = -"USum is a summation that works like Sum. It may be faster that Sum for \ -multiple summations where each summation reduces the number of terms. This \ -is typically the case in isospin indices summations."; - -USumHeld::usage = -"USumHeld is a symbol substituted for USum when the option HoldSums of \ -SUNReduce is set to True."; - -SUNReduce::usage = -"SUNReduce[a] finds SU(n) objects, simplifies using SU(2) or SU(3) rules \ -and sums over pairs of indices not in $ConstantIsoIndices. Indices are \ -summed over only if they have head SUNIndex. NOTICE: With the option \ -Explicit set to True, large expressions that can be expanded to \ -a sum, should be expanded before applying SUNReduce (this will reduce \ -computation time dramatically)."; - -SUDFSymmetrize::usage = -"SUDFSymmetrize[exp] renames factors multiplying SUND[i,j,k], \ -SU3D[i,j,k], SUNF[i,j,k], SU2F[i,j,k] or SU3F[i,j,k] in an attempt to \ -reduce exp."; - -IsoFunction::usage = -"IsoFunction is a head recognized by SUNReduce, so that for e.g. \ -IsoFunction[f][SUNIndex[i]*SUNDelta[SUNIndex[i],SUNIndex[j]] ocurring in an \ -expression will imply a sum over SUNIndex[i]."; - -HoldSums::usage = -"HoldSums is an option for SUNReduce relevant \ -when the option Explicit is set to True. When set to True, the \ -isospin summations are not performed and USum is substituted with USumHeld. \ -Default value : True."; - -IndicesCleanup::usage = -"IndicesCleanup[expr] renames dummy indices in expr in a systematic way \ -in order to get cancellations and a simpler expression. The expression expr \ -should be in PHI notation, that is, involving the products NM and/or Times, \ -not DOT or NonCommutativeMultiply.\n -NOTICE : IndicesCleanup does not work \ -properly when the indices are nested more than one level down in factors. \ -The only exceptions to this are terms like NM[UTrace[NM[a]],UTrace[NM[b]]] with \ -a and b having isospin or Lorentz index dependence. For these however, it may \ -be necessary to apply IndicesCleanup repeatedly.\n -NOTICE : IndicesCleanup does not work for D-dimensional Lorentz indices like \ -LorentzIndex[li, D]."; - -CNM::usage = -"CNM[a,b] renames contracted Lorentz and SU(N) indices."; - -ExtendedCleanup::usage = -"ExtendedCleanup is an option for IndicesCleanup. When set to True, \ -contractions within a mixing of Times and NM will also be renamed, so that in \ -a mixed product there will be no multiple pairs of the same index. When set \ -to False, there will be multiple pairs of the same index in mixed products. \ -This will give wrong results with e.g. FeynRule. Default value : True."; - -FCleanup::usage = -"FCleanup is an option for IndicesCleanup. When set to True, special \ -attention is given to renaming the indices of SU2F, SU3F and SUNF in order to \ -get cancellations. Default value : False."; - -IsoDummy::usage = -"IsoDummy is a head used by IndicesCleanup for temporary renaming of \ -indices."; - -NM1::usage = -"NM1 is a head used by IndicesCleanup for temporary renaming of Times."; - -NM2::usage = -"NM2 is a head used by IndicesCleanup for temporary renaming of DOT."; - -IsoExternDummy::usage = -"IsoExternDummy is a head used by IndicesCleanup for temporary renaming \ -of indices."; - -IsoInternDummy::usage = -"IsoInternDummy is a head used by IndicesCleanup for temporary renaming \ -of indices."; - -LorentzDummy::usage = -"LorentzDummy is a head used by IndicesCleanup for temporary renaming of \ -indices."; - -LorentzExternDummy::usage = -"LorentzExternDummy is a head used by IndicesCleanup for temporary \ -renaming of indices."; - -LorentzInternDummy::usage = -"LorentzInternDummy is a head used by IndicesCleanup for temporary \ -renaming of indices."; - -DerivativeExternDummy::usage = -"DerivativeExternDummy is a head used by IndicesCleanup for temporary \ -renaming of indices."; - -DerivativeInternDummy::usage = -"DerivativeInternDummy is a head used by IndicesCleanup for temporary \ -renaming of indices."; - -IsoDummys::usage = -"IsoDummys is an option for IndicesCleanup and CNM. It should be a list of two \ -three strings. Default value : {\"j\",\"k\",\"l\"}."; - -LorentzDummys::usage = -"LorentzDummys is an option for IndicesCleanup and CNM. It should be a list of \ -five strings. Default value : {\"\[Xi]\",\"\[Rho]\",\"\[Sigma]\",\"\[Tau]\",\ -\"\[Omega]\"}."; - - -Begin["`Package`"] -End[] - -Begin["`Channels`Private`"]; - -(* -Boxes -*) - -sumstart[{_, ss_, _, _}] := - ss; - -sumstart[{_, ss_, _}] := - ss; - -sumstart[{_, _}] := - 1; - -sumstart[{_}] := - 1; - -sumvar[{ss_, __}] := - MakeBoxes[TraditionalForm[ss]]; - -sumvar[{_}] := - "."; - -sv[bb__, rr_] := - sumvar[{bb}[[rr]]]; - -sumeq[{_}] := - "."; - -sumeq[{_, __}] := - "=."; - -USumHeld /: - MakeBoxes[USumHeld[a__, b : _List ..], TraditionalForm] := - RowBox[Join[Table[UnderoverscriptBox["\[CapitalSigma]", - RowBox[{sv[b, rep], sumeq[{b}[[rep]]], - sumstart[{b}[[rep]]]}], {b}[[rep]][[-1]]], {rep, - Length[{b}]}], {MakeBoxes[TraditionalForm[a]]}]]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* FeynCalc functions *) -fccombs := - fccombs = MakeFeynCalcPrivateContext["CombinationLists"]; -(* FeynArts functions *) - -faso := - faso = FeynArts`SumOver; - -(* Defaults *) - -$IsoSpinProjectionRules = {PionPlus -> (Iso[PhiMeson, {1}] - - I*Iso[PhiMeson, {2}])/Sqrt[2], - PionMinus -> (Iso[PhiMeson, {1}] + I*Iso[PhiMeson, {2}])/Sqrt[2], - PionZero -> Iso[PhiMeson, {3}], - KaonPlus -> (Iso[PhiMeson, {4}] - I*Iso[PhiMeson, {5}])/Sqrt[2], - KaonMinus -> (Iso[PhiMeson, {4}] + I*Iso[PhiMeson, {5}])/Sqrt[2], - KaonZero -> (Iso[PhiMeson, {6}] - I*Iso[PhiMeson, {7}])/Sqrt[2], - KaonZeroBar -> (Iso[PhiMeson, {6}] + I*Iso[PhiMeson, {7}])/Sqrt[2], - EtaMeson -> Iso[PhiMeson, {8}]}; -Options[FieldProjection] = {Channel -> PionPlus}; -Options[AmplitudeProjection] = {Channel -> {{Pion, Pion} -> {Pion, - Pion}, 2}, (*CommutatorReduce -> True,*) OnMassShell -> True, - MassArguments -> {RenormalizationState[0]}, - MomentumVariablesString -> "p"(*, HoldSums -> False, - Explicit -> True, SUNN -> 2*)(*Dunno what these options were doing here. 5.4.2002*)}; -Options[SUNReduce] = {HoldSums -> True, CommutatorReduce -> False, - Explicit -> False, FullReduce -> False, SUNN -> 2, - UDimension -> Automatic(*Commented out 11/5-2003*)(*, RemoveIntegerIndices -> False*)}; -Options[IndicesCleanup] := - {IsoDummys -> {"j", "k", "l"}, - LorentzDummys -> {"\[Xi]", "\[Rho]", "\[Sigma]", "\[Tau]", "\[Omega]"}, - ExtendedCleanup -> True, FCleanup -> False, CommutatorReduce -> True}; -Options[CNM] = {IsoDummys -> {"p", "q", "r", "s"}, - LorentzDummys -> {"\[Zeta]", "\[Eta]", "\[Theta]", "\[Kappa]"}} - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Isospin simplification and summation *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* A summation function for multiple sums that remembers previously calculated - sums and uses these for the ensuing summations: *) - -USum[a_, b___List] := - (sumlims[i_] := - ({b}[[i]]); - recfun[0] = a; - Do[recfun[rep] = - Sum1[recfun[rep - 1], sumlims[rep]] /. Sum1 -> Sum, {rep, 1, - Length[{b}]}]; - recfun[Length[{b}]]); -USum[a_, {}] := - a; -USumHeld[a_] := - a; - - - -(* Finding pairs in a list of indices (ignoring integers and elements from - $ConstantIsoIndices): *) - -su3summationindices[{a__}, gennr2_] := - (us = (Complement[ - Union[Complement[Sort[Flatten[{a}]], - Sort[Flatten[{a}]] //. {cc___, b_, b_, c___} -> {cc, c}]], - Join[$ConstantIsoIndices, - SUNIndex/@ $ConstantIsoIndices]]) //. {{cc___, _Integer, - c___} -> {cc, c}, {cc___, (fcsuni|ExplicitSUNIndex)[_Integer], c___} -> {cc, c}}; - Table[{removesun[us[[icount]]], gennr2}, {icount, Length[us]}]); -su3summationindices[{}, ___] := - {}; - - - -(* Support functions for SUNReduce for removing SUNIndex and UIndex heads: *) - -removesun[(SUNIndex| ExplicitSUNIndex | UIndex)[iii_]] := - iii; -removesun[iii /; FreeQ[iii, (SUNIndex| ExplicitSUNIndex | UIndex)]] := - iii; - - - -(* Support functions for SUNReduce for removing SUNIndex and UIndex heads from - constants: *) - -removesunc[(SUNIndex| ExplicitSUNIndex | UIndex)[iii_]] /; - (IntegerQ[iii] || (!FreeQ[$ConstantIsoIndices, iii])) := - tmpsuni[iii]; -removesunc[(SUNIndex| ExplicitSUNIndex)[iii_]] /; - (!IntegerQ[iii] && (FreeQ[$ConstantIsoIndices, iii])) := - fcsuni[iii]; -removesunc[UIndex[iii_]] /; - (!IntegerQ[iii] && (FreeQ[$ConstantIsoIndices, iii])) := - UIndex[iii]; -removesunc[iii_] /; FreeQ[{iii}, (SUNIndex| ExplicitSUNIndex | UIndex)] := - iii; - - - - -(* Adding a head to the inner index of PhiProjection: *) -(* This PhiProjection business is not necessary. Dropped, 11/5-2003 *) -(*NTo3Rules1 = (PhiProjection[pa_, ___][pb_]) :> SUNDelta[pa, pb];*) -NTo3Rules3 = {(SUNDelta|SU2Delta|SU3Delta)[i_, j:((fcsuni(*|ExplicitSUNIndex*)(*Bug fix, 11/5-2003*))[_])]* - QuantumField[a___, j_, b___][x_] -> - QuantumField[a, fcsuni[i], b][x]}; - - - -(* Removing heads from constants and changing from FeynCalc to PHI functions: *) - -NTo3Rules2[2] = {SU2D[_, _, _] :> 0, - SU2F[x1_, x2_, x3_] :> - SU2F[removesunc[x1], removesunc[x2], removesunc[x3]], - SU2Delta[x1_, x2_] :> SU2Delta[removesunc[x1], removesunc[x2]], - SUND[_, _, _] :> 0, - SUNF[x1_, x2_, x3_] :> - SU2F[removesunc[x1], removesunc[x2], removesunc[x3]], - SUNDelta[x1_, x2_] :> SU2Delta[removesunc[x1], removesunc[x2]]}; -NTo3Rules2[3] = {SU3D[x1_, x2_, x3_] :> - SU3D[removesunc[x1], removesunc[x2], removesunc[x3]], - SU3F[x1_, x2_, x3_] :> - SU3F[removesunc[x1], removesunc[x2], removesunc[x3]], - SU3Delta[x1_, x2_] :> SU3Delta[removesunc[x1], removesunc[x2]], - SUND[x1_, x2_, x3_] :> - SU3D[removesunc[x1], removesunc[x2], removesunc[x3]], - SUNF[x1_, x2_, x3_] :> - SU3F[removesunc[x1], removesunc[x2], removesunc[x3]], - SUNDelta[x1_, x2_] :> SU3Delta[removesunc[x1], removesunc[x2]]}; -NTo3iRules2[2] = {SUND[_, _, _] :> 0, SUNF :> SU2F, - SUNDelta :> SU2Delta}; -NTo3iRules2[3] = {SUND :> SU3D, SUNF :> SU3F, SUNDelta :> SU3Delta}; - -NTo3Rules2[_] = {}; -NTo3iRules2[_] = {}; - - - -(* A function for selecting the members of a list with head SUNIndex: *) - -su3test[a_] := - {} /; Head[a]=!=SUNIndex; -su3test[a_SUNIndex] := - a; -su3list[{a___}] := - Flatten[su3test /@ Flatten[{a}]]; - - - -(* Distributivity: *) - -SUNReduce1[aa_, OptionsPattern[]] /; (FreeQ[aa, SUNIndex| ExplicitSUNIndex]) := - aa; -SUNReduce1[aa_ bb_, opts:OptionsPattern[]] /; (FreeQ[aa, SUNIndex| ExplicitSUNIndex]) := - aa*SUNReduce1[bb, opts]; -SUNReduce1[aa_Plus, opts___] := - SUNReduce1[#, opts] & /@ aa; -SUNReduce1[aa_, opts___] /; - (((Explicit /. Flatten[{opts}] /. - Options[SUNReduce]) == True) && FreeQ[{aa}, Plus]) := - SUNReduce2[aa, opts]; -SUNReduce1[aa_, opts___] /; - ((Explicit /. Flatten[{opts}] /. Options[SUNReduce]) == False) := - SUNReduce2[aa, opts]; - - -(* Explicit summation: *) - -SUNReduce2[aa_, - opts___] /; (Explicit /. Flatten[{opts}] /. Options[SUNReduce]) == - True := - (FCPrint[2, "Finding indices to sum over"]; - gennr1 = If[ FreeQ[aa, _SU3F | _SU3D | _SU3Delta] && - FreeQ[aa, - SUNN -> 3], - (SUNN^2 - 1 /. Flatten[{opts}] /. - Options[SUNReduce]), - 8 - ]; - flatlist = - List1[(aa (*Commented out 11/5-2003*)(*/. NTo3Rules1*) /. - NTo3Rules2[(SUNN /. Flatten[{opts}] /. - Options[SUNReduce])]) /. {NM -> List1, - Times -> - List1}(*writing out powers*)/. - ((at_ /; !FreeQ[at, fcsuni])^ex_Integer :> - Table[NM[at], {ex}])]; - flatlist1 = Flatten[flatlist /. List1 -> List]; - sumlist = - su3summationindices[ - su3list[Flatten[(flatlist1 //. {ff_[a___, fcsuni[ind_], b___][_] /; - FreeQ[ff, List] -> {ff[a, b], fcsuni[ind]}, - ff_[fcsuni[ind_], b___][_] /; FreeQ[ff, List] -> {ff[b], - fcsuni[ind]}, - ff_[a___, fcsuni[ind_]][_] /; FreeQ[ff, List] -> {ff[a], - fcsuni[ind]}, - ff_[a___, fcsuni[ind_], b___] /; - FreeQ[ff, List] -> {ff[a, b], fcsuni[ind]}, - ff_[fcsuni[ind_], b___] /; FreeQ[ff, List] -> {ff[b], - fcsuni[ind]}, - ff_[a___, fcsuni[ind_]] /; FreeQ[ff, List] -> {ff[a], - fcsuni[ind]}})]], gennr1]; - FCPrint[3, "Found:\n", sumlist]; - FCPrint[2, "Summing"]; - tmpres = USum1[(aa (*Commented out 11/5-2003*)(*/. NTo3Rules1*) /. - NTo3Rules2[(SUNN /. Flatten[{opts}] /. - Options[SUNReduce])]), ##] & @@ sumlist /. - If[ (HoldSums /. Flatten[{opts}] /. Options[SUNReduce]), - USum1 -> USumHeld, - USum1 -> USum - ]; - If[ (CommutatorReduce /. Flatten[{opts}] /. - Options[SUNReduce]), - FCPrint[2,"Applying CommutatorReduce"]; - CommutatorReduce[tmpres,opts], - tmpres - ]); - - - -(* To determine if there are identical indices in the two f-functions of a -product, we have to compare them all pairwise, that is, construct all -possible combinations with Outer: *) - - - -twoselect[{a_, b_, c_}, {d_, e_, f_}] := - twoselect[{a, b, c}, {d, e, f}] = - Select[Join @@ - Outer[List, {a, b, c}, {d, e, f}], (#[[1]] == #[[2]] && - Head[#[[1]]] === SUNIndex&& Head[#[[2]]] === fcsuni) &]; - - - -(* This function gives the signature of the permutations needed to turn one e.g. -{a,b,cc},{c,a,b} into {a,b,cc},{a,b,c}: *) - -sig1[{___, a_, mm___, b_, ___}, {___, a_, m___, b_, ___}] := - (-1)^(Length[{mm}] - Length[{m}]); -sig1[{___, a_, mm___, b_, ___}, {___, b_, m___, a_, ___}] := - (-1)^(Length[{mm}] - Length[{m}] + 1); - - - -(* This function gives the signature of the permutations needed to turn one e.g. -{a,b,c},{c,aa,bb} into {a,b,c},{aa,bb,c}: *) -(*Bug fixed 25/5-2001: There might be an identical constant index in - the two argument lists besides the index to be permuted*) - -sig2[{a___, m_?((!IntegerQ[#] && Head[#] =!= tmpsuni)&), ___}, -{aa___, m_?((!IntegerQ[#] && Head[#] =!= tmpsuni)&), ___}] := - (-1)^(Length[{a}] - Length[{aa}]); - - - -(* Implicit summation: *) - -$SUNDeltaRules =(*the delta functions are orderless, - so we need not be carefull with the order*) {SU3Delta[fcsuni[i_], - fcsuni[i_]] :> 8, - SU3Delta[i_, fcsuni[j_]]*SU3Delta[fcsuni[j_], k_] :> SU3Delta[i, k], - SU3Delta[i_Integer|(i:tmpsuni[_Integer]), i_Integer|(i:tmpsuni[_Integer])] :> 1, - SU3Delta[i:tmpsuni[_]|_Integer, j:tmpsuni[_]|_Integer]^_ :> SU3Delta[i, j], - SU3Delta[i:tmpsuni[_Integer]|_Integer, k_]* - SU3Delta[j:tmpsuni[_Integer]|_Integer, k_] :> 0/; - ((i/.tmpsuni->Identity) =!= (j/.tmpsuni->Identity)), - SU3Delta[tmpsuni[_], fcsuni[_]]^n_ /; EvenQ[n] :> 1, - SU3Delta[fcsuni[_], tmpsuni[_]]^n_ /; EvenQ[n] :> 1, - SU3Delta[_Integer, fcsuni[_]]^n_ /; EvenQ[n] :> 1, - SU3Delta[fcsuni[_], _Integer]^n_ /; EvenQ[n] :> 1, - SU3Delta[i_?((IntegerQ[#] || Head[#] === tmpsuni) &), - j_?((IntegerQ[#] || Head[#] === tmpsuni) &)]^_ :> SU3Delta[i, j], - SU3Delta[fcsuni[_], fcsuni[_]]^n_ /; EvenQ[n] :> 8^(n/2), - SU3Delta[i_, j_SUNIndex]* - expr_ :> (expr /. j -> i) /; (!FreeQ[expr, j] && - (FreeQ[expr, QuantumField[___, j, ___]] || !(IntegerQ[i]||Head[i]===tmpsuni&&IntegerQ[i[[1]]]))), - SU2Delta[fcsuni[i_], fcsuni[i_]] :> 3, - SU2Delta[i_, fcsuni[j_]]*SU2Delta[fcsuni[j_], k_] :> SU2Delta[i, k], - SU2Delta[i_Integer|(i:tmpsuni[_Integer]), i_Integer|(i:tmpsuni[_Integer])] :> 1, - SU2Delta[i:tmpsuni[_]|_Integer, j:tmpsuni[_]|_Integer]^_ :> SU2Delta[i, j], - SU2Delta[i:tmpsuni[_Integer]|_Integer, k_]* - SU2Delta[j:tmpsuni[_Integer]|_Integer, k_] :> 0 /; - ((i/.tmpsuni->Identity) =!= (j/.tmpsuni->Identity)), - SU2Delta[tmpsuni[_], fcsuni[_]]^n_ /; EvenQ[n] :> 1, - SU2Delta[fcsuni[_], tmpsuni[_]]^n_ /; EvenQ[n] :> 1, - SU2Delta[_Integer, fcsuni[_]]^n_ /; EvenQ[n] :> 1, - SU2Delta[fcsuni[_], _Integer]^n_ /; EvenQ[n] :> 1, - SU2Delta[i_?(IntegerQ[#] || Head[#] === tmpsuni), - j_?(IntegerQ[#] || Head[#] === tmpsuni)]^_ :> SU2Delta[i, j], - SU2Delta[fcsuni[_], fcsuni[_]]^n_ /; EvenQ[n] :> 3^(n/2), - SU2Delta[i_, j_SUNIndex]* - expr_ :> (expr /. j -> i) /; (!FreeQ[expr, j] && - (FreeQ[expr, QuantumField[___, j, ___]] || !(IntegerQ[i]||Head[i]===tmpsuni&&IntegerQ[i[[1]]])))(*Commented out 11/5-2003*)(*, - PhiProjection[i_Integer][fcsuni[j_]]^n_ /; EvenQ[n] :> 1, - PhiProjection[i_Integer][j_Integer] /; (i =!= j) :> 0, - PhiProjection[i_Integer][(fcsuni|ExplicitSUNIndex)[j_Integer]]/;(*fixed problem when missing one head 9/10-2001*) - ((i/.tmpsuni->Identity) =!= (j/.tmpsuni->Identity)) :> 0*)}; - -$SUNDFRules = {(*contraction of three indices*) - SU2F[_SUNIndex, _SUNIndex, _SUNIndex]^2 :> 6, - SU3F[_SUNIndex, _SUNIndex, _SUNIndex]^2 :> 24, - SU3D[_SUNIndex, _SUNIndex, _SUNIndex]^2 :> - 40/3,(*contraction of two indices*) - SU2F[a_, b_, (*Added tmpsuni->Identity to catch ExplicitSUNIndex. 16/9-2002*) - c_]^2 /; (Sort[Head /@ ({a, b, c}/.tmpsuni->Identity)] == {Integer, fcsuni, fcsuni}) :> - 2, SU3F[a_, b_, - c_]^2 /; (Sort[Head /@ ({a, b, c}/.tmpsuni->Identity)] == {Integer, fcsuni, fcsuni}) :> - 3(*Bug fix 12/1 - 2000, was 6*), - SU3D[a_, b_, - c_]^2 /; (Sort[Head /@ ({a, b, c}/.tmpsuni->Identity)] == {Integer, fcsuni, fcsuni}) :> - 5/3, (SU2F[a_, b_, c_]*SU2F[d_, e_, f_]* - rest___) /; (Length[twoselect[{a, b, c}, {d, e, f}]] == 2) :> - 2*(SU2Delta @@ - Complement[{a, b, c, d, e, - f}, (Join @@ twoselect[{a, b, c}, {d, e, f}])])*(sig1[{a, b, - c}, {d, e, f}])* - rest, (SU3F[a_, b_, c_]*SU3F[d_, e_, f_]* - rest___) /; (Length[twoselect[{a, b, c}, {d, e, f}]] == 2) :> - 3*(SU3Delta @@ - Complement[{a, b, c, d, e, - f}, (Join @@ twoselect[{a, b, c}, {d, e, f}])])*(sig1[{a, b, - c}, {d, e, f}])* - rest, (SU3D[a_, b_, c_]*SU3D[d_, e_, f_]* - rest___) /; (Length[twoselect[{a, b, c}, {d, e, f}]] == 2) :> - rest*5/3*SU3Delta @@ - Complement[{a, b, c, d, e, - f}, (Join @@ twoselect[{a, b, c}, {d, e, f}])], - (SU3D[a_, b_, c_]*SU3F[d_, e_, f_]*___) /; - (Length[twoselect[{a, b, c}, {d, e, f}]] == 2) :> 0, - (*contraction of one index - is this formula true for SU(3)?*) - (*NO it's not - fixed, but correct formula not really useful, 16/12/1999*) - (SU2F[a_, b_, c_]*SU2F[d_, e_, f_]*rest___) /; - (Length[twoselect[{a, b, c}, {d, e, f}]] == 1) :> - (((SU2Delta[#1, #3]*SU2Delta[#2, #4] - SU2Delta[#2, #3]*SU2Delta[#1, #4])& @@ - Join[Complement[{a, b, c}, {twoselect[{a, b, c}, {d, e, f}][[1, 1]]}], - Complement[{d, e, f}, {twoselect[{a, b, c}, {d, e, f}][[1, 1]]}]])* - sig2[{a, b, c}, {d, e, f}])*rest, - (SU2F[a_, b_, c_]^2) /; - (Length[twoselect[{a, b, c}, {a, b, c}]] == 1) :> - (((SU2Delta[#1, #3]*SU2Delta[#2, #4] - SU2Delta[#2, #3]*SU2Delta[#1, #4])& @@ - Join[Complement[{a, b, c}, {twoselect[{a, b, c}, {a, b, c}][[1, 1]]}], - Complement[{a, b, c}, {twoselect[{a, b, c}, {a, b, c}][[1, 1]]}]])* - sig2[{a, b, c}, {a, b, c}]), - (*Integers should already be sorted and put first - - the following should also take care of SU2F[a_integer, c_integer, - d_SUNIndex]^2, ...*) - SU2F[a_, b_Integer, c_Integer] :> - (-1)^(Complement[{1, 2, 3}, {b, c}][[1]] + 1)* - (SU2Delta[#, a] & @@ (Complement[{1, 2, 3}, {b, c}])), - SU2F[a_Integer, b_Integer, c_] :> - (-1)^(Complement[{1, 2, 3}, {a, b}][[1]] + 1)* - (SU2Delta[#, c] & @@ (Complement[{1, 2, 3}, {a, b}])), - SU2F[a_, (b:tmpsuni[_Integer]), (c:tmpsuni[_Integer])] :> - (-1)^(Complement[{1, 2, 3}, {b[[1]], c[[1]]}][[1]] + 1)* - (SU2Delta[#, a] & @@ (Complement[tmpsuni/@{1, 2, 3}, {b, c}])), - SU2F[(a:tmpsuni[_Integer]), (b:tmpsuni[_Integer]), c_] :> - (-1)^(Complement[{1, 2, 3}, {a[[1]], b[[1]]}][[1]] + 1)* - (SU2Delta[#, c] & @@ (Complement[tmpsuni/@{1, 2, 3}, {a, b}])) }; - - -$SUNRules = - Join[$SUNDeltaRules, $SUNDFRules, $SU3FReduceList, $SU3DReduceList]; - -(*Completeness of SU(N) - see Gasser & Leutwyler 1985*) -$SUNCompletenessRules = {HoldPattern[ - NM[UTrace1[NM[f___, - UMatrix[UGenerator[SUNIndex[j_]]], a___]], - UTrace1[NM[g___, - UMatrix[UGenerator[SUNIndex[j_]]], b___]]]] :> - 2 UTrace[NM[a, f, b, g]] - 2/SUNN NM[UTrace[NM[a, f]], UTrace[NM[b, g]]], - HoldPattern[ - Times[UTrace1[NM[f___, - UMatrix[UGenerator[SUNIndex[j_]]], a___]], - UTrace1[NM[g___, - UMatrix[UGenerator[SUNIndex[j_]]], b___]]]] :> - 2 UTrace[NM[a, f, b, g]] + -2/SUNN NM[UTrace[NM[a, f]], UTrace[NM[b, g]]], - HoldPattern[ - UTrace1[NM[f___, - UMatrix[UGenerator[SUNIndex[_]]], a___]]^2] :> - 2 UTrace[NM[a, f, a, f]] - 2/SUNN NM[UTrace[NM[a, f]], UTrace[NM[a, f]]], - HoldPattern[ - UTrace1[NM[f___, - UMatrix[UGenerator[SUNIndex[j_]]], a___, - UMatrix[UGenerator[SUNIndex[j_]]], b___]]] :> - -2/SUNN UTrace[ - NM[a, b, f]] + 2NM[UTrace[NM[a]], UTrace[NM[b, f]]]}; - -applyCompletenessRules[expr_, opts___Rule] := - expr /. $SUNCompletenessRules /. - SUNN -> (SUNN /. Flatten[{opts}] /. Options[SUNReduce]) /. - (UTrace1[]|UTrace[]) -> - Phi`Objects`Private`gaugedimcheck[SUNReduce, opts, expr]; - -SUNReduce2[aa_, opts___] /; -((Explicit /. Flatten[{opts}] /. Options[SUNReduce]) == False) := - Block[ {bb, cc}, - FCPrint[2, "Applying reduction rules on ", StandardForm[aa]]; - FCPrint[3, "Reduction rules are:\n", $SUNRules]; - bb = - (*Commented out 11/5-2003*)(*If[(RemoveIntegerIndices /. Flatten[{opts}] /. Options[SUNReduce]), - aa,*) - aa (*/. NTo3Rules1*) (*7/4.2002*) /. NTo3Rules3(*]*) /. - - NTo3Rules2[(SUNN /. Flatten[{opts}] /.Options[SUNReduce])]; - FCPrint[2, "Entered SUNReduce2; expression is:\n", StandardForm[bb]]; - cc = bb /. NTo3iRules2[(SUNN /. Flatten[{opts}] /. Options[SUNReduce])]; - FCPrint[2, "After NTo3iRules2, expression is:\n", StandardForm[cc]]; - - (*Changed below, 13/5-2003, to have $SU3FReduceList, $SU3DReduceList from - $SUNRules catch ExplicitSUNIndex[1], ... *) - cc /. ($SUNRules/.(SUNIndex| ExplicitSUNIndex | UIndex)[iii_Integer]->tmpsuni[iii]) - ]; - -SUNReduce[aa_, opts___] /; - (((Explicit /. Flatten[{opts}] /. Options[SUNReduce]) == False) && - (FullReduce /. Flatten[{opts}] /. Options[SUNReduce]) === True) := - Block[ {op}, - op = Join[{FullReduce->False}, - Select[Flatten[{opts}],FreeQ[#,FullReduce,Infinity,Heads->True]]]; - FCPrint[2, "Iterating with options ", op]; - FixedPoint[(SUNReduce[applyCompletenessRules[ - ExpandAll[#],opts], - Sequence@@op]&),aa] - ]; - -SUNReduce[aa_Plus, opts___] := - SUNReduce[#, opts] & /@ aa; - - -(*Added 7/6-2001 - might slow down too much ? ... - well, yes it did*) -(*SUNReduce[Times[ -aa:((_?((FreeQ[#,fcsuni|SU2Delta|SU3Delta|SUNDelta|SU2F|SU3F|SU3D|SUNF|SUND]===True)&))..), -bb:((_?((FreeQ[#,fcsuni|SU2Delta|SU3Delta|SUNDelta|SU2F|SU3F|SU3D|SUNF|SUND]===False)&))..)], -opts___] := -Times[aa]*SUNReduce[Times[bb]];*) - -SUNReduce[aa_, opts___] /; ((Explicit /. Flatten[{opts}] /. - Options[SUNReduce]) == False && (FullReduce /. Flatten[{opts}] /. - Options[SUNReduce]) =!= True) := - (FCPrint[2, - "Will use reduction rules"]; - Collect[FCPrint[2, "Collecting"]; - SUNReduce1[ - Expand[aa](*Change 5/3 - 1999 - - FA likes to use indices more than twice in a product*) - (*Changed again 16/12/1999*)(*SUNDelta[fcsuni[i_?! NumberQ], fcsuni[i_!NumberQ]]*)/. - SUNDelta[ - fcsuni[i_?((NumberQ[#] == False && - FreeQ[$ConstantIsoIndices, #]) &)], - fcsuni[i_?((NumberQ[#] == False && - FreeQ[$ConstantIsoIndices, #]) &)]] :> - (SUNN /. Flatten[{opts}] /. Options[SUNReduce])^2 - 1, - opts], {_fcfad, _SU2Delta, _SU2F, _SU2D}] /. - tmpsuni -> SUNIndex/.{faso[_Integer,___] -> - 1, faso[(fcsuni|ExplicitSUNIndex)[_Integer],___] -> 1}); - -SUNReduce[aa_, - opts___] /; ((Explicit /. Flatten[{opts}] /. - Options[SUNReduce]) == True) := - (FCPrint[2, - "Will sum explicitly"]; - Collect[FCPrint[2, "Collecting"]; - SUNReduce1[ - Expand[aa /. - Plus[bb_, bbb__] /; FreeQ[{bb, bbb}, fcsuni] -> - tempplus[ttt[Plus[bb, bbb]] /. Plus -> ppl]], - opts] /. Plus -> ppl /. tempplus[cc___] -> cc /. - ppl -> Plus /. - ttt -> Together, {_fcfad, _SU2Delta, _SU3Delta, _SU2F, _SU3F, _SU3D}] /. - tmpsuni -> SUNIndex/. - faso[_Integer,___]-> 1); - - -$SymSUNDFRules1 = { - Times[dd___, (sud:(SUND|SU3D))[a_, b_, c_], d___] :> - Block[ {inds0, originds, originds0, originds1, inds}, - originds0 = {a, b, c} /. SUNIndex-> Identity; - inds0 =(*Select instead of Intersection is used to preserve the order*) - Select[Sort[Cases[{dd, d}, QuantumField[___, fcsuni[_], ___], Infinity, - Heads -> True]] /. QuantumField[___, fcsuni[e_], ___] -> e, (MemberQ[originds0, #]) &]; - originds1 = Select[originds0, (MemberQ[inds0, #]) &]; - originds = Join[Complement[originds0, originds1], originds1]; - inds = Join[Complement[originds, inds0], inds0]; - If[ Length[inds0] > 1 && Length[inds] < 4, - sud[a, b, c]*(Times[dd, d] /. ((Rule @@ #) & /@ Transpose[{originds, inds}])), - sud[a, b, c]*Times[dd, d] - ] - ], - Times[dd___, (suf:(SUNF|SU2F|SU3F))[a_, b_, c_], d___] :> - Block[ {inds0, originds, originds0, originds1, inds}, - originds0 = {a, b, c} /. SUNIndex-> Identity; - inds0 =(*Select instead of Intersection is used to preserve the order*) - Select[Sort[Cases[{dd, d}, QuantumField[___, fcsuni[_], ___], Infinity, - Heads -> True]] /. QuantumField[___, fcsuni[e_], ___] -> e, (MemberQ[originds0, #]) &]; - originds1 = Select[originds0, (MemberQ[inds0, #]) &]; - originds = Join[Complement[originds0, originds1], originds1]; - inds = Join[Complement[originds, inds0], inds0]; - If[ Length[inds0] > 1 && Length[inds] < 4, - sig1[originds, inds]* - suf[a, b, c]* - (Times[dd, d] /. ((Rule @@ #) & /@ Transpose[{originds, inds}])), - suf[a, b, c]*Times[dd, d] - ] - ] - }; - -$SymSUNDFRules2 = { - Times[dd___, (sud:(SUND|SU3D))[a_, b_, c_], d___] :> - Block[ {inds0, originds, originds0, originds1, inds}, - originds0 = {a, b, c} /. SUNIndex-> Identity; - inds0 =(*Select instead of Intersection is used to preserve the order*) - Select[Cases[{dd, d}, UMatrix[UGenerator[fcsuni[_]]], Infinity, - Heads -> True] /. - UMatrix[UGenerator[fcsuni[e_]]] -> e, (MemberQ[originds0, #]) &]; - originds1 = Select[originds0, (MemberQ[inds0, #]) &]; - originds = Join[Complement[originds0, originds1], originds1]; - inds = Join[Complement[originds, inds0], inds0]; - If[ Length[inds0] > 1 && Length[inds] < 4, - sud[a, b, c]*(Times[dd, d] /. ((Rule @@ #) & /@ Transpose[{originds, inds}])), - sud[a, b, c]*Times[dd, d] - ] - ], - Times[dd___, (suf:(SUNF|SU2F|SU3F))[a_, b_, c_], d___] :> - Block[ {inds0, originds, originds0, originds1, inds}, - originds0 = {a, b, c} /. SUNIndex-> Identity; - inds0 =(*Select instead of Intersection is used to preserve the order*) - Select[Cases[{dd, d}, UMatrix[UGenerator[fcsuni[_]]], Infinity, - Heads -> True] /. - UMatrix[UGenerator[fcsuni[e_]]] -> e, (MemberQ[originds0, #]) &]; - originds1 = Select[originds0, (MemberQ[inds0, #]) &]; - originds = Join[Complement[originds0, originds1], originds1]; - inds = Join[Complement[originds, inds0], inds0]; - If[ Length[inds0] > 1 && Length[inds] < 4, - sig1[originds, inds]* - suf[a, b, c]* - (Times[dd, d] /. ((Rule @@ #) & /@ Transpose[{originds, inds}])), - suf[a, b, c]*Times[dd, d] - ] - ] - }; - - -SUDFSymmetrize[exp_] := - exp /. $SymSUNDFRules1 /. $SymSUNDFRules2; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Cleaning up indices *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Sorting indices *) - -(*Clean up contracted indices*) -sortRules1 = {(nm : (Times | NM))[a__, b__] :> - ((nm[a, b] /. ((Rule @@ #) & /@ - Transpose[{Cases[{a}, LorentzIndex[__], Infinity, - Heads -> True], - Sort[Cases[{a}, LorentzIndex[__], Infinity, - Heads -> True]]}]))) /; (Sort[ - Cases[{a}, LorentzIndex[__], Infinity, Heads -> True]] === - Sort[Cases[{b}, LorentzIndex[__], Infinity, Heads -> True]] && - Cases[{a}, LorentzIndex[__], Infinity, Heads -> True] =!= - Sort[Cases[{a}, LorentzIndex[__], Infinity, - Heads -> True]]), (nm : (Times | NM))[a__, - b__] :> (ablors = - Intersection[ - alors = Cases[{a}, LorentzIndex[__], Infinity, Heads -> True], - blors = Cases[{b}, LorentzIndex[__], Infinity, Heads -> True]]; - test = (alors =!= {} && blors =!= {} && ablors === {} && - Join[alors, blors] =!= Sort[Join[alors, blors]] && - Sort[alors] === Sort[Join[Union[alors], Union[alors]]] && - Sort[blors] === Sort[Join[Union[blors], Union[blors]]]); - If[ test, - nm[a, b] /. ((Rule @@ #) & /@ - Transpose[{Join[alors, blors], Sort[Join[alors, blors]]}]), - nm[a, b] - ]) /; (Cases[{a}, LorentzIndex[__], Infinity, - Heads -> True] =!= {} && - Cases[{b}, LorentzIndex[__], Infinity, Heads -> True] =!= {} && - Join[Cases[{a}, LorentzIndex[__], Infinity, Heads -> True], - Cases[{b}, LorentzIndex[__], Infinity, Heads -> True]] =!= - Sort[Join[Cases[{a}, LorentzIndex[__], Infinity, Heads -> True], - Cases[{b}, LorentzIndex[__], Infinity, - Heads -> True]]] && ((Sort[#] === - Sort[Join[Union[#], Union[#]]]) &[ - Cases[{a}, LorentzIndex[__], Infinity, - Heads -> - True]]) && ((Sort[#] === - Sort[Join[Union[#], Union[#]]]) &[ - Cases[{b}, LorentzIndex[__], Infinity, Heads -> True]]))}; - -sortRules2 = sortRules1 //. {HoldPattern[LorentzIndex] -> fcsuni, LorentzIndex -> fcsuni}; - -sortRules3 = sortRules1 //. {HoldPattern[LorentzIndex] -> UIndex, LorentzIndex -> UIndex}; - -(* Cleaning up contracted Lorentz indices. co is the number of factors that will be - considered; in e.g. u[mu2] gamma[mu1] gamma[mu1] u[mu2], two will suffice. *) - -lorentzCleanup[exp_] := - (exp1 = exp; - Do[ders = - fccombs[ - Union[Cases[exp, LorentzIndex[__], Infinity, Heads -> True]], co]; - ruls = ((RuleDelayed1[Power1[PatternTest1[a_, func[ - And @@ Table[Count1[yo, #[[i]], Infinity, Heads -> True] == 1, {i, co}]]], 2], - Condition1[ReplaceAll1[a^2, Map1[(Rule1 @@ #) &, - Transpose1[{Cases1[{a}, LorentzIndex[__], Infinity, Heads -> True], Sort[#]}]]], - SameQ1[Sort1[Cases1[{a}, LorentzIndex[__], Infinity, Heads -> True]], Sort1[#]] && - UnsameQ1[Cases1[{a}, LorentzIndex[__], Infinity, Heads -> True], - Sort1[#]]]]) & /@ ders) /. PatternTest1 -> PatternTest /. - Count1 -> Count /. yo -> # /. func -> Function /. - RuleDelayed1 -> RuleDelayed /. ReplaceAll1 -> ReplaceAll /. - Condition1 -> Condition /. UnsameQ1 -> UnsameQ /. SameQ1 -> SameQ /. - Cases1 -> Cases /. Sort1 -> Sort /. ReplaceAll1 -> ReplaceAll /. - Transpose1 -> Transpose /. Rule1 -> Rule /. Map1 -> Map /. Power1 -> Power; - exp1 = exp1 /. ruls, {co, 2, 2}]; - exp1); - -(* In case we would want to do the same for NM products*) - -(*lorentzCleanupNM[exp_] := (exp1 = exp; - Do[ders = - fccombs[ - Union[Cases[exp, LorentzIndex[__], Infinity, Heads -> True]], co]; - ruls = ((RuleDelayed1[ - NM[PatternTest1[a_, - func[And @@ Table[Count1[yo, #[[i]], - Infinity, Heads -> True] == 1, {i, - co}]]], PatternTest1[b_, - func[And @@ Table[Count1[yo, #[[i]], - Infinity, Heads -> True] == 1, {i, - co}]]]], Condition1[ - ReplaceAll1[NM[a, b], - Map1[(Rule1 @@ #) &, - Transpose1[{Cases1[{b}, LorentzIndex[__], - Infinity, Heads -> True], Sort[#]}]]], - SameQ1[Sort1[Cases1[{b}, LorentzIndex[__], - Infinity, Heads -> True]], Sort1[#]] && - UnsameQ1[Cases1[{b}, LorentzIndex[__], - Infinity, Heads -> True], - Sort1[#]]]]) & /@ ders) /. - PatternTest1 -> PatternTest /. - Count1 -> Count /. yo -> # /. - func -> Function /. - RuleDelayed1 -> RuleDelayed /. - ReplaceAll1 -> ReplaceAll /. - Condition1 -> Condition /. - UnsameQ1 -> UnsameQ /. SameQ1 -> SameQ /. - Cases1 -> Cases /. Sort1 -> Sort /. - ReplaceAll1 -> ReplaceAll /. Transpose1 -> Transpose /. - Rule1 -> Rule /. Map1 -> Map /. Power1 -> Power; - exp1 = exp1 /. ruls, {co, 2, 2}]; exp1);*) - -(* Cleaning up contracted SU(N) indices. co is the number of factors that will be - considered; in e.g. u[mu2] gamma[mu1] gamma[mu1] u[mu2], two will suffice. *) - -sunCleanup[exp_] := - (exp1 = exp; - Do[ders = - fccombs[ - Union[Cases[exp, fcsuni[__], Infinity, Heads -> True]], co]; - ruls = ((RuleDelayed1[Power1[PatternTest1[a_, func[ - And @@ Table[Count1[yo, #[[i]], Infinity, Heads -> True] == 1, {i, co}]]], 2], - Condition1[ReplaceAll1[a^2, Map1[(Rule1 @@ #) &, - Transpose1[{Cases1[{a}, fcsuni[__], Infinity, Heads -> True], Sort[#]}]]], - SameQ1[Sort1[Cases1[{a}, fcsuni[__], Infinity, Heads -> True]], Sort1[#]] && - UnsameQ1[Cases1[{a}, fcsuni[__], Infinity, Heads -> True], - Sort1[#]]]]) & /@ ders) /. PatternTest1 -> PatternTest /. - Count1 -> Count /. yo -> # /. func -> Function /. - RuleDelayed1 -> RuleDelayed /. ReplaceAll1 -> ReplaceAll /. - Condition1 -> Condition /. UnsameQ1 -> UnsameQ /. SameQ1 -> SameQ /. - Cases1 -> Cases /. Sort1 -> Sort /. ReplaceAll1 -> ReplaceAll /. - Transpose1 -> Transpose /. Rule1 -> Rule /. Map1 -> Map /. Power1 -> Power; - exp1 = exp1 /. ruls, {co, 2, 2}]; - exp1); - -(* Sort differentation Lorentz indices. *) - -SetAttributes[nmm, Flat]; - -sortDiff := - (# //. - FieldDerivative[f_, x_, LorentzIndex[li_]] :> - nmm[Derivativex[x, LorentzIndex[li]], f] /. - nmm[dl : (Derivativex[_, LorentzIndex[_]] ..)] :> - nmm @@ Sort[{dl}] //. - nmm[Derivativex[x_, LorentzIndex[li_]], f_] :> - FieldDerivative[f, x, LorentzIndex[li]] /; - FreeQ[f, Derivativex, Infinity] /. nmm -> NM)&; - -(* Change order of differentation if appropriate. *) - -lorentzDerCleanupRules = {HoldPattern[ - a__ UTrace1[ - NM[b___, - FieldDerivative[ - fd : (FieldDerivative[f_, x_, LorentzIndex[li2_]] | - Adjoint[ - FieldDerivative[f_, x_, LorentzIndex[li2_]]]), x_, - LorentzIndex[li1_]], - c___]]] :> (a UTrace1[ - NM[b, FieldDerivative[ - fd /. {li1 -> li2, li2 -> li1}, x, LorentzIndex[li2]], - c]] /. {li1 -> li2, li2 -> li1}) /; - Cases[{a, b, c}, LorentzIndex[__], Infinity, - Heads -> True] === {LorentzIndex[li1], LorentzIndex[li2]}, - HoldPattern[ - a__ UTrace1[ - NM[b___, - Adjoint[FieldDerivative[ - fd : (FieldDerivative[f_, x_, LorentzIndex[li2_]] | - Adjoint[ - FieldDerivative[f_, x_, LorentzIndex[li2_]]]), - x_, LorentzIndex[li1_]]], - c___]]] :> (a UTrace1[ - NM[b, Adjoint[ - FieldDerivative[ - fd /. {li1 -> li2, li2 -> li1}, x, LorentzIndex[li2]]], - c]] /. {li1 -> li2, li2 -> li1}) /; - Cases[{a, b, c}, LorentzIndex[__], Infinity, - Heads -> True] === {LorentzIndex[li1], LorentzIndex[li2]}, - HoldPattern[ - NM[a__, UTrace1[ - NM[b___, - FieldDerivative[ - fd : (FieldDerivative[f_, x_, LorentzIndex[li2_]] | - Adjoint[ - FieldDerivative[f_, x_, LorentzIndex[li2_]]]), x_, - LorentzIndex[li1_]], c___]]]] :> (NM[a, - UTrace1[NM[b, - FieldDerivative[ - fd /. {li1 -> li2, li2 -> li1}, x, LorentzIndex[li2]], - c]]] /. {li1 -> li2, li2 -> li1}) /; - Cases[{a, b, c}, LorentzIndex[__], Infinity, - Heads -> True] === {LorentzIndex[li1], LorentzIndex[li2]}, - HoldPattern[ - NM[a__, UTrace1[ - NM[b___, - Adjoint[FieldDerivative[ - fd : (FieldDerivative[f_, x_, LorentzIndex[li2_]] | - Adjoint[ - FieldDerivative[f_, x_, LorentzIndex[li2_]]]), - x_, LorentzIndex[li1_]]], c___]]]] :> (NM[a, - UTrace1[NM[b, - Adjoint[ - FieldDerivative[ - fd /. {li1 -> li2, li2 -> li1}, x, LorentzIndex[li2]]], c]]] /. - {li1 -> li2, li2 -> li1}) /; - Cases[{a, b, c}, LorentzIndex[__], Infinity, - Heads -> True] === {LorentzIndex[li1], LorentzIndex[li2]}} - -lorentzDerCleanup := - ((# /. lorentzDerCleanupRules) &); - -(* Field strength tensors *) - -fstrules = {n : - (FieldStrengthTensorFull|FieldStrengthTensor)[LorentzIndex[mu1_], - QuantumField[__, - LorentzIndex[mu2_]][ - x_], x_, ___] :> (-n /. {mu1 -> mu2, mu2 -> mu1}) /; - Sort[LorentzIndex /@ {mu1, - mu2}] =!= \ -(LorentzIndex /@ {mu1, mu2}), - n : NM[a___, - (FieldStrengthTensorFull|FieldStrengthTensor)[LorentzIndex[mu1_], - QuantumField[__, - LorentzIndex[mu2_]][ - x_], x_, ___], b___] :> (n /. {mu1 -> mu2, mu2 -> mu1}) /; - Sort[Cases[{a, b}, - LorentzIndex[ - mu1 | mu2], Infinity, Heads -> True]] == - Sort[LorentzIndex /@ \ -{mu1, mu2}] && - Cases[{a, b}, - LorentzIndex[ - mu1 | mu2], Infinity, Heads -> True] =!= - Sort[LorentzIndex /@ \ -{mu1, mu2}]}; - -fstCleanup := - ((# //. fstrules) &); - -(* Final sorting function *) - -SortIndices = ((Expand[NMExpand[#]] /. sortRules1 /. sortRules2 /. sortRules3 // - sortDiff// lorentzCleanup // sunCleanup // lorentzDerCleanup // fstCleanup)&); - -(*------------------------------------------------------------------------------*) - - -(* These rules substitute "real" index names instead of the internal code names: *) - -dummynames[li_List, - ll_List] := - {fcsuni[IsoDummy][n_] :> - fcsuni[ToExpression[li[[1]] <> ToString[n]]], - fcsuni[IsoExternDummy][n_] :> fcsuni[ToExpression[li[[2]] <> ToString[ - n]]], fcsuni[IsoInternDummy][n_] :> fcsuni[ToExpression[li[[3]] <> ToString[ - n]]], LorentzIndex[LorentzDummy][n_] :> LorentzIndex[ToExpression[ll[[1]] <> ToString[ - n]]], - LorentzIndex[LorentzExternDummy][n_] :> LorentzIndex[ToExpression[ll[[2]] <> ToString[ - n]]], LorentzIndex[LorentzInternDummy][n_] :> - LorentzIndex[ToExpression[ll[[3]] <> ToString[n]]], - LorentzIndex[DerivativeExternDummy][n_] :> LorentzIndex[ToExpression[ll[[4]] <> ToString[ - n]]], LorentzIndex[DerivativeInternDummy][n_] :> - LorentzIndex[ToExpression[ll[[5]] <> ToString[n]]]}; - - - -(* The aim is to make a unique dummy substitution ending with as few dummys as -possible. The uniqueness should then make terms cancel... *) - - -(* We have to be carefull with the iso f function, since it is not orderless: *) - -dummyrulesf3 = {ff_[a_, b_, c_]* - facc_ :> (res = - ff[a, b, c]*facc /. - Map[Apply[Rule, #] &, - Transpose[{Select[{a, b, c}, ! FreeQ[facc, #] &], - Table[fcsuni[IsoDummy][rep], {rep, isodummycounter, - isodummycounter + 2}]}]]; - isodummycounter += 3; - res)/; - (Count[{! FreeQ[facc, a], ! FreeQ[facc, b], - !FreeQ[facc, c]}, True] == 3 && - Count[Select[{a, b, c}, ! FreeQ[facc, #] &], -_SUNIndex] == 3 && - FreeQ[Select[{a, b, c}, ! FreeQ[facc, #] &], _Integer] && - FreeQ[{a, b, c}, IsoDummy] && - FreeQ[Select[{a, b, c}, ! FreeQ[facc, #] &], - Alternatives @@ $ConstantIsoIndices])}; - -dummyrulesf2 = {ff_[a_, b_, c_]* - facc_ :> (res = - ff[a, b, c]*facc /. - Map[Apply[Rule, #] &, - Transpose[{Select[{a, b, c}, ! FreeQ[facc, #] &], - Table[fcsuni[IsoDummy][rep], {rep, isodummycounter, - isodummycounter + 1}]}]]; - isodummycounter += 2; - res)/; - (Count[{! FreeQ[facc, a], ! FreeQ[facc, b], - !FreeQ[facc, c]}, True] == 2 && - Count[Select[{a, b, c}, ! FreeQ[facc, #] &], -_SUNIndex] == 2 && - FreeQ[Select[{a, b, c}, ! FreeQ[facc, #] &], _Integer] && - FreeQ[{a, b, c}, IsoDummy] && - FreeQ[Select[{a, b, c}, ! FreeQ[facc, #] &], - Alternatives @@ $ConstantIsoIndices]) }; - -dummyrulesf1 = {ff_[a_, b_, c_]* - facc_ :> (res = - ff[a, b, c]*facc /. - Map[Apply[Rule, #] &, - Transpose[{Select[{a, b, c}, ! FreeQ[facc, #] &], - Table[fcsuni[IsoDummy][rep], {rep, isodummycounter, - isodummycounter + 0}]}]]; - isodummycounter += 1; - res)/; (Count[{! FreeQ[facc, a], ! FreeQ[facc, b], - !FreeQ[facc, c]}, True] == 1 && - Count[Select[{a, b,c}, ! FreeQ[facc, #] &], -_SUNIndex] == 1 && - FreeQ[Select[{a, b, c}, ! FreeQ[facc, #] &], _Integer] && - FreeQ[{a, b, c}, IsoDummy] && - FreeQ[Select[{a, b, c}, ! FreeQ[facc, #] &], - Alternatives @@ $ConstantIsoIndices])}; - - - -(* Now we can deal with general functions, which are assumed to be orderless in -iso-indices, derivative indices and Lorentz indices. This last point means -that we may miss cancellation of e.g. some space-time tensors... Again we -device a unique substitution of dummys. *) - -(* Label factors in nested structures like NM[NM[..]+NM[..], NM[..]+NM[..]]. - The problem is that we cannot use identical indices on both sides. Thus, - we label the NM's sequentially and take one label out on each run. *) - -(*Put on an isowait[..] tag if an NM product is of the above form*) -(*Applied only once*) -isowaitrules1 = -(aa : HoldPattern[ -(NM | NM1 | NM2)[(Plus(*|UTrace1*))[ - (___*(NM | NM1 | NM2)[__?(FreeQ[#, _(NM | NM1 | NM2)] &)] | -(NM | NM1 | NM2)[__?(FreeQ[#, (NM | NM1 | NM2)[__]] &)] | - _?(FreeQ[#, (NM | NM1 | NM2)[__]] &)) ..] ..]]) :> -(waitcounter = 0; -((waitcounter++; -Replace[#, (nm1 : NM | NM1 | NM2)[b__] :> -nm1[b, isowait[waitcounter]] /; FreeQ[{b}, isowait[__]], {1, 3}]) &) /@ aa)/; -!FreeQ[aa,fcsuni[_]]; - - -(*remove the highest tag*) -(*Applied only once*) -isowaitrules0 = -aa : HoldPattern[ -(NM | NM1 | NM2)[(Plus(*|UTrace1*))[(___*(NM | NM1 | NM2)[__?(FreeQ[#, (NM | NM1 | NM2)[__]] &), isowait[__]] | -(NM | NM1 | NM2)[__?(FreeQ[#, (NM | NM1 | NM2)[__]] &), isowait[__]] | - _?(FreeQ[#, (NM | NM1 | NM2)[__]] &)) ..] ..,___]] :> -(aa /. (isowait[(Max[(#[[1]]) & /@ Cases[aa, isowait[__], {3, 4}]])] -> - (seq[])) /. seq -> Sequence)/; -!FreeQ[aa,fcsuni[_]]; - -(*If an NM product is of the above form, already has a tag and ends with -a factor that has no NM's, remove the highest tag and increment isoexterndummycounter by one*) -(*Applied repeatdly (with IndicesCleanup1)*) -isowaitrules2 = -aa : HoldPattern[ -(NM | NM1 | NM2)[___, -(Plus(*|UTrace1*))[(___*(NM | NM1 | NM2)[__?(FreeQ[#, (NM | NM1 | NM2)[__]] &), isowait[__],___] | -(NM | NM1 | NM2)[__?(FreeQ[#, (NM | NM1 | NM2)[__]] &), - isowait[__],___] | _?(FreeQ[#, (NM | NM1 | NM2)[__]] &)) ..] .., - (_?((FreeQ[#,isowait[__]] && - FreeQ[#,fcsuni[_?(FreeQ[#,IsoDummy|IsoExternDummy|IsoInternDummy]&)]])&))..]] :> -(aa /. (isowait[(Max[(#[[1]]) & /@ Cases[aa, isowait[__], {3, 4}]])] -> -(isoexterndummycounter = Max[Union[{0},Cases[{aa}, fcsuni[IsoExternDummy][_], Infinity, - Heads -> True]] /. - fcsuni[IsoExternDummy][na_] -> na]+1; -seq[])) /. seq -> Sequence)/; -!FreeQ[aa,fcsuni[_]]; - -(*Same as above but no check fo last factor NM's*) -(*Hmm, the way it is applied, it seems to be redundant. 26/8-2001*) -isowaitrules3 = -aa : HoldPattern[ -(NM | NM1 | NM2)[___, -(Plus(*|UTrace1*))[(___*(NM | NM1 | NM2)[__?(FreeQ[#, (NM | NM1 | NM2)[__]] &), isowait[__],___] | -(NM | NM1 | NM2)[__?(FreeQ[#, (NM | NM1 | NM2)[__]] &), - isowait[__],___] | _?(FreeQ[#, (NM | NM1 | NM2)[__]] &)) ..] .., - (_?((FreeQ[#,isowait[__]])&))..]] :> -(aa /. (isowait[(Max[(#[[1]]) & /@ Cases[aa, isowait[__], {3, 4}]])] -> -(isoexterndummycounter = Max[Union[{0},Cases[{aa}, fcsuni[IsoExternDummy][_], Infinity, - Heads -> True]] /. - fcsuni[IsoExternDummy][na_] -> na]+1; -seq[])) /. seq -> Sequence)/; -!FreeQ[aa,fcsuni[_]]; - -(* Rules for UTraces. This is the one exception to only allowing one level of nesting. - The strategy is to take out SUNIndices in UTraces via SUNDeltas, leaving a dummy - index without SUNIndex head in the UTrace and then later substitute back in the index *) - -tracerule1 = { - -NM[a___, UTrace1[b_?(!FreeQ[#,LorentzIndex]&)], c___]*d_ :> - (Times @@ (inxlist = (SUNDelta[#, fcsuni[suninx[Unique["dum"]]]] & /@ - Select[ - Cases[Cases[{a,UTrace1[b],c,d}, UTrace1[_], Infinity, Heads->True], - fcsuni[_], Infinity, Heads->True], - FreeQ[#,suninx]&])))* - (*Lorentz stuff added 23/9-2001*) - (Times @@ (linxlist = (Pair[#, LorentzIndex[linx[Unique["dum"]]]] & /@ - Select[ - Cases[Cases[{a,UTrace1[b],c,d}, UTrace1[_], Infinity, Heads->True], - LorentzIndex[_], Infinity, Heads->True], - FreeQ[#,linx]&])))(**)* - (NM[a, UTrace1[b], c] /. - (UTrace1[e_] :> - UTrace1[e/.((Rule[#[[1]], suninx0@@#[[2,1]]])& /@ inxlist)/. - (*PartialD automatically put on head LorentzIndex which screws up things*) - ((Rule[FCPartialD[#[[1]]],partd[linx0@@#[[2,1]]]])& /@ linxlist)/. - ((Rule[#[[1]],linx0@@#[[2,1]]])& /@ linxlist)]))*(d), - -(nm:(NM|Times))[a___, UTrace1[b_?(!FreeQ[#,LorentzIndex]&)], c___] :> - (Times @@ (inxlist = (SUNDelta[#, fcsuni[suninx[Unique["dum"]]]] & /@ - Select[ - Cases[Cases[{a,UTrace1[b],c}, UTrace1[_], Infinity, Heads->True], - fcsuni[_], Infinity, Heads -> True], - FreeQ[#,suninx]&])))* - (Times @@ (linxlist = (Pair[#, LorentzIndex[linx[Unique["dum"]]]] & /@ - Select[ - Cases[Cases[{a,UTrace1[b],c}, UTrace1[_], Infinity, Heads->True], - LorentzIndex[_], Infinity, Heads -> True], - FreeQ[#,linx]&])))* - (nm[a, UTrace1[b], c]/. - UTrace1[e_]:> - UTrace1[e/.((Rule[#[[1]],suninx0@@#[[2,1]]])& /@ inxlist)/. - ((Rule[FCPartialD[#[[1]]],partd[linx0@@#[[2,1]]]])& /@ linxlist)/. - ((Rule[#[[1]],linx0@@#[[2,1]]])& /@ linxlist)])}; - -tracerule2 = {SUNDelta[fcsuni[suninx[f_]], j_]* - a_?((!FreeQ[#, suninx0[f_]])&) :> (a /. suninx0[f] -> j), - Pair[LorentzIndex[linx[f_]], j_]*a_?((!FreeQ[#, linx0[f_]])&) :> - (a /. linx0[f] -> j)}; - -tracerule3 = {SUNDelta[fcsuni[suninx[_]], _]->1, Pair[LorentzIndex[linx[_]], _]->1, partd->FCPartialD}; - -(* Comparison between factors: *) - -(*Iso - indices*) - dummyrulesiso1a = -{(nm1 : NM | NM1 | NM2)[ - fac___, gg_[fi___, a_SUNIndex, la___][x_], - facc___] :> - (( (nm1[fac, gg[fi, a, la][x], facc] /. - a -> fcsuni[IsoExternDummy][isoexterndummycounter]) /; - (!FreeQ[{fac, facc}, a] && FreeQ[{fac, facc}, IsoExternDummy] && - FreeQ[{fac, facc}, _isowait] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___, _?((FreeQ[{##}, isomult] && - FreeQ[{##}, _SUNIndex] === - False)&), ___] - ] - ) ) ) - }; -(*Iso - indices*) - dummyrulesiso1b = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_SUNIndex, la___], - facc___] :> (((nm1[fac, - gg[fi, a, la], facc] /. - a -> fcsuni[IsoExternDummy][isoexterndummycounter]) /; (! FreeQ[{fac, facc}, a] && - FreeQ[{fac, facc}, IsoExternDummy] && FreeQ[{fac, facc}, _isowait] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___, _?((FreeQ[{##}, isomult] && - FreeQ[{##}, _SUNIndex] === - False) &), ___] - - ]) ))}; -(*Iso - indices*) - dummyrulesiso2 = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_SUNIndex, la___][ - x_], facc___] :> (nm1[fac, - gg[fi, a, la][x], facc] /. - a -> fcsuni[IsoExternDummy][ - Max[Union[{0},Cases[{fac, facc}, fcsuni[IsoExternDummy][_], Infinity, - Heads -> True]] /. - fcsuni[IsoExternDummy][na_] -> na] + 1]) /; - (! FreeQ[{fac, facc}, a] && - FreeQ[{fac, facc}, _isowait] && FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},isomult]&)]]), - (nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_SUNIndex, la___], - facc___] :> (nm1[fac, - gg[fi, a, la], facc] /. - a -> fcsuni[IsoExternDummy][ - Max[Union[{0},Cases[{fac, facc}, fcsuni[IsoExternDummy][_], Infinity, - Heads -> True]] /. - fcsuni[IsoExternDummy][na_] -> na] + 1]) /; - (! FreeQ[{fac, facc}, a] && - FreeQ[{fac, facc}, _isowait] && FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},isomult]&)]]) }; - -(*Derivative indices*) - dummyrulesder1a = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, - FCPartialD[a_LorentzIndex], - la___][x_], - facc___] :> (nm1[fac, - gg[fi, FCPartialD[a], la][x], facc] /. - a -> LorentzIndex[DerivativeExternDummy][1]) /; (! FreeQ[{fac, facc}, a] && - FreeQ[{fac, facc}, DerivativeExternDummy] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},lorentzmult]&)]]), - (ff_[FCPartialD[LorentzIndex[a_]], fi___,LorentzIndex[a_],if___][x_]) :> (ff[ - FCPartialD[LorentzIndex[DerivativeInternDummy][0]], - fi,LorentzIndex[DerivativeInternDummy][0],if][x])/; - (FreeQ[a, DerivativeInternDummy])}; -(*Derivative indices*) - dummyrulesder1b = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, - FCPartialD[a_LorentzIndex], - la___], facc___] :> (nm1[fac, - gg[fi, FCPartialD[a], la], facc] /. - a -> LorentzIndex[DerivativeExternDummy][1])/; (! FreeQ[{fac, facc}, a] && - FreeQ[{fac, facc}, DerivativeExternDummy] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},lorentzmult]&)]])}; -(*Derivative indices*) - dummyrulesder2 = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, - FCPartialD[a_LorentzIndex], - la___][x_], - facc___] :> (nm1[fac, - gg[fi, FCPartialD[a], la][x], facc] /. - a -> LorentzIndex[DerivativeExternDummy][ - Max[Cases[{fac, facc}, LorentzIndex[DerivativeExternDummy][_], - Infinity, Heads -> True] /. - LorentzIndex[DerivativeExternDummy][na_] -> na] + 1])/; - (! FreeQ[{fac, facc}, a] && !FreeQ[{fac, facc}, DerivativeExternDummy] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},lorentzmult]&)]]), - (nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, - FCPartialD[a_LorentzIndex], - la___], facc___] :> (nm1[fac, - gg[fi, FCPartialD[a], la], facc] /. - a -> LorentzIndex[DerivativeExternDummy][ - Max[Cases[{fac, facc}, LorentzIndex[DerivativeExternDummy][_], - Infinity, Heads -> True] /. - LorentzIndex[DerivativeExternDummy][na_] -> na] + 1])/; - (! FreeQ[{fac, facc}, a] && !FreeQ[{fac, facc}, DerivativeExternDummy] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},lorentzmult]&)]])}; -(*Lorentz indices*) - dummyruleslor1 = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_LorentzIndex, - la___][x_], - facc___] :> (nm1[fac, - gg[fi, a, la][x], facc] /. - a -> LorentzIndex[LorentzExternDummy][1])/; (! FreeQ[{fac, facc}, a] && - FreeQ[{fac, facc}, LorentzExternDummy] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},lorentzmult]&)]]), - (nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_LorentzIndex, - la___], facc___] :> (nm1[fac, - gg[fi, a, la], facc] /. - a -> LorentzIndex[LorentzExternDummy][1])/; (! FreeQ[{fac, facc}, a] && - FreeQ[{fac, facc}, LorentzExternDummy] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},lorentzmult]&)]])}; -(*Lorentz indices*) - dummyruleslor2 = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_LorentzIndex, - la___][x_], - facc___] :> (nm1[fac, - gg[fi, a, la][x], facc] /. - a -> LorentzIndex[LorentzExternDummy][ - Max[Cases[{fac, facc}, LorentzIndex[LorentzExternDummy][_], Infinity, - Heads -> True] /. - LorentzIndex[LorentzExternDummy][na_] -> na] + 1])/; - (!FreeQ[{fac, facc}, a] && !FreeQ[{fac, facc}, LorentzExternDummy] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},lorentzmult]&)]]), - (nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_LorentzIndex, - la___], - facc___] :> (nm1[fac, - gg[fi, a, la], facc] /. - a -> - LorentzIndex[LorentzExternDummy][ - Max[Cases[{fac, facc}, LorentzIndex[LorentzExternDummy][_], Infinity, - Heads -> True] /. - LorentzIndex[LorentzExternDummy][na_] -> na] + 1])/; - (! FreeQ[{fac, facc}, a] && !FreeQ[{fac, facc}, LorentzExternDummy] && - FreeQ[{fac, facc}, - (NM | NM1 | NM2)[___?(FreeQ[{##},lorentzmult]&)]])}; - - -(* Comparison internally in functions: *) - -(*Iso - indices*) - dummyrulesisoint1 = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_SUNIndex, la___][ - x_], facc___] :> (nm1[fac, gg[fi, a, la][x], - facc] /. - a -> fcsuni[IsoInternDummy][1])/; (! FreeQ[{fac, facc}, a] && - FreeQ[{fi, la}, IsoInternDummy]), (nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_SUNIndex, la___], - facc___] :> (nm1[fac, gg[fi, a, la], - facc] /. a -> fcsuni[IsoInternDummy][1])/; (! FreeQ[{fac, facc}, a] && - FreeQ[{fi, la}, IsoInternDummy])}; -(*Iso - indices*) - dummyrulesisoint2 = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_SUNIndex, la___][ - x_], facc___] :> (nm1[fac, - gg[fi, a, la][x], facc] /. - a -> fcsuni[IsoInternDummy][ - Max[Cases[{fi, la}, fcsuni[IsoInternDummy][_], Infinity, - Heads -> True] /. - fcsuni[IsoInternDummy][na_] -> na] + 1])/; (! FreeQ[{fac, facc}, a] && - !FreeQ[{fi, la}, IsoInternDummy]), (nm1 : - NM | NM1 | NM2)[fac___, - gg_[fi___, a_SUNIndex, la___], - facc___] :> (nm1[fac, gg[fi, a, la], - facc] /. - a -> fcsuni[IsoInternDummy][ - Max[Cases[{fi, la}, fcsuni[IsoInternDummy][_], Infinity, - Heads -> True] /. - fcsuni[IsoInternDummy][na_] -> na] + 1])/; (! FreeQ[{fac, facc}, a] && - !FreeQ[{fi, la}, IsoInternDummy])}; - -(*Lorentz indices*) - dummyruleslorint1 = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_LorentzIndex, - la___][x_], - facc___] :> (nm1[fac, - gg[fi, a, la][x], facc] /. - a -> LorentzIndex[LorentzInternDummy][1]) /; (! FreeQ[{fac, facc}, a] && - FreeQ[{fi, la}, LorentzInternDummy]), (nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_LorentzIndex, - la___], - facc___] :> (nm1[fac, gg[fi, a, la], - facc] /. a -> LorentzIndex[LorentzInternDummy][1])/; (! FreeQ[{fac, facc}, a] && - FreeQ[{fi, la}, LorentzInternDummy])}; -(*Lorentz indices*) - dummyruleslorint2 = {(nm1 : NM | NM1 | NM2)[fac___, - gg_[fi___, a_LorentzIndex, - la___][x_], - facc___] :> (nm1[fac, - gg[fi, a, la][x], facc] /. - a -> - LorentzIndex[LorentzInternDummy][ - Max[Cases[{fi, la}, LorentzIndex[LorentzInternDummy][_], Infinity, - Heads -> True] /. - LorentzIndex[LorentzInternDummy][na_] -> na] + 1])/; - (! FreeQ[{fac, facc}, a] && !FreeQ[{fi, la}, LorentzInternDummy]), (nm1 : - NM | NM1 | NM2)[fac___, - gg_[fi___, a_LorentzIndex, - la___], - facc___] :> (nm1[fac, - gg[fi, a, la], facc] /. - a -> LorentzIndex[LorentzInternDummy][ - Max[Cases[{fi, la}, LorentzIndex[LorentzInternDummy][_], Infinity, - Heads -> True] /. - LorentzIndex[LorentzInternDummy][na_] -> na] + 1])/; (! FreeQ[{fac, facc}, a] && - !FreeQ[{fi, la}, LorentzInternDummy])}; - - - -(* Squared objects will not be caught by the previous rules (and we don't have -higher powers with one iso-spin index), so we need a special set of rules: *) - -dummyrulessq1 = { - (ff_[fi___, a_SUNIndex, - la___][x_])^2 :> (res = (ff[fi, fcsuni[IsoDummy][isodummycounter], la][x])^2; - isodummycounter += 1; - res) /; (FreeQ[a, IsoDummy]), - - (ff_[fi___, a_SUNIndex, - la___])^2 :> (res = (ff[fi, fcsuni[IsoDummy][isodummycounter], la])^2; - isodummycounter += 1; - res)/; (FreeQ[a, IsoDummy]), - - (ff_[fi___, a_LorentzIndex, - la___][x_])^2 :> (ff[fi, LorentzIndex[LorentzDummy][1], la][x])^2 /; (FreeQ[a, LorentzDummy]), - - (ff_[fi___, a_LorentzIndex, - la___])^2 :> (ff[fi, LorentzIndex[LorentzDummy][1], la])^2/; (FreeQ[a, LorentzDummy]), - - (ff_[FCPartialD[LorentzIndex[a_]], fi__][x_])^2 :> (ff[ - FCPartialD[LorentzIndex[DerivativeExternDummy][1]], fi][x])^2/; (FreeQ[a, DerivativeExternDummy]), - - (ff_[FCPartialD[LorentzIndex[a_]], fi__])^2 :> - (ff[FCPartialD[LorentzIndex[DerivativeExternDummy][1]], fi])^2 /; (FreeQ[a, DerivativeExternDummy])}; - -dummyrulessq2 = { - (ff_[fi___, fcsuni[ld_][ll_], fcsuni[ln_], la___][x_])^2 :> - (ff[fi, fcsuni[ld][ll], fcsuni[ln][ll + 1], la][x])^2, - (ff_[fi___, fcsuni[ld_][ll_], fcsuni[ln_], la___])^2 :> - (ff[fi, fcsuni[ld][ll], fcsuni[ln][ll + 1], la])^2, - (ff_[fi___, LorentzIndex[ld_][ll_], LorentzIndex[ln_], la___][x_])^2 :> - (ff[fi, LorentzIndex[ld][ll], LorentzIndex[ln][ll + 1], la][x])^2, - (ff_[fi___, LorentzIndex[ld_][ll_], LorentzIndex[ln_], la___])^2 :> - (ff[fi, LorentzIndex[ld][ll], LorentzIndex[ln][ll + 1], la])^2, - (ff_[FCPartialD[LorentzIndex[ld_][ll_]], FCPartialD[LorentzIndex[ln_]], fi__][x_])^2 :> - (ff[FCPartialD[LorentzIndex[ld][ll]], FCPartialD[LorentzIndex[ln][ll + 1]], fi][x])^2, - (ff_[FCPartialD[LorentzIndex[ld_][ll_]], FCPartialD[LorentzIndex[ln_]], fi__])^2 :> - (ff[FCPartialD[LorentzIndex[ld][ll]], FCPartialD[LorentzIndex[ln][ll + 1]], fi])^2}; - -(* This is to clean up products of QuantumField[ - PartialD[LorentzIndex[DerivativeInternDummy][0]], p, - LorentzIndex[DerivativeInternDummy][0]][x] *) -fixderindices1 = {NM->nmm1, NM1->nmm1}; -fixderindices2 = {nmm1[a__]?((FreeQ[#, nmm1[__?(!FreeQ[#, - LorentzIndex[DerivativeInternDummy][0]]&)]] && !FreeQ[#, DerivativeInternDummy])&) :> - (derindcounter = Max[Union[{0}, - Cases[{a}, LorentzIndex[DerivativeInternDummy][_], Infinity, Heads->True] /. - LorentzIndex[DerivativeInternDummy] -> Identity]]; - nmm1 @@ ((# /. QuantumField[ - FCPartialD[LorentzIndex[DerivativeInternDummy][0]], p__, - LorentzIndex[DerivativeInternDummy][0], r___] :> - (++derindcounter; - QuantumField[FCPartialD[LorentzIndex[ - DerivativeInternDummy][derindcounter]], p, LorentzIndex[ - DerivativeInternDummy][derindcounter], r]))& /@ {a}))}; -fixderindices3 = {nmm1->NM1}; - -allpatterns = (Blank | BlankSequence | BlankNullSequence | Pattern); - -(*Expand traces of products of sums and products of sums of traces*) -fixtraceplus = {aa:HoldPattern[UTrace1[NM[___, - Plus[___,_?(!FreeQ[#,SUNIndex, - Heads->True]&),___],___]]] :> -(FCPrint[1,"Found UTrace of NM Product of sums. Applying NMExpand"]; -NMExpand[aa]), -aa:(NM[___, _?((!FreeQ[#, UTrace1, Heads -> True] && - !FreeQ[#,SUNIndex] && - !MatchQ[#, UTrace1[_] | _*UTrace1[_]]) &), ___]) :> - (FCPrint[1,"Found NM Product of sums of UTraces. Applying NMExpand"]; - NMExpand[aa]), -aa:(Times[___, _?((!FreeQ[#, UTrace1, Heads -> True] && - !FreeQ[#,SUNIndex] && - !MatchQ[#, UTrace1[_] | _*UTrace1[_]]) &), ___]) :> - (FCPrint[1,"Found Product of sums of UTraces. Applying Expand"]; - Expand[aa])}; - -(*Very cheap hacks to catch a few nested indices*) -cheapnesthackrule = {f_[LorentzIndex[li__]][x_] :> f[x, lihusk][LorentzIndex[li]] /; !MatchQ[x,LorentzIndex[__]], -HoldPattern[FieldStrengthTensor[LorentzIndex[li1__], - QuantumField[p__, l:(LorentzIndex[__]..)][x_], x_]] :> - FieldStrengthTensor[LorentzIndex[li1], l, QuantumField[p][x], x]}; -cheapnesthackruleback = {f_[x_, lihusk][LorentzIndex[li__]] :> f[LorentzIndex[li]][x], -HoldPattern[FieldStrengthTensor[LorentzIndex[li1_], l:(LorentzIndex[__]..), -QuantumField[p__][x_], x_]] :> FieldStrengthTensor[LorentzIndex[li1], - QuantumField[p, l][x], x] -}; - -(* The final cleanup function *) - -IndicesCleanup1[w_, OptionsPattern[]] := - w /. - dummyrulesiso1a /. dummyrulesiso1b /. dummyrulesiso2 /. - dummyrulesder1a /. dummyrulesder1b /. dummyrulesder2 /. - dummyruleslor1 /. dummyruleslor2 //. - fixderindices1 //. fixderindices2 //. fixderindices3 /. - {(nm1:NM|NM1|NM2)[fac___] :> nm1[fac,isomult] /; - FreeQ[{fac},fcsuni[_?((FreeQ[#,IsoDummy|IsoExternDummy|IsoInternDummy]&&!UScalarQ[#])&)]] && - FreeQ[{fac},isomult], - (nm1:NM|NM1|NM2)[fac___] :> nm1[fac,lorentzmult] /; - FreeQ[{fac},fcsuni[_?((FreeQ[#,LorentzDummy|LorentzExternDummy|LorentzInternDummy| - DerivativeExternDummy]&&!UScalarQ[#])&)]] && FreeQ[{fac},lorentzmult]} /. isowaitrules2; - - -SetAttributes[NM1, Flat]; -SetAttributes[NM2, Flat]; - -IndicesCleanup[ww_, opts___] := - ( - - declutr = False; - w = ww /. - - (* If UTrace1 has been declared UScalar, NMPower's of it will be Power's - and contracted indices woun't be seen. Hack to fix this *) - If[ ExtendedCleanup /. Flatten[{opts}] /. Options[IndicesCleanup], - If[ UScalarQ[UTrace1], - declutr = True; - FCPrint[2,"UndeclareUScalar[UTrace1]"]; - UndeclareUScalar[UTrace1] - ]; - Power[utr_UTrace1, po_] :> NM@@Table[utr,{po}], - Power[utr_UTrace1, po_] :> NM@@Table[utr,{po}] - ] /. - - cheapnesthackrule/.fixtraceplus//.tracerule1/.isowaitrules1/.isowaitrules0; - larul = {{}, {}, {}}; - Which[ - !FreeQ[w,LorentzIndex[_, D] | Momentum[_, D]], - - If[ ExtendedCleanup /. Flatten[{opts}] /. Options[IndicesCleanup], - FCPrint[1, - "Found occurence of D, using this as number of \ -space-time dimensions for all momenta, Dirac gamma matrices and Lorentz \ -indices"]; - larul = {LorentzIndex[llii_] -> LorentzIndex[llii, D], - dg[dig_] -> dg[dig, D], - Momentum[mo_] -> Momentum[mo, D]} - ];, - - - !FreeQ[w, LorentzIndex[_, D] | Momentum[_, D]], - If[ ExtendedCleanup /. Flatten[{opts}] /. Options[IndicesCleanup], - FCPrint[1, - "Found occurence of D, using this as number of space-time \ -dimensions for all momenta, Dirac gamma matrices and Lorentz indices"]; - larul = {LorentzIndex[llii_] -> LorentzIndex[llii, D], dg[dig_] -> dg[dig, D], - Momentum[mo_] -> Momentum[mo, D]} - ]; - ]; - isodummycounter = 1; - isoexterndummycounter = 1; - w1 = If[ ExtendedCleanup /. Flatten[{opts}] /. Options[IndicesCleanup], - FCPrint[1, "Using ExtendedCleanup->True"]; - w /. {SU2Delta -> su2delta1, SU2F -> su2f1, - SU3Delta -> su3delta1, SU3F -> su3f1, SU3D -> su3d1, - SUNDelta -> sundelta1, SUNF -> sunf1, - SUND -> sund1}, - FCPrint[1, - "Using ExtendedCleanup->False\nWill not work if mixed Times \ -and NM products are present"]w - ] /. - (*Cleaned up a bit below. 20/6-2003*) - (((fcsuni[#] -> protectisoconstant[#])&) /@ (((#[[1]])&) /@ - Cases[w, faso[_?((Head[#]=!=fcsuni)&),___], Infinity])) /. - - faso[fcsuni[a_], b___] -> faso[protectisoconstant[a], b]; - FCPrint[3,"Doing reduction on ", w1//StandardForm]; - subres = FixedPoint[ - (If[ FreeQ[#,isowait], - w2 = #/.isowaitrules3, - w2 = # - ]; - FixedPoint[(FCPrint[2, "Applying renaming rules"]; - IndicesCleanup1[#, opts]) &, - If[ FCleanup /. Flatten[{opts}] /. Options[IndicesCleanup], - FCPrint[2, "Using FCleanup->True"]; - FCPrint[2, - "Renaming product functions and protecting constants"]; - w2 /. {fcsuni[a_] :> protectisoconstant[a]/; (UScalarQ[a] || - !FreeQ[$ConstantIsoIndices, a]), - LorentzIndex[a_] :> protectliconstant[a] /; UScalarQ[a]} /. - dummyrulesf3 /. dummyrulesf2 /. - dummyrulesf1 /. {NM -> NM1, - Times -> NM1, - DOT -> NM2,(*change 19/1 - 1999*) - Power[a_, b_ /; b > 0 && IntegerQ[b]] :> - NM1 @@ Table[a, {ddum, 1, b}]}, - FCPrint[2, - "Renaming product functions and protecting constants"]; - w2 /. {fcsuni[a_/; (UScalarQ[a] || !FreeQ[$ConstantIsoIndices, a])] -> - protectisoconstant[a], - LorentzIndex[a_] :> protectliconstant[a] /; UScalarQ[a] } /. {NM -> - NM1, Times -> NM1, DOT -> NM2, - Power[a_, b_ /; b > 0 && IntegerQ[b]] :> - NM1 @@ Table[a, {ddum, 1, b}]} - ]])&,w1]; - FCPrint[2, - "Putting back product function names and constants"]; - subres /. {isomult->Sequence[],lorentzmult->Sequence[]} /. - {NM1 ->NM, NM2 -> DOT} /. {protectisoconstant -> fcsuni, - protectliconstant -> LorentzIndex} /. - (*Commented out 20/6-2003*)(*faso[fcsuni[ii_]] -> faso[ii] /.*) {su2delta1 -> SU2Delta, - su2f1 -> SU2F, su3delta1 -> SU3Delta, su3f1 -> SU3F, - su3d1 -> SU3D, sundelta1 -> SUNDelta, sunf1 -> SUNF, - sund1 -> SUND} /. - dummynames[ - IsoDummys /. Flatten[{opts}] /. Options[IndicesCleanup], - LorentzDummys /. Flatten[{opts}] /. - Options[IndicesCleanup]] /. - DiracGamma -> dg /. Flatten[{larul[[1]], larul[[3]]}] /. - larul[[2]] /. dg -> DiracGamma /. Null->Sequence[] //. - tracerule2 /. tracerule3 /. cheapnesthackruleback // - (If[ declutr, - FCPrint[2, "DeclareUScalar[UTrace1]"]; - DeclareUScalar[UTrace1] - ]; - If[ (CommutatorReduce /. Flatten[{opts}] /. Options[IndicesCleanup]), - FCPrint[2, "Applying CommutatorReduce"]; - # // ( CommutatorReduce[#,opts])&, - # - ])& // - If[ (ExtendedCleanup /. Flatten[{opts}] /. Options[IndicesCleanup]), - FCPrint[2, "Applying SortIndices"]; - # // ( SortIndices[#,opts])&, - # - ]&); - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Multiplication of factors containing contracted indices *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Replace NM with CNM and contracted indices in factors will be renamed *) - -CNM[a_, b_, opts___Rule] := - Block[ {ais = {}, bis = {}, ais1 = {}, bis1 = {}, isos, - lors, is, dum, j, jj, nm, nma, nmb}, - siCNM = 0; - liCNM = 0; - a /. ((NM | Times)[___, - j_?(! FreeQ[#, fcsuni[__] | LorentzIndex[__]] &), ___, - jj_?(! FreeQ[#, fcsuni[__] | LorentzIndex[__]] &), ___]) :> - dum /; ((ais = - Intersection[ - Cases[j, fcsuni[__] | LorentzIndex[__], Infinity, - Heads -> True], - Cases[jj, fcsuni[__] | LorentzIndex[__], Infinity, - Heads -> True]]) =!= {}); - ais1 = Cases[ - Cases[{a}, ((_?(! FreeQ[#, fcsuni[__] | LorentzIndex[__]] &))^2), - Infinity, Heads -> True], fcsuni[_], Infinity, Heads -> True]; - b /. ((NM | Times)[___, - j_?(! FreeQ[#, fcsuni[__] | LorentzIndex[__]] &), ___, - jj_?(! FreeQ[#, fcsuni[__] | LorentzIndex[__]] &), ___]) :> - dum /; ((bis = - Intersection[ - Cases[j, fcsuni[__] | LorentzIndex[__], Infinity, - Heads -> True], - Cases[jj, fcsuni[__] | LorentzIndex[__], Infinity, - Heads -> True]]) =!= {}); - bis1 = Cases[ - Cases[{b}, ((_?(! FreeQ[#, fcsuni[__] | LorentzIndex[__]] &))^2), - Infinity, Heads -> True], fcsuni[__] | LorentzIndex[__], - Infinity, Heads -> True]; - If[ (is = Intersection[Union[ais, ais1], Union[bis, bis1]]) =!= {}, - isos = IsoDummys /. {opts} /. Options[CNM]; - lors = LorentzDummys /. {opts} /. Options[CNM]; - NM[a, b /. (Rule[#, - If[ Head[#] === fcsuni, - ++siCNM; - fcsuni[isos[[siCNM]]], - ++liCNM; - LorentzIndex[lors[[liCNM]]] - ]] &/@ is)], - NM[a, b] - ] - ]; - -CNM[aa_, bb_, cc__?(!MatchQ[#,Rule]&),opts___Rule] := - Block[ {isos = IsoDummys /. {opts} /. Options[CNM], - lors = LorentzDummys /. {opts} /. Options[CNM]}, - CNM[CNM[aa, bb, opts], cc, IsoDummys -> Drop[isos, siCNM], - LorentzDummys -> Drop[lors, siCNM]] - ]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Isospin projection *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(*!!This whole section should be reworked if it's to be of any use, - e.g. using ClebschGordan. - Think it even might be wrong!!*) - -(* Projecting out IsoVectors in particle channels: *) - -FieldProjection[ - IsoVector[ - QuantumField[ders___, Particle[p : Alternatives @@ $Particles, pp___], - la___], ___], - opts___] := - (Select[$IsoSpinProjectionRules, (!FreeQ[#, (Channel /. Flatten[{opts}] /. - Options[FieldProjection]) -> _] &)])[[1, 2]] /. - Iso[par_, {i_}] -> QuantumField[ders, Particle[par, pp], fcsuni[i], la]; -FieldProjection[ - IsoVector[ - QuantumField[ders___, Particle[p : Alternatives @@ $Particles, pp___], - la___], ___][x_], - opts___] := - (Select[$IsoSpinProjectionRules, (!FreeQ[#, (Channel /. Flatten[{opts}] /. - Options[FieldProjection]) -> _] &)])[[1, 2]] /. - Iso[par_, {i_}] -> QuantumField[ders, Particle[par, pp], fcsuni[i], la][x]; - - - -(* Support functions for AmplitudeProjection: *) - - -(* The in and out particles are arranged as {tou,in}: *) - -processfieldproduct[a_List -> b_List] := - Join[ChargeConjugate /@ Reverse[b], a]; - - - -(* On-mass-shell rules: *) - -processmasses[a_List -> b_List, opts___][ - i_] := - (ParticleMass[#, - Sequence @@ (MassArguments /. Flatten[{opts}] /. - Options[AmplitudeProjection])] & /@ Join[a, b])[[i]]; -momentarules[ - opts___] := - (mv[i_] := - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[AmplitudeProjection]) <> ToString[i]]; - Flatten[Join[{ - If[ (OnMassShell /. Flatten[{opts}] /. - Options[AmplitudeProjection]), - Table[Pair[Momentum[mv[irep], ___], - Momentum[mv[ - irep], ___]] -> (processmasses[(Channel /. - Flatten[{opts}] /. - Options[AmplitudeProjection])[[1]]][ - irep])^2, {irep, - Length[(Channel /. Flatten[{opts}] /. - Options[AmplitudeProjection])[[1, 1]]] + - Length[(Channel /. Flatten[{opts}] /. - Options[AmplitudeProjection])[[1, - 2]]]}], - {} - ]}]]); - - - -(* Projecting amplitudes out in particle channels: *) - -AmplitudeProjection[amp_, - opts___Rule] := - (Expand[ - NMExpand[ - NM @@ (processfieldproduct[(Channel /. Flatten[{opts}] /. - Options[ - AmplitudeProjection])[[1]]] /. \ - ($IsoSpinProjectionRules /. Iso -> iso1)) /. - ChargeConjugate[Plus[a_, b___]] :> - Plus @@ ChargeConjugate /@ {a, b}]] /. - NM -> amp1) /. {iso1[PhiMeson, {aa_Integer|(aa:ExplicitSUNIndex[_Integer])}] -> aa, - iso1[Pion, {aa_Integer|(aa:ExplicitSUNIndex[_Integer])}] -> aa} /. - iso1[_, {aa_Integer|(aa:ExplicitSUNIndex[_Integer])}] -> aa /. momentarules[opts] /. amp1 -> amp; - - - -(* PionKaonIsoSpin->3/2: *) - -AmplitudeProjection[amp_, - opts___Rule] /; ((Channel /. Flatten[{opts}] /. - Options[AmplitudeProjection]) === {{Pion, Kaon} -> {Kaon, Pion}, - 3/2}) := - AmplitudeProjection[amp, - Channel -> {{PionPlus, KaonPlus} -> {KaonPlus, PionPlus}}, - Sequence[opts]]; - - - -(* PionKaonIsoSpin->1/2: *) - -AmplitudeProjection[amp_, - opts___Rule] /; ((Channel /. Flatten[{opts}] /. - Options[AmplitudeProjection]) === {{Pion, Kaon} -> {Kaon, Pion}, - 1/2}) := - -1/2* - AmplitudeProjection[amp, - Channel -> {{PionPlus, KaonPlus} -> {KaonPlus, PionPlus}}, - Sequence[opts]] + - 3/2*AmplitudeProjection[amp, - Channel -> {{KaonPlus, PionMinus} -> {KaonPlus, PionMinus}}, - Sequence[opts]]; - - - -(* PionPionIsoSpin->2: *) - -AmplitudeProjection[amp_, - opts___Rule] /; ((Channel /. Flatten[{opts}] /. - Options[AmplitudeProjection])) === {{Pion, Pion} -> {Pion, - Pion}, 2} := - AmplitudeProjection[amp, - Channel -> {{PionPlus, PionPlus} -> {PionPlus, PionPlus}}, - Sequence[opts]]; - - - -(* PionPionIsoSpin->1: *) - -AmplitudeProjection[amp_, - opts___Rule] /; ((Channel /. Flatten[{opts}] /. - Options[AmplitudeProjection]) === {{Pion, Pion} -> {Pion, Pion}, - 1}) := - 2* - AmplitudeProjection[amp, - Channel -> {{PionPlus, PionZero} -> {PionPlus, PionZero}}, - Sequence[opts]] - - AmplitudeProjection[amp, - Channel -> {{PionPlus, PionPlus} -> {PionPlus, PionPlus}}, - Sequence[opts]]; - - - -(* PionPionIsoSpin->0: *) - -AmplitudeProjection[amp_, - opts___Rule] /; ((Channel /. Flatten[{opts}] /. - Options[AmplitudeProjection]) === {{Pion, Pion} -> {Pion, Pion}, - 0}) := - 3* - AmplitudeProjection[amp, - Channel -> {{PionZero, PionZero} -> {PionZero, PionZero}}, - Sequence[opts]] - - 2*AmplitudeProjection[amp, - Channel -> {{PionPlus, PionPlus} -> {PionPlus, PionPlus}}, - Sequence[opts]]; - - -FCPrint[1,"PHI: Channels.m loaded."]; -End[]; diff --git a/FeynCalc/Phi/Configurations/BChPT2.conf b/FeynCalc/Phi/Configurations/BChPT2.conf deleted file mode 100644 index a8c0bc808..000000000 --- a/FeynCalc/Phi/Configurations/BChPT2.conf +++ /dev/null @@ -1,629 +0,0 @@ -(* ************************************************************** *) -(* *) -(* BChPT2 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - Lagrangians BChPT2 for PHI - -Description: Definitions for the relativistic - ChPT BChPT lagrangians. - - The definitions follow - J. Gasser, M. E. Sainio and - A. Svarc (1988), Nucl. Phys, B307, 779-853. -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPT2::usage= -"Lagrangian[ChPT2[2]] is the pionic Chiral Perturbation Theory -lagrangian written in terms of a matrix representation -of the meson fields to second order in the energy. Lagrangian[ChPT2[4]] -is the pionic Chiral Perturbation Theory lagrangian -to four'th order in the energy (first written down by Gasser and -Leutwyler). To evaluate use ArgumentsSupply."; - -Phi`Objects`BChPT2::usage= -"Lagrangian[BChPT2[2]] is the lowest order nucleon-pion -Chiral Perturbation Theory lagrangian. To evaluate -use ArgumentsSupply."; - -Phi`Objects`USmall::usage= -"USmall[mu] is the u-field of BChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204)."; - -Phi`Objects`UGamma::usage= -"UGamma[mu] is the gamma-field of BChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply. -UGamma[mu,opts][x] is the evaluated gamma-field."; - -Phi`Objects`UChiPlus::usage= -"UChiPlus[opts] is the chi_plus-field of BChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply"; - -Phi`Objects`UChiMinus::usage= -"UChiMinus[opts] is the chi_minus-field of BChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UFMinus::usage= -"UFMinus[mu,nu] is the f_minus-field of BChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UFPlus::usage= -"UFPlus[mu,nu] is the f_plus-field of BChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UVTensor::usage= -"UVTensor[mu,nu] is the v-tensor of BChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -It uses the Vector[1]. -To evaluate use ArgumentsSupply."; - -Phi`Objects`GasserDelta::usage= -"GasserDelta[mu] is the delta field of J. Gasser, M. E. Sainio and -A. Svarc (1988), Nucl. Phys, B307, 779-853."; - -Phi`Objects`NucleonLeftComponent::usage="" - -Phi`Objects`NucleonRightComponent::usage="" - -Phi`Objects`MesonLeftComponent::usage="" - -Phi`Objects`MesonRightComponent::usage="" - -(* ************************************************************** *) - -(* Box definitions *) - -ClearAll[Vector,AxialVector]; - -Vector/:MakeBoxes[Vector[1],TraditionalForm]:= -SuperscriptBox[MakeBoxes[ -StyleForm["v",FontSlant->"Italic"]][[1]],"(s)"]; - -Vector/:MakeBoxes[Vector[_],TraditionalForm]:= -MakeBoxes[StyleForm["v",FontSlant->"Italic"]]; - -AxialVector/:MakeBoxes[AxialVector[_],TraditionalForm]:= -MakeBoxes[StyleForm["a",FontSlant->"Italic"]]; - -SetFAField/@{Vector,AxialVector}; - -VariableBoxes["J",ParticlesNumber->12]; - - CovariantNucleonFieldDerivative /: - MakeBoxes[CovariantNucleonFieldDerivative[a_,_,lis___fcpd], -TraditionalForm] := - RowBox[{SubscriptBox[ -MakeBoxes[ StyleForm["D",FontSlant->"Italic"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{lis}]],"(", - MakeBoxes[TraditionalForm[a]],")"}]; - - CovariantNucleonFieldDerivative /: - MakeBoxes[CovariantNucleonFieldDerivative[a_,{lis___}], -TraditionalForm] := - RowBox[{SubscriptBox[ -MakeBoxes[ StyleForm["D",FontSlant->"Italic"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{lis}]],"(", - MakeBoxes[TraditionalForm[a]],")"}]; - -NucleonLeftComponent /: MakeBoxes[NucleonLeftComponent, TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptCapitalL]", FontSlant -> "Italic"]]; - -NucleonRightComponent /: MakeBoxes[NucleonRightComponent, TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptCapitalR]", FontSlant -> "Italic"]]; - -NucleonLeftComponent /: MakeBoxes[NucleonLeftComponent[__], TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptCapitalL]", FontSlant -> "Italic"]]; - -NucleonRightComponent /: MakeBoxes[NucleonRightComponent[__], TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptCapitalR]", FontSlant -> "Italic"]]; - - -MesonLeftComponent /: MakeBoxes[MesonLeftComponent, TraditionalForm] := - MakeBoxes[StyleForm["\[GothicCapitalL]", FontSlant -> "Italic"]]; - -MesonRightComponent /: MakeBoxes[MesonRightComponent, TraditionalForm] := - MakeBoxes[StyleForm["\[GothicCapitalR]", FontSlant -> "Italic"]]; - -MesonLeftComponent /: MakeBoxes[MesonLeftComponent[__], TraditionalForm] := - MakeBoxes[StyleForm["\[GothicCapitalL]", FontSlant -> "Italic"]]; - -MesonRightComponent /: MakeBoxes[MesonRightComponent[__], TraditionalForm] := - MakeBoxes[StyleForm["\[GothicCapitalR]", FontSlant -> "Italic"]]; - -(* ************************************************************** *) - -(* Attributes and data types *) - -DeclareNonCommutative[UVector, MM, SMM]; -UnDeclareNonCommutative[QuantumField,PartialD]; -DeclareNonCommutative[QuantumField[__][_]?(! FreeQ[#, _Fermion] &)]; - -(* ************************************************************** *) - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[Scalar[0],st___RenormalizationState, -sc___RenormalizationScheme,qs___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -UQuarkMassMatrix[st,sc,qs,opts]; - -(* ************************************************************** *) - - -QuantumField[aa___, Particle[NucleonLeftComponent[a_,opts0___Rule],i___],bb___(*,(opts___Rule|opts___List)*)][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x])+ - NM[UNucleonChargeMatrix[],QuantumField[aa,Particle[Photon,i],bb][x]]; - -QuantumField[aa___, Particle[NucleonRightComponent[a_,opts0___Rule],i___],bb___(*,(opts___Rule|opts___List)*)][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x])+ - NM[UNucleonChargeMatrix[],QuantumField[aa,Particle[Photon,i],bb][x]]; - - -QuantumField[aa___, Particle[MesonLeftComponent[a_,opts0___Rule],i___],bb___(*,(opts___Rule|opts___List)*)][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x])+ - NM[UQuarkChargeMatrix[],QuantumField[aa,Particle[Photon,i],bb][x]]; - -QuantumField[aa___, Particle[MesonRightComponent[a_,opts0___Rule],i___],bb___(*,(opts___Rule|opts___List)*)][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x])+ - NM[UQuarkChargeMatrix[],QuantumField[aa,Particle[Photon,i],bb][x]]; - - - - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Adjoint[QuantumField[d___,p:(Particle[ -Fermion[_],___]),r___][x_]] = QuantumField[d,Adjoint[p],r][x]; - -Adjoint[QuantumField[d___,p:(Particle[ -Fermion[_],___]),r___]] = QuantumField[d,Adjoint[p],r]; - -Adjoint[QuantumField[d___,p:(DiracBar[Particle[ -Fermion[_],___]]),r___][x_]] = QuantumField[d,Adjoint[p],r][x]; - -Adjoint[QuantumField[d___,p:(DiracBar[Particle[ -Fermion[_],___]]),r___]] = QuantumField[d,Adjoint[p],r]; - - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Source fields: -We set the vector- and the axial vactor- source fields to zero -*) - - -QuantumField[___,Particle[PseudoScalar[0],___],___][_]:=0; -IsoVector[QuantumField[Particle[PseudoScalar[0],___],___],___][_]:=0; -IsoVector[QuantumField[Particle[Scalar[0],___],___],___][_]:=0; -IsoVector[QuantumField[Particle[Scalar[2],___],___],___][_]:=0; -QuantumField[Particle[Scalar[2],___],___][_]:=0; -QuantumField[Particle[Vector[0],___],___][_]:=0; -QuantumField[Particle[AxialVector[0],___],___][_]:=0; - - -(* ************************************************************** *) - -(* Antiparticles *) -(* -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; -*) -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -(*ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0;*) - -(*CouplingConstant[ChPT2[4],1,___][___]=0; -CouplingConstant[ChPT2[4],2,___][___]=0; -CouplingConstant[ChPT2[4],3,___][___]=0; -CouplingConstant[ChPT2[4],4,___][___]=0; -CouplingConstant[ChPT2[4],5,___][___]=0; -CouplingConstant[ChPT2[4],6,___][___]=0; -CouplingConstant[ChPT2[4],7,___][___]=0; -CouplingConstant[ChPT2[4],8,___][___]=0; -CouplingConstant[ChPT2[4],9,___][___]=0; -CouplingConstant[ChPT2[4],10,___][___]=0; -CouplingConstant[ChPT2[4],11,___][___]=0; -CouplingConstant[ChPT2[4],12,___][___]=0;*) - -(* ************************************************************** *) - -(* Redefinition of the left and right components -Gasser et al. write them out in vectors and axial-vectors, -but with this I can reuse some of the Ecker stuff. They are -interchanged and multiplied with two compared to the default *) -(*Paul has this commented out - F.Orellana*) -(* -IsoVector[QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___], -bb___],opts___][x_]/;(Explicit/.{opts0}/.Options[LeftComponent]):= -( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]- -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -IsoVector[QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___], -opts___][x_]/;(Explicit/.{opts0}/.Options[RightComponent]):=( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]+ -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); -*) - -(* ************************************************************** *) - -(* The u_mu field *) - -(* We're overriding *) -$Substitutions = Select[$Substitutions, -(!MatchQ[#, (_?((! FreeQ[#, USmall, Heads -> True]) &)) :> _])&]; - - -$Substitutions = Append[$Substitutions, -USmall[mu_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -I*NM[Adjoint[SMM[x,ar,br,cr,opts]],FDr[SMM[x,ar,br,cr,opts],x,{mu}]]+ - -NM[Adjoint[SMM[x,ar,br,cr,opts]], -QuantumField[Particle[MesonRightComponent[0],ar,br,cr],{mu}][x], -SMM[x,ar,br,cr,opts]]- - -I*NM[SMM,FDr[Adjoint[SMM[x,ar,br,cr,opts]],x,{mu}]]- - -NM[SMM[x,ar,br,cr,opts], -QuantumField[Particle[MesonLeftComponent[0],ar,br,cr],{mu}][x], -Adjoint[SMM[x,ar,br,cr,opts]]]]; - - -$Substitutions = Append[$Substitutions, -USmall[mu_] :> - -I*NM[Adjoint[SMM],FDr[SMM,{mu}]]+ - -NM[Adjoint[SMM], -QuantumField[Particle[MesonRightComponent[0]],{mu}],SMM]- - -I*NM[SMM,FDr[Adjoint[SMM],{mu}]]- - -NM[SMM, -QuantumField[Particle[MesonLeftComponent[0]],{mu}],Adjoint[SMM]]]; - -(* ************************************************************** *) - -(* The Gamma_mu field *) - -(* We're overriding *) -$Substitutions = Select[$Substitutions, -(!MatchQ[#, (_?((! FreeQ[#, UGamma, Heads -> True]) &)) :> _])&]; - -$Substitutions = Append[$Substitutions, -UGamma[mu_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -1/2*( - -NM[Adjoint[SMM[x,ar,br,cr,opts]], -FDr[SMM[x,ar,br,cr,opts],x,{mu}]]- - -NM[FDr[SMM[x,ar,br,cr,opts],x,{mu}], -Adjoint[SMM[x,ar,br,cr,opts]]]- - -I*NM[Adjoint[SMM[x,ar,br,cr,opts]], -QuantumField[Particle[NucleonRightComponent[0], -ar,br,cr],{mu}][x], -SMM[x,ar,br,cr,opts]]- - -I*NM[SMM[x,ar,br,cr,opts], -QuantumField[Particle[NucleonLeftComponent[0], -ar,br,cr],{mu}][x], -Adjoint[SMM[x,ar,br,cr,opts]]] - -)]; - -$Substitutions = Append[$Substitutions, -UGamma[mu_] :> - -1/2*( - -NM[Adjoint[SMM],FDr[SMM,{mu}]]- - -I*NM[Adjoint[SMM], -QuantumField[Particle[NucleonRightComponent[0]],{mu}],SMM]+ - -NM[SMM,FDr[Adjoint[SMM],{mu}]]- - -I*NM[SMM, -QuantumField[Particle[NucleonLeftComponent[0]],{mu}],Adjoint[SMM]] - -)]; - - -(* ************************************************************** *) - -(* Redefinition of the field strength tensor: -I instead of I *) -(*Paul has this commented out - F.Orellana*) -(* - -FST[p_,mu_LorentzIndex, - nu_LorentzIndex,x_, - a___RenormalizationState, - b___RenormalizationScheme,(opts___Rule|opts___List)]:= -FieldStrengthTensor[mu, -UGeneratorMatrixIsoDotFull[QuantumField[ -Particle[p,a,b],nu][x],opts],x]-2*I* - UGeneratorMatrixIsoDotFull[ - IsoCross[( - IsoVector[QuantumField[Particle[p,a,b],mu],##]&@@ - OptionsSelect[IsoVector,opts])[ - x],(IsoVector[QuantumField[Particle[p,a,b],nu],##]&@@ - OptionsSelect[IsoVector,opts])[x]],opts]; -*) - -(* ************************************************************** *) - -(* The iso-singlet v field. -The field Vector[1] is used *) - -$Substitutions = Append[$Substitutions, -UVTensor[mu_,nu_, - a___RenormalizationState, - b___RenormalizationScheme,(opts___Rule|opts___List)][x_] :> -UIdentityMatrix[opts]* -FieldStrengthTensor[{mu}, -QuantumField[Particle[Vector[1],a,b],{nu}][x],opts]]; - -$Substitutions = Append[$Substitutions, -UVTensor[mu_,nu_] :> -UIdentityMatrix* -FieldStrengthTensor[{mu}, -QuantumField[Particle[Vector[1]],{nu}]]]; - -(* ************************************************************** *) - -(* The delta field of Gasser et al. *) - -$Substitutions = Append[$Substitutions, -GasserDelta[mu_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> -1/2*NM[Adjoint[SMM[x,ar,br,cr,opts]],CDr[MM[x,ar,br,cr,opts],x,{mu}], -Adjoint[SMM[x,ar,br,cr,opts]]]]; - -$Substitutions = Append[$Substitutions, -GasserDelta[mu_] :> -1/2*NM[Adjoint[SMM],CDr[MM,{mu}],Adjoint[SMM]]]; - -(* ************************************************************** *) - -(* The covariant derivatives *) - -CNDr:=CovariantNucleonFieldDerivative; - -(* -------------------------------------------------------------- *) - -(* Supplying LorentzIndex *) - -CovariantNucleonFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantNucleonFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -(* The nucleon *) - -CovariantNucleonFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] := -( -ggu=(SUNN/.Options[UMatrix]); -ggi=(SUNN/.Options[IsoVector]); -ggg=(SUNN/.Options[CovariantFieldDerivative]); - -SetOptions[UMatrix,SUNN->ggg]; -SetOptions[IsoVector,SUNN->ggg]; - - -cfdr=NM[UIdentityMatrix[##]&@@OptionsSelect[UMatrix,opts], - FieldDerivative[aa,x,lori]] + -UDot[ -UGamma[lori[[1]],ar,br,cr,Sequence@@Join[Flatten[{opts}], -Select[{DiagonalToU->True, -ExpansionOrder->2,DropOrder->2}, -FreeQ[Part[#,1]&/@Flatten[{opts}],#[[1]]]&]]][x],aa]; - -SetOptions[UMatrix,SUNN->ggu]; -SetOptions[IsoVector,SUNN->ggi]; - -cfdr -); - -(* -------------------------------------------------------------- *) - -(* The pion *) -(* Notice that in contrast to ChPT2.conf, -we use e.g -QuantumField[Particle[LeftComponent[0],ar,br],lori][x] -instead of -UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br],lori][x],opts], - -that is, we consider the source field as one -field, and not as a matrix generated by 3 -fields plus a singlet field *) - -CovariantFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] := - -FieldDerivative[aa,x,lori] + - -I*NM[aa,QuantumField[Particle[MesonLeftComponent[0],ar,br],lori][x]] - - -I*NM[QuantumField[Particle[MesonRightComponent[0],ar,br],lori][x],aa]; - -(* ************************************************************** *) -(* Modify the nucleon propagator to use renormalized masses -in the spinors *) - - -Phi`Couplings`GenProps[a:$FermionHeads]:={ -FeynArts`AnalyticalPropagator[ -FeynArts`External][ s a[i, mom] ] == -NonCommutative[ -(*Tag, so WFRenormalize can do its thing*) -Phi`Couplings`Private`propSpinor[ --mom, FeynArts`Mass[ a[i] ], -Sequence @@ Drop[{i},1], RenormalizationState[1] ] ], -FeynArts`AnalyticalPropagator[ -FeynArts`Internal][ s a[i,mom] ] == -NonCommutative[ -Phi`Couplings`Private`propGamma[ --mom, FeynArts`Mass[a[i]]] ]* -I*PropagatorDenominator[ mom , -FeynArts`Mass[a[i]] ]}; - - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - - -(* We use the sigma-parameterization for the matrix U, of course only -in SU(2) ;-) *) - -$UExpansionCoefficients = {1, 1, 1/2, 0, -1/8, 0, 1/16, 0, -5/128, 0, 7/256}; - -(* We use a different definition of the Pauli matrices *) - -$SUNBasis[2,1/2] = {{{0,1},{1,0}},{{0,-I},{I,0}},{{1,0},{0,-1}}}; - -FixSUN; - -$ParticlesInUse={Pion,Nucleon,Vector[1],Vector[0],AxialVector[0]}; - -$ExpansionQuantities=Join[$ExpansionQuantities, -{CouplingConstant[BChPT2[2],a___], DiracMatrix[_], -NonCommutative[DiracMatrix[_]..]}]; - -$PropagatorMassesStates={Pion[0]->{RenormalizationState[0]}, - Nucleon[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - Vector[0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{Pion[0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Nucleon[0]->{{IsoRange->{1,2},IsoIndicesString->"J"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"II"}}, -Vector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"II"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{(*Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, - AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Photon[0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}*)}; - -Options[CovariantNucleonFieldDerivative]:= -{SUNN->2,DiagonalToU->True, -ExpansionOrder->2,DropOrder->2}; - -Options[CovariantFieldDerivative]= -{DiagonalToU->True, -SUNN->2,UDimension->Automatic, -ExpansionOrder->2,DropOrder->2}; - -SetOptions[UQuarkMass, QuarkToMesonMasses -> False]; - - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/ChPT2.conf b/FeynCalc/Phi/Configurations/ChPT2.conf deleted file mode 100644 index a63daec27..000000000 --- a/FeynCalc/Phi/Configurations/ChPT2.conf +++ /dev/null @@ -1,258 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPT2 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - lagrangians ChPT2 for PHI - -Description: Definitions for standard ChPT lagrangians. - - The definitions follow - J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPT2::usage= -"Lagrangian[ChPT2[2]] is the pionic Chiral Perturbation Theory -lagrangian written in terms of a matrix representation -of the meson fields to second order in the energy. -Lagrangian[ChPT2[4]] is the pionic Chiral Perturbation Theory lagrangian -to four'th order in the energy (first written down by Gasser and -Leutwyler). To evaluate use ArgumentsSupply."; - -(* ************************************************************** *) - -(* Source fields *) - -(* The setting below expands the zero'th Scalar[0] -source around the quark mass. The Scalar[1] source with SUNIndex[0] is -then the perturbation. Iso-spin breaking and pseudo-scalar -sources can be controlled by (un)setting the relevant sources -to zero *) - -(*Added 15/6-2001*) -IsoVector[QuantumField[Particle[ -Scalar[0],ar___RenormalizationState, -br___RenormalizationScheme,cr___ExpansionState, -opts___Rule|opts___List]],opts1___][x_]:= -IsoVector[QuantumField[Particle[Scalar[1],ar,br,cr]],opts1][x]; - -QuantumField[Particle[ -Scalar[0],ar___RenormalizationState, -br___RenormalizationScheme,cr___ExpansionState, -opts___Rule|opts___List], SUNIndex[0]][x_]:= -ParticleMass[Pion,ar,br,cr]^2/ -(2*QuarkCondensate[ar,br,cr,Sequence@@OptionsSelect[QuarkCondensate,opts]])+ -QuantumField[Particle[Scalar[1],ar,br,cr, -Sequence@@OptionsSelect[Particle,opts]], -SUNIndex[0]][x]; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -(*ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0;*) - -(*CouplingConstant[ChPT2[4],1,___]=0; -CouplingConstant[ChPT2[4],2,___]=0; -CouplingConstant[ChPT2[4],3,___]=0; -CouplingConstant[ChPT2[4],4,___]=0; -CouplingConstant[ChPT2[4],5,___]=0; -CouplingConstant[ChPT2[4],6,___]=0; -CouplingConstant[ChPT2[4],7,___]=0; -CouplingConstant[ChPT2[4],8,___]=0; -CouplingConstant[ChPT2[4],9,___]=0; -CouplingConstant[ChPT2[4],10,___]=0; -CouplingConstant[ChPT2[4],11,___]=0; -CouplingConstant[ChPT2[4],12,___]=0;*) - -(* ************************************************************** *) - -(* The nabla of the u_mu field *) - -Options[CovariantNabla] = {Explicit -> True}; - -CovariantNabla[aa_,x_,loris__LorentzIndex,lori1_LorentzIndex, opts___Rule]:= -(newfuncc[1]=CovariantNabla[aa,x,lori1, opts]; -Do[newfuncc[rep+1]=CovariantNabla[ -newfuncc[rep],x,##,opts]&@@Take[{loris},{-rep}], -{rep,1,Length[{loris}]}];newfuncc[Length[{loris}]+1]); - -CovariantNabla[aa_,x_,{loris__},rest___] := -CovariantNabla[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -CovariantNabla[aa_,{lori_},(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,{lori}] + - -NM[UGamma[lori],aa] - -NM[aa,UGamma[lori]]; - -CovariantNabla[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,x,lori] + - -NM[UGamma[lori,ar,br,cr,opts][x],aa] - -NM[aa,UGamma[lori,ar,br,cr,opts][x]]; - - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -(* Standard ChPT - Donoghue, Golowich, Holstein *) - -CovariantFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantFieldDerivative]) := - -FieldDerivative[aa,x,lori] + - -I*NM[UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br],lori][x],opts],aa] - - -I*NM[aa,UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0],ar,br],lori][x],opts]]; - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - -$ParticlesInUse={Pion,Scalar[0], - Scalar[1],Scalar[2],PseudoScalar[0],Vector[0],AxialVector[0]}; - -$PropagatorMassesStates={Pion[0]->{RenormalizationState[0]}, - Scalar[0]->{RenormalizationState[0]}, - Scalar[1]->{RenormalizationState[0]}, - Scalar[2]->{RenormalizationState[0]}, - PseudoScalar[0]->{RenormalizationState[0]}, - Vector[0]->{RenormalizationState[0]}, - AxialVector[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{Pion[0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Scalar[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Scalar[1][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Scalar[2][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - PseudoScalar[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Vector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}}; - -(* FeynArts does not appear to accept other mixing fields than VS *) - -$MixingFields= -{}; - -(* Switch to Majorana fields *) - -(*SelfConjugation[Vector[0]]:=False;*) - -$InsertOnly= -{Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Scalar[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Scalar[1][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Scalar[2][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -PseudoScalar[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/ChPT3.conf b/FeynCalc/Phi/Configurations/ChPT3.conf deleted file mode 100644 index fa03d12ae..000000000 --- a/FeynCalc/Phi/Configurations/ChPT3.conf +++ /dev/null @@ -1,426 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPT3 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 1999 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - Lagrangians ChPT3 for PHI - -Description: Definitions for standard ChPT lagrangians. - - The definitions follow - J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* SU(3) meson matrix PhiMeson instead of Pion *) - -BeginPackage["Phi`Objects`", {"Phi`", -"FeynCalc`"}]; -Begin["`Private`"]; - -MM[x_?(! NumberQ[#] &), h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MM]) := - - UFieldMatrix[fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -MM[ii_?NumberQ, x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MM]) := - UFieldMatrix[ii, fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -SMM[x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[SMM]) := MM[1/2, x, h, opts]; -MMS[x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MMS]) := - UFieldMatrixSeries[fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; - -End[]; -EndPackage[]; - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPT3::usage= -"Lagrangian[ChPT3[2]] is the mesonic Chiral Perturbation Theory \ -lagrangian written in terms of a matrix representation \ -of the meson fields to second order in the energy. \ -Lagrangian[ChPT3[4]] is the mesonic Chiral Perturbation Theory lagrangian \ -to four'th order in the energy (first written down by Gasser and \ -Leutwyler). To evaluate use ArgumentsSupply."; - -MM::usage="MM[x] := -UFieldMatrix[QuantumField[Particle[PhiMeson]][x]]. -MM takes two optional arguments with head RenormalizationState -and RenormalizationScheme respectively."; - -Phi`Objects`CovariantNabla::usage= -"CovariantNabla[f[x],x,{li1,li2,...},opts] is \ -the covariant derivative of a h h^(-1) transforming quantity f[x] with respect to \ -space-time variables x and with Lorentz indices li0, li1, li2,... \ -(See e.g ChPT (Ecker, Kambor and Wyler (1992), CERN-TH.6610/92) \ -- and note that a gamma is used that follows Holstein, Golowich and \ -Donoghue's LR convention instead of the inverse Bernese convention). \ -To evaluate use ArgumentsSupply."; - -(* ************************************************************** *) - -(* Source fields *) - -(* Strip off options passed to Particle[PseudoScalar[0],___]*) - -Particle[PseudoScalar[0],o___,__Rule]:=Particle[PseudoScalar[0],o]; - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[Scalar[0],st___RenormalizationState, -sc___RenormalizationScheme,qs___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -UQuarkMassMatrix[st,sc,qs,opts]; - -(* ************************************************************** *) - -(* Redefinition of the left and right components -Ecker, Kambor and Wyler have them the other way round. -Also its necessary in order to not have the AxialVector (Vector) -part set to zero *) - -IsoVector[QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___], -bb___],opts___][x_]/;(Explicit/.{opts0}/.Options[LeftComponent]):= -1/2*( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]- -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -IsoVector[QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___], -opts___][x_]/;(Explicit/.{opts0}/.Options[RightComponent]):=1/2*( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]+ -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -1/2*(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -1/2*(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0; - -(*CouplingConstant[ChPT3[4],1,___]=0; -CouplingConstant[ChPT3[4],2,___]=0; -CouplingConstant[ChPT3[4],3,___]=0; -CouplingConstant[ChPT3[4],4,___]=0; -CouplingConstant[ChPT3[4],5,___]=0; -CouplingConstant[ChPT3[4],6,___]=0; -CouplingConstant[ChPT3[4],7,___]=0; -CouplingConstant[ChPT3[4],8,___]=0; -CouplingConstant[ChPT3[4],9,___]=0; -CouplingConstant[ChPT3[4],10,___]=0; -CouplingConstant[ChPT3[4],11,___]=0; -CouplingConstant[ChPT3[4],12,___]=0;*) - - -(* ************************************************************** *) - -(* The nabla of the u_mu field *) - -Options[CovariantNabla] = {Explicit -> True}; - -CovariantNabla[aa_,x_,loris__LorentzIndex,lori1_LorentzIndex, opts___Rule]:= -(newfuncc[1]=CovariantNabla[aa,x,lori1, opts]; -Do[newfuncc[rep+1]=CovariantNabla[ -newfuncc[rep],x,##,opts]&@@Take[{loris},{-rep}], -{rep,1,Length[{loris}]}];newfuncc[Length[{loris}]+1]); - -CovariantNabla[aa_,x_,{loris__},rest___] := -CovariantNabla[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -CovariantNabla[aa_,{lori_},(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,{lori}] + - -NM[UGamma[lori],aa] - -NM[aa,UGamma[lori]]; - -CovariantNabla[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,x,lori] + - -NM[UGamma[lori,ar,br,cr,opts][x],aa] - -NM[aa,UGamma[lori,ar,br,cr,opts][x]]; - - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -(* Standard ChPT - Donoghue, Golowich, Holstein *) - -CovariantFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantFieldDerivative]) := - -FieldDerivative[aa,x,lori] + - -I*NM[UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br],lori][x],opts],aa] - - -I*NM[aa,UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0],ar,br],lori][x],opts]]; - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - -SetOptions[Renormalize,SUNN->3]; -SetOptions[WriteOutUMatrices,SUNN->3]; -SetOptions[WriteOutIsoVectors,SUNN->3]; -SetOptions[UQuarkMass,SUNN->3,DiagonalToU->True]; -SetOptions[UMatrix,SUNN->3]; -SetOptions[IsoVector,SUNN->3]; -SetOptions[UGenerator,SUNN->3]; -SetOptions[UTrace,SUNN->3]; -SetOptions[SUNReduce,SUNN->3]; -SetOptions[ExpandU,SUNN->3]; -SetOptions[FAToFC,EqualMasses->False]; -SetOptions[DiscardTerms, -Retain->{Particle[PhiMeson,RenormalizationState[0]]->4}]; -SetOptions[CovariantFieldDerivative,SUNN->3]; -SetOptions[UPerturb, SUNN -> 3]; -SetOptions[UReduce, SUNN -> 3, UDimension -> 3]; -SetOptions[SMMToMM, SUNN -> 3]; -SetOptions[CharacteristicCoefficient, UDimension -> 3]; -SetOptions[CayleyHamilton, UDimension -> 3]; -SetOptions[CayleyHamiltonRules, SUNN -> 3, UDimension -> 3]; -tmpoptscdr=Options[CovariantFieldDerivative]; -tmpoptsmm=Options[MM]; -SetOptions[CovariantFieldDerivative, Explicit -> False]; -SetOptions[MM, Explicit -> False]; -SetOptions[CayleyHamiltonTrick, SUNN -> 3, UDimension -> 3, - UMatrices :> {{I NM[ - Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]], - I NM[Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]]}}]; -SetOptions[CovariantFieldDerivative, Sequence@@tmpoptscdr]; -SetOptions[MM, Sequence@@tmpoptsmm]; - -$EOMRules = {UTrace1[ - NM[Adjoint[MM[x_]], - CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], - Adjoint[UMatrix[UChi[]][x_]], - CovariantFieldDerivative[MM[x_], x, - LorentzIndex[mu_]]]] -> -(UTrace1[ - NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]^2/ - 6 - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])/3 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]]^2/6 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x]]]/2 - - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x]]]/ - 2 - (-UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[MM[x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[]][x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]]])), - UTrace1[NM[ - Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]]], - MM[x_], Adjoint[UMatrix[UChi[]][x_]], - CovariantFieldDerivative[MM[x_], x, - LorentzIndex[mu_]]]] -> (UTrace1[ - NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]^2/ - 6 - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])/3 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]]^2/6 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x]]]/2 - - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x]]]/ - 2 - (-UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]]] - - UTrace1[NM[ - Adjoint[ - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]] - - UTrace1[NM[MM[x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]], - UMatrix[UChi[]][x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]]]))}; - -$ParticlesInUse= -{PhiMeson,Pion,Kaon,KaonPlus,KaonMinus, -KaonZero,KaonZeroBar,EtaMeson, -Photon,Vector[0],AxialVector[0], -PseudoScalar[0],Scalar[0],Scalar[2]}; - -$ExpansionQuantities= -{FourVector[__],ParticleMass[Pion,a___], -ParticleMass[PhiMeson,b___],ParticleMass[KaonZero,c___], -ParticleMass[KaonPlus,d___],ParticleMass[EtaMeson,d___], -CouplingConstant[QED[2],e___]}; - -$PropagatorMassesStates={ - PhiMeson[0]->{RenormalizationState[0]}, - Pion[0]->{RenormalizationState[0]}, - Kaon[0]->{RenormalizationState[0]}, - KaonPlus[0]->{RenormalizationState[0]}, - KaonMinus[0]->{RenormalizationState[0]}, - KaonZero[0]->{RenormalizationState[0]}, - KaonZeroBar[0]->{RenormalizationState[0]}, - EtaMeson[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - PseudoScalar[0][0]->{RenormalizationState[0]}, - Vector[0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{PhiMeson[0]->{{IsoRange->{0,1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - PseudoScalar[0][0]->{{IsoRange->{0,1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - Scalar[1][0]->{{IsoRange->{0,1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - Scalar[2][0]->{{IsoRange->{0,1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - PseudoScalar[0][0]->{{IsoRange->{0,1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - AxialVector[0][0]->{{IsoRange->{0,1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - Vector[0][0]->{{IsoRange->{0,1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{Scalar[1][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Scalar[2][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -PseudoScalar[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}(*, -Photon[0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}*)}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/ChPTEM2.conf b/FeynCalc/Phi/Configurations/ChPTEM2.conf deleted file mode 100644 index f72c93db0..000000000 --- a/FeynCalc/Phi/Configurations/ChPTEM2.conf +++ /dev/null @@ -1,217 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTEM2 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 2001 - -Mathematica Version: 4.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - lagrangians ChPTEM2 for PHI - -Description: Definitions for standard ChPT lagrangians. - - The definitions follow - Ulf-G. Meissner, G. Mueller, S. Steininger - (1997), hep-ph/9704377 -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPTEM2::usage= -"Lagrangian[ChPTEM2[2] is the pionic Chiral -Perturbation Theory lagrangian with couplings to virtual photons -written in terms of a matrix -representation of the meson fields to second order in the energy -and the electron charge."; - -(* ************************************************************** *) - -(* Source fields *) - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[Scalar[0],st___RenormalizationState, -sc___RenormalizationScheme,qs___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -UQuarkMassMatrix[st,sc,qs,opts]; - -(* To simplify algebra, the iso-vector components -of the vector and axial-vector sources should be set to zero. -Below we identify the iso-spin zero or iso-scalar component of the -vector field with the photon field of the covariant derivative -below *) - -QuantumField[a___,Particle[Vector[1],b___],c___,SUNIndex[0]][x_]:= -QuantumField[a,Particle[Vector[1],b],c][x]; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -(*ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0;*) - -(*CouplingConstant[ChPTPhoton2[4],1,___][___]=0; -CouplingConstant[ChPTPhoton2[4],2,___][___]=0; -CouplingConstant[ChPTPhoton2[4],3,___][___]=0; -CouplingConstant[ChPTPhoton2[4],4,___][___]=0; -CouplingConstant[ChPTPhoton2[4],5,___][___]=0; -CouplingConstant[ChPTPhoton2[4],6,___][___]=0; -CouplingConstant[ChPTPhoton2[4],7,___][___]=0; -CouplingConstant[ChPTPhoton2[4],8,___][___]=0; -CouplingConstant[ChPTPhoton2[4],9,___][___]=0; -CouplingConstant[ChPTPhoton2[4],10,___][___]=0; -CouplingConstant[ChPTPhoton2[4],11,___][___]=0; -CouplingConstant[ChPTPhoton2[4],12,___][___]=0;*) - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -(* EM-ChPT - Meissner, Mueller, Steininger *) - -CovariantFieldDerivative[aa_,x_,lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantFieldDerivative]) := - -FieldDerivative[aa,x,lori] + - -I*NM[UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br],lori][x],opts],aa] - - -I*NM[aa,UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0],ar,br],lori][x],opts]]- - -I* -NM[UQuarkChargeMatrix[ar,br,cr,opts], -QuantumField[Particle[Photon,ar,br],lori][x],aa]+ - -I* -NM[aa,UQuarkChargeMatrix[ar,br,cr,opts], -QuantumField[Particle[Photon,ar,br],lori][x]]; - -(* ************************************************************** *) -(* Modify the photon propagator to general Lorentz gange *) - -Phi`Couplings`GenProps[a:Vector1] := -{FeynArts`AnalyticalPropagator[ -FeynArts`External][s a[i, mom, {li2}]] == -PolarizationVector[a[i], mom, li2], -FeynArts`AnalyticalPropagator[ -FeynArts`Internal][s a[i, mom, {li1} -> {li2}]] == -I*PropagatorDenominator[mom, FeynArts`Mass[a[i]]]* -(-MetricTensor[li1, li2] + -(1 - 1/$Gauge)* -FourVector[mom, li1]*FourVector[mom, li2]* -1/(PropagatorDenominator1[mom, FeynArts`Mass[a[i]]]) -)}; - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - -$IsoSpinProjectionRules = - {PionPlus -> (Iso[Pion, {1}] - I*Iso[Pion, {2}])/Sqrt[2], - PionMinus -> (Iso[Pion, {1}] + I*Iso[Pion, {2}])/Sqrt[2], - PionZero -> Iso[Pion, {3}]}; - -$ExpansionQuantities=Union[$ExpansionQuantities,{MetricTensor[__],Pair[__]}]; - -$ParticlesInUse={Pion,PionPlus,PionMinus,PionZero,Photon,AxialVector[0](*,Vector[0]*)}; - -$PropagatorMassesStates={Pion[0]->{RenormalizationState[0]}, - Kaon[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - Vector[0][0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{Pion[0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Kaon[0]->{{IsoRange->{1,2},IsoIndicesString->"J"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, -Vector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{(*Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, - AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Photon[0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}*)}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/ChPTPhoton2.conf b/FeynCalc/Phi/Configurations/ChPTPhoton2.conf deleted file mode 100644 index d485e8be5..000000000 --- a/FeynCalc/Phi/Configurations/ChPTPhoton2.conf +++ /dev/null @@ -1,200 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTPhoton2 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - Lagrangians ChPTPhoton2 for PHI - -Description: Definitions for standard ChPT lagrangians. - - The definitions follow - J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPTPhoton2::usage= -"Lagrangian[ChPTPhoton2[2]] is the pionic Chiral Perturbation Theory -lagrangian written in terms of a matrix representation -of the meson fields to second order in the energy. -Lagrangian[ChPTPhoton2[4]] -is the pionic Chiral Perturbation Theory lagrangian -to four'th order in the energy (first written down by Gasser and -Leutwyler). To evaluate use ArgumentsSupply."; - -(* ************************************************************** *) - -(* Source fields *) - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[Scalar[0],st___RenormalizationState, -sc___RenormalizationScheme,qs___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -UQuarkMassMatrix[st,sc,qs,opts]; - -(* To simplify algebra, the iso-vector components -of the vector and axial-vector sources should be set to zero. -Below we identify the iso-spin zero or iso-scalar component of the -vector field with the photon field of the covariant derivative -below *) - -QuantumField[a___,Particle[Vector[1],b___],c___,SUNIndex[0]][x_]:= -QuantumField[a,Particle[Vector[1],b],c][x]; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0; - -(*CouplingConstant[ChPTPhoton2[4],1,___][___]=0; -CouplingConstant[ChPTPhoton2[4],2,___][___]=0; -CouplingConstant[ChPTPhoton2[4],3,___][___]=0; -CouplingConstant[ChPTPhoton2[4],4,___][___]=0; -CouplingConstant[ChPTPhoton2[4],5,___][___]=0; -CouplingConstant[ChPTPhoton2[4],6,___][___]=0; -CouplingConstant[ChPTPhoton2[4],7,___][___]=0; -CouplingConstant[ChPTPhoton2[4],8,___][___]=0; -CouplingConstant[ChPTPhoton2[4],9,___][___]=0; -CouplingConstant[ChPTPhoton2[4],10,___][___]=0; -CouplingConstant[ChPTPhoton2[4],11,___][___]=0; -CouplingConstant[ChPTPhoton2[4],12,___][___]=0;*) - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -Options[CovariantFieldDerivative]= -{DiagonalToU->False, -SUNN->2,UDimension->Automatic}; - -(* -------------------------------------------------------------- *) - -(* Standard ChPT - Donoghue, Golowich, Holstein *) - -CovariantFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] := - -FieldDerivative[aa,x,lori] + - -(* Notice that the covariant derivative now -uses Vector[1] instead of the default Vector[0] *) - -I*NM[UQuarkChargeMatrix[ar,br,cr,opts], -QuantumField[Particle[Photon,ar,br],lori][x],aa]- - -I*NM[aa,UQuarkChargeMatrix[ar,br,cr,opts], -QuantumField[Particle[Photon,ar,br],lori][x]]; - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - -$ExpansionQuantities=Union[$ExpansionQuantities,{MetricTensor[__],Pair[__]}]; - -$ParticlesInUse={Pion,Kaon,Photon(*,Vector[0],AxialVector[0]*)}; - -$PropagatorMassesStates={Pion[0]->{RenormalizationState[0]}, - Kaon[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - Vector[0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{Pion[0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Kaon[0]->{{IsoRange->{1,2},IsoIndicesString->"J"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, -Vector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{(*Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, - AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External},*) -Photon[0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/ChPTPhotonsLeptons3.conf b/FeynCalc/Phi/Configurations/ChPTPhotonsLeptons3.conf deleted file mode 100644 index 3ba1e29d4..000000000 --- a/FeynCalc/Phi/Configurations/ChPTPhotonsLeptons3.conf +++ /dev/null @@ -1,1245 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTPhotonsLeptons3 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 2002 - -Mathematica Version: 4.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - lagrangians ChPTPhotonsLeptons3 for PHI - -Description: Definitions for standard ChPT lagrangians - with virtual photons. - - The definitions follow - M. Knecht, H. Neufeld, H. Rupertsberger, P. Talavera - (1999), hep-ph/9909284 -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`UChiralSpurionLeft1Matrix::usage = - "UChiralSpurionLeft1Matrix[opts] := UMatrix[UChiralSpurionLeft1[opts],opts]."; - -Phi`Objects`UChiralSpurionLeft1::usage = - "UMatrix[UChiralSpurionLeft1[opts],opts] represents CKM matrix with non-relevant \ -entries set to zero."; - -Phi`Objects`VUD::usage= -"VUD is a CKM matrix element."; - -Phi`Objects`VUS::usage= -"VUS is a CKM matrix element."; - -Phi`Objects`FermiConstant::usage = - "FermiConstant is the Fermi coupling constant."; - -Phi`Objects`$ChargeEliminate::usage = - "$ChargeEliminate is a substitution rule, valid to lowest order \ -in the chiral expansion, for replacing the unit charge with the electromagnetic \ -pion mass difference."; - -Phi`Objects`$ChargedMassesEliminate::usage = - "$ChargedMassesEliminate is a substitution rule, valid to lowest order in the \ -chiral expansion, for replacing the charged pion \ -and kaon masses with the unit charge. NOTICE : When using this rule, it is \ -assumed that the neutral - charged kaon mass difference is due solely to \ -the electromagnetic interaction."; - -Phi`Objects`$NeutralMassesEliminate::usage = - "$NeutralMassesEliminate is a substitution rule, valid to lowest order in the \ -chiral expansion, for replacing the neutral pion \ -and kaon masses with the unit charge. NOTICE : When using this rule, it is \ -assumed that the neutral - charged kaon mass difference is due solely to \ -the electromagnetic interaction."; - -Phi`Objects`$CEliminate::usage = - "$CEliminate is a substitution rule, valid to lowest order in the \ -chiral expansion, for replacing the proportionality constant C with the \ -neutral to charged mass difference and the unit electric charge."; - -Phi`Objects`$ChargedNeutralMassesCancel::usage = - "$ChargedNeutralMassesCancel is a substitution rule, valid to lowest order in the \ -chiral expansion, for replacing the difference of the squared charged pion mass \ -and the squared neutral pion mass or the difference of the squared charged kaon mass \ -and the squared neutral kaon mass with the unit charge."; - -Phi`Objects`ChargeEliminate::usage = - "ChargeEliminate[exp] applies $ChargeEliminate to exp."; - -Phi`Objects`ChargedMassesEliminate::usage = - "ChargedMassesEliminate[exp] applies $ChargedMassesEliminate to exp."; - -Phi`Objects`NeutralMassesEliminate::usage = - "NeutralMassesEliminate[exp] applies $NeutralMassesEliminate to exp."; - -Phi`Objects`ChargedNeutralMassesCancel::usage = - "ChargedNeutralMassesCancel[exp] applies $ChargedNeutralMassesCancel to exp."; - -Phi`Objects`CEliminate::usage = - "CEliminate[exp] applies $CEliminate to exp."; - -(**) - -Phi`Objects`ChPTPhotonsLeptons3::usage= -"Lagrangian[ChPTPhotonsLeptons3[2] is the mesonic Chiral \ -Perturbation Theory lagrangian with couplings to virtual photons and leptons\ -written in terms of a matrix representation of the meson fields to second \ -order in the energy and the electron charge. Lagrangian[ChPTPhotonsLeptons24]] \ -is the lagrangian to four'th order in the energy and the electron charge."; - -Phi`Objects`GRight::usage= -"GRight[mu] is the right-handed G field of \ -(Res Urech (1994), hep-ph/9405341). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`GLeft::usage= -"GLeft[mu] is the left-handed G field of \ -(Res Urech (1994), hep-ph/9405341). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`HRight::usage= -"HRight is the right-handed H field of \ -(Res Urech (1994), hep-ph/9405341)."; - -Phi`Objects`HLeft::usage= -"HLeft is the left-handed H field of \ -(Res Urech (1994), hep-ph/9405341)."; - -Phi`Objects`CQRight::usage= -"CQRight[mu] is the covariant derivative of the right-handed \ -Q source of \ -(Res Urech (1994), hep-ph/9405341). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`CQLeft::usage= -"CQLeft[mu] is the covariant derivative of the Left-handed \ -Q source of \ -(Res Urech (1994), hep-ph/9405341). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`CovariantNabla::usage= -"CovariantNabla[f[x],x,{li1,li2,...},opts] is -the covariant nabla of f[x] with respect to -space-time variables x and with Lorentz indices li0, li1, li2,... -as defined in WChPT Ecker, Kambor and Wyler (1992), CERN-TH.6610/92. -To evaluate use ArgumentsSupply."; - -MM::usage="MM[x] := -UFieldMatrix[QuantumField[Particle[PhiMeson]][x]]. -MM takes two optional arguments with head RenormalizationState -and RenormalizationScheme respectively."; - -(* ************************************************************** *) - -(* Box definitions *) - -UChiralSpurionLeft1Matrix /: - MakeBoxes[UChiralSpurionLeft1Matrix, TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]], - MakeBoxes[StyleForm["W", FontSlant -> "Plain"]]]; - -UChiralSpurionLeft1 /: - MakeBoxes[UChiralSpurionLeft1[___], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]], - MakeBoxes[StyleForm["W", FontSlant -> "Plain"]]]; - -VUS /: - MakeBoxes[VUS, TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["V", FontSlant -> "Italic", - FontWeight -> "Bold"]], MakeBoxes[StyleForm["us", FontSlant -> "Plain"]]]; - -VUD /: - MakeBoxes[VUD, TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["V", FontSlant -> "Italic", - FontWeight -> "Bold"]], MakeBoxes[StyleForm["ud", FontSlant -> "Plain"]]]; - -FermiConstant /: - MakeBoxes[FermiConstant, TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["G", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["F", FontSlant -> "Plain"]]]; - -(**) - -Vector /: MakeBoxes[Vector[1], TraditionalForm] := - MakeBoxes[StyleForm["A", FontSlant -> "Italic"]]; - -GRight /: MakeBoxes[GRight[mu__,___Rule][_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]]; - -GRight /: MakeBoxes[GRight[mu__,___Rule], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]]; - -GLeft /: MakeBoxes[GLeft[mu__,___Rule][_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]]; - -GLeft /: MakeBoxes[GLeft[mu__,___Rule], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]]; - -HRight /: MakeBoxes[HRight[___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]]; - -HRight /: MakeBoxes[HRight, TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]]; - -HLeft /: MakeBoxes[HLeft[___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]]; - -HLeft /: MakeBoxes[HLeft, TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]]; - -CQRight /: MakeBoxes[CQRight[mu__,___Rule][_], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]]}]; - -CQRight /: MakeBoxes[CQRight[mu__,___Rule], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm["R"]]]}]; - -CQLeft /: MakeBoxes[CQLeft[mu__,___Rule][_], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm["L"]]]}]; - -CQLeft /: MakeBoxes[CQLeft[mu__,___Rule], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]]}]; - -(* ************************************************************** *) - -(* Source fields *) - -IsoVector[QuantumField[Particle[Scalar[0],___],___],___][_]:=0; -IsoVector[QuantumField[Particle[PseudoScalar[0],___],___],___][_]:=0; -IsoVector[QuantumField[Particle[Vector[0],___],___],___][_]:=0; -(*IsoVector[QuantumField[Particle[AxialVector[0],___],___],___][_]:=0;*) - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[Scalar[0],st___RenormalizationState, -sc___RenormalizationScheme,qs___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -UQuarkMassMatrix[st,sc,qs,opts]; -QuantumField[___,Particle[PseudoScalar[0],___],___][_]:=0; -QuantumField[___,Particle[Vector[0],___],___][_]:=0; -(*QuantumField[___,Particle[AxialVector[0],___],___][_]:=0;*) -QuantumField[Particle[AxialVector[0], ___], ___, SUNIndex[0]][_]:=0; - -(* To simplify algebra, above we set the iso-vector components -of the vector and axial-vector sources to zero and below -we identify the iso-spin zero or iso-scalar component of the -vector field with the photon field of the covariant derivative -below *) - -QuantumField[a___,Particle[Vector[1],b___],c___,SUNIndex[0]][x_]:= -QuantumField[a,Particle[Vector[1],b],c][x]; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -(*ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0;*) - -(*CouplingConstant[ChPTPhoton2[4],1,___][___]=0; -CouplingConstant[ChPTPhoton2[4],2,___][___]=0; -CouplingConstant[ChPTPhoton2[4],3,___][___]=0; -CouplingConstant[ChPTPhoton2[4],4,___][___]=0; -CouplingConstant[ChPTPhoton2[4],5,___][___]=0; -CouplingConstant[ChPTPhoton2[4],6,___][___]=0; -CouplingConstant[ChPTPhoton2[4],7,___][___]=0; -CouplingConstant[ChPTPhoton2[4],8,___][___]=0; -CouplingConstant[ChPTPhoton2[4],9,___][___]=0; -CouplingConstant[ChPTPhoton2[4],10,___][___]=0; -CouplingConstant[ChPTPhoton2[4],11,___][___]=0; -CouplingConstant[ChPTPhoton2[4],12,___][___]=0;*) - -(* ************************************************************** *) - -(* SU(3) meson matrix PhiMeson instead of Pion *) - -BeginPackage["Phi`Objects`", {"Phi`", -"FeynCalc`"}]; -Begin["`Private`"]; - -MM[x_?(! NumberQ[#]&), h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MM]) := - - UFieldMatrix[fcqf[(Particle[PhiMeson, h])][x], ##]& @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -MM[i_?NumberQ, x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MM]) := - UFieldMatrix[i, fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -SMM[x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[SMM]) := MM[1/2, x, h, opts]; -MMS[x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MMS]) := - UFieldMatrixSeries[fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; - -End[]; -EndPackage[]; - -(* ************************************************************** *) - -(* Redefinition of the left and right components. -Urech have them the other way round and without the 1/2. -Also its necessary in order to not have the AxialVector (Vector) -part set to zero *) - -IsoVector[QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___], -bb___],opts___][x_]/;(Explicit/.{opts0}/.Options[LeftComponent]):= -( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]- -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -IsoVector[QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___], -opts___][x_]/;(Explicit/.{opts0}/.Options[RightComponent]):=( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]+ -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -(* ************************************************************** *) - -(* Spurions *) - -(* I think we always want this ?*) - -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurion[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurionRight[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurionLeft[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; - - - -(* ************************************************************** *) - -(* The H fields *) - -$Substitutions = Append[$Substitutions, -HRight[x_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] :> -NM[Adjoint[SMM[x,ar,br,cr]], UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -SMM[x,ar,br,cr]] + -NM[SMM[x,ar,br,cr], UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -Adjoint[SMM[x,ar,br,cr]]]]; - -$Substitutions = Append[$Substitutions, -HLeft[x_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] :> -NM[Adjoint[SMM[x,ar,br,cr]], UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -SMM[x,ar,br,cr]] - -NM[SMM[x,ar,br,cr], UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -Adjoint[SMM[x,ar,br,cr]]]]; - - -$Substitutions = Append[$Substitutions, -HRight :> NM[Adjoint[SMM],UMatrix[UChiralSpurionRight[],SMM]] + - NM[SMM,UMatrix[UChiralSpurionLeft[],Adjoint[SMM]]]]; - -$Substitutions = Append[$Substitutions, -HLeft :> NM[Adjoint[SMM],UMatrix[UChiralSpurionRight[],SMM]] - - NM[SMM,UMatrix[UChiralSpurionLeft[],Adjoint[SMM]]]]; - - - - -(* ************************************************************** *) - -(* The G fields *) - -$Substitutions = Append[$Substitutions, -GRight[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[RightComponent[0, - Sequence@@OptionsSelect[RightComponent,opts]],ar,br,cr],{mu}][x]]+ - NM[UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - QuantumField[Particle[Photon,ar,br,cr],{mu}][x]]]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[LeftComponent[0, - Sequence@@OptionsSelect[LeftComponent,opts]],ar,br,cr],{mu}][x]]+ - NM[UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - QuantumField[Particle[Photon,ar,br,cr],{mu}][x]]]; - -$Substitutions = Append[$Substitutions, -GRight[mu_, nu_?(FreeQ[#, - RenormalizationState | RenormalizationScheme | ExpansionState | - Rule] &), ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> -FieldDerivative[GRight[nu,ar,br,cr,opts][x], x, {mu}] - - FieldDerivative[GRight[mu,ar,br,cr,opts][x],x, {nu}] - -I*(NM[GRight[mu,ar,br,cr,opts][x], GRight[nu,ar,br,cr,opts][x]] - -NM[GRight[nu,ar,br,cr,opts][x], GRight[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_, nu_?(FreeQ[#, - RenormalizationState | RenormalizationScheme | ExpansionState | - Rule] &), ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> -FieldDerivative[GLeft[nu,ar,br,cr,opts][x], x, {mu}] - - FieldDerivative[GLeft[mu,ar,br,cr,opts][x],x, {nu}] - -I*(NM[GLeft[mu,ar,br,cr,opts][x], GLeft[nu,ar,br,cr,opts][x]] - -NM[GLeft[nu,ar,br,cr,opts][x], GLeft[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -CQRight[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> FieldDerivative[UMatrix[UChiralSpurionRight@@ -OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], x, {mu}]- - I*(NM[GRight[mu,ar,br,cr,opts][x], - UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x]]- - NM[UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - GRight[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -CQLeft[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> FieldDerivative[UMatrix[UChiralSpurionLeft@@ -OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], x, {mu}]- - I*(NM[GLeft[mu,ar,br,cr,opts][x], - UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x]]- - NM[UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - GLeft[mu,ar,br,cr,opts][x]])]; - - -$Substitutions = Append[$Substitutions, -GRight[mu_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[RightComponent[0]],{mu}]]+ - NM[UMatrix[UChiralSpurionRight[]], - QuantumField[Particle[Photon],{mu}]] ]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[LeftComponent[0]],{mu}]]+ - NM[UMatrix[UChiralSpurionLeft[]], - QuantumField[Particle[Photon],{mu}]]]; - -$Substitutions = Append[$Substitutions, -GRight[mu_, nu_] :> FieldDerivative[GRight[nu], {mu}] - - FieldDerivative[GRight[mu], {nu}] - -I*(NM[GRight[mu], GRight[nu]] - NM[GRight[nu], GRight[mu]])]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_, nu_] :> FieldDerivative[GLeft[nu], {mu}] - - FieldDerivative[GLeft[mu], {nu}] - -I*(NM[GLeft[mu], GLeft[nu]] - NM[GLeft[nu], GLeft[mu]])]; - - - -$Substitutions = Append[$Substitutions, -CQRight[mu_] :> FieldDerivative[UMatrix[UChiralSpurionRight[]],{mu}]- - I*(NM[GRight[mu], UMatrix[UChiralSpurionRight[]]]- - NM[UMatrix[UChiralSpurionRight[]], GRight[mu]])]; - -$Substitutions = Append[$Substitutions, -CQLeft[mu_] :> FieldDerivative[UMatrix[UChiralSpurionLeft[]],{mu}]- - I*(NM[GLeft[mu], UMatrix[UChiralSpurionLeft[]]]- - NM[UMatrix[UChiralSpurionLeft[]], GLeft[mu]])]; - - -(*Added 8/2-2002*) - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GRight[mu_] :> GRight[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GLeft[mu_] :> GLeft[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GRight[mu_, nu_] :> GRight[mu, nu, SubArgs][SubX] /; -FreeQ[{nu}, Rule|RenormalizationsState|RenormalizationScheme|ExpansionState]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GLeft[mu_, nu_] :> GLeft[mu, nu, SubArgs][SubX] /; -FreeQ[{nu}, Rule|RenormalizationsState|RenormalizationScheme|ExpansionState]]; - - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -CQRight[mu_] :> CQRight[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -CQLeft[mu_] :> CQLeft[mu, SubArgs][SubX]]; - - -(* ************************************************************** *) - -(* The Gamma_mu field *) - -(* We're overriding *) -$Substitutions = Select[$Substitutions, -(!MatchQ[#, (_?((! FreeQ[#, UGamma, Heads -> True]) &)) :> _])&]; - -$Substitutions = Append[$Substitutions, -UGamma[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -1/2*( - -NM[Adjoint[SMM[x,ar,br,cr,opts]], -FDr[SMM[x,ar,br,cr,opts],x,{mu}]]- - -I*NM[Adjoint[SMM[x,ar,br,cr,opts]], -GRight[mu,ar,br,cr,opts][x], -SMM[x,ar,br,cr,opts]]+ - -NM[SMM[x,ar,br,cr,opts], -FDr[Adjoint[SMM[x,ar,br,cr,opts]],x,{mu}]]- - -I*NM[SMM[x,ar,br,cr,opts], -GLeft[mu,ar,br,cr,opts][x], -Adjoint[SMM[x,ar,br,cr,opts]]] - -)]; - -$Substitutions = Append[$Substitutions, UGamma[mu_] :> - -1/2*( - -NM[Adjoint[SMM],FDr[SMM,{mu}]]- - -I*NM[Adjoint[SMM],GRight[mu],SMM]+ - -NM[SMM,FDr[Adjoint[SMM],{mu}]]- - -I*NM[SMM,GLeft[mu],Adjoint[SMM]] - -)]; - -(* ************************************************************** *) - -(* The nabla of the u_mu field *) - -Options[CovariantNabla] = {Explicit -> True}; - -CovariantNabla[aa_,x_,loris__LorentzIndex,lori1_LorentzIndex, opts___Rule]:= -(newfuncc[1]=CovariantNabla[aa,x,lori1, opts]; -Do[newfuncc[rep+1]=CovariantNabla[ -newfuncc[rep],x,##,opts]&@@Take[{loris},{-rep}], -{rep,1,Length[{loris}]}];newfuncc[Length[{loris}]+1]); - -CovariantNabla[aa_,x_,{loris__},rest___] := -CovariantNabla[aa,x,##,rest]& @@ LorentzIndex /@ {loris}; - -(* -------------------------------------------------------------- *) - -CovariantNabla[aa_,{lori_},(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,{lori}] + - -NM[UGamma[lori],aa] - -NM[aa,UGamma[lori]]; - -CovariantNabla[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,opts___Rule] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,x,lori] + - -NM[UGamma[lori,ar,br,cr, -Sequence@@Select[{opts},FreeQ[#,Explicit]&]][x],aa] - -NM[aa,UGamma[lori,ar,br,cr, -Sequence@@Select[{opts},FreeQ[#,Explicit]&]][x]]; - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]& @@ LorentzIndex /@ {loris}; - -(* -------------------------------------------------------------- *) - -CovariantFieldDerivative[aa_,x_,lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantFieldDerivative]) := - -FieldDerivative[aa,x,lori] + - -I*NM[aa,UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br],lori][x],opts]] - - -I*NM[UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0],ar,br],lori][x],opts],aa]+ - -I* -NM[aa,UMatrix[UChiralSpurionLeft[ar,br,cr, -Sequence@@OptionsSelect[UChiralSpurionLeft,opts]], -Sequence@@OptionsSelect[UMatrix,opts]][x], -QuantumField[Particle[Photon,ar,br],lori][x]]+ - -I* -NM[aa,DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]][x]], -DiracMatrix[LorentzIndex[lori]], -DiracMatrix[7], -QuantumField[Particle[Neutrino],SUNIndex[i]][x]], -UMatrix[UChiralSpurionLeft1[ar,br,cr, -Sequence@@OptionsSelect[UChiralSpurionLeft1,opts]], -Sequence@@OptionsSelect[UMatrix,opts]][x]]+ - - -I* -NM[aa,DOT[DiracBar[QuantumField[Particle[Neutrino],SUNIndex[i]][x]], -DiracMatrix[6], -DiracMatrix[LorentzIndex[lori]], -QuantumField[Particle[Lepton],SUNIndex[i]][x]], -Adjoint[UMatrix[UChiralSpurionLeft1[ar,br,cr, -Sequence@@OptionsSelect[UChiralSpurionLeft1,opts]], -Sequence@@OptionsSelect[UMatrix,opts]][x]]]- - -I* -NM[UMatrix[UChiralSpurionRight[ar,br,cr, -Sequence@@OptionsSelect[UChiralSpurionRight,opts]], -Sequence@@OptionsSelect[UMatrix,opts]][x], -QuantumField[Particle[Photon,ar,br],lori][x],aa]; - -(* ************************************************************** *) -(* Modify the photon propagator to general Lorentz gange *) - -Phi`Couplings`GenProps[a:Vector1] := -{FeynArts`AnalyticalPropagator[ -FeynArts`External][s a[i, mom, {li2}]] == -PolarizationVector[a[i], mom, li2], -FeynArts`AnalyticalPropagator[ -FeynArts`Internal][s a[i, mom, {li1} -> {li2}]] == -I*PropagatorDenominator[mom, FeynArts`Mass[a[i]]]* -(-MetricTensor[li1, li2] + -(1 - 1/$Gauge)* -FourVector[mom, li1]*FourVector[mom, li2]* -1/(PropagatorDenominator1[mom, FeynArts`Mass[a[i]]]) -)}; - -(* ************************************************************** *) - -(* An identity easily shown *) - -Phi`Objects`HLeftRightTrick::usage = - "HLeftRightTrick[exp] expresses CovariantNabla[HRight[x], x, {li}] \ -and CovariantNabla[HLeft[x], x, {li}] in terms of \ -SMM, USmall, HRight and HLeft"; - -HLeftRightTrick[exp_] := - exp /. - {CovariantNabla[HRight[x_, opts___Rule], x_, {li_} | LorentzIndex[li_]] :> - I/2 UCommutator[USmall[LorentzIndex[li], opts][x], HLeft[x, opts]] + - NM[Adjoint[SMM[x, opts]], CQRight[LorentzIndex[li], opts][x], SMM[x, opts]] + - NM[SMM[x, opts], CQLeft[LorentzIndex[li], opts][x], Adjoint[SMM[x, opts]]], - - CovariantNabla[HLeft[x_, opts___Rule], x_, {li_} | LorentzIndex[li_]] :> - I/2 UCommutator[USmall[LorentzIndex[li], opts][x], HRight[x, opts]] + - NM[Adjoint[SMM[x, opts]], CQRight[LorentzIndex[li], opts][x], SMM[x, opts]] - - NM[SMM[x, opts], CQLeft[LorentzIndex[li], opts][x], Adjoint[SMM[x, opts]]], - - (*Swap order of UGamma HRight and UGamma HLeft*) - NM[UGamma[li_, opts1___Rule][x_], HRight[x, opts2___Rule]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - CovariantNabla[HRight[x, opts2], x, {li}] - - FieldDerivative[HRight[x, opts2], x, {li}] + - NM[HRight[x, opts2], UGamma[li, opts1][x]]], - - NM[UGamma[li_, opts1___Rule][x_], HLeft[x, opts2___Rule]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - CovariantNabla[HLeft[x, opts2], x, {li}] - - FieldDerivative[HLeft[x, opts2], x, {li}] + - NM[HLeft[x, opts2], UGamma[li, opts1][x]]], - - UTrace1[NM[HRight[x, opts2___Rule], m__, - UGamma[li_, opts1___Rule][x_]]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - UTrace1[NM[m, CovariantNabla[HRight[x, opts2], x, {li}] - - FieldDerivative[HRight[x, opts2], x, {li}] + - NM[HRight[x, opts2], UGamma[li, opts1][x]]]]], - - UTrace1[NM[HLeft[x, opts2___Rule], m__, - UGamma[li_, opts1___Rule][x_]]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - UTrace1[NM[m, CovariantNabla[HLeft[x, opts2], x, {li}] - - FieldDerivative[HLeft[x, opts2], x, {li}] + - NM[HLeft[x, opts2], UGamma[li, opts1][x]]]]]}; - -(* ************************************************************** *) - -(* Setting of options and $-variables, etc. *) - -SetOptions[Renormalize,SUNN->3]; -SetOptions[WriteOutUMatrices,SUNN->3]; -SetOptions[WriteOutIsoVectors,SUNN->3]; -SetOptions[UQuarkMass,SUNN->3,DiagonalToU->True]; -SetOptions[UMatrix,SUNN->3]; -SetOptions[IsoVector,SUNN->3]; -SetOptions[UGenerator,SUNN->3]; -SetOptions[UTrace,SUNN->3]; -SetOptions[SUNReduce,SUNN->3]; -SetOptions[ExpandU,SUNN->3]; -SetOptions[FAToFC,EqualMasses->False]; -SetOptions[DiscardTerms, -Retain->{Particle[PhiMeson,RenormalizationState[0]]->4}]; -SetOptions[CovariantFieldDerivative,SUNN->3]; -SetOptions[UPerturb, SUNN -> 3]; -SetOptions[UReduce, SUNN -> 3, UDimension -> 3]; -SetOptions[SMMToMM,SUNN -> 3]; -SetOptions[CharacteristicCoefficient, UDimension -> 3]; -SetOptions[CayleyHamilton, UDimension -> 3]; -SetOptions[CayleyHamiltonRules, SUNN -> 3, UDimension -> 3]; -tmpoptscdr=Options[CovariantFieldDerivative]; -tmpoptsmm=Options[MM]; -SetOptions[CovariantFieldDerivative, Explicit -> False]; -SetOptions[MM, Explicit -> False]; -SetOptions[CayleyHamiltonTrick, SUNN -> 3, UDimension -> 3, - UMatrices :> {{I NM[ - Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]], - I NM[Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]]}}]; -SetOptions[CovariantFieldDerivative, Sequence@@tmpoptscdr]; -SetOptions[MM,Sequence@@tmpoptsmm]; - -DeclareUScalar /@ {VUD, VUS, FermiConstant}; - -(* Auxiliary functions*) - -SetOptions[UPerturb, -UFields -> {HRight, HLeft, USmall, UChiPlus, UChiMinus, UFPlus, UFMinus, MM}]; - -xi[x_] := -IsoDot[IsoVector[QuantumField[Particle[PseudoScalar[12]]]][x], - IsoVector[UMatrix[UGenerator[]]]]; - -(*See Ecker 1992, CERN-TH-6660/92*) - -uExpRight[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule]:= - NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[PhiMeson,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]]]; - -uExpLeftAdj[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule]:= - NM[UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[PhiMeson,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]]; - -(* The u_mu field *) - -(*Keep things compact*) -SetOptions[CovariantNabla, Explicit -> False]; - -UCoefficient[USmall][0][li_, x_] = USmall[li][x]; -UCoefficient[USmall][1][li_, x_] = - -Sqrt[2]/DecayConstant[PhiMeson] CovariantNabla[xi[x], x, {li}] + -Sqrt[2]QuantumField[Particle[UPerturbation], LorentzIndex[li]][x]HLeft[x]; -UCoefficient[USmall][2][li_, x_] = -1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], - UCommutator[USmall[li][x], xi[x]]] - -I/DecayConstant[PhiMeson]QuantumField[Particle[UPerturbation], - LorentzIndex[li]][x]UCommutator[xi[x], HRight[x]]; -UCoefficient[USmall][do_?((# > 2) &)][li_, x_] := - UCoefficient[USmall][do][li, x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - I*NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - CDr[NM[uExpRight[x, ExpansionOrder -> do], - uExpLeftAdj[x, ExpansionOrder -> do]], x, {li}, - Explicit -> True], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] /. {QuantumField[pd___, Particle[Photon], LorentzIndex[l_]][xx_] -> - QuantumField[pd, Particle[Photon], {l}][xx] + - Sqrt[2]QuantumField[Particle[UPerturbation], {l}][xx]} // - NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(* The H_R - field*) - -UCoefficient[HRight][0][x_] = HRight[x]; -UCoefficient[HRight][1][x_] = --I/Sqrt[2]/DecayConstant[PhiMeson]UCommutator[xi[x], HLeft[x]]; -UCoefficient[HRight][2][x_] = --1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], - UCommutator[xi[x], HRight[x]]]; -UCoefficient[HRight][do_?((# > 2) &)][x_] := - UCoefficient[HRight][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ -NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChiralSpurionRight[]][x], - uExpRight[x, ExpansionOrder -> do]] + - NM[uExpLeftAdj[x, ExpansionOrder -> do], - UMatrix[UChiralSpurionLeft[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // - Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(* The H_L - field*) - -UCoefficient[HLeft][0][x_] = HLeft[x]; -UCoefficient[HLeft][1][x_] = --I/Sqrt[2]/DecayConstant[PhiMeson]UCommutator[xi[x], HRight[x]]; -UCoefficient[HLeft][2][x_] = --1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], - UCommutator[xi[x], HLeft[x]]]; -UCoefficient[HLeft][do_?((# > 2) &)][x_] := - UCoefficient[HLeft][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ -NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChiralSpurionRight[]][x], - uExpRight[x, ExpansionOrder -> do]] - - NM[uExpLeftAdj[x, ExpansionOrder -> do], - UMatrix[UChiralSpurionLeft[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // - Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(*Return to defaults*) -SetOptions[CovariantNabla, Explicit -> True]; - -(* (7.14) and (7.20) from Gasser and Leutwyler (1985) *) - -gammaRule := -FieldDerivative[UGamma[LorentzIndex[li1_],opts___Rule][x_], x_, LorentzIndex[li2_]] /; -Sort[{li1,li2}] =!= {li1,li2} :> - FieldDerivative[UGamma[LorentzIndex[li2],opts][x], x, - LorentzIndex[li1]] + - UCommutator[UGamma[LorentzIndex[li1],opts][x], - UGamma[LorentzIndex[li2],opts][x]] - - 1/4 UCommutator[USmall[LorentzIndex[li1],Sequence@@OptionsSelect[USmall,opts]][x], - USmall[LorentzIndex[li2],Sequence@@OptionsSelect[USmall,opts]][x]] + - 1/2 I NM[Adjoint[SMM[x,Sequence@@OptionsSelect[SMM,opts]]], - GRight[LorentzIndex[li1],LorentzIndex[li2],opts][x], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]] + - 1/2 I NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - GLeft[LorentzIndex[li1],LorentzIndex[li2],opts][x], - Adjoint[SMM[x,Sequence@@OptionsSelect[SMM,opts]]]]; - - -UGammaTrick[exp_] := exp /. gammaRule; - -(* The chi_+ field*) - -UCoefficient[UChiPlus][0][x_] = UChiPlus[x]; -UCoefficient[UChiPlus][1][x_] = --I/Sqrt[2]/DecayConstant[PhiMeson]UAntiCommutator[xi[x], - UChiMinus[x]]; -UCoefficient[UChiPlus][2][x_] = - -1/4/DecayConstant[PhiMeson]^2 UAntiCommutator[xi[x], - UAntiCommutator[xi[x], UChiPlus[x]]]; -UCoefficient[UChiPlus][do_?((# > 2) &)][x_] := - UCoefficient[UChiPlus][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChi[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] + - NM[uExpLeftAdj[x, ExpansionOrder -> do], - Adjoint[UMatrix[UChi[]][x]], - uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -$EOMRules := - -{UTrace1[NM[Adjoint[MM[x_]], CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], -Adjoint[UMatrix[UChi[]][x_]], CovariantFieldDerivative[MM[x_], x_, - LorentzIndex[mu_]]]] -> --(UTrace1[ - NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]^2/ - 6 - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])/3 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]]^2/6 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x]]]/2 - - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x]]]/ - 2 - (-UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[MM[x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[]][x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]]]))+ - -(-2*CouplingConstant[ChPTPhotonsLeptons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], UMatrix[UChi[]][x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[1]]^2 - -(2*CouplingConstant[ChPTPhotonsLeptons2[2]]* -UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[1]]^2 + -(2*CouplingConstant[ChPTPhotonsLeptons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x], UMatrix[UChiralSpurionLeft[]][x]]])/ -DecayConstant[PseudoScalar[1]]^2 + (2*CouplingConstant[ChPTPhotonsLeptons2[2]]* -UTrace1[NM[MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x], Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x]]])/ -DecayConstant[PseudoScalar[1]]^2, - -UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]]], -CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], - Adjoint[UMatrix[UChi[chopts___]][x_]], MM[x_]]] -> --(-(UTrace1[ - NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]^2/ - 6 - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])/3 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]]^2/6 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x]]]/2 - - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x]]]/ - 2 - (-UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[MM[x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[]][x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]]]))+ - -(-2*CouplingConstant[ChPTPhotonsLeptons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], UMatrix[UChi[]][x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[1]]^2 - -(2*CouplingConstant[ChPTPhotonsLeptons2[2]]* -UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[1]]^2 + -(2*CouplingConstant[ChPTPhotonsLeptons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x], UMatrix[UChiralSpurionLeft[]][x]]])/ -DecayConstant[PseudoScalar[1]]^2 + (2*CouplingConstant[ChPTPhotonsLeptons2[2]]* -UTrace1[NM[MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x], Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x]]])/ -DecayConstant[PseudoScalar[1]]^2)}; - -(* Elimination of either the unit charge or the charged pion and kaon masses -or the proportionality constant. Careful! Valid only to leading order. *) - -$ChargeEliminate = -CouplingConstant[QED[1], r___]^n_ :> - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^n/ - (2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]])^(n/2)* - (ParticleMass[PionPlus, r]^2 - ParticleMass[PionZero, r]^2)^(n/2); - -$ChargedMassesEliminate = -{ParticleMass[PionPlus, r___]^n_ -> -(ParticleMass[PionZero, r]^2 + -CouplingConstant[QED[1], r]^2* -(2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)^(n/2), -ParticleMass[KaonPlus, r___]^n_ -> (ParticleMass[KaonZero, r]^2 + -CouplingConstant[QED[1], r]^2* -(2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)^(n/2)}; - -$NeutralMassesEliminate = -{ParticleMass[PionZero, r___]^n_ -> -(ParticleMass[PionPlus, r]^2 - -CouplingConstant[QED[1], r]^2* -(2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)^(n/2), -ParticleMass[KaonZero, r___]^n_ -> (ParticleMass[KaonPlus, r]^2 - -CouplingConstant[QED[1], r]^2* -(2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)^(n/2)}; - -$CEliminate = -CouplingConstant[ChPTPhotonsLeptons3[2], r___] :> -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2( -(ParticleMass[PionPlus, r]^2 - ParticleMass[PionZero, r]^2))/ -(2 CouplingConstant[QED[1], r]^2); - -ChargeEliminate[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $ChargeEliminate /. -pm -> ParticleMass]; - -ChargedMassesEliminate[exp_] := Block[{l, s, pm, ex}, ex = exp // Together; -(Numerator[ex] /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $ChargedMassesEliminate /. -pm -> ParticleMass) / Denominator[ex]]; - -NeutralMassesEliminate[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $NeutralMassesEliminate /. -pm -> ParticleMass]; - -CEliminate[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $CEliminate /. -pm -> ParticleMass]; - -$ChargedNeutralMassesCancel = { -ParticleMass[PseudoScalar[3], r___]^2 - - ParticleMass[PseudoScalar[4], r___]^2 -> -(2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], r]^2)/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2, - ParticleMass[PseudoScalar[4], r___]^2 - - ParticleMass[PseudoScalar[3], r___]^2 -> --(2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* - CouplingConstant[QED[1], r]^2)/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2, - -ParticleMass[PseudoScalar[7], r___]^2 - ParticleMass[PseudoScalar[8], r___]^2 -> -(2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], r]^2)/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[8], r___]^2 - ParticleMass[PseudoScalar[7], r___]^2 -> --(2 CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], r]^2)/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}; - -ChargedNeutralMassesCancel[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $ChargedNeutralMassesCancel /. -pm -> ParticleMass]; - -$ExpansionQuantities=Union[$ExpansionQuantities, -{MetricTensor[__],Pair[__],ParticleMass[Kaon, g___],ParticleMass[KaonPlus, b___], -ParticleMass[KaonZero, c___],ParticleMass[EtaMeson, d___],ParticleMass[PionPlus, e___], -ParticleMass[PionZero, f___]}]; - -DeclareUMatrix[MM,SMM,UChiMatrix,USmall,UFPlus,UFMinus,UChiPlus,UChiMinus,UGamma, -GRight,GLeft,HRight,HLeft,CQLeft,CQRight,UQuarkChargeMatrix,UChiralSpurionLeft1Matrix]; - -$ParticlesInUse={PhiMeson, Pion, PionPlus, PionZero, Kaon, KaonPlus, KaonZero, - EtaMeson, Photon, Lepton, Neutrino, Electron, Muon, - ElectronNeutrino, MuonNeutrino(*,Vector[0],AxialVector[0]*)}; - -$PropagatorMassesStates={PhiMeson[0]->{RenormalizationState[0]}, - Kaon[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - Vector[0][0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}, - Lepton[0]->{RenormalizationState[0]}, - Lepton[1]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{PhiMeson[0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - Kaon[0]->{{IsoRange->{1,2},IsoIndicesString->"J"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, -Vector[0][0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - Lepton[0]->{{IsoRange->{1,2},IsoIndicesString->"J"}}, - Lepton[1]->{{IsoRange->{1,2},IsoIndicesString->"J"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{(*Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, - AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Photon[0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}*)}; - - -$LastModelRules = {(*Not very pretty, but it works*) -Fermion[1, 1] -> Fermion[2], -Fermion[1][1, {i_}] -> Fermion[2][0,{i}], -(*Could also just set $Gauge=1*) -$Gauge -> 1}; - -$IsoSpinProjectionRules = -Union[$IsoSpinProjectionRules, {Fermion[7] -> Iso[Fermion[1], {1}], - Fermion[8] -> Iso[Fermion[1], {2}], Fermion[9] -> Iso[Fermion[1], {3}], - Fermion[3] -> Iso[Fermion[2], {1}], Fermion[4] -> Iso[Fermion[2], {2}], - Fermion[5] -> Iso[Fermion[2], {3}]}]; - -$ConstantIsoIndices = Union[$ConstantIsoIndices, {J1, J2, J3, J4}]; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/ChPTVirtualPhotons2.conf b/FeynCalc/Phi/Configurations/ChPTVirtualPhotons2.conf deleted file mode 100644 index 168582a96..000000000 --- a/FeynCalc/Phi/Configurations/ChPTVirtualPhotons2.conf +++ /dev/null @@ -1,1041 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTVirtualPhotons2 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 2001 - -Mathematica Version: 4.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - lagrangians ChPTVirtualPhotons2 for PHI - -Description: Definitions for standard ChPT lagrangians - with virtual photons. - - The definitions follow - Marc Knecht and Res Urech - (1997), hep-ph/9709348 -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPTVirtualPhotons2::usage= -"Lagrangian[ChPTVirtualPhotons2[2] is the pionic Chiral \ -Perturbation Theory lagrangian with couplings to virtual photons \ -written in terms of a matrix representation of the meson fields to second \ -order in the energy and the electron charge. Lagrangian[ChPTVirtualPhotons24]] \ -is the lagrangian to four'th order in the energy and the electron charge."; - -Phi`Objects`GRight::usage= -"GRight[mu] is the right-handed G field of \ -(M. Knecht and R. Urech (1997), hep-ph/9709348). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`GLeft::usage= -"GLeft[mu] is the left-handed G field of \ -(M. Knecht and R. Urech (1997), hep-ph/9709348). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`HRight::usage= -"HRight is the right-handed H field of \ -(M. Knecht and R. Urech (1997), hep-ph/9709348)."; - -Phi`Objects`HLeft::usage= -"HLeft is the left-handed H field of \ -(M. Knecht and R. Urech (1997), hep-ph/9709348)."; - -Phi`Objects`CQRight::usage= -"CQRight[mu] is the covariant derivative of the right-handed \ -Q source of \ -(M. Knecht and R. Urech (1997), hep-ph/9709348). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`CQLeft::usage= -"CQLeft[mu] is the covariant derivative of the Left-handed \ -Q source of \ -(M. Knecht and R. Urech (1997), hep-ph/9709348). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`CovariantNabla::usage= -"CovariantNabla[f[x],x,{li1,li2,...},opts] is -the covariant nabla of f[x] with respect to -space-time variables x and with Lorentz indices li0, li1, li2,... -as defined in Ecker, Kambor and Wyler (1992), CERN-TH.6610/92. -To evaluate use ArgumentsSupply."; - -Phi`Objects`$ChargeEliminate::usage = - "$ChargeEliminate is a substitution rule, valid to lowest order \ -in the chiral expansion, for replacing the unit charge with the electromagnetic \ -pion mass difference."; - -Phi`Objects`$ChargedMassesEliminate::usage = - "$ChargedMassesEliminate is a substitution rule, valid to lowest order in the \ -chiral expansion, for replacing the charged pion mass with the unit charge"; - -Phi`Objects`$NeutralMassesEliminate::usage = - "$NeutralMassesEliminate is a substitution rule, valid to lowest order in the \ -chiral expansion, for replacing the neutral pion mass with the unit charge."; - -Phi`Objects`$CEliminate::usage = - "$CEliminate is a substitution rule, valid to lowest order in the \ -chiral expansion, for replacing the proportionality constant C with the \ -neutral to charged mass difference and the unit electric charge."; - -Phi`Objects`$ChargedNeutralMassesCancel::usage = - "$ChargedNeutralMassesCancel is a substitution rule, valid to lowest order in the \ -chiral expansion, for replacing the difference of the squared charged pion mass \ -and the squared neutral pion mass with the unit charge."; - -Phi`Objects`ChargeEliminate::usage = - "ChargeEliminate[exp] applies $ChargeEliminate to exp."; - -Phi`Objects`ChargedMassesEliminate::usage = - "ChargedMassesEliminate[exp] applies $ChargedMassesEliminate to exp."; - -Phi`Objects`NeutralMassesEliminate::usage = - "NeutralMassesEliminate[exp] applies $ChargedMassesEliminate to exp."; - -Phi`Objects`ChargedNeutralMassesCancel::usage = - "ChargedNeutralMassesCancel[exp] applies $ChargedNeutralMassesCancel to exp."; - -Phi`Objects`CEliminate::usage = - "CEliminate[exp] applies $CEliminate to exp."; - -(* ************************************************************** *) - -(* Box definitions *) - -GRight /: MakeBoxes[GRight[mu__,___Rule][_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["R"]]]; - -GRight /: MakeBoxes[GRight[mu__,___Rule], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["R"]]]; - -GLeft /: MakeBoxes[GLeft[mu__,___Rule][_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["L"]]]; - -GLeft /: MakeBoxes[GLeft[mu__,___Rule], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["L"]]]; - -HRight /: MakeBoxes[HRight[___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["R"]]]; - -HRight /: MakeBoxes[HRight, TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["R"]]]; - -HLeft /: MakeBoxes[HLeft[___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["L"]]]; - -HLeft /: MakeBoxes[HLeft, TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["L"]]]; - -CQRight /: MakeBoxes[CQRight[mu__,___Rule][_], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["R"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["R"]]]}]; - -CQRight /: MakeBoxes[CQRight[mu__,___Rule], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["R"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["R"]]]}]; - -CQLeft /: MakeBoxes[CQLeft[mu__,___Rule][_], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["L"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["L"]]]}]; - -CQLeft /: MakeBoxes[CQLeft[mu__,___Rule], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["L"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["L"]]]}]; - -(* ************************************************************** *) - -(* Source fields *) - -IsoVector[QuantumField[Particle[Scalar[0],___],___],___][_]:=0; -IsoVector[QuantumField[Particle[PseudoScalar[0],___],___],___][_]:=0; -(*IsoVector[QuantumField[Particle[Vector[0],___],___],___][_]:=0; -IsoVector[QuantumField[Particle[AxialVector[0],___],___],___][_]:=0;*) - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[Scalar[0],st___RenormalizationState, -sc___RenormalizationScheme,qs___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -UQuarkMassMatrix[st,sc,qs,opts]; -QuantumField[___,Particle[PseudoScalar[0],___],___][_]:=0; -(*QuantumField[___,Particle[Vector[0],___],___][_]:=0; -QuantumField[___,Particle[AxialVector[0],___],___][_]:=0;*) -QuantumField[Particle[AxialVector[0], ___], ___, SUNIndex[0]][_]:=0; - -(* To simplify algebra, above we set the iso-vector components -of the vector and axial-vector sources to zero and below -we identify the iso-spin zero or iso-scalar component of the -vector field with the photon field of the covariant derivative -below *) - -QuantumField[a___,Particle[Vector[1],b___],c___,SUNIndex[0]][x_]:= -QuantumField[a,Particle[Vector[1],b],c][x]; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -(*ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0;*) - -(*CouplingConstant[ChPTPhoton2[4],1,___][___]=0; -CouplingConstant[ChPTPhoton2[4],2,___][___]=0; -CouplingConstant[ChPTPhoton2[4],3,___][___]=0; -CouplingConstant[ChPTPhoton2[4],4,___][___]=0; -CouplingConstant[ChPTPhoton2[4],5,___][___]=0; -CouplingConstant[ChPTPhoton2[4],6,___][___]=0; -CouplingConstant[ChPTPhoton2[4],7,___][___]=0; -CouplingConstant[ChPTPhoton2[4],8,___][___]=0; -CouplingConstant[ChPTPhoton2[4],9,___][___]=0; -CouplingConstant[ChPTPhoton2[4],10,___][___]=0; -CouplingConstant[ChPTPhoton2[4],11,___][___]=0; -CouplingConstant[ChPTPhoton2[4],12,___][___]=0;*) - -(* ************************************************************** *) - -(* Redefinition of the left and right components. -Knecht and Urech have them the other way round and without the 1/2. -Also its necessary in order to not have the AxialVector (Vector) -part set to zero *) - -IsoVector[QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___], -bb___],opts___][x_]/;(Explicit/.{opts0}/.Options[LeftComponent]):= -( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]- -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -IsoVector[QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___], -opts___][x_]/;(Explicit/.{opts0}/.Options[RightComponent]):=( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]+ -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -(* ************************************************************** *) - -(* Spurions *) - -(* I think we always want this ?*) - -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurion[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurionRight[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurionLeft[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; - -(* ************************************************************** *) - -(* The H fields *) - -$Substitutions = Append[$Substitutions, -HRight[x_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] :> -NM[Adjoint[SMM[x,ar,br,cr]], UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -SMM[x,ar,br,cr]] + -NM[SMM[x,ar,br,cr], UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -Adjoint[SMM[x,ar,br,cr]]]]; - -$Substitutions = Append[$Substitutions, -HLeft[x_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] :> -NM[Adjoint[SMM[x,ar,br,cr]], UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -SMM[x,ar,br,cr]] - -NM[SMM[x,ar,br,cr], UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -Adjoint[SMM[x,ar,br,cr]]]]; - - -$Substitutions = Append[$Substitutions, -HRight :> NM[Adjoint[SMM],UMatrix[UChiralSpurionRight[],SMM]] + - NM[SMM,UMatrix[UChiralSpurionLeft[],Adjoint[SMM]]]]; - -$Substitutions = Append[$Substitutions, -HLeft :> NM[Adjoint[SMM],UMatrix[UChiralSpurionRight[],SMM]] - - NM[SMM,UMatrix[UChiralSpurionLeft[],Adjoint[SMM]]]]; - - - - -(* ************************************************************** *) - -(* The G fields *) - -$Substitutions = Append[$Substitutions, -GRight[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[RightComponent[0, - Sequence@@OptionsSelect[RightComponent,opts]],ar,br,cr],{mu}][x]]+ - NM[UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - QuantumField[Particle[Photon,ar,br,cr],{mu}][x]]]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[LeftComponent[0, - Sequence@@OptionsSelect[LeftComponent,opts]],ar,br,cr],{mu}][x]]+ - NM[UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - QuantumField[Particle[Photon,ar,br,cr],{mu}][x]]]; - -$Substitutions = Append[$Substitutions, -GRight[mu_, nu_?(FreeQ[#, - RenormalizationState | RenormalizationScheme | ExpansionState | - Rule] &), ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> -FieldDerivative[GRight[nu,ar,br,cr,opts][x], x, {mu}] - - FieldDerivative[GRight[mu,ar,br,cr,opts][x],x, {nu}] - -I*(NM[GRight[mu,ar,br,cr,opts][x], GRight[nu,ar,br,cr,opts][x]] - -NM[GRight[nu,ar,br,cr,opts][x], GRight[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_, nu_?(FreeQ[#, - RenormalizationState | RenormalizationScheme | ExpansionState | - Rule] &), ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> -FieldDerivative[GLeft[nu,ar,br,cr,opts][x], x, {mu}] - - FieldDerivative[GLeft[mu,ar,br,cr,opts][x],x, {nu}] - -I*(NM[GLeft[mu,ar,br,cr,opts][x], GLeft[nu,ar,br,cr,opts][x]] - -NM[GLeft[nu,ar,br,cr,opts][x], GLeft[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -CQRight[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> FieldDerivative[UMatrix[UChiralSpurionRight@@ -OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], x, {mu}]- - I*(NM[GRight[mu,ar,br,cr,opts][x], - UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x]]- - NM[UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - GRight[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -CQLeft[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> FieldDerivative[UMatrix[UChiralSpurionLeft@@ -OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], x, {mu}]- - I*(NM[GLeft[mu,ar,br,cr,opts][x], - UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x]]- - NM[UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - GLeft[mu,ar,br,cr,opts][x]])]; - - -$Substitutions = Append[$Substitutions, -GRight[mu_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[RightComponent[0]],{mu}]]+ - NM[UMatrix[UChiralSpurionRight[]], - QuantumField[Particle[Photon],{mu}]] ]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[LeftComponent[0]],{mu}]]+ - NM[UMatrix[UChiralSpurionLeft[]], - QuantumField[Particle[Photon],{mu}]]]; - -$Substitutions = Append[$Substitutions, -GRight[mu_, nu_] :> FieldDerivative[GRight[nu], {mu}] - - FieldDerivative[GRight[mu], {nu}] - -I*(NM[GRight[mu], GRight[nu]] - NM[GRight[nu], GRight[mu]])]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_, nu_] :> FieldDerivative[GLeft[nu], {mu}] - - FieldDerivative[GLeft[mu], {nu}] - -I*(NM[GLeft[mu], GLeft[nu]] - NM[GLeft[nu], GLeft[mu]])]; - - - -$Substitutions = Append[$Substitutions, -CQRight[mu_] :> FieldDerivative[UMatrix[UChiralSpurionRight[]],{mu}]- - I*(NM[GRight[mu], UMatrix[UChiralSpurionRight[]]]- - NM[UMatrix[UChiralSpurionRight[]], GRight[mu]])]; - -$Substitutions = Append[$Substitutions, -CQLeft[mu_] :> FieldDerivative[UMatrix[UChiralSpurionLeft[]],{mu}]- - I*(NM[GLeft[mu], UMatrix[UChiralSpurionLeft[]]]- - NM[UMatrix[UChiralSpurionLeft[]], GLeft[mu]])]; - - -(*Added 8/2-2002*) - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GRight[mu_] :> GRight[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GLeft[mu_] :> GLeft[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GRight[mu_, nu_] :> GRight[mu, nu, SubArgs][SubX] /; -FreeQ[{nu}, Rule|RenormalizationsState|RenormalizationScheme|ExpansionState]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GLeft[mu_, nu_] :> GLeft[mu, nu, SubArgs][SubX] /; -FreeQ[{nu}, Rule|RenormalizationsState|RenormalizationScheme|ExpansionState]]; - - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -CQRight[mu_] :> CQRight[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -CQLeft[mu_] :> CQLeft[mu, SubArgs][SubX]]; - - -(* ************************************************************** *) - -(* The Gamma_mu field *) - -(* We're overriding *) -$Substitutions = Select[$Substitutions, -(!MatchQ[#, (_?((! FreeQ[#, UGamma, Heads -> True]) &)) :> _])&]; - -$Substitutions = Append[$Substitutions, -UGamma[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -1/2*( - -NM[Adjoint[SMM[x,ar,br,cr,opts]], -FDr[SMM[x,ar,br,cr,opts],x,{mu}]]- - -I*NM[Adjoint[SMM[x,ar,br,cr,opts]], -GRight[mu,ar,br,cr,opts][x], -SMM[x,ar,br,cr,opts]]+ - -NM[SMM[x,ar,br,cr,opts], -FDr[Adjoint[SMM[x,ar,br,cr,opts]],x,{mu}]]- - -I*NM[SMM[x,ar,br,cr,opts], -GLeft[mu,ar,br,cr,opts][x], -Adjoint[SMM[x,ar,br,cr,opts]]] - -)]; - -$Substitutions = Append[$Substitutions, UGamma[mu_] :> - -1/2*( - -NM[Adjoint[SMM],FDr[SMM,{mu}]]- - -I*NM[Adjoint[SMM],GRight[mu],SMM]+ - -NM[SMM,FDr[Adjoint[SMM],{mu}]]- - -I*NM[SMM,GLeft[mu],Adjoint[SMM]] - -)]; - -(* ************************************************************** *) - -(* The nabla of the u_mu field *) - -Options[CovariantNabla] = {Explicit -> True}; - -CovariantNabla[aa_,x_,loris__LorentzIndex,lori1_LorentzIndex, opts___Rule]:= -(newfuncc[1]=CovariantNabla[aa,x,lori1, opts]; -Do[newfuncc[rep+1]=CovariantNabla[ -newfuncc[rep],x,##,opts]&@@Take[{loris},{-rep}], -{rep,1,Length[{loris}]}];newfuncc[Length[{loris}]+1]); - -CovariantNabla[aa_,x_,{loris__},rest___] := -CovariantNabla[aa,x,##,rest]& @@ LorentzIndex /@ {loris}; - -(* -------------------------------------------------------------- *) - -CovariantNabla[aa_,{lori_},(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,{lori}] + - -NM[UGamma[lori],aa] - -NM[aa,UGamma[lori]]; - -CovariantNabla[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,opts___Rule] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,x,lori] + - -NM[UGamma[lori,ar,br,cr, -Sequence@@Select[{opts},FreeQ[#,Explicit]&]][x],aa] - -NM[aa,UGamma[lori,ar,br,cr, -Sequence@@Select[{opts},FreeQ[#,Explicit]&]][x]]; - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]& @@ LorentzIndex /@ {loris}; - -(* -------------------------------------------------------------- *) - -(* EM-ChPT - Knecht & Urech *) - -CovariantFieldDerivative[aa_,x_,lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantFieldDerivative]) := - -FieldDerivative[aa,x,lori] + - -I*NM[aa,UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br],lori][x],opts]] - - -I*NM[UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0],ar,br],lori][x],opts],aa]+ - -I* -NM[aa,UMatrix[UChiralSpurionLeft[ar,br,cr, -Sequence@@OptionsSelect[UChiralSpurionLeft,opts]], -Sequence@@OptionsSelect[UMatrix,opts]][x], -QuantumField[Particle[Photon,ar,br],lori][x]]- - -I* -NM[UMatrix[UChiralSpurionRight[ar,br,cr, -Sequence@@OptionsSelect[UChiralSpurionRight,opts]], -Sequence@@OptionsSelect[UMatrix,opts]][x], -QuantumField[Particle[Photon,ar,br],lori][x],aa]; - -(* ************************************************************** *) -(* Modify the photon propagator to general Lorentz gange *) - -Phi`Couplings`GenProps[a:Vector1] := -{FeynArts`AnalyticalPropagator[ -FeynArts`External][s a[i, mom, {li2}]] == -PolarizationVector[a[i], mom, li2], -FeynArts`AnalyticalPropagator[ -FeynArts`Internal][s a[i, mom, {li1} -> {li2}]] == -I*PropagatorDenominator[mom, FeynArts`Mass[a[i]]]* -(-MetricTensor[li1, li2] + -(1 - 1/$Gauge)* -FourVector[mom, li1]*FourVector[mom, li2]* -1/(PropagatorDenominator1[mom, FeynArts`Mass[a[i]]]) -)}; - -(* This means that we have to explicitly specify any other - (axial-)vector propagator we want to use *) - -Phi`Couplings`GenProps[a:AxialVector0] := -{FeynArts`AnalyticalPropagator[ -FeynArts`External][ s a[i, mom, {li2}] ] == -PolarizationVector[ a[i], mom, li2 ], -FeynArts`AnalyticalPropagator[ -FeynArts`Internal][ s a[i,mom,{li1}->{li2}] ] == -I*PropagatorDenominator[ mom , -FeynArts`Mass[a[i]] ]* -(-MetricTensor[li1, li2])}; - -(* ************************************************************** *) - -(* An identity easily shown *) - -Phi`Objects`HLeftRightTrick::usage = - "HLeftRightTrick[exp] expresses CovariantNabla[HRight[x], x, {li}] \ -and CovariantNabla[HLeft[x], x, {li}] in terms of \ -SMM, USmall, HRight and HLeft"; - -HLeftRightTrick[exp_] := - exp /. - {CovariantNabla[HRight[x_, opts___Rule], x_, {li_} | LorentzIndex[li_]] :> - I/2 UCommutator[USmall[LorentzIndex[li], opts][x], HLeft[x, opts]] + - NM[Adjoint[SMM[x, opts]], CQRight[LorentzIndex[li], opts][x], SMM[x, opts]] + - NM[SMM[x, opts], CQLeft[LorentzIndex[li], opts][x], Adjoint[SMM[x, opts]]], - - CovariantNabla[HLeft[x_, opts___Rule], x_, {li_} | LorentzIndex[li_]] :> - I/2 UCommutator[USmall[LorentzIndex[li], opts][x], HRight[x, opts]] + - NM[Adjoint[SMM[x, opts]], CQRight[LorentzIndex[li], opts][x], SMM[x, opts]] - - NM[SMM[x, opts], CQLeft[LorentzIndex[li], opts][x], Adjoint[SMM[x, opts]]], - - (*Swap order of UGamma HRight and UGamma HLeft*) - NM[UGamma[li_, opts1___Rule][x_], HRight[x, opts2___Rule]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - CovariantNabla[HRight[x, opts2], x, {li}] - - FieldDerivative[HRight[x, opts2], x, {li}] + - NM[HRight[x, opts2], UGamma[li, opts1][x]]], - - NM[UGamma[li_, opts1___Rule][x_], HLeft[x, opts2___Rule]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - CovariantNabla[HLeft[x, opts2], x, {li}] - - FieldDerivative[HLeft[x, opts2], x, {li}] + - NM[HLeft[x, opts2], UGamma[li, opts1][x]]], - - UTrace1[NM[HRight[x, opts2___Rule], m__, - UGamma[li_, opts1___Rule][x_]]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - UTrace1[NM[m, CovariantNabla[HRight[x, opts2], x, {li}] - - FieldDerivative[HRight[x, opts2], x, {li}] + - NM[HRight[x, opts2], UGamma[li, opts1][x]]]]], - - UTrace1[NM[HLeft[x, opts2___Rule], m__, - UGamma[li_, opts1___Rule][x_]]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - UTrace1[NM[m, CovariantNabla[HLeft[x, opts2], x, {li}] - - FieldDerivative[HLeft[x, opts2], x, {li}] + - NM[HLeft[x, opts2], UGamma[li, opts1][x]]]]]}; - -(* ************************************************************** *) - -(* Setting of options and $-variables, etc. *) - -SetOptions[UPerturb, -UFields -> {HRight, HLeft, USmall, UChiPlus, UChiMinus, UFPlus, UFMinus, MM}]; - -(* Auxiliary functions*) - -xi[x_] := -IsoDot[IsoVector[QuantumField[Particle[PseudoScalar[12]]]][x], - IsoVector[UMatrix[UGenerator[]]]]; - -(*See Ecker 1992, CERN-TH-6660/92*) - -uExpRight[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule]:= - NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[PhiMeson,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]]]; - -uExpLeftAdj[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule]:= - NM[UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[PhiMeson,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]]; - -(* The u_mu field *) - -(*Keep things compact*) -SetOptions[CovariantNabla, Explicit -> False]; - -UCoefficient[USmall][0][li_, x_] = USmall[li][x]; -UCoefficient[USmall][1][li_, x_] = - -Sqrt[2]/DecayConstant[Pion] CovariantNabla[xi[x], x, {li}] + -Sqrt[2]QuantumField[Particle[UPerturbation], LorentzIndex[li]][x]HLeft[x]; -UCoefficient[USmall][2][li_, x_] = -1/4/DecayConstant[Pion]^2 UCommutator[xi[x], - UCommutator[USmall[li][x], xi[x]]] - -I/DecayConstant[Pion]QuantumField[Particle[UPerturbation], - LorentzIndex[li]][x]UCommutator[xi[x], HRight[x]]; -UCoefficient[USmall][do_?((# > 2) &)][li_, x_] := - UCoefficient[USmall][do][li, x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - I*NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - CDr[NM[uExpRight[x, ExpansionOrder -> do], - uExpLeftAdj[x, ExpansionOrder -> do]], x, {li}, - Explicit -> True], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] /. {QuantumField[pd___, Particle[Photon], LorentzIndex[l_]][xx_] -> - QuantumField[pd, Particle[Photon], {l}][xx] + - Sqrt[2]QuantumField[Particle[UPerturbation], {l}][xx]} // - NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(* The H_R - field*) - -UCoefficient[HRight][0][x_] = HRight[x]; -UCoefficient[HRight][1][x_] = --I/Sqrt[2]/DecayConstant[Pion]UCommutator[xi[x], HLeft[x]]; -UCoefficient[HRight][2][x_] = --1/4/DecayConstant[Pion]^2 UCommutator[xi[x], - UCommutator[xi[x], HRight[x]]]; -UCoefficient[HRight][do_?((# > 2) &)][x_] := - UCoefficient[HRight][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ -NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChiralSpurionRight[]][x], - uExpRight[x, ExpansionOrder -> do]] + - NM[uExpLeftAdj[x, ExpansionOrder -> do], - UMatrix[UChiralSpurionLeft[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // - Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(* The H_L - field*) - -UCoefficient[HLeft][0][x_] = HLeft[x]; -UCoefficient[HLeft][1][x_] = --I/Sqrt[2]/DecayConstant[Pion]UCommutator[xi[x], HRight[x]]; -UCoefficient[HLeft][2][x_] = --1/4/DecayConstant[Pion]^2 UCommutator[xi[x], - UCommutator[xi[x], HLeft[x]]]; -UCoefficient[HLeft][do_?((# > 2) &)][x_] := - UCoefficient[HLeft][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ -NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChiralSpurionRight[]][x], - uExpRight[x, ExpansionOrder -> do]] - - NM[uExpLeftAdj[x, ExpansionOrder -> do], - UMatrix[UChiralSpurionLeft[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // - Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(*Return to defaults*) -SetOptions[CovariantNabla, Explicit -> True]; - -(* (7.14) and (7.20) from Gasser and Leutwyler (1985) *) - -gammaRule := -FieldDerivative[UGamma[LorentzIndex[li1_],opts___Rule][x_], x_, LorentzIndex[li2_]] /; -Sort[{li1,li2}] =!= {li1,li2} :> - FieldDerivative[UGamma[LorentzIndex[li2],opts][x], x, - LorentzIndex[li1]] + - UCommutator[UGamma[LorentzIndex[li1],opts][x], - UGamma[LorentzIndex[li2],opts][x]] - - 1/4 UCommutator[USmall[LorentzIndex[li1],Sequence@@OptionsSelect[USmall,opts]][x], - USmall[LorentzIndex[li2],Sequence@@OptionsSelect[USmall,opts]][x]] + - 1/2 I NM[Adjoint[SMM[x,Sequence@@OptionsSelect[SMM,opts]]], - GRight[LorentzIndex[li1],LorentzIndex[li2],opts][x], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]] + - 1/2 I NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - GLeft[LorentzIndex[li1],LorentzIndex[li2],opts][x], - Adjoint[SMM[x,Sequence@@OptionsSelect[SMM,opts]]]]; - - -UGammaTrick[exp_] := exp /. gammaRule; - -(* The chi_+ field*) - -UCoefficient[UChiPlus][0][x_] = UChiPlus[x]; -UCoefficient[UChiPlus][1][x_] = --I/Sqrt[2]/DecayConstant[Pion]UAntiCommutator[xi[x], - UChiMinus[x]]; -UCoefficient[UChiPlus][2][x_] = - -1/4/DecayConstant[Pion]^2 UAntiCommutator[xi[x], - UAntiCommutator[xi[x], UChiPlus[x]]]; -UCoefficient[UChiPlus][do_?((# > 2) &)][x_] := - UCoefficient[UChiPlus][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChi[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] + - NM[uExpLeftAdj[x, ExpansionOrder -> do], - Adjoint[UMatrix[UChi[]][x]], - uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -$EOMRules := -{UTrace1[NM[Adjoint[MM[x_]], CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], - Adjoint[UMatrix[UChi[chopts___]][x_]], CovariantFieldDerivative[MM[x_], x_, - LorentzIndex[mu_]]]] -> --UTrace1[NM[MM[x], Adjoint[CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[chopts]][x], - Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]]]- -Det[Adjoint[UMatrix[UChi[chopts]][x]]]/2 - Det[UMatrix[UChi[chopts]][x]]/2 + -((-2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], UMatrix[UChi[]][x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[2]]^2 - -(2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[2]]^2 + -(2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x], UMatrix[UChiralSpurionLeft[]][x]]])/ -DecayConstant[PseudoScalar[2]]^2 + (2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x], Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x]]])/ -DecayConstant[PseudoScalar[2]]^2) - -UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, LorentzIndex[mu]]]] - -UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, - LorentzIndex[mu]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]] + -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]^2/4 + -(UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]])/2 + -UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]]^2/4 - -UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], UMatrix[UChi[chopts]][x]]], - -UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]]], -CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], - Adjoint[UMatrix[UChi[chopts___]][x_]], MM[x_]]] -> --(-UTrace1[NM[MM[x], Adjoint[CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[chopts]][x], - Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]]]- -Det[Adjoint[UMatrix[UChi[chopts]][x]]]/2 - Det[UMatrix[UChi[chopts]][x]]/2 + -((-2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], UMatrix[UChi[]][x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[2]]^2 - -(2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[2]]^2 + -(2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x], UMatrix[UChiralSpurionLeft[]][x]]])/ -DecayConstant[PseudoScalar[2]]^2 + (2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x], Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x]]])/ -DecayConstant[PseudoScalar[2]]^2) - -UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, LorentzIndex[mu]]]] - -UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, - LorentzIndex[mu]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]] + -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]^2/4 + -(UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]])/2 + -UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]]^2/4 - -UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], UMatrix[UChi[chopts]][x]]])}; - -$ChargeEliminate = -CouplingConstant[QED[1], r___]^n_ :> - DecayConstant[PseudoScalar[2], RenormalizationState[0]]^n/ - (2 CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]])^(n/2)* - (ParticleMass[PionPlus, r]^2 - ParticleMass[PionZero, r]^2)^(n/2); - -$ChargedMassesEliminate = -{ParticleMass[PionPlus, r___]^n_ -> -(ParticleMass[PionZero, r]^2 + -CouplingConstant[QED[1], r]^2* -(2 CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]])/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)^(n/2)}; - -$NeutralMassesEliminate = -{ParticleMass[PionZero, r___]^n_ -> -(ParticleMass[PionPlus, r]^2 - -CouplingConstant[QED[1], r]^2* -(2 CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]])/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)^(n/2)}; - -$CEliminate = -CouplingConstant[ChPTVirtualPhotons2[2], r___] :> -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2( -(ParticleMass[PionPlus, r]^2 - ParticleMass[PionZero, r]^2))/ -(2 CouplingConstant[QED[1], r]^2); - -ChargeEliminate[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $ChargeEliminate /. -pm -> ParticleMass]; - -ChargedMassesEliminate[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $ChargedMassesEliminate /. -pm -> ParticleMass]; - -NeutralMassesEliminate[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $NeutralMassesEliminate /. -pm -> ParticleMass]; - -CEliminate[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $CEliminate /. -pm -> ParticleMass]; - -$ChargedNeutralMassesCancel = {ParticleMass[PseudoScalar[3], r___]^2 - - ParticleMass[PseudoScalar[4], r___]^2 -> - (2 CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - CouplingConstant[QED[1], r]^2)/ - DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2, - ParticleMass[PseudoScalar[4], r___]^2 - - ParticleMass[PseudoScalar[3], r___]^2 -> - -(2 CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - CouplingConstant[QED[1], r]^2)/ - DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}; - -ChargedNeutralMassesCancel[exp_] := Block[{l, s, pm}, exp /. -(l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> -(l[s] /. ParticleMass -> pm) /. $ChargedNeutralMassesCancel /. -pm -> ParticleMass]; - -$IsoSpinProjectionRules = { - PionPlus -> (Iso[Pion, {1}] - I*Iso[Pion, {2}])/Sqrt[2], - PionMinus -> (Iso[Pion, {1}] + I*Iso[Pion, {2}])/Sqrt[2], - PionZero -> Iso[Pion, {3}]}; - -$QuarkToPionMassesRules = {ParticleMass[UpQuark, - rest___] -> (ParticleMass[PionZero, rest])^2/(2*QuarkCondensate[rest]), - ParticleMass[DownQuark, - rest___] -> (ParticleMass[PionZero, rest])^2/(2* - QuarkCondensate[rest])}; - -$ExpansionQuantities=Union[$ExpansionQuantities, -{MetricTensor[__], Pair[__], -ParticleMass[PionZero, d___], ParticleMass[PionPlus, e___]}]; - -DeclareUMatrix[MM,SMM,UChiMatrix,USmall,UFPlus,UFMinus,UChiPlus,UChiMinus,UGamma, -GRight,GLeft,HRight,HLeft,CQLeft,CQRight,UQuarkChargeMatrix]; - -$ParticlesInUse={Pion, PionPlus, PionZero, - Photon, Vector[0], AxialVector[0]}; - -$PropagatorMassesStates={Pion[0]->{RenormalizationState[0]}, - Kaon[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - Vector[0][0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{Pion[0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Kaon[0]->{{IsoRange->{1,2},IsoIndicesString->"J"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, -Vector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{(*Vector[0][0]->{ - FeynArts`Incoming, - FeynArts`Outgoing, - FeynArts`External},*) - AxialVector[0][0]->{ - FeynArts`Incoming, - FeynArts`Outgoing, - FeynArts`External}}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/ChPTVirtualPhotons3.conf b/FeynCalc/Phi/Configurations/ChPTVirtualPhotons3.conf deleted file mode 100644 index ea61af28e..000000000 --- a/FeynCalc/Phi/Configurations/ChPTVirtualPhotons3.conf +++ /dev/null @@ -1,1022 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTVirtualPhotons3 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 2002 - -Mathematica Version: 4.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - lagrangians ChPTVirtualPhotons3 for PHI - -Description: Definitions for standard ChPT lagrangians - with virtual photons. - - The definitions follow - Res Urech - (1994), hep-ph/9405341 -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPTVirtualPhotons3::usage= -"Lagrangian[ChPTVirtualPhotons3[2] is the mesonic Chiral \ -Perturbation Theory lagrangian with couplings to virtual photons \ -written in terms of a matrix representation of the meson fields to second \ -order in the energy and the electron charge. Lagrangian[ChPTVirtualPhotons24]] \ -is the lagrangian to four'th order in the energy and the electron charge."; - -Phi`Objects`GRight::usage= -"GRight[mu] is the right-handed G field of \ -(Res Urech (1994), hep-ph/9405341). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`GLeft::usage= -"GLeft[mu] is the left-handed G field of \ -(Res Urech (1994), hep-ph/9405341). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`HRight::usage= -"HRight is the right-handed H field of \ -(Res Urech (1994), hep-ph/9405341)."; - -Phi`Objects`HLeft::usage= -"HLeft is the left-handed H field of \ -(Res Urech (1994), hep-ph/9405341)."; - -Phi`Objects`CQRight::usage= -"CQRight[mu] is the covariant derivative of the right-handed \ -Q source of \ -(Res Urech (1994), hep-ph/9405341). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`CQLeft::usage= -"CQLeft[mu] is the covariant derivative of the Left-handed \ -Q source of \ -(Res Urech (1994), hep-ph/9405341). \ -With two arguments it's the field strength tensor."; - -Phi`Objects`CovariantNabla::usage= -"CovariantNabla[f[x],x,{li1,li2,...},opts] is -the covariant nabla of f[x] with respect to -space-time variables x and with Lorentz indices li0, li1, li2,... -as defined in Ecker, Kambor and Wyler (1992), CERN-TH.6610/92. -To evaluate use ArgumentsSupply."; - -MM::usage="MM[x] := -UFieldMatrix[QuantumField[Particle[PhiMeson]][x]]. -MM takes two optional arguments with head RenormalizationState -and RenormalizationScheme respectively."; - -(* ************************************************************** *) - -(* Box definitions *) - -GRight /: MakeBoxes[GRight[mu__,___Rule][_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["R"]]]; - -GRight /: MakeBoxes[GRight[mu__,___Rule], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["R"]]]; - -GLeft /: MakeBoxes[GLeft[mu__,___Rule][_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["L"]]]; - -GLeft /: MakeBoxes[GLeft[mu__,___Rule], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["G", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["L"]]]; - -HRight /: MakeBoxes[HRight[___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["R"]]]; - -HRight /: MakeBoxes[HRight, TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["R"]]]; - -HLeft /: MakeBoxes[HLeft[___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["L"]]]; - -HLeft /: MakeBoxes[HLeft, TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["H", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["L"]]]; - -CQRight /: MakeBoxes[CQRight[mu__,___Rule][_], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["R"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["R"]]]}]; - -CQRight /: MakeBoxes[CQRight[mu__,___Rule], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["R"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["R"]]]}]; - -CQLeft /: MakeBoxes[CQLeft[mu__,___Rule][_], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["L"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["L"]]]}]; - -CQLeft /: MakeBoxes[CQLeft[mu__,___Rule], TraditionalForm] := - RowBox[{SubsuperscriptBox[ - MakeBoxes[ - StyleForm["c", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]]&/@{mu}], - MakeBoxes[TraditionalForm["L"]]], - SubscriptBox[ - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - MakeBoxes[TraditionalForm["L"]]]}]; - -(* ************************************************************** *) - -(* Source fields *) - -IsoVector[QuantumField[Particle[Scalar[0],___],___],___][_]:=0; -IsoVector[QuantumField[Particle[PseudoScalar[0],___],___],___][_]:=0; -IsoVector[QuantumField[Particle[Vector[0],___],___],___][_]:=0; -(*IsoVector[QuantumField[Particle[AxialVector[0],___],___],___][_]:=0;*) - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[Scalar[0],st___RenormalizationState, -sc___RenormalizationScheme,qs___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -UQuarkMassMatrix[st,sc,qs,opts]; -QuantumField[___,Particle[PseudoScalar[0],___],___][_]:=0; -QuantumField[___,Particle[Vector[0],___],___][_]:=0; -(*QuantumField[___,Particle[AxialVector[0],___],___][_]:=0;*) -QuantumField[Particle[AxialVector[0], ___], ___, SUNIndex[0]][_]:=0; - -(* To simplify algebra, above we set the iso-vector components -of the vector and axial-vector sources to zero and below -we identify the iso-spin zero or iso-scalar component of the -vector field with the photon field of the covariant derivative -below *) - -QuantumField[a___,Particle[Vector[1],b___],c___,SUNIndex[0]][x_]:= -QuantumField[a,Particle[Vector[1],b],c][x]; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -(*ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0;*) - -(*CouplingConstant[ChPTPhoton2[4],1,___][___]=0; -CouplingConstant[ChPTPhoton2[4],2,___][___]=0; -CouplingConstant[ChPTPhoton2[4],3,___][___]=0; -CouplingConstant[ChPTPhoton2[4],4,___][___]=0; -CouplingConstant[ChPTPhoton2[4],5,___][___]=0; -CouplingConstant[ChPTPhoton2[4],6,___][___]=0; -CouplingConstant[ChPTPhoton2[4],7,___][___]=0; -CouplingConstant[ChPTPhoton2[4],8,___][___]=0; -CouplingConstant[ChPTPhoton2[4],9,___][___]=0; -CouplingConstant[ChPTPhoton2[4],10,___][___]=0; -CouplingConstant[ChPTPhoton2[4],11,___][___]=0; -CouplingConstant[ChPTPhoton2[4],12,___][___]=0;*) - -(* ************************************************************** *) - -(* SU(3) meson matrix PhiMeson instead of Pion *) - -BeginPackage["Phi`Objects`", {"Phi`", -"FeynCalc`"}]; -Begin["`Private`"]; - -MM[x_?(! NumberQ[#] &), h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MM]) := - - UFieldMatrix[fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -MM[ii_?NumberQ, x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MM]) := - UFieldMatrix[ii, fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -SMM[x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[SMM]) := MM[1/2, x, h, opts]; -MMS[x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MMS]) := - UFieldMatrixSeries[fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; - -End[]; -EndPackage[]; - -(* ************************************************************** *) - -(* Redefinition of the left and right components. -Urech have them the other way round and without the 1/2. -Also its necessary in order to not have the AxialVector (Vector) -part set to zero *) - -IsoVector[QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___], -bb___],opts___][x_]/;(Explicit/.{opts0}/.Options[LeftComponent]):= -( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]- -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -IsoVector[QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___], -opts___][x_]/;(Explicit/.{opts0}/.Options[RightComponent]):=( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]+ -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -(* ************************************************************** *) - -(* Spurions *) - -(* I think we always want this ?*) - -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurion[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurionRight[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; -$Substitutions = Append[$Substitutions, -UMatrix[UChiralSpurionLeft[___]][___] :> -UQuarkChargeMatrix[RenormalizationState[0], DiagonalToU -> True]]; - -(* ************************************************************** *) - -(* The H fields *) - -$Substitutions = Append[$Substitutions, -HRight[x_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] :> -NM[Adjoint[SMM[x,ar,br,cr]], UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -SMM[x,ar,br,cr]] + -NM[SMM[x,ar,br,cr], UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -Adjoint[SMM[x,ar,br,cr]]]]; - -$Substitutions = Append[$Substitutions, -HLeft[x_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] :> -NM[Adjoint[SMM[x,ar,br,cr]], UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -SMM[x,ar,br,cr]] - -NM[SMM[x,ar,br,cr], UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], -Adjoint[SMM[x,ar,br,cr]]]]; - - -$Substitutions = Append[$Substitutions, -HRight :> NM[Adjoint[SMM],UMatrix[UChiralSpurionRight[],SMM]] + - NM[SMM,UMatrix[UChiralSpurionLeft[],Adjoint[SMM]]]]; - -$Substitutions = Append[$Substitutions, -HLeft :> NM[Adjoint[SMM],UMatrix[UChiralSpurionRight[],SMM]] - - NM[SMM,UMatrix[UChiralSpurionLeft[],Adjoint[SMM]]]]; - - - - -(* ************************************************************** *) - -(* The G fields *) - -$Substitutions = Append[$Substitutions, -GRight[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[RightComponent[0, - Sequence@@OptionsSelect[RightComponent,opts]],ar,br,cr],{mu}][x]]+ - NM[UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - QuantumField[Particle[Photon,ar,br,cr],{mu}][x]]]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[LeftComponent[0, - Sequence@@OptionsSelect[LeftComponent,opts]],ar,br,cr],{mu}][x]]+ - NM[UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - QuantumField[Particle[Photon,ar,br,cr],{mu}][x]]]; - -$Substitutions = Append[$Substitutions, -GRight[mu_, nu_?(FreeQ[#, - RenormalizationState | RenormalizationScheme | ExpansionState | - Rule] &), ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> -FieldDerivative[GRight[nu,ar,br,cr,opts][x], x, {mu}] - - FieldDerivative[GRight[mu,ar,br,cr,opts][x],x, {nu}] - -I*(NM[GRight[mu,ar,br,cr,opts][x], GRight[nu,ar,br,cr,opts][x]] - -NM[GRight[nu,ar,br,cr,opts][x], GRight[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_, nu_?(FreeQ[#, - RenormalizationState | RenormalizationScheme | ExpansionState | - Rule] &), ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> -FieldDerivative[GLeft[nu,ar,br,cr,opts][x], x, {mu}] - - FieldDerivative[GLeft[mu,ar,br,cr,opts][x],x, {nu}] - -I*(NM[GLeft[mu,ar,br,cr,opts][x], GLeft[nu,ar,br,cr,opts][x]] - -NM[GLeft[nu,ar,br,cr,opts][x], GLeft[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -CQRight[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> FieldDerivative[UMatrix[UChiralSpurionRight@@ -OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], x, {mu}]- - I*(NM[GRight[mu,ar,br,cr,opts][x], - UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x]]- - NM[UMatrix[UChiralSpurionRight@@OptionsSelect[UChiralSpurionRight,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - GRight[mu,ar,br,cr,opts][x]])]; - -$Substitutions = Append[$Substitutions, -CQLeft[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> FieldDerivative[UMatrix[UChiralSpurionLeft@@ -OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], x, {mu}]- - I*(NM[GLeft[mu,ar,br,cr,opts][x], - UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x]]- - NM[UMatrix[UChiralSpurionLeft@@OptionsSelect[UChiralSpurionLeft,opts], - Sequence@@OptionsSelect[UMatrix,opts]][x], - GLeft[mu,ar,br,cr,opts][x]])]; - - -$Substitutions = Append[$Substitutions, -GRight[mu_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[RightComponent[0]],{mu}]]+ - NM[UMatrix[UChiralSpurionRight[]], - QuantumField[Particle[Photon],{mu}]] ]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_] :> UGeneratorMatrixIsoDot[QuantumField[ - Particle[LeftComponent[0]],{mu}]]+ - NM[UMatrix[UChiralSpurionLeft[]], - QuantumField[Particle[Photon],{mu}]]]; - -$Substitutions = Append[$Substitutions, -GRight[mu_, nu_] :> FieldDerivative[GRight[nu], {mu}] - - FieldDerivative[GRight[mu], {nu}] - -I*(NM[GRight[mu], GRight[nu]] - NM[GRight[nu], GRight[mu]])]; - -$Substitutions = Append[$Substitutions, -GLeft[mu_, nu_] :> FieldDerivative[GLeft[nu], {mu}] - - FieldDerivative[GLeft[mu], {nu}] - -I*(NM[GLeft[mu], GLeft[nu]] - NM[GLeft[nu], GLeft[mu]])]; - - - -$Substitutions = Append[$Substitutions, -CQRight[mu_] :> FieldDerivative[UMatrix[UChiralSpurionRight[]],{mu}]- - I*(NM[GRight[mu], UMatrix[UChiralSpurionRight[]]]- - NM[UMatrix[UChiralSpurionRight[]], GRight[mu]])]; - -$Substitutions = Append[$Substitutions, -CQLeft[mu_] :> FieldDerivative[UMatrix[UChiralSpurionLeft[]],{mu}]- - I*(NM[GLeft[mu], UMatrix[UChiralSpurionLeft[]]]- - NM[UMatrix[UChiralSpurionLeft[]], GLeft[mu]])]; - - -(*Added 8/2-2002*) - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GRight[mu_] :> GRight[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GLeft[mu_] :> GLeft[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GRight[mu_, nu_] :> GRight[mu, nu, SubArgs][SubX] /; -FreeQ[{nu}, Rule|RenormalizationsState|RenormalizationScheme|ExpansionState]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -GLeft[mu_, nu_] :> GLeft[mu, nu, SubArgs][SubX] /; -FreeQ[{nu}, Rule|RenormalizationsState|RenormalizationScheme|ExpansionState]]; - - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -CQRight[mu_] :> CQRight[mu, SubArgs][SubX]]; - -$PreSubstitutions[0] = Append[$PreSubstitutions[0], -CQLeft[mu_] :> CQLeft[mu, SubArgs][SubX]]; - - -(* ************************************************************** *) - -(* The Gamma_mu field *) - -(* We're overriding *) -$Substitutions = Select[$Substitutions, -(!MatchQ[#, (_?((! FreeQ[#, UGamma, Heads -> True]) &)) :> _])&]; - -$Substitutions = Append[$Substitutions, -UGamma[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -1/2*( - -NM[Adjoint[SMM[x,ar,br,cr,opts]], -FDr[SMM[x,ar,br,cr,opts],x,{mu}]]- - -I*NM[Adjoint[SMM[x,ar,br,cr,opts]], -GRight[mu,ar,br,cr,opts][x], -SMM[x,ar,br,cr,opts]]+ - -NM[SMM[x,ar,br,cr,opts], -FDr[Adjoint[SMM[x,ar,br,cr,opts]],x,{mu}]]- - -I*NM[SMM[x,ar,br,cr,opts], -GLeft[mu,ar,br,cr,opts][x], -Adjoint[SMM[x,ar,br,cr,opts]]] - -)]; - -$Substitutions = Append[$Substitutions, UGamma[mu_] :> - -1/2*( - -NM[Adjoint[SMM],FDr[SMM,{mu}]]- - -I*NM[Adjoint[SMM],GRight[mu],SMM]+ - -NM[SMM,FDr[Adjoint[SMM],{mu}]]- - -I*NM[SMM,GLeft[mu],Adjoint[SMM]] - -)]; - -(* ************************************************************** *) - -(* The nabla of the u_mu field *) - -Options[CovariantNabla] = {Explicit -> True}; - -CovariantNabla[aa_,x_,loris__LorentzIndex,lori1_LorentzIndex, opts___Rule]:= -(newfuncc[1]=CovariantNabla[aa,x,lori1, opts]; -Do[newfuncc[rep+1]=CovariantNabla[ -newfuncc[rep],x,##,opts]&@@Take[{loris},{-rep}], -{rep,1,Length[{loris}]}];newfuncc[Length[{loris}]+1]); - -CovariantNabla[aa_,x_,{loris__},rest___] := -CovariantNabla[aa,x,##,rest]& @@ LorentzIndex /@ {loris}; - -(* -------------------------------------------------------------- *) - -CovariantNabla[aa_,{lori_},(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,{lori}] + - -NM[UGamma[lori],aa] - -NM[aa,UGamma[lori]]; - -CovariantNabla[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,opts___Rule] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,x,lori] + - -NM[UGamma[lori,ar,br,cr, -Sequence@@Select[{opts},FreeQ[#,Explicit]&]][x],aa] - -NM[aa,UGamma[lori,ar,br,cr, -Sequence@@Select[{opts},FreeQ[#,Explicit]&]][x]]; - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]& @@ LorentzIndex /@ {loris}; - -(* -------------------------------------------------------------- *) - -(* EM-ChPT - Urech *) - -CovariantFieldDerivative[aa_,x_,lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantFieldDerivative]) := - -FieldDerivative[aa,x,lori] + - -I*NM[aa,UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br],lori][x],opts]] - - -I*NM[UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0],ar,br],lori][x],opts],aa]+ - -I* -NM[aa,UMatrix[UChiralSpurionLeft[ar,br,cr, -Sequence@@OptionsSelect[UChiralSpurionLeft,opts]], -Sequence@@OptionsSelect[UMatrix,opts]][x], -QuantumField[Particle[Photon,ar,br],lori][x]]- - -I* -NM[UMatrix[UChiralSpurionRight[ar,br,cr, -Sequence@@OptionsSelect[UChiralSpurionRight,opts]], -Sequence@@OptionsSelect[UMatrix,opts]][x], -QuantumField[Particle[Photon,ar,br],lori][x],aa]; - -(* ************************************************************** *) -(* Modify the photon propagator to general Lorentz gange *) - -Phi`Couplings`GenProps[a:Vector1] := -{FeynArts`AnalyticalPropagator[ -FeynArts`External][s a[i, mom, {li2}]] == -PolarizationVector[a[i], mom, li2], -FeynArts`AnalyticalPropagator[ -FeynArts`Internal][s a[i, mom, {li1} -> {li2}]] == -I*PropagatorDenominator[mom, FeynArts`Mass[a[i]]]* -(-MetricTensor[li1, li2] + -(1 - 1/$Gauge)* -FourVector[mom, li1]*FourVector[mom, li2]* -1/(PropagatorDenominator1[mom, FeynArts`Mass[a[i]]]) -)}; - -(* ************************************************************** *) - -(* An identity easily shown *) - -Phi`Objects`HLeftRightTrick::usage = - "HLeftRightTrick[exp] expresses CovariantNabla[HRight[x], x, {li}] \ -and CovariantNabla[HLeft[x], x, {li}] in terms of \ -SMM, USmall, HRight and HLeft"; - -HLeftRightTrick[exp_] := - exp /. - {CovariantNabla[HRight[x_, opts___Rule], x_, {li_} | LorentzIndex[li_]] :> - I/2 UCommutator[USmall[LorentzIndex[li], opts][x], HLeft[x, opts]] + - NM[Adjoint[SMM[x, opts]], CQRight[LorentzIndex[li], opts][x], SMM[x, opts]] + - NM[SMM[x, opts], CQLeft[LorentzIndex[li], opts][x], Adjoint[SMM[x, opts]]], - - CovariantNabla[HLeft[x_, opts___Rule], x_, {li_} | LorentzIndex[li_]] :> - I/2 UCommutator[USmall[LorentzIndex[li], opts][x], HRight[x, opts]] + - NM[Adjoint[SMM[x, opts]], CQRight[LorentzIndex[li], opts][x], SMM[x, opts]] - - NM[SMM[x, opts], CQLeft[LorentzIndex[li], opts][x], Adjoint[SMM[x, opts]]], - - (*Swap order of UGamma HRight and UGamma HLeft*) - NM[UGamma[li_, opts1___Rule][x_], HRight[x, opts2___Rule]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - CovariantNabla[HRight[x, opts2], x, {li}] - - FieldDerivative[HRight[x, opts2], x, {li}] + - NM[HRight[x, opts2], UGamma[li, opts1][x]]], - - NM[UGamma[li_, opts1___Rule][x_], HLeft[x, opts2___Rule]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - CovariantNabla[HLeft[x, opts2], x, {li}] - - FieldDerivative[HLeft[x, opts2], x, {li}] + - NM[HLeft[x, opts2], UGamma[li, opts1][x]]], - - UTrace1[NM[HRight[x, opts2___Rule], m__, - UGamma[li_, opts1___Rule][x_]]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - UTrace1[NM[m, CovariantNabla[HRight[x, opts2], x, {li}] - - FieldDerivative[HRight[x, opts2], x, {li}] + - NM[HRight[x, opts2], UGamma[li, opts1][x]]]]], - - UTrace1[NM[HLeft[x, opts2___Rule], m__, - UGamma[li_, opts1___Rule][x_]]] :> - Block[{opts}, - opts = Sequence @@ OptionsSelect[CovariantNabla, opts1, opts2]; - UTrace1[NM[m, CovariantNabla[HLeft[x, opts2], x, {li}] - - FieldDerivative[HLeft[x, opts2], x, {li}] + - NM[HLeft[x, opts2], UGamma[li, opts1][x]]]]]}; - -(* ************************************************************** *) - -(* Setting of options and $-variables, etc. *) - -SetOptions[Renormalize,SUNN->3]; -SetOptions[WriteOutUMatrices,SUNN->3]; -SetOptions[WriteOutIsoVectors,SUNN->3]; -SetOptions[UQuarkMass,SUNN->3,DiagonalToU->True]; -SetOptions[UMatrix,SUNN->3]; -SetOptions[IsoVector,SUNN->3]; -SetOptions[UGenerator,SUNN->3]; -SetOptions[UTrace,SUNN->3]; -SetOptions[SUNReduce,SUNN->3]; -SetOptions[ExpandU,SUNN->3]; -SetOptions[FAToFC,EqualMasses->False]; -SetOptions[DiscardTerms, -Retain->{Particle[PhiMeson,RenormalizationState[0]]->4}]; -SetOptions[CovariantFieldDerivative,SUNN->3]; -SetOptions[UPerturb, SUNN -> 3]; -SetOptions[UReduce, SUNN -> 3, UDimension -> 3]; -SetOptions[SMMToMM,SUNN -> 3]; -SetOptions[CharacteristicCoefficient, UDimension -> 3]; -SetOptions[CayleyHamilton, UDimension -> 3]; -SetOptions[CayleyHamiltonRules, SUNN -> 3, UDimension -> 3]; -tmpoptscdr=Options[CovariantFieldDerivative]; -tmpoptsmm=Options[MM]; -SetOptions[CovariantFieldDerivative, Explicit -> False]; -SetOptions[MM, Explicit -> False]; -SetOptions[CayleyHamiltonTrick, SUNN -> 3, UDimension -> 3, - UMatrices :> {{I NM[ - Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]], - I NM[Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]]}}]; -SetOptions[CovariantFieldDerivative, Sequence@@tmpoptscdr]; -SetOptions[MM,Sequence@@tmpoptsmm]; - -(* Auxiliary functions *) - -SetOptions[UPerturb, -UFields -> {HRight, HLeft, USmall, UChiPlus, UChiMinus, UFPlus, UFMinus, MM}]; - -xi[x_] := -IsoDot[IsoVector[QuantumField[Particle[PseudoScalar[12]]]][x], - IsoVector[UMatrix[UGenerator[]]]]; - -(*See Ecker 1992, CERN-TH-6660/92*) - -uExpRight[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule]:= - NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[PhiMeson,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]]]; - -uExpLeftAdj[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule]:= - NM[UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[PhiMeson,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]]; - -(* The u_mu field *) - -(*Keep things compact*) -SetOptions[CovariantNabla, Explicit -> False]; - -UCoefficient[USmall][0][li_, x_] = USmall[li][x]; -UCoefficient[USmall][1][li_, x_] = - -Sqrt[2]/DecayConstant[PhiMeson] CovariantNabla[xi[x], x, {li}] + -Sqrt[2]QuantumField[Particle[UPerturbation], LorentzIndex[li]][x]HLeft[x]; -UCoefficient[USmall][2][li_, x_] = -1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], - UCommutator[USmall[li][x], xi[x]]] - -I/DecayConstant[PhiMeson]QuantumField[Particle[UPerturbation], - LorentzIndex[li]][x]UCommutator[xi[x], HRight[x]]; -UCoefficient[USmall][do_?((# > 2) &)][li_, x_] := - UCoefficient[USmall][do][li, x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - I*NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - CDr[NM[uExpRight[x, ExpansionOrder -> do], - uExpLeftAdj[x, ExpansionOrder -> do]], x, {li}, - Explicit -> True], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] /. {QuantumField[pd___, Particle[Photon], LorentzIndex[l_]][xx_] -> - QuantumField[pd, Particle[Photon], {l}][xx] + - Sqrt[2]QuantumField[Particle[UPerturbation], {l}][xx]} // - NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(* The H_R - field*) - -UCoefficient[HRight][0][x_] = HRight[x]; -UCoefficient[HRight][1][x_] = --I/Sqrt[2]/DecayConstant[PhiMeson]UCommutator[xi[x], HLeft[x]]; -UCoefficient[HRight][2][x_] = --1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], - UCommutator[xi[x], HRight[x]]]; -UCoefficient[HRight][do_?((# > 2) &)][x_] := - UCoefficient[HRight][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ -NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChiralSpurionRight[]][x], - uExpRight[x, ExpansionOrder -> do]] + - NM[uExpLeftAdj[x, ExpansionOrder -> do], - UMatrix[UChiralSpurionLeft[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // - Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(* The H_L - field *) - -UCoefficient[HLeft][0][x_] = HLeft[x]; -UCoefficient[HLeft][1][x_] = --I/Sqrt[2]/DecayConstant[PhiMeson]UCommutator[xi[x], HRight[x]]; -UCoefficient[HLeft][2][x_] = --1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], - UCommutator[xi[x], HLeft[x]]]; -UCoefficient[HLeft][do_?((# > 2) &)][x_] := - UCoefficient[HLeft][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ -NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChiralSpurionRight[]][x], - uExpRight[x, ExpansionOrder -> do]] - - NM[uExpLeftAdj[x, ExpansionOrder -> do], - UMatrix[UChiralSpurionLeft[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // - Expand, Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -(*Return to defaults*) -SetOptions[CovariantNabla, Explicit -> True]; - -(* (7.14) and (7.20) from Gasser and Leutwyler (1985) *) - -gammaRule := -FieldDerivative[UGamma[LorentzIndex[li1_],opts___Rule][x_], x_, LorentzIndex[li2_]] /; -Sort[{li1,li2}] =!= {li1,li2} :> - FieldDerivative[UGamma[LorentzIndex[li2],opts][x], x, - LorentzIndex[li1]] + - UCommutator[UGamma[LorentzIndex[li1],opts][x], - UGamma[LorentzIndex[li2],opts][x]] - - 1/4 UCommutator[USmall[LorentzIndex[li1],Sequence@@OptionsSelect[USmall,opts]][x], - USmall[LorentzIndex[li2],Sequence@@OptionsSelect[USmall,opts]][x]] + - 1/2 I NM[Adjoint[SMM[x,Sequence@@OptionsSelect[SMM,opts]]], - GRight[LorentzIndex[li1],LorentzIndex[li2],opts][x], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]] + - 1/2 I NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - GLeft[LorentzIndex[li1],LorentzIndex[li2],opts][x], - Adjoint[SMM[x,Sequence@@OptionsSelect[SMM,opts]]]]; - - -UGammaTrick[exp_] := exp /. gammaRule; - -(* The chi_+ field*) - -UCoefficient[UChiPlus][0][x_] = UChiPlus[x]; -UCoefficient[UChiPlus][1][x_] = --I/Sqrt[2]/DecayConstant[PhiMeson]UAntiCommutator[xi[x], - UChiMinus[x]]; -UCoefficient[UChiPlus][2][x_] = - -1/4/DecayConstant[PhiMeson]^2 UAntiCommutator[xi[x], - UAntiCommutator[xi[x], UChiPlus[x]]]; -UCoefficient[UChiPlus][do_?((# > 2) &)][x_] := - UCoefficient[UChiPlus][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChi[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] + - NM[uExpLeftAdj[x, ExpansionOrder -> do], - Adjoint[UMatrix[UChi[]][x]], - uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] // UReduce); - -$EOMRules := - -{UTrace1[NM[Adjoint[MM[x_]], CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], -Adjoint[UMatrix[UChi[]][x_]], CovariantFieldDerivative[MM[x_], x_, - LorentzIndex[mu_]]]] -> --(UTrace1[ - NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]^2/ - 6 - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])/3 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]]^2/6 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x]]]/2 - - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x]]]/ - 2 - (-UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[MM[x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[]][x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]]]))+ - -(-2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], UMatrix[UChi[]][x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[1]]^2 - -(2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[1]]^2 + -(2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x], UMatrix[UChiralSpurionLeft[]][x]]])/ -DecayConstant[PseudoScalar[1]]^2 + (2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x], Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x]]])/ -DecayConstant[PseudoScalar[1]]^2, - -UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]]], -CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], - Adjoint[UMatrix[UChi[chopts___]][x_]], MM[x_]]] -> --(-(UTrace1[ - NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]^2/ - 6 - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]])/3 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x]]]^2/6 + - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChi[]][x]]] - - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x]]]/2 - - UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x]]]/ - 2 - (-UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[Adjoint[ - CovariantFieldDerivative[UMatrix[UChi[]][x], x, - LorentzIndex[mu]]], - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]] - - UTrace1[ - NM[MM[x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[]][x], - Adjoint[ - CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]]]]))+ - -(-2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], UMatrix[UChi[]][x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[1]]^2 - -(2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[UMatrix[UChi[]][x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - UMatrix[UChiralSpurionLeft[]][x]]])/DecayConstant[PseudoScalar[1]]^2 + -(2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x], MM[x], - Adjoint[UMatrix[UChi[]][x]], MM[x], UMatrix[UChiralSpurionLeft[]][x]]])/ -DecayConstant[PseudoScalar[1]]^2 + (2*CouplingConstant[ChPTVirtualPhotons2[2]]* -UTrace1[NM[MM[x], UMatrix[UChiralSpurionLeft[]][x], Adjoint[MM[x]], - UMatrix[UChi[]][x], Adjoint[MM[x]], UMatrix[UChiralSpurionRight[]][x]]])/ -DecayConstant[PseudoScalar[1]]^2)}; - - -$ExpansionQuantities=Union[$ExpansionQuantities, -{MetricTensor[__],Pair[__]}]; - -DeclareUMatrix[MM,SMM,UChiMatrix,USmall,UFPlus,UFMinus,UChiPlus,UChiMinus,UGamma, -GRight,GLeft,HRight,HLeft,CQLeft,CQRight,UQuarkChargeMatrix]; - -$ParticlesInUse={PhiMeson,Pion,Kaon,Photon(*,Vector[0],AxialVector[0]*)}; - -$PropagatorMassesStates={PhiMeson[0]->{RenormalizationState[0]}, - Kaon[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - Vector[0][0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{PhiMeson[0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - Kaon[0]->{{IsoRange->{1,2},IsoIndicesString->"J"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, -Vector[0][0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{(*Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, - AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Photon[0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}*)}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/ChPTW3.conf b/FeynCalc/Phi/Configurations/ChPTW3.conf deleted file mode 100644 index d951e90fb..000000000 --- a/FeynCalc/Phi/Configurations/ChPTW3.conf +++ /dev/null @@ -1,705 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTW3 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 2000 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - Lagrangians ChPTW3 for PHI - -Description: Definitions for standard weak ChPT lagrangians - The definitions follow - Ecker, Kambor and Wyler (1992), CERN-TH.6610/92. - -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* SU(3) meson matrix PhiMeson instead of Pion *) - -BeginPackage["Phi`Objects`", {"Phi`", -"FeynCalc`"}]; -Begin["`Private`"]; - -MM[x_?(! NumberQ[#] &), h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MM]) := - - UFieldMatrix[fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -MM[ii_?NumberQ, x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MM]) := - UFieldMatrix[ii, fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -SMM[x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[SMM]) := MM[1/2, x, h, opts]; -MMS[x_, h___, opts___Rule] /; (fcexpt/.Flatten[{opts}]/.Options[MMS]) := - UFieldMatrixSeries[fcqf[(Particle[PhiMeson, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; - -End[]; -EndPackage[]; - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPTW3::usage= -"Lagrangian[ChPTW3[2]] is the weak mesonic Chiral Perturbation Theory -lagrangian written in terms of a matrix representation -of the meson fields to second order in the energy. Lagrangian[ChPTW3[4]] -is the weak mesonic Chiral Perturbation Theory lagrangian -to four'th order in the energy. To evaluate use ArgumentsSupply"; - -Phi`Objects`ChPT3; - -MM::usage="MM[x] := -UFieldMatrix[QuantumField[Particle[PhiMeson]][x]]. -MM takes two optional arguments with head RenormalizationState -and RenormalizationScheme respectively."; - -Phi`Objects`UDelta::usage= -"UDelta is the delta-field of WChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UNablaHatDelta::usage= -"UNablaHatDelta[mu] is the nabla hat of the -delta-field of WChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UOmega::usage= -"UOmega[mu,nu] is the omega-field of WChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -Phi`Objects`CovariantNabla::usage= -"CovariantNabla[f[x],x,{li1,li2,...},opts] is -the covariant derivative of a h h^(-1) transforming quantity f[x] with respect to -space-time variables x and with Lorentz indices li0, li1, li2,... -(See e.g ChPT (Ecker, Kambor and Wyler (1992), CERN-TH.6610/92)). -To evaluate use ArgumentsSupply."; - -Phi`Objects`NablaChiPlus::usage= -"NablaChiPlus is CovariantNabla acting on UChiPlus."; - -Phi`Objects`NablaChiMinus::usage= -"NablaChiPlus is CovariantNabla acting on UChiMinus."; - -Phi`Objects`C8::usage= -"C8 is the coefficient C_8 of Kambor, Missimer and Wyler, \ -Nucl.Phys.B346:17-64,1990."; - -Phi`Objects`C8Dot::usage= -"C8Dot is the coefficient C_8' of Kambor, Missimer and Wyler, \ -Nucl.Phys.B346:17-64,1990."; - -Phi`Objects`C8::usage= -"C27 is the coefficient C_27 of Kambor, Missimer and Wyler, \ -Nucl.Phys.B346:17-64,1990."; - -Phi`Objects`FW::usage= -"FW[a,b] is the coefficient f^a_b of Kambor, Missimer and Wyler, \ -Nucl.Phys.B346:17-64,1990."; - -Phi`Objects`QW::usage= -"QW[a,b] is an SU(3) generator matrix Q_a^b in the Cartan-Weyl basis, \ -as used in Kambor, Missimer and Wyler, \ -Nucl.Phys.B346:17-64,1990."; - -Phi`Objects`KW::usage= -"KW[a,b] is the K^a_b of Kambor, Missimer and Wyler, \ -Nucl.Phys.B346:17-64,1990."; - -Phi`Objects`TW::usage= -"TW[a,b,c,d] is the t^{a b}_{c d} of Kambor, Missimer and Wyler, \ -Nucl.Phys.B346:17-64,1990."; - -(* ************************************************************** *) - -(* Box definitions *) - -UOmega /: MakeBoxes[UOmega[mu_,nu_], TraditionalForm] := - SuperscriptBox[ - MakeBoxes[ - StyleForm["\[Omega]", FontSlant -> "Italic", - FontWeight -> "Bold"]][[1]], - RowBox[{MakeBoxes[TraditionalForm[mu]], - MakeBoxes[TraditionalForm[nu]]}]]; - -FW /: MakeBoxes[FW[a_,b_], TraditionalForm] := - SubsuperscriptBox[ - "f", MakeBoxes[TraditionalForm[b]], - MakeBoxes[TraditionalForm[a]]]; - -QW /: MakeBoxes[QW[a_,b_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["Q", (*FontSlant -> "Italic",*) - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm[b]], - MakeBoxes[TraditionalForm[a]]]; - -KW /: MakeBoxes[KW[a_,b_][x_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["K", (*FontSlant -> "Italic",*) - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm[b]], - MakeBoxes[TraditionalForm[a]]]; - -KW /: MakeBoxes[KW[a_,b_], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[ - StyleForm["K", (*FontSlant -> "Italic",*) - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm[b]], - MakeBoxes[TraditionalForm[a]]]; - -TW /: MakeBoxes[TW[a_,b_,c_,d_], TraditionalForm] := - SubsuperscriptBox[ - "t", RowBox[{MakeBoxes[TraditionalForm[c]], - MakeBoxes[TraditionalForm[d]]}], - RowBox[{MakeBoxes[TraditionalForm[a]], - MakeBoxes[TraditionalForm[b]]}]]; - -UDelta /: MakeBoxes[UDelta, TraditionalForm] := - MakeBoxes[ - StyleForm["\[CapitalDelta]", - FontSlant -> "Italic",FontWeight->"Bold"]]; - -C8 /: MakeBoxes[C8, TraditionalForm] := - SubscriptBox["C","8"]; - -C8Dot /: MakeBoxes[C8Dot, TraditionalForm] := - SubsuperscriptBox["C","8","\[Prime]"]; - -C27 /: MakeBoxes[C27, TraditionalForm] := - SubscriptBox["C","27"]; - -UNablaHatDelta /: MakeBoxes[UNablaHatDelta[mu_], TraditionalForm] := - RowBox[{SubscriptBox[MakeBoxes[OverHat["\[Del]"]], - MakeBoxes[TraditionalForm[mu]]], - MakeBoxes[ - StyleForm["\[CapitalDelta]", - FontSlant -> "Italic",FontWeight->"Bold"]]}]; - -NablaChiPlus /: MakeBoxes[NablaChiPlus[mu_], TraditionalForm] := - RowBox[{SubscriptBox[MakeBoxes[OverHat["\[Del]"]], - MakeBoxes[TraditionalForm[mu]]], - SubscriptBox[MakeBoxes["\[Chi]"], - MakeBoxes["+"]]}]; - -(* ************************************************************** *) - -(* Source fields *) - -(* Strip off options passed to Particle[PseudoScalar[0],___]*) -Particle[PseudoScalar[0],o___,__Rule]:=Particle[PseudoScalar[0],o]; - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[Scalar[0],st___RenormalizationState, -sc___RenormalizationScheme,qs___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -UQuarkMassMatrix[st,sc,qs,opts]; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2|12],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0; - -(*Strong part*) -(*CouplingConstant[ChPT3[4],1,___]=0; -CouplingConstant[ChPT3[4],2,___]=0; -CouplingConstant[ChPT3[4],3,___]=0; -CouplingConstant[ChPT3[4],4,___]=0; -CouplingConstant[ChPT3[4],5,___]=0; -CouplingConstant[ChPT3[4],6,___]=0; -CouplingConstant[ChPT3[4],7,___]=0; -CouplingConstant[ChPT3[4],8,___]=0; -CouplingConstant[ChPT3[4],9,___]=0; -CouplingConstant[ChPT3[4],10,___]=0; -CouplingConstant[ChPT3[4],11,___]=0*) - -(*Weak part*) -(*CouplingConstant[ChPTW3[4],1,___]=0; -CouplingConstant[ChPTW3[4],2,___]=0; -CouplingConstant[ChPTW3[4],3,___]=0; -CouplingConstant[ChPTW3[4],4,___]=0;*) -(*CouplingConstant[ChPTW3[4],5,___]=0; -CouplingConstant[ChPTW3[4],6,___]=0; -CouplingConstant[ChPTW3[4],7,___]=0; -CouplingConstant[ChPTW3[4],8,___]=0; -CouplingConstant[ChPTW3[4],9,___]=0; -CouplingConstant[ChPTW3[4],10,___]=0; -CouplingConstant[ChPTW3[4],11,___]=0; -CouplingConstant[ChPTW3[4],12,___]=0; -CouplingConstant[ChPTW3[4],13,___]=0;*) -(*CouplingConstant[ChPTW3[4],14,___]=0; -CouplingConstant[ChPTW3[4],15,___]=0; -CouplingConstant[ChPTW3[4],16,___]=0; -CouplingConstant[ChPTW3[4],17,___]=0;*) -(*CouplingConstant[ChPTW3[4],18,___]=0;*) -(*CouplingConstant[ChPTW3[4],19,___]=0; -CouplingConstant[ChPTW3[4],20,___]=0; -CouplingConstant[ChPTW3[4],21,___]=0; -CouplingConstant[ChPTW3[4],22,___]=0; -CouplingConstant[ChPTW3[4],23,___]=0; -CouplingConstant[ChPTW3[4],24,___]=0;*) -(*CouplingConstant[ChPTW3[4],25,___]=0; -CouplingConstant[ChPTW3[4],26,___]=0; -CouplingConstant[ChPTW3[4],27,___]=0; -CouplingConstant[ChPTW3[4],28,___]=0; -CouplingConstant[ChPTW3[4],29,___]=0; -CouplingConstant[ChPTW3[4],30,___]=0; -CouplingConstant[ChPTW3[4],31,___]=0; -CouplingConstant[ChPTW3[4],32,___]=0; -CouplingConstant[ChPTW3[4],33,___]=0; -CouplingConstant[ChPTW3[4],34,___]=0; -CouplingConstant[ChPTW3[4],35,___]=0; -CouplingConstant[ChPTW3[4],36,___]=0; -CouplingConstant[ChPTW3[4],37,___]=0;*) - -(* ************************************************************** *) - -(* Redefinition of the left and right components. -Ecker, Kambor and Wyler have them the other way round. -Also it's necessary in order to not have the AxialVector (Vector) -part set to zero *) - -IsoVector[QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___], -bb___],opts___][x_]/;(Explicit/.{opts0}/.Options[LeftComponent]):= -1/2*( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]- -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -IsoVector[QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___], -opts___][x_]/;(Explicit/.{opts0}/.Options[RightComponent]):=1/2*( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]+ -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -1/2*(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -1/2*(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -(* ************************************************************** *) - -(* Redefinition of the field strength tensor: -I instead of I *) - -FST[p_,mu_LorentzIndex, - nu_LorentzIndex,x_, - a___RenormalizationState, - b___RenormalizationScheme,(opts___Rule|opts___List)]:= -FieldStrengthTensor[mu, -UGeneratorMatrixIsoDotFull[QuantumField[ -Particle[p,a,b],nu][x],opts],x]-2*I* - UGeneratorMatrixIsoDot[ - IsoCross[( - IsoVector[QuantumField[Particle[p,a,b],mu],##]&@@ - OptionsSelect[IsoVector,opts])[ - x],(IsoVector[QuantumField[Particle[p,a,b],nu],##]&@@ - OptionsSelect[IsoVector,opts])[x]],opts]; - -(* ************************************************************** *) - -(* The capital delta field *) - -$Substitutions = Append[$Substitutions, UDelta :> -NM[SMM, -UGeneratorMatrix[SUNIndex[6]], -Adjoint[SMM]]]; - -$Substitutions = Append[$Substitutions, UDelta[x_] :> -NM[SMM[x], -UGeneratorMatrix[SUNIndex[6]], -Adjoint[SMM[x]]]]; - -(* ************************************************************** *) - -(* The K field of Kambor, Missimer and Wyler *) - -$Substitutions = Append[$Substitutions, KW[a_, b_][x_] :> -NM[SMM[x], QW[a, b], Adjoint[SMM[x]]]]; - -$Substitutions = Append[$Substitutions, KW[a_, b_] :> -NM[SMM, QW[a, b], Adjoint[SMM]]]; - -$Substitutions = Append[$Substitutions, KW :> -NM[SMM, QW, Adjoint[SMM]]]; - -(* ************************************************************** *) - -(* The nabla hat of the capital delta field *) - -(* Uncomment one and comment the other of the definitions below; -the first is without and the second with -coupling to a scalar source *) - -$Substitutions = Append[$Substitutions, UNablaHatDelta[mu_] :> - -(* The standard definition *) --I*NM[SMM, -UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0]],{mu}]], -UGeneratorMatrix[SUNIndex[6]], -Adjoint[SMM]]+ -I*NM[SMM, -UGeneratorMatrix[SUNIndex[6]], -UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0]],{mu}]], -Adjoint[SMM]] - -(* Including a scalar 'source' with momentum. Forget about the -vector and axial-vector sources *) -(*NM[SMM,NM[ -FDr[QuantumField[Particle[Scalar[1]]],{mu}], -UGeneratorMatrix[SUNIndex[6]], -Adjoint[SMM]]]*) -]; - -(* ************************************************************** *) - -(* The omega field *) - -$Substitutions = Append[$Substitutions, UOmega[mu_,nu_] :> - -CovariantNabla[USmall[mu],{nu}]+CovariantNabla[USmall[nu],{mu}]]; - -(* ************************************************************** *) - -(* The Gamma_mu field *) - -$Substitutions = Append[$Substitutions, -UGamma[mu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -1/2*( - -NM[Adjoint[SMM[x,ar,br,cr,opts]], -FDr[SMM[x,ar,br,cr,opts],x,{mu}]]- - -I*NM[Adjoint[SMM[x,ar,br,cr,opts]], -UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0],ar,br,cr],{mu}][x]], -SMM[x,ar,br,cr,opts]]+ - -NM[SMM[x,ar,br,cr,opts], -FDr[Adjoint[SMM[x,ar,br,cr,opts]],x,{mu}]]- - -I*NM[SMM[x,ar,br,cr,opts], -UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br,cr],{mu}][x]], -Adjoint[SMM[x,ar,br,cr,opts]]] - -)]; - -$Substitutions = Append[$Substitutions, UGamma[mu_] :> - -1/2*( - -NM[Adjoint[SMM],FDr[SMM,{mu}]]- - -I*NM[Adjoint[SMM], -UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0]],{mu}]],SMM]+ - -NM[SMM,FDr[Adjoint[SMM],{mu}]]- - -I*NM[SMM, -UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0]],{mu}]],Adjoint[SMM]] - -)]; - -(* ************************************************************** *) - -(* The nabla of the u_mu field *) - -Options[CovariantNabla] = {Explicit -> True}; - -CovariantNabla[aa_,x_,loris__LorentzIndex,lori1_LorentzIndex, opts___Rule]:= -(newfuncc[1]=CovariantNabla[aa,x,lori1, opts]; -Do[newfuncc[rep+1]=CovariantNabla[ -newfuncc[rep],x,##,opts]&@@Take[{loris},{-rep}], -{rep,1,Length[{loris}]}];newfuncc[Length[{loris}]+1]); - -CovariantNabla[aa_,x_,{loris__},rest___] := -CovariantNabla[aa,x,##,rest]& @@ LorentzIndex /@ {loris}; - -(* -------------------------------------------------------------- *) - -CovariantNabla[aa_,{lori_},(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,{lori}] + - -NM[UGamma[lori],aa] - -NM[aa,UGamma[lori]]; - -CovariantNabla[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantNabla]) := - -FieldDerivative[aa,x,lori] + - -NM[UGamma[lori,ar,br,cr,opts][x],aa] - -NM[aa,UGamma[lori,ar,br,cr,opts][x]]; - - -(* ************************************************************** *) - -(* The nabla of the Chi_plus/Chi_minus fields *) - -$Substitutions = Append[$Substitutions, NablaChiPlus[mu_] :> -NM[SMM,CDr[Adjoint[UChiMatrix],{mu}],SMM]+ -NM[Adjoint[SMM],CDr[UChiMatrix,{mu}],Adjoint[SMM]]+ -I/2*(NM[USmall[mu],UChiMinus]+NM[UChiMinus,USmall[mu]])]; - -(* Not used *) -$Substitutions = Append[$Substitutions, NablaChiMinus[mu_] :> -NM[SMM,CDr[Adjoint[UChiMatrix],{mu}],SMM]- -NM[Adjoint[SMM],CDr[UChiMatrix,{mu}],Adjoint[SMM]]+ -I/2*(NM[USmall[mu],UChiPlus]+NM[UChiPlus,USmall[mu]])]; - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]& @@ LorentzIndex /@ {loris}; - -(* -------------------------------------------------------------- *) - -(* Standard ChPT - Donoghue, Golowich, Holstein *) -(* commuted 14/1-2001*) - -CovariantFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] /; -(Explicit /. Flatten[{opts}] /. Options[CovariantFieldDerivative]) := - -FieldDerivative[aa,x,lori] + - -I*NM[aa,UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0],ar,br],lori][x],opts]] - - -I*NM[UGeneratorMatrixIsoDot[QuantumField[Particle[ -RightComponent[0],ar,br],lori][x],opts],aa]; - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - -SetOptions[WriteOutUMatrices,SUNN->3]; -SetOptions[UQuarkMass,SUNN->3,DiagonalToU->True]; -SetOptions[UGenerator,SUNN->3]; -SetOptions[WriteOutIsoVectors,SUNN->3]; -SetOptions[UIdentity,SUNN->3]; -SetOptions[UMatrix,SUNN->3]; -SetOptions[IsoVector,SUNN->3]; -SetOptions[UTrace,SUNN->3]; -SetOptions[SUNReduce,SUNN->3]; -SetOptions[ExpandU,SUNN->3]; -SetOptions[FAToFC,EqualMasses->False]; -SetOptions[DiscardTerms, -Retain->{Particle[PhiMeson,RenormalizationState[0]]->2, -Particle[AxialVector[0],RenormalizationState[0]]->1}]; -SetOptions[CovariantFieldDerivative,SUNN->3]; -SetOptions[DiscardTopologies,PerturbationOrder -> 1, -OrderingPatterns -> {(*Vertices with a scalar are always weak*) -FullVertex[___,Scalar1[0], ___],(*so are odd vertices without a scalar*) -FullVertex[v__] /; (OddQ[Length[{v}]] && FreeQ[{v}, Scalar1[0]])}]; -SetOptions[UPerturb, SUNN -> 3]; -SetOptions[CayleyHamiltonRules, UDimension -> 2]; -SetOptions[CayleyHamiltonTrick, UDimension -> 3, - UMatrices :> {{I NM[ - Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]], - I NM[Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]]}}]; -SetOptions[UReduce] = {UDimension -> 3}; - -DeclareUMatrix[MM,SMM,UChiMatrix,USmall,UFPlus,UFMinus,UChiPlus,UChiMinus,UGamma,QW,KW]; - -(* Auxiliary functions *) - -SetOptions[UPerturb, -UFields -> {USmall, UChiPlus, UChiMinus, UFPlus, UFMinus, MM, KW}]; - -xi[x_] := -IsoDot[IsoVector[QuantumField[Particle[PseudoScalar[12]]]][x], - IsoVector[UMatrix[UGenerator[]]]]; - -(*See Ecker 1992, CERN-TH-6660/92*) - -uExpRight[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule]:= - NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[PhiMeson,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]]]; - -uExpLeftAdj[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule]:= - NM[UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[PhiMeson,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]]; - -(* The K field of Kambor, Missimer and Wyler *) - -UCoefficient[KW][0][a_,b_,x_]=KW[a,b][x] - -UCoefficient[KW][1][a_,b_,x_]= -I/Sqrt[2]/DecayConstant[PhiMeson]UCommutator[xi[x],KW[a,b][x]] - -UCoefficient[KW][2][a_,b_, - x_]=-1/4/DecayConstant[PhiMeson]^2UCommutator[xi[x], - UCommutator[xi[x],KW[a,b][x]]] - -UCoefficient[KW][do_?((#>2)&)][a_,b_,x_]:= - UCoefficient[KW][do][a,b,x]=(Message[UPerturb::"nocoeff",do]; - DiscardTerms[ - NM[uExpLeftAdj[x,ExpansionOrder -> do],QW[a,b], - Adjoint[uExpLeftAdj[x,ExpansionOrder -> do]]]//NMExpand// - Expand,Retain -> {Particle[UPerturbation] -> do}]// - UReduce); - -$ParticlesInUse= -{PhiMeson,Pion,Kaon,KaonPlus,KaonMinus, -KaonZero,KaonZeroBar,(*EtaMeson, -Photon,Vector[0],*)AxialVector[0],Scalar[1],Scalar[2], -PseudoScalar[0]}; - -$ExpansionQuantities= -{FourVector[__],ParticleMass[Pion,a___], -ParticleMass[PhiMeson,b___],ParticleMass[KaonZero,c___], -ParticleMass[KaonPlus,d___],ParticleMass[EtaMeson,d___](*, -CouplingConstant[ChPTW3[2],h___]*)}; - -$PropagatorMassesStates={ - PhiMeson[0]->{RenormalizationState[0]}, - Pion[0]->{RenormalizationState[0]}, - Kaon[0]->{RenormalizationState[0]}, - KaonPlus[0]->{RenormalizationState[0]}, - KaonMinus[0]->{RenormalizationState[0]}, - KaonZero[0]->{RenormalizationState[0]}, - KaonZeroBar[0]->{RenormalizationState[0]}, - EtaMeson[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - PseudoScalar[0][0]->{RenormalizationState[0]}, - Vector[0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{PhiMeson[0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - PseudoScalar[0][0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - Scalar[2][0]->{{IsoRange->{0,1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}, - Vector[0][0]->{{IsoRange->{1,2,3,4,5,6,7,8},IsoIndicesString->"I"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{Scalar[1][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Scalar[2][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -PseudoScalar[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Photon[0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/FCBoxes.m b/FeynCalc/Phi/Configurations/FCBoxes.m deleted file mode 100644 index b3dde77a5..000000000 --- a/FeynCalc/Phi/Configurations/FCBoxes.m +++ /dev/null @@ -1,216 +0,0 @@ -(* ************************************************************** *) -(* *) -(* FCBoxes.m *) -(* *) -(* ************************************************************** *) - -(* - Author: F.Orellana 2000 - - Mathematica Version: 3.0 - - Requirements: FeynCalc > 3, PHI - - Description: The definitions in this file modifies the - way QuantumFields are displayed, so that - outputs of calculations with PHI look nicer. - -*) - -(* ************************************************************** *) - -(* Box definitions for FeynCalc *) - -ClearAll[QuantumField]; - -Begin["FeynCalc`QuantumField`Private`"] - -QuantumField /: -MakeBoxes[ QuantumField[a_][_], TraditionalForm - ] := TBox[a](*[[1]]*); - -QuantumField /: -MakeBoxes[ QuantumField[f_, lo_[mu_,___]][_], TraditionalForm - ] := SubscriptBox[TBox[f](*[[1]]*), TBox[mu]] /; - lo === LorentzIndex || - lo === Phi`Objects`UIndex; - -QuantumField /: - MakeBoxes[ QuantumField[f_, lori:lo_[_,___].., suni:sun_[_].. - ][_], TraditionalForm - ] := -SubsuperscriptBox[TBox[f](*[[1]]*), TBox[lori], TBox[suni]]/; - MatchQ[lo, LorentzIndex | Momentum | Phi`Objects`UIndex] && - (sun === SUNIndex || sun === ExplicitSUNIndex); - -QuantumField /: - MakeBoxes[ QuantumField[ - FCPartialD[pa_], a_, -lori___LorentzIndex | -lori___Phi`Objects`UIndex, -suni___SUNIndex | -suni___ExplicitSUNIndex - ][_], - TraditionalForm] := -RowBox[{SubscriptBox["\[PartialD]" , TBox[pa]], -SubsuperscriptBox[TBox[a](*[[1]]*), TBox[lori], TBox[suni]] - }]; - -QuantumField /: - MakeBoxes[ QuantumField[ - FCPartialD[pa_]^m_, a_, -(*lori___Momentum,*) -lori___LorentzIndex | -lori___Phi`Objects`UIndex, -suni___SUNIndex | -suni___ExplicitSUNIndex - ][_], - TraditionalForm] := - RowBox[{SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]], -SubsuperscriptBox[TBox[a](*[[1]]*), TBox[lori], TBox[suni]] - }]; - -QuantumField /: - MakeBoxes[ QuantumField[ - pa__FCPartialD, a_, -(*lori___Momentum,*) -lori___LorentzIndex | -lori___Phi`Objects`UIndex, -suni___SUNIndex | -suni___ExplicitSUNIndex - ][_], - TraditionalForm - ] := RowBox[{TBox[pa], -SubsuperscriptBox[TBox[a](*[[1]]*), TBox[lori], TBox[suni]] - }]; - -(*----------------------------------------------------------------*) - -QuantumField /: - MakeBoxes[ QuantumField[f_,suni:sun_[_].. - ][_], TraditionalForm] := - SuperscriptBox[TBox[f](*[[1]]*),TBox[suni]] /; - (sun === SUNIndex || sun === ExplicitSUNIndex); - -QuantumField /: - MakeBoxes[ QuantumField[f_,suni:sun_[_].. - ], TraditionalForm - ] := SuperscriptBox[TBox[f](*[[1]]*),TBox[suni] - ] /; - (sun === SUNIndex || sun === ExplicitSUNIndex); - -(*----------------------------------------------------------------*) - -(* Modified original FeynCalc definitions*) - -QuantumField[f___,g_/;Head[g]=!=List,{lilo___}] := - QuantumField@@Join[{f,g},LorentzIndex/@{lilo}]; - -QuantumField[f___,g_/;Head[g]=!=List,{lilo___},{suli___}] := - QuantumField@@Join[{f,g},LorentzIndex/@{lilo},SUNIndex/@{suli}]; - -QuantumField[f___,g_/;Head[g]=!=List,{lilo___},{suli___}, {ui___}] := - QuantumField@@Join[{f,g},LorentzIndex/@{lilo},SUNIndex/@{suli}, - Phi`Objects`UIndex/@{ui}]; - -QuantumField[f1_QuantumField] := - f1; - - -QuantumField /: - MakeBoxes[ QuantumField[a_][_], TraditionalForm - ] := TBox[a](*[[1]]*); - -QuantumField /: - MakeBoxes[ QuantumField[a_], TraditionalForm - ] := TBox[a](*[[1]]*); - -QuantumField /: - MakeBoxes[ QuantumField[f_, lo_[mu_,___]], TraditionalForm - ] := SubscriptBox[TBox[f](*[[1]]*), TBox[mu]] /; - lo === LorentzIndex || - lo === Phi`Objects`UIndex; - -QuantumField /: - MakeBoxes[ - QuantumField[f_, - lol : (((LorentzIndex| - Phi`Objects`UIndex)[_, ___])..)], - TraditionalForm] := SubscriptBox[TBox[f][[1(*, 1*)]], TBox[lol]]; - -QuantumField /: - MakeBoxes[ QuantumField[f_, lori:lo_[_,___].., suni:sun_[_].. - ], TraditionalForm -] := SubsuperscriptBox[TBox[f](*[[1]]*), TBox[lori], TBox[suni] - ] /; MatchQ[lo, LorentzIndex | Momentum | Phi`Objects`UIndex - ] && (sun === SUNIndex || sun === ExplicitSUNIndex); - -QuantumField /: - MakeBoxes[ QuantumField[f_, lori:lo_[_,___].., suni:sun_[_].. - ][_], TraditionalForm -] := SubsuperscriptBox[TBox[f](*[[1]]*), TBox[lori], TBox[suni]] /; - MatchQ[lo, LorentzIndex | Momentum | Phi`Objects`UIndex] && - (sun === SUNIndex || sun === ExplicitSUNIndex); -QuantumField /: - MakeBoxes[ QuantumField[ - FCPartialD[pa_], a_, -lori___LorentzIndex | -lori___Phi`Objects`UIndex, -suni___SUNIndex | -suni___ExplicitSUNIndex - ], - TraditionalForm - ] := RowBox[{SubscriptBox["\[PartialD]" , TBox[pa]], - SubsuperscriptBox[TBox[a](*[[1]]*), TBox[lori], TBox[suni]] - }]; - -QuantumField /: - MakeBoxes[ QuantumField[ - FCPartialD[pa_]^m_, a_, -(*lori___Momentum,*) -lori___LorentzIndex | -lori___Phi`Objects`UIndex, -suni___SUNIndex | -suni___ExplicitSUNIndex - ], - TraditionalForm - ] := RowBox[{SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]], - SubsuperscriptBox[TBox[a](*[[1]]*), TBox[lori], TBox[suni]] - }]; - -QuantumField /: - MakeBoxes[ QuantumField[ - pa__FCPartialD, a_, -(*lori___Momentum,*) -lori___LorentzIndex | -lori___Phi`Objects`UIndex, -suni___SUNIndex | -suni___ExplicitSUNIndex - ], - TraditionalForm - ] := RowBox[{TBox[pa], - SubsuperscriptBox[TBox[a](*[[1]]*), - TBox[lori], TBox[suni]] - }]; - -(* ************************************************************** *) - -End[] - -(* ************************************************************** *) - -(* Additional definitions from Objects.m *) - -QuantumField[ders___FCPartialD,a__, lors___LorentzIndex, - iis___SUNIndex|iis___ExplicitSUNIndex][ - isosp_SUNIndex|isosp_ExplicitSUNIndex] := - QuantumField[ders,a,lors,isosp,iis]; - -QuantumField[ -ders___FCPartialD, a__, lors___LorentzIndex, - iis___SUNIndex|iis___ExplicitSUNIndex][ui_UIndex] := - QuantumField[ders, a, lors, iis, ui]; - -Phi`Objects`Private`setLeftRightComponents; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/HBChPT2.conf b/FeynCalc/Phi/Configurations/HBChPT2.conf deleted file mode 100644 index 806146ba9..000000000 --- a/FeynCalc/Phi/Configurations/HBChPT2.conf +++ /dev/null @@ -1,448 +0,0 @@ -(* ************************************************************** *) -(* *) -(* HBChPT2 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 1999 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the family of - Lagrangians HBChPT2 for PHI - -Description: Definitions for HBChPT lagrangians. - - The definitions follow - G.Ecker and M. Mojzis (1995), - hep-ph/9508204 -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* Usage definitions *) - -Phi`Objects`ChPT2::usage= -"Lagrangian[ChPT2[2]] is the pionic Chiral Perturbation Theory -lagrangian written in terms of a matrix representation -of the pion fields to second order in the energy. Lagrangian[ChPT2[4]] -is the pionic Chiral Perturbation Theory lagrangian -to four'th order in the energy (first written down by Gasser and -Leutwyler). To evaluate use ArgumentsSupply."; - -Phi`Objects`HBChPT2::usage= -"Lagrangian[HBChPT2[2]] is the lowest order nucleon-pion -Chiral Perturbation Theory lagrangian. To evaluate -use ArgumentsSupply."; - -Phi`Objects`USmall::usage= -"USmall[mu] is the u-field of HBChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UGamma::usage= -"UGamma[mu] is the gamma-field of HBChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply. -UGamma[mu,opts][x] is the evaluated gamma-field."; - -Phi`Objects`UChiPlus::usage= -"UChiPlus[opts] is the chi_plus-field of HBChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UChiMinus::usage= -"UChiMinus[opts] is the chi_minus-field of HBChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply"; - -Phi`Objects`UFMinus::usage= -"UFMinus[mu,nu] is the f_minus-field of HBChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UFPlus::usage= -"UFPlus[mu,nu] is the f_plus-field of HBChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -To evaluate use ArgumentsSupply."; - -Phi`Objects`UVTensor::usage= -"UVTensor[mu,nu] is the v-tensor of HBChPT -(G.Ecker and M. Mojzis (1995), hep-ph/9508204). -It uses the Vector[1]. -To evaluate use ArgumentsSupply."; - - -(* ************************************************************** *) - -(* Box definitions *) - -ClearAll[Vector,AxialVector]; - -Vector/:MakeBoxes[Vector[1],TraditionalForm]:= -SuperscriptBox[MakeBoxes[ -StyleForm["v",FontSlant->"Italic"]][[1]],"(s)"]; - -Vector/:MakeBoxes[Vector[_],TraditionalForm]:= -MakeBoxes[StyleForm["v",FontSlant->"Italic"]]; - -AxialVector/:MakeBoxes[AxialVector[_],TraditionalForm]:= -MakeBoxes[StyleForm["a",FontSlant->"Italic"]]; - -SetFAField/@{Vector,AxialVector}; - -VariableBoxes["J",ParticlesNumber->12]; - -(* ************************************************************** *) - -(* Attributes and data types *) - -DeclareNonCommutative[UVector, MM, SMM]; -UnDeclareNonCommutative[QuantumField, PartialD]; -DeclareNonCommutative[QuantumField[__][_]?(! FreeQ[#, _Fermion] &)]; - -(* ************************************************************** *) - - -(* Source fields *) - -(* The scalar source is set to the quark mass matrix *) - -QuantumField[Particle[ -Scalar[0],ar___RenormalizationState, -br___RenormalizationScheme,cr___ExpansionState, -opts___Rule|opts___List],SUNIndex[0]][x_]:= -ParticleMass[Pion,ar,br,cr,opts]^2/(2*QuarkCondensate[ar,br,cr,opts]); - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Antiparticles *) - -ChargeConjugate[Pion] = Pion; -ChargeConjugate[Vector[0]] = Vector[0]; -ChargeConjugate[AxialVector[0]] = AxialVector[0]; -ChargeConjugate[Scalar[0]] = Scalar[0]; -ChargeConjugate[Scalar[1]] = Scalar[1]; -ChargeConjugate[PseudoScalar[0]] = PseudoScalar[0]; -ChargeConjugate[PseudoScalar[1]] = PseudoScalar[1]; -ChargeConjugate[PionPlus] = PionMinus; -ChargeConjugate[PionMinus] = PionPlus; -ChargeConjugate[PionZero] = PionZero; -ChargeConjugate[KaonMinus] = KaonPlus; -ChargeConjugate[KaonPlus] = KaonMinus; -ChargeConjugate[KaonZero] = KaonZeroBar; -ChargeConjugate[KaonZeroBar] = KaonZero; -ChargeConjugate[EtaMeson] = EtaMeson; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -ParticleMass[Photon,___]:=0; -ParticleMass[Photon[0],___]:=0; - -(*CouplingConstant[ChPT2[4],1,___][___]=0; -CouplingConstant[ChPT2[4],2,___][___]=0; -CouplingConstant[ChPT2[4],3,___][___]=0; -CouplingConstant[ChPT2[4],4,___][___]=0; -CouplingConstant[ChPT2[4],5,___][___]=0; -CouplingConstant[ChPT2[4],6,___][___]=0;*) -CouplingConstant[ChPT2[4],7,___][___]=0; -(*CouplingConstant[ChPT2[4],8,___][___]=0;*) -CouplingConstant[ChPT2[4],9,___][___]=0; -CouplingConstant[ChPT2[4],10,___][___]=0; -CouplingConstant[ChPT2[4],11,___][___]=0; -CouplingConstant[ChPT2[4],12,___][___]=0; - -(* ************************************************************** *) - -(* Redefinition of the left and right components -G.Ecker and M. Mojzis have them the other way round *) - -IsoVector[QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___], -bb___],opts___][x_]/;(Explicit/.{opts0}/.Options[LeftComponent]):= -1/2*( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]- -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -IsoVector[QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___], -opts___][x_]/;(Explicit/.{opts0}/.Options[RightComponent]):=1/2*( -IsoVector[QuantumField[aa, Particle[Vector[a],i],bb],opts][x]+ -IsoVector[QuantumField[aa, Particle[AxialVector[a],i],bb],opts][x]); - -QuantumField[aa___, Particle[LeftComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[LeftComponent]):= -1/2*(QuantumField[aa, Particle[Vector[a],i],bb][x]- - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -QuantumField[aa___, Particle[RightComponent[a_,opts0___Rule],i___],bb___][x_]/; -(Explicit/.{opts0} /. Options[RightComponent]):= -1/2*(QuantumField[aa, Particle[Vector[a],i],bb][x]+ - QuantumField[aa, Particle[AxialVector[a],i],bb][x]); - -(* ************************************************************** *) - -(* The u_mu field *) - -(* We're overriding *) -$Substitutions = Select[$Substitutions, -(!MatchQ[#, (_?((! FreeQ[#, USmall, Heads -> True]) &)) :> _])&]; - - -$Substitutions = Append[$Substitutions, -USmall[mu_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -I*NM[Adjoint[SMM[x,ar,br,cr,opts]],FDr[SMM[x,ar,br,cr,opts],x,{mu}]]+ - -NM[Adjoint[SMM[x,ar,br,cr,opts]], -QuantumField[Particle[RightComponent[0],ar,br,cr],{mu}][x], -SMM[x,ar,br,cr,opts]]- - -I*NM[SMM,FDr[Adjoint[SMM[x,ar,br,cr,opts]],x,{mu}]]- - -NM[SMM[x,ar,br,cr,opts], -QuantumField[Particle[LeftComponent[0],ar,br,cr],{mu}][x], -Adjoint[SMM[x,ar,br,cr,opts]]]]; - - -$Substitutions = Append[$Substitutions, -USmall[mu_] :> - -I*NM[Adjoint[SMM],FDr[SMM,{mu}]]+ - -NM[Adjoint[SMM], -QuantumField[Particle[RightComponent[0]],{mu}],SMM]- - -I*NM[SMM,FDr[Adjoint[SMM],{mu}]]- - -NM[SMM, -QuantumField[Particle[LeftComponent[0]],{mu}],Adjoint[SMM]]]; - -(* ************************************************************** *) - -(* The Gamma_mu field *) - -(* We're overriding *) -$Substitutions = Select[$Substitutions, -(!MatchQ[#, (_?((! FreeQ[#, UGamma, Heads -> True]) &)) :> _])&]; - -$Substitutions = Append[$Substitutions, -UGamma[mu_, ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -1/2*( - -NM[Adjoint[SMM[x,ar,br,cr,opts]], -FDr[SMM[x,ar,br,cr,opts],x,{mu}]]- - -NM[FDr[SMM[x,ar,br,cr,opts],x,{mu}], -Adjoint[SMM[x,ar,br,cr,opts]]]- - -I*NM[Adjoint[SMM[x,ar,br,cr,opts]], -QuantumField[Particle[RightComponent[0], -ar,br,cr],{mu}][x], -SMM[x,ar,br,cr,opts]]- - -I*NM[SMM[x,ar,br,cr,opts], -QuantumField[Particle[LeftComponent[0], -ar,br,cr],{mu}][x], -Adjoint[SMM[x,ar,br,cr,opts]]] - -)]; - -$Substitutions = Append[$Substitutions, -UGamma[mu_] :> - -1/2*( - -NM[Adjoint[SMM],FDr[SMM,{mu}]]- - -I*NM[Adjoint[SMM], -QuantumField[Particle[RightComponent[0]],{mu}],SMM]+ - -NM[SMM,FDr[Adjoint[SMM],{mu}]]- - -I*NM[SMM, -QuantumField[Particle[LeftComponent[0]],{mu}],Adjoint[SMM]] - -)]; - - -(* ************************************************************** *) - -(* Redefinition of the field strength tensor: -I instead of I *) - -FST[p_,mu_LorentzIndex, - nu_LorentzIndex,x_, - a___RenormalizationState, - b___RenormalizationScheme,(opts___Rule|opts___List)]:= -FieldStrengthTensor[mu, -UGeneratorMatrixIsoDotFull[QuantumField[ -Particle[p,a,b],nu][x],opts],x]-2*I* - UGeneratorMatrixIsoDotFull[ - IsoCross[( - IsoVector[QuantumField[Particle[p,a,b],mu],##]&@@ - OptionsSelect[IsoVector,opts])[ - x],(IsoVector[QuantumField[Particle[p,a,b],nu],##]&@@ - OptionsSelect[IsoVector,opts])[x]],opts]; - -(* ************************************************************** *) - -(* The iso-singlet v field. -The field Vector[1] is used *) - -$Substitutions = Append[$Substitutions, -UVTensor[mu_,nu_, - a___RenormalizationState, - b___RenormalizationScheme,(opts___Rule|opts___List)][x_] :> -UIdentityMatrix[opts]* -FieldStrengthTensor[{mu}, -QuantumField[Particle[Vector[1],a,b],{nu}][x],opts]]; - -$Substitutions = Append[$Substitutions, -UVTensor[mu_,nu_] :> -UIdentityMatrix* -FieldStrengthTensor[{mu}, -QuantumField[Particle[Vector[1]],{nu}]]]; - -(* ************************************************************** *) - -(* The covariant derivative *) - -Options[CovariantFieldDerivative]= -{DiagonalToU->True, -SUNN->2,UDimension->Automatic, -ExpansionOrder->2,DropOrder->2}; - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -CovariantFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] := -( -ggu=(SUNN/.Options[UMatrix]); -ggi=(SUNN/.Options[IsoVector]); -ggg=(SUNN/.Options[CovariantFieldDerivative]); - -SetOptions[UMatrix,SUNN->ggg]; -SetOptions[IsoVector,SUNN->ggg]; - - -cfdr=NM[UIdentityMatrix[##]&@@OptionsSelect[UMatrix,opts], - FieldDerivative[aa,x,lori]]+ - -UDot[((UGamma[lori[[1]],Sequence@@Join[Flatten[{opts}], -Select[{DiagonalToU->True, -ExpansionOrder->2,DropOrder->2}, -FreeQ[Part[#,1]&/@Flatten[{opts}],#[[1]]]&]]][x])- - -I*(UIdentityMatrix[##]&@@OptionsSelect[UMatrix,opts])* - QuantumField[Particle[Vector[1]],lori][x]),aa]; - -SetOptions[UMatrix,SUNN->ggu]; -SetOptions[IsoVector,SUNN->ggi]; - -cfdr -); - -(* ************************************************************** *) -(* Modify the nucleon propagator to use renormalized masses -in the spinors *) - - -Phi`Couplings`GenProps[a:$FermionHeads]:={ -FeynArts`AnalyticalPropagator[ -FeynArts`External][ s a[i, mom] ] == -NonCommutative[ -(*Tag, so WFRenormalize can do its thing*) -Phi`Couplings`Private`propSpinor[ --mom, FeynArts`Mass[ a[i] ], -Sequence @@ Drop[{i},1], RenormalizationState[1] ] ], -FeynArts`AnalyticalPropagator[ -FeynArts`Internal][ s a[i,mom] ] == -NonCommutative[ -Phi`Couplings`Private`propGamma[ --mom, FeynArts`Mass[a[i]]] ]* -I*PropagatorDenominator[ mom , -FeynArts`Mass[a[i]] ]}; - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - -$ParticlesInUse={Pion,Nucleon,Vector[1],Vector[0],AxialVector[0]}; - -$ExpansionQuantities=Join[$ExpansionQuantities, -{CouplingConstant[HBChPT2[2],a___], DiracMatrix[_], -NonCommutative[DiracMatrix[_]..]}]; - -$PropagatorMassesStates={Pion[0]->{RenormalizationState[0]}, - Nucleon[0]->{RenormalizationState[0]}, - AxialVector[0][0]->{RenormalizationState[0]}, - Vector[0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = -{Pion[0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}, - Nucleon[0]->{{IsoRange->{1,2},IsoIndicesString->"J"}}, - AxialVector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"II"}}, -Vector[0][0]->{{IsoRange->{1,2,3},IsoIndicesString->"II"}}}; - -$MixingFields= -{}; - -$InsertOnly= -{(*Vector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, - AxialVector[0][0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}, -Photon[0]->{ -FeynArts`Incoming, -FeynArts`Outgoing, -FeynArts`External}*)}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/QED.conf b/FeynCalc/Phi/Configurations/QED.conf deleted file mode 100644 index 64c78a7f6..000000000 --- a/FeynCalc/Phi/Configurations/QED.conf +++ /dev/null @@ -1,135 +0,0 @@ -(* ************************************************************** *) -(* *) -(* QED *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the lagrangians - QED1 and QED2 for PHI - -Description: Definitions for the (electron) QED - lagrangians and the counterterm - lagrangian. - - The definitions follow - Bjoerken and Drell, - "Relativistic Quantum Fields", - McGraw-Hill 1965 and - S .Weinberg (1995), - "The Quantum Theory of Fields", - Cambridge University Press - (Adapted to the usual space- - time metric (1,-1,-1,-1)) -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* A new box definition for the photon - -to avoid confusion with the Dirac matrices *) - -ClearAll[Vector,Fermion]; - -Vector/:MakeBoxes[Vector[1],TraditionalForm]:= -MakeBoxes[StyleForm["A",FontSlant->"Italic"]][[1]]; - -Fermion/:MakeBoxes[Fermion[7],TraditionalForm]:= -MakeBoxes[StyleForm["\[Psi]"]][[1]]; - -SetFAField/@{Vector,Fermion}; - -(* ************************************************************** *) - -(* Superscripts *) - -$RenormalizationSuperscripts={"0",""}; -$RSSuperscripts={"",""}; -$ExpansionSuperscripts={"",""}; - -(* Uncomment below if you don't want the dimension space dimensions -of polarization vectors displayed *) - -(*SpaceDimensions/: Format[SpaceDimensions,TraditionalForm] :="";*) - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -(*ParticleMass[Photon,___]:=0;*) - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -CovariantFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] := - -FieldDerivative[aa,x,lori] + - -I*CouplingConstant[QED[1],RenormalizationState[0]]* -fcqf[Particle[Photon,ar,br],lori][x]*aa; - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - -$ParticlesInUse={Electron,Photon}; - -$PropagatorMassesStates={Electron[0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = - {}; - -$MixingFields= - {}; - -$InsertOnly= - {}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/Configurations/QED2.conf b/FeynCalc/Phi/Configurations/QED2.conf deleted file mode 100644 index a08edcd52..000000000 --- a/FeynCalc/Phi/Configurations/QED2.conf +++ /dev/null @@ -1,143 +0,0 @@ -(* ************************************************************** *) -(* *) -(* QED2 *) -(* *) -(* ************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Configuration file for the lagrangians - QED21 and QED22 for PHI - -Description: Definitions for the (three leptons) QED2 - lagrangians and the counterterm - lagrangian. - - The definitions follow - Bjoerken and Drell, - "Relativistic Quantum Fields", - McGraw-Hill 1965 and - S .Weinberg (1995), - "The Quantum Theory of Fields", - Cambridge University Press - (Adapted to the usual space- - time metric (1,-1,-1,-1)) -*) - -(* ************************************************************** *) - -(* Modified box definitions for FeynCalc *) - -<<"FCBoxes.m" - -(* ************************************************************** *) - -(* A new box definition for the photon - -to avoid confusion with the Dirac matrices *) - -ClearAll[Vector,Fermion]; - -Vector/:MakeBoxes[Vector[1],TraditionalForm]:= -MakeBoxes[StyleForm["A",FontSlant->"Italic"]][[1]]; - -Fermion/:MakeBoxes[Fermion[1],TraditionalForm]:= -MakeBoxes[StyleForm["\[Psi]"]][[1]]; - -SetFAField/@{Vector,Fermion}; - -(* ************************************************************** *) - -(* Superscripts *) - -$RenormalizationSuperscripts={"0",""}; -$RSSuperscripts={"",""}; -$ExpansionSuperscripts={"",""}; - -(* Uncomment below if you don't want the dimension space dimensions -of polarization vectors displayed *) - -(*SpaceDimensions/: Format[SpaceDimensions,TraditionalForm] :="";*) - -(* ************************************************************** *) - -(* Labels for Feynman diagrams *) - -FeynArts`TheLabel[Vector1]:="A"; -FALabel[Photon,0]:="A"; -FALabel[Photon[0],_]:="A"; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Adjoint[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Unprotect[Conjugate]; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___][_]] = p; - -Conjugate[p:QuantumField[___,Particle[ -(Vector|AxialVector|Scalar|PseudoScalar)[0|1|2],___],___]] = p; - -Protect[Conjugate]; - -(* ************************************************************** *) - -(* Constants *) - -(* When calculating infrared divergences, the photon mass -should not be set to zero *) - -(*ParticleMass[Photon,___]:=0;*) - -(* ************************************************************** *) - -(* The covariant derivative *) - -CovariantFieldDerivative[aa_,x_,{loris__},rest___] := -CovariantFieldDerivative[aa,x,##,rest]&@@ -LorentzIndex/@{loris}; - -(* -------------------------------------------------------------- *) - -CovariantFieldDerivative[aa_,x_, -lori_LorentzIndex, -ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)] := - -FieldDerivative[aa,x,lori] + - -I*CouplingConstant[QED[1],RenormalizationState[0]]* -fcqf[Particle[Photon,ar,br],lori][x]*aa; - -(* ************************************************************** *) - -(* Re-setting of options and $-variables *) - -$ParticlesInUse={Lepton,Photon}; - -$PropagatorMassesStates={Lepton[0]->{RenormalizationState[0]}, - Photon[0]->{RenormalizationState[0]}}; - -$CouplingIsoIndicesSpecifications = - {Lepton[0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}}}; - -$MixingFields= - {}; - -$InsertOnly= - {}; - -(* ************************************************************** *) diff --git a/FeynCalc/Phi/CouplingVectors/BChPT2F200F200P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/BChPT2F200F200P20P20o2.Gen deleted file mode 100644 index 30aeb0be5..000000000 --- a/FeynCalc/Phi/CouplingVectors/BChPT2F200F200P20P20o2.Gen +++ /dev/null @@ -1,4 +0,0 @@ -{((4*I)*MomentaScalarProduct[p1, p3]*MomentaScalarProduct[p1, p4])/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2 + -((4*I)*MomentaScalarProduct[p2, p3]*MomentaScalarProduct[p2, p4])/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/BChPT2F200F200P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/BChPT2F200F200P20P20o2.Mod deleted file mode 100644 index 55721e199..000000000 --- a/FeynCalc/Phi/CouplingVectors/BChPT2F200F200P20P20o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{SUNDelta[I3, I4]*SUNDelta[J1, J2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2A00P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2A00P20P20P20o2.Gen deleted file mode 100644 index 13bb2f0ef..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2A00P20P20P20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1], FourVector[p3, \[Mu]1], FourVector[p4, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2A00P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2A00P20P20P20o2.Mod deleted file mode 100644 index a2152524e..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2A00P20P20P20o2.Mod +++ /dev/null @@ -1,15 +0,0 @@ -{{(5*SUNDelta[I1, I4]*SUNDelta[I2, I3] + 5*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 10*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - 3*SUNF[I1, I4, k1]*SUNF[I2, I3, k1] - 3*SUNF[I1, I3, k1]* - SUNF[I2, I4, k1])/(12*DecayConstant[PseudoScalar[2], - RenormalizationState[0]])}, -{(5*SUNDelta[I1, I4]*SUNDelta[I2, I3] - 10*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 5*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 3*SUNF[I1, I4, k1]*SUNF[I2, I3, k1] - 3*SUNF[I1, I2, k1]* - SUNF[I3, I4, k1])/(12*DecayConstant[PseudoScalar[2], - RenormalizationState[0]])}, -{(-10*SUNDelta[I1, I4]*SUNDelta[I2, I3] + 5*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 5*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 3*SUNF[I1, I3, k1]*SUNF[I2, I4, k1] + 3*SUNF[I1, I2, k1]* - SUNF[I3, I4, k1])/(12*DecayConstant[PseudoScalar[2], - RenormalizationState[0]])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20P20P20o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20P20P20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20P20P20o2.Mod deleted file mode 100644 index 76db45855..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20P20P20o2.Mod +++ /dev/null @@ -1,3 +0,0 @@ -{{(((-2*I)/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I3]*SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o2.Gen deleted file mode 100644 index 7611e11db..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{0} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o2.Mod deleted file mode 100644 index d8f234e31..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{0}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o4.Gen deleted file mode 100644 index 03bcc9279..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o4.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o4.Mod deleted file mode 100644 index ed879704f..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20S20o4.Mod +++ /dev/null @@ -1,7 +0,0 @@ -{{((64*I)*(2*CouplingConstant[ChPT2[4], 6, RenormalizationState[0]]* - SUNDelta[0, I3]*SUNDelta[I1, I2] + CouplingConstant[ChPT2[4], 8, - RenormalizationState[0]]*SUNDelta[0, I3]*SUNDelta[I1, I2] + - 2*CouplingConstant[ChPT2[4], 7, RenormalizationState[0]]*SUNDelta[0, I1]* - SUNDelta[I2, I3] + CouplingConstant[ChPT2[4], 8, - RenormalizationState[0]]*SUNDelta[0, I1]*SUNDelta[I2, I3]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o2.Mod deleted file mode 100644 index 47ae25561..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{(2*I)*DecayConstant[PseudoScalar[2], RenormalizationState[0]]* -SUNDelta[I1, I2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o4.Gen deleted file mode 100644 index d27dfa082..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o4.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o4.Mod deleted file mode 100644 index c83a699fb..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P00P20o4.Mod +++ /dev/null @@ -1,4 +0,0 @@ -{{((32*I)*(2*CouplingConstant[ChPT2[4], 6, RenormalizationState[0]] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[0]])* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20P20P20o2.Gen deleted file mode 100644 index 642672e37..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20P20P20o2.Gen +++ /dev/null @@ -1,9 +0,0 @@ -{MomentaScalarProduct[p5, p6], MomentaScalarProduct[p1, p2], -MomentaScalarProduct[p3, p4], ParticleMass[PseudoScalar[2], -RenormalizationState[0]]^2, MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p2, p4], MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p4, p6], -MomentaScalarProduct[p3, p5], MomentaScalarProduct[p2, p5], -MomentaScalarProduct[p1, p5], MomentaScalarProduct[p4, p5], -MomentaScalarProduct[p3, p6], MomentaScalarProduct[p2, p6], -MomentaScalarProduct[p1, p6]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20P20P20o2.Mod deleted file mode 100644 index 73231b8c7..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20P20P20o2.Mod +++ /dev/null @@ -1,256 +0,0 @@ -{{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{((-I/15)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20S20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20S20o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20S20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20S20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20S20o2.Mod deleted file mode 100644 index 36fcfb715..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20S20o2.Mod +++ /dev/null @@ -1,3 +0,0 @@ -{{(((2*I)/3)*SUNDelta[0, I5]*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I3]*SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o2.Gen deleted file mode 100644 index cf506a630..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o2.Gen +++ /dev/null @@ -1,4 +0,0 @@ -{MomentaScalarProduct[p1, p2], MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p1, p3], MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p2, p3], -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o2.Mod deleted file mode 100644 index 68a0110dc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o2.Mod +++ /dev/null @@ -1,21 +0,0 @@ -{{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((I/3)*(2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - SUNDelta[I1, I3]* - SUNDelta[I2, I4] - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((I/3)*(2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - SUNDelta[I1, I3]* - SUNDelta[I2, I4] - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o4.Gen deleted file mode 100644 index d1cb02b3a..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o4.Gen +++ /dev/null @@ -1,13 +0,0 @@ -{MomentaScalarProduct[p1, p4]*MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p3]*MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p1, p4]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p3]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p4]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p3, p4]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o4.Mod deleted file mode 100644 index 1b3779e56..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20P20P20o4.Mod +++ /dev/null @@ -1,105 +0,0 @@ -{{((16*I)*(2*CouplingConstant[ChPT2[4], 1, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 3, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + CouplingConstant[ChPT2[4], 2, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 2, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{((16*I)*(CouplingConstant[ChPT2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 2*CouplingConstant[ChPT2[4], 1, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 3, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + CouplingConstant[ChPT2[4], 2, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{((16*I)*(CouplingConstant[ChPT2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 2, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 2*CouplingConstant[ChPT2[4], 1, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT2[4], 3, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((8*I)/3)*(10*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((8*I)/3)*(10*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((-8*I)/3)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] - 10*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((-8*I)/3)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] - 10*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((-8*I)/3)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + 2*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 10*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-8*I)/3)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + 2*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 10*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((64*I)/3)*(2*CouplingConstant[ChPT2[4], 6, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + 2*CouplingConstant[ChPT2[4], 6, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 2*CouplingConstant[ChPT2[4], 6, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o2.Mod deleted file mode 100644 index 18c2df5ac..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{(-2*I)*SUNDelta[0, I3]*SUNDelta[I1, I2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o4.Gen deleted file mode 100644 index ec5f92201..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o4.Gen +++ /dev/null @@ -1,3 +0,0 @@ -{MomentaScalarProduct[p1, p2]*QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o4.Mod deleted file mode 100644 index 4c08e3605..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT2P20P20S20o4.Mod +++ /dev/null @@ -1,8 +0,0 @@ -{{((-16*I)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[0, I3]*SUNDelta[I1, I2] + CouplingConstant[ChPT2[4], 5, - RenormalizationState[0]]*SUNDelta[0, I3]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-64*I)*(2*CouplingConstant[ChPT2[4], 6, RenormalizationState[0]]* - SUNDelta[0, I3]*SUNDelta[I1, I2] + CouplingConstant[ChPT2[4], 8, - RenormalizationState[0]]*SUNDelta[0, I3]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10P10P10o2.Gen deleted file mode 100644 index fe318ccec..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10P10P10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{FourVector[p6, \[Mu]1], FourVector[p5, \[Mu]1], FourVector[p2, \[Mu]1], -FourVector[p4, \[Mu]1], FourVector[p3, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10P10P10o2.Mod deleted file mode 100644 index 504c299bd..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10P10P10o2.Mod +++ /dev/null @@ -1,4679 +0,0 @@ -{{(108*SUND[I1, I5, I6]*SUND[I2, I3, I4] + 108*SUND[I1, I4, I6]* - SUND[I2, I3, I5] - 72*SUND[I1, I4, I5]*SUND[I2, I3, I6] + - 108*SUND[I1, I3, I6]*SUND[I2, I4, I5] - 72*SUND[I1, I3, I5]* - SUND[I2, I4, I6] - 72*SUND[I1, I3, I4]*SUND[I2, I5, I6] + - 108*SUND[I1, I2, I6]*SUND[I3, I4, I5] - 72*SUND[I1, I2, I5]* - SUND[I3, I4, I6] - 72*SUND[I1, I2, I4]*SUND[I3, I5, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUND[I3, i4, I6]*SUND[i4, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I6]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I6]*SUND[I3, I5, i8]*SUND[i4, I4, i6] - - 18*SUND[I1, i4, I6]*SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUND[i4, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, I6]*SUND[I3, i6, i8]*SUND[i4, I4, i6] - - 18*SUND[I1, i4, I6]*SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, I5, i8]*SUND[i4, I4, I6] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUND[i4, I4, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[i4, I4, I6] + - 72*SUND[I1, i4, i6]*SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUND[i4, I4, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUND[I3, i4, I6]*SUND[i4, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I6]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I6]*SUND[I3, I4, i8]*SUND[i4, I5, i6] - - 18*SUND[I1, i4, I6]*SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUND[i4, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, I6]*SUND[I3, i6, i8]*SUND[i4, I5, i6] - - 18*SUND[I1, i4, I6]*SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUND[i4, I4, I6]*SUND[i4, I5, i6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I4, I6]*SUND[i4, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUND[i4, I4, I6]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUND[I3, i4, i6]*SUND[i4, I5, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[i4, I5, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, I4, i8]*SUND[i4, I5, I6] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUND[i4, I5, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[i4, I5, I6] + - 72*SUND[I1, i4, i6]*SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUND[i4, I5, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUND[i4, I4, i6]*SUND[i4, I5, I6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I4, i6]*SUND[i4, I5, I6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUND[i4, I4, i6]*SUND[i4, I5, I6] - - 72*SUND[I1, I2, I3]*SUND[I4, I5, I6] - 108*SUND[I1, i6, i8]* - SUND[I2, i4, I6]*SUND[I3, i4, i6]*SUND[I4, I5, i8] - - 18*SUND[I1, i4, I6]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[I4, I5, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I6]*SUND[I4, I5, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, i4, I6]*SUND[I4, I5, i8] - - 18*SUND[I1, i4, I6]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[I4, I5, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I6]*SUND[I3, i6, i8]*SUND[I4, I5, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, I6]*SUND[I3, i4, i6]*SUND[I4, i6, i8] - - 18*SUND[I1, i4, I6]*SUND[I2, I5, i8]*SUND[I3, i4, i6]*SUND[I4, i6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I6]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I5, i8]*SUND[I3, i4, I6]*SUND[I4, i6, i8] - - 18*SUND[I1, i4, I6]*SUND[I2, i4, i6]*SUND[I3, I5, i8]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I6]*SUND[I3, I5, i8]*SUND[I4, i6, i8] - - 18*SUND[I1, i4, I6]*SUND[I2, I3, i8]*SUND[i4, I5, i6]*SUND[I4, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I6]*SUND[i4, I5, i6]*SUND[I4, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I6]*SUND[i4, I5, i6]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i8]*SUND[i4, I5, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[i4, I5, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, i6]*SUND[i4, I5, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, I6]*SUND[I3, i4, i6]*SUND[I5, i6, i8] - - 18*SUND[I1, i4, I6]*SUND[I2, I4, i8]*SUND[I3, i4, i6]*SUND[I5, i6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I6]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I4, i8]*SUND[I3, i4, I6]*SUND[I5, i6, i8] - - 18*SUND[I1, i4, I6]*SUND[I2, i4, i6]*SUND[I3, I4, i8]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I6]*SUND[I3, I4, i8]*SUND[I5, i6, i8] - - 18*SUND[I1, i4, I6]*SUND[I2, I3, i8]*SUND[i4, I4, i6]*SUND[I5, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I6]*SUND[i4, I4, i6]*SUND[I5, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I6]*SUND[i4, I4, i6]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i8]*SUND[i4, I4, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[i4, I4, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I6]*SUND[I5, i6, i8] + - 36*SUND[I3, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I2] + - 36*SUND[I3, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I2] + - 36*SUND[I3, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I2] + - 36*SUND[I2, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I3] + - 36*SUND[I2, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I3] + - 36*SUND[I2, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I3] + - 36*SUND[I2, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I1, I4] + - 36*SUND[I2, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I1, I4] + - 36*SUND[I2, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I4] + - 36*SUND[I2, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I1, I5] + - 36*SUND[I2, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I1, I5] + - 36*SUND[I2, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I1, I5] - - 48*SUND[I2, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I1, I6] - - 48*SUND[I2, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I1, I6] - - 48*SUND[I2, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I1, I6] - - 24*SUND[I1, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I2, I3] - - 24*SUND[I1, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I2, I3] - - 24*SUND[I1, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I3] - - 24*SUND[I1, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I2, I4] - - 24*SUND[I1, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I2, I4] - - 24*SUND[I1, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I4] - - 24*SUND[I1, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I2, I5] - - 24*SUND[I1, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I2, I5] - - 24*SUND[I1, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I2, I5] + - 12*SUND[I1, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I2, I6] + - 12*SUND[I1, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I2, I6] + - 12*SUND[I1, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I2, I6] - - 24*SUND[I1, i5, I6]*SUND[I2, i5, I5]*SUNDelta[I3, I4] - - 24*SUND[I1, i5, I5]*SUND[I2, i5, I6]*SUNDelta[I3, I4] - - 24*SUND[I1, I2, i5]*SUND[i5, I5, I6]*SUNDelta[I3, I4] - - 32*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 24*SUND[I1, i5, I6]*SUND[I2, I4, i5]*SUNDelta[I3, I5] - - 24*SUND[I1, I4, i5]*SUND[I2, i5, I6]*SUNDelta[I3, I5] - - 24*SUND[I1, I2, i5]*SUND[I4, i5, I6]*SUNDelta[I3, I5] - - 32*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - 12*SUND[I1, i5, I5]*SUND[I2, I4, i5]*SUNDelta[I3, I6] + - 12*SUND[I1, I4, i5]*SUND[I2, i5, I5]*SUNDelta[I3, I6] + - 12*SUND[I1, I2, i5]*SUND[I4, i5, I5]*SUNDelta[I3, I6] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 24*SUND[I1, i5, I6]*SUND[I2, I3, i5]*SUNDelta[I4, I5] - - 24*SUND[I1, I3, i5]*SUND[I2, i5, I6]*SUNDelta[I4, I5] - - 24*SUND[I1, I2, i5]*SUND[I3, i5, I6]*SUNDelta[I4, I5] - - 32*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - 12*SUND[I1, i5, I5]*SUND[I2, I3, i5]*SUNDelta[I4, I6] + - 12*SUND[I1, I3, i5]*SUND[I2, i5, I5]*SUNDelta[I4, I6] + - 12*SUND[I1, I2, i5]*SUND[I3, i5, I5]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - 12*SUND[I1, I4, i5]*SUND[I2, I3, i5]*SUNDelta[I5, I6] + - 12*SUND[I1, I3, i5]*SUND[I2, I4, i5]*SUNDelta[I5, I6] + - 12*SUND[I1, I2, i5]*SUND[I3, I4, i5]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6] + - (45*I)*SUND[i1, I5, i8]*SUND[I3, i6, i8]*SUND[I4, i6, I6]* - SUNF[i1, I1, I2] + (45*I)*SUND[i1, I5, i8]*SUND[I3, i6, I6]* - SUND[I4, i6, i8]*SUNF[i1, I1, I2] + (45*I)*SUND[i1, I4, i8]* - SUND[I3, i6, i8]*SUND[I5, i6, I6]*SUNF[i1, I1, I2] + - (45*I)*SUND[i1, I3, i8]*SUND[I4, i6, i8]*SUND[I5, i6, I6]* - SUNF[i1, I1, I2] + (45*I)*SUND[i1, I4, i8]*SUND[I3, i6, I6]* - SUND[I5, i6, i8]*SUNF[i1, I1, I2] + (45*I)*SUND[i1, I3, i8]* - SUND[I4, i6, I6]*SUND[I5, i6, i8]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I5, I6]*SUNDelta[I3, I4]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I4, I6]*SUNDelta[I3, I5]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I4, I5]*SUNDelta[I3, I6]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I3, I6]*SUNDelta[I4, I5]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I3, I5]*SUNDelta[I4, I6]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I3, I4]*SUNDelta[I5, I6]*SUNF[i1, I1, I2] + - (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, i8]*SUND[I4, i6, I6]* - SUNF[i1, I1, I3] + (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, I6]* - SUND[I4, i6, i8]*SUNF[i1, I1, I3] + (45*I)*SUND[i1, I4, i8]* - SUND[I2, i6, i8]*SUND[I5, i6, I6]*SUNF[i1, I1, I3] + - (45*I)*SUND[i1, I2, i8]*SUND[I4, i6, i8]*SUND[I5, i6, I6]* - SUNF[i1, I1, I3] + (45*I)*SUND[i1, I4, i8]*SUND[I2, i6, I6]* - SUND[I5, i6, i8]*SUNF[i1, I1, I3] + (45*I)*SUND[i1, I2, i8]* - SUND[I4, i6, I6]*SUND[I5, i6, i8]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I5, I6]*SUNDelta[I2, I4]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I4, I6]*SUNDelta[I2, I5]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I4, I5]*SUNDelta[I2, I6]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I2, I6]*SUNDelta[I4, I5]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I2, I5]*SUNDelta[I4, I6]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I2, I4]*SUNDelta[I5, I6]*SUNF[i1, I1, I3] + - (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, i6, I6]* - SUNF[i1, I1, I4] + (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, I6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I4] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, i6, i8]*SUND[I5, i6, I6]*SUNF[i1, I1, I4] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, i6, i8]*SUND[I5, i6, I6]* - SUNF[i1, I1, I4] + (45*I)*SUND[i1, I3, i8]*SUND[I2, i6, I6]* - SUND[I5, i6, i8]*SUNF[i1, I1, I4] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, i6, I6]*SUND[I5, i6, i8]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I5, I6]*SUNDelta[I2, I3]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I3, I6]*SUNDelta[I2, I5]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I3, I5]*SUNDelta[I2, I6]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I2, I6]*SUNDelta[I3, I5]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I2, I5]*SUNDelta[I3, I6]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I2, I3]*SUNDelta[I5, I6]*SUNF[i1, I1, I4] + - (45*I)*SUND[i1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i6, I6]* - SUNF[i1, I1, I5] + (45*I)*SUND[i1, I4, i8]*SUND[I2, i6, I6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I5] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, i6, i8]*SUND[I4, i6, I6]*SUNF[i1, I1, I5] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, i6, i8]*SUND[I4, i6, I6]* - SUNF[i1, I1, I5] + (45*I)*SUND[i1, I3, i8]*SUND[I2, i6, I6]* - SUND[I4, i6, i8]*SUNF[i1, I1, I5] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, i6, I6]*SUND[I4, i6, i8]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I4, I6]*SUNDelta[I2, I3]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I3, I6]*SUNDelta[I2, I4]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I3, I4]*SUNDelta[I2, I6]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I2, I6]*SUNDelta[I3, I4]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I2, I4]*SUNDelta[I3, I6]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I2, I3]*SUNDelta[I4, I6]*SUNF[i1, I1, I5] + - (72*I)*SUND[i1, I5, I6]*SUND[I2, i6, i8]*SUND[I3, I4, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I4, I6]*SUND[I2, i6, i8]* - SUND[I3, I5, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I5, I6]* - SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I4, I6]*SUND[I2, I5, i8]*SUND[I3, i6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I6]*SUND[I2, i6, i8]* - SUND[I4, I5, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I6]* - SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I5, I6]*SUND[I2, I3, i8]*SUND[I4, i6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I6]*SUND[I2, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I6]* - SUND[I3, I5, i8]*SUND[I4, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I4, I6]*SUND[I2, I3, i8]*SUND[I5, i6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I6]*SUND[I2, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I6]* - SUND[I3, I4, i8]*SUND[I5, i6, i8]*SUNF[i1, I1, i6] - - (108*I)*SUND[i1, I5, i6]*SUND[I2, i6, I6]*SUND[I3, I4, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I4, i6]*SUND[I2, i6, I6]* - SUND[I3, I5, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]* - SUND[I2, I4, i8]*SUND[I3, i6, I6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I4, i6]*SUND[I2, I5, i8]*SUND[I3, i6, I6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]*SUND[I2, i6, I6]* - SUND[I4, I5, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I2, i6]* - SUND[I3, i6, I6]*SUND[I4, I5, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I5, i6]*SUND[I2, I3, i8]*SUND[I4, i6, I6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]*SUND[I2, I5, i8]* - SUND[I4, i6, I6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I2, i6]* - SUND[I3, I5, i8]*SUND[I4, i6, I6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I4, i6]*SUND[I2, I3, i8]*SUND[I5, i6, I6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]*SUND[I2, I4, i8]* - SUND[I5, i6, I6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I2, i6]* - SUND[I3, I4, i8]*SUND[I5, i6, I6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I5, I6]*SUND[I1, i6, i8]*SUND[I3, I4, i8]* - SUNF[i1, I2, i6] - (108*I)*SUND[i1, I4, I6]*SUND[I1, i6, i8]* - SUND[I3, I5, i8]*SUNF[i1, I2, i6] + (27*I)*SUND[i1, I5, I6]* - SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUNF[i1, I2, i6] + - (27*I)*SUND[i1, I4, I6]*SUND[I1, I5, i8]*SUND[I3, i6, i8]* - SUNF[i1, I2, i6] - (108*I)*SUND[i1, I3, I6]*SUND[I1, i6, i8]* - SUND[I4, I5, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[i1, I2, i6] + - (27*I)*SUND[i1, I5, I6]*SUND[I1, I3, i8]*SUND[I4, i6, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I6]*SUND[I1, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I3, I5, i8]*SUND[I4, i6, i8]*SUNF[i1, I2, i6] + - (27*I)*SUND[i1, I4, I6]*SUND[I1, I3, i8]*SUND[I5, i6, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I6]*SUND[I1, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I3, I4, i8]*SUND[I5, i6, i8]*SUNF[i1, I2, i6] - - (18*I)*SUND[i1, I5, i6]*SUND[I1, i6, I6]*SUND[I3, I4, i8]* - SUNF[i1, I2, i8] - (18*I)*SUND[i1, I4, i6]*SUND[I1, i6, I6]* - SUND[I3, I5, i8]*SUNF[i1, I2, i8] + (27*I)*SUND[i1, I5, i6]* - SUND[I1, I4, i8]*SUND[I3, i6, I6]*SUNF[i1, I2, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I5, i8]*SUND[I3, i6, I6]* - SUNF[i1, I2, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, i6, I6]* - SUND[I4, I5, i8]*SUNF[i1, I2, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I3, i6, I6]*SUND[I4, I5, i8]*SUNF[i1, I2, i8] + - (27*I)*SUND[i1, I5, i6]*SUND[I1, I3, i8]*SUND[I4, i6, I6]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, I3, i6]*SUND[I1, I5, i8]* - SUND[I4, i6, I6]*SUNF[i1, I2, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I3, I5, i8]*SUND[I4, i6, I6]*SUNF[i1, I2, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I3, i8]*SUND[I5, i6, I6]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, I3, i6]*SUND[I1, I4, i8]* - SUND[I5, i6, I6]*SUNF[i1, I2, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I3, I4, i8]*SUND[I5, i6, I6]*SUNF[i1, I2, i8] - - (108*I)*SUND[i1, I5, I6]*SUND[I1, i6, i8]*SUND[I2, I4, i8]* - SUNF[i1, I3, i6] - (108*I)*SUND[i1, I4, I6]*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUNF[i1, I3, i6] + (27*I)*SUND[i1, I5, I6]* - SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUNF[i1, I3, i6] + - (27*I)*SUND[i1, I4, I6]*SUND[I1, I5, i8]*SUND[I2, i6, i8]* - SUNF[i1, I3, i6] - (108*I)*SUND[i1, I2, I6]*SUND[I1, i6, i8]* - SUND[I4, I5, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, i6, i8]*SUND[I4, I5, i8]*SUNF[i1, I3, i6] + - (27*I)*SUND[i1, I5, I6]*SUND[I1, I2, i8]*SUND[I4, i6, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, I5, i8]*SUND[I4, i6, i8]*SUNF[i1, I3, i6] + - (27*I)*SUND[i1, I4, I6]*SUND[I1, I2, i8]*SUND[I5, i6, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, I4, i8]*SUND[I5, i6, i8]*SUNF[i1, I3, i6] - - (18*I)*SUND[i1, I5, i6]*SUND[I1, i6, I6]*SUND[I2, I4, i8]* - SUNF[i1, I3, i8] - (18*I)*SUND[i1, I4, i6]*SUND[I1, i6, I6]* - SUND[I2, I5, i8]*SUNF[i1, I3, i8] + (27*I)*SUND[i1, I5, i6]* - SUND[I1, I4, i8]*SUND[I2, i6, I6]*SUNF[i1, I3, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I5, i8]*SUND[I2, i6, I6]* - SUNF[i1, I3, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, i6, I6]* - SUND[I4, I5, i8]*SUNF[i1, I3, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, i6, I6]*SUND[I4, I5, i8]*SUNF[i1, I3, i8] + - (27*I)*SUND[i1, I5, i6]*SUND[I1, I2, i8]*SUND[I4, i6, I6]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I5, i8]* - SUND[I4, i6, I6]*SUNF[i1, I3, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I5, i8]*SUND[I4, i6, I6]*SUNF[i1, I3, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I2, i8]*SUND[I5, i6, I6]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I4, i8]* - SUND[I5, i6, I6]*SUNF[i1, I3, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I4, i8]*SUND[I5, i6, I6]*SUNF[i1, I3, i8] - - (108*I)*SUND[i1, I5, I6]*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUNF[i1, I4, i6] - (108*I)*SUND[i1, I3, I6]*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUNF[i1, I4, i6] + (27*I)*SUND[i1, I5, I6]* - SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i1, I4, i6] + - (27*I)*SUND[i1, I3, I6]*SUND[I1, I5, i8]*SUND[I2, i6, i8]* - SUNF[i1, I4, i6] - (108*I)*SUND[i1, I2, I6]*SUND[I1, i6, i8]* - SUND[I3, I5, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUNF[i1, I4, i6] + - (27*I)*SUND[i1, I5, I6]*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I5, i8]* - SUND[I3, i6, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUNF[i1, I4, i6] + - (27*I)*SUND[i1, I3, I6]*SUND[I1, I2, i8]*SUND[I5, i6, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I3, i8]* - SUND[I5, i6, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, I3, i8]*SUND[I5, i6, i8]*SUNF[i1, I4, i6] - - (18*I)*SUND[i1, I5, i6]*SUND[I1, i6, I6]*SUND[I2, I3, i8]* - SUNF[i1, I4, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, i6, I6]* - SUND[I2, I5, i8]*SUNF[i1, I4, i8] + (27*I)*SUND[i1, I5, i6]* - SUND[I1, I3, i8]*SUND[I2, i6, I6]*SUNF[i1, I4, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I5, i8]*SUND[I2, i6, I6]* - SUNF[i1, I4, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, i6, I6]* - SUND[I3, I5, i8]*SUNF[i1, I4, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, i6, I6]*SUND[I3, I5, i8]*SUNF[i1, I4, i8] + - (27*I)*SUND[i1, I5, i6]*SUND[I1, I2, i8]*SUND[I3, i6, I6]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I5, i8]* - SUND[I3, i6, I6]*SUNF[i1, I4, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I5, i8]*SUND[I3, i6, I6]*SUNF[i1, I4, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I2, i8]*SUND[I5, i6, I6]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I3, i8]* - SUND[I5, i6, I6]*SUNF[i1, I4, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i8]*SUND[I5, i6, I6]*SUNF[i1, I4, i8] - - (108*I)*SUND[i1, I4, I6]*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUNF[i1, I5, i6] - (108*I)*SUND[i1, I3, I6]*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUNF[i1, I5, i6] + (27*I)*SUND[i1, I4, I6]* - SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i1, I5, i6] + - (27*I)*SUND[i1, I3, I6]*SUND[I1, I4, i8]*SUND[I2, i6, i8]* - SUNF[i1, I5, i6] - (108*I)*SUND[i1, I2, I6]*SUND[I1, i6, i8]* - SUND[I3, I4, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUNF[i1, I5, i6] + - (27*I)*SUND[i1, I4, I6]*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I4, i8]* - SUND[I3, i6, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUNF[i1, I5, i6] + - (27*I)*SUND[i1, I3, I6]*SUND[I1, I2, i8]*SUND[I4, i6, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I3, i8]* - SUND[I4, i6, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I6]* - SUND[I2, I3, i8]*SUND[I4, i6, i8]*SUNF[i1, I5, i6] - - (18*I)*SUND[i1, I4, i6]*SUND[I1, i6, I6]*SUND[I2, I3, i8]* - SUNF[i1, I5, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, i6, I6]* - SUND[I2, I4, i8]*SUNF[i1, I5, i8] + (27*I)*SUND[i1, I4, i6]* - SUND[I1, I3, i8]*SUND[I2, i6, I6]*SUNF[i1, I5, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I4, i8]*SUND[I2, i6, I6]* - SUNF[i1, I5, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, i6, I6]* - SUND[I3, I4, i8]*SUNF[i1, I5, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, i6, I6]*SUND[I3, I4, i8]*SUNF[i1, I5, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I2, i8]*SUND[I3, i6, I6]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I4, i8]* - SUND[I3, i6, I6]*SUNF[i1, I5, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I4, i8]*SUND[I3, i6, I6]*SUNF[i1, I5, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I2, i8]*SUND[I4, i6, I6]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I3, i8]* - SUND[I4, i6, I6]*SUNF[i1, I5, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i8]*SUND[I4, i6, I6]*SUNF[i1, I5, i8] - - 45*SUND[i1, I5, I6]*SUND[i3, I4, i8]*SUNF[i1, I3, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I4, I6]*SUND[i3, I5, i8]*SUNF[i1, I3, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I5, I6]*SUND[i3, I3, i8]*SUNF[i1, I4, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I6]*SUND[i3, I5, i8]*SUNF[i1, I4, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I4, I6]*SUND[i3, I3, i8]*SUNF[i1, I5, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I6]*SUND[i3, I4, i8]*SUNF[i1, I5, i8]*SUNF[I1, I2, i3] + - (120*I)*SUND[I4, i5, I5]*SUNDelta[I3, I6]*SUNF[I1, I2, i5] + - (120*I)*SUND[I3, i5, I5]*SUNDelta[I4, I6]*SUNF[I1, I2, i5] + - (120*I)*SUND[I3, I4, i5]*SUNDelta[I5, I6]*SUNF[I1, I2, i5] - - 45*SUND[i1, I5, i8]*SUND[I4, I6, i8]*SUNF[i1, I3, i5]*SUNF[I1, I2, i5] - - 45*SUND[i1, I4, i8]*SUND[I5, I6, i8]*SUNF[i1, I3, i5]*SUNF[I1, I2, i5] - - 45*SUND[i1, I5, i8]*SUND[I3, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, I2, i5] - - 45*SUND[i1, I3, i8]*SUND[I5, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, I2, i5] + - 45*SUND[i1, I4, i8]*SUND[I3, I6, i8]*SUNF[i1, i5, I5]*SUNF[I1, I2, i5] + - 45*SUND[i1, I3, i8]*SUND[I4, I6, i8]*SUNF[i1, i5, I5]*SUNF[I1, I2, i5] - - (180*I)*SUND[I3, I4, I5]*SUNF[I1, I2, I6] + 45*SUND[i1, I5, I6]* - SUND[i3, I4, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I4, I6]*SUND[i3, I5, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I5, I6]*SUND[I2, i3, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I6]*SUND[i3, I5, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I4, I6]*SUND[I2, i3, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I6]*SUND[i3, I4, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I5, I6]*SUND[i3, I3, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I3, I6]*SUND[i3, I5, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I5, I6]*SUND[I2, i3, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I6]*SUND[i3, I5, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I3, I6]*SUND[I2, i3, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I6]*SUND[i3, I3, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I4, I6]*SUND[i3, I3, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I3, I6]*SUND[i3, I4, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I4, I6]*SUND[I2, i3, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I2, I6]*SUND[i3, I4, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I3, I6]*SUND[I2, i3, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I2, I6]*SUND[i3, I3, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I5] - - 108*SUND[i1, I5, I6]*SUND[I3, I4, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] - - 108*SUND[i1, I4, I6]*SUND[I3, I5, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] - - 108*SUND[i1, I3, I6]*SUND[I4, I5, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I5, I6]*SUND[I2, I4, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I4, I6]*SUND[I2, I5, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I6]*SUND[I4, I5, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I5, I6]*SUND[I2, I3, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I6]*SUND[I2, I5, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I6]*SUND[I3, I5, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I4, I6]*SUND[I2, I3, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I6]*SUND[I2, I4, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I6]*SUND[I3, I4, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - (120*I)*SUND[I4, i5, I5]*SUNDelta[I2, I6]*SUNF[I1, I3, i5] + - (120*I)*SUND[I2, i5, I5]*SUNDelta[I4, I6]*SUNF[I1, I3, i5] + - (120*I)*SUND[I2, I4, i5]*SUNDelta[I5, I6]*SUNF[I1, I3, i5] - - 45*SUND[i1, I5, i8]*SUND[I4, I6, i8]*SUNF[i1, I2, i5]*SUNF[I1, I3, i5] - - 45*SUND[i1, I4, i8]*SUND[I5, I6, i8]*SUNF[i1, I2, i5]*SUNF[I1, I3, i5] - - 45*SUND[i1, I5, i8]*SUND[I2, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, I3, i5] - - 45*SUND[i1, I2, i8]*SUND[I5, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, I3, i5] + - 45*SUND[i1, I4, i8]*SUND[I2, I6, i8]*SUNF[i1, i5, I5]*SUNF[I1, I3, i5] + - 45*SUND[i1, I2, i8]*SUND[I4, I6, i8]*SUNF[i1, i5, I5]*SUNF[I1, I3, i5] - - (180*I)*SUND[I2, I4, I5]*SUNF[I1, I3, I6] - (18*I)*SUND[I2, i6, i8]* - SUND[I3, I5, i8]*SUND[i4, I4, i6]*SUNF[I1, i4, I6] - - (18*I)*SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUND[i4, I4, i6]* - SUNF[I1, i4, I6] - (18*I)*SUND[I2, i6, i8]*SUND[I3, I4, i8]* - SUND[i4, I5, i6]*SUNF[I1, i4, I6] - (18*I)*SUND[I2, I4, i8]* - SUND[I3, i6, i8]*SUND[i4, I5, i6]*SUNF[I1, i4, I6] - - (18*I)*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[I4, I5, i8]* - SUNF[I1, i4, I6] - (18*I)*SUND[I2, i4, i6]*SUND[I3, i6, i8]* - SUND[I4, I5, i8]*SUNF[I1, i4, I6] - (18*I)*SUND[I2, I5, i8]* - SUND[I3, i4, i6]*SUND[I4, i6, i8]*SUNF[I1, i4, I6] - - (18*I)*SUND[I2, i4, i6]*SUND[I3, I5, i8]*SUND[I4, i6, i8]* - SUNF[I1, i4, I6] - (18*I)*SUND[I2, I3, i8]*SUND[i4, I5, i6]* - SUND[I4, i6, i8]*SUNF[I1, i4, I6] - (18*I)*SUND[I2, I4, i8]* - SUND[I3, i4, i6]*SUND[I5, i6, i8]*SUNF[I1, i4, I6] - - (18*I)*SUND[I2, i4, i6]*SUND[I3, I4, i8]*SUND[I5, i6, i8]* - SUNF[I1, i4, I6] - (18*I)*SUND[I2, I3, i8]*SUND[i4, I4, i6]* - SUND[I5, i6, i8]*SUNF[I1, i4, I6] + (120*I)*SUND[I3, i5, I5]* - SUNDelta[I2, I6]*SUNF[I1, I4, i5] + (120*I)*SUND[I2, i5, I5]* - SUNDelta[I3, I6]*SUNF[I1, I4, i5] + (120*I)*SUND[I2, I3, i5]* - SUNDelta[I5, I6]*SUNF[I1, I4, i5] - 45*SUND[i1, I5, i8]*SUND[I3, I6, i8]* - SUNF[i1, I2, i5]*SUNF[I1, I4, i5] - 45*SUND[i1, I3, i8]*SUND[I5, I6, i8]* - SUNF[i1, I2, i5]*SUNF[I1, I4, i5] - 45*SUND[i1, I5, i8]*SUND[I2, I6, i8]* - SUNF[i1, I3, i5]*SUNF[I1, I4, i5] - 45*SUND[i1, I2, i8]*SUND[I5, I6, i8]* - SUNF[i1, I3, i5]*SUNF[I1, I4, i5] + 45*SUND[i1, I3, i8]*SUND[I2, I6, i8]* - SUNF[i1, i5, I5]*SUNF[I1, I4, i5] + 45*SUND[i1, I2, i8]*SUND[I3, I6, i8]* - SUNF[i1, i5, I5]*SUNF[I1, I4, i5] - (180*I)*SUND[I2, I3, I5]* - SUNF[I1, I4, I6] - (120*I)*SUND[I3, I4, i5]*SUNDelta[I2, I6]* - SUNF[I1, i5, I5] - (120*I)*SUND[I2, I4, i5]*SUNDelta[I3, I6]* - SUNF[I1, i5, I5] - (120*I)*SUND[I2, I3, i5]*SUNDelta[I4, I6]* - SUNF[I1, i5, I5] + 45*SUND[i1, I4, i8]*SUND[I3, I6, i8]*SUNF[i1, I2, i5]* - SUNF[I1, i5, I5] + 45*SUND[i1, I3, i8]*SUND[I4, I6, i8]*SUNF[i1, I2, i5]* - SUNF[I1, i5, I5] + 45*SUND[i1, I4, i8]*SUND[I2, I6, i8]*SUNF[i1, I3, i5]* - SUNF[I1, i5, I5] + 45*SUND[i1, I2, i8]*SUND[I4, I6, i8]*SUNF[i1, I3, i5]* - SUNF[I1, i5, I5] + 45*SUND[i1, I3, i8]*SUND[I2, I6, i8]*SUNF[i1, I4, i5]* - SUNF[I1, i5, I5] + 45*SUND[i1, I2, i8]*SUND[I3, I6, i8]*SUNF[i1, I4, i5]* - SUNF[I1, i5, I5] - (24*I)*SUND[I4, i5, I5]*SUNDelta[I2, I3]* - SUNF[I1, i5, I6] - (24*I)*SUND[I3, i5, I5]*SUNDelta[I2, I4]* - SUNF[I1, i5, I6] - (24*I)*SUND[I3, I4, i5]*SUNDelta[I2, I5]* - SUNF[I1, i5, I6] - (24*I)*SUND[I2, i5, I5]*SUNDelta[I3, I4]* - SUNF[I1, i5, I6] - (24*I)*SUND[I2, I4, i5]*SUNDelta[I3, I5]* - SUNF[I1, i5, I6] - (24*I)*SUND[I2, I3, i5]*SUNDelta[I4, I5]* - SUNF[I1, i5, I6] - (180*I)*SUND[I2, I3, I4]*SUNF[I1, I5, I6] - - 18*SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[I1, i3, I6]*SUNF[I2, i3, i6] - - 18*SUND[I3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, i3, i6] - - 18*SUND[I3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, i3, i6] + - 72*SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I6] + - 72*SUND[I3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I6] + - 72*SUND[I3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I6] + - 72*SUND[i1, I5, I6]*SUND[I3, I4, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] + - 72*SUND[i1, I4, I6]*SUND[I3, I5, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] + - 72*SUND[i1, I3, I6]*SUND[I4, I5, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I5, I6]*SUND[I1, I4, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I4, I6]*SUND[I1, I5, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I6]*SUND[I4, I5, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I5, I6]*SUND[I1, I3, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I6]*SUND[I1, I5, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I6]*SUND[I3, I5, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] - - 27*SUND[i1, I4, I6]*SUND[I1, I3, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I6]*SUND[I1, I4, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I6]*SUND[I3, I4, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] - - 18*SUND[i3, I5, i6]*SUND[I3, I4, i8]*SUNF[I1, i6, I6]*SUNF[I2, i3, i8] - - 18*SUND[i3, I4, i6]*SUND[I3, I5, i8]*SUNF[I1, i6, I6]*SUNF[I2, i3, i8] - - 18*SUND[i3, I3, i6]*SUND[I4, I5, i8]*SUNF[I1, i6, I6]*SUNF[I2, i3, i8] - - (108*I)*SUND[I1, i6, i8]*SUND[I3, I5, i8]*SUND[i4, I4, i6]* - SUNF[I2, i4, I6] + (27*I)*SUND[I1, I5, i8]*SUND[I3, i6, i8]* - SUND[i4, I4, i6]*SUNF[I2, i4, I6] - (108*I)*SUND[I1, i6, i8]* - SUND[I3, I4, i8]*SUND[i4, I5, i6]*SUNF[I2, i4, I6] + - (27*I)*SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUND[i4, I5, i6]* - SUNF[I2, i4, I6] - (108*I)*SUND[I1, i6, i8]*SUND[I3, i4, i6]* - SUND[I4, I5, i8]*SUNF[I2, i4, I6] + (72*I)*SUND[I1, i4, i6]* - SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[I2, i4, I6] + - (27*I)*SUND[I1, I5, i8]*SUND[I3, i4, i6]*SUND[I4, i6, i8]* - SUNF[I2, i4, I6] + (72*I)*SUND[I1, i4, i6]*SUND[I3, I5, i8]* - SUND[I4, i6, i8]*SUNF[I2, i4, I6] + (27*I)*SUND[I1, I3, i8]* - SUND[i4, I5, i6]*SUND[I4, i6, i8]*SUNF[I2, i4, I6] + - (27*I)*SUND[I1, I4, i8]*SUND[I3, i4, i6]*SUND[I5, i6, i8]* - SUNF[I2, i4, I6] + (72*I)*SUND[I1, i4, i6]*SUND[I3, I4, i8]* - SUND[I5, i6, i8]*SUNF[I2, i4, I6] + (27*I)*SUND[I1, I3, i8]* - SUND[i4, I4, i6]*SUND[I5, i6, i8]*SUNF[I2, i4, I6] + - (36*I)*SUND[I4, i5, I5]*SUNDelta[I1, I3]*SUNF[I2, i5, I6] + - (36*I)*SUND[I3, i5, I5]*SUNDelta[I1, I4]*SUNF[I2, i5, I6] + - (36*I)*SUND[I3, I4, i5]*SUNDelta[I1, I5]*SUNF[I2, i5, I6] - - (24*I)*SUND[I1, i5, I5]*SUNDelta[I3, I4]*SUNF[I2, i5, I6] - - (24*I)*SUND[I1, I4, i5]*SUNDelta[I3, I5]*SUNF[I2, i5, I6] - - (24*I)*SUND[I1, I3, i5]*SUNDelta[I4, I5]*SUNF[I2, i5, I6] + - 45*SUND[i3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i6, I6] + - 45*SUND[i3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i6, I6] + - 45*SUND[i3, I5, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i6, I6] + - 45*SUND[i3, I3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i6, I6] + - 45*SUND[i3, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i6, I6] + - 45*SUND[i3, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i6, I6] - - 108*SUND[i3, I5, i6]*SUND[I3, I4, i8]*SUNF[I1, i3, i8]*SUNF[I2, i6, I6] - - 108*SUND[i3, I4, i6]*SUND[I3, I5, i8]*SUNF[I1, i3, i8]*SUNF[I2, i6, I6] - - 108*SUND[i3, I3, i6]*SUND[I4, I5, i8]*SUNF[I1, i3, i8]*SUNF[I2, i6, I6] - - 120*SUNDelta[I4, I5]*SUNF[I1, I3, i6]*SUNF[I2, i6, I6] - - 120*SUNDelta[I3, I5]*SUNF[I1, I4, i6]*SUNF[I2, i6, I6] - - 120*SUNDelta[I3, I4]*SUNF[I1, I5, i6]*SUNF[I2, i6, I6] - - (45*I)*SUND[i1, I5, I6]*SUNF[i1, I4, i9]*SUNF[I1, I3, i8]* - SUNF[I2, i8, i9] - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I5, i9]* - SUNF[I1, I3, i8]*SUNF[I2, i8, i9] - (45*I)*SUND[i1, I5, I6]* - SUNF[i1, I3, i9]*SUNF[I1, I4, i8]*SUNF[I2, i8, i9] - - (45*I)*SUND[i1, I3, I6]*SUNF[i1, I5, i9]*SUNF[I1, I4, i8]* - SUNF[I2, i8, i9] - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I3, i9]* - SUNF[I1, I5, i8]*SUNF[I2, i8, i9] - (45*I)*SUND[i1, I3, I6]* - SUNF[i1, I4, i9]*SUNF[I1, I5, i8]*SUNF[I2, i8, i9] - - (108*I)*SUND[I4, I5, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, I6]* - SUNF[i3, I3, i5] - (18*I)*SUND[I4, I5, i8]*SUNF[I1, i3, I6]* - SUNF[I2, i5, i8]*SUNF[i3, I3, i5] + 18*SUND[I2, i6, i8]*SUND[I4, I5, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I3, i6] + 18*SUND[I2, I5, i8]*SUND[I4, i6, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I3, i6] + 18*SUND[I2, I4, i8]*SUND[I5, i6, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I3, i6] + 108*SUND[I1, i6, i8]* - SUND[I4, I5, i8]*SUNF[I2, i3, I6]*SUNF[i3, I3, i6] - - 27*SUND[I1, I5, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I3, i6] - - 27*SUND[I1, I4, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I3, i6] - - 72*SUND[I2, i6, i8]*SUND[I4, I5, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I6] - - 72*SUND[I2, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I6] - - 72*SUND[I2, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I6] - - (108*I)*SUND[I4, I5, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I6] + 108*SUND[I1, i6, i8]*SUND[I4, I5, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I6] - 27*SUND[I1, I5, i8]*SUND[I4, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I6] - 27*SUND[I1, I4, i8]*SUND[I5, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I6] - (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I4, i5]*SUNF[I2, i3, i8]*SUNF[i3, I3, I6] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I5]*SUNF[I2, i3, i8]* - SUNF[i3, I3, I6] + (72*I)*SUND[I4, I5, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I6] - 72*SUND[i1, I5, I6]*SUND[I2, I4, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - 72*SUND[i1, I4, I6]*SUND[I2, I5, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - 72*SUND[i1, I2, I6]*SUND[I4, I5, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - 27*SUND[i1, I5, I6]*SUND[I1, I4, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I3, i8] - 27*SUND[i1, I4, I6]*SUND[I1, I5, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I3, i8] + 18*SUND[i1, I1, I6]*SUND[I4, I5, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I3, i8] + 27*SUND[i1, I5, I6]*SUND[I1, I2, i8]* - SUNF[i1, i3, I4]*SUNF[i3, I3, i8] + 27*SUND[i1, I2, I6]*SUND[I1, I5, i8]* - SUNF[i1, i3, I4]*SUNF[i3, I3, i8] - 18*SUND[i1, I1, I6]*SUND[I2, I5, i8]* - SUNF[i1, i3, I4]*SUNF[i3, I3, i8] + 27*SUND[i1, I4, I6]*SUND[I1, I2, i8]* - SUNF[i1, i3, I5]*SUNF[i3, I3, i8] + 27*SUND[i1, I2, I6]*SUND[I1, I4, i8]* - SUNF[i1, i3, I5]*SUNF[i3, I3, i8] - 18*SUND[i1, I1, I6]*SUND[I2, I4, i8]* - SUNF[i1, i3, I5]*SUNF[i3, I3, i8] + 18*SUND[I2, I5, i8]*SUND[i3, I4, i6]* - SUNF[I1, i6, I6]*SUNF[i3, I3, i8] + 18*SUND[I2, I4, i8]*SUND[i3, I5, i6]* - SUNF[I1, i6, I6]*SUNF[i3, I3, i8] + 18*SUND[I2, i3, i6]*SUND[I4, I5, i8]* - SUNF[I1, i6, I6]*SUNF[i3, I3, i8] - (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I4, i5]*SUNF[I2, i3, I6]*SUNF[i3, I3, i8] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I5]*SUNF[I2, i3, I6]* - SUNF[i3, I3, i8] - 27*SUND[I1, I5, i8]*SUND[i3, I4, i6]*SUNF[I2, i6, I6]* - SUNF[i3, I3, i8] - 27*SUND[I1, I4, i8]*SUND[i3, I5, i6]*SUNF[I2, i6, I6]* - SUNF[i3, I3, i8] - 72*SUND[I1, i3, i6]*SUND[I4, I5, i8]*SUNF[I2, i6, I6]* - SUNF[i3, I3, i8] - (108*I)*SUND[I3, I5, i8]*SUNF[I1, i5, i8]* - SUNF[I2, i3, I6]*SUNF[i3, I4, i5] - (18*I)*SUND[I3, I5, i8]* - SUNF[I1, i3, I6]*SUNF[I2, i5, i8]*SUNF[i3, I4, i5] + - (108*I)*SUND[I2, I5, i8]*SUNF[I1, i5, i8]*SUNF[i3, I3, I6]* - SUNF[i3, I4, i5] - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I3, I6]*SUNF[i3, I4, i5] + 18*SUND[I2, i6, i8]*SUND[I3, I5, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I4, i6] + 18*SUND[I2, I5, i8]*SUND[I3, i6, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I4, i6] + 18*SUND[I2, I3, i8]*SUND[I5, i6, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I4, i6] + 108*SUND[I1, i6, i8]* - SUND[I3, I5, i8]*SUNF[I2, i3, I6]*SUNF[i3, I4, i6] - - 27*SUND[I1, I5, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I4, i6] - - 27*SUND[I1, I3, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUNF[i3, I3, I6]*SUNF[i3, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I6]*SUNF[i3, I4, i6] + - 27*SUND[I1, I2, i8]*SUND[I5, i6, i8]*SUNF[i3, I3, I6]*SUNF[i3, I4, i6] - - 72*SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUNF[I1, i3, i6]*SUNF[i3, I4, I6] - - 72*SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I4, I6] - - 72*SUND[I2, I3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I4, I6] - - (108*I)*SUND[I3, I5, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I4, I6] + 108*SUND[I1, i6, i8]*SUND[I3, I5, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I4, I6] - 27*SUND[I1, I5, i8]*SUND[I3, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I4, I6] - 27*SUND[I1, I3, i8]*SUND[I5, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I4, I6] - (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I3, i5]*SUNF[I2, i3, i8]*SUNF[i3, I4, I6] + - (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I5]*SUNF[I2, i3, i8]* - SUNF[i3, I4, I6] + (72*I)*SUND[I3, I5, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i5, i8]*SUNF[i3, I4, I6] + (108*I)*SUND[I2, I5, i8]* - SUNF[I1, i5, i8]*SUNF[i3, I3, i5]*SUNF[i3, I4, I6] - - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i5, i8]*SUNF[i3, I3, i5]* - SUNF[i3, I4, I6] - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I4, I6] + 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I4, I6] + 27*SUND[I1, I2, i8]*SUND[I5, i6, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I4, I6] + (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, i8]*SUNF[i3, I4, I6] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I5]*SUNF[i3, I3, i8]* - SUNF[i3, I4, I6] - 72*SUND[i1, I5, I6]*SUND[I2, I3, i8]*SUNF[i1, I1, i3]* - SUNF[i3, I4, i8] - 72*SUND[i1, I3, I6]*SUND[I2, I5, i8]*SUNF[i1, I1, i3]* - SUNF[i3, I4, i8] - 72*SUND[i1, I2, I6]*SUND[I3, I5, i8]*SUNF[i1, I1, i3]* - SUNF[i3, I4, i8] - 27*SUND[i1, I5, I6]*SUND[I1, I3, i8]*SUNF[i1, I2, i3]* - SUNF[i3, I4, i8] - 27*SUND[i1, I3, I6]*SUND[I1, I5, i8]*SUNF[i1, I2, i3]* - SUNF[i3, I4, i8] + 18*SUND[i1, I1, I6]*SUND[I3, I5, i8]*SUNF[i1, I2, i3]* - SUNF[i3, I4, i8] + 27*SUND[i1, I5, I6]*SUND[I1, I2, i8]*SUNF[i1, i3, I3]* - SUNF[i3, I4, i8] + 27*SUND[i1, I2, I6]*SUND[I1, I5, i8]*SUNF[i1, i3, I3]* - SUNF[i3, I4, i8] - 18*SUND[i1, I1, I6]*SUND[I2, I5, i8]*SUNF[i1, i3, I3]* - SUNF[i3, I4, i8] + 27*SUND[i1, I3, I6]*SUND[I1, I2, i8]*SUNF[i1, i3, I5]* - SUNF[i3, I4, i8] + 27*SUND[i1, I2, I6]*SUND[I1, I3, i8]*SUNF[i1, i3, I5]* - SUNF[i3, I4, i8] - 18*SUND[i1, I1, I6]*SUND[I2, I3, i8]*SUNF[i1, i3, I5]* - SUNF[i3, I4, i8] + 18*SUND[I2, I5, i8]*SUND[i3, I3, i6]*SUNF[I1, i6, I6]* - SUNF[i3, I4, i8] + 18*SUND[I2, I3, i8]*SUND[i3, I5, i6]*SUNF[I1, i6, I6]* - SUNF[i3, I4, i8] + 18*SUND[I2, i3, i6]*SUND[I3, I5, i8]*SUNF[I1, i6, I6]* - SUNF[i3, I4, i8] - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I3, i5]* - SUNF[I2, i3, I6]*SUNF[i3, I4, i8] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, i5, I5]*SUNF[I2, i3, I6]*SUNF[i3, I4, i8] - - 27*SUND[I1, I5, i8]*SUND[i3, I3, i6]*SUNF[I2, i6, I6]*SUNF[i3, I4, i8] - - 27*SUND[I1, I3, i8]*SUND[i3, I5, i6]*SUNF[I2, i6, I6]*SUNF[i3, I4, i8] - - 72*SUND[I1, i3, i6]*SUND[I3, I5, i8]*SUNF[I2, i6, I6]*SUNF[i3, I4, i8] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I2, i5]*SUNF[i3, I3, I6]* - SUNF[i3, I4, i8] - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I5]* - SUNF[i3, I3, I6]*SUNF[i3, I4, i8] + (108*I)*SUND[I3, I4, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I6]*SUNF[i3, i5, I5] + - (18*I)*SUND[I3, I4, i8]*SUNF[I1, i3, I6]*SUNF[I2, i5, i8]* - SUNF[i3, i5, I5] - (108*I)*SUND[I2, I4, i8]*SUNF[I1, i5, i8]* - SUNF[i3, I3, I6]*SUNF[i3, i5, I5] + (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I6]*SUNF[i3, i5, I5] - - (108*I)*SUND[I2, I3, i8]*SUNF[I1, i5, i8]*SUNF[i3, I4, I6]* - SUNF[i3, i5, I5] + (27*I)*SUND[I1, I3, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I4, I6]*SUNF[i3, i5, I5] + 18*SUND[I2, i6, i8]*SUND[I3, I4, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I5, i6] + 18*SUND[I2, I4, i8]*SUND[I3, i6, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I5, i6] + 18*SUND[I2, I3, i8]*SUND[I4, i6, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I5, i6] + 108*SUND[I1, i6, i8]* - SUND[I3, I4, i8]*SUNF[I2, i3, I6]*SUNF[i3, I5, i6] - - 27*SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I5, i6] - - 27*SUND[I1, I3, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUNF[i3, I3, I6]*SUNF[i3, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I6]*SUNF[i3, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[I4, i6, i8]*SUNF[i3, I3, I6]*SUNF[i3, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUNF[i3, I4, I6]*SUNF[i3, I5, i6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i3, I4, I6]*SUNF[i3, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUNF[i3, I4, I6]*SUNF[i3, I5, i6] - - 72*SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUNF[I1, i3, i6]*SUNF[i3, I5, I6] - - 72*SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I5, I6] - - 72*SUND[I2, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I5, I6] - - (108*I)*SUND[I3, I4, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I5, I6] + 108*SUND[I1, i6, i8]*SUND[I3, I4, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I5, I6] - 27*SUND[I1, I4, i8]*SUND[I3, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I5, I6] - 27*SUND[I1, I3, i8]*SUND[I4, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I5, I6] - (45*I)*SUND[I4, i5, i8]* - SUNF[I1, I3, i5]*SUNF[I2, i3, i8]*SUNF[i3, I5, I6] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, i8]* - SUNF[i3, I5, I6] + (72*I)*SUND[I3, I4, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i5, i8]*SUNF[i3, I5, I6] + (108*I)*SUND[I2, I4, i8]* - SUNF[I1, i5, i8]*SUNF[i3, I3, i5]*SUNF[i3, I5, I6] - - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i5, i8]*SUNF[i3, I3, i5]* - SUNF[i3, I5, I6] - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I5, I6] + 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I5, I6] + 27*SUND[I1, I2, i8]*SUND[I4, i6, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I5, I6] + (45*I)*SUND[I4, i5, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, i8]*SUNF[i3, I5, I6] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i5]*SUNF[i3, I3, i8]* - SUNF[i3, I5, I6] + (108*I)*SUND[I2, I3, i8]*SUNF[I1, i5, i8]* - SUNF[i3, I4, i5]*SUNF[i3, I5, I6] - (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i5, i8]*SUNF[i3, I4, i5]*SUNF[i3, I5, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUNF[i3, I4, i6]*SUNF[i3, I5, I6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i3, I4, i6]*SUNF[i3, I5, I6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUNF[i3, I4, i6]*SUNF[i3, I5, I6] + - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I2, i5]*SUNF[i3, I4, i8]* - SUNF[i3, I5, I6] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, I3, i5]* - SUNF[i3, I4, i8]*SUNF[i3, I5, I6] - 72*SUND[i1, I4, I6]*SUND[I2, I3, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - 72*SUND[i1, I3, I6]*SUND[I2, I4, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - 72*SUND[i1, I2, I6]*SUND[I3, I4, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - 27*SUND[i1, I4, I6]*SUND[I1, I3, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I5, i8] - 27*SUND[i1, I3, I6]*SUND[I1, I4, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I5, i8] + 18*SUND[i1, I1, I6]*SUND[I3, I4, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I5, i8] + 27*SUND[i1, I4, I6]*SUND[I1, I2, i8]* - SUNF[i1, i3, I3]*SUNF[i3, I5, i8] + 27*SUND[i1, I2, I6]*SUND[I1, I4, i8]* - SUNF[i1, i3, I3]*SUNF[i3, I5, i8] - 18*SUND[i1, I1, I6]*SUND[I2, I4, i8]* - SUNF[i1, i3, I3]*SUNF[i3, I5, i8] + 27*SUND[i1, I3, I6]*SUND[I1, I2, i8]* - SUNF[i1, i3, I4]*SUNF[i3, I5, i8] + 27*SUND[i1, I2, I6]*SUND[I1, I3, i8]* - SUNF[i1, i3, I4]*SUNF[i3, I5, i8] - 18*SUND[i1, I1, I6]*SUND[I2, I3, i8]* - SUNF[i1, i3, I4]*SUNF[i3, I5, i8] + 18*SUND[I2, I4, i8]*SUND[i3, I3, i6]* - SUNF[I1, i6, I6]*SUNF[i3, I5, i8] + 18*SUND[I2, I3, i8]*SUND[i3, I4, i6]* - SUNF[I1, i6, I6]*SUNF[i3, I5, i8] + 18*SUND[I2, i3, i6]*SUND[I3, I4, i8]* - SUNF[I1, i6, I6]*SUNF[i3, I5, i8] - (45*I)*SUND[I4, i5, i8]* - SUNF[I1, I3, i5]*SUNF[I2, i3, I6]*SUNF[i3, I5, i8] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, I6]* - SUNF[i3, I5, i8] - 27*SUND[I1, I4, i8]*SUND[i3, I3, i6]*SUNF[I2, i6, I6]* - SUNF[i3, I5, i8] - 27*SUND[I1, I3, i8]*SUND[i3, I4, i6]*SUNF[I2, i6, I6]* - SUNF[i3, I5, i8] - 72*SUND[I1, i3, i6]*SUND[I3, I4, i8]*SUNF[I2, i6, I6]* - SUNF[i3, I5, i8] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, I2, i5]* - SUNF[i3, I3, I6]*SUNF[i3, I5, i8] + (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I4, i5]*SUNF[i3, I3, I6]*SUNF[i3, I5, i8] + - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I2, i5]*SUNF[i3, I4, I6]* - SUNF[i3, I5, i8] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, I3, i5]* - SUNF[i3, I4, I6]*SUNF[i3, I5, i8] - (108*I)*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUND[i4, I4, i6]*SUNF[I3, i4, I6] + - (27*I)*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[i4, I4, i6]* - SUNF[I3, i4, I6] - (108*I)*SUND[I1, i6, i8]*SUND[I2, I4, i8]* - SUND[i4, I5, i6]*SUNF[I3, i4, I6] + (27*I)*SUND[I1, I4, i8]* - SUND[I2, i6, i8]*SUND[i4, I5, i6]*SUNF[I3, i4, I6] - - (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I4, I5, i8]* - SUNF[I3, i4, I6] + (72*I)*SUND[I1, i4, i6]*SUND[I2, i6, i8]* - SUND[I4, I5, i8]*SUNF[I3, i4, I6] + (27*I)*SUND[I1, I5, i8]* - SUND[I2, i4, i6]*SUND[I4, i6, i8]*SUNF[I3, i4, I6] + - (72*I)*SUND[I1, i4, i6]*SUND[I2, I5, i8]*SUND[I4, i6, i8]* - SUNF[I3, i4, I6] + (27*I)*SUND[I1, I2, i8]*SUND[i4, I5, i6]* - SUND[I4, i6, i8]*SUNF[I3, i4, I6] + (27*I)*SUND[I1, I4, i8]* - SUND[I2, i4, i6]*SUND[I5, i6, i8]*SUNF[I3, i4, I6] + - (72*I)*SUND[I1, i4, i6]*SUND[I2, I4, i8]*SUND[I5, i6, i8]* - SUNF[I3, i4, I6] + (27*I)*SUND[I1, I2, i8]*SUND[i4, I4, i6]* - SUND[I5, i6, i8]*SUNF[I3, i4, I6] + (36*I)*SUND[I4, i5, I5]* - SUNDelta[I1, I2]*SUNF[I3, i5, I6] + (36*I)*SUND[I2, i5, I5]* - SUNDelta[I1, I4]*SUNF[I3, i5, I6] + (36*I)*SUND[I2, I4, i5]* - SUNDelta[I1, I5]*SUNF[I3, i5, I6] - (24*I)*SUND[I1, i5, I5]* - SUNDelta[I2, I4]*SUNF[I3, i5, I6] - (24*I)*SUND[I1, I4, i5]* - SUNDelta[I2, I5]*SUNF[I3, i5, I6] - (24*I)*SUND[I1, I2, i5]* - SUNDelta[I4, I5]*SUNF[I3, i5, I6] - (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I4, i7]*SUNF[I2, I6, i8]*SUNF[I3, i5, i7] - - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I5, i7]*SUNF[I2, I6, i8]* - SUNF[I3, i5, i7] + (18*I)*SUND[I4, I5, i8]*SUNF[I1, i3, I6]* - SUNF[I2, i3, i5]*SUNF[I3, i5, i8] - (72*I)*SUND[I4, I5, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I6]*SUNF[I3, i5, i8] - - (18*I)*SUND[I2, I5, i8]*SUNF[I1, i3, I6]*SUNF[i3, I4, i5]* - SUNF[I3, i5, i8] + (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I6]* - SUNF[i3, I4, i5]*SUNF[I3, i5, i8] + (72*I)*SUND[I2, I5, i8]* - SUNF[I1, i3, i5]*SUNF[i3, I4, I6]*SUNF[I3, i5, i8] + - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, i5]*SUNF[i3, I4, I6]* - SUNF[I3, i5, i8] + (18*I)*SUND[I2, I4, i8]*SUNF[I1, i3, I6]* - SUNF[i3, i5, I5]*SUNF[I3, i5, i8] - (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i3, I6]*SUNF[i3, i5, I5]*SUNF[I3, i5, i8] + - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I4, I6]*SUNF[i3, i5, I5]* - SUNF[I3, i5, i8] + (72*I)*SUND[I2, I4, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I5, I6]*SUNF[I3, i5, i8] + (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I5, I6]*SUNF[I3, i5, i8] - - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I4, i5]*SUNF[i3, I5, I6]* - SUNF[I3, i5, i8] - 45*SUND[i3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I3, i6, I6] - 45*SUND[i3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I3, i6, I6] - 120*SUNDelta[I4, I5]*SUNF[I1, I2, i6]* - SUNF[I3, i6, I6] + 45*SUND[I2, i6, i8]*SUND[i3, I5, i8]*SUNF[I1, i3, I4]* - SUNF[I3, i6, I6] + 45*SUND[I2, i3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I4]* - SUNF[I3, i6, I6] + 45*SUND[I2, i6, i8]*SUND[i3, I4, i8]*SUNF[I1, i3, I5]* - SUNF[I3, i6, I6] + 45*SUND[I2, i3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I5]* - SUNF[I3, i6, I6] - 108*SUND[I2, I5, i8]*SUND[i3, I4, i6]* - SUNF[I1, i3, i8]*SUNF[I3, i6, I6] - 108*SUND[I2, I4, i8]* - SUND[i3, I5, i6]*SUNF[I1, i3, i8]*SUNF[I3, i6, I6] - - 108*SUND[I2, i3, i6]*SUND[I4, I5, i8]*SUNF[I1, i3, i8]*SUNF[I3, i6, I6] - - 120*SUNDelta[I2, I5]*SUNF[I1, I4, i6]*SUNF[I3, i6, I6] - - 120*SUNDelta[I2, I4]*SUNF[I1, I5, i6]*SUNF[I3, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[i3, I4, i6]*SUNF[I2, i3, i8]*SUNF[I3, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[i3, I5, i6]*SUNF[I2, i3, i8]*SUNF[I3, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I4, I5, i8]*SUNF[I2, i3, i8]*SUNF[I3, i6, I6] - - 27*SUND[I1, I5, i8]*SUND[I2, i3, i6]*SUNF[i3, I4, i8]*SUNF[I3, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I2, I5, i8]*SUNF[i3, I4, i8]*SUNF[I3, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[i3, I5, i6]*SUNF[i3, I4, i8]*SUNF[I3, i6, I6] - - 27*SUND[I1, I4, i8]*SUND[I2, i3, i6]*SUNF[i3, I5, i8]*SUNF[I3, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I2, I4, i8]*SUNF[i3, I5, i8]*SUNF[I3, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[i3, I4, i6]*SUNF[i3, I5, i8]*SUNF[I3, i6, I6] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I4, i7]*SUNF[I2, i5, i7]* - SUNF[I3, I6, i8] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I5, i7]* - SUNF[I2, i5, i7]*SUNF[I3, I6, i8] - (45*I)*SUND[i1, I5, I6]* - SUNF[i1, I4, i9]*SUNF[I1, I2, i8]*SUNF[I3, i8, i9] - - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I5, i9]*SUNF[I1, I2, i8]* - SUNF[I3, i8, i9] - (45*I)*SUND[i1, I5, I6]*SUNF[i1, I2, i9]* - SUNF[I1, I4, i8]*SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I6]* - SUNF[i1, I5, i9]*SUNF[I1, I4, i8]*SUNF[I3, i8, i9] - - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I2, i9]*SUNF[I1, I5, i8]* - SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I6]*SUNF[i1, I4, i9]* - SUNF[I1, I5, i8]*SUNF[I3, i8, i9] + (108*I)*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUND[I3, i4, i6]*SUNF[i4, I4, I6] - - (27*I)*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]* - SUNF[i4, I4, I6] + (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]* - SUND[I3, I5, i8]*SUNF[i4, I4, I6] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUNF[i4, I4, I6] - - (27*I)*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]* - SUNF[i4, I4, I6] - (72*I)*SUND[I1, i4, i6]*SUND[I2, I5, i8]* - SUND[I3, i6, i8]*SUNF[i4, I4, I6] + (108*I)*SUND[I1, i6, i8]* - SUND[I2, I3, i8]*SUND[i4, I5, i6]*SUNF[i4, I4, I6] - - (27*I)*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I5, i6]* - SUNF[i4, I4, I6] - (27*I)*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUND[i4, I5, i6]*SUNF[i4, I4, I6] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, I3, i8]*SUND[I5, i6, i8]*SUNF[i4, I4, I6] - - (27*I)*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[I5, i6, i8]* - SUNF[i4, I4, I6] - (27*I)*SUND[I1, I2, i8]*SUND[I3, i4, i6]* - SUND[I5, i6, i8]*SUNF[i4, I4, I6] + (108*I)*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUND[I3, i4, i6]*SUNF[i4, I5, I6] - - (27*I)*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]* - SUNF[i4, I5, I6] + (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]* - SUND[I3, I4, i8]*SUNF[i4, I5, I6] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUNF[i4, I5, I6] - - (27*I)*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]* - SUNF[i4, I5, I6] - (72*I)*SUND[I1, i4, i6]*SUND[I2, I4, i8]* - SUND[I3, i6, i8]*SUNF[i4, I5, I6] + (108*I)*SUND[I1, i6, i8]* - SUND[I2, I3, i8]*SUND[i4, I4, i6]*SUNF[i4, I5, I6] - - (27*I)*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I4, i6]* - SUNF[i4, I5, I6] - (27*I)*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUND[i4, I4, i6]*SUNF[i4, I5, I6] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, I3, i8]*SUND[I4, i6, i8]*SUNF[i4, I5, I6] - - (27*I)*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[I4, i6, i8]* - SUNF[i4, I5, I6] - (27*I)*SUND[I1, I2, i8]*SUND[I3, i4, i6]* - SUND[I4, i6, i8]*SUNF[i4, I5, I6] + (36*I)*SUND[I3, i5, I5]* - SUNDelta[I1, I2]*SUNF[I4, i5, I6] + (36*I)*SUND[I2, i5, I5]* - SUNDelta[I1, I3]*SUNF[I4, i5, I6] + (36*I)*SUND[I2, I3, i5]* - SUNDelta[I1, I5]*SUNF[I4, i5, I6] - (24*I)*SUND[I1, i5, I5]* - SUNDelta[I2, I3]*SUNF[I4, i5, I6] - (24*I)*SUND[I1, I3, i5]* - SUNDelta[I2, I5]*SUNF[I4, i5, I6] - (24*I)*SUND[I1, I2, i5]* - SUNDelta[I3, I5]*SUNF[I4, i5, I6] - (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I3, i7]*SUNF[I2, I6, i8]*SUNF[I4, i5, i7] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I5, i7]*SUNF[I2, I6, i8]* - SUNF[I4, i5, i7] - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I2, i7]* - SUNF[I3, I6, i8]*SUNF[I4, i5, i7] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I5, i7]*SUNF[I3, I6, i8]*SUNF[I4, i5, i7] + - (18*I)*SUND[I3, I5, i8]*SUNF[I1, i3, I6]*SUNF[I2, i3, i5]* - SUNF[I4, i5, i8] - (72*I)*SUND[I3, I5, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I6]*SUNF[I4, i5, i8] - (18*I)*SUND[I2, I5, i8]* - SUNF[I1, i3, I6]*SUNF[i3, I3, i5]*SUNF[I4, i5, i8] + - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I6]*SUNF[i3, I3, i5]* - SUNF[I4, i5, i8] + (72*I)*SUND[I2, I5, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I3, I6]*SUNF[I4, i5, i8] + (27*I)*SUND[I1, I5, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I3, I6]*SUNF[I4, i5, i8] + - (18*I)*SUND[I2, I3, i8]*SUNF[I1, i3, I6]*SUNF[i3, i5, I5]* - SUNF[I4, i5, i8] - (27*I)*SUND[I1, I3, i8]*SUNF[I2, i3, I6]* - SUNF[i3, i5, I5]*SUNF[I4, i5, i8] + (27*I)*SUND[I1, I2, i8]* - SUNF[i3, I3, I6]*SUNF[i3, i5, I5]*SUNF[I4, i5, i8] + - (72*I)*SUND[I2, I3, i8]*SUNF[I1, i3, i5]*SUNF[i3, I5, I6]* - SUNF[I4, i5, i8] + (27*I)*SUND[I1, I3, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I5, I6]*SUNF[I4, i5, i8] - (27*I)*SUND[I1, I2, i8]* - SUNF[i3, I3, i5]*SUNF[i3, I5, I6]*SUNF[I4, i5, i8] - - 45*SUND[i3, I5, i8]*SUND[I3, i6, i8]*SUNF[I1, I2, i3]*SUNF[I4, i6, I6] - - 45*SUND[i3, I3, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i3]*SUNF[I4, i6, I6] - - 120*SUNDelta[I3, I5]*SUNF[I1, I2, i6]*SUNF[I4, i6, I6] + - 45*SUND[I2, i6, i8]*SUND[i3, I5, i8]*SUNF[I1, i3, I3]*SUNF[I4, i6, I6] + - 45*SUND[I2, i3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I3]*SUNF[I4, i6, I6] + - 45*SUND[I2, i6, i8]*SUND[i3, I3, i8]*SUNF[I1, i3, I5]*SUNF[I4, i6, I6] + - 45*SUND[I2, i3, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I5]*SUNF[I4, i6, I6] - - 108*SUND[I2, I5, i8]*SUND[i3, I3, i6]*SUNF[I1, i3, i8]*SUNF[I4, i6, I6] - - 108*SUND[I2, I3, i8]*SUND[i3, I5, i6]*SUNF[I1, i3, i8]*SUNF[I4, i6, I6] - - 108*SUND[I2, i3, i6]*SUND[I3, I5, i8]*SUNF[I1, i3, i8]*SUNF[I4, i6, I6] - - 120*SUNDelta[I2, I5]*SUNF[I1, I3, i6]*SUNF[I4, i6, I6] - - 120*SUNDelta[I2, I3]*SUNF[I1, I5, i6]*SUNF[I4, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[i3, I3, i6]*SUNF[I2, i3, i8]*SUNF[I4, i6, I6] + - 27*SUND[I1, I3, i8]*SUND[i3, I5, i6]*SUNF[I2, i3, i8]*SUNF[I4, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I3, I5, i8]*SUNF[I2, i3, i8]*SUNF[I4, i6, I6] - - 27*SUND[I1, I5, i8]*SUND[I2, i3, i6]*SUNF[i3, I3, i8]*SUNF[I4, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I2, I5, i8]*SUNF[i3, I3, i8]*SUNF[I4, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[i3, I5, i6]*SUNF[i3, I3, i8]*SUNF[I4, i6, I6] - - 27*SUND[I1, I3, i8]*SUND[I2, i3, i6]*SUNF[i3, I5, i8]*SUNF[I4, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I2, I3, i8]*SUNF[i3, I5, i8]*SUNF[I4, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[i3, I3, i6]*SUNF[i3, I5, i8]*SUNF[I4, i6, I6] - - 45*SUNF[I1, I5, i6]*SUNF[I2, i8, i9]*SUNF[I3, I6, i9]*SUNF[I4, i6, i8] - - 45*SUNF[I1, I5, i6]*SUNF[I2, I6, i9]*SUNF[I3, i8, i9]*SUNF[I4, i6, i8] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I3, i7]*SUNF[I2, i5, i7]* - SUNF[I4, I6, i8] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I5, i7]* - SUNF[I2, i5, i7]*SUNF[I4, I6, i8] - (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I2, i7]*SUNF[I3, i5, i7]*SUNF[I4, I6, i8] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I5, i7]*SUNF[I3, i5, i7]* - SUNF[I4, I6, i8] - 45*SUNF[I1, I5, i6]*SUNF[I2, i8, i9]*SUNF[I3, i6, i8]* - SUNF[I4, I6, i9] - 45*SUNF[I1, I5, i6]*SUNF[I2, i6, i8]*SUNF[I3, i8, i9]* - SUNF[I4, I6, i9] - (45*I)*SUND[i1, I5, I6]*SUNF[i1, I3, i9]* - SUNF[I1, I2, i8]*SUNF[I4, i8, i9] - (45*I)*SUND[i1, I3, I6]* - SUNF[i1, I5, i9]*SUNF[I1, I2, i8]*SUNF[I4, i8, i9] - - (45*I)*SUND[i1, I5, I6]*SUNF[i1, I2, i9]*SUNF[I1, I3, i8]* - SUNF[I4, i8, i9] - (45*I)*SUND[i1, I2, I6]*SUNF[i1, I5, i9]* - SUNF[I1, I3, i8]*SUNF[I4, i8, i9] - (45*I)*SUND[i1, I3, I6]* - SUNF[i1, I2, i9]*SUNF[I1, I5, i8]*SUNF[I4, i8, i9] - - (45*I)*SUND[i1, I2, I6]*SUNF[i1, I3, i9]*SUNF[I1, I5, i8]* - SUNF[I4, i8, i9] - 45*SUNF[I1, I5, i6]*SUNF[I2, I6, i9]*SUNF[I3, i6, i8]* - SUNF[I4, i8, i9] - 45*SUNF[I1, I5, i6]*SUNF[I2, i6, i8]*SUNF[I3, I6, i9]* - SUNF[I4, i8, i9] - (36*I)*SUND[I3, I4, i5]*SUNDelta[I1, I2]* - SUNF[i5, I5, I6] - (36*I)*SUND[I2, I4, i5]*SUNDelta[I1, I3]* - SUNF[i5, I5, I6] - (36*I)*SUND[I2, I3, i5]*SUNDelta[I1, I4]* - SUNF[i5, I5, I6] + (24*I)*SUND[I1, I4, i5]*SUNDelta[I2, I3]* - SUNF[i5, I5, I6] + (24*I)*SUND[I1, I3, i5]*SUNDelta[I2, I4]* - SUNF[i5, I5, I6] + (24*I)*SUND[I1, I2, i5]*SUNDelta[I3, I4]* - SUNF[i5, I5, I6] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i7]* - SUNF[I2, I6, i8]*SUNF[i5, I5, i7] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I4, i7]*SUNF[I2, I6, i8]*SUNF[i5, I5, i7] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I2, i7]*SUNF[I3, I6, i8]* - SUNF[i5, I5, i7] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i7]* - SUNF[I3, I6, i8]*SUNF[i5, I5, i7] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I2, i7]*SUNF[I4, I6, i8]*SUNF[i5, I5, i7] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I3, i7]*SUNF[I4, I6, i8]* - SUNF[i5, I5, i7] - (18*I)*SUND[I3, I4, i8]*SUNF[I1, i3, I6]* - SUNF[I2, i3, i5]*SUNF[i5, I5, i8] + (72*I)*SUND[I3, I4, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I6]*SUNF[i5, I5, i8] + - (18*I)*SUND[I2, I4, i8]*SUNF[I1, i3, I6]*SUNF[i3, I3, i5]* - SUNF[i5, I5, i8] - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, I6]* - SUNF[i3, I3, i5]*SUNF[i5, I5, i8] - (72*I)*SUND[I2, I4, i8]* - SUNF[I1, i3, i5]*SUNF[i3, I3, I6]*SUNF[i5, I5, i8] - - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, i5]*SUNF[i3, I3, I6]* - SUNF[i5, I5, i8] + (18*I)*SUND[I2, I3, i8]*SUNF[I1, i3, I6]* - SUNF[i3, I4, i5]*SUNF[i5, I5, i8] - (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I6]*SUNF[i3, I4, i5]*SUNF[i5, I5, i8] + - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I6]*SUNF[i3, I4, i5]* - SUNF[i5, I5, i8] - (72*I)*SUND[I2, I3, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I4, I6]*SUNF[i5, I5, i8] - (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I4, I6]*SUNF[i5, I5, i8] + - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, i5]*SUNF[i3, I4, I6]* - SUNF[i5, I5, i8] - 45*SUND[i3, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I5, i6, I6] - 45*SUND[i3, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I5, i6, I6] - 120*SUNDelta[I3, I4]*SUNF[I1, I2, i6]* - SUNF[I5, i6, I6] + 45*SUND[I2, i6, i8]*SUND[i3, I4, i8]*SUNF[I1, i3, I3]* - SUNF[I5, i6, I6] + 45*SUND[I2, i3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I3]* - SUNF[I5, i6, I6] + 45*SUND[I2, i6, i8]*SUND[i3, I3, i8]*SUNF[I1, i3, I4]* - SUNF[I5, i6, I6] + 45*SUND[I2, i3, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I4]* - SUNF[I5, i6, I6] - 108*SUND[I2, I4, i8]*SUND[i3, I3, i6]* - SUNF[I1, i3, i8]*SUNF[I5, i6, I6] - 108*SUND[I2, I3, i8]* - SUND[i3, I4, i6]*SUNF[I1, i3, i8]*SUNF[I5, i6, I6] - - 108*SUND[I2, i3, i6]*SUND[I3, I4, i8]*SUNF[I1, i3, i8]*SUNF[I5, i6, I6] - - 120*SUNDelta[I2, I4]*SUNF[I1, I3, i6]*SUNF[I5, i6, I6] - - 120*SUNDelta[I2, I3]*SUNF[I1, I4, i6]*SUNF[I5, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[i3, I3, i6]*SUNF[I2, i3, i8]*SUNF[I5, i6, I6] + - 27*SUND[I1, I3, i8]*SUND[i3, I4, i6]*SUNF[I2, i3, i8]*SUNF[I5, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I3, I4, i8]*SUNF[I2, i3, i8]*SUNF[I5, i6, I6] - - 27*SUND[I1, I4, i8]*SUND[I2, i3, i6]*SUNF[i3, I3, i8]*SUNF[I5, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I2, I4, i8]*SUNF[i3, I3, i8]*SUNF[I5, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[i3, I4, i6]*SUNF[i3, I3, i8]*SUNF[I5, i6, I6] - - 27*SUND[I1, I3, i8]*SUND[I2, i3, i6]*SUNF[i3, I4, i8]*SUNF[I5, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I2, I3, i8]*SUNF[i3, I4, i8]*SUNF[I5, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[i3, I3, i6]*SUNF[i3, I4, i8]*SUNF[I5, i6, I6] - - 45*SUNF[I1, I4, i6]*SUNF[I2, i8, i9]*SUNF[I3, I6, i9]*SUNF[I5, i6, i8] - - 45*SUNF[I1, I4, i6]*SUNF[I2, I6, i9]*SUNF[I3, i8, i9]*SUNF[I5, i6, i8] - - 45*SUNF[I1, I3, i6]*SUNF[I2, i8, i9]*SUNF[I4, I6, i9]*SUNF[I5, i6, i8] - - 45*SUNF[I1, I2, i6]*SUNF[I3, i8, i9]*SUNF[I4, I6, i9]*SUNF[I5, i6, i8] - - 45*SUNF[I1, I3, i6]*SUNF[I2, I6, i9]*SUNF[I4, i8, i9]*SUNF[I5, i6, i8] - - 45*SUNF[I1, I2, i6]*SUNF[I3, I6, i9]*SUNF[I4, i8, i9]*SUNF[I5, i6, i8] - - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i7]*SUNF[I2, i5, i7]* - SUNF[I5, I6, i8] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I4, i7]* - SUNF[I2, i5, i7]*SUNF[I5, I6, i8] - (45*I)*SUND[I4, i5, i8]* - SUNF[I1, I2, i7]*SUNF[I3, i5, i7]*SUNF[I5, I6, i8] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i7]*SUNF[I3, i5, i7]* - SUNF[I5, I6, i8] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I2, i7]* - SUNF[I4, i5, i7]*SUNF[I5, I6, i8] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I3, i7]*SUNF[I4, i5, i7]*SUNF[I5, I6, i8] - - 45*SUNF[I1, I4, i6]*SUNF[I2, i8, i9]*SUNF[I3, i6, i8]*SUNF[I5, I6, i9] - - 45*SUNF[I1, I4, i6]*SUNF[I2, i6, i8]*SUNF[I3, i8, i9]*SUNF[I5, I6, i9] - - 45*SUNF[I1, I3, i6]*SUNF[I2, i8, i9]*SUNF[I4, i6, i8]*SUNF[I5, I6, i9] - - 45*SUNF[I1, I2, i6]*SUNF[I3, i8, i9]*SUNF[I4, i6, i8]*SUNF[I5, I6, i9] - - 45*SUNF[I1, I3, i6]*SUNF[I2, i6, i8]*SUNF[I4, i8, i9]*SUNF[I5, I6, i9] - - 45*SUNF[I1, I2, i6]*SUNF[I3, i6, i8]*SUNF[I4, i8, i9]*SUNF[I5, I6, i9] - - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I3, i9]*SUNF[I1, I2, i8]* - SUNF[I5, i8, i9] - (45*I)*SUND[i1, I3, I6]*SUNF[i1, I4, i9]* - SUNF[I1, I2, i8]*SUNF[I5, i8, i9] - (45*I)*SUND[i1, I4, I6]* - SUNF[i1, I2, i9]*SUNF[I1, I3, i8]*SUNF[I5, i8, i9] - - (45*I)*SUND[i1, I2, I6]*SUNF[i1, I4, i9]*SUNF[I1, I3, i8]* - SUNF[I5, i8, i9] - (45*I)*SUND[i1, I3, I6]*SUNF[i1, I2, i9]* - SUNF[I1, I4, i8]*SUNF[I5, i8, i9] - (45*I)*SUND[i1, I2, I6]* - SUNF[i1, I3, i9]*SUNF[I1, I4, i8]*SUNF[I5, i8, i9] - - 45*SUNF[I1, I4, i6]*SUNF[I2, I6, i9]*SUNF[I3, i6, i8]*SUNF[I5, i8, i9] - - 45*SUNF[I1, I4, i6]*SUNF[I2, i6, i8]*SUNF[I3, I6, i9]*SUNF[I5, i8, i9] - - 45*SUNF[I1, I3, i6]*SUNF[I2, I6, i9]*SUNF[I4, i6, i8]*SUNF[I5, i8, i9] - - 45*SUNF[I1, I2, i6]*SUNF[I3, I6, i9]*SUNF[I4, i6, i8]*SUNF[I5, i8, i9] - - 45*SUNF[I1, I3, i6]*SUNF[I2, i6, i8]*SUNF[I4, I6, i9]*SUNF[I5, i8, i9] - - 45*SUNF[I1, I2, i6]*SUNF[I3, i6, i8]*SUNF[I4, I6, i9]*SUNF[I5, i8, i9])/ -(1080*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(108*SUND[I1, I5, I6]*SUND[I2, I3, I4] - 72*SUND[I1, I4, I6]* - SUND[I2, I3, I5] + 108*SUND[I1, I4, I5]*SUND[I2, I3, I6] - - 72*SUND[I1, I3, I6]*SUND[I2, I4, I5] + 108*SUND[I1, I3, I5]* - SUND[I2, I4, I6] - 72*SUND[I1, I3, I4]*SUND[I2, I5, I6] - - 72*SUND[I1, I2, I6]*SUND[I3, I4, I5] + 108*SUND[I1, I2, I5]* - SUND[I3, I4, I6] - 72*SUND[I1, I2, I4]*SUND[I3, I5, I6] + - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I5] - - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I5] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[i4, I4, I5] + - 72*SUND[I1, i4, i6]*SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUND[i4, I4, I5] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, I6, i8]*SUND[i4, I4, I5] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUND[i4, I4, I5] + - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I5]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUND[I3, i4, I5]*SUND[i4, I4, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, I5]*SUND[I3, i6, i8]*SUND[i4, I4, i6] - - 18*SUND[I1, i4, I5]*SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I5]*SUND[I3, I6, i8]*SUND[i4, I4, i6] - - 18*SUND[I1, i4, I5]*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUND[I3, i4, i6]*SUND[i4, I5, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[i4, I5, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, I4, i8]*SUND[i4, I5, I6] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUND[i4, I5, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[i4, I5, I6] + - 72*SUND[I1, i4, i6]*SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUND[i4, I5, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUND[i4, I4, i6]*SUND[i4, I5, I6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I4, i6]*SUND[i4, I5, I6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUND[i4, I4, i6]*SUND[i4, I5, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUND[I3, i4, I5]*SUND[i4, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I5]*SUND[i4, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I5]*SUND[I3, I4, i8]*SUND[i4, i6, I6] - - 18*SUND[I1, i4, I5]*SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUND[i4, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, I5]*SUND[I3, i6, i8]*SUND[i4, i6, I6] - - 18*SUND[I1, i4, I5]*SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUND[i4, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUND[i4, I4, I5]*SUND[i4, i6, I6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I4, I5]*SUND[i4, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUND[i4, I4, I5]*SUND[i4, i6, I6] - - 72*SUND[I1, I2, I3]*SUND[I4, I5, I6] + 27*SUND[I1, I6, i8]* - SUND[I2, i4, i6]*SUND[I3, i4, I5]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I6, i8]*SUND[I3, i4, I5]*SUND[I4, i6, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, I5]*SUND[I3, i4, i6]*SUND[I4, i6, i8] - - 18*SUND[I1, i4, I5]*SUND[I2, I6, i8]*SUND[I3, i4, i6]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I5]*SUND[I3, I6, i8]*SUND[I4, i6, i8] - - 18*SUND[I1, i4, I5]*SUND[I2, i4, i6]*SUND[I3, I6, i8]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i8]*SUND[i4, I5, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[i4, I5, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, i6]*SUND[i4, I5, I6]*SUND[I4, i6, i8] - - 18*SUND[I1, i4, I5]*SUND[I2, I3, i8]*SUND[i4, i6, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I5]*SUND[i4, i6, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I5]*SUND[i4, i6, I6]*SUND[I4, i6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I5]*SUND[I4, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, i4, I5]*SUND[I4, I6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I5]*SUND[I3, i4, i6]*SUND[I4, I6, i8] - - 18*SUND[I1, i4, I5]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[I4, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I5]*SUND[I3, i6, i8]*SUND[I4, I6, i8] - - 18*SUND[I1, i4, I5]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[I4, I6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I5]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I4, i8]*SUND[I3, i4, I5]*SUND[i6, I6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, I5]*SUND[I3, i4, i6]*SUND[i6, I6, i8] - - 18*SUND[I1, i4, I5]*SUND[I2, I4, i8]*SUND[I3, i4, i6]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I5]*SUND[I3, I4, i8]*SUND[i6, I6, i8] - - 18*SUND[I1, i4, I5]*SUND[I2, i4, i6]*SUND[I3, I4, i8]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i8]*SUND[i4, I4, I5]*SUND[i6, I6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[i4, I4, I5]*SUND[i6, I6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I5]*SUND[i6, I6, i8] - - 18*SUND[I1, i4, I5]*SUND[I2, I3, i8]*SUND[i4, I4, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I5]*SUND[i4, I4, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I5]*SUND[i4, I4, i6]*SUND[i6, I6, i8] + - 36*SUND[I3, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I2] + - 36*SUND[I3, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I2] + - 36*SUND[I3, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I2] + - 36*SUND[I2, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I3] + - 36*SUND[I2, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I3] + - 36*SUND[I2, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I3] + - 36*SUND[I2, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I1, I4] + - 36*SUND[I2, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I1, I4] + - 36*SUND[I2, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I4] - - 48*SUND[I2, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I1, I5] - - 48*SUND[I2, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I1, I5] - - 48*SUND[I2, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I1, I5] + - 36*SUND[I2, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I1, I6] + - 36*SUND[I2, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I1, I6] + - 36*SUND[I2, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I1, I6] - - 24*SUND[I1, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I2, I3] - - 24*SUND[I1, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I2, I3] - - 24*SUND[I1, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I3] - - 24*SUND[I1, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I2, I4] - - 24*SUND[I1, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I2, I4] - - 24*SUND[I1, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I4] + - 12*SUND[I1, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I2, I5] + - 12*SUND[I1, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I2, I5] + - 12*SUND[I1, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I2, I5] - - 24*SUND[I1, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I2, I6] - - 24*SUND[I1, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I2, I6] - - 24*SUND[I1, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I2, I6] - - 24*SUND[I1, i5, I6]*SUND[I2, i5, I5]*SUNDelta[I3, I4] - - 24*SUND[I1, i5, I5]*SUND[I2, i5, I6]*SUNDelta[I3, I4] - - 24*SUND[I1, I2, i5]*SUND[i5, I5, I6]*SUNDelta[I3, I4] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 32*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - 12*SUND[I1, i5, I6]*SUND[I2, I4, i5]*SUNDelta[I3, I5] + - 12*SUND[I1, I4, i5]*SUND[I2, i5, I6]*SUNDelta[I3, I5] + - 12*SUND[I1, I2, i5]*SUND[I4, i5, I6]*SUNDelta[I3, I5] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 24*SUND[I1, i5, I5]*SUND[I2, I4, i5]*SUNDelta[I3, I6] - - 24*SUND[I1, I4, i5]*SUND[I2, i5, I5]*SUNDelta[I3, I6] - - 24*SUND[I1, I2, i5]*SUND[I4, i5, I5]*SUNDelta[I3, I6] - - 32*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - 12*SUND[I1, i5, I6]*SUND[I2, I3, i5]*SUNDelta[I4, I5] + - 12*SUND[I1, I3, i5]*SUND[I2, i5, I6]*SUNDelta[I4, I5] + - 12*SUND[I1, I2, i5]*SUND[I3, i5, I6]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 24*SUND[I1, i5, I5]*SUND[I2, I3, i5]*SUNDelta[I4, I6] - - 24*SUND[I1, I3, i5]*SUND[I2, i5, I5]*SUNDelta[I4, I6] - - 24*SUND[I1, I2, i5]*SUND[I3, i5, I5]*SUNDelta[I4, I6] - - 32*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - 12*SUND[I1, I4, i5]*SUND[I2, I3, i5]*SUNDelta[I5, I6] + - 12*SUND[I1, I3, i5]*SUND[I2, I4, i5]*SUNDelta[I5, I6] + - 12*SUND[I1, I2, i5]*SUND[I3, I4, i5]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6] + - (45*I)*SUND[i1, I6, i8]*SUND[I3, i6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I1, I2] + (45*I)*SUND[i1, I6, i8]*SUND[I3, I5, i6]* - SUND[I4, i6, i8]*SUNF[i1, I1, I2] + (45*I)*SUND[i1, I4, i8]* - SUND[I3, i6, i8]*SUND[I5, i6, I6]*SUNF[i1, I1, I2] + - (45*I)*SUND[i1, I3, i8]*SUND[I4, i6, i8]*SUND[I5, i6, I6]* - SUNF[i1, I1, I2] + (45*I)*SUND[i1, I4, i8]*SUND[I3, I5, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I2] + (45*I)*SUND[i1, I3, i8]* - SUND[I4, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I5, I6]*SUNDelta[I3, I4]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I4, I6]*SUNDelta[I3, I5]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I4, I5]*SUNDelta[I3, I6]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I3, I6]*SUNDelta[I4, I5]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I3, I5]*SUNDelta[I4, I6]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I3, I4]*SUNDelta[I5, I6]*SUNF[i1, I1, I2] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, i6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I1, I3] + (45*I)*SUND[i1, I6, i8]*SUND[I2, I5, i6]* - SUND[I4, i6, i8]*SUNF[i1, I1, I3] + (45*I)*SUND[i1, I4, i8]* - SUND[I2, i6, i8]*SUND[I5, i6, I6]*SUNF[i1, I1, I3] + - (45*I)*SUND[i1, I2, i8]*SUND[I4, i6, i8]*SUND[I5, i6, I6]* - SUNF[i1, I1, I3] + (45*I)*SUND[i1, I4, i8]*SUND[I2, I5, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I3] + (45*I)*SUND[i1, I2, i8]* - SUND[I4, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I5, I6]*SUNDelta[I2, I4]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I4, I6]*SUNDelta[I2, I5]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I4, I5]*SUNDelta[I2, I6]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I2, I6]*SUNDelta[I4, I5]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I2, I5]*SUNDelta[I4, I6]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I2, I4]*SUNDelta[I5, I6]*SUNF[i1, I1, I3] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, I5, i6]* - SUNF[i1, I1, I4] + (45*I)*SUND[i1, I6, i8]*SUND[I2, I5, i6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I4] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, i6, i8]*SUND[I5, i6, I6]*SUNF[i1, I1, I4] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, i6, i8]*SUND[I5, i6, I6]* - SUNF[i1, I1, I4] + (45*I)*SUND[i1, I3, i8]*SUND[I2, I5, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I4] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I5, I6]*SUNDelta[I2, I3]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I3, I6]*SUNDelta[I2, I5]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I3, I5]*SUNDelta[I2, I6]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I2, I6]*SUNDelta[I3, I5]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I2, I5]*SUNDelta[I3, I6]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I2, I3]*SUNDelta[I5, I6]*SUNF[i1, I1, I4] + - (72*I)*SUND[i1, I5, I6]*SUND[I2, i6, i8]*SUND[I3, I4, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I5, I6]*SUND[I2, I4, i8]* - SUND[I3, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I4, I5]* - SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I4, I5]*SUND[I2, i6, i8]*SUND[I3, I6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I5, I6]*SUND[I2, I3, i8]* - SUND[I4, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I5]* - SUND[I2, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I2, I5]*SUND[I3, I6, i8]*SUND[I4, i6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I5]*SUND[I2, i6, i8]* - SUND[I4, I6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I5]* - SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I4, I5]*SUND[I2, I3, i8]*SUND[i6, I6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I5]*SUND[I2, I4, i8]* - SUND[i6, I6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I5]* - SUND[I3, I4, i8]*SUND[i6, I6, i8]*SUNF[i1, I1, i6] + - (45*I)*SUND[i1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, I5, i6]* - SUNF[i1, I1, I6] + (45*I)*SUND[i1, I4, i8]*SUND[I2, I5, i6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I6] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, i6, i8]*SUND[I4, I5, i6]*SUNF[i1, I1, I6] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, i6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I1, I6] + (45*I)*SUND[i1, I3, i8]*SUND[I2, I5, i6]* - SUND[I4, i6, i8]*SUNF[i1, I1, I6] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, I5, i6]*SUND[I4, i6, i8]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I4, I5]*SUNDelta[I2, I3]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I3, I5]*SUNDelta[I2, I4]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I3, I4]*SUNDelta[I2, I5]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I2, I5]*SUNDelta[I3, I4]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I2, I4]*SUNDelta[I3, I5]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I2, I3]*SUNDelta[I4, I5]*SUNF[i1, I1, I6] - - (108*I)*SUND[i1, i6, I6]*SUND[I2, I5, i6]*SUND[I3, I4, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, i6, I6]*SUND[I2, I4, i8]* - SUND[I3, I5, i6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I4, i6]* - SUND[I2, I6, i8]*SUND[I3, I5, i6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I4, i6]*SUND[I2, I5, i6]*SUND[I3, I6, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, i6, I6]*SUND[I2, I3, i8]* - SUND[I4, I5, i6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]* - SUND[I2, I6, i8]*SUND[I4, I5, i6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I2, i6]*SUND[I3, I6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]*SUND[I2, I5, i6]* - SUND[I4, I6, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I2, i6]* - SUND[I3, I5, i6]*SUND[I4, I6, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I4, i6]*SUND[I2, I3, i8]*SUND[I5, i6, I6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]*SUND[I2, I4, i8]* - SUND[I5, i6, I6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I2, i6]* - SUND[I3, I4, i8]*SUND[I5, i6, I6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I5, I6]*SUND[I1, i6, i8]*SUND[I3, I4, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I5, I6]*SUND[I1, I4, i8]* - SUND[I3, i6, i8]*SUNF[i1, I2, i6] + (27*I)*SUND[i1, I4, I5]* - SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[i1, I2, i6] - - (108*I)*SUND[i1, I4, I5]*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I5, I6]*SUND[I1, I3, i8]* - SUND[I4, i6, i8]*SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I5]* - SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I2, i6] - - (18*I)*SUND[i1, I1, I5]*SUND[I3, I6, i8]*SUND[I4, i6, i8]* - SUNF[i1, I2, i6] - (108*I)*SUND[i1, I3, I5]*SUND[I1, i6, i8]* - SUND[I4, I6, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I5]* - SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[i1, I2, i6] + - (27*I)*SUND[i1, I4, I5]*SUND[I1, I3, i8]*SUND[i6, I6, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I5]*SUND[I1, I4, i8]* - SUND[i6, I6, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I5]* - SUND[I3, I4, i8]*SUND[i6, I6, i8]*SUNF[i1, I2, i6] - - (18*I)*SUND[i1, i6, I6]*SUND[I1, I5, i6]*SUND[I3, I4, i8]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I4, i8]* - SUND[I3, I5, i6]*SUNF[i1, I2, i8] + (27*I)*SUND[i1, I4, i6]* - SUND[I1, I6, i8]*SUND[I3, I5, i6]*SUNF[i1, I2, i8] - - (18*I)*SUND[i1, I4, i6]*SUND[I1, I5, i6]*SUND[I3, I6, i8]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I3, i8]* - SUND[I4, I5, i6]*SUNF[i1, I2, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I6, i8]*SUND[I4, I5, i6]*SUNF[i1, I2, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I3, I6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I2, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, I5, i6]* - SUND[I4, I6, i8]*SUNF[i1, I2, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I3, I5, i6]*SUND[I4, I6, i8]*SUNF[i1, I2, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I3, i8]*SUND[I5, i6, I6]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, I3, i6]*SUND[I1, I4, i8]* - SUND[I5, i6, I6]*SUNF[i1, I2, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I3, I4, i8]*SUND[I5, i6, I6]*SUNF[i1, I2, i8] - - (108*I)*SUND[i1, I5, I6]*SUND[I1, i6, i8]*SUND[I2, I4, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I5, I6]*SUND[I1, I4, i8]* - SUND[I2, i6, i8]*SUNF[i1, I3, i6] + (27*I)*SUND[i1, I4, I5]* - SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i1, I3, i6] - - (108*I)*SUND[i1, I4, I5]*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I5, I6]*SUND[I1, I2, i8]* - SUND[I4, i6, i8]*SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I5]* - SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I3, i6] - - (18*I)*SUND[i1, I1, I5]*SUND[I2, I6, i8]*SUND[I4, i6, i8]* - SUNF[i1, I3, i6] - (108*I)*SUND[i1, I2, I5]*SUND[I1, i6, i8]* - SUND[I4, I6, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I5]* - SUND[I2, i6, i8]*SUND[I4, I6, i8]*SUNF[i1, I3, i6] + - (27*I)*SUND[i1, I4, I5]*SUND[I1, I2, i8]*SUND[i6, I6, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I5]*SUND[I1, I4, i8]* - SUND[i6, I6, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I5]* - SUND[I2, I4, i8]*SUND[i6, I6, i8]*SUNF[i1, I3, i6] - - (18*I)*SUND[i1, i6, I6]*SUND[I1, I5, i6]*SUND[I2, I4, i8]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I4, i8]* - SUND[I2, I5, i6]*SUNF[i1, I3, i8] + (27*I)*SUND[i1, I4, i6]* - SUND[I1, I6, i8]*SUND[I2, I5, i6]*SUNF[i1, I3, i8] - - (18*I)*SUND[i1, I4, i6]*SUND[I1, I5, i6]*SUND[I2, I6, i8]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I2, i8]* - SUND[I4, I5, i6]*SUNF[i1, I3, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I6, i8]*SUND[I4, I5, i6]*SUNF[i1, I3, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I3, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I5, i6]* - SUND[I4, I6, i8]*SUNF[i1, I3, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I5, i6]*SUND[I4, I6, i8]*SUNF[i1, I3, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I2, i8]*SUND[I5, i6, I6]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I4, i8]* - SUND[I5, i6, I6]*SUNF[i1, I3, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I4, i8]*SUND[I5, i6, I6]*SUNF[i1, I3, i8] - - (108*I)*SUND[i1, I5, I6]*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I5, I6]*SUND[I1, I3, i8]* - SUND[I2, i6, i8]*SUNF[i1, I4, i6] + (27*I)*SUND[i1, I3, I5]* - SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i1, I4, i6] - - (108*I)*SUND[i1, I3, I5]*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I5, I6]*SUND[I1, I2, i8]* - SUND[I3, i6, i8]*SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I5]* - SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[i1, I4, i6] - - (18*I)*SUND[i1, I1, I5]*SUND[I2, I6, i8]*SUND[I3, i6, i8]* - SUNF[i1, I4, i6] - (108*I)*SUND[i1, I2, I5]*SUND[I1, i6, i8]* - SUND[I3, I6, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I5]* - SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUNF[i1, I4, i6] + - (27*I)*SUND[i1, I3, I5]*SUND[I1, I2, i8]*SUND[i6, I6, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I5]*SUND[I1, I3, i8]* - SUND[i6, I6, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I5]* - SUND[I2, I3, i8]*SUND[i6, I6, i8]*SUNF[i1, I4, i6] - - (18*I)*SUND[i1, i6, I6]*SUND[I1, I5, i6]*SUND[I2, I3, i8]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I3, i8]* - SUND[I2, I5, i6]*SUNF[i1, I4, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I6, i8]*SUND[I2, I5, i6]*SUNF[i1, I4, i8] - - (18*I)*SUND[i1, I3, i6]*SUND[I1, I5, i6]*SUND[I2, I6, i8]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I2, i8]* - SUND[I3, I5, i6]*SUNF[i1, I4, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I6, i8]*SUND[I3, I5, i6]*SUNF[i1, I4, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I6, i8]*SUND[I3, I5, i6]* - SUNF[i1, I4, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I5, i6]* - SUND[I3, I6, i8]*SUNF[i1, I4, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I5, i6]*SUND[I3, I6, i8]*SUNF[i1, I4, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I2, i8]*SUND[I5, i6, I6]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I3, i8]* - SUND[I5, i6, I6]*SUNF[i1, I4, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i8]*SUND[I5, i6, I6]*SUNF[i1, I4, i8] + - (108*I)*SUND[i1, I4, I5]*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUNF[i1, i6, I6] + (108*I)*SUND[i1, I3, I5]*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUNF[i1, i6, I6] - (27*I)*SUND[i1, I4, I5]* - SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I3, I5]*SUND[I1, I4, i8]*SUND[I2, i6, i8]* - SUNF[i1, i6, I6] + (108*I)*SUND[i1, I2, I5]*SUND[I1, i6, i8]* - SUND[I3, I4, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I5]* - SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I4, I5]*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I5]*SUND[I1, I4, i8]* - SUND[I3, i6, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I5]* - SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I3, I5]*SUND[I1, I2, i8]*SUND[I4, i6, i8]* - SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I5]*SUND[I1, I3, i8]* - SUND[I4, i6, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I5]* - SUND[I2, I3, i8]*SUND[I4, i6, i8]*SUNF[i1, i6, I6] - - (18*I)*SUND[i1, I4, i6]*SUND[I1, I5, i6]*SUND[I2, I3, i8]* - SUNF[i1, I6, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, I5, i6]* - SUND[I2, I4, i8]*SUNF[i1, I6, i8] + (27*I)*SUND[i1, I4, i6]* - SUND[I1, I3, i8]*SUND[I2, I5, i6]*SUNF[i1, I6, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I4, i8]*SUND[I2, I5, i6]* - SUNF[i1, I6, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I5, i6]* - SUND[I3, I4, i8]*SUNF[i1, I6, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I5, i6]*SUND[I3, I4, i8]*SUNF[i1, I6, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I2, i8]*SUND[I3, I5, i6]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I4, i8]* - SUND[I3, I5, i6]*SUNF[i1, I6, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I4, i8]*SUND[I3, I5, i6]*SUNF[i1, I6, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I2, i8]*SUND[I4, I5, i6]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I3, i8]* - SUND[I4, I5, i6]*SUNF[i1, I6, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i8]*SUND[I4, I5, i6]*SUNF[i1, I6, i8] - - 45*SUND[i1, I5, I6]*SUND[i3, I4, i8]*SUNF[i1, I3, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I4, I5]*SUND[i3, I6, i8]*SUNF[i1, I3, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I5, I6]*SUND[i3, I3, i8]*SUNF[i1, I4, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I5]*SUND[i3, I6, i8]*SUNF[i1, I4, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I4, I5]*SUND[i3, I3, i8]*SUNF[i1, I6, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I5]*SUND[i3, I4, i8]*SUNF[i1, I6, i8]*SUNF[I1, I2, i3] + - (120*I)*SUND[I4, i5, I6]*SUNDelta[I3, I5]*SUNF[I1, I2, i5] + - (120*I)*SUND[I3, i5, I6]*SUNDelta[I4, I5]*SUNF[I1, I2, i5] + - (120*I)*SUND[I3, I4, i5]*SUNDelta[I5, I6]*SUNF[I1, I2, i5] - - 45*SUND[i1, I6, i8]*SUND[I4, I5, i8]*SUNF[i1, I3, i5]*SUNF[I1, I2, i5] - - 45*SUND[i1, I4, i8]*SUND[I5, I6, i8]*SUNF[i1, I3, i5]*SUNF[I1, I2, i5] - - 45*SUND[i1, I6, i8]*SUND[I3, I5, i8]*SUNF[i1, I4, i5]*SUNF[I1, I2, i5] - - 45*SUND[i1, I3, i8]*SUND[I5, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, I2, i5] + - 45*SUND[i1, I4, i8]*SUND[I3, I5, i8]*SUNF[i1, i5, I6]*SUNF[I1, I2, i5] + - 45*SUND[i1, I3, i8]*SUND[I4, I5, i8]*SUNF[i1, i5, I6]*SUNF[I1, I2, i5] - - (180*I)*SUND[I3, I4, I6]*SUNF[I1, I2, I5] + 45*SUND[i1, I5, I6]* - SUND[i3, I4, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I4, I5]*SUND[i3, I6, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I5, I6]*SUND[I2, i3, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I5]*SUND[i3, I6, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I4, I5]*SUND[I2, i3, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I5]*SUND[i3, I4, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I5, I6]*SUND[i3, I3, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I3, I5]*SUND[i3, I6, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I5, I6]*SUND[I2, i3, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I5]*SUND[i3, I6, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I3, I5]*SUND[I2, i3, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I5]*SUND[i3, I3, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I4, I5]*SUND[i3, I3, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I3, I5]*SUND[i3, I4, i8]*SUNF[i1, I2, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I4, I5]*SUND[I2, i3, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I2, I5]*SUND[i3, I4, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I3, I5]*SUND[I2, i3, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I2, I5]*SUND[i3, I3, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I6] - - 108*SUND[i1, I5, I6]*SUND[I3, I4, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] - - 108*SUND[i1, I4, I5]*SUND[I3, I6, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] - - 108*SUND[i1, I3, I5]*SUND[I4, I6, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I5, I6]*SUND[I2, I4, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I4, I5]*SUND[I2, I6, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I5]*SUND[I4, I6, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I5, I6]*SUND[I2, I3, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I5]*SUND[I2, I6, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I5]*SUND[I3, I6, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I4, I5]*SUND[I2, I3, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I5]*SUND[I2, I4, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I5]*SUND[I3, I4, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - (120*I)*SUND[I4, i5, I6]*SUNDelta[I2, I5]*SUNF[I1, I3, i5] + - (120*I)*SUND[I2, i5, I6]*SUNDelta[I4, I5]*SUNF[I1, I3, i5] + - (120*I)*SUND[I2, I4, i5]*SUNDelta[I5, I6]*SUNF[I1, I3, i5] - - 45*SUND[i1, I6, i8]*SUND[I4, I5, i8]*SUNF[i1, I2, i5]*SUNF[I1, I3, i5] - - 45*SUND[i1, I4, i8]*SUND[I5, I6, i8]*SUNF[i1, I2, i5]*SUNF[I1, I3, i5] - - 45*SUND[i1, I6, i8]*SUND[I2, I5, i8]*SUNF[i1, I4, i5]*SUNF[I1, I3, i5] - - 45*SUND[i1, I2, i8]*SUND[I5, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, I3, i5] + - 45*SUND[i1, I4, i8]*SUND[I2, I5, i8]*SUNF[i1, i5, I6]*SUNF[I1, I3, i5] + - 45*SUND[i1, I2, i8]*SUND[I4, I5, i8]*SUNF[i1, i5, I6]*SUNF[I1, I3, i5] - - (180*I)*SUND[I2, I4, I6]*SUNF[I1, I3, I5] - (18*I)*SUND[I2, I6, i8]* - SUND[I3, i6, i8]*SUND[i4, I4, i6]*SUNF[I1, i4, I5] - - (18*I)*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUND[i4, I4, i6]* - SUNF[I1, i4, I5] - (18*I)*SUND[I2, i6, i8]*SUND[I3, I4, i8]* - SUND[i4, i6, I6]*SUNF[I1, i4, I5] - (18*I)*SUND[I2, I4, i8]* - SUND[I3, i6, i8]*SUND[i4, i6, I6]*SUNF[I1, i4, I5] - - (18*I)*SUND[I2, I6, i8]*SUND[I3, i4, i6]*SUND[I4, i6, i8]* - SUNF[I1, i4, I5] - (18*I)*SUND[I2, i4, i6]*SUND[I3, I6, i8]* - SUND[I4, i6, i8]*SUNF[I1, i4, I5] - (18*I)*SUND[I2, I3, i8]* - SUND[i4, i6, I6]*SUND[I4, i6, i8]*SUNF[I1, i4, I5] - - (18*I)*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[I4, I6, i8]* - SUNF[I1, i4, I5] - (18*I)*SUND[I2, i4, i6]*SUND[I3, i6, i8]* - SUND[I4, I6, i8]*SUNF[I1, i4, I5] - (18*I)*SUND[I2, I4, i8]* - SUND[I3, i4, i6]*SUND[i6, I6, i8]*SUNF[I1, i4, I5] - - (18*I)*SUND[I2, i4, i6]*SUND[I3, I4, i8]*SUND[i6, I6, i8]* - SUNF[I1, i4, I5] - (18*I)*SUND[I2, I3, i8]*SUND[i4, I4, i6]* - SUND[i6, I6, i8]*SUNF[I1, i4, I5] + (120*I)*SUND[I3, i5, I6]* - SUNDelta[I2, I5]*SUNF[I1, I4, i5] + (120*I)*SUND[I2, i5, I6]* - SUNDelta[I3, I5]*SUNF[I1, I4, i5] + (120*I)*SUND[I2, I3, i5]* - SUNDelta[I5, I6]*SUNF[I1, I4, i5] - 45*SUND[i1, I6, i8]*SUND[I3, I5, i8]* - SUNF[i1, I2, i5]*SUNF[I1, I4, i5] - 45*SUND[i1, I3, i8]*SUND[I5, I6, i8]* - SUNF[i1, I2, i5]*SUNF[I1, I4, i5] - 45*SUND[i1, I6, i8]*SUND[I2, I5, i8]* - SUNF[i1, I3, i5]*SUNF[I1, I4, i5] - 45*SUND[i1, I2, i8]*SUND[I5, I6, i8]* - SUNF[i1, I3, i5]*SUNF[I1, I4, i5] + 45*SUND[i1, I3, i8]*SUND[I2, I5, i8]* - SUNF[i1, i5, I6]*SUNF[I1, I4, i5] + 45*SUND[i1, I2, i8]*SUND[I3, I5, i8]* - SUNF[i1, i5, I6]*SUNF[I1, I4, i5] - (180*I)*SUND[I2, I3, I6]* - SUNF[I1, I4, I5] - (24*I)*SUND[I4, i5, I6]*SUNDelta[I2, I3]* - SUNF[I1, i5, I5] - (24*I)*SUND[I3, i5, I6]*SUNDelta[I2, I4]* - SUNF[I1, i5, I5] - (24*I)*SUND[I3, I4, i5]*SUNDelta[I2, I6]* - SUNF[I1, i5, I5] - (24*I)*SUND[I2, i5, I6]*SUNDelta[I3, I4]* - SUNF[I1, i5, I5] - (24*I)*SUND[I2, I4, i5]*SUNDelta[I3, I6]* - SUNF[I1, i5, I5] - (24*I)*SUND[I2, I3, i5]*SUNDelta[I4, I6]* - SUNF[I1, i5, I5] - (120*I)*SUND[I3, I4, i5]*SUNDelta[I2, I5]* - SUNF[I1, i5, I6] - (120*I)*SUND[I2, I4, i5]*SUNDelta[I3, I5]* - SUNF[I1, i5, I6] - (120*I)*SUND[I2, I3, i5]*SUNDelta[I4, I5]* - SUNF[I1, i5, I6] + 45*SUND[i1, I4, i8]*SUND[I3, I5, i8]*SUNF[i1, I2, i5]* - SUNF[I1, i5, I6] + 45*SUND[i1, I3, i8]*SUND[I4, I5, i8]*SUNF[i1, I2, i5]* - SUNF[I1, i5, I6] + 45*SUND[i1, I4, i8]*SUND[I2, I5, i8]*SUNF[i1, I3, i5]* - SUNF[I1, i5, I6] + 45*SUND[i1, I2, i8]*SUND[I4, I5, i8]*SUNF[i1, I3, i5]* - SUNF[I1, i5, I6] + 45*SUND[i1, I3, i8]*SUND[I2, I5, i8]*SUNF[i1, I4, i5]* - SUNF[I1, i5, I6] + 45*SUND[i1, I2, i8]*SUND[I3, I5, i8]*SUNF[i1, I4, i5]* - SUNF[I1, i5, I6] + (180*I)*SUND[I2, I3, I4]*SUNF[I1, I5, I6] + - 72*SUND[I3, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I5] + - 72*SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I5] + - 72*SUND[I3, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I5] - - 18*SUND[I3, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i3, i6] - - 18*SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i3, i6] - - 18*SUND[I3, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i3, i6] + - 72*SUND[i1, I5, I6]*SUND[I3, I4, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] + - 72*SUND[i1, I4, I5]*SUND[I3, I6, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] + - 72*SUND[i1, I3, I5]*SUND[I4, I6, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I5, I6]*SUND[I1, I4, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I4, I5]*SUND[I1, I6, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I5]*SUND[I4, I6, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I5, I6]*SUND[I1, I3, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I5]*SUND[I1, I6, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I5]*SUND[I3, I6, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] - - 27*SUND[i1, I4, I5]*SUND[I1, I3, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I5]*SUND[I1, I4, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I5]*SUND[I3, I4, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] + - 18*SUND[i3, i6, I6]*SUND[I3, I4, i8]*SUNF[I1, I5, i6]*SUNF[I2, i3, i8] + - 18*SUND[i3, I4, i6]*SUND[I3, I6, i8]*SUNF[I1, I5, i6]*SUNF[I2, i3, i8] + - 18*SUND[i3, I3, i6]*SUND[I4, I6, i8]*SUNF[I1, I5, i6]*SUNF[I2, i3, i8] + - (27*I)*SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUND[i4, I4, i6]* - SUNF[I2, i4, I5] - (108*I)*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUND[i4, I4, i6]*SUNF[I2, i4, I5] - (108*I)*SUND[I1, i6, i8]* - SUND[I3, I4, i8]*SUND[i4, i6, I6]*SUNF[I2, i4, I5] + - (27*I)*SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUND[i4, i6, I6]* - SUNF[I2, i4, I5] + (27*I)*SUND[I1, I6, i8]*SUND[I3, i4, i6]* - SUND[I4, i6, i8]*SUNF[I2, i4, I5] + (72*I)*SUND[I1, i4, i6]* - SUND[I3, I6, i8]*SUND[I4, i6, i8]*SUNF[I2, i4, I5] + - (27*I)*SUND[I1, I3, i8]*SUND[i4, i6, I6]*SUND[I4, i6, i8]* - SUNF[I2, i4, I5] - (108*I)*SUND[I1, i6, i8]*SUND[I3, i4, i6]* - SUND[I4, I6, i8]*SUNF[I2, i4, I5] + (72*I)*SUND[I1, i4, i6]* - SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[I2, i4, I5] + - (27*I)*SUND[I1, I4, i8]*SUND[I3, i4, i6]*SUND[i6, I6, i8]* - SUNF[I2, i4, I5] + (72*I)*SUND[I1, i4, i6]*SUND[I3, I4, i8]* - SUND[i6, I6, i8]*SUNF[I2, i4, I5] + (27*I)*SUND[I1, I3, i8]* - SUND[i4, I4, i6]*SUND[i6, I6, i8]*SUNF[I2, i4, I5] + - (36*I)*SUND[I4, i5, I6]*SUNDelta[I1, I3]*SUNF[I2, i5, I5] + - (36*I)*SUND[I3, i5, I6]*SUNDelta[I1, I4]*SUNF[I2, i5, I5] + - (36*I)*SUND[I3, I4, i5]*SUNDelta[I1, I6]*SUNF[I2, i5, I5] - - (24*I)*SUND[I1, i5, I6]*SUNDelta[I3, I4]*SUNF[I2, i5, I5] - - (24*I)*SUND[I1, I4, i5]*SUNDelta[I3, I6]*SUNF[I2, i5, I5] - - (24*I)*SUND[I1, I3, i5]*SUNDelta[I4, I6]*SUNF[I2, i5, I5] - - 45*SUND[i3, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, I5, i6] - - 45*SUND[i3, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, I5, i6] - - 45*SUND[i3, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, I5, i6] - - 45*SUND[i3, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I4]*SUNF[I2, I5, i6] - - 45*SUND[i3, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I5, i6] - - 45*SUND[i3, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I5, i6] + - 108*SUND[i3, i6, I6]*SUND[I3, I4, i8]*SUNF[I1, i3, i8]*SUNF[I2, I5, i6] + - 108*SUND[i3, I4, i6]*SUND[I3, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I5, i6] + - 108*SUND[i3, I3, i6]*SUND[I4, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I5, i6] + - 120*SUNDelta[I4, I6]*SUNF[I1, I3, i6]*SUNF[I2, I5, i6] + - 120*SUNDelta[I3, I6]*SUNF[I1, I4, i6]*SUNF[I2, I5, i6] - - 120*SUNDelta[I3, I4]*SUNF[I1, i6, I6]*SUNF[I2, I5, i6] - - (45*I)*SUND[i1, I5, I6]*SUNF[i1, I4, i9]*SUNF[I1, I3, i8]* - SUNF[I2, i8, i9] - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I6, i9]* - SUNF[I1, I3, i8]*SUNF[I2, i8, i9] - (45*I)*SUND[i1, I5, I6]* - SUNF[i1, I3, i9]*SUNF[I1, I4, i8]*SUNF[I2, i8, i9] - - (45*I)*SUND[i1, I3, I5]*SUNF[i1, I6, i9]*SUNF[I1, I4, i8]* - SUNF[I2, i8, i9] - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I3, i9]* - SUNF[I1, I6, i8]*SUNF[I2, i8, i9] - (45*I)*SUND[i1, I3, I5]* - SUNF[i1, I4, i9]*SUNF[I1, I6, i8]*SUNF[I2, i8, i9] - - (108*I)*SUND[I4, I6, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, I5]* - SUNF[i3, I3, i5] - (18*I)*SUND[I4, I6, i8]*SUNF[I1, i3, I5]* - SUNF[I2, i5, i8]*SUNF[i3, I3, i5] - 72*SUND[I2, I6, i8]*SUND[I4, i6, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I3, I5] - 72*SUND[I2, i6, i8]*SUND[I4, I6, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I3, I5] - 72*SUND[I2, I4, i8]*SUND[i6, I6, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I3, I5] - (108*I)*SUND[I4, I6, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, i5]*SUNF[i3, I3, I5] - - 27*SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I3, I5] + - 108*SUND[I1, i6, i8]*SUND[I4, I6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I3, I5] - - 27*SUND[I1, I4, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I3, I5] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, i8]* - SUNF[i3, I3, I5] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, i8]*SUNF[i3, I3, I5] + (72*I)*SUND[I4, I6, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i5, i8]*SUNF[i3, I3, I5] + - 18*SUND[I2, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I5]*SUNF[i3, I3, i6] + - 18*SUND[I2, i6, i8]*SUND[I4, I6, i8]*SUNF[I1, i3, I5]*SUNF[i3, I3, i6] + - 18*SUND[I2, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]*SUNF[i3, I3, i6] - - 27*SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I3, i6] + - 108*SUND[I1, i6, i8]*SUND[I4, I6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I3, i6] - - 27*SUND[I1, I4, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I3, i6] - - 72*SUND[i1, I5, I6]*SUND[I2, I4, i8]*SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - - 72*SUND[i1, I4, I5]*SUND[I2, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - - 72*SUND[i1, I2, I5]*SUND[I4, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - - 27*SUND[i1, I5, I6]*SUND[I1, I4, i8]*SUNF[i1, I2, i3]*SUNF[i3, I3, i8] - - 27*SUND[i1, I4, I5]*SUND[I1, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I3, i8] + - 18*SUND[i1, I1, I5]*SUND[I4, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I3, i8] + - 27*SUND[i1, I5, I6]*SUND[I1, I2, i8]*SUNF[i1, i3, I4]*SUNF[i3, I3, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I6, i8]*SUNF[i1, i3, I4]*SUNF[i3, I3, i8] - - 18*SUND[i1, I1, I5]*SUND[I2, I6, i8]*SUNF[i1, i3, I4]*SUNF[i3, I3, i8] + - 27*SUND[i1, I4, I5]*SUND[I1, I2, i8]*SUNF[i1, i3, I6]*SUNF[i3, I3, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I4, i8]*SUNF[i1, i3, I6]*SUNF[i3, I3, i8] - - 18*SUND[i1, I1, I5]*SUND[I2, I4, i8]*SUNF[i1, i3, I6]*SUNF[i3, I3, i8] - - 18*SUND[I2, I6, i8]*SUND[i3, I4, i6]*SUNF[I1, I5, i6]*SUNF[i3, I3, i8] - - 18*SUND[I2, I4, i8]*SUND[i3, i6, I6]*SUNF[I1, I5, i6]*SUNF[i3, I3, i8] - - 18*SUND[I2, i3, i6]*SUND[I4, I6, i8]*SUNF[I1, I5, i6]*SUNF[i3, I3, i8] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, I5]* - SUNF[i3, I3, i8] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, I5]*SUNF[i3, I3, i8] + 27*SUND[I1, I6, i8]*SUND[i3, I4, i6]* - SUNF[I2, I5, i6]*SUNF[i3, I3, i8] + 27*SUND[I1, I4, i8]*SUND[i3, i6, I6]* - SUNF[I2, I5, i6]*SUNF[i3, I3, i8] + 72*SUND[I1, i3, i6]*SUND[I4, I6, i8]* - SUNF[I2, I5, i6]*SUNF[i3, I3, i8] - (108*I)*SUND[I3, I6, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I5]*SUNF[i3, I4, i5] - - (18*I)*SUND[I3, I6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i5, i8]* - SUNF[i3, I4, i5] + (108*I)*SUND[I2, I6, i8]*SUNF[I1, i5, i8]* - SUNF[i3, I3, I5]*SUNF[i3, I4, i5] - (27*I)*SUND[I1, I6, i8]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I5]*SUNF[i3, I4, i5] - - 72*SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I4, I5] - - 72*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I4, I5] - - 72*SUND[I2, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I4, I5] - - (108*I)*SUND[I3, I6, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I4, I5] - 27*SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, i6]* - SUNF[i3, I4, I5] + 108*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I4, I5] - 27*SUND[I1, I3, i8]*SUND[i6, I6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I4, I5] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I3, i5]*SUNF[I2, i3, i8]*SUNF[i3, I4, I5] + - (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I6]*SUNF[I2, i3, i8]* - SUNF[i3, I4, I5] + (72*I)*SUND[I3, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i5, i8]*SUNF[i3, I4, I5] + (108*I)*SUND[I2, I6, i8]* - SUNF[I1, i5, i8]*SUNF[i3, I3, i5]*SUNF[i3, I4, I5] - - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i5, i8]*SUNF[i3, I3, i5]* - SUNF[i3, I4, I5] + 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, i6]* - SUNF[i3, I4, I5] - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I4, I5] + 27*SUND[I1, I2, i8]*SUND[i6, I6, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I4, I5] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, i8]*SUNF[i3, I4, I5] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I6]*SUNF[i3, I3, i8]* - SUNF[i3, I4, I5] + 18*SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I5]* - SUNF[i3, I4, i6] + 18*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUNF[I1, i3, I5]* - SUNF[i3, I4, i6] + 18*SUND[I2, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]* - SUNF[i3, I4, i6] - 27*SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I5]* - SUNF[i3, I4, i6] + 108*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUNF[I2, i3, I5]*SUNF[i3, I4, i6] - 27*SUND[I1, I3, i8]*SUND[i6, I6, i8]* - SUNF[I2, i3, I5]*SUNF[i3, I4, i6] + 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]* - SUNF[i3, I3, I5]*SUNF[i3, I4, i6] - 108*SUND[I1, i6, i8]* - SUND[I2, I6, i8]*SUNF[i3, I3, I5]*SUNF[i3, I4, i6] + - 27*SUND[I1, I2, i8]*SUND[i6, I6, i8]*SUNF[i3, I3, I5]*SUNF[i3, I4, i6] - - 72*SUND[i1, I5, I6]*SUND[I2, I3, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] - - 72*SUND[i1, I3, I5]*SUND[I2, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] - - 72*SUND[i1, I2, I5]*SUND[I3, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] - - 27*SUND[i1, I5, I6]*SUND[I1, I3, i8]*SUNF[i1, I2, i3]*SUNF[i3, I4, i8] - - 27*SUND[i1, I3, I5]*SUND[I1, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I4, i8] + - 18*SUND[i1, I1, I5]*SUND[I3, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I4, i8] + - 27*SUND[i1, I5, I6]*SUND[I1, I2, i8]*SUNF[i1, i3, I3]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I6, i8]*SUNF[i1, i3, I3]*SUNF[i3, I4, i8] - - 18*SUND[i1, I1, I5]*SUND[I2, I6, i8]*SUNF[i1, i3, I3]*SUNF[i3, I4, i8] + - 27*SUND[i1, I3, I5]*SUND[I1, I2, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I3, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] - - 18*SUND[i1, I1, I5]*SUND[I2, I3, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] - - 18*SUND[I2, I6, i8]*SUND[i3, I3, i6]*SUNF[I1, I5, i6]*SUNF[i3, I4, i8] - - 18*SUND[I2, I3, i8]*SUND[i3, i6, I6]*SUNF[I1, I5, i6]*SUNF[i3, I4, i8] - - 18*SUND[I2, i3, i6]*SUND[I3, I6, i8]*SUNF[I1, I5, i6]*SUNF[i3, I4, i8] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I3, i5]*SUNF[I2, i3, I5]* - SUNF[i3, I4, i8] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, I5]*SUNF[i3, I4, i8] + 27*SUND[I1, I6, i8]*SUND[i3, I3, i6]* - SUNF[I2, I5, i6]*SUNF[i3, I4, i8] + 27*SUND[I1, I3, i8]*SUND[i3, i6, I6]* - SUNF[I2, I5, i6]*SUNF[i3, I4, i8] + 72*SUND[I1, i3, i6]*SUND[I3, I6, i8]* - SUNF[I2, I5, i6]*SUNF[i3, I4, i8] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, I5]*SUNF[i3, I4, i8] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I6]*SUNF[i3, I3, I5]* - SUNF[i3, I4, i8] + (108*I)*SUND[I3, I4, i8]*SUNF[I1, i5, i8]* - SUNF[I2, i3, I5]*SUNF[i3, i5, I6] + (18*I)*SUND[I3, I4, i8]* - SUNF[I1, i3, I5]*SUNF[I2, i5, i8]*SUNF[i3, i5, I6] - - (108*I)*SUND[I2, I4, i8]*SUNF[I1, i5, i8]*SUNF[i3, I3, I5]* - SUNF[i3, i5, I6] + (27*I)*SUND[I1, I4, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I3, I5]*SUNF[i3, i5, I6] - (108*I)*SUND[I2, I3, i8]* - SUNF[I1, i5, i8]*SUNF[i3, I4, I5]*SUNF[i3, i5, I6] + - (27*I)*SUND[I1, I3, i8]*SUNF[I2, i5, i8]*SUNF[i3, I4, I5]* - SUNF[i3, i5, I6] + 72*SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUNF[I1, i3, i6]* - SUNF[i3, I5, I6] + 72*SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, i6]* - SUNF[i3, I5, I6] + 72*SUND[I2, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, i6]* - SUNF[i3, I5, I6] + (108*I)*SUND[I3, I4, i8]*SUNF[I1, i5, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I5, I6] - 108*SUND[I1, i6, i8]* - SUND[I3, I4, i8]*SUNF[I2, i3, i6]*SUNF[i3, I5, I6] + - 27*SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I5, I6] + - 27*SUND[I1, I3, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I5, I6] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i5]*SUNF[I2, i3, i8]* - SUNF[i3, I5, I6] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, I4, i5]* - SUNF[I2, i3, i8]*SUNF[i3, I5, I6] - (72*I)*SUND[I3, I4, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i5, i8]*SUNF[i3, I5, I6] - - (108*I)*SUND[I2, I4, i8]*SUNF[I1, i5, i8]*SUNF[i3, I3, i5]* - SUNF[i3, I5, I6] + (27*I)*SUND[I1, I4, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I3, i5]*SUNF[i3, I5, I6] + 108*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUNF[i3, I3, i6]*SUNF[i3, I5, I6] - - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, i6]*SUNF[i3, I5, I6] - - 27*SUND[I1, I2, i8]*SUND[I4, i6, i8]*SUNF[i3, I3, i6]*SUNF[i3, I5, I6] - - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I2, i5]*SUNF[i3, I3, i8]* - SUNF[i3, I5, I6] - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i5]* - SUNF[i3, I3, i8]*SUNF[i3, I5, I6] - (108*I)*SUND[I2, I3, i8]* - SUNF[I1, i5, i8]*SUNF[i3, I4, i5]*SUNF[i3, I5, I6] + - (27*I)*SUND[I1, I3, i8]*SUNF[I2, i5, i8]*SUNF[i3, I4, i5]* - SUNF[i3, I5, I6] + 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUNF[i3, I4, i6]*SUNF[i3, I5, I6] - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]* - SUNF[i3, I4, i6]*SUNF[i3, I5, I6] - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUNF[i3, I4, i6]*SUNF[i3, I5, I6] - (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I4, i8]*SUNF[i3, I5, I6] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I3, i5]*SUNF[i3, I4, i8]* - SUNF[i3, I5, I6] - 18*SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUNF[I1, i3, I5]* - SUNF[i3, i6, I6] - 18*SUND[I2, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I5]* - SUNF[i3, i6, I6] - 18*SUND[I2, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I5]* - SUNF[i3, i6, I6] - 108*SUND[I1, i6, i8]*SUND[I3, I4, i8]* - SUNF[I2, i3, I5]*SUNF[i3, i6, I6] + 27*SUND[I1, I4, i8]*SUND[I3, i6, i8]* - SUNF[I2, i3, I5]*SUNF[i3, i6, I6] + 27*SUND[I1, I3, i8]*SUND[I4, i6, i8]* - SUNF[I2, i3, I5]*SUNF[i3, i6, I6] + 108*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUNF[i3, I3, I5]*SUNF[i3, i6, I6] - - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I5]*SUNF[i3, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[I4, i6, i8]*SUNF[i3, I3, I5]*SUNF[i3, i6, I6] + - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUNF[i3, I4, I5]*SUNF[i3, i6, I6] - - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i3, I4, I5]*SUNF[i3, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUNF[i3, I4, I5]*SUNF[i3, i6, I6] - - 72*SUND[i1, I4, I5]*SUND[I2, I3, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 72*SUND[i1, I3, I5]*SUND[I2, I4, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 72*SUND[i1, I2, I5]*SUND[I3, I4, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 27*SUND[i1, I4, I5]*SUND[I1, I3, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] - - 27*SUND[i1, I3, I5]*SUND[I1, I4, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] + - 18*SUND[i1, I1, I5]*SUND[I3, I4, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I4, I5]*SUND[I1, I2, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I4, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I5]*SUND[I2, I4, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I3, I5]*SUND[I1, I2, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I3, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I5]*SUND[I2, I3, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] - - 18*SUND[I2, I4, i8]*SUND[i3, I3, i6]*SUNF[I1, I5, i6]*SUNF[i3, I6, i8] - - 18*SUND[I2, I3, i8]*SUND[i3, I4, i6]*SUNF[I1, I5, i6]*SUNF[i3, I6, i8] - - 18*SUND[I2, i3, i6]*SUND[I3, I4, i8]*SUNF[I1, I5, i6]*SUNF[i3, I6, i8] - - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i5]*SUNF[I2, i3, I5]* - SUNF[i3, I6, i8] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I4, i5]* - SUNF[I2, i3, I5]*SUNF[i3, I6, i8] + 27*SUND[I1, I4, i8]*SUND[i3, I3, i6]* - SUNF[I2, I5, i6]*SUNF[i3, I6, i8] + 27*SUND[I1, I3, i8]*SUND[i3, I4, i6]* - SUNF[I2, I5, i6]*SUNF[i3, I6, i8] + 72*SUND[I1, i3, i6]*SUND[I3, I4, i8]* - SUNF[I2, I5, i6]*SUNF[i3, I6, i8] + (45*I)*SUND[I4, i5, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, I5]*SUNF[i3, I6, i8] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i5]*SUNF[i3, I3, I5]* - SUNF[i3, I6, i8] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, I2, i5]* - SUNF[i3, I4, I5]*SUNF[i3, I6, i8] + (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I3, i5]*SUNF[i3, I4, I5]*SUNF[i3, I6, i8] + - (27*I)*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[i4, I4, i6]* - SUNF[I3, i4, I5] - (108*I)*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUND[i4, I4, i6]*SUNF[I3, i4, I5] - (108*I)*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUND[i4, i6, I6]*SUNF[I3, i4, I5] + - (27*I)*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[i4, i6, I6]* - SUNF[I3, i4, I5] + (27*I)*SUND[I1, I6, i8]*SUND[I2, i4, i6]* - SUND[I4, i6, i8]*SUNF[I3, i4, I5] + (72*I)*SUND[I1, i4, i6]* - SUND[I2, I6, i8]*SUND[I4, i6, i8]*SUNF[I3, i4, I5] + - (27*I)*SUND[I1, I2, i8]*SUND[i4, i6, I6]*SUND[I4, i6, i8]* - SUNF[I3, i4, I5] - (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]* - SUND[I4, I6, i8]*SUNF[I3, i4, I5] + (72*I)*SUND[I1, i4, i6]* - SUND[I2, i6, i8]*SUND[I4, I6, i8]*SUNF[I3, i4, I5] + - (27*I)*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[i6, I6, i8]* - SUNF[I3, i4, I5] + (72*I)*SUND[I1, i4, i6]*SUND[I2, I4, i8]* - SUND[i6, I6, i8]*SUNF[I3, i4, I5] + (27*I)*SUND[I1, I2, i8]* - SUND[i4, I4, i6]*SUND[i6, I6, i8]*SUNF[I3, i4, I5] + - (36*I)*SUND[I4, i5, I6]*SUNDelta[I1, I2]*SUNF[I3, i5, I5] + - (36*I)*SUND[I2, i5, I6]*SUNDelta[I1, I4]*SUNF[I3, i5, I5] + - (36*I)*SUND[I2, I4, i5]*SUNDelta[I1, I6]*SUNF[I3, i5, I5] - - (24*I)*SUND[I1, i5, I6]*SUNDelta[I2, I4]*SUNF[I3, i5, I5] - - (24*I)*SUND[I1, I4, i5]*SUNDelta[I2, I6]*SUNF[I3, i5, I5] - - (24*I)*SUND[I1, I2, i5]*SUNDelta[I4, I6]*SUNF[I3, i5, I5] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i7]*SUNF[I2, I5, i8]* - SUNF[I3, i5, i7] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, I5, i8]*SUNF[I3, i5, i7] + (18*I)*SUND[I4, I6, i8]* - SUNF[I1, i3, I5]*SUNF[I2, i3, i5]*SUNF[I3, i5, i8] - - (72*I)*SUND[I4, I6, i8]*SUNF[I1, i3, i5]*SUNF[I2, i3, I5]* - SUNF[I3, i5, i8] - (18*I)*SUND[I2, I6, i8]*SUNF[I1, i3, I5]* - SUNF[i3, I4, i5]*SUNF[I3, i5, i8] + (27*I)*SUND[I1, I6, i8]* - SUNF[I2, i3, I5]*SUNF[i3, I4, i5]*SUNF[I3, i5, i8] + - (72*I)*SUND[I2, I6, i8]*SUNF[I1, i3, i5]*SUNF[i3, I4, I5]* - SUNF[I3, i5, i8] + (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I4, I5]*SUNF[I3, i5, i8] + (18*I)*SUND[I2, I4, i8]* - SUNF[I1, i3, I5]*SUNF[i3, i5, I6]*SUNF[I3, i5, i8] - - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, I5]*SUNF[i3, i5, I6]* - SUNF[I3, i5, i8] + (27*I)*SUND[I1, I2, i8]*SUNF[i3, I4, I5]* - SUNF[i3, i5, I6]*SUNF[I3, i5, i8] - (72*I)*SUND[I2, I4, i8]* - SUNF[I1, i3, i5]*SUNF[i3, I5, I6]*SUNF[I3, i5, i8] - - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, i5]*SUNF[i3, I5, I6]* - SUNF[I3, i5, i8] + (27*I)*SUND[I1, I2, i8]*SUNF[i3, I4, i5]* - SUNF[i3, I5, I6]*SUNF[I3, i5, i8] + 45*SUND[i3, I6, i8]*SUND[I4, i6, i8]* - SUNF[I1, I2, i3]*SUNF[I3, I5, i6] + 45*SUND[i3, I4, i8]*SUND[i6, I6, i8]* - SUNF[I1, I2, i3]*SUNF[I3, I5, i6] + 120*SUNDelta[I4, I6]* - SUNF[I1, I2, i6]*SUNF[I3, I5, i6] - 45*SUND[I2, i6, i8]*SUND[i3, I6, i8]* - SUNF[I1, i3, I4]*SUNF[I3, I5, i6] - 45*SUND[I2, i3, i8]*SUND[i6, I6, i8]* - SUNF[I1, i3, I4]*SUNF[I3, I5, i6] - 45*SUND[I2, i6, i8]*SUND[i3, I4, i8]* - SUNF[I1, i3, I6]*SUNF[I3, I5, i6] - 45*SUND[I2, i3, i8]*SUND[I4, i6, i8]* - SUNF[I1, i3, I6]*SUNF[I3, I5, i6] + 108*SUND[I2, I6, i8]* - SUND[i3, I4, i6]*SUNF[I1, i3, i8]*SUNF[I3, I5, i6] + - 108*SUND[I2, I4, i8]*SUND[i3, i6, I6]*SUNF[I1, i3, i8]*SUNF[I3, I5, i6] + - 108*SUND[I2, i3, i6]*SUND[I4, I6, i8]*SUNF[I1, i3, i8]*SUNF[I3, I5, i6] + - 120*SUNDelta[I2, I6]*SUNF[I1, I4, i6]*SUNF[I3, I5, i6] - - 120*SUNDelta[I2, I4]*SUNF[I1, i6, I6]*SUNF[I3, I5, i6] - - 27*SUND[I1, I6, i8]*SUND[i3, I4, i6]*SUNF[I2, i3, i8]*SUNF[I3, I5, i6] - - 27*SUND[I1, I4, i8]*SUND[i3, i6, I6]*SUNF[I2, i3, i8]*SUNF[I3, I5, i6] - - 72*SUND[I1, i3, i6]*SUND[I4, I6, i8]*SUNF[I2, i3, i8]*SUNF[I3, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i3, i6]*SUNF[i3, I4, i8]*SUNF[I3, I5, i6] + - 72*SUND[I1, i3, i6]*SUND[I2, I6, i8]*SUNF[i3, I4, i8]*SUNF[I3, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[i3, i6, I6]*SUNF[i3, I4, i8]*SUNF[I3, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[I2, i3, i6]*SUNF[i3, I6, i8]*SUNF[I3, I5, i6] + - 72*SUND[I1, i3, i6]*SUND[I2, I4, i8]*SUNF[i3, I6, i8]*SUNF[I3, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[i3, I4, i6]*SUNF[i3, I6, i8]*SUNF[I3, I5, i6] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i7]*SUNF[I2, i5, i7]* - SUNF[I3, I5, i8] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, i5, i7]*SUNF[I3, I5, i8] - (45*I)*SUND[i1, I5, I6]* - SUNF[i1, I4, i9]*SUNF[I1, I2, i8]*SUNF[I3, i8, i9] - - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I6, i9]*SUNF[I1, I2, i8]* - SUNF[I3, i8, i9] - (45*I)*SUND[i1, I5, I6]*SUNF[i1, I2, i9]* - SUNF[I1, I4, i8]*SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I5]* - SUNF[i1, I6, i9]*SUNF[I1, I4, i8]*SUNF[I3, i8, i9] - - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I2, i9]*SUNF[I1, I6, i8]* - SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I4, i9]* - SUNF[I1, I6, i8]*SUNF[I3, i8, i9] - (27*I)*SUND[I1, I6, i8]* - SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUNF[i4, I4, I5] + - (108*I)*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUND[I3, i4, i6]* - SUNF[i4, I4, I5] - (27*I)*SUND[I1, I6, i8]*SUND[I2, i4, i6]* - SUND[I3, i6, i8]*SUNF[i4, I4, I5] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUNF[i4, I4, I5] + - (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, I6, i8]* - SUNF[i4, I4, I5] - (72*I)*SUND[I1, i4, i6]*SUND[I2, i6, i8]* - SUND[I3, I6, i8]*SUNF[i4, I4, I5] + (108*I)*SUND[I1, i6, i8]* - SUND[I2, I3, i8]*SUND[i4, i6, I6]*SUNF[i4, I4, I5] - - (27*I)*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, i6, I6]* - SUNF[i4, I4, I5] - (27*I)*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUND[i4, i6, I6]*SUNF[i4, I4, I5] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, I3, i8]*SUND[i6, I6, i8]*SUNF[i4, I4, I5] - - (27*I)*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[i6, I6, i8]* - SUNF[i4, I4, I5] - (27*I)*SUND[I1, I2, i8]*SUND[I3, i4, i6]* - SUND[i6, I6, i8]*SUNF[i4, I4, I5] - (108*I)*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUND[I3, i4, i6]*SUNF[i4, I5, I6] + - (27*I)*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]* - SUNF[i4, I5, I6] - (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]* - SUND[I3, I4, i8]*SUNF[i4, I5, I6] + (72*I)*SUND[I1, i4, i6]* - SUND[I2, i6, i8]*SUND[I3, I4, i8]*SUNF[i4, I5, I6] + - (27*I)*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]* - SUNF[i4, I5, I6] + (72*I)*SUND[I1, i4, i6]*SUND[I2, I4, i8]* - SUND[I3, i6, i8]*SUNF[i4, I5, I6] - (108*I)*SUND[I1, i6, i8]* - SUND[I2, I3, i8]*SUND[i4, I4, i6]*SUNF[i4, I5, I6] + - (27*I)*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I4, i6]* - SUNF[i4, I5, I6] + (27*I)*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUND[i4, I4, i6]*SUNF[i4, I5, I6] + (72*I)*SUND[I1, i4, i6]* - SUND[I2, I3, i8]*SUND[I4, i6, i8]*SUNF[i4, I5, I6] + - (27*I)*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[I4, i6, i8]* - SUNF[i4, I5, I6] + (27*I)*SUND[I1, I2, i8]*SUND[I3, i4, i6]* - SUND[I4, i6, i8]*SUNF[i4, I5, I6] + (36*I)*SUND[I3, i5, I6]* - SUNDelta[I1, I2]*SUNF[I4, i5, I5] + (36*I)*SUND[I2, i5, I6]* - SUNDelta[I1, I3]*SUNF[I4, i5, I5] + (36*I)*SUND[I2, I3, i5]* - SUNDelta[I1, I6]*SUNF[I4, i5, I5] - (24*I)*SUND[I1, i5, I6]* - SUNDelta[I2, I3]*SUNF[I4, i5, I5] - (24*I)*SUND[I1, I3, i5]* - SUNDelta[I2, I6]*SUNF[I4, i5, I5] - (24*I)*SUND[I1, I2, i5]* - SUNDelta[I3, I6]*SUNF[I4, i5, I5] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I3, i7]*SUNF[I2, I5, i8]*SUNF[I4, i5, i7] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I6, i7]*SUNF[I2, I5, i8]* - SUNF[I4, i5, i7] - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I2, i7]* - SUNF[I3, I5, i8]*SUNF[I4, i5, i7] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I6, i7]*SUNF[I3, I5, i8]*SUNF[I4, i5, i7] + - (18*I)*SUND[I3, I6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i3, i5]* - SUNF[I4, i5, i8] - (72*I)*SUND[I3, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I5]*SUNF[I4, i5, i8] - (18*I)*SUND[I2, I6, i8]* - SUNF[I1, i3, I5]*SUNF[i3, I3, i5]*SUNF[I4, i5, i8] + - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I3, i5]* - SUNF[I4, i5, i8] + (72*I)*SUND[I2, I6, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I3, I5]*SUNF[I4, i5, i8] + (27*I)*SUND[I1, I6, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I3, I5]*SUNF[I4, i5, i8] + - (18*I)*SUND[I2, I3, i8]*SUNF[I1, i3, I5]*SUNF[i3, i5, I6]* - SUNF[I4, i5, i8] - (27*I)*SUND[I1, I3, i8]*SUNF[I2, i3, I5]* - SUNF[i3, i5, I6]*SUNF[I4, i5, i8] + (27*I)*SUND[I1, I2, i8]* - SUNF[i3, I3, I5]*SUNF[i3, i5, I6]*SUNF[I4, i5, i8] - - (72*I)*SUND[I2, I3, i8]*SUNF[I1, i3, i5]*SUNF[i3, I5, I6]* - SUNF[I4, i5, i8] - (27*I)*SUND[I1, I3, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I5, I6]*SUNF[I4, i5, i8] + (27*I)*SUND[I1, I2, i8]* - SUNF[i3, I3, i5]*SUNF[i3, I5, I6]*SUNF[I4, i5, i8] + - 45*SUND[i3, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, I2, i3]*SUNF[I4, I5, i6] + - 45*SUND[i3, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, I2, i3]*SUNF[I4, I5, i6] + - 120*SUNDelta[I3, I6]*SUNF[I1, I2, i6]*SUNF[I4, I5, i6] - - 45*SUND[I2, i6, i8]*SUND[i3, I6, i8]*SUNF[I1, i3, I3]*SUNF[I4, I5, i6] - - 45*SUND[I2, i3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I3]*SUNF[I4, I5, i6] - - 45*SUND[I2, i6, i8]*SUND[i3, I3, i8]*SUNF[I1, i3, I6]*SUNF[I4, I5, i6] - - 45*SUND[I2, i3, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I6]*SUNF[I4, I5, i6] + - 108*SUND[I2, I6, i8]*SUND[i3, I3, i6]*SUNF[I1, i3, i8]*SUNF[I4, I5, i6] + - 108*SUND[I2, I3, i8]*SUND[i3, i6, I6]*SUNF[I1, i3, i8]*SUNF[I4, I5, i6] + - 108*SUND[I2, i3, i6]*SUND[I3, I6, i8]*SUNF[I1, i3, i8]*SUNF[I4, I5, i6] + - 120*SUNDelta[I2, I6]*SUNF[I1, I3, i6]*SUNF[I4, I5, i6] - - 120*SUNDelta[I2, I3]*SUNF[I1, i6, I6]*SUNF[I4, I5, i6] - - 27*SUND[I1, I6, i8]*SUND[i3, I3, i6]*SUNF[I2, i3, i8]*SUNF[I4, I5, i6] - - 27*SUND[I1, I3, i8]*SUND[i3, i6, I6]*SUNF[I2, i3, i8]*SUNF[I4, I5, i6] - - 72*SUND[I1, i3, i6]*SUND[I3, I6, i8]*SUNF[I2, i3, i8]*SUNF[I4, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i3, i6]*SUNF[i3, I3, i8]*SUNF[I4, I5, i6] + - 72*SUND[I1, i3, i6]*SUND[I2, I6, i8]*SUNF[i3, I3, i8]*SUNF[I4, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[i3, i6, I6]*SUNF[i3, I3, i8]*SUNF[I4, I5, i6] + - 27*SUND[I1, I3, i8]*SUND[I2, i3, i6]*SUNF[i3, I6, i8]*SUNF[I4, I5, i6] + - 72*SUND[I1, i3, i6]*SUND[I2, I3, i8]*SUNF[i3, I6, i8]*SUNF[I4, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[i3, I3, i6]*SUNF[i3, I6, i8]*SUNF[I4, I5, i6] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I3, i7]*SUNF[I2, i5, i7]* - SUNF[I4, I5, i8] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, i5, i7]*SUNF[I4, I5, i8] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I2, i7]*SUNF[I3, i5, i7]*SUNF[I4, I5, i8] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I6, i7]*SUNF[I3, i5, i7]* - SUNF[I4, I5, i8] + 45*SUNF[I1, i6, I6]*SUNF[I2, i8, i9]*SUNF[I3, i6, i8]* - SUNF[I4, I5, i9] + 45*SUNF[I1, i6, I6]*SUNF[I2, i6, i8]*SUNF[I3, i8, i9]* - SUNF[I4, I5, i9] + 45*SUNF[I1, i6, I6]*SUNF[I2, i8, i9]*SUNF[I3, I5, i9]* - SUNF[I4, i6, i8] + 45*SUNF[I1, i6, I6]*SUNF[I2, I5, i9]*SUNF[I3, i8, i9]* - SUNF[I4, i6, i8] - (45*I)*SUND[i1, I5, I6]*SUNF[i1, I3, i9]* - SUNF[I1, I2, i8]*SUNF[I4, i8, i9] - (45*I)*SUND[i1, I3, I5]* - SUNF[i1, I6, i9]*SUNF[I1, I2, i8]*SUNF[I4, i8, i9] - - (45*I)*SUND[i1, I5, I6]*SUNF[i1, I2, i9]*SUNF[I1, I3, i8]* - SUNF[I4, i8, i9] - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I6, i9]* - SUNF[I1, I3, i8]*SUNF[I4, i8, i9] - (45*I)*SUND[i1, I3, I5]* - SUNF[i1, I2, i9]*SUNF[I1, I6, i8]*SUNF[I4, i8, i9] - - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I3, i9]*SUNF[I1, I6, i8]* - SUNF[I4, i8, i9] + 45*SUNF[I1, i6, I6]*SUNF[I2, i6, i8]*SUNF[I3, I5, i9]* - SUNF[I4, i8, i9] + 45*SUNF[I1, i6, I6]*SUNF[I2, I5, i9]*SUNF[I3, i6, i8]* - SUNF[I4, i8, i9] + (36*I)*SUND[I3, I4, i5]*SUNDelta[I1, I2]* - SUNF[i5, I5, I6] + (36*I)*SUND[I2, I4, i5]*SUNDelta[I1, I3]* - SUNF[i5, I5, I6] + (36*I)*SUND[I2, I3, i5]*SUNDelta[I1, I4]* - SUNF[i5, I5, I6] - (24*I)*SUND[I1, I4, i5]*SUNDelta[I2, I3]* - SUNF[i5, I5, I6] - (24*I)*SUND[I1, I3, i5]*SUNDelta[I2, I4]* - SUNF[i5, I5, I6] - (24*I)*SUND[I1, I2, i5]*SUNDelta[I3, I4]* - SUNF[i5, I5, I6] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i7]* - SUNF[I2, I5, i8]*SUNF[i5, I6, i7] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I4, i7]*SUNF[I2, I5, i8]*SUNF[i5, I6, i7] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I2, i7]*SUNF[I3, I5, i8]* - SUNF[i5, I6, i7] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i7]* - SUNF[I3, I5, i8]*SUNF[i5, I6, i7] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I2, i7]*SUNF[I4, I5, i8]*SUNF[i5, I6, i7] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I3, i7]*SUNF[I4, I5, i8]* - SUNF[i5, I6, i7] - (18*I)*SUND[I3, I4, i8]*SUNF[I1, i3, I5]* - SUNF[I2, i3, i5]*SUNF[i5, I6, i8] + (72*I)*SUND[I3, I4, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I5]*SUNF[i5, I6, i8] + - (18*I)*SUND[I2, I4, i8]*SUNF[I1, i3, I5]*SUNF[i3, I3, i5]* - SUNF[i5, I6, i8] - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, I5]* - SUNF[i3, I3, i5]*SUNF[i5, I6, i8] - (72*I)*SUND[I2, I4, i8]* - SUNF[I1, i3, i5]*SUNF[i3, I3, I5]*SUNF[i5, I6, i8] - - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, i5]*SUNF[i3, I3, I5]* - SUNF[i5, I6, i8] + (18*I)*SUND[I2, I3, i8]*SUNF[I1, i3, I5]* - SUNF[i3, I4, i5]*SUNF[i5, I6, i8] - (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I5]*SUNF[i3, I4, i5]*SUNF[i5, I6, i8] + - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I5]*SUNF[i3, I4, i5]* - SUNF[i5, I6, i8] - (72*I)*SUND[I2, I3, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I4, I5]*SUNF[i5, I6, i8] - (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I4, I5]*SUNF[i5, I6, i8] + - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, i5]*SUNF[i3, I4, I5]* - SUNF[i5, I6, i8] + 45*SUND[i3, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I5, i6, I6] + 45*SUND[i3, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I5, i6, I6] + 120*SUNDelta[I3, I4]*SUNF[I1, I2, i6]* - SUNF[I5, i6, I6] - 45*SUND[I2, i6, i8]*SUND[i3, I4, i8]*SUNF[I1, i3, I3]* - SUNF[I5, i6, I6] - 45*SUND[I2, i3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I3]* - SUNF[I5, i6, I6] - 45*SUND[I2, i6, i8]*SUND[i3, I3, i8]*SUNF[I1, i3, I4]* - SUNF[I5, i6, I6] - 45*SUND[I2, i3, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I4]* - SUNF[I5, i6, I6] + 108*SUND[I2, I4, i8]*SUND[i3, I3, i6]* - SUNF[I1, i3, i8]*SUNF[I5, i6, I6] + 108*SUND[I2, I3, i8]* - SUND[i3, I4, i6]*SUNF[I1, i3, i8]*SUNF[I5, i6, I6] + - 108*SUND[I2, i3, i6]*SUND[I3, I4, i8]*SUNF[I1, i3, i8]*SUNF[I5, i6, I6] + - 120*SUNDelta[I2, I4]*SUNF[I1, I3, i6]*SUNF[I5, i6, I6] + - 120*SUNDelta[I2, I3]*SUNF[I1, I4, i6]*SUNF[I5, i6, I6] - - 27*SUND[I1, I4, i8]*SUND[i3, I3, i6]*SUNF[I2, i3, i8]*SUNF[I5, i6, I6] - - 27*SUND[I1, I3, i8]*SUND[i3, I4, i6]*SUNF[I2, i3, i8]*SUNF[I5, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I3, I4, i8]*SUNF[I2, i3, i8]*SUNF[I5, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i3, i6]*SUNF[i3, I3, i8]*SUNF[I5, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I2, I4, i8]*SUNF[i3, I3, i8]*SUNF[I5, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[i3, I4, i6]*SUNF[i3, I3, i8]*SUNF[I5, i6, I6] + - 27*SUND[I1, I3, i8]*SUND[I2, i3, i6]*SUNF[i3, I4, i8]*SUNF[I5, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I2, I3, i8]*SUNF[i3, I4, i8]*SUNF[I5, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[i3, I3, i6]*SUNF[i3, I4, i8]*SUNF[I5, i6, I6] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i7]*SUNF[I2, i5, i7]* - SUNF[I5, I6, i8] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, I4, i7]* - SUNF[I2, i5, i7]*SUNF[I5, I6, i8] + (45*I)*SUND[I4, i5, i8]* - SUNF[I1, I2, i7]*SUNF[I3, i5, i7]*SUNF[I5, I6, i8] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i7]*SUNF[I3, i5, i7]* - SUNF[I5, I6, i8] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, I2, i7]* - SUNF[I4, i5, i7]*SUNF[I5, I6, i8] + (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I3, i7]*SUNF[I4, i5, i7]*SUNF[I5, I6, i8] + - 45*SUNF[I1, I4, i6]*SUNF[I2, i8, i9]*SUNF[I3, i6, i8]*SUNF[I5, I6, i9] + - 45*SUNF[I1, I4, i6]*SUNF[I2, i6, i8]*SUNF[I3, i8, i9]*SUNF[I5, I6, i9] + - 45*SUNF[I1, I3, i6]*SUNF[I2, i8, i9]*SUNF[I4, i6, i8]*SUNF[I5, I6, i9] + - 45*SUNF[I1, I2, i6]*SUNF[I3, i8, i9]*SUNF[I4, i6, i8]*SUNF[I5, I6, i9] + - 45*SUNF[I1, I3, i6]*SUNF[I2, i6, i8]*SUNF[I4, i8, i9]*SUNF[I5, I6, i9] + - 45*SUNF[I1, I2, i6]*SUNF[I3, i6, i8]*SUNF[I4, i8, i9]*SUNF[I5, I6, i9] + - 45*SUNF[I1, I4, i6]*SUNF[I2, i8, i9]*SUNF[I3, I5, i9]*SUNF[i6, I6, i8] + - 45*SUNF[I1, I4, i6]*SUNF[I2, I5, i9]*SUNF[I3, i8, i9]*SUNF[i6, I6, i8] + - 45*SUNF[I1, I3, i6]*SUNF[I2, i8, i9]*SUNF[I4, I5, i9]*SUNF[i6, I6, i8] + - 45*SUNF[I1, I2, i6]*SUNF[I3, i8, i9]*SUNF[I4, I5, i9]*SUNF[i6, I6, i8] + - 45*SUNF[I1, I3, i6]*SUNF[I2, I5, i9]*SUNF[I4, i8, i9]*SUNF[i6, I6, i8] + - 45*SUNF[I1, I2, i6]*SUNF[I3, I5, i9]*SUNF[I4, i8, i9]*SUNF[i6, I6, i8] - - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I3, i9]*SUNF[I1, I2, i8]* - SUNF[I6, i8, i9] - (45*I)*SUND[i1, I3, I5]*SUNF[i1, I4, i9]* - SUNF[I1, I2, i8]*SUNF[I6, i8, i9] - (45*I)*SUND[i1, I4, I5]* - SUNF[i1, I2, i9]*SUNF[I1, I3, i8]*SUNF[I6, i8, i9] - - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I4, i9]*SUNF[I1, I3, i8]* - SUNF[I6, i8, i9] - (45*I)*SUND[i1, I3, I5]*SUNF[i1, I2, i9]* - SUNF[I1, I4, i8]*SUNF[I6, i8, i9] - (45*I)*SUND[i1, I2, I5]* - SUNF[i1, I3, i9]*SUNF[I1, I4, i8]*SUNF[I6, i8, i9] - - 45*SUNF[I1, I4, i6]*SUNF[I2, i6, i8]*SUNF[I3, I5, i9]*SUNF[I6, i8, i9] - - 45*SUNF[I1, I4, i6]*SUNF[I2, I5, i9]*SUNF[I3, i6, i8]*SUNF[I6, i8, i9] - - 45*SUNF[I1, I3, i6]*SUNF[I2, i6, i8]*SUNF[I4, I5, i9]*SUNF[I6, i8, i9] - - 45*SUNF[I1, I2, i6]*SUNF[I3, i6, i8]*SUNF[I4, I5, i9]*SUNF[I6, i8, i9] - - 45*SUNF[I1, I3, i6]*SUNF[I2, I5, i9]*SUNF[I4, i6, i8]*SUNF[I6, i8, i9] - - 45*SUNF[I1, I2, i6]*SUNF[I3, I5, i9]*SUNF[I4, i6, i8]*SUNF[I6, i8, i9])/ -(1080*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-72*SUND[I1, I5, I6]*SUND[I2, I3, I4] - 72*SUND[I1, I4, I6]* - SUND[I2, I3, I5] - 72*SUND[I1, I4, I5]*SUND[I2, I3, I6] - - 72*SUND[I1, I3, I6]*SUND[I2, I4, I5] - 72*SUND[I1, I3, I5]* - SUND[I2, I4, I6] - 72*SUND[I1, I3, I4]*SUND[I2, I5, I6] + - 108*SUND[I1, I2, I6]*SUND[I3, I4, I5] + 108*SUND[I1, I2, I5]* - SUND[I3, I4, I6] + 108*SUND[I1, I2, I4]*SUND[I3, I5, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I6]*SUND[I3, I5, i8]*SUND[i4, I4, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, I5]*SUND[I3, i6, i8]*SUND[i4, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, I6]*SUND[I3, i6, i8]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I5]*SUND[I3, I6, i8]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I6]*SUND[I3, I4, i8]*SUND[i4, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, I4]*SUND[I3, i6, i8]*SUND[i4, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, I6]*SUND[I3, i6, i8]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I4]*SUND[I3, I6, i8]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I5]*SUND[I3, I4, i8]*SUND[i4, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I4]*SUND[I3, I5, i8]*SUND[i4, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, I4]*SUND[I3, i6, i8]*SUND[i4, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, I5]*SUND[I3, i6, i8]*SUND[i4, i6, I6] + - 108*SUND[I1, I2, I3]*SUND[I4, I5, I6] - 108*SUND[I1, i6, i8]* - SUND[I2, i4, I6]*SUND[I3, i4, i6]*SUND[I4, I5, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I6]*SUND[I3, i6, i8]*SUND[I4, I5, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i4]*SUND[i4, i6, I6]*SUND[I4, I5, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, i6, i8]*SUND[i4, i6, I6]*SUND[I4, I5, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, I5]*SUND[I3, i4, i6]*SUND[I4, i6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, I6]*SUND[I3, i4, i6]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I6]*SUND[I3, I5, i8]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I5]*SUND[I3, I6, i8]*SUND[I4, i6, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, I3, i4]*SUND[i4, I5, i6]*SUND[I4, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I6]*SUND[i4, I5, i6]*SUND[I4, i6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, I6, i8]*SUND[i4, I5, i6]*SUND[I4, i6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, I3, i4]*SUND[i4, i6, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I5]*SUND[i4, i6, I6]*SUND[I4, i6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, I5, i8]*SUND[i4, i6, I6]*SUND[I4, i6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I5]*SUND[I3, i4, i6]*SUND[I4, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I5]*SUND[I3, i6, i8]*SUND[I4, I6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i4]*SUND[i4, I5, i6]*SUND[I4, I6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, i6, i8]*SUND[i4, I5, i6]*SUND[I4, I6, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, I4]*SUND[I3, i4, i6]*SUND[I5, i6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, I6]*SUND[I3, i4, i6]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I6]*SUND[I3, I4, i8]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I4]*SUND[I3, I6, i8]*SUND[I5, i6, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, I3, i4]*SUND[i4, I4, i6]*SUND[I5, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I6]*SUND[i4, I4, i6]*SUND[I5, i6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, I6, i8]*SUND[i4, I4, i6]*SUND[I5, i6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, I3, i4]*SUND[i4, i6, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I4]*SUND[i4, i6, I6]*SUND[I5, i6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, I4, i8]*SUND[i4, i6, I6]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i4]*SUND[I4, I6, i8]*SUND[I5, i6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, i4, i6]*SUND[I4, I6, i8]*SUND[I5, i6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I4]*SUND[I3, i4, i6]*SUND[I5, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I4]*SUND[I3, i6, i8]*SUND[I5, I6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i4]*SUND[i4, I4, i6]*SUND[I5, I6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, i6, i8]*SUND[i4, I4, i6]*SUND[I5, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i4]*SUND[I4, i6, i8]*SUND[I5, I6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, i4, i6]*SUND[I4, i6, i8]*SUND[I5, I6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, I4]*SUND[I3, i4, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, I5]*SUND[I3, i4, i6]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I5]*SUND[I3, I4, i8]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I4]*SUND[I3, I5, i8]*SUND[i6, I6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, I3, i4]*SUND[i4, I4, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I5]*SUND[i4, I4, i6]*SUND[i6, I6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, I5, i8]*SUND[i4, I4, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, I3, i4]*SUND[i4, I5, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I4]*SUND[i4, I5, i6]*SUND[i6, I6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, I4, i8]*SUND[i4, I5, i6]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i4]*SUND[I4, I5, i8]*SUND[i6, I6, i8] - - 18*SUND[I1, I2, i4]*SUND[I3, i4, i6]*SUND[I4, I5, i8]*SUND[i6, I6, i8] - - 48*SUND[I3, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I2] - - 48*SUND[I3, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I2] - - 48*SUND[I3, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I2] + - 36*SUND[I2, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I3] + - 36*SUND[I2, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I3] + - 36*SUND[I2, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I3] + - 36*SUND[I2, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I1, I4] + - 36*SUND[I2, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I1, I4] + - 36*SUND[I2, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I4] + - 36*SUND[I2, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I1, I5] + - 36*SUND[I2, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I1, I5] + - 36*SUND[I2, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I1, I5] + - 36*SUND[I2, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I1, I6] + - 36*SUND[I2, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I1, I6] + - 36*SUND[I2, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I1, I6] + - 12*SUND[I1, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I2, I3] + - 12*SUND[I1, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I2, I3] + - 12*SUND[I1, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I3] + - 12*SUND[I1, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I2, I4] + - 12*SUND[I1, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I2, I4] + - 12*SUND[I1, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I4] + - 12*SUND[I1, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I2, I5] + - 12*SUND[I1, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I2, I5] + - 12*SUND[I1, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I2, I5] + - 12*SUND[I1, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I2, I6] + - 12*SUND[I1, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I2, I6] + - 12*SUND[I1, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I2, I6] - - 24*SUND[I1, i5, I6]*SUND[I2, i5, I5]*SUNDelta[I3, I4] - - 24*SUND[I1, i5, I5]*SUND[I2, i5, I6]*SUNDelta[I3, I4] - - 24*SUND[I1, I2, i5]*SUND[i5, I5, I6]*SUNDelta[I3, I4] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 24*SUND[I1, i5, I6]*SUND[I2, I4, i5]*SUNDelta[I3, I5] - - 24*SUND[I1, I4, i5]*SUND[I2, i5, I6]*SUNDelta[I3, I5] - - 24*SUND[I1, I2, i5]*SUND[I4, i5, I6]*SUNDelta[I3, I5] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 24*SUND[I1, i5, I5]*SUND[I2, I4, i5]*SUNDelta[I3, I6] - - 24*SUND[I1, I4, i5]*SUND[I2, i5, I5]*SUNDelta[I3, I6] - - 24*SUND[I1, I2, i5]*SUND[I4, i5, I5]*SUNDelta[I3, I6] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 24*SUND[I1, i5, I6]*SUND[I2, I3, i5]*SUNDelta[I4, I5] - - 24*SUND[I1, I3, i5]*SUND[I2, i5, I6]*SUNDelta[I4, I5] - - 24*SUND[I1, I2, i5]*SUND[I3, i5, I6]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 32*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 24*SUND[I1, i5, I5]*SUND[I2, I3, i5]*SUNDelta[I4, I6] - - 24*SUND[I1, I3, i5]*SUND[I2, i5, I5]*SUNDelta[I4, I6] - - 24*SUND[I1, I2, i5]*SUND[I3, i5, I5]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 32*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 24*SUND[I1, I4, i5]*SUND[I2, I3, i5]*SUNDelta[I5, I6] - - 24*SUND[I1, I3, i5]*SUND[I2, I4, i5]*SUNDelta[I5, I6] - - 24*SUND[I1, I2, i5]*SUND[I3, I4, i5]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 32*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, I5, i6]*SUND[I4, i6, i8]* - SUNF[i1, I1, I3] + (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, I6]* - SUND[I4, i6, i8]*SUNF[i1, I1, I3] + (45*I)*SUND[i1, I6, i8]* - SUND[I2, I4, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I3] + - (45*I)*SUND[i1, I4, i8]*SUND[I2, i6, I6]*SUND[I5, i6, i8]* - SUNF[i1, I1, I3] + (45*I)*SUND[i1, I5, i8]*SUND[I2, I4, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I3] + (45*I)*SUND[i1, I4, i8]* - SUND[I2, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I5, I6]*SUNDelta[I2, I4]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I4, I6]*SUNDelta[I2, I5]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I4, I5]*SUNDelta[I2, I6]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I2, I6]*SUNDelta[I4, I5]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I2, I5]*SUNDelta[I4, I6]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I2, I4]*SUNDelta[I5, I6]*SUNF[i1, I1, I3] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, I5, i6]*SUND[I3, i6, i8]* - SUNF[i1, I1, I4] + (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, I6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I4] + (45*I)*SUND[i1, I6, i8]* - SUND[I2, I3, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I4] + - (45*I)*SUND[i1, I3, i8]*SUND[I2, i6, I6]*SUND[I5, i6, i8]* - SUNF[i1, I1, I4] + (45*I)*SUND[i1, I5, i8]*SUND[I2, I3, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I4] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I5, I6]*SUNDelta[I2, I3]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I3, I6]*SUNDelta[I2, I5]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I3, I5]*SUNDelta[I2, I6]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I2, I6]*SUNDelta[I3, I5]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I2, I5]*SUNDelta[I3, I6]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I2, I3]*SUNDelta[I5, I6]*SUNF[i1, I1, I4] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, I4, i6]*SUND[I3, i6, i8]* - SUNF[i1, I1, I5] + (45*I)*SUND[i1, I4, i8]*SUND[I2, i6, I6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I5] + (45*I)*SUND[i1, I6, i8]* - SUND[I2, I3, i6]*SUND[I4, i6, i8]*SUNF[i1, I1, I5] + - (45*I)*SUND[i1, I3, i8]*SUND[I2, i6, I6]*SUND[I4, i6, i8]* - SUNF[i1, I1, I5] + (45*I)*SUND[i1, I4, i8]*SUND[I2, I3, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I5] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, I4, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I4, I6]*SUNDelta[I2, I3]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I3, I6]*SUNDelta[I2, I4]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I3, I4]*SUNDelta[I2, I6]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I2, I6]*SUNDelta[I3, I4]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I2, I4]*SUNDelta[I3, I6]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I2, I3]*SUNDelta[I4, I6]*SUNF[i1, I1, I5] + - (72*I)*SUND[i1, I2, I6]*SUND[I3, i6, i8]*SUND[I4, I5, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I6]*SUND[I3, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I5]* - SUND[I3, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I2, I5]*SUND[I3, i6, i8]*SUND[I4, I6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I6]*SUND[I3, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I4]* - SUND[I3, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I2, I3]*SUND[I4, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I4]*SUND[I3, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I3]* - SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I2, I5]*SUND[I3, I4, i8]*SUND[i6, I6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I4]*SUND[I3, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I3]* - SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I1, i6] + - (45*I)*SUND[i1, I5, i8]*SUND[I2, I4, i6]*SUND[I3, i6, i8]* - SUNF[i1, I1, I6] + (45*I)*SUND[i1, I4, i8]*SUND[I2, I5, i6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I6] + (45*I)*SUND[i1, I5, i8]* - SUND[I2, I3, i6]*SUND[I4, i6, i8]*SUNF[i1, I1, I6] + - (45*I)*SUND[i1, I3, i8]*SUND[I2, I5, i6]*SUND[I4, i6, i8]* - SUNF[i1, I1, I6] + (45*I)*SUND[i1, I4, i8]*SUND[I2, I3, i6]* - SUND[I5, i6, i8]*SUNF[i1, I1, I6] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, I4, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I4, I5]*SUNDelta[I2, I3]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I3, I5]*SUNDelta[I2, I4]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I3, I4]*SUNDelta[I2, I5]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I2, I5]*SUNDelta[I3, I4]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I2, I4]*SUNDelta[I3, I5]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I2, I3]*SUNDelta[I4, I5]*SUNF[i1, I1, I6] - - (108*I)*SUND[i1, i6, I6]*SUND[I2, I5, i6]*SUND[I3, I4, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]*SUND[I2, i6, I6]* - SUND[I3, I4, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, i6, I6]* - SUND[I2, I4, i6]*SUND[I3, I5, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I4, i6]*SUND[I2, i6, I6]*SUND[I3, I5, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]*SUND[I2, I4, i6]* - SUND[I3, I6, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I4, i6]* - SUND[I2, I5, i6]*SUND[I3, I6, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, i6, I6]*SUND[I2, I3, i6]*SUND[I4, I5, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]*SUND[I2, i6, I6]* - SUND[I4, I5, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]* - SUND[I2, I3, i6]*SUND[I4, I6, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I3, i6]*SUND[I2, I5, i6]*SUND[I4, I6, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I4, i6]*SUND[I2, I3, i6]* - SUND[I5, I6, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]* - SUND[I2, I4, i6]*SUND[I5, I6, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I2, I6]*SUND[I1, i6, i8]*SUND[I4, I5, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I5]* - SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I3, i6] - - (108*I)*SUND[i1, I2, I5]*SUND[I1, i6, i8]*SUND[I4, I6, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I4]* - SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I3, i6] - - (18*I)*SUND[i1, I1, I2]*SUND[I4, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I3, i6] - (108*I)*SUND[i1, I2, I4]*SUND[I1, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I2]* - SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I3, i6] + - (27*I)*SUND[i1, I2, I5]*SUND[I1, I4, i8]*SUND[i6, I6, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I4]*SUND[I1, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I2]* - SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I3, i6] + - (27*I)*SUND[i1, i6, I6]*SUND[I1, I5, i8]*SUND[I2, I4, i6]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I6, i8]* - SUND[I2, I4, i6]*SUNF[i1, I3, i8] + (27*I)*SUND[i1, i6, I6]* - SUND[I1, I4, i8]*SUND[I2, I5, i6]*SUNF[i1, I3, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I6, i8]*SUND[I2, I5, i6]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I4, i8]* - SUND[I2, i6, I6]*SUNF[i1, I3, i8] + (27*I)*SUND[i1, I4, i6]* - SUND[I1, I5, i8]*SUND[I2, i6, I6]*SUNF[i1, I3, i8] - - (18*I)*SUND[i1, i6, I6]*SUND[I1, I2, i6]*SUND[I4, I5, i8]* - SUNF[i1, I3, i8] + (72*I)*SUND[i1, I1, i6]*SUND[I2, i6, I6]* - SUND[I4, I5, i8]*SUNF[i1, I3, i8] - (18*I)*SUND[i1, I5, i6]* - SUND[I1, I2, i6]*SUND[I4, I6, i8]*SUNF[i1, I3, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I5, i6]*SUND[I4, I6, i8]* - SUNF[i1, I3, i8] - (18*I)*SUND[i1, I4, i6]*SUND[I1, I2, i6]* - SUND[I5, I6, i8]*SUNF[i1, I3, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I4, i6]*SUND[I5, I6, i8]*SUNF[i1, I3, i8] - - (108*I)*SUND[i1, I2, I6]*SUND[I1, i6, i8]*SUND[I3, I5, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I5, i8]* - SUND[I3, i6, i8]*SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I5]* - SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[i1, I4, i6] - - (108*I)*SUND[i1, I2, I5]*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I3, i8]* - SUND[I5, i6, i8]*SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I3]* - SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I4, i6] - - (18*I)*SUND[i1, I1, I2]*SUND[I3, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I4, i6] - (108*I)*SUND[i1, I2, I3]*SUND[I1, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I2]* - SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I4, i6] + - (27*I)*SUND[i1, I2, I5]*SUND[I1, I3, i8]*SUND[i6, I6, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I3]*SUND[I1, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I2]* - SUND[I3, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I4, i6] + - (27*I)*SUND[i1, i6, I6]*SUND[I1, I5, i8]*SUND[I2, I3, i6]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I6, i8]* - SUND[I2, I3, i6]*SUNF[i1, I4, i8] + (27*I)*SUND[i1, i6, I6]* - SUND[I1, I3, i8]*SUND[I2, I5, i6]*SUNF[i1, I4, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I6, i8]*SUND[I2, I5, i6]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I3, i8]* - SUND[I2, i6, I6]*SUNF[i1, I4, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I5, i8]*SUND[I2, i6, I6]*SUNF[i1, I4, i8] - - (18*I)*SUND[i1, i6, I6]*SUND[I1, I2, i6]*SUND[I3, I5, i8]* - SUNF[i1, I4, i8] + (72*I)*SUND[i1, I1, i6]*SUND[I2, i6, I6]* - SUND[I3, I5, i8]*SUNF[i1, I4, i8] - (18*I)*SUND[i1, I5, i6]* - SUND[I1, I2, i6]*SUND[I3, I6, i8]*SUNF[i1, I4, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I5, i6]*SUND[I3, I6, i8]* - SUNF[i1, I4, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, I2, i6]* - SUND[I5, I6, i8]*SUNF[i1, I4, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i6]*SUND[I5, I6, i8]*SUNF[i1, I4, i8] - - (108*I)*SUND[i1, I2, I6]*SUND[I1, i6, i8]*SUND[I3, I4, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I4, i8]* - SUND[I3, i6, i8]*SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I4]* - SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[i1, I5, i6] - - (108*I)*SUND[i1, I2, I4]*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I6]*SUND[I1, I3, i8]* - SUND[I4, i6, i8]*SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I3]* - SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I5, i6] - - (18*I)*SUND[i1, I1, I2]*SUND[I3, I6, i8]*SUND[I4, i6, i8]* - SUNF[i1, I5, i6] - (108*I)*SUND[i1, I2, I3]*SUND[I1, i6, i8]* - SUND[I4, I6, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I2]* - SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[i1, I5, i6] + - (27*I)*SUND[i1, I2, I4]*SUND[I1, I3, i8]*SUND[i6, I6, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I3]*SUND[I1, I4, i8]* - SUND[i6, I6, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I2]* - SUND[I3, I4, i8]*SUND[i6, I6, i8]*SUNF[i1, I5, i6] + - (27*I)*SUND[i1, i6, I6]*SUND[I1, I4, i8]*SUND[I2, I3, i6]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, I4, i6]*SUND[I1, I6, i8]* - SUND[I2, I3, i6]*SUNF[i1, I5, i8] + (27*I)*SUND[i1, i6, I6]* - SUND[I1, I3, i8]*SUND[I2, I4, i6]*SUNF[i1, I5, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I6, i8]*SUND[I2, I4, i6]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, I4, i6]*SUND[I1, I3, i8]* - SUND[I2, i6, I6]*SUNF[i1, I5, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I4, i8]*SUND[I2, i6, I6]*SUNF[i1, I5, i8] - - (18*I)*SUND[i1, i6, I6]*SUND[I1, I2, i6]*SUND[I3, I4, i8]* - SUNF[i1, I5, i8] + (72*I)*SUND[i1, I1, i6]*SUND[I2, i6, I6]* - SUND[I3, I4, i8]*SUNF[i1, I5, i8] - (18*I)*SUND[i1, I4, i6]* - SUND[I1, I2, i6]*SUND[I3, I6, i8]*SUNF[i1, I5, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I4, i6]*SUND[I3, I6, i8]* - SUNF[i1, I5, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, I2, i6]* - SUND[I4, I6, i8]*SUNF[i1, I5, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i6]*SUND[I4, I6, i8]*SUNF[i1, I5, i8] + - (108*I)*SUND[i1, I2, I5]*SUND[I1, i6, i8]*SUND[I3, I4, i8]* - SUNF[i1, i6, I6] + (108*I)*SUND[i1, I2, I4]*SUND[I1, i6, i8]* - SUND[I3, I5, i8]*SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I5]* - SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I2, I4]*SUND[I1, I5, i8]*SUND[I3, i6, i8]* - SUNF[i1, i6, I6] + (108*I)*SUND[i1, I2, I3]*SUND[I1, i6, i8]* - SUND[I4, I5, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I2]* - SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I2, I5]*SUND[I1, I3, i8]*SUND[I4, i6, i8]* - SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I3]*SUND[I1, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I2]* - SUND[I3, I5, i8]*SUND[I4, i6, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I2, I4]*SUND[I1, I3, i8]*SUND[I5, i6, i8]* - SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I3]*SUND[I1, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I2]* - SUND[I3, I4, i8]*SUND[I5, i6, i8]*SUNF[i1, i6, I6] + - (27*I)*SUND[i1, I5, i6]*SUND[I1, I4, i8]*SUND[I2, I3, i6]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I4, i6]*SUND[I1, I5, i8]* - SUND[I2, I3, i6]*SUNF[i1, I6, i8] + (27*I)*SUND[i1, I5, i6]* - SUND[I1, I3, i8]*SUND[I2, I4, i6]*SUNF[i1, I6, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I5, i8]*SUND[I2, I4, i6]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I4, i6]*SUND[I1, I3, i8]* - SUND[I2, I5, i6]*SUNF[i1, I6, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I4, i8]*SUND[I2, I5, i6]*SUNF[i1, I6, i8] - - (18*I)*SUND[i1, I5, i6]*SUND[I1, I2, i6]*SUND[I3, I4, i8]* - SUNF[i1, I6, i8] + (72*I)*SUND[i1, I1, i6]*SUND[I2, I5, i6]* - SUND[I3, I4, i8]*SUNF[i1, I6, i8] - (18*I)*SUND[i1, I4, i6]* - SUND[I1, I2, i6]*SUND[I3, I5, i8]*SUNF[i1, I6, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I4, i6]*SUND[I3, I5, i8]* - SUNF[i1, I6, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, I2, i6]* - SUND[I4, I5, i8]*SUNF[i1, I6, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i6]*SUND[I4, I5, i8]*SUNF[i1, I6, i8] + - (180*I)*SUND[I4, I5, I6]*SUNF[I1, I2, I3] + (18*I)*SUND[I3, i6, i8]* - SUND[i4, i6, I6]*SUND[I4, I5, i8]*SUNF[I1, I2, i4] + - (18*I)*SUND[I3, I6, i8]*SUND[i4, I5, i6]*SUND[I4, i6, i8]* - SUNF[I1, I2, i4] + (18*I)*SUND[I3, I5, i8]*SUND[i4, i6, I6]* - SUND[I4, i6, i8]*SUNF[I1, I2, i4] + (18*I)*SUND[I3, i6, i8]* - SUND[i4, I5, i6]*SUND[I4, I6, i8]*SUNF[I1, I2, i4] + - (18*I)*SUND[I3, I6, i8]*SUND[i4, I4, i6]*SUND[I5, i6, i8]* - SUNF[I1, I2, i4] + (18*I)*SUND[I3, I4, i8]*SUND[i4, i6, I6]* - SUND[I5, i6, i8]*SUNF[I1, I2, i4] + (18*I)*SUND[I3, i4, i6]* - SUND[I4, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i4] + - (18*I)*SUND[I3, i6, i8]*SUND[i4, I4, i6]*SUND[I5, I6, i8]* - SUNF[I1, I2, i4] + (18*I)*SUND[I3, i4, i6]*SUND[I4, i6, i8]* - SUND[I5, I6, i8]*SUNF[I1, I2, i4] + (18*I)*SUND[I3, I5, i8]* - SUND[i4, I4, i6]*SUND[i6, I6, i8]*SUNF[I1, I2, i4] + - (18*I)*SUND[I3, I4, i8]*SUND[i4, I5, i6]*SUND[i6, I6, i8]* - SUNF[I1, I2, i4] + (18*I)*SUND[I3, i4, i6]*SUND[I4, I5, i8]* - SUND[i6, I6, i8]*SUNF[I1, I2, i4] + (180*I)*SUND[I3, I5, I6]* - SUNF[I1, I2, I4] + (24*I)*SUND[i5, I5, I6]*SUNDelta[I3, I4]* - SUNF[I1, I2, i5] + (24*I)*SUND[I4, i5, I6]*SUNDelta[I3, I5]* - SUNF[I1, I2, i5] + (24*I)*SUND[I4, i5, I5]*SUNDelta[I3, I6]* - SUNF[I1, I2, i5] + (24*I)*SUND[I3, i5, I6]*SUNDelta[I4, I5]* - SUNF[I1, I2, i5] + (24*I)*SUND[I3, i5, I5]*SUNDelta[I4, I6]* - SUNF[I1, I2, i5] + (24*I)*SUND[I3, I4, i5]*SUNDelta[I5, I6]* - SUNF[I1, I2, i5] + (180*I)*SUND[I3, I4, I6]*SUNF[I1, I2, I5] + - (180*I)*SUND[I3, I4, I5]*SUNF[I1, I2, I6] + 45*SUND[i1, I2, I6]* - SUND[i3, I5, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I5]*SUND[i3, I6, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I6]*SUND[i3, I4, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I4]*SUND[i3, I6, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I5]*SUND[i3, I4, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I4]*SUND[i3, I5, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I3] + - 45*SUND[i1, I2, I6]*SUND[i3, I5, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I5]*SUND[i3, I6, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I6]*SUND[i3, I3, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I3]*SUND[i3, I6, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I5]*SUND[i3, I3, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I3]*SUND[i3, I5, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I4] + - 45*SUND[i1, I2, I6]*SUND[i3, I4, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I2, I4]*SUND[i3, I6, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I2, I6]*SUND[i3, I3, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I2, I3]*SUND[i3, I6, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I2, I4]*SUND[i3, I3, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I2, I3]*SUND[i3, I4, i8]*SUNF[i1, I6, i8]*SUNF[I1, i3, I5] + - 45*SUND[i1, I2, I5]*SUND[i3, I4, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I2, I4]*SUND[i3, I5, i8]*SUNF[i1, I3, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I2, I5]*SUND[i3, I3, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I2, I3]*SUND[i3, I5, i8]*SUNF[i1, I4, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I2, I4]*SUND[i3, I3, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I6] + - 45*SUND[i1, I2, I3]*SUND[i3, I4, i8]*SUNF[i1, I5, i8]*SUNF[I1, i3, I6] + - 108*SUND[i1, I2, I6]*SUND[I4, I5, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I5]*SUND[I4, I6, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I4]*SUND[I5, I6, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I6]*SUND[I3, I5, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I5]*SUND[I3, I6, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I3]*SUND[I5, I6, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I6]*SUND[I3, I4, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I4]*SUND[I3, I6, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I3]*SUND[I4, I6, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I5]*SUND[I3, I4, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I4]*SUND[I3, I5, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I3]*SUND[I4, I5, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - (120*I)*SUND[i5, I5, I6]*SUNDelta[I2, I4]*SUNF[I1, I3, i5] + - (120*I)*SUND[I4, i5, I6]*SUNDelta[I2, I5]*SUNF[I1, I3, i5] + - (120*I)*SUND[I4, i5, I5]*SUNDelta[I2, I6]*SUNF[I1, I3, i5] - - 45*SUND[i1, I6, i8]*SUND[I2, I5, i8]*SUNF[i1, I4, i5]*SUNF[I1, I3, i5] - - 45*SUND[i1, I5, i8]*SUND[I2, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, I3, i5] + - 45*SUND[i1, I6, i8]*SUND[I2, I4, i8]*SUNF[i1, i5, I5]*SUNF[I1, I3, i5] + - 45*SUND[i1, I4, i8]*SUND[I2, I6, i8]*SUNF[i1, i5, I5]*SUNF[I1, I3, i5] + - 45*SUND[i1, I5, i8]*SUND[I2, I4, i8]*SUNF[i1, i5, I6]*SUNF[I1, I3, i5] + - 45*SUND[i1, I4, i8]*SUND[I2, I5, i8]*SUNF[i1, i5, I6]*SUNF[I1, I3, i5] + - (120*I)*SUND[i5, I5, I6]*SUNDelta[I2, I3]*SUNF[I1, I4, i5] + - (120*I)*SUND[I3, i5, I6]*SUNDelta[I2, I5]*SUNF[I1, I4, i5] + - (120*I)*SUND[I3, i5, I5]*SUNDelta[I2, I6]*SUNF[I1, I4, i5] - - 45*SUND[i1, I6, i8]*SUND[I2, I5, i8]*SUNF[i1, I3, i5]*SUNF[I1, I4, i5] - - 45*SUND[i1, I5, i8]*SUND[I2, I6, i8]*SUNF[i1, I3, i5]*SUNF[I1, I4, i5] + - 45*SUND[i1, I6, i8]*SUND[I2, I3, i8]*SUNF[i1, i5, I5]*SUNF[I1, I4, i5] + - 45*SUND[i1, I3, i8]*SUND[I2, I6, i8]*SUNF[i1, i5, I5]*SUNF[I1, I4, i5] + - 45*SUND[i1, I5, i8]*SUND[I2, I3, i8]*SUNF[i1, i5, I6]*SUNF[I1, I4, i5] + - 45*SUND[i1, I3, i8]*SUND[I2, I5, i8]*SUNF[i1, i5, I6]*SUNF[I1, I4, i5] - - (120*I)*SUND[I4, i5, I6]*SUNDelta[I2, I3]*SUNF[I1, i5, I5] - - (120*I)*SUND[I3, i5, I6]*SUNDelta[I2, I4]*SUNF[I1, i5, I5] - - (120*I)*SUND[I3, I4, i5]*SUNDelta[I2, I6]*SUNF[I1, i5, I5] + - 45*SUND[i1, I6, i8]*SUND[I2, I4, i8]*SUNF[i1, I3, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I4, i8]*SUND[I2, I6, i8]*SUNF[i1, I3, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I6, i8]*SUND[I2, I3, i8]*SUNF[i1, I4, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I3, i8]*SUND[I2, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, i5, I5] - - 45*SUND[i1, I4, i8]*SUND[I2, I3, i8]*SUNF[i1, i5, I6]*SUNF[I1, i5, I5] - - 45*SUND[i1, I3, i8]*SUND[I2, I4, i8]*SUNF[i1, i5, I6]*SUNF[I1, i5, I5] - - (120*I)*SUND[I4, i5, I5]*SUNDelta[I2, I3]*SUNF[I1, i5, I6] - - (120*I)*SUND[I3, i5, I5]*SUNDelta[I2, I4]*SUNF[I1, i5, I6] - - (120*I)*SUND[I3, I4, i5]*SUNDelta[I2, I5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I5, i8]*SUND[I2, I4, i8]*SUNF[i1, I3, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I4, i8]*SUND[I2, I5, i8]*SUNF[i1, I3, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I5, i8]*SUND[I2, I3, i8]*SUNF[i1, I4, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I3, i8]*SUND[I2, I5, i8]*SUNF[i1, I4, i5]*SUNF[I1, i5, I6] - - 45*SUND[i1, I4, i8]*SUND[I2, I3, i8]*SUNF[i1, i5, I5]*SUNF[I1, i5, I6] - - 45*SUND[i1, I3, i8]*SUND[I2, I4, i8]*SUNF[i1, i5, I5]*SUNF[I1, i5, I6] - - 72*SUND[I4, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I3] - - 72*SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I3] - - 72*SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I3] - - 72*SUND[I3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I4] - - 72*SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I4] - - 72*SUND[I3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I4] - - 72*SUND[I3, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I5] - - 72*SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I5] - - 72*SUND[I3, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I5] - - 72*SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I6] - - 72*SUND[I3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I6] - - 72*SUND[I3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I6] - - (108*I)*SUND[I1, i6, i8]*SUND[i4, i6, I6]*SUND[I4, I5, i8]* - SUNF[I2, I3, i4] + (27*I)*SUND[I1, I6, i8]*SUND[i4, I5, i6]* - SUND[I4, i6, i8]*SUNF[I2, I3, i4] + (27*I)*SUND[I1, I5, i8]* - SUND[i4, i6, I6]*SUND[I4, i6, i8]*SUNF[I2, I3, i4] - - (108*I)*SUND[I1, i6, i8]*SUND[i4, I5, i6]*SUND[I4, I6, i8]* - SUNF[I2, I3, i4] + (27*I)*SUND[I1, I6, i8]*SUND[i4, I4, i6]* - SUND[I5, i6, i8]*SUNF[I2, I3, i4] + (27*I)*SUND[I1, I4, i8]* - SUND[i4, i6, I6]*SUND[I5, i6, i8]*SUNF[I2, I3, i4] + - (72*I)*SUND[I1, i4, i6]*SUND[I4, I6, i8]*SUND[I5, i6, i8]* - SUNF[I2, I3, i4] - (108*I)*SUND[I1, i6, i8]*SUND[i4, I4, i6]* - SUND[I5, I6, i8]*SUNF[I2, I3, i4] + (72*I)*SUND[I1, i4, i6]* - SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[I2, I3, i4] + - (27*I)*SUND[I1, I5, i8]*SUND[i4, I4, i6]*SUND[i6, I6, i8]* - SUNF[I2, I3, i4] + (27*I)*SUND[I1, I4, i8]*SUND[i4, I5, i6]* - SUND[i6, I6, i8]*SUNF[I2, I3, i4] + (72*I)*SUND[I1, i4, i6]* - SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[I2, I3, i4] + - (36*I)*SUND[i5, I5, I6]*SUNDelta[I1, I4]*SUNF[I2, I3, i5] + - (36*I)*SUND[I4, i5, I6]*SUNDelta[I1, I5]*SUNF[I2, I3, i5] + - (36*I)*SUND[I4, i5, I5]*SUNDelta[I1, I6]*SUNF[I2, I3, i5] - - (24*I)*SUND[I1, i5, I6]*SUNDelta[I4, I5]*SUNF[I2, I3, i5] - - (24*I)*SUND[I1, i5, I5]*SUNDelta[I4, I6]*SUNF[I2, I3, i5] - - (24*I)*SUND[I1, I4, i5]*SUNDelta[I5, I6]*SUNF[I2, I3, i5] + - 45*SUND[i3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, I3, i6] + - 45*SUND[i3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I4]*SUNF[I2, I3, i6] + - 45*SUND[i3, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, I3, i6] + - 45*SUND[i3, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]*SUNF[I2, I3, i6] + - 45*SUND[i3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I3, i6] + - 45*SUND[i3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I3, i6] - - 108*SUND[i3, i6, I6]*SUND[I4, I5, i8]*SUNF[I1, i3, i8]*SUNF[I2, I3, i6] - - 108*SUND[i3, I5, i6]*SUND[I4, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I3, i6] - - 108*SUND[i3, I4, i6]*SUND[I5, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I3, i6] - - 120*SUNDelta[I5, I6]*SUNF[I1, I4, i6]*SUNF[I2, I3, i6] - - 120*SUNDelta[I4, I6]*SUNF[I1, I5, i6]*SUNF[I2, I3, i6] + - 120*SUNDelta[I4, I5]*SUNF[I1, i6, I6]*SUNF[I2, I3, i6] - - (27*I)*SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUND[i4, I5, i6]* - SUNF[I2, i4, I4] + (108*I)*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUND[i4, I5, i6]*SUNF[I2, i4, I4] + (108*I)*SUND[I1, i6, i8]* - SUND[I3, I5, i8]*SUND[i4, i6, I6]*SUNF[I2, i4, I4] - - (27*I)*SUND[I1, I5, i8]*SUND[I3, i6, i8]*SUND[i4, i6, I6]* - SUNF[I2, i4, I4] - (27*I)*SUND[I1, I6, i8]*SUND[I3, i4, i6]* - SUND[I5, i6, i8]*SUNF[I2, i4, I4] - (72*I)*SUND[I1, i4, i6]* - SUND[I3, I6, i8]*SUND[I5, i6, i8]*SUNF[I2, i4, I4] - - (27*I)*SUND[I1, I3, i8]*SUND[i4, i6, I6]*SUND[I5, i6, i8]* - SUNF[I2, i4, I4] + (108*I)*SUND[I1, i6, i8]*SUND[I3, i4, i6]* - SUND[I5, I6, i8]*SUNF[I2, i4, I4] - (72*I)*SUND[I1, i4, i6]* - SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[I2, i4, I4] - - (27*I)*SUND[I1, I5, i8]*SUND[I3, i4, i6]*SUND[i6, I6, i8]* - SUNF[I2, i4, I4] - (72*I)*SUND[I1, i4, i6]*SUND[I3, I5, i8]* - SUND[i6, I6, i8]*SUNF[I2, i4, I4] - (27*I)*SUND[I1, I3, i8]* - SUND[i4, I5, i6]*SUND[i6, I6, i8]*SUNF[I2, i4, I4] - - (27*I)*SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUND[i4, I4, i6]* - SUNF[I2, i4, I5] + (108*I)*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUND[i4, I4, i6]*SUNF[I2, i4, I5] + (108*I)*SUND[I1, i6, i8]* - SUND[I3, I4, i8]*SUND[i4, i6, I6]*SUNF[I2, i4, I5] - - (27*I)*SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUND[i4, i6, I6]* - SUNF[I2, i4, I5] - (27*I)*SUND[I1, I6, i8]*SUND[I3, i4, i6]* - SUND[I4, i6, i8]*SUNF[I2, i4, I5] - (72*I)*SUND[I1, i4, i6]* - SUND[I3, I6, i8]*SUND[I4, i6, i8]*SUNF[I2, i4, I5] - - (27*I)*SUND[I1, I3, i8]*SUND[i4, i6, I6]*SUND[I4, i6, i8]* - SUNF[I2, i4, I5] + (108*I)*SUND[I1, i6, i8]*SUND[I3, i4, i6]* - SUND[I4, I6, i8]*SUNF[I2, i4, I5] - (72*I)*SUND[I1, i4, i6]* - SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[I2, i4, I5] - - (27*I)*SUND[I1, I4, i8]*SUND[I3, i4, i6]*SUND[i6, I6, i8]* - SUNF[I2, i4, I5] - (72*I)*SUND[I1, i4, i6]*SUND[I3, I4, i8]* - SUND[i6, I6, i8]*SUNF[I2, i4, I5] - (27*I)*SUND[I1, I3, i8]* - SUND[i4, I4, i6]*SUND[i6, I6, i8]*SUNF[I2, i4, I5] + - (108*I)*SUND[I1, i6, i8]*SUND[I3, I5, i8]*SUND[i4, I4, i6]* - SUNF[I2, i4, I6] - (27*I)*SUND[I1, I5, i8]*SUND[I3, i6, i8]* - SUND[i4, I4, i6]*SUNF[I2, i4, I6] + (108*I)*SUND[I1, i6, i8]* - SUND[I3, I4, i8]*SUND[i4, I5, i6]*SUNF[I2, i4, I6] - - (27*I)*SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUND[i4, I5, i6]* - SUNF[I2, i4, I6] + (108*I)*SUND[I1, i6, i8]*SUND[I3, i4, i6]* - SUND[I4, I5, i8]*SUNF[I2, i4, I6] - (72*I)*SUND[I1, i4, i6]* - SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[I2, i4, I6] - - (27*I)*SUND[I1, I5, i8]*SUND[I3, i4, i6]*SUND[I4, i6, i8]* - SUNF[I2, i4, I6] - (72*I)*SUND[I1, i4, i6]*SUND[I3, I5, i8]* - SUND[I4, i6, i8]*SUNF[I2, i4, I6] - (27*I)*SUND[I1, I3, i8]* - SUND[i4, I5, i6]*SUND[I4, i6, i8]*SUNF[I2, i4, I6] - - (27*I)*SUND[I1, I4, i8]*SUND[I3, i4, i6]*SUND[I5, i6, i8]* - SUNF[I2, i4, I6] - (72*I)*SUND[I1, i4, i6]*SUND[I3, I4, i8]* - SUND[I5, i6, i8]*SUNF[I2, i4, I6] - (27*I)*SUND[I1, I3, i8]* - SUND[i4, I4, i6]*SUND[I5, i6, i8]*SUNF[I2, i4, I6] + - (36*I)*SUND[i5, I5, I6]*SUNDelta[I1, I3]*SUNF[I2, I4, i5] + - (36*I)*SUND[I3, i5, I6]*SUNDelta[I1, I5]*SUNF[I2, I4, i5] + - (36*I)*SUND[I3, i5, I5]*SUNDelta[I1, I6]*SUNF[I2, I4, i5] - - (24*I)*SUND[I1, i5, I6]*SUNDelta[I3, I5]*SUNF[I2, I4, i5] - - (24*I)*SUND[I1, i5, I5]*SUNDelta[I3, I6]*SUNF[I2, I4, i5] - - (24*I)*SUND[I1, I3, i5]*SUNDelta[I5, I6]*SUNF[I2, I4, i5] + - 45*SUND[i3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, I4, i6] + - 45*SUND[i3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, I4, i6] + - 45*SUND[i3, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, I4, i6] + - 45*SUND[i3, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]*SUNF[I2, I4, i6] + - 45*SUND[i3, I5, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I4, i6] + - 45*SUND[i3, I3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I4, i6] - - 108*SUND[i3, i6, I6]*SUND[I3, I5, i8]*SUNF[I1, i3, i8]*SUNF[I2, I4, i6] - - 108*SUND[i3, I5, i6]*SUND[I3, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I4, i6] - - 108*SUND[i3, I3, i6]*SUND[I5, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I4, i6] - - 120*SUNDelta[I5, I6]*SUNF[I1, I3, i6]*SUNF[I2, I4, i6] - - 120*SUNDelta[I3, I6]*SUNF[I1, I5, i6]*SUNF[I2, I4, i6] + - 120*SUNDelta[I3, I5]*SUNF[I1, i6, I6]*SUNF[I2, I4, i6] - - (36*I)*SUND[I4, i5, I6]*SUNDelta[I1, I3]*SUNF[I2, i5, I5] - - (36*I)*SUND[I3, i5, I6]*SUNDelta[I1, I4]*SUNF[I2, i5, I5] - - (36*I)*SUND[I3, I4, i5]*SUNDelta[I1, I6]*SUNF[I2, i5, I5] + - (24*I)*SUND[I1, i5, I6]*SUNDelta[I3, I4]*SUNF[I2, i5, I5] + - (24*I)*SUND[I1, I4, i5]*SUNDelta[I3, I6]*SUNF[I2, i5, I5] + - (24*I)*SUND[I1, I3, i5]*SUNDelta[I4, I6]*SUNF[I2, i5, I5] - - (36*I)*SUND[I4, i5, I5]*SUNDelta[I1, I3]*SUNF[I2, i5, I6] - - (36*I)*SUND[I3, i5, I5]*SUNDelta[I1, I4]*SUNF[I2, i5, I6] - - (36*I)*SUND[I3, I4, i5]*SUNDelta[I1, I5]*SUNF[I2, i5, I6] + - (24*I)*SUND[I1, i5, I5]*SUNDelta[I3, I4]*SUNF[I2, i5, I6] + - (24*I)*SUND[I1, I4, i5]*SUNDelta[I3, I5]*SUNF[I2, i5, I6] + - (24*I)*SUND[I1, I3, i5]*SUNDelta[I4, I5]*SUNF[I2, i5, I6] + - 45*SUND[i3, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, I5, i6] + - 45*SUND[i3, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, I5, i6] + - 45*SUND[i3, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, I5, i6] + - 45*SUND[i3, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I4]*SUNF[I2, I5, i6] + - 45*SUND[i3, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I5, i6] + - 45*SUND[i3, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I5, i6] - - 108*SUND[i3, i6, I6]*SUND[I3, I4, i8]*SUNF[I1, i3, i8]*SUNF[I2, I5, i6] - - 108*SUND[i3, I4, i6]*SUND[I3, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I5, i6] - - 108*SUND[i3, I3, i6]*SUND[I4, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I5, i6] - - 120*SUNDelta[I4, I6]*SUNF[I1, I3, i6]*SUNF[I2, I5, i6] - - 120*SUNDelta[I3, I6]*SUNF[I1, I4, i6]*SUNF[I2, I5, i6] + - 120*SUNDelta[I3, I4]*SUNF[I1, i6, I6]*SUNF[I2, I5, i6] - - 45*SUND[i3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i6, I6] - - 45*SUND[i3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i6, I6] - - 45*SUND[i3, I5, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i6, I6] - - 45*SUND[i3, I3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i6, I6] - - 45*SUND[i3, I4, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i6, I6] - - 45*SUND[i3, I3, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, i6, I6] + - 108*SUND[i3, I5, i6]*SUND[I3, I4, i8]*SUNF[I1, i3, i8]*SUNF[I2, i6, I6] + - 108*SUND[i3, I4, i6]*SUND[I3, I5, i8]*SUNF[I1, i3, i8]*SUNF[I2, i6, I6] + - 108*SUND[i3, I3, i6]*SUND[I4, I5, i8]*SUNF[I1, i3, i8]*SUNF[I2, i6, I6] + - 120*SUNDelta[I4, I5]*SUNF[I1, I3, i6]*SUNF[I2, i6, I6] + - 120*SUNDelta[I3, I5]*SUNF[I1, I4, i6]*SUNF[I2, i6, I6] + - 120*SUNDelta[I3, I4]*SUNF[I1, I5, i6]*SUNF[I2, i6, I6] + - (108*I)*SUND[I5, I6, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, I4]* - SUNF[i3, I3, i5] + (108*I)*SUND[I4, I6, i8]*SUNF[I1, i5, i8]* - SUNF[I2, i3, I5]*SUNF[i3, I3, i5] + (108*I)*SUND[I4, I5, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I6]*SUNF[i3, I3, i5] - - 18*SUND[I4, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I3, i6] - - 18*SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I3, i6] - - 18*SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I3, i6] + - 27*SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I3, i6] - - 108*SUND[I1, i6, i8]*SUND[I5, I6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I3, i6] + - 27*SUND[I1, I5, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I3, i6] + - 27*SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I3, i6] - - 108*SUND[I1, i6, i8]*SUND[I4, I6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I3, i6] + - 27*SUND[I1, I4, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I3, i6] - - 108*SUND[I1, i6, i8]*SUND[I4, I5, i8]*SUNF[I2, i3, I6]*SUNF[i3, I3, i6] + - 27*SUND[I1, I5, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I3, i6] + - 27*SUND[I1, I4, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I3, i6] - - 72*SUND[i1, I2, I6]*SUND[I4, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - - 72*SUND[i1, I2, I5]*SUND[I4, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - - 72*SUND[i1, I2, I4]*SUND[I5, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I3, i8] + - 27*SUND[i1, I2, I6]*SUND[I1, I5, i8]*SUNF[i1, i3, I4]*SUNF[i3, I3, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I6, i8]*SUNF[i1, i3, I4]*SUNF[i3, I3, i8] - - 18*SUND[i1, I1, I2]*SUND[I5, I6, i8]*SUNF[i1, i3, I4]*SUNF[i3, I3, i8] + - 27*SUND[i1, I2, I6]*SUND[I1, I4, i8]*SUNF[i1, i3, I5]*SUNF[i3, I3, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I6, i8]*SUNF[i1, i3, I5]*SUNF[i3, I3, i8] - - 18*SUND[i1, I1, I2]*SUND[I4, I6, i8]*SUNF[i1, i3, I5]*SUNF[i3, I3, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I4, i8]*SUNF[i1, i3, I6]*SUNF[i3, I3, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I5, i8]*SUNF[i1, i3, I6]*SUNF[i3, I3, i8] - - 18*SUND[i1, I1, I2]*SUND[I4, I5, i8]*SUNF[i1, i3, I6]*SUNF[i3, I3, i8] - - 18*SUND[i3, i6, I6]*SUND[I4, I5, i8]*SUNF[I1, I2, i6]*SUNF[i3, I3, i8] - - 18*SUND[i3, I5, i6]*SUND[I4, I6, i8]*SUNF[I1, I2, i6]*SUNF[i3, I3, i8] - - 18*SUND[i3, I4, i6]*SUND[I5, I6, i8]*SUNF[I1, I2, i6]*SUNF[i3, I3, i8] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, i5, I5]*SUNF[I2, i3, I4]* - SUNF[i3, I3, i8] - (45*I)*SUND[i5, I5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, I4]*SUNF[i3, I3, i8] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I4, i5]*SUNF[I2, i3, I5]*SUNF[i3, I3, i8] - - (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I6]*SUNF[I2, i3, I5]* - SUNF[i3, I3, i8] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, I4, i5]* - SUNF[I2, i3, I6]*SUNF[i3, I3, i8] - (45*I)*SUND[I4, i5, i8]* - SUNF[I1, i5, I5]*SUNF[I2, i3, I6]*SUNF[i3, I3, i8] - - 27*SUND[I1, I6, i8]*SUND[i3, I5, i6]*SUNF[I2, I4, i6]*SUNF[i3, I3, i8] - - 27*SUND[I1, I5, i8]*SUND[i3, i6, I6]*SUNF[I2, I4, i6]*SUNF[i3, I3, i8] - - 72*SUND[I1, i3, i6]*SUND[I5, I6, i8]*SUNF[I2, I4, i6]*SUNF[i3, I3, i8] - - 27*SUND[I1, I6, i8]*SUND[i3, I4, i6]*SUNF[I2, I5, i6]*SUNF[i3, I3, i8] - - 27*SUND[I1, I4, i8]*SUND[i3, i6, I6]*SUNF[I2, I5, i6]*SUNF[i3, I3, i8] - - 72*SUND[I1, i3, i6]*SUND[I4, I6, i8]*SUNF[I2, I5, i6]*SUNF[i3, I3, i8] + - 27*SUND[I1, I5, i8]*SUND[i3, I4, i6]*SUNF[I2, i6, I6]*SUNF[i3, I3, i8] + - 27*SUND[I1, I4, i8]*SUND[i3, I5, i6]*SUNF[I2, i6, I6]*SUNF[i3, I3, i8] + - 72*SUND[I1, i3, i6]*SUND[I4, I5, i8]*SUNF[I2, i6, I6]*SUNF[i3, I3, i8] + - (108*I)*SUND[I5, I6, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, I3]* - SUNF[i3, I4, i5] + (108*I)*SUND[I3, I6, i8]*SUNF[I1, i5, i8]* - SUNF[I2, i3, I5]*SUNF[i3, I4, i5] + (108*I)*SUND[I3, I5, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I6]*SUNF[i3, I4, i5] - - 18*SUND[I3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I4, i6] - - 18*SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I4, i6] - - 18*SUND[I3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I4, i6] + - 27*SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I5, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I4, i6] + - 27*SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I3, I6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I4, i6] + - 27*SUND[I1, I3, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I5]*SUNF[i3, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I3, I5, i8]*SUNF[I2, i3, I6]*SUNF[i3, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I4, i6] + - 27*SUND[I1, I3, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I4, i6] - - 72*SUND[i1, I2, I6]*SUND[I3, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] - - 72*SUND[i1, I2, I5]*SUND[I3, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] - - 72*SUND[i1, I2, I3]*SUND[I5, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I6]*SUND[I1, I5, i8]*SUNF[i1, i3, I3]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I6, i8]*SUNF[i1, i3, I3]*SUNF[i3, I4, i8] - - 18*SUND[i1, I1, I2]*SUND[I5, I6, i8]*SUNF[i1, i3, I3]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I6]*SUND[I1, I3, i8]*SUNF[i1, i3, I5]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I6, i8]*SUNF[i1, i3, I5]*SUNF[i3, I4, i8] - - 18*SUND[i1, I1, I2]*SUND[I3, I6, i8]*SUNF[i1, i3, I5]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I3, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I5, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] - - 18*SUND[i1, I1, I2]*SUND[I3, I5, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] - - 18*SUND[i3, i6, I6]*SUND[I3, I5, i8]*SUNF[I1, I2, i6]*SUNF[i3, I4, i8] - - 18*SUND[i3, I5, i6]*SUND[I3, I6, i8]*SUNF[I1, I2, i6]*SUNF[i3, I4, i8] - - 18*SUND[i3, I3, i6]*SUND[I5, I6, i8]*SUNF[I1, I2, i6]*SUNF[i3, I4, i8] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, i5, I5]*SUNF[I2, i3, I3]* - SUNF[i3, I4, i8] - (45*I)*SUND[i5, I5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, I3]*SUNF[i3, I4, i8] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I3, i5]*SUNF[I2, i3, I5]*SUNF[i3, I4, i8] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I6]*SUNF[I2, i3, I5]* - SUNF[i3, I4, i8] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, I3, i5]* - SUNF[I2, i3, I6]*SUNF[i3, I4, i8] - (45*I)*SUND[I3, i5, i8]* - SUNF[I1, i5, I5]*SUNF[I2, i3, I6]*SUNF[i3, I4, i8] - - 27*SUND[I1, I6, i8]*SUND[i3, I5, i6]*SUNF[I2, I3, i6]*SUNF[i3, I4, i8] - - 27*SUND[I1, I5, i8]*SUND[i3, i6, I6]*SUNF[I2, I3, i6]*SUNF[i3, I4, i8] - - 72*SUND[I1, i3, i6]*SUND[I5, I6, i8]*SUNF[I2, I3, i6]*SUNF[i3, I4, i8] - - 27*SUND[I1, I6, i8]*SUND[i3, I3, i6]*SUNF[I2, I5, i6]*SUNF[i3, I4, i8] - - 27*SUND[I1, I3, i8]*SUND[i3, i6, I6]*SUNF[I2, I5, i6]*SUNF[i3, I4, i8] - - 72*SUND[I1, i3, i6]*SUND[I3, I6, i8]*SUNF[I2, I5, i6]*SUNF[i3, I4, i8] + - 27*SUND[I1, I5, i8]*SUND[i3, I3, i6]*SUNF[I2, i6, I6]*SUNF[i3, I4, i8] + - 27*SUND[I1, I3, i8]*SUND[i3, I5, i6]*SUNF[I2, i6, I6]*SUNF[i3, I4, i8] + - 72*SUND[I1, i3, i6]*SUND[I3, I5, i8]*SUNF[I2, i6, I6]*SUNF[i3, I4, i8] - - (108*I)*SUND[I4, I6, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, I3]* - SUNF[i3, i5, I5] - (108*I)*SUND[I3, I6, i8]*SUNF[I1, i5, i8]* - SUNF[I2, i3, I4]*SUNF[i3, i5, I5] - (108*I)*SUND[I3, I4, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I6]*SUNF[i3, i5, I5] - - (108*I)*SUND[I4, I5, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, I3]* - SUNF[i3, i5, I6] - (108*I)*SUND[I3, I5, i8]*SUNF[I1, i5, i8]* - SUNF[I2, i3, I4]*SUNF[i3, i5, I6] - (108*I)*SUND[I3, I4, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I5]*SUNF[i3, i5, I6] - - 18*SUND[I3, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I5, i6] - - 18*SUND[I3, i6, i8]*SUND[I4, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I5, i6] - - 18*SUND[I3, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I4, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I3, I6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I5, i6] + - 27*SUND[I1, I3, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I3, I4, i8]*SUNF[I2, i3, I6]*SUNF[i3, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I5, i6] + - 27*SUND[I1, I3, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I6]*SUNF[i3, I5, i6] - - 72*SUND[i1, I2, I6]*SUND[I3, I4, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - - 72*SUND[i1, I2, I4]*SUND[I3, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - - 72*SUND[i1, I2, I3]*SUND[I4, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I6]*SUND[I1, I4, i8]*SUNF[i1, i3, I3]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I6, i8]*SUNF[i1, i3, I3]*SUNF[i3, I5, i8] - - 18*SUND[i1, I1, I2]*SUND[I4, I6, i8]*SUNF[i1, i3, I3]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I6]*SUND[I1, I3, i8]*SUNF[i1, i3, I4]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I6, i8]*SUNF[i1, i3, I4]*SUNF[i3, I5, i8] - - 18*SUND[i1, I1, I2]*SUND[I3, I6, i8]*SUNF[i1, i3, I4]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I3, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I4, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] - - 18*SUND[i1, I1, I2]*SUND[I3, I4, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] - - 18*SUND[i3, i6, I6]*SUND[I3, I4, i8]*SUNF[I1, I2, i6]*SUNF[i3, I5, i8] - - 18*SUND[i3, I4, i6]*SUND[I3, I6, i8]*SUNF[I1, I2, i6]*SUNF[i3, I5, i8] - - 18*SUND[i3, I3, i6]*SUND[I4, I6, i8]*SUNF[I1, I2, i6]*SUNF[i3, I5, i8] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, I3]* - SUNF[i3, I5, i8] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, I3]*SUNF[i3, I5, i8] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I3, i5]*SUNF[I2, i3, I4]*SUNF[i3, I5, i8] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I6]*SUNF[I2, i3, I4]* - SUNF[i3, I5, i8] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i5]* - SUNF[I2, i3, I6]*SUNF[i3, I5, i8] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I4, i5]*SUNF[I2, i3, I6]*SUNF[i3, I5, i8] - - 27*SUND[I1, I6, i8]*SUND[i3, I4, i6]*SUNF[I2, I3, i6]*SUNF[i3, I5, i8] - - 27*SUND[I1, I4, i8]*SUND[i3, i6, I6]*SUNF[I2, I3, i6]*SUNF[i3, I5, i8] - - 72*SUND[I1, i3, i6]*SUND[I4, I6, i8]*SUNF[I2, I3, i6]*SUNF[i3, I5, i8] - - 27*SUND[I1, I6, i8]*SUND[i3, I3, i6]*SUNF[I2, I4, i6]*SUNF[i3, I5, i8] - - 27*SUND[I1, I3, i8]*SUND[i3, i6, I6]*SUNF[I2, I4, i6]*SUNF[i3, I5, i8] - - 72*SUND[I1, i3, i6]*SUND[I3, I6, i8]*SUNF[I2, I4, i6]*SUNF[i3, I5, i8] + - 27*SUND[I1, I4, i8]*SUND[i3, I3, i6]*SUNF[I2, i6, I6]*SUNF[i3, I5, i8] + - 27*SUND[I1, I3, i8]*SUND[i3, I4, i6]*SUNF[I2, i6, I6]*SUNF[i3, I5, i8] + - 72*SUND[I1, i3, i6]*SUND[I3, I4, i8]*SUNF[I2, i6, I6]*SUNF[i3, I5, i8] + - 18*SUND[I3, i6, i8]*SUND[I4, I5, i8]*SUNF[I1, I2, i3]*SUNF[i3, i6, I6] + - 18*SUND[I3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, I2, i3]*SUNF[i3, i6, I6] + - 18*SUND[I3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i3]*SUNF[i3, i6, I6] + - 108*SUND[I1, i6, i8]*SUND[I4, I5, i8]*SUNF[I2, i3, I3]*SUNF[i3, i6, I6] - - 27*SUND[I1, I5, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I3]*SUNF[i3, i6, I6] - - 27*SUND[I1, I4, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I3]*SUNF[i3, i6, I6] + - 108*SUND[I1, i6, i8]*SUND[I3, I5, i8]*SUNF[I2, i3, I4]*SUNF[i3, i6, I6] - - 27*SUND[I1, I5, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I4]*SUNF[i3, i6, I6] - - 27*SUND[I1, I3, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I4]*SUNF[i3, i6, I6] + - 108*SUND[I1, i6, i8]*SUND[I3, I4, i8]*SUNF[I2, i3, I5]*SUNF[i3, i6, I6] - - 27*SUND[I1, I4, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I5]*SUNF[i3, i6, I6] - - 27*SUND[I1, I3, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I5]*SUNF[i3, i6, I6] - - 72*SUND[i1, I2, I5]*SUND[I3, I4, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 72*SUND[i1, I2, I4]*SUND[I3, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 72*SUND[i1, I2, I3]*SUND[I4, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I4, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I5, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I2]*SUND[I4, I5, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I5]*SUND[I1, I3, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I5, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I2]*SUND[I3, I5, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I3, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I4, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I2]*SUND[I3, I4, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] - - 18*SUND[i3, I5, i6]*SUND[I3, I4, i8]*SUNF[I1, I2, i6]*SUNF[i3, I6, i8] - - 18*SUND[i3, I4, i6]*SUND[I3, I5, i8]*SUNF[I1, I2, i6]*SUNF[i3, I6, i8] - - 18*SUND[i3, I3, i6]*SUND[I4, I5, i8]*SUNF[I1, I2, i6]*SUNF[i3, I6, i8] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, I3]* - SUNF[i3, I6, i8] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I5]* - SUNF[I2, i3, I3]*SUNF[i3, I6, i8] + (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I3, i5]*SUNF[I2, i3, I4]*SUNF[i3, I6, i8] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I5]*SUNF[I2, i3, I4]* - SUNF[i3, I6, i8] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i5]* - SUNF[I2, i3, I5]*SUNF[i3, I6, i8] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I4, i5]*SUNF[I2, i3, I5]*SUNF[i3, I6, i8] - - 27*SUND[I1, I5, i8]*SUND[i3, I4, i6]*SUNF[I2, I3, i6]*SUNF[i3, I6, i8] - - 27*SUND[I1, I4, i8]*SUND[i3, I5, i6]*SUNF[I2, I3, i6]*SUNF[i3, I6, i8] - - 72*SUND[I1, i3, i6]*SUND[I4, I5, i8]*SUNF[I2, I3, i6]*SUNF[i3, I6, i8] - - 27*SUND[I1, I5, i8]*SUND[i3, I3, i6]*SUNF[I2, I4, i6]*SUNF[i3, I6, i8] - - 27*SUND[I1, I3, i8]*SUND[i3, I5, i6]*SUNF[I2, I4, i6]*SUNF[i3, I6, i8] - - 72*SUND[I1, i3, i6]*SUND[I3, I5, i8]*SUNF[I2, I4, i6]*SUNF[i3, I6, i8] - - 27*SUND[I1, I4, i8]*SUND[i3, I3, i6]*SUNF[I2, I5, i6]*SUNF[i3, I6, i8] - - 27*SUND[I1, I3, i8]*SUND[i3, I4, i6]*SUNF[I2, I5, i6]*SUNF[i3, I6, i8] - - 72*SUND[I1, i3, i6]*SUND[I3, I4, i8]*SUNF[I2, I5, i6]*SUNF[i3, I6, i8] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I5, i7]*SUNF[I2, I4, i8]* - SUNF[I3, i5, i7] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, I4, i8]*SUNF[I3, i5, i7] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I4, i7]*SUNF[I2, I5, i8]*SUNF[I3, i5, i7] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I6, i7]*SUNF[I2, I5, i8]* - SUNF[I3, i5, i7] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, I4, i7]* - SUNF[I2, I6, i8]*SUNF[I3, i5, i7] + (45*I)*SUND[I4, i5, i8]* - SUNF[I1, I5, i7]*SUNF[I2, I6, i8]*SUNF[I3, i5, i7] + - (72*I)*SUND[I5, I6, i8]*SUNF[I1, i3, i5]*SUNF[I2, i3, I4]* - SUNF[I3, i5, i8] + (72*I)*SUND[I4, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I5]*SUNF[I3, i5, i8] + (72*I)*SUND[I4, I5, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I6]*SUNF[I3, i5, i8] + - (18*I)*SUND[I5, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I4, i5]* - SUNF[I3, i5, i8] - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I5]* - SUNF[i3, I4, i5]*SUNF[I3, i5, i8] - (27*I)*SUND[I1, I5, i8]* - SUNF[I2, i3, I6]*SUNF[i3, I4, i5]*SUNF[I3, i5, i8] - - (18*I)*SUND[I4, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, i5, I5]* - SUNF[I3, i5, i8] + (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I4]* - SUNF[i3, i5, I5]*SUNF[I3, i5, i8] + (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i3, I6]*SUNF[i3, i5, I5]*SUNF[I3, i5, i8] - - (18*I)*SUND[I4, I5, i8]*SUNF[I1, I2, i3]*SUNF[i3, i5, I6]* - SUNF[I3, i5, i8] + (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I4]* - SUNF[i3, i5, I6]*SUNF[I3, i5, i8] + (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i3, I5]*SUNF[i3, i5, I6]*SUNF[I3, i5, i8] - - (45*I)*SUND[i1, I2, I6]*SUNF[i1, I5, i9]*SUNF[I1, I4, i8]* - SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I6, i9]* - SUNF[I1, I4, i8]*SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I6]* - SUNF[i1, I4, i9]*SUNF[I1, I5, i8]*SUNF[I3, i8, i9] - - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I6, i9]*SUNF[I1, I5, i8]* - SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I4, i9]* - SUNF[I1, I6, i8]*SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I4]* - SUNF[i1, I5, i9]*SUNF[I1, I6, i8]*SUNF[I3, i8, i9] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I5, i7]*SUNF[I2, I3, i8]* - SUNF[I4, i5, i7] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, I3, i8]*SUNF[I4, i5, i7] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I3, i7]*SUNF[I2, I5, i8]*SUNF[I4, i5, i7] + - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I6, i7]*SUNF[I2, I5, i8]* - SUNF[I4, i5, i7] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, I3, i7]* - SUNF[I2, I6, i8]*SUNF[I4, i5, i7] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I5, i7]*SUNF[I2, I6, i8]*SUNF[I4, i5, i7] + - (72*I)*SUND[I5, I6, i8]*SUNF[I1, i3, i5]*SUNF[I2, i3, I3]* - SUNF[I4, i5, i8] + (72*I)*SUND[I3, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I5]*SUNF[I4, i5, i8] + (72*I)*SUND[I3, I5, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I6]*SUNF[I4, i5, i8] + - (18*I)*SUND[I5, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I3, i5]* - SUNF[I4, i5, i8] - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I5]* - SUNF[i3, I3, i5]*SUNF[I4, i5, i8] - (27*I)*SUND[I1, I5, i8]* - SUNF[I2, i3, I6]*SUNF[i3, I3, i5]*SUNF[I4, i5, i8] - - (18*I)*SUND[I3, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, i5, I5]* - SUNF[I4, i5, i8] + (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I3]* - SUNF[i3, i5, I5]*SUNF[I4, i5, i8] + (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I6]*SUNF[i3, i5, I5]*SUNF[I4, i5, i8] - - (18*I)*SUND[I3, I5, i8]*SUNF[I1, I2, i3]*SUNF[i3, i5, I6]* - SUNF[I4, i5, i8] + (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I3]* - SUNF[i3, i5, I6]*SUNF[I4, i5, i8] + (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I5]*SUNF[i3, i5, I6]*SUNF[I4, i5, i8] - - 45*SUNF[I1, i6, I6]*SUNF[I2, I5, i9]*SUNF[I3, i8, i9]*SUNF[I4, i6, i8] + - 45*SUNF[I1, I5, i6]*SUNF[I2, I6, i9]*SUNF[I3, i8, i9]*SUNF[I4, i6, i8] - - (45*I)*SUND[i1, I2, I6]*SUNF[i1, I5, i9]*SUNF[I1, I3, i8]* - SUNF[I4, i8, i9] - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I6, i9]* - SUNF[I1, I3, i8]*SUNF[I4, i8, i9] - (45*I)*SUND[i1, I2, I6]* - SUNF[i1, I3, i9]*SUNF[I1, I5, i8]*SUNF[I4, i8, i9] - - (45*I)*SUND[i1, I2, I3]*SUNF[i1, I6, i9]*SUNF[I1, I5, i8]* - SUNF[I4, i8, i9] - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I3, i9]* - SUNF[I1, I6, i8]*SUNF[I4, i8, i9] - (45*I)*SUND[i1, I2, I3]* - SUNF[i1, I5, i9]*SUNF[I1, I6, i8]*SUNF[I4, i8, i9] - - 45*SUNF[I1, i6, I6]*SUNF[I2, I5, i9]*SUNF[I3, i6, i8]*SUNF[I4, i8, i9] + - 45*SUNF[I1, I5, i6]*SUNF[I2, I6, i9]*SUNF[I3, i6, i8]*SUNF[I4, i8, i9] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i7]*SUNF[I2, I3, i8]* - SUNF[i5, I5, i7] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, I3, i8]*SUNF[i5, I5, i7] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I3, i7]*SUNF[I2, I4, i8]*SUNF[i5, I5, i7] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I6, i7]*SUNF[I2, I4, i8]* - SUNF[i5, I5, i7] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i7]* - SUNF[I2, I6, i8]*SUNF[i5, I5, i7] - (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I4, i7]*SUNF[I2, I6, i8]*SUNF[i5, I5, i7] - - (72*I)*SUND[I4, I6, i8]*SUNF[I1, i3, i5]*SUNF[I2, i3, I3]* - SUNF[i5, I5, i8] - (72*I)*SUND[I3, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I4]*SUNF[i5, I5, i8] - (72*I)*SUND[I3, I4, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I6]*SUNF[i5, I5, i8] - - (18*I)*SUND[I4, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I3, i5]* - SUNF[i5, I5, i8] + (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I4]* - SUNF[i3, I3, i5]*SUNF[i5, I5, i8] + (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i3, I6]*SUNF[i3, I3, i5]*SUNF[i5, I5, i8] - - (18*I)*SUND[I3, I6, i8]*SUNF[I1, I2, i3]*SUNF[i3, I4, i5]* - SUNF[i5, I5, i8] + (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I3]* - SUNF[i3, I4, i5]*SUNF[i5, I5, i8] + (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I6]*SUNF[i3, I4, i5]*SUNF[i5, I5, i8] + - (18*I)*SUND[I3, I4, i8]*SUNF[I1, I2, i3]*SUNF[i3, i5, I6]* - SUNF[i5, I5, i8] - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, I3]* - SUNF[i3, i5, I6]*SUNF[i5, I5, i8] - (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I4]*SUNF[i3, i5, I6]*SUNF[i5, I5, i8] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I4, i7]*SUNF[I2, I3, i8]* - SUNF[i5, I6, i7] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I5, i7]* - SUNF[I2, I3, i8]*SUNF[i5, I6, i7] - (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I3, i7]*SUNF[I2, I4, i8]*SUNF[i5, I6, i7] - - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I5, i7]*SUNF[I2, I4, i8]* - SUNF[i5, I6, i7] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I3, i7]* - SUNF[I2, I5, i8]*SUNF[i5, I6, i7] - (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I4, i7]*SUNF[I2, I5, i8]*SUNF[i5, I6, i7] - - (72*I)*SUND[I4, I5, i8]*SUNF[I1, i3, i5]*SUNF[I2, i3, I3]* - SUNF[i5, I6, i8] - (72*I)*SUND[I3, I5, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I4]*SUNF[i5, I6, i8] - (72*I)*SUND[I3, I4, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I5]*SUNF[i5, I6, i8] - - (18*I)*SUND[I4, I5, i8]*SUNF[I1, I2, i3]*SUNF[i3, I3, i5]* - SUNF[i5, I6, i8] + (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I4]* - SUNF[i3, I3, i5]*SUNF[i5, I6, i8] + (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i3, I5]*SUNF[i3, I3, i5]*SUNF[i5, I6, i8] - - (18*I)*SUND[I3, I5, i8]*SUNF[I1, I2, i3]*SUNF[i3, I4, i5]* - SUNF[i5, I6, i8] + (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I3]* - SUNF[i3, I4, i5]*SUNF[i5, I6, i8] + (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I5]*SUNF[i3, I4, i5]*SUNF[i5, I6, i8] + - (18*I)*SUND[I3, I4, i8]*SUNF[I1, I2, i3]*SUNF[i3, i5, I5]* - SUNF[i5, I6, i8] - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, I3]* - SUNF[i3, i5, I5]*SUNF[i5, I6, i8] - (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I4]*SUNF[i3, i5, I5]*SUNF[i5, I6, i8] - - 45*SUNF[I1, i6, I6]*SUNF[I2, I4, i9]*SUNF[I3, i8, i9]*SUNF[I5, i6, i8] + - 45*SUNF[I1, I4, i6]*SUNF[I2, I6, i9]*SUNF[I3, i8, i9]*SUNF[I5, i6, i8] - - 45*SUNF[I1, i6, I6]*SUNF[I2, I3, i9]*SUNF[I4, i8, i9]*SUNF[I5, i6, i8] + - 45*SUNF[I1, I3, i6]*SUNF[I2, I6, i9]*SUNF[I4, i8, i9]*SUNF[I5, i6, i8] - - (45*I)*SUND[i1, I2, I6]*SUNF[i1, I4, i9]*SUNF[I1, I3, i8]* - SUNF[I5, i8, i9] - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I6, i9]* - SUNF[I1, I3, i8]*SUNF[I5, i8, i9] - (45*I)*SUND[i1, I2, I6]* - SUNF[i1, I3, i9]*SUNF[I1, I4, i8]*SUNF[I5, i8, i9] - - (45*I)*SUND[i1, I2, I3]*SUNF[i1, I6, i9]*SUNF[I1, I4, i8]* - SUNF[I5, i8, i9] - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I3, i9]* - SUNF[I1, I6, i8]*SUNF[I5, i8, i9] - (45*I)*SUND[i1, I2, I3]* - SUNF[i1, I4, i9]*SUNF[I1, I6, i8]*SUNF[I5, i8, i9] - - 45*SUNF[I1, i6, I6]*SUNF[I2, I4, i9]*SUNF[I3, i6, i8]*SUNF[I5, i8, i9] + - 45*SUNF[I1, I4, i6]*SUNF[I2, I6, i9]*SUNF[I3, i6, i8]*SUNF[I5, i8, i9] - - 45*SUNF[I1, i6, I6]*SUNF[I2, I3, i9]*SUNF[I4, i6, i8]*SUNF[I5, i8, i9] + - 45*SUNF[I1, I3, i6]*SUNF[I2, I6, i9]*SUNF[I4, i6, i8]*SUNF[I5, i8, i9] - - 45*SUNF[I1, I5, i6]*SUNF[I2, I4, i9]*SUNF[I3, i8, i9]*SUNF[i6, I6, i8] - - 45*SUNF[I1, I4, i6]*SUNF[I2, I5, i9]*SUNF[I3, i8, i9]*SUNF[i6, I6, i8] - - 45*SUNF[I1, I5, i6]*SUNF[I2, I3, i9]*SUNF[I4, i8, i9]*SUNF[i6, I6, i8] - - 45*SUNF[I1, I3, i6]*SUNF[I2, I5, i9]*SUNF[I4, i8, i9]*SUNF[i6, I6, i8] - - 45*SUNF[I1, I4, i6]*SUNF[I2, I3, i9]*SUNF[I5, i8, i9]*SUNF[i6, I6, i8] - - 45*SUNF[I1, I3, i6]*SUNF[I2, I4, i9]*SUNF[I5, i8, i9]*SUNF[i6, I6, i8] - - (45*I)*SUND[i1, I2, I5]*SUNF[i1, I4, i9]*SUNF[I1, I3, i8]* - SUNF[I6, i8, i9] - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I5, i9]* - SUNF[I1, I3, i8]*SUNF[I6, i8, i9] - (45*I)*SUND[i1, I2, I5]* - SUNF[i1, I3, i9]*SUNF[I1, I4, i8]*SUNF[I6, i8, i9] - - (45*I)*SUND[i1, I2, I3]*SUNF[i1, I5, i9]*SUNF[I1, I4, i8]* - SUNF[I6, i8, i9] - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I3, i9]* - SUNF[I1, I5, i8]*SUNF[I6, i8, i9] - (45*I)*SUND[i1, I2, I3]* - SUNF[i1, I4, i9]*SUNF[I1, I5, i8]*SUNF[I6, i8, i9] + - 45*SUNF[I1, I5, i6]*SUNF[I2, I4, i9]*SUNF[I3, i6, i8]*SUNF[I6, i8, i9] + - 45*SUNF[I1, I4, i6]*SUNF[I2, I5, i9]*SUNF[I3, i6, i8]*SUNF[I6, i8, i9] + - 45*SUNF[I1, I5, i6]*SUNF[I2, I3, i9]*SUNF[I4, i6, i8]*SUNF[I6, i8, i9] + - 45*SUNF[I1, I3, i6]*SUNF[I2, I5, i9]*SUNF[I4, i6, i8]*SUNF[I6, i8, i9] + - 45*SUNF[I1, I4, i6]*SUNF[I2, I3, i9]*SUNF[I5, i6, i8]*SUNF[I6, i8, i9] + - 45*SUNF[I1, I3, i6]*SUNF[I2, I4, i9]*SUNF[I5, i6, i8]*SUNF[I6, i8, i9])/ -(1080*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-72*SUND[I1, I5, I6]*SUND[I2, I3, I4] + 108*SUND[I1, I4, I6]* - SUND[I2, I3, I5] + 108*SUND[I1, I4, I5]*SUND[I2, I3, I6] - - 72*SUND[I1, I3, I6]*SUND[I2, I4, I5] - 72*SUND[I1, I3, I5]* - SUND[I2, I4, I6] + 108*SUND[I1, I3, I4]*SUND[I2, I5, I6] - - 72*SUND[I1, I2, I6]*SUND[I3, I4, I5] - 72*SUND[I1, I2, I5]* - SUND[I3, I4, I6] + 108*SUND[I1, I2, I4]*SUND[I3, I5, I6] + - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I5] - - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I5] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[i4, I4, I5] + - 72*SUND[I1, i4, i6]*SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUND[i4, I4, I5] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, I6, i8]*SUND[i4, I4, I5] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUND[i4, I4, I5] - - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, I5, i8]*SUND[i4, I4, I6] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUND[i4, I4, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[i4, I4, I6] + - 72*SUND[I1, i4, i6]*SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUND[i4, I4, I6] + - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I4]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUND[I3, i4, I4]*SUND[i4, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, I4]*SUND[I3, i6, i8]*SUND[i4, I5, i6] - - 18*SUND[I1, i4, I4]*SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I4]*SUND[I3, I6, i8]*SUND[i4, I5, i6] - - 18*SUND[I1, i4, I4]*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUND[i4, I4, I6]*SUND[i4, I5, i6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I4, I6]*SUND[i4, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUND[i4, I4, I6]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUND[I3, i4, I4]*SUND[i4, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I4]*SUND[i4, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I4]*SUND[I3, I5, i8]*SUND[i4, i6, I6] - - 18*SUND[I1, i4, I4]*SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUND[i4, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, I4]*SUND[I3, i6, i8]*SUND[i4, i6, I6] - - 18*SUND[I1, i4, I4]*SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUND[i4, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUND[i4, I4, I5]*SUND[i4, i6, I6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUND[i4, I4, I5]*SUND[i4, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUND[i4, I4, I5]*SUND[i4, i6, I6] - - 72*SUND[I1, I2, I3]*SUND[I4, I5, I6] + 27*SUND[I1, I6, i8]* - SUND[I2, i4, i6]*SUND[I3, i4, I4]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I6, i8]*SUND[I3, i4, I4]*SUND[I5, i6, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, I4]*SUND[I3, i4, i6]*SUND[I5, i6, i8] - - 18*SUND[I1, i4, I4]*SUND[I2, I6, i8]*SUND[I3, i4, i6]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I4]*SUND[I3, I6, i8]*SUND[I5, i6, i8] - - 18*SUND[I1, i4, I4]*SUND[I2, i4, i6]*SUND[I3, I6, i8]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i8]*SUND[i4, I4, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[i4, I4, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I6]*SUND[I5, i6, i8] - - 18*SUND[I1, i4, I4]*SUND[I2, I3, i8]*SUND[i4, i6, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I4]*SUND[i4, i6, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I4]*SUND[i4, i6, I6]*SUND[I5, i6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I4]*SUND[I5, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, i4, I4]*SUND[I5, I6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, I4]*SUND[I3, i4, i6]*SUND[I5, I6, i8] - - 18*SUND[I1, i4, I4]*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[I5, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I4]*SUND[I3, i6, i8]*SUND[I5, I6, i8] - - 18*SUND[I1, i4, I4]*SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUND[I5, I6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I4]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I5, i8]*SUND[I3, i4, I4]*SUND[i6, I6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, I4]*SUND[I3, i4, i6]*SUND[i6, I6, i8] - - 18*SUND[I1, i4, I4]*SUND[I2, I5, i8]*SUND[I3, i4, i6]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i4, I4]*SUND[I3, I5, i8]*SUND[i6, I6, i8] - - 18*SUND[I1, i4, I4]*SUND[I2, i4, i6]*SUND[I3, I5, i8]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i8]*SUND[i4, I4, I5]*SUND[i6, I6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, i6]*SUND[i4, I4, I5]*SUND[i6, I6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, i6]*SUND[i4, I4, I5]*SUND[i6, I6, i8] - - 18*SUND[I1, i4, I4]*SUND[I2, I3, i8]*SUND[i4, I5, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I3, i8]*SUND[I2, i4, I4]*SUND[i4, I5, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I4]*SUND[i4, I5, i6]*SUND[i6, I6, i8] + - 36*SUND[I3, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I2] + - 36*SUND[I3, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I2] + - 36*SUND[I3, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I2] + - 36*SUND[I2, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I3] + - 36*SUND[I2, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I3] + - 36*SUND[I2, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I3] - - 48*SUND[I2, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I1, I4] - - 48*SUND[I2, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I1, I4] - - 48*SUND[I2, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I4] + - 36*SUND[I2, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I1, I5] + - 36*SUND[I2, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I1, I5] + - 36*SUND[I2, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I1, I5] + - 36*SUND[I2, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I1, I6] + - 36*SUND[I2, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I1, I6] + - 36*SUND[I2, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I1, I6] - - 24*SUND[I1, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I2, I3] - - 24*SUND[I1, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I2, I3] - - 24*SUND[I1, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I3] + - 12*SUND[I1, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I2, I4] + - 12*SUND[I1, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I2, I4] + - 12*SUND[I1, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I4] - - 24*SUND[I1, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I2, I5] - - 24*SUND[I1, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I2, I5] - - 24*SUND[I1, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I2, I5] - - 24*SUND[I1, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I2, I6] - - 24*SUND[I1, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I2, I6] - - 24*SUND[I1, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I2, I6] + - 12*SUND[I1, i5, I6]*SUND[I2, i5, I5]*SUNDelta[I3, I4] + - 12*SUND[I1, i5, I5]*SUND[I2, i5, I6]*SUNDelta[I3, I4] + - 12*SUND[I1, I2, i5]*SUND[i5, I5, I6]*SUNDelta[I3, I4] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 24*SUND[I1, i5, I6]*SUND[I2, I4, i5]*SUNDelta[I3, I5] - - 24*SUND[I1, I4, i5]*SUND[I2, i5, I6]*SUNDelta[I3, I5] - - 24*SUND[I1, I2, i5]*SUND[I4, i5, I6]*SUNDelta[I3, I5] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 32*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 24*SUND[I1, i5, I5]*SUND[I2, I4, i5]*SUNDelta[I3, I6] - - 24*SUND[I1, I4, i5]*SUND[I2, i5, I5]*SUNDelta[I3, I6] - - 24*SUND[I1, I2, i5]*SUND[I4, i5, I5]*SUNDelta[I3, I6] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 32*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - 12*SUND[I1, i5, I6]*SUND[I2, I3, i5]*SUNDelta[I4, I5] + - 12*SUND[I1, I3, i5]*SUND[I2, i5, I6]*SUNDelta[I4, I5] + - 12*SUND[I1, I2, i5]*SUND[I3, i5, I6]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - 12*SUND[I1, i5, I5]*SUND[I2, I3, i5]*SUNDelta[I4, I6] + - 12*SUND[I1, I3, i5]*SUND[I2, i5, I5]*SUNDelta[I4, I6] + - 12*SUND[I1, I2, i5]*SUND[I3, i5, I5]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 24*SUND[I1, I4, i5]*SUND[I2, I3, i5]*SUNDelta[I5, I6] - - 24*SUND[I1, I3, i5]*SUND[I2, I4, i5]*SUNDelta[I5, I6] - - 24*SUND[I1, I2, i5]*SUND[I3, I4, i5]*SUNDelta[I5, I6] - - 32*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6] + - (45*I)*SUND[i1, I6, i8]*SUND[I3, i6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I1, I2] + (45*I)*SUND[i1, I5, i8]*SUND[I3, i6, i8]* - SUND[I4, i6, I6]*SUNF[i1, I1, I2] + (45*I)*SUND[i1, I6, i8]* - SUND[I3, I4, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I2] + - (45*I)*SUND[i1, I3, i8]*SUND[I4, i6, I6]*SUND[I5, i6, i8]* - SUNF[i1, I1, I2] + (45*I)*SUND[i1, I5, i8]*SUND[I3, I4, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I2] + (45*I)*SUND[i1, I3, i8]* - SUND[I4, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I5, I6]*SUNDelta[I3, I4]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I4, I6]*SUNDelta[I3, I5]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I4, I5]*SUNDelta[I3, I6]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I3, I6]*SUNDelta[I4, I5]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I3, I5]*SUNDelta[I4, I6]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I3, I4]*SUNDelta[I5, I6]*SUNF[i1, I1, I2] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, i6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I1, I3] + (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, i8]* - SUND[I4, i6, I6]*SUNF[i1, I1, I3] + (45*I)*SUND[i1, I6, i8]* - SUND[I2, I4, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I3] + - (45*I)*SUND[i1, I2, i8]*SUND[I4, i6, I6]*SUND[I5, i6, i8]* - SUNF[i1, I1, I3] + (45*I)*SUND[i1, I5, i8]*SUND[I2, I4, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I3] + (45*I)*SUND[i1, I2, i8]* - SUND[I4, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I5, I6]*SUNDelta[I2, I4]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I4, I6]*SUNDelta[I2, I5]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I4, I5]*SUNDelta[I2, I6]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I2, I6]*SUNDelta[I4, I5]*SUNF[i1, I1, I3] + - (60*I)*SUND[i1, I2, I5]*SUNDelta[I4, I6]*SUNF[i1, I1, I3] + - (120*I)*SUND[i1, I2, I4]*SUNDelta[I5, I6]*SUNF[i1, I1, I3] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, I4, i6]* - SUNF[i1, I1, I5] + (45*I)*SUND[i1, I6, i8]*SUND[I2, I4, i6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I5] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, i6, i8]*SUND[I4, i6, I6]*SUNF[i1, I1, I5] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, i6, i8]*SUND[I4, i6, I6]* - SUNF[i1, I1, I5] + (45*I)*SUND[i1, I3, i8]*SUND[I2, I4, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I5] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, I4, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I4, I6]*SUNDelta[I2, I3]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I3, I6]*SUNDelta[I2, I4]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I3, I4]*SUNDelta[I2, I6]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I2, I6]*SUNDelta[I3, I4]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I2, I4]*SUNDelta[I3, I6]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I2, I3]*SUNDelta[I4, I6]*SUNF[i1, I1, I5] + - (72*I)*SUND[i1, I4, I6]*SUND[I2, i6, i8]*SUND[I3, I5, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I4, I6]*SUND[I2, I5, i8]* - SUND[I3, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I4, I5]* - SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I4, I5]*SUND[I2, i6, i8]*SUND[I3, I6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I4, I6]*SUND[I2, I3, i8]* - SUND[I5, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I4]* - SUND[I2, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I2, I4]*SUND[I3, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I4]*SUND[I2, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I4]* - SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I4, I5]*SUND[I2, I3, i8]*SUND[i6, I6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I4]*SUND[I2, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I4]* - SUND[I3, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I1, i6] + - (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, I4, i6]* - SUNF[i1, I1, I6] + (45*I)*SUND[i1, I5, i8]*SUND[I2, I4, i6]* - SUND[I3, i6, i8]*SUNF[i1, I1, I6] + (45*I)*SUND[i1, I3, i8]* - SUND[I2, i6, i8]*SUND[I4, I5, i6]*SUNF[i1, I1, I6] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, i6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I1, I6] + (45*I)*SUND[i1, I3, i8]*SUND[I2, I4, i6]* - SUND[I5, i6, i8]*SUNF[i1, I1, I6] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, I4, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I4, I5]*SUNDelta[I2, I3]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I3, I5]*SUNDelta[I2, I4]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I3, I4]*SUNDelta[I2, I5]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I2, I5]*SUNDelta[I3, I4]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I2, I4]*SUNDelta[I3, I5]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I2, I3]*SUNDelta[I4, I5]*SUNF[i1, I1, I6] - - (108*I)*SUND[i1, i6, I6]*SUND[I2, I5, i8]*SUND[I3, I4, i6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]*SUND[I2, I6, i8]* - SUND[I3, I4, i6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, i6, I6]* - SUND[I2, I4, i6]*SUND[I3, I5, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I5, i6]*SUND[I2, I4, i6]*SUND[I3, I6, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, i6, I6]*SUND[I2, I3, i8]* - SUND[I4, I5, i6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]* - SUND[I2, I6, i8]*SUND[I4, I5, i6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I2, i6]*SUND[I3, I6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]*SUND[I2, I3, i8]* - SUND[I4, i6, I6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]* - SUND[I2, I5, i8]*SUND[I4, i6, I6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I2, i6]*SUND[I3, I5, i8]*SUND[I4, i6, I6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I3, i6]*SUND[I2, I4, i6]* - SUND[I5, I6, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I2, i6]* - SUND[I3, I4, i6]*SUND[I5, I6, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I4, I6]*SUND[I1, i6, i8]*SUND[I3, I5, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I4, I6]*SUND[I1, I5, i8]* - SUND[I3, i6, i8]*SUNF[i1, I2, i6] + (27*I)*SUND[i1, I4, I5]* - SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[i1, I2, i6] - - (108*I)*SUND[i1, I4, I5]*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I4, I6]*SUND[I1, I3, i8]* - SUND[I5, i6, i8]*SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I4]* - SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I2, i6] - - (18*I)*SUND[i1, I1, I4]*SUND[I3, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I2, i6] - (108*I)*SUND[i1, I3, I4]*SUND[I1, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I4]* - SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I2, i6] + - (27*I)*SUND[i1, I4, I5]*SUND[I1, I3, i8]*SUND[i6, I6, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I4]*SUND[I1, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I4]* - SUND[I3, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I2, i6] + - (27*I)*SUND[i1, i6, I6]*SUND[I1, I5, i8]*SUND[I3, I4, i6]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I6, i8]* - SUND[I3, I4, i6]*SUNF[i1, I2, i8] - (18*I)*SUND[i1, i6, I6]* - SUND[I1, I4, i6]*SUND[I3, I5, i8]*SUNF[i1, I2, i8] - - (18*I)*SUND[i1, I5, i6]*SUND[I1, I4, i6]*SUND[I3, I6, i8]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I3, i8]* - SUND[I4, I5, i6]*SUNF[i1, I2, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I6, i8]*SUND[I4, I5, i6]*SUNF[i1, I2, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I3, I6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I3, i8]* - SUND[I4, i6, I6]*SUNF[i1, I2, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I5, i8]*SUND[I4, i6, I6]*SUNF[i1, I2, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I3, I5, i8]*SUND[I4, i6, I6]* - SUNF[i1, I2, i8] - (18*I)*SUND[i1, I3, i6]*SUND[I1, I4, i6]* - SUND[I5, I6, i8]*SUNF[i1, I2, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I3, I4, i6]*SUND[I5, I6, i8]*SUNF[i1, I2, i8] - - (108*I)*SUND[i1, I4, I6]*SUND[I1, i6, i8]*SUND[I2, I5, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I4, I6]*SUND[I1, I5, i8]* - SUND[I2, i6, i8]*SUNF[i1, I3, i6] + (27*I)*SUND[i1, I4, I5]* - SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i1, I3, i6] - - (108*I)*SUND[i1, I4, I5]*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I4, I6]*SUND[I1, I2, i8]* - SUND[I5, i6, i8]*SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I4]* - SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I3, i6] - - (18*I)*SUND[i1, I1, I4]*SUND[I2, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I3, i6] - (108*I)*SUND[i1, I2, I4]*SUND[I1, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I4]* - SUND[I2, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I3, i6] + - (27*I)*SUND[i1, I4, I5]*SUND[I1, I2, i8]*SUND[i6, I6, i8]* - SUNF[i1, I3, i6] + (27*I)*SUND[i1, I2, I4]*SUND[I1, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I3, i6] - (18*I)*SUND[i1, I1, I4]* - SUND[I2, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I3, i6] + - (27*I)*SUND[i1, i6, I6]*SUND[I1, I5, i8]*SUND[I2, I4, i6]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I6, i8]* - SUND[I2, I4, i6]*SUNF[i1, I3, i8] - (18*I)*SUND[i1, i6, I6]* - SUND[I1, I4, i6]*SUND[I2, I5, i8]*SUNF[i1, I3, i8] - - (18*I)*SUND[i1, I5, i6]*SUND[I1, I4, i6]*SUND[I2, I6, i8]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I2, i8]* - SUND[I4, I5, i6]*SUNF[i1, I3, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I6, i8]*SUND[I4, I5, i6]*SUNF[i1, I3, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I6, i8]*SUND[I4, I5, i6]* - SUNF[i1, I3, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I2, i8]* - SUND[I4, i6, I6]*SUNF[i1, I3, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I5, i8]*SUND[I4, i6, I6]*SUNF[i1, I3, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I5, i8]*SUND[I4, i6, I6]* - SUNF[i1, I3, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I4, i6]* - SUND[I5, I6, i8]*SUNF[i1, I3, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I4, i6]*SUND[I5, I6, i8]*SUNF[i1, I3, i8] - - (108*I)*SUND[i1, I4, I6]*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I4, I6]*SUND[I1, I3, i8]* - SUND[I2, i6, i8]*SUNF[i1, I5, i6] + (27*I)*SUND[i1, I3, I4]* - SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i1, I5, i6] - - (108*I)*SUND[i1, I3, I4]*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I4, I6]*SUND[I1, I2, i8]* - SUND[I3, i6, i8]*SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I4]* - SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUNF[i1, I5, i6] - - (18*I)*SUND[i1, I1, I4]*SUND[I2, I6, i8]*SUND[I3, i6, i8]* - SUNF[i1, I5, i6] - (108*I)*SUND[i1, I2, I4]*SUND[I1, i6, i8]* - SUND[I3, I6, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I4]* - SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUNF[i1, I5, i6] + - (27*I)*SUND[i1, I3, I4]*SUND[I1, I2, i8]*SUND[i6, I6, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I4]*SUND[I1, I3, i8]* - SUND[i6, I6, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I4]* - SUND[I2, I3, i8]*SUND[i6, I6, i8]*SUNF[i1, I5, i6] - - (18*I)*SUND[i1, i6, I6]*SUND[I1, I4, i6]*SUND[I2, I3, i8]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I3, i8]* - SUND[I2, I4, i6]*SUNF[i1, I5, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I6, i8]*SUND[I2, I4, i6]*SUNF[i1, I5, i8] - - (18*I)*SUND[i1, I3, i6]*SUND[I1, I4, i6]*SUND[I2, I6, i8]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I2, i8]* - SUND[I3, I4, i6]*SUNF[i1, I5, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I6, i8]*SUND[I3, I4, i6]*SUNF[i1, I5, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I6, i8]*SUND[I3, I4, i6]* - SUNF[i1, I5, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I4, i6]* - SUND[I3, I6, i8]*SUNF[i1, I5, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I4, i6]*SUND[I3, I6, i8]*SUNF[i1, I5, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I2, i8]*SUND[I4, i6, I6]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I3, i8]* - SUND[I4, i6, I6]*SUNF[i1, I5, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i8]*SUND[I4, i6, I6]*SUNF[i1, I5, i8] + - (108*I)*SUND[i1, I4, I5]*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUNF[i1, i6, I6] + (108*I)*SUND[i1, I3, I4]*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUNF[i1, i6, I6] - (27*I)*SUND[i1, I4, I5]* - SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I3, I4]*SUND[I1, I5, i8]*SUND[I2, i6, i8]* - SUNF[i1, i6, I6] + (108*I)*SUND[i1, I2, I4]*SUND[I1, i6, i8]* - SUND[I3, I5, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I4]* - SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I4, I5]*SUND[I1, I2, i8]*SUND[I3, i6, i8]* - SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I4]*SUND[I1, I5, i8]* - SUND[I3, i6, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I4]* - SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I3, I4]*SUND[I1, I2, i8]*SUND[I5, i6, i8]* - SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I4]*SUND[I1, I3, i8]* - SUND[I5, i6, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I4]* - SUND[I2, I3, i8]*SUND[I5, i6, i8]*SUNF[i1, i6, I6] - - (18*I)*SUND[i1, I5, i6]*SUND[I1, I4, i6]*SUND[I2, I3, i8]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I3, i8]* - SUND[I2, I4, i6]*SUNF[i1, I6, i8] + (27*I)*SUND[i1, I3, i6]* - SUND[I1, I5, i8]*SUND[I2, I4, i6]*SUNF[i1, I6, i8] - - (18*I)*SUND[i1, I3, i6]*SUND[I1, I4, i6]*SUND[I2, I5, i8]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I2, i8]* - SUND[I3, I4, i6]*SUNF[i1, I6, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I5, i8]*SUND[I3, I4, i6]*SUNF[i1, I6, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I5, i8]*SUND[I3, I4, i6]* - SUNF[i1, I6, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I4, i6]* - SUND[I3, I5, i8]*SUNF[i1, I6, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I4, i6]*SUND[I3, I5, i8]*SUNF[i1, I6, i8] + - (27*I)*SUND[i1, I3, i6]*SUND[I1, I2, i8]*SUND[I4, I5, i6]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I2, i6]*SUND[I1, I3, i8]* - SUND[I4, I5, i6]*SUNF[i1, I6, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i8]*SUND[I4, I5, i6]*SUNF[i1, I6, i8] - - 45*SUND[i1, I4, I6]*SUND[i3, I5, i8]*SUNF[i1, I3, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I4, I5]*SUND[i3, I6, i8]*SUNF[i1, I3, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I4, I6]*SUND[i3, I3, i8]*SUNF[i1, I5, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I4]*SUND[i3, I6, i8]*SUNF[i1, I5, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I4, I5]*SUND[i3, I3, i8]*SUNF[i1, I6, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I4]*SUND[i3, I5, i8]*SUNF[i1, I6, i8]*SUNF[I1, I2, i3] - - (180*I)*SUND[I3, I5, I6]*SUNF[I1, I2, I4] + (120*I)*SUND[i5, I5, I6]* - SUNDelta[I3, I4]*SUNF[I1, I2, i5] + (120*I)*SUND[I3, i5, I6]* - SUNDelta[I4, I5]*SUNF[I1, I2, i5] + (120*I)*SUND[I3, i5, I5]* - SUNDelta[I4, I6]*SUNF[I1, I2, i5] - 45*SUND[i1, I6, i8]*SUND[I4, I5, i8]* - SUNF[i1, I3, i5]*SUNF[I1, I2, i5] - 45*SUND[i1, I5, i8]*SUND[I4, I6, i8]* - SUNF[i1, I3, i5]*SUNF[I1, I2, i5] + 45*SUND[i1, I6, i8]*SUND[I3, I4, i8]* - SUNF[i1, i5, I5]*SUNF[I1, I2, i5] + 45*SUND[i1, I3, i8]*SUND[I4, I6, i8]* - SUNF[i1, i5, I5]*SUNF[I1, I2, i5] + 45*SUND[i1, I5, i8]*SUND[I3, I4, i8]* - SUNF[i1, i5, I6]*SUNF[I1, I2, i5] + 45*SUND[i1, I3, i8]*SUND[I4, I5, i8]* - SUNF[i1, i5, I6]*SUNF[I1, I2, i5] + 45*SUND[i1, I4, I6]*SUND[i3, I5, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I3] + 45*SUND[i1, I4, I5]*SUND[i3, I6, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I3] + 45*SUND[i1, I4, I6]*SUND[I2, i3, i8]* - SUNF[i1, I5, i8]*SUNF[I1, i3, I3] + 45*SUND[i1, I2, I4]*SUND[i3, I6, i8]* - SUNF[i1, I5, i8]*SUNF[I1, i3, I3] + 45*SUND[i1, I4, I5]*SUND[I2, i3, i8]* - SUNF[i1, I6, i8]*SUNF[I1, i3, I3] + 45*SUND[i1, I2, I4]*SUND[i3, I5, i8]* - SUNF[i1, I6, i8]*SUNF[I1, i3, I3] + 45*SUND[i1, I4, I6]*SUND[i3, I3, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I3, I4]*SUND[i3, I6, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I4, I6]*SUND[I2, i3, i8]* - SUNF[i1, I3, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I2, I4]*SUND[i3, I6, i8]* - SUNF[i1, I3, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I3, I4]*SUND[I2, i3, i8]* - SUNF[i1, I6, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I2, I4]*SUND[i3, I3, i8]* - SUNF[i1, I6, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I4, I5]*SUND[i3, I3, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I3, I4]*SUND[i3, I5, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I4, I5]*SUND[I2, i3, i8]* - SUNF[i1, I3, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I2, I4]*SUND[i3, I5, i8]* - SUNF[i1, I3, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I3, I4]*SUND[I2, i3, i8]* - SUNF[i1, I5, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I2, I4]*SUND[i3, I3, i8]* - SUNF[i1, I5, i8]*SUNF[I1, i3, I6] - 108*SUND[i1, I4, I6]* - SUND[I3, I5, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] - - 108*SUND[i1, I4, I5]*SUND[I3, I6, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] - - 108*SUND[i1, I3, I4]*SUND[I5, I6, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I4, I6]*SUND[I2, I5, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I4, I5]*SUND[I2, I6, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I4]*SUND[I5, I6, i8]*SUNF[i1, i3, I3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I4, I6]*SUND[I2, I3, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I4]*SUND[I2, I6, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I4]*SUND[I3, I6, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I4, I5]*SUND[I2, I3, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I4]*SUND[I2, I5, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I4]*SUND[I3, I5, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] - - (180*I)*SUND[I2, I5, I6]*SUNF[I1, I3, I4] + (120*I)*SUND[i5, I5, I6]* - SUNDelta[I2, I4]*SUNF[I1, I3, i5] + (120*I)*SUND[I2, i5, I6]* - SUNDelta[I4, I5]*SUNF[I1, I3, i5] + (120*I)*SUND[I2, i5, I5]* - SUNDelta[I4, I6]*SUNF[I1, I3, i5] - 45*SUND[i1, I6, i8]*SUND[I4, I5, i8]* - SUNF[i1, I2, i5]*SUNF[I1, I3, i5] - 45*SUND[i1, I5, i8]*SUND[I4, I6, i8]* - SUNF[i1, I2, i5]*SUNF[I1, I3, i5] + 45*SUND[i1, I6, i8]*SUND[I2, I4, i8]* - SUNF[i1, i5, I5]*SUNF[I1, I3, i5] + 45*SUND[i1, I2, i8]*SUND[I4, I6, i8]* - SUNF[i1, i5, I5]*SUNF[I1, I3, i5] + 45*SUND[i1, I5, i8]*SUND[I2, I4, i8]* - SUNF[i1, i5, I6]*SUNF[I1, I3, i5] + 45*SUND[i1, I2, i8]*SUND[I4, I5, i8]* - SUNF[i1, i5, I6]*SUNF[I1, I3, i5] - (18*I)*SUND[I2, I6, i8]* - SUND[I3, i6, i8]*SUND[i4, I5, i6]*SUNF[I1, i4, I4] - - (18*I)*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUND[i4, I5, i6]* - SUNF[I1, i4, I4] - (18*I)*SUND[I2, i6, i8]*SUND[I3, I5, i8]* - SUND[i4, i6, I6]*SUNF[I1, i4, I4] - (18*I)*SUND[I2, I5, i8]* - SUND[I3, i6, i8]*SUND[i4, i6, I6]*SUNF[I1, i4, I4] - - (18*I)*SUND[I2, I6, i8]*SUND[I3, i4, i6]*SUND[I5, i6, i8]* - SUNF[I1, i4, I4] - (18*I)*SUND[I2, i4, i6]*SUND[I3, I6, i8]* - SUND[I5, i6, i8]*SUNF[I1, i4, I4] - (18*I)*SUND[I2, I3, i8]* - SUND[i4, i6, I6]*SUND[I5, i6, i8]*SUNF[I1, i4, I4] - - (18*I)*SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUND[I5, I6, i8]* - SUNF[I1, i4, I4] - (18*I)*SUND[I2, i4, i6]*SUND[I3, i6, i8]* - SUND[I5, I6, i8]*SUNF[I1, i4, I4] - (18*I)*SUND[I2, I5, i8]* - SUND[I3, i4, i6]*SUND[i6, I6, i8]*SUNF[I1, i4, I4] - - (18*I)*SUND[I2, i4, i6]*SUND[I3, I5, i8]*SUND[i6, I6, i8]* - SUNF[I1, i4, I4] - (18*I)*SUND[I2, I3, i8]*SUND[i4, I5, i6]* - SUND[i6, I6, i8]*SUNF[I1, i4, I4] + (24*I)*SUND[i5, I5, I6]* - SUNDelta[I2, I3]*SUNF[I1, I4, i5] + (24*I)*SUND[I3, i5, I6]* - SUNDelta[I2, I5]*SUNF[I1, I4, i5] + (24*I)*SUND[I3, i5, I5]* - SUNDelta[I2, I6]*SUNF[I1, I4, i5] + (24*I)*SUND[I2, i5, I6]* - SUNDelta[I3, I5]*SUNF[I1, I4, i5] + (24*I)*SUND[I2, i5, I5]* - SUNDelta[I3, I6]*SUNF[I1, I4, i5] + (24*I)*SUND[I2, I3, i5]* - SUNDelta[I5, I6]*SUNF[I1, I4, i5] + (180*I)*SUND[I2, I3, I6]* - SUNF[I1, I4, I5] + (180*I)*SUND[I2, I3, I5]*SUNF[I1, I4, I6] - - (120*I)*SUND[I3, i5, I6]*SUNDelta[I2, I4]*SUNF[I1, i5, I5] - - (120*I)*SUND[I2, i5, I6]*SUNDelta[I3, I4]*SUNF[I1, i5, I5] - - (120*I)*SUND[I2, I3, i5]*SUNDelta[I4, I6]*SUNF[I1, i5, I5] + - 45*SUND[i1, I6, i8]*SUND[I3, I4, i8]*SUNF[i1, I2, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I3, i8]*SUND[I4, I6, i8]*SUNF[i1, I2, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I6, i8]*SUND[I2, I4, i8]*SUNF[i1, I3, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I2, i8]*SUND[I4, I6, i8]*SUNF[i1, I3, i5]*SUNF[I1, i5, I5] - - 45*SUND[i1, I3, i8]*SUND[I2, I4, i8]*SUNF[i1, i5, I6]*SUNF[I1, i5, I5] - - 45*SUND[i1, I2, i8]*SUND[I3, I4, i8]*SUNF[i1, i5, I6]*SUNF[I1, i5, I5] - - (120*I)*SUND[I3, i5, I5]*SUNDelta[I2, I4]*SUNF[I1, i5, I6] - - (120*I)*SUND[I2, i5, I5]*SUNDelta[I3, I4]*SUNF[I1, i5, I6] - - (120*I)*SUND[I2, I3, i5]*SUNDelta[I4, I5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I5, i8]*SUND[I3, I4, i8]*SUNF[i1, I2, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I3, i8]*SUND[I4, I5, i8]*SUNF[i1, I2, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I5, i8]*SUND[I2, I4, i8]*SUNF[i1, I3, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I2, i8]*SUND[I4, I5, i8]*SUNF[i1, I3, i5]*SUNF[I1, i5, I6] - - 45*SUND[i1, I3, i8]*SUND[I2, I4, i8]*SUNF[i1, i5, I5]*SUNF[I1, i5, I6] - - 45*SUND[i1, I2, i8]*SUND[I3, I4, i8]*SUNF[i1, i5, I5]*SUNF[I1, i5, I6] + - 72*SUND[I3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I4] + - 72*SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I4] + - 72*SUND[I3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I4] - - 18*SUND[I3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i3, i6] - - 18*SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i3, i6] - - 18*SUND[I3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i3, i6] + - 72*SUND[i1, I4, I6]*SUND[I3, I5, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] + - 72*SUND[i1, I4, I5]*SUND[I3, I6, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] + - 72*SUND[i1, I3, I4]*SUND[I5, I6, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I4, I6]*SUND[I1, I5, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I4, I5]*SUND[I1, I6, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I4]*SUND[I5, I6, i8]*SUNF[i1, i3, I3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I4, I6]*SUND[I1, I3, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I4]*SUND[I1, I6, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I4]*SUND[I3, I6, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] - - 27*SUND[i1, I4, I5]*SUND[I1, I3, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I4]*SUND[I1, I5, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I4]*SUND[I3, I5, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] + - 18*SUND[i3, i6, I6]*SUND[I3, I5, i8]*SUNF[I1, I4, i6]*SUNF[I2, i3, i8] + - 18*SUND[i3, I5, i6]*SUND[I3, I6, i8]*SUNF[I1, I4, i6]*SUNF[I2, i3, i8] + - 18*SUND[i3, I3, i6]*SUND[I5, I6, i8]*SUNF[I1, I4, i6]*SUNF[I2, i3, i8] + - (27*I)*SUND[I1, I6, i8]*SUND[I3, i6, i8]*SUND[i4, I5, i6]* - SUNF[I2, i4, I4] - (108*I)*SUND[I1, i6, i8]*SUND[I3, I6, i8]* - SUND[i4, I5, i6]*SUNF[I2, i4, I4] - (108*I)*SUND[I1, i6, i8]* - SUND[I3, I5, i8]*SUND[i4, i6, I6]*SUNF[I2, i4, I4] + - (27*I)*SUND[I1, I5, i8]*SUND[I3, i6, i8]*SUND[i4, i6, I6]* - SUNF[I2, i4, I4] + (27*I)*SUND[I1, I6, i8]*SUND[I3, i4, i6]* - SUND[I5, i6, i8]*SUNF[I2, i4, I4] + (72*I)*SUND[I1, i4, i6]* - SUND[I3, I6, i8]*SUND[I5, i6, i8]*SUNF[I2, i4, I4] + - (27*I)*SUND[I1, I3, i8]*SUND[i4, i6, I6]*SUND[I5, i6, i8]* - SUNF[I2, i4, I4] - (108*I)*SUND[I1, i6, i8]*SUND[I3, i4, i6]* - SUND[I5, I6, i8]*SUNF[I2, i4, I4] + (72*I)*SUND[I1, i4, i6]* - SUND[I3, i6, i8]*SUND[I5, I6, i8]*SUNF[I2, i4, I4] + - (27*I)*SUND[I1, I5, i8]*SUND[I3, i4, i6]*SUND[i6, I6, i8]* - SUNF[I2, i4, I4] + (72*I)*SUND[I1, i4, i6]*SUND[I3, I5, i8]* - SUND[i6, I6, i8]*SUNF[I2, i4, I4] + (27*I)*SUND[I1, I3, i8]* - SUND[i4, I5, i6]*SUND[i6, I6, i8]*SUNF[I2, i4, I4] - - (36*I)*SUND[i5, I5, I6]*SUNDelta[I1, I3]*SUNF[I2, I4, i5] - - (36*I)*SUND[I3, i5, I6]*SUNDelta[I1, I5]*SUNF[I2, I4, i5] - - (36*I)*SUND[I3, i5, I5]*SUNDelta[I1, I6]*SUNF[I2, I4, i5] + - (24*I)*SUND[I1, i5, I6]*SUNDelta[I3, I5]*SUNF[I2, I4, i5] + - (24*I)*SUND[I1, i5, I5]*SUNDelta[I3, I6]*SUNF[I2, I4, i5] + - (24*I)*SUND[I1, I3, i5]*SUNDelta[I5, I6]*SUNF[I2, I4, i5] - - 45*SUND[i3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, I4, i6] - - 45*SUND[i3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, I4, i6] - - 45*SUND[i3, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, I4, i6] - - 45*SUND[i3, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]*SUNF[I2, I4, i6] - - 45*SUND[i3, I5, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I4, i6] - - 45*SUND[i3, I3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I4, i6] + - 108*SUND[i3, i6, I6]*SUND[I3, I5, i8]*SUNF[I1, i3, i8]*SUNF[I2, I4, i6] + - 108*SUND[i3, I5, i6]*SUND[I3, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I4, i6] + - 108*SUND[i3, I3, i6]*SUND[I5, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I4, i6] + - 120*SUNDelta[I5, I6]*SUNF[I1, I3, i6]*SUNF[I2, I4, i6] + - 120*SUNDelta[I3, I6]*SUNF[I1, I5, i6]*SUNF[I2, I4, i6] - - 120*SUNDelta[I3, I5]*SUNF[I1, i6, I6]*SUNF[I2, I4, i6] - - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I5, i9]*SUNF[I1, I3, i8]* - SUNF[I2, i8, i9] - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I6, i9]* - SUNF[I1, I3, i8]*SUNF[I2, i8, i9] - (45*I)*SUND[i1, I4, I6]* - SUNF[i1, I3, i9]*SUNF[I1, I5, i8]*SUNF[I2, i8, i9] - - (45*I)*SUND[i1, I3, I4]*SUNF[i1, I6, i9]*SUNF[I1, I5, i8]* - SUNF[I2, i8, i9] - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I3, i9]* - SUNF[I1, I6, i8]*SUNF[I2, i8, i9] - (45*I)*SUND[i1, I3, I4]* - SUNF[i1, I5, i9]*SUNF[I1, I6, i8]*SUNF[I2, i8, i9] - - 72*SUND[I2, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I4] - - 72*SUND[I2, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I4] - - 72*SUND[I2, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I4] - - (108*I)*SUND[I5, I6, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I4] - 27*SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, i6]* - SUNF[i3, I3, I4] + 108*SUND[I1, i6, i8]*SUND[I5, I6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I4] - 27*SUND[I1, I5, i8]*SUND[i6, I6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I4] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, i5, I5]*SUNF[I2, i3, i8]*SUNF[i3, I3, I4] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, i5, I6]*SUNF[I2, i3, i8]* - SUNF[i3, I3, I4] + (72*I)*SUND[I5, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I4] - (108*I)*SUND[I5, I6, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I4]*SUNF[i3, I3, i5] - - (18*I)*SUND[I5, I6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i5, i8]* - SUNF[i3, I3, i5] + 18*SUND[I2, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I4]* - SUNF[i3, I3, i6] + 18*SUND[I2, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, I4]* - SUNF[i3, I3, i6] + 18*SUND[I2, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I4]* - SUNF[i3, I3, i6] - 27*SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I4]* - SUNF[i3, I3, i6] + 108*SUND[I1, i6, i8]*SUND[I5, I6, i8]* - SUNF[I2, i3, I4]*SUNF[i3, I3, i6] - 27*SUND[I1, I5, i8]*SUND[i6, I6, i8]* - SUNF[I2, i3, I4]*SUNF[i3, I3, i6] - 72*SUND[i1, I4, I6]*SUND[I2, I5, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - 72*SUND[i1, I4, I5]*SUND[I2, I6, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - 72*SUND[i1, I2, I4]*SUND[I5, I6, i8]* - SUNF[i1, I1, i3]*SUNF[i3, I3, i8] - 27*SUND[i1, I4, I6]*SUND[I1, I5, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I3, i8] - 27*SUND[i1, I4, I5]*SUND[I1, I6, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I3, i8] + 18*SUND[i1, I1, I4]*SUND[I5, I6, i8]* - SUNF[i1, I2, i3]*SUNF[i3, I3, i8] + 27*SUND[i1, I4, I6]*SUND[I1, I2, i8]* - SUNF[i1, i3, I5]*SUNF[i3, I3, i8] + 27*SUND[i1, I2, I4]*SUND[I1, I6, i8]* - SUNF[i1, i3, I5]*SUNF[i3, I3, i8] - 18*SUND[i1, I1, I4]*SUND[I2, I6, i8]* - SUNF[i1, i3, I5]*SUNF[i3, I3, i8] + 27*SUND[i1, I4, I5]*SUND[I1, I2, i8]* - SUNF[i1, i3, I6]*SUNF[i3, I3, i8] + 27*SUND[i1, I2, I4]*SUND[I1, I5, i8]* - SUNF[i1, i3, I6]*SUNF[i3, I3, i8] - 18*SUND[i1, I1, I4]*SUND[I2, I5, i8]* - SUNF[i1, i3, I6]*SUNF[i3, I3, i8] - 18*SUND[I2, I6, i8]*SUND[i3, I5, i6]* - SUNF[I1, I4, i6]*SUNF[i3, I3, i8] - 18*SUND[I2, I5, i8]*SUND[i3, i6, I6]* - SUNF[I1, I4, i6]*SUNF[i3, I3, i8] - 18*SUND[I2, i3, i6]*SUND[I5, I6, i8]* - SUNF[I1, I4, i6]*SUNF[i3, I3, i8] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, i5, I5]*SUNF[I2, i3, I4]*SUNF[i3, I3, i8] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, i5, I6]*SUNF[I2, i3, I4]* - SUNF[i3, I3, i8] + 27*SUND[I1, I6, i8]*SUND[i3, I5, i6]*SUNF[I2, I4, i6]* - SUNF[i3, I3, i8] + 27*SUND[I1, I5, i8]*SUND[i3, i6, I6]*SUNF[I2, I4, i6]* - SUNF[i3, I3, i8] + 72*SUND[I1, i3, i6]*SUND[I5, I6, i8]*SUNF[I2, I4, i6]* - SUNF[i3, I3, i8] + 72*SUND[I2, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, i6]* - SUNF[i3, I4, I5] + 72*SUND[I2, i6, i8]*SUND[I3, I6, i8]*SUNF[I1, i3, i6]* - SUNF[i3, I4, I5] + 72*SUND[I2, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]* - SUNF[i3, I4, I5] + (108*I)*SUND[I3, I6, i8]*SUNF[I1, i5, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I4, I5] + 27*SUND[I1, I6, i8]*SUND[I3, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I4, I5] - 108*SUND[I1, i6, i8]* - SUND[I3, I6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I4, I5] + - 27*SUND[I1, I3, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I4, I5] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I3, i5]*SUNF[I2, i3, i8]* - SUNF[i3, I4, I5] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, i8]*SUNF[i3, I4, I5] - (72*I)*SUND[I3, I6, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i5, i8]*SUNF[i3, I4, I5] - - (108*I)*SUND[I2, I6, i8]*SUNF[I1, i5, i8]*SUNF[i3, I3, i5]* - SUNF[i3, I4, I5] + (27*I)*SUND[I1, I6, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I3, i5]*SUNF[i3, I4, I5] - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]* - SUNF[i3, I3, i6]*SUNF[i3, I4, I5] + 108*SUND[I1, i6, i8]* - SUND[I2, I6, i8]*SUNF[i3, I3, i6]*SUNF[i3, I4, I5] - - 27*SUND[I1, I2, i8]*SUND[i6, I6, i8]*SUNF[i3, I3, i6]*SUNF[i3, I4, I5] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I2, i5]*SUNF[i3, I3, i8]* - SUNF[i3, I4, I5] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I6]* - SUNF[i3, I3, i8]*SUNF[i3, I4, I5] + 72*SUND[I2, i6, i8]*SUND[I3, I5, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I4, I6] + 72*SUND[I2, I5, i8]*SUND[I3, i6, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I4, I6] + 72*SUND[I2, I3, i8]*SUND[I5, i6, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I4, I6] + (108*I)*SUND[I3, I5, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, i5]*SUNF[i3, I4, I6] - - 108*SUND[I1, i6, i8]*SUND[I3, I5, i8]*SUNF[I2, i3, i6]*SUNF[i3, I4, I6] + - 27*SUND[I1, I5, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I4, I6] + - 27*SUND[I1, I3, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I4, I6] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I3, i5]*SUNF[I2, i3, i8]* - SUNF[i3, I4, I6] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I5]* - SUNF[I2, i3, i8]*SUNF[i3, I4, I6] - (72*I)*SUND[I3, I5, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i5, i8]*SUNF[i3, I4, I6] - - (108*I)*SUND[I2, I5, i8]*SUNF[I1, i5, i8]*SUNF[i3, I3, i5]* - SUNF[i3, I4, I6] + (27*I)*SUND[I1, I5, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I3, i5]*SUNF[i3, I4, I6] + 108*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUNF[i3, I3, i6]*SUNF[i3, I4, I6] - - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, i6]*SUNF[i3, I4, I6] - - 27*SUND[I1, I2, i8]*SUND[I5, i6, i8]*SUNF[i3, I3, i6]*SUNF[i3, I4, I6] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I2, i5]*SUNF[i3, I3, i8]* - SUNF[i3, I4, I6] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I5]* - SUNF[i3, I3, i8]*SUNF[i3, I4, I6] + (108*I)*SUND[I3, I6, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I4]*SUNF[i3, i5, I5] + - (18*I)*SUND[I3, I6, i8]*SUNF[I1, i3, I4]*SUNF[I2, i5, i8]* - SUNF[i3, i5, I5] - (108*I)*SUND[I2, I6, i8]*SUNF[I1, i5, i8]* - SUNF[i3, I3, I4]*SUNF[i3, i5, I5] + (27*I)*SUND[I1, I6, i8]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I4]*SUNF[i3, i5, I5] + - (108*I)*SUND[I2, I3, i8]*SUNF[I1, i5, i8]*SUNF[i3, I4, I6]* - SUNF[i3, i5, I5] - (27*I)*SUND[I1, I3, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I4, I6]*SUNF[i3, i5, I5] + (108*I)*SUND[I3, I5, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I4]*SUNF[i3, i5, I6] + - (18*I)*SUND[I3, I5, i8]*SUNF[I1, i3, I4]*SUNF[I2, i5, i8]* - SUNF[i3, i5, I6] - (108*I)*SUND[I2, I5, i8]*SUNF[I1, i5, i8]* - SUNF[i3, I3, I4]*SUNF[i3, i5, I6] + (27*I)*SUND[I1, I5, i8]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I4]*SUNF[i3, i5, I6] + - (108*I)*SUND[I2, I3, i8]*SUNF[I1, i5, i8]*SUNF[i3, I4, I5]* - SUNF[i3, i5, I6] - (27*I)*SUND[I1, I3, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I4, I5]*SUNF[i3, i5, I6] + 18*SUND[I2, I6, i8]*SUND[I3, i6, i8]* - SUNF[I1, i3, I4]*SUNF[i3, I5, i6] + 18*SUND[I2, i6, i8]*SUND[I3, I6, i8]* - SUNF[I1, i3, I4]*SUNF[i3, I5, i6] + 18*SUND[I2, I3, i8]*SUND[i6, I6, i8]* - SUNF[I1, i3, I4]*SUNF[i3, I5, i6] - 27*SUND[I1, I6, i8]*SUND[I3, i6, i8]* - SUNF[I2, i3, I4]*SUNF[i3, I5, i6] + 108*SUND[I1, i6, i8]* - SUND[I3, I6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I5, i6] - - 27*SUND[I1, I3, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I4]*SUNF[i3, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUNF[i3, I3, I4]*SUNF[i3, I5, i6] + - 27*SUND[I1, I2, i8]*SUND[i6, I6, i8]*SUNF[i3, I3, I4]*SUNF[i3, I5, i6] + - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUNF[i3, I4, I6]*SUNF[i3, I5, i6] - - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i3, I4, I6]*SUNF[i3, I5, i6] - - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUNF[i3, I4, I6]*SUNF[i3, I5, i6] - - 72*SUND[i1, I4, I6]*SUND[I2, I3, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - - 72*SUND[i1, I3, I4]*SUND[I2, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - - 72*SUND[i1, I2, I4]*SUND[I3, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - - 27*SUND[i1, I4, I6]*SUND[I1, I3, i8]*SUNF[i1, I2, i3]*SUNF[i3, I5, i8] - - 27*SUND[i1, I3, I4]*SUND[I1, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I5, i8] + - 18*SUND[i1, I1, I4]*SUND[I3, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I5, i8] + - 27*SUND[i1, I4, I6]*SUND[I1, I2, i8]*SUNF[i1, i3, I3]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I6, i8]*SUNF[i1, i3, I3]*SUNF[i3, I5, i8] - - 18*SUND[i1, I1, I4]*SUND[I2, I6, i8]*SUNF[i1, i3, I3]*SUNF[i3, I5, i8] + - 27*SUND[i1, I3, I4]*SUND[I1, I2, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I3, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] - - 18*SUND[i1, I1, I4]*SUND[I2, I3, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] - - 18*SUND[I2, I6, i8]*SUND[i3, I3, i6]*SUNF[I1, I4, i6]*SUNF[i3, I5, i8] - - 18*SUND[I2, I3, i8]*SUND[i3, i6, I6]*SUNF[I1, I4, i6]*SUNF[i3, I5, i8] - - 18*SUND[I2, i3, i6]*SUND[I3, I6, i8]*SUNF[I1, I4, i6]*SUNF[i3, I5, i8] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I3, i5]*SUNF[I2, i3, I4]* - SUNF[i3, I5, i8] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, I4]*SUNF[i3, I5, i8] + 27*SUND[I1, I6, i8]*SUND[i3, I3, i6]* - SUNF[I2, I4, i6]*SUNF[i3, I5, i8] + 27*SUND[I1, I3, i8]*SUND[i3, i6, I6]* - SUNF[I2, I4, i6]*SUNF[i3, I5, i8] + 72*SUND[I1, i3, i6]*SUND[I3, I6, i8]* - SUNF[I2, I4, i6]*SUNF[i3, I5, i8] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, I4]*SUNF[i3, I5, i8] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I6]*SUNF[i3, I3, I4]* - SUNF[i3, I5, i8] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I2, i5]* - SUNF[i3, I4, I6]*SUNF[i3, I5, i8] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I3, i5]*SUNF[i3, I4, I6]*SUNF[i3, I5, i8] - - 18*SUND[I2, i6, i8]*SUND[I3, I5, i8]*SUNF[I1, i3, I4]*SUNF[i3, i6, I6] - - 18*SUND[I2, I5, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I4]*SUNF[i3, i6, I6] - - 18*SUND[I2, I3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I4]*SUNF[i3, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I3, I5, i8]*SUNF[I2, i3, I4]*SUNF[i3, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I3, i6, i8]*SUNF[I2, i3, I4]*SUNF[i3, i6, I6] + - 27*SUND[I1, I3, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I4]*SUNF[i3, i6, I6] + - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUNF[i3, I3, I4]*SUNF[i3, i6, I6] - - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I4]*SUNF[i3, i6, I6] - - 27*SUND[I1, I2, i8]*SUND[I5, i6, i8]*SUNF[i3, I3, I4]*SUNF[i3, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i8]*SUNF[i3, I4, I5]*SUNF[i3, i6, I6] + - 27*SUND[I1, I3, i8]*SUND[I2, i6, i8]*SUNF[i3, I4, I5]*SUNF[i3, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUNF[i3, I4, I5]*SUNF[i3, i6, I6] - - 72*SUND[i1, I4, I5]*SUND[I2, I3, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 72*SUND[i1, I3, I4]*SUND[I2, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 72*SUND[i1, I2, I4]*SUND[I3, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 27*SUND[i1, I4, I5]*SUND[I1, I3, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] - - 27*SUND[i1, I3, I4]*SUND[I1, I5, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] + - 18*SUND[i1, I1, I4]*SUND[I3, I5, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I4, I5]*SUND[I1, I2, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I5, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I4]*SUND[I2, I5, i8]*SUNF[i1, i3, I3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I3, I4]*SUND[I1, I2, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I4]*SUND[I1, I3, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I4]*SUND[I2, I3, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] - - 18*SUND[I2, I5, i8]*SUND[i3, I3, i6]*SUNF[I1, I4, i6]*SUNF[i3, I6, i8] - - 18*SUND[I2, I3, i8]*SUND[i3, I5, i6]*SUNF[I1, I4, i6]*SUNF[i3, I6, i8] - - 18*SUND[I2, i3, i6]*SUND[I3, I5, i8]*SUNF[I1, I4, i6]*SUNF[i3, I6, i8] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I3, i5]*SUNF[I2, i3, I4]* - SUNF[i3, I6, i8] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, i5, I5]* - SUNF[I2, i3, I4]*SUNF[i3, I6, i8] + 27*SUND[I1, I5, i8]*SUND[i3, I3, i6]* - SUNF[I2, I4, i6]*SUNF[i3, I6, i8] + 27*SUND[I1, I3, i8]*SUND[i3, I5, i6]* - SUNF[I2, I4, i6]*SUNF[i3, I6, i8] + 72*SUND[I1, i3, i6]*SUND[I3, I5, i8]* - SUNF[I2, I4, i6]*SUNF[i3, I6, i8] + (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, I4]*SUNF[i3, I6, i8] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I5]*SUNF[i3, I3, I4]* - SUNF[i3, I6, i8] - (45*I)*SUND[I3, i5, i8]*SUNF[I1, I2, i5]* - SUNF[i3, I4, I5]*SUNF[i3, I6, i8] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I3, i5]*SUNF[i3, I4, I5]*SUNF[i3, I6, i8] + - (27*I)*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[i4, I5, i6]* - SUNF[I3, i4, I4] - (108*I)*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUND[i4, I5, i6]*SUNF[I3, i4, I4] - (108*I)*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUND[i4, i6, I6]*SUNF[I3, i4, I4] + - (27*I)*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[i4, i6, I6]* - SUNF[I3, i4, I4] + (27*I)*SUND[I1, I6, i8]*SUND[I2, i4, i6]* - SUND[I5, i6, i8]*SUNF[I3, i4, I4] + (72*I)*SUND[I1, i4, i6]* - SUND[I2, I6, i8]*SUND[I5, i6, i8]*SUNF[I3, i4, I4] + - (27*I)*SUND[I1, I2, i8]*SUND[i4, i6, I6]*SUND[I5, i6, i8]* - SUNF[I3, i4, I4] - (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]* - SUND[I5, I6, i8]*SUNF[I3, i4, I4] + (72*I)*SUND[I1, i4, i6]* - SUND[I2, i6, i8]*SUND[I5, I6, i8]*SUNF[I3, i4, I4] + - (27*I)*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[i6, I6, i8]* - SUNF[I3, i4, I4] + (72*I)*SUND[I1, i4, i6]*SUND[I2, I5, i8]* - SUND[i6, I6, i8]*SUNF[I3, i4, I4] + (27*I)*SUND[I1, I2, i8]* - SUND[i4, I5, i6]*SUND[i6, I6, i8]*SUNF[I3, i4, I4] - - (36*I)*SUND[i5, I5, I6]*SUNDelta[I1, I2]*SUNF[I3, I4, i5] - - (36*I)*SUND[I2, i5, I6]*SUNDelta[I1, I5]*SUNF[I3, I4, i5] - - (36*I)*SUND[I2, i5, I5]*SUNDelta[I1, I6]*SUNF[I3, I4, i5] + - (24*I)*SUND[I1, i5, I6]*SUNDelta[I2, I5]*SUNF[I3, I4, i5] + - (24*I)*SUND[I1, i5, I5]*SUNDelta[I2, I6]*SUNF[I3, I4, i5] + - (24*I)*SUND[I1, I2, i5]*SUNDelta[I5, I6]*SUNF[I3, I4, i5] + - 45*SUND[i3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i3]*SUNF[I3, I4, i6] + - 45*SUND[i3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, I2, i3]*SUNF[I3, I4, i6] + - 120*SUNDelta[I5, I6]*SUNF[I1, I2, i6]*SUNF[I3, I4, i6] - - 45*SUND[I2, i6, i8]*SUND[i3, I6, i8]*SUNF[I1, i3, I5]*SUNF[I3, I4, i6] - - 45*SUND[I2, i3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]*SUNF[I3, I4, i6] - - 45*SUND[I2, i6, i8]*SUND[i3, I5, i8]*SUNF[I1, i3, I6]*SUNF[I3, I4, i6] - - 45*SUND[I2, i3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I6]*SUNF[I3, I4, i6] + - 108*SUND[I2, I6, i8]*SUND[i3, I5, i6]*SUNF[I1, i3, i8]*SUNF[I3, I4, i6] + - 108*SUND[I2, I5, i8]*SUND[i3, i6, I6]*SUNF[I1, i3, i8]*SUNF[I3, I4, i6] + - 108*SUND[I2, i3, i6]*SUND[I5, I6, i8]*SUNF[I1, i3, i8]*SUNF[I3, I4, i6] + - 120*SUNDelta[I2, I6]*SUNF[I1, I5, i6]*SUNF[I3, I4, i6] - - 120*SUNDelta[I2, I5]*SUNF[I1, i6, I6]*SUNF[I3, I4, i6] - - 27*SUND[I1, I6, i8]*SUND[i3, I5, i6]*SUNF[I2, i3, i8]*SUNF[I3, I4, i6] - - 27*SUND[I1, I5, i8]*SUND[i3, i6, I6]*SUNF[I2, i3, i8]*SUNF[I3, I4, i6] - - 72*SUND[I1, i3, i6]*SUND[I5, I6, i8]*SUNF[I2, i3, i8]*SUNF[I3, I4, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i3, i6]*SUNF[i3, I5, i8]*SUNF[I3, I4, i6] + - 72*SUND[I1, i3, i6]*SUND[I2, I6, i8]*SUNF[i3, I5, i8]*SUNF[I3, I4, i6] + - 27*SUND[I1, I2, i8]*SUND[i3, i6, I6]*SUNF[i3, I5, i8]*SUNF[I3, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[I2, i3, i6]*SUNF[i3, I6, i8]*SUNF[I3, I4, i6] + - 72*SUND[I1, i3, i6]*SUND[I2, I5, i8]*SUNF[i3, I6, i8]*SUNF[I3, I4, i6] + - 27*SUND[I1, I2, i8]*SUND[i3, I5, i6]*SUNF[i3, I6, i8]*SUNF[I3, I4, i6] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I5, i7]*SUNF[I2, i5, i7]* - SUNF[I3, I4, i8] - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, i5, i7]*SUNF[I3, I4, i8] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I5, i7]*SUNF[I2, I4, i8]*SUNF[I3, i5, i7] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I6, i7]*SUNF[I2, I4, i8]* - SUNF[I3, i5, i7] - (72*I)*SUND[I5, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I4]*SUNF[I3, i5, i8] + (18*I)*SUND[I5, I6, i8]* - SUNF[I1, i3, I4]*SUNF[I2, i3, i5]*SUNF[I3, i5, i8] - - (72*I)*SUND[I2, I6, i8]*SUNF[I1, i3, i5]*SUNF[i3, I4, I5]* - SUNF[I3, i5, i8] - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I4, I5]*SUNF[I3, i5, i8] - (72*I)*SUND[I2, I5, i8]* - SUNF[I1, i3, i5]*SUNF[i3, I4, I6]*SUNF[I3, i5, i8] - - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, i5]*SUNF[i3, I4, I6]* - SUNF[I3, i5, i8] + (18*I)*SUND[I2, I6, i8]*SUNF[I1, i3, I4]* - SUNF[i3, i5, I5]*SUNF[I3, i5, i8] - (27*I)*SUND[I1, I6, i8]* - SUNF[I2, i3, I4]*SUNF[i3, i5, I5]*SUNF[I3, i5, i8] - - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I4, I6]*SUNF[i3, i5, I5]* - SUNF[I3, i5, i8] + (18*I)*SUND[I2, I5, i8]*SUNF[I1, i3, I4]* - SUNF[i3, i5, I6]*SUNF[I3, i5, i8] - (27*I)*SUND[I1, I5, i8]* - SUNF[I2, i3, I4]*SUNF[i3, i5, I6]*SUNF[I3, i5, i8] - - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I4, I5]*SUNF[i3, i5, I6]* - SUNF[I3, i5, i8] - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I5, i9]* - SUNF[I1, I2, i8]*SUNF[I3, i8, i9] - (45*I)*SUND[i1, I4, I5]* - SUNF[i1, I6, i9]*SUNF[I1, I2, i8]*SUNF[I3, i8, i9] - - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I2, i9]*SUNF[I1, I5, i8]* - SUNF[I3, i8, i9] - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I6, i9]* - SUNF[I1, I5, i8]*SUNF[I3, i8, i9] - (45*I)*SUND[i1, I4, I5]* - SUNF[i1, I2, i9]*SUNF[I1, I6, i8]*SUNF[I3, i8, i9] - - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I5, i9]*SUNF[I1, I6, i8]* - SUNF[I3, i8, i9] + (27*I)*SUND[I1, I6, i8]*SUND[I2, i6, i8]* - SUND[I3, i4, i6]*SUNF[i4, I4, I5] - (108*I)*SUND[I1, i6, i8]* - SUND[I2, I6, i8]*SUND[I3, i4, i6]*SUNF[i4, I4, I5] + - (27*I)*SUND[I1, I6, i8]*SUND[I2, i4, i6]*SUND[I3, i6, i8]* - SUNF[i4, I4, I5] + (72*I)*SUND[I1, i4, i6]*SUND[I2, I6, i8]* - SUND[I3, i6, i8]*SUNF[i4, I4, I5] - (108*I)*SUND[I1, i6, i8]* - SUND[I2, i4, i6]*SUND[I3, I6, i8]*SUNF[i4, I4, I5] + - (72*I)*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, I6, i8]* - SUNF[i4, I4, I5] - (108*I)*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUND[i4, i6, I6]*SUNF[i4, I4, I5] + (27*I)*SUND[I1, I3, i8]* - SUND[I2, i6, i8]*SUND[i4, i6, I6]*SUNF[i4, I4, I5] + - (27*I)*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUND[i4, i6, I6]* - SUNF[i4, I4, I5] + (72*I)*SUND[I1, i4, i6]*SUND[I2, I3, i8]* - SUND[i6, I6, i8]*SUNF[i4, I4, I5] + (27*I)*SUND[I1, I3, i8]* - SUND[I2, i4, i6]*SUND[i6, I6, i8]*SUNF[i4, I4, I5] + - (27*I)*SUND[I1, I2, i8]*SUND[I3, i4, i6]*SUND[i6, I6, i8]* - SUNF[i4, I4, I5] - (108*I)*SUND[I1, i6, i8]*SUND[I2, I5, i8]* - SUND[I3, i4, i6]*SUNF[i4, I4, I6] + (27*I)*SUND[I1, I5, i8]* - SUND[I2, i6, i8]*SUND[I3, i4, i6]*SUNF[i4, I4, I6] - - (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, I5, i8]* - SUNF[i4, I4, I6] + (72*I)*SUND[I1, i4, i6]*SUND[I2, i6, i8]* - SUND[I3, I5, i8]*SUNF[i4, I4, I6] + (27*I)*SUND[I1, I5, i8]* - SUND[I2, i4, i6]*SUND[I3, i6, i8]*SUNF[i4, I4, I6] + - (72*I)*SUND[I1, i4, i6]*SUND[I2, I5, i8]*SUND[I3, i6, i8]* - SUNF[i4, I4, I6] - (108*I)*SUND[I1, i6, i8]*SUND[I2, I3, i8]* - SUND[i4, I5, i6]*SUNF[i4, I4, I6] + (27*I)*SUND[I1, I3, i8]* - SUND[I2, i6, i8]*SUND[i4, I5, i6]*SUNF[i4, I4, I6] + - (27*I)*SUND[I1, I2, i8]*SUND[I3, i6, i8]*SUND[i4, I5, i6]* - SUNF[i4, I4, I6] + (72*I)*SUND[I1, i4, i6]*SUND[I2, I3, i8]* - SUND[I5, i6, i8]*SUNF[i4, I4, I6] + (27*I)*SUND[I1, I3, i8]* - SUND[I2, i4, i6]*SUND[I5, i6, i8]*SUNF[i4, I4, I6] + - (27*I)*SUND[I1, I2, i8]*SUND[I3, i4, i6]*SUND[I5, i6, i8]* - SUNF[i4, I4, I6] - (36*I)*SUND[I3, i5, I6]*SUNDelta[I1, I2]* - SUNF[I4, i5, I5] - (36*I)*SUND[I2, i5, I6]*SUNDelta[I1, I3]* - SUNF[I4, i5, I5] - (36*I)*SUND[I2, I3, i5]*SUNDelta[I1, I6]* - SUNF[I4, i5, I5] + (24*I)*SUND[I1, i5, I6]*SUNDelta[I2, I3]* - SUNF[I4, i5, I5] + (24*I)*SUND[I1, I3, i5]*SUNDelta[I2, I6]* - SUNF[I4, i5, I5] + (24*I)*SUND[I1, I2, i5]*SUNDelta[I3, I6]* - SUNF[I4, i5, I5] - (36*I)*SUND[I3, i5, I5]*SUNDelta[I1, I2]* - SUNF[I4, i5, I6] - (36*I)*SUND[I2, i5, I5]*SUNDelta[I1, I3]* - SUNF[I4, i5, I6] - (36*I)*SUND[I2, I3, i5]*SUNDelta[I1, I5]* - SUNF[I4, i5, I6] + (24*I)*SUND[I1, i5, I5]*SUNDelta[I2, I3]* - SUNF[I4, i5, I6] + (24*I)*SUND[I1, I3, i5]*SUNDelta[I2, I5]* - SUNF[I4, i5, I6] + (24*I)*SUND[I1, I2, i5]*SUNDelta[I3, I5]* - SUNF[I4, i5, I6] - 45*SUND[i3, I6, i8]*SUND[I3, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I4, I5, i6] - 45*SUND[i3, I3, i8]*SUND[i6, I6, i8]*SUNF[I1, I2, i3]* - SUNF[I4, I5, i6] - 120*SUNDelta[I3, I6]*SUNF[I1, I2, i6]* - SUNF[I4, I5, i6] + 45*SUND[I2, i6, i8]*SUND[i3, I6, i8]*SUNF[I1, i3, I3]* - SUNF[I4, I5, i6] + 45*SUND[I2, i3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I3]* - SUNF[I4, I5, i6] + 45*SUND[I2, i6, i8]*SUND[i3, I3, i8]*SUNF[I1, i3, I6]* - SUNF[I4, I5, i6] + 45*SUND[I2, i3, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I6]* - SUNF[I4, I5, i6] - 108*SUND[I2, I6, i8]*SUND[i3, I3, i6]* - SUNF[I1, i3, i8]*SUNF[I4, I5, i6] - 108*SUND[I2, I3, i8]* - SUND[i3, i6, I6]*SUNF[I1, i3, i8]*SUNF[I4, I5, i6] - - 108*SUND[I2, i3, i6]*SUND[I3, I6, i8]*SUNF[I1, i3, i8]*SUNF[I4, I5, i6] - - 120*SUNDelta[I2, I6]*SUNF[I1, I3, i6]*SUNF[I4, I5, i6] + - 120*SUNDelta[I2, I3]*SUNF[I1, i6, I6]*SUNF[I4, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[i3, I3, i6]*SUNF[I2, i3, i8]*SUNF[I4, I5, i6] + - 27*SUND[I1, I3, i8]*SUND[i3, i6, I6]*SUNF[I2, i3, i8]*SUNF[I4, I5, i6] + - 72*SUND[I1, i3, i6]*SUND[I3, I6, i8]*SUNF[I2, i3, i8]*SUNF[I4, I5, i6] - - 27*SUND[I1, I6, i8]*SUND[I2, i3, i6]*SUNF[i3, I3, i8]*SUNF[I4, I5, i6] - - 72*SUND[I1, i3, i6]*SUND[I2, I6, i8]*SUNF[i3, I3, i8]*SUNF[I4, I5, i6] - - 27*SUND[I1, I2, i8]*SUND[i3, i6, I6]*SUNF[i3, I3, i8]*SUNF[I4, I5, i6] - - 27*SUND[I1, I3, i8]*SUND[I2, i3, i6]*SUNF[i3, I6, i8]*SUNF[I4, I5, i6] - - 72*SUND[I1, i3, i6]*SUND[I2, I3, i8]*SUNF[i3, I6, i8]*SUNF[I4, I5, i6] - - 27*SUND[I1, I2, i8]*SUND[i3, I3, i6]*SUNF[i3, I6, i8]*SUNF[I4, I5, i6] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I3, i7]*SUNF[I2, i5, i7]* - SUNF[I4, I5, i8] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, i5, i7]*SUNF[I4, I5, i8] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I2, i7]*SUNF[I3, i5, i7]*SUNF[I4, I5, i8] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I6, i7]*SUNF[I3, i5, i7]* - SUNF[I4, I5, i8] - 45*SUNF[I1, i6, I6]*SUNF[I2, i8, i9]*SUNF[I3, i6, i8]* - SUNF[I4, I5, i9] - 45*SUNF[I1, i6, I6]*SUNF[I2, i6, i8]*SUNF[I3, i8, i9]* - SUNF[I4, I5, i9] + 45*SUND[i3, I5, i8]*SUND[I3, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I4, i6, I6] + 45*SUND[i3, I3, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i3]* - SUNF[I4, i6, I6] + 120*SUNDelta[I3, I5]*SUNF[I1, I2, i6]* - SUNF[I4, i6, I6] - 45*SUND[I2, i6, i8]*SUND[i3, I5, i8]*SUNF[I1, i3, I3]* - SUNF[I4, i6, I6] - 45*SUND[I2, i3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I3]* - SUNF[I4, i6, I6] - 45*SUND[I2, i6, i8]*SUND[i3, I3, i8]*SUNF[I1, i3, I5]* - SUNF[I4, i6, I6] - 45*SUND[I2, i3, i8]*SUND[I3, i6, i8]*SUNF[I1, i3, I5]* - SUNF[I4, i6, I6] + 108*SUND[I2, I5, i8]*SUND[i3, I3, i6]* - SUNF[I1, i3, i8]*SUNF[I4, i6, I6] + 108*SUND[I2, I3, i8]* - SUND[i3, I5, i6]*SUNF[I1, i3, i8]*SUNF[I4, i6, I6] + - 108*SUND[I2, i3, i6]*SUND[I3, I5, i8]*SUNF[I1, i3, i8]*SUNF[I4, i6, I6] + - 120*SUNDelta[I2, I5]*SUNF[I1, I3, i6]*SUNF[I4, i6, I6] + - 120*SUNDelta[I2, I3]*SUNF[I1, I5, i6]*SUNF[I4, i6, I6] - - 27*SUND[I1, I5, i8]*SUND[i3, I3, i6]*SUNF[I2, i3, i8]*SUNF[I4, i6, I6] - - 27*SUND[I1, I3, i8]*SUND[i3, I5, i6]*SUNF[I2, i3, i8]*SUNF[I4, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I3, I5, i8]*SUNF[I2, i3, i8]*SUNF[I4, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i3, i6]*SUNF[i3, I3, i8]*SUNF[I4, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I2, I5, i8]*SUNF[i3, I3, i8]*SUNF[I4, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[i3, I5, i6]*SUNF[i3, I3, i8]*SUNF[I4, i6, I6] + - 27*SUND[I1, I3, i8]*SUND[I2, i3, i6]*SUNF[i3, I5, i8]*SUNF[I4, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I2, I3, i8]*SUNF[i3, I5, i8]*SUNF[I4, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[i3, I3, i6]*SUNF[i3, I5, i8]*SUNF[I4, i6, I6] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I3, i7]*SUNF[I2, i5, i7]* - SUNF[I4, I6, i8] + (45*I)*SUND[I3, i5, i8]*SUNF[I1, I5, i7]* - SUNF[I2, i5, i7]*SUNF[I4, I6, i8] + (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I2, i7]*SUNF[I3, i5, i7]*SUNF[I4, I6, i8] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I5, i7]*SUNF[I3, i5, i7]* - SUNF[I4, I6, i8] + 45*SUNF[I1, I5, i6]*SUNF[I2, i8, i9]*SUNF[I3, i6, i8]* - SUNF[I4, I6, i9] + 45*SUNF[I1, I5, i6]*SUNF[I2, i6, i8]*SUNF[I3, i8, i9]* - SUNF[I4, I6, i9] + (45*I)*SUND[i5, I6, i8]*SUNF[I1, I3, i7]* - SUNF[I2, I4, i8]*SUNF[i5, I5, i7] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I6, i7]*SUNF[I2, I4, i8]*SUNF[i5, I5, i7] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I2, i7]*SUNF[I3, I4, i8]* - SUNF[i5, I5, i7] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, I6, i7]* - SUNF[I3, I4, i8]*SUNF[i5, I5, i7] - (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I2, i7]*SUNF[I4, I6, i8]*SUNF[i5, I5, i7] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I3, i7]*SUNF[I4, I6, i8]* - SUNF[i5, I5, i7] + (72*I)*SUND[I3, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I4]*SUNF[i5, I5, i8] - (18*I)*SUND[I3, I6, i8]* - SUNF[I1, i3, I4]*SUNF[I2, i3, i5]*SUNF[i5, I5, i8] - - (72*I)*SUND[I2, I6, i8]*SUNF[I1, i3, i5]*SUNF[i3, I3, I4]* - SUNF[i5, I5, i8] - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I4]*SUNF[i5, I5, i8] + (18*I)*SUND[I2, I6, i8]* - SUNF[I1, i3, I4]*SUNF[i3, I3, i5]*SUNF[i5, I5, i8] - - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I4]*SUNF[i3, I3, i5]* - SUNF[i5, I5, i8] + (72*I)*SUND[I2, I3, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I4, I6]*SUNF[i5, I5, i8] + (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I4, I6]*SUNF[i5, I5, i8] - - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, i5]*SUNF[i3, I4, I6]* - SUNF[i5, I5, i8] - (18*I)*SUND[I2, I3, i8]*SUNF[I1, i3, I4]* - SUNF[i3, i5, I6]*SUNF[i5, I5, i8] + (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I4]*SUNF[i3, i5, I6]*SUNF[i5, I5, i8] - - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I4]*SUNF[i3, i5, I6]* - SUNF[i5, I5, i8] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, I3, i7]* - SUNF[I2, I4, i8]*SUNF[i5, I6, i7] + (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I5, i7]*SUNF[I2, I4, i8]*SUNF[i5, I6, i7] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I2, i7]*SUNF[I3, I4, i8]* - SUNF[i5, I6, i7] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, I5, i7]* - SUNF[I3, I4, i8]*SUNF[i5, I6, i7] - (45*I)*SUND[I3, i5, i8]* - SUNF[I1, I2, i7]*SUNF[I4, I5, i8]*SUNF[i5, I6, i7] - - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I3, i7]*SUNF[I4, I5, i8]* - SUNF[i5, I6, i7] + (72*I)*SUND[I3, I5, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i3, I4]*SUNF[i5, I6, i8] - (18*I)*SUND[I3, I5, i8]* - SUNF[I1, i3, I4]*SUNF[I2, i3, i5]*SUNF[i5, I6, i8] - - (72*I)*SUND[I2, I5, i8]*SUNF[I1, i3, i5]*SUNF[i3, I3, I4]* - SUNF[i5, I6, i8] - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I4]*SUNF[i5, I6, i8] + (18*I)*SUND[I2, I5, i8]* - SUNF[I1, i3, I4]*SUNF[i3, I3, i5]*SUNF[i5, I6, i8] - - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I4]*SUNF[i3, I3, i5]* - SUNF[i5, I6, i8] + (72*I)*SUND[I2, I3, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I4, I5]*SUNF[i5, I6, i8] + (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I4, I5]*SUNF[i5, I6, i8] - - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, i5]*SUNF[i3, I4, I5]* - SUNF[i5, I6, i8] - (18*I)*SUND[I2, I3, i8]*SUNF[I1, i3, I4]* - SUNF[i3, i5, I5]*SUNF[i5, I6, i8] + (27*I)*SUND[I1, I3, i8]* - SUNF[I2, i3, I4]*SUNF[i3, i5, I5]*SUNF[i5, I6, i8] - - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I4]*SUNF[i3, i5, I5]* - SUNF[i5, I6, i8] + 45*SUNF[I1, i6, I6]*SUNF[I2, i8, i9]*SUNF[I3, I4, i9]* - SUNF[I5, i6, i8] + 45*SUNF[I1, i6, I6]*SUNF[I2, I4, i9]*SUNF[I3, i8, i9]* - SUNF[I5, i6, i8] + 45*SUNF[I1, I3, i6]*SUNF[I2, i8, i9]*SUNF[I4, I6, i9]* - SUNF[I5, i6, i8] + 45*SUNF[I1, I2, i6]*SUNF[I3, i8, i9]*SUNF[I4, I6, i9]* - SUNF[I5, i6, i8] - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I3, i9]* - SUNF[I1, I2, i8]*SUNF[I5, i8, i9] - (45*I)*SUND[i1, I3, I4]* - SUNF[i1, I6, i9]*SUNF[I1, I2, i8]*SUNF[I5, i8, i9] - - (45*I)*SUND[i1, I4, I6]*SUNF[i1, I2, i9]*SUNF[I1, I3, i8]* - SUNF[I5, i8, i9] - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I6, i9]* - SUNF[I1, I3, i8]*SUNF[I5, i8, i9] - (45*I)*SUND[i1, I3, I4]* - SUNF[i1, I2, i9]*SUNF[I1, I6, i8]*SUNF[I5, i8, i9] - - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I3, i9]*SUNF[I1, I6, i8]* - SUNF[I5, i8, i9] + 45*SUNF[I1, i6, I6]*SUNF[I2, i6, i8]*SUNF[I3, I4, i9]* - SUNF[I5, i8, i9] + 45*SUNF[I1, i6, I6]*SUNF[I2, I4, i9]*SUNF[I3, i6, i8]* - SUNF[I5, i8, i9] + 45*SUNF[I1, I3, i6]*SUNF[I2, i6, i8]*SUNF[I4, I6, i9]* - SUNF[I5, i8, i9] + 45*SUNF[I1, I2, i6]*SUNF[I3, i6, i8]*SUNF[I4, I6, i9]* - SUNF[I5, i8, i9] + 45*SUNF[I1, I5, i6]*SUNF[I2, i8, i9]*SUNF[I3, I4, i9]* - SUNF[i6, I6, i8] + 45*SUNF[I1, I5, i6]*SUNF[I2, I4, i9]*SUNF[I3, i8, i9]* - SUNF[i6, I6, i8] - 45*SUNF[I1, I3, i6]*SUNF[I2, i8, i9]*SUNF[I4, I5, i9]* - SUNF[i6, I6, i8] - 45*SUNF[I1, I2, i6]*SUNF[I3, i8, i9]*SUNF[I4, I5, i9]* - SUNF[i6, I6, i8] + 45*SUNF[I1, I3, i6]*SUNF[I2, I4, i9]*SUNF[I5, i8, i9]* - SUNF[i6, I6, i8] + 45*SUNF[I1, I2, i6]*SUNF[I3, I4, i9]*SUNF[I5, i8, i9]* - SUNF[i6, I6, i8] - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I3, i9]* - SUNF[I1, I2, i8]*SUNF[I6, i8, i9] - (45*I)*SUND[i1, I3, I4]* - SUNF[i1, I5, i9]*SUNF[I1, I2, i8]*SUNF[I6, i8, i9] - - (45*I)*SUND[i1, I4, I5]*SUNF[i1, I2, i9]*SUNF[I1, I3, i8]* - SUNF[I6, i8, i9] - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I5, i9]* - SUNF[I1, I3, i8]*SUNF[I6, i8, i9] - (45*I)*SUND[i1, I3, I4]* - SUNF[i1, I2, i9]*SUNF[I1, I5, i8]*SUNF[I6, i8, i9] - - (45*I)*SUND[i1, I2, I4]*SUNF[i1, I3, i9]*SUNF[I1, I5, i8]* - SUNF[I6, i8, i9] - 45*SUNF[I1, I5, i6]*SUNF[I2, i6, i8]*SUNF[I3, I4, i9]* - SUNF[I6, i8, i9] - 45*SUNF[I1, I5, i6]*SUNF[I2, I4, i9]*SUNF[I3, i6, i8]* - SUNF[I6, i8, i9] + 45*SUNF[I1, I3, i6]*SUNF[I2, i6, i8]*SUNF[I4, I5, i9]* - SUNF[I6, i8, i9] + 45*SUNF[I1, I2, i6]*SUNF[I3, i6, i8]*SUNF[I4, I5, i9]* - SUNF[I6, i8, i9] - 45*SUNF[I1, I3, i6]*SUNF[I2, I4, i9]*SUNF[I5, i6, i8]* - SUNF[I6, i8, i9] - 45*SUNF[I1, I2, i6]*SUNF[I3, I4, i9]*SUNF[I5, i6, i8]* - SUNF[I6, i8, i9])/(1080*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3)}, -{(-72*SUND[I1, I5, I6]*SUND[I2, I3, I4] - 72*SUND[I1, I4, I6]* - SUND[I2, I3, I5] - 72*SUND[I1, I4, I5]*SUND[I2, I3, I6] + - 108*SUND[I1, I3, I6]*SUND[I2, I4, I5] + 108*SUND[I1, I3, I5]* - SUND[I2, I4, I6] + 108*SUND[I1, I3, I4]*SUND[I2, I5, I6] - - 72*SUND[I1, I2, I6]*SUND[I3, I4, I5] - 72*SUND[I1, I2, I5]* - SUND[I3, I4, I6] - 72*SUND[I1, I2, I4]*SUND[I3, I5, I6] + - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I5]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUND[I3, i4, I5]*SUND[i4, I4, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUND[I3, i4, I6]*SUND[i4, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I6]*SUND[i4, I4, i6] + - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I4]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUND[I3, i4, I4]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUND[I3, i4, I6]*SUND[i4, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I6]*SUND[i4, I5, i6] - - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUND[I3, i4, I4]*SUND[i4, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I4]*SUND[i4, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUND[I3, i4, I5]*SUND[i4, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[I3, i4, I5]*SUND[i4, i6, I6] + - 108*SUND[I1, I2, I3]*SUND[I4, I5, I6] - 108*SUND[I1, i6, i8]* - SUND[I2, i4, i6]*SUND[I3, i4, I6]*SUND[I4, I5, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, i4, I6]*SUND[I4, I5, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i4]*SUND[i4, i6, I6]*SUND[I4, I5, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, i6, i8]*SUND[i4, i6, I6]*SUND[I4, I5, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I5]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I6, i8]*SUND[I3, i4, I5]*SUND[I4, i6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I6]*SUND[I4, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I5, i8]*SUND[I3, i4, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, I3, i4]*SUND[i4, I5, i6]*SUND[I4, i6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, I6, i8]*SUND[i4, I5, i6]*SUND[I4, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I6]*SUND[i4, I5, i6]*SUND[I4, i6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, I3, i4]*SUND[i4, i6, I6]*SUND[I4, i6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, I5, i8]*SUND[i4, i6, I6]*SUND[I4, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I5]*SUND[i4, i6, I6]*SUND[I4, i6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I5]*SUND[I4, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, i4, I5]*SUND[I4, I6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i4]*SUND[i4, I5, i6]*SUND[I4, I6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, i6, i8]*SUND[i4, I5, i6]*SUND[I4, I6, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I4]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I6, i8]*SUND[I3, i4, I4]*SUND[I5, i6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I6]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I4, i8]*SUND[I3, i4, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I6, i8]*SUND[I2, I3, i4]*SUND[i4, I4, i6]*SUND[I5, i6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, I6, i8]*SUND[i4, I4, i6]*SUND[I5, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I6]*SUND[i4, I4, i6]*SUND[I5, i6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, I3, i4]*SUND[i4, i6, I6]*SUND[I5, i6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, I4, i8]*SUND[i4, i6, I6]*SUND[I5, i6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I4]*SUND[i4, i6, I6]*SUND[I5, i6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i4]*SUND[I4, I6, i8]*SUND[I5, i6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, i4, i6]*SUND[I4, I6, i8]*SUND[I5, i6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I4]*SUND[I5, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, i6, i8]*SUND[I3, i4, I4]*SUND[I5, I6, i8] - - 108*SUND[I1, i6, i8]*SUND[I2, I3, i4]*SUND[i4, I4, i6]*SUND[I5, I6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, i6, i8]*SUND[i4, I4, i6]*SUND[I5, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i4]*SUND[I4, i6, i8]*SUND[I5, I6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, i4, i6]*SUND[I4, i6, i8]*SUND[I5, I6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I4]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I5, i8]*SUND[I3, i4, I4]*SUND[i6, I6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I3, i4, I5]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I4, i8]*SUND[I3, i4, I5]*SUND[i6, I6, i8] + - 27*SUND[I1, I5, i8]*SUND[I2, I3, i4]*SUND[i4, I4, i6]*SUND[i6, I6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, I5, i8]*SUND[i4, I4, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I5]*SUND[i4, I4, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I4, i8]*SUND[I2, I3, i4]*SUND[i4, I5, i6]*SUND[i6, I6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, I4, i8]*SUND[i4, I5, i6]*SUND[i6, I6, i8] + - 27*SUND[I1, I2, i8]*SUND[I3, i4, I4]*SUND[i4, I5, i6]*SUND[i6, I6, i8] + - 72*SUND[I1, i4, i6]*SUND[I2, I3, i4]*SUND[I4, I5, i8]*SUND[i6, I6, i8] - - 18*SUND[I1, I3, i4]*SUND[I2, i4, i6]*SUND[I4, I5, i8]*SUND[i6, I6, i8] + - 36*SUND[I3, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I2] + - 36*SUND[I3, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I2] + - 36*SUND[I3, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I2] - - 48*SUND[I2, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I1, I3] - - 48*SUND[I2, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I1, I3] - - 48*SUND[I2, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I3] + - 36*SUND[I2, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I1, I4] + - 36*SUND[I2, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I1, I4] + - 36*SUND[I2, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I1, I4] + - 36*SUND[I2, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I1, I5] + - 36*SUND[I2, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I1, I5] + - 36*SUND[I2, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I1, I5] + - 36*SUND[I2, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I1, I6] + - 36*SUND[I2, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I1, I6] + - 36*SUND[I2, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I1, I6] + - 12*SUND[I1, i5, I6]*SUND[I4, i5, I5]*SUNDelta[I2, I3] + - 12*SUND[I1, i5, I5]*SUND[I4, i5, I6]*SUNDelta[I2, I3] + - 12*SUND[I1, I4, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I3] - - 24*SUND[I1, i5, I6]*SUND[I3, i5, I5]*SUNDelta[I2, I4] - - 24*SUND[I1, i5, I5]*SUND[I3, i5, I6]*SUNDelta[I2, I4] - - 24*SUND[I1, I3, i5]*SUND[i5, I5, I6]*SUNDelta[I2, I4] - - 24*SUND[I1, i5, I6]*SUND[I3, I4, i5]*SUNDelta[I2, I5] - - 24*SUND[I1, I4, i5]*SUND[I3, i5, I6]*SUNDelta[I2, I5] - - 24*SUND[I1, I3, i5]*SUND[I4, i5, I6]*SUNDelta[I2, I5] - - 24*SUND[I1, i5, I5]*SUND[I3, I4, i5]*SUNDelta[I2, I6] - - 24*SUND[I1, I4, i5]*SUND[I3, i5, I5]*SUNDelta[I2, I6] - - 24*SUND[I1, I3, i5]*SUND[I4, i5, I5]*SUNDelta[I2, I6] + - 12*SUND[I1, i5, I6]*SUND[I2, i5, I5]*SUNDelta[I3, I4] + - 12*SUND[I1, i5, I5]*SUND[I2, i5, I6]*SUNDelta[I3, I4] + - 12*SUND[I1, I2, i5]*SUND[i5, I5, I6]*SUNDelta[I3, I4] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - 12*SUND[I1, i5, I6]*SUND[I2, I4, i5]*SUNDelta[I3, I5] + - 12*SUND[I1, I4, i5]*SUND[I2, i5, I6]*SUNDelta[I3, I5] + - 12*SUND[I1, I2, i5]*SUND[I4, i5, I6]*SUNDelta[I3, I5] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - 12*SUND[I1, i5, I5]*SUND[I2, I4, i5]*SUNDelta[I3, I6] + - 12*SUND[I1, I4, i5]*SUND[I2, i5, I5]*SUNDelta[I3, I6] + - 12*SUND[I1, I2, i5]*SUND[I4, i5, I5]*SUNDelta[I3, I6] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 24*SUND[I1, i5, I6]*SUND[I2, I3, i5]*SUNDelta[I4, I5] - - 24*SUND[I1, I3, i5]*SUND[I2, i5, I6]*SUNDelta[I4, I5] - - 24*SUND[I1, I2, i5]*SUND[I3, i5, I6]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 32*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 24*SUND[I1, i5, I5]*SUND[I2, I3, i5]*SUNDelta[I4, I6] - - 24*SUND[I1, I3, i5]*SUND[I2, i5, I5]*SUNDelta[I4, I6] - - 24*SUND[I1, I2, i5]*SUND[I3, i5, I5]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 32*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 24*SUND[I1, I4, i5]*SUND[I2, I3, i5]*SUNDelta[I5, I6] - - 24*SUND[I1, I3, i5]*SUND[I2, I4, i5]*SUNDelta[I5, I6] - - 24*SUND[I1, I2, i5]*SUND[I3, I4, i5]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 32*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - 8*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6] + - (45*I)*SUND[i1, I6, i8]*SUND[I3, I5, i6]*SUND[I4, i6, i8]* - SUNF[i1, I1, I2] + (45*I)*SUND[i1, I5, i8]*SUND[I3, i6, I6]* - SUND[I4, i6, i8]*SUNF[i1, I1, I2] + (45*I)*SUND[i1, I6, i8]* - SUND[I3, I4, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I2] + - (45*I)*SUND[i1, I4, i8]*SUND[I3, i6, I6]*SUND[I5, i6, i8]* - SUNF[i1, I1, I2] + (45*I)*SUND[i1, I5, i8]*SUND[I3, I4, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I2] + (45*I)*SUND[i1, I4, i8]* - SUND[I3, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I5, I6]*SUNDelta[I3, I4]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I4, I6]*SUNDelta[I3, I5]*SUNF[i1, I1, I2] + - (60*I)*SUND[i1, I4, I5]*SUNDelta[I3, I6]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I3, I6]*SUNDelta[I4, I5]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I3, I5]*SUNDelta[I4, I6]*SUNF[i1, I1, I2] + - (120*I)*SUND[i1, I3, I4]*SUNDelta[I5, I6]*SUNF[i1, I1, I2] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, I5, i6]* - SUNF[i1, I1, I4] + (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, i8]* - SUND[I3, i6, I6]*SUNF[i1, I1, I4] + (45*I)*SUND[i1, I6, i8]* - SUND[I2, I3, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I4] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, i6, I6]*SUND[I5, i6, i8]* - SUNF[i1, I1, I4] + (45*I)*SUND[i1, I5, i8]*SUND[I2, I3, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I4] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, I5, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I5, I6]*SUNDelta[I2, I3]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I3, I6]*SUNDelta[I2, I5]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I3, I5]*SUNDelta[I2, I6]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I2, I6]*SUNDelta[I3, I5]*SUNF[i1, I1, I4] + - (60*I)*SUND[i1, I2, I5]*SUNDelta[I3, I6]*SUNF[i1, I1, I4] + - (120*I)*SUND[i1, I2, I3]*SUNDelta[I5, I6]*SUNF[i1, I1, I4] + - (45*I)*SUND[i1, I6, i8]*SUND[I2, i6, i8]*SUND[I3, I4, i6]* - SUNF[i1, I1, I5] + (45*I)*SUND[i1, I4, i8]*SUND[I2, i6, i8]* - SUND[I3, i6, I6]*SUNF[i1, I1, I5] + (45*I)*SUND[i1, I6, i8]* - SUND[I2, I3, i6]*SUND[I4, i6, i8]*SUNF[i1, I1, I5] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, i6, I6]*SUND[I4, i6, i8]* - SUNF[i1, I1, I5] + (45*I)*SUND[i1, I4, i8]*SUND[I2, I3, i6]* - SUND[i6, I6, i8]*SUNF[i1, I1, I5] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, I4, i6]*SUND[i6, I6, i8]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I4, I6]*SUNDelta[I2, I3]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I3, I6]*SUNDelta[I2, I4]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I3, I4]*SUNDelta[I2, I6]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I2, I6]*SUNDelta[I3, I4]*SUNF[i1, I1, I5] + - (60*I)*SUND[i1, I2, I4]*SUNDelta[I3, I6]*SUNF[i1, I1, I5] + - (120*I)*SUND[i1, I2, I3]*SUNDelta[I4, I6]*SUNF[i1, I1, I5] + - (72*I)*SUND[i1, I3, I6]*SUND[I2, i6, i8]*SUND[I4, I5, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I6]*SUND[I2, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I5]* - SUND[I2, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I3, I5]*SUND[I2, i6, i8]*SUND[I4, I6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I6]*SUND[I2, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I4]* - SUND[I2, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I2, I3]*SUND[I4, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I4]*SUND[I2, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I3]* - SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I1, i6] + - (72*I)*SUND[i1, I3, I5]*SUND[I2, I4, i8]*SUND[i6, I6, i8]* - SUNF[i1, I1, i6] + (72*I)*SUND[i1, I3, I4]*SUND[I2, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I1, i6] + (72*I)*SUND[i1, I2, I3]* - SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I1, i6] + - (45*I)*SUND[i1, I5, i8]*SUND[I2, i6, i8]*SUND[I3, I4, i6]* - SUNF[i1, I1, I6] + (45*I)*SUND[i1, I4, i8]*SUND[I2, i6, i8]* - SUND[I3, I5, i6]*SUNF[i1, I1, I6] + (45*I)*SUND[i1, I5, i8]* - SUND[I2, I3, i6]*SUND[I4, i6, i8]*SUNF[i1, I1, I6] + - (45*I)*SUND[i1, I2, i8]*SUND[I3, I5, i6]*SUND[I4, i6, i8]* - SUNF[i1, I1, I6] + (45*I)*SUND[i1, I4, i8]*SUND[I2, I3, i6]* - SUND[I5, i6, i8]*SUNF[i1, I1, I6] + (45*I)*SUND[i1, I2, i8]* - SUND[I3, I4, i6]*SUND[I5, i6, i8]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I4, I5]*SUNDelta[I2, I3]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I3, I5]*SUNDelta[I2, I4]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I3, I4]*SUNDelta[I2, I5]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I2, I5]*SUNDelta[I3, I4]*SUNF[i1, I1, I6] + - (60*I)*SUND[i1, I2, I4]*SUNDelta[I3, I5]*SUNF[i1, I1, I6] + - (120*I)*SUND[i1, I2, I3]*SUNDelta[I4, I5]*SUNF[i1, I1, I6] - - (108*I)*SUND[i1, i6, I6]*SUND[I2, I5, i8]*SUND[I3, I4, i6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]*SUND[I2, I6, i8]* - SUND[I3, I4, i6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, i6, I6]* - SUND[I2, I4, i8]*SUND[I3, I5, i6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I4, i6]*SUND[I2, I6, i8]*SUND[I3, I5, i6]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]*SUND[I2, I4, i8]* - SUND[I3, i6, I6]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I4, i6]* - SUND[I2, I5, i8]*SUND[I3, i6, I6]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, i6, I6]*SUND[I2, I3, i6]*SUND[I4, I5, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I2, i6]*SUND[I3, i6, I6]* - SUND[I4, I5, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I5, i6]* - SUND[I2, I3, i6]*SUND[I4, I6, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I2, i6]*SUND[I3, I5, i6]*SUND[I4, I6, i8]* - SUNF[i1, I1, i8] - (108*I)*SUND[i1, I4, i6]*SUND[I2, I3, i6]* - SUND[I5, I6, i8]*SUNF[i1, I1, i8] - (108*I)*SUND[i1, I2, i6]* - SUND[I3, I4, i6]*SUND[I5, I6, i8]*SUNF[i1, I1, i8] - - (108*I)*SUND[i1, I3, I6]*SUND[I1, i6, i8]*SUND[I4, I5, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I6]*SUND[I1, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I5]* - SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I2, i6] - - (108*I)*SUND[i1, I3, I5]*SUND[I1, i6, i8]*SUND[I4, I6, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I6]*SUND[I1, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I4]* - SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I2, i6] - - (18*I)*SUND[i1, I1, I3]*SUND[I4, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I2, i6] - (108*I)*SUND[i1, I3, I4]*SUND[I1, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I3]* - SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I2, i6] + - (27*I)*SUND[i1, I3, I5]*SUND[I1, I4, i8]*SUND[i6, I6, i8]* - SUNF[i1, I2, i6] + (27*I)*SUND[i1, I3, I4]*SUND[I1, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I2, i6] - (18*I)*SUND[i1, I1, I3]* - SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I2, i6] + - (27*I)*SUND[i1, i6, I6]*SUND[I1, I5, i8]*SUND[I3, I4, i6]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I6, i8]* - SUND[I3, I4, i6]*SUNF[i1, I2, i8] + (27*I)*SUND[i1, i6, I6]* - SUND[I1, I4, i8]*SUND[I3, I5, i6]*SUNF[i1, I2, i8] + - (27*I)*SUND[i1, I4, i6]*SUND[I1, I6, i8]*SUND[I3, I5, i6]* - SUNF[i1, I2, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I4, i8]* - SUND[I3, i6, I6]*SUNF[i1, I2, i8] + (27*I)*SUND[i1, I4, i6]* - SUND[I1, I5, i8]*SUND[I3, i6, I6]*SUNF[i1, I2, i8] - - (18*I)*SUND[i1, i6, I6]*SUND[I1, I3, i6]*SUND[I4, I5, i8]* - SUNF[i1, I2, i8] + (72*I)*SUND[i1, I1, i6]*SUND[I3, i6, I6]* - SUND[I4, I5, i8]*SUNF[i1, I2, i8] - (18*I)*SUND[i1, I5, i6]* - SUND[I1, I3, i6]*SUND[I4, I6, i8]*SUNF[i1, I2, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I3, I5, i6]*SUND[I4, I6, i8]* - SUNF[i1, I2, i8] - (18*I)*SUND[i1, I4, i6]*SUND[I1, I3, i6]* - SUND[I5, I6, i8]*SUNF[i1, I2, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I3, I4, i6]*SUND[I5, I6, i8]*SUNF[i1, I2, i8] - - (108*I)*SUND[i1, I3, I6]*SUND[I1, i6, i8]*SUND[I2, I5, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I3, I6]*SUND[I1, I5, i8]* - SUND[I2, i6, i8]*SUNF[i1, I4, i6] + (27*I)*SUND[i1, I3, I5]* - SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i1, I4, i6] - - (108*I)*SUND[i1, I3, I5]*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I3, I6]*SUND[I1, I2, i8]* - SUND[I5, i6, i8]*SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I3]* - SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[i1, I4, i6] - - (18*I)*SUND[i1, I1, I3]*SUND[I2, I6, i8]*SUND[I5, i6, i8]* - SUNF[i1, I4, i6] - (108*I)*SUND[i1, I2, I3]*SUND[I1, i6, i8]* - SUND[I5, I6, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I3]* - SUND[I2, i6, i8]*SUND[I5, I6, i8]*SUNF[i1, I4, i6] + - (27*I)*SUND[i1, I3, I5]*SUND[I1, I2, i8]*SUND[i6, I6, i8]* - SUNF[i1, I4, i6] + (27*I)*SUND[i1, I2, I3]*SUND[I1, I5, i8]* - SUND[i6, I6, i8]*SUNF[i1, I4, i6] - (18*I)*SUND[i1, I1, I3]* - SUND[I2, I5, i8]*SUND[i6, I6, i8]*SUNF[i1, I4, i6] + - (27*I)*SUND[i1, i6, I6]*SUND[I1, I5, i8]*SUND[I2, I3, i6]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I6, i8]* - SUND[I2, I3, i6]*SUNF[i1, I4, i8] - (18*I)*SUND[i1, i6, I6]* - SUND[I1, I3, i6]*SUND[I2, I5, i8]*SUNF[i1, I4, i8] - - (18*I)*SUND[i1, I5, i6]*SUND[I1, I3, i6]*SUND[I2, I6, i8]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I2, i8]* - SUND[I3, I5, i6]*SUNF[i1, I4, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I6, i8]*SUND[I3, I5, i6]*SUNF[i1, I4, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I6, i8]*SUND[I3, I5, i6]* - SUNF[i1, I4, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I2, i8]* - SUND[I3, i6, I6]*SUNF[i1, I4, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I5, i8]*SUND[I3, i6, I6]*SUNF[i1, I4, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I5, i8]*SUND[I3, i6, I6]* - SUNF[i1, I4, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I3, i6]* - SUND[I5, I6, i8]*SUNF[i1, I4, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i6]*SUND[I5, I6, i8]*SUNF[i1, I4, i8] - - (108*I)*SUND[i1, I3, I6]*SUND[I1, i6, i8]*SUND[I2, I4, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I3, I6]*SUND[I1, I4, i8]* - SUND[I2, i6, i8]*SUNF[i1, I5, i6] + (27*I)*SUND[i1, I3, I4]* - SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i1, I5, i6] - - (108*I)*SUND[i1, I3, I4]*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I3, I6]*SUND[I1, I2, i8]* - SUND[I4, i6, i8]*SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I3]* - SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[i1, I5, i6] - - (18*I)*SUND[i1, I1, I3]*SUND[I2, I6, i8]*SUND[I4, i6, i8]* - SUNF[i1, I5, i6] - (108*I)*SUND[i1, I2, I3]*SUND[I1, i6, i8]* - SUND[I4, I6, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I3]* - SUND[I2, i6, i8]*SUND[I4, I6, i8]*SUNF[i1, I5, i6] + - (27*I)*SUND[i1, I3, I4]*SUND[I1, I2, i8]*SUND[i6, I6, i8]* - SUNF[i1, I5, i6] + (27*I)*SUND[i1, I2, I3]*SUND[I1, I4, i8]* - SUND[i6, I6, i8]*SUNF[i1, I5, i6] - (18*I)*SUND[i1, I1, I3]* - SUND[I2, I4, i8]*SUND[i6, I6, i8]*SUNF[i1, I5, i6] + - (27*I)*SUND[i1, i6, I6]*SUND[I1, I4, i8]*SUND[I2, I3, i6]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, I4, i6]*SUND[I1, I6, i8]* - SUND[I2, I3, i6]*SUNF[i1, I5, i8] - (18*I)*SUND[i1, i6, I6]* - SUND[I1, I3, i6]*SUND[I2, I4, i8]*SUNF[i1, I5, i8] - - (18*I)*SUND[i1, I4, i6]*SUND[I1, I3, i6]*SUND[I2, I6, i8]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, i6, I6]*SUND[I1, I2, i8]* - SUND[I3, I4, i6]*SUNF[i1, I5, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I6, i8]*SUND[I3, I4, i6]*SUNF[i1, I5, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I6, i8]*SUND[I3, I4, i6]* - SUNF[i1, I5, i8] + (27*I)*SUND[i1, I4, i6]*SUND[I1, I2, i8]* - SUND[I3, i6, I6]*SUNF[i1, I5, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I4, i8]*SUND[I3, i6, I6]*SUNF[i1, I5, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I4, i8]*SUND[I3, i6, I6]* - SUNF[i1, I5, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I3, i6]* - SUND[I4, I6, i8]*SUNF[i1, I5, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i6]*SUND[I4, I6, i8]*SUNF[i1, I5, i8] + - (108*I)*SUND[i1, I3, I5]*SUND[I1, i6, i8]*SUND[I2, I4, i8]* - SUNF[i1, i6, I6] + (108*I)*SUND[i1, I3, I4]*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUNF[i1, i6, I6] - (27*I)*SUND[i1, I3, I5]* - SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I3, I4]*SUND[I1, I5, i8]*SUND[I2, i6, i8]* - SUNF[i1, i6, I6] + (108*I)*SUND[i1, I2, I3]*SUND[I1, i6, i8]* - SUND[I4, I5, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I3]* - SUND[I2, i6, i8]*SUND[I4, I5, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I3, I5]*SUND[I1, I2, i8]*SUND[I4, i6, i8]* - SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I3]*SUND[I1, I5, i8]* - SUND[I4, i6, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I3]* - SUND[I2, I5, i8]*SUND[I4, i6, i8]*SUNF[i1, i6, I6] - - (27*I)*SUND[i1, I3, I4]*SUND[I1, I2, i8]*SUND[I5, i6, i8]* - SUNF[i1, i6, I6] - (27*I)*SUND[i1, I2, I3]*SUND[I1, I4, i8]* - SUND[I5, i6, i8]*SUNF[i1, i6, I6] + (18*I)*SUND[i1, I1, I3]* - SUND[I2, I4, i8]*SUND[I5, i6, i8]*SUNF[i1, i6, I6] + - (27*I)*SUND[i1, I5, i6]*SUND[I1, I4, i8]*SUND[I2, I3, i6]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I4, i6]*SUND[I1, I5, i8]* - SUND[I2, I3, i6]*SUNF[i1, I6, i8] - (18*I)*SUND[i1, I5, i6]* - SUND[I1, I3, i6]*SUND[I2, I4, i8]*SUNF[i1, I6, i8] - - (18*I)*SUND[i1, I4, i6]*SUND[I1, I3, i6]*SUND[I2, I5, i8]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I5, i6]*SUND[I1, I2, i8]* - SUND[I3, I4, i6]*SUNF[i1, I6, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I5, i8]*SUND[I3, I4, i6]*SUNF[i1, I6, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I5, i8]*SUND[I3, I4, i6]* - SUNF[i1, I6, i8] + (27*I)*SUND[i1, I4, i6]*SUND[I1, I2, i8]* - SUND[I3, I5, i6]*SUNF[i1, I6, i8] + (27*I)*SUND[i1, I2, i6]* - SUND[I1, I4, i8]*SUND[I3, I5, i6]*SUNF[i1, I6, i8] + - (72*I)*SUND[i1, I1, i6]*SUND[I2, I4, i8]*SUND[I3, I5, i6]* - SUNF[i1, I6, i8] - (18*I)*SUND[i1, I2, i6]*SUND[I1, I3, i6]* - SUND[I4, I5, i8]*SUNF[i1, I6, i8] + (72*I)*SUND[i1, I1, i6]* - SUND[I2, I3, i6]*SUND[I4, I5, i8]*SUNF[i1, I6, i8] - - 45*SUND[i1, I3, I6]*SUND[i3, I5, i8]*SUNF[i1, I4, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I5]*SUND[i3, I6, i8]*SUNF[i1, I4, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I6]*SUND[i3, I4, i8]*SUNF[i1, I5, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I4]*SUND[i3, I6, i8]*SUNF[i1, I5, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I5]*SUND[i3, I4, i8]*SUNF[i1, I6, i8]*SUNF[I1, I2, i3] - - 45*SUND[i1, I3, I4]*SUND[i3, I5, i8]*SUNF[i1, I6, i8]*SUNF[I1, I2, i3] - - (180*I)*SUND[I4, I5, I6]*SUNF[I1, I2, I3] + (120*I)*SUND[i5, I5, I6]* - SUNDelta[I3, I4]*SUNF[I1, I2, i5] + (120*I)*SUND[I4, i5, I6]* - SUNDelta[I3, I5]*SUNF[I1, I2, i5] + (120*I)*SUND[I4, i5, I5]* - SUNDelta[I3, I6]*SUNF[I1, I2, i5] - 45*SUND[i1, I6, i8]*SUND[I3, I5, i8]* - SUNF[i1, I4, i5]*SUNF[I1, I2, i5] - 45*SUND[i1, I5, i8]*SUND[I3, I6, i8]* - SUNF[i1, I4, i5]*SUNF[I1, I2, i5] + 45*SUND[i1, I6, i8]*SUND[I3, I4, i8]* - SUNF[i1, i5, I5]*SUNF[I1, I2, i5] + 45*SUND[i1, I4, i8]*SUND[I3, I6, i8]* - SUNF[i1, i5, I5]*SUNF[I1, I2, i5] + 45*SUND[i1, I5, i8]*SUND[I3, I4, i8]* - SUNF[i1, i5, I6]*SUNF[I1, I2, i5] + 45*SUND[i1, I4, i8]*SUND[I3, I5, i8]* - SUNF[i1, i5, I6]*SUNF[I1, I2, i5] + 45*SUND[i1, I3, I6]*SUND[i3, I5, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I4] + 45*SUND[i1, I3, I5]*SUND[i3, I6, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I4] + 45*SUND[i1, I3, I6]*SUND[I2, i3, i8]* - SUNF[i1, I5, i8]*SUNF[I1, i3, I4] + 45*SUND[i1, I2, I3]*SUND[i3, I6, i8]* - SUNF[i1, I5, i8]*SUNF[I1, i3, I4] + 45*SUND[i1, I3, I5]*SUND[I2, i3, i8]* - SUNF[i1, I6, i8]*SUNF[I1, i3, I4] + 45*SUND[i1, I2, I3]*SUND[i3, I5, i8]* - SUNF[i1, I6, i8]*SUNF[I1, i3, I4] + 45*SUND[i1, I3, I6]*SUND[i3, I4, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I3, I4]*SUND[i3, I6, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I3, I6]*SUND[I2, i3, i8]* - SUNF[i1, I4, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I2, I3]*SUND[i3, I6, i8]* - SUNF[i1, I4, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I3, I4]*SUND[I2, i3, i8]* - SUNF[i1, I6, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I2, I3]*SUND[i3, I4, i8]* - SUNF[i1, I6, i8]*SUNF[I1, i3, I5] + 45*SUND[i1, I3, I5]*SUND[i3, I4, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I3, I4]*SUND[i3, I5, i8]* - SUNF[i1, I2, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I3, I5]*SUND[I2, i3, i8]* - SUNF[i1, I4, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I2, I3]*SUND[i3, I5, i8]* - SUNF[i1, I4, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I3, I4]*SUND[I2, i3, i8]* - SUNF[i1, I5, i8]*SUNF[I1, i3, I6] + 45*SUND[i1, I2, I3]*SUND[i3, I4, i8]* - SUNF[i1, I5, i8]*SUNF[I1, i3, I6] - 108*SUND[i1, I3, I6]* - SUND[I4, I5, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] - - 108*SUND[i1, I3, I5]*SUND[I4, I6, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] - - 108*SUND[i1, I3, I4]*SUND[I5, I6, i8]*SUNF[i1, I2, i3]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I6]*SUND[I2, I5, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I5]*SUND[I2, I6, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I3]*SUND[I5, I6, i8]*SUNF[i1, i3, I4]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I6]*SUND[I2, I4, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I4]*SUND[I2, I6, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I3]*SUND[I4, I6, i8]*SUNF[i1, i3, I5]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I5]*SUND[I2, I4, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - 108*SUND[i1, I3, I4]*SUND[I2, I5, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - 108*SUND[i1, I2, I3]*SUND[I4, I5, i8]*SUNF[i1, i3, I6]*SUNF[I1, i3, i8] + - (18*I)*SUND[I2, i6, i8]*SUND[i4, i6, I6]*SUND[I4, I5, i8]* - SUNF[I1, I3, i4] + (18*I)*SUND[I2, I6, i8]*SUND[i4, I5, i6]* - SUND[I4, i6, i8]*SUNF[I1, I3, i4] + (18*I)*SUND[I2, I5, i8]* - SUND[i4, i6, I6]*SUND[I4, i6, i8]*SUNF[I1, I3, i4] + - (18*I)*SUND[I2, i6, i8]*SUND[i4, I5, i6]*SUND[I4, I6, i8]* - SUNF[I1, I3, i4] + (18*I)*SUND[I2, I6, i8]*SUND[i4, I4, i6]* - SUND[I5, i6, i8]*SUNF[I1, I3, i4] + (18*I)*SUND[I2, I4, i8]* - SUND[i4, i6, I6]*SUND[I5, i6, i8]*SUNF[I1, I3, i4] + - (18*I)*SUND[I2, i4, i6]*SUND[I4, I6, i8]*SUND[I5, i6, i8]* - SUNF[I1, I3, i4] + (18*I)*SUND[I2, i6, i8]*SUND[i4, I4, i6]* - SUND[I5, I6, i8]*SUNF[I1, I3, i4] + (18*I)*SUND[I2, i4, i6]* - SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, I3, i4] + - (18*I)*SUND[I2, I5, i8]*SUND[i4, I4, i6]*SUND[i6, I6, i8]* - SUNF[I1, I3, i4] + (18*I)*SUND[I2, I4, i8]*SUND[i4, I5, i6]* - SUND[i6, I6, i8]*SUNF[I1, I3, i4] + (18*I)*SUND[I2, i4, i6]* - SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, I3, i4] + - (180*I)*SUND[I2, I5, I6]*SUNF[I1, I3, I4] + (24*I)*SUND[i5, I5, I6]* - SUNDelta[I2, I4]*SUNF[I1, I3, i5] + (24*I)*SUND[I4, i5, I6]* - SUNDelta[I2, I5]*SUNF[I1, I3, i5] + (24*I)*SUND[I4, i5, I5]* - SUNDelta[I2, I6]*SUNF[I1, I3, i5] + (24*I)*SUND[I2, i5, I6]* - SUNDelta[I4, I5]*SUNF[I1, I3, i5] + (24*I)*SUND[I2, i5, I5]* - SUNDelta[I4, I6]*SUNF[I1, I3, i5] + (24*I)*SUND[I2, I4, i5]* - SUNDelta[I5, I6]*SUNF[I1, I3, i5] + (180*I)*SUND[I2, I4, I6]* - SUNF[I1, I3, I5] + (180*I)*SUND[I2, I4, I5]*SUNF[I1, I3, I6] + - (120*I)*SUND[i5, I5, I6]*SUNDelta[I2, I3]*SUNF[I1, I4, i5] + - (120*I)*SUND[I2, i5, I6]*SUNDelta[I3, I5]*SUNF[I1, I4, i5] + - (120*I)*SUND[I2, i5, I5]*SUNDelta[I3, I6]*SUNF[I1, I4, i5] - - 45*SUND[i1, I6, i8]*SUND[I3, I5, i8]*SUNF[i1, I2, i5]*SUNF[I1, I4, i5] - - 45*SUND[i1, I5, i8]*SUND[I3, I6, i8]*SUNF[i1, I2, i5]*SUNF[I1, I4, i5] + - 45*SUND[i1, I6, i8]*SUND[I2, I3, i8]*SUNF[i1, i5, I5]*SUNF[I1, I4, i5] + - 45*SUND[i1, I2, i8]*SUND[I3, I6, i8]*SUNF[i1, i5, I5]*SUNF[I1, I4, i5] + - 45*SUND[i1, I5, i8]*SUND[I2, I3, i8]*SUNF[i1, i5, I6]*SUNF[I1, I4, i5] + - 45*SUND[i1, I2, i8]*SUND[I3, I5, i8]*SUNF[i1, i5, I6]*SUNF[I1, I4, i5] - - (120*I)*SUND[I4, i5, I6]*SUNDelta[I2, I3]*SUNF[I1, i5, I5] - - (120*I)*SUND[I2, i5, I6]*SUNDelta[I3, I4]*SUNF[I1, i5, I5] - - (120*I)*SUND[I2, I4, i5]*SUNDelta[I3, I6]*SUNF[I1, i5, I5] + - 45*SUND[i1, I6, i8]*SUND[I3, I4, i8]*SUNF[i1, I2, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I4, i8]*SUND[I3, I6, i8]*SUNF[i1, I2, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I6, i8]*SUND[I2, I3, i8]*SUNF[i1, I4, i5]*SUNF[I1, i5, I5] + - 45*SUND[i1, I2, i8]*SUND[I3, I6, i8]*SUNF[i1, I4, i5]*SUNF[I1, i5, I5] - - 45*SUND[i1, I4, i8]*SUND[I2, I3, i8]*SUNF[i1, i5, I6]*SUNF[I1, i5, I5] - - 45*SUND[i1, I2, i8]*SUND[I3, I4, i8]*SUNF[i1, i5, I6]*SUNF[I1, i5, I5] - - (120*I)*SUND[I4, i5, I5]*SUNDelta[I2, I3]*SUNF[I1, i5, I6] - - (120*I)*SUND[I2, i5, I5]*SUNDelta[I3, I4]*SUNF[I1, i5, I6] - - (120*I)*SUND[I2, I4, i5]*SUNDelta[I3, I5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I5, i8]*SUND[I3, I4, i8]*SUNF[i1, I2, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I4, i8]*SUND[I3, I5, i8]*SUNF[i1, I2, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I5, i8]*SUND[I2, I3, i8]*SUNF[i1, I4, i5]*SUNF[I1, i5, I6] + - 45*SUND[i1, I2, i8]*SUND[I3, I5, i8]*SUNF[i1, I4, i5]*SUNF[I1, i5, I6] - - 45*SUND[i1, I4, i8]*SUND[I2, I3, i8]*SUNF[i1, i5, I5]*SUNF[I1, i5, I6] - - 45*SUND[i1, I2, i8]*SUND[I3, I4, i8]*SUNF[i1, i5, I5]*SUNF[I1, i5, I6] + - 72*SUND[I4, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I3] + - 72*SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I3] + - 72*SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[I2, i3, I3] - - 18*SUND[I4, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i3, i6] - - 18*SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i3, i6] - - 18*SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i3, i6] + - 72*SUND[i1, I3, I6]*SUND[I4, I5, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] + - 72*SUND[i1, I3, I5]*SUND[I4, I6, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] + - 72*SUND[i1, I3, I4]*SUND[I5, I6, i8]*SUNF[i1, I1, i3]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I6]*SUND[I1, I5, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I5]*SUND[I1, I6, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I3]*SUND[I5, I6, i8]*SUNF[i1, i3, I4]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I6]*SUND[I1, I4, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I4]*SUND[I1, I6, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I3]*SUND[I4, I6, i8]*SUNF[i1, i3, I5]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I5]*SUND[I1, I4, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] - - 27*SUND[i1, I3, I4]*SUND[I1, I5, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] + - 18*SUND[i1, I1, I3]*SUND[I4, I5, i8]*SUNF[i1, i3, I6]*SUNF[I2, i3, i8] + - 18*SUND[i3, i6, I6]*SUND[I4, I5, i8]*SUNF[I1, I3, i6]*SUNF[I2, i3, i8] + - 18*SUND[i3, I5, i6]*SUND[I4, I6, i8]*SUNF[I1, I3, i6]*SUNF[I2, i3, i8] + - 18*SUND[i3, I4, i6]*SUND[I5, I6, i8]*SUNF[I1, I3, i6]*SUNF[I2, i3, i8] + - (108*I)*SUND[I1, i6, i8]*SUND[i4, i6, I6]*SUND[I4, I5, i8]* - SUNF[I2, I3, i4] - (27*I)*SUND[I1, I6, i8]*SUND[i4, I5, i6]* - SUND[I4, i6, i8]*SUNF[I2, I3, i4] - (27*I)*SUND[I1, I5, i8]* - SUND[i4, i6, I6]*SUND[I4, i6, i8]*SUNF[I2, I3, i4] + - (108*I)*SUND[I1, i6, i8]*SUND[i4, I5, i6]*SUND[I4, I6, i8]* - SUNF[I2, I3, i4] - (27*I)*SUND[I1, I6, i8]*SUND[i4, I4, i6]* - SUND[I5, i6, i8]*SUNF[I2, I3, i4] - (27*I)*SUND[I1, I4, i8]* - SUND[i4, i6, I6]*SUND[I5, i6, i8]*SUNF[I2, I3, i4] - - (72*I)*SUND[I1, i4, i6]*SUND[I4, I6, i8]*SUND[I5, i6, i8]* - SUNF[I2, I3, i4] + (108*I)*SUND[I1, i6, i8]*SUND[i4, I4, i6]* - SUND[I5, I6, i8]*SUNF[I2, I3, i4] - (72*I)*SUND[I1, i4, i6]* - SUND[I4, i6, i8]*SUND[I5, I6, i8]*SUNF[I2, I3, i4] - - (27*I)*SUND[I1, I5, i8]*SUND[i4, I4, i6]*SUND[i6, I6, i8]* - SUNF[I2, I3, i4] - (27*I)*SUND[I1, I4, i8]*SUND[i4, I5, i6]* - SUND[i6, I6, i8]*SUNF[I2, I3, i4] - (72*I)*SUND[I1, i4, i6]* - SUND[I4, I5, i8]*SUND[i6, I6, i8]*SUNF[I2, I3, i4] - - (36*I)*SUND[i5, I5, I6]*SUNDelta[I1, I4]*SUNF[I2, I3, i5] - - (36*I)*SUND[I4, i5, I6]*SUNDelta[I1, I5]*SUNF[I2, I3, i5] - - (36*I)*SUND[I4, i5, I5]*SUNDelta[I1, I6]*SUNF[I2, I3, i5] + - (24*I)*SUND[I1, i5, I6]*SUNDelta[I4, I5]*SUNF[I2, I3, i5] + - (24*I)*SUND[I1, i5, I5]*SUNDelta[I4, I6]*SUNF[I2, I3, i5] + - (24*I)*SUND[I1, I4, i5]*SUNDelta[I5, I6]*SUNF[I2, I3, i5] - - 45*SUND[i3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I4]*SUNF[I2, I3, i6] - - 45*SUND[i3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I4]*SUNF[I2, I3, i6] - - 45*SUND[i3, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I5]*SUNF[I2, I3, i6] - - 45*SUND[i3, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]*SUNF[I2, I3, i6] - - 45*SUND[i3, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I3, i6] - - 45*SUND[i3, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I6]*SUNF[I2, I3, i6] + - 108*SUND[i3, i6, I6]*SUND[I4, I5, i8]*SUNF[I1, i3, i8]*SUNF[I2, I3, i6] + - 108*SUND[i3, I5, i6]*SUND[I4, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I3, i6] + - 108*SUND[i3, I4, i6]*SUND[I5, I6, i8]*SUNF[I1, i3, i8]*SUNF[I2, I3, i6] + - 120*SUNDelta[I5, I6]*SUNF[I1, I4, i6]*SUNF[I2, I3, i6] + - 120*SUNDelta[I4, I6]*SUNF[I1, I5, i6]*SUNF[I2, I3, i6] - - 120*SUNDelta[I4, I5]*SUNF[I1, i6, I6]*SUNF[I2, I3, i6] - - (45*I)*SUND[i1, I3, I6]*SUNF[i1, I5, i9]*SUNF[I1, I4, i8]* - SUNF[I2, i8, i9] - (45*I)*SUND[i1, I3, I5]*SUNF[i1, I6, i9]* - SUNF[I1, I4, i8]*SUNF[I2, i8, i9] - (45*I)*SUND[i1, I3, I6]* - SUNF[i1, I4, i9]*SUNF[I1, I5, i8]*SUNF[I2, i8, i9] - - (45*I)*SUND[i1, I3, I4]*SUNF[i1, I6, i9]*SUNF[I1, I5, i8]* - SUNF[I2, i8, i9] - (45*I)*SUND[i1, I3, I5]*SUNF[i1, I4, i9]* - SUNF[I1, I6, i8]*SUNF[I2, i8, i9] - (45*I)*SUND[i1, I3, I4]* - SUNF[i1, I5, i9]*SUNF[I1, I6, i8]*SUNF[I2, i8, i9] + - 72*SUND[I2, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I4] + - 72*SUND[I2, i6, i8]*SUND[I5, I6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I4] + - 72*SUND[I2, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I4] + - (108*I)*SUND[I5, I6, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I4] + 27*SUND[I1, I6, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, i6]* - SUNF[i3, I3, I4] - 108*SUND[I1, i6, i8]*SUND[I5, I6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I4] + 27*SUND[I1, I5, i8]*SUND[i6, I6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I4] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, i5, I5]*SUNF[I2, i3, i8]*SUNF[i3, I3, I4] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, i5, I6]*SUNF[I2, i3, i8]* - SUNF[i3, I3, I4] - (72*I)*SUND[I5, I6, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I4] + 72*SUND[I2, I6, i8]*SUND[I4, i6, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I3, I5] + 72*SUND[I2, i6, i8]*SUND[I4, I6, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I3, I5] + 72*SUND[I2, I4, i8]*SUND[i6, I6, i8]* - SUNF[I1, i3, i6]*SUNF[i3, I3, I5] + (108*I)*SUND[I4, I6, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, i5]*SUNF[i3, I3, I5] + - 27*SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I3, I5] - - 108*SUND[I1, i6, i8]*SUND[I4, I6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I3, I5] + - 27*SUND[I1, I4, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, i6]*SUNF[i3, I3, I5] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, i8]* - SUNF[i3, I3, I5] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, i8]*SUNF[i3, I3, I5] - (72*I)*SUND[I4, I6, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i5, i8]*SUNF[i3, I3, I5] + - 72*SUND[I2, i6, i8]*SUND[I4, I5, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I6] + - 72*SUND[I2, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I6] + - 72*SUND[I2, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, i6]*SUNF[i3, I3, I6] + - (108*I)*SUND[I4, I5, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I6] - 108*SUND[I1, i6, i8]*SUND[I4, I5, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I6] + 27*SUND[I1, I5, i8]*SUND[I4, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I6] + 27*SUND[I1, I4, i8]*SUND[I5, i6, i8]* - SUNF[I2, i3, i6]*SUNF[i3, I3, I6] + (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I4, i5]*SUNF[I2, i3, i8]*SUNF[i3, I3, I6] - - (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I5]*SUNF[I2, i3, i8]* - SUNF[i3, I3, I6] - (72*I)*SUND[I4, I5, i8]*SUNF[I1, i3, i5]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I6] - (108*I)*SUND[I5, I6, i8]* - SUNF[I1, i5, i8]*SUNF[I2, i3, I3]*SUNF[i3, I4, i5] - - (18*I)*SUND[I5, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i5, i8]* - SUNF[i3, I4, i5] - (108*I)*SUND[I2, I6, i8]*SUNF[I1, i5, i8]* - SUNF[i3, I3, I5]*SUNF[i3, I4, i5] + (27*I)*SUND[I1, I6, i8]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I5]*SUNF[i3, I4, i5] - - (108*I)*SUND[I2, I5, i8]*SUNF[I1, i5, i8]*SUNF[i3, I3, I6]* - SUNF[i3, I4, i5] + (27*I)*SUND[I1, I5, i8]*SUNF[I2, i5, i8]* - SUNF[i3, I3, I6]*SUNF[i3, I4, i5] + 18*SUND[I2, I6, i8]*SUND[I5, i6, i8]* - SUNF[I1, i3, I3]*SUNF[i3, I4, i6] + 18*SUND[I2, i6, i8]*SUND[I5, I6, i8]* - SUNF[I1, i3, I3]*SUNF[i3, I4, i6] + 18*SUND[I2, I5, i8]*SUND[i6, I6, i8]* - SUNF[I1, i3, I3]*SUNF[i3, I4, i6] - 27*SUND[I1, I6, i8]*SUND[I5, i6, i8]* - SUNF[I2, i3, I3]*SUNF[i3, I4, i6] + 108*SUND[I1, i6, i8]* - SUND[I5, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I4, i6] - - 27*SUND[I1, I5, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I4, i6] - - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I5]*SUNF[i3, I4, i6] + - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUNF[i3, I3, I5]*SUNF[i3, I4, i6] - - 27*SUND[I1, I2, i8]*SUND[i6, I6, i8]*SUNF[i3, I3, I5]*SUNF[i3, I4, i6] + - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUNF[i3, I3, I6]*SUNF[i3, I4, i6] - - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I6]*SUNF[i3, I4, i6] - - 27*SUND[I1, I2, i8]*SUND[I5, i6, i8]*SUNF[i3, I3, I6]*SUNF[i3, I4, i6] - - 72*SUND[i1, I3, I6]*SUND[I2, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] - - 72*SUND[i1, I3, I5]*SUND[I2, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] - - 72*SUND[i1, I2, I3]*SUND[I5, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I4, i8] - - 27*SUND[i1, I3, I6]*SUND[I1, I5, i8]*SUNF[i1, I2, i3]*SUNF[i3, I4, i8] - - 27*SUND[i1, I3, I5]*SUND[I1, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I4, i8] + - 18*SUND[i1, I1, I3]*SUND[I5, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I4, i8] + - 27*SUND[i1, I3, I6]*SUND[I1, I2, i8]*SUNF[i1, i3, I5]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I6, i8]*SUNF[i1, i3, I5]*SUNF[i3, I4, i8] - - 18*SUND[i1, I1, I3]*SUND[I2, I6, i8]*SUNF[i1, i3, I5]*SUNF[i3, I4, i8] + - 27*SUND[i1, I3, I5]*SUND[I1, I2, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I5, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] - - 18*SUND[i1, I1, I3]*SUND[I2, I5, i8]*SUNF[i1, i3, I6]*SUNF[i3, I4, i8] - - 18*SUND[I2, I6, i8]*SUND[i3, I5, i6]*SUNF[I1, I3, i6]*SUNF[i3, I4, i8] - - 18*SUND[I2, I5, i8]*SUND[i3, i6, I6]*SUNF[I1, I3, i6]*SUNF[i3, I4, i8] - - 18*SUND[I2, i3, i6]*SUND[I5, I6, i8]*SUNF[I1, I3, i6]*SUNF[i3, I4, i8] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, i5, I5]*SUNF[I2, i3, I3]* - SUNF[i3, I4, i8] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, I3]*SUNF[i3, I4, i8] + 27*SUND[I1, I6, i8]*SUND[i3, I5, i6]* - SUNF[I2, I3, i6]*SUNF[i3, I4, i8] + 27*SUND[I1, I5, i8]*SUND[i3, i6, I6]* - SUNF[I2, I3, i6]*SUNF[i3, I4, i8] + 72*SUND[I1, i3, i6]*SUND[I5, I6, i8]* - SUNF[I2, I3, i6]*SUNF[i3, I4, i8] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, I5]*SUNF[i3, I4, i8] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I6]*SUNF[i3, I3, I5]* - SUNF[i3, I4, i8] - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I2, i5]* - SUNF[i3, I3, I6]*SUNF[i3, I4, i8] + (45*I)*SUND[I2, i5, i8]* - SUNF[I1, i5, I5]*SUNF[i3, I3, I6]*SUNF[i3, I4, i8] + - (108*I)*SUND[I4, I6, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, I3]* - SUNF[i3, i5, I5] + (18*I)*SUND[I4, I6, i8]*SUNF[I1, i3, I3]* - SUNF[I2, i5, i8]*SUNF[i3, i5, I5] + (108*I)*SUND[I2, I6, i8]* - SUNF[I1, i5, i8]*SUNF[i3, I3, I4]*SUNF[i3, i5, I5] - - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i5, i8]*SUNF[i3, I3, I4]* - SUNF[i3, i5, I5] + (108*I)*SUND[I2, I4, i8]*SUNF[I1, i5, i8]* - SUNF[i3, I3, I6]*SUNF[i3, i5, I5] - (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I6]*SUNF[i3, i5, I5] + - (108*I)*SUND[I4, I5, i8]*SUNF[I1, i5, i8]*SUNF[I2, i3, I3]* - SUNF[i3, i5, I6] + (18*I)*SUND[I4, I5, i8]*SUNF[I1, i3, I3]* - SUNF[I2, i5, i8]*SUNF[i3, i5, I6] + (108*I)*SUND[I2, I5, i8]* - SUNF[I1, i5, i8]*SUNF[i3, I3, I4]*SUNF[i3, i5, I6] - - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i5, i8]*SUNF[i3, I3, I4]* - SUNF[i3, i5, I6] + (108*I)*SUND[I2, I4, i8]*SUNF[I1, i5, i8]* - SUNF[i3, I3, I5]*SUNF[i3, i5, I6] - (27*I)*SUND[I1, I4, i8]* - SUNF[I2, i5, i8]*SUNF[i3, I3, I5]*SUNF[i3, i5, I6] + - 18*SUND[I2, I6, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I3]*SUNF[i3, I5, i6] + - 18*SUND[I2, i6, i8]*SUND[I4, I6, i8]*SUNF[I1, i3, I3]*SUNF[i3, I5, i6] + - 18*SUND[I2, I4, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I3]*SUNF[i3, I5, i6] - - 27*SUND[I1, I6, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I5, i6] + - 108*SUND[I1, i6, i8]*SUND[I4, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I5, i6] - - 27*SUND[I1, I4, i8]*SUND[i6, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I5, i6] - - 27*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I4]*SUNF[i3, I5, i6] + - 108*SUND[I1, i6, i8]*SUND[I2, I6, i8]*SUNF[i3, I3, I4]*SUNF[i3, I5, i6] - - 27*SUND[I1, I2, i8]*SUND[i6, I6, i8]*SUNF[i3, I3, I4]*SUNF[i3, I5, i6] + - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUNF[i3, I3, I6]*SUNF[i3, I5, i6] - - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I6]*SUNF[i3, I5, i6] - - 27*SUND[I1, I2, i8]*SUND[I4, i6, i8]*SUNF[i3, I3, I6]*SUNF[i3, I5, i6] - - 72*SUND[i1, I3, I6]*SUND[I2, I4, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - - 72*SUND[i1, I3, I4]*SUND[I2, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - - 72*SUND[i1, I2, I3]*SUND[I4, I6, i8]*SUNF[i1, I1, i3]*SUNF[i3, I5, i8] - - 27*SUND[i1, I3, I6]*SUND[I1, I4, i8]*SUNF[i1, I2, i3]*SUNF[i3, I5, i8] - - 27*SUND[i1, I3, I4]*SUND[I1, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I5, i8] + - 18*SUND[i1, I1, I3]*SUND[I4, I6, i8]*SUNF[i1, I2, i3]*SUNF[i3, I5, i8] + - 27*SUND[i1, I3, I6]*SUND[I1, I2, i8]*SUNF[i1, i3, I4]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I6, i8]*SUNF[i1, i3, I4]*SUNF[i3, I5, i8] - - 18*SUND[i1, I1, I3]*SUND[I2, I6, i8]*SUNF[i1, i3, I4]*SUNF[i3, I5, i8] + - 27*SUND[i1, I3, I4]*SUND[I1, I2, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I4, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] - - 18*SUND[i1, I1, I3]*SUND[I2, I4, i8]*SUNF[i1, i3, I6]*SUNF[i3, I5, i8] - - 18*SUND[I2, I6, i8]*SUND[i3, I4, i6]*SUNF[I1, I3, i6]*SUNF[i3, I5, i8] - - 18*SUND[I2, I4, i8]*SUND[i3, i6, I6]*SUNF[I1, I3, i6]*SUNF[i3, I5, i8] - - 18*SUND[I2, i3, i6]*SUND[I4, I6, i8]*SUNF[I1, I3, i6]*SUNF[i3, I5, i8] - - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, I3]* - SUNF[i3, I5, i8] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I6]* - SUNF[I2, i3, I3]*SUNF[i3, I5, i8] + 27*SUND[I1, I6, i8]*SUND[i3, I4, i6]* - SUNF[I2, I3, i6]*SUNF[i3, I5, i8] + 27*SUND[I1, I4, i8]*SUND[i3, i6, I6]* - SUNF[I2, I3, i6]*SUNF[i3, I5, i8] + 72*SUND[I1, i3, i6]*SUND[I4, I6, i8]* - SUNF[I2, I3, i6]*SUNF[i3, I5, i8] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, I4]*SUNF[i3, I5, i8] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I6]*SUNF[i3, I3, I4]* - SUNF[i3, I5, i8] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I2, i5]* - SUNF[i3, I3, I6]*SUNF[i3, I5, i8] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I4, i5]*SUNF[i3, I3, I6]*SUNF[i3, I5, i8] - - 18*SUND[I2, i6, i8]*SUND[I4, I5, i8]*SUNF[I1, i3, I3]*SUNF[i3, i6, I6] - - 18*SUND[I2, I5, i8]*SUND[I4, i6, i8]*SUNF[I1, i3, I3]*SUNF[i3, i6, I6] - - 18*SUND[I2, I4, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I3]*SUNF[i3, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I4, I5, i8]*SUNF[I2, i3, I3]*SUNF[i3, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I4, i6, i8]*SUNF[I2, i3, I3]*SUNF[i3, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[I5, i6, i8]*SUNF[I2, i3, I3]*SUNF[i3, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUNF[i3, I3, I4]*SUNF[i3, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I4]*SUNF[i3, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[I5, i6, i8]*SUNF[i3, I3, I4]*SUNF[i3, i6, I6] - - 108*SUND[I1, i6, i8]*SUND[I2, I4, i8]*SUNF[i3, I3, I5]*SUNF[i3, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUNF[i3, I3, I5]*SUNF[i3, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[I4, i6, i8]*SUNF[i3, I3, I5]*SUNF[i3, i6, I6] - - 72*SUND[i1, I3, I5]*SUND[I2, I4, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 72*SUND[i1, I3, I4]*SUND[I2, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 72*SUND[i1, I2, I3]*SUND[I4, I5, i8]*SUNF[i1, I1, i3]*SUNF[i3, I6, i8] - - 27*SUND[i1, I3, I5]*SUND[I1, I4, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] - - 27*SUND[i1, I3, I4]*SUND[I1, I5, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] + - 18*SUND[i1, I1, I3]*SUND[I4, I5, i8]*SUNF[i1, I2, i3]*SUNF[i3, I6, i8] + - 27*SUND[i1, I3, I5]*SUND[I1, I2, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I5, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I3]*SUND[I2, I5, i8]*SUNF[i1, i3, I4]*SUNF[i3, I6, i8] + - 27*SUND[i1, I3, I4]*SUND[I1, I2, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] + - 27*SUND[i1, I2, I3]*SUND[I1, I4, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] - - 18*SUND[i1, I1, I3]*SUND[I2, I4, i8]*SUNF[i1, i3, I5]*SUNF[i3, I6, i8] - - 18*SUND[I2, I5, i8]*SUND[i3, I4, i6]*SUNF[I1, I3, i6]*SUNF[i3, I6, i8] - - 18*SUND[I2, I4, i8]*SUND[i3, I5, i6]*SUNF[I1, I3, i6]*SUNF[i3, I6, i8] - - 18*SUND[I2, i3, i6]*SUND[I4, I5, i8]*SUNF[I1, I3, i6]*SUNF[i3, I6, i8] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I4, i5]*SUNF[I2, i3, I3]* - SUNF[i3, I6, i8] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, i5, I5]* - SUNF[I2, i3, I3]*SUNF[i3, I6, i8] + 27*SUND[I1, I5, i8]*SUND[i3, I4, i6]* - SUNF[I2, I3, i6]*SUNF[i3, I6, i8] + 27*SUND[I1, I4, i8]*SUND[i3, I5, i6]* - SUNF[I2, I3, i6]*SUNF[i3, I6, i8] + 72*SUND[I1, i3, i6]*SUND[I4, I5, i8]* - SUNF[I2, I3, i6]*SUNF[i3, I6, i8] - (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I2, i5]*SUNF[i3, I3, I4]*SUNF[i3, I6, i8] + - (45*I)*SUND[I2, i5, i8]*SUNF[I1, i5, I5]*SUNF[i3, I3, I4]* - SUNF[i3, I6, i8] - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I2, i5]* - SUNF[i3, I3, I5]*SUNF[i3, I6, i8] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I4, i5]*SUNF[i3, I3, I5]*SUNF[i3, I6, i8] - - (27*I)*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[i4, I5, i6]* - SUNF[I3, i4, I4] + (108*I)*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUND[i4, I5, i6]*SUNF[I3, i4, I4] + (108*I)*SUND[I1, i6, i8]* - SUND[I2, I5, i8]*SUND[i4, i6, I6]*SUNF[I3, i4, I4] - - (27*I)*SUND[I1, I5, i8]*SUND[I2, i6, i8]*SUND[i4, i6, I6]* - SUNF[I3, i4, I4] - (27*I)*SUND[I1, I6, i8]*SUND[I2, i4, i6]* - SUND[I5, i6, i8]*SUNF[I3, i4, I4] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, I6, i8]*SUND[I5, i6, i8]*SUNF[I3, i4, I4] - - (27*I)*SUND[I1, I2, i8]*SUND[i4, i6, I6]*SUND[I5, i6, i8]* - SUNF[I3, i4, I4] + (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]* - SUND[I5, I6, i8]*SUNF[I3, i4, I4] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, i6, i8]*SUND[I5, I6, i8]*SUNF[I3, i4, I4] - - (27*I)*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[i6, I6, i8]* - SUNF[I3, i4, I4] - (72*I)*SUND[I1, i4, i6]*SUND[I2, I5, i8]* - SUND[i6, I6, i8]*SUNF[I3, i4, I4] - (27*I)*SUND[I1, I2, i8]* - SUND[i4, I5, i6]*SUND[i6, I6, i8]*SUNF[I3, i4, I4] - - (27*I)*SUND[I1, I6, i8]*SUND[I2, i6, i8]*SUND[i4, I4, i6]* - SUNF[I3, i4, I5] + (108*I)*SUND[I1, i6, i8]*SUND[I2, I6, i8]* - SUND[i4, I4, i6]*SUNF[I3, i4, I5] + (108*I)*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUND[i4, i6, I6]*SUNF[I3, i4, I5] - - (27*I)*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[i4, i6, I6]* - SUNF[I3, i4, I5] - (27*I)*SUND[I1, I6, i8]*SUND[I2, i4, i6]* - SUND[I4, i6, i8]*SUNF[I3, i4, I5] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, I6, i8]*SUND[I4, i6, i8]*SUNF[I3, i4, I5] - - (27*I)*SUND[I1, I2, i8]*SUND[i4, i6, I6]*SUND[I4, i6, i8]* - SUNF[I3, i4, I5] + (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]* - SUND[I4, I6, i8]*SUNF[I3, i4, I5] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, i6, i8]*SUND[I4, I6, i8]*SUNF[I3, i4, I5] - - (27*I)*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[i6, I6, i8]* - SUNF[I3, i4, I5] - (72*I)*SUND[I1, i4, i6]*SUND[I2, I4, i8]* - SUND[i6, I6, i8]*SUNF[I3, i4, I5] - (27*I)*SUND[I1, I2, i8]* - SUND[i4, I4, i6]*SUND[i6, I6, i8]*SUNF[I3, i4, I5] + - (108*I)*SUND[I1, i6, i8]*SUND[I2, I5, i8]*SUND[i4, I4, i6]* - SUNF[I3, i4, I6] - (27*I)*SUND[I1, I5, i8]*SUND[I2, i6, i8]* - SUND[i4, I4, i6]*SUNF[I3, i4, I6] + (108*I)*SUND[I1, i6, i8]* - SUND[I2, I4, i8]*SUND[i4, I5, i6]*SUNF[I3, i4, I6] - - (27*I)*SUND[I1, I4, i8]*SUND[I2, i6, i8]*SUND[i4, I5, i6]* - SUNF[I3, i4, I6] + (108*I)*SUND[I1, i6, i8]*SUND[I2, i4, i6]* - SUND[I4, I5, i8]*SUNF[I3, i4, I6] - (72*I)*SUND[I1, i4, i6]* - SUND[I2, i6, i8]*SUND[I4, I5, i8]*SUNF[I3, i4, I6] - - (27*I)*SUND[I1, I5, i8]*SUND[I2, i4, i6]*SUND[I4, i6, i8]* - SUNF[I3, i4, I6] - (72*I)*SUND[I1, i4, i6]*SUND[I2, I5, i8]* - SUND[I4, i6, i8]*SUNF[I3, i4, I6] - (27*I)*SUND[I1, I2, i8]* - SUND[i4, I5, i6]*SUND[I4, i6, i8]*SUNF[I3, i4, I6] - - (27*I)*SUND[I1, I4, i8]*SUND[I2, i4, i6]*SUND[I5, i6, i8]* - SUNF[I3, i4, I6] - (72*I)*SUND[I1, i4, i6]*SUND[I2, I4, i8]* - SUND[I5, i6, i8]*SUNF[I3, i4, I6] - (27*I)*SUND[I1, I2, i8]* - SUND[i4, I4, i6]*SUND[I5, i6, i8]*SUNF[I3, i4, I6] + - (36*I)*SUND[i5, I5, I6]*SUNDelta[I1, I2]*SUNF[I3, I4, i5] + - (36*I)*SUND[I2, i5, I6]*SUNDelta[I1, I5]*SUNF[I3, I4, i5] + - (36*I)*SUND[I2, i5, I5]*SUNDelta[I1, I6]*SUNF[I3, I4, i5] - - (24*I)*SUND[I1, i5, I6]*SUNDelta[I2, I5]*SUNF[I3, I4, i5] - - (24*I)*SUND[I1, i5, I5]*SUNDelta[I2, I6]*SUNF[I3, I4, i5] - - (24*I)*SUND[I1, I2, i5]*SUNDelta[I5, I6]*SUNF[I3, I4, i5] - - 45*SUND[i3, I6, i8]*SUND[I5, i6, i8]*SUNF[I1, I2, i3]*SUNF[I3, I4, i6] - - 45*SUND[i3, I5, i8]*SUND[i6, I6, i8]*SUNF[I1, I2, i3]*SUNF[I3, I4, i6] - - 120*SUNDelta[I5, I6]*SUNF[I1, I2, i6]*SUNF[I3, I4, i6] + - 45*SUND[I2, i6, i8]*SUND[i3, I6, i8]*SUNF[I1, i3, I5]*SUNF[I3, I4, i6] + - 45*SUND[I2, i3, i8]*SUND[i6, I6, i8]*SUNF[I1, i3, I5]*SUNF[I3, I4, i6] + - 45*SUND[I2, i6, i8]*SUND[i3, I5, i8]*SUNF[I1, i3, I6]*SUNF[I3, I4, i6] + - 45*SUND[I2, i3, i8]*SUND[I5, i6, i8]*SUNF[I1, i3, I6]*SUNF[I3, I4, i6] - - 108*SUND[I2, I6, i8]*SUND[i3, I5, i6]*SUNF[I1, i3, i8]*SUNF[I3, I4, i6] - - 108*SUND[I2, I5, i8]*SUND[i3, i6, I6]*SUNF[I1, i3, i8]*SUNF[I3, I4, i6] - - 108*SUND[I2, i3, i6]*SUND[I5, I6, i8]*SUNF[I1, i3, i8]*SUNF[I3, I4, i6] - - 120*SUNDelta[I2, I6]*SUNF[I1, I5, i6]*SUNF[I3, I4, i6] + - 120*SUNDelta[I2, I5]*SUNF[I1, i6, I6]*SUNF[I3, I4, i6] + - 27*SUND[I1, I6, i8]*SUND[i3, I5, i6]*SUNF[I2, i3, i8]*SUNF[I3, I4, i6] + - 27*SUND[I1, I5, i8]*SUND[i3, i6, I6]*SUNF[I2, i3, i8]*SUNF[I3, I4, i6] + - 72*SUND[I1, i3, i6]*SUND[I5, I6, i8]*SUNF[I2, i3, i8]*SUNF[I3, I4, i6] - - 27*SUND[I1, I6, i8]*SUND[I2, i3, i6]*SUNF[i3, I5, i8]*SUNF[I3, I4, i6] - - 72*SUND[I1, i3, i6]*SUND[I2, I6, i8]*SUNF[i3, I5, i8]*SUNF[I3, I4, i6] - - 27*SUND[I1, I2, i8]*SUND[i3, i6, I6]*SUNF[i3, I5, i8]*SUNF[I3, I4, i6] - - 27*SUND[I1, I5, i8]*SUND[I2, i3, i6]*SUNF[i3, I6, i8]*SUNF[I3, I4, i6] - - 72*SUND[I1, i3, i6]*SUND[I2, I5, i8]*SUNF[i3, I6, i8]*SUNF[I3, I4, i6] - - 27*SUND[I1, I2, i8]*SUND[i3, I5, i6]*SUNF[i3, I6, i8]*SUNF[I3, I4, i6] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I5, i7]*SUNF[I2, i5, i7]* - SUNF[I3, I4, i8] + (45*I)*SUND[i5, I5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, i5, i7]*SUNF[I3, I4, i8] - (36*I)*SUND[I4, i5, I6]* - SUNDelta[I1, I2]*SUNF[I3, i5, I5] - (36*I)*SUND[I2, i5, I6]* - SUNDelta[I1, I4]*SUNF[I3, i5, I5] - (36*I)*SUND[I2, I4, i5]* - SUNDelta[I1, I6]*SUNF[I3, i5, I5] + (24*I)*SUND[I1, i5, I6]* - SUNDelta[I2, I4]*SUNF[I3, i5, I5] + (24*I)*SUND[I1, I4, i5]* - SUNDelta[I2, I6]*SUNF[I3, i5, I5] + (24*I)*SUND[I1, I2, i5]* - SUNDelta[I4, I6]*SUNF[I3, i5, I5] - (36*I)*SUND[I4, i5, I5]* - SUNDelta[I1, I2]*SUNF[I3, i5, I6] - (36*I)*SUND[I2, i5, I5]* - SUNDelta[I1, I4]*SUNF[I3, i5, I6] - (36*I)*SUND[I2, I4, i5]* - SUNDelta[I1, I5]*SUNF[I3, i5, I6] + (24*I)*SUND[I1, i5, I5]* - SUNDelta[I2, I4]*SUNF[I3, i5, I6] + (24*I)*SUND[I1, I4, i5]* - SUNDelta[I2, I5]*SUNF[I3, i5, I6] + (24*I)*SUND[I1, I2, i5]* - SUNDelta[I4, I5]*SUNF[I3, i5, I6] - 45*SUND[i3, I6, i8]*SUND[I4, i6, i8]* - SUNF[I1, I2, i3]*SUNF[I3, I5, i6] - 45*SUND[i3, I4, i8]*SUND[i6, I6, i8]* - SUNF[I1, I2, i3]*SUNF[I3, I5, i6] - 120*SUNDelta[I4, I6]* - SUNF[I1, I2, i6]*SUNF[I3, I5, i6] + 45*SUND[I2, i6, i8]*SUND[i3, I6, i8]* - SUNF[I1, i3, I4]*SUNF[I3, I5, i6] + 45*SUND[I2, i3, i8]*SUND[i6, I6, i8]* - SUNF[I1, i3, I4]*SUNF[I3, I5, i6] + 45*SUND[I2, i6, i8]*SUND[i3, I4, i8]* - SUNF[I1, i3, I6]*SUNF[I3, I5, i6] + 45*SUND[I2, i3, i8]*SUND[I4, i6, i8]* - SUNF[I1, i3, I6]*SUNF[I3, I5, i6] - 108*SUND[I2, I6, i8]* - SUND[i3, I4, i6]*SUNF[I1, i3, i8]*SUNF[I3, I5, i6] - - 108*SUND[I2, I4, i8]*SUND[i3, i6, I6]*SUNF[I1, i3, i8]*SUNF[I3, I5, i6] - - 108*SUND[I2, i3, i6]*SUND[I4, I6, i8]*SUNF[I1, i3, i8]*SUNF[I3, I5, i6] - - 120*SUNDelta[I2, I6]*SUNF[I1, I4, i6]*SUNF[I3, I5, i6] + - 120*SUNDelta[I2, I4]*SUNF[I1, i6, I6]*SUNF[I3, I5, i6] + - 27*SUND[I1, I6, i8]*SUND[i3, I4, i6]*SUNF[I2, i3, i8]*SUNF[I3, I5, i6] + - 27*SUND[I1, I4, i8]*SUND[i3, i6, I6]*SUNF[I2, i3, i8]*SUNF[I3, I5, i6] + - 72*SUND[I1, i3, i6]*SUND[I4, I6, i8]*SUNF[I2, i3, i8]*SUNF[I3, I5, i6] - - 27*SUND[I1, I6, i8]*SUND[I2, i3, i6]*SUNF[i3, I4, i8]*SUNF[I3, I5, i6] - - 72*SUND[I1, i3, i6]*SUND[I2, I6, i8]*SUNF[i3, I4, i8]*SUNF[I3, I5, i6] - - 27*SUND[I1, I2, i8]*SUND[i3, i6, I6]*SUNF[i3, I4, i8]*SUNF[I3, I5, i6] - - 27*SUND[I1, I4, i8]*SUND[I2, i3, i6]*SUNF[i3, I6, i8]*SUNF[I3, I5, i6] - - 72*SUND[I1, i3, i6]*SUND[I2, I4, i8]*SUNF[i3, I6, i8]*SUNF[I3, I5, i6] - - 27*SUND[I1, I2, i8]*SUND[i3, I4, i6]*SUNF[i3, I6, i8]*SUNF[I3, I5, i6] + - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I4, i7]*SUNF[I2, i5, i7]* - SUNF[I3, I5, i8] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, I6, i7]* - SUNF[I2, i5, i7]*SUNF[I3, I5, i8] + 45*SUND[i3, I5, i8]*SUND[I4, i6, i8]* - SUNF[I1, I2, i3]*SUNF[I3, i6, I6] + 45*SUND[i3, I4, i8]*SUND[I5, i6, i8]* - SUNF[I1, I2, i3]*SUNF[I3, i6, I6] + 120*SUNDelta[I4, I5]* - SUNF[I1, I2, i6]*SUNF[I3, i6, I6] - 45*SUND[I2, i6, i8]*SUND[i3, I5, i8]* - SUNF[I1, i3, I4]*SUNF[I3, i6, I6] - 45*SUND[I2, i3, i8]*SUND[I5, i6, i8]* - SUNF[I1, i3, I4]*SUNF[I3, i6, I6] - 45*SUND[I2, i6, i8]*SUND[i3, I4, i8]* - SUNF[I1, i3, I5]*SUNF[I3, i6, I6] - 45*SUND[I2, i3, i8]*SUND[I4, i6, i8]* - SUNF[I1, i3, I5]*SUNF[I3, i6, I6] + 108*SUND[I2, I5, i8]* - SUND[i3, I4, i6]*SUNF[I1, i3, i8]*SUNF[I3, i6, I6] + - 108*SUND[I2, I4, i8]*SUND[i3, I5, i6]*SUNF[I1, i3, i8]*SUNF[I3, i6, I6] + - 108*SUND[I2, i3, i6]*SUND[I4, I5, i8]*SUNF[I1, i3, i8]*SUNF[I3, i6, I6] + - 120*SUNDelta[I2, I5]*SUNF[I1, I4, i6]*SUNF[I3, i6, I6] + - 120*SUNDelta[I2, I4]*SUNF[I1, I5, i6]*SUNF[I3, i6, I6] - - 27*SUND[I1, I5, i8]*SUND[i3, I4, i6]*SUNF[I2, i3, i8]*SUNF[I3, i6, I6] - - 27*SUND[I1, I4, i8]*SUND[i3, I5, i6]*SUNF[I2, i3, i8]*SUNF[I3, i6, I6] - - 72*SUND[I1, i3, i6]*SUND[I4, I5, i8]*SUNF[I2, i3, i8]*SUNF[I3, i6, I6] + - 27*SUND[I1, I5, i8]*SUND[I2, i3, i6]*SUNF[i3, I4, i8]*SUNF[I3, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I2, I5, i8]*SUNF[i3, I4, i8]*SUNF[I3, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[i3, I5, i6]*SUNF[i3, I4, i8]*SUNF[I3, i6, I6] + - 27*SUND[I1, I4, i8]*SUND[I2, i3, i6]*SUNF[i3, I5, i8]*SUNF[I3, i6, I6] + - 72*SUND[I1, i3, i6]*SUND[I2, I4, i8]*SUNF[i3, I5, i8]*SUNF[I3, i6, I6] + - 27*SUND[I1, I2, i8]*SUND[i3, I4, i6]*SUNF[i3, I5, i8]*SUNF[I3, i6, I6] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I4, i7]*SUNF[I2, i5, i7]* - SUNF[I3, I6, i8] + (45*I)*SUND[I4, i5, i8]*SUNF[I1, I5, i7]* - SUNF[I2, i5, i7]*SUNF[I3, I6, i8] - (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I5, i7]*SUNF[I2, I3, i8]*SUNF[I4, i5, i7] - - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I6, i7]*SUNF[I2, I3, i8]* - SUNF[I4, i5, i7] + (45*I)*SUND[i5, I6, i8]*SUNF[I1, I2, i7]* - SUNF[I3, I5, i8]*SUNF[I4, i5, i7] + (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I6, i7]*SUNF[I3, I5, i8]*SUNF[I4, i5, i7] + - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I2, i7]*SUNF[I3, I6, i8]* - SUNF[I4, i5, i7] + (45*I)*SUND[I2, i5, i8]*SUNF[I1, I5, i7]* - SUNF[I3, I6, i8]*SUNF[I4, i5, i7] - (72*I)*SUND[I5, I6, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I3]*SUNF[I4, i5, i8] + - (18*I)*SUND[I5, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i3, i5]* - SUNF[I4, i5, i8] - (72*I)*SUND[I2, I6, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I3, I5]*SUNF[I4, i5, i8] - (27*I)*SUND[I1, I6, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I3, I5]*SUNF[I4, i5, i8] - - (72*I)*SUND[I2, I5, i8]*SUNF[I1, i3, i5]*SUNF[i3, I3, I6]* - SUNF[I4, i5, i8] - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I6]*SUNF[I4, i5, i8] + (18*I)*SUND[I2, I6, i8]* - SUNF[I1, i3, I3]*SUNF[i3, i5, I5]*SUNF[I4, i5, i8] - - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, i5, I5]* - SUNF[I4, i5, i8] - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I6]* - SUNF[i3, i5, I5]*SUNF[I4, i5, i8] + (18*I)*SUND[I2, I5, i8]* - SUNF[I1, i3, I3]*SUNF[i3, i5, I6]*SUNF[I4, i5, i8] - - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I3]*SUNF[i3, i5, I6]* - SUNF[I4, i5, i8] - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I5]* - SUNF[i3, i5, I6]*SUNF[I4, i5, i8] - 45*SUNF[I1, i6, I6]*SUNF[I2, i8, i9]* - SUNF[I3, I5, i9]*SUNF[I4, i6, i8] + 45*SUNF[I1, I5, i6]*SUNF[I2, i8, i9]* - SUNF[I3, I6, i9]*SUNF[I4, i6, i8] - (45*I)*SUND[i1, I3, I6]* - SUNF[i1, I5, i9]*SUNF[I1, I2, i8]*SUNF[I4, i8, i9] - - (45*I)*SUND[i1, I3, I5]*SUNF[i1, I6, i9]*SUNF[I1, I2, i8]* - SUNF[I4, i8, i9] - (45*I)*SUND[i1, I3, I6]*SUNF[i1, I2, i9]* - SUNF[I1, I5, i8]*SUNF[I4, i8, i9] - (45*I)*SUND[i1, I2, I3]* - SUNF[i1, I6, i9]*SUNF[I1, I5, i8]*SUNF[I4, i8, i9] - - (45*I)*SUND[i1, I3, I5]*SUNF[i1, I2, i9]*SUNF[I1, I6, i8]* - SUNF[I4, i8, i9] - (45*I)*SUND[i1, I2, I3]*SUNF[i1, I5, i9]* - SUNF[I1, I6, i8]*SUNF[I4, i8, i9] - 45*SUNF[I1, i6, I6]*SUNF[I2, i6, i8]* - SUNF[I3, I5, i9]*SUNF[I4, i8, i9] + 45*SUNF[I1, I5, i6]*SUNF[I2, i6, i8]* - SUNF[I3, I6, i9]*SUNF[I4, i8, i9] + (45*I)*SUND[i5, I6, i8]* - SUNF[I1, I4, i7]*SUNF[I2, I3, i8]*SUNF[i5, I5, i7] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I6, i7]*SUNF[I2, I3, i8]* - SUNF[i5, I5, i7] - (45*I)*SUND[i5, I6, i8]*SUNF[I1, I2, i7]* - SUNF[I3, I4, i8]*SUNF[i5, I5, i7] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I6, i7]*SUNF[I3, I4, i8]*SUNF[i5, I5, i7] - - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I2, i7]*SUNF[I3, I6, i8]* - SUNF[i5, I5, i7] - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i7]* - SUNF[I3, I6, i8]*SUNF[i5, I5, i7] + (72*I)*SUND[I4, I6, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I3]*SUNF[i5, I5, i8] - - (18*I)*SUND[I4, I6, i8]*SUNF[I1, i3, I3]*SUNF[I2, i3, i5]* - SUNF[i5, I5, i8] + (72*I)*SUND[I2, I6, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I3, I4]*SUNF[i5, I5, i8] + (27*I)*SUND[I1, I6, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I3, I4]*SUNF[i5, I5, i8] + - (72*I)*SUND[I2, I4, i8]*SUNF[I1, i3, i5]*SUNF[i3, I3, I6]* - SUNF[i5, I5, i8] + (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I6]*SUNF[i5, I5, i8] + (18*I)*SUND[I2, I6, i8]* - SUNF[I1, i3, I3]*SUNF[i3, I4, i5]*SUNF[i5, I5, i8] - - (27*I)*SUND[I1, I6, i8]*SUNF[I2, i3, I3]*SUNF[i3, I4, i5]* - SUNF[i5, I5, i8] - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I6]* - SUNF[i3, I4, i5]*SUNF[i5, I5, i8] - (18*I)*SUND[I2, I4, i8]* - SUNF[I1, i3, I3]*SUNF[i3, i5, I6]*SUNF[i5, I5, i8] + - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, I3]*SUNF[i3, i5, I6]* - SUNF[i5, I5, i8] + (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I4]* - SUNF[i3, i5, I6]*SUNF[i5, I5, i8] + (45*I)*SUND[i5, I5, i8]* - SUNF[I1, I4, i7]*SUNF[I2, I3, i8]*SUNF[i5, I6, i7] + - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I5, i7]*SUNF[I2, I3, i8]* - SUNF[i5, I6, i7] - (45*I)*SUND[i5, I5, i8]*SUNF[I1, I2, i7]* - SUNF[I3, I4, i8]*SUNF[i5, I6, i7] - (45*I)*SUND[I2, i5, i8]* - SUNF[I1, I5, i7]*SUNF[I3, I4, i8]*SUNF[i5, I6, i7] - - (45*I)*SUND[I4, i5, i8]*SUNF[I1, I2, i7]*SUNF[I3, I5, i8]* - SUNF[i5, I6, i7] - (45*I)*SUND[I2, i5, i8]*SUNF[I1, I4, i7]* - SUNF[I3, I5, i8]*SUNF[i5, I6, i7] + (72*I)*SUND[I4, I5, i8]* - SUNF[I1, i3, i5]*SUNF[I2, i3, I3]*SUNF[i5, I6, i8] - - (18*I)*SUND[I4, I5, i8]*SUNF[I1, i3, I3]*SUNF[I2, i3, i5]* - SUNF[i5, I6, i8] + (72*I)*SUND[I2, I5, i8]*SUNF[I1, i3, i5]* - SUNF[i3, I3, I4]*SUNF[i5, I6, i8] + (27*I)*SUND[I1, I5, i8]* - SUNF[I2, i3, i5]*SUNF[i3, I3, I4]*SUNF[i5, I6, i8] + - (72*I)*SUND[I2, I4, i8]*SUNF[I1, i3, i5]*SUNF[i3, I3, I5]* - SUNF[i5, I6, i8] + (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, i5]* - SUNF[i3, I3, I5]*SUNF[i5, I6, i8] + (18*I)*SUND[I2, I5, i8]* - SUNF[I1, i3, I3]*SUNF[i3, I4, i5]*SUNF[i5, I6, i8] - - (27*I)*SUND[I1, I5, i8]*SUNF[I2, i3, I3]*SUNF[i3, I4, i5]* - SUNF[i5, I6, i8] - (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I5]* - SUNF[i3, I4, i5]*SUNF[i5, I6, i8] - (18*I)*SUND[I2, I4, i8]* - SUNF[I1, i3, I3]*SUNF[i3, i5, I5]*SUNF[i5, I6, i8] + - (27*I)*SUND[I1, I4, i8]*SUNF[I2, i3, I3]*SUNF[i3, i5, I5]* - SUNF[i5, I6, i8] + (27*I)*SUND[I1, I2, i8]*SUNF[i3, I3, I4]* - SUNF[i3, i5, I5]*SUNF[i5, I6, i8] - 45*SUNF[I1, i6, I6]*SUNF[I2, i8, i9]* - SUNF[I3, I4, i9]*SUNF[I5, i6, i8] + 45*SUNF[I1, I4, i6]*SUNF[I2, i8, i9]* - SUNF[I3, I6, i9]*SUNF[I5, i6, i8] + 45*SUNF[I1, i6, I6]*SUNF[I2, I3, i9]* - SUNF[I4, i8, i9]*SUNF[I5, i6, i8] + 45*SUNF[I1, I2, i6]*SUNF[I3, I6, i9]* - SUNF[I4, i8, i9]*SUNF[I5, i6, i8] - (45*I)*SUND[i1, I3, I6]* - SUNF[i1, I4, i9]*SUNF[I1, I2, i8]*SUNF[I5, i8, i9] - - (45*I)*SUND[i1, I3, I4]*SUNF[i1, I6, i9]*SUNF[I1, I2, i8]* - SUNF[I5, i8, i9] - (45*I)*SUND[i1, I3, I6]*SUNF[i1, I2, i9]* - SUNF[I1, I4, i8]*SUNF[I5, i8, i9] - (45*I)*SUND[i1, I2, I3]* - SUNF[i1, I6, i9]*SUNF[I1, I4, i8]*SUNF[I5, i8, i9] - - (45*I)*SUND[i1, I3, I4]*SUNF[i1, I2, i9]*SUNF[I1, I6, i8]* - SUNF[I5, i8, i9] - (45*I)*SUND[i1, I2, I3]*SUNF[i1, I4, i9]* - SUNF[I1, I6, i8]*SUNF[I5, i8, i9] - 45*SUNF[I1, i6, I6]*SUNF[I2, i6, i8]* - SUNF[I3, I4, i9]*SUNF[I5, i8, i9] + 45*SUNF[I1, I4, i6]*SUNF[I2, i6, i8]* - SUNF[I3, I6, i9]*SUNF[I5, i8, i9] + 45*SUNF[I1, i6, I6]*SUNF[I2, I3, i9]* - SUNF[I4, i6, i8]*SUNF[I5, i8, i9] + 45*SUNF[I1, I2, i6]*SUNF[I3, I6, i9]* - SUNF[I4, i6, i8]*SUNF[I5, i8, i9] - 45*SUNF[I1, I5, i6]*SUNF[I2, i8, i9]* - SUNF[I3, I4, i9]*SUNF[i6, I6, i8] - 45*SUNF[I1, I4, i6]*SUNF[I2, i8, i9]* - SUNF[I3, I5, i9]*SUNF[i6, I6, i8] + 45*SUNF[I1, I5, i6]*SUNF[I2, I3, i9]* - SUNF[I4, i8, i9]*SUNF[i6, I6, i8] - 45*SUNF[I1, I2, i6]*SUNF[I3, I5, i9]* - SUNF[I4, i8, i9]*SUNF[i6, I6, i8] + 45*SUNF[I1, I4, i6]*SUNF[I2, I3, i9]* - SUNF[I5, i8, i9]*SUNF[i6, I6, i8] - 45*SUNF[I1, I2, i6]*SUNF[I3, I4, i9]* - SUNF[I5, i8, i9]*SUNF[i6, I6, i8] - (45*I)*SUND[i1, I3, I5]* - SUNF[i1, I4, i9]*SUNF[I1, I2, i8]*SUNF[I6, i8, i9] - - (45*I)*SUND[i1, I3, I4]*SUNF[i1, I5, i9]*SUNF[I1, I2, i8]* - SUNF[I6, i8, i9] - (45*I)*SUND[i1, I3, I5]*SUNF[i1, I2, i9]* - SUNF[I1, I4, i8]*SUNF[I6, i8, i9] - (45*I)*SUND[i1, I2, I3]* - SUNF[i1, I5, i9]*SUNF[I1, I4, i8]*SUNF[I6, i8, i9] - - (45*I)*SUND[i1, I3, I4]*SUNF[i1, I2, i9]*SUNF[I1, I5, i8]* - SUNF[I6, i8, i9] - (45*I)*SUND[i1, I2, I3]*SUNF[i1, I4, i9]* - SUNF[I1, I5, i8]*SUNF[I6, i8, i9] + 45*SUNF[I1, I5, i6]*SUNF[I2, i6, i8]* - SUNF[I3, I4, i9]*SUNF[I6, i8, i9] + 45*SUNF[I1, I4, i6]*SUNF[I2, i6, i8]* - SUNF[I3, I5, i9]*SUNF[I6, i8, i9] - 45*SUNF[I1, I5, i6]*SUNF[I2, I3, i9]* - SUNF[I4, i6, i8]*SUNF[I6, i8, i9] + 45*SUNF[I1, I2, i6]*SUNF[I3, I5, i9]* - SUNF[I4, i6, i8]*SUNF[I6, i8, i9] - 45*SUNF[I1, I4, i6]*SUNF[I2, I3, i9]* - SUNF[I5, i6, i8]*SUNF[I6, i8, i9] + 45*SUNF[I1, I2, i6]*SUNF[I3, I4, i9]* - SUNF[I5, i6, i8]*SUNF[I6, i8, i9])/ -(1080*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o2.Gen deleted file mode 100644 index 13bb2f0ef..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1], FourVector[p3, \[Mu]1], FourVector[p4, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o2.Mod deleted file mode 100644 index 43c31e46b..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o2.Mod +++ /dev/null @@ -1,21 +0,0 @@ -{{(-15*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] - 15*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] + 30*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 9*SU3F[I1, I4, k1]*SU3F[I2, I3, k1] + 9*SU3F[I1, I3, k1]* - SU3F[I2, I4, k1] - 10*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 10*SUNDelta[I1, I3]*SUNDelta[I2, I4] + 20*SUNDelta[I1, I2]* - SUNDelta[I3, I4])/(36*DecayConstant[PseudoScalar[1], - RenormalizationState[0]])}, -{(-15*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] + 30*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] - 15*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] - - 9*SU3F[I1, I4, k1]*SU3F[I2, I3, k1] + 9*SU3F[I1, I2, k1]* - SU3F[I3, I4, k1] - 10*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 20*SUNDelta[I1, I3]*SUNDelta[I2, I4] - 10*SUNDelta[I1, I2]* - SUNDelta[I3, I4])/(36*DecayConstant[PseudoScalar[1], - RenormalizationState[0]])}, -{(30*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] - 15*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] - 15*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] - - 9*SU3F[I1, I3, k1]*SU3F[I2, I4, k1] - 9*SU3F[I1, I2, k1]* - SU3F[I3, I4, k1] + 20*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 10*SUNDelta[I1, I3]*SUNDelta[I2, I4] - 10*SUNDelta[I1, I2]* - SUNDelta[I3, I4])/(36*DecayConstant[PseudoScalar[1], - RenormalizationState[0]])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o4.Gen deleted file mode 100644 index bb23c3857..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o4.Gen +++ /dev/null @@ -1,17 +0,0 @@ -{FourVector[p4, \[Mu]1]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, FourVector[p3, \[Mu]1]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -FourVector[p4, \[Mu]1]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, FourVector[p3, \[Mu]1]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -FourVector[p4, \[Mu]1]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, FourVector[p3, \[Mu]1]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, FourVector[p2, \[Mu]1]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, FourVector[p2, \[Mu]1]* -MomentaScalarProduct[p3, p4], FourVector[p3, \[Mu]1]* -MomentaScalarProduct[p2, p4], FourVector[p4, \[Mu]1]* -MomentaScalarProduct[p2, p3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o4.Mod deleted file mode 100644 index d1aec9ec6..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10P10P10o4.Mod +++ /dev/null @@ -1,1658 +0,0 @@ -{{(CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((20*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 - 2*SU3F[I1, I3, k5]* - SU3F[I2, I4, k5] - 2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5] + - (88*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9) + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((44*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 + 4*SU3D[3, k5, k6]* - SU3D[I1, I4, k5]*SU3D[I2, I3, k6] - - (4*SU3D[8, k5, k6]*SU3D[I1, I4, k5]*SU3D[I2, I3, k6])/Sqrt[3] + - 2*SU3D[3, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6] - - (2*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 - 2*SU3D[3, I3, k5]* - SU3D[I1, k5, k6]*SU3D[I2, I4, k6] + - (2*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] - - (SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/3 + - (SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) + - (11*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/3 - - (11*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 - 2*SU3D[3, I2, k5]* - SU3D[I1, k5, k6]*SU3D[I3, I4, k6] + - (2*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] + - (SU3D[3, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) - - (SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/3 + - (SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (11*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/3 - - (11*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/3 + - (4*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/3 + - (4*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (4*SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/3 - - (4*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (I/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[3, I1, k5] - - (I/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I1, k5] - - ((4*I)/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I1, k5] + - (I/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I2, k5] - - ((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I2, k5] + - (I/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[3, I3, k5] - - ((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[3, I3, k5] - - (2*I)*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[3, I4, k5] + - (I/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[3, I4, k5] + - (I/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[3, I4, k5] - - (4*I)*SU3D[I1, I4, k3]*SU3D[I2, I3, k6]*SU3F[3, k3, k6] + - ((I/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((I/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - (((4*I)/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - ((2*I)*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - ((4*I)*SU3D[I1, I4, k3]*SU3D[I2, I3, k6]*SU3F[8, k3, k6])/Sqrt[3] + - ((5*I)/3)*SU3D[3, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6] - - (((5*I)/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] + - ((2*I)/3)*SU3D[3, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6] - - (((2*I)/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] - - (4*SU3D[I4, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I2, k6])/3 + - (5*SU3D[I3, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I2, k6])/3 + - (4*SU3D[I4, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) - - (5*SU3D[I3, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) + - ((5*I)/3)*SU3D[3, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6] - - (((5*I)/3)*SU3D[8, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] + - ((2*I)/3)*SU3D[3, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6] - - (((2*I)/3)*SU3D[8, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] - - (4*SU3D[I4, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I3, k6])/3 + - (5*SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I3, k6])/3 + - (4*SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) - - (5*SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) - - (I/3)*SU3D[3, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6] + - ((I/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] - - (I/3)*SU3D[3, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6] + - ((I/3)*SU3D[8, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] - - (SU3D[I3, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I4, k6])/3 - - (SU3D[I2, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I4, k6])/3 + - (SU3D[I3, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) + - (SU3D[I2, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) + - (2*I)*SU3D[3, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6] - - ((2*I)*SU3D[8, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*I)*SU3D[3, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*I)*SU3D[3, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - 2*SU3D[I2, I3, k5]*SU3F[3, I4, k6]*SU3F[I1, k5, k6] + - (2*SU3D[I2, I3, k5]*SU3F[8, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5])/3 - I*SU3D[3, I1, k5]* - SU3D[I3, k5, k6]*SU3F[I2, I4, k6] + - (I*SU3D[8, I1, k5]*SU3D[I3, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] - - SU3D[I3, k5, k6]*SU3F[3, I1, k5]*SU3F[I2, I4, k6] + - 2*SU3D[I1, k5, k6]*SU3F[3, I3, k5]*SU3F[I2, I4, k6] + - (SU3D[I3, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I4, k6])/Sqrt[3] - - (2*SU3D[I1, k5, k6]*SU3F[8, I3, k5]*SU3F[I2, I4, k6])/Sqrt[3] + - (2*I)*SU3F[3, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6] - - ((2*I)*SU3F[8, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] - - (I/3)*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6] + - ((I/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - ((11*I)/3)*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6] - - (((11*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6])/ - Sqrt[3] + (I/3)*SU3D[3, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (SU3D[I3, I4, k5]*SU3F[3, I1, k6]*SU3F[I2, k5, k6])/3 + - (SU3D[I1, I4, k5]*SU3F[3, I3, k6]*SU3F[I2, k5, k6])/3 + - (SU3D[I1, I3, k5]*SU3F[3, I4, k6]*SU3F[I2, k5, k6])/3 + - (SU3D[I3, I4, k5]*SU3F[8, I1, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I4, k5]*SU3F[8, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I3, k5]*SU3F[8, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (5*SU3D[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/3 + - (5*SU3D[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - ((5*I)/3)*SU3F[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6] - - (((5*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (SU3D[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/3 - - (SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (I/3)*SU3F[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6] + - ((I/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5])/3 - I*SU3D[3, I1, k5]* - SU3D[I2, k5, k6]*SU3F[I3, I4, k6] + - (I*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - SU3D[I2, k5, k6]*SU3F[3, I1, k5]*SU3F[I3, I4, k6] + - 2*SU3D[I1, k5, k6]*SU3F[3, I2, k5]*SU3F[I3, I4, k6] + - (SU3D[I2, k5, k6]*SU3F[8, I1, k5]*SU3F[I3, I4, k6])/Sqrt[3] - - (2*SU3D[I1, k5, k6]*SU3F[8, I2, k5]*SU3F[I3, I4, k6])/Sqrt[3] + - (2*I)*SU3F[3, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6] - - ((2*I)*SU3F[8, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - SU3D[3, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6] - - (SU3D[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - I*SU3F[3, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6] + - (I*SU3F[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - (I/3)*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6] + - ((I/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - ((11*I)/3)*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6] - - (((11*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] + (I/3)*SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (SU3D[I2, I4, k5]*SU3F[3, I1, k6]*SU3F[I3, k5, k6])/3 + - (SU3D[I1, I4, k5]*SU3F[3, I2, k6]*SU3F[I3, k5, k6])/3 + - (SU3D[I1, I2, k5]*SU3F[3, I4, k6]*SU3F[I3, k5, k6])/3 + - (SU3D[I2, I4, k5]*SU3F[8, I1, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I4, k5]*SU3F[8, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I2, k5]*SU3F[8, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (5*SU3D[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/3 + - (5*SU3D[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - ((5*I)/3)*SU3F[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6] - - (((5*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (SU3D[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/3 - - (SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (I/3)*SU3F[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6] + - ((I/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - SU3D[3, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6] - - (SU3D[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - I*SU3F[3, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6] + - (I*SU3F[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6] + - (((4*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6] + - (((4*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6] - - (((4*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (4*SU3D[I2, I3, k5]*SU3F[3, I1, k6]*SU3F[I4, k5, k6])/3 - - (2*SU3D[I1, I3, k5]*SU3F[3, I2, k6]*SU3F[I4, k5, k6])/3 - - (2*SU3D[I1, I2, k5]*SU3F[3, I3, k6]*SU3F[I4, k5, k6])/3 + - (4*SU3D[I2, I3, k5]*SU3F[8, I1, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I3, k5]*SU3F[8, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I2, k5]*SU3F[8, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (2*SU3D[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/3 + - (2*SU3D[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - ((4*I)/3)*SU3F[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6] + - (((4*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (2*SU3D[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/3 + - (2*SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - ((4*I)/3)*SU3F[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6] + - (((4*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (4*SU3D[I2, I3, I4]*SUNDelta[3, I1])/3 + - (2*SU3D[I1, I3, I4]*SUNDelta[3, I2])/9 + ((2*I)/3)*SU3F[I1, I3, I4]* - SUNDelta[3, I2] + (2*SU3D[I1, I2, I4]*SUNDelta[3, I3])/9 + - ((2*I)/3)*SU3F[I1, I2, I4]*SUNDelta[3, I3] + - (8*SU3D[I1, I2, I3]*SUNDelta[3, I4])/9 - - (4*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) - - (2*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) - - (((2*I)/3)*SU3F[I1, I3, I4]*SUNDelta[8, I2])/Sqrt[3] - - (2*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) - - (((2*I)/3)*SU3F[I1, I2, I4]*SUNDelta[8, I3])/Sqrt[3] - - (8*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) - - (10*SU3D[3, I3, I4]*SUNDelta[I1, I2])/9 + - (10*SU3D[8, I3, I4]*SUNDelta[I1, I2])/(9*Sqrt[3]) - - ((2*I)/3)*SU3F[3, I3, I4]*SUNDelta[I1, I2] + - (((2*I)/3)*SU3F[8, I3, I4]*SUNDelta[I1, I2])/Sqrt[3] - - (10*SU3D[3, I2, I4]*SUNDelta[I1, I3])/9 + - (10*SU3D[8, I2, I4]*SUNDelta[I1, I3])/(9*Sqrt[3]) - - ((2*I)/3)*SU3F[3, I2, I4]*SUNDelta[I1, I3] + - (((2*I)/3)*SU3F[8, I2, I4]*SUNDelta[I1, I3])/Sqrt[3] + - (44*SU3D[3, I1, I4]*SUNDelta[I2, I3])/9 - - (44*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) + - ((4*I)/9)*SU3F[3, I1, I4]*SUNDelta[I2, I3] - - (((4*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] + - (88*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 - - (10*SU3D[3, I1, I3]*SUNDelta[I2, I4])/9 + - (10*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) - - ((2*I)/9)*SU3F[3, I1, I3]*SUNDelta[I2, I4] + - (((2*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 - - (10*SU3D[3, I1, I2]*SUNDelta[I3, I4])/9 + - (10*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) - - ((2*I)/9)*SU3F[3, I1, I2]*SUNDelta[I3, I4] + - (((2*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 + - (20*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 - 2*SU3F[I1, I4, k5]* - SU3F[I2, I3, k5] + 2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 + - (88*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9) + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 - 2*SU3D[3, I4, k5]* - SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - (2*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] + - (44*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 + 4*SU3D[3, k5, k6]* - SU3D[I1, I3, k5]*SU3D[I2, I4, k6] - - (4*SU3D[8, k5, k6]*SU3D[I1, I3, k5]*SU3D[I2, I4, k6])/Sqrt[3] + - 2*SU3D[3, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6] - - (2*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] + - (11*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/3 - - (11*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/3 + - (SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 - 2*SU3D[3, I2, k5]* - SU3D[I1, k5, k6]*SU3D[I3, I4, k6] + - (2*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] + - (SU3D[3, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) - - (4*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/3 + - (4*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/3 + - (4*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (4*SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/3 - - (4*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/3 + - (SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (11*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/3 - - (11*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (I/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[3, I1, k5] - - ((4*I)/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I1, k5] - - (I/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I1, k5] - - ((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I2, k5] + - (I/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I2, k5] - - (2*I)*SU3D[I1, k5, k6]*SU3D[I2, I4, k6]*SU3F[3, I3, k5] + - (I/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[3, I3, k5] + - (I/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[3, I3, k5] + - (I/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[3, I4, k5] - - ((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[3, I4, k5] - - (4*I)*SU3D[I1, I3, k3]*SU3D[I2, I4, k6]*SU3F[3, k3, k6] + - ((I/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] + - (((4*I)/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((I/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - ((2*I)*SU3D[I1, k5, k6]*SU3D[I2, I4, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - ((4*I)*SU3D[I1, I3, k3]*SU3D[I2, I4, k6]*SU3F[8, k3, k6])/Sqrt[3] + - ((2*I)/3)*SU3D[3, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6] - - (((2*I)/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] + - ((5*I)/3)*SU3D[3, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6] - - (((5*I)/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] + - (5*SU3D[I4, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I2, k6])/3 - - (4*SU3D[I3, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I2, k6])/3 - - (5*SU3D[I4, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) + - (4*SU3D[I3, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) - - (I/3)*SU3D[3, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6] + - ((I/3)*SU3D[8, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] - - (I/3)*SU3D[3, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6] + - ((I/3)*SU3D[8, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] - - (SU3D[I4, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I3, k6])/3 - - (SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I3, k6])/3 + - (SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - (SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - ((5*I)/3)*SU3D[3, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6] - - (((5*I)/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] + - ((2*I)/3)*SU3D[3, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6] - - (((2*I)/3)*SU3D[8, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] - - (4*SU3D[I3, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I4, k6])/3 + - (5*SU3D[I2, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I4, k6])/3 + - (4*SU3D[I3, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) - - (5*SU3D[I2, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) - - (2*I)*SU3D[3, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*I)*SU3D[3, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6] - - ((2*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*I)*SU3D[3, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - 2*SU3D[I2, I4, k5]*SU3F[3, I3, k6]*SU3F[I1, k5, k6] + - (2*SU3D[I2, I4, k5]*SU3F[8, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I4, k5]*SU3F[I2, I3, k5])/3 - I*SU3D[3, I1, k5]* - SU3D[I4, k5, k6]*SU3F[I2, I3, k6] + - (I*SU3D[8, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] - - SU3D[I4, k5, k6]*SU3F[3, I1, k5]*SU3F[I2, I3, k6] + - 2*SU3D[I1, k5, k6]*SU3F[3, I4, k5]*SU3F[I2, I3, k6] + - (SU3D[I4, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I3, k6])/Sqrt[3] - - (2*SU3D[I1, k5, k6]*SU3F[8, I4, k5]*SU3F[I2, I3, k6])/Sqrt[3] + - (2*I)*SU3F[3, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6] - - ((2*I)*SU3F[8, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] + - ((11*I)/3)*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6] - - (((11*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/ - Sqrt[3] - (I/3)*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6] + - ((I/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (I/3)*SU3D[3, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (SU3D[I3, I4, k5]*SU3F[3, I1, k6]*SU3F[I2, k5, k6])/3 + - (SU3D[I1, I4, k5]*SU3F[3, I3, k6]*SU3F[I2, k5, k6])/3 + - (SU3D[I1, I3, k5]*SU3F[3, I4, k6]*SU3F[I2, k5, k6])/3 + - (SU3D[I3, I4, k5]*SU3F[8, I1, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I4, k5]*SU3F[8, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I3, k5]*SU3F[8, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/3 - - (SU3D[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (I/3)*SU3F[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6] + - ((I/3)*SU3F[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (5*SU3D[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/3 + - (5*SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - ((5*I)/3)*SU3F[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6] - - (((5*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5])/3 + I*SU3D[3, I1, k5]* - SU3D[I2, k5, k6]*SU3F[I3, I4, k6] - - (I*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - SU3D[I2, k5, k6]*SU3F[3, I1, k5]*SU3F[I3, I4, k6] - - 2*SU3D[I1, k5, k6]*SU3F[3, I2, k5]*SU3F[I3, I4, k6] - - (SU3D[I2, k5, k6]*SU3F[8, I1, k5]*SU3F[I3, I4, k6])/Sqrt[3] + - (2*SU3D[I1, k5, k6]*SU3F[8, I2, k5]*SU3F[I3, I4, k6])/Sqrt[3] - - (2*I)*SU3F[3, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6] + - ((2*I)*SU3F[8, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - SU3D[3, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6] + - (SU3D[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - I*SU3F[3, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6] - - (I*SU3F[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6] + - (((4*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6] + - (((4*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6] - - (((4*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (4*SU3D[I2, I4, k5]*SU3F[3, I1, k6]*SU3F[I3, k5, k6])/3 - - (2*SU3D[I1, I4, k5]*SU3F[3, I2, k6]*SU3F[I3, k5, k6])/3 - - (2*SU3D[I1, I2, k5]*SU3F[3, I4, k6]*SU3F[I3, k5, k6])/3 + - (4*SU3D[I2, I4, k5]*SU3F[8, I1, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I4, k5]*SU3F[8, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I2, k5]*SU3F[8, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (2*SU3D[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/3 + - (2*SU3D[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - ((4*I)/3)*SU3F[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6] + - (((4*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (2*SU3D[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/3 + - (2*SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - ((4*I)/3)*SU3F[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6] + - (((4*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (I/3)*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6] + - ((I/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - ((11*I)/3)*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6] - - (((11*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/ - Sqrt[3] + (I/3)*SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (SU3D[I2, I3, k5]*SU3F[3, I1, k6]*SU3F[I4, k5, k6])/3 + - (SU3D[I1, I3, k5]*SU3F[3, I2, k6]*SU3F[I4, k5, k6])/3 + - (SU3D[I1, I2, k5]*SU3F[3, I3, k6]*SU3F[I4, k5, k6])/3 + - (SU3D[I2, I3, k5]*SU3F[8, I1, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I3, k5]*SU3F[8, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I2, k5]*SU3F[8, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (5*SU3D[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/3 + - (5*SU3D[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - ((5*I)/3)*SU3F[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6] - - (((5*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (SU3D[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/3 - - (SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (I/3)*SU3F[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6] + - ((I/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - SU3D[3, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6] - - (SU3D[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - I*SU3F[3, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6] + - (I*SU3F[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (4*SU3D[I2, I3, I4]*SUNDelta[3, I1])/3 + - (2*SU3D[I1, I3, I4]*SUNDelta[3, I2])/9 - ((2*I)/3)*SU3F[I1, I3, I4]* - SUNDelta[3, I2] + (8*SU3D[I1, I2, I4]*SUNDelta[3, I3])/9 + - (2*SU3D[I1, I2, I3]*SUNDelta[3, I4])/9 + ((2*I)/3)*SU3F[I1, I2, I3]* - SUNDelta[3, I4] - (4*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) - - (2*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) + - (((2*I)/3)*SU3F[I1, I3, I4]*SUNDelta[8, I2])/Sqrt[3] - - (8*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) - - (2*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) - - (((2*I)/3)*SU3F[I1, I2, I3]*SUNDelta[8, I4])/Sqrt[3] - - (10*SU3D[3, I3, I4]*SUNDelta[I1, I2])/9 + - (10*SU3D[8, I3, I4]*SUNDelta[I1, I2])/(9*Sqrt[3]) + - ((2*I)/3)*SU3F[3, I3, I4]*SUNDelta[I1, I2] - - (((2*I)/3)*SU3F[8, I3, I4]*SUNDelta[I1, I2])/Sqrt[3] - - (10*SU3D[3, I2, I3]*SUNDelta[I1, I4])/9 + - (10*SU3D[8, I2, I3]*SUNDelta[I1, I4])/(9*Sqrt[3]) - - ((2*I)/3)*SU3F[3, I2, I3]*SUNDelta[I1, I4] + - (((2*I)/3)*SU3F[8, I2, I3]*SUNDelta[I1, I4])/Sqrt[3] - - (10*SU3D[3, I1, I4]*SUNDelta[I2, I3])/9 + - (10*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) - - ((2*I)/9)*SU3F[3, I1, I4]*SUNDelta[I2, I3] + - (((2*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 + - (44*SU3D[3, I1, I3]*SUNDelta[I2, I4])/9 - - (44*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) + - ((4*I)/9)*SU3F[3, I1, I3]*SUNDelta[I2, I4] - - (((4*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] + - (88*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 - - (10*SU3D[3, I1, I2]*SUNDelta[I3, I4])/9 + - (10*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) - - ((2*I)/9)*SU3F[3, I1, I2]*SUNDelta[I3, I4] + - (((2*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((20*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 - 2*SU3F[I1, I3, k5]* - SU3F[I2, I4, k5] - 2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5] + - (88*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9) + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((44*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 - 4*SU3D[3, k5, k6]* - SU3D[I1, I4, k5]*SU3D[I2, I3, k6] - - (4*SU3D[8, k5, k6]*SU3D[I1, I4, k5]*SU3D[I2, I3, k6])/Sqrt[3] - - 2*SU3D[3, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6] - - (2*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 + 2*SU3D[3, I3, k5]* - SU3D[I1, k5, k6]*SU3D[I2, I4, k6] + - (2*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] + - (SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/3 + - (SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (11*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/3 - - (11*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 + 2*SU3D[3, I2, k5]* - SU3D[I1, k5, k6]*SU3D[I3, I4, k6] + - (2*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] - - (SU3D[3, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) + - (SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/3 + - (SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (11*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/3 - - (11*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (4*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/3 + - (4*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (4*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/3 + - (4*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/3 - - (4*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (I/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[3, I1, k5] + - (I/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I1, k5] + - ((4*I)/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I1, k5] - - (I/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I2, k5] + - ((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I2, k5] - - (I/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[3, I3, k5] + - ((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[3, I3, k5] + - (2*I)*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[3, I4, k5] - - (I/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[3, I4, k5] - - (I/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[3, I4, k5] + - (4*I)*SU3D[I1, I4, k3]*SU3D[I2, I3, k6]*SU3F[3, k3, k6] + - ((I/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((I/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - (((4*I)/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - ((2*I)*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - ((4*I)*SU3D[I1, I4, k3]*SU3D[I2, I3, k6]*SU3F[8, k3, k6])/Sqrt[3] - - ((5*I)/3)*SU3D[3, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6] - - (((5*I)/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] - - ((2*I)/3)*SU3D[3, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6] - - (((2*I)/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] + - (4*SU3D[I4, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I2, k6])/3 - - (5*SU3D[I3, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I2, k6])/3 + - (4*SU3D[I4, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) - - (5*SU3D[I3, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) - - ((5*I)/3)*SU3D[3, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6] - - (((5*I)/3)*SU3D[8, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] - - ((2*I)/3)*SU3D[3, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6] - - (((2*I)/3)*SU3D[8, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] + - (4*SU3D[I4, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I3, k6])/3 - - (5*SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I3, k6])/3 + - (4*SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) - - (5*SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - (I/3)*SU3D[3, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6] + - ((I/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] + - (I/3)*SU3D[3, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6] + - ((I/3)*SU3D[8, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] + - (SU3D[I3, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I4, k6])/3 + - (SU3D[I2, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I4, k6])/3 + - (SU3D[I3, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) + - (SU3D[I2, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) - - (2*I)*SU3D[3, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6] - - ((2*I)*SU3D[8, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*I)*SU3D[3, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*I)*SU3D[3, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - 2*SU3D[I2, I3, k5]*SU3F[3, I4, k6]*SU3F[I1, k5, k6] + - (2*SU3D[I2, I3, k5]*SU3F[8, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5])/3 + I*SU3D[3, I1, k5]* - SU3D[I3, k5, k6]*SU3F[I2, I4, k6] + - (I*SU3D[8, I1, k5]*SU3D[I3, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] + - SU3D[I3, k5, k6]*SU3F[3, I1, k5]*SU3F[I2, I4, k6] - - 2*SU3D[I1, k5, k6]*SU3F[3, I3, k5]*SU3F[I2, I4, k6] + - (SU3D[I3, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I4, k6])/Sqrt[3] - - (2*SU3D[I1, k5, k6]*SU3F[8, I3, k5]*SU3F[I2, I4, k6])/Sqrt[3] - - (2*I)*SU3F[3, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6] - - ((2*I)*SU3F[8, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] + - (I/3)*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6] + - ((I/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - ((11*I)/3)*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6] - - (((11*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6])/ - Sqrt[3] - (I/3)*SU3D[3, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (SU3D[I3, I4, k5]*SU3F[3, I1, k6]*SU3F[I2, k5, k6])/3 - - (SU3D[I1, I4, k5]*SU3F[3, I3, k6]*SU3F[I2, k5, k6])/3 - - (SU3D[I1, I3, k5]*SU3F[3, I4, k6]*SU3F[I2, k5, k6])/3 + - (SU3D[I3, I4, k5]*SU3F[8, I1, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I4, k5]*SU3F[8, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I3, k5]*SU3F[8, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (5*SU3D[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/3 + - (5*SU3D[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - ((5*I)/3)*SU3F[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6] - - (((5*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (SU3D[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/3 - - (SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (I/3)*SU3F[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6] + - ((I/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5])/3 + I*SU3D[3, I1, k5]* - SU3D[I2, k5, k6]*SU3F[I3, I4, k6] + - (I*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - SU3D[I2, k5, k6]*SU3F[3, I1, k5]*SU3F[I3, I4, k6] - - 2*SU3D[I1, k5, k6]*SU3F[3, I2, k5]*SU3F[I3, I4, k6] + - (SU3D[I2, k5, k6]*SU3F[8, I1, k5]*SU3F[I3, I4, k6])/Sqrt[3] - - (2*SU3D[I1, k5, k6]*SU3F[8, I2, k5]*SU3F[I3, I4, k6])/Sqrt[3] - - (2*I)*SU3F[3, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6] - - ((2*I)*SU3F[8, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - SU3D[3, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6] - - (SU3D[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - I*SU3F[3, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6] + - (I*SU3F[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - (I/3)*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6] + - ((I/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - ((11*I)/3)*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6] - - (((11*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] - (I/3)*SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (SU3D[I2, I4, k5]*SU3F[3, I1, k6]*SU3F[I3, k5, k6])/3 - - (SU3D[I1, I4, k5]*SU3F[3, I2, k6]*SU3F[I3, k5, k6])/3 - - (SU3D[I1, I2, k5]*SU3F[3, I4, k6]*SU3F[I3, k5, k6])/3 + - (SU3D[I2, I4, k5]*SU3F[8, I1, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I4, k5]*SU3F[8, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I2, k5]*SU3F[8, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (5*SU3D[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/3 + - (5*SU3D[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - ((5*I)/3)*SU3F[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6] - - (((5*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (SU3D[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/3 - - (SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (I/3)*SU3F[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6] + - ((I/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - SU3D[3, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6] - - (SU3D[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - I*SU3F[3, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6] + - (I*SU3F[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6] + - (((4*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6] + - (((4*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6] - - (((4*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (4*SU3D[I2, I3, k5]*SU3F[3, I1, k6]*SU3F[I4, k5, k6])/3 + - (2*SU3D[I1, I3, k5]*SU3F[3, I2, k6]*SU3F[I4, k5, k6])/3 + - (2*SU3D[I1, I2, k5]*SU3F[3, I3, k6]*SU3F[I4, k5, k6])/3 + - (4*SU3D[I2, I3, k5]*SU3F[8, I1, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I3, k5]*SU3F[8, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I2, k5]*SU3F[8, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/3 + - (2*SU3D[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - ((4*I)/3)*SU3F[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6] + - (((4*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (2*SU3D[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/3 + - (2*SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - ((4*I)/3)*SU3F[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6] + - (((4*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (4*SU3D[I2, I3, I4]*SUNDelta[3, I1])/3 - - (2*SU3D[I1, I3, I4]*SUNDelta[3, I2])/9 - ((2*I)/3)*SU3F[I1, I3, I4]* - SUNDelta[3, I2] - (2*SU3D[I1, I2, I4]*SUNDelta[3, I3])/9 - - ((2*I)/3)*SU3F[I1, I2, I4]*SUNDelta[3, I3] - - (8*SU3D[I1, I2, I3]*SUNDelta[3, I4])/9 - - (4*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) - - (2*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) - - (((2*I)/3)*SU3F[I1, I3, I4]*SUNDelta[8, I2])/Sqrt[3] - - (2*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) - - (((2*I)/3)*SU3F[I1, I2, I4]*SUNDelta[8, I3])/Sqrt[3] - - (8*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) + - (10*SU3D[3, I3, I4]*SUNDelta[I1, I2])/9 + - (10*SU3D[8, I3, I4]*SUNDelta[I1, I2])/(9*Sqrt[3]) + - ((2*I)/3)*SU3F[3, I3, I4]*SUNDelta[I1, I2] + - (((2*I)/3)*SU3F[8, I3, I4]*SUNDelta[I1, I2])/Sqrt[3] + - (10*SU3D[3, I2, I4]*SUNDelta[I1, I3])/9 + - (10*SU3D[8, I2, I4]*SUNDelta[I1, I3])/(9*Sqrt[3]) + - ((2*I)/3)*SU3F[3, I2, I4]*SUNDelta[I1, I3] + - (((2*I)/3)*SU3F[8, I2, I4]*SUNDelta[I1, I3])/Sqrt[3] - - (44*SU3D[3, I1, I4]*SUNDelta[I2, I3])/9 - - (44*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) - - ((4*I)/9)*SU3F[3, I1, I4]*SUNDelta[I2, I3] - - (((4*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] + - (88*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 + - (10*SU3D[3, I1, I3]*SUNDelta[I2, I4])/9 + - (10*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) + - ((2*I)/9)*SU3F[3, I1, I3]*SUNDelta[I2, I4] + - (((2*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 + - (10*SU3D[3, I1, I2]*SUNDelta[I3, I4])/9 + - (10*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) + - ((2*I)/9)*SU3F[3, I1, I2]*SUNDelta[I3, I4] + - (((2*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 + - (20*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 - 2*SU3F[I1, I4, k5]* - SU3F[I2, I3, k5] + 2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 + - (88*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9) + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 + 2*SU3D[3, I4, k5]* - SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - (2*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] + - (44*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 - 4*SU3D[3, k5, k6]* - SU3D[I1, I3, k5]*SU3D[I2, I4, k6] - - (4*SU3D[8, k5, k6]*SU3D[I1, I3, k5]*SU3D[I2, I4, k6])/Sqrt[3] - - 2*SU3D[3, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6] - - (2*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] - - (11*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/3 - - (11*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/3 + - (SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 + 2*SU3D[3, I2, k5]* - SU3D[I1, k5, k6]*SU3D[I3, I4, k6] + - (2*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] - - (SU3D[3, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) + - (4*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/3 + - (4*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (4*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/3 + - (4*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/3 - - (4*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/3 + - (SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (11*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/3 - - (11*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (I/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[3, I1, k5] + - ((4*I)/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I1, k5] + - (I/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I1, k5] + - ((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I2, k5] - - (I/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I2, k5] + - (2*I)*SU3D[I1, k5, k6]*SU3D[I2, I4, k6]*SU3F[3, I3, k5] - - (I/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[3, I3, k5] - - (I/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[3, I3, k5] - - (I/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[3, I4, k5] + - ((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[3, I4, k5] + - (4*I)*SU3D[I1, I3, k3]*SU3D[I2, I4, k6]*SU3F[3, k3, k6] + - ((I/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] + - (((4*I)/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((I/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - ((2*I)*SU3D[I1, k5, k6]*SU3D[I2, I4, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - ((4*I)*SU3D[I1, I3, k3]*SU3D[I2, I4, k6]*SU3F[8, k3, k6])/Sqrt[3] - - ((2*I)/3)*SU3D[3, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6] - - (((2*I)/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] - - ((5*I)/3)*SU3D[3, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6] - - (((5*I)/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] - - (5*SU3D[I4, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I2, k6])/3 + - (4*SU3D[I3, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I2, k6])/3 - - (5*SU3D[I4, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) + - (4*SU3D[I3, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) + - (I/3)*SU3D[3, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6] + - ((I/3)*SU3D[8, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] + - (I/3)*SU3D[3, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6] + - ((I/3)*SU3D[8, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] + - (SU3D[I4, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I3, k6])/3 + - (SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I3, k6])/3 + - (SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - (SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) - - ((5*I)/3)*SU3D[3, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6] - - (((5*I)/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] - - ((2*I)/3)*SU3D[3, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6] - - (((2*I)/3)*SU3D[8, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] + - (4*SU3D[I3, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I4, k6])/3 - - (5*SU3D[I2, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I4, k6])/3 + - (4*SU3D[I3, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) - - (5*SU3D[I2, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) + - (2*I)*SU3D[3, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*I)*SU3D[3, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6] - - ((2*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*I)*SU3D[3, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - 2*SU3D[I2, I4, k5]*SU3F[3, I3, k6]*SU3F[I1, k5, k6] + - (2*SU3D[I2, I4, k5]*SU3F[8, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I4, k5]*SU3F[I2, I3, k5])/3 + I*SU3D[3, I1, k5]* - SU3D[I4, k5, k6]*SU3F[I2, I3, k6] + - (I*SU3D[8, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] + - SU3D[I4, k5, k6]*SU3F[3, I1, k5]*SU3F[I2, I3, k6] - - 2*SU3D[I1, k5, k6]*SU3F[3, I4, k5]*SU3F[I2, I3, k6] + - (SU3D[I4, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I3, k6])/Sqrt[3] - - (2*SU3D[I1, k5, k6]*SU3F[8, I4, k5]*SU3F[I2, I3, k6])/Sqrt[3] - - (2*I)*SU3F[3, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6] - - ((2*I)*SU3F[8, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] - - ((11*I)/3)*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6] - - (((11*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/ - Sqrt[3] + (I/3)*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6] + - ((I/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (I/3)*SU3D[3, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (SU3D[I3, I4, k5]*SU3F[3, I1, k6]*SU3F[I2, k5, k6])/3 - - (SU3D[I1, I4, k5]*SU3F[3, I3, k6]*SU3F[I2, k5, k6])/3 - - (SU3D[I1, I3, k5]*SU3F[3, I4, k6]*SU3F[I2, k5, k6])/3 + - (SU3D[I3, I4, k5]*SU3F[8, I1, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I4, k5]*SU3F[8, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I3, k5]*SU3F[8, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/3 - - (SU3D[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (I/3)*SU3F[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6] + - ((I/3)*SU3F[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (5*SU3D[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/3 + - (5*SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - ((5*I)/3)*SU3F[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6] - - (((5*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5])/3 - I*SU3D[3, I1, k5]* - SU3D[I2, k5, k6]*SU3F[I3, I4, k6] - - (I*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - SU3D[I2, k5, k6]*SU3F[3, I1, k5]*SU3F[I3, I4, k6] + - 2*SU3D[I1, k5, k6]*SU3F[3, I2, k5]*SU3F[I3, I4, k6] - - (SU3D[I2, k5, k6]*SU3F[8, I1, k5]*SU3F[I3, I4, k6])/Sqrt[3] + - (2*SU3D[I1, k5, k6]*SU3F[8, I2, k5]*SU3F[I3, I4, k6])/Sqrt[3] + - (2*I)*SU3F[3, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6] + - ((2*I)*SU3F[8, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - SU3D[3, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6] + - (SU3D[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - I*SU3F[3, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6] - - (I*SU3F[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6] + - (((4*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6] + - (((4*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6] - - (((4*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (4*SU3D[I2, I4, k5]*SU3F[3, I1, k6]*SU3F[I3, k5, k6])/3 + - (2*SU3D[I1, I4, k5]*SU3F[3, I2, k6]*SU3F[I3, k5, k6])/3 + - (2*SU3D[I1, I2, k5]*SU3F[3, I4, k6]*SU3F[I3, k5, k6])/3 + - (4*SU3D[I2, I4, k5]*SU3F[8, I1, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I4, k5]*SU3F[8, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I2, k5]*SU3F[8, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/3 + - (2*SU3D[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - ((4*I)/3)*SU3F[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6] + - (((4*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (2*SU3D[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/3 + - (2*SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - ((4*I)/3)*SU3F[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6] + - (((4*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (I/3)*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6] + - ((I/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - ((11*I)/3)*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6] - - (((11*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/ - Sqrt[3] - (I/3)*SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (SU3D[I2, I3, k5]*SU3F[3, I1, k6]*SU3F[I4, k5, k6])/3 - - (SU3D[I1, I3, k5]*SU3F[3, I2, k6]*SU3F[I4, k5, k6])/3 - - (SU3D[I1, I2, k5]*SU3F[3, I3, k6]*SU3F[I4, k5, k6])/3 + - (SU3D[I2, I3, k5]*SU3F[8, I1, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I3, k5]*SU3F[8, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I2, k5]*SU3F[8, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (5*SU3D[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/3 + - (5*SU3D[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - ((5*I)/3)*SU3F[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6] - - (((5*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (SU3D[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/3 - - (SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (I/3)*SU3F[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6] + - ((I/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - SU3D[3, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6] - - (SU3D[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - I*SU3F[3, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6] + - (I*SU3F[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (4*SU3D[I2, I3, I4]*SUNDelta[3, I1])/3 - - (2*SU3D[I1, I3, I4]*SUNDelta[3, I2])/9 + ((2*I)/3)*SU3F[I1, I3, I4]* - SUNDelta[3, I2] - (8*SU3D[I1, I2, I4]*SUNDelta[3, I3])/9 - - (2*SU3D[I1, I2, I3]*SUNDelta[3, I4])/9 - ((2*I)/3)*SU3F[I1, I2, I3]* - SUNDelta[3, I4] - (4*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) - - (2*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) + - (((2*I)/3)*SU3F[I1, I3, I4]*SUNDelta[8, I2])/Sqrt[3] - - (8*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) - - (2*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) - - (((2*I)/3)*SU3F[I1, I2, I3]*SUNDelta[8, I4])/Sqrt[3] + - (10*SU3D[3, I3, I4]*SUNDelta[I1, I2])/9 + - (10*SU3D[8, I3, I4]*SUNDelta[I1, I2])/(9*Sqrt[3]) - - ((2*I)/3)*SU3F[3, I3, I4]*SUNDelta[I1, I2] - - (((2*I)/3)*SU3F[8, I3, I4]*SUNDelta[I1, I2])/Sqrt[3] + - (10*SU3D[3, I2, I3]*SUNDelta[I1, I4])/9 + - (10*SU3D[8, I2, I3]*SUNDelta[I1, I4])/(9*Sqrt[3]) + - ((2*I)/3)*SU3F[3, I2, I3]*SUNDelta[I1, I4] + - (((2*I)/3)*SU3F[8, I2, I3]*SUNDelta[I1, I4])/Sqrt[3] + - (10*SU3D[3, I1, I4]*SUNDelta[I2, I3])/9 + - (10*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) + - ((2*I)/9)*SU3F[3, I1, I4]*SUNDelta[I2, I3] + - (((2*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 - - (44*SU3D[3, I1, I3]*SUNDelta[I2, I4])/9 - - (44*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) - - ((4*I)/9)*SU3F[3, I1, I3]*SUNDelta[I2, I4] - - (((4*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] + - (88*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 + - (10*SU3D[3, I1, I2]*SUNDelta[I3, I4])/9 + - (10*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) + - ((2*I)/9)*SU3F[3, I1, I2]*SUNDelta[I3, I4] + - (((2*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((20*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 - 2*SU3F[I1, I3, k5]* - SU3F[I2, I4, k5] - 2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5] + - (88*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9) + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((44*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 + - (8*SU3D[8, k5, k6]*SU3D[I1, I4, k5]*SU3D[I2, I3, k6])/Sqrt[3] + - (4*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 - - (4*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] - - (2*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) + - (22*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 - - (4*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] + - (2*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) - - (2*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (22*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (8*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (8*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (8*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] - - (((2*I)/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] - - (((8*I)/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - (((4*I)/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - (((4*I)/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((4*I)*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[8, I4, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((8*I)*SU3D[I1, I4, k3]*SU3D[I2, I3, k6]*SU3F[8, k3, k6])/Sqrt[3] + - (((10*I)/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/ - Sqrt[3] + (((4*I)/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]* - SU3F[I1, I2, k6])/Sqrt[3] - (8*SU3D[I4, k5, k6]*SU3F[8, I3, k5]* - SU3F[I1, I2, k6])/(3*Sqrt[3]) + (10*SU3D[I3, k5, k6]*SU3F[8, I4, k5]* - SU3F[I1, I2, k6])/(3*Sqrt[3]) + (((10*I)/3)*SU3D[8, I4, k5]* - SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] + - (((4*I)/3)*SU3D[8, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] - - (8*SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - (10*SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] - - (((2*I)/3)*SU3D[8, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] - - (2*SU3D[I3, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) - - (2*SU3D[I2, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) + - ((4*I)*SU3D[8, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - ((4*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - ((4*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (4*SU3D[I2, I3, k5]*SU3F[8, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5])/3 - - ((2*I)*SU3D[8, I1, k5]*SU3D[I3, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] - - (2*SU3D[I3, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I4, k6])/Sqrt[3] + - (4*SU3D[I1, k5, k6]*SU3F[8, I3, k5]*SU3F[I2, I4, k6])/Sqrt[3] + - ((4*I)*SU3F[8, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] - - (((2*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (((22*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6])/ - Sqrt[3] + (((2*I)/3)*SU3D[8, I1, k5]*SU3D[I3, I4, k6]* - SU3F[I2, k5, k6])/Sqrt[3] - (2*SU3D[I3, I4, k5]*SU3F[8, I1, k6]* - SU3F[I2, k5, k6])/(3*Sqrt[3]) + (2*SU3D[I1, I4, k5]*SU3F[8, I3, k6]* - SU3F[I2, k5, k6])/(3*Sqrt[3]) + (2*SU3D[I1, I3, k5]*SU3F[8, I4, k6]* - SU3F[I2, k5, k6])/(3*Sqrt[3]) - (10*SU3D[8, I4, k5]*SU3F[I1, I3, k6]* - SU3F[I2, k5, k6])/(3*Sqrt[3]) + (((10*I)/3)*SU3F[8, I4, k5]* - SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (2*SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5])/3 - - ((2*I)*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - (2*SU3D[I2, k5, k6]*SU3F[8, I1, k5]*SU3F[I3, I4, k6])/Sqrt[3] + - (4*SU3D[I1, k5, k6]*SU3F[8, I2, k5]*SU3F[I3, I4, k6])/Sqrt[3] + - ((4*I)*SU3F[8, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - (2*SU3D[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - ((2*I)*SU3F[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - (((2*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (((22*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] + (((2*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I4, k6]* - SU3F[I3, k5, k6])/Sqrt[3] - (2*SU3D[I2, I4, k5]*SU3F[8, I1, k6]* - SU3F[I3, k5, k6])/(3*Sqrt[3]) + (2*SU3D[I1, I4, k5]*SU3F[8, I2, k6]* - SU3F[I3, k5, k6])/(3*Sqrt[3]) + (2*SU3D[I1, I2, k5]*SU3F[8, I4, k6]* - SU3F[I3, k5, k6])/(3*Sqrt[3]) - (10*SU3D[8, I4, k5]*SU3F[I1, I2, k6]* - SU3F[I3, k5, k6])/(3*Sqrt[3]) + (((10*I)/3)*SU3F[8, I4, k5]* - SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (2*SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (2*SU3D[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - ((2*I)*SU3F[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (((8*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (((8*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (((8*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (8*SU3D[I2, I3, k5]*SU3F[8, I1, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[I1, I3, k5]*SU3F[8, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[I1, I2, k5]*SU3F[8, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (((8*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (4*SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (((8*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (8*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) + - (4*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) + - (((4*I)/3)*SU3F[I1, I3, I4]*SUNDelta[8, I2])/Sqrt[3] + - (4*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) + - (((4*I)/3)*SU3F[I1, I2, I4]*SUNDelta[8, I3])/Sqrt[3] + - (16*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) - - (20*SU3D[8, I3, I4]*SUNDelta[I1, I2])/(9*Sqrt[3]) - - (((4*I)/3)*SU3F[8, I3, I4]*SUNDelta[I1, I2])/Sqrt[3] - - (20*SU3D[8, I2, I4]*SUNDelta[I1, I3])/(9*Sqrt[3]) - - (((4*I)/3)*SU3F[8, I2, I4]*SUNDelta[I1, I3])/Sqrt[3] + - (88*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) + - (((8*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] + - (88*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 - - (20*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) - - (((4*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 - - (20*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) - - (((4*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 + - (20*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 - 2*SU3F[I1, I4, k5]* - SU3F[I2, I3, k5] + 2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 + - (88*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9) + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 - - (4*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] + - (44*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 + - (8*SU3D[8, k5, k6]*SU3D[I1, I3, k5]*SU3D[I2, I4, k6])/Sqrt[3] + - (4*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] + - (22*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (2*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (10*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 - - (4*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] + - (2*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) - - (8*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (8*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (8*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (2*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (22*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] - - (((8*I)/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] - - (((2*I)/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] - - (((4*I)/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((4*I)*SU3D[I1, k5, k6]*SU3D[I2, I4, k6]*SU3F[8, I3, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] - - (((4*I)/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((8*I)*SU3D[I1, I3, k3]*SU3D[I2, I4, k6]*SU3F[8, k3, k6])/Sqrt[3] + - (((4*I)/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] + - (((10*I)/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/ - Sqrt[3] + (10*SU3D[I4, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I2, k6])/ - (3*Sqrt[3]) - (8*SU3D[I3, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I2, k6])/ - (3*Sqrt[3]) - (((2*I)/3)*SU3D[8, I4, k5]*SU3D[I2, k5, k6]* - SU3F[I1, I3, k6])/Sqrt[3] - (((2*I)/3)*SU3D[8, I2, k5]* - SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] - - (2*SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) - - (2*SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - (((10*I)/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/ - Sqrt[3] + (((4*I)/3)*SU3D[8, I2, k5]*SU3D[I3, k5, k6]* - SU3F[I1, I4, k6])/Sqrt[3] - (8*SU3D[I3, k5, k6]*SU3F[8, I2, k5]* - SU3F[I1, I4, k6])/(3*Sqrt[3]) + (10*SU3D[I2, k5, k6]*SU3F[8, I3, k5]* - SU3F[I1, I4, k6])/(3*Sqrt[3]) - ((4*I)*SU3D[8, I4, k5]* - SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - ((4*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - ((4*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (4*SU3D[I2, I4, k5]*SU3F[8, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*SU3F[I1, I4, k5]*SU3F[I2, I3, k5])/3 - - ((2*I)*SU3D[8, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] - - (2*SU3D[I4, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I3, k6])/Sqrt[3] + - (4*SU3D[I1, k5, k6]*SU3F[8, I4, k5]*SU3F[I2, I3, k6])/Sqrt[3] + - ((4*I)*SU3F[8, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] + - (((22*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/ - Sqrt[3] - (((2*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]* - SU3F[I2, k5, k6])/Sqrt[3] + (((2*I)/3)*SU3D[8, I1, k5]* - SU3D[I3, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (2*SU3D[I3, I4, k5]*SU3F[8, I1, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I4, k5]*SU3F[8, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I3, k5]*SU3F[8, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (10*SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (((10*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/ - Sqrt[3] + (2*SU3F[I1, I2, k5]*SU3F[I3, I4, k5])/3 + - ((2*I)*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - (2*SU3D[I2, k5, k6]*SU3F[8, I1, k5]*SU3F[I3, I4, k6])/Sqrt[3] - - (4*SU3D[I1, k5, k6]*SU3F[8, I2, k5]*SU3F[I3, I4, k6])/Sqrt[3] - - ((4*I)*SU3F[8, I2, k5]*SU3F[I1, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - (2*SU3D[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] + - ((2*I)*SU3F[8, I1, k5]*SU3F[I2, k5, k6]*SU3F[I3, I4, k6])/Sqrt[3] - - (((8*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (((8*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (((8*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (8*SU3D[I2, I4, k5]*SU3F[8, I1, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[I1, I4, k5]*SU3F[8, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[I1, I2, k5]*SU3F[8, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (((8*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (4*SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (((8*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (((2*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (((22*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/ - Sqrt[3] + (((2*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]* - SU3F[I4, k5, k6])/Sqrt[3] - (2*SU3D[I2, I3, k5]*SU3F[8, I1, k6]* - SU3F[I4, k5, k6])/(3*Sqrt[3]) + (2*SU3D[I1, I3, k5]*SU3F[8, I2, k6]* - SU3F[I4, k5, k6])/(3*Sqrt[3]) + (2*SU3D[I1, I2, k5]*SU3F[8, I3, k6]* - SU3F[I4, k5, k6])/(3*Sqrt[3]) - (10*SU3D[8, I3, k5]*SU3F[I1, I2, k6]* - SU3F[I4, k5, k6])/(3*Sqrt[3]) + (((10*I)/3)*SU3F[8, I3, k5]* - SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (2*SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (2*SU3D[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - ((2*I)*SU3F[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (8*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) + - (4*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) - - (((4*I)/3)*SU3F[I1, I3, I4]*SUNDelta[8, I2])/Sqrt[3] + - (16*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) + - (4*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) + - (((4*I)/3)*SU3F[I1, I2, I3]*SUNDelta[8, I4])/Sqrt[3] - - (20*SU3D[8, I3, I4]*SUNDelta[I1, I2])/(9*Sqrt[3]) + - (((4*I)/3)*SU3F[8, I3, I4]*SUNDelta[I1, I2])/Sqrt[3] - - (20*SU3D[8, I2, I3]*SUNDelta[I1, I4])/(9*Sqrt[3]) - - (((4*I)/3)*SU3F[8, I2, I3]*SUNDelta[I1, I4])/Sqrt[3] - - (20*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) - - (((4*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 + - (88*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) + - (((8*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] + - (88*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 - - (20*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) - - (((4*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] - - (20*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 + 2*SU3D[3, I4, k5]* - SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - (2*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 + 2*SU3D[3, I3, k5]* - SU3D[I1, k5, k6]*SU3D[I2, I4, k6] + - (2*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] + - (4*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/3 + - (4*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) + - (4*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/3 + - (4*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) + - (44*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 - 4*SU3D[3, k5, k6]* - SU3D[I1, I2, k5]*SU3D[I3, I4, k6] - - (4*SU3D[8, k5, k6]*SU3D[I1, I2, k5]*SU3D[I3, I4, k6])/Sqrt[3] - - 2*SU3D[3, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6] - - (2*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] - - (4*SU3D[3, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/3 - - (4*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) - - (11*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/3 - - (11*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/3 + - (SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (11*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/3 - - (11*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/3 + - (SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - ((4*I)/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[3, I1, k5] + - (I/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I1, k5] + - (I/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I1, k5] + - (2*I)*SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[3, I2, k5] - - (I/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I2, k5] - - (I/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I2, k5] + - ((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[3, I3, k5] - - (I/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[3, I3, k5] + - ((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[3, I4, k5] - - (I/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[3, I4, k5] + - (4*I)*SU3D[I1, I2, k3]*SU3D[I3, I4, k6]*SU3F[3, k3, k6] + - (((4*I)/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((I/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((I/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((2*I)*SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - ((4*I)*SU3D[I1, I2, k3]*SU3D[I3, I4, k6]*SU3F[8, k3, k6])/Sqrt[3] + - (I/3)*SU3D[3, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6] + - ((I/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] + - (I/3)*SU3D[3, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6] + - ((I/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] + - (SU3D[I4, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I2, k6])/3 + - (SU3D[I3, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I2, k6])/3 + - (SU3D[I4, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) + - (SU3D[I3, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) - - ((2*I)/3)*SU3D[3, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6] - - (((2*I)/3)*SU3D[8, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] - - ((5*I)/3)*SU3D[3, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6] - - (((5*I)/3)*SU3D[8, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] - - (5*SU3D[I4, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I3, k6])/3 + - (4*SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I3, k6])/3 - - (5*SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - (4*SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) - - ((2*I)/3)*SU3D[3, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6] - - (((2*I)/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] - - ((5*I)/3)*SU3D[3, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6] - - (((5*I)/3)*SU3D[8, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] - - (5*SU3D[I3, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I4, k6])/3 + - (4*SU3D[I2, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I4, k6])/3 - - (5*SU3D[I3, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) + - (4*SU3D[I2, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) + - (2*I)*SU3D[3, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*I)*SU3D[3, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*I)*SU3D[3, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6] - - ((2*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - 2*SU3D[I3, I4, k5]*SU3F[3, I2, k6]*SU3F[I1, k5, k6] + - (2*SU3D[I3, I4, k5]*SU3F[8, I2, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*SU3F[I1, I4, k5]*SU3F[I2, I3, k5])/3 - I*SU3D[3, I1, k5]* - SU3D[I4, k5, k6]*SU3F[I2, I3, k6] - - (I*SU3D[8, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] - - SU3D[I4, k5, k6]*SU3F[3, I1, k5]*SU3F[I2, I3, k6] + - 2*SU3D[I1, k5, k6]*SU3F[3, I4, k5]*SU3F[I2, I3, k6] - - (SU3D[I4, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I3, k6])/Sqrt[3] + - (2*SU3D[I1, k5, k6]*SU3F[8, I4, k5]*SU3F[I2, I3, k6])/Sqrt[3] + - (2*I)*SU3F[3, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6] + - ((2*I)*SU3F[8, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] + - (2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5])/3 - I*SU3D[3, I1, k5]* - SU3D[I3, k5, k6]*SU3F[I2, I4, k6] - - (I*SU3D[8, I1, k5]*SU3D[I3, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] - - SU3D[I3, k5, k6]*SU3F[3, I1, k5]*SU3F[I2, I4, k6] + - 2*SU3D[I1, k5, k6]*SU3F[3, I3, k5]*SU3F[I2, I4, k6] - - (SU3D[I3, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I4, k6])/Sqrt[3] + - (2*SU3D[I1, k5, k6]*SU3F[8, I3, k5]*SU3F[I2, I4, k6])/Sqrt[3] + - (2*I)*SU3F[3, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6] + - ((2*I)*SU3F[8, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6] + - (((4*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6] + - (((4*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6] - - (((4*I)/3)*SU3D[8, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (4*SU3D[I3, I4, k5]*SU3F[3, I1, k6]*SU3F[I2, k5, k6])/3 + - (2*SU3D[I1, I4, k5]*SU3F[3, I3, k6]*SU3F[I2, k5, k6])/3 + - (2*SU3D[I1, I3, k5]*SU3F[3, I4, k6]*SU3F[I2, k5, k6])/3 + - (4*SU3D[I3, I4, k5]*SU3F[8, I1, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I4, k5]*SU3F[8, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I3, k5]*SU3F[8, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/3 + - (2*SU3D[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - ((4*I)/3)*SU3F[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6] + - (((4*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (2*SU3D[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/3 + - (2*SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - ((4*I)/3)*SU3F[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6] + - (((4*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - ((11*I)/3)*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6] - - (((11*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] + (I/3)*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6] + - ((I/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (I/3)*SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (SU3D[I2, I4, k5]*SU3F[3, I1, k6]*SU3F[I3, k5, k6])/3 - - (SU3D[I1, I4, k5]*SU3F[3, I2, k6]*SU3F[I3, k5, k6])/3 - - (SU3D[I1, I2, k5]*SU3F[3, I4, k6]*SU3F[I3, k5, k6])/3 + - (SU3D[I2, I4, k5]*SU3F[8, I1, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I4, k5]*SU3F[8, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I2, k5]*SU3F[8, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/3 - - (SU3D[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (I/3)*SU3F[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6] + - ((I/3)*SU3F[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (5*SU3D[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/3 + - (5*SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - ((5*I)/3)*SU3F[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6] - - (((5*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - SU3D[3, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6] + - (SU3D[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - I*SU3F[3, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6] - - (I*SU3F[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - ((11*I)/3)*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6] - - (((11*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6])/ - Sqrt[3] + (I/3)*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6] + - ((I/3)*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (I/3)*SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (SU3D[I2, I3, k5]*SU3F[3, I1, k6]*SU3F[I4, k5, k6])/3 - - (SU3D[I1, I3, k5]*SU3F[3, I2, k6]*SU3F[I4, k5, k6])/3 - - (SU3D[I1, I2, k5]*SU3F[3, I3, k6]*SU3F[I4, k5, k6])/3 + - (SU3D[I2, I3, k5]*SU3F[8, I1, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I3, k5]*SU3F[8, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I2, k5]*SU3F[8, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/3 - - (SU3D[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (I/3)*SU3F[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6] + - ((I/3)*SU3F[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (5*SU3D[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/3 + - (5*SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - ((5*I)/3)*SU3F[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6] - - (((5*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - SU3D[3, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6] + - (SU3D[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - I*SU3F[3, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6] - - (I*SU3F[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (4*SU3D[I2, I3, I4]*SUNDelta[3, I1])/3 - - (8*SU3D[I1, I3, I4]*SUNDelta[3, I2])/9 - - (2*SU3D[I1, I2, I4]*SUNDelta[3, I3])/9 + ((2*I)/3)*SU3F[I1, I2, I4]* - SUNDelta[3, I3] - (2*SU3D[I1, I2, I3]*SUNDelta[3, I4])/9 + - ((2*I)/3)*SU3F[I1, I2, I3]*SUNDelta[3, I4] - - (4*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) - - (8*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) - - (2*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) + - (((2*I)/3)*SU3F[I1, I2, I4]*SUNDelta[8, I3])/Sqrt[3] - - (2*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) + - (((2*I)/3)*SU3F[I1, I2, I3]*SUNDelta[8, I4])/Sqrt[3] + - (10*SU3D[3, I2, I4]*SUNDelta[I1, I3])/9 + - (10*SU3D[8, I2, I4]*SUNDelta[I1, I3])/(9*Sqrt[3]) - - ((2*I)/3)*SU3F[3, I2, I4]*SUNDelta[I1, I3] - - (((2*I)/3)*SU3F[8, I2, I4]*SUNDelta[I1, I3])/Sqrt[3] + - (10*SU3D[3, I2, I3]*SUNDelta[I1, I4])/9 + - (10*SU3D[8, I2, I3]*SUNDelta[I1, I4])/(9*Sqrt[3]) - - ((2*I)/3)*SU3F[3, I2, I3]*SUNDelta[I1, I4] - - (((2*I)/3)*SU3F[8, I2, I3]*SUNDelta[I1, I4])/Sqrt[3] + - (10*SU3D[3, I1, I4]*SUNDelta[I2, I3])/9 + - (10*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) + - ((2*I)/9)*SU3F[3, I1, I4]*SUNDelta[I2, I3] + - (((2*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 + - (10*SU3D[3, I1, I3]*SUNDelta[I2, I4])/9 + - (10*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) + - ((2*I)/9)*SU3F[3, I1, I3]*SUNDelta[I2, I4] + - (((2*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 - - (44*SU3D[3, I1, I2]*SUNDelta[I3, I4])/9 - - (44*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) - - ((4*I)/9)*SU3F[3, I1, I2]*SUNDelta[I3, I4] - - (((4*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] + - (88*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27) + - CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 + - (20*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 + 2*SU3F[I1, I4, k5]* - SU3F[I2, I3, k5] + 2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 + - (88*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 - 2*SU3D[3, I4, k5]* - SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - (2*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 - 2*SU3D[3, I3, k5]* - SU3D[I1, k5, k6]*SU3D[I2, I4, k6] + - (2*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] - - (4*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/3 + - (4*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/3 + - (4*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) + - (44*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 + 4*SU3D[3, k5, k6]* - SU3D[I1, I2, k5]*SU3D[I3, I4, k6] - - (4*SU3D[8, k5, k6]*SU3D[I1, I2, k5]*SU3D[I3, I4, k6])/Sqrt[3] + - 2*SU3D[3, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6] - - (2*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] + - (4*SU3D[3, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/3 - - (4*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) + - (11*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/3 - - (11*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/3 + - (SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (11*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/3 - - (11*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/3 + - (SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/3 - - (SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - ((4*I)/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[3, I1, k5] - - (I/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I1, k5] - - (I/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I1, k5] - - (2*I)*SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[3, I2, k5] + - (I/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[3, I2, k5] + - (I/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[3, I2, k5] - - ((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[3, I3, k5] + - (I/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[3, I3, k5] - - ((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[3, I4, k5] + - (I/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[3, I4, k5] - - (4*I)*SU3D[I1, I2, k3]*SU3D[I3, I4, k6]*SU3F[3, k3, k6] + - (((4*I)/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((I/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((I/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] + - ((2*I)*SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((I/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - ((4*I)*SU3D[I1, I2, k3]*SU3D[I3, I4, k6]*SU3F[8, k3, k6])/Sqrt[3] - - (I/3)*SU3D[3, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6] + - ((I/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] - - (I/3)*SU3D[3, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6] + - ((I/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] - - (SU3D[I4, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I2, k6])/3 - - (SU3D[I3, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I2, k6])/3 + - (SU3D[I4, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) + - (SU3D[I3, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) + - ((2*I)/3)*SU3D[3, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6] - - (((2*I)/3)*SU3D[8, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] + - ((5*I)/3)*SU3D[3, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6] - - (((5*I)/3)*SU3D[8, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] + - (5*SU3D[I4, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I3, k6])/3 - - (4*SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[I1, I3, k6])/3 - - (5*SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - (4*SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/(3*Sqrt[3]) + - ((2*I)/3)*SU3D[3, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6] - - (((2*I)/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] + - ((5*I)/3)*SU3D[3, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6] - - (((5*I)/3)*SU3D[8, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] + - (5*SU3D[I3, k5, k6]*SU3F[3, I2, k5]*SU3F[I1, I4, k6])/3 - - (4*SU3D[I2, k5, k6]*SU3F[3, I3, k5]*SU3F[I1, I4, k6])/3 - - (5*SU3D[I3, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) + - (4*SU3D[I2, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) - - (2*I)*SU3D[3, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (2*I)*SU3D[3, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6] + - ((2*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*I)*SU3D[3, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6] - - ((2*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - 2*SU3D[I3, I4, k5]*SU3F[3, I2, k6]*SU3F[I1, k5, k6] + - (2*SU3D[I3, I4, k5]*SU3F[8, I2, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*SU3F[I1, I4, k5]*SU3F[I2, I3, k5])/3 + I*SU3D[3, I1, k5]* - SU3D[I4, k5, k6]*SU3F[I2, I3, k6] - - (I*SU3D[8, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] + - SU3D[I4, k5, k6]*SU3F[3, I1, k5]*SU3F[I2, I3, k6] - - 2*SU3D[I1, k5, k6]*SU3F[3, I4, k5]*SU3F[I2, I3, k6] - - (SU3D[I4, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I3, k6])/Sqrt[3] + - (2*SU3D[I1, k5, k6]*SU3F[8, I4, k5]*SU3F[I2, I3, k6])/Sqrt[3] - - (2*I)*SU3F[3, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6] + - ((2*I)*SU3F[8, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] + - (2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5])/3 + I*SU3D[3, I1, k5]* - SU3D[I3, k5, k6]*SU3F[I2, I4, k6] - - (I*SU3D[8, I1, k5]*SU3D[I3, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] + - SU3D[I3, k5, k6]*SU3F[3, I1, k5]*SU3F[I2, I4, k6] - - 2*SU3D[I1, k5, k6]*SU3F[3, I3, k5]*SU3F[I2, I4, k6] - - (SU3D[I3, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I4, k6])/Sqrt[3] + - (2*SU3D[I1, k5, k6]*SU3F[8, I3, k5]*SU3F[I2, I4, k6])/Sqrt[3] - - (2*I)*SU3F[3, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6] + - ((2*I)*SU3F[8, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6] + - (((4*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - ((4*I)/3)*SU3D[3, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6] + - (((4*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - ((4*I)/3)*SU3D[3, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6] - - (((4*I)/3)*SU3D[8, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (4*SU3D[I3, I4, k5]*SU3F[3, I1, k6]*SU3F[I2, k5, k6])/3 - - (2*SU3D[I1, I4, k5]*SU3F[3, I3, k6]*SU3F[I2, k5, k6])/3 - - (2*SU3D[I1, I3, k5]*SU3F[3, I4, k6]*SU3F[I2, k5, k6])/3 + - (4*SU3D[I3, I4, k5]*SU3F[8, I1, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I4, k5]*SU3F[8, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I3, k5]*SU3F[8, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (2*SU3D[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/3 + - (2*SU3D[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - ((4*I)/3)*SU3F[3, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6] + - (((4*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (2*SU3D[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/3 + - (2*SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - ((4*I)/3)*SU3F[3, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6] + - (((4*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - ((11*I)/3)*SU3D[3, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6] - - (((11*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] - (I/3)*SU3D[3, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6] + - ((I/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - (I/3)*SU3D[3, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (SU3D[I2, I4, k5]*SU3F[3, I1, k6]*SU3F[I3, k5, k6])/3 + - (SU3D[I1, I4, k5]*SU3F[3, I2, k6]*SU3F[I3, k5, k6])/3 + - (SU3D[I1, I2, k5]*SU3F[3, I4, k6]*SU3F[I3, k5, k6])/3 + - (SU3D[I2, I4, k5]*SU3F[8, I1, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I4, k5]*SU3F[8, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I2, k5]*SU3F[8, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/3 - - (SU3D[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (I/3)*SU3F[3, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6] + - ((I/3)*SU3F[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (5*SU3D[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/3 + - (5*SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - ((5*I)/3)*SU3F[3, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6] - - (((5*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - SU3D[3, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6] + - (SU3D[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - I*SU3F[3, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6] - - (I*SU3F[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] + - ((11*I)/3)*SU3D[3, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6] - - (((11*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3F[I4, k5, k6])/ - Sqrt[3] - (I/3)*SU3D[3, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6] + - ((I/3)*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (I/3)*SU3D[3, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6] - - ((I/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (SU3D[I2, I3, k5]*SU3F[3, I1, k6]*SU3F[I4, k5, k6])/3 + - (SU3D[I1, I3, k5]*SU3F[3, I2, k6]*SU3F[I4, k5, k6])/3 + - (SU3D[I1, I2, k5]*SU3F[3, I3, k6]*SU3F[I4, k5, k6])/3 + - (SU3D[I2, I3, k5]*SU3F[8, I1, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I3, k5]*SU3F[8, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (SU3D[I1, I2, k5]*SU3F[8, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (SU3D[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/3 - - (SU3D[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (I/3)*SU3F[3, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6] + - ((I/3)*SU3F[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (5*SU3D[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/3 + - (5*SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - ((5*I)/3)*SU3F[3, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6] - - (((5*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - SU3D[3, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6] + - (SU3D[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - I*SU3F[3, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6] - - (I*SU3F[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (4*SU3D[I2, I3, I4]*SUNDelta[3, I1])/3 + - (8*SU3D[I1, I3, I4]*SUNDelta[3, I2])/9 + - (2*SU3D[I1, I2, I4]*SUNDelta[3, I3])/9 - ((2*I)/3)*SU3F[I1, I2, I4]* - SUNDelta[3, I3] + (2*SU3D[I1, I2, I3]*SUNDelta[3, I4])/9 - - ((2*I)/3)*SU3F[I1, I2, I3]*SUNDelta[3, I4] - - (4*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) - - (8*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) - - (2*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) + - (((2*I)/3)*SU3F[I1, I2, I4]*SUNDelta[8, I3])/Sqrt[3] - - (2*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) + - (((2*I)/3)*SU3F[I1, I2, I3]*SUNDelta[8, I4])/Sqrt[3] - - (10*SU3D[3, I2, I4]*SUNDelta[I1, I3])/9 + - (10*SU3D[8, I2, I4]*SUNDelta[I1, I3])/(9*Sqrt[3]) + - ((2*I)/3)*SU3F[3, I2, I4]*SUNDelta[I1, I3] - - (((2*I)/3)*SU3F[8, I2, I4]*SUNDelta[I1, I3])/Sqrt[3] - - (10*SU3D[3, I2, I3]*SUNDelta[I1, I4])/9 + - (10*SU3D[8, I2, I3]*SUNDelta[I1, I4])/(9*Sqrt[3]) + - ((2*I)/3)*SU3F[3, I2, I3]*SUNDelta[I1, I4] - - (((2*I)/3)*SU3F[8, I2, I3]*SUNDelta[I1, I4])/Sqrt[3] - - (10*SU3D[3, I1, I4]*SUNDelta[I2, I3])/9 + - (10*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) - - ((2*I)/9)*SU3F[3, I1, I4]*SUNDelta[I2, I3] + - (((2*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 - - (10*SU3D[3, I1, I3]*SUNDelta[I2, I4])/9 + - (10*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) - - ((2*I)/9)*SU3F[3, I1, I3]*SUNDelta[I2, I4] + - (((2*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 + - (44*SU3D[3, I1, I2]*SUNDelta[I3, I4])/9 - - (44*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) + - ((4*I)/9)*SU3F[3, I1, I2]*SUNDelta[I3, I4] - - (((4*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] + - (88*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27) + - CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 + - (20*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 + 2*SU3F[I1, I4, k5]* - SU3F[I2, I3, k5] + 2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 + - (88*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/9 - - (4*SU3D[8, I4, k5]*SU3D[I1, k5, k6]*SU3D[I2, I3, k6])/Sqrt[3] - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/9 - - (4*SU3D[8, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/Sqrt[3] - - (8*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) - - (8*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/(3*Sqrt[3]) + - (44*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/9 + - (8*SU3D[8, k5, k6]*SU3D[I1, I2, k5]*SU3D[I3, I4, k6])/Sqrt[3] + - (4*SU3D[8, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/Sqrt[3] + - (8*SU3D[8, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/(3*Sqrt[3]) + - (22*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) - - (2*SU3D[8, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[8, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/(3*Sqrt[3]) + - (22*SU3D[8, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (2*SU3D[8, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/(3*Sqrt[3]) - - (((8*I)/3)*SU3D[I2, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I1, k5])/Sqrt[3] - - (((2*I)/3)*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] - - (((2*I)/3)*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I1, k5])/Sqrt[3] - - ((4*I)*SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[8, I2, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[8, I2, k5])/Sqrt[3] - - (((4*I)/3)*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[8, I3, k5])/Sqrt[3] - - (((4*I)/3)*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] + - (((2*I)/3)*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[8, I4, k5])/Sqrt[3] - - ((8*I)*SU3D[I1, I2, k3]*SU3D[I3, I4, k6]*SU3F[8, k3, k6])/Sqrt[3] - - (((2*I)/3)*SU3D[8, I4, k5]*SU3D[I3, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] - - (((2*I)/3)*SU3D[8, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/Sqrt[3] - - (2*SU3D[I4, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) - - (2*SU3D[I3, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I2, k6])/(3*Sqrt[3]) + - (((4*I)/3)*SU3D[8, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/Sqrt[3] + - (((10*I)/3)*SU3D[8, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/ - Sqrt[3] + (10*SU3D[I4, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I3, k6])/ - (3*Sqrt[3]) - (8*SU3D[I2, k5, k6]*SU3F[8, I4, k5]*SU3F[I1, I3, k6])/ - (3*Sqrt[3]) + (((4*I)/3)*SU3D[8, I3, k5]*SU3D[I2, k5, k6]* - SU3F[I1, I4, k6])/Sqrt[3] + (((10*I)/3)*SU3D[8, I2, k5]* - SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/Sqrt[3] + - (10*SU3D[I3, k5, k6]*SU3F[8, I2, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) - - (8*SU3D[I2, k5, k6]*SU3F[8, I3, k5]*SU3F[I1, I4, k6])/(3*Sqrt[3]) - - ((4*I)*SU3D[8, I4, k5]*SU3D[I2, I3, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - ((4*I)*SU3D[8, I3, k5]*SU3D[I2, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - ((4*I)*SU3D[8, I2, k5]*SU3D[I3, I4, k6]*SU3F[I1, k5, k6])/Sqrt[3] - - (4*SU3D[I3, I4, k5]*SU3F[8, I2, k6]*SU3F[I1, k5, k6])/Sqrt[3] + - (2*SU3F[I1, I4, k5]*SU3F[I2, I3, k5])/3 + - ((2*I)*SU3D[8, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] + - (2*SU3D[I4, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I3, k6])/Sqrt[3] - - (4*SU3D[I1, k5, k6]*SU3F[8, I4, k5]*SU3F[I2, I3, k6])/Sqrt[3] - - ((4*I)*SU3F[8, I4, k5]*SU3F[I1, k5, k6]*SU3F[I2, I3, k6])/Sqrt[3] + - (2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5])/3 + - ((2*I)*SU3D[8, I1, k5]*SU3D[I3, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] + - (2*SU3D[I3, k5, k6]*SU3F[8, I1, k5]*SU3F[I2, I4, k6])/Sqrt[3] - - (4*SU3D[I1, k5, k6]*SU3F[8, I3, k5]*SU3F[I2, I4, k6])/Sqrt[3] - - ((4*I)*SU3F[8, I3, k5]*SU3F[I1, k5, k6]*SU3F[I2, I4, k6])/Sqrt[3] - - (((8*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (((8*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (((8*I)/3)*SU3D[8, I1, k5]*SU3D[I3, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (8*SU3D[I3, I4, k5]*SU3F[8, I1, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[I1, I4, k5]*SU3F[8, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[I1, I3, k5]*SU3F[8, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (4*SU3D[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (((8*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I3, k6]*SU3F[I2, k5, k6])/Sqrt[3] - - (4*SU3D[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/(3*Sqrt[3]) - - (((8*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I4, k6]*SU3F[I2, k5, k6])/Sqrt[3] + - (((22*I)/3)*SU3D[8, I4, k5]*SU3D[I1, I2, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] - (((2*I)/3)*SU3D[8, I2, k5]*SU3D[I1, I4, k6]* - SU3F[I3, k5, k6])/Sqrt[3] + (((2*I)/3)*SU3D[8, I1, k5]* - SU3D[I2, I4, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (2*SU3D[I2, I4, k5]*SU3F[8, I1, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I4, k5]*SU3F[8, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I2, k5]*SU3F[8, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3F[8, I4, k5]*SU3F[I1, I2, k6]*SU3F[I3, k5, k6])/Sqrt[3] - - (10*SU3D[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/(3*Sqrt[3]) + - (((10*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I4, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] - (2*SU3D[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] + ((2*I)*SU3F[8, I1, k5]*SU3F[I2, I4, k6]*SU3F[I3, k5, k6])/ - Sqrt[3] + (((22*I)/3)*SU3D[8, I3, k5]*SU3D[I1, I2, k6]* - SU3F[I4, k5, k6])/Sqrt[3] - (((2*I)/3)*SU3D[8, I2, k5]* - SU3D[I1, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] + - (((2*I)/3)*SU3D[8, I1, k5]*SU3D[I2, I3, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (2*SU3D[I2, I3, k5]*SU3F[8, I1, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I3, k5]*SU3F[8, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[I1, I2, k5]*SU3F[8, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (2*SU3D[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) - - (((2*I)/3)*SU3F[8, I3, k5]*SU3F[I1, I2, k6]*SU3F[I4, k5, k6])/Sqrt[3] - - (10*SU3D[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/(3*Sqrt[3]) + - (((10*I)/3)*SU3F[8, I2, k5]*SU3F[I1, I3, k6]*SU3F[I4, k5, k6])/ - Sqrt[3] - (2*SU3D[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/ - Sqrt[3] + ((2*I)*SU3F[8, I1, k5]*SU3F[I2, I3, k6]*SU3F[I4, k5, k6])/ - Sqrt[3] + (8*SU3D[I2, I3, I4]*SUNDelta[8, I1])/(3*Sqrt[3]) + - (16*SU3D[I1, I3, I4]*SUNDelta[8, I2])/(9*Sqrt[3]) + - (4*SU3D[I1, I2, I4]*SUNDelta[8, I3])/(9*Sqrt[3]) - - (((4*I)/3)*SU3F[I1, I2, I4]*SUNDelta[8, I3])/Sqrt[3] + - (4*SU3D[I1, I2, I3]*SUNDelta[8, I4])/(9*Sqrt[3]) - - (((4*I)/3)*SU3F[I1, I2, I3]*SUNDelta[8, I4])/Sqrt[3] - - (20*SU3D[8, I2, I4]*SUNDelta[I1, I3])/(9*Sqrt[3]) + - (((4*I)/3)*SU3F[8, I2, I4]*SUNDelta[I1, I3])/Sqrt[3] - - (20*SU3D[8, I2, I3]*SUNDelta[I1, I4])/(9*Sqrt[3]) + - (((4*I)/3)*SU3F[8, I2, I3]*SUNDelta[I1, I4])/Sqrt[3] - - (20*SU3D[8, I1, I4]*SUNDelta[I2, I3])/(9*Sqrt[3]) - - (((4*I)/9)*SU3F[8, I1, I4]*SUNDelta[I2, I3])/Sqrt[3] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/27 - - (20*SU3D[8, I1, I3]*SUNDelta[I2, I4])/(9*Sqrt[3]) - - (((4*I)/9)*SU3F[8, I1, I3]*SUNDelta[I2, I4])/Sqrt[3] - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/27 + - (88*SU3D[8, I1, I2]*SUNDelta[I3, I4])/(9*Sqrt[3]) + - (((8*I)/9)*SU3F[8, I1, I2]*SUNDelta[I3, I4])/Sqrt[3] + - (88*SUNDelta[I1, I2]*SUNDelta[I3, I4])/27) + - CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - ((-10*SU3D[I1, I4, k5]*SU3D[I2, I3, k5])/3 - - (10*SU3D[I1, I3, k5]*SU3D[I2, I4, k5])/3 + - (20*SU3D[I1, I2, k5]*SU3D[I3, I4, k5])/3 + 2*SU3F[I1, I4, k5]* - SU3F[I2, I3, k5] + 2*SU3F[I1, I3, k5]*SU3F[I2, I4, k5] - - (20*SUNDelta[I1, I4]*SUNDelta[I2, I3])/9 - - (20*SUNDelta[I1, I3]*SUNDelta[I2, I4])/9 + - (88*SUNDelta[I1, I2]*SUNDelta[I3, I4])/9))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - (16*SUNDelta[I1, I4]*SUNDelta[I2, I3] + 16*SUNDelta[I1, I3]* - SUNDelta[I2, I4]) + 32*CouplingConstant[ChPT3[4], 1, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - (16*SU3D[I1, I2, k5]*SU3D[I3, I4, k5] + - (32*SUNDelta[I1, I2]*SUNDelta[I3, I4])/3))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(32*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*(16*SU3D[I1, I3, k5]*SU3D[I2, I4, k5] + - (32*SUNDelta[I1, I3]*SUNDelta[I2, I4])/3) + - CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - (16*SUNDelta[I1, I4]*SUNDelta[I2, I3] + 16*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3}, -{(32*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*(16*SU3D[I1, I4, k5]*SU3D[I2, I3, k5] + - (32*SUNDelta[I1, I4]*SUNDelta[I2, I3])/3) + - CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - (16*SUNDelta[I1, I3]*SUNDelta[I2, I4] + 16*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o2.Gen deleted file mode 100644 index a32126124..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o2.Mod deleted file mode 100644 index 16dabe029..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{-(DecayConstant[PseudoScalar[1], RenormalizationState[0]]* - SUNDelta[I1, I2])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o4.Gen deleted file mode 100644 index cc42775f9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o4.Gen +++ /dev/null @@ -1,5 +0,0 @@ -{FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, FourVector[p2, \[Mu]1]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o4.Mod deleted file mode 100644 index 233b723bf..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3A00P10o4.Mod +++ /dev/null @@ -1,15 +0,0 @@ -{{(CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - ((-16*SU3D[8, I1, I2])/Sqrt[3] - (8*SUNDelta[I1, I2])/3) - - 8*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]}, -{(CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - (-8*SU3D[3, I1, I2] + (8*SU3D[8, I1, I2])/Sqrt[3] - - (8*SUNDelta[I1, I2])/3) - 8*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}, -{(CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - (8*SU3D[3, I1, I2] + (8*SU3D[8, I1, I2])/Sqrt[3] - - (8*SUNDelta[I1, I2])/3) - 8*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o2.Gen deleted file mode 100644 index 7611e11db..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{0} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o2.Mod deleted file mode 100644 index d8f234e31..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{0}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o4.Gen deleted file mode 100644 index 03bcc9279..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o4.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o4.Mod deleted file mode 100644 index 46a23086b..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P00o4.Mod +++ /dev/null @@ -1,3 +0,0 @@ -{{(-16*I)*(2*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - SUNDelta[I1, I2] - CouplingConstant[ChPT3[4], 12, - RenormalizationState[0]]*SUNDelta[I1, I2])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10P10P10o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10P10P10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10P10P10o2.Mod deleted file mode 100644 index ace33a35c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10P10P10o2.Mod +++ /dev/null @@ -1,6 +0,0 @@ -{{(((-2*I)/9)*(3*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] + - 3*SU3D[I1, I3, k1]*SU3D[I2, I4, k1] + 3*SU3D[I1, I2, k1]* - SU3D[I3, I4, k1] + 9*SU3D[I2, I3, I4]*SUNDelta[0, I1] + - 2*SUNDelta[I1, I4]*SUNDelta[I2, I3] + 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o2.Gen deleted file mode 100644 index 7611e11db..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{0} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o2.Mod deleted file mode 100644 index d8f234e31..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{0}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o4.Gen deleted file mode 100644 index 03bcc9279..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o4.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o4.Mod deleted file mode 100644 index 292a7cd54..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10S20o4.Mod +++ /dev/null @@ -1,7 +0,0 @@ -{{((64*I)*(CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - (SU3D[I1, I2, I3] + SUNDelta[0, I3]*SUNDelta[I1, I2] + - SUNDelta[0, I1]*SUNDelta[I2, I3]) + - 3*(CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - SUNDelta[0, I3]*SUNDelta[I1, I2] + CouplingConstant[ChPT3[4], 7, - RenormalizationState[0]]*SUNDelta[0, I1]*SUNDelta[I2, I3])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o2.Mod deleted file mode 100644 index 3c7e5b620..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{(2*I)*DecayConstant[PseudoScalar[1], RenormalizationState[0]]* - SUNDelta[I1, I2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o4.Gen deleted file mode 100644 index b465853da..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o4.Gen +++ /dev/null @@ -1,6 +0,0 @@ -{ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o4.Mod deleted file mode 100644 index e16ce0691..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P00P10o4.Mod +++ /dev/null @@ -1,20 +0,0 @@ -{{(((-32*I)/3)*(3*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - SU3D[3, I1, I2] + Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*SU3D[8, I1, I2] - - 3*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - SUNDelta[I1, I2] - CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}, -{(((32*I)/3)*(3*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - SU3D[3, I1, I2] - Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*SU3D[8, I1, I2] + - 3*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - SUNDelta[I1, I2] + CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}, -{(((32*I)/3)*(2*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*SU3D[8, I1, I2] + - 3*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - SUNDelta[I1, I2] + CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10P10P10o2.Gen deleted file mode 100644 index ce2b8af04..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10P10P10o2.Gen +++ /dev/null @@ -1,11 +0,0 @@ -{MomentaScalarProduct[p1, p4], MomentaScalarProduct[p2, p5], -MomentaScalarProduct[p3, p6], MomentaScalarProduct[p1, p6], -MomentaScalarProduct[p5, p6], MomentaScalarProduct[p4, p5], -MomentaScalarProduct[p2, p3], MomentaScalarProduct[p1, p2], -MomentaScalarProduct[p3, p4], MomentaScalarProduct[p3, p5], -MomentaScalarProduct[p2, p6], MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p2, p4], MomentaScalarProduct[p4, p6], -MomentaScalarProduct[p1, p5], ParticleMass[PseudoScalar[2], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[7], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[8], -RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10P10P10o2.Mod deleted file mode 100644 index b5efb17be..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10P10P10o2.Mod +++ /dev/null @@ -1,26653 +0,0 @@ -{ -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (180*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(720*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{I*(-UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]/ - (720*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I6]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I6]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]/(1440*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10S20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10S20o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10S20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10S20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10S20o2.Mod deleted file mode 100644 index 033d100f1..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10S20o2.Mod +++ /dev/null @@ -1,41 +0,0 @@ -{{((I/36)*(3*SU3D[I1, k1, k2]*SU3D[I2, I5, k2]*SU3D[I3, I4, k1] + - 3*SU3D[I1, k1, k2]*SU3D[I2, I5, k1]*SU3D[I3, I4, k2] + - 6*SU3D[I1, I5, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] + - 3*SU3D[I1, k1, k2]*SU3D[I2, I4, k2]*SU3D[I3, I5, k1] + - 3*SU3D[I1, k1, k2]*SU3D[I2, I4, k1]*SU3D[I3, I5, k2] + - 6*SU3D[I1, I4, k1]*SU3D[I2, k1, k2]*SU3D[I3, I5, k2] + - 6*SU3D[I1, I5, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] + - 6*SU3D[I1, I4, k1]*SU3D[I2, I5, k2]*SU3D[I3, k1, k2] + - 3*SU3D[I1, k1, k2]*SU3D[I2, I3, k2]*SU3D[I4, I5, k1] + - 3*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]*SU3D[I4, I5, k2] + - 6*SU3D[I1, I3, k1]*SU3D[I2, k1, k2]*SU3D[I4, I5, k2] + - 6*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]*SU3D[I4, I5, k2] + - 6*SU3D[I1, I5, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] + - 6*SU3D[I1, I3, k1]*SU3D[I2, I5, k2]*SU3D[I4, k1, k2] + - 6*SU3D[I1, I2, k1]*SU3D[I3, I5, k2]*SU3D[I4, k1, k2] + - 6*SU3D[I3, I4, k1]*SU3F[I1, k1, k2]*SU3F[I2, I5, k2] + - 6*SU3D[I3, I4, k1]*SU3F[I1, I5, k2]*SU3F[I2, k1, k2] + - 6*SU3D[I2, I4, k1]*SU3F[I1, k1, k2]*SU3F[I3, I5, k2] + - 6*SU3D[I1, I4, k1]*SU3F[I2, k1, k2]*SU3F[I3, I5, k2] + - 6*SU3D[I2, I4, k1]*SU3F[I1, I5, k2]*SU3F[I3, k1, k2] + - 6*SU3D[I1, I4, k1]*SU3F[I2, I5, k2]*SU3F[I3, k1, k2] + - 6*SU3D[I2, I3, k1]*SU3F[I1, k1, k2]*SU3F[I4, I5, k2] + - 6*SU3D[I1, I3, k1]*SU3F[I2, k1, k2]*SU3F[I4, I5, k2] + - 6*SU3D[I1, I2, k1]*SU3F[I3, k1, k2]*SU3F[I4, I5, k2] + - 6*SU3D[I2, I3, k1]*SU3F[I1, I5, k2]*SU3F[I4, k1, k2] + - 6*SU3D[I1, I3, k1]*SU3F[I2, I5, k2]*SU3F[I4, k1, k2] + - 6*SU3D[I1, I2, k1]*SU3F[I3, I5, k2]*SU3F[I4, k1, k2] + - 24*SU3D[I1, I4, k1]*SU3D[I2, I3, k1]*SUNDelta[0, I5] + - 24*SU3D[I1, I3, k1]*SU3D[I2, I4, k1]*SUNDelta[0, I5] + - 24*SU3D[I1, I2, k1]*SU3D[I3, I4, k1]*SUNDelta[0, I5] + - 8*SU3D[I3, I4, I5]*SUNDelta[I1, I2] + 8*SU3D[I2, I4, I5]* - SUNDelta[I1, I3] + 8*SU3D[I2, I3, I5]*SUNDelta[I1, I4] + - 12*SU3D[I2, I3, I4]*SUNDelta[I1, I5] + 8*SU3D[I1, I4, I5]* - SUNDelta[I2, I3] + 16*SUNDelta[0, I5]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + 8*SU3D[I1, I3, I5]*SUNDelta[I2, I4] + - 16*SUNDelta[0, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 12*SU3D[I1, I3, I4]*SUNDelta[I2, I5] + 8*SU3D[I1, I2, I5]* - SUNDelta[I3, I4] + 16*SUNDelta[0, I5]*SUNDelta[I1, I2]* - SUNDelta[I3, I4] + 12*SU3D[I1, I2, I4]*SUNDelta[I3, I5] + - 12*SU3D[I1, I2, I3]*SUNDelta[I4, I5]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o2.Gen deleted file mode 100644 index e04e40412..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o2.Gen +++ /dev/null @@ -1,6 +0,0 @@ -{ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p3], MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p1, p2], MomentaScalarProduct[p3, p4]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o2.Mod deleted file mode 100644 index 56d3f8421..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o2.Mod +++ /dev/null @@ -1,209 +0,0 @@ -{{((24*I)*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] - (18*I)*SU3D[3, I4, k1]* - SU3D[I1, k1, k2]*SU3D[I2, I3, k2] - (6*I)*Sqrt[3]*SU3D[8, I4, k1]* - SU3D[I1, k1, k2]*SU3D[I2, I3, k2] + (24*I)*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] - (18*I)*SU3D[3, I3, k1]*SU3D[I1, k1, k2]* - SU3D[I2, I4, k2] - (6*I)*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, k1, k2]* - SU3D[I2, I4, k2] - (18*I)*SU3D[3, I4, k1]*SU3D[I1, I3, k2]* - SU3D[I2, k1, k2] - (6*I)*Sqrt[3]*SU3D[8, I4, k1]*SU3D[I1, I3, k2]* - SU3D[I2, k1, k2] - (18*I)*SU3D[3, I3, k1]*SU3D[I1, I4, k2]* - SU3D[I2, k1, k2] - (6*I)*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I4, k2]* - SU3D[I2, k1, k2] + (24*I)*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] - - (18*I)*SU3D[3, I2, k1]*SU3D[I1, k1, k2]*SU3D[I3, I4, k2] - - (6*I)*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]*SU3D[I3, I4, k2] - - (18*I)*SU3D[3, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] - - (6*I)*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] - - (18*I)*SU3D[3, I4, k1]*SU3D[I1, I2, k2]*SU3D[I3, k1, k2] - - (6*I)*Sqrt[3]*SU3D[8, I4, k1]*SU3D[I1, I2, k2]*SU3D[I3, k1, k2] - - (18*I)*SU3D[3, I2, k1]*SU3D[I1, I4, k2]*SU3D[I3, k1, k2] - - (6*I)*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I4, k2]*SU3D[I3, k1, k2] - - (18*I)*SU3D[3, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] - - (6*I)*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] - - (18*I)*SU3D[3, I3, k1]*SU3D[I1, I2, k2]*SU3D[I4, k1, k2] - - (6*I)*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I2, k2]*SU3D[I4, k1, k2] - - (18*I)*SU3D[3, I2, k1]*SU3D[I1, I3, k2]*SU3D[I4, k1, k2] - - (6*I)*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I3, k2]*SU3D[I4, k1, k2] - - (18*I)*SU3D[3, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] - - (6*I)*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] - - 3*Sqrt[3]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2]*SU3F[8, I1, k1] + - 3*Sqrt[3]*SU3D[I2, k1, k2]*SU3D[I3, I4, k1]*SU3F[8, I1, k2] - - 3*Sqrt[3]*SU3D[I1, k1, k2]*SU3D[I3, I4, k2]*SU3F[8, I2, k1] + - 3*Sqrt[3]*SU3D[I1, k1, k2]*SU3D[I3, I4, k1]*SU3F[8, I2, k2] - - 3*Sqrt[3]*SU3D[I1, k1, k2]*SU3D[I2, I4, k2]*SU3F[8, I3, k1] + - 3*Sqrt[3]*SU3D[I1, k1, k2]*SU3D[I2, I4, k1]*SU3F[8, I3, k2] - - 3*Sqrt[3]*SU3D[I1, k1, k2]*SU3D[I2, I3, k2]*SU3F[8, I4, k1] + - 3*Sqrt[3]*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]*SU3F[8, I4, k2] + - (18*I)*SU3D[I3, I4, k1]*SU3F[3, I2, k2]*SU3F[I1, k1, k2] + - (18*I)*SU3D[I2, I4, k1]*SU3F[3, I3, k2]*SU3F[I1, k1, k2] + - (18*I)*SU3D[I2, I3, k1]*SU3F[3, I4, k2]*SU3F[I1, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I3, I4, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I2, I4, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I2, I3, k1]*SU3F[8, I4, k2]*SU3F[I1, k1, k2] + - (18*I)*SU3D[I3, I4, k1]*SU3F[3, I1, k2]*SU3F[I2, k1, k2] + - (18*I)*SU3D[I1, I4, k1]*SU3F[3, I3, k2]*SU3F[I2, k1, k2] + - (18*I)*SU3D[I1, I3, k1]*SU3F[3, I4, k2]*SU3F[I2, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I3, I4, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I1, I4, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I1, I3, k1]*SU3F[8, I4, k2]*SU3F[I2, k1, k2] + - (18*I)*SU3D[I2, I4, k1]*SU3F[3, I1, k2]*SU3F[I3, k1, k2] + - (18*I)*SU3D[I1, I4, k1]*SU3F[3, I2, k2]*SU3F[I3, k1, k2] + - (18*I)*SU3D[I1, I2, k1]*SU3F[3, I4, k2]*SU3F[I3, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I2, I4, k1]*SU3F[8, I1, k2]*SU3F[I3, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I1, I4, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I1, I2, k1]*SU3F[8, I4, k2]*SU3F[I3, k1, k2] + - (18*I)*SU3D[I2, I3, k1]*SU3F[3, I1, k2]*SU3F[I4, k1, k2] + - (18*I)*SU3D[I1, I3, k1]*SU3F[3, I2, k2]*SU3F[I4, k1, k2] + - (18*I)*SU3D[I1, I2, k1]*SU3F[3, I3, k2]*SU3F[I4, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I2, I3, k1]*SU3F[8, I1, k2]*SU3F[I4, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I1, I3, k1]*SU3F[8, I2, k2]*SU3F[I4, k1, k2] + - (6*I)*Sqrt[3]*SU3D[I1, I2, k1]*SU3F[8, I3, k2]*SU3F[I4, k1, k2] - - (36*I)*SU3D[I2, I3, I4]*SUNDelta[3, I1] - (36*I)*SU3D[I1, I3, I4]* - SUNDelta[3, I2] - (36*I)*SU3D[I1, I2, I4]*SUNDelta[3, I3] - - (36*I)*SU3D[I1, I2, I3]*SUNDelta[3, I4] - (12*I)*Sqrt[3]*SU3D[I2, I3, I4]* - SUNDelta[8, I1] - (12*I)*Sqrt[3]*SU3D[I1, I3, I4]*SUNDelta[8, I2] - - (12*I)*Sqrt[3]*SU3D[I1, I2, I4]*SUNDelta[8, I3] - - (12*I)*Sqrt[3]*SU3D[I1, I2, I3]*SUNDelta[8, I4] - - (24*I)*SU3D[3, I3, I4]*SUNDelta[I1, I2] - (8*I)*Sqrt[3]*SU3D[8, I3, I4]* - SUNDelta[I1, I2] - (24*I)*SU3D[3, I2, I4]*SUNDelta[I1, I3] - - (8*I)*Sqrt[3]*SU3D[8, I2, I4]*SUNDelta[I1, I3] - - (24*I)*SU3D[3, I2, I3]*SUNDelta[I1, I4] - (8*I)*Sqrt[3]*SU3D[8, I2, I3]* - SUNDelta[I1, I4] - (24*I)*SU3D[3, I1, I4]*SUNDelta[I2, I3] - - (8*I)*Sqrt[3]*SU3D[8, I1, I4]*SUNDelta[I2, I3] + - (16*I)*SUNDelta[I1, I4]*SUNDelta[I2, I3] - (24*I)*SU3D[3, I1, I3]* - SUNDelta[I2, I4] - (8*I)*Sqrt[3]*SU3D[8, I1, I3]*SUNDelta[I2, I4] + - (16*I)*SUNDelta[I1, I3]*SUNDelta[I2, I4] - (24*I)*SU3D[3, I1, I2]* - SUNDelta[I3, I4] - (8*I)*Sqrt[3]*SU3D[8, I1, I2]*SUNDelta[I3, I4] + - (16*I)*SUNDelta[I1, I2]*SUNDelta[I3, I4])/ -(216*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{((I/108)*(12*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] + - 9*SU3D[3, I4, k1]*SU3D[I1, k1, k2]*SU3D[I2, I3, k2] - - 3*Sqrt[3]*SU3D[8, I4, k1]*SU3D[I1, k1, k2]*SU3D[I2, I3, k2] + - 12*SU3D[I1, I3, k1]*SU3D[I2, I4, k1] + 9*SU3D[3, I3, k1]* - SU3D[I1, k1, k2]*SU3D[I2, I4, k2] - 3*Sqrt[3]*SU3D[8, I3, k1]* - SU3D[I1, k1, k2]*SU3D[I2, I4, k2] + 9*SU3D[3, I4, k1]*SU3D[I1, I3, k2]* - SU3D[I2, k1, k2] - 3*Sqrt[3]*SU3D[8, I4, k1]*SU3D[I1, I3, k2]* - SU3D[I2, k1, k2] + 9*SU3D[3, I3, k1]*SU3D[I1, I4, k2]* - SU3D[I2, k1, k2] - 3*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I4, k2]* - SU3D[I2, k1, k2] + 12*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 9*SU3D[3, I2, k1]*SU3D[I1, k1, k2]*SU3D[I3, I4, k2] - - 3*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]*SU3D[I3, I4, k2] + - 9*SU3D[3, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] - - 3*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] + - 9*SU3D[3, I4, k1]*SU3D[I1, I2, k2]*SU3D[I3, k1, k2] - - 3*Sqrt[3]*SU3D[8, I4, k1]*SU3D[I1, I2, k2]*SU3D[I3, k1, k2] + - 9*SU3D[3, I2, k1]*SU3D[I1, I4, k2]*SU3D[I3, k1, k2] - - 3*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I4, k2]*SU3D[I3, k1, k2] + - 9*SU3D[3, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] - - 3*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] + - 9*SU3D[3, I3, k1]*SU3D[I1, I2, k2]*SU3D[I4, k1, k2] - - 3*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I2, k2]*SU3D[I4, k1, k2] + - 9*SU3D[3, I2, k1]*SU3D[I1, I3, k2]*SU3D[I4, k1, k2] - - 3*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I3, k2]*SU3D[I4, k1, k2] + - 9*SU3D[3, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] - - 3*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] - - 9*SU3D[I3, I4, k1]*SU3F[3, I2, k2]*SU3F[I1, k1, k2] - - 9*SU3D[I2, I4, k1]*SU3F[3, I3, k2]*SU3F[I1, k1, k2] - - 9*SU3D[I2, I3, k1]*SU3F[3, I4, k2]*SU3F[I1, k1, k2] + - 3*Sqrt[3]*SU3D[I3, I4, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] + - 3*Sqrt[3]*SU3D[I2, I4, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] + - 3*Sqrt[3]*SU3D[I2, I3, k1]*SU3F[8, I4, k2]*SU3F[I1, k1, k2] - - 9*SU3D[I3, I4, k1]*SU3F[3, I1, k2]*SU3F[I2, k1, k2] - - 9*SU3D[I1, I4, k1]*SU3F[3, I3, k2]*SU3F[I2, k1, k2] - - 9*SU3D[I1, I3, k1]*SU3F[3, I4, k2]*SU3F[I2, k1, k2] + - 3*Sqrt[3]*SU3D[I3, I4, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] + - 3*Sqrt[3]*SU3D[I1, I4, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] + - 3*Sqrt[3]*SU3D[I1, I3, k1]*SU3F[8, I4, k2]*SU3F[I2, k1, k2] - - 9*SU3D[I2, I4, k1]*SU3F[3, I1, k2]*SU3F[I3, k1, k2] - - 9*SU3D[I1, I4, k1]*SU3F[3, I2, k2]*SU3F[I3, k1, k2] - - 9*SU3D[I1, I2, k1]*SU3F[3, I4, k2]*SU3F[I3, k1, k2] + - 3*Sqrt[3]*SU3D[I2, I4, k1]*SU3F[8, I1, k2]*SU3F[I3, k1, k2] + - 3*Sqrt[3]*SU3D[I1, I4, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] + - 3*Sqrt[3]*SU3D[I1, I2, k1]*SU3F[8, I4, k2]*SU3F[I3, k1, k2] - - 9*SU3D[I2, I3, k1]*SU3F[3, I1, k2]*SU3F[I4, k1, k2] - - 9*SU3D[I1, I3, k1]*SU3F[3, I2, k2]*SU3F[I4, k1, k2] - - 9*SU3D[I1, I2, k1]*SU3F[3, I3, k2]*SU3F[I4, k1, k2] + - 3*Sqrt[3]*SU3D[I2, I3, k1]*SU3F[8, I1, k2]*SU3F[I4, k1, k2] + - 3*Sqrt[3]*SU3D[I1, I3, k1]*SU3F[8, I2, k2]*SU3F[I4, k1, k2] + - 3*Sqrt[3]*SU3D[I1, I2, k1]*SU3F[8, I3, k2]*SU3F[I4, k1, k2] + - 18*SU3D[I2, I3, I4]*SUNDelta[3, I1] + 18*SU3D[I1, I3, I4]* - SUNDelta[3, I2] + 18*SU3D[I1, I2, I4]*SUNDelta[3, I3] + - 18*SU3D[I1, I2, I3]*SUNDelta[3, I4] - 6*Sqrt[3]*SU3D[I2, I3, I4]* - SUNDelta[8, I1] - 6*Sqrt[3]*SU3D[I1, I3, I4]*SUNDelta[8, I2] - - 6*Sqrt[3]*SU3D[I1, I2, I4]*SUNDelta[8, I3] - 6*Sqrt[3]*SU3D[I1, I2, I3]* - SUNDelta[8, I4] + 12*SU3D[3, I3, I4]*SUNDelta[I1, I2] - - 4*Sqrt[3]*SU3D[8, I3, I4]*SUNDelta[I1, I2] + 12*SU3D[3, I2, I4]* - SUNDelta[I1, I3] - 4*Sqrt[3]*SU3D[8, I2, I4]*SUNDelta[I1, I3] + - 12*SU3D[3, I2, I3]*SUNDelta[I1, I4] - 4*Sqrt[3]*SU3D[8, I2, I3]* - SUNDelta[I1, I4] + 12*SU3D[3, I1, I4]*SUNDelta[I2, I3] - - 4*Sqrt[3]*SU3D[8, I1, I4]*SUNDelta[I2, I3] + 8*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + 12*SU3D[3, I1, I3]*SUNDelta[I2, I4] - - 4*Sqrt[3]*SU3D[8, I1, I3]*SUNDelta[I2, I4] + 8*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 12*SU3D[3, I1, I2]*SUNDelta[I3, I4] - - 4*Sqrt[3]*SU3D[8, I1, I2]*SUNDelta[I3, I4] + 8*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2}, -{((I/54)*(6*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] + 3*Sqrt[3]*SU3D[8, I4, k1]* - SU3D[I1, k1, k2]*SU3D[I2, I3, k2] + 6*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] + 3*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, k1, k2]* - SU3D[I2, I4, k2] + 3*Sqrt[3]*SU3D[8, I4, k1]*SU3D[I1, I3, k2]* - SU3D[I2, k1, k2] + 3*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I4, k2]* - SU3D[I2, k1, k2] + 6*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 3*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]*SU3D[I3, I4, k2] + - 3*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] + - 3*Sqrt[3]*SU3D[8, I4, k1]*SU3D[I1, I2, k2]*SU3D[I3, k1, k2] + - 3*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I4, k2]*SU3D[I3, k1, k2] + - 3*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] + - 3*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I2, k2]*SU3D[I4, k1, k2] + - 3*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I3, k2]*SU3D[I4, k1, k2] + - 3*Sqrt[3]*SU3D[8, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] - - 3*Sqrt[3]*SU3D[I3, I4, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] - - 3*Sqrt[3]*SU3D[I2, I4, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] - - 3*Sqrt[3]*SU3D[I2, I3, k1]*SU3F[8, I4, k2]*SU3F[I1, k1, k2] - - 3*Sqrt[3]*SU3D[I3, I4, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] - - 3*Sqrt[3]*SU3D[I1, I4, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] - - 3*Sqrt[3]*SU3D[I1, I3, k1]*SU3F[8, I4, k2]*SU3F[I2, k1, k2] - - 3*Sqrt[3]*SU3D[I2, I4, k1]*SU3F[8, I1, k2]*SU3F[I3, k1, k2] - - 3*Sqrt[3]*SU3D[I1, I4, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] - - 3*Sqrt[3]*SU3D[I1, I2, k1]*SU3F[8, I4, k2]*SU3F[I3, k1, k2] - - 3*Sqrt[3]*SU3D[I2, I3, k1]*SU3F[8, I1, k2]*SU3F[I4, k1, k2] - - 3*Sqrt[3]*SU3D[I1, I3, k1]*SU3F[8, I2, k2]*SU3F[I4, k1, k2] - - 3*Sqrt[3]*SU3D[I1, I2, k1]*SU3F[8, I3, k2]*SU3F[I4, k1, k2] + - 6*Sqrt[3]*SU3D[I2, I3, I4]*SUNDelta[8, I1] + 6*Sqrt[3]*SU3D[I1, I3, I4]* - SUNDelta[8, I2] + 6*Sqrt[3]*SU3D[I1, I2, I4]*SUNDelta[8, I3] + - 6*Sqrt[3]*SU3D[I1, I2, I3]*SUNDelta[8, I4] + 4*Sqrt[3]*SU3D[8, I3, I4]* - SUNDelta[I1, I2] + 4*Sqrt[3]*SU3D[8, I2, I4]*SUNDelta[I1, I3] + - 4*Sqrt[3]*SU3D[8, I2, I3]*SUNDelta[I1, I4] + 4*Sqrt[3]*SU3D[8, I1, I4]* - SUNDelta[I2, I3] + 4*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 4*Sqrt[3]*SU3D[8, I1, I3]*SUNDelta[I2, I4] + 4*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 4*Sqrt[3]*SU3D[8, I1, I2]*SUNDelta[I3, I4] + - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((I/9)*(6*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] - 3*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] - 3*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((I/9)*(6*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] - 3*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] - 3*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/9)*(3*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] - 6*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] + 3*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - 4*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/9)*(3*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] - 6*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] + 3*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - 4*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/9)*(3*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] + 3*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] - 6*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 2*SUNDelta[I1, I4]*SUNDelta[I2, I3] + 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/9)*(3*SU3D[I1, I4, k1]*SU3D[I2, I3, k1] + 3*SU3D[I1, I3, k1]* - SU3D[I2, I4, k1] - 6*SU3D[I1, I2, k1]*SU3D[I3, I4, k1] + - 2*SUNDelta[I1, I4]*SUNDelta[I2, I3] + 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o4.Gen deleted file mode 100644 index e80180621..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o4.Gen +++ /dev/null @@ -1,39 +0,0 @@ -{MomentaScalarProduct[p1, p4]*MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p3]*MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p1, p4]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p4]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p2, p4]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p4]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p3]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p3]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -MomentaScalarProduct[p3, p4]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, MomentaScalarProduct[p3, p4]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p2]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p2, p4]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p4]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p3]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -MomentaScalarProduct[p2, p3]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, MomentaScalarProduct[p3, p4]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o4.Mod deleted file mode 100644 index 5386c6d1f..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10P10P10o4.Mod +++ /dev/null @@ -1,17798 +0,0 @@ -{{(I*(2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(I*(2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(I*(2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 2, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 1, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 3, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPT3[4], 3, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/18)*(6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 4, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/54)*(12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 36*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/54)*(12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 36*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 48*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/27)*(12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 108*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 108*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/27)*(12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/27)*(12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 8*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/27)*(6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPT3[4], 6, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 16*Sqrt[3]*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPT3[4], 8, - RenormalizationState[0]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o2.Mod deleted file mode 100644 index 9bb9fc41e..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{(-2*I)*(SU3D[I1, I2, I3] + SUNDelta[0, I3]*SUNDelta[I1, I2])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o4.Gen deleted file mode 100644 index 52faf677f..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o4.Gen +++ /dev/null @@ -1,7 +0,0 @@ -{MomentaScalarProduct[p1, p2]*QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o4.Mod deleted file mode 100644 index ccdbbb309..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPT3P10P10S20o4.Mod +++ /dev/null @@ -1,64 +0,0 @@ -{{((-16*I)*(3*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - SUNDelta[0, I3]*SUNDelta[I1, I2] + CouplingConstant[ChPT3[4], 5, - RenormalizationState[0]]*(SU3D[I1, I2, I3] + SUNDelta[0, I3]* - SUNDelta[I1, I2])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2}, -{(((-16*I)/9)*(18*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - (SU3D[I1, I2, I3] + 2*SUNDelta[0, I3]*(Sqrt[3]*SU3D[8, I1, I2] + - SUNDelta[I1, I2])) + 24*Sqrt[3]*CouplingConstant[ChPT3[4], 7, - RenormalizationState[0]]*(SUNDelta[8, I2]*SUNDelta[I1, I3] + - SUNDelta[8, I1]*SUNDelta[I2, I3]) + - CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - (12*SU3D[I1, I2, I3] + 6*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I2, k1] + - 9*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I3, k1] + 9*Sqrt[3]*SU3D[8, I1, k1]* - SU3D[I2, I3, k1] + 3*Sqrt[3]*SU3F[8, I2, k1]*SU3F[I1, I3, k1] + - 3*Sqrt[3]*SU3F[8, I1, k1]*SU3F[I2, I3, k1] + - 24*Sqrt[3]*SU3D[8, I1, I2]*SUNDelta[0, I3] + 12*SUNDelta[0, I3]* - SUNDelta[I1, I2] + 4*Sqrt[3]*SUNDelta[8, I3]*SUNDelta[I1, I2] + - 6*Sqrt[3]*SUNDelta[8, I2]*SUNDelta[I1, I3] + 6*Sqrt[3]*SUNDelta[8, I1]* - SUNDelta[I2, I3])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2}, -{(((-8*I)/9)*(36*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - (SU3D[I1, I2, I3] + SUNDelta[0, I3]*(3*SU3D[3, I1, I2] - - Sqrt[3]*SU3D[8, I1, I2] + 2*SUNDelta[I1, I2])) + - CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - (24*SU3D[I1, I2, I3] + 18*SU3D[3, I3, k1]*SU3D[I1, I2, k1] - - 6*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I2, k1] + 27*SU3D[3, I2, k1]* - SU3D[I1, I3, k1] - 9*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I3, k1] + - 27*SU3D[3, I1, k1]*SU3D[I2, I3, k1] - 9*Sqrt[3]*SU3D[8, I1, k1]* - SU3D[I2, I3, k1] + 9*SU3F[3, I2, k1]*SU3F[I1, I3, k1] - - 3*Sqrt[3]*SU3F[8, I2, k1]*SU3F[I1, I3, k1] + 9*SU3F[3, I1, k1]* - SU3F[I2, I3, k1] - 3*Sqrt[3]*SU3F[8, I1, k1]*SU3F[I2, I3, k1] + - 72*SU3D[3, I1, I2]*SUNDelta[0, I3] - 24*Sqrt[3]*SU3D[8, I1, I2]* - SUNDelta[0, I3] + 24*SUNDelta[0, I3]*SUNDelta[I1, I2] + - 12*SUNDelta[3, I3]*SUNDelta[I1, I2] - 4*Sqrt[3]*SUNDelta[8, I3]* - SUNDelta[I1, I2] + 18*SUNDelta[3, I2]*SUNDelta[I1, I3] - - 6*Sqrt[3]*SUNDelta[8, I2]*SUNDelta[I1, I3] + 18*SUNDelta[3, I1]* - SUNDelta[I2, I3] - 6*Sqrt[3]*SUNDelta[8, I1]*SUNDelta[I2, I3]) + - 24*CouplingConstant[ChPT3[4], 7, RenormalizationState[0]]* - (3*SUNDelta[3, I2]*SUNDelta[I1, I3] - Sqrt[3]*SUNDelta[8, I2]* - SUNDelta[I1, I3] + (3*SUNDelta[3, I1] - Sqrt[3]*SUNDelta[8, I1])* - SUNDelta[I2, I3])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2}, -{(((-8*I)/9)*(36*CouplingConstant[ChPT3[4], 6, RenormalizationState[0]]* - (SU3D[I1, I2, I3] - SUNDelta[0, I3]*(3*SU3D[3, I1, I2] + - Sqrt[3]*SU3D[8, I1, I2] - 2*SUNDelta[I1, I2])) + - CouplingConstant[ChPT3[4], 8, RenormalizationState[0]]* - (24*SU3D[I1, I2, I3] - 18*SU3D[3, I3, k1]*SU3D[I1, I2, k1] - - 6*Sqrt[3]*SU3D[8, I3, k1]*SU3D[I1, I2, k1] - 27*SU3D[3, I2, k1]* - SU3D[I1, I3, k1] - 9*Sqrt[3]*SU3D[8, I2, k1]*SU3D[I1, I3, k1] - - 27*SU3D[3, I1, k1]*SU3D[I2, I3, k1] - 9*Sqrt[3]*SU3D[8, I1, k1]* - SU3D[I2, I3, k1] - 9*SU3F[3, I2, k1]*SU3F[I1, I3, k1] - - 3*Sqrt[3]*SU3F[8, I2, k1]*SU3F[I1, I3, k1] - 9*SU3F[3, I1, k1]* - SU3F[I2, I3, k1] - 3*Sqrt[3]*SU3F[8, I1, k1]*SU3F[I2, I3, k1] - - 72*SU3D[3, I1, I2]*SUNDelta[0, I3] - 24*Sqrt[3]*SU3D[8, I1, I2]* - SUNDelta[0, I3] + 24*SUNDelta[0, I3]*SUNDelta[I1, I2] - - 12*SUNDelta[3, I3]*SUNDelta[I1, I2] - 4*Sqrt[3]*SUNDelta[8, I3]* - SUNDelta[I1, I2] - 18*SUNDelta[3, I2]*SUNDelta[I1, I3] - - 6*Sqrt[3]*SUNDelta[8, I2]*SUNDelta[I1, I3] - 18*SUNDelta[3, I1]* - SUNDelta[I2, I3] - 6*Sqrt[3]*SUNDelta[8, I1]*SUNDelta[I2, I3]) - - 24*CouplingConstant[ChPT3[4], 7, RenormalizationState[0]]* - (3*SUNDelta[3, I2]*SUNDelta[I1, I3] + Sqrt[3]*SUNDelta[8, I2]* - SUNDelta[I1, I3] + (3*SUNDelta[3, I1] + Sqrt[3]*SUNDelta[8, I1])* - SUNDelta[I2, I3])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20P20P20o2.Gen deleted file mode 100644 index 297769e43..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20P20P20o2.Gen +++ /dev/null @@ -1,10 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p6], MomentaScalarProduct[p2, p6], -MomentaScalarProduct[p3, p6], MomentaScalarProduct[p4, p5], -MomentaScalarProduct[p1, p5], MomentaScalarProduct[p2, p5], -MomentaScalarProduct[p3, p5], MomentaScalarProduct[p4, p6], -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p2, p4], MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p3, p4], MomentaScalarProduct[p1, p2], -MomentaScalarProduct[p5, p6]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20P20P20o2.Mod deleted file mode 100644 index 91ce5f77c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20P20P20o2.Mod +++ /dev/null @@ -1,377 +0,0 @@ -{{(((32*I)/45)*(CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* - SUNDelta[3, I5]*SUNDelta[3, I6]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I4]* - SUNDelta[3, I6]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I4]* - SUNDelta[3, I5]*SUNDelta[I1, I6]*SUNDelta[I2, I3] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I5]* - SUNDelta[3, I6]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I6]*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I5]*SUNDelta[I1, I6]*SUNDelta[I2, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I4]* - SUNDelta[3, I6]*SUNDelta[I1, I3]*SUNDelta[I2, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I6]*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I4]*SUNDelta[I1, I6]*SUNDelta[I2, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I4]* - SUNDelta[3, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I5]* - SUNDelta[3, I6]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I6]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I5]*SUNDelta[I1, I6]*SUNDelta[I3, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I6]* - SUNDelta[I2, I5]*SUNDelta[I3, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I5]* - SUNDelta[I2, I6]*SUNDelta[I3, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I4]* - SUNDelta[3, I6]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I6]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I4]*SUNDelta[I1, I6]*SUNDelta[I3, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I6]* - SUNDelta[I2, I4]*SUNDelta[I3, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I6]*SUNDelta[I3, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I4]* - SUNDelta[3, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I5]*SUNDelta[I1, I4]*SUNDelta[I3, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I4]*SUNDelta[I1, I5]*SUNDelta[I3, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I5]* - SUNDelta[I2, I4]*SUNDelta[I3, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I5]*SUNDelta[I3, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I6]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I6]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I3]*SUNDelta[I1, I6]*SUNDelta[I4, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I6]* - SUNDelta[I2, I3]*SUNDelta[I4, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I6]*SUNDelta[I4, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I6]*SUNDelta[I4, I5] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I5]*SUNDelta[I1, I2]*SUNDelta[I4, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I5]*SUNDelta[I1, I3]*SUNDelta[I4, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I3]*SUNDelta[I1, I5]*SUNDelta[I4, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I5]* - SUNDelta[I2, I3]*SUNDelta[I4, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I5]*SUNDelta[I4, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I5]*SUNDelta[I4, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I3]* - SUNDelta[3, I4]*SUNDelta[I1, I2]*SUNDelta[I5, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I4]*SUNDelta[I1, I3]*SUNDelta[I5, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I3]*SUNDelta[I1, I4]*SUNDelta[I5, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3]*SUNDelta[I5, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4]*SUNDelta[I5, I6] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6] - - 3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^6}, -{((-I/15)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10V10o2.Gen deleted file mode 100644 index 1680d22c5..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]5, \[Mu]6]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10V10o2.Mod deleted file mode 100644 index e2c5232f9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10V10o2.Mod +++ /dev/null @@ -1,9 +0,0 @@ -{{(((4*I)/3)*(SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 2*SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[3, I1]*SUNDelta[3, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10o2.Gen deleted file mode 100644 index dfe15a510..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10o2.Gen +++ /dev/null @@ -1,4 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p4, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p3, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]5]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10o2.Mod deleted file mode 100644 index 1bdb16768..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20V10o2.Mod +++ /dev/null @@ -1,12 +0,0 @@ -{{(2*(SU2F[3, I3, I4]*SUNDelta[I1, I2] + SU2F[3, I2, I4]*SUNDelta[I1, I3] + - SU2F[3, I1, I4]*SUNDelta[I2, I3]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(-2*(SU2F[3, I3, I4]*SUNDelta[I1, I2] - SU2F[3, I2, I3]*SUNDelta[I1, I4] - - SU2F[3, I1, I3]*SUNDelta[I2, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(-2*(SU2F[3, I2, I4]*SUNDelta[I1, I3] + SU2F[3, I2, I3]*SUNDelta[I1, I4] - - SU2F[3, I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(-2*(SU2F[3, I1, I4]*SUNDelta[I2, I3] + SU2F[3, I1, I3]*SUNDelta[I2, I4] + - SU2F[3, I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o2.Gen deleted file mode 100644 index 746c624c8..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o2.Gen +++ /dev/null @@ -1,5 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p3], MomentaScalarProduct[p2, p4], -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2], MomentaScalarProduct[p3, p4]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o2.Mod deleted file mode 100644 index 43c2fbf5e..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o2.Mod +++ /dev/null @@ -1,37 +0,0 @@ -{{(((-4*I)/3)*(CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I4]*SUNDelta[I1, I3] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I2]* - SUNDelta[3, I3]*SUNDelta[I1, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I4]*SUNDelta[I2, I3] - 2*CouplingConstant[ChPTEM2[2], - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I3]*SUNDelta[I2, I4] - 2*CouplingConstant[ChPTEM2[2], - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPTEM2[2], RenormalizationState[0]]*SUNDelta[3, I1]* - SUNDelta[3, I2]*SUNDelta[I3, I4] - 2*CouplingConstant[ChPTEM2[2], - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{((I/3)*(2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - SUNDelta[I1, I3]* - SUNDelta[I2, I4] - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((I/3)*(2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - SUNDelta[I1, I3]* - SUNDelta[I2, I4] - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o4.Gen deleted file mode 100644 index 4b8b2e0d4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o4.Gen +++ /dev/null @@ -1,27 +0,0 @@ -{MomentaScalarProduct[p1, p4]*MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p3]*MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p1, p4]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p3]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p4]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p3, p4]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4, -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p2, p3], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p1, p4], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p2, p4], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p1, p3], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p3, p4], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p1, p2], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o4.Mod deleted file mode 100644 index d68aa4297..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20P20P20o4.Mod +++ /dev/null @@ -1,376 +0,0 @@ -{{((16*I)*(2*CouplingConstant[ChPT2[4], 1, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 3, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + CouplingConstant[ChPT2[4], 2, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 2, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{((16*I)*(CouplingConstant[ChPT2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 2*CouplingConstant[ChPT2[4], 1, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 3, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + CouplingConstant[ChPT2[4], 2, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{((16*I)*(CouplingConstant[ChPT2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 2, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 2*CouplingConstant[ChPT2[4], 1, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT2[4], 3, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((8*I)/3)*(10*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((8*I)/3)*(10*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((-8*I)/3)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] - 10*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((-8*I)/3)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] - 10*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((-8*I)/3)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + 2*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 10*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-8*I)/3)*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + 2*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 10*CouplingConstant[ChPT2[4], 4, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - 5*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((64*I)/3)*(2*CouplingConstant[ChPT2[4], 6, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[0]]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + 2*CouplingConstant[ChPT2[4], 6, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[0]]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 2*CouplingConstant[ChPT2[4], 6, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[0]]*SUNDelta[I1, I2]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^4}, -{(((-2*I)/27)*(54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I3]*SU2F[3, I2, I4] + - 54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 144*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 72*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 108*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 128*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 20*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((-2*I)/27)*(54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I3]*SU2F[3, I2, I4] + - 54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 108*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 144*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] + - 72*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 128*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 20*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((-2*I)/27)*(54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I4]*SU2F[3, I2, I3] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I4]*SU2F[3, I2, I3] - - 54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] + 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 144*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 72*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] + - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 108*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 128*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 20*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((-2*I)/27)*(54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I4]*SU2F[3, I2, I3] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I4]*SU2F[3, I2, I3] - - 54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] + 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 108*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] + - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 144*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 72*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 128*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 20*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((2*I)/27)*(54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I4]*SU2F[3, I2, I3] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I4]*SU2F[3, I2, I3] + - 54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I3]*SU2F[3, I2, I4] - - 144*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 72*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] + - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 108*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 128*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 20*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((2*I)/27)*(54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I4]*SU2F[3, I2, I3] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I4]*SU2F[3, I2, I3] + - 54*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] - 27*CouplingConstant[ChPTEM2[4], 4, - RenormalizationState[0]]*SU2F[3, I1, I3]*SU2F[3, I2, I4] - - 108*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] + - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 36*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 18*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 144*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 72*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 128*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 20*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((-20*I)/27)*(18*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 18*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 18*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 18*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 37*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - CouplingConstant[ChPTEM2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 18*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 37*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - CouplingConstant[ChPTEM2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 18*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 37*CouplingConstant[ChPTEM2[4], 7, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] - - CouplingConstant[ChPTEM2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10V10o2.Gen deleted file mode 100644 index 2cc0c303d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10V10o2.Mod deleted file mode 100644 index 166dd3a47..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{(-2*I)*(SUNDelta[3, I1]*SUNDelta[3, I2] - SUNDelta[I1, I2])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o2.Gen deleted file mode 100644 index e275e87e4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o2.Mod deleted file mode 100644 index 12f89349d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{SU2F[3, I1, I2]}, {-SU2F[3, I1, I2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o4.Gen deleted file mode 100644 index 077145276..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o4.Gen +++ /dev/null @@ -1,10 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -MomentaScalarProduct[p1, p3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -MomentaScalarProduct[p2, p3], -CouplingConstant[QED[1], RenormalizationState[0]]^3*FourVector[p1, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]^3*FourVector[p2, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o4.Mod deleted file mode 100644 index 66650d490..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2P20P20V10o4.Mod +++ /dev/null @@ -1,18 +0,0 @@ -{{(-4*CouplingConstant[ChPT2[4], 9, RenormalizationState[0]]*SU2F[3, I1, I2])/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(4*CouplingConstant[ChPT2[4], 9, RenormalizationState[0]]*SU2F[3, I1, I2])/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(20*(CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SU2F[3, I1, I2] + CouplingConstant[ChPTEM2[4], 10, - RenormalizationState[0]]*SU2F[3, I1, I2]))/9}, -{(-20*(CouplingConstant[ChPTEM2[4], 2, RenormalizationState[0]]* - SU2F[3, I1, I2] + CouplingConstant[ChPTEM2[4], 10, - RenormalizationState[0]]*SU2F[3, I1, I2]))/9}, -{(8*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SU2F[3, I1, I2] + CouplingConstant[ChPT2[4], 5, - RenormalizationState[0]]*SU2F[3, I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(-8*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]]* - SU2F[3, I1, I2] + CouplingConstant[ChPT2[4], 5, - RenormalizationState[0]]*SU2F[3, I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTEM2V10V10o2.Gen deleted file mode 100644 index b346d7325..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2V10V10o2.Gen +++ /dev/null @@ -1,3 +0,0 @@ -{FourVector[p1, \[Mu]2]*FourVector[p2, \[Mu]1], -FourVector[p1, \[Mu]1]*FourVector[p2, \[Mu]2], -MetricTensor[\[Mu]1, \[Mu]2]*MomentaScalarProduct[p1, p2]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTEM2V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTEM2V10V10o2.Mod deleted file mode 100644 index afaf75fbf..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTEM2V10V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{-I}, {I*$Gauge}, {I}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10V10o2.Gen deleted file mode 100644 index 1680d22c5..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]5, \[Mu]6]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10V10o2.Mod deleted file mode 100644 index b3555bafe..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10V10o2.Mod +++ /dev/null @@ -1,11 +0,0 @@ -{{((I/24)*(5*SU2F[3, I1, I4]*SU2F[3, I2, I3] + 5*SU2F[3, I1, I3]* - SU2F[3, I2, I4] + 5*SU2F[3, I1, I2]*SU2F[3, I3, I4] + - 42*SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 32*SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 22*SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - 22*SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 54*SUNDelta[I1, I4]*SUNDelta[I2, I3] + 32*SUNDelta[3, I1]* - SUNDelta[3, I3]*SUNDelta[I2, I4] - 64*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + 42*SUNDelta[3, I1]*SUNDelta[3, I2]* - SUNDelta[I3, I4] - 74*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10o2.Gen deleted file mode 100644 index dfe15a510..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10o2.Gen +++ /dev/null @@ -1,4 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p4, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p3, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]5]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10o2.Mod deleted file mode 100644 index 47e1ad0ad..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20P20P20V10o2.Mod +++ /dev/null @@ -1,12 +0,0 @@ -{{(-2*(SU2F[3, I3, I4]*SUNDelta[I1, I2] + SU2F[3, I2, I4]*SUNDelta[I1, I3] + - SU2F[3, I1, I4]*SUNDelta[I2, I3]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(2*(SU2F[3, I3, I4]*SUNDelta[I1, I2] - SU2F[3, I2, I3]*SUNDelta[I1, I4] - - SU2F[3, I1, I3]*SUNDelta[I2, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(2*(SU2F[3, I2, I4]*SUNDelta[I1, I3] + SU2F[3, I2, I3]*SUNDelta[I1, I4] - - SU2F[3, I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(2*(SU2F[3, I1, I4]*SUNDelta[I2, I3] + SU2F[3, I1, I3]*SUNDelta[I2, I4] + - SU2F[3, I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o2.Gen deleted file mode 100644 index 2cc0c303d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o2.Mod deleted file mode 100644 index 166dd3a47..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{(-2*I)*(SUNDelta[3, I1]*SUNDelta[3, I2] - SUNDelta[I1, I2])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o4.Gen deleted file mode 100644 index 64fe24da9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o4.Gen +++ /dev/null @@ -1,20 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]*MomentaScalarProduct[p1, p3], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]*MomentaScalarProduct[p1, p4], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]*MomentaScalarProduct[p2, p3], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]*MomentaScalarProduct[p2, p4], -CouplingConstant[QED[1], RenormalizationState[0]]^2*FourVector[p1, \[Mu]3]* -FourVector[p3, \[Mu]4], CouplingConstant[QED[1], RenormalizationState[0]]^2* -FourVector[p2, \[Mu]3]*FourVector[p3, \[Mu]4], -CouplingConstant[QED[1], RenormalizationState[0]]^2*FourVector[p1, \[Mu]4]* -FourVector[p4, \[Mu]3], CouplingConstant[QED[1], RenormalizationState[0]]^2* -FourVector[p2, \[Mu]4]*FourVector[p4, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]^2*FourVector[p3, \[Mu]4]* -FourVector[p4, \[Mu]3], CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]*MomentaScalarProduct[p3, p4]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o4.Mod deleted file mode 100644 index 2ed7eb26a..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10V10o4.Mod +++ /dev/null @@ -1,47 +0,0 @@ -{{((-16*I)*(2*CouplingConstant[ChPTPhoton2[4], 4, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] + CouplingConstant[ChPTPhoton2[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] - - 2*CouplingConstant[ChPTPhoton2[4], 4, RenormalizationState[0]]* - SUNDelta[I1, I2] - CouplingConstant[ChPTPhoton2[4], 5, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((4*I)*(CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 9, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((4*I)*(CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 9, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((4*I)*(CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 9, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((4*I)*(CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 9, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-4*I)*(CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 9, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-4*I)*(CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 9, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-4*I)*(CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 9, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-4*I)*(CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 9, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((8*I)*(CouplingConstant[ChPTPhoton2[4], 10, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 10, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-8*I)*(CouplingConstant[ChPTPhoton2[4], 10, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2] - CouplingConstant[ChPTPhoton2[4], 10, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o2.Gen deleted file mode 100644 index e275e87e4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o2.Mod deleted file mode 100644 index 9e437230a..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{-SU2F[3, I1, I2]}, {SU2F[3, I1, I2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o4.Gen deleted file mode 100644 index c6a74c4e9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o4.Gen +++ /dev/null @@ -1,8 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -MomentaScalarProduct[p1, p3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -MomentaScalarProduct[p2, p3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o4.Mod deleted file mode 100644 index a4b38ceb2..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhoton2P20P20V10o4.Mod +++ /dev/null @@ -1,12 +0,0 @@ -{{(-4*CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SU2F[3, I1, I2])/DecayConstant[PseudoScalar[2], RenormalizationState[0]]^ - 2}, {(4*CouplingConstant[ChPTPhoton2[4], 9, RenormalizationState[0]]* - SU2F[3, I1, I2])/DecayConstant[PseudoScalar[2], RenormalizationState[0]]^ - 2}, {(-8*(2*CouplingConstant[ChPTPhoton2[4], 4, RenormalizationState[0]]* - SU2F[3, I1, I2] + CouplingConstant[ChPTPhoton2[4], 5, - RenormalizationState[0]]*SU2F[3, I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(8*(2*CouplingConstant[ChPTPhoton2[4], 4, RenormalizationState[0]]* - SU2F[3, I1, I2] + CouplingConstant[ChPTPhoton2[4], 5, - RenormalizationState[0]]*SU2F[3, I1, I2]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o2.Gen deleted file mode 100644 index 79c75493b..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{NonCommutative[CouplingConstant[QED[1], RenormalizationState[0]]* -DiracGamma[\[Mu]3]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o2.Mod deleted file mode 100644 index aa7c5acf7..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{I*SUNDelta[J1, J2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o4.Gen deleted file mode 100644 index aacf80b48..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o4.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{NonCommutative[CouplingConstant[QED[1], RenormalizationState[0]]^3* -DiracGamma[\[Mu]3]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o4.Mod deleted file mode 100644 index 52dcf9f6c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F10V10o4.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{I*CouplingConstant[ChPTPhotonsLeptons3[4], 37, RenormalizationState[0]]* -SUNDelta[J1, J2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10V10o2.Gen deleted file mode 100644 index 4d53ac8f9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{NonCommutative[FermiConstant*CouplingConstant[QED[1], - RenormalizationState[0]]*DiracGamma[\[Mu]4], DiracGamma[7]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10V10o2.Mod deleted file mode 100644 index cbb11161f..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10V10o2.Mod +++ /dev/null @@ -1,7 +0,0 @@ -{{Sqrt[2]*VUD*DecayConstant[PseudoScalar[1], RenormalizationState[0]]* - SUNDelta[1, I3]*SUNDelta[J1, J2] + I*Sqrt[2]*VUD* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]*SUNDelta[2, I3]* - SUNDelta[J1, J2] + Sqrt[2]*VUS*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]*SUNDelta[4, I3]*SUNDelta[J1, J2] + -I*Sqrt[2]*VUS*DecayConstant[PseudoScalar[1], RenormalizationState[0]]* - SUNDelta[5, I3]*SUNDelta[J1, J2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o2.Gen deleted file mode 100644 index 68da720f1..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{NonCommutative[FermiConstant*DiracSlash[p3], DiracGamma[7]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o2.Mod deleted file mode 100644 index 49422023d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o2.Mod +++ /dev/null @@ -1,7 +0,0 @@ -{{-(Sqrt[2]*VUD*DecayConstant[PseudoScalar[1], RenormalizationState[0]]* - SUNDelta[1, I3]*SUNDelta[J1, J2]) - I*Sqrt[2]*VUD* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]*SUNDelta[2, I3]* - SUNDelta[J1, J2] - Sqrt[2]*VUS*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]*SUNDelta[4, I3]*SUNDelta[J1, J2] - -I*Sqrt[2]*VUS*DecayConstant[PseudoScalar[1], RenormalizationState[0]]* - SUNDelta[5, I3]*SUNDelta[J1, J2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o4.Gen deleted file mode 100644 index 5e44c6e6c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o4.Gen +++ /dev/null @@ -1,7 +0,0 @@ -{NonCommutative[CouplingConstant[QED[1], RenormalizationState[0]]^2* -DiracSlash[p3], DiracGamma[7]], NonCommutative[ -DiracSlash[p3]*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -DiracGamma[7]], NonCommutative[DiracSlash[p3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, DiracGamma[7]], -NonCommutative[DiracSlash[p3]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, DiracGamma[7]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o4.Mod deleted file mode 100644 index d8dac97bb..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3F10F11P10o4.Mod +++ /dev/null @@ -1,27 +0,0 @@ -{{(-2*Sqrt[2]*FermiConstant*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[0]] + 12*CouplingConstant[ChPTPhotonsLeptons3[4], - 14, RenormalizationState[0]] + - 10*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[ - 0]] + 10*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]] - 3*CouplingConstant[ChPTPhotonsLeptons3[4], - 32, RenormalizationState[0]] - - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 33, RenormalizationState[0]])* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]* - (VUD*SUNDelta[1, I3] + I*VUD*SUNDelta[2, I3] + - VUS*(SUNDelta[4, I3] + I*SUNDelta[5, I3]))*SUNDelta[J1, J2])/9}, -{(-8*Sqrt[2]*FermiConstant*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[0]]*(VUD*SUNDelta[1, I3] + I*VUD*SUNDelta[2, I3] + - VUS*(SUNDelta[4, I3] + I*SUNDelta[5, I3]))*SUNDelta[J1, J2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}, -{(-8*Sqrt[2]*FermiConstant*(VUD*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*(SUNDelta[1, I3] + I*SUNDelta[2, I3]) + - CouplingConstant[ChPTPhotonsLeptons3[4], 4, RenormalizationState[0]]* - (VUD*SUNDelta[1, I3] + I*VUD*SUNDelta[2, I3] + VUS*SUNDelta[4, I3] + - I*VUS*SUNDelta[5, I3]))*SUNDelta[J1, J2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}, -{(-8*Sqrt[2]*FermiConstant*(VUS*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*(SUNDelta[4, I3] + I*SUNDelta[5, I3]) + - CouplingConstant[ChPTPhotonsLeptons3[4], 4, RenormalizationState[0]]* - (VUD*SUNDelta[1, I3] + I*VUD*SUNDelta[2, I3] + VUS*SUNDelta[4, I3] + - I*VUS*SUNDelta[5, I3]))*SUNDelta[J1, J2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10P10P10o2.Gen deleted file mode 100644 index 7a0566d99..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10P10P10o2.Gen +++ /dev/null @@ -1,7 +0,0 @@ -{MomentaScalarProduct[p3, p4], MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p3], MomentaScalarProduct[p1, p2], -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10P10P10o2.Mod deleted file mode 100644 index fc9e40083..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10P10P10o2.Mod +++ /dev/null @@ -1,1796 +0,0 @@ -{{((I/24)*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/24)*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/24)*(UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/24)*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/24)*(UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-I/24)*(UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((I/144)*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((I/144)*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((I/144)*(UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((I/144)*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* - (Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10V10o2.Gen deleted file mode 100644 index 2cc0c303d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10V10o2.Mod deleted file mode 100644 index 0bcd18ede..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10V10o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{(2*I)*(SUNDelta[1, I1]*SUNDelta[1, I2] + SUNDelta[2, I1]*SUNDelta[2, I2] + - SUNDelta[4, I1]*SUNDelta[4, I2] + SUNDelta[5, I1]*SUNDelta[5, I2])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o2.Gen deleted file mode 100644 index e275e87e4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o2.Mod deleted file mode 100644 index da242a459..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o2.Mod +++ /dev/null @@ -1,4 +0,0 @@ -{{SUNDelta[1, I2]*SUNDelta[2, I1] - SUNDelta[1, I1]*SUNDelta[2, I2] + -SUNDelta[4, I2]*SUNDelta[5, I1] - SUNDelta[4, I1]*SUNDelta[5, I2]}, -{-(SUNDelta[1, I2]*SUNDelta[2, I1]) + SUNDelta[1, I1]*SUNDelta[2, I2] - -SUNDelta[4, I2]*SUNDelta[5, I1] + SUNDelta[4, I1]*SUNDelta[5, I2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o4.Gen deleted file mode 100644 index 69a16069f..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o4.Gen +++ /dev/null @@ -1,18 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -MomentaScalarProduct[p1, p3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -MomentaScalarProduct[p2, p3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -CouplingConstant[QED[1], RenormalizationState[0]]^3*FourVector[p2, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]^3*FourVector[p1, \[Mu]3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o4.Mod deleted file mode 100644 index 99b5eca47..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTPhotonsLeptons3P10P10V10o4.Mod +++ /dev/null @@ -1,847 +0,0 @@ -{{(-4*CouplingConstant[ChPTPhotonsLeptons3[4], 9, RenormalizationState[0]]* - (3*SU3F[3, I1, I2] + Sqrt[3]*SU3F[8, I1, I2]))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{(4*CouplingConstant[ChPTPhotonsLeptons3[4], 9, RenormalizationState[0]]* - (3*SU3F[3, I1, I2] + Sqrt[3]*SU3F[8, I1, I2]))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{(4*((-3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, I2] + - I*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, I2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] + - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 4, RenormalizationState[0]]* - SU3F[3, I1, I2] + 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, I2] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[3, I1, k3] - - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[0]]*SU3F[8, I1, I2] + - Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, I2] - - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] + - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3F[3, I2, k3]*SU3F[8, I1, k3] - - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[8, I1, k3]*SU3F[8, I2, k3] + - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] - - (2*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] + - (2*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] - - (2*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{(-4*((3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, I2] - - I*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, I2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] - - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 4, RenormalizationState[0]]* - SU3F[3, I1, I2] + 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, I2] + - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[3, I1, k3] - - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[0]]*SU3F[8, I1, I2] + - Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] + 3*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[3, I1, k3]* - SU3F[8, I2, k3] - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[8, I2, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[8, I2, k3] - - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] - - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] + - (2*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] - - (2*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] + - (2*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{(2*((9*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, I2, k3] - - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, I2] + - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] - - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] - - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - 36*CouplingConstant[ChPTPhotonsLeptons3[4], 4, RenormalizationState[0]]* - SU3F[3, I1, I2] + 12*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, I2] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3F[3, I1, k3] - 9*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[8, I2, k3]* - SU3F[3, I1, k3] - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[3, I2, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] + - (9*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, I2, k3] + - 12*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 8*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] - - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3F[3, I2, k3]*SU3F[8, I1, k3] - 3*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[3, I1, k3]* - SU3F[8, I2, k3] + 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[8, I2, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[8, I2, k3] - - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] + - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] - - (2*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] - - (4*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{(-2*((-9*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, I2, k3] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, I2] + - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] - - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] + - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - 36*CouplingConstant[ChPTPhotonsLeptons3[4], 4, RenormalizationState[0]]* - SU3F[3, I1, I2] + 12*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, I2] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3F[3, I1, k3] - 3*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[8, I2, k3]* - SU3F[3, I1, k3] - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[3, I2, k3] + - 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] - - (9*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, I2, k3] + - 12*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 8*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] - - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3F[3, I2, k3]*SU3F[8, I1, k3] - 9*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[3, I1, k3]* - SU3F[8, I2, k3] + 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[8, I2, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[8, I2, k3] + - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] - - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] + - (2*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] + - (4*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{(-2*((-6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, I2] + - (9*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, I2, k3] - - (2*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, I2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] + - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - 36*CouplingConstant[ChPTPhotonsLeptons3[4], 4, RenormalizationState[0]]* - SU3F[3, I1, I2] + 6*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, I2] - - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3F[3, I1, k3] - 3*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[8, I2, k3]* - SU3F[3, I1, k3] + 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[3, I2, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] + - (9*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, I2, k3] + - 12*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 2*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, I2] - - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] - - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3F[3, I2, k3]*SU3F[8, I1, k3] + 3*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[3, I1, k3]* - SU3F[8, I2, k3] + 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[8, I2, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[8, I2, k3] + - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] + - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] + - (2*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] + - (2*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] + - (2*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] - - (8*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{(2*((6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, I2] - - (9*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, I2, k3] + - (2*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, I2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] - - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - 36*CouplingConstant[ChPTPhotonsLeptons3[4], 4, RenormalizationState[0]]* - SU3F[3, I1, I2] + 6*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, I2] - - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3F[3, I1, k3] - 3*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[8, I2, k3]* - SU3F[3, I1, k3] + 9*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[3, I2, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] - - (9*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, I2, k3] + - 12*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 2*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, I2] - - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] - - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]* - SU3F[3, I2, k3]*SU3F[8, I1, k3] + 3*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[0]]*SU3D[3, I1, k3]* - SU3F[8, I2, k3] + 3*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[8, I2, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[8, I2, k3] - - (3*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] - - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] - - (2*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] - - (2*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] - - (2*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] + - (8*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 5, - RenormalizationState[0]]*SUNDelta[I1, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{((-12*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, I2] - - (12*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, I2] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, I2, k3] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, I2, k3] - - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, I2] - - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, I2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] - - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k4]*SU3D[3, k3, k4]* - SU3D[8, I1, k3] - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, I2, k4]*SU3D[3, k3, k4]* - SU3D[8, I1, k3] + (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[3, k3, k4]* - SU3D[8, I1, k4] + (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[3, k3, k4]* - SU3D[8, I1, k4] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] + - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - 144*CouplingConstant[ChPTPhotonsLeptons3[4], 13, RenormalizationState[0]]* - SU3F[3, I1, I2] + 144*CouplingConstant[ChPTPhotonsLeptons3[4], 14, - RenormalizationState[0]]*SU3F[3, I1, I2] + - 60*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3F[3, I1, I2] + 60*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I1, I2] + - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3F[3, I1, k3] + - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3F[3, I1, k3] - - 27*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, I2, k4]*SU3D[3, k3, k4]*SU3F[3, I1, k3] - - 27*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I2, k4]*SU3D[3, k3, k4]*SU3F[3, I1, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[3, I1, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[3, I1, k3] - - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[8, I2, k4]*SU3D[8, k3, k4]*SU3F[3, I1, k3] - - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I2, k4]*SU3D[8, k3, k4]*SU3F[3, I1, k3] + - 27*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3D[3, k3, k4]*SU3F[3, I1, k4] + - 27*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3D[3, k3, k4]*SU3F[3, I1, k4] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3D[8, k3, k4]*SU3F[3, I1, k4] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3D[8, k3, k4]*SU3F[3, I1, k4] + - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, I1, k3]*SU3F[3, I2, k3] + - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I1, k3]*SU3F[3, I2, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] - - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, I2, k3] - - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, I2, k3] + - (54*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[3, I1, k4]* - SU3F[3, I2, k3] + (54*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[3, I1, k4]* - SU3F[3, I2, k3] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[8, k3, k4]* - SU3F[3, I1, k4]*SU3F[3, I2, k3] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, k3, k4]*SU3F[3, I1, k4]*SU3F[3, I2, k3] - - 54*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, I1, k3]*SU3D[3, k3, k4]*SU3F[3, I2, k4] - - 54*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I1, k3]*SU3D[3, k3, k4]*SU3F[3, I2, k4] - - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3D[8, I1, k3]* - SU3F[3, I2, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, k3, k4]*SU3D[8, I1, k3]* - SU3F[3, I2, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, k3, k4]* - SU3F[3, I2, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, k3, k4]* - SU3F[3, I2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, k3, k4]* - SU3F[3, I2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, k3, k4]* - SU3F[3, I2, k4] - 54*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, I1, k4]*SU3F[3, I2, k2]* - SU3F[3, k2, k4] - 54*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I1, k4]*SU3F[3, I2, k2]* - SU3F[3, k2, k4] + (54*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k2]*SU3F[3, I2, k4]* - SU3F[3, k2, k4] + (54*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k2]*SU3F[3, I2, k4]* - SU3F[3, k2, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[8, I1, k2]* - SU3F[3, I2, k4]*SU3F[3, k2, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I1, k2]*SU3F[3, I2, k4]*SU3F[3, k2, k4] + - 48*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 48*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 14, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 20*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 20*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] - - 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k4]*SU3D[3, k3, k4]* - SU3F[8, I1, k3] - 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k4]*SU3D[3, k3, k4]* - SU3F[8, I1, k3] + 6*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[8, I1, k3] + - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] - - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k4]*SU3D[8, k3, k4]* - SU3F[8, I1, k3] - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I2, k4]*SU3D[8, k3, k4]* - SU3F[8, I1, k3] - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3F[3, I2, k3]*SU3F[8, I1, k3] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I2, k3]*SU3F[8, I1, k3] + - 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[3, k3, k4]* - SU3F[8, I1, k4] + 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[3, k3, k4]* - SU3F[8, I1, k4] + 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3D[8, k3, k4]* - SU3F[8, I1, k4] + 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3D[8, k3, k4]* - SU3F[8, I1, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[3, k3, k4]* - SU3F[3, I2, k3]*SU3F[8, I1, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, k3, k4]*SU3F[3, I2, k3]*SU3F[8, I1, k4] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[3, I2, k3]* - SU3F[8, I1, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[3, I2, k3]* - SU3F[8, I1, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3F[3, I2, k3]*SU3F[3, k3, k4]* - SU3F[8, I1, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3F[3, I2, k3]*SU3F[3, k3, k4]* - SU3F[8, I1, k4] + 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[8, I2, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[8, I2, k3] + - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[8, I1, k3]*SU3F[8, I2, k3] + - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I1, k3]*SU3F[8, I2, k3] - (6*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3F[3, I1, k3]*SU3F[8, I2, k3] - (6*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3F[3, I1, k3]*SU3F[8, I2, k3] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, k3, k4]*SU3F[3, I1, k4]*SU3F[8, I2, k3] + - (18*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[3, I1, k4]* - SU3F[8, I2, k3] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[3, I1, k4]* - SU3F[8, I2, k3] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[3, I1, k4]* - SU3F[8, I2, k3] - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] - - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[8, I1, k4]* - SU3F[8, I2, k3] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[8, I1, k4]* - SU3F[8, I2, k3] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[8, I1, k4]* - SU3F[8, I2, k3] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[8, I1, k4]* - SU3F[8, I2, k3] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, k3, k4]*SU3F[8, I1, k4]* - SU3F[8, I2, k3] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, k3, k4]*SU3F[8, I1, k4]* - SU3F[8, I2, k3] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, k3, k4]* - SU3F[8, I2, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, k3, k4]* - SU3F[8, I2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3D[8, I1, k3]* - SU3F[8, I2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3D[8, I1, k3]* - SU3F[8, I2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, k3, k4]* - SU3F[8, I2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, k3, k4]* - SU3F[8, I2, k4] - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, k3, k4]* - SU3F[8, I2, k4] - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, k3, k4]* - SU3F[8, I2, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[3, I1, k3]* - SU3F[3, k3, k4]*SU3F[8, I2, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I1, k3]*SU3F[3, k3, k4]*SU3F[8, I2, k4] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, k3, k4]* - SU3F[8, I2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, k3, k4]* - SU3F[8, I2, k4] + 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, k3, k4]* - SU3F[8, I2, k4] + 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, k3, k4]* - SU3F[8, I2, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[3, I1, k2]* - SU3F[3, I2, k4]*SU3F[8, k2, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I1, k2]*SU3F[3, I2, k4]*SU3F[8, k2, k4] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k2]*SU3F[3, I2, k4]* - SU3F[8, k2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k2]*SU3F[3, I2, k4]* - SU3F[8, k2, k4] + 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3F[3, I1, k2]*SU3F[3, I2, k4]* - SU3F[8, k2, k4] + 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3F[3, I1, k2]*SU3F[3, I2, k4]* - SU3F[8, k2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, I2, k2]*SU3F[8, I1, k4]* - SU3F[8, k2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I2, k2]*SU3F[8, I1, k4]* - SU3F[8, k2, k4] - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[8, I1, k4]*SU3F[8, I2, k2]* - SU3F[8, k2, k4] - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[8, I1, k4]*SU3F[8, I2, k2]* - SU3F[8, k2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[8, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[8, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] + 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] + 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] + (12*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] + - (12*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] + - (4*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] + - (4*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] - - (16*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[I1, I2] - - (16*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[I1, I2])/54}, -{((-12*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, I2] - - (12*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, I2] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, I2, k3] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, I2, k3] - - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, I2] - - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, I2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, I1, k3] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[8, I2, k3] - - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k4]*SU3D[3, k3, k4]* - SU3D[8, I2, k3] - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, I1, k4]*SU3D[3, k3, k4]* - SU3D[8, I2, k3] + (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, I2, k3] + - (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, k3, k4]* - SU3D[8, I2, k4] + (9*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, k3, k4]* - SU3D[8, I2, k4] - 144*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[0]]*SU3F[3, I1, I2] - - 144*CouplingConstant[ChPTPhotonsLeptons3[4], 14, RenormalizationState[0]]* - SU3F[3, I1, I2] - 60*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, I1, I2] - - 60*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3F[3, I1, I2] + 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[3, I1, k3] + - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3F[3, I1, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[3, I1, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[3, I1, k3] - - 54*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3D[3, k3, k4]*SU3F[3, I1, k4] - - 54*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3D[3, k3, k4]*SU3F[3, I1, k4] - - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3D[8, I2, k3]* - SU3F[3, I1, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, k3, k4]*SU3D[8, I2, k3]* - SU3F[3, I1, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, k3, k4]* - SU3F[3, I1, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, k3, k4]* - SU3F[3, I1, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3D[8, k3, k4]* - SU3F[3, I1, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3D[8, k3, k4]* - SU3F[3, I1, k4] + 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[3, I2, k3] + - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I1, k3]*SU3F[3, I2, k3] - - 27*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, I1, k4]*SU3D[3, k3, k4]*SU3F[3, I2, k3] - - 27*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I1, k4]*SU3D[3, k3, k4]*SU3F[3, I2, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[3, I2, k3] - - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[8, I1, k4]*SU3D[8, k3, k4]*SU3F[3, I2, k3] - - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I1, k4]*SU3D[8, k3, k4]*SU3F[3, I2, k3] - - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, I2, k3] - - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, I2, k3] + - 27*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, I1, k3]*SU3D[3, k3, k4]*SU3F[3, I2, k4] + - 27*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I1, k3]*SU3D[3, k3, k4]*SU3F[3, I2, k4] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[8, I1, k3]*SU3D[8, k3, k4]*SU3F[3, I2, k4] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I1, k3]*SU3D[8, k3, k4]*SU3F[3, I2, k4] + - (54*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[3, I1, k3]* - SU3F[3, I2, k4] + (54*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[3, I1, k3]* - SU3F[3, I2, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[8, k3, k4]* - SU3F[3, I1, k3]*SU3F[3, I2, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, k3, k4]*SU3F[3, I1, k3]*SU3F[3, I2, k4] + - (54*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k2]*SU3F[3, I1, k4]* - SU3F[3, k2, k4] + (54*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k2]*SU3F[3, I1, k4]* - SU3F[3, k2, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[8, I2, k2]* - SU3F[3, I1, k4]*SU3F[3, k2, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I2, k2]*SU3F[3, I1, k4]*SU3F[3, k2, k4] - - 54*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3F[3, I1, k2]*SU3F[3, I2, k4]*SU3F[3, k2, k4] - - 54*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3F[3, I1, k2]*SU3F[3, I2, k4]*SU3F[3, k2, k4] - - 48*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[0]]*SU3F[8, I1, I2] - - 48*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 14, - RenormalizationState[0]]*SU3F[8, I1, I2] - - 20*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[8, I1, I2] - - 20*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[8, I1, I2] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3F[8, I1, k3] + - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] + - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I2, k3]*SU3F[8, I1, k3] - (6*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3F[3, I2, k3]*SU3F[8, I1, k3] - (6*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3F[3, I2, k3]*SU3F[8, I1, k3] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]* - SU3D[3, k3, k4]*SU3F[3, I2, k4]*SU3F[8, I1, k3] + - (18*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[3, I2, k4]* - SU3F[8, I1, k3] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[3, I2, k4]* - SU3F[8, I1, k3] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[3, I2, k4]* - SU3F[8, I1, k3] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[3, k3, k4]* - SU3F[8, I1, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[3, k3, k4]* - SU3F[8, I1, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3D[8, I2, k3]* - SU3F[8, I1, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3D[8, I2, k3]* - SU3F[8, I1, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, k3, k4]* - SU3F[8, I1, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k3]*SU3D[8, k3, k4]* - SU3F[8, I1, k4] - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3D[8, k3, k4]* - SU3F[8, I1, k4] - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3D[8, k3, k4]* - SU3F[8, I1, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[3, I2, k3]* - SU3F[3, k3, k4]*SU3F[8, I1, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I2, k3]*SU3F[3, k3, k4]*SU3F[8, I1, k4] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[3, k3, k4]* - SU3F[8, I1, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I2, k3]*SU3F[3, k3, k4]* - SU3F[8, I1, k4] + 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3F[3, I2, k3]*SU3F[3, k3, k4]* - SU3F[8, I1, k4] + 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3F[3, I2, k3]*SU3F[3, k3, k4]* - SU3F[8, I1, k4] + 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[8, I2, k3] + - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3F[8, I2, k3] - - 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k4]*SU3D[3, k3, k4]* - SU3F[8, I2, k3] - 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k4]*SU3D[3, k3, k4]* - SU3F[8, I2, k3] + 6*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3F[8, I2, k3] + - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[8, I1, k3]*SU3F[8, I2, k3] - - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k4]*SU3D[8, k3, k4]* - SU3F[8, I2, k3] - 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k4]*SU3D[8, k3, k4]* - SU3F[8, I2, k3] - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[8, I2, k3] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[8, I2, k3] - - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] - - (6*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[8, I1, k3]*SU3F[8, I2, k3] + - 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, k3, k4]* - SU3F[8, I2, k4] + 9*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I1, k3]*SU3D[3, k3, k4]* - SU3F[8, I2, k4] + 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, k3, k4]* - SU3F[8, I2, k4] + 3*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I1, k3]*SU3D[8, k3, k4]* - SU3F[8, I2, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[3, k3, k4]* - SU3F[3, I1, k3]*SU3F[8, I2, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, k3, k4]*SU3F[3, I1, k3]*SU3F[8, I2, k4] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[3, I1, k3]* - SU3F[8, I2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[3, I1, k3]* - SU3F[8, I2, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, k3, k4]* - SU3F[8, I2, k4] - 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3F[3, I1, k3]*SU3F[3, k3, k4]* - SU3F[8, I2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[8, I1, k3]* - SU3F[8, I2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, k3, k4]*SU3F[8, I1, k3]* - SU3F[8, I2, k4] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[8, I1, k3]* - SU3F[8, I2, k4] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[8, k3, k4]*SU3F[8, I1, k3]* - SU3F[8, I2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, k3, k4]*SU3F[8, I1, k3]* - SU3F[8, I2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, k3, k4]*SU3F[8, I1, k3]* - SU3F[8, I2, k4] + (18*I)*Sqrt[3]*CouplingConstant[ - ChPTPhotonsLeptons3[4], 17, RenormalizationState[0]]*SU3D[3, I2, k2]* - SU3F[3, I1, k4]*SU3F[8, k2, k4] + (18*I)*Sqrt[3]* - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[0]]* - SU3D[3, I2, k2]*SU3F[3, I1, k4]*SU3F[8, k2, k4] + - (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[8, I2, k2]*SU3F[3, I1, k4]* - SU3F[8, k2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[8, I2, k2]*SU3F[3, I1, k4]* - SU3F[8, k2, k4] + 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3F[3, I1, k4]*SU3F[3, I2, k2]* - SU3F[8, k2, k4] + 18*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3F[3, I1, k4]*SU3F[3, I2, k2]* - SU3F[8, k2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3D[3, I2, k2]*SU3F[8, I1, k4]* - SU3F[8, k2, k4] + (18*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3D[3, I2, k2]*SU3F[8, I1, k4]* - SU3F[8, k2, k4] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[0]]*SU3D[8, I2, k2]*SU3F[8, I1, k4]* - SU3F[8, k2, k4] + (6*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[0]]*SU3D[8, I2, k2]*SU3F[8, I1, k4]* - SU3F[8, k2, k4] + 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, I2, k2]*SU3F[8, I1, k4]* - SU3F[8, k2, k4] + 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I2, k2]*SU3F[8, I1, k4]* - SU3F[8, k2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[3, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[3, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SU3F[8, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] - 6*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SU3F[8, I1, k2]*SU3F[8, I2, k4]* - SU3F[8, k2, k4] + (12*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] + - (12*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[8, I1] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[8, I2] + - (4*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] + - (4*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[8, I1]*SUNDelta[8, I2] - - (16*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[0]]*SUNDelta[I1, I2] - - (16*I)*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[0]]*SUNDelta[I1, I2])/54}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20P20P20o2.Gen deleted file mode 100644 index 13bb2f0ef..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20P20P20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1], FourVector[p3, \[Mu]1], FourVector[p4, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20P20P20o2.Mod deleted file mode 100644 index bc37985e8..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20P20P20o2.Mod +++ /dev/null @@ -1,9 +0,0 @@ -{{(-4*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]])}, -{(-4*(SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]])}, -{(4*(2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - SUNDelta[I1, I3]* - SUNDelta[I2, I4] - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20V10o2.Gen deleted file mode 100644 index 96e0dbcaf..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]* -MetricTensor[\[Mu]1, \[Mu]3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20V10o2.Mod deleted file mode 100644 index 91ffffcc4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2A00P20V10o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{(-2*I)*DecayConstant[PseudoScalar[2], RenormalizationState[0]]* -SUNF[3, I1, I2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20P20P20o2.Gen deleted file mode 100644 index c9ae1731d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20P20P20o2.Gen +++ /dev/null @@ -1,10 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p6], MomentaScalarProduct[p2, p6], -MomentaScalarProduct[p3, p6], MomentaScalarProduct[p4, p5], -MomentaScalarProduct[p1, p5], MomentaScalarProduct[p2, p5], -MomentaScalarProduct[p3, p5], MomentaScalarProduct[p4, p6], -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p2, p4], MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p3, p4], MomentaScalarProduct[p1, p2], -MomentaScalarProduct[p5, p6]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20P20P20o2.Mod deleted file mode 100644 index 52acdb2e6..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20P20P20o2.Mod +++ /dev/null @@ -1,378 +0,0 @@ -{{(((32*I)/45)*(CouplingConstant[ChPTVirtualPhotons2[2], - RenormalizationState[0]]*SUNDelta[3, I5]*SUNDelta[3, I6]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I4]*SUNDelta[3, I6]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I4]*SUNDelta[3, I5]*SUNDelta[I1, I6]*SUNDelta[I2, I3] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I5]*SUNDelta[3, I6]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I6]*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I5]*SUNDelta[I1, I6]*SUNDelta[I2, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I4]*SUNDelta[3, I6]*SUNDelta[I1, I3]*SUNDelta[I2, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I6]*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I6]*SUNDelta[I2, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I4]*SUNDelta[3, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I5]*SUNDelta[3, I6]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I6]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I5]*SUNDelta[I1, I6]*SUNDelta[I3, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I4]*SUNDelta[3, I6]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I6]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I6]*SUNDelta[I3, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I4]*SUNDelta[3, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I5]*SUNDelta[I1, I4]*SUNDelta[I3, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I5]*SUNDelta[I3, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I6]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I6]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I6]*SUNDelta[I4, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I5]*SUNDelta[I1, I2]*SUNDelta[I4, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I5]*SUNDelta[I1, I3]*SUNDelta[I4, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I5]*SUNDelta[I4, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2]*SUNDelta[I5, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3]*SUNDelta[I5, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4]*SUNDelta[I5, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6] - - 3*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^6}, -{((-I/15)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - 4*SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - 4*SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-4*I)/45)*(4*SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - 4*SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] - - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] - - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] - - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] - - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] + - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((4*I)/45)*(SUNDelta[I1, I6]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[I1, I5]*SUNDelta[I2, I6]*SUNDelta[I3, I4] + - SUNDelta[I1, I6]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - SUNDelta[I1, I4]*SUNDelta[I2, I6]*SUNDelta[I3, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I4]*SUNDelta[I3, I6] + - SUNDelta[I1, I4]*SUNDelta[I2, I5]*SUNDelta[I3, I6] + - SUNDelta[I1, I6]*SUNDelta[I2, I3]*SUNDelta[I4, I5] + - SUNDelta[I1, I3]*SUNDelta[I2, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I2]*SUNDelta[I3, I6]*SUNDelta[I4, I5] + - SUNDelta[I1, I5]*SUNDelta[I2, I3]*SUNDelta[I4, I6] + - SUNDelta[I1, I3]*SUNDelta[I2, I5]*SUNDelta[I4, I6] + - SUNDelta[I1, I2]*SUNDelta[I3, I5]*SUNDelta[I4, I6] - - 4*SUNDelta[I1, I4]*SUNDelta[I2, I3]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I3]*SUNDelta[I2, I4]*SUNDelta[I5, I6] - - 4*SUNDelta[I1, I2]*SUNDelta[I3, I4]*SUNDelta[I5, I6]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10V10o2.Gen deleted file mode 100644 index 1680d22c5..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]5, \[Mu]6]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10V10o2.Mod deleted file mode 100644 index 605979aca..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10V10o2.Mod +++ /dev/null @@ -1,7 +0,0 @@ -{{(((4*I)/3)*(SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[3, I3]*(SUNDelta[3, I4]*SUNDelta[I1, I2] + - SUNDelta[3, I2]*SUNDelta[I1, I4] + SUNDelta[3, I1]*SUNDelta[I2, I4]) - - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4] + SUNDelta[3, I2]* - (SUNDelta[3, I4]*SUNDelta[I1, I3] + SUNDelta[3, I1]*SUNDelta[I3, I4])))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10o2.Gen deleted file mode 100644 index dfe15a510..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10o2.Gen +++ /dev/null @@ -1,4 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p4, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p3, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]5], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]5]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10o2.Mod deleted file mode 100644 index 1bdb16768..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20V10o2.Mod +++ /dev/null @@ -1,12 +0,0 @@ -{{(2*(SU2F[3, I3, I4]*SUNDelta[I1, I2] + SU2F[3, I2, I4]*SUNDelta[I1, I3] + - SU2F[3, I1, I4]*SUNDelta[I2, I3]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(-2*(SU2F[3, I3, I4]*SUNDelta[I1, I2] - SU2F[3, I2, I3]*SUNDelta[I1, I4] - - SU2F[3, I1, I3]*SUNDelta[I2, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(-2*(SU2F[3, I2, I4]*SUNDelta[I1, I3] + SU2F[3, I2, I3]*SUNDelta[I1, I4] - - SU2F[3, I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}, -{(-2*(SU2F[3, I1, I4]*SUNDelta[I2, I3] + SU2F[3, I1, I3]*SUNDelta[I2, I4] + - SU2F[3, I1, I2]*SUNDelta[I3, I4]))/ -(3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o2.Gen deleted file mode 100644 index 4de0d06c3..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o2.Gen +++ /dev/null @@ -1,5 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p3], MomentaScalarProduct[p2, p4], -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2], MomentaScalarProduct[p3, p4]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o2.Mod deleted file mode 100644 index 6c09fc61b..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o2.Mod +++ /dev/null @@ -1,40 +0,0 @@ -{{(((-4*I)/3)*(CouplingConstant[ChPTVirtualPhotons2[2], - RenormalizationState[0]]*SUNDelta[3, I3]*SUNDelta[3, I4]* - SUNDelta[I1, I2] + CouplingConstant[ChPTVirtualPhotons2[2], - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] + CouplingConstant[ChPTVirtualPhotons2[2], - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + CouplingConstant[ChPTVirtualPhotons2[2], - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 2*CouplingConstant[ChPTVirtualPhotons2[2], - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 2*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 2*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{((I/3)*(2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - SUNDelta[I1, I3]* - SUNDelta[I2, I4] - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((I/3)*(2*SUNDelta[I1, I4]*SUNDelta[I2, I3] - SUNDelta[I1, I3]* - SUNDelta[I2, I4] - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] - 2*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] + SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{((-I/3)*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I4] - 2*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o4.Gen deleted file mode 100644 index 0f66475c4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o4.Gen +++ /dev/null @@ -1,19 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^4, -MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p1, p3]*MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p1, p4]*MomentaScalarProduct[p2, p3], -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^4, -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p2, p3], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p1, p4], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p2, p4], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p1, p3], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p3, p4], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -MomentaScalarProduct[p1, p2], -CouplingConstant[QED[1], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o4.Mod deleted file mode 100644 index 28fc9a830..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20P20P20o4.Mod +++ /dev/null @@ -1,374 +0,0 @@ -{{((4*I)/27)*(162*CouplingConstant[ChPTVirtualPhotons2[4], 24, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2]* - SUNDelta[3, I3]*SUNDelta[3, I4] - - 5*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 64*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 5*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] - - 64*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] - - 5*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] - - 64*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I3]*SUNDelta[I1, I4] - - 5*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] - - 64*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I4]*SUNDelta[I2, I3] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 74*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 5*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 64*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 74*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 5*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 64*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 74*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4])}, -{((4*I)*(CouplingConstant[ChPTVirtualPhotons2[4], 2, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPTVirtualPhotons2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 2*CouplingConstant[ChPTVirtualPhotons2[4], 1, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{((4*I)*(CouplingConstant[ChPTVirtualPhotons2[4], 2, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 2*CouplingConstant[ChPTVirtualPhotons2[4], 1, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPTVirtualPhotons2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{((4*I)*(2*CouplingConstant[ChPTVirtualPhotons2[4], 1, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPTVirtualPhotons2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPTVirtualPhotons2[4], 2, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((8*I)/3)*(CouplingConstant[ChPTVirtualPhotons2[4], 3, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - CouplingConstant[ChPTVirtualPhotons2[4], 3, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - CouplingConstant[ChPTVirtualPhotons2[4], 3, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4}, -{(((-2*I)/27)*(54*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SU2F[3, I1, I3]*SU2F[3, I2, I4] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] + - 54*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 144*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] - 72*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + 108*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 20*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 128*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((-2*I)/27)*(54*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SU2F[3, I1, I3]*SU2F[3, I2, I4] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] + - 54*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I2]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - 108*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + 144*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 72*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 20*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 128*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((-2*I)/27)*(54*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SU2F[3, I1, I4]*SU2F[3, I2, I3] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I4]*SU2F[3, I2, I3] - - 54*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 144*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] - 72*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] + 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] + 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 108*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I3]* - SUNDelta[I2, I4] - 20*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 128*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((-2*I)/27)*(54*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SU2F[3, I1, I4]*SU2F[3, I2, I3] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I4]*SU2F[3, I2, I3] - - 54*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I2]*SU2F[3, I3, I4] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I3]*SUNDelta[3, I4]*SUNDelta[I1, I2] + - 108*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] + 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] + 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 144*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I3]* - SUNDelta[I2, I4] - 72*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I3]* - SUNDelta[I2, I4] - 20*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 128*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((2*I)/27)*(54*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SU2F[3, I1, I4]*SU2F[3, I2, I3] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I4]*SU2F[3, I2, I3] + - 54*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] - - 144*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I3]*SUNDelta[3, I4]* - SUNDelta[I1, I2] + 72*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I3]*SUNDelta[3, I4]* - SUNDelta[I1, I2] + 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] + 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 108*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2]* - SUNDelta[I3, I4] + 20*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 128*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((2*I)/27)*(54*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SU2F[3, I1, I4]*SU2F[3, I2, I3] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I4]*SU2F[3, I2, I3] + - 54*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] + - 27*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SU2F[3, I1, I3]*SU2F[3, I2, I4] - - 108*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[3, I3]*SUNDelta[3, I4]* - SUNDelta[I1, I2] + 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] + 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 36*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 18*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 144*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2]* - SUNDelta[I3, I4] + 72*CouplingConstant[ChPTVirtualPhotons2[4], 14, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I2]* - SUNDelta[I3, I4] + 20*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - 128*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(((-4*I)/27)*(90*CouplingConstant[ChPTVirtualPhotons2[4], 16, - RenormalizationState[0]]*SUNDelta[3, I3]*SUNDelta[3, I4]* - SUNDelta[I1, I2] + 90*CouplingConstant[ChPTVirtualPhotons2[4], 18, - RenormalizationState[0]]*SUNDelta[3, I3]*SUNDelta[3, I4]* - SUNDelta[I1, I2] + 90*CouplingConstant[ChPTVirtualPhotons2[4], 16, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] + 90*CouplingConstant[ChPTVirtualPhotons2[4], 18, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I4]* - SUNDelta[I1, I3] + 90*CouplingConstant[ChPTVirtualPhotons2[4], 16, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + 90*CouplingConstant[ChPTVirtualPhotons2[4], 18, - RenormalizationState[0]]*SUNDelta[3, I2]*SUNDelta[3, I3]* - SUNDelta[I1, I4] + 90*CouplingConstant[ChPTVirtualPhotons2[4], 16, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] + 90*CouplingConstant[ChPTVirtualPhotons2[4], 18, - RenormalizationState[0]]*SUNDelta[3, I1]*SUNDelta[3, I4]* - SUNDelta[I2, I3] - 5*CouplingConstant[ChPTVirtualPhotons2[4], 15, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 185*CouplingConstant[ChPTVirtualPhotons2[4], 16, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - CouplingConstant[ChPTVirtualPhotons2[4], 17, RenormalizationState[0]]* - SUNDelta[I1, I4]*SUNDelta[I2, I3] - - 180*CouplingConstant[ChPTVirtualPhotons2[4], 18, - RenormalizationState[0]]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - 90*CouplingConstant[ChPTVirtualPhotons2[4], 16, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] + - 90*CouplingConstant[ChPTVirtualPhotons2[4], 18, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I3]*SUNDelta[I2, I4] - - 5*CouplingConstant[ChPTVirtualPhotons2[4], 15, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 185*CouplingConstant[ChPTVirtualPhotons2[4], 16, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - CouplingConstant[ChPTVirtualPhotons2[4], 17, RenormalizationState[0]]* - SUNDelta[I1, I3]*SUNDelta[I2, I4] - - 180*CouplingConstant[ChPTVirtualPhotons2[4], 18, - RenormalizationState[0]]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - 90*CouplingConstant[ChPTVirtualPhotons2[4], 16, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - 90*CouplingConstant[ChPTVirtualPhotons2[4], 18, RenormalizationState[0]]* - SUNDelta[3, I1]*SUNDelta[3, I2]*SUNDelta[I3, I4] - - 5*CouplingConstant[ChPTVirtualPhotons2[4], 15, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] - - 185*CouplingConstant[ChPTVirtualPhotons2[4], 16, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - CouplingConstant[ChPTVirtualPhotons2[4], 17, RenormalizationState[0]]* - SUNDelta[I1, I2]*SUNDelta[I3, I4] - - 180*CouplingConstant[ChPTVirtualPhotons2[4], 18, - RenormalizationState[0]]*SUNDelta[I1, I2]*SUNDelta[I3, I4]))/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10V10o2.Gen deleted file mode 100644 index 2cc0c303d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]^2* -MetricTensor[\[Mu]3, \[Mu]4]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10V10o2.Mod deleted file mode 100644 index 166dd3a47..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{(-2*I)*(SUNDelta[3, I1]*SUNDelta[3, I2] - SUNDelta[I1, I2])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o2.Gen deleted file mode 100644 index e275e87e4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o2.Mod deleted file mode 100644 index 12f89349d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{SU2F[3, I1, I2]}, {-SU2F[3, I1, I2]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o4.Gen deleted file mode 100644 index 6a1ba6cd7..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o4.Gen +++ /dev/null @@ -1,6 +0,0 @@ -{CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p2, \[Mu]3]* -MomentaScalarProduct[p1, p3], -CouplingConstant[QED[1], RenormalizationState[0]]*FourVector[p1, \[Mu]3]* -MomentaScalarProduct[p2, p3], -CouplingConstant[QED[1], RenormalizationState[0]]^3*FourVector[p1, \[Mu]3], -CouplingConstant[QED[1], RenormalizationState[0]]^3*FourVector[p2, \[Mu]3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o4.Mod deleted file mode 100644 index 52d8dbbba..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2P20P20V10o4.Mod +++ /dev/null @@ -1,11 +0,0 @@ -{{(-2*CouplingConstant[ChPTVirtualPhotons2[4], 6, RenormalizationState[0]]* - SU2F[3, I1, I2])/DecayConstant[PseudoScalar[2], RenormalizationState[0]]^ - 2}, {(2*CouplingConstant[ChPTVirtualPhotons2[4], 6, - RenormalizationState[0]]*SU2F[3, I1, I2])/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2}, -{(20*(CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SU2F[3, I1, I2] + CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SU2F[3, I1, I2]))/9}, -{(-20*(CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[0]]* - SU2F[3, I1, I2] + CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[0]]*SU2F[3, I1, I2]))/9}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2V10V10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2V10V10o2.Gen deleted file mode 100644 index b346d7325..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2V10V10o2.Gen +++ /dev/null @@ -1,3 +0,0 @@ -{FourVector[p1, \[Mu]2]*FourVector[p2, \[Mu]1], -FourVector[p1, \[Mu]1]*FourVector[p2, \[Mu]2], -MetricTensor[\[Mu]1, \[Mu]2]*MomentaScalarProduct[p1, p2]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2V10V10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2V10V10o2.Mod deleted file mode 100644 index afaf75fbf..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTVirtualPhotons2V10V10o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{-I}, {I*$Gauge}, {I}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10S10o2.Gen deleted file mode 100644 index 94f7a8f73..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10S10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{FourVector[p2, \[Mu]1], FourVector[p3, \[Mu]1], FourVector[p4, \[Mu]1], -FourVector[p5, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10S10o2.Mod deleted file mode 100644 index 631866ad8..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10S10o2.Mod +++ /dev/null @@ -1,4087 +0,0 @@ -{{(CouplingConstant[ChPTW3[2], 1]*((72*I)*SU3D[6, I4, I5]*SU3D[I1, I2, I3] + - (72*I)*SU3D[6, I3, I5]*SU3D[I1, I2, I4] + (72*I)*SU3D[6, I3, I4]* - SU3D[I1, I2, I5] - (48*I)*SU3D[6, I2, I5]*SU3D[I1, I3, I4] - - (48*I)*SU3D[6, I2, I4]*SU3D[I1, I3, I5] - (48*I)*SU3D[6, I2, I3]* - SU3D[I1, I4, I5] - (60*I)*SU3D[6, I1, I5]*SU3D[I2, I3, I4] - - (60*I)*SU3D[6, I1, I4]*SU3D[I2, I3, I5] - (60*I)*SU3D[6, I1, I3]* - SU3D[I2, I4, I5] + (108*I)*SU3D[6, I1, I2]*SU3D[I3, I4, I5] - - (54*I)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k9] - (36*I)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3D[I3, I4, k9] - (54*I)*SU3D[6, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9] - - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k9] + (54*I)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k9]*SU3D[I3, k7, k8] + (54*I)*SU3D[6, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8] + - (27*I)*SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8] + (27*I)*SU3D[6, I4, k7]*SU3D[I1, I5, k9]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8] - (36*I)*SU3D[6, I5, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9] - - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]* - SU3D[I3, k8, k9] - (54*I)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3D[I4, I5, k9] - (36*I)*SU3D[6, I3, k7]* - SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9] - - (54*I)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k9] - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, I5, k9] + (36*I)*SU3D[6, I2, k7]* - SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k9] - (27*I)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3D[I4, k6, k9] + (54*I)*SU3D[6, I5, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8] + - (54*I)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]* - SU3D[I4, k7, k8] + (27*I)*SU3D[6, I5, k7]*SU3D[I1, I3, k9]* - SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + (27*I)*SU3D[6, I3, k7]* - SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8] - - (54*I)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I5, k9]* - SU3D[I4, k7, k8] - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k9]*SU3D[I4, k7, k8] + (18*I)*SU3D[6, I2, k7]* - SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k9] - (36*I)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, I3, k9]*SU3D[I4, k8, k9] - (36*I)*SU3D[6, I3, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9] + - (36*I)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]* - SU3D[I4, k8, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k9]*SU3D[I4, k8, k9] - (27*I)*SU3D[6, I5, k8]* - SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9] + - (18*I)*SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, I5, k8]* - SU3D[I3, k7, k9]*SU3D[I4, k8, k9] - (27*I)*SU3D[6, I4, k8]* - SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9] - - (27*I)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k9] + (54*I)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k9]*SU3D[I5, k7, k8] + (54*I)*SU3D[6, I3, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8] + - (27*I)*SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8] + (27*I)*SU3D[6, I3, k7]*SU3D[I1, I4, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k7, k8] - (54*I)*SU3D[6, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8] - - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]* - SU3D[I5, k7, k8] + (18*I)*SU3D[6, I2, k7]*SU3D[I1, I4, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + (18*I)*SU3D[6, I2, k7]* - SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, I3, k8]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k9] - (36*I)*SU3D[6, I4, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9] - - (36*I)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]* - SU3D[I5, k8, k9] + (36*I)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, I4, k9]*SU3D[I5, k8, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9] - - (27*I)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]* - SU3D[I5, k8, k9] + (18*I)*SU3D[6, I2, k7]*SU3D[I1, I4, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I4, k8]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9] - - (27*I)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k6, k9]* - SU3D[I5, k8, k9] + (18*I)*SU3D[6, I2, k7]*SU3D[I1, I3, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I3, k8]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9] + - 36*SU3D[I3, I4, I5]*SU3F[6, I1, I2] - 84*SU3D[I2, I4, I5]* - SU3F[6, I1, I3] - 84*SU3D[I2, I3, I5]*SU3F[6, I1, I4] - - 84*SU3D[I2, I3, I4]*SU3F[6, I1, I5] - 18*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I1, k7] + - 18*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I1, k7] - - 18*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] - - 24*SU3D[I1, I4, I5]*SU3F[6, I2, I3] - 24*SU3D[I1, I3, I5]* - SU3F[6, I2, I4] - 24*SU3D[I1, I3, I4]*SU3F[6, I2, I5] - - 36*SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I2, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I2, k7] - - 36*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I2, k7] - - 18*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I2, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7] - - 18*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I2, k7] - - 36*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] - - 18*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] - - 18*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] - - 18*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] - - 18*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I3, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I3, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I3, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7] - - 27*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I3, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I3, k7] + - 27*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I3, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I3, k7] - - 27*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I3, k7] + - 27*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I3, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]*SU3F[6, I4, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3F[6, I4, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3F[6, I4, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7] - - 27*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3F[6, I4, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k8]*SU3F[6, I4, k7] + - 27*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I4, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I5, k7, k8]*SU3F[6, I4, k7] - - 27*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I4, k7] + - 27*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I4, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]*SU3F[6, I5, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3F[6, I5, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3F[6, I5, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3F[6, I5, k7] - - 27*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3F[6, I5, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3F[6, I5, k7] + - 27*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I5, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3F[6, I5, k7] - - 27*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I5, k7] + - 27*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I5, k7] + - 24*SU3D[6, I4, I5]*SU3F[I1, I2, I3] + 24*SU3D[6, I3, I5]* - SU3F[I1, I2, I4] + 24*SU3D[6, I3, I4]*SU3F[I1, I2, I5] + - 9*SU3D[6, I5, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I1, I2, k6] + - 9*SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I1, I2, k6] + - 9*SU3D[6, I4, k9]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, I2, k6] + - 9*SU3D[6, I3, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, I2, k6] + - 9*SU3D[6, I4, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, I2, k6] + - 9*SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, I2, k6] + - (9*I)*SU3D[I4, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[I1, I2, k6] + (9*I)*SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k8]*SU3F[I1, I2, k6] + (9*I)*SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I2, k6] + - (9*I)*SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[I1, I2, k6] + (9*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I5, k8]*SU3F[I1, I2, k6] + (9*I)*SU3D[I3, k6, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I2, k6] + - 9*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[I1, I3, k6] + - 9*SU3D[6, I4, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, I3, k6] - - (18*I)*SU3D[I4, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[I1, I3, k6] - (18*I)*SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6] - (36*I)*SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I3, k6] - - (9*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[I1, I3, k6] - (36*I)*SU3D[I2, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I5, k8]*SU3F[I1, I3, k6] - (9*I)*SU3D[I2, k6, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I3, k6] - - 18*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9] - - 36*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]*SU3F[I1, I3, k9] - - 18*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9] - - 18*SU3D[6, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9] - - 36*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]*SU3F[I1, I3, k9] - - 18*SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[I1, I3, k9] + - 9*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3D[I3, k7, k9]*SU3F[I1, I4, k6] + - 9*SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, I4, k6] - - (18*I)*SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[I1, I4, k6] - (18*I)*SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6] - (36*I)*SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I4, k6] - - (9*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[I1, I4, k6] - (36*I)*SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k8]*SU3F[I1, I4, k6] - (9*I)*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6] - - 18*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9] - - 36*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3F[I1, I4, k9] - - 18*SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9] - - 18*SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9] - - 36*SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]*SU3F[I1, I4, k9] - - 18*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]*SU3F[I1, I4, k9] + - 9*SU3D[6, I4, k9]*SU3D[I2, k6, k7]*SU3D[I3, k7, k9]*SU3F[I1, I5, k6] + - 9*SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[I1, I5, k6] - - (18*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k8]* - SU3F[I1, I5, k6] - (18*I)*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6] - (36*I)*SU3D[I2, k7, k8]* - SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I5, k6] - - (9*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]* - SU3F[I1, I5, k6] - (36*I)*SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k8]*SU3F[I1, I5, k6] - (9*I)*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I5, k6] - - 18*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9] - - 36*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3F[I1, I5, k9] - - 18*SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9] - - 18*SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9] - - 36*SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]*SU3F[I1, I5, k9] - - 18*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]*SU3F[I1, I5, k9] - - (54*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]* - SU3F[I1, k6, k8] - (54*I)*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k8] - - (54*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8] - - (54*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8] - - (54*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8] + - 54*SU3D[6, I5, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + - 54*SU3D[6, I4, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9] - - 54*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I3, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9] + - 54*SU3D[6, I2, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9] - - 54*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] - - (36*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]* - SU3F[I1, k7, k9] - (36*I)*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9] - (36*I)*SU3D[I3, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I4, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]* - SU3F[6, I5, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9] - - 36*SU3D[6, I5, k8]*SU3D[I2, k6, k9]*SU3D[I3, I4, k6]*SU3F[I1, k8, k9] - - 36*SU3D[6, I4, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]*SU3F[I1, k8, k9] - - 36*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9] + - 36*SU3D[6, I2, k8]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9] - - 36*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] + - 36*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] + - 36*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] - - 18*SU3D[6, I1, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[I2, I3, k6] - - 18*SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[I2, I3, k6] - - (18*I)*SU3D[I4, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[I2, I3, k6] - (18*I)*SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k8]*SU3F[I2, I3, k6] - 18*SU3D[6, I1, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I2, I4, k6] - 18*SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I2, I4, k6] - (18*I)*SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[I2, I4, k6] - - (18*I)*SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]* - SU3F[I2, I4, k6] - 18*SU3D[6, I1, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]* - SU3F[I2, I5, k6] - 18*SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[I2, I5, k6] - (18*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I5, k6] - (18*I)*SU3D[I3, k6, k7]* - SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I5, k6] - - (18*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I1, k7]* - SU3F[I2, k6, k8] - (18*I)*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k6, k8] - (18*I)*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] + (27*I)*SU3D[I1, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k6, k8] + (27*I)*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k8] + (27*I)*SU3D[I1, I5, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k6, k8] + (27*I)*SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I2, k6, k8] + (27*I)*SU3D[I1, I4, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k6, k8] + (27*I)*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8] + - 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]*SU3F[I2, k6, k9] + - 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]*SU3F[I2, k6, k9] - - 27*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9] - - 27*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9] + - 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9] - - 27*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] - - 27*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] - - 27*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] - - 27*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] - - 9*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]*SU3F[I2, k6, k9] - - 9*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I3, k9]*SU3F[I2, k6, k9] - - 9*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]*SU3F[I2, k6, k9] - - 9*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I4, k9]*SU3F[I2, k6, k9] - - 9*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]*SU3F[I2, k6, k9] - - 9*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I5, k9]*SU3F[I2, k6, k9] - - (36*I)*SU3D[6, I5, k8]*SU3D[I3, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] - (36*I)*SU3D[6, I4, k8]*SU3D[I3, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9] - (36*I)*SU3D[6, I3, k8]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - 36*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - 36*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - 36*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] - - (18*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9] - (18*I)*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9] - (18*I)*SU3D[I3, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] + (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I4, k9]*SU3F[I2, k7, k9] + (54*I)*SU3D[I1, k6, k7]* - SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9] - - (36*I)*SU3D[6, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I2, k7, k9] - (36*I)*SU3D[6, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] + 36*SU3D[I5, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] + 36*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] - (36*I)*SU3D[6, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k6]*SU3F[I2, k7, k9] - - (36*I)*SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] + 36*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] + 36*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] - (36*I)*SU3D[6, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9] - (36*I)*SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] + - 36*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] + - 36*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] - - 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3F[I2, k8, k9] - - 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]*SU3F[I2, k8, k9] - - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I4, I5, k6]*SU3F[I2, k8, k9] + - 18*SU3D[6, I1, k8]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]*SU3F[I2, k8, k9] + - 18*SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9]*SU3F[I2, k8, k9] + - 18*SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9]*SU3F[I2, k8, k9] + - (9*I)*SU3D[6, I5, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I2, k8, k9] + (9*I)*SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9] + (9*I)*SU3D[6, I5, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9] + - (9*I)*SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9] + (9*I)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I2, k8, k9] + (9*I)*SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9] - - (54*I)*SU3D[6, I5, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9] - (54*I)*SU3D[6, I4, k8]*SU3D[I3, I5, k6]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9] - (54*I)*SU3D[6, I3, k8]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + - 54*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + - 54*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + - 54*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + - 9*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] - - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - 9*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I5, k7, k8]*SU3F[I3, k6, k7] - - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I5, k7, k8]*SU3F[I3, k6, k7] - - 18*SU3D[6, I5, k7]*SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8] - - 18*SU3D[6, I4, k7]*SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8] + - (18*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] + (18*I)*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8] + (18*I)*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8] + - (36*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k8] + (18*I)*SU3D[I1, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k6, k8] + (18*I)*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] - (27*I)*SU3D[I1, I2, k8]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8] - - (27*I)*SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k6, k8] + 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k6, k9] + 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I5, k6]* - SU3F[I3, k6, k9] - 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k6, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k6, k9] - 18*SU3D[6, I5, k6]*SU3D[I1, I2, k8]*SU3D[I4, k8, k9]* - SU3F[I3, k6, k9] - 18*SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I3, k6, k9] - 18*SU3D[6, I4, k6]*SU3D[I1, I2, k8]*SU3D[I5, k8, k9]* - SU3F[I3, k6, k9] - 18*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I3, k6, k9] - (18*I)*SU3D[6, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I3, k6, k9] - (18*I)*SU3D[6, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k8]*SU3F[I3, k6, k9] - - (18*I)*SU3D[6, I5, k7]*SU3D[I4, k6, k7]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k9] - (18*I)*SU3D[6, I4, k7]*SU3D[I5, k6, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9] + 9*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9] - 18*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9] - 36*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9] - 18*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I5, k9]*SU3F[I3, k6, k9] - 36*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I3, k6, k9] - (36*I)*SU3D[6, I5, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - - (36*I)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + (36*I)*SU3D[6, I2, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - 36*SU3D[I4, I5, k6]*SU3F[6, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + 36*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + 36*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I5, k6, k7]*SU3F[I2, I4, k9]*SU3F[I3, k6, k9] - - 18*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]*SU3F[I3, k6, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9] - 18*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9] + (18*I)*SU3D[6, I1, k8]*SU3D[I4, I5, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[I4, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + (9*I)*SU3D[6, I5, k8]* - SU3D[I2, k6, k7]*SU3F[I1, I4, k6]*SU3F[I3, k7, k8] + - (9*I)*SU3D[6, I4, k8]*SU3D[I2, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k8] - (18*I)*SU3D[6, I1, k8]*SU3D[I5, k6, k7]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k8] - (18*I)*SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[I2, I5, k6]*SU3F[I3, k7, k8] + - (36*I)*SU3F[6, I5, k9]*SU3F[I1, I4, k7]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k8] + (36*I)*SU3F[6, I4, k9]*SU3F[I1, I5, k7]* - SU3F[I2, k8, k9]*SU3F[I3, k7, k8] + 9*SU3D[6, I5, k7]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k7, k9] + 9*SU3D[6, I4, k7]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k7, k9] + (18*I)*SU3D[I2, k6, k7]* - SU3D[I4, I5, k6]*SU3F[6, I1, k9]*SU3F[I3, k7, k9] - - (18*I)*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] - (18*I)*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9] + (54*I)*SU3D[I1, k6, k7]* - SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9] - - (18*I)*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9] - (18*I)*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]* - SU3F[6, I2, k9]*SU3F[I3, k7, k9] - (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9] - - (27*I)*SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + (27*I)*SU3D[I1, I2, k6]*SU3D[I5, k6, k7]* - SU3F[6, I4, k9]*SU3F[I3, k7, k9] - (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9] - - (27*I)*SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I3, k7, k9] + (27*I)*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[6, I5, k9]*SU3F[I3, k7, k9] - (9*I)*SU3D[6, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] - - (9*I)*SU3D[6, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, I2, k6]* - SU3F[I3, k7, k9] - 9*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]* - SU3F[I3, k7, k9] - 9*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]* - SU3F[I3, k7, k9] - (18*I)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] - (18*I)*SU3D[6, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I4, k6]*SU3F[I3, k7, k9] + - 18*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]*SU3F[I3, k7, k9] + - 9*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I4, k6]*SU3F[I3, k7, k9] - - (18*I)*SU3D[6, I4, k9]*SU3D[I2, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] - (18*I)*SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9] + 9*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9] + 18*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9] + (9*I)*SU3D[6, I5, k7]* - SU3D[I1, I4, k6]*SU3F[I2, k6, k9]*SU3F[I3, k7, k9] + - (9*I)*SU3D[6, I4, k7]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]* - SU3F[I3, k7, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9] - 9*SU3D[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9] + 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k8, k9] + 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]* - SU3F[I3, k8, k9] + 18*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I2, k6, k9]* - SU3F[I3, k8, k9] + 18*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]* - SU3F[I3, k8, k9] - 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k8, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k8, k9] - 9*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I4, k6, k9]* - SU3F[I3, k8, k9] + 18*SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I4, k6, k9]* - SU3F[I3, k8, k9] - 9*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I5, k6, k9]* - SU3F[I3, k8, k9] + 18*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I5, k6, k9]* - SU3F[I3, k8, k9] + (9*I)*SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I3, k8, k9] + (9*I)*SU3D[6, I4, k7]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I3, k8, k9] + - (36*I)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3F[I1, I4, k9]* - SU3F[I3, k8, k9] + (18*I)*SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I3, k8, k9] + (36*I)*SU3D[6, I4, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9] + - (18*I)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]* - SU3F[I3, k8, k9] + (54*I)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] + (54*I)*SU3D[6, I4, k8]* - SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - - (54*I)*SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + 54*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] - 54*SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] - 54*SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + (18*I)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + (18*I)*SU3D[6, I4, k8]* - SU3D[I1, I5, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] - - (18*I)*SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + 18*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] - 27*SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] - 27*SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + (9*I)*SU3F[6, I5, k9]*SU3F[I1, I4, k7]* - SU3F[I2, k7, k8]*SU3F[I3, k8, k9] + (9*I)*SU3F[6, I4, k9]* - SU3F[I1, I5, k7]*SU3F[I2, k7, k8]*SU3F[I3, k8, k9] - - 36*SU3D[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9] - - 36*SU3D[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9] + - 9*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3F[I4, k6, k7] - - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + - 9*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I5, k7, k8]*SU3F[I4, k6, k7] - - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I5, k7, k8]*SU3F[I4, k6, k7] - - 18*SU3D[6, I5, k7]*SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[I4, k6, k8] - - 18*SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k8] + - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I1, k7]* - SU3F[I4, k6, k8] + (18*I)*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] + (18*I)*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8] + - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I2, k7]* - SU3F[I4, k6, k8] + (18*I)*SU3D[I1, I5, k8]*SU3D[I3, k6, k7]* - SU3F[6, I2, k7]*SU3F[I4, k6, k8] + (18*I)*SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]* - SU3F[I4, k6, k8] - (27*I)*SU3D[I1, I2, k8]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8] - - (27*I)*SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I4, k6, k8] - 18*SU3D[6, I5, k6]*SU3F[I1, I2, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k8] + 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k6, k9] + 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I5, k6]* - SU3F[I4, k6, k9] - 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]* - SU3F[I4, k6, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]* - SU3F[I4, k6, k9] - 18*SU3D[6, I5, k6]*SU3D[I1, I2, k8]*SU3D[I3, k8, k9]* - SU3F[I4, k6, k9] - 18*SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I4, k6, k9] - 18*SU3D[6, I3, k6]*SU3D[I1, I2, k8]*SU3D[I5, k8, k9]* - SU3F[I4, k6, k9] - 18*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I4, k6, k9] - (18*I)*SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I4, k6, k9] - (18*I)*SU3D[6, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k8]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I5, k7]*SU3D[I3, k6, k7]*SU3F[I1, I2, k9]* - SU3F[I4, k6, k9] - (18*I)*SU3D[6, I3, k7]*SU3D[I5, k6, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9] + 9*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9] - 18*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9] - 36*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9] - 18*SU3D[I3, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I5, k9]*SU3F[I4, k6, k9] - 36*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I5, k9]*SU3F[I4, k6, k9] - (36*I)*SU3D[6, I5, k8]* - SU3D[I2, I3, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] - - (36*I)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9] + (36*I)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] - 36*SU3D[I3, I5, k6]*SU3F[6, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + 36*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + 36*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I5, k6, k7]*SU3F[I2, I3, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]*SU3F[I4, k6, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k9] - 18*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k9] + (18*I)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[I3, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - (9*I)*SU3D[6, I5, k8]* - SU3D[I1, I2, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I5, k6]*SU3D[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9] + (18*I)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + - 27*SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + - (9*I)*SU3D[6, I5, k8]*SU3D[I2, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k8] + (9*I)*SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k8] - (18*I)*SU3D[6, I1, k8]* - SU3D[I5, k6, k7]*SU3F[I2, I3, k6]*SU3F[I4, k7, k8] - - (18*I)*SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[I2, I5, k6]* - SU3F[I4, k7, k8] + (36*I)*SU3F[6, I5, k9]*SU3F[I1, I3, k7]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k8] + (36*I)*SU3F[6, I3, k9]* - SU3F[I1, I5, k7]*SU3F[I2, k8, k9]*SU3F[I4, k7, k8] + - (9*I)*SU3F[6, I5, k9]*SU3F[I1, I2, k7]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k8] + (18*I)*SU3F[6, I2, k9]*SU3F[I1, I5, k7]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k8] + (18*I)*SU3F[6, I1, k9]* - SU3F[I2, I5, k7]*SU3F[I3, k8, k9]*SU3F[I4, k7, k8] + - 9*SU3D[6, I5, k7]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3F[I4, k7, k9] + - 9*SU3D[6, I3, k7]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3F[I4, k7, k9] + - 18*SU3D[6, I1, k7]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3F[I4, k7, k9] + - 18*SU3D[6, I1, k7]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9]*SU3F[I4, k7, k9] + - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I1, k9]* - SU3F[I4, k7, k9] - (18*I)*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] - (18*I)*SU3D[I2, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]* - SU3F[I4, k7, k9] - (18*I)*SU3D[I1, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] - (18*I)*SU3D[I1, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]* - SU3F[I4, k7, k9] - (27*I)*SU3D[I1, I5, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + (27*I)*SU3D[I1, I2, k6]* - SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]* - SU3F[I4, k7, k9] - (27*I)*SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[6, I5, k9]*SU3F[I4, k7, k9] + (27*I)*SU3D[I1, I2, k6]* - SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9] - - (9*I)*SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3F[I1, I2, k6]* - SU3F[I4, k7, k9] - (9*I)*SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9] - 9*SU3D[I5, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9] - 9*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9] - (18*I)*SU3D[6, I5, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I3, k6]*SU3F[I4, k7, k9] - - (18*I)*SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9] + 18*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9] + 9*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9] - (18*I)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9] - (18*I)*SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I5, k6]*SU3F[I4, k7, k9] + - 18*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]*SU3F[I4, k7, k9] + - 9*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]*SU3F[I4, k7, k9] + - 18*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]*SU3F[I4, k7, k9] + - 18*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]*SU3F[I4, k7, k9] + - (9*I)*SU3D[6, I5, k7]*SU3D[I1, I3, k6]*SU3F[I2, k6, k9]* - SU3F[I4, k7, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I1, I5, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k7, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k9] - 9*SU3D[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9] + (18*I)*SU3F[6, I5, k7]* - SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9] - - 18*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9] - - 18*SU3D[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9] + - 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3F[I4, k8, k9] + - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3F[I4, k8, k9] + - 18*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3F[I4, k8, k9] + - 18*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3F[I4, k8, k9] - - 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]*SU3F[I4, k8, k9] - - 18*SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]*SU3F[I4, k8, k9] - - 9*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3F[I4, k8, k9] + - 18*SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]*SU3F[I4, k8, k9] - - 9*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I5, k6, k9]*SU3F[I4, k8, k9] + - 18*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I5, k6, k9]*SU3F[I4, k8, k9] + - (9*I)*SU3D[6, I5, k7]*SU3D[I3, k7, k8]*SU3F[I1, I2, k9]* - SU3F[I4, k8, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9] + (36*I)*SU3D[6, I5, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9] + - (18*I)*SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I4, k8, k9] + (36*I)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I4, k8, k9] + (18*I)*SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9] + - (54*I)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] + (54*I)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - (54*I)*SU3D[6, I2, k8]* - SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + - 54*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - - 54*SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - - 54*SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + - (18*I)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - (18*I)*SU3D[6, I1, k8]* - SU3D[I3, I5, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + - 18*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - - 27*SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - - 27*SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + - (9*I)*SU3F[6, I5, k9]*SU3F[I1, I3, k7]*SU3F[I2, k7, k8]* - SU3F[I4, k8, k9] + (9*I)*SU3F[6, I3, k9]*SU3F[I1, I5, k7]* - SU3F[I2, k7, k8]*SU3F[I4, k8, k9] - 36*SU3D[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9] - 36*SU3D[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9] - 18*SU3D[6, I5, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] - (9*I)*SU3D[6, I5, k8]* - SU3D[I1, I2, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - - (18*I)*SU3D[6, I5, k6]*SU3D[I1, I2, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I2, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - - 18*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - - 18*SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + - 27*SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + - (9*I)*SU3F[6, I5, k9]*SU3F[I1, I2, k7]*SU3F[I3, k7, k8]* - SU3F[I4, k8, k9] + (18*I)*SU3F[6, I2, k9]*SU3F[I1, I5, k7]* - SU3F[I3, k7, k8]*SU3F[I4, k8, k9] + (18*I)*SU3F[6, I1, k9]* - SU3F[I2, I5, k7]*SU3F[I3, k7, k8]*SU3F[I4, k8, k9] - - 9*SU3D[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k7, k9]*SU3F[I4, k8, k9] + - (18*I)*SU3F[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k7, k9]* - SU3F[I4, k8, k9] - 18*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k7, k9]* - SU3F[I4, k8, k9] - 18*SU3D[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k7, k9]* - SU3F[I4, k8, k9] + 9*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3F[I5, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3F[I5, k6, k7] + 9*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3F[I5, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3F[I5, k6, k7] - 18*SU3D[6, I4, k7]*SU3D[I1, I2, k8]*SU3D[I3, k6, k7]* - SU3F[I5, k6, k8] - 18*SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I5, k6, k8] + (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8] + (18*I)*SU3D[I2, I4, k8]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8] + - (18*I)*SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I5, k6, k8] + (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I2, k7]*SU3F[I5, k6, k8] + (18*I)*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8] + - (18*I)*SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I5, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k8] - (27*I)*SU3D[I1, I2, k8]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]* - SU3F[I5, k6, k8] - (27*I)*SU3D[I1, I2, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I5, k6, k8] - 18*SU3D[6, I4, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8] - 18*SU3D[6, I3, k6]*SU3F[I1, I2, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8] + 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k6, k9] + 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9] - 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9] - 18*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I1, I2, k8]*SU3F[I5, k6, k9] - - (18*I)*SU3D[6, I3, k6]*SU3D[I4, k8, k9]*SU3F[I1, I2, k8]* - SU3F[I5, k6, k9] - (18*I)*SU3D[6, I4, k7]*SU3D[I3, k6, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I3, k7]* - SU3D[I4, k6, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9] + - 9*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9] + - 9*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9] - - 18*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9] - - 36*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9] - - 18*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9] - - 36*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9] - - (36*I)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9] - (36*I)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + (36*I)*SU3D[6, I2, k8]* - SU3D[I3, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] - - 36*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k9] - 18*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k9] - 18*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k9] + (18*I)*SU3D[6, I1, k8]* - SU3D[I3, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - - (9*I)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - (18*I)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9] + (18*I)*SU3D[6, I2, k8]* - SU3D[I1, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9] + - (18*I)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - 18*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - 18*SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] + 27*SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - (9*I)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I3, k6]* - SU3D[I1, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + - (18*I)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[I2, I3, k6]*SU3F[6, I1, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + 27*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + (9*I)*SU3D[6, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I1, I3, k6]*SU3F[I5, k7, k8] + - (9*I)*SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I5, k7, k8] - (18*I)*SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k8] - (18*I)*SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[I2, I4, k6]*SU3F[I5, k7, k8] + - (36*I)*SU3F[6, I4, k9]*SU3F[I1, I3, k7]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k8] + (36*I)*SU3F[6, I3, k9]*SU3F[I1, I4, k7]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k8] + (9*I)*SU3F[6, I4, k9]* - SU3F[I1, I2, k7]*SU3F[I3, k8, k9]*SU3F[I5, k7, k8] + - (18*I)*SU3F[6, I2, k9]*SU3F[I1, I4, k7]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k8] + (18*I)*SU3F[6, I1, k9]*SU3F[I2, I4, k7]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k8] + (9*I)*SU3F[6, I3, k9]* - SU3F[I1, I2, k7]*SU3F[I4, k8, k9]*SU3F[I5, k7, k8] + - (18*I)*SU3F[6, I2, k9]*SU3F[I1, I3, k7]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k8] + (18*I)*SU3F[6, I1, k9]*SU3F[I2, I3, k7]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k8] + 9*SU3D[6, I4, k7]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k7, k9] + 9*SU3D[6, I3, k7]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k7, k9] + (18*I)*SU3D[I2, k6, k7]* - SU3D[I3, I4, k6]*SU3F[6, I1, k9]*SU3F[I5, k7, k9] - - (18*I)*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I5, k7, k9] - (18*I)*SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9] + (54*I)*SU3D[I1, k6, k7]* - SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9] - - (18*I)*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]* - SU3F[I5, k7, k9] - (18*I)*SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I5, k7, k9] - (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9] - - (27*I)*SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I5, k7, k9] + (27*I)*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k9]*SU3F[I5, k7, k9] - (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9] - - (27*I)*SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I5, k7, k9] + (27*I)*SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SU3F[6, I4, k9]*SU3F[I5, k7, k9] - (9*I)*SU3D[6, I4, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I2, k6]*SU3F[I5, k7, k9] - - (9*I)*SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9] - 9*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9] - 9*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9] - (18*I)*SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9] - (18*I)*SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9] + - 18*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9] + - 9*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9] - - (18*I)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I5, k7, k9] - (18*I)*SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9] + 18*SU3D[I3, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9] + 9*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9] + 18*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9] + (9*I)*SU3D[6, I4, k7]* - SU3D[I1, I3, k6]*SU3F[I2, k6, k9]*SU3F[I5, k7, k9] + - (9*I)*SU3D[6, I3, k7]*SU3D[I1, I4, k6]*SU3F[I2, k6, k9]* - SU3F[I5, k7, k9] - 9*SU3D[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k9] - 9*SU3D[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k9] - 9*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9] + (18*I)*SU3F[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9] - 18*SU3D[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9] - 18*SU3D[6, I1, k7]*SU3F[I2, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9] - 9*SU3D[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k9] + (18*I)*SU3F[6, I3, k7]* - SU3F[I1, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] - - 18*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] - - 18*SU3D[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] + - 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3F[I5, k8, k9] + - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3F[I5, k8, k9] + - 18*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3F[I5, k8, k9] + - 18*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3F[I5, k8, k9] - - 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3F[I5, k8, k9] - - 18*SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, I4, k6]*SU3F[I5, k8, k9] - - 9*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3F[I5, k8, k9] + - 18*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k6, k9]*SU3F[I5, k8, k9] + - 18*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]*SU3F[I5, k8, k9] + - (9*I)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]*SU3F[I1, I2, k9]* - SU3F[I5, k8, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9] + (36*I)*SU3D[6, I4, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I5, k8, k9] + (36*I)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9] + - (54*I)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9] + (54*I)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9] - (54*I)*SU3D[6, I2, k8]* - SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + - 54*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] - - 54*SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] - - 54*SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] + (18*I)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] - (18*I)*SU3D[6, I1, k8]* - SU3D[I3, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + - 18*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9] - - 27*SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9] - - 27*SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + - (9*I)*SU3F[6, I4, k9]*SU3F[I1, I3, k7]*SU3F[I2, k7, k8]* - SU3F[I5, k8, k9] + (9*I)*SU3F[6, I3, k9]*SU3F[I1, I4, k7]* - SU3F[I2, k7, k8]*SU3F[I5, k8, k9] - 36*SU3D[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9] - 36*SU3D[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9] - 18*SU3D[6, I4, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9] - (9*I)*SU3D[6, I4, k8]* - SU3D[I1, I2, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - - (18*I)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9] + (18*I)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I2, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - - 18*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - - 18*SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + - 27*SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + - (9*I)*SU3F[6, I4, k9]*SU3F[I1, I2, k7]*SU3F[I3, k7, k8]* - SU3F[I5, k8, k9] + (18*I)*SU3F[6, I2, k9]*SU3F[I1, I4, k7]* - SU3F[I3, k7, k8]*SU3F[I5, k8, k9] + (18*I)*SU3F[6, I1, k9]* - SU3F[I2, I4, k7]*SU3F[I3, k7, k8]*SU3F[I5, k8, k9] - - 9*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3F[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k7, k9]* - SU3F[I5, k8, k9] - 18*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k7, k9]* - SU3F[I5, k8, k9] - 18*SU3D[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k7, k9]* - SU3F[I5, k8, k9] - 18*SU3D[6, I3, k6]*SU3F[I1, I2, k9]*SU3F[I4, k6, k8]* - SU3F[I5, k8, k9] - (9*I)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] - (18*I)*SU3D[6, I3, k6]* - SU3D[I1, I2, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] - 18*SU3D[I2, I3, k6]*SU3F[6, I1, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] - 18*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + 27*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + (9*I)*SU3F[6, I3, k9]* - SU3F[I1, I2, k7]*SU3F[I4, k7, k8]*SU3F[I5, k8, k9] + - (18*I)*SU3F[6, I2, k9]*SU3F[I1, I3, k7]*SU3F[I4, k7, k8]* - SU3F[I5, k8, k9] + (18*I)*SU3F[6, I1, k9]*SU3F[I2, I3, k7]* - SU3F[I4, k7, k8]*SU3F[I5, k8, k9] - 9*SU3D[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9] + (18*I)*SU3F[6, I3, k7]* - SU3F[I1, I2, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] - - 18*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] - - 18*SU3D[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] + - (24*I)*SU3D[I2, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I1] + - (24*I)*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I1] + - (24*I)*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1] - - 48*SU3D[I4, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I1] - - 48*SU3D[I3, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I1] - - 48*SU3D[I3, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I1] + - (12*I)*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - (12*I)*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - (12*I)*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2] - - 84*SU3D[I4, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I2] - - 84*SU3D[I3, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I2] - - 84*SU3D[I3, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I2] + - (30*I)*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3] + - (30*I)*SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3] - - (96*I)*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - 30*SU3D[I2, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I3] + - 30*SU3D[I2, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I3] + - 18*SU3D[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3] - - (18*I)*SU3F[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3] + - 18*SU3D[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3] - - (18*I)*SU3F[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3] + - (30*I)*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4] + - (30*I)*SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4] - - (96*I)*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - 30*SU3D[I2, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I4] + - 30*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I4] + - 18*SU3D[I1, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I4] - - (18*I)*SU3F[I1, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I4] + - 18*SU3D[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4] - - (18*I)*SU3F[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4] + - (30*I)*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5] + - (30*I)*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5] - - (96*I)*SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - 30*SU3D[I2, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I5] + - 30*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I5] + - 18*SU3D[I1, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I5] - - (18*I)*SU3F[I1, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I5] + - 18*SU3D[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5] - - (18*I)*SU3F[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5] + - (18*I)*SU3D[6, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[I1, I3] + - (18*I)*SU3D[6, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[I1, I3] + - (24*I)*SU3D[6, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[I1, I3] - - 24*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3] - - 18*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3] - - 18*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3] + - 18*SU3D[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3] + - (18*I)*SU3F[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3] + - 18*SU3D[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3] + - (18*I)*SU3F[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3] + - (18*I)*SU3D[6, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[I1, I4] + - (18*I)*SU3D[6, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[I1, I4] + - (24*I)*SU3D[6, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[I1, I4] - - 24*SU3D[I3, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I4] - - 18*SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4] - - 18*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4] + - 18*SU3D[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4] + - (18*I)*SU3F[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4] + - 18*SU3D[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4] + - (18*I)*SU3F[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4] + - (18*I)*SU3D[6, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[I1, I5] + - (18*I)*SU3D[6, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[I1, I5] + - (24*I)*SU3D[6, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[I1, I5] - - 24*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5] - - 18*SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5] - - 18*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5] + - 18*SU3D[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5] + - (18*I)*SU3F[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5] + - 18*SU3D[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5] + - (18*I)*SU3F[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5] + - (12*I)*SU3D[6, I5, k6]*SU3D[I1, I4, k6]*SUNDelta[I2, I3] + - (12*I)*SU3D[6, I4, k6]*SU3D[I1, I5, k6]*SUNDelta[I2, I3] + - (24*I)*SU3D[6, I1, k6]*SU3D[I4, I5, k6]*SUNDelta[I2, I3] - - 24*SU3D[I4, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I3] - - 12*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3] - - 12*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3] + - 60*SU3D[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3] + - (60*I)*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3] + - 60*SU3D[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3] + - (60*I)*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3] + - (20*I)*SUNDelta[6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - (20*I)*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - (12*I)*SU3D[6, I5, k6]*SU3D[I1, I3, k6]*SUNDelta[I2, I4] + - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I5, k6]*SUNDelta[I2, I4] + - (24*I)*SU3D[6, I1, k6]*SU3D[I3, I5, k6]*SUNDelta[I2, I4] - - 24*SU3D[I3, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I4] - - 12*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4] - - 12*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4] + - 60*SU3D[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4] + - (60*I)*SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4] + - 60*SU3D[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4] + - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4] + - (20*I)*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - (20*I)*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - (12*I)*SU3D[6, I4, k6]*SU3D[I1, I3, k6]*SUNDelta[I2, I5] + - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I4, k6]*SUNDelta[I2, I5] + - (24*I)*SU3D[6, I1, k6]*SU3D[I3, I4, k6]*SUNDelta[I2, I5] - - 24*SU3D[I3, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I5] - - 12*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5] - - 12*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5] + - 60*SU3D[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5] + - (60*I)*SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5] + - 60*SU3D[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5] + - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5] + - (20*I)*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5] + - (20*I)*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5] - - (60*I)*SU3D[6, I5, k6]*SU3D[I1, I2, k6]*SUNDelta[I3, I4] - - (12*I)*SU3D[6, I2, k6]*SU3D[I1, I5, k6]*SUNDelta[I3, I4] + - 12*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4] + - 60*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4] - - 12*SU3D[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4] - - (12*I)*SU3F[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4] - - 60*SU3D[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4] - - (60*I)*SU3F[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4] - - 24*SU3D[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4] - - (24*I)*SU3F[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4] - - (64*I)*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - (8*I)*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - (60*I)*SU3D[6, I4, k6]*SU3D[I1, I2, k6]*SUNDelta[I3, I5] - - (12*I)*SU3D[6, I2, k6]*SU3D[I1, I4, k6]*SUNDelta[I3, I5] + - 12*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5] + - 60*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5] - - 12*SU3D[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5] - - (12*I)*SU3F[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5] - - 60*SU3D[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5] - - (60*I)*SU3F[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5] - - 24*SU3D[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5] - - (24*I)*SU3F[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5] - - (64*I)*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - (8*I)*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5] - - (60*I)*SU3D[6, I3, k6]*SU3D[I1, I2, k6]*SUNDelta[I4, I5] - - (12*I)*SU3D[6, I2, k6]*SU3D[I1, I3, k6]*SUNDelta[I4, I5] + - 12*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5] + - 60*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5] - - 12*SU3D[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5] - - (12*I)*SU3F[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5] - - 60*SU3D[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5] - - (60*I)*SU3F[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5] - - 24*SU3D[6, I1, k6]*SU3F[I2, I3, k6]*SUNDelta[I4, I5] - - (24*I)*SU3F[6, I1, k6]*SU3F[I2, I3, k6]*SUNDelta[I4, I5] - - (64*I)*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - (8*I)*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ -(108*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*((72*I)*SU3D[6, I4, I5]*SU3D[I1, I2, I3] - - (48*I)*SU3D[6, I3, I5]*SU3D[I1, I2, I4] - (48*I)*SU3D[6, I3, I4]* - SU3D[I1, I2, I5] + (72*I)*SU3D[6, I2, I5]*SU3D[I1, I3, I4] + - (72*I)*SU3D[6, I2, I4]*SU3D[I1, I3, I5] - (48*I)*SU3D[6, I2, I3]* - SU3D[I1, I4, I5] - (60*I)*SU3D[6, I1, I5]*SU3D[I2, I3, I4] - - (60*I)*SU3D[6, I1, I4]*SU3D[I2, I3, I5] + (108*I)*SU3D[6, I1, I3]* - SU3D[I2, I4, I5] - (60*I)*SU3D[6, I1, I2]*SU3D[I3, I4, I5] + - (54*I)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k9] - (36*I)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3D[I3, I4, k9] + (54*I)*SU3D[6, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9] - - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k9] - (54*I)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k9]*SU3D[I3, k7, k8] - (54*I)*SU3D[6, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8] - - (36*I)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]* - SU3D[I3, k8, k9] - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I2, I5, k9]*SU3D[I3, k8, k9] + (27*I)*SU3D[6, I5, k7]* - SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9] + - (27*I)*SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9] - (54*I)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3D[I4, I5, k9] + (36*I)*SU3D[6, I3, k7]* - SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9] - - (54*I)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, I5, k9] - (36*I)*SU3D[6, I2, k7]* - SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9] - - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k9] - (27*I)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3D[I4, k6, k9] + (54*I)*SU3D[6, I5, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8] - - (54*I)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]* - SU3D[I4, k7, k8] + (18*I)*SU3D[6, I3, k7]*SU3D[I1, I5, k9]* - SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + (54*I)*SU3D[6, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8] + - (27*I)*SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8] + (27*I)*SU3D[6, I2, k7]*SU3D[I1, I5, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k7, k8] - (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k8]* - SU3D[I4, k7, k9] - (36*I)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, I3, k9]*SU3D[I4, k8, k9] + (36*I)*SU3D[6, I3, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9] - - (27*I)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]* - SU3D[I4, k8, k9] + (18*I)*SU3D[6, I3, k7]*SU3D[I1, I5, k9]* - SU3D[I2, k7, k8]*SU3D[I4, k8, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, k7, k9]*SU3D[I3, I5, k8]*SU3D[I4, k8, k9] - - (36*I)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]* - SU3D[I4, k8, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, I5, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k8, k9] - (27*I)*SU3D[6, I4, k8]* - SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I5, k6, k9] - - (27*I)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k9] + (54*I)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k9]*SU3D[I5, k7, k8] - (54*I)*SU3D[6, I3, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8] + - (18*I)*SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8] + (54*I)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k9]*SU3D[I5, k7, k8] + (27*I)*SU3D[6, I4, k7]* - SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + - (27*I)*SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8] - (18*I)*SU3D[6, I1, k7]*SU3D[I2, I4, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + (18*I)*SU3D[6, I3, k7]* - SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k8]* - SU3D[I5, k7, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, I3, k8]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k9] - (36*I)*SU3D[6, I4, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9] + - (36*I)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]* - SU3D[I5, k8, k9] - (27*I)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3D[I5, k8, k9] + (18*I)*SU3D[6, I3, k7]* - SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k9]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9] - (36*I)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, I4, k9]*SU3D[I5, k8, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] - - (27*I)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]* - SU3D[I5, k8, k9] + (18*I)*SU3D[6, I3, k7]*SU3D[I1, I2, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I3, k8]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9] - - 84*SU3D[I3, I4, I5]*SU3F[6, I1, I2] + 36*SU3D[I2, I4, I5]* - SU3F[6, I1, I3] - 84*SU3D[I2, I3, I5]*SU3F[6, I1, I4] - - 84*SU3D[I2, I3, I4]*SU3F[6, I1, I5] + 18*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I1, k7] - - 18*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] + - 24*SU3D[I1, I4, I5]*SU3F[6, I2, I3] + 36*SU3D[I1, k7, k8]* - SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I2, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I2, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I2, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7] - - 27*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I2, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] + - 27*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] - - 27*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] + - 27*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] - - 24*SU3D[I1, I2, I5]*SU3F[6, I3, I4] - 24*SU3D[I1, I2, I4]* - SU3F[6, I3, I5] - 36*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7] + 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7] - 36*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k8]* - SU3F[6, I3, k7] - 18*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k8]* - SU3F[6, I3, k7] + 54*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I4, k7, k8]* - SU3F[6, I3, k7] - 18*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]*SU3D[I4, k7, k8]* - SU3F[6, I3, k7] - 36*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k8]* - SU3F[6, I3, k7] - 18*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I5, k6, k8]* - SU3F[6, I3, k7] - 18*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]* - SU3F[6, I3, k7] + 54*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I5, k7, k8]* - SU3F[6, I3, k7] - 18*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]*SU3D[I5, k7, k8]* - SU3F[6, I3, k7] - 18*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]* - SU3F[6, I3, k7] + 36*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3F[6, I4, k7] - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]* - SU3F[6, I4, k7] + 36*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]* - SU3F[6, I4, k7] - 27*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k8]* - SU3F[6, I4, k7] + 54*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3F[6, I4, k7] + 36*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k8]* - SU3F[6, I4, k7] + 27*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I5, k6, k8]* - SU3F[6, I4, k7] - 54*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I5, k7, k8]* - SU3F[6, I4, k7] + 27*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]*SU3D[I5, k7, k8]* - SU3F[6, I4, k7] - 27*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]* - SU3F[6, I4, k7] + 36*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3F[6, I5, k7] - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]* - SU3F[6, I5, k7] + 36*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]* - SU3F[6, I5, k7] - 27*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k8]* - SU3F[6, I5, k7] + 54*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3F[6, I5, k7] + 36*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3F[6, I5, k7] + 27*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k8]* - SU3F[6, I5, k7] - 54*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3F[6, I5, k7] + 27*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]*SU3D[I4, k7, k8]* - SU3F[6, I5, k7] - 27*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]* - SU3F[6, I5, k7] - 24*SU3D[6, I4, I5]*SU3F[I1, I2, I3] + - 9*SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I1, I2, k6] + - 9*SU3D[6, I4, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, I2, k6] - - (18*I)*SU3D[I4, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[I1, I2, k6] - (18*I)*SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k8]*SU3F[I1, I2, k6] - (36*I)*SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I2, k6] - - (9*I)*SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[I1, I2, k6] - (36*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I5, k8]*SU3F[I1, I2, k6] - (9*I)*SU3D[I3, k6, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I2, k6] - - 18*SU3D[6, I5, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[I1, I2, k9] - - 36*SU3D[6, I5, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]*SU3F[I1, I2, k9] - - 18*SU3D[6, I4, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9] - - 18*SU3D[6, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9] - - 36*SU3D[6, I4, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]*SU3F[I1, I2, k9] - - 18*SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[I1, I2, k9] + - 24*SU3D[6, I2, I5]*SU3F[I1, I3, I4] + 24*SU3D[6, I2, I4]* - SU3F[I1, I3, I5] + 9*SU3D[6, I5, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I3, k6] + 9*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[I1, I3, k6] + 9*SU3D[6, I4, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6] + 9*SU3D[6, I2, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6] + 9*SU3D[6, I4, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]* - SU3F[I1, I3, k6] + 9*SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[I1, I3, k6] + (9*I)*SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6] + (9*I)*SU3D[I4, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I3, k6] + - (9*I)*SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[I1, I3, k6] + (9*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k8]*SU3F[I1, I3, k6] + (9*I)*SU3D[I2, k7, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6] + - (9*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]* - SU3F[I1, I3, k6] + 9*SU3D[6, I5, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I4, k6] + 9*SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]* - SU3F[I1, I4, k6] - (36*I)*SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6] - (9*I)*SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I4, k6] - - (18*I)*SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[I1, I4, k6] - (18*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k8]*SU3F[I1, I4, k6] - (9*I)*SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I4, k6] - - (36*I)*SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]* - SU3F[I1, I4, k6] - 36*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9] - 18*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3F[I1, I4, k9] - 18*SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I4, k9] - 18*SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I4, k9] - 18*SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]* - SU3F[I1, I4, k9] - 36*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[I1, I4, k9] + 9*SU3D[6, I4, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I5, k6] + 9*SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[I1, I5, k6] - (36*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6] - (9*I)*SU3D[I3, k6, k7]* - SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I5, k6] - - (18*I)*SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]* - SU3F[I1, I5, k6] - (18*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]* - SU3F[6, I3, k8]*SU3F[I1, I5, k6] - (9*I)*SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I5, k6] - - (36*I)*SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]* - SU3F[I1, I5, k6] - 36*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9] - 18*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3F[I1, I5, k9] - 18*SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I1, I5, k9] - 18*SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I1, I5, k9] - 18*SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I5, k9] - 36*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I5, k9] - (54*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8] + (54*I)*SU3D[I3, I5, k8]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - (54*I)*SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k8] - (54*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I3, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8] - - (54*I)*SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I5, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8] + - (54*I)*SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I5, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I4, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8] + - (54*I)*SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k8] - 54*SU3D[6, I5, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]* - SU3F[I1, k6, k9] - 54*SU3D[6, I4, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]* - SU3F[I1, k6, k9] + 54*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9] + 54*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9] + 54*SU3D[6, I3, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k6, k9] + 54*SU3D[6, I2, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k6, k9] - 54*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]* - SU3F[I1, k6, k9] + 54*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, k6, k9] - 54*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, k6, k9] - 54*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9] + 54*SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9] - 54*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9] + (36*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I3, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, k7, k9] - (36*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I3, k9]*SU3F[I1, k7, k9] - (36*I)*SU3D[I2, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9] - - (36*I)*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I4, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I5, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I4, k6]* - SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9] - 36*SU3D[6, I5, k8]*SU3D[I2, k6, k9]*SU3D[I3, I4, k6]* - SU3F[I1, k8, k9] - 36*SU3D[6, I4, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]* - SU3F[I1, k8, k9] - 36*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3F[I1, k8, k9] - 36*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]* - SU3F[I1, k8, k9] + 36*SU3D[6, I3, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9] - 36*SU3D[6, I2, k8]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9] - 36*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]* - SU3F[I1, k8, k9] + 36*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k9]* - SU3F[I1, k8, k9] - 36*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9]* - SU3F[I1, k8, k9] - 36*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9]* - SU3F[I1, k8, k9] + 36*SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9]* - SU3F[I1, k8, k9] - 36*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9]* - SU3F[I1, k8, k9] + 18*SU3D[6, I1, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]* - SU3F[I2, I3, k6] + 18*SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[I2, I3, k6] + (18*I)*SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I3, k6] + (18*I)*SU3D[I4, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I3, k6] + - 9*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]*SU3F[I2, k6, k7] - - 18*SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + - 9*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I5, k7, k8]*SU3F[I2, k6, k7] - - 18*SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[I2, k6, k7] - - 18*SU3D[6, I5, k7]*SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8] - - 18*SU3D[6, I4, k7]*SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8] + - (18*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I1, k7]* - SU3F[I2, k6, k8] + (18*I)*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k6, k8] + (18*I)*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8] + - (36*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] + (18*I)*SU3D[I1, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k6, k8] + (18*I)*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k8] - (27*I)*SU3D[I1, I3, k8]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8] - - (27*I)*SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k6, k8] + 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]* - SU3F[I2, k6, k9] + 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]* - SU3F[I2, k6, k9] - 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I2, k6, k9] - 18*SU3D[6, I1, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I2, k6, k9] - 18*SU3D[6, I5, k6]*SU3D[I1, I3, k8]*SU3D[I4, k8, k9]* - SU3F[I2, k6, k9] - 18*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I2, k6, k9] - 18*SU3D[6, I4, k6]*SU3D[I1, I3, k8]*SU3D[I5, k8, k9]* - SU3F[I2, k6, k9] - 18*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I2, k6, k9] - (18*I)*SU3D[6, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I2, k6, k9] - (18*I)*SU3D[6, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k8]*SU3F[I2, k6, k9] - - (18*I)*SU3D[6, I5, k7]*SU3D[I4, k6, k7]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k9] - (18*I)*SU3D[6, I4, k7]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k9]*SU3F[I2, k6, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I3, k9]*SU3F[I2, k6, k9] + 9*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I2, k6, k9] - 18*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I4, k9]*SU3F[I2, k6, k9] - 36*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I2, k6, k9] - 18*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I5, k9]*SU3F[I2, k6, k9] - 36*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I2, k6, k9] - (36*I)*SU3D[6, I5, k8]* - SU3D[I3, I4, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] - - (36*I)*SU3D[6, I4, k8]*SU3D[I3, I5, k6]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] + (36*I)*SU3D[6, I3, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9] - 36*SU3D[I4, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + 36*SU3D[I3, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + 36*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + (9*I)*SU3D[6, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k6]*SU3F[I2, k7, k8] + - (9*I)*SU3D[6, I4, k8]*SU3D[I3, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I2, k7, k8] + 9*SU3D[6, I5, k7]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]* - SU3F[I2, k7, k9] + 9*SU3D[6, I4, k7]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]* - SU3F[I2, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9]* - SU3F[I2, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9]* - SU3F[I2, k7, k9] + (18*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9] - (18*I)*SU3D[I3, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9] - - (18*I)*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9] + (54*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I3, k9]*SU3F[I2, k7, k9] - (18*I)*SU3D[I1, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9] - - (18*I)*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I4, k9]*SU3F[I2, k7, k9] - (27*I)*SU3D[I1, I5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9] + - (27*I)*SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9] - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I5, k9]*SU3F[I2, k7, k9] - (27*I)*SU3D[I1, I4, k6]* - SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9] + - (27*I)*SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9] - (9*I)*SU3D[6, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] - (9*I)*SU3D[6, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I3, k6]*SU3F[I2, k7, k9] - - 9*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I3, k6]*SU3F[I2, k7, k9] - - 9*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I3, k6]*SU3F[I2, k7, k9] - - (18*I)*SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] - (18*I)*SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9] + 18*SU3D[I5, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9] + 9*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9] - (18*I)*SU3D[6, I4, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] - - (18*I)*SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I2, k7, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]* - SU3F[I2, k7, k9] + 9*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I5, k6]* - SU3F[I2, k7, k9] + 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]* - SU3F[I2, k8, k9] + 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]* - SU3F[I2, k8, k9] + 18*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]* - SU3F[I2, k8, k9] + 18*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]* - SU3F[I2, k8, k9] - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I2, k8, k9] - 18*SU3D[6, I1, k8]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I2, k8, k9] - 9*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]* - SU3F[I2, k8, k9] + 18*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I4, k6, k9]* - SU3F[I2, k8, k9] - 9*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I5, k6, k9]* - SU3F[I2, k8, k9] + 18*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I5, k6, k9]* - SU3F[I2, k8, k9] + (9*I)*SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9] + (9*I)*SU3D[6, I4, k7]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9] + - (36*I)*SU3D[6, I5, k7]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9] + (18*I)*SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I2, k8, k9] + (36*I)*SU3D[6, I4, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9] + - (18*I)*SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]* - SU3F[I2, k8, k9] + (54*I)*SU3D[6, I5, k8]*SU3D[I3, I4, k6]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + (54*I)*SU3D[6, I4, k8]* - SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] - - (54*I)*SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9] + 54*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9] - 54*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9] - 54*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9] - 18*SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[I3, I4, k6] - 18*SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]* - SU3F[I3, I4, k6] - (18*I)*SU3D[I2, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I4, k6] - (18*I)*SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I4, k6] - - (18*I)*SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[I2, k7, k8]* - SU3F[I3, I4, k6] + 18*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I3, I4, k6] + (18*I)*SU3D[6, I1, k7]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k9] - 18*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k9] - 18*SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I3, I5, k6] - 18*SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I3, I5, k6] - (18*I)*SU3D[I2, k7, k8]* - SU3D[I4, k6, k7]*SU3F[6, I1, k8]*SU3F[I3, I5, k6] - - (18*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]* - SU3F[I3, I5, k6] - (18*I)*SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[I2, k7, k8]*SU3F[I3, I5, k6] + 18*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6] + (18*I)*SU3D[6, I1, k7]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, I5, k9] - - 18*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]*SU3F[I3, I5, k9] - - (18*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] - (18*I)*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8] - (18*I)*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k8] + (27*I)*SU3D[I1, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k6, k8] + (27*I)*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + (27*I)*SU3D[I1, I5, k8]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k6, k8] + (27*I)*SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]* - SU3F[I3, k6, k8] + (27*I)*SU3D[I1, I4, k8]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I3, k6, k8] + (27*I)*SU3D[I1, I2, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8] + - 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]*SU3F[I3, k6, k9] + - 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I5, k6]*SU3F[I3, k6, k9] - - 27*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3F[I3, k6, k9] - - 27*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3F[I3, k6, k9] + - 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I4, I5, k6]*SU3F[I3, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]*SU3F[I3, k6, k9] - - 27*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I4, k8, k9]*SU3F[I3, k6, k9] - - 27*SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I4, k8, k9]*SU3F[I3, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I4, k8, k9]*SU3F[I3, k6, k9] - - 27*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] - - 27*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] - - 9*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I2, k9]*SU3F[I3, k6, k9] - - 9*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I2, k9]*SU3F[I3, k6, k9] - - 9*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]*SU3F[I3, k6, k9] - - 9*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I4, k9]*SU3F[I3, k6, k9] - - 9*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9] - - 9*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9] - - (36*I)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] - (36*I)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - (36*I)*SU3D[6, I2, k8]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - 36*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - 36*SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - 36*SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - (9*I)*SU3D[6, I5, k7]*SU3D[I1, I4, k6]*SU3F[I2, k7, k9]* - SU3F[I3, k6, k9] + (9*I)*SU3D[6, I4, k7]*SU3D[I1, I5, k6]* - SU3F[I2, k7, k9]*SU3F[I3, k6, k9] + (18*I)*SU3D[6, I5, k8]* - SU3D[I1, I4, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + - (18*I)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9] - (18*I)*SU3D[6, I1, k8]*SU3D[I4, I5, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + 18*SU3D[I4, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - 27*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - 27*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + (9*I)*SU3F[6, I5, k9]* - SU3F[I1, I4, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k8] + - (9*I)*SU3F[6, I4, k9]*SU3F[I1, I5, k7]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k8] - (18*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9] - (18*I)*SU3D[I2, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9] - - (18*I)*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] + (54*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I2, k9]*SU3F[I3, k7, k9] + (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]* - SU3F[I3, k7, k9] - (36*I)*SU3D[6, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I3, k7, k9] - (36*I)*SU3D[6, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] + - 36*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] + - 36*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] - - (36*I)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k9] - (36*I)*SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] + 36*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] + 36*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] - (36*I)*SU3D[6, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I5, k6]*SU3F[I3, k7, k9] - - (36*I)*SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] + 36*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] + 36*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] - 36*SU3D[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9] - 36*SU3D[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9] - 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k8, k9] - 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]* - SU3F[I3, k8, k9] - 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k8, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k8, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k9]* - SU3F[I3, k8, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9]* - SU3F[I3, k8, k9] + (9*I)*SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I3, k8, k9] + (9*I)*SU3D[6, I4, k7]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I3, k8, k9] + - (9*I)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3F[I1, I4, k9]* - SU3F[I3, k8, k9] + (9*I)*SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I3, k8, k9] + (9*I)*SU3D[6, I4, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9] + - (9*I)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]* - SU3F[I3, k8, k9] - (54*I)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - (54*I)*SU3D[6, I4, k8]* - SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - - (54*I)*SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + 54*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + 54*SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + 54*SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + (18*I)*SU3D[6, I1, k8]*SU3D[I4, I5, k6]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9] - 18*SU3D[I4, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + (36*I)*SU3F[6, I5, k9]* - SU3F[I1, I4, k7]*SU3F[I2, k7, k8]*SU3F[I3, k8, k9] + - (36*I)*SU3F[6, I4, k9]*SU3F[I1, I5, k7]*SU3F[I2, k7, k8]* - SU3F[I3, k8, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k7, k9]* - SU3F[I3, k8, k9] - 9*SU3D[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k7, k9]* - SU3F[I3, k8, k9] + 9*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3F[I4, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]* - SU3F[I4, k6, k7] + 9*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I5, k7, k8]* - SU3F[I4, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I5, k7, k8]* - SU3F[I4, k6, k7] - 18*SU3D[6, I5, k7]*SU3D[I1, I3, k8]*SU3D[I2, k6, k7]* - SU3F[I4, k6, k8] - 18*SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I5, k6, k7]* - SU3F[I4, k6, k8] + (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] + (18*I)*SU3D[I2, I5, k8]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8] + - (18*I)*SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k8] - (27*I)*SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8] + - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]* - SU3F[I4, k6, k8] + (18*I)*SU3D[I1, I5, k8]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + (18*I)*SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]* - SU3F[I4, k6, k8] - (27*I)*SU3D[I1, I3, k8]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k6, k8] - 18*SU3D[6, I5, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k6, k9] - 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9] - 18*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9] + 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9] - 36*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9] - (18*I)*SU3D[6, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I1, I3, k8]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[I1, I3, k8]* - SU3F[I4, k6, k9] - (18*I)*SU3D[6, I5, k7]*SU3D[I2, k6, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9] - (18*I)*SU3D[6, I2, k7]* - SU3D[I5, k6, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9] + - 9*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9] + - 9*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9] - - 36*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]*SU3F[I4, k6, k9] - - (36*I)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9] + (36*I)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] - (36*I)*SU3D[6, I2, k8]* - SU3D[I3, I5, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + - 36*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] - - 36*SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + - 36*SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k9] + 18*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k9] - (9*I)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - (18*I)*SU3D[6, I5, k6]* - SU3D[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + - (18*I)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I3, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[I3, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + 27*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, k6, k7]*SU3F[I3, I5, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I5, k9]*SU3F[I4, k6, k9] + - (18*I)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9] - 18*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9] + (9*I)*SU3D[6, I5, k8]*SU3D[I3, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k8] + (9*I)*SU3D[6, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I1, I5, k6]*SU3F[I4, k7, k8] + - (18*I)*SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[I2, I3, k6]* - SU3F[I4, k7, k8] + (9*I)*SU3F[6, I5, k9]*SU3F[I1, I3, k7]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k8] + (18*I)*SU3F[6, I3, k9]* - SU3F[I1, I5, k7]*SU3F[I2, k8, k9]*SU3F[I4, k7, k8] - - (18*I)*SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[I3, I5, k6]* - SU3F[I4, k7, k8] + (18*I)*SU3F[6, I1, k9]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k7]*SU3F[I4, k7, k8] + (36*I)*SU3F[6, I5, k9]* - SU3F[I1, I2, k7]*SU3F[I3, k8, k9]*SU3F[I4, k7, k8] + - (36*I)*SU3F[6, I2, k9]*SU3F[I1, I5, k7]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k8] + 18*SU3D[6, I1, k7]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]* - SU3F[I4, k7, k9] + 9*SU3D[6, I5, k7]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]* - SU3F[I4, k7, k9] + 9*SU3D[6, I2, k7]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]* - SU3F[I4, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9]* - SU3F[I4, k7, k9] - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] + (18*I)*SU3D[I2, I5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9] - - (18*I)*SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I4, k7, k9] - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] - (27*I)*SU3D[I1, I5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9] + - (27*I)*SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I4, k7, k9] + (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] - (18*I)*SU3D[I1, I5, k6]* - SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9] - - (18*I)*SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]* - SU3F[I4, k7, k9] - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[6, I5, k9]*SU3F[I4, k7, k9] + (27*I)*SU3D[I1, I3, k6]* - SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9] - - (27*I)*SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I4, k7, k9] - (18*I)*SU3D[6, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9] - (18*I)*SU3D[6, I3, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9] + - 18*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9] + - 9*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9] - - (9*I)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9] - (9*I)*SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9] - 9*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9] - 9*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9] - (18*I)*SU3D[6, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I5, k6]*SU3F[I4, k7, k9] - - (18*I)*SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9] + 9*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9] + 18*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9] - 18*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]* - SU3F[I4, k7, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k7, k9] + (18*I)*SU3F[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k9] - 18*SU3D[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k9] + 18*SU3D[I2, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, I5, k6]*SU3F[I4, k7, k9] - 18*SU3D[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9] + (9*I)*SU3D[6, I5, k7]* - SU3D[I1, I2, k6]*SU3F[I3, k6, k9]*SU3F[I4, k7, k9] + - (9*I)*SU3D[6, I2, k7]*SU3D[I1, I5, k6]*SU3F[I3, k6, k9]* - SU3F[I4, k7, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9] - 9*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9] + 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k8, k9] - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]* - SU3F[I4, k8, k9] - 9*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]* - SU3F[I4, k8, k9] + 18*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]* - SU3F[I4, k8, k9] + 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]* - SU3F[I4, k8, k9] + 18*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]* - SU3F[I4, k8, k9] + 18*SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]* - SU3F[I4, k8, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]* - SU3F[I4, k8, k9] + 18*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I5, k6, k9]* - SU3F[I4, k8, k9] - 9*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I5, k6, k9]* - SU3F[I4, k8, k9] + (36*I)*SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9] + (18*I)*SU3D[6, I3, k7]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I4, k8, k9] + - (9*I)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I4, k8, k9] + (9*I)*SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I4, k8, k9] + (18*I)*SU3D[6, I3, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9] + - (36*I)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]* - SU3F[I4, k8, k9] + (54*I)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - (54*I)*SU3D[6, I3, k8]* - SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + - (54*I)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] - 54*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] + 54*SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] - 54*SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] - 18*SU3D[6, I5, k6]*SU3F[I1, I3, k9]*SU3F[I2, k6, k8]* - SU3F[I4, k8, k9] - (9*I)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - (18*I)*SU3D[6, I5, k6]* - SU3D[I1, I3, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + - (18*I)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I3, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - 18*SU3D[I3, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - 18*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + 27*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + (9*I)*SU3F[6, I5, k9]* - SU3F[I1, I3, k7]*SU3F[I2, k7, k8]*SU3F[I4, k8, k9] + - (18*I)*SU3F[6, I3, k9]*SU3F[I1, I5, k7]*SU3F[I2, k7, k8]* - SU3F[I4, k8, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k7, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3F[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9] - 18*SU3D[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9] + (18*I)*SU3F[6, I1, k9]* - SU3F[I2, k7, k8]*SU3F[I3, I5, k7]*SU3F[I4, k8, k9] - - 18*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8]*SU3F[I4, k8, k9] + - (18*I)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - (18*I)*SU3D[6, I1, k8]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + - 18*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - - 27*SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - - 27*SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + - (9*I)*SU3F[6, I5, k9]*SU3F[I1, I2, k7]*SU3F[I3, k7, k8]* - SU3F[I4, k8, k9] + (9*I)*SU3F[6, I2, k9]*SU3F[I1, I5, k7]* - SU3F[I3, k7, k8]*SU3F[I4, k8, k9] - 36*SU3D[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9] - 36*SU3D[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9] + 9*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k7, k8]*SU3F[I5, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k7] + 9*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k7, k8]*SU3F[I5, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[I5, k6, k7] - 18*SU3D[6, I4, k7]*SU3D[I1, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I5, k6, k8] - 18*SU3D[6, I2, k7]*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8] + (18*I)*SU3D[I2, k6, k7]* - SU3D[I3, I4, k8]*SU3F[6, I1, k7]*SU3F[I5, k6, k8] + - (18*I)*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[I5, k6, k8] + (18*I)*SU3D[I2, I3, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8] - - (27*I)*SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I5, k6, k8] + (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k8] + (18*I)*SU3D[I1, I4, k8]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8] + - (18*I)*SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I5, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k8]* - SU3F[6, I4, k7]*SU3F[I5, k6, k8] - (27*I)*SU3D[I1, I3, k8]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8] - - 18*SU3D[6, I4, k6]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9]*SU3F[I5, k6, k8] - - 18*SU3D[6, I2, k6]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9]*SU3F[I5, k6, k8] + - 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]*SU3F[I5, k6, k9] - - 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]*SU3F[I5, k6, k9] - - 18*SU3D[6, I4, k6]*SU3D[I1, I3, k8]*SU3D[I2, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]*SU3F[I5, k6, k9] - - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9] - - 36*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9] - - (18*I)*SU3D[6, I4, k6]*SU3D[I2, k8, k9]*SU3F[I1, I3, k8]* - SU3F[I5, k6, k9] - (18*I)*SU3D[6, I2, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I4, k7]* - SU3D[I2, k6, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9] - - (18*I)*SU3D[6, I2, k7]*SU3D[I4, k6, k7]*SU3F[I1, I3, k9]* - SU3F[I5, k6, k9] + 9*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I5, k6, k9] + 9*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]* - SU3F[I5, k6, k9] - 36*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I5, k6, k9] - 18*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]* - SU3F[I5, k6, k9] - (36*I)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + (36*I)*SU3D[6, I3, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] - - (36*I)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9] + 36*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9] - 36*SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9] + 36*SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9] - (18*I)*SU3D[6, I1, k7]*SU3D[I4, k6, k7]* - SU3F[I2, I3, k9]*SU3F[I5, k6, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, I3, k9]*SU3F[I5, k6, k9] - (9*I)*SU3D[6, I4, k8]* - SU3D[I1, I3, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - - (18*I)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I3, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + - 27*SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]*SU3F[I3, I4, k9]* - SU3F[I5, k6, k9] - 18*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I4, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[I2, I4, k6]*SU3F[6, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9] + (18*I)*SU3D[6, I3, k8]* - SU3D[I1, I2, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - - (9*I)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9] - (18*I)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + - 27*SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - - 18*SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + - (9*I)*SU3D[6, I4, k8]*SU3D[I3, k6, k7]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k8] + (9*I)*SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k8] + (18*I)*SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[I2, I3, k6]*SU3F[I5, k7, k8] + - (9*I)*SU3F[6, I4, k9]*SU3F[I1, I3, k7]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k8] + (18*I)*SU3F[6, I3, k9]*SU3F[I1, I4, k7]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k8] - (18*I)*SU3D[6, I1, k8]* - SU3D[I2, k6, k7]*SU3F[I3, I4, k6]*SU3F[I5, k7, k8] + - (18*I)*SU3F[6, I1, k9]*SU3F[I2, k8, k9]*SU3F[I3, I4, k7]* - SU3F[I5, k7, k8] + (36*I)*SU3F[6, I4, k9]*SU3F[I1, I2, k7]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k8] + (36*I)*SU3F[6, I2, k9]* - SU3F[I1, I4, k7]*SU3F[I3, k8, k9]*SU3F[I5, k7, k8] + - (18*I)*SU3F[6, I3, k9]*SU3F[I1, I2, k7]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k8] + (9*I)*SU3F[6, I2, k9]*SU3F[I1, I3, k7]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k8] - (18*I)*SU3F[6, I1, k9]* - SU3F[I2, I3, k7]*SU3F[I4, k8, k9]*SU3F[I5, k7, k8] + - 18*SU3D[6, I1, k7]*SU3D[I2, k6, k9]*SU3D[I3, I4, k6]*SU3F[I5, k7, k9] + - 9*SU3D[6, I4, k7]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3F[I5, k7, k9] + - 9*SU3D[6, I2, k7]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3F[I5, k7, k9] + - 18*SU3D[6, I1, k7]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]*SU3F[I5, k7, k9] - - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I1, k9]* - SU3F[I5, k7, k9] + (18*I)*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9] - (18*I)*SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]* - SU3F[I5, k7, k9] - (27*I)*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]* - SU3F[6, I2, k9]*SU3F[I5, k7, k9] + (27*I)*SU3D[I1, I3, k6]* - SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]* - SU3F[I5, k7, k9] - (18*I)*SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k9]*SU3F[I5, k7, k9] - (18*I)*SU3D[I1, I2, k6]* - SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]* - SU3F[I5, k7, k9] + (27*I)*SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[6, I4, k9]*SU3F[I5, k7, k9] - (27*I)*SU3D[I1, I2, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9] - - (18*I)*SU3D[6, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9] - (18*I)*SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9] + 9*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9] - (9*I)*SU3D[6, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9] - - (9*I)*SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9] - 9*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9] - 9*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9] - (18*I)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9] - (18*I)*SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k6]*SU3F[I5, k7, k9] + - 9*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]*SU3F[I5, k7, k9] + - 18*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]*SU3F[I5, k7, k9] - - 18*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]*SU3F[I5, k7, k9] - - 9*SU3D[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9] + - (18*I)*SU3F[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k9] - 18*SU3D[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k9] + 18*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I4, k6]* - SU3F[I5, k7, k9] - 18*SU3D[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8]* - SU3F[I5, k7, k9] + (9*I)*SU3D[6, I4, k7]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I5, k7, k9] + (9*I)*SU3D[6, I2, k7]* - SU3D[I1, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k7, k9] - - 9*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9] - - 9*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9] - - 18*SU3D[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] - - 9*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] + - (18*I)*SU3F[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k9] + 18*SU3D[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k9] + 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]* - SU3F[I5, k8, k9] - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]* - SU3F[I5, k8, k9] - 9*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]* - SU3F[I5, k8, k9] + 18*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k6, k9]* - SU3F[I5, k8, k9] + 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]* - SU3F[I5, k8, k9] + 18*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]* - SU3F[I5, k8, k9] + 18*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]* - SU3F[I5, k8, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3F[I5, k8, k9] + 18*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k6, k9]* - SU3F[I5, k8, k9] - 9*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]* - SU3F[I5, k8, k9] + (36*I)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[I1, I2, k9]*SU3F[I5, k8, k9] + - (9*I)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I5, k8, k9] + (9*I)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I3, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9] + - (36*I)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9]* - SU3F[I5, k8, k9] + (54*I)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9] - (54*I)*SU3D[6, I3, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + - (54*I)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9] - 54*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9] + 54*SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9] - 54*SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9] - 18*SU3D[6, I4, k6]*SU3F[I1, I3, k9]*SU3F[I2, k6, k8]* - SU3F[I5, k8, k9] - (9*I)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] - (18*I)*SU3D[6, I4, k6]* - SU3D[I1, I3, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I3, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] - 18*SU3D[I3, I4, k6]*SU3F[6, I1, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] - 18*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + 27*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + (9*I)*SU3F[6, I4, k9]* - SU3F[I1, I3, k7]*SU3F[I2, k7, k8]*SU3F[I5, k8, k9] + - (18*I)*SU3F[6, I3, k9]*SU3F[I1, I4, k7]*SU3F[I2, k7, k8]* - SU3F[I5, k8, k9] - 9*SU3D[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k7, k9]* - SU3F[I5, k8, k9] + (18*I)*SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9] - 18*SU3D[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9] + (18*I)*SU3F[6, I1, k9]* - SU3F[I2, k7, k8]*SU3F[I3, I4, k7]*SU3F[I5, k8, k9] - - 18*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I4, k8]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9] + (18*I)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - (18*I)*SU3D[6, I1, k8]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + - 18*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - - 27*SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - - 27*SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + - (9*I)*SU3F[6, I4, k9]*SU3F[I1, I2, k7]*SU3F[I3, k7, k8]* - SU3F[I5, k8, k9] + (9*I)*SU3F[6, I2, k9]*SU3F[I1, I4, k7]* - SU3F[I3, k7, k8]*SU3F[I5, k8, k9] - 36*SU3D[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9] - 36*SU3D[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9] - 18*SU3D[6, I2, k6]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k8]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I3, k8]* - SU3D[I1, I2, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9] - - (9*I)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9] - (18*I)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9] - - 18*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + - 27*SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9] - - 18*SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3F[6, I3, k9]*SU3F[I1, I2, k7]*SU3F[I4, k7, k8]* - SU3F[I5, k8, k9] + (9*I)*SU3F[6, I2, k9]*SU3F[I1, I3, k7]* - SU3F[I4, k7, k8]*SU3F[I5, k8, k9] - (18*I)*SU3F[6, I1, k9]* - SU3F[I2, I3, k7]*SU3F[I4, k7, k8]*SU3F[I5, k8, k9] - - 18*SU3D[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3F[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k7, k9]* - SU3F[I5, k8, k9] + 18*SU3D[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k7, k9]* - SU3F[I5, k8, k9] + (24*I)*SU3D[I2, I5, k6]*SU3D[I3, I4, k6]* - SUNDelta[6, I1] + (24*I)*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]* - SUNDelta[6, I1] + (24*I)*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]* - SUNDelta[6, I1] + 48*SU3D[I4, I5, k6]*SU3F[I2, I3, k6]* - SUNDelta[6, I1] - 48*SU3D[I2, I5, k6]*SU3F[I3, I4, k6]* - SUNDelta[6, I1] - 48*SU3D[I2, I4, k6]*SU3F[I3, I5, k6]* - SUNDelta[6, I1] + (30*I)*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]* - SUNDelta[6, I2] + (30*I)*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]* - SUNDelta[6, I2] - (96*I)*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]* - SUNDelta[6, I2] + 30*SU3D[I3, I5, k6]*SU3F[I1, I4, k6]* - SUNDelta[6, I2] + 30*SU3D[I3, I4, k6]*SU3F[I1, I5, k6]* - SUNDelta[6, I2] + 18*SU3D[I1, I5, k6]*SU3F[I3, I4, k6]* - SUNDelta[6, I2] - (18*I)*SU3F[I1, I5, k6]*SU3F[I3, I4, k6]* - SUNDelta[6, I2] + 18*SU3D[I1, I4, k6]*SU3F[I3, I5, k6]* - SUNDelta[6, I2] - (18*I)*SU3F[I1, I4, k6]*SU3F[I3, I5, k6]* - SUNDelta[6, I2] + (12*I)*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]* - SUNDelta[6, I3] + (12*I)*SU3D[I1, I4, k6]*SU3D[I2, I5, k6]* - SUNDelta[6, I3] + (12*I)*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]* - SUNDelta[6, I3] - 84*SU3D[I4, I5, k6]*SU3F[I1, I2, k6]* - SUNDelta[6, I3] - 84*SU3D[I2, I5, k6]*SU3F[I1, I4, k6]* - SUNDelta[6, I3] - 84*SU3D[I2, I4, k6]*SU3F[I1, I5, k6]* - SUNDelta[6, I3] + (30*I)*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]* - SUNDelta[6, I4] - (96*I)*SU3D[I1, I3, k6]*SU3D[I2, I5, k6]* - SUNDelta[6, I4] + (30*I)*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]* - SUNDelta[6, I4] + 30*SU3D[I3, I5, k6]*SU3F[I1, I2, k6]* - SUNDelta[6, I4] + 30*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]* - SUNDelta[6, I4] - 18*SU3D[I1, I5, k6]*SU3F[I2, I3, k6]* - SUNDelta[6, I4] + (18*I)*SU3F[I1, I5, k6]*SU3F[I2, I3, k6]* - SUNDelta[6, I4] + 18*SU3D[I1, I2, k6]*SU3F[I3, I5, k6]* - SUNDelta[6, I4] - (18*I)*SU3F[I1, I2, k6]*SU3F[I3, I5, k6]* - SUNDelta[6, I4] + (30*I)*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]* - SUNDelta[6, I5] - (96*I)*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]* - SUNDelta[6, I5] + (30*I)*SU3D[I1, I2, k6]*SU3D[I3, I4, k6]* - SUNDelta[6, I5] + 30*SU3D[I3, I4, k6]*SU3F[I1, I2, k6]* - SUNDelta[6, I5] + 30*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]* - SUNDelta[6, I5] - 18*SU3D[I1, I4, k6]*SU3F[I2, I3, k6]* - SUNDelta[6, I5] + (18*I)*SU3F[I1, I4, k6]*SU3F[I2, I3, k6]* - SUNDelta[6, I5] + 18*SU3D[I1, I2, k6]*SU3F[I3, I4, k6]* - SUNDelta[6, I5] - (18*I)*SU3F[I1, I2, k6]*SU3F[I3, I4, k6]* - SUNDelta[6, I5] + (18*I)*SU3D[6, I5, k6]*SU3D[I3, I4, k6]* - SUNDelta[I1, I2] + (18*I)*SU3D[6, I4, k6]*SU3D[I3, I5, k6]* - SUNDelta[I1, I2] + (24*I)*SU3D[6, I3, k6]*SU3D[I4, I5, k6]* - SUNDelta[I1, I2] - 24*SU3D[I4, I5, k5]*SU3F[6, I3, k5]* - SUNDelta[I1, I2] - 18*SU3D[I3, I5, k5]*SU3F[6, I4, k5]* - SUNDelta[I1, I2] - 18*SU3D[I3, I4, k5]*SU3F[6, I5, k5]* - SUNDelta[I1, I2] + 18*SU3D[6, I5, k6]*SU3F[I3, I4, k6]* - SUNDelta[I1, I2] + (18*I)*SU3F[6, I5, k6]*SU3F[I3, I4, k6]* - SUNDelta[I1, I2] + 18*SU3D[6, I4, k6]*SU3F[I3, I5, k6]* - SUNDelta[I1, I2] + (18*I)*SU3F[6, I4, k6]*SU3F[I3, I5, k6]* - SUNDelta[I1, I2] + (18*I)*SU3D[6, I5, k6]*SU3D[I2, I3, k6]* - SUNDelta[I1, I4] + (24*I)*SU3D[6, I3, k6]*SU3D[I2, I5, k6]* - SUNDelta[I1, I4] + (18*I)*SU3D[6, I2, k6]*SU3D[I3, I5, k6]* - SUNDelta[I1, I4] - 18*SU3D[I3, I5, k5]*SU3F[6, I2, k5]* - SUNDelta[I1, I4] - 24*SU3D[I2, I5, k5]*SU3F[6, I3, k5]* - SUNDelta[I1, I4] - 18*SU3D[I2, I3, k5]*SU3F[6, I5, k5]* - SUNDelta[I1, I4] - 18*SU3D[6, I5, k6]*SU3F[I2, I3, k6]* - SUNDelta[I1, I4] - (18*I)*SU3F[6, I5, k6]*SU3F[I2, I3, k6]* - SUNDelta[I1, I4] + 18*SU3D[6, I2, k6]*SU3F[I3, I5, k6]* - SUNDelta[I1, I4] + (18*I)*SU3F[6, I2, k6]*SU3F[I3, I5, k6]* - SUNDelta[I1, I4] + (18*I)*SU3D[6, I4, k6]*SU3D[I2, I3, k6]* - SUNDelta[I1, I5] + (24*I)*SU3D[6, I3, k6]*SU3D[I2, I4, k6]* - SUNDelta[I1, I5] + (18*I)*SU3D[6, I2, k6]*SU3D[I3, I4, k6]* - SUNDelta[I1, I5] - 18*SU3D[I3, I4, k5]*SU3F[6, I2, k5]* - SUNDelta[I1, I5] - 24*SU3D[I2, I4, k5]*SU3F[6, I3, k5]* - SUNDelta[I1, I5] - 18*SU3D[I2, I3, k5]*SU3F[6, I4, k5]* - SUNDelta[I1, I5] - 18*SU3D[6, I4, k6]*SU3F[I2, I3, k6]* - SUNDelta[I1, I5] - (18*I)*SU3F[6, I4, k6]*SU3F[I2, I3, k6]* - SUNDelta[I1, I5] + 18*SU3D[6, I2, k6]*SU3F[I3, I4, k6]* - SUNDelta[I1, I5] + (18*I)*SU3F[6, I2, k6]*SU3F[I3, I4, k6]* - SUNDelta[I1, I5] + (12*I)*SU3D[6, I5, k6]*SU3D[I1, I4, k6]* - SUNDelta[I2, I3] + (12*I)*SU3D[6, I4, k6]*SU3D[I1, I5, k6]* - SUNDelta[I2, I3] + (24*I)*SU3D[6, I1, k6]*SU3D[I4, I5, k6]* - SUNDelta[I2, I3] - 24*SU3D[I4, I5, k5]*SU3F[6, I1, k5]* - SUNDelta[I2, I3] - 12*SU3D[I1, I5, k5]*SU3F[6, I4, k5]* - SUNDelta[I2, I3] - 12*SU3D[I1, I4, k5]*SU3F[6, I5, k5]* - SUNDelta[I2, I3] + 60*SU3D[6, I5, k6]*SU3F[I1, I4, k6]* - SUNDelta[I2, I3] + (60*I)*SU3F[6, I5, k6]*SU3F[I1, I4, k6]* - SUNDelta[I2, I3] + 60*SU3D[6, I4, k6]*SU3F[I1, I5, k6]* - SUNDelta[I2, I3] + (60*I)*SU3F[6, I4, k6]*SU3F[I1, I5, k6]* - SUNDelta[I2, I3] + (20*I)*SUNDelta[6, I5]*SUNDelta[I1, I4]* - SUNDelta[I2, I3] + (20*I)*SUNDelta[6, I4]*SUNDelta[I1, I5]* - SUNDelta[I2, I3] - (60*I)*SU3D[6, I5, k6]*SU3D[I1, I3, k6]* - SUNDelta[I2, I4] - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I5, k6]* - SUNDelta[I2, I4] + 12*SU3D[I1, I5, k5]*SU3F[6, I3, k5]* - SUNDelta[I2, I4] + 60*SU3D[I1, I3, k5]*SU3F[6, I5, k5]* - SUNDelta[I2, I4] - 12*SU3D[6, I5, k6]*SU3F[I1, I3, k6]* - SUNDelta[I2, I4] - (12*I)*SU3F[6, I5, k6]*SU3F[I1, I3, k6]* - SUNDelta[I2, I4] - 60*SU3D[6, I3, k6]*SU3F[I1, I5, k6]* - SUNDelta[I2, I4] - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I5, k6]* - SUNDelta[I2, I4] - 24*SU3D[6, I1, k6]*SU3F[I3, I5, k6]* - SUNDelta[I2, I4] - (24*I)*SU3F[6, I1, k6]*SU3F[I3, I5, k6]* - SUNDelta[I2, I4] - (64*I)*SUNDelta[6, I5]*SUNDelta[I1, I3]* - SUNDelta[I2, I4] + (8*I)*SUNDelta[6, I3]*SUNDelta[I1, I5]* - SUNDelta[I2, I4] - (60*I)*SU3D[6, I4, k6]*SU3D[I1, I3, k6]* - SUNDelta[I2, I5] - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I4, k6]* - SUNDelta[I2, I5] + 12*SU3D[I1, I4, k5]*SU3F[6, I3, k5]* - SUNDelta[I2, I5] + 60*SU3D[I1, I3, k5]*SU3F[6, I4, k5]* - SUNDelta[I2, I5] - 12*SU3D[6, I4, k6]*SU3F[I1, I3, k6]* - SUNDelta[I2, I5] - (12*I)*SU3F[6, I4, k6]*SU3F[I1, I3, k6]* - SUNDelta[I2, I5] - 60*SU3D[6, I3, k6]*SU3F[I1, I4, k6]* - SUNDelta[I2, I5] - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I4, k6]* - SUNDelta[I2, I5] - 24*SU3D[6, I1, k6]*SU3F[I3, I4, k6]* - SUNDelta[I2, I5] - (24*I)*SU3F[6, I1, k6]*SU3F[I3, I4, k6]* - SUNDelta[I2, I5] - (64*I)*SUNDelta[6, I4]*SUNDelta[I1, I3]* - SUNDelta[I2, I5] + (8*I)*SUNDelta[6, I3]*SUNDelta[I1, I4]* - SUNDelta[I2, I5] + (12*I)*SU3D[6, I5, k6]*SU3D[I1, I2, k6]* - SUNDelta[I3, I4] + (12*I)*SU3D[6, I2, k6]*SU3D[I1, I5, k6]* - SUNDelta[I3, I4] + (24*I)*SU3D[6, I1, k6]*SU3D[I2, I5, k6]* - SUNDelta[I3, I4] - 24*SU3D[I2, I5, k5]*SU3F[6, I1, k5]* - SUNDelta[I3, I4] - 12*SU3D[I1, I5, k5]*SU3F[6, I2, k5]* - SUNDelta[I3, I4] - 12*SU3D[I1, I2, k5]*SU3F[6, I5, k5]* - SUNDelta[I3, I4] + 60*SU3D[6, I5, k6]*SU3F[I1, I2, k6]* - SUNDelta[I3, I4] + (60*I)*SU3F[6, I5, k6]*SU3F[I1, I2, k6]* - SUNDelta[I3, I4] + 60*SU3D[6, I2, k6]*SU3F[I1, I5, k6]* - SUNDelta[I3, I4] + (60*I)*SU3F[6, I2, k6]*SU3F[I1, I5, k6]* - SUNDelta[I3, I4] + (20*I)*SUNDelta[6, I5]*SUNDelta[I1, I2]* - SUNDelta[I3, I4] + (20*I)*SUNDelta[6, I2]*SUNDelta[I1, I5]* - SUNDelta[I3, I4] + (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I5]* - SUNDelta[I3, I4] + (12*I)*SU3D[6, I4, k6]*SU3D[I1, I2, k6]* - SUNDelta[I3, I5] + (12*I)*SU3D[6, I2, k6]*SU3D[I1, I4, k6]* - SUNDelta[I3, I5] + (24*I)*SU3D[6, I1, k6]*SU3D[I2, I4, k6]* - SUNDelta[I3, I5] - 24*SU3D[I2, I4, k5]*SU3F[6, I1, k5]* - SUNDelta[I3, I5] - 12*SU3D[I1, I4, k5]*SU3F[6, I2, k5]* - SUNDelta[I3, I5] - 12*SU3D[I1, I2, k5]*SU3F[6, I4, k5]* - SUNDelta[I3, I5] + 60*SU3D[6, I4, k6]*SU3F[I1, I2, k6]* - SUNDelta[I3, I5] + (60*I)*SU3F[6, I4, k6]*SU3F[I1, I2, k6]* - SUNDelta[I3, I5] + 60*SU3D[6, I2, k6]*SU3F[I1, I4, k6]* - SUNDelta[I3, I5] + (60*I)*SU3F[6, I2, k6]*SU3F[I1, I4, k6]* - SUNDelta[I3, I5] + (20*I)*SUNDelta[6, I4]*SUNDelta[I1, I2]* - SUNDelta[I3, I5] + (20*I)*SUNDelta[6, I2]*SUNDelta[I1, I4]* - SUNDelta[I3, I5] + (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I4]* - SUNDelta[I3, I5] - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I2, k6]* - SUNDelta[I4, I5] - (60*I)*SU3D[6, I2, k6]*SU3D[I1, I3, k6]* - SUNDelta[I4, I5] + 60*SU3D[I1, I3, k5]*SU3F[6, I2, k5]* - SUNDelta[I4, I5] + 12*SU3D[I1, I2, k5]*SU3F[6, I3, k5]* - SUNDelta[I4, I5] - 60*SU3D[6, I3, k6]*SU3F[I1, I2, k6]* - SUNDelta[I4, I5] - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I2, k6]* - SUNDelta[I4, I5] - 12*SU3D[6, I2, k6]*SU3F[I1, I3, k6]* - SUNDelta[I4, I5] - (12*I)*SU3F[6, I2, k6]*SU3F[I1, I3, k6]* - SUNDelta[I4, I5] + 24*SU3D[6, I1, k6]*SU3F[I2, I3, k6]* - SUNDelta[I4, I5] + (24*I)*SU3F[6, I1, k6]*SU3F[I2, I3, k6]* - SUNDelta[I4, I5] + (8*I)*SUNDelta[6, I3]*SUNDelta[I1, I2]* - SUNDelta[I4, I5] - (64*I)*SUNDelta[6, I2]*SUNDelta[I1, I3]* - SUNDelta[I4, I5] + (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I3]* - SUNDelta[I4, I5]))/(108*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*((-48*I)*SU3D[6, I4, I5]*SU3D[I1, I2, I3] + - (72*I)*SU3D[6, I3, I5]*SU3D[I1, I2, I4] - (48*I)*SU3D[6, I3, I4]* - SU3D[I1, I2, I5] + (72*I)*SU3D[6, I2, I5]*SU3D[I1, I3, I4] - - (48*I)*SU3D[6, I2, I4]*SU3D[I1, I3, I5] + (72*I)*SU3D[6, I2, I3]* - SU3D[I1, I4, I5] - (60*I)*SU3D[6, I1, I5]*SU3D[I2, I3, I4] + - (108*I)*SU3D[6, I1, I4]*SU3D[I2, I3, I5] - (60*I)*SU3D[6, I1, I3]* - SU3D[I2, I4, I5] - (60*I)*SU3D[6, I1, I2]*SU3D[I3, I4, I5] + - (54*I)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k9] - (36*I)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3D[I3, I4, k9] - (54*I)*SU3D[6, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9] + - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k9] - (27*I)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3D[I3, k6, k9] + (54*I)*SU3D[6, I5, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8] - - (54*I)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]* - SU3D[I3, k7, k8] + (18*I)*SU3D[6, I4, k7]*SU3D[I1, I5, k9]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8] - (36*I)*SU3D[6, I5, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9] + - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]* - SU3D[I3, k8, k9] - (27*I)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3D[I3, k8, k9] + (18*I)*SU3D[6, I4, k7]* - SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k9]* - SU3D[I4, I5, k8] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, k8, k9]*SU3D[I4, I5, k8] + (54*I)*SU3D[6, I3, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I4, I5, k9] - - (36*I)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k9] + (54*I)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, I5, k9] - (36*I)*SU3D[6, I2, k7]* - SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9] - - (54*I)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]* - SU3D[I4, k7, k8] - (54*I)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k9]*SU3D[I4, k7, k8] - (54*I)*SU3D[6, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]* - SU3D[I4, k7, k8] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, I5, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k7, k8] - (36*I)*SU3D[6, I5, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9] - - (36*I)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]* - SU3D[I4, k8, k9] + (27*I)*SU3D[6, I5, k7]*SU3D[I1, I3, k9]* - SU3D[I2, k7, k8]*SU3D[I4, k8, k9] + (27*I)*SU3D[6, I3, k7]* - SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9] - - (36*I)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]* - SU3D[I4, k8, k9] - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k9]*SU3D[I4, k8, k9] + (27*I)*SU3D[6, I5, k7]* - SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + - (27*I)*SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9] - (18*I)*SU3D[6, I1, k7]*SU3D[I2, I5, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k8, k9] - (27*I)*SU3D[6, I3, k8]* - SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I5, k6, k9] - - (27*I)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k9] - (54*I)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k9]*SU3D[I5, k7, k8] + (54*I)*SU3D[6, I3, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8] + - (18*I)*SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8] + (54*I)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k9]*SU3D[I5, k7, k8] + (18*I)*SU3D[6, I4, k7]* - SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + - (27*I)*SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + (27*I)*SU3D[6, I2, k7]*SU3D[I1, I3, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8] - (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k8]* - SU3D[I5, k7, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k9] + (36*I)*SU3D[6, I4, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9] - - (36*I)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]* - SU3D[I5, k8, k9] - (27*I)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3D[I5, k8, k9] + (18*I)*SU3D[6, I4, k7]* - SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k9]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9] - (36*I)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, I4, k9]*SU3D[I5, k8, k9] - (27*I)*SU3D[6, I2, k8]* - SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9] + - (18*I)*SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]* - SU3D[I3, k7, k9]*SU3D[I5, k8, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] - - 84*SU3D[I3, I4, I5]*SU3F[6, I1, I2] - 84*SU3D[I2, I4, I5]* - SU3F[6, I1, I3] + 36*SU3D[I2, I3, I5]*SU3F[6, I1, I4] - - 84*SU3D[I2, I3, I4]*SU3F[6, I1, I5] - 18*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I1, k7] + - 18*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] + - 24*SU3D[I1, I3, I5]*SU3F[6, I2, I4] + 36*SU3D[I1, k7, k8]* - SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I2, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I2, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I2, k7] - - 27*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I2, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] + - 27*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] + - 27*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] - - 27*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] + - 24*SU3D[I1, I2, I5]*SU3F[6, I3, I4] + 36*SU3D[I1, k7, k8]* - SU3D[I2, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I3, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I3, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I3, k7] - - 27*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I3, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I3, k7] + - 27*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I3, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I3, k7] + - 27*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I3, k7] - - 27*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I3, k7] - - 24*SU3D[I1, I2, I3]*SU3F[6, I4, I5] - 36*SU3D[I1, k7, k8]* - SU3D[I2, k6, k8]*SU3D[I3, I5, k6]*SU3F[6, I4, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3F[6, I4, k7] - - 36*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3F[6, I4, k7] - - 18*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k8]*SU3F[6, I4, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7] - - 18*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3F[6, I4, k7] - - 36*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k8]*SU3F[6, I4, k7] - - 18*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I4, k7] - - 18*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I4, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I5, k7, k8]*SU3F[6, I4, k7] - - 18*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I4, k7] - - 18*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I4, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]*SU3F[6, I5, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3F[6, I5, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3F[6, I5, k7] + - 27*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k8]*SU3F[6, I5, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3F[6, I5, k7] + - 27*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3F[6, I5, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3F[6, I5, k7] - - 27*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I5, k7] - - 27*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I5, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3F[6, I5, k7] - - 24*SU3D[6, I3, I5]*SU3F[I1, I2, I4] + 9*SU3D[6, I5, k9]*SU3D[I3, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I2, k6] + 9*SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I2, k6] - (36*I)*SU3D[I4, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I2, k6] - - (9*I)*SU3D[I4, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[I1, I2, k6] - (18*I)*SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[I1, I2, k6] - (18*I)*SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I2, k6] - - (9*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]* - SU3F[I1, I2, k6] - (36*I)*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]* - SU3F[6, I5, k8]*SU3F[I1, I2, k6] - 36*SU3D[6, I5, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I2, k9] - 18*SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I2, k9] - 18*SU3D[6, I4, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9] - 18*SU3D[6, I3, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9] - 18*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9] - 36*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9] - 24*SU3D[6, I2, I5]* - SU3F[I1, I3, I4] + 9*SU3D[6, I5, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I3, k6] + 9*SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[I1, I3, k6] - (36*I)*SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6] - (9*I)*SU3D[I4, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I3, k6] - - (18*I)*SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[I1, I3, k6] - (18*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k8]*SU3F[I1, I3, k6] - (9*I)*SU3D[I2, k7, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6] - - (36*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]* - SU3F[I1, I3, k6] - 36*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9] - 18*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k9] - 18*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9] - 18*SU3D[6, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9] - 18*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]* - SU3F[I1, I3, k9] - 36*SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[I1, I3, k9] + 24*SU3D[6, I2, I3]*SU3F[I1, I4, I5] + - 9*SU3D[6, I5, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3F[I1, I4, k6] + - 9*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3D[I3, k7, k9]*SU3F[I1, I4, k6] + - 9*SU3D[6, I3, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6] + - 9*SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6] + - 9*SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, I4, k6] + - 9*SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, I4, k6] + - (9*I)*SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[I1, I4, k6] + (9*I)*SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6] + (9*I)*SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I4, k6] + - (9*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[I1, I4, k6] + (9*I)*SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k8]*SU3F[I1, I4, k6] + (9*I)*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6] + - 9*SU3D[6, I3, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6] + - 9*SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6] - - (9*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k8]* - SU3F[I1, I5, k6] - (36*I)*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6] - (9*I)*SU3D[I2, k7, k8]* - SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I5, k6] - - (36*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]* - SU3F[I1, I5, k6] - (18*I)*SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k8]*SU3F[I1, I5, k6] - (18*I)*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I5, k6] - - 18*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9] - - 18*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3F[I1, I5, k9] - - 36*SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9] - - 36*SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9] - - 18*SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]*SU3F[I1, I5, k9] - - 18*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]*SU3F[I1, I5, k9] + - (54*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]* - SU3F[I1, k6, k8] - (54*I)*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8] + (54*I)*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - (54*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8] - - (54*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8] + - (54*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8] - - 54*SU3D[6, I5, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + - 54*SU3D[6, I4, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9] - - 54*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I3, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9] - - 54*SU3D[6, I2, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9] + - 54*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - (36*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I3, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9] - - (36*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] - (36*I)*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I4, k9]*SU3F[I1, k7, k9] - (36*I)*SU3D[I2, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]* - SU3F[6, I5, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9] - - 36*SU3D[6, I5, k8]*SU3D[I2, k6, k9]*SU3D[I3, I4, k6]*SU3F[I1, k8, k9] + - 36*SU3D[6, I4, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]*SU3F[I1, k8, k9] - - 36*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]*SU3F[I1, k8, k9] + - 36*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9] - - 36*SU3D[6, I2, k8]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9] - - 36*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] + - 36*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] + - 18*SU3D[6, I1, k9]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I2, I4, k6] + - 18*SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I2, I4, k6] + - (18*I)*SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[I2, I4, k6] + (18*I)*SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k8]*SU3F[I2, I4, k6] + 9*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k7, k8]*SU3F[I2, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k7] + 9*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k7, k8]*SU3F[I2, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[I2, k6, k7] - 18*SU3D[6, I5, k7]*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k8] - 18*SU3D[6, I3, k7]*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8] + (18*I)*SU3D[I3, k6, k7]* - SU3D[I4, I5, k8]*SU3F[6, I1, k7]*SU3F[I2, k6, k8] + - (18*I)*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k6, k8] + (18*I)*SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8] - - (27*I)*SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] + (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I2, k6, k8] + (18*I)*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8] + - (18*I)*SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I5, k7]*SU3F[I2, k6, k8] - (27*I)*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8] + - 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]*SU3F[I2, k6, k9] - - 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]*SU3F[I2, k6, k9] - - 18*SU3D[6, I5, k6]*SU3D[I1, I4, k8]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9] - - 18*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9] + - 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9] - - 18*SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] - - 18*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] - - 18*SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] - - 18*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]*SU3F[I2, k6, k9] - - 36*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I3, k9]*SU3F[I2, k6, k9] - - (18*I)*SU3D[6, I5, k6]*SU3D[I3, k8, k9]*SU3F[I1, I4, k8]* - SU3F[I2, k6, k9] - (18*I)*SU3D[6, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I2, k6, k9] - (18*I)*SU3D[6, I5, k7]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k9]*SU3F[I2, k6, k9] - - (18*I)*SU3D[6, I3, k7]*SU3D[I5, k6, k7]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k9] + 9*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k9] - 36*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9] - 18*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9] - (36*I)*SU3D[6, I5, k8]*SU3D[I3, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + (36*I)*SU3D[6, I4, k8]* - SU3D[I3, I5, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] - - (36*I)*SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] + 36*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] - 36*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] + 36*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] + (9*I)*SU3D[6, I5, k8]*SU3D[I4, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k8] + (9*I)*SU3D[6, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, I5, k6]*SU3F[I2, k7, k8] + - 18*SU3D[6, I1, k7]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]*SU3F[I2, k7, k9] + - 9*SU3D[6, I5, k7]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]*SU3F[I2, k7, k9] + - 9*SU3D[6, I3, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k9]*SU3F[I2, k7, k9] + - 18*SU3D[6, I1, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9]*SU3F[I2, k7, k9] - - (18*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9] + (18*I)*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9] - (18*I)*SU3D[I3, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] - (27*I)*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k9]*SU3F[I2, k7, k9] + (27*I)*SU3D[I1, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9] - (18*I)*SU3D[I1, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I4, k9]*SU3F[I2, k7, k9] - (18*I)*SU3D[I1, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9] + (27*I)*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]* - SU3F[6, I5, k9]*SU3F[I2, k7, k9] - (27*I)*SU3D[I1, I3, k6]* - SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9] - - (18*I)*SU3D[6, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I2, k7, k9] - (18*I)*SU3D[6, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] + 18*SU3D[I5, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] + 9*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] - (9*I)*SU3D[6, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k6]*SU3F[I2, k7, k9] - - (9*I)*SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] - 9*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] - 9*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] - (18*I)*SU3D[6, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9] - (18*I)*SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] + - 9*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] + - 18*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] + - 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3F[I2, k8, k9] - - 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]*SU3F[I2, k8, k9] - - 9*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3F[I2, k8, k9] + - 18*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]*SU3F[I2, k8, k9] + - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I4, I5, k6]*SU3F[I2, k8, k9] + - 18*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]*SU3F[I2, k8, k9] + - 18*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I4, k6, k9]*SU3F[I2, k8, k9] - - 18*SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9]*SU3F[I2, k8, k9] + - 18*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I5, k6, k9]*SU3F[I2, k8, k9] - - 9*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I5, k6, k9]*SU3F[I2, k8, k9] + - (36*I)*SU3D[6, I5, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I2, k8, k9] + (18*I)*SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9] + (9*I)*SU3D[6, I5, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9] + - (9*I)*SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9] + (18*I)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I2, k8, k9] + (36*I)*SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9] + - (54*I)*SU3D[6, I5, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9] - (54*I)*SU3D[6, I4, k8]*SU3D[I3, I5, k6]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + (54*I)*SU3D[6, I3, k8]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] - - 54*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + - 54*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] - - 54*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + - 18*SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[I3, I4, k6] + - 18*SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[I3, I4, k6] + - (18*I)*SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[I3, I4, k6] + (18*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k8]*SU3F[I3, I4, k6] + (18*I)*SU3D[6, I1, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k7, k8]*SU3F[I3, I4, k6] - - 18*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]*SU3F[I3, I4, k6] - - (18*I)*SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I4, k9] + 18*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I4, k9] + 9*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3F[I3, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, k7, k8]*SU3D[I4, I5, k6]* - SU3F[I3, k6, k7] + 9*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I5, k7, k8]* - SU3F[I3, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I5, k7, k8]* - SU3F[I3, k6, k7] - 18*SU3D[6, I5, k7]*SU3D[I1, I4, k8]*SU3D[I2, k6, k7]* - SU3F[I3, k6, k8] - 18*SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I3, k6, k8] + (18*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8] + (18*I)*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8] + - (18*I)*SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I2, k7]*SU3F[I3, k6, k8] - (27*I)*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8] + - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + (18*I)*SU3D[I1, I5, k8]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k6, k8] + (18*I)*SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]* - SU3F[I3, k6, k8] - (27*I)*SU3D[I1, I4, k8]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I3, k6, k8] - 18*SU3D[6, I5, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9] - 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9] - 18*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9] + 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9] - 36*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9] - (18*I)*SU3D[6, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I1, I4, k8]*SU3F[I3, k6, k9] - - (18*I)*SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[I1, I4, k8]* - SU3F[I3, k6, k9] - (18*I)*SU3D[6, I5, k7]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9] - (18*I)*SU3D[6, I2, k7]* - SU3D[I5, k6, k7]*SU3F[I1, I4, k9]*SU3F[I3, k6, k9] + - 9*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]*SU3F[I3, k6, k9] + - 9*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I4, k9]*SU3F[I3, k6, k9] - - 36*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9] - - 18*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9] - - (36*I)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + (36*I)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - (36*I)*SU3D[6, I2, k8]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - 36*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - - 36*SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - 36*SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - - (18*I)*SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k9] + 18*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k9] - (9*I)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - (18*I)*SU3D[6, I5, k6]* - SU3D[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + - (18*I)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I4, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[I4, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + 27*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + (9*I)*SU3D[6, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k8] + - (9*I)*SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k8] + (18*I)*SU3D[6, I1, k8]*SU3D[I5, k6, k7]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k8] + (9*I)*SU3F[6, I5, k9]* - SU3F[I1, I4, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k8] + - (18*I)*SU3F[6, I4, k9]*SU3F[I1, I5, k7]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k8] + 18*SU3D[6, I1, k7]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k7, k9] + 9*SU3D[6, I5, k7]*SU3D[I1, I2, k6]*SU3D[I4, k6, k9]* - SU3F[I3, k7, k9] + 9*SU3D[6, I2, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k9]* - SU3F[I3, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9]* - SU3F[I3, k7, k9] - (18*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9] + (18*I)*SU3D[I2, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9] - - (18*I)*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] - (54*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I2, k9]*SU3F[I3, k7, k9] - (27*I)*SU3D[I1, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9] + - (27*I)*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9] + (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]* - SU3F[6, I4, k9]*SU3F[I3, k7, k9] - (18*I)*SU3D[I1, I5, k6]* - SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9] - - (18*I)*SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[6, I5, k9]*SU3F[I3, k7, k9] + (27*I)*SU3D[I1, I4, k6]* - SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9] - - (27*I)*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I3, k7, k9] - (18*I)*SU3D[6, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I3, k7, k9] - (18*I)*SU3D[6, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] + - 18*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] + - 9*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] - - (9*I)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k9] - (9*I)*SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] - 9*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] - 9*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] - (18*I)*SU3D[6, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I5, k6]*SU3F[I3, k7, k9] - - (18*I)*SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] + 9*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] + 18*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] - 18*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I3, k7, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9] + (18*I)*SU3F[6, I5, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k7, k9] - 18*SU3D[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k7, k9] + 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k8, k9] - 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k8, k9] - 9*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9] + 18*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9] + 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9] + 18*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9] + 18*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9] + 18*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9] - 9*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9] + (36*I)*SU3D[6, I5, k7]* - SU3D[I4, k7, k8]*SU3F[I1, I2, k9]*SU3F[I3, k8, k9] + - (18*I)*SU3D[6, I4, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]* - SU3F[I3, k8, k9] + (9*I)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I3, k8, k9] + (9*I)*SU3D[6, I2, k7]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9] + - (18*I)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]* - SU3F[I3, k8, k9] + (36*I)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I3, k8, k9] + (54*I)*SU3D[6, I5, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - - (54*I)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + (54*I)*SU3D[6, I2, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - 54*SU3D[I4, I5, k6]*SU3F[6, I2, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] + 54*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - 54*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - 18*SU3D[6, I5, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k8]*SU3F[I3, k8, k9] - (9*I)*SU3D[6, I5, k8]* - SU3D[I1, I4, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] - - (18*I)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + (18*I)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] - - 18*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] - - 18*SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + - 27*SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + - (9*I)*SU3F[6, I5, k9]*SU3F[I1, I4, k7]*SU3F[I2, k7, k8]* - SU3F[I3, k8, k9] + (18*I)*SU3F[6, I4, k9]*SU3F[I1, I5, k7]* - SU3F[I2, k7, k8]*SU3F[I3, k8, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9] + (18*I)*SU3F[6, I5, k7]* - SU3F[I1, I4, k8]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9] - - 18*SU3D[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9] - - 18*SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3F[I4, I5, k6] - - 18*SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k7, k9]*SU3F[I4, I5, k6] - - (18*I)*SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]* - SU3F[I4, I5, k6] - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I1, k8]*SU3F[I4, I5, k6] - (18*I)*SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k7, k8]*SU3F[I4, I5, k6] + - 18*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]*SU3F[I4, I5, k6] - - (18*I)*SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8]* - SU3F[I4, I5, k6] + 18*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k6] + (18*I)*SU3F[6, I1, k9]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k8]*SU3F[I4, I5, k7] + (18*I)*SU3F[6, I1, k9]* - SU3F[I2, k7, k8]*SU3F[I3, k8, k9]*SU3F[I4, I5, k7] - - 18*SU3D[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8] - - 18*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8] + - (18*I)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9] - 18*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9] - 18*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9] - (18*I)*SU3D[I2, k6, k7]* - SU3D[I3, I5, k8]*SU3F[6, I1, k7]*SU3F[I4, k6, k8] - - (18*I)*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k6, k8] - (18*I)*SU3D[I2, I3, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8] + - (27*I)*SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k6, k8] + (27*I)*SU3D[I1, I3, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I4, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8] + - (27*I)*SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k6, k8] + (27*I)*SU3D[I1, I2, k8]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8] + - (27*I)*SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I4, k6, k8] + (27*I)*SU3D[I1, I2, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k6, k8] + 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k6, k9] + 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9] - 27*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9] - 27*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9] + 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9] - 27*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9] - 27*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9] - 27*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9] - 27*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9] - 9*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9] - 9*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9] - 9*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9] - 9*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9] - 9*SU3D[I3, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I5, k9]*SU3F[I4, k6, k9] - 9*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I5, k9]*SU3F[I4, k6, k9] - (36*I)*SU3D[6, I5, k8]* - SU3D[I2, I3, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] - - (36*I)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9] - (36*I)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + 36*SU3D[I3, I5, k6]*SU3F[6, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + 36*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + 36*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + (9*I)*SU3D[6, I5, k7]* - SU3D[I1, I3, k6]*SU3F[I2, k7, k9]*SU3F[I4, k6, k9] + - (9*I)*SU3D[6, I3, k7]*SU3D[I1, I5, k6]*SU3F[I2, k7, k9]* - SU3F[I4, k6, k9] + (18*I)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + (18*I)*SU3D[6, I3, k8]* - SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9] + 18*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9] - 27*SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9] - 27*SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9] + (9*I)*SU3D[6, I5, k7]*SU3D[I1, I2, k6]* - SU3F[I3, k7, k9]*SU3F[I4, k6, k9] + (9*I)*SU3D[6, I2, k7]* - SU3D[I1, I5, k6]*SU3F[I3, k7, k9]*SU3F[I4, k6, k9] + - (18*I)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9] + (18*I)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - (18*I)*SU3D[6, I1, k8]* - SU3D[I2, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + - 18*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - - 27*SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - - 27*SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + - (9*I)*SU3F[6, I5, k9]*SU3F[I1, I3, k7]*SU3F[I2, k8, k9]* - SU3F[I4, k7, k8] + (9*I)*SU3F[6, I3, k9]*SU3F[I1, I5, k7]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k8] + (9*I)*SU3F[6, I5, k9]* - SU3F[I1, I2, k7]*SU3F[I3, k8, k9]*SU3F[I4, k7, k8] + - (9*I)*SU3F[6, I2, k9]*SU3F[I1, I5, k7]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k8] - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] - (18*I)*SU3D[I2, I5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9] - - (18*I)*SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I4, k7, k9] + (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] + (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]* - SU3F[I4, k7, k9] - (36*I)*SU3D[6, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9] - (36*I)*SU3D[6, I3, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9] + - 36*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9] + - 36*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9] - - (36*I)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9] - (36*I)*SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9] + 36*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9] + 36*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9] - (36*I)*SU3D[6, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I5, k6]*SU3F[I4, k7, k9] - - (36*I)*SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9] + 36*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9] + 36*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9] - 36*SU3D[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k7, k9] - 36*SU3D[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k7, k9] - 36*SU3D[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9] - 36*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9] - 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k8, k9] - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]* - SU3F[I4, k8, k9] - 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]* - SU3F[I4, k8, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]* - SU3F[I4, k8, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]* - SU3F[I4, k8, k9] + 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9]* - SU3F[I4, k8, k9] + (9*I)*SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9] + (9*I)*SU3D[6, I3, k7]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I4, k8, k9] + - (9*I)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I4, k8, k9] + (9*I)*SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I4, k8, k9] + (9*I)*SU3D[6, I3, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9] + - (9*I)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]* - SU3F[I4, k8, k9] - (54*I)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - (54*I)*SU3D[6, I3, k8]* - SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - - (54*I)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] + 54*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] + 54*SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] + 54*SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - 18*SU3D[I3, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + (36*I)*SU3F[6, I5, k9]* - SU3F[I1, I3, k7]*SU3F[I2, k7, k8]*SU3F[I4, k8, k9] + - (36*I)*SU3F[6, I3, k9]*SU3F[I1, I5, k7]*SU3F[I2, k7, k8]* - SU3F[I4, k8, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k7, k9]* - SU3F[I4, k8, k9] - 9*SU3D[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k7, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - 18*SU3D[I2, I5, k6]*SU3F[6, I1, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + (36*I)*SU3F[6, I5, k9]* - SU3F[I1, I2, k7]*SU3F[I3, k7, k8]*SU3F[I4, k8, k9] + - (36*I)*SU3F[6, I2, k9]*SU3F[I1, I5, k7]*SU3F[I3, k7, k8]* - SU3F[I4, k8, k9] - 9*SU3D[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k7, k9]* - SU3F[I4, k8, k9] - 9*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k7, k9]* - SU3F[I4, k8, k9] + 9*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3F[I5, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]* - SU3F[I5, k6, k7] + 9*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3F[I5, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3F[I5, k6, k7] - 18*SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I2, k6, k7]* - SU3F[I5, k6, k8] - 18*SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I3, k6, k7]* - SU3F[I5, k6, k8] + (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8] + (18*I)*SU3D[I2, I4, k8]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8] + - (18*I)*SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I5, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I2, k7]*SU3F[I5, k6, k8] - (27*I)*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]* - SU3F[I5, k6, k8] - (27*I)*SU3D[I1, I4, k8]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I5, k6, k8] + (36*I)*SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8] + - (18*I)*SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k6, k8] + (18*I)*SU3D[I1, I2, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I5, k6, k8] - 18*SU3D[6, I3, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k8] - 18*SU3D[6, I2, k6]*SU3F[I1, I4, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8] - 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k6, k9] + 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9] - 18*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9] + 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9] - 18*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9] - 36*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9] - 18*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9] - 36*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I3, k9]*SU3F[I5, k6, k9] - 18*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I3, k9]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I1, I4, k8]*SU3F[I5, k6, k9] - - (18*I)*SU3D[6, I2, k6]*SU3D[I3, k8, k9]*SU3F[I1, I4, k8]* - SU3F[I5, k6, k9] - (18*I)*SU3D[6, I3, k7]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k9]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I2, k7]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9] + - 9*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9] + - 9*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9] + - (36*I)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9] - (36*I)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] - (36*I)*SU3D[6, I2, k8]* - SU3D[I3, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] - - 36*SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] - - (18*I)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, I4, k9]* - SU3F[I5, k6, k9] + 18*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - (9*I)*SU3D[6, I3, k8]* - SU3D[I1, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - - (18*I)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I3, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[I3, I4, k6]*SU3F[6, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + 27*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I1, k7]* - SU3D[I2, k6, k7]*SU3F[I3, I4, k9]*SU3F[I5, k6, k9] + - 18*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I4, k9]*SU3F[I5, k6, k9] + - (18*I)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - (9*I)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I2, k6]* - SU3D[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9] + - (18*I)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - 18*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] + 27*SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - 18*SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - 18*SU3D[I2, I3, k6]*SU3F[6, I1, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + (9*I)*SU3D[6, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, I2, k6]*SU3F[I5, k7, k8] + - (9*I)*SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k8] + (18*I)*SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k8] + (18*I)*SU3F[6, I4, k9]* - SU3F[I1, I3, k7]*SU3F[I2, k8, k9]*SU3F[I5, k7, k8] + - (9*I)*SU3F[6, I3, k9]*SU3F[I1, I4, k7]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k8] + (18*I)*SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3F[I3, I4, k6]*SU3F[I5, k7, k8] - (18*I)*SU3F[6, I1, k9]* - SU3F[I2, k8, k9]*SU3F[I3, I4, k7]*SU3F[I5, k7, k8] + - (18*I)*SU3F[6, I4, k9]*SU3F[I1, I2, k7]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k8] + (9*I)*SU3F[6, I2, k9]*SU3F[I1, I4, k7]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k8] - (18*I)*SU3F[6, I1, k9]* - SU3F[I2, I4, k7]*SU3F[I3, k8, k9]*SU3F[I5, k7, k8] + - (36*I)*SU3F[6, I3, k9]*SU3F[I1, I2, k7]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k8] + (36*I)*SU3F[6, I2, k9]*SU3F[I1, I3, k7]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k8] + 18*SU3D[6, I1, k7]*SU3D[I2, k6, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k7, k9] + 9*SU3D[6, I3, k7]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k7, k9] + 9*SU3D[6, I2, k7]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k7, k9] - (18*I)*SU3D[I2, k6, k7]* - SU3D[I3, I4, k6]*SU3F[6, I1, k9]*SU3F[I5, k7, k9] - - (18*I)*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I5, k7, k9] + (18*I)*SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9] - (54*I)*SU3D[I1, k6, k7]* - SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9] + - (27*I)*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]* - SU3F[I5, k7, k9] - (27*I)*SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I5, k7, k9] - (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9] + - (27*I)*SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I5, k7, k9] - (27*I)*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k9]*SU3F[I5, k7, k9] + (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9] - - (18*I)*SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I5, k7, k9] - (18*I)*SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SU3F[6, I4, k9]*SU3F[I5, k7, k9] - (18*I)*SU3D[6, I4, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I2, k6]*SU3F[I5, k7, k9] - - (18*I)*SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9] + 9*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9] + 18*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9] - (18*I)*SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9] - (18*I)*SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9] + - 9*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9] + - 18*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9] - - (9*I)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I5, k7, k9] - (9*I)*SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9] - 9*SU3D[I3, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9] - 9*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9] - 18*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9] - 18*SU3D[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9] - 9*SU3D[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9] + (18*I)*SU3F[6, I3, k7]* - SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9] - - 18*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I4, k6]*SU3F[I5, k7, k9] + - 18*SU3D[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8]*SU3F[I5, k7, k9] - - 18*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9] - - 9*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9] + - (18*I)*SU3F[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9] + 18*SU3D[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I1, I2, k6]* - SU3F[I4, k6, k9]*SU3F[I5, k7, k9] + (9*I)*SU3D[6, I2, k7]* - SU3D[I1, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k7, k9] - - 9*SU3D[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] - - 9*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] - - 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3F[I5, k8, k9] + - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3F[I5, k8, k9] + - 18*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3F[I5, k8, k9] + - 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3F[I5, k8, k9] + - 18*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3F[I5, k8, k9] + - 18*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k6, k9]*SU3F[I5, k8, k9] + - 18*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]*SU3F[I5, k8, k9] - - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]*SU3F[I1, I2, k9]* - SU3F[I5, k8, k9] + (36*I)*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I4, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9] + - (36*I)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I5, k8, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I5, k8, k9] + (9*I)*SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9] - - (54*I)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9] + (54*I)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + (54*I)*SU3D[6, I2, k8]* - SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] - - 54*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] - - 54*SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + - 54*SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] - - 18*SU3D[6, I3, k6]*SU3F[I1, I4, k9]*SU3F[I2, k6, k8]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] - (9*I)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] - (18*I)*SU3D[6, I3, k6]* - SU3D[I1, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] - 18*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] + 27*SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] - 18*SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] + (18*I)*SU3F[6, I4, k9]*SU3F[I1, I3, k7]* - SU3F[I2, k7, k8]*SU3F[I5, k8, k9] + (9*I)*SU3F[6, I3, k9]* - SU3F[I1, I4, k7]*SU3F[I2, k7, k8]*SU3F[I5, k8, k9] - - 18*SU3D[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k7, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k7, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3F[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k7, k9]* - SU3F[I5, k8, k9] - (18*I)*SU3F[6, I1, k9]*SU3F[I2, k7, k8]* - SU3F[I3, I4, k7]*SU3F[I5, k8, k9] + 18*SU3D[6, I1, k7]*SU3F[I2, k7, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k8, k9] - 18*SU3D[6, I2, k6]*SU3F[I1, I4, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I4, k8]* - SU3D[I1, I2, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - - (9*I)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9] - (18*I)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I2, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - - 18*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + - 27*SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] - - 18*SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3F[6, I4, k9]*SU3F[I1, I2, k7]*SU3F[I3, k7, k8]* - SU3F[I5, k8, k9] + (9*I)*SU3F[6, I2, k9]*SU3F[I1, I4, k7]* - SU3F[I3, k7, k8]*SU3F[I5, k8, k9] - (18*I)*SU3F[6, I1, k9]* - SU3F[I2, I4, k7]*SU3F[I3, k7, k8]*SU3F[I5, k8, k9] - - 18*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3F[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k7, k9]* - SU3F[I5, k8, k9] + 18*SU3D[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k7, k9]* - SU3F[I5, k8, k9] + (18*I)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + (18*I)*SU3D[6, I2, k8]* - SU3D[I1, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9] - - (18*I)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9] + 18*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9] - 27*SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9] - 27*SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9] + (9*I)*SU3F[6, I3, k9]*SU3F[I1, I2, k7]* - SU3F[I4, k7, k8]*SU3F[I5, k8, k9] + (9*I)*SU3F[6, I2, k9]* - SU3F[I1, I3, k7]*SU3F[I4, k7, k8]*SU3F[I5, k8, k9] - - 36*SU3D[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] - - 36*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] + - (24*I)*SU3D[I2, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I1] + - (24*I)*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I1] + - (24*I)*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - 48*SU3D[I3, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I1] + - 48*SU3D[I2, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I1] - - 48*SU3D[I2, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I1] + - (30*I)*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2] - - (96*I)*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - (30*I)*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - 30*SU3D[I4, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I2] + - 30*SU3D[I3, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I2] - - 18*SU3D[I1, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I2] + - (18*I)*SU3F[I1, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I2] + - 18*SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2] - - (18*I)*SU3F[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2] + - (30*I)*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3] - - (96*I)*SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3] + - (30*I)*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - 30*SU3D[I4, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I3] + - 30*SU3D[I2, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I3] - - 18*SU3D[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3] + - (18*I)*SU3F[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3] + - 18*SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3] - - (18*I)*SU3F[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3] + - (12*I)*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4] + - (12*I)*SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4] + - (12*I)*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4] - - 84*SU3D[I3, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I4] - - 84*SU3D[I2, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I4] - - 84*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I4] - - (96*I)*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5] + - (30*I)*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5] + - (30*I)*SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - 30*SU3D[I3, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I5] + - 30*SU3D[I2, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I5] - - 18*SU3D[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5] + - (18*I)*SU3F[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5] - - 18*SU3D[I1, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I5] + - (18*I)*SU3F[I1, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I5] + - (18*I)*SU3D[6, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[I1, I2] + - (24*I)*SU3D[6, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[I1, I2] + - (18*I)*SU3D[6, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[I1, I2] - - 18*SU3D[I4, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I2] - - 24*SU3D[I3, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I2] - - 18*SU3D[I3, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I2] - - 18*SU3D[6, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I2] - - (18*I)*SU3F[6, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I2] + - 18*SU3D[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2] + - (18*I)*SU3F[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2] + - (18*I)*SU3D[6, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[I1, I3] + - (24*I)*SU3D[6, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[I1, I3] + - (18*I)*SU3D[6, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[I1, I3] - - 18*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3] - - 24*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3] - - 18*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3] - - 18*SU3D[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3] - - (18*I)*SU3F[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3] + - 18*SU3D[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3] + - (18*I)*SU3F[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3] + - (24*I)*SU3D[6, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[I1, I5] + - (18*I)*SU3D[6, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[I1, I5] + - (18*I)*SU3D[6, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[I1, I5] - - 18*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5] - - 18*SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5] - - 24*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5] - - 18*SU3D[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5] - - (18*I)*SU3F[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5] - - 18*SU3D[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5] - - (18*I)*SU3F[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5] - - (60*I)*SU3D[6, I5, k6]*SU3D[I1, I4, k6]*SUNDelta[I2, I3] - - (12*I)*SU3D[6, I4, k6]*SU3D[I1, I5, k6]*SUNDelta[I2, I3] + - 12*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3] + - 60*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3] - - 12*SU3D[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3] - - (12*I)*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3] - - 60*SU3D[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3] - - (60*I)*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3] - - 24*SU3D[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3] - - (24*I)*SU3F[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3] - - (64*I)*SUNDelta[6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - (8*I)*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - (12*I)*SU3D[6, I5, k6]*SU3D[I1, I3, k6]*SUNDelta[I2, I4] + - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I5, k6]*SUNDelta[I2, I4] + - (24*I)*SU3D[6, I1, k6]*SU3D[I3, I5, k6]*SUNDelta[I2, I4] - - 24*SU3D[I3, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I4] - - 12*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4] - - 12*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4] + - 60*SU3D[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4] + - (60*I)*SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4] + - 60*SU3D[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4] + - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4] + - (20*I)*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - (20*I)*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4] - - (12*I)*SU3D[6, I4, k6]*SU3D[I1, I3, k6]*SUNDelta[I2, I5] - - (60*I)*SU3D[6, I3, k6]*SU3D[I1, I4, k6]*SUNDelta[I2, I5] + - 60*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5] + - 12*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5] - - 60*SU3D[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5] - - (60*I)*SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5] - - 12*SU3D[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5] - - (12*I)*SU3F[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5] + - 24*SU3D[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5] + - (24*I)*SU3F[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5] + - (8*I)*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5] - - (64*I)*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - (12*I)*SU3D[6, I5, k6]*SU3D[I1, I2, k6]*SUNDelta[I3, I4] + - (12*I)*SU3D[6, I2, k6]*SU3D[I1, I5, k6]*SUNDelta[I3, I4] + - (24*I)*SU3D[6, I1, k6]*SU3D[I2, I5, k6]*SUNDelta[I3, I4] - - 24*SU3D[I2, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I4] - - 12*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4] - - 12*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4] + - 60*SU3D[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4] + - (60*I)*SU3F[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4] + - 60*SU3D[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4] + - (60*I)*SU3F[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4] + - (20*I)*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - (20*I)*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4] - - (12*I)*SU3D[6, I4, k6]*SU3D[I1, I2, k6]*SUNDelta[I3, I5] - - (60*I)*SU3D[6, I2, k6]*SU3D[I1, I4, k6]*SUNDelta[I3, I5] + - 60*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5] + - 12*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5] - - 60*SU3D[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5] - - (60*I)*SU3F[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5] - - 12*SU3D[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5] - - (12*I)*SU3F[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5] + - 24*SU3D[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5] + - (24*I)*SU3F[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5] + - (8*I)*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5] - - (64*I)*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I2, k6]*SUNDelta[I4, I5] + - (12*I)*SU3D[6, I2, k6]*SU3D[I1, I3, k6]*SUNDelta[I4, I5] + - (24*I)*SU3D[6, I1, k6]*SU3D[I2, I3, k6]*SUNDelta[I4, I5] - - 24*SU3D[I2, I3, k5]*SU3F[6, I1, k5]*SUNDelta[I4, I5] - - 12*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5] - - 12*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5] + - 60*SU3D[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5] + - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5] + - 60*SU3D[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5] + - (60*I)*SU3F[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5] + - (20*I)*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - (20*I)*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ -(108*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*((-48*I)*SU3D[6, I4, I5]*SU3D[I1, I2, I3] - - (48*I)*SU3D[6, I3, I5]*SU3D[I1, I2, I4] + (72*I)*SU3D[6, I3, I4]* - SU3D[I1, I2, I5] - (48*I)*SU3D[6, I2, I5]*SU3D[I1, I3, I4] + - (72*I)*SU3D[6, I2, I4]*SU3D[I1, I3, I5] + (72*I)*SU3D[6, I2, I3]* - SU3D[I1, I4, I5] + (108*I)*SU3D[6, I1, I5]*SU3D[I2, I3, I4] - - (60*I)*SU3D[6, I1, I4]*SU3D[I2, I3, I5] - (60*I)*SU3D[6, I1, I3]* - SU3D[I2, I4, I5] - (60*I)*SU3D[6, I1, I2]*SU3D[I3, I4, I5] - - (54*I)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k9] + (36*I)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3D[I3, I4, k9] + (54*I)*SU3D[6, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9] - - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k9] - (27*I)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3D[I3, k6, k9] - (54*I)*SU3D[6, I5, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8] + - (54*I)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]* - SU3D[I3, k7, k8] + (18*I)*SU3D[6, I5, k7]*SU3D[I1, I4, k9]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8] + (36*I)*SU3D[6, I5, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9] - - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]* - SU3D[I3, k8, k9] - (27*I)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3D[I3, k8, k9] + (18*I)*SU3D[6, I5, k7]* - SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k9]* - SU3D[I4, I5, k8] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, k8, k9]*SU3D[I4, I5, k8] + (54*I)*SU3D[6, I3, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I4, I5, k9] - - (36*I)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k9] + (54*I)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, I5, k9] - (36*I)*SU3D[6, I2, k7]* - SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9] - - (27*I)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k9] - (27*I)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3D[I4, k6, k9] - (54*I)*SU3D[6, I5, k7]* - SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8] + - (54*I)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]* - SU3D[I4, k7, k8] + (18*I)*SU3D[6, I5, k7]*SU3D[I1, I3, k9]* - SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + (54*I)*SU3D[6, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8] + - (18*I)*SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k8]*SU3D[I4, k7, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I5, k8]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9] + - (36*I)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]* - SU3D[I4, k8, k9] - (36*I)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, I5, k9]*SU3D[I4, k8, k9] - (27*I)*SU3D[6, I3, k8]* - SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I4, k8, k9] + - (18*I)*SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, I5, k8]*SU3D[I4, k8, k9] - (36*I)*SU3D[6, I2, k7]* - SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9] - - (27*I)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]* - SU3D[I4, k8, k9] + (18*I)*SU3D[6, I5, k7]*SU3D[I1, I2, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I5, k8]*SU3D[I3, k7, k9]*SU3D[I4, k8, k9] - - (54*I)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]* - SU3D[I5, k7, k8] - (54*I)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k9]*SU3D[I5, k7, k8] - (54*I)*SU3D[6, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8] + - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]* - SU3D[I5, k7, k8] + (18*I)*SU3D[6, I1, k7]*SU3D[I2, I4, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8] - - (36*I)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]* - SU3D[I5, k8, k9] - (36*I)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, I4, k9]*SU3D[I5, k8, k9] + (27*I)*SU3D[6, I4, k7]* - SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9] + - (27*I)*SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9] - (36*I)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, I4, k9]*SU3D[I5, k8, k9] - (18*I)*SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9] + - (27*I)*SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9] + (27*I)*SU3D[6, I2, k7]*SU3D[I1, I4, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k8, k9] - (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + - (27*I)*SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9] + (27*I)*SU3D[6, I2, k7]*SU3D[I1, I3, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9] - (18*I)*SU3D[6, I1, k7]* - SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] - - 84*SU3D[I3, I4, I5]*SU3F[6, I1, I2] - 84*SU3D[I2, I4, I5]* - SU3F[6, I1, I3] - 84*SU3D[I2, I3, I5]*SU3F[6, I1, I4] + - 36*SU3D[I2, I3, I4]*SU3F[6, I1, I5] - 18*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I1, k7] - - 18*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] + - 18*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] - - 18*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[6, I1, k7] + - 24*SU3D[I1, I3, I4]*SU3F[6, I2, I5] + 36*SU3D[I1, k7, k8]* - SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I2, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I2, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I2, k7] + - 27*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I2, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7] + - 27*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I2, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] - - 27*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] - - 27*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I2, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I2, k7] + - 24*SU3D[I1, I2, I4]*SU3F[6, I3, I5] + 36*SU3D[I1, k7, k8]* - SU3D[I2, k6, k8]*SU3D[I4, I5, k6]*SU3F[6, I3, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I4, I5, k6]*SU3F[6, I3, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k8]*SU3F[6, I3, k7] + - 27*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I3, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7] + - 27*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I3, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k8]*SU3F[6, I3, k7] - - 27*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I3, k7] - - 27*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I3, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I5, k7, k8]*SU3F[6, I3, k7] + - 24*SU3D[I1, I2, I3]*SU3F[6, I4, I5] + 36*SU3D[I1, k7, k8]* - SU3D[I2, k6, k8]*SU3D[I3, I5, k6]*SU3F[6, I4, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3F[6, I4, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3F[6, I4, k7] + - 27*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k8]*SU3F[6, I4, k7] - - 54*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7] + - 27*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3F[6, I4, k7] + - 36*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k8]*SU3F[6, I4, k7] - - 27*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I4, k7] - - 27*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[6, I4, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I5, k7, k8]*SU3F[6, I4, k7] - - 36*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]*SU3F[6, I5, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3F[6, I5, k7] - - 36*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3F[6, I5, k7] - - 18*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k8]*SU3F[6, I5, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3F[6, I5, k7] - - 18*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3F[6, I5, k7] - - 36*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3F[6, I5, k7] - - 18*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I5, k7] - - 18*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[6, I5, k7] + - 54*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3F[6, I5, k7] - - 18*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I5, k7] - - 18*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[6, I5, k7] - - 24*SU3D[6, I3, I4]*SU3F[I1, I2, I5] + 9*SU3D[6, I4, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6] + 9*SU3D[6, I3, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6] - (9*I)*SU3D[I4, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I2, k6] - - (36*I)*SU3D[I4, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[I1, I2, k6] - (9*I)*SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[I1, I2, k6] - (36*I)*SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I2, k6] - - (18*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]* - SU3F[I1, I2, k6] - (18*I)*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]* - SU3F[6, I5, k8]*SU3F[I1, I2, k6] - 18*SU3D[6, I5, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I2, k9] - 18*SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I2, k9] - 36*SU3D[6, I4, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9] - 36*SU3D[6, I3, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9] - 18*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9] - 18*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9] - 24*SU3D[6, I2, I4]* - SU3F[I1, I3, I5] + 9*SU3D[6, I4, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6] + 9*SU3D[6, I2, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6] - (9*I)*SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6] - (36*I)*SU3D[I4, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I3, k6] - - (9*I)*SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[I1, I3, k6] - (36*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k8]*SU3F[I1, I3, k6] - (18*I)*SU3D[I2, k7, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6] - - (18*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]* - SU3F[I1, I3, k6] - 18*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9] - 18*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k9] - 36*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9] - 36*SU3D[6, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9] - 18*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]* - SU3F[I1, I3, k9] - 18*SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[I1, I3, k9] - 24*SU3D[6, I2, I3]*SU3F[I1, I4, I5] + - 9*SU3D[6, I3, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6] + - 9*SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6] - - (9*I)*SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[I1, I4, k6] - (36*I)*SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6] - (9*I)*SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I4, k6] - - (36*I)*SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[I1, I4, k6] - (18*I)*SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k8]*SU3F[I1, I4, k6] - (18*I)*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6] - - 18*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9] - - 18*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3F[I1, I4, k9] - - 36*SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9] - - 36*SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9] - - 18*SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]*SU3F[I1, I4, k9] - - 18*SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]*SU3F[I1, I4, k9] + - 9*SU3D[6, I4, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3F[I1, I5, k6] + - 9*SU3D[6, I4, k9]*SU3D[I2, k6, k7]*SU3D[I3, k7, k9]*SU3F[I1, I5, k6] + - 9*SU3D[6, I3, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6] + - 9*SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6] + - 9*SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[I1, I5, k6] + - 9*SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I1, I5, k6] + - (9*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k8]* - SU3F[I1, I5, k6] + (9*I)*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6] + (9*I)*SU3D[I2, k7, k8]* - SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I5, k6] + - (9*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]* - SU3F[I1, I5, k6] + (9*I)*SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k8]*SU3F[I1, I5, k6] + (9*I)*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I5, k6] + - (54*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - (54*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8] + - (54*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] + (54*I)*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8] - - (54*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I1, k6, k8] - (54*I)*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8] + - 54*SU3D[6, I5, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9] - - 54*SU3D[6, I4, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9] + - 54*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I3, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9] - - 54*SU3D[6, I2, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9] + - 54*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] - - 54*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - 54*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - (36*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I3, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9] + - (36*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I4, k9]*SU3F[I1, k7, k9] + (36*I)*SU3D[I2, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9] - - (36*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9] - (36*I)*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]* - SU3F[6, I5, k9]*SU3F[I1, k7, k9] - (36*I)*SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9] + - 36*SU3D[6, I5, k8]*SU3D[I2, k6, k9]*SU3D[I3, I4, k6]*SU3F[I1, k8, k9] - - 36*SU3D[6, I4, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]*SU3F[I1, k8, k9] + - 36*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9] - - 36*SU3D[6, I2, k8]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9] + - 36*SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] - - 36*SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9]*SU3F[I1, k8, k9] + - 18*SU3D[6, I1, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I2, I5, k6] + - 18*SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I2, I5, k6] + - (18*I)*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k8]* - SU3F[I2, I5, k6] + (18*I)*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k8]*SU3F[I2, I5, k6] + 9*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k7, k8]*SU3F[I2, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k7] + 9*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k7, k8]*SU3F[I2, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[I2, k6, k7] - 18*SU3D[6, I4, k7]*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k8] - 18*SU3D[6, I3, k7]*SU3D[I1, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8] + (18*I)*SU3D[I3, k6, k7]* - SU3D[I4, I5, k8]*SU3F[6, I1, k7]*SU3F[I2, k6, k8] + - (18*I)*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k6, k8] + (18*I)*SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8] - - (27*I)*SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I2, k6, k8] - (27*I)*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8] + - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I2, k6, k8] + (18*I)*SU3D[I1, I4, k8]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k6, k8] + (18*I)*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8] - - 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]*SU3F[I2, k6, k9] + - 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]*SU3F[I2, k6, k9] - - 18*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9] - - 18*SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9] + - 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9] - - 18*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] - - 18*SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] - - 18*SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] - - 36*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]*SU3F[I2, k6, k9] - - 18*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I3, k9]*SU3F[I2, k6, k9] - - 36*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]*SU3F[I2, k6, k9] - - 18*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I4, k9]*SU3F[I2, k6, k9] - - (18*I)*SU3D[6, I4, k6]*SU3D[I3, k8, k9]*SU3F[I1, I5, k8]* - SU3F[I2, k6, k9] - (18*I)*SU3D[6, I3, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I2, k6, k9] - (18*I)*SU3D[6, I4, k7]* - SU3D[I3, k6, k7]*SU3F[I1, I5, k9]*SU3F[I2, k6, k9] - - (18*I)*SU3D[6, I3, k7]*SU3D[I4, k6, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9] + 9*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9] + 9*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9] + (36*I)*SU3D[6, I5, k8]*SU3D[I3, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9] - (36*I)*SU3D[6, I4, k8]* - SU3D[I3, I5, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] - - (36*I)*SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] + 36*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] + 36*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] - 36*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9] + (9*I)*SU3D[6, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k8] + (9*I)*SU3D[6, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I1, I4, k6]*SU3F[I2, k7, k8] + - 18*SU3D[6, I1, k7]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]*SU3F[I2, k7, k9] + - 18*SU3D[6, I1, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9]*SU3F[I2, k7, k9] + - 9*SU3D[6, I4, k7]*SU3D[I1, I3, k6]*SU3D[I5, k6, k9]*SU3F[I2, k7, k9] + - 9*SU3D[6, I3, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k9]*SU3F[I2, k7, k9] - - (18*I)*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9] - (18*I)*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9] + (18*I)*SU3D[I3, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] + (27*I)*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k9]*SU3F[I2, k7, k9] - (27*I)*SU3D[I1, I4, k6]* - SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9] + (27*I)*SU3D[I1, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I4, k9]*SU3F[I2, k7, k9] - (27*I)*SU3D[I1, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9] - (18*I)*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]* - SU3F[6, I5, k9]*SU3F[I2, k7, k9] - (18*I)*SU3D[I1, I3, k6]* - SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9] - - (18*I)*SU3D[6, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I2, k7, k9] - (18*I)*SU3D[6, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9] - (18*I)*SU3D[6, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k6]*SU3F[I2, k7, k9] - - (18*I)*SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] + 18*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9] - (9*I)*SU3D[6, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9] - (9*I)*SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] - - 9*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] - - 9*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I5, k6]*SU3F[I2, k7, k9] - - 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3F[I2, k8, k9] + - 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]*SU3F[I2, k8, k9] + - 18*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3F[I2, k8, k9] - - 9*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]*SU3F[I2, k8, k9] + - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I4, I5, k6]*SU3F[I2, k8, k9] + - 18*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]*SU3F[I2, k8, k9] - - 9*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I4, k6, k9]*SU3F[I2, k8, k9] + - 18*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I5, k6, k9]*SU3F[I2, k8, k9] + - 18*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I5, k6, k9]*SU3F[I2, k8, k9] - - 18*SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9]*SU3F[I2, k8, k9] + - (18*I)*SU3D[6, I5, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I2, k8, k9] + (36*I)*SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9] + (18*I)*SU3D[6, I5, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9] + - (36*I)*SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9] + (9*I)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I2, k8, k9] + (9*I)*SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9] - - (54*I)*SU3D[6, I5, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9] + (54*I)*SU3D[6, I4, k8]*SU3D[I3, I5, k6]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + (54*I)*SU3D[6, I3, k8]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] - - 54*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] - - 54*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + - 54*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9] + - 18*SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[I3, I5, k6] + - 18*SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[I3, I5, k6] + - (18*I)*SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k8]* - SU3F[I3, I5, k6] + (18*I)*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k8]*SU3F[I3, I5, k6] + (18*I)*SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k7, k8]*SU3F[I3, I5, k6] - - 18*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]*SU3F[I3, I5, k6] - - (18*I)*SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I5, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I5, k9] + 9*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3F[I3, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, k7, k8]*SU3D[I4, I5, k6]* - SU3F[I3, k6, k7] + 9*SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I4, k7, k8]* - SU3F[I3, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I4, k7, k8]* - SU3F[I3, k6, k7] - 18*SU3D[6, I4, k7]*SU3D[I1, I5, k8]*SU3D[I2, k6, k7]* - SU3F[I3, k6, k8] - 18*SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I4, k6, k7]* - SU3F[I3, k6, k8] + (18*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8] + (18*I)*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8] + - (18*I)*SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I2, k7]*SU3F[I3, k6, k8] - (27*I)*SU3D[I1, I5, k8]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] - (27*I)*SU3D[I1, I5, k8]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k6, k8] + (36*I)*SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8] + - (18*I)*SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k6, k8] + (18*I)*SU3D[I1, I2, k8]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I3, k6, k8] - 18*SU3D[6, I4, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k8] - 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9] + 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9] - 18*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9] + 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9] - 18*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9] - 36*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9] - 18*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9] - 36*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9] - 18*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9] - (18*I)*SU3D[6, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I1, I5, k8]*SU3F[I3, k6, k9] - - (18*I)*SU3D[6, I2, k6]*SU3D[I4, k8, k9]*SU3F[I1, I5, k8]* - SU3F[I3, k6, k9] - (18*I)*SU3D[6, I4, k7]*SU3D[I2, k6, k7]* - SU3F[I1, I5, k9]*SU3F[I3, k6, k9] - (18*I)*SU3D[6, I2, k7]* - SU3D[I4, k6, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9] + - 9*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9] + - 9*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9] + - (36*I)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] - (36*I)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - (36*I)*SU3D[6, I2, k8]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - 36*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - 36*SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - - 36*SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] - - (18*I)*SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9] + 18*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9] + (18*I)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - (9*I)*SU3D[6, I4, k8]* - SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - - (18*I)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I4, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[I4, I5, k6]*SU3F[6, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + 27*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] - 18*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + (9*I)*SU3D[6, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k8] + - (9*I)*SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k8] + (18*I)*SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k8] + (18*I)*SU3F[6, I5, k9]* - SU3F[I1, I4, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k8] + - (9*I)*SU3F[6, I4, k9]*SU3F[I1, I5, k7]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k8] + 18*SU3D[6, I1, k7]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k7, k9] + 18*SU3D[6, I1, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k9]* - SU3F[I3, k7, k9] + 9*SU3D[6, I4, k7]*SU3D[I1, I2, k6]*SU3D[I5, k6, k9]* - SU3F[I3, k7, k9] + 9*SU3D[6, I2, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k9]* - SU3F[I3, k7, k9] - (18*I)*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9] - (18*I)*SU3D[I2, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9] + - (18*I)*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] - (54*I)*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I2, k9]*SU3F[I3, k7, k9] + (27*I)*SU3D[I1, I5, k6]* - SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9] - - (27*I)*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9] - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]* - SU3F[6, I4, k9]*SU3F[I3, k7, k9] + (27*I)*SU3D[I1, I5, k6]* - SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9] - - (27*I)*SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[6, I5, k9]*SU3F[I3, k7, k9] - (18*I)*SU3D[I1, I4, k6]* - SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9] - - (18*I)*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I3, k7, k9] - (18*I)*SU3D[6, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I3, k7, k9] - (18*I)*SU3D[6, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] + - 9*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] + - 18*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9] - - (18*I)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k9] - (18*I)*SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] + 18*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9] - (9*I)*SU3D[6, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I5, k6]*SU3F[I3, k7, k9] - - (9*I)*SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] - 9*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] - 9*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9] - 18*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]* - SU3F[I3, k7, k9] - 18*SU3D[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9] - 9*SU3D[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9] + (18*I)*SU3F[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k7, k9] - 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k8, k9] + 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k8, k9] + 18*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9] - 9*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9] + 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9] + 18*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9] - 9*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9] + 18*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9] + 18*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9] + (18*I)*SU3D[6, I5, k7]* - SU3D[I4, k7, k8]*SU3F[I1, I2, k9]*SU3F[I3, k8, k9] + - (36*I)*SU3D[6, I4, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]* - SU3F[I3, k8, k9] + (18*I)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I3, k8, k9] + (36*I)*SU3D[6, I2, k7]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9] + - (9*I)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]* - SU3F[I3, k8, k9] + (9*I)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I3, k8, k9] - (54*I)*SU3D[6, I5, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9] + - (54*I)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + (54*I)*SU3D[6, I2, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - 54*SU3D[I4, I5, k6]*SU3F[6, I2, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - 54*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] + 54*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9] - 18*SU3D[6, I4, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k8]*SU3F[I3, k8, k9] + (18*I)*SU3D[6, I5, k8]* - SU3D[I1, I4, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] - - (9*I)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] - (18*I)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] - - 18*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + - 27*SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] - - 18*SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + - (18*I)*SU3F[6, I5, k9]*SU3F[I1, I4, k7]*SU3F[I2, k7, k8]* - SU3F[I3, k8, k9] + (9*I)*SU3F[6, I4, k9]*SU3F[I1, I5, k7]* - SU3F[I2, k7, k8]*SU3F[I3, k8, k9] - 18*SU3D[6, I5, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9] - 9*SU3D[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9] + (18*I)*SU3F[6, I4, k7]* - SU3F[I1, I5, k8]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9] + - 18*SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3F[I4, I5, k6] + - 18*SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k7, k9]*SU3F[I4, I5, k6] + - (18*I)*SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]* - SU3F[I4, I5, k6] + (18*I)*SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I1, k8]*SU3F[I4, I5, k6] + (18*I)*SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k7, k8]*SU3F[I4, I5, k6] - - 18*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]*SU3F[I4, I5, k6] + - (18*I)*SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8]* - SU3F[I4, I5, k6] - 18*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k6] - (18*I)*SU3F[6, I1, k9]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k8]*SU3F[I4, I5, k7] - (18*I)*SU3F[6, I1, k9]* - SU3F[I2, k7, k8]*SU3F[I3, k8, k9]*SU3F[I4, I5, k7] + - 18*SU3D[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8] + - 18*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8] - - (18*I)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9] + 18*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9] - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9] + 18*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9] + 9*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k7, k8]*SU3F[I4, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k7] + 9*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] - 18*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] - 18*SU3D[6, I3, k7]*SU3D[I1, I5, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k8] - 18*SU3D[6, I2, k7]*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k8] + (18*I)*SU3D[I2, k6, k7]* - SU3D[I3, I5, k8]*SU3F[6, I1, k7]*SU3F[I4, k6, k8] + - (18*I)*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k6, k8] + (18*I)*SU3D[I2, I3, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] - (36*I)*SU3D[I1, k6, k7]* - SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8] - - (27*I)*SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k6, k8] - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] - (27*I)*SU3D[I1, I5, k8]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8] + - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]* - SU3F[I4, k6, k8] + (18*I)*SU3D[I1, I3, k8]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k6, k8] + (18*I)*SU3D[I1, I2, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8] - - 18*SU3D[6, I3, k6]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9]*SU3F[I4, k6, k8] - - 18*SU3D[6, I2, k6]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9]*SU3F[I4, k6, k8] - - 36*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]*SU3F[I4, k6, k9] + - 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I5, k6]*SU3F[I4, k6, k9] - - 18*SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3F[I4, k6, k9] - - 18*SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3D[I2, k8, k9]*SU3F[I4, k6, k9] + - 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]*SU3F[I4, k6, k9] - - 18*SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3F[I4, k6, k9] - - 18*SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3D[I3, k8, k9]*SU3F[I4, k6, k9] - - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I5, k8, k9]*SU3F[I4, k6, k9] - - 36*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I2, k9]*SU3F[I4, k6, k9] - - 36*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I3, k6]*SU3D[I2, k8, k9]*SU3F[I1, I5, k8]* - SU3F[I4, k6, k9] - (18*I)*SU3D[6, I2, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I4, k6, k9] - (18*I)*SU3D[6, I3, k7]* - SU3D[I2, k6, k7]*SU3F[I1, I5, k9]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I2, k7]*SU3D[I3, k6, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9] + 9*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9] + 9*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9] + (36*I)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] - (36*I)*SU3D[6, I3, k8]* - SU3D[I2, I5, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] - - (36*I)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9] + 36*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9] + 36*SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9] - 36*SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9] - (18*I)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]* - SU3F[I2, I5, k9]*SU3F[I4, k6, k9] + 18*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, I5, k9]*SU3F[I4, k6, k9] + (18*I)*SU3D[6, I5, k8]* - SU3D[I1, I3, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - - (9*I)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9] - (18*I)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I3, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + - 27*SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - - 18*SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]*SU3F[I3, I5, k9]* - SU3F[I4, k6, k9] + 18*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I5, k9]* - SU3F[I4, k6, k9] + (18*I)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - (9*I)*SU3D[6, I2, k8]* - SU3D[I1, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - - (18*I)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[I2, I5, k6]*SU3F[6, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + 27*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] - 18*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + (9*I)*SU3D[6, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I4, k7, k8] + - (9*I)*SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k8] + (18*I)*SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k8] + (18*I)*SU3F[6, I5, k9]* - SU3F[I1, I3, k7]*SU3F[I2, k8, k9]*SU3F[I4, k7, k8] + - (9*I)*SU3F[6, I3, k9]*SU3F[I1, I5, k7]*SU3F[I2, k8, k9]* - SU3F[I4, k7, k8] + (18*I)*SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3F[I3, I5, k6]*SU3F[I4, k7, k8] - (18*I)*SU3F[6, I1, k9]* - SU3F[I2, k8, k9]*SU3F[I3, I5, k7]*SU3F[I4, k7, k8] + - (18*I)*SU3F[6, I5, k9]*SU3F[I1, I2, k7]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k8] + (9*I)*SU3F[6, I2, k9]*SU3F[I1, I5, k7]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k8] - (18*I)*SU3F[6, I1, k9]* - SU3F[I2, I5, k7]*SU3F[I3, k8, k9]*SU3F[I4, k7, k8] + - 18*SU3D[6, I1, k7]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]*SU3F[I4, k7, k9] + - 18*SU3D[6, I1, k7]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3F[I4, k7, k9] + - 9*SU3D[6, I3, k7]*SU3D[I1, I2, k6]*SU3D[I5, k6, k9]*SU3F[I4, k7, k9] + - 9*SU3D[6, I2, k7]*SU3D[I1, I3, k6]*SU3D[I5, k6, k9]*SU3F[I4, k7, k9] - - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I1, k9]* - SU3F[I4, k7, k9] - (18*I)*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] + (18*I)*SU3D[I2, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]* - SU3F[I4, k7, k9] + (27*I)*SU3D[I1, I5, k6]*SU3D[I3, k6, k7]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] - (27*I)*SU3D[I1, I3, k6]* - SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9] - - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]* - SU3F[I4, k7, k9] + (27*I)*SU3D[I1, I5, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] - (27*I)*SU3D[I1, I2, k6]* - SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]* - SU3F[I4, k7, k9] - (18*I)*SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[6, I5, k9]*SU3F[I4, k7, k9] - (18*I)*SU3D[I1, I2, k6]* - SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9] - - (18*I)*SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3F[I1, I2, k6]* - SU3F[I4, k7, k9] - (18*I)*SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9] + 18*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9] - (18*I)*SU3D[6, I5, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I3, k6]*SU3F[I4, k7, k9] - - (18*I)*SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9] + 9*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9] + 18*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9] - (9*I)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9] - (9*I)*SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I5, k6]*SU3F[I4, k7, k9] - - 9*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]*SU3F[I4, k7, k9] - - 9*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]*SU3F[I4, k7, k9] - - 18*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]*SU3F[I4, k7, k9] - - 18*SU3D[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9] - - 9*SU3D[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9] + - (18*I)*SU3F[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k7, k9] - 18*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I5, k6]* - SU3F[I4, k7, k9] + 18*SU3D[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8]* - SU3F[I4, k7, k9] - 18*SU3D[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9] - 9*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9] + (18*I)*SU3F[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9] + 18*SU3D[6, I1, k7]*SU3F[I2, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9] - 54*SU3D[6, I5, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k8, k9] + 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k8, k9] + 18*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9] - 9*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9] + 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k8, k9] + 18*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9] - 9*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9] + 18*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9] + 18*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9] - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9] + (18*I)*SU3D[6, I5, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I2, k9]*SU3F[I4, k8, k9] + - (36*I)*SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I4, k8, k9] + (36*I)*SU3D[6, I2, k7]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9] + - (9*I)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]* - SU3F[I4, k8, k9] + (9*I)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I4, k8, k9] - (54*I)*SU3D[6, I5, k8]* - SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + - (54*I)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9] + (54*I)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - 54*SU3D[I3, I5, k6]*SU3F[6, I2, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - 54*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + 54*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] - 18*SU3D[6, I3, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9] + (18*I)*SU3D[6, I5, k8]* - SU3D[I1, I3, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - - (9*I)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9] - (18*I)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + (18*I)*SU3D[6, I1, k6]* - SU3D[I3, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - - 18*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + - 27*SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] - - 18*SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + - (18*I)*SU3F[6, I5, k9]*SU3F[I1, I3, k7]*SU3F[I2, k7, k8]* - SU3F[I4, k8, k9] + (9*I)*SU3F[6, I3, k9]*SU3F[I1, I5, k7]* - SU3F[I2, k7, k8]*SU3F[I4, k8, k9] - 18*SU3D[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9] - 9*SU3D[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9] + (18*I)*SU3F[6, I3, k7]* - SU3F[I1, I5, k8]*SU3F[I2, k7, k9]*SU3F[I4, k8, k9] - - (18*I)*SU3F[6, I1, k9]*SU3F[I2, k7, k8]*SU3F[I3, I5, k7]* - SU3F[I4, k8, k9] + 18*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8]* - SU3F[I4, k8, k9] - 18*SU3D[6, I2, k6]*SU3F[I1, I5, k9]*SU3F[I3, k6, k8]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - (9*I)*SU3D[6, I2, k8]* - SU3D[I1, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - - (18*I)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9] + (18*I)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - 18*SU3D[I2, I5, k6]*SU3F[6, I1, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + 27*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] - 18*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + (18*I)*SU3F[6, I5, k9]* - SU3F[I1, I2, k7]*SU3F[I3, k7, k8]*SU3F[I4, k8, k9] + - (9*I)*SU3F[6, I2, k9]*SU3F[I1, I5, k7]*SU3F[I3, k7, k8]* - SU3F[I4, k8, k9] - (18*I)*SU3F[6, I1, k9]*SU3F[I2, I5, k7]* - SU3F[I3, k7, k8]*SU3F[I4, k8, k9] - 18*SU3D[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9] - 9*SU3D[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9] + (18*I)*SU3F[6, I2, k7]* - SU3F[I1, I5, k8]*SU3F[I3, k7, k9]*SU3F[I4, k8, k9] + - 18*SU3D[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k7, k9]*SU3F[I4, k8, k9] - - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I1, k7]* - SU3F[I5, k6, k8] - (18*I)*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8] - (18*I)*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]* - SU3F[I5, k6, k8] + (27*I)*SU3D[I1, I4, k8]*SU3D[I3, k6, k7]* - SU3F[6, I2, k7]*SU3F[I5, k6, k8] + (27*I)*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]* - SU3F[I5, k6, k8] + (27*I)*SU3D[I1, I4, k8]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I5, k6, k8] + (27*I)*SU3D[I1, I2, k8]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8] - - (36*I)*SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]* - SU3F[I5, k6, k8] + (27*I)*SU3D[I1, I3, k8]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[I5, k6, k8] + (27*I)*SU3D[I1, I2, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8] + - 36*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]*SU3F[I5, k6, k9] + - 36*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]*SU3F[I5, k6, k9] - - 27*SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3F[I5, k6, k9] - - 27*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]*SU3F[I5, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]*SU3F[I5, k6, k9] - - 27*SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3F[I5, k6, k9] - - 27*SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]*SU3F[I5, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3F[I5, k6, k9] - - 27*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] - - 27*SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] - - 9*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9] - - 9*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9] - - 9*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9] - - 9*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9] - - 9*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9] - - 9*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9] - - (36*I)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9] - (36*I)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] - (36*I)*SU3D[6, I2, k8]* - SU3D[I3, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - 36*SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + - (9*I)*SU3D[6, I4, k7]*SU3D[I1, I3, k6]*SU3F[I2, k7, k9]* - SU3F[I5, k6, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I1, I4, k6]* - SU3F[I2, k7, k9]*SU3F[I5, k6, k9] + (18*I)*SU3D[6, I4, k8]* - SU3D[I1, I3, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + - (18*I)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9] - (18*I)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + 18*SU3D[I3, I4, k6]*SU3F[6, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - 27*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] - 27*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + (9*I)*SU3D[6, I4, k7]* - SU3D[I1, I2, k6]*SU3F[I3, k7, k9]*SU3F[I5, k6, k9] + - (9*I)*SU3D[6, I2, k7]*SU3D[I1, I4, k6]*SU3F[I3, k7, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9] + (18*I)*SU3D[6, I2, k8]* - SU3D[I1, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9] - - (18*I)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] + 18*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - 27*SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] - 27*SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I1, I2, k6]* - SU3F[I4, k7, k9]*SU3F[I5, k6, k9] + (9*I)*SU3D[6, I2, k7]* - SU3D[I1, I3, k6]*SU3F[I4, k7, k9]*SU3F[I5, k6, k9] + - (18*I)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9] + (18*I)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - (18*I)*SU3D[6, I1, k8]* - SU3D[I2, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + - 18*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - - 27*SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] - - 27*SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + - (9*I)*SU3F[6, I4, k9]*SU3F[I1, I3, k7]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k8] + (9*I)*SU3F[6, I3, k9]*SU3F[I1, I4, k7]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k8] + (9*I)*SU3F[6, I4, k9]* - SU3F[I1, I2, k7]*SU3F[I3, k8, k9]*SU3F[I5, k7, k8] + - (9*I)*SU3F[6, I2, k9]*SU3F[I1, I4, k7]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k8] + (9*I)*SU3F[6, I3, k9]*SU3F[I1, I2, k7]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k8] + (9*I)*SU3F[6, I2, k9]* - SU3F[I1, I3, k7]*SU3F[I4, k8, k9]*SU3F[I5, k7, k8] - - (18*I)*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I1, k9]* - SU3F[I5, k7, k9] - (18*I)*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9] - (18*I)*SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9] + - (54*I)*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]* - SU3F[I5, k7, k9] + (54*I)*SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[6, I3, k9]*SU3F[I5, k7, k9] + (54*I)*SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9] - - (36*I)*SU3D[6, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9] - (36*I)*SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9] + 36*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9] + 36*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9] - (36*I)*SU3D[6, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9] - - (36*I)*SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9] + 36*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9] + 36*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9] - (36*I)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9] - (36*I)*SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k6]*SU3F[I5, k7, k9] + - 36*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]*SU3F[I5, k7, k9] + - 36*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]*SU3F[I5, k7, k9] - - 36*SU3D[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9] - - 36*SU3D[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9] - - 36*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9] - - 36*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9] - - 36*SU3D[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] - - 36*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9] - - 54*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3F[I5, k8, k9] - - 54*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3F[I5, k8, k9] - - 54*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3F[I5, k8, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, I4, k6]*SU3F[I5, k8, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]*SU3F[I5, k8, k9] + - 18*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]*SU3F[I5, k8, k9] + - (9*I)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]*SU3F[I1, I2, k9]* - SU3F[I5, k8, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9] + (9*I)*SU3D[6, I4, k7]* - SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9] + - (9*I)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]* - SU3F[I5, k8, k9] + (9*I)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I5, k8, k9] + (9*I)*SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9] - - (54*I)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9] - (54*I)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9] - (54*I)*SU3D[6, I2, k8]* - SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + - 54*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + - 54*SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + - 54*SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] - 18*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9] + (36*I)*SU3F[6, I4, k9]*SU3F[I1, I3, k7]* - SU3F[I2, k7, k8]*SU3F[I5, k8, k9] + (36*I)*SU3F[6, I3, k9]* - SU3F[I1, I4, k7]*SU3F[I2, k7, k8]*SU3F[I5, k8, k9] - - 9*SU3D[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k7, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k7, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9] - 18*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9] + (36*I)*SU3F[6, I4, k9]*SU3F[I1, I2, k7]* - SU3F[I3, k7, k8]*SU3F[I5, k8, k9] + (36*I)*SU3F[6, I2, k9]* - SU3F[I1, I4, k7]*SU3F[I3, k7, k8]*SU3F[I5, k8, k9] - - 9*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9] + - (18*I)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9] - 18*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9] + (36*I)*SU3F[6, I3, k9]*SU3F[I1, I2, k7]* - SU3F[I4, k7, k8]*SU3F[I5, k8, k9] + (36*I)*SU3F[6, I2, k9]* - SU3F[I1, I3, k7]*SU3F[I4, k7, k8]*SU3F[I5, k8, k9] - - 9*SU3D[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] - - 9*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9] + - (24*I)*SU3D[I2, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I1] + - (24*I)*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I1] + - (24*I)*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - 48*SU3D[I3, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I1] + - 48*SU3D[I2, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I1] + - 48*SU3D[I2, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I1] - - (96*I)*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - (30*I)*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - (30*I)*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - 30*SU3D[I4, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I2] + - 30*SU3D[I3, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I2] - - 18*SU3D[I1, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I2] + - (18*I)*SU3F[I1, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I2] - - 18*SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2] + - (18*I)*SU3F[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2] - - (96*I)*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3] + - (30*I)*SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3] + - (30*I)*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - 30*SU3D[I4, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I3] + - 30*SU3D[I2, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I3] - - 18*SU3D[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3] + - (18*I)*SU3F[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3] - - 18*SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3] + - (18*I)*SU3F[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3] - - (96*I)*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4] + - (30*I)*SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4] + - (30*I)*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - 30*SU3D[I3, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I4] + - 30*SU3D[I2, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I4] - - 18*SU3D[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4] + - (18*I)*SU3F[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4] - - 18*SU3D[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4] + - (18*I)*SU3F[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4] + - (12*I)*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5] + - (12*I)*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5] + - (12*I)*SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5] - - 84*SU3D[I3, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I5] - - 84*SU3D[I2, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I5] - - 84*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I5] + - (24*I)*SU3D[6, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[I1, I2] + - (18*I)*SU3D[6, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[I1, I2] + - (18*I)*SU3D[6, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[I1, I2] - - 18*SU3D[I4, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I2] - - 18*SU3D[I3, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I2] - - 24*SU3D[I3, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I2] - - 18*SU3D[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2] - - (18*I)*SU3F[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2] - - 18*SU3D[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2] - - (18*I)*SU3F[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2] + - (24*I)*SU3D[6, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[I1, I3] + - (18*I)*SU3D[6, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[I1, I3] + - (18*I)*SU3D[6, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[I1, I3] - - 18*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3] - - 18*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3] - - 24*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3] - - 18*SU3D[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3] - - (18*I)*SU3F[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3] - - 18*SU3D[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3] - - (18*I)*SU3F[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3] + - (24*I)*SU3D[6, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[I1, I4] + - (18*I)*SU3D[6, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[I1, I4] + - (18*I)*SU3D[6, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[I1, I4] - - 18*SU3D[I3, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I4] - - 18*SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4] - - 24*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4] - - 18*SU3D[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4] - - (18*I)*SU3F[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4] - - 18*SU3D[6, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I4] - - (18*I)*SU3F[6, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I4] - - (12*I)*SU3D[6, I5, k6]*SU3D[I1, I4, k6]*SUNDelta[I2, I3] - - (60*I)*SU3D[6, I4, k6]*SU3D[I1, I5, k6]*SUNDelta[I2, I3] + - 60*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3] + - 12*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3] - - 60*SU3D[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3] - - (60*I)*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3] - - 12*SU3D[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3] - - (12*I)*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3] + - 24*SU3D[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3] + - (24*I)*SU3F[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3] + - (8*I)*SUNDelta[6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - (64*I)*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3] - - (12*I)*SU3D[6, I5, k6]*SU3D[I1, I3, k6]*SUNDelta[I2, I4] - - (60*I)*SU3D[6, I3, k6]*SU3D[I1, I5, k6]*SUNDelta[I2, I4] + - 60*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4] + - 12*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4] - - 60*SU3D[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4] - - (60*I)*SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4] - - 12*SU3D[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4] - - (12*I)*SU3F[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4] + - 24*SU3D[6, I1, k6]*SU3F[I3, I5, k6]*SUNDelta[I2, I4] + - (24*I)*SU3F[6, I1, k6]*SU3F[I3, I5, k6]*SUNDelta[I2, I4] + - (8*I)*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - (64*I)*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - (12*I)*SU3D[6, I4, k6]*SU3D[I1, I3, k6]*SUNDelta[I2, I5] + - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I4, k6]*SUNDelta[I2, I5] + - (24*I)*SU3D[6, I1, k6]*SU3D[I3, I4, k6]*SUNDelta[I2, I5] - - 24*SU3D[I3, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I5] - - 12*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5] - - 12*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5] + - 60*SU3D[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5] + - (60*I)*SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5] + - 60*SU3D[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5] + - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5] + - (20*I)*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5] + - (20*I)*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5] - - (12*I)*SU3D[6, I5, k6]*SU3D[I1, I2, k6]*SUNDelta[I3, I4] - - (60*I)*SU3D[6, I2, k6]*SU3D[I1, I5, k6]*SUNDelta[I3, I4] + - 60*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4] + - 12*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4] - - 60*SU3D[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4] - - (60*I)*SU3F[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4] - - 12*SU3D[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4] - - (12*I)*SU3F[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4] + - 24*SU3D[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4] + - (24*I)*SU3F[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4] + - (8*I)*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4] - - (64*I)*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - (12*I)*SU3D[6, I4, k6]*SU3D[I1, I2, k6]*SUNDelta[I3, I5] + - (12*I)*SU3D[6, I2, k6]*SU3D[I1, I4, k6]*SUNDelta[I3, I5] + - (24*I)*SU3D[6, I1, k6]*SU3D[I2, I4, k6]*SUNDelta[I3, I5] - - 24*SU3D[I2, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I5] - - 12*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5] - - 12*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5] + - 60*SU3D[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5] + - (60*I)*SU3F[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5] + - 60*SU3D[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5] + - (60*I)*SU3F[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5] + - (20*I)*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - (20*I)*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - (12*I)*SU3D[6, I3, k6]*SU3D[I1, I2, k6]*SUNDelta[I4, I5] + - (12*I)*SU3D[6, I2, k6]*SU3D[I1, I3, k6]*SUNDelta[I4, I5] + - (24*I)*SU3D[6, I1, k6]*SU3D[I2, I3, k6]*SUNDelta[I4, I5] - - 24*SU3D[I2, I3, k5]*SU3F[6, I1, k5]*SUNDelta[I4, I5] - - 12*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5] - - 12*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5] + - 60*SU3D[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5] + - (60*I)*SU3F[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5] + - 60*SU3D[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5] + - (60*I)*SU3F[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5] + - (20*I)*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - (20*I)*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - (16*I)*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ -(108*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10o2.Gen deleted file mode 100644 index 46e6953fd..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{FourVector[p3, \[Mu]1], FourVector[p2, \[Mu]1], FourVector[p4, \[Mu]1], -FourVector[p5, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10o2.Mod deleted file mode 100644 index 0b8027ca7..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10P10o2.Mod +++ /dev/null @@ -1,2936 +0,0 @@ -{{(CouplingConstant[ChPTW3[2], 1]*(((-4*I)/9)*SU3D[6, I3, I5]* - SU3D[I1, I2, I4] - ((4*I)/9)*SU3D[6, I3, I4]*SU3D[I1, I2, I5] - - ((4*I)/9)*SU3D[6, I2, I3]*SU3D[I1, I4, I5] - ((5*I)/9)*SU3D[6, I1, I5]* - SU3D[I2, I3, I4] - ((5*I)/9)*SU3D[6, I1, I4]*SU3D[I2, I3, I5] + - I*SU3D[6, I1, I3]*SU3D[I2, I4, I5] - ((5*I)/9)*SU3D[6, I1, I2]* - SU3D[I3, I4, I5] - (7*SU3D[I3, I4, I5]*SU3F[6, I1, I2])/9 + - (SU3D[I2, I4, I5]*SU3F[6, I1, I3])/3 - - (7*SU3D[I2, I3, I5]*SU3F[6, I1, I4])/9 - - (7*SU3D[I2, I3, I4]*SU3F[6, I1, I5])/9 + - (2*SU3D[I1, I4, I5]*SU3F[6, I2, I3])/9 - - (2*SU3D[I1, I2, I5]*SU3F[6, I3, I4])/9 - - (2*SU3D[I1, I2, I4]*SU3F[6, I3, I5])/9 + SU3D[6, I4, I5]* - (((2*I)/3)*SU3D[I1, I2, I3] - (2*SU3F[I1, I2, I3])/9) + - SU3D[6, I2, I5]*(((2*I)/3)*SU3D[I1, I3, I4] + (2*SU3F[I1, I3, I4])/9) + - SU3D[6, I2, I4]*(((2*I)/3)*SU3D[I1, I3, I5] + (2*SU3F[I1, I3, I5])/9) + - SU3D[I4, I5, k2]*(SU3D[6, I2, k1]*((-I/2)*SU3F[I1, k2, k3]* - SU3F[I3, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]) + - SU3D[6, I1, k1]*((I/6)*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] - - (I/6)*SU3F[I2, k1, k3]*SU3F[I3, k2, k3])) + - SU3D[I5, k2, k3]*(SU3D[I3, I4, k1]*((-I/2)*SU3F[6, I2, k2]* - SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]*SU3F[I2, k1, k3]) + - SU3D[I2, I4, k1]*((I/2)*SU3F[6, I3, k2]*SU3F[I1, k1, k3] + - (I/6)*SU3F[6, I1, k2]*SU3F[I3, k1, k3]) + SU3D[I1, I4, k1]* - ((-I/6)*SU3F[6, I3, k2]*SU3F[I2, k1, k3] - (I/4)*SU3F[6, I2, k2]* - SU3F[I3, k1, k3]) + SU3D[I2, I3, k1]* - ((-I/2)*SU3F[6, I4, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I4, k1, k3]) + SU3D[I1, I3, k1]* - ((I/4)*SU3F[6, I4, k2]*SU3F[I2, k1, k3] + (I/4)*SU3F[6, I2, k2]* - SU3F[I4, k1, k3]) + SU3D[I1, I2, k1]* - ((-I/4)*SU3F[6, I4, k2]*SU3F[I3, k1, k3] - (I/6)*SU3F[6, I3, k2]* - SU3F[I4, k1, k3])) + SU3D[6, I3, k1]*SU3D[I1, I5, k2]* - SU3D[I2, k1, k3]*((I/6)*SU3D[I4, k2, k3] - SU3F[I4, k2, k3]/6) + - SU3D[I5, k1, k2]*((-I/6)*SU3D[I1, I4, k1]*SU3F[6, I3, k3]* - SU3F[I2, k2, k3] + SU3D[I3, I4, k1]*((I/3)*SU3F[6, I2, k3]* - SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]*SU3F[I2, k2, k3]) + - SU3F[6, I4, k2]*((SU3F[I1, I3, k3]*SU3F[I2, k1, k3])/12 - - (SU3F[I1, I2, k3]*SU3F[I3, k1, k3])/12) + SU3D[I2, I4, k1]* - ((-I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I4, k3]* - (-(SU3F[I1, I3, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I3, k2, k3])/3) + SU3F[6, I3, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I2, k1, k3])/6 - - (SU3F[I1, I2, k3]*SU3F[I4, k1, k3])/6) + SU3F[6, I2, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I3, k1, k3])/12 + - (SU3F[I1, I3, k3]*SU3F[I4, k1, k3])/12) + SU3F[6, I1, k2]* - (-(SU3F[I2, k1, k3]*SU3F[I3, I4, k3])/6 + - (SU3F[I2, I3, k3]*SU3F[I4, k1, k3])/6) - (I/6)*SU3D[I1, I2, k1]* - SU3F[6, I3, k3]*SU3F[I4, k2, k3] + SU3D[I2, I3, k1]* - ((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I4, k2, k3]) + SU3D[I1, I3, k1]* - ((I/4)*SU3F[6, I4, k3]*SU3F[I2, k2, k3] + (I/4)*SU3F[6, I2, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I3, k3]* - ((SU3F[I1, I4, k1]*SU3F[I2, k2, k3])/6 + - (SU3F[I1, I2, k1]*SU3F[I4, k2, k3])/6) + SU3F[6, I2, k3]* - ((SU3F[I1, I4, k1]*SU3F[I3, k2, k3])/3 - - (SU3F[I1, I3, k1]*SU3F[I4, k2, k3])/12) + SU3F[6, I1, k3]* - ((SU3F[I2, k2, k3]*SU3F[I3, I4, k1])/6 - - (SU3F[I2, I3, k1]*SU3F[I4, k2, k3])/6)) + - SU3D[I1, I5, k2]*(SU3D[6, I2, k1]*(-(SU3D[I4, k1, k3]*SU3F[I3, k2, k3])/ - 4 + (I/4)*SU3F[I3, k2, k3]*SU3F[I4, k1, k3]) + - SU3D[6, I3, k1]*((SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/6 - - (SU3D[I4, k1, k3]*SU3F[I2, k2, k3])/6 + (I/6)*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I2, k1, k3]*SU3F[I4, k2, k3])) + - SU3D[I1, k2, k3]*((I/2)*SU3D[6, I4, k1]*SU3D[I2, k1, k2]* - SU3D[I3, I5, k3] - (I/2)*SU3D[6, I3, k1]*SU3D[I2, k1, k3]* - SU3D[I4, I5, k2] - (I/2)*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3D[I4, I5, k3] + SU3D[6, I3, k1]*((-I/2)*SU3D[I2, I5, k2]* - SU3D[I4, k1, k3] - (I/2)*SU3D[I2, I4, k2]*SU3D[I5, k1, k3] - - (SU3D[I4, I5, k3]*SU3F[I2, k1, k2])/2) - - (SU3D[6, I2, k1]*SU3D[I4, I5, k3]*SU3F[I3, k1, k2])/2 + - SU3D[6, I2, k1]*SU3D[I3, I5, k3]*((I/2)*SU3D[I4, k1, k2] + - SU3F[I4, k1, k2]/2) - (SU3D[6, I3, k1]*SU3D[I2, I5, k3]* - SU3F[I4, k1, k2])/2 + SU3D[6, I4, k1]* - ((-I/2)*SU3D[I2, I5, k3]*SU3D[I3, k1, k2] + - (SU3D[I3, I5, k3]*SU3F[I2, k1, k2])/2 - - (SU3D[I2, I5, k3]*SU3F[I3, k1, k2])/2 + SU3D[I2, I3, k3]* - ((I/2)*SU3D[I5, k1, k2] + SU3F[I5, k1, k2]/2)) + - SU3D[6, I2, k1]*SU3D[I3, I4, k3]*((I/2)*SU3D[I5, k1, k2] + - SU3F[I5, k1, k2]/2) - (SU3D[6, I3, k1]*SU3D[I2, I4, k3]* - SU3F[I5, k1, k2])/2) + SU3D[I4, k2, k3]* - (SU3D[I5, k1, k3]*(-(SU3D[I2, I3, k1]*SU3F[6, I1, k2])/6 + - (SU3D[I1, I3, k1]*SU3F[6, I2, k2])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I3, k2])/6) + SU3D[I3, I5, k1]* - ((-I/2)*SU3F[6, I2, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I2, k1, k3]) + SU3D[I2, I5, k1]* - ((I/2)*SU3F[6, I3, k2]*SU3F[I1, k1, k3] + (I/6)*SU3F[6, I1, k2]* - SU3F[I3, k1, k3]) + SU3D[I1, I5, k1]* - ((-I/6)*SU3F[6, I3, k2]*SU3F[I2, k1, k3] - (I/4)*SU3F[6, I2, k2]* - SU3F[I3, k1, k3]) + SU3D[I2, I3, k1]* - ((-I/2)*SU3F[6, I5, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I3, k1]* - ((I/4)*SU3F[6, I5, k2]*SU3F[I2, k1, k3] + (I/4)*SU3F[6, I2, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I2, k1]* - ((-I/4)*SU3F[6, I5, k2]*SU3F[I3, k1, k3] - (I/6)*SU3F[6, I3, k2]* - SU3F[I5, k1, k3])) + SU3D[I3, k2, k3]* - (-(SU3D[I2, I5, k1]*SU3D[I4, k1, k3]*SU3F[6, I1, k2])/6 - - (SU3D[I2, I4, k1]*SU3D[I5, k1, k3]*SU3F[6, I1, k2])/6 + - SU3D[I4, I5, k3]*(-(SU3D[6, I2, k1]*SU3F[I1, k1, k2])/3 - - (SU3D[6, I1, k1]*SU3F[I2, k1, k2])/6) + SU3D[6, I2, k1]* - SU3D[I1, I5, k2]*((I/4)*SU3D[I4, k1, k3] + SU3F[I4, k1, k3]/4) + - SU3D[I2, I5, k1]*((I/2)*SU3F[6, I4, k2]*SU3F[I1, k1, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I4, k1, k3]) + SU3D[6, I1, k1]* - (SU3D[I2, I5, k2]*((-I/6)*SU3D[I4, k1, k3] - SU3F[I4, k1, k3]/6) + - SU3D[I2, I4, k2]*((-I/6)*SU3D[I5, k1, k3] - SU3F[I5, k1, k3]/6)) + - SU3D[6, I2, k1]*SU3D[I1, I4, k2]*((I/4)*SU3D[I5, k1, k3] + - SU3F[I5, k1, k3]/4) + SU3D[I2, I4, k1]* - ((I/2)*SU3F[6, I5, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I5, k1, k3]) + SU3D[6, I2, k1]* - (-(SU3D[I5, k1, k2]*SU3F[I1, I4, k3])/12 - - (SU3D[I4, k1, k2]*SU3F[I1, I5, k3])/12 + (I/12)*SU3F[I1, I5, k2]* - SU3F[I4, k1, k3] + (I/12)*SU3F[I1, I4, k2]*SU3F[I5, k1, k3])) + - SU3D[I2, k2, k3]*((I/6)*SU3D[6, I1, k1]*SU3D[I3, k1, k2]* - SU3D[I4, I5, k3] + SU3D[I5, k1, k3]* - (-(SU3D[I1, I4, k1]*SU3F[6, I3, k2])/6 + - (SU3D[I1, I3, k1]*SU3F[6, I4, k2])/4) + SU3D[I4, k1, k3]* - (-(SU3D[I1, I5, k1]*SU3F[6, I3, k2])/6 + - (SU3D[I1, I3, k1]*SU3F[6, I5, k2])/4) + SU3D[I3, k1, k3]* - (-(SU3D[I1, I5, k1]*SU3F[6, I4, k2])/4 - - (SU3D[I1, I4, k1]*SU3F[6, I5, k2])/4) + - (SU3D[6, I1, k1]*SU3D[I4, I5, k3]*SU3F[I3, k1, k2])/6 + - (SU3D[6, I1, k1]*SU3D[I3, I5, k3]*SU3F[I4, k1, k2])/6 + - SU3D[6, I3, k1]*SU3D[I1, I5, k2]*((I/6)*SU3D[I4, k1, k3] + - SU3F[I4, k1, k3]/6) + SU3D[I1, I5, k1]* - ((-I/4)*SU3F[6, I4, k2]*SU3F[I3, k1, k3] - (I/6)*SU3F[6, I3, k2]* - SU3F[I4, k1, k3]) + SU3D[6, I3, k1]*SU3D[I1, I4, k2]* - ((I/6)*SU3D[I5, k1, k3] + SU3F[I5, k1, k3]/6) + - SU3D[I1, I4, k1]*((-I/4)*SU3F[6, I5, k2]*SU3F[I3, k1, k3] - - (I/6)*SU3F[6, I3, k2]*SU3F[I5, k1, k3]) + SU3D[I1, I3, k1]* - ((I/4)*SU3F[6, I5, k2]*SU3F[I4, k1, k3] + (I/4)*SU3F[6, I4, k2]* - SU3F[I5, k1, k3]) + SU3D[6, I4, k1]* - ((SU3D[I5, k1, k2]*SU3F[I1, I3, k3])/12 - - (SU3D[I3, k1, k2]*SU3F[I1, I5, k3])/3 - - (SU3D[I3, I5, k3]*SU3F[I1, k1, k2])/3 + (I/3)*SU3F[I1, I5, k2]* - SU3F[I3, k1, k3] + SU3D[I1, I3, k2]*((-I/4)*SU3D[I5, k1, k3] - - SU3F[I5, k1, k3]/4) - (I/12)*SU3F[I1, I3, k2]*SU3F[I5, k1, k3]) + - SU3D[6, I3, k1]*(-(SU3D[I5, k1, k2]*SU3F[I1, I4, k3])/6 - - (SU3D[I4, k1, k2]*SU3F[I1, I5, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I1, k1, k2])/3 + (I/6)*SU3F[I1, I5, k2]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I1, I4, k2]*SU3F[I5, k1, k3]) + - SU3D[6, I1, k1]*((I/6)*SU3D[I3, I5, k2]*SU3D[I4, k1, k3] + - (I/6)*SU3D[I3, I4, k2]*SU3D[I5, k1, k3] - - (SU3D[I5, k1, k2]*SU3F[I3, I4, k3])/6 - - (SU3D[I4, k1, k2]*SU3F[I3, I5, k3])/6 + (I/6)*SU3F[I3, I5, k2]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I3, I4, k2]*SU3F[I5, k1, k3])) + - SU3D[I3, I4, k3]*((SU3D[6, I1, k1]*SU3D[I2, k2, k3]*SU3F[I5, k1, k2])/ - 6 + SU3D[I1, k1, k2]*((SU3D[I5, k2, k3]*SU3F[6, I2, k1])/3 + - (SU3D[I2, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I2, k2, k3] + SU3D[6, I2, k1]*((-I/3)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/3) - (I/3)*SU3F[6, I2, k1]*SU3F[I5, k2, k3])) + - SU3D[I1, k1, k2]*(SU3D[I3, k2, k3]*SU3D[I4, I5, k3]* - ((-I/3)*SU3D[6, I2, k1] + SU3F[6, I2, k1]/3) + - (SU3D[I3, k1, k3]*SU3D[I4, I5, k2]*SU3F[6, I2, k3])/2 + - (SU3D[I2, I4, k2]*SU3D[I5, k1, k3]*SU3F[6, I3, k3])/2 + - SU3D[I2, k2, k3]*((-I/3)*SU3D[6, I4, k1]*SU3D[I3, I5, k3] + - (I/3)*SU3D[6, I3, k1]*SU3D[I4, I5, k3] - - (SU3D[I4, I5, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, I5, k3]*SU3F[6, I4, k1])/3) + SU3D[I5, k1, k3]* - (-(SU3D[I3, I4, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I3, k2]*SU3F[6, I4, k3])/2) + SU3D[I2, I5, k2]* - ((SU3D[I4, k1, k3]*SU3F[6, I3, k3])/2 + - (SU3D[I3, k1, k3]*SU3F[6, I4, k3])/2) + - (SU3D[I2, I4, k2]*SU3D[I3, k1, k3]*SU3F[6, I5, k3])/2 + - SU3D[I4, k1, k3]*(-(SU3D[I3, I5, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I3, k2]*SU3F[6, I5, k3])/2) + SU3D[I2, k1, k3]* - ((SU3D[I4, I5, k2]*SU3F[6, I3, k3])/2 - - (SU3D[I3, I5, k2]*SU3F[6, I4, k3])/2 - - (SU3D[I3, I4, k2]*SU3F[6, I5, k3])/2) + - (SU3D[6, I3, k1]*SU3D[I4, I5, k3]*SU3F[I2, k2, k3])/3 + - SU3D[I4, I5, k3]*((I/3)*SU3F[6, I3, k1]*SU3F[I2, k2, k3] - - (SU3D[6, I2, k1]*SU3F[I3, k2, k3])/3 - (I/3)*SU3F[6, I2, k1]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k1]* - ((I/2)*SU3F[6, I3, k3]*SU3F[I2, k2, k3] + (I/2)*SU3F[6, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I3, I5, k3]* - ((SU3D[I4, k2, k3]*SU3F[6, I2, k1])/3 - (I/3)*SU3F[6, I4, k1]* - SU3F[I2, k2, k3] + SU3D[6, I2, k1]*((-I/3)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/3) - (I/3)*SU3F[6, I2, k1]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k1]*((-I/2)*SU3F[6, I4, k3]*SU3F[I2, k2, k3] - - (I/2)*SU3F[6, I2, k3]*SU3F[I4, k2, k3]) + SU3D[I2, I5, k3]* - (-(SU3D[I4, k2, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, k2, k3]*SU3F[6, I4, k1])/3 - (I/3)*SU3F[6, I4, k1]* - SU3F[I3, k2, k3] + SU3D[6, I3, k1]*((I/3)*SU3D[I4, k2, k3] + - SU3F[I4, k2, k3]/3) + (I/3)*SU3F[6, I3, k1]*SU3F[I4, k2, k3]) + - SU3D[I2, I5, k1]*((I/2)*SU3F[6, I4, k3]*SU3F[I3, k2, k3] + - (I/2)*SU3F[6, I3, k3]*SU3F[I4, k2, k3]) + SU3D[6, I4, k1]* - (-(SU3D[I3, I5, k3]*SU3F[I2, k2, k3])/3 + SU3D[I2, I5, k3]* - ((-I/3)*SU3D[I3, k2, k3] - SU3F[I3, k2, k3]/3) + - SU3D[I2, I3, k3]*((-I/3)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/3)) + - SU3D[I3, I4, k1]*((-I/2)*SU3F[6, I5, k3]*SU3F[I2, k2, k3] - - (I/2)*SU3F[6, I2, k3]*SU3F[I5, k2, k3]) + SU3D[I2, I4, k3]* - (-(SU3D[I5, k2, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I3, k2, k3] + SU3D[6, I3, k1]*((I/3)*SU3D[I5, k2, k3] + - SU3F[I5, k2, k3]/3) + (I/3)*SU3F[6, I3, k1]*SU3F[I5, k2, k3]) + - SU3D[I2, I4, k1]*((I/2)*SU3F[6, I5, k3]*SU3F[I3, k2, k3] + - (I/2)*SU3F[6, I3, k3]*SU3F[I5, k2, k3]) + SU3D[I2, I3, k3]* - ((SU3D[I5, k2, k3]*SU3F[6, I4, k1])/3 + - (SU3D[I4, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I4, k2, k3] - (I/3)*SU3F[6, I4, k1]*SU3F[I5, k2, k3]) + - SU3D[I2, I3, k1]*((-I/2)*SU3F[6, I5, k3]*SU3F[I4, k2, k3] - - (I/2)*SU3F[6, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I3, k1, k2]*(SU3D[I5, k2, k3]*((SU3D[I2, I4, k1]*SU3F[6, I1, k3])/ - 6 - (SU3D[I1, I4, k1]*SU3F[6, I2, k3])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I4, k3])/4 - (I/12)*SU3F[6, I4, k3]* - SU3F[I1, I2, k1] - (I/12)*SU3F[6, I2, k3]*SU3F[I1, I4, k1]) + - SU3D[I5, k1, k3]*((-I/3)*SU3F[6, I4, k2]*SU3F[I1, I2, k3] - - (I/3)*SU3F[6, I2, k2]*SU3F[I1, I4, k3]) + SU3D[I4, k2, k3]* - ((SU3D[I2, I5, k1]*SU3F[6, I1, k3])/6 - - (SU3D[I1, I5, k1]*SU3F[6, I2, k3])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I5, k3])/4 - (I/12)*SU3F[6, I5, k3]* - SU3F[I1, I2, k1] - (I/12)*SU3F[6, I2, k3]*SU3F[I1, I5, k1]) + - SU3D[I4, k1, k3]*((-I/3)*SU3F[6, I5, k2]*SU3F[I1, I2, k3] - - (I/3)*SU3F[6, I2, k2]*SU3F[I1, I5, k3]) + SU3D[I4, I5, k3]* - (-(SU3D[6, I2, k1]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[6, I2, k1]* - SU3F[I1, k2, k3] + (SU3D[6, I1, k1]*SU3F[I2, k2, k3])/6 + - (I/6)*SU3F[6, I1, k1]*SU3F[I2, k2, k3]) + SU3D[I4, I5, k1]* - ((I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I2, k2, k3]) + SU3F[6, I5, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, I2, k3]*SU3F[I4, k1, k3])/3) + SU3D[I2, I5, k1]* - ((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I4, k2, k3]) + SU3D[I1, I5, k1]* - ((-I/4)*SU3F[6, I4, k3]*SU3F[I2, k2, k3] - (I/4)*SU3F[6, I2, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I4, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I4, k2, k3])/12) + SU3F[6, I4, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, I2, k3]*SU3F[I5, k1, k3])/3) + SU3F[6, I2, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, I4, k3]*SU3F[I5, k1, k3])/3) + SU3D[I2, I4, k1]* - ((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I4, k1]* - ((-I/4)*SU3F[6, I5, k3]*SU3F[I2, k2, k3] - (I/4)*SU3F[6, I2, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I2, k1]* - ((-I/4)*SU3F[6, I5, k3]*SU3F[I4, k2, k3] - (I/4)*SU3F[6, I4, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I5, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I5, k2, k3])/12) + SU3F[6, I2, k3]* - ((SU3F[I1, I5, k1]*SU3F[I4, k2, k3])/12 + - (SU3F[I1, I4, k1]*SU3F[I5, k2, k3])/12) + SU3D[6, I2, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I4, k3])/3 - - (SU3D[I4, k2, k3]*SU3F[I1, I5, k3])/3 + (I/3)*SU3F[I1, I5, k3]* - SU3F[I4, k2, k3] + (I/3)*SU3F[I1, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I4, k1, k2]*(SU3D[I5, k2, k3]*(-(SU3D[I2, I3, k1]*SU3F[6, I1, k3])/ - 6 + (SU3D[I1, I3, k1]*SU3F[6, I2, k3])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I3, k3])/6 - (I/6)*SU3F[6, I3, k3]* - SU3F[I1, I2, k1] + (I/12)*SU3F[6, I2, k3]*SU3F[I1, I3, k1] + - (I/6)*SU3F[6, I1, k3]*SU3F[I2, I3, k1]) + SU3D[I5, k1, k3]* - ((-I/6)*SU3F[6, I3, k2]*SU3F[I1, I2, k3] + (I/12)*SU3F[6, I2, k2]* - SU3F[I1, I3, k3] + (I/6)*SU3F[6, I1, k2]*SU3F[I2, I3, k3]) - - (I/6)*SU3D[I1, I5, k1]*SU3F[6, I3, k3]*SU3F[I2, k2, k3] + - SU3D[I3, I5, k1]*((I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I2, k2, k3]) + SU3F[6, I5, k2]* - ((SU3F[I1, I3, k3]*SU3F[I2, k1, k3])/12 - - (SU3F[I1, I2, k3]*SU3F[I3, k1, k3])/12) + SU3D[I2, I5, k1]* - ((-I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I5, k3]* - (-(SU3F[I1, I3, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I3, k2, k3])/3) + SU3F[6, I3, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I2, k1, k3])/6 - - (SU3F[I1, I2, k3]*SU3F[I5, k1, k3])/6) + SU3F[6, I2, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I3, k1, k3])/12 + - (SU3F[I1, I3, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I1, k2]* - (-(SU3F[I2, k1, k3]*SU3F[I3, I5, k3])/6 + - (SU3F[I2, I3, k3]*SU3F[I5, k1, k3])/6) - (I/6)*SU3D[I1, I2, k1]* - SU3F[6, I3, k3]*SU3F[I5, k2, k3] + SU3D[I2, I3, k1]* - ((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I3, k1]* - ((I/4)*SU3F[6, I5, k3]*SU3F[I2, k2, k3] + (I/4)*SU3F[6, I2, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I3, k3]* - ((SU3F[I1, I5, k1]*SU3F[I2, k2, k3])/6 + - (SU3F[I1, I2, k1]*SU3F[I5, k2, k3])/6) + SU3F[6, I2, k3]* - ((SU3F[I1, I5, k1]*SU3F[I3, k2, k3])/3 - - (SU3F[I1, I3, k1]*SU3F[I5, k2, k3])/12) + SU3F[6, I1, k3]* - ((SU3F[I2, k2, k3]*SU3F[I3, I5, k1])/6 - - (SU3F[I2, I3, k1]*SU3F[I5, k2, k3])/6)) + - SU3D[I1, I4, k2]*(SU3D[6, I2, k1]*(-(SU3D[I5, k1, k3]*SU3F[I3, k2, k3])/ - 4 + (I/4)*SU3F[I3, k2, k3]*SU3F[I5, k1, k3]) + - SU3D[6, I3, k1]*SU3D[I2, k1, k3]*((I/6)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/6) + SU3D[6, I3, k1]* - ((SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I2, k2, k3])/6 + (I/6)*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I2, k1, k3]*SU3F[I5, k2, k3])) + - SU3D[I2, k1, k2]*(-(SU3D[I3, k1, k3]*SU3D[I4, I5, k2]*SU3F[6, I1, k3])/ - 6 + SU3D[I3, k2, k3]*(SU3D[I4, I5, k3]*((-I/6)*SU3D[6, I1, k1] + - SU3F[6, I1, k1]/6) - (I/3)*SU3F[6, I5, k3]*SU3F[I1, I4, k1] - - (I/3)*SU3F[6, I4, k3]*SU3F[I1, I5, k1]) + SU3D[I3, k1, k3]* - ((-I/12)*SU3F[6, I5, k2]*SU3F[I1, I4, k3] - (I/12)*SU3F[6, I4, k2]* - SU3F[I1, I5, k3]) + SU3D[I5, k2, k3]* - (-(SU3D[I1, I4, k1]*SU3F[6, I3, k3])/6 + - (SU3D[I1, I3, k1]*SU3F[6, I4, k3])/4 + (I/12)*SU3F[6, I4, k3]* - SU3F[I1, I3, k1] - (I/6)*SU3F[6, I3, k3]*SU3F[I1, I4, k1] - - (I/6)*SU3F[6, I1, k3]*SU3F[I3, I4, k1]) + SU3D[I5, k1, k3]* - (-(SU3D[I3, I4, k2]*SU3F[6, I1, k3])/6 + (I/12)*SU3F[6, I4, k2]* - SU3F[I1, I3, k3] - (I/6)*SU3F[6, I3, k2]*SU3F[I1, I4, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I3, I4, k3]) + SU3D[I4, k2, k3]* - (-(SU3D[I1, I5, k1]*SU3F[6, I3, k3])/6 + - (SU3D[I1, I3, k1]*SU3F[6, I5, k3])/4 + (I/12)*SU3F[6, I5, k3]* - SU3F[I1, I3, k1] - (I/6)*SU3F[6, I3, k3]*SU3F[I1, I5, k1] - - (I/6)*SU3F[6, I1, k3]*SU3F[I3, I5, k1]) + SU3D[I4, k1, k3]* - (-(SU3D[I3, I5, k2]*SU3F[6, I1, k3])/6 + (I/12)*SU3F[6, I5, k2]* - SU3F[I1, I3, k3] - (I/6)*SU3F[6, I3, k2]*SU3F[I1, I5, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I3, I5, k3]) + SU3D[I4, I5, k3]* - ((-I/2)*SU3F[6, I3, k1]*SU3F[I1, k2, k3] - - (SU3D[6, I1, k1]*SU3F[I3, k2, k3])/6 - (I/6)*SU3F[6, I1, k1]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k1]* - ((-I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I5, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I3, k1, k3])/12 + - (SU3F[I1, I3, k3]*SU3F[I4, k1, k3])/12) - (I/6)*SU3D[I1, I5, k1]* - SU3F[6, I3, k3]*SU3F[I4, k2, k3] + SU3D[I3, I5, k3]* - (-(SU3D[I4, k2, k3]*SU3F[6, I1, k1])/6 + (I/2)*SU3F[6, I4, k1]* - SU3F[I1, k2, k3] + SU3D[6, I1, k1]*((I/6)*SU3D[I4, k2, k3] + - SU3F[I4, k2, k3]/6) + (I/6)*SU3F[6, I1, k1]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k1]*((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I4, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I4, k1]*SU3F[I3, k2, k3])/3 - - (SU3F[I1, I3, k1]*SU3F[I4, k2, k3])/12) + SU3F[6, I4, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I3, k1, k3])/12 + - (SU3F[I1, I3, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I3, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I1, I4, k3]*SU3F[I5, k1, k3])/6) + SU3F[6, I1, k2]* - (-(SU3F[I3, I5, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I3, I4, k3]*SU3F[I5, k1, k3])/6) - (I/6)*SU3D[I1, I4, k1]* - SU3F[6, I3, k3]*SU3F[I5, k2, k3] + SU3D[I3, I4, k3]* - (-(SU3D[I5, k2, k3]*SU3F[6, I1, k1])/6 + (I/2)*SU3F[6, I5, k1]* - SU3F[I1, k2, k3] + SU3D[6, I1, k1]*((I/6)*SU3D[I5, k2, k3] + - SU3F[I5, k2, k3]/6) + (I/6)*SU3F[6, I1, k1]*SU3F[I5, k2, k3]) + - SU3D[I3, I4, k1]*((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I5, k2, k3]) + SU3D[I1, I3, k1]* - ((I/4)*SU3F[6, I5, k3]*SU3F[I4, k2, k3] + (I/4)*SU3F[6, I4, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I5, k1]*SU3F[I3, k2, k3])/3 - - (SU3F[I1, I3, k1]*SU3F[I5, k2, k3])/12) + SU3D[6, I4, k1]* - ((SU3D[I5, k2, k3]*SU3F[I1, I3, k3])/12 - - (SU3D[I3, k2, k3]*SU3F[I1, I5, k3])/12 + - (SU3D[I3, I5, k3]*SU3F[I1, k2, k3])/2 + (I/12)*SU3F[I1, I5, k3]* - SU3F[I3, k2, k3] - (I/12)*SU3F[I1, I3, k3]*SU3F[I5, k2, k3]) + - SU3F[6, I3, k3]*((SU3F[I1, I5, k1]*SU3F[I4, k2, k3])/6 + - (SU3F[I1, I4, k1]*SU3F[I5, k2, k3])/6) + SU3D[6, I3, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I4, k3])/6 - - (SU3D[I4, k2, k3]*SU3F[I1, I5, k3])/6 - - (SU3D[I4, I5, k3]*SU3F[I1, k2, k3])/2 + (I/6)*SU3F[I1, I5, k3]* - SU3F[I4, k2, k3] + (I/6)*SU3F[I1, I4, k3]*SU3F[I5, k2, k3]) + - SU3F[6, I1, k3]*((SU3F[I3, I5, k1]*SU3F[I4, k2, k3])/6 + - (SU3F[I3, I4, k1]*SU3F[I5, k2, k3])/6) + SU3D[6, I1, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I3, I4, k3])/6 - - (SU3D[I4, k2, k3]*SU3F[I3, I5, k3])/6 + (I/6)*SU3F[I3, I5, k3]* - SU3F[I4, k2, k3] + (I/6)*SU3F[I3, I4, k3]*SU3F[I5, k2, k3])) + - SU3F[I1, I5, k1]*((-I/6)*SU3F[I3, I4, k1]*SUNDelta[6, I2] + - (I/6)*SU3F[I2, I3, k1]*SUNDelta[6, I4]) + SU3F[I1, I4, k1]* - ((-I/6)*SU3F[I3, I5, k1]*SUNDelta[6, I2] + (I/6)*SU3F[I2, I3, k1]* - SUNDelta[6, I5]) + SU3F[I1, I2, k1]* - ((-I/6)*SU3F[I3, I5, k1]*SUNDelta[6, I4] - (I/6)*SU3F[I3, I4, k1]* - SUNDelta[6, I5]) + SU3D[I3, I5, k1]* - (SU3F[6, I4, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/6) + - (5*SU3F[I1, I4, k1]*SUNDelta[6, I2])/18 + - (5*SU3F[I1, I2, k1]*SUNDelta[6, I4])/18 - - (SU3F[6, I4, k1]*SUNDelta[I1, I2])/6 - - (SU3F[6, I2, k1]*SUNDelta[I1, I4])/6) + SU3D[I3, I4, k1]* - (SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/6) + - (5*SU3F[I1, I5, k1]*SUNDelta[6, I2])/18 + - (5*SU3F[I1, I2, k1]*SUNDelta[6, I5])/18 - - (SU3F[6, I5, k1]*SUNDelta[I1, I2])/6 - - (SU3F[6, I2, k1]*SUNDelta[I1, I5])/6) + SU3D[I2, I3, k1]* - (SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I4, k2]* - ((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6) + ((2*I)/9)*SU3D[I4, I5, k1]* - SUNDelta[6, I1] + ((5*I)/18)*SU3D[I1, I5, k1]*SUNDelta[6, I4] + - (5*SU3F[I1, I5, k1]*SUNDelta[6, I4])/18 + ((5*I)/18)*SU3D[I1, I4, k1]* - SUNDelta[6, I5] + (5*SU3F[I1, I4, k1]*SUNDelta[6, I5])/18 - - (SU3F[6, I5, k1]*SUNDelta[I1, I4])/6 - - (SU3F[6, I4, k1]*SUNDelta[I1, I5])/6) + SU3D[I4, I5, k1]* - (SU3F[6, I3, k2]*(-(SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I1, k2]* - ((SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/6) + - (4*SU3F[I2, I3, k1]*SUNDelta[6, I1])/9 - - (7*SU3F[I1, I2, k1]*SUNDelta[6, I3])/9 - - (2*SU3F[6, I3, k1]*SUNDelta[I1, I2])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I2, I3])/9) + SU3D[I2, I5, k1]* - (SU3F[6, I4, k2]*((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I3, k2]* - (-(SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/6 + - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6) + ((2*I)/9)*SU3D[I3, I4, k1]* - SUNDelta[6, I1] - (4*SU3F[I3, I4, k1]*SUNDelta[6, I1])/9 + - (I/9)*SU3D[I1, I4, k1]*SUNDelta[6, I3] - - (7*SU3F[I1, I4, k1]*SUNDelta[6, I3])/9 - ((8*I)/9)*SU3D[I1, I3, k1]* - SUNDelta[6, I4] - (2*SU3F[6, I3, k1]*SUNDelta[I1, I4])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I3, I4])/9) + SU3D[I1, I5, k1]* - (-(SU3F[6, I4, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/4 - - (SU3F[6, I2, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/4 + - SU3F[6, I3, k2]*(-(SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/6) + ((5*I)/18)*SU3D[I3, I4, k1]* - SUNDelta[6, I2] + (SU3F[I3, I4, k1]*SUNDelta[6, I2])/6 - - (SU3F[I2, I3, k1]*SUNDelta[6, I4])/6 - - (SU3F[6, I4, k1]*SUNDelta[I2, I3])/9 + - (SU3F[6, I3, k1]*SUNDelta[I2, I4])/9 - - (SU3F[6, I2, k1]*SUNDelta[I3, I4])/9) + SU3F[6, I5, k1]* - ((-I/3)*SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] + - (I/12)*SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3] - - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3] - - (I/3)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3] + - SU3F[I2, k1, k3]*((-I/12)*SU3F[I1, I4, k2]*SU3F[I3, k2, k3] + - (I/12)*SU3F[I1, I3, k2]*SU3F[I4, k2, k3]) + (I/6)*SU3F[I3, I4, k1]* - SUNDelta[I1, I2] - (I/6)*SU3F[I2, I3, k1]*SUNDelta[I1, I4] + - ((5*I)/9)*SU3F[I1, I4, k1]*SUNDelta[I2, I3] - (I/9)*SU3F[I1, I3, k1]* - SUNDelta[I2, I4] + ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I3, I4]) + - SU3D[6, I5, k1]*((SU3D[I2, I4, k2]*SU3D[I3, k1, k3]*SU3F[I1, k2, k3])/ - 2 + SU3D[I3, I4, k3]*(-(SU3D[I2, k2, k3]*SU3F[I1, k1, k2])/3 + - SU3D[I1, k1, k2]*((-I/3)*SU3D[I2, k2, k3] - SU3F[I2, k2, k3]/3)) + - SU3D[I3, I4, k2]*((I/2)*SU3F[I1, k2, k3]*SU3F[I2, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) - - (SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/3 + - SU3D[I4, k2, k3]*(-(SU3D[I2, I3, k2]*SU3F[I1, k1, k3])/3 - - (I/12)*SU3F[I1, I3, k2]*SU3F[I2, k1, k3] + (I/3)*SU3F[I1, I2, k2]* - SU3F[I3, k1, k3]) + SU3D[I4, k1, k3]* - (-(SU3D[I2, I3, k2]*SU3F[I1, k2, k3])/2 + - (SU3D[I1, I3, k2]*SU3F[I2, k2, k3])/4 - - (SU3D[I1, I2, k2]*SU3F[I3, k2, k3])/4) + SU3D[I4, k1, k2]* - ((-I/12)*SU3F[I1, I3, k3]*SU3F[I2, k2, k3] + (I/12)*SU3F[I1, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I2, I4, k2]* - ((-I/2)*SU3F[I1, k2, k3]*SU3F[I3, k1, k3] - (I/3)*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, I4, k2]* - (-(SU3D[I2, k1, k3]*SU3F[I3, k2, k3])/4 + (I/4)*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, k2, k3]* - ((I/2)*SU3D[I2, k1, k2]*SU3D[I3, I4, k3] + - (SU3D[I3, I4, k3]*SU3F[I2, k1, k2])/2 + SU3D[I2, I4, k3]* - ((-I/2)*SU3D[I3, k1, k2] - SU3F[I3, k1, k2]/2) + - SU3D[I2, I3, k3]*((I/2)*SU3D[I4, k1, k2] + SU3F[I4, k1, k2]/2)) + - (SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/12 + - (I/4)*SU3D[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3] - - (SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/12 + - SU3D[I3, k2, k3]*((I/4)*SU3D[I1, I2, k2]*SU3D[I4, k1, k3] - - (SU3D[I4, k1, k2]*SU3F[I1, I2, k3])/12 - - (SU3D[I2, I4, k2]*SU3F[I1, k1, k3])/3 + SU3D[I1, I4, k2]* - ((I/4)*SU3D[I2, k1, k3] + SU3F[I2, k1, k3]/4) + - (I/12)*SU3F[I1, I4, k2]*SU3F[I2, k1, k3] + - (SU3D[I1, I2, k2]*SU3F[I4, k1, k3])/4 + (I/12)*SU3F[I1, I2, k2]* - SU3F[I4, k1, k3]) + SU3D[I2, k2, k3]* - ((-I/4)*SU3D[I1, I3, k2]*SU3D[I4, k1, k3] + - (SU3D[I4, k1, k2]*SU3F[I1, I3, k3])/12 - - (SU3D[I3, k1, k2]*SU3F[I1, I4, k3])/3 + (I/3)*SU3F[I1, I4, k2]* - SU3F[I3, k1, k3] - (SU3D[I1, I3, k2]*SU3F[I4, k1, k3])/4 - - (I/12)*SU3F[I1, I3, k2]*SU3F[I4, k1, k3]) + - SU3D[I1, k1, k2]*(SU3D[I2, I4, k3]*((-I/3)*SU3D[I3, k2, k3] - - SU3F[I3, k2, k3]/3) + SU3D[I2, I3, k3]*((-I/3)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/3)) + SU3D[I1, I3, k2]*SU3D[I2, k1, k3]* - ((-I/4)*SU3D[I4, k2, k3] + SU3F[I4, k2, k3]/4) - - (SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/3 + - SU3D[I3, k1, k2]*(-(SU3D[I4, k2, k3]*SU3F[I1, I2, k3])/3 + - (I/3)*SU3F[I1, I4, k3]*SU3F[I2, k2, k3] + (I/3)*SU3F[I1, I2, k3]* - SU3F[I4, k2, k3]) + SU3F[I2, k1, k3]* - (-(SU3F[I1, I4, k2]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k2]*SU3F[I4, k2, k3])/12) + SU3D[I2, k1, k2]* - ((SU3D[I4, k2, k3]*SU3F[I1, I3, k3])/12 - - (SU3D[I3, k2, k3]*SU3F[I1, I4, k3])/12 + - (SU3D[I3, I4, k3]*SU3F[I1, k2, k3])/2 + (I/12)*SU3F[I1, I4, k3]* - SU3F[I3, k2, k3] - (I/12)*SU3F[I1, I3, k3]*SU3F[I4, k2, k3]) + - SU3D[I2, I3, k2]*((I/2)*SU3F[I1, k2, k3]*SU3F[I4, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) + SU3D[I1, I3, k2]* - (-(SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/4 - (I/4)*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] - (I/4)*SU3F[I2, k1, k3]*SU3F[I4, k2, k3]) + - (I/6)*SU3D[I3, I4, k1]*SUNDelta[I1, I2] + - (SU3F[I3, I4, k1]*SUNDelta[I1, I2])/6 + (I/6)*SU3D[I2, I3, k1]* - SUNDelta[I1, I4] - (SU3F[I2, I3, k1]*SUNDelta[I1, I4])/6 + - (I/9)*SU3D[I1, I4, k1]*SUNDelta[I2, I3] + - (5*SU3F[I1, I4, k1]*SUNDelta[I2, I3])/9 - ((5*I)/9)*SU3D[I1, I3, k1]* - SUNDelta[I2, I4] - (SU3F[I1, I3, k1]*SUNDelta[I2, I4])/9 + - (I/9)*SU3D[I1, I2, k1]*SUNDelta[I3, I4] + - (5*SU3F[I1, I2, k1]*SUNDelta[I3, I4])/9) + - SUNDelta[6, I5]*(((5*I)/27)*SUNDelta[I1, I4]*SUNDelta[I2, I3] - - ((16*I)/27)*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - ((5*I)/27)*SUNDelta[I1, I2]*SUNDelta[I3, I4]) + - SU3D[I2, I4, k1]*(SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/ - 3 + (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + - SU3F[6, I3, k2]*(-(SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/6 + - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/6) + ((2*I)/9)*SU3D[I3, I5, k1]* - SUNDelta[6, I1] - (4*SU3F[I3, I5, k1]*SUNDelta[6, I1])/9 + - (I/9)*SU3D[I1, I5, k1]*SUNDelta[6, I3] - - (7*SU3F[I1, I5, k1]*SUNDelta[6, I3])/9 - ((8*I)/9)*SU3D[I1, I3, k1]* - SUNDelta[6, I5] - (2*SU3F[6, I3, k1]*SUNDelta[I1, I5])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I3, I5])/9) + SU3D[I1, I4, k1]* - (-(SU3F[6, I5, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/4 - - (SU3F[6, I2, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/4 + - SU3F[6, I3, k2]*(-(SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/6) + ((5*I)/18)*SU3D[I3, I5, k1]* - SUNDelta[6, I2] + (SU3F[I3, I5, k1]*SUNDelta[6, I2])/6 - - (SU3F[I2, I3, k1]*SUNDelta[6, I5])/6 - - (SU3F[6, I5, k1]*SUNDelta[I2, I3])/9 + - (SU3F[6, I3, k1]*SUNDelta[I2, I5])/9 - - (SU3F[6, I2, k1]*SUNDelta[I3, I5])/9) + SU3F[6, I4, k1]* - ((-I/3)*SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] + - (I/12)*SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3] - - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3] - - (I/3)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3] + - SU3F[I2, k1, k3]*((-I/12)*SU3F[I1, I5, k2]*SU3F[I3, k2, k3] + - (I/12)*SU3F[I1, I3, k2]*SU3F[I5, k2, k3]) + (I/6)*SU3F[I3, I5, k1]* - SUNDelta[I1, I2] - (I/6)*SU3F[I2, I3, k1]*SUNDelta[I1, I5] + - ((5*I)/9)*SU3F[I1, I5, k1]*SUNDelta[I2, I3] - (I/9)*SU3F[I1, I3, k1]* - SUNDelta[I2, I5] + ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I3, I5]) + - SU3D[6, I4, k1]*(-(SU3D[I2, I3, k2]*SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/ - 2 + SU3D[I3, I5, k2]*((I/2)*SU3F[I1, k2, k3]*SU3F[I2, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) - - (SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/3 + - SU3D[I5, k2, k3]*((-I/12)*SU3F[I1, I3, k2]*SU3F[I2, k1, k3] + - (I/3)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]) + (I/4)*SU3D[I1, I5, k2]* - SU3F[I2, k1, k3]*SU3F[I3, k2, k3] + SU3D[I5, k1, k2]* - ((-I/12)*SU3F[I1, I3, k3]*SU3F[I2, k2, k3] + (I/12)*SU3F[I1, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I2, I5, k2]* - ((SU3D[I3, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I3, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]) + - (SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/12 - - (SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/12 + - SU3D[I3, k2, k3]*((I/4)*SU3D[I1, I5, k2]*SU3D[I2, k1, k3] - - (SU3D[I5, k1, k2]*SU3F[I1, I2, k3])/12 - - (SU3D[I2, I5, k2]*SU3F[I1, k1, k3])/3 + - (SU3D[I1, I5, k2]*SU3F[I2, k1, k3])/4 + (I/12)*SU3F[I1, I5, k2]* - SU3F[I2, k1, k3] + SU3D[I1, I2, k2]*((I/4)*SU3D[I5, k1, k3] + - SU3F[I5, k1, k3]/4) + (I/12)*SU3F[I1, I2, k2]*SU3F[I5, k1, k3]) + - SU3D[I1, I2, k2]*(-(SU3D[I5, k1, k3]*SU3F[I3, k2, k3])/4 + - (I/4)*SU3F[I3, k2, k3]*SU3F[I5, k1, k3]) + SU3D[I2, k1, k3]* - (-(SU3D[I1, I5, k2]*SU3F[I3, k2, k3])/4 + SU3D[I1, I3, k2]* - ((-I/4)*SU3D[I5, k2, k3] + SU3F[I5, k2, k3]/4)) - - (SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/3 + - SU3D[I3, k1, k2]*(-(SU3D[I5, k2, k3]*SU3F[I1, I2, k3])/3 + - (I/3)*SU3F[I1, I5, k3]*SU3F[I2, k2, k3] + (I/3)*SU3F[I1, I2, k3]* - SU3F[I5, k2, k3]) + SU3F[I2, k1, k3]* - (-(SU3F[I1, I5, k2]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k2]*SU3F[I5, k2, k3])/12) + SU3D[I2, I3, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I1, I3, k2]*(-(SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/4 + - (SU3D[I5, k1, k3]*SU3F[I2, k2, k3])/4 - (I/4)*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] - (I/4)*SU3F[I2, k1, k3]*SU3F[I5, k2, k3]) + - (I/6)*SU3D[I3, I5, k1]*SUNDelta[I1, I2] + - (SU3F[I3, I5, k1]*SUNDelta[I1, I2])/6 + (I/6)*SU3D[I2, I3, k1]* - SUNDelta[I1, I5] - (SU3F[I2, I3, k1]*SUNDelta[I1, I5])/6 + - (I/9)*SU3D[I1, I5, k1]*SUNDelta[I2, I3] + - (5*SU3F[I1, I5, k1]*SUNDelta[I2, I3])/9 - ((5*I)/9)*SU3D[I1, I3, k1]* - SUNDelta[I2, I5] - (SU3F[I1, I3, k1]*SUNDelta[I2, I5])/9 + - (I/9)*SU3D[I1, I2, k1]*SUNDelta[I3, I5] + - (5*SU3F[I1, I2, k1]*SUNDelta[I3, I5])/9) + - SUNDelta[6, I4]*(((5*I)/27)*SUNDelta[I1, I5]*SUNDelta[I2, I3] - - ((16*I)/27)*SUNDelta[I1, I3]*SUNDelta[I2, I5] + - ((5*I)/27)*SUNDelta[I1, I2]*SUNDelta[I3, I5]) + - SU3D[I1, I3, k1]*(SU3F[6, I5, k2]*((SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/ - 4 + (SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/4) + - SU3F[6, I4, k2]*((SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/4 + - (SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/4) + SU3F[6, I2, k2]* - ((SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/4 + - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/4) - ((8*I)/9)*SU3D[I4, I5, k1]* - SUNDelta[6, I2] + (5*SU3F[6, I5, k1]*SUNDelta[I2, I4])/9 + - (5*SU3F[6, I4, k1]*SUNDelta[I2, I5])/9 + - (5*SU3F[6, I2, k1]*SUNDelta[I4, I5])/9) + SU3D[I1, I2, k1]* - (-(SU3F[6, I5, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/4 - - (SU3F[6, I4, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/4 + - SU3F[6, I3, k2]*(-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6) + (I/9)*SU3D[I4, I5, k1]* - SUNDelta[6, I3] + ((5*I)/18)*SU3D[I3, I5, k1]*SUNDelta[6, I4] + - (SU3F[I3, I5, k1]*SUNDelta[6, I4])/6 + ((5*I)/18)*SU3D[I3, I4, k1]* - SUNDelta[6, I5] + (SU3F[I3, I4, k1]*SUNDelta[6, I5])/6 - - (SU3F[6, I5, k1]*SUNDelta[I3, I4])/9 - - (SU3F[6, I4, k1]*SUNDelta[I3, I5])/9 + - (SU3F[6, I3, k1]*SUNDelta[I4, I5])/9) + SU3D[6, I3, k1]* - (SU3D[I4, I5, k2]*((-I/2)*SU3F[I1, k2, k3]*SU3F[I2, k1, k3] + - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) - - (SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/6 + - SU3D[I5, k2, k3]*((I/6)*SU3F[I1, I4, k2]*SU3F[I2, k1, k3] + - (I/6)*SU3F[I1, I2, k2]*SU3F[I4, k1, k3]) + SU3D[I5, k1, k2]* - ((I/6)*SU3F[I1, I4, k3]*SU3F[I2, k2, k3] + (I/6)*SU3F[I1, I2, k3]* - SU3F[I4, k2, k3]) + SU3D[I2, I5, k2]* - ((SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I4, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I4, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) - - (SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/6 + - SU3D[I4, k2, k3]*(-(SU3D[I5, k1, k2]*SU3F[I1, I2, k3])/6 + - (I/6)*SU3F[I1, I5, k2]*SU3F[I2, k1, k3] + (I/6)*SU3F[I1, I2, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I2, k2]*SU3D[I4, k1, k3]* - ((I/6)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/6) + - SU3D[I4, k1, k2]*(-(SU3D[I5, k2, k3]*SU3F[I1, I2, k3])/6 + - (I/6)*SU3F[I1, I5, k3]*SU3F[I2, k2, k3] + (I/6)*SU3F[I1, I2, k3]* - SU3F[I5, k2, k3]) + SU3F[I2, k1, k3]* - (-(SU3F[I1, I5, k2]*SU3F[I4, k2, k3])/6 - - (SU3F[I1, I4, k2]*SU3F[I5, k2, k3])/6) + SU3D[I2, I4, k2]* - ((SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3F[I1, I2, k2]*(-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6) + SU3D[I1, I2, k2]* - ((SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I4, k2, k3])/6 + SU3D[I4, k2, k3]* - ((I/6)*SU3D[I5, k1, k3] + SU3F[I5, k1, k3]/6) + - (I/6)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] + (I/6)*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3]) + ((2*I)/9)*SU3D[I4, I5, k1]*SUNDelta[I1, I2] + - ((2*I)/9)*SU3D[I2, I5, k1]*SUNDelta[I1, I4] + - ((2*I)/9)*SU3D[I2, I4, k1]*SUNDelta[I1, I5] - (I/9)*SU3D[I1, I5, k1]* - SUNDelta[I2, I4] - (5*SU3F[I1, I5, k1]*SUNDelta[I2, I4])/9 - - (I/9)*SU3D[I1, I4, k1]*SUNDelta[I2, I5] - - (5*SU3F[I1, I4, k1]*SUNDelta[I2, I5])/9 - (I/9)*SU3D[I1, I2, k1]* - SUNDelta[I4, I5] - (5*SU3F[I1, I2, k1]*SUNDelta[I4, I5])/9) + - SU3F[6, I3, k1]*((-I/6)*SU3F[I1, I5, k2]*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] - (I/6)*SU3F[I1, I4, k2]*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] + SU3F[I2, k1, k3]*((-I/6)*SU3F[I1, I5, k2]* - SU3F[I4, k2, k3] - (I/6)*SU3F[I1, I4, k2]*SU3F[I5, k2, k3]) + - SU3F[I1, I2, k2]*((-I/6)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] - - (I/6)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) - - ((5*I)/9)*SU3F[I1, I5, k1]*SUNDelta[I2, I4] - - ((5*I)/9)*SU3F[I1, I4, k1]*SUNDelta[I2, I5] - - ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I4, I5]) + - SU3D[6, I2, k1]*(-(SU3D[I3, I4, k2]*SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/ - 2 + SU3D[I5, k2, k3]*((I/3)*SU3F[I1, I4, k2]*SU3F[I3, k1, k3] - - (I/12)*SU3F[I1, I3, k2]*SU3F[I4, k1, k3]) + - SU3D[I5, k1, k2]*((I/12)*SU3F[I1, I4, k3]*SU3F[I3, k2, k3] - - (I/12)*SU3F[I1, I3, k3]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k2]*(-(SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/3 + - (I/2)*SU3F[I1, k2, k3]*SU3F[I4, k1, k3] - (I/3)*SU3F[I1, k1, k3]* - SU3F[I4, k2, k3]) + SU3F[I1, I5, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/12 - - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/3) + SU3D[I4, k2, k3]* - ((SU3D[I5, k1, k2]*SU3F[I1, I3, k3])/12 + (I/3)*SU3F[I1, I5, k2]* - SU3F[I3, k1, k3] - (I/12)*SU3F[I1, I3, k2]*SU3F[I5, k1, k3]) + - SU3D[I4, k1, k3]*(-(SU3D[I3, I5, k2]*SU3F[I1, k2, k3])/2 + - SU3D[I1, I3, k2]*((-I/4)*SU3D[I5, k2, k3] + SU3F[I5, k2, k3]/4)) + - SU3D[I4, k1, k2]*((SU3D[I5, k2, k3]*SU3F[I1, I3, k3])/12 + - (I/12)*SU3F[I1, I5, k3]*SU3F[I3, k2, k3] - (I/12)*SU3F[I1, I3, k3]* - SU3F[I5, k2, k3]) + SU3D[I3, I4, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3F[I1, I4, k2]*(-(SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/12 - - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/3) + SU3D[I1, I3, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/4 + - (SU3D[I5, k1, k3]*SU3F[I4, k2, k3])/4 + SU3D[I4, k2, k3]* - ((-I/4)*SU3D[I5, k1, k3] - SU3F[I5, k1, k3]/4) - - (I/4)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] - (I/4)*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3]) + SU3F[I1, I3, k2]* - ((SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/12 + - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/12) + (I/6)*SU3D[I3, I5, k1]* - SUNDelta[I1, I4] + (SU3F[I3, I5, k1]*SUNDelta[I1, I4])/6 + - (I/6)*SU3D[I3, I4, k1]*SUNDelta[I1, I5] + - (SU3F[I3, I4, k1]*SUNDelta[I1, I5])/6 + (I/9)*SU3D[I1, I5, k1]* - SUNDelta[I3, I4] + (5*SU3F[I1, I5, k1]*SUNDelta[I3, I4])/9 + - (I/9)*SU3D[I1, I4, k1]*SUNDelta[I3, I5] + - (5*SU3F[I1, I4, k1]*SUNDelta[I3, I5])/9 - ((5*I)/9)*SU3D[I1, I3, k1]* - SUNDelta[I4, I5] - (SU3F[I1, I3, k1]*SUNDelta[I4, I5])/9) + - SU3F[6, I2, k1]*(SU3F[I1, I5, k2]*((-I/12)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] - (I/3)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3]) + - SU3F[I1, I4, k2]*((-I/12)*SU3F[I3, k2, k3]*SU3F[I5, k1, k3] - - (I/3)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3]) + SU3F[I1, I3, k2]* - ((I/12)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] + (I/12)*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3]) + (I/6)*SU3F[I3, I5, k1]*SUNDelta[I1, I4] + - (I/6)*SU3F[I3, I4, k1]*SUNDelta[I1, I5] + ((5*I)/9)*SU3F[I1, I5, k1]* - SUNDelta[I3, I4] + ((5*I)/9)*SU3F[I1, I4, k1]*SUNDelta[I3, I5] - - (I/9)*SU3F[I1, I3, k1]*SUNDelta[I4, I5]) + - SU3F[6, I1, k1]*((I/6)*SU3F[I2, I3, k2]*SU3F[I4, k2, k3]* - SU3F[I5, k1, k3] + SU3F[I2, k2, k3]*((-I/6)*SU3F[I3, I5, k2]* - SU3F[I4, k1, k3] - (I/6)*SU3F[I3, I4, k2]*SU3F[I5, k1, k3]) + - (I/6)*SU3F[I2, I3, k2]*SU3F[I4, k1, k3]*SU3F[I5, k2, k3] + - SU3F[I2, k1, k2]*((I/6)*SU3F[I3, I5, k3]*SU3F[I4, k2, k3] + - (I/6)*SU3F[I3, I4, k3]*SU3F[I5, k2, k3]) - - ((2*I)/9)*SU3F[I3, I5, k1]*SUNDelta[I2, I4] - - ((2*I)/9)*SU3F[I3, I4, k1]*SUNDelta[I2, I5] + - ((2*I)/9)*SU3F[I2, I3, k1]*SUNDelta[I4, I5]) + - SU3D[6, I1, k1]*(SU3D[I5, k2, k3]*((I/6)*SU3F[I2, k1, k3]* - SU3F[I3, I4, k2] - (I/6)*SU3F[I2, I3, k2]*SU3F[I4, k1, k3]) + - SU3D[I5, k1, k3]*(-(SU3D[I3, I4, k2]*SU3F[I2, k2, k3])/6 - - (SU3D[I2, I3, k2]*SU3F[I4, k2, k3])/6) + SU3D[I5, k1, k2]* - ((I/6)*SU3F[I2, k2, k3]*SU3F[I3, I4, k3] - (I/6)*SU3F[I2, I3, k3]* - SU3F[I4, k2, k3]) + SU3D[I3, I5, k2]* - ((SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/6 + (I/6)*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I2, k1, k3]*SU3F[I4, k2, k3]) + - SU3D[I2, I5, k2]*(SU3D[I4, k2, k3]*((I/6)*SU3D[I3, k1, k3] + - SU3F[I3, k1, k3]/6) + (SU3D[I4, k1, k3]*SU3F[I3, k2, k3])/6 - - (I/6)*SU3F[I3, k2, k3]*SU3F[I4, k1, k3] - - (SU3D[I3, k1, k3]*SU3F[I4, k2, k3])/6 + (I/6)*SU3F[I3, k1, k3]* - SU3F[I4, k2, k3]) + (SU3F[I2, I3, k2]*SU3F[I4, k2, k3]* - SU3F[I5, k1, k3])/6 + SU3D[I4, k2, k3]* - ((I/6)*SU3D[I2, I3, k2]*SU3D[I5, k1, k3] + - (SU3D[I5, k1, k2]*SU3F[I2, I3, k3])/6 + (I/6)*SU3F[I2, k1, k3]* - SU3F[I3, I5, k2] + (SU3D[I2, I3, k2]*SU3F[I5, k1, k3])/6 - - (I/6)*SU3F[I2, I3, k2]*SU3F[I5, k1, k3]) + SU3F[I2, k2, k3]* - (-(SU3F[I3, I5, k2]*SU3F[I4, k1, k3])/6 - - (SU3F[I3, I4, k2]*SU3F[I5, k1, k3])/6) + SU3D[I4, k1, k3]* - (-(SU3D[I3, I5, k2]*SU3F[I2, k2, k3])/6 + SU3D[I2, I3, k2]* - ((I/6)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/6)) + - SU3D[I2, I4, k2]*SU3D[I3, k1, k3]*((I/6)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/6) + (SU3F[I2, I3, k2]*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3])/6 + SU3D[I4, k1, k2]* - ((SU3D[I5, k2, k3]*SU3F[I2, I3, k3])/6 + (I/6)*SU3F[I2, k2, k3]* - SU3F[I3, I5, k3] - (I/6)*SU3F[I2, I3, k3]*SU3F[I5, k2, k3]) + - SU3D[I3, I4, k2]*((SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/6 + - (I/6)*SU3F[I2, k2, k3]*SU3F[I5, k1, k3] + (I/6)*SU3F[I2, k1, k3]* - SU3F[I5, k2, k3]) + SU3F[I2, k1, k2]* - ((SU3F[I3, I5, k3]*SU3F[I4, k2, k3])/6 + - (SU3F[I3, I4, k3]*SU3F[I5, k2, k3])/6) + SU3D[I2, I4, k2]* - ((SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/6 + - (SU3D[I5, k1, k3]*SU3F[I3, k2, k3])/6 - (I/6)*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I2, I3, k2]*((SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/6 + - (I/6)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] + (I/6)*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3]) + ((2*I)/9)*SU3D[I4, I5, k1]*SUNDelta[I2, I3] - - (2*SU3F[I3, I5, k1]*SUNDelta[I2, I4])/9 - - (2*SU3F[I3, I4, k1]*SUNDelta[I2, I5])/9 + ((2*I)/9)*SU3D[I2, I5, k1]* - SUNDelta[I3, I4] + ((2*I)/9)*SU3D[I2, I4, k1]*SUNDelta[I3, I5] + - (2*SU3F[I2, I3, k1]*SUNDelta[I4, I5])/9) + - SUNDelta[6, I3]*(((2*I)/27)*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - ((2*I)/27)*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - ((2*I)/27)*SUNDelta[I1, I2]*SUNDelta[I4, I5]) + - SUNDelta[6, I2]*(((5*I)/27)*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - ((5*I)/27)*SUNDelta[I1, I4]*SUNDelta[I3, I5] - - ((16*I)/27)*SUNDelta[I1, I3]*SUNDelta[I4, I5]) + - SUNDelta[6, I1]*(((4*I)/27)*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - ((4*I)/27)*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - ((4*I)/27)*SUNDelta[I2, I3]*SUNDelta[I4, I5])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(CouplingConstant[ChPTW3[2], 1]*(((-4*I)/9)*SU3D[6, I2, I5]* - SU3D[I1, I3, I4] - ((4*I)/9)*SU3D[6, I2, I4]*SU3D[I1, I3, I5] - - ((4*I)/9)*SU3D[6, I2, I3]*SU3D[I1, I4, I5] - ((5*I)/9)*SU3D[6, I1, I5]* - SU3D[I2, I3, I4] - ((5*I)/9)*SU3D[6, I1, I4]*SU3D[I2, I3, I5] - - ((5*I)/9)*SU3D[6, I1, I3]*SU3D[I2, I4, I5] + - I*SU3D[6, I1, I2]*SU3D[I3, I4, I5] + (SU3D[I3, I4, I5]*SU3F[6, I1, I2])/ - 3 - (7*SU3D[I2, I4, I5]*SU3F[6, I1, I3])/9 - - (7*SU3D[I2, I3, I5]*SU3F[6, I1, I4])/9 - - (7*SU3D[I2, I3, I4]*SU3F[6, I1, I5])/9 - - (2*SU3D[I1, I4, I5]*SU3F[6, I2, I3])/9 - - (2*SU3D[I1, I3, I5]*SU3F[6, I2, I4])/9 - - (2*SU3D[I1, I3, I4]*SU3F[6, I2, I5])/9 + SU3D[6, I4, I5]* - (((2*I)/3)*SU3D[I1, I2, I3] + (2*SU3F[I1, I2, I3])/9) + - SU3D[6, I3, I5]*(((2*I)/3)*SU3D[I1, I2, I4] + (2*SU3F[I1, I2, I4])/9) + - SU3D[6, I3, I4]*(((2*I)/3)*SU3D[I1, I2, I5] + (2*SU3F[I1, I2, I5])/9) + - SU3D[I4, I5, k2]*(SU3D[6, I3, k1]*((-I/2)*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) + - SU3D[6, I1, k1]*((-I/6)*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] + - (I/6)*SU3F[I2, k1, k3]*SU3F[I3, k2, k3])) + - SU3D[I5, k2, k3]*(SU3D[I3, I4, k1]*((I/2)*SU3F[6, I2, k2]* - SU3F[I1, k1, k3] + (I/6)*SU3F[6, I1, k2]*SU3F[I2, k1, k3]) + - SU3D[I2, I4, k1]*((-I/2)*SU3F[6, I3, k2]*SU3F[I1, k1, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I3, k1, k3]) + SU3D[I1, I4, k1]* - ((-I/4)*SU3F[6, I3, k2]*SU3F[I2, k1, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I3, k1, k3]) + SU3D[I2, I3, k1]* - ((-I/2)*SU3F[6, I4, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I4, k1, k3]) + SU3D[I1, I3, k1]* - ((-I/4)*SU3F[6, I4, k2]*SU3F[I2, k1, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I4, k1, k3]) + SU3D[I1, I2, k1]* - ((I/4)*SU3F[6, I4, k2]*SU3F[I3, k1, k3] + (I/4)*SU3F[6, I3, k2]* - SU3F[I4, k1, k3])) + SU3D[I5, k1, k2]* - (SU3D[I3, I4, k1]*((-I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I2, k2, k3]) + SU3F[6, I4, k2]* - (-(SU3F[I1, I3, k3]*SU3F[I2, k1, k3])/12 + - (SU3F[I1, I2, k3]*SU3F[I3, k1, k3])/12) - (I/6)*SU3D[I1, I4, k1]* - SU3F[6, I2, k3]*SU3F[I3, k2, k3] + SU3D[I2, I4, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I3, k1]*SU3F[I2, k2, k3])/3 - - (SU3F[I1, I2, k1]*SU3F[I3, k2, k3])/12) + SU3F[6, I3, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I2, k1, k3])/12 + - (SU3F[I1, I2, k3]*SU3F[I4, k1, k3])/12) + SU3F[6, I2, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I1, I3, k3]*SU3F[I4, k1, k3])/6) + SU3F[6, I1, k2]* - (-(SU3F[I2, I4, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I2, I3, k3]*SU3F[I4, k1, k3])/6) - (I/6)*SU3D[I1, I3, k1]* - SU3F[6, I2, k3]*SU3F[I4, k2, k3] + SU3D[I2, I3, k1]* - ((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I4, k2, k3]) + SU3D[I1, I2, k1]* - ((I/4)*SU3F[6, I4, k3]*SU3F[I3, k2, k3] + (I/4)*SU3F[6, I3, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I3, k3]* - ((SU3F[I1, I4, k1]*SU3F[I2, k2, k3])/3 - - (SU3F[I1, I2, k1]*SU3F[I4, k2, k3])/12) + SU3F[6, I2, k3]* - ((SU3F[I1, I4, k1]*SU3F[I3, k2, k3])/6 + - (SU3F[I1, I3, k1]*SU3F[I4, k2, k3])/6) + SU3F[6, I1, k3]* - ((SU3F[I2, I4, k1]*SU3F[I3, k2, k3])/6 + - (SU3F[I2, I3, k1]*SU3F[I4, k2, k3])/6)) + - SU3D[I1, I5, k2]*(SU3D[6, I2, k1]*SU3D[I3, k2, k3]* - ((I/6)*SU3D[I4, k1, k3] + SU3F[I4, k1, k3]/6) + - SU3D[6, I3, k1]*(-(SU3D[I4, k1, k3]*SU3F[I2, k2, k3])/4 + - (I/4)*SU3F[I2, k2, k3]*SU3F[I4, k1, k3]) + SU3D[6, I2, k1]* - ((SU3D[I4, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3D[I4, k1, k3]*SU3F[I3, k2, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])) + - SU3D[I1, k2, k3]*((-I/2)*SU3D[6, I2, k1]*SU3D[I3, k1, k3]* - SU3D[I4, I5, k2] + SU3D[I2, k1, k2]*((-I/2)*SU3D[6, I4, k1]* - SU3D[I3, I5, k3] - (I/2)*SU3D[6, I3, k1]*SU3D[I4, I5, k3]) - - (SU3D[6, I3, k1]*SU3D[I4, I5, k3]*SU3F[I2, k1, k2])/2 + - SU3D[6, I2, k1]*((-I/2)*SU3D[I3, I5, k2]*SU3D[I4, k1, k3] - - (I/2)*SU3D[I3, I4, k2]*SU3D[I5, k1, k3] - - (SU3D[I4, I5, k3]*SU3F[I3, k1, k2])/2) + SU3D[6, I3, k1]* - SU3D[I2, I5, k3]*((I/2)*SU3D[I4, k1, k2] + SU3F[I4, k1, k2]/2) - - (SU3D[6, I2, k1]*SU3D[I3, I5, k3]*SU3F[I4, k1, k2])/2 + - SU3D[6, I4, k1]*((I/2)*SU3D[I2, I5, k3]*SU3D[I3, k1, k2] - - (SU3D[I3, I5, k3]*SU3F[I2, k1, k2])/2 + - (SU3D[I2, I5, k3]*SU3F[I3, k1, k2])/2 + SU3D[I2, I3, k3]* - ((I/2)*SU3D[I5, k1, k2] + SU3F[I5, k1, k2]/2)) + - SU3D[6, I3, k1]*SU3D[I2, I4, k3]*((I/2)*SU3D[I5, k1, k2] + - SU3F[I5, k1, k2]/2) - (SU3D[6, I2, k1]*SU3D[I3, I4, k3]* - SU3F[I5, k1, k2])/2) + SU3D[I4, k2, k3]* - (SU3D[I5, k1, k3]*(-(SU3D[I2, I3, k1]*SU3F[6, I1, k2])/6 - - (SU3D[I1, I3, k1]*SU3F[6, I2, k2])/6 + - (SU3D[I1, I2, k1]*SU3F[6, I3, k2])/4) + SU3D[I3, I5, k1]* - ((I/2)*SU3F[6, I2, k2]*SU3F[I1, k1, k3] + (I/6)*SU3F[6, I1, k2]* - SU3F[I2, k1, k3]) + SU3D[I2, I5, k1]* - ((-I/2)*SU3F[6, I3, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I3, k1, k3]) + SU3D[I1, I5, k1]* - ((-I/4)*SU3F[6, I3, k2]*SU3F[I2, k1, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I3, k1, k3]) + SU3D[I2, I3, k1]* - ((-I/2)*SU3F[6, I5, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I3, k1]* - ((-I/4)*SU3F[6, I5, k2]*SU3F[I2, k1, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I2, k1]* - ((I/4)*SU3F[6, I5, k2]*SU3F[I3, k1, k3] + (I/4)*SU3F[6, I3, k2]* - SU3F[I5, k1, k3])) + SU3D[I2, k2, k3]* - ((-I/6)*SU3D[6, I1, k1]*SU3D[I3, k1, k2]*SU3D[I4, I5, k3] - - (SU3D[6, I1, k1]*SU3D[I4, I5, k3]*SU3F[I3, k1, k2])/6 + - SU3D[6, I1, k1]*SU3D[I3, I5, k3]*((-I/6)*SU3D[I4, k1, k2] - - SU3F[I4, k1, k2]/6) + SU3D[6, I3, k1]*SU3D[I1, I5, k2]* - ((I/4)*SU3D[I4, k1, k3] + SU3F[I4, k1, k3]/4) + - SU3D[6, I3, k1]*SU3D[I1, I4, k2]*((I/4)*SU3D[I5, k1, k3] + - SU3F[I5, k1, k3]/4) + SU3D[6, I4, k1]* - ((I/4)*SU3D[I1, I5, k2]*SU3D[I3, k1, k3] - - (SU3D[I5, k1, k2]*SU3F[I1, I3, k3])/12 - - (SU3D[I3, k1, k2]*SU3F[I1, I5, k3])/12 - - (SU3D[I3, I5, k3]*SU3F[I1, k1, k2])/3 + - (SU3D[I1, I5, k2]*SU3F[I3, k1, k3])/4 + (I/12)*SU3F[I1, I5, k2]* - SU3F[I3, k1, k3] + SU3D[I1, I3, k2]*((I/4)*SU3D[I5, k1, k3] + - SU3F[I5, k1, k3]/4) + (I/12)*SU3F[I1, I3, k2]*SU3F[I5, k1, k3]) + - SU3D[6, I3, k1]*(-(SU3D[I5, k1, k2]*SU3F[I1, I4, k3])/12 - - (SU3D[I4, k1, k2]*SU3F[I1, I5, k3])/12 - - (SU3D[I4, I5, k3]*SU3F[I1, k1, k2])/3 + (I/12)*SU3F[I1, I5, k2]* - SU3F[I4, k1, k3] + (I/12)*SU3F[I1, I4, k2]*SU3F[I5, k1, k3])) + - SU3D[I3, k2, k3]*(SU3D[I5, k1, k3]*(-(SU3D[I2, I4, k1]*SU3F[6, I1, k2])/ - 6 - (SU3D[I1, I4, k1]*SU3F[6, I2, k2])/6 + - (SU3D[I1, I2, k1]*SU3F[6, I4, k2])/4) + SU3D[I4, k1, k3]* - (-(SU3D[I2, I5, k1]*SU3F[6, I1, k2])/6 - - (SU3D[I1, I5, k1]*SU3F[6, I2, k2])/6 + - (SU3D[I1, I2, k1]*SU3F[6, I5, k2])/4) + - (SU3D[6, I1, k1]*SU3D[I4, I5, k3]*SU3F[I2, k1, k2])/6 + - SU3D[I2, I5, k1]*((-I/2)*SU3F[6, I4, k2]*SU3F[I1, k1, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I4, k1, k3]) + SU3D[I1, I5, k1]* - ((-I/4)*SU3F[6, I4, k2]*SU3F[I2, k1, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I4, k1, k3]) + SU3D[I2, I4, k1]* - ((-I/2)*SU3F[6, I5, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I4, k1]* - ((-I/4)*SU3F[6, I5, k2]*SU3F[I2, k1, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I2, k1]* - ((I/4)*SU3F[6, I5, k2]*SU3F[I4, k1, k3] + (I/4)*SU3F[6, I4, k2]* - SU3F[I5, k1, k3]) + SU3D[6, I2, k1]* - (-(SU3D[I5, k1, k2]*SU3F[I1, I4, k3])/6 - - (SU3D[I4, k1, k2]*SU3F[I1, I5, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I1, k1, k2])/3 + (I/6)*SU3F[I1, I5, k2]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I1, I4, k2]*SU3F[I5, k1, k3]) + - SU3D[6, I1, k1]*((I/6)*SU3D[I2, I5, k2]*SU3D[I4, k1, k3] + - (I/6)*SU3D[I2, I4, k2]*SU3D[I5, k1, k3] - - (SU3D[I5, k1, k2]*SU3F[I2, I4, k3])/6 - - (SU3D[I4, k1, k2]*SU3F[I2, I5, k3])/6 + - (SU3D[I2, I5, k2]*SU3F[I4, k1, k3])/6 + (I/6)*SU3F[I2, I5, k2]* - SU3F[I4, k1, k3] + (SU3D[I2, I4, k2]*SU3F[I5, k1, k3])/6 + - (I/6)*SU3F[I2, I4, k2]*SU3F[I5, k1, k3])) + - SU3D[I3, k1, k3]*(SU3D[6, I2, k1]*SU3D[I1, I5, k2]* - ((I/6)*SU3D[I4, k2, k3] - SU3F[I4, k2, k3]/6) + - SU3D[6, I1, k1]*(SU3D[I2, I5, k2]*((I/6)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/6) + SU3D[I2, I4, k2]*((I/6)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/6))) + SU3D[I3, I4, k3]* - (SU3D[6, I1, k1]*SU3D[I2, k2, k3]*((-I/6)*SU3D[I5, k1, k2] - - SU3F[I5, k1, k2]/6) + SU3D[I1, k1, k2]* - (-(SU3D[I5, k2, k3]*SU3F[6, I2, k1])/3 + - (SU3D[I2, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I2, k2, k3] + SU3D[6, I2, k1]*((I/3)*SU3D[I5, k2, k3] + - SU3F[I5, k2, k3]/3) + (I/3)*SU3F[6, I2, k1]*SU3F[I5, k2, k3])) + - SU3D[I1, k1, k2]*(SU3D[I3, k2, k3]*((I/3)*SU3D[6, I2, k1]* - SU3D[I4, I5, k3] - (SU3D[I4, I5, k3]*SU3F[6, I2, k1])/3) + - (SU3D[I2, k1, k3]*SU3D[I4, I5, k2]*SU3F[6, I3, k3])/2 + - SU3D[I2, k2, k3]*((-I/3)*SU3D[6, I4, k1]*SU3D[I3, I5, k3] - - (I/3)*SU3D[6, I3, k1]*SU3D[I4, I5, k3] + - (SU3D[I4, I5, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, I5, k3]*SU3F[6, I4, k1])/3) + - (SU3D[I2, k1, k3]*SU3D[I3, I5, k2]*SU3F[6, I4, k3])/2 + - SU3D[I5, k1, k3]*((SU3D[I3, I4, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I4, k2]*SU3F[6, I3, k3])/2 - - (SU3D[I2, I3, k2]*SU3F[6, I4, k3])/2) + - (SU3D[I2, k1, k3]*SU3D[I3, I4, k2]*SU3F[6, I5, k3])/2 + - SU3D[I4, k1, k3]*((SU3D[I3, I5, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I5, k2]*SU3F[6, I3, k3])/2 - - (SU3D[I2, I3, k2]*SU3F[6, I5, k3])/2) + SU3D[I3, k1, k3]* - ((SU3D[I4, I5, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I5, k2]*SU3F[6, I4, k3])/2 - - (SU3D[I2, I4, k2]*SU3F[6, I5, k3])/2) - - (SU3D[6, I3, k1]*SU3D[I4, I5, k3]*SU3F[I2, k2, k3])/3 + - (SU3D[6, I2, k1]*SU3D[I4, I5, k3]*SU3F[I3, k2, k3])/3 + - SU3D[I4, I5, k3]*((-I/3)*SU3F[6, I3, k1]*SU3F[I2, k2, k3] + - (I/3)*SU3F[6, I2, k1]*SU3F[I3, k2, k3]) + SU3D[I4, I5, k1]* - ((I/2)*SU3F[6, I3, k3]*SU3F[I2, k2, k3] + (I/2)*SU3F[6, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I3, I5, k3]* - (-(SU3D[I4, k2, k3]*SU3F[6, I2, k1])/3 - (I/3)*SU3F[6, I4, k1]* - SU3F[I2, k2, k3] + SU3D[6, I2, k1]*((I/3)*SU3D[I4, k2, k3] + - SU3F[I4, k2, k3]/3) + (I/3)*SU3F[6, I2, k1]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k1]*((I/2)*SU3F[6, I4, k3]*SU3F[I2, k2, k3] + - (I/2)*SU3F[6, I2, k3]*SU3F[I4, k2, k3]) + SU3D[I2, I5, k3]* - ((SU3D[I4, k2, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, k2, k3]*SU3F[6, I4, k1])/3 - (I/3)*SU3F[6, I4, k1]* - SU3F[I3, k2, k3] + SU3D[6, I3, k1]*((-I/3)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/3) - (I/3)*SU3F[6, I3, k1]*SU3F[I4, k2, k3]) + - SU3D[I2, I5, k1]*((-I/2)*SU3F[6, I4, k3]*SU3F[I3, k2, k3] - - (I/2)*SU3F[6, I3, k3]*SU3F[I4, k2, k3]) + SU3D[6, I4, k1]* - (-(SU3D[I3, I5, k3]*SU3F[I2, k2, k3])/3 + SU3D[I2, I5, k3]* - ((-I/3)*SU3D[I3, k2, k3] - SU3F[I3, k2, k3]/3) + - SU3D[I2, I3, k3]*((-I/3)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/3)) + - SU3D[I3, I4, k1]*((I/2)*SU3F[6, I5, k3]*SU3F[I2, k2, k3] + - (I/2)*SU3F[6, I2, k3]*SU3F[I5, k2, k3]) + SU3D[I2, I4, k3]* - ((SU3D[I5, k2, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I3, k2, k3] + SU3D[6, I3, k1]*((-I/3)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/3) - (I/3)*SU3F[6, I3, k1]*SU3F[I5, k2, k3]) + - SU3D[I2, I4, k1]*((-I/2)*SU3F[6, I5, k3]*SU3F[I3, k2, k3] - - (I/2)*SU3F[6, I3, k3]*SU3F[I5, k2, k3]) + SU3D[I2, I3, k3]* - ((SU3D[I5, k2, k3]*SU3F[6, I4, k1])/3 + - (SU3D[I4, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I4, k2, k3] - (I/3)*SU3F[6, I4, k1]*SU3F[I5, k2, k3]) + - SU3D[I2, I3, k1]*((-I/2)*SU3F[6, I5, k3]*SU3F[I4, k2, k3] - - (I/2)*SU3F[6, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I2, k1, k2]*(SU3D[I5, k2, k3]*(-(SU3D[I1, I4, k1]*SU3F[6, I3, k3])/ - 4 - (SU3D[I1, I3, k1]*SU3F[6, I4, k3])/4 - (I/12)*SU3F[6, I4, k3]* - SU3F[I1, I3, k1] - (I/12)*SU3F[6, I3, k3]*SU3F[I1, I4, k1]) + - SU3D[I5, k1, k3]*((SU3D[I3, I4, k2]*SU3F[6, I1, k3])/6 - - (I/3)*SU3F[6, I4, k2]*SU3F[I1, I3, k3] - (I/3)*SU3F[6, I3, k2]* - SU3F[I1, I4, k3]) + SU3D[I4, k2, k3]* - (-(SU3D[I1, I5, k1]*SU3F[6, I3, k3])/4 - - (SU3D[I1, I3, k1]*SU3F[6, I5, k3])/4 - (I/12)*SU3F[6, I5, k3]* - SU3F[I1, I3, k1] - (I/12)*SU3F[6, I3, k3]*SU3F[I1, I5, k1]) + - SU3D[I3, k2, k3]*(SU3D[I4, I5, k3]*((I/6)*SU3D[6, I1, k1] - - SU3F[6, I1, k1]/6) - (SU3D[I1, I5, k1]*SU3F[6, I4, k3])/4 - - (SU3D[I1, I4, k1]*SU3F[6, I5, k3])/4 - (I/12)*SU3F[6, I5, k3]* - SU3F[I1, I4, k1] - (I/12)*SU3F[6, I4, k3]*SU3F[I1, I5, k1]) + - SU3D[I4, k1, k3]*((SU3D[I3, I5, k2]*SU3F[6, I1, k3])/6 - - (I/3)*SU3F[6, I5, k2]*SU3F[I1, I3, k3] - (I/3)*SU3F[6, I3, k2]* - SU3F[I1, I5, k3]) + SU3D[I3, k1, k3]* - ((SU3D[I4, I5, k2]*SU3F[6, I1, k3])/6 - (I/3)*SU3F[6, I5, k2]* - SU3F[I1, I4, k3] - (I/3)*SU3F[6, I4, k2]*SU3F[I1, I5, k3]) + - SU3D[I4, I5, k3]*((-I/2)*SU3F[6, I3, k1]*SU3F[I1, k2, k3] + - (SU3D[6, I1, k1]*SU3F[I3, k2, k3])/6 + (I/6)*SU3F[6, I1, k1]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I5, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, I3, k3]*SU3F[I4, k1, k3])/3) + SU3D[I3, I5, k3]* - (-(SU3D[I4, k2, k3]*SU3F[6, I1, k1])/6 - (I/2)*SU3F[6, I4, k1]* - SU3F[I1, k2, k3] + SU3D[6, I1, k1]*((I/6)*SU3D[I4, k2, k3] + - SU3F[I4, k2, k3]/6) + (I/6)*SU3F[6, I1, k1]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k1]*((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] + - (I/6)*SU3F[6, I1, k3]*SU3F[I4, k2, k3]) + SU3D[I1, I5, k1]* - ((-I/4)*SU3F[6, I4, k3]*SU3F[I3, k2, k3] - (I/4)*SU3F[6, I3, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I4, k1]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k1]*SU3F[I4, k2, k3])/12) + SU3F[6, I4, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, I3, k3]*SU3F[I5, k1, k3])/3) + SU3F[6, I3, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, I4, k3]*SU3F[I5, k1, k3])/3) + SU3D[I3, I4, k3]* - (-(SU3D[I5, k2, k3]*SU3F[6, I1, k1])/6 - (I/2)*SU3F[6, I5, k1]* - SU3F[I1, k2, k3] + SU3D[6, I1, k1]*((I/6)*SU3D[I5, k2, k3] + - SU3F[I5, k2, k3]/6) + (I/6)*SU3F[6, I1, k1]*SU3F[I5, k2, k3]) + - SU3D[I3, I4, k1]*((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] + - (I/6)*SU3F[6, I1, k3]*SU3F[I5, k2, k3]) + SU3D[I1, I4, k1]* - ((-I/4)*SU3F[6, I5, k3]*SU3F[I3, k2, k3] - (I/4)*SU3F[6, I3, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I3, k1]* - ((-I/4)*SU3F[6, I5, k3]*SU3F[I4, k2, k3] - (I/4)*SU3F[6, I4, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I5, k1]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k1]*SU3F[I5, k2, k3])/12) + SU3D[6, I4, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I3, k3])/3 - - (SU3D[I3, k2, k3]*SU3F[I1, I5, k3])/3 - - (SU3D[I3, I5, k3]*SU3F[I1, k2, k3])/2 + (I/3)*SU3F[I1, I5, k3]* - SU3F[I3, k2, k3] + (I/3)*SU3F[I1, I3, k3]*SU3F[I5, k2, k3]) + - SU3F[6, I3, k3]*((SU3F[I1, I5, k1]*SU3F[I4, k2, k3])/12 + - (SU3F[I1, I4, k1]*SU3F[I5, k2, k3])/12) + SU3D[6, I3, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I4, k3])/3 - - (SU3D[I4, k2, k3]*SU3F[I1, I5, k3])/3 - - (SU3D[I4, I5, k3]*SU3F[I1, k2, k3])/2 + (I/3)*SU3F[I1, I5, k3]* - SU3F[I4, k2, k3] + (I/3)*SU3F[I1, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I4, k1, k2]*(SU3D[I5, k2, k3]*(-(SU3D[I2, I3, k1]*SU3F[6, I1, k3])/ - 6 - (SU3D[I1, I3, k1]*SU3F[6, I2, k3])/6 + - (SU3D[I1, I2, k1]*SU3F[6, I3, k3])/4 + (I/12)*SU3F[6, I3, k3]* - SU3F[I1, I2, k1] - (I/6)*SU3F[6, I2, k3]*SU3F[I1, I3, k1] - - (I/6)*SU3F[6, I1, k3]*SU3F[I2, I3, k1]) + SU3D[I5, k1, k3]* - ((I/12)*SU3F[6, I3, k2]*SU3F[I1, I2, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I1, I3, k3] - (I/6)*SU3F[6, I1, k2]*SU3F[I2, I3, k3]) + - SU3D[I3, I5, k1]*((-I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I2, k2, k3]) + SU3F[6, I5, k2]* - (-(SU3F[I1, I3, k3]*SU3F[I2, k1, k3])/12 + - (SU3F[I1, I2, k3]*SU3F[I3, k1, k3])/12) - (I/6)*SU3D[I1, I5, k1]* - SU3F[6, I2, k3]*SU3F[I3, k2, k3] + SU3D[I2, I5, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I3, k1]*SU3F[I2, k2, k3])/3 - - (SU3F[I1, I2, k1]*SU3F[I3, k2, k3])/12) + SU3F[6, I3, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I2, k1, k3])/12 + - (SU3F[I1, I2, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I2, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I1, I3, k3]*SU3F[I5, k1, k3])/6) + SU3F[6, I1, k2]* - (-(SU3F[I2, I5, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I2, I3, k3]*SU3F[I5, k1, k3])/6) - (I/6)*SU3D[I1, I3, k1]* - SU3F[6, I2, k3]*SU3F[I5, k2, k3] + SU3D[I2, I3, k1]* - ((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I2, k1]* - ((I/4)*SU3F[6, I5, k3]*SU3F[I3, k2, k3] + (I/4)*SU3F[6, I3, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I3, k3]* - ((SU3F[I1, I5, k1]*SU3F[I2, k2, k3])/3 - - (SU3F[I1, I2, k1]*SU3F[I5, k2, k3])/12) + SU3F[6, I2, k3]* - ((SU3F[I1, I5, k1]*SU3F[I3, k2, k3])/6 + - (SU3F[I1, I3, k1]*SU3F[I5, k2, k3])/6) + SU3F[6, I1, k3]* - ((SU3F[I2, I5, k1]*SU3F[I3, k2, k3])/6 + - (SU3F[I2, I3, k1]*SU3F[I5, k2, k3])/6)) + - SU3D[I3, k1, k2]*(SU3D[I5, k2, k3]*(-(SU3D[I2, I4, k1]*SU3F[6, I1, k3])/ - 6 - (SU3D[I1, I4, k1]*SU3F[6, I2, k3])/6 + - (SU3D[I1, I2, k1]*SU3F[6, I4, k3])/4 + (I/12)*SU3F[6, I4, k3]* - SU3F[I1, I2, k1] - (I/6)*SU3F[6, I2, k3]*SU3F[I1, I4, k1] - - (I/6)*SU3F[6, I1, k3]*SU3F[I2, I4, k1]) + SU3D[I5, k1, k3]* - ((I/12)*SU3F[6, I4, k2]*SU3F[I1, I2, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I1, I4, k3] - (I/6)*SU3F[6, I1, k2]*SU3F[I2, I4, k3]) + - SU3D[I4, k2, k3]*(-(SU3D[I2, I5, k1]*SU3F[6, I1, k3])/6 - - (SU3D[I1, I5, k1]*SU3F[6, I2, k3])/6 + - (SU3D[I1, I2, k1]*SU3F[6, I5, k3])/4 + (I/12)*SU3F[6, I5, k3]* - SU3F[I1, I2, k1] - (I/6)*SU3F[6, I2, k3]*SU3F[I1, I5, k1] - - (I/6)*SU3F[6, I1, k3]*SU3F[I2, I5, k1]) + SU3D[I4, k1, k3]* - ((I/12)*SU3F[6, I5, k2]*SU3F[I1, I2, k3] - (I/6)*SU3F[6, I2, k2]* - SU3F[I1, I5, k3] - (I/6)*SU3F[6, I1, k2]*SU3F[I2, I5, k3]) + - SU3D[I4, I5, k3]*((-I/2)*SU3F[6, I2, k1]*SU3F[I1, k2, k3] - - (SU3D[6, I1, k1]*SU3F[I2, k2, k3])/6 - (I/6)*SU3F[6, I1, k1]* - SU3F[I2, k2, k3]) + SU3D[I4, I5, k1]* - ((-I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I2, k2, k3]) + SU3F[6, I5, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I2, k1, k3])/12 + - (SU3F[I1, I2, k3]*SU3F[I4, k1, k3])/12) - (I/6)*SU3D[I1, I5, k1]* - SU3F[6, I2, k3]*SU3F[I4, k2, k3] + SU3D[I2, I5, k1]* - ((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I4, k1]*SU3F[I2, k2, k3])/3 - - (SU3F[I1, I2, k1]*SU3F[I4, k2, k3])/12) + SU3F[6, I4, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I2, k1, k3])/12 + - (SU3F[I1, I2, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I2, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I1, I4, k3]*SU3F[I5, k1, k3])/6) + SU3F[6, I1, k2]* - (-(SU3F[I2, I5, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I2, I4, k3]*SU3F[I5, k1, k3])/6) - (I/6)*SU3D[I1, I4, k1]* - SU3F[6, I2, k3]*SU3F[I5, k2, k3] + SU3D[I2, I4, k1]* - ((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I2, k1]* - ((I/4)*SU3F[6, I5, k3]*SU3F[I4, k2, k3] + (I/4)*SU3F[6, I4, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I5, k1]*SU3F[I2, k2, k3])/3 - - (SU3F[I1, I2, k1]*SU3F[I5, k2, k3])/12) + SU3F[6, I2, k3]* - ((SU3F[I1, I5, k1]*SU3F[I4, k2, k3])/6 + - (SU3F[I1, I4, k1]*SU3F[I5, k2, k3])/6) + SU3D[6, I2, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I4, k3])/6 - - (SU3D[I4, k2, k3]*SU3F[I1, I5, k3])/6 - - (SU3D[I4, I5, k3]*SU3F[I1, k2, k3])/2 + (I/6)*SU3F[I1, I5, k3]* - SU3F[I4, k2, k3] + (I/6)*SU3F[I1, I4, k3]*SU3F[I5, k2, k3]) + - SU3F[6, I1, k3]*((SU3F[I2, I5, k1]*SU3F[I4, k2, k3])/6 + - (SU3F[I2, I4, k1]*SU3F[I5, k2, k3])/6) + SU3D[6, I1, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I2, I4, k3])/6 - - (SU3D[I4, k2, k3]*SU3F[I2, I5, k3])/6 + (I/6)*SU3F[I2, I5, k3]* - SU3F[I4, k2, k3] + (I/6)*SU3F[I2, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I1, I4, k2]*(SU3D[6, I2, k1]*SU3D[I3, k2, k3]* - ((I/6)*SU3D[I5, k1, k3] + SU3F[I5, k1, k3]/6) + - SU3D[6, I3, k1]*(-(SU3D[I5, k1, k3]*SU3F[I2, k2, k3])/4 + - (I/4)*SU3F[I2, k2, k3]*SU3F[I5, k1, k3]) + SU3D[6, I2, k1]* - SU3D[I3, k1, k3]*((I/6)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/6) + - SU3D[6, I2, k1]*((SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I3, k2, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])) + - SU3F[I1, I5, k1]*((-I/6)*SU3F[I2, I4, k1]*SUNDelta[6, I3] - - (I/6)*SU3F[I2, I3, k1]*SUNDelta[6, I4]) + SU3F[I1, I4, k1]* - ((-I/6)*SU3F[I2, I5, k1]*SUNDelta[6, I3] - (I/6)*SU3F[I2, I3, k1]* - SUNDelta[6, I5]) + SU3F[I1, I3, k1]* - ((-I/6)*SU3F[I2, I5, k1]*SUNDelta[6, I4] - (I/6)*SU3F[I2, I4, k1]* - SUNDelta[6, I5]) + SU3D[I2, I5, k1]* - (SU3F[6, I4, k2]*((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I3, k2]* - ((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6) + ((2*I)/9)*SU3D[I3, I4, k1]* - SUNDelta[6, I1] + ((5*I)/18)*SU3D[I1, I4, k1]*SUNDelta[6, I3] + - (5*SU3F[I1, I4, k1]*SUNDelta[6, I3])/18 + ((5*I)/18)*SU3D[I1, I3, k1]* - SUNDelta[6, I4] + (5*SU3F[I1, I3, k1]*SUNDelta[6, I4])/18 - - (SU3F[6, I4, k1]*SUNDelta[I1, I3])/6 - - (SU3F[6, I3, k1]*SUNDelta[I1, I4])/6) + SU3D[I2, I4, k1]* - (SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I3, k2]* - ((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/6) + ((2*I)/9)*SU3D[I3, I5, k1]* - SUNDelta[6, I1] + ((5*I)/18)*SU3D[I1, I5, k1]*SUNDelta[6, I3] + - (5*SU3F[I1, I5, k1]*SUNDelta[6, I3])/18 + ((5*I)/18)*SU3D[I1, I3, k1]* - SUNDelta[6, I5] + (5*SU3F[I1, I3, k1]*SUNDelta[6, I5])/18 - - (SU3F[6, I5, k1]*SUNDelta[I1, I3])/6 - - (SU3F[6, I3, k1]*SUNDelta[I1, I5])/6) + SU3D[I2, I3, k1]* - (SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I4, k2]* - ((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6) + ((2*I)/9)*SU3D[I4, I5, k1]* - SUNDelta[6, I1] + ((5*I)/18)*SU3D[I1, I5, k1]*SUNDelta[6, I4] + - (5*SU3F[I1, I5, k1]*SUNDelta[6, I4])/18 + ((5*I)/18)*SU3D[I1, I4, k1]* - SUNDelta[6, I5] + (5*SU3F[I1, I4, k1]*SUNDelta[6, I5])/18 - - (SU3F[6, I5, k1]*SUNDelta[I1, I4])/6 - - (SU3F[6, I4, k1]*SUNDelta[I1, I5])/6) + SU3D[I4, I5, k1]* - (SU3F[6, I3, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - (-(SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/6 + - (SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/6) - - (4*SU3F[I2, I3, k1]*SUNDelta[6, I1])/9 - - (7*SU3F[I1, I3, k1]*SUNDelta[6, I2])/9 - - (2*SU3F[6, I2, k1]*SUNDelta[I1, I3])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I2, I3])/9) + SU3D[I3, I5, k1]* - (SU3F[6, I4, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - (-(SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/6 + - (SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/6) - - (4*SU3F[I2, I4, k1]*SUNDelta[6, I1])/9 - - (7*SU3F[I1, I4, k1]*SUNDelta[6, I2])/9 - - (2*SU3F[6, I2, k1]*SUNDelta[I1, I4])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I2, I4])/9) + SU3D[I3, I4, k1]* - (SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - (-(SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/6 + - (SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/6) - - (4*SU3F[I2, I5, k1]*SUNDelta[6, I1])/9 - - (7*SU3F[I1, I5, k1]*SUNDelta[6, I2])/9 - - (2*SU3F[6, I2, k1]*SUNDelta[I1, I5])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I2, I5])/9) + SU3D[I1, I5, k1]* - (-(SU3F[6, I4, k2]*SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/4 - - (SU3F[6, I3, k2]*SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/4 + - SU3F[6, I2, k2]*(-(SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6) + (I/9)*SU3D[I3, I4, k1]* - SUNDelta[6, I2] + (SU3F[I2, I4, k1]*SUNDelta[6, I3])/6 + - (SU3F[I2, I3, k1]*SUNDelta[6, I4])/6 - - (SU3F[6, I4, k1]*SUNDelta[I2, I3])/9 - - (SU3F[6, I3, k1]*SUNDelta[I2, I4])/9 + - (SU3F[6, I2, k1]*SUNDelta[I3, I4])/9) + SU3D[6, I5, k1]* - (SU3D[I3, I4, k3]*(-(SU3D[I2, k2, k3]*SU3F[I1, k1, k2])/3 + - SU3D[I1, k1, k2]*((-I/3)*SU3D[I2, k2, k3] - SU3F[I2, k2, k3]/3)) + - SU3D[I3, I4, k2]*((-I/2)*SU3F[I1, k2, k3]*SU3F[I2, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) - - (SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/12 + - SU3D[I4, k2, k3]*(-(SU3D[I2, I3, k2]*SU3F[I1, k1, k3])/3 + - (I/3)*SU3F[I1, I3, k2]*SU3F[I2, k1, k3] - (I/12)*SU3F[I1, I2, k2]* - SU3F[I3, k1, k3]) + SU3D[I1, I4, k2]* - (-(SU3D[I3, k1, k3]*SU3F[I2, k2, k3])/4 + (I/4)*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3]) + SU3D[I4, k1, k3]* - (-(SU3D[I2, I3, k2]*SU3F[I1, k2, k3])/2 + - (SU3D[I1, I2, k2]*SU3F[I3, k2, k3])/4) + SU3D[I4, k1, k2]* - ((I/12)*SU3F[I1, I3, k3]*SU3F[I2, k2, k3] - (I/12)*SU3F[I1, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I2, I4, k2]* - ((I/2)*SU3F[I1, k2, k3]*SU3F[I3, k1, k3] - (I/3)*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, k2, k3]* - ((-I/2)*SU3D[I2, k1, k2]*SU3D[I3, I4, k3] - - (SU3D[I3, I4, k3]*SU3F[I2, k1, k2])/2 + SU3D[I2, I4, k3]* - ((I/2)*SU3D[I3, k1, k2] + SU3F[I3, k1, k2]/2) + - SU3D[I2, I3, k3]*((I/2)*SU3D[I4, k1, k2] + SU3F[I4, k1, k2]/2)) - - (SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/12 + - (SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/12 + - SU3D[I3, k2, k3]*((-I/4)*SU3D[I1, I2, k2]*SU3D[I4, k1, k3] + - (SU3D[I4, k1, k2]*SU3F[I1, I2, k3])/12 - - (SU3D[I2, I4, k2]*SU3F[I1, k1, k3])/3 + (I/3)*SU3F[I1, I4, k2]* - SU3F[I2, k1, k3] - (SU3D[I1, I2, k2]*SU3F[I4, k1, k3])/4 - - (I/12)*SU3F[I1, I2, k2]*SU3F[I4, k1, k3]) + - SU3D[I2, k2, k3]*(-(SU3D[I4, k1, k2]*SU3F[I1, I3, k3])/12 - - (SU3D[I3, k1, k2]*SU3F[I1, I4, k3])/12 + SU3D[I1, I4, k2]* - ((I/4)*SU3D[I3, k1, k3] + SU3F[I3, k1, k3]/4) + - (I/12)*SU3F[I1, I4, k2]*SU3F[I3, k1, k3] + SU3D[I1, I3, k2]* - ((I/4)*SU3D[I4, k1, k3] + SU3F[I4, k1, k3]/4) + - (I/12)*SU3F[I1, I3, k2]*SU3F[I4, k1, k3]) + - SU3D[I1, I3, k2]*(-(SU3D[I4, k1, k3]*SU3F[I2, k2, k3])/4 + - (I/4)*SU3F[I2, k2, k3]*SU3F[I4, k1, k3]) + SU3D[I1, k1, k2]* - (SU3D[I2, I4, k3]*((-I/3)*SU3D[I3, k2, k3] - SU3F[I3, k2, k3]/3) + - SU3D[I2, I3, k3]*((-I/3)*SU3D[I4, k2, k3] - SU3F[I4, k2, k3]/3)) + - SU3D[I3, k1, k3]*(-(SU3D[I2, I4, k2]*SU3F[I1, k2, k3])/2 + - SU3D[I1, I2, k2]*((-I/4)*SU3D[I4, k2, k3] + SU3F[I4, k2, k3]/4)) + - (SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/12 + - SU3D[I3, k1, k2]*((SU3D[I4, k2, k3]*SU3F[I1, I2, k3])/12 + - (I/12)*SU3F[I1, I4, k3]*SU3F[I2, k2, k3] - (I/12)*SU3F[I1, I2, k3]* - SU3F[I4, k2, k3]) + SU3F[I2, k1, k3]* - (-(SU3F[I1, I4, k2]*SU3F[I3, k2, k3])/3 - - (SU3F[I1, I3, k2]*SU3F[I4, k2, k3])/3) + SU3D[I2, k1, k2]* - (-(SU3D[I4, k2, k3]*SU3F[I1, I3, k3])/3 - - (SU3D[I3, k2, k3]*SU3F[I1, I4, k3])/3 - - (SU3D[I3, I4, k3]*SU3F[I1, k2, k3])/2 + (I/3)*SU3F[I1, I4, k3]* - SU3F[I3, k2, k3] + (I/3)*SU3F[I1, I3, k3]*SU3F[I4, k2, k3]) + - SU3D[I2, I3, k2]*((I/2)*SU3F[I1, k2, k3]*SU3F[I4, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) + SU3D[I1, I2, k2]* - (-(SU3D[I4, k2, k3]*SU3F[I3, k1, k3])/4 - (I/4)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] - (I/4)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3]) + - (I/6)*SU3D[I2, I4, k1]*SUNDelta[I1, I3] + - (SU3F[I2, I4, k1]*SUNDelta[I1, I3])/6 + (I/6)*SU3D[I2, I3, k1]* - SUNDelta[I1, I4] + (SU3F[I2, I3, k1]*SUNDelta[I1, I4])/6 + - (I/9)*SU3D[I1, I4, k1]*SUNDelta[I2, I3] + - (5*SU3F[I1, I4, k1]*SUNDelta[I2, I3])/9 + (I/9)*SU3D[I1, I3, k1]* - SUNDelta[I2, I4] + (5*SU3F[I1, I3, k1]*SUNDelta[I2, I4])/9 - - ((5*I)/9)*SU3D[I1, I2, k1]*SUNDelta[I3, I4] - - (SU3F[I1, I2, k1]*SUNDelta[I3, I4])/9) + SU3F[6, I5, k1]* - ((-I/12)*SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] - - (I/12)*SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3] + - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3] + - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3] + - SU3F[I2, k1, k3]*((-I/3)*SU3F[I1, I4, k2]*SU3F[I3, k2, k3] - - (I/3)*SU3F[I1, I3, k2]*SU3F[I4, k2, k3]) + (I/6)*SU3F[I2, I4, k1]* - SUNDelta[I1, I3] + (I/6)*SU3F[I2, I3, k1]*SUNDelta[I1, I4] + - ((5*I)/9)*SU3F[I1, I4, k1]*SUNDelta[I2, I3] + - ((5*I)/9)*SU3F[I1, I3, k1]*SUNDelta[I2, I4] - (I/9)*SU3F[I1, I2, k1]* - SUNDelta[I3, I4]) + SUNDelta[6, I5]* - (((5*I)/27)*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - ((5*I)/27)*SUNDelta[I1, I3]*SUNDelta[I2, I4] - - ((16*I)/27)*SUNDelta[I1, I2]*SUNDelta[I3, I4]) + - SU3D[I1, I4, k1]*(-(SU3F[6, I5, k2]*SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/ - 4 - (SU3F[6, I3, k2]*SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/4 + - SU3F[6, I2, k2]*(-(SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/6) + (I/9)*SU3D[I3, I5, k1]* - SUNDelta[6, I2] + (SU3F[I2, I5, k1]*SUNDelta[6, I3])/6 + - (SU3F[I2, I3, k1]*SUNDelta[6, I5])/6 - - (SU3F[6, I5, k1]*SUNDelta[I2, I3])/9 - - (SU3F[6, I3, k1]*SUNDelta[I2, I5])/9 + - (SU3F[6, I2, k1]*SUNDelta[I3, I5])/9) + SU3D[6, I4, k1]* - (-(SU3D[I2, I3, k2]*SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/2 + - SU3D[I3, I5, k2]*((-I/2)*SU3F[I1, k2, k3]*SU3F[I2, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) + (I/4)*SU3D[I1, I5, k2]* - SU3F[I2, k2, k3]*SU3F[I3, k1, k3] - - (SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/12 + - SU3D[I5, k2, k3]*((I/3)*SU3F[I1, I3, k2]*SU3F[I2, k1, k3] - - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]) + - SU3D[I5, k1, k2]*((I/12)*SU3F[I1, I3, k3]*SU3F[I2, k2, k3] - - (I/12)*SU3F[I1, I2, k3]*SU3F[I3, k2, k3]) + - SU3D[I2, I5, k2]*((I/2)*SU3F[I1, k2, k3]*SU3F[I3, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]) - - (SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/12 + - (SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/12 + - SU3D[I3, k2, k3]*((SU3D[I5, k1, k2]*SU3F[I1, I2, k3])/12 - - (SU3D[I2, I5, k2]*SU3F[I1, k1, k3])/3 + (I/3)*SU3F[I1, I5, k2]* - SU3F[I2, k1, k3] + SU3D[I1, I2, k2]*((-I/4)*SU3D[I5, k1, k3] - - SU3F[I5, k1, k3]/4) - (I/12)*SU3F[I1, I2, k2]*SU3F[I5, k1, k3]) + - SU3D[I1, I3, k2]*(-(SU3D[I5, k1, k3]*SU3F[I2, k2, k3])/4 + - (I/4)*SU3F[I2, k2, k3]*SU3F[I5, k1, k3]) + SU3D[I3, k1, k3]* - (-(SU3D[I2, I5, k2]*SU3F[I1, k2, k3])/2 - - (SU3D[I1, I5, k2]*SU3F[I2, k2, k3])/4 + SU3D[I1, I2, k2]* - ((-I/4)*SU3D[I5, k2, k3] + SU3F[I5, k2, k3]/4)) + - (SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/12 + - SU3D[I3, k1, k2]*((SU3D[I5, k2, k3]*SU3F[I1, I2, k3])/12 + - (I/12)*SU3F[I1, I5, k3]*SU3F[I2, k2, k3] - (I/12)*SU3F[I1, I2, k3]* - SU3F[I5, k2, k3]) + SU3F[I2, k1, k3]* - (-(SU3F[I1, I5, k2]*SU3F[I3, k2, k3])/3 - - (SU3F[I1, I3, k2]*SU3F[I5, k2, k3])/3) + SU3D[I2, I3, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I1, I2, k2]*(-(SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/4 + - (SU3D[I5, k1, k3]*SU3F[I3, k2, k3])/4 - (I/4)*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] - (I/4)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3]) + - (I/6)*SU3D[I2, I5, k1]*SUNDelta[I1, I3] + - (SU3F[I2, I5, k1]*SUNDelta[I1, I3])/6 + (I/6)*SU3D[I2, I3, k1]* - SUNDelta[I1, I5] + (SU3F[I2, I3, k1]*SUNDelta[I1, I5])/6 + - (I/9)*SU3D[I1, I5, k1]*SUNDelta[I2, I3] + - (5*SU3F[I1, I5, k1]*SUNDelta[I2, I3])/9 + (I/9)*SU3D[I1, I3, k1]* - SUNDelta[I2, I5] + (5*SU3F[I1, I3, k1]*SUNDelta[I2, I5])/9 - - ((5*I)/9)*SU3D[I1, I2, k1]*SUNDelta[I3, I5] - - (SU3F[I1, I2, k1]*SUNDelta[I3, I5])/9) + SU3F[6, I4, k1]* - ((-I/12)*SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] - - (I/12)*SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3] + - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3] + - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3] + - SU3F[I2, k1, k3]*((-I/3)*SU3F[I1, I5, k2]*SU3F[I3, k2, k3] - - (I/3)*SU3F[I1, I3, k2]*SU3F[I5, k2, k3]) + (I/6)*SU3F[I2, I5, k1]* - SUNDelta[I1, I3] + (I/6)*SU3F[I2, I3, k1]*SUNDelta[I1, I5] + - ((5*I)/9)*SU3F[I1, I5, k1]*SUNDelta[I2, I3] + - ((5*I)/9)*SU3F[I1, I3, k1]*SUNDelta[I2, I5] - (I/9)*SU3F[I1, I2, k1]* - SUNDelta[I3, I5]) + SUNDelta[6, I4]* - (((5*I)/27)*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - ((5*I)/27)*SUNDelta[I1, I3]*SUNDelta[I2, I5] - - ((16*I)/27)*SUNDelta[I1, I2]*SUNDelta[I3, I5]) + - SU3D[I1, I3, k1]*(-(SU3F[6, I5, k2]*SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/ - 4 - (SU3F[6, I4, k2]*SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/4 + - SU3F[6, I2, k2]*(-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6) + (I/9)*SU3D[I4, I5, k1]* - SUNDelta[6, I2] + (SU3F[I2, I5, k1]*SUNDelta[6, I4])/6 + - (SU3F[I2, I4, k1]*SUNDelta[6, I5])/6 - - (SU3F[6, I5, k1]*SUNDelta[I2, I4])/9 - - (SU3F[6, I4, k1]*SUNDelta[I2, I5])/9 + - (SU3F[6, I2, k1]*SUNDelta[I4, I5])/9) + SU3D[I1, I2, k1]* - (SU3F[6, I5, k2]*((SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/4 + - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/4) + SU3F[6, I4, k2]* - ((SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/4 + - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/4) + SU3F[6, I3, k2]* - ((SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/4 + - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/4) - ((8*I)/9)*SU3D[I4, I5, k1]* - SUNDelta[6, I3] - ((8*I)/9)*SU3D[I3, I5, k1]*SUNDelta[6, I4] - - ((8*I)/9)*SU3D[I3, I4, k1]*SUNDelta[6, I5] + - (5*SU3F[6, I5, k1]*SUNDelta[I3, I4])/9 + - (5*SU3F[6, I4, k1]*SUNDelta[I3, I5])/9 + - (5*SU3F[6, I3, k1]*SUNDelta[I4, I5])/9) + - SU3D[6, I3, k1]*(-(SU3D[I2, I4, k2]*SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/ - 2 - (SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/12 + - SU3D[I5, k2, k3]*((I/3)*SU3F[I1, I4, k2]*SU3F[I2, k1, k3] - - (I/12)*SU3F[I1, I2, k2]*SU3F[I4, k1, k3]) + - SU3D[I5, k1, k2]*((I/12)*SU3F[I1, I4, k3]*SU3F[I2, k2, k3] - - (I/12)*SU3F[I1, I2, k3]*SU3F[I4, k2, k3]) + - SU3D[I2, I5, k2]*(-(SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/3 + - (I/2)*SU3F[I1, k2, k3]*SU3F[I4, k1, k3] - (I/3)*SU3F[I1, k1, k3]* - SU3F[I4, k2, k3]) - (SU3F[I1, I4, k2]*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3])/12 + SU3D[I4, k2, k3]* - ((SU3D[I5, k1, k2]*SU3F[I1, I2, k3])/12 + (I/3)*SU3F[I1, I5, k2]* - SU3F[I2, k1, k3] - (I/12)*SU3F[I1, I2, k2]*SU3F[I5, k1, k3]) + - SU3D[I4, k1, k3]*(-(SU3D[I2, I5, k2]*SU3F[I1, k2, k3])/2 + - SU3D[I1, I2, k2]*((-I/4)*SU3D[I5, k2, k3] + SU3F[I5, k2, k3]/4)) + - SU3D[I4, k1, k2]*((SU3D[I5, k2, k3]*SU3F[I1, I2, k3])/12 + - (I/12)*SU3F[I1, I5, k3]*SU3F[I2, k2, k3] - (I/12)*SU3F[I1, I2, k3]* - SU3F[I5, k2, k3]) + SU3F[I2, k1, k3]* - (-(SU3F[I1, I5, k2]*SU3F[I4, k2, k3])/3 - - (SU3F[I1, I4, k2]*SU3F[I5, k2, k3])/3) + SU3D[I2, I4, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I1, I2, k2]*(-(SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/4 + - (SU3D[I5, k1, k3]*SU3F[I4, k2, k3])/4 + SU3D[I4, k2, k3]* - ((-I/4)*SU3D[I5, k1, k3] - SU3F[I5, k1, k3]/4) - - (I/4)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] - (I/4)*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3]) + SU3F[I1, I2, k2]* - ((SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/12 + - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/12) + (I/6)*SU3D[I2, I5, k1]* - SUNDelta[I1, I4] + (SU3F[I2, I5, k1]*SUNDelta[I1, I4])/6 + - (I/6)*SU3D[I2, I4, k1]*SUNDelta[I1, I5] + - (SU3F[I2, I4, k1]*SUNDelta[I1, I5])/6 + (I/9)*SU3D[I1, I5, k1]* - SUNDelta[I2, I4] + (5*SU3F[I1, I5, k1]*SUNDelta[I2, I4])/9 + - (I/9)*SU3D[I1, I4, k1]*SUNDelta[I2, I5] + - (5*SU3F[I1, I4, k1]*SUNDelta[I2, I5])/9 - ((5*I)/9)*SU3D[I1, I2, k1]* - SUNDelta[I4, I5] - (SU3F[I1, I2, k1]*SUNDelta[I4, I5])/9) + - SU3F[6, I3, k1]*((-I/12)*SU3F[I1, I5, k2]*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] - (I/12)*SU3F[I1, I4, k2]*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] + SU3F[I2, k1, k3]*((-I/3)*SU3F[I1, I5, k2]* - SU3F[I4, k2, k3] - (I/3)*SU3F[I1, I4, k2]*SU3F[I5, k2, k3]) + - SU3F[I1, I2, k2]*((I/12)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] + - (I/12)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) + (I/6)*SU3F[I2, I5, k1]* - SUNDelta[I1, I4] + (I/6)*SU3F[I2, I4, k1]*SUNDelta[I1, I5] + - ((5*I)/9)*SU3F[I1, I5, k1]*SUNDelta[I2, I4] + - ((5*I)/9)*SU3F[I1, I4, k1]*SUNDelta[I2, I5] - (I/9)*SU3F[I1, I2, k1]* - SUNDelta[I4, I5]) + SU3D[6, I2, k1]* - ((SU3D[I3, I5, k2]*SU3D[I4, k1, k3]*SU3F[I1, k2, k3])/2 + - (SU3D[I3, I4, k2]*SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/2 + - SU3D[I4, I5, k2]*((-I/2)*SU3F[I1, k2, k3]*SU3F[I3, k1, k3] + - (I/3)*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]) + SU3D[I5, k2, k3]* - ((I/6)*SU3F[I1, I4, k2]*SU3F[I3, k1, k3] + (I/6)*SU3F[I1, I3, k2]* - SU3F[I4, k1, k3]) + SU3D[I5, k1, k2]* - ((I/6)*SU3F[I1, I4, k3]*SU3F[I3, k2, k3] + (I/6)*SU3F[I1, I3, k3]* - SU3F[I4, k2, k3]) + SU3D[I3, I5, k2]* - ((SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/3 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I4, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) + - SU3F[I1, I5, k2]*(-(SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6) + SU3D[I4, k2, k3]* - (-(SU3D[I5, k1, k2]*SU3F[I1, I3, k3])/6 + (I/6)*SU3F[I1, I5, k2]* - SU3F[I3, k1, k3] + (I/6)*SU3F[I1, I3, k2]*SU3F[I5, k1, k3]) + - SU3D[I4, k1, k2]*(-(SU3D[I5, k2, k3]*SU3F[I1, I3, k3])/6 + - (I/6)*SU3F[I1, I5, k3]*SU3F[I3, k2, k3] + (I/6)*SU3F[I1, I3, k3]* - SU3F[I5, k2, k3]) + SU3D[I3, I4, k2]* - ((SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3F[I1, I4, k2]*(-(SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/6) + SU3F[I1, I3, k2]* - (-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6) + SU3D[I1, I3, k2]* - ((SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I4, k2, k3])/6 + SU3D[I4, k2, k3]* - ((I/6)*SU3D[I5, k1, k3] + SU3F[I5, k1, k3]/6) + - (I/6)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] + SU3D[I4, k1, k3]* - ((I/6)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/6) + - (I/6)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) + - ((2*I)/9)*SU3D[I4, I5, k1]*SUNDelta[I1, I3] + - ((2*I)/9)*SU3D[I3, I5, k1]*SUNDelta[I1, I4] + - ((2*I)/9)*SU3D[I3, I4, k1]*SUNDelta[I1, I5] - (I/9)*SU3D[I1, I5, k1]* - SUNDelta[I3, I4] - (5*SU3F[I1, I5, k1]*SUNDelta[I3, I4])/9 - - (I/9)*SU3D[I1, I4, k1]*SUNDelta[I3, I5] - - (5*SU3F[I1, I4, k1]*SUNDelta[I3, I5])/9 - (I/9)*SU3D[I1, I3, k1]* - SUNDelta[I4, I5] - (5*SU3F[I1, I3, k1]*SUNDelta[I4, I5])/9) + - SU3F[6, I2, k1]*(SU3F[I1, I5, k2]*((-I/6)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] - (I/6)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3]) + - SU3F[I1, I4, k2]*((-I/6)*SU3F[I3, k2, k3]*SU3F[I5, k1, k3] - - (I/6)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3]) + SU3F[I1, I3, k2]* - ((-I/6)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] - (I/6)*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3]) - ((5*I)/9)*SU3F[I1, I5, k1]*SUNDelta[I3, I4] - - ((5*I)/9)*SU3F[I1, I4, k1]*SUNDelta[I3, I5] - - ((5*I)/9)*SU3F[I1, I3, k1]*SUNDelta[I4, I5]) + - SU3D[6, I1, k1]*(-(SU3F[I2, I5, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/ - 6 + SU3D[I5, k2, k3]*((I/6)*SU3F[I2, I4, k2]*SU3F[I3, k1, k3] + - (I/6)*SU3F[I2, I3, k2]*SU3F[I4, k1, k3]) + SU3D[I5, k1, k3]* - ((SU3D[I3, I4, k2]*SU3F[I2, k2, k3])/6 - - (SU3D[I2, I4, k2]*SU3F[I3, k2, k3])/6 - - (SU3D[I2, I3, k2]*SU3F[I4, k2, k3])/6) + SU3D[I5, k1, k2]* - ((I/6)*SU3F[I2, I4, k3]*SU3F[I3, k2, k3] + (I/6)*SU3F[I2, I3, k3]* - SU3F[I4, k2, k3]) + SU3D[I3, I5, k2]* - ((SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/6 - (I/6)*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I2, k1, k3]*SU3F[I4, k2, k3]) + - SU3D[I2, I5, k2]*((SU3D[I4, k2, k3]*SU3F[I3, k1, k3])/6 + - (I/6)*SU3F[I3, k2, k3]*SU3F[I4, k1, k3] + (I/6)*SU3F[I3, k1, k3]* - SU3F[I4, k2, k3]) - (SU3F[I2, I4, k2]*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3])/6 - (SU3F[I2, I3, k2]*SU3F[I4, k2, k3]* - SU3F[I5, k1, k3])/6 + SU3D[I4, k2, k3]* - ((I/6)*SU3D[I2, I3, k2]*SU3D[I5, k1, k3] - - (SU3D[I5, k1, k2]*SU3F[I2, I3, k3])/6 + (I/6)*SU3F[I2, I5, k2]* - SU3F[I3, k1, k3] + (SU3D[I2, I3, k2]*SU3F[I5, k1, k3])/6 + - (I/6)*SU3F[I2, I3, k2]*SU3F[I5, k1, k3]) + SU3D[I4, k1, k3]* - ((SU3D[I3, I5, k2]*SU3F[I2, k2, k3])/6 - - (SU3D[I2, I5, k2]*SU3F[I3, k2, k3])/6 + SU3D[I2, I3, k2]* - ((I/6)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/6)) - - (SU3F[I2, I3, k2]*SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6 + - SU3D[I4, k1, k2]*(-(SU3D[I5, k2, k3]*SU3F[I2, I3, k3])/6 + - (I/6)*SU3F[I2, I5, k3]*SU3F[I3, k2, k3] + (I/6)*SU3F[I2, I3, k3]* - SU3F[I5, k2, k3]) + SU3F[I3, k1, k3]* - (-(SU3F[I2, I5, k2]*SU3F[I4, k2, k3])/6 - - (SU3F[I2, I4, k2]*SU3F[I5, k2, k3])/6) + SU3D[I3, I4, k2]* - ((SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/6 - (I/6)*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I2, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I2, I4, k2]*((SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/6 + - (I/6)*SU3F[I3, k2, k3]*SU3F[I5, k1, k3] + (I/6)*SU3F[I3, k1, k3]* - SU3F[I5, k2, k3]) + SU3D[I2, I3, k2]* - ((SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/6 + (I/6)*SU3F[I4, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) + - ((2*I)/9)*SU3D[I4, I5, k1]*SUNDelta[I2, I3] + - ((2*I)/9)*SU3D[I3, I5, k1]*SUNDelta[I2, I4] + - ((2*I)/9)*SU3D[I3, I4, k1]*SUNDelta[I2, I5] - - (2*SU3F[I2, I5, k1]*SUNDelta[I3, I4])/9 - - (2*SU3F[I2, I4, k1]*SUNDelta[I3, I5])/9 - - (2*SU3F[I2, I3, k1]*SUNDelta[I4, I5])/9) + - SU3F[6, I1, k1]*((-I/6)*SU3F[I2, I5, k2]*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] - (I/6)*SU3F[I2, I4, k2]*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] - (I/6)*SU3F[I2, I3, k2]*SU3F[I4, k2, k3]* - SU3F[I5, k1, k3] - (I/6)*SU3F[I2, I3, k2]*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3] + SU3F[I3, k1, k3]*((-I/6)*SU3F[I2, I5, k2]* - SU3F[I4, k2, k3] - (I/6)*SU3F[I2, I4, k2]*SU3F[I5, k2, k3]) - - ((2*I)/9)*SU3F[I2, I5, k1]*SUNDelta[I3, I4] - - ((2*I)/9)*SU3F[I2, I4, k1]*SUNDelta[I3, I5] - - ((2*I)/9)*SU3F[I2, I3, k1]*SUNDelta[I4, I5]) + - SUNDelta[6, I3]*(((5*I)/27)*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - ((5*I)/27)*SUNDelta[I1, I4]*SUNDelta[I2, I5] - - ((16*I)/27)*SUNDelta[I1, I2]*SUNDelta[I4, I5]) + - SUNDelta[6, I2]*(((2*I)/27)*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - ((2*I)/27)*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - ((2*I)/27)*SUNDelta[I1, I3]*SUNDelta[I4, I5]) + - SUNDelta[6, I1]*(((4*I)/27)*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - ((4*I)/27)*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - ((4*I)/27)*SUNDelta[I2, I3]*SUNDelta[I4, I5])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(CouplingConstant[ChPTW3[2], 1]*(((-4*I)/9)*SU3D[6, I4, I5]* - SU3D[I1, I2, I3] - ((4*I)/9)*SU3D[6, I3, I4]*SU3D[I1, I2, I5] - - ((4*I)/9)*SU3D[6, I2, I4]*SU3D[I1, I3, I5] - ((5*I)/9)*SU3D[6, I1, I5]* - SU3D[I2, I3, I4] + I*SU3D[6, I1, I4]*SU3D[I2, I3, I5] - - ((5*I)/9)*SU3D[6, I1, I3]*SU3D[I2, I4, I5] - ((5*I)/9)*SU3D[6, I1, I2]* - SU3D[I3, I4, I5] - (7*SU3D[I3, I4, I5]*SU3F[6, I1, I2])/9 - - (7*SU3D[I2, I4, I5]*SU3F[6, I1, I3])/9 + - (SU3D[I2, I3, I5]*SU3F[6, I1, I4])/3 - - (7*SU3D[I2, I3, I4]*SU3F[6, I1, I5])/9 + - (2*SU3D[I1, I3, I5]*SU3F[6, I2, I4])/9 + - (2*SU3D[I1, I2, I5]*SU3F[6, I3, I4])/9 - - (2*SU3D[I1, I2, I3]*SU3F[6, I4, I5])/9 + SU3D[6, I3, I5]* - (((2*I)/3)*SU3D[I1, I2, I4] - (2*SU3F[I1, I2, I4])/9) + - SU3D[6, I2, I5]*(((2*I)/3)*SU3D[I1, I3, I4] - (2*SU3F[I1, I3, I4])/9) + - SU3D[6, I2, I3]*(((2*I)/3)*SU3D[I1, I4, I5] + (2*SU3F[I1, I4, I5])/9) + - SU3D[I4, I5, k2]*(SU3D[6, I3, k1]*((I/2)*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) + - SU3D[6, I2, k1]*((I/2)*SU3F[I1, k2, k3]*SU3F[I3, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I3, k2, k3])) + - SU3D[I5, k2, k3]*(SU3D[I3, I4, k1]*((-I/2)*SU3F[6, I2, k2]* - SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]*SU3F[I2, k1, k3]) + - SU3D[I2, I4, k1]*((-I/2)*SU3F[6, I3, k2]*SU3F[I1, k1, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I3, k1, k3]) + SU3D[I1, I4, k1]* - ((I/4)*SU3F[6, I3, k2]*SU3F[I2, k1, k3] + (I/4)*SU3F[6, I2, k2]* - SU3F[I3, k1, k3]) + SU3D[I2, I3, k1]* - ((I/2)*SU3F[6, I4, k2]*SU3F[I1, k1, k3] + (I/6)*SU3F[6, I1, k2]* - SU3F[I4, k1, k3]) + SU3D[I1, I3, k1]* - ((-I/6)*SU3F[6, I4, k2]*SU3F[I2, k1, k3] - (I/4)*SU3F[6, I2, k2]* - SU3F[I4, k1, k3]) + SU3D[I1, I2, k1]* - ((-I/6)*SU3F[6, I4, k2]*SU3F[I3, k1, k3] - (I/4)*SU3F[6, I3, k2]* - SU3F[I4, k1, k3])) + SU3D[I5, k1, k2]* - ((-I/6)*SU3D[I1, I3, k1]*SU3F[6, I4, k3]*SU3F[I2, k2, k3] + - SU3D[I3, I4, k1]*((I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I2, k2, k3]) + SU3F[6, I4, k2]* - (-(SU3F[I1, I3, k3]*SU3F[I2, k1, k3])/6 - - (SU3F[I1, I2, k3]*SU3F[I3, k1, k3])/6) + SU3F[6, I1, k2]* - ((SU3F[I2, k1, k3]*SU3F[I3, I4, k3])/6 + - (SU3F[I2, I4, k3]*SU3F[I3, k1, k3])/6) - (I/6)*SU3D[I1, I2, k1]* - SU3F[6, I4, k3]*SU3F[I3, k2, k3] + SU3D[I2, I4, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, I4, k1]* - ((I/4)*SU3F[6, I3, k3]*SU3F[I2, k2, k3] + (I/4)*SU3F[6, I2, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I3, k1]*SU3F[I2, k2, k3])/6 + - (SU3F[I1, I2, k1]*SU3F[I3, k2, k3])/6) + SU3F[6, I1, k3]* - (-(SU3F[I2, k2, k3]*SU3F[I3, I4, k1])/6 - - (SU3F[I2, I4, k1]*SU3F[I3, k2, k3])/6) + SU3F[6, I3, k2]* - ((SU3F[I1, I4, k3]*SU3F[I2, k1, k3])/12 - - (SU3F[I1, I2, k3]*SU3F[I4, k1, k3])/12) + SU3F[6, I2, k2]* - ((SU3F[I1, I4, k3]*SU3F[I3, k1, k3])/12 - - (SU3F[I1, I3, k3]*SU3F[I4, k1, k3])/12) + SU3D[I2, I3, k1]* - ((-I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I3, k3]* - (-(SU3F[I1, I4, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I4, k2, k3])/3) + SU3F[6, I2, k3]* - (-(SU3F[I1, I4, k1]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k1]*SU3F[I4, k2, k3])/3)) + - SU3D[I3, I5, k2]*(SU3D[6, I2, k1]*(-(SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/ - 3 + (SU3D[I4, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I4, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) + - SU3D[6, I1, k1]*(-(SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/6 - - (SU3D[I4, k1, k3]*SU3F[I2, k2, k3])/6 + (I/6)*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] - (I/6)*SU3F[I2, k1, k3]*SU3F[I4, k2, k3])) + - SU3D[I2, I5, k2]*(SU3D[6, I1, k1]*SU3D[I3, k2, k3]* - ((I/6)*SU3D[I4, k1, k3] + SU3F[I4, k1, k3]/6) + - SU3D[6, I1, k1]*SU3D[I3, k1, k3]*((-I/6)*SU3D[I4, k2, k3] + - SU3F[I4, k2, k3]/6) + SU3D[6, I3, k1]* - (-(SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I4, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I4, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) + - SU3D[6, I1, k1]*(-(SU3D[I4, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3D[I4, k1, k3]*SU3F[I3, k2, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] - (I/6)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])) + - SU3D[I1, I5, k2]*(SU3D[6, I3, k1]*((SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/ - 4 + (I/4)*SU3F[I2, k1, k3]*SU3F[I4, k2, k3]) + - SU3D[6, I2, k1]*((SU3D[I4, k2, k3]*SU3F[I3, k1, k3])/4 + - (I/4)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])) + - SU3D[I1, k2, k3]*((I/2)*SU3D[6, I3, k1]*SU3D[I2, k1, k2]* - SU3D[I4, I5, k3] + (I/2)*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3D[I4, I5, k3] + (SU3D[6, I3, k1]*SU3D[I4, I5, k3]* - SU3F[I2, k1, k2])/2 + (SU3D[6, I2, k1]*SU3D[I4, I5, k3]* - SU3F[I3, k1, k2])/2 + SU3D[6, I3, k1]*SU3D[I2, I5, k3]* - ((-I/2)*SU3D[I4, k1, k2] - SU3F[I4, k1, k2]/2) + - SU3D[6, I2, k1]*SU3D[I3, I5, k3]*((-I/2)*SU3D[I4, k1, k2] - - SU3F[I4, k1, k2]/2) + SU3D[6, I3, k1]*SU3D[I2, I4, k3]* - ((I/2)*SU3D[I5, k1, k2] + SU3F[I5, k1, k2]/2) + - SU3D[6, I2, k1]*SU3D[I3, I4, k3]*((I/2)*SU3D[I5, k1, k2] + - SU3F[I5, k1, k2]/2) + SU3D[6, I4, k1]* - ((-I/2)*SU3D[I2, k1, k3]*SU3D[I3, I5, k2] - (I/2)*SU3D[I2, I5, k2]* - SU3D[I3, k1, k3] - (I/2)*SU3D[I2, I3, k2]*SU3D[I5, k1, k3] - - (SU3D[I3, I5, k3]*SU3F[I2, k1, k2])/2 - - (SU3D[I2, I5, k3]*SU3F[I3, k1, k2])/2 - - (SU3D[I2, I3, k3]*SU3F[I5, k1, k2])/2)) + - SU3D[I4, k2, k3]*(-(SU3D[I2, I3, k1]*SU3D[I5, k1, k3]*SU3F[6, I1, k2])/ - 6 + SU3D[I3, I5, k1]*((I/2)*SU3F[6, I2, k2]*SU3F[I1, k1, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I2, k1, k3]) + SU3D[I2, I5, k1]* - ((I/2)*SU3F[6, I3, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I3, k1, k3]) + SU3D[I2, I3, k1]* - ((I/2)*SU3F[6, I5, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I5, k1, k3])) + SU3D[I3, k2, k3]* - (SU3D[I5, k1, k3]*(-(SU3D[I2, I4, k1]*SU3F[6, I1, k2])/6 + - (SU3D[I1, I4, k1]*SU3F[6, I2, k2])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I4, k2])/6) + SU3D[I4, k1, k3]* - ((SU3D[I2, I5, k1]*SU3F[6, I1, k2])/6 - - (SU3D[I1, I5, k1]*SU3F[6, I2, k2])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I5, k2])/4) - - (SU3D[6, I2, k1]*SU3D[I4, I5, k3]*SU3F[I1, k1, k2])/3 + - SU3D[I2, I5, k1]*((I/2)*SU3F[6, I4, k2]*SU3F[I1, k1, k3] + - (I/6)*SU3F[6, I1, k2]*SU3F[I4, k1, k3]) + SU3D[I1, I5, k1]* - ((-I/6)*SU3F[6, I4, k2]*SU3F[I2, k1, k3] - (I/4)*SU3F[6, I2, k2]* - SU3F[I4, k1, k3]) + SU3D[I2, I4, k1]* - ((-I/2)*SU3F[6, I5, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I4, k1]* - ((I/4)*SU3F[6, I5, k2]*SU3F[I2, k1, k3] + (I/4)*SU3F[6, I2, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I2, k1]* - ((-I/4)*SU3F[6, I5, k2]*SU3F[I4, k1, k3] - (I/6)*SU3F[6, I4, k2]* - SU3F[I5, k1, k3]) + SU3D[6, I2, k1]* - ((SU3D[I5, k1, k2]*SU3F[I1, I4, k3])/12 - - (SU3D[I4, k1, k2]*SU3F[I1, I5, k3])/3 + (I/3)*SU3F[I1, I5, k2]* - SU3F[I4, k1, k3] - (I/12)*SU3F[I1, I4, k2]*SU3F[I5, k1, k3]) + - SU3D[6, I1, k1]*((I/6)*SU3D[I2, I4, k2]*SU3D[I5, k1, k3] + - (SU3D[I5, k1, k2]*SU3F[I2, I4, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I2, k1, k2])/6 + (I/6)*SU3F[I2, k1, k3]* - SU3F[I4, I5, k2] + (SU3D[I2, I4, k2]*SU3F[I5, k1, k3])/6 - - (I/6)*SU3F[I2, I4, k2]*SU3F[I5, k1, k3])) + - SU3D[I2, k2, k3]*(SU3D[I5, k1, k3]*((SU3D[I1, I4, k1]*SU3F[6, I3, k2])/ - 4 - (SU3D[I1, I3, k1]*SU3F[6, I4, k2])/6) + - SU3D[I4, k1, k3]*(-(SU3D[I1, I5, k1]*SU3F[6, I3, k2])/4 - - (SU3D[I1, I3, k1]*SU3F[6, I5, k2])/4) + SU3D[I3, k1, k3]* - ((I/6)*SU3D[6, I1, k1]*SU3D[I4, I5, k2] - - (SU3D[I1, I5, k1]*SU3F[6, I4, k2])/6 + - (SU3D[I1, I4, k1]*SU3F[6, I5, k2])/4) - - (SU3D[6, I1, k1]*SU3D[I3, k1, k2]*SU3F[I4, I5, k3])/6 + - SU3D[6, I1, k1]*SU3D[I3, I5, k3]*((I/6)*SU3D[I4, k1, k2] + - SU3F[I4, k1, k2]/6) + SU3D[I1, I5, k1]* - ((-I/6)*SU3F[6, I4, k2]*SU3F[I3, k1, k3] - (I/4)*SU3F[6, I3, k2]* - SU3F[I4, k1, k3]) + SU3D[6, I3, k1]*SU3D[I1, I4, k2]* - ((-I/4)*SU3D[I5, k1, k3] - SU3F[I5, k1, k3]/4) + - SU3D[I1, I4, k1]*((I/4)*SU3F[6, I5, k2]*SU3F[I3, k1, k3] + - (I/4)*SU3F[6, I3, k2]*SU3F[I5, k1, k3]) + SU3D[I1, I3, k1]* - ((-I/4)*SU3F[6, I5, k2]*SU3F[I4, k1, k3] - (I/6)*SU3F[6, I4, k2]* - SU3F[I5, k1, k3]) + SU3D[6, I4, k1]* - ((I/6)*SU3D[I1, I5, k2]*SU3D[I3, k1, k3] - - (SU3D[I5, k1, k2]*SU3F[I1, I3, k3])/6 - - (SU3D[I3, k1, k2]*SU3F[I1, I5, k3])/6 + - (SU3D[I3, I5, k3]*SU3F[I1, k1, k2])/3 + - (SU3D[I1, I5, k2]*SU3F[I3, k1, k3])/6 + (I/6)*SU3F[I1, I5, k2]* - SU3F[I3, k1, k3] + SU3D[I1, I3, k2]*((I/6)*SU3D[I5, k1, k3] + - SU3F[I5, k1, k3]/6) + (I/6)*SU3F[I1, I3, k2]*SU3F[I5, k1, k3]) + - SU3D[6, I3, k1]*((SU3D[I5, k1, k2]*SU3F[I1, I4, k3])/12 - - (SU3D[I4, k1, k2]*SU3F[I1, I5, k3])/3 - - (SU3D[I4, I5, k3]*SU3F[I1, k1, k2])/3 + (I/3)*SU3F[I1, I5, k2]* - SU3F[I4, k1, k3] - (I/12)*SU3F[I1, I4, k2]*SU3F[I5, k1, k3]) + - SU3D[6, I1, k1]*((I/6)*SU3D[I3, I4, k2]*SU3D[I5, k1, k3] + - (SU3D[I5, k1, k2]*SU3F[I3, I4, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I3, k1, k2])/6 + (I/6)*SU3F[I3, k1, k3]* - SU3F[I4, I5, k2] - (I/6)*SU3F[I3, I4, k2]*SU3F[I5, k1, k3])) + - SU3D[I3, k1, k3]*(SU3D[6, I2, k1]*SU3D[I1, I5, k2]* - ((I/4)*SU3D[I4, k2, k3] - SU3F[I4, k2, k3]/4) + - SU3D[6, I1, k1]*SU3D[I2, I4, k2]*((I/6)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/6) + SU3D[6, I2, k1]*SU3D[I1, I4, k2]* - ((-I/4)*SU3D[I5, k2, k3] + SU3F[I5, k2, k3]/4)) + - SU3D[I2, k1, k3]*(SU3D[6, I3, k1]*SU3D[I1, I5, k2]* - ((I/4)*SU3D[I4, k2, k3] - SU3F[I4, k2, k3]/4) + - SU3D[6, I3, k1]*SU3D[I1, I4, k2]*((-I/4)*SU3D[I5, k2, k3] + - SU3F[I5, k2, k3]/4)) + SU3D[I3, I4, k3]* - ((SU3D[6, I1, k1]*SU3D[I2, k2, k3]*SU3F[I5, k1, k2])/6 + - SU3D[I1, k1, k2]*((SU3D[I5, k2, k3]*SU3F[6, I2, k1])/3 + - (SU3D[I2, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I2, k2, k3] + SU3D[6, I2, k1]*((-I/3)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/3) - (I/3)*SU3F[6, I2, k1]*SU3F[I5, k2, k3])) + - SU3D[I1, k1, k2]*((SU3D[I3, I5, k2]*SU3D[I4, k1, k3]*SU3F[6, I2, k3])/ - 2 + SU3D[I5, k1, k3]*(-(SU3D[I3, I4, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I4, k2]*SU3F[6, I3, k3])/2) + SU3D[I3, k2, k3]* - (SU3D[I4, I5, k3]*((-I/3)*SU3D[6, I2, k1] + SU3F[6, I2, k1]/3) - - (SU3D[I2, I5, k3]*SU3F[6, I4, k1])/3) + SU3D[I2, k2, k3]* - ((I/3)*SU3D[6, I4, k1]*SU3D[I3, I5, k3] - (I/3)*SU3D[6, I3, k1]* - SU3D[I4, I5, k3] + (SU3D[I4, I5, k3]*SU3F[6, I3, k1])/3 - - (SU3D[I3, I5, k3]*SU3F[6, I4, k1])/3) + - (SU3D[I2, I3, k2]*SU3D[I5, k1, k3]*SU3F[6, I4, k3])/2 + - SU3D[I2, I5, k2]*((SU3D[I4, k1, k3]*SU3F[6, I3, k3])/2 + - (SU3D[I3, k1, k3]*SU3F[6, I4, k3])/2) + - (SU3D[I2, I3, k2]*SU3D[I4, k1, k3]*SU3F[6, I5, k3])/2 + - SU3D[I3, k1, k3]*(-(SU3D[I4, I5, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I4, k2]*SU3F[6, I5, k3])/2) + SU3D[I2, k1, k3]* - (-(SU3D[I4, I5, k2]*SU3F[6, I3, k3])/2 + - (SU3D[I3, I5, k2]*SU3F[6, I4, k3])/2 - - (SU3D[I3, I4, k2]*SU3F[6, I5, k3])/2) - - (SU3D[6, I3, k1]*SU3D[I4, I5, k3]*SU3F[I2, k2, k3])/3 + - SU3D[I4, I5, k3]*((-I/3)*SU3F[6, I3, k1]*SU3F[I2, k2, k3] - - (SU3D[6, I2, k1]*SU3F[I3, k2, k3])/3 - (I/3)*SU3F[6, I2, k1]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k1]* - ((-I/2)*SU3F[6, I3, k3]*SU3F[I2, k2, k3] - (I/2)*SU3F[6, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I3, I5, k3]* - ((SU3D[I4, k2, k3]*SU3F[6, I2, k1])/3 + (I/3)*SU3F[6, I4, k1]* - SU3F[I2, k2, k3] + SU3D[6, I2, k1]*((-I/3)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/3) - (I/3)*SU3F[6, I2, k1]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k1]*((I/2)*SU3F[6, I4, k3]*SU3F[I2, k2, k3] + - (I/2)*SU3F[6, I2, k3]*SU3F[I4, k2, k3]) + SU3D[I2, I5, k3]* - ((SU3D[I4, k2, k3]*SU3F[6, I3, k1])/3 + (I/3)*SU3F[6, I4, k1]* - SU3F[I3, k2, k3] + SU3D[6, I3, k1]*((-I/3)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/3) - (I/3)*SU3F[6, I3, k1]*SU3F[I4, k2, k3]) + - SU3D[I2, I5, k1]*((I/2)*SU3F[6, I4, k3]*SU3F[I3, k2, k3] + - (I/2)*SU3F[6, I3, k3]*SU3F[I4, k2, k3]) + SU3D[6, I4, k1]* - ((I/3)*SU3D[I2, I5, k3]*SU3D[I3, k2, k3] + - (SU3D[I3, I5, k3]*SU3F[I2, k2, k3])/3 + - (SU3D[I2, I5, k3]*SU3F[I3, k2, k3])/3 + SU3D[I2, I3, k3]* - ((I/3)*SU3D[I5, k2, k3] + SU3F[I5, k2, k3]/3)) + - SU3D[I3, I4, k1]*((-I/2)*SU3F[6, I5, k3]*SU3F[I2, k2, k3] - - (I/2)*SU3F[6, I2, k3]*SU3F[I5, k2, k3]) + SU3D[I2, I4, k3]* - ((SU3D[I5, k2, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I3, k2, k3] + SU3D[6, I3, k1]*((-I/3)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/3) - (I/3)*SU3F[6, I3, k1]*SU3F[I5, k2, k3]) + - SU3D[I2, I4, k1]*((-I/2)*SU3F[6, I5, k3]*SU3F[I3, k2, k3] - - (I/2)*SU3F[6, I3, k3]*SU3F[I5, k2, k3]) + SU3D[I2, I3, k3]* - (-(SU3D[I5, k2, k3]*SU3F[6, I4, k1])/3 + - (SU3D[I4, k2, k3]*SU3F[6, I5, k1])/3 - (I/3)*SU3F[6, I5, k1]* - SU3F[I4, k2, k3] + (I/3)*SU3F[6, I4, k1]*SU3F[I5, k2, k3]) + - SU3D[I2, I3, k1]*((I/2)*SU3F[6, I5, k3]*SU3F[I4, k2, k3] + - (I/2)*SU3F[6, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I4, k1, k2]*(SU3D[I5, k2, k3]*((SU3D[I2, I3, k1]*SU3F[6, I1, k3])/ - 6 - (SU3D[I1, I3, k1]*SU3F[6, I2, k3])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I3, k3])/4 - (I/12)*SU3F[6, I3, k3]* - SU3F[I1, I2, k1] - (I/12)*SU3F[6, I2, k3]*SU3F[I1, I3, k1]) + - SU3D[I5, k1, k3]*((-I/3)*SU3F[6, I3, k2]*SU3F[I1, I2, k3] - - (I/3)*SU3F[6, I2, k2]*SU3F[I1, I3, k3]) + SU3D[I3, I5, k1]* - ((I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I2, k2, k3]) + SU3F[6, I5, k2]* - (-(SU3F[I1, I3, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, I2, k3]*SU3F[I3, k1, k3])/3) + SU3D[I2, I5, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, I5, k1]* - ((-I/4)*SU3F[6, I3, k3]*SU3F[I2, k2, k3] - (I/4)*SU3F[6, I2, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I3, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I3, k2, k3])/12) + SU3F[6, I3, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, I2, k3]*SU3F[I5, k1, k3])/3) + SU3F[6, I2, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, I3, k3]*SU3F[I5, k1, k3])/3) + SU3D[I2, I3, k1]* - ((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I3, k1]* - ((-I/4)*SU3F[6, I5, k3]*SU3F[I2, k2, k3] - (I/4)*SU3F[6, I2, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I2, k1]* - ((-I/4)*SU3F[6, I5, k3]*SU3F[I3, k2, k3] - (I/4)*SU3F[6, I3, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I3, k3]* - ((SU3F[I1, I5, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I5, k2, k3])/12) + SU3F[6, I2, k3]* - ((SU3F[I1, I5, k1]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k1]*SU3F[I5, k2, k3])/12)) + - SU3D[I3, k1, k2]*(SU3D[I4, k2, k3]*(-(SU3D[I2, I5, k1]*SU3F[6, I1, k3])/ - 6 - (I/3)*SU3F[6, I5, k3]*SU3F[I1, I2, k1] - (I/3)*SU3F[6, I2, k3]* - SU3F[I1, I5, k1]) + SU3D[I4, k1, k3]* - ((-I/12)*SU3F[6, I5, k2]*SU3F[I1, I2, k3] - (I/12)*SU3F[6, I2, k2]* - SU3F[I1, I5, k3]) + SU3D[I5, k2, k3]* - (-(SU3D[I2, I4, k1]*SU3F[6, I1, k3])/6 + - (SU3D[I1, I4, k1]*SU3F[6, I2, k3])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I4, k3])/6 - (I/6)*SU3F[6, I4, k3]* - SU3F[I1, I2, k1] + (I/12)*SU3F[6, I2, k3]*SU3F[I1, I4, k1] + - (I/6)*SU3F[6, I1, k3]*SU3F[I2, I4, k1]) + SU3D[I5, k1, k3]* - ((-I/6)*SU3F[6, I4, k2]*SU3F[I1, I2, k3] + (I/12)*SU3F[6, I2, k2]* - SU3F[I1, I4, k3] + (I/6)*SU3F[6, I1, k2]*SU3F[I2, I4, k3]) - - (I/6)*SU3D[I1, I5, k1]*SU3F[6, I4, k3]*SU3F[I2, k2, k3] + - SU3D[I4, I5, k3]*((SU3D[6, I2, k1]*SU3F[I1, k2, k3])/2 + - (I/2)*SU3F[6, I2, k1]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k1]* - SU3F[I2, k2, k3]) + SU3D[I4, I5, k1]* - ((I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I2, k2, k3]) + SU3F[6, I5, k2]* - ((SU3F[I1, I4, k3]*SU3F[I2, k1, k3])/12 - - (SU3F[I1, I2, k3]*SU3F[I4, k1, k3])/12) + SU3D[I2, I5, k1]* - ((-I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I5, k3]* - (-(SU3F[I1, I4, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I4, k2, k3])/3) + SU3F[6, I4, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I2, k1, k3])/6 - - (SU3F[I1, I2, k3]*SU3F[I5, k1, k3])/6) + SU3F[6, I2, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I4, k1, k3])/12 + - (SU3F[I1, I4, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I1, k2]* - (-(SU3F[I2, k1, k3]*SU3F[I4, I5, k3])/6 + - (SU3F[I2, I4, k3]*SU3F[I5, k1, k3])/6) - (I/6)*SU3D[I1, I2, k1]* - SU3F[6, I4, k3]*SU3F[I5, k2, k3] + SU3D[I2, I4, k1]* - ((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3D[I1, I4, k1]* - ((I/4)*SU3F[6, I5, k3]*SU3F[I2, k2, k3] + (I/4)*SU3F[6, I2, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I5, k1]*SU3F[I2, k2, k3])/6 + - (SU3F[I1, I2, k1]*SU3F[I5, k2, k3])/6) + SU3F[6, I2, k3]* - ((SU3F[I1, I5, k1]*SU3F[I4, k2, k3])/3 - - (SU3F[I1, I4, k1]*SU3F[I5, k2, k3])/12) + SU3D[6, I2, k1]* - ((SU3D[I5, k2, k3]*SU3F[I1, I4, k3])/12 - - (SU3D[I4, k2, k3]*SU3F[I1, I5, k3])/12 + (I/12)*SU3F[I1, I5, k3]* - SU3F[I4, k2, k3] - (I/12)*SU3F[I1, I4, k3]*SU3F[I5, k2, k3]) + - SU3F[6, I1, k3]*((SU3F[I2, k2, k3]*SU3F[I4, I5, k1])/6 - - (SU3F[I2, I4, k1]*SU3F[I5, k2, k3])/6) + SU3D[6, I1, k1]* - ((SU3D[I5, k2, k3]*SU3F[I2, I4, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I2, k2, k3])/6 + (I/6)*SU3F[I2, k2, k3]* - SU3F[I4, I5, k3] - (I/6)*SU3F[I2, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I2, k1, k2]*(-(SU3D[I3, I5, k2]*SU3D[I4, k1, k3]*SU3F[6, I1, k3])/ - 6 + SU3D[I4, k2, k3]*((-I/3)*SU3F[6, I5, k3]*SU3F[I1, I3, k1] - - (I/3)*SU3F[6, I3, k3]*SU3F[I1, I5, k1]) + SU3D[I4, k1, k3]* - ((-I/12)*SU3F[6, I5, k2]*SU3F[I1, I3, k3] - (I/12)*SU3F[6, I3, k2]* - SU3F[I1, I5, k3]) + SU3D[I5, k2, k3]* - ((SU3D[I1, I4, k1]*SU3F[6, I3, k3])/4 - - (SU3D[I1, I3, k1]*SU3F[6, I4, k3])/6 - (I/6)*SU3F[6, I4, k3]* - SU3F[I1, I3, k1] + (I/12)*SU3F[6, I3, k3]*SU3F[I1, I4, k1] + - (I/6)*SU3F[6, I1, k3]*SU3F[I3, I4, k1]) + SU3D[I5, k1, k3]* - (-(SU3D[I3, I4, k2]*SU3F[6, I1, k3])/6 - (I/6)*SU3F[6, I4, k2]* - SU3F[I1, I3, k3] + (I/12)*SU3F[6, I3, k2]*SU3F[I1, I4, k3] + - (I/6)*SU3F[6, I1, k2]*SU3F[I3, I4, k3]) - (I/6)*SU3D[I1, I5, k1]* - SU3F[6, I4, k3]*SU3F[I3, k2, k3] + SU3D[I4, I5, k3]* - ((I/2)*SU3F[6, I3, k1]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k1]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3D[I3, k2, k3]* - (-(SU3D[I4, I5, k3]*SU3F[6, I1, k1])/6 - - (SU3D[I1, I5, k1]*SU3F[6, I4, k3])/6 + - (SU3D[I1, I4, k1]*SU3F[6, I5, k3])/4 + (I/12)*SU3F[6, I5, k3]* - SU3F[I1, I4, k1] - (I/6)*SU3F[6, I4, k3]*SU3F[I1, I5, k1] - - (I/6)*SU3F[6, I1, k3]*SU3F[I4, I5, k1] + SU3D[6, I1, k1]* - ((I/6)*SU3D[I4, I5, k3] - SU3F[I4, I5, k3]/6)) + - SU3D[I3, k1, k3]*(-(SU3D[I4, I5, k2]*SU3F[6, I1, k3])/6 + - (I/12)*SU3F[6, I5, k2]*SU3F[I1, I4, k3] - (I/6)*SU3F[6, I4, k2]* - SU3F[I1, I5, k3] - (I/6)*SU3F[6, I1, k2]*SU3F[I4, I5, k3]) + - SU3F[6, I5, k2]*((SU3F[I1, I4, k3]*SU3F[I3, k1, k3])/12 - - (SU3F[I1, I3, k3]*SU3F[I4, k1, k3])/12) + SU3D[I3, I5, k3]* - ((SU3D[I4, k2, k3]*SU3F[6, I1, k1])/6 - (I/2)*SU3F[6, I4, k1]* - SU3F[I1, k2, k3] + SU3D[6, I1, k1]*((-I/6)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/6) - (I/6)*SU3F[6, I1, k1]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k1]*((-I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I4, k2, k3]) + SU3F[6, I5, k3]* - (-(SU3F[I1, I4, k1]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k1]*SU3F[I4, k2, k3])/3) + SU3F[6, I4, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I1, I3, k3]*SU3F[I5, k1, k3])/6) + SU3F[6, I3, k2]* - (-(SU3F[I1, I5, k3]*SU3F[I4, k1, k3])/12 + - (SU3F[I1, I4, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I1, k2]* - (-(SU3F[I3, k1, k3]*SU3F[I4, I5, k3])/6 + - (SU3F[I3, I4, k3]*SU3F[I5, k1, k3])/6) - (I/6)*SU3D[I1, I3, k1]* - SU3F[6, I4, k3]*SU3F[I5, k2, k3] + SU3D[I3, I4, k3]* - (-(SU3D[I5, k2, k3]*SU3F[6, I1, k1])/6 + (I/2)*SU3F[6, I5, k1]* - SU3F[I1, k2, k3] + SU3D[6, I1, k1]*((I/6)*SU3D[I5, k2, k3] + - SU3F[I5, k2, k3]/6) + (I/6)*SU3F[6, I1, k1]*SU3F[I5, k2, k3]) + - SU3D[I3, I4, k1]*((I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I5, k2, k3]) + SU3D[I1, I4, k1]* - ((I/4)*SU3F[6, I5, k3]*SU3F[I3, k2, k3] + (I/4)*SU3F[6, I3, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I5, k1]*SU3F[I3, k2, k3])/6 + - (SU3F[I1, I3, k1]*SU3F[I5, k2, k3])/6) + SU3D[6, I4, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I3, k3])/6 - - (SU3D[I3, k2, k3]*SU3F[I1, I5, k3])/6 - - (SU3D[I3, I5, k3]*SU3F[I1, k2, k3])/2 + (I/6)*SU3F[I1, I5, k3]* - SU3F[I3, k2, k3] + (I/6)*SU3F[I1, I3, k3]*SU3F[I5, k2, k3]) + - SU3F[6, I3, k3]*((SU3F[I1, I5, k1]*SU3F[I4, k2, k3])/3 - - (SU3F[I1, I4, k1]*SU3F[I5, k2, k3])/12) + SU3D[6, I3, k1]* - ((SU3D[I5, k2, k3]*SU3F[I1, I4, k3])/12 - - (SU3D[I4, k2, k3]*SU3F[I1, I5, k3])/12 + - (SU3D[I4, I5, k3]*SU3F[I1, k2, k3])/2 + (I/12)*SU3F[I1, I5, k3]* - SU3F[I4, k2, k3] - (I/12)*SU3F[I1, I4, k3]*SU3F[I5, k2, k3]) + - SU3F[6, I1, k3]*((SU3F[I3, k2, k3]*SU3F[I4, I5, k1])/6 - - (SU3F[I3, I4, k1]*SU3F[I5, k2, k3])/6) + SU3D[6, I1, k1]* - ((SU3D[I5, k2, k3]*SU3F[I3, I4, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I3, k2, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I4, I5, k3] - (I/6)*SU3F[I3, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I1, I4, k2]*(SU3D[6, I2, k1]*SU3D[I3, k2, k3]* - ((-I/4)*SU3D[I5, k1, k3] - SU3F[I5, k1, k3]/4) + - SU3D[6, I3, k1]*(-(SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/4 + - (SU3D[I5, k1, k3]*SU3F[I2, k2, k3])/4 - (I/4)*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] - (I/4)*SU3F[I2, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[6, I2, k1]*(-(SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/4 + - (SU3D[I5, k1, k3]*SU3F[I3, k2, k3])/4 - (I/4)*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] - (I/4)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])) + - SU3F[I1, I5, k1]*((I/6)*SU3F[I3, I4, k1]*SUNDelta[6, I2] + - (I/6)*SU3F[I2, I4, k1]*SUNDelta[6, I3]) + SU3F[I1, I3, k1]* - ((-I/6)*SU3F[I4, I5, k1]*SUNDelta[6, I2] + (I/6)*SU3F[I2, I4, k1]* - SUNDelta[6, I5]) + SU3F[I1, I2, k1]* - ((-I/6)*SU3F[I4, I5, k1]*SUNDelta[6, I3] + (I/6)*SU3F[I3, I4, k1]* - SUNDelta[6, I5]) + SU3D[I4, I5, k1]* - (SU3F[6, I3, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/6) + - (5*SU3F[I1, I3, k1]*SUNDelta[6, I2])/18 + - (5*SU3F[I1, I2, k1]*SUNDelta[6, I3])/18 - - (SU3F[6, I3, k1]*SUNDelta[I1, I2])/6 - - (SU3F[6, I2, k1]*SUNDelta[I1, I3])/6) + SU3D[I3, I4, k1]* - (SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/6) + - (5*SU3F[I1, I5, k1]*SUNDelta[6, I2])/18 + - (5*SU3F[I1, I2, k1]*SUNDelta[6, I5])/18 - - (SU3F[6, I5, k1]*SUNDelta[I1, I2])/6 - - (SU3F[6, I2, k1]*SUNDelta[I1, I5])/6) + SU3D[I2, I4, k1]* - (SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I3, k2]* - ((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/6) + ((2*I)/9)*SU3D[I3, I5, k1]* - SUNDelta[6, I1] + ((5*I)/18)*SU3D[I1, I5, k1]*SUNDelta[6, I3] + - (5*SU3F[I1, I5, k1]*SUNDelta[6, I3])/18 + ((5*I)/18)*SU3D[I1, I3, k1]* - SUNDelta[6, I5] + (5*SU3F[I1, I3, k1]*SUNDelta[6, I5])/18 - - (SU3F[6, I5, k1]*SUNDelta[I1, I3])/6 - - (SU3F[6, I3, k1]*SUNDelta[I1, I5])/6) + SU3D[I3, I5, k1]* - (SU3F[6, I4, k2]*(-(SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I1, k2]* - ((SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/6) + - (4*SU3F[I2, I4, k1]*SUNDelta[6, I1])/9 - - (7*SU3F[I1, I2, k1]*SUNDelta[6, I4])/9 - - (2*SU3F[6, I4, k1]*SUNDelta[I1, I2])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I2, I4])/9) + SU3D[I2, I5, k1]* - (SU3F[6, I4, k2]*(-(SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I3, k2]* - ((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I1, k2]* - ((SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6) + ((2*I)/9)*SU3D[I3, I4, k1]* - SUNDelta[6, I1] + (4*SU3F[I3, I4, k1]*SUNDelta[6, I1])/9 - - ((8*I)/9)*SU3D[I1, I4, k1]*SUNDelta[6, I3] + (I/9)*SU3D[I1, I3, k1]* - SUNDelta[6, I4] - (7*SU3F[I1, I3, k1]*SUNDelta[6, I4])/9 - - (2*SU3F[6, I4, k1]*SUNDelta[I1, I3])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I3, I4])/9) + SU3D[I1, I5, k1]* - (SU3F[6, I4, k2]*(-(SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/6) - - (SU3F[6, I3, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/4 - - (SU3F[6, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/4 + - ((5*I)/18)*SU3D[I3, I4, k1]*SUNDelta[6, I2] - - (SU3F[I3, I4, k1]*SUNDelta[6, I2])/6 - - (SU3F[I2, I4, k1]*SUNDelta[6, I3])/6 + - (SU3F[6, I4, k1]*SUNDelta[I2, I3])/9 - - (SU3F[6, I3, k1]*SUNDelta[I2, I4])/9 - - (SU3F[6, I2, k1]*SUNDelta[I3, I4])/9) + SU3F[6, I5, k1]* - ((I/12)*SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] - - (I/3)*SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3] - - (I/3)*SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3] - - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3] + - SU3F[I2, k1, k3]*((I/12)*SU3F[I1, I4, k2]*SU3F[I3, k2, k3] - - (I/12)*SU3F[I1, I3, k2]*SU3F[I4, k2, k3]) - (I/6)*SU3F[I3, I4, k1]* - SUNDelta[I1, I2] - (I/6)*SU3F[I2, I4, k1]*SUNDelta[I1, I3] - - (I/9)*SU3F[I1, I4, k1]*SUNDelta[I2, I3] + ((5*I)/9)*SU3F[I1, I3, k1]* - SUNDelta[I2, I4] + ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I3, I4]) + - SU3D[6, I5, k1]*((SU3D[I2, I3, k2]*SU3D[I4, k1, k3]*SU3F[I1, k2, k3])/ - 2 + SU3D[I3, I4, k3]*(-(SU3D[I2, k2, k3]*SU3F[I1, k1, k2])/3 + - SU3D[I1, k1, k2]*((-I/3)*SU3D[I2, k2, k3] - SU3F[I2, k2, k3]/3)) + - SU3D[I3, I4, k2]*((I/2)*SU3F[I1, k2, k3]*SU3F[I2, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) + - (SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/12 + - SU3D[I4, k2, k3]*(-(SU3D[I2, I3, k2]*SU3F[I1, k1, k3])/3 + - (SU3D[I1, I3, k2]*SU3F[I2, k1, k3])/4 + (I/12)*SU3F[I1, I3, k2]* - SU3F[I2, k1, k3] + (SU3D[I1, I2, k2]*SU3F[I3, k1, k3])/4 + - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]) + - SU3D[I4, k1, k2]*((I/3)*SU3F[I1, I3, k3]*SU3F[I2, k2, k3] + - (I/3)*SU3F[I1, I2, k3]*SU3F[I3, k2, k3]) + SU3D[I2, I4, k2]* - ((I/2)*SU3F[I1, k2, k3]*SU3F[I3, k1, k3] - (I/3)*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, I4, k2]* - (-(SU3D[I3, k2, k3]*SU3F[I2, k1, k3])/4 - (I/4)*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3] - (I/4)*SU3F[I2, k1, k3]*SU3F[I3, k2, k3]) + - SU3D[I1, k2, k3]*((I/2)*SU3D[I2, k1, k2]*SU3D[I3, I4, k3] + - (SU3D[I3, I4, k3]*SU3F[I2, k1, k2])/2 + SU3D[I2, I4, k3]* - ((I/2)*SU3D[I3, k1, k2] + SU3F[I3, k1, k2]/2) + - SU3D[I2, I3, k3]*((-I/2)*SU3D[I4, k1, k2] - SU3F[I4, k1, k2]/2)) - - (SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/3 + - SU3D[I3, k2, k3]*(-(SU3D[I4, k1, k2]*SU3F[I1, I2, k3])/3 - - (SU3D[I2, I4, k2]*SU3F[I1, k1, k3])/3 - (I/12)*SU3F[I1, I4, k2]* - SU3F[I2, k1, k3] + (I/3)*SU3F[I1, I2, k2]*SU3F[I4, k1, k3]) + - SU3D[I2, k2, k3]*((-I/4)*SU3D[I1, I4, k2]*SU3D[I3, k1, k3] - - (SU3D[I4, k1, k2]*SU3F[I1, I3, k3])/3 + - (SU3D[I3, k1, k2]*SU3F[I1, I4, k3])/12 - - (SU3D[I1, I4, k2]*SU3F[I3, k1, k3])/4 - (I/12)*SU3F[I1, I4, k2]* - SU3F[I3, k1, k3] + (I/3)*SU3F[I1, I3, k2]*SU3F[I4, k1, k3]) + - SU3D[I1, k1, k2]*(SU3D[I2, I4, k3]*((-I/3)*SU3D[I3, k2, k3] - - SU3F[I3, k2, k3]/3) + SU3D[I2, I3, k3]*((-I/3)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/3)) + (I/4)*SU3D[I1, I3, k2]*SU3F[I2, k1, k3]* - SU3F[I4, k2, k3] + (I/4)*SU3D[I1, I2, k2]*SU3F[I3, k1, k3]* - SU3F[I4, k2, k3] - (SU3F[I1, I2, k2]*SU3F[I3, k1, k3]* - SU3F[I4, k2, k3])/12 + SU3D[I3, k1, k3]* - ((I/4)*SU3D[I1, I2, k2]*SU3D[I4, k2, k3] - - (SU3D[I2, I4, k2]*SU3F[I1, k2, k3])/2 + - (SU3D[I1, I4, k2]*SU3F[I2, k2, k3])/4 - - (SU3D[I1, I2, k2]*SU3F[I4, k2, k3])/4) + SU3D[I2, k1, k3]* - ((I/4)*SU3D[I1, I3, k2]*SU3D[I4, k2, k3] + SU3D[I1, I4, k2]* - ((-I/4)*SU3D[I3, k2, k3] + SU3F[I3, k2, k3]/4) - - (SU3D[I1, I3, k2]*SU3F[I4, k2, k3])/4) + SU3D[I3, k1, k2]* - (-(SU3D[I4, k2, k3]*SU3F[I1, I2, k3])/12 - (I/12)*SU3F[I1, I4, k3]* - SU3F[I2, k2, k3] + (I/12)*SU3F[I1, I2, k3]*SU3F[I4, k2, k3]) + - SU3F[I2, k1, k3]*((SU3F[I1, I4, k2]*SU3F[I3, k2, k3])/12 - - (SU3F[I1, I3, k2]*SU3F[I4, k2, k3])/12) + SU3D[I2, k1, k2]* - (-(SU3D[I4, k2, k3]*SU3F[I1, I3, k3])/12 + - (SU3D[I3, k2, k3]*SU3F[I1, I4, k3])/12 + - (SU3D[I3, I4, k3]*SU3F[I1, k2, k3])/2 - (I/12)*SU3F[I1, I4, k3]* - SU3F[I3, k2, k3] + (I/12)*SU3F[I1, I3, k3]*SU3F[I4, k2, k3]) + - SU3D[I2, I3, k2]*((-I/2)*SU3F[I1, k2, k3]*SU3F[I4, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) + (I/6)*SU3D[I3, I4, k1]* - SUNDelta[I1, I2] - (SU3F[I3, I4, k1]*SUNDelta[I1, I2])/6 + - (I/6)*SU3D[I2, I4, k1]*SUNDelta[I1, I3] - - (SU3F[I2, I4, k1]*SUNDelta[I1, I3])/6 - ((5*I)/9)*SU3D[I1, I4, k1]* - SUNDelta[I2, I3] - (SU3F[I1, I4, k1]*SUNDelta[I2, I3])/9 + - (I/9)*SU3D[I1, I3, k1]*SUNDelta[I2, I4] + - (5*SU3F[I1, I3, k1]*SUNDelta[I2, I4])/9 + (I/9)*SU3D[I1, I2, k1]* - SUNDelta[I3, I4] + (5*SU3F[I1, I2, k1]*SUNDelta[I3, I4])/9) + - SUNDelta[6, I5]*(((-16*I)/27)*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - ((5*I)/27)*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - ((5*I)/27)*SUNDelta[I1, I2]*SUNDelta[I3, I4]) + - SU3D[I1, I4, k1]*(SU3F[6, I5, k2]*((SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/ - 4 + (SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/4) + - SU3F[6, I3, k2]*((SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/4 + - (SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/4) + SU3F[6, I2, k2]* - ((SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/4 + - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/4) - ((8*I)/9)*SU3D[I3, I5, k1]* - SUNDelta[6, I2] + (5*SU3F[6, I5, k1]*SUNDelta[I2, I3])/9 + - (5*SU3F[6, I3, k1]*SUNDelta[I2, I5])/9 + - (5*SU3F[6, I2, k1]*SUNDelta[I3, I5])/9) + - SU3D[6, I4, k1]*(SU3D[I3, I5, k2]*((-I/2)*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) - - (SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/6 + - SU3D[I5, k2, k3]*((I/6)*SU3F[I1, I3, k2]*SU3F[I2, k1, k3] + - (I/6)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]) + SU3D[I5, k1, k2]* - ((I/6)*SU3F[I1, I3, k3]*SU3F[I2, k2, k3] + (I/6)*SU3F[I1, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I2, I5, k2]* - ((SU3D[I3, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I3, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I3, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]) + - SU3D[I1, I5, k2]*((SU3D[I3, k2, k3]*SU3F[I2, k1, k3])/6 + - (I/6)*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] + (I/6)*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]) - (SU3F[I1, I3, k2]*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3])/6 - (SU3F[I1, I2, k2]*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3])/6 + SU3D[I3, k2, k3]* - (-(SU3D[I5, k1, k2]*SU3F[I1, I2, k3])/6 + (I/6)*SU3F[I1, I5, k2]* - SU3F[I2, k1, k3] + SU3D[I1, I2, k2]*((I/6)*SU3D[I5, k1, k3] + - SU3F[I5, k1, k3]/6) + (I/6)*SU3F[I1, I2, k2]*SU3F[I5, k1, k3]) + - SU3D[I3, k1, k3]*(-(SU3D[I1, I5, k2]*SU3F[I2, k2, k3])/6 + - SU3D[I1, I2, k2]*((I/6)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/6)) + - SU3D[I2, k1, k3]*(SU3D[I1, I5, k2]*((I/6)*SU3D[I3, k2, k3] - - SU3F[I3, k2, k3]/6) + SU3D[I1, I3, k2]*((I/6)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/6)) - (SU3F[I1, I2, k2]*SU3F[I3, k1, k3]* - SU3F[I5, k2, k3])/6 + SU3D[I3, k1, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I2, k3])/6 + (I/6)*SU3F[I1, I5, k3]* - SU3F[I2, k2, k3] + (I/6)*SU3F[I1, I2, k3]*SU3F[I5, k2, k3]) + - SU3F[I2, k1, k3]*(-(SU3F[I1, I5, k2]*SU3F[I3, k2, k3])/6 - - (SU3F[I1, I3, k2]*SU3F[I5, k2, k3])/6) + SU3D[I2, I3, k2]* - ((SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I1, I3, k2]*((SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I2, k2, k3])/6 + (I/6)*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I2, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I1, I2, k2]*((SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I3, k2, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3]) + - ((2*I)/9)*SU3D[I3, I5, k1]*SUNDelta[I1, I2] + - ((2*I)/9)*SU3D[I2, I5, k1]*SUNDelta[I1, I3] + - ((2*I)/9)*SU3D[I2, I3, k1]*SUNDelta[I1, I5] - (I/9)*SU3D[I1, I5, k1]* - SUNDelta[I2, I3] - (5*SU3F[I1, I5, k1]*SUNDelta[I2, I3])/9 - - (I/9)*SU3D[I1, I3, k1]*SUNDelta[I2, I5] - - (5*SU3F[I1, I3, k1]*SUNDelta[I2, I5])/9 - (I/9)*SU3D[I1, I2, k1]* - SUNDelta[I3, I5] - (5*SU3F[I1, I2, k1]*SUNDelta[I3, I5])/9) + - SU3F[6, I4, k1]*((-I/6)*SU3F[I1, I5, k2]*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3] - (I/6)*SU3F[I1, I3, k2]*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] - (I/6)*SU3F[I1, I2, k2]*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] - (I/6)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]* - SU3F[I5, k2, k3] + SU3F[I2, k1, k3]*((-I/6)*SU3F[I1, I5, k2]* - SU3F[I3, k2, k3] - (I/6)*SU3F[I1, I3, k2]*SU3F[I5, k2, k3]) - - ((5*I)/9)*SU3F[I1, I5, k1]*SUNDelta[I2, I3] - - ((5*I)/9)*SU3F[I1, I3, k1]*SUNDelta[I2, I5] - - ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I3, I5]) + - SU3F[6, I1, k1]*((I/6)*SU3F[I2, I4, k2]*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] + SU3F[I2, k2, k3]*((-I/6)*SU3F[I3, k1, k3]* - SU3F[I4, I5, k2] + (I/6)*SU3F[I3, I4, k2]*SU3F[I5, k1, k3]) + - (I/6)*SU3F[I2, I4, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3] + - SU3F[I2, k1, k2]*((I/6)*SU3F[I3, k2, k3]*SU3F[I4, I5, k3] - - (I/6)*SU3F[I3, I4, k3]*SU3F[I5, k2, k3]) - - ((2*I)/9)*SU3F[I4, I5, k1]*SUNDelta[I2, I3] + - ((2*I)/9)*SU3F[I3, I4, k1]*SUNDelta[I2, I5] + - ((2*I)/9)*SU3F[I2, I4, k1]*SUNDelta[I3, I5]) + - SUNDelta[6, I4]*(((2*I)/27)*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - ((2*I)/27)*SUNDelta[I1, I3]*SUNDelta[I2, I5] + - ((2*I)/27)*SUNDelta[I1, I2]*SUNDelta[I3, I5]) + - SU3D[6, I1, k1]*(SU3D[I5, k2, k3]*((-I/6)*SU3F[I2, k1, k3]* - SU3F[I3, I4, k2] - (I/6)*SU3F[I2, I4, k2]*SU3F[I3, k1, k3]) + - SU3D[I5, k1, k3]*(-(SU3D[I3, I4, k2]*SU3F[I2, k2, k3])/6 - - (SU3D[I2, I4, k2]*SU3F[I3, k2, k3])/6) + SU3D[I5, k1, k2]* - ((-I/6)*SU3F[I2, k2, k3]*SU3F[I3, I4, k3] - (I/6)*SU3F[I2, I4, k3]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k2]* - ((I/6)*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] + (I/6)*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]) + SU3D[I2, I3, k2]*SU3D[I4, k2, k3]* - ((-I/6)*SU3D[I5, k1, k3] - SU3F[I5, k1, k3]/6) + - (SU3F[I2, I4, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/6 + - SU3F[I2, k2, k3]*(-(SU3F[I3, k1, k3]*SU3F[I4, I5, k2])/6 + - (SU3F[I3, I4, k2]*SU3F[I5, k1, k3])/6) + SU3D[I2, I3, k2]* - SU3D[I4, k1, k3]*((I/6)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/6) + - (SU3F[I2, I4, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/6 + - SU3D[I3, I4, k2]*((SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/6 + - (I/6)*SU3F[I2, k2, k3]*SU3F[I5, k1, k3] + (I/6)*SU3F[I2, k1, k3]* - SU3F[I5, k2, k3]) + SU3F[I2, k1, k2]* - ((SU3F[I3, k2, k3]*SU3F[I4, I5, k3])/6 - - (SU3F[I3, I4, k3]*SU3F[I5, k2, k3])/6) + SU3D[I2, I4, k2]* - ((SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I2, I3, k2]*((SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/6 + - (SU3D[I5, k1, k3]*SU3F[I4, k2, k3])/6 - (I/6)*SU3F[I4, k2, k3]* - SU3F[I5, k1, k3] + (I/6)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) - - (2*SU3F[I4, I5, k1]*SUNDelta[I2, I3])/9 + ((2*I)/9)*SU3D[I3, I5, k1]* - SUNDelta[I2, I4] + (2*SU3F[I3, I4, k1]*SUNDelta[I2, I5])/9 + - ((2*I)/9)*SU3D[I2, I5, k1]*SUNDelta[I3, I4] + - (2*SU3F[I2, I4, k1]*SUNDelta[I3, I5])/9 + ((2*I)/9)*SU3D[I2, I3, k1]* - SUNDelta[I4, I5]) + SU3D[I2, I3, k1]* - (SU3F[6, I5, k2]*((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I4, k2]* - (-(SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/6 + - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6) + ((2*I)/9)*SU3D[I4, I5, k1]* - SUNDelta[6, I1] - (4*SU3F[I4, I5, k1]*SUNDelta[6, I1])/9 + - (I/9)*SU3D[I1, I5, k1]*SUNDelta[6, I4] - - (7*SU3F[I1, I5, k1]*SUNDelta[6, I4])/9 - ((8*I)/9)*SU3D[I1, I4, k1]* - SUNDelta[6, I5] - (2*SU3F[6, I4, k1]*SUNDelta[I1, I5])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I4, I5])/9) + SU3D[I1, I3, k1]* - (-(SU3F[6, I5, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/4 - - (SU3F[6, I2, k2]*SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/4 + - SU3F[6, I4, k2]*(-(SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/6) + ((5*I)/18)*SU3D[I4, I5, k1]* - SUNDelta[6, I2] + (SU3F[I4, I5, k1]*SUNDelta[6, I2])/6 - - (SU3F[I2, I4, k1]*SUNDelta[6, I5])/6 - - (SU3F[6, I5, k1]*SUNDelta[I2, I4])/9 + - (SU3F[6, I4, k1]*SUNDelta[I2, I5])/9 - - (SU3F[6, I2, k1]*SUNDelta[I4, I5])/9) + SU3D[I1, I2, k1]* - (-(SU3F[6, I5, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/4 - - (SU3F[6, I3, k2]*SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/4 + - SU3F[6, I4, k2]*(-(SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/6) + ((5*I)/18)*SU3D[I4, I5, k1]* - SUNDelta[6, I3] + (SU3F[I4, I5, k1]*SUNDelta[6, I3])/6 + - (I/9)*SU3D[I3, I5, k1]*SUNDelta[6, I4] + ((5*I)/18)*SU3D[I3, I4, k1]* - SUNDelta[6, I5] - (SU3F[I3, I4, k1]*SUNDelta[6, I5])/6 - - (SU3F[6, I5, k1]*SUNDelta[I3, I4])/9 + - (SU3F[6, I4, k1]*SUNDelta[I3, I5])/9 - - (SU3F[6, I3, k1]*SUNDelta[I4, I5])/9) + SU3F[6, I3, k1]* - ((-I/3)*SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3] + - (I/12)*SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3] + - SU3F[I2, k1, k3]*((-I/12)*SU3F[I1, I5, k2]*SU3F[I4, k2, k3] + - (I/12)*SU3F[I1, I4, k2]*SU3F[I5, k2, k3]) + - SU3F[I1, I2, k2]*((-I/12)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] - - (I/3)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) + (I/6)*SU3F[I4, I5, k1]* - SUNDelta[I1, I2] - (I/6)*SU3F[I2, I4, k1]*SUNDelta[I1, I5] + - ((5*I)/9)*SU3F[I1, I5, k1]*SUNDelta[I2, I4] - (I/9)*SU3F[I1, I4, k1]* - SUNDelta[I2, I5] + ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I4, I5]) + - SU3D[6, I3, k1]*(-(SU3D[I2, I4, k2]*SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/ - 2 - (SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/3 + - SU3D[I5, k2, k3]*((-I/12)*SU3F[I1, I4, k2]*SU3F[I2, k1, k3] + - (I/3)*SU3F[I1, I2, k2]*SU3F[I4, k1, k3]) + SU3D[I5, k1, k2]* - ((-I/12)*SU3F[I1, I4, k3]*SU3F[I2, k2, k3] + (I/12)*SU3F[I1, I2, k3]* - SU3F[I4, k2, k3]) + (SU3F[I1, I4, k2]*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3])/12 + SU3D[I4, k2, k3]* - (-(SU3D[I5, k1, k2]*SU3F[I1, I2, k3])/12 + (I/12)*SU3F[I1, I5, k2]* - SU3F[I2, k1, k3] + SU3D[I1, I2, k2]*((I/4)*SU3D[I5, k1, k3] + - SU3F[I5, k1, k3]/4) + (I/12)*SU3F[I1, I2, k2]*SU3F[I5, k1, k3]) + - SU3D[I1, I2, k2]*(-(SU3D[I5, k1, k3]*SU3F[I4, k2, k3])/4 + - (I/4)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3]) + SU3D[I4, k1, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I2, k3])/3 + (I/3)*SU3F[I1, I5, k3]* - SU3F[I2, k2, k3] + (I/3)*SU3F[I1, I2, k3]*SU3F[I5, k2, k3]) + - SU3F[I2, k1, k3]*(-(SU3F[I1, I5, k2]*SU3F[I4, k2, k3])/12 + - (SU3F[I1, I4, k2]*SU3F[I5, k2, k3])/12) + SU3D[I2, I4, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3F[I1, I2, k2]*(-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/12 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/3) + (I/6)*SU3D[I4, I5, k1]* - SUNDelta[I1, I2] + (SU3F[I4, I5, k1]*SUNDelta[I1, I2])/6 + - (I/6)*SU3D[I2, I4, k1]*SUNDelta[I1, I5] - - (SU3F[I2, I4, k1]*SUNDelta[I1, I5])/6 + (I/9)*SU3D[I1, I5, k1]* - SUNDelta[I2, I4] + (5*SU3F[I1, I5, k1]*SUNDelta[I2, I4])/9 - - ((5*I)/9)*SU3D[I1, I4, k1]*SUNDelta[I2, I5] - - (SU3F[I1, I4, k1]*SUNDelta[I2, I5])/9 + (I/9)*SU3D[I1, I2, k1]* - SUNDelta[I4, I5] + (5*SU3F[I1, I2, k1]*SUNDelta[I4, I5])/9) + - SU3F[6, I2, k1]*(SU3F[I1, I5, k2]*((-I/3)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] - (I/12)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3]) + - SU3F[I1, I4, k2]*((I/12)*SU3F[I3, k2, k3]*SU3F[I5, k1, k3] + - (I/12)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3]) + - SU3F[I1, I3, k2]*((-I/12)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] - - (I/3)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) + (I/6)*SU3F[I4, I5, k1]* - SUNDelta[I1, I3] - (I/6)*SU3F[I3, I4, k1]*SUNDelta[I1, I5] + - ((5*I)/9)*SU3F[I1, I5, k1]*SUNDelta[I3, I4] - (I/9)*SU3F[I1, I4, k1]* - SUNDelta[I3, I5] + ((5*I)/9)*SU3F[I1, I3, k1]*SUNDelta[I4, I5]) + - SU3D[6, I2, k1]*(-(SU3D[I3, I4, k2]*SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/ - 2 + SU3D[I5, k2, k3]*((-I/12)*SU3F[I1, I4, k2]*SU3F[I3, k1, k3] + - (I/3)*SU3F[I1, I3, k2]*SU3F[I4, k1, k3]) + SU3D[I5, k1, k2]* - ((-I/12)*SU3F[I1, I4, k3]*SU3F[I3, k2, k3] + (I/12)*SU3F[I1, I3, k3]* - SU3F[I4, k2, k3]) + SU3F[I1, I5, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/12) + SU3D[I4, k2, k3]* - (-(SU3D[I5, k1, k2]*SU3F[I1, I3, k3])/12 + (I/12)*SU3F[I1, I5, k2]* - SU3F[I3, k1, k3] + SU3D[I1, I3, k2]*((I/4)*SU3D[I5, k1, k3] + - SU3F[I5, k1, k3]/4) + (I/12)*SU3F[I1, I3, k2]*SU3F[I5, k1, k3]) + - SU3D[I1, I3, k2]*(-(SU3D[I5, k1, k3]*SU3F[I4, k2, k3])/4 + - (I/4)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3]) + SU3D[I4, k1, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I3, k3])/3 + (I/3)*SU3F[I1, I5, k3]* - SU3F[I3, k2, k3] + (I/3)*SU3F[I1, I3, k3]*SU3F[I5, k2, k3]) + - SU3D[I3, I4, k2]*(-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + - (I/2)*SU3F[I1, k2, k3]*SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]* - SU3F[I5, k2, k3]) + SU3F[I1, I4, k2]* - ((SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/12 + - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/12) + SU3F[I1, I3, k2]* - (-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/12 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/3) + (I/6)*SU3D[I4, I5, k1]* - SUNDelta[I1, I3] + (SU3F[I4, I5, k1]*SUNDelta[I1, I3])/6 + - (I/6)*SU3D[I3, I4, k1]*SUNDelta[I1, I5] - - (SU3F[I3, I4, k1]*SUNDelta[I1, I5])/6 + (I/9)*SU3D[I1, I5, k1]* - SUNDelta[I3, I4] + (5*SU3F[I1, I5, k1]*SUNDelta[I3, I4])/9 - - ((5*I)/9)*SU3D[I1, I4, k1]*SUNDelta[I3, I5] - - (SU3F[I1, I4, k1]*SUNDelta[I3, I5])/9 + (I/9)*SU3D[I1, I3, k1]* - SUNDelta[I4, I5] + (5*SU3F[I1, I3, k1]*SUNDelta[I4, I5])/9) + - SUNDelta[6, I3]*(((5*I)/27)*SUNDelta[I1, I5]*SUNDelta[I2, I4] - - ((16*I)/27)*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - ((5*I)/27)*SUNDelta[I1, I2]*SUNDelta[I4, I5]) + - SUNDelta[6, I2]*(((5*I)/27)*SUNDelta[I1, I5]*SUNDelta[I3, I4] - - ((16*I)/27)*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - ((5*I)/27)*SUNDelta[I1, I3]*SUNDelta[I4, I5]) + - SUNDelta[6, I1]*(((4*I)/27)*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - ((4*I)/27)*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - ((4*I)/27)*SUNDelta[I2, I3]*SUNDelta[I4, I5])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(CouplingConstant[ChPTW3[2], 1]*(((-4*I)/9)*SU3D[6, I4, I5]* - SU3D[I1, I2, I3] - ((4*I)/9)*SU3D[6, I3, I5]*SU3D[I1, I2, I4] - - ((4*I)/9)*SU3D[6, I2, I5]*SU3D[I1, I3, I4] + - I*SU3D[6, I1, I5]*SU3D[I2, I3, I4] - ((5*I)/9)*SU3D[6, I1, I4]* - SU3D[I2, I3, I5] - ((5*I)/9)*SU3D[6, I1, I3]*SU3D[I2, I4, I5] - - ((5*I)/9)*SU3D[6, I1, I2]*SU3D[I3, I4, I5] - - (7*SU3D[I3, I4, I5]*SU3F[6, I1, I2])/9 - - (7*SU3D[I2, I4, I5]*SU3F[6, I1, I3])/9 - - (7*SU3D[I2, I3, I5]*SU3F[6, I1, I4])/9 + - (SU3D[I2, I3, I4]*SU3F[6, I1, I5])/3 + - (2*SU3D[I1, I3, I4]*SU3F[6, I2, I5])/9 + - (2*SU3D[I1, I2, I4]*SU3F[6, I3, I5])/9 + - (2*SU3D[I1, I2, I3]*SU3F[6, I4, I5])/9 + SU3D[6, I3, I4]* - (((2*I)/3)*SU3D[I1, I2, I5] - (2*SU3F[I1, I2, I5])/9) + - SU3D[6, I2, I4]*(((2*I)/3)*SU3D[I1, I3, I5] - (2*SU3F[I1, I3, I5])/9) + - SU3D[6, I2, I3]*(((2*I)/3)*SU3D[I1, I4, I5] - (2*SU3F[I1, I4, I5])/9) + - SU3D[I4, I5, k2]*(SU3D[6, I3, k1]*((I/2)*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) + - SU3D[6, I2, k1]*((I/2)*SU3F[I1, k2, k3]*SU3F[I3, k1, k3] - - (I/3)*SU3F[I1, k1, k3]*SU3F[I3, k2, k3])) + - SU3D[I5, k2, k3]*(SU3D[I3, I4, k1]*((I/2)*SU3F[6, I2, k2]* - SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]*SU3F[I2, k1, k3]) + - SU3D[I2, I4, k1]*((I/2)*SU3F[6, I3, k2]*SU3F[I1, k1, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I3, k1, k3]) + SU3D[I2, I3, k1]* - ((I/2)*SU3F[6, I4, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I4, k1, k3])) + SU3D[I5, k1, k2]* - (SU3D[I3, I4, k1]*((I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] + - (I/6)*SU3F[6, I1, k3]*SU3F[I2, k2, k3]) + SU3F[6, I4, k2]* - (-(SU3F[I1, I3, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, I2, k3]*SU3F[I3, k1, k3])/3) + SU3D[I2, I4, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, I4, k1]* - ((-I/4)*SU3F[6, I3, k3]*SU3F[I2, k2, k3] - (I/4)*SU3F[6, I2, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I4, k3]* - ((SU3F[I1, I3, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I3, k2, k3])/12) + SU3F[6, I3, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, I2, k3]*SU3F[I4, k1, k3])/3) + SU3F[6, I2, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, I3, k3]*SU3F[I4, k1, k3])/3) + SU3D[I2, I3, k1]* - ((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k3]* - SU3F[I4, k2, k3]) + SU3D[I1, I3, k1]* - ((-I/4)*SU3F[6, I4, k3]*SU3F[I2, k2, k3] - (I/4)*SU3F[6, I2, k3]* - SU3F[I4, k2, k3]) + SU3D[I1, I2, k1]* - ((-I/4)*SU3F[6, I4, k3]*SU3F[I3, k2, k3] - (I/4)*SU3F[6, I3, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I3, k3]* - ((SU3F[I1, I4, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I4, k2, k3])/12) + SU3F[6, I2, k3]* - ((SU3F[I1, I4, k1]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k1]*SU3F[I4, k2, k3])/12)) + - SU3D[I1, I5, k2]*(SU3D[6, I2, k1]*SU3D[I3, k2, k3]* - ((-I/4)*SU3D[I4, k1, k3] - SU3F[I4, k1, k3]/4) + - SU3D[6, I3, k1]*(-(SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/4 + - (SU3D[I4, k1, k3]*SU3F[I2, k2, k3])/4 - (I/4)*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] - (I/4)*SU3F[I2, k1, k3]*SU3F[I4, k2, k3]) + - SU3D[6, I2, k1]*(-(SU3D[I4, k2, k3]*SU3F[I3, k1, k3])/4 + - (SU3D[I4, k1, k3]*SU3F[I3, k2, k3])/4 - (I/4)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] - (I/4)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])) + - SU3D[I1, k2, k3]*((I/2)*SU3D[6, I3, k1]*SU3D[I2, k1, k2]* - SU3D[I4, I5, k3] + (I/2)*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3D[I4, I5, k3] + (SU3D[6, I3, k1]*SU3D[I4, I5, k3]* - SU3F[I2, k1, k2])/2 + (SU3D[6, I2, k1]*SU3D[I4, I5, k3]* - SU3F[I3, k1, k2])/2 + SU3D[6, I3, k1]*SU3D[I2, I5, k3]* - ((I/2)*SU3D[I4, k1, k2] + SU3F[I4, k1, k2]/2) + - SU3D[6, I2, k1]*SU3D[I3, I5, k3]*((I/2)*SU3D[I4, k1, k2] + - SU3F[I4, k1, k2]/2) + SU3D[6, I4, k1]* - ((I/2)*SU3D[I2, k1, k2]*SU3D[I3, I5, k3] + - (SU3D[I3, I5, k3]*SU3F[I2, k1, k2])/2 + SU3D[I2, I5, k3]* - ((I/2)*SU3D[I3, k1, k2] + SU3F[I3, k1, k2]/2) + - SU3D[I2, I3, k3]*((-I/2)*SU3D[I5, k1, k2] - SU3F[I5, k1, k2]/2)) + - SU3D[6, I3, k1]*SU3D[I2, I4, k3]*((-I/2)*SU3D[I5, k1, k2] - - SU3F[I5, k1, k2]/2) + SU3D[6, I2, k1]*SU3D[I3, I4, k3]* - ((-I/2)*SU3D[I5, k1, k2] - SU3F[I5, k1, k2]/2)) + - SU3D[I4, k2, k3]*(SU3D[I5, k1, k3]*((SU3D[I2, I3, k1]*SU3F[6, I1, k2])/ - 6 - (SU3D[I1, I3, k1]*SU3F[6, I2, k2])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I3, k2])/4) + SU3D[I3, I5, k1]* - ((-I/2)*SU3F[6, I2, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I2, k1, k3]) + SU3D[I2, I5, k1]* - ((-I/2)*SU3F[6, I3, k2]*SU3F[I1, k1, k3] - (I/6)*SU3F[6, I1, k2]* - SU3F[I3, k1, k3]) + SU3D[I1, I5, k1]* - ((I/4)*SU3F[6, I3, k2]*SU3F[I2, k1, k3] + (I/4)*SU3F[6, I2, k2]* - SU3F[I3, k1, k3]) + SU3D[I2, I3, k1]* - ((I/2)*SU3F[6, I5, k2]*SU3F[I1, k1, k3] + (I/6)*SU3F[6, I1, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I3, k1]* - ((-I/6)*SU3F[6, I5, k2]*SU3F[I2, k1, k3] - (I/4)*SU3F[6, I2, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I2, k1]* - ((-I/6)*SU3F[6, I5, k2]*SU3F[I3, k1, k3] - (I/4)*SU3F[6, I3, k2]* - SU3F[I5, k1, k3])) + SU3D[I3, k2, k3]* - (SU3D[I5, k1, k3]*((SU3D[I2, I4, k1]*SU3F[6, I1, k2])/6 - - (SU3D[I1, I4, k1]*SU3F[6, I2, k2])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I4, k2])/4) + SU3D[I4, k1, k3]* - (-(SU3D[I2, I5, k1]*SU3F[6, I1, k2])/6 + - (SU3D[I1, I5, k1]*SU3F[6, I2, k2])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I5, k2])/6) - - (SU3D[6, I2, k1]*SU3D[I4, I5, k3]*SU3F[I1, k1, k2])/3 + - SU3D[I2, I5, k1]*((-I/2)*SU3F[6, I4, k2]*SU3F[I1, k1, k3] - - (I/6)*SU3F[6, I1, k2]*SU3F[I4, k1, k3]) + SU3D[I1, I5, k1]* - ((I/4)*SU3F[6, I4, k2]*SU3F[I2, k1, k3] + (I/4)*SU3F[6, I2, k2]* - SU3F[I4, k1, k3]) + SU3D[6, I1, k1]* - ((I/6)*SU3D[I2, I5, k2]*SU3D[I4, k1, k3] + - (SU3D[I4, k1, k2]*SU3F[I2, I5, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I2, k1, k2])/6 - (I/6)*SU3F[I2, k1, k3]* - SU3F[I4, I5, k2] + (SU3D[I2, I5, k2]*SU3F[I4, k1, k3])/6 - - (I/6)*SU3F[I2, I5, k2]*SU3F[I4, k1, k3]) + SU3D[I2, I4, k1]* - ((I/2)*SU3F[6, I5, k2]*SU3F[I1, k1, k3] + (I/6)*SU3F[6, I1, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I4, k1]* - ((-I/6)*SU3F[6, I5, k2]*SU3F[I2, k1, k3] - (I/4)*SU3F[6, I2, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I2, k1]* - ((-I/6)*SU3F[6, I5, k2]*SU3F[I4, k1, k3] - (I/4)*SU3F[6, I4, k2]* - SU3F[I5, k1, k3]) + SU3D[6, I2, k1]* - (-(SU3D[I5, k1, k2]*SU3F[I1, I4, k3])/3 + - (SU3D[I4, k1, k2]*SU3F[I1, I5, k3])/12 - (I/12)*SU3F[I1, I5, k2]* - SU3F[I4, k1, k3] + (I/3)*SU3F[I1, I4, k2]*SU3F[I5, k1, k3])) + - SU3D[I2, k2, k3]*(SU3D[I5, k1, k3]*(-(SU3D[I1, I4, k1]*SU3F[6, I3, k2])/ - 4 - (SU3D[I1, I3, k1]*SU3F[6, I4, k2])/4) + - SU3D[I4, k1, k3]*((SU3D[I1, I5, k1]*SU3F[6, I3, k2])/4 - - (SU3D[I1, I3, k1]*SU3F[6, I5, k2])/6) + SU3D[I3, k1, k3]* - ((I/6)*SU3D[6, I1, k1]*SU3D[I4, I5, k2] + - (SU3D[I1, I5, k1]*SU3F[6, I4, k2])/4 - - (SU3D[I1, I4, k1]*SU3F[6, I5, k2])/6) + - (SU3D[6, I1, k1]*SU3D[I3, k1, k2]*SU3F[I4, I5, k3])/6 + - (SU3D[6, I1, k1]*SU3D[I3, I5, k3]*SU3F[I4, k1, k2])/6 + - SU3D[6, I3, k1]*SU3D[I1, I5, k2]*((-I/4)*SU3D[I4, k1, k3] - - SU3F[I4, k1, k3]/4) + SU3D[I1, I5, k1]* - ((I/4)*SU3F[6, I4, k2]*SU3F[I3, k1, k3] + (I/4)*SU3F[6, I3, k2]* - SU3F[I4, k1, k3]) + SU3D[6, I1, k1]* - ((I/6)*SU3D[I3, I5, k2]*SU3D[I4, k1, k3] + - (SU3D[I4, k1, k2]*SU3F[I3, I5, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I3, k1, k2])/6 - (I/6)*SU3F[I3, k1, k3]* - SU3F[I4, I5, k2] - (I/6)*SU3F[I3, I5, k2]*SU3F[I4, k1, k3]) + - SU3D[6, I1, k1]*SU3D[I3, I4, k3]*((I/6)*SU3D[I5, k1, k2] + - SU3F[I5, k1, k2]/6) + SU3D[I1, I4, k1]* - ((-I/6)*SU3F[6, I5, k2]*SU3F[I3, k1, k3] - (I/4)*SU3F[6, I3, k2]* - SU3F[I5, k1, k3]) + SU3D[I1, I3, k1]* - ((-I/6)*SU3F[6, I5, k2]*SU3F[I4, k1, k3] - (I/4)*SU3F[6, I4, k2]* - SU3F[I5, k1, k3]) + SU3D[6, I4, k1]* - ((-I/4)*SU3D[I1, I5, k2]*SU3D[I3, k1, k3] - - (SU3D[I5, k1, k2]*SU3F[I1, I3, k3])/3 + - (SU3D[I3, k1, k2]*SU3F[I1, I5, k3])/12 - - (SU3D[I3, I5, k3]*SU3F[I1, k1, k2])/3 - - (SU3D[I1, I5, k2]*SU3F[I3, k1, k3])/4 - (I/12)*SU3F[I1, I5, k2]* - SU3F[I3, k1, k3] + (I/3)*SU3F[I1, I3, k2]*SU3F[I5, k1, k3]) + - SU3D[6, I3, k1]*(-(SU3D[I5, k1, k2]*SU3F[I1, I4, k3])/3 + - (SU3D[I4, k1, k2]*SU3F[I1, I5, k3])/12 - - (SU3D[I4, I5, k3]*SU3F[I1, k1, k2])/3 - (I/12)*SU3F[I1, I5, k2]* - SU3F[I4, k1, k3] + (I/3)*SU3F[I1, I4, k2]*SU3F[I5, k1, k3])) + - SU3D[I3, k1, k3]*(SU3D[6, I1, k1]*SU3D[I2, I5, k2]* - ((I/6)*SU3D[I4, k2, k3] - SU3F[I4, k2, k3]/6) + - SU3D[6, I2, k1]*SU3D[I1, I5, k2]*((-I/4)*SU3D[I4, k2, k3] + - SU3F[I4, k2, k3]/4) + SU3D[6, I2, k1]*SU3D[I1, I4, k2]* - ((I/4)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/4)) + - SU3D[I2, k1, k3]*(SU3D[I1, k1, k2]*(-(SU3D[I4, I5, k2]*SU3F[6, I3, k3])/ - 2 - (SU3D[I3, I5, k2]*SU3F[6, I4, k3])/2) + - (SU3D[I1, k1, k2]*SU3D[I3, I4, k2]*SU3F[6, I5, k3])/2 + - SU3D[6, I3, k1]*SU3D[I1, I5, k2]*((-I/4)*SU3D[I4, k2, k3] + - SU3F[I4, k2, k3]/4) + SU3D[6, I4, k1]* - (SU3D[I1, I5, k2]*((-I/4)*SU3D[I3, k2, k3] + SU3F[I3, k2, k3]/4) + - SU3D[I1, I3, k2]*((I/4)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/4)) + - SU3D[6, I3, k1]*SU3D[I1, I4, k2]*((I/4)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/4)) + SU3D[I2, k1, k2]*SU3D[I3, I4, k3]* - ((SU3D[I5, k2, k3]*SU3F[6, I1, k1])/6 - (I/2)*SU3F[6, I5, k1]* - SU3F[I1, k2, k3] + SU3D[6, I1, k1]*((-I/6)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/6) - (I/6)*SU3F[6, I1, k1]*SU3F[I5, k2, k3]) + - SU3D[I1, k1, k2]*(SU3D[I3, k2, k3]*SU3D[I4, I5, k3]* - ((-I/3)*SU3D[6, I2, k1] + SU3F[6, I2, k1]/3) + - SU3D[I4, k1, k3]*(-(SU3D[I3, I5, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I5, k2]*SU3F[6, I3, k3])/2) + SU3D[I3, k1, k3]* - (-(SU3D[I4, I5, k2]*SU3F[6, I2, k3])/2 - - (SU3D[I2, I5, k2]*SU3F[6, I4, k3])/2) + SU3D[I2, k2, k3]* - ((-I/3)*SU3D[6, I4, k1]*SU3D[I3, I5, k3] - (I/3)*SU3D[6, I3, k1]* - SU3D[I4, I5, k3] + (SU3D[I4, I5, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, I5, k3]*SU3F[6, I4, k1])/3 - - (SU3D[I3, I4, k3]*SU3F[6, I5, k1])/3) + SU3D[I2, I4, k2]* - ((SU3D[I5, k1, k3]*SU3F[6, I3, k3])/2 + - (SU3D[I3, k1, k3]*SU3F[6, I5, k3])/2) + SU3D[I2, I3, k2]* - ((SU3D[I5, k1, k3]*SU3F[6, I4, k3])/2 + - (SU3D[I4, k1, k3]*SU3F[6, I5, k3])/2) - - (SU3D[6, I3, k1]*SU3D[I4, I5, k3]*SU3F[I2, k2, k3])/3 + - SU3D[I4, I5, k3]*((-I/3)*SU3F[6, I3, k1]*SU3F[I2, k2, k3] - - (SU3D[6, I2, k1]*SU3F[I3, k2, k3])/3 - (I/3)*SU3F[6, I2, k1]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k1]* - ((-I/2)*SU3F[6, I3, k3]*SU3F[I2, k2, k3] - (I/2)*SU3F[6, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I3, I5, k3]* - ((SU3D[I4, k2, k3]*SU3F[6, I2, k1])/3 - (I/3)*SU3F[6, I4, k1]* - SU3F[I2, k2, k3] + SU3D[6, I2, k1]*((-I/3)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/3) - (I/3)*SU3F[6, I2, k1]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k1]*((-I/2)*SU3F[6, I4, k3]*SU3F[I2, k2, k3] - - (I/2)*SU3F[6, I2, k3]*SU3F[I4, k2, k3]) + SU3D[I2, I5, k3]* - ((SU3D[I4, k2, k3]*SU3F[6, I3, k1])/3 + - (SU3D[I3, k2, k3]*SU3F[6, I4, k1])/3 - (I/3)*SU3F[6, I4, k1]* - SU3F[I3, k2, k3] + SU3D[6, I3, k1]*((-I/3)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/3) - (I/3)*SU3F[6, I3, k1]*SU3F[I4, k2, k3]) + - SU3D[I2, I5, k1]*((-I/2)*SU3F[6, I4, k3]*SU3F[I3, k2, k3] - - (I/2)*SU3F[6, I3, k3]*SU3F[I4, k2, k3]) + SU3D[6, I4, k1]* - (-(SU3D[I3, I5, k3]*SU3F[I2, k2, k3])/3 + SU3D[I2, I5, k3]* - ((-I/3)*SU3D[I3, k2, k3] - SU3F[I3, k2, k3]/3) + - SU3D[I2, I3, k3]*((-I/3)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/3)) + - SU3D[I3, I4, k3]*((SU3D[I5, k2, k3]*SU3F[6, I2, k1])/3 + - (I/3)*SU3F[6, I5, k1]*SU3F[I2, k2, k3] + SU3D[6, I2, k1]* - ((-I/3)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/3) - - (I/3)*SU3F[6, I2, k1]*SU3F[I5, k2, k3]) + SU3D[I3, I4, k1]* - ((I/2)*SU3F[6, I5, k3]*SU3F[I2, k2, k3] + (I/2)*SU3F[6, I2, k3]* - SU3F[I5, k2, k3]) + SU3D[I2, I4, k3]* - ((SU3D[I5, k2, k3]*SU3F[6, I3, k1])/3 - - (SU3D[I3, k2, k3]*SU3F[6, I5, k1])/3 + (I/3)*SU3F[6, I5, k1]* - SU3F[I3, k2, k3] + SU3D[6, I3, k1]*((-I/3)*SU3D[I5, k2, k3] - - SU3F[I5, k2, k3]/3) - (I/3)*SU3F[6, I3, k1]*SU3F[I5, k2, k3]) + - SU3D[I2, I4, k1]*((I/2)*SU3F[6, I5, k3]*SU3F[I3, k2, k3] + - (I/2)*SU3F[6, I3, k3]*SU3F[I5, k2, k3]) + SU3D[I2, I3, k3]* - ((SU3D[I5, k2, k3]*SU3F[6, I4, k1])/3 - - (SU3D[I4, k2, k3]*SU3F[6, I5, k1])/3 + (I/3)*SU3F[6, I5, k1]* - SU3F[I4, k2, k3] - (I/3)*SU3F[6, I4, k1]*SU3F[I5, k2, k3]) + - SU3D[I2, I3, k1]*((I/2)*SU3F[6, I5, k3]*SU3F[I4, k2, k3] + - (I/2)*SU3F[6, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I4, k1, k2]*(SU3D[I5, k2, k3]*(-(SU3D[I2, I3, k1]*SU3F[6, I1, k3])/ - 6 - (I/3)*SU3F[6, I3, k3]*SU3F[I1, I2, k1] - (I/3)*SU3F[6, I2, k3]* - SU3F[I1, I3, k1]) + SU3D[I5, k1, k3]* - ((-I/12)*SU3F[6, I3, k2]*SU3F[I1, I2, k3] - (I/12)*SU3F[6, I2, k2]* - SU3F[I1, I3, k3]) - (I/6)*SU3D[I1, I3, k1]*SU3F[6, I5, k3]* - SU3F[I2, k2, k3] + SU3D[I3, I5, k1]*((I/3)*SU3F[6, I2, k3]* - SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]*SU3F[I2, k2, k3]) + - SU3F[6, I5, k2]*(-(SU3F[I1, I3, k3]*SU3F[I2, k1, k3])/6 - - (SU3F[I1, I2, k3]*SU3F[I3, k1, k3])/6) + SU3F[6, I1, k2]* - ((SU3F[I2, k1, k3]*SU3F[I3, I5, k3])/6 + - (SU3F[I2, I5, k3]*SU3F[I3, k1, k3])/6) - (I/6)*SU3D[I1, I2, k1]* - SU3F[6, I5, k3]*SU3F[I3, k2, k3] + SU3D[I2, I5, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, I5, k1]* - ((I/4)*SU3F[6, I3, k3]*SU3F[I2, k2, k3] + (I/4)*SU3F[6, I2, k3]* - SU3F[I3, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I3, k1]*SU3F[I2, k2, k3])/6 + - (SU3F[I1, I2, k1]*SU3F[I3, k2, k3])/6) + SU3F[6, I1, k3]* - (-(SU3F[I2, k2, k3]*SU3F[I3, I5, k1])/6 - - (SU3F[I2, I5, k1]*SU3F[I3, k2, k3])/6) + SU3F[6, I3, k2]* - ((SU3F[I1, I5, k3]*SU3F[I2, k1, k3])/12 - - (SU3F[I1, I2, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I2, k2]* - ((SU3F[I1, I5, k3]*SU3F[I3, k1, k3])/12 - - (SU3F[I1, I3, k3]*SU3F[I5, k1, k3])/12) + SU3D[I2, I3, k1]* - ((-I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I3, k3]* - (-(SU3F[I1, I5, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I5, k2, k3])/3) + SU3F[6, I2, k3]* - (-(SU3F[I1, I5, k1]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k1]*SU3F[I5, k2, k3])/3)) + - SU3D[I3, k1, k2]*(SU3D[I5, k2, k3]*(-(SU3D[I2, I4, k1]*SU3F[6, I1, k3])/ - 6 - (I/3)*SU3F[6, I4, k3]*SU3F[I1, I2, k1] - (I/3)*SU3F[6, I2, k3]* - SU3F[I1, I4, k1]) + SU3D[I5, k1, k3]* - ((-I/12)*SU3F[6, I4, k2]*SU3F[I1, I2, k3] - (I/12)*SU3F[6, I2, k2]* - SU3F[I1, I4, k3]) + SU3D[I4, k2, k3]* - (-(SU3D[I2, I5, k1]*SU3F[6, I1, k3])/6 + - (SU3D[I1, I5, k1]*SU3F[6, I2, k3])/4 - - (SU3D[I1, I2, k1]*SU3F[6, I5, k3])/6 - (I/6)*SU3F[6, I5, k3]* - SU3F[I1, I2, k1] + (I/12)*SU3F[6, I2, k3]*SU3F[I1, I5, k1] + - (I/6)*SU3F[6, I1, k3]*SU3F[I2, I5, k1]) + SU3D[I4, k1, k3]* - ((-I/6)*SU3F[6, I5, k2]*SU3F[I1, I2, k3] + (I/12)*SU3F[6, I2, k2]* - SU3F[I1, I5, k3] + (I/6)*SU3F[6, I1, k2]*SU3F[I2, I5, k3]) - - (I/6)*SU3D[I1, I4, k1]*SU3F[6, I5, k3]*SU3F[I2, k2, k3] + - SU3D[I4, I5, k3]*((SU3D[6, I2, k1]*SU3F[I1, k2, k3])/2 + - (I/2)*SU3F[6, I2, k1]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k1]* - SU3F[I2, k2, k3]) + SU3D[I4, I5, k1]* - ((I/3)*SU3F[6, I2, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I2, k2, k3]) + SU3F[6, I5, k2]* - (-(SU3F[I1, I4, k3]*SU3F[I2, k1, k3])/6 - - (SU3F[I1, I2, k3]*SU3F[I4, k1, k3])/6) + SU3F[6, I1, k2]* - ((SU3F[I2, k1, k3]*SU3F[I4, I5, k3])/6 + - (SU3F[I2, I5, k3]*SU3F[I4, k1, k3])/6) - (I/6)*SU3D[I1, I2, k1]* - SU3F[6, I5, k3]*SU3F[I4, k2, k3] + SU3D[I2, I5, k1]* - ((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I4, k2, k3]) + SU3D[I1, I5, k1]* - ((I/4)*SU3F[6, I4, k3]*SU3F[I2, k2, k3] + (I/4)*SU3F[6, I2, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I4, k1]*SU3F[I2, k2, k3])/6 + - (SU3F[I1, I2, k1]*SU3F[I4, k2, k3])/6) + SU3F[6, I1, k3]* - (-(SU3F[I2, k2, k3]*SU3F[I4, I5, k1])/6 - - (SU3F[I2, I5, k1]*SU3F[I4, k2, k3])/6) + SU3D[6, I1, k1]* - ((SU3D[I4, k2, k3]*SU3F[I2, I5, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I2, k2, k3])/6 - (I/6)*SU3F[I2, k2, k3]* - SU3F[I4, I5, k3] - (I/6)*SU3F[I2, I5, k3]*SU3F[I4, k2, k3]) + - SU3F[6, I4, k2]*((SU3F[I1, I5, k3]*SU3F[I2, k1, k3])/12 - - (SU3F[I1, I2, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I2, k2]* - ((SU3F[I1, I5, k3]*SU3F[I4, k1, k3])/12 - - (SU3F[I1, I4, k3]*SU3F[I5, k1, k3])/12) + SU3D[I2, I4, k1]* - ((-I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I4, k3]* - (-(SU3F[I1, I5, k1]*SU3F[I2, k2, k3])/12 + - (SU3F[I1, I2, k1]*SU3F[I5, k2, k3])/3) + SU3F[6, I2, k3]* - (-(SU3F[I1, I5, k1]*SU3F[I4, k2, k3])/12 + - (SU3F[I1, I4, k1]*SU3F[I5, k2, k3])/3) + SU3D[6, I2, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I4, k3])/12 + - (SU3D[I4, k2, k3]*SU3F[I1, I5, k3])/12 - (I/12)*SU3F[I1, I5, k3]* - SU3F[I4, k2, k3] + (I/12)*SU3F[I1, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I2, k1, k2]*(SU3D[I5, k2, k3]*((-I/3)*SU3F[6, I4, k3]* - SU3F[I1, I3, k1] - (I/3)*SU3F[6, I3, k3]*SU3F[I1, I4, k1]) + - SU3D[I5, k1, k3]*((-I/12)*SU3F[6, I4, k2]*SU3F[I1, I3, k3] - - (I/12)*SU3F[6, I3, k2]*SU3F[I1, I4, k3]) + SU3D[I4, k2, k3]* - ((SU3D[I1, I5, k1]*SU3F[6, I3, k3])/4 - - (SU3D[I1, I3, k1]*SU3F[6, I5, k3])/6 - (I/6)*SU3F[6, I5, k3]* - SU3F[I1, I3, k1] + (I/12)*SU3F[6, I3, k3]*SU3F[I1, I5, k1] + - (I/6)*SU3F[6, I1, k3]*SU3F[I3, I5, k1]) + SU3D[I4, k1, k3]* - (-(SU3D[I3, I5, k2]*SU3F[6, I1, k3])/6 - (I/6)*SU3F[6, I5, k2]* - SU3F[I1, I3, k3] + (I/12)*SU3F[6, I3, k2]*SU3F[I1, I5, k3] + - (I/6)*SU3F[6, I1, k2]*SU3F[I3, I5, k3]) - (I/6)*SU3D[I1, I4, k1]* - SU3F[6, I5, k3]*SU3F[I3, k2, k3] + SU3D[I4, I5, k3]* - ((I/2)*SU3F[6, I3, k1]*SU3F[I1, k2, k3] + (I/6)*SU3F[6, I1, k1]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k1]* - ((I/3)*SU3F[6, I3, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I3, k2, k3]) + SU3D[I3, k2, k3]* - (-(SU3D[I4, I5, k3]*SU3F[6, I1, k1])/6 + - (SU3D[I1, I5, k1]*SU3F[6, I4, k3])/4 - - (SU3D[I1, I4, k1]*SU3F[6, I5, k3])/6 - (I/6)*SU3F[6, I5, k3]* - SU3F[I1, I4, k1] + (I/12)*SU3F[6, I4, k3]*SU3F[I1, I5, k1] + - (I/6)*SU3F[6, I1, k3]*SU3F[I4, I5, k1] + SU3D[6, I1, k1]* - ((I/6)*SU3D[I4, I5, k3] + SU3F[I4, I5, k3]/6)) + - SU3D[I3, k1, k3]*(-(SU3D[I4, I5, k2]*SU3F[6, I1, k3])/6 - - (I/6)*SU3F[6, I5, k2]*SU3F[I1, I4, k3] + (I/12)*SU3F[6, I4, k2]* - SU3F[I1, I5, k3] + (I/6)*SU3F[6, I1, k2]*SU3F[I4, I5, k3]) + - SU3F[6, I5, k2]*(-(SU3F[I1, I4, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I1, I3, k3]*SU3F[I4, k1, k3])/6) + SU3F[6, I1, k2]* - ((SU3F[I3, k1, k3]*SU3F[I4, I5, k3])/6 + - (SU3F[I3, I5, k3]*SU3F[I4, k1, k3])/6) - (I/6)*SU3D[I1, I3, k1]* - SU3F[6, I5, k3]*SU3F[I4, k2, k3] + SU3D[I3, I5, k3]* - (-(SU3D[I4, k2, k3]*SU3F[6, I1, k1])/6 + (I/2)*SU3F[6, I4, k1]* - SU3F[I1, k2, k3] + SU3D[6, I1, k1]*((I/6)*SU3D[I4, k2, k3] + - SU3F[I4, k2, k3]/6) + (I/6)*SU3F[6, I1, k1]*SU3F[I4, k2, k3]) + - SU3D[I3, I5, k1]*((I/3)*SU3F[6, I4, k3]*SU3F[I1, k2, k3] - - (I/6)*SU3F[6, I1, k3]*SU3F[I4, k2, k3]) + SU3D[I1, I5, k1]* - ((I/4)*SU3F[6, I4, k3]*SU3F[I3, k2, k3] + (I/4)*SU3F[6, I3, k3]* - SU3F[I4, k2, k3]) + SU3F[6, I5, k3]* - ((SU3F[I1, I4, k1]*SU3F[I3, k2, k3])/6 + - (SU3F[I1, I3, k1]*SU3F[I4, k2, k3])/6) + SU3F[6, I1, k3]* - (-(SU3F[I3, k2, k3]*SU3F[I4, I5, k1])/6 - - (SU3F[I3, I5, k1]*SU3F[I4, k2, k3])/6) + SU3D[6, I1, k1]* - ((SU3D[I4, k2, k3]*SU3F[I3, I5, k3])/6 + - (SU3D[I4, I5, k3]*SU3F[I3, k2, k3])/6 - (I/6)*SU3F[I3, k2, k3]* - SU3F[I4, I5, k3] - (I/6)*SU3F[I3, I5, k3]*SU3F[I4, k2, k3]) + - SU3F[6, I4, k2]*((SU3F[I1, I5, k3]*SU3F[I3, k1, k3])/12 - - (SU3F[I1, I3, k3]*SU3F[I5, k1, k3])/12) + SU3F[6, I3, k2]* - ((SU3F[I1, I5, k3]*SU3F[I4, k1, k3])/12 - - (SU3F[I1, I4, k3]*SU3F[I5, k1, k3])/12) + SU3D[I3, I4, k1]* - ((-I/3)*SU3F[6, I5, k3]*SU3F[I1, k2, k3] - (I/6)*SU3F[6, I1, k3]* - SU3F[I5, k2, k3]) + SU3F[6, I4, k3]* - (-(SU3F[I1, I5, k1]*SU3F[I3, k2, k3])/12 + - (SU3F[I1, I3, k1]*SU3F[I5, k2, k3])/3) + SU3F[6, I3, k3]* - (-(SU3F[I1, I5, k1]*SU3F[I4, k2, k3])/12 + - (SU3F[I1, I4, k1]*SU3F[I5, k2, k3])/3) + SU3D[6, I3, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I4, k3])/12 + - (SU3D[I4, k2, k3]*SU3F[I1, I5, k3])/12 + - (SU3D[I4, I5, k3]*SU3F[I1, k2, k3])/2 - (I/12)*SU3F[I1, I5, k3]* - SU3F[I4, k2, k3] + (I/12)*SU3F[I1, I4, k3]*SU3F[I5, k2, k3])) + - SU3D[I3, I4, k2]*(-(SU3D[I2, k1, k2]*SU3D[I5, k1, k3]*SU3F[6, I1, k3])/ - 6 + (SU3D[I1, k1, k2]*SU3D[I5, k1, k3]*SU3F[6, I2, k3])/2 + - SU3D[6, I2, k1]*(-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[6, I1, k1]*(-(SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I2, k2, k3])/6 + (I/6)*SU3F[I2, k2, k3]* - SU3F[I5, k1, k3] - (I/6)*SU3F[I2, k1, k3]*SU3F[I5, k2, k3])) + - SU3D[I2, I4, k2]*(SU3D[6, I1, k1]*SU3D[I3, k2, k3]* - ((I/6)*SU3D[I5, k1, k3] + SU3F[I5, k1, k3]/6) + - SU3D[6, I1, k1]*SU3D[I3, k1, k3]*((-I/6)*SU3D[I5, k2, k3] + - SU3F[I5, k2, k3]/6) + SU3D[6, I3, k1]* - (-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[6, I1, k1]*(-(SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I3, k2, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I5, k1, k3] - (I/6)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])) + - SU3D[I1, I4, k2]*(SU3D[6, I3, k1]*((SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/ - 4 + (I/4)*SU3F[I2, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[6, I2, k1]*((SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/4 + - (I/4)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])) + - SU3F[I1, I4, k1]*((I/6)*SU3F[I3, I5, k1]*SUNDelta[6, I2] + - (I/6)*SU3F[I2, I5, k1]*SUNDelta[6, I3]) + SU3F[I1, I3, k1]* - ((I/6)*SU3F[I4, I5, k1]*SUNDelta[6, I2] + (I/6)*SU3F[I2, I5, k1]* - SUNDelta[6, I4]) + SU3F[I1, I2, k1]* - ((I/6)*SU3F[I4, I5, k1]*SUNDelta[6, I3] + (I/6)*SU3F[I3, I5, k1]* - SUNDelta[6, I4]) + SU3D[I4, I5, k1]* - (SU3F[6, I3, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/6) + - (5*SU3F[I1, I3, k1]*SUNDelta[6, I2])/18 + - (5*SU3F[I1, I2, k1]*SUNDelta[6, I3])/18 - - (SU3F[6, I3, k1]*SUNDelta[I1, I2])/6 - - (SU3F[6, I2, k1]*SUNDelta[I1, I3])/6) + SU3D[I3, I5, k1]* - (SU3F[6, I4, k2]*((SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/6) + - (5*SU3F[I1, I4, k1]*SUNDelta[6, I2])/18 + - (5*SU3F[I1, I2, k1]*SUNDelta[6, I4])/18 - - (SU3F[6, I4, k1]*SUNDelta[I1, I2])/6 - - (SU3F[6, I2, k1]*SUNDelta[I1, I4])/6) + SU3D[I2, I5, k1]* - (SU3F[6, I4, k2]*((SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + SU3F[6, I3, k2]* - ((SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/3 - - (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + SU3F[6, I1, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6) + ((2*I)/9)*SU3D[I3, I4, k1]* - SUNDelta[6, I1] + ((5*I)/18)*SU3D[I1, I4, k1]*SUNDelta[6, I3] + - (5*SU3F[I1, I4, k1]*SUNDelta[6, I3])/18 + ((5*I)/18)*SU3D[I1, I3, k1]* - SUNDelta[6, I4] + (5*SU3F[I1, I3, k1]*SUNDelta[6, I4])/18 - - (SU3F[6, I4, k1]*SUNDelta[I1, I3])/6 - - (SU3F[6, I3, k1]*SUNDelta[I1, I4])/6) + SU3D[I3, I4, k1]* - (SU3F[6, I5, k2]*(-(SU3F[I1, k2, k3]*SU3F[I2, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I2, k2, k3])/2) + SU3F[6, I2, k2]* - ((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - ((SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I5, k2, k3])/6) + - (4*SU3F[I2, I5, k1]*SUNDelta[6, I1])/9 - - (7*SU3F[I1, I2, k1]*SUNDelta[6, I5])/9 - - (2*SU3F[6, I5, k1]*SUNDelta[I1, I2])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I2, I5])/9) + SU3D[I1, I5, k1]* - (SU3F[6, I4, k2]*((SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/4 + - (SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/4) + SU3F[6, I3, k2]* - ((SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/4 + - (SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/4) + SU3F[6, I2, k2]* - ((SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/4 + - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/4) - ((8*I)/9)*SU3D[I3, I4, k1]* - SUNDelta[6, I2] + (5*SU3F[6, I4, k1]*SUNDelta[I2, I3])/9 + - (5*SU3F[6, I3, k1]*SUNDelta[I2, I4])/9 + - (5*SU3F[6, I2, k1]*SUNDelta[I3, I4])/9) + - SU3D[6, I5, k1]*(-(SU3D[I2, k1, k2]*SU3D[I3, I4, k3]*SU3F[I1, k2, k3])/ - 2 + SU3D[I3, I4, k2]*((-I/2)*SU3F[I1, k2, k3]*SU3F[I2, k1, k3] + - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) - - (SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/6 + - SU3D[I4, k2, k3]*((I/6)*SU3F[I1, I3, k2]*SU3F[I2, k1, k3] + - (I/6)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]) + SU3D[I4, k1, k3]* - (-(SU3D[I1, I3, k2]*SU3F[I2, k2, k3])/6 - - (SU3D[I1, I2, k2]*SU3F[I3, k2, k3])/6) + SU3D[I4, k1, k2]* - ((I/6)*SU3F[I1, I3, k3]*SU3F[I2, k2, k3] + (I/6)*SU3F[I1, I2, k3]* - SU3F[I3, k2, k3]) + SU3D[I2, I4, k2]* - ((SU3D[I3, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I3, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I3, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]) + - SU3D[I1, I4, k2]*((SU3D[I3, k2, k3]*SU3F[I2, k1, k3])/6 + - (I/6)*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] + (I/6)*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, k2, k3]* - ((-I/2)*SU3D[I2, k1, k3]*SU3D[I3, I4, k2] - (I/2)*SU3D[I2, I4, k2]* - SU3D[I3, k1, k3] - (I/2)*SU3D[I2, I3, k2]*SU3D[I4, k1, k3] - - (SU3D[I3, I4, k3]*SU3F[I2, k1, k2])/2 - - (SU3D[I2, I4, k3]*SU3F[I3, k1, k2])/2 - - (SU3D[I2, I3, k3]*SU3F[I4, k1, k2])/2) - - (SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/6 + - SU3D[I3, k2, k3]*((I/6)*SU3D[I1, I2, k2]*SU3D[I4, k1, k3] - - (SU3D[I4, k1, k2]*SU3F[I1, I2, k3])/6 + (I/6)*SU3F[I1, I4, k2]* - SU3F[I2, k1, k3] + (SU3D[I1, I2, k2]*SU3F[I4, k1, k3])/6 + - (I/6)*SU3F[I1, I2, k2]*SU3F[I4, k1, k3]) + SU3D[I2, k2, k3]* - ((I/6)*SU3D[I1, I4, k2]*SU3D[I3, k1, k3] + (I/6)*SU3D[I1, I3, k2]* - SU3D[I4, k1, k3] - (SU3D[I4, k1, k2]*SU3F[I1, I3, k3])/6 - - (SU3D[I3, k1, k2]*SU3F[I1, I4, k3])/6 + - (SU3D[I3, I4, k3]*SU3F[I1, k1, k2])/3 + - (SU3D[I1, I4, k2]*SU3F[I3, k1, k3])/6 + (I/6)*SU3F[I1, I4, k2]* - SU3F[I3, k1, k3] + (SU3D[I1, I3, k2]*SU3F[I4, k1, k3])/6 + - (I/6)*SU3F[I1, I3, k2]*SU3F[I4, k1, k3]) + SU3D[I3, k1, k3]* - (-(SU3D[I1, I4, k2]*SU3F[I2, k2, k3])/6 + SU3D[I1, I2, k2]* - ((I/6)*SU3D[I4, k2, k3] - SU3F[I4, k2, k3]/6)) + - SU3D[I2, k1, k3]*(SU3D[I1, I4, k2]*((I/6)*SU3D[I3, k2, k3] - - SU3F[I3, k2, k3]/6) + SU3D[I1, I3, k2]*((I/6)*SU3D[I4, k2, k3] - - SU3F[I4, k2, k3]/6)) + SU3D[I1, k1, k2]* - ((I/3)*SU3D[I2, k2, k3]*SU3D[I3, I4, k3] + - (SU3D[I3, I4, k3]*SU3F[I2, k2, k3])/3 + SU3D[I2, I4, k3]* - ((I/3)*SU3D[I3, k2, k3] + SU3F[I3, k2, k3]/3) + - SU3D[I2, I3, k3]*((I/3)*SU3D[I4, k2, k3] + SU3F[I4, k2, k3]/3)) - - (SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6 + - SU3D[I3, k1, k2]*(-(SU3D[I4, k2, k3]*SU3F[I1, I2, k3])/6 + - (I/6)*SU3F[I1, I4, k3]*SU3F[I2, k2, k3] + (I/6)*SU3F[I1, I2, k3]* - SU3F[I4, k2, k3]) + SU3F[I2, k1, k3]* - (-(SU3F[I1, I4, k2]*SU3F[I3, k2, k3])/6 - - (SU3F[I1, I3, k2]*SU3F[I4, k2, k3])/6) + SU3D[I2, k1, k2]* - (-(SU3D[I4, k2, k3]*SU3F[I1, I3, k3])/6 - - (SU3D[I3, k2, k3]*SU3F[I1, I4, k3])/6 + (I/6)*SU3F[I1, I4, k3]* - SU3F[I3, k2, k3] + (I/6)*SU3F[I1, I3, k3]*SU3F[I4, k2, k3]) + - SU3D[I2, I3, k2]*((SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I4, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I4, k1, k3] + (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) + - SU3D[I1, I3, k2]*((SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/6 + - (I/6)*SU3F[I2, k2, k3]*SU3F[I4, k1, k3] + (I/6)*SU3F[I2, k1, k3]* - SU3F[I4, k2, k3]) + SU3D[I1, I2, k2]* - ((SU3D[I4, k2, k3]*SU3F[I3, k1, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3]) + - ((2*I)/9)*SU3D[I3, I4, k1]*SUNDelta[I1, I2] + - ((2*I)/9)*SU3D[I2, I4, k1]*SUNDelta[I1, I3] + - ((2*I)/9)*SU3D[I2, I3, k1]*SUNDelta[I1, I4] - (I/9)*SU3D[I1, I4, k1]* - SUNDelta[I2, I3] - (5*SU3F[I1, I4, k1]*SUNDelta[I2, I3])/9 - - (I/9)*SU3D[I1, I3, k1]*SUNDelta[I2, I4] - - (5*SU3F[I1, I3, k1]*SUNDelta[I2, I4])/9 - (I/9)*SU3D[I1, I2, k1]* - SUNDelta[I3, I4] - (5*SU3F[I1, I2, k1]*SUNDelta[I3, I4])/9) + - SU3F[6, I5, k1]*((-I/6)*SU3F[I1, I4, k2]*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3] - (I/6)*SU3F[I1, I3, k2]*SU3F[I2, k2, k3]* - SU3F[I4, k1, k3] - (I/6)*SU3F[I1, I2, k2]*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] - (I/6)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]* - SU3F[I4, k2, k3] + SU3F[I2, k1, k3]*((-I/6)*SU3F[I1, I4, k2]* - SU3F[I3, k2, k3] - (I/6)*SU3F[I1, I3, k2]*SU3F[I4, k2, k3]) - - ((5*I)/9)*SU3F[I1, I4, k1]*SUNDelta[I2, I3] - - ((5*I)/9)*SU3F[I1, I3, k1]*SUNDelta[I2, I4] - - ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I3, I4]) + - SU3F[6, I1, k1]*((I/6)*SU3F[I2, I5, k2]*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] + SU3F[I2, k2, k3]*((I/6)*SU3F[I3, k1, k3]* - SU3F[I4, I5, k2] + (I/6)*SU3F[I3, I5, k2]*SU3F[I4, k1, k3]) + - (I/6)*SU3F[I2, I5, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3] + - SU3F[I2, k1, k2]*((-I/6)*SU3F[I3, k2, k3]*SU3F[I4, I5, k3] - - (I/6)*SU3F[I3, I5, k3]*SU3F[I4, k2, k3]) + - ((2*I)/9)*SU3F[I4, I5, k1]*SUNDelta[I2, I3] + - ((2*I)/9)*SU3F[I3, I5, k1]*SUNDelta[I2, I4] + - ((2*I)/9)*SU3F[I2, I5, k1]*SUNDelta[I3, I4]) + - SUNDelta[6, I5]*(((2*I)/27)*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - ((2*I)/27)*SUNDelta[I1, I3]*SUNDelta[I2, I4] + - ((2*I)/27)*SUNDelta[I1, I2]*SUNDelta[I3, I4]) + - SU3D[I2, I4, k1]*(SU3F[6, I5, k2]*(-(SU3F[I1, k2, k3]*SU3F[I3, k1, k3])/ - 3 + (SU3F[I1, k1, k3]*SU3F[I3, k2, k3])/2) + - SU3F[6, I3, k2]*((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - ((SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/6) + ((2*I)/9)*SU3D[I3, I5, k1]* - SUNDelta[6, I1] + (4*SU3F[I3, I5, k1]*SUNDelta[6, I1])/9 - - ((8*I)/9)*SU3D[I1, I5, k1]*SUNDelta[6, I3] + (I/9)*SU3D[I1, I3, k1]* - SUNDelta[6, I5] - (7*SU3F[I1, I3, k1]*SUNDelta[6, I5])/9 - - (2*SU3F[6, I5, k1]*SUNDelta[I1, I3])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I3, I5])/9) + SU3D[I1, I4, k1]* - (SU3F[6, I5, k2]*(-(SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I3, k2, k3])/6) - - (SU3F[6, I3, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/4 - - (SU3F[6, I2, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/4 + - ((5*I)/18)*SU3D[I3, I5, k1]*SUNDelta[6, I2] - - (SU3F[I3, I5, k1]*SUNDelta[6, I2])/6 - - (SU3F[I2, I5, k1]*SUNDelta[6, I3])/6 + - (SU3F[6, I5, k1]*SUNDelta[I2, I3])/9 - - (SU3F[6, I3, k1]*SUNDelta[I2, I5])/9 - - (SU3F[6, I2, k1]*SUNDelta[I3, I5])/9) + SU3F[6, I4, k1]* - ((I/12)*SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] - - (I/3)*SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3] - - (I/3)*SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3] - - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3] + - SU3F[I2, k1, k3]*((I/12)*SU3F[I1, I5, k2]*SU3F[I3, k2, k3] - - (I/12)*SU3F[I1, I3, k2]*SU3F[I5, k2, k3]) - (I/6)*SU3F[I3, I5, k1]* - SUNDelta[I1, I2] - (I/6)*SU3F[I2, I5, k1]*SUNDelta[I1, I3] - - (I/9)*SU3F[I1, I5, k1]*SUNDelta[I2, I3] + ((5*I)/9)*SU3F[I1, I3, k1]* - SUNDelta[I2, I5] + ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I3, I5]) + - SU3D[6, I4, k1]*(SU3D[I3, I5, k2]*((I/2)*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]) + - (SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3])/12 + - SU3D[I5, k2, k3]*((I/12)*SU3F[I1, I3, k2]*SU3F[I2, k1, k3] + - (I/12)*SU3F[I1, I2, k2]*SU3F[I3, k1, k3]) + - SU3D[I5, k1, k2]*((I/3)*SU3F[I1, I3, k3]*SU3F[I2, k2, k3] + - (I/3)*SU3F[I1, I2, k3]*SU3F[I3, k2, k3]) + SU3D[I2, I5, k2]* - ((I/2)*SU3F[I1, k2, k3]*SU3F[I3, k1, k3] - (I/3)*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]) + SU3D[I1, I5, k2]* - (-(SU3D[I3, k2, k3]*SU3F[I2, k1, k3])/4 - (I/4)*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3] - (I/4)*SU3F[I2, k1, k3]*SU3F[I3, k2, k3]) - - (SU3F[I1, I3, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I1, I2, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/3 + - SU3D[I3, k2, k3]*(-(SU3D[I5, k1, k2]*SU3F[I1, I2, k3])/3 - - (SU3D[I2, I5, k2]*SU3F[I1, k1, k3])/3 - (I/12)*SU3F[I1, I5, k2]* - SU3F[I2, k1, k3] + (I/3)*SU3F[I1, I2, k2]*SU3F[I5, k1, k3]) + - SU3D[I3, k1, k3]*(-(SU3D[I2, I5, k2]*SU3F[I1, k2, k3])/2 + - (SU3D[I1, I5, k2]*SU3F[I2, k2, k3])/4 + SU3D[I1, I2, k2]* - ((I/4)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/4)) - - (SU3F[I1, I2, k2]*SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/12 + - SU3D[I3, k1, k2]*(-(SU3D[I5, k2, k3]*SU3F[I1, I2, k3])/12 - - (I/12)*SU3F[I1, I5, k3]*SU3F[I2, k2, k3] + (I/12)*SU3F[I1, I2, k3]* - SU3F[I5, k2, k3]) + SU3F[I2, k1, k3]* - ((SU3F[I1, I5, k2]*SU3F[I3, k2, k3])/12 - - (SU3F[I1, I3, k2]*SU3F[I5, k2, k3])/12) + SU3D[I2, k1, k2]* - (-(SU3D[I5, k2, k3]*SU3F[I1, I3, k3])/12 + - (SU3D[I3, k2, k3]*SU3F[I1, I5, k3])/12 + - (SU3D[I3, I5, k3]*SU3F[I1, k2, k3])/2 - (I/12)*SU3F[I1, I5, k3]* - SU3F[I3, k2, k3] + (I/12)*SU3F[I1, I3, k3]*SU3F[I5, k2, k3]) + - SU3D[I2, I3, k2]*(-(SU3D[I5, k2, k3]*SU3F[I1, k1, k3])/3 + - (SU3D[I5, k1, k3]*SU3F[I1, k2, k3])/2 - (I/2)*SU3F[I1, k2, k3]* - SU3F[I5, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I5, k2, k3]) + - SU3D[I1, I3, k2]*((SU3D[I5, k2, k3]*SU3F[I2, k1, k3])/4 + - (I/4)*SU3F[I2, k1, k3]*SU3F[I5, k2, k3]) + SU3D[I1, I2, k2]* - ((SU3D[I5, k2, k3]*SU3F[I3, k1, k3])/4 + (I/4)*SU3F[I3, k1, k3]* - SU3F[I5, k2, k3]) + (I/6)*SU3D[I3, I5, k1]*SUNDelta[I1, I2] - - (SU3F[I3, I5, k1]*SUNDelta[I1, I2])/6 + (I/6)*SU3D[I2, I5, k1]* - SUNDelta[I1, I3] - (SU3F[I2, I5, k1]*SUNDelta[I1, I3])/6 - - ((5*I)/9)*SU3D[I1, I5, k1]*SUNDelta[I2, I3] - - (SU3F[I1, I5, k1]*SUNDelta[I2, I3])/9 + (I/9)*SU3D[I1, I3, k1]* - SUNDelta[I2, I5] + (5*SU3F[I1, I3, k1]*SUNDelta[I2, I5])/9 + - (I/9)*SU3D[I1, I2, k1]*SUNDelta[I3, I5] + - (5*SU3F[I1, I2, k1]*SUNDelta[I3, I5])/9) + - SUNDelta[6, I4]*(((-16*I)/27)*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - ((5*I)/27)*SUNDelta[I1, I3]*SUNDelta[I2, I5] + - ((5*I)/27)*SUNDelta[I1, I2]*SUNDelta[I3, I5]) + - SU3D[6, I1, k1]*(SU3D[I4, k2, k3]*((-I/6)*SU3F[I2, k1, k3]* - SU3F[I3, I5, k2] - (I/6)*SU3F[I2, I5, k2]*SU3F[I3, k1, k3]) + - SU3D[I4, k1, k3]*(-(SU3D[I3, I5, k2]*SU3F[I2, k2, k3])/6 - - (SU3D[I2, I5, k2]*SU3F[I3, k2, k3])/6) + SU3D[I4, k1, k2]* - ((-I/6)*SU3F[I2, k2, k3]*SU3F[I3, I5, k3] - (I/6)*SU3F[I2, I5, k3]* - SU3F[I3, k2, k3]) + SU3D[I4, I5, k2]* - ((I/6)*SU3F[I2, k2, k3]*SU3F[I3, k1, k3] + (I/6)*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]) + (SU3F[I2, I5, k2]*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3])/6 + SU3F[I2, k2, k3]* - ((SU3F[I3, k1, k3]*SU3F[I4, I5, k2])/6 + - (SU3F[I3, I5, k2]*SU3F[I4, k1, k3])/6) + - (SU3F[I2, I5, k2]*SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6 + - SU3D[I3, I5, k2]*((SU3D[I4, k2, k3]*SU3F[I2, k1, k3])/6 + - (I/6)*SU3F[I2, k2, k3]*SU3F[I4, k1, k3] + (I/6)*SU3F[I2, k1, k3]* - SU3F[I4, k2, k3]) + SU3F[I2, k1, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I4, I5, k3])/6 - - (SU3F[I3, I5, k3]*SU3F[I4, k2, k3])/6) + SU3D[I2, I5, k2]* - ((SU3D[I4, k2, k3]*SU3F[I3, k1, k3])/6 + (I/6)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] + (I/6)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3]) + - SU3D[I2, I3, k2]*(-(SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3D[I5, k1, k3]*SU3F[I4, k2, k3])/6 + SU3D[I4, k2, k3]* - ((I/6)*SU3D[I5, k1, k3] + SU3F[I5, k1, k3]/6) + - (I/6)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] + SU3D[I4, k1, k3]* - ((-I/6)*SU3D[I5, k2, k3] + SU3F[I5, k2, k3]/6) - - (I/6)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) + - (2*SU3F[I4, I5, k1]*SUNDelta[I2, I3])/9 + - (2*SU3F[I3, I5, k1]*SUNDelta[I2, I4])/9 + ((2*I)/9)*SU3D[I3, I4, k1]* - SUNDelta[I2, I5] + (2*SU3F[I2, I5, k1]*SUNDelta[I3, I4])/9 + - ((2*I)/9)*SU3D[I2, I4, k1]*SUNDelta[I3, I5] + - ((2*I)/9)*SU3D[I2, I3, k1]*SUNDelta[I4, I5]) + - SU3D[I2, I3, k1]*(SU3F[6, I5, k2]*(-(SU3F[I1, k2, k3]*SU3F[I4, k1, k3])/ - 3 + (SU3F[I1, k1, k3]*SU3F[I4, k2, k3])/2) + - SU3F[6, I4, k2]*((SU3F[I1, k2, k3]*SU3F[I5, k1, k3])/3 + - (SU3F[I1, k1, k3]*SU3F[I5, k2, k3])/2) + SU3F[6, I1, k2]* - ((SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/6 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/6) + ((2*I)/9)*SU3D[I4, I5, k1]* - SUNDelta[6, I1] + (4*SU3F[I4, I5, k1]*SUNDelta[6, I1])/9 - - ((8*I)/9)*SU3D[I1, I5, k1]*SUNDelta[6, I4] + (I/9)*SU3D[I1, I4, k1]* - SUNDelta[6, I5] - (7*SU3F[I1, I4, k1]*SUNDelta[6, I5])/9 - - (2*SU3F[6, I5, k1]*SUNDelta[I1, I4])/9 - - (2*SU3F[6, I1, k1]*SUNDelta[I4, I5])/9) + SU3D[I1, I3, k1]* - (SU3F[6, I5, k2]*(-(SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I2, k1, k3]*SU3F[I4, k2, k3])/6) - - (SU3F[6, I4, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/4 - - (SU3F[6, I2, k2]*SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/4 + - ((5*I)/18)*SU3D[I4, I5, k1]*SUNDelta[6, I2] - - (SU3F[I4, I5, k1]*SUNDelta[6, I2])/6 - - (SU3F[I2, I5, k1]*SUNDelta[6, I4])/6 + - (SU3F[6, I5, k1]*SUNDelta[I2, I4])/9 - - (SU3F[6, I4, k1]*SUNDelta[I2, I5])/9 - - (SU3F[6, I2, k1]*SUNDelta[I4, I5])/9) + SU3D[I1, I2, k1]* - (SU3F[6, I5, k2]*(-(SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/6 - - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/6) - - (SU3F[6, I4, k2]*SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/4 - - (SU3F[6, I3, k2]*SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/4 + - ((5*I)/18)*SU3D[I4, I5, k1]*SUNDelta[6, I3] - - (SU3F[I4, I5, k1]*SUNDelta[6, I3])/6 + ((5*I)/18)*SU3D[I3, I5, k1]* - SUNDelta[6, I4] - (SU3F[I3, I5, k1]*SUNDelta[6, I4])/6 + - (I/9)*SU3D[I3, I4, k1]*SUNDelta[6, I5] + - (SU3F[6, I5, k1]*SUNDelta[I3, I4])/9 - - (SU3F[6, I4, k1]*SUNDelta[I3, I5])/9 - - (SU3F[6, I3, k1]*SUNDelta[I4, I5])/9) + SU3F[6, I3, k1]* - ((I/12)*SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3] - - (I/3)*SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3] + - SU3F[I2, k1, k3]*((I/12)*SU3F[I1, I5, k2]*SU3F[I4, k2, k3] - - (I/12)*SU3F[I1, I4, k2]*SU3F[I5, k2, k3]) + - SU3F[I1, I2, k2]*((-I/3)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] - - (I/12)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) - (I/6)*SU3F[I4, I5, k1]* - SUNDelta[I1, I2] - (I/6)*SU3F[I2, I5, k1]*SUNDelta[I1, I4] - - (I/9)*SU3F[I1, I5, k1]*SUNDelta[I2, I4] + ((5*I)/9)*SU3F[I1, I4, k1]* - SUNDelta[I2, I5] + ((5*I)/9)*SU3F[I1, I2, k1]*SUNDelta[I4, I5]) + - SU3D[6, I3, k1]*((SU3F[I1, I5, k2]*SU3F[I2, k2, k3]*SU3F[I4, k1, k3])/ - 12 + SU3D[I5, k2, k3]*((I/12)*SU3F[I1, I4, k2]*SU3F[I2, k1, k3] + - (I/12)*SU3F[I1, I2, k2]*SU3F[I4, k1, k3]) + - SU3D[I5, k1, k2]*((I/3)*SU3F[I1, I4, k3]*SU3F[I2, k2, k3] + - (I/3)*SU3F[I1, I2, k3]*SU3F[I4, k2, k3]) + SU3D[I2, I5, k2]* - (-(SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/3 + (I/2)*SU3F[I1, k2, k3]* - SU3F[I4, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) - - (SU3F[I1, I4, k2]*SU3F[I2, k2, k3]*SU3F[I5, k1, k3])/3 + - SU3D[I4, k2, k3]*(-(SU3D[I5, k1, k2]*SU3F[I1, I2, k3])/3 - - (I/12)*SU3F[I1, I5, k2]*SU3F[I2, k1, k3] + (I/3)*SU3F[I1, I2, k2]* - SU3F[I5, k1, k3]) + SU3D[I4, k1, k3]* - (-(SU3D[I2, I5, k2]*SU3F[I1, k2, k3])/2 + SU3D[I1, I2, k2]* - ((I/4)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/4)) + - SU3D[I4, k1, k2]*(-(SU3D[I5, k2, k3]*SU3F[I1, I2, k3])/12 - - (I/12)*SU3F[I1, I5, k3]*SU3F[I2, k2, k3] + (I/12)*SU3F[I1, I2, k3]* - SU3F[I5, k2, k3]) + SU3F[I2, k1, k3]* - ((SU3F[I1, I5, k2]*SU3F[I4, k2, k3])/12 - - (SU3F[I1, I4, k2]*SU3F[I5, k2, k3])/12) + SU3F[I1, I2, k2]* - (-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/12) + SU3D[I1, I2, k2]* - ((SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/4 + (I/4)*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3]) + (I/6)*SU3D[I4, I5, k1]*SUNDelta[I1, I2] - - (SU3F[I4, I5, k1]*SUNDelta[I1, I2])/6 + (I/6)*SU3D[I2, I5, k1]* - SUNDelta[I1, I4] - (SU3F[I2, I5, k1]*SUNDelta[I1, I4])/6 - - ((5*I)/9)*SU3D[I1, I5, k1]*SUNDelta[I2, I4] - - (SU3F[I1, I5, k1]*SUNDelta[I2, I4])/9 + (I/9)*SU3D[I1, I4, k1]* - SUNDelta[I2, I5] + (5*SU3F[I1, I4, k1]*SUNDelta[I2, I5])/9 + - (I/9)*SU3D[I1, I2, k1]*SUNDelta[I4, I5] + - (5*SU3F[I1, I2, k1]*SUNDelta[I4, I5])/9) + - SU3F[6, I2, k1]*(SU3F[I1, I5, k2]*((I/12)*SU3F[I3, k2, k3]* - SU3F[I4, k1, k3] + (I/12)*SU3F[I3, k1, k3]*SU3F[I4, k2, k3]) + - SU3F[I1, I4, k2]*((-I/3)*SU3F[I3, k2, k3]*SU3F[I5, k1, k3] - - (I/12)*SU3F[I3, k1, k3]*SU3F[I5, k2, k3]) + - SU3F[I1, I3, k2]*((-I/3)*SU3F[I4, k2, k3]*SU3F[I5, k1, k3] - - (I/12)*SU3F[I4, k1, k3]*SU3F[I5, k2, k3]) - (I/6)*SU3F[I4, I5, k1]* - SUNDelta[I1, I3] - (I/6)*SU3F[I3, I5, k1]*SUNDelta[I1, I4] - - (I/9)*SU3F[I1, I5, k1]*SUNDelta[I3, I4] + ((5*I)/9)*SU3F[I1, I4, k1]* - SUNDelta[I3, I5] + ((5*I)/9)*SU3F[I1, I3, k1]*SUNDelta[I4, I5]) + - SU3D[6, I2, k1]*(SU3D[I5, k2, k3]*((I/12)*SU3F[I1, I4, k2]* - SU3F[I3, k1, k3] + (I/12)*SU3F[I1, I3, k2]*SU3F[I4, k1, k3]) + - SU3D[I5, k1, k2]*((I/3)*SU3F[I1, I4, k3]*SU3F[I3, k2, k3] + - (I/3)*SU3F[I1, I3, k3]*SU3F[I4, k2, k3]) + SU3D[I3, I5, k2]* - (-(SU3D[I4, k2, k3]*SU3F[I1, k1, k3])/3 + (I/2)*SU3F[I1, k2, k3]* - SU3F[I4, k1, k3] - (I/3)*SU3F[I1, k1, k3]*SU3F[I4, k2, k3]) + - SU3F[I1, I5, k2]*((SU3F[I3, k2, k3]*SU3F[I4, k1, k3])/12 + - (SU3F[I3, k1, k3]*SU3F[I4, k2, k3])/12) + SU3D[I4, k2, k3]* - (-(SU3D[I5, k1, k2]*SU3F[I1, I3, k3])/3 - (I/12)*SU3F[I1, I5, k2]* - SU3F[I3, k1, k3] + (I/3)*SU3F[I1, I3, k2]*SU3F[I5, k1, k3]) + - SU3D[I4, k1, k3]*(-(SU3D[I3, I5, k2]*SU3F[I1, k2, k3])/2 + - SU3D[I1, I3, k2]*((I/4)*SU3D[I5, k2, k3] - SU3F[I5, k2, k3]/4)) + - SU3D[I4, k1, k2]*(-(SU3D[I5, k2, k3]*SU3F[I1, I3, k3])/12 - - (I/12)*SU3F[I1, I5, k3]*SU3F[I3, k2, k3] + (I/12)*SU3F[I1, I3, k3]* - SU3F[I5, k2, k3]) + SU3F[I1, I4, k2]* - (-(SU3F[I3, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I3, k1, k3]*SU3F[I5, k2, k3])/12) + SU3F[I1, I3, k2]* - (-(SU3F[I4, k2, k3]*SU3F[I5, k1, k3])/3 - - (SU3F[I4, k1, k3]*SU3F[I5, k2, k3])/12) + SU3D[I1, I3, k2]* - ((SU3D[I5, k2, k3]*SU3F[I4, k1, k3])/4 + (I/4)*SU3F[I4, k1, k3]* - SU3F[I5, k2, k3]) + (I/6)*SU3D[I4, I5, k1]*SUNDelta[I1, I3] - - (SU3F[I4, I5, k1]*SUNDelta[I1, I3])/6 + (I/6)*SU3D[I3, I5, k1]* - SUNDelta[I1, I4] - (SU3F[I3, I5, k1]*SUNDelta[I1, I4])/6 - - ((5*I)/9)*SU3D[I1, I5, k1]*SUNDelta[I3, I4] - - (SU3F[I1, I5, k1]*SUNDelta[I3, I4])/9 + (I/9)*SU3D[I1, I4, k1]* - SUNDelta[I3, I5] + (5*SU3F[I1, I4, k1]*SUNDelta[I3, I5])/9 + - (I/9)*SU3D[I1, I3, k1]*SUNDelta[I4, I5] + - (5*SU3F[I1, I3, k1]*SUNDelta[I4, I5])/9) + - SUNDelta[6, I3]*(((-16*I)/27)*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - ((5*I)/27)*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - ((5*I)/27)*SUNDelta[I1, I2]*SUNDelta[I4, I5]) + - SUNDelta[6, I2]*(((-16*I)/27)*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - ((5*I)/27)*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - ((5*I)/27)*SUNDelta[I1, I3]*SUNDelta[I4, I5]) + - SUNDelta[6, I1]*(((4*I)/27)*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - ((4*I)/27)*SUNDelta[I2, I4]*SUNDelta[I3, I5] + - ((4*I)/27)*SUNDelta[I2, I3]*SUNDelta[I4, I5])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10S10o2.Gen deleted file mode 100644 index 13bb2f0ef..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10S10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1], FourVector[p3, \[Mu]1], FourVector[p4, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10S10o2.Mod deleted file mode 100644 index 62bf2a5ac..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10S10o2.Mod +++ /dev/null @@ -1,330 +0,0 @@ -{{-(CouplingConstant[ChPTW3[2], 1]*(18*SU3D[6, I4, k6]*SU3D[I1, k6, k7]* - SU3D[I2, I3, k7] + 18*SU3D[6, I3, k6]*SU3D[I1, k6, k7]* - SU3D[I2, I4, k7] + 12*SU3D[6, I4, k7]*SU3D[I1, I3, k5]* - SU3D[I2, k5, k7] + 12*SU3D[6, I3, k7]*SU3D[I1, I4, k5]* - SU3D[I2, k5, k7] - 18*SU3D[6, I2, k7]*SU3D[I1, k5, k7]* - SU3D[I3, I4, k5] - 12*SU3D[6, I1, k7]*SU3D[I2, k5, k7]* - SU3D[I3, I4, k5] - 15*SU3D[6, I4, k7]*SU3D[I1, I2, k5]* - SU3D[I3, k5, k7] + 3*SU3D[6, I2, k7]*SU3D[I1, I4, k5]* - SU3D[I3, k5, k7] - 3*SU3D[6, I1, k7]*SU3D[I2, I4, k5]* - SU3D[I3, k5, k7] - 15*SU3D[6, I3, k7]*SU3D[I1, I2, k5]* - SU3D[I4, k5, k7] + 3*SU3D[6, I2, k7]*SU3D[I1, I3, k5]* - SU3D[I4, k5, k7] - 3*SU3D[6, I1, k7]*SU3D[I2, I3, k5]* - SU3D[I4, k5, k7] - (12*I)*SU3D[I2, k5, k6]*SU3D[I3, I4, k5]* - SU3F[6, I1, k6] - (3*I)*SU3D[I2, I4, k5]*SU3D[I3, k5, k6]* - SU3F[6, I1, k6] - (3*I)*SU3D[I2, I3, k5]*SU3D[I4, k5, k6]* - SU3F[6, I1, k6] - (18*I)*SU3D[I1, k5, k6]*SU3D[I3, I4, k5]* - SU3F[6, I2, k6] + (3*I)*SU3D[I1, I4, k5]*SU3D[I3, k5, k6]* - SU3F[6, I2, k6] + (3*I)*SU3D[I1, I3, k5]*SU3D[I4, k5, k6]* - SU3F[6, I2, k6] + (18*I)*SU3D[I1, k5, k6]*SU3D[I2, I4, k5]* - SU3F[6, I3, k6] + (12*I)*SU3D[I1, I4, k5]*SU3D[I2, k5, k6]* - SU3F[6, I3, k6] - (15*I)*SU3D[I1, I2, k5]*SU3D[I4, k5, k6]* - SU3F[6, I3, k6] + (18*I)*SU3D[I1, k5, k6]*SU3D[I2, I3, k5]* - SU3F[6, I4, k6] + (12*I)*SU3D[I1, I3, k5]*SU3D[I2, k5, k6]* - SU3F[6, I4, k6] - (15*I)*SU3D[I1, I2, k5]*SU3D[I3, k5, k6]* - SU3F[6, I4, k6] - (3*I)*SU3D[6, I4, k6]*SU3D[I3, k5, k6]* - SU3F[I1, I2, k5] - (3*I)*SU3D[6, I3, k6]*SU3D[I4, k5, k6]* - SU3F[I1, I2, k5] + 3*SU3D[I4, k5, k6]*SU3F[6, I3, k6]* - SU3F[I1, I2, k5] + 3*SU3D[I3, k5, k6]*SU3F[6, I4, k6]* - SU3F[I1, I2, k5] + (6*I)*SU3D[6, I4, k6]*SU3D[I2, k5, k6]* - SU3F[I1, I3, k5] + (15*I)*SU3D[6, I2, k6]*SU3D[I4, k5, k6]* - SU3F[I1, I3, k5] - 15*SU3D[I4, k5, k6]*SU3F[6, I2, k6]* - SU3F[I1, I3, k5] - 6*SU3D[I2, k5, k6]*SU3F[6, I4, k6]* - SU3F[I1, I3, k5] + (6*I)*SU3D[6, I3, k6]*SU3D[I2, k5, k6]* - SU3F[I1, I4, k5] + (15*I)*SU3D[6, I2, k6]*SU3D[I3, k5, k6]* - SU3F[I1, I4, k5] - 15*SU3D[I3, k5, k6]*SU3F[6, I2, k6]* - SU3F[I1, I4, k5] - 6*SU3D[I2, k5, k6]*SU3F[6, I3, k6]* - SU3F[I1, I4, k5] + (9*I)*SU3D[6, I4, k7]*SU3D[I2, I3, k5]* - SU3F[I1, k5, k7] - (9*I)*SU3D[6, I4, k5]*SU3D[I2, I3, k7]* - SU3F[I1, k5, k7] + (9*I)*SU3D[6, I3, k7]*SU3D[I2, I4, k5]* - SU3F[I1, k5, k7] - (9*I)*SU3D[6, I3, k5]*SU3D[I2, I4, k7]* - SU3F[I1, k5, k7] + (18*I)*SU3D[6, I2, k5]*SU3D[I3, I4, k7]* - SU3F[I1, k5, k7] + 18*SU3D[I3, I4, k5]*SU3F[6, I2, k7]* - SU3F[I1, k5, k7] - 18*SU3D[I2, I4, k5]*SU3F[6, I3, k7]* - SU3F[I1, k5, k7] - 18*SU3D[I2, I3, k5]*SU3F[6, I4, k7]* - SU3F[I1, k5, k7] + (6*I)*SU3D[6, I1, k6]*SU3D[I4, k5, k6]* - SU3F[I2, I3, k5] - 9*SU3D[I4, k5, k6]*SU3F[6, I1, k6]* - SU3F[I2, I3, k5] - (9*I)*SU3F[6, I4, k7]*SU3F[I1, k6, k7]* - SU3F[I2, I3, k6] + (3*I)*SU3D[6, I1, k6]*SU3D[I4, k6, k7]* - SU3F[I2, I3, k7] - 9*SU3D[6, I4, k5]*SU3F[I1, k5, k7]* - SU3F[I2, I3, k7] + 9*SU3D[6, I4, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I3, k7] - (9*I)*SU3F[6, I4, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I3, k7] + (6*I)*SU3D[6, I1, k6]*SU3D[I3, k5, k6]* - SU3F[I2, I4, k5] - 9*SU3D[I3, k5, k6]*SU3F[6, I1, k6]* - SU3F[I2, I4, k5] - (9*I)*SU3F[6, I3, k7]*SU3F[I1, k6, k7]* - SU3F[I2, I4, k6] + (3*I)*SU3D[6, I1, k6]*SU3D[I3, k6, k7]* - SU3F[I2, I4, k7] - 9*SU3D[6, I3, k5]*SU3F[I1, k5, k7]* - SU3F[I2, I4, k7] + 9*SU3D[6, I3, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I4, k7] - (9*I)*SU3F[6, I3, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I4, k7] + (3*I)*SU3D[6, I4, k7]*SU3D[I1, I3, k5]* - SU3F[I2, k5, k7] - (9*I)*SU3D[6, I4, k5]*SU3D[I1, I3, k7]* - SU3F[I2, k5, k7] + (3*I)*SU3D[6, I3, k7]*SU3D[I1, I4, k5]* - SU3F[I2, k5, k7] - (9*I)*SU3D[6, I3, k5]*SU3D[I1, I4, k7]* - SU3F[I2, k5, k7] + (12*I)*SU3D[6, I1, k5]*SU3D[I3, I4, k7]* - SU3F[I2, k5, k7] + 12*SU3D[I3, I4, k5]*SU3F[6, I1, k7]* - SU3F[I2, k5, k7] - 12*SU3D[I1, I4, k5]*SU3F[6, I3, k7]* - SU3F[I2, k5, k7] - 12*SU3D[I1, I3, k5]*SU3F[6, I4, k7]* - SU3F[I2, k5, k7] + 9*SU3D[6, I4, k5]*SU3F[I1, I3, k7]* - SU3F[I2, k5, k7] + 9*SU3D[6, I3, k5]*SU3F[I1, I4, k7]* - SU3F[I2, k5, k7] - 3*SU3D[6, I4, k6]*SU3F[I1, I3, k7]* - SU3F[I2, k6, k7] + (6*I)*SU3F[6, I4, k6]*SU3F[I1, I3, k7]* - SU3F[I2, k6, k7] - 3*SU3D[6, I3, k6]*SU3F[I1, I4, k7]* - SU3F[I2, k6, k7] + (6*I)*SU3F[6, I3, k6]*SU3F[I1, I4, k7]* - SU3F[I2, k6, k7] + (15*I)*SU3D[6, I4, k5]*SU3D[I1, I2, k7]* - SU3F[I3, k5, k7] - (3*I)*SU3D[6, I2, k5]*SU3D[I1, I4, k7]* - SU3F[I3, k5, k7] + (3*I)*SU3D[6, I1, k5]*SU3D[I2, I4, k7]* - SU3F[I3, k5, k7] + 3*SU3D[I2, I4, k5]*SU3F[6, I1, k7]* - SU3F[I3, k5, k7] - 3*SU3D[I1, I4, k5]*SU3F[6, I2, k7]* - SU3F[I3, k5, k7] + 15*SU3D[I1, I2, k5]*SU3F[6, I4, k7]* - SU3F[I3, k5, k7] - 3*SU3D[6, I4, k5]*SU3F[I1, I2, k7]* - SU3F[I3, k5, k7] + 15*SU3D[6, I2, k5]*SU3F[I1, I4, k7]* - SU3F[I3, k5, k7] + 9*SU3D[6, I1, k5]*SU3F[I2, I4, k7]* - SU3F[I3, k5, k7] - (3*I)*SU3F[6, I4, k6]*SU3F[I1, I2, k7]* - SU3F[I3, k6, k7] + (15*I)*SU3F[6, I2, k6]*SU3F[I1, I4, k7]* - SU3F[I3, k6, k7] - (3*I)*SU3F[6, I1, k7]*SU3F[I2, I4, k6]* - SU3F[I3, k6, k7] + (6*I)*SU3F[6, I1, k6]*SU3F[I2, I4, k7]* - SU3F[I3, k6, k7] + (15*I)*SU3D[6, I3, k5]*SU3D[I1, I2, k7]* - SU3F[I4, k5, k7] - (3*I)*SU3D[6, I2, k5]*SU3D[I1, I3, k7]* - SU3F[I4, k5, k7] + (3*I)*SU3D[6, I1, k5]*SU3D[I2, I3, k7]* - SU3F[I4, k5, k7] + 3*SU3D[I2, I3, k5]*SU3F[6, I1, k7]* - SU3F[I4, k5, k7] - 3*SU3D[I1, I3, k5]*SU3F[6, I2, k7]* - SU3F[I4, k5, k7] + 15*SU3D[I1, I2, k5]*SU3F[6, I3, k7]* - SU3F[I4, k5, k7] - 3*SU3D[6, I3, k5]*SU3F[I1, I2, k7]* - SU3F[I4, k5, k7] + 15*SU3D[6, I2, k5]*SU3F[I1, I3, k7]* - SU3F[I4, k5, k7] + 9*SU3D[6, I1, k5]*SU3F[I2, I3, k7]* - SU3F[I4, k5, k7] - (3*I)*SU3F[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7] + (15*I)*SU3F[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7] - (3*I)*SU3F[6, I1, k7]*SU3F[I2, I3, k6]* - SU3F[I4, k6, k7] + (6*I)*SU3F[6, I1, k6]*SU3F[I2, I3, k7]* - SU3F[I4, k6, k7] - 12*SU3D[I2, I3, I4]*SUNDelta[6, I1] - - 8*SU3D[I1, I3, I4]*SUNDelta[6, I2] + 10*SU3D[I1, I2, I4]* - SUNDelta[6, I3] - (6*I)*SU3F[I1, I2, I4]*SUNDelta[6, I3] + - 10*SU3D[I1, I2, I3]*SUNDelta[6, I4] - (6*I)*SU3F[I1, I2, I3]* - SUNDelta[6, I4] + 10*SU3D[6, I2, I4]*SUNDelta[I1, I3] - - (6*I)*SU3F[6, I2, I4]*SUNDelta[I1, I3] + 10*SU3D[6, I2, I3]* - SUNDelta[I1, I4] - (6*I)*SU3F[6, I2, I3]*SUNDelta[I1, I4] + - 10*SU3D[6, I1, I4]*SUNDelta[I2, I3] - (14*I)*SU3F[6, I1, I4]* - SUNDelta[I2, I3] + 10*SU3D[6, I1, I3]*SUNDelta[I2, I4] - - (14*I)*SU3F[6, I1, I3]*SUNDelta[I2, I4] - 20*SU3D[6, I1, I2]* - SUNDelta[I3, I4] + (4*I)*SU3F[6, I1, I2]*SUNDelta[I3, I4]))/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(CouplingConstant[ChPTW3[2], 1]*(-18*SU3D[6, I4, k6]*SU3D[I1, k6, k7]* - SU3D[I2, I3, k7] + 18*SU3D[6, I3, k7]*SU3D[I1, k5, k7]* - SU3D[I2, I4, k5] + 15*SU3D[6, I4, k7]*SU3D[I1, I3, k5]* - SU3D[I2, k5, k7] - 3*SU3D[6, I3, k7]*SU3D[I1, I4, k5]* - SU3D[I2, k5, k7] + 3*SU3D[6, I1, k7]*SU3D[I2, k5, k7]* - SU3D[I3, I4, k5] - 18*SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3D[I3, I4, k7] - 12*SU3D[6, I4, k7]*SU3D[I1, I2, k5]* - SU3D[I3, k5, k7] - 12*SU3D[6, I2, k7]*SU3D[I1, I4, k5]* - SU3D[I3, k5, k7] + 12*SU3D[6, I1, k7]*SU3D[I2, I4, k5]* - SU3D[I3, k5, k7] - 3*SU3D[6, I3, k7]*SU3D[I1, I2, k5]* - SU3D[I4, k5, k7] + 15*SU3D[6, I2, k7]*SU3D[I1, I3, k5]* - SU3D[I4, k5, k7] + 3*SU3D[6, I1, k7]*SU3D[I2, I3, k5]* - SU3D[I4, k5, k7] + (3*I)*SU3D[I2, k5, k6]*SU3D[I3, I4, k5]* - SU3F[6, I1, k6] + (12*I)*SU3D[I2, I4, k5]*SU3D[I3, k5, k6]* - SU3F[6, I1, k6] + (3*I)*SU3D[I2, I3, k5]*SU3D[I4, k5, k6]* - SU3F[6, I1, k6] - (18*I)*SU3D[I1, k5, k6]*SU3D[I3, I4, k5]* - SU3F[6, I2, k6] - (12*I)*SU3D[I1, I4, k5]*SU3D[I3, k5, k6]* - SU3F[6, I2, k6] + (15*I)*SU3D[I1, I3, k5]*SU3D[I4, k5, k6]* - SU3F[6, I2, k6] + (18*I)*SU3D[I1, k5, k6]*SU3D[I2, I4, k5]* - SU3F[6, I3, k6] - (3*I)*SU3D[I1, I4, k5]*SU3D[I2, k5, k6]* - SU3F[6, I3, k6] - (3*I)*SU3D[I1, I2, k5]*SU3D[I4, k5, k6]* - SU3F[6, I3, k6] - (18*I)*SU3D[I1, k5, k6]*SU3D[I2, I3, k5]* - SU3F[6, I4, k6] + (15*I)*SU3D[I1, I3, k5]*SU3D[I2, k5, k6]* - SU3F[6, I4, k6] - (12*I)*SU3D[I1, I2, k5]*SU3D[I3, k5, k6]* - SU3F[6, I4, k6] - (6*I)*SU3D[6, I4, k6]*SU3D[I3, k5, k6]* - SU3F[I1, I2, k5] - (15*I)*SU3D[6, I3, k6]*SU3D[I4, k5, k6]* - SU3F[I1, I2, k5] + 15*SU3D[I4, k5, k6]*SU3F[6, I3, k6]* - SU3F[I1, I2, k5] + 6*SU3D[I3, k5, k6]*SU3F[6, I4, k6]* - SU3F[I1, I2, k5] + (3*I)*SU3D[6, I4, k6]*SU3D[I2, k5, k6]* - SU3F[I1, I3, k5] + (3*I)*SU3D[6, I2, k6]*SU3D[I4, k5, k6]* - SU3F[I1, I3, k5] - 3*SU3D[I4, k5, k6]*SU3F[6, I2, k6]* - SU3F[I1, I3, k5] - 3*SU3D[I2, k5, k6]*SU3F[6, I4, k6]* - SU3F[I1, I3, k5] - (15*I)*SU3D[6, I3, k6]*SU3D[I2, k5, k6]* - SU3F[I1, I4, k5] - (6*I)*SU3D[6, I2, k6]*SU3D[I3, k5, k6]* - SU3F[I1, I4, k5] + 6*SU3D[I3, k5, k6]*SU3F[6, I2, k6]* - SU3F[I1, I4, k5] + 15*SU3D[I2, k5, k6]*SU3F[6, I3, k6]* - SU3F[I1, I4, k5] - (9*I)*SU3D[6, I4, k7]*SU3D[I2, I3, k5]* - SU3F[I1, k5, k7] + (9*I)*SU3D[6, I4, k5]*SU3D[I2, I3, k7]* - SU3F[I1, k5, k7] - (18*I)*SU3D[6, I3, k5]*SU3D[I2, I4, k7]* - SU3F[I1, k5, k7] - (9*I)*SU3D[6, I2, k7]*SU3D[I3, I4, k5]* - SU3F[I1, k5, k7] + (9*I)*SU3D[6, I2, k5]*SU3D[I3, I4, k7]* - SU3F[I1, k5, k7] + 18*SU3D[I3, I4, k5]*SU3F[6, I2, k7]* - SU3F[I1, k5, k7] - 18*SU3D[I2, I4, k5]*SU3F[6, I3, k7]* - SU3F[I1, k5, k7] + 18*SU3D[I2, I3, k5]*SU3F[6, I4, k7]* - SU3F[I1, k5, k7] + (6*I)*SU3D[6, I1, k6]*SU3D[I4, k5, k6]* - SU3F[I2, I3, k5] - 9*SU3D[I4, k5, k6]*SU3F[6, I1, k6]* - SU3F[I2, I3, k5] - (9*I)*SU3F[6, I4, k7]*SU3F[I1, k6, k7]* - SU3F[I2, I3, k6] + (3*I)*SU3D[6, I1, k6]*SU3D[I4, k6, k7]* - SU3F[I2, I3, k7] - 9*SU3D[6, I4, k5]*SU3F[I1, k5, k7]* - SU3F[I2, I3, k7] + 9*SU3D[6, I4, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I3, k7] - (9*I)*SU3F[6, I4, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I3, k7] - (15*I)*SU3D[6, I4, k5]*SU3D[I1, I3, k7]* - SU3F[I2, k5, k7] + (3*I)*SU3D[6, I3, k5]*SU3D[I1, I4, k7]* - SU3F[I2, k5, k7] - (3*I)*SU3D[6, I1, k5]*SU3D[I3, I4, k7]* - SU3F[I2, k5, k7] - 3*SU3D[I3, I4, k5]*SU3F[6, I1, k7]* - SU3F[I2, k5, k7] + 3*SU3D[I1, I4, k5]*SU3F[6, I3, k7]* - SU3F[I2, k5, k7] - 15*SU3D[I1, I3, k5]*SU3F[6, I4, k7]* - SU3F[I2, k5, k7] + 3*SU3D[6, I4, k5]*SU3F[I1, I3, k7]* - SU3F[I2, k5, k7] - 15*SU3D[6, I3, k5]*SU3F[I1, I4, k7]* - SU3F[I2, k5, k7] + (3*I)*SU3F[6, I4, k6]*SU3F[I1, I3, k7]* - SU3F[I2, k6, k7] - (15*I)*SU3F[6, I3, k6]*SU3F[I1, I4, k7]* - SU3F[I2, k6, k7] - (6*I)*SU3D[6, I1, k6]*SU3D[I2, k5, k6]* - SU3F[I3, I4, k5] + 9*SU3D[I2, k5, k6]*SU3F[6, I1, k6]* - SU3F[I3, I4, k5] + (9*I)*SU3F[6, I2, k7]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k6] + (3*I)*SU3F[6, I1, k7]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k6] - (3*I)*SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3F[I3, I4, k7] + 9*SU3D[6, I2, k5]*SU3F[I1, k5, k7]* - SU3F[I3, I4, k7] - 9*SU3D[6, I2, k6]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k7] + (9*I)*SU3F[6, I2, k6]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k7] - 9*SU3D[6, I1, k5]*SU3F[I2, k5, k7]* - SU3F[I3, I4, k7] - (6*I)*SU3F[6, I1, k6]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k7] - (3*I)*SU3D[6, I4, k7]*SU3D[I1, I2, k5]* - SU3F[I3, k5, k7] + (9*I)*SU3D[6, I4, k5]*SU3D[I1, I2, k7]* - SU3F[I3, k5, k7] - (3*I)*SU3D[6, I2, k7]*SU3D[I1, I4, k5]* - SU3F[I3, k5, k7] + (9*I)*SU3D[6, I2, k5]*SU3D[I1, I4, k7]* - SU3F[I3, k5, k7] - (12*I)*SU3D[6, I1, k5]*SU3D[I2, I4, k7]* - SU3F[I3, k5, k7] - 12*SU3D[I2, I4, k5]*SU3F[6, I1, k7]* - SU3F[I3, k5, k7] + 12*SU3D[I1, I4, k5]*SU3F[6, I2, k7]* - SU3F[I3, k5, k7] + 12*SU3D[I1, I2, k5]*SU3F[6, I4, k7]* - SU3F[I3, k5, k7] - 9*SU3D[6, I4, k5]*SU3F[I1, I2, k7]* - SU3F[I3, k5, k7] - 9*SU3D[6, I2, k5]*SU3F[I1, I4, k7]* - SU3F[I3, k5, k7] + 3*SU3D[6, I4, k6]*SU3F[I1, I2, k7]* - SU3F[I3, k6, k7] - (6*I)*SU3F[6, I4, k6]*SU3F[I1, I2, k7]* - SU3F[I3, k6, k7] + 3*SU3D[6, I2, k6]*SU3F[I1, I4, k7]* - SU3F[I3, k6, k7] - (6*I)*SU3F[6, I2, k6]*SU3F[I1, I4, k7]* - SU3F[I3, k6, k7] + (3*I)*SU3D[6, I3, k5]*SU3D[I1, I2, k7]* - SU3F[I4, k5, k7] - (15*I)*SU3D[6, I2, k5]*SU3D[I1, I3, k7]* - SU3F[I4, k5, k7] - (3*I)*SU3D[6, I1, k5]*SU3D[I2, I3, k7]* - SU3F[I4, k5, k7] - 3*SU3D[I2, I3, k5]*SU3F[6, I1, k7]* - SU3F[I4, k5, k7] - 15*SU3D[I1, I3, k5]*SU3F[6, I2, k7]* - SU3F[I4, k5, k7] + 3*SU3D[I1, I2, k5]*SU3F[6, I3, k7]* - SU3F[I4, k5, k7] - 15*SU3D[6, I3, k5]*SU3F[I1, I2, k7]* - SU3F[I4, k5, k7] + 3*SU3D[6, I2, k5]*SU3F[I1, I3, k7]* - SU3F[I4, k5, k7] + 9*SU3D[6, I1, k5]*SU3F[I2, I3, k7]* - SU3F[I4, k5, k7] - (15*I)*SU3F[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7] + (3*I)*SU3F[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7] - (3*I)*SU3F[6, I1, k7]*SU3F[I2, I3, k6]* - SU3F[I4, k6, k7] + (6*I)*SU3F[6, I1, k6]*SU3F[I2, I3, k7]* - SU3F[I4, k6, k7] + 12*SU3D[I2, I3, I4]*SUNDelta[6, I1] - - 10*SU3D[I1, I3, I4]*SUNDelta[6, I2] + (6*I)*SU3F[I1, I3, I4]* - SUNDelta[6, I2] + 8*SU3D[I1, I2, I4]*SUNDelta[6, I3] - - 10*SU3D[I1, I2, I3]*SUNDelta[6, I4] - (6*I)*SU3F[I1, I2, I3]* - SUNDelta[6, I4] - 10*SU3D[6, I3, I4]*SUNDelta[I1, I2] + - (6*I)*SU3F[6, I3, I4]*SUNDelta[I1, I2] - 10*SU3D[6, I2, I3]* - SUNDelta[I1, I4] - (6*I)*SU3F[6, I2, I3]*SUNDelta[I1, I4] - - 10*SU3D[6, I1, I4]*SUNDelta[I2, I3] + (14*I)*SU3F[6, I1, I4]* - SUNDelta[I2, I3] + 20*SU3D[6, I1, I3]*SUNDelta[I2, I4] - - (4*I)*SU3F[6, I1, I3]*SUNDelta[I2, I4] - 10*SU3D[6, I1, I2]* - SUNDelta[I3, I4] + (14*I)*SU3F[6, I1, I2]*SUNDelta[I3, I4]))/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(CouplingConstant[ChPTW3[2], 1]*(18*SU3D[6, I4, k7]*SU3D[I1, k5, k7]* - SU3D[I2, I3, k5] - 18*SU3D[6, I3, k6]*SU3D[I1, k6, k7]* - SU3D[I2, I4, k7] - 3*SU3D[6, I4, k7]*SU3D[I1, I3, k5]* - SU3D[I2, k5, k7] + 15*SU3D[6, I3, k7]*SU3D[I1, I4, k5]* - SU3D[I2, k5, k7] + 3*SU3D[6, I1, k7]*SU3D[I2, k5, k7]* - SU3D[I3, I4, k5] - 18*SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3D[I3, I4, k7] - 3*SU3D[6, I4, k7]*SU3D[I1, I2, k5]* - SU3D[I3, k5, k7] + 15*SU3D[6, I2, k7]*SU3D[I1, I4, k5]* - SU3D[I3, k5, k7] + 3*SU3D[6, I1, k7]*SU3D[I2, I4, k5]* - SU3D[I3, k5, k7] - 12*SU3D[6, I3, k7]*SU3D[I1, I2, k5]* - SU3D[I4, k5, k7] - 12*SU3D[6, I2, k7]*SU3D[I1, I3, k5]* - SU3D[I4, k5, k7] + 12*SU3D[6, I1, k7]*SU3D[I2, I3, k5]* - SU3D[I4, k5, k7] + (3*I)*SU3D[I2, k5, k6]*SU3D[I3, I4, k5]* - SU3F[6, I1, k6] + (3*I)*SU3D[I2, I4, k5]*SU3D[I3, k5, k6]* - SU3F[6, I1, k6] + (12*I)*SU3D[I2, I3, k5]*SU3D[I4, k5, k6]* - SU3F[6, I1, k6] - (18*I)*SU3D[I1, k5, k6]*SU3D[I3, I4, k5]* - SU3F[6, I2, k6] + (15*I)*SU3D[I1, I4, k5]*SU3D[I3, k5, k6]* - SU3F[6, I2, k6] - (12*I)*SU3D[I1, I3, k5]*SU3D[I4, k5, k6]* - SU3F[6, I2, k6] - (18*I)*SU3D[I1, k5, k6]*SU3D[I2, I4, k5]* - SU3F[6, I3, k6] + (15*I)*SU3D[I1, I4, k5]*SU3D[I2, k5, k6]* - SU3F[6, I3, k6] - (12*I)*SU3D[I1, I2, k5]*SU3D[I4, k5, k6]* - SU3F[6, I3, k6] + (18*I)*SU3D[I1, k5, k6]*SU3D[I2, I3, k5]* - SU3F[6, I4, k6] - (3*I)*SU3D[I1, I3, k5]*SU3D[I2, k5, k6]* - SU3F[6, I4, k6] - (3*I)*SU3D[I1, I2, k5]*SU3D[I3, k5, k6]* - SU3F[6, I4, k6] - (15*I)*SU3D[6, I4, k6]*SU3D[I3, k5, k6]* - SU3F[I1, I2, k5] - (6*I)*SU3D[6, I3, k6]*SU3D[I4, k5, k6]* - SU3F[I1, I2, k5] + 6*SU3D[I4, k5, k6]*SU3F[6, I3, k6]* - SU3F[I1, I2, k5] + 15*SU3D[I3, k5, k6]*SU3F[6, I4, k6]* - SU3F[I1, I2, k5] - (15*I)*SU3D[6, I4, k6]*SU3D[I2, k5, k6]* - SU3F[I1, I3, k5] - (6*I)*SU3D[6, I2, k6]*SU3D[I4, k5, k6]* - SU3F[I1, I3, k5] + 6*SU3D[I4, k5, k6]*SU3F[6, I2, k6]* - SU3F[I1, I3, k5] + 15*SU3D[I2, k5, k6]*SU3F[6, I4, k6]* - SU3F[I1, I3, k5] + (3*I)*SU3D[6, I3, k6]*SU3D[I2, k5, k6]* - SU3F[I1, I4, k5] + (3*I)*SU3D[6, I2, k6]*SU3D[I3, k5, k6]* - SU3F[I1, I4, k5] - 3*SU3D[I3, k5, k6]*SU3F[6, I2, k6]* - SU3F[I1, I4, k5] - 3*SU3D[I2, k5, k6]*SU3F[6, I3, k6]* - SU3F[I1, I4, k5] - (18*I)*SU3D[6, I4, k5]*SU3D[I2, I3, k7]* - SU3F[I1, k5, k7] - (9*I)*SU3D[6, I3, k7]*SU3D[I2, I4, k5]* - SU3F[I1, k5, k7] + (9*I)*SU3D[6, I3, k5]*SU3D[I2, I4, k7]* - SU3F[I1, k5, k7] - (9*I)*SU3D[6, I2, k7]*SU3D[I3, I4, k5]* - SU3F[I1, k5, k7] + (9*I)*SU3D[6, I2, k5]*SU3D[I3, I4, k7]* - SU3F[I1, k5, k7] + 18*SU3D[I3, I4, k5]*SU3F[6, I2, k7]* - SU3F[I1, k5, k7] + 18*SU3D[I2, I4, k5]*SU3F[6, I3, k7]* - SU3F[I1, k5, k7] - 18*SU3D[I2, I3, k5]*SU3F[6, I4, k7]* - SU3F[I1, k5, k7] + (6*I)*SU3D[6, I1, k6]*SU3D[I3, k5, k6]* - SU3F[I2, I4, k5] - 9*SU3D[I3, k5, k6]*SU3F[6, I1, k6]* - SU3F[I2, I4, k5] - (9*I)*SU3F[6, I3, k7]*SU3F[I1, k6, k7]* - SU3F[I2, I4, k6] + (3*I)*SU3D[6, I1, k6]*SU3D[I3, k6, k7]* - SU3F[I2, I4, k7] - 9*SU3D[6, I3, k5]*SU3F[I1, k5, k7]* - SU3F[I2, I4, k7] + 9*SU3D[6, I3, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I4, k7] - (9*I)*SU3F[6, I3, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I4, k7] + (3*I)*SU3D[6, I4, k5]*SU3D[I1, I3, k7]* - SU3F[I2, k5, k7] - (15*I)*SU3D[6, I3, k5]*SU3D[I1, I4, k7]* - SU3F[I2, k5, k7] - (3*I)*SU3D[6, I1, k5]*SU3D[I3, I4, k7]* - SU3F[I2, k5, k7] - 3*SU3D[I3, I4, k5]*SU3F[6, I1, k7]* - SU3F[I2, k5, k7] - 15*SU3D[I1, I4, k5]*SU3F[6, I3, k7]* - SU3F[I2, k5, k7] + 3*SU3D[I1, I3, k5]*SU3F[6, I4, k7]* - SU3F[I2, k5, k7] - 15*SU3D[6, I4, k5]*SU3F[I1, I3, k7]* - SU3F[I2, k5, k7] + 3*SU3D[6, I3, k5]*SU3F[I1, I4, k7]* - SU3F[I2, k5, k7] - (15*I)*SU3F[6, I4, k6]*SU3F[I1, I3, k7]* - SU3F[I2, k6, k7] + (3*I)*SU3F[6, I3, k6]*SU3F[I1, I4, k7]* - SU3F[I2, k6, k7] + (6*I)*SU3D[6, I1, k6]*SU3D[I2, k5, k6]* - SU3F[I3, I4, k5] - 9*SU3D[I2, k5, k6]*SU3F[6, I1, k6]* - SU3F[I3, I4, k5] - (9*I)*SU3F[6, I2, k7]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k6] - (3*I)*SU3F[6, I1, k7]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k6] + (3*I)*SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3F[I3, I4, k7] - 9*SU3D[6, I2, k5]*SU3F[I1, k5, k7]* - SU3F[I3, I4, k7] + 9*SU3D[6, I2, k6]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k7] - (9*I)*SU3F[6, I2, k6]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k7] + 9*SU3D[6, I1, k5]*SU3F[I2, k5, k7]* - SU3F[I3, I4, k7] + (6*I)*SU3F[6, I1, k6]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k7] + (3*I)*SU3D[6, I4, k5]*SU3D[I1, I2, k7]* - SU3F[I3, k5, k7] - (15*I)*SU3D[6, I2, k5]*SU3D[I1, I4, k7]* - SU3F[I3, k5, k7] - (3*I)*SU3D[6, I1, k5]*SU3D[I2, I4, k7]* - SU3F[I3, k5, k7] - 3*SU3D[I2, I4, k5]*SU3F[6, I1, k7]* - SU3F[I3, k5, k7] - 15*SU3D[I1, I4, k5]*SU3F[6, I2, k7]* - SU3F[I3, k5, k7] + 3*SU3D[I1, I2, k5]*SU3F[6, I4, k7]* - SU3F[I3, k5, k7] - 15*SU3D[6, I4, k5]*SU3F[I1, I2, k7]* - SU3F[I3, k5, k7] + 3*SU3D[6, I2, k5]*SU3F[I1, I4, k7]* - SU3F[I3, k5, k7] + 9*SU3D[6, I1, k5]*SU3F[I2, I4, k7]* - SU3F[I3, k5, k7] - (15*I)*SU3F[6, I4, k6]*SU3F[I1, I2, k7]* - SU3F[I3, k6, k7] + (3*I)*SU3F[6, I2, k6]*SU3F[I1, I4, k7]* - SU3F[I3, k6, k7] - (3*I)*SU3F[6, I1, k7]*SU3F[I2, I4, k6]* - SU3F[I3, k6, k7] + (6*I)*SU3F[6, I1, k6]*SU3F[I2, I4, k7]* - SU3F[I3, k6, k7] - (3*I)*SU3D[6, I3, k7]*SU3D[I1, I2, k5]* - SU3F[I4, k5, k7] + (9*I)*SU3D[6, I3, k5]*SU3D[I1, I2, k7]* - SU3F[I4, k5, k7] - (3*I)*SU3D[6, I2, k7]*SU3D[I1, I3, k5]* - SU3F[I4, k5, k7] + (9*I)*SU3D[6, I2, k5]*SU3D[I1, I3, k7]* - SU3F[I4, k5, k7] - (12*I)*SU3D[6, I1, k5]*SU3D[I2, I3, k7]* - SU3F[I4, k5, k7] - 12*SU3D[I2, I3, k5]*SU3F[6, I1, k7]* - SU3F[I4, k5, k7] + 12*SU3D[I1, I3, k5]*SU3F[6, I2, k7]* - SU3F[I4, k5, k7] + 12*SU3D[I1, I2, k5]*SU3F[6, I3, k7]* - SU3F[I4, k5, k7] - 9*SU3D[6, I3, k5]*SU3F[I1, I2, k7]* - SU3F[I4, k5, k7] - 9*SU3D[6, I2, k5]*SU3F[I1, I3, k7]* - SU3F[I4, k5, k7] + 3*SU3D[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7] - (6*I)*SU3F[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7] + 3*SU3D[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7] - (6*I)*SU3F[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7] + 12*SU3D[I2, I3, I4]*SUNDelta[6, I1] - - 10*SU3D[I1, I3, I4]*SUNDelta[6, I2] - (6*I)*SU3F[I1, I3, I4]* - SUNDelta[6, I2] - 10*SU3D[I1, I2, I4]*SUNDelta[6, I3] - - (6*I)*SU3F[I1, I2, I4]*SUNDelta[6, I3] + 8*SU3D[I1, I2, I3]* - SUNDelta[6, I4] - 10*SU3D[6, I3, I4]*SUNDelta[I1, I2] - - (6*I)*SU3F[6, I3, I4]*SUNDelta[I1, I2] - 10*SU3D[6, I2, I4]* - SUNDelta[I1, I3] - (6*I)*SU3F[6, I2, I4]*SUNDelta[I1, I3] + - 20*SU3D[6, I1, I4]*SUNDelta[I2, I3] - (4*I)*SU3F[6, I1, I4]* - SUNDelta[I2, I3] - 10*SU3D[6, I1, I3]*SUNDelta[I2, I4] + - (14*I)*SU3F[6, I1, I3]*SUNDelta[I2, I4] - 10*SU3D[6, I1, I2]* - SUNDelta[I3, I4] + (14*I)*SU3F[6, I1, I2]*SUNDelta[I3, I4]))/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10o2.Gen deleted file mode 100644 index 13bb2f0ef..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1], FourVector[p3, \[Mu]1], FourVector[p4, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10o2.Mod deleted file mode 100644 index 5f80523d9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10P10o2.Mod +++ /dev/null @@ -1,375 +0,0 @@ -{{(-18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, k1, k2]* - SU3D[I2, I3, k2] - 18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3D[I2, I4, k2] - 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I4, k1]*SU3D[I1, I3, k2]*SU3D[I2, k1, k2] - - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I4, k2]* - SU3D[I2, k1, k2] + 18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3D[I3, I4, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] + - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, I2, k2]* - SU3D[I3, k1, k2] - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I4, k2]*SU3D[I3, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] + - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k2]* - SU3D[I4, k1, k2] - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I3, k2]*SU3D[I4, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] + - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k1]* - SU3F[6, I1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I4, k1]* - SU3D[I3, k1, k2]*SU3F[6, I1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I3, k1]*SU3D[I4, k1, k2]*SU3F[6, I1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I3, I4, k1]* - SU3F[6, I2, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I3, k1]*SU3D[I4, k1, k2]*SU3F[6, I2, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I2, I4, k1]* - SU3F[6, I3, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3D[I2, k1, k2]*SU3F[6, I3, k2] + (15*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, k1]*SU3D[I4, k1, k2]*SU3F[6, I3, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I4, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]* - SU3D[I2, k1, k2]*SU3F[6, I4, k2] + (15*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I4, k2] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I4, k1, k2]*SU3F[6, I3, k2]* - SU3F[I1, I2, k1] - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, k1, k2]* - SU3F[6, I4, k2]*SU3F[I1, I2, k1] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I4, k1]*SU3D[I3, k1, k2]*SU3F[I1, I2, k2] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I4, k1, k2]* - SU3F[I1, I2, k2] + 15*CouplingConstant[ChPTW3[2], 1]*SU3D[I4, k1, k2]* - SU3F[6, I2, k2]*SU3F[I1, I3, k1] + 6*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, k1, k2]*SU3F[6, I4, k2]*SU3F[I1, I3, k1] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I2, k1, k2]* - SU3F[I1, I3, k2] - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I4, k1, k2]*SU3F[I1, I3, k2] + 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2]*SU3F[I1, I4, k1] + - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2]* - SU3F[I1, I4, k1] - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I2, k1, k2]*SU3F[I1, I4, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3F[I1, I4, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]* - SU3D[I2, I3, k2]*SU3F[I1, k1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I2, I4, k2]* - SU3F[I1, k1, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I3, I4, k2]*SU3F[I1, k1, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - SU3D[I3, I4, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I4, k1]*SU3F[6, I3, k2]* - SU3F[I1, k1, k2] + 18*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]* - SU3F[6, I4, k2]*SU3F[I1, k1, k2] + 9*CouplingConstant[ChPTW3[2], 1]* - SU3D[I4, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I4, k1, k2]* - SU3F[I2, I3, k2] + 9*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2]*SU3F[I2, I4, k1] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I3, k1, k2]*SU3F[I2, I4, k2] + - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, I3, k2]* - SU3F[I2, k1, k2] + (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I1, I4, k2]*SU3F[I2, k1, k2] - - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I3, I4, k2]* - SU3F[I2, k1, k2] - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, I4, k1]* - SU3F[6, I1, k2]*SU3F[I2, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I4, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I4, k2]* - SU3F[I2, k1, k2] - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]* - SU3F[I1, I3, k2]*SU3F[I2, k1, k2] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I4, k1]*SU3F[I1, I3, k2]*SU3F[I2, k1, k2] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3F[I1, I4, k2]* - SU3F[I2, k1, k2] - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]* - SU3F[I1, I4, k2]*SU3F[I2, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, I2, k2]* - SU3F[I3, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I4, k2]*SU3F[I3, k1, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, I4, k2]*SU3F[I3, k1, k2] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I4, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3F[6, I2, k2]*SU3F[I3, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, k1]*SU3F[6, I4, k2]*SU3F[I3, k1, k2] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3F[I1, I2, k2]* - SU3F[I3, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I4, k1]* - SU3F[I1, I2, k2]*SU3F[I3, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I2, k1]*SU3F[I1, I4, k2]*SU3F[I3, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]*SU3F[I1, I4, k2]* - SU3F[I3, k1, k2] - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]* - SU3F[I2, I4, k2]*SU3F[I3, k1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I1, k1]*SU3F[I2, I4, k2]*SU3F[I3, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k2]* - SU3F[I4, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I3, k2]*SU3F[I4, k1, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, I3, k2]*SU3F[I4, k1, k2] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]* - SU3F[I4, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]* - SU3F[6, I2, k2]*SU3F[I4, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, k1]*SU3F[6, I3, k2]*SU3F[I4, k1, k2] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3F[I1, I2, k2]* - SU3F[I4, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]* - SU3F[I1, I2, k2]*SU3F[I4, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I2, k1]*SU3F[I1, I3, k2]*SU3F[I4, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]*SU3F[I1, I3, k2]* - SU3F[I4, k1, k2] - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]* - SU3F[I2, I3, k2]*SU3F[I4, k1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I1, k1]*SU3F[I2, I3, k2]*SU3F[I4, k1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, I4]*SUNDelta[6, I1] + - 8*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, I4]*SUNDelta[6, I2] - - 10*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, I4]*SUNDelta[6, I3] + - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[I1, I2, I4]*SUNDelta[6, I3] - - 10*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, I3]*SUNDelta[6, I4] + - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[I1, I2, I3]*SUNDelta[6, I4] - - 10*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, I4]*SUNDelta[I1, I3] + - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, I4]*SUNDelta[I1, I3] - - 10*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, I3]*SUNDelta[I1, I4] + - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, I3]*SUNDelta[I1, I4] - - 10*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, I4]*SUNDelta[I2, I3] + - (14*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, I4]*SUNDelta[I2, I3] - - 10*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, I3]*SUNDelta[I2, I4] + - (14*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, I3]*SUNDelta[I2, I4] + - 20*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, I2]*SUNDelta[I3, I4] - - (4*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, I2]*SUNDelta[I3, I4])/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, k1, k2]* - SU3D[I2, I3, k2] + 18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3D[I2, I4, k2] + 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I4, k1]*SU3D[I1, I3, k2]*SU3D[I2, k1, k2] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I4, k2]* - SU3D[I2, k1, k2] - 18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3D[I3, I4, k2] + 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] - - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, I2, k2]* - SU3D[I3, k1, k2] - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I4, k2]*SU3D[I3, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k2]* - SU3D[I4, k1, k2] + 15*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I3, k2]*SU3D[I4, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k1]* - SU3F[6, I1, k2] + (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I4, k1]* - SU3D[I3, k1, k2]*SU3F[6, I1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I3, k1]*SU3D[I4, k1, k2]*SU3F[6, I1, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I3, I4, k1]* - SU3F[6, I2, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2] + (15*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I3, k1]*SU3D[I4, k1, k2]*SU3F[6, I2, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I2, I4, k1]* - SU3F[6, I3, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3D[I2, k1, k2]*SU3F[6, I3, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, k1]*SU3D[I4, k1, k2]*SU3F[6, I3, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I4, k2] + (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]* - SU3D[I2, k1, k2]*SU3F[6, I4, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I4, k2] + - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[I4, k1, k2]*SU3F[6, I3, k2]* - SU3F[I1, I2, k1] + 6*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, k1, k2]* - SU3F[6, I4, k2]*SU3F[I1, I2, k1] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I4, k1]*SU3D[I3, k1, k2]*SU3F[I1, I2, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I4, k1, k2]* - SU3F[I1, I2, k2] - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I4, k1, k2]* - SU3F[6, I2, k2]*SU3F[I1, I3, k1] - 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, k1, k2]*SU3F[6, I4, k2]*SU3F[I1, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I2, k1, k2]* - SU3F[I1, I3, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I4, k1, k2]*SU3F[I1, I3, k2] + 6*CouplingConstant[ChPTW3[2], 1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2]*SU3F[I1, I4, k1] + - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2]* - SU3F[I1, I4, k1] - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I2, k1, k2]*SU3F[I1, I4, k2] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I2, k1]*SU3D[I3, k1, k2]*SU3F[I1, I4, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I2, I3, k2]* - SU3F[I1, k1, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I2, I4, k2]*SU3F[I1, k1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I3, I4, k2]* - SU3F[I1, k1, k2] + 18*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, I4, k1]* - SU3F[6, I2, k2]*SU3F[I1, k1, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I4, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I4, k2]* - SU3F[I1, k1, k2] - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[I4, k1, k2]* - SU3F[6, I1, k2]*SU3F[I2, I3, k1] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I4, k1, k2]*SU3F[I2, I3, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, I3, k2]* - SU3F[I2, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I1, I4, k2]*SU3F[I2, k1, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I3, I4, k2]*SU3F[I2, k1, k2] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, I4, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3F[6, I3, k2]*SU3F[I2, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I3, k1]*SU3F[6, I4, k2]*SU3F[I2, k1, k2] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3F[I1, I3, k2]* - SU3F[I2, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I4, k1]* - SU3F[I1, I3, k2]*SU3F[I2, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I3, k1]*SU3F[I1, I4, k2]*SU3F[I2, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]*SU3F[I1, I4, k2]* - SU3F[I2, k1, k2] + 9*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2]*SU3F[I3, I4, k1] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, k1, k2]*SU3F[I3, I4, k2] - - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, k1, k2]* - SU3F[I3, I4, k2] - (9*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]* - SU3F[I2, k1, k2]*SU3F[I3, I4, k2] + - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, I2, k2]* - SU3F[I3, k1, k2] + (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I4, k2]*SU3F[I3, k1, k2] - - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I4, k2]* - SU3F[I3, k1, k2] - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I4, k1]* - SU3F[6, I1, k2]*SU3F[I3, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I4, k1]*SU3F[6, I2, k2]*SU3F[I3, k1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I4, k2]* - SU3F[I3, k1, k2] - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]* - SU3F[I1, I2, k2]*SU3F[I3, k1, k2] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I4, k1]*SU3F[I1, I2, k2]*SU3F[I3, k1, k2] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3F[I1, I4, k2]* - SU3F[I3, k1, k2] - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]* - SU3F[I1, I4, k2]*SU3F[I3, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I3, k1]*SU3D[I1, I2, k2]*SU3F[I4, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k2]* - SU3F[I4, k1, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]* - SU3D[I2, I3, k2]*SU3F[I4, k1, k2] - 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[I4, k1, k2] - - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k2]* - SU3F[I4, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]* - SU3F[6, I3, k2]*SU3F[I4, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I3, k1]*SU3F[I1, I2, k2]*SU3F[I4, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]*SU3F[I1, I2, k2]* - SU3F[I4, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3F[I1, I3, k2]*SU3F[I4, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I2, k1]*SU3F[I1, I3, k2]*SU3F[I4, k1, k2] + - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, I3, k2]* - SU3F[I4, k1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]* - SU3F[I2, I3, k2]*SU3F[I4, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I3, I4]*SUNDelta[6, I1] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I3, I4]*SUNDelta[6, I2] + (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[I1, I3, I4]*SUNDelta[6, I2] + 8*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, I4]*SUNDelta[6, I3] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, I3]*SUNDelta[6, I4] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[I1, I2, I3]*SUNDelta[6, I4] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I3, I4]*SUNDelta[I1, I2] + (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I3, I4]*SUNDelta[I1, I2] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I2, I3]*SUNDelta[I1, I4] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I2, I3]*SUNDelta[I1, I4] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, I4]*SUNDelta[I2, I3] + (14*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I1, I4]*SUNDelta[I2, I3] + 20*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, I3]*SUNDelta[I2, I4] - (4*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I1, I3]*SUNDelta[I2, I4] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, I2]*SUNDelta[I3, I4] + (14*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I1, I2]*SUNDelta[I3, I4])/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, k1, k2]* - SU3D[I2, I3, k2] - 18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3D[I2, I4, k2] - 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I4, k1]*SU3D[I1, I3, k2]*SU3D[I2, k1, k2] + - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I4, k2]* - SU3D[I2, k1, k2] - 18*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3D[I3, I4, k2] + 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, I2, k2]* - SU3D[I3, k1, k2] + 15*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I4, k2]*SU3D[I3, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] - - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k2]* - SU3D[I4, k1, k2] - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I3, k2]*SU3D[I4, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k1]* - SU3F[6, I1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I4, k1]* - SU3D[I3, k1, k2]*SU3F[6, I1, k2] + (12*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I3, k1]*SU3D[I4, k1, k2]*SU3F[6, I1, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I3, I4, k1]* - SU3F[6, I2, k2] + (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I3, k1]*SU3D[I4, k1, k2]*SU3F[6, I2, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I2, I4, k1]* - SU3F[6, I3, k2] + (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3D[I2, k1, k2]*SU3F[6, I3, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, k1]*SU3D[I4, k1, k2]*SU3F[6, I3, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I4, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]* - SU3D[I2, k1, k2]*SU3F[6, I4, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I4, k2] + - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[I4, k1, k2]*SU3F[6, I3, k2]* - SU3F[I1, I2, k1] + 15*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, k1, k2]* - SU3F[6, I4, k2]*SU3F[I1, I2, k1] - (15*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I4, k1]*SU3D[I3, k1, k2]*SU3F[I1, I2, k2] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I4, k1, k2]* - SU3F[I1, I2, k2] + 6*CouplingConstant[ChPTW3[2], 1]*SU3D[I4, k1, k2]* - SU3F[6, I2, k2]*SU3F[I1, I3, k1] + 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, k1, k2]*SU3F[6, I4, k2]*SU3F[I1, I3, k1] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I2, k1, k2]* - SU3F[I1, I3, k2] - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I4, k1, k2]*SU3F[I1, I3, k2] - 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2]*SU3F[I1, I4, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2]* - SU3F[I1, I4, k1] + (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I2, k1, k2]*SU3F[I1, I4, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I2, k1]*SU3D[I3, k1, k2]*SU3F[I1, I4, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I2, I3, k2]* - SU3F[I1, k1, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I2, I4, k2]*SU3F[I1, k1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I3, I4, k2]* - SU3F[I1, k1, k2] + 18*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, I4, k1]* - SU3F[6, I2, k2]*SU3F[I1, k1, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I4, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I4, k2]* - SU3F[I1, k1, k2] - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2]*SU3F[I2, I4, k1] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I3, k1, k2]*SU3F[I2, I4, k2] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3D[I1, I3, k2]* - SU3F[I2, k1, k2] - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3D[I1, I4, k2]*SU3F[I2, k1, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I3, I4, k2]*SU3F[I2, k1, k2] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I3, I4, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]* - SU3F[6, I3, k2]*SU3F[I2, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I3, k1]*SU3F[6, I4, k2]*SU3F[I2, k1, k2] - - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I4, k1]*SU3F[I1, I3, k2]* - SU3F[I2, k1, k2] - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I4, k1]* - SU3F[I1, I3, k2]*SU3F[I2, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I3, k1]*SU3F[I1, I4, k2]*SU3F[I2, k1, k2] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]*SU3F[I1, I4, k2]* - SU3F[I2, k1, k2] - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2]*SU3F[I3, I4, k1] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, k1]*SU3D[I2, k1, k2]*SU3F[I3, I4, k2] + - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, k1, k2]* - SU3F[I3, I4, k2] + (9*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]* - SU3F[I2, k1, k2]*SU3F[I3, I4, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I4, k1]*SU3D[I1, I2, k2]*SU3F[I3, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I4, k2]* - SU3F[I3, k1, k2] - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]* - SU3D[I2, I4, k2]*SU3F[I3, k1, k2] - 3*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I4, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - 15*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I4, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]* - SU3F[6, I4, k2]*SU3F[I3, k1, k2] - 15*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I4, k1]*SU3F[I1, I2, k2]*SU3F[I3, k1, k2] - - (15*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I4, k1]*SU3F[I1, I2, k2]* - SU3F[I3, k1, k2] + 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3F[I1, I4, k2]*SU3F[I3, k1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I2, k1]*SU3F[I1, I4, k2]*SU3F[I3, k1, k2] + - 9*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, I4, k2]* - SU3F[I3, k1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]* - SU3F[I2, I4, k2]*SU3F[I3, k1, k2] + - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k2]* - SU3F[I4, k1, k2] + (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]* - SU3D[I1, I3, k2]*SU3F[I4, k1, k2] - - (12*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k2]* - SU3F[I4, k1, k2] - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2]*SU3F[I4, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I3, k1]*SU3F[6, I2, k2]*SU3F[I4, k1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k2]* - SU3F[I4, k1, k2] - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]* - SU3F[I1, I2, k2]*SU3F[I4, k1, k2] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I3, k1]*SU3F[I1, I2, k2]*SU3F[I4, k1, k2] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3F[I1, I3, k2]* - SU3F[I4, k1, k2] - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]* - SU3F[I1, I3, k2]*SU3F[I4, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - SU3D[I2, I3, I4]*SUNDelta[6, I1] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I3, I4]*SUNDelta[6, I2] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[I1, I3, I4]*SUNDelta[6, I2] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, I4]*SUNDelta[6, I3] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[I1, I2, I4]*SUNDelta[6, I3] + 8*CouplingConstant[ChPTW3[2], 1]* - SU3D[I1, I2, I3]*SUNDelta[6, I4] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I3, I4]*SUNDelta[I1, I2] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I3, I4]*SUNDelta[I1, I2] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I2, I4]*SUNDelta[I1, I3] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I2, I4]*SUNDelta[I1, I3] + 20*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, I4]*SUNDelta[I2, I3] - (4*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I1, I4]*SUNDelta[I2, I3] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, I3]*SUNDelta[I2, I4] + (14*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I1, I3]*SUNDelta[I2, I4] - 10*CouplingConstant[ChPTW3[2], 1]* - SU3D[6, I1, I2]*SUNDelta[I3, I4] + (14*I)*CouplingConstant[ChPTW3[2], 1]* - SU3F[6, I1, I2]*SUNDelta[I3, I4])/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o2.Gen deleted file mode 100644 index 774901bc9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1], FourVector[p3, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o2.Mod deleted file mode 100644 index 08ca4de9d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o2.Mod +++ /dev/null @@ -1,28 +0,0 @@ -{{((6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3F[I1, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] + - (4*I)*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I3]*SUNDelta[I1, I2] - - (2*I)*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I2]*SUNDelta[I1, I3] - - (2*I)*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{((-3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]*SU3F[I1, I2, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, I3, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] - - (2*I)*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I3]*SUNDelta[I1, I2] + - (4*I)*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I2]*SUNDelta[I1, I3] - - (2*I)*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o4.Gen deleted file mode 100644 index c7294dcf4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o4.Gen +++ /dev/null @@ -1,50 +0,0 @@ -{FourVector[p3, \[Mu]1]*MomentaScalarProduct[p2, p4], -FourVector[p2, \[Mu]1]*MomentaScalarProduct[p3, p4], -FourVector[p4, \[Mu]1]*MomentaScalarProduct[p2, p3], -FourVector[p3, \[Mu]1]*MomentaScalarProduct[p3, p4], -FourVector[p3, \[Mu]1]*MomentaScalarProduct[p1, p4], -FourVector[p4, \[Mu]1]*MomentaScalarProduct[p1, p3], -FourVector[p2, \[Mu]1]*MomentaScalarProduct[p2, p4], -FourVector[p2, \[Mu]1]*MomentaScalarProduct[p1, p4], -FourVector[p4, \[Mu]1]*MomentaScalarProduct[p1, p2], -FourVector[p1, \[Sigma]]*FourVector[p3, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Rho]]*FourVector[p3, \[Nu]]* -FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p2, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Rho]]*FourVector[p2, \[Nu]]* -FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p2, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Rho]]*FourVector[p2, \[Nu]]* -FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p2, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Sigma]]* -FourVector[p3, \[Nu]]*FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Rho]], -FourVector[p1, \[Rho]]*FourVector[p2, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Sigma]], FourVector[p1, \[Rho]]* -FourVector[p3, \[Nu]]*FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p3, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Rho]]*FourVector[p3, \[Nu]]* -FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p2, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Sigma]]* -FourVector[p3, \[Nu]]*FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Rho]], -FourVector[p1, \[Rho]]*FourVector[p2, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Sigma]], FourVector[p1, \[Rho]]* -FourVector[p3, \[Nu]]*FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p3, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Rho]]*FourVector[p3, \[Nu]]* -FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p3, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Rho]]*FourVector[p3, \[Nu]]* -FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p2, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Rho]]*FourVector[p2, \[Nu]]* -FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p1, \[Sigma]]*FourVector[p2, \[Nu]]*FourVector[p4, \[Mu]]* -MetricTensor[\[Mu]1, \[Rho]], FourVector[p1, \[Rho]]*FourVector[p2, \[Nu]]* -FourVector[p4, \[Mu]]*MetricTensor[\[Mu]1, \[Sigma]], -FourVector[p4, \[Mu]1]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, FourVector[p4, \[Mu]1]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -FourVector[p4, \[Mu]1]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o4.Mod deleted file mode 100644 index 6df1f0f96..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10S10o4.Mod +++ /dev/null @@ -1,1637 +0,0 @@ -{{(I*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(I*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/2)*CouplingConstant[ChPTW3[2], 1]* - (CouplingConstant[ChPTW3[4], 25]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) - - (CouplingConstant[ChPTW3[4], 20] - CouplingConstant[ChPTW3[4], 26])* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I/2)*CouplingConstant[ChPTW3[2], 1]* - (CouplingConstant[ChPTW3[4], 25]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) + - (CouplingConstant[ChPTW3[4], 20] + CouplingConstant[ChPTW3[4], 26])* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/2)*CouplingConstant[ChPTW3[2], 1]* - (CouplingConstant[ChPTW3[4], 25]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]) - - (CouplingConstant[ChPTW3[4], 20] - CouplingConstant[ChPTW3[4], 26])* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I/2)*CouplingConstant[ChPTW3[2], 1]* - (CouplingConstant[ChPTW3[4], 25]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]) + - (CouplingConstant[ChPTW3[4], 20] + CouplingConstant[ChPTW3[4], 26])* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 32]* - Eps[\[Mu], \[Nu], \[Rho], \[Sigma]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ -(2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{((I/24)*CouplingConstant[ChPTW3[2], 1]* - (4*CouplingConstant[ChPTW3[4], 24]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]) + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]) - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]) + 2*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 2*CouplingConstant[ChPTW3[4], 21]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I/24)*CouplingConstant[ChPTW3[2], 1]* - (4*CouplingConstant[ChPTW3[4], 24]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]) - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]* - (-UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]) - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]) - 2*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 4*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 4*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 8*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 2*CouplingConstant[ChPTW3[4], 21]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I/12)*CouplingConstant[ChPTW3[2], 1]* - (4*Sqrt[3]*CouplingConstant[ChPTW3[4], 24]* - (UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]) + - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]) + - (UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]])* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]])) - - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 4*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 4*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 4*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 4*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 4*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 4*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 4*CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 2*CouplingConstant[ChPTW3[4], 21]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o2.Gen deleted file mode 100644 index fe6015203..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p3, \[Mu]1], FourVector[p2, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o2.Mod deleted file mode 100644 index cfbb8fab6..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o2.Mod +++ /dev/null @@ -1,20 +0,0 @@ -{{(CouplingConstant[ChPTW3[2], 1]*((-3*I)*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - (6*I)*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - (3*I)*SU3D[6, I1, k1]* - SU3D[I2, I3, k1] + 3*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 6*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + 3*SU3D[I1, I2, k1]* - SU3F[6, I3, k1] + 3*SU3D[6, I3, k1]*SU3F[I1, I2, k1] + - (3*I)*SU3F[6, I3, k1]*SU3F[I1, I2, k1] - 3*SU3D[6, I1, k1]* - SU3F[I2, I3, k1] - (3*I)*SU3F[6, I1, k1]*SU3F[I2, I3, k1] - - (2*I)*SUNDelta[6, I3]*SUNDelta[I1, I2] + (4*I)*SUNDelta[6, I2]* - SUNDelta[I1, I3] - (2*I)*SUNDelta[6, I1]*SUNDelta[I2, I3]))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}, -{(CouplingConstant[ChPTW3[2], 1]*((6*I)*SU3D[6, I3, k1]*SU3D[I1, I2, k1] - - (3*I)*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - (3*I)*SU3D[6, I1, k1]* - SU3D[I2, I3, k1] + 3*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + - 3*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - 6*SU3D[I1, I2, k1]* - SU3F[6, I3, k1] + 3*SU3D[6, I2, k1]*SU3F[I1, I3, k1] + - (3*I)*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + 3*SU3D[6, I1, k1]* - SU3F[I2, I3, k1] + (3*I)*SU3F[6, I1, k1]*SU3F[I2, I3, k1] + - (4*I)*SUNDelta[6, I3]*SUNDelta[I1, I2] - (2*I)*SUNDelta[6, I2]* - SUNDelta[I1, I3] - (2*I)*SUNDelta[6, I1]*SUNDelta[I2, I3]))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o4.Gen deleted file mode 100644 index ba3dc7582..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o4.Gen +++ /dev/null @@ -1,13 +0,0 @@ -{FourVector[p2, \[Mu]1]*MomentaScalarProduct[p2, p3], -FourVector[p3, \[Mu]1]*MomentaScalarProduct[p2, p3], -FourVector[p2, \[Mu]1]*MomentaScalarProduct[p1, p3], -FourVector[p3, \[Mu]1]*MomentaScalarProduct[p1, p2], -FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, FourVector[p3, \[Mu]1]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, FourVector[p3, \[Mu]1]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, FourVector[p3, \[Mu]1]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o4.Mod deleted file mode 100644 index 7e9c604a8..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10P10o4.Mod +++ /dev/null @@ -1,1680 +0,0 @@ -{{(-8*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(-8*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(2*((3*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I3, k1]*SU3D[I1, I2, k1] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I2, k1]*SU3D[I1, I3, k1] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I3, k1]*SU3F[I1, I2, k1] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3F[6, I3, k1]*SU3F[I1, I2, k1] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3F[6, I3, k1]*SU3F[I1, I2, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I2, k1]*SU3F[I1, I3, k1] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[6, I2, k1]*SU3F[I1, I3, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3F[6, I2, k1]*SU3F[I1, I3, k1] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I1, k1]*SU3F[I2, I3, k1] + (6*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 16]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] + - (2*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SUNDelta[6, I3]*SUNDelta[I1, I2] + (2*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SUNDelta[6, I3]*SUNDelta[I1, I2] - - (2*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SUNDelta[6, I2]*SUNDelta[I1, I3] - (2*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SUNDelta[6, I2]*SUNDelta[I1, I3]))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(2*((-3*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I3, k1]*SU3D[I1, I2, k1] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I2, k1]*SU3D[I1, I3, k1] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I3, k1]*SU3F[I1, I2, k1] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3F[6, I3, k1]*SU3F[I1, I2, k1] + (3*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3F[6, I3, k1]*SU3F[I1, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I2, k1]*SU3F[I1, I3, k1] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3D[6, I2, k1]*SU3F[I1, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3F[6, I2, k1]*SU3F[I1, I3, k1] - (3*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SU3D[6, I1, k1]*SU3F[I2, I3, k1] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 16]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] - - (2*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SUNDelta[6, I3]*SUNDelta[I1, I2] - (2*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SUNDelta[6, I3]*SUNDelta[I1, I2] + - (2*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 16]* - SUNDelta[6, I2]*SUNDelta[I1, I3] + (2*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 17]*SUNDelta[6, I2]*SUNDelta[I1, I3]))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{((24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k1] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, k1, k2]*SU3D[6, I3, k1]* - SU3D[I1, I2, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[8, k1, k2]* - SU3D[I1, I2, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3D[8, I2, k2]*SU3D[I1, I3, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3D[8, I2, k1]*SU3D[I1, I3, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3D[6, I2, k2]*SU3D[I1, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[6, I2, k1]*SU3D[8, I3, k2]*SU3D[I1, k1, k2] - - (12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[I2, I3, k1] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I3, k1]*SU3D[6, I1, k2]* - SU3D[I2, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3D[8, I3, k2]* - SU3D[I2, k1, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, 6, k1]*SU3D[I1, I2, k2]* - SU3D[I3, k1, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, 8, k1]*SU3D[I1, I2, k2]* - SU3D[I3, k1, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]* - SU3F[3, 6, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3D[I1, I3, k2]* - SU3F[3, I2, k1] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, I3, k1]*SU3D[I1, k1, k2]* - SU3F[3, I2, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[I1, I2, k2]* - SU3F[3, k1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, 8, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[I3, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[I3, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I1, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[I3, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[I2, I3, k1]*SU3F[3, k1, k2]*SU3F[6, I1, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[I2, I3, k1]*SU3F[3, k1, k2]*SU3F[6, I1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I3, k1]*SU3D[I1, k1, k2]* - SU3F[6, I2, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I3, k1]*SU3D[I1, k1, k2]* - SU3F[6, I2, k2] - 48*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I2, k1]*SU3D[I1, k1, k2]*SU3F[6, I3, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I2, k1]*SU3D[I1, k1, k2]*SU3F[6, I3, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I1, k1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I2, k1, k2]*SU3F[3, I1, k1]*SU3F[6, I3, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I3, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[I1, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I3, k2] - - (72*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, I2, k1]*SU3F[3, k1, k2]*SU3F[6, I3, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3F[3, k1, k2]*SU3F[6, I3, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[I1, I3, k1]*SU3F[3, I2, k2]*SU3F[6, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[I2, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I1, k1] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[I1, I3, k2]*SU3F[8, I2, k1] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[I1, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I2, k1] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I1, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I2, k1] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, I3, k1]*SU3D[I1, k1, k2]*SU3F[8, I2, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I1, I3, k1]*SU3F[6, k1, k2]*SU3F[8, I2, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k2]*SU3F[8, k1, k2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[8, k1, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[8, k1, k2] + - (24*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[I1, I2, k1]*SU3F[6, I3, k2]*SU3F[8, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[I1, I2, k1]*SU3F[6, I3, k2]*SU3F[8, k1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3F[I1, I3, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3D[8, I2, k2]* - SU3F[I1, I3, k1] + (12*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I2, k1]*SU3F[I1, I3, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3F[3, I2, k1]*SU3F[I1, I3, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[3, I2, k1]*SU3F[6, k1, k2]*SU3F[I1, I3, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3F[8, I2, k1]*SU3F[I1, I3, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, k1, k2]*SU3F[8, I2, k1]*SU3F[I1, I3, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3D[6, I2, k2]*SU3F[I1, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[8, I3, k2]*SU3F[I1, k1, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, I3, k1]*SU3F[3, I2, k2]*SU3F[I1, k1, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I3, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[8, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[3, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[3, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3F[I2, I3, k1] + (12*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[3, k1, k2]*SU3F[6, I1, k1]*SU3F[I2, I3, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[3, k1, k2]*SU3F[6, I1, k1]*SU3F[I2, I3, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, k1]*SU3F[8, k1, k2]*SU3F[I2, I3, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, k1]*SU3F[8, k1, k2]*SU3F[I2, I3, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3D[6, I1, k2]*SU3F[I2, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[8, I3, k2]*SU3F[I2, k1, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[8, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[3, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I3, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, 6, k1]*SU3D[I1, I2, k2]*SU3F[I3, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, 8, k1]*SU3D[I1, I2, k2]*SU3F[I3, k1, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3F[3, 6, k2]*SU3F[I3, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[I1, I2, k1]*SU3F[6, 8, k2]*SU3F[I3, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, I3]*SUNDelta[3, I1] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*SU3F[6, I2, I3]*SUNDelta[3, I1] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I1, I3]*SUNDelta[3, I2] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*SU3F[6, I1, I3]*SUNDelta[3, I2] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, I3]*SUNDelta[3, I2] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, I3]*SUNDelta[3, I2] - - (48*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, I2]*SUNDelta[3, I3] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[3, I3] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[3, I3] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*SU3F[6, I1, I2]*SUNDelta[3, I3] - - (24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I2, I3]*SUNDelta[6, I1] + (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I2, I3]*SUNDelta[6, I1] - (24*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I1, I3]*SUNDelta[6, I2] + - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I1, I3]*SUNDelta[6, I2] + - (24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I1, I2]*SUNDelta[6, I3] - (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I1, I2]*SUNDelta[6, I3] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I1, I2]*SUNDelta[6, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[8, I1, I2]*SUNDelta[6, I3] - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, I3]*SUNDelta[8, I1] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I2, I3]*SUNDelta[8, I1] - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, I3]*SUNDelta[8, I2] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I1, I3]*SUNDelta[8, I2] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I3]*SUNDelta[8, I2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I3]*SUNDelta[8, I2] + (16*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, I2]*SUNDelta[8, I3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[8, I3] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[8, I3] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 24]*SU3F[6, I1, I2]*SUNDelta[8, I3] + - (16*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I3]*SUNDelta[I1, I2] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, 6, I2]*SUNDelta[I1, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, 8, I2]*SUNDelta[I1, I3] - (8*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I2]*SUNDelta[I1, I3] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[3, 6, I1]*SUNDelta[I2, I3] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[3, 6, I1]*SUNDelta[I2, I3] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, 8, I1]*SUNDelta[I2, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 23]*SU3F[6, 8, I1]*SUNDelta[I2, I3] - - (8*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{((-12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I3, k2]*SU3D[I1, I2, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3D[8, I3, k1]*SU3D[I1, I2, k2] + - (24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[I1, I3, k1] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, k1, k2]*SU3D[6, I2, k1]* - SU3D[I1, I3, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I2, k1]*SU3D[8, k1, k2]* - SU3D[I1, I3, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[6, I3, k2]* - SU3D[I1, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[8, I2, k2]* - SU3D[I1, k1, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, 6, k1]*SU3D[I1, I3, k2]*SU3D[I2, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[6, 8, k1]*SU3D[I1, I3, k2]*SU3D[I2, k1, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I2, k1]*SU3D[6, I1, k2]*SU3D[I3, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[6, I1, k1]*SU3D[8, I2, k2]*SU3D[I3, k1, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3D[I2, k1, k2]*SU3F[3, 6, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[I1, I2, k2]*SU3F[3, I3, k1] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, I2, k1]*SU3D[I1, k1, k2]*SU3F[3, I3, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[I1, I3, k2]*SU3F[3, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, 8, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I2, k1, k2]*SU3F[3, I3, k1]* - SU3F[6, I1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, k1, k2]*SU3F[3, I3, k1]* - SU3F[6, I1, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, k1, k2]*SU3F[3, I3, k1]* - SU3F[6, I1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, I3, k1]*SU3F[3, k1, k2]* - SU3F[6, I1, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, I3, k1]*SU3F[3, k1, k2]* - SU3F[6, I1, k2] - 48*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I3, k1]*SU3D[I1, k1, k2]*SU3F[6, I2, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I3, k1]*SU3D[I1, k1, k2]*SU3F[6, I2, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I1, k1]*SU3D[I3, k1, k2]*SU3F[6, I2, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3D[I3, k1, k2]*SU3F[6, I2, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I3, k1, k2]*SU3F[3, I1, k1]*SU3F[6, I2, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, k1, k2]*SU3F[3, I3, k1]*SU3F[6, I2, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[I1, k1, k2]*SU3F[3, I3, k1]*SU3F[6, I2, k2] - - (72*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, I3, k1]*SU3F[3, k1, k2]*SU3F[6, I2, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3F[3, k1, k2]*SU3F[6, I2, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[I1, k1, k2]* - SU3F[6, I3, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]* - SU3F[6, I3, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I1, I2, k1]*SU3F[3, I3, k2]* - SU3F[6, k1, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I3, k1, k2]*SU3F[6, I2, k2]* - SU3F[8, I1, k1] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3D[I1, I2, k2]* - SU3F[8, I3, k1] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[8, I3, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[8, I3, k1] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[8, I3, k1] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]* - SU3F[8, I3, k1] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]* - SU3F[8, I3, k1] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, I2, k1]*SU3D[I1, k1, k2]* - SU3F[8, I3, k2] - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I1, I2, k1]*SU3F[6, k1, k2]* - SU3F[8, I3, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I2, k1]*SU3D[I1, I3, k2]* - SU3F[8, k1, k2] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]* - SU3F[8, k1, k2] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]* - SU3F[8, k1, k2] + (24*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I1, I3, k1]*SU3F[6, I2, k2]* - SU3F[8, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[6, I2, k2]* - SU3F[8, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I3, k2]*SU3F[I1, I2, k1] + - (12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3F[6, I3, k1]*SU3F[I1, I2, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3D[8, I3, k1]* - SU3F[I1, I2, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3F[3, I3, k1]* - SU3F[I1, I2, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I3, k1]*SU3F[6, k1, k2]* - SU3F[I1, I2, k2] - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3F[8, I3, k1]* - SU3F[I1, I2, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[6, k1, k2]*SU3F[8, I3, k1]* - SU3F[I1, I2, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[6, I3, k2]* - SU3F[I1, k1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[8, I2, k2]* - SU3F[I1, k1, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, I2, k1]*SU3F[3, I3, k2]* - SU3F[I1, k1, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[8, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3F[6, I3, k2]* - SU3F[I1, k1, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3F[6, I3, k2]* - SU3F[I1, k1, k2] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, I2, k1]*SU3F[8, I3, k2]* - SU3F[I1, k1, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, k1]*SU3F[8, I3, k2]* - SU3F[I1, k1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[6, I2, k1]*SU3F[8, I3, k2]* - SU3F[I1, k1, k2] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3F[I2, I3, k1] - - (12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3F[6, I1, k1]*SU3F[I2, I3, k1] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, k1, k2]*SU3F[6, I1, k2]* - SU3F[I2, I3, k1] - (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, k1, k2]*SU3F[6, I1, k2]* - SU3F[I2, I3, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, k1, k2]*SU3F[6, I1, k2]* - SU3F[I2, I3, k1] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, k1, k2]*SU3F[6, I1, k2]* - SU3F[I2, I3, k1] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[3, k1, k2]*SU3F[6, I1, k1]* - SU3F[I2, I3, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[3, k1, k2]*SU3F[6, I1, k1]* - SU3F[I2, I3, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, k1]*SU3F[8, k1, k2]* - SU3F[I2, I3, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, k1]*SU3F[8, k1, k2]* - SU3F[I2, I3, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, 6, k1]*SU3D[I1, I3, k2]* - SU3F[I2, k1, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, 8, k1]*SU3D[I1, I3, k2]* - SU3F[I2, k1, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[3, 6, k2]* - SU3F[I2, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[6, 8, k2]* - SU3F[I2, k1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[6, I1, k1]*SU3F[8, I3, k2]* - SU3F[I2, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, k1]*SU3F[8, I3, k2]* - SU3F[I2, k1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, k1]*SU3F[8, I3, k2]* - SU3F[I2, k1, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[6, I1, k2]* - SU3F[I3, k1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3D[8, I2, k2]* - SU3F[I3, k1, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[3, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[8, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[3, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, k1]*SU3F[8, I1, k2]* - SU3F[I3, k1, k2] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, I3]*SUNDelta[3, I1] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I2, I3]*SUNDelta[3, I1] - (48*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, I3]*SUNDelta[3, I2] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, I3]*SUNDelta[3, I2] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, I3]*SUNDelta[3, I2] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - SU3F[6, I1, I3]*SUNDelta[3, I2] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, I2]*SUNDelta[3, I3] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I1, I2]*SUNDelta[3, I3] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[3, I3] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[3, I3] - (24*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, I3]*SUNDelta[6, I1] + - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I2, I3]*SUNDelta[6, I1] + - (24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I1, I3]*SUNDelta[6, I2] - (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I1, I3]*SUNDelta[6, I2] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I1, I3]*SUNDelta[6, I2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[8, I1, I3]*SUNDelta[6, I2] - (24*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I1, I2]*SUNDelta[6, I3] + - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I1, I2]*SUNDelta[6, I3] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, I3]*SUNDelta[8, I1] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 6]*SU3F[6, I2, I3]*SUNDelta[8, I1] + - (16*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[6, I1, I3]*SUNDelta[8, I2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, I3]*SUNDelta[8, I2] + 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, I3]*SUNDelta[8, I2] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - SU3F[6, I1, I3]*SUNDelta[8, I2] - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, I2]*SUNDelta[8, I3] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I1, I2]*SUNDelta[8, I3] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[8, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[8, I3] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, 6, I3]*SUNDelta[I1, I2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, 8, I3]*SUNDelta[I1, I2] - (8*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I3]*SUNDelta[I1, I2] + - (16*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I2]*SUNDelta[I1, I3] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[3, 6, I1]*SUNDelta[I2, I3] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[3, 6, I1]*SUNDelta[I2, I3] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, 8, I1]*SUNDelta[I2, I3] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, 8, I1]*SUNDelta[I2, I3] - (8*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{((24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k1] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, k1, k2]*SU3D[6, I3, k1]* - SU3D[I1, I2, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[8, k1, k2]* - SU3D[I1, I2, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3D[8, I2, k2]*SU3D[I1, I3, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3D[8, I2, k1]*SU3D[I1, I3, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3D[6, I2, k2]*SU3D[I1, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[6, I2, k1]*SU3D[8, I3, k2]*SU3D[I1, k1, k2] - - (12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[I2, I3, k1] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I3, k1]*SU3D[6, I1, k2]* - SU3D[I2, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3D[8, I3, k2]* - SU3D[I2, k1, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, 6, k1]*SU3D[I1, I2, k2]* - SU3D[I3, k1, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, 8, k1]*SU3D[I1, I2, k2]* - SU3D[I3, k1, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]* - SU3F[3, 6, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3D[I1, I3, k2]* - SU3F[3, I2, k1] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, I3, k1]*SU3D[I1, k1, k2]* - SU3F[3, I2, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[I1, I2, k2]* - SU3F[3, k1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, 8, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[I3, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[I3, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[I3, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[I2, I3, k1]*SU3F[3, k1, k2]*SU3F[6, I1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[I2, I3, k1]*SU3F[3, k1, k2]*SU3F[6, I1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I3, k1]*SU3D[I1, k1, k2]* - SU3F[6, I2, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I3, k1]*SU3D[I1, k1, k2]* - SU3F[6, I2, k2] - 48*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I2, k1]*SU3D[I1, k1, k2]*SU3F[6, I3, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I2, k1]*SU3D[I1, k1, k2]*SU3F[6, I3, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I1, k1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I2, k1, k2]*SU3F[3, I1, k1]*SU3F[6, I3, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I3, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[I1, k1, k2]*SU3F[3, I2, k1]*SU3F[6, I3, k2] + - (72*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, I2, k1]*SU3F[3, k1, k2]*SU3F[6, I3, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3F[3, k1, k2]*SU3F[6, I3, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[I1, I3, k1]*SU3F[3, I2, k2]*SU3F[6, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[I2, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I1, k1] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[I1, I3, k2]*SU3F[8, I2, k1] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[I1, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I2, k1] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I1, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I2, k1] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, I3, k1]*SU3D[I1, k1, k2]*SU3F[8, I2, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I1, I3, k1]*SU3F[6, k1, k2]*SU3F[8, I2, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k2]*SU3F[8, k1, k2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[8, k1, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[8, k1, k2] + - (24*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[I1, I2, k1]*SU3F[6, I3, k2]*SU3F[8, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[I1, I2, k1]*SU3F[6, I3, k2]*SU3F[8, k1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3F[I1, I3, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3D[8, I2, k2]* - SU3F[I1, I3, k1] + (12*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I2, k1]*SU3F[I1, I3, k2] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3F[3, I2, k1]*SU3F[I1, I3, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[3, I2, k1]*SU3F[6, k1, k2]*SU3F[I1, I3, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3F[8, I2, k1]*SU3F[I1, I3, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, k1, k2]*SU3F[8, I2, k1]*SU3F[I1, I3, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3D[6, I2, k2]*SU3F[I1, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[8, I3, k2]*SU3F[I1, k1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, I3, k1]*SU3F[3, I2, k2]*SU3F[I1, k1, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I3, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[8, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[3, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[3, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3F[I2, I3, k1] + (12*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[3, k1, k2]*SU3F[6, I1, k1]*SU3F[I2, I3, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[3, k1, k2]*SU3F[6, I1, k1]*SU3F[I2, I3, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, k1]*SU3F[8, k1, k2]*SU3F[I2, I3, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, k1]*SU3F[8, k1, k2]*SU3F[I2, I3, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3D[6, I1, k2]*SU3F[I2, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[8, I3, k2]*SU3F[I2, k1, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[8, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[3, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I3, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, 6, k1]*SU3D[I1, I2, k2]*SU3F[I3, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, 8, k1]*SU3D[I1, I2, k2]*SU3F[I3, k1, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3F[3, 6, k2]*SU3F[I3, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[I1, I2, k1]*SU3F[6, 8, k2]*SU3F[I3, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[3, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, I3]*SUNDelta[3, I1] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*SU3F[6, I2, I3]*SUNDelta[3, I1] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I1, I3]*SUNDelta[3, I2] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*SU3F[6, I1, I3]*SUNDelta[3, I2] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, I3]*SUNDelta[3, I2] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, I3]*SUNDelta[3, I2] + - (48*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, I2]*SUNDelta[3, I3] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[3, I3] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[3, I3] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*SU3F[6, I1, I2]*SUNDelta[3, I3] + - (24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I2, I3]*SUNDelta[6, I1] + (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I2, I3]*SUNDelta[6, I1] + (24*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I1, I3]*SUNDelta[6, I2] + - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I1, I3]*SUNDelta[6, I2] - - (24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I1, I2]*SUNDelta[6, I3] - (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I1, I2]*SUNDelta[6, I3] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I1, I2]*SUNDelta[6, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[8, I1, I2]*SUNDelta[6, I3] - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, I3]*SUNDelta[8, I1] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I2, I3]*SUNDelta[8, I1] - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, I3]*SUNDelta[8, I2] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I1, I3]*SUNDelta[8, I2] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I3]*SUNDelta[8, I2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I3]*SUNDelta[8, I2] + (16*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, I2]*SUNDelta[8, I3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[8, I3] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[8, I3] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 24]*SU3F[6, I1, I2]*SUNDelta[8, I3] + - (16*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I3]*SUNDelta[I1, I2] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, 6, I2]*SUNDelta[I1, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, 8, I2]*SUNDelta[I1, I3] - (8*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I2]*SUNDelta[I1, I3] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[3, 6, I1]*SUNDelta[I2, I3] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[3, 6, I1]*SUNDelta[I2, I3] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, 8, I1]*SUNDelta[I2, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 23]*SU3F[6, 8, I1]*SUNDelta[I2, I3] - - (8*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{((-12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I3, k2]*SU3D[I1, I2, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3D[8, I3, k1]*SU3D[I1, I2, k2] + - (24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[I1, I3, k1] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, k1, k2]*SU3D[6, I2, k1]* - SU3D[I1, I3, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I2, k1]*SU3D[8, k1, k2]* - SU3D[I1, I3, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[6, I3, k2]* - SU3D[I1, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[8, I2, k2]* - SU3D[I1, k1, k2] - (12*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, 6, k1]*SU3D[I1, I3, k2]*SU3D[I2, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[6, 8, k1]*SU3D[I1, I3, k2]*SU3D[I2, k1, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I2, k1]*SU3D[6, I1, k2]*SU3D[I3, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[6, I1, k1]*SU3D[8, I2, k2]*SU3D[I3, k1, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3D[I2, k1, k2]*SU3F[3, 6, k2] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[I1, I2, k2]*SU3F[3, I3, k1] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, I2, k1]*SU3D[I1, k1, k2]*SU3F[3, I3, k2] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[I1, I3, k2]*SU3F[3, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, 8, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k2] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I2, k1, k2]*SU3F[3, I3, k1]* - SU3F[6, I1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, k1, k2]*SU3F[3, I3, k1]* - SU3F[6, I1, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, k1, k2]*SU3F[3, I3, k1]* - SU3F[6, I1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, I3, k1]*SU3F[3, k1, k2]* - SU3F[6, I1, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, I3, k1]*SU3F[3, k1, k2]* - SU3F[6, I1, k2] - 48*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I3, k1]*SU3D[I1, k1, k2]*SU3F[6, I2, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I3, k1]*SU3D[I1, k1, k2]*SU3F[6, I2, k2] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I1, k1]*SU3D[I3, k1, k2]*SU3F[6, I2, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3D[I3, k1, k2]*SU3F[6, I2, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I3, k1, k2]*SU3F[3, I1, k1]*SU3F[6, I2, k2] - - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, k1, k2]*SU3F[3, I3, k1]*SU3F[6, I2, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[I1, k1, k2]*SU3F[3, I3, k1]*SU3F[6, I2, k2] + - (72*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, I3, k1]*SU3F[3, k1, k2]*SU3F[6, I2, k2] + - (36*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3F[3, k1, k2]*SU3F[6, I2, k2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[I1, k1, k2]* - SU3F[6, I3, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]* - SU3F[6, I3, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I1, I2, k1]*SU3F[3, I3, k2]* - SU3F[6, k1, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I3, k1, k2]*SU3F[6, I2, k2]* - SU3F[8, I1, k1] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3D[I1, I2, k2]* - SU3F[8, I3, k1] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[8, I3, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[8, I3, k1] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[8, I3, k1] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]* - SU3F[8, I3, k1] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]* - SU3F[8, I3, k1] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, I2, k1]*SU3D[I1, k1, k2]* - SU3F[8, I3, k2] - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[I1, I2, k1]*SU3F[6, k1, k2]* - SU3F[8, I3, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I2, k1]*SU3D[I1, I3, k2]* - SU3F[8, k1, k2] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]* - SU3F[8, k1, k2] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]* - SU3F[8, k1, k2] + (24*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[I1, I3, k1]*SU3F[6, I2, k2]* - SU3F[8, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[6, I2, k2]* - SU3F[8, k1, k2] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I3, k2]*SU3F[I1, I2, k1] + - (12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3F[6, I3, k1]*SU3F[I1, I2, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3D[8, I3, k1]* - SU3F[I1, I2, k2] - (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3F[3, I3, k1]* - SU3F[I1, I2, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I3, k1]*SU3F[6, k1, k2]* - SU3F[I1, I2, k2] - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, k1, k2]*SU3F[8, I3, k1]* - SU3F[I1, I2, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[6, k1, k2]*SU3F[8, I3, k1]* - SU3F[I1, I2, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[6, I3, k2]* - SU3F[I1, k1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[8, I2, k2]* - SU3F[I1, k1, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, I2, k1]*SU3F[3, I3, k2]* - SU3F[I1, k1, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[8, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3F[6, I3, k2]* - SU3F[I1, k1, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3F[6, I3, k2]* - SU3F[I1, k1, k2] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3D[6, I2, k1]*SU3F[8, I3, k2]* - SU3F[I1, k1, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, k1]*SU3F[8, I3, k2]* - SU3F[I1, k1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[6, I2, k1]*SU3F[8, I3, k2]* - SU3F[I1, k1, k2] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3F[I2, I3, k1] - - (12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3F[6, I1, k1]*SU3F[I2, I3, k1] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, k1, k2]*SU3F[6, I1, k2]* - SU3F[I2, I3, k1] + (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, k1, k2]*SU3F[6, I1, k2]* - SU3F[I2, I3, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, k1, k2]*SU3F[6, I1, k2]* - SU3F[I2, I3, k1] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, k1, k2]*SU3F[6, I1, k2]* - SU3F[I2, I3, k1] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[3, k1, k2]*SU3F[6, I1, k1]* - SU3F[I2, I3, k2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[3, k1, k2]*SU3F[6, I1, k1]* - SU3F[I2, I3, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, k1]*SU3F[8, k1, k2]* - SU3F[I2, I3, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, k1]*SU3F[8, k1, k2]* - SU3F[I2, I3, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, 6, k1]*SU3D[I1, I3, k2]* - SU3F[I2, k1, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, 8, k1]*SU3D[I1, I3, k2]* - SU3F[I2, k1, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[3, 6, k2]* - SU3F[I2, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[6, 8, k2]* - SU3F[I2, k1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[6, I1, k1]*SU3F[8, I3, k2]* - SU3F[I2, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, k1]*SU3F[8, I3, k2]* - SU3F[I2, k1, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, k1]*SU3F[8, I3, k2]* - SU3F[I2, k1, k2] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3D[6, I1, k2]* - SU3F[I3, k1, k2] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3D[8, I2, k2]* - SU3F[I3, k1, k2] - (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + (18*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[3, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[3, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[8, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3D[8, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + (36*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[3, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] + (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[8, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[3, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, k1]*SU3F[8, I1, k2]* - SU3F[I3, k1, k2] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, I3]*SUNDelta[3, I1] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I2, I3]*SUNDelta[3, I1] + (48*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, I3]*SUNDelta[3, I2] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, I3]*SUNDelta[3, I2] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, I3]*SUNDelta[3, I2] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - SU3F[6, I1, I3]*SUNDelta[3, I2] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, I2]*SUNDelta[3, I3] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I1, I2]*SUNDelta[3, I3] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[3, I3] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[3, I3] + (24*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I2, I3]*SUNDelta[6, I1] + - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I2, I3]*SUNDelta[6, I1] - - (24*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[3, I1, I3]*SUNDelta[6, I2] - (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I1, I3]*SUNDelta[6, I2] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, I1, I3]*SUNDelta[6, I2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[8, I1, I3]*SUNDelta[6, I2] + (24*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[3, I1, I2]*SUNDelta[6, I3] + - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I1, I2]*SUNDelta[6, I3] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, I3]*SUNDelta[8, I1] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 6]*SU3F[6, I2, I3]*SUNDelta[8, I1] + - (16*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[6, I1, I3]*SUNDelta[8, I2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, I3]*SUNDelta[8, I2] + 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, I3]*SUNDelta[8, I2] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - SU3F[6, I1, I3]*SUNDelta[8, I2] - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, I2]*SUNDelta[8, I3] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I1, I2]*SUNDelta[8, I3] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[8, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[8, I3] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*SU3F[3, 6, I3]*SUNDelta[I1, I2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, 8, I3]*SUNDelta[I1, I2] - (8*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I3]*SUNDelta[I1, I2] + - (16*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I2]*SUNDelta[I1, I3] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[3, 6, I1]*SUNDelta[I2, I3] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[3, 6, I1]*SUNDelta[I2, I3] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, 8, I1]*SUNDelta[I2, I3] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, 8, I1]*SUNDelta[I2, I3] - (8*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(2*((12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k1] + (12*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[8, k1, k2]*SU3D[I1, I2, k2] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[I1, I3, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I2, k2]*SU3D[I1, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3D[8, I2, k1]*SU3D[I1, I3, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[6, I2, k1]*SU3D[8, I3, k2]*SU3D[I1, k1, k2] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[I2, I3, k1] - (12*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[8, I3, k2]*SU3D[I2, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[6, 8, k1]*SU3D[I1, I2, k2]*SU3D[I3, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, 8, k2] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] + 12*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I3, k1]*SU3D[I1, k1, k2]*SU3F[6, I2, k2] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 8]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] - 24*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, k1, k2]*SU3D[I1, I2, k1]*SU3F[6, I3, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I2, k1]*SU3D[I1, k1, k2]*SU3F[6, I3, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[I2, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I1, k1] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[I1, I3, k2]*SU3F[8, I2, k1] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 21]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[I1, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I2, k1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I1, k1, k2]*SU3F[6, I3, k2]*SU3F[8, I2, k1] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, I3, k1]*SU3D[I1, k1, k2]*SU3F[8, I2, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I1, I3, k1]*SU3F[6, k1, k2]*SU3F[8, I2, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k2]*SU3F[8, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[8, k1, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[8, k1, k2] - - (24*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[I1, I2, k1]*SU3F[6, I3, k2]*SU3F[8, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[I1, I2, k1]*SU3F[6, I3, k2]*SU3F[8, k1, k2] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3F[I1, I3, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I2, k2]*SU3F[I1, I3, k1] + - (6*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3F[6, I2, k1]*SU3F[I1, I3, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I2, k1]*SU3F[I1, I3, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3F[8, I2, k1]*SU3F[I1, I3, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, k1, k2]*SU3F[8, I2, k1]*SU3F[I1, I3, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[8, I3, k2]*SU3F[I1, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[8, I3, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[8, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3F[I2, I3, k1] + (6*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, k1]*SU3F[8, k1, k2]*SU3F[I2, I3, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, k1]*SU3F[8, k1, k2]*SU3F[I2, I3, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[8, I3, k2]*SU3F[I2, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 23]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[8, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I3, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, 8, k1]*SU3D[I1, I2, k2]*SU3F[I3, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[I1, I2, k1]*SU3F[6, 8, k2]*SU3F[I3, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] - - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I2, I3]*SUNDelta[6, I1] - (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I1, I3]*SUNDelta[6, I2] + (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I1, I2]*SUNDelta[6, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 21]*SU3F[8, I1, I2]*SUNDelta[6, I3] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, I3]*SUNDelta[8, I1] + 24*Sqrt[3]*CouplingConstant[ - ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]*SU3F[6, I2, I3]* - SUNDelta[8, I1] + 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, I3]*SUNDelta[8, I2] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SU3F[6, I1, I3]*SUNDelta[8, I2] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I3]*SUNDelta[8, I2] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I3]*SUNDelta[8, I2] - (16*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, I2]*SUNDelta[8, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[8, I3] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[8, I3] - 24*Sqrt[3]*CouplingConstant[ - ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]*SU3F[6, I1, I2]* - SUNDelta[8, I3] + (8*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I3]*SUNDelta[I1, I2] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, 8, I2]*SUNDelta[I1, I3] - (4*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I2]*SUNDelta[I1, I3] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, 8, I1]*SUNDelta[I2, I3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 23]*SU3F[6, 8, I1]*SUNDelta[I2, I3] - - (4*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I1]*SUNDelta[I2, I3]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{(2*((-6*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[I1, I2, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I3, k2]*SU3D[I1, I2, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3D[8, I3, k1]*SU3D[I1, I2, k2] + - (12*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[I1, I3, k1] + (12*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[8, k1, k2]*SU3D[I1, I3, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[6, I3, k1]*SU3D[8, I2, k2]*SU3D[I1, k1, k2] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[I2, I3, k1] + (12*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, 8, k1]*SU3D[I1, I3, k2]*SU3D[I2, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[6, I1, k1]*SU3D[8, I2, k2]*SU3D[I3, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, 8, k2] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, k1, k2]*SU3D[I2, I3, k1]*SU3F[6, I1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3D[8, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 8]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I3, k1]*SU3F[6, I2, k1] - 24*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, k1, k2]*SU3D[I1, I3, k1]*SU3F[6, I2, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I3, k1]*SU3D[I1, k1, k2]*SU3F[6, I2, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3D[I3, k1, k2]*SU3F[6, I2, k2] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] + 12*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I2, k1]*SU3D[I1, k1, k2]*SU3F[6, I3, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[I3, k1, k2]*SU3F[6, I2, k2]*SU3F[8, I1, k1] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[I1, I2, k2]*SU3F[8, I3, k1] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 21]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I3, k1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I3, k1] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]*SU3F[8, I3, k1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]*SU3F[8, I3, k1] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, I2, k1]*SU3D[I1, k1, k2]*SU3F[8, I3, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[I1, I2, k1]*SU3F[6, k1, k2]*SU3F[8, I3, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I2, k1]*SU3D[I1, I3, k2]*SU3F[8, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[8, k1, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[8, k1, k2] - - (24*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[I1, I3, k1]*SU3F[6, I2, k2]*SU3F[8, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[6, I2, k2]*SU3F[8, k1, k2] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3F[I1, I2, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I3, k2]*SU3F[I1, I2, k1] + - (6*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3F[6, I3, k1]*SU3F[I1, I2, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3D[6, k1, k2]*SU3D[8, I3, k1]*SU3F[I1, I2, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, k1, k2]*SU3F[8, I3, k1]*SU3F[I1, I2, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, k1, k2]*SU3F[8, I3, k1]*SU3F[I1, I2, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I3, k1]*SU3D[8, I2, k2]*SU3F[I1, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[8, I3, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3D[6, I2, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - SU3F[6, I2, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3F[I2, I3, k1] - (6*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, I3, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, k1]*SU3F[8, k1, k2]*SU3F[I2, I3, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, k1]*SU3F[8, k1, k2]*SU3F[I2, I3, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, 8, k1]*SU3D[I1, I3, k2]*SU3F[I2, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[I1, I3, k1]*SU3F[6, 8, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 23]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 21]*SU3F[6, I1, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[6, I1, k1]*SU3D[8, I2, k2]*SU3F[I3, k1, k2] + - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 9]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 22]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 23]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - (12*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 5]*SU3D[8, I1, k1]*SU3F[6, I2, k2]*SU3F[I3, k1, k2] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, k1]*SU3F[8, I1, k2]*SU3F[I3, k1, k2] - - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I2, I3]*SUNDelta[6, I1] + (8*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SU3D[8, I1, I3]*SUNDelta[6, I2] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 21]*SU3F[8, I1, I3]*SUNDelta[6, I2] - - (8*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 9]*SU3D[8, I1, I2]*SUNDelta[6, I3] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, I3]*SUNDelta[8, I1] - 24*Sqrt[3]*CouplingConstant[ - ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]*SU3F[6, I2, I3]* - SUNDelta[8, I1] - (16*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SU3D[6, I1, I3]*SUNDelta[8, I2] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, I1, I3]*SUNDelta[8, I2] - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 23]*SU3F[6, I1, I3]*SUNDelta[8, I2] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 24]*SU3F[6, I1, I3]*SUNDelta[8, I2] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I1, I2]*SUNDelta[8, I3] + 24*Sqrt[3]*CouplingConstant[ - ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]*SU3F[6, I1, I2]* - SUNDelta[8, I3] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*SU3F[6, I1, I2]*SUNDelta[8, I3] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - SU3F[6, I1, I2]*SUNDelta[8, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 21]*SU3F[6, 8, I3]*SUNDelta[I1, I2] - - (4*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I3]*SUNDelta[I1, I2] + (8*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*SUNDelta[6, I2]*SUNDelta[I1, I3] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - SU3F[6, 8, I1]*SUNDelta[I2, I3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 23]*SU3F[6, 8, I1]*SUNDelta[I2, I3] - - (4*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - SUNDelta[6, I1]*SUNDelta[I2, I3]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o2.Gen deleted file mode 100644 index a32126124..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o2.Mod deleted file mode 100644 index f08475792..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{(-4*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, I2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o4.Gen deleted file mode 100644 index 9797ea491..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o4.Gen +++ /dev/null @@ -1,8 +0,0 @@ -{FourVector[p3, \[Mu]1]*MomentaScalarProduct[p1, p2], -FourVector[p2, \[Mu]1]*MomentaScalarProduct[p1, p3], -FourVector[p2, \[Mu]1]*MomentaScalarProduct[p2, p3], -FourVector[p3, \[Mu]1]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, FourVector[p3, \[Mu]1]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -FourVector[p3, \[Mu]1]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o4.Mod deleted file mode 100644 index b95e1d380..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10S10o4.Mod +++ /dev/null @@ -1,46 +0,0 @@ -{{(2*CouplingConstant[ChPTW3[2], 1]*(CouplingConstant[ChPTW3[4], 20] + - CouplingConstant[ChPTW3[4], 26])*UTrace1[UMatrix[UGenerator[6]]* - UMatrix[UGenerator[I1]]*UMatrix[UGenerator[I2]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(2*CouplingConstant[ChPTW3[2], 1]*(CouplingConstant[ChPTW3[4], 20] - - CouplingConstant[ChPTW3[4], 26])*UTrace1[UMatrix[UGenerator[6]]* - UMatrix[UGenerator[I1]]*UMatrix[UGenerator[I2]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(4*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3}, -{(-2*CouplingConstant[ChPTW3[2], 1]*(CouplingConstant[ChPTW3[4], 24]* - UTrace1[UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]]* - (3*UTrace1[UMatrix[UGenerator[3]]*UMatrix[UGenerator[I2]]] + - Sqrt[3]*UTrace1[UMatrix[UGenerator[8]]*UMatrix[UGenerator[I2]]]) - - (CouplingConstant[ChPTW3[4], 22] + 2*CouplingConstant[ChPTW3[4], 23])* - (UTrace1[UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]] - 3*UTrace1[UMatrix[UGenerator[3]]* - UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]] - Sqrt[3]*UTrace1[UMatrix[UGenerator[6]]* - UMatrix[UGenerator[8]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]])))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(2*CouplingConstant[ChPTW3[2], 1]*(CouplingConstant[ChPTW3[4], 24]* - UTrace1[UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]]* - (3*UTrace1[UMatrix[UGenerator[3]]*UMatrix[UGenerator[I2]]] - - Sqrt[3]*UTrace1[UMatrix[UGenerator[8]]*UMatrix[UGenerator[I2]]]) + - (CouplingConstant[ChPTW3[4], 22] + 2*CouplingConstant[ChPTW3[4], 23])* - (UTrace1[UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]] + 3*UTrace1[UMatrix[UGenerator[3]]* - UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]] - Sqrt[3]*UTrace1[UMatrix[UGenerator[6]]* - UMatrix[UGenerator[8]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]])))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(2*CouplingConstant[ChPTW3[2], 1]* - (2*Sqrt[3]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]]* - UTrace1[UMatrix[UGenerator[8]]*UMatrix[UGenerator[I2]]] + - (CouplingConstant[ChPTW3[4], 22] + 2*CouplingConstant[ChPTW3[4], 23])* - (UTrace1[UMatrix[UGenerator[6]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]] + 2*Sqrt[3]*UTrace1[UMatrix[UGenerator[6]]* - UMatrix[UGenerator[8]]*UMatrix[UGenerator[I1]]* - UMatrix[UGenerator[I2]]])))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o2.Gen deleted file mode 100644 index a32126124..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{FourVector[p2, \[Mu]1]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o2.Mod deleted file mode 100644 index f08475792..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{(-4*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, I2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o4.Gen deleted file mode 100644 index cc42775f9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o4.Gen +++ /dev/null @@ -1,5 +0,0 @@ -{FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, FourVector[p2, \[Mu]1]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -FourVector[p2, \[Mu]1]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o4.Mod deleted file mode 100644 index 23dc807a3..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3A00P10o4.Mod +++ /dev/null @@ -1,111 +0,0 @@ -{{(-8*(3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I1, I2] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 8]*SU3D[6, I1, I2] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[7, I1, I2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[6, I2, k1]*SU3D[8, I1, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I1, k1]*SU3D[8, I2, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I2, k1]*SU3F[6, I1, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3F[6, I2, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I2, k1]*SU3F[8, I1, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I2, k1]*SU3F[8, I1, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[6, I1, k1]*SU3F[8, I2, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I1, k1]*SU3F[8, I2, k1] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SUNDelta[6, I2]*SUNDelta[8, I1] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SUNDelta[6, I2]*SUNDelta[8, I1] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SUNDelta[6, I1]*SUNDelta[8, I2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 6]* - SUNDelta[6, I1]*SUNDelta[8, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-4*(6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I1, I2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 8]*SU3D[6, I1, I2] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I2, k1]*SU3D[6, I1, k1] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[3, I1, k1]*SU3D[6, I2, k1] + - (18*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[7, I1, I2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[6, I2, k1]*SU3D[8, I1, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I1, k1]*SU3D[8, I2, k1] - (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[6, I2, k1]*SU3F[3, I1, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I1, k1]*SU3F[3, I2, k1] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[3, I2, k1]*SU3F[6, I1, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[8, I2, k1]*SU3F[6, I1, k1] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[3, I2, k1]*SU3F[6, I1, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I1, k1]*SU3F[6, I2, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3F[6, I2, k1] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[3, I1, k1]*SU3F[6, I2, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[6, I2, k1]*SU3F[8, I1, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, k1]*SU3F[8, I1, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I1, k1]*SU3F[8, I2, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, k1]*SU3F[8, I2, k1] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SUNDelta[3, I2]*SUNDelta[6, I1] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*SUNDelta[3, I2]*SUNDelta[6, I1] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SUNDelta[3, I1]*SUNDelta[6, I2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*SUNDelta[3, I1]*SUNDelta[6, I2] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SUNDelta[6, I2]*SUNDelta[8, I1] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 6]*SUNDelta[6, I2]*SUNDelta[8, I1] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SUNDelta[6, I1]*SUNDelta[8, I2] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 6]*SUNDelta[6, I1]*SUNDelta[8, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-4*(24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I1, I2] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 8]*SU3D[6, I1, I2] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I2, k1]*SU3D[6, I1, k1] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[3, I1, k1]*SU3D[6, I2, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I2, k1]*SU3D[8, I1, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3D[6, I1, k1]*SU3D[8, I2, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I2, k1]*SU3F[3, I1, k1] + (9*I)*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3D[6, I1, k1]*SU3F[3, I2, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I2, k1]*SU3F[6, I1, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I2, k1]*SU3F[6, I1, k1] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[3, I2, k1]*SU3F[6, I1, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[3, I1, k1]*SU3F[6, I2, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[8, I1, k1]*SU3F[6, I2, k1] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*SU3F[3, I1, k1]*SU3F[6, I2, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 5]*SU3D[6, I2, k1]*SU3F[8, I1, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3F[6, I2, k1]*SU3F[8, I1, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SU3D[6, I1, k1]*SU3F[8, I2, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 5]*SU3F[6, I1, k1]*SU3F[8, I2, k1] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SUNDelta[3, I2]*SUNDelta[6, I1] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*SUNDelta[3, I2]*SUNDelta[6, I1] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SUNDelta[3, I1]*SUNDelta[6, I2] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*SUNDelta[3, I1]*SUNDelta[6, I2] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SUNDelta[6, I2]*SUNDelta[8, I1] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 6]*SUNDelta[6, I2]*SUNDelta[8, I1] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - SUNDelta[6, I1]*SUNDelta[8, I2] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 1]*CouplingConstant[ChPTW3[4], 6]*SUNDelta[6, I1]*SUNDelta[8, I2]))/ -(9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o2.Gen deleted file mode 100644 index 7611e11db..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{0} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o2.Mod deleted file mode 100644 index d8f234e31..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o2.Mod +++ /dev/null @@ -1 +0,0 @@ -{{0}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o4.Gen deleted file mode 100644 index 03bcc9279..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o4.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o4.Mod deleted file mode 100644 index 7b21bf970..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P00o4.Mod +++ /dev/null @@ -1,10 +0,0 @@ -{{((-32*I)*CouplingConstant[ChPTW3[2], 1]* - (2*CouplingConstant[ChPTW3[4], 12]*SU3D[6, I1, I2] - - 2*CouplingConstant[ChPTW3[4], 36]*SU3D[6, I1, I2] + - 2*CouplingConstant[ChPTW3[4], 12]*SUNDelta[0, I2]*SUNDelta[6, I1] + - 3*CouplingConstant[ChPTW3[4], 13]*SUNDelta[0, I2]*SUNDelta[6, I1] - - 2*CouplingConstant[ChPTW3[4], 36]*SUNDelta[0, I2]*SUNDelta[6, I1] + - 2*CouplingConstant[ChPTW3[4], 12]*SUNDelta[0, I1]*SUNDelta[6, I2] + - 3*CouplingConstant[ChPTW3[4], 13]*SUNDelta[0, I1]*SUNDelta[6, I2] - - 2*CouplingConstant[ChPTW3[4], 36]*SUNDelta[0, I1]*SUNDelta[6, I2]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10P10o2.Gen deleted file mode 100644 index 13886c34c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10P10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10P10o2.Mod deleted file mode 100644 index db6ed1420..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10P10o2.Mod +++ /dev/null @@ -1,70 +0,0 @@ -{{((-2*I)/9)*CouplingConstant[ChPTW3[2], 2]* -(6*SU3D[6, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, I4, k2] + - 3*SU3D[6, I2, k1]*SU3D[I1, I4, k2]*SU3D[I3, k1, k2] + - 6*SU3D[6, I1, k1]*SU3D[I2, I4, k2]*SU3D[I3, k1, k2] + - 3*SU3D[6, I2, k1]*SU3D[I1, I3, k2]*SU3D[I4, k1, k2] + - 6*SU3D[6, I1, k1]*SU3D[I2, I3, k2]*SU3D[I4, k1, k2] + - (6*I)*SU3D[I2, k1, k2]*SU3D[I3, I4, k1]*SU3F[6, I1, k2] + - (6*I)*SU3D[I2, I4, k1]*SU3D[I3, k1, k2]*SU3F[6, I1, k2] + - (6*I)*SU3D[I2, I3, k1]*SU3D[I4, k1, k2]*SU3F[6, I1, k2] + - (3*I)*SU3D[I1, I4, k1]*SU3D[I3, k1, k2]*SU3F[6, I2, k2] + - (3*I)*SU3D[I1, I3, k1]*SU3D[I4, k1, k2]*SU3F[6, I2, k2] + - (3*I)*SU3D[I1, I4, k1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2] + - (3*I)*SU3D[I1, I2, k1]*SU3D[I4, k1, k2]*SU3F[6, I3, k2] + - (3*I)*SU3D[I1, I3, k1]*SU3D[I2, k1, k2]*SU3F[6, I4, k2] + - (3*I)*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]*SU3F[6, I4, k2] + - 3*SU3D[I4, k1, k2]*SU3F[6, I3, k2]*SU3F[I1, I2, k1] + - 3*SU3D[I3, k1, k2]*SU3F[6, I4, k2]*SU3F[I1, I2, k1] + - 3*SU3D[I4, k1, k2]*SU3F[6, I2, k2]*SU3F[I1, I3, k1] + - 3*SU3D[I2, k1, k2]*SU3F[6, I4, k2]*SU3F[I1, I3, k1] - - (3*I)*SU3D[6, I2, k1]*SU3D[I4, k1, k2]*SU3F[I1, I3, k2] + - 3*SU3D[I3, k1, k2]*SU3F[6, I2, k2]*SU3F[I1, I4, k1] + - 3*SU3D[I2, k1, k2]*SU3F[6, I3, k2]*SU3F[I1, I4, k1] - - (3*I)*SU3D[6, I2, k1]*SU3D[I3, k1, k2]*SU3F[I1, I4, k2] - - (6*I)*SU3D[6, I1, k1]*SU3D[I3, I4, k2]*SU3F[I2, k1, k2] - - 6*SU3D[I3, I4, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - 3*SU3D[I1, I4, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] - - 3*SU3D[I1, I3, k1]*SU3F[6, I4, k2]*SU3F[I2, k1, k2] - - (3*I)*SU3F[6, I4, k1]*SU3F[I1, I3, k2]*SU3F[I2, k1, k2] - - (3*I)*SU3F[6, I3, k1]*SU3F[I1, I4, k2]*SU3F[I2, k1, k2] - - (3*I)*SU3D[6, I2, k1]*SU3D[I1, I4, k2]*SU3F[I3, k1, k2] - - (6*I)*SU3D[6, I1, k1]*SU3D[I2, I4, k2]*SU3F[I3, k1, k2] - - 6*SU3D[I2, I4, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - 3*SU3D[I1, I4, k1]*SU3F[6, I2, k2]*SU3F[I3, k1, k2] - - 3*SU3D[I1, I2, k1]*SU3F[6, I4, k2]*SU3F[I3, k1, k2] - - (3*I)*SU3F[6, I4, k1]*SU3F[I1, I2, k2]*SU3F[I3, k1, k2] - - 3*SU3D[6, I2, k1]*SU3F[I1, I4, k2]*SU3F[I3, k1, k2] - - (3*I)*SU3F[6, I2, k1]*SU3F[I1, I4, k2]*SU3F[I3, k1, k2] - - (3*I)*SU3D[6, I2, k1]*SU3D[I1, I3, k2]*SU3F[I4, k1, k2] - - (6*I)*SU3D[6, I1, k1]*SU3D[I2, I3, k2]*SU3F[I4, k1, k2] - - 6*SU3D[I2, I3, k1]*SU3F[6, I1, k2]*SU3F[I4, k1, k2] - - 3*SU3D[I1, I3, k1]*SU3F[6, I2, k2]*SU3F[I4, k1, k2] - - 3*SU3D[I1, I2, k1]*SU3F[6, I3, k2]*SU3F[I4, k1, k2] - - (3*I)*SU3F[6, I3, k1]*SU3F[I1, I2, k2]*SU3F[I4, k1, k2] - - 3*SU3D[6, I2, k1]*SU3F[I1, I3, k2]*SU3F[I4, k1, k2] - - (3*I)*SU3F[6, I2, k1]*SU3F[I1, I3, k2]*SU3F[I4, k1, k2] + - 12*SU3D[6, I2, k1]*SU3D[I3, I4, k1]*SUNDelta[0, I1] + - (12*I)*SU3D[I3, I4, k1]*SU3F[6, I2, k1]*SUNDelta[0, I1] + - (12*I)*SU3D[I2, I4, k1]*SU3F[6, I3, k1]*SUNDelta[0, I1] + - (12*I)*SU3D[I2, I3, k1]*SU3F[6, I4, k1]*SUNDelta[0, I1] + - 3*SU3D[6, I4, k1]*((-I)*SU3D[I3, k1, k2]*SU3F[I1, I2, k2] - - I*SU3D[I2, k1, k2]*SU3F[I1, I3, k2] + SU3D[I1, I3, k2]* - (SU3D[I2, k1, k2] - I*SU3F[I2, k1, k2]) - SU3F[I1, I3, k2]* - SU3F[I2, k1, k2] + SU3D[I1, I2, k2]*(SU3D[I3, k1, k2] - - I*SU3F[I3, k1, k2]) - SU3F[I1, I2, k2]*SU3F[I3, k1, k2] + - 4*SU3D[I2, I3, k1]*SUNDelta[0, I1]) + 3*SU3D[6, I3, k1]* - ((-I)*SU3D[I4, k1, k2]*SU3F[I1, I2, k2] - I*SU3D[I2, k1, k2]* - SU3F[I1, I4, k2] + SU3D[I1, I4, k2]*(SU3D[I2, k1, k2] - - I*SU3F[I2, k1, k2]) - SU3F[I1, I4, k2]*SU3F[I2, k1, k2] + - SU3D[I1, I2, k2]*(SU3D[I4, k1, k2] - I*SU3F[I4, k1, k2]) - - SU3F[I1, I2, k2]*SU3F[I4, k1, k2] + 4*SU3D[I2, I4, k1]* - SUNDelta[0, I1]) + 12*SU3D[I2, I3, I4]*SUNDelta[6, I1] + - 4*SU3D[I1, I3, I4]*SUNDelta[6, I2] + 4*SU3D[I1, I2, I4]*SUNDelta[6, I3] + - 4*SU3D[I1, I2, I3]*SUNDelta[6, I4] + 4*SU3D[6, I3, I4]*SUNDelta[I1, I2] + - 4*SU3D[6, I2, I4]*SUNDelta[I1, I3] + 4*SU3D[6, I2, I3]*SUNDelta[I1, I4] + - 4*SU3D[6, I1, I4]*SUNDelta[I2, I3] + (4*I)*SU3F[6, I1, I4]* - SUNDelta[I2, I3] + 8*SUNDelta[0, I1]*SUNDelta[6, I4]*SUNDelta[I2, I3] + - 4*SU3D[6, I1, I3]*SUNDelta[I2, I4] + (4*I)*SU3F[6, I1, I3]* - SUNDelta[I2, I4] + 8*SUNDelta[0, I1]*SUNDelta[6, I3]*SUNDelta[I2, I4] + - 4*SU3D[6, I1, I2]*SUNDelta[I3, I4] + (4*I)*SU3F[6, I1, I2]* - SUNDelta[I3, I4] + 8*SUNDelta[0, I1]*SUNDelta[6, I2]*SUNDelta[I3, I4])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10o2.Gen deleted file mode 100644 index c828fa1ab..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]/DecayConstant[PseudoScalar[1], -RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10o2.Mod deleted file mode 100644 index fbdf234c8..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10P10o2.Mod +++ /dev/null @@ -1,10 +0,0 @@ -{{(2*CouplingConstant[ChPTW3[2], 2]*(-6*SU3D[6, I1, k1]*SU3D[I2, I3, k1] - - (6*I)*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + (3*I)*SU3D[I1, I3, k1]* - SU3F[6, I2, k1] + (3*I)*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - 3*SU3D[6, I3, k1]*(SU3D[I1, I2, k1] - I*SU3F[I1, I2, k1]) + - 3*SU3F[6, I3, k1]*SU3F[I1, I2, k1] + 3*SU3D[6, I2, k1]* - (SU3D[I1, I3, k1] - I*SU3F[I1, I3, k1]) + 3*SU3F[6, I2, k1]* - SU3F[I1, I3, k1] + 2*SUNDelta[6, I3]*SUNDelta[I1, I2] + - 2*SUNDelta[6, I2]*SUNDelta[I1, I3] - 4*SUNDelta[6, I1]* - SUNDelta[I2, I3]))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o2.Mod deleted file mode 100644 index 9e6da99e7..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o2.Mod +++ /dev/null @@ -1,3 +0,0 @@ -{{((8*I)*(CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2] + - CouplingConstant[ChPTW3[2], 2]*SUNDelta[0, I1]*SUNDelta[6, I2]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o4.Gen deleted file mode 100644 index b15699e3c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o4.Gen +++ /dev/null @@ -1 +0,0 @@ -{MomentaScalarProduct[p1, p3], MomentaScalarProduct[p2, p3]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o4.Mod deleted file mode 100644 index fd3ef218c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10S10o4.Mod +++ /dev/null @@ -1,19 +0,0 @@ -{{((-2*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - QuarkCondensate[RenormalizationState[0]]* - (2*SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3}, -{((-2*I)*CouplingConstant[ChPTW3[2], 1]*(CouplingConstant[ChPTW3[4], 22] + - 2*CouplingConstant[ChPTW3[4], 23])*QuarkCondensate[ - RenormalizationState[0]]*(2*SUNDelta[0, I1]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o2.Gen deleted file mode 100644 index c828fa1ab..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]/DecayConstant[PseudoScalar[1], -RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o2.Mod deleted file mode 100644 index feecdef0a..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{(8*I)*CouplingConstant[ChPTW3[2], 2]*(SU3D[6, I1, I2] + - SUNDelta[0, I1]*SUNDelta[6, I2])}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o4.Gen deleted file mode 100644 index 1c15fd8b3..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o4.Gen +++ /dev/null @@ -1,3 +0,0 @@ -{ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o4.Mod deleted file mode 100644 index d7790fb2c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P00P10o4.Mod +++ /dev/null @@ -1,305 +0,0 @@ -{{(((-4*I)/3)*CouplingConstant[ChPTW3[2], 1]*QuarkCondensate[ - RenormalizationState[0]]*(-6*CouplingConstant[ChPTW3[4], 11]* - SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 4*CouplingConstant[ChPTW3[4], 12]* - SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]*SUNDelta[0, I1]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]*SUNDelta[0, I1]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + CouplingConstant[ChPTW3[4], 13]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]* - (Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]) + - SUNDelta[0, I1]*(-6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]])) - - 3*CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[4], 10]* - (-2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - SUNDelta[0, I1]*(-4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]) - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(((4*I)/3)*CouplingConstant[ChPTW3[2], 1]*QuarkCondensate[ - RenormalizationState[0]]*(6*CouplingConstant[ChPTW3[4], 11]* - SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 4*CouplingConstant[ChPTW3[4], 12]* - SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]*SUNDelta[0, I1]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]*SUNDelta[0, I1]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + CouplingConstant[ChPTW3[4], 13]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]* - (Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]) + - SUNDelta[0, I1]*(6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]])) + - 3*CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[4], 10]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - SUNDelta[0, I1]*(4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]) + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{(((4*I)/3)*CouplingConstant[ChPTW3[2], 1]*QuarkCondensate[ - RenormalizationState[0]]*(CouplingConstant[ChPTW3[4], 11]* - (6*SUNDelta[0, I1]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]) + - 3*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])) + - 2*(CouplingConstant[ChPTW3[4], 13]* - (Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]) + 3*SUNDelta[0, I1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[ - UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[ - UGenerator[I2]], UMatrix[UGenerator[8]]]]))) + - CouplingConstant[ChPTW3[4], 12]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*SUNDelta[0, I1]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[ - UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[ - UGenerator[I2]], UMatrix[UGenerator[8]]]])) + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]])) + - 2*CouplingConstant[ChPTW3[4], 10]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*SUNDelta[0, I1]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]])) + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10S10o2.Gen deleted file mode 100644 index f87d0e408..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10S10o2.Gen +++ /dev/null @@ -1,8 +0,0 @@ -{MomentaScalarProduct[p3, p4], MomentaScalarProduct[p3, p5], -MomentaScalarProduct[p1, p2], MomentaScalarProduct[p4, p5], -MomentaScalarProduct[p2, p4], MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p2, p3], ParticleMass[PseudoScalar[2], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[8], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[7], -RenormalizationState[0]]^2, MomentaScalarProduct[p1, p4], -MomentaScalarProduct[p2, p5], MomentaScalarProduct[p1, p5]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10S10o2.Mod deleted file mode 100644 index 74ae76788..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10S10o2.Mod +++ /dev/null @@ -1,50043 +0,0 @@ -{{CouplingConstant[ChPTW3[2], 1]*((SU3D[6, I4, I5]*SU3D[I1, I2, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I5]*SU3D[I1, I2, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I3, I4]*SU3D[I1, I2, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I2, I5]*SU3D[I1, I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I4]*SU3D[I1, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I3]*SU3D[I2, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k9]*(SU3D[6, I5, k7]*(SU3D[I1, k8, k9]*SU3D[I2, k7, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k8, k9]) + SU3D[6, I2, k7]* - (SU3D[I1, k8, k9]*SU3D[I5, k7, k8] + SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]) + SU3D[6, I1, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I5, k8, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I4, I5]*SU3F[6, I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I3, I5]*SU3F[6, I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, I5]*SU3F[6, I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I3, I5]*SU3F[6, I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]* - SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I2, I4]*SU3F[6, I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I2, I3]*SU3F[6, I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/4)*(SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]* - SU3F[6, I1, k7] + SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I2, k7] + SU3D[I1, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]* - SU3F[6, I2, k7] + SU3D[I1, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]* - SU3F[6, I2, k7] + SU3D[I1, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]* - SU3F[6, I2, k7] + SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3F[6, I5, k7] + SU3D[I2, I4, k6]*SU3D[I3, k6, k8]* - (SU3D[I5, k7, k8]*SU3F[6, I1, k7] + SU3D[I1, k7, k8]* - SU3F[6, I5, k7]) + SU3D[I2, k7, k8]* - (SU3D[I4, k6, k8]*(SU3D[I3, I5, k6]*SU3F[6, I1, k7] + - SU3D[I1, I3, k6]*SU3F[6, I5, k7]) + SU3D[I3, k6, k8]* - (SU3D[I4, I5, k6]*SU3F[6, I1, k7] + SU3D[I1, I4, k6]* - SU3F[6, I5, k7]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k9]*SU3D[I2, k7, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I2, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I2, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]* - SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I2, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k9]*SU3D[I1, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k7, k9]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I3, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I5, k9]*SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k7, k9]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I3, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, I3, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I3, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k9]*SU3D[I2, k6, k7]*SU3F[I1, k7, k9]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, k8, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3D[I2, I4, k8]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k7]*SU3D[I1, I2, k8]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I1, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k8, k9]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[I1, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I2, k6, k7]*SU3F[I1, I4, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I5, k6, k7]*SU3F[I1, I4, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I2, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I4, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[I2, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I4, I5, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, I4, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k8]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I3, k6, k7]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[I1, k7, k9]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[I3, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]*SU3F[I3, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k6, k8]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k7]*SU3D[I1, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k8, k9]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[I1, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I2, k6, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I5, k6, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I2, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[I2, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3F[I2, I3, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, I3, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]*SU3F[I3, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k6, k7]*SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k6, k7]*SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, I3, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k6, k8]* - SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I4, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I3, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I3, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[I4, k6, k7]*(SU3D[I3, I5, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, I3, k8]* - (SU3F[6, I5, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I5, k6, k8]) + SU3D[I1, I3, k8]* - (SU3F[6, I5, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I5, k6, k8])) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, I4, k8]* - (SU3F[6, I5, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I5, k6, k8]) + SU3D[I1, I4, k8]* - (SU3F[6, I5, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I5, k6, k8])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*SU3D[I3, I4, k6]*(SU3D[6, I5, k8]* - (SU3D[I2, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I2, k6, k9]) + SU3D[6, I2, k8]* - (SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I5, k6, k9]) + SU3D[6, I1, k8]* - (SU3D[I5, k8, k9]*SU3F[I2, k6, k9] + SU3D[I2, k8, k9]* - SU3F[I5, k6, k9])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[6, I5, k6]*(SU3D[I4, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k8] + - SU3F[I1, I3, k8]*SU3F[I2, k6, k9]) + SU3D[I3, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I2, I4, k8] + SU3F[I1, I4, k8]* - SU3F[I2, k6, k9])) + SU3D[6, I2, k6]* - (SU3D[I4, k8, k9]*(-(SU3F[I1, k6, k9]*SU3F[I3, I5, k8]) + - SU3F[I1, I3, k8]*SU3F[I5, k6, k9]) + SU3D[I3, k8, k9]* - (-(SU3F[I1, k6, k9]*SU3F[I4, I5, k8]) + SU3F[I1, I4, k8]* - SU3F[I5, k6, k9])) + SU3D[6, I1, k6]* - (SU3D[I4, k8, k9]*(-(SU3F[I2, k6, k9]*SU3F[I3, I5, k8]) + - SU3F[I2, I3, k8]*SU3F[I5, k6, k9]) + SU3D[I3, k8, k9]* - (-(SU3F[I2, k6, k9]*SU3F[I4, I5, k8]) + SU3F[I2, I4, k8]* - SU3F[I5, k6, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I3, k9] + SU3F[I1, I3, k9]* - SU3F[I2, k6, k9]) + SU3F[6, I3, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I2, k6, k9])) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*(-(SU3F[I1, k6, k9]*SU3F[I3, I5, k9]) + - SU3F[I1, I3, k9]*SU3F[I5, k6, k9]) + SU3F[6, I3, k7]* - (-(SU3F[I1, k6, k9]*SU3F[I4, I5, k9]) + SU3F[I1, I4, k9]* - SU3F[I5, k6, k9])) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*(-(SU3F[I2, k6, k9]*SU3F[I3, I5, k9]) + - SU3F[I2, I3, k9]*SU3F[I5, k6, k9]) + SU3F[6, I3, k7]* - (-(SU3F[I2, k6, k9]*SU3F[I4, I5, k9]) + SU3F[I2, I4, k9]* - SU3F[I5, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k9]*SU3D[I2, k6, k7]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I4, k6, k7]*(SU3D[I3, I5, k6]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, I3, k6]* - (SU3F[6, I5, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I5, k7, k9]) + SU3D[I1, I3, k6]* - (SU3F[6, I5, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I5, k7, k9])) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k6]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, I4, k6]* - (SU3F[6, I5, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I5, k7, k9]) + SU3D[I1, I4, k6]* - (SU3F[6, I5, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I5, k7, k9])))/(4*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I3, k6] + SU3F[I1, I3, k6]* - SU3F[I2, k7, k9]) + SU3F[6, I3, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I4, k6] + SU3F[I1, I4, k6]* - SU3F[I2, k7, k9])) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k9]*(-(SU3F[I1, k7, k9]*SU3F[I3, I5, k6]) + - SU3F[I1, I3, k6]*SU3F[I5, k7, k9]) + SU3F[6, I3, k9]* - (-(SU3F[I1, k7, k9]*SU3F[I4, I5, k6]) + SU3F[I1, I4, k6]* - SU3F[I5, k7, k9])) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k9]*(-(SU3F[I2, k7, k9]*SU3F[I3, I5, k6]) + - SU3F[I2, I3, k6]*SU3F[I5, k7, k9]) + SU3F[6, I3, k9]* - (-(SU3F[I2, k7, k9]*SU3F[I4, I5, k6]) + SU3F[I2, I4, k6]* - SU3F[I5, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, k7, k9]*SU3F[I2, I4, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k7, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I4, k9]*SU3F[I3, k6, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I3, k9]*SU3F[I4, k6, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*(SU3D[I4, I5, k6]*SU3F[6, I3, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I2, k8, k9]) + SU3D[I3, I5, k6]*SU3F[6, I4, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I2, k8, k9]) + SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9] + SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/6)*SU3D[I3, I4, k6]*(SU3D[6, I5, k8]* - (SU3D[I2, k6, k9]*SU3F[I1, k8, k9] + SU3D[I1, k6, k9]* - SU3F[I2, k8, k9]) + SU3D[6, I2, k8]* - (SU3D[I5, k6, k9]*SU3F[I1, k8, k9] + SU3D[I1, k6, k9]* - SU3F[I5, k8, k9]) + SU3D[6, I1, k8]* - (SU3D[I5, k6, k9]*SU3F[I2, k8, k9] + SU3D[I2, k6, k9]* - SU3F[I5, k8, k9])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[I3, I4, k6]*(SU3D[6, I5, k8]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[6, I2, k8]* - (SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I5, k8, k9]) + SU3D[6, I1, k8]* - (SU3F[I2, k8, k9]*SU3F[I5, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*(SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I3, k9] + - SU3F[I1, I3, k9]*SU3F[I2, k8, k9]) + SU3D[I3, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I2, k8, k9])) + SU3D[6, I2, k7]* - (SU3D[I4, k7, k8]*(-(SU3F[I1, k8, k9]*SU3F[I3, I5, k9]) + - SU3F[I1, I3, k9]*SU3F[I5, k8, k9]) + SU3D[I3, k7, k8]* - (-(SU3F[I1, k8, k9]*SU3F[I4, I5, k9]) + SU3F[I1, I4, k9]* - SU3F[I5, k8, k9])) + SU3D[6, I1, k7]* - (SU3D[I4, k7, k8]*(-(SU3F[I2, k8, k9]*SU3F[I3, I5, k9]) + - SU3F[I2, I3, k9]*SU3F[I5, k8, k9]) + SU3D[I3, k7, k8]* - (-(SU3F[I2, k8, k9]*SU3F[I4, I5, k9]) + SU3F[I2, I4, k9]* - SU3F[I5, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (2*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]* - SUNDelta[6, I1])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (2*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]* - SUNDelta[6, I1])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[I3, I4, k6]*(SU3D[I2, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SUNDelta[6, I2] + SU3D[I1, I2, k6]*SUNDelta[6, I5]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I3, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I2, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I4, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I2, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I3, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I4, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I1, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I4, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I1, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I3, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I3, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I3, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[I3, I4, k5]*(SU3D[6, I5, k5]*SUNDelta[I1, I2] + - SU3D[6, I2, k5]*SUNDelta[I1, I5] + SU3D[6, I1, k5]*SUNDelta[I2, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I5, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I2, k5]*SU3D[I1, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I1, k5]*SU3D[I2, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[I2, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I1, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I2, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I1, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I1, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I3, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 1]*((SU3D[6, I4, I5]*SU3D[I1, I2, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I3, I5]*SU3D[I1, I2, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I4]*SU3D[I1, I2, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I5]*SU3D[I1, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I2, I4]*SU3D[I1, I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I3]*SU3D[I2, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I5, k9]*(SU3D[6, I4, k7]*(SU3D[I1, k8, k9]*SU3D[I2, k7, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k8, k9]) + SU3D[6, I2, k7]* - (SU3D[I1, k8, k9]*SU3D[I4, k7, k8] + SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]) + SU3D[6, I1, k7]* - (SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I4, k8, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*(SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I3, I4, k9] + - SU3D[I2, I3, k9]*SU3D[I4, k7, k8]) + SU3D[I1, k7, k8]* - (SU3D[I2, k8, k9]*SU3D[I3, I4, k9] + SU3D[I2, I3, k9]* - SU3D[I4, k8, k9]) + SU3D[I1, I3, k9]* - (SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I4, k8, k9])) + SU3D[6, I3, k7]* - (SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I4, I5, k9] + - SU3D[I2, I5, k9]*SU3D[I4, k7, k8]) + SU3D[I1, k7, k8]* - (SU3D[I2, k8, k9]*SU3D[I4, I5, k9] + SU3D[I2, I5, k9]* - SU3D[I4, k8, k9]) + SU3D[I1, I5, k9]* - (SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I4, I5]*SU3F[6, I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I3, I4]*SU3F[6, I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, I5]*SU3F[6, I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I3, I4]*SU3F[6, I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]* - SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I2, I5]*SU3F[6, I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, I3]*SU3F[6, I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*SU3D[I3, I5, k6]*((SU3D[I1, k7, k8]*SU3D[I4, k6, k8] + - SU3D[I1, k6, k8]*SU3D[I4, k7, k8])*SU3F[6, I2, k7] + - SU3D[I2, k7, k8]*(SU3D[I4, k6, k8]*SU3F[6, I1, k7] + - SU3D[I1, k6, k8]*SU3F[6, I4, k7]) + SU3D[I2, k6, k8]* - (SU3D[I4, k7, k8]*SU3F[6, I1, k7] + SU3D[I1, k7, k8]* - SU3F[6, I4, k7])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/4)*(SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]* - SU3F[6, I1, k7] + SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I2, k7] + SU3D[I1, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]* - SU3F[6, I2, k7] + SU3D[I1, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]* - SU3F[6, I2, k7] + SU3D[I1, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]* - SU3F[6, I2, k7] + SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k8]* - SU3F[6, I4, k7] + SU3D[I2, I5, k6]*SU3D[I3, k6, k8]* - (SU3D[I4, k7, k8]*SU3F[6, I1, k7] + SU3D[I1, k7, k8]* - SU3F[6, I4, k7]) + SU3D[I2, k7, k8]* - (SU3D[I5, k6, k8]*(SU3D[I3, I4, k6]*SU3F[6, I1, k7] + - SU3D[I1, I3, k6]*SU3F[6, I4, k7]) + SU3D[I3, k6, k8]* - (SU3D[I4, I5, k6]*SU3F[6, I1, k7] + SU3D[I1, I5, k6]* - SU3F[6, I4, k7]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I2, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I2, k7, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I2, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I3, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I3, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I3, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I5, k6, k7]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3D[I2, I5, k8]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I5, k8]* - SU3D[I2, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k7]*SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k8, k9]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I4, k8, k9]*SU3F[I1, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I2, k6, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I4, k6, k7]*SU3F[I1, I5, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I2, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I4, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, k8, k9]*SU3F[I2, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I4, I5, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, I5, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k8]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I3, k6, k7]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[I3, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]*SU3F[I3, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k6, k8]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I5, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I4, k6, k8]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I4, k6, k8])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[I5, k6, k7]*(SU3D[I3, I4, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, I3, k8]* - (SU3F[6, I4, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I4, k6, k8]) + SU3D[I1, I3, k8]* - (SU3F[6, I4, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I4, k6, k8])) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, I5, k8]* - (SU3F[6, I4, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I4, k6, k8]) + SU3D[I1, I5, k8]* - (SU3F[6, I4, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I4, k6, k8])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k6]*SU3D[I5, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k6]*SU3D[I3, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*SU3D[I3, I5, k6]*(SU3D[6, I4, k8]* - (SU3D[I2, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I2, k6, k9]) + SU3D[6, I2, k8]* - (SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I4, k6, k9]) + SU3D[6, I1, k8]* - (SU3D[I4, k8, k9]*SU3F[I2, k6, k9] + SU3D[I2, k8, k9]* - SU3F[I4, k6, k9])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I5, k8]*((SU3D[I1, k8, k9]*SU3D[I3, I4, k6] + - SU3D[I1, I3, k6]*SU3D[I4, k8, k9])*SU3F[I2, k6, k9] + - SU3D[I2, k8, k9]*(SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I3, k6]*SU3F[I4, k6, k9]) + SU3D[I2, I3, k6]* - (SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I4, k6, k9])) + SU3D[6, I3, k8]* - ((SU3D[I1, k8, k9]*SU3D[I4, I5, k6] + SU3D[I1, I5, k6]* - SU3D[I4, k8, k9])*SU3F[I2, k6, k9] + SU3D[I2, k8, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k6, k9] + SU3D[I1, I5, k6]* - SU3F[I4, k6, k9]) + SU3D[I2, I5, k6]* - (SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I4, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I3, k9] + SU3F[I1, I3, k9]* - SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (-(SU3F[I1, k6, k9]*SU3F[I3, I4, k9]) + SU3F[I1, I3, k9]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k7]* - (-(SU3F[I2, k6, k9]*SU3F[I3, I4, k9]) + SU3F[I2, I3, k9]* - SU3F[I4, k6, k9])) + SU3D[I3, k6, k7]* - (SU3F[6, I4, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I5, k9] + - SU3F[I1, I5, k9]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k6, k9]*SU3F[I4, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k6, k9]*SU3F[I4, I5, k9] + SU3F[I2, I5, k9]* - SU3F[I4, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k6]*(SU3D[I4, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I4, k7, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[I5, k6, k7]*(SU3D[I3, I4, k6]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, I3, k6]* - (SU3F[6, I4, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, I3, k6]* - (SU3F[6, I4, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I4, k7, k9])) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k6]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, I5, k6]* - (SU3F[6, I4, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, I5, k6]* - (SU3F[6, I4, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I4, k7, k9])))/(4*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[6, I5, k9]*(SU3D[I4, k6, k7]*(SU3F[I1, k7, k9]*SU3F[I2, I3, k6] + - SU3F[I1, I3, k6]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (-(SU3F[I1, k7, k9]*SU3F[I3, I4, k6]) + SU3F[I1, I3, k6]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (-(SU3F[I2, k7, k9]*SU3F[I3, I4, k6]) + SU3F[I2, I3, k6]* - SU3F[I4, k7, k9])) + SU3D[6, I3, k9]* - (SU3D[I4, k6, k7]*(SU3F[I1, k7, k9]*SU3F[I2, I5, k6] + - SU3F[I1, I5, k6]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[I1, k7, k9]*SU3F[I4, I5, k6] + SU3F[I1, I5, k6]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k7, k9]*SU3F[I4, I5, k6] + SU3F[I2, I5, k6]* - SU3F[I4, k7, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I3, k6] + SU3F[I1, I3, k6]* - SU3F[I2, k7, k9]) + SU3F[6, I2, k9]* - (-(SU3F[I1, k7, k9]*SU3F[I3, I4, k6]) + SU3F[I1, I3, k6]* - SU3F[I4, k7, k9]) + SU3F[6, I1, k9]* - (-(SU3F[I2, k7, k9]*SU3F[I3, I4, k6]) + SU3F[I2, I3, k6]* - SU3F[I4, k7, k9])) + SU3D[I3, k6, k7]* - (SU3F[6, I4, k9]*(SU3F[I1, k7, k9]*SU3F[I2, I5, k6] + - SU3F[I1, I5, k6]*SU3F[I2, k7, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I4, I5, k6] + SU3F[I1, I5, k6]* - SU3F[I4, k7, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k7, k9]*SU3F[I4, I5, k6] + SU3F[I2, I5, k6]* - SU3F[I4, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I5, k9]*SU3F[I3, k6, k8]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*(SU3D[I4, I5, k6]*SU3F[6, I3, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I2, k8, k9]) + SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I2, k8, k9]) + SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/6)*SU3D[I3, I5, k6]*(SU3D[6, I4, k8]* - (SU3D[I2, k6, k9]*SU3F[I1, k8, k9] + SU3D[I1, k6, k9]* - SU3F[I2, k8, k9]) + SU3D[6, I2, k8]* - (SU3D[I4, k6, k9]*SU3F[I1, k8, k9] + SU3D[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[6, I1, k8]* - (SU3D[I4, k6, k9]*SU3F[I2, k8, k9] + SU3D[I2, k6, k9]* - SU3F[I4, k8, k9])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[I3, I5, k6]*(SU3D[6, I4, k8]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[6, I2, k8]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[6, I1, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I5, k6]*(SU3F[6, I4, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I2, k8, k9]) + SU3F[6, I2, k8]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3F[6, I1, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[6, I5, k8]*((SU3D[I1, k6, k9]*SU3D[I3, I4, k6] + - SU3D[I1, I3, k6]*SU3D[I4, k6, k9])*SU3F[I2, k8, k9] + - SU3D[I2, k6, k9]*(SU3D[I3, I4, k6]*SU3F[I1, k8, k9] + - SU3D[I1, I3, k6]*SU3F[I4, k8, k9]) + SU3D[I2, I3, k6]* - (SU3D[I4, k6, k9]*SU3F[I1, k8, k9] + SU3D[I1, k6, k9]* - SU3F[I4, k8, k9])) + SU3D[6, I3, k8]* - ((SU3D[I1, k6, k9]*SU3D[I4, I5, k6] + SU3D[I1, I5, k6]* - SU3D[I4, k6, k9])*SU3F[I2, k8, k9] + SU3D[I2, k6, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k8, k9] + SU3D[I1, I5, k6]* - SU3F[I4, k8, k9]) + SU3D[I2, I5, k6]* - (SU3D[I4, k6, k9]*SU3F[I1, k8, k9] + SU3D[I1, k6, k9]* - SU3F[I4, k8, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[6, I5, k7]*(SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I3, k9] + - SU3F[I1, I3, k9]*SU3F[I2, k8, k9]) + SU3D[I2, k7, k8]* - (-(SU3F[I1, k8, k9]*SU3F[I3, I4, k9]) + SU3F[I1, I3, k9]* - SU3F[I4, k8, k9]) + SU3D[I1, k7, k8]* - (-(SU3F[I2, k8, k9]*SU3F[I3, I4, k9]) + SU3F[I2, I3, k9]* - SU3F[I4, k8, k9])) + SU3D[6, I3, k7]* - (SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I5, k9] + - SU3F[I1, I5, k9]*SU3F[I2, k8, k9]) + SU3D[I2, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I4, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I4, k8, k9]) + SU3D[I1, k7, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, I5, k9] + SU3F[I2, I5, k9]* - SU3F[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*(SU3D[I3, I4, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[I2, I3, k6]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[I1, I3, k6]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])) + SU3D[6, I3, k8]* - (SU3D[I4, I5, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[I2, I5, k6]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[I1, I5, k6]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*(SU3D[6, I5, k7]*(SU3F[I1, k8, k9]* - (SU3F[I2, k7, k9]*SU3F[I3, I4, k8] - SU3F[I2, I3, k8]* - SU3F[I4, k7, k9]) + SU3F[I1, k7, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, I4, k8] - SU3F[I2, I3, k8]* - SU3F[I4, k8, k9]) - SU3F[I1, I3, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, k7, k9] + SU3F[I2, k7, k9]* - SU3F[I4, k8, k9])) - SU3D[6, I3, k7]* - (SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I4, I5, k8] + - SU3F[I2, I5, k8]*SU3F[I4, k7, k9]) + SU3F[I1, k7, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, I5, k8] + SU3F[I2, I5, k8]* - SU3F[I4, k8, k9]) + SU3F[I1, I5, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, k7, k9] + SU3F[I2, k7, k9]* - SU3F[I4, k8, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3F[6, I5, k7]*(SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I3, I4, k8] - - SU3F[I2, I3, k8]*SU3F[I4, k7, k9]) + SU3F[I1, k7, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, I4, k8] - SU3F[I2, I3, k8]* - SU3F[I4, k8, k9]) - SU3F[I1, I3, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, k7, k9] + SU3F[I2, k7, k9]* - SU3F[I4, k8, k9])) - SU3F[6, I3, k7]* - (SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I4, I5, k8] + - SU3F[I2, I5, k8]*SU3F[I4, k7, k9]) + SU3F[I1, k7, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, I5, k8] + SU3F[I2, I5, k8]* - SU3F[I4, k8, k9]) + SU3F[I1, I5, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, k7, k9] + SU3F[I2, k7, k9]* - SU3F[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k7]*SU3D[I1, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k8, k9]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k8, k9]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I3, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I3, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I4, k8, k9]*SU3F[I1, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I2, k6, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I4, k6, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, k8, k9]*SU3F[I2, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]*SU3F[I3, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k6, k7]*SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k6, k7]*SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, I3, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, I4, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k6, k8]* - SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I2, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I1])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I2, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I4, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I2, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I3, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I4, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I4, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[I3, I5, k5]*(SU3D[6, I4, k5]*SUNDelta[I1, I2] + - SU3D[6, I2, k5]*SUNDelta[I1, I4] + SU3D[6, I1, k5]*SUNDelta[I2, I4]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I3, I5, k5]*(SU3F[6, I4, k5]*SUNDelta[I1, I2] + - SU3F[6, I2, k5]*SUNDelta[I1, I4] + SU3F[6, I1, k5]*SUNDelta[I2, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I3, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I1, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I4, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[I2, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I2, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I1, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I1, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I3, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 1]* -((-4*(SU3D[6, I4, I5]*SU3D[I1, I2, I3] + SU3D[6, I3, I5]* - SU3D[I1, I2, I4] + SU3D[6, I3, I4]*SU3D[I1, I2, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I5]*SU3D[I1, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I4]*SU3D[I1, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I3]*SU3D[I2, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I1, k8, k9]*SU3D[I2, k6, k9] + SU3D[I1, k6, k9]*SU3D[I2, k8, k9])* - (SU3D[6, I5, k8]*SU3D[I3, I4, k6] + SU3D[6, I4, k8]*SU3D[I3, I5, k6] + - SU3D[6, I3, k8]*SU3D[I4, I5, k6]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*SU3D[I2, I4, I5]*SU3F[6, I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I3, I5]*SU3F[6, I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I3, I4]*SU3F[6, I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I4, I5]*SU3F[6, I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I3, I5]*SU3F[6, I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I3, I4]*SU3F[6, I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]* - SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*(SU3D[I3, k7, k8]*SU3D[I4, I5, k6] + SU3D[I3, I5, k6]* - SU3D[I4, k7, k8] + SU3D[I3, I4, k6]*SU3D[I5, k7, k8])* - (SU3D[I2, k6, k8]*SU3F[6, I1, k7] + SU3D[I1, k6, k8]*SU3F[6, I2, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/6)*(SU3D[I3, k6, k8]*SU3D[I4, I5, k6] + SU3D[I3, I5, k6]* - SU3D[I4, k6, k8] + SU3D[I3, I4, k6]*SU3D[I5, k6, k8])* - (SU3D[I2, k7, k8]*SU3F[6, I1, k7] + SU3D[I1, k7, k8]*SU3F[6, I2, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k9]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k9]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I2, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I2, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I2, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I2, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I2, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I2, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I2, k8]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I4, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k7, k9]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k7, k9]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*(SU3D[6, I5, k7]*SU3D[I3, I4, k8] + SU3D[6, I4, k7]* - SU3D[I3, I5, k8] + SU3D[6, I3, k7]*SU3D[I4, I5, k8])* - (SU3D[I2, k6, k7]*SU3F[I1, k6, k8] + SU3D[I1, k6, k7]* - SU3F[I2, k6, k8]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[I3, k6, k7]*SU3D[I4, I5, k8] + SU3D[I3, I5, k8]*SU3D[I4, k6, k7] + - SU3D[I3, I4, k8]*SU3D[I5, k6, k7])*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/3)*(SU3D[6, I5, k6]*SU3D[I3, I4, k8] + SU3D[6, I4, k6]* - SU3D[I3, I5, k8] + SU3D[6, I3, k6]*SU3D[I4, I5, k8])* - (SU3D[I2, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I2, k6, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I5, k6]*(SU3D[I4, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k8] + - SU3F[I1, I3, k8]*SU3F[I2, k6, k9]) + SU3D[I3, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I2, I4, k8] + SU3F[I1, I4, k8]* - SU3F[I2, k6, k9])) + SU3D[6, I4, k6]* - (SU3D[I5, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k8] + - SU3F[I1, I3, k8]*SU3F[I2, k6, k9]) + SU3D[I3, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I2, I5, k8] + SU3F[I1, I5, k8]* - SU3F[I2, k6, k9])) + SU3D[6, I3, k6]* - (SU3D[I5, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I2, I4, k8] + - SU3F[I1, I4, k8]*SU3F[I2, k6, k9]) + SU3D[I4, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I2, I5, k8] + SU3F[I1, I5, k8]* - SU3F[I2, k6, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k9] + - SU3F[I1, I3, k9]*SU3F[I2, k6, k9]) + SU3D[I3, k6, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I2, k6, k9])) + SU3D[6, I4, k7]* - (SU3D[I5, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k9] + - SU3F[I1, I3, k9]*SU3F[I2, k6, k9]) + SU3D[I3, k6, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I2, k6, k9])) + SU3D[6, I3, k7]* - (SU3D[I5, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I4, k9] + - SU3F[I1, I4, k9]*SU3F[I2, k6, k9]) + SU3D[I4, k6, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I2, k6, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I3, k9] + SU3F[I1, I3, k9]* - SU3F[I2, k6, k9]) + SU3F[6, I3, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I2, k6, k9])) + SU3D[I4, k6, k7]* - (SU3F[6, I5, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k9] + - SU3F[I1, I3, k9]*SU3F[I2, k6, k9]) + SU3F[6, I3, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I2, k6, k9])) + SU3D[I3, k6, k7]* - (SU3F[6, I5, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I4, k9] + - SU3F[I1, I4, k9]*SU3F[I2, k6, k9]) + SU3F[6, I4, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I2, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I3, k6, k7]*SU3D[I4, I5, k6] + SU3D[I3, I5, k6]*SU3D[I4, k6, k7] + - SU3D[I3, I4, k6]*SU3D[I5, k6, k7])*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I3, k6] + SU3F[I1, I3, k6]* - SU3F[I2, k7, k9]) + SU3F[6, I3, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I4, k6] + SU3F[I1, I4, k6]* - SU3F[I2, k7, k9])) + SU3D[I4, k6, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k7, k9]*SU3F[I2, I3, k6] + - SU3F[I1, I3, k6]*SU3F[I2, k7, k9]) + SU3F[6, I3, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I5, k6] + SU3F[I1, I5, k6]* - SU3F[I2, k7, k9])) + SU3D[I3, k6, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k7, k9]*SU3F[I2, I4, k6] + - SU3F[I1, I4, k6]*SU3F[I2, k7, k9]) + SU3F[6, I4, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I5, k6] + SU3F[I1, I5, k6]* - SU3F[I2, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[6, I5, k6]*SU3D[I3, I4, k8] + SU3D[6, I4, k6]*SU3D[I3, I5, k8] + - SU3D[6, I3, k6]*SU3D[I4, I5, k8])*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*(SU3D[I4, I5, k6]*SU3F[6, I3, k8] + SU3D[I3, I5, k6]* - SU3F[6, I4, k8] + SU3D[I3, I4, k6]*SU3F[6, I5, k8])* - (SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I2, k8, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[6, I5, k7]*(SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I3, k9] + - SU3F[I1, I3, k9]*SU3F[I2, k8, k9]) + SU3D[I3, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I2, k8, k9])) + SU3D[6, I4, k7]* - (SU3D[I5, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I3, k9] + - SU3F[I1, I3, k9]*SU3F[I2, k8, k9]) + SU3D[I3, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I2, k8, k9])) + SU3D[6, I3, k7]* - (SU3D[I5, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I4, k9] + - SU3F[I1, I4, k9]*SU3F[I2, k8, k9]) + SU3D[I4, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I2, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k8, k9]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k9]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I2, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I2, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, I4, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, I5, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k8]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k8]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k8, k9]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I2, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, I3, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k7, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k8, k9]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I2, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, I3, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, I4, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k7, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, I4, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I3, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, I3, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k7, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, I3, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*SU3D[I4, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I3, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I3, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I4, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I3, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I3, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I2, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/9)*SU3D[I2, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/9)*SU3D[I2, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/9)*SU3D[I2, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*(SU3D[6, I5, k5]*SU3D[I3, I4, k5] + SU3D[6, I4, k5]*SU3D[I3, I5, k5] + - SU3D[6, I3, k5]*SU3D[I4, I5, k5])*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[I4, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I3, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I3, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I5, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I2, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I2, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I2, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I2, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I2, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I2, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I4, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I1, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I1, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*(SU3D[I4, I5, k5]*(SU3F[6, I2, k5]*SUNDelta[I1, I3] + - SU3F[6, I1, k5]*SUNDelta[I2, I3]) + SU3D[I3, I5, k5]* - (SU3F[6, I2, k5]*SUNDelta[I1, I4] + SU3F[6, I1, k5]* - SUNDelta[I2, I4]) + SU3D[I3, I4, k5]* - (SU3F[6, I2, k5]*SUNDelta[I1, I5] + SU3F[6, I1, k5]* - SUNDelta[I2, I5])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (4*(SUNDelta[6, I5]*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I3]*SUNDelta[I2, I4]) + SUNDelta[6, I4]* - (SUNDelta[I1, I5]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I5]) + SUNDelta[6, I3]* - (SUNDelta[I1, I5]*SUNDelta[I2, I4] + SUNDelta[I1, I4]* - SUNDelta[I2, I5])))/(27*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (4*SU3D[6, I5, k5]*SU3D[I1, I2, k5]* - SUNDelta[I3, I4])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (((4*I)/9)*SU3D[I1, I2, k5]* - SU3F[6, I5, k5]*SUNDelta[I3, I4])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (((2*I)/9)*SU3D[6, I2, k6]* - SU3F[I1, I5, k6]*SUNDelta[I3, I4])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (2*SU3F[6, I2, k6]*SU3F[I1, I5, k6]* - SUNDelta[I3, I4])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I4, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I3, k5]*SU3D[I1, I2, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k6]*SU3F[I2, I3, k6]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I3, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 1]*((-2*SU3D[6, I4, I5]*SU3D[I1, I2, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I5]*SU3D[I1, I2, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I4]*SU3D[I1, I2, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I5]*SU3D[I1, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I4]*SU3D[I1, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I3]*SU3D[I2, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*(SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I3, I4, k9] + - SU3D[I2, I4, k9]*SU3D[I3, k7, k8]) + SU3D[I1, k7, k8]* - (SU3D[I2, k8, k9]*SU3D[I3, I4, k9] + SU3D[I2, I4, k9]* - SU3D[I3, k8, k9]) + SU3D[I1, I4, k9]* - (SU3D[I2, k8, k9]*SU3D[I3, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k8, k9])) + SU3D[6, I4, k7]* - (SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I3, I5, k9] + - SU3D[I2, I5, k9]*SU3D[I3, k7, k8]) + SU3D[I1, k7, k8]* - (SU3D[I2, k8, k9]*SU3D[I3, I5, k9] + SU3D[I2, I5, k9]* - SU3D[I3, k8, k9]) + SU3D[I1, I5, k9]* - (SU3D[I2, k8, k9]*SU3D[I3, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I5, k6]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I3, I5]*SU3F[6, I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I3, I4]*SU3F[6, I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/4)*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, I5]*SU3F[6, I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I3, I4]*SU3F[6, I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/4)*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]* - SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, I5]*SU3F[6, I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I2, I4]*SU3F[6, I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k8]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*SU3D[I4, I5, k6]*((SU3D[I1, k7, k8]*SU3D[I3, k6, k8] + - SU3D[I1, k6, k8]*SU3D[I3, k7, k8])*SU3F[6, I2, k7] + - SU3D[I2, k7, k8]*(SU3D[I3, k6, k8]*SU3F[6, I1, k7] + - SU3D[I1, k6, k8]*SU3F[6, I3, k7]) + SU3D[I2, k6, k8]* - (SU3D[I3, k7, k8]*SU3F[6, I1, k7] + SU3D[I1, k7, k8]* - SU3F[6, I3, k7])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k9]*SU3D[I2, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I3, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I2, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k9]*SU3D[I1, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3F[I1, k7, k9]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, k8, k9]*SU3F[I2, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I4, k6, k7]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I3, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k7, k9]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I4, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9]*SU3F[I2, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3F[I1, I4, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k7, k9]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I4, k6, k7]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k9]*SU3D[I2, k6, k7]*SU3F[I1, k7, k9]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I4, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I4, I5, k8]*(SU3D[I3, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I3, k6, k8]) + SU3D[I1, k6, k7]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I3, k6, k8])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k6]*SU3D[I5, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k6]*SU3D[I4, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k8]*SU3D[I4, I5, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I5, k8]*((SU3D[I1, k8, k9]*SU3D[I3, I4, k6] + - SU3D[I1, I4, k6]*SU3D[I3, k8, k9])*SU3F[I2, k6, k9] + - SU3D[I2, k8, k9]*(SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I4, k6]*SU3F[I3, k6, k9]) + SU3D[I2, I4, k6]* - (SU3D[I3, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I3, k6, k9])) + SU3D[6, I4, k8]* - ((SU3D[I1, k8, k9]*SU3D[I3, I5, k6] + SU3D[I1, I5, k6]* - SU3D[I3, k8, k9])*SU3F[I2, k6, k9] + SU3D[I2, k8, k9]* - (SU3D[I3, I5, k6]*SU3F[I1, k6, k9] + SU3D[I1, I5, k6]* - SU3F[I3, k6, k9]) + SU3D[I2, I5, k6]* - (SU3D[I3, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I3, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, I4, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[I4, I5, k6]*(SU3D[I3, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I3, k7, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*SU3D[I4, I5, k6]*(SU3F[6, I3, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I2, k8, k9]) + SU3F[6, I2, k8]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]) + SU3F[6, I1, k8]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[6, I5, k8]*((SU3D[I1, k6, k9]*SU3D[I3, I4, k6] + - SU3D[I1, I4, k6]*SU3D[I3, k6, k9])*SU3F[I2, k8, k9] + - SU3D[I2, k6, k9]*(SU3D[I3, I4, k6]*SU3F[I1, k8, k9] + - SU3D[I1, I4, k6]*SU3F[I3, k8, k9]) + SU3D[I2, I4, k6]* - (SU3D[I3, k6, k9]*SU3F[I1, k8, k9] + SU3D[I1, k6, k9]* - SU3F[I3, k8, k9])) + SU3D[6, I4, k8]* - ((SU3D[I1, k6, k9]*SU3D[I3, I5, k6] + SU3D[I1, I5, k6]* - SU3D[I3, k6, k9])*SU3F[I2, k8, k9] + SU3D[I2, k6, k9]* - (SU3D[I3, I5, k6]*SU3F[I1, k8, k9] + SU3D[I1, I5, k6]* - SU3F[I3, k8, k9]) + SU3D[I2, I5, k6]* - (SU3D[I3, k6, k9]*SU3F[I1, k8, k9] + SU3D[I1, k6, k9]* - SU3F[I3, k8, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I5, k8]*(SU3D[I3, I4, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[I2, I4, k6]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]) + SU3D[I1, I4, k6]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])) + SU3D[6, I4, k8]* - (SU3D[I3, I5, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[I2, I5, k6]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]) + SU3D[I1, I5, k6]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/12)*(SU3D[6, I5, k7]*(SU3F[I1, k8, k9]* - (SU3F[I2, k7, k9]*SU3F[I3, I4, k8] + SU3F[I2, I4, k8]* - SU3F[I3, k7, k9]) + SU3F[I1, k7, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, I4, k8] + SU3F[I2, I4, k8]* - SU3F[I3, k8, k9]) + SU3F[I1, I4, k8]* - (SU3F[I2, k8, k9]*SU3F[I3, k7, k9] + SU3F[I2, k7, k9]* - SU3F[I3, k8, k9])) + SU3D[6, I4, k7]* - (SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I3, I5, k8] + - SU3F[I2, I5, k8]*SU3F[I3, k7, k9]) + SU3F[I1, k7, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, I5, k8] + SU3F[I2, I5, k8]* - SU3F[I3, k8, k9]) + SU3F[I1, I5, k8]* - (SU3F[I2, k8, k9]*SU3F[I3, k7, k9] + SU3F[I2, k7, k9]* - SU3F[I3, k8, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3F[6, I5, k7]*(SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I3, I4, k8] + - SU3F[I2, I4, k8]*SU3F[I3, k7, k9]) + SU3F[I1, k7, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, I4, k8] + SU3F[I2, I4, k8]* - SU3F[I3, k8, k9]) + SU3F[I1, I4, k8]* - (SU3F[I2, k8, k9]*SU3F[I3, k7, k9] + SU3F[I2, k7, k9]* - SU3F[I3, k8, k9])) + SU3F[6, I4, k7]* - (SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I3, I5, k8] + - SU3F[I2, I5, k8]*SU3F[I3, k7, k9]) + SU3F[I1, k7, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, I5, k8] + SU3F[I2, I5, k8]* - SU3F[I3, k8, k9]) + SU3F[I1, I5, k8]* - (SU3F[I2, k8, k9]*SU3F[I3, k7, k9] + SU3F[I2, k7, k9]* - SU3F[I3, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I5, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k8, k9]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I5, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I5, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, k8, k9]*SU3F[I1, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I2, k6, k7]*SU3F[I1, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I3, k6, k7]*SU3F[I1, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]*SU3F[I2, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k6, k7]*SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]*SU3F[I3, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k6, k7]*SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k6, k7]*SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k6, k8]* - SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I5, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k7]*SU3D[I1, k6, k7]*SU3D[I2, I4, k8]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I1, I2, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k8, k9]*SU3F[I2, I4, k9]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k8, k9]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I4, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I4, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, k8, k9]*SU3F[I1, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I2, k6, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I3, k6, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]*SU3F[I2, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k6, k7]*SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]*SU3F[I3, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k6, k7]*SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k6, k7]*SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, I4, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, I4, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k6, k8]* - SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I4, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I2, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (2*SU3D[I2, I5, k6]*SU3D[I3, I4, k6]* - SUNDelta[6, I1])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (2*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]* - SUNDelta[6, I1])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (2*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]* - SUNDelta[6, I1])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SU3D[6, I3, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I2, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I2, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I3, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I2, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I3, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I1, k5]*SU3D[I4, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I4, I5, k5]*(SU3F[6, I3, k5]*SUNDelta[I1, I2] + - SU3F[6, I2, k5]*SUNDelta[I1, I3] + SU3F[6, I1, k5]*SUNDelta[I2, I3]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I5, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I3, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I3, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I3, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I1, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I1, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I3, k5]*SU3D[I1, I2, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I2, k5]*SU3D[I1, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[I2, I3, k5]*SU3F[6, I1, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 1]*((SU3D[6, I4, I5]*SU3D[I1, I2, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I3, I5]*SU3D[I1, I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I4]*SU3D[I1, I2, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I5]*SU3D[I1, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I2, I4]*SU3D[I1, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I3]*SU3D[I2, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*(SU3D[I3, k8, k9]*(SU3D[I1, I4, k6]*SU3D[I2, k6, k9] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k9]) + SU3D[I1, k8, k9]* - (SU3D[I2, k6, k9]*SU3D[I3, I4, k6] + SU3D[I2, I3, k6]* - SU3D[I4, k6, k9])) + SU3D[6, I3, k8]* - (SU3D[I1, k8, k9]*(SU3D[I2, k6, k9]*SU3D[I4, I5, k6] + - SU3D[I2, I5, k6]*SU3D[I4, k6, k9]) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k9] + SU3D[I1, I2, k6]* - SU3D[I4, k6, k9])*SU3D[I5, k8, k9]) + SU3D[6, I1, k8]* - (SU3D[I4, k6, k9]*(SU3D[I2, I5, k6]*SU3D[I3, k8, k9] + - SU3D[I2, I3, k6]*SU3D[I5, k8, k9]) + SU3D[I2, k6, k9]* - (SU3D[I3, k8, k9]*SU3D[I4, I5, k6] + SU3D[I3, I4, k6]* - SU3D[I5, k8, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*(SU3D[I3, k8, k9]*(SU3D[I1, I4, k9]*SU3D[I2, k7, k8] + - SU3D[I1, I2, k9]*SU3D[I4, k7, k8]) + SU3D[I1, k8, k9]* - (SU3D[I2, k7, k8]*SU3D[I3, I4, k9] + SU3D[I2, I3, k9]* - SU3D[I4, k7, k8])) + SU3D[6, I3, k7]* - (SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I4, I5, k9] + - SU3D[I2, I5, k9]*SU3D[I4, k7, k8]) + - (SU3D[I1, I4, k9]*SU3D[I2, k7, k8] + SU3D[I1, I2, k9]* - SU3D[I4, k7, k8])*SU3D[I5, k8, k9]) + SU3D[6, I1, k7]* - (SU3D[I4, k7, k8]*(SU3D[I2, I5, k9]*SU3D[I3, k8, k9] + - SU3D[I2, I3, k9]*SU3D[I5, k8, k9]) + SU3D[I2, k7, k8]* - (SU3D[I3, k8, k9]*SU3D[I4, I5, k9] + SU3D[I3, I4, k9]* - SU3D[I5, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, I5]*SU3F[6, I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I3, I5]*SU3F[6, I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/4)*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I4, I5]*SU3F[6, I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I3, I4]*SU3F[6, I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, I5]*SU3F[6, I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I2, I3]*SU3F[6, I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/3)*(SU3D[I2, k7, k8]*SU3D[I4, k6, k8] + SU3D[I2, k6, k8]* - SU3D[I4, k7, k8])*(SU3D[I3, I5, k6]*SU3F[6, I1, k7] + - SU3D[I1, I5, k6]*SU3F[6, I3, k7] + SU3D[I1, I3, k6]*SU3F[6, I5, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*(SU3D[I2, k7, k8]*((SU3D[I1, k6, k8]*SU3D[I4, I5, k6] + - SU3D[I1, I4, k6]*SU3D[I5, k6, k8])*SU3F[6, I3, k7] + - SU3D[I3, k6, k8]*(SU3D[I4, I5, k6]*SU3F[6, I1, k7] + - SU3D[I1, I4, k6]*SU3F[6, I5, k7]) + SU3D[I3, I4, k6]* - (SU3D[I5, k6, k8]*SU3F[6, I1, k7] + SU3D[I1, k6, k8]* - SU3F[6, I5, k7])) + SU3D[I4, k7, k8]* - (SU3D[I2, I5, k6]*(SU3D[I3, k6, k8]*SU3F[6, I1, k7] + - SU3D[I1, k6, k8]*SU3F[6, I3, k7]) + SU3D[I2, I3, k6]* - (SU3D[I5, k6, k8]*SU3F[6, I1, k7] + SU3D[I1, k6, k8]* - SU3F[6, I5, k7]) + SU3D[I1, I2, k6]* - (SU3D[I5, k6, k8]*SU3F[6, I3, k7] + SU3D[I3, k6, k8]* - SU3F[6, I5, k7]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k7, k9]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I3, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k7, k9]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k7]*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I1, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I3, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[I1, I4, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I3, k6, k7]*SU3F[I1, I4, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I5, k6, k7]*SU3F[I1, I4, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I4, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k7, k9]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, k7, k9]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*(SU3D[6, I5, k9]*(SU3D[I3, k7, k9]*(SU3D[I4, k6, k7]* - SU3F[I1, I2, k6] + SU3D[I2, k6, k7]*SU3F[I1, I4, k6]) + - SU3D[I1, k7, k9]*(-(SU3D[I4, k6, k7]*SU3F[I2, I3, k6]) + - SU3D[I2, k6, k7]*SU3F[I3, I4, k6])) + SU3D[6, I3, k9]* - (SU3D[I4, k6, k7]*(SU3D[I5, k7, k9]*SU3F[I1, I2, k6] - - SU3D[I1, k7, k9]*SU3F[I2, I5, k6]) + SU3D[I2, k6, k7]* - (SU3D[I5, k7, k9]*SU3F[I1, I4, k6] - SU3D[I1, k7, k9]* - SU3F[I4, I5, k6])) - SU3D[6, I1, k9]* - (SU3D[I4, k6, k7]*(SU3D[I5, k7, k9]*SU3F[I2, I3, k6] + - SU3D[I3, k7, k9]*SU3F[I2, I5, k6]) + SU3D[I2, k6, k7]* - (-(SU3D[I5, k7, k9]*SU3F[I3, I4, k6]) + SU3D[I3, k7, k9]* - SU3F[I4, I5, k6]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[I4, k7, k8]*(SU3D[I5, k6, k7]*(SU3F[6, I3, k8]*SU3F[I1, I2, k6] - - SU3F[6, I1, k8]*SU3F[I2, I3, k6]) + SU3D[I3, k6, k7]* - (SU3F[6, I5, k8]*SU3F[I1, I2, k6] - SU3F[6, I1, k8]* - SU3F[I2, I5, k6]) - SU3D[I1, k6, k7]* - (SU3F[6, I5, k8]*SU3F[I2, I3, k6] + SU3F[6, I3, k8]* - SU3F[I2, I5, k6])) + SU3D[I2, k7, k8]* - (SU3D[I5, k6, k7]*(SU3F[6, I3, k8]*SU3F[I1, I4, k6] + - SU3F[6, I1, k8]*SU3F[I3, I4, k6]) + SU3D[I3, k6, k7]* - (SU3F[6, I5, k8]*SU3F[I1, I4, k6] - SU3F[6, I1, k8]* - SU3F[I4, I5, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k8]*SU3F[I3, I4, k6] - SU3F[6, I3, k8]* - SU3F[I4, I5, k6])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k8, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, k7, k9]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*(SU3D[6, I5, k7]*(SU3D[I3, k8, k9]* - (SU3D[I4, k7, k8]*SU3F[I1, I2, k9] + SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]) + SU3D[I1, k8, k9]* - (-(SU3D[I4, k7, k8]*SU3F[I2, I3, k9]) + SU3D[I2, k7, k8]* - SU3F[I3, I4, k9])) + SU3D[6, I3, k7]* - (SU3D[I4, k7, k8]*(SU3D[I5, k8, k9]*SU3F[I1, I2, k9] - - SU3D[I1, k8, k9]*SU3F[I2, I5, k9]) + SU3D[I2, k7, k8]* - (SU3D[I5, k8, k9]*SU3F[I1, I4, k9] - SU3D[I1, k8, k9]* - SU3F[I4, I5, k9])) - SU3D[6, I1, k7]* - (SU3D[I4, k7, k8]*(SU3D[I5, k8, k9]*SU3F[I2, I3, k9] + - SU3D[I3, k8, k9]*SU3F[I2, I5, k9]) + SU3D[I2, k7, k8]* - (-(SU3D[I5, k8, k9]*SU3F[I3, I4, k9]) + SU3D[I3, k8, k9]* - SU3F[I4, I5, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k7]*SU3D[I1, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I1, I5, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[I1, I2, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I3, k6, k7]*SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I5, k6, k7]*SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[I2, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3F[I2, I3, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, I3, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]*SU3F[I2, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k6, k7]*SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, I3, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I2, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I3, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((SU3D[I4, k6, k7]*SU3F[6, I2, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k7])* - (SU3D[I3, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I3, k6, k8] + SU3D[I1, I3, k8]*SU3F[I5, k6, k8]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8] + - SU3D[I3, I4, k8]*SU3F[6, I2, k7]*(SU3D[I5, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3F[I5, k6, k8]) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k8] + - (SU3D[I1, I4, k8]*SU3F[6, I2, k7] + SU3D[I1, I2, k8]*SU3F[6, I4, k7])* - SU3F[I5, k6, k8]))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/6)*(SU3D[6, I4, k8]*SU3D[I2, k8, k9] + SU3D[6, I2, k8]* - SU3D[I4, k8, k9])*(SU3D[I3, I5, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I5, k6]*SU3F[I3, k6, k9] + SU3D[I1, I3, k6]* - SU3F[I5, k6, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[6, I5, k8]*(SU3D[I4, k8, k9]* - (SU3D[I2, I3, k6]*SU3F[I1, k6, k9] + SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + SU3D[I1, I4, k6]* - SU3F[I3, k6, k9])) + SU3D[6, I3, k8]* - (SU3D[I4, k8, k9]*(SU3D[I2, I5, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k6]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k6, k9] + SU3D[I1, I4, k6]* - SU3F[I5, k6, k9])) + SU3D[6, I1, k8]* - (SU3D[I4, k8, k9]*(SU3D[I2, I5, k6]*SU3F[I3, k6, k9] + - SU3D[I2, I3, k6]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I4, I5, k6]*SU3F[I3, k6, k9] + SU3D[I3, I4, k6]* - SU3F[I5, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/4)*(SU3D[6, I5, k6]*(SU3D[I4, k8, k9]*(SU3D[I2, I3, k8]* - SU3F[I1, k6, k9] + SU3D[I1, I2, k8]*SU3F[I3, k6, k9]) + - SU3D[I2, k8, k9]*(SU3D[I3, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I1, I4, k8]*SU3F[I3, k6, k9])) + SU3D[6, I3, k6]* - (SU3D[I4, k8, k9]*(SU3D[I2, I5, k8]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k8]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I4, k8]* - SU3F[I5, k6, k9])) + SU3D[6, I1, k6]* - (SU3D[I4, k8, k9]*(SU3D[I2, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I2, I3, k8]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I4, I5, k8]*SU3F[I3, k6, k9] + SU3D[I3, I4, k8]* - SU3F[I5, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I5, k6]*(SU3D[I4, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k8] - - SU3F[I1, I2, k8]*SU3F[I3, k6, k9]) - SU3D[I2, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I3, I4, k8] + SU3F[I1, I4, k8]* - SU3F[I3, k6, k9])) + SU3D[6, I3, k6]* - (SU3D[I4, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I2, I5, k8] - - SU3F[I1, I2, k8]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I4, I5, k8] - SU3F[I1, I4, k8]* - SU3F[I5, k6, k9])) + SU3D[6, I1, k6]* - (SU3D[I4, k8, k9]*(SU3F[I2, I5, k8]*SU3F[I3, k6, k9] + - SU3F[I2, I3, k8]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3F[I3, k6, k9]*SU3F[I4, I5, k8] - SU3F[I3, I4, k8]* - SU3F[I5, k6, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I3, k9] - SU3F[I1, I2, k9]* - SU3F[I3, k6, k9]) - SU3F[6, I2, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I3, k6, k9])) + SU3D[I3, k6, k7]* - (SU3F[6, I4, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I5, k9] - - SU3F[I1, I2, k9]*SU3F[I5, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k6, k9]*SU3F[I4, I5, k9] - SU3F[I1, I4, k9]* - SU3F[I5, k6, k9])) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*(SU3F[I2, I5, k9]*SU3F[I3, k6, k9] + - SU3F[I2, I3, k9]*SU3F[I5, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[I3, k6, k9]*SU3F[I4, I5, k9] - SU3F[I3, I4, k9]* - SU3F[I5, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I4, k6, k7]*SU3F[6, I2, k9] + SU3D[I2, k6, k7]*SU3F[6, I4, k9])* - (SU3D[I3, I5, k6]*SU3F[I1, k7, k9] + SU3D[I1, I5, k6]* - SU3F[I3, k7, k9] + SU3D[I1, I3, k6]*SU3F[I5, k7, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9] + - SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9] + - SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9] + - SU3D[I3, I4, k6]*SU3F[6, I2, k9]*(SU3D[I5, k6, k7]*SU3F[I1, k7, k9] + - SU3D[I1, k6, k7]*SU3F[I5, k7, k9]) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I1, k7, k9] + - (SU3D[I1, I4, k6]*SU3F[6, I2, k9] + SU3D[I1, I2, k6]*SU3F[6, I4, k9])* - SU3F[I5, k7, k9]))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I3, k6] - SU3F[I1, I2, k6]* - SU3F[I3, k7, k9]) - SU3F[6, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I3, I4, k6] + SU3F[I1, I4, k6]* - SU3F[I3, k7, k9])) + SU3D[I3, k6, k7]* - (SU3F[6, I4, k9]*(SU3F[I1, k7, k9]*SU3F[I2, I5, k6] - - SU3F[I1, I2, k6]*SU3F[I5, k7, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I4, I5, k6] - SU3F[I1, I4, k6]* - SU3F[I5, k7, k9])) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k9]*(SU3F[I2, I5, k6]*SU3F[I3, k7, k9] + - SU3F[I2, I3, k6]*SU3F[I5, k7, k9]) + SU3F[6, I2, k9]* - (SU3F[I3, k7, k9]*SU3F[I4, I5, k6] - SU3F[I3, I4, k6]* - SU3F[I5, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I4, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k7, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*(SU3D[6, I4, k8]*SU3D[I2, k6, k9] + SU3D[6, I2, k8]* - SU3D[I4, k6, k9])*(SU3D[I3, I5, k6]*SU3F[I1, k8, k9] + - SU3D[I1, I5, k6]*SU3F[I3, k8, k9] + SU3D[I1, I3, k6]* - SU3F[I5, k8, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[6, I4, k8]*SU3F[I2, k6, k9] + SU3D[6, I2, k8]*SU3F[I4, k6, k9])* - (SU3D[I3, I5, k6]*SU3F[I1, k8, k9] + SU3D[I1, I5, k6]* - SU3F[I3, k8, k9] + SU3D[I1, I3, k6]*SU3F[I5, k8, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*(SU3F[6, I4, k8]*SU3F[I2, k6, k9] + SU3F[6, I2, k8]* - SU3F[I4, k6, k9])*(SU3D[I3, I5, k6]*SU3F[I1, k8, k9] + - SU3D[I1, I5, k6]*SU3F[I3, k8, k9] + SU3D[I1, I3, k6]* - SU3F[I5, k8, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/4)*(SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + SU3D[I4, I5, k6]*SU3F[I2, k6, k9]* - (SU3F[6, I3, k8]*SU3F[I1, k8, k9] + SU3F[6, I1, k8]* - SU3F[I3, k8, k9]) + SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[I2, I5, k6]*SU3F[6, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + SU3D[I2, I3, k6]*SU3F[6, I1, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + SU3D[I3, I4, k6]*SU3F[I2, k6, k9]* - (SU3F[6, I5, k8]*SU3F[I1, k8, k9] + SU3F[6, I1, k8]* - SU3F[I5, k8, k9])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[6, I5, k6]*(SU3D[I3, I4, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I4, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + - (SU3D[I2, I3, k8]*SU3F[I1, k8, k9] + SU3D[I1, I2, k8]* - SU3F[I3, k8, k9])*SU3F[I4, k6, k9]) + SU3D[6, I3, k6]* - (SU3D[I4, I5, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I2, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + - (SU3D[I1, I4, k8]*SU3F[I2, k6, k9] + SU3D[I1, I2, k8]* - SU3F[I4, k6, k9])*SU3F[I5, k8, k9]) + SU3D[6, I1, k6]* - (SU3D[I4, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + - SU3D[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + - (SU3D[I3, I4, k8]*SU3F[I2, k6, k9] + SU3D[I2, I3, k8]* - SU3F[I4, k6, k9])*SU3F[I5, k8, k9]))/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*(SU3F[I3, k8, k9]*(SU3F[I1, I4, k8]*SU3F[I2, k7, k9] + - SU3F[I1, I2, k8]*SU3F[I4, k7, k9]) + SU3F[I1, k8, k9]* - (SU3F[I2, k7, k9]*SU3F[I3, I4, k8] - SU3F[I2, I3, k8]* - SU3F[I4, k7, k9])) - SU3F[6, I3, k7]* - (SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I4, I5, k8] + - SU3F[I2, I5, k8]*SU3F[I4, k7, k9]) - - (SU3F[I1, I4, k8]*SU3F[I2, k7, k9] + SU3F[I1, I2, k8]* - SU3F[I4, k7, k9])*SU3F[I5, k8, k9]) - SU3F[6, I1, k7]* - (SU3F[I4, k7, k9]*(SU3F[I2, I5, k8]*SU3F[I3, k8, k9] + - SU3F[I2, I3, k8]*SU3F[I5, k8, k9]) + SU3F[I2, k7, k9]* - (SU3F[I3, k8, k9]*SU3F[I4, I5, k8] - SU3F[I3, I4, k8]* - SU3F[I5, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*(SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I3, k9] - - SU3F[I1, I2, k9]*SU3F[I3, k8, k9]) - SU3D[I2, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I3, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I3, k8, k9])) + SU3D[6, I3, k7]* - (SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I5, k9] - - SU3F[I1, I2, k9]*SU3F[I5, k8, k9]) + SU3D[I2, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I4, I5, k9] - SU3F[I1, I4, k9]* - SU3F[I5, k8, k9])) + SU3D[6, I1, k7]* - (SU3D[I4, k7, k8]*(SU3F[I2, I5, k9]*SU3F[I3, k8, k9] + - SU3F[I2, I3, k9]*SU3F[I5, k8, k9]) + SU3D[I2, k7, k8]* - (SU3F[I3, k8, k9]*SU3F[I4, I5, k9] - SU3F[I3, I4, k9]* - SU3F[I5, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*(SU3D[6, I5, k6]*(SU3F[I3, k8, k9]* - (SU3F[I1, I4, k9]*SU3F[I2, k6, k8] + SU3F[I1, I2, k9]* - SU3F[I4, k6, k8]) + SU3F[I1, k8, k9]* - (SU3F[I2, k6, k8]*SU3F[I3, I4, k9] - SU3F[I2, I3, k9]* - SU3F[I4, k6, k8])) - SU3D[6, I3, k6]* - (SU3F[I1, k8, k9]*(SU3F[I2, k6, k8]*SU3F[I4, I5, k9] + - SU3F[I2, I5, k9]*SU3F[I4, k6, k8]) - - (SU3F[I1, I4, k9]*SU3F[I2, k6, k8] + SU3F[I1, I2, k9]* - SU3F[I4, k6, k8])*SU3F[I5, k8, k9]) - SU3D[6, I1, k6]* - (SU3F[I4, k6, k8]*(SU3F[I2, I5, k9]*SU3F[I3, k8, k9] + - SU3F[I2, I3, k9]*SU3F[I5, k8, k9]) + SU3F[I2, k6, k8]* - (SU3F[I3, k8, k9]*SU3F[I4, I5, k9] - SU3F[I3, I4, k9]* - SU3F[I5, k8, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (2*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]* - SUNDelta[6, I1])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/9)*SU3D[I4, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I3, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*(SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SUNDelta[6, I1] + - SU3D[I1, I4, k6]*SUNDelta[6, I3]) + SU3D[I2, I3, k6]* - (SU3D[I4, I5, k6]*SUNDelta[6, I1] + SU3D[I1, I4, k6]* - SUNDelta[6, I5]) + SU3D[I1, I2, k6]* - (SU3D[I4, I5, k6]*SUNDelta[6, I3] + SU3D[I3, I4, k6]* - SUNDelta[6, I5])))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I5, k5]*SU3D[I3, I4, k5]* - SUNDelta[I1, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I4, k5]*SU3D[I3, I5, k5]* - SUNDelta[I1, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I3, k5]*SU3D[I4, I5, k5]* - SUNDelta[I1, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I4, k5]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (((2*I)/9)*SU3D[6, I5, k5]* - SU3F[I3, I4, k5]*SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (2*SU3F[6, I5, k6]*SU3F[I3, I4, k6]* - SUNDelta[I1, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I4, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I5, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I2, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I2, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I3, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I4, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I1, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I4, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I5, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I3, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I1, k5]*SU3D[I3, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*(SU3D[I3, I5, k5]*SU3F[6, I1, k5] + SU3D[I1, I5, k5]* - SU3F[6, I3, k5] + SU3D[I1, I3, k5]*SU3F[6, I5, k5])*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I3, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I1, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I2, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I2, I3, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*(SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4] + - SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4] + - SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3] + - SU3D[I4, I5, k5]*(SU3F[6, I3, k5]*SUNDelta[I1, I2] + - SU3F[6, I1, k5]*SUNDelta[I2, I3]) + SU3D[I1, I4, k5]*SU3F[6, I3, k5]* - SUNDelta[I2, I5] + SU3D[I3, I4, k5]* - (SU3F[6, I5, k5]*SUNDelta[I1, I2] + SU3F[6, I1, k5]* - SUNDelta[I2, I5]) + SU3D[I2, I5, k5]*SU3F[6, I1, k5]* - SUNDelta[I3, I4] + SU3D[I1, I2, k5]*SU3F[6, I5, k5]* - SUNDelta[I3, I4] + SU3D[I2, I3, k5]*SU3F[6, I1, k5]* - SUNDelta[I4, I5] + SU3D[I1, I2, k5]*SU3F[6, I3, k5]* - SUNDelta[I4, I5]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5)}, -{CouplingConstant[ChPTW3[2], 1]*((SU3D[6, I3, I5]*SU3D[I1, I2, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I4]*SU3D[I1, I2, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*(SU3D[6, I4, I5]*SU3D[I1, I2, I3] + SU3D[6, I2, I5]*SU3D[I1, I3, I4] + - SU3D[6, I2, I4]*SU3D[I1, I3, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I1, I3]*SU3D[I2, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I1, k8, k9]*SU3D[I3, k6, k9] + SU3D[I1, k6, k9]*SU3D[I3, k8, k9])* - (SU3D[6, I5, k8]*SU3D[I2, I4, k6] + SU3D[6, I4, k8]*SU3D[I2, I5, k6] + - SU3D[6, I2, k8]*SU3D[I4, I5, k6]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*(SU3D[I3, k8, k9]*(SU3D[I1, I4, k9]*SU3D[I2, k7, k8] + - SU3D[I1, I2, k9]*SU3D[I4, k7, k8]) + SU3D[I1, k8, k9]* - (SU3D[I2, k7, k8]*SU3D[I3, I4, k9] + SU3D[I2, I3, k9]* - SU3D[I4, k7, k8])) + SU3D[6, I4, k7]* - (SU3D[I3, k8, k9]*(SU3D[I1, I5, k9]*SU3D[I2, k7, k8] + - SU3D[I1, I2, k9]*SU3D[I5, k7, k8]) + SU3D[I1, k8, k9]* - (SU3D[I2, k7, k8]*SU3D[I3, I5, k9] + SU3D[I2, I3, k9]* - SU3D[I5, k7, k8])) + SU3D[6, I2, k7]* - (SU3D[I3, k8, k9]*(SU3D[I1, I5, k9]*SU3D[I4, k7, k8] + - SU3D[I1, I4, k9]*SU3D[I5, k7, k8]) + SU3D[I1, k8, k9]* - (SU3D[I3, I5, k9]*SU3D[I4, k7, k8] + SU3D[I3, I4, k9]* - SU3D[I5, k7, k8])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I3, k6]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I3, k6, k8]* - SU3D[I4, I5, k6]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/3)*(SU3D[I3, I4, I5]*SU3F[6, I1, I2] + SU3D[I2, I3, I5]* - SU3F[6, I1, I4] + SU3D[I2, I3, I4]*SU3F[6, I1, I5] - - SU3D[I1, I4, I5]*SU3F[6, I2, I3] + SU3D[I1, I2, I5]*SU3F[6, I3, I4] + - SU3D[I1, I2, I4]*SU3F[6, I3, I5]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k8]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*(SU3D[I2, k7, k8]*SU3D[I4, I5, k6] + SU3D[I2, I5, k6]* - SU3D[I4, k7, k8] + SU3D[I2, I4, k6]*SU3D[I5, k7, k8])* - (SU3D[I3, k6, k8]*SU3F[6, I1, k7] + SU3D[I1, k6, k8]*SU3F[6, I3, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/6)*(SU3D[I2, k6, k8]*SU3D[I4, I5, k6] + SU3D[I2, I5, k6]* - SU3D[I4, k6, k8] + SU3D[I2, I4, k6]*SU3D[I5, k6, k8])* - (SU3D[I3, k7, k8]*SU3F[6, I1, k7] + SU3D[I1, k7, k8]*SU3F[6, I3, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I2, k7, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I2, k7, k9]* - SU3D[I3, k6, k7]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, I4, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I1, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I5, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[I2, k7, k8]*SU3D[I5, k6, k7] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8])* - (SU3F[6, I3, k8]*SU3F[I1, I4, k6] + SU3F[6, I1, k8]* - SU3F[I3, I4, k6]) + SU3D[I4, k7, k8]* - (SU3D[I5, k6, k7]*(SU3F[6, I3, k8]*SU3F[I1, I2, k6] - - SU3F[6, I1, k8]*SU3F[I2, I3, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k8]*SU3F[I1, I5, k6] + SU3F[6, I1, k8]* - SU3F[I3, I5, k6])) + SU3D[I4, k6, k7]* - (SU3D[I5, k7, k8]*(SU3F[6, I3, k8]*SU3F[I1, I2, k6] - - SU3F[6, I1, k8]*SU3F[I2, I3, k6]) + SU3D[I2, k7, k8]* - (SU3F[6, I3, k8]*SU3F[I1, I5, k6] + SU3F[6, I1, k8]* - SU3F[I3, I5, k6])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[6, I5, k7]*(SU3D[I3, k8, k9]* - (SU3D[I4, k7, k8]*SU3F[I1, I2, k9] + SU3D[I2, k7, k8]* - SU3F[I1, I4, k9]) + SU3D[I1, k8, k9]* - (-(SU3D[I4, k7, k8]*SU3F[I2, I3, k9]) + SU3D[I2, k7, k8]* - SU3F[I3, I4, k9])) + SU3D[6, I4, k7]* - (SU3D[I3, k8, k9]*(SU3D[I5, k7, k8]*SU3F[I1, I2, k9] + - SU3D[I2, k7, k8]*SU3F[I1, I5, k9]) + SU3D[I1, k8, k9]* - (-(SU3D[I5, k7, k8]*SU3F[I2, I3, k9]) + SU3D[I2, k7, k8]* - SU3F[I3, I5, k9])) + SU3D[6, I2, k7]* - (SU3D[I3, k8, k9]*(SU3D[I5, k7, k8]*SU3F[I1, I4, k9] + - SU3D[I4, k7, k8]*SU3F[I1, I5, k9]) + SU3D[I1, k8, k9]* - (SU3D[I5, k7, k8]*SU3F[I3, I4, k9] + SU3D[I4, k7, k8]* - SU3F[I3, I5, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/3)*(SU3D[6, I5, k7]*SU3D[I2, I4, k8] + SU3D[6, I4, k7]* - SU3D[I2, I5, k8] + SU3D[6, I2, k7]*SU3D[I4, I5, k8])* - (SU3D[I3, k6, k7]*SU3F[I1, k6, k8] + SU3D[I1, k6, k7]* - SU3F[I3, k6, k8]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[I4, I5, k8]*SU3F[6, I2, k7] + SU3D[I2, I5, k8]*SU3F[6, I4, k7] + - SU3D[I2, I4, k8]*SU3F[6, I5, k7])*(SU3D[I3, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3F[I3, k6, k8]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I2, k6, k7]*SU3D[I4, I5, k8] + SU3D[I2, I5, k8]*SU3D[I4, k6, k7] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7])*(SU3F[6, I3, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I3, k6, k8]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*(SU3D[6, I2, k7]*(SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k8] + SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k6, k8] + (SU3D[I1, I5, k8]*SU3D[I4, k6, k7] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7])*SU3F[I3, k6, k8]) + - SU3D[6, I5, k7]*(SU3D[I4, k6, k7]*(SU3D[I2, I3, k8]*SU3F[I1, k6, k8] + - SU3D[I1, I2, k8]*SU3F[I3, k6, k8]) + SU3D[I2, k6, k7]* - (SU3D[I3, I4, k8]*SU3F[I1, k6, k8] + SU3D[I1, I4, k8]* - SU3F[I3, k6, k8])) + SU3D[6, I4, k7]* - (SU3D[I5, k6, k7]*(SU3D[I2, I3, k8]*SU3F[I1, k6, k8] + - SU3D[I1, I2, k8]*SU3F[I3, k6, k8]) + SU3D[I2, k6, k7]* - (SU3D[I3, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I3, k6, k8]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/3)*(SU3D[6, I5, k6]*SU3D[I2, I4, k8] + SU3D[6, I4, k6]* - SU3D[I2, I5, k8] + SU3D[6, I2, k6]*SU3D[I4, I5, k8])* - (SU3D[I3, k8, k9]*SU3F[I1, k6, k9] + SU3D[I1, k8, k9]* - SU3F[I3, k6, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I2, k8]*(SU3D[I3, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, k6, k9] + SU3D[I3, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9] + (SU3D[I1, I5, k6]*SU3D[I4, k8, k9] + - SU3D[I1, I4, k6]*SU3D[I5, k8, k9])*SU3F[I3, k6, k9]) + - SU3D[6, I5, k8]*(SU3D[I4, k8, k9]*(SU3D[I2, I3, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + SU3D[I1, I4, k6]* - SU3F[I3, k6, k9])) + SU3D[6, I4, k8]* - (SU3D[I5, k8, k9]*(SU3D[I2, I3, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I5, k6]*SU3F[I1, k6, k9] + SU3D[I1, I5, k6]* - SU3F[I3, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I2, k6]*(SU3D[I3, I5, k8]*SU3D[I4, k8, k9]* - SU3F[I1, k6, k9] + SU3D[I3, I4, k8]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9] + (SU3D[I1, I5, k8]*SU3D[I4, k8, k9] + - SU3D[I1, I4, k8]*SU3D[I5, k8, k9])*SU3F[I3, k6, k9]) + - SU3D[6, I5, k6]*(SU3D[I4, k8, k9]*(SU3D[I2, I3, k8]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k8]*SU3F[I3, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k8]*SU3F[I1, k6, k9] + SU3D[I1, I4, k8]* - SU3F[I3, k6, k9])) + SU3D[6, I4, k6]* - (SU3D[I5, k8, k9]*(SU3D[I2, I3, k8]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k8]*SU3F[I3, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I5, k8]* - SU3F[I3, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[6, I5, k6]*(SU3D[I4, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k8] - - SU3F[I1, I2, k8]*SU3F[I3, k6, k9]) - SU3D[I2, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I3, I4, k8] + SU3F[I1, I4, k8]* - SU3F[I3, k6, k9])) + SU3D[6, I4, k6]* - (SU3D[I5, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k8] - - SU3F[I1, I2, k8]*SU3F[I3, k6, k9]) - SU3D[I2, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I3, I5, k8] + SU3F[I1, I5, k8]* - SU3F[I3, k6, k9])) - SU3D[6, I2, k6]* - (SU3D[I5, k8, k9]*(SU3F[I1, k6, k9]*SU3F[I3, I4, k8] + - SU3F[I1, I4, k8]*SU3F[I3, k6, k9]) + SU3D[I4, k8, k9]* - (SU3F[I1, k6, k9]*SU3F[I3, I5, k8] + SU3F[I1, I5, k8]* - SU3F[I3, k6, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k9] - - SU3F[I1, I2, k9]*SU3F[I3, k6, k9]) - SU3D[I2, k6, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I3, k6, k9])) + SU3D[6, I4, k7]* - (SU3D[I5, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k9] - - SU3F[I1, I2, k9]*SU3F[I3, k6, k9]) - SU3D[I2, k6, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I3, k6, k9])) - SU3D[6, I2, k7]* - (SU3D[I5, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I3, I4, k9] + - SU3F[I1, I4, k9]*SU3F[I3, k6, k9]) + SU3D[I4, k6, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I3, k6, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I3, k9] - SU3F[I1, I2, k9]* - SU3F[I3, k6, k9]) - SU3F[6, I2, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I3, k6, k9])) + SU3D[I4, k6, k7]* - (SU3F[6, I5, k7]*(SU3F[I1, k6, k9]*SU3F[I2, I3, k9] - - SU3F[I1, I2, k9]*SU3F[I3, k6, k9]) - SU3F[6, I2, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I3, k6, k9])) - SU3D[I2, k6, k7]* - (SU3F[6, I5, k7]*(SU3F[I1, k6, k9]*SU3F[I3, I4, k9] + - SU3F[I1, I4, k9]*SU3F[I3, k6, k9]) + SU3F[6, I4, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I3, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I4, I5, k6]*SU3F[6, I2, k9] + SU3D[I2, I5, k6]*SU3F[6, I4, k9] + - SU3D[I2, I4, k6]*SU3F[6, I5, k9])*(SU3D[I3, k6, k7]*SU3F[I1, k7, k9] + - SU3D[I1, k6, k7]*SU3F[I3, k7, k9]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I2, k6, k7]*SU3D[I4, I5, k6] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7] + - SU3D[I2, I4, k6]*SU3D[I5, k6, k7])*(SU3F[6, I3, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I3, k7, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I3, k6] - SU3F[I1, I2, k6]* - SU3F[I3, k7, k9]) - SU3F[6, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I3, I4, k6] + SU3F[I1, I4, k6]* - SU3F[I3, k7, k9])) + SU3D[I4, k6, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k7, k9]*SU3F[I2, I3, k6] - - SU3F[I1, I2, k6]*SU3F[I3, k7, k9]) - SU3F[6, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I3, I5, k6] + SU3F[I1, I5, k6]* - SU3F[I3, k7, k9])) - SU3D[I2, k6, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k7, k9]*SU3F[I3, I4, k6] + - SU3F[I1, I4, k6]*SU3F[I3, k7, k9]) + SU3F[6, I4, k9]* - (SU3F[I1, k7, k9]*SU3F[I3, I5, k6] + SU3F[I1, I5, k6]* - SU3F[I3, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[6, I5, k6]*SU3D[I2, I4, k8] + SU3D[6, I4, k6]*SU3D[I2, I5, k8] + - SU3D[6, I2, k6]*SU3D[I4, I5, k8])*(SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I3, k8, k9]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*(SU3D[I4, I5, k6]*SU3F[6, I2, k8] + SU3D[I2, I5, k6]* - SU3F[6, I4, k8] + SU3D[I2, I4, k6]*SU3F[6, I5, k8])* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I5, k7]*(SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I3, k9] - - SU3F[I1, I2, k9]*SU3F[I3, k8, k9]) - SU3D[I2, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I3, I4, k9] + SU3F[I1, I4, k9]* - SU3F[I3, k8, k9])) + SU3D[6, I4, k7]* - (SU3D[I5, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I3, k9] - - SU3F[I1, I2, k9]*SU3F[I3, k8, k9]) - SU3D[I2, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I3, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I3, k8, k9])) - SU3D[6, I2, k7]* - (SU3D[I5, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I3, I4, k9] + - SU3F[I1, I4, k9]*SU3F[I3, k8, k9]) + SU3D[I4, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I3, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I3, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, I5, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, I3, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, k7, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I5, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*(SU3D[6, I5, k6]*(SU3F[I3, k8, k9]* - (SU3F[I1, I4, k9]*SU3F[I2, k6, k8] + SU3F[I1, I2, k9]* - SU3F[I4, k6, k8]) + SU3F[I1, k8, k9]* - (SU3F[I2, k6, k8]*SU3F[I3, I4, k9] - SU3F[I2, I3, k9]* - SU3F[I4, k6, k8])) + SU3D[6, I4, k6]* - (SU3F[I3, k8, k9]*(SU3F[I1, I5, k9]*SU3F[I2, k6, k8] + - SU3F[I1, I2, k9]*SU3F[I5, k6, k8]) + SU3F[I1, k8, k9]* - (SU3F[I2, k6, k8]*SU3F[I3, I5, k9] - SU3F[I2, I3, k9]* - SU3F[I5, k6, k8])) + SU3D[6, I2, k6]* - (SU3F[I3, k8, k9]*(SU3F[I1, I5, k9]*SU3F[I4, k6, k8] + - SU3F[I1, I4, k9]*SU3F[I5, k6, k8]) + SU3F[I1, k8, k9]* - (SU3F[I3, I5, k9]*SU3F[I4, k6, k8] + SU3F[I3, I4, k9]* - SU3F[I5, k6, k8]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/6)*(SU3F[6, I3, k8]*SU3F[I1, k8, k9] + SU3F[6, I1, k8]* - SU3F[I3, k8, k9])*(SU3D[I4, I5, k6]*SU3F[I2, k6, k9] + - SU3D[I2, I5, k6]*SU3F[I4, k6, k9] + SU3D[I2, I4, k6]* - SU3F[I5, k6, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I5, k6]*(SU3D[I3, I4, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I4, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + - (SU3D[I2, I3, k8]*SU3F[I1, k8, k9] + SU3D[I1, I2, k8]* - SU3F[I3, k8, k9])*SU3F[I4, k6, k9]) + SU3D[6, I4, k6]* - (SU3D[I3, I5, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9] + - (SU3D[I2, I3, k8]*SU3F[I1, k8, k9] + SU3D[I1, I2, k8]* - SU3F[I3, k8, k9])*SU3F[I5, k6, k9]) + SU3D[6, I2, k6]* - (SU3D[I3, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I1, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + - (SU3D[I3, I4, k8]*SU3F[I1, k8, k9] + SU3D[I1, I4, k8]* - SU3F[I3, k8, k9])*SU3F[I5, k6, k9]))/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I5, k7]*(SU3F[I3, k8, k9]*(SU3F[I1, I4, k8]*SU3F[I2, k7, k9] + - SU3F[I1, I2, k8]*SU3F[I4, k7, k9]) + SU3F[I1, k8, k9]* - (SU3F[I2, k7, k9]*SU3F[I3, I4, k8] - SU3F[I2, I3, k8]* - SU3F[I4, k7, k9])) + SU3F[6, I4, k7]* - (SU3F[I3, k8, k9]*(SU3F[I1, I5, k8]*SU3F[I2, k7, k9] + - SU3F[I1, I2, k8]*SU3F[I5, k7, k9]) + SU3F[I1, k8, k9]* - (SU3F[I2, k7, k9]*SU3F[I3, I5, k8] - SU3F[I2, I3, k8]* - SU3F[I5, k7, k9])) + SU3F[6, I2, k7]* - (SU3F[I3, k8, k9]*(SU3F[I1, I5, k8]*SU3F[I4, k7, k9] + - SU3F[I1, I4, k8]*SU3F[I5, k7, k9]) + SU3F[I1, k8, k9]* - (SU3F[I3, I5, k8]*SU3F[I4, k7, k9] + SU3F[I3, I4, k8]* - SU3F[I5, k7, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, I3, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I4, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, k7, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, I4, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I4, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k7, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/9)*SU3D[I3, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I3, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I4, I5, k6]*(SU3D[I2, I3, k6]*SUNDelta[6, I1] + - SU3D[I1, I2, k6]*SUNDelta[6, I3]) + SU3D[I2, I5, k6]* - (SU3D[I3, I4, k6]*SUNDelta[6, I1] + SU3D[I1, I4, k6]* - SUNDelta[6, I3]) + SU3D[I2, I4, k6]* - (SU3D[I3, I5, k6]*SUNDelta[6, I1] + SU3D[I1, I5, k6]*SUNDelta[6, I3]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*(SU3D[I4, I5, k6]*(-(SU3F[I2, I3, k6]*SUNDelta[6, I1]) + - SU3F[I1, I2, k6]*SUNDelta[6, I3]) + SU3D[I2, I5, k6]* - (SU3F[I3, I4, k6]*SUNDelta[6, I1] + SU3F[I1, I4, k6]* - SUNDelta[6, I3]) + SU3D[I2, I4, k6]* - (SU3F[I3, I5, k6]*SUNDelta[6, I1] + SU3F[I1, I5, k6]* - SUNDelta[6, I3])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (2*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]* - SUNDelta[6, I4])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (2*SU3D[I1, I3, k6]*SU3D[I2, I5, k6]* - SUNDelta[6, I4])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (2*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]* - SUNDelta[6, I4])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/9)*SU3D[I3, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/9)*SU3D[I3, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I3, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*(SU3D[6, I5, k5]*SU3D[I2, I4, k5] + SU3D[6, I4, k5]*SU3D[I2, I5, k5] + - SU3D[6, I2, k5]*SU3D[I4, I5, k5])*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I3, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I4, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I5, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I1, k6]*SU3F[I3, I5, k6]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I4, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I2, k6]*SU3F[I1, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*(SU3D[I3, I4, k5]*SUNDelta[I1, I2] + - SU3D[I2, I3, k5]*SUNDelta[I1, I4] + SU3D[I1, I4, k5]* - SUNDelta[I2, I3] + SU3D[I1, I2, k5]*SUNDelta[I3, I4]) + - SU3D[6, I4, k5]*(SU3D[I3, I5, k5]*SUNDelta[I1, I2] + - SU3D[I2, I3, k5]*SUNDelta[I1, I5] + SU3D[I1, I5, k5]* - SUNDelta[I2, I3] + SU3D[I1, I2, k5]*SUNDelta[I3, I5]) + - SU3D[6, I2, k5]*(SU3D[I3, I5, k5]*SUNDelta[I1, I4] + - SU3D[I3, I4, k5]*SUNDelta[I1, I5] + SU3D[I1, I5, k5]* - SUNDelta[I3, I4] + SU3D[I1, I4, k5]*SUNDelta[I3, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*(SU3D[I4, I5, k5]*(SU3F[6, I3, k5]*SUNDelta[I1, I2] + - SU3F[6, I1, k5]*SUNDelta[I2, I3]) + SU3D[I2, I5, k5]* - (SU3F[6, I3, k5]*SUNDelta[I1, I4] + SU3F[6, I1, k5]* - SUNDelta[I3, I4]) + SU3D[I2, I4, k5]* - (SU3F[6, I3, k5]*SUNDelta[I1, I5] + SU3F[6, I1, k5]* - SUNDelta[I3, I5])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (((2*I)/9)*(SU3D[6, I5, k5]*(SU3F[I3, I4, k5]*SUNDelta[I1, I2] - - SU3F[I2, I3, k5]*SUNDelta[I1, I4] + SU3F[I1, I4, k5]* - SUNDelta[I2, I3] + SU3F[I1, I2, k5]*SUNDelta[I3, I4]) + - SU3D[6, I4, k5]*(SU3F[I3, I5, k5]*SUNDelta[I1, I2] - - SU3F[I2, I3, k5]*SUNDelta[I1, I5] + SU3F[I1, I5, k5]* - SUNDelta[I2, I3] + SU3F[I1, I2, k5]*SUNDelta[I3, I5]) + - SU3D[6, I2, k5]*(SU3F[I3, I5, k5]*SUNDelta[I1, I4] + - SU3F[I3, I4, k5]*SUNDelta[I1, I5] + SU3F[I1, I5, k5]* - SUNDelta[I3, I4] + SU3F[I1, I4, k5]*SUNDelta[I3, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (4*(SUNDelta[6, I5]*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I2]*SUNDelta[I3, I4]) + SUNDelta[6, I4]* - (SUNDelta[I1, I5]*SUNDelta[I2, I3] + SUNDelta[I1, I2]* - SUNDelta[I3, I5]) + SUNDelta[6, I2]* - (SUNDelta[I1, I5]*SUNDelta[I3, I4] + SUNDelta[I1, I4]* - SUNDelta[I3, I5])))/(27*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (4*SU3D[6, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[I4, I5])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (((4*I)/9)*SU3D[I1, I3, k5]* - SU3F[6, I2, k5]*SUNDelta[I4, I5])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (((2*I)/9)*SU3D[6, I3, k6]* - SU3F[I1, I2, k6]*SUNDelta[I4, I5])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (((2*I)/9)*SU3D[6, I1, k6]* - SU3F[I2, I3, k6]*SUNDelta[I4, I5])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (2*SUNDelta[6, I3]*SUNDelta[I1, I2]* - SUNDelta[I4, I5])/(27*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (4*SUNDelta[6, I2]*SUNDelta[I1, I3]* - SUNDelta[I4, I5])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (2*SUNDelta[6, I1]*SUNDelta[I2, I3]* - SUNDelta[I4, I5])/(27*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (2*((SU3F[6, I3, k6]*SU3F[I1, I5, k6] + SU3F[6, I1, k6]*SU3F[I3, I5, k6])* - SUNDelta[I2, I4] + (SU3F[6, I3, k6]*SU3F[I1, I4, k6] + - SU3F[6, I1, k6]*SU3F[I3, I4, k6])*SUNDelta[I2, I5] + - (SU3F[6, I3, k6]*SU3F[I1, I2, k6] - SU3F[6, I1, k6]*SU3F[I2, I3, k6])* - SUNDelta[I4, I5]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 1]*((-4*SU3D[6, I4, I5]*SU3D[I1, I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I5]*SU3D[I1, I2, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I4]*SU3D[I1, I2, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I5]*SU3D[I1, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I4]*SU3D[I1, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I3]*SU3D[I2, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9]*SU3D[I4, I5, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*(SU3D[I1, k8, k9]*(SU3D[I2, k6, k9]*SU3D[I3, I4, k6] + - SU3D[I2, I4, k6]*SU3D[I3, k6, k9]) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k9] + SU3D[I1, I2, k6]* - SU3D[I3, k6, k9])*SU3D[I4, k8, k9]) + SU3D[6, I4, k8]* - (SU3D[I1, k8, k9]*(SU3D[I2, k6, k9]*SU3D[I3, I5, k6] + - SU3D[I2, I5, k6]*SU3D[I3, k6, k9]) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k9] + SU3D[I1, I2, k6]* - SU3D[I3, k6, k9])*SU3D[I5, k8, k9]) + SU3D[6, I1, k8]* - (SU3D[I3, k6, k9]*(SU3D[I2, I5, k6]*SU3D[I4, k8, k9] + - SU3D[I2, I4, k6]*SU3D[I5, k8, k9]) + SU3D[I2, k6, k9]* - (SU3D[I3, I5, k6]*SU3D[I4, k8, k9] + SU3D[I3, I4, k6]* - SU3D[I5, k8, k9])))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*(SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I3, I4, k9] + - SU3D[I2, I4, k9]*SU3D[I3, k7, k8]) + - (SU3D[I1, I3, k9]*SU3D[I2, k7, k8] + SU3D[I1, I2, k9]* - SU3D[I3, k7, k8])*SU3D[I4, k8, k9]) + SU3D[6, I4, k7]* - (SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I3, I5, k9] + - SU3D[I2, I5, k9]*SU3D[I3, k7, k8]) + - (SU3D[I1, I3, k9]*SU3D[I2, k7, k8] + SU3D[I1, I2, k9]* - SU3D[I3, k7, k8])*SU3D[I5, k8, k9]) + SU3D[6, I1, k7]* - (SU3D[I3, k7, k8]*(SU3D[I2, I5, k9]*SU3D[I4, k8, k9] + - SU3D[I2, I4, k9]*SU3D[I5, k8, k9]) + SU3D[I2, k7, k8]* - (SU3D[I3, I5, k9]*SU3D[I4, k8, k9] + SU3D[I3, I4, k9]* - SU3D[I5, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, I5]*SU3F[6, I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I4, I5]*SU3F[6, I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I3, I5]*SU3F[6, I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I3, I4]*SU3F[6, I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/6)*SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I2, I5]*SU3F[6, I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I2, I4]*SU3F[6, I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/3)*(SU3D[I2, k7, k8]*SU3D[I3, k6, k8] + SU3D[I2, k6, k8]* - SU3D[I3, k7, k8])*(SU3D[I4, I5, k6]*SU3F[6, I1, k7] + - SU3D[I1, I5, k6]*SU3F[6, I4, k7] + SU3D[I1, I4, k6]*SU3F[6, I5, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/6)*SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I1, k7, k9]* - SU3D[I3, k6, k7]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k7, k9]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, k8, k9]*SU3F[I2, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[I1, k7, k9]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9]*SU3F[I2, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, k6, k7]* - SU3D[I3, I5, k8]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k7]*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k7]*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I3, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I5, k8, k9]*SU3F[I1, I3, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I4, k6, k7]*SU3F[I1, I3, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I5, k6, k7]*SU3F[I1, I3, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I3, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k9]*SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k7, k9]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I2, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k6]*SU3D[I1, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I5, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, k7, k9]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (-((SU3D[I1, k7, k8]*SU3D[I5, k6, k7] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8])*(SU3F[6, I3, k8]*SU3F[I2, I4, k6] + - SU3F[6, I2, k8]*SU3F[I3, I4, k6])) + SU3D[I4, k7, k8]* - (SU3D[I5, k6, k7]*(SU3F[6, I3, k8]*SU3F[I1, I2, k6] + - SU3F[6, I2, k8]*SU3F[I1, I3, k6]) - SU3D[I1, k6, k7]* - (SU3F[6, I3, k8]*SU3F[I2, I5, k6] + SU3F[6, I2, k8]* - SU3F[I3, I5, k6])) + SU3D[I4, k6, k7]* - (SU3D[I5, k7, k8]*(SU3F[6, I3, k8]*SU3F[I1, I2, k6] + - SU3F[6, I2, k8]*SU3F[I1, I3, k6]) - SU3D[I1, k7, k8]* - (SU3F[6, I3, k8]*SU3F[I2, I5, k6] + SU3F[6, I2, k8]* - SU3F[I3, I5, k6])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I1, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I5, k7]*(SU3D[I3, k8, k9]* - (SU3D[I4, k7, k8]*SU3F[I1, I2, k9] - SU3D[I1, k7, k8]* - SU3F[I2, I4, k9]) + SU3D[I2, k8, k9]* - (SU3D[I4, k7, k8]*SU3F[I1, I3, k9] - SU3D[I1, k7, k8]* - SU3F[I3, I4, k9])) + SU3D[6, I4, k7]* - (SU3D[I3, k8, k9]*(SU3D[I5, k7, k8]*SU3F[I1, I2, k9] - - SU3D[I1, k7, k8]*SU3F[I2, I5, k9]) + SU3D[I2, k8, k9]* - (SU3D[I5, k7, k8]*SU3F[I1, I3, k9] - SU3D[I1, k7, k8]* - SU3F[I3, I5, k9])) - SU3D[6, I1, k7]* - (SU3D[I3, k8, k9]*(SU3D[I5, k7, k8]*SU3F[I2, I4, k9] + - SU3D[I4, k7, k8]*SU3F[I2, I5, k9]) + SU3D[I2, k8, k9]* - (SU3D[I5, k7, k8]*SU3F[I3, I4, k9] + SU3D[I4, k7, k8]* - SU3F[I3, I5, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I5, k8]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k7]*SU3D[I1, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k7]*SU3D[I1, I5, k8]* - SU3D[I2, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k7]*SU3D[I1, I2, k8]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I5, k8, k9]*SU3F[I1, I2, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I4, k6, k7]*SU3F[I1, I2, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I5, k6, k7]*SU3F[I1, I2, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k8]*SU3D[I4, I5, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[I2, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k6, k7]*SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I4, k8, k9]*SU3F[I2, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, I4, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, I5, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I5, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, I5, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k7, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, k7, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I4, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((SU3D[I3, k6, k7]*SU3F[6, I2, k7] + SU3D[I2, k6, k7]*SU3F[6, I3, k7])* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k8] + SU3D[I1, I4, k8]*SU3F[I5, k6, k8]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[6, I5, k8]*(SU3D[I3, k8, k9]* - (SU3D[I2, I4, k6]*SU3F[I1, k6, k9] + SU3D[I1, I2, k6]* - SU3F[I4, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + SU3D[I1, I3, k6]* - SU3F[I4, k6, k9])) + SU3D[6, I4, k8]* - (SU3D[I3, k8, k9]*(SU3D[I2, I5, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k6]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I5, k6]*SU3F[I1, k6, k9] + SU3D[I1, I3, k6]* - SU3F[I5, k6, k9])) + SU3D[6, I1, k8]* - (SU3D[I3, k8, k9]*(SU3D[I2, I5, k6]*SU3F[I4, k6, k9] + - SU3D[I2, I4, k6]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I5, k6]*SU3F[I4, k6, k9] + SU3D[I3, I4, k6]* - SU3F[I5, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/4)*(SU3D[6, I5, k6]*(SU3D[I3, k8, k9]*(SU3D[I2, I4, k8]* - SU3F[I1, k6, k9] + SU3D[I1, I2, k8]*SU3F[I4, k6, k9]) + - SU3D[I2, k8, k9]*(SU3D[I3, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I1, I3, k8]*SU3F[I4, k6, k9])) + SU3D[6, I4, k6]* - (SU3D[I3, k8, k9]*(SU3D[I2, I5, k8]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k8]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I3, k8]* - SU3F[I5, k6, k9])) + SU3D[6, I1, k6]* - (SU3D[I3, k8, k9]*(SU3D[I2, I5, k8]*SU3F[I4, k6, k9] + - SU3D[I2, I4, k8]*SU3F[I5, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I5, k8]*SU3F[I4, k6, k9] + SU3D[I3, I4, k8]* - SU3F[I5, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I3, k6, k7]*SU3F[6, I2, k9] + SU3D[I2, k6, k7]*SU3F[6, I3, k9])* - (SU3D[I4, I5, k6]*SU3F[I1, k7, k9] + SU3D[I1, I5, k6]* - SU3F[I4, k7, k9] + SU3D[I1, I4, k6]*SU3F[I5, k7, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k7, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I2, k7]*SU3F[I1, k7, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k7, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*(SU3F[6, I3, k8]*SU3F[I2, k6, k9] + SU3F[6, I2, k8]* - SU3F[I3, k6, k9])*(SU3D[I4, I5, k6]*SU3F[I1, k8, k9] + - SU3D[I1, I5, k6]*SU3F[I4, k8, k9] + SU3D[I1, I4, k6]* - SU3F[I5, k8, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[6, I5, k6]*(SU3D[I3, I4, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I2, I4, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - (SU3D[I1, I3, k8]*SU3F[I2, k6, k9] + SU3D[I1, I2, k8]* - SU3F[I3, k6, k9])*SU3F[I4, k8, k9]) + SU3D[6, I4, k6]* - (SU3D[I3, I5, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I2, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - (SU3D[I1, I3, k8]*SU3F[I2, k6, k9] + SU3D[I1, I2, k8]* - SU3F[I3, k6, k9])*SU3F[I5, k8, k9]) + SU3D[6, I1, k6]* - (SU3D[I3, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + - SU3D[I2, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + - (SU3D[I3, I4, k8]*SU3F[I2, k6, k9] + SU3D[I2, I4, k8]* - SU3F[I3, k6, k9])*SU3F[I5, k8, k9]))/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I5, k7]*(SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I3, I4, k8] + - SU3F[I2, I4, k8]*SU3F[I3, k7, k9]) - - (SU3F[I1, I3, k8]*SU3F[I2, k7, k9] + SU3F[I1, I2, k8]* - SU3F[I3, k7, k9])*SU3F[I4, k8, k9]) + SU3F[6, I4, k7]* - (SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I3, I5, k8] + - SU3F[I2, I5, k8]*SU3F[I3, k7, k9]) - - (SU3F[I1, I3, k8]*SU3F[I2, k7, k9] + SU3F[I1, I2, k8]* - SU3F[I3, k7, k9])*SU3F[I5, k8, k9]) + SU3F[6, I1, k7]* - (SU3F[I3, k7, k9]*(SU3F[I2, I5, k8]*SU3F[I4, k8, k9] + - SU3F[I2, I4, k8]*SU3F[I5, k8, k9]) + SU3F[I2, k7, k9]* - (SU3F[I3, I5, k8]*SU3F[I4, k8, k9] + SU3F[I3, I4, k8]* - SU3F[I5, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/12)*(SU3D[6, I5, k6]*(SU3F[I1, k8, k9]* - (SU3F[I2, k6, k8]*SU3F[I3, I4, k9] + SU3F[I2, I4, k9]* - SU3F[I3, k6, k8]) - (SU3F[I1, I3, k9]*SU3F[I2, k6, k8] + - SU3F[I1, I2, k9]*SU3F[I3, k6, k8])*SU3F[I4, k8, k9]) + - SU3D[6, I4, k6]*(SU3F[I1, k8, k9]*(SU3F[I2, k6, k8]*SU3F[I3, I5, k9] + - SU3F[I2, I5, k9]*SU3F[I3, k6, k8]) - - (SU3F[I1, I3, k9]*SU3F[I2, k6, k8] + SU3F[I1, I2, k9]* - SU3F[I3, k6, k8])*SU3F[I5, k8, k9]) + SU3D[6, I1, k6]* - (SU3F[I3, k6, k8]*(SU3F[I2, I5, k9]*SU3F[I4, k8, k9] + - SU3F[I2, I4, k9]*SU3F[I5, k8, k9]) + SU3F[I2, k6, k8]* - (SU3F[I3, I5, k9]*SU3F[I4, k8, k9] + SU3F[I3, I4, k9]* - SU3F[I5, k8, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (2*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]* - SUNDelta[6, I1])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/9)*SU3D[I3, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I3, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I2, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*(-(SU3D[I4, I5, k6]*(SU3F[I1, I3, k6]*SUNDelta[6, I2] + - SU3F[I1, I2, k6]*SUNDelta[6, I3])) + SU3D[I1, I5, k6]* - (SU3F[I3, I4, k6]*SUNDelta[6, I2] + SU3F[I2, I4, k6]* - SUNDelta[6, I3]) + SU3D[I1, I4, k6]* - (SU3F[I3, I5, k6]*SUNDelta[6, I2] + SU3F[I2, I5, k6]* - SUNDelta[6, I3])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (2*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]* - SUNDelta[6, I4])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*(SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SUNDelta[6, I1] + - SU3D[I1, I3, k6]*SUNDelta[6, I4]) + SU3D[I2, I4, k6]* - (SU3D[I3, I5, k6]*SUNDelta[6, I1] + SU3D[I1, I3, k6]* - SUNDelta[6, I5]) + SU3D[I1, I2, k6]* - (SU3D[I3, I5, k6]*SUNDelta[6, I4] + SU3D[I3, I4, k6]* - SUNDelta[6, I5])))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I5, k5]*SU3D[I3, I4, k5]* - SUNDelta[I1, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I4, k5]*SU3D[I3, I5, k5]* - SUNDelta[I1, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I3, k5]*SU3D[I4, I5, k5]* - SUNDelta[I1, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I3, k5]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I4, k5]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I5, k5]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (((2*I)/9)*SU3D[6, I5, k5]* - SU3F[I3, I4, k5]*SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (2*SU3F[6, I5, k6]*SU3F[I3, I4, k6]* - SUNDelta[I1, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I3, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I2, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I2, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I5, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SU3D[6, I4, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[6, I5, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I4, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I1, k5]*SU3D[I4, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*(SU3D[I4, I5, k5]*SU3F[6, I1, k5] + SU3D[I1, I5, k5]* - SU3F[6, I4, k5] + SU3D[I1, I4, k5]*SU3F[6, I5, k5])*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I5, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I1, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I3, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I3, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I3, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I5, k5]*SU3F[I1, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I3, k5]*SU3F[6, I1, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I2, k6]*SU3F[I1, I3, k6]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*((SU3F[6, I3, k6]*SU3F[I2, I5, k6] + SU3F[6, I2, k6]*SU3F[I3, I5, k6])* - SUNDelta[I1, I4] + (SU3F[6, I3, k6]*SU3F[I2, I4, k6] + - SU3F[6, I2, k6]*SU3F[I3, I4, k6])*SUNDelta[I1, I5] - - (SU3F[6, I3, k6]*SU3F[I1, I2, k6] + SU3F[6, I2, k6]*SU3F[I1, I3, k6])* - SUNDelta[I4, I5]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (4*SUNDelta[I2, I3]*(SUNDelta[6, I5]*SUNDelta[I1, I4] + - SUNDelta[6, I4]*SUNDelta[I1, I5] + SUNDelta[6, I1]*SUNDelta[I4, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 2]* -((4*(SU3D[6, I3, k7]*SU3D[8, I4, I5]*SU3D[I1, I2, k7] + - SU3D[6, I2, k7]*SU3D[8, I4, I5]*SU3D[I1, I3, k7] + - SU3D[6, I3, k7]*SU3D[8, I2, I5]*SU3D[I1, I4, k7] + - SU3D[6, I2, k7]*SU3D[8, I3, I5]*SU3D[I1, I4, k7] + - SU3D[6, I3, k7]*SU3D[8, I2, I4]*SU3D[I1, I5, k7] + - SU3D[6, I2, k7]*SU3D[8, I3, I4]*SU3D[I1, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I4, I5]*SU3D[I2, I3, k7] + - SU3D[6, I3, k7]*SU3D[8, I1, I5]*SU3D[I2, I4, k7] + - SU3D[6, I1, k7]*SU3D[8, I3, I5]*SU3D[I2, I4, k7] + - SU3D[6, I3, k7]*SU3D[8, I1, I4]*SU3D[I2, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I3, I4]*SU3D[I2, I5, k7] + - SU3D[6, I2, k7]*SU3D[8, I1, I5]*SU3D[I3, I4, k7] + - SU3D[6, I1, k7]*SU3D[8, I2, I5]*SU3D[I3, I4, k7] + - SU3D[6, I5, k7]*(SU3D[8, I3, I4]*SU3D[I1, I2, k7] + - SU3D[8, I2, I4]*SU3D[I1, I3, k7] + SU3D[8, I2, I3]* - SU3D[I1, I4, k7] + SU3D[8, I1, I4]*SU3D[I2, I3, k7] + - SU3D[8, I1, I3]*SU3D[I2, I4, k7] + SU3D[8, I1, I2]* - SU3D[I3, I4, k7]) + SU3D[6, I2, k7]*SU3D[8, I1, I4]* - SU3D[I3, I5, k7] + SU3D[6, I1, k7]*SU3D[8, I2, I4]*SU3D[I3, I5, k7] + - SU3D[6, I4, k7]*(SU3D[8, I3, I5]*SU3D[I1, I2, k7] + - SU3D[8, I2, I5]*SU3D[I1, I3, k7] + SU3D[8, I2, I3]* - SU3D[I1, I5, k7] + SU3D[8, I1, I5]*SU3D[I2, I3, k7] + - SU3D[8, I1, I3]*SU3D[I2, I5, k7] + SU3D[8, I1, I2]* - SU3D[I3, I5, k7]) + SU3D[6, I3, k7]*SU3D[8, I1, I2]* - SU3D[I4, I5, k7] + SU3D[6, I2, k7]*SU3D[8, I1, I3]*SU3D[I4, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I2, I3]*SU3D[I4, I5, k7]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*(SU3D[6, I3, I4]*SU3D[8, I5, k8]*SU3D[I1, I2, k8] + - SU3D[6, I2, I5]*SU3D[8, I4, k8]*SU3D[I1, I3, k8] + - SU3D[6, I2, I4]*SU3D[8, I5, k8]*SU3D[I1, I3, k8] + - SU3D[6, I2, I5]*SU3D[8, I3, k8]*SU3D[I1, I4, k8] + - SU3D[6, I2, I3]*SU3D[8, I5, k8]*SU3D[I1, I4, k8] + - SU3D[6, I3, I4]*SU3D[8, I2, k8]*SU3D[I1, I5, k8] + - SU3D[6, I2, I4]*SU3D[8, I3, k8]*SU3D[I1, I5, k8] + - SU3D[6, I2, I3]*SU3D[8, I4, k8]*SU3D[I1, I5, k8] + - SU3D[6, I1, I5]*SU3D[8, I4, k8]*SU3D[I2, I3, k8] + - SU3D[6, I1, I4]*SU3D[8, I5, k8]*SU3D[I2, I3, k8] + - SU3D[6, I4, I5]*(SU3D[8, I3, k8]*SU3D[I1, I2, k8] + - SU3D[8, I2, k8]*SU3D[I1, I3, k8] + SU3D[8, I1, k8]* - SU3D[I2, I3, k8]) + SU3D[6, I1, I5]*SU3D[8, I3, k8]* - SU3D[I2, I4, k8] + SU3D[6, I1, I3]*SU3D[8, I5, k8]*SU3D[I2, I4, k8] + - SU3D[6, I3, I5]*(SU3D[8, I4, k8]*SU3D[I1, I2, k8] + - SU3D[8, I2, k8]*SU3D[I1, I4, k8] + SU3D[8, I1, k8]* - SU3D[I2, I4, k8]) + SU3D[6, I3, I4]*SU3D[8, I1, k8]* - SU3D[I2, I5, k8] + SU3D[6, I1, I4]*SU3D[8, I3, k8]*SU3D[I2, I5, k8] + - SU3D[6, I1, I3]*SU3D[8, I4, k8]*SU3D[I2, I5, k8] + - SU3D[6, I2, I5]*SU3D[8, I1, k8]*SU3D[I3, I4, k8] + - SU3D[6, I1, I5]*SU3D[8, I2, k8]*SU3D[I3, I4, k8] + - SU3D[6, I1, I2]*SU3D[8, I5, k8]*SU3D[I3, I4, k8] + - SU3D[6, I2, I4]*SU3D[8, I1, k8]*SU3D[I3, I5, k8] + - SU3D[6, I1, I4]*SU3D[8, I2, k8]*SU3D[I3, I5, k8] + - SU3D[6, I1, I2]*SU3D[8, I4, k8]*SU3D[I3, I5, k8] + - SU3D[6, I2, I3]*SU3D[8, I1, k8]*SU3D[I4, I5, k8] + - SU3D[6, I1, I3]*SU3D[8, I2, k8]*SU3D[I4, I5, k8] + - SU3D[6, I1, I2]*SU3D[8, I3, k8]*SU3D[I4, I5, k8]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I1, k11, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I1, k10, k7]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[8, I5, k9]* - SU3D[I1, k11, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[8, I5, k9]*SU3D[I2, k11, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[8, I5, k9]*SU3D[I1, k10, k7]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I5, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11] + - SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I1, k11, k9]*SU3D[I2, k10, k11]* - SU3D[I4, k10, k7] + SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I1, k10, k11]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k7] + SU3D[6, I2, k7]*SU3D[8, I5, k9]* - SU3D[I1, k11, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k7] + - SU3D[6, I1, k7]*SU3D[8, I5, k9]*SU3D[I2, k11, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k7] + SU3D[6, I2, k7]*SU3D[8, I5, k9]*SU3D[I1, k10, k11]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k7] + SU3D[6, I1, k7]*SU3D[8, I5, k9]* - SU3D[I2, k10, k11]*SU3D[I3, k11, k9]*SU3D[I4, k10, k7] + - SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I1, k10, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I1, k10, k11]* - SU3D[I2, k10, k7]*SU3D[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k9]* - SU3D[I1, k10, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k9] + - SU3D[6, I1, k7]*SU3D[8, I5, k9]*SU3D[I2, k10, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k9]*SU3D[I1, k10, k11]* - SU3D[I3, k10, k7]*SU3D[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I5, k9]* - SU3D[I2, k10, k11]*SU3D[I3, k10, k7]*SU3D[I4, k11, k9] + - SU3D[6, I5, k7]*(SU3D[8, I4, k9]*(SU3D[I1, k11, k9]* - (SU3D[I2, k10, k7]*SU3D[I3, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I3, k10, k7]) + SU3D[I1, k10, k7]* - (SU3D[I2, k11, k9]*SU3D[I3, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I3, k11, k9]) + SU3D[I1, k10, k11]* - (SU3D[I2, k11, k9]*SU3D[I3, k10, k7] + SU3D[I2, k10, k7]* - SU3D[I3, k11, k9])) + SU3D[8, I2, k9]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k11] + SU3D[8, I1, k9]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k11] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k11, k9]* - SU3D[I4, k10, k11] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k11] + SU3D[8, I2, k9]* - SU3D[I1, k11, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k7] + - SU3D[8, I1, k9]*SU3D[I2, k11, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k7] + SU3D[8, I2, k9]*SU3D[I1, k10, k11]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k7] + SU3D[8, I1, k9]* - SU3D[I2, k10, k11]*SU3D[I3, k11, k9]*SU3D[I4, k10, k7] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k9] + SU3D[8, I2, k9]* - SU3D[I1, k10, k11]*SU3D[I3, k10, k7]*SU3D[I4, k11, k9] + - SU3D[8, I1, k9]*SU3D[I2, k10, k11]*SU3D[I3, k10, k7]* - SU3D[I4, k11, k9] + SU3D[8, I3, k9]* - (SU3D[I1, k11, k9]*(SU3D[I2, k10, k7]*SU3D[I4, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I4, k10, k7]) + SU3D[I1, k10, k7]* - (SU3D[I2, k11, k9]*SU3D[I4, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I4, k11, k9]) + SU3D[I1, k10, k11]* - (SU3D[I2, k11, k9]*SU3D[I4, k10, k7] + SU3D[I2, k10, k7]* - SU3D[I4, k11, k9]))) + SU3D[6, I3, k7]*SU3D[8, I4, k9]* - SU3D[I1, k11, k9]*SU3D[I2, k10, k7]*SU3D[I5, k10, k11] + - SU3D[6, I3, k7]*SU3D[8, I4, k9]*SU3D[I1, k10, k7]*SU3D[I2, k11, k9]* - SU3D[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k7]*SU3D[I5, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I4, k9]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I1, k10, k7]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I4, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I1, k11, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I1, k11, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I2, k11, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I3, k9]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I3, k11, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I3, k11, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I1, k10, k7]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I3, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I4, k9]* - SU3D[I1, k11, k9]*SU3D[I2, k10, k11]*SU3D[I5, k10, k7] + - SU3D[6, I3, k7]*SU3D[8, I4, k9]*SU3D[I1, k10, k11]*SU3D[I2, k11, k9]* - SU3D[I5, k10, k7] + SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k7] + SU3D[6, I1, k7]*SU3D[8, I4, k9]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k11]*SU3D[I5, k10, k7] + - SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I1, k10, k11]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k7] + SU3D[6, I1, k7]*SU3D[8, I4, k9]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k7] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I1, k11, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k7] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I1, k11, k9]*SU3D[I4, k10, k11]* - SU3D[I5, k10, k7] + SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I2, k11, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k7] + SU3D[6, I1, k7]*SU3D[8, I3, k9]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k7] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3D[I5, k10, k7] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I3, k11, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k7] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k9]*SU3D[I5, k10, k7] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I1, k10, k11]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k7] + SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k7] + SU3D[6, I1, k7]*SU3D[8, I3, k9]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k9]*SU3D[I5, k10, k7] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I3, k10, k11]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k7] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k7] + SU3D[6, I3, k7]*SU3D[8, I4, k9]* - SU3D[I1, k10, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k9] + - SU3D[6, I3, k7]*SU3D[8, I4, k9]*SU3D[I1, k10, k11]*SU3D[I2, k10, k7]* - SU3D[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I1, k10, k11]*SU3D[I3, k10, k7]* - SU3D[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k9]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k7]*SU3D[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I1, k10, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I3, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I1, k10, k11]*SU3D[I4, k10, k7]*SU3D[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I1, k10, k11]*SU3D[I4, k10, k7]* - SU3D[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I4, k10, k7]*SU3D[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I3, k9]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k7]*SU3D[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k7]* - SU3D[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k7]*SU3D[I5, k11, k9] + SU3D[6, I4, k7]* - (SU3D[8, I5, k9]*(SU3D[I1, k11, k9]*(SU3D[I2, k10, k7]* - SU3D[I3, k10, k11] + SU3D[I2, k10, k11]*SU3D[I3, k10, k7]) + - SU3D[I1, k10, k7]*(SU3D[I2, k11, k9]*SU3D[I3, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I3, k11, k9]) + SU3D[I1, k10, k11]* - (SU3D[I2, k11, k9]*SU3D[I3, k10, k7] + SU3D[I2, k10, k7]* - SU3D[I3, k11, k9])) + SU3D[8, I2, k9]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k7]*SU3D[I5, k10, k11] + SU3D[8, I1, k9]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k11] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k11] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k11] + SU3D[8, I2, k9]* - SU3D[I1, k11, k9]*SU3D[I3, k10, k11]*SU3D[I5, k10, k7] + - SU3D[8, I1, k9]*SU3D[I2, k11, k9]*SU3D[I3, k10, k11]* - SU3D[I5, k10, k7] + SU3D[8, I2, k9]*SU3D[I1, k10, k11]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k7] + SU3D[8, I1, k9]* - SU3D[I2, k10, k11]*SU3D[I3, k11, k9]*SU3D[I5, k10, k7] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I1, k10, k11]*SU3D[I3, k10, k7]*SU3D[I5, k11, k9] + - SU3D[8, I1, k9]*SU3D[I2, k10, k11]*SU3D[I3, k10, k7]* - SU3D[I5, k11, k9] + SU3D[8, I3, k9]* - (SU3D[I1, k11, k9]*(SU3D[I2, k10, k7]*SU3D[I5, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I5, k10, k7]) + SU3D[I1, k10, k7]* - (SU3D[I2, k11, k9]*SU3D[I5, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I5, k11, k9]) + SU3D[I1, k10, k11]* - (SU3D[I2, k11, k9]*SU3D[I5, k10, k7] + SU3D[I2, k10, k7]* - SU3D[I5, k11, k9]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((8*I)/45)*(SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SU3F[6, 8, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SU3F[6, 8, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I2] + - SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I3] + - SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SU3F[6, 8, I4] + - SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SU3F[6, 8, I4] + - SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SU3F[6, 8, I1] + - SU3D[I1, I4, k6]*SU3F[6, 8, I3] + SU3D[I1, I3, k6]*SU3F[6, 8, I4]) + - SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SU3F[6, 8, I5] + - SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SU3F[6, 8, I5] + - SU3D[I2, I4, k6]*(SU3D[I3, I5, k6]*SU3F[6, 8, I1] + - SU3D[I1, I5, k6]*SU3F[6, 8, I3] + SU3D[I1, I3, k6]*SU3F[6, 8, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/45)*(SU3D[8, I3, I4]*SU3D[I2, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I5]*SU3D[I3, I4, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I4]*SU3D[I3, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I3]*SU3D[I4, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I3, I4]*SU3D[I1, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I5]*SU3D[I3, I4, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I4]*SU3D[I3, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I3]*SU3D[I4, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I2, I5]*SU3D[I1, I4, k6]*SU3F[6, I3, k6] + - SU3D[8, I2, I4]*SU3D[I1, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I5]*SU3D[I2, I4, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I4]*SU3D[I2, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I2]*SU3D[I4, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I4, I5]*(SU3D[I2, I3, k6]*SU3F[6, I1, k6] + - SU3D[I1, I3, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I3, k6]) + SU3D[8, I2, I5]*SU3D[I1, I3, k6]* - SU3F[6, I4, k6] + SU3D[8, I2, I3]*SU3D[I1, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I5]*SU3D[I2, I3, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I3]*SU3D[I2, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I2]*SU3D[I3, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I3, I5]*(SU3D[I2, I4, k6]*SU3F[6, I1, k6] + - SU3D[I1, I4, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I4, k6]) + SU3D[8, I3, I4]*SU3D[I1, I2, k6]* - SU3F[6, I5, k6] + SU3D[8, I2, I4]*SU3D[I1, I3, k6]*SU3F[6, I5, k6] + - SU3D[8, I2, I3]*SU3D[I1, I4, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I4]*SU3D[I2, I3, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I3]*SU3D[I2, I4, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I2]*SU3D[I3, I4, k6]*SU3F[6, I5, k6]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k8] + - SU3D[8, I2, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k8] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I3, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[8, I5, k7]*(SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I1, k8] + - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k8] + SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3F[6, I4, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3F[6, I4, k8] + SU3D[I2, k8, k9]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k10, k9])*SU3F[6, I3, k8] + SU3D[I3, k10, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I4, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I4, k8]))) + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k8] + SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k8] + - SU3D[I2, k8, k9]*((SU3D[I1, k10, k9]*SU3D[I5, k10, k7] + - SU3D[I1, k10, k7]*SU3D[I5, k10, k9])*SU3F[6, I3, k8] + - SU3D[I3, k10, k9]*(SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[I1, k10, k7]*SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I5, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I5, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I5, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I5, k8])))))/(Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I1, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[8, I1, k6] + - SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I1, k6] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I1, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[8, I1, k6] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[8, I1, k6] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I1, k6] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I1, k6] + - SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6] + - SU3D[6, I2, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I2, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[8, I2, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I2, k6] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I2, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[8, I2, k6] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[8, I2, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I2, k6] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I2, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6] + - SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[8, I3, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I3, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[8, I3, k6] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[8, I3, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I3, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I3, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6] + - SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I4, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3D[I3, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I4, k6] + - SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3D[I5, k10, k9]*SU3F[8, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I4, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]*SU3D[I5, k10, k9]* - SU3F[8, I4, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[8, I4, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]* - SU3D[I3, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I4, k6] + - SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[8, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I4, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6] + - SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6] + SU3D[6, I5, k9]*(SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k9]*SU3F[8, I1, k6] + SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6] + - SU3D[I1, k6, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3F[8, I2, k6] + SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I2, k6] + SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[8, I2, k6] + - SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[8, I2, k6] + SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6] + SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]* - SU3F[8, I3, k6] + SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3F[8, I4, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[8, I4, k6] + SU3D[I2, k6, k7]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k10, k9])*SU3F[8, I3, k6] + SU3D[I3, k10, k9]* - (SU3D[I4, k10, k7]*SU3F[8, I1, k6] + SU3D[I1, k10, k7]* - SU3F[8, I4, k6]) + SU3D[I3, k10, k7]* - (SU3D[I4, k10, k9]*SU3F[8, I1, k6] + SU3D[I1, k10, k9]* - SU3F[8, I4, k6])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k6, k7]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k6, k7])*SU3F[8, I3, k6] + SU3D[I3, k6, k7]* - (SU3D[I4, k10, k7]*SU3F[8, I1, k6] + SU3D[I1, k10, k7]* - SU3F[8, I4, k6]) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*SU3F[8, I1, k6] + SU3D[I1, k6, k7]* - SU3F[8, I4, k6]))) + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3F[8, I5, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I5, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k7]*SU3F[8, I5, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3F[8, I5, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[8, I5, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k9]*SU3F[8, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[8, I5, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[8, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k9]*SU3F[8, I5, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I5, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I5, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6] + SU3D[6, I4, k9]* - (SU3D[I2, k10, k7]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[8, I1, k6] + SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6] + SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k7]*SU3F[8, I2, k6] + - SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[8, I2, k6] + SU3D[I1, k10, k7]* - SU3D[I3, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I2, k6] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6] + SU3D[I1, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3D[I5, k10, k9]*SU3F[8, I3, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3F[8, I5, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k6, k7]*SU3F[8, I5, k6] + - SU3D[I2, k6, k7]*((SU3D[I1, k10, k9]*SU3D[I5, k10, k7] + - SU3D[I1, k10, k7]*SU3D[I5, k10, k9])*SU3F[8, I3, k6] + - SU3D[I3, k10, k9]*(SU3D[I5, k10, k7]*SU3F[8, I1, k6] + - SU3D[I1, k10, k7]*SU3F[8, I5, k6]) + SU3D[I3, k10, k7]* - (SU3D[I5, k10, k9]*SU3F[8, I1, k6] + SU3D[I1, k10, k9]* - SU3F[8, I5, k6])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k6, k7]*SU3D[I5, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I5, k6, k7])*SU3F[8, I3, k6] + SU3D[I3, k6, k7]* - (SU3D[I5, k10, k7]*SU3F[8, I1, k6] + SU3D[I1, k10, k7]* - SU3F[8, I5, k6]) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*SU3F[8, I1, k6] + SU3D[I1, k6, k7]* - SU3F[8, I5, k6])))))/(Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I1, k6] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8]*SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8]*SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I1, k6] + - SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I2, k6] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8]*SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I2, k6] + - SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I3, k6] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[8, I3, k6] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I1, k8]*SU3F[8, I3, k6] + - SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I3, k6] + SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I3, k6] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[6, I5, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I3, k6] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I3, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[6, I3, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I5, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I5, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[6, I2, k8]* - SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[6, I3, k8]* - SU3F[8, I5, k6] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I3, k8]*SU3F[8, I5, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I3, k8, k9]*(SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[6, I5, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I5, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I5, k6] + SU3D[I4, k7, k9]*(SU3D[I5, k6, k7]* - (SU3F[6, I2, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I2, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6])) + SU3D[I4, k6, k7]* - (SU3D[I5, k7, k9]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k7, k9]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k7, k9]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6]))) + SU3D[I3, k7, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I4, k8, k9]*(SU3D[I5, k6, k7]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6])) + SU3D[I4, k6, k7]* - (SU3D[I5, k8, k9]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k8, k9]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k8, k9]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((4*I)/45)*(SU3D[6, I3, I4]*SU3D[I2, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I5]*SU3D[I3, I4, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I4]*SU3D[I3, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I3]*SU3D[I4, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I3, I4]*SU3D[I1, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I5]*SU3D[I3, I4, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I4]*SU3D[I3, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I3]*SU3D[I4, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I2, I5]*SU3D[I1, I4, k7]*SU3F[8, I3, k7] + - SU3D[6, I2, I4]*SU3D[I1, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I5]*SU3D[I2, I4, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I4]*SU3D[I2, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I2]*SU3D[I4, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I4, I5]*(SU3D[I2, I3, k7]*SU3F[8, I1, k7] + - SU3D[I1, I3, k7]*SU3F[8, I2, k7] + SU3D[I1, I2, k7]* - SU3F[8, I3, k7]) + SU3D[6, I2, I5]*SU3D[I1, I3, k7]* - SU3F[8, I4, k7] + SU3D[6, I2, I3]*SU3D[I1, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I5]*SU3D[I2, I3, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I3]*SU3D[I2, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I2]*SU3D[I3, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I3, I5]*(SU3D[I2, I4, k7]*SU3F[8, I1, k7] + - SU3D[I1, I4, k7]*SU3F[8, I2, k7] + SU3D[I1, I2, k7]* - SU3F[8, I4, k7]) + SU3D[6, I3, I4]*SU3D[I1, I2, k7]* - SU3F[8, I5, k7] + SU3D[6, I2, I4]*SU3D[I1, I3, k7]*SU3F[8, I5, k7] + - SU3D[6, I2, I3]*SU3D[I1, I4, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I4]*SU3D[I2, I3, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I3]*SU3D[I2, I4, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I2]*SU3D[I3, I4, k7]*SU3F[8, I5, k7]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I1, k10, k6] + - SU3D[8, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[8, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I2, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I3, k10, k6] + - SU3D[8, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I4, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I4, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I4, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6]))) + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I1, k7]* - SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I2, k7]*SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k10, k6] + - SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I5, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I5, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k11]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k11]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I4, k11]*SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3F[6, I4, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[6, I2, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I3, k11]*SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I3, k11]*SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3F[6, I1, k7]* - SU3F[8, I2, k11]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + - SU3F[6, I3, k7]*(SU3F[8, I4, k11]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k6]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I2, k11]*SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k11]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I2, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I1, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I2, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I3, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I3, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k11]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k11]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I2, k11]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I1, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I2, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I3, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I3, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I5, k11]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3F[6, I1, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3F[6, I5, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[6, I2, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I3, k11]*SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I3, k11]*SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3F[6, I1, k7]* - SU3F[8, I2, k11]*SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + - SU3F[6, I3, k7]*(SU3F[8, I5, k11]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k6]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I2, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I5, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k9] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I3, k10, k9] + SU3D[8, I4, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k9])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I4, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I4, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I4, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I4, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I4, k10, k9]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + SU3D[8, I5, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k9])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I5, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I5, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I5, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I5, k10, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I2, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I1, k10, k9] + - SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k10, k9] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I2, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k10, k9] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I2, k6]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I3, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k9] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I1, k6]*SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I2, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I2, k6]*SU3F[I4, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I3, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[8, I5, k6]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[8, I5, k6]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[8, I5, k6]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[8, I5, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[8, I5, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I4, k10, k9] + - SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k9] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k9] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k9] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I4, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[8, I3, k6]*SU3F[I4, k10, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[8, I2, k6]* - SU3F[I1, k10, k9] + SU3F[8, I1, k6]*SU3F[I2, k10, k9]) + - SU3D[I2, k10, k7]*(SU3F[8, I4, k6]*SU3F[I1, k10, k9] + - SU3F[8, I1, k6]*SU3F[I4, k10, k9]) + SU3D[I1, k10, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k10, k9] + SU3F[8, I2, k6]* - SU3F[I4, k10, k9])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k10, k9] + - SU3F[8, I1, k6]*SU3F[I2, k10, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I1, k10, k9] + SU3F[8, I1, k6]* - SU3F[I4, k10, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k10, k9] + SU3F[8, I2, k6]* - SU3F[I4, k10, k9]))) + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I1, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I1, k6]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I1, k6]*SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I2, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I2, k6]*SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I3, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I4, k6]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[8, I4, k6]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[8, I4, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[8, I4, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[8, I4, k6]*SU3F[I5, k10, k9] + SU3D[6, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k9] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k9] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k9] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I5, k10, k9] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[8, I2, k6]* - SU3F[I1, k10, k9] + SU3F[8, I1, k6]*SU3F[I2, k10, k9]) + - SU3D[I2, k10, k7]*(SU3F[8, I5, k6]*SU3F[I1, k10, k9] + - SU3F[8, I1, k6]*SU3F[I5, k10, k9]) + SU3D[I1, k10, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k10, k9] + SU3F[8, I2, k6]* - SU3F[I5, k10, k9])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k10, k9] + - SU3F[8, I1, k6]*SU3F[I2, k10, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I1, k10, k9] + SU3F[8, I1, k6]* - SU3F[I5, k10, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k10, k9] + SU3F[8, I2, k6]* - SU3F[I5, k10, k9]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I1, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6] + SU3D[6, I2, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I1, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[8, I5, k11]*SU3F[I1, k11, k6] + - SU3D[6, I3, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]* - SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I1, k11]*SU3F[I2, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I2, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k7, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I2, k11, k6] + - SU3D[6, I1, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[8, I5, k11]*SU3F[I2, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k11]*SU3F[I3, k11, k6] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I3, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I4, k11]*SU3F[I3, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I3, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[8, I5, k11]*SU3F[I3, k11, k6] + - SU3D[6, I3, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[8, I1, k11]*SU3F[I4, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I5, k6, k7]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k11]*SU3F[I4, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I3, k11]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3F[8, I5, k11]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k11]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3F[8, I5, k11]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k7, k9]* - SU3F[8, I5, k11]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k9]*SU3F[8, I5, k11]*SU3F[I4, k11, k6] + - SU3D[6, I5, k9]*(SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3D[I1, k7, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[8, I1, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[8, I4, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3F[8, I3, k11]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k7, k9]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[I3, k7, k9]*(SU3D[I4, k6, k7]*(SU3F[8, I2, k11]* - SU3F[I1, k11, k6] + SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k6, k7]*(SU3F[8, I4, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I4, k11, k6]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I4, k11, k6])) + SU3D[I3, k6, k7]* - (SU3D[I4, k7, k9]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3D[I2, k7, k9]* - (SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I4, k11, k6]) + SU3D[I1, k7, k9]* - (SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I4, k11, k6]))) + SU3D[6, I3, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[8, I1, k11]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]* - SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[8, I1, k11]*SU3F[I5, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k11]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k7, k9]*SU3F[8, I2, k11]*SU3F[I5, k11, k6] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[8, I2, k11]* - SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I4, k6, k7]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k11]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[8, I4, k11]*SU3F[I5, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[8, I4, k11]* - SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3F[8, I4, k11]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k11]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k7, k9]*SU3F[8, I4, k11]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k7, k9]* - SU3F[8, I4, k11]*SU3F[I5, k11, k6] + SU3D[6, I4, k9]* - (SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3D[I1, k7, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[8, I1, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k7, k9]*SU3F[8, I3, k11]*SU3F[I5, k11, k6] + - SU3D[I3, k7, k9]*(SU3D[I5, k6, k7]*(SU3F[8, I2, k11]* - SU3F[I1, k11, k6] + SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k6, k7]*(SU3F[8, I5, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I5, k11, k6]) + SU3D[I1, k6, k7]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I5, k11, k6])) + SU3D[I3, k6, k7]* - (SU3D[I5, k7, k9]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3D[I2, k7, k9]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I5, k11, k6]) + SU3D[I1, k7, k9]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I5, k11, k6]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k11]*SU3F[I1, k11, k6] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I2, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I2, k11, k6] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I4, k11]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I4, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I1, k11]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I1, k11]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I2, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I3, k11]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I5, k11]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I5, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I5, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I4, k11]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I4, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]* - SU3F[I5, k11, k6] + SU3D[I4, k7, k8]* - (SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I3, k11, k6])) + SU3D[I2, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I2, k11]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I5, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I5, k11, k6]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I3, k11, k6])) + SU3D[I2, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I3, k8]*SU3F[8, I2, k11]*SU3F[I5, k11, k6] + - SU3D[I2, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[I3, k7, k8]* - (SU3F[6, I5, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I5, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I5, k11, k6])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I2, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I2, k10, k7]*SU3F[I3, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k11]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I4, k11]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[6, I4, k10]* - (SU3F[8, I3, k11]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[6, I2, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3F[6, I1, k10]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + - SU3F[6, I2, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I3, k11]*SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3F[6, I1, k10]* - SU3F[8, I2, k11]*SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + - SU3F[6, I3, k10]*(SU3F[8, I4, k11]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I4, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I4, k11, k6]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I2, k11]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k11]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k11]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I4, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I5, k11]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[6, I5, k10]* - (SU3F[8, I3, k11]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[6, I2, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3F[6, I1, k10]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + - SU3F[6, I2, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I3, k11]*SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3F[6, I1, k10]* - SU3F[8, I2, k11]*SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + - SU3F[6, I3, k10]*(SU3F[8, I5, k11]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I5, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I5, k11, k6]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I4, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3F[6, I4, k10]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I3, k6]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I3, k6]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[6, I1, k10]* - SU3F[8, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3F[6, I3, k10]*(SU3F[8, I4, k6]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[8, I2, k6]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I2, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I4, k6, k7]*(SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I5, k6]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3F[6, I1, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3F[6, I5, k10]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I3, k6]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I3, k6]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[6, I1, k10]* - SU3F[8, I2, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3F[6, I3, k10]*(SU3F[8, I5, k6]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3F[I2, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I5, k9]* - (SU3D[8, I4, k7]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[8, I2, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[8, I1, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[8, I2, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[8, I2, k7]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[8, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k7]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[8, I3, k7]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3F[I2, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3F[I2, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3F[I2, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3F[I2, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k9]* - SU3D[8, I4, k7]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3F[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I4, k9]* - (SU3D[8, I5, k7]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[8, I2, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I2, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I1, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[8, I2, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3D[8, I1, k7]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k7]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[8, I5, k7]*(SU3F[6, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I4, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I5, k7]*(SU3F[8, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[8, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[8, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[8, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[8, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[8, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[8, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I4, k7]* - (SU3F[8, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[8, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[8, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[8, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[8, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[8, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[8, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I1, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I3, k8, k9]*SU3D[I4, k11, k7]*SU3F[I1, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I1, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I1, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k8, k9]*SU3D[I5, k11, k7]*SU3F[I1, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I1, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k7]*SU3F[I1, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I1, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I1, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k8, k9]*SU3F[I1, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I1, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I2, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k8, k9]*SU3D[I4, k11, k7]*SU3F[I2, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I2, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I2, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k7]*SU3F[I2, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I2, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k7]*SU3F[I2, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I2, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k8, k9]*SU3F[I2, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I3, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I2, k8, k9]*SU3D[I4, k11, k7]*SU3F[I3, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I3, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I3, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I3, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I3, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k8, k9]*SU3F[I3, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I3, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I2, k8, k9]*SU3F[I4, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k8, k9]*SU3D[I3, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I3, k8, k9]*SU3F[I4, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I3, k8, k9]* - SU3F[I4, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k7]*SU3F[I4, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k11, k7]*SU3F[I4, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I4, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I1, k11, k7]*SU3D[I5, k8, k9]*SU3F[I4, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I4, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I4, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I5, k8, k9]*SU3F[I4, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I4, k11, k8] + SU3D[6, I5, k9]*(SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k11, k7]*SU3D[I4, k8, k9]*SU3F[I1, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k11, k7]* - SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I2, k11, k8] + SU3D[8, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I4, k11, k7]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k11, k7]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k8, k9]*SU3F[I3, k11, k8] + - SU3D[8, I4, k7]*((SU3D[I1, k8, k9]*SU3D[I3, k11, k7] + - SU3D[I1, k11, k7]*SU3D[I3, k8, k9])*SU3F[I2, k11, k8] + - SU3D[I2, k8, k9]*(SU3D[I3, k11, k7]*SU3F[I1, k11, k8] + - SU3D[I1, k11, k7]*SU3F[I3, k11, k8]) + SU3D[I2, k11, k7]* - (SU3D[I3, k8, k9]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3F[I3, k11, k8])) + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k7]*SU3F[I4, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k11, k7]*SU3D[I3, k8, k9]* - SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I3, k8, k9]*SU3F[I4, k11, k8] + SU3D[8, I3, k7]* - ((SU3D[I1, k8, k9]*SU3D[I4, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I4, k8, k9])*SU3F[I2, k11, k8] + SU3D[I2, k8, k9]* - (SU3D[I4, k11, k7]*SU3F[I1, k11, k8] + SU3D[I1, k11, k7]* - SU3F[I4, k11, k8]) + SU3D[I2, k11, k7]* - (SU3D[I4, k8, k9]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]*SU3D[I2, k8, k9]* - SU3F[I5, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]*SU3D[I3, k8, k9]* - SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]* - SU3D[I3, k8, k9]*SU3F[I5, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I4, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k8, k9]*SU3D[I4, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k11, k7]*SU3D[I4, k8, k9]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I5, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k8, k9]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I5, k11, k8] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I1, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k11, k7]*SU3F[I2, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k8, k9]*SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I3, k11, k8] + SU3D[8, I5, k7]* - ((SU3D[I1, k8, k9]*SU3D[I3, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I3, k8, k9])*SU3F[I2, k11, k8] + SU3D[I2, k8, k9]* - (SU3D[I3, k11, k7]*SU3F[I1, k11, k8] + SU3D[I1, k11, k7]* - SU3F[I3, k11, k8]) + SU3D[I2, k11, k7]* - (SU3D[I3, k8, k9]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3F[I3, k11, k8])) + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k7]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k11, k7]*SU3D[I3, k8, k9]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I3, k8, k9]*SU3F[I5, k11, k8] + SU3D[8, I3, k7]* - ((SU3D[I1, k8, k9]*SU3D[I5, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I5, k8, k9])*SU3F[I2, k11, k8] + SU3D[I2, k8, k9]* - (SU3D[I5, k11, k7]*SU3F[I1, k11, k8] + SU3D[I1, k11, k7]* - SU3F[I5, k11, k8]) + SU3D[I2, k11, k7]* - (SU3D[I5, k8, k9]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[8, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I1, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[8, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[8, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, k8, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[8, I5, k7]*(SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I4, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I4, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I4, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8]))) + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I1, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I2, k11]*SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I5, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I5, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[8, I2, k6]*SU3F[I1, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I1, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I1, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I2, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I2, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I3, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I2, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I3, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I5, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I2, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I4, k7, k8]*(SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I2, k6, k7]*SU3F[6, I5, k11]* - SU3F[8, I1, k6]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[8, I5, k6]*SU3F[I3, k11, k8] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I3, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I3, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I3, k11, k8])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[8, I1, k6]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[8, I3, k6]*SU3F[I5, k11, k8] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I5, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I5, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I5, k11, k8]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I3, k11]* - SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I5, k11]* - SU3F[8, I1, k6]*SU3F[I3, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k7, k8]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k8]*SU3F[6, I2, k11]* - SU3F[8, I5, k6]*SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I3, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I3, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k11]* - SU3F[8, I1, k6]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k7, k8]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k7, k8]*SU3F[6, I2, k11]* - SU3F[8, I3, k6]*SU3F[I5, k11, k8] + SU3D[I3, k7, k8]* - (SU3F[6, I5, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I5, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I5, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[8, I3, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[8, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[6, I2, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]* - SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[8, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[8, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[8, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[8, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[8, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[8, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[8, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3F[8, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[8, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[8, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[8, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[8, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[8, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[8, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I5, k10, k7]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k7]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I5, k9]*(SU3D[8, I2, k7]*SU3D[I4, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I4, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k9] + SU3D[8, I4, k7]* - (SU3D[I3, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k10, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k9])) + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3D[I3, k10, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k9] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[8, I1, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[8, I3, k7]*(SU3D[I4, k10, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k7]*SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k7]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k10, k7]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k7]*SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k7]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k10, k7]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I5, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k9] + SU3D[8, I5, k7]* - (SU3D[I3, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k10, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k9])) + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[8, I2, k7]* - SU3D[I3, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[8, I1, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3D[8, I3, k7]*(SU3D[I5, k10, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k9]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I2, k11, k9] + - SU3D[6, I3, k7]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I2, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[6, I2, k7]*SU3D[8, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + - SU3D[6, I1, k7]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[6, I2, k7]*SU3D[8, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + - SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I2, k7]*SU3D[8, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k7]*SU3D[8, I5, k9]* - SU3D[I1, k6, k7]*SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + - SU3D[6, I1, k7]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + - SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + - SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k9]* - SU3D[I1, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[6, I1, k7]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[6, I5, k7]*(SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + - SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[8, I4, k9]* - (SU3D[I3, k6, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3D[I2, k6, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[8, I3, k9]*(SU3D[I4, k6, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k7]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I2, k7]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[6, I3, k7]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[6, I1, k7]*SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k7]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[6, I3, k7]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + - SU3D[6, I1, k7]*SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I4, k7]* - (SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[8, I5, k9]* - (SU3D[I3, k6, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3D[I2, k6, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[8, I3, k9]*(SU3D[I5, k6, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k11, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k11, k9]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I2, k11, k9] + SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I2, k11, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k6] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k9]))) + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I4, k9]*(SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k11, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I2, k11, k9] + SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I2, k11, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k11, k9] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I3, k11, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I2, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[I4, k6, k7]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k9]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I3, k6]*SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + - SU3D[I1, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[I1, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[8, I4, k6]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k11, k9]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I2, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I4, k9]*(SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I5, k6]*SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[I5, k6, k7]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k9]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I3, k6]*SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + - SU3D[I1, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[I1, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[8, I5, k6]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k11, k9]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k11, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k11, k7]*SU3F[I1, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3D[I4, k11, k7]*SU3F[I1, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I2, k11, k7]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3D[I5, k11, k7]*SU3F[I1, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3D[I5, k11, k7]* - SU3F[I1, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k11, k7]*SU3F[I1, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3D[I5, k11, k7]*SU3F[I1, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I2, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I1, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I3, k11, k7]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I4, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I1, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k11, k7]*SU3F[I2, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3D[I4, k11, k7]*SU3F[I2, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I1, k11, k7]*SU3D[I4, k6, k7]* - SU3F[I2, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I4, k9]* - SU3D[I1, k6, k7]*SU3D[I5, k11, k7]*SU3F[I2, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3D[I5, k11, k7]* - SU3F[I2, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k11, k7]*SU3F[I2, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3D[I5, k11, k7]*SU3F[I2, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I1, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I3, k11, k7]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I1, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I4, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k11, k7]*SU3F[I3, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]* - SU3D[I2, k6, k7]*SU3D[I4, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I1, k11, k7]*SU3D[I4, k6, k7]* - SU3F[I3, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I2, k11, k7]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I4, k9]* - SU3D[I1, k6, k7]*SU3D[I5, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I2, k6, k7]*SU3D[I5, k11, k7]* - SU3F[I3, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k11, k7]*SU3F[I3, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3D[I5, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I1, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I3, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I2, k11, k7]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I1, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I4, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I3, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I5, k9]* - SU3D[I1, k11, k7]*SU3D[I2, k6, k7]*SU3F[I4, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]*SU3D[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]* - SU3D[I1, k11, k7]*SU3D[I3, k6, k7]*SU3F[I4, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I2, k11, k7]*SU3D[I3, k6, k7]* - SU3F[I4, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I3, k9]* - SU3D[I1, k6, k7]*SU3D[I5, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3D[I5, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I3, k9]* - SU3D[I1, k11, k7]*SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I2, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I2, k11, k7]* - SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I1, k9]* - SU3D[I3, k11, k7]*SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I3, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I4, k6, k9] + SU3D[6, I5, k11]*(SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k11, k7]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]* - SU3D[I3, k11, k7]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k11, k7]* - SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k9] + SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3D[I4, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k11, k7]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I4, k6, k7]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9] + - SU3D[8, I4, k9]*((SU3D[I1, k6, k7]*SU3D[I3, k11, k7] + - SU3D[I1, k11, k7]*SU3D[I3, k6, k7])*SU3F[I2, k6, k9] + - SU3D[I2, k6, k7]*(SU3D[I3, k11, k7]*SU3F[I1, k6, k9] + - SU3D[I1, k11, k7]*SU3F[I3, k6, k9]) + SU3D[I2, k11, k7]* - (SU3D[I3, k6, k7]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3F[I3, k6, k9])) + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3D[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k11, k7]*SU3D[I3, k6, k7]* - SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I3, k6, k7]*SU3F[I4, k6, k9] + SU3D[8, I3, k9]* - ((SU3D[I1, k6, k7]*SU3D[I4, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I4, k6, k7])*SU3F[I2, k6, k9] + SU3D[I2, k6, k7]* - (SU3D[I4, k11, k7]*SU3F[I1, k6, k9] + SU3D[I1, k11, k7]* - SU3F[I4, k6, k9]) + SU3D[I2, k11, k7]* - (SU3D[I4, k6, k7]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3F[I4, k6, k9]))) + SU3D[6, I3, k11]*SU3D[8, I4, k9]* - SU3D[I1, k6, k7]*SU3D[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I1, k11, k7]*SU3D[I2, k6, k7]* - SU3F[I5, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3D[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I1, k11, k7]*SU3D[I3, k6, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I2, k11, k7]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3D[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3D[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I1, k11, k7]*SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I1, k11, k7]*SU3D[I4, k6, k7]* - SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]* - SU3D[I2, k11, k7]*SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I3, k11, k7]*SU3D[I4, k6, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + SU3D[6, I4, k11]* - (SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k11, k7]* - SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k11, k7]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3D[I5, k11, k7]*SU3F[I2, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k11, k7]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3D[I5, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k11, k7]*SU3D[I5, k6, k7]* - SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + SU3D[8, I5, k9]* - ((SU3D[I1, k6, k7]*SU3D[I3, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I3, k6, k7])*SU3F[I2, k6, k9] + SU3D[I2, k6, k7]* - (SU3D[I3, k11, k7]*SU3F[I1, k6, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3D[I2, k11, k7]* - (SU3D[I3, k6, k7]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3F[I3, k6, k9])) + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3D[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k11, k7]*SU3D[I3, k6, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]* - ((SU3D[I1, k6, k7]*SU3D[I5, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I5, k6, k7])*SU3F[I2, k6, k9] + SU3D[I2, k6, k7]* - (SU3D[I5, k11, k7]*SU3F[I1, k6, k9] + SU3D[I1, k11, k7]* - SU3F[I5, k6, k9]) + SU3D[I2, k11, k7]* - (SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3F[I5, k6, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I1, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I2, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I4, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9]))) + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I1, k10]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I1, k10]*SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I2, k10]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I2, k10]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I5, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I1, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k7]*SU3F[8, I4, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I4, k8]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I2, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I2, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I4, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I4, k8]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I2, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I3, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I3, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I4, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I4, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k7]*SU3F[8, I4, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I3, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I1, k8]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k7]*SU3F[8, I1, k8]*SU3F[I4, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I1, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k8]*SU3F[I4, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I1, k8]* - SU3F[I4, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I2, k8]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I2, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I2, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I2, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I3, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I3, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I5, k8]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I5, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I5, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k8]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I4, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k8]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I4, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I4, k8]* - SU3F[I5, k6, k9] + SU3D[I4, k8, k9]*(SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I1, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I2, k8]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I5, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I5, k8]*SU3F[I3, k6, k9] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I5, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I5, k6, k9]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I1, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I2, k8]*SU3F[I3, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I2, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I5, k8, k9]*(SU3F[6, I3, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, - k9] + SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I3, k6, k9])) + SU3D[I2, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I3, k8, k9]* - (SU3F[6, I5, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I5, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I5, k6, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I2, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I2, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I5, k9]* - SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]* - SU3D[I1, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I5, k11]*(SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I4, k9]*(SU3D[I3, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I3, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k9]))) + SU3D[6, I3, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I4, k11]* - (SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I5, k9]*(SU3D[I3, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I3, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*(SU3D[I5, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k6, k9]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I2, k6, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k11]*(SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k9]))) + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I5, k6, k7]*(SU3F[6, I3, k11]* - (SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k6, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I2, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k7, k8] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I3, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k7, k8] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I4, k6]* - SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I4, k6]*SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I5, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I5, k6]*SU3F[I1, k7, k8] + - SU3D[6, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I1, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k7, k8] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I3, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k6]*SU3F[I2, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I4, k6]* - SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I4, k6]*SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k7, k8] + - SU3D[6, I1, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I5, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I5, k6]*SU3F[I2, k7, k8] + - SU3D[6, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I1, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I2, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k6]*SU3F[I3, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I4, k6]* - SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I4, k6]*SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I5, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I5, k6]*SU3F[I3, k7, k8] + - SU3D[6, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[8, I1, k6]*SU3F[I4, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I1, k6]* - SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I2, k6]* - SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I2, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I3, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[8, I3, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k8, k9]* - SU3F[8, I5, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[8, I5, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k8, k9]* - SU3F[8, I5, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k8, k9]*SU3F[8, I5, k6]*SU3F[I4, k7, k8] + - SU3D[6, I5, k9]*(SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k7, k8] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I3, k6]* - SU3F[I1, k7, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k7, k8] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I3, k6]* - SU3F[I2, k7, k8] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k7, k8] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I1, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I2, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I4, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k7, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I3, k6]* - SU3F[I4, k7, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k7, k8] + - SU3F[8, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I1, k7, k8] + SU3F[8, I1, k6]* - SU3F[I4, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k7, k8] + SU3F[8, I2, k6]* - SU3F[I4, k7, k8])) + SU3D[I3, k6, k7]* - (SU3D[I4, k8, k9]*(SU3F[8, I2, k6]*SU3F[I1, k7, k8] + - SU3F[8, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k8, k9]* - (SU3F[8, I4, k6]*SU3F[I1, k7, k8] + SU3F[8, I1, k6]* - SU3F[I4, k7, k8]) + SU3D[I1, k8, k9]* - (SU3F[8, I4, k6]*SU3F[I2, k7, k8] + SU3F[8, I2, k6]* - SU3F[I4, k7, k8]))) + SU3D[6, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I1, k6]*SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I1, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I2, k6]*SU3F[I5, k7, k8] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I2, k6]* - SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I3, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I3, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]* - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I4, k6]* - SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[8, I4, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[8, I4, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[8, I4, k6]*SU3F[I5, k7, k8] + SU3D[6, I4, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k7, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I3, k6]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I3, k6]*SU3F[I2, k7, k8] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k7, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I1, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I2, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I5, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I5, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I3, k6]*SU3F[I5, k7, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k6, k7]*(SU3F[8, I2, k6]* - SU3F[I1, k7, k8] + SU3F[8, I1, k6]*SU3F[I2, k7, k8]) + - SU3D[I2, k6, k7]*(SU3F[8, I5, k6]*SU3F[I1, k7, k8] + - SU3F[8, I1, k6]*SU3F[I5, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k7, k8] + SU3F[8, I2, k6]* - SU3F[I5, k7, k8])) + SU3D[I3, k6, k7]* - (SU3D[I5, k8, k9]*(SU3F[8, I2, k6]*SU3F[I1, k7, k8] + - SU3F[8, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k8, k9]* - (SU3F[8, I5, k6]*SU3F[I1, k7, k8] + SU3F[8, I1, k6]* - SU3F[I5, k7, k8]) + SU3D[I1, k8, k9]* - (SU3F[8, I5, k6]*SU3F[I2, k7, k8] + SU3F[8, I2, k6]* - SU3F[I5, k7, k8]))))/(30*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k11]*SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + - SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I2, k7, k9] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I2, k7, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]* - SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I3, k7, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6]*SU3F[I3, k7, k9] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3F[8, I5, k11]*SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k9] + SU3D[I1, k6, k7]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k7, k9] + SU3D[I4, k6, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + SU3F[8, I2, k11]* - (SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k9]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k9])) + SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I3, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + - SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k9] + SU3D[I2, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + SU3D[I1, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + - SU3D[I3, k6, k7]*(SU3F[8, I4, k11]*(SU3F[I1, k7, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + - SU3F[8, I2, k11]*(SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k7, k9]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k7, k9]))) + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]*SU3F[I1, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]*SU3F[I2, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]* - SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3F[8, I4, k11]*SU3F[I2, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k11]*SU3F[I3, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[8, I1, k11]*SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[8, I1, k11]*SU3F[I4, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[8, I2, k11]*SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I4, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[8, I1, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I4, k9]* - (SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6]*SU3F[I3, k7, k9] + - SU3D[I1, k6, k7]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k9] + SU3D[I5, k6, k7]*(SU3F[8, I3, k11]* - (SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I2, k7, k9]) + SU3F[8, I2, k11]* - (SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k9]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k9])) + SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I3, k11]*SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[I2, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[I1, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + - SU3D[I3, k6, k7]*(SU3F[8, I5, k11]*(SU3F[I1, k7, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + - SU3F[8, I2, k11]*(SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k7, k9]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k7, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I3, k11]* - SU3F[8, I5, k8]*SU3F[I1, k10, k9]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k9]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9] + - SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I4, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I5, k8]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k8, k9] + SU3F[6, I5, k11]* - (SU3F[8, I4, k8]*(SU3F[I1, k8, k9]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k8, k9])) + SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[8, I1, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[8, I2, k8]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9] + - SU3F[8, I1, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k8, k9] + SU3F[8, I3, k8]*(SU3F[I1, k8, k9]* - (SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k8, k9]))) + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k9]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k9]*SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I2, k11]* - SU3F[8, I3, k8]*SU3F[I1, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k8, k9] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I4, k8]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I2, k11]* - SU3F[8, I3, k8]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I3, k8]*SU3F[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I2, k8]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I4, k11]* - (SU3F[8, I5, k8]*(SU3F[I1, k8, k9]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k8, k9])) + SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[8, I1, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[8, I2, k8]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k8, k9] + - SU3F[8, I1, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k8, k9] + SU3F[8, I3, k8]*(SU3F[I1, k8, k9]* - (SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k8, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[I3, I4, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I3, I4, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I2, I5, k6]*SU3F[8, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[8, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*SU3F[8, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[8, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I4, I5, k6]*((SU3F[8, I3, k8]*SU3F[I2, k6, k8] + - SU3F[8, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[6, I1] + - (SU3F[8, I3, k8]*SU3F[I1, k6, k8] + SU3F[8, I1, k8]* - SU3F[I3, k6, k8])*SUNDelta[6, I2] + - (SU3F[8, I2, k8]*SU3F[I1, k6, k8] + SU3F[8, I1, k8]* - SU3F[I2, k6, k8])*SUNDelta[6, I3]) + SU3D[I2, I5, k6]* - SU3F[8, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[8, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I5, k6]*SU3F[8, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[8, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I3, I5, k6]*((SU3F[8, I4, k8]*SU3F[I2, k6, k8] + - SU3F[8, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[6, I1] + - (SU3F[8, I4, k8]*SU3F[I1, k6, k8] + SU3F[8, I1, k8]* - SU3F[I4, k6, k8])*SUNDelta[6, I2] + - (SU3F[8, I2, k8]*SU3F[I1, k6, k8] + SU3F[8, I1, k8]* - SU3F[I2, k6, k8])*SUNDelta[6, I4]) + SU3D[I3, I4, k6]* - SU3F[8, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[8, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[8, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I3, I4, k6]*SU3F[8, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[8, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[8, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[8, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[8, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[8, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[8, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*(SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SUNDelta[6, I1] + - SU3D[I1, I4, k6]*SUNDelta[6, I3] + SU3D[I1, I3, k6]* - SUNDelta[6, I4]) + SU3D[I1, I4, k6]*SU3D[I2, I3, k6]* - SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*(SU3D[I3, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SUNDelta[6, I3] + SU3D[I1, I3, k6]* - SUNDelta[6, I5])))/(135*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (((2*I)/45)*(SU3D[I3, I4, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I1] + SU3D[I2, I5, k7]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I1] + SU3D[I2, I4, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I1] + SU3D[I2, I3, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I1] + SU3D[I2, I3, k7]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I1] + SU3D[I3, I4, k7]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I2] + SU3D[I1, I5, k7]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I2] + SU3D[I1, I4, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I2] + SU3D[I1, I3, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I2] + SU3D[I1, I3, k7]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k7]*SU3F[8, I1, k6]* - SUNDelta[6, I3] + SU3D[I2, I5, k7]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SUNDelta[6, I3] + SU3D[I2, I4, k7]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k7]*SU3F[8, I2, k6]* - SUNDelta[6, I3] + SU3D[I1, I5, k7]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SUNDelta[6, I3] + SU3D[I1, I4, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k7]*SU3F[8, I4, k6]* - SUNDelta[6, I3] + SU3D[I1, I5, k7]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SUNDelta[6, I3] + SU3D[I1, I2, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I3] + SU3D[I1, I4, k7]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I3] + SU3D[I1, I2, k7]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I3] + SU3D[I2, I3, k7]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SUNDelta[6, I4] + SU3D[I1, I3, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I4] + SU3D[I1, I5, k7]*SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I4] + SU3D[I1, I2, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I4] + SU3D[I1, I3, k7]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I4] + SU3D[I3, I5, k7]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k6]*SUNDelta[6, I1] + - SU3F[8, I1, k6]*SUNDelta[6, I2]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k6]*SUNDelta[6, I1] + SU3F[8, I1, k6]* - SUNDelta[6, I4]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k6]*SUNDelta[6, I2] + SU3F[8, I2, k6]* - SUNDelta[6, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k7]* - SU3F[8, I1, k6]*SUNDelta[6, I5] + SU3D[I2, I3, k7]*SU3D[I4, k6, k7]* - SU3F[8, I1, k6]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k7]* - SU3F[8, I2, k6]*SUNDelta[6, I5] + SU3D[I1, I3, k7]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k7]* - SU3F[8, I3, k6]*SUNDelta[6, I5] + SU3D[I1, I4, k7]*SU3D[I2, k6, k7]* - SU3F[8, I3, k6]*SUNDelta[6, I5] + SU3D[I1, I2, k7]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k7]* - SU3F[8, I4, k6]*SUNDelta[6, I5] + SU3D[I1, I3, k7]*SU3D[I2, k6, k7]* - SU3F[8, I4, k6]*SUNDelta[6, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k7]*SU3F[8, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k7]*SU3F[8, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k7]*SU3F[8, I5, k6]*SUNDelta[6, I2] + - SU3D[I4, I5, k7]*(SU3F[8, I2, k6]*SUNDelta[6, I1] + - SU3F[8, I1, k6]*SUNDelta[6, I2]) + SU3D[I1, I5, k7]* - SU3F[8, I2, k6]*SUNDelta[6, I4] + SU3D[I1, I2, k7]*SU3F[8, I5, k6]* - SUNDelta[6, I4] + SU3D[I2, I5, k7]*(SU3F[8, I4, k6]* - SUNDelta[6, I1] + SU3F[8, I1, k6]*SUNDelta[6, I4]) + - SU3D[I2, I4, k7]*SU3F[8, I1, k6]*SUNDelta[6, I5] + - SU3D[I1, I4, k7]*SU3F[8, I2, k6]*SUNDelta[6, I5] + - SU3D[I1, I2, k7]*SU3F[8, I4, k6]*SUNDelta[6, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/45)*(SU3D[8, I3, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[6, I2] + SU3D[8, I3, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[6, I2] + SU3D[8, I3, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I2] + SU3D[8, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[6, I3] + SU3D[8, I2, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[6, I3] + SU3D[8, I2, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I3] + SU3D[8, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I3, k8]*SU3D[I1, I2, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k8]*SU3D[I1, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k8]*SU3D[I2, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[6, I4] + SU3D[8, I5, k8]*(SU3D[I2, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[6, I1] + SU3D[I1, I4, k6]*SU3F[I3, k6, k8]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[6, I2] + SU3D[I3, I4, k6]*(SU3F[I2, k6, k8]* - SUNDelta[6, I1] + SU3F[I1, k6, k8]*SUNDelta[6, I2]) + - SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*(SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3F[I1, k6, k8]*SUNDelta[6, I3]) + SU3D[I2, I3, k6]* - SU3F[I1, k6, k8]*SUNDelta[6, I4] + SU3D[I1, I3, k6]* - SU3F[I2, k6, k8]*SUNDelta[6, I4] + SU3D[I1, I2, k6]* - SU3F[I3, k6, k8]*SUNDelta[6, I4]) + SU3D[8, I3, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I3, k8]*SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[8, I4, k8]*(SU3D[I2, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I3, I5, k6]*(SU3F[I2, k6, k8]*SUNDelta[6, I1] + - SU3F[I1, k6, k8]*SUNDelta[6, I2]) + SU3D[I1, I5, k6]* - SU3F[I2, k6, k8]*SUNDelta[6, I3] + SU3D[I1, I2, k6]* - SU3F[I5, k6, k8]*SUNDelta[6, I3] + SU3D[I2, I5, k6]* - (SU3F[I3, k6, k8]*SUNDelta[6, I1] + SU3F[I1, k6, k8]* - SUNDelta[6, I3]) + SU3D[I2, I3, k6]*SU3F[I1, k6, k8]* - SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3F[I2, k6, k8]* - SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3F[I3, k6, k8]* - SUNDelta[6, I5])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (2*(SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[6, I2] + - SU3D[8, I3, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I2] + - SU3D[8, I3, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I2] + - SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[6, I3] + - SU3D[8, I2, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I3] + - SU3D[8, I2, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I3] + - SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k8]*SUNDelta[6, I4] + - SU3D[8, I3, k7]*SU3D[I1, I5, k8]*SU3D[I2, k7, k8]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[6, I4] + - SU3D[8, I3, k7]*SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I4] + - SU3D[8, I5, k7]*(SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I2] + - SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k8]*(SU3D[I3, k7, k8]*SUNDelta[6, I1] + - SU3D[I1, k7, k8]*SUNDelta[6, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[6, I4] + SU3D[I1, I2, k8]* - SU3D[I3, k7, k8]*SUNDelta[6, I4] + SU3D[I2, k7, k8]* - (SU3D[I3, I4, k8]*SUNDelta[6, I1] + SU3D[I1, I4, k8]* - SUNDelta[6, I3] + SU3D[I1, I3, k8]*SUNDelta[6, I4])) + - SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k8]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I4, k8]*SU3D[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I4, k7]*(SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I2] + - SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[6, I3] + - SU3D[I2, I5, k8]*(SU3D[I3, k7, k8]*SUNDelta[6, I1] + - SU3D[I1, k7, k8]*SUNDelta[6, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[6, I5] + SU3D[I1, I2, k8]* - SU3D[I3, k7, k8]*SUNDelta[6, I5] + SU3D[I2, k7, k8]* - (SU3D[I3, I5, k8]*SUNDelta[6, I1] + SU3D[I1, I5, k8]* - SUNDelta[6, I3] + SU3D[I1, I3, k8]*SUNDelta[6, I5]))))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/90)*(SU3D[I2, I5, k9]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k6] + SU3D[I2, I5, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9]*SU3F[I1, k10, k6] + SU3D[I2, I4, k9]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k11]*SU3F[I1, k10, k6] + - SU3D[I2, I3, k9]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k6] + SU3D[I2, I4, k9]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k9]*SU3F[I1, k10, k6] + SU3D[I2, I3, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I1, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I3, k10, k11]*SU3D[I4, I5, k9]* - SU3F[I2, k10, k6] + SU3D[I1, k10, k11]*SU3D[I3, k11, k9]* - SU3D[I4, I5, k9]*SU3F[I2, k10, k6] + SU3D[I1, k11, k9]* - SU3D[I3, I5, k9]*SU3D[I4, k10, k11]*SU3F[I2, k10, k6] + - SU3D[I1, I5, k9]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I1, k10, k11]*SU3D[I3, I5, k9]* - SU3D[I4, k11, k9]*SU3F[I2, k10, k6] + SU3D[I1, I5, k9]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k9]*SU3F[I2, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I3, I4, k9]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I1, I4, k9]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k6] + SU3D[I1, I3, k9]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k11]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k11]*SU3D[I3, I4, k9]*SU3D[I5, k11, k9]* - SU3F[I2, k10, k6] + SU3D[I1, I4, k9]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k9]*SU3F[I2, k10, k6] + SU3D[I1, I3, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I2, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I2, I5, k9]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k9]* - SU3D[I4, k11, k9]*SU3F[I3, k10, k6] + SU3D[I1, k11, k9]* - SU3D[I2, I4, k9]*SU3D[I5, k10, k11]*SU3F[I3, k10, k6] + - SU3D[I1, I2, k9]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I4, k9]* - SU3D[I5, k11, k9]*SU3F[I3, k10, k6] + SU3D[I1, I2, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I3, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I2, I5, k9]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k9]* - SU3D[I3, k11, k9]*SU3F[I4, k10, k6] + SU3D[I1, k11, k9]* - SU3D[I2, I3, k9]*SU3D[I5, k10, k11]*SU3F[I4, k10, k6] + - SU3D[I1, I2, k9]*SU3D[I3, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k9]* - SU3D[I5, k11, k9]*SU3F[I4, k10, k6] + SU3D[I1, I2, k9]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k9]*SU3F[I4, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I2, I4, k9]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I4, k9]* - SU3D[I3, k11, k9]*SU3F[I5, k10, k6] + SU3D[I1, k11, k9]* - SU3D[I2, I3, k9]*SU3D[I4, k10, k11]*SU3F[I5, k10, k6] + - SU3D[I1, I2, k9]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k9]* - SU3D[I4, k11, k9]*SU3F[I5, k10, k6] + SU3D[I1, I2, k9]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[I2, k11, k9]*(SU3D[I3, I4, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k6] + SU3D[I1, k10, k11]*SU3D[I4, I5, k9]* - SU3F[I3, k10, k6] + SU3D[I1, I5, k9]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, I4, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, I3, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I3, I5, k9]*(SU3D[I4, k10, k11]* - SU3F[I1, k10, k6] + SU3D[I1, k10, k11]*SU3F[I4, k10, k6]) + - SU3D[I1, k10, k11]*SU3D[I3, I4, k9]*SU3F[I5, k10, k6] + - SU3D[I1, I3, k9]*SU3D[I4, k10, k11]*SU3F[I5, k10, k6] + - SU3D[I3, k10, k11]*(SU3D[I4, I5, k9]*SU3F[I1, k10, k6] + - SU3D[I1, I5, k9]*SU3F[I4, k10, k6] + SU3D[I1, I4, k9]* - SU3F[I5, k10, k6])) + SU3D[I2, k10, k11]* - (SU3D[I3, I4, k9]*SU3D[I5, k11, k9]*SU3F[I1, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I4, I5, k9]*SU3F[I3, k10, k6] + - SU3D[I1, I5, k9]*SU3D[I4, k11, k9]*SU3F[I3, k10, k6] + - SU3D[I1, I4, k9]*SU3D[I5, k11, k9]*SU3F[I3, k10, k6] + - SU3D[I1, I3, k9]*SU3D[I5, k11, k9]*SU3F[I4, k10, k6] + - SU3D[I3, I5, k9]*(SU3D[I4, k11, k9]*SU3F[I1, k10, k6] + - SU3D[I1, k11, k9]*SU3F[I4, k10, k6]) + SU3D[I1, k11, k9]* - SU3D[I3, I4, k9]*SU3F[I5, k10, k6] + SU3D[I1, I3, k9]* - SU3D[I4, k11, k9]*SU3F[I5, k10, k6] + SU3D[I3, k11, k9]* - (SU3D[I4, I5, k9]*SU3F[I1, k10, k6] + SU3D[I1, I5, k9]* - SU3F[I4, k10, k6] + SU3D[I1, I4, k9]*SU3F[I5, k10, k6])))* - SUNDelta[6, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((SU3D[I3, I4, k9]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3D[I3, I4, k9]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k6] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k9]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I2, I5, k9]*SU3D[I4, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I2, I4, k9]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k9]*SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I1, I5, k9]*SU3D[I4, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k9]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I2, I5, k9]*SU3D[I4, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I2, I4, k9]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I1, I5, k9]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, I4, k9]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + SU3D[I2, I3, k9]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, I3, k9]*SU3D[I5, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k9]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k9]* - SU3D[I2, k10, k9]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k9]*SU3D[I5, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I2, I3, k9]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k6] + SU3D[I1, I3, k9]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, I5, k9]*SU3D[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[I1, I2, k9]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I3, I5, k9]*(SU3D[I4, k10, k9]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k6]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6])) + SU3D[I2, k10, k9]*SU3D[I3, I4, k9]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + SU3D[I2, I3, k9]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k9]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k9]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k9]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k9]*SU3D[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k9]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k9]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I3, k9]*SU3D[I2, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k10, k9]*SU3D[I3, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + SU3D[I2, I3, k9]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I3, k9]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k9]*SU3D[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k9]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I3, k9]*SU3D[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k9]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + SU3D[I1, I5, k9]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + SU3D[I2, I5, k9]* - (SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I4, k11, k6]) + SU3D[I2, I4, k9]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k9]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I4, k9]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6]))*SUNDelta[6, k6])/ - (90*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/90)*(SU3D[I4, I5, k9]*(SU3F[I1, k11, k9]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[I1, k10, k6]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, I5, k9]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k9]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + - SU3D[I2, I5, k9]*SU3F[I1, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[I1, I5, k9]*SU3F[I2, k10, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[I2, I5, k9]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + - SU3D[I1, I5, k9]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + SU3D[I1, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + - SU3D[I2, I5, k9]*SU3F[I1, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[I1, I5, k9]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[I2, I5, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9] + - SU3D[I1, I5, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k11, k9] + SU3D[I3, I5, k9]* - (SU3F[I1, k11, k9]*(SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k6]) + SU3F[I1, k10, k6]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I4, k11, k9])) + SU3D[I3, I4, k9]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I3, I4, k9]* - SU3F[I1, k10, k6]*SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I2, I4, k9]*SU3F[I1, k11, k9]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k9]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, I4, k9]* - SU3F[I1, k10, k6]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k9]*SU3F[I2, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k9]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, I3, k9]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k9]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k9]*SU3F[I1, k10, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + SU3D[I1, I3, k9]* - SU3F[I2, k10, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k9]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I3, I4, k9]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I3, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]*SU3F[I5, k10, k6] + - SU3D[I2, I4, k9]*SU3F[I1, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I1, I4, k9]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + - SU3D[I1, I4, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k6] + SU3D[I2, I3, k9]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, I3, k9]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + - SU3D[I1, I2, k9]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, I3, k9]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + SU3D[I1, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[I1, I2, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[I3, I4, k9]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + SU3D[I3, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]*SU3F[I5, k11, k9] + - SU3D[I2, I4, k9]*SU3F[I1, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I4, k9]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[I2, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I5, k11, k9] + - SU3D[I1, I4, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k11, k9] + SU3D[I2, I3, k9]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[I1, I3, k9]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[I1, I2, k9]*SU3F[I3, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I2, I3, k9]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + SU3D[I1, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + - SU3D[I1, I2, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9])*SUNDelta[6, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((SU3D[I3, I4, k11]*SU3D[I5, k10, k9]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k6] + SU3D[I3, I4, k11]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k6]*SU3F[I2, k11, k9] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k11]*SU3F[I1, k11, k9]*SU3F[I3, k10, k6] + - SU3D[I2, I5, k11]*SU3D[I4, k10, k9]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k6] + SU3D[I2, I4, k11]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k11]*SU3F[I2, k11, k9]*SU3F[I3, k10, k6] + - SU3D[I1, I5, k11]*SU3D[I4, k10, k9]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k6] + SU3D[I1, I4, k11]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k11]*SU3F[I1, k10, k6]*SU3F[I3, k11, k9] + - SU3D[I2, I5, k11]*SU3D[I4, k10, k9]*SU3F[I1, k10, k6]* - SU3F[I3, k11, k9] + SU3D[I2, I4, k11]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k6]*SU3F[I3, k11, k9] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k11]*SU3F[I2, k10, k6]*SU3F[I3, k11, k9] + - SU3D[I1, I5, k11]*SU3D[I4, k10, k9]*SU3F[I2, k10, k6]* - SU3F[I3, k11, k9] + SU3D[I1, I4, k11]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k6]*SU3F[I3, k11, k9] + SU3D[I2, I3, k11]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k9]*SU3F[I4, k10, k6] + - SU3D[I1, I3, k11]*SU3D[I5, k10, k9]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k6] + SU3D[I1, k10, k9]*SU3D[I2, I5, k11]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + SU3D[I1, I5, k11]* - SU3D[I2, k10, k9]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + - SU3D[I1, I2, k11]*SU3D[I5, k10, k9]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k6] + SU3D[I2, I3, k11]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k6]*SU3F[I4, k11, k9] + SU3D[I1, I3, k11]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k6]*SU3F[I4, k11, k9] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k11, k9] + SU3D[I1, I5, k11]*SU3D[I2, k10, k9]* - SU3F[I3, k10, k6]*SU3F[I4, k11, k9] + SU3D[I1, I2, k11]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9] + - SU3D[I3, I5, k11]*(SU3D[I4, k10, k9]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k6] + SU3F[I1, k10, k6]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k9]*SU3F[I4, k10, k6] + - SU3F[I1, k10, k6]*SU3F[I4, k11, k9]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I4, k11, k9])) + SU3D[I2, k10, k9]*SU3D[I3, I4, k11]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k6] + SU3D[I2, I3, k11]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k9]*SU3F[I5, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k11]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k6] + SU3D[I1, I3, k11]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k9]*SU3F[I5, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k11]*SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + - SU3D[I1, I4, k11]*SU3D[I2, k10, k9]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k6] + SU3D[I1, I2, k11]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k11]*SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[I1, I3, k11]*SU3D[I2, k10, k9]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[I2, k10, k9]*SU3D[I3, I4, k11]* - SU3F[I1, k10, k6]*SU3F[I5, k11, k9] + SU3D[I2, I3, k11]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k6]*SU3F[I5, k11, k9] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k11, k9] + SU3D[I1, I3, k11]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k6]*SU3F[I5, k11, k9] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k11]*SU3F[I3, k10, k6]*SU3F[I5, k11, k9] + - SU3D[I1, I4, k11]*SU3D[I2, k10, k9]*SU3F[I3, k10, k6]* - SU3F[I5, k11, k9] + SU3D[I1, I2, k11]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k6]*SU3F[I5, k11, k9] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k11]*SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + - SU3D[I1, I3, k11]*SU3D[I2, k10, k9]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k11]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k6] + - SU3F[I1, k10, k6]*SU3F[I2, k11, k9]) + SU3D[I1, I5, k11]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k6] + SU3D[I1, I5, k11]* - SU3F[I2, k10, k6]*SU3F[I4, k11, k9] + SU3D[I2, I5, k11]* - (SU3F[I1, k11, k9]*SU3F[I4, k10, k6] + SU3F[I1, k10, k6]* - SU3F[I4, k11, k9]) + SU3D[I2, I4, k11]*SU3F[I1, k11, k9]* - SU3F[I5, k10, k6] + SU3D[I1, I4, k11]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k6] + SU3D[I1, I2, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[I2, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I5, k11, k9] + SU3D[I1, I4, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k11, k9] + SU3D[I1, I2, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9]))*SUNDelta[6, k6])/ - (90*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*(SU3D[I1, I5, k8]*SU3D[I2, I3, I4] + SU3D[I1, I4, k8]* - SU3D[I2, I3, I5] + SU3D[I1, I4, I5]*SU3D[I2, I3, k8] + - SU3D[I1, I3, k8]*SU3D[I2, I4, I5] + SU3D[I1, I3, I5]* - SU3D[I2, I4, k8] + SU3D[I1, I3, I4]*SU3D[I2, I5, k8] + - SU3D[I1, I2, k8]*SU3D[I3, I4, I5] + SU3D[I1, I2, I5]* - SU3D[I3, I4, k8] + SU3D[I1, I2, I4]*SU3D[I3, I5, k8] + - SU3D[I1, I2, I3]*SU3D[I4, I5, k8])*SUNDelta[6, k8])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I1, k10, k11]*SU3D[I2, k11, k6]*SU3D[I3, k10, k9]* - SU3D[I4, I5, k6] + SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3D[I3, k11, k6]*SU3D[I4, I5, k6] + SU3D[I1, I5, k6]* - SU3D[I2, k11, k6]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I2, k10, k9]*SU3D[I3, k11, k6]* - SU3D[I4, k10, k11] + SU3D[I1, k10, k11]*SU3D[I2, k11, k6]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k9] + SU3D[I1, I5, k6]* - SU3D[I2, k11, k6]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9] + - SU3D[I1, k10, k11]*SU3D[I2, I5, k6]*SU3D[I3, k11, k6]* - SU3D[I4, k10, k9] + SU3D[I1, I5, k6]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k6]*SU3D[I4, k10, k9] + SU3D[I1, k10, k11]* - SU3D[I2, k10, k9]*SU3D[I3, I5, k6]*SU3D[I4, k11, k6] + - SU3D[I1, I5, k6]*SU3D[I2, k10, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k6] + SU3D[I1, I5, k6]* - SU3D[I2, k10, k11]*SU3D[I3, k10, k9]*SU3D[I4, k11, k6] + - SU3D[I1, I4, k6]*SU3D[I2, k11, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I1, I4, k6]*SU3D[I2, k10, k9]* - SU3D[I3, k11, k6]*SU3D[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3D[I2, k11, k6]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I2, k10, k9]* - SU3D[I4, k11, k6]*SU3D[I5, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k6]*SU3D[I5, k10, k11] + - SU3D[I1, k10, k11]*SU3D[I2, k11, k6]*SU3D[I3, I4, k6]* - SU3D[I5, k10, k9] + SU3D[I1, I4, k6]*SU3D[I2, k11, k6]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k9] + SU3D[I1, k10, k11]* - SU3D[I2, I4, k6]*SU3D[I3, k11, k6]*SU3D[I5, k10, k9] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k11]*SU3D[I3, k11, k6]* - SU3D[I5, k10, k9] + SU3D[I1, I3, k6]*SU3D[I2, k11, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + SU3D[I1, I2, k6]* - SU3D[I3, k11, k6]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I1, k10, k11]*SU3D[I2, I3, k6]*SU3D[I4, k11, k6]* - SU3D[I5, k10, k9] + SU3D[I1, I3, k6]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k6]*SU3D[I5, k10, k9] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k6]*SU3D[I5, k10, k9] + - SU3D[I1, k11, k6]*(SU3D[I2, I5, k6]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k11] + SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k9] + SU3D[I2, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I2, I3, k6]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I2, k10, k9]* - (SU3D[I3, k10, k11]*SU3D[I4, I5, k6] + SU3D[I3, I5, k6]* - SU3D[I4, k10, k11] + SU3D[I3, I4, k6]*SU3D[I5, k10, k11]) + - SU3D[I2, I4, k6]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I2, I3, k6]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I2, k10, k11]*(SU3D[I3, k10, k9]*SU3D[I4, I5, k6] + - SU3D[I3, I5, k6]*SU3D[I4, k10, k9] + SU3D[I3, I4, k6]* - SU3D[I5, k10, k9])) + SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3D[I3, I4, k6]*SU3D[I5, k11, k6] + SU3D[I1, I4, k6]* - SU3D[I2, k10, k9]*SU3D[I3, k10, k11]*SU3D[I5, k11, k6] + - SU3D[I1, k10, k11]*SU3D[I2, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k6] + SU3D[I1, I4, k6]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k9]*SU3D[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k11]*SU3D[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k9]*SU3D[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3D[I5, k11, k6] + SU3D[I1, k10, k9]* - (SU3D[I2, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k11] + - SU3D[I2, I5, k6]*SU3D[I3, k10, k11]*SU3D[I4, k11, k6] + - SU3D[I2, I4, k6]*SU3D[I3, k11, k6]*SU3D[I5, k10, k11] + - SU3D[I2, I3, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k11] + - SU3D[I2, k11, k6]*(SU3D[I3, k10, k11]*SU3D[I4, I5, k6] + - SU3D[I3, I5, k6]*SU3D[I4, k10, k11] + SU3D[I3, I4, k6]* - SU3D[I5, k10, k11]) + SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k6] + SU3D[I2, I3, k6]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k6] + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k6]*SU3D[I4, I5, k6] + SU3D[I3, I5, k6]* - SU3D[I4, k11, k6] + SU3D[I3, I4, k6]*SU3D[I5, k11, k6])))* - SUNDelta[6, k9])/(90*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/90)*(SU3D[I2, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I2, I5, k6]*SU3D[I3, k10, k9]* - SU3D[I4, k11, k6]*SU3F[I1, k10, k11] + SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[I2, I3, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I2, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k6]*SU3F[I1, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I1, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I3, k10, k9]*SU3D[I4, I5, k6]* - SU3F[I2, k10, k11] + SU3D[I1, k10, k9]*SU3D[I3, k11, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11] + SU3D[I1, k10, k9]*SU3D[I3, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I2, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k6]*SU3F[I2, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[I1, I4, k6]*SU3D[I3, k11, k6]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k6]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I2, k10, k11] + SU3D[I1, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k6]*SU3F[I2, k10, k11] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I2, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I4, k6]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I4, k6]* - SU3D[I5, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3D[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I3, k6]* - SU3D[I5, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k9]*SU3D[I5, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I4, k6]*SU3D[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I3, k6]* - SU3D[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I2, k11, k6]*(SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I1, k10, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I5, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, I3, k6]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I3, I5, k6]* - (SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I4, k10, k11]) + SU3D[I1, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I4, k6]*SU3F[I5, k10, k11])) + - SU3D[I2, k10, k9]*(SU3D[I3, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I1, k10, k11] + SU3D[I1, k11, k6]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I5, k6]*SU3D[I4, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I3, k6]*SU3D[I5, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I3, I5, k6]* - (SU3D[I4, k11, k6]*SU3F[I1, k10, k11] + SU3D[I1, k11, k6]* - SU3F[I4, k10, k11]) + SU3D[I1, k11, k6]*SU3D[I3, I4, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k11, k6]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I4, k6]*SU3F[I5, k10, k11])))* - SUNDelta[6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/90)*(SU3D[I2, I5, k6]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k6] + SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9]*SU3F[I1, k10, k6] + SU3D[I2, I4, k6]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k11]*SU3F[I1, k10, k6] + - SU3D[I2, I3, k6]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k6] + SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k9]*SU3F[I1, k10, k6] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I1, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I3, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I2, k10, k6] + SU3D[I1, k10, k11]*SU3D[I3, k11, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k6] + SU3D[I1, k11, k9]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k11]*SU3F[I2, k10, k6] + - SU3D[I1, I5, k6]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I1, k10, k11]*SU3D[I3, I5, k6]* - SU3D[I4, k11, k9]*SU3F[I2, k10, k6] + SU3D[I1, I5, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k9]*SU3F[I2, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I1, I4, k6]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k11]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3D[I5, k11, k9]* - SU3F[I2, k10, k6] + SU3D[I1, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k9]*SU3F[I2, k10, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I2, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I2, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I4, k11, k9]*SU3F[I3, k10, k6] + SU3D[I1, k11, k9]* - SU3D[I2, I4, k6]*SU3D[I5, k10, k11]*SU3F[I3, k10, k6] + - SU3D[I1, I2, k6]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I5, k11, k9]*SU3F[I3, k10, k6] + SU3D[I1, I2, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I3, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I3, k11, k9]*SU3F[I4, k10, k6] + SU3D[I1, k11, k9]* - SU3D[I2, I3, k6]*SU3D[I5, k10, k11]*SU3F[I4, k10, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I5, k11, k9]*SU3F[I4, k10, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k9]*SU3F[I4, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I3, k11, k9]*SU3F[I5, k10, k6] + SU3D[I1, k11, k9]* - SU3D[I2, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k10, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I4, k11, k9]*SU3F[I5, k10, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[I2, k11, k9]*(SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k6] + SU3D[I1, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k6] + SU3D[I1, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, I3, k6]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I3, I5, k6]*(SU3D[I4, k10, k11]* - SU3F[I1, k10, k6] + SU3D[I1, k10, k11]*SU3F[I4, k10, k6]) + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3F[I5, k10, k6] + - SU3D[I1, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k10, k6] + - SU3D[I3, k10, k11]*(SU3D[I4, I5, k6]*SU3F[I1, k10, k6] + - SU3D[I1, I5, k6]*SU3F[I4, k10, k6] + SU3D[I1, I4, k6]* - SU3F[I5, k10, k6])) + SU3D[I2, k10, k11]* - (SU3D[I3, I4, k6]*SU3D[I5, k11, k9]*SU3F[I1, k10, k6] + - SU3D[I1, k11, k9]*SU3D[I4, I5, k6]*SU3F[I3, k10, k6] + - SU3D[I1, I5, k6]*SU3D[I4, k11, k9]*SU3F[I3, k10, k6] + - SU3D[I1, I4, k6]*SU3D[I5, k11, k9]*SU3F[I3, k10, k6] + - SU3D[I1, I3, k6]*SU3D[I5, k11, k9]*SU3F[I4, k10, k6] + - SU3D[I3, I5, k6]*(SU3D[I4, k11, k9]*SU3F[I1, k10, k6] + - SU3D[I1, k11, k9]*SU3F[I4, k10, k6]) + SU3D[I1, k11, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k10, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k9]*SU3F[I5, k10, k6] + SU3D[I3, k11, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k6] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k6] + SU3D[I1, I4, k6]*SU3F[I5, k10, k6])))* - SUNDelta[6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((SU3D[I3, I4, k6]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k6] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I2, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I2, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + SU3D[I2, I3, k6]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I5, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I2, k10, k9]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I5, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I2, I3, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, I5, k6]*SU3D[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I3, I5, k6]*(SU3D[I4, k10, k9]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k6]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6])) + SU3D[I2, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k6]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + SU3D[I1, I5, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + SU3D[I2, I5, k6]* - (SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I4, k11, k6]) + SU3D[I2, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6]))*SUNDelta[6, k9])/ - (90*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/30)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k6]*SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + - SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + - SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[I2, I3, k6]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I1, I3, k6]* - SU3D[I5, k6, k7]*SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I1, I2, k6]* - SU3D[I5, k6, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[I3, I5, k6]*(SU3D[I4, k6, k7]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3D[I2, k6, k7]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3D[I2, I4, k6]*SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3D[I2, I4, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k6]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3D[I1, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, I5, k6]* - (SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I4, k11, k7]) + SU3D[I2, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I1, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I1, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7]))*SUNDelta[7, k10])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[I1, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[I2, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[I2, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I4, k7, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I5, k7, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I5, k7, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[I5, k11, k7] + - SU3D[I2, k7, k8]*(SU3D[I3, I4, k6]*SU3D[I5, k6, k8]* - SU3F[I1, k11, k7] + SU3D[I1, k6, k8]*SU3D[I4, I5, k6]* - SU3F[I3, k11, k7] + SU3D[I1, I5, k6]*SU3D[I4, k6, k8]* - SU3F[I3, k11, k7] + SU3D[I1, I4, k6]*SU3D[I5, k6, k8]* - SU3F[I3, k11, k7] + SU3D[I1, I3, k6]*SU3D[I5, k6, k8]* - SU3F[I4, k11, k7] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k8]*SU3F[I1, k11, k7] + SU3D[I1, k6, k8]* - SU3F[I4, k11, k7]) + SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3F[I5, k11, k7] + SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k8]* - (SU3D[I4, I5, k6]*SU3F[I1, k11, k7] + SU3D[I1, I5, k6]* - SU3F[I4, k11, k7] + SU3D[I1, I4, k6]*SU3F[I5, k11, k7])) + - SU3D[I2, k6, k8]*(SU3D[I3, I4, k6]*SU3D[I5, k7, k8]* - SU3F[I1, k11, k7] + SU3D[I1, k7, k8]*SU3D[I4, I5, k6]* - SU3F[I3, k11, k7] + SU3D[I1, I5, k6]*SU3D[I4, k7, k8]* - SU3F[I3, k11, k7] + SU3D[I1, I4, k6]*SU3D[I5, k7, k8]* - SU3F[I3, k11, k7] + SU3D[I1, I3, k6]*SU3D[I5, k7, k8]* - SU3F[I4, k11, k7] + SU3D[I3, I5, k6]* - (SU3D[I4, k7, k8]*SU3F[I1, k11, k7] + SU3D[I1, k7, k8]* - SU3F[I4, k11, k7]) + SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3F[I5, k11, k7] + SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3F[I5, k11, k7] + SU3D[I3, k7, k8]* - (SU3D[I4, I5, k6]*SU3F[I1, k11, k7] + SU3D[I1, I5, k6]* - SU3F[I4, k11, k7] + SU3D[I1, I4, k6]*SU3F[I5, k11, k7])))* - SUNDelta[7, k11])/(30*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/30)*(SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I2, k6, k8] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k8])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[I4, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I3, k6, k7]*(SU3D[I4, I5, k8]*(SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k8]) + - SU3D[I1, I5, k8]*SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I5, k8]*SU3F[I2, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I2, I5, k8]*(SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k8]) + SU3D[I2, I4, k8]* - SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + SU3D[I1, I4, k8]* - SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + SU3D[I1, I2, k8]* - SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + SU3D[I2, I4, k8]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + SU3D[I1, I4, k8]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + SU3D[I1, I2, k8]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k8]))*SUNDelta[7, k11])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/15)*(SU3D[I1, I5, k3]*SU3D[I2, I3, I4] + - SU3D[I1, I4, k3]*SU3D[I2, I3, I5] + SU3D[I1, I4, I5]* - SU3D[I2, I3, k3] + SU3D[I1, I3, k3]*SU3D[I2, I4, I5] + - SU3D[I1, I3, I5]*SU3D[I2, I4, k3] + SU3D[I1, I3, I4]* - SU3D[I2, I5, k3] + SU3D[I1, I2, k3]*SU3D[I3, I4, I5] + - SU3D[I1, I2, I5]*SU3D[I3, I4, k3] + SU3D[I1, I2, I4]* - SU3D[I3, I5, k3] + SU3D[I1, I2, I3]*SU3D[I4, I5, k3])* - SUNDelta[7, k3])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/30)*(SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6] + SU3D[I1, k6, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6] + SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k9] + SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, k6, k9] + SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8] + SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9]* - SU3D[I4, k7, k8] + SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8] + SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8] + SU3D[I1, k6, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9] + SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k9]* - SU3D[I4, k8, k9] + SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9] + SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9] + SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k9] + SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k9] + SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k9] + SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k9] + SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k9] + SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k9] + SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8] + SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I4, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, k8, k9]* - (SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k9] + - SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k7, k8] + - SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k9] + - SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k9] + - SU3D[I2, k7, k8]*(SU3D[I3, k6, k9]*SU3D[I4, I5, k6] + - SU3D[I3, I5, k6]*SU3D[I4, k6, k9] + SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]) + SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I2, I3, k6]*SU3D[I4, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I2, k6, k9]*(SU3D[I3, k7, k8]* - SU3D[I4, I5, k6] + SU3D[I3, I5, k6]*SU3D[I4, k7, k8] + - SU3D[I3, I4, k6]*SU3D[I5, k7, k8])) + SU3D[I1, k6, k9]* - SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9] + - SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9] + - SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9] + - SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9] + - SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, k7, k8]*(SU3D[I2, I5, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9] + - SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9] + - SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9] + - SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9] + - SU3D[I2, k8, k9]*(SU3D[I3, k6, k9]*SU3D[I4, I5, k6] + - SU3D[I3, I5, k6]*SU3D[I4, k6, k9] + SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]) + SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3D[I5, k8, k9] + SU3D[I2, I3, k6]*SU3D[I4, k6, k9]* - SU3D[I5, k8, k9] + SU3D[I2, k6, k9]*(SU3D[I3, k8, k9]* - SU3D[I4, I5, k6] + SU3D[I3, I5, k6]*SU3D[I4, k8, k9] + - SU3D[I3, I4, k6]*SU3D[I5, k8, k9])))*SUNDelta[7, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/30)*(SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k8]* - SU3F[I2, k11, k6] + SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I2, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I1, k11, k8]*SU3F[I3, k11, k6] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k8]* - SU3F[I3, k11, k6] + SU3D[I2, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k8]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k11, k8]*SU3F[I3, k11, k6] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k8]* - SU3F[I3, k11, k6] + SU3D[I1, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k8]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I1, k11, k6]*SU3F[I3, k11, k8] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k8] + SU3D[I2, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k11, k6]*SU3F[I3, k11, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k8] + SU3D[I1, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k8] + SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k8]*SU3F[I4, k11, k6] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, I5, k8]* - SU3F[I3, k11, k8]*SU3F[I4, k11, k6] + SU3D[I1, I5, k8]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k8]*SU3F[I4, k11, k6] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k11, k8]* - SU3F[I4, k11, k6] + SU3D[I2, I3, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k8] + SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k11, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k8] + SU3D[I1, I5, k8]*SU3D[I2, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k8] + SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*(SU3F[I1, k11, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k11, k8]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k8]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k8])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I1, k11, k8]*SU3F[I5, k11, k6] + SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I1, I3, k8]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k8]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[I3, k11, k8]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k8]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I4, k11, k8]*SU3F[I5, k11, k6] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k8] + SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I1, I3, k8]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[I3, k11, k6]*SU3F[I5, k11, k8] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I1, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I4, k11, k6]*SU3F[I5, k11, k8] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*(SU3F[I1, k11, k8]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k8]) + SU3D[I1, I5, k8]* - SU3F[I2, k11, k8]*SU3F[I4, k11, k6] + SU3D[I1, I5, k8]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k8] + SU3D[I2, I5, k8]* - (SU3F[I1, k11, k8]*SU3F[I4, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I4, k11, k8]) + SU3D[I2, I4, k8]*SU3F[I1, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k8]*SU3F[I2, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k8]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I2, I4, k8]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I1, I4, k8]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I1, I2, k8]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k8]))*SUNDelta[7, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((SU3D[I2, I5, k8]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I2, I4, k8]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I2, I3, k8]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3D[I4, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, I5, k8]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, I4, k8]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, I3, k8]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3D[I4, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3D[I3, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3D[I5, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3D[I3, k8, k9]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] + - SU3D[I2, k8, k9]*(SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I1, k6, k7]*SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9] + SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I1, I4, k8]*SU3F[I5, k6, k9])) + - SU3D[I2, k6, k7]*(SU3D[I3, I4, k8]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I4, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, I5, k8]*SU3D[I4, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, I4, k8]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, I3, k8]*SU3D[I5, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I3, I5, k8]*(SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3F[I4, k6, k9]) + SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9] + SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9] + SU3D[I3, k8, k9]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I1, I4, k8]*SU3F[I5, k6, k9])))* - SUNDelta[7, k7])/(30*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((SU3D[I4, I5, k6]*(SU3F[I1, k11, k6]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k6]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k6])) + SU3D[I2, I5, k6]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[I2, I5, k6]*SU3F[I1, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I5, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I2, I5, k6]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[I1, I5, k6]*SU3F[I2, k11, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I2, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k9] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6]*SU3F[I4, k10, k9] + - SU3D[I2, I5, k6]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, I5, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[I2, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k6] + - SU3D[I1, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k6] + SU3D[I3, I5, k6]* - (SU3F[I1, k11, k6]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k6])) + SU3D[I3, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k9]*SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I2, I4, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k6]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3F[I3, k11, k6]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k6]*SU3F[I1, k10, k9]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I3, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I2, I4, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k9] + SU3D[I2, I3, k6]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I2, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k9] + SU3D[I3, I4, k6]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I2, I4, k6]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k6] + SU3D[I2, I3, k6]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I2, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k6])*SUNDelta[7, k9])/ - (30*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I2, I5, k8]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k9]*SU3D[I4, I5, k8]*SU3F[I2, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[I4, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3D[I3, k7, k9]*SU3F[I4, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I4, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3D[I5, k7, k9]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I4, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3D[I3, k7, k9]*SU3F[I5, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3D[I4, k7, k9]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I5, k6, k8] + - SU3D[I2, k7, k9]*(SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3F[I4, k6, k8]) + SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8] + SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8] + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k8] + SU3D[I1, I4, k8]*SU3F[I5, k6, k8])) + - SU3D[I2, k6, k7]*(SU3D[I3, I4, k8]*SU3D[I5, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I4, I5, k8]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k9]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I1, k7, k9]*SU3F[I4, k6, k8]) + SU3D[I1, k7, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8] + SU3D[I1, I3, k8]* - SU3D[I4, k7, k9]*SU3F[I5, k6, k8] + SU3D[I3, k7, k9]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k8] + SU3D[I1, I4, k8]*SU3F[I5, k6, k8])))* - SUNDelta[7, k9])/(30*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (2*(SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I1] + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I2] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I4, I5, k6]*((SU3F[6, I3, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[8, I1] + - (SU3F[6, I3, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]* - SU3F[I3, k6, k8])*SUNDelta[8, I2] + - (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]* - SU3F[I2, k6, k8])*SUNDelta[8, I3]) + SU3D[I2, I5, k6]* - SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I3, I5, k6]*((SU3F[6, I4, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[8, I1] + - (SU3F[6, I4, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]* - SU3F[I4, k6, k8])*SUNDelta[8, I2] + - (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]* - SU3F[I2, k6, k8])*SUNDelta[8, I4]) + SU3D[I3, I4, k6]* - SU3F[6, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*(SU3D[I2, I3, I5]*SUNDelta[6, I4]*SUNDelta[8, I1] + - SU3D[I2, I3, I4]*SUNDelta[6, I5]*SUNDelta[8, I1] + - SU3D[I1, I4, I5]*SUNDelta[6, I3]*SUNDelta[8, I2] + - SU3D[I1, I3, I5]*SUNDelta[6, I4]*SUNDelta[8, I2] + - SU3D[I1, I3, I4]*SUNDelta[6, I5]*SUNDelta[8, I2] + - SU3D[I3, I4, I5]*(SUNDelta[6, I2]*SUNDelta[8, I1] + - SUNDelta[6, I1]*SUNDelta[8, I2]) + SU3D[I1, I4, I5]*SUNDelta[6, I2]* - SUNDelta[8, I3] + SU3D[I1, I2, I5]*SUNDelta[6, I4]*SUNDelta[8, I3] + - SU3D[I1, I2, I4]*SUNDelta[6, I5]*SUNDelta[8, I3] + - SU3D[I2, I4, I5]*(SUNDelta[6, I3]*SUNDelta[8, I1] + - SUNDelta[6, I1]*SUNDelta[8, I3]) + SU3D[I2, I3, I5]*SUNDelta[6, I1]* - SUNDelta[8, I4] + SU3D[I1, I3, I5]*SUNDelta[6, I2]*SUNDelta[8, I4] + - SU3D[I1, I2, I5]*SUNDelta[6, I3]*SUNDelta[8, I4] + - SU3D[I1, I2, I3]*SUNDelta[6, I5]*SUNDelta[8, I4] + - SU3D[I2, I3, I4]*SUNDelta[6, I1]*SUNDelta[8, I5] + - SU3D[I1, I3, I4]*SUNDelta[6, I2]*SUNDelta[8, I5] + - SU3D[I1, I2, I4]*SUNDelta[6, I3]*SUNDelta[8, I5] + - SU3D[I1, I2, I3]*SUNDelta[6, I4]*SUNDelta[8, I5]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SUNDelta[8, I1] + - SU3F[6, I1, k7]*SUNDelta[8, I2]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[8, I1] + SU3F[6, I1, k7]* - SUNDelta[8, I4]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[8, I2] + SU3F[6, I2, k7]* - SUNDelta[8, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k7]*SUNDelta[8, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I2, k7]*SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[6, I4, k7]*SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SUNDelta[8, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[6, I5, k7]*SUNDelta[8, I1] + - SU3D[I1, I5, k6]*SU3F[6, I4, k7]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k7]*SUNDelta[8, I2] + - SU3D[I4, I5, k6]*(SU3F[6, I2, k7]*SUNDelta[8, I1] + - SU3F[6, I1, k7]*SUNDelta[8, I2]) + SU3D[I1, I5, k6]* - SU3F[6, I2, k7]*SUNDelta[8, I4] + SU3D[I1, I2, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I2, I5, k6]*(SU3F[6, I4, k7]* - SUNDelta[8, I1] + SU3F[6, I1, k7]*SUNDelta[8, I4]) + - SU3D[I2, I4, k6]*SU3F[6, I1, k7]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k7]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k7]*SUNDelta[8, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/45)*(SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I5, k8]*(SU3D[I2, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[I1, I4, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[I3, I4, k6]*(SU3F[I2, k6, k8]* - SUNDelta[8, I1] + SU3F[I1, k6, k8]*SUNDelta[8, I2]) + - SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*(SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3F[I1, k6, k8]*SUNDelta[8, I3]) + SU3D[I2, I3, k6]* - SU3F[I1, k6, k8]*SUNDelta[8, I4] + SU3D[I1, I3, k6]* - SU3F[I2, k6, k8]*SUNDelta[8, I4] + SU3D[I1, I2, k6]* - SU3F[I3, k6, k8]*SUNDelta[8, I4]) + SU3D[6, I3, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I4, k8]*(SU3D[I2, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I1, I5, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I3, I5, k6]*(SU3F[I2, k6, k8]*SUNDelta[8, I1] + - SU3F[I1, k6, k8]*SUNDelta[8, I2]) + SU3D[I1, I5, k6]* - SU3F[I2, k6, k8]*SUNDelta[8, I3] + SU3D[I1, I2, k6]* - SU3F[I5, k6, k8]*SUNDelta[8, I3] + SU3D[I2, I5, k6]* - (SU3F[I3, k6, k8]*SUNDelta[8, I1] + SU3F[I1, k6, k8]* - SUNDelta[8, I3]) + SU3D[I2, I3, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I5] + SU3D[I1, I2, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I5])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (2*(SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I2] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I3] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I2, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I5, k7]*(SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k8]*(SU3D[I3, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SUNDelta[8, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[8, I4] + SU3D[I1, I2, k8]* - SU3D[I3, k7, k8]*SUNDelta[8, I4] + SU3D[I2, k7, k8]* - (SU3D[I3, I4, k8]*SUNDelta[8, I1] + SU3D[I1, I4, k8]* - SUNDelta[8, I3] + SU3D[I1, I3, k8]*SUNDelta[8, I4])) + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I2, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I4, k7]*(SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[I2, I5, k8]*(SU3D[I3, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SUNDelta[8, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[8, I5] + SU3D[I1, I2, k8]* - SU3D[I3, k7, k8]*SUNDelta[8, I5] + SU3D[I2, k7, k8]* - (SU3D[I3, I5, k8]*SUNDelta[8, I1] + SU3D[I1, I5, k8]* - SUNDelta[8, I3] + SU3D[I1, I3, k8]*SUNDelta[8, I5]))))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[7, k8]*(SU3D[I3, I4, k5]*SU3F[I5, k5, k8]*SUNDelta[I1, I2] + - SU3D[I2, I5, k5]*SU3F[I4, k5, k8]*SUNDelta[I1, I3] + - SU3D[I2, I4, k5]*SU3F[I5, k5, k8]*SUNDelta[I1, I3] + - SU3D[I2, I5, k5]*SU3F[I3, k5, k8]*SUNDelta[I1, I4] + - SU3D[I2, I3, k5]*SU3F[I5, k5, k8]*SUNDelta[I1, I4] + - SU3D[I3, I4, k5]*SU3F[I2, k5, k8]*SUNDelta[I1, I5] + - SU3D[I2, I4, k5]*SU3F[I3, k5, k8]*SUNDelta[I1, I5] + - SU3D[I2, I3, k5]*SU3F[I4, k5, k8]*SUNDelta[I1, I5] + - SU3D[I1, I5, k5]*SU3F[I4, k5, k8]*SUNDelta[I2, I3] + - SU3D[I1, I4, k5]*SU3F[I5, k5, k8]*SUNDelta[I2, I3] + - SU3D[I4, I5, k5]*(SU3F[I3, k5, k8]*SUNDelta[I1, I2] + - SU3F[I2, k5, k8]*SUNDelta[I1, I3] + SU3F[I1, k5, k8]* - SUNDelta[I2, I3]) + SU3D[I1, I5, k5]*SU3F[I3, k5, k8]* - SUNDelta[I2, I4] + SU3D[I1, I3, k5]*SU3F[I5, k5, k8]* - SUNDelta[I2, I4] + SU3D[I3, I5, k5]* - (SU3F[I4, k5, k8]*SUNDelta[I1, I2] + SU3F[I2, k5, k8]* - SUNDelta[I1, I4] + SU3F[I1, k5, k8]*SUNDelta[I2, I4]) + - SU3D[I3, I4, k5]*SU3F[I1, k5, k8]*SUNDelta[I2, I5] + - SU3D[I1, I4, k5]*SU3F[I3, k5, k8]*SUNDelta[I2, I5] + - SU3D[I1, I3, k5]*SU3F[I4, k5, k8]*SUNDelta[I2, I5] + - SU3D[I2, I5, k5]*SU3F[I1, k5, k8]*SUNDelta[I3, I4] + - SU3D[I1, I5, k5]*SU3F[I2, k5, k8]*SUNDelta[I3, I4] + - SU3D[I1, I2, k5]*SU3F[I5, k5, k8]*SUNDelta[I3, I4] + - SU3D[I2, I4, k5]*SU3F[I1, k5, k8]*SUNDelta[I3, I5] + - SU3D[I1, I4, k5]*SU3F[I2, k5, k8]*SUNDelta[I3, I5] + - SU3D[I1, I2, k5]*SU3F[I4, k5, k8]*SUNDelta[I3, I5] + - SU3D[I2, I3, k5]*SU3F[I1, k5, k8]*SUNDelta[I4, I5] + - SU3D[I1, I3, k5]*SU3F[I2, k5, k8]*SUNDelta[I4, I5] + - SU3D[I1, I2, k5]*SU3F[I3, k5, k8]*SUNDelta[I4, I5]))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/135)*SUNDelta[6, k5]*(SU3D[I3, I4, k8]*SU3F[I5, k5, k8]* - SUNDelta[I1, I2] + SU3D[I2, I5, k8]*SU3F[I4, k5, k8]* - SUNDelta[I1, I3] + SU3D[I2, I4, k8]*SU3F[I5, k5, k8]* - SUNDelta[I1, I3] + SU3D[I2, I5, k8]*SU3F[I3, k5, k8]* - SUNDelta[I1, I4] + SU3D[I2, I3, k8]*SU3F[I5, k5, k8]* - SUNDelta[I1, I4] + SU3D[I3, I4, k8]*SU3F[I2, k5, k8]* - SUNDelta[I1, I5] + SU3D[I2, I4, k8]*SU3F[I3, k5, k8]* - SUNDelta[I1, I5] + SU3D[I2, I3, k8]*SU3F[I4, k5, k8]* - SUNDelta[I1, I5] + SU3D[I1, I5, k8]*SU3F[I4, k5, k8]* - SUNDelta[I2, I3] + SU3D[I1, I4, k8]*SU3F[I5, k5, k8]* - SUNDelta[I2, I3] + SU3D[I4, I5, k8]* - (SU3F[I3, k5, k8]*SUNDelta[I1, I2] + SU3F[I2, k5, k8]* - SUNDelta[I1, I3] + SU3F[I1, k5, k8]*SUNDelta[I2, I3]) + - SU3D[I1, I5, k8]*SU3F[I3, k5, k8]*SUNDelta[I2, I4] + - SU3D[I1, I3, k8]*SU3F[I5, k5, k8]*SUNDelta[I2, I4] + - SU3D[I3, I5, k8]*(SU3F[I4, k5, k8]*SUNDelta[I1, I2] + - SU3F[I2, k5, k8]*SUNDelta[I1, I4] + SU3F[I1, k5, k8]* - SUNDelta[I2, I4]) + SU3D[I3, I4, k8]*SU3F[I1, k5, k8]* - SUNDelta[I2, I5] + SU3D[I1, I4, k8]*SU3F[I3, k5, k8]* - SUNDelta[I2, I5] + SU3D[I1, I3, k8]*SU3F[I4, k5, k8]* - SUNDelta[I2, I5] + SU3D[I2, I5, k8]*SU3F[I1, k5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I5, k8]*SU3F[I2, k5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I2, k8]*SU3F[I5, k5, k8]* - SUNDelta[I3, I4] + SU3D[I2, I4, k8]*SU3F[I1, k5, k8]* - SUNDelta[I3, I5] + SU3D[I1, I4, k8]*SU3F[I2, k5, k8]* - SUNDelta[I3, I5] + SU3D[I1, I2, k8]*SU3F[I4, k5, k8]* - SUNDelta[I3, I5] + SU3D[I2, I3, k8]*SU3F[I1, k5, k8]* - SUNDelta[I4, I5] + SU3D[I1, I3, k8]*SU3F[I2, k5, k8]* - SUNDelta[I4, I5] + SU3D[I1, I2, k8]*SU3F[I3, k5, k8]* - SUNDelta[I4, I5]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (8*(SU3D[8, I3, I4]*SUNDelta[6, I5]*SUNDelta[I1, I2] + - SU3D[8, I2, I5]*SUNDelta[6, I4]*SUNDelta[I1, I3] + - SU3D[8, I2, I4]*SUNDelta[6, I5]*SUNDelta[I1, I3] + - SU3D[8, I2, I5]*SUNDelta[6, I3]*SUNDelta[I1, I4] + - SU3D[8, I2, I3]*SUNDelta[6, I5]*SUNDelta[I1, I4] + - SU3D[8, I3, I4]*SUNDelta[6, I2]*SUNDelta[I1, I5] + - SU3D[8, I2, I4]*SUNDelta[6, I3]*SUNDelta[I1, I5] + - SU3D[8, I2, I3]*SUNDelta[6, I4]*SUNDelta[I1, I5] + - SU3D[8, I1, I5]*SUNDelta[6, I4]*SUNDelta[I2, I3] + - SU3D[8, I1, I4]*SUNDelta[6, I5]*SUNDelta[I2, I3] + - SU3D[8, I4, I5]*(SUNDelta[6, I3]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I3] + SUNDelta[6, I1]* - SUNDelta[I2, I3]) + SU3D[8, I1, I5]*SUNDelta[6, I3]* - SUNDelta[I2, I4] + SU3D[8, I1, I3]*SUNDelta[6, I5]*SUNDelta[I2, I4] + - SU3D[8, I3, I5]*(SUNDelta[6, I4]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I4] + SUNDelta[6, I1]* - SUNDelta[I2, I4]) + SU3D[8, I3, I4]*SUNDelta[6, I1]* - SUNDelta[I2, I5] + SU3D[8, I1, I4]*SUNDelta[6, I3]*SUNDelta[I2, I5] + - SU3D[8, I1, I3]*SUNDelta[6, I4]*SUNDelta[I2, I5] + - SU3D[8, I2, I5]*SUNDelta[6, I1]*SUNDelta[I3, I4] + - SU3D[8, I1, I5]*SUNDelta[6, I2]*SUNDelta[I3, I4] + - SU3D[8, I1, I2]*SUNDelta[6, I5]*SUNDelta[I3, I4] + - SU3D[8, I2, I4]*SUNDelta[6, I1]*SUNDelta[I3, I5] + - SU3D[8, I1, I4]*SUNDelta[6, I2]*SUNDelta[I3, I5] + - SU3D[8, I1, I2]*SUNDelta[6, I4]*SUNDelta[I3, I5] + - SU3D[8, I2, I3]*SUNDelta[6, I1]*SUNDelta[I4, I5] + - SU3D[8, I1, I3]*SUNDelta[6, I2]*SUNDelta[I4, I5] + - SU3D[8, I1, I2]*SUNDelta[6, I3]*SUNDelta[I4, I5]))/ - (135*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 5) + (8*(SU3D[6, I3, I4]*SUNDelta[8, I5]*SUNDelta[I1, I2] + - SU3D[6, I2, I5]*SUNDelta[8, I4]*SUNDelta[I1, I3] + - SU3D[6, I2, I4]*SUNDelta[8, I5]*SUNDelta[I1, I3] + - SU3D[6, I2, I5]*SUNDelta[8, I3]*SUNDelta[I1, I4] + - SU3D[6, I2, I3]*SUNDelta[8, I5]*SUNDelta[I1, I4] + - SU3D[6, I3, I4]*SUNDelta[8, I2]*SUNDelta[I1, I5] + - SU3D[6, I2, I4]*SUNDelta[8, I3]*SUNDelta[I1, I5] + - SU3D[6, I2, I3]*SUNDelta[8, I4]*SUNDelta[I1, I5] + - SU3D[6, I1, I5]*SUNDelta[8, I4]*SUNDelta[I2, I3] + - SU3D[6, I1, I4]*SUNDelta[8, I5]*SUNDelta[I2, I3] + - SU3D[6, I4, I5]*(SUNDelta[8, I3]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I3] + SUNDelta[8, I1]* - SUNDelta[I2, I3]) + SU3D[6, I1, I5]*SUNDelta[8, I3]* - SUNDelta[I2, I4] + SU3D[6, I1, I3]*SUNDelta[8, I5]*SUNDelta[I2, I4] + - SU3D[6, I3, I5]*(SUNDelta[8, I4]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I4] + SUNDelta[8, I1]* - SUNDelta[I2, I4]) + SU3D[6, I3, I4]*SUNDelta[8, I1]* - SUNDelta[I2, I5] + SU3D[6, I1, I4]*SUNDelta[8, I3]*SUNDelta[I2, I5] + - SU3D[6, I1, I3]*SUNDelta[8, I4]*SUNDelta[I2, I5] + - SU3D[6, I2, I5]*SUNDelta[8, I1]*SUNDelta[I3, I4] + - SU3D[6, I1, I5]*SUNDelta[8, I2]*SUNDelta[I3, I4] + - SU3D[6, I1, I2]*SUNDelta[8, I5]*SUNDelta[I3, I4] + - SU3D[6, I2, I4]*SUNDelta[8, I1]*SUNDelta[I3, I5] + - SU3D[6, I1, I4]*SUNDelta[8, I2]*SUNDelta[I3, I5] + - SU3D[6, I1, I2]*SUNDelta[8, I4]*SUNDelta[I3, I5] + - SU3D[6, I2, I3]*SUNDelta[8, I1]*SUNDelta[I4, I5] + - SU3D[6, I1, I3]*SUNDelta[8, I2]*SUNDelta[I4, I5] + - SU3D[6, I1, I2]*SUNDelta[8, I3]*SUNDelta[I4, I5]))/ - (135*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 5) - (((16*I)/135)*(SU3F[6, 8, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SU3F[6, 8, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - SU3F[6, 8, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - SU3F[6, 8, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - SUNDelta[I2, I5]*(SU3F[6, 8, I4]*SUNDelta[I1, I3] + - SU3F[6, 8, I3]*SUNDelta[I1, I4] + SU3F[6, 8, I1]*SUNDelta[I3, I4]) + - SU3F[6, 8, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - SU3F[6, 8, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - SUNDelta[I2, I4]*(SU3F[6, 8, I5]*SUNDelta[I1, I3] + - SU3F[6, 8, I3]*SUNDelta[I1, I5] + SU3F[6, 8, I1]*SUNDelta[I3, I5]) + - SU3F[6, 8, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - SU3F[6, 8, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - SU3F[6, 8, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (8*(SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[6, I5]*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I3]*SUNDelta[I2, I4] + SUNDelta[I1, I2]* - SUNDelta[I3, I4]) + SUNDelta[6, I2]*SUNDelta[I1, I4]* - SUNDelta[I3, I5] + SUNDelta[6, I1]*SUNDelta[I2, I4]* - SUNDelta[I3, I5] + SUNDelta[6, I4]* - (SUNDelta[I1, I5]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I5] + SUNDelta[I1, I2]*SUNDelta[I3, I5]) + - SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ - (405*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/45)*SUNDelta[7, k6]*(SU3D[I3, I4, k5]*SU3D[I5, k5, k6]* - SUNDelta[I1, I2] + SU3D[I2, k5, k6]*SU3D[I4, I5, k5]* - SUNDelta[I1, I3] + SU3D[I2, I5, k5]*SU3D[I4, k5, k6]* - SUNDelta[I1, I3] + SU3D[I2, I4, k5]*SU3D[I5, k5, k6]* - SUNDelta[I1, I3] + SU3D[I2, I3, k5]*SU3D[I5, k5, k6]* - SUNDelta[I1, I4] + SU3D[I2, k5, k6]*SU3D[I3, I4, k5]* - SUNDelta[I1, I5] + SU3D[I2, I3, k5]*SU3D[I4, k5, k6]* - SUNDelta[I1, I5] + SU3D[I1, k5, k6]*SU3D[I4, I5, k5]* - SUNDelta[I2, I3] + SU3D[I1, I5, k5]*SU3D[I4, k5, k6]* - SUNDelta[I2, I3] + SU3D[I1, I4, k5]*SU3D[I5, k5, k6]* - SUNDelta[I2, I3] + SU3D[I1, I3, k5]*SU3D[I5, k5, k6]* - SUNDelta[I2, I4] + SU3D[I3, I5, k5]* - (SU3D[I4, k5, k6]*SUNDelta[I1, I2] + SU3D[I2, k5, k6]* - SUNDelta[I1, I4] + SU3D[I1, k5, k6]*SUNDelta[I2, I4]) + - SU3D[I1, k5, k6]*SU3D[I3, I4, k5]*SUNDelta[I2, I5] + - SU3D[I1, I3, k5]*SU3D[I4, k5, k6]*SUNDelta[I2, I5] + - SU3D[I1, k5, k6]*SU3D[I2, I5, k5]*SUNDelta[I3, I4] + - SU3D[I1, I5, k5]*SU3D[I2, k5, k6]*SUNDelta[I3, I4] + - SU3D[I1, I2, k5]*SU3D[I5, k5, k6]*SUNDelta[I3, I4] + - SU3D[I1, k5, k6]*SU3D[I2, I4, k5]*SUNDelta[I3, I5] + - SU3D[I1, I4, k5]*SU3D[I2, k5, k6]*SUNDelta[I3, I5] + - SU3D[I1, I2, k5]*SU3D[I4, k5, k6]*SUNDelta[I3, I5] + - SU3D[I1, k5, k6]*SU3D[I2, I3, k5]*SUNDelta[I4, I5] + - SU3D[I1, I3, k5]*SU3D[I2, k5, k6]*SUNDelta[I4, I5] + - SU3D[I3, k5, k6]*(SU3D[I4, I5, k5]*SUNDelta[I1, I2] + - SU3D[I2, I5, k5]*SUNDelta[I1, I4] + SU3D[I2, I4, k5]* - SUNDelta[I1, I5] + SU3D[I1, I5, k5]*SUNDelta[I2, I4] + - SU3D[I1, I4, k5]*SUNDelta[I2, I5] + SU3D[I1, I2, k5]* - SUNDelta[I4, I5])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (2*SUNDelta[6, k8]*(SU3D[I3, I4, k5]*SU3D[I5, k5, k8]*SUNDelta[I1, I2] + - SU3D[I2, k5, k8]*SU3D[I4, I5, k5]*SUNDelta[I1, I3] + - SU3D[I2, I5, k5]*SU3D[I4, k5, k8]*SUNDelta[I1, I3] + - SU3D[I2, I4, k5]*SU3D[I5, k5, k8]*SUNDelta[I1, I3] + - SU3D[I2, I3, k5]*SU3D[I5, k5, k8]*SUNDelta[I1, I4] + - SU3D[I2, k5, k8]*SU3D[I3, I4, k5]*SUNDelta[I1, I5] + - SU3D[I2, I3, k5]*SU3D[I4, k5, k8]*SUNDelta[I1, I5] + - SU3D[I1, k5, k8]*SU3D[I4, I5, k5]*SUNDelta[I2, I3] + - SU3D[I1, I5, k5]*SU3D[I4, k5, k8]*SUNDelta[I2, I3] + - SU3D[I1, I4, k5]*SU3D[I5, k5, k8]*SUNDelta[I2, I3] + - SU3D[I1, I3, k5]*SU3D[I5, k5, k8]*SUNDelta[I2, I4] + - SU3D[I3, I5, k5]*(SU3D[I4, k5, k8]*SUNDelta[I1, I2] + - SU3D[I2, k5, k8]*SUNDelta[I1, I4] + SU3D[I1, k5, k8]* - SUNDelta[I2, I4]) + SU3D[I1, k5, k8]*SU3D[I3, I4, k5]* - SUNDelta[I2, I5] + SU3D[I1, I3, k5]*SU3D[I4, k5, k8]* - SUNDelta[I2, I5] + SU3D[I1, k5, k8]*SU3D[I2, I5, k5]* - SUNDelta[I3, I4] + SU3D[I1, I5, k5]*SU3D[I2, k5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I2, k5]*SU3D[I5, k5, k8]* - SUNDelta[I3, I4] + SU3D[I1, k5, k8]*SU3D[I2, I4, k5]* - SUNDelta[I3, I5] + SU3D[I1, I4, k5]*SU3D[I2, k5, k8]* - SUNDelta[I3, I5] + SU3D[I1, I2, k5]*SU3D[I4, k5, k8]* - SUNDelta[I3, I5] + SU3D[I1, k5, k8]*SU3D[I2, I3, k5]* - SUNDelta[I4, I5] + SU3D[I1, I3, k5]*SU3D[I2, k5, k8]* - SUNDelta[I4, I5] + SU3D[I3, k5, k8]* - (SU3D[I4, I5, k5]*SUNDelta[I1, I2] + SU3D[I2, I5, k5]* - SUNDelta[I1, I4] + SU3D[I2, I4, k5]*SUNDelta[I1, I5] + - SU3D[I1, I5, k5]*SUNDelta[I2, I4] + SU3D[I1, I4, k5]* - SUNDelta[I2, I5] + SU3D[I1, I2, k5]*SUNDelta[I4, I5])))/ - (135*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 2]* -((-2*(SU3D[3, I3, k7]*SU3D[6, I4, I5]*SU3D[I1, I2, k7] + - SU3D[3, I2, k7]*SU3D[6, I4, I5]*SU3D[I1, I3, k7] + - SU3D[3, I3, k7]*SU3D[6, I2, I5]*SU3D[I1, I4, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, I5]*SU3D[I1, I4, k7] + - SU3D[3, I3, k7]*SU3D[6, I2, I4]*SU3D[I1, I5, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, I4]*SU3D[I1, I5, k7] + - SU3D[3, I1, k7]*SU3D[6, I4, I5]*SU3D[I2, I3, k7] + - SU3D[3, I3, k7]*SU3D[6, I1, I5]*SU3D[I2, I4, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, I5]*SU3D[I2, I4, k7] + - SU3D[3, I3, k7]*SU3D[6, I1, I4]*SU3D[I2, I5, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, I4]*SU3D[I2, I5, k7] + - SU3D[3, I2, k7]*SU3D[6, I1, I5]*SU3D[I3, I4, k7] + - SU3D[3, I1, k7]*SU3D[6, I2, I5]*SU3D[I3, I4, k7] + - SU3D[3, I5, k7]*(SU3D[6, I3, I4]*SU3D[I1, I2, k7] + - SU3D[6, I2, I4]*SU3D[I1, I3, k7] + SU3D[6, I2, I3]* - SU3D[I1, I4, k7] + SU3D[6, I1, I4]*SU3D[I2, I3, k7] + - SU3D[6, I1, I3]*SU3D[I2, I4, k7] + SU3D[6, I1, I2]* - SU3D[I3, I4, k7]) + SU3D[3, I2, k7]*SU3D[6, I1, I4]* - SU3D[I3, I5, k7] + SU3D[3, I1, k7]*SU3D[6, I2, I4]*SU3D[I3, I5, k7] + - SU3D[3, I4, k7]*(SU3D[6, I3, I5]*SU3D[I1, I2, k7] + - SU3D[6, I2, I5]*SU3D[I1, I3, k7] + SU3D[6, I2, I3]* - SU3D[I1, I5, k7] + SU3D[6, I1, I5]*SU3D[I2, I3, k7] + - SU3D[6, I1, I3]*SU3D[I2, I5, k7] + SU3D[6, I1, I2]* - SU3D[I3, I5, k7]) + SU3D[3, I3, k7]*SU3D[6, I1, I2]* - SU3D[I4, I5, k7] + SU3D[3, I2, k7]*SU3D[6, I1, I3]*SU3D[I4, I5, k7] + - SU3D[3, I1, k7]*SU3D[6, I2, I3]*SU3D[I4, I5, k7]))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[3, I3, I4]*SU3D[6, I5, k7]*SU3D[I1, I2, k7] + - SU3D[3, I2, I5]*SU3D[6, I4, k7]*SU3D[I1, I3, k7] + - SU3D[3, I2, I4]*SU3D[6, I5, k7]*SU3D[I1, I3, k7] + - SU3D[3, I2, I5]*SU3D[6, I3, k7]*SU3D[I1, I4, k7] + - SU3D[3, I2, I3]*SU3D[6, I5, k7]*SU3D[I1, I4, k7] + - SU3D[3, I3, I4]*SU3D[6, I2, k7]*SU3D[I1, I5, k7] + - SU3D[3, I2, I4]*SU3D[6, I3, k7]*SU3D[I1, I5, k7] + - SU3D[3, I2, I3]*SU3D[6, I4, k7]*SU3D[I1, I5, k7] + - SU3D[3, I1, I5]*SU3D[6, I4, k7]*SU3D[I2, I3, k7] + - SU3D[3, I1, I4]*SU3D[6, I5, k7]*SU3D[I2, I3, k7] + - SU3D[3, I4, I5]*(SU3D[6, I3, k7]*SU3D[I1, I2, k7] + - SU3D[6, I2, k7]*SU3D[I1, I3, k7] + SU3D[6, I1, k7]* - SU3D[I2, I3, k7]) + SU3D[3, I1, I5]*SU3D[6, I3, k7]* - SU3D[I2, I4, k7] + SU3D[3, I1, I3]*SU3D[6, I5, k7]*SU3D[I2, I4, k7] + - SU3D[3, I3, I5]*(SU3D[6, I4, k7]*SU3D[I1, I2, k7] + - SU3D[6, I2, k7]*SU3D[I1, I4, k7] + SU3D[6, I1, k7]* - SU3D[I2, I4, k7]) + SU3D[3, I3, I4]*SU3D[6, I1, k7]* - SU3D[I2, I5, k7] + SU3D[3, I1, I4]*SU3D[6, I3, k7]*SU3D[I2, I5, k7] + - SU3D[3, I1, I3]*SU3D[6, I4, k7]*SU3D[I2, I5, k7] + - SU3D[3, I2, I5]*SU3D[6, I1, k7]*SU3D[I3, I4, k7] + - SU3D[3, I1, I5]*SU3D[6, I2, k7]*SU3D[I3, I4, k7] + - SU3D[3, I1, I2]*SU3D[6, I5, k7]*SU3D[I3, I4, k7] + - SU3D[3, I2, I4]*SU3D[6, I1, k7]*SU3D[I3, I5, k7] + - SU3D[3, I1, I4]*SU3D[6, I2, k7]*SU3D[I3, I5, k7] + - SU3D[3, I1, I2]*SU3D[6, I4, k7]*SU3D[I3, I5, k7] + - SU3D[3, I2, I3]*SU3D[6, I1, k7]*SU3D[I4, I5, k7] + - SU3D[3, I1, I3]*SU3D[6, I2, k7]*SU3D[I4, I5, k7] + - SU3D[3, I1, I2]*SU3D[6, I3, k7]*SU3D[I4, I5, k7]))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[6, I3, k7]*SU3D[8, I4, I5]*SU3D[I1, I2, k7] + - SU3D[6, I2, k7]*SU3D[8, I4, I5]*SU3D[I1, I3, k7] + - SU3D[6, I3, k7]*SU3D[8, I2, I5]*SU3D[I1, I4, k7] + - SU3D[6, I2, k7]*SU3D[8, I3, I5]*SU3D[I1, I4, k7] + - SU3D[6, I3, k7]*SU3D[8, I2, I4]*SU3D[I1, I5, k7] + - SU3D[6, I2, k7]*SU3D[8, I3, I4]*SU3D[I1, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I4, I5]*SU3D[I2, I3, k7] + - SU3D[6, I3, k7]*SU3D[8, I1, I5]*SU3D[I2, I4, k7] + - SU3D[6, I1, k7]*SU3D[8, I3, I5]*SU3D[I2, I4, k7] + - SU3D[6, I3, k7]*SU3D[8, I1, I4]*SU3D[I2, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I3, I4]*SU3D[I2, I5, k7] + - SU3D[6, I2, k7]*SU3D[8, I1, I5]*SU3D[I3, I4, k7] + - SU3D[6, I1, k7]*SU3D[8, I2, I5]*SU3D[I3, I4, k7] + - SU3D[6, I5, k7]*(SU3D[8, I3, I4]*SU3D[I1, I2, k7] + - SU3D[8, I2, I4]*SU3D[I1, I3, k7] + SU3D[8, I2, I3]* - SU3D[I1, I4, k7] + SU3D[8, I1, I4]*SU3D[I2, I3, k7] + - SU3D[8, I1, I3]*SU3D[I2, I4, k7] + SU3D[8, I1, I2]* - SU3D[I3, I4, k7]) + SU3D[6, I2, k7]*SU3D[8, I1, I4]* - SU3D[I3, I5, k7] + SU3D[6, I1, k7]*SU3D[8, I2, I4]*SU3D[I3, I5, k7] + - SU3D[6, I4, k7]*(SU3D[8, I3, I5]*SU3D[I1, I2, k7] + - SU3D[8, I2, I5]*SU3D[I1, I3, k7] + SU3D[8, I2, I3]* - SU3D[I1, I5, k7] + SU3D[8, I1, I5]*SU3D[I2, I3, k7] + - SU3D[8, I1, I3]*SU3D[I2, I5, k7] + SU3D[8, I1, I2]* - SU3D[I3, I5, k7]) + SU3D[6, I3, k7]*SU3D[8, I1, I2]* - SU3D[I4, I5, k7] + SU3D[6, I2, k7]*SU3D[8, I1, I3]*SU3D[I4, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I2, I3]*SU3D[I4, I5, k7]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[6, I3, I4]*SU3D[8, I5, k7]*SU3D[I1, I2, k7] + - SU3D[6, I2, I5]*SU3D[8, I4, k7]*SU3D[I1, I3, k7] + - SU3D[6, I2, I4]*SU3D[8, I5, k7]*SU3D[I1, I3, k7] + - SU3D[6, I2, I5]*SU3D[8, I3, k7]*SU3D[I1, I4, k7] + - SU3D[6, I2, I3]*SU3D[8, I5, k7]*SU3D[I1, I4, k7] + - SU3D[6, I3, I4]*SU3D[8, I2, k7]*SU3D[I1, I5, k7] + - SU3D[6, I2, I4]*SU3D[8, I3, k7]*SU3D[I1, I5, k7] + - SU3D[6, I2, I3]*SU3D[8, I4, k7]*SU3D[I1, I5, k7] + - SU3D[6, I1, I5]*SU3D[8, I4, k7]*SU3D[I2, I3, k7] + - SU3D[6, I1, I4]*SU3D[8, I5, k7]*SU3D[I2, I3, k7] + - SU3D[6, I4, I5]*(SU3D[8, I3, k7]*SU3D[I1, I2, k7] + - SU3D[8, I2, k7]*SU3D[I1, I3, k7] + SU3D[8, I1, k7]* - SU3D[I2, I3, k7]) + SU3D[6, I1, I5]*SU3D[8, I3, k7]* - SU3D[I2, I4, k7] + SU3D[6, I1, I3]*SU3D[8, I5, k7]*SU3D[I2, I4, k7] + - SU3D[6, I3, I5]*(SU3D[8, I4, k7]*SU3D[I1, I2, k7] + - SU3D[8, I2, k7]*SU3D[I1, I4, k7] + SU3D[8, I1, k7]* - SU3D[I2, I4, k7]) + SU3D[6, I3, I4]*SU3D[8, I1, k7]* - SU3D[I2, I5, k7] + SU3D[6, I1, I4]*SU3D[8, I3, k7]*SU3D[I2, I5, k7] + - SU3D[6, I1, I3]*SU3D[8, I4, k7]*SU3D[I2, I5, k7] + - SU3D[6, I2, I5]*SU3D[8, I1, k7]*SU3D[I3, I4, k7] + - SU3D[6, I1, I5]*SU3D[8, I2, k7]*SU3D[I3, I4, k7] + - SU3D[6, I1, I2]*SU3D[8, I5, k7]*SU3D[I3, I4, k7] + - SU3D[6, I2, I4]*SU3D[8, I1, k7]*SU3D[I3, I5, k7] + - SU3D[6, I1, I4]*SU3D[8, I2, k7]*SU3D[I3, I5, k7] + - SU3D[6, I1, I2]*SU3D[8, I4, k7]*SU3D[I3, I5, k7] + - SU3D[6, I2, I3]*SU3D[8, I1, k7]*SU3D[I4, I5, k7] + - SU3D[6, I1, I3]*SU3D[8, I2, k7]*SU3D[I4, I5, k7] + - SU3D[6, I1, I2]*SU3D[8, I3, k7]*SU3D[I4, I5, k7]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I1, k11, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I5, k7]* - SU3D[I1, k11, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I5, k7]*SU3D[I2, k11, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I5, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I5, k7]* - SU3D[I2, k10, k7]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11] + - SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I1, k11, k9]*SU3D[I2, k10, k11]* - SU3D[I4, k10, k7] + SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I1, k10, k11]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k7] + SU3D[3, I2, k9]*SU3D[6, I5, k7]* - SU3D[I1, k11, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k7] + - SU3D[3, I1, k9]*SU3D[6, I5, k7]*SU3D[I2, k11, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k7] + SU3D[3, I2, k9]*SU3D[6, I5, k7]*SU3D[I1, k10, k11]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k7] + SU3D[3, I1, k9]*SU3D[6, I5, k7]* - SU3D[I2, k10, k11]*SU3D[I3, k11, k9]*SU3D[I4, k10, k7] + - SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I1, k10, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I1, k10, k11]* - SU3D[I2, k10, k7]*SU3D[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k7]* - SU3D[I1, k10, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k9] + - SU3D[3, I1, k9]*SU3D[6, I5, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k7]*SU3D[I1, k10, k11]* - SU3D[I3, k10, k7]*SU3D[I4, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I5, k7]* - SU3D[I2, k10, k11]*SU3D[I3, k10, k7]*SU3D[I4, k11, k9] + - SU3D[3, I5, k9]*(SU3D[6, I4, k7]*(SU3D[I1, k11, k9]* - (SU3D[I2, k10, k7]*SU3D[I3, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I3, k10, k7]) + SU3D[I1, k10, k7]* - (SU3D[I2, k11, k9]*SU3D[I3, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I3, k11, k9]) + SU3D[I1, k10, k11]* - (SU3D[I2, k11, k9]*SU3D[I3, k10, k7] + SU3D[I2, k10, k7]* - SU3D[I3, k11, k9])) + SU3D[6, I2, k7]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k11] + SU3D[6, I1, k7]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k11] + - SU3D[6, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k11, k9]* - SU3D[I4, k10, k11] + SU3D[6, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k11] + SU3D[6, I2, k7]* - SU3D[I1, k11, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k7] + - SU3D[6, I1, k7]*SU3D[I2, k11, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k7] + SU3D[6, I2, k7]*SU3D[I1, k10, k11]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k7] + SU3D[6, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I3, k11, k9]*SU3D[I4, k10, k7] + - SU3D[6, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k9] + SU3D[6, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k10, k7]*SU3D[I4, k11, k9] + - SU3D[6, I1, k7]*SU3D[I2, k10, k11]*SU3D[I3, k10, k7]* - SU3D[I4, k11, k9] + SU3D[6, I3, k7]* - (SU3D[I1, k11, k9]*(SU3D[I2, k10, k7]*SU3D[I4, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I4, k10, k7]) + SU3D[I1, k10, k7]* - (SU3D[I2, k11, k9]*SU3D[I4, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I4, k11, k9]) + SU3D[I1, k10, k11]* - (SU3D[I2, k11, k9]*SU3D[I4, k10, k7] + SU3D[I2, k10, k7]* - SU3D[I4, k11, k9]))) + SU3D[3, I3, k9]*SU3D[6, I4, k7]* - SU3D[I1, k11, k9]*SU3D[I2, k10, k7]*SU3D[I5, k10, k11] + - SU3D[3, I3, k9]*SU3D[6, I4, k7]*SU3D[I1, k10, k7]*SU3D[I2, k11, k9]* - SU3D[I5, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k7]*SU3D[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I4, k7]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I1, k10, k7]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I4, k7]*SU3D[I2, k10, k7]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I1, k11, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I1, k11, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I2, k11, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I3, k7]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I3, k11, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I3, k11, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I1, k10, k7]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I1, k10, k7]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I3, k7]* - SU3D[I2, k10, k7]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I3, k10, k7]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I4, k7]* - SU3D[I1, k11, k9]*SU3D[I2, k10, k11]*SU3D[I5, k10, k7] + - SU3D[3, I3, k9]*SU3D[6, I4, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k9]* - SU3D[I5, k10, k7] + SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k7] + SU3D[3, I1, k9]*SU3D[6, I4, k7]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k11]*SU3D[I5, k10, k7] + - SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k7] + SU3D[3, I1, k9]*SU3D[6, I4, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k7] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I1, k11, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k7] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I1, k11, k9]*SU3D[I4, k10, k11]* - SU3D[I5, k10, k7] + SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I2, k11, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k7] + SU3D[3, I1, k9]*SU3D[6, I3, k7]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k7] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3D[I5, k10, k7] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I3, k11, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k7] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k9]*SU3D[I5, k10, k7] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k7] + SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k7] + SU3D[3, I1, k9]*SU3D[6, I3, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k9]*SU3D[I5, k10, k7] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k7] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9]*SU3D[I5, k10, k7] + SU3D[3, I3, k9]*SU3D[6, I4, k7]* - SU3D[I1, k10, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k9] + - SU3D[3, I3, k9]*SU3D[6, I4, k7]*SU3D[I1, k10, k11]*SU3D[I2, k10, k7]* - SU3D[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I4, k7]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I1, k10, k11]*SU3D[I3, k10, k7]* - SU3D[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I4, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k7]*SU3D[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I1, k10, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I1, k10, k7]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I3, k7]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k10, k7]*SU3D[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I1, k10, k11]*SU3D[I4, k10, k7]* - SU3D[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k10, k7]*SU3D[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I3, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k7]*SU3D[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I3, k10, k11]*SU3D[I4, k10, k7]* - SU3D[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k7]*SU3D[I5, k11, k9] + SU3D[3, I4, k9]* - (SU3D[6, I5, k7]*(SU3D[I1, k11, k9]*(SU3D[I2, k10, k7]* - SU3D[I3, k10, k11] + SU3D[I2, k10, k11]*SU3D[I3, k10, k7]) + - SU3D[I1, k10, k7]*(SU3D[I2, k11, k9]*SU3D[I3, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I3, k11, k9]) + SU3D[I1, k10, k11]* - (SU3D[I2, k11, k9]*SU3D[I3, k10, k7] + SU3D[I2, k10, k7]* - SU3D[I3, k11, k9])) + SU3D[6, I2, k7]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k7]*SU3D[I5, k10, k11] + SU3D[6, I1, k7]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k11] + SU3D[6, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k11] + SU3D[6, I2, k7]* - SU3D[I1, k11, k9]*SU3D[I3, k10, k11]*SU3D[I5, k10, k7] + - SU3D[6, I1, k7]*SU3D[I2, k11, k9]*SU3D[I3, k10, k11]* - SU3D[I5, k10, k7] + SU3D[6, I2, k7]*SU3D[I1, k10, k11]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k7] + SU3D[6, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I3, k11, k9]*SU3D[I5, k10, k7] + - SU3D[6, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k9] + SU3D[6, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k10, k7]*SU3D[I5, k11, k9] + - SU3D[6, I1, k7]*SU3D[I2, k10, k11]*SU3D[I3, k10, k7]* - SU3D[I5, k11, k9] + SU3D[6, I3, k7]* - (SU3D[I1, k11, k9]*(SU3D[I2, k10, k7]*SU3D[I5, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I5, k10, k7]) + SU3D[I1, k10, k7]* - (SU3D[I2, k11, k9]*SU3D[I5, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I5, k11, k9]) + SU3D[I1, k10, k11]* - (SU3D[I2, k11, k9]*SU3D[I5, k10, k7] + SU3D[I2, k10, k7]* - SU3D[I5, k11, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k7, k8]*SU3D[I2, k11, k8]* - SU3D[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I5, k10]* - SU3D[I1, k11, k8]*SU3D[I2, k7, k8]*SU3D[I4, k10, k11] + - SU3D[6, I2, k7]*SU3D[8, I5, k10]*SU3D[I1, k7, k8]*SU3D[I3, k11, k8]* - SU3D[I4, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I5, k10]*SU3D[I2, k7, k8]* - SU3D[I3, k11, k8]*SU3D[I4, k10, k11] + SU3D[6, I2, k7]* - SU3D[8, I5, k10]*SU3D[I1, k11, k8]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k11] + SU3D[6, I1, k7]*SU3D[8, I5, k10]* - SU3D[I2, k11, k8]*SU3D[I3, k7, k8]*SU3D[I4, k10, k11] + - SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k7, k8]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[8, I5, k10]* - SU3D[I1, k10, k11]*SU3D[I2, k7, k8]*SU3D[I4, k11, k8] + - SU3D[6, I2, k7]*SU3D[8, I5, k10]*SU3D[I1, k7, k8]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k8] + SU3D[6, I1, k7]*SU3D[8, I5, k10]*SU3D[I2, k7, k8]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k8] + SU3D[6, I2, k7]* - SU3D[8, I5, k10]*SU3D[I1, k10, k11]*SU3D[I3, k7, k8]* - SU3D[I4, k11, k8] + SU3D[6, I1, k7]*SU3D[8, I5, k10]* - SU3D[I2, k10, k11]*SU3D[I3, k7, k8]*SU3D[I4, k11, k8] + - SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k11, k8]*SU3D[I2, k10, k11]* - SU3D[I4, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k10, k11]* - SU3D[I2, k11, k8]*SU3D[I4, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I5, k10]* - SU3D[I1, k11, k8]*SU3D[I3, k10, k11]*SU3D[I4, k7, k8] + - SU3D[6, I1, k7]*SU3D[8, I5, k10]*SU3D[I2, k11, k8]*SU3D[I3, k10, k11]* - SU3D[I4, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I5, k10]*SU3D[I1, k10, k11]* - SU3D[I3, k11, k8]*SU3D[I4, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I5, k10]* - SU3D[I2, k10, k11]*SU3D[I3, k11, k8]*SU3D[I4, k7, k8] + - SU3D[6, I5, k7]*(SU3D[8, I4, k10]*(SU3D[I1, k7, k8]* - (SU3D[I2, k11, k8]*SU3D[I3, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I3, k11, k8]) + SU3D[I1, k11, k8]* - (SU3D[I2, k7, k8]*SU3D[I3, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I3, k7, k8]) + SU3D[I1, k10, k11]* - (SU3D[I2, k7, k8]*SU3D[I3, k11, k8] + SU3D[I2, k11, k8]* - SU3D[I3, k7, k8])) + SU3D[8, I2, k10]*SU3D[I1, k7, k8]* - SU3D[I3, k11, k8]*SU3D[I4, k10, k11] + SU3D[8, I1, k10]* - SU3D[I2, k7, k8]*SU3D[I3, k11, k8]*SU3D[I4, k10, k11] + - SU3D[8, I2, k10]*SU3D[I1, k11, k8]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k11] + SU3D[8, I1, k10]*SU3D[I2, k11, k8]* - SU3D[I3, k7, k8]*SU3D[I4, k10, k11] + SU3D[8, I2, k10]* - SU3D[I1, k7, k8]*SU3D[I3, k10, k11]*SU3D[I4, k11, k8] + - SU3D[8, I1, k10]*SU3D[I2, k7, k8]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k8] + SU3D[8, I2, k10]*SU3D[I1, k10, k11]* - SU3D[I3, k7, k8]*SU3D[I4, k11, k8] + SU3D[8, I1, k10]* - SU3D[I2, k10, k11]*SU3D[I3, k7, k8]*SU3D[I4, k11, k8] + - SU3D[8, I2, k10]*SU3D[I1, k11, k8]*SU3D[I3, k10, k11]* - SU3D[I4, k7, k8] + SU3D[8, I1, k10]*SU3D[I2, k11, k8]* - SU3D[I3, k10, k11]*SU3D[I4, k7, k8] + SU3D[8, I2, k10]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k8]*SU3D[I4, k7, k8] + - SU3D[8, I1, k10]*SU3D[I2, k10, k11]*SU3D[I3, k11, k8]* - SU3D[I4, k7, k8] + SU3D[8, I3, k10]* - (SU3D[I1, k7, k8]*(SU3D[I2, k11, k8]*SU3D[I4, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I4, k11, k8]) + SU3D[I1, k11, k8]* - (SU3D[I2, k7, k8]*SU3D[I4, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I4, k7, k8]) + SU3D[I1, k10, k11]* - (SU3D[I2, k7, k8]*SU3D[I4, k11, k8] + SU3D[I2, k11, k8]* - SU3D[I4, k7, k8]))) + SU3D[6, I3, k7]*SU3D[8, I4, k10]* - SU3D[I1, k7, k8]*SU3D[I2, k11, k8]*SU3D[I5, k10, k11] + - SU3D[6, I3, k7]*SU3D[8, I4, k10]*SU3D[I1, k11, k8]*SU3D[I2, k7, k8]* - SU3D[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k7, k8]* - SU3D[I3, k11, k8]*SU3D[I5, k10, k11] + SU3D[6, I1, k7]* - SU3D[8, I4, k10]*SU3D[I2, k7, k8]*SU3D[I3, k11, k8]* - SU3D[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[8, I4, k10]* - SU3D[I1, k11, k8]*SU3D[I3, k7, k8]*SU3D[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[8, I4, k10]*SU3D[I2, k11, k8]*SU3D[I3, k7, k8]* - SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I2, k10]*SU3D[I1, k7, k8]* - SU3D[I4, k11, k8]*SU3D[I5, k10, k11] + SU3D[6, I2, k7]* - SU3D[8, I3, k10]*SU3D[I1, k7, k8]*SU3D[I4, k11, k8]* - SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k7, k8]* - SU3D[I4, k11, k8]*SU3D[I5, k10, k11] + SU3D[6, I1, k7]* - SU3D[8, I3, k10]*SU3D[I2, k7, k8]*SU3D[I4, k11, k8]* - SU3D[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[8, I1, k10]*SU3D[I3, k7, k8]* - SU3D[I4, k11, k8]*SU3D[I5, k10, k11] + SU3D[6, I1, k7]* - SU3D[8, I2, k10]*SU3D[I3, k7, k8]*SU3D[I4, k11, k8]* - SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I2, k10]* - SU3D[I1, k11, k8]*SU3D[I4, k7, k8]*SU3D[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[8, I3, k10]*SU3D[I1, k11, k8]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I1, k10]* - SU3D[I2, k11, k8]*SU3D[I4, k7, k8]*SU3D[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[8, I3, k10]*SU3D[I2, k11, k8]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[8, I1, k10]* - SU3D[I3, k11, k8]*SU3D[I4, k7, k8]*SU3D[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k11, k8]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[8, I4, k10]*SU3D[I1, k7, k8]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k8] + SU3D[6, I3, k7]* - SU3D[8, I4, k10]*SU3D[I1, k10, k11]*SU3D[I2, k7, k8]* - SU3D[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k7, k8]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[8, I4, k10]*SU3D[I2, k7, k8]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[8, I4, k10]* - SU3D[I1, k10, k11]*SU3D[I3, k7, k8]*SU3D[I5, k11, k8] + - SU3D[6, I1, k7]*SU3D[8, I4, k10]*SU3D[I2, k10, k11]*SU3D[I3, k7, k8]* - SU3D[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[8, I2, k10]*SU3D[I1, k7, k8]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[8, I3, k10]*SU3D[I1, k7, k8]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k7, k8]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[8, I3, k10]*SU3D[I2, k7, k8]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[8, I1, k10]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[8, I2, k10]*SU3D[I3, k7, k8]*SU3D[I4, k10, k11]* - SU3D[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[8, I2, k10]* - SU3D[I1, k10, k11]*SU3D[I4, k7, k8]*SU3D[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[8, I3, k10]*SU3D[I1, k10, k11]*SU3D[I4, k7, k8]* - SU3D[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[8, I1, k10]* - SU3D[I2, k10, k11]*SU3D[I4, k7, k8]*SU3D[I5, k11, k8] + - SU3D[6, I1, k7]*SU3D[8, I3, k10]*SU3D[I2, k10, k11]*SU3D[I4, k7, k8]* - SU3D[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[8, I1, k10]* - SU3D[I3, k10, k11]*SU3D[I4, k7, k8]*SU3D[I5, k11, k8] + - SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k10, k11]*SU3D[I4, k7, k8]* - SU3D[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[8, I4, k10]*SU3D[I1, k11, k8]* - SU3D[I2, k10, k11]*SU3D[I5, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I4, k10]* - SU3D[I1, k10, k11]*SU3D[I2, k11, k8]*SU3D[I5, k7, k8] + - SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k11, k8]*SU3D[I3, k10, k11]* - SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I4, k10]*SU3D[I2, k11, k8]* - SU3D[I3, k10, k11]*SU3D[I5, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I4, k10]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k8]*SU3D[I5, k7, k8] + - SU3D[6, I1, k7]*SU3D[8, I4, k10]*SU3D[I2, k10, k11]*SU3D[I3, k11, k8]* - SU3D[I5, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I2, k10]*SU3D[I1, k11, k8]* - SU3D[I4, k10, k11]*SU3D[I5, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I3, k10]* - SU3D[I1, k11, k8]*SU3D[I4, k10, k11]*SU3D[I5, k7, k8] + - SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k11, k8]*SU3D[I4, k10, k11]* - SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I3, k10]*SU3D[I2, k11, k8]* - SU3D[I4, k10, k11]*SU3D[I5, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I1, k10]* - SU3D[I3, k11, k8]*SU3D[I4, k10, k11]*SU3D[I5, k7, k8] + - SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k11, k8]*SU3D[I4, k10, k11]* - SU3D[I5, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I2, k10]*SU3D[I1, k10, k11]* - SU3D[I4, k11, k8]*SU3D[I5, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I3, k10]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k8]*SU3D[I5, k7, k8] + - SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k10, k11]*SU3D[I4, k11, k8]* - SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I3, k10]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k8]*SU3D[I5, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I1, k10]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k8]*SU3D[I5, k7, k8] + - SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k10, k11]*SU3D[I4, k11, k8]* - SU3D[I5, k7, k8] + SU3D[6, I4, k7]* - (SU3D[8, I5, k10]*(SU3D[I1, k7, k8]*(SU3D[I2, k11, k8]* - SU3D[I3, k10, k11] + SU3D[I2, k10, k11]*SU3D[I3, k11, k8]) + - SU3D[I1, k11, k8]*(SU3D[I2, k7, k8]*SU3D[I3, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I3, k7, k8]) + SU3D[I1, k10, k11]* - (SU3D[I2, k7, k8]*SU3D[I3, k11, k8] + SU3D[I2, k11, k8]* - SU3D[I3, k7, k8])) + SU3D[8, I2, k10]*SU3D[I1, k7, k8]* - SU3D[I3, k11, k8]*SU3D[I5, k10, k11] + SU3D[8, I1, k10]* - SU3D[I2, k7, k8]*SU3D[I3, k11, k8]*SU3D[I5, k10, k11] + - SU3D[8, I2, k10]*SU3D[I1, k11, k8]*SU3D[I3, k7, k8]* - SU3D[I5, k10, k11] + SU3D[8, I1, k10]*SU3D[I2, k11, k8]* - SU3D[I3, k7, k8]*SU3D[I5, k10, k11] + SU3D[8, I2, k10]* - SU3D[I1, k7, k8]*SU3D[I3, k10, k11]*SU3D[I5, k11, k8] + - SU3D[8, I1, k10]*SU3D[I2, k7, k8]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k8] + SU3D[8, I2, k10]*SU3D[I1, k10, k11]* - SU3D[I3, k7, k8]*SU3D[I5, k11, k8] + SU3D[8, I1, k10]* - SU3D[I2, k10, k11]*SU3D[I3, k7, k8]*SU3D[I5, k11, k8] + - SU3D[8, I2, k10]*SU3D[I1, k11, k8]*SU3D[I3, k10, k11]* - SU3D[I5, k7, k8] + SU3D[8, I1, k10]*SU3D[I2, k11, k8]* - SU3D[I3, k10, k11]*SU3D[I5, k7, k8] + SU3D[8, I2, k10]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k8]*SU3D[I5, k7, k8] + - SU3D[8, I1, k10]*SU3D[I2, k10, k11]*SU3D[I3, k11, k8]* - SU3D[I5, k7, k8] + SU3D[8, I3, k10]* - (SU3D[I1, k7, k8]*(SU3D[I2, k11, k8]*SU3D[I5, k10, k11] + - SU3D[I2, k10, k11]*SU3D[I5, k11, k8]) + SU3D[I1, k11, k8]* - (SU3D[I2, k7, k8]*SU3D[I5, k10, k11] + SU3D[I2, k10, k11]* - SU3D[I5, k7, k8]) + SU3D[I1, k10, k11]* - (SU3D[I2, k7, k8]*SU3D[I5, k11, k8] + SU3D[I2, k11, k8]* - SU3D[I5, k7, k8]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((4*I)/45)*(SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SU3F[3, 6, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SU3F[3, 6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SU3F[3, 6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SU3F[3, 6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SU3F[3, 6, I3] + - SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SU3F[3, 6, I4] + - SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SU3F[3, 6, I4] + - SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SU3F[3, 6, I1] + - SU3D[I1, I4, k6]*SU3F[3, 6, I3] + SU3D[I1, I3, k6]*SU3F[3, 6, I4]) + - SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SU3F[3, 6, I5] + - SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SU3F[3, 6, I5] + - SU3D[I2, I4, k6]*(SU3D[I3, I5, k6]*SU3F[3, 6, I1] + - SU3D[I1, I5, k6]*SU3F[3, 6, I3] + SU3D[I1, I3, k6]*SU3F[3, 6, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/60)*(SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[3, I1, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[3, I1, k6] + - SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I1, k6] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I1, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[3, I1, k6] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[3, I1, k6] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I1, k6] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I1, k6] + - SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6] + - SU3D[6, I2, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[3, I2, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[3, I2, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I2, k6] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I2, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[3, I2, k6] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[3, I2, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I2, k6] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I2, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I2, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6] + - SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[3, I3, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I3, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[3, I3, k6] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[3, I3, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I3, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I3, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6] + - SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k7]*SU3F[3, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I4, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]*SU3D[I5, k10, k7]* - SU3F[3, I4, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k7]*SU3F[3, I4, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3D[I3, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I4, k6] + - SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3D[I5, k10, k9]*SU3F[3, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I4, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]*SU3D[I5, k10, k9]* - SU3F[3, I4, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[3, I4, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]* - SU3D[I3, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I4, k6] + - SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[3, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I4, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I4, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6] + - SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6] + SU3D[6, I5, k9]*(SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k9]*SU3F[3, I1, k6] + SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k6] + - SU3D[I1, k6, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3F[3, I2, k6] + SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I2, k6] + SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[3, I2, k6] + - SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[3, I2, k6] + SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I2, k6] + SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[3, I2, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]* - SU3F[3, I3, k6] + SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I3, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3F[3, I4, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[3, I4, k6] + SU3D[I2, k6, k7]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k10, k9])*SU3F[3, I3, k6] + SU3D[I3, k10, k9]* - (SU3D[I4, k10, k7]*SU3F[3, I1, k6] + SU3D[I1, k10, k7]* - SU3F[3, I4, k6]) + SU3D[I3, k10, k7]* - (SU3D[I4, k10, k9]*SU3F[3, I1, k6] + SU3D[I1, k10, k9]* - SU3F[3, I4, k6])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k6, k7]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k6, k7])*SU3F[3, I3, k6] + SU3D[I3, k6, k7]* - (SU3D[I4, k10, k7]*SU3F[3, I1, k6] + SU3D[I1, k10, k7]* - SU3F[3, I4, k6]) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*SU3F[3, I1, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]))) + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3F[3, I5, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[3, I5, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k7]*SU3F[3, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k7]*SU3F[3, I5, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[3, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I5, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3F[3, I5, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[3, I5, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k9]*SU3F[3, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[3, I5, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[3, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3D[I4, k10, k9]*SU3F[3, I5, k6] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k6, k7]*SU3F[3, I5, k6] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[3, I5, k6] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6] + SU3D[6, I4, k9]* - (SU3D[I2, k10, k7]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[3, I1, k6] + SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6] + SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k7]*SU3F[3, I2, k6] + - SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I2, k6] + SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[3, I2, k6] + SU3D[I1, k10, k7]* - SU3D[I3, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I2, k6] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6] + SU3D[I1, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k6, k7]*SU3F[3, I2, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3D[I5, k10, k9]*SU3F[3, I3, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3F[3, I5, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k6, k7]*SU3F[3, I5, k6] + - SU3D[I2, k6, k7]*((SU3D[I1, k10, k9]*SU3D[I5, k10, k7] + - SU3D[I1, k10, k7]*SU3D[I5, k10, k9])*SU3F[3, I3, k6] + - SU3D[I3, k10, k9]*(SU3D[I5, k10, k7]*SU3F[3, I1, k6] + - SU3D[I1, k10, k7]*SU3F[3, I5, k6]) + SU3D[I3, k10, k7]* - (SU3D[I5, k10, k9]*SU3F[3, I1, k6] + SU3D[I1, k10, k9]* - SU3F[3, I5, k6])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k6, k7]*SU3D[I5, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I5, k6, k7])*SU3F[3, I3, k6] + SU3D[I3, k6, k7]* - (SU3D[I5, k10, k7]*SU3F[3, I1, k6] + SU3D[I1, k10, k7]* - SU3F[3, I5, k6]) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*SU3F[3, I1, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (((2*I)/45)*(SU3D[6, I3, I4]*SU3D[I2, I5, k7]*SU3F[3, I1, k7] + - SU3D[6, I2, I5]*SU3D[I3, I4, k7]*SU3F[3, I1, k7] + - SU3D[6, I2, I4]*SU3D[I3, I5, k7]*SU3F[3, I1, k7] + - SU3D[6, I2, I3]*SU3D[I4, I5, k7]*SU3F[3, I1, k7] + - SU3D[6, I3, I4]*SU3D[I1, I5, k7]*SU3F[3, I2, k7] + - SU3D[6, I1, I5]*SU3D[I3, I4, k7]*SU3F[3, I2, k7] + - SU3D[6, I1, I4]*SU3D[I3, I5, k7]*SU3F[3, I2, k7] + - SU3D[6, I1, I3]*SU3D[I4, I5, k7]*SU3F[3, I2, k7] + - SU3D[6, I2, I5]*SU3D[I1, I4, k7]*SU3F[3, I3, k7] + - SU3D[6, I2, I4]*SU3D[I1, I5, k7]*SU3F[3, I3, k7] + - SU3D[6, I1, I5]*SU3D[I2, I4, k7]*SU3F[3, I3, k7] + - SU3D[6, I1, I4]*SU3D[I2, I5, k7]*SU3F[3, I3, k7] + - SU3D[6, I1, I2]*SU3D[I4, I5, k7]*SU3F[3, I3, k7] + - SU3D[6, I4, I5]*(SU3D[I2, I3, k7]*SU3F[3, I1, k7] + - SU3D[I1, I3, k7]*SU3F[3, I2, k7] + SU3D[I1, I2, k7]* - SU3F[3, I3, k7]) + SU3D[6, I2, I5]*SU3D[I1, I3, k7]* - SU3F[3, I4, k7] + SU3D[6, I2, I3]*SU3D[I1, I5, k7]*SU3F[3, I4, k7] + - SU3D[6, I1, I5]*SU3D[I2, I3, k7]*SU3F[3, I4, k7] + - SU3D[6, I1, I3]*SU3D[I2, I5, k7]*SU3F[3, I4, k7] + - SU3D[6, I1, I2]*SU3D[I3, I5, k7]*SU3F[3, I4, k7] + - SU3D[6, I3, I5]*(SU3D[I2, I4, k7]*SU3F[3, I1, k7] + - SU3D[I1, I4, k7]*SU3F[3, I2, k7] + SU3D[I1, I2, k7]* - SU3F[3, I4, k7]) + SU3D[6, I3, I4]*SU3D[I1, I2, k7]* - SU3F[3, I5, k7] + SU3D[6, I2, I4]*SU3D[I1, I3, k7]*SU3F[3, I5, k7] + - SU3D[6, I2, I3]*SU3D[I1, I4, k7]*SU3F[3, I5, k7] + - SU3D[6, I1, I4]*SU3D[I2, I3, k7]*SU3F[3, I5, k7] + - SU3D[6, I1, I3]*SU3D[I2, I4, k7]*SU3F[3, I5, k7] + - SU3D[6, I1, I2]*SU3D[I3, I4, k7]*SU3F[3, I5, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((4*I)/45)*(SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SU3F[6, 8, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SU3F[6, 8, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I2] + - SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I3] + - SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SU3F[6, 8, I4] + - SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SU3F[6, 8, I4] + - SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SU3F[6, 8, I1] + - SU3D[I1, I4, k6]*SU3F[6, 8, I3] + SU3D[I1, I3, k6]*SU3F[6, 8, I4]) + - SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SU3F[6, 8, I5] + - SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SU3F[6, 8, I5] + - SU3D[I2, I4, k6]*(SU3D[I3, I5, k6]*SU3F[6, 8, I1] + - SU3D[I1, I5, k6]*SU3F[6, 8, I3] + SU3D[I1, I3, k6]*SU3F[6, 8, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/45)*(SU3D[3, I3, I4]*SU3D[I2, I5, k6]*SU3F[6, I1, k6] + - SU3D[3, I2, I5]*SU3D[I3, I4, k6]*SU3F[6, I1, k6] + - SU3D[3, I2, I4]*SU3D[I3, I5, k6]*SU3F[6, I1, k6] + - SU3D[3, I2, I3]*SU3D[I4, I5, k6]*SU3F[6, I1, k6] + - SU3D[3, I3, I4]*SU3D[I1, I5, k6]*SU3F[6, I2, k6] + - SU3D[3, I1, I5]*SU3D[I3, I4, k6]*SU3F[6, I2, k6] + - SU3D[3, I1, I4]*SU3D[I3, I5, k6]*SU3F[6, I2, k6] + - SU3D[3, I1, I3]*SU3D[I4, I5, k6]*SU3F[6, I2, k6] + - SU3D[3, I2, I5]*SU3D[I1, I4, k6]*SU3F[6, I3, k6] + - SU3D[3, I2, I4]*SU3D[I1, I5, k6]*SU3F[6, I3, k6] + - SU3D[3, I1, I5]*SU3D[I2, I4, k6]*SU3F[6, I3, k6] + - SU3D[3, I1, I4]*SU3D[I2, I5, k6]*SU3F[6, I3, k6] + - SU3D[3, I1, I2]*SU3D[I4, I5, k6]*SU3F[6, I3, k6] + - SU3D[3, I4, I5]*(SU3D[I2, I3, k6]*SU3F[6, I1, k6] + - SU3D[I1, I3, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I3, k6]) + SU3D[3, I2, I5]*SU3D[I1, I3, k6]* - SU3F[6, I4, k6] + SU3D[3, I2, I3]*SU3D[I1, I5, k6]*SU3F[6, I4, k6] + - SU3D[3, I1, I5]*SU3D[I2, I3, k6]*SU3F[6, I4, k6] + - SU3D[3, I1, I3]*SU3D[I2, I5, k6]*SU3F[6, I4, k6] + - SU3D[3, I1, I2]*SU3D[I3, I5, k6]*SU3F[6, I4, k6] + - SU3D[3, I3, I5]*(SU3D[I2, I4, k6]*SU3F[6, I1, k6] + - SU3D[I1, I4, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I4, k6]) + SU3D[3, I3, I4]*SU3D[I1, I2, k6]* - SU3F[6, I5, k6] + SU3D[3, I2, I4]*SU3D[I1, I3, k6]*SU3F[6, I5, k6] + - SU3D[3, I2, I3]*SU3D[I1, I4, k6]*SU3F[6, I5, k6] + - SU3D[3, I1, I4]*SU3D[I2, I3, k6]*SU3F[6, I5, k6] + - SU3D[3, I1, I3]*SU3D[I2, I4, k6]*SU3F[6, I5, k6] + - SU3D[3, I1, I2]*SU3D[I3, I4, k6]*SU3F[6, I5, k6]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/45)*(SU3D[8, I3, I4]*SU3D[I2, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I5]*SU3D[I3, I4, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I4]*SU3D[I3, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I3]*SU3D[I4, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I3, I4]*SU3D[I1, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I5]*SU3D[I3, I4, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I4]*SU3D[I3, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I3]*SU3D[I4, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I2, I5]*SU3D[I1, I4, k6]*SU3F[6, I3, k6] + - SU3D[8, I2, I4]*SU3D[I1, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I5]*SU3D[I2, I4, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I4]*SU3D[I2, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I2]*SU3D[I4, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I4, I5]*(SU3D[I2, I3, k6]*SU3F[6, I1, k6] + - SU3D[I1, I3, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I3, k6]) + SU3D[8, I2, I5]*SU3D[I1, I3, k6]* - SU3F[6, I4, k6] + SU3D[8, I2, I3]*SU3D[I1, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I5]*SU3D[I2, I3, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I3]*SU3D[I2, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I2]*SU3D[I3, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I3, I5]*(SU3D[I2, I4, k6]*SU3F[6, I1, k6] + - SU3D[I1, I4, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I4, k6]) + SU3D[8, I3, I4]*SU3D[I1, I2, k6]* - SU3F[6, I5, k6] + SU3D[8, I2, I4]*SU3D[I1, I3, k6]*SU3F[6, I5, k6] + - SU3D[8, I2, I3]*SU3D[I1, I4, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I4]*SU3D[I2, I3, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I3]*SU3D[I2, I4, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I2]*SU3D[I3, I4, k6]*SU3F[6, I5, k6]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[3, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[3, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[3, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I1, k8] + SU3D[3, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[3, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[3, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[3, I3, k7]*SU3D[I2, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[3, I2, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[3, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[3, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[3, I3, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k8] + - SU3D[3, I2, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[3, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[3, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[3, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[3, I1, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[3, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k8] + - SU3D[3, I1, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I3, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I3, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I3, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I3, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I3, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k8] + - SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[3, I5, k7]*(SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I1, k8] + - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k8] + SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3F[6, I4, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3F[6, I4, k8] + SU3D[I2, k8, k9]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k10, k9])*SU3F[6, I3, k8] + SU3D[I3, k10, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I4, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I4, k8]))) + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[3, I4, k7]* - (SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k8] + SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k8] + - SU3D[I2, k8, k9]*((SU3D[I1, k10, k9]*SU3D[I5, k10, k7] + - SU3D[I1, k10, k7]*SU3D[I5, k10, k9])*SU3F[6, I3, k8] + - SU3D[I3, k10, k9]*(SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[I1, k10, k7]*SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I5, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I5, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I5, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I5, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k8] + - SU3D[8, I2, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k8] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I3, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[8, I5, k7]*(SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I1, k8] + - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k8] + SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3F[6, I4, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3F[6, I4, k8] + SU3D[I2, k8, k9]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k10, k9])*SU3F[6, I3, k8] + SU3D[I3, k10, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I4, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I4, k8]))) + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k8] + SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k8] + - SU3D[I2, k8, k9]*((SU3D[I1, k10, k9]*SU3D[I5, k10, k7] + - SU3D[I1, k10, k7]*SU3D[I5, k10, k9])*SU3F[6, I3, k8] + - SU3D[I3, k10, k9]*(SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[I1, k10, k7]*SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I5, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I5, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I5, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I5, k8])))))/(Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I2, k6]* - SU3F[6, I1, k8] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[3, I2, k6]*SU3F[6, I1, k8] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I1, k8] + - SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I1, k8] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I3, k6]*SU3F[6, I1, k8] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[3, I3, k6]*SU3F[6, I1, k8] + - SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]* - SU3F[6, I1, k8] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[3, I3, k6]*SU3F[6, I1, k8] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I4, k6]*SU3F[6, I1, k8] + - SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]* - SU3F[6, I1, k8] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[6, I1, k8] + - SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I2, k8] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[3, I1, k6]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I2, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I3, k6]*SU3F[6, I2, k8] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[3, I3, k6]*SU3F[6, I2, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]* - SU3F[6, I2, k8] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[3, I3, k6]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I4, k6]*SU3F[6, I2, k8] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[6, I2, k8] + - SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I3, k8] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I3, k8] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I1, k6]*SU3F[6, I3, k8] + - SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I3, k8] + SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k6]*SU3F[6, I3, k8] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[3, I1, k6]*SU3F[6, I3, k8] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I2, k6]*SU3F[6, I3, k8] + - SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I2, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I2, k6]*SU3F[6, I3, k8] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[3, I2, k6]*SU3F[6, I3, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I4, k6]*SU3F[6, I3, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I4, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k6]*SU3F[6, I3, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[3, I4, k6]*SU3F[6, I3, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I5, k6]*SU3F[6, I3, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[3, I5, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I5, k6]*SU3F[6, I3, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[6, I3, k8] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I4, k8] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k6]*SU3F[6, I4, k8] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I2, k6]*SU3F[6, I4, k8] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k6]* - SU3F[6, I4, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I4, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I3, k6]* - SU3F[6, I4, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[3, I3, k6]*SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[3, I3, k6]*SU3F[6, I4, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]* - SU3F[6, I4, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k8] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I5, k8] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I1, k6]*SU3F[6, I5, k8] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I2, k6]*SU3F[6, I5, k8] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[3, I2, k6]* - SU3F[6, I5, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I5, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[3, I3, k6]* - SU3F[6, I5, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[3, I3, k6]*SU3F[6, I5, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I3, k6]*SU3F[6, I5, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3F[3, I3, k6]* - SU3F[6, I5, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I5, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k8] + - SU3D[I3, k8, k9]*(SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I1, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I4, k6]* - SU3F[6, I1, k8] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I2, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I4, k6]* - SU3F[6, I2, k8] + SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I4, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I4, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I2, k6]* - SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[6, I4, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[3, I5, k6]* - SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I5, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[3, I4, k6]* - SU3F[6, I5, k8] + SU3D[I4, k7, k9]*(SU3D[I5, k6, k7]* - (SU3F[3, I2, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I2, k8]) + SU3D[I2, k6, k7]* - (SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I5, k8]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3F[3, I2, k6]* - SU3F[6, I5, k8])) + SU3D[I4, k6, k7]* - (SU3D[I5, k7, k9]*(SU3F[3, I2, k6]*SU3F[6, I1, k8] + - SU3F[3, I1, k6]*SU3F[6, I2, k8]) + SU3D[I2, k7, k9]* - (SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I5, k8]) + SU3D[I1, k7, k9]* - (SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3F[3, I2, k6]* - SU3F[6, I5, k8]))) + SU3D[I3, k7, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]*SU3F[6, I1, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I2, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]*SU3F[6, I2, k8] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I1, k6]*SU3F[6, I4, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k6]*SU3F[6, I4, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I5, k6]*SU3F[6, I4, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I4, k6]*SU3F[6, I5, k8] + - SU3D[I4, k8, k9]*(SU3D[I5, k6, k7]*(SU3F[3, I2, k6]*SU3F[6, I1, k8] + - SU3F[3, I1, k6]*SU3F[6, I2, k8]) + SU3D[I2, k6, k7]* - (SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I5, k8]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3F[3, I2, k6]* - SU3F[6, I5, k8])) + SU3D[I4, k6, k7]* - (SU3D[I5, k8, k9]*(SU3F[3, I2, k6]*SU3F[6, I1, k8] + - SU3F[3, I1, k6]*SU3F[6, I2, k8]) + SU3D[I2, k8, k9]* - (SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I5, k8]) + SU3D[I1, k8, k9]* - (SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3F[3, I2, k6]* - SU3F[6, I5, k8]))))/(60*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I1, k6] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8]*SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8]*SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I1, k6] + - SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I2, k6] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8]*SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I2, k6] + - SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I3, k6] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[8, I3, k6] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I1, k8]*SU3F[8, I3, k6] + - SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I3, k6] + SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I3, k6] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[6, I5, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I3, k6] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I3, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[6, I3, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I5, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I5, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[6, I2, k8]* - SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[6, I3, k8]* - SU3F[8, I5, k6] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I3, k8]*SU3F[8, I5, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I3, k8, k9]*(SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[6, I5, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I5, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I5, k6] + SU3D[I4, k7, k9]*(SU3D[I5, k6, k7]* - (SU3F[6, I2, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I2, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6])) + SU3D[I4, k6, k7]* - (SU3D[I5, k7, k9]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k7, k9]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k7, k9]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6]))) + SU3D[I3, k7, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I4, k8, k9]*(SU3D[I5, k6, k7]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6])) + SU3D[I4, k6, k7]* - (SU3D[I5, k8, k9]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k8, k9]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k8, k9]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/45)*(SU3D[6, I3, I4]*SU3D[I2, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I5]*SU3D[I3, I4, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I4]*SU3D[I3, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I3]*SU3D[I4, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I3, I4]*SU3D[I1, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I5]*SU3D[I3, I4, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I4]*SU3D[I3, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I3]*SU3D[I4, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I2, I5]*SU3D[I1, I4, k7]*SU3F[8, I3, k7] + - SU3D[6, I2, I4]*SU3D[I1, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I5]*SU3D[I2, I4, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I4]*SU3D[I2, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I2]*SU3D[I4, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I4, I5]*(SU3D[I2, I3, k7]*SU3F[8, I1, k7] + - SU3D[I1, I3, k7]*SU3F[8, I2, k7] + SU3D[I1, I2, k7]* - SU3F[8, I3, k7]) + SU3D[6, I2, I5]*SU3D[I1, I3, k7]* - SU3F[8, I4, k7] + SU3D[6, I2, I3]*SU3D[I1, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I5]*SU3D[I2, I3, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I3]*SU3D[I2, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I2]*SU3D[I3, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I3, I5]*(SU3D[I2, I4, k7]*SU3F[8, I1, k7] + - SU3D[I1, I4, k7]*SU3F[8, I2, k7] + SU3D[I1, I2, k7]* - SU3F[8, I4, k7]) + SU3D[6, I3, I4]*SU3D[I1, I2, k7]* - SU3F[8, I5, k7] + SU3D[6, I2, I4]*SU3D[I1, I3, k7]*SU3F[8, I5, k7] + - SU3D[6, I2, I3]*SU3D[I1, I4, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I4]*SU3D[I2, I3, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I3]*SU3D[I2, I4, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I2]*SU3D[I3, I4, k7]*SU3F[8, I5, k7]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I1, k8] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[8, I1, k8] + - SU3D[6, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[8, I1, k8] + SU3D[6, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[8, I1, k8] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[8, I1, k8] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[8, I1, k8] + SU3D[6, I3, k7]*SU3D[I2, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[8, I1, k8] + SU3D[6, I2, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[8, I1, k8] + - SU3D[6, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[8, I1, k8] + SU3D[6, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[8, I1, k8] + SU3D[6, I3, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[8, I1, k8] + - SU3D[6, I2, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I1, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I2, k8] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[8, I2, k8] + - SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[8, I2, k8] + SU3D[6, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[8, I2, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[8, I2, k8] + - SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[8, I2, k8] + SU3D[6, I3, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[8, I2, k8] + SU3D[6, I1, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[8, I2, k8] + - SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[8, I2, k8] + SU3D[6, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[8, I2, k8] + SU3D[6, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[8, I2, k8] + - SU3D[6, I1, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I2, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I3, k8] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[8, I3, k8] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[8, I3, k8] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[8, I3, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[8, I3, k8] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[8, I3, k8] + SU3D[6, I2, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[8, I3, k8] + SU3D[6, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[8, I3, k8] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[8, I3, k8] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[8, I3, k8] + SU3D[6, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[8, I3, k8] + - SU3D[6, I1, k7]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I3, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I4, k8] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k7]*SU3F[8, I4, k8] + - SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k7]* - SU3F[8, I4, k8] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k7]*SU3F[8, I4, k8] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k7]*SU3F[8, I4, k8] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[8, I4, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k10, k9]*SU3F[8, I4, k8] + SU3D[6, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k9]*SU3F[8, I4, k8] + - SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k9]* - SU3F[8, I4, k8] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[8, I4, k8] + SU3D[6, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[8, I4, k8] + - SU3D[6, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[8, I4, k8] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k8, k9]*SU3F[8, I4, k8] + SU3D[6, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k8, k9]*SU3F[8, I4, k8] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[8, I4, k8] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k8, k9]*SU3F[8, I4, k8] + SU3D[6, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9]*SU3F[8, I4, k8] + - SU3D[6, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I4, k8] + SU3D[6, I5, k7]*(SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[8, I1, k8] + SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[8, I1, k8] + - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3F[8, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[8, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[8, I2, k8] + - SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[8, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[8, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[8, I2, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]* - SU3F[8, I3, k8] + SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3F[8, I3, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3F[8, I4, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3F[8, I4, k8] + SU3D[I2, k8, k9]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k10, k9])*SU3F[8, I3, k8] + SU3D[I3, k10, k9]* - (SU3D[I4, k10, k7]*SU3F[8, I1, k8] + SU3D[I1, k10, k7]* - SU3F[8, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k10, k9]*SU3F[8, I1, k8] + SU3D[I1, k10, k9]* - SU3F[8, I4, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k8, k9])*SU3F[8, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k10, k7]*SU3F[8, I1, k8] + SU3D[I1, k10, k7]* - SU3F[8, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k8, k9]*SU3F[8, I1, k8] + SU3D[I1, k8, k9]* - SU3F[8, I4, k8]))) + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3F[8, I5, k8] + - SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]* - SU3F[8, I5, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k7]*SU3F[8, I5, k8] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k7]*SU3F[8, I5, k8] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]* - SU3F[8, I5, k8] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[8, I5, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3F[8, I5, k8] + - SU3D[6, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3F[8, I5, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k9]*SU3F[8, I5, k8] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[8, I5, k8] + - SU3D[6, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[8, I5, k8] + SU3D[6, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[8, I5, k8] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k8, k9]*SU3F[8, I5, k8] + - SU3D[6, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3F[8, I5, k8] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[8, I5, k8] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k8, k9]*SU3F[8, I5, k8] + - SU3D[6, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3F[8, I5, k8] + SU3D[6, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3F[8, I5, k8] + SU3D[6, I4, k7]* - (SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[8, I1, k8] + SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[8, I1, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k7]*SU3F[8, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[8, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[8, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[8, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[8, I2, k8] + SU3D[I1, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[8, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I5, k10, k9]*SU3F[8, I3, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I5, k8, k9]* - SU3F[8, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3F[8, I5, k8] + SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3F[8, I5, k8] + - SU3D[I2, k8, k9]*((SU3D[I1, k10, k9]*SU3D[I5, k10, k7] + - SU3D[I1, k10, k7]*SU3D[I5, k10, k9])*SU3F[8, I3, k8] + - SU3D[I3, k10, k9]*(SU3D[I5, k10, k7]*SU3F[8, I1, k8] + - SU3D[I1, k10, k7]*SU3F[8, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k10, k9]*SU3F[8, I1, k8] + SU3D[I1, k10, k9]* - SU3F[8, I5, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I5, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I5, k8, k9])*SU3F[8, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I5, k10, k7]*SU3F[8, I1, k8] + SU3D[I1, k10, k7]* - SU3F[8, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k8, k9]*SU3F[8, I1, k8] + SU3D[I1, k8, k9]* - SU3F[8, I5, k8])))))/(Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[6, I2, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k9]*SU3D[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k9]*SU3D[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I5, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k11, k7]*SU3F[I3, k10, k11] + SU3D[8, I4, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k11])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I4, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I4, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I4, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I4, k10, k11]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]*SU3D[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k9]*SU3D[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + SU3D[8, I5, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k11])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I5, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I5, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I5, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I5, k10, k11])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3D[3, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k10, k6] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I1, k10, k6] + - SU3D[3, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3D[3, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I2, k10, k6] + SU3D[3, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k10, k6] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[3, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I2, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I3, k10, k6] + SU3D[3, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I3, k10, k6] + - SU3D[3, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I3, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I4, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k10, k6] + - SU3D[3, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I4, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[3, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I4, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I4, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6]))) + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I1, k7]* - SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I2, k7]*SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k10, k6] + - SU3D[3, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[3, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I5, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I5, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I1, k10, k6] + - SU3D[8, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[8, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I2, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I3, k10, k6] + - SU3D[8, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I4, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I4, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I4, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6]))) + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I1, k7]* - SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I2, k7]*SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k10, k6] + - SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I5, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I5, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k7]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I5, k7]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k7]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k7]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k7]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k7]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I5, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I5, k6, k7]* - (SU3F[3, I2, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[3, I2, k11]* - SU3F[6, I4, k7]*SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + - SU3F[3, I1, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3F[3, I4, k11]* - (SU3F[6, I3, k7]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[6, I2, k7]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[6, I1, k7]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[3, I2, k11]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3F[3, I1, k11]* - SU3F[6, I3, k7]*SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + - SU3F[3, I2, k11]*SU3F[6, I1, k7]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3F[3, I1, k11]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3F[3, I2, k11]* - SU3F[6, I3, k7]*SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + - SU3F[3, I1, k11]*SU3F[6, I3, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3F[3, I2, k11]*SU3F[6, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3F[3, I1, k11]* - SU3F[6, I2, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + - SU3F[3, I3, k11]*(SU3F[6, I4, k7]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[6, I2, k7]*(SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k10, k6]) + SU3F[6, I1, k7]* - (SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k6]))) + SU3D[I3, k6, k7]*SU3F[3, I4, k11]* - SU3F[6, I2, k7]*SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k7]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k7]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k7]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k7]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k7]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I2, k7]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I4, k7]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I1, k7]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k7]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k7]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k7]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I3, k7]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k7]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k7]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I2, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I4, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I1, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I3, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I4, k6, k7]*(SU3F[3, I2, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[3, I1, k11]* - SU3F[6, I5, k7]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + - SU3F[3, I2, k11]*SU3F[6, I5, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3F[3, I1, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3F[3, I5, k11]* - (SU3F[6, I3, k7]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[6, I2, k7]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[6, I1, k7]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[3, I2, k11]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3F[3, I1, k11]* - SU3F[6, I3, k7]*SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + - SU3F[3, I2, k11]*SU3F[6, I1, k7]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3F[3, I1, k11]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3F[3, I2, k11]* - SU3F[6, I3, k7]*SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + - SU3F[3, I1, k11]*SU3F[6, I3, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3F[3, I2, k11]*SU3F[6, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3F[3, I1, k11]* - SU3F[6, I2, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + - SU3F[3, I3, k11]*(SU3F[6, I5, k7]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[6, I2, k7]*(SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k10, k6]) + SU3F[6, I1, k7]* - (SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k6]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k11]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k11]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I4, k11]*SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3F[6, I4, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[6, I2, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I3, k11]*SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I3, k11]*SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3F[6, I1, k7]* - SU3F[8, I2, k11]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + - SU3F[6, I3, k7]*(SU3F[8, I4, k11]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k6]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I2, k11]*SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k11]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I2, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I1, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I2, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I3, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I3, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k11]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k11]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I2, k11]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I1, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I2, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I3, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I3, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I5, k11]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3F[6, I1, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3F[6, I5, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[6, I2, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I3, k11]*SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I3, k11]*SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3F[6, I1, k7]* - SU3F[8, I2, k11]*SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + - SU3F[6, I3, k7]*(SU3F[8, I5, k11]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k6]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k9]* - SU3D[I4, k10, k11]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k9]*SU3F[I1, k10, k7] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k9]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]* - SU3D[8, I4, k7]*SU3D[I3, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k9]*SU3F[I1, k10, k7] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I1, k10, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k9]* - SU3D[I4, k10, k11]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k9]*SU3F[I2, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k9]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I3, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k9]*SU3F[I2, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I2, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I2, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k9]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k9]*SU3F[I3, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I4, k11, k9]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I4, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k9]*SU3F[I3, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k9]*SU3F[I3, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I3, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k9]* - SU3D[I2, k10, k11]*SU3F[I4, k10, k7] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k9]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k11, k9]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k9]*SU3F[I4, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I3, k11, k9]* - SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k7] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k9]*SU3F[I4, k10, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k9]*SU3F[I4, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k9]*SU3F[I4, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I4, k10, k7] + SU3D[6, I5, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k7] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k9]*SU3F[I1, k10, k7] + SU3D[8, I1, k7]* - SU3D[I3, k11, k9]*SU3D[I4, k10, k11]*SU3F[I2, k10, k7] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k9]* - SU3F[I2, k10, k7] + SU3D[8, I2, k7]*SU3D[I1, k11, k9]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k7] + SU3D[8, I1, k7]* - SU3D[I2, k11, k9]*SU3D[I4, k10, k11]*SU3F[I3, k10, k7] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k9]* - SU3F[I3, k10, k7] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k9]*SU3F[I3, k10, k7] + SU3D[8, I4, k7]* - ((SU3D[I1, k11, k9]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k9])*SU3F[I2, k10, k7] + SU3D[I2, k11, k9]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k7] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k7]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k9]*SU3F[I1, k10, k7] + SU3D[I1, k11, k9]* - SU3F[I3, k10, k7])) + SU3D[8, I2, k7]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k7] + SU3D[8, I1, k7]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k11]*SU3F[I4, k10, k7] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k9]* - SU3F[I4, k10, k7] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k9]*SU3F[I4, k10, k7] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k9]*SU3D[I4, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I4, k11, k9])*SU3F[I2, k10, k7] + SU3D[I2, k11, k9]* - (SU3D[I4, k10, k11]*SU3F[I1, k10, k7] + SU3D[I1, k10, k11]* - SU3F[I4, k10, k7]) + SU3D[I2, k10, k11]* - (SU3D[I4, k11, k9]*SU3F[I1, k10, k7] + SU3D[I1, k11, k9]* - SU3F[I4, k10, k7]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k9]*SU3D[I2, k10, k11]*SU3F[I5, k10, k7] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k9]* - SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k11, k9]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k9]*SU3F[I5, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I3, k11, k9]* - SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k7] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k7] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k11, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k9]*SU3F[I5, k10, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k9]* - SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k9]*SU3F[I5, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I4, k11, k9]* - SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k9]*SU3F[I5, k10, k7] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k9]* - SU3F[I5, k10, k7] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k7] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k9]*SU3F[I1, k10, k7] + SU3D[8, I1, k7]* - SU3D[I3, k11, k9]*SU3D[I5, k10, k11]*SU3F[I2, k10, k7] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I2, k10, k7] + SU3D[8, I2, k7]*SU3D[I1, k11, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k7] + SU3D[8, I1, k7]* - SU3D[I2, k11, k9]*SU3D[I5, k10, k11]*SU3F[I3, k10, k7] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I5, k11, k9]* - SU3F[I3, k10, k7] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I5, k11, k9]*SU3F[I3, k10, k7] + SU3D[8, I5, k7]* - ((SU3D[I1, k11, k9]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k9])*SU3F[I2, k10, k7] + SU3D[I2, k11, k9]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k7] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k7]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k9]*SU3F[I1, k10, k7] + SU3D[I1, k11, k9]* - SU3F[I3, k10, k7])) + SU3D[8, I2, k7]*SU3D[I1, k11, k9]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k7] + SU3D[8, I1, k7]* - SU3D[I2, k11, k9]*SU3D[I3, k10, k11]*SU3F[I5, k10, k7] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k9]* - SU3F[I5, k10, k7] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k9]*SU3F[I5, k10, k7] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k9]*SU3D[I5, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I5, k11, k9])*SU3F[I2, k10, k7] + SU3D[I2, k11, k9]* - (SU3D[I5, k10, k11]*SU3F[I1, k10, k7] + SU3D[I1, k10, k11]* - SU3F[I5, k10, k7]) + SU3D[I2, k10, k11]* - (SU3D[I5, k11, k9]*SU3F[I1, k10, k7] + SU3D[I1, k11, k9]* - SU3F[I5, k10, k7])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[3, I3, k7]*SU3D[6, I5, k8]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I1, k10, k8] + SU3D[3, I2, k7]* - SU3D[6, I5, k8]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k8]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I1, k10, k8] + - SU3D[3, I2, k7]*SU3D[6, I5, k8]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I1, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I4, k8]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k8] + SU3D[3, I2, k7]* - SU3D[6, I4, k8]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k8]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k8] + SU3D[3, I2, k7]* - SU3D[6, I3, k8]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I4, k8]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k8] + - SU3D[3, I2, k7]*SU3D[6, I4, k8]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k8]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k8]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k8]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I2, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I5, k8]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k8]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I2, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I5, k8]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I4, k8]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I4, k8]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k8]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I3, k8]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I4, k8]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I4, k8]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k8]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I3, k8]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k8]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I5, k8]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k8]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I3, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I5, k8]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k8]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I4, k8]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k8]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I2, k8]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k8]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I4, k8]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k8]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k8]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k8]*SU3D[I1, k11, k7]* - SU3D[I2, k10, k11]*SU3F[I4, k10, k8] + SU3D[3, I3, k7]* - SU3D[6, I5, k8]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I4, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k8]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I5, k8]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k8]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I4, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I5, k8]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k8]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k8] + SU3D[3, I2, k7]* - SU3D[6, I3, k8]*SU3D[I1, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k8]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I3, k8]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k8]*SU3D[I3, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I2, k8]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k8]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k8]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k8]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I3, k8]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k8]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k8]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k8] + SU3D[3, I5, k7]* - (SU3D[6, I2, k8]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I1, k10, k8] + SU3D[6, I1, k8]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k11]*SU3F[I2, k10, k8] + - SU3D[6, I1, k8]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k8] + SU3D[6, I1, k8]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k11]*SU3F[I3, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I3, k10, k8] + SU3D[6, I4, k8]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k8] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k8] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k8]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k8] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k8])) + SU3D[6, I2, k8]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k8] + SU3D[6, I1, k8]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I4, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I4, k10, k8] + SU3D[6, I3, k8]* - ((SU3D[I1, k11, k7]*SU3D[I4, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I4, k11, k7])*SU3F[I2, k10, k8] + SU3D[I2, k11, k7]* - (SU3D[I4, k10, k11]*SU3F[I1, k10, k8] + SU3D[I1, k10, k11]* - SU3F[I4, k10, k8]) + SU3D[I2, k10, k11]* - (SU3D[I4, k11, k7]*SU3F[I1, k10, k8] + SU3D[I1, k11, k7]* - SU3F[I4, k10, k8]))) + SU3D[3, I3, k7]*SU3D[6, I4, k8]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k11]*SU3F[I5, k10, k8] + - SU3D[3, I3, k7]*SU3D[6, I4, k8]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I5, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k8]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I4, k8]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k8]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I5, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I4, k8]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k8]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k8] + SU3D[3, I2, k7]* - SU3D[6, I3, k8]*SU3D[I1, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k8]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I3, k8]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k8]*SU3D[I3, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k8] + SU3D[3, I1, k7]* - SU3D[6, I2, k8]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k8]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k8]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k8]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I3, k8]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k8]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k8]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k8] + SU3D[3, I4, k7]* - (SU3D[6, I2, k8]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I1, k10, k8] + SU3D[6, I1, k8]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k11]*SU3F[I2, k10, k8] + - SU3D[6, I1, k8]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k8] + SU3D[6, I1, k8]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k11]*SU3F[I3, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I3, k10, k8] + SU3D[6, I5, k8]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k8] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k8] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k8]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k8] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k8])) + SU3D[6, I2, k8]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k8] + SU3D[6, I1, k8]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I5, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I5, k10, k8] + SU3D[6, I3, k8]* - ((SU3D[I1, k11, k7]*SU3D[I5, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I5, k11, k7])*SU3F[I2, k10, k8] + SU3D[I2, k11, k7]* - (SU3D[I5, k10, k11]*SU3F[I1, k10, k8] + SU3D[I1, k10, k11]* - SU3F[I5, k10, k8]) + SU3D[I2, k10, k11]* - (SU3D[I5, k11, k7]*SU3F[I1, k10, k8] + SU3D[I1, k11, k7]* - SU3F[I5, k10, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I2, k6]* - SU3F[I1, k10, k8] + SU3D[6, I3, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6]*SU3F[I1, k10, k8] + - SU3D[6, I2, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I1, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I4, k6]*SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I4, k6]*SU3F[I1, k10, k8] + - SU3D[6, I3, k8]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I1, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I5, k6]*SU3F[I1, k10, k8] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I5, k6]* - SU3F[I1, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k10, k8] + - SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I1, k6]* - SU3F[I2, k10, k8] + SU3D[6, I3, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[I2, k10, k8] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6]*SU3F[I2, k10, k8] + - SU3D[6, I1, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I4, k6]*SU3F[I2, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I4, k6]*SU3F[I2, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I2, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I2, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I5, k6]*SU3F[I2, k10, k8] + - SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I5, k6]* - SU3F[I2, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I2, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I2, k10, k8] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I1, k6]* - SU3F[I3, k10, k8] + SU3D[6, I2, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I2, k6]*SU3F[I3, k10, k8] + - SU3D[6, I1, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I3, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I4, k6]*SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I4, k6]*SU3F[I3, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I3, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I5, k6]*SU3F[I3, k10, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I5, k6]* - SU3F[I3, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I3, k10, k8] + - SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I1, k6]* - SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I1, k6]*SU3F[I4, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[I4, k10, k8] + - SU3D[6, I2, k8]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I4, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I2, k6]*SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I2, k6]*SU3F[I4, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6]*SU3F[I4, k10, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I3, k6]* - SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6]*SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[3, I5, k6]* - SU3F[I4, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[3, I5, k6]*SU3F[I4, k10, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[3, I5, k6]* - SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[I4, k10, k8] + - SU3D[6, I5, k8]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I3, k6]* - SU3F[I1, k10, k8] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[I1, k10, k8] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I3, k6]*SU3F[I2, k10, k8] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k8] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[3, I1, k6]*SU3F[I3, k10, k8] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k10, k8] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I2, k6]* - SU3F[I3, k10, k8] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I2, k6]*SU3F[I3, k10, k8] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[3, I4, k6]*SU3F[I3, k10, k8] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k10, k8] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[3, I3, k6]*SU3F[I4, k10, k8] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k10, k8] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[3, I2, k6]* - SU3F[I1, k10, k8] + SU3F[3, I1, k6]*SU3F[I2, k10, k8]) + - SU3D[I2, k10, k7]*(SU3F[3, I4, k6]*SU3F[I1, k10, k8] + - SU3F[3, I1, k6]*SU3F[I4, k10, k8]) + SU3D[I1, k10, k7]* - (SU3F[3, I4, k6]*SU3F[I2, k10, k8] + SU3F[3, I2, k6]* - SU3F[I4, k10, k8])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k6]*SU3F[I1, k10, k8] + - SU3F[3, I1, k6]*SU3F[I2, k10, k8]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k6]*SU3F[I1, k10, k8] + SU3F[3, I1, k6]* - SU3F[I4, k10, k8]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k6]*SU3F[I2, k10, k8] + SU3F[3, I2, k6]* - SU3F[I4, k10, k8]))) + SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I1, k6]*SU3F[I5, k10, k8] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I1, k6]* - SU3F[I5, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I1, k6]*SU3F[I5, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I1, k6]*SU3F[I5, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I2, k6]* - SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[3, I2, k6]*SU3F[I5, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I2, k6]*SU3F[I5, k10, k8] + - SU3D[6, I1, k8]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[3, I2, k6]* - SU3F[I5, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[3, I3, k6]*SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I3, k6]*SU3F[I5, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]* - SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[I5, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[3, I4, k6]*SU3F[I5, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I5, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[3, I4, k6]*SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[3, I4, k6]*SU3F[I5, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[3, I4, k6]* - SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[3, I4, k6]*SU3F[I5, k10, k8] + SU3D[6, I4, k8]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I3, k6]* - SU3F[I1, k10, k8] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6]*SU3F[I1, k10, k8] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6]*SU3F[I2, k10, k8] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k8] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I1, k6]*SU3F[I3, k10, k8] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k10, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I2, k6]* - SU3F[I3, k10, k8] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I3, k10, k8] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[3, I5, k6]*SU3F[I3, k10, k8] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[I3, k10, k8] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[3, I3, k6]*SU3F[I5, k10, k8] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I5, k10, k8] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[3, I2, k6]* - SU3F[I1, k10, k8] + SU3F[3, I1, k6]*SU3F[I2, k10, k8]) + - SU3D[I2, k10, k7]*(SU3F[3, I5, k6]*SU3F[I1, k10, k8] + - SU3F[3, I1, k6]*SU3F[I5, k10, k8]) + SU3D[I1, k10, k7]* - (SU3F[3, I5, k6]*SU3F[I2, k10, k8] + SU3F[3, I2, k6]* - SU3F[I5, k10, k8])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[3, I2, k6]*SU3F[I1, k10, k8] + - SU3F[3, I1, k6]*SU3F[I2, k10, k8]) + SU3D[I2, k6, k7]* - (SU3F[3, I5, k6]*SU3F[I1, k10, k8] + SU3F[3, I1, k6]* - SU3F[I5, k10, k8]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k6]*SU3F[I2, k10, k8] + SU3F[3, I2, k6]* - SU3F[I5, k10, k8]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I2, k6]* - SU3F[I1, k10, k8] + SU3D[6, I3, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I1, k10, k8] + - SU3D[6, I2, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I1, k10, k8] + - SU3D[6, I3, k8]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I1, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I1, k10, k8] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I1, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I1, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k10, k8] + - SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I2, k10, k8] + SU3D[6, I3, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I2, k10, k8] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k8] + - SU3D[6, I1, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I2, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I2, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I2, k10, k8] + - SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I2, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I2, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k10, k8] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I3, k10, k8] + SU3D[6, I2, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I2, k6]*SU3F[I3, k10, k8] + - SU3D[6, I1, k8]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I3, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I3, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I3, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I3, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k8] + - SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I1, k6]*SU3F[I4, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k10, k8] + - SU3D[6, I2, k8]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I2, k6]*SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I2, k6]*SU3F[I4, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I3, k6]* - SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6]*SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[8, I5, k6]* - SU3F[I4, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[8, I5, k6]*SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[8, I5, k6]*SU3F[I4, k10, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[8, I5, k6]* - SU3F[I4, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[8, I5, k6]*SU3F[I4, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I4, k10, k8] + - SU3D[6, I5, k8]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k8] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k10, k8] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k8] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k8] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k8] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k10, k8] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k8] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k10, k8] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I4, k6]*SU3F[I3, k10, k8] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k10, k8] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[8, I3, k6]*SU3F[I4, k10, k8] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k8] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[8, I2, k6]* - SU3F[I1, k10, k8] + SU3F[8, I1, k6]*SU3F[I2, k10, k8]) + - SU3D[I2, k10, k7]*(SU3F[8, I4, k6]*SU3F[I1, k10, k8] + - SU3F[8, I1, k6]*SU3F[I4, k10, k8]) + SU3D[I1, k10, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k10, k8] + SU3F[8, I2, k6]* - SU3F[I4, k10, k8])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k10, k8] + - SU3F[8, I1, k6]*SU3F[I2, k10, k8]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I1, k10, k8] + SU3F[8, I1, k6]* - SU3F[I4, k10, k8]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k10, k8] + SU3F[8, I2, k6]* - SU3F[I4, k10, k8]))) + SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I1, k6]*SU3F[I5, k10, k8] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I1, k6]* - SU3F[I5, k10, k8] + SU3D[6, I3, k8]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I1, k6]*SU3F[I5, k10, k8] + SU3D[6, I2, k8]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I5, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I2, k6]* - SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I2, k6]*SU3F[I5, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I5, k10, k8] + - SU3D[6, I1, k8]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I5, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I3, k6]*SU3F[I5, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I4, k6]*SU3F[I5, k10, k8] + - SU3D[6, I3, k8]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I5, k10, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[8, I4, k6]*SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[8, I4, k6]*SU3F[I5, k10, k8] + - SU3D[6, I2, k8]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[8, I4, k6]* - SU3F[I5, k10, k8] + SU3D[6, I1, k8]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[8, I4, k6]*SU3F[I5, k10, k8] + SU3D[6, I4, k8]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k8] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k10, k8] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k8] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k8] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k8] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k10, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k8] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k10, k8] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k8] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k10, k8] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k8] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I5, k10, k8] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[8, I2, k6]* - SU3F[I1, k10, k8] + SU3F[8, I1, k6]*SU3F[I2, k10, k8]) + - SU3D[I2, k10, k7]*(SU3F[8, I5, k6]*SU3F[I1, k10, k8] + - SU3F[8, I1, k6]*SU3F[I5, k10, k8]) + SU3D[I1, k10, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k10, k8] + SU3F[8, I2, k6]* - SU3F[I5, k10, k8])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k10, k8] + - SU3F[8, I1, k6]*SU3F[I2, k10, k8]) + SU3D[I2, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I1, k10, k8] + SU3F[8, I1, k6]* - SU3F[I5, k10, k8]) + SU3D[I1, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k10, k8] + SU3F[8, I2, k6]* - SU3F[I5, k10, k8]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I2, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I5, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k9] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I3, k10, k9] + SU3D[8, I4, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k9])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I4, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I4, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I4, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I4, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I4, k10, k9]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + SU3D[8, I5, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k9])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I5, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I5, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I5, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I5, k10, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I1, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I2, k11]*SU3F[I1, k11, k6] + SU3D[6, I2, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[I1, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I3, k11]* - SU3F[I1, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k11]*SU3F[I1, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[I1, k11, k6] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I4, k11]* - SU3F[I1, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I4, k11]*SU3F[I1, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I5, k11]*SU3F[I1, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I5, k11]*SU3F[I1, k11, k6] + - SU3D[6, I3, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]* - SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I1, k11]*SU3F[I2, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I3, k11]* - SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[I2, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I4, k11]* - SU3F[I2, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I4, k11]*SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k7, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k11]*SU3F[I2, k11, k6] + - SU3D[6, I1, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]* - SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I5, k11]*SU3F[I2, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I5, k11]*SU3F[I2, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k11, k6] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I1, k11]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[I3, k11, k6] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I2, k11]* - SU3F[I3, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k11]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[I3, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I4, k11]* - SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I4, k11]*SU3F[I3, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k11]*SU3F[I3, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]* - SU3F[I3, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I5, k11]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I5, k11]*SU3F[I3, k11, k6] + - SU3D[6, I3, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k11]*SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I1, k11]*SU3F[I4, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I1, k11]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k11]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[I4, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I2, k11]* - SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I2, k11]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I3, k11]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I3, k11]*SU3F[I4, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3F[3, I5, k11]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k7, k9]* - SU3F[3, I5, k11]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k9]*SU3F[3, I5, k11]*SU3F[I4, k11, k6] + - SU3D[6, I5, k9]*(SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I3, k11]*SU3F[I1, k11, k6] + SU3D[I1, k7, k9]* - SU3D[I4, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3F[3, I3, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[3, I1, k11]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I1, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I2, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[3, I4, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k7, k9]*SU3F[3, I3, k11]*SU3F[I4, k11, k6] + - SU3D[I3, k7, k9]*(SU3D[I4, k6, k7]*(SU3F[3, I2, k11]* - SU3F[I1, k11, k6] + SU3F[3, I1, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k6, k7]*(SU3F[3, I4, k11]*SU3F[I1, k11, k6] + - SU3F[3, I1, k11]*SU3F[I4, k11, k6]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k11]*SU3F[I2, k11, k6] + SU3F[3, I2, k11]* - SU3F[I4, k11, k6])) + SU3D[I3, k6, k7]* - (SU3D[I4, k7, k9]*(SU3F[3, I2, k11]*SU3F[I1, k11, k6] + - SU3F[3, I1, k11]*SU3F[I2, k11, k6]) + SU3D[I2, k7, k9]* - (SU3F[3, I4, k11]*SU3F[I1, k11, k6] + SU3F[3, I1, k11]* - SU3F[I4, k11, k6]) + SU3D[I1, k7, k9]* - (SU3F[3, I4, k11]*SU3F[I2, k11, k6] + SU3F[3, I2, k11]* - SU3F[I4, k11, k6]))) + SU3D[6, I3, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[3, I1, k11]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]* - SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I1, k11]*SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I1, k11]*SU3F[I5, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I2, k11]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I2, k11]*SU3F[I5, k11, k6] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[3, I2, k11]* - SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I4, k6, k7]* - SU3F[3, I3, k11]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I4, k6, k7]*SU3F[3, I3, k11]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3F[3, I3, k11]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I3, k11]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[I5, k11, k6] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[3, I4, k11]* - SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k11]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k7, k9]* - SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k7, k9]*SU3F[3, I4, k11]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k7, k9]* - SU3F[3, I4, k11]*SU3F[I5, k11, k6] + SU3D[6, I4, k9]* - (SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I3, k11]*SU3F[I1, k11, k6] + SU3D[I1, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I3, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k11]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I1, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I2, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[3, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k7, k9]*SU3F[3, I3, k11]*SU3F[I5, k11, k6] + - SU3D[I3, k7, k9]*(SU3D[I5, k6, k7]*(SU3F[3, I2, k11]* - SU3F[I1, k11, k6] + SU3F[3, I1, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k6, k7]*(SU3F[3, I5, k11]*SU3F[I1, k11, k6] + - SU3F[3, I1, k11]*SU3F[I5, k11, k6]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k11]*SU3F[I2, k11, k6] + SU3F[3, I2, k11]* - SU3F[I5, k11, k6])) + SU3D[I3, k6, k7]* - (SU3D[I5, k7, k9]*(SU3F[3, I2, k11]*SU3F[I1, k11, k6] + - SU3F[3, I1, k11]*SU3F[I2, k11, k6]) + SU3D[I2, k7, k9]* - (SU3F[3, I5, k11]*SU3F[I1, k11, k6] + SU3F[3, I1, k11]* - SU3F[I5, k11, k6]) + SU3D[I1, k7, k9]* - (SU3F[3, I5, k11]*SU3F[I2, k11, k6] + SU3F[3, I2, k11]* - SU3F[I5, k11, k6]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]* - SU3F[6, I2, k8]*SU3F[I1, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I3, k8]*SU3F[I1, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k8]* - SU3F[I1, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I4, k8]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I4, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I4, k8]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I4, k8]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I5, k8]*SU3F[I1, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k8]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I1, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k8]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I3, k8]*SU3F[I2, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k8]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I4, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I4, k8]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I4, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k8]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I4, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k8]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I5, k8]*SU3F[I2, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k8]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I1, k8]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I2, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I2, k8]*SU3F[I3, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k8]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I4, k8]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I4, k8]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I4, k8]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I5, k8]*SU3F[I3, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k8]* - SU3F[I4, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I1, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I1, k8]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I1, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I1, k8]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I1, k8]*SU3F[I4, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k8]* - SU3F[I4, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I2, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I2, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I2, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I2, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k8]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I3, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I3, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I3, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I3, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I5, k8]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I5, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I5, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I5, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k8]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I1, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I2, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I2, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I3, k8]*SU3F[I5, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k8]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I4, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I4, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I4, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I4, k8]*SU3F[I5, k11, k6] + - SU3D[I4, k7, k8]*(SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[6, I5, k8]*SU3F[I1, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I3, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k8]* - SU3F[I2, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]* - SU3F[6, I1, k8]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k8]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I5, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[6, I5, k8]*SU3F[I3, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[3, I3, k11]*(SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3F[6, I1, k8]*SU3F[I2, k11, k6]) + SU3F[3, I2, k11]* - (SU3F[6, I3, k8]*SU3F[I1, k11, k6] + SU3F[6, I1, k8]* - SU3F[I3, k11, k6]) + SU3F[3, I1, k11]* - (SU3F[6, I3, k8]*SU3F[I2, k11, k6] + SU3F[6, I2, k8]* - SU3F[I3, k11, k6])) + SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[6, I1, k8]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k8]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[6, I3, k8]*SU3F[I5, k11, k6] + SU3D[I3, k6, k7]* - (SU3F[3, I5, k11]*(SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3F[6, I1, k8]*SU3F[I2, k11, k6]) + SU3F[3, I2, k11]* - (SU3F[6, I5, k8]*SU3F[I1, k11, k6] + SU3F[6, I1, k8]* - SU3F[I5, k11, k6]) + SU3F[3, I1, k11]* - (SU3F[6, I5, k8]*SU3F[I2, k11, k6] + SU3F[6, I2, k8]* - SU3F[I5, k11, k6]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[3, I5, k11]*SU3F[6, I3, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k7, k8]*SU3F[3, I3, k11]* - SU3F[6, I5, k8]*SU3F[I1, k11, k6] + SU3D[I1, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I3, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3F[3, I3, k11]*SU3F[6, I5, k8]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k8]*SU3F[3, I5, k11]* - SU3F[6, I1, k8]*SU3F[I3, k11, k6] + SU3D[I1, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I2, k8]*SU3F[I3, k11, k6] + - SU3D[I2, k7, k8]*SU3F[3, I1, k11]*SU3F[6, I5, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k8]*SU3F[3, I2, k11]* - SU3F[6, I5, k8]*SU3F[I3, k11, k6] + SU3D[I5, k7, k8]* - (SU3F[3, I3, k11]*(SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3F[6, I1, k8]*SU3F[I2, k11, k6]) + SU3F[3, I2, k11]* - (SU3F[6, I3, k8]*SU3F[I1, k11, k6] + SU3F[6, I1, k8]* - SU3F[I3, k11, k6]) + SU3F[3, I1, k11]* - (SU3F[6, I3, k8]*SU3F[I2, k11, k6] + SU3F[6, I2, k8]* - SU3F[I3, k11, k6])) + SU3D[I2, k7, k8]*SU3F[3, I3, k11]* - SU3F[6, I1, k8]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I2, k8]*SU3F[I5, k11, k6] + - SU3D[I2, k7, k8]*SU3F[3, I1, k11]*SU3F[6, I3, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k7, k8]*SU3F[3, I2, k11]* - SU3F[6, I3, k8]*SU3F[I5, k11, k6] + SU3D[I3, k7, k8]* - (SU3F[3, I5, k11]*(SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3F[6, I1, k8]*SU3F[I2, k11, k6]) + SU3F[3, I2, k11]* - (SU3F[6, I5, k8]*SU3F[I1, k11, k6] + SU3F[6, I1, k8]* - SU3F[I5, k11, k6]) + SU3F[3, I1, k11]* - (SU3F[6, I5, k8]*SU3F[I2, k11, k6] + SU3F[6, I2, k8]* - SU3F[I5, k11, k6])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k11]*SU3F[I1, k11, k6] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I2, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I2, k11, k6] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I4, k11]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I4, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I1, k11]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I1, k11]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I2, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I3, k11]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I5, k11]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I5, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I5, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I4, k11]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I4, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]* - SU3F[I5, k11, k6] + SU3D[I4, k7, k8]* - (SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I3, k11, k6])) + SU3D[I2, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I2, k11]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I5, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I5, k11, k6]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I3, k11, k6])) + SU3D[I2, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I3, k8]*SU3F[8, I2, k11]*SU3F[I5, k11, k6] + - SU3D[I2, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[I3, k7, k8]* - (SU3F[6, I5, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I5, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I5, k11, k6])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[3, I3, k9]*SU3D[6, I5, k6]*SU3D[I4, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I2, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I5, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k6] + - SU3D[3, I3, k9]*SU3D[6, I4, k6]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I5, k6]*SU3D[I4, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I4, k6]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I5, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I4, k6]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I5, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I4, k6]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + - SU3D[3, I3, k9]*SU3D[6, I5, k6]*SU3D[I2, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I5, k6]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I2, k6]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I3, k6]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I5, k6]*SU3D[I1, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I5, k6]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + - SU3D[3, I3, k9]*SU3D[6, I1, k6]*SU3D[I5, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I3, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I5, k6]* - SU3D[I1, k10, k9]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I5, k6]*SU3D[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I1, k6]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I2, k6]* - SU3D[I5, k10, k9]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + - SU3D[3, I3, k9]*SU3D[6, I5, k6]*SU3D[I2, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I5, k6]*SU3D[I3, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I2, k6]* - SU3D[I5, k10, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I3, k6]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I5, k6]*SU3D[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I5, k6]* - SU3D[I3, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + - SU3D[3, I3, k9]*SU3D[6, I1, k6]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I3, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I5, k6]* - SU3D[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + - SU3D[3, I1, k9]*SU3D[6, I5, k6]*SU3D[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I1, k6]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I2, k6]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + - SU3D[3, I5, k9]*(SU3D[6, I2, k6]*SU3D[I4, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k11] + SU3D[6, I1, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3D[6, I2, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + - SU3D[6, I1, k6]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k6] + SU3D[6, I4, k6]* - (SU3D[I3, k10, k9]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + SU3D[I2, k10, k9]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k6]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k6])) + SU3D[6, I2, k6]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + SU3D[6, I1, k6]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + - SU3D[6, I2, k6]*SU3D[I1, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[6, I1, k6]*SU3D[I2, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[6, I2, k6]* - SU3D[I3, k10, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k6] + - SU3D[6, I1, k6]*SU3D[I3, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k6] + SU3D[6, I2, k6]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[6, I1, k6]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + - SU3D[6, I3, k6]*(SU3D[I4, k10, k9]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k6]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6]))) + SU3D[3, I3, k9]*SU3D[6, I4, k6]* - SU3D[I2, k10, k9]*SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I4, k6]*SU3D[I3, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + - SU3D[3, I3, k9]*SU3D[6, I4, k6]*SU3D[I1, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I4, k6]*SU3D[I3, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I1, k6]* - SU3D[I4, k10, k9]*SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I3, k6]*SU3D[I4, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I4, k6]*SU3D[I1, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I4, k6]* - SU3D[I2, k10, k9]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I1, k6]*SU3D[I4, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I2, k6]* - SU3D[I1, k10, k9]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I3, k6]*SU3D[I1, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I1, k6]*SU3D[I2, k10, k9]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I3, k6]* - SU3D[I2, k10, k9]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I1, k6]*SU3D[I3, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[3, I1, k9]*SU3D[6, I2, k6]*SU3D[I3, k10, k9]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I4, k6]* - SU3D[I2, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I4, k6]*SU3D[I3, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + - SU3D[3, I3, k9]*SU3D[6, I4, k6]*SU3D[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I4, k6]*SU3D[I3, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I1, k6]* - SU3D[I4, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + - SU3D[3, I1, k9]*SU3D[6, I3, k6]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I4, k6]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I4, k6]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I1, k6]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I2, k6]* - SU3D[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I3, k6]*SU3D[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I1, k6]*SU3D[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I3, k6]* - SU3D[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I1, k6]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I2, k6]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + SU3D[3, I4, k9]* - (SU3D[6, I2, k6]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k11] + SU3D[6, I1, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3D[6, I2, k6]* - SU3D[I5, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + - SU3D[6, I1, k6]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k6] + SU3D[6, I5, k6]* - (SU3D[I3, k10, k9]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + SU3D[I2, k10, k9]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k6]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k6])) + SU3D[6, I2, k6]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + SU3D[6, I1, k6]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + - SU3D[6, I2, k6]*SU3D[I1, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[6, I1, k6]*SU3D[I2, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[6, I2, k6]* - SU3D[I3, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + - SU3D[6, I1, k6]*SU3D[I3, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[6, I2, k6]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[6, I1, k6]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + - SU3D[6, I3, k6]*(SU3D[I5, k10, k9]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k6]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k6]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I1, k10, k7]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I1, k10, k7]*SU3F[I2, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I1, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I2, k10, k7]*SU3F[I3, k11, k6] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k10]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k10]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I5, k10]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k10]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k10]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k10]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k10]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k10]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k10]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k10]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k10]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k10]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I5, k10]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k10]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k10]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k10]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k10]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k10]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k10]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k10]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[3, I2, k11]*SU3F[6, I4, k10]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[3, I2, k11]* - SU3F[6, I4, k10]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[3, I1, k11]*SU3F[6, I4, k10]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[3, I4, k11]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[3, I2, k11]*SU3F[6, I3, k10]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3F[3, I1, k11]* - SU3F[6, I3, k10]*SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + - SU3F[3, I2, k11]*SU3F[6, I1, k10]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3F[3, I1, k11]*SU3F[6, I2, k10]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3F[3, I2, k11]* - SU3F[6, I3, k10]*SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + - SU3F[3, I1, k11]*SU3F[6, I3, k10]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3F[3, I2, k11]*SU3F[6, I1, k10]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3F[3, I1, k11]* - SU3F[6, I2, k10]*SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + - SU3F[3, I3, k11]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I4, k11, k6]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I4, k11, k6]))) + SU3D[I3, k6, k7]*SU3F[3, I4, k11]* - SU3F[6, I2, k10]*SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k10]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k10]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k10]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k10]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k10]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k10]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k10]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I2, k10]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I4, k10]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k10]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I1, k10]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k10]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k10]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k10]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I3, k10]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I2, k10]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k10]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k10]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k10]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k10]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k10]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k10]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k10]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I2, k10]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I4, k10]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k10]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I1, k10]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k10]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k10]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k10]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I3, k10]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I4, k6, k7]* - (SU3F[3, I2, k11]*SU3F[6, I5, k10]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[3, I1, k11]*SU3F[6, I5, k10]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[3, I2, k11]* - SU3F[6, I5, k10]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[3, I5, k11]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[3, I2, k11]*SU3F[6, I3, k10]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3F[3, I1, k11]* - SU3F[6, I3, k10]*SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + - SU3F[3, I2, k11]*SU3F[6, I1, k10]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3F[3, I1, k11]*SU3F[6, I2, k10]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3F[3, I2, k11]* - SU3F[6, I3, k10]*SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + - SU3F[3, I1, k11]*SU3F[6, I3, k10]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3F[3, I2, k11]*SU3F[6, I1, k10]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3F[3, I1, k11]* - SU3F[6, I2, k10]*SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + - SU3F[3, I3, k11]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I5, k11, k6]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I5, k11, k6]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I2, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I2, k10, k7]*SU3F[I3, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k11]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I4, k11]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[6, I4, k10]* - (SU3F[8, I3, k11]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[6, I2, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3F[6, I1, k10]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + - SU3F[6, I2, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I3, k11]*SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3F[6, I1, k10]* - SU3F[8, I2, k11]*SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + - SU3F[6, I3, k10]*(SU3F[8, I4, k11]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I4, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I4, k11, k6]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I2, k11]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k11]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k11]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I4, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I5, k11]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[6, I5, k10]* - (SU3F[8, I3, k11]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[6, I2, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3F[6, I1, k10]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + - SU3F[6, I2, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I3, k11]*SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3F[6, I1, k10]* - SU3F[8, I2, k11]*SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + - SU3F[6, I3, k10]*(SU3F[8, I5, k11]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I5, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I5, k11, k6]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I2, k10]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k10]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I5, k10]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k10]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I1, k10]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k10]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I5, k10]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k10]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I1, k10]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I2, k10]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I5, k10]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I5, k10]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I2, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I1, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I1, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I2, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I5, k6, k7]* - (SU3F[3, I2, k6]*SU3F[6, I4, k10]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[3, I2, k6]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3F[3, I1, k6]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3F[3, I4, k6]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[3, I2, k6]*SU3F[6, I3, k10]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3F[3, I1, k6]* - SU3F[6, I3, k10]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3F[3, I2, k6]*SU3F[6, I1, k10]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[3, I1, k6]*SU3F[6, I2, k10]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[3, I2, k6]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3F[3, I1, k6]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3F[3, I2, k6]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[3, I1, k6]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3F[3, I3, k6]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]))) + SU3D[I3, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I2, k10]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I3, k10]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k10]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k10]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k10]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I3, k10]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k10]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k10]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I2, k10]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I4, k10]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I1, k10]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I1, k10]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I2, k10]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I2, k10]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I3, k10]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I3, k10]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I2, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I4, k6, k7]*(SU3F[3, I2, k6]*SU3F[6, I5, k10]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[3, I1, k6]* - SU3F[6, I5, k10]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[3, I2, k6]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3F[3, I1, k6]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3F[3, I5, k6]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[3, I2, k6]*SU3F[6, I3, k10]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3F[3, I1, k6]* - SU3F[6, I3, k10]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3F[3, I2, k6]*SU3F[6, I1, k10]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[3, I1, k6]*SU3F[6, I2, k10]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[3, I2, k6]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3F[3, I1, k6]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3F[3, I2, k6]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[3, I1, k6]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3F[3, I3, k6]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k7]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I4, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3F[6, I4, k10]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I3, k6]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I3, k6]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[6, I1, k10]* - SU3F[8, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3F[6, I3, k10]*(SU3F[8, I4, k6]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[8, I2, k6]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I2, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I4, k6, k7]*(SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I5, k6]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3F[6, I1, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3F[6, I5, k10]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I3, k6]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I3, k6]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[6, I1, k10]* - SU3F[8, I2, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3F[6, I3, k10]*(SU3F[8, I5, k6]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[3, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3F[3, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[3, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I1, k7]*SU3F[3, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[3, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I1, k7]*SU3F[3, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I5, k7]*(SU3F[3, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[3, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[3, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[3, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[3, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[3, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[3, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[3, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[3, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[3, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[3, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[3, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k7]*SU3F[3, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I3, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I4, k7]* - (SU3F[3, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[3, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[3, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[3, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[3, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[3, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[3, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[3, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[3, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[3, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[3, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[3, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[3, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[3, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[3, I5, k7]*(SU3F[6, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[3, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[3, I4, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[8, I5, k7]*(SU3F[6, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I4, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I5, k7]*(SU3F[8, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[8, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[8, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[8, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[8, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[8, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[8, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I4, k7]* - (SU3F[8, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[8, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[8, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[8, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[8, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[8, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[8, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k11, k7]*SU3F[I1, k11, k8] + - SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k11, k7]*SU3F[I1, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I3, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k7]*SU3F[I1, k11, k8] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I2, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k8, k9]*SU3F[I1, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I4, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k11, k7]*SU3F[I2, k11, k8] + - SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k7]*SU3F[I2, k11, k8] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k7]*SU3F[I2, k11, k8] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k8, k9]*SU3F[I2, k11, k8] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I1, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k9]* - SU3D[I2, k8, k9]*SU3D[I4, k11, k7]*SU3F[I3, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I1, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I2, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k8, k9]*SU3F[I3, k11, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I3, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k8, k9]* - SU3D[I2, k11, k7]*SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I1, k11, k7]*SU3D[I2, k8, k9]*SU3F[I4, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I1, k8, k9]*SU3D[I3, k11, k7]* - SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k11, k7]*SU3D[I3, k8, k9]*SU3F[I4, k11, k8] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k11, k7]*SU3D[I3, k8, k9]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I3, k9]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k7]*SU3F[I4, k11, k8] + - SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k11, k7]*SU3F[I4, k11, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I3, k9]* - SU3D[I1, k11, k7]*SU3D[I5, k8, k9]*SU3F[I4, k11, k8] + - SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k11, k7]*SU3D[I5, k8, k9]*SU3F[I4, k11, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I4, k11, k8] + SU3D[3, I5, k7]*(SU3D[6, I2, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I1, k11, k8] + SU3D[6, I2, k9]* - SU3D[I3, k11, k7]*SU3D[I4, k8, k9]*SU3F[I1, k11, k8] + - SU3D[6, I1, k9]*SU3D[I3, k8, k9]*SU3D[I4, k11, k7]* - SU3F[I2, k11, k8] + SU3D[6, I1, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I2, k11, k8] + SU3D[6, I2, k9]* - SU3D[I1, k8, k9]*SU3D[I4, k11, k7]*SU3F[I3, k11, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I4, k11, k7]* - SU3F[I3, k11, k8] + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I3, k11, k8] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I4, k8, k9]*SU3F[I3, k11, k8] + - SU3D[6, I4, k9]*((SU3D[I1, k8, k9]*SU3D[I3, k11, k7] + - SU3D[I1, k11, k7]*SU3D[I3, k8, k9])*SU3F[I2, k11, k8] + - SU3D[I2, k8, k9]*(SU3D[I3, k11, k7]*SU3F[I1, k11, k8] + - SU3D[I1, k11, k7]*SU3F[I3, k11, k8]) + SU3D[I2, k11, k7]* - (SU3D[I3, k8, k9]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3F[I3, k11, k8])) + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I1, k9]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k7]*SU3F[I4, k11, k8] + - SU3D[6, I2, k9]*SU3D[I1, k11, k7]*SU3D[I3, k8, k9]* - SU3F[I4, k11, k8] + SU3D[6, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I3, k8, k9]*SU3F[I4, k11, k8] + SU3D[6, I3, k9]* - ((SU3D[I1, k8, k9]*SU3D[I4, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I4, k8, k9])*SU3F[I2, k11, k8] + SU3D[I2, k8, k9]* - (SU3D[I4, k11, k7]*SU3F[I1, k11, k8] + SU3D[I1, k11, k7]* - SU3F[I4, k11, k8]) + SU3D[I2, k11, k7]* - (SU3D[I4, k8, k9]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3F[I4, k11, k8]))) + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k8, k9]*SU3D[I2, k11, k7]*SU3F[I5, k11, k8] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k11, k7]*SU3D[I2, k8, k9]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I4, k9]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k7]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k11, k7]*SU3D[I3, k8, k9]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k11, k7]* - SU3D[I3, k8, k9]*SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k8, k9]*SU3D[I4, k11, k7]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k9]* - SU3D[I2, k8, k9]*SU3D[I4, k11, k7]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k8, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k11, k7]*SU3D[I4, k8, k9]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k9]* - SU3D[I2, k11, k7]*SU3D[I4, k8, k9]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k11, k7]*SU3D[I4, k8, k9]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k8, k9]*SU3F[I5, k11, k8] + SU3D[3, I4, k7]* - (SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k11, k8] + SU3D[6, I2, k9]*SU3D[I3, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I1, k11, k8] + SU3D[6, I1, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k11, k7]*SU3F[I2, k11, k8] + - SU3D[6, I1, k9]*SU3D[I3, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + SU3D[6, I1, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k11, k7]*SU3F[I3, k11, k8] + - SU3D[6, I2, k9]*SU3D[I1, k11, k7]*SU3D[I5, k8, k9]* - SU3F[I3, k11, k8] + SU3D[6, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I5, k8, k9]*SU3F[I3, k11, k8] + SU3D[6, I5, k9]* - ((SU3D[I1, k8, k9]*SU3D[I3, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I3, k8, k9])*SU3F[I2, k11, k8] + SU3D[I2, k8, k9]* - (SU3D[I3, k11, k7]*SU3F[I1, k11, k8] + SU3D[I1, k11, k7]* - SU3F[I3, k11, k8]) + SU3D[I2, k11, k7]* - (SU3D[I3, k8, k9]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3F[I3, k11, k8])) + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k9]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[I1, k11, k7]*SU3D[I3, k8, k9]* - SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I3, k8, k9]*SU3F[I5, k11, k8] + SU3D[6, I3, k9]* - ((SU3D[I1, k8, k9]*SU3D[I5, k11, k7] + SU3D[I1, k11, k7]* - SU3D[I5, k8, k9])*SU3F[I2, k11, k8] + SU3D[I2, k8, k9]* - (SU3D[I5, k11, k7]*SU3F[I1, k11, k8] + SU3D[I1, k11, k7]* - SU3F[I5, k11, k8]) + SU3D[I2, k11, k7]* - (SU3D[I5, k8, k9]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3F[I5, k11, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[3, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I1, k11, k8] + - SU3D[3, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[3, I3, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[3, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[3, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[3, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[3, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[3, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[3, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[3, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[3, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, k8, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[3, I5, k7]*(SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I4, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I4, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I4, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8]))) + SU3D[3, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I1, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I2, k11]*SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[3, I1, k7]*SU3D[I3, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[3, I4, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I5, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I5, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I1, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[8, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[8, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, k8, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[8, I5, k7]*(SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I4, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I4, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I4, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8]))) + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I1, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I2, k11]*SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I5, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I5, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I2, k11]*SU3F[I1, k11, k8] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k6]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I2, k6]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k6]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I5, k11]* - SU3F[I1, k11, k8] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I1, k11]*SU3F[I2, k11, k8] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I1, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k6]* - SU3F[6, I3, k11]*SU3F[I2, k11, k8] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k6]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k6]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I2, k6]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I5, k6]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I2, k6]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I3, k6]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k6]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I3, k6]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k6]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I5, k6]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k6]* - SU3F[6, I2, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[I4, k7, k8]* - (SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[I5, k6, k7]* - (SU3F[3, I3, k6]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k6]* - (SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I3, k11, k8]) + SU3F[3, I1, k6]* - (SU3F[6, I3, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I3, k6, k7]* - (SU3F[3, I5, k6]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k6]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3F[3, I1, k6]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[3, I5, k6]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k8]*SU3F[3, I3, k6]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I5, k6]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k7, k8]*SU3F[3, I5, k6]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I5, k6]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[I2, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[3, I3, k6]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k6]* - (SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I3, k11, k8]) + SU3F[3, I1, k6]* - (SU3F[6, I3, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[3, I3, k6]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I3, k6]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[I2, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[I1, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I3, k7, k8]* - (SU3F[3, I5, k6]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k6]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3F[3, I1, k6]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[8, I2, k11]* - SU3F[I1, k11, k8] + SU3D[6, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I2, k11]*SU3F[I1, k11, k8] + SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I3, k11]*SU3F[I1, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I3, k11]* - SU3F[I1, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[8, I4, k11]*SU3F[I1, k11, k8] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I4, k11]*SU3F[I1, k11, k8] + - SU3D[6, I3, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I4, k11]* - SU3F[I1, k11, k8] + SU3D[6, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I4, k11]*SU3F[I1, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[8, I5, k11]*SU3F[I1, k11, k8] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[8, I5, k11]* - SU3F[I1, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[8, I5, k11]*SU3F[I1, k11, k8] + SU3D[6, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[8, I5, k11]*SU3F[I1, k11, k8] + - SU3D[6, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[8, I1, k11]* - SU3F[I2, k11, k8] + SU3D[6, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I1, k11]*SU3F[I2, k11, k8] + SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I3, k11]*SU3F[I2, k11, k8] + - SU3D[6, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[8, I4, k11]*SU3F[I2, k11, k8] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I4, k11]*SU3F[I2, k11, k8] + - SU3D[6, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I4, k11]* - SU3F[I2, k11, k8] + SU3D[6, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I4, k11]*SU3F[I2, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[8, I5, k11]*SU3F[I2, k11, k8] + - SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[8, I5, k11]* - SU3F[I2, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[8, I5, k11]*SU3F[I2, k11, k8] + SU3D[6, I1, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[8, I5, k11]*SU3F[I2, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[8, I1, k11]* - SU3F[I3, k11, k8] + SU3D[6, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I1, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I2, k11]*SU3F[I3, k11, k8] + - SU3D[6, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I2, k11]* - SU3F[I3, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[8, I4, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I4, k11]*SU3F[I3, k11, k8] + - SU3D[6, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I4, k11]* - SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I4, k11]*SU3F[I3, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[8, I5, k11]*SU3F[I3, k11, k8] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[8, I5, k11]* - SU3F[I3, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[8, I5, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[8, I5, k11]*SU3F[I3, k11, k8] + - SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[8, I1, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k9]* - SU3F[8, I1, k11]*SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[8, I1, k11]*SU3F[I4, k11, k8] + - SU3D[6, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I1, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[8, I2, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I2, k11]*SU3F[I4, k11, k8] + - SU3D[6, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I2, k11]* - SU3F[I4, k11, k8] + SU3D[6, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I2, k11]*SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I3, k11]*SU3F[I4, k11, k8] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[8, I3, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I3, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[8, I3, k11]*SU3F[I4, k11, k8] + - SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3F[8, I5, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3F[8, I5, k11]*SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k9]*SU3F[8, I5, k11]*SU3F[I4, k11, k8] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k9]*SU3F[8, I5, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]* - SU3F[8, I5, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, k8, k9]*SU3F[8, I5, k11]*SU3F[I4, k11, k8] + - SU3D[6, I5, k7]*(SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[8, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[8, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[8, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[8, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[8, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[8, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[8, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[8, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[8, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[8, I3, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[8, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k9]*(SU3F[8, I2, k11]* - SU3F[I1, k11, k8] + SU3F[8, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[8, I4, k11]*SU3F[I1, k11, k8] + - SU3F[8, I1, k11]*SU3F[I4, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[8, I4, k11]*SU3F[I2, k11, k8] + SU3F[8, I2, k11]* - SU3F[I4, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I4, k8, k9]*(SU3F[8, I2, k11]*SU3F[I1, k11, k8] + - SU3F[8, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[8, I4, k11]*SU3F[I1, k11, k8] + SU3F[8, I1, k11]* - SU3F[I4, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[8, I4, k11]*SU3F[I2, k11, k8] + SU3F[8, I2, k11]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[8, I1, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[8, I1, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[8, I1, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[8, I1, k11]*SU3F[I5, k11, k8] + - SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[8, I2, k11]* - SU3F[I5, k11, k8] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]* - SU3F[8, I2, k11]*SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k9]* - SU3D[I4, k8, k9]*SU3F[8, I2, k11]*SU3F[I5, k11, k8] + - SU3D[6, I1, k7]*SU3D[I3, k7, k9]*SU3D[I4, k8, k9]*SU3F[8, I2, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3F[8, I3, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[8, I3, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[8, I3, k11]* - SU3F[I5, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[8, I3, k11]*SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[8, I4, k11]*SU3F[I5, k11, k8] + - SU3D[6, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[8, I4, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k9]* - SU3F[8, I4, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k9]*SU3F[8, I4, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]*SU3F[8, I4, k11]* - SU3F[I5, k11, k8] + SU3D[6, I1, k7]*SU3D[I2, k7, k9]*SU3D[I3, k8, k9]* - SU3F[8, I4, k11]*SU3F[I5, k11, k8] + SU3D[6, I4, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[8, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[8, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[8, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[8, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k7, k9]*SU3F[8, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[8, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[8, I5, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[8, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[8, I3, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[8, I3, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k7, k9]*(SU3F[8, I2, k11]* - SU3F[I1, k11, k8] + SU3F[8, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[8, I5, k11]*SU3F[I1, k11, k8] + - SU3F[8, I1, k11]*SU3F[I5, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k8] + SU3F[8, I2, k11]* - SU3F[I5, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I5, k8, k9]*(SU3F[8, I2, k11]*SU3F[I1, k11, k8] + - SU3F[8, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k8] + SU3F[8, I1, k11]* - SU3F[I5, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k8] + SU3F[8, I2, k11]* - SU3F[I5, k11, k8]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[8, I2, k6]*SU3F[I1, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I1, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I1, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I2, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I2, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I3, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I2, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I3, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I5, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I2, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I4, k7, k8]*(SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I2, k6, k7]*SU3F[6, I5, k11]* - SU3F[8, I1, k6]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[8, I5, k6]*SU3F[I3, k11, k8] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I3, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I3, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I3, k11, k8])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[8, I1, k6]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[8, I3, k6]*SU3F[I5, k11, k8] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I5, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I5, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I5, k11, k8]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I3, k11]* - SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I5, k11]* - SU3F[8, I1, k6]*SU3F[I3, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k7, k8]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k8]*SU3F[6, I2, k11]* - SU3F[8, I5, k6]*SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I3, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I3, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k11]* - SU3F[8, I1, k6]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k7, k8]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k7, k8]*SU3F[6, I2, k11]* - SU3F[8, I3, k6]*SU3F[I5, k11, k8] + SU3D[I3, k7, k8]* - (SU3F[6, I5, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I5, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I5, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I5, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[6, I3, k8]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[6, I2, k8]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[6, I2, k8]*SU3D[8, I4, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + - SU3D[6, I1, k8]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[6, I2, k8]*SU3D[8, I5, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[6, I2, k8]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I4, k7]* - SU3D[I5, k10, k7]*SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + - SU3D[6, I3, k8]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k8]*SU3D[8, I5, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I2, k8]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I5, k7]*SU3D[I1, k10, k7]* - SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I5, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I3, k8]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I2, k8]*SU3D[8, I5, k7]* - SU3D[I1, k10, k7]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k8]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k8]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I3, k8]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k8]*SU3D[8, I5, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I3, k8]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I2, k8]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k8]*SU3D[8, I5, k7]*SU3D[I1, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I5, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I3, k8]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I2, k8]*SU3D[8, I5, k7]* - SU3D[I1, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I1, k8]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k8]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I5, k8]*(SU3D[8, I2, k7]*SU3D[I4, k10, k7]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I4, k10, k7]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[8, I4, k7]* - (SU3D[I3, k10, k7]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k10, k7]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3D[I3, k10, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[8, I3, k7]*(SU3D[I4, k10, k7]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k10, k7]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k8]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k8]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[6, I2, k8]*SU3D[8, I3, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I3, k8]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]* - SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I1, k7]* - SU3D[I4, k10, k7]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k8]*SU3D[8, I3, k7]*SU3D[I4, k10, k7]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k8]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k8]*SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I2, k7]* - SU3D[I1, k10, k7]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k8]*SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I3, k7]* - SU3D[I2, k10, k7]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k8]*SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I1, k8]*SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + SU3D[6, I3, k8]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k8]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k8]*SU3D[8, I3, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I3, k8]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[8, I1, k7]* - SU3D[I4, k10, k7]*SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I1, k8]*SU3D[8, I3, k7]*SU3D[I4, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k8]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k8]*SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[8, I2, k7]* - SU3D[I1, k10, k7]*SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k8]*SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I3, k7]* - SU3D[I2, k10, k7]*SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k8]*SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I1, k8]*SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I4, k8]* - (SU3D[8, I2, k7]*SU3D[I5, k10, k7]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[8, I5, k7]* - (SU3D[I3, k10, k7]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k10, k7]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[8, I2, k7]* - SU3D[I3, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[8, I3, k7]*(SU3D[I5, k10, k7]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k10, k7]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[6, I2, k7]* - SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[3, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]* - SU3D[I5, k7, k8]*SU3F[3, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[3, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[3, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[3, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[3, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[3, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[3, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[3, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[3, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[3, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[3, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[3, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[3, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[3, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[3, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[3, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[3, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[3, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[3, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[3, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[3, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[3, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[3, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[3, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[3, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[3, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[3, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[3, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[3, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[3, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[3, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[3, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3F[3, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[3, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[3, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[3, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[3, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[3, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[3, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[3, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[3, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[3, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[3, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[3, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[3, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[3, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[3, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[3, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[3, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[3, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[3, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[3, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[3, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[3, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[3, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[3, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[3, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[3, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[3, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[3, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[3, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[3, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[3, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[3, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[3, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[3, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[3, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[3, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[3, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[3, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[3, I3, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[3, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[3, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[3, I2, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[3, I1, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[3, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[3, I2, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[3, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[3, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[8, I3, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[8, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[6, I2, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]* - SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[8, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[8, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[8, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[8, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[8, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[8, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[8, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3F[8, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[8, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[8, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[8, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[8, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[8, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[8, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I4, k8, k9]*SU3F[I1, k11, k8]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I5, k8, k9]* - SU3F[I1, k11, k8]*SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I4, k8, k9]*SU3F[I1, k11, k7]*SU3F[I2, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I5, k8, k9]*SU3F[I1, k11, k7]* - SU3F[I2, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I4, k8, k9]* - SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I5, k8, k9]*SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I4, k8, k9]*SU3F[I2, k11, k8]* - SU3F[I3, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I4, k8, k9]*SU3F[I1, k11, k7]*SU3F[I3, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I5, k8, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I4, k8, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I5, k8, k9]*SU3F[I2, k11, k7]*SU3F[I3, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k8, k9]*SU3F[I1, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k8, k9]* - SU3F[I1, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I5, k8, k9]*SU3F[I1, k11, k8]*SU3F[I4, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I5, k8, k9]*SU3F[I1, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k8, k9]* - SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k8, k9]*SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I5, k8, k9]*SU3F[I2, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k8, k9]*SU3F[I3, k11, k8]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k8, k9]*SU3F[I3, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I5, k8, k9]* - SU3F[I3, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I5, k8, k9]*SU3F[I3, k11, k8]*SU3F[I4, k11, k7] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k8, k9]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k8, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I5, k8, k9]*SU3F[I1, k11, k7]*SU3F[I4, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I5, k8, k9]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k8, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k8, k9]*SU3F[I2, k11, k7]*SU3F[I4, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I5, k8, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k8, k9]*SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k8, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I5, k8, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I5, k8, k9]*SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + - SU3D[6, I5, k9]*(SU3D[8, I2, k7]*SU3D[I4, k8, k9]*SU3F[I1, k11, k8]* - SU3F[I3, k11, k7] + SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + SU3D[8, I2, k7]* - SU3D[I4, k8, k9]*SU3F[I1, k11, k7]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I4, k8, k9]*SU3F[I2, k11, k7]* - SU3F[I3, k11, k8] + SU3D[8, I4, k7]* - (SU3D[I3, k8, k9]*(SU3F[I1, k11, k8]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k8])) + SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3F[I1, k11, k8]*SU3F[I4, k11, k7] + SU3D[8, I1, k7]* - SU3D[I3, k8, k9]*SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + - SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3F[I3, k11, k8]* - SU3F[I4, k11, k7] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3F[I3, k11, k8]*SU3F[I4, k11, k7] + SU3D[8, I2, k7]* - SU3D[I3, k8, k9]*SU3F[I1, k11, k7]*SU3F[I4, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k8, k9]*SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + - SU3D[8, I3, k7]*(SU3D[I4, k8, k9]*(SU3F[I1, k11, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k8]) + - SU3D[I2, k8, k9]*(SU3F[I1, k11, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k8, k9]*SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k8, k9]*SU3F[I1, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k8, k9]* - SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k8, k9]*SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k8, k9]*SU3F[I2, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k8, k9]* - SU3F[I2, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k8, k9]*SU3F[I2, k11, k8]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k8, k9]*SU3F[I2, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k8, k9]* - SU3F[I3, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k8, k9]*SU3F[I3, k11, k8]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k8, k9]*SU3F[I3, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k8, k9]* - SU3F[I3, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k8, k9]*SU3F[I4, k11, k8]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3F[I4, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k8, k9]*SU3F[I4, k11, k8]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3F[I4, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k8, k9]*SU3F[I1, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k8, k9]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k8, k9]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k8, k9]*SU3F[I1, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k8, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k8, k9]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k8, k9]*SU3F[I2, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k8, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k8, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k8, k9]*SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k8, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k8, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k8, k9]*SU3F[I4, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k8, k9]*SU3F[I4, k11, k7]*SU3F[I5, k11, k8] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I5, k8, k9]*SU3F[I1, k11, k8]* - SU3F[I3, k11, k7] + SU3D[8, I1, k7]*SU3D[I5, k8, k9]* - SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + SU3D[8, I2, k7]* - SU3D[I5, k8, k9]*SU3F[I1, k11, k7]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I5, k8, k9]*SU3F[I2, k11, k7]* - SU3F[I3, k11, k8] + SU3D[8, I5, k7]* - (SU3D[I3, k8, k9]*(SU3F[I1, k11, k8]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k8])) + SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]* - SU3D[I3, k8, k9]*SU3F[I2, k11, k8]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3F[I3, k11, k8]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3F[I3, k11, k8]*SU3F[I5, k11, k7] + SU3D[8, I2, k7]* - SU3D[I3, k8, k9]*SU3F[I1, k11, k7]*SU3F[I5, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k8, k9]*SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + - SU3D[8, I3, k7]*(SU3D[I5, k8, k9]*(SU3F[I1, k11, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k8]) + - SU3D[I2, k8, k9]*(SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[I2, k11, k8]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k11, k8]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8]*SU3F[I2, k11, k7] + SU3D[6, I3, k8]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k8]* - SU3F[I2, k11, k7] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I2, k11, k8] + SU3D[6, I3, k8]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I2, k11, k8] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + SU3D[6, I2, k8]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k8]* - SU3F[I3, k11, k7] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k8]* - SU3F[I3, k11, k7] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k11, k8] + SU3D[6, I2, k8]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k8] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k8] + SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I3, k11, k8] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I2, k8]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I2, k8]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I1, k8]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I1, k8]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8]*SU3F[I4, k11, k7] + SU3D[6, I1, k8]* - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k11, k8]* - SU3F[I4, k11, k7] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I2, k8]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I2, k8]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I1, k8]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I1, k8]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[6, I1, k8]* - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k8] + SU3D[6, I5, k8]*(SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k8] + SU3D[I4, k6, k7]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k8]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k8]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k8]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k8])) + SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I3, k6]*SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k11, k8]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k11, k8]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k11, k7]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + SU3D[I1, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k11, k7]*SU3F[I4, k11, k8] + - SU3D[I3, k6, k7]*(SU3F[8, I4, k6]*(SU3F[I1, k11, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k8]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k11, k8]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k8]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k8]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I2, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I2, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I1, k8]* - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I3, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I2, k8]* - SU3D[I3, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[8, I2, k6]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8]*SU3F[I5, k11, k7] + SU3D[6, I1, k8]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k7] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I2, k8]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I2, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k8]* - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I2, k8]* - SU3D[I3, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[8, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k8] + SU3D[6, I1, k8]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k8] + SU3D[6, I4, k8]*(SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I5, k6]*SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k8] + SU3D[I5, k6, k7]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k8]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k8]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k8]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k8]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k8]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k8])) + SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I3, k6]*SU3F[I2, k11, k8]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k11, k8]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k11, k8]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k11, k7]*SU3F[I5, k11, k8] + - SU3D[I1, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k8] + SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k11, k7]*SU3F[I5, k11, k8] + - SU3D[I3, k6, k7]*(SU3F[8, I5, k6]*(SU3F[I1, k11, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k8]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k8]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k11, k8]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k8]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[3, I3, k9]*SU3D[6, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[3, I3, k9]* - SU3D[6, I5, k6]*SU3F[I1, k10, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I5, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I5, k6]*SU3F[I2, k11, k9]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I5, k6]* - SU3F[I1, k10, k6]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I5, k6]*SU3F[I2, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I5, k6]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + - SU3D[3, I3, k9]*SU3D[6, I5, k6]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[6, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[3, I1, k9]* - SU3D[6, I5, k6]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[6, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + - SU3D[3, I1, k9]*SU3D[6, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k6] + SU3D[3, I3, k9]*SU3D[6, I5, k6]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[3, I3, k9]* - SU3D[6, I5, k6]*SU3F[I1, k10, k11]*SU3F[I2, k10, k6]* - SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k6]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[6, I5, k6]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9] + - SU3D[3, I1, k9]*SU3D[6, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k11, k9] + SU3D[3, I5, k9]* - (SU3D[6, I4, k6]*(SU3F[I1, k11, k9]*(SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k6]) + - SU3F[I1, k10, k6]*(SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I3, k11, k9])) + SU3D[6, I2, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[6, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + - SU3D[6, I2, k6]*SU3F[I1, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I1, k6]*SU3F[I2, k10, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I2, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + - SU3D[6, I1, k6]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[6, I2, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + SU3D[6, I1, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + - SU3D[6, I2, k6]*SU3F[I1, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I1, k6]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I2, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9] + - SU3D[6, I1, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k11, k9] + SU3D[6, I3, k6]*(SU3F[I1, k11, k9]* - (SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k6]) + SU3F[I1, k10, k6]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I4, k11, k9]))) + SU3D[3, I3, k9]*SU3D[6, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + - SU3D[3, I3, k9]*SU3D[6, I4, k6]*SU3F[I1, k10, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I4, k6]*SU3F[I2, k11, k9]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I4, k6]* - SU3F[I1, k10, k6]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I4, k6]*SU3F[I2, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I2, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I3, k6]*SU3F[I1, k11, k9]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I3, k6]*SU3F[I2, k11, k9]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I1, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I2, k6]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I2, k6]* - SU3F[I1, k10, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k9]*SU3D[6, I3, k6]*SU3F[I1, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I1, k6]* - SU3F[I2, k10, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I3, k6]*SU3F[I2, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I2, k9]*SU3D[6, I1, k6]* - SU3F[I3, k10, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k9]*SU3D[6, I2, k6]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k9]*SU3D[6, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + - SU3D[3, I3, k9]*SU3D[6, I4, k6]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[6, I4, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[3, I1, k9]* - SU3D[6, I4, k6]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[6, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + - SU3D[3, I1, k9]*SU3D[6, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[6, I2, k6]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[3, I2, k9]* - SU3D[6, I3, k6]*SU3F[I1, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[6, I1, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[3, I1, k9]* - SU3D[6, I3, k6]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[6, I1, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[3, I1, k9]* - SU3D[6, I2, k6]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[6, I2, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[3, I2, k9]*SU3D[6, I3, k6]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[6, I1, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[3, I1, k9]*SU3D[6, I3, k6]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[6, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[3, I1, k9]*SU3D[6, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[6, I4, k6]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I3, k9]* - SU3D[6, I4, k6]*SU3F[I1, k10, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I4, k6]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[6, I4, k6]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I5, k11, k9] + - SU3D[3, I1, k9]*SU3D[6, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k6]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I2, k9]* - SU3D[6, I3, k6]*SU3F[I1, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I1, k6]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[6, I3, k6]*SU3F[I2, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I1, k6]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[6, I2, k6]*SU3F[I3, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I3, k6]*SU3F[I1, k10, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I1, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + - SU3D[3, I1, k9]*SU3D[6, I3, k6]*SU3F[I2, k10, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + - SU3D[3, I1, k9]*SU3D[6, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9] + SU3D[3, I4, k9]* - (SU3D[6, I5, k6]*(SU3F[I1, k11, k9]*(SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k6]) + - SU3F[I1, k10, k6]*(SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I3, k11, k9])) + SU3D[6, I2, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[6, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + - SU3D[6, I2, k6]*SU3F[I1, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k6]*SU3F[I2, k10, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I2, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + - SU3D[6, I1, k6]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[6, I2, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + SU3D[6, I1, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + - SU3D[6, I2, k6]*SU3F[I1, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k6]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I2, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I5, k11, k9] + - SU3D[6, I1, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*(SU3F[I1, k11, k9]* - (SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k6]) + SU3F[I1, k10, k6]* - (SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I5, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I5, k11, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[6, I3, k6]*SU3D[8, I5, k9]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[6, I3, k6]* - SU3D[8, I5, k9]*SU3F[I1, k10, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k6]*SU3D[8, I5, k9]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + - SU3D[6, I1, k6]*SU3D[8, I5, k9]*SU3F[I2, k11, k9]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[6, I2, k6]*SU3D[8, I5, k9]* - SU3F[I1, k10, k6]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k6]*SU3D[8, I5, k9]*SU3F[I2, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k6]*SU3D[8, I5, k9]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + - SU3D[6, I3, k6]*SU3D[8, I5, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k6] + SU3D[6, I2, k6]*SU3D[8, I5, k9]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[6, I1, k6]* - SU3D[8, I5, k9]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[6, I2, k6]*SU3D[8, I5, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + - SU3D[6, I1, k6]*SU3D[8, I5, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k6] + SU3D[6, I3, k6]*SU3D[8, I5, k9]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I3, k6]* - SU3D[8, I5, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k6]* - SU3F[I4, k11, k9] + SU3D[6, I2, k6]*SU3D[8, I5, k9]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k6]* - SU3D[8, I5, k9]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k6]*SU3D[8, I5, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9] + - SU3D[6, I1, k6]*SU3D[8, I5, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k11, k9] + SU3D[6, I5, k6]* - (SU3D[8, I4, k9]*(SU3F[I1, k11, k9]*(SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k6]) + - SU3F[I1, k10, k6]*(SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I3, k11, k9])) + SU3D[8, I2, k9]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[8, I1, k9]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + - SU3D[8, I2, k9]*SU3F[I1, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[8, I1, k9]*SU3F[I2, k10, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[8, I2, k9]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + - SU3D[8, I1, k9]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6] + - SU3D[8, I2, k9]*SU3F[I1, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[8, I1, k9]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9] + - SU3D[8, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*(SU3F[I1, k11, k9]* - (SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k6]) + SU3F[I1, k10, k6]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k6]*SU3D[8, I4, k9]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + - SU3D[6, I3, k6]*SU3D[8, I4, k9]*SU3F[I1, k10, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k6]*SU3D[8, I4, k9]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + - SU3D[6, I1, k6]*SU3D[8, I4, k9]*SU3F[I2, k11, k9]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[6, I2, k6]*SU3D[8, I4, k9]* - SU3F[I1, k10, k6]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k6]*SU3D[8, I4, k9]*SU3F[I2, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k6]*SU3D[8, I2, k9]* - SU3F[I1, k11, k9]*SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + - SU3D[6, I2, k6]*SU3D[8, I3, k9]*SU3F[I1, k11, k9]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[6, I3, k6]*SU3D[8, I1, k9]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + - SU3D[6, I1, k6]*SU3D[8, I3, k9]*SU3F[I2, k11, k9]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[6, I2, k6]*SU3D[8, I1, k9]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + - SU3D[6, I1, k6]*SU3D[8, I2, k9]*SU3F[I3, k11, k9]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[6, I3, k6]*SU3D[8, I2, k9]* - SU3F[I1, k10, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k6]*SU3D[8, I3, k9]*SU3F[I1, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k6]*SU3D[8, I1, k9]* - SU3F[I2, k10, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k6]*SU3D[8, I3, k9]*SU3F[I2, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k6]*SU3D[8, I1, k9]* - SU3F[I3, k10, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k6]*SU3D[8, I2, k9]*SU3F[I3, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k6]*SU3D[8, I4, k9]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + - SU3D[6, I3, k6]*SU3D[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k6] + SU3D[6, I2, k6]*SU3D[8, I4, k9]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[6, I1, k6]* - SU3D[8, I4, k9]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[6, I2, k6]*SU3D[8, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + - SU3D[6, I1, k6]*SU3D[8, I4, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k6] + SU3D[6, I3, k6]*SU3D[8, I2, k9]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[6, I2, k6]* - SU3D[8, I3, k9]*SU3F[I1, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[6, I3, k6]*SU3D[8, I1, k9]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[6, I1, k6]* - SU3D[8, I3, k9]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[6, I2, k6]*SU3D[8, I1, k9]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[6, I1, k6]* - SU3D[8, I2, k9]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[6, I3, k6]*SU3D[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[6, I2, k6]*SU3D[8, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[6, I3, k6]*SU3D[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[6, I1, k6]*SU3D[8, I3, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[6, I2, k6]*SU3D[8, I1, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k10, k6] + - SU3D[6, I1, k6]*SU3D[8, I2, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k6] + SU3D[6, I3, k6]*SU3D[8, I4, k9]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k6]* - SU3D[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k11, k9] + SU3D[6, I2, k6]*SU3D[8, I4, k9]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[8, I4, k9]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k6]*SU3D[8, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I5, k11, k9] + - SU3D[6, I1, k6]*SU3D[8, I4, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[8, I2, k9]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I2, k6]* - SU3D[8, I3, k9]*SU3F[I1, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[8, I1, k9]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[8, I3, k9]*SU3F[I2, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k6]*SU3D[8, I1, k9]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[8, I2, k9]*SU3F[I3, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + - SU3D[6, I2, k6]*SU3D[8, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + - SU3D[6, I1, k6]*SU3D[8, I3, k9]*SU3F[I2, k10, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9] + SU3D[6, I2, k6]*SU3D[8, I1, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6]*SU3F[I5, k11, k9] + - SU3D[6, I1, k6]*SU3D[8, I2, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k11, k9] + SU3D[6, I4, k6]* - (SU3D[8, I5, k9]*(SU3F[I1, k11, k9]*(SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k6]) + - SU3F[I1, k10, k6]*(SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I3, k11, k9])) + SU3D[8, I2, k9]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[8, I1, k9]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + - SU3D[8, I2, k9]*SU3F[I1, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[8, I1, k9]*SU3F[I2, k10, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[8, I2, k9]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + - SU3D[8, I1, k9]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + SU3D[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3F[I1, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[8, I1, k9]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6]*SU3F[I5, k11, k9] + - SU3D[8, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*(SU3F[I1, k11, k9]* - (SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k6]) + SU3F[I1, k10, k6]* - (SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k9]*SU3F[I5, k10, k6] + SU3F[I2, k10, k6]* - SU3F[I5, k11, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I4, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I4, k7]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I5, k7]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I2, k11, k9] + - SU3D[3, I3, k9]*SU3D[6, I4, k7]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I2, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k7]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I4, k7]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + - SU3D[3, I1, k9]*SU3D[6, I5, k7]*SU3D[I4, k6, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I4, k7]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I5, k7]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I5, k7]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I4, k7]* - SU3D[I5, k6, k7]*SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + - SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I2, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I5, k7]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I5, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I1, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I5, k7]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I3, k7]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I5, k7]* - SU3D[I1, k6, k7]*SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + - SU3D[3, I1, k9]*SU3D[6, I5, k7]*SU3D[I2, k6, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I5, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I2, k7]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + - SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I2, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k7]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I5, k7]*SU3D[I1, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I5, k7]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + - SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I3, k7]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k7]* - SU3D[I1, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[3, I1, k9]*SU3D[6, I5, k7]*SU3D[I2, k6, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I5, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I2, k7]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[3, I5, k9]*(SU3D[6, I2, k7]*SU3D[I4, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[6, I1, k7]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[6, I2, k7]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + - SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[6, I4, k7]* - (SU3D[I3, k6, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3D[I2, k6, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[6, I2, k7]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k7]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[6, I2, k7]*SU3D[I1, k6, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k7]* - SU3D[I3, k6, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[6, I3, k7]*(SU3D[I4, k6, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k9]))) + SU3D[3, I3, k9]*SU3D[6, I4, k7]* - SU3D[I2, k6, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I3, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I2, k7]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I3, k7]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[3, I3, k9]*SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I4, k7]*SU3D[I3, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I1, k7]* - SU3D[I4, k6, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[3, I1, k9]*SU3D[6, I3, k7]*SU3D[I4, k6, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I4, k7]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I1, k6, k7]*SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I1, k6, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I3, k7]* - SU3D[I2, k6, k7]*SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I3, k6, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[6, I4, k7]* - SU3D[I2, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I3, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k7]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I3, k7]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[3, I3, k9]*SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I4, k7]*SU3D[I3, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I1, k7]* - SU3D[I4, k6, k7]*SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + - SU3D[3, I1, k9]*SU3D[6, I3, k7]*SU3D[I4, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[6, I4, k7]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I4, k7]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k7]* - SU3D[I1, k6, k7]*SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I3, k7]*SU3D[I1, k6, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I3, k7]* - SU3D[I2, k6, k7]*SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + - SU3D[3, I2, k9]*SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I1, k9]*SU3D[6, I2, k7]*SU3D[I3, k6, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I4, k9]* - (SU3D[6, I2, k7]*SU3D[I5, k6, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[6, I1, k7]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[6, I2, k7]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + - SU3D[6, I1, k7]*SU3D[I5, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[6, I5, k7]* - (SU3D[I3, k6, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3D[I2, k6, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[6, I2, k7]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k7]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k7]*SU3D[I1, k6, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I2, k7]* - SU3D[I3, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k7]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[6, I3, k7]*(SU3D[I5, k6, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k11, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k11, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + SU3D[6, I3, k6]* - SU3D[I4, k8, k9]*SU3F[3, I5, k8]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[I1, k11, k6]*SU3F[I2, k11, k9] + SU3D[6, I3, k6]* - SU3D[I4, k8, k9]*SU3F[3, I5, k8]*SU3F[I1, k11, k6]* - SU3F[I2, k11, k9] + SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[6, I2, k6]* - SU3D[I4, k8, k9]*SU3F[3, I5, k8]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[6, I1, k6]* - SU3D[I4, k8, k9]*SU3F[3, I5, k8]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k6] + SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + SU3D[6, I2, k6]* - SU3D[I4, k8, k9]*SU3F[3, I5, k8]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[6, I1, k6]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[6, I1, k6]* - SU3D[I4, k8, k9]*SU3F[3, I5, k8]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[3, I2, k8]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k6]* - SU3D[I5, k8, k9]*SU3F[3, I3, k8]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k6]*SU3D[I2, k8, k9]*SU3F[3, I5, k8]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k6]* - SU3D[I3, k8, k9]*SU3F[3, I5, k8]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[3, I1, k8]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k6]* - SU3D[I5, k8, k9]*SU3F[3, I3, k8]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[3, I5, k8]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k6]* - SU3D[I3, k8, k9]*SU3F[3, I5, k8]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[3, I1, k8]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k6]* - SU3D[I5, k8, k9]*SU3F[3, I2, k8]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[3, I5, k8]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k6]* - SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[3, I2, k8]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I2, k6]* - SU3D[I5, k8, k9]*SU3F[3, I3, k8]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I3, k6]*SU3D[I2, k8, k9]*SU3F[3, I5, k8]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I2, k6]* - SU3D[I3, k8, k9]*SU3F[3, I5, k8]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[3, I1, k8]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I1, k6]* - SU3D[I5, k8, k9]*SU3F[3, I3, k8]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[3, I5, k8]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I1, k6]* - SU3D[I3, k8, k9]*SU3F[3, I5, k8]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[3, I1, k8]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I1, k6]* - SU3D[I5, k8, k9]*SU3F[3, I2, k8]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[3, I5, k8]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[6, I1, k6]* - SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[6, I5, k6]*(SU3D[I2, k8, k9]*SU3F[3, I4, k8]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k8, k9]* - SU3F[3, I4, k8]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k8, k9]*SU3F[3, I4, k8]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k8, k9]*SU3F[3, I4, k8]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I4, k8, k9]* - (SU3F[3, I3, k8]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[3, I2, k8]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[3, I1, k8]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k8, k9]*SU3F[3, I3, k8]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[I1, k8, k9]* - SU3F[3, I3, k8]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k8, k9]*SU3F[3, I1, k8]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k8, k9]*SU3F[3, I2, k8]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[I2, k8, k9]* - SU3F[3, I3, k8]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I1, k8, k9]*SU3F[3, I3, k8]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[I2, k8, k9]*SU3F[3, I1, k8]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[I1, k8, k9]* - SU3F[3, I2, k8]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I3, k8, k9]*(SU3F[3, I4, k8]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[3, I2, k8]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k9]) + SU3F[3, I1, k8]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k6]*SU3D[I4, k8, k9]* - SU3F[3, I2, k8]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k6]*SU3D[I4, k8, k9]*SU3F[3, I3, k8]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k6]*SU3D[I2, k8, k9]*SU3F[3, I4, k8]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I2, k6]* - SU3D[I3, k8, k9]*SU3F[3, I4, k8]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k6]*SU3D[I4, k8, k9]*SU3F[3, I1, k8]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k6]* - SU3D[I4, k8, k9]*SU3F[3, I3, k8]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[3, I4, k8]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k6]* - SU3D[I3, k8, k9]*SU3F[3, I4, k8]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I2, k6]*SU3D[I4, k8, k9]*SU3F[3, I1, k8]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k6]* - SU3D[I4, k8, k9]*SU3F[3, I2, k8]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[3, I4, k8]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k6]* - SU3D[I2, k8, k9]*SU3F[3, I4, k8]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k6]*SU3D[I2, k8, k9]*SU3F[3, I1, k8]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I2, k6]* - SU3D[I3, k8, k9]*SU3F[3, I1, k8]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[3, I2, k8]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k6]* - SU3D[I3, k8, k9]*SU3F[3, I2, k8]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[3, I3, k8]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k6]* - SU3D[I2, k8, k9]*SU3F[3, I3, k8]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k6]*SU3D[I4, k8, k9]*SU3F[3, I2, k8]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I2, k6]* - SU3D[I4, k8, k9]*SU3F[3, I3, k8]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[I2, k8, k9]*SU3F[3, I4, k8]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I2, k6]* - SU3D[I3, k8, k9]*SU3F[3, I4, k8]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[I4, k8, k9]*SU3F[3, I1, k8]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[I4, k8, k9]*SU3F[3, I3, k8]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[3, I4, k8]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[I3, k8, k9]*SU3F[3, I4, k8]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I2, k6]*SU3D[I4, k8, k9]*SU3F[3, I1, k8]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[I4, k8, k9]*SU3F[3, I2, k8]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[3, I4, k8]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[I2, k8, k9]*SU3F[3, I4, k8]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[I2, k8, k9]*SU3F[3, I1, k8]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I2, k6]* - SU3D[I3, k8, k9]*SU3F[3, I1, k8]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[3, I2, k8]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[I3, k8, k9]*SU3F[3, I2, k8]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[3, I3, k8]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[6, I1, k6]* - SU3D[I2, k8, k9]*SU3F[3, I3, k8]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[6, I4, k6]*(SU3D[I2, k8, k9]*SU3F[3, I5, k8]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k8, k9]* - SU3F[3, I5, k8]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k8, k9]*SU3F[3, I5, k8]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I5, k8, k9]* - (SU3F[3, I3, k8]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[3, I2, k8]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[3, I1, k8]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k8, k9]*SU3F[3, I3, k8]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[I1, k8, k9]* - SU3F[3, I3, k8]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k8, k9]*SU3F[3, I1, k8]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k8, k9]*SU3F[3, I2, k8]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[I2, k8, k9]* - SU3F[3, I3, k8]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I1, k8, k9]*SU3F[3, I3, k8]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[I2, k8, k9]*SU3F[3, I1, k8]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[I1, k8, k9]* - SU3F[3, I2, k8]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I3, k8, k9]*(SU3F[3, I5, k8]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[3, I2, k8]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k11, k9]) + SU3F[3, I1, k8]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k11, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + SU3D[3, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I2, k11, k9] + SU3D[3, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I2, k11, k9] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[3, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k6] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + SU3D[3, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k9]))) + SU3D[3, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I4, k9]*(SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k11, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I2, k11, k9] + SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I2, k11, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k6] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k9]))) + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I4, k9]*(SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k11, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3D[3, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I1, k6, k9] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I1, k6, k9] + - SU3D[3, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3D[3, I3, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I1, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I1, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I2, k6, k9] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[3, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I2, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I2, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I3, k6, k9] + - SU3D[3, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I4, k6, k9] + - SU3D[3, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I4, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[3, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I4, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9]))) + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I1, k10]* - SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I1, k10]*SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I2, k10]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I2, k10]*SU3F[I5, k6, k9] + - SU3D[3, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[3, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I5, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I1, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I2, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I4, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9]))) + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I1, k10]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I1, k10]*SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I2, k10]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I2, k10]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I5, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]* - SU3F[6, I2, k7]*SU3F[I1, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k8]*SU3F[6, I2, k7]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[6, I3, k7]*SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I4, k7]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I3, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I2, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k8]*SU3F[6, I1, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[6, I3, k7]*SU3F[I2, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I1, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I4, k7]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I3, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I2, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k8]*SU3F[6, I1, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[6, I2, k7]*SU3F[I3, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I1, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k8]* - SU3F[6, I4, k7]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I2, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I3, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I2, k8]*SU3F[6, I1, k7]*SU3F[I4, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k8]*SU3F[6, I1, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k8]*SU3F[6, I1, k7]*SU3F[I4, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I1, k7]* - SU3F[I4, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k8]*SU3F[6, I2, k7]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I2, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k8]*SU3F[6, I3, k7]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I3, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I5, k7]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[3, I1, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I2, k8]*SU3F[6, I5, k7]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I2, k8]* - SU3F[6, I5, k7]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I3, k8]*SU3F[6, I5, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[3, I4, k8]*SU3F[6, I1, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I4, k8]*SU3F[6, I2, k7]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I4, k8]* - SU3F[6, I2, k7]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I4, k8]*SU3F[6, I3, k7]* - SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I4, k7]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[3, I1, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I2, k8]*SU3F[6, I4, k7]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I2, k8]* - SU3F[6, I4, k7]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I3, k8]*SU3F[6, I4, k7]* - SU3F[I5, k6, k9] + SU3D[I4, k8, k9]*(SU3D[I2, k6, k7]*SU3F[3, I5, k8]* - SU3F[6, I3, k7]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I5, k7]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I5, k8]* - SU3F[6, I3, k7]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I5, k7]*SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3F[3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I5, k8]* - SU3F[6, I2, k7]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I5, k7]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I2, k8]* - SU3F[6, I5, k7]*SU3F[I3, k6, k9] + SU3D[I5, k6, k7]* - (SU3F[3, I3, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k9] + - SU3F[6, I1, k7]*SU3F[I2, k6, k9]) + SU3F[3, I2, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k9] + SU3F[6, I1, k7]* - SU3F[I3, k6, k9]) + SU3F[3, I1, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k9] + SU3F[6, I2, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I2, k7]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I2, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k9] + SU3D[I3, k6, k7]* - (SU3F[3, I5, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k9] + - SU3F[6, I1, k7]*SU3F[I2, k6, k9]) + SU3F[3, I2, k8]* - (SU3F[6, I5, k7]*SU3F[I1, k6, k9] + SU3F[6, I1, k7]* - SU3F[I5, k6, k9]) + SU3F[3, I1, k8]* - (SU3F[6, I5, k7]*SU3F[I2, k6, k9] + SU3F[6, I2, k7]* - SU3F[I5, k6, k9]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I3, k7]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3F[3, I3, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3F[3, I3, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k9] + - SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I1, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k9] + - SU3D[I2, k8, k9]*SU3F[3, I1, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[3, I2, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k9] + - SU3D[I5, k8, k9]*(SU3F[3, I3, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, - k9] + SU3F[6, I1, k7]*SU3F[I2, k6, k9]) + SU3F[3, I2, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k9] + SU3F[6, I1, k7]* - SU3F[I3, k6, k9]) + SU3F[3, I1, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k9] + SU3F[6, I2, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k8, k9]*SU3F[3, I3, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[3, I3, k8]* - SU3F[6, I2, k7]*SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3F[3, I1, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[3, I2, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k9] + SU3D[I3, k8, k9]* - (SU3F[3, I5, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k9] + - SU3F[6, I1, k7]*SU3F[I2, k6, k9]) + SU3F[3, I2, k8]* - (SU3F[6, I5, k7]*SU3F[I1, k6, k9] + SU3F[6, I1, k7]* - SU3F[I5, k6, k9]) + SU3F[3, I1, k8]* - (SU3F[6, I5, k7]*SU3F[I2, k6, k9] + SU3F[6, I2, k7]* - SU3F[I5, k6, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I1, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k7]*SU3F[8, I4, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I4, k8]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I2, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I2, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I4, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I4, k8]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I2, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I3, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I3, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I4, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I4, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k7]*SU3F[8, I4, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I3, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I1, k8]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k7]*SU3F[8, I1, k8]*SU3F[I4, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I1, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k8]*SU3F[I4, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I1, k8]* - SU3F[I4, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I2, k8]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I2, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I2, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I2, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I3, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I3, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I5, k8]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I5, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I5, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k8]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I4, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k8]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I4, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I4, k8]* - SU3F[I5, k6, k9] + SU3D[I4, k8, k9]*(SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I1, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I2, k8]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I5, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I5, k8]*SU3F[I3, k6, k9] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I5, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I5, k6, k9]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I1, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I2, k8]*SU3F[I3, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I2, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I5, k8, k9]*(SU3F[6, I3, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, - k9] + SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I3, k6, k9])) + SU3D[I2, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I3, k8, k9]* - (SU3F[6, I5, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I5, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I5, k6, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k10]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I2, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I2, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k10, k7]*SU3F[I2, k6, k9] + - SU3D[6, I3, k10]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k10, k7]* - SU3F[I2, k6, k9] + SU3D[6, I2, k10]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I3, k10, k7] + SU3D[6, I2, k10]*SU3D[8, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, k10, k7] + - SU3D[6, I1, k10]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I3, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k10, k7] + SU3D[6, I2, k10]*SU3D[8, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k10, k7]*SU3F[I3, k6, k9] + - SU3D[6, I2, k10]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k10, k7]* - SU3F[I3, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k10, k7]*SU3F[I3, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I2, k10, k7]*SU3F[I3, k6, k9] + - SU3D[6, I3, k10]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I4, k10, k7] + SU3D[6, I2, k10]*SU3D[8, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I4, k10, k7] + - SU3D[6, I2, k10]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I4, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, k10, k7] + - SU3D[6, I3, k10]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I4, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, k10, k7] + SU3D[6, I2, k10]*SU3D[8, I5, k9]* - SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k10, k7] + - SU3D[6, I1, k10]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I4, k10, k7] + SU3D[6, I2, k10]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k10, k7] + - SU3D[6, I3, k10]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k10, k7]* - SU3F[I4, k6, k9] + SU3D[6, I2, k10]*SU3D[8, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k10, k7]*SU3F[I4, k6, k9] + SU3D[6, I3, k10]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k10, k7]*SU3F[I4, k6, k9] + - SU3D[6, I2, k10]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k10, k7]* - SU3F[I4, k6, k9] + SU3D[6, I3, k10]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k10, k7]*SU3F[I4, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k10, k7]*SU3F[I4, k6, k9] + - SU3D[6, I3, k10]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k10, k7]* - SU3F[I4, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k10, k7]*SU3F[I4, k6, k9] + SU3D[6, I2, k10]*SU3D[8, I5, k9]* - SU3D[I1, k6, k7]*SU3F[I3, k10, k7]*SU3F[I4, k6, k9] + - SU3D[6, I1, k10]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I3, k10, k7]* - SU3F[I4, k6, k9] + SU3D[6, I2, k10]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I3, k10, k7]*SU3F[I4, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I3, k10, k7]*SU3F[I4, k6, k9] + - SU3D[6, I5, k10]*(SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I3, k10, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k10, k7] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k10, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I2, k10, k7]*SU3F[I3, k6, k9] + - SU3D[8, I4, k9]*(SU3D[I3, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I3, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I3, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k6, k9])) + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, k10, k7] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, k10, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k10, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k10, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, k10, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, k10, k7]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k10, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k10, k7]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I4, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I4, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I4, k6, k9]))) + SU3D[6, I3, k10]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, k6, k9]*SU3F[I5, k10, k7] + - SU3D[6, I2, k10]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I5, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I5, k10, k7] + SU3D[6, I2, k10]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k9]*SU3F[I5, k10, k7] + - SU3D[6, I3, k10]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I5, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I5, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k9]*SU3F[I5, k10, k7] + - SU3D[6, I1, k10]*SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I5, k10, k7] + SU3D[6, I2, k10]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k10, k7] + - SU3D[6, I2, k10]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I5, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3F[I4, k6, k9]*SU3F[I5, k10, k7] + - SU3D[6, I2, k10]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[I4, k6, k9]* - SU3F[I5, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I4, k6, k9]*SU3F[I5, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k9]*SU3F[I5, k10, k7] + - SU3D[6, I2, k10]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I4, k6, k9]* - SU3F[I5, k10, k7] + SU3D[6, I1, k10]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I4, k6, k9]*SU3F[I5, k10, k7] + SU3D[6, I3, k10]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, k10, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k10]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k10, k7]* - SU3F[I5, k6, k9] + SU3D[6, I3, k10]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k10, k7]*SU3F[I5, k6, k9] + SU3D[6, I2, k10]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k10, k7]*SU3F[I5, k6, k9] + - SU3D[6, I3, k10]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]*SU3F[I2, k10, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k10, k7]*SU3F[I5, k6, k9] + SU3D[6, I3, k10]*SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[I2, k10, k7]*SU3F[I5, k6, k9] + - SU3D[6, I1, k10]*SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[I2, k10, k7]* - SU3F[I5, k6, k9] + SU3D[6, I2, k10]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k10, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k10, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k10]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I3, k10, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I3, k10, k7]*SU3F[I5, k6, k9] + SU3D[6, I3, k10]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3F[I4, k10, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k10]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[I4, k10, k7]* - SU3F[I5, k6, k9] + SU3D[6, I3, k10]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I4, k10, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I4, k10, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k10]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I4, k10, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k10]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I4, k10, k7]*SU3F[I5, k6, k9] + SU3D[6, I4, k10]* - (SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, k10, k7] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, k10, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k10, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k10, k7]*SU3F[I3, k6, k9] + - SU3D[8, I5, k9]*(SU3D[I3, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I3, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I3, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k6, k9])) + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I5, k10, k7] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I5, k10, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k10, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k10, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, k10, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, k10, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k10, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k10, k7]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*(SU3D[I5, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I5, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I5, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I5, k6, k9]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I2, k6, k9] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[3, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k11]*(SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k9]))) + SU3D[3, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I4, k9]* - (SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I5, k6, k7]*(SU3F[6, I3, k11]* - (SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k6, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I2, k6, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k11]*(SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k9]))) + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I5, k6, k7]*(SU3F[6, I3, k11]* - (SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k6, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[3, I3, k7]*SU3D[6, I5, k11]*SU3D[I2, k8, k9]* - SU3D[I4, k11, k9]*SU3F[I1, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k11]* - SU3D[I3, k8, k9]*SU3D[I4, k11, k9]*SU3F[I1, k7, k8] + - SU3D[3, I3, k7]*SU3D[6, I5, k11]*SU3D[I2, k11, k9]*SU3D[I4, k8, k9]* - SU3F[I1, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k11]*SU3D[I3, k11, k9]* - SU3D[I4, k8, k9]*SU3F[I1, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I4, k11]* - SU3D[I2, k8, k9]*SU3D[I5, k11, k9]*SU3F[I1, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I4, k11]*SU3D[I3, k8, k9]*SU3D[I5, k11, k9]* - SU3F[I1, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k11]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k9]*SU3F[I1, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I3, k11]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k9]*SU3F[I1, k7, k8] + - SU3D[3, I3, k7]*SU3D[6, I4, k11]*SU3D[I2, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I1, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k11]*SU3D[I3, k11, k9]* - SU3D[I5, k8, k9]*SU3F[I1, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k11]* - SU3D[I4, k11, k9]*SU3D[I5, k8, k9]*SU3F[I1, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k11]*SU3D[I4, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I1, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k11]*SU3D[I1, k8, k9]* - SU3D[I4, k11, k9]*SU3F[I2, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k11]* - SU3D[I3, k8, k9]*SU3D[I4, k11, k9]*SU3F[I2, k7, k8] + - SU3D[3, I3, k7]*SU3D[6, I5, k11]*SU3D[I1, k11, k9]*SU3D[I4, k8, k9]* - SU3F[I2, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k11]*SU3D[I3, k11, k9]* - SU3D[I4, k8, k9]*SU3F[I2, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I4, k11]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k9]*SU3F[I2, k7, k8] + - SU3D[3, I1, k7]*SU3D[6, I4, k11]*SU3D[I3, k8, k9]*SU3D[I5, k11, k9]* - SU3F[I2, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k11]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k9]*SU3F[I2, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k11]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k9]*SU3F[I2, k7, k8] + - SU3D[3, I3, k7]*SU3D[6, I4, k11]*SU3D[I1, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I2, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I4, k11]*SU3D[I3, k11, k9]* - SU3D[I5, k8, k9]*SU3F[I2, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k11]* - SU3D[I4, k11, k9]*SU3D[I5, k8, k9]*SU3F[I2, k7, k8] + - SU3D[3, I1, k7]*SU3D[6, I3, k11]*SU3D[I4, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I2, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k11]*SU3D[I1, k8, k9]* - SU3D[I4, k11, k9]*SU3F[I3, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k11]* - SU3D[I2, k8, k9]*SU3D[I4, k11, k9]*SU3F[I3, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I5, k11]*SU3D[I1, k11, k9]*SU3D[I4, k8, k9]* - SU3F[I3, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k11]*SU3D[I2, k11, k9]* - SU3D[I4, k8, k9]*SU3F[I3, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k11]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k9]*SU3F[I3, k7, k8] + - SU3D[3, I1, k7]*SU3D[6, I4, k11]*SU3D[I2, k8, k9]*SU3D[I5, k11, k9]* - SU3F[I3, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k11]*SU3D[I4, k8, k9]* - SU3D[I5, k11, k9]*SU3F[I3, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I2, k11]* - SU3D[I4, k8, k9]*SU3D[I5, k11, k9]*SU3F[I3, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I4, k11]*SU3D[I1, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I3, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I4, k11]*SU3D[I2, k11, k9]* - SU3D[I5, k8, k9]*SU3F[I3, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k11]* - SU3D[I4, k11, k9]*SU3D[I5, k8, k9]*SU3F[I3, k7, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k11]*SU3D[I4, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I3, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k11]*SU3D[I1, k8, k9]* - SU3D[I2, k11, k9]*SU3F[I4, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I5, k11]* - SU3D[I1, k11, k9]*SU3D[I2, k8, k9]*SU3F[I4, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I5, k11]*SU3D[I1, k8, k9]*SU3D[I3, k11, k9]* - SU3F[I4, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I5, k11]*SU3D[I2, k8, k9]* - SU3D[I3, k11, k9]*SU3F[I4, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I5, k11]* - SU3D[I1, k11, k9]*SU3D[I3, k8, k9]*SU3F[I4, k7, k8] + - SU3D[3, I1, k7]*SU3D[6, I5, k11]*SU3D[I2, k11, k9]*SU3D[I3, k8, k9]* - SU3F[I4, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k11]*SU3D[I1, k8, k9]* - SU3D[I5, k11, k9]*SU3F[I4, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I3, k11]* - SU3D[I1, k8, k9]*SU3D[I5, k11, k9]*SU3F[I4, k7, k8] + - SU3D[3, I3, k7]*SU3D[6, I1, k11]*SU3D[I2, k8, k9]*SU3D[I5, k11, k9]* - SU3F[I4, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k11]*SU3D[I2, k8, k9]* - SU3D[I5, k11, k9]*SU3F[I4, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k11]* - SU3D[I3, k8, k9]*SU3D[I5, k11, k9]*SU3F[I4, k7, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k11]*SU3D[I3, k8, k9]*SU3D[I5, k11, k9]* - SU3F[I4, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k11]*SU3D[I1, k11, k9]* - SU3D[I5, k8, k9]*SU3F[I4, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I3, k11]* - SU3D[I1, k11, k9]*SU3D[I5, k8, k9]*SU3F[I4, k7, k8] + - SU3D[3, I3, k7]*SU3D[6, I1, k11]*SU3D[I2, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I4, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k11]*SU3D[I2, k11, k9]* - SU3D[I5, k8, k9]*SU3F[I4, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I1, k11]* - SU3D[I3, k11, k9]*SU3D[I5, k8, k9]*SU3F[I4, k7, k8] + - SU3D[3, I1, k7]*SU3D[6, I2, k11]*SU3D[I3, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I4, k7, k8] + SU3D[3, I5, k7]*(SU3D[6, I2, k11]*SU3D[I3, k8, k9]* - SU3D[I4, k11, k9]*SU3F[I1, k7, k8] + SU3D[6, I2, k11]* - SU3D[I3, k11, k9]*SU3D[I4, k8, k9]*SU3F[I1, k7, k8] + - SU3D[6, I1, k11]*SU3D[I3, k8, k9]*SU3D[I4, k11, k9]* - SU3F[I2, k7, k8] + SU3D[6, I1, k11]*SU3D[I3, k11, k9]* - SU3D[I4, k8, k9]*SU3F[I2, k7, k8] + SU3D[6, I2, k11]* - SU3D[I1, k8, k9]*SU3D[I4, k11, k9]*SU3F[I3, k7, k8] + - SU3D[6, I1, k11]*SU3D[I2, k8, k9]*SU3D[I4, k11, k9]* - SU3F[I3, k7, k8] + SU3D[6, I2, k11]*SU3D[I1, k11, k9]* - SU3D[I4, k8, k9]*SU3F[I3, k7, k8] + SU3D[6, I1, k11]* - SU3D[I2, k11, k9]*SU3D[I4, k8, k9]*SU3F[I3, k7, k8] + - SU3D[6, I4, k11]*((SU3D[I1, k8, k9]*SU3D[I3, k11, k9] + - SU3D[I1, k11, k9]*SU3D[I3, k8, k9])*SU3F[I2, k7, k8] + - SU3D[I2, k8, k9]*(SU3D[I3, k11, k9]*SU3F[I1, k7, k8] + - SU3D[I1, k11, k9]*SU3F[I3, k7, k8]) + SU3D[I2, k11, k9]* - (SU3D[I3, k8, k9]*SU3F[I1, k7, k8] + SU3D[I1, k8, k9]* - SU3F[I3, k7, k8])) + SU3D[6, I2, k11]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k9]*SU3F[I4, k7, k8] + SU3D[6, I1, k11]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k9]*SU3F[I4, k7, k8] + - SU3D[6, I2, k11]*SU3D[I1, k11, k9]*SU3D[I3, k8, k9]* - SU3F[I4, k7, k8] + SU3D[6, I1, k11]*SU3D[I2, k11, k9]* - SU3D[I3, k8, k9]*SU3F[I4, k7, k8] + SU3D[6, I3, k11]* - ((SU3D[I1, k8, k9]*SU3D[I4, k11, k9] + SU3D[I1, k11, k9]* - SU3D[I4, k8, k9])*SU3F[I2, k7, k8] + SU3D[I2, k8, k9]* - (SU3D[I4, k11, k9]*SU3F[I1, k7, k8] + SU3D[I1, k11, k9]* - SU3F[I4, k7, k8]) + SU3D[I2, k11, k9]* - (SU3D[I4, k8, k9]*SU3F[I1, k7, k8] + SU3D[I1, k8, k9]* - SU3F[I4, k7, k8]))) + SU3D[3, I3, k7]*SU3D[6, I4, k11]* - SU3D[I1, k8, k9]*SU3D[I2, k11, k9]*SU3F[I5, k7, k8] + - SU3D[3, I3, k7]*SU3D[6, I4, k11]*SU3D[I1, k11, k9]*SU3D[I2, k8, k9]* - SU3F[I5, k7, k8] + SU3D[3, I2, k7]*SU3D[6, I4, k11]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k9]*SU3F[I5, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I4, k11]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k9]*SU3F[I5, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I4, k11]*SU3D[I1, k11, k9]*SU3D[I3, k8, k9]* - SU3F[I5, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I4, k11]*SU3D[I2, k11, k9]* - SU3D[I3, k8, k9]*SU3F[I5, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k11]* - SU3D[I1, k8, k9]*SU3D[I4, k11, k9]*SU3F[I5, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k11]*SU3D[I1, k8, k9]*SU3D[I4, k11, k9]* - SU3F[I5, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k11]*SU3D[I2, k8, k9]* - SU3D[I4, k11, k9]*SU3F[I5, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k11]* - SU3D[I2, k8, k9]*SU3D[I4, k11, k9]*SU3F[I5, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I1, k11]*SU3D[I3, k8, k9]*SU3D[I4, k11, k9]* - SU3F[I5, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I2, k11]*SU3D[I3, k8, k9]* - SU3D[I4, k11, k9]*SU3F[I5, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I2, k11]* - SU3D[I1, k11, k9]*SU3D[I4, k8, k9]*SU3F[I5, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I3, k11]*SU3D[I1, k11, k9]*SU3D[I4, k8, k9]* - SU3F[I5, k7, k8] + SU3D[3, I3, k7]*SU3D[6, I1, k11]*SU3D[I2, k11, k9]* - SU3D[I4, k8, k9]*SU3F[I5, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I3, k11]* - SU3D[I2, k11, k9]*SU3D[I4, k8, k9]*SU3F[I5, k7, k8] + - SU3D[3, I2, k7]*SU3D[6, I1, k11]*SU3D[I3, k11, k9]*SU3D[I4, k8, k9]* - SU3F[I5, k7, k8] + SU3D[3, I1, k7]*SU3D[6, I2, k11]*SU3D[I3, k11, k9]* - SU3D[I4, k8, k9]*SU3F[I5, k7, k8] + SU3D[3, I4, k7]* - (SU3D[6, I2, k11]*SU3D[I3, k8, k9]*SU3D[I5, k11, k9]* - SU3F[I1, k7, k8] + SU3D[6, I2, k11]*SU3D[I3, k11, k9]* - SU3D[I5, k8, k9]*SU3F[I1, k7, k8] + SU3D[6, I1, k11]* - SU3D[I3, k8, k9]*SU3D[I5, k11, k9]*SU3F[I2, k7, k8] + - SU3D[6, I1, k11]*SU3D[I3, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I2, k7, k8] + SU3D[6, I2, k11]*SU3D[I1, k8, k9]* - SU3D[I5, k11, k9]*SU3F[I3, k7, k8] + SU3D[6, I1, k11]* - SU3D[I2, k8, k9]*SU3D[I5, k11, k9]*SU3F[I3, k7, k8] + - SU3D[6, I2, k11]*SU3D[I1, k11, k9]*SU3D[I5, k8, k9]* - SU3F[I3, k7, k8] + SU3D[6, I1, k11]*SU3D[I2, k11, k9]* - SU3D[I5, k8, k9]*SU3F[I3, k7, k8] + SU3D[6, I5, k11]* - ((SU3D[I1, k8, k9]*SU3D[I3, k11, k9] + SU3D[I1, k11, k9]* - SU3D[I3, k8, k9])*SU3F[I2, k7, k8] + SU3D[I2, k8, k9]* - (SU3D[I3, k11, k9]*SU3F[I1, k7, k8] + SU3D[I1, k11, k9]* - SU3F[I3, k7, k8]) + SU3D[I2, k11, k9]* - (SU3D[I3, k8, k9]*SU3F[I1, k7, k8] + SU3D[I1, k8, k9]* - SU3F[I3, k7, k8])) + SU3D[6, I2, k11]*SU3D[I1, k8, k9]* - SU3D[I3, k11, k9]*SU3F[I5, k7, k8] + SU3D[6, I1, k11]* - SU3D[I2, k8, k9]*SU3D[I3, k11, k9]*SU3F[I5, k7, k8] + - SU3D[6, I2, k11]*SU3D[I1, k11, k9]*SU3D[I3, k8, k9]* - SU3F[I5, k7, k8] + SU3D[6, I1, k11]*SU3D[I2, k11, k9]* - SU3D[I3, k8, k9]*SU3F[I5, k7, k8] + SU3D[6, I3, k11]* - ((SU3D[I1, k8, k9]*SU3D[I5, k11, k9] + SU3D[I1, k11, k9]* - SU3D[I5, k8, k9])*SU3F[I2, k7, k8] + SU3D[I2, k8, k9]* - (SU3D[I5, k11, k9]*SU3F[I1, k7, k8] + SU3D[I1, k11, k9]* - SU3F[I5, k7, k8]) + SU3D[I2, k11, k9]* - (SU3D[I5, k8, k9]*SU3F[I1, k7, k8] + SU3D[I1, k8, k9]* - SU3F[I5, k7, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I2, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I1, k7, k8] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[I1, k7, k8] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]* - SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k6]*SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I5, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[I1, k7, k8] + - SU3D[6, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I2, k7, k8] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[I2, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]* - SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k6]*SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I2, k7, k8] + - SU3D[6, I1, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I5, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[I2, k7, k8] + - SU3D[6, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[I3, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]* - SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k6]*SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I5, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[I3, k7, k8] + - SU3D[6, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[3, I1, k6]*SU3F[I4, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I1, k6]* - SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k6]* - SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I2, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I3, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[3, I3, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k8, k9]* - SU3F[3, I5, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I5, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k8, k9]* - SU3F[3, I5, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k8, k9]*SU3F[3, I5, k6]*SU3F[I4, k7, k8] + - SU3D[6, I5, k9]*(SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]* - SU3F[I1, k7, k8] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3F[3, I3, k6]* - SU3F[I1, k7, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k7, k8] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[3, I3, k6]* - SU3F[I2, k7, k8] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k6]* - SU3F[I3, k7, k8] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3F[3, I1, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I2, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[3, I2, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I4, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I3, k6]* - SU3F[I4, k7, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I3, k6]* - SU3F[I4, k7, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k6]*SU3F[I1, k7, k8] + - SU3F[3, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k6]*SU3F[I1, k7, k8] + SU3F[3, I1, k6]* - SU3F[I4, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k6]*SU3F[I2, k7, k8] + SU3F[3, I2, k6]* - SU3F[I4, k7, k8])) + SU3D[I3, k6, k7]* - (SU3D[I4, k8, k9]*(SU3F[3, I2, k6]*SU3F[I1, k7, k8] + - SU3F[3, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k8, k9]* - (SU3F[3, I4, k6]*SU3F[I1, k7, k8] + SU3F[3, I1, k6]* - SU3F[I4, k7, k8]) + SU3D[I1, k8, k9]* - (SU3F[3, I4, k6]*SU3F[I2, k7, k8] + SU3F[3, I2, k6]* - SU3F[I4, k7, k8]))) + SU3D[6, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[3, I1, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k6]* - SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I1, k6]*SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I1, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[3, I2, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]* - SU3F[3, I2, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I2, k6]*SU3F[I5, k7, k8] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[3, I2, k6]* - SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[3, I3, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[3, I3, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I3, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]* - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I4, k6]* - SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I4, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[3, I4, k6]*SU3F[I5, k7, k8] + SU3D[6, I4, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I1, k7, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I2, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]*SU3F[I2, k7, k8] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k7, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I1, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I5, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I5, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I3, k6]*SU3F[I5, k7, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k6, k7]*(SU3F[3, I2, k6]* - SU3F[I1, k7, k8] + SU3F[3, I1, k6]*SU3F[I2, k7, k8]) + - SU3D[I2, k6, k7]*(SU3F[3, I5, k6]*SU3F[I1, k7, k8] + - SU3F[3, I1, k6]*SU3F[I5, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k6]*SU3F[I2, k7, k8] + SU3F[3, I2, k6]* - SU3F[I5, k7, k8])) + SU3D[I3, k6, k7]* - (SU3D[I5, k8, k9]*(SU3F[3, I2, k6]*SU3F[I1, k7, k8] + - SU3F[3, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k8, k9]* - (SU3F[3, I5, k6]*SU3F[I1, k7, k8] + SU3F[3, I1, k6]* - SU3F[I5, k7, k8]) + SU3D[I1, k8, k9]* - (SU3F[3, I5, k6]*SU3F[I2, k7, k8] + SU3F[3, I2, k6]* - SU3F[I5, k7, k8]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I2, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k7, k8] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I3, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k7, k8] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I4, k6]* - SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I4, k6]*SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I5, k6]*SU3F[I1, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I5, k6]*SU3F[I1, k7, k8] + - SU3D[6, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I1, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k7, k8] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I3, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k6]*SU3F[I2, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I4, k6]* - SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I4, k6]*SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k7, k8] + - SU3D[6, I1, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I5, k6]*SU3F[I2, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I5, k6]*SU3F[I2, k7, k8] + - SU3D[6, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I1, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I2, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I4, k6]*SU3F[I3, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I4, k6]* - SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I4, k6]*SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I5, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I5, k6]*SU3F[I3, k7, k8] + - SU3D[6, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[8, I1, k6]*SU3F[I4, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I1, k6]* - SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I2, k6]* - SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I2, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[8, I3, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[8, I3, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I4, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k8, k9]* - SU3F[8, I5, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k9]*SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[8, I5, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k8, k9]* - SU3F[8, I5, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k8, k9]*SU3F[8, I5, k6]*SU3F[I4, k7, k8] + - SU3D[6, I5, k9]*(SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k7, k8] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I3, k6]* - SU3F[I1, k7, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k7, k8] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I3, k6]* - SU3F[I2, k7, k8] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k7, k8] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I1, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I2, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I4, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k7, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I3, k6]* - SU3F[I4, k7, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k7, k8] + - SU3F[8, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I1, k7, k8] + SU3F[8, I1, k6]* - SU3F[I4, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k7, k8] + SU3F[8, I2, k6]* - SU3F[I4, k7, k8])) + SU3D[I3, k6, k7]* - (SU3D[I4, k8, k9]*(SU3F[8, I2, k6]*SU3F[I1, k7, k8] + - SU3F[8, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k8, k9]* - (SU3F[8, I4, k6]*SU3F[I1, k7, k8] + SU3F[8, I1, k6]* - SU3F[I4, k7, k8]) + SU3D[I1, k8, k9]* - (SU3F[8, I4, k6]*SU3F[I2, k7, k8] + SU3F[8, I2, k6]* - SU3F[I4, k7, k8]))) + SU3D[6, I3, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I1, k6]*SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I1, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k8, k9]*SU3F[8, I2, k6]*SU3F[I5, k7, k8] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I2, k6]* - SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3F[8, I3, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[8, I3, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k9]*SU3D[I1, k8, k9]* - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I4, k6]* - SU3F[I5, k7, k8] + SU3D[6, I2, k9]*SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[8, I4, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[8, I4, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[8, I4, k6]*SU3F[I5, k7, k8] + SU3D[6, I4, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k7, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I3, k6]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I3, k6]*SU3F[I2, k7, k8] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k7, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I1, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[8, I2, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I5, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I5, k7, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[8, I3, k6]*SU3F[I5, k7, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k6, k7]*(SU3F[8, I2, k6]* - SU3F[I1, k7, k8] + SU3F[8, I1, k6]*SU3F[I2, k7, k8]) + - SU3D[I2, k6, k7]*(SU3F[8, I5, k6]*SU3F[I1, k7, k8] + - SU3F[8, I1, k6]*SU3F[I5, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k7, k8] + SU3F[8, I2, k6]* - SU3F[I5, k7, k8])) + SU3D[I3, k6, k7]* - (SU3D[I5, k8, k9]*(SU3F[8, I2, k6]*SU3F[I1, k7, k8] + - SU3F[8, I1, k6]*SU3F[I2, k7, k8]) + SU3D[I2, k8, k9]* - (SU3F[8, I5, k6]*SU3F[I1, k7, k8] + SU3F[8, I1, k6]* - SU3F[I5, k7, k8]) + SU3D[I1, k8, k9]* - (SU3F[8, I5, k6]*SU3F[I2, k7, k8] + SU3F[8, I2, k6]* - SU3F[I5, k7, k8]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[3, I3, k11]*SU3D[6, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I2, k7, k8] + - SU3D[3, I3, k11]*SU3D[6, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I2, k7, k8] + SU3D[3, I2, k11]*SU3D[6, I5, k8]*SU3D[I4, k6, k7]* - SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + SU3D[3, I2, k11]*SU3D[6, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + - SU3D[3, I1, k11]*SU3D[6, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k7, k8]* - SU3F[I3, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3D[3, I2, k11]*SU3D[6, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k7, k8] + - SU3D[3, I2, k11]*SU3D[6, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I5, k8]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k11, k6]*SU3F[I3, k7, k8] + - SU3D[3, I3, k11]*SU3D[6, I5, k8]*SU3D[I2, k6, k7]*SU3F[I1, k7, k8]* - SU3F[I4, k11, k6] + SU3D[3, I2, k11]*SU3D[6, I5, k8]*SU3D[I3, k6, k7]* - SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + - SU3D[3, I2, k11]*SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k7, k8]* - SU3F[I4, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I5, k8]*SU3D[I1, k6, k7]* - SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + - SU3D[3, I3, k11]*SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[I2, k7, k8]* - SU3F[I4, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I3, k8]*SU3D[I5, k6, k7]* - SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + SU3D[3, I2, k11]*SU3D[6, I5, k8]* - SU3D[I1, k6, k7]*SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + - SU3D[3, I1, k11]*SU3D[6, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8]* - SU3F[I4, k11, k6] + SU3D[3, I2, k11]*SU3D[6, I1, k8]*SU3D[I5, k6, k7]* - SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + - SU3D[3, I3, k11]*SU3D[6, I5, k8]*SU3D[I2, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k7, k8] + SU3D[3, I2, k11]*SU3D[6, I5, k8]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + SU3D[3, I3, k11]*SU3D[6, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + - SU3D[3, I2, k11]*SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k7, k8] + SU3D[3, I3, k11]*SU3D[6, I5, k8]*SU3D[I1, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + - SU3D[3, I3, k11]*SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I3, k8]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + SU3D[3, I2, k11]*SU3D[6, I5, k8]* - SU3D[I1, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + - SU3D[3, I1, k11]*SU3D[6, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k8] + SU3D[3, I2, k11]*SU3D[6, I1, k8]*SU3D[I5, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + - SU3D[3, I5, k11]*(SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[I1, k7, k8]* - SU3F[I3, k11, k6] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3D[6, I2, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k6]*SU3F[I3, k7, k8] + - SU3D[6, I4, k8]*(SU3D[I3, k6, k7]*(SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I3, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k8])) + SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k8]*(SU3D[I4, k6, k7]*(SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k7, k8]))) + SU3D[3, I3, k11]*SU3D[6, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3D[3, I2, k11]*SU3D[6, I4, k8]*SU3D[I3, k6, k7]*SU3F[I1, k7, k8]* - SU3F[I5, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + SU3D[3, I2, k11]*SU3D[6, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3D[3, I3, k11]*SU3D[6, I4, k8]*SU3D[I1, k6, k7]*SU3F[I2, k7, k8]* - SU3F[I5, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I4, k8]*SU3D[I3, k6, k7]* - SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + - SU3D[3, I1, k11]*SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k7, k8]* - SU3F[I5, k11, k6] + SU3D[3, I2, k11]*SU3D[6, I4, k8]*SU3D[I1, k6, k7]* - SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + - SU3D[3, I2, k11]*SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8]* - SU3F[I5, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I2, k8]* - SU3D[I1, k6, k7]*SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + - SU3D[3, I2, k11]*SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[I4, k7, k8]* - SU3F[I5, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + - SU3D[3, I2, k11]*SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[I4, k7, k8]* - SU3F[I5, k11, k6] + SU3D[3, I1, k11]*SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + SU3D[3, I3, k11]*SU3D[6, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[3, I2, k11]*SU3D[6, I4, k8]*SU3D[I3, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k7, k8] + SU3D[3, I3, k11]*SU3D[6, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + SU3D[3, I2, k11]*SU3D[6, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[3, I3, k11]*SU3D[6, I4, k8]*SU3D[I1, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I4, k8]*SU3D[I3, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k7, k8] + SU3D[3, I3, k11]*SU3D[6, I1, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k11, k6]*SU3F[I5, k7, k8] + - SU3D[3, I1, k11]*SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k8] + SU3D[3, I2, k11]*SU3D[6, I4, k8]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + - SU3D[3, I2, k11]*SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + SU3D[3, I3, k11]*SU3D[6, I2, k8]* - SU3D[I1, k6, k7]*SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + - SU3D[3, I2, k11]*SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k8] + SU3D[3, I3, k11]*SU3D[6, I1, k8]*SU3D[I2, k6, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + - SU3D[3, I2, k11]*SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k8] + SU3D[3, I1, k11]*SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + SU3D[3, I4, k11]* - (SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + - SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + - SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k6]*SU3F[I3, k7, k8] + - SU3D[6, I5, k8]*(SU3D[I3, k6, k7]*(SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I3, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k8])) + SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I1, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[I2, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k8]*(SU3D[I5, k6, k7]*(SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k7, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k7, k8]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]* - SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]* - SU3F[3, I5, k11]*SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + - SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I2, k7, k8] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]* - SU3F[3, I4, k11]*SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k7, k8]* - SU3F[I3, k11, k6] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]* - SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[3, I5, k11]*SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + - SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k11, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k8] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]* - SU3F[3, I3, k11]*SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k7, k8]* - SU3F[I4, k11, k6] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]* - SU3F[3, I1, k11]*SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k7, k8]* - SU3F[I4, k11, k6] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[3, I5, k11]* - SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[I3, k7, k8]* - SU3F[I4, k11, k6] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I3, k7, k8]* - SU3F[I4, k11, k6] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]* - SU3F[3, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]* - SU3F[3, I1, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[3, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k8] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k8] + SU3D[6, I5, k8]*(SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k7, k8] + SU3D[I4, k6, k7]* - (SU3F[3, I3, k11]*(SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + SU3F[3, I2, k11]* - (SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k8]) + SU3F[3, I1, k11]* - (SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k8])) + SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[I3, k7, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + - SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k8] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + - SU3D[I3, k6, k7]*(SU3F[3, I4, k11]*(SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + - SU3F[3, I2, k11]*(SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k7, k8]) + SU3F[3, I1, k11]* - (SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k7, k8]))) + SU3D[6, I3, k8]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]*SU3F[I1, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[3, I4, k11]*SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]*SU3F[I2, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]* - SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[I2, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[I3, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[I4, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[I4, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[3, I4, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I4, k8]* - (SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k7, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]* - SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[I1, k11, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k8] + SU3D[I5, k6, k7]*(SU3F[3, I3, k11]* - (SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I2, k7, k8]) + SU3F[3, I2, k11]* - (SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k8]) + SU3F[3, I1, k11]* - (SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k8])) + SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[I3, k7, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k8] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + - SU3D[I3, k6, k7]*(SU3F[3, I5, k11]*(SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + - SU3F[3, I2, k11]*(SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k7, k8]) + SU3F[3, I1, k11]* - (SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k7, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]* - SU3F[8, I5, k11]*SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + - SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I2, k7, k8] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I2, k7, k8] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k8]* - SU3F[I3, k11, k6] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]* - SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + - SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k8] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I3, k7, k8] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6]*SU3F[I3, k7, k8] + - SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k8] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k8]* - SU3F[I4, k11, k6] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]* - SU3F[8, I1, k11]*SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k7, k8]* - SU3F[I4, k11, k6] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k8]* - SU3F[I4, k11, k6] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3F[8, I5, k11]*SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I3, k7, k8]* - SU3F[I4, k11, k6] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k8]*SU3D[I5, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k7, k8] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + SU3D[6, I3, k8]*SU3D[I5, k6, k7]* - SU3F[8, I1, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I2, k8]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k8] + SU3D[6, I1, k8]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + SU3D[6, I2, k8]*SU3D[I1, k6, k7]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + - SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k8] + SU3D[6, I5, k8]*(SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k8] + SU3D[I1, k6, k7]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k7, k8] + SU3D[I4, k6, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + SU3F[8, I2, k11]* - (SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k8]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k8])) + SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I3, k11]*SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k8]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k8] + - SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k8] + SU3D[I2, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + SU3D[I1, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k8] + - SU3D[I3, k6, k7]*(SU3F[8, I4, k11]*(SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + - SU3F[8, I2, k11]*(SU3F[I1, k7, k8]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k7, k8]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k8]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k7, k8]))) + SU3D[6, I3, k8]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]*SU3F[I1, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]*SU3F[I2, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]* - SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[8, I4, k11]*SU3F[I2, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I4, k11]*SU3F[I3, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3F[8, I1, k11]*SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[8, I1, k11]*SU3F[I4, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[8, I2, k11]*SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I4, k7, k8]* - SU3F[I5, k11, k6] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I4, k7, k8]*SU3F[I5, k11, k6] + SU3D[6, I3, k8]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I2, k8]*SU3D[I3, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I3, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I1, k8]*SU3D[I3, k6, k7]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I2, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I4, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I3, k8]*SU3D[I2, k6, k7]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I3, k6, k7]*SU3F[8, I1, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I3, k8]*SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I3, k6, k7]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + - SU3D[6, I2, k8]*SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k8] + SU3D[6, I1, k8]*SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k8] + SU3D[6, I4, k8]* - (SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6]*SU3F[I3, k7, k8] + - SU3D[I1, k6, k7]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k8] + SU3D[I5, k6, k7]*(SU3F[8, I3, k11]* - (SU3F[I1, k7, k8]*SU3F[I2, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I2, k7, k8]) + SU3F[8, I2, k11]* - (SU3F[I1, k7, k8]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k8]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k8]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k8])) + SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I3, k11]*SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k8]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k8] + - SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k8] + SU3D[I2, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + SU3D[I1, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k8] + - SU3D[I3, k6, k7]*(SU3F[8, I5, k11]*(SU3F[I1, k7, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k8]) + - SU3F[8, I2, k11]*(SU3F[I1, k7, k8]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k7, k8]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k8]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k7, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I3, k11]* - SU3F[8, I5, k8]*SU3F[I1, k10, k9]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k9]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9] + - SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I4, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I5, k8]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k8, k9] + SU3F[6, I5, k11]* - (SU3F[8, I4, k8]*(SU3F[I1, k8, k9]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k8, k9])) + SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[8, I1, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[8, I2, k8]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9] + - SU3F[8, I1, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k8, k9] + SU3F[8, I3, k8]*(SU3F[I1, k8, k9]* - (SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k8, k9]))) + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k9]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k9]*SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I2, k11]* - SU3F[8, I3, k8]*SU3F[I1, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k8, k9] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I4, k8]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I2, k11]* - SU3F[8, I3, k8]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I3, k8]*SU3F[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I2, k8]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I4, k11]* - (SU3F[8, I5, k8]*(SU3F[I1, k8, k9]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k8, k9])) + SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[8, I1, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[8, I2, k8]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k8, k9] + - SU3F[8, I1, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k8, k9] + SU3F[8, I3, k8]*(SU3F[I1, k8, k9]* - (SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k8, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3F[3, I3, k8]*SU3F[6, I5, k10]*SU3F[I1, k8, k9]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[3, I3, k8]* - SU3F[6, I5, k10]*SU3F[I1, k11, k9]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I5, k10]* - SU3F[I1, k8, k9]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I5, k10]*SU3F[I2, k8, k9]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I5, k10]* - SU3F[I1, k11, k9]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I5, k10]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + - SU3F[3, I3, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I4, k11, k9] + SU3F[3, I2, k8]*SU3F[6, I5, k10]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3F[3, I1, k8]* - SU3F[6, I5, k10]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3F[3, I2, k8]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k11, k9] + - SU3F[3, I1, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I4, k11, k9] + SU3F[3, I3, k8]*SU3F[6, I5, k10]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9] + - SU3F[3, I3, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9]* - SU3F[I4, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[3, I1, k8]* - SU3F[6, I5, k10]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I4, k8, k9] + - SU3F[3, I1, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I4, k8, k9] + SU3F[3, I5, k8]* - (SU3F[6, I4, k10]*(SU3F[I1, k8, k9]*(SU3F[I2, k11, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k11, k9]) + - SU3F[I1, k11, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k11, k9] + SU3F[I2, k11, k9]* - SU3F[I3, k8, k9])) + SU3F[6, I2, k10]*SU3F[I1, k8, k9]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3F[6, I1, k10]* - SU3F[I2, k8, k9]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3F[6, I2, k10]*SU3F[I1, k11, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[6, I1, k10]*SU3F[I2, k11, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + SU3F[6, I2, k10]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3F[6, I1, k10]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3F[6, I2, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I4, k11, k9] + SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k11, k9] + - SU3F[6, I2, k10]*SU3F[I1, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[6, I1, k10]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[6, I2, k10]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I4, k8, k9] + - SU3F[6, I1, k10]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I4, k8, k9] + SU3F[6, I3, k10]*(SU3F[I1, k8, k9]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9]) + SU3F[I1, k11, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I4, k11, k9] + SU3F[I2, k11, k9]* - SU3F[I4, k8, k9]))) + SU3F[3, I3, k8]*SU3F[6, I4, k10]* - SU3F[I1, k8, k9]*SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + - SU3F[3, I3, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k9]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I4, k10]* - SU3F[I1, k8, k9]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I4, k10]*SU3F[I2, k8, k9]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k9]*SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I4, k10]*SU3F[I2, k11, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I2, k10]* - SU3F[I1, k8, k9]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3F[3, I2, k8]*SU3F[6, I3, k10]*SU3F[I1, k8, k9]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I1, k10]* - SU3F[I2, k8, k9]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I3, k10]*SU3F[I2, k8, k9]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I1, k10]* - SU3F[I3, k8, k9]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I2, k10]*SU3F[I3, k8, k9]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I2, k10]* - SU3F[I1, k11, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[3, I2, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I1, k10]* - SU3F[I2, k11, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I1, k10]* - SU3F[I3, k11, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I4, k10]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + - SU3F[3, I3, k8]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I5, k11, k9] + SU3F[3, I2, k8]*SU3F[6, I4, k10]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3F[3, I1, k8]* - SU3F[6, I4, k10]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3F[3, I2, k8]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k11, k9] + - SU3F[3, I1, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I5, k11, k9] + SU3F[3, I3, k8]*SU3F[6, I2, k10]*SU3F[I1, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3F[3, I2, k8]* - SU3F[6, I3, k10]*SU3F[I1, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3F[3, I3, k8]*SU3F[6, I1, k10]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3F[3, I1, k8]* - SU3F[6, I3, k10]*SU3F[I2, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3F[3, I2, k8]*SU3F[6, I1, k10]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3F[3, I1, k8]* - SU3F[6, I2, k10]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3F[3, I3, k8]*SU3F[6, I2, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k11, k9] + - SU3F[3, I2, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k11, k9] + SU3F[3, I3, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k11, k9] + - SU3F[3, I1, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k11, k9] + SU3F[3, I2, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k11, k9] + - SU3F[3, I1, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k11, k9] + SU3F[3, I3, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11]*SU3F[I5, k8, k9] + - SU3F[3, I3, k8]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9]* - SU3F[I5, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[3, I1, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I5, k8, k9] + - SU3F[3, I1, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I5, k8, k9] + SU3F[3, I3, k8]*SU3F[6, I2, k10]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[3, I2, k8]* - SU3F[6, I3, k10]*SU3F[I1, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[3, I3, k8]*SU3F[6, I1, k10]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[3, I1, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[3, I1, k8]* - SU3F[6, I2, k10]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[3, I3, k8]*SU3F[6, I2, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k8, k9] + - SU3F[3, I2, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k8, k9] + SU3F[3, I3, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k8, k9] + - SU3F[3, I1, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9]*SU3F[I5, k8, k9] + - SU3F[3, I1, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9]* - SU3F[I5, k8, k9] + SU3F[3, I4, k8]* - (SU3F[6, I5, k10]*(SU3F[I1, k8, k9]*(SU3F[I2, k11, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k11, k9]) + - SU3F[I1, k11, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k11, k9] + SU3F[I2, k11, k9]* - SU3F[I3, k8, k9])) + SU3F[6, I2, k10]*SU3F[I1, k8, k9]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3F[6, I1, k10]* - SU3F[I2, k8, k9]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k10]*SU3F[I1, k11, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I1, k10]*SU3F[I2, k11, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + SU3F[6, I2, k10]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3F[6, I1, k10]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3F[6, I2, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I5, k11, k9] + SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k11, k9] + - SU3F[6, I2, k10]*SU3F[I1, k11, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I1, k10]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I2, k10]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k10]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9]* - SU3F[I5, k8, k9] + SU3F[6, I3, k10]*(SU3F[I1, k8, k9]* - (SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k9]) + SU3F[I1, k11, k9]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I5, k11, k9] + SU3F[I2, k11, k9]* - SU3F[I5, k8, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I1] + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I1] + - SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I2] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I2] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I3] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I3] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I3] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I3] + - SU3D[I4, I5, k6]*((SU3F[6, I3, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[3, I1] + - (SU3F[6, I3, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]*SU3F[I3, k6, k8])* - SUNDelta[3, I2] + (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + - SU3F[6, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[3, I3]) + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I4] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I4] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I4] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I4] + - SU3D[I3, I5, k6]*((SU3F[6, I4, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[3, I1] + - (SU3F[6, I4, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]*SU3F[I4, k6, k8])* - SUNDelta[3, I2] + (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + - SU3F[6, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[3, I4]) + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I5] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I5] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I5] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I5] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I5] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I5])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[3, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[3, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[3, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[3, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[3, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[3, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I1, k7]* - SUNDelta[3, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[3, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[3, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k7]* - SUNDelta[3, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[3, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[3, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k7]* - SUNDelta[3, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[3, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[3, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[3, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[3, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[3, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SUNDelta[3, I1] + - SU3F[6, I1, k7]*SUNDelta[3, I2]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[3, I1] + SU3F[6, I1, k7]* - SUNDelta[3, I4]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[3, I2] + SU3F[6, I2, k7]* - SUNDelta[3, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k7]*SUNDelta[3, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SUNDelta[3, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I2, k7]*SUNDelta[3, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SUNDelta[3, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[6, I3, k7]*SUNDelta[3, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[3, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[3, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[6, I4, k7]*SUNDelta[3, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SUNDelta[3, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[6, I5, k7]*SUNDelta[3, I1] + - SU3D[I1, I5, k6]*SU3F[6, I4, k7]*SUNDelta[3, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k7]*SUNDelta[3, I2] + - SU3D[I4, I5, k6]*(SU3F[6, I2, k7]*SUNDelta[3, I1] + - SU3F[6, I1, k7]*SUNDelta[3, I2]) + SU3D[I1, I5, k6]* - SU3F[6, I2, k7]*SUNDelta[3, I4] + SU3D[I1, I2, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I4] + SU3D[I2, I5, k6]*(SU3F[6, I4, k7]* - SUNDelta[3, I1] + SU3F[6, I1, k7]*SUNDelta[3, I4]) + - SU3D[I2, I4, k6]*SU3F[6, I1, k7]*SUNDelta[3, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k7]*SUNDelta[3, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k7]*SUNDelta[3, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/45)*(SU3D[6, I3, k7]*SU3D[I4, I5, k6]*SU3F[I2, k6, k7]* - SUNDelta[3, I1] + SU3D[6, I2, k7]*SU3D[I4, I5, k6]*SU3F[I3, k6, k7]* - SUNDelta[3, I1] + SU3D[6, I3, k7]*SU3D[I2, I5, k6]*SU3F[I4, k6, k7]* - SUNDelta[3, I1] + SU3D[6, I2, k7]*SU3D[I3, I5, k6]*SU3F[I4, k6, k7]* - SUNDelta[3, I1] + SU3D[6, I3, k7]*SU3D[I2, I4, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I1] + SU3D[6, I2, k7]*SU3D[I3, I4, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I1] + SU3D[6, I3, k7]*SU3D[I4, I5, k6]*SU3F[I1, k6, k7]* - SUNDelta[3, I2] + SU3D[6, I1, k7]*SU3D[I4, I5, k6]*SU3F[I3, k6, k7]* - SUNDelta[3, I2] + SU3D[6, I3, k7]*SU3D[I1, I5, k6]*SU3F[I4, k6, k7]* - SUNDelta[3, I2] + SU3D[6, I1, k7]*SU3D[I3, I5, k6]*SU3F[I4, k6, k7]* - SUNDelta[3, I2] + SU3D[6, I3, k7]*SU3D[I1, I4, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I2] + SU3D[6, I1, k7]*SU3D[I3, I4, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I2] + SU3D[6, I2, k7]*SU3D[I4, I5, k6]*SU3F[I1, k6, k7]* - SUNDelta[3, I3] + SU3D[6, I1, k7]*SU3D[I4, I5, k6]*SU3F[I2, k6, k7]* - SUNDelta[3, I3] + SU3D[6, I2, k7]*SU3D[I1, I5, k6]*SU3F[I4, k6, k7]* - SUNDelta[3, I3] + SU3D[6, I1, k7]*SU3D[I2, I5, k6]*SU3F[I4, k6, k7]* - SUNDelta[3, I3] + SU3D[6, I2, k7]*SU3D[I1, I4, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I3] + SU3D[6, I1, k7]*SU3D[I2, I4, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I3] + SU3D[6, I3, k7]*SU3D[I2, I5, k6]*SU3F[I1, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I2, k7]*SU3D[I3, I5, k6]*SU3F[I1, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I3, k7]*SU3D[I1, I5, k6]*SU3F[I2, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I1, k7]*SU3D[I3, I5, k6]*SU3F[I2, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I2, k7]*SU3D[I1, I5, k6]*SU3F[I3, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I1, k7]*SU3D[I2, I5, k6]*SU3F[I3, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I3, k7]*SU3D[I1, I2, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I2, k7]*SU3D[I1, I3, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I1, k7]*SU3D[I2, I3, k6]*SU3F[I5, k6, k7]* - SUNDelta[3, I4] + SU3D[6, I5, k7]*(SU3D[I2, I3, k6]*SU3F[I4, k6, k7]* - SUNDelta[3, I1] + SU3D[I1, I4, k6]*SU3F[I3, k6, k7]* - SUNDelta[3, I2] + SU3D[I1, I3, k6]*SU3F[I4, k6, k7]* - SUNDelta[3, I2] + SU3D[I3, I4, k6]*(SU3F[I2, k6, k7]* - SUNDelta[3, I1] + SU3F[I1, k6, k7]*SUNDelta[3, I2]) + - SU3D[I1, I4, k6]*SU3F[I2, k6, k7]*SUNDelta[3, I3] + - SU3D[I1, I2, k6]*SU3F[I4, k6, k7]*SUNDelta[3, I3] + - SU3D[I2, I4, k6]*(SU3F[I3, k6, k7]*SUNDelta[3, I1] + - SU3F[I1, k6, k7]*SUNDelta[3, I3]) + SU3D[I2, I3, k6]* - SU3F[I1, k6, k7]*SUNDelta[3, I4] + SU3D[I1, I3, k6]* - SU3F[I2, k6, k7]*SUNDelta[3, I4] + SU3D[I1, I2, k6]* - SU3F[I3, k6, k7]*SUNDelta[3, I4]) + SU3D[6, I3, k7]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I3, I4, k6]*SU3F[I1, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I3, k7]*SU3D[I1, I4, k6]*SU3F[I2, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I3, I4, k6]*SU3F[I2, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I1, I4, k6]*SU3F[I3, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I2, I4, k6]*SU3F[I3, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I3, k7]*SU3D[I1, I2, k6]*SU3F[I4, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I1, I3, k6]*SU3F[I4, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I2, I3, k6]*SU3F[I4, k6, k7]*SUNDelta[3, I5] + - SU3D[6, I4, k7]*(SU3D[I2, I3, k6]*SU3F[I5, k6, k7]*SUNDelta[3, I1] + - SU3D[I1, I5, k6]*SU3F[I3, k6, k7]*SUNDelta[3, I2] + - SU3D[I1, I3, k6]*SU3F[I5, k6, k7]*SUNDelta[3, I2] + - SU3D[I3, I5, k6]*(SU3F[I2, k6, k7]*SUNDelta[3, I1] + - SU3F[I1, k6, k7]*SUNDelta[3, I2]) + SU3D[I1, I5, k6]* - SU3F[I2, k6, k7]*SUNDelta[3, I3] + SU3D[I1, I2, k6]* - SU3F[I5, k6, k7]*SUNDelta[3, I3] + SU3D[I2, I5, k6]* - (SU3F[I3, k6, k7]*SUNDelta[3, I1] + SU3F[I1, k6, k7]* - SUNDelta[3, I3]) + SU3D[I2, I3, k6]*SU3F[I1, k6, k7]* - SUNDelta[3, I5] + SU3D[I1, I3, k6]*SU3F[I2, k6, k7]* - SUNDelta[3, I5] + SU3D[I1, I2, k6]*SU3F[I3, k6, k7]* - SUNDelta[3, I5])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I1] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I1] + - SU3D[6, I3, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I1] + - SU3D[6, I2, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I1] + - SU3D[6, I3, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I1] + - SU3D[6, I2, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I1] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I2] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I2] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I2] + - SU3D[6, I1, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I2] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I2] + - SU3D[6, I1, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I2] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I3] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I3] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I3] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I3] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I3] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I3] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k8]*SUNDelta[3, I4] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I2, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[3, I4] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[3, I4] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I5, k7]*(SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[3, I2] + - SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I2] + - SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I3] + - SU3D[I2, I4, k8]*(SU3D[I3, k7, k8]*SUNDelta[3, I1] + - SU3D[I1, k7, k8]*SUNDelta[3, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[3, I4] + SU3D[I1, I2, k8]*SU3D[I3, k7, k8]* - SUNDelta[3, I4] + SU3D[I2, k7, k8]*(SU3D[I3, I4, k8]* - SUNDelta[3, I1] + SU3D[I1, I4, k8]*SUNDelta[3, I3] + - SU3D[I1, I3, k8]*SUNDelta[3, I4])) + SU3D[6, I3, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I4, k8]*SUNDelta[3, I5] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I2, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I4, k7]*(SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[3, I2] + - SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I2] + - SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I3] + - SU3D[I2, I5, k8]*(SU3D[I3, k7, k8]*SUNDelta[3, I1] + - SU3D[I1, k7, k8]*SUNDelta[3, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[3, I5] + SU3D[I1, I2, k8]*SU3D[I3, k7, k8]* - SUNDelta[3, I5] + SU3D[I2, k7, k8]*(SU3D[I3, I5, k8]* - SUNDelta[3, I1] + SU3D[I1, I5, k8]*SUNDelta[3, I3] + - SU3D[I1, I3, k8]*SUNDelta[3, I5])))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3F[3, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[3, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[3, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[3, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[3, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[3, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[3, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[3, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[3, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[3, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[3, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[3, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[3, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I3, I4, k6]*SU3F[3, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[3, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[3, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I2, I5, k6]*SU3F[3, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[3, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[3, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[3, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*SU3F[3, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[3, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[3, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[3, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[3, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[3, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I4, I5, k6]*((SU3F[3, I3, k8]*SU3F[I2, k6, k8] + - SU3F[3, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[6, I1] + - (SU3F[3, I3, k8]*SU3F[I1, k6, k8] + SU3F[3, I1, k8]*SU3F[I3, k6, k8])* - SUNDelta[6, I2] + (SU3F[3, I2, k8]*SU3F[I1, k6, k8] + - SU3F[3, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[6, I3]) + - SU3D[I2, I5, k6]*SU3F[3, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[3, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[3, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[3, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I5, k6]*SU3F[3, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[3, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[3, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[3, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[3, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[3, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I3, I5, k6]*((SU3F[3, I4, k8]*SU3F[I2, k6, k8] + - SU3F[3, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[6, I1] + - (SU3F[3, I4, k8]*SU3F[I1, k6, k8] + SU3F[3, I1, k8]*SU3F[I4, k6, k8])* - SUNDelta[6, I2] + (SU3F[3, I2, k8]*SU3F[I1, k6, k8] + - SU3F[3, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[6, I4]) + - SU3D[I3, I4, k6]*SU3F[3, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[3, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[3, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I3, I4, k6]*SU3F[3, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[3, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[3, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[3, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[3, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[3, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[3, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[3, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[3, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I3, I4, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I2, I5, k6]*SU3F[8, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[8, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*SU3F[8, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[8, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I4, I5, k6]*((SU3F[8, I3, k8]*SU3F[I2, k6, k8] + - SU3F[8, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[6, I1] + - (SU3F[8, I3, k8]*SU3F[I1, k6, k8] + SU3F[8, I1, k8]*SU3F[I3, k6, k8])* - SUNDelta[6, I2] + (SU3F[8, I2, k8]*SU3F[I1, k6, k8] + - SU3F[8, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[6, I3]) + - SU3D[I2, I5, k6]*SU3F[8, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[8, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I5, k6]*SU3F[8, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[8, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I3, I5, k6]*((SU3F[8, I4, k8]*SU3F[I2, k6, k8] + - SU3F[8, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[6, I1] + - (SU3F[8, I4, k8]*SU3F[I1, k6, k8] + SU3F[8, I1, k8]*SU3F[I4, k6, k8])* - SUNDelta[6, I2] + (SU3F[8, I2, k8]*SU3F[I1, k6, k8] + - SU3F[8, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[6, I4]) + - SU3D[I3, I4, k6]*SU3F[8, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[8, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[8, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I3, I4, k6]*SU3F[8, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[8, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[8, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[8, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[8, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[8, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[8, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5])/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[I2, I3, I5]*SUNDelta[3, I4]*SUNDelta[6, I1] + - SU3D[I2, I3, I4]*SUNDelta[3, I5]*SUNDelta[6, I1] + - SU3D[I1, I4, I5]*SUNDelta[3, I3]*SUNDelta[6, I2] + - SU3D[I1, I3, I5]*SUNDelta[3, I4]*SUNDelta[6, I2] + - SU3D[I1, I3, I4]*SUNDelta[3, I5]*SUNDelta[6, I2] + - SU3D[I3, I4, I5]*(SUNDelta[3, I2]*SUNDelta[6, I1] + - SUNDelta[3, I1]*SUNDelta[6, I2]) + SU3D[I1, I4, I5]*SUNDelta[3, I2]* - SUNDelta[6, I3] + SU3D[I1, I2, I5]*SUNDelta[3, I4]*SUNDelta[6, I3] + - SU3D[I1, I2, I4]*SUNDelta[3, I5]*SUNDelta[6, I3] + - SU3D[I2, I4, I5]*(SUNDelta[3, I3]*SUNDelta[6, I1] + - SUNDelta[3, I1]*SUNDelta[6, I3]) + SU3D[I2, I3, I5]*SUNDelta[3, I1]* - SUNDelta[6, I4] + SU3D[I1, I3, I5]*SUNDelta[3, I2]*SUNDelta[6, I4] + - SU3D[I1, I2, I5]*SUNDelta[3, I3]*SUNDelta[6, I4] + - SU3D[I1, I2, I3]*SUNDelta[3, I5]*SUNDelta[6, I4] + - SU3D[I2, I3, I4]*SUNDelta[3, I1]*SUNDelta[6, I5] + - SU3D[I1, I3, I4]*SUNDelta[3, I2]*SUNDelta[6, I5] + - SU3D[I1, I2, I4]*SUNDelta[3, I3]*SUNDelta[6, I5] + - SU3D[I1, I2, I3]*SUNDelta[3, I4]*SUNDelta[6, I5]))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (8*(SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SUNDelta[6, I1] + - SU3D[I1, I4, k6]*SUNDelta[6, I3] + SU3D[I1, I3, k6]* - SUNDelta[6, I4]) + SU3D[I1, I4, k6]*SU3D[I2, I3, k6]* - SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*(SU3D[I3, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SUNDelta[6, I3] + SU3D[I1, I3, k6]* - SUNDelta[6, I5])))/(135*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I2, k7]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[3, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[3, I4, k7]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I1, k7]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[3, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[3, I4, k7]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[3, I1, k7]* - SUNDelta[6, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[3, I1, k7]* - SUNDelta[6, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I1, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[3, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[3, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[3, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[3, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[3, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[3, I1, k7]* - SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[3, I2, k7]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[3, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k7]*SUNDelta[6, I1] + - SU3F[3, I1, k7]*SUNDelta[6, I2]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k7]*SUNDelta[6, I1] + SU3F[3, I1, k7]* - SUNDelta[6, I4]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k7]*SUNDelta[6, I2] + SU3F[3, I2, k7]* - SUNDelta[6, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[3, I1, k7]*SUNDelta[6, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[3, I1, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[3, I2, k7]*SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[3, I2, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[3, I3, k7]*SUNDelta[6, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[3, I3, k7]*SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[3, I3, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[3, I4, k7]*SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[3, I4, k7]*SUNDelta[6, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[3, I5, k7]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3F[3, I4, k7]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[3, I5, k7]*SUNDelta[6, I2] + - SU3D[I4, I5, k6]*(SU3F[3, I2, k7]*SUNDelta[6, I1] + - SU3F[3, I1, k7]*SUNDelta[6, I2]) + SU3D[I1, I5, k6]* - SU3F[3, I2, k7]*SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I4] + SU3D[I2, I5, k6]*(SU3F[3, I4, k7]* - SUNDelta[6, I1] + SU3F[3, I1, k7]*SUNDelta[6, I4]) + - SU3D[I2, I4, k6]*SU3F[3, I1, k7]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[3, I2, k7]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[3, I4, k7]*SUNDelta[6, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I2, k7]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[8, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[8, I4, k7]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I1, k7]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[8, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[8, I4, k7]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[8, I1, k7]* - SUNDelta[6, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[8, I1, k7]* - SUNDelta[6, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I1, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[8, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[8, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[8, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[8, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[8, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[8, I1, k7]* - SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[8, I2, k7]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[8, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k7]*SUNDelta[6, I1] + - SU3F[8, I1, k7]*SUNDelta[6, I2]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k7]*SUNDelta[6, I1] + SU3F[8, I1, k7]* - SUNDelta[6, I4]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k7]*SUNDelta[6, I2] + SU3F[8, I2, k7]* - SUNDelta[6, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[8, I1, k7]*SUNDelta[6, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[8, I1, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[8, I2, k7]*SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[8, I2, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[8, I3, k7]*SUNDelta[6, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[8, I3, k7]*SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[8, I3, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[8, I4, k7]*SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[8, I4, k7]*SUNDelta[6, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[8, I5, k7]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3F[8, I4, k7]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[8, I5, k7]*SUNDelta[6, I2] + - SU3D[I4, I5, k6]*(SU3F[8, I2, k7]*SUNDelta[6, I1] + - SU3F[8, I1, k7]*SUNDelta[6, I2]) + SU3D[I1, I5, k6]* - SU3F[8, I2, k7]*SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I4] + SU3D[I2, I5, k6]*(SU3F[8, I4, k7]* - SUNDelta[6, I1] + SU3F[8, I1, k7]*SUNDelta[6, I4]) + - SU3D[I2, I4, k6]*SU3F[8, I1, k7]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[8, I2, k7]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[8, I4, k7]*SUNDelta[6, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/45)*(SU3D[3, I3, k7]*SU3D[I4, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I2, k7]*SU3D[I4, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I3, k7]*SU3D[I2, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I2, k7]*SU3D[I3, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I3, k7]*SU3D[I2, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I2, k7]*SU3D[I3, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I3, k7]*SU3D[I4, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I1, k7]*SU3D[I4, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I3, k7]*SU3D[I1, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I1, k7]*SU3D[I3, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I3, k7]*SU3D[I1, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I1, k7]*SU3D[I3, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I2, k7]*SU3D[I4, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I1, k7]*SU3D[I4, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I2, k7]*SU3D[I1, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I1, k7]*SU3D[I2, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I2, k7]*SU3D[I1, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I1, k7]*SU3D[I2, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I3, k7]*SU3D[I2, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I2, k7]*SU3D[I3, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I3, k7]*SU3D[I1, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I1, k7]*SU3D[I3, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I2, k7]*SU3D[I1, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I1, k7]*SU3D[I2, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I3, k7]*SU3D[I1, I2, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I2, k7]*SU3D[I1, I3, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I1, k7]*SU3D[I2, I3, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I5, k7]*(SU3D[I2, I3, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[I1, I4, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I2] + SU3D[I1, I3, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[I3, I4, k8]*(SU3F[I2, k7, k8]* - SUNDelta[6, I1] + SU3F[I1, k7, k8]*SUNDelta[6, I2]) + - SU3D[I1, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k8]*(SU3F[I3, k7, k8]*SUNDelta[6, I1] + - SU3F[I1, k7, k8]*SUNDelta[6, I3]) + SU3D[I2, I3, k8]* - SU3F[I1, k7, k8]*SUNDelta[6, I4] + SU3D[I1, I3, k8]* - SU3F[I2, k7, k8]*SUNDelta[6, I4] + SU3D[I1, I2, k8]* - SU3F[I3, k7, k8]*SUNDelta[6, I4]) + SU3D[3, I3, k7]* - SU3D[I2, I4, k8]*SU3F[I1, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I3, I4, k8]*SU3F[I1, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I3, k7]*SU3D[I1, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I3, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, I4, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, I4, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I3, k7]*SU3D[I1, I2, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, I3, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, I3, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I4, k7]*(SU3D[I2, I3, k8]*SU3F[I5, k7, k8]*SUNDelta[6, I1] + - SU3D[I1, I5, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k8]*SU3F[I5, k7, k8]*SUNDelta[6, I2] + - SU3D[I3, I5, k8]*(SU3F[I2, k7, k8]*SUNDelta[6, I1] + - SU3F[I1, k7, k8]*SUNDelta[6, I2]) + SU3D[I1, I5, k8]* - SU3F[I2, k7, k8]*SUNDelta[6, I3] + SU3D[I1, I2, k8]* - SU3F[I5, k7, k8]*SUNDelta[6, I3] + SU3D[I2, I5, k8]* - (SU3F[I3, k7, k8]*SUNDelta[6, I1] + SU3F[I1, k7, k8]* - SUNDelta[6, I3]) + SU3D[I2, I3, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I5] + SU3D[I1, I3, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I5] + SU3D[I1, I2, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I5])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/45)*(SU3D[8, I3, k7]*SU3D[I4, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k7]*SU3D[I4, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k7]*SU3D[I2, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k7]*SU3D[I3, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k7]*SU3D[I2, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k7]*SU3D[I3, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k7]*SU3D[I4, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k7]*SU3D[I4, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I3, k7]*SU3D[I1, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k7]*SU3D[I3, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I3, k7]*SU3D[I1, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k7]*SU3D[I3, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I2, k7]*SU3D[I4, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k7]*SU3D[I4, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I2, k7]*SU3D[I1, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k7]*SU3D[I2, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I2, k7]*SU3D[I1, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k7]*SU3D[I2, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I3, k7]*SU3D[I2, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k7]*SU3D[I3, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I3, k7]*SU3D[I1, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k7]*SU3D[I3, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k7]*SU3D[I1, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k7]*SU3D[I2, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I3, k7]*SU3D[I1, I2, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k7]*SU3D[I1, I3, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k7]*SU3D[I2, I3, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I5, k7]*(SU3D[I2, I3, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[I1, I4, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I2] + SU3D[I1, I3, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[I3, I4, k8]*(SU3F[I2, k7, k8]* - SUNDelta[6, I1] + SU3F[I1, k7, k8]*SUNDelta[6, I2]) + - SU3D[I1, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k8]*(SU3F[I3, k7, k8]*SUNDelta[6, I1] + - SU3F[I1, k7, k8]*SUNDelta[6, I3]) + SU3D[I2, I3, k8]* - SU3F[I1, k7, k8]*SUNDelta[6, I4] + SU3D[I1, I3, k8]* - SU3F[I2, k7, k8]*SUNDelta[6, I4] + SU3D[I1, I2, k8]* - SU3F[I3, k7, k8]*SUNDelta[6, I4]) + SU3D[8, I3, k7]* - SU3D[I2, I4, k8]*SU3F[I1, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I3, I4, k8]*SU3F[I1, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I3, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I4, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I4, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I2, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I3, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I3, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I4, k7]*(SU3D[I2, I3, k8]*SU3F[I5, k7, k8]*SUNDelta[6, I1] + - SU3D[I1, I5, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k8]*SU3F[I5, k7, k8]*SUNDelta[6, I2] + - SU3D[I3, I5, k8]*(SU3F[I2, k7, k8]*SUNDelta[6, I1] + - SU3F[I1, k7, k8]*SUNDelta[6, I2]) + SU3D[I1, I5, k8]* - SU3F[I2, k7, k8]*SUNDelta[6, I3] + SU3D[I1, I2, k8]* - SU3F[I5, k7, k8]*SUNDelta[6, I3] + SU3D[I2, I5, k8]* - (SU3F[I3, k7, k8]*SUNDelta[6, I1] + SU3F[I1, k7, k8]* - SUNDelta[6, I3]) + SU3D[I2, I3, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I5] + SU3D[I1, I3, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I5] + SU3D[I1, I2, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I5])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[3, I3, k7]*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[3, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[3, I3, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[3, I2, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[3, I3, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[3, I2, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[3, I3, k7]*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[3, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[3, I3, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[3, I1, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[3, I3, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[3, I1, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[3, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[3, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[3, I2, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[3, I1, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[3, I2, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[3, I1, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[3, I3, k7]*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SUNDelta[6, I4] + - SU3D[3, I3, k7]*SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I2, k7]*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[3, I1, k7]*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[3, I2, k7]*SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I1, k7]*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I3, k7]*SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I2, k7]*SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I1, k7]*SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I5, k7]*(SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*(SU3D[I3, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SUNDelta[6, I3]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SUNDelta[6, I4] + SU3D[I2, k6, k7]*(SU3D[I3, I4, k6]* - SUNDelta[6, I1] + SU3D[I1, I4, k6]*SUNDelta[6, I3] + - SU3D[I1, I3, k6]*SUNDelta[6, I4])) + SU3D[3, I3, k7]* - SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SUNDelta[6, I5] + - SU3D[3, I3, k7]*SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I3, k7]*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I4, k7]*(SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*(SU3D[I3, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SUNDelta[6, I3]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SUNDelta[6, I5] + SU3D[I2, k6, k7]*(SU3D[I3, I5, k6]* - SUNDelta[6, I1] + SU3D[I1, I5, k6]*SUNDelta[6, I3] + - SU3D[I1, I3, k6]*SUNDelta[6, I5])))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k7]*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[8, I3, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[8, I3, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[8, I2, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[8, I2, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[8, I3, k7]*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SUNDelta[6, I4] + - SU3D[8, I3, k7]*SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I3, k7]*SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I5, k7]*(SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*(SU3D[I3, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SUNDelta[6, I3]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SUNDelta[6, I4] + SU3D[I2, k6, k7]*(SU3D[I3, I4, k6]* - SUNDelta[6, I1] + SU3D[I1, I4, k6]*SUNDelta[6, I3] + - SU3D[I1, I3, k6]*SUNDelta[6, I4])) + SU3D[8, I3, k7]* - SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I4, k7]*(SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*(SU3D[I3, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SUNDelta[6, I3]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SUNDelta[6, I5] + SU3D[I2, k6, k7]*(SU3D[I3, I5, k6]* - SUNDelta[6, I1] + SU3D[I1, I5, k6]*SUNDelta[6, I3] + - SU3D[I1, I3, k6]*SUNDelta[6, I5])))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I2, k6, k8] + - SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k8])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[I4, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I3, k6, k7]*(SU3D[I4, I5, k8]*(SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k8]) + - SU3D[I1, I5, k8]*SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I5, k8]*SU3F[I2, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I2, I5, k8]*(SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k8]) + SU3D[I2, I4, k8]* - SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + SU3D[I1, I4, k8]* - SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + SU3D[I1, I2, k8]* - SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + SU3D[I2, I4, k8]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + SU3D[I1, I4, k8]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + SU3D[I1, I2, k8]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k8]))*SUNDelta[6, k11])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*(SU3D[I1, I5, k8]*SU3D[I2, I3, I4] + SU3D[I1, I4, k8]* - SU3D[I2, I3, I5] + SU3D[I1, I4, I5]*SU3D[I2, I3, k8] + - SU3D[I1, I3, k8]*SU3D[I2, I4, I5] + SU3D[I1, I3, I5]* - SU3D[I2, I4, k8] + SU3D[I1, I3, I4]*SU3D[I2, I5, k8] + - SU3D[I1, I2, k8]*SU3D[I3, I4, I5] + SU3D[I1, I2, I5]* - SU3D[I3, I4, k8] + SU3D[I1, I2, I4]*SU3D[I3, I5, k8] + - SU3D[I1, I2, I3]*SU3D[I4, I5, k8])*SUNDelta[6, k8])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I1, k10, k11]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, I5, k11] + SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I4, I5, k11] + SU3D[I1, I5, k11]* - SU3D[I2, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11] + - SU3D[I1, I5, k11]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k11] + SU3D[I1, k10, k11]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k11]*SU3D[I4, k10, k9] + SU3D[I1, I5, k11]* - SU3D[I2, k8, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9] + - SU3D[I1, k10, k11]*SU3D[I2, I5, k11]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9] + SU3D[I1, I5, k11]*SU3D[I2, k10, k11]* - SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + SU3D[I1, k10, k11]* - SU3D[I2, k10, k9]*SU3D[I3, I5, k11]*SU3D[I4, k8, k9] + - SU3D[I1, I5, k11]*SU3D[I2, k10, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k8, k9] + SU3D[I1, k10, k11]*SU3D[I2, I5, k11]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + SU3D[I1, I5, k11]* - SU3D[I2, k10, k11]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + - SU3D[I1, I4, k11]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I1, I4, k11]*SU3D[I2, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k11] + SU3D[I1, I3, k11]* - SU3D[I2, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11] + - SU3D[I1, I2, k11]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I1, I3, k11]*SU3D[I2, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k11] + SU3D[I1, I2, k11]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k11] + - SU3D[I1, k10, k11]*SU3D[I2, k8, k9]*SU3D[I3, I4, k11]* - SU3D[I5, k10, k9] + SU3D[I1, I4, k11]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k9] + SU3D[I1, k10, k11]* - SU3D[I2, I4, k11]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9] + - SU3D[I1, I4, k11]*SU3D[I2, k10, k11]*SU3D[I3, k8, k9]* - SU3D[I5, k10, k9] + SU3D[I1, I3, k11]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + SU3D[I1, I2, k11]* - SU3D[I3, k8, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I1, k10, k11]*SU3D[I2, I3, k11]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9] + SU3D[I1, I3, k11]*SU3D[I2, k10, k11]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + SU3D[I1, I2, k11]* - SU3D[I3, k10, k11]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + - SU3D[I1, k8, k9]*(SU3D[I2, I5, k11]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k11] + SU3D[I2, I5, k11]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k9] + SU3D[I2, I4, k11]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I2, I3, k11]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I2, k10, k9]* - (SU3D[I3, k10, k11]*SU3D[I4, I5, k11] + SU3D[I3, I5, k11]* - SU3D[I4, k10, k11] + SU3D[I3, I4, k11]*SU3D[I5, k10, k11]) + - SU3D[I2, I4, k11]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I2, I3, k11]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I2, k10, k11]*(SU3D[I3, k10, k9]*SU3D[I4, I5, k11] + - SU3D[I3, I5, k11]*SU3D[I4, k10, k9] + SU3D[I3, I4, k11]* - SU3D[I5, k10, k9])) + SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3D[I3, I4, k11]*SU3D[I5, k8, k9] + SU3D[I1, I4, k11]* - SU3D[I2, k10, k9]*SU3D[I3, k10, k11]*SU3D[I5, k8, k9] + - SU3D[I1, k10, k11]*SU3D[I2, I4, k11]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9] + SU3D[I1, I4, k11]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + SU3D[I1, I3, k11]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k11]*SU3D[I5, k8, k9] + - SU3D[I1, I2, k11]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3D[I5, k8, k9] + SU3D[I1, k10, k11]*SU3D[I2, I3, k11]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + SU3D[I1, I3, k11]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + - SU3D[I1, I2, k11]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9] + SU3D[I1, k10, k9]* - (SU3D[I2, I5, k11]*SU3D[I3, k8, k9]*SU3D[I4, k10, k11] + - SU3D[I2, I5, k11]*SU3D[I3, k10, k11]*SU3D[I4, k8, k9] + - SU3D[I2, I4, k11]*SU3D[I3, k8, k9]*SU3D[I5, k10, k11] + - SU3D[I2, I3, k11]*SU3D[I4, k8, k9]*SU3D[I5, k10, k11] + - SU3D[I2, k8, k9]*(SU3D[I3, k10, k11]*SU3D[I4, I5, k11] + - SU3D[I3, I5, k11]*SU3D[I4, k10, k11] + SU3D[I3, I4, k11]* - SU3D[I5, k10, k11]) + SU3D[I2, I4, k11]*SU3D[I3, k10, k11]* - SU3D[I5, k8, k9] + SU3D[I2, I3, k11]*SU3D[I4, k10, k11]* - SU3D[I5, k8, k9] + SU3D[I2, k10, k11]* - (SU3D[I3, k8, k9]*SU3D[I4, I5, k11] + SU3D[I3, I5, k11]* - SU3D[I4, k8, k9] + SU3D[I3, I4, k11]*SU3D[I5, k8, k9])))* - SUNDelta[6, k8])/(45*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/45)*(SU3D[I2, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I2, I5, k6]*SU3D[I3, k10, k9]* - SU3D[I4, k11, k6]*SU3F[I1, k10, k11] + SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[I2, I3, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I2, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k6]*SU3F[I1, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I1, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I3, k10, k9]*SU3D[I4, I5, k6]* - SU3F[I2, k10, k11] + SU3D[I1, k10, k9]*SU3D[I3, k11, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11] + SU3D[I1, k10, k9]*SU3D[I3, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I2, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k6]*SU3F[I2, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[I1, I4, k6]*SU3D[I3, k11, k6]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k6]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I2, k10, k11] + SU3D[I1, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k6]*SU3F[I2, k10, k11] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I2, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I4, k6]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I4, k6]* - SU3D[I5, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3D[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I3, k6]* - SU3D[I5, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k9]*SU3D[I5, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I4, k6]*SU3D[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I3, k6]* - SU3D[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I2, k11, k6]*(SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I1, k10, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I5, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, I3, k6]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I3, I5, k6]* - (SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I4, k10, k11]) + SU3D[I1, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I4, k6]*SU3F[I5, k10, k11])) + - SU3D[I2, k10, k9]*(SU3D[I3, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I1, k10, k11] + SU3D[I1, k11, k6]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I5, k6]*SU3D[I4, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I3, k6]*SU3D[I5, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I3, I5, k6]* - (SU3D[I4, k11, k6]*SU3F[I1, k10, k11] + SU3D[I1, k11, k6]* - SU3F[I4, k10, k11]) + SU3D[I1, k11, k6]*SU3D[I3, I4, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k11, k6]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I4, k6]*SU3F[I5, k10, k11])))* - SUNDelta[6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/45)*(SU3D[I2, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k6]*SU3F[I1, k10, k9] + SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + - SU3D[I2, I3, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k6]*SU3F[I1, k10, k9] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k6]*SU3F[I1, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I3, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I2, k10, k9] + SU3D[I1, k10, k11]*SU3D[I3, k11, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k9] + SU3D[I1, k11, k6]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + - SU3D[I1, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k9] + SU3D[I1, k10, k11]*SU3D[I3, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I2, k10, k9] + SU3D[I1, I5, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[I1, I4, k6]*SU3D[I3, k11, k6]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k6]*SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I2, k10, k9] + SU3D[I1, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k6]*SU3F[I2, k10, k9] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I3, k10, k9] + SU3D[I1, k11, k6]* - SU3D[I2, I4, k6]*SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + - SU3D[I1, I2, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I5, k11, k6]*SU3F[I3, k10, k9] + SU3D[I1, I2, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I3, k11, k6]*SU3F[I4, k10, k9] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I5, k11, k6]*SU3F[I4, k10, k9] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k6]*SU3F[I4, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3F[I5, k10, k9] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I4, k11, k6]*SU3F[I5, k10, k9] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I2, k11, k6]*(SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[I1, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k9] + SU3D[I1, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k9] + SU3D[I1, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[I1, I3, k6]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I3, I5, k6]*(SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[I1, k10, k11]*SU3F[I4, k10, k9]) + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[I3, k10, k11]*(SU3D[I4, I5, k6]*SU3F[I1, k10, k9] + - SU3D[I1, I5, k6]*SU3F[I4, k10, k9] + SU3D[I1, I4, k6]* - SU3F[I5, k10, k9])) + SU3D[I2, k10, k11]* - (SU3D[I3, I4, k6]*SU3D[I5, k11, k6]*SU3F[I1, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I4, I5, k6]*SU3F[I3, k10, k9] + - SU3D[I1, I5, k6]*SU3D[I4, k11, k6]*SU3F[I3, k10, k9] + - SU3D[I1, I4, k6]*SU3D[I5, k11, k6]*SU3F[I3, k10, k9] + - SU3D[I1, I3, k6]*SU3D[I5, k11, k6]*SU3F[I4, k10, k9] + - SU3D[I3, I5, k6]*(SU3D[I4, k11, k6]*SU3F[I1, k10, k9] + - SU3D[I1, k11, k6]*SU3F[I4, k10, k9]) + SU3D[I1, k11, k6]* - SU3D[I3, I4, k6]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k6]*SU3F[I5, k10, k9] + SU3D[I3, k11, k6]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k9] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k9] + SU3D[I1, I4, k6]*SU3F[I5, k10, k9])))* - SUNDelta[6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/45)*(SU3D[I4, I5, k6]*(SU3F[I1, k11, k6]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k6]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k6])) + SU3D[I2, I5, k6]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[I2, I5, k6]*SU3F[I1, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I5, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I2, I5, k6]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[I1, I5, k6]*SU3F[I2, k11, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I2, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k9] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6]*SU3F[I4, k10, k9] + - SU3D[I2, I5, k6]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, I5, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[I2, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k6] + - SU3D[I1, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k6] + SU3D[I3, I5, k6]* - (SU3F[I1, k11, k6]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k6])) + SU3D[I3, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k9]*SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I2, I4, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k6]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3F[I3, k11, k6]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k6]*SU3F[I1, k10, k9]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I3, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I2, I4, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k9] + SU3D[I2, I3, k6]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I2, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k9] + SU3D[I3, I4, k6]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I2, I4, k6]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k6] + SU3D[I2, I3, k6]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I2, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k6])*SUNDelta[6, k9])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((SU3D[I3, I4, k6]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k6] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I2, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I2, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + SU3D[I2, I3, k6]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I5, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I2, k10, k9]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I5, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I2, I3, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, I5, k6]*SU3D[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I3, I5, k6]*(SU3D[I4, k10, k9]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k6]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6])) + SU3D[I2, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k6]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + SU3D[I1, I5, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + SU3D[I2, I5, k6]* - (SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I4, k11, k6]) + SU3D[I2, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6]))*SUNDelta[6, k9])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/45)*(SU3D[I2, I5, k6]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k11, k6] + SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k6] + SU3D[I2, I4, k6]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k11]*SU3F[I1, k11, k6] + - SU3D[I2, I3, k6]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k6] + SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k6] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I2, k11, k6] + SU3D[I1, k10, k11]*SU3D[I3, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k11]*SU3F[I2, k11, k6] + - SU3D[I1, I5, k6]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k10, k11]*SU3D[I3, I5, k6]* - SU3D[I4, k10, k9]*SU3F[I2, k11, k6] + SU3D[I1, I5, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k10, k9]*SU3F[I2, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I2, k11, k6] + SU3D[I1, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6] + SU3D[I1, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k10, k9]*SU3F[I2, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I2, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I4, k10, k9]*SU3F[I3, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k6]*SU3D[I5, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I1, I2, k6]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I5, k10, k9]*SU3F[I3, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I3, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I3, k10, k9]*SU3F[I4, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3D[I5, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I5, k10, k9]*SU3F[I4, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k9]*SU3F[I4, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I3, k10, k9]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I5, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k10, k9]*(SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k6] + SU3D[I1, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I3, k11, k6] + SU3D[I1, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, I3, k6]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I3, I5, k6]*(SU3D[I4, k10, k11]* - SU3F[I1, k11, k6] + SU3D[I1, k10, k11]*SU3F[I4, k11, k6]) + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3F[I5, k11, k6] + - SU3D[I1, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I3, k10, k11]*(SU3D[I4, I5, k6]*SU3F[I1, k11, k6] + - SU3D[I1, I5, k6]*SU3F[I4, k11, k6] + SU3D[I1, I4, k6]* - SU3F[I5, k11, k6])) + SU3D[I2, k10, k11]* - (SU3D[I3, I4, k6]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I4, I5, k6]*SU3F[I3, k11, k6] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k9]*SU3F[I3, k11, k6] + - SU3D[I1, I4, k6]*SU3D[I5, k10, k9]*SU3F[I3, k11, k6] + - SU3D[I1, I3, k6]*SU3D[I5, k10, k9]*SU3F[I4, k11, k6] + - SU3D[I3, I5, k6]*(SU3D[I4, k10, k9]*SU3F[I1, k11, k6] + - SU3D[I1, k10, k9]*SU3F[I4, k11, k6]) + SU3D[I1, k10, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I5, k11, k6] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k11, k6] + SU3D[I1, I5, k6]* - SU3F[I4, k11, k6] + SU3D[I1, I4, k6]*SU3F[I5, k11, k6])))* - SUNDelta[6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[I3, I4, k6]*SU3D[I5, k10, k6]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3D[I3, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k9] + SU3D[I2, k10, k6]* - SU3D[I4, I5, k6]*SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11] + SU3D[I2, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3D[I1, k10, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k6]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[I2, k10, k6]* - SU3D[I4, I5, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9] + SU3D[I2, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + SU3D[I1, k10, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k6]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k9] + SU3D[I1, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + SU3D[I2, I3, k6]* - SU3D[I5, k10, k6]*SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I5, k10, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k6]*SU3D[I2, I5, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I2, k10, k6]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I5, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[I2, I3, k6]*SU3D[I5, k10, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + SU3D[I1, I3, k6]* - SU3D[I5, k10, k6]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + - SU3D[I1, k10, k6]*SU3D[I2, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[I1, I5, k6]*SU3D[I2, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[I1, I2, k6]* - SU3D[I5, k10, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[I3, I5, k6]*(SU3D[I4, k10, k6]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k6]*(SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k9]) + SU3D[I1, k10, k6]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9])) + SU3D[I2, k10, k6]*SU3D[I3, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k6]*SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I1, k10, k6]*SU3D[I3, I4, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k10, k6]* - SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3D[I1, k10, k6]* - SU3D[I2, I4, k6]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3D[I4, k10, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[I1, k10, k6]* - SU3D[I2, I3, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I2, k10, k6]*SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k6]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[I1, k10, k6]*SU3D[I3, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I3, k6]*SU3D[I4, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + SU3D[I1, k10, k6]* - SU3D[I2, I4, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I2, k6]*SU3D[I4, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[I1, k10, k6]* - SU3D[I2, I3, k6]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I3, k10, k6]* - (SU3D[I4, I5, k6]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + SU3D[I1, I5, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[I2, I5, k6]* - (SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I4, k11, k9]) + SU3D[I2, I4, k6]*SU3F[I1, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I2, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9]))*SUNDelta[6, k9])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I1] + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I2] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I4, I5, k6]*((SU3F[6, I3, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[8, I1] + - (SU3F[6, I3, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]*SU3F[I3, k6, k8])* - SUNDelta[8, I2] + (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + - SU3F[6, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[8, I3]) + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I3, I5, k6]*((SU3F[6, I4, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[8, I1] + - (SU3F[6, I4, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]*SU3F[I4, k6, k8])* - SUNDelta[8, I2] + (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + - SU3F[6, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[8, I4]) + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5])/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[I2, I3, I5]*SUNDelta[6, I4]*SUNDelta[8, I1] + - SU3D[I2, I3, I4]*SUNDelta[6, I5]*SUNDelta[8, I1] + - SU3D[I1, I4, I5]*SUNDelta[6, I3]*SUNDelta[8, I2] + - SU3D[I1, I3, I5]*SUNDelta[6, I4]*SUNDelta[8, I2] + - SU3D[I1, I3, I4]*SUNDelta[6, I5]*SUNDelta[8, I2] + - SU3D[I3, I4, I5]*(SUNDelta[6, I2]*SUNDelta[8, I1] + - SUNDelta[6, I1]*SUNDelta[8, I2]) + SU3D[I1, I4, I5]*SUNDelta[6, I2]* - SUNDelta[8, I3] + SU3D[I1, I2, I5]*SUNDelta[6, I4]*SUNDelta[8, I3] + - SU3D[I1, I2, I4]*SUNDelta[6, I5]*SUNDelta[8, I3] + - SU3D[I2, I4, I5]*(SUNDelta[6, I3]*SUNDelta[8, I1] + - SUNDelta[6, I1]*SUNDelta[8, I3]) + SU3D[I2, I3, I5]*SUNDelta[6, I1]* - SUNDelta[8, I4] + SU3D[I1, I3, I5]*SUNDelta[6, I2]*SUNDelta[8, I4] + - SU3D[I1, I2, I5]*SUNDelta[6, I3]*SUNDelta[8, I4] + - SU3D[I1, I2, I3]*SUNDelta[6, I5]*SUNDelta[8, I4] + - SU3D[I2, I3, I4]*SUNDelta[6, I1]*SUNDelta[8, I5] + - SU3D[I1, I3, I4]*SUNDelta[6, I2]*SUNDelta[8, I5] + - SU3D[I1, I2, I4]*SUNDelta[6, I3]*SUNDelta[8, I5] + - SU3D[I1, I2, I3]*SUNDelta[6, I4]*SUNDelta[8, I5]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SUNDelta[8, I1] + - SU3F[6, I1, k7]*SUNDelta[8, I2]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[8, I1] + SU3F[6, I1, k7]* - SUNDelta[8, I4]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[8, I2] + SU3F[6, I2, k7]* - SUNDelta[8, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k7]*SUNDelta[8, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I2, k7]*SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[6, I4, k7]*SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SUNDelta[8, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[6, I5, k7]*SUNDelta[8, I1] + - SU3D[I1, I5, k6]*SU3F[6, I4, k7]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k7]*SUNDelta[8, I2] + - SU3D[I4, I5, k6]*(SU3F[6, I2, k7]*SUNDelta[8, I1] + - SU3F[6, I1, k7]*SUNDelta[8, I2]) + SU3D[I1, I5, k6]* - SU3F[6, I2, k7]*SUNDelta[8, I4] + SU3D[I1, I2, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I2, I5, k6]*(SU3F[6, I4, k7]* - SUNDelta[8, I1] + SU3F[6, I1, k7]*SUNDelta[8, I4]) + - SU3D[I2, I4, k6]*SU3F[6, I1, k7]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k7]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k7]*SUNDelta[8, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/45)*(SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I5, k8]*(SU3D[I2, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[I1, I4, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[I3, I4, k6]*(SU3F[I2, k6, k8]* - SUNDelta[8, I1] + SU3F[I1, k6, k8]*SUNDelta[8, I2]) + - SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*(SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3F[I1, k6, k8]*SUNDelta[8, I3]) + SU3D[I2, I3, k6]* - SU3F[I1, k6, k8]*SUNDelta[8, I4] + SU3D[I1, I3, k6]* - SU3F[I2, k6, k8]*SUNDelta[8, I4] + SU3D[I1, I2, k6]* - SU3F[I3, k6, k8]*SUNDelta[8, I4]) + SU3D[6, I3, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I4, k8]*(SU3D[I2, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I1, I5, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I3, I5, k6]*(SU3F[I2, k6, k8]*SUNDelta[8, I1] + - SU3F[I1, k6, k8]*SUNDelta[8, I2]) + SU3D[I1, I5, k6]* - SU3F[I2, k6, k8]*SUNDelta[8, I3] + SU3D[I1, I2, k6]* - SU3F[I5, k6, k8]*SUNDelta[8, I3] + SU3D[I2, I5, k6]* - (SU3F[I3, k6, k8]*SUNDelta[8, I1] + SU3F[I1, k6, k8]* - SUNDelta[8, I3]) + SU3D[I2, I3, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I5] + SU3D[I1, I2, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I5])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I2] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I3] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I2, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I5, k7]*(SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k8]*(SU3D[I3, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SUNDelta[8, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[8, I4] + SU3D[I1, I2, k8]*SU3D[I3, k7, k8]* - SUNDelta[8, I4] + SU3D[I2, k7, k8]*(SU3D[I3, I4, k8]* - SUNDelta[8, I1] + SU3D[I1, I4, k8]*SUNDelta[8, I3] + - SU3D[I1, I3, k8]*SUNDelta[8, I4])) + SU3D[6, I3, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I2, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I4, k7]*(SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[I2, I5, k8]*(SU3D[I3, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SUNDelta[8, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[8, I5] + SU3D[I1, I2, k8]*SU3D[I3, k7, k8]* - SUNDelta[8, I5] + SU3D[I2, k7, k8]*(SU3D[I3, I5, k8]* - SUNDelta[8, I1] + SU3D[I1, I5, k8]*SUNDelta[8, I3] + - SU3D[I1, I3, k8]*SUNDelta[8, I5])))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((4*I)/135)*SUNDelta[6, k8]*(SU3D[I3, I4, k5]*SU3F[I5, k5, k8]* - SUNDelta[I1, I2] + SU3D[I2, I5, k5]*SU3F[I4, k5, k8]* - SUNDelta[I1, I3] + SU3D[I2, I4, k5]*SU3F[I5, k5, k8]* - SUNDelta[I1, I3] + SU3D[I2, I5, k5]*SU3F[I3, k5, k8]* - SUNDelta[I1, I4] + SU3D[I2, I3, k5]*SU3F[I5, k5, k8]* - SUNDelta[I1, I4] + SU3D[I3, I4, k5]*SU3F[I2, k5, k8]* - SUNDelta[I1, I5] + SU3D[I2, I4, k5]*SU3F[I3, k5, k8]* - SUNDelta[I1, I5] + SU3D[I2, I3, k5]*SU3F[I4, k5, k8]* - SUNDelta[I1, I5] + SU3D[I1, I5, k5]*SU3F[I4, k5, k8]* - SUNDelta[I2, I3] + SU3D[I1, I4, k5]*SU3F[I5, k5, k8]* - SUNDelta[I2, I3] + SU3D[I4, I5, k5]* - (SU3F[I3, k5, k8]*SUNDelta[I1, I2] + SU3F[I2, k5, k8]* - SUNDelta[I1, I3] + SU3F[I1, k5, k8]*SUNDelta[I2, I3]) + - SU3D[I1, I5, k5]*SU3F[I3, k5, k8]*SUNDelta[I2, I4] + - SU3D[I1, I3, k5]*SU3F[I5, k5, k8]*SUNDelta[I2, I4] + - SU3D[I3, I5, k5]*(SU3F[I4, k5, k8]*SUNDelta[I1, I2] + - SU3F[I2, k5, k8]*SUNDelta[I1, I4] + SU3F[I1, k5, k8]* - SUNDelta[I2, I4]) + SU3D[I3, I4, k5]*SU3F[I1, k5, k8]* - SUNDelta[I2, I5] + SU3D[I1, I4, k5]*SU3F[I3, k5, k8]* - SUNDelta[I2, I5] + SU3D[I1, I3, k5]*SU3F[I4, k5, k8]* - SUNDelta[I2, I5] + SU3D[I2, I5, k5]*SU3F[I1, k5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I5, k5]*SU3F[I2, k5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I2, k5]*SU3F[I5, k5, k8]* - SUNDelta[I3, I4] + SU3D[I2, I4, k5]*SU3F[I1, k5, k8]* - SUNDelta[I3, I5] + SU3D[I1, I4, k5]*SU3F[I2, k5, k8]* - SUNDelta[I3, I5] + SU3D[I1, I2, k5]*SU3F[I4, k5, k8]* - SUNDelta[I3, I5] + SU3D[I2, I3, k5]*SU3F[I1, k5, k8]* - SUNDelta[I4, I5] + SU3D[I1, I3, k5]*SU3F[I2, k5, k8]* - SUNDelta[I4, I5] + SU3D[I1, I2, k5]*SU3F[I3, k5, k8]* - SUNDelta[I4, I5]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (4*(SU3D[6, I3, I4]*SUNDelta[3, I5]*SUNDelta[I1, I2] + - SU3D[6, I2, I5]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - SU3D[6, I2, I4]*SUNDelta[3, I5]*SUNDelta[I1, I3] + - SU3D[6, I2, I5]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - SU3D[6, I2, I3]*SUNDelta[3, I5]*SUNDelta[I1, I4] + - SU3D[6, I3, I4]*SUNDelta[3, I2]*SUNDelta[I1, I5] + - SU3D[6, I2, I4]*SUNDelta[3, I3]*SUNDelta[I1, I5] + - SU3D[6, I2, I3]*SUNDelta[3, I4]*SUNDelta[I1, I5] + - SU3D[6, I1, I5]*SUNDelta[3, I4]*SUNDelta[I2, I3] + - SU3D[6, I1, I4]*SUNDelta[3, I5]*SUNDelta[I2, I3] + - SU3D[6, I4, I5]*(SUNDelta[3, I3]*SUNDelta[I1, I2] + - SUNDelta[3, I2]*SUNDelta[I1, I3] + SUNDelta[3, I1]* - SUNDelta[I2, I3]) + SU3D[6, I1, I5]*SUNDelta[3, I3]* - SUNDelta[I2, I4] + SU3D[6, I1, I3]*SUNDelta[3, I5]*SUNDelta[I2, I4] + - SU3D[6, I3, I5]*(SUNDelta[3, I4]*SUNDelta[I1, I2] + - SUNDelta[3, I2]*SUNDelta[I1, I4] + SUNDelta[3, I1]* - SUNDelta[I2, I4]) + SU3D[6, I3, I4]*SUNDelta[3, I1]* - SUNDelta[I2, I5] + SU3D[6, I1, I4]*SUNDelta[3, I3]*SUNDelta[I2, I5] + - SU3D[6, I1, I3]*SUNDelta[3, I4]*SUNDelta[I2, I5] + - SU3D[6, I2, I5]*SUNDelta[3, I1]*SUNDelta[I3, I4] + - SU3D[6, I1, I5]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - SU3D[6, I1, I2]*SUNDelta[3, I5]*SUNDelta[I3, I4] + - SU3D[6, I2, I4]*SUNDelta[3, I1]*SUNDelta[I3, I5] + - SU3D[6, I1, I4]*SUNDelta[3, I2]*SUNDelta[I3, I5] + - SU3D[6, I1, I2]*SUNDelta[3, I4]*SUNDelta[I3, I5] + - SU3D[6, I2, I3]*SUNDelta[3, I1]*SUNDelta[I4, I5] + - SU3D[6, I1, I3]*SUNDelta[3, I2]*SUNDelta[I4, I5] + - SU3D[6, I1, I2]*SUNDelta[3, I3]*SUNDelta[I4, I5]))/ - (135*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*(SU3D[3, I3, I4]*SUNDelta[6, I5]*SUNDelta[I1, I2] + - SU3D[3, I2, I5]*SUNDelta[6, I4]*SUNDelta[I1, I3] + - SU3D[3, I2, I4]*SUNDelta[6, I5]*SUNDelta[I1, I3] + - SU3D[3, I2, I5]*SUNDelta[6, I3]*SUNDelta[I1, I4] + - SU3D[3, I2, I3]*SUNDelta[6, I5]*SUNDelta[I1, I4] + - SU3D[3, I3, I4]*SUNDelta[6, I2]*SUNDelta[I1, I5] + - SU3D[3, I2, I4]*SUNDelta[6, I3]*SUNDelta[I1, I5] + - SU3D[3, I2, I3]*SUNDelta[6, I4]*SUNDelta[I1, I5] + - SU3D[3, I1, I5]*SUNDelta[6, I4]*SUNDelta[I2, I3] + - SU3D[3, I1, I4]*SUNDelta[6, I5]*SUNDelta[I2, I3] + - SU3D[3, I4, I5]*(SUNDelta[6, I3]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I3] + SUNDelta[6, I1]* - SUNDelta[I2, I3]) + SU3D[3, I1, I5]*SUNDelta[6, I3]* - SUNDelta[I2, I4] + SU3D[3, I1, I3]*SUNDelta[6, I5]*SUNDelta[I2, I4] + - SU3D[3, I3, I5]*(SUNDelta[6, I4]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I4] + SUNDelta[6, I1]* - SUNDelta[I2, I4]) + SU3D[3, I3, I4]*SUNDelta[6, I1]* - SUNDelta[I2, I5] + SU3D[3, I1, I4]*SUNDelta[6, I3]*SUNDelta[I2, I5] + - SU3D[3, I1, I3]*SUNDelta[6, I4]*SUNDelta[I2, I5] + - SU3D[3, I2, I5]*SUNDelta[6, I1]*SUNDelta[I3, I4] + - SU3D[3, I1, I5]*SUNDelta[6, I2]*SUNDelta[I3, I4] + - SU3D[3, I1, I2]*SUNDelta[6, I5]*SUNDelta[I3, I4] + - SU3D[3, I2, I4]*SUNDelta[6, I1]*SUNDelta[I3, I5] + - SU3D[3, I1, I4]*SUNDelta[6, I2]*SUNDelta[I3, I5] + - SU3D[3, I1, I2]*SUNDelta[6, I4]*SUNDelta[I3, I5] + - SU3D[3, I2, I3]*SUNDelta[6, I1]*SUNDelta[I4, I5] + - SU3D[3, I1, I3]*SUNDelta[6, I2]*SUNDelta[I4, I5] + - SU3D[3, I1, I2]*SUNDelta[6, I3]*SUNDelta[I4, I5]))/ - (135*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*(SU3D[8, I3, I4]*SUNDelta[6, I5]*SUNDelta[I1, I2] + - SU3D[8, I2, I5]*SUNDelta[6, I4]*SUNDelta[I1, I3] + - SU3D[8, I2, I4]*SUNDelta[6, I5]*SUNDelta[I1, I3] + - SU3D[8, I2, I5]*SUNDelta[6, I3]*SUNDelta[I1, I4] + - SU3D[8, I2, I3]*SUNDelta[6, I5]*SUNDelta[I1, I4] + - SU3D[8, I3, I4]*SUNDelta[6, I2]*SUNDelta[I1, I5] + - SU3D[8, I2, I4]*SUNDelta[6, I3]*SUNDelta[I1, I5] + - SU3D[8, I2, I3]*SUNDelta[6, I4]*SUNDelta[I1, I5] + - SU3D[8, I1, I5]*SUNDelta[6, I4]*SUNDelta[I2, I3] + - SU3D[8, I1, I4]*SUNDelta[6, I5]*SUNDelta[I2, I3] + - SU3D[8, I4, I5]*(SUNDelta[6, I3]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I3] + SUNDelta[6, I1]* - SUNDelta[I2, I3]) + SU3D[8, I1, I5]*SUNDelta[6, I3]* - SUNDelta[I2, I4] + SU3D[8, I1, I3]*SUNDelta[6, I5]*SUNDelta[I2, I4] + - SU3D[8, I3, I5]*(SUNDelta[6, I4]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I4] + SUNDelta[6, I1]* - SUNDelta[I2, I4]) + SU3D[8, I3, I4]*SUNDelta[6, I1]* - SUNDelta[I2, I5] + SU3D[8, I1, I4]*SUNDelta[6, I3]*SUNDelta[I2, I5] + - SU3D[8, I1, I3]*SUNDelta[6, I4]*SUNDelta[I2, I5] + - SU3D[8, I2, I5]*SUNDelta[6, I1]*SUNDelta[I3, I4] + - SU3D[8, I1, I5]*SUNDelta[6, I2]*SUNDelta[I3, I4] + - SU3D[8, I1, I2]*SUNDelta[6, I5]*SUNDelta[I3, I4] + - SU3D[8, I2, I4]*SUNDelta[6, I1]*SUNDelta[I3, I5] + - SU3D[8, I1, I4]*SUNDelta[6, I2]*SUNDelta[I3, I5] + - SU3D[8, I1, I2]*SUNDelta[6, I4]*SUNDelta[I3, I5] + - SU3D[8, I2, I3]*SUNDelta[6, I1]*SUNDelta[I4, I5] + - SU3D[8, I1, I3]*SUNDelta[6, I2]*SUNDelta[I4, I5] + - SU3D[8, I1, I2]*SUNDelta[6, I3]*SUNDelta[I4, I5]))/ - (135*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 5) - (4*(SU3D[6, I3, I4]*SUNDelta[8, I5]*SUNDelta[I1, I2] + - SU3D[6, I2, I5]*SUNDelta[8, I4]*SUNDelta[I1, I3] + - SU3D[6, I2, I4]*SUNDelta[8, I5]*SUNDelta[I1, I3] + - SU3D[6, I2, I5]*SUNDelta[8, I3]*SUNDelta[I1, I4] + - SU3D[6, I2, I3]*SUNDelta[8, I5]*SUNDelta[I1, I4] + - SU3D[6, I3, I4]*SUNDelta[8, I2]*SUNDelta[I1, I5] + - SU3D[6, I2, I4]*SUNDelta[8, I3]*SUNDelta[I1, I5] + - SU3D[6, I2, I3]*SUNDelta[8, I4]*SUNDelta[I1, I5] + - SU3D[6, I1, I5]*SUNDelta[8, I4]*SUNDelta[I2, I3] + - SU3D[6, I1, I4]*SUNDelta[8, I5]*SUNDelta[I2, I3] + - SU3D[6, I4, I5]*(SUNDelta[8, I3]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I3] + SUNDelta[8, I1]* - SUNDelta[I2, I3]) + SU3D[6, I1, I5]*SUNDelta[8, I3]* - SUNDelta[I2, I4] + SU3D[6, I1, I3]*SUNDelta[8, I5]*SUNDelta[I2, I4] + - SU3D[6, I3, I5]*(SUNDelta[8, I4]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I4] + SUNDelta[8, I1]* - SUNDelta[I2, I4]) + SU3D[6, I3, I4]*SUNDelta[8, I1]* - SUNDelta[I2, I5] + SU3D[6, I1, I4]*SUNDelta[8, I3]*SUNDelta[I2, I5] + - SU3D[6, I1, I3]*SUNDelta[8, I4]*SUNDelta[I2, I5] + - SU3D[6, I2, I5]*SUNDelta[8, I1]*SUNDelta[I3, I4] + - SU3D[6, I1, I5]*SUNDelta[8, I2]*SUNDelta[I3, I4] + - SU3D[6, I1, I2]*SUNDelta[8, I5]*SUNDelta[I3, I4] + - SU3D[6, I2, I4]*SUNDelta[8, I1]*SUNDelta[I3, I5] + - SU3D[6, I1, I4]*SUNDelta[8, I2]*SUNDelta[I3, I5] + - SU3D[6, I1, I2]*SUNDelta[8, I4]*SUNDelta[I3, I5] + - SU3D[6, I2, I3]*SUNDelta[8, I1]*SUNDelta[I4, I5] + - SU3D[6, I1, I3]*SUNDelta[8, I2]*SUNDelta[I4, I5] + - SU3D[6, I1, I2]*SUNDelta[8, I3]*SUNDelta[I4, I5]))/ - (135*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 5) - (((8*I)/135)*(SU3F[3, 6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SU3F[3, 6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - SU3F[3, 6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - SU3F[3, 6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - SUNDelta[I2, I5]*(SU3F[3, 6, I4]*SUNDelta[I1, I3] + - SU3F[3, 6, I3]*SUNDelta[I1, I4] + SU3F[3, 6, I1]*SUNDelta[I3, I4]) + - SU3F[3, 6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - SU3F[3, 6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - SUNDelta[I2, I4]*(SU3F[3, 6, I5]*SUNDelta[I1, I3] + - SU3F[3, 6, I3]*SUNDelta[I1, I5] + SU3F[3, 6, I1]*SUNDelta[I3, I5]) + - SU3F[3, 6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - SU3F[3, 6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - SU3F[3, 6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((8*I)/135)*(SU3F[6, 8, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SU3F[6, 8, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - SU3F[6, 8, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - SU3F[6, 8, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - SUNDelta[I2, I5]*(SU3F[6, 8, I4]*SUNDelta[I1, I3] + - SU3F[6, 8, I3]*SUNDelta[I1, I4] + SU3F[6, 8, I1]*SUNDelta[I3, I4]) + - SU3F[6, 8, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - SU3F[6, 8, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - SUNDelta[I2, I4]*(SU3F[6, 8, I5]*SUNDelta[I1, I3] + - SU3F[6, 8, I3]*SUNDelta[I1, I5] + SU3F[6, 8, I1]*SUNDelta[I3, I5]) + - SU3F[6, 8, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - SU3F[6, 8, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - SU3F[6, 8, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (16*(SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[6, I5]*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I3]*SUNDelta[I2, I4] + SUNDelta[I1, I2]* - SUNDelta[I3, I4]) + SUNDelta[6, I2]*SUNDelta[I1, I4]* - SUNDelta[I3, I5] + SUNDelta[6, I1]*SUNDelta[I2, I4]* - SUNDelta[I3, I5] + SUNDelta[6, I4]* - (SUNDelta[I1, I5]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I5] + SUNDelta[I1, I2]*SUNDelta[I3, I5]) + - SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ - (405*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, k7]*(SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[I1, I2] + - SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[I1, I3] + - SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[I1, I3] + - SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[I1, I3] + - SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[I1, I4] + - SU3D[I2, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[I1, I5] + - SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[I1, I5] + - SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[I2, I3] + - SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[I2, I3] + - SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[I2, I3] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[I2, I4] + - SU3D[I3, I5, k8]*(SU3D[I4, k7, k8]*SUNDelta[I1, I2] + - SU3D[I2, k7, k8]*SUNDelta[I1, I4] + SU3D[I1, k7, k8]* - SUNDelta[I2, I4]) + SU3D[I1, k7, k8]*SU3D[I3, I4, k8]* - SUNDelta[I2, I5] + SU3D[I1, I3, k8]*SU3D[I4, k7, k8]* - SUNDelta[I2, I5] + SU3D[I1, k7, k8]*SU3D[I2, I5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I5, k8]*SU3D[I2, k7, k8]* - SUNDelta[I3, I4] + SU3D[I1, I2, k8]*SU3D[I5, k7, k8]* - SUNDelta[I3, I4] + SU3D[I1, k7, k8]*SU3D[I2, I4, k8]* - SUNDelta[I3, I5] + SU3D[I1, I4, k8]*SU3D[I2, k7, k8]* - SUNDelta[I3, I5] + SU3D[I1, I2, k8]*SU3D[I4, k7, k8]* - SUNDelta[I3, I5] + SU3D[I1, k7, k8]*SU3D[I2, I3, k8]* - SUNDelta[I4, I5] + SU3D[I1, I3, k8]*SU3D[I2, k7, k8]* - SUNDelta[I4, I5] + SU3D[I3, k7, k8]* - (SU3D[I4, I5, k8]*SUNDelta[I1, I2] + SU3D[I2, I5, k8]* - SUNDelta[I1, I4] + SU3D[I2, I4, k8]*SUNDelta[I1, I5] + - SU3D[I1, I5, k8]*SUNDelta[I2, I4] + SU3D[I1, I4, k8]* - SUNDelta[I2, I5] + SU3D[I1, I2, k8]*SUNDelta[I4, I5])))/ - (135*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 2]* -((2*(SU3D[3, I3, k7]*SU3D[6, I4, I5]*SU3D[I1, I2, k7] + - SU3D[3, I2, k7]*SU3D[6, I4, I5]*SU3D[I1, I3, k7] + - SU3D[3, I3, k7]*SU3D[6, I2, I5]*SU3D[I1, I4, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, I5]*SU3D[I1, I4, k7] + - SU3D[3, I3, k7]*SU3D[6, I2, I4]*SU3D[I1, I5, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, I4]*SU3D[I1, I5, k7] + - SU3D[3, I1, k7]*SU3D[6, I4, I5]*SU3D[I2, I3, k7] + - SU3D[3, I3, k7]*SU3D[6, I1, I5]*SU3D[I2, I4, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, I5]*SU3D[I2, I4, k7] + - SU3D[3, I3, k7]*SU3D[6, I1, I4]*SU3D[I2, I5, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, I4]*SU3D[I2, I5, k7] + - SU3D[3, I2, k7]*SU3D[6, I1, I5]*SU3D[I3, I4, k7] + - SU3D[3, I1, k7]*SU3D[6, I2, I5]*SU3D[I3, I4, k7] + - SU3D[3, I5, k7]*(SU3D[6, I3, I4]*SU3D[I1, I2, k7] + - SU3D[6, I2, I4]*SU3D[I1, I3, k7] + SU3D[6, I2, I3]* - SU3D[I1, I4, k7] + SU3D[6, I1, I4]*SU3D[I2, I3, k7] + - SU3D[6, I1, I3]*SU3D[I2, I4, k7] + SU3D[6, I1, I2]* - SU3D[I3, I4, k7]) + SU3D[3, I2, k7]*SU3D[6, I1, I4]* - SU3D[I3, I5, k7] + SU3D[3, I1, k7]*SU3D[6, I2, I4]*SU3D[I3, I5, k7] + - SU3D[3, I4, k7]*(SU3D[6, I3, I5]*SU3D[I1, I2, k7] + - SU3D[6, I2, I5]*SU3D[I1, I3, k7] + SU3D[6, I2, I3]* - SU3D[I1, I5, k7] + SU3D[6, I1, I5]*SU3D[I2, I3, k7] + - SU3D[6, I1, I3]*SU3D[I2, I5, k7] + SU3D[6, I1, I2]* - SU3D[I3, I5, k7]) + SU3D[3, I3, k7]*SU3D[6, I1, I2]* - SU3D[I4, I5, k7] + SU3D[3, I2, k7]*SU3D[6, I1, I3]*SU3D[I4, I5, k7] + - SU3D[3, I1, k7]*SU3D[6, I2, I3]*SU3D[I4, I5, k7]))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*(SU3D[3, I3, I4]*SU3D[6, I5, k7]*SU3D[I1, I2, k7] + - SU3D[3, I2, I5]*SU3D[6, I4, k7]*SU3D[I1, I3, k7] + - SU3D[3, I2, I4]*SU3D[6, I5, k7]*SU3D[I1, I3, k7] + - SU3D[3, I2, I5]*SU3D[6, I3, k7]*SU3D[I1, I4, k7] + - SU3D[3, I2, I3]*SU3D[6, I5, k7]*SU3D[I1, I4, k7] + - SU3D[3, I3, I4]*SU3D[6, I2, k7]*SU3D[I1, I5, k7] + - SU3D[3, I2, I4]*SU3D[6, I3, k7]*SU3D[I1, I5, k7] + - SU3D[3, I2, I3]*SU3D[6, I4, k7]*SU3D[I1, I5, k7] + - SU3D[3, I1, I5]*SU3D[6, I4, k7]*SU3D[I2, I3, k7] + - SU3D[3, I1, I4]*SU3D[6, I5, k7]*SU3D[I2, I3, k7] + - SU3D[3, I4, I5]*(SU3D[6, I3, k7]*SU3D[I1, I2, k7] + - SU3D[6, I2, k7]*SU3D[I1, I3, k7] + SU3D[6, I1, k7]* - SU3D[I2, I3, k7]) + SU3D[3, I1, I5]*SU3D[6, I3, k7]* - SU3D[I2, I4, k7] + SU3D[3, I1, I3]*SU3D[6, I5, k7]*SU3D[I2, I4, k7] + - SU3D[3, I3, I5]*(SU3D[6, I4, k7]*SU3D[I1, I2, k7] + - SU3D[6, I2, k7]*SU3D[I1, I4, k7] + SU3D[6, I1, k7]* - SU3D[I2, I4, k7]) + SU3D[3, I3, I4]*SU3D[6, I1, k7]* - SU3D[I2, I5, k7] + SU3D[3, I1, I4]*SU3D[6, I3, k7]*SU3D[I2, I5, k7] + - SU3D[3, I1, I3]*SU3D[6, I4, k7]*SU3D[I2, I5, k7] + - SU3D[3, I2, I5]*SU3D[6, I1, k7]*SU3D[I3, I4, k7] + - SU3D[3, I1, I5]*SU3D[6, I2, k7]*SU3D[I3, I4, k7] + - SU3D[3, I1, I2]*SU3D[6, I5, k7]*SU3D[I3, I4, k7] + - SU3D[3, I2, I4]*SU3D[6, I1, k7]*SU3D[I3, I5, k7] + - SU3D[3, I1, I4]*SU3D[6, I2, k7]*SU3D[I3, I5, k7] + - SU3D[3, I1, I2]*SU3D[6, I4, k7]*SU3D[I3, I5, k7] + - SU3D[3, I2, I3]*SU3D[6, I1, k7]*SU3D[I4, I5, k7] + - SU3D[3, I1, I3]*SU3D[6, I2, k7]*SU3D[I4, I5, k7] + - SU3D[3, I1, I2]*SU3D[6, I3, k7]*SU3D[I4, I5, k7]))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[6, I3, k7]*SU3D[8, I4, I5]*SU3D[I1, I2, k7] + - SU3D[6, I2, k7]*SU3D[8, I4, I5]*SU3D[I1, I3, k7] + - SU3D[6, I3, k7]*SU3D[8, I2, I5]*SU3D[I1, I4, k7] + - SU3D[6, I2, k7]*SU3D[8, I3, I5]*SU3D[I1, I4, k7] + - SU3D[6, I3, k7]*SU3D[8, I2, I4]*SU3D[I1, I5, k7] + - SU3D[6, I2, k7]*SU3D[8, I3, I4]*SU3D[I1, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I4, I5]*SU3D[I2, I3, k7] + - SU3D[6, I3, k7]*SU3D[8, I1, I5]*SU3D[I2, I4, k7] + - SU3D[6, I1, k7]*SU3D[8, I3, I5]*SU3D[I2, I4, k7] + - SU3D[6, I3, k7]*SU3D[8, I1, I4]*SU3D[I2, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I3, I4]*SU3D[I2, I5, k7] + - SU3D[6, I2, k7]*SU3D[8, I1, I5]*SU3D[I3, I4, k7] + - SU3D[6, I1, k7]*SU3D[8, I2, I5]*SU3D[I3, I4, k7] + - SU3D[6, I5, k7]*(SU3D[8, I3, I4]*SU3D[I1, I2, k7] + - SU3D[8, I2, I4]*SU3D[I1, I3, k7] + SU3D[8, I2, I3]* - SU3D[I1, I4, k7] + SU3D[8, I1, I4]*SU3D[I2, I3, k7] + - SU3D[8, I1, I3]*SU3D[I2, I4, k7] + SU3D[8, I1, I2]* - SU3D[I3, I4, k7]) + SU3D[6, I2, k7]*SU3D[8, I1, I4]* - SU3D[I3, I5, k7] + SU3D[6, I1, k7]*SU3D[8, I2, I4]*SU3D[I3, I5, k7] + - SU3D[6, I4, k7]*(SU3D[8, I3, I5]*SU3D[I1, I2, k7] + - SU3D[8, I2, I5]*SU3D[I1, I3, k7] + SU3D[8, I2, I3]* - SU3D[I1, I5, k7] + SU3D[8, I1, I5]*SU3D[I2, I3, k7] + - SU3D[8, I1, I3]*SU3D[I2, I5, k7] + SU3D[8, I1, I2]* - SU3D[I3, I5, k7]) + SU3D[6, I3, k7]*SU3D[8, I1, I2]* - SU3D[I4, I5, k7] + SU3D[6, I2, k7]*SU3D[8, I1, I3]*SU3D[I4, I5, k7] + - SU3D[6, I1, k7]*SU3D[8, I2, I3]*SU3D[I4, I5, k7]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[6, I3, I4]*SU3D[8, I5, k7]*SU3D[I1, I2, k7] + - SU3D[6, I2, I5]*SU3D[8, I4, k7]*SU3D[I1, I3, k7] + - SU3D[6, I2, I4]*SU3D[8, I5, k7]*SU3D[I1, I3, k7] + - SU3D[6, I2, I5]*SU3D[8, I3, k7]*SU3D[I1, I4, k7] + - SU3D[6, I2, I3]*SU3D[8, I5, k7]*SU3D[I1, I4, k7] + - SU3D[6, I3, I4]*SU3D[8, I2, k7]*SU3D[I1, I5, k7] + - SU3D[6, I2, I4]*SU3D[8, I3, k7]*SU3D[I1, I5, k7] + - SU3D[6, I2, I3]*SU3D[8, I4, k7]*SU3D[I1, I5, k7] + - SU3D[6, I1, I5]*SU3D[8, I4, k7]*SU3D[I2, I3, k7] + - SU3D[6, I1, I4]*SU3D[8, I5, k7]*SU3D[I2, I3, k7] + - SU3D[6, I4, I5]*(SU3D[8, I3, k7]*SU3D[I1, I2, k7] + - SU3D[8, I2, k7]*SU3D[I1, I3, k7] + SU3D[8, I1, k7]* - SU3D[I2, I3, k7]) + SU3D[6, I1, I5]*SU3D[8, I3, k7]* - SU3D[I2, I4, k7] + SU3D[6, I1, I3]*SU3D[8, I5, k7]*SU3D[I2, I4, k7] + - SU3D[6, I3, I5]*(SU3D[8, I4, k7]*SU3D[I1, I2, k7] + - SU3D[8, I2, k7]*SU3D[I1, I4, k7] + SU3D[8, I1, k7]* - SU3D[I2, I4, k7]) + SU3D[6, I3, I4]*SU3D[8, I1, k7]* - SU3D[I2, I5, k7] + SU3D[6, I1, I4]*SU3D[8, I3, k7]*SU3D[I2, I5, k7] + - SU3D[6, I1, I3]*SU3D[8, I4, k7]*SU3D[I2, I5, k7] + - SU3D[6, I2, I5]*SU3D[8, I1, k7]*SU3D[I3, I4, k7] + - SU3D[6, I1, I5]*SU3D[8, I2, k7]*SU3D[I3, I4, k7] + - SU3D[6, I1, I2]*SU3D[8, I5, k7]*SU3D[I3, I4, k7] + - SU3D[6, I2, I4]*SU3D[8, I1, k7]*SU3D[I3, I5, k7] + - SU3D[6, I1, I4]*SU3D[8, I2, k7]*SU3D[I3, I5, k7] + - SU3D[6, I1, I2]*SU3D[8, I4, k7]*SU3D[I3, I5, k7] + - SU3D[6, I2, I3]*SU3D[8, I1, k7]*SU3D[I4, I5, k7] + - SU3D[6, I1, I3]*SU3D[8, I2, k7]*SU3D[I4, I5, k7] + - SU3D[6, I1, I2]*SU3D[8, I3, k7]*SU3D[I4, I5, k7]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[3, I3, k10]*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3D[I4, k10, k9] + SU3D[3, I3, k10]*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3D[I4, k10, k9] + SU3D[3, I2, k10]*SU3D[6, I5, k7]* - SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9] + - SU3D[3, I1, k10]*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k9] + SU3D[3, I2, k10]*SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + SU3D[3, I1, k10]*SU3D[6, I5, k7]* - SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + - SU3D[3, I3, k10]*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k7, k8] + SU3D[3, I3, k10]*SU3D[6, I5, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + SU3D[3, I2, k10]*SU3D[6, I5, k7]* - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8] + - SU3D[3, I1, k10]*SU3D[6, I5, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8] + SU3D[3, I2, k10]*SU3D[6, I5, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + SU3D[3, I1, k10]*SU3D[6, I5, k7]* - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + - SU3D[3, I3, k10]*SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, k10, k9]* - SU3D[I4, k8, k9] + SU3D[3, I3, k10]*SU3D[6, I5, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k7, k8]*SU3D[I4, k8, k9] + SU3D[3, I2, k10]*SU3D[6, I5, k7]* - SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + - SU3D[3, I1, k10]*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9] + SU3D[3, I2, k10]*SU3D[6, I5, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + SU3D[3, I1, k10]*SU3D[6, I5, k7]* - SU3D[I2, k10, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + - SU3D[3, I5, k10]*(SU3D[6, I4, k7]*(SU3D[I1, k8, k9]* - (SU3D[I2, k7, k8]*SU3D[I3, k10, k9] + SU3D[I2, k10, k9]* - SU3D[I3, k7, k8]) + SU3D[I1, k7, k8]* - (SU3D[I2, k8, k9]*SU3D[I3, k10, k9] + SU3D[I2, k10, k9]* - SU3D[I3, k8, k9]) + SU3D[I1, k10, k9]* - (SU3D[I2, k8, k9]*SU3D[I3, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k8, k9])) + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k10, k9] + SU3D[6, I1, k7]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + - SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + - SU3D[6, I3, k7]*(SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]* - SU3D[I4, k10, k9] + SU3D[I2, k10, k9]*SU3D[I4, k7, k8]) + - SU3D[I1, k7, k8]*(SU3D[I2, k8, k9]*SU3D[I4, k10, k9] + - SU3D[I2, k10, k9]*SU3D[I4, k8, k9]) + SU3D[I1, k10, k9]* - (SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]))) + SU3D[3, I3, k10]*SU3D[6, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I5, k10, k9] + - SU3D[3, I3, k10]*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3D[I5, k10, k9] + SU3D[3, I2, k10]*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k10, k9] + SU3D[3, I1, k10]*SU3D[6, I4, k7]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I5, k10, k9] + - SU3D[3, I2, k10]*SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I5, k10, k9] + SU3D[3, I1, k10]*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9] + SU3D[3, I3, k10]*SU3D[6, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I4, k7, k8]*SU3D[I5, k10, k9] + - SU3D[3, I2, k10]*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9] + SU3D[3, I3, k10]*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9] + SU3D[3, I1, k10]*SU3D[6, I3, k7]* - SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3D[I5, k10, k9] + - SU3D[3, I2, k10]*SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9] + SU3D[3, I1, k10]*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9] + SU3D[3, I3, k10]*SU3D[6, I2, k7]* - SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + - SU3D[3, I2, k10]*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9] + SU3D[3, I3, k10]*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + SU3D[3, I1, k10]*SU3D[6, I3, k7]* - SU3D[I2, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + - SU3D[3, I2, k10]*SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9] + SU3D[3, I1, k10]*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + SU3D[3, I3, k10]*SU3D[6, I4, k7]* - SU3D[I1, k8, k9]*SU3D[I2, k10, k9]*SU3D[I5, k7, k8] + - SU3D[3, I3, k10]*SU3D[6, I4, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8] + SU3D[3, I2, k10]*SU3D[6, I4, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k7, k8] + SU3D[3, I1, k10]*SU3D[6, I4, k7]* - SU3D[I2, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k7, k8] + - SU3D[3, I2, k10]*SU3D[6, I4, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8] + SU3D[3, I1, k10]*SU3D[6, I4, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + SU3D[3, I3, k10]*SU3D[6, I2, k7]* - SU3D[I1, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8] + - SU3D[3, I2, k10]*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k7, k8] + SU3D[3, I3, k10]*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8] + SU3D[3, I1, k10]*SU3D[6, I3, k7]* - SU3D[I2, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8] + - SU3D[3, I2, k10]*SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k7, k8] + SU3D[3, I1, k10]*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8] + SU3D[3, I3, k10]*SU3D[6, I2, k7]* - SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + - SU3D[3, I2, k10]*SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[3, I3, k10]*SU3D[6, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + SU3D[3, I1, k10]*SU3D[6, I3, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + - SU3D[3, I2, k10]*SU3D[6, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[3, I1, k10]*SU3D[6, I2, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + SU3D[3, I3, k10]*SU3D[6, I4, k7]* - SU3D[I1, k7, k8]*SU3D[I2, k10, k9]*SU3D[I5, k8, k9] + - SU3D[3, I3, k10]*SU3D[6, I4, k7]*SU3D[I1, k10, k9]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9] + SU3D[3, I2, k10]*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + SU3D[3, I1, k10]*SU3D[6, I4, k7]* - SU3D[I2, k7, k8]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + - SU3D[3, I2, k10]*SU3D[6, I4, k7]*SU3D[I1, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9] + SU3D[3, I1, k10]*SU3D[6, I4, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + SU3D[3, I3, k10]*SU3D[6, I2, k7]* - SU3D[I1, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + - SU3D[3, I2, k10]*SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9] + SU3D[3, I3, k10]*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + SU3D[3, I1, k10]*SU3D[6, I3, k7]* - SU3D[I2, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + - SU3D[3, I2, k10]*SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9] + SU3D[3, I1, k10]*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + SU3D[3, I3, k10]*SU3D[6, I2, k7]* - SU3D[I1, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[3, I2, k10]*SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9] + SU3D[3, I3, k10]*SU3D[6, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + SU3D[3, I1, k10]*SU3D[6, I3, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[3, I2, k10]*SU3D[6, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9] + SU3D[3, I1, k10]*SU3D[6, I2, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + SU3D[3, I4, k10]* - (SU3D[6, I5, k7]*(SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]* - SU3D[I3, k10, k9] + SU3D[I2, k10, k9]*SU3D[I3, k7, k8]) + - SU3D[I1, k7, k8]*(SU3D[I2, k8, k9]*SU3D[I3, k10, k9] + - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]) + SU3D[I1, k10, k9]* - (SU3D[I2, k8, k9]*SU3D[I3, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k8, k9])) + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k10, k9] + SU3D[6, I1, k7]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I5, k10, k9] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9] + - SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k7, k8] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k7, k8] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + - SU3D[6, I3, k7]*(SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]* - SU3D[I5, k10, k9] + SU3D[I2, k10, k9]*SU3D[I5, k7, k8]) + - SU3D[I1, k7, k8]*(SU3D[I2, k8, k9]*SU3D[I5, k10, k9] + - SU3D[I2, k10, k9]*SU3D[I5, k8, k9]) + SU3D[I1, k10, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3D[I4, k10, k9] + SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3D[I4, k10, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k10]* - SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9] + - SU3D[6, I1, k7]*SU3D[8, I5, k10]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k10]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + SU3D[6, I1, k7]*SU3D[8, I5, k10]* - SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + - SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I5, k10]* - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8] + - SU3D[6, I1, k7]*SU3D[8, I5, k10]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I5, k10]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I5, k10]* - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + - SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k7, k8]*SU3D[I2, k10, k9]* - SU3D[I4, k8, k9] + SU3D[6, I3, k7]*SU3D[8, I5, k10]*SU3D[I1, k10, k9]* - SU3D[I2, k7, k8]*SU3D[I4, k8, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k10]* - SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + - SU3D[6, I1, k7]*SU3D[8, I5, k10]*SU3D[I2, k7, k8]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9] + SU3D[6, I2, k7]*SU3D[8, I5, k10]*SU3D[I1, k10, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + SU3D[6, I1, k7]*SU3D[8, I5, k10]* - SU3D[I2, k10, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + - SU3D[6, I5, k7]*(SU3D[8, I4, k10]*(SU3D[I1, k8, k9]* - (SU3D[I2, k7, k8]*SU3D[I3, k10, k9] + SU3D[I2, k10, k9]* - SU3D[I3, k7, k8]) + SU3D[I1, k7, k8]* - (SU3D[I2, k8, k9]*SU3D[I3, k10, k9] + SU3D[I2, k10, k9]* - SU3D[I3, k8, k9]) + SU3D[I1, k10, k9]* - (SU3D[I2, k8, k9]*SU3D[I3, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k8, k9])) + SU3D[8, I2, k10]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k10, k9] + SU3D[8, I1, k10]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9] + - SU3D[8, I2, k10]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9] + SU3D[8, I1, k10]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + SU3D[8, I2, k10]* - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8] + - SU3D[8, I1, k10]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8] + SU3D[8, I2, k10]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + SU3D[8, I1, k10]* - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8] + - SU3D[8, I2, k10]*SU3D[I1, k7, k8]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9] + SU3D[8, I1, k10]*SU3D[I2, k7, k8]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + SU3D[8, I2, k10]* - SU3D[I1, k10, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9] + - SU3D[8, I1, k10]*SU3D[I2, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9] + SU3D[8, I3, k10]* - (SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I4, k10, k9] + - SU3D[I2, k10, k9]*SU3D[I4, k7, k8]) + SU3D[I1, k7, k8]* - (SU3D[I2, k8, k9]*SU3D[I4, k10, k9] + SU3D[I2, k10, k9]* - SU3D[I4, k8, k9]) + SU3D[I1, k10, k9]* - (SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]))) + SU3D[6, I3, k7]*SU3D[8, I4, k10]* - SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I5, k10, k9] + - SU3D[6, I3, k7]*SU3D[8, I4, k10]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3D[I5, k10, k9] + SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k10, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k10]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I5, k10, k9] + - SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I5, k10, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k10]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k10]* - SU3D[I1, k8, k9]*SU3D[I4, k7, k8]*SU3D[I5, k10, k9] + - SU3D[6, I2, k7]*SU3D[8, I3, k10]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9] + SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9] + SU3D[6, I1, k7]*SU3D[8, I3, k10]* - SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3D[I5, k10, k9] + - SU3D[6, I2, k7]*SU3D[8, I1, k10]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k10]* - SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + - SU3D[6, I2, k7]*SU3D[8, I3, k10]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9] + SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + SU3D[6, I1, k7]*SU3D[8, I3, k10]* - SU3D[I2, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + - SU3D[6, I2, k7]*SU3D[8, I1, k10]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + SU3D[6, I3, k7]*SU3D[8, I4, k10]* - SU3D[I1, k8, k9]*SU3D[I2, k10, k9]*SU3D[I5, k7, k8] + - SU3D[6, I3, k7]*SU3D[8, I4, k10]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8] + SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I4, k10]* - SU3D[I2, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k7, k8] + - SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I4, k10]*SU3D[I2, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I2, k10]* - SU3D[I1, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8] + - SU3D[6, I2, k7]*SU3D[8, I3, k10]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I3, k10]* - SU3D[I2, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8] + - SU3D[6, I2, k7]*SU3D[8, I1, k10]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I2, k10]* - SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + - SU3D[6, I2, k7]*SU3D[8, I3, k10]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I3, k10]* - SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + - SU3D[6, I2, k7]*SU3D[8, I1, k10]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8] + SU3D[6, I3, k7]*SU3D[8, I4, k10]* - SU3D[I1, k7, k8]*SU3D[I2, k10, k9]*SU3D[I5, k8, k9] + - SU3D[6, I3, k7]*SU3D[8, I4, k10]*SU3D[I1, k10, k9]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9] + SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k7, k8]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k10]* - SU3D[I2, k7, k8]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + - SU3D[6, I2, k7]*SU3D[8, I4, k10]*SU3D[I1, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9] + SU3D[6, I1, k7]*SU3D[8, I4, k10]*SU3D[I2, k10, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k10]* - SU3D[I1, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + - SU3D[6, I2, k7]*SU3D[8, I3, k10]*SU3D[I1, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9] + SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k7, k8]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + SU3D[6, I1, k7]*SU3D[8, I3, k10]* - SU3D[I2, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + - SU3D[6, I2, k7]*SU3D[8, I1, k10]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + SU3D[6, I3, k7]*SU3D[8, I2, k10]* - SU3D[I1, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[6, I2, k7]*SU3D[8, I3, k10]*SU3D[I1, k10, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9] + SU3D[6, I3, k7]*SU3D[8, I1, k10]*SU3D[I2, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + SU3D[6, I1, k7]*SU3D[8, I3, k10]* - SU3D[I2, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[6, I2, k7]*SU3D[8, I1, k10]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9] + SU3D[6, I1, k7]*SU3D[8, I2, k10]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + SU3D[6, I4, k7]* - (SU3D[8, I5, k10]*(SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]* - SU3D[I3, k10, k9] + SU3D[I2, k10, k9]*SU3D[I3, k7, k8]) + - SU3D[I1, k7, k8]*(SU3D[I2, k8, k9]*SU3D[I3, k10, k9] + - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]) + SU3D[I1, k10, k9]* - (SU3D[I2, k8, k9]*SU3D[I3, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k8, k9])) + SU3D[8, I2, k10]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k10, k9] + SU3D[8, I1, k10]* - SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I5, k10, k9] + - SU3D[8, I2, k10]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I5, k10, k9] + SU3D[8, I1, k10]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9] + SU3D[8, I2, k10]* - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k7, k8] + - SU3D[8, I1, k10]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k7, k8] + SU3D[8, I2, k10]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + SU3D[8, I1, k10]* - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8] + - SU3D[8, I2, k10]*SU3D[I1, k7, k8]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9] + SU3D[8, I1, k10]*SU3D[I2, k7, k8]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + SU3D[8, I2, k10]* - SU3D[I1, k10, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + - SU3D[8, I1, k10]*SU3D[I2, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9] + SU3D[8, I3, k10]* - (SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I5, k10, k9] + - SU3D[I2, k10, k9]*SU3D[I5, k7, k8]) + SU3D[I1, k7, k8]* - (SU3D[I2, k8, k9]*SU3D[I5, k10, k9] + SU3D[I2, k10, k9]* - SU3D[I5, k8, k9]) + SU3D[I1, k10, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/45)*(SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SU3F[3, 6, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SU3F[3, 6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SU3F[3, 6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SU3F[3, 6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SU3F[3, 6, I3] + - SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SU3F[3, 6, I4] + - SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SU3F[3, 6, I4] + - SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SU3F[3, 6, I1] + - SU3D[I1, I4, k6]*SU3F[3, 6, I3] + SU3D[I1, I3, k6]*SU3F[3, 6, I4]) + - SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SU3F[3, 6, I5] + - SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SU3F[3, 6, I5] + - SU3D[I2, I4, k6]*(SU3D[I3, I5, k6]*SU3F[3, 6, I1] + - SU3D[I1, I5, k6]*SU3F[3, 6, I3] + SU3D[I1, I3, k6]*SU3F[3, 6, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/60)*(SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9]*SU3F[3, I1, k10] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9]*SU3F[3, I1, k10] + - SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9]* - SU3F[3, I1, k10] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[3, I1, k10] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8]*SU3F[3, I1, k10] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8]* - SU3F[3, I1, k10] + SU3D[6, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I1, k10] + SU3D[6, I2, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I1, k10] + - SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[3, I1, k10] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9]*SU3F[3, I1, k10] + SU3D[6, I3, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I1, k10] + - SU3D[6, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I1, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9]*SU3F[3, I2, k10] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9]*SU3F[3, I2, k10] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9]* - SU3F[3, I2, k10] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[3, I2, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8]*SU3F[3, I2, k10] + - SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8]* - SU3F[3, I2, k10] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I2, k10] + SU3D[6, I1, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I2, k10] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[3, I2, k10] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9]*SU3F[3, I2, k10] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I2, k10] + - SU3D[6, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I2, k10] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9]*SU3F[3, I3, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9]*SU3F[3, I3, k10] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9]* - SU3F[3, I3, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[3, I3, k10] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8]*SU3F[3, I3, k10] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8]* - SU3F[3, I3, k10] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I3, k10] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I3, k10] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[3, I3, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9]*SU3F[3, I3, k10] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I3, k10] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I3, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3D[I5, k10, k9]*SU3F[3, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k9]*SU3F[3, I4, k10] + - SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I5, k10, k9]* - SU3F[3, I4, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k10, k9]*SU3F[3, I4, k10] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[3, I4, k10] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[3, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k7, k8]*SU3F[3, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I4, k10] + - SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k7, k8]* - SU3F[3, I4, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k7, k8]*SU3F[3, I4, k10] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I4, k10] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[3, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k10, k9]* - SU3D[I5, k8, k9]*SU3F[3, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I4, k10] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[3, I4, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[3, I4, k10] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I4, k10] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I4, k10] + SU3D[6, I5, k7]* - (SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3F[3, I1, k10] + SU3D[I2, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I1, k10] + SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k10, k9]*SU3F[3, I2, k10] + - SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[3, I2, k10] + SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8]*SU3F[3, I2, k10] + SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[3, I2, k10] + - SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3F[3, I2, k10] + SU3D[I1, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I2, k10] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k7, k8]*SU3F[3, I3, k10] + - SU3D[I1, k7, k8]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3F[3, I3, k10] + SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k7, k8]*SU3F[3, I4, k10] + SU3D[I1, k7, k8]* - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3F[3, I4, k10] + - SU3D[I2, k8, k9]*((SU3D[I1, k7, k8]*SU3D[I4, k10, k9] + - SU3D[I1, k10, k9]*SU3D[I4, k7, k8])*SU3F[3, I3, k10] + - SU3D[I3, k7, k8]*(SU3D[I4, k10, k9]*SU3F[3, I1, k10] + - SU3D[I1, k10, k9]*SU3F[3, I4, k10]) + SU3D[I3, k10, k9]* - (SU3D[I4, k7, k8]*SU3F[3, I1, k10] + SU3D[I1, k7, k8]* - SU3F[3, I4, k10])) + SU3D[I2, k7, k8]* - ((SU3D[I1, k8, k9]*SU3D[I4, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I4, k8, k9])*SU3F[3, I3, k10] + SU3D[I3, k8, k9]* - (SU3D[I4, k10, k9]*SU3F[3, I1, k10] + SU3D[I1, k10, k9]* - SU3F[3, I4, k10]) + SU3D[I3, k10, k9]* - (SU3D[I4, k8, k9]*SU3F[3, I1, k10] + SU3D[I1, k8, k9]* - SU3F[3, I4, k10]))) + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3D[I4, k10, k9]*SU3F[3, I5, k10] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3F[3, I5, k10] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k9]*SU3F[3, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k10, k9]*SU3F[3, I5, k10] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[3, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[3, I5, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k7, k8]*SU3F[3, I5, k10] + - SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[3, I5, k10] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8]*SU3F[3, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k7, k8]*SU3F[3, I5, k10] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3F[3, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[3, I5, k10] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3F[3, I5, k10] + - SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I5, k10] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3F[3, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[3, I5, k10] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I5, k10] + SU3D[6, I4, k7]* - (SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[3, I1, k10] + SU3D[I2, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[3, I1, k10] + SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k10, k9]*SU3F[3, I2, k10] + - SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[3, I2, k10] + SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k7, k8]*SU3F[3, I2, k10] + SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I2, k10] + - SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[3, I2, k10] + SU3D[I1, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[3, I2, k10] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I5, k7, k8]*SU3F[3, I3, k10] + - SU3D[I1, k7, k8]*SU3D[I2, k10, k9]*SU3D[I5, k8, k9]* - SU3F[3, I3, k10] + SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k7, k8]*SU3F[3, I5, k10] + SU3D[I1, k7, k8]* - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3F[3, I5, k10] + - SU3D[I2, k8, k9]*((SU3D[I1, k7, k8]*SU3D[I5, k10, k9] + - SU3D[I1, k10, k9]*SU3D[I5, k7, k8])*SU3F[3, I3, k10] + - SU3D[I3, k7, k8]*(SU3D[I5, k10, k9]*SU3F[3, I1, k10] + - SU3D[I1, k10, k9]*SU3F[3, I5, k10]) + SU3D[I3, k10, k9]* - (SU3D[I5, k7, k8]*SU3F[3, I1, k10] + SU3D[I1, k7, k8]* - SU3F[3, I5, k10])) + SU3D[I2, k7, k8]* - ((SU3D[I1, k8, k9]*SU3D[I5, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I5, k8, k9])*SU3F[3, I3, k10] + SU3D[I3, k8, k9]* - (SU3D[I5, k10, k9]*SU3F[3, I1, k10] + SU3D[I1, k10, k9]* - SU3F[3, I5, k10]) + SU3D[I3, k10, k9]* - (SU3D[I5, k8, k9]*SU3F[3, I1, k10] + SU3D[I1, k8, k9]* - SU3F[3, I5, k10])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (((2*I)/45)*(SU3D[6, I3, I4]*SU3D[I2, I5, k7]*SU3F[3, I1, k7] + - SU3D[6, I2, I5]*SU3D[I3, I4, k7]*SU3F[3, I1, k7] + - SU3D[6, I2, I4]*SU3D[I3, I5, k7]*SU3F[3, I1, k7] + - SU3D[6, I2, I3]*SU3D[I4, I5, k7]*SU3F[3, I1, k7] + - SU3D[6, I3, I4]*SU3D[I1, I5, k7]*SU3F[3, I2, k7] + - SU3D[6, I1, I5]*SU3D[I3, I4, k7]*SU3F[3, I2, k7] + - SU3D[6, I1, I4]*SU3D[I3, I5, k7]*SU3F[3, I2, k7] + - SU3D[6, I1, I3]*SU3D[I4, I5, k7]*SU3F[3, I2, k7] + - SU3D[6, I2, I5]*SU3D[I1, I4, k7]*SU3F[3, I3, k7] + - SU3D[6, I2, I4]*SU3D[I1, I5, k7]*SU3F[3, I3, k7] + - SU3D[6, I1, I5]*SU3D[I2, I4, k7]*SU3F[3, I3, k7] + - SU3D[6, I1, I4]*SU3D[I2, I5, k7]*SU3F[3, I3, k7] + - SU3D[6, I1, I2]*SU3D[I4, I5, k7]*SU3F[3, I3, k7] + - SU3D[6, I4, I5]*(SU3D[I2, I3, k7]*SU3F[3, I1, k7] + - SU3D[I1, I3, k7]*SU3F[3, I2, k7] + SU3D[I1, I2, k7]* - SU3F[3, I3, k7]) + SU3D[6, I2, I5]*SU3D[I1, I3, k7]* - SU3F[3, I4, k7] + SU3D[6, I2, I3]*SU3D[I1, I5, k7]*SU3F[3, I4, k7] + - SU3D[6, I1, I5]*SU3D[I2, I3, k7]*SU3F[3, I4, k7] + - SU3D[6, I1, I3]*SU3D[I2, I5, k7]*SU3F[3, I4, k7] + - SU3D[6, I1, I2]*SU3D[I3, I5, k7]*SU3F[3, I4, k7] + - SU3D[6, I3, I5]*(SU3D[I2, I4, k7]*SU3F[3, I1, k7] + - SU3D[I1, I4, k7]*SU3F[3, I2, k7] + SU3D[I1, I2, k7]* - SU3F[3, I4, k7]) + SU3D[6, I3, I4]*SU3D[I1, I2, k7]* - SU3F[3, I5, k7] + SU3D[6, I2, I4]*SU3D[I1, I3, k7]*SU3F[3, I5, k7] + - SU3D[6, I2, I3]*SU3D[I1, I4, k7]*SU3F[3, I5, k7] + - SU3D[6, I1, I4]*SU3D[I2, I3, k7]*SU3F[3, I5, k7] + - SU3D[6, I1, I3]*SU3D[I2, I4, k7]*SU3F[3, I5, k7] + - SU3D[6, I1, I2]*SU3D[I3, I4, k7]*SU3F[3, I5, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((4*I)/45)*(SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SU3F[6, 8, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SU3F[6, 8, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I2] + - SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SU3F[6, 8, I3] + - SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SU3F[6, 8, I4] + - SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SU3F[6, 8, I4] + - SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SU3F[6, 8, I1] + - SU3D[I1, I4, k6]*SU3F[6, 8, I3] + SU3D[I1, I3, k6]*SU3F[6, 8, I4]) + - SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SU3F[6, 8, I5] + - SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SU3F[6, 8, I5] + - SU3D[I2, I4, k6]*(SU3D[I3, I5, k6]*SU3F[6, 8, I1] + - SU3D[I1, I5, k6]*SU3F[6, 8, I3] + SU3D[I1, I3, k6]*SU3F[6, 8, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/45)*(SU3D[3, I3, I4]*SU3D[I2, I5, k6]*SU3F[6, I1, k6] + - SU3D[3, I2, I5]*SU3D[I3, I4, k6]*SU3F[6, I1, k6] + - SU3D[3, I2, I4]*SU3D[I3, I5, k6]*SU3F[6, I1, k6] + - SU3D[3, I2, I3]*SU3D[I4, I5, k6]*SU3F[6, I1, k6] + - SU3D[3, I3, I4]*SU3D[I1, I5, k6]*SU3F[6, I2, k6] + - SU3D[3, I1, I5]*SU3D[I3, I4, k6]*SU3F[6, I2, k6] + - SU3D[3, I1, I4]*SU3D[I3, I5, k6]*SU3F[6, I2, k6] + - SU3D[3, I1, I3]*SU3D[I4, I5, k6]*SU3F[6, I2, k6] + - SU3D[3, I2, I5]*SU3D[I1, I4, k6]*SU3F[6, I3, k6] + - SU3D[3, I2, I4]*SU3D[I1, I5, k6]*SU3F[6, I3, k6] + - SU3D[3, I1, I5]*SU3D[I2, I4, k6]*SU3F[6, I3, k6] + - SU3D[3, I1, I4]*SU3D[I2, I5, k6]*SU3F[6, I3, k6] + - SU3D[3, I1, I2]*SU3D[I4, I5, k6]*SU3F[6, I3, k6] + - SU3D[3, I4, I5]*(SU3D[I2, I3, k6]*SU3F[6, I1, k6] + - SU3D[I1, I3, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I3, k6]) + SU3D[3, I2, I5]*SU3D[I1, I3, k6]* - SU3F[6, I4, k6] + SU3D[3, I2, I3]*SU3D[I1, I5, k6]*SU3F[6, I4, k6] + - SU3D[3, I1, I5]*SU3D[I2, I3, k6]*SU3F[6, I4, k6] + - SU3D[3, I1, I3]*SU3D[I2, I5, k6]*SU3F[6, I4, k6] + - SU3D[3, I1, I2]*SU3D[I3, I5, k6]*SU3F[6, I4, k6] + - SU3D[3, I3, I5]*(SU3D[I2, I4, k6]*SU3F[6, I1, k6] + - SU3D[I1, I4, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I4, k6]) + SU3D[3, I3, I4]*SU3D[I1, I2, k6]* - SU3F[6, I5, k6] + SU3D[3, I2, I4]*SU3D[I1, I3, k6]*SU3F[6, I5, k6] + - SU3D[3, I2, I3]*SU3D[I1, I4, k6]*SU3F[6, I5, k6] + - SU3D[3, I1, I4]*SU3D[I2, I3, k6]*SU3F[6, I5, k6] + - SU3D[3, I1, I3]*SU3D[I2, I4, k6]*SU3F[6, I5, k6] + - SU3D[3, I1, I2]*SU3D[I3, I4, k6]*SU3F[6, I5, k6]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/45)*(SU3D[8, I3, I4]*SU3D[I2, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I5]*SU3D[I3, I4, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I4]*SU3D[I3, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I2, I3]*SU3D[I4, I5, k6]*SU3F[6, I1, k6] + - SU3D[8, I3, I4]*SU3D[I1, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I5]*SU3D[I3, I4, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I4]*SU3D[I3, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I1, I3]*SU3D[I4, I5, k6]*SU3F[6, I2, k6] + - SU3D[8, I2, I5]*SU3D[I1, I4, k6]*SU3F[6, I3, k6] + - SU3D[8, I2, I4]*SU3D[I1, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I5]*SU3D[I2, I4, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I4]*SU3D[I2, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I1, I2]*SU3D[I4, I5, k6]*SU3F[6, I3, k6] + - SU3D[8, I4, I5]*(SU3D[I2, I3, k6]*SU3F[6, I1, k6] + - SU3D[I1, I3, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I3, k6]) + SU3D[8, I2, I5]*SU3D[I1, I3, k6]* - SU3F[6, I4, k6] + SU3D[8, I2, I3]*SU3D[I1, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I5]*SU3D[I2, I3, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I3]*SU3D[I2, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I1, I2]*SU3D[I3, I5, k6]*SU3F[6, I4, k6] + - SU3D[8, I3, I5]*(SU3D[I2, I4, k6]*SU3F[6, I1, k6] + - SU3D[I1, I4, k6]*SU3F[6, I2, k6] + SU3D[I1, I2, k6]* - SU3F[6, I4, k6]) + SU3D[8, I3, I4]*SU3D[I1, I2, k6]* - SU3F[6, I5, k6] + SU3D[8, I2, I4]*SU3D[I1, I3, k6]*SU3F[6, I5, k6] + - SU3D[8, I2, I3]*SU3D[I1, I4, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I4]*SU3D[I2, I3, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I3]*SU3D[I2, I4, k6]*SU3F[6, I5, k6] + - SU3D[8, I1, I2]*SU3D[I3, I4, k6]*SU3F[6, I5, k6]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[3, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[3, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[3, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I1, k8] + SU3D[3, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[3, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[3, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[3, I3, k7]*SU3D[I2, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[3, I2, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[3, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[3, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[3, I3, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k8] + - SU3D[3, I2, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[3, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[3, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[3, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[3, I1, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[3, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k8] + - SU3D[3, I1, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I3, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I3, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I3, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I3, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I3, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k8] + - SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[3, I5, k7]*(SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I1, k8] + - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k8] + SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3F[6, I4, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3F[6, I4, k8] + SU3D[I2, k8, k9]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k10, k9])*SU3F[6, I3, k8] + SU3D[I3, k10, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I4, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I4, k8]))) + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[3, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[3, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[3, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[3, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[3, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[3, I4, k7]* - (SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k8] + SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k8] + - SU3D[I2, k8, k9]*((SU3D[I1, k10, k9]*SU3D[I5, k10, k7] + - SU3D[I1, k10, k7]*SU3D[I5, k10, k9])*SU3F[6, I3, k8] + - SU3D[I3, k10, k9]*(SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[I1, k10, k7]*SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I5, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I5, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I5, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I5, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I1, k8] + - SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k8] + - SU3D[8, I2, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k8] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I3, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k7]*SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I3, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k7]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k7]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k8] + - SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8] + SU3D[8, I5, k7]*(SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I1, k8] + - SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k10, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k8] + SU3D[I1, k10, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k10, k9]*SU3F[6, I4, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3F[6, I4, k8] + SU3D[I2, k8, k9]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k10, k9])*SU3F[6, I3, k8] + SU3D[I3, k10, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I4, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I4, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I4, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I4, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I4, k8]) + SU3D[I3, k10, k7]* - (SU3D[I4, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I4, k8]))) + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k7]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k10, k7]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k7]*SU3F[6, I5, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[6, I5, k8] + SU3D[8, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k10, k7]*SU3D[I4, k8, k9]*SU3F[6, I5, k8] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[6, I1, k8] + SU3D[I2, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k7]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k10, k7]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k10, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k8] + SU3D[I1, k10, k7]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[6, I2, k8] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8] + SU3D[I1, k10, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k8] + - SU3D[I1, k10, k9]*SU3D[I2, k10, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k8] + SU3D[I1, k10, k9]* - SU3D[I2, k10, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k8] + - SU3D[I2, k8, k9]*((SU3D[I1, k10, k9]*SU3D[I5, k10, k7] + - SU3D[I1, k10, k7]*SU3D[I5, k10, k9])*SU3F[6, I3, k8] + - SU3D[I3, k10, k9]*(SU3D[I5, k10, k7]*SU3F[6, I1, k8] + - SU3D[I1, k10, k7]*SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k10, k9]*SU3F[6, I1, k8] + SU3D[I1, k10, k9]* - SU3F[6, I5, k8])) + SU3D[I2, k10, k9]* - ((SU3D[I1, k8, k9]*SU3D[I5, k10, k7] + SU3D[I1, k10, k7]* - SU3D[I5, k8, k9])*SU3F[6, I3, k8] + SU3D[I3, k8, k9]* - (SU3D[I5, k10, k7]*SU3F[6, I1, k8] + SU3D[I1, k10, k7]* - SU3F[6, I5, k8]) + SU3D[I3, k10, k7]* - (SU3D[I5, k8, k9]*SU3F[6, I1, k8] + SU3D[I1, k8, k9]* - SU3F[6, I5, k8])))))/(Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I2, k6]* - SU3F[6, I1, k8] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[3, I2, k6]*SU3F[6, I1, k8] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I1, k8] + - SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I1, k8] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I3, k6]*SU3F[6, I1, k8] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[3, I3, k6]*SU3F[6, I1, k8] + - SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]* - SU3F[6, I1, k8] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[3, I3, k6]*SU3F[6, I1, k8] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I4, k6]*SU3F[6, I1, k8] + - SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]* - SU3F[6, I1, k8] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[6, I1, k8] + - SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I2, k8] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[3, I1, k6]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I2, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[3, I3, k6]*SU3F[6, I2, k8] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[3, I3, k6]*SU3F[6, I2, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]* - SU3F[6, I2, k8] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[3, I3, k6]*SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I4, k6]*SU3F[6, I2, k8] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]* - SU3F[6, I2, k8] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[6, I2, k8] + - SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I3, k8] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I3, k8] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I1, k6]*SU3F[6, I3, k8] + - SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I3, k8] + SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k6]*SU3F[6, I3, k8] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[3, I1, k6]*SU3F[6, I3, k8] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I2, k6]*SU3F[6, I3, k8] + - SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I2, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I2, k6]*SU3F[6, I3, k8] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[3, I2, k6]*SU3F[6, I3, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I4, k6]*SU3F[6, I3, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[3, I4, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k6]*SU3F[6, I3, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[3, I4, k6]*SU3F[6, I3, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I3, k8] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I5, k6]*SU3F[6, I3, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[3, I5, k6]* - SU3F[6, I3, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I5, k6]*SU3F[6, I3, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[3, I5, k6]*SU3F[6, I3, k8] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I4, k8] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k6]*SU3F[6, I4, k8] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[3, I2, k6]*SU3F[6, I4, k8] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k6]* - SU3F[6, I4, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I4, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I3, k6]* - SU3F[6, I4, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[3, I3, k6]*SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[3, I3, k6]*SU3F[6, I4, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[3, I3, k6]* - SU3F[6, I4, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k8] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I5, k8] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]* - SU3F[3, I1, k6]*SU3F[6, I5, k8] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[3, I2, k6]*SU3F[6, I5, k8] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[3, I2, k6]* - SU3F[6, I5, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I5, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[3, I3, k6]* - SU3F[6, I5, k8] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[3, I3, k6]*SU3F[6, I5, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k8, k9]*SU3F[3, I3, k6]*SU3F[6, I5, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3F[3, I3, k6]* - SU3F[6, I5, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I5, k8] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k8] + - SU3D[I3, k8, k9]*(SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I1, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I4, k6]* - SU3F[6, I1, k8] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I2, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I4, k6]* - SU3F[6, I2, k8] + SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I4, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I1, k6]* - SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I4, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[3, I2, k6]* - SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[6, I4, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[3, I5, k6]* - SU3F[6, I4, k8] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I5, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[3, I4, k6]* - SU3F[6, I5, k8] + SU3D[I4, k7, k9]*(SU3D[I5, k6, k7]* - (SU3F[3, I2, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I2, k8]) + SU3D[I2, k6, k7]* - (SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I5, k8]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3F[3, I2, k6]* - SU3F[6, I5, k8])) + SU3D[I4, k6, k7]* - (SU3D[I5, k7, k9]*(SU3F[3, I2, k6]*SU3F[6, I1, k8] + - SU3F[3, I1, k6]*SU3F[6, I2, k8]) + SU3D[I2, k7, k9]* - (SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I5, k8]) + SU3D[I1, k7, k9]* - (SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3F[3, I2, k6]* - SU3F[6, I5, k8]))) + SU3D[I3, k7, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]*SU3F[6, I1, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I2, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k6]*SU3F[6, I2, k8] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I1, k6]*SU3F[6, I4, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k8] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k6]*SU3F[6, I4, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I5, k6]*SU3F[6, I4, k8] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I4, k6]*SU3F[6, I5, k8] + - SU3D[I4, k8, k9]*(SU3D[I5, k6, k7]*(SU3F[3, I2, k6]*SU3F[6, I1, k8] + - SU3F[3, I1, k6]*SU3F[6, I2, k8]) + SU3D[I2, k6, k7]* - (SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I5, k8]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3F[3, I2, k6]* - SU3F[6, I5, k8])) + SU3D[I4, k6, k7]* - (SU3D[I5, k8, k9]*(SU3F[3, I2, k6]*SU3F[6, I1, k8] + - SU3F[3, I1, k6]*SU3F[6, I2, k8]) + SU3D[I2, k8, k9]* - (SU3F[3, I5, k6]*SU3F[6, I1, k8] + SU3F[3, I1, k6]* - SU3F[6, I5, k8]) + SU3D[I1, k8, k9]* - (SU3F[3, I5, k6]*SU3F[6, I2, k8] + SU3F[3, I2, k6]* - SU3F[6, I5, k8]))))/(60*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/60)*(SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9]*SU3F[8, I1, k10] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9]*SU3F[8, I1, k10] + - SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9]* - SU3F[8, I1, k10] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[8, I1, k10] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8]*SU3F[8, I1, k10] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8]* - SU3F[8, I1, k10] + SU3D[6, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I1, k10] + SU3D[6, I2, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I1, k10] + - SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I1, k10] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9]*SU3F[8, I1, k10] + SU3D[6, I3, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I1, k10] + - SU3D[6, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I1, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9]*SU3F[8, I2, k10] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9]*SU3F[8, I2, k10] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9]* - SU3F[8, I2, k10] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[8, I2, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8]*SU3F[8, I2, k10] + - SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8]* - SU3F[8, I2, k10] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I2, k10] + SU3D[6, I1, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I2, k10] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I2, k10] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9]*SU3F[8, I2, k10] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I2, k10] + - SU3D[6, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I2, k10] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k10, k9]*SU3F[8, I3, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k10, k9]*SU3F[8, I3, k10] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9]* - SU3F[8, I3, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9]*SU3F[8, I3, k10] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k7, k8]*SU3F[8, I3, k10] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k7, k8]* - SU3F[8, I3, k10] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I3, k10] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I3, k10] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I3, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9]*SU3F[8, I3, k10] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I3, k10] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I3, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3D[I5, k10, k9]*SU3F[8, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3D[I5, k10, k9]*SU3F[8, I4, k10] + - SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I5, k10, k9]* - SU3F[8, I4, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k10, k9]*SU3F[8, I4, k10] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k9]*SU3F[8, I4, k10] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[8, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k7, k8]*SU3F[8, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I4, k10] + - SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k7, k8]*SU3F[8, I4, k10] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I4, k10] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k10, k9]* - SU3D[I5, k8, k9]*SU3F[8, I4, k10] + SU3D[6, I3, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I4, k10] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I4, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9]*SU3F[8, I4, k10] + SU3D[6, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I4, k10] + - SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I4, k10] + SU3D[6, I5, k7]* - (SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3F[8, I1, k10] + SU3D[I2, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I1, k10] + SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k10, k9]*SU3F[8, I2, k10] + - SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[8, I2, k10] + SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8]*SU3F[8, I2, k10] + SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[8, I2, k10] + - SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9]* - SU3F[8, I2, k10] + SU3D[I1, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I2, k10] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k7, k8]*SU3F[8, I3, k10] + - SU3D[I1, k7, k8]*SU3D[I2, k10, k9]*SU3D[I4, k8, k9]* - SU3F[8, I3, k10] + SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k7, k8]*SU3F[8, I4, k10] + SU3D[I1, k7, k8]* - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3F[8, I4, k10] + - SU3D[I2, k8, k9]*((SU3D[I1, k7, k8]*SU3D[I4, k10, k9] + - SU3D[I1, k10, k9]*SU3D[I4, k7, k8])*SU3F[8, I3, k10] + - SU3D[I3, k7, k8]*(SU3D[I4, k10, k9]*SU3F[8, I1, k10] + - SU3D[I1, k10, k9]*SU3F[8, I4, k10]) + SU3D[I3, k10, k9]* - (SU3D[I4, k7, k8]*SU3F[8, I1, k10] + SU3D[I1, k7, k8]* - SU3F[8, I4, k10])) + SU3D[I2, k7, k8]* - ((SU3D[I1, k8, k9]*SU3D[I4, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I4, k8, k9])*SU3F[8, I3, k10] + SU3D[I3, k8, k9]* - (SU3D[I4, k10, k9]*SU3F[8, I1, k10] + SU3D[I1, k10, k9]* - SU3F[8, I4, k10]) + SU3D[I3, k10, k9]* - (SU3D[I4, k8, k9]*SU3F[8, I1, k10] + SU3D[I1, k8, k9]* - SU3F[8, I4, k10]))) + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3D[I4, k10, k9]*SU3F[8, I5, k10] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, k10, k9]* - SU3F[8, I5, k10] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k10, k9]*SU3F[8, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I4, k10, k9]*SU3F[8, I5, k10] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3F[8, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9]*SU3F[8, I5, k10] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k7, k8]*SU3F[8, I5, k10] + - SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[8, I5, k10] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k7, k8]*SU3F[8, I5, k10] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3F[8, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k10, k9]*SU3D[I4, k8, k9]*SU3F[8, I5, k10] + - SU3D[6, I3, k7]*SU3D[I1, k10, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I5, k10] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k10, k9]* - SU3D[I4, k8, k9]*SU3F[8, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3F[8, I5, k10] + - SU3D[6, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I5, k10] + SU3D[6, I1, k7]*SU3D[I2, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I5, k10] + SU3D[6, I4, k7]* - (SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[8, I1, k10] + SU3D[I2, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[8, I1, k10] + SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3D[I5, k10, k9]*SU3F[8, I2, k10] + - SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9]* - SU3F[8, I2, k10] + SU3D[I1, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k7, k8]*SU3F[8, I2, k10] + SU3D[I1, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I2, k10] + - SU3D[I1, k7, k8]*SU3D[I3, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I2, k10] + SU3D[I1, k10, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[8, I2, k10] + SU3D[I1, k8, k9]* - SU3D[I2, k10, k9]*SU3D[I5, k7, k8]*SU3F[8, I3, k10] + - SU3D[I1, k7, k8]*SU3D[I2, k10, k9]*SU3D[I5, k8, k9]* - SU3F[8, I3, k10] + SU3D[I1, k8, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k7, k8]*SU3F[8, I5, k10] + SU3D[I1, k7, k8]* - SU3D[I2, k10, k9]*SU3D[I3, k8, k9]*SU3F[8, I5, k10] + - SU3D[I2, k8, k9]*((SU3D[I1, k7, k8]*SU3D[I5, k10, k9] + - SU3D[I1, k10, k9]*SU3D[I5, k7, k8])*SU3F[8, I3, k10] + - SU3D[I3, k7, k8]*(SU3D[I5, k10, k9]*SU3F[8, I1, k10] + - SU3D[I1, k10, k9]*SU3F[8, I5, k10]) + SU3D[I3, k10, k9]* - (SU3D[I5, k7, k8]*SU3F[8, I1, k10] + SU3D[I1, k7, k8]* - SU3F[8, I5, k10])) + SU3D[I2, k7, k8]* - ((SU3D[I1, k8, k9]*SU3D[I5, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I5, k8, k9])*SU3F[8, I3, k10] + SU3D[I3, k8, k9]* - (SU3D[I5, k10, k9]*SU3F[8, I1, k10] + SU3D[I1, k10, k9]* - SU3F[8, I5, k10]) + SU3D[I3, k10, k9]* - (SU3D[I5, k8, k9]*SU3F[8, I1, k10] + SU3D[I1, k8, k9]* - SU3F[8, I5, k10])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I1, k6] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8]*SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8]*SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I1, k6] + - SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I2, k6] + SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k8]*SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]* - SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3D[I1, k7, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I2, k6] + - SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I3, k6] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[8, I3, k6] + SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I1, k8]*SU3F[8, I3, k6] + - SU3D[I2, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I3, k6] + SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I3, k6] + SU3D[I2, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I4, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I2, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I4, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I3, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I3, k6] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[6, I5, k8]*SU3F[8, I3, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k8]* - SU3F[8, I3, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3D[I4, k8, k9]* - SU3F[6, I5, k8]*SU3F[8, I3, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I3, k6] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I3, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k8, k9]*SU3F[6, I3, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I4, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I5, k6] + SU3D[I2, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]* - SU3F[6, I1, k8]*SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3D[I4, k7, k9]*SU3F[6, I2, k8]*SU3F[8, I5, k6] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[6, I2, k8]* - SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3D[I4, k7, k9]*SU3F[6, I3, k8]* - SU3F[8, I5, k6] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I3, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k8, k9]*SU3F[6, I3, k8]*SU3F[8, I5, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k8]* - SU3F[8, I5, k6] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k8]*SU3F[8, I5, k6] + SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I3, k8, k9]*(SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I1, k6] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I2, k6] + SU3D[I2, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I1, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k9]*SU3F[6, I2, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I4, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[6, I5, k8]* - SU3F[8, I4, k6] + SU3D[I1, k7, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I5, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k9]*SU3F[6, I4, k8]* - SU3F[8, I5, k6] + SU3D[I4, k7, k9]*(SU3D[I5, k6, k7]* - (SU3F[6, I2, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I2, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6])) + SU3D[I4, k6, k7]* - (SU3D[I5, k7, k9]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k7, k9]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k7, k9]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6]))) + SU3D[I3, k7, k9]* - (SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I1, k6] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I2, k6] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k8]*SU3F[8, I4, k6] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k8]*SU3F[8, I5, k6] + - SU3D[I4, k8, k9]*(SU3D[I5, k6, k7]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6])) + SU3D[I4, k6, k7]* - (SU3D[I5, k8, k9]*(SU3F[6, I2, k8]*SU3F[8, I1, k6] + - SU3F[6, I1, k8]*SU3F[8, I2, k6]) + SU3D[I2, k8, k9]* - (SU3F[6, I5, k8]*SU3F[8, I1, k6] + SU3F[6, I1, k8]* - SU3F[8, I5, k6]) + SU3D[I1, k8, k9]* - (SU3F[6, I5, k8]*SU3F[8, I2, k6] + SU3F[6, I2, k8]* - SU3F[8, I5, k6]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/45)*(SU3D[6, I3, I4]*SU3D[I2, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I5]*SU3D[I3, I4, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I4]*SU3D[I3, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I2, I3]*SU3D[I4, I5, k7]*SU3F[8, I1, k7] + - SU3D[6, I3, I4]*SU3D[I1, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I5]*SU3D[I3, I4, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I4]*SU3D[I3, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I1, I3]*SU3D[I4, I5, k7]*SU3F[8, I2, k7] + - SU3D[6, I2, I5]*SU3D[I1, I4, k7]*SU3F[8, I3, k7] + - SU3D[6, I2, I4]*SU3D[I1, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I5]*SU3D[I2, I4, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I4]*SU3D[I2, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I1, I2]*SU3D[I4, I5, k7]*SU3F[8, I3, k7] + - SU3D[6, I4, I5]*(SU3D[I2, I3, k7]*SU3F[8, I1, k7] + - SU3D[I1, I3, k7]*SU3F[8, I2, k7] + SU3D[I1, I2, k7]* - SU3F[8, I3, k7]) + SU3D[6, I2, I5]*SU3D[I1, I3, k7]* - SU3F[8, I4, k7] + SU3D[6, I2, I3]*SU3D[I1, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I5]*SU3D[I2, I3, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I3]*SU3D[I2, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I1, I2]*SU3D[I3, I5, k7]*SU3F[8, I4, k7] + - SU3D[6, I3, I5]*(SU3D[I2, I4, k7]*SU3F[8, I1, k7] + - SU3D[I1, I4, k7]*SU3F[8, I2, k7] + SU3D[I1, I2, k7]* - SU3F[8, I4, k7]) + SU3D[6, I3, I4]*SU3D[I1, I2, k7]* - SU3F[8, I5, k7] + SU3D[6, I2, I4]*SU3D[I1, I3, k7]*SU3F[8, I5, k7] + - SU3D[6, I2, I3]*SU3D[I1, I4, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I4]*SU3D[I2, I3, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I3]*SU3D[I2, I4, k7]*SU3F[8, I5, k7] + - SU3D[6, I1, I2]*SU3D[I3, I4, k7]*SU3F[8, I5, k7]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[3, I2, k7]* - SU3D[6, I5, k9]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I1, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k9]*SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I2, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I2, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I2, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k9]*SU3D[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k11, k7]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k11, k7]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k9]*SU3D[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I2, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I5, k7]* - (SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + SU3D[6, I1, k9]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k11, k7]*SU3F[I3, k10, k11] + SU3D[6, I4, k9]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k11])) + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I3, k9]* - ((SU3D[I1, k11, k7]*SU3D[I4, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I4, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I4, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I4, k10, k11]))) + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k9]*SU3D[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k11, k7]*SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k11, k7]*SU3D[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k9]*SU3D[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I4, k7]* - (SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + SU3D[6, I1, k9]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + SU3D[6, I5, k9]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k11])) + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]* - ((SU3D[I1, k11, k7]*SU3D[I5, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I5, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I5, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I5, k10, k11])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[6, I2, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I2, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k9]*SU3D[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k11, k7]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k9]*SU3D[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I5, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k11, k7]*SU3F[I3, k10, k11] + SU3D[8, I4, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k11])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I4, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I4, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I4, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I4, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I4, k10, k11]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]*SU3D[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k9]*SU3D[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[8, I2, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I5, k11, k7]*SU3F[I3, k10, k11] + SU3D[8, I5, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k11])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I5, k10, k9] + SU3D[I1, k10, k9]* - SU3D[I5, k11, k7])*SU3F[I2, k10, k11] + SU3D[I2, k11, k7]* - (SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I5, k10, k11]) + SU3D[I2, k10, k9]* - (SU3D[I5, k11, k7]*SU3F[I1, k10, k11] + SU3D[I1, k11, k7]* - SU3F[I5, k10, k11])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3D[3, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k10, k6] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I1, k10, k6] + - SU3D[3, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3D[3, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I2, k10, k6] + SU3D[3, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k10, k6] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[3, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I2, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I3, k10, k6] + SU3D[3, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I3, k10, k6] + - SU3D[3, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I3, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I4, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k10, k6] + - SU3D[3, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I4, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[3, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I4, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I4, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6]))) + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I1, k7]* - SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I2, k7]*SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k10, k6] + - SU3D[3, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[3, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[3, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[3, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[3, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I5, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I5, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I1, k10, k6] + - SU3D[8, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[8, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I2, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k10, k6] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I3, k10, k6] + - SU3D[8, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k7]*SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k7]*SU3F[I3, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I2, k7]*SU3F[I4, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]*SU3F[6, I5, k7]* - SU3F[I4, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[I4, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k10, k6] + - SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I4, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I4, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I4, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I4, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I4, k10, k6]))) + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I1, k7]* - SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I2, k7]*SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k10, k6] + - SU3D[8, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[8, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3F[6, I4, k7]*SU3F[I5, k10, k6] + - SU3D[8, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I5, k10, k6] + SU3D[8, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[I5, k10, k6] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6] + SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[6, I3, k7]*SU3F[I2, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6] + SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[6, I1, k7]*SU3F[I3, k10, k6] + SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k9]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[6, I5, k7]*SU3F[I3, k10, k6] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[6, I3, k7]*SU3F[I5, k10, k6] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k10, k6] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k9]*(SU3F[6, I2, k7]* - SU3F[I1, k10, k6] + SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + - SU3D[I2, k10, k9]*(SU3F[6, I5, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I5, k10, k6]) + SU3D[I1, k10, k9]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6])) + SU3D[I3, k10, k9]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k7]*SU3F[I1, k10, k6] + - SU3F[6, I1, k7]*SU3F[I2, k10, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I1, k10, k6] + SU3F[6, I1, k7]* - SU3F[I5, k10, k6]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k7]*SU3F[I2, k10, k6] + SU3F[6, I2, k7]* - SU3F[I5, k10, k6]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k7]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I5, k7]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k7]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k7]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k7]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k7]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k7]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k7]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I5, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I5, k6, k7]* - (SU3F[3, I2, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[3, I2, k11]* - SU3F[6, I4, k7]*SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + - SU3F[3, I1, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3F[3, I4, k11]* - (SU3F[6, I3, k7]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[6, I2, k7]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[6, I1, k7]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[3, I2, k11]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3F[3, I1, k11]* - SU3F[6, I3, k7]*SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + - SU3F[3, I2, k11]*SU3F[6, I1, k7]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3F[3, I1, k11]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3F[3, I2, k11]* - SU3F[6, I3, k7]*SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + - SU3F[3, I1, k11]*SU3F[6, I3, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3F[3, I2, k11]*SU3F[6, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3F[3, I1, k11]* - SU3F[6, I2, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + - SU3F[3, I3, k11]*(SU3F[6, I4, k7]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[6, I2, k7]*(SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k10, k6]) + SU3F[6, I1, k7]* - (SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k6]))) + SU3D[I3, k6, k7]*SU3F[3, I4, k11]* - SU3F[6, I2, k7]*SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k7]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k7]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k7]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k7]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k7]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I2, k7]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I4, k7]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k7]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I1, k7]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k7]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k7]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k7]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I3, k7]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k7]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k7]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k7]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I2, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I4, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I1, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I3, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I4, k6, k7]*(SU3F[3, I2, k11]*SU3F[6, I5, k7]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[3, I1, k11]* - SU3F[6, I5, k7]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + - SU3F[3, I2, k11]*SU3F[6, I5, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3F[3, I1, k11]*SU3F[6, I5, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3F[3, I5, k11]* - (SU3F[6, I3, k7]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[6, I2, k7]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[6, I1, k7]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[3, I2, k11]*SU3F[6, I3, k7]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3F[3, I1, k11]* - SU3F[6, I3, k7]*SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + - SU3F[3, I2, k11]*SU3F[6, I1, k7]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3F[3, I1, k11]*SU3F[6, I2, k7]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3F[3, I2, k11]* - SU3F[6, I3, k7]*SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + - SU3F[3, I1, k11]*SU3F[6, I3, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3F[3, I2, k11]*SU3F[6, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3F[3, I1, k11]* - SU3F[6, I2, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + - SU3F[3, I3, k11]*(SU3F[6, I5, k7]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[6, I2, k7]*(SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k10, k6]) + SU3F[6, I1, k7]* - (SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k6]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k6]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k11]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I2, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k11]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I3, k11]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I3, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I5, k11]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I3, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I4, k11]*SU3F[I1, k10, k11]*SU3F[I3, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k6] + SU3F[6, I4, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[6, I2, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I3, k11]*SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I4, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I4, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I3, k11]*SU3F[I1, k10, k11]*SU3F[I4, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k6] + SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + SU3F[6, I1, k7]* - SU3F[8, I2, k11]*SU3F[I3, k10, k11]*SU3F[I4, k10, k6] + - SU3F[6, I3, k7]*(SU3F[8, I4, k11]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k10, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k6]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I2, k11]*SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k11]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I2, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I1, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I2, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I3, k11]* - SU3F[I4, k10, k6]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I3, k11]*SU3F[I4, k10, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k11]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k11]* - SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I1, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I2, k11]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I4, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k11]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I1, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I2, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[8, I3, k11]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I3, k11]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k6] + SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SU3F[8, I5, k11]* - SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I5, k11]*SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I5, k11]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k6] + SU3F[6, I1, k7]*SU3F[8, I5, k11]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k6] + SU3F[6, I5, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k10, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k10, k6]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k6])) + SU3F[6, I2, k7]*SU3F[8, I3, k11]* - SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + SU3F[6, I1, k7]* - SU3F[8, I3, k11]*SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + - SU3F[6, I2, k7]*SU3F[8, I1, k11]*SU3F[I3, k10, k6]* - SU3F[I5, k10, k11] + SU3F[6, I1, k7]*SU3F[8, I2, k11]* - SU3F[I3, k10, k6]*SU3F[I5, k10, k11] + SU3F[6, I2, k7]* - SU3F[8, I3, k11]*SU3F[I1, k10, k11]*SU3F[I5, k10, k6] + - SU3F[6, I1, k7]*SU3F[8, I3, k11]*SU3F[I2, k10, k11]* - SU3F[I5, k10, k6] + SU3F[6, I2, k7]*SU3F[8, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + SU3F[6, I1, k7]* - SU3F[8, I2, k11]*SU3F[I3, k10, k11]*SU3F[I5, k10, k6] + - SU3F[6, I3, k7]*(SU3F[8, I5, k11]*(SU3F[I1, k10, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k10, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k10, k6]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k10, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k10, k6]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k6]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I2, k6]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I3, k6]*SU3F[I1, k10, k7] + - SU3D[6, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[3, I4, k6]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I4, k6]*SU3F[I1, k10, k7] + - SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[3, I5, k6]*SU3F[I1, k10, k7] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[3, I5, k6]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k10, k7] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I1, k6]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I3, k6]*SU3F[I2, k10, k7] + - SU3D[6, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[3, I4, k6]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I4, k6]*SU3F[I2, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I2, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[3, I5, k6]*SU3F[I2, k10, k7] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[3, I5, k6]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I2, k10, k7] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I1, k6]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I2, k6]*SU3F[I3, k10, k7] + - SU3D[6, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[3, I4, k6]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I4, k6]*SU3F[I3, k10, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[3, I5, k6]*SU3F[I3, k10, k7] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[3, I5, k6]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I3, k10, k7] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I1, k6]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[3, I1, k6]*SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[I4, k10, k7] + - SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[3, I2, k6]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I2, k6]*SU3F[I4, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I4, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I3, k6]*SU3F[I4, k10, k7] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I3, k6]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]*SU3F[3, I5, k6]* - SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3F[3, I5, k6]*SU3F[I4, k10, k7] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]*SU3F[3, I5, k6]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[I4, k10, k7] + - SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[3, I3, k6]* - SU3F[I1, k10, k7] + SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[I1, k10, k7] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[3, I3, k6]*SU3F[I2, k10, k7] + - SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k7] + SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[3, I1, k6]*SU3F[I3, k10, k7] + SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k10, k7] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[3, I2, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I2, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[3, I4, k6]*SU3F[I3, k10, k7] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[3, I3, k6]*SU3F[I4, k10, k7] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k10, k7] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k9]*(SU3F[3, I2, k6]* - SU3F[I1, k10, k7] + SU3F[3, I1, k6]*SU3F[I2, k10, k7]) + - SU3D[I2, k10, k9]*(SU3F[3, I4, k6]*SU3F[I1, k10, k7] + - SU3F[3, I1, k6]*SU3F[I4, k10, k7]) + SU3D[I1, k10, k9]* - (SU3F[3, I4, k6]*SU3F[I2, k10, k7] + SU3F[3, I2, k6]* - SU3F[I4, k10, k7])) + SU3D[I3, k10, k9]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k6]*SU3F[I1, k10, k7] + - SU3F[3, I1, k6]*SU3F[I2, k10, k7]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k6]*SU3F[I1, k10, k7] + SU3F[3, I1, k6]* - SU3F[I4, k10, k7]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k6]*SU3F[I2, k10, k7] + SU3F[3, I2, k6]* - SU3F[I4, k10, k7]))) + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[3, I1, k6]*SU3F[I5, k10, k7] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[3, I1, k6]* - SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I1, k6]*SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[3, I1, k6]*SU3F[I5, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[3, I2, k6]* - SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[3, I2, k6]*SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k6, k7]*SU3F[3, I2, k6]*SU3F[I5, k10, k7] + - SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[3, I2, k6]* - SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3F[3, I3, k6]*SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[3, I3, k6]*SU3F[I5, k10, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]* - SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[3, I4, k6]*SU3F[I5, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3F[3, I4, k6]*SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3F[3, I4, k6]*SU3F[I5, k10, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3F[3, I4, k6]* - SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k6]*SU3F[I5, k10, k7] + SU3D[6, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I3, k6]* - SU3F[I1, k10, k7] + SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6]*SU3F[I1, k10, k7] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[3, I3, k6]*SU3F[I2, k10, k7] + - SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k7] + SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[3, I1, k6]*SU3F[I3, k10, k7] + SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k10, k7] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k9]*SU3F[3, I2, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[3, I5, k6]*SU3F[I3, k10, k7] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[3, I3, k6]*SU3F[I5, k10, k7] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I5, k10, k7] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k9]*(SU3F[3, I2, k6]* - SU3F[I1, k10, k7] + SU3F[3, I1, k6]*SU3F[I2, k10, k7]) + - SU3D[I2, k10, k9]*(SU3F[3, I5, k6]*SU3F[I1, k10, k7] + - SU3F[3, I1, k6]*SU3F[I5, k10, k7]) + SU3D[I1, k10, k9]* - (SU3F[3, I5, k6]*SU3F[I2, k10, k7] + SU3F[3, I2, k6]* - SU3F[I5, k10, k7])) + SU3D[I3, k10, k9]* - (SU3D[I5, k6, k7]*(SU3F[3, I2, k6]*SU3F[I1, k10, k7] + - SU3F[3, I1, k6]*SU3F[I2, k10, k7]) + SU3D[I2, k6, k7]* - (SU3F[3, I5, k6]*SU3F[I1, k10, k7] + SU3F[3, I1, k6]* - SU3F[I5, k10, k7]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k6]*SU3F[I2, k10, k7] + SU3F[3, I2, k6]* - SU3F[I5, k10, k7]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I2, k6]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I3, k6]*SU3F[I1, k10, k7] + - SU3D[6, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[8, I4, k6]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I4, k6]*SU3F[I1, k10, k7] + - SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[8, I5, k6]*SU3F[I1, k10, k7] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[8, I5, k6]* - SU3F[I1, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I1, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k10, k7] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I1, k6]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I3, k6]*SU3F[I2, k10, k7] + - SU3D[6, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[8, I4, k6]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I4, k6]*SU3F[I2, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[8, I5, k6]*SU3F[I2, k10, k7] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[8, I5, k6]* - SU3F[I2, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I2, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k10, k7] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I1, k6]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I2, k6]*SU3F[I3, k10, k7] + - SU3D[6, I1, k9]*SU3D[I4, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[8, I4, k6]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I4, k6]*SU3F[I3, k10, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[8, I5, k6]*SU3F[I3, k10, k7] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[8, I5, k6]* - SU3F[I3, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I3, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k7] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I1, k6]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k9]* - SU3F[8, I1, k6]*SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k10, k7] + - SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k9]* - SU3F[8, I2, k6]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I2, k6]*SU3F[I4, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I3, k6]*SU3F[I4, k10, k7] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I3, k6]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k9]*SU3F[8, I5, k6]* - SU3F[I4, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]* - SU3F[8, I5, k6]*SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k9]*SU3F[8, I5, k6]*SU3F[I4, k10, k7] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k9]*SU3F[8, I5, k6]* - SU3F[I4, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]* - SU3F[8, I5, k6]*SU3F[I4, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I4, k10, k7] + - SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k9]*SU3F[8, I3, k6]* - SU3F[I1, k10, k7] + SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k10, k7] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k9]*SU3F[8, I3, k6]*SU3F[I2, k10, k7] + - SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k7] + SU3D[I2, k6, k7]*SU3D[I4, k10, k9]* - SU3F[8, I1, k6]*SU3F[I3, k10, k7] + SU3D[I2, k10, k9]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k10, k7] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[8, I2, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[8, I4, k6]*SU3F[I3, k10, k7] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[8, I3, k6]*SU3F[I4, k10, k7] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k7] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k9]*(SU3F[8, I2, k6]* - SU3F[I1, k10, k7] + SU3F[8, I1, k6]*SU3F[I2, k10, k7]) + - SU3D[I2, k10, k9]*(SU3F[8, I4, k6]*SU3F[I1, k10, k7] + - SU3F[8, I1, k6]*SU3F[I4, k10, k7]) + SU3D[I1, k10, k9]* - (SU3F[8, I4, k6]*SU3F[I2, k10, k7] + SU3F[8, I2, k6]* - SU3F[I4, k10, k7])) + SU3D[I3, k10, k9]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k10, k7] + - SU3F[8, I1, k6]*SU3F[I2, k10, k7]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I1, k10, k7] + SU3F[8, I1, k6]* - SU3F[I4, k10, k7]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k10, k7] + SU3F[8, I2, k6]* - SU3F[I4, k10, k7]))) + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[8, I1, k6]*SU3F[I5, k10, k7] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]*SU3F[8, I1, k6]* - SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I1, k6]*SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I5, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]*SU3F[8, I2, k6]* - SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k9]* - SU3F[8, I2, k6]*SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I5, k10, k7] + - SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k9]* - SU3F[8, I3, k6]*SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k9]*SU3F[8, I3, k6]*SU3F[I5, k10, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[8, I4, k6]*SU3F[I5, k10, k7] + - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I5, k10, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k9]* - SU3F[8, I4, k6]*SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k9]*SU3F[8, I4, k6]*SU3F[I5, k10, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3D[I3, k6, k7]*SU3F[8, I4, k6]* - SU3F[I5, k10, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]*SU3D[I3, k6, k7]* - SU3F[8, I4, k6]*SU3F[I5, k10, k7] + SU3D[6, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I3, k6]* - SU3F[I1, k10, k7] + SU3D[I2, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k10, k7] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k9]*SU3F[8, I3, k6]*SU3F[I2, k10, k7] + - SU3D[I1, k10, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k7] + SU3D[I2, k6, k7]*SU3D[I5, k10, k9]* - SU3F[8, I1, k6]*SU3F[I3, k10, k7] + SU3D[I2, k10, k9]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k10, k7] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k9]*SU3F[8, I2, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k10, k9]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k9]*SU3F[8, I5, k6]*SU3F[I3, k10, k7] + - SU3D[I1, k10, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3D[I2, k10, k9]* - SU3F[8, I3, k6]*SU3F[I5, k10, k7] + SU3D[I1, k10, k9]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I5, k10, k7] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k9]*(SU3F[8, I2, k6]* - SU3F[I1, k10, k7] + SU3F[8, I1, k6]*SU3F[I2, k10, k7]) + - SU3D[I2, k10, k9]*(SU3F[8, I5, k6]*SU3F[I1, k10, k7] + - SU3F[8, I1, k6]*SU3F[I5, k10, k7]) + SU3D[I1, k10, k9]* - (SU3F[8, I5, k6]*SU3F[I2, k10, k7] + SU3F[8, I2, k6]* - SU3F[I5, k10, k7])) + SU3D[I3, k10, k9]* - (SU3D[I5, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k10, k7] + - SU3F[8, I1, k6]*SU3F[I2, k10, k7]) + SU3D[I2, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I1, k10, k7] + SU3F[8, I1, k6]* - SU3F[I5, k10, k7]) + SU3D[I1, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k10, k7] + SU3F[8, I2, k6]* - SU3F[I5, k10, k7]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I1, k10, k9] + SU3D[3, I2, k7]* - SU3D[6, I5, k9]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + - SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I1, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[3, I2, k7]* - SU3D[6, I4, k9]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[3, I2, k7]* - SU3D[6, I3, k9]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I5, k9]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I2, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I4, k9]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I3, k9]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I5, k9]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I3, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I4, k9]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I2, k9]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k11, k7]* - SU3D[I2, k10, k11]*SU3F[I4, k10, k9] + SU3D[3, I3, k7]* - SU3D[6, I5, k9]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I5, k9]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[3, I2, k7]* - SU3D[6, I3, k9]*SU3D[I1, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I3, k9]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[3, I5, k7]* - (SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + SU3D[6, I1, k9]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I3, k10, k9] + SU3D[6, I4, k9]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k9])) + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I3, k9]* - ((SU3D[I1, k11, k7]*SU3D[I4, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I4, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I4, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I4, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I4, k10, k9]))) + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I4, k9]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I2, k7]* - SU3D[6, I3, k9]*SU3D[I1, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I3, k9]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I4, k7]* - (SU3D[6, I2, k9]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + SU3D[6, I1, k9]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + SU3D[6, I5, k9]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k9])) + SU3D[6, I2, k9]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k9]* - ((SU3D[I1, k11, k7]*SU3D[I5, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I5, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I5, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I5, k10, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I4, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I2, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I5, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I2, k10, k9] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I4, k10, k11]*SU3F[I3, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I3, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k11, k7]*SU3F[I3, k10, k9] + SU3D[8, I4, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k9])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I4, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I4, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I4, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I4, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I4, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I4, k10, k9]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k11, k7]*SU3D[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k11]*SU3D[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k11, k7]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k11, k7]* - SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k11, k7]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + SU3D[8, I1, k7]* - SU3D[I3, k11, k7]*SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I2, k10, k9] + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I5, k11, k7]* - SU3F[I3, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I5, k11, k7]*SU3F[I3, k10, k9] + SU3D[8, I5, k7]* - ((SU3D[I1, k11, k7]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I3, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I3, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I3, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I3, k10, k9])) + SU3D[8, I2, k7]*SU3D[I1, k11, k7]* - SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]* - SU3D[I2, k11, k7]*SU3D[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]* - ((SU3D[I1, k11, k7]*SU3D[I5, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I5, k11, k7])*SU3F[I2, k10, k9] + SU3D[I2, k11, k7]* - (SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + SU3D[I1, k10, k11]* - SU3F[I5, k10, k9]) + SU3D[I2, k10, k11]* - (SU3D[I5, k11, k7]*SU3F[I1, k10, k9] + SU3D[I1, k11, k7]* - SU3F[I5, k10, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I2, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I4, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I4, k6]*SU3F[I1, k10, k9] + - SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I5, k6]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I5, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k10, k9] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I1, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I4, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I4, k6]*SU3F[I2, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I5, k6]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I5, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I2, k10, k9] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I1, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I1, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I2, k6]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I4, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I4, k6]*SU3F[I3, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I4, k6]*SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I5, k6]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I5, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I5, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I3, k10, k9] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I1, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I1, k6]*SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[I4, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I2, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I2, k6]*SU3F[I4, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I3, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[3, I5, k6]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[3, I5, k6]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[3, I5, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[I4, k10, k9] + - SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I3, k6]* - SU3F[I1, k10, k9] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[I1, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I3, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k9] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[3, I1, k6]*SU3F[I3, k10, k9] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I2, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I2, k6]*SU3F[I3, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[3, I4, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[3, I3, k6]*SU3F[I4, k10, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k10, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[3, I2, k6]* - SU3F[I1, k10, k9] + SU3F[3, I1, k6]*SU3F[I2, k10, k9]) + - SU3D[I2, k10, k7]*(SU3F[3, I4, k6]*SU3F[I1, k10, k9] + - SU3F[3, I1, k6]*SU3F[I4, k10, k9]) + SU3D[I1, k10, k7]* - (SU3F[3, I4, k6]*SU3F[I2, k10, k9] + SU3F[3, I2, k6]* - SU3F[I4, k10, k9])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k6]*SU3F[I1, k10, k9] + - SU3F[3, I1, k6]*SU3F[I2, k10, k9]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k6]*SU3F[I1, k10, k9] + SU3F[3, I1, k6]* - SU3F[I4, k10, k9]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k6]*SU3F[I2, k10, k9] + SU3F[3, I2, k6]* - SU3F[I4, k10, k9]))) + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I1, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I1, k6]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I1, k6]*SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I1, k6]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[3, I2, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[3, I2, k6]*SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[3, I2, k6]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[3, I2, k6]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[3, I3, k6]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[3, I3, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[3, I3, k6]*SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[3, I4, k6]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[3, I4, k6]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[3, I4, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[3, I4, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[3, I4, k6]*SU3F[I5, k10, k9] + SU3D[6, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I3, k6]* - SU3F[I1, k10, k9] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I3, k6]*SU3F[I1, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[3, I3, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[I2, k10, k9] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[3, I1, k6]*SU3F[I3, k10, k9] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[3, I2, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[3, I2, k6]*SU3F[I3, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[3, I5, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[3, I3, k6]*SU3F[I5, k10, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I5, k10, k9] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[3, I2, k6]* - SU3F[I1, k10, k9] + SU3F[3, I1, k6]*SU3F[I2, k10, k9]) + - SU3D[I2, k10, k7]*(SU3F[3, I5, k6]*SU3F[I1, k10, k9] + - SU3F[3, I1, k6]*SU3F[I5, k10, k9]) + SU3D[I1, k10, k7]* - (SU3F[3, I5, k6]*SU3F[I2, k10, k9] + SU3F[3, I2, k6]* - SU3F[I5, k10, k9])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[3, I2, k6]*SU3F[I1, k10, k9] + - SU3F[3, I1, k6]*SU3F[I2, k10, k9]) + SU3D[I2, k6, k7]* - (SU3F[3, I5, k6]*SU3F[I1, k10, k9] + SU3F[3, I1, k6]* - SU3F[I5, k10, k9]) + SU3D[I1, k6, k7]* - (SU3F[3, I5, k6]*SU3F[I2, k10, k9] + SU3F[3, I2, k6]* - SU3F[I5, k10, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I2, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I1, k10, k9] + - SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I1, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I1, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I1, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k10, k9] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I2, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I2, k10, k9] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I2, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I2, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k10, k9] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I2, k6]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I4, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I4, k6]*SU3F[I3, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I4, k6]*SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I5, k6]* - SU3F[I3, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I5, k6]*SU3F[I3, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k9] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I1, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I1, k6]*SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I2, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I2, k6]*SU3F[I4, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I3, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[8, I5, k6]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[8, I5, k6]*SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[8, I5, k6]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[8, I5, k6]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[8, I5, k6]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I4, k10, k9] + - SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k9] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k9] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k9] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I4, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[8, I3, k6]*SU3F[I4, k10, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k10, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[8, I2, k6]* - SU3F[I1, k10, k9] + SU3F[8, I1, k6]*SU3F[I2, k10, k9]) + - SU3D[I2, k10, k7]*(SU3F[8, I4, k6]*SU3F[I1, k10, k9] + - SU3F[8, I1, k6]*SU3F[I4, k10, k9]) + SU3D[I1, k10, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k10, k9] + SU3F[8, I2, k6]* - SU3F[I4, k10, k9])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k10, k9] + - SU3F[8, I1, k6]*SU3F[I2, k10, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I1, k10, k9] + SU3F[8, I1, k6]* - SU3F[I4, k10, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k6]*SU3F[I2, k10, k9] + SU3F[8, I2, k6]* - SU3F[I4, k10, k9]))) + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I1, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I1, k6]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I1, k6]*SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I1, k6]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[8, I2, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I2, k6]*SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[8, I3, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I4, k6]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[8, I4, k6]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[8, I4, k6]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[8, I4, k6]* - SU3F[I5, k10, k9] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[8, I4, k6]*SU3F[I5, k10, k9] + SU3D[6, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I3, k6]* - SU3F[I1, k10, k9] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[8, I3, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[8, I3, k6]* - SU3F[I2, k10, k9] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[8, I1, k6]*SU3F[I3, k10, k9] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[8, I2, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k10, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[8, I5, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k10, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[8, I3, k6]*SU3F[I5, k10, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I5, k10, k9] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[8, I2, k6]* - SU3F[I1, k10, k9] + SU3F[8, I1, k6]*SU3F[I2, k10, k9]) + - SU3D[I2, k10, k7]*(SU3F[8, I5, k6]*SU3F[I1, k10, k9] + - SU3F[8, I1, k6]*SU3F[I5, k10, k9]) + SU3D[I1, k10, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k10, k9] + SU3F[8, I2, k6]* - SU3F[I5, k10, k9])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[8, I2, k6]*SU3F[I1, k10, k9] + - SU3F[8, I1, k6]*SU3F[I2, k10, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I1, k10, k9] + SU3F[8, I1, k6]* - SU3F[I5, k10, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I5, k6]*SU3F[I2, k10, k9] + SU3F[8, I2, k6]* - SU3F[I5, k10, k9]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]* - SU3F[6, I2, k8]*SU3F[I1, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I3, k8]*SU3F[I1, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k8]* - SU3F[I1, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I4, k8]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I4, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I4, k8]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I4, k8]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I5, k8]*SU3F[I1, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k8]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I1, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k8]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I3, k8]*SU3F[I2, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k8]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I4, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I4, k8]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I4, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k8]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I4, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k8]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I5, k8]*SU3F[I2, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k8]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I1, k8]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I2, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I2, k8]*SU3F[I3, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k8]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I4, k8]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I4, k8]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I4, k8]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I5, k8]*SU3F[I3, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k8]* - SU3F[I4, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I1, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I1, k8]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I1, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I1, k8]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I1, k8]*SU3F[I4, k11, k6] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k8]* - SU3F[I4, k11, k6] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I2, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I2, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I2, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I2, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k8]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I3, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I3, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I3, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I3, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I5, k8]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I5, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I5, k8]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I5, k8]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k8]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I1, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I2, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I2, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I4, k11]*SU3F[6, I3, k8]*SU3F[I5, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k8]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I1, k11]*SU3F[6, I4, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[3, I2, k11]*SU3F[6, I4, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I4, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I4, k8]*SU3F[I5, k11, k6] + - SU3D[I4, k7, k8]*(SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[6, I5, k8]*SU3F[I1, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I3, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k8]* - SU3F[I2, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]* - SU3F[6, I1, k8]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k8]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I5, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[6, I5, k8]*SU3F[I3, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[3, I3, k11]*(SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3F[6, I1, k8]*SU3F[I2, k11, k6]) + SU3F[3, I2, k11]* - (SU3F[6, I3, k8]*SU3F[I1, k11, k6] + SU3F[6, I1, k8]* - SU3F[I3, k11, k6]) + SU3F[3, I1, k11]* - (SU3F[6, I3, k8]*SU3F[I2, k11, k6] + SU3F[6, I2, k8]* - SU3F[I3, k11, k6])) + SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[6, I1, k8]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k8]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[6, I3, k8]*SU3F[I5, k11, k6] + SU3D[I3, k6, k7]* - (SU3F[3, I5, k11]*(SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3F[6, I1, k8]*SU3F[I2, k11, k6]) + SU3F[3, I2, k11]* - (SU3F[6, I5, k8]*SU3F[I1, k11, k6] + SU3F[6, I1, k8]* - SU3F[I5, k11, k6]) + SU3F[3, I1, k11]* - (SU3F[6, I5, k8]*SU3F[I2, k11, k6] + SU3F[6, I2, k8]* - SU3F[I5, k11, k6]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[3, I5, k11]*SU3F[6, I3, k8]* - SU3F[I1, k11, k6] + SU3D[I2, k7, k8]*SU3F[3, I3, k11]* - SU3F[6, I5, k8]*SU3F[I1, k11, k6] + SU3D[I1, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I3, k8]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3F[3, I3, k11]*SU3F[6, I5, k8]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k8]*SU3F[3, I5, k11]* - SU3F[6, I1, k8]*SU3F[I3, k11, k6] + SU3D[I1, k7, k8]* - SU3F[3, I5, k11]*SU3F[6, I2, k8]*SU3F[I3, k11, k6] + - SU3D[I2, k7, k8]*SU3F[3, I1, k11]*SU3F[6, I5, k8]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k8]*SU3F[3, I2, k11]* - SU3F[6, I5, k8]*SU3F[I3, k11, k6] + SU3D[I5, k7, k8]* - (SU3F[3, I3, k11]*(SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3F[6, I1, k8]*SU3F[I2, k11, k6]) + SU3F[3, I2, k11]* - (SU3F[6, I3, k8]*SU3F[I1, k11, k6] + SU3F[6, I1, k8]* - SU3F[I3, k11, k6]) + SU3F[3, I1, k11]* - (SU3F[6, I3, k8]*SU3F[I2, k11, k6] + SU3F[6, I2, k8]* - SU3F[I3, k11, k6])) + SU3D[I2, k7, k8]*SU3F[3, I3, k11]* - SU3F[6, I1, k8]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3F[3, I3, k11]*SU3F[6, I2, k8]*SU3F[I5, k11, k6] + - SU3D[I2, k7, k8]*SU3F[3, I1, k11]*SU3F[6, I3, k8]* - SU3F[I5, k11, k6] + SU3D[I1, k7, k8]*SU3F[3, I2, k11]* - SU3F[6, I3, k8]*SU3F[I5, k11, k6] + SU3D[I3, k7, k8]* - (SU3F[3, I5, k11]*(SU3F[6, I2, k8]*SU3F[I1, k11, k6] + - SU3F[6, I1, k8]*SU3F[I2, k11, k6]) + SU3F[3, I2, k11]* - (SU3F[6, I5, k8]*SU3F[I1, k11, k6] + SU3F[6, I1, k8]* - SU3F[I5, k11, k6]) + SU3F[3, I1, k11]* - (SU3F[6, I5, k8]*SU3F[I2, k11, k6] + SU3F[6, I2, k8]* - SU3F[I5, k11, k6])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k11]*SU3F[I1, k11, k6] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I1, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I2, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I2, k11, k6] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I4, k11]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I4, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I4, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I5, k11]*SU3F[I3, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[8, I1, k11]*SU3F[I4, k11, k6] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I1, k11]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I2, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I3, k11]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I5, k11]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I5, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I5, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I4, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I4, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I1, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I2, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]* - SU3F[8, I2, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[8, I3, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]* - SU3F[8, I4, k11]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I4, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[8, I4, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I4, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I4, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I4, k11]* - SU3F[I5, k11, k6] + SU3D[I4, k7, k8]* - (SU3D[I2, k6, k7]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k6, k7]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I3, k11, k6])) + SU3D[I2, k6, k7]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k8]*SU3F[8, I2, k11]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I5, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I5, k11, k6]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6] + SU3D[I2, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I5, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k7, k8]*SU3F[6, I3, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6] + SU3D[I2, k7, k8]*SU3F[6, I5, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I5, k8]*SU3F[8, I2, k11]*SU3F[I3, k11, k6] + - SU3D[I2, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I3, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I3, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I3, k11, k6])) + SU3D[I2, k7, k8]*SU3F[6, I3, k8]* - SU3F[8, I1, k11]*SU3F[I5, k11, k6] + SU3D[I1, k7, k8]* - SU3F[6, I3, k8]*SU3F[8, I2, k11]*SU3F[I5, k11, k6] + - SU3D[I2, k7, k8]*SU3F[6, I1, k8]*SU3F[8, I3, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k7, k8]*SU3F[6, I2, k8]* - SU3F[8, I3, k11]*SU3F[I5, k11, k6] + SU3D[I3, k7, k8]* - (SU3F[6, I5, k8]*(SU3F[8, I2, k11]*SU3F[I1, k11, k6] + - SU3F[8, I1, k11]*SU3F[I2, k11, k6]) + SU3F[6, I2, k8]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k6] + SU3F[8, I1, k11]* - SU3F[I5, k11, k6]) + SU3F[6, I1, k8]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k6] + SU3F[8, I2, k11]* - SU3F[I5, k11, k6])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I1, k10, k7]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I1, k10, k7]*SU3F[I2, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I1, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I4, k10]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I5, k10]* - SU3F[I2, k10, k7]*SU3F[I3, k11, k6] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k10]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k10]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I5, k10]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k10]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k10]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k10]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k10]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k10]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k10]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k10]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I2, k10]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k10]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I5, k10]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k10]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k10]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I3, k10]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[6, I5, k10]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[6, I1, k10]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[6, I2, k10]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I5, k10]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[3, I2, k11]*SU3F[6, I4, k10]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[3, I2, k11]* - SU3F[6, I4, k10]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[3, I1, k11]*SU3F[6, I4, k10]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[3, I4, k11]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[3, I2, k11]*SU3F[6, I3, k10]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3F[3, I1, k11]* - SU3F[6, I3, k10]*SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + - SU3F[3, I2, k11]*SU3F[6, I1, k10]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3F[3, I1, k11]*SU3F[6, I2, k10]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3F[3, I2, k11]* - SU3F[6, I3, k10]*SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + - SU3F[3, I1, k11]*SU3F[6, I3, k10]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3F[3, I2, k11]*SU3F[6, I1, k10]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3F[3, I1, k11]* - SU3F[6, I2, k10]*SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + - SU3F[3, I3, k11]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I4, k11, k6]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I4, k11, k6]))) + SU3D[I3, k6, k7]*SU3F[3, I4, k11]* - SU3F[6, I2, k10]*SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I3, k10]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k10]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k10]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k10]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k10]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k10]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k10]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I2, k10]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I4, k10]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k10]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I1, k10]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k10]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k10]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k10]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I3, k10]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I2, k10]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k10]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I4, k10]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k10]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k10]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I3, k10]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I4, k10]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[6, I1, k10]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[6, I2, k10]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I4, k10]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I4, k10]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I2, k11]*SU3F[6, I1, k10]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I1, k10]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I2, k10]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[6, I2, k10]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[6, I3, k10]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[6, I3, k10]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I4, k6, k7]* - (SU3F[3, I2, k11]*SU3F[6, I5, k10]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[3, I1, k11]*SU3F[6, I5, k10]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[3, I2, k11]* - SU3F[6, I5, k10]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[3, I1, k11]*SU3F[6, I5, k10]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[3, I5, k11]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[3, I2, k11]*SU3F[6, I3, k10]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3F[3, I1, k11]* - SU3F[6, I3, k10]*SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + - SU3F[3, I2, k11]*SU3F[6, I1, k10]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3F[3, I1, k11]*SU3F[6, I2, k10]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3F[3, I2, k11]* - SU3F[6, I3, k10]*SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + - SU3F[3, I1, k11]*SU3F[6, I3, k10]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3F[3, I2, k11]*SU3F[6, I1, k10]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3F[3, I1, k11]* - SU3F[6, I2, k10]*SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + - SU3F[3, I3, k11]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I5, k11, k6]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I5, k11, k6]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I2, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I2, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k11]* - SU3F[I2, k10, k7]*SU3F[I3, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k11]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k11]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k11]* - SU3F[I2, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k11]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I3, k10, k7]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I4, k11]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[6, I4, k10]* - (SU3F[8, I3, k11]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[6, I2, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + SU3F[6, I1, k10]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + - SU3F[6, I2, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I3, k11]*SU3F[I1, k10, k7]*SU3F[I4, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I4, k11, k6] + SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + SU3F[6, I1, k10]* - SU3F[8, I2, k11]*SU3F[I3, k10, k7]*SU3F[I4, k11, k6] + - SU3F[6, I3, k10]*(SU3F[8, I4, k11]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I4, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I4, k11, k6]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I2, k11]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k11]* - SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I1, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I2, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k11]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k11]*SU3F[I3, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k11]* - SU3F[I4, k10, k7]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k11]*SU3F[I4, k10, k7]* - SU3F[I5, k11, k6] + SU3D[I4, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I5, k11]*SU3F[I1, k10, k7]*SU3F[I3, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I5, k11]*SU3F[I2, k10, k7]* - SU3F[I3, k11, k6] + SU3F[6, I5, k10]* - (SU3F[8, I3, k11]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + SU3F[8, I2, k11]* - (SU3F[I1, k11, k6]*SU3F[I3, k10, k7] + SU3F[I1, k10, k7]* - SU3F[I3, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I3, k11, k6])) + SU3F[6, I2, k10]*SU3F[8, I3, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + SU3F[6, I1, k10]* - SU3F[8, I3, k11]*SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + - SU3F[6, I2, k10]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k7] + SU3F[6, I1, k10]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k7] + SU3F[6, I2, k10]* - SU3F[8, I3, k11]*SU3F[I1, k10, k7]*SU3F[I5, k11, k6] + - SU3F[6, I1, k10]*SU3F[8, I3, k11]*SU3F[I2, k10, k7]* - SU3F[I5, k11, k6] + SU3F[6, I2, k10]*SU3F[8, I1, k11]* - SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + SU3F[6, I1, k10]* - SU3F[8, I2, k11]*SU3F[I3, k10, k7]*SU3F[I5, k11, k6] + - SU3F[6, I3, k10]*(SU3F[8, I5, k11]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k7] + SU3F[I1, k10, k7]*SU3F[I2, k11, k6]) + - SU3F[8, I2, k11]*(SU3F[I1, k11, k6]*SU3F[I5, k10, k7] + - SU3F[I1, k10, k7]*SU3F[I5, k11, k6]) + SU3F[8, I1, k11]* - (SU3F[I2, k11, k6]*SU3F[I5, k10, k7] + SU3F[I2, k10, k7]* - SU3F[I5, k11, k6]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I1, k11, k7] + SU3D[3, I2, k7]* - SU3D[6, I5, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k9]*SU3F[I1, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I1, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I1, k11, k7] + SU3D[3, I2, k7]* - SU3D[6, I4, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I1, k11, k7] + SU3D[3, I2, k7]* - SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k11]*SU3D[I5, k10, k9]*SU3F[I1, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I1, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I2, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I5, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I2, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k11]*SU3D[I4, k10, k9]*SU3F[I2, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I4, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I2, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I2, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k11]*SU3D[I5, k10, k9]*SU3F[I2, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I2, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I3, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I5, k9]*SU3D[I2, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I3, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k11]*SU3D[I4, k10, k9]*SU3F[I3, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I4, k9]*SU3D[I2, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I2, k9]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k11]*SU3D[I5, k10, k9]*SU3F[I3, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I3, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I3, k7]* - SU3D[6, I5, k9]*SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k9]* - SU3D[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I5, k9]*SU3D[I2, k10, k9]*SU3D[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k11]*SU3D[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k11]*SU3D[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I2, k7]* - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k11]*SU3D[I5, k10, k9]*SU3F[I4, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I4, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I2, k10, k11]*SU3D[I5, k10, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I4, k11, k7] + SU3D[3, I5, k7]* - (SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k11, k7] + SU3D[6, I2, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k11]*SU3F[I2, k11, k7] + - SU3D[6, I1, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k11]*SU3F[I3, k11, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I4, k10, k9]*SU3F[I3, k11, k7] + SU3D[6, I4, k9]* - ((SU3D[I1, k10, k9]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k10, k9])*SU3F[I2, k11, k7] + SU3D[I2, k10, k9]* - (SU3D[I3, k10, k11]*SU3F[I1, k11, k7] + SU3D[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3D[I2, k10, k11]* - (SU3D[I3, k10, k9]*SU3F[I1, k11, k7] + SU3D[I1, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3D[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k10, k9]*SU3D[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k11]*SU3D[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I3, k9]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I4, k10, k9])*SU3F[I2, k11, k7] + SU3D[I2, k10, k9]* - (SU3D[I4, k10, k11]*SU3F[I1, k11, k7] + SU3D[I1, k10, k11]* - SU3F[I4, k11, k7]) + SU3D[I2, k10, k11]* - (SU3D[I4, k10, k9]*SU3F[I1, k11, k7] + SU3D[I1, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k9]*SU3D[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k9]* - SU3D[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I4, k9]*SU3D[I2, k10, k9]*SU3D[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I1, k10, k11]*SU3D[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I2, k10, k11]*SU3D[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I2, k7]* - SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I3, k9]*SU3D[I2, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k11]*SU3D[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I2, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3D[I3, k10, k11]*SU3D[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I4, k7]* - (SU3D[6, I2, k9]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k7] + SU3D[6, I2, k9]*SU3D[I3, k10, k11]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k11]*SU3F[I2, k11, k7] + - SU3D[6, I1, k9]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k10, k9]*SU3D[I5, k10, k11]*SU3F[I3, k11, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I5, k10, k9]*SU3F[I3, k11, k7] + SU3D[6, I5, k9]* - ((SU3D[I1, k10, k9]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k10, k9])*SU3F[I2, k11, k7] + SU3D[I2, k10, k9]* - (SU3D[I3, k10, k11]*SU3F[I1, k11, k7] + SU3D[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3D[I2, k10, k11]* - (SU3D[I3, k10, k9]*SU3F[I1, k11, k7] + SU3D[I1, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3D[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k10, k9]*SU3D[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[I1, k10, k11]*SU3D[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k9]* - ((SU3D[I1, k10, k9]*SU3D[I5, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I5, k10, k9])*SU3F[I2, k11, k7] + SU3D[I2, k10, k9]* - (SU3D[I5, k10, k11]*SU3F[I1, k11, k7] + SU3D[I1, k10, k11]* - SU3F[I5, k11, k7]) + SU3D[I2, k10, k11]* - (SU3D[I5, k10, k9]*SU3F[I1, k11, k7] + SU3D[I1, k10, k9]* - SU3F[I5, k11, k7])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I1, k11, k7] + SU3D[6, I2, k9]* - SU3D[8, I5, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k9]*SU3F[I1, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I1, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I1, k11, k7] + SU3D[6, I2, k9]* - SU3D[8, I4, k7]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I1, k11, k7] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k10, k9]*SU3F[I1, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I1, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I2, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k10, k9]*SU3F[I2, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k10, k9]*SU3F[I2, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I2, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k10, k9]*SU3F[I3, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k10, k9]*SU3F[I3, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I3, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k9]* - SU3D[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3D[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k11]*SU3D[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I5, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I5, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I5, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k11, k7] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k7] + SU3D[8, I1, k7]* - SU3D[I3, k10, k9]*SU3D[I4, k10, k11]*SU3F[I2, k11, k7] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k7] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I3, k11, k7] + SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k11]*SU3F[I3, k11, k7] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k7] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I4, k10, k9]*SU3F[I3, k11, k7] + SU3D[8, I4, k7]* - ((SU3D[I1, k10, k9]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k10, k9])*SU3F[I2, k11, k7] + SU3D[I2, k10, k9]* - (SU3D[I3, k10, k11]*SU3F[I1, k11, k7] + SU3D[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3D[I2, k10, k11]* - (SU3D[I3, k10, k9]*SU3F[I1, k11, k7] + SU3D[I1, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3D[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[8, I3, k7]* - ((SU3D[I1, k10, k9]*SU3D[I4, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I4, k10, k9])*SU3F[I2, k11, k7] + SU3D[I2, k10, k9]* - (SU3D[I4, k10, k11]*SU3F[I1, k11, k7] + SU3D[I1, k10, k11]* - SU3F[I4, k11, k7]) + SU3D[I2, k10, k11]* - (SU3D[I4, k10, k9]*SU3F[I1, k11, k7] + SU3D[I1, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k9]*SU3D[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3D[I2, k10, k9]*SU3D[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I1, k10, k11]*SU3D[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I2, k10, k11]*SU3D[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3D[I2, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k11]*SU3D[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I2, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3D[I3, k10, k11]*SU3D[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k7] + SU3D[8, I2, k7]*SU3D[I3, k10, k11]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k7] + SU3D[8, I1, k7]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k11]*SU3F[I2, k11, k7] + - SU3D[8, I1, k7]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I3, k11, k7] + SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3D[I5, k10, k11]*SU3F[I3, k11, k7] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k7] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I5, k10, k9]*SU3F[I3, k11, k7] + SU3D[8, I5, k7]* - ((SU3D[I1, k10, k9]*SU3D[I3, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I3, k10, k9])*SU3F[I2, k11, k7] + SU3D[I2, k10, k9]* - (SU3D[I3, k10, k11]*SU3F[I1, k11, k7] + SU3D[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3D[I2, k10, k11]* - (SU3D[I3, k10, k9]*SU3F[I1, k11, k7] + SU3D[I1, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3D[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3D[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3D[I1, k10, k11]*SU3D[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k7]* - ((SU3D[I1, k10, k9]*SU3D[I5, k10, k11] + SU3D[I1, k10, k11]* - SU3D[I5, k10, k9])*SU3F[I2, k11, k7] + SU3D[I2, k10, k9]* - (SU3D[I5, k10, k11]*SU3F[I1, k11, k7] + SU3D[I1, k10, k11]* - SU3F[I5, k11, k7]) + SU3D[I2, k10, k11]* - (SU3D[I5, k10, k9]*SU3F[I1, k11, k7] + SU3D[I1, k10, k9]* - SU3F[I5, k11, k7])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I4, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I4, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I4, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I4, k9]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + - SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I5, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I5, k9]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I5, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I2, k9]* - SU3D[I5, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I5, k10, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I5, k9]* - SU3D[I3, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + - SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I2, k9]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[3, I5, k7]*(SU3D[6, I2, k9]*SU3D[I4, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3D[6, I1, k9]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[6, I4, k9]* - (SU3D[I3, k10, k9]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3D[I2, k10, k9]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I2, k9]* - SU3D[I3, k10, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I3, k9]*(SU3D[I4, k10, k9]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]))) + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k9]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I3, k9]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k9]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I4, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I3, k9]* - SU3D[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I3, k9]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I3, k9]* - SU3D[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I4, k7]* - (SU3D[6, I2, k9]*SU3D[I5, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]* - SU3D[I5, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3D[6, I1, k9]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[6, I5, k9]* - (SU3D[I3, k10, k9]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3D[I2, k10, k9]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3D[6, I2, k9]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I2, k9]* - SU3D[I3, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[I3, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I3, k9]*(SU3D[I5, k10, k9]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k7]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I5, k9]*(SU3D[8, I2, k7]*SU3D[I4, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3D[8, I1, k7]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[8, I4, k7]* - (SU3D[I3, k10, k9]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3D[I2, k10, k9]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3D[8, I2, k7]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3D[I3, k10, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[8, I3, k7]*(SU3D[I4, k10, k9]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k9]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k9]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I5, k10, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I5, k10, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3D[8, I1, k7]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[8, I5, k7]* - (SU3D[I3, k10, k9]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3D[I2, k10, k9]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3D[8, I2, k7]*SU3D[I3, k10, k9]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k10, k9]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I2, k7]* - SU3D[I3, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I1, k7]*SU3D[I3, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I2, k7]*SU3D[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]* - SU3D[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I3, k7]*(SU3D[I5, k10, k9]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k7]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I2, k10]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k10]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I5, k10]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k10]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I1, k10]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k10]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I5, k10]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k10]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I1, k10]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I2, k10]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I5, k10]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I5, k10]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I2, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I1, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I1, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I2, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I1, k6]*SU3F[6, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I5, k6, k7]* - (SU3F[3, I2, k6]*SU3F[6, I4, k10]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[3, I2, k6]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3F[3, I1, k6]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3F[3, I4, k6]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[3, I2, k6]*SU3F[6, I3, k10]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3F[3, I1, k6]* - SU3F[6, I3, k10]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3F[3, I2, k6]*SU3F[6, I1, k10]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[3, I1, k6]*SU3F[6, I2, k10]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[3, I2, k6]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3F[3, I1, k6]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3F[3, I2, k6]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[3, I1, k6]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3F[3, I3, k6]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]))) + SU3D[I3, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I2, k10]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I3, k10]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k10]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k10]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k10]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I3, k10]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k10]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k10]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I2, k10]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I4, k10]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I1, k10]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I1, k10]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I2, k10]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I2, k10]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I3, k10]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I3, k10]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I2, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[6, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I4, k6, k7]*(SU3F[3, I2, k6]*SU3F[6, I5, k10]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[3, I1, k6]* - SU3F[6, I5, k10]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[3, I2, k6]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3F[3, I1, k6]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3F[3, I5, k6]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[3, I2, k6]*SU3F[6, I3, k10]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3F[3, I1, k6]* - SU3F[6, I3, k10]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3F[3, I2, k6]*SU3F[6, I1, k10]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[3, I1, k6]*SU3F[6, I2, k10]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[3, I2, k6]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3F[3, I1, k6]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3F[3, I2, k6]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[3, I1, k6]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3F[3, I3, k6]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k7]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I2, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I3, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I3, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[8, I1, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k10]*SU3F[8, I2, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I1, k10]*SU3F[8, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I5, k6, k7]* - (SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I4, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3F[6, I4, k10]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I3, k6]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I3, k6]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[6, I1, k10]* - SU3F[8, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3F[6, I3, k10]*(SU3F[8, I4, k6]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]))) + SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[8, I2, k6]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I2, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I4, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k10]*SU3F[8, I2, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I4, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I4, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I1, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k10]*SU3F[8, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I2, k6, k7]*SU3F[6, I1, k10]*SU3F[8, I3, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I2, k10]*SU3F[8, I3, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I4, k6, k7]*(SU3F[6, I2, k10]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I5, k6]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3F[6, I1, k10]*SU3F[8, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3F[6, I5, k10]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k10]*SU3F[8, I3, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I1, k10]* - SU3F[8, I3, k6]*SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + - SU3F[6, I2, k10]*SU3F[8, I1, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[6, I1, k10]*SU3F[8, I2, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I2, k10]* - SU3F[8, I3, k6]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3F[6, I1, k10]*SU3F[8, I3, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3F[6, I2, k10]*SU3F[8, I1, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[6, I1, k10]* - SU3F[8, I2, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3F[6, I3, k10]*(SU3F[8, I5, k6]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k7]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3D[3, I3, k7]* - SU3D[6, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9] + - SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I3, k7]* - SU3D[6, I5, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[3, I5, k7]* - (SU3D[6, I4, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3F[I2, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3F[I2, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3F[I2, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I4, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I2, k7]* - SU3D[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I3, k9]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]* - SU3D[6, I2, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I3, k7]* - SU3D[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I4, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I2, k7]* - SU3D[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I3, k9]*SU3F[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]* - SU3D[6, I2, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3D[6, I1, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I4, k7]* - (SU3D[6, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3F[I2, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I3, k9]* - SU3D[8, I5, k7]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I5, k7]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[6, I5, k9]* - (SU3D[8, I4, k7]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[8, I2, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[8, I1, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[8, I2, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[8, I2, k7]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[8, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k7]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3D[8, I3, k7]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3F[I2, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3F[I2, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3F[I2, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3F[I1, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3F[I2, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3F[I2, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k9]* - SU3D[8, I4, k7]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I4, k7]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[8, I3, k7]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I3, k7]*SU3F[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[8, I2, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[8, I1, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I4, k9]* - (SU3D[8, I5, k7]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3D[8, I2, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I2, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I1, k7]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[8, I2, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I2, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3D[8, I1, k7]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k7]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[3, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3F[3, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[3, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I1, k7]*SU3F[3, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[3, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I1, k7]*SU3F[3, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[3, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I5, k7]*(SU3F[3, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[3, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[3, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[3, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[3, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[3, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[3, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[3, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[3, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[3, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[3, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[3, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k7]*SU3F[3, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[3, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[3, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I3, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[3, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[3, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[3, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I4, k7]* - (SU3F[3, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[3, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[3, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[3, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[3, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[3, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[3, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[3, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[3, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[3, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[3, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[3, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[3, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[3, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[3, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[3, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[3, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[3, I5, k7]*(SU3F[6, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[3, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[3, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[3, I4, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[8, I1, k7]*SU3F[6, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[8, I5, k7]*(SU3F[6, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[8, I3, k7]*SU3F[6, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I3, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k7]*SU3F[6, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k7]*SU3F[6, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k7]*SU3F[6, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[8, I4, k7]* - (SU3F[6, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[6, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[6, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[6, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[6, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[6, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[6, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[6, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[6, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[6, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k11, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I5, k9]* - SU3F[I1, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[6, I1, k7]*SU3F[8, I5, k9]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I5, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I5, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3D[6, I5, k7]*(SU3F[8, I4, k9]*(SU3F[I1, k11, k7]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[8, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[8, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[8, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[8, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + SU3F[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7] + - SU3F[8, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7] + SU3F[8, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]))) + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k11, k7]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k9] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k10, k9] + SU3D[6, I3, k7]*SU3F[8, I4, k9]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I3, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I4, k9]* - SU3F[I2, k10, k9]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I4, k9]*SU3F[I1, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I4, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I3, k9]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k7]*SU3F[8, I1, k9]*SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I3, k9]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k7]*SU3F[8, I1, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k7]*SU3F[8, I2, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k7] + SU3D[6, I4, k7]* - (SU3F[8, I5, k9]*(SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k7])) + SU3F[8, I2, k9]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[8, I1, k9]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3F[8, I2, k9]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[8, I1, k9]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[8, I2, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + SU3F[8, I1, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7]*SU3F[I5, k10, k9] + - SU3F[8, I2, k9]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3F[8, I1, k9]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3F[8, I2, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k7] + - SU3F[8, I1, k9]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k7] + SU3F[8, I3, k9]* - (SU3F[I1, k11, k7]*(SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k7]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k7]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k11, k7]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[3, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I1, k11, k8] + - SU3D[3, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[3, I3, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[3, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I1, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[3, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[3, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[3, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[3, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[3, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[3, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[3, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[3, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, k8, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[3, I5, k7]*(SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I4, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I4, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I4, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8]))) + SU3D[3, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I1, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I2, k11]*SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[3, I1, k7]*SU3D[I3, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[3, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[3, I1, k7]*SU3D[I2, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[3, I4, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I5, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I5, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I1, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I1, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[8, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[8, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I4, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[8, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[8, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k9]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]* - SU3D[I3, k8, k9]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[8, I5, k7]*(SU3D[I2, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I4, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I4, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I4, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I4, k11, k8]))) + SU3D[8, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I1, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I3, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I2, k11]*SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k9]* - SU3D[I4, k8, k9]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[8, I1, k7]*SU3D[I3, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I4, k8, k9]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I4, k8, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[8, I3, k7]*SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k9]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I1, k7, k9]*SU3D[I3, k8, k9]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[8, I1, k7]*SU3D[I2, k7, k9]*SU3D[I3, k8, k9]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I5, k7, k9]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I5, k8, k9]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k8, k9]*SU3D[I5, k7, k9]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k9]* - SU3D[I5, k8, k9]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k8, k9]*SU3D[I5, k7, k9]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k9]*SU3D[I5, k8, k9]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k9]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k9]*SU3D[I2, k8, k9]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k8, k9]*SU3D[I2, k7, k9]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k9]* - SU3D[I2, k8, k9]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k8, k9]*(SU3D[I5, k7, k9]*(SU3F[6, I2, k11]* - SU3F[I1, k11, k8] + SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + - SU3D[I2, k7, k9]*(SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I5, k11, k8]) + SU3D[I1, k7, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8])) + SU3D[I3, k7, k9]* - (SU3D[I5, k8, k9]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3D[I2, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3D[I1, k8, k9]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I2, k11]*SU3F[I1, k11, k8] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k6]* - SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I2, k6]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I4, k11]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k6]* - SU3F[6, I4, k11]*SU3F[I1, k11, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k11]*SU3F[I1, k11, k8] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I5, k11]* - SU3F[I1, k11, k8] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I1, k11]*SU3F[I2, k11, k8] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I1, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I3, k11]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k6]* - SU3F[6, I3, k11]*SU3F[I2, k11, k8] + SU3D[I3, k7, k8]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I4, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k11]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k6]* - SU3F[6, I4, k11]*SU3F[I2, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I1, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I2, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k6]* - SU3F[6, I2, k11]*SU3F[I3, k11, k8] + SU3D[I2, k7, k8]* - SU3D[I5, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I2, k6]*SU3F[6, I4, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I4, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I5, k6]* - SU3F[6, I4, k11]*SU3F[I3, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I5, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I2, k6]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I3, k6]* - SU3F[6, I1, k11]*SU3F[I4, k11, k8] + SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I1, k11]*SU3F[I4, k11, k8] + - SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k6]*SU3F[6, I1, k11]* - SU3F[I4, k11, k8] + SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[I3, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I3, k6]* - SU3F[6, I2, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I2, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k6]*SU3F[6, I2, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I5, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I3, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I5, k6]*SU3F[6, I3, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I5, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I5, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k6]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I1, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I2, k11]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k6]* - SU3F[6, I2, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[6, I3, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I4, k6]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I1, k6]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I4, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I4, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I4, k11]* - SU3F[I5, k11, k8] + SU3D[I4, k7, k8]* - (SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k6, k7]*SU3F[3, I3, k6]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[I5, k6, k7]* - (SU3F[3, I3, k6]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k6]* - (SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I3, k11, k8]) + SU3F[3, I1, k6]* - (SU3F[6, I3, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k6, k7]*SU3F[3, I3, k6]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I3, k6, k7]* - (SU3F[3, I5, k6]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k6]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3F[3, I1, k6]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[3, I5, k6]*SU3F[6, I3, k11]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k8]*SU3F[3, I3, k6]* - SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I5, k6]*SU3F[6, I3, k11]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I3, k6]*SU3F[6, I5, k11]* - SU3F[I2, k11, k8] + SU3D[I2, k7, k8]*SU3F[3, I5, k6]* - SU3F[6, I1, k11]*SU3F[I3, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I5, k6]*SU3F[6, I2, k11]*SU3F[I3, k11, k8] + - SU3D[I2, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I5, k11]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I5, k11]*SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[3, I3, k6]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k6]* - (SU3F[6, I3, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I3, k11, k8]) + SU3F[3, I1, k6]* - (SU3F[6, I3, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[3, I3, k6]* - SU3F[6, I1, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I3, k6]*SU3F[6, I2, k11]*SU3F[I5, k11, k8] + - SU3D[I2, k7, k8]*SU3F[3, I1, k6]*SU3F[6, I3, k11]* - SU3F[I5, k11, k8] + SU3D[I1, k7, k8]*SU3F[3, I2, k6]* - SU3F[6, I3, k11]*SU3F[I5, k11, k8] + SU3D[I3, k7, k8]* - (SU3F[3, I5, k6]*(SU3F[6, I2, k11]*SU3F[I1, k11, k8] + - SU3F[6, I1, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k6]* - (SU3F[6, I5, k11]*SU3F[I1, k11, k8] + SU3F[6, I1, k11]* - SU3F[I5, k11, k8]) + SU3F[3, I1, k6]* - (SU3F[6, I5, k11]*SU3F[I2, k11, k8] + SU3F[6, I2, k11]* - SU3F[I5, k11, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[8, I2, k6]*SU3F[I1, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I1, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I1, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I1, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I2, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I2, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I3, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I2, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I4, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I4, k6]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I5, k6]*SU3F[I3, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I1, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I1, k6]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I2, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I4, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I5, k6]*SU3F[I4, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I1, k6]* - SU3F[I5, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I1, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I2, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k11]*SU3F[8, I3, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I2, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I1, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I3, k7, k8]* - SU3F[6, I2, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I4, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3D[I2, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I4, k6]*SU3F[I5, k11, k8] + - SU3D[I4, k7, k8]*(SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I2, k6, k7]*SU3F[6, I5, k11]* - SU3F[8, I1, k6]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[8, I5, k6]*SU3F[I3, k11, k8] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I3, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I3, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I3, k11, k8])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[8, I1, k6]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[8, I3, k6]*SU3F[I5, k11, k8] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I5, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I5, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I5, k11, k8]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k11]*SU3F[8, I3, k6]* - SU3F[I1, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I3, k11]* - SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I3, k6]*SU3F[I2, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k11]*SU3F[8, I5, k6]* - SU3F[I2, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I5, k11]* - SU3F[8, I1, k6]*SU3F[I3, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I5, k11]*SU3F[8, I2, k6]*SU3F[I3, k11, k8] + - SU3D[I2, k7, k8]*SU3F[6, I1, k11]*SU3F[8, I5, k6]* - SU3F[I3, k11, k8] + SU3D[I1, k7, k8]*SU3F[6, I2, k11]* - SU3F[8, I5, k6]*SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I3, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I3, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k11]* - SU3F[8, I1, k6]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I3, k11]*SU3F[8, I2, k6]*SU3F[I5, k11, k8] + - SU3D[I2, k7, k8]*SU3F[6, I1, k11]*SU3F[8, I3, k6]* - SU3F[I5, k11, k8] + SU3D[I1, k7, k8]*SU3F[6, I2, k11]* - SU3F[8, I3, k6]*SU3F[I5, k11, k8] + SU3D[I3, k7, k8]* - (SU3F[6, I5, k11]*(SU3F[8, I2, k6]*SU3F[I1, k11, k8] + - SU3F[8, I1, k6]*SU3F[I2, k11, k8]) + SU3F[6, I2, k11]* - (SU3F[8, I5, k6]*SU3F[I1, k11, k8] + SU3F[8, I1, k6]* - SU3F[I5, k11, k8]) + SU3F[6, I1, k11]* - (SU3F[8, I5, k6]*SU3F[I2, k11, k8] + SU3F[8, I2, k6]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[6, I2, k7]* - SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[3, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[3, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[3, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]* - SU3D[I5, k7, k8]*SU3F[3, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[3, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[3, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[3, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[3, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[3, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[3, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[3, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[3, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[3, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[3, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[3, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[3, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[3, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[3, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[3, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[3, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[3, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[3, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[3, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[3, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[3, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[3, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[3, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[3, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[3, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[3, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[3, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[3, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[3, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[3, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[3, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[3, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[3, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[3, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3F[3, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[3, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[3, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[3, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[3, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[3, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[3, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[3, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[3, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[3, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[3, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[3, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[3, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[3, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[3, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[3, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[3, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[3, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[3, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[3, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[3, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[3, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[3, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[3, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[3, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[3, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[3, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[3, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[3, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[3, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[3, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[3, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[3, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[3, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[3, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[3, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[3, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[3, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[3, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[3, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[3, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[3, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[3, I3, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[3, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[3, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[3, I2, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[3, I1, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[3, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[3, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[3, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[3, I2, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[3, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[3, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[3, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[3, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[3, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[3, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[3, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[8, I3, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[8, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I5, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[8, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I4, k7, k8]* - SU3F[6, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]* - SU3F[6, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[8, I1, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]* - SU3F[6, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I4, k7, k8]*SU3F[6, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I2, k7]* - SU3D[I3, k7, k8]*SU3F[6, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I3, k7]*SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I3, k7, k8]*SU3F[6, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I2, k7]*SU3D[I1, k7, k8]*SU3F[6, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[8, I1, k7]* - SU3D[I2, k7, k8]*SU3F[6, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[8, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[6, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[6, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[6, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[6, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[6, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[6, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[6, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[6, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[6, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[6, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[6, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[6, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[6, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[6, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + SU3D[6, I3, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I2, k11, k8] + - SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3D[6, I2, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I3, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I2, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[6, I2, k7]* - SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I5, k10]*SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I1, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I5, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]* - SU3F[8, I1, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I5, k10]*SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I5, k10]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[8, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I5, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k8] + SU3D[6, I5, k7]* - (SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I4, k7, k8]* - (SU3F[8, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[8, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[8, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + - SU3D[I2, k7, k8]*SU3F[8, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I4, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I4, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I3, k10]*SU3F[I1, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k8] + SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I3, k10, k11]*SU3F[I4, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[8, I4, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[8, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k8]))) + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I4, k10]*SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I1, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I4, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3F[8, I1, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I4, k10]*SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[8, I1, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[8, I1, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[8, I2, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I4, k11, k8]*SU3F[I5, k10, k11] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[8, I3, k10]*SU3F[I4, k11, k8]* - SU3F[I5, k10, k11] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3F[8, I2, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I4, k10]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I4, k7, k8]*SU3F[8, I2, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I4, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I4, k10]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I2, k7]* - SU3D[I3, k7, k8]*SU3F[8, I1, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I3, k7, k8]*SU3F[8, I2, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[8, I3, k10]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k8] + SU3D[6, I1, k7]* - SU3D[I2, k7, k8]*SU3F[8, I3, k10]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k8] + SU3D[6, I4, k7]* - (SU3D[I2, k7, k8]*SU3F[8, I5, k10]*SU3F[I1, k11, k8]* - SU3F[I3, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I5, k10]* - SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I5, k10]*SU3F[I1, k10, k11]*SU3F[I3, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I5, k10]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k8] + SU3D[I5, k7, k8]* - (SU3F[8, I3, k10]*(SU3F[I1, k11, k8]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + SU3F[8, I2, k10]* - (SU3F[I1, k11, k8]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k8])) + SU3D[I2, k7, k8]*SU3F[8, I3, k10]* - SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + SU3D[I1, k7, k8]* - SU3F[8, I3, k10]*SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + - SU3D[I2, k7, k8]*SU3F[8, I1, k10]*SU3F[I3, k11, k8]* - SU3F[I5, k10, k11] + SU3D[I1, k7, k8]*SU3F[8, I2, k10]* - SU3F[I3, k11, k8]*SU3F[I5, k10, k11] + SU3D[I2, k7, k8]* - SU3F[8, I3, k10]*SU3F[I1, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I1, k7, k8]*SU3F[8, I3, k10]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k8] + SU3D[I2, k7, k8]*SU3F[8, I1, k10]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + SU3D[I1, k7, k8]* - SU3F[8, I2, k10]*SU3F[I3, k10, k11]*SU3F[I5, k11, k8] + - SU3D[I3, k7, k8]*(SU3F[8, I5, k10]*(SU3F[I1, k11, k8]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k8]) + - SU3F[8, I2, k10]*(SU3F[I1, k11, k8]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k8]) + SU3F[8, I1, k10]* - (SU3F[I2, k11, k8]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k8])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I2, k11]* - SU3F[I1, k11, k9] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I2, k11]*SU3F[I1, k11, k9] + SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I3, k11]*SU3F[I1, k11, k9] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I3, k11]* - SU3F[I1, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[I1, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I4, k11]*SU3F[I1, k11, k9] + - SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I4, k11]* - SU3F[I1, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I4, k11]*SU3F[I1, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[3, I5, k11]*SU3F[I1, k11, k9] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[3, I5, k11]* - SU3F[I1, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I5, k11]*SU3F[I1, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I5, k11]*SU3F[I1, k11, k9] + - SU3D[6, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I1, k11]* - SU3F[I2, k11, k9] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I1, k11]*SU3F[I2, k11, k9] + SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I3, k11]*SU3F[I2, k11, k9] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I3, k11]* - SU3F[I2, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[I2, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I4, k11]*SU3F[I2, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I4, k11]* - SU3F[I2, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I4, k11]*SU3F[I2, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[3, I5, k11]*SU3F[I2, k11, k9] + - SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[3, I5, k11]* - SU3F[I2, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I5, k11]*SU3F[I2, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I5, k11]*SU3F[I2, k11, k9] + - SU3D[6, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I1, k11]* - SU3F[I3, k11, k9] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I1, k11]*SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I2, k11]*SU3F[I3, k11, k9] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I2, k11]* - SU3F[I3, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k8]* - SU3F[3, I4, k11]*SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I4, k11]*SU3F[I3, k11, k9] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I4, k11]* - SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I4, k11]*SU3F[I3, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[3, I5, k11]*SU3F[I3, k11, k9] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3F[3, I5, k11]* - SU3F[I3, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I5, k11]*SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I5, k11]*SU3F[I3, k11, k9] + - SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I1, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[3, I1, k11]*SU3F[I4, k11, k9] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I1, k11]* - SU3F[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k8]* - SU3F[3, I2, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I2, k11]*SU3F[I4, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I2, k11]* - SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I2, k11]*SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I3, k11]*SU3F[I4, k11, k9] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I3, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I3, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[3, I3, k11]*SU3F[I4, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3F[3, I5, k11]* - SU3F[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3F[3, I5, k11]*SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[3, I5, k11]*SU3F[I4, k11, k9] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3F[3, I5, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]* - SU3F[3, I5, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[3, I5, k11]*SU3F[I4, k11, k9] + - SU3D[6, I5, k7]*(SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3F[3, I3, k11]* - SU3F[I1, k11, k9] + SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I3, k11]*SU3F[I1, k11, k9] + SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[3, I3, k11]*SU3F[I2, k11, k9] + - SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3F[3, I3, k11]* - SU3F[I2, k11, k9] + SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[3, I1, k11]*SU3F[I3, k11, k9] + SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I1, k11]*SU3F[I3, k11, k9] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k8]*SU3F[3, I2, k11]* - SU3F[I3, k11, k9] + SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I2, k11]*SU3F[I3, k11, k9] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3F[3, I4, k11]*SU3F[I3, k11, k9] + - SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3F[3, I4, k11]* - SU3F[I3, k11, k9] + SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[3, I3, k11]*SU3F[I4, k11, k9] + SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[3, I3, k11]*SU3F[I4, k11, k9] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k8]*(SU3F[3, I2, k11]* - SU3F[I1, k11, k9] + SU3F[3, I1, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k7, k8]*(SU3F[3, I4, k11]*SU3F[I1, k11, k9] + - SU3F[3, I1, k11]*SU3F[I4, k11, k9]) + SU3D[I1, k7, k8]* - (SU3F[3, I4, k11]*SU3F[I2, k11, k9] + SU3F[3, I2, k11]* - SU3F[I4, k11, k9])) + SU3D[I3, k7, k8]* - (SU3D[I4, k8, k9]*(SU3F[3, I2, k11]*SU3F[I1, k11, k9] + - SU3F[3, I1, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k8, k9]* - (SU3F[3, I4, k11]*SU3F[I1, k11, k9] + SU3F[3, I1, k11]* - SU3F[I4, k11, k9]) + SU3D[I1, k8, k9]* - (SU3F[3, I4, k11]*SU3F[I2, k11, k9] + SU3F[3, I2, k11]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[3, I1, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[3, I1, k11]* - SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I1, k11]*SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I1, k11]*SU3F[I5, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]*SU3F[3, I2, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3F[3, I2, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[3, I2, k11]*SU3F[I5, k11, k9] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]*SU3F[3, I2, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3F[3, I3, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[3, I3, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3F[3, I3, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[3, I3, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3F[3, I4, k11]*SU3F[I5, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3F[3, I4, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[3, I4, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3F[3, I4, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3F[3, I4, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3F[3, I4, k11]*SU3F[I5, k11, k9] + SU3D[6, I4, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I3, k11]* - SU3F[I1, k11, k9] + SU3D[I2, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I3, k11]*SU3F[I1, k11, k9] + SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[3, I3, k11]*SU3F[I2, k11, k9] + - SU3D[I1, k7, k8]*SU3D[I5, k8, k9]*SU3F[3, I3, k11]* - SU3F[I2, k11, k9] + SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[3, I1, k11]*SU3F[I3, k11, k9] + SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[3, I1, k11]*SU3F[I3, k11, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k7, k8]*SU3F[3, I2, k11]* - SU3F[I3, k11, k9] + SU3D[I1, k7, k8]*SU3D[I5, k8, k9]* - SU3F[3, I2, k11]*SU3F[I3, k11, k9] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3F[3, I5, k11]*SU3F[I3, k11, k9] + - SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3F[3, I5, k11]* - SU3F[I3, k11, k9] + SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[3, I3, k11]*SU3F[I5, k11, k9] + SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[3, I3, k11]*SU3F[I5, k11, k9] + - SU3D[I3, k8, k9]*(SU3D[I5, k7, k8]*(SU3F[3, I2, k11]* - SU3F[I1, k11, k9] + SU3F[3, I1, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k7, k8]*(SU3F[3, I5, k11]*SU3F[I1, k11, k9] + - SU3F[3, I1, k11]*SU3F[I5, k11, k9]) + SU3D[I1, k7, k8]* - (SU3F[3, I5, k11]*SU3F[I2, k11, k9] + SU3F[3, I2, k11]* - SU3F[I5, k11, k9])) + SU3D[I3, k7, k8]* - (SU3D[I5, k8, k9]*(SU3F[3, I2, k11]*SU3F[I1, k11, k9] + - SU3F[3, I1, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k8, k9]* - (SU3F[3, I5, k11]*SU3F[I1, k11, k9] + SU3F[3, I1, k11]* - SU3F[I5, k11, k9]) + SU3D[I1, k8, k9]* - (SU3F[3, I5, k11]*SU3F[I2, k11, k9] + SU3F[3, I2, k11]* - SU3F[I5, k11, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I2, k11]* - SU3F[I1, k11, k9] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I2, k11]*SU3F[I1, k11, k9] + SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I3, k11]*SU3F[I1, k11, k9] + - SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I3, k11]* - SU3F[I1, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[8, I4, k11]*SU3F[I1, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I4, k11]*SU3F[I1, k11, k9] + - SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I4, k11]* - SU3F[I1, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I4, k11]*SU3F[I1, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[8, I5, k11]*SU3F[I1, k11, k9] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[8, I5, k11]* - SU3F[I1, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I5, k11]*SU3F[I1, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I5, k11]*SU3F[I1, k11, k9] + - SU3D[6, I3, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I1, k11]* - SU3F[I2, k11, k9] + SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I1, k11]*SU3F[I2, k11, k9] + SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k9] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k8]* - SU3F[8, I4, k11]*SU3F[I2, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I4, k11]*SU3F[I2, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I4, k11]* - SU3F[I2, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I4, k11]*SU3F[I2, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[8, I5, k11]*SU3F[I2, k11, k9] + - SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[8, I5, k11]* - SU3F[I2, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I5, k11]*SU3F[I2, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I5, k11]*SU3F[I2, k11, k9] + - SU3D[6, I2, k7]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I1, k11]* - SU3F[I3, k11, k9] + SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I1, k11]*SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I2, k11]*SU3F[I3, k11, k9] + - SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I2, k11]* - SU3F[I3, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k8]* - SU3F[8, I4, k11]*SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I4, k11]*SU3F[I3, k11, k9] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I4, k11]* - SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I4, k11]*SU3F[I3, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[8, I5, k11]*SU3F[I3, k11, k9] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3F[8, I5, k11]* - SU3F[I3, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I5, k11]*SU3F[I3, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I5, k11]*SU3F[I3, k11, k9] + - SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I1, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[8, I1, k11]*SU3F[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[8, I1, k11]*SU3F[I4, k11, k9] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I1, k11]* - SU3F[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k8]* - SU3F[8, I2, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I2, k11]*SU3F[I4, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I2, k11]* - SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I2, k11]*SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I3, k11]*SU3F[I4, k11, k9] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I3, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I3, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[8, I3, k11]*SU3F[I4, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3F[8, I5, k11]* - SU3F[I4, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]* - SU3F[8, I5, k11]*SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[8, I5, k11]*SU3F[I4, k11, k9] + - SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3F[8, I5, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]* - SU3F[8, I5, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[8, I5, k11]*SU3F[I4, k11, k9] + - SU3D[6, I5, k7]*(SU3D[I2, k8, k9]*SU3D[I4, k7, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k9] + SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I3, k11]*SU3F[I1, k11, k9] + SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k9] + - SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k9] + SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k9] + SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I1, k11]*SU3F[I3, k11, k9] + - SU3D[I1, k8, k9]*SU3D[I4, k7, k8]*SU3F[8, I2, k11]* - SU3F[I3, k11, k9] + SU3D[I1, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I2, k11]*SU3F[I3, k11, k9] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3F[8, I4, k11]*SU3F[I3, k11, k9] + - SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3F[8, I4, k11]* - SU3F[I3, k11, k9] + SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[8, I3, k11]*SU3F[I4, k11, k9] + SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[8, I3, k11]*SU3F[I4, k11, k9] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k8]*(SU3F[8, I2, k11]* - SU3F[I1, k11, k9] + SU3F[8, I1, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k7, k8]*(SU3F[8, I4, k11]*SU3F[I1, k11, k9] + - SU3F[8, I1, k11]*SU3F[I4, k11, k9]) + SU3D[I1, k7, k8]* - (SU3F[8, I4, k11]*SU3F[I2, k11, k9] + SU3F[8, I2, k11]* - SU3F[I4, k11, k9])) + SU3D[I3, k7, k8]* - (SU3D[I4, k8, k9]*(SU3F[8, I2, k11]*SU3F[I1, k11, k9] + - SU3F[8, I1, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k8, k9]* - (SU3F[8, I4, k11]*SU3F[I1, k11, k9] + SU3F[8, I1, k11]* - SU3F[I4, k11, k9]) + SU3D[I1, k8, k9]* - (SU3F[8, I4, k11]*SU3F[I2, k11, k9] + SU3F[8, I2, k11]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[8, I1, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]*SU3F[8, I1, k11]* - SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I1, k11]*SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I1, k11]*SU3F[I5, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]*SU3F[8, I2, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3F[8, I2, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[8, I2, k11]*SU3F[I5, k11, k9] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]*SU3F[8, I2, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I4, k7, k8]* - SU3F[8, I3, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[8, I3, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, k8, k9]*SU3F[8, I3, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[8, I3, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3F[8, I4, k11]*SU3F[I5, k11, k9] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3F[8, I4, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[8, I4, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3F[8, I4, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3F[8, I4, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3F[8, I4, k11]*SU3F[I5, k11, k9] + SU3D[6, I4, k7]* - (SU3D[I2, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I3, k11]* - SU3F[I1, k11, k9] + SU3D[I2, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I3, k11]*SU3F[I1, k11, k9] + SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[8, I3, k11]*SU3F[I2, k11, k9] + - SU3D[I1, k7, k8]*SU3D[I5, k8, k9]*SU3F[8, I3, k11]* - SU3F[I2, k11, k9] + SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[8, I1, k11]*SU3F[I3, k11, k9] + SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[8, I1, k11]*SU3F[I3, k11, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k7, k8]*SU3F[8, I2, k11]* - SU3F[I3, k11, k9] + SU3D[I1, k7, k8]*SU3D[I5, k8, k9]* - SU3F[8, I2, k11]*SU3F[I3, k11, k9] + SU3D[I1, k8, k9]* - SU3D[I2, k7, k8]*SU3F[8, I5, k11]*SU3F[I3, k11, k9] + - SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3F[8, I5, k11]* - SU3F[I3, k11, k9] + SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[8, I3, k11]*SU3F[I5, k11, k9] + SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[8, I3, k11]*SU3F[I5, k11, k9] + - SU3D[I3, k8, k9]*(SU3D[I5, k7, k8]*(SU3F[8, I2, k11]* - SU3F[I1, k11, k9] + SU3F[8, I1, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k7, k8]*(SU3F[8, I5, k11]*SU3F[I1, k11, k9] + - SU3F[8, I1, k11]*SU3F[I5, k11, k9]) + SU3D[I1, k7, k8]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k9] + SU3F[8, I2, k11]* - SU3F[I5, k11, k9])) + SU3D[I3, k7, k8]* - (SU3D[I5, k8, k9]*(SU3F[8, I2, k11]*SU3F[I1, k11, k9] + - SU3F[8, I1, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k8, k9]* - (SU3F[8, I5, k11]*SU3F[I1, k11, k9] + SU3F[8, I1, k11]* - SU3F[I5, k11, k9]) + SU3D[I1, k8, k9]* - (SU3F[8, I5, k11]*SU3F[I2, k11, k9] + SU3F[8, I2, k11]* - SU3F[I5, k11, k9]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I4, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I5, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I4, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]* - SU3D[I5, k10, k7]*SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I4, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I4, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I4, k9]* - SU3D[I5, k10, k7]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + - SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I5, k10, k7]*SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I5, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I5, k9]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I5, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k7]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I5, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I2, k9]* - SU3D[I5, k10, k7]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]*SU3D[I3, k10, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I5, k10, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k9] + SU3D[3, I3, k7]*SU3D[6, I5, k9]*SU3D[I1, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I5, k9]* - SU3D[I3, k10, k7]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + - SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I5, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I5, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[3, I2, k7]*SU3D[6, I5, k9]* - SU3D[I1, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[3, I1, k7]*SU3D[6, I5, k9]*SU3D[I2, k10, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I5, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I2, k9]* - SU3D[I5, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[3, I5, k7]*(SU3D[6, I2, k9]*SU3D[I4, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[I4, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k9] + SU3D[6, I4, k9]* - (SU3D[I3, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k10, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k9])) + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I2, k9]* - SU3D[I3, k10, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I3, k9]*(SU3D[I4, k10, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9]))) + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k7]*SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I3, k9]* - SU3D[I4, k10, k7]*SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k7]*SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k7]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k7]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I3, k9]* - SU3D[I2, k10, k7]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + SU3D[3, I3, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k7]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I2, k7]*SU3D[6, I3, k9]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[3, I3, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I4, k9]*SU3D[I3, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]* - SU3D[I4, k10, k7]*SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + - SU3D[3, I1, k7]*SU3D[6, I3, k9]*SU3D[I4, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I2, k7]*SU3D[6, I4, k9]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I4, k9]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I4, k10, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I4, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I3, k7]*SU3D[6, I2, k9]* - SU3D[I1, k10, k7]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[3, I2, k7]*SU3D[6, I3, k9]*SU3D[I1, k10, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I3, k7]*SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I3, k9]* - SU3D[I2, k10, k7]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[3, I2, k7]*SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[3, I1, k7]*SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[3, I4, k7]* - (SU3D[6, I2, k9]*SU3D[I5, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]* - SU3D[I5, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[6, I1, k9]*SU3D[I5, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k9] + SU3D[6, I5, k9]* - (SU3D[I3, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k10, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k9])) + SU3D[6, I2, k9]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[I1, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[I2, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I2, k9]* - SU3D[I3, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I1, k9]*SU3D[I3, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I3, k9]*(SU3D[I5, k10, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I2, k11, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I2, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I4, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I5, k10, k7]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k7]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I5, k7]*SU3D[I1, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I5, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I5, k7]* - SU3D[I1, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I1, k9]*SU3D[8, I5, k7]*SU3D[I2, k10, k7]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[6, I5, k9]*(SU3D[8, I2, k7]*SU3D[I4, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I4, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k9] + SU3D[8, I4, k7]* - (SU3D[I3, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k10, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k9])) + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[8, I2, k7]* - SU3D[I3, k10, k7]*SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I4, k11, k9] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[8, I1, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[8, I3, k7]*(SU3D[I4, k10, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k7]*SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k7]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k10, k7]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + SU3D[6, I3, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I3, k7]* - SU3D[I4, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I3, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I4, k7]*SU3D[I3, k10, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]* - SU3D[I4, k10, k7]*SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I1, k9]*SU3D[8, I3, k7]*SU3D[I4, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[8, I4, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I4, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I4, k10, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I4, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I2, k7]* - SU3D[I1, k10, k7]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I3, k7]*SU3D[I1, k10, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I3, k7]* - SU3D[I2, k10, k7]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[6, I2, k9]*SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[6, I1, k9]*SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + SU3D[6, I4, k9]* - (SU3D[8, I2, k7]*SU3D[I5, k10, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11] + SU3D[8, I1, k7]*SU3D[I5, k10, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[8, I2, k7]* - SU3D[I5, k10, k7]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[8, I1, k7]*SU3D[I5, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k9] + SU3D[8, I5, k7]* - (SU3D[I3, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + SU3D[I2, k10, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I3, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k9])) + SU3D[8, I2, k7]*SU3D[I3, k10, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + SU3D[8, I1, k7]* - SU3D[I3, k10, k7]*SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + - SU3D[8, I2, k7]*SU3D[I1, k10, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[8, I1, k7]*SU3D[I2, k10, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[8, I2, k7]* - SU3D[I3, k10, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[8, I1, k7]*SU3D[I3, k10, k7]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[8, I2, k7]*SU3D[I1, k10, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[8, I1, k7]* - SU3D[I2, k10, k7]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3D[8, I3, k7]*(SU3D[I5, k10, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I5, k11, k9]) + SU3D[I1, k10, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k11, k9]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + SU3D[3, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I2, k11, k9] + SU3D[3, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I2, k11, k9] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[3, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k6] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + SU3D[3, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[3, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k9]))) + SU3D[3, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[3, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[3, I4, k9]*(SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k11, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I2, k11, k9] + SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I2, k11, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k6] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k6] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I3, k11, k9] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k9] + SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I4, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I4, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k9]))) + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k6] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k6] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I2, k9]* - SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I4, k11, k6]*SU3F[I5, k11, k9] + SU3D[8, I1, k9]* - SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k9] + SU3D[8, I4, k9]*(SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I5, k7]*SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k9] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + SU3F[6, I2, k7]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[6, I3, k7]*SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k7]*SU3F[I3, k11, k6]*SU3F[I5, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k7]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k9]) + - SU3F[6, I2, k7]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k11, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k11, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I2, k11, k9] + SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I2, k11, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k11, k9] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[3, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I3, k11, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I5, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I5, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I2, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[3, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[3, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[3, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I4, k6]*SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[3, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[I4, k6, k7]* - (SU3F[3, I3, k6]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + SU3F[3, I2, k6]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k9]) + SU3F[3, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[3, I3, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + - SU3D[I1, k6, k7]*SU3F[3, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[3, I4, k6]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + - SU3F[3, I2, k6]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k11, k9]) + SU3F[3, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[3, I2, k6]*SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k6]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[3, I3, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I4, k6]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[3, I2, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I1, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I2, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I3, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[3, I2, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[3, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[3, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[3, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[3, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I4, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[3, I4, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I1, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[3, I1, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I2, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[3, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I3, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[3, I3, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I4, k9]*(SU3D[I2, k6, k7]*SU3F[3, I5, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I5, k6]*SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[3, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[3, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[I5, k6, k7]* - (SU3F[3, I3, k6]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + SU3F[3, I2, k6]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k9]) + SU3F[3, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[3, I3, k6]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[3, I3, k6]*SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[3, I1, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[3, I2, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[3, I3, k6]*SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + - SU3D[I1, k6, k7]*SU3F[3, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[I2, k6, k7]*SU3F[3, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[I1, k6, k7]* - SU3F[3, I2, k6]*SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[3, I5, k6]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + - SU3F[3, I2, k6]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k11, k9]) + SU3F[3, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k11, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I2, k11, k9] + SU3D[6, I3, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I2, k11, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k9]* - SU3F[I3, k11, k7] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I3, k11, k9] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I3, k11, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I2, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I5, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I5, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I3, k11, k7]* - SU3F[I4, k11, k9] + SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I4, k6]*SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[I4, k6, k7]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k9]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I3, k6]*SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k11, k7]*SU3F[I4, k11, k9] + - SU3D[I1, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I4, k11, k9] + SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + SU3D[I1, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k11, k7]*SU3F[I4, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[8, I4, k6]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k11, k9]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k11, k9]))) + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k6]*SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I2, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k11, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I2, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I2, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I4, k6, k7]*SU3F[8, I2, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I4, k6]*SU3F[I3, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I2, k9]* - SU3D[I3, k6, k7]*SU3F[8, I1, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I3, k6, k7]*SU3F[8, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I3, k6]* - SU3F[I4, k11, k7]*SU3F[I5, k11, k9] + SU3D[6, I1, k9]* - SU3D[I2, k6, k7]*SU3F[8, I3, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k11, k9] + SU3D[6, I4, k9]*(SU3D[I2, k6, k7]*SU3F[8, I5, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I5, k6]*SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I5, k6]*SU3F[I1, k11, k7]* - SU3F[I3, k11, k9] + SU3D[I1, k6, k7]*SU3F[8, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I3, k11, k9] + SU3D[I5, k6, k7]* - (SU3F[8, I3, k6]*(SU3F[I1, k11, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + SU3F[8, I2, k6]* - (SU3F[I1, k11, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k11, k9]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k11, k9])) + SU3D[I2, k6, k7]*SU3F[8, I3, k6]* - SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[8, I3, k6]*SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[8, I1, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[8, I2, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[8, I3, k6]*SU3F[I1, k11, k7]*SU3F[I5, k11, k9] + - SU3D[I1, k6, k7]*SU3F[8, I3, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k11, k9] + SU3D[I2, k6, k7]*SU3F[8, I1, k6]* - SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + SU3D[I1, k6, k7]* - SU3F[8, I2, k6]*SU3F[I3, k11, k7]*SU3F[I5, k11, k9] + - SU3D[I3, k6, k7]*(SU3F[8, I5, k6]*(SU3F[I1, k11, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k11, k9]) + - SU3F[8, I2, k6]*(SU3F[I1, k11, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k11, k9]) + SU3F[8, I1, k6]* - (SU3F[I2, k11, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k11, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3D[3, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I1, k6, k9] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I1, k6, k9] + - SU3D[3, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3D[3, I3, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I1, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I1, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I2, k6, k9] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[3, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I2, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I2, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I3, k6, k9] + - SU3D[3, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I4, k6, k9] + - SU3D[3, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I4, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[3, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I4, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9]))) + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I1, k10]* - SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I1, k10]*SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I2, k10]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I2, k10]*SU3F[I5, k6, k9] + - SU3D[3, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[3, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[3, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I5, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I1, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I1, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I2, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I2, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I4, k10]*SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I5, k10]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I1, k10]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I2, k10]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I2, k10]* - SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3D[I3, k10, k7]*SU3F[6, I5, k10]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I5, k10]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]* - SU3D[I3, k6, k7]*SU3F[6, I5, k10]*SU3F[I4, k6, k9] + - SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I4, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I4, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I4, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I4, k6, k9]))) + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I1, k10]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I1, k10]*SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I1, k10]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I2, k10]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k10, k7]* - SU3D[I4, k6, k7]*SU3F[6, I2, k10]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I2, k10]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I4, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k10, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I4, k6, k7]*SU3F[6, I3, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I4, k6, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3D[I3, k10, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k10, k7]*SU3F[6, I4, k10]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k10, k7]*SU3D[I3, k6, k7]*SU3F[6, I4, k10]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k10, k7]*SU3D[I3, k6, k7]* - SU3F[6, I4, k10]*SU3F[I5, k6, k9] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I3, k10]* - SU3F[I1, k6, k9] + SU3D[I2, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I3, k10]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I5, k10, k7]*SU3F[6, I3, k10]*SU3F[I2, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I5, k6, k7]*SU3F[6, I3, k10]* - SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k10, k7]* - SU3F[6, I1, k10]*SU3F[I3, k6, k9] + SU3D[I2, k10, k7]* - SU3D[I5, k6, k7]*SU3F[6, I1, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I5, k10, k7]*SU3F[6, I2, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k10, k7]*SU3D[I5, k6, k7]* - SU3F[6, I2, k10]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]* - SU3D[I2, k10, k7]*SU3F[6, I5, k10]*SU3F[I3, k6, k9] + - SU3D[I1, k10, k7]*SU3D[I2, k6, k7]*SU3F[6, I5, k10]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k10, k7]* - SU3F[6, I3, k10]*SU3F[I5, k6, k9] + SU3D[I1, k10, k7]* - SU3D[I2, k6, k7]*SU3F[6, I3, k10]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3D[I5, k10, k7]*(SU3F[6, I2, k10]* - SU3F[I1, k6, k9] + SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + - SU3D[I2, k10, k7]*(SU3F[6, I5, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I5, k6, k9]) + SU3D[I1, k10, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9])) + SU3D[I3, k10, k7]* - (SU3D[I5, k6, k7]*(SU3F[6, I2, k10]*SU3F[I1, k6, k9] + - SU3F[6, I1, k10]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I1, k6, k9] + SU3F[6, I1, k10]* - SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I5, k10]*SU3F[I2, k6, k9] + SU3F[6, I2, k10]* - SU3F[I5, k6, k9]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]* - SU3F[6, I2, k7]*SU3F[I1, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k8]*SU3F[6, I2, k7]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[6, I3, k7]*SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I2, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I4, k7]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I3, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I2, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k8]*SU3F[6, I1, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[6, I3, k7]*SU3F[I2, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I1, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I4, k7]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I3, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I2, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I4, k8]*SU3F[6, I1, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I4, k8]* - SU3F[6, I2, k7]*SU3F[I3, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I1, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k8]* - SU3F[6, I4, k7]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I2, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I4, k8]*SU3F[6, I5, k7]* - SU3F[I3, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I2, k8]*SU3F[6, I1, k7]*SU3F[I4, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k8]*SU3F[6, I1, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k8]*SU3F[6, I1, k7]*SU3F[I4, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I1, k7]* - SU3F[I4, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k8]*SU3F[6, I2, k7]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I3, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I2, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[3, I1, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k8]*SU3F[6, I3, k7]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[3, I2, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I3, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I5, k7]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[3, I1, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I2, k8]*SU3F[6, I5, k7]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I2, k8]* - SU3F[6, I5, k7]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I3, k8]*SU3F[6, I5, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[3, I4, k8]*SU3F[6, I1, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I4, k8]*SU3F[6, I2, k7]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I4, k8]* - SU3F[6, I2, k7]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I4, k8]*SU3F[6, I3, k7]* - SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I4, k7]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[3, I1, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[3, I2, k8]*SU3F[6, I4, k7]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[3, I2, k8]* - SU3F[6, I4, k7]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[3, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[3, I3, k8]*SU3F[6, I4, k7]* - SU3F[I5, k6, k9] + SU3D[I4, k8, k9]*(SU3D[I2, k6, k7]*SU3F[3, I5, k8]* - SU3F[6, I3, k7]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I5, k7]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I5, k8]* - SU3F[6, I3, k7]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I5, k7]*SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3F[3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I5, k8]* - SU3F[6, I2, k7]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I5, k7]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I2, k8]* - SU3F[6, I5, k7]*SU3F[I3, k6, k9] + SU3D[I5, k6, k7]* - (SU3F[3, I3, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k9] + - SU3F[6, I1, k7]*SU3F[I2, k6, k9]) + SU3F[3, I2, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k9] + SU3F[6, I1, k7]* - SU3F[I3, k6, k9]) + SU3F[3, I1, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k9] + SU3F[6, I2, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I3, k8]* - SU3F[6, I2, k7]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[3, I1, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[3, I2, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k9] + SU3D[I3, k6, k7]* - (SU3F[3, I5, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k9] + - SU3F[6, I1, k7]*SU3F[I2, k6, k9]) + SU3F[3, I2, k8]* - (SU3F[6, I5, k7]*SU3F[I1, k6, k9] + SU3F[6, I1, k7]* - SU3F[I5, k6, k9]) + SU3F[3, I1, k8]* - (SU3F[6, I5, k7]*SU3F[I2, k6, k9] + SU3F[6, I2, k7]* - SU3F[I5, k6, k9]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I3, k7]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3F[3, I3, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3F[3, I3, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k9] + - SU3D[I2, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I1, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[3, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k9] + - SU3D[I2, k8, k9]*SU3F[3, I1, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[3, I2, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k9] + - SU3D[I5, k8, k9]*(SU3F[3, I3, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, - k9] + SU3F[6, I1, k7]*SU3F[I2, k6, k9]) + SU3F[3, I2, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k9] + SU3F[6, I1, k7]* - SU3F[I3, k6, k9]) + SU3F[3, I1, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k9] + SU3F[6, I2, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k8, k9]*SU3F[3, I3, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[3, I3, k8]* - SU3F[6, I2, k7]*SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3F[3, I1, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[3, I2, k8]* - SU3F[6, I3, k7]*SU3F[I5, k6, k9] + SU3D[I3, k8, k9]* - (SU3F[3, I5, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k9] + - SU3F[6, I1, k7]*SU3F[I2, k6, k9]) + SU3F[3, I2, k8]* - (SU3F[6, I5, k7]*SU3F[I1, k6, k9] + SU3F[6, I1, k7]* - SU3F[I5, k6, k9]) + SU3F[3, I1, k8]* - (SU3F[6, I5, k7]*SU3F[I2, k6, k9] + SU3F[6, I2, k7]* - SU3F[I5, k6, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I1, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[8, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k7]*SU3F[8, I4, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I4, k8]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I1, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I1, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I2, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I2, k6, k9] + - SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I4, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I4, k8]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I2, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I2, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I3, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I3, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I4, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I4, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k7]*SU3F[8, I4, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[8, I4, k8]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k7]* - SU3F[8, I4, k8]*SU3F[I3, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I5, k8]* - SU3F[I3, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I1, k8]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I2, k7]*SU3F[8, I1, k8]*SU3F[I4, k6, k9] + - SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I1, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I1, k8]*SU3F[I4, k6, k9] + - SU3D[I2, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I1, k8]* - SU3F[I4, k6, k9] + SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I2, k8]*SU3F[I4, k6, k9] + SU3D[I3, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I2, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[8, I2, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I2, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I2, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I5, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I3, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I3, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I5, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I5, k8]*SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I5, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I5, k8]*SU3F[I4, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I4, k7]*SU3F[8, I1, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[8, I2, k8]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I4, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SU3F[8, I3, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I4, k7]*SU3F[8, I3, k8]* - SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I4, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3D[I3, k8, k9]* - SU3F[6, I1, k7]*SU3F[8, I4, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[8, I4, k8]* - SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I4, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SU3F[8, I4, k8]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I4, k8]* - SU3F[I5, k6, k9] + SU3D[I4, k8, k9]*(SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I1, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[8, I2, k8]*SU3F[I3, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I5, k8]*SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I5, k8]*SU3F[I3, k6, k9] + SU3D[I5, k6, k7]* - (SU3F[6, I3, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I3, k6, k7]* - (SU3F[6, I5, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I5, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I5, k6, k9]))) + SU3D[I4, k6, k7]* - (SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I1, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I3, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I3, k7]*SU3F[8, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I1, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I5, k7]*SU3F[8, I2, k8]*SU3F[I3, k6, k9] + - SU3D[I2, k8, k9]*SU3F[6, I1, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3F[6, I2, k7]*SU3F[8, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I5, k8, k9]*(SU3F[6, I3, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, - k9] + SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I3, k6, k9])) + SU3D[I2, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I1, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[6, I3, k7]* - SU3F[8, I2, k8]*SU3F[I5, k6, k9] + SU3D[I2, k8, k9]*SU3F[6, I1, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I1, k8, k9]*SU3F[6, I2, k7]* - SU3F[8, I3, k8]*SU3F[I5, k6, k9] + SU3D[I3, k8, k9]* - (SU3F[6, I5, k7]*(SU3F[8, I2, k8]*SU3F[I1, k6, k9] + - SU3F[8, I1, k8]*SU3F[I2, k6, k9]) + SU3F[6, I2, k7]* - (SU3F[8, I5, k8]*SU3F[I1, k6, k9] + SU3F[8, I1, k8]* - SU3F[I5, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[8, I5, k8]*SU3F[I2, k6, k9] + SU3F[8, I2, k8]* - SU3F[I5, k6, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[3, I3, k9]*SU3D[6, I5, k11]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I4, k11]*SU3D[I5, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I5, k11]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I2, k6, k9] + - SU3D[3, I3, k9]*SU3D[6, I4, k11]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I2, k6, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k11]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3D[3, I2, k9]*SU3D[6, I4, k11]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[3, I1, k9]*SU3D[6, I5, k11]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I3, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I4, k11]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[3, I2, k9]*SU3D[6, I5, k11]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[3, I2, k9]*SU3D[6, I4, k11]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I5, k11]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I4, k11]* - SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[3, I3, k9]*SU3D[6, I5, k11]*SU3D[I2, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[6, I5, k11]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I2, k11]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I2, k9]*SU3D[6, I3, k11]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I5, k11]*SU3D[I1, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I5, k11]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I3, k9]*SU3D[6, I1, k11]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I3, k11]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[6, I5, k11]* - SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k9]*SU3D[6, I5, k11]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[6, I1, k11]*SU3D[I5, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I2, k11]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I3, k9]*SU3D[6, I5, k11]*SU3D[I2, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k11]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k11]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I2, k9]*SU3D[6, I3, k11]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[6, I5, k11]*SU3D[I1, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I5, k11]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I3, k9]*SU3D[6, I1, k11]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I3, k11]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[6, I5, k11]* - SU3D[I1, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[6, I5, k11]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[6, I1, k11]*SU3D[I5, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I2, k11]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I5, k9]*(SU3D[6, I2, k11]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k11]*SU3D[I4, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k11]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I1, k11]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[6, I4, k11]* - (SU3D[I3, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[6, I2, k11]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k11]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I2, k11]*SU3D[I1, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I1, k11]*SU3D[I2, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k11]* - SU3D[I3, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I1, k11]*SU3D[I3, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I1, k11]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I3, k11]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k9]))) + SU3D[3, I3, k9]*SU3D[6, I4, k11]* - SU3D[I2, k6, k7]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[6, I4, k11]*SU3D[I3, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I2, k11]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I2, k9]*SU3D[6, I3, k11]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I3, k9]*SU3D[6, I4, k11]*SU3D[I1, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I4, k11]*SU3D[I3, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I1, k11]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k9]*SU3D[6, I3, k11]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k9]*SU3D[6, I4, k11]*SU3D[I1, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I4, k11]* - SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[6, I1, k11]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I2, k11]*SU3D[I4, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I2, k11]* - SU3D[I1, k6, k7]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[6, I3, k11]*SU3D[I1, k6, k7]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I1, k11]*SU3D[I2, k6, k7]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I3, k11]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[6, I1, k11]*SU3D[I3, k6, k7]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[6, I2, k11]*SU3D[I3, k6, k7]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[6, I4, k11]* - SU3D[I2, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[6, I4, k11]*SU3D[I3, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k11]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[6, I3, k11]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I3, k9]*SU3D[6, I4, k11]*SU3D[I1, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I4, k11]*SU3D[I3, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[6, I1, k11]* - SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I1, k9]*SU3D[6, I3, k11]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[6, I4, k11]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I4, k11]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[6, I1, k11]*SU3D[I4, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I2, k11]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[6, I2, k11]* - SU3D[I1, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[6, I3, k11]*SU3D[I1, k6, k7]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[6, I1, k11]*SU3D[I2, k6, k7]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I3, k11]* - SU3D[I2, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[6, I1, k11]*SU3D[I3, k6, k7]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[6, I2, k11]*SU3D[I3, k6, k7]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I4, k9]* - (SU3D[6, I2, k11]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k11]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k11]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I1, k11]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[6, I5, k11]* - (SU3D[I3, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + SU3D[I2, k6, k7]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[6, I2, k11]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k11]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[I1, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[I2, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k11]* - SU3D[I3, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I1, k11]*SU3D[I3, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I2, k11]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k11]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I3, k11]*(SU3D[I5, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k6, k9]))))/ - (60*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I2, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I2, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I3, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I5, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]* - SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I5, k9]* - SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I5, k9]*SU3D[I1, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I5, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I5, k9]* - SU3D[I1, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I5, k9]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[6, I5, k11]*(SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[8, I2, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I4, k9]*(SU3D[I3, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I3, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k9]))) + SU3D[6, I3, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[6, I3, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I3, k9]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I3, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I1, k9]* - SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I1, k11]*SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I2, k11]*SU3D[8, I4, k9]*SU3D[I1, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I4, k9]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I2, k9]* - SU3D[I1, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I3, k11]*SU3D[8, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I3, k9]* - SU3D[I2, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[6, I2, k11]*SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[6, I1, k11]*SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[6, I4, k11]* - (SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I5, k9]*(SU3D[I3, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I3, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k9]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*(SU3D[I5, k6, k7]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k6, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k6, k9]))))/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/60)*(SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I2, k6, k9] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I2, k6, k9] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[3, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[3, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[3, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k11]*(SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k9]))) + SU3D[3, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[3, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[3, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[3, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[3, I4, k9]* - (SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I5, k6, k7]*(SU3F[6, I3, k11]* - (SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k6, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/60)*(SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I2, k6, k9] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I2, k6, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + - SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I5, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I5, k11]* - SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I5, k6, k7]* - SU3F[6, I1, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I5, k11]*SU3F[I2, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I2, k9]*SU3D[I5, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I1, k9]*SU3D[I5, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[8, I2, k9]*SU3D[I1, k6, k7]* - SU3F[6, I5, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I3, k11, k7]* - SU3F[I4, k6, k9] + SU3D[8, I5, k9]*(SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k11]*SU3F[I1, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I1, k6, k7]*SU3F[6, I4, k11]* - SU3F[I2, k11, k7]*SU3F[I3, k6, k9] + SU3D[I4, k6, k7]* - (SU3F[6, I3, k11]*(SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I4, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I4, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I4, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I4, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I4, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k9]))) + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k6, k9]* - SU3F[I5, k11, k7] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k6, k9]*SU3F[I5, k11, k7] + SU3D[8, I3, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]*SU3F[I1, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I3, k6, k7]* - SU3F[6, I4, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I3, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]*SU3F[6, I3, k11]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]* - SU3F[6, I4, k11]*SU3F[I2, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I1, k9]*SU3D[I3, k6, k7]*SU3F[6, I4, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I2, k9]*SU3D[I4, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I4, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I4, k11]*SU3F[I3, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I4, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I2, k6, k7]* - SU3F[6, I1, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I3, k6, k7]*SU3F[6, I1, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I3, k9]*SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I3, k6, k7]* - SU3F[6, I2, k11]*SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + - SU3D[8, I2, k9]*SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I4, k11, k7]* - SU3F[I5, k6, k9] + SU3D[8, I1, k9]*SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k9] + SU3D[8, I4, k9]* - (SU3D[I2, k6, k7]*SU3F[6, I5, k11]*SU3F[I1, k6, k9]* - SU3F[I3, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I5, k11]* - SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I5, k11]*SU3F[I1, k11, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I5, k11]*SU3F[I2, k11, k7]* - SU3F[I3, k6, k9] + SU3D[I5, k6, k7]*(SU3F[6, I3, k11]* - (SU3F[I1, k6, k9]*SU3F[I2, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I2, k6, k9]) + SU3F[6, I2, k11]* - (SU3F[I1, k6, k9]*SU3F[I3, k11, k7] + SU3F[I1, k11, k7]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I3, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I3, k6, k9])) + SU3D[I2, k6, k7]*SU3F[6, I3, k11]* - SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3F[6, I3, k11]*SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3F[6, I1, k11]*SU3F[I3, k6, k9]* - SU3F[I5, k11, k7] + SU3D[I1, k6, k7]*SU3F[6, I2, k11]* - SU3F[I3, k6, k9]*SU3F[I5, k11, k7] + SU3D[I2, k6, k7]* - SU3F[6, I3, k11]*SU3F[I1, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3F[6, I3, k11]*SU3F[I2, k11, k7]* - SU3F[I5, k6, k9] + SU3D[I2, k6, k7]*SU3F[6, I1, k11]* - SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + SU3D[I1, k6, k7]* - SU3F[6, I2, k11]*SU3F[I3, k11, k7]*SU3F[I5, k6, k9] + - SU3D[I3, k6, k7]*(SU3F[6, I5, k11]*(SU3F[I1, k6, k9]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k9]) + - SU3F[6, I2, k11]*(SU3F[I1, k6, k9]*SU3F[I5, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I5, k6, k9]) + SU3F[6, I1, k11]* - (SU3F[I2, k6, k9]*SU3F[I5, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I5, k6, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k11]*SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + - SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I2, k7, k9] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I2, k7, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k11]*SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]* - SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[3, I5, k11]*SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[3, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I3, k7, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k11, k6]*SU3F[I3, k7, k9] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[3, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[3, I3, k11]*SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I5, k11]* - SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[3, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[3, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[3, I1, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[3, I5, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[3, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3F[3, I5, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k9] + SU3D[I1, k6, k7]*SU3F[3, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k7, k9] + SU3D[I4, k6, k7]* - (SU3F[3, I3, k11]*(SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + SU3F[3, I2, k11]* - (SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k9]) + SU3F[3, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k9])) + SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + - SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k9] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + - SU3D[I3, k6, k7]*(SU3F[3, I4, k11]*(SU3F[I1, k7, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + - SU3F[3, I2, k11]*(SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k7, k9]) + SU3F[3, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k7, k9]))) + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]*SU3F[I1, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k11]*SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]*SU3F[I2, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]* - SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[I2, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[I3, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[I4, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[I4, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[3, I4, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[3, I3, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[3, I4, k11]*SU3F[I2, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3F[3, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[3, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I4, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[3, I4, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[3, I1, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[3, I1, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[3, I2, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I4, k9]* - (SU3D[I2, k6, k7]*SU3F[3, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I5, k11]* - SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I5, k11]*SU3F[I1, k11, k6]*SU3F[I3, k7, k9] + - SU3D[I1, k6, k7]*SU3F[3, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k9] + SU3D[I5, k6, k7]*(SU3F[3, I3, k11]* - (SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I2, k7, k9]) + SU3F[3, I2, k11]* - (SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k9]) + SU3F[3, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k9])) + SU3D[I2, k6, k7]*SU3F[3, I3, k11]* - SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[3, I3, k11]*SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[3, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[3, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[3, I3, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[I1, k6, k7]*SU3F[3, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[I2, k6, k7]*SU3F[3, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[I1, k6, k7]* - SU3F[3, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + - SU3D[I3, k6, k7]*(SU3F[3, I5, k11]*(SU3F[I1, k7, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + - SU3F[3, I2, k11]*(SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k7, k9]) + SU3F[3, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k7, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k11]*SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + - SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I2, k7, k9] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I2, k7, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]* - SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I3, k7, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6]*SU3F[I3, k7, k9] + - SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3F[8, I5, k11]*SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I5, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[8, I5, k11]* - SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I3, k9]*SU3D[I5, k6, k7]* - SU3F[8, I1, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[8, I5, k11]*SU3F[I2, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I2, k9]*SU3D[I5, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I1, k9]*SU3D[I5, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3F[8, I5, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + - SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I3, k11, k6]* - SU3F[I4, k7, k9] + SU3D[6, I5, k9]*(SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I4, k11]*SU3F[I1, k11, k6]* - SU3F[I3, k7, k9] + SU3D[I1, k6, k7]*SU3F[8, I4, k11]* - SU3F[I2, k11, k6]*SU3F[I3, k7, k9] + SU3D[I4, k6, k7]* - (SU3F[8, I3, k11]*(SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + SU3F[8, I2, k11]* - (SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k9]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k9])) + SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I3, k11]*SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I4, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I4, k7, k9] + - SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I4, k7, k9] + SU3D[I2, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + SU3D[I1, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I4, k7, k9] + - SU3D[I3, k6, k7]*(SU3F[8, I4, k11]*(SU3F[I1, k7, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + - SU3F[8, I2, k11]*(SU3F[I1, k7, k9]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k7, k9]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k7, k9]))) + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]*SU3F[I1, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]*SU3F[I2, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]* - SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3F[8, I4, k11]*SU3F[I2, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k11]*SU3F[I3, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[8, I1, k11]*SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[8, I1, k11]*SU3F[I4, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[8, I2, k11]*SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I4, k7, k9]* - SU3F[I5, k11, k6] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I4, k7, k9]*SU3F[I5, k11, k6] + SU3D[6, I3, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]*SU3F[I1, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I2, k9]*SU3D[I3, k6, k7]* - SU3F[8, I4, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I3, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]*SU3F[8, I3, k11]* - SU3F[I2, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3F[8, I4, k11]*SU3F[I2, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I1, k9]*SU3D[I3, k6, k7]*SU3F[8, I4, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I2, k9]*SU3D[I4, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I4, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I4, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3F[8, I1, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I3, k6, k7]*SU3F[8, I1, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[8, I2, k11]*SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + - SU3D[6, I2, k9]*SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k7, k9] + SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k7, k9] + SU3D[6, I4, k9]* - (SU3D[I2, k6, k7]*SU3F[8, I5, k11]*SU3F[I1, k7, k9]* - SU3F[I3, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I5, k11]* - SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I5, k11]*SU3F[I1, k11, k6]*SU3F[I3, k7, k9] + - SU3D[I1, k6, k7]*SU3F[8, I5, k11]*SU3F[I2, k11, k6]* - SU3F[I3, k7, k9] + SU3D[I5, k6, k7]*(SU3F[8, I3, k11]* - (SU3F[I1, k7, k9]*SU3F[I2, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I2, k7, k9]) + SU3F[8, I2, k11]* - (SU3F[I1, k7, k9]*SU3F[I3, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I3, k7, k9]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I3, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I3, k7, k9])) + SU3D[I2, k6, k7]*SU3F[8, I3, k11]* - SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3F[8, I3, k11]*SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k6, k7]*SU3F[8, I1, k11]*SU3F[I3, k7, k9]* - SU3F[I5, k11, k6] + SU3D[I1, k6, k7]*SU3F[8, I2, k11]* - SU3F[I3, k7, k9]*SU3F[I5, k11, k6] + SU3D[I2, k6, k7]* - SU3F[8, I3, k11]*SU3F[I1, k11, k6]*SU3F[I5, k7, k9] + - SU3D[I1, k6, k7]*SU3F[8, I3, k11]*SU3F[I2, k11, k6]* - SU3F[I5, k7, k9] + SU3D[I2, k6, k7]*SU3F[8, I1, k11]* - SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + SU3D[I1, k6, k7]* - SU3F[8, I2, k11]*SU3F[I3, k11, k6]*SU3F[I5, k7, k9] + - SU3D[I3, k6, k7]*(SU3F[8, I5, k11]*(SU3F[I1, k7, k9]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k7, k9]) + - SU3F[8, I2, k11]*(SU3F[I1, k7, k9]*SU3F[I5, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I5, k7, k9]) + SU3F[8, I1, k11]* - (SU3F[I2, k7, k9]*SU3F[I5, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I5, k7, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/60)*(SU3F[3, I3, k8]*SU3F[6, I5, k11]*SU3F[I1, k8, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[3, I3, k8]* - SU3F[6, I5, k11]*SU3F[I1, k10, k9]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I5, k11]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I5, k11]*SU3F[I2, k8, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I5, k11]* - SU3F[I1, k10, k9]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I5, k11]*SU3F[I2, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I5, k11]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9] + - SU3F[3, I3, k8]*SU3F[6, I5, k11]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k9] + SU3F[3, I2, k8]*SU3F[6, I5, k11]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + SU3F[3, I1, k8]* - SU3F[6, I5, k11]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[3, I2, k8]*SU3F[6, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + - SU3F[3, I1, k8]*SU3F[6, I5, k11]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k9] + SU3F[3, I3, k8]*SU3F[6, I5, k11]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9] + - SU3F[3, I3, k8]*SU3F[6, I5, k11]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I4, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I5, k11]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[3, I1, k8]* - SU3F[6, I5, k11]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I5, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9] + - SU3F[3, I1, k8]*SU3F[6, I5, k11]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k8, k9] + SU3F[3, I5, k8]* - (SU3F[6, I4, k11]*(SU3F[I1, k8, k9]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k8, k9])) + SU3F[6, I2, k11]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I1, k11]* - SU3F[I2, k8, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I2, k11]*SU3F[I1, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[6, I1, k11]*SU3F[I2, k10, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + SU3F[6, I2, k11]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I1, k11]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k11]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + SU3F[6, I1, k11]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + - SU3F[6, I2, k11]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[6, I1, k11]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[6, I2, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9] + - SU3F[6, I1, k11]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k8, k9] + SU3F[6, I3, k11]*(SU3F[I1, k8, k9]* - (SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k8, k9]))) + SU3F[3, I3, k8]*SU3F[6, I4, k11]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[3, I3, k8]*SU3F[6, I4, k11]*SU3F[I1, k10, k9]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I4, k11]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I4, k11]*SU3F[I2, k8, k9]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I4, k11]* - SU3F[I1, k10, k9]*SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I4, k11]*SU3F[I2, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I2, k11]* - SU3F[I1, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[3, I2, k8]*SU3F[6, I3, k11]*SU3F[I1, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I1, k11]* - SU3F[I2, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I3, k11]*SU3F[I2, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I1, k11]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I2, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I2, k11]* - SU3F[I1, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[3, I2, k8]*SU3F[6, I3, k11]*SU3F[I1, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I1, k11]* - SU3F[I2, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I3, k11]*SU3F[I2, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I2, k8]*SU3F[6, I1, k11]* - SU3F[I3, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[3, I1, k8]*SU3F[6, I2, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[3, I3, k8]*SU3F[6, I4, k11]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3F[3, I3, k8]*SU3F[6, I4, k11]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k9] + SU3F[3, I2, k8]*SU3F[6, I4, k11]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3F[3, I1, k8]* - SU3F[6, I4, k11]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[3, I2, k8]*SU3F[6, I4, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + - SU3F[3, I1, k8]*SU3F[6, I4, k11]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k9] + SU3F[3, I3, k8]*SU3F[6, I2, k11]*SU3F[I1, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[3, I2, k8]* - SU3F[6, I3, k11]*SU3F[I1, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[3, I3, k8]*SU3F[6, I1, k11]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[3, I1, k8]* - SU3F[6, I3, k11]*SU3F[I2, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[3, I2, k8]*SU3F[6, I1, k11]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[3, I1, k8]* - SU3F[6, I2, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[3, I3, k8]*SU3F[6, I2, k11]* - SU3F[I1, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[3, I2, k8]*SU3F[6, I3, k11]*SU3F[I1, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[3, I3, k8]*SU3F[6, I1, k11]* - SU3F[I2, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[3, I1, k8]*SU3F[6, I3, k11]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[3, I2, k8]*SU3F[6, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[3, I1, k8]*SU3F[6, I2, k11]*SU3F[I3, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[3, I3, k8]*SU3F[6, I4, k11]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k8, k9] + - SU3F[3, I3, k8]*SU3F[6, I4, k11]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I4, k11]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[3, I1, k8]* - SU3F[6, I4, k11]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I4, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k8, k9] + - SU3F[3, I1, k8]*SU3F[6, I4, k11]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k8, k9] + SU3F[3, I3, k8]*SU3F[6, I2, k11]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[3, I2, k8]* - SU3F[6, I3, k11]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[3, I3, k8]*SU3F[6, I1, k11]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[3, I1, k8]* - SU3F[6, I3, k11]*SU3F[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I1, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[3, I1, k8]* - SU3F[6, I2, k11]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[3, I3, k8]*SU3F[6, I2, k11]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[3, I2, k8]*SU3F[6, I3, k11]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[3, I3, k8]*SU3F[6, I1, k11]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[3, I1, k8]*SU3F[6, I3, k11]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[3, I2, k8]*SU3F[6, I1, k11]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[3, I1, k8]*SU3F[6, I2, k11]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[3, I4, k8]* - (SU3F[6, I5, k11]*(SU3F[I1, k8, k9]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k8, k9])) + SU3F[6, I2, k11]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[6, I1, k11]* - SU3F[I2, k8, k9]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k11]*SU3F[I1, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I1, k11]*SU3F[I2, k10, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + SU3F[6, I2, k11]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I2, k11]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I1, k11]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I2, k11]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*(SU3F[I1, k8, k9]* - (SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k8, k9])))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/60)*(SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[6, I3, k11]* - SU3F[8, I5, k8]*SU3F[I1, k10, k9]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k9]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9] + - SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9] + - SU3F[6, I3, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I4, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I5, k8]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I5, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I5, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k8, k9] + SU3F[6, I5, k11]* - (SU3F[8, I4, k8]*(SU3F[I1, k8, k9]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k8, k9])) + SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k11] + SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3F[8, I1, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3F[8, I2, k8]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k8, k9] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9] + SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9] + - SU3F[8, I1, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k8, k9] + SU3F[8, I3, k8]*(SU3F[I1, k8, k9]* - (SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k8, k9]))) + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k9]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k9]*SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k9]*SU3F[I4, k8, k9]*SU3F[I5, k10, k11] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k9]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k11] + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k11]*SU3F[I2, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I4, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k11]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I2, k11]* - SU3F[8, I3, k8]*SU3F[I1, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I3, k8]*SU3F[I2, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3F[6, I1, k11]* - SU3F[8, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k11]*SU3F[I4, k8, k9]*SU3F[I5, k10, k9] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k11]*SU3F[I4, k8, k9]* - SU3F[I5, k10, k9] + SU3F[6, I3, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k9]*SU3F[I2, k10, k11]*SU3F[I5, k8, k9] + - SU3F[6, I3, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k11]*SU3F[I2, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]*SU3F[I1, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I4, k8]*SU3F[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I4, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I4, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I2, k11]* - SU3F[8, I3, k8]*SU3F[I1, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I3, k8]*SU3F[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]*SU3F[I3, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k8, k9] + SU3F[6, I1, k11]* - SU3F[8, I2, k8]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I2, k11]*SU3F[8, I3, k8]*SU3F[I1, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I3, k11]*SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I3, k8]*SU3F[I2, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I2, k11]*SU3F[8, I1, k8]* - SU3F[I3, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k8, k9] + - SU3F[6, I1, k11]*SU3F[8, I2, k8]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k8, k9] + SU3F[6, I4, k11]* - (SU3F[8, I5, k8]*(SU3F[I1, k8, k9]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k8, k9]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k8, k9])) + SU3F[8, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3F[8, I1, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k8, k9]* - SU3F[I5, k10, k11] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k11] + SU3F[8, I2, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + - SU3F[8, I1, k8]*SU3F[I2, k8, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3F[8, I2, k8]*SU3F[I1, k10, k11]* - SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + SU3F[8, I1, k8]* - SU3F[I2, k10, k11]*SU3F[I3, k8, k9]*SU3F[I5, k10, k9] + - SU3F[8, I2, k8]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k8, k9] + SU3F[8, I1, k8]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k8, k9] + SU3F[8, I2, k8]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k8, k9] + - SU3F[8, I1, k8]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k8, k9] + SU3F[8, I3, k8]*(SU3F[I1, k8, k9]* - (SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I5, k8, k9]) + SU3F[I1, k10, k11]* - (SU3F[I2, k8, k9]*SU3F[I5, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I5, k8, k9])))))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I1] + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I1] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I1] + - SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I2] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I2] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I3] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I3] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I3] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I3] + - SU3D[I4, I5, k6]*((SU3F[6, I3, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[3, I1] + - (SU3F[6, I3, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]*SU3F[I3, k6, k8])* - SUNDelta[3, I2] + (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + - SU3F[6, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[3, I3]) + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I4] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I4] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I4] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I4] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[3, I4] + - SU3D[I3, I5, k6]*((SU3F[6, I4, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[3, I1] + - (SU3F[6, I4, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]*SU3F[I4, k6, k8])* - SUNDelta[3, I2] + (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + - SU3F[6, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[3, I4]) + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I5] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I5] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[3, I5] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[3, I5] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[3, I5] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I5] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[3, I5])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[3, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[3, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[3, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[3, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[3, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[3, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I1, k7]* - SUNDelta[3, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[3, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[3, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k7]* - SUNDelta[3, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[3, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[3, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k7]* - SUNDelta[3, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[3, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[3, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[3, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[3, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[3, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[3, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[3, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SUNDelta[3, I1] + - SU3F[6, I1, k7]*SUNDelta[3, I2]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[3, I1] + SU3F[6, I1, k7]* - SUNDelta[3, I4]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[3, I2] + SU3F[6, I2, k7]* - SUNDelta[3, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k7]*SUNDelta[3, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SUNDelta[3, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I2, k7]*SUNDelta[3, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SUNDelta[3, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[6, I3, k7]*SUNDelta[3, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[3, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[3, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[6, I4, k7]*SUNDelta[3, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SUNDelta[3, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[6, I5, k7]*SUNDelta[3, I1] + - SU3D[I1, I5, k6]*SU3F[6, I4, k7]*SUNDelta[3, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k7]*SUNDelta[3, I2] + - SU3D[I4, I5, k6]*(SU3F[6, I2, k7]*SUNDelta[3, I1] + - SU3F[6, I1, k7]*SUNDelta[3, I2]) + SU3D[I1, I5, k6]* - SU3F[6, I2, k7]*SUNDelta[3, I4] + SU3D[I1, I2, k6]*SU3F[6, I5, k7]* - SUNDelta[3, I4] + SU3D[I2, I5, k6]*(SU3F[6, I4, k7]* - SUNDelta[3, I1] + SU3F[6, I1, k7]*SUNDelta[3, I4]) + - SU3D[I2, I4, k6]*SU3F[6, I1, k7]*SUNDelta[3, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k7]*SUNDelta[3, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k7]*SUNDelta[3, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/45)*(SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[3, I1] + SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[3, I1] + SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[3, I1] + SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[3, I1] + SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I1] + SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I1] + SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[3, I2] + SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[3, I2] + SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[3, I2] + SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[3, I2] + SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I2] + SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I2] + SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[3, I3] + SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[3, I3] + SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[3, I3] + SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[3, I3] + SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I3] + SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I3] + SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[3, I4] + SU3D[6, I5, k8]*(SU3D[I2, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[3, I1] + SU3D[I1, I4, k6]*SU3F[I3, k6, k8]* - SUNDelta[3, I2] + SU3D[I1, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[3, I2] + SU3D[I3, I4, k6]*(SU3F[I2, k6, k8]* - SUNDelta[3, I1] + SU3F[I1, k6, k8]*SUNDelta[3, I2]) + - SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[3, I3] + - SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[3, I3] + - SU3D[I2, I4, k6]*(SU3F[I3, k6, k8]*SUNDelta[3, I1] + - SU3F[I1, k6, k8]*SUNDelta[3, I3]) + SU3D[I2, I3, k6]* - SU3F[I1, k6, k8]*SUNDelta[3, I4] + SU3D[I1, I3, k6]* - SU3F[I2, k6, k8]*SUNDelta[3, I4] + SU3D[I1, I2, k6]* - SU3F[I3, k6, k8]*SUNDelta[3, I4]) + SU3D[6, I3, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[3, I5] + - SU3D[6, I4, k8]*(SU3D[I2, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[3, I1] + - SU3D[I1, I5, k6]*SU3F[I3, k6, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[3, I2] + - SU3D[I3, I5, k6]*(SU3F[I2, k6, k8]*SUNDelta[3, I1] + - SU3F[I1, k6, k8]*SUNDelta[3, I2]) + SU3D[I1, I5, k6]* - SU3F[I2, k6, k8]*SUNDelta[3, I3] + SU3D[I1, I2, k6]* - SU3F[I5, k6, k8]*SUNDelta[3, I3] + SU3D[I2, I5, k6]* - (SU3F[I3, k6, k8]*SUNDelta[3, I1] + SU3F[I1, k6, k8]* - SUNDelta[3, I3]) + SU3D[I2, I3, k6]*SU3F[I1, k6, k8]* - SUNDelta[3, I5] + SU3D[I1, I3, k6]*SU3F[I2, k6, k8]* - SUNDelta[3, I5] + SU3D[I1, I2, k6]*SU3F[I3, k6, k8]* - SUNDelta[3, I5])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I1] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I1] + - SU3D[6, I3, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I1] + - SU3D[6, I2, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I1] + - SU3D[6, I3, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I1] + - SU3D[6, I2, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I1] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I2] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I2] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I2] + - SU3D[6, I1, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I2] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I2] + - SU3D[6, I1, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I2] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I3] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[3, I3] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I3] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I3] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I3] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I3] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k8]*SUNDelta[3, I4] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I2, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[3, I4] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[3, I4] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I4] + - SU3D[6, I5, k7]*(SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[3, I2] + - SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I2] + - SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I3] + - SU3D[I2, I4, k8]*(SU3D[I3, k7, k8]*SUNDelta[3, I1] + - SU3D[I1, k7, k8]*SUNDelta[3, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[3, I4] + SU3D[I1, I2, k8]*SU3D[I3, k7, k8]* - SUNDelta[3, I4] + SU3D[I2, k7, k8]*(SU3D[I3, I4, k8]* - SUNDelta[3, I1] + SU3D[I1, I4, k8]*SUNDelta[3, I3] + - SU3D[I1, I3, k8]*SUNDelta[3, I4])) + SU3D[6, I3, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I4, k8]*SUNDelta[3, I5] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I2, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[3, I5] + - SU3D[6, I4, k7]*(SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[3, I2] + - SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[3, I2] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I2] + - SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[3, I3] + - SU3D[I2, I5, k8]*(SU3D[I3, k7, k8]*SUNDelta[3, I1] + - SU3D[I1, k7, k8]*SUNDelta[3, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[3, I5] + SU3D[I1, I2, k8]*SU3D[I3, k7, k8]* - SUNDelta[3, I5] + SU3D[I2, k7, k8]*(SU3D[I3, I5, k8]* - SUNDelta[3, I1] + SU3D[I1, I5, k8]*SUNDelta[3, I3] + - SU3D[I1, I3, k8]*SUNDelta[3, I5])))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k6]*SU3F[3, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[3, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[3, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[3, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[3, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[3, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[3, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[3, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[3, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[3, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[3, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[3, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[3, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I3, I4, k6]*SU3F[3, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[3, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[3, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I2, I5, k6]*SU3F[3, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[3, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[3, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[3, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*SU3F[3, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[3, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[3, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[3, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[3, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[3, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I4, I5, k6]*((SU3F[3, I3, k8]*SU3F[I2, k6, k8] + - SU3F[3, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[6, I1] + - (SU3F[3, I3, k8]*SU3F[I1, k6, k8] + SU3F[3, I1, k8]*SU3F[I3, k6, k8])* - SUNDelta[6, I2] + (SU3F[3, I2, k8]*SU3F[I1, k6, k8] + - SU3F[3, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[6, I3]) + - SU3D[I2, I5, k6]*SU3F[3, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[3, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[3, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[3, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I5, k6]*SU3F[3, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[3, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[3, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[3, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[3, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[3, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I3, I5, k6]*((SU3F[3, I4, k8]*SU3F[I2, k6, k8] + - SU3F[3, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[6, I1] + - (SU3F[3, I4, k8]*SU3F[I1, k6, k8] + SU3F[3, I1, k8]*SU3F[I4, k6, k8])* - SUNDelta[6, I2] + (SU3F[3, I2, k8]*SU3F[I1, k6, k8] + - SU3F[3, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[6, I4]) + - SU3D[I3, I4, k6]*SU3F[3, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[3, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[3, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I3, I4, k6]*SU3F[3, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[3, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[3, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[3, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[3, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[3, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[3, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[3, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[3, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I5, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I4, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I2, I3, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I1] + - SU3D[I3, I4, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I2] + - SU3D[I3, I4, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I2] + - SU3D[I2, I5, k6]*SU3F[8, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[8, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*SU3F[8, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3F[8, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[8, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[8, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I3] + - SU3D[I4, I5, k6]*((SU3F[8, I3, k8]*SU3F[I2, k6, k8] + - SU3F[8, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[6, I1] + - (SU3F[8, I3, k8]*SU3F[I1, k6, k8] + SU3F[8, I1, k8]*SU3F[I3, k6, k8])* - SUNDelta[6, I2] + (SU3F[8, I2, k8]*SU3F[I1, k6, k8] + - SU3F[8, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[6, I3]) + - SU3D[I2, I5, k6]*SU3F[8, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[8, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[8, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[8, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I5, k6]*SU3F[8, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I5, k6]*SU3F[8, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[8, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I4] + - SU3D[I2, I3, k6]*SU3F[8, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I3, k6]*SU3F[8, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3F[8, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[6, I4] + - SU3D[I3, I5, k6]*((SU3F[8, I4, k8]*SU3F[I2, k6, k8] + - SU3F[8, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[6, I1] + - (SU3F[8, I4, k8]*SU3F[I1, k6, k8] + SU3F[8, I1, k8]*SU3F[I4, k6, k8])* - SUNDelta[6, I2] + (SU3F[8, I2, k8]*SU3F[I1, k6, k8] + - SU3F[8, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[6, I4]) + - SU3D[I3, I4, k6]*SU3F[8, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[8, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[8, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[6, I5] + - SU3D[I3, I4, k6]*SU3F[8, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[8, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[8, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*SU3F[8, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[8, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[8, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[6, I5] + - SU3D[I2, I3, k6]*SU3F[8, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I3, k6]*SU3F[8, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[8, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[6, I5])/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*(SU3D[I2, I3, I5]*SUNDelta[3, I4]*SUNDelta[6, I1] + - SU3D[I2, I3, I4]*SUNDelta[3, I5]*SUNDelta[6, I1] + - SU3D[I1, I4, I5]*SUNDelta[3, I3]*SUNDelta[6, I2] + - SU3D[I1, I3, I5]*SUNDelta[3, I4]*SUNDelta[6, I2] + - SU3D[I1, I3, I4]*SUNDelta[3, I5]*SUNDelta[6, I2] + - SU3D[I3, I4, I5]*(SUNDelta[3, I2]*SUNDelta[6, I1] + - SUNDelta[3, I1]*SUNDelta[6, I2]) + SU3D[I1, I4, I5]*SUNDelta[3, I2]* - SUNDelta[6, I3] + SU3D[I1, I2, I5]*SUNDelta[3, I4]*SUNDelta[6, I3] + - SU3D[I1, I2, I4]*SUNDelta[3, I5]*SUNDelta[6, I3] + - SU3D[I2, I4, I5]*(SUNDelta[3, I3]*SUNDelta[6, I1] + - SUNDelta[3, I1]*SUNDelta[6, I3]) + SU3D[I2, I3, I5]*SUNDelta[3, I1]* - SUNDelta[6, I4] + SU3D[I1, I3, I5]*SUNDelta[3, I2]*SUNDelta[6, I4] + - SU3D[I1, I2, I5]*SUNDelta[3, I3]*SUNDelta[6, I4] + - SU3D[I1, I2, I3]*SUNDelta[3, I5]*SUNDelta[6, I4] + - SU3D[I2, I3, I4]*SUNDelta[3, I1]*SUNDelta[6, I5] + - SU3D[I1, I3, I4]*SUNDelta[3, I2]*SUNDelta[6, I5] + - SU3D[I1, I2, I4]*SUNDelta[3, I3]*SUNDelta[6, I5] + - SU3D[I1, I2, I3]*SUNDelta[3, I4]*SUNDelta[6, I5]))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*(SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4] + - SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SUNDelta[6, I1] + - SU3D[I1, I4, k6]*SUNDelta[6, I3] + SU3D[I1, I3, k6]* - SUNDelta[6, I4]) + SU3D[I1, I4, k6]*SU3D[I2, I3, k6]* - SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[I2, I4, k6]*(SU3D[I3, I5, k6]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SUNDelta[6, I3] + SU3D[I1, I3, k6]* - SUNDelta[6, I5])))/(135*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I2, k7]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[3, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[3, I4, k7]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I1, k7]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[3, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[3, I4, k7]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[3, I1, k7]* - SUNDelta[6, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[3, I1, k7]* - SUNDelta[6, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I1, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[3, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[3, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[3, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[3, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[3, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[3, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[3, I1, k7]* - SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[3, I2, k7]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[3, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[3, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[3, I5, k7]* - SUNDelta[6, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k7]*SUNDelta[6, I1] + - SU3F[3, I1, k7]*SUNDelta[6, I2]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k7]*SUNDelta[6, I1] + SU3F[3, I1, k7]* - SUNDelta[6, I4]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k7]*SUNDelta[6, I2] + SU3F[3, I2, k7]* - SUNDelta[6, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[3, I1, k7]*SUNDelta[6, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[3, I1, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[3, I2, k7]*SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[3, I2, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[3, I3, k7]*SUNDelta[6, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[3, I3, k7]*SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[3, I3, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[3, I4, k7]*SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[3, I4, k7]*SUNDelta[6, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[3, I5, k7]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3F[3, I4, k7]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[3, I5, k7]*SUNDelta[6, I2] + - SU3D[I4, I5, k6]*(SU3F[3, I2, k7]*SUNDelta[6, I1] + - SU3F[3, I1, k7]*SUNDelta[6, I2]) + SU3D[I1, I5, k6]* - SU3F[3, I2, k7]*SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3F[3, I5, k7]* - SUNDelta[6, I4] + SU3D[I2, I5, k6]*(SU3F[3, I4, k7]* - SUNDelta[6, I1] + SU3F[3, I1, k7]*SUNDelta[6, I4]) + - SU3D[I2, I4, k6]*SU3F[3, I1, k7]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[3, I2, k7]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[3, I4, k7]*SUNDelta[6, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I2, k7]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[8, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[8, I4, k7]* - SUNDelta[6, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I1, k7]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[8, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[8, I4, k7]* - SUNDelta[6, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[8, I1, k7]* - SUNDelta[6, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[8, I1, k7]* - SUNDelta[6, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I1, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[8, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[8, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[8, I2, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[8, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[8, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[8, I4, k7]* - SUNDelta[6, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[8, I1, k7]* - SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[8, I2, k7]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[8, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[8, I3, k7]* - SUNDelta[6, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[8, I5, k7]* - SUNDelta[6, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k7]*SUNDelta[6, I1] + - SU3F[8, I1, k7]*SUNDelta[6, I2]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k7]*SUNDelta[6, I1] + SU3F[8, I1, k7]* - SUNDelta[6, I4]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k7]*SUNDelta[6, I2] + SU3F[8, I2, k7]* - SUNDelta[6, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[8, I1, k7]*SUNDelta[6, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[8, I1, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[8, I2, k7]*SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[8, I2, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[8, I3, k7]*SUNDelta[6, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[8, I3, k7]*SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[8, I3, k7]*SUNDelta[6, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[8, I4, k7]*SUNDelta[6, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[8, I4, k7]*SUNDelta[6, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[8, I5, k7]*SUNDelta[6, I1] + - SU3D[I1, I5, k6]*SU3F[8, I4, k7]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3F[8, I5, k7]*SUNDelta[6, I2] + - SU3D[I4, I5, k6]*(SU3F[8, I2, k7]*SUNDelta[6, I1] + - SU3F[8, I1, k7]*SUNDelta[6, I2]) + SU3D[I1, I5, k6]* - SU3F[8, I2, k7]*SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3F[8, I5, k7]* - SUNDelta[6, I4] + SU3D[I2, I5, k6]*(SU3F[8, I4, k7]* - SUNDelta[6, I1] + SU3F[8, I1, k7]*SUNDelta[6, I4]) + - SU3D[I2, I4, k6]*SU3F[8, I1, k7]*SUNDelta[6, I5] + - SU3D[I1, I4, k6]*SU3F[8, I2, k7]*SUNDelta[6, I5] + - SU3D[I1, I2, k6]*SU3F[8, I4, k7]*SUNDelta[6, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/45)*(SU3D[3, I3, k7]*SU3D[I4, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I2, k7]*SU3D[I4, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I3, k7]*SU3D[I2, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I2, k7]*SU3D[I3, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I3, k7]*SU3D[I2, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I2, k7]*SU3D[I3, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I1] + SU3D[3, I3, k7]*SU3D[I4, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I1, k7]*SU3D[I4, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I3, k7]*SU3D[I1, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I1, k7]*SU3D[I3, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I3, k7]*SU3D[I1, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I1, k7]*SU3D[I3, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I2] + SU3D[3, I2, k7]*SU3D[I4, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I1, k7]*SU3D[I4, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I2, k7]*SU3D[I1, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I1, k7]*SU3D[I2, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I2, k7]*SU3D[I1, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I1, k7]*SU3D[I2, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I3] + SU3D[3, I3, k7]*SU3D[I2, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I2, k7]*SU3D[I3, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I3, k7]*SU3D[I1, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I1, k7]*SU3D[I3, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I2, k7]*SU3D[I1, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I1, k7]*SU3D[I2, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I3, k7]*SU3D[I1, I2, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I2, k7]*SU3D[I1, I3, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I1, k7]*SU3D[I2, I3, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[3, I5, k7]*(SU3D[I2, I3, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[I1, I4, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I2] + SU3D[I1, I3, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[I3, I4, k8]*(SU3F[I2, k7, k8]* - SUNDelta[6, I1] + SU3F[I1, k7, k8]*SUNDelta[6, I2]) + - SU3D[I1, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k8]*(SU3F[I3, k7, k8]*SUNDelta[6, I1] + - SU3F[I1, k7, k8]*SUNDelta[6, I3]) + SU3D[I2, I3, k8]* - SU3F[I1, k7, k8]*SUNDelta[6, I4] + SU3D[I1, I3, k8]* - SU3F[I2, k7, k8]*SUNDelta[6, I4] + SU3D[I1, I2, k8]* - SU3F[I3, k7, k8]*SUNDelta[6, I4]) + SU3D[3, I3, k7]* - SU3D[I2, I4, k8]*SU3F[I1, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I3, I4, k8]*SU3F[I1, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I3, k7]*SU3D[I1, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I3, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, I4, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, I4, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I3, k7]*SU3D[I1, I2, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, I3, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, I3, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[3, I4, k7]*(SU3D[I2, I3, k8]*SU3F[I5, k7, k8]*SUNDelta[6, I1] + - SU3D[I1, I5, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k8]*SU3F[I5, k7, k8]*SUNDelta[6, I2] + - SU3D[I3, I5, k8]*(SU3F[I2, k7, k8]*SUNDelta[6, I1] + - SU3F[I1, k7, k8]*SUNDelta[6, I2]) + SU3D[I1, I5, k8]* - SU3F[I2, k7, k8]*SUNDelta[6, I3] + SU3D[I1, I2, k8]* - SU3F[I5, k7, k8]*SUNDelta[6, I3] + SU3D[I2, I5, k8]* - (SU3F[I3, k7, k8]*SUNDelta[6, I1] + SU3F[I1, k7, k8]* - SUNDelta[6, I3]) + SU3D[I2, I3, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I5] + SU3D[I1, I3, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I5] + SU3D[I1, I2, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I5])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/45)*(SU3D[8, I3, k7]*SU3D[I4, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k7]*SU3D[I4, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k7]*SU3D[I2, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k7]*SU3D[I3, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k7]*SU3D[I2, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I2, k7]*SU3D[I3, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I1] + SU3D[8, I3, k7]*SU3D[I4, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k7]*SU3D[I4, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I3, k7]*SU3D[I1, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k7]*SU3D[I3, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I3, k7]*SU3D[I1, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I1, k7]*SU3D[I3, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I2] + SU3D[8, I2, k7]*SU3D[I4, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k7]*SU3D[I4, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I2, k7]*SU3D[I1, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k7]*SU3D[I2, I5, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I2, k7]*SU3D[I1, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I1, k7]*SU3D[I2, I4, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I3] + SU3D[8, I3, k7]*SU3D[I2, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k7]*SU3D[I3, I5, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I3, k7]*SU3D[I1, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k7]*SU3D[I3, I5, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k7]*SU3D[I1, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k7]*SU3D[I2, I5, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I3, k7]*SU3D[I1, I2, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I2, k7]*SU3D[I1, I3, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I1, k7]*SU3D[I2, I3, k8]*SU3F[I5, k7, k8]* - SUNDelta[6, I4] + SU3D[8, I5, k7]*(SU3D[I2, I3, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I1] + SU3D[I1, I4, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I2] + SU3D[I1, I3, k8]*SU3F[I4, k7, k8]* - SUNDelta[6, I2] + SU3D[I3, I4, k8]*(SU3F[I2, k7, k8]* - SUNDelta[6, I1] + SU3F[I1, k7, k8]*SUNDelta[6, I2]) + - SU3D[I1, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I3] + - SU3D[I1, I2, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I3] + - SU3D[I2, I4, k8]*(SU3F[I3, k7, k8]*SUNDelta[6, I1] + - SU3F[I1, k7, k8]*SUNDelta[6, I3]) + SU3D[I2, I3, k8]* - SU3F[I1, k7, k8]*SUNDelta[6, I4] + SU3D[I1, I3, k8]* - SU3F[I2, k7, k8]*SUNDelta[6, I4] + SU3D[I1, I2, k8]* - SU3F[I3, k7, k8]*SUNDelta[6, I4]) + SU3D[8, I3, k7]* - SU3D[I2, I4, k8]*SU3F[I1, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I3, I4, k8]*SU3F[I1, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I3, I4, k8]*SU3F[I2, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I4, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I4, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I2, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I3, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I3, k8]*SU3F[I4, k7, k8]*SUNDelta[6, I5] + - SU3D[8, I4, k7]*(SU3D[I2, I3, k8]*SU3F[I5, k7, k8]*SUNDelta[6, I1] + - SU3D[I1, I5, k8]*SU3F[I3, k7, k8]*SUNDelta[6, I2] + - SU3D[I1, I3, k8]*SU3F[I5, k7, k8]*SUNDelta[6, I2] + - SU3D[I3, I5, k8]*(SU3F[I2, k7, k8]*SUNDelta[6, I1] + - SU3F[I1, k7, k8]*SUNDelta[6, I2]) + SU3D[I1, I5, k8]* - SU3F[I2, k7, k8]*SUNDelta[6, I3] + SU3D[I1, I2, k8]* - SU3F[I5, k7, k8]*SUNDelta[6, I3] + SU3D[I2, I5, k8]* - (SU3F[I3, k7, k8]*SUNDelta[6, I1] + SU3F[I1, k7, k8]* - SUNDelta[6, I3]) + SU3D[I2, I3, k8]*SU3F[I1, k7, k8]* - SUNDelta[6, I5] + SU3D[I1, I3, k8]*SU3F[I2, k7, k8]* - SUNDelta[6, I5] + SU3D[I1, I2, k8]*SU3F[I3, k7, k8]* - SUNDelta[6, I5])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[3, I3, k7]*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[3, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[3, I3, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[3, I2, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[3, I3, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[3, I2, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[3, I3, k7]*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[3, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[3, I3, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[3, I1, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[3, I3, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[3, I1, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[3, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[3, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[3, I2, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[3, I1, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[3, I2, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[3, I1, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[3, I3, k7]*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SUNDelta[6, I4] + - SU3D[3, I3, k7]*SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I2, k7]*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[3, I1, k7]*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[3, I2, k7]*SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I1, k7]*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I3, k7]*SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I2, k7]*SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I1, k7]*SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[3, I5, k7]*(SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*(SU3D[I3, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SUNDelta[6, I3]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SUNDelta[6, I4] + SU3D[I2, k6, k7]*(SU3D[I3, I4, k6]* - SUNDelta[6, I1] + SU3D[I1, I4, k6]*SUNDelta[6, I3] + - SU3D[I1, I3, k6]*SUNDelta[6, I4])) + SU3D[3, I3, k7]* - SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SUNDelta[6, I5] + - SU3D[3, I3, k7]*SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I3, k7]*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I2, k7]*SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I1, k7]*SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[3, I4, k7]*(SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*(SU3D[I3, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SUNDelta[6, I3]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SUNDelta[6, I5] + SU3D[I2, k6, k7]*(SU3D[I3, I5, k6]* - SUNDelta[6, I1] + SU3D[I1, I5, k6]*SUNDelta[6, I3] + - SU3D[I1, I3, k6]*SUNDelta[6, I5])))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[8, I3, k7]*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[8, I2, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[8, I3, k7]*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[8, I3, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[8, I3, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[8, I1, k7]*SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[8, I2, k7]*SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[8, I2, k7]*SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[8, I1, k7]*SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[8, I3, k7]*SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SUNDelta[6, I4] + - SU3D[8, I3, k7]*SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I3, k7]*SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I2, k7]*SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I1, k7]*SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I4] + - SU3D[8, I5, k7]*(SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I2] + - SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I3] + - SU3D[I2, I4, k6]*(SU3D[I3, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SUNDelta[6, I3]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SUNDelta[6, I4] + SU3D[I2, k6, k7]*(SU3D[I3, I4, k6]* - SUNDelta[6, I1] + SU3D[I1, I4, k6]*SUNDelta[6, I3] + - SU3D[I1, I3, k6]*SUNDelta[6, I4])) + SU3D[8, I3, k7]* - SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I3, k7]*SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I2, k7]*SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I1, k7]*SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SUNDelta[6, I5] + - SU3D[8, I4, k7]*(SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I2] + - SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SUNDelta[6, I3] + - SU3D[I2, I5, k6]*(SU3D[I3, k6, k7]*SUNDelta[6, I1] + - SU3D[I1, k6, k7]*SUNDelta[6, I3]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SUNDelta[6, I5] + SU3D[I1, I2, k6]*SU3D[I3, k6, k7]* - SUNDelta[6, I5] + SU3D[I2, k6, k7]*(SU3D[I3, I5, k6]* - SUNDelta[6, I1] + SU3D[I1, I5, k6]*SUNDelta[6, I3] + - SU3D[I1, I3, k6]*SUNDelta[6, I5])))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I2, k6, k8] + - SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k8])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[I4, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I3, k6, k7]*(SU3D[I4, I5, k8]*(SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k8]) + - SU3D[I1, I5, k8]*SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I5, k8]*SU3F[I2, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I2, I5, k8]*(SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k8]) + SU3D[I2, I4, k8]* - SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + SU3D[I1, I4, k8]* - SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + SU3D[I1, I2, k8]* - SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + SU3D[I2, I4, k8]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + SU3D[I1, I4, k8]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + SU3D[I1, I2, k8]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k8]))*SUNDelta[6, k11])/ - (90*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*(SU3D[I1, I5, k8]*SU3D[I2, I3, I4] + SU3D[I1, I4, k8]* - SU3D[I2, I3, I5] + SU3D[I1, I4, I5]*SU3D[I2, I3, k8] + - SU3D[I1, I3, k8]*SU3D[I2, I4, I5] + SU3D[I1, I3, I5]* - SU3D[I2, I4, k8] + SU3D[I1, I3, I4]*SU3D[I2, I5, k8] + - SU3D[I1, I2, k8]*SU3D[I3, I4, I5] + SU3D[I1, I2, I5]* - SU3D[I3, I4, k8] + SU3D[I1, I2, I4]*SU3D[I3, I5, k8] + - SU3D[I1, I2, I3]*SU3D[I4, I5, k8])*SUNDelta[6, k8])/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I1, k10, k11]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I4, I5, k11] + SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I4, I5, k11] + SU3D[I1, I5, k11]* - SU3D[I2, k8, k9]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11] + - SU3D[I1, I5, k11]*SU3D[I2, k10, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k11] + SU3D[I1, k10, k11]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k11]*SU3D[I4, k10, k9] + SU3D[I1, I5, k11]* - SU3D[I2, k8, k9]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9] + - SU3D[I1, k10, k11]*SU3D[I2, I5, k11]*SU3D[I3, k8, k9]* - SU3D[I4, k10, k9] + SU3D[I1, I5, k11]*SU3D[I2, k10, k11]* - SU3D[I3, k8, k9]*SU3D[I4, k10, k9] + SU3D[I1, k10, k11]* - SU3D[I2, k10, k9]*SU3D[I3, I5, k11]*SU3D[I4, k8, k9] + - SU3D[I1, I5, k11]*SU3D[I2, k10, k9]*SU3D[I3, k10, k11]* - SU3D[I4, k8, k9] + SU3D[I1, k10, k11]*SU3D[I2, I5, k11]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + SU3D[I1, I5, k11]* - SU3D[I2, k10, k11]*SU3D[I3, k10, k9]*SU3D[I4, k8, k9] + - SU3D[I1, I4, k11]*SU3D[I2, k8, k9]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I1, I4, k11]*SU3D[I2, k10, k9]* - SU3D[I3, k8, k9]*SU3D[I5, k10, k11] + SU3D[I1, I3, k11]* - SU3D[I2, k8, k9]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11] + - SU3D[I1, I2, k11]*SU3D[I3, k8, k9]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I1, I3, k11]*SU3D[I2, k10, k9]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k11] + SU3D[I1, I2, k11]* - SU3D[I3, k10, k9]*SU3D[I4, k8, k9]*SU3D[I5, k10, k11] + - SU3D[I1, k10, k11]*SU3D[I2, k8, k9]*SU3D[I3, I4, k11]* - SU3D[I5, k10, k9] + SU3D[I1, I4, k11]*SU3D[I2, k8, k9]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k9] + SU3D[I1, k10, k11]* - SU3D[I2, I4, k11]*SU3D[I3, k8, k9]*SU3D[I5, k10, k9] + - SU3D[I1, I4, k11]*SU3D[I2, k10, k11]*SU3D[I3, k8, k9]* - SU3D[I5, k10, k9] + SU3D[I1, I3, k11]*SU3D[I2, k8, k9]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + SU3D[I1, I2, k11]* - SU3D[I3, k8, k9]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I1, k10, k11]*SU3D[I2, I3, k11]*SU3D[I4, k8, k9]* - SU3D[I5, k10, k9] + SU3D[I1, I3, k11]*SU3D[I2, k10, k11]* - SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + SU3D[I1, I2, k11]* - SU3D[I3, k10, k11]*SU3D[I4, k8, k9]*SU3D[I5, k10, k9] + - SU3D[I1, k8, k9]*(SU3D[I2, I5, k11]*SU3D[I3, k10, k9]* - SU3D[I4, k10, k11] + SU3D[I2, I5, k11]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k9] + SU3D[I2, I4, k11]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I2, I3, k11]*SU3D[I4, k10, k9]* - SU3D[I5, k10, k11] + SU3D[I2, k10, k9]* - (SU3D[I3, k10, k11]*SU3D[I4, I5, k11] + SU3D[I3, I5, k11]* - SU3D[I4, k10, k11] + SU3D[I3, I4, k11]*SU3D[I5, k10, k11]) + - SU3D[I2, I4, k11]*SU3D[I3, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I2, I3, k11]*SU3D[I4, k10, k11]*SU3D[I5, k10, k9] + - SU3D[I2, k10, k11]*(SU3D[I3, k10, k9]*SU3D[I4, I5, k11] + - SU3D[I3, I5, k11]*SU3D[I4, k10, k9] + SU3D[I3, I4, k11]* - SU3D[I5, k10, k9])) + SU3D[I1, k10, k11]*SU3D[I2, k10, k9]* - SU3D[I3, I4, k11]*SU3D[I5, k8, k9] + SU3D[I1, I4, k11]* - SU3D[I2, k10, k9]*SU3D[I3, k10, k11]*SU3D[I5, k8, k9] + - SU3D[I1, k10, k11]*SU3D[I2, I4, k11]*SU3D[I3, k10, k9]* - SU3D[I5, k8, k9] + SU3D[I1, I4, k11]*SU3D[I2, k10, k11]* - SU3D[I3, k10, k9]*SU3D[I5, k8, k9] + SU3D[I1, I3, k11]* - SU3D[I2, k10, k9]*SU3D[I4, k10, k11]*SU3D[I5, k8, k9] + - SU3D[I1, I2, k11]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3D[I5, k8, k9] + SU3D[I1, k10, k11]*SU3D[I2, I3, k11]* - SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + SU3D[I1, I3, k11]* - SU3D[I2, k10, k11]*SU3D[I4, k10, k9]*SU3D[I5, k8, k9] + - SU3D[I1, I2, k11]*SU3D[I3, k10, k11]*SU3D[I4, k10, k9]* - SU3D[I5, k8, k9] + SU3D[I1, k10, k9]* - (SU3D[I2, I5, k11]*SU3D[I3, k8, k9]*SU3D[I4, k10, k11] + - SU3D[I2, I5, k11]*SU3D[I3, k10, k11]*SU3D[I4, k8, k9] + - SU3D[I2, I4, k11]*SU3D[I3, k8, k9]*SU3D[I5, k10, k11] + - SU3D[I2, I3, k11]*SU3D[I4, k8, k9]*SU3D[I5, k10, k11] + - SU3D[I2, k8, k9]*(SU3D[I3, k10, k11]*SU3D[I4, I5, k11] + - SU3D[I3, I5, k11]*SU3D[I4, k10, k11] + SU3D[I3, I4, k11]* - SU3D[I5, k10, k11]) + SU3D[I2, I4, k11]*SU3D[I3, k10, k11]* - SU3D[I5, k8, k9] + SU3D[I2, I3, k11]*SU3D[I4, k10, k11]* - SU3D[I5, k8, k9] + SU3D[I2, k10, k11]* - (SU3D[I3, k8, k9]*SU3D[I4, I5, k11] + SU3D[I3, I5, k11]* - SU3D[I4, k8, k9] + SU3D[I3, I4, k11]*SU3D[I5, k8, k9])))* - SUNDelta[6, k8])/(90*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/90)*(SU3D[I2, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I2, I5, k6]*SU3D[I3, k10, k9]* - SU3D[I4, k11, k6]*SU3F[I1, k10, k11] + SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3D[I5, k10, k9]*SU3F[I1, k10, k11] + - SU3D[I2, I3, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I2, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k6]*SU3F[I1, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I1, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I3, k10, k9]*SU3D[I4, I5, k6]* - SU3F[I2, k10, k11] + SU3D[I1, k10, k9]*SU3D[I3, k11, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11] + SU3D[I1, k10, k9]*SU3D[I3, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I2, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k6]*SU3F[I2, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11] + SU3D[I1, I4, k6]*SU3D[I3, k11, k6]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k6]*SU3D[I5, k10, k9]*SU3F[I2, k10, k11] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I2, k10, k11] + SU3D[I1, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k11, k6]*SU3F[I2, k10, k11] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I2, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I4, k6]*SU3D[I5, k10, k9]*SU3F[I3, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I4, k6]* - SU3D[I5, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I3, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3D[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I5, k10, k9]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I3, k6]* - SU3D[I5, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k9]*SU3D[I5, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, k11, k6]*SU3D[I2, I4, k6]*SU3D[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I3, k6]* - SU3D[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k9]*SU3D[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I2, k11, k6]*(SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11] + SU3D[I1, k10, k9]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I5, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I3, k10, k11] + SU3D[I1, I3, k6]*SU3D[I5, k10, k9]* - SU3F[I4, k10, k11] + SU3D[I3, I5, k6]* - (SU3D[I4, k10, k9]*SU3F[I1, k10, k11] + SU3D[I1, k10, k9]* - SU3F[I4, k10, k11]) + SU3D[I1, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I4, k6]*SU3F[I5, k10, k11])) + - SU3D[I2, k10, k9]*(SU3D[I3, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I1, k10, k11] + SU3D[I1, k11, k6]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I5, k6]*SU3D[I4, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I3, k6]*SU3D[I5, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I3, I5, k6]* - (SU3D[I4, k11, k6]*SU3F[I1, k10, k11] + SU3D[I1, k11, k6]* - SU3F[I4, k10, k11]) + SU3D[I1, k11, k6]*SU3D[I3, I4, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I3, k11, k6]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I4, k6]*SU3F[I5, k10, k11])))* - SUNDelta[6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/90)*(SU3D[I2, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3D[I4, k11, k6]*SU3F[I1, k10, k9] + SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3D[I5, k10, k11]*SU3F[I1, k10, k9] + - SU3D[I2, I3, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k6]*SU3F[I1, k10, k9] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k6]*SU3F[I1, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I3, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I2, k10, k9] + SU3D[I1, k10, k11]*SU3D[I3, k11, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k9] + SU3D[I1, k11, k6]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k11]*SU3F[I2, k10, k9] + - SU3D[I1, I5, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k11]* - SU3F[I2, k10, k9] + SU3D[I1, k10, k11]*SU3D[I3, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I2, k10, k9] + SU3D[I1, I5, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I2, k10, k9] + SU3D[I1, I4, k6]*SU3D[I3, k11, k6]* - SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k6]*SU3D[I5, k10, k11]*SU3F[I2, k10, k9] + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3D[I5, k11, k6]* - SU3F[I2, k10, k9] + SU3D[I1, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k11, k6]*SU3F[I2, k10, k9] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k6]*SU3F[I2, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I4, k11, k6]*SU3F[I3, k10, k9] + SU3D[I1, k11, k6]* - SU3D[I2, I4, k6]*SU3D[I5, k10, k11]*SU3F[I3, k10, k9] + - SU3D[I1, I2, k6]*SU3D[I4, k11, k6]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I5, k11, k6]*SU3F[I3, k10, k9] + SU3D[I1, I2, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k11, k6]*SU3F[I3, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I3, k11, k6]*SU3F[I4, k10, k9] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I5, k10, k11]*SU3F[I4, k10, k9] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I5, k11, k6]*SU3F[I4, k10, k9] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I5, k11, k6]*SU3F[I4, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I3, k11, k6]*SU3F[I5, k10, k9] + SU3D[I1, k11, k6]* - SU3D[I2, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3D[I3, k11, k6]*SU3D[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I4, k11, k6]*SU3F[I5, k10, k9] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I2, k11, k6]*(SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I1, k10, k9] + SU3D[I1, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I3, k10, k9] + SU3D[I1, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k10, k9] + SU3D[I1, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I3, k10, k9] + SU3D[I1, I3, k6]*SU3D[I5, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I3, I5, k6]*(SU3D[I4, k10, k11]* - SU3F[I1, k10, k9] + SU3D[I1, k10, k11]*SU3F[I4, k10, k9]) + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[I3, k10, k11]*(SU3D[I4, I5, k6]*SU3F[I1, k10, k9] + - SU3D[I1, I5, k6]*SU3F[I4, k10, k9] + SU3D[I1, I4, k6]* - SU3F[I5, k10, k9])) + SU3D[I2, k10, k11]* - (SU3D[I3, I4, k6]*SU3D[I5, k11, k6]*SU3F[I1, k10, k9] + - SU3D[I1, k11, k6]*SU3D[I4, I5, k6]*SU3F[I3, k10, k9] + - SU3D[I1, I5, k6]*SU3D[I4, k11, k6]*SU3F[I3, k10, k9] + - SU3D[I1, I4, k6]*SU3D[I5, k11, k6]*SU3F[I3, k10, k9] + - SU3D[I1, I3, k6]*SU3D[I5, k11, k6]*SU3F[I4, k10, k9] + - SU3D[I3, I5, k6]*(SU3D[I4, k11, k6]*SU3F[I1, k10, k9] + - SU3D[I1, k11, k6]*SU3F[I4, k10, k9]) + SU3D[I1, k11, k6]* - SU3D[I3, I4, k6]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3D[I4, k11, k6]*SU3F[I5, k10, k9] + SU3D[I3, k11, k6]* - (SU3D[I4, I5, k6]*SU3F[I1, k10, k9] + SU3D[I1, I5, k6]* - SU3F[I4, k10, k9] + SU3D[I1, I4, k6]*SU3F[I5, k10, k9])))* - SUNDelta[6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/90)*(SU3D[I4, I5, k6]*(SU3F[I1, k11, k6]* - (SU3F[I2, k10, k9]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I3, k11, k6]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k6])) + SU3D[I2, I5, k6]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[I2, I5, k6]*SU3F[I1, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I5, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I2, I5, k6]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[I1, I5, k6]*SU3F[I2, k11, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I2, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k9] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6]*SU3F[I4, k10, k9] + - SU3D[I2, I5, k6]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, I5, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[I2, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k6] + - SU3D[I1, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k6] + SU3D[I3, I5, k6]* - (SU3F[I1, k11, k6]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k6])) + SU3D[I3, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k9]*SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I2, I4, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k6]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3F[I3, k11, k6]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k6]*SU3F[I1, k10, k9]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I3, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I2, I4, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k9] + SU3D[I2, I3, k6]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I2, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k9] + SU3D[I3, I4, k6]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I2, I4, k6]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k6] + SU3D[I2, I3, k6]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I2, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k6])*SUNDelta[6, k9])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((SU3D[I3, I4, k6]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k6] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k9]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I2, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + SU3D[I2, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k9]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I2, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k9]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6] + SU3D[I2, I3, k6]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I5, k10, k9]*SU3F[I2, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k9]*SU3D[I2, I5, k6]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I2, k10, k9]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I5, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I2, I3, k6]*SU3D[I5, k10, k9]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I5, k10, k9]*SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, I5, k6]*SU3D[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I5, k10, k9]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I3, I5, k6]*(SU3D[I4, k10, k9]*(SU3F[I1, k11, k6]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + - SU3D[I2, k10, k9]*(SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k6]) + SU3D[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6])) + SU3D[I2, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, k10, k9]*SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I1, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I3, k6]*SU3D[I4, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k6]*SU3D[I4, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k6]*(SU3F[I1, k11, k6]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]) + SU3D[I1, I5, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6] + SU3D[I2, I5, k6]* - (SU3F[I1, k11, k6]*SU3F[I4, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I4, k11, k6]) + SU3D[I2, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6]))*SUNDelta[6, k9])/ - (90*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/90)*(SU3D[I2, I5, k6]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I1, k11, k6] + SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3D[I4, k10, k9]*SU3F[I1, k11, k6] + SU3D[I2, I4, k6]* - SU3D[I3, k10, k9]*SU3D[I5, k10, k11]*SU3F[I1, k11, k6] + - SU3D[I2, I3, k6]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k6] + SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k10, k9]*SU3F[I1, k11, k6] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I3, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I2, k11, k6] + SU3D[I1, k10, k11]*SU3D[I3, k10, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I3, I5, k6]*SU3D[I4, k10, k11]*SU3F[I2, k11, k6] + - SU3D[I1, I5, k6]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I2, k11, k6] + SU3D[I1, k10, k11]*SU3D[I3, I5, k6]* - SU3D[I4, k10, k9]*SU3F[I2, k11, k6] + SU3D[I1, I5, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k10, k9]*SU3F[I2, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I2, k11, k6] + SU3D[I1, I4, k6]*SU3D[I3, k10, k9]* - SU3D[I5, k10, k11]*SU3F[I2, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k9]*SU3D[I5, k10, k11]*SU3F[I2, k11, k6] + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3D[I5, k10, k9]* - SU3F[I2, k11, k6] + SU3D[I1, I4, k6]*SU3D[I3, k10, k11]* - SU3D[I5, k10, k9]*SU3F[I2, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I2, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I4, k10, k9]*SU3F[I3, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I4, k6]*SU3D[I5, k10, k11]*SU3F[I3, k11, k6] + - SU3D[I1, I2, k6]*SU3D[I4, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I5, k10, k9]*SU3F[I3, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I4, k10, k11]*SU3D[I5, k10, k9]*SU3F[I3, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I5, k6]*SU3D[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I5, k6]* - SU3D[I3, k10, k9]*SU3F[I4, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3D[I5, k10, k11]*SU3F[I4, k11, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k10, k9]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I5, k10, k9]*SU3F[I4, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I5, k10, k9]*SU3F[I4, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I2, I4, k6]*SU3D[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I4, k6]* - SU3D[I3, k10, k9]*SU3F[I5, k11, k6] + SU3D[I1, k10, k9]* - SU3D[I2, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k10, k9]*SU3D[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, k10, k11]*SU3D[I2, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I5, k11, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k10, k11]*SU3D[I4, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I2, k10, k9]*(SU3D[I3, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I1, k11, k6] + SU3D[I1, k10, k11]*SU3D[I4, I5, k6]* - SU3F[I3, k11, k6] + SU3D[I1, I5, k6]*SU3D[I4, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, I4, k6]*SU3D[I5, k10, k11]* - SU3F[I3, k11, k6] + SU3D[I1, I3, k6]*SU3D[I5, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I3, I5, k6]*(SU3D[I4, k10, k11]* - SU3F[I1, k11, k6] + SU3D[I1, k10, k11]*SU3F[I4, k11, k6]) + - SU3D[I1, k10, k11]*SU3D[I3, I4, k6]*SU3F[I5, k11, k6] + - SU3D[I1, I3, k6]*SU3D[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I3, k10, k11]*(SU3D[I4, I5, k6]*SU3F[I1, k11, k6] + - SU3D[I1, I5, k6]*SU3F[I4, k11, k6] + SU3D[I1, I4, k6]* - SU3F[I5, k11, k6])) + SU3D[I2, k10, k11]* - (SU3D[I3, I4, k6]*SU3D[I5, k10, k9]*SU3F[I1, k11, k6] + - SU3D[I1, k10, k9]*SU3D[I4, I5, k6]*SU3F[I3, k11, k6] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k9]*SU3F[I3, k11, k6] + - SU3D[I1, I4, k6]*SU3D[I5, k10, k9]*SU3F[I3, k11, k6] + - SU3D[I1, I3, k6]*SU3D[I5, k10, k9]*SU3F[I4, k11, k6] + - SU3D[I3, I5, k6]*(SU3D[I4, k10, k9]*SU3F[I1, k11, k6] + - SU3D[I1, k10, k9]*SU3F[I4, k11, k6]) + SU3D[I1, k10, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3D[I4, k10, k9]*SU3F[I5, k11, k6] + SU3D[I3, k10, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k11, k6] + SU3D[I1, I5, k6]* - SU3F[I4, k11, k6] + SU3D[I1, I4, k6]*SU3F[I5, k11, k6])))* - SUNDelta[6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((SU3D[I3, I4, k6]*SU3D[I5, k10, k6]*SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3D[I3, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k9] + SU3D[I2, k10, k6]* - SU3D[I4, I5, k6]*SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k6]*SU3F[I1, k11, k9]* - SU3F[I3, k10, k11] + SU3D[I2, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I1, k11, k9]*SU3F[I3, k10, k11] + SU3D[I1, k10, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k6]*SU3F[I2, k11, k9]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I2, k11, k9]*SU3F[I3, k10, k11] + SU3D[I2, k10, k6]* - SU3D[I4, I5, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + - SU3D[I2, I5, k6]*SU3D[I4, k10, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k9] + SU3D[I2, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k9] + SU3D[I1, k10, k6]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + - SU3D[I1, I5, k6]*SU3D[I4, k10, k6]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k9] + SU3D[I1, I4, k6]*SU3D[I5, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k9] + SU3D[I2, I3, k6]* - SU3D[I5, k10, k6]*SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I5, k10, k6]*SU3F[I2, k11, k9]* - SU3F[I4, k10, k11] + SU3D[I1, k10, k6]*SU3D[I2, I5, k6]* - SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I2, k10, k6]*SU3F[I3, k11, k9]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I5, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I4, k10, k11] + SU3D[I2, I3, k6]*SU3D[I5, k10, k6]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k9] + SU3D[I1, I3, k6]* - SU3D[I5, k10, k6]*SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + - SU3D[I1, k10, k6]*SU3D[I2, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k9] + SU3D[I1, I5, k6]*SU3D[I2, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + SU3D[I1, I2, k6]* - SU3D[I5, k10, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k9] + - SU3D[I3, I5, k6]*(SU3D[I4, k10, k6]*(SU3F[I1, k11, k9]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + - SU3D[I2, k10, k6]*(SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k9]) + SU3D[I1, k10, k6]* - (SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k9])) + SU3D[I2, k10, k6]*SU3D[I3, I4, k6]* - SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k6]*SU3F[I1, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I1, k10, k6]*SU3D[I3, I4, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k10, k6]* - SU3F[I2, k11, k9]*SU3F[I5, k10, k11] + SU3D[I1, k10, k6]* - SU3D[I2, I4, k6]*SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k6]*SU3F[I3, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3D[I4, k10, k6]* - SU3F[I3, k11, k9]*SU3F[I5, k10, k11] + SU3D[I1, k10, k6]* - SU3D[I2, I3, k6]*SU3F[I4, k11, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I2, k10, k6]*SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + SU3D[I2, I3, k6]* - SU3D[I4, k10, k6]*SU3F[I1, k10, k11]*SU3F[I5, k11, k9] + - SU3D[I1, k10, k6]*SU3D[I3, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I3, k6]*SU3D[I4, k10, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k9] + SU3D[I1, k10, k6]* - SU3D[I2, I4, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + - SU3D[I1, I4, k6]*SU3D[I2, k10, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I2, k6]*SU3D[I4, k10, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k9] + SU3D[I1, k10, k6]* - SU3D[I2, I3, k6]*SU3F[I4, k10, k11]*SU3F[I5, k11, k9] + - SU3D[I1, I3, k6]*SU3D[I2, k10, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I3, k10, k6]* - (SU3D[I4, I5, k6]*(SU3F[I1, k11, k9]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k9]) + SU3D[I1, I5, k6]* - SU3F[I2, k11, k9]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k9] + SU3D[I2, I5, k6]* - (SU3F[I1, k11, k9]*SU3F[I4, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I4, k11, k9]) + SU3D[I2, I4, k6]*SU3F[I1, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3F[I4, k11, k9]* - SU3F[I5, k10, k11] + SU3D[I2, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k9] + SU3D[I1, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k9]))*SUNDelta[6, k9])/ - (90*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/30)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k7] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k6]*SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + - SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I3, k10, k11] + SU3D[I1, k6, k7]* - SU3D[I4, I5, k6]*SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + - SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I3, k10, k11] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I3, k10, k11] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k6]*SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + - SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k7] + SU3D[I1, k6, k7]* - SU3D[I4, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + - SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[I2, k10, k11]* - SU3F[I3, k11, k7] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k7] + SU3D[I2, I3, k6]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]* - SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k10, k11] + - SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I4, k10, k11] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]* - SU3F[I1, k10, k11]*SU3F[I4, k11, k7] + SU3D[I1, I3, k6]* - SU3D[I5, k6, k7]*SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k7] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + SU3D[I1, I2, k6]* - SU3D[I5, k6, k7]*SU3F[I3, k10, k11]*SU3F[I4, k11, k7] + - SU3D[I3, I5, k6]*(SU3D[I4, k6, k7]*(SU3F[I1, k11, k7]* - SU3F[I2, k10, k11] + SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + - SU3D[I2, k6, k7]*(SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I4, k11, k7]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k7])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3D[I2, I4, k6]*SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k7]*SU3F[I5, k10, k11] + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SU3F[I4, k11, k7]*SU3F[I5, k10, k11] + - SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + SU3D[I2, I3, k6]* - SU3D[I4, k6, k7]*SU3F[I1, k10, k11]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3D[I2, I4, k6]*SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + - SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k7] + SU3D[I1, k6, k7]* - SU3D[I2, I3, k6]*SU3F[I4, k10, k11]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k6]*(SU3F[I1, k11, k7]*SU3F[I2, k10, k11] + - SU3F[I1, k10, k11]*SU3F[I2, k11, k7]) + SU3D[I1, I5, k6]* - SU3F[I2, k11, k7]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k7] + SU3D[I2, I5, k6]* - (SU3F[I1, k11, k7]*SU3F[I4, k10, k11] + SU3F[I1, k10, k11]* - SU3F[I4, k11, k7]) + SU3D[I2, I4, k6]*SU3F[I1, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I1, I2, k6]*SU3F[I4, k11, k7]* - SU3F[I5, k10, k11] + SU3D[I2, I4, k6]*SU3F[I1, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I1, I4, k6]*SU3F[I2, k10, k11]* - SU3F[I5, k11, k7] + SU3D[I1, I2, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k7]))*SUNDelta[7, k10])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[I1, k11, k7] + - SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[I1, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]*SU3F[I2, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]*SU3F[I2, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I3, I5, k6]*SU3D[I4, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I5, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[I2, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I3, I4, k6]*SU3D[I5, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I4, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, I3, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[I2, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I4, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I4, k7, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I5, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I5, k7, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k8]*SU3D[I5, k7, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I5, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I5, k7, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I5, k7, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k7, k8]*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k8]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I2, k6]*SU3D[I3, k6, k8]*SU3D[I4, k7, k8]*SU3F[I5, k11, k7] + - SU3D[I2, k7, k8]*(SU3D[I3, I4, k6]*SU3D[I5, k6, k8]* - SU3F[I1, k11, k7] + SU3D[I1, k6, k8]*SU3D[I4, I5, k6]* - SU3F[I3, k11, k7] + SU3D[I1, I5, k6]*SU3D[I4, k6, k8]* - SU3F[I3, k11, k7] + SU3D[I1, I4, k6]*SU3D[I5, k6, k8]* - SU3F[I3, k11, k7] + SU3D[I1, I3, k6]*SU3D[I5, k6, k8]* - SU3F[I4, k11, k7] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k8]*SU3F[I1, k11, k7] + SU3D[I1, k6, k8]* - SU3F[I4, k11, k7]) + SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3F[I5, k11, k7] + SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3F[I5, k11, k7] + SU3D[I3, k6, k8]* - (SU3D[I4, I5, k6]*SU3F[I1, k11, k7] + SU3D[I1, I5, k6]* - SU3F[I4, k11, k7] + SU3D[I1, I4, k6]*SU3F[I5, k11, k7])) + - SU3D[I2, k6, k8]*(SU3D[I3, I4, k6]*SU3D[I5, k7, k8]* - SU3F[I1, k11, k7] + SU3D[I1, k7, k8]*SU3D[I4, I5, k6]* - SU3F[I3, k11, k7] + SU3D[I1, I5, k6]*SU3D[I4, k7, k8]* - SU3F[I3, k11, k7] + SU3D[I1, I4, k6]*SU3D[I5, k7, k8]* - SU3F[I3, k11, k7] + SU3D[I1, I3, k6]*SU3D[I5, k7, k8]* - SU3F[I4, k11, k7] + SU3D[I3, I5, k6]* - (SU3D[I4, k7, k8]*SU3F[I1, k11, k7] + SU3D[I1, k7, k8]* - SU3F[I4, k11, k7]) + SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3F[I5, k11, k7] + SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3F[I5, k11, k7] + SU3D[I3, k7, k8]* - (SU3D[I4, I5, k6]*SU3F[I1, k11, k7] + SU3D[I1, I5, k6]* - SU3F[I4, k11, k7] + SU3D[I1, I4, k6]*SU3F[I5, k11, k7])))* - SUNDelta[7, k11])/(30*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/30)*(SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k7]*SU3F[I2, k6, k8] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8]*SU3F[I3, k11, k7] + - SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I3, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*(SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + SU3F[I2, k11, k7]* - SU3F[I4, k6, k8])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + - SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[I4, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k11, k7]*SU3F[I5, k6, k8] + - SU3D[I3, k6, k7]*(SU3D[I4, I5, k8]*(SU3F[I1, k6, k8]* - SU3F[I2, k11, k7] + SU3F[I1, k11, k7]*SU3F[I2, k6, k8]) + - SU3D[I1, I5, k8]*SU3F[I2, k6, k8]*SU3F[I4, k11, k7] + - SU3D[I1, I5, k8]*SU3F[I2, k11, k7]*SU3F[I4, k6, k8] + - SU3D[I2, I5, k8]*(SU3F[I1, k6, k8]*SU3F[I4, k11, k7] + - SU3F[I1, k11, k7]*SU3F[I4, k6, k8]) + SU3D[I2, I4, k8]* - SU3F[I1, k6, k8]*SU3F[I5, k11, k7] + SU3D[I1, I4, k8]* - SU3F[I2, k6, k8]*SU3F[I5, k11, k7] + SU3D[I1, I2, k8]* - SU3F[I4, k6, k8]*SU3F[I5, k11, k7] + SU3D[I2, I4, k8]* - SU3F[I1, k11, k7]*SU3F[I5, k6, k8] + SU3D[I1, I4, k8]* - SU3F[I2, k11, k7]*SU3F[I5, k6, k8] + SU3D[I1, I2, k8]* - SU3F[I4, k11, k7]*SU3F[I5, k6, k8]))*SUNDelta[7, k11])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/15)*(SU3D[I1, I5, k3]*SU3D[I2, I3, I4] + - SU3D[I1, I4, k3]*SU3D[I2, I3, I5] + SU3D[I1, I4, I5]* - SU3D[I2, I3, k3] + SU3D[I1, I3, k3]*SU3D[I2, I4, I5] + - SU3D[I1, I3, I5]*SU3D[I2, I4, k3] + SU3D[I1, I3, I4]* - SU3D[I2, I5, k3] + SU3D[I1, I2, k3]*SU3D[I3, I4, I5] + - SU3D[I1, I2, I5]*SU3D[I3, I4, k3] + SU3D[I1, I2, I4]* - SU3D[I3, I5, k3] + SU3D[I1, I2, I3]*SU3D[I4, I5, k3])* - SUNDelta[7, k3])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/30)*(SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6] + SU3D[I1, k6, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6] + SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k9] + SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I4, k6, k9] + SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8] + SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9]* - SU3D[I4, k7, k8] + SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8] + SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9]* - SU3D[I4, k7, k8] + SU3D[I1, k6, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9] + SU3D[I1, I5, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k9]* - SU3D[I4, k8, k9] + SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9] + SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9] + SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k9] + SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]* - SU3D[I5, k6, k9] + SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k9] + SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k9] + SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k9] + SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3D[I5, k6, k9] + SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8] + SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I3, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I4, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8] + SU3D[I1, k8, k9]* - (SU3D[I2, I5, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k9] + - SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k7, k8] + - SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k6, k9] + - SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k6, k9] + - SU3D[I2, k7, k8]*(SU3D[I3, k6, k9]*SU3D[I4, I5, k6] + - SU3D[I3, I5, k6]*SU3D[I4, k6, k9] + SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]) + SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I2, I3, k6]*SU3D[I4, k6, k9]* - SU3D[I5, k7, k8] + SU3D[I2, k6, k9]*(SU3D[I3, k7, k8]* - SU3D[I4, I5, k6] + SU3D[I3, I5, k6]*SU3D[I4, k7, k8] + - SU3D[I3, I4, k6]*SU3D[I5, k7, k8])) + SU3D[I1, k6, k9]* - SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9] + - SU3D[I1, I4, k6]*SU3D[I2, k7, k8]*SU3D[I3, k6, k9]*SU3D[I5, k8, k9] + - SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, I3, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9] + - SU3D[I1, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9] + - SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, I2, k6]*SU3D[I3, k6, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9] + - SU3D[I1, k7, k8]*(SU3D[I2, I5, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9] + - SU3D[I2, I5, k6]*SU3D[I3, k6, k9]*SU3D[I4, k8, k9] + - SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9] + - SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9] + - SU3D[I2, k8, k9]*(SU3D[I3, k6, k9]*SU3D[I4, I5, k6] + - SU3D[I3, I5, k6]*SU3D[I4, k6, k9] + SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]) + SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3D[I5, k8, k9] + SU3D[I2, I3, k6]*SU3D[I4, k6, k9]* - SU3D[I5, k8, k9] + SU3D[I2, k6, k9]*(SU3D[I3, k8, k9]* - SU3D[I4, I5, k6] + SU3D[I3, I5, k6]*SU3D[I4, k8, k9] + - SU3D[I3, I4, k6]*SU3D[I5, k8, k9])))*SUNDelta[7, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/30)*(SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k11, k8]* - SU3F[I2, k11, k6] + SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I2, k11, k8] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I1, k11, k8]*SU3F[I3, k11, k6] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k8]* - SU3F[I3, k11, k6] + SU3D[I2, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k8]*SU3F[I3, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k11, k8]*SU3F[I3, k11, k6] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k8]* - SU3F[I3, k11, k6] + SU3D[I1, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k8]*SU3F[I3, k11, k6] + SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I1, k11, k6]*SU3F[I3, k11, k8] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I1, k11, k6]* - SU3F[I3, k11, k8] + SU3D[I2, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I3, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k11, k6]*SU3F[I3, k11, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k11, k6]* - SU3F[I3, k11, k8] + SU3D[I1, I4, k8]*SU3D[I5, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I3, k11, k8] + SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k11, k8]*SU3F[I4, k11, k6] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I2, k11, k8]* - SU3F[I4, k11, k6] + SU3D[I1, k6, k7]*SU3D[I2, I5, k8]* - SU3F[I3, k11, k8]*SU3F[I4, k11, k6] + SU3D[I1, I5, k8]* - SU3D[I2, k6, k7]*SU3F[I3, k11, k8]*SU3F[I4, k11, k6] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[I3, k11, k8]* - SU3F[I4, k11, k6] + SU3D[I2, I3, k8]*SU3D[I5, k6, k7]* - SU3F[I1, k11, k6]*SU3F[I4, k11, k8] + SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k11, k6]*SU3F[I4, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[I3, k11, k6]* - SU3F[I4, k11, k8] + SU3D[I1, I5, k8]*SU3D[I2, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I4, k11, k8] + SU3D[I1, I2, k8]* - SU3D[I5, k6, k7]*SU3F[I3, k11, k6]*SU3F[I4, k11, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*(SU3F[I1, k11, k8]* - SU3F[I2, k11, k6] + SU3F[I1, k11, k6]*SU3F[I2, k11, k8]) + - SU3D[I2, k6, k7]*(SU3F[I1, k11, k8]*SU3F[I4, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I4, k11, k8]) + SU3D[I1, k6, k7]* - (SU3F[I2, k11, k8]*SU3F[I4, k11, k6] + SU3F[I2, k11, k6]* - SU3F[I4, k11, k8])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I1, k11, k8]*SU3F[I5, k11, k6] + SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k8]*SU3F[I5, k11, k6] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I1, I3, k8]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k8]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[I3, k11, k8]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k8]*SU3F[I5, k11, k6] + SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I4, k11, k8]*SU3F[I5, k11, k6] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[I1, k11, k6]*SU3F[I5, k11, k8] + SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k11, k6]*SU3F[I5, k11, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I1, I3, k8]*SU3D[I4, k6, k7]* - SU3F[I2, k11, k6]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[I3, k11, k6]*SU3F[I5, k11, k8] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I1, I2, k8]*SU3D[I4, k6, k7]* - SU3F[I3, k11, k6]*SU3F[I5, k11, k8] + SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I4, k11, k6]*SU3F[I5, k11, k8] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*(SU3F[I1, k11, k8]*SU3F[I2, k11, k6] + - SU3F[I1, k11, k6]*SU3F[I2, k11, k8]) + SU3D[I1, I5, k8]* - SU3F[I2, k11, k8]*SU3F[I4, k11, k6] + SU3D[I1, I5, k8]* - SU3F[I2, k11, k6]*SU3F[I4, k11, k8] + SU3D[I2, I5, k8]* - (SU3F[I1, k11, k8]*SU3F[I4, k11, k6] + SU3F[I1, k11, k6]* - SU3F[I4, k11, k8]) + SU3D[I2, I4, k8]*SU3F[I1, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k8]*SU3F[I2, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I1, I2, k8]*SU3F[I4, k11, k8]* - SU3F[I5, k11, k6] + SU3D[I2, I4, k8]*SU3F[I1, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I1, I4, k8]*SU3F[I2, k11, k6]* - SU3F[I5, k11, k8] + SU3D[I1, I2, k8]*SU3F[I4, k11, k6]* - SU3F[I5, k11, k8]))*SUNDelta[7, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((SU3D[I2, I5, k8]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I2, I4, k8]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I2, I3, k8]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, k8, k9]*SU3D[I4, I5, k8]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, I5, k8]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, I4, k8]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, I3, k8]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3D[I4, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I4, k8, k9]*SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3D[I3, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I3, k8, k9]*SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3D[I5, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3D[I5, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3D[I3, k8, k9]*SU3F[I5, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I3, k8, k9]*SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] + - SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3D[I4, k8, k9]*SU3F[I5, k6, k9] + - SU3D[I2, k8, k9]*(SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k9] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k9] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*SU3F[I1, k6, k9] + - SU3D[I1, k6, k7]*SU3F[I4, k6, k9]) + SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9] + SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k9] + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I1, I4, k8]*SU3F[I5, k6, k9])) + - SU3D[I2, k6, k7]*(SU3D[I3, I4, k8]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3D[I4, I5, k8]*SU3F[I3, k6, k9] + - SU3D[I1, I5, k8]*SU3D[I4, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, I4, k8]*SU3D[I5, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, I3, k8]*SU3D[I5, k8, k9]*SU3F[I4, k6, k9] + - SU3D[I3, I5, k8]*(SU3D[I4, k8, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k8, k9]*SU3F[I4, k6, k9]) + SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9] + SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9] + SU3D[I3, k8, k9]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k9] + SU3D[I1, I4, k8]*SU3F[I5, k6, k9])))* - SUNDelta[7, k7])/(30*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((SU3D[I4, I5, k6]*(SU3F[I1, k11, k6]*(SU3F[I2, k10, k9]* - SU3F[I3, k10, k11] + SU3F[I2, k10, k11]*SU3F[I3, k10, k9]) + - SU3F[I1, k10, k9]*(SU3F[I2, k11, k6]*SU3F[I3, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I3, k11, k6]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k6]*SU3F[I3, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I3, k11, k6])) + SU3D[I2, I5, k6]*SU3F[I1, k11, k6]* - SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + SU3D[I1, I5, k6]* - SU3F[I2, k11, k6]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11] + - SU3D[I2, I5, k6]*SU3F[I1, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I4, k10, k11] + SU3D[I1, I5, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k11] + SU3D[I2, I5, k6]* - SU3F[I1, k11, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9] + - SU3D[I1, I5, k6]*SU3F[I2, k11, k6]*SU3F[I3, k10, k11]* - SU3F[I4, k10, k9] + SU3D[I2, I5, k6]*SU3F[I1, k10, k11]* - SU3F[I3, k11, k6]*SU3F[I4, k10, k9] + SU3D[I1, I5, k6]* - SU3F[I2, k10, k11]*SU3F[I3, k11, k6]*SU3F[I4, k10, k9] + - SU3D[I2, I5, k6]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I4, k11, k6] + SU3D[I1, I5, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I4, k11, k6] + SU3D[I2, I5, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I4, k11, k6] + - SU3D[I1, I5, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I4, k11, k6] + SU3D[I3, I5, k6]* - (SU3F[I1, k11, k6]*(SU3F[I2, k10, k9]*SU3F[I4, k10, k11] + - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]) + SU3F[I1, k10, k9]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k11] + SU3F[I2, k10, k11]* - SU3F[I4, k11, k6]) + SU3F[I1, k10, k11]* - (SU3F[I2, k11, k6]*SU3F[I4, k10, k9] + SU3F[I2, k10, k9]* - SU3F[I4, k11, k6])) + SU3D[I3, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k9]*SU3F[I5, k10, k11] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k9]*SU3F[I2, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I2, I4, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k9]*SU3F[I5, k10, k11] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k9]*SU3F[I3, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k9]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k6]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k9]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3F[I3, k11, k6]*SU3F[I4, k10, k9]* - SU3F[I5, k10, k11] + SU3D[I2, I3, k6]*SU3F[I1, k10, k9]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k9]*SU3F[I4, k11, k6]*SU3F[I5, k10, k11] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k9]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k11] + SU3D[I3, I4, k6]*SU3F[I1, k11, k6]* - SU3F[I2, k10, k11]*SU3F[I5, k10, k9] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I2, I4, k6]*SU3F[I1, k11, k6]*SU3F[I3, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I1, I4, k6]*SU3F[I2, k11, k6]* - SU3F[I3, k10, k11]*SU3F[I5, k10, k9] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k11, k6]* - SU3F[I5, k10, k9] + SU3D[I2, I3, k6]*SU3F[I1, k11, k6]* - SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3F[I2, k11, k6]*SU3F[I4, k10, k11]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k11, k6]*SU3F[I4, k10, k11]* - SU3F[I5, k10, k9] + SU3D[I2, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k11, k6]*SU3F[I5, k10, k9] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k11, k6]*SU3F[I5, k10, k9] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k11, k6]* - SU3F[I5, k10, k9] + SU3D[I3, I4, k6]*SU3F[I1, k10, k9]* - SU3F[I2, k10, k11]*SU3F[I5, k11, k6] + SU3D[I3, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I2, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I2, I4, k6]*SU3F[I1, k10, k9]*SU3F[I3, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I1, I4, k6]*SU3F[I2, k10, k9]* - SU3F[I3, k10, k11]*SU3F[I5, k11, k6] + SU3D[I2, I4, k6]* - SU3F[I1, k10, k11]*SU3F[I3, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I1, I4, k6]*SU3F[I2, k10, k11]*SU3F[I3, k10, k9]* - SU3F[I5, k11, k6] + SU3D[I2, I3, k6]*SU3F[I1, k10, k9]* - SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k9]*SU3F[I4, k10, k11]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k9]*SU3F[I4, k10, k11]* - SU3F[I5, k11, k6] + SU3D[I2, I3, k6]*SU3F[I1, k10, k11]* - SU3F[I4, k10, k9]*SU3F[I5, k11, k6] + SU3D[I1, I3, k6]* - SU3F[I2, k10, k11]*SU3F[I4, k10, k9]*SU3F[I5, k11, k6] + - SU3D[I1, I2, k6]*SU3F[I3, k10, k11]*SU3F[I4, k10, k9]* - SU3F[I5, k11, k6])*SUNDelta[7, k9])/ - (30*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I2, I5, k8]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[I2, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k9]*SU3D[I4, I5, k8]*SU3F[I2, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[I2, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[I2, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k7, k9]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3D[I5, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[I4, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3D[I3, k7, k9]*SU3F[I4, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I3, k7, k9]*SU3D[I5, k6, k7]*SU3F[I4, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3D[I5, k7, k9]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3D[I5, k7, k9]*SU3F[I4, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3D[I3, k7, k9]*SU3F[I5, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I3, k7, k9]*SU3D[I4, k6, k7]*SU3F[I5, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3D[I4, k7, k9]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3D[I4, k7, k9]*SU3F[I5, k6, k8] + - SU3D[I2, k7, k9]*(SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3F[I4, k6, k8]) + SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8] + SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8] + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k8] + SU3D[I1, I4, k8]*SU3F[I5, k6, k8])) + - SU3D[I2, k6, k7]*(SU3D[I3, I4, k8]*SU3D[I5, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I1, k7, k9]*SU3D[I4, I5, k8]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I5, k7, k9]*SU3F[I3, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k9]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k7, k9]*SU3F[I1, k6, k8] + - SU3D[I1, k7, k9]*SU3F[I4, k6, k8]) + SU3D[I1, k7, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8] + SU3D[I1, I3, k8]* - SU3D[I4, k7, k9]*SU3F[I5, k6, k8] + SU3D[I3, k7, k9]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k8] + SU3D[I1, I4, k8]*SU3F[I5, k6, k8])))* - SUNDelta[7, k9])/(30*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I1] + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I2] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I3] + - SU3D[I4, I5, k6]*((SU3F[6, I3, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I3, k6, k8])*SUNDelta[8, I1] + - (SU3F[6, I3, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]*SU3F[I3, k6, k8])* - SUNDelta[8, I2] + (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + - SU3F[6, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[8, I3]) + - SU3D[I2, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I5, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I5, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I2, k6]*SU3F[6, I5, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I4] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I5, k6, k8]*SUNDelta[8, I4] + - SU3D[I3, I5, k6]*((SU3F[6, I4, k8]*SU3F[I2, k6, k8] + - SU3F[6, I2, k8]*SU3F[I4, k6, k8])*SUNDelta[8, I1] + - (SU3F[6, I4, k8]*SU3F[I1, k6, k8] + SU3F[6, I1, k8]*SU3F[I4, k6, k8])* - SUNDelta[8, I2] + (SU3F[6, I2, k8]*SU3F[I1, k6, k8] + - SU3F[6, I1, k8]*SU3F[I2, k6, k8])*SUNDelta[8, I4]) + - SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I4, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I3, k6]*SU3F[6, I4, k8]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I3, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I3, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k8]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I3, k8]*SU3F[I4, k6, k8]*SUNDelta[8, I5])/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SU3D[I2, I3, I5]*SUNDelta[6, I4]*SUNDelta[8, I1] + - SU3D[I2, I3, I4]*SUNDelta[6, I5]*SUNDelta[8, I1] + - SU3D[I1, I4, I5]*SUNDelta[6, I3]*SUNDelta[8, I2] + - SU3D[I1, I3, I5]*SUNDelta[6, I4]*SUNDelta[8, I2] + - SU3D[I1, I3, I4]*SUNDelta[6, I5]*SUNDelta[8, I2] + - SU3D[I3, I4, I5]*(SUNDelta[6, I2]*SUNDelta[8, I1] + - SUNDelta[6, I1]*SUNDelta[8, I2]) + SU3D[I1, I4, I5]*SUNDelta[6, I2]* - SUNDelta[8, I3] + SU3D[I1, I2, I5]*SUNDelta[6, I4]*SUNDelta[8, I3] + - SU3D[I1, I2, I4]*SUNDelta[6, I5]*SUNDelta[8, I3] + - SU3D[I2, I4, I5]*(SUNDelta[6, I3]*SUNDelta[8, I1] + - SUNDelta[6, I1]*SUNDelta[8, I3]) + SU3D[I2, I3, I5]*SUNDelta[6, I1]* - SUNDelta[8, I4] + SU3D[I1, I3, I5]*SUNDelta[6, I2]*SUNDelta[8, I4] + - SU3D[I1, I2, I5]*SUNDelta[6, I3]*SUNDelta[8, I4] + - SU3D[I1, I2, I3]*SUNDelta[6, I5]*SUNDelta[8, I4] + - SU3D[I2, I3, I4]*SUNDelta[6, I1]*SUNDelta[8, I5] + - SU3D[I1, I3, I4]*SUNDelta[6, I2]*SUNDelta[8, I5] + - SU3D[I1, I2, I4]*SUNDelta[6, I3]*SUNDelta[8, I5] + - SU3D[I1, I2, I3]*SUNDelta[6, I4]*SUNDelta[8, I5]))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/45)*(SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I1] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I1] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I1] + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I1] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I1] + SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I2] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I2] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I2] + SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]* - SUNDelta[8, I3] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I3] + SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]* - SUNDelta[8, I4] + SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]* - SUNDelta[8, I4] + SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]* - SUNDelta[8, I4] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k7]*SUNDelta[8, I1] + - SU3F[6, I1, k7]*SUNDelta[8, I2]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[8, I1] + SU3F[6, I1, k7]* - SUNDelta[8, I4]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k7]*SUNDelta[8, I2] + SU3F[6, I2, k7]* - SUNDelta[8, I4])) + SU3D[I2, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I1, k7]*SUNDelta[8, I5] + SU3D[I2, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I1, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I3, I4, k6]* - SU3F[6, I2, k7]*SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3D[I4, k6, k7]* - SU3F[6, I2, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I2, I4, k6]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, I4, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, I2, k6]*SU3D[I4, k6, k7]* - SU3F[6, I3, k7]*SUNDelta[8, I5] + SU3D[I1, k6, k7]*SU3D[I2, I3, k6]* - SU3F[6, I4, k7]*SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3D[I2, k6, k7]* - SU3F[6, I4, k7]*SUNDelta[8, I5] + SU3D[I3, k6, k7]* - (SU3D[I2, I4, k6]*SU3F[6, I5, k7]*SUNDelta[8, I1] + - SU3D[I1, I5, k6]*SU3F[6, I4, k7]*SUNDelta[8, I2] + - SU3D[I1, I4, k6]*SU3F[6, I5, k7]*SUNDelta[8, I2] + - SU3D[I4, I5, k6]*(SU3F[6, I2, k7]*SUNDelta[8, I1] + - SU3F[6, I1, k7]*SUNDelta[8, I2]) + SU3D[I1, I5, k6]* - SU3F[6, I2, k7]*SUNDelta[8, I4] + SU3D[I1, I2, k6]*SU3F[6, I5, k7]* - SUNDelta[8, I4] + SU3D[I2, I5, k6]*(SU3F[6, I4, k7]* - SUNDelta[8, I1] + SU3F[6, I1, k7]*SUNDelta[8, I4]) + - SU3D[I2, I4, k6]*SU3F[6, I1, k7]*SUNDelta[8, I5] + - SU3D[I1, I4, k6]*SU3F[6, I2, k7]*SUNDelta[8, I5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k7]*SUNDelta[8, I5])))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/45)*(SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I1] + SU3D[6, I3, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I2] + SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I3] + SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I5, k6, k8]* - SUNDelta[8, I4] + SU3D[6, I5, k8]*(SU3D[I2, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I1] + SU3D[I1, I4, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I2] + SU3D[I1, I3, k6]*SU3F[I4, k6, k8]* - SUNDelta[8, I2] + SU3D[I3, I4, k6]*(SU3F[I2, k6, k8]* - SUNDelta[8, I1] + SU3F[I1, k6, k8]*SUNDelta[8, I2]) + - SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I3] + - SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k6]*(SU3F[I3, k6, k8]*SUNDelta[8, I1] + - SU3F[I1, k6, k8]*SUNDelta[8, I3]) + SU3D[I2, I3, k6]* - SU3F[I1, k6, k8]*SUNDelta[8, I4] + SU3D[I1, I3, k6]* - SU3F[I2, k6, k8]*SUNDelta[8, I4] + SU3D[I1, I2, k6]* - SU3F[I3, k6, k8]*SUNDelta[8, I4]) + SU3D[6, I3, k8]* - SU3D[I2, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k8]*SUNDelta[8, I5] + - SU3D[6, I4, k8]*(SU3D[I2, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[8, I1] + - SU3D[I1, I5, k6]*SU3F[I3, k6, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k6]*SU3F[I5, k6, k8]*SUNDelta[8, I2] + - SU3D[I3, I5, k6]*(SU3F[I2, k6, k8]*SUNDelta[8, I1] + - SU3F[I1, k6, k8]*SUNDelta[8, I2]) + SU3D[I1, I5, k6]* - SU3F[I2, k6, k8]*SUNDelta[8, I3] + SU3D[I1, I2, k6]* - SU3F[I5, k6, k8]*SUNDelta[8, I3] + SU3D[I2, I5, k6]* - (SU3F[I3, k6, k8]*SUNDelta[8, I1] + SU3F[I1, k6, k8]* - SUNDelta[8, I3]) + SU3D[I2, I3, k6]*SU3F[I1, k6, k8]* - SUNDelta[8, I5] + SU3D[I1, I3, k6]*SU3F[I2, k6, k8]* - SUNDelta[8, I5] + SU3D[I1, I2, k6]*SU3F[I3, k6, k8]* - SUNDelta[8, I5])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I2, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I2] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I1, k7]*SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[8, I3] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I3, k7]*SU3D[I1, I5, k8]*SU3D[I2, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I4] + - SU3D[6, I5, k7]*(SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I2] + - SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I3] + - SU3D[I2, I4, k8]*(SU3D[I3, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SUNDelta[8, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[8, I4] + SU3D[I1, I2, k8]*SU3D[I3, k7, k8]* - SUNDelta[8, I4] + SU3D[I2, k7, k8]*(SU3D[I3, I4, k8]* - SUNDelta[8, I1] + SU3D[I1, I4, k8]*SUNDelta[8, I3] + - SU3D[I1, I3, k8]*SUNDelta[8, I4])) + SU3D[6, I3, k7]* - SU3D[I1, k7, k8]*SU3D[I2, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k7]*SU3D[I1, I4, k8]*SU3D[I2, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, I4, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I3, k7]*SU3D[I1, I2, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I2, k7]*SU3D[I1, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I1, k7]*SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[8, I5] + - SU3D[6, I4, k7]*(SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SU3D[I3, I5, k8]*SUNDelta[8, I2] + - SU3D[I1, I5, k8]*SU3D[I3, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I2] + - SU3D[I1, I2, k8]*SU3D[I5, k7, k8]*SUNDelta[8, I3] + - SU3D[I2, I5, k8]*(SU3D[I3, k7, k8]*SUNDelta[8, I1] + - SU3D[I1, k7, k8]*SUNDelta[8, I3]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k8]*SUNDelta[8, I5] + SU3D[I1, I2, k8]*SU3D[I3, k7, k8]* - SUNDelta[8, I5] + SU3D[I2, k7, k8]*(SU3D[I3, I5, k8]* - SUNDelta[8, I1] + SU3D[I1, I5, k8]*SUNDelta[8, I3] + - SU3D[I1, I3, k8]*SUNDelta[8, I5])))/ - (45*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/135)*SUNDelta[6, k8]*(SU3D[I3, I4, k5]*SU3F[I5, k5, k8]* - SUNDelta[I1, I2] + SU3D[I2, I5, k5]*SU3F[I4, k5, k8]* - SUNDelta[I1, I3] + SU3D[I2, I4, k5]*SU3F[I5, k5, k8]* - SUNDelta[I1, I3] + SU3D[I2, I5, k5]*SU3F[I3, k5, k8]* - SUNDelta[I1, I4] + SU3D[I2, I3, k5]*SU3F[I5, k5, k8]* - SUNDelta[I1, I4] + SU3D[I3, I4, k5]*SU3F[I2, k5, k8]* - SUNDelta[I1, I5] + SU3D[I2, I4, k5]*SU3F[I3, k5, k8]* - SUNDelta[I1, I5] + SU3D[I2, I3, k5]*SU3F[I4, k5, k8]* - SUNDelta[I1, I5] + SU3D[I1, I5, k5]*SU3F[I4, k5, k8]* - SUNDelta[I2, I3] + SU3D[I1, I4, k5]*SU3F[I5, k5, k8]* - SUNDelta[I2, I3] + SU3D[I4, I5, k5]* - (SU3F[I3, k5, k8]*SUNDelta[I1, I2] + SU3F[I2, k5, k8]* - SUNDelta[I1, I3] + SU3F[I1, k5, k8]*SUNDelta[I2, I3]) + - SU3D[I1, I5, k5]*SU3F[I3, k5, k8]*SUNDelta[I2, I4] + - SU3D[I1, I3, k5]*SU3F[I5, k5, k8]*SUNDelta[I2, I4] + - SU3D[I3, I5, k5]*(SU3F[I4, k5, k8]*SUNDelta[I1, I2] + - SU3F[I2, k5, k8]*SUNDelta[I1, I4] + SU3F[I1, k5, k8]* - SUNDelta[I2, I4]) + SU3D[I3, I4, k5]*SU3F[I1, k5, k8]* - SUNDelta[I2, I5] + SU3D[I1, I4, k5]*SU3F[I3, k5, k8]* - SUNDelta[I2, I5] + SU3D[I1, I3, k5]*SU3F[I4, k5, k8]* - SUNDelta[I2, I5] + SU3D[I2, I5, k5]*SU3F[I1, k5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I5, k5]*SU3F[I2, k5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I2, k5]*SU3F[I5, k5, k8]* - SUNDelta[I3, I4] + SU3D[I2, I4, k5]*SU3F[I1, k5, k8]* - SUNDelta[I3, I5] + SU3D[I1, I4, k5]*SU3F[I2, k5, k8]* - SUNDelta[I3, I5] + SU3D[I1, I2, k5]*SU3F[I4, k5, k8]* - SUNDelta[I3, I5] + SU3D[I2, I3, k5]*SU3F[I1, k5, k8]* - SUNDelta[I4, I5] + SU3D[I1, I3, k5]*SU3F[I2, k5, k8]* - SUNDelta[I4, I5] + SU3D[I1, I2, k5]*SU3F[I3, k5, k8]* - SUNDelta[I4, I5]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (2*SUNDelta[7, k8]*(SU3D[I3, I4, k5]*SU3F[I5, k5, k8]*SUNDelta[I1, I2] + - SU3D[I2, I5, k5]*SU3F[I4, k5, k8]*SUNDelta[I1, I3] + - SU3D[I2, I4, k5]*SU3F[I5, k5, k8]*SUNDelta[I1, I3] + - SU3D[I2, I5, k5]*SU3F[I3, k5, k8]*SUNDelta[I1, I4] + - SU3D[I2, I3, k5]*SU3F[I5, k5, k8]*SUNDelta[I1, I4] + - SU3D[I3, I4, k5]*SU3F[I2, k5, k8]*SUNDelta[I1, I5] + - SU3D[I2, I4, k5]*SU3F[I3, k5, k8]*SUNDelta[I1, I5] + - SU3D[I2, I3, k5]*SU3F[I4, k5, k8]*SUNDelta[I1, I5] + - SU3D[I1, I5, k5]*SU3F[I4, k5, k8]*SUNDelta[I2, I3] + - SU3D[I1, I4, k5]*SU3F[I5, k5, k8]*SUNDelta[I2, I3] + - SU3D[I4, I5, k5]*(SU3F[I3, k5, k8]*SUNDelta[I1, I2] + - SU3F[I2, k5, k8]*SUNDelta[I1, I3] + SU3F[I1, k5, k8]* - SUNDelta[I2, I3]) + SU3D[I1, I5, k5]*SU3F[I3, k5, k8]* - SUNDelta[I2, I4] + SU3D[I1, I3, k5]*SU3F[I5, k5, k8]* - SUNDelta[I2, I4] + SU3D[I3, I5, k5]* - (SU3F[I4, k5, k8]*SUNDelta[I1, I2] + SU3F[I2, k5, k8]* - SUNDelta[I1, I4] + SU3F[I1, k5, k8]*SUNDelta[I2, I4]) + - SU3D[I3, I4, k5]*SU3F[I1, k5, k8]*SUNDelta[I2, I5] + - SU3D[I1, I4, k5]*SU3F[I3, k5, k8]*SUNDelta[I2, I5] + - SU3D[I1, I3, k5]*SU3F[I4, k5, k8]*SUNDelta[I2, I5] + - SU3D[I2, I5, k5]*SU3F[I1, k5, k8]*SUNDelta[I3, I4] + - SU3D[I1, I5, k5]*SU3F[I2, k5, k8]*SUNDelta[I3, I4] + - SU3D[I1, I2, k5]*SU3F[I5, k5, k8]*SUNDelta[I3, I4] + - SU3D[I2, I4, k5]*SU3F[I1, k5, k8]*SUNDelta[I3, I5] + - SU3D[I1, I4, k5]*SU3F[I2, k5, k8]*SUNDelta[I3, I5] + - SU3D[I1, I2, k5]*SU3F[I4, k5, k8]*SUNDelta[I3, I5] + - SU3D[I2, I3, k5]*SU3F[I1, k5, k8]*SUNDelta[I4, I5] + - SU3D[I1, I3, k5]*SU3F[I2, k5, k8]*SUNDelta[I4, I5] + - SU3D[I1, I2, k5]*SU3F[I3, k5, k8]*SUNDelta[I4, I5]))/ - (45*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*(SU3D[6, I3, I4]*SUNDelta[3, I5]*SUNDelta[I1, I2] + - SU3D[6, I2, I5]*SUNDelta[3, I4]*SUNDelta[I1, I3] + - SU3D[6, I2, I4]*SUNDelta[3, I5]*SUNDelta[I1, I3] + - SU3D[6, I2, I5]*SUNDelta[3, I3]*SUNDelta[I1, I4] + - SU3D[6, I2, I3]*SUNDelta[3, I5]*SUNDelta[I1, I4] + - SU3D[6, I3, I4]*SUNDelta[3, I2]*SUNDelta[I1, I5] + - SU3D[6, I2, I4]*SUNDelta[3, I3]*SUNDelta[I1, I5] + - SU3D[6, I2, I3]*SUNDelta[3, I4]*SUNDelta[I1, I5] + - SU3D[6, I1, I5]*SUNDelta[3, I4]*SUNDelta[I2, I3] + - SU3D[6, I1, I4]*SUNDelta[3, I5]*SUNDelta[I2, I3] + - SU3D[6, I4, I5]*(SUNDelta[3, I3]*SUNDelta[I1, I2] + - SUNDelta[3, I2]*SUNDelta[I1, I3] + SUNDelta[3, I1]* - SUNDelta[I2, I3]) + SU3D[6, I1, I5]*SUNDelta[3, I3]* - SUNDelta[I2, I4] + SU3D[6, I1, I3]*SUNDelta[3, I5]*SUNDelta[I2, I4] + - SU3D[6, I3, I5]*(SUNDelta[3, I4]*SUNDelta[I1, I2] + - SUNDelta[3, I2]*SUNDelta[I1, I4] + SUNDelta[3, I1]* - SUNDelta[I2, I4]) + SU3D[6, I3, I4]*SUNDelta[3, I1]* - SUNDelta[I2, I5] + SU3D[6, I1, I4]*SUNDelta[3, I3]*SUNDelta[I2, I5] + - SU3D[6, I1, I3]*SUNDelta[3, I4]*SUNDelta[I2, I5] + - SU3D[6, I2, I5]*SUNDelta[3, I1]*SUNDelta[I3, I4] + - SU3D[6, I1, I5]*SUNDelta[3, I2]*SUNDelta[I3, I4] + - SU3D[6, I1, I2]*SUNDelta[3, I5]*SUNDelta[I3, I4] + - SU3D[6, I2, I4]*SUNDelta[3, I1]*SUNDelta[I3, I5] + - SU3D[6, I1, I4]*SUNDelta[3, I2]*SUNDelta[I3, I5] + - SU3D[6, I1, I2]*SUNDelta[3, I4]*SUNDelta[I3, I5] + - SU3D[6, I2, I3]*SUNDelta[3, I1]*SUNDelta[I4, I5] + - SU3D[6, I1, I3]*SUNDelta[3, I2]*SUNDelta[I4, I5] + - SU3D[6, I1, I2]*SUNDelta[3, I3]*SUNDelta[I4, I5]))/ - (135*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*(SU3D[3, I3, I4]*SUNDelta[6, I5]*SUNDelta[I1, I2] + - SU3D[3, I2, I5]*SUNDelta[6, I4]*SUNDelta[I1, I3] + - SU3D[3, I2, I4]*SUNDelta[6, I5]*SUNDelta[I1, I3] + - SU3D[3, I2, I5]*SUNDelta[6, I3]*SUNDelta[I1, I4] + - SU3D[3, I2, I3]*SUNDelta[6, I5]*SUNDelta[I1, I4] + - SU3D[3, I3, I4]*SUNDelta[6, I2]*SUNDelta[I1, I5] + - SU3D[3, I2, I4]*SUNDelta[6, I3]*SUNDelta[I1, I5] + - SU3D[3, I2, I3]*SUNDelta[6, I4]*SUNDelta[I1, I5] + - SU3D[3, I1, I5]*SUNDelta[6, I4]*SUNDelta[I2, I3] + - SU3D[3, I1, I4]*SUNDelta[6, I5]*SUNDelta[I2, I3] + - SU3D[3, I4, I5]*(SUNDelta[6, I3]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I3] + SUNDelta[6, I1]* - SUNDelta[I2, I3]) + SU3D[3, I1, I5]*SUNDelta[6, I3]* - SUNDelta[I2, I4] + SU3D[3, I1, I3]*SUNDelta[6, I5]*SUNDelta[I2, I4] + - SU3D[3, I3, I5]*(SUNDelta[6, I4]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I4] + SUNDelta[6, I1]* - SUNDelta[I2, I4]) + SU3D[3, I3, I4]*SUNDelta[6, I1]* - SUNDelta[I2, I5] + SU3D[3, I1, I4]*SUNDelta[6, I3]*SUNDelta[I2, I5] + - SU3D[3, I1, I3]*SUNDelta[6, I4]*SUNDelta[I2, I5] + - SU3D[3, I2, I5]*SUNDelta[6, I1]*SUNDelta[I3, I4] + - SU3D[3, I1, I5]*SUNDelta[6, I2]*SUNDelta[I3, I4] + - SU3D[3, I1, I2]*SUNDelta[6, I5]*SUNDelta[I3, I4] + - SU3D[3, I2, I4]*SUNDelta[6, I1]*SUNDelta[I3, I5] + - SU3D[3, I1, I4]*SUNDelta[6, I2]*SUNDelta[I3, I5] + - SU3D[3, I1, I2]*SUNDelta[6, I4]*SUNDelta[I3, I5] + - SU3D[3, I2, I3]*SUNDelta[6, I1]*SUNDelta[I4, I5] + - SU3D[3, I1, I3]*SUNDelta[6, I2]*SUNDelta[I4, I5] + - SU3D[3, I1, I2]*SUNDelta[6, I3]*SUNDelta[I4, I5]))/ - (135*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*(SU3D[8, I3, I4]*SUNDelta[6, I5]*SUNDelta[I1, I2] + - SU3D[8, I2, I5]*SUNDelta[6, I4]*SUNDelta[I1, I3] + - SU3D[8, I2, I4]*SUNDelta[6, I5]*SUNDelta[I1, I3] + - SU3D[8, I2, I5]*SUNDelta[6, I3]*SUNDelta[I1, I4] + - SU3D[8, I2, I3]*SUNDelta[6, I5]*SUNDelta[I1, I4] + - SU3D[8, I3, I4]*SUNDelta[6, I2]*SUNDelta[I1, I5] + - SU3D[8, I2, I4]*SUNDelta[6, I3]*SUNDelta[I1, I5] + - SU3D[8, I2, I3]*SUNDelta[6, I4]*SUNDelta[I1, I5] + - SU3D[8, I1, I5]*SUNDelta[6, I4]*SUNDelta[I2, I3] + - SU3D[8, I1, I4]*SUNDelta[6, I5]*SUNDelta[I2, I3] + - SU3D[8, I4, I5]*(SUNDelta[6, I3]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I3] + SUNDelta[6, I1]* - SUNDelta[I2, I3]) + SU3D[8, I1, I5]*SUNDelta[6, I3]* - SUNDelta[I2, I4] + SU3D[8, I1, I3]*SUNDelta[6, I5]*SUNDelta[I2, I4] + - SU3D[8, I3, I5]*(SUNDelta[6, I4]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I4] + SUNDelta[6, I1]* - SUNDelta[I2, I4]) + SU3D[8, I3, I4]*SUNDelta[6, I1]* - SUNDelta[I2, I5] + SU3D[8, I1, I4]*SUNDelta[6, I3]*SUNDelta[I2, I5] + - SU3D[8, I1, I3]*SUNDelta[6, I4]*SUNDelta[I2, I5] + - SU3D[8, I2, I5]*SUNDelta[6, I1]*SUNDelta[I3, I4] + - SU3D[8, I1, I5]*SUNDelta[6, I2]*SUNDelta[I3, I4] + - SU3D[8, I1, I2]*SUNDelta[6, I5]*SUNDelta[I3, I4] + - SU3D[8, I2, I4]*SUNDelta[6, I1]*SUNDelta[I3, I5] + - SU3D[8, I1, I4]*SUNDelta[6, I2]*SUNDelta[I3, I5] + - SU3D[8, I1, I2]*SUNDelta[6, I4]*SUNDelta[I3, I5] + - SU3D[8, I2, I3]*SUNDelta[6, I1]*SUNDelta[I4, I5] + - SU3D[8, I1, I3]*SUNDelta[6, I2]*SUNDelta[I4, I5] + - SU3D[8, I1, I2]*SUNDelta[6, I3]*SUNDelta[I4, I5]))/ - (135*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 5) - (4*(SU3D[6, I3, I4]*SUNDelta[8, I5]*SUNDelta[I1, I2] + - SU3D[6, I2, I5]*SUNDelta[8, I4]*SUNDelta[I1, I3] + - SU3D[6, I2, I4]*SUNDelta[8, I5]*SUNDelta[I1, I3] + - SU3D[6, I2, I5]*SUNDelta[8, I3]*SUNDelta[I1, I4] + - SU3D[6, I2, I3]*SUNDelta[8, I5]*SUNDelta[I1, I4] + - SU3D[6, I3, I4]*SUNDelta[8, I2]*SUNDelta[I1, I5] + - SU3D[6, I2, I4]*SUNDelta[8, I3]*SUNDelta[I1, I5] + - SU3D[6, I2, I3]*SUNDelta[8, I4]*SUNDelta[I1, I5] + - SU3D[6, I1, I5]*SUNDelta[8, I4]*SUNDelta[I2, I3] + - SU3D[6, I1, I4]*SUNDelta[8, I5]*SUNDelta[I2, I3] + - SU3D[6, I4, I5]*(SUNDelta[8, I3]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I3] + SUNDelta[8, I1]* - SUNDelta[I2, I3]) + SU3D[6, I1, I5]*SUNDelta[8, I3]* - SUNDelta[I2, I4] + SU3D[6, I1, I3]*SUNDelta[8, I5]*SUNDelta[I2, I4] + - SU3D[6, I3, I5]*(SUNDelta[8, I4]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I4] + SUNDelta[8, I1]* - SUNDelta[I2, I4]) + SU3D[6, I3, I4]*SUNDelta[8, I1]* - SUNDelta[I2, I5] + SU3D[6, I1, I4]*SUNDelta[8, I3]*SUNDelta[I2, I5] + - SU3D[6, I1, I3]*SUNDelta[8, I4]*SUNDelta[I2, I5] + - SU3D[6, I2, I5]*SUNDelta[8, I1]*SUNDelta[I3, I4] + - SU3D[6, I1, I5]*SUNDelta[8, I2]*SUNDelta[I3, I4] + - SU3D[6, I1, I2]*SUNDelta[8, I5]*SUNDelta[I3, I4] + - SU3D[6, I2, I4]*SUNDelta[8, I1]*SUNDelta[I3, I5] + - SU3D[6, I1, I4]*SUNDelta[8, I2]*SUNDelta[I3, I5] + - SU3D[6, I1, I2]*SUNDelta[8, I4]*SUNDelta[I3, I5] + - SU3D[6, I2, I3]*SUNDelta[8, I1]*SUNDelta[I4, I5] + - SU3D[6, I1, I3]*SUNDelta[8, I2]*SUNDelta[I4, I5] + - SU3D[6, I1, I2]*SUNDelta[8, I3]*SUNDelta[I4, I5]))/ - (135*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 5) + (((8*I)/135)*(SU3F[3, 6, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SU3F[3, 6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - SU3F[3, 6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - SU3F[3, 6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - SUNDelta[I2, I5]*(SU3F[3, 6, I4]*SUNDelta[I1, I3] + - SU3F[3, 6, I3]*SUNDelta[I1, I4] + SU3F[3, 6, I1]*SUNDelta[I3, I4]) + - SU3F[3, 6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - SU3F[3, 6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - SUNDelta[I2, I4]*(SU3F[3, 6, I5]*SUNDelta[I1, I3] + - SU3F[3, 6, I3]*SUNDelta[I1, I5] + SU3F[3, 6, I1]*SUNDelta[I3, I5]) + - SU3F[3, 6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - SU3F[3, 6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - SU3F[3, 6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((8*I)/135)*(SU3F[6, 8, I5]*SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SU3F[6, 8, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3] + - SU3F[6, 8, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4] + - SU3F[6, 8, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - SUNDelta[I2, I5]*(SU3F[6, 8, I4]*SUNDelta[I1, I3] + - SU3F[6, 8, I3]*SUNDelta[I1, I4] + SU3F[6, 8, I1]*SUNDelta[I3, I4]) + - SU3F[6, 8, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5] + - SU3F[6, 8, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5] + - SUNDelta[I2, I4]*(SU3F[6, 8, I5]*SUNDelta[I1, I3] + - SU3F[6, 8, I3]*SUNDelta[I1, I5] + SU3F[6, 8, I1]*SUNDelta[I3, I5]) + - SU3F[6, 8, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - SU3F[6, 8, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - SU3F[6, 8, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (8*(SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4] + - SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5] + - SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4] + - SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4] + - SUNDelta[6, I5]*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I3]*SUNDelta[I2, I4] + SUNDelta[I1, I2]* - SUNDelta[I3, I4]) + SUNDelta[6, I2]*SUNDelta[I1, I4]* - SUNDelta[I3, I5] + SUNDelta[6, I1]*SUNDelta[I2, I4]* - SUNDelta[I3, I5] + SUNDelta[6, I4]* - (SUNDelta[I1, I5]*SUNDelta[I2, I3] + SUNDelta[I1, I3]* - SUNDelta[I2, I5] + SUNDelta[I1, I2]*SUNDelta[I3, I5]) + - SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5] + - SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5] + - SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5]))/ - (405*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/45)*SUNDelta[7, k6]*(SU3D[I3, I4, k5]*SU3D[I5, k5, k6]* - SUNDelta[I1, I2] + SU3D[I2, k5, k6]*SU3D[I4, I5, k5]* - SUNDelta[I1, I3] + SU3D[I2, I5, k5]*SU3D[I4, k5, k6]* - SUNDelta[I1, I3] + SU3D[I2, I4, k5]*SU3D[I5, k5, k6]* - SUNDelta[I1, I3] + SU3D[I2, I3, k5]*SU3D[I5, k5, k6]* - SUNDelta[I1, I4] + SU3D[I2, k5, k6]*SU3D[I3, I4, k5]* - SUNDelta[I1, I5] + SU3D[I2, I3, k5]*SU3D[I4, k5, k6]* - SUNDelta[I1, I5] + SU3D[I1, k5, k6]*SU3D[I4, I5, k5]* - SUNDelta[I2, I3] + SU3D[I1, I5, k5]*SU3D[I4, k5, k6]* - SUNDelta[I2, I3] + SU3D[I1, I4, k5]*SU3D[I5, k5, k6]* - SUNDelta[I2, I3] + SU3D[I1, I3, k5]*SU3D[I5, k5, k6]* - SUNDelta[I2, I4] + SU3D[I3, I5, k5]* - (SU3D[I4, k5, k6]*SUNDelta[I1, I2] + SU3D[I2, k5, k6]* - SUNDelta[I1, I4] + SU3D[I1, k5, k6]*SUNDelta[I2, I4]) + - SU3D[I1, k5, k6]*SU3D[I3, I4, k5]*SUNDelta[I2, I5] + - SU3D[I1, I3, k5]*SU3D[I4, k5, k6]*SUNDelta[I2, I5] + - SU3D[I1, k5, k6]*SU3D[I2, I5, k5]*SUNDelta[I3, I4] + - SU3D[I1, I5, k5]*SU3D[I2, k5, k6]*SUNDelta[I3, I4] + - SU3D[I1, I2, k5]*SU3D[I5, k5, k6]*SUNDelta[I3, I4] + - SU3D[I1, k5, k6]*SU3D[I2, I4, k5]*SUNDelta[I3, I5] + - SU3D[I1, I4, k5]*SU3D[I2, k5, k6]*SUNDelta[I3, I5] + - SU3D[I1, I2, k5]*SU3D[I4, k5, k6]*SUNDelta[I3, I5] + - SU3D[I1, k5, k6]*SU3D[I2, I3, k5]*SUNDelta[I4, I5] + - SU3D[I1, I3, k5]*SU3D[I2, k5, k6]*SUNDelta[I4, I5] + - SU3D[I3, k5, k6]*(SU3D[I4, I5, k5]*SUNDelta[I1, I2] + - SU3D[I2, I5, k5]*SUNDelta[I1, I4] + SU3D[I2, I4, k5]* - SUNDelta[I1, I5] + SU3D[I1, I5, k5]*SUNDelta[I2, I4] + - SU3D[I1, I4, k5]*SUNDelta[I2, I5] + SU3D[I1, I2, k5]* - SUNDelta[I4, I5])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (2*SUNDelta[6, k7]*(SU3D[I3, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[I1, I2] + - SU3D[I2, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[I1, I3] + - SU3D[I2, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[I1, I3] + - SU3D[I2, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[I1, I3] + - SU3D[I2, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[I1, I4] + - SU3D[I2, k7, k8]*SU3D[I3, I4, k8]*SUNDelta[I1, I5] + - SU3D[I2, I3, k8]*SU3D[I4, k7, k8]*SUNDelta[I1, I5] + - SU3D[I1, k7, k8]*SU3D[I4, I5, k8]*SUNDelta[I2, I3] + - SU3D[I1, I5, k8]*SU3D[I4, k7, k8]*SUNDelta[I2, I3] + - SU3D[I1, I4, k8]*SU3D[I5, k7, k8]*SUNDelta[I2, I3] + - SU3D[I1, I3, k8]*SU3D[I5, k7, k8]*SUNDelta[I2, I4] + - SU3D[I3, I5, k8]*(SU3D[I4, k7, k8]*SUNDelta[I1, I2] + - SU3D[I2, k7, k8]*SUNDelta[I1, I4] + SU3D[I1, k7, k8]* - SUNDelta[I2, I4]) + SU3D[I1, k7, k8]*SU3D[I3, I4, k8]* - SUNDelta[I2, I5] + SU3D[I1, I3, k8]*SU3D[I4, k7, k8]* - SUNDelta[I2, I5] + SU3D[I1, k7, k8]*SU3D[I2, I5, k8]* - SUNDelta[I3, I4] + SU3D[I1, I5, k8]*SU3D[I2, k7, k8]* - SUNDelta[I3, I4] + SU3D[I1, I2, k8]*SU3D[I5, k7, k8]* - SUNDelta[I3, I4] + SU3D[I1, k7, k8]*SU3D[I2, I4, k8]* - SUNDelta[I3, I5] + SU3D[I1, I4, k8]*SU3D[I2, k7, k8]* - SUNDelta[I3, I5] + SU3D[I1, I2, k8]*SU3D[I4, k7, k8]* - SUNDelta[I3, I5] + SU3D[I1, k7, k8]*SU3D[I2, I3, k8]* - SUNDelta[I4, I5] + SU3D[I1, I3, k8]*SU3D[I2, k7, k8]* - SUNDelta[I4, I5] + SU3D[I3, k7, k8]* - (SU3D[I4, I5, k8]*SUNDelta[I1, I2] + SU3D[I2, I5, k8]* - SUNDelta[I1, I4] + SU3D[I2, I4, k8]*SUNDelta[I1, I5] + - SU3D[I1, I5, k8]*SUNDelta[I2, I4] + SU3D[I1, I4, k8]* - SUNDelta[I2, I5] + SU3D[I1, I2, k8]*SUNDelta[I4, I5])))/ - (135*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 1]*((-4*SU3D[6, I3, I5]*SU3D[I1, I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I2, I5]*SU3D[I1, I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, I5]*SU3D[I1, I2, I3] + SU3D[6, I3, I4]*SU3D[I1, I2, I5] + - SU3D[6, I2, I4]*SU3D[I1, I3, I5] + SU3D[6, I1, I5]*SU3D[I2, I3, I4] + - SU3D[6, I1, I3]*SU3D[I2, I4, I5] + SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I5, k6]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k8, k9]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I5, k6]*SU3D[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3D[I3, k8, k9]*SU3D[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*(SU3D[I1, k8, k9]*(SU3D[I2, k7, k8]*SU3D[I3, I4, k9] + - SU3D[I2, I4, k9]*SU3D[I3, k7, k8]) + - (SU3D[I1, I3, k9]*SU3D[I2, k7, k8] + SU3D[I1, I2, k9]* - SU3D[I3, k7, k8])*SU3D[I4, k8, k9]) + SU3D[6, I3, k7]* - (SU3D[I4, k8, k9]*(SU3D[I1, I5, k9]*SU3D[I2, k7, k8] + - SU3D[I1, I2, k9]*SU3D[I5, k7, k8]) + SU3D[I1, k8, k9]* - (SU3D[I2, k7, k8]*SU3D[I4, I5, k9] + SU3D[I2, I4, k9]* - SU3D[I5, k7, k8])) + SU3D[6, I2, k7]* - (SU3D[I4, k8, k9]*(SU3D[I1, I5, k9]*SU3D[I3, k7, k8] + - SU3D[I1, I3, k9]*SU3D[I5, k7, k8]) + SU3D[I1, k8, k9]* - (SU3D[I3, k7, k8]*SU3D[I4, I5, k9] + SU3D[I3, I4, k9]* - SU3D[I5, k7, k8])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k6, k9]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, k7, k8]*SU3D[I3, I5, k6]*SU3D[I4, k6, k8]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, k6, k8]* - SU3D[I4, I5, k6]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I4, I5, k6]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/3)*(SU3D[I3, I4, I5]*SU3F[6, I1, I2] + SU3D[I2, I4, I5]* - SU3F[6, I1, I3] + SU3D[I2, I3, I4]*SU3F[6, I1, I5] - - SU3D[I1, I3, I5]*SU3F[6, I2, I4] - SU3D[I1, I2, I5]*SU3F[6, I3, I4] + - SU3D[I1, I2, I3]*SU3F[6, I4, I5]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*((SU3D[I3, k7, k8]*SU3D[I5, k6, k8] + SU3D[I3, k6, k8]* - SU3D[I5, k7, k8])*(SU3D[I2, I4, k6]*SU3F[6, I1, k7] + - SU3D[I1, I2, k6]*SU3F[6, I4, k7]) + SU3D[I2, k7, k8]* - (SU3D[I5, k6, k8]*(SU3D[I3, I4, k6]*SU3F[6, I1, k7] + - SU3D[I1, I3, k6]*SU3F[6, I4, k7]) + SU3D[I3, k6, k8]* - (SU3D[I4, I5, k6]*SU3F[6, I1, k7] + SU3D[I1, I5, k6]* - SU3F[6, I4, k7])) + SU3D[I2, k6, k8]* - (SU3D[I5, k7, k8]*(SU3D[I3, I4, k6]*SU3F[6, I1, k7] + - SU3D[I1, I3, k6]*SU3F[6, I4, k7]) + SU3D[I3, k7, k8]* - (SU3D[I4, I5, k6]*SU3F[6, I1, k7] + SU3D[I1, I5, k6]* - SU3F[6, I4, k7]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k7]*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I3, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*SU3D[6, I5, k6]*SU3D[I2, I3, k8]*SU3D[I4, k8, k9]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I2, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k7, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9]*SU3F[I2, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k9]* - SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, k8, k9]*SU3F[I2, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, I3, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I3, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I4, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I5, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I5, k8]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I2, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[I1, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k6]*SU3D[I1, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I3, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I2, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I5, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]* - SU3F[I2, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k9]*SU3D[I5, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I5, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I5, k6, k7]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I4, I5, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, k6, k8]*SU3F[I2, I4, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/6)*(SU3D[6, I5, k9]*(SU3D[I3, k7, k9]*(SU3D[I4, k6, k7]* - SU3F[I1, I2, k6] - SU3D[I1, k6, k7]*SU3F[I2, I4, k6]) + - SU3D[I2, k7, k9]*(SU3D[I4, k6, k7]*SU3F[I1, I3, k6] - - SU3D[I1, k6, k7]*SU3F[I3, I4, k6])) + SU3D[6, I3, k9]* - (SU3D[I4, k6, k7]*(SU3D[I5, k7, k9]*SU3F[I1, I2, k6] + - SU3D[I2, k7, k9]*SU3F[I1, I5, k6]) + SU3D[I1, k6, k7]* - (-(SU3D[I5, k7, k9]*SU3F[I2, I4, k6]) + SU3D[I2, k7, k9]* - SU3F[I4, I5, k6])) + SU3D[6, I2, k9]* - (SU3D[I4, k6, k7]*(SU3D[I5, k7, k9]*SU3F[I1, I3, k6] + - SU3D[I3, k7, k9]*SU3F[I1, I5, k6]) + SU3D[I1, k6, k7]* - (-(SU3D[I5, k7, k9]*SU3F[I3, I4, k6]) + SU3D[I3, k7, k9]* - SU3F[I4, I5, k6]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[I4, k7, k8]*(SU3D[I5, k6, k7]*(SU3F[6, I3, k8]*SU3F[I1, I2, k6] + - SU3F[6, I2, k8]*SU3F[I1, I3, k6]) + SU3D[I3, k6, k7]* - (SU3F[6, I5, k8]*SU3F[I1, I2, k6] + SU3F[6, I2, k8]* - SU3F[I1, I5, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k8]*SU3F[I1, I3, k6] + SU3F[6, I3, k8]* - SU3F[I1, I5, k6])) - SU3D[I1, k7, k8]* - (SU3D[I5, k6, k7]*(SU3F[6, I3, k8]*SU3F[I2, I4, k6] + - SU3F[6, I2, k8]*SU3F[I3, I4, k6]) + SU3D[I3, k6, k7]* - (SU3F[6, I5, k8]*SU3F[I2, I4, k6] - SU3F[6, I2, k8]* - SU3F[I4, I5, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I5, k8]*SU3F[I3, I4, k6] - SU3F[6, I3, k8]* - SU3F[I4, I5, k6])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I3, k8, k9]*SU3F[I1, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[I2, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[I3, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I1, k7]*SU3F[I2, k7, k9]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I2, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k6, k7]*SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I5, k7]*(SU3D[I3, k8, k9]* - (SU3D[I4, k7, k8]*SU3F[I1, I2, k9] - SU3D[I1, k7, k8]* - SU3F[I2, I4, k9]) + SU3D[I2, k8, k9]* - (SU3D[I4, k7, k8]*SU3F[I1, I3, k9] - SU3D[I1, k7, k8]* - SU3F[I3, I4, k9])) + SU3D[6, I3, k7]* - (SU3D[I4, k7, k8]*(SU3D[I5, k8, k9]*SU3F[I1, I2, k9] + - SU3D[I2, k8, k9]*SU3F[I1, I5, k9]) + SU3D[I1, k7, k8]* - (-(SU3D[I5, k8, k9]*SU3F[I2, I4, k9]) + SU3D[I2, k8, k9]* - SU3F[I4, I5, k9])) + SU3D[6, I2, k7]* - (SU3D[I4, k7, k8]*(SU3D[I5, k8, k9]*SU3F[I1, I3, k9] + - SU3D[I3, k8, k9]*SU3F[I1, I5, k9]) + SU3D[I1, k7, k8]* - (-(SU3D[I5, k8, k9]*SU3F[I3, I4, k9]) + SU3D[I3, k8, k9]* - SU3F[I4, I5, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I5, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I5, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[I3, I5, k8]*SU3F[6, I2, k7] + SU3D[I2, I5, k8]*SU3F[6, I3, k7] + - SU3D[I2, I3, k8]*SU3F[6, I5, k7])*(SU3D[I4, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3F[I4, k6, k8]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8] + - SU3D[I3, I4, k8]*(SU3D[I5, k6, k7]*SU3F[6, I2, k7] + - SU3D[I2, k6, k7]*SU3F[6, I5, k7])*SU3F[I1, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8] + - SU3D[I3, k6, k7]*(SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8] + - (SU3D[I1, I5, k8]*SU3F[6, I2, k7] + SU3D[I1, I2, k8]*SU3F[6, I5, k7])* - SU3F[I4, k6, k8]))/(4*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/6)*(SU3D[6, I5, k7]*(SU3D[I3, k6, k7]*(SU3D[I2, I4, k8]* - SU3F[I1, k6, k8] + SU3D[I1, I2, k8]*SU3F[I4, k6, k8]) + - SU3D[I2, k6, k7]*(SU3D[I3, I4, k8]*SU3F[I1, k6, k8] + - SU3D[I1, I3, k8]*SU3F[I4, k6, k8])) + SU3D[6, I3, k7]* - (SU3D[I5, k6, k7]*(SU3D[I2, I4, k8]*SU3F[I1, k6, k8] + - SU3D[I1, I2, k8]*SU3F[I4, k6, k8]) + SU3D[I2, k6, k7]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k8])) + SU3D[6, I2, k7]* - (SU3D[I5, k6, k7]*(SU3D[I3, I4, k8]*SU3F[I1, k6, k8] + - SU3D[I1, I3, k8]*SU3F[I4, k6, k8]) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k8] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k8]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I5, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I5, k8, k9]*SU3F[I1, I2, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I3, k6, k7]*SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k6, k7]*SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I5, k8, k9]*SU3F[I1, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I2, k6, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k6, k7]*SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I3, k8, k9]*SU3F[I1, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I2, k6, k7]*SU3F[I1, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k6, k7]*SU3F[I1, I5, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I2, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*(SU3D[I2, k8, k9]*SU3D[I3, I5, k6] + SU3D[I2, I5, k6]* - SU3D[I3, k8, k9] + SU3D[I2, I3, k6]*SU3D[I5, k8, k9])* - (SU3D[6, I4, k8]*SU3F[I1, k6, k9] + SU3D[6, I1, k8]*SU3F[I4, k6, k9]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I5, k8]*(SU3D[I3, k8, k9]* - (SU3D[I2, I4, k6]*SU3F[I1, k6, k9] + SU3D[I1, I2, k6]* - SU3F[I4, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + SU3D[I1, I3, k6]* - SU3F[I4, k6, k9])) + SU3D[6, I3, k8]* - (SU3D[I5, k8, k9]*(SU3D[I2, I4, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k6]*SU3F[I4, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k6, k9] + SU3D[I1, I5, k6]* - SU3F[I4, k6, k9])) + SU3D[6, I2, k8]* - (SU3D[I5, k8, k9]*(SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I3, k6]*SU3F[I4, k6, k9]) + SU3D[I3, k8, k9]* - (SU3D[I4, I5, k6]*SU3F[I1, k6, k9] + SU3D[I1, I5, k6]* - SU3F[I4, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I5, k6]*(SU3D[I3, k8, k9]* - (SU3D[I2, I4, k8]*SU3F[I1, k6, k9] + SU3D[I1, I2, k8]* - SU3F[I4, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k8]*SU3F[I1, k6, k9] + SU3D[I1, I3, k8]* - SU3F[I4, k6, k9])) + SU3D[6, I3, k6]* - (SU3D[I5, k8, k9]*(SU3D[I2, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I1, I2, k8]*SU3F[I4, k6, k9]) + SU3D[I2, k8, k9]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k9])) + SU3D[6, I2, k6]* - (SU3D[I5, k8, k9]*(SU3D[I3, I4, k8]*SU3F[I1, k6, k9] + - SU3D[I1, I3, k8]*SU3F[I4, k6, k9]) + SU3D[I3, k8, k9]* - (SU3D[I4, I5, k8]*SU3F[I1, k6, k9] + SU3D[I1, I5, k8]* - SU3F[I4, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I3, I5, k6]*SU3F[6, I2, k9] + SU3D[I2, I5, k6]*SU3F[6, I3, k9] + - SU3D[I2, I3, k6]*SU3F[6, I5, k9])*(SU3D[I4, k6, k7]*SU3F[I1, k7, k9] + - SU3D[I1, k6, k7]*SU3F[I4, k7, k9]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I1, k7, k9] + - SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9] + - SU3D[I3, I4, k6]*(SU3D[I5, k6, k7]*SU3F[6, I2, k9] + - SU3D[I2, k6, k7]*SU3F[6, I5, k9])*SU3F[I1, k7, k9] + - SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9] + - SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9] + - SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9] + - SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9] + - (SU3D[I1, I5, k6]*SU3F[6, I2, k9] + SU3D[I1, I2, k6]*SU3F[6, I5, k9])* - SU3F[I4, k7, k9]))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*(SU3D[I2, k6, k9]*SU3D[I3, I5, k6] + SU3D[I2, I5, k6]* - SU3D[I3, k6, k9] + SU3D[I2, I3, k6]*SU3D[I5, k6, k9])* - (SU3D[6, I4, k8]*SU3F[I1, k8, k9] + SU3D[6, I1, k8]*SU3F[I4, k8, k9]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*(SU3D[6, I5, k6]*(SU3F[I1, k8, k9]* - (SU3F[I2, k6, k8]*SU3F[I3, I4, k9] + SU3F[I2, I4, k9]* - SU3F[I3, k6, k8]) - (SU3F[I1, I3, k9]*SU3F[I2, k6, k8] + - SU3F[I1, I2, k9]*SU3F[I3, k6, k8])*SU3F[I4, k8, k9]) - - SU3D[6, I3, k6]*(SU3F[I4, k8, k9]*(SU3F[I1, I5, k9]*SU3F[I2, k6, k8] + - SU3F[I1, I2, k9]*SU3F[I5, k6, k8]) + SU3F[I1, k8, k9]* - (SU3F[I2, k6, k8]*SU3F[I4, I5, k9] - SU3F[I2, I4, k9]* - SU3F[I5, k6, k8])) - SU3D[6, I2, k6]* - (SU3F[I4, k8, k9]*(SU3F[I1, I5, k9]*SU3F[I3, k6, k8] + - SU3F[I1, I3, k9]*SU3F[I5, k6, k8]) + SU3F[I1, k8, k9]* - (SU3F[I3, k6, k8]*SU3F[I4, I5, k9] - SU3F[I3, I4, k9]* - SU3F[I5, k6, k8]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I4, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((SU3D[6, I4, k8]*SU3F[I1, k8, k9] + SU3D[6, I1, k8]*SU3F[I4, k8, k9])* - (SU3D[I3, I5, k6]*SU3F[I2, k6, k9] + SU3D[I2, I5, k6]* - SU3F[I3, k6, k9] + SU3D[I2, I3, k6]*SU3F[I5, k6, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*(SU3F[6, I4, k8]*SU3F[I1, k8, k9] + SU3F[6, I1, k8]* - SU3F[I4, k8, k9])*(SU3D[I3, I5, k6]*SU3F[I2, k6, k9] + - SU3D[I2, I5, k6]*SU3F[I3, k6, k9] + SU3D[I2, I3, k6]* - SU3F[I5, k6, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + SU3D[I4, I5, k6]*SU3F[I1, k8, k9]* - (SU3F[6, I3, k8]*SU3F[I2, k6, k9] + SU3F[6, I2, k8]* - SU3F[I3, k6, k9]) + SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + SU3D[I3, I4, k6]*SU3F[I1, k8, k9]* - (SU3F[6, I5, k8]*SU3F[I2, k6, k9] + SU3F[6, I2, k8]* - SU3F[I5, k6, k9])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I5, k6]*(SU3D[I3, I4, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I2, I4, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - (SU3D[I1, I3, k8]*SU3F[I2, k6, k9] + SU3D[I1, I2, k8]* - SU3F[I3, k6, k9])*SU3F[I4, k8, k9]) + SU3D[6, I3, k6]* - (SU3D[I4, I5, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3D[I1, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + - (SU3D[I2, I4, k8]*SU3F[I1, k8, k9] + SU3D[I1, I2, k8]* - SU3F[I4, k8, k9])*SU3F[I5, k6, k9]) + SU3D[6, I2, k6]* - (SU3D[I4, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + - SU3D[I1, I5, k8]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + - (SU3D[I3, I4, k8]*SU3F[I1, k8, k9] + SU3D[I1, I3, k8]* - SU3F[I4, k8, k9])*SU3F[I5, k6, k9]))/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k9]*SU3D[I3, k6, k7]*SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I5, k7]*(SU3F[I1, k8, k9]*(SU3F[I2, k7, k9]*SU3F[I3, I4, k8] + - SU3F[I2, I4, k8]*SU3F[I3, k7, k9]) - - (SU3F[I1, I3, k8]*SU3F[I2, k7, k9] + SU3F[I1, I2, k8]* - SU3F[I3, k7, k9])*SU3F[I4, k8, k9]) - SU3F[6, I3, k7]* - (SU3F[I4, k8, k9]*(SU3F[I1, I5, k8]*SU3F[I2, k7, k9] + - SU3F[I1, I2, k8]*SU3F[I5, k7, k9]) + SU3F[I1, k8, k9]* - (SU3F[I2, k7, k9]*SU3F[I4, I5, k8] - SU3F[I2, I4, k8]* - SU3F[I5, k7, k9])) - SU3F[6, I2, k7]* - (SU3F[I4, k8, k9]*(SU3F[I1, I5, k8]*SU3F[I3, k7, k9] + - SU3F[I1, I3, k8]*SU3F[I5, k7, k9]) + SU3F[I1, k8, k9]* - (SU3F[I3, k7, k9]*SU3F[I4, I5, k8] - SU3F[I3, I4, k8]* - SU3F[I5, k7, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, I4, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I4, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]* - SU3F[I3, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, I4, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k7, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I2, k9]*SU3F[I4, k6, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*SU3D[I3, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/9)*(-(SU3D[I1, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I2]) + - SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[I2, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I3] - - SU3D[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[I4, I5, k6]*(SU3F[I1, I3, k6]*SUNDelta[6, I2] + - SU3F[I1, I2, k6]*SUNDelta[6, I3]) + SU3D[I2, I4, k6]* - SU3F[I1, I3, k6]*SUNDelta[6, I5] - SU3D[I1, I3, k6]*SU3F[I2, I4, k6]* - SUNDelta[6, I5] - SU3D[I1, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[6, I5] + - SU3D[I3, I4, k6]*(SU3F[I1, I5, k6]*SUNDelta[6, I2] + - SU3F[I1, I2, k6]*SUNDelta[6, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[6, I5, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I3, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I2, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[I3, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SU3D[6, I5, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (4*SUNDelta[6, I5]*SUNDelta[I1, I3]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I3, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I3, I4, k6]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I5, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (4*SUNDelta[6, I5]*SUNDelta[I1, I2]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[I1, I4]*(SUNDelta[6, I5]*SUNDelta[I2, I3] + - SUNDelta[6, I3]*SUNDelta[I2, I5] + SUNDelta[6, I2]*SUNDelta[I3, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I1, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (4*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(-(SU3F[6, I5, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I2]) + - SU3F[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2] - - SU3F[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3] + - SU3F[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3] - - SU3F[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5] - - SU3F[6, I2, k6]*SU3F[I3, I4, k6]*SUNDelta[I1, I5] + - SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4] + - SU3F[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4] + - (SU3F[6, I5, k6]*SU3F[I1, I2, k6] + SU3F[6, I2, k6]*SU3F[I1, I5, k6])* - SUNDelta[I3, I4] + (SU3F[6, I3, k6]*SU3F[I1, I2, k6] + - SU3F[6, I2, k6]*SU3F[I1, I3, k6])*SUNDelta[I4, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*(SU3D[I3, I4, k5]*SUNDelta[I1, I2] + - SU3D[I2, I4, k5]*SUNDelta[I1, I3] + SU3D[I1, I3, k5]* - SUNDelta[I2, I4] + SU3D[I1, I2, k5]*SUNDelta[I3, I4]) + - SU3D[6, I3, k5]*(SU3D[I4, I5, k5]*SUNDelta[I1, I2] + - SU3D[I2, I4, k5]*SUNDelta[I1, I5] + SU3D[I1, I5, k5]* - SUNDelta[I2, I4] + SU3D[I1, I2, k5]*SUNDelta[I4, I5]) + - SU3D[6, I2, k5]*(SU3D[I4, I5, k5]*SUNDelta[I1, I3] + - SU3D[I3, I4, k5]*SUNDelta[I1, I5] + SU3D[I1, I5, k5]* - SUNDelta[I3, I4] + SU3D[I1, I3, k5]*SUNDelta[I4, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*(SU3D[6, I5, k5]*(-(SU3F[I3, I4, k5]*SUNDelta[I1, I2]) - - SU3F[I2, I4, k5]*SUNDelta[I1, I3] + SU3F[I1, I3, k5]* - SUNDelta[I2, I4] + SU3F[I1, I2, k5]*SUNDelta[I3, I4]) + - SU3D[6, I3, k5]*(SU3F[I4, I5, k5]*SUNDelta[I1, I2] - - SU3F[I2, I4, k5]*SUNDelta[I1, I5] + SU3F[I1, I5, k5]* - SUNDelta[I2, I4] + SU3F[I1, I2, k5]*SUNDelta[I4, I5]) + - SU3D[6, I2, k5]*(SU3F[I4, I5, k5]*SUNDelta[I1, I3] - - SU3F[I3, I4, k5]*SUNDelta[I1, I5] + SU3F[I1, I5, k5]* - SUNDelta[I3, I4] + SU3F[I1, I3, k5]*SUNDelta[I4, I5])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{CouplingConstant[ChPTW3[2], 1]*((SU3D[6, I4, I5]*SU3D[I1, I2, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, I5]*SU3D[I1, I2, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I3, I4]*SU3D[I1, I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I2, I5]*SU3D[I1, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I4]*SU3D[I1, I3, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I4]*SU3D[I2, I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I1, I3]*SU3D[I2, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, k6, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3D[I2, k6, k9]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, k8, k9]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I3, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I4, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I1, k8, k9]*SU3D[I3, I4, k9] + SU3D[I1, I4, k9]*SU3D[I3, k8, k9] + - SU3D[I1, I3, k9]*SU3D[I4, k8, k9])*(SU3D[6, I5, k7]*SU3D[I2, k7, k8] + - SU3D[6, I2, k7]*SU3D[I5, k7, k8]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I3, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I4, k9]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k6, k9]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k6, k9]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, k6, k9]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I1, k7, k8]*SU3D[I3, I4, k9] + SU3D[I1, I4, k9]*SU3D[I3, k7, k8] + - SU3D[I1, I3, k9]*SU3D[I4, k7, k8])*(SU3D[6, I5, k7]*SU3D[I2, k8, k9] + - SU3D[6, I2, k7]*SU3D[I5, k8, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, I5]*SU3F[6, I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I3, I4]*SU3F[6, I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/4)*SU3D[I2, k6, k8]*SU3D[I3, k7, k8]*SU3D[I4, I5, k6]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[I1, I4, I5]*SU3F[6, I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I3, I5]*SU3F[6, I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, I4]*SU3F[6, I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, I3]*SU3F[6, I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[I2, k7, k8]*((SU3D[I1, k6, k8]*SU3D[I4, I5, k6] + - SU3D[I1, I5, k6]*SU3D[I4, k6, k8])*SU3F[6, I3, k7] + - SU3D[I3, k6, k8]*(SU3D[I4, I5, k6]*SU3F[6, I1, k7] + - SU3D[I1, I5, k6]*SU3F[6, I4, k7]) + SU3D[I3, I5, k6]* - (SU3D[I4, k6, k8]*SU3F[6, I1, k7] + SU3D[I1, k6, k8]* - SU3F[6, I4, k7])) + SU3D[I5, k7, k8]* - (SU3D[I2, I4, k6]*(SU3D[I3, k6, k8]*SU3F[6, I1, k7] + - SU3D[I1, k6, k8]*SU3F[6, I3, k7]) + SU3D[I2, I3, k6]* - (SU3D[I4, k6, k8]*SU3F[6, I1, k7] + SU3D[I1, k6, k8]* - SU3F[6, I4, k7]) + SU3D[I1, I2, k6]* - (SU3D[I4, k6, k8]*SU3F[6, I3, k7] + SU3D[I3, k6, k8]* - SU3F[6, I4, k7]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k9]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I1, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I1, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I1, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3D[I3, k6, k9]* - SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I1, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I3, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I3, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I5, k6, k7]* - SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I1, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I2, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I4, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3D[I3, I5, k8]* - SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I3, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I3, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k7]*SU3D[I1, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I1, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I2, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I4, k8, k9]*SU3F[I1, I5, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I3, k6, k7]*SU3F[I1, I5, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I4, k6, k7]*SU3F[I1, I5, k9]*SU3F[I2, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I5, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I5, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I3, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I4, I5, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I5, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I5, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I4, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I4, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k7, k9]* - SU3D[I2, k6, k7]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I1, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, k8, k9]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k8]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I1, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I2, I4, k6]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I4, I5, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I5, k9]*SU3F[I2, k6, k8]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I4, I5, k8]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k9]*SU3D[I1, k7, k9]*SU3D[I2, k6, k7]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, k7, k8]*SU3F[6, I3, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[I4, k7, k8]*(SU3D[I5, k6, k7]*(SU3F[6, I3, k8]*SU3F[I1, I2, k6] - - SU3F[6, I1, k8]*SU3F[I2, I3, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k8]*SU3F[I1, I5, k6] + SU3F[6, I1, k8]* - SU3F[I3, I5, k6])) + SU3D[I3, k7, k8]* - (SU3D[I5, k6, k7]*(SU3F[6, I4, k8]*SU3F[I1, I2, k6] - - SU3F[6, I1, k8]*SU3F[I2, I4, k6]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k8]*SU3F[I1, I5, k6] + SU3F[6, I1, k8]* - SU3F[I4, I5, k6])) + SU3D[I1, k7, k8]* - (-(SU3D[I5, k6, k7]*(SU3F[6, I4, k8]*SU3F[I2, I3, k6] + - SU3F[6, I3, k8]*SU3F[I2, I4, k6])) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k8]*SU3F[I3, I5, k6] + SU3F[6, I3, k8]* - SU3F[I4, I5, k6])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[I2, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]*SU3F[I2, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, k8, k9]*SU3F[I2, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, k8, k9]*SU3F[I3, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k8, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k7]*SU3D[I1, k6, k7]* - SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k7]*SU3D[I2, k7, k8]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k6, k8]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/12)*(SU3D[6, I5, k7]*(-((SU3D[I1, k8, k9]*SU3D[I4, k7, k8] + - SU3D[I1, k7, k8]*SU3D[I4, k8, k9])*SU3F[I2, I3, k9]) + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k8]*SU3F[I1, I2, k9] - - SU3D[I1, k7, k8]*SU3F[I2, I4, k9]) + SU3D[I3, k7, k8]* - (SU3D[I4, k8, k9]*SU3F[I1, I2, k9] - SU3D[I1, k8, k9]* - SU3F[I2, I4, k9])) + SU3D[6, I2, k7]* - ((SU3D[I1, k8, k9]*SU3D[I4, k7, k8] + SU3D[I1, k7, k8]* - SU3D[I4, k8, k9])*SU3F[I3, I5, k9] + SU3D[I3, k8, k9]* - (SU3D[I4, k7, k8]*SU3F[I1, I5, k9] + SU3D[I1, k7, k8]* - SU3F[I4, I5, k9]) + SU3D[I3, k7, k8]* - (SU3D[I4, k8, k9]*SU3F[I1, I5, k9] + SU3D[I1, k8, k9]* - SU3F[I4, I5, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I5, k9]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8] + - SU3D[I3, I5, k8]*SU3F[6, I2, k7]*(SU3D[I4, k6, k7]*SU3F[I1, k6, k8] + - SU3D[I1, k6, k7]*SU3F[I4, k6, k8]) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8] + - (SU3D[I1, I5, k8]*SU3F[6, I2, k7] + SU3D[I1, I2, k8]*SU3F[6, I5, k7])* - SU3F[I4, k6, k8]))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, I2, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I2, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k6]*SU3D[I5, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/6)*(SU3D[6, I5, k8]*SU3D[I2, k8, k9] + SU3D[6, I2, k8]* - SU3D[I5, k8, k9])*(SU3D[I3, I4, k6]*SU3F[I1, k6, k9] + - SU3D[I1, I4, k6]*SU3F[I3, k6, k9] + SU3D[I1, I3, k6]* - SU3F[I4, k6, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I3, k9] - SU3F[I1, I2, k9]* - SU3F[I3, k6, k9]) + SU3F[6, I3, k7]* - (SU3F[I1, k6, k9]*SU3F[I2, I4, k9] - SU3F[I1, I2, k9]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[I2, I4, k9]*SU3F[I3, k6, k9] + SU3F[I2, I3, k9]* - SU3F[I4, k6, k9])) - SU3D[I2, k6, k7]* - (SU3F[6, I4, k7]*(SU3F[I1, k6, k9]*SU3F[I3, I5, k9] + - SU3F[I1, I5, k9]*SU3F[I3, k6, k9]) + SU3F[6, I3, k7]* - (SU3F[I1, k6, k9]*SU3F[I4, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k7]* - (SU3F[I3, k6, k9]*SU3F[I4, I5, k9] + SU3F[I3, I5, k9]* - SU3F[I4, k6, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, I2, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I5, k9]* - SU3F[I2, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, I5, k8]*SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9] + - SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9] + - SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9] + - SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9] + - SU3D[I3, I5, k6]*SU3F[6, I2, k9]*(SU3D[I4, k6, k7]*SU3F[I1, k7, k9] + - SU3D[I1, k6, k7]*SU3F[I4, k7, k9]) + SU3D[I3, k6, k7]* - (SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9] + - (SU3D[I1, I5, k6]*SU3F[6, I2, k9] + SU3D[I1, I2, k6]*SU3F[6, I5, k9])* - SU3F[I4, k7, k9]))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - (SU3D[6, I5, k9]*(SU3D[I4, k6, k7]*(SU3F[I1, k7, k9]*SU3F[I2, I3, k6] - - SU3F[I1, I2, k6]*SU3F[I3, k7, k9]) + SU3D[I3, k6, k7]* - (SU3F[I1, k7, k9]*SU3F[I2, I4, k6] - SU3F[I1, I2, k6]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[I2, I4, k6]*SU3F[I3, k7, k9] + SU3F[I2, I3, k6]* - SU3F[I4, k7, k9])) - SU3D[6, I2, k9]* - (SU3D[I4, k6, k7]*(SU3F[I1, k7, k9]*SU3F[I3, I5, k6] + - SU3F[I1, I5, k6]*SU3F[I3, k7, k9]) + SU3D[I3, k6, k7]* - (SU3F[I1, k7, k9]*SU3F[I4, I5, k6] + SU3F[I1, I5, k6]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[I3, k7, k9]*SU3F[I4, I5, k6] + SU3F[I3, I5, k6]* - SU3F[I4, k7, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + - ((I/12)*(SU3D[I5, k6, k7]*(SU3F[6, I4, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I3, k6] - SU3F[I1, I2, k6]* - SU3F[I3, k7, k9]) + SU3F[6, I3, k9]* - (SU3F[I1, k7, k9]*SU3F[I2, I4, k6] - SU3F[I1, I2, k6]* - SU3F[I4, k7, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, I4, k6]*SU3F[I3, k7, k9] + SU3F[I2, I3, k6]* - SU3F[I4, k7, k9])) - SU3D[I2, k6, k7]* - (SU3F[6, I4, k9]*(SU3F[I1, k7, k9]*SU3F[I3, I5, k6] + - SU3F[I1, I5, k6]*SU3F[I3, k7, k9]) + SU3F[6, I3, k9]* - (SU3F[I1, k7, k9]*SU3F[I4, I5, k6] + SU3F[I1, I5, k6]* - SU3F[I4, k7, k9]) + SU3F[6, I1, k9]* - (SU3F[I3, k7, k9]*SU3F[I4, I5, k6] + SU3F[I3, I5, k6]* - SU3F[I4, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, k6, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k7]*SU3D[I5, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I2, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I5, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I5, k7, k8]*SU3F[I2, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I5, k9]*SU3F[I2, k6, k8]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I5, k8]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, I5, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I5, k8]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I1, k6]*SU3F[I2, k6, k8]*SU3F[I3, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I2, k7]*SU3F[I1, I5, k8]*SU3F[I3, k7, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*(SU3D[6, I5, k8]*SU3D[I2, k6, k9] + SU3D[6, I2, k8]* - SU3D[I5, k6, k9])*(SU3D[I3, I4, k6]*SU3F[I1, k8, k9] + - SU3D[I1, I4, k6]*SU3F[I3, k8, k9] + SU3D[I1, I3, k6]* - SU3F[I4, k8, k9]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I5, k7]*(SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I2, I3, k9] - - SU3F[I1, I2, k9]*SU3F[I3, k8, k9]) + SU3D[I3, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I2, I4, k9] - SU3F[I1, I2, k9]* - SU3F[I4, k8, k9]) + SU3D[I1, k7, k8]* - (SU3F[I2, I4, k9]*SU3F[I3, k8, k9] + SU3F[I2, I3, k9]* - SU3F[I4, k8, k9])) - SU3D[6, I2, k7]* - (SU3D[I4, k7, k8]*(SU3F[I1, k8, k9]*SU3F[I3, I5, k9] + - SU3F[I1, I5, k9]*SU3F[I3, k8, k9]) + SU3D[I3, k7, k8]* - (SU3F[I1, k8, k9]*SU3F[I4, I5, k9] + SU3F[I1, I5, k9]* - SU3F[I4, k8, k9]) + SU3D[I1, k7, k8]* - (SU3F[I3, k8, k9]*SU3F[I4, I5, k9] + SU3F[I3, I5, k9]* - SU3F[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I3, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k7]*SU3D[I1, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I1, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I2, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I1, k7]*SU3D[I2, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k8, k9]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I4, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I2, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I3, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k6]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I1, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k6]*SU3D[I2, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I4, k8, k9]*SU3F[I1, I2, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I3, k6, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I4, k6, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I4, k8, k9]*SU3F[I2, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I4, k6, k7]*SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I3, k8, k9]*SU3F[I2, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k6, k7]*SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I3, k6, k7]*SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((SU3D[I3, I4, k6]*SU3F[I1, k8, k9] + SU3D[I1, I4, k6]*SU3F[I3, k8, k9] + - SU3D[I1, I3, k6]*SU3F[I4, k8, k9])*(SU3D[6, I5, k8]*SU3F[I2, k6, k9] + - SU3D[6, I2, k8]*SU3F[I5, k6, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*(SU3D[I1, I5, k6]*SU3F[6, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + SU3D[I4, I5, k6]*SU3F[I2, k6, k9]* - (SU3F[6, I3, k8]*SU3F[I1, k8, k9] + SU3F[6, I1, k8]* - SU3F[I3, k8, k9]) + SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[I3, I5, k6]*SU3F[I2, k6, k9]* - (SU3F[6, I4, k8]*SU3F[I1, k8, k9] + SU3F[6, I1, k8]* - SU3F[I4, k8, k9]) + SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9] + SU3D[I2, I4, k6]*SU3F[6, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9] + SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9] + SU3D[I2, I3, k6]*SU3F[6, I1, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9] + SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I4, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I3, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, I3, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I4, k8]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, I4, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k6]*SU3D[I3, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I4, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, I4, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I2, k9]*SU3F[I4, k6, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k6]*SU3F[I2, I3, k9]* - SU3F[I4, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k6]*SU3D[I2, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I1, k7]*SU3F[I2, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I2, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/9)*SU3D[I4, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I3, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/9)*SU3D[I1, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[I2, I5, k6]*(SU3D[I3, I4, k6]*SUNDelta[6, I1] + - SU3D[I1, I4, k6]*SUNDelta[6, I3] + SU3D[I1, I3, k6]*SUNDelta[6, I4]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I1, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I3, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I4, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I4, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I3, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I2, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I4, k6]*SU3F[I2, I3, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I2, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I3, k6]*SU3F[I2, I4, k6]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I4, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I4, I5, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I3, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I1, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I3, I5, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I1, k6]*SU3F[I3, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I4, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I3, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[I3, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I1, k5]*SU3D[I2, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I2, I5, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I2, k6]*SU3F[I1, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I1]*SUNDelta[I2, I5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*(SU3D[6, I5, k6]*(-(SU3F[I2, I4, k6]*SUNDelta[I1, I3]) - - SU3F[I2, I3, k6]*SUNDelta[I1, I4] + SU3F[I1, I2, k6]* - SUNDelta[I3, I4]) + SU3D[6, I2, k6]* - (SU3F[I4, I5, k6]*SUNDelta[I1, I3] + SU3F[I3, I5, k6]* - SUNDelta[I1, I4] + SU3F[I1, I5, k6]*SUNDelta[I3, I4])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I2, I4, k6]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I2, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I3, k6]*SU3F[I1, I2, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[6, I1, k5]*SU3F[I2, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (2*SU3F[6, I1, k6]*SU3F[I2, I3, k6]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I1]*SUNDelta[I2, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*(SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5] + - SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5] + - SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3] + - SU3D[I4, I5, k5]*(SU3F[6, I3, k5]*SUNDelta[I1, I2] + - SU3F[6, I1, k5]*SUNDelta[I2, I3]) + SU3D[I1, I5, k5]*SU3F[6, I3, k5]* - SUNDelta[I2, I4] + SU3D[I3, I5, k5]* - (SU3F[6, I4, k5]*SUNDelta[I1, I2] + SU3F[6, I1, k5]* - SUNDelta[I2, I4]) + SU3D[I2, I4, k5]*SU3F[6, I1, k5]* - SUNDelta[I3, I5] + SU3D[I1, I2, k5]*SU3F[6, I4, k5]* - SUNDelta[I3, I5] + SU3D[I2, I3, k5]*SU3F[6, I1, k5]* - SUNDelta[I4, I5] + SU3D[I1, I2, k5]*SU3F[6, I3, k5]* - SUNDelta[I4, I5]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[6, I5, k5]*(SU3D[I3, I4, k5]*SUNDelta[I1, I2] + - SU3D[I1, I4, k5]*SUNDelta[I2, I3] + SU3D[I1, I3, k5]* - SUNDelta[I2, I4]) + SU3D[6, I2, k5]* - (SU3D[I3, I4, k5]*SUNDelta[I1, I5] + SU3D[I1, I4, k5]* - SUNDelta[I3, I5] + SU3D[I1, I3, k5]*SUNDelta[I4, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SUNDelta[6, I5]*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I3]*SUNDelta[I2, I4] + SUNDelta[I1, I2]* - SUNDelta[I3, I4]) + SUNDelta[6, I2]* - (SUNDelta[I1, I5]*SUNDelta[I3, I4] + SUNDelta[I1, I4]* - SUNDelta[I3, I5] + SUNDelta[I1, I3]*SUNDelta[I4, I5])))/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}, -{CouplingConstant[ChPTW3[2], 1]*((-4*SU3D[6, I3, I4]*SU3D[I1, I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I2, I4]*SU3D[I1, I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SU3D[6, I2, I3]*SU3D[I1, I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[6, I1, I5]*SU3D[I2, I3, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, I5]*SU3D[I1, I2, I3] + SU3D[6, I3, I5]*SU3D[I1, I2, I4] + - SU3D[6, I2, I5]*SU3D[I1, I3, I4] + SU3D[6, I1, I4]*SU3D[I2, I3, I5] + - SU3D[6, I1, I3]*SU3D[I2, I4, I5] + SU3D[6, I1, I2]*SU3D[I3, I4, I5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, k8, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, k8, k9]*SU3D[I4, I5, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, k7, k8]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, k8, k9]*SU3D[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k8, k9]*SU3D[I3, I5, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k8, k9]*SU3D[I4, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I5, k6]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3D[I2, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I5, k9]*SU3D[I2, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I5, k6]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3D[I3, I5, k9]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k7]*SU3D[I2, I5, k9]*SU3D[I3, k7, k8]*SU3D[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, k8, k9]*SU3D[I2, I3, k6]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, k8, k9]*SU3D[I2, I4, k6]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I3, k6]*SU3D[I2, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I4, k6]*SU3D[I2, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]*SU3D[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k8]*SU3D[I1, I2, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I4, k6]*SU3D[I3, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k8]*SU3D[I1, I2, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k8]*SU3D[I1, I3, k6]*SU3D[I4, k8, k9]*SU3D[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3D[I5, k7, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((SU3D[I2, k8, k9]*SU3D[I3, I4, k9] + SU3D[I2, I4, k9]*SU3D[I3, k8, k9] + - SU3D[I2, I3, k9]*SU3D[I4, k8, k9])*(SU3D[6, I5, k7]*SU3D[I1, k7, k8] + - SU3D[6, I1, k7]*SU3D[I5, k7, k8]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I3, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I4, k9]*SU3D[I2, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, k6, k9]*SU3D[I3, I4, k6]*SU3D[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I1, I2, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3D[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((SU3D[I2, k7, k8]*SU3D[I3, I4, k9] + SU3D[I2, I4, k9]*SU3D[I3, k7, k8] + - SU3D[I2, I3, k9]*SU3D[I4, k7, k8])*(SU3D[6, I5, k7]*SU3D[I1, k8, k9] + - SU3D[6, I1, k7]*SU3D[I5, k8, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*SU3D[I3, I4, I5]*SU3F[6, I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I4, I5]*SU3F[6, I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I3, I5]*SU3F[6, I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/6)*SU3D[I2, k7, k8]*SU3D[I3, I4, k6]*SU3D[I5, k6, k8]* - SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I2, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I1, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I3, I4]*SU3F[6, I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I3, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I3, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I3, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I2, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, I4]*SU3F[6, I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I4, I5, k6]* - SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I4, I5, k6]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I4, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I4, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I4, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I4, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3D[I4, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I3, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, I2, I3]*SU3F[6, I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]*SU3D[I3, I5, k6]* - SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I5, k6]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k7, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, k6, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3D[I2, k6, k8]* - SU3D[I3, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3D[I2, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3D[I3, k7, k8]* - SU3D[I5, k6, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I3, k6]*SU3D[I2, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, I2, k6]*SU3D[I3, k6, k8]* - SU3D[I5, k7, k8]*SU3F[6, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, k6, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, k7, k8]* - SU3D[I3, I4, k6]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I4, k6]* - SU3D[I3, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[I1, k7, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k6, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, k6, k8]*SU3D[I2, I3, k6]* - SU3D[I4, k7, k8]*SU3F[6, I5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*((SU3D[I3, k7, k8]*SU3D[I4, k6, k8] + SU3D[I3, k6, k8]* - SU3D[I4, k7, k8])*(SU3D[I2, I5, k6]*SU3F[6, I1, k7] + - SU3D[I1, I2, k6]*SU3F[6, I5, k7]) + SU3D[I2, k7, k8]* - (SU3D[I4, k6, k8]*(SU3D[I3, I5, k6]*SU3F[6, I1, k7] + - SU3D[I1, I3, k6]*SU3F[6, I5, k7]) + SU3D[I3, k6, k8]* - (SU3D[I4, I5, k6]*SU3F[6, I1, k7] + SU3D[I1, I4, k6]* - SU3F[6, I5, k7])) + SU3D[I2, k6, k8]* - (SU3D[I4, k7, k8]*(SU3D[I3, I5, k6]*SU3F[6, I1, k7] + - SU3D[I1, I3, k6]*SU3F[6, I5, k7]) + SU3D[I3, k7, k8]* - (SU3D[I4, I5, k6]*SU3F[6, I1, k7] + SU3D[I1, I4, k6]* - SU3F[6, I5, k7]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I3, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I2, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I2, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k9]*SU3D[I2, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k9]*SU3D[I4, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I4, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I4, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I3, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I4, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I3, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k9]*SU3D[I2, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k9]*SU3D[I3, k7, k9]* - SU3D[I5, k6, k7]*SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k6, k7]*SU3D[I5, k7, k8]* - SU3F[6, I2, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I5, k7, k8]*SU3F[6, I3, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I5, k8]*SU3F[I1, I4, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k8, k9]*SU3D[I5, k7, k8]* - SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k8, k9]* - SU3D[I5, k7, k8]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I3, k7, k8]* - SU3D[I5, k8, k9]*SU3F[I1, I4, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I2, k6, k7]* - SU3D[I3, I5, k8]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I2, I5, k8]* - SU3D[I3, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I2, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I3, k6, k7]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I2, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I3, I5, k8]* - SU3D[I4, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k7]*SU3D[I2, I3, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I2, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I3, I4, k8]* - SU3D[I5, k6, k7]*SU3F[I1, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]* - SU3F[6, I2, k7]*SU3F[I1, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I1, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, k8, k9]*SU3D[I3, I5, k6]* - SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I2, I5, k8]* - SU3D[I3, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I2, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I3, I5, k8]* - SU3D[I4, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I4, k6]*SU3D[I2, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I2, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I3, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I1, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]* - SU3F[6, I2, k9]*SU3F[I1, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I1, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k6, k7]*SU3D[I3, k7, k9]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I3, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k8]*SU3F[I2, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9]*SU3F[I2, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9]*SU3F[I2, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I3, k7, k8]* - SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I3, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k9]* - SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9]*SU3F[I2, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I2, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9]*SU3F[I2, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I2, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]*SU3D[I3, I4, k6]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I2, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I3, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I4, I5, k8]*SU3F[I1, k8, k9]*SU3F[I2, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I2, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I3, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I3, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I3, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I2, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, I3, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I3, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k9]*SU3D[I3, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I4, k6]* - SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I2, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]* - SU3D[I3, I4, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I3, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I3, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I3, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I3, I4, k6]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I4, I5, k8]*SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I4, I5, k6]*SU3F[6, I3, k8]*SU3F[I1, k6, k9]* - SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I2, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k9]*SU3D[I1, k6, k7]* - SU3D[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I4, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I4, k6, k7]* - SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[6, I1, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k8]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9]*SU3F[I3, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I4, k8, k9]*SU3F[I1, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I1, k8, k9]*SU3F[I2, k6, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, k8, k9]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I4, k7, k8]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I4, k8, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I2, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I4, k6, k7]*SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k8]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, k6, k9]*SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, k8, k9]*SU3F[I3, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]* - SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I5, k7]*SU3F[I3, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k8, k9]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I4, I5, k8]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k7]*SU3F[I1, I2, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I4, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I2, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I4, I5, k8]*SU3F[I1, k8, k9]*SU3F[I3, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k7]* - SU3F[I2, I5, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]* - SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I3, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I5, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k9]*SU3D[I4, k6, k7]*SU3F[I1, I2, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I4, k9]*SU3F[I1, I2, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I4, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I4, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I4, k6, k7]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, I5, k6]*SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I3, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I4, k6]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I4, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I4, I5, k6]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I4, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I4, k6]* - SU3D[I5, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I4, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I4, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I2, I4, k6]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I4, I5, k8]*SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I4, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I4, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I4, k7, k8]*SU3F[I2, I5, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, k6, k8]*SU3F[I2, I5, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I4, k6]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I4, I5, k6]*SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I4, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I4, k8]* - SU3F[I2, k7, k9]*SU3F[I3, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[6, I3, k9]*SU3D[I1, k6, k7]*SU3D[I2, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k9]*SU3D[I1, k6, k7]* - SU3D[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k7, k8]*SU3D[I3, k6, k7]* - SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I3, k7, k8]*SU3F[6, I1, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k7, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k8]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I2, k6, k7]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - (SU3D[I4, k7, k8]*(SU3D[I5, k6, k7]*(SU3F[6, I3, k8]*SU3F[I1, I2, k6] + - SU3F[6, I2, k8]*SU3F[I1, I3, k6]) - SU3D[I1, k6, k7]* - (SU3F[6, I3, k8]*SU3F[I2, I5, k6] + SU3F[6, I2, k8]* - SU3F[I3, I5, k6])) + SU3D[I3, k7, k8]* - (SU3D[I5, k6, k7]*(SU3F[6, I4, k8]*SU3F[I1, I2, k6] + - SU3F[6, I2, k8]*SU3F[I1, I4, k6]) - SU3D[I1, k6, k7]* - (SU3F[6, I4, k8]*SU3F[I2, I5, k6] + SU3F[6, I2, k8]* - SU3F[I4, I5, k6])) + SU3D[I2, k7, k8]* - (SU3D[I5, k6, k7]*(SU3F[6, I4, k8]*SU3F[I1, I3, k6] + - SU3F[6, I3, k8]*SU3F[I1, I4, k6]) - SU3D[I1, k6, k7]* - (SU3F[6, I4, k8]*SU3F[I3, I5, k6] + SU3F[6, I3, k8]* - SU3F[I4, I5, k6])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, k8, k9]*SU3F[I1, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, k8, k9]*SU3F[I2, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, k8, k9]*SU3F[I2, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]*SU3F[I2, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, k8, k9]*SU3F[I3, k6, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]*SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, k7, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, k7, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k8, k9]*SU3D[I2, k7, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3D[I2, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k8, k9]* - SU3D[I3, k7, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3D[I3, k8, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k7]*SU3D[I2, k6, k7]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I3, k6, k7]*SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, k6, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]* - SU3F[I1, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k8, k9]*SU3F[I2, k6, k8]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]* - SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k7]*SU3D[I1, k7, k8]* - SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k8]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, k6, k9]*SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k7]*SU3D[I1, k7, k8]* - SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, k8, k9]*SU3F[I4, I5, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9]* - SU3F[I4, I5, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - ((I/12)*(SU3D[6, I5, k7]*((SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + - SU3D[I2, k7, k8]*SU3D[I4, k8, k9])*SU3F[I1, I3, k9] + - SU3D[I3, k8, k9]*(SU3D[I4, k7, k8]*SU3F[I1, I2, k9] + - SU3D[I2, k7, k8]*SU3F[I1, I4, k9]) + SU3D[I3, k7, k8]* - (SU3D[I4, k8, k9]*SU3F[I1, I2, k9] + SU3D[I2, k8, k9]* - SU3F[I1, I4, k9])) - SU3D[6, I1, k7]* - ((SU3D[I2, k8, k9]*SU3D[I4, k7, k8] + SU3D[I2, k7, k8]* - SU3D[I4, k8, k9])*SU3F[I3, I5, k9] + SU3D[I3, k8, k9]* - (SU3D[I4, k7, k8]*SU3F[I2, I5, k9] + SU3D[I2, k7, k8]* - SU3F[I4, I5, k9]) + SU3D[I3, k7, k8]* - (SU3D[I4, k8, k9]*SU3F[I2, I5, k9] + SU3D[I2, k8, k9]* - SU3F[I4, I5, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[I2, k6, k7]*SU3D[I3, I5, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I1, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k8]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k8]*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k8]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I5, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k8]*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k8]*SU3D[I3, k6, k7]*SU3F[6, I5, k7]*SU3F[I4, k6, k8])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k8, k9]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k8, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I5, k8]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/4)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I2, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I2, k6]*SU3D[I5, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k7]* - SU3F[I1, I3, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k8, k9]*SU3F[I4, k6, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]*SU3F[I1, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I2, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k7]* - SU3F[I2, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k7]*SU3F[I3, I5, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k7]* - SU3F[I3, I5, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I5, k6]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I1, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I5, k6]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I3, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I5, k6]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I4, k7, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I5, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k9]*SU3D[I3, k6, k7]*SU3F[I1, I2, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I2, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I5, k9]*SU3D[I2, k6, k7]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I5, k6, k7]*SU3F[6, I2, k9]*SU3F[I1, I3, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I5, k9]* - SU3F[I1, I3, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I1, k9]*SU3D[I3, k6, k7]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I2, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k8, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, I3, k8]*SU3F[I2, k8, k9]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k9]*SU3D[I2, k6, k7]*SU3F[I3, I5, k6]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I1, k9]*SU3F[I3, I5, k6]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, I5, k6]*SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I2, k7]*SU3F[I1, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k8, k9]*SU3F[I3, I5, k8]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, k8, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k8, k9]* - SU3F[I4, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, I5, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[6, I5, k8]*SU3D[I1, k6, k9]*SU3D[I2, I3, k6]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I3, k8]*SU3D[I1, I5, k6]* - SU3D[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, k6, k9]* - SU3D[I3, I5, k6]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I2, k8]*SU3D[I1, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I1, k8]*SU3D[I2, I5, k6]* - SU3D[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/6)*SU3D[6, I1, k8]*SU3D[I2, I3, k6]* - SU3D[I5, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I5, k7, k8]*SU3F[I1, I2, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I5, k7, k8]*SU3F[I1, I3, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I5, k8]*SU3D[I2, I3, k6]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I5, k8]*SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/4)*SU3D[I3, I5, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I5, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I3, k7]*SU3F[I1, k7, k9]* - SU3F[I2, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I1, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I3, k7, k8]*SU3F[I2, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, k6, k8]*SU3F[I2, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k8]*SU3D[I1, I5, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I3, I5, k6]*SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, I5, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I3, k6]*SU3F[6, I5, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3F[6, I2, k7]*SU3F[I1, k7, k9]*SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, k7, k9]*SU3F[I3, I5, k8]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, k7, k9]* - SU3F[I3, I5, k8]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I1, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k7]*SU3D[I2, k7, k8]*SU3F[I3, I5, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[6, I2, k6]*SU3F[I1, k6, k8]*SU3F[I3, I5, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I5, k8]*SU3D[I1, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k8]*SU3D[I1, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I1, k8]*SU3D[I2, I5, k6]*SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I2, I5, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[I1, I5, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I1, I2, k6]*SU3F[6, I5, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I5, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I1, k7]*SU3F[I2, I5, k8]*SU3F[I3, k7, k9]* - SU3F[I4, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3F[6, I1, k7]*SU3F[I2, I5, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*SU3D[6, I4, k7]*SU3D[I1, k6, k7]*SU3D[I2, I3, k8]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k7]*SU3D[I1, k6, k7]* - SU3D[I2, I4, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I4, k8]* - SU3D[I2, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I4, k7]*SU3D[I1, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, I4, k8]* - SU3D[I3, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I3, k7]*SU3D[I1, I2, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/6)*SU3D[6, I2, k7]*SU3D[I1, I3, k8]* - SU3D[I4, k6, k7]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[I2, k6, k7]*SU3D[I3, I4, k8]* - SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k8]*SU3D[I3, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I1, k7]*SU3F[I5, k6, k8])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I3, I4, k8]*SU3F[6, I2, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I4, k8]*SU3F[6, I3, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I1, k6, k7]*SU3D[I2, I3, k8]*SU3F[6, I4, k7]*SU3F[I5, k6, k8])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I3, k9]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I4, k9]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I2, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I3, k9]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k8])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - - (SU3D[I2, k6, k7]*SU3D[I4, I5, k8]*SU3F[6, I3, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I5, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, k6, k8] + - SU3D[I3, I5, k8]*(SU3D[I4, k6, k7]*SU3F[6, I2, k7] + - SU3D[I2, k6, k7]*SU3F[6, I4, k7])*SU3F[I1, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I4, k8]*SU3D[I2, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I2, k8]*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I5, k6, k8] + - SU3D[I1, I3, k8]*SU3D[I2, k6, k7]*SU3F[6, I4, k7]*SU3F[I5, k6, k8] + - SU3D[I3, k6, k7]*(SU3D[I4, I5, k8]*SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3D[I2, I5, k8]*SU3F[6, I4, k7]*SU3F[I1, k6, k8] + - (SU3D[I1, I4, k8]*SU3F[6, I2, k7] + SU3D[I1, I2, k8]*SU3F[6, I4, k7])* - SU3F[I5, k6, k8]))/(4*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) - ((I/3)*SU3D[6, I4, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I3, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I3, k6]*SU3D[I1, k8, k9]* - SU3D[I2, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I3, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I4, k6]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I4, k8]* - SU3D[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/3)*SU3D[6, I2, k6]*SU3D[I1, k8, k9]* - SU3D[I3, I4, k8]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k8]*SU3D[I1, I2, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I4, k6]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, I4, k8]* - SU3D[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k8]*SU3D[I1, I2, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k8]*SU3D[I1, I3, k6]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[6, I2, k6]*SU3D[I1, I3, k8]* - SU3D[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I3, k8, k9]* - SU3F[I1, I2, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I4, k8, k9]*SU3F[I1, I2, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I3, k6, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I4, k6, k7]*SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k7]*SU3F[I1, I2, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I2, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I4, k8, k9]*SU3F[I1, I3, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k7]*SU3D[I2, k6, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I4, k6, k7]*SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I3, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k7]* - SU3F[I1, I3, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I2, k8, k9]* - SU3F[I1, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I3, k8, k9]*SU3F[I1, I4, k8]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k7]*SU3D[I2, k6, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k7]*SU3D[I3, k6, k7]*SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k7]*SU3F[I1, I4, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k7]* - SU3F[I1, I4, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I2, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I4, k8]*SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I3, I4, k6]*SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I4, k6]*SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I1, k8]*SU3D[I2, I3, k6]*SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k8, k9]* - SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - ((I/4)*SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k8, k9]*SU3F[I5, k6, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + - ((I/6)*(SU3D[I2, k8, k9]*SU3D[I3, I4, k6] + SU3D[I2, I4, k6]* - SU3D[I3, k8, k9] + SU3D[I2, I3, k6]*SU3D[I4, k8, k9])* - (SU3D[6, I5, k8]*SU3F[I1, k6, k9] + SU3D[6, I1, k8]*SU3F[I5, k6, k9]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (SU3D[I2, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I4, k6]*SU3D[I3, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[I2, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]*SU3F[I5, k7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I3, I4, k6]*SU3F[6, I2, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I4, k6]*SU3F[6, I3, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, k6, k7]*SU3D[I2, I3, k6]*SU3F[6, I4, k9]*SU3F[I5, k7, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, I2, k6]* - SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I2, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, I3, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I3, k6, k7]*SU3F[6, I2, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[I2, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, I4, k6]*SU3F[I5, k7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I4, k7]*SU3F[I1, I2, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, I2, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k8, k9]*SU3F[I5, k7, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, k6, k7]*SU3D[I4, I5, k6]*SU3F[6, I3, k9]*SU3F[I1, k7, k9] + - SU3D[I2, I5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I1, k7, k9] + - SU3D[I3, I5, k6]*(SU3D[I4, k6, k7]*SU3F[6, I2, k9] + - SU3D[I2, k6, k7]*SU3F[6, I4, k9])*SU3F[I1, k7, k9] + - SU3D[I1, I3, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]*SU3F[I5, k7, k9] + - SU3D[I1, I4, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9] + - SU3D[I1, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]*SU3F[I5, k7, k9] + - SU3D[I1, I3, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]*SU3F[I5, k7, k9] + - SU3D[I3, k6, k7]*(SU3D[I4, I5, k6]*SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3D[I2, I5, k6]*SU3F[6, I4, k9]*SU3F[I1, k7, k9] + - (SU3D[I1, I4, k6]*SU3F[6, I2, k9] + SU3D[I1, I2, k6]*SU3F[6, I4, k9])* - SU3F[I5, k7, k9]))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5) + (SU3D[6, I4, k7]*SU3D[I3, k7, k8]* - SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I4, k7, k8]*SU3F[I1, I2, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k7]*SU3D[I2, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I4, k7, k8]*SU3F[I1, I3, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k7]*SU3D[I2, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k7]*SU3D[I3, k7, k8]*SU3F[I1, I4, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I4, k6]*SU3D[I2, I3, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I3, k6]*SU3D[I2, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3D[6, I2, k6]*SU3D[I3, I4, k8]*SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, k6]*SU3F[6, I2, k8]*SU3F[I1, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I4, k6]*SU3F[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/3)*SU3D[I2, I3, k6]*SU3F[6, I4, k8]* - SU3F[I1, k6, k9]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I4, k9]* - SU3F[I2, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k6]*SU3D[I1, I4, k8]*SU3F[I2, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I3, I4, k6]*SU3F[6, I1, k8]*SU3F[I2, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I3, k7]*SU3F[I1, I4, k8]*SU3F[I2, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I4, k6]*SU3F[I1, I2, k9]*SU3F[I3, k6, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I4, k9]* - SU3F[I3, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I4, k6]*SU3D[I1, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, I4, k8]*SU3F[I3, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I2, I4, k6]*SU3F[6, I1, k8]*SU3F[I3, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I4, k7]*SU3F[I1, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, I4, k8]*SU3F[I3, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*SU3D[6, I3, k6]*SU3F[I1, I2, k9]*SU3F[I4, k6, k8]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + ((I/12)*SU3D[6, I2, k6]*SU3F[I1, I3, k9]* - SU3F[I4, k6, k8]*SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 - (SU3D[6, I3, k6]*SU3D[I1, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k6]*SU3D[I1, I3, k8]*SU3F[I4, k6, k9]*SU3F[I5, k8, k9])/ - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/6)*SU3D[I2, I3, k6]*SU3F[6, I1, k8]*SU3F[I4, k6, k9]* - SU3F[I5, k8, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^5 + (SU3F[6, I3, k7]*SU3F[I1, I2, k8]* - SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (SU3F[6, I2, k7]*SU3F[I1, I3, k8]*SU3F[I4, k7, k9]*SU3F[I5, k8, k9])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*(SU3D[I2, k6, k9]*SU3D[I3, I4, k6] + SU3D[I2, I4, k6]* - SU3D[I3, k6, k9] + SU3D[I2, I3, k6]*SU3D[I4, k6, k9])* - (SU3D[6, I5, k8]*SU3F[I1, k8, k9] + SU3D[6, I1, k8]*SU3F[I5, k8, k9]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((SU3D[I3, I4, k6]*SU3F[I2, k6, k9] + SU3D[I2, I4, k6]*SU3F[I3, k6, k9] + - SU3D[I2, I3, k6]*SU3F[I4, k6, k9])*(SU3D[6, I5, k8]*SU3F[I1, k8, k9] + - SU3D[6, I1, k8]*SU3F[I5, k8, k9]))/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/12)*(SU3D[I2, I5, k6]*SU3F[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + SU3D[I4, I5, k6]*SU3F[I1, k8, k9]* - (SU3F[6, I3, k8]*SU3F[I2, k6, k9] + SU3F[6, I2, k8]* - SU3F[I3, k6, k9]) + SU3D[I2, I5, k6]*SU3F[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[I3, I5, k6]*SU3F[I1, k8, k9]* - (SU3F[6, I4, k8]*SU3F[I2, k6, k9] + SU3F[6, I2, k8]* - SU3F[I4, k6, k9]) + SU3D[I1, I4, k6]*SU3F[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + SU3D[I1, I3, k6]*SU3F[6, I4, k8]* - SU3F[I2, k6, k9]*SU3F[I5, k8, k9] + SU3D[I1, I4, k6]*SU3F[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + SU3D[I1, I2, k6]*SU3F[6, I4, k8]* - SU3F[I3, k6, k9]*SU3F[I5, k8, k9] + SU3D[I1, I3, k6]*SU3F[6, I2, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9] + SU3D[I1, I2, k6]*SU3F[6, I3, k8]* - SU3F[I4, k6, k9]*SU3F[I5, k8, k9]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I2, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I2, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I1])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/3)*SU3D[I3, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - ((I/3)*SU3D[I2, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[I1, I5, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I2])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I4, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I5, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I3])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I4, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I2, k6]*SU3D[I4, I5, k6]*SUNDelta[6, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[I1, I5, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I3, k6]*SU3D[I2, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3D[I1, I2, k6]*SU3D[I3, I5, k6]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - ((I/6)*(SU3D[I1, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I2] + - SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2] - - SU3D[I2, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I3] + - SU3D[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3] + - SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3] - - SU3D[I4, I5, k6]*(SU3F[I1, I3, k6]*SUNDelta[6, I2] + - SU3F[I1, I2, k6]*SUNDelta[6, I3]) - SU3D[I2, I5, k6]* - SU3F[I1, I3, k6]*SUNDelta[6, I4] + SU3D[I1, I3, k6]*SU3F[I2, I5, k6]* - SUNDelta[6, I4] + SU3D[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4] - - SU3D[I3, I5, k6]*(SU3F[I1, I4, k6]*SUNDelta[6, I2] + - SU3F[I1, I2, k6]*SUNDelta[6, I4])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((5*I)/18)*(-(SU3D[I1, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I2]) - - SU3D[I1, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I2] + - SU3D[I2, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I3] - - SU3D[I1, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[6, I3] - - SU3D[I1, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[6, I3] + - SU3D[I4, I5, k6]*(SU3F[I1, I3, k6]*SUNDelta[6, I2] + - SU3F[I1, I2, k6]*SUNDelta[6, I3]) + SU3D[I2, I5, k6]* - SU3F[I1, I3, k6]*SUNDelta[6, I4] - SU3D[I1, I3, k6]*SU3F[I2, I5, k6]* - SUNDelta[6, I4] - SU3D[I1, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[6, I4] + - SU3D[I3, I5, k6]*(SU3F[I1, I4, k6]*SUNDelta[6, I2] + - SU3F[I1, I2, k6]*SUNDelta[6, I4])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[I1, I4, k6]*SU3D[I2, I3, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I3, k6]*SU3D[I2, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[I1, I2, k6]*SU3D[I3, I4, k6]*SUNDelta[6, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/3)*SU3D[I3, I4, k6]*SU3F[I1, I2, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/3)*SU3D[I2, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[6, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I3, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I4, I5, k5]*SUNDelta[I1, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I4, I5, k5]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I4, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I2, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I4, I5, k5]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I3, k5]*SU3D[I2, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I3, I5, k5]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I2, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I3, I5, k5]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3D[6, I4, k5]*SU3D[I2, I3, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I3, k5]*SU3D[I2, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[I1, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((2*I)/9)*SU3D[I3, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I2, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I1, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (4*SU3D[6, I4, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I5, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I1, k6]*SU3F[I4, I5, k6]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I4]*SUNDelta[I1, I5]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I3, k5]*SU3D[I1, I5, k5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I5, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I1, k6]*SU3F[I3, I5, k6]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I3]*SUNDelta[I1, I5]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I4, k5]*SU3D[I1, I3, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I4, k5]*SUNDelta[I2, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I3, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I3, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I4, k5]*SUNDelta[I2, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (4*SUNDelta[6, I4]*SUNDelta[I1, I3]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I3]*SUNDelta[I1, I4]*SUNDelta[I2, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SU3D[6, I2, k5]*SU3D[I1, I5, k5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (((4*I)/9)*SU3D[I1, I5, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (2*SU3F[6, I5, k6]*SU3F[I1, I2, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*SU3F[6, I1, k6]*SU3F[I2, I5, k6]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (4*SUNDelta[6, I2]*SUNDelta[I1, I5]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (((2*I)/9)*(SU3D[6, I5, k6]*(SU3F[I1, I4, k6]*SUNDelta[I2, I3] + - SU3F[I1, I3, k6]*SUNDelta[I2, I4] + SU3F[I1, I2, k6]* - SUNDelta[I3, I4]) - SU3D[6, I1, k6]* - (SU3F[I4, I5, k6]*SUNDelta[I2, I3] + SU3F[I3, I5, k6]* - SUNDelta[I2, I4] + SU3F[I2, I5, k6]*SUNDelta[I3, I4])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (SU3D[6, I4, k5]*SU3D[I1, I2, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[I3, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I4, k5]*SU3F[6, I1, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I4, k5]*SU3F[6, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I4, k5]*SU3F[I1, I2, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I1, I4, k5]*SUNDelta[I3, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (4*SUNDelta[6, I4]*SUNDelta[I1, I2]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I4]*SUNDelta[I3, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I3, k5]*SU3D[I1, I2, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I2, k5]*SU3D[I1, I3, k5]*SUNDelta[I4, I5])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - ((I/9)*SU3D[I2, I3, k5]*SU3F[6, I1, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - ((I/9)*SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I3, k5]*SU3F[I1, I2, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 + - (((2*I)/9)*SU3D[6, I2, k5]*SU3F[I1, I3, k5]*SUNDelta[I4, I5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5 - - (4*SUNDelta[6, I3]*SUNDelta[I1, I2]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (4*SUNDelta[6, I2]*SUNDelta[I1, I3]*SUNDelta[I4, I5])/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + - (2*(SU3F[6, I4, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I2] + - SU3F[6, I3, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I2] + - SU3F[6, I4, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I3] + - SU3F[6, I2, k6]*SU3F[I4, I5, k6]*SUNDelta[I1, I3] + - SU3F[6, I3, k6]*SU3F[I2, I5, k6]*SUNDelta[I1, I4] + - SU3F[6, I2, k6]*SU3F[I3, I5, k6]*SUNDelta[I1, I4] - - SU3F[6, I4, k6]*SU3F[I1, I3, k6]*SUNDelta[I2, I5] - - SU3F[6, I3, k6]*SU3F[I1, I4, k6]*SUNDelta[I2, I5] - - (SU3F[6, I4, k6]*SU3F[I1, I2, k6] + SU3F[6, I2, k6]*SU3F[I1, I4, k6])* - SUNDelta[I3, I5] - (SU3F[6, I3, k6]*SU3F[I1, I2, k6] + - SU3F[6, I2, k6]*SU3F[I1, I3, k6])*SUNDelta[I4, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (SU3D[6, I5, k5]*(SU3D[I3, I4, k5]*SUNDelta[I1, I2] + - SU3D[I2, I4, k5]*SUNDelta[I1, I3] + SU3D[I2, I3, k5]* - SUNDelta[I1, I4]) + SU3D[6, I1, k5]* - (SU3D[I3, I4, k5]*SUNDelta[I2, I5] + SU3D[I2, I4, k5]* - SUNDelta[I3, I5] + SU3D[I2, I3, k5]*SUNDelta[I4, I5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - - (2*(SUNDelta[6, I5]*(SUNDelta[I1, I4]*SUNDelta[I2, I3] + - SUNDelta[I1, I3]*SUNDelta[I2, I4] + SUNDelta[I1, I2]* - SUNDelta[I3, I4]) + SUNDelta[6, I1]* - (SUNDelta[I2, I5]*SUNDelta[I3, I4] + SUNDelta[I2, I4]* - SUNDelta[I3, I5] + SUNDelta[I2, I3]*SUNDelta[I4, I5])))/ - (27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5))}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10o2.Gen deleted file mode 100644 index 8d5515403..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10o2.Gen +++ /dev/null @@ -1,8 +0,0 @@ -{MomentaScalarProduct[p1, p5], MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p2, p3], MomentaScalarProduct[p2, p5], -MomentaScalarProduct[p1, p3], MomentaScalarProduct[p4, p5], -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p3, p5], -MomentaScalarProduct[p1, p2], MomentaScalarProduct[p3, p4], -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10o2.Mod deleted file mode 100644 index 65d64780c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10P10o2.Mod +++ /dev/null @@ -1,12000 +0,0 @@ -{{-(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{-(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{-(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{-(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{-(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]])/ - (24*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 1]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ - (12*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{-(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]])/ - (120*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(120*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{-(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) - -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I5]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5) + -(CouplingConstant[ChPTW3[2], 2]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I5]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/(60*Sqrt[3]* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10S10o2.Gen deleted file mode 100644 index f3c821bae..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10S10o2.Gen +++ /dev/null @@ -1,6 +0,0 @@ -{MomentaScalarProduct[p1, p2], MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p2, p4], MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p1, p3], -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10S10o2.Mod deleted file mode 100644 index f743e93ac..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10S10o2.Mod +++ /dev/null @@ -1,3819 +0,0 @@ -{{CouplingConstant[ChPTW3[2], 1]* -(((-I/6)*(SU3D[6, I4, k6]*(SU3D[I1, k5, k6]*SU3D[I2, I3, k5] + - SU3D[I1, I3, k5]*SU3D[I2, k5, k6]) + SU3D[6, I3, k6]* - (SU3D[I1, k5, k6]*SU3D[I2, I4, k5] + SU3D[I1, I4, k5]* - SU3D[I2, k5, k6])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/2)*(SU3D[6, I4, k5]*(SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - SU3D[I1, I3, k6]*SU3D[I2, k5, k6]) + SU3D[6, I3, k5]* - (SU3D[I1, k5, k6]*SU3D[I2, I4, k6] + SU3D[I1, I4, k6]* - SU3D[I2, k5, k6])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[6, I2, k6]* - SU3D[I1, k5, k6]*SU3D[I3, I4, k5])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[6, I1, k6]* - SU3D[I2, k5, k6]*SU3D[I3, I4, k5])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[6, I4, k5]* - SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[6, I3, k5]* - SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (2*SU3D[I3, I4, k6]*(SU3D[I2, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I2, k5]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, k5, k6]*SU3D[I2, I4, k6]*SU3F[6, I3, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[6, I3, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[6, I3, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I4, k5, k6]*SU3F[6, I2, k5]*SU3F[I1, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - ((I/3)*SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[I1, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[6, I4, k6]*SU3D[I2, k6, k7]*SU3F[I1, I3, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I2, k5]*SU3F[I1, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - ((I/3)*SU3D[I2, k5, k6]*SU3F[6, I3, k5]*SU3F[I1, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[6, I3, k6]*SU3D[I2, k6, k7]*SU3F[I1, I4, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((2*I)/3)*SU3D[I2, I4, k5]*SU3F[6, I3, k7]*SU3F[I1, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[I2, I3, k5]*SU3F[6, I4, k7]*SU3F[I1, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (2*SU3D[6, I2, k6]*SU3D[I3, I4, k7]*SU3F[I1, k6, k7])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I4, k5]*SU3D[I1, k5, k6]*SU3F[I2, I3, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I4, k5, k6]*SU3F[6, I1, k5]*SU3F[I2, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - ((I/3)*SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[I2, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[6, I4, k6]*SU3D[I1, k6, k7]*SU3F[I2, I3, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I3, k5]*SU3D[I1, k5, k6]*SU3F[I2, I4, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I1, k5]*SU3D[I3, k5, k6]*SU3F[I2, I4, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I1, k5]*SU3F[I2, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - ((I/3)*SU3D[I1, k5, k6]*SU3F[6, I3, k5]*SU3F[I2, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[6, I3, k6]*SU3D[I1, k6, k7]*SU3F[I2, I4, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((2*I)/3)*SU3D[I1, I4, k5]*SU3F[6, I3, k7]*SU3F[I2, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[I1, I3, k5]*SU3F[6, I4, k7]*SU3F[I2, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((2*I)/3)*SU3D[I3, I4, k5]*(SU3F[6, I2, k7]*SU3F[I1, k5, k7] + - SU3F[6, I1, k7]*SU3F[I2, k5, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I4, k5]*(SU3D[I2, I3, k7]*SU3F[I1, k5, k7] + - SU3D[I1, I3, k7]*SU3F[I2, k5, k7]) + SU3D[6, I3, k5]* - (SU3D[I2, I4, k7]*SU3F[I1, k5, k7] + SU3D[I1, I4, k7]* - SU3F[I2, k5, k7]))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/6)*(SU3D[6, I4, k5]*(SU3F[I1, k5, k7]*SU3F[I2, I3, k7] + - SU3F[I1, I3, k7]*SU3F[I2, k5, k7]) + SU3D[6, I3, k5]* - (SU3F[I1, k5, k7]*SU3F[I2, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I2, k5, k7])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I1, k6]*SU3D[I3, I4, k7]* - SU3F[I2, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I4, k6]*(SU3D[I2, I3, k7]*SU3F[I1, k6, k7] + - SU3D[I1, I3, k7]*SU3F[I2, k6, k7]) + SU3D[6, I3, k6]* - (SU3D[I2, I4, k7]*SU3F[I1, k6, k7] + SU3D[I1, I4, k7]* - SU3F[I2, k6, k7]))/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/2)*(SU3D[6, I4, k6]*(SU3F[I1, k6, k7]*SU3F[I2, I3, k7] + - SU3F[I1, I3, k7]*SU3F[I2, k6, k7]) + SU3D[6, I3, k6]* - (SU3F[I1, k6, k7]*SU3F[I2, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I2, k6, k7])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (SU3F[6, I4, k6]*(SU3F[I1, k6, k7]*SU3F[I2, I3, k7] + - SU3F[I1, I3, k7]*SU3F[I2, k6, k7]) + SU3F[6, I3, k6]* - (SU3F[I1, k6, k7]*SU3F[I2, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I2, k6, k7]))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((2*I)/3)*SU3D[I1, I2, k5]* - SU3F[6, I4, k7]*SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I2, k5]*SU3F[I1, I4, k7]* - SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I1, k5]*SU3F[I2, I4, k7]* - SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I4, k6]*SU3D[I1, I2, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3F[6, I2, k6]*SU3F[I1, I4, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3F[6, I1, k6]*SU3F[I2, I4, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((2*I)/3)*SU3D[I1, I2, k5]* - SU3F[6, I3, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I2, k5]*SU3F[I1, I3, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I1, k5]*SU3F[I2, I3, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I3, k6]*SU3D[I1, I2, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3F[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3F[6, I1, k6]*SU3F[I2, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (((4*I)/9)*(SU3D[I2, I3, I4]*SUNDelta[6, I1] + SU3D[I1, I3, I4]* - SUNDelta[6, I2]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((4*I)/9)*SU3D[I1, I2, I4]* - SUNDelta[6, I3])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((4*I)/9)*SU3D[I1, I2, I3]* - SUNDelta[6, I4])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((8*I)/9)*SU3D[6, I3, I4]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((4*I)/9)*SU3D[6, I2, I4]* - SUNDelta[I1, I3])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (4*SU3F[6, I2, I4]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I2, I3]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (4*SU3F[6, I2, I3]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I1, I4]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (4*SU3F[6, I1, I4]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I1, I3]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (4*SU3F[6, I1, I3]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((8*I)/9)*SU3D[6, I1, I2]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{CouplingConstant[ChPTW3[2], 1]* -((((2*I)/3)*SU3D[6, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[6, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[6, I4, k6]*SU3D[I1, I2, k5]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I2, k6]*SU3D[I1, I4, k5]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I1, k6]*SU3D[I2, I4, k5]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[6, I3, k6]*SU3D[I1, I2, k5]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I2, k6]*SU3D[I1, I3, k5]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I1, k6]*SU3D[I2, I3, k5]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (2*SU3D[I2, I4, k6]*SU3D[I3, k5, k6]*SU3F[6, I1, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I1, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[6, I2, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I2, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I3, I4, k6]*(SU3D[I2, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I2, k5]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[6, I3, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I4, k5]*SU3D[I2, k5, k6]*SU3F[I1, I3, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/3)*SU3D[I4, k5, k6]*SU3F[6, I2, k5]*SU3F[I1, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/3)*SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[I1, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[I1, I3, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I2, k5]*SU3D[I3, k5, k6]*SU3F[I1, I4, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I2, k5]*SU3F[I1, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/3)*SU3D[I2, k5, k6]*SU3F[6, I3, k5]*SU3F[I1, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3F[I1, I4, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[6, I2, k6]*SU3D[I3, I4, k7]*SU3F[I1, k6, k7])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I4, k5]*SU3D[I1, k5, k6]*SU3F[I2, I3, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/3)*SU3D[I4, k5, k6]*SU3F[6, I1, k5]*SU3F[I2, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/3)*SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[I2, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[I2, I3, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I3, k5]*SU3D[I1, k5, k6]*SU3F[I2, I4, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I1, k5]*SU3D[I3, k5, k6]*SU3F[I2, I4, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I1, k5]*SU3F[I2, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/3)*SU3D[I1, k5, k6]*SU3F[6, I3, k5]*SU3F[I2, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3F[I2, I4, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((2*I)/3)*SU3D[I3, I4, k5]*(SU3F[6, I2, k7]*SU3F[I1, k5, k7] + - SU3F[6, I1, k7]*SU3F[I2, k5, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - ((I/3)*(SU3D[6, I4, k5]*(SU3F[I1, k5, k7]*SU3F[I2, I3, k7] + - SU3F[I1, I3, k7]*SU3F[I2, k5, k7]) + SU3D[6, I3, k5]* - (SU3F[I1, k5, k7]*SU3F[I2, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I2, k5, k7])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I1, k6]*SU3D[I3, I4, k7]* - SU3F[I2, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3F[6, I4, k6]*(SU3F[I1, k6, k7]*SU3F[I2, I3, k7] + - SU3F[I1, I3, k7]*SU3F[I2, k6, k7]) + SU3F[6, I3, k6]* - (SU3F[I1, k6, k7]*SU3F[I2, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I2, k6, k7]))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I2, k5]*SU3D[I1, I4, k7]* - SU3F[I3, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k5]*SU3D[I2, I4, k7]* - SU3F[I3, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (((2*I)/3)*SU3D[I2, I4, k5]* - SU3F[6, I1, k7]*SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[I1, I4, k5]* - SU3F[6, I2, k7]*SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((2*I)/3)*SU3D[I1, I2, k5]* - SU3F[6, I4, k7]*SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/6)*SU3D[6, I2, k5]*SU3F[I1, I4, k7]* - SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/6)*SU3D[6, I1, k5]*SU3F[I2, I4, k7]* - SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I4, k6]*SU3D[I1, I2, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I2, k6]*SU3D[I1, I4, k7]* - SU3F[I3, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k6]*SU3D[I2, I4, k7]* - SU3F[I3, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/2)*SU3D[6, I2, k6]*SU3F[I1, I4, k7]* - SU3F[I3, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I2, k6]*SU3F[I1, I4, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/2)*SU3D[6, I1, k6]*SU3F[I2, I4, k7]* - SU3F[I3, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I1, k6]*SU3F[I2, I4, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I2, k5]*SU3D[I1, I3, k7]* - SU3F[I4, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k5]*SU3D[I2, I3, k7]* - SU3F[I4, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (((2*I)/3)*SU3D[I2, I3, k5]* - SU3F[6, I1, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[I1, I3, k5]* - SU3F[6, I2, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((2*I)/3)*SU3D[I1, I2, k5]* - SU3F[6, I3, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/6)*SU3D[6, I2, k5]*SU3F[I1, I3, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/6)*SU3D[6, I1, k5]*SU3F[I2, I3, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I3, k6]*SU3D[I1, I2, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I2, k6]*SU3D[I1, I3, k7]* - SU3F[I4, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k6]*SU3D[I2, I3, k7]* - SU3F[I4, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/2)*SU3D[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/2)*SU3D[6, I1, k6]*SU3F[I2, I3, k7]* - SU3F[I4, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I1, k6]*SU3F[I2, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((4*I)/9)*SU3D[I2, I3, I4]* - SUNDelta[6, I1])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((4*I)/9)*SU3D[I1, I3, I4]* - SUNDelta[6, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((4*I)/9)*SU3D[I1, I2, I4]* - SUNDelta[6, I3])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((4*I)/9)*SU3D[I1, I2, I3]* - SUNDelta[6, I4])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((8*I)/9)*SU3D[6, I3, I4]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((4*I)/9)*SU3D[6, I2, I4]* - SUNDelta[I1, I3])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (4*SU3F[6, I2, I4]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I2, I3]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (4*SU3F[6, I2, I3]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I1, I4]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (4*SU3F[6, I1, I4]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I1, I3]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (4*SU3F[6, I1, I3]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((8*I)/9)*SU3D[6, I1, I2]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{CouplingConstant[ChPTW3[2], 1]* -((((2*I)/3)*SU3D[6, I4, k6]*SU3D[I1, I3, k5]*SU3D[I2, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I3, k6]*SU3D[I1, I4, k5]*SU3D[I2, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I1, k6]*SU3D[I2, k5, k6]*SU3D[I3, I4, k5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[I2, I4, k6]*(SU3D[6, I3, k5]*SU3D[I1, k5, k6] + - SU3D[6, I1, k5]*SU3D[I3, k5, k6]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I3, k6]*SU3D[I1, I2, k5]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[6, I2, k6]*SU3D[I1, I3, k5]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I1, k6]*SU3D[I2, I3, k5]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I1, k5]*SU3D[I2, I3, k6]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (2*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I2, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I2, I4, k6]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*(SU3D[I4, k5, k6]*(SU3D[I2, I3, k6]*SU3F[6, I1, k5] + - SU3D[I1, I2, k6]*SU3F[6, I3, k5]) + SU3D[I2, k5, k6]* - (SU3D[I3, I4, k6]*SU3F[6, I1, k5] + SU3D[I1, I4, k6]* - SU3F[6, I3, k5])))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (2*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]* - SU3F[6, I4, k5])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3D[6, I3, k5]*SU3D[I4, k5, k6]* - SU3F[I1, I2, k6])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I4, k5]* - SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I3, k6]*SU3D[I4, k6, k7]* - SU3F[I1, I2, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3D[6, I3, k5]*SU3D[I2, k5, k6]* - SU3F[I1, I4, k6])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I2, k5]* - SU3F[I1, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I3, k6]*SU3D[I2, k6, k7]* - SU3F[I1, I4, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k5]*SU3D[I4, k5, k6]* - SU3F[I2, I3, k6])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/3)*SU3D[I1, k5, k6]*SU3F[6, I4, k5]* - SU3F[I2, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3D[6, I1, k6]*SU3D[I4, k6, k7]* - SU3F[I2, I3, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I3, k5]*SU3D[I1, I4, k7]* - SU3F[I2, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k5]*SU3D[I3, I4, k7]* - SU3F[I2, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (((2*I)/3)*SU3D[I3, I4, k5]* - SU3F[6, I1, k7]*SU3F[I2, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[I1, I4, k5]* - SU3F[6, I3, k7]*SU3F[I2, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((2*I)/3)*SU3D[I1, I3, k5]* - SU3F[6, I4, k7]*SU3F[I2, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/6)*SU3D[6, I3, k5]*SU3F[I1, I4, k7]* - SU3F[I2, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I4, k6]*SU3D[I1, I3, k7]* - SU3F[I2, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I3, k6]*SU3D[I1, I4, k7]* - SU3F[I2, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k6]*SU3D[I3, I4, k7]* - SU3F[I2, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/2)*SU3D[6, I3, k6]*SU3F[I1, I4, k7]* - SU3F[I2, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I3, k6]*SU3F[I1, I4, k7]* - SU3F[I2, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3D[6, I1, k5]*SU3D[I2, k5, k6]* - SU3F[I3, I4, k6])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/3)*SU3D[I1, k5, k6]*SU3F[6, I2, k5]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (SU3D[6, I4, k5]*(SU3D[I3, k5, k6]*SU3F[I1, I2, k6] - - SU3D[I1, k5, k6]*SU3F[I2, I3, k6]) + SU3D[6, I2, k5]* - (SU3D[I3, k5, k6]*SU3F[I1, I4, k6] + SU3D[I1, k5, k6]* - SU3F[I3, I4, k6]))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/3)*(SU3D[I4, k5, k6]*(SU3F[6, I3, k5]*SU3F[I1, I2, k6] - - SU3F[6, I1, k5]*SU3F[I2, I3, k6]) + SU3D[I2, k5, k6]* - (SU3F[6, I3, k5]*SU3F[I1, I4, k6] + SU3F[6, I1, k5]* - SU3F[I3, I4, k6])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3F[I3, I4, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/6)*SU3D[6, I1, k5]*SU3F[I2, k5, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/2)*SU3D[6, I1, k6]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I1, k6]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((2*I)/3)*SU3D[I2, I4, k5]* - (SU3F[6, I3, k7]*SU3F[I1, k5, k7] + SU3F[6, I1, k7]*SU3F[I3, k5, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/3)*(SU3D[6, I4, k5]*(SU3F[I1, k5, k7]*SU3F[I2, I3, k7] - - SU3F[I1, I2, k7]*SU3F[I3, k5, k7]) - SU3D[6, I2, k5]* - (SU3F[I1, k5, k7]*SU3F[I3, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I3, k5, k7])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (2*SU3D[I2, I4, k7]*(SU3D[6, I3, k6]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3F[I3, k6, k7]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3F[6, I4, k6]*(SU3F[I1, k6, k7]*SU3F[I2, I3, k7] - - SU3F[I1, I2, k7]*SU3F[I3, k6, k7]) - SU3F[6, I2, k6]* - (SU3F[I1, k6, k7]*SU3F[I3, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I3, k6, k7]))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I3, k5]*SU3D[I1, I2, k7]* - SU3F[I4, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k5]*SU3D[I2, I3, k7]* - SU3F[I4, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (((2*I)/3)*SU3D[I2, I3, k5]* - SU3F[6, I1, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((2*I)/3)*SU3D[I1, I3, k5]* - SU3F[6, I2, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[I1, I2, k5]* - SU3F[6, I3, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/6)*SU3D[6, I3, k5]*SU3F[I1, I2, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*SU3D[6, I1, k5]*SU3F[I2, I3, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I3, k6]*SU3D[I1, I2, k7]* - SU3F[I4, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (2*SU3D[6, I2, k6]*SU3D[I1, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k6]*SU3D[I2, I3, k7]* - SU3F[I4, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/2)*SU3D[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/2)*SU3D[6, I1, k6]*SU3F[I2, I3, k7]* - SU3F[I4, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3F[6, I1, k6]*SU3F[I2, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (((4*I)/9)*SU3D[I1, I3, I4]* - SUNDelta[6, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (((4*I)/9)*(SU3D[I2, I3, I4]*SUNDelta[6, I1] + SU3D[I1, I2, I4]* - SUNDelta[6, I3]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((4*I)/9)*SU3D[I1, I2, I3]* - SUNDelta[6, I4])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((4*I)/9)*SU3D[6, I3, I4]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (4*SU3F[6, I3, I4]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((8*I)/9)*SU3D[6, I2, I4]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((4*I)/9)*SU3D[6, I2, I3]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (4*SU3F[6, I2, I3]*SUNDelta[I1, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I1, I4]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (4*SU3F[6, I1, I4]*SUNDelta[I2, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((8*I)/9)*SU3D[6, I1, I3]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((4*I)/9)*SU3D[6, I1, I2]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (4*SU3F[6, I1, I2]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{CouplingConstant[ChPTW3[2], 1]* -(((-I/6)*SU3D[6, I4, k6]*SU3D[I1, I3, k5]*SU3D[I2, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[6, I3, k6]*SU3D[I1, I4, k5]*SU3D[I2, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I1, k6]*SU3D[I2, k5, k6]*SU3D[I3, I4, k5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I4, k6]*SU3D[I1, I2, k5]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I4, k5]*SU3D[I1, I2, k6]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[6, I2, k6]*SU3D[I1, I4, k5]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I1, k6]*SU3D[I2, I4, k5]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[I2, I3, k6]*(SU3D[6, I4, k5]*SU3D[I1, k5, k6] + - SU3D[6, I1, k5]*SU3D[I4, k5, k6]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (2*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I1, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[6, I2, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[6, I3, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*(SU3D[I3, k5, k6]*(SU3D[I2, I4, k6]*SU3F[6, I1, k5] + - SU3D[I1, I2, k6]*SU3F[6, I4, k5]) + SU3D[I2, k5, k6]* - (SU3D[I3, I4, k6]*SU3F[6, I1, k5] + SU3D[I1, I3, k6]* - SU3F[6, I4, k5])))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I3, k5]*SU3D[I4, k5, k6]* - SU3F[I1, I2, k6])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I4, k5]* - SU3F[I1, I2, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I2, k5]*SU3D[I4, k5, k6]* - SU3F[I1, I3, k6])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/3)*SU3D[I2, k5, k6]*SU3F[6, I4, k5]* - SU3F[I1, I3, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((2*I)/3)*SU3D[I2, I3, k5]* - SU3F[6, I4, k7]*SU3F[I1, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3D[6, I3, k5]*SU3D[I1, k5, k6]* - SU3F[I2, I4, k6])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I1, k5]* - SU3F[I2, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I3, k5]*SU3F[I1, k5, k7]* - SU3F[I2, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3F[6, I3, k6]*SU3F[I1, k6, k7]* - SU3F[I2, I4, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I4, k5]*SU3D[I1, I3, k7]* - SU3F[I2, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k5]*SU3D[I3, I4, k7]* - SU3F[I2, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (((2*I)/3)*SU3D[I3, I4, k5]* - SU3F[6, I1, k7]*SU3F[I2, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((2*I)/3)*SU3D[I1, I4, k5]* - SU3F[6, I3, k7]*SU3F[I2, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[I1, I3, k5]* - SU3F[6, I4, k7]*SU3F[I2, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/6)*SU3D[6, I4, k5]*SU3F[I1, I3, k7]* - SU3F[I2, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I4, k6]*SU3D[I1, I3, k7]* - SU3F[I2, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (2*SU3D[6, I3, k6]*SU3D[I1, I4, k7]* - SU3F[I2, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k6]*SU3D[I3, I4, k7]* - SU3F[I2, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/2)*SU3D[6, I4, k6]*SU3F[I1, I3, k7]* - SU3F[I2, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I4, k6]*SU3F[I1, I3, k7]* - SU3F[I2, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3D[6, I2, k5]*SU3D[I1, k5, k6]* - SU3F[I3, I4, k6])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/3)*SU3D[I2, k5, k6]*SU3F[6, I1, k5]* - SU3F[I3, I4, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (SU3D[6, I4, k5]*(SU3D[I3, k5, k6]*SU3F[I1, I2, k6] + - SU3D[I2, k5, k6]*SU3F[I1, I3, k6]) - SU3D[6, I1, k5]* - (SU3D[I3, k5, k6]*SU3F[I2, I4, k6] + SU3D[I2, k5, k6]* - SU3F[I3, I4, k6]))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/3)*(SU3D[I4, k5, k6]*(SU3F[6, I3, k5]*SU3F[I1, I2, k6] + - SU3F[6, I2, k5]*SU3F[I1, I3, k6]) - SU3D[I1, k5, k6]* - (SU3F[6, I3, k5]*SU3F[I2, I4, k6] + SU3F[6, I2, k5]* - SU3F[I3, I4, k6])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I2, k5]*SU3F[I1, k5, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3F[6, I2, k6]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/6)*SU3D[6, I1, k5]*SU3F[I2, k5, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/2)*SU3D[6, I1, k6]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3F[6, I1, k6]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I4, k6]*(SU3D[I3, k6, k7]*SU3F[I1, I2, k7] + - SU3D[I2, k6, k7]*SU3F[I1, I3, k7]) - SU3D[6, I1, k6]* - (SU3D[I3, k6, k7]*SU3F[I2, I4, k7] + SU3D[I2, k6, k7]* - SU3F[I3, I4, k7]))/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I4, k5]*SU3D[I1, I2, k7]* - SU3F[I3, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k5]*SU3D[I2, I4, k7]* - SU3F[I3, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (((2*I)/3)*SU3D[I2, I4, k5]* - SU3F[6, I1, k7]*SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((2*I)/3)*SU3D[I1, I4, k5]* - SU3F[6, I2, k7]*SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[I1, I2, k5]* - SU3F[6, I4, k7]*SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/6)*SU3D[6, I4, k5]*SU3F[I1, I2, k7]* - SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*SU3D[6, I1, k5]*SU3F[I2, I4, k7]* - SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I4, k6]*SU3D[I1, I2, k7]* - SU3F[I3, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (2*SU3D[6, I2, k6]*SU3D[I1, I4, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I1, k6]*SU3D[I2, I4, k7]* - SU3F[I3, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/2)*SU3D[6, I4, k6]*SU3F[I1, I2, k7]* - SU3F[I3, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I4, k6]*SU3F[I1, I2, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/2)*SU3D[6, I1, k6]*SU3F[I2, I4, k7]* - SU3F[I3, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3F[6, I1, k6]*SU3F[I2, I4, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((2*I)/3)*SU3D[I2, I3, k5]* - SU3F[6, I1, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/3)*SU3D[6, I3, k5]*SU3F[I1, I2, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/3)*SU3D[6, I2, k5]*SU3F[I1, I3, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3F[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (2*SU3D[I2, I3, k7]*(SU3D[6, I4, k6]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3F[I4, k6, k7]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((4*I)/9)*SU3D[I1, I3, I4]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((4*I)/9)*SU3D[I1, I2, I4]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((4*I)/9)*(SU3D[I2, I3, I4]*SUNDelta[6, I1] + SU3D[I1, I2, I3]* - SUNDelta[6, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((4*I)/9)*SU3D[6, I3, I4]* - SUNDelta[I1, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (4*SU3F[6, I3, I4]*SUNDelta[I1, I2])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I2, I4]*SUNDelta[I1, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (4*SU3F[6, I2, I4]*SUNDelta[I1, I3])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((8*I)/9)*SU3D[6, I2, I3]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((8*I)/9)*SU3D[6, I1, I4]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((4*I)/9)*SU3D[6, I1, I3]*SUNDelta[I2, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (4*SU3F[6, I1, I3]*SUNDelta[I2, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((4*I)/9)*SU3D[6, I1, I2]*SUNDelta[I3, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (4*SU3F[6, I1, I2]*SUNDelta[I3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{CouplingConstant[ChPTW3[2], 1]* -(((-I/6)*SU3D[6, I3, k6]*SU3D[I1, k5, k6]*SU3D[I2, I4, k5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I3, k5]*SU3D[I1, k5, k6]*SU3D[I2, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[6, I3, k5]*SU3D[I1, I4, k6]*SU3D[I2, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I2, k6]*SU3D[I1, k5, k6]*SU3D[I3, I4, k5])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[6, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I3, k6]*SU3D[I1, I2, k5]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I3, k5]*SU3D[I1, I2, k6]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*SU3D[6, I2, k6]*SU3D[I1, I3, k5]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/2)*SU3D[6, I2, k5]*SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[I2, I3, k5]*(SU3D[6, I4, k6]*SU3D[I1, k5, k6] + - SU3D[6, I1, k6]*SU3D[I4, k5, k6]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (2*SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I1, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[6, I2, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[6, I2, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I2, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, k5, k6]*SU3D[I2, I4, k6]*SU3F[6, I3, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I4, k6]*SU3D[I2, k5, k6]*SU3F[6, I3, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[6, I3, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I4, k5]*SU3F[I1, I2, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[6, I3, k6]*SU3D[I4, k6, k7]*SU3F[I1, I2, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I2, k5]*SU3D[I4, k5, k6]*SU3F[I1, I3, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[I1, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[I1, I3, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I3, k5]*SU3D[I2, I4, k7]*SU3F[I1, k5, k7])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I2, k5]*SU3D[I3, I4, k7]*SU3F[I1, k5, k7])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((2*I)/3)*SU3D[I2, I3, k5]*SU3F[6, I4, k7]*SU3F[I1, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I3, k6]*SU3D[I2, I4, k7]*SU3F[I1, k6, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I2, k6]*SU3D[I3, I4, k7]*SU3F[I1, k6, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I3, k5]*SU3D[I1, k5, k6]*SU3F[I2, I4, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I1, k5]*SU3F[I2, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I3, k6]*SU3D[I1, k6, k7]*SU3F[I2, I4, k7])/ - (2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/6)*SU3D[6, I3, k5]*SU3F[I1, k5, k7]*SU3F[I2, I4, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - ((I/2)*SU3D[6, I3, k6]*SU3F[I1, k6, k7]*SU3F[I2, I4, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3F[6, I3, k6]*SU3F[I1, k6, k7]*SU3F[I2, I4, k7])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (((2*I)/3)*SU3D[I1, I4, k5]*SU3F[6, I3, k7]*SU3F[I2, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/3)*SU3D[6, I4, k5]*SU3F[I1, I3, k7]*SU3F[I2, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (2*SU3D[6, I3, k6]*SU3D[I1, I4, k7]*SU3F[I2, k6, k7])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3F[6, I4, k6]*SU3F[I1, I3, k7]*SU3F[I2, k6, k7])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I2, k5]*SU3D[I1, k5, k6]*SU3F[I3, I4, k6])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/3)*SU3D[I2, k5, k6]*SU3F[6, I1, k5]*SU3F[I3, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[6, I4, k5]*(SU3D[I3, k5, k6]*SU3F[I1, I2, k6] + - SU3D[I2, k5, k6]*SU3F[I1, I3, k6]) - SU3D[6, I1, k5]* - (SU3D[I3, k5, k6]*SU3F[I2, I4, k6] + SU3D[I2, k5, k6]* - SU3F[I3, I4, k6]))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/3)*(SU3D[I4, k5, k6]*(SU3F[6, I3, k5]*SU3F[I1, I2, k6] + - SU3F[6, I2, k5]*SU3F[I1, I3, k6]) - SU3D[I1, k5, k6]* - (SU3F[6, I3, k5]*SU3F[I2, I4, k6] + SU3F[6, I2, k5]* - SU3F[I3, I4, k6])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3F[I3, I4, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/6)*SU3D[6, I2, k5]*SU3F[I1, k5, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/2)*SU3D[6, I2, k6]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I2, k6]*SU3F[I1, k6, k7]* - SU3F[I3, I4, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + ((I/3)*SU3D[6, I1, k5]*SU3F[I2, k5, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3F[6, I1, k6]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((2*I)/3)*SU3D[I1, I4, k5]* - SU3F[6, I2, k7]*SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I4, k5]*SU3F[I1, I2, k7]* - SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/3)*SU3D[6, I1, k5]*SU3F[I2, I4, k7]* - SU3F[I3, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I2, k6]*SU3D[I1, I4, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3F[6, I4, k6]*SU3F[I1, I2, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3F[6, I1, k6]*SU3F[I2, I4, k7]* - SU3F[I3, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I3, k5]*SU3D[I1, I2, k7]* - SU3F[I4, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I2, k5]*SU3D[I1, I3, k7]* - SU3F[I4, k5, k7])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((2*I)/3)*SU3D[I2, I3, k5]* - SU3F[6, I1, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*SU3D[6, I3, k5]*SU3F[I1, I2, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*SU3D[6, I2, k5]*SU3F[I1, I3, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (((2*I)/3)*(SU3D[I3, I4, k5]*SU3F[6, I2, k7]*SU3F[I1, k5, k7] + - SU3D[I2, I4, k5]*SU3F[6, I3, k7]*SU3F[I1, k5, k7] + - (SU3D[I1, I3, k5]*SU3F[6, I2, k7] + SU3D[I1, I2, k5]*SU3F[6, I3, k7])* - SU3F[I4, k5, k7]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (SU3D[6, I3, k6]*SU3D[I1, I2, k7]* - SU3F[I4, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3D[6, I2, k6]*SU3D[I1, I3, k7]* - SU3F[I4, k6, k7])/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/2)*SU3D[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3F[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - ((I/2)*SU3D[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3F[6, I2, k6]*SU3F[I1, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (2*SU3D[I2, I3, k7]*(SU3D[6, I4, k6]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3F[I4, k6, k7]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((4*I)/9)*SU3D[I2, I3, I4]*SUNDelta[6, I1])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((4*I)/9)*SU3D[I1, I3, I4]*SUNDelta[6, I2])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((4*I)/9)*SU3D[I1, I2, I4]*SUNDelta[6, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((4*I)/9)*SU3D[I1, I2, I3]*SUNDelta[6, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((8*I)/9)*SU3D[6, I2, I3]*SUNDelta[I1, I4])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((8*I)/9)*SU3D[6, I1, I4]*SUNDelta[I2, I3])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((4*I)/9)*(SU3D[6, I3, I4]*SUNDelta[I1, I2] + SU3D[6, I2, I4]* - SUNDelta[I1, I3] + SU3D[6, I1, I3]*SUNDelta[I2, I4] + - SU3D[6, I1, I2]*SUNDelta[I3, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (4*(SU3F[6, I3, I4]*SUNDelta[I1, I2] + SU3F[6, I2, I4]*SUNDelta[I1, I3] - - SU3F[6, I1, I3]*SUNDelta[I2, I4] - SU3F[6, I1, I2]*SUNDelta[I3, I4]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{CouplingConstant[ChPTW3[2], 1]* -((((2*I)/3)*SU3D[6, I4, k5]*SU3D[I1, I3, k6]*SU3D[I2, k5, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*SU3D[I2, I4, k5]*(SU3D[6, I3, k6]*SU3D[I1, k5, k6] + - SU3D[6, I1, k6]*SU3D[I3, k5, k6]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/6)*(SU3D[6, I4, k6]*(SU3D[I1, k5, k6]*SU3D[I2, I3, k5] + - SU3D[I1, I2, k5]*SU3D[I3, k5, k6]) + SU3D[6, I2, k6]* - (SU3D[I1, k5, k6]*SU3D[I3, I4, k5] + SU3D[I1, I4, k5]* - SU3D[I3, k5, k6])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/2)*(SU3D[6, I4, k5]*(SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - SU3D[I1, I2, k6]*SU3D[I3, k5, k6]) + SU3D[6, I2, k5]* - (SU3D[I1, k5, k6]*SU3D[I3, I4, k6] + SU3D[I1, I4, k6]* - SU3D[I3, k5, k6])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((2*I)/3)*SU3D[6, I2, k5]* - SU3D[I1, I3, k6]*SU3D[I4, k5, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[I1, k5, k6]*SU3D[I3, I4, k6]* - SU3F[6, I2, k5])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (2*SU3D[I1, I4, k6]*SU3D[I3, k5, k6]* - SU3F[6, I2, k5])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (2*SU3D[I1, I3, k6]*SU3D[I4, k5, k6]* - SU3F[6, I2, k5])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (2*SU3D[I2, I4, k6]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, k5, k6]*SU3D[I2, I3, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*SU3D[I1, I3, k6]*SU3D[I2, k5, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (2*SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[6, I4, k5])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, I2, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I4, k5]*SU3F[I1, I2, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[6, I3, k5]*SU3D[I2, k5, k6]*SU3F[I1, I4, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I3, k5, k6]*SU3F[6, I2, k5]*SU3F[I1, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I1, k5]*SU3D[I4, k5, k6]*SU3F[I2, I3, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/3)*SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[I2, I3, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((2*I)/3)*SU3D[I1, I3, k5]*SU3F[6, I4, k7]*SU3F[I2, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/3)*SU3D[6, I3, k5]*SU3F[I1, I4, k7]*SU3F[I2, k5, k7])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (2*SU3D[6, I4, k6]*SU3D[I1, I3, k7]*SU3F[I2, k6, k7])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3F[6, I3, k6]*SU3F[I1, I4, k7]*SU3F[I2, k6, k7])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[6, I1, k5]*SU3D[I2, k5, k6]*SU3F[I3, I4, k6])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/3)*SU3D[I1, k5, k6]*SU3F[6, I2, k5]*SU3F[I3, I4, k6])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[6, I4, k5]*(SU3D[I3, k5, k6]*SU3F[I1, I2, k6] - - SU3D[I1, k5, k6]*SU3F[I2, I3, k6]) + SU3D[6, I2, k5]* - (SU3D[I3, k5, k6]*SU3F[I1, I4, k6] + SU3D[I1, k5, k6]* - SU3F[I3, I4, k6]))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/3)*(SU3D[I4, k5, k6]*(SU3F[6, I3, k5]*SU3F[I1, I2, k6] - - SU3F[6, I1, k5]*SU3F[I2, I3, k6]) + SU3D[I2, k5, k6]* - (SU3F[6, I3, k5]*SU3F[I1, I4, k6] + SU3F[6, I1, k5]* - SU3F[I3, I4, k6])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I1, k5]*SU3F[I2, k5, k7]* - SU3F[I3, I4, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (SU3F[6, I1, k6]*SU3F[I2, k6, k7]* - SU3F[I3, I4, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[6, I4, k6]*(SU3D[I3, k6, k7]*SU3F[I1, I2, k7] - - SU3D[I1, k6, k7]*SU3F[I2, I3, k7]) + SU3D[6, I2, k6]* - (SU3D[I3, k6, k7]*SU3F[I1, I4, k7] + SU3D[I1, k6, k7]* - SU3F[I3, I4, k7]))/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((2*I)/3)*SU3D[I2, I4, k5]* - (SU3F[6, I3, k7]*SU3F[I1, k5, k7] + SU3F[6, I1, k7]*SU3F[I3, k5, k7]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((2*I)/3)*(SU3D[I3, I4, k5]*SU3F[6, I2, k7]*SU3F[I1, k5, k7] + - SU3D[I2, I3, k5]*SU3F[6, I4, k7]*SU3F[I1, k5, k7] + - (SU3D[I1, I4, k5]*SU3F[6, I2, k7] + SU3D[I1, I2, k5]*SU3F[6, I4, k7])* - SU3F[I3, k5, k7]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (SU3D[6, I4, k5]*(SU3D[I2, I3, k7]*SU3F[I1, k5, k7] + - SU3D[I1, I2, k7]*SU3F[I3, k5, k7]) + SU3D[6, I2, k5]* - (SU3D[I3, I4, k7]*SU3F[I1, k5, k7] + SU3D[I1, I4, k7]* - SU3F[I3, k5, k7]))/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/6)*(SU3D[6, I4, k5]*(SU3F[I1, k5, k7]*SU3F[I2, I3, k7] - - SU3F[I1, I2, k7]*SU3F[I3, k5, k7]) - SU3D[6, I2, k5]* - (SU3F[I1, k5, k7]*SU3F[I3, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I3, k5, k7])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (2*SU3D[I2, I4, k7]*(SU3D[6, I3, k6]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3F[I3, k6, k7]))/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[6, I4, k6]*(SU3D[I2, I3, k7]*SU3F[I1, k6, k7] + - SU3D[I1, I2, k7]*SU3F[I3, k6, k7]) + SU3D[6, I2, k6]* - (SU3D[I3, I4, k7]*SU3F[I1, k6, k7] + SU3D[I1, I4, k7]* - SU3F[I3, k6, k7]))/(2*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/2)*(SU3D[6, I4, k6]*(SU3F[I1, k6, k7]*SU3F[I2, I3, k7] - - SU3F[I1, I2, k7]*SU3F[I3, k6, k7]) - SU3D[6, I2, k6]* - (SU3F[I1, k6, k7]*SU3F[I3, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I3, k6, k7])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (SU3F[6, I4, k6]*(SU3F[I1, k6, k7]*SU3F[I2, I3, k7] - - SU3F[I1, I2, k7]*SU3F[I3, k6, k7]) - SU3F[6, I2, k6]* - (SU3F[I1, k6, k7]*SU3F[I3, I4, k7] + SU3F[I1, I4, k7]* - SU3F[I3, k6, k7]))/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((2*I)/3)*SU3D[I1, I3, k5]* - SU3F[6, I2, k7]*SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/3)*SU3D[6, I3, k5]*SU3F[I1, I2, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/3)*SU3D[6, I1, k5]*SU3F[I2, I3, k7]* - SU3F[I4, k5, k7])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (2*SU3D[6, I2, k6]*SU3D[I1, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + (SU3F[6, I3, k6]*SU3F[I1, I2, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (SU3F[6, I1, k6]*SU3F[I2, I3, k7]* - SU3F[I4, k6, k7])/(3*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - (((4*I)/9)*SU3D[I1, I3, I4]* - SUNDelta[6, I2])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (((4*I)/9)*(SU3D[I2, I3, I4]*SUNDelta[6, I1] + SU3D[I1, I2, I4]* - SUNDelta[6, I3]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - (((4*I)/9)*SU3D[I1, I2, I3]* - SUNDelta[6, I4])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((8*I)/9)*SU3D[6, I2, I4]* - SUNDelta[I1, I3])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + (((8*I)/9)*SU3D[6, I1, I3]* - SUNDelta[I2, I4])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (((4*I)/9)*(SU3D[6, I3, I4]*SUNDelta[I1, I2] + SU3D[6, I2, I3]* - SUNDelta[I1, I4] + SU3D[6, I1, I4]*SUNDelta[I2, I3] + - SU3D[6, I1, I2]*SUNDelta[I3, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (4*(SU3F[6, I3, I4]*SUNDelta[I1, I2] - SU3F[6, I2, I3]*SUNDelta[I1, I4] + - SU3F[6, I1, I4]*SUNDelta[I2, I3] + SU3F[6, I1, I2]*SUNDelta[I3, I4]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{CouplingConstant[ChPTW3[2], 2]* -((((-2*I)/9)*(SU3D[3, I3, I4]*SU3D[6, I1, I2] + SU3D[3, I2, I4]* - SU3D[6, I1, I3] + SU3D[3, I2, I3]*SU3D[6, I1, I4] + - SU3D[3, I1, I4]*SU3D[6, I2, I3] + SU3D[3, I1, I3]*SU3D[6, I2, I4] + - SU3D[3, I1, I2]*SU3D[6, I3, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (((2*I)/9)*(SU3D[6, I3, I4]*SU3D[8, I1, I2] + SU3D[6, I2, I4]* - SU3D[8, I1, I3] + SU3D[6, I2, I3]*SU3D[8, I1, I4] + - SU3D[6, I1, I4]*SU3D[8, I2, I3] + SU3D[6, I1, I3]*SU3D[8, I2, I4] + - SU3D[6, I1, I2]*SU3D[8, I3, I4]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/9)*(SU3D[6, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6] + - SU3D[6, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6] + - SU3D[6, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6] + - SU3D[6, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6] + - SU3D[6, I4, k5]*(SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - SU3D[I1, I3, k6]*SU3D[I2, k5, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k5, k6]) + SU3D[6, I2, k5]*SU3D[I1, I3, k6]* - SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[I2, I3, k6]* - SU3D[I4, k5, k6] + SU3D[6, I3, k5]* - (SU3D[I1, k5, k6]*SU3D[I2, I4, k6] + SU3D[I1, I4, k6]* - SU3D[I2, k5, k6] + SU3D[I1, I2, k6]*SU3D[I4, k5, k6])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - ((I/12)*(SU3D[3, I2, k8]*SU3D[6, I4, k5]*SU3D[I1, k6, k8]* - SU3D[I3, k5, k6] + SU3D[3, I1, k8]*SU3D[6, I4, k5]*SU3D[I2, k6, k8]* - SU3D[I3, k5, k6] + SU3D[3, I2, k8]*SU3D[6, I4, k5]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k8] + SU3D[3, I1, k8]*SU3D[6, I4, k5]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k8] + SU3D[3, I4, k8]* - (SU3D[6, I3, k5]*(SU3D[I1, k6, k8]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k8]) + SU3D[6, I2, k5]* - (SU3D[I1, k6, k8]*SU3D[I3, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I3, k6, k8]) + SU3D[6, I1, k5]* - (SU3D[I2, k6, k8]*SU3D[I3, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I3, k6, k8])) + SU3D[3, I2, k8]*SU3D[6, I3, k5]* - SU3D[I1, k6, k8]*SU3D[I4, k5, k6] + SU3D[3, I1, k8]*SU3D[6, I3, k5]* - SU3D[I2, k6, k8]*SU3D[I4, k5, k6] + SU3D[3, I2, k8]*SU3D[6, I1, k5]* - SU3D[I3, k6, k8]*SU3D[I4, k5, k6] + SU3D[3, I1, k8]*SU3D[6, I2, k5]* - SU3D[I3, k6, k8]*SU3D[I4, k5, k6] + SU3D[3, I2, k8]*SU3D[6, I3, k5]* - SU3D[I1, k5, k6]*SU3D[I4, k6, k8] + SU3D[3, I1, k8]*SU3D[6, I3, k5]* - SU3D[I2, k5, k6]*SU3D[I4, k6, k8] + SU3D[3, I2, k8]*SU3D[6, I1, k5]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k8] + SU3D[3, I1, k8]*SU3D[6, I2, k5]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k8] + SU3D[3, I3, k8]* - (SU3D[6, I4, k5]*(SU3D[I1, k6, k8]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k8]) + SU3D[6, I2, k5]* - (SU3D[I1, k6, k8]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k8]) + SU3D[6, I1, k5]* - (SU3D[I2, k6, k8]*SU3D[I4, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I4, k6, k8]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3D[6, I2, k5]*SU3D[8, I4, k8]*SU3D[I1, k6, k8]* - SU3D[I3, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I4, k8]*SU3D[I2, k6, k8]* - SU3D[I3, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I4, k8]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k8] + SU3D[6, I1, k5]*SU3D[8, I4, k8]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k8] + SU3D[6, I4, k5]* - (SU3D[8, I3, k8]*(SU3D[I1, k6, k8]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k8]) + SU3D[8, I2, k8]* - (SU3D[I1, k6, k8]*SU3D[I3, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I3, k6, k8]) + SU3D[8, I1, k8]* - (SU3D[I2, k6, k8]*SU3D[I3, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I3, k6, k8])) + SU3D[6, I2, k5]*SU3D[8, I3, k8]* - SU3D[I1, k6, k8]*SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I3, k8]* - SU3D[I2, k6, k8]*SU3D[I4, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I1, k8]* - SU3D[I3, k6, k8]*SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I2, k8]* - SU3D[I3, k6, k8]*SU3D[I4, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I3, k8]* - SU3D[I1, k5, k6]*SU3D[I4, k6, k8] + SU3D[6, I1, k5]*SU3D[8, I3, k8]* - SU3D[I2, k5, k6]*SU3D[I4, k6, k8] + SU3D[6, I2, k5]*SU3D[8, I1, k8]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k8] + SU3D[6, I1, k5]*SU3D[8, I2, k8]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k8] + SU3D[6, I3, k5]* - (SU3D[8, I4, k8]*(SU3D[I1, k6, k8]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k8]) + SU3D[8, I2, k8]* - (SU3D[I1, k6, k8]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k8]) + SU3D[8, I1, k8]* - (SU3D[I2, k6, k8]*SU3D[I4, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I4, k6, k8]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[3, I1, k8] + - SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[3, I1, k8] + - SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[3, I2, k8] + - SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[3, I2, k8] + - SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[3, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[3, I3, k8] + - SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k8] + - SU3D[6, I4, k6]*((SU3D[I1, k7, k8]*SU3D[I3, k6, k7] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8])*SU3F[3, I2, k8] + - SU3D[I2, k7, k8]*(SU3D[I3, k6, k7]*SU3F[3, I1, k8] + - SU3D[I1, k6, k7]*SU3F[3, I3, k8]) + SU3D[I2, k6, k7]* - (SU3D[I3, k7, k8]*SU3F[3, I1, k8] + SU3D[I1, k7, k8]* - SU3F[3, I3, k8])) + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I4, k8] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k8] + SU3D[6, I3, k6]* - ((SU3D[I1, k7, k8]*SU3D[I4, k6, k7] + SU3D[I1, k6, k7]* - SU3D[I4, k7, k8])*SU3F[3, I2, k8] + SU3D[I2, k7, k8]* - (SU3D[I4, k6, k7]*SU3F[3, I1, k8] + SU3D[I1, k6, k7]* - SU3F[3, I4, k8]) + SU3D[I2, k6, k7]* - (SU3D[I4, k7, k8]*SU3F[3, I1, k8] + SU3D[I1, k7, k8]* - SU3F[3, I4, k8])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[6, I2, k5] + - SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[6, I2, k5] + - SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I2, k5] + - SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[I2, I4, k6]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]) + SU3D[I1, k5, k6]*SU3D[I2, I3, k6]* - SU3F[6, I4, k5] + SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[6, I4, k5] + - SU3D[I2, k5, k6]*(SU3D[I3, I4, k6]*SU3F[6, I1, k5] + - SU3D[I1, I4, k6]*SU3F[6, I3, k5] + SU3D[I1, I3, k6]*SU3F[6, I4, k5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[3, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I1, k5] + - SU3D[3, I2, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k5] + - SU3D[3, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I2, k5] + - SU3D[3, I1, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k5] + - SU3D[3, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[3, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[3, I2, k7]*SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[3, I1, k7]*SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[3, I4, k7]*((SU3D[I1, k6, k7]*SU3D[I3, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I3, k6, k7])*SU3F[6, I2, k5] + - SU3D[I2, k6, k7]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]) + SU3D[I2, k5, k6]* - (SU3D[I3, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I3, k5])) + SU3D[3, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[3, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[3, I2, k7]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[3, I1, k7]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[3, I3, k7]* - ((SU3D[I1, k6, k7]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k7])*SU3F[6, I2, k5] + SU3D[I2, k6, k7]* - (SU3D[I4, k5, k6]*SU3F[6, I1, k5] + SU3D[I1, k5, k6]* - SU3F[6, I4, k5]) + SU3D[I2, k5, k6]* - (SU3D[I4, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I4, k5])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[8, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I1, k5] + - SU3D[8, I2, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k5] + - SU3D[8, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I2, k5] + - SU3D[8, I1, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k5] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[8, I2, k7]*SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[8, I1, k7]*SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[8, I4, k7]*((SU3D[I1, k6, k7]*SU3D[I3, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I3, k6, k7])*SU3F[6, I2, k5] + - SU3D[I2, k6, k7]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]) + SU3D[I2, k5, k6]* - (SU3D[I3, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I3, k5])) + SU3D[8, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[8, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[8, I2, k7]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[8, I1, k7]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[8, I3, k7]* - ((SU3D[I1, k6, k7]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k7])*SU3F[6, I2, k5] + SU3D[I2, k6, k7]* - (SU3D[I4, k5, k6]*SU3F[6, I1, k5] + SU3D[I1, k5, k6]* - SU3F[6, I4, k5]) + SU3D[I2, k5, k6]* - (SU3D[I4, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I4, k5])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/12)*(SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[3, I3, k7]* - SU3F[6, I1, k5] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k7]* - SU3F[6, I1, k5] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[3, I3, k7]* - SU3F[6, I2, k5] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k7]* - SU3F[6, I2, k5] + SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[3, I1, k7]* - SU3F[6, I3, k5] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[3, I1, k7]* - SU3F[6, I3, k5] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[3, I2, k7]* - SU3F[6, I3, k5] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[3, I2, k7]* - SU3F[6, I3, k5] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[3, I4, k7]* - SU3F[6, I3, k5] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[3, I4, k7]* - SU3F[6, I3, k5] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[3, I3, k7]* - SU3F[6, I4, k5] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[3, I3, k7]* - SU3F[6, I4, k5] + SU3D[I3, k6, k7]* - (SU3D[I4, k5, k6]*(SU3F[3, I2, k7]*SU3F[6, I1, k5] + - SU3F[3, I1, k7]*SU3F[6, I2, k5]) + SU3D[I2, k5, k6]* - (SU3F[3, I4, k7]*SU3F[6, I1, k5] + SU3F[3, I1, k7]* - SU3F[6, I4, k5]) + SU3D[I1, k5, k6]* - (SU3F[3, I4, k7]*SU3F[6, I2, k5] + SU3F[3, I2, k7]* - SU3F[6, I4, k5])) + SU3D[I3, k5, k6]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k7]*SU3F[6, I1, k5] + - SU3F[3, I1, k7]*SU3F[6, I2, k5]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k7]*SU3F[6, I1, k5] + SU3F[3, I1, k7]* - SU3F[6, I4, k5]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k7]*SU3F[6, I2, k5] + SU3F[3, I2, k7]* - SU3F[6, I4, k5]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I1, k7] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I1, k7] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I2, k7] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I2, k7] + SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I1, k5]* - SU3F[8, I3, k7] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I2, k5]* - SU3F[8, I3, k7] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[6, I4, k5]* - SU3F[8, I3, k7] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I4, k7] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I4, k7] + SU3D[I3, k6, k7]* - (SU3D[I4, k5, k6]*(SU3F[6, I2, k5]*SU3F[8, I1, k7] + - SU3F[6, I1, k5]*SU3F[8, I2, k7]) + SU3D[I2, k5, k6]* - (SU3F[6, I4, k5]*SU3F[8, I1, k7] + SU3F[6, I1, k5]* - SU3F[8, I4, k7]) + SU3D[I1, k5, k6]* - (SU3F[6, I4, k5]*SU3F[8, I2, k7] + SU3F[6, I2, k5]* - SU3F[8, I4, k7])) + SU3D[I3, k5, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k5]*SU3F[8, I1, k7] + - SU3F[6, I1, k5]*SU3F[8, I2, k7]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k5]*SU3F[8, I1, k7] + SU3F[6, I1, k5]* - SU3F[8, I4, k7]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k5]*SU3F[8, I2, k7] + SU3F[6, I2, k5]* - SU3F[8, I4, k7]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k8] + - SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k8] + - SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I2, k8] + - SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I2, k8] + - SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k8] + - SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k8] + - SU3D[6, I4, k6]*((SU3D[I1, k7, k8]*SU3D[I3, k6, k7] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8])*SU3F[8, I2, k8] + - SU3D[I2, k7, k8]*(SU3D[I3, k6, k7]*SU3F[8, I1, k8] + - SU3D[I1, k6, k7]*SU3F[8, I3, k8]) + SU3D[I2, k6, k7]* - (SU3D[I3, k7, k8]*SU3F[8, I1, k8] + SU3D[I1, k7, k8]* - SU3F[8, I3, k8])) + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k8] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k8] + SU3D[6, I3, k6]* - ((SU3D[I1, k7, k8]*SU3D[I4, k6, k7] + SU3D[I1, k6, k7]* - SU3D[I4, k7, k8])*SU3F[8, I2, k8] + SU3D[I2, k7, k8]* - (SU3D[I4, k6, k7]*SU3F[8, I1, k8] + SU3D[I1, k6, k7]* - SU3F[8, I4, k8]) + SU3D[I2, k6, k7]* - (SU3D[I4, k7, k8]*SU3F[8, I1, k8] + SU3D[I1, k7, k8]* - SU3F[8, I4, k8])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/9)*(SU3D[I2, I3, k5]*SU3F[6, I4, k7]*SU3F[I1, k5, k7] + - SU3D[I1, I4, k5]*SU3F[6, I3, k7]*SU3F[I2, k5, k7] + - SU3D[I1, I3, k5]*SU3F[6, I4, k7]*SU3F[I2, k5, k7] + - SU3D[I3, I4, k5]*(SU3F[6, I2, k7]*SU3F[I1, k5, k7] + - SU3F[6, I1, k7]*SU3F[I2, k5, k7]) + SU3D[I1, I4, k5]*SU3F[6, I2, k7]* - SU3F[I3, k5, k7] + SU3D[I1, I2, k5]*SU3F[6, I4, k7]* - SU3F[I3, k5, k7] + SU3D[I2, I4, k5]* - (SU3F[6, I3, k7]*SU3F[I1, k5, k7] + SU3F[6, I1, k7]* - SU3F[I3, k5, k7]) + SU3D[I2, I3, k5]*SU3F[6, I1, k7]* - SU3F[I4, k5, k7] + SU3D[I1, I3, k5]*SU3F[6, I2, k7]* - SU3F[I4, k5, k7] + SU3D[I1, I2, k5]*SU3F[6, I3, k7]* - SU3F[I4, k5, k7]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (SU3D[6, I2, k6]*SU3D[I3, I4, k7]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3D[I3, I4, k7]*SU3F[I2, k6, k7] + - SU3D[6, I2, k6]*SU3D[I1, I4, k7]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[I2, I4, k7]*SU3F[I3, k6, k7] + - SU3D[6, I4, k6]*(SU3D[I2, I3, k7]*SU3F[I1, k6, k7] + - SU3D[I1, I3, k7]*SU3F[I2, k6, k7] + SU3D[I1, I2, k7]* - SU3F[I3, k6, k7]) + SU3D[6, I2, k6]*SU3D[I1, I3, k7]* - SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, I3, k7]*SU3F[I4, k6, k7] + - SU3D[6, I3, k6]*(SU3D[I2, I4, k7]*SU3F[I1, k6, k7] + - SU3D[I1, I4, k7]*SU3F[I2, k6, k7] + SU3D[I1, I2, k7]* - SU3F[I4, k6, k7]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[3, I2, k8]*SU3D[6, I4, k6]*SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + - SU3D[3, I2, k8]*SU3D[6, I3, k6]*SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + - SU3D[3, I1, k8]*SU3D[6, I4, k6]*SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + - SU3D[3, I1, k8]*SU3D[6, I3, k6]*SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + - SU3D[3, I2, k8]*SU3D[6, I4, k6]*SU3D[I1, k7, k8]*SU3F[I3, k6, k7] + - SU3D[3, I1, k8]*SU3D[6, I4, k6]*SU3D[I2, k7, k8]*SU3F[I3, k6, k7] + - SU3D[3, I2, k8]*SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[3, I1, k8]*SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[3, I4, k8]*(SU3D[6, I3, k6]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[6, I2, k6]* - (SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I3, k6, k7]) + SU3D[6, I1, k6]* - (SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I3, k6, k7])) + SU3D[3, I2, k8]*SU3D[6, I3, k6]* - SU3D[I1, k7, k8]*SU3F[I4, k6, k7] + SU3D[3, I1, k8]*SU3D[6, I3, k6]* - SU3D[I2, k7, k8]*SU3F[I4, k6, k7] + SU3D[3, I2, k8]*SU3D[6, I1, k6]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[3, I1, k8]*SU3D[6, I2, k6]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[3, I3, k8]* - (SU3D[6, I4, k6]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[6, I2, k6]* - (SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I4, k6, k7]) + SU3D[6, I1, k6]* - (SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I4, k6, k7])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I3, k8]*SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I3, k8]*SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I1, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I2, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I1, k8]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I2, k8]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I4, k6]*(SU3D[8, I3, k8]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[8, I2, k8]* - (SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I3, k6, k7]) + SU3D[8, I1, k8]* - (SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I3, k6, k7])) + SU3D[6, I2, k6]*SU3D[8, I3, k8]* - SU3D[I1, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[8, I3, k8]* - SU3D[I2, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I2, k6]*SU3D[8, I1, k8]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[8, I2, k8]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I3, k6]* - (SU3D[8, I4, k8]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[8, I2, k8]* - (SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I4, k6, k7]) + SU3D[8, I1, k8]* - (SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I4, k6, k7])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/12)*(SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[3, I3, k8]* - SU3F[I1, k6, k7] + SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3F[3, I4, k8]* - SU3F[I1, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[3, I3, k8]* - SU3F[I2, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3F[3, I4, k8]* - SU3F[I2, k6, k7] + SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[3, I1, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[3, I2, k8]* - SU3F[I3, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3F[3, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3F[3, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[3, I2, k8]*SU3F[I1, k6, k7] + - SU3F[3, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[3, I3, k8]*SU3F[I1, k6, k7] + SU3F[3, I1, k8]* - SU3F[I3, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[3, I3, k8]*SU3F[I2, k6, k7] + SU3F[3, I2, k8]* - SU3F[I3, k6, k7])) + SU3D[6, I2, k6]*SU3D[I3, k7, k8]* - SU3F[3, I1, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]* - SU3F[3, I2, k8]*SU3F[I4, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3F[3, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3F[3, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[3, I2, k8]*SU3F[I1, k6, k7] + - SU3F[3, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[3, I4, k8]*SU3F[I1, k6, k7] + SU3F[3, I1, k8]* - SU3F[I4, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[3, I4, k8]*SU3F[I2, k6, k7] + SU3F[3, I2, k8]* - SU3F[I4, k6, k7]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/12)*(SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[8, I3, k8]* - SU3F[I1, k6, k7] + SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3F[8, I4, k8]* - SU3F[I1, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[8, I3, k8]* - SU3F[I2, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3F[8, I4, k8]* - SU3F[I2, k6, k7] + SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[8, I1, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[8, I2, k8]* - SU3F[I3, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3F[8, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3F[8, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[8, I2, k8]*SU3F[I1, k6, k7] + - SU3F[8, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k7] + SU3F[8, I1, k8]* - SU3F[I3, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k7] + SU3F[8, I2, k8]* - SU3F[I3, k6, k7])) + SU3D[6, I2, k6]*SU3D[I3, k7, k8]* - SU3F[8, I1, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]* - SU3F[8, I2, k8]*SU3F[I4, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3F[8, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3F[8, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[8, I2, k8]*SU3F[I1, k6, k7] + - SU3F[8, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[8, I4, k8]*SU3F[I1, k6, k7] + SU3F[8, I1, k8]* - SU3F[I4, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[8, I4, k8]*SU3F[I2, k6, k7] + SU3F[8, I2, k8]* - SU3F[I4, k6, k7]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/12)*(SU3D[3, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] + SU3D[3, I2, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] + SU3D[3, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] + SU3D[3, I1, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k8] + SU3D[3, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] + SU3D[3, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k8] + SU3D[3, I2, k6]*SU3D[I1, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[3, I1, k6]*SU3D[I2, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[3, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I3, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I3, k6, k8])) + SU3D[3, I2, k6]*SU3D[I3, k7, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] + SU3D[3, I1, k6]*SU3D[I3, k7, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k8] + SU3D[3, I2, k6]*SU3D[I1, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[3, I1, k6]*SU3D[I2, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[3, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I4, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I4, k6, k8]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/12)*(SU3D[8, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] + SU3D[8, I2, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] + SU3D[8, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] + SU3D[8, I1, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k8] + SU3D[8, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] + SU3D[8, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k8] + SU3D[8, I2, k6]*SU3D[I1, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[8, I1, k6]*SU3D[I2, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[8, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I3, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I3, k6, k8])) + SU3D[8, I2, k6]*SU3D[I3, k7, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3D[I3, k7, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3D[I1, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3D[I2, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[8, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I4, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I4, k6, k8]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, k5, k6]*SU3F[3, I4, k9]*SU3F[6, I3, k5]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I3, k9]*SU3F[6, I4, k5]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I4, k9]*SU3F[6, I3, k5]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I3, k9]*SU3F[6, I4, k5]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I4, k9]*SU3F[6, I1, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I4, k9]*SU3F[6, I2, k5]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I1, k9]*SU3F[6, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I2, k9]*SU3F[6, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[3, I3, k9]*(SU3F[6, I2, k5]*SU3F[I1, k6, k9] + - SU3F[6, I1, k5]*SU3F[I2, k6, k9]) + SU3F[3, I2, k9]* - (SU3F[6, I3, k5]*SU3F[I1, k6, k9] + SU3F[6, I1, k5]* - SU3F[I3, k6, k9]) + SU3F[3, I1, k9]* - (SU3F[6, I3, k5]*SU3F[I2, k6, k9] + SU3F[6, I2, k5]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[3, I3, k9]* - SU3F[6, I1, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[3, I3, k9]* - SU3F[6, I2, k5]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[3, I1, k9]* - SU3F[6, I3, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[3, I2, k9]* - SU3F[6, I3, k5]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[3, I4, k9]*(SU3F[6, I2, k5]*SU3F[I1, k6, k9] + - SU3F[6, I1, k5]*SU3F[I2, k6, k9]) + SU3F[3, I2, k9]* - (SU3F[6, I4, k5]*SU3F[I1, k6, k9] + SU3F[6, I1, k5]* - SU3F[I4, k6, k9]) + SU3F[3, I1, k9]* - (SU3F[6, I4, k5]*SU3F[I2, k6, k9] + SU3F[6, I2, k5]* - SU3F[I4, k6, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[6, I3, k9]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I3, k5]*SU3F[6, I4, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I4, k5]*SU3F[6, I3, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I3, k5]*SU3F[6, I4, k9]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[6, I1, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I4, k5]*SU3F[6, I2, k9]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I1, k5]*SU3F[6, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I2, k5]*SU3F[6, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[3, I3, k5]*(SU3F[6, I2, k9]*SU3F[I1, k6, k9] + - SU3F[6, I1, k9]*SU3F[I2, k6, k9]) + SU3F[3, I2, k5]* - (SU3F[6, I3, k9]*SU3F[I1, k6, k9] + SU3F[6, I1, k9]* - SU3F[I3, k6, k9]) + SU3F[3, I1, k5]* - (SU3F[6, I3, k9]*SU3F[I2, k6, k9] + SU3F[6, I2, k9]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[3, I3, k5]* - SU3F[6, I1, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[3, I3, k5]* - SU3F[6, I2, k9]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[3, I1, k5]* - SU3F[6, I3, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[3, I2, k5]* - SU3F[6, I3, k9]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[3, I4, k5]*(SU3F[6, I2, k9]*SU3F[I1, k6, k9] + - SU3F[6, I1, k9]*SU3F[I2, k6, k9]) + SU3F[3, I2, k5]* - (SU3F[6, I4, k9]*SU3F[I1, k6, k9] + SU3F[6, I1, k9]* - SU3F[I4, k6, k9]) + SU3F[3, I1, k5]* - (SU3F[6, I4, k9]*SU3F[I2, k6, k9] + SU3F[6, I2, k9]* - SU3F[I4, k6, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[I2, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I3, k5]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I3, k9]*SU3F[8, I4, k5]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I3, k5]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I3, k9]*SU3F[8, I4, k5]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I1, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I2, k5]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I1, k9]*SU3F[8, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I2, k9]*SU3F[8, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[6, I3, k9]*(SU3F[8, I2, k5]*SU3F[I1, k6, k9] + - SU3F[8, I1, k5]*SU3F[I2, k6, k9]) + SU3F[6, I2, k9]* - (SU3F[8, I3, k5]*SU3F[I1, k6, k9] + SU3F[8, I1, k5]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k9]* - (SU3F[8, I3, k5]*SU3F[I2, k6, k9] + SU3F[8, I2, k5]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[6, I3, k9]* - SU3F[8, I1, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I3, k9]* - SU3F[8, I2, k5]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[6, I1, k9]* - SU3F[8, I3, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I2, k9]* - SU3F[8, I3, k5]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[6, I4, k9]*(SU3F[8, I2, k5]*SU3F[I1, k6, k9] + - SU3F[8, I1, k5]*SU3F[I2, k6, k9]) + SU3F[6, I2, k9]* - (SU3F[8, I4, k5]*SU3F[I1, k6, k9] + SU3F[8, I1, k5]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k9]* - (SU3F[8, I4, k5]*SU3F[I2, k6, k9] + SU3F[8, I2, k5]* - SU3F[I4, k6, k9])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I3, k9]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I3, k5]*SU3F[8, I4, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I3, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]*SU3F[8, I4, k9]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I1, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I2, k9]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[6, I3, k5]*(SU3F[8, I2, k9]*SU3F[I1, k6, k9] + - SU3F[8, I1, k9]*SU3F[I2, k6, k9]) + SU3F[6, I2, k5]* - (SU3F[8, I3, k9]*SU3F[I1, k6, k9] + SU3F[8, I1, k9]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k5]* - (SU3F[8, I3, k9]*SU3F[I2, k6, k9] + SU3F[8, I2, k9]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I1, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I2, k9]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[6, I1, k5]* - SU3F[8, I3, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I2, k5]* - SU3F[8, I3, k9]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[6, I4, k5]*(SU3F[8, I2, k9]*SU3F[I1, k6, k9] + - SU3F[8, I1, k9]*SU3F[I2, k6, k9]) + SU3F[6, I2, k5]* - (SU3F[8, I4, k9]*SU3F[I1, k6, k9] + SU3F[8, I1, k9]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k5]* - (SU3F[8, I4, k9]*SU3F[I2, k6, k9] + SU3F[8, I2, k9]* - SU3F[I4, k6, k9])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[3, I2, k8]*SU3D[6, I4, k6]*SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + - SU3D[3, I2, k8]*SU3D[6, I3, k6]*SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + - SU3D[3, I1, k8]*SU3D[6, I4, k6]*SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + - SU3D[3, I1, k8]*SU3D[6, I3, k6]*SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + - SU3D[3, I2, k8]*SU3D[6, I4, k6]*SU3D[I1, k6, k7]*SU3F[I3, k7, k8] + - SU3D[3, I1, k8]*SU3D[6, I4, k6]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8] + - SU3D[3, I2, k8]*SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[3, I1, k8]*SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[3, I4, k8]*(SU3D[6, I3, k6]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[6, I2, k6]* - (SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I3, k7, k8]) + SU3D[6, I1, k6]* - (SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I3, k7, k8])) + SU3D[3, I2, k8]*SU3D[6, I3, k6]* - SU3D[I1, k6, k7]*SU3F[I4, k7, k8] + SU3D[3, I1, k8]*SU3D[6, I3, k6]* - SU3D[I2, k6, k7]*SU3F[I4, k7, k8] + SU3D[3, I2, k8]*SU3D[6, I1, k6]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[3, I1, k8]*SU3D[6, I2, k6]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[3, I3, k8]* - (SU3D[6, I4, k6]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[6, I2, k6]* - (SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I4, k7, k8]) + SU3D[6, I1, k6]* - (SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I4, k7, k8])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I3, k8]*SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I1, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I1, k8]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I4, k6]*(SU3D[8, I3, k8]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[8, I2, k8]* - (SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I3, k7, k8]) + SU3D[8, I1, k8]* - (SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I3, k7, k8])) + SU3D[6, I2, k6]*SU3D[8, I3, k8]* - SU3D[I1, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I1, k6]*SU3D[8, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I2, k6]*SU3D[8, I1, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I1, k6]*SU3D[8, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I3, k6]* - (SU3D[8, I4, k8]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[8, I2, k8]* - (SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I4, k7, k8]) + SU3D[8, I1, k8]* - (SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I4, k7, k8])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/12)*(SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k9]* - SU3F[I1, k7, k9] + SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3F[3, I4, k9]* - SU3F[I1, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k9]* - SU3F[I2, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3F[3, I4, k9]* - SU3F[I2, k7, k9] + SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[3, I1, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[3, I2, k9]* - SU3F[I3, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3F[3, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3F[3, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[3, I2, k9]*SU3F[I1, k7, k9] + - SU3F[3, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[3, I3, k9]*SU3F[I1, k7, k9] + SU3F[3, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[3, I3, k9]*SU3F[I2, k7, k9] + SU3F[3, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[6, I2, k6]*SU3D[I3, k6, k7]* - SU3F[3, I1, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]* - SU3F[3, I2, k9]*SU3F[I4, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3F[3, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3F[3, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k9]*SU3F[I1, k7, k9] + - SU3F[3, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k9]*SU3F[I1, k7, k9] + SU3F[3, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k9]*SU3F[I2, k7, k9] + SU3F[3, I2, k9]* - SU3F[I4, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/12)*(SU3D[3, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + SU3D[3, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] + SU3D[3, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] + SU3D[3, I1, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9] + SU3D[3, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] + SU3D[3, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9] + SU3D[3, I2, k6]*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[3, I1, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[3, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[3, I2, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] + SU3D[3, I1, k6]*SU3D[I3, k6, k7]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] + SU3D[3, I2, k6]*SU3D[I1, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[3, I1, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[3, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I4, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/12)*(SU3D[8, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + SU3D[8, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] + SU3D[8, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] + SU3D[8, I1, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9] + SU3D[8, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] + SU3D[8, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9] + SU3D[8, I2, k6]*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[8, I1, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[8, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[8, I2, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] + SU3D[8, I1, k6]*SU3D[I3, k6, k7]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] + SU3D[8, I2, k6]*SU3D[I1, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[8, I1, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[8, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/12)*(SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k9]* - SU3F[I1, k7, k9] + SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3F[8, I4, k9]* - SU3F[I1, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k9]* - SU3F[I2, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3F[8, I4, k9]* - SU3F[I2, k7, k9] + SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[8, I1, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[8, I2, k9]* - SU3F[I3, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3F[8, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3F[8, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[8, I2, k9]*SU3F[I1, k7, k9] + - SU3F[8, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I3, k9]*SU3F[I1, k7, k9] + SU3F[8, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I3, k9]*SU3F[I2, k7, k9] + SU3F[8, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[6, I2, k6]*SU3D[I3, k6, k7]* - SU3F[8, I1, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]* - SU3F[8, I2, k9]*SU3F[I4, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3F[8, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3F[8, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k9]*SU3F[I1, k7, k9] + - SU3F[8, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k9]*SU3F[I1, k7, k9] + SU3F[8, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k9]*SU3F[I2, k7, k9] + SU3F[8, I2, k9]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/12)*(SU3F[3, I2, k9]*SU3F[6, I4, k8]*SU3F[I1, k7, k9]* - SU3F[I3, k7, k8] + SU3F[3, I1, k9]*SU3F[6, I4, k8]*SU3F[I2, k7, k9]* - SU3F[I3, k7, k8] + SU3F[3, I2, k9]*SU3F[6, I4, k8]*SU3F[I1, k7, k8]* - SU3F[I3, k7, k9] + SU3F[3, I1, k9]*SU3F[6, I4, k8]*SU3F[I2, k7, k8]* - SU3F[I3, k7, k9] + SU3F[3, I4, k9]* - (SU3F[6, I3, k8]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[6, I2, k8]* - (SU3F[I1, k7, k9]*SU3F[I3, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I3, k7, k9]) + SU3F[6, I1, k8]* - (SU3F[I2, k7, k9]*SU3F[I3, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I3, k7, k9])) + SU3F[3, I2, k9]*SU3F[6, I3, k8]* - SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[3, I1, k9]*SU3F[6, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[3, I2, k9]*SU3F[6, I1, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[3, I1, k9]*SU3F[6, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[3, I2, k9]*SU3F[6, I3, k8]* - SU3F[I1, k7, k8]*SU3F[I4, k7, k9] + SU3F[3, I1, k9]*SU3F[6, I3, k8]* - SU3F[I2, k7, k8]*SU3F[I4, k7, k9] + SU3F[3, I2, k9]*SU3F[6, I1, k8]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[3, I1, k9]*SU3F[6, I2, k8]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[3, I3, k9]* - (SU3F[6, I4, k8]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[6, I2, k8]* - (SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I4, k7, k9]) + SU3F[6, I1, k8]* - (SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I4, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3F[6, I2, k8]*SU3F[8, I4, k9]*SU3F[I1, k7, k9]* - SU3F[I3, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I4, k9]*SU3F[I2, k7, k9]* - SU3F[I3, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I4, k9]*SU3F[I1, k7, k8]* - SU3F[I3, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I4, k9]*SU3F[I2, k7, k8]* - SU3F[I3, k7, k9] + SU3F[6, I4, k8]* - (SU3F[8, I3, k9]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I3, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I3, k7, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k7, k9]*SU3F[I3, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I3, k7, k9])) + SU3F[6, I2, k8]*SU3F[8, I3, k9]* - SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I3, k9]* - SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I1, k9]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I2, k9]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I3, k9]* - SU3F[I1, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I3, k9]* - SU3F[I2, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I2, k8]*SU3F[8, I1, k9]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I2, k9]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I3, k8]* - (SU3F[8, I4, k9]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I4, k7, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[6, I2, k5]*SU3F[3, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I1, k5]*SU3F[3, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I2, k5]*SU3F[3, I4, k9]*SU3F[I1, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I1, k5]*SU3F[3, I4, k9]*SU3F[I2, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I4, k5]*(SU3F[3, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[3, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I3, k8, k9]) + SU3F[3, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I3, k8, k9])) + SU3D[6, I2, k5]*SU3F[3, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[3, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[3, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[3, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[3, I3, k9]* - SU3F[I1, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[3, I3, k9]* - SU3F[I2, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I2, k5]*SU3F[3, I1, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[3, I2, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I3, k5]* - (SU3F[3, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[3, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I4, k8, k9]) + SU3F[3, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I1, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I2, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I4, k5]*(SU3F[8, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I3, k8, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I3, k8, k9])) + SU3D[6, I2, k5]*SU3F[8, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[8, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[8, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[8, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[8, I3, k9]* - SU3F[I1, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[8, I3, k9]* - SU3F[I2, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I2, k5]*SU3F[8, I1, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[8, I2, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I3, k5]* - (SU3F[8, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I4, k8, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I4, k8, k9])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[3, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + - SU3D[3, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + - SU3D[3, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9] + - SU3D[3, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k6, k8]*SU3F[I3, k8, k9] + - SU3D[3, I4, k6]*(SU3F[6, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I3, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I3, k8, k9])) + SU3D[3, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3D[3, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3D[3, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[3, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[3, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k6, k8]*SU3F[I4, k8, k9] + SU3D[3, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9] + SU3D[3, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[3, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[3, I3, k6]* - (SU3F[6, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I4, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[8, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + - SU3D[8, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + - SU3D[8, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9] + - SU3D[8, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k6, k8]*SU3F[I3, k8, k9] + - SU3D[8, I4, k6]*(SU3F[6, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I3, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I3, k8, k9])) + SU3D[8, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I3, k6]* - (SU3F[6, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I4, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I4, k8, k9])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/12)*(SU3D[3, I2, k6]*SU3D[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + SU3D[3, I1, k6]*SU3D[6, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9] + SU3D[3, I2, k6]*SU3D[6, I4, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + SU3D[3, I1, k6]*SU3D[6, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + SU3D[3, I4, k6]* - (SU3D[6, I3, k8]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[6, I2, k8]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]) + SU3D[6, I1, k8]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])) + SU3D[3, I2, k6]*SU3D[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[3, I1, k6]*SU3D[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3D[3, I2, k6]*SU3D[6, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[3, I1, k6]*SU3D[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[3, I2, k6]*SU3D[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + SU3D[3, I1, k6]*SU3D[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[3, I2, k6]*SU3D[6, I1, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[3, I1, k6]*SU3D[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[3, I3, k6]* - (SU3D[6, I4, k8]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[6, I2, k8]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[6, I1, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3D[6, I2, k8]*SU3D[8, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I4, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I4, k6]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I4, k6]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + SU3D[6, I4, k8]* - (SU3D[8, I3, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[8, I2, k6]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]) + SU3D[8, I1, k6]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])) + SU3D[6, I2, k8]*SU3D[8, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I1, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I3, k6]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I2, k8]*SU3D[8, I1, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I3, k8]* - (SU3D[8, I4, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[8, I2, k6]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[8, I1, k6]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[3, I1] + - SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[3, I2] + - SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[3, I2] + - SU3D[I3, I4, k5]*(SU3F[6, I2, k5]*SUNDelta[3, I1] + - SU3F[6, I1, k5]*SUNDelta[3, I2]) + SU3D[I1, I4, k5]*SU3F[6, I2, k5]* - SUNDelta[3, I3] + SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[3, I3] + - SU3D[I2, I4, k5]*(SU3F[6, I3, k5]*SUNDelta[3, I1] + - SU3F[6, I1, k5]*SUNDelta[3, I3]) + SU3D[I2, I3, k5]*SU3F[6, I1, k5]* - SUNDelta[3, I4] + SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[3, I4] + - SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/9)*(SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[3, I1] + - SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[3, I2] + - SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[3, I3] + - SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[3, I3] + - SU3D[6, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[3, I1] + - SU3D[I1, I3, k5]*SUNDelta[3, I2] + SU3D[I1, I2, k5]* - SUNDelta[3, I3]) + SU3D[6, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[3, I4] + SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[3, I4] + - SU3D[6, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[3, I1] + - SU3D[I1, I4, k5]*SUNDelta[3, I2] + SU3D[I1, I2, k5]* - SUNDelta[3, I4])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (((4*I)/9)*(SU3D[I2, I3, I4]*SUNDelta[6, I1] + SU3D[I1, I3, I4]* - SUNDelta[6, I2] + SU3D[I1, I2, I4]*SUNDelta[6, I3] + - SU3D[I1, I2, I3]*SUNDelta[6, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[I2, I3, k5]*SU3F[3, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SU3F[3, I3, k5]*SUNDelta[6, I2] + - SU3D[I1, I3, k5]*SU3F[3, I4, k5]*SUNDelta[6, I2] + - SU3D[I3, I4, k5]*(SU3F[3, I2, k5]*SUNDelta[6, I1] + - SU3F[3, I1, k5]*SUNDelta[6, I2]) + SU3D[I1, I4, k5]*SU3F[3, I2, k5]* - SUNDelta[6, I3] + SU3D[I1, I2, k5]*SU3F[3, I4, k5]*SUNDelta[6, I3] + - SU3D[I2, I4, k5]*(SU3F[3, I3, k5]*SUNDelta[6, I1] + - SU3F[3, I1, k5]*SUNDelta[6, I3]) + SU3D[I2, I3, k5]*SU3F[3, I1, k5]* - SUNDelta[6, I4] + SU3D[I1, I3, k5]*SU3F[3, I2, k5]*SUNDelta[6, I4] + - SU3D[I1, I2, k5]*SU3F[3, I3, k5]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[I2, I3, k5]*SU3F[8, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SU3F[8, I3, k5]*SUNDelta[6, I2] + - SU3D[I1, I3, k5]*SU3F[8, I4, k5]*SUNDelta[6, I2] + - SU3D[I3, I4, k5]*(SU3F[8, I2, k5]*SUNDelta[6, I1] + - SU3F[8, I1, k5]*SUNDelta[6, I2]) + SU3D[I1, I4, k5]*SU3F[8, I2, k5]* - SUNDelta[6, I3] + SU3D[I1, I2, k5]*SU3F[8, I4, k5]*SUNDelta[6, I3] + - SU3D[I2, I4, k5]*(SU3F[8, I3, k5]*SUNDelta[6, I1] + - SU3F[8, I1, k5]*SUNDelta[6, I3]) + SU3D[I2, I3, k5]*SU3F[8, I1, k5]* - SUNDelta[6, I4] + SU3D[I1, I3, k5]*SU3F[8, I2, k5]*SUNDelta[6, I4] + - SU3D[I1, I2, k5]*SU3F[8, I3, k5]*SUNDelta[6, I4])/ - (9*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/9)*(SU3D[3, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I1] + - SU3D[3, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I2] + - SU3D[3, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[6, I3] + - SU3D[3, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[6, I3] + - SU3D[3, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[6, I1] + - SU3D[I1, I3, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I3]) + SU3D[3, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[6, I4] + SU3D[3, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[6, I4] + - SU3D[3, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I4])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/9)*(SU3D[8, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I1] + - SU3D[8, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I2] + - SU3D[8, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[6, I3] + - SU3D[8, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[6, I3] + - SU3D[8, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[6, I1] + - SU3D[I1, I3, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I3]) + SU3D[8, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[6, I4] + SU3D[8, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[6, I4] + - SU3D[8, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I4])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/9)*(SU3D[I1, I4, k9]*SU3D[I2, k6, k9]*SU3D[I3, k5, k6] + - SU3D[I1, I4, k9]*SU3D[I2, k5, k6]*SU3D[I3, k6, k9] + - SU3D[I1, I3, k9]*SU3D[I2, k6, k9]*SU3D[I4, k5, k6] + - SU3D[I1, I2, k9]*SU3D[I3, k6, k9]*SU3D[I4, k5, k6] + - SU3D[I1, k6, k9]*(SU3D[I2, k5, k6]*SU3D[I3, I4, k9] + - SU3D[I2, I4, k9]*SU3D[I3, k5, k6] + SU3D[I2, I3, k9]* - SU3D[I4, k5, k6]) + SU3D[I1, I3, k9]*SU3D[I2, k5, k6]* - SU3D[I4, k6, k9] + SU3D[I1, I2, k9]*SU3D[I3, k5, k6]* - SU3D[I4, k6, k9] + SU3D[I1, k5, k6]* - (SU3D[I2, k6, k9]*SU3D[I3, I4, k9] + SU3D[I2, I4, k9]* - SU3D[I3, k6, k9] + SU3D[I2, I3, k9]*SU3D[I4, k6, k9]))* - SUNDelta[6, k5])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3F[I3, k7, k8] + - SU3D[I2, I4, k9]*(SU3D[I3, k8, k9]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3F[I3, k7, k8]) + SU3D[I1, k8, k9]* - SU3D[I2, I3, k9]*SU3F[I4, k7, k8] + SU3D[I1, I2, k9]*SU3D[I3, k8, k9]* - SU3F[I4, k7, k8] + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k9]*SU3F[I1, k7, k8] + SU3D[I1, I4, k9]* - SU3F[I3, k7, k8] + SU3D[I1, I3, k9]*SU3F[I4, k7, k8]))* - SUNDelta[6, k7])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3F[I2, k8, k9] + - SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3F[I2, k8, k9] + - SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3F[I2, k8, k9] + - SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3F[I3, k8, k9] + - SU3D[I2, I4, k9]*(SU3D[I3, k7, k8]*SU3F[I1, k8, k9] + - SU3D[I1, k7, k8]*SU3F[I3, k8, k9]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k9]*SU3F[I4, k8, k9] + SU3D[I1, I2, k9]*SU3D[I3, k7, k8]* - SU3F[I4, k8, k9] + SU3D[I2, k7, k8]* - (SU3D[I3, I4, k9]*SU3F[I1, k8, k9] + SU3D[I1, I4, k9]* - SU3F[I3, k8, k9] + SU3D[I1, I3, k9]*SU3F[I4, k8, k9]))* - SUNDelta[6, k7])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/9)*(SU3D[I3, I4, k5]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k9] + - SU3F[I1, k5, k9]*SU3F[I2, k8, k9]) + SU3D[I1, I4, k5]* - SU3F[I2, k8, k9]*SU3F[I3, k5, k9] + SU3D[I1, I4, k5]*SU3F[I2, k5, k9]* - SU3F[I3, k8, k9] + SU3D[I2, I4, k5]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k9] + SU3F[I1, k5, k9]* - SU3F[I3, k8, k9]) + SU3D[I2, I3, k5]*SU3F[I1, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I1, I3, k5]*SU3F[I2, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I1, I2, k5]*SU3F[I3, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I2, I3, k5]*SU3F[I1, k5, k9]* - SU3F[I4, k8, k9] + SU3D[I1, I3, k5]*SU3F[I2, k5, k9]* - SU3F[I4, k8, k9] + SU3D[I1, I2, k5]*SU3F[I3, k5, k9]* - SU3F[I4, k8, k9])*SUNDelta[6, k8])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[8, I1] + - SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[8, I2] + - SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[8, I2] + - SU3D[I3, I4, k5]*(SU3F[6, I2, k5]*SUNDelta[8, I1] + - SU3F[6, I1, k5]*SUNDelta[8, I2]) + SU3D[I1, I4, k5]*SU3F[6, I2, k5]* - SUNDelta[8, I3] + SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[8, I3] + - SU3D[I2, I4, k5]*(SU3F[6, I3, k5]*SUNDelta[8, I1] + - SU3F[6, I1, k5]*SUNDelta[8, I3]) + SU3D[I2, I3, k5]*SU3F[6, I1, k5]* - SUNDelta[8, I4] + SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[8, I4] + - SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[8, I4])/ - (9*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/9)*(SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[8, I1] + - SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[8, I2] + - SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[8, I3] + - SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[8, I3] + - SU3D[6, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[8, I1] + - SU3D[I1, I3, k5]*SUNDelta[8, I2] + SU3D[I1, I2, k5]* - SUNDelta[8, I3]) + SU3D[6, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[8, I4] + SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[8, I4] + - SU3D[6, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[8, I1] + - SU3D[I1, I4, k5]*SUNDelta[8, I2] + SU3D[I1, I2, k5]* - SUNDelta[8, I4])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (((4*I)/27)*(SU3D[6, I3, I4]*SUNDelta[I1, I2] + SU3D[6, I2, I4]* - SUNDelta[I1, I3] + SU3D[6, I2, I3]*SUNDelta[I1, I4] + - SU3D[6, I1, I4]*SUNDelta[I2, I3] + SU3D[6, I1, I3]*SUNDelta[I2, I4] + - SU3D[6, I1, I2]*SUNDelta[I3, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (((4*I)/27)*SUNDelta[6, k4]*(SU3D[I3, I4, k4]*SUNDelta[I1, I2] + - SU3D[I2, I4, k4]*SUNDelta[I1, I3] + SU3D[I2, I3, k4]* - SUNDelta[I1, I4] + SU3D[I1, I4, k4]*SUNDelta[I2, I3] + - SU3D[I1, I3, k4]*SUNDelta[I2, I4] + SU3D[I1, I2, k4]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (((2*I)/27)*(SUNDelta[3, I2]*SUNDelta[6, I4]*SUNDelta[I1, I3] + - SUNDelta[3, I2]*SUNDelta[6, I3]*SUNDelta[I1, I4] + - SUNDelta[3, I1]*SUNDelta[6, I4]*SUNDelta[I2, I3] + - SUNDelta[3, I4]*(SUNDelta[6, I3]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I3] + SUNDelta[6, I1]* - SUNDelta[I2, I3]) + SUNDelta[3, I1]*SUNDelta[6, I3]* - SUNDelta[I2, I4] + SUNDelta[3, I3]* - (SUNDelta[6, I4]*SUNDelta[I1, I2] + SUNDelta[6, I2]* - SUNDelta[I1, I4] + SUNDelta[6, I1]*SUNDelta[I2, I4]) + - SUNDelta[3, I2]*SUNDelta[6, I1]*SUNDelta[I3, I4] + - SUNDelta[3, I1]*SUNDelta[6, I2]*SUNDelta[I3, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((2*I)/27)*(SUNDelta[6, I2]*SUNDelta[8, I4]*SUNDelta[I1, I3] + - SUNDelta[6, I2]*SUNDelta[8, I3]*SUNDelta[I1, I4] + - SUNDelta[6, I1]*SUNDelta[8, I4]*SUNDelta[I2, I3] + - SUNDelta[6, I4]*(SUNDelta[8, I3]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I3] + SUNDelta[8, I1]* - SUNDelta[I2, I3]) + SUNDelta[6, I1]*SUNDelta[8, I3]* - SUNDelta[I2, I4] + SUNDelta[6, I3]* - (SUNDelta[8, I4]*SUNDelta[I1, I2] + SUNDelta[8, I2]* - SUNDelta[I1, I4] + SUNDelta[8, I1]*SUNDelta[I2, I4]) + - SUNDelta[6, I2]*SUNDelta[8, I1]*SUNDelta[I3, I4] + - SUNDelta[6, I1]*SUNDelta[8, I2]*SUNDelta[I3, I4]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{CouplingConstant[ChPTW3[2], 2]* -((((2*I)/9)*(SU3D[3, I3, I4]*SU3D[6, I1, I2] + SU3D[3, I2, I4]* - SU3D[6, I1, I3] + SU3D[3, I2, I3]*SU3D[6, I1, I4] + - SU3D[3, I1, I4]*SU3D[6, I2, I3] + SU3D[3, I1, I3]*SU3D[6, I2, I4] + - SU3D[3, I1, I2]*SU3D[6, I3, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (((2*I)/9)*(SU3D[6, I3, I4]*SU3D[8, I1, I2] + SU3D[6, I2, I4]* - SU3D[8, I1, I3] + SU3D[6, I2, I3]*SU3D[8, I1, I4] + - SU3D[6, I1, I4]*SU3D[8, I2, I3] + SU3D[6, I1, I3]*SU3D[8, I2, I4] + - SU3D[6, I1, I2]*SU3D[8, I3, I4]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/9)*(SU3D[6, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6] + - SU3D[6, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6] + - SU3D[6, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6] + - SU3D[6, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6] + - SU3D[6, I4, k5]*(SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - SU3D[I1, I3, k6]*SU3D[I2, k5, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k5, k6]) + SU3D[6, I2, k5]*SU3D[I1, I3, k6]* - SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[I2, I3, k6]* - SU3D[I4, k5, k6] + SU3D[6, I3, k5]* - (SU3D[I1, k5, k6]*SU3D[I2, I4, k6] + SU3D[I1, I4, k6]* - SU3D[I2, k5, k6] + SU3D[I1, I2, k6]*SU3D[I4, k5, k6])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - ((I/12)*(SU3D[3, I2, k8]*SU3D[6, I4, k5]*SU3D[I1, k6, k8]* - SU3D[I3, k5, k6] + SU3D[3, I1, k8]*SU3D[6, I4, k5]*SU3D[I2, k6, k8]* - SU3D[I3, k5, k6] + SU3D[3, I2, k8]*SU3D[6, I4, k5]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k8] + SU3D[3, I1, k8]*SU3D[6, I4, k5]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k8] + SU3D[3, I4, k8]* - (SU3D[6, I3, k5]*(SU3D[I1, k6, k8]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k8]) + SU3D[6, I2, k5]* - (SU3D[I1, k6, k8]*SU3D[I3, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I3, k6, k8]) + SU3D[6, I1, k5]* - (SU3D[I2, k6, k8]*SU3D[I3, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I3, k6, k8])) + SU3D[3, I2, k8]*SU3D[6, I3, k5]* - SU3D[I1, k6, k8]*SU3D[I4, k5, k6] + SU3D[3, I1, k8]*SU3D[6, I3, k5]* - SU3D[I2, k6, k8]*SU3D[I4, k5, k6] + SU3D[3, I2, k8]*SU3D[6, I1, k5]* - SU3D[I3, k6, k8]*SU3D[I4, k5, k6] + SU3D[3, I1, k8]*SU3D[6, I2, k5]* - SU3D[I3, k6, k8]*SU3D[I4, k5, k6] + SU3D[3, I2, k8]*SU3D[6, I3, k5]* - SU3D[I1, k5, k6]*SU3D[I4, k6, k8] + SU3D[3, I1, k8]*SU3D[6, I3, k5]* - SU3D[I2, k5, k6]*SU3D[I4, k6, k8] + SU3D[3, I2, k8]*SU3D[6, I1, k5]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k8] + SU3D[3, I1, k8]*SU3D[6, I2, k5]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k8] + SU3D[3, I3, k8]* - (SU3D[6, I4, k5]*(SU3D[I1, k6, k8]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k8]) + SU3D[6, I2, k5]* - (SU3D[I1, k6, k8]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k8]) + SU3D[6, I1, k5]* - (SU3D[I2, k6, k8]*SU3D[I4, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I4, k6, k8]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3D[6, I2, k5]*SU3D[8, I4, k8]*SU3D[I1, k6, k8]* - SU3D[I3, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I4, k8]*SU3D[I2, k6, k8]* - SU3D[I3, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I4, k8]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k8] + SU3D[6, I1, k5]*SU3D[8, I4, k8]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k8] + SU3D[6, I4, k5]* - (SU3D[8, I3, k8]*(SU3D[I1, k6, k8]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k8]) + SU3D[8, I2, k8]* - (SU3D[I1, k6, k8]*SU3D[I3, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I3, k6, k8]) + SU3D[8, I1, k8]* - (SU3D[I2, k6, k8]*SU3D[I3, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I3, k6, k8])) + SU3D[6, I2, k5]*SU3D[8, I3, k8]* - SU3D[I1, k6, k8]*SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I3, k8]* - SU3D[I2, k6, k8]*SU3D[I4, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I1, k8]* - SU3D[I3, k6, k8]*SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I2, k8]* - SU3D[I3, k6, k8]*SU3D[I4, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I3, k8]* - SU3D[I1, k5, k6]*SU3D[I4, k6, k8] + SU3D[6, I1, k5]*SU3D[8, I3, k8]* - SU3D[I2, k5, k6]*SU3D[I4, k6, k8] + SU3D[6, I2, k5]*SU3D[8, I1, k8]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k8] + SU3D[6, I1, k5]*SU3D[8, I2, k8]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k8] + SU3D[6, I3, k5]* - (SU3D[8, I4, k8]*(SU3D[I1, k6, k8]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k8]) + SU3D[8, I2, k8]* - (SU3D[I1, k6, k8]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k8]) + SU3D[8, I1, k8]* - (SU3D[I2, k6, k8]*SU3D[I4, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I4, k6, k8]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[3, I1, k8] + - SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[3, I1, k8] + - SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[3, I2, k8] + - SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[3, I2, k8] + - SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[3, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[3, I3, k8] + - SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[3, I3, k8] + - SU3D[6, I4, k6]*((SU3D[I1, k7, k8]*SU3D[I3, k6, k7] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8])*SU3F[3, I2, k8] + - SU3D[I2, k7, k8]*(SU3D[I3, k6, k7]*SU3F[3, I1, k8] + - SU3D[I1, k6, k7]*SU3F[3, I3, k8]) + SU3D[I2, k6, k7]* - (SU3D[I3, k7, k8]*SU3F[3, I1, k8] + SU3D[I1, k7, k8]* - SU3F[3, I3, k8])) + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[3, I4, k8] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[3, I4, k8] + SU3D[6, I3, k6]* - ((SU3D[I1, k7, k8]*SU3D[I4, k6, k7] + SU3D[I1, k6, k7]* - SU3D[I4, k7, k8])*SU3F[3, I2, k8] + SU3D[I2, k7, k8]* - (SU3D[I4, k6, k7]*SU3F[3, I1, k8] + SU3D[I1, k6, k7]* - SU3F[3, I4, k8]) + SU3D[I2, k6, k7]* - (SU3D[I4, k7, k8]*SU3F[3, I1, k8] + SU3D[I1, k7, k8]* - SU3F[3, I4, k8])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[6, I2, k5] + - SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[6, I2, k5] + - SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I2, k5] + - SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[I2, I4, k6]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]) + SU3D[I1, k5, k6]*SU3D[I2, I3, k6]* - SU3F[6, I4, k5] + SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[6, I4, k5] + - SU3D[I2, k5, k6]*(SU3D[I3, I4, k6]*SU3F[6, I1, k5] + - SU3D[I1, I4, k6]*SU3F[6, I3, k5] + SU3D[I1, I3, k6]*SU3F[6, I4, k5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[3, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I1, k5] + - SU3D[3, I2, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k5] + - SU3D[3, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I2, k5] + - SU3D[3, I1, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k5] + - SU3D[3, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[3, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[3, I2, k7]*SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[3, I1, k7]*SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[3, I4, k7]*((SU3D[I1, k6, k7]*SU3D[I3, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I3, k6, k7])*SU3F[6, I2, k5] + - SU3D[I2, k6, k7]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]) + SU3D[I2, k5, k6]* - (SU3D[I3, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I3, k5])) + SU3D[3, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[3, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[3, I2, k7]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[3, I1, k7]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[3, I3, k7]* - ((SU3D[I1, k6, k7]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k7])*SU3F[6, I2, k5] + SU3D[I2, k6, k7]* - (SU3D[I4, k5, k6]*SU3F[6, I1, k5] + SU3D[I1, k5, k6]* - SU3F[6, I4, k5]) + SU3D[I2, k5, k6]* - (SU3D[I4, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I4, k5])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[8, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I1, k5] + - SU3D[8, I2, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k5] + - SU3D[8, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I2, k5] + - SU3D[8, I1, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k5] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[8, I2, k7]*SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[8, I1, k7]*SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[8, I4, k7]*((SU3D[I1, k6, k7]*SU3D[I3, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I3, k6, k7])*SU3F[6, I2, k5] + - SU3D[I2, k6, k7]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]) + SU3D[I2, k5, k6]* - (SU3D[I3, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I3, k5])) + SU3D[8, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[8, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[8, I2, k7]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[8, I1, k7]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[8, I3, k7]* - ((SU3D[I1, k6, k7]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k7])*SU3F[6, I2, k5] + SU3D[I2, k6, k7]* - (SU3D[I4, k5, k6]*SU3F[6, I1, k5] + SU3D[I1, k5, k6]* - SU3F[6, I4, k5]) + SU3D[I2, k5, k6]* - (SU3D[I4, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I4, k5])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/12)*(SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[3, I3, k7]* - SU3F[6, I1, k5] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k7]* - SU3F[6, I1, k5] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[3, I3, k7]* - SU3F[6, I2, k5] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k7]* - SU3F[6, I2, k5] + SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[3, I1, k7]* - SU3F[6, I3, k5] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[3, I1, k7]* - SU3F[6, I3, k5] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[3, I2, k7]* - SU3F[6, I3, k5] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[3, I2, k7]* - SU3F[6, I3, k5] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[3, I4, k7]* - SU3F[6, I3, k5] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[3, I4, k7]* - SU3F[6, I3, k5] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[3, I3, k7]* - SU3F[6, I4, k5] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[3, I3, k7]* - SU3F[6, I4, k5] + SU3D[I3, k6, k7]* - (SU3D[I4, k5, k6]*(SU3F[3, I2, k7]*SU3F[6, I1, k5] + - SU3F[3, I1, k7]*SU3F[6, I2, k5]) + SU3D[I2, k5, k6]* - (SU3F[3, I4, k7]*SU3F[6, I1, k5] + SU3F[3, I1, k7]* - SU3F[6, I4, k5]) + SU3D[I1, k5, k6]* - (SU3F[3, I4, k7]*SU3F[6, I2, k5] + SU3F[3, I2, k7]* - SU3F[6, I4, k5])) + SU3D[I3, k5, k6]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k7]*SU3F[6, I1, k5] + - SU3F[3, I1, k7]*SU3F[6, I2, k5]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k7]*SU3F[6, I1, k5] + SU3F[3, I1, k7]* - SU3F[6, I4, k5]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k7]*SU3F[6, I2, k5] + SU3F[3, I2, k7]* - SU3F[6, I4, k5]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I1, k7] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I1, k7] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I2, k7] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I2, k7] + SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I1, k5]* - SU3F[8, I3, k7] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I2, k5]* - SU3F[8, I3, k7] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[6, I4, k5]* - SU3F[8, I3, k7] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I4, k7] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I4, k7] + SU3D[I3, k6, k7]* - (SU3D[I4, k5, k6]*(SU3F[6, I2, k5]*SU3F[8, I1, k7] + - SU3F[6, I1, k5]*SU3F[8, I2, k7]) + SU3D[I2, k5, k6]* - (SU3F[6, I4, k5]*SU3F[8, I1, k7] + SU3F[6, I1, k5]* - SU3F[8, I4, k7]) + SU3D[I1, k5, k6]* - (SU3F[6, I4, k5]*SU3F[8, I2, k7] + SU3F[6, I2, k5]* - SU3F[8, I4, k7])) + SU3D[I3, k5, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k5]*SU3F[8, I1, k7] + - SU3F[6, I1, k5]*SU3F[8, I2, k7]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k5]*SU3F[8, I1, k7] + SU3F[6, I1, k5]* - SU3F[8, I4, k7]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k5]*SU3F[8, I2, k7] + SU3F[6, I2, k5]* - SU3F[8, I4, k7]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k8] + - SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k8] + - SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I2, k8] + - SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I2, k8] + - SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k8] + - SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k8] + - SU3D[6, I4, k6]*((SU3D[I1, k7, k8]*SU3D[I3, k6, k7] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8])*SU3F[8, I2, k8] + - SU3D[I2, k7, k8]*(SU3D[I3, k6, k7]*SU3F[8, I1, k8] + - SU3D[I1, k6, k7]*SU3F[8, I3, k8]) + SU3D[I2, k6, k7]* - (SU3D[I3, k7, k8]*SU3F[8, I1, k8] + SU3D[I1, k7, k8]* - SU3F[8, I3, k8])) + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k8] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k8] + SU3D[6, I3, k6]* - ((SU3D[I1, k7, k8]*SU3D[I4, k6, k7] + SU3D[I1, k6, k7]* - SU3D[I4, k7, k8])*SU3F[8, I2, k8] + SU3D[I2, k7, k8]* - (SU3D[I4, k6, k7]*SU3F[8, I1, k8] + SU3D[I1, k6, k7]* - SU3F[8, I4, k8]) + SU3D[I2, k6, k7]* - (SU3D[I4, k7, k8]*SU3F[8, I1, k8] + SU3D[I1, k7, k8]* - SU3F[8, I4, k8])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/9)*(SU3D[I2, I3, k5]*SU3F[6, I4, k7]*SU3F[I1, k5, k7] + - SU3D[I1, I4, k5]*SU3F[6, I3, k7]*SU3F[I2, k5, k7] + - SU3D[I1, I3, k5]*SU3F[6, I4, k7]*SU3F[I2, k5, k7] + - SU3D[I3, I4, k5]*(SU3F[6, I2, k7]*SU3F[I1, k5, k7] + - SU3F[6, I1, k7]*SU3F[I2, k5, k7]) + SU3D[I1, I4, k5]*SU3F[6, I2, k7]* - SU3F[I3, k5, k7] + SU3D[I1, I2, k5]*SU3F[6, I4, k7]* - SU3F[I3, k5, k7] + SU3D[I2, I4, k5]* - (SU3F[6, I3, k7]*SU3F[I1, k5, k7] + SU3F[6, I1, k7]* - SU3F[I3, k5, k7]) + SU3D[I2, I3, k5]*SU3F[6, I1, k7]* - SU3F[I4, k5, k7] + SU3D[I1, I3, k5]*SU3F[6, I2, k7]* - SU3F[I4, k5, k7] + SU3D[I1, I2, k5]*SU3F[6, I3, k7]* - SU3F[I4, k5, k7]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (SU3D[6, I2, k6]*SU3D[I3, I4, k7]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3D[I3, I4, k7]*SU3F[I2, k6, k7] + - SU3D[6, I2, k6]*SU3D[I1, I4, k7]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[I2, I4, k7]*SU3F[I3, k6, k7] + - SU3D[6, I4, k6]*(SU3D[I2, I3, k7]*SU3F[I1, k6, k7] + - SU3D[I1, I3, k7]*SU3F[I2, k6, k7] + SU3D[I1, I2, k7]* - SU3F[I3, k6, k7]) + SU3D[6, I2, k6]*SU3D[I1, I3, k7]* - SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, I3, k7]*SU3F[I4, k6, k7] + - SU3D[6, I3, k6]*(SU3D[I2, I4, k7]*SU3F[I1, k6, k7] + - SU3D[I1, I4, k7]*SU3F[I2, k6, k7] + SU3D[I1, I2, k7]* - SU3F[I4, k6, k7]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[3, I2, k8]*SU3D[6, I4, k6]*SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + - SU3D[3, I2, k8]*SU3D[6, I3, k6]*SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + - SU3D[3, I1, k8]*SU3D[6, I4, k6]*SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + - SU3D[3, I1, k8]*SU3D[6, I3, k6]*SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + - SU3D[3, I2, k8]*SU3D[6, I4, k6]*SU3D[I1, k7, k8]*SU3F[I3, k6, k7] + - SU3D[3, I1, k8]*SU3D[6, I4, k6]*SU3D[I2, k7, k8]*SU3F[I3, k6, k7] + - SU3D[3, I2, k8]*SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[3, I1, k8]*SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[3, I4, k8]*(SU3D[6, I3, k6]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[6, I2, k6]* - (SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I3, k6, k7]) + SU3D[6, I1, k6]* - (SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I3, k6, k7])) + SU3D[3, I2, k8]*SU3D[6, I3, k6]* - SU3D[I1, k7, k8]*SU3F[I4, k6, k7] + SU3D[3, I1, k8]*SU3D[6, I3, k6]* - SU3D[I2, k7, k8]*SU3F[I4, k6, k7] + SU3D[3, I2, k8]*SU3D[6, I1, k6]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[3, I1, k8]*SU3D[6, I2, k6]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[3, I3, k8]* - (SU3D[6, I4, k6]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[6, I2, k6]* - (SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I4, k6, k7]) + SU3D[6, I1, k6]* - (SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I4, k6, k7])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I3, k8]*SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I3, k8]*SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I1, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I2, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I1, k8]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I2, k8]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I4, k6]*(SU3D[8, I3, k8]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[8, I2, k8]* - (SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I3, k6, k7]) + SU3D[8, I1, k8]* - (SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I3, k6, k7])) + SU3D[6, I2, k6]*SU3D[8, I3, k8]* - SU3D[I1, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[8, I3, k8]* - SU3D[I2, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I2, k6]*SU3D[8, I1, k8]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[8, I2, k8]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I3, k6]* - (SU3D[8, I4, k8]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[8, I2, k8]* - (SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I4, k6, k7]) + SU3D[8, I1, k8]* - (SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I4, k6, k7])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/12)*(SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[3, I3, k8]* - SU3F[I1, k6, k7] + SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3F[3, I4, k8]* - SU3F[I1, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[3, I3, k8]* - SU3F[I2, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3F[3, I4, k8]* - SU3F[I2, k6, k7] + SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[3, I1, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[3, I2, k8]* - SU3F[I3, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3F[3, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3F[3, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[3, I2, k8]*SU3F[I1, k6, k7] + - SU3F[3, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[3, I3, k8]*SU3F[I1, k6, k7] + SU3F[3, I1, k8]* - SU3F[I3, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[3, I3, k8]*SU3F[I2, k6, k7] + SU3F[3, I2, k8]* - SU3F[I3, k6, k7])) + SU3D[6, I2, k6]*SU3D[I3, k7, k8]* - SU3F[3, I1, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]* - SU3F[3, I2, k8]*SU3F[I4, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3F[3, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3F[3, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[3, I2, k8]*SU3F[I1, k6, k7] + - SU3F[3, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[3, I4, k8]*SU3F[I1, k6, k7] + SU3F[3, I1, k8]* - SU3F[I4, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[3, I4, k8]*SU3F[I2, k6, k7] + SU3F[3, I2, k8]* - SU3F[I4, k6, k7]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/12)*(SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[8, I3, k8]* - SU3F[I1, k6, k7] + SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3F[8, I4, k8]* - SU3F[I1, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[8, I3, k8]* - SU3F[I2, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3F[8, I4, k8]* - SU3F[I2, k6, k7] + SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[8, I1, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[8, I2, k8]* - SU3F[I3, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3F[8, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3F[8, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[8, I2, k8]*SU3F[I1, k6, k7] + - SU3F[8, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k7] + SU3F[8, I1, k8]* - SU3F[I3, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k7] + SU3F[8, I2, k8]* - SU3F[I3, k6, k7])) + SU3D[6, I2, k6]*SU3D[I3, k7, k8]* - SU3F[8, I1, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]* - SU3F[8, I2, k8]*SU3F[I4, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3F[8, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3F[8, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[8, I2, k8]*SU3F[I1, k6, k7] + - SU3F[8, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[8, I4, k8]*SU3F[I1, k6, k7] + SU3F[8, I1, k8]* - SU3F[I4, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[8, I4, k8]*SU3F[I2, k6, k7] + SU3F[8, I2, k8]* - SU3F[I4, k6, k7]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/12)*(SU3D[3, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] + SU3D[3, I2, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] + SU3D[3, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] + SU3D[3, I1, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k8] + SU3D[3, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] + SU3D[3, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k8] + SU3D[3, I2, k6]*SU3D[I1, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[3, I1, k6]*SU3D[I2, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[3, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I3, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I3, k6, k8])) + SU3D[3, I2, k6]*SU3D[I3, k7, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] + SU3D[3, I1, k6]*SU3D[I3, k7, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k8] + SU3D[3, I2, k6]*SU3D[I1, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[3, I1, k6]*SU3D[I2, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[3, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I4, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I4, k6, k8]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/12)*(SU3D[8, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] + SU3D[8, I2, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] + SU3D[8, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] + SU3D[8, I1, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k8] + SU3D[8, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] + SU3D[8, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k8] + SU3D[8, I2, k6]*SU3D[I1, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[8, I1, k6]*SU3D[I2, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[8, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I3, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I3, k6, k8])) + SU3D[8, I2, k6]*SU3D[I3, k7, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3D[I3, k7, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3D[I1, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3D[I2, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[8, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I4, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I4, k6, k8]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[I2, k5, k6]*SU3F[3, I4, k9]*SU3F[6, I3, k5]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I3, k9]*SU3F[6, I4, k5]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I4, k9]*SU3F[6, I3, k5]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I3, k9]*SU3F[6, I4, k5]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I4, k9]*SU3F[6, I1, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I4, k9]*SU3F[6, I2, k5]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I1, k9]*SU3F[6, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I2, k9]*SU3F[6, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[3, I3, k9]*(SU3F[6, I2, k5]*SU3F[I1, k6, k9] + - SU3F[6, I1, k5]*SU3F[I2, k6, k9]) + SU3F[3, I2, k9]* - (SU3F[6, I3, k5]*SU3F[I1, k6, k9] + SU3F[6, I1, k5]* - SU3F[I3, k6, k9]) + SU3F[3, I1, k9]* - (SU3F[6, I3, k5]*SU3F[I2, k6, k9] + SU3F[6, I2, k5]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[3, I3, k9]* - SU3F[6, I1, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[3, I3, k9]* - SU3F[6, I2, k5]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[3, I1, k9]* - SU3F[6, I3, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[3, I2, k9]* - SU3F[6, I3, k5]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[3, I4, k9]*(SU3F[6, I2, k5]*SU3F[I1, k6, k9] + - SU3F[6, I1, k5]*SU3F[I2, k6, k9]) + SU3F[3, I2, k9]* - (SU3F[6, I4, k5]*SU3F[I1, k6, k9] + SU3F[6, I1, k5]* - SU3F[I4, k6, k9]) + SU3F[3, I1, k9]* - (SU3F[6, I4, k5]*SU3F[I2, k6, k9] + SU3F[6, I2, k5]* - SU3F[I4, k6, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[6, I3, k9]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I3, k5]*SU3F[6, I4, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I4, k5]*SU3F[6, I3, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I3, k5]*SU3F[6, I4, k9]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I4, k5]*SU3F[6, I1, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I4, k5]*SU3F[6, I2, k9]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[3, I1, k5]*SU3F[6, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[3, I2, k5]*SU3F[6, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[3, I3, k5]*(SU3F[6, I2, k9]*SU3F[I1, k6, k9] + - SU3F[6, I1, k9]*SU3F[I2, k6, k9]) + SU3F[3, I2, k5]* - (SU3F[6, I3, k9]*SU3F[I1, k6, k9] + SU3F[6, I1, k9]* - SU3F[I3, k6, k9]) + SU3F[3, I1, k5]* - (SU3F[6, I3, k9]*SU3F[I2, k6, k9] + SU3F[6, I2, k9]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[3, I3, k5]* - SU3F[6, I1, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[3, I3, k5]* - SU3F[6, I2, k9]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[3, I1, k5]* - SU3F[6, I3, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[3, I2, k5]* - SU3F[6, I3, k9]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[3, I4, k5]*(SU3F[6, I2, k9]*SU3F[I1, k6, k9] + - SU3F[6, I1, k9]*SU3F[I2, k6, k9]) + SU3F[3, I2, k5]* - (SU3F[6, I4, k9]*SU3F[I1, k6, k9] + SU3F[6, I1, k9]* - SU3F[I4, k6, k9]) + SU3F[3, I1, k5]* - (SU3F[6, I4, k9]*SU3F[I2, k6, k9] + SU3F[6, I2, k9]* - SU3F[I4, k6, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[I2, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I3, k5]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I3, k9]*SU3F[8, I4, k5]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I3, k5]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I3, k9]*SU3F[8, I4, k5]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I1, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I2, k5]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I1, k9]*SU3F[8, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I2, k9]*SU3F[8, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[6, I3, k9]*(SU3F[8, I2, k5]*SU3F[I1, k6, k9] + - SU3F[8, I1, k5]*SU3F[I2, k6, k9]) + SU3F[6, I2, k9]* - (SU3F[8, I3, k5]*SU3F[I1, k6, k9] + SU3F[8, I1, k5]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k9]* - (SU3F[8, I3, k5]*SU3F[I2, k6, k9] + SU3F[8, I2, k5]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[6, I3, k9]* - SU3F[8, I1, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I3, k9]* - SU3F[8, I2, k5]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[6, I1, k9]* - SU3F[8, I3, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I2, k9]* - SU3F[8, I3, k5]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[6, I4, k9]*(SU3F[8, I2, k5]*SU3F[I1, k6, k9] + - SU3F[8, I1, k5]*SU3F[I2, k6, k9]) + SU3F[6, I2, k9]* - (SU3F[8, I4, k5]*SU3F[I1, k6, k9] + SU3F[8, I1, k5]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k9]* - (SU3F[8, I4, k5]*SU3F[I2, k6, k9] + SU3F[8, I2, k5]* - SU3F[I4, k6, k9])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I3, k9]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I3, k5]*SU3F[8, I4, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I3, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]*SU3F[8, I4, k9]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I1, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I2, k9]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[6, I3, k5]*(SU3F[8, I2, k9]*SU3F[I1, k6, k9] + - SU3F[8, I1, k9]*SU3F[I2, k6, k9]) + SU3F[6, I2, k5]* - (SU3F[8, I3, k9]*SU3F[I1, k6, k9] + SU3F[8, I1, k9]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k5]* - (SU3F[8, I3, k9]*SU3F[I2, k6, k9] + SU3F[8, I2, k9]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I1, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I2, k9]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[6, I1, k5]* - SU3F[8, I3, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I2, k5]* - SU3F[8, I3, k9]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[6, I4, k5]*(SU3F[8, I2, k9]*SU3F[I1, k6, k9] + - SU3F[8, I1, k9]*SU3F[I2, k6, k9]) + SU3F[6, I2, k5]* - (SU3F[8, I4, k9]*SU3F[I1, k6, k9] + SU3F[8, I1, k9]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k5]* - (SU3F[8, I4, k9]*SU3F[I2, k6, k9] + SU3F[8, I2, k9]* - SU3F[I4, k6, k9])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[3, I2, k8]*SU3D[6, I4, k6]*SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + - SU3D[3, I2, k8]*SU3D[6, I3, k6]*SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + - SU3D[3, I1, k8]*SU3D[6, I4, k6]*SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + - SU3D[3, I1, k8]*SU3D[6, I3, k6]*SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + - SU3D[3, I2, k8]*SU3D[6, I4, k6]*SU3D[I1, k6, k7]*SU3F[I3, k7, k8] + - SU3D[3, I1, k8]*SU3D[6, I4, k6]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8] + - SU3D[3, I2, k8]*SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[3, I1, k8]*SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[3, I4, k8]*(SU3D[6, I3, k6]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[6, I2, k6]* - (SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I3, k7, k8]) + SU3D[6, I1, k6]* - (SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I3, k7, k8])) + SU3D[3, I2, k8]*SU3D[6, I3, k6]* - SU3D[I1, k6, k7]*SU3F[I4, k7, k8] + SU3D[3, I1, k8]*SU3D[6, I3, k6]* - SU3D[I2, k6, k7]*SU3F[I4, k7, k8] + SU3D[3, I2, k8]*SU3D[6, I1, k6]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[3, I1, k8]*SU3D[6, I2, k6]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[3, I3, k8]* - (SU3D[6, I4, k6]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[6, I2, k6]* - (SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I4, k7, k8]) + SU3D[6, I1, k6]* - (SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I4, k7, k8])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I3, k8]*SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I1, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I1, k8]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I4, k6]*(SU3D[8, I3, k8]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[8, I2, k8]* - (SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I3, k7, k8]) + SU3D[8, I1, k8]* - (SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I3, k7, k8])) + SU3D[6, I2, k6]*SU3D[8, I3, k8]* - SU3D[I1, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I1, k6]*SU3D[8, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I2, k6]*SU3D[8, I1, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I1, k6]*SU3D[8, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I3, k6]* - (SU3D[8, I4, k8]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[8, I2, k8]* - (SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I4, k7, k8]) + SU3D[8, I1, k8]* - (SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I4, k7, k8])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/12)*(SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k9]* - SU3F[I1, k7, k9] + SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3F[3, I4, k9]* - SU3F[I1, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[3, I3, k9]* - SU3F[I2, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3F[3, I4, k9]* - SU3F[I2, k7, k9] + SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[3, I1, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[3, I2, k9]* - SU3F[I3, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3F[3, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3F[3, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[3, I2, k9]*SU3F[I1, k7, k9] + - SU3F[3, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[3, I3, k9]*SU3F[I1, k7, k9] + SU3F[3, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[3, I3, k9]*SU3F[I2, k7, k9] + SU3F[3, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[6, I2, k6]*SU3D[I3, k6, k7]* - SU3F[3, I1, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]* - SU3F[3, I2, k9]*SU3F[I4, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3F[3, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3F[3, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[3, I2, k9]*SU3F[I1, k7, k9] + - SU3F[3, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[3, I4, k9]*SU3F[I1, k7, k9] + SU3F[3, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[3, I4, k9]*SU3F[I2, k7, k9] + SU3F[3, I2, k9]* - SU3F[I4, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3D[3, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + SU3D[3, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] + SU3D[3, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] + SU3D[3, I1, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9] + SU3D[3, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] + SU3D[3, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9] + SU3D[3, I2, k6]*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[3, I1, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[3, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[3, I2, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] + SU3D[3, I1, k6]*SU3D[I3, k6, k7]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] + SU3D[3, I2, k6]*SU3D[I1, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[3, I1, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[3, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I4, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/12)*(SU3D[8, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + SU3D[8, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] + SU3D[8, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] + SU3D[8, I1, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9] + SU3D[8, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] + SU3D[8, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9] + SU3D[8, I2, k6]*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[8, I1, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[8, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[8, I2, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] + SU3D[8, I1, k6]*SU3D[I3, k6, k7]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] + SU3D[8, I2, k6]*SU3D[I1, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[8, I1, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[8, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/12)*(SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k9]* - SU3F[I1, k7, k9] + SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3F[8, I4, k9]* - SU3F[I1, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k9]* - SU3F[I2, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3F[8, I4, k9]* - SU3F[I2, k7, k9] + SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[8, I1, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[8, I2, k9]* - SU3F[I3, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3F[8, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3F[8, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[8, I2, k9]*SU3F[I1, k7, k9] + - SU3F[8, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I3, k9]*SU3F[I1, k7, k9] + SU3F[8, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I3, k9]*SU3F[I2, k7, k9] + SU3F[8, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[6, I2, k6]*SU3D[I3, k6, k7]* - SU3F[8, I1, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]* - SU3F[8, I2, k9]*SU3F[I4, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3F[8, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3F[8, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k9]*SU3F[I1, k7, k9] + - SU3F[8, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k9]*SU3F[I1, k7, k9] + SU3F[8, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k9]*SU3F[I2, k7, k9] + SU3F[8, I2, k9]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/12)*(SU3F[3, I2, k9]*SU3F[6, I4, k8]*SU3F[I1, k7, k9]* - SU3F[I3, k7, k8] + SU3F[3, I1, k9]*SU3F[6, I4, k8]*SU3F[I2, k7, k9]* - SU3F[I3, k7, k8] + SU3F[3, I2, k9]*SU3F[6, I4, k8]*SU3F[I1, k7, k8]* - SU3F[I3, k7, k9] + SU3F[3, I1, k9]*SU3F[6, I4, k8]*SU3F[I2, k7, k8]* - SU3F[I3, k7, k9] + SU3F[3, I4, k9]* - (SU3F[6, I3, k8]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[6, I2, k8]* - (SU3F[I1, k7, k9]*SU3F[I3, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I3, k7, k9]) + SU3F[6, I1, k8]* - (SU3F[I2, k7, k9]*SU3F[I3, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I3, k7, k9])) + SU3F[3, I2, k9]*SU3F[6, I3, k8]* - SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[3, I1, k9]*SU3F[6, I3, k8]* - SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[3, I2, k9]*SU3F[6, I1, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[3, I1, k9]*SU3F[6, I2, k8]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[3, I2, k9]*SU3F[6, I3, k8]* - SU3F[I1, k7, k8]*SU3F[I4, k7, k9] + SU3F[3, I1, k9]*SU3F[6, I3, k8]* - SU3F[I2, k7, k8]*SU3F[I4, k7, k9] + SU3F[3, I2, k9]*SU3F[6, I1, k8]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[3, I1, k9]*SU3F[6, I2, k8]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[3, I3, k9]* - (SU3F[6, I4, k8]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[6, I2, k8]* - (SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I4, k7, k9]) + SU3F[6, I1, k8]* - (SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I4, k7, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3F[6, I2, k8]*SU3F[8, I4, k9]*SU3F[I1, k7, k9]* - SU3F[I3, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I4, k9]*SU3F[I2, k7, k9]* - SU3F[I3, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I4, k9]*SU3F[I1, k7, k8]* - SU3F[I3, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I4, k9]*SU3F[I2, k7, k8]* - SU3F[I3, k7, k9] + SU3F[6, I4, k8]* - (SU3F[8, I3, k9]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I3, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I3, k7, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k7, k9]*SU3F[I3, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I3, k7, k9])) + SU3F[6, I2, k8]*SU3F[8, I3, k9]* - SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I3, k9]* - SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I1, k9]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I2, k9]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I3, k9]* - SU3F[I1, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I3, k9]* - SU3F[I2, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I2, k8]*SU3F[8, I1, k9]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I2, k9]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I3, k8]* - (SU3F[8, I4, k9]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I4, k7, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k5]*SU3F[3, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I1, k5]*SU3F[3, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I2, k5]*SU3F[3, I4, k9]*SU3F[I1, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I1, k5]*SU3F[3, I4, k9]*SU3F[I2, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I4, k5]*(SU3F[3, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[3, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I3, k8, k9]) + SU3F[3, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I3, k8, k9])) + SU3D[6, I2, k5]*SU3F[3, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[3, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[3, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[3, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[3, I3, k9]* - SU3F[I1, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[3, I3, k9]* - SU3F[I2, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I2, k5]*SU3F[3, I1, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[3, I2, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I3, k5]* - (SU3F[3, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[3, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I4, k8, k9]) + SU3F[3, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I1, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I2, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I4, k5]*(SU3F[8, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I3, k8, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I3, k8, k9])) + SU3D[6, I2, k5]*SU3F[8, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[8, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[8, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[8, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[8, I3, k9]* - SU3F[I1, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[8, I3, k9]* - SU3F[I2, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I2, k5]*SU3F[8, I1, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[8, I2, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I3, k5]* - (SU3F[8, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I4, k8, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I4, k8, k9])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[3, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + - SU3D[3, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + - SU3D[3, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9] + - SU3D[3, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k6, k8]*SU3F[I3, k8, k9] + - SU3D[3, I4, k6]*(SU3F[6, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I3, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I3, k8, k9])) + SU3D[3, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3D[3, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3D[3, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[3, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[3, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k6, k8]*SU3F[I4, k8, k9] + SU3D[3, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9] + SU3D[3, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[3, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[3, I3, k6]* - (SU3F[6, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I4, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I4, k8, k9])))/(12*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[8, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + - SU3D[8, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + - SU3D[8, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9] + - SU3D[8, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k6, k8]*SU3F[I3, k8, k9] + - SU3D[8, I4, k6]*(SU3F[6, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I3, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I3, k8, k9])) + SU3D[8, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I3, k6]* - (SU3F[6, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I4, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I4, k8, k9])))/(12*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/12)*(SU3D[3, I2, k6]*SU3D[6, I4, k8]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + SU3D[3, I1, k6]*SU3D[6, I4, k8]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9] + SU3D[3, I2, k6]*SU3D[6, I4, k8]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + SU3D[3, I1, k6]*SU3D[6, I4, k8]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + SU3D[3, I4, k6]* - (SU3D[6, I3, k8]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[6, I2, k8]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]) + SU3D[6, I1, k8]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])) + SU3D[3, I2, k6]*SU3D[6, I3, k8]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[3, I1, k6]*SU3D[6, I3, k8]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3D[3, I2, k6]*SU3D[6, I1, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[3, I1, k6]*SU3D[6, I2, k8]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[3, I2, k6]*SU3D[6, I3, k8]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + SU3D[3, I1, k6]*SU3D[6, I3, k8]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[3, I2, k6]*SU3D[6, I1, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[3, I1, k6]*SU3D[6, I2, k8]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[3, I3, k6]* - (SU3D[6, I4, k8]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[6, I2, k8]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[6, I1, k8]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9]))))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/12)*(SU3D[6, I2, k8]*SU3D[8, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I4, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I4, k6]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I4, k6]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + SU3D[6, I4, k8]* - (SU3D[8, I3, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[8, I2, k6]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]) + SU3D[8, I1, k6]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])) + SU3D[6, I2, k8]*SU3D[8, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I1, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I3, k6]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I2, k8]*SU3D[8, I1, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I3, k8]* - (SU3D[8, I4, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[8, I2, k6]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[8, I1, k6]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[3, I1] + - SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[3, I2] + - SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[3, I2] + - SU3D[I3, I4, k5]*(SU3F[6, I2, k5]*SUNDelta[3, I1] + - SU3F[6, I1, k5]*SUNDelta[3, I2]) + SU3D[I1, I4, k5]*SU3F[6, I2, k5]* - SUNDelta[3, I3] + SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[3, I3] + - SU3D[I2, I4, k5]*(SU3F[6, I3, k5]*SUNDelta[3, I1] + - SU3F[6, I1, k5]*SUNDelta[3, I3]) + SU3D[I2, I3, k5]*SU3F[6, I1, k5]* - SUNDelta[3, I4] + SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[3, I4] + - SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[3, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/9)*(SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[3, I1] + - SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[3, I2] + - SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[3, I3] + - SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[3, I3] + - SU3D[6, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[3, I1] + - SU3D[I1, I3, k5]*SUNDelta[3, I2] + SU3D[I1, I2, k5]* - SUNDelta[3, I3]) + SU3D[6, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[3, I4] + SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[3, I4] + - SU3D[6, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[3, I1] + - SU3D[I1, I4, k5]*SUNDelta[3, I2] + SU3D[I1, I2, k5]* - SUNDelta[3, I4])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/9)*(SU3D[I2, I3, I4]*SUNDelta[6, I1] + SU3D[I1, I3, I4]* - SUNDelta[6, I2] + SU3D[I1, I2, I4]*SUNDelta[6, I3] + - SU3D[I1, I2, I3]*SUNDelta[6, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[I2, I3, k5]*SU3F[3, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SU3F[3, I3, k5]*SUNDelta[6, I2] + - SU3D[I1, I3, k5]*SU3F[3, I4, k5]*SUNDelta[6, I2] + - SU3D[I3, I4, k5]*(SU3F[3, I2, k5]*SUNDelta[6, I1] + - SU3F[3, I1, k5]*SUNDelta[6, I2]) + SU3D[I1, I4, k5]*SU3F[3, I2, k5]* - SUNDelta[6, I3] + SU3D[I1, I2, k5]*SU3F[3, I4, k5]*SUNDelta[6, I3] + - SU3D[I2, I4, k5]*(SU3F[3, I3, k5]*SUNDelta[6, I1] + - SU3F[3, I1, k5]*SUNDelta[6, I3]) + SU3D[I2, I3, k5]*SU3F[3, I1, k5]* - SUNDelta[6, I4] + SU3D[I1, I3, k5]*SU3F[3, I2, k5]*SUNDelta[6, I4] + - SU3D[I1, I2, k5]*SU3F[3, I3, k5]*SUNDelta[6, I4])/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[I2, I3, k5]*SU3F[8, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SU3F[8, I3, k5]*SUNDelta[6, I2] + - SU3D[I1, I3, k5]*SU3F[8, I4, k5]*SUNDelta[6, I2] + - SU3D[I3, I4, k5]*(SU3F[8, I2, k5]*SUNDelta[6, I1] + - SU3F[8, I1, k5]*SUNDelta[6, I2]) + SU3D[I1, I4, k5]*SU3F[8, I2, k5]* - SUNDelta[6, I3] + SU3D[I1, I2, k5]*SU3F[8, I4, k5]*SUNDelta[6, I3] + - SU3D[I2, I4, k5]*(SU3F[8, I3, k5]*SUNDelta[6, I1] + - SU3F[8, I1, k5]*SUNDelta[6, I3]) + SU3D[I2, I3, k5]*SU3F[8, I1, k5]* - SUNDelta[6, I4] + SU3D[I1, I3, k5]*SU3F[8, I2, k5]*SUNDelta[6, I4] + - SU3D[I1, I2, k5]*SU3F[8, I3, k5]*SUNDelta[6, I4])/ - (9*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/9)*(SU3D[3, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I1] + - SU3D[3, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I2] + - SU3D[3, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[6, I3] + - SU3D[3, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[6, I3] + - SU3D[3, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[6, I1] + - SU3D[I1, I3, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I3]) + SU3D[3, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[6, I4] + SU3D[3, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[6, I4] + - SU3D[3, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I4])))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/9)*(SU3D[8, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I1] + - SU3D[8, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I2] + - SU3D[8, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[6, I3] + - SU3D[8, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[6, I3] + - SU3D[8, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[6, I1] + - SU3D[I1, I3, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I3]) + SU3D[8, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[6, I4] + SU3D[8, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[6, I4] + - SU3D[8, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I4])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/18)*(SU3D[I1, I4, k9]*SU3D[I2, k6, k9]*SU3D[I3, k5, k6] + - SU3D[I1, I4, k9]*SU3D[I2, k5, k6]*SU3D[I3, k6, k9] + - SU3D[I1, I3, k9]*SU3D[I2, k6, k9]*SU3D[I4, k5, k6] + - SU3D[I1, I2, k9]*SU3D[I3, k6, k9]*SU3D[I4, k5, k6] + - SU3D[I1, k6, k9]*(SU3D[I2, k5, k6]*SU3D[I3, I4, k9] + - SU3D[I2, I4, k9]*SU3D[I3, k5, k6] + SU3D[I2, I3, k9]* - SU3D[I4, k5, k6]) + SU3D[I1, I3, k9]*SU3D[I2, k5, k6]* - SU3D[I4, k6, k9] + SU3D[I1, I2, k9]*SU3D[I3, k5, k6]* - SU3D[I4, k6, k9] + SU3D[I1, k5, k6]* - (SU3D[I2, k6, k9]*SU3D[I3, I4, k9] + SU3D[I2, I4, k9]* - SU3D[I3, k6, k9] + SU3D[I2, I3, k9]*SU3D[I4, k6, k9]))* - SUNDelta[6, k5])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3F[I3, k7, k8] + - SU3D[I2, I4, k9]*(SU3D[I3, k8, k9]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3F[I3, k7, k8]) + SU3D[I1, k8, k9]* - SU3D[I2, I3, k9]*SU3F[I4, k7, k8] + SU3D[I1, I2, k9]*SU3D[I3, k8, k9]* - SU3F[I4, k7, k8] + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k9]*SU3F[I1, k7, k8] + SU3D[I1, I4, k9]* - SU3F[I3, k7, k8] + SU3D[I1, I3, k9]*SU3F[I4, k7, k8]))* - SUNDelta[6, k7])/(18*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3F[I2, k8, k9] + - SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3F[I2, k8, k9] + - SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3F[I2, k8, k9] + - SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3F[I3, k8, k9] + - SU3D[I2, I4, k9]*(SU3D[I3, k7, k8]*SU3F[I1, k8, k9] + - SU3D[I1, k7, k8]*SU3F[I3, k8, k9]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k9]*SU3F[I4, k8, k9] + SU3D[I1, I2, k9]*SU3D[I3, k7, k8]* - SU3F[I4, k8, k9] + SU3D[I2, k7, k8]* - (SU3D[I3, I4, k9]*SU3F[I1, k8, k9] + SU3D[I1, I4, k9]* - SU3F[I3, k8, k9] + SU3D[I1, I3, k9]*SU3F[I4, k8, k9]))* - SUNDelta[6, k7])/(18*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/18)*(SU3D[I3, I4, k5]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k9] + - SU3F[I1, k5, k9]*SU3F[I2, k8, k9]) + SU3D[I1, I4, k5]* - SU3F[I2, k8, k9]*SU3F[I3, k5, k9] + SU3D[I1, I4, k5]*SU3F[I2, k5, k9]* - SU3F[I3, k8, k9] + SU3D[I2, I4, k5]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k9] + SU3F[I1, k5, k9]* - SU3F[I3, k8, k9]) + SU3D[I2, I3, k5]*SU3F[I1, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I1, I3, k5]*SU3F[I2, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I1, I2, k5]*SU3F[I3, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I2, I3, k5]*SU3F[I1, k5, k9]* - SU3F[I4, k8, k9] + SU3D[I1, I3, k5]*SU3F[I2, k5, k9]* - SU3F[I4, k8, k9] + SU3D[I1, I2, k5]*SU3F[I3, k5, k9]* - SU3F[I4, k8, k9])*SUNDelta[6, k8])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (SU3D[I2, I3, I4]*SUNDelta[7, I1] + SU3D[I1, I3, I4]*SUNDelta[7, I2] + - SU3D[I1, I2, I4]*SUNDelta[7, I3] + SU3D[I1, I2, I3]*SUNDelta[7, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((SU3D[I1, I4, k7]*SU3D[I2, k6, k7]*SU3D[I3, k5, k6] + - SU3D[I1, I4, k7]*SU3D[I2, k5, k6]*SU3D[I3, k6, k7] + - SU3D[I1, I3, k7]*SU3D[I2, k6, k7]*SU3D[I4, k5, k6] + - SU3D[I1, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6] + - SU3D[I1, k6, k7]*(SU3D[I2, k5, k6]*SU3D[I3, I4, k7] + - SU3D[I2, I4, k7]*SU3D[I3, k5, k6] + SU3D[I2, I3, k7]* - SU3D[I4, k5, k6]) + SU3D[I1, I3, k7]*SU3D[I2, k5, k6]* - SU3D[I4, k6, k7] + SU3D[I1, I2, k7]*SU3D[I3, k5, k6]* - SU3D[I4, k6, k7] + SU3D[I1, k5, k6]* - (SU3D[I2, k6, k7]*SU3D[I3, I4, k7] + SU3D[I2, I4, k7]* - SU3D[I3, k6, k7] + SU3D[I2, I3, k7]*SU3D[I4, k6, k7]))* - SUNDelta[7, k5])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/6)*(SU3D[I2, I3, k5]*SU3D[I4, k6, k7]*SU3F[I1, k5, k7] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k5]*SU3F[I2, k5, k7] + - SU3D[I1, I4, k5]*SU3D[I3, k6, k7]*SU3F[I2, k5, k7] + - SU3D[I1, I3, k5]*SU3D[I4, k6, k7]*SU3F[I2, k5, k7] + - SU3D[I1, I2, k5]*SU3D[I4, k6, k7]*SU3F[I3, k5, k7] + - SU3D[I2, I4, k5]*(SU3D[I3, k6, k7]*SU3F[I1, k5, k7] + - SU3D[I1, k6, k7]*SU3F[I3, k5, k7]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k5]*SU3F[I4, k5, k7] + SU3D[I1, I2, k5]*SU3D[I3, k6, k7]* - SU3F[I4, k5, k7] + SU3D[I2, k6, k7]* - (SU3D[I3, I4, k5]*SU3F[I1, k5, k7] + SU3D[I1, I4, k5]* - SU3F[I3, k5, k7] + SU3D[I1, I3, k5]*SU3F[I4, k5, k7]))* - SUNDelta[7, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((I/6)*(SU3D[I2, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3D[I3, I4, k5]*SU3F[I2, k6, k9] + - SU3D[I1, I4, k5]*SU3D[I3, k5, k6]*SU3F[I2, k6, k9] + - SU3D[I1, I3, k5]*SU3D[I4, k5, k6]*SU3F[I2, k6, k9] + - SU3D[I1, I2, k5]*SU3D[I4, k5, k6]*SU3F[I3, k6, k9] + - SU3D[I2, I4, k5]*(SU3D[I3, k5, k6]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[I3, k6, k9]) + SU3D[I1, k5, k6]* - SU3D[I2, I3, k5]*SU3F[I4, k6, k9] + SU3D[I1, I2, k5]*SU3D[I3, k5, k6]* - SU3F[I4, k6, k9] + SU3D[I2, k5, k6]* - (SU3D[I3, I4, k5]*SU3F[I1, k6, k9] + SU3D[I1, I4, k5]* - SU3F[I3, k6, k9] + SU3D[I1, I3, k5]*SU3F[I4, k6, k9]))* - SUNDelta[7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((SU3D[I3, I4, k5]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3D[I1, I4, k5]* - SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + SU3D[I1, I4, k5]*SU3F[I2, k5, k8]* - SU3F[I3, k8, k9] + SU3D[I2, I4, k5]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I3, k8, k9]) + SU3D[I2, I3, k5]*SU3F[I1, k8, k9]* - SU3F[I4, k5, k8] + SU3D[I1, I3, k5]*SU3F[I2, k8, k9]* - SU3F[I4, k5, k8] + SU3D[I1, I2, k5]*SU3F[I3, k8, k9]* - SU3F[I4, k5, k8] + SU3D[I2, I3, k5]*SU3F[I1, k5, k8]* - SU3F[I4, k8, k9] + SU3D[I1, I3, k5]*SU3F[I2, k5, k8]* - SU3F[I4, k8, k9] + SU3D[I1, I2, k5]*SU3F[I3, k5, k8]* - SU3F[I4, k8, k9])*SUNDelta[7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[8, I1] + - SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[8, I2] + - SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[8, I2] + - SU3D[I3, I4, k5]*(SU3F[6, I2, k5]*SUNDelta[8, I1] + - SU3F[6, I1, k5]*SUNDelta[8, I2]) + SU3D[I1, I4, k5]*SU3F[6, I2, k5]* - SUNDelta[8, I3] + SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[8, I3] + - SU3D[I2, I4, k5]*(SU3F[6, I3, k5]*SUNDelta[8, I1] + - SU3F[6, I1, k5]*SUNDelta[8, I3]) + SU3D[I2, I3, k5]*SU3F[6, I1, k5]* - SUNDelta[8, I4] + SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[8, I4] + - SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[8, I4])/ - (9*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - ((I/9)*(SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[8, I1] + - SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[8, I2] + - SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[8, I3] + - SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[8, I3] + - SU3D[6, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[8, I1] + - SU3D[I1, I3, k5]*SUNDelta[8, I2] + SU3D[I1, I2, k5]* - SUNDelta[8, I3]) + SU3D[6, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[8, I4] + SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[8, I4] + - SU3D[6, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[8, I1] + - SU3D[I1, I4, k5]*SUNDelta[8, I2] + SU3D[I1, I2, k5]* - SUNDelta[8, I4])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (((4*I)/27)*(SU3D[6, I3, I4]*SUNDelta[I1, I2] + SU3D[6, I2, I4]* - SUNDelta[I1, I3] + SU3D[6, I2, I3]*SUNDelta[I1, I4] + - SU3D[6, I1, I4]*SUNDelta[I2, I3] + SU3D[6, I1, I3]*SUNDelta[I2, I4] + - SU3D[6, I1, I2]*SUNDelta[I3, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((2*I)/27)*SUNDelta[6, k4]*(SU3D[I3, I4, k4]*SUNDelta[I1, I2] + - SU3D[I2, I4, k4]*SUNDelta[I1, I3] + SU3D[I2, I3, k4]* - SUNDelta[I1, I4] + SU3D[I1, I4, k4]*SUNDelta[I2, I3] + - SU3D[I1, I3, k4]*SUNDelta[I2, I4] + SU3D[I1, I2, k4]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - (2*SUNDelta[7, k4]*(SU3D[I3, I4, k4]*SUNDelta[I1, I2] + - SU3D[I2, I4, k4]*SUNDelta[I1, I3] + SU3D[I2, I3, k4]* - SUNDelta[I1, I4] + SU3D[I1, I4, k4]*SUNDelta[I2, I3] + - SU3D[I1, I3, k4]*SUNDelta[I2, I4] + SU3D[I1, I2, k4]* - SUNDelta[I3, I4]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (((2*I)/27)*(SUNDelta[3, I2]*SUNDelta[6, I4]*SUNDelta[I1, I3] + - SUNDelta[3, I2]*SUNDelta[6, I3]*SUNDelta[I1, I4] + - SUNDelta[3, I1]*SUNDelta[6, I4]*SUNDelta[I2, I3] + - SUNDelta[3, I4]*(SUNDelta[6, I3]*SUNDelta[I1, I2] + - SUNDelta[6, I2]*SUNDelta[I1, I3] + SUNDelta[6, I1]* - SUNDelta[I2, I3]) + SUNDelta[3, I1]*SUNDelta[6, I3]* - SUNDelta[I2, I4] + SUNDelta[3, I3]* - (SUNDelta[6, I4]*SUNDelta[I1, I2] + SUNDelta[6, I2]* - SUNDelta[I1, I4] + SUNDelta[6, I1]*SUNDelta[I2, I4]) + - SUNDelta[3, I2]*SUNDelta[6, I1]*SUNDelta[I3, I4] + - SUNDelta[3, I1]*SUNDelta[6, I2]*SUNDelta[I3, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((2*I)/27)*(SUNDelta[6, I2]*SUNDelta[8, I4]*SUNDelta[I1, I3] + - SUNDelta[6, I2]*SUNDelta[8, I3]*SUNDelta[I1, I4] + - SUNDelta[6, I1]*SUNDelta[8, I4]*SUNDelta[I2, I3] + - SUNDelta[6, I4]*(SUNDelta[8, I3]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I3] + SUNDelta[8, I1]* - SUNDelta[I2, I3]) + SUNDelta[6, I1]*SUNDelta[8, I3]* - SUNDelta[I2, I4] + SUNDelta[6, I3]* - (SUNDelta[8, I4]*SUNDelta[I1, I2] + SUNDelta[8, I2]* - SUNDelta[I1, I4] + SUNDelta[8, I1]*SUNDelta[I2, I4]) + - SUNDelta[6, I2]*SUNDelta[8, I1]*SUNDelta[I3, I4] + - SUNDelta[6, I1]*SUNDelta[8, I2]*SUNDelta[I3, I4]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}, -{CouplingConstant[ChPTW3[2], 2]* -((((4*I)/9)*(SU3D[6, I3, I4]*SU3D[8, I1, I2] + SU3D[6, I2, I4]* - SU3D[8, I1, I3] + SU3D[6, I2, I3]*SU3D[8, I1, I4] + - SU3D[6, I1, I4]*SU3D[8, I2, I3] + SU3D[6, I1, I3]*SU3D[8, I2, I4] + - SU3D[6, I1, I2]*SU3D[8, I3, I4]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((I/9)*(SU3D[6, I2, k5]*SU3D[I1, k5, k6]*SU3D[I3, I4, k6] + - SU3D[6, I1, k5]*SU3D[I2, k5, k6]*SU3D[I3, I4, k6] + - SU3D[6, I2, k5]*SU3D[I1, I4, k6]*SU3D[I3, k5, k6] + - SU3D[6, I1, k5]*SU3D[I2, I4, k6]*SU3D[I3, k5, k6] + - SU3D[6, I4, k5]*(SU3D[I1, k5, k6]*SU3D[I2, I3, k6] + - SU3D[I1, I3, k6]*SU3D[I2, k5, k6] + SU3D[I1, I2, k6]* - SU3D[I3, k5, k6]) + SU3D[6, I2, k5]*SU3D[I1, I3, k6]* - SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[I2, I3, k6]* - SU3D[I4, k5, k6] + SU3D[6, I3, k5]* - (SU3D[I1, k5, k6]*SU3D[I2, I4, k6] + SU3D[I1, I4, k6]* - SU3D[I2, k5, k6] + SU3D[I1, I2, k6]*SU3D[I4, k5, k6])))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - ((I/6)*(SU3D[6, I2, k5]*SU3D[8, I4, k9]*SU3D[I1, k6, k9]* - SU3D[I3, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I4, k9]*SU3D[I2, k6, k9]* - SU3D[I3, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I4, k9]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k9] + SU3D[6, I1, k5]*SU3D[8, I4, k9]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k9] + SU3D[6, I4, k5]* - (SU3D[8, I3, k9]*(SU3D[I1, k6, k9]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k9]) + SU3D[8, I2, k9]* - (SU3D[I1, k6, k9]*SU3D[I3, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I3, k6, k9]) + SU3D[8, I1, k9]* - (SU3D[I2, k6, k9]*SU3D[I3, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I3, k6, k9])) + SU3D[6, I2, k5]*SU3D[8, I3, k9]* - SU3D[I1, k6, k9]*SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I3, k9]* - SU3D[I2, k6, k9]*SU3D[I4, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I1, k9]* - SU3D[I3, k6, k9]*SU3D[I4, k5, k6] + SU3D[6, I1, k5]*SU3D[8, I2, k9]* - SU3D[I3, k6, k9]*SU3D[I4, k5, k6] + SU3D[6, I2, k5]*SU3D[8, I3, k9]* - SU3D[I1, k5, k6]*SU3D[I4, k6, k9] + SU3D[6, I1, k5]*SU3D[8, I3, k9]* - SU3D[I2, k5, k6]*SU3D[I4, k6, k9] + SU3D[6, I2, k5]*SU3D[8, I1, k9]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k9] + SU3D[6, I1, k5]*SU3D[8, I2, k9]* - SU3D[I3, k5, k6]*SU3D[I4, k6, k9] + SU3D[6, I3, k5]* - (SU3D[8, I4, k9]*(SU3D[I1, k6, k9]*SU3D[I2, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I2, k6, k9]) + SU3D[8, I2, k9]* - (SU3D[I1, k6, k9]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k9]) + SU3D[8, I1, k9]* - (SU3D[I2, k6, k9]*SU3D[I4, k5, k6] + SU3D[I2, k5, k6]* - SU3D[I4, k6, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3D[I3, I4, k6]*SU3F[6, I2, k5] + - SU3D[I1, I4, k6]*SU3D[I3, k5, k6]*SU3F[6, I2, k5] + - SU3D[I1, I3, k6]*SU3D[I4, k5, k6]*SU3F[6, I2, k5] + - SU3D[I1, I2, k6]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[I2, I4, k6]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]) + SU3D[I1, k5, k6]*SU3D[I2, I3, k6]* - SU3F[6, I4, k5] + SU3D[I1, I2, k6]*SU3D[I3, k5, k6]*SU3F[6, I4, k5] + - SU3D[I2, k5, k6]*(SU3D[I3, I4, k6]*SU3F[6, I1, k5] + - SU3D[I1, I4, k6]*SU3F[6, I3, k5] + SU3D[I1, I3, k6]*SU3F[6, I4, k5]))/ - (9*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (SU3D[8, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I1, k5] + - SU3D[8, I2, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k5] + - SU3D[8, I1, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I2, k5] + - SU3D[8, I1, k7]*SU3D[I3, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k5] + - SU3D[8, I2, k7]*SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[8, I1, k7]*SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5] + - SU3D[8, I2, k7]*SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[8, I1, k7]*SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5] + - SU3D[8, I4, k7]*((SU3D[I1, k6, k7]*SU3D[I3, k5, k6] + - SU3D[I1, k5, k6]*SU3D[I3, k6, k7])*SU3F[6, I2, k5] + - SU3D[I2, k6, k7]*(SU3D[I3, k5, k6]*SU3F[6, I1, k5] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]) + SU3D[I2, k5, k6]* - (SU3D[I3, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I3, k5])) + SU3D[8, I2, k7]*SU3D[I1, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[8, I1, k7]*SU3D[I2, k6, k7]* - SU3D[I3, k5, k6]*SU3F[6, I4, k5] + SU3D[8, I2, k7]*SU3D[I1, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[8, I1, k7]*SU3D[I2, k5, k6]* - SU3D[I3, k6, k7]*SU3F[6, I4, k5] + SU3D[8, I3, k7]* - ((SU3D[I1, k6, k7]*SU3D[I4, k5, k6] + SU3D[I1, k5, k6]* - SU3D[I4, k6, k7])*SU3F[6, I2, k5] + SU3D[I2, k6, k7]* - (SU3D[I4, k5, k6]*SU3F[6, I1, k5] + SU3D[I1, k5, k6]* - SU3F[6, I4, k5]) + SU3D[I2, k5, k6]* - (SU3D[I4, k6, k7]*SU3F[6, I1, k5] + SU3D[I1, k6, k7]* - SU3F[6, I4, k5])))/(6*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/6)*(SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I1, k7] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I1, k7] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I2, k7] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I2, k7] + SU3D[I2, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I1, k5]* - SU3F[8, I3, k7] + SU3D[I2, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I4, k5, k6]*SU3F[6, I2, k5]* - SU3F[8, I3, k7] + SU3D[I1, k5, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[6, I4, k5]* - SU3F[8, I3, k7] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k5]* - SU3F[8, I3, k7] + SU3D[I1, k6, k7]*SU3D[I2, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I4, k7] + SU3D[I1, k5, k6]*SU3D[I2, k6, k7]*SU3F[6, I3, k5]* - SU3F[8, I4, k7] + SU3D[I3, k6, k7]* - (SU3D[I4, k5, k6]*(SU3F[6, I2, k5]*SU3F[8, I1, k7] + - SU3F[6, I1, k5]*SU3F[8, I2, k7]) + SU3D[I2, k5, k6]* - (SU3F[6, I4, k5]*SU3F[8, I1, k7] + SU3F[6, I1, k5]* - SU3F[8, I4, k7]) + SU3D[I1, k5, k6]* - (SU3F[6, I4, k5]*SU3F[8, I2, k7] + SU3F[6, I2, k5]* - SU3F[8, I4, k7])) + SU3D[I3, k5, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k5]*SU3F[8, I1, k7] + - SU3F[6, I1, k5]*SU3F[8, I2, k7]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k5]*SU3F[8, I1, k7] + SU3F[6, I1, k5]* - SU3F[8, I4, k7]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k5]*SU3F[8, I2, k7] + SU3F[6, I2, k5]* - SU3F[8, I4, k7]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I1, k8] + - SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I1, k8] + - SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I2, k8] + - SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I2, k8] + - SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3D[I4, k6, k7]*SU3F[8, I3, k8] + - SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k8] + - SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3D[I4, k7, k8]*SU3F[8, I3, k8] + - SU3D[6, I4, k6]*((SU3D[I1, k7, k8]*SU3D[I3, k6, k7] + - SU3D[I1, k6, k7]*SU3D[I3, k7, k8])*SU3F[8, I2, k8] + - SU3D[I2, k7, k8]*(SU3D[I3, k6, k7]*SU3F[8, I1, k8] + - SU3D[I1, k6, k7]*SU3F[8, I3, k8]) + SU3D[I2, k6, k7]* - (SU3D[I3, k7, k8]*SU3F[8, I1, k8] + SU3D[I1, k7, k8]* - SU3F[8, I3, k8])) + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3D[I3, k6, k7]*SU3F[8, I4, k8] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k8] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3D[I3, k7, k8]*SU3F[8, I4, k8] + SU3D[6, I3, k6]* - ((SU3D[I1, k7, k8]*SU3D[I4, k6, k7] + SU3D[I1, k6, k7]* - SU3D[I4, k7, k8])*SU3F[8, I2, k8] + SU3D[I2, k7, k8]* - (SU3D[I4, k6, k7]*SU3F[8, I1, k8] + SU3D[I1, k6, k7]* - SU3F[8, I4, k8]) + SU3D[I2, k6, k7]* - (SU3D[I4, k7, k8]*SU3F[8, I1, k8] + SU3D[I1, k7, k8]* - SU3F[8, I4, k8])))/(6*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/9)*(SU3D[I2, I3, k5]*SU3F[6, I4, k7]*SU3F[I1, k5, k7] + - SU3D[I1, I4, k5]*SU3F[6, I3, k7]*SU3F[I2, k5, k7] + - SU3D[I1, I3, k5]*SU3F[6, I4, k7]*SU3F[I2, k5, k7] + - SU3D[I3, I4, k5]*(SU3F[6, I2, k7]*SU3F[I1, k5, k7] + - SU3F[6, I1, k7]*SU3F[I2, k5, k7]) + SU3D[I1, I4, k5]*SU3F[6, I2, k7]* - SU3F[I3, k5, k7] + SU3D[I1, I2, k5]*SU3F[6, I4, k7]* - SU3F[I3, k5, k7] + SU3D[I2, I4, k5]* - (SU3F[6, I3, k7]*SU3F[I1, k5, k7] + SU3F[6, I1, k7]* - SU3F[I3, k5, k7]) + SU3D[I2, I3, k5]*SU3F[6, I1, k7]* - SU3F[I4, k5, k7] + SU3D[I1, I3, k5]*SU3F[6, I2, k7]* - SU3F[I4, k5, k7] + SU3D[I1, I2, k5]*SU3F[6, I3, k7]* - SU3F[I4, k5, k7]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (SU3D[6, I2, k6]*SU3D[I3, I4, k7]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3D[I3, I4, k7]*SU3F[I2, k6, k7] + - SU3D[6, I2, k6]*SU3D[I1, I4, k7]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[I2, I4, k7]*SU3F[I3, k6, k7] + - SU3D[6, I4, k6]*(SU3D[I2, I3, k7]*SU3F[I1, k6, k7] + - SU3D[I1, I3, k7]*SU3F[I2, k6, k7] + SU3D[I1, I2, k7]* - SU3F[I3, k6, k7]) + SU3D[6, I2, k6]*SU3D[I1, I3, k7]* - SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, I3, k7]*SU3F[I4, k6, k7] + - SU3D[6, I3, k6]*(SU3D[I2, I4, k7]*SU3F[I1, k6, k7] + - SU3D[I1, I4, k7]*SU3F[I2, k6, k7] + SU3D[I1, I2, k7]* - SU3F[I4, k6, k7]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I3, k8]*SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I3, k8]*SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I1, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I2, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I2, k6]*SU3D[8, I1, k8]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I1, k6]*SU3D[8, I2, k8]*SU3D[I4, k7, k8]*SU3F[I3, k6, k7] + - SU3D[6, I4, k6]*(SU3D[8, I3, k8]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[8, I2, k8]* - (SU3D[I3, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I3, k6, k7]) + SU3D[8, I1, k8]* - (SU3D[I3, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I3, k6, k7])) + SU3D[6, I2, k6]*SU3D[8, I3, k8]* - SU3D[I1, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[8, I3, k8]* - SU3D[I2, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I2, k6]*SU3D[8, I1, k8]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[8, I2, k8]* - SU3D[I3, k7, k8]*SU3F[I4, k6, k7] + SU3D[6, I3, k6]* - (SU3D[8, I4, k8]*(SU3D[I2, k7, k8]*SU3F[I1, k6, k7] + - SU3D[I1, k7, k8]*SU3F[I2, k6, k7]) + SU3D[8, I2, k8]* - (SU3D[I4, k7, k8]*SU3F[I1, k6, k7] + SU3D[I1, k7, k8]* - SU3F[I4, k6, k7]) + SU3D[8, I1, k8]* - (SU3D[I4, k7, k8]*SU3F[I2, k6, k7] + SU3D[I2, k7, k8]* - SU3F[I4, k6, k7])))/(6*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/6)*(SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[8, I3, k8]* - SU3F[I1, k6, k7] + SU3D[6, I2, k6]*SU3D[I3, k7, k8]*SU3F[8, I4, k8]* - SU3F[I1, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[8, I3, k8]* - SU3F[I2, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]*SU3F[8, I4, k8]* - SU3F[I2, k6, k7] + SU3D[6, I2, k6]*SU3D[I4, k7, k8]*SU3F[8, I1, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I4, k7, k8]*SU3F[8, I2, k8]* - SU3F[I3, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]*SU3F[8, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]*SU3F[8, I4, k8]* - SU3F[I3, k6, k7] + SU3D[6, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[8, I2, k8]*SU3F[I1, k6, k7] + - SU3F[8, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[8, I3, k8]*SU3F[I1, k6, k7] + SU3F[8, I1, k8]* - SU3F[I3, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[8, I3, k8]*SU3F[I2, k6, k7] + SU3F[8, I2, k8]* - SU3F[I3, k6, k7])) + SU3D[6, I2, k6]*SU3D[I3, k7, k8]* - SU3F[8, I1, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I3, k7, k8]* - SU3F[8, I2, k8]*SU3F[I4, k6, k7] + SU3D[6, I2, k6]*SU3D[I1, k7, k8]* - SU3F[8, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I1, k6]*SU3D[I2, k7, k8]* - SU3F[8, I3, k8]*SU3F[I4, k6, k7] + SU3D[6, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[8, I2, k8]*SU3F[I1, k6, k7] + - SU3F[8, I1, k8]*SU3F[I2, k6, k7]) + SU3D[I2, k7, k8]* - (SU3F[8, I4, k8]*SU3F[I1, k6, k7] + SU3F[8, I1, k8]* - SU3F[I4, k6, k7]) + SU3D[I1, k7, k8]* - (SU3F[8, I4, k8]*SU3F[I2, k6, k7] + SU3F[8, I2, k8]* - SU3F[I4, k6, k7]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/6)*(SU3D[8, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I1, k6, k8] + SU3D[8, I2, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I1, k6, k8] + SU3D[8, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I3, k7]* - SU3F[I2, k6, k8] + SU3D[8, I1, k6]*SU3D[I3, k7, k8]*SU3F[6, I4, k7]* - SU3F[I2, k6, k8] + SU3D[8, I2, k6]*SU3D[I4, k7, k8]*SU3F[6, I1, k7]* - SU3F[I3, k6, k8] + SU3D[8, I1, k6]*SU3D[I4, k7, k8]*SU3F[6, I2, k7]* - SU3F[I3, k6, k8] + SU3D[8, I2, k6]*SU3D[I1, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[8, I1, k6]*SU3D[I2, k7, k8]*SU3F[6, I4, k7]* - SU3F[I3, k6, k8] + SU3D[8, I4, k6]* - (SU3D[I3, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I3, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I3, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I3, k6, k8])) + SU3D[8, I2, k6]*SU3D[I3, k7, k8]* - SU3F[6, I1, k7]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3D[I3, k7, k8]* - SU3F[6, I2, k7]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3D[I1, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3D[I2, k7, k8]* - SU3F[6, I3, k7]*SU3F[I4, k6, k8] + SU3D[8, I3, k6]* - (SU3D[I4, k7, k8]*(SU3F[6, I2, k7]*SU3F[I1, k6, k8] + - SU3F[6, I1, k7]*SU3F[I2, k6, k8]) + SU3D[I2, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I1, k6, k8] + SU3F[6, I1, k7]* - SU3F[I4, k6, k8]) + SU3D[I1, k7, k8]* - (SU3F[6, I4, k7]*SU3F[I2, k6, k8] + SU3F[6, I2, k7]* - SU3F[I4, k6, k8]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[I2, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I3, k5]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I3, k9]*SU3F[8, I4, k5]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I3, k5]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I3, k9]*SU3F[8, I4, k5]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I1, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k9]*SU3F[8, I2, k5]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I1, k9]*SU3F[8, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I2, k9]*SU3F[8, I4, k5]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[6, I3, k9]*(SU3F[8, I2, k5]*SU3F[I1, k6, k9] + - SU3F[8, I1, k5]*SU3F[I2, k6, k9]) + SU3F[6, I2, k9]* - (SU3F[8, I3, k5]*SU3F[I1, k6, k9] + SU3F[8, I1, k5]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k9]* - (SU3F[8, I3, k5]*SU3F[I2, k6, k9] + SU3F[8, I2, k5]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[6, I3, k9]* - SU3F[8, I1, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I3, k9]* - SU3F[8, I2, k5]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[6, I1, k9]* - SU3F[8, I3, k5]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I2, k9]* - SU3F[8, I3, k5]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[6, I4, k9]*(SU3F[8, I2, k5]*SU3F[I1, k6, k9] + - SU3F[8, I1, k5]*SU3F[I2, k6, k9]) + SU3F[6, I2, k9]* - (SU3F[8, I4, k5]*SU3F[I1, k6, k9] + SU3F[8, I1, k5]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k9]* - (SU3F[8, I4, k5]*SU3F[I2, k6, k9] + SU3F[8, I2, k5]* - SU3F[I4, k6, k9])))/(6*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I3, k9]*SU3F[I1, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I3, k5]*SU3F[8, I4, k9]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I3, k9]*SU3F[I2, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I3, k5]*SU3F[8, I4, k9]*SU3F[I2, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I1, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I4, k5]*SU3F[8, I2, k9]*SU3F[I3, k6, k9] + - SU3D[I2, k5, k6]*SU3F[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I1, k5, k6]*SU3F[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I3, k6, k9] + - SU3D[I4, k5, k6]*(SU3F[6, I3, k5]*(SU3F[8, I2, k9]*SU3F[I1, k6, k9] + - SU3F[8, I1, k9]*SU3F[I2, k6, k9]) + SU3F[6, I2, k5]* - (SU3F[8, I3, k9]*SU3F[I1, k6, k9] + SU3F[8, I1, k9]* - SU3F[I3, k6, k9]) + SU3F[6, I1, k5]* - (SU3F[8, I3, k9]*SU3F[I2, k6, k9] + SU3F[8, I2, k9]* - SU3F[I3, k6, k9])) + SU3D[I2, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I1, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I3, k5]* - SU3F[8, I2, k9]*SU3F[I4, k6, k9] + SU3D[I2, k5, k6]*SU3F[6, I1, k5]* - SU3F[8, I3, k9]*SU3F[I4, k6, k9] + SU3D[I1, k5, k6]*SU3F[6, I2, k5]* - SU3F[8, I3, k9]*SU3F[I4, k6, k9] + SU3D[I3, k5, k6]* - (SU3F[6, I4, k5]*(SU3F[8, I2, k9]*SU3F[I1, k6, k9] + - SU3F[8, I1, k9]*SU3F[I2, k6, k9]) + SU3F[6, I2, k5]* - (SU3F[8, I4, k9]*SU3F[I1, k6, k9] + SU3F[8, I1, k9]* - SU3F[I4, k6, k9]) + SU3F[6, I1, k5]* - (SU3F[8, I4, k9]*SU3F[I2, k6, k9] + SU3F[8, I2, k9]* - SU3F[I4, k6, k9])))/(6*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I3, k8]*SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I3, k8]*SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I4, k8]*SU3D[I1, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I4, k8]*SU3D[I2, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I2, k6]*SU3D[8, I1, k8]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I1, k6]*SU3D[8, I2, k8]*SU3D[I4, k6, k7]*SU3F[I3, k7, k8] + - SU3D[6, I4, k6]*(SU3D[8, I3, k8]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[8, I2, k8]* - (SU3D[I3, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I3, k7, k8]) + SU3D[8, I1, k8]* - (SU3D[I3, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I3, k7, k8])) + SU3D[6, I2, k6]*SU3D[8, I3, k8]* - SU3D[I1, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I1, k6]*SU3D[8, I3, k8]* - SU3D[I2, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I2, k6]*SU3D[8, I1, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I1, k6]*SU3D[8, I2, k8]* - SU3D[I3, k6, k7]*SU3F[I4, k7, k8] + SU3D[6, I3, k6]* - (SU3D[8, I4, k8]*(SU3D[I2, k6, k7]*SU3F[I1, k7, k8] + - SU3D[I1, k6, k7]*SU3F[I2, k7, k8]) + SU3D[8, I2, k8]* - (SU3D[I4, k6, k7]*SU3F[I1, k7, k8] + SU3D[I1, k6, k7]* - SU3F[I4, k7, k8]) + SU3D[8, I1, k8]* - (SU3D[I4, k6, k7]*SU3F[I2, k7, k8] + SU3D[I2, k6, k7]* - SU3F[I4, k7, k8])))/(6*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/6)*(SU3D[8, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I1, k7, k9] + SU3D[8, I2, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I1, k7, k9] + SU3D[8, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I3, k9]* - SU3F[I2, k7, k9] + SU3D[8, I1, k6]*SU3D[I3, k6, k7]*SU3F[6, I4, k9]* - SU3F[I2, k7, k9] + SU3D[8, I2, k6]*SU3D[I4, k6, k7]*SU3F[6, I1, k9]* - SU3F[I3, k7, k9] + SU3D[8, I1, k6]*SU3D[I4, k6, k7]*SU3F[6, I2, k9]* - SU3F[I3, k7, k9] + SU3D[8, I2, k6]*SU3D[I1, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[8, I1, k6]*SU3D[I2, k6, k7]*SU3F[6, I4, k9]* - SU3F[I3, k7, k9] + SU3D[8, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I3, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[8, I2, k6]*SU3D[I3, k6, k7]* - SU3F[6, I1, k9]*SU3F[I4, k7, k9] + SU3D[8, I1, k6]*SU3D[I3, k6, k7]* - SU3F[6, I2, k9]*SU3F[I4, k7, k9] + SU3D[8, I2, k6]*SU3D[I1, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[8, I1, k6]*SU3D[I2, k6, k7]* - SU3F[6, I3, k9]*SU3F[I4, k7, k9] + SU3D[8, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[6, I2, k9]*SU3F[I1, k7, k9] + - SU3F[6, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I1, k7, k9] + SU3F[6, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[6, I4, k9]*SU3F[I2, k7, k9] + SU3F[6, I2, k9]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/6)*(SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k9]* - SU3F[I1, k7, k9] + SU3D[6, I2, k6]*SU3D[I3, k6, k7]*SU3F[8, I4, k9]* - SU3F[I1, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[8, I3, k9]* - SU3F[I2, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]*SU3F[8, I4, k9]* - SU3F[I2, k7, k9] + SU3D[6, I2, k6]*SU3D[I4, k6, k7]*SU3F[8, I1, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I4, k6, k7]*SU3F[8, I2, k9]* - SU3F[I3, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]*SU3F[8, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]*SU3F[8, I4, k9]* - SU3F[I3, k7, k9] + SU3D[6, I4, k6]* - (SU3D[I3, k6, k7]*(SU3F[8, I2, k9]*SU3F[I1, k7, k9] + - SU3F[8, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I3, k9]*SU3F[I1, k7, k9] + SU3F[8, I1, k9]* - SU3F[I3, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I3, k9]*SU3F[I2, k7, k9] + SU3F[8, I2, k9]* - SU3F[I3, k7, k9])) + SU3D[6, I2, k6]*SU3D[I3, k6, k7]* - SU3F[8, I1, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I3, k6, k7]* - SU3F[8, I2, k9]*SU3F[I4, k7, k9] + SU3D[6, I2, k6]*SU3D[I1, k6, k7]* - SU3F[8, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I1, k6]*SU3D[I2, k6, k7]* - SU3F[8, I3, k9]*SU3F[I4, k7, k9] + SU3D[6, I3, k6]* - (SU3D[I4, k6, k7]*(SU3F[8, I2, k9]*SU3F[I1, k7, k9] + - SU3F[8, I1, k9]*SU3F[I2, k7, k9]) + SU3D[I2, k6, k7]* - (SU3F[8, I4, k9]*SU3F[I1, k7, k9] + SU3F[8, I1, k9]* - SU3F[I4, k7, k9]) + SU3D[I1, k6, k7]* - (SU3F[8, I4, k9]*SU3F[I2, k7, k9] + SU3F[8, I2, k9]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/6)*(SU3F[6, I2, k8]*SU3F[8, I4, k9]*SU3F[I1, k7, k9]* - SU3F[I3, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I4, k9]*SU3F[I2, k7, k9]* - SU3F[I3, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I4, k9]*SU3F[I1, k7, k8]* - SU3F[I3, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I4, k9]*SU3F[I2, k7, k8]* - SU3F[I3, k7, k9] + SU3F[6, I4, k8]* - (SU3F[8, I3, k9]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I3, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I3, k7, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k7, k9]*SU3F[I3, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I3, k7, k9])) + SU3F[6, I2, k8]*SU3F[8, I3, k9]* - SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I3, k9]* - SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I1, k9]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I1, k8]*SU3F[8, I2, k9]* - SU3F[I3, k7, k9]*SU3F[I4, k7, k8] + SU3F[6, I2, k8]*SU3F[8, I3, k9]* - SU3F[I1, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I3, k9]* - SU3F[I2, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I2, k8]*SU3F[8, I1, k9]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I1, k8]*SU3F[8, I2, k9]* - SU3F[I3, k7, k8]*SU3F[I4, k7, k9] + SU3F[6, I3, k8]* - (SU3F[8, I4, k9]*(SU3F[I1, k7, k9]*SU3F[I2, k7, k8] + - SU3F[I1, k7, k8]*SU3F[I2, k7, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k7, k9]*SU3F[I4, k7, k8] + SU3F[I1, k7, k8]* - SU3F[I4, k7, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k7, k9]*SU3F[I4, k7, k8] + SU3F[I2, k7, k8]* - SU3F[I4, k7, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - (SU3D[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + - SU3D[6, I2, k5]*SU3F[8, I4, k9]*SU3F[I1, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I1, k5]*SU3F[8, I4, k9]*SU3F[I2, k5, k8]*SU3F[I3, k8, k9] + - SU3D[6, I4, k5]*(SU3F[8, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I3, k8, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I3, k8, k9])) + SU3D[6, I2, k5]*SU3F[8, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[8, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[8, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I1, k5]*SU3F[8, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k5, k8] + SU3D[6, I2, k5]*SU3F[8, I3, k9]* - SU3F[I1, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[8, I3, k9]* - SU3F[I2, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I2, k5]*SU3F[8, I1, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I1, k5]*SU3F[8, I2, k9]* - SU3F[I3, k5, k8]*SU3F[I4, k8, k9] + SU3D[6, I3, k5]* - (SU3F[8, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3F[8, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I4, k8, k9]) + SU3F[8, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k5, k8] + SU3F[I2, k5, k8]* - SU3F[I4, k8, k9])))/(6*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (SU3D[8, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + - SU3D[8, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + - SU3D[8, I2, k6]*SU3F[6, I4, k9]*SU3F[I1, k6, k8]*SU3F[I3, k8, k9] + - SU3D[8, I1, k6]*SU3F[6, I4, k9]*SU3F[I2, k6, k8]*SU3F[I3, k8, k9] + - SU3D[8, I4, k6]*(SU3F[6, I3, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I3, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I3, k8, k9])) + SU3D[8, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k8] + SU3D[8, I2, k6]*SU3F[6, I3, k9]* - SU3F[I1, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I1, k6]*SU3F[6, I3, k9]* - SU3F[I2, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I2, k6]*SU3F[6, I1, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I1, k6]*SU3F[6, I2, k9]* - SU3F[I3, k6, k8]*SU3F[I4, k8, k9] + SU3D[8, I3, k6]* - (SU3F[6, I4, k9]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k8] + - SU3F[I1, k6, k8]*SU3F[I2, k8, k9]) + SU3F[6, I2, k9]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k8] + SU3F[I1, k6, k8]* - SU3F[I4, k8, k9]) + SU3F[6, I1, k9]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k8] + SU3F[I2, k6, k8]* - SU3F[I4, k8, k9])))/(6*Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/6)*(SU3D[6, I2, k8]*SU3D[8, I4, k6]*SU3F[I1, k8, k9]* - SU3F[I3, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I4, k6]*SU3F[I2, k8, k9]* - SU3F[I3, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I4, k6]*SU3F[I1, k6, k9]* - SU3F[I3, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I4, k6]*SU3F[I2, k6, k9]* - SU3F[I3, k8, k9] + SU3D[6, I4, k8]* - (SU3D[8, I3, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[8, I2, k6]* - (SU3F[I1, k8, k9]*SU3F[I3, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I3, k8, k9]) + SU3D[8, I1, k6]* - (SU3F[I2, k8, k9]*SU3F[I3, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I3, k8, k9])) + SU3D[6, I2, k8]*SU3D[8, I3, k6]* - SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I3, k6]* - SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I1, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I1, k8]*SU3D[8, I2, k6]* - SU3F[I3, k8, k9]*SU3F[I4, k6, k9] + SU3D[6, I2, k8]*SU3D[8, I3, k6]* - SU3F[I1, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I3, k6]* - SU3F[I2, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I2, k8]*SU3D[8, I1, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I1, k8]*SU3D[8, I2, k6]* - SU3F[I3, k6, k9]*SU3F[I4, k8, k9] + SU3D[6, I3, k8]* - (SU3D[8, I4, k6]*(SU3F[I1, k8, k9]*SU3F[I2, k6, k9] + - SU3F[I1, k6, k9]*SU3F[I2, k8, k9]) + SU3D[8, I2, k6]* - (SU3F[I1, k8, k9]*SU3F[I4, k6, k9] + SU3F[I1, k6, k9]* - SU3F[I4, k8, k9]) + SU3D[8, I1, k6]* - (SU3F[I2, k8, k9]*SU3F[I4, k6, k9] + SU3F[I2, k6, k9]* - SU3F[I4, k8, k9]))))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/9)*(SU3D[I2, I3, I4]*SUNDelta[6, I1] + SU3D[I1, I3, I4]* - SUNDelta[6, I2] + SU3D[I1, I2, I4]*SUNDelta[6, I3] + - SU3D[I1, I2, I3]*SUNDelta[6, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (2*(SU3D[I2, I3, k5]*SU3F[8, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SU3F[8, I3, k5]*SUNDelta[6, I2] + - SU3D[I1, I3, k5]*SU3F[8, I4, k5]*SUNDelta[6, I2] + - SU3D[I3, I4, k5]*(SU3F[8, I2, k5]*SUNDelta[6, I1] + - SU3F[8, I1, k5]*SUNDelta[6, I2]) + SU3D[I1, I4, k5]*SU3F[8, I2, k5]* - SUNDelta[6, I3] + SU3D[I1, I2, k5]*SU3F[8, I4, k5]*SUNDelta[6, I3] + - SU3D[I2, I4, k5]*(SU3F[8, I3, k5]*SUNDelta[6, I1] + - SU3F[8, I1, k5]*SUNDelta[6, I3]) + SU3D[I2, I3, k5]*SU3F[8, I1, k5]* - SUNDelta[6, I4] + SU3D[I1, I3, k5]*SU3F[8, I2, k5]*SUNDelta[6, I4] + - SU3D[I1, I2, k5]*SU3F[8, I3, k5]*SUNDelta[6, I4]))/ - (9*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((2*I)/9)*(SU3D[8, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I1] + - SU3D[8, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[6, I2] + - SU3D[8, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[6, I3] + - SU3D[8, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[6, I3] + - SU3D[8, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[6, I1] + - SU3D[I1, I3, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I3]) + SU3D[8, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[6, I4] + SU3D[8, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[6, I4] + - SU3D[8, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[6, I1] + - SU3D[I1, I4, k5]*SUNDelta[6, I2] + SU3D[I1, I2, k5]* - SUNDelta[6, I4])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/18)*(SU3D[I1, I4, k9]*SU3D[I2, k6, k9]*SU3D[I3, k5, k6] + - SU3D[I1, I4, k9]*SU3D[I2, k5, k6]*SU3D[I3, k6, k9] + - SU3D[I1, I3, k9]*SU3D[I2, k6, k9]*SU3D[I4, k5, k6] + - SU3D[I1, I2, k9]*SU3D[I3, k6, k9]*SU3D[I4, k5, k6] + - SU3D[I1, k6, k9]*(SU3D[I2, k5, k6]*SU3D[I3, I4, k9] + - SU3D[I2, I4, k9]*SU3D[I3, k5, k6] + SU3D[I2, I3, k9]* - SU3D[I4, k5, k6]) + SU3D[I1, I3, k9]*SU3D[I2, k5, k6]* - SU3D[I4, k6, k9] + SU3D[I1, I2, k9]*SU3D[I3, k5, k6]* - SU3D[I4, k6, k9] + SU3D[I1, k5, k6]* - (SU3D[I2, k6, k9]*SU3D[I3, I4, k9] + SU3D[I2, I4, k9]* - SU3D[I3, k6, k9] + SU3D[I2, I3, k9]*SU3D[I4, k6, k9]))* - SUNDelta[6, k5])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((SU3D[I2, I3, k9]*SU3D[I4, k8, k9]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3D[I3, I4, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I4, k9]*SU3D[I3, k8, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I3, k9]*SU3D[I4, k8, k9]*SU3F[I2, k7, k8] + - SU3D[I1, I2, k9]*SU3D[I4, k8, k9]*SU3F[I3, k7, k8] + - SU3D[I2, I4, k9]*(SU3D[I3, k8, k9]*SU3F[I1, k7, k8] + - SU3D[I1, k8, k9]*SU3F[I3, k7, k8]) + SU3D[I1, k8, k9]* - SU3D[I2, I3, k9]*SU3F[I4, k7, k8] + SU3D[I1, I2, k9]*SU3D[I3, k8, k9]* - SU3F[I4, k7, k8] + SU3D[I2, k8, k9]* - (SU3D[I3, I4, k9]*SU3F[I1, k7, k8] + SU3D[I1, I4, k9]* - SU3F[I3, k7, k8] + SU3D[I1, I3, k9]*SU3F[I4, k7, k8]))* - SUNDelta[6, k7])/(18*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((SU3D[I2, I3, k9]*SU3D[I4, k7, k8]*SU3F[I1, k8, k9] + - SU3D[I1, k7, k8]*SU3D[I3, I4, k9]*SU3F[I2, k8, k9] + - SU3D[I1, I4, k9]*SU3D[I3, k7, k8]*SU3F[I2, k8, k9] + - SU3D[I1, I3, k9]*SU3D[I4, k7, k8]*SU3F[I2, k8, k9] + - SU3D[I1, I2, k9]*SU3D[I4, k7, k8]*SU3F[I3, k8, k9] + - SU3D[I2, I4, k9]*(SU3D[I3, k7, k8]*SU3F[I1, k8, k9] + - SU3D[I1, k7, k8]*SU3F[I3, k8, k9]) + SU3D[I1, k7, k8]* - SU3D[I2, I3, k9]*SU3F[I4, k8, k9] + SU3D[I1, I2, k9]*SU3D[I3, k7, k8]* - SU3F[I4, k8, k9] + SU3D[I2, k7, k8]* - (SU3D[I3, I4, k9]*SU3F[I1, k8, k9] + SU3D[I1, I4, k9]* - SU3F[I3, k8, k9] + SU3D[I1, I3, k9]*SU3F[I4, k8, k9]))* - SUNDelta[6, k7])/(18*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) - - ((I/18)*(SU3D[I3, I4, k5]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k9] + - SU3F[I1, k5, k9]*SU3F[I2, k8, k9]) + SU3D[I1, I4, k5]* - SU3F[I2, k8, k9]*SU3F[I3, k5, k9] + SU3D[I1, I4, k5]*SU3F[I2, k5, k9]* - SU3F[I3, k8, k9] + SU3D[I2, I4, k5]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k9] + SU3F[I1, k5, k9]* - SU3F[I3, k8, k9]) + SU3D[I2, I3, k5]*SU3F[I1, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I1, I3, k5]*SU3F[I2, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I1, I2, k5]*SU3F[I3, k8, k9]* - SU3F[I4, k5, k9] + SU3D[I2, I3, k5]*SU3F[I1, k5, k9]* - SU3F[I4, k8, k9] + SU3D[I1, I3, k5]*SU3F[I2, k5, k9]* - SU3F[I4, k8, k9] + SU3D[I1, I2, k5]*SU3F[I3, k5, k9]* - SU3F[I4, k8, k9])*SUNDelta[6, k8])/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - (SU3D[I2, I3, I4]*SUNDelta[7, I1] + SU3D[I1, I3, I4]*SUNDelta[7, I2] + - SU3D[I1, I2, I4]*SUNDelta[7, I3] + SU3D[I1, I2, I3]*SUNDelta[7, I4])/ - (3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - ((SU3D[I1, I4, k7]*SU3D[I2, k6, k7]*SU3D[I3, k5, k6] + - SU3D[I1, I4, k7]*SU3D[I2, k5, k6]*SU3D[I3, k6, k7] + - SU3D[I1, I3, k7]*SU3D[I2, k6, k7]*SU3D[I4, k5, k6] + - SU3D[I1, I2, k7]*SU3D[I3, k6, k7]*SU3D[I4, k5, k6] + - SU3D[I1, k6, k7]*(SU3D[I2, k5, k6]*SU3D[I3, I4, k7] + - SU3D[I2, I4, k7]*SU3D[I3, k5, k6] + SU3D[I2, I3, k7]* - SU3D[I4, k5, k6]) + SU3D[I1, I3, k7]*SU3D[I2, k5, k6]* - SU3D[I4, k6, k7] + SU3D[I1, I2, k7]*SU3D[I3, k5, k6]* - SU3D[I4, k6, k7] + SU3D[I1, k5, k6]* - (SU3D[I2, k6, k7]*SU3D[I3, I4, k7] + SU3D[I2, I4, k7]* - SU3D[I3, k6, k7] + SU3D[I2, I3, k7]*SU3D[I4, k6, k7]))* - SUNDelta[7, k5])/(6*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - ((I/6)*(SU3D[I2, I3, k5]*SU3D[I4, k6, k7]*SU3F[I1, k5, k7] + - SU3D[I1, k6, k7]*SU3D[I3, I4, k5]*SU3F[I2, k5, k7] + - SU3D[I1, I4, k5]*SU3D[I3, k6, k7]*SU3F[I2, k5, k7] + - SU3D[I1, I3, k5]*SU3D[I4, k6, k7]*SU3F[I2, k5, k7] + - SU3D[I1, I2, k5]*SU3D[I4, k6, k7]*SU3F[I3, k5, k7] + - SU3D[I2, I4, k5]*(SU3D[I3, k6, k7]*SU3F[I1, k5, k7] + - SU3D[I1, k6, k7]*SU3F[I3, k5, k7]) + SU3D[I1, k6, k7]* - SU3D[I2, I3, k5]*SU3F[I4, k5, k7] + SU3D[I1, I2, k5]*SU3D[I3, k6, k7]* - SU3F[I4, k5, k7] + SU3D[I2, k6, k7]* - (SU3D[I3, I4, k5]*SU3F[I1, k5, k7] + SU3D[I1, I4, k5]* - SU3F[I3, k5, k7] + SU3D[I1, I3, k5]*SU3F[I4, k5, k7]))* - SUNDelta[7, k6])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - ((I/6)*(SU3D[I2, I3, k5]*SU3D[I4, k5, k6]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3D[I3, I4, k5]*SU3F[I2, k6, k9] + - SU3D[I1, I4, k5]*SU3D[I3, k5, k6]*SU3F[I2, k6, k9] + - SU3D[I1, I3, k5]*SU3D[I4, k5, k6]*SU3F[I2, k6, k9] + - SU3D[I1, I2, k5]*SU3D[I4, k5, k6]*SU3F[I3, k6, k9] + - SU3D[I2, I4, k5]*(SU3D[I3, k5, k6]*SU3F[I1, k6, k9] + - SU3D[I1, k5, k6]*SU3F[I3, k6, k9]) + SU3D[I1, k5, k6]* - SU3D[I2, I3, k5]*SU3F[I4, k6, k9] + SU3D[I1, I2, k5]*SU3D[I3, k5, k6]* - SU3F[I4, k6, k9] + SU3D[I2, k5, k6]* - (SU3D[I3, I4, k5]*SU3F[I1, k6, k9] + SU3D[I1, I4, k5]* - SU3F[I3, k6, k9] + SU3D[I1, I3, k5]*SU3F[I4, k6, k9]))* - SUNDelta[7, k9])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - - ((SU3D[I3, I4, k5]*(SU3F[I1, k8, k9]*SU3F[I2, k5, k8] + - SU3F[I1, k5, k8]*SU3F[I2, k8, k9]) + SU3D[I1, I4, k5]* - SU3F[I2, k8, k9]*SU3F[I3, k5, k8] + SU3D[I1, I4, k5]*SU3F[I2, k5, k8]* - SU3F[I3, k8, k9] + SU3D[I2, I4, k5]* - (SU3F[I1, k8, k9]*SU3F[I3, k5, k8] + SU3F[I1, k5, k8]* - SU3F[I3, k8, k9]) + SU3D[I2, I3, k5]*SU3F[I1, k8, k9]* - SU3F[I4, k5, k8] + SU3D[I1, I3, k5]*SU3F[I2, k8, k9]* - SU3F[I4, k5, k8] + SU3D[I1, I2, k5]*SU3F[I3, k8, k9]* - SU3F[I4, k5, k8] + SU3D[I2, I3, k5]*SU3F[I1, k5, k8]* - SU3F[I4, k8, k9] + SU3D[I1, I3, k5]*SU3F[I2, k5, k8]* - SU3F[I4, k8, k9] + SU3D[I1, I2, k5]*SU3F[I3, k5, k8]* - SU3F[I4, k8, k9])*SUNDelta[7, k9])/ - (6*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) - - (2*(SU3D[I2, I3, k5]*SU3F[6, I4, k5]*SUNDelta[8, I1] + - SU3D[I1, I4, k5]*SU3F[6, I3, k5]*SUNDelta[8, I2] + - SU3D[I1, I3, k5]*SU3F[6, I4, k5]*SUNDelta[8, I2] + - SU3D[I3, I4, k5]*(SU3F[6, I2, k5]*SUNDelta[8, I1] + - SU3F[6, I1, k5]*SUNDelta[8, I2]) + SU3D[I1, I4, k5]*SU3F[6, I2, k5]* - SUNDelta[8, I3] + SU3D[I1, I2, k5]*SU3F[6, I4, k5]*SUNDelta[8, I3] + - SU3D[I2, I4, k5]*(SU3F[6, I3, k5]*SUNDelta[8, I1] + - SU3F[6, I1, k5]*SUNDelta[8, I3]) + SU3D[I2, I3, k5]*SU3F[6, I1, k5]* - SUNDelta[8, I4] + SU3D[I1, I3, k5]*SU3F[6, I2, k5]*SUNDelta[8, I4] + - SU3D[I1, I2, k5]*SU3F[6, I3, k5]*SUNDelta[8, I4]))/ - (9*Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) + - (((2*I)/9)*(SU3D[6, I2, k5]*SU3D[I3, I4, k5]*SUNDelta[8, I1] + - SU3D[6, I1, k5]*SU3D[I3, I4, k5]*SUNDelta[8, I2] + - SU3D[6, I2, k5]*SU3D[I1, I4, k5]*SUNDelta[8, I3] + - SU3D[6, I1, k5]*SU3D[I2, I4, k5]*SUNDelta[8, I3] + - SU3D[6, I4, k5]*(SU3D[I2, I3, k5]*SUNDelta[8, I1] + - SU3D[I1, I3, k5]*SUNDelta[8, I2] + SU3D[I1, I2, k5]* - SUNDelta[8, I3]) + SU3D[6, I2, k5]*SU3D[I1, I3, k5]* - SUNDelta[8, I4] + SU3D[6, I1, k5]*SU3D[I2, I3, k5]*SUNDelta[8, I4] + - SU3D[6, I3, k5]*(SU3D[I2, I4, k5]*SUNDelta[8, I1] + - SU3D[I1, I4, k5]*SUNDelta[8, I2] + SU3D[I1, I2, k5]* - SUNDelta[8, I4])))/(Sqrt[3]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (((4*I)/27)*(SU3D[6, I3, I4]*SUNDelta[I1, I2] + SU3D[6, I2, I4]* - SUNDelta[I1, I3] + SU3D[6, I2, I3]*SUNDelta[I1, I4] + - SU3D[6, I1, I4]*SUNDelta[I2, I3] + SU3D[6, I1, I3]*SUNDelta[I2, I4] + - SU3D[6, I1, I2]*SUNDelta[I3, I4]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - (((2*I)/27)*SUNDelta[6, k4]*(SU3D[I3, I4, k4]*SUNDelta[I1, I2] + - SU3D[I2, I4, k4]*SUNDelta[I1, I3] + SU3D[I2, I3, k4]* - SUNDelta[I1, I4] + SU3D[I1, I4, k4]*SUNDelta[I2, I3] + - SU3D[I1, I3, k4]*SUNDelta[I2, I4] + SU3D[I1, I2, k4]* - SUNDelta[I3, I4]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - (2*SUNDelta[7, k4]*(SU3D[I3, I4, k4]*SUNDelta[I1, I2] + - SU3D[I2, I4, k4]*SUNDelta[I1, I3] + SU3D[I2, I3, k4]* - SUNDelta[I1, I4] + SU3D[I1, I4, k4]*SUNDelta[I2, I3] + - SU3D[I1, I3, k4]*SUNDelta[I2, I4] + SU3D[I1, I2, k4]* - SUNDelta[I3, I4]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4) + - (((4*I)/27)*(SUNDelta[6, I2]*SUNDelta[8, I4]*SUNDelta[I1, I3] + - SUNDelta[6, I2]*SUNDelta[8, I3]*SUNDelta[I1, I4] + - SUNDelta[6, I1]*SUNDelta[8, I4]*SUNDelta[I2, I3] + - SUNDelta[6, I4]*(SUNDelta[8, I3]*SUNDelta[I1, I2] + - SUNDelta[8, I2]*SUNDelta[I1, I3] + SUNDelta[8, I1]* - SUNDelta[I2, I3]) + SUNDelta[6, I1]*SUNDelta[8, I3]* - SUNDelta[I2, I4] + SUNDelta[6, I3]* - (SUNDelta[8, I4]*SUNDelta[I1, I2] + SUNDelta[8, I2]* - SUNDelta[I1, I4] + SUNDelta[8, I1]*SUNDelta[I2, I4]) + - SUNDelta[6, I2]*SUNDelta[8, I1]*SUNDelta[I3, I4] + - SUNDelta[6, I1]*SUNDelta[8, I2]*SUNDelta[I3, I4]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4))}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10o2.Gen deleted file mode 100644 index c720f1c90..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10o2.Gen +++ /dev/null @@ -1,6 +0,0 @@ -{MomentaScalarProduct[p2, p4], MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p1, p4], MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p1, p2], MomentaScalarProduct[p2, p3], -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10o2.Mod deleted file mode 100644 index cd7aa6037..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10P10o2.Mod +++ /dev/null @@ -1,1492 +0,0 @@ -{{((-I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((-I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((-I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/6)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/12)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/4)*CouplingConstant[ChPTW3[2], 1]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 - ((I/24)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - -((I/24)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/24)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]))/ - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - -((I/24)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}, -{((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/36)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + ((I/12)*CouplingConstant[ChPTW3[2], 2]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I4]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I4]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ - (Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o2.Gen deleted file mode 100644 index 531a98fd9..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o2.Gen +++ /dev/null @@ -1,5 +0,0 @@ -{MomentaScalarProduct[p2, p3], MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p1, p2], ParticleMass[PseudoScalar[8], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[2], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[7], -RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o2.Mod deleted file mode 100644 index 3962e1510..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o2.Mod +++ /dev/null @@ -1,479 +0,0 @@ -{{(3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]*SU3F[I1, I2, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3F[I1, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I3]*SUNDelta[I1, I2] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I2]*SUNDelta[I1, I3] - - 4*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]*SU3F[I1, I2, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I3]*SUNDelta[I1, I2] - - 4*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I2]*SUNDelta[I1, I3] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3F[I1, I3, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, I3, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] - - 4*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I3]*SUNDelta[I1, I2] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I2]*SUNDelta[I1, I3] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3D[6, I2, k2]* - SU3D[I1, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3D[6, I3, k2]*SU3D[I1, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I3, k1]*SU3D[8, I2, k2]*SU3D[I1, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[8, I3, k2]* - SU3D[I1, k1, k2] + 12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I2, I3, k1] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3D[6, I1, k2]*SU3D[I2, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, k1]*SU3D[6, I3, k2]*SU3D[I2, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[8, I1, k2]* - SU3D[I2, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I3, k2]*SU3D[I2, k1, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[6, I1, k2]* - SU3D[I3, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3D[6, I2, k2]*SU3D[I3, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3D[8, I1, k2]*SU3D[I3, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[8, I2, k2]* - SU3D[I3, k1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I2, k1, k2]*SU3F[3, I1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[I3, k1, k2]*SU3F[3, I1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, k1, k2]* - SU3F[3, I2, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I3, k1, k2]*SU3F[3, I2, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[I1, k1, k2]*SU3F[3, I3, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3F[3, I3, k2] + (12*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k1] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3D[I2, k1, k2]*SU3F[6, I1, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3D[I3, k1, k2]*SU3F[6, I1, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]* - SU3F[3, I2, k1]*SU3F[6, I1, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I2, k1, k2]*SU3F[3, I3, k1]*SU3F[6, I1, k2] + - (12*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]*SU3F[3, I1, k2]* - SU3F[6, I2, k1] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3D[I1, k1, k2]*SU3F[6, I2, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3D[I1, k1, k2]* - SU3F[6, I2, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3D[I3, k1, k2]* - SU3F[6, I2, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]* - SU3F[3, I3, k1]*SU3F[6, I2, k2] + (12*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I2, k1, k2]*SU3F[3, I1, k2]*SU3F[6, I3, k1] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3F[3, I2, k2]* - SU3F[6, I3, k1] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3D[I1, k1, k2]*SU3F[6, I3, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]* - SU3F[6, I3, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3D[I2, k1, k2]*SU3F[6, I3, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3D[I2, k1, k2]* - SU3F[6, I3, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[I2, k1, k2]*SU3F[8, I1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I3, k1, k2]*SU3F[8, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I3, k1, k2]*SU3F[6, I2, k1]*SU3F[8, I1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[6, I3, k1]* - SU3F[8, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3F[8, I2, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I3, k1, k2]* - SU3F[8, I2, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, k1, k2]*SU3F[6, I3, k1]*SU3F[8, I2, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[8, I3, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, k1, k2]*SU3F[6, I2, k2]*SU3F[8, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3F[8, I3, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3F[8, I3, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3D[6, I2, k2]*SU3F[I1, k1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3D[6, I3, k2]*SU3F[I1, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[8, I2, k2]*SU3F[I1, k1, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[8, I3, k2]* - SU3F[I1, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3F[3, I2, k2]*SU3F[I1, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[3, I3, k2]*SU3F[I1, k1, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I3, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3F[6, I3, k2]*SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SU3F[6, I3, k2]* - SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k1]* - SU3F[8, I2, k2]*SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]* - SU3F[8, I3, k2]*SU3F[I1, k1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I3, k1]*SU3D[6, I1, k2]*SU3F[I2, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[6, I3, k2]* - SU3F[I2, k1, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[8, I1, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[8, I3, k2]*SU3F[I2, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3F[3, I1, k2]*SU3F[I2, k1, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[3, I3, k2]* - SU3F[I2, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3F[6, I1, k2]*SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3F[6, I3, k2]*SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]*SU3F[6, I3, k2]* - SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k1]* - SU3F[8, I1, k2]*SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I1, k1]* - SU3F[8, I3, k2]*SU3F[I2, k1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3D[6, I1, k2]*SU3F[I3, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[6, I2, k2]* - SU3F[I3, k1, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[8, I1, k2]*SU3F[I3, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[8, I2, k2]*SU3F[I3, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[3, I1, k2]*SU3F[I3, k1, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[3, I2, k2]* - SU3F[I3, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3F[6, I1, k2]*SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3F[6, I2, k2]*SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, k1]*SU3F[6, I2, k2]*SU3F[I3, k1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k2]*SU3F[I3, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]* - SU3F[8, I1, k2]*SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I1, k1]* - SU3F[8, I2, k2]*SU3F[I3, k1, k2] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, I3]*SUNDelta[3, I1] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I3]*SUNDelta[3, I2] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I2]*SUNDelta[3, I3] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, I3]*SUNDelta[6, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, I3]*SUNDelta[6, I1] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, I3]*SUNDelta[6, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I3]*SUNDelta[6, I2] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, I2]*SUNDelta[6, I3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I2]*SUNDelta[6, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, I3]* - SUNDelta[8, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I3]*SUNDelta[8, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, I2]*SUNDelta[8, I3] + 8*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I3]*SUNDelta[I1, I2] + 8*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I2]*SUNDelta[I1, I3] + 8*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-2*(3*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I3, k1]*SU3D[I1, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I2, k1]*SU3D[I1, I3, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[8, I2, k2]* - SU3D[I1, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[8, I3, k2]*SU3D[I1, k1, k2] + - 3*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I1, k1]*SU3D[I2, I3, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[8, I1, k2]* - SU3D[I2, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I3, k2]*SU3D[I2, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[8, I1, k2]* - SU3D[I3, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I2, k2]*SU3D[I3, k1, k2] + - (3*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I2, k1, k2]*SU3F[6, I1, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + (3*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]* - SU3F[6, I2, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I3, k1]*SU3D[I1, k1, k2]*SU3F[6, I2, k2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2] + (3*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]* - SU3F[6, I3, k2] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I1, k1]*SU3D[I2, k1, k2]*SU3F[6, I3, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, I3, k1]*SU3F[7, I1, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]*SU3F[7, I2, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]*SU3F[7, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I2, k1, k2]*SU3F[8, I1, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3F[8, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[I3, k1, k2]*SU3F[6, I2, k1]*SU3F[8, I1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]* - SU3F[6, I3, k1]*SU3F[8, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3F[8, I2, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I3, k1, k2]* - SU3F[8, I2, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, k1, k2]*SU3F[6, I3, k1]*SU3F[8, I2, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2]*SU3F[8, I3, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]*SU3F[8, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3F[8, I3, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3F[8, I3, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[8, I2, k2]*SU3F[I1, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[8, I3, k2]*SU3F[I1, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3F[8, I2, k2]* - SU3F[I1, k1, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3F[8, I3, k2]* - SU3F[I1, k1, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I2, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[8, I1, k2]*SU3F[I2, k1, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[8, I3, k2]* - SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3F[6, I3, k2]* - SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k1]* - SU3F[8, I1, k2]*SU3F[I2, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[8, I3, k2]* - SU3F[I2, k1, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[8, I1, k2]*SU3F[I3, k1, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[8, I2, k2]* - SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k2]*SU3F[I3, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]* - SU3F[8, I1, k2]*SU3F[I3, k1, k2] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[8, I2, k2]* - SU3F[I3, k1, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, I3]* - SUNDelta[6, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I1, I3]*SUNDelta[6, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I2]*SUNDelta[6, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, I3]* - SUNDelta[8, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I3]*SUNDelta[8, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, I2]*SUNDelta[8, I3] + 2*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I3]*SUNDelta[I1, I2] + (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[7, I3]*SUNDelta[I1, I2] + 2*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I2]*SUNDelta[I1, I3] + (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[7, I2]*SUNDelta[I1, I3] + 2*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I1]*SUNDelta[I2, I3] + (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[7, I1]*SUNDelta[I2, I3]))/ -(27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-6*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - (18*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I3, k1]*SU3D[I1, I2, k1] - - 6*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] + - (18*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I2, k1]*SU3D[I1, I3, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3D[6, I2, k2]* - SU3D[I1, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3D[6, I3, k2]*SU3D[I1, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I3, k1]*SU3D[8, I2, k2]*SU3D[I1, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[8, I3, k2]* - SU3D[I1, k1, k2] - 6*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I2, I3, k1] + (18*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I1, k1]* - SU3D[I2, I3, k1] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3D[6, I1, k2]*SU3D[I2, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, k1]*SU3D[6, I3, k2]*SU3D[I2, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[8, I1, k2]* - SU3D[I2, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I3, k2]*SU3D[I2, k1, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[6, I1, k2]* - SU3D[I3, k1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3D[6, I2, k2]*SU3D[I3, k1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3D[8, I1, k2]*SU3D[I3, k1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[8, I2, k2]* - SU3D[I3, k1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I2, k1, k2]*SU3F[3, I1, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[I3, k1, k2]*SU3F[3, I1, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, k1, k2]* - SU3F[3, I2, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I3, k1, k2]*SU3F[3, I2, k2] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[I1, k1, k2]*SU3F[3, I3, k2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3F[3, I3, k2] - (6*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, I3, k1]* - SU3F[6, I1, k1] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3D[I2, k1, k2]*SU3F[6, I1, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3D[I3, k1, k2]*SU3F[6, I1, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]* - SU3F[3, I2, k1]*SU3F[6, I1, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I2, k1, k2]*SU3F[3, I3, k1]*SU3F[6, I1, k2] - - (6*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]*SU3F[3, I1, k2]* - SU3F[6, I2, k1] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3D[I1, k1, k2]*SU3F[6, I2, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3D[I1, k1, k2]* - SU3F[6, I2, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3D[I3, k1, k2]*SU3F[6, I2, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3D[I3, k1, k2]* - SU3F[6, I2, k2] - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]* - SU3F[3, I3, k1]*SU3F[6, I2, k2] - (6*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, I2, k1]*SU3F[6, I3, k1] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I2, k1, k2]*SU3F[3, I1, k2]*SU3F[6, I3, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3F[3, I2, k2]* - SU3F[6, I3, k1] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3D[I1, k1, k2]*SU3F[6, I3, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]* - SU3F[6, I3, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3D[I2, k1, k2]*SU3F[6, I3, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3D[I2, k1, k2]* - SU3F[6, I3, k2] - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, I3, k1]* - SU3F[7, I1, k1] - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]* - SU3F[7, I2, k1] - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]* - SU3F[7, I3, k1] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[I2, k1, k2]*SU3F[8, I1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I3, k1, k2]*SU3F[8, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I3, k1, k2]*SU3F[6, I2, k1]*SU3F[8, I1, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[6, I3, k1]* - SU3F[8, I1, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[8, I2, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3F[8, I2, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I3, k1, k2]* - SU3F[8, I2, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, k1, k2]*SU3F[6, I3, k1]*SU3F[8, I2, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[8, I3, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, k1, k2]*SU3F[6, I2, k2]*SU3F[8, I3, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3F[8, I3, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3F[8, I3, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3D[6, I2, k2]*SU3F[I1, k1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3D[6, I3, k2]*SU3F[I1, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[8, I2, k2]*SU3F[I1, k1, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[8, I3, k2]* - SU3F[I1, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3F[3, I2, k2]*SU3F[I1, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[3, I3, k2]*SU3F[I1, k1, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I3, k1]*SU3F[6, I2, k2]*SU3F[I1, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I3, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3F[6, I3, k2]*SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I3, k2]*SU3F[I1, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SU3F[6, I3, k2]* - SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3F[8, I2, k2]*SU3F[I1, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k1]* - SU3F[8, I2, k2]*SU3F[I1, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3F[8, I3, k2]*SU3F[I1, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]* - SU3F[8, I3, k2]*SU3F[I1, k1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I3, k1]*SU3D[6, I1, k2]*SU3F[I2, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[6, I3, k2]* - SU3F[I2, k1, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[8, I1, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[8, I3, k2]*SU3F[I2, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3F[3, I1, k2]*SU3F[I2, k1, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[3, I3, k2]* - SU3F[I2, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]* - SU3F[6, I1, k2]*SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I3, k1]*SU3F[6, I1, k2]*SU3F[I2, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I3, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3F[6, I3, k2]*SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, k1]*SU3F[6, I3, k2]*SU3F[I2, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]*SU3F[6, I3, k2]* - SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3F[8, I1, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k1]* - SU3F[8, I1, k2]*SU3F[I2, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, k1]*SU3F[8, I3, k2]*SU3F[I2, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I1, k1]* - SU3F[8, I3, k2]*SU3F[I2, k1, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3D[6, I1, k2]*SU3F[I3, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[6, I2, k2]* - SU3F[I3, k1, k2] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[8, I1, k2]*SU3F[I3, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[8, I2, k2]*SU3F[I3, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[3, I1, k2]*SU3F[I3, k1, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[3, I2, k2]* - SU3F[I3, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]* - SU3F[6, I1, k2]*SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I1, k2]*SU3F[I3, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] + 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]* - SU3F[6, I2, k2]*SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, k1]*SU3F[6, I2, k2]*SU3F[I3, k1, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k2]*SU3F[I3, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]* - SU3F[8, I1, k2]*SU3F[I3, k1, k2] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, k1]*SU3F[8, I2, k2]*SU3F[I3, k1, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I1, k1]* - SU3F[8, I2, k2]*SU3F[I3, k1, k2] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, I3]*SUNDelta[3, I1] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I3]*SUNDelta[3, I2] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I2]*SUNDelta[3, I3] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, I3]*SUNDelta[6, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, I3]*SUNDelta[6, I1] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, I3]*SUNDelta[6, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I3]*SUNDelta[6, I2] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, I2]*SUNDelta[6, I3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I2]*SUNDelta[6, I3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, I3]* - SUNDelta[8, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I3]*SUNDelta[8, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, I2]*SUNDelta[8, I3] - 4*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I3]*SUNDelta[I1, I2] + (12*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[7, I3]*SUNDelta[I1, I2] - 4*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I2]*SUNDelta[I1, I3] + (12*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[7, I2]*SUNDelta[I1, I3] - 4*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[6, I1]*SUNDelta[I2, I3] + (12*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[7, I1]*SUNDelta[I2, I3])/ -(27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o4.Gen deleted file mode 100644 index e26fd408c..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o4.Gen +++ /dev/null @@ -1,23 +0,0 @@ -{MomentaScalarProduct[p1, p3]*MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p1, p4]*MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p2, p3]*MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p2, p3]*MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p1, p3]*MomentaScalarProduct[p1, p4], -MomentaScalarProduct[p1, p3]*MomentaScalarProduct[p3, p4], -MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p1, p4], -MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p2, p4], -MomentaScalarProduct[p3, p4]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p3, p4]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p3, p4]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p4]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p2, p4]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p4]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p4]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p4]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p4]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o4.Mod deleted file mode 100644 index d99044d0d..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S10o4.Mod +++ /dev/null @@ -1,4746 +0,0 @@ -{{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]) + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]) - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 19]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5}, -{(6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/ -(36*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]])/ -(36*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/ -(36*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/ -(36*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(18*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(36*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 24]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 21]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(36*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S20o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S20o2.Mod deleted file mode 100644 index 68544b2f5..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10S20o2.Mod +++ /dev/null @@ -1,66 +0,0 @@ -{{(-2*CouplingConstant[ChPTW3[2], 2]*(3*SU3D[6, I2, k1]*SU3D[I1, k1, k2]* - SU3D[I3, I4, k2] + 3*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3D[I3, I4, k2] + 3*SU3D[6, I2, k1]*SU3D[I1, I4, k2]* - SU3D[I3, k1, k2] + 3*SU3D[6, I1, k1]*SU3D[I2, I4, k2]* - SU3D[I3, k1, k2] + (3*I)*SU3D[I2, k1, k2]*SU3D[I3, I4, k1]* - SU3F[6, I1, k2] + (3*I)*SU3D[I2, I4, k1]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2] + (3*I)*SU3D[I1, k1, k2]*SU3D[I3, I4, k1]* - SU3F[6, I2, k2] + (3*I)*SU3D[I1, I4, k1]*SU3D[I3, k1, k2]* - SU3F[6, I2, k2] + (3*I)*SU3D[I1, k1, k2]*SU3D[I2, I4, k1]* - SU3F[6, I3, k2] + (3*I)*SU3D[I1, I4, k1]*SU3D[I2, k1, k2]* - SU3F[6, I3, k2] - (6*I)*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, I4, k2] - (6*I)*SU3D[I1, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, I4, k2] - (6*I)*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, I4, k2] + (3*I)*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3F[I1, I4, k2] - 3*SU3D[I3, k1, k2]*SU3F[6, I2, k1]* - SU3F[I1, I4, k2] - 3*SU3D[I2, k1, k2]*SU3F[6, I3, k1]* - SU3F[I1, I4, k2] - (3*I)*SU3D[6, I2, k1]*SU3D[I3, I4, k2]* - SU3F[I1, k1, k2] - 3*SU3D[I3, I4, k1]*SU3F[6, I2, k2]* - SU3F[I1, k1, k2] - 3*SU3D[I2, I4, k1]*SU3F[6, I3, k2]* - SU3F[I1, k1, k2] + 6*SU3D[I2, I3, k1]*SU3F[6, I4, k2]* - SU3F[I1, k1, k2] + (3*I)*SU3D[6, I1, k1]*SU3D[I3, k1, k2]* - SU3F[I2, I4, k2] - 3*SU3D[I3, k1, k2]*SU3F[6, I1, k1]* - SU3F[I2, I4, k2] - 3*SU3D[I1, k1, k2]*SU3F[6, I3, k1]* - SU3F[I2, I4, k2] + (3*I)*SU3F[6, I3, k1]*SU3F[I1, k1, k2]* - SU3F[I2, I4, k2] - (3*I)*SU3D[6, I1, k1]*SU3D[I3, I4, k2]* - SU3F[I2, k1, k2] - 3*SU3D[I3, I4, k1]*SU3F[6, I1, k2]* - SU3F[I2, k1, k2] - 3*SU3D[I1, I4, k1]*SU3F[6, I3, k2]* - SU3F[I2, k1, k2] + 6*SU3D[I1, I3, k1]*SU3F[6, I4, k2]* - SU3F[I2, k1, k2] + (3*I)*SU3F[6, I3, k1]*SU3F[I1, I4, k2]* - SU3F[I2, k1, k2] + 3*SU3D[6, I3, k1]* - (I*SU3D[I2, k1, k2]*SU3F[I1, I4, k2] - I*SU3D[I2, I4, k2]* - SU3F[I1, k1, k2] + SU3D[I1, k1, k2]*(SU3D[I2, I4, k2] + - I*SU3F[I2, I4, k2]) + SU3F[I1, k1, k2]*SU3F[I2, I4, k2] + - SU3D[I1, I4, k2]*(SU3D[I2, k1, k2] - I*SU3F[I2, k1, k2]) + - SU3F[I1, I4, k2]*SU3F[I2, k1, k2]) + (3*I)*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3F[I3, I4, k2] + (3*I)*SU3D[6, I1, k1]* - SU3D[I2, k1, k2]*SU3F[I3, I4, k2] - 3*SU3D[I2, k1, k2]*SU3F[6, I1, k1]* - SU3F[I3, I4, k2] - 3*SU3D[I1, k1, k2]*SU3F[6, I2, k1]* - SU3F[I3, I4, k2] + 3*SU3D[6, I2, k1]*SU3F[I1, k1, k2]* - SU3F[I3, I4, k2] + (3*I)*SU3F[6, I2, k1]*SU3F[I1, k1, k2]* - SU3F[I3, I4, k2] + 3*SU3D[6, I1, k1]*SU3F[I2, k1, k2]* - SU3F[I3, I4, k2] + (3*I)*SU3F[6, I1, k1]*SU3F[I2, k1, k2]* - SU3F[I3, I4, k2] - (3*I)*SU3D[6, I2, k1]*SU3D[I1, I4, k2]* - SU3F[I3, k1, k2] - (3*I)*SU3D[6, I1, k1]*SU3D[I2, I4, k2]* - SU3F[I3, k1, k2] - 3*SU3D[I2, I4, k1]*SU3F[6, I1, k2]* - SU3F[I3, k1, k2] - 3*SU3D[I1, I4, k1]*SU3F[6, I2, k2]* - SU3F[I3, k1, k2] + 6*SU3D[I1, I2, k1]*SU3F[6, I4, k2]* - SU3F[I3, k1, k2] + 3*SU3D[6, I2, k1]*SU3F[I1, I4, k2]* - SU3F[I3, k1, k2] + (3*I)*SU3F[6, I2, k1]*SU3F[I1, I4, k2]* - SU3F[I3, k1, k2] + 3*SU3D[6, I1, k1]*SU3F[I2, I4, k2]* - SU3F[I3, k1, k2] + (3*I)*SU3F[6, I1, k1]*SU3F[I2, I4, k2]* - SU3F[I3, k1, k2] - 6*SU3D[6, I4, k1]* - (SU3D[I1, k1, k2]*SU3D[I2, I3, k2] + SU3D[I1, I2, k2]* - SU3D[I3, k1, k2] - I*SU3D[I2, I3, k2]*SU3F[I1, k1, k2] + - SU3D[I1, I3, k2]*(SU3D[I2, k1, k2] - I*SU3F[I2, k1, k2]) - - I*SU3D[I1, I2, k2]*SU3F[I3, k1, k2]) + 4*SU3D[I2, I3, I4]* - SUNDelta[6, I1] + 4*SU3D[I1, I3, I4]*SUNDelta[6, I2] + - 4*SU3D[I1, I2, I4]*SUNDelta[6, I3] - 12*SU3D[I1, I2, I3]* - SUNDelta[6, I4] - 4*SU3D[6, I3, I4]*SUNDelta[I1, I2] + - (4*I)*SU3F[6, I3, I4]*SUNDelta[I1, I2] - 4*SU3D[6, I2, I4]* - SUNDelta[I1, I3] + (4*I)*SU3F[6, I2, I4]*SUNDelta[I1, I3] + - 4*SU3D[6, I2, I3]*SUNDelta[I1, I4] - 4*SU3D[6, I1, I4]* - SUNDelta[I2, I3] + (4*I)*SU3F[6, I1, I4]*SUNDelta[I2, I3] + - 4*SU3D[6, I1, I3]*SUNDelta[I2, I4] + 4*SU3D[6, I1, I2]* - SUNDelta[I3, I4]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o2.Gen deleted file mode 100644 index 6113ac651..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o2.Gen +++ /dev/null @@ -1,5 +0,0 @@ -{MomentaScalarProduct[p2, p3], MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p1, p2], ParticleMass[PseudoScalar[8], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[7], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[2], -RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o2.Mod deleted file mode 100644 index 3cfb14eb4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o2.Mod +++ /dev/null @@ -1,635 +0,0 @@ -{{(3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]*SU3F[I1, I2, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3F[I1, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I3]*SUNDelta[I1, I2] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I2]*SUNDelta[I1, I3] - - 4*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] - - 6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3F[I1, I2, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I3, k1]*SU3F[I1, I2, k1] - - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I3]*SUNDelta[I1, I2] - - 4*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I2]*SUNDelta[I1, I3] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-6*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I3, k1]*SU3D[I1, I2, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3D[I1, I3, k1] + - 3*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3D[I2, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I2, I3, k1]*SU3F[6, I1, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I3, k1]*SU3F[6, I2, k1] - - (6*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[I1, I2, k1]*SU3F[6, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I2, k1]*SU3F[I1, I3, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I2, k1]*SU3F[I1, I3, k1] + - (3*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, k1]*SU3F[I2, I3, k1] - - 3*CouplingConstant[ChPTW3[2], 1]*SU3F[6, I1, k1]*SU3F[I2, I3, k1] - - 4*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I3]*SUNDelta[I1, I2] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I2]*SUNDelta[I1, I3] + - 2*CouplingConstant[ChPTW3[2], 1]*SUNDelta[6, I1]*SUNDelta[I2, I3])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, I3]*SUNDelta[3, I1] + - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I3]*SUNDelta[3, I2] + - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2]*SUNDelta[3, I3] - - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I1, k2, k3]* - SU3D[I2, I3, k3]*SUNDelta[3, k1] - 18*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, k1, k2]*SU3D[I1, I3, k3]*SU3D[I2, k2, k3]*SUNDelta[3, k1] - - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I1, I2, k3]* - SU3D[I3, k2, k3]*SUNDelta[3, k1] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I3, k2]*SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[3, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]*SU3F[I1, k1, k3]* - SU3F[I2, k2, k3]*SUNDelta[3, k1] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I2, k2]*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[3, k1] + - (18*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I2, I3, k3]* - SU3F[I1, k1, k3]*SUNDelta[3, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[I2, k2, k3]*SU3F[I1, k1, k3]*SUNDelta[3, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I3, k2, k3]* - SU3F[I1, k1, k3]*SUNDelta[3, k2] + (18*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, k1, k2]*SU3D[I1, I3, k3]*SU3F[I2, k1, k3]*SUNDelta[3, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[3, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[I3, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[3, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[3, k2] + (18*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, k1, k2]*SU3D[I1, I2, k3]*SU3F[I3, k1, k3]*SUNDelta[3, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I1, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[3, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[I2, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[3, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3F[I1, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[3, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[3, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I2, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[3, k3] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[I3, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[3, k3] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]*SU3F[6, I2, k1]* - SU3F[I1, k2, k3]*SUNDelta[3, k3] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I2, k1, k2]*SU3F[6, I3, k1]*SU3F[I1, k2, k3]*SUNDelta[3, k3] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, k1, k2]* - SU3F[I2, k2, k3]*SUNDelta[3, k3] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[I3, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[3, k3] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3F[6, I3, k1]* - SU3F[I2, k2, k3]*SUNDelta[3, k3] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[I1, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[3, k3] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3F[I3, k2, k3]*SUNDelta[3, k3] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, I3]*SUNDelta[6, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, I3]*SUNDelta[6, I1] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, I3]*SUNDelta[6, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I3]*SUNDelta[6, I2] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, I2]*SUNDelta[6, I3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I2]*SUNDelta[6, I3] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I3, k1, k2]*SU3F[3, I2, k3]*SU3F[I1, k2, k3]*SUNDelta[6, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[3, I3, k3]* - SU3F[I1, k2, k3]*SUNDelta[6, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I3, k1, k2]*SU3F[8, I2, k3]*SU3F[I1, k2, k3]*SUNDelta[6, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[8, I3, k3]* - SU3F[I1, k2, k3]*SUNDelta[6, k1] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3F[3, I3, k2]*SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[8, I3, k2]* - SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3F[3, I3, k3]* - SU3F[I2, k2, k3]*SUNDelta[6, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I1, k1, k2]*SU3F[8, I3, k3]*SU3F[I2, k2, k3]*SUNDelta[6, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I3, k2]*SU3F[I1, k1, k3]* - SU3F[I2, k2, k3]*SUNDelta[6, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[8, I3, k2]*SU3F[I1, k1, k3]* - SU3F[I2, k2, k3]*SUNDelta[6, k1] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3F[3, I2, k2]*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[8, I2, k2]* - SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k1] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3D[I1, k2, k3]* - SU3D[I2, k1, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I3, k1]*SU3D[I1, k2, k3]*SU3D[I2, k1, k3]*SUNDelta[6, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[I1, k2, k3]* - SU3D[I3, k1, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3D[I1, k2, k3]*SU3D[I3, k1, k3]*SUNDelta[6, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[I2, k2, k3]* - SU3D[I3, k1, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, k1]*SU3D[I2, k2, k3]*SU3D[I3, k1, k3]*SUNDelta[6, k2] - - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, I3, k1]*SU3F[3, k2, k3]* - SU3F[I1, k1, k3]*SUNDelta[6, k2] - 18*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, I3, k1]*SU3F[3, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I3, k1]*SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k2] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3F[I1, k1, k3]* - SU3F[I2, k2, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I3, k1]*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[6, k2] - - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]*SU3F[3, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[6, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3F[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3F[I1, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[6, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, k1]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[6, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[6, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, k1]*SU3F[I2, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[6, k2] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I3, k1]*SU3D[I1, k1, k2]*SU3D[I2, k2, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3D[I1, k1, k2]* - SU3D[I2, k2, k3]*SUNDelta[6, k3] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3D[I1, k1, k2]*SU3D[I3, k2, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]* - SU3D[I3, k2, k3]*SUNDelta[6, k3] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, k1]*SU3D[I2, k1, k2]*SU3D[I3, k2, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3D[I2, k1, k2]* - SU3D[I3, k2, k3]*SUNDelta[6, k3] - (18*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, k1, k2]*SU3D[I2, I3, k1]*SU3F[3, k2, k3]*SUNDelta[6, k3] - - (18*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]*SU3D[I2, k1, k2]* - SU3F[3, k2, k3]*SUNDelta[6, k3] - (18*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, I2, k1]*SU3D[I3, k1, k2]*SU3F[3, k2, k3]*SUNDelta[6, k3] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3D[I2, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[6, k3] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3D[I2, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[6, k3] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3D[I3, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I3, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[6, k3] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]*SU3F[3, I2, k1]* - SU3F[I1, k2, k3]*SUNDelta[6, k3] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I2, k1, k2]*SU3F[3, I3, k1]*SU3F[I1, k2, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]*SU3F[8, I1, k2]* - SU3F[I2, k1, k3]*SUNDelta[6, k3] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I3, k1]*SU3D[I1, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I1, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[6, k3] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[I3, k1, k2]* - SU3F[I2, k2, k3]*SUNDelta[6, k3] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3D[I3, k1, k2]* - SU3F[I2, k2, k3]*SUNDelta[6, k3] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, k1, k2]*SU3F[3, I3, k1]*SU3F[I2, k2, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[8, I1, k2]* - SU3F[I3, k1, k3]*SUNDelta[6, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I1, k1, k2]*SU3F[8, I2, k2]*SU3F[I3, k1, k3]*SUNDelta[6, k3] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[I1, k1, k2]* - SU3F[I3, k2, k3]*SUNDelta[6, k3] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I1, k1, k2]* - SU3F[I3, k2, k3]*SUNDelta[6, k3] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, k1]*SU3D[I2, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I2, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[6, k3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, I3]* - SUNDelta[8, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I3]*SUNDelta[8, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, I2]*SUNDelta[8, I3] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I1, k2, k3]* - SU3D[I2, I3, k3]*SUNDelta[8, k1] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, k1, k2]*SU3D[I1, I3, k3]*SU3D[I2, k2, k3]*SUNDelta[8, k1] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I1, I2, k3]* - SU3D[I3, k2, k3]*SUNDelta[8, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[8, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]*SU3F[I1, k1, k3]* - SU3F[I2, k2, k3]*SUNDelta[8, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k2]*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[8, k1] + (6*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I2, I3, k3]* - SU3F[I1, k1, k3]*SUNDelta[8, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I2, k2, k3]* - SU3F[I1, k1, k3]*SUNDelta[8, k2] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I3, k2, k3]* - SU3F[I1, k1, k3]*SUNDelta[8, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I2, I3, k1]*SU3F[6, k2, k3]*SU3F[I1, k1, k3]*SUNDelta[8, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I1, I3, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I3, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]*SU3F[6, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[8, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I3, k1]*SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I1, I2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I2, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]*SU3F[6, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[8, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3F[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[8, k2] + (6*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, k2, k3]*SUNDelta[8, k3] + (6*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, k2, k3]*SUNDelta[8, k3] + (6*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, k2, k3]*SUNDelta[8, k3] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I2, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[8, k3] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[8, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, k1, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I3, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[8, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[I3, k1, k3]*SUNDelta[8, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]*SU3F[I3, k1, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I2, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[8, k3] - - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SUNDelta[3, k1]* - SUNDelta[I1, I2] - (12*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I3, k1]* - SUNDelta[6, k1]*SUNDelta[I1, I2] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I3, k1]*SUNDelta[8, k1]*SUNDelta[I1, I2] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k1]* - SUNDelta[8, k1]*SUNDelta[I1, I2] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SUNDelta[3, k1]*SUNDelta[I1, I3] - - (12*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SUNDelta[6, k1]* - SUNDelta[I1, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SUNDelta[8, k1]*SUNDelta[I1, I3] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]* - SUNDelta[8, k1]*SUNDelta[I1, I3] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SUNDelta[3, k1]*SUNDelta[I2, I3] - - (12*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]*SUNDelta[6, k1]* - SUNDelta[I2, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SUNDelta[8, k1]*SUNDelta[I2, I3] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I1, k1]* - SUNDelta[8, k1]*SUNDelta[I2, I3])/ -(27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, I3]*SUNDelta[3, I1] - - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I3]*SUNDelta[3, I2] - - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2]*SUNDelta[3, I3] + - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I1, k2, k3]* - SU3D[I2, I3, k3]*SUNDelta[3, k1] + 18*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, k1, k2]*SU3D[I1, I3, k3]*SU3D[I2, k2, k3]*SUNDelta[3, k1] + - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I1, I2, k3]* - SU3D[I3, k2, k3]*SUNDelta[3, k1] - (18*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, k1, k2]*SU3D[I2, I3, k3]*SU3F[I1, k2, k3]*SUNDelta[3, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[3, k1] - (18*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, k1, k2]*SU3D[I1, I3, k3]*SU3F[I2, k2, k3]*SUNDelta[3, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]*SU3F[I1, k1, k3]* - SU3F[I2, k2, k3]*SUNDelta[3, k1] - (18*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, k1, k2]*SU3D[I1, I2, k3]*SU3F[I3, k2, k3]*SUNDelta[3, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k2]*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[3, k1] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[3, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3F[I1, k1, k3]* - SU3F[I2, k2, k3]*SUNDelta[3, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[3, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[3, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[3, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[3, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[I1, k2, k3]*SU3D[I2, k1, k2]*SUNDelta[3, k3] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, k1, k2]* - SU3D[I2, k2, k3]*SUNDelta[3, k3] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[I1, k2, k3]*SU3D[I3, k1, k2]*SUNDelta[3, k3] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k2, k3]* - SU3D[I3, k1, k2]*SUNDelta[3, k3] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3D[I1, k1, k2]*SU3D[I3, k2, k3]*SUNDelta[3, k3] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3D[I3, k2, k3]*SUNDelta[3, k3] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[I2, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[3, k3] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[3, k3] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I3, k1, k2]*SU3F[6, I2, k1]*SU3F[I1, k2, k3]*SUNDelta[3, k3] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[6, I3, k1]* - SU3F[I1, k2, k3]*SUNDelta[3, k3] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I3, k1]*SU3D[I1, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[3, k3] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I3, k1, k2]* - SU3F[I2, k2, k3]*SUNDelta[3, k3] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, k1, k2]*SU3F[6, I3, k1]*SU3F[I2, k2, k3]*SUNDelta[3, k3] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I1, k1, k2]* - SU3F[I3, k2, k3]*SUNDelta[3, k3] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[I2, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[3, k3] - - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, I3]*SUNDelta[6, I1] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, I3]* - SUNDelta[6, I1] - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, I3]* - SUNDelta[6, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I1, I3]*SUNDelta[6, I2] - 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, I2]*SUNDelta[6, I3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I2]*SUNDelta[6, I3] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I3, k2]*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[6, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[8, I3, k2]*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[6, k1] + (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3F[3, I3, k2]*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[6, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[8, I3, k2]* - SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[6, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k2]*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[6, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[8, I2, k2]*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[6, k1] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I3, k1]*SU3D[I2, k2, k3]*SU3F[I1, k1, k3]*SUNDelta[6, k2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I2, k2, k3]*SU3F[I1, k1, k3]*SUNDelta[6, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[I3, k2, k3]* - SU3F[I1, k1, k3]*SUNDelta[6, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I3, k2, k3]* - SU3F[I1, k1, k3]*SUNDelta[6, k2] + 18*CouplingConstant[ChPTW3[2], 2]* - SU3D[I2, I3, k1]*SU3F[3, k2, k3]*SU3F[I1, k1, k3]*SUNDelta[6, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3D[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[6, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3D[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[6, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, k1]*SU3D[I3, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I3, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k2] + - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]*SU3F[3, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[6, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I3, k1]*SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[6, k2] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I3, k1]*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3F[I1, k1, k3]* - SU3F[I2, k2, k3]*SUNDelta[6, k2] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3D[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[I2, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[6, k2] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3D[I2, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[6, k2] + 18*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, I2, k1]*SU3F[3, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3F[I1, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, k1]*SU3F[I2, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3F[I1, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[6, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, k1]*SU3F[I2, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k2] + - (18*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]* - SU3F[3, k2, k3]*SUNDelta[6, k3] + (18*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[I1, I3, k1]*SU3D[I2, k1, k2]*SU3F[3, k2, k3]*SUNDelta[6, k3] + - (18*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]* - SU3F[3, k2, k3]*SUNDelta[6, k3] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I3, k1]*SU3D[I2, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I2, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[6, k3] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[I3, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[6, k3] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]*SU3D[I3, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[6, k3] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[I3, k1, k2]*SU3F[3, I2, k1]*SU3F[I1, k2, k3]*SUNDelta[6, k3] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[3, I3, k1]* - SU3F[I1, k2, k3]*SUNDelta[6, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I3, k1, k2]*SU3F[8, I1, k2]*SU3F[I2, k1, k3]*SUNDelta[6, k3] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I3, k1]*SU3D[I1, k1, k2]* - SU3F[I2, k2, k3]*SUNDelta[6, k3] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]*SU3D[I1, k1, k2]* - SU3F[I2, k2, k3]*SUNDelta[6, k3] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I1, k1]*SU3D[I3, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I3, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[6, k3] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3F[3, I3, k1]* - SU3F[I2, k2, k3]*SUNDelta[6, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I2, k1, k2]*SU3F[8, I1, k2]*SU3F[I3, k1, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3F[8, I2, k2]* - SU3F[I3, k1, k3]*SUNDelta[6, k3] - (9*I)*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3D[I1, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I1, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[6, k3] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[I2, k1, k2]* - SU3F[I3, k2, k3]*SUNDelta[6, k3] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]*SU3D[I2, k1, k2]* - SU3F[I3, k2, k3]*SUNDelta[6, k3] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, I3]*SUNDelta[8, I1] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I3]* - SUNDelta[8, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I2]*SUNDelta[8, I3] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, k1, k2]*SU3D[I1, k2, k3]*SU3D[I2, I3, k3]*SUNDelta[8, k1] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I1, I3, k3]* - SU3D[I2, k2, k3]*SUNDelta[8, k1] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, k1, k2]*SU3D[I1, I2, k3]*SU3D[I3, k2, k3]*SUNDelta[8, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]* - SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]* - SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[8, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k2]* - SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[8, k1] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I2, I3, k3]*SU3F[I1, k1, k3]*SUNDelta[8, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, I3, k1]*SU3F[6, k2, k3]* - SU3F[I1, k1, k3]*SUNDelta[8, k2] + (6*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]*SU3D[I1, I3, k3]* - SU3F[I2, k1, k3]*SUNDelta[8, k2] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I1, I3, k1]*SU3F[6, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3F[I1, k2, k3]* - SU3F[I2, k1, k3]*SUNDelta[8, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I3, k1]*SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[8, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I1, I2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]*SU3F[6, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[8, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3F[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[I2, k2, k3]* - SU3F[I3, k1, k3]*SUNDelta[8, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[8, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3F[I2, k1, k3]* - SU3F[I3, k2, k3]*SUNDelta[8, k2] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I3, k1]*SU3D[I1, k2, k3]*SU3D[I2, k1, k2]*SUNDelta[8, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I1, k1, k2]* - SU3D[I2, k2, k3]*SUNDelta[8, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3D[I1, k2, k3]*SU3D[I3, k1, k2]*SUNDelta[8, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k2, k3]* - SU3D[I3, k1, k2]*SUNDelta[8, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I2, k1]*SU3D[I1, k1, k2]*SU3D[I3, k2, k3]*SUNDelta[8, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SU3D[I2, k1, k2]* - SU3D[I3, k2, k3]*SUNDelta[8, k3] + (6*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]*SU3D[I2, I3, k1]* - SU3F[6, k2, k3]*SUNDelta[8, k3] + (6*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]*SU3D[I2, k1, k2]* - SU3F[6, k2, k3]*SUNDelta[8, k3] + (6*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]*SU3D[I3, k1, k2]* - SU3F[6, k2, k3]*SUNDelta[8, k3] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SU3D[I2, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[8, k3] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SU3D[I3, k1, k2]* - SU3F[I1, k2, k3]*SUNDelta[8, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I3, k1, k2]*SU3F[6, I1, k2]*SU3F[I2, k1, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I3, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[8, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]*SU3F[6, I1, k2]* - SU3F[I3, k1, k3]*SUNDelta[8, k3] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[I1, k1, k2]*SU3F[6, I2, k2]*SU3F[I3, k1, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I2, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[8, k3] + - 12*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SUNDelta[3, k1]* - SUNDelta[I1, I2] + (12*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I3, k1]* - SUNDelta[6, k1]*SUNDelta[I1, I2] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I3, k1]*SUNDelta[8, k1]*SUNDelta[I1, I2] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k1]* - SUNDelta[8, k1]*SUNDelta[I1, I2] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SUNDelta[3, k1]*SUNDelta[I1, I3] + - (12*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SUNDelta[6, k1]* - SUNDelta[I1, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SUNDelta[8, k1]*SUNDelta[I1, I3] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]* - SUNDelta[8, k1]*SUNDelta[I1, I3] + 12*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SUNDelta[3, k1]*SUNDelta[I2, I3] + - (12*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]*SUNDelta[6, k1]* - SUNDelta[I2, I3] - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SUNDelta[8, k1]*SUNDelta[I2, I3] + - (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I1, k1]* - SUNDelta[8, k1]*SUNDelta[I2, I3])/ -(27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(-2*(4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, I3]* - SUNDelta[6, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[8, I1, I3]*SUNDelta[6, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I1, I2]*SUNDelta[6, I3] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]* - SU3F[8, I2, k3]*SU3F[I1, k2, k3]*SUNDelta[6, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]* - SU3F[8, I3, k3]*SU3F[I1, k2, k3]*SUNDelta[6, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[8, I3, k2]* - SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]* - SU3F[8, I3, k3]*SU3F[I2, k2, k3]*SUNDelta[6, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[8, I3, k2]* - SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[6, k1] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[8, I2, k2]* - SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I1, k2, k3]*SU3D[I2, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I1, k2, k3]*SU3D[I3, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I2, k2, k3]*SU3D[I3, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3F[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3F[I2, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3F[I2, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[6, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I1, k1, k2]*SU3D[I2, k2, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I1, k1, k2]*SU3D[I3, k2, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I2, k1, k2]*SU3D[I3, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I2, k2, k3]*SU3F[I1, k1, k2]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I3, k2, k3]*SU3F[I1, k1, k2]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I2, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I3, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I1, k2, k3]*SU3F[I2, k1, k2]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I3, k2, k3]*SU3F[I2, k1, k2]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]* - SU3F[8, I1, k2]*SU3F[I2, k1, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I3, k1]* - SU3D[I1, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I3, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I1, k2, k3]*SU3F[I3, k1, k2]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I2, k2, k3]*SU3F[I3, k1, k2]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]* - SU3F[8, I1, k2]*SU3F[I3, k1, k3]*SUNDelta[6, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]* - SU3F[8, I2, k2]*SU3F[I3, k1, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I2, k1]* - SU3D[I1, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[6, k3] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3D[I2, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[6, k3] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, I3]* - SUNDelta[8, I1] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, I3]*SUNDelta[8, I2] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[6, I1, I2]*SUNDelta[8, I3] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I1, k2, k3]*SU3D[I2, I3, k3]*SUNDelta[8, k1] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I1, I3, k3]*SU3D[I2, k2, k3]*SUNDelta[8, k1] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I1, I2, k3]*SU3D[I3, k2, k3]*SUNDelta[8, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]* - SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I3, k2]* - SU3F[I1, k1, k3]*SU3F[I2, k2, k3]*SUNDelta[8, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k2]* - SU3F[I1, k1, k3]*SU3F[I3, k2, k3]*SUNDelta[8, k1] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I2, I3, k3]*SU3F[I1, k1, k3]*SUNDelta[8, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, I3, k1]* - SU3F[6, k2, k3]*SU3F[I1, k1, k3]*SUNDelta[8, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I1, I3, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]* - SU3F[6, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3F[I1, k2, k3]*SU3F[I2, k1, k3]*SUNDelta[8, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, k1, k2]* - SU3D[I1, I2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]* - SU3F[6, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3F[I1, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3F[I2, k2, k3]*SU3F[I3, k1, k3]*SUNDelta[8, k2] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]* - SU3D[I2, I3, k1]*SU3F[6, k2, k3]*SUNDelta[8, k3] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I3, k1]* - SU3D[I2, k1, k2]*SU3F[6, k2, k3]*SUNDelta[8, k3] + - (6*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, I2, k1]* - SU3D[I3, k1, k2]*SU3F[6, k2, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I2, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I3, k1, k2]*SU3F[I1, k2, k3]*SUNDelta[8, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I3, k1, k2]* - SU3F[6, I1, k2]*SU3F[I2, k1, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]* - SU3D[I1, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I3, k1, k2]*SU3F[I2, k2, k3]*SUNDelta[8, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I2, k1, k2]* - SU3F[6, I1, k2]*SU3F[I3, k1, k3]*SUNDelta[8, k3] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[I1, k1, k2]* - SU3F[6, I2, k2]*SU3F[I3, k1, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[I1, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[8, k3] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3D[I2, k1, k2]*SU3F[I3, k2, k3]*SUNDelta[8, k3] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I3, k1]*SUNDelta[8, k1]* - SUNDelta[I1, I2] + (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I3, k1]*SUNDelta[8, k1]*SUNDelta[I1, I2] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]*SUNDelta[8, k1]* - SUNDelta[I1, I3] + (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I2, k1]*SUNDelta[8, k1]*SUNDelta[I1, I3] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]*SUNDelta[8, k1]* - SUNDelta[I2, I3] + (4*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SUNDelta[8, k1]*SUNDelta[I2, I3]))/ -(27*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o4.Gen deleted file mode 100644 index c2bd10e5e..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o4.Gen +++ /dev/null @@ -1,23 +0,0 @@ -{MomentaScalarProduct[p2, p3]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p3]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p2, p3]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p3]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p3]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p2]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o4.Mod deleted file mode 100644 index ca1a6b4ae..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10P10o4.Mod +++ /dev/null @@ -1,25935 +0,0 @@ -{{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]) + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]) + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]) + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]) + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]) + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]) + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]) - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]) - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]) - - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 7]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 6]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 9]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 9]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]])/ -(108*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 50*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 78*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 90*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]])/ -(108*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]])/ -(108*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 60*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]])/ -(108*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 54*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 20*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 9*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 27*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 54*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 18*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]])/ -(54*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}, -{(-12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 72*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 13]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 25*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 39*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 13]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 27*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 45*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 9*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 40*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 40*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] - 40*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 40*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 40*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 40*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 48*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 36*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 24*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 18*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 36*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 48*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 72*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 36*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]])/ -(108*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^5)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o2.Gen deleted file mode 100644 index c927422e2..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o2.Gen +++ /dev/null @@ -1,4 +0,0 @@ -{MomentaScalarProduct[p1, p2], ParticleMass[PseudoScalar[7], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[8], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[2], -RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o2.Mod deleted file mode 100644 index 66512accf..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o2.Mod +++ /dev/null @@ -1,72 +0,0 @@ -{{((-4*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, I2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-6*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[6, I1, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[6, I2, k1] + - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I1, I2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[8, I1, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I2, k1] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[3, I1, k1] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3F[3, I2, k1] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3F[6, I1, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I1, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SU3F[6, I1, k1] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3F[6, I2, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3F[6, I2, k1] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]* - SU3F[6, I2, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]*SU3F[8, I1, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3F[8, I2, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SU3F[8, I2, k1] - (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[3, I2]*SUNDelta[6, I1] - (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[3, I1]*SUNDelta[6, I2] + (2*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I2]*SUNDelta[8, I1] + - (2*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I1]* - SUNDelta[8, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2)}, -{((-24*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[6, I1, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[6, I2, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[8, I1, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I2, k1] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[3, I1, k1] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3F[3, I2, k1] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3F[6, I1, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I1, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SU3F[6, I1, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3F[6, I2, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3F[6, I2, k1] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]* - SU3F[6, I2, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]*SU3F[8, I1, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3F[8, I2, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SU3F[8, I2, k1] + (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[3, I2]*SUNDelta[6, I1] + (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[3, I1]*SUNDelta[6, I2] + (2*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I2]*SUNDelta[8, I1] + - (2*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I1]* - SUNDelta[8, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2)}, -{(2*((-3*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I1, I2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[8, I1, k1] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I2, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I1, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3F[6, I2, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]*SU3F[8, I1, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3F[8, I2, k1] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SU3F[8, I2, k1] - (2*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I2]*SUNDelta[8, I1] - - (2*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I1]* - SUNDelta[8, I2]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o4.Gen deleted file mode 100644 index f14b7165b..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o4.Gen +++ /dev/null @@ -1,11 +0,0 @@ -{MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p1, p3], -MomentaScalarProduct[p1, p2]*MomentaScalarProduct[p2, p3], -MomentaScalarProduct[p2, p3]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, MomentaScalarProduct[p2, p3]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p2, p3]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p3]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p3]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p3]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o4.Mod deleted file mode 100644 index 0bff9edc6..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S10o4.Mod +++ /dev/null @@ -1,532 +0,0 @@ -{{((2*I)*(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 20]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((2*I)*(CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 20]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 20]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((-I/6)*(6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 4*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/6)*(6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 4*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/3)*(2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 24]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I/6)*(6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 4*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 4*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/6)*(6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 4*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/3)*(2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ - ChPTW3[4], 24]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 24]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 23]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 22]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 23]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S20o4.Gen deleted file mode 100644 index 2c2746854..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S20o4.Gen +++ /dev/null @@ -1,7 +0,0 @@ -{MomentaScalarProduct[p1, p2]*QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S20o4.Mod deleted file mode 100644 index 3443de0b5..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10S20o4.Mod +++ /dev/null @@ -1,1277 +0,0 @@ -{{(CouplingConstant[ChPTW3[2], 1]*SUNDelta[0, I3]* - ((-8*I)*CouplingConstant[ChPTW3[4], 5]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) - - (12*I)*CouplingConstant[ChPTW3[4], 8]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])) + - CouplingConstant[ChPTW3[2], 1]*((-8*I)*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - (4*I)*CouplingConstant[ChPTW3[4], 6]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]) - - (4*I)*CouplingConstant[ChPTW3[4], 5]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(CouplingConstant[ChPTW3[2], 1]*SUNDelta[0, I3]* - (((8*I)/3)*CouplingConstant[ChPTW3[4], 13]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]])) - - ((8*I)/3)*CouplingConstant[ChPTW3[4], 10]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) - ((4*I)/3)*CouplingConstant[ChPTW3[4], - 12]*(4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) + - ((2*I)/3)*CouplingConstant[ChPTW3[4], 11]* - (12*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*(-4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] + 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))) + - CouplingConstant[ChPTW3[2], 1]* - (((-4*I)/3)*CouplingConstant[ChPTW3[4], 13]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]) - - ((2*I)/3)*CouplingConstant[ChPTW3[4], 11]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 2*(3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[ - UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[ - UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[ - UGenerator[I2]], UMatrix[UGenerator[I1]]]]))) - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]) + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]) - ((2*I)/3)*CouplingConstant[ChPTW3[4], - 12]*(2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) - - ((2*I)/3)*CouplingConstant[ChPTW3[4], 10]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(CouplingConstant[ChPTW3[2], 1]*SUNDelta[0, I3]* - (((-8*I)/3)*CouplingConstant[ChPTW3[4], 13]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]])) - - ((2*I)/3)*CouplingConstant[ChPTW3[4], 11]* - (12*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) - ((8*I)/3)*CouplingConstant[ChPTW3[4], - 10]*(2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) - ((4*I)/3)*CouplingConstant[ChPTW3[4], - 12]*(4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - CouplingConstant[ChPTW3[2], 1]* - (((-4*I)/3)*CouplingConstant[ChPTW3[4], 13]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]]) - - ((2*I)/3)*CouplingConstant[ChPTW3[4], 11]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]) + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]]) - ((2*I)/3)*CouplingConstant[ChPTW3[4], - 12]*(2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) - - ((2*I)/3)*CouplingConstant[ChPTW3[4], 10]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(CouplingConstant[ChPTW3[2], 1]*SUNDelta[0, I3]* - (((-16*I)*CouplingConstant[ChPTW3[4], 13]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]))/Sqrt[3] - - ((16*I)/3)*CouplingConstant[ChPTW3[4], 10]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) - - ((8*I)/3)*CouplingConstant[ChPTW3[4], 12]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) - - ((4*I)/3)*CouplingConstant[ChPTW3[4], 11]* - (4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*(2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[ - I1]], UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[ - I2]], UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])))) + - CouplingConstant[ChPTW3[2], 1]* - (((-8*I)/3)*CouplingConstant[ChPTW3[4], 13]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[ - 8]], UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]) + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]])) - - ((2*I)/3)*CouplingConstant[ChPTW3[4], 11]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[ - I2]], UMatrix[UGenerator[I1]]]])) + - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]]) + - 3*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]])) - - ((4*I)/3)*CouplingConstant[ChPTW3[4], 12]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) - ((4*I)/3)*CouplingConstant[ChPTW3[4], - 10]*(2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]])))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o2.Gen deleted file mode 100644 index c927422e2..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o2.Gen +++ /dev/null @@ -1,4 +0,0 @@ -{MomentaScalarProduct[p1, p2], ParticleMass[PseudoScalar[7], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[8], -RenormalizationState[0]]^2, ParticleMass[PseudoScalar[2], -RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o2.Mod deleted file mode 100644 index 66512accf..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o2.Mod +++ /dev/null @@ -1,72 +0,0 @@ -{{((-4*I)*CouplingConstant[ChPTW3[2], 1]*SU3D[6, I1, I2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2}, -{((-6*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[6, I1, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[6, I2, k1] + - 18*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I1, I2] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[8, I1, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I2, k1] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[3, I1, k1] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3F[3, I2, k1] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3F[6, I1, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I1, k1] - - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SU3F[6, I1, k1] + - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3F[6, I2, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3F[6, I2, k1] - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]* - SU3F[6, I2, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]*SU3F[8, I1, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3F[8, I2, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SU3F[8, I2, k1] - (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[3, I2]*SUNDelta[6, I1] - (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[3, I1]*SUNDelta[6, I2] + (2*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I2]*SUNDelta[8, I1] + - (2*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I1]* - SUNDelta[8, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2)}, -{((-24*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I2, k1]*SU3D[6, I1, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3D[6, I2, k1] + - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[8, I1, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I2, k1] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[3, I1, k1] + 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3F[3, I2, k1] - 9*CouplingConstant[ChPTW3[2], 2]* - SU3D[3, I2, k1]*SU3F[6, I1, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I1, k1] + - (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I2, k1]*SU3F[6, I1, k1] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[3, I1, k1]*SU3F[6, I2, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3F[6, I2, k1] + (9*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[3, I1, k1]* - SU3F[6, I2, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k1] + (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]*SU3F[8, I1, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3F[8, I2, k1] + (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SU3F[8, I2, k1] + (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[3, I2]*SUNDelta[6, I1] + (6*I)*CouplingConstant[ChPTW3[2], 2]* - SUNDelta[3, I1]*SUNDelta[6, I2] + (2*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I2]*SUNDelta[8, I1] + - (2*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I1]* - SUNDelta[8, I2])/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2)}, -{(2*((-3*I)*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, I2] - - 9*CouplingConstant[ChPTW3[2], 2]*SU3D[7, I1, I2] - - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I2, k1]* - SU3D[8, I1, k1] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I1, k1]*SU3D[8, I2, k1] + 3*Sqrt[3]*CouplingConstant[ChPTW3[2], - 2]*SU3D[8, I2, k1]*SU3F[6, I1, k1] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[8, I1, k1]* - SU3F[6, I2, k1] - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3D[6, I2, k1]*SU3F[8, I1, k1] - (3*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SU3F[6, I2, k1]*SU3F[8, I1, k1] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SU3D[6, I1, k1]* - SU3F[8, I2, k1] - (3*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]* - SU3F[6, I1, k1]*SU3F[8, I2, k1] - (2*I)*Sqrt[3]* - CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I2]*SUNDelta[8, I1] - - (2*I)*Sqrt[3]*CouplingConstant[ChPTW3[2], 2]*SUNDelta[6, I1]* - SUNDelta[8, I2]))/(9*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o4.Gen deleted file mode 100644 index cb8084996..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o4.Gen +++ /dev/null @@ -1,14 +0,0 @@ -{MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p2]* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o4.Mod deleted file mode 100644 index 529f1af08..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10P10o4.Mod +++ /dev/null @@ -1,3083 +0,0 @@ -{{(((-2*I)/3)*CouplingConstant[ChPTW3[2], 1]* - (CouplingConstant[ChPTW3[4], 6]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]])) + - CouplingConstant[ChPTW3[4], 7]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]])* - (UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) + - 2*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(((2*I)/3)*CouplingConstant[ChPTW3[2], 1]* - (CouplingConstant[ChPTW3[4], 6]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]])) + - CouplingConstant[ChPTW3[4], 7]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]])* - (UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) - - 2*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{(((-2*I)/3)*CouplingConstant[ChPTW3[2], 1]* - (2*Sqrt[3]*CouplingConstant[ChPTW3[4], 6]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]]) + - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 7]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]]* - (UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) + - 2*CouplingConstant[ChPTW3[4], 5]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[4], 8]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 5]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I/18)*CouplingConstant[ChPTW3[2], 1]* - (9*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 8*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[4], 13]* - (-2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]* - (-6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]* - (-6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]])) + - 9*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 8*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 2*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 18*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 12*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 18*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 12*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 24*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 24*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 12*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 6*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 12*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + CouplingConstant[ChPTW3[4], 11]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]* - (-4*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]* - (-4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*(Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 3*(5*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 5*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]])) + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((-I/18)*CouplingConstant[ChPTW3[2], 1]* - (9*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 8*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[4], 13]* - (-2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]* - (6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]* - (6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]])) + - 9*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 8*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 2*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 18*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 18*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 12*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 24*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 12*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 12*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 24*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 12*CouplingConstant[ChPTW3[4], 12]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 12*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 12*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + CouplingConstant[ChPTW3[4], 11]* - (-(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]*(4*Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*(Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[ - UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], UMatrix[ - UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[8]], UMatrix[UGenerator[ - I1]], UMatrix[UGenerator[I2]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], UMatrix[ - UGenerator[I2]]]] - 2*UTrace1[NonCommutative[UMatrix[ - UGenerator[I1]], UMatrix[UGenerator[8]], UMatrix[ - UGenerator[I2]]]] + Sqrt[3]*UTrace1[NonCommutative[UMatrix[ - UGenerator[I1]], UMatrix[UGenerator[I2]], UMatrix[ - UGenerator[3]]]] - UTrace1[NonCommutative[UMatrix[UGenerator[ - I1]], UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[ - UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[ - UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[ - UGenerator[I1]], UMatrix[UGenerator[3]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))) + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) + - 3*(5*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 5*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]])) + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]]]] - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]]]] + 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 3*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((I/9)*CouplingConstant[ChPTW3[2], 1]* - (-9*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 8*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*CouplingConstant[ChPTW3[4], 13]* - (2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]) + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]) - 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 8*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 2*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 6*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + CouplingConstant[ChPTW3[4], 11]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]* - (4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 3*(UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 3*(-5*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 5*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 2*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]) - UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]]]])) + - 9*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 3*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 3*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 18*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] - 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] - 18*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[3]]]] + 6*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 9*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[3]]]] - - 3*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4}, -{((-I/18)*CouplingConstant[ChPTW3[2], 1]* - (9*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 8*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 8*CouplingConstant[ChPTW3[4], 13]* - (Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]) + - 3*(UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]) + - (UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]))) + - 9*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 8*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - 2*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 2*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 12*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 16*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 16*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 16*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 16*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 8*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 4*Sqrt[3]*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + CouplingConstant[ChPTW3[4], 11]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]* - (2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*(UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 3*(5*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 5*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 4*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]])) + 12*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 12*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 12]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] - 24*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 12*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 24*CouplingConstant[ChPTW3[4], 10]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]]]] + 12*CouplingConstant[ChPTW3[4], 10]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((-I/18)*CouplingConstant[ChPTW3[2], 1]* - (4*CouplingConstant[ChPTW3[4], 13]* - (Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]))) + - CouplingConstant[ChPTW3[4], 11]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]* - (2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*(Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - (UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 3*(10*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 10*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]])) + - 2*(2*CouplingConstant[ChPTW3[4], 12]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) + - CouplingConstant[ChPTW3[4], 10]* - (9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 12*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 12*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 12*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 12*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}, -{((I/18)*CouplingConstant[ChPTW3[2], 1]* - (4*CouplingConstant[ChPTW3[4], 13]* - (-(Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]]) - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]]*(UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]]))) + - CouplingConstant[ChPTW3[4], 11]* - (6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]]]]* - (2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - (UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]]* - (-2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + - 3*(Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) - - 3*(10*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 10*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 4*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]])) - - 2*(2*CouplingConstant[ChPTW3[4], 12]* - (4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 4*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) + - CouplingConstant[ChPTW3[4], 10]* - (9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] + - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] - - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 9*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]]]] + 2*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - 12*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] + - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] - 12*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] + - 4*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] + 6*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 2*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]] - 3*UTrace1[NonCommutative[ - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[3]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]]]] - 3*Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I2]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 12*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 12*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] + - 6*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] + - 12*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[8]]]] - - 3*Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[3]]]] - - 6*UTrace1[NonCommutative[UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[8]]]]))))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10S20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10S20o4.Gen deleted file mode 100644 index 7af5663d4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10S20o4.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{MomentaScalarProduct[p1, p2]*QuarkCondensate[RenormalizationState[0]], -MomentaScalarProduct[p2, p3]*QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10S20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10S20o4.Mod deleted file mode 100644 index dd9404673..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10S20o4.Mod +++ /dev/null @@ -1,15 +0,0 @@ -{{(4*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - (UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] - UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I3]], - UMatrix[UGenerator[I1]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3}, -{(2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 22]* - (SUNDelta[0, I3]*(-UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]]) - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I3]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I3]]]]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o2.Gen deleted file mode 100644 index 3ecdd602a..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o2.Mod deleted file mode 100644 index 827245c86..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o2.Mod +++ /dev/null @@ -1,4 +0,0 @@ -{{((4*I)*CouplingConstant[ChPTW3[2], 2]*SUNDelta[7, I1])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}, -{((-4*I)*CouplingConstant[ChPTW3[2], 2]*SUNDelta[7, I1])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o4.Gen deleted file mode 100644 index 33e3db7e6..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o4.Gen +++ /dev/null @@ -1,5 +0,0 @@ -{MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2, MomentaScalarProduct[p1, p2]* -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, -MomentaScalarProduct[p1, p2]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o4.Mod deleted file mode 100644 index 712975d78..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S10o4.Mod +++ /dev/null @@ -1,26 +0,0 @@ -{{(2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - (-3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[3]], UMatrix[UGenerator[I1]]]] + - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[3]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(4*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 21]* - (-UTrace1[NonCommutative[UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I1]]]] + UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[8]]]]))/ -(Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o2.Gen deleted file mode 100644 index 7996ac8bc..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o2.Gen +++ /dev/null @@ -1 +0,0 @@ -{QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o2.Mod deleted file mode 100644 index ec7ef6438..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{((8*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[6, I1, I2])/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o4.Gen deleted file mode 100644 index d89cefd8a..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o4.Gen +++ /dev/null @@ -1,6 +0,0 @@ -{ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]], -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2* -QuarkCondensate[RenormalizationState[0]]} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o4.Mod deleted file mode 100644 index d4e21aa17..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10S20o4.Mod +++ /dev/null @@ -1,129 +0,0 @@ -{{(4*CouplingConstant[ChPTW3[2], 1]*(3*CouplingConstant[ChPTW3[4], 11]* - (2*Sqrt[3]*SUNDelta[0, I2]* - (-UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) + - 2*CouplingConstant[ChPTW3[4], 10]*(2*Sqrt[3]*SUNDelta[0, I2]* - (-UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]]) + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[I1]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] + Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] - Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]])))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(4*CouplingConstant[ChPTW3[2], 1]*(3*CouplingConstant[ChPTW3[4], 11]* - (SUNDelta[0, I2]*(3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) + - CouplingConstant[ChPTW3[4], 10]*(2*SUNDelta[0, I2]* - (3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]])))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}, -{(4*CouplingConstant[ChPTW3[2], 1]*(3*CouplingConstant[ChPTW3[4], 11]* - (SUNDelta[0, I2]*(-3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]]) + - CouplingConstant[ChPTW3[4], 10]* - (SUNDelta[0, I2]*(-6*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]]]] + - 6*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]]]] + - 2*Sqrt[3]*(UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]] - - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]]]])) + - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]]]] - - 2*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[6]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[I2]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I2]]]] - - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]]]] + - 3*UTrace1[NonCommutative[UMatrix[UGenerator[3]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]], - UMatrix[UGenerator[6]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]], UMatrix[UGenerator[I1]]]] - - Sqrt[3]*UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[8]], - UMatrix[UGenerator[I2]]]] - Sqrt[3]* - UTrace1[NonCommutative[UMatrix[UGenerator[6]], - UMatrix[UGenerator[I1]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]]]] + Sqrt[3]*UTrace1[NonCommutative[ - UMatrix[UGenerator[6]], UMatrix[UGenerator[I2]], - UMatrix[UGenerator[8]], UMatrix[UGenerator[I1]]]])))/ -(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3)}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10o2.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10o2.Gen deleted file mode 100644 index f2745f394..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10o2.Gen +++ /dev/null @@ -1,3 +0,0 @@ -{ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10o2.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10o2.Mod deleted file mode 100644 index 8d1352ddb..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10o2.Mod +++ /dev/null @@ -1,8 +0,0 @@ -{{((-8*I)*CouplingConstant[ChPTW3[2], 2]*SU3F[6, 8, I1])/ -(Sqrt[3]*DecayConstant[PseudoScalar[1], RenormalizationState[0]])}, -{(((-4*I)/3)*CouplingConstant[ChPTW3[2], 2]*(3*SU3F[3, 6, I1] - - Sqrt[3]*SU3F[6, 8, I1]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]}, -{(((4*I)/3)*CouplingConstant[ChPTW3[2], 2]*(3*SU3F[3, 6, I1] + - Sqrt[3]*SU3F[6, 8, I1]))/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]}} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10o4.Gen b/FeynCalc/Phi/CouplingVectors/ChPTW3P10o4.Gen deleted file mode 100644 index 9f43180de..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10o4.Gen +++ /dev/null @@ -1,6 +0,0 @@ -{ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^4, -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2, -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2} diff --git a/FeynCalc/Phi/CouplingVectors/ChPTW3P10o4.Mod b/FeynCalc/Phi/CouplingVectors/ChPTW3P10o4.Mod deleted file mode 100644 index 5c63307a4..000000000 --- a/FeynCalc/Phi/CouplingVectors/ChPTW3P10o4.Mod +++ /dev/null @@ -1,13 +0,0 @@ -{{((8*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 11]* - SUNDelta[7, I1])/DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 3}, {((-8*I)*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], - 11]*SUNDelta[7, I1])/DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^3}, -{((8*I)*(2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - SUNDelta[7, I1] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*SUNDelta[7, I1]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}, -{((-8*I)*(2*CouplingConstant[ChPTW3[2], 1]*CouplingConstant[ChPTW3[4], 10]* - SUNDelta[7, I1] + CouplingConstant[ChPTW3[2], 1]* - CouplingConstant[ChPTW3[4], 11]*SUNDelta[7, I1]))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^3}} diff --git a/FeynCalc/Phi/CouplingVectors/HBChPT2F200F200P20o2.Gen b/FeynCalc/Phi/CouplingVectors/HBChPT2F200F200P20o2.Gen deleted file mode 100644 index 8862da7d0..000000000 --- a/FeynCalc/Phi/CouplingVectors/HBChPT2F200F200P20o2.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{NonCommutative[CouplingConstant[HBChPT2[2], RenormalizationState[0]]* -DiracSlash[p3]]} diff --git a/FeynCalc/Phi/CouplingVectors/HBChPT2F200F200P20o2.Mod b/FeynCalc/Phi/CouplingVectors/HBChPT2F200F200P20o2.Mod deleted file mode 100644 index 7576bfe02..000000000 --- a/FeynCalc/Phi/CouplingVectors/HBChPT2F200F200P20o2.Mod +++ /dev/null @@ -1,2 +0,0 @@ -{{-UGenerator[I3][J1, J2]/(2*DecayConstant[PseudoScalar[2], - RenormalizationState[0]])}} diff --git a/FeynCalc/Phi/CouplingVectors/QEDF70F70V10o1.Gen b/FeynCalc/Phi/CouplingVectors/QEDF70F70V10o1.Gen deleted file mode 100644 index 79c75493b..000000000 --- a/FeynCalc/Phi/CouplingVectors/QEDF70F70V10o1.Gen +++ /dev/null @@ -1,2 +0,0 @@ -{NonCommutative[CouplingConstant[QED[1], RenormalizationState[0]]* -DiracGamma[\[Mu]3]]} diff --git a/FeynCalc/Phi/CouplingVectors/QEDF70F70V10o1.Mod b/FeynCalc/Phi/CouplingVectors/QEDF70F70V10o1.Mod deleted file mode 100644 index a32c3e9a2..000000000 --- a/FeynCalc/Phi/CouplingVectors/QEDF70F70V10o1.Mod +++ /dev/null @@ -1 +0,0 @@ -{{I}} diff --git a/FeynCalc/Phi/Couplings.m b/FeynCalc/Phi/Couplings.m deleted file mode 100644 index 3ce6c9ca0..000000000 --- a/FeynCalc/Phi/Couplings.m +++ /dev/null @@ -1,2686 +0,0 @@ -(* Wolfram Language package *) - -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: Couplings *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Utilities for generating coupling definitions for - FeynArts >2 and using them for calculating amplitudes *) - -(* ------------------------------------------------------------------------ *) - - -FAParticleMass::usage = -"FAParticleMass is a function used internally by the FeynArts model -Automatic.mod provided by PHI. It is used for setting the ParticleMass of \ -the different PHI particles."; - -PropagatorDenominator1::usage = -"PropagatorDenominator1 is a head for extra PropagatorDenominator's \ -used in the definition of propagators for FeynArts (FeynArts doesn't seem \ -to like products of PropagatorDenominator's). It is replaced with \ -PropagatorDenominator by FAToFC."; - -Wrap::usage = -"Wrap is the head used by FixCouplingIndices to tag couplings with dummy \ -indices."; - -FixCouplingIndices::usage = -"FixCouplingIndices (evaluated with no arguments) scans \ -M$CouplingMatrices, checking for couplings with dummy indices (to be summed \ -over) and wraps both the couplings and the indices in Wrap. FAToFC will then \ -rename as needed to avoid problems with Feynman graphs that have two vertices \ -with the same dummy indices (giving e.g. a product with four occurences of \ -the same dummy index, which e.g. SUNReduce is unable to handle). The \ -renaming consists in prepending the first letter of an index to the index; \ -e.g. k1 would be renamed to kk1 or kkk1 or ... FixCouplingIndices is \ -evaluated automatically by the model \"Automatic\"."; - -CheckCouplingSign::usage = -"CheckCouplingSign[c] calculates the symmetry sign of the coupling c, \ -where c is a coupling vector like the elements of M$GenericCouplings."; - -FixCouplingSigns::usage = -"FixCouplingSigns checks the symmetry (specified by G[1] or G[-1]) \ -of all coupling vectors in M$GenericCouplings and fixes them if they are wrong."; - -Compare1::usage = -"Compare1 is like Compare except symmetry factors are not changed.."; - -AddCT::usage = -"AddCT[t], where t is a list of non-counterterm topologies with head \ -TopologyList, generates diagrams with one of the vertices of the original \ -topologies replaced by a counterterm vertex. This is a usefull hack to \ -generate the diagrams necessary in e.g. weak ChPT, where one needs to work \ -with meson fields that couple directly to the vacuum."; - -DiscardCT::usage = -"DiscardCT[t], where t is a list of topologies with head TopologyList, \ -converts conterterm topologies to non-counterterm topologies discarding \ -topologies with vertices of higher counter term order than one. This is a \ -usefull hack to generate the diagrams necessary in e.g. weak ChPT, where one \ -needs to work with meson fields that couple directly to the vacuum."; - -AddExternalLegs::usage = -"AddExternalLegs[t], where t is a list of topologies with head \ -TopologyList, puts on extra propagators on external legs. This is usefull in \ -e.g. ChPT, where one often needs to work with external sources which couple \ -via two-vertices to mesons, but which don't propagate internally."; - -ExternalPropagators::usage = -"ExternalPropagators is an option for AddExternalLegs specifying the \ -number of external legs of each topology onto which an external propagator \ -should be put. Default value : 1."; - -DiscardTopologies::usage = -"DiscardTopologies discards topologies with more than a specified number \ -(specified by the option PerturbationOrder) of a specified type of vertex \ -(specified by the option OrderingPatterns). This can be handy when expanding \ -not only in loops, but additionally in some extra coupling constant (like in \ -weak ChPT)."; - -OrderingPatterns::usage = -"OrderingPatterns is an option for DiscardTopologies specifying a type of \ -vertex that counts as of order 1 in some expansion (besides the loop \ -expansion). It must be a list of patterns each with head FullVertex (the \ -matching is done against the list of vertices returned VerticesExtract). \ -Default value : {}."; - -$GenObjects::usage = -"$GenObjects is a list of strings used by GenSave to determine which \ -definitions should be saved. Default value : \ -{\"M$GenericPropagators\",\"M$GenericCouplings\",\"M$FermionFlipRule\",\"M$\ -LastGenericRules\"}."; - -$ModObjects::usage = -"$ModObjects is a list of strings used by ModSave to determine which \ -definitions should be saved. Default value : \ -{\"$ScreenSymbolFont\",\"M$ClassesDescription\",\"M$CouplingMatrices\",\"M$\ -LastModelRules\"}."; - -GenSave::usage = -"GenSave[\"model_name\"] generates a generic coupling file for use with \ -FeynArts using the current definitions of the functions PropagatorType, \ -PropagatorArrow and KinematicIndices and the values of the variables \ -ToExpression/@$GenObjects. The file is saved in the Model directory under the \ -name \"model_name.gen\"."; - -ModSave::usage = -"ModSave[\"model_name\"] generates a classes coupling file for use with \ -FeynArts using the current definitions of the functions PropagatorType, \ -PropagatorArrow and KinematicIndices and the values of the variables \ -ToExpression/@$GenObjects. The file is saved in the Model directory under the \ -name \"model_name.mod\". NOTICE : ModSave uses a temporary file \"dum\" in \ -the model directory."; - -VerticesExtract::usage = -"VerticesExtract[top] returns a list of the vertices of top, where top is \ -an element of the list of topologies and insertions returned by InsertFields. \ -The vertices are given as FullVertex[field1,field2,..]."; - -FullVertex::usage = -"FullVertex[field1,field2,..] is a representation of a vertex. \ -field1,field2,.. are the Phi fields used by with FeynArts like e.g. \ -PseudoScalar2[0]."; - -VerticesSymmetryFactor::usage = -"VerticesSymmetryFactor[top], where top is an element of the list of \ -topologies and insertions returned by InsertFields, supplies for n absolutely \ -identical (including signs - e.g. -Fermion7[0]!=Fermion7[0]) vertices a \ -factor n! to the combinatorical number."; - -LoopsSymmetryFactor::usage = -"LoopsSymmetryFactor[top], where top is an element of the list of \ -topologies and insertions returned by InsertFields, supplies for each set of \ -identical progators with scalar, pseudoscalar, vector or axial-vector fields \ -a factor n!, where n is the number of propagators in the set a factor n! to \ -the combinatorical number."; - -$VerticesSpecifications::usage = -"$VerticesSpecifications is a variable used by the FeynArts model files \ -Automatic.gen and Automatic.mod. It is a list specifying the options of \ -XName, and it determines which of the files in the directory CouplingVectors \ -of Phi are loaded by Automatic.gen and Automatic.mod. Default value : \ -{{VertexFields->{Pion[0],Pion[0],Pion[0],Pion[0]},PerturbationOrder->{2},\ -CouplingSign->1,PhiModel->ChPT2,XFileName->Automatic},{VertexFields->{Pion[0],\ -Pion[0],Pion[0],Pion[0],Pion[0],Pion[0]},PerturbationOrder->{2},\ -CouplingSign->1,PhiModel->ChPT2,XFileName->Automatic}}."; - -VerticesSpecifications::usage = -"VerticesSpecifications[conf, faparts, parttypes] returns \ -a list usable as the setting of $VerticesSpecifications, by reading the \ -directory of coupling vectors \"CouplingVectors\". conf is a configuration \ -(possible setting of $Configuration), faparts is a list of FeynArts particle \ -heads (possible setting of $FAParticlesInUse), parttypes is a list of \ -allowed PHI particle heads (possible setting of $ParticleTypes). \ -VerticesSpecifications[$Configuration, $FAParticlesInUse, $ParticleTypes] \ -will return all vertices found in \"CouplingVectors\" belonging to the current model. \ -NOTICE : Currently, fermion number violating vertices cannot be handled by VerticesSpecifications; \ -for such models you have to write $VerticesSpecifications by hand."; - -PhiModel::usage = -"PhiModel is one of the parameters in $VerticesSpecifications that should \ -be set before doing loop calculations with Phi and FeynArts. Default value \ -: ChPT2."; - -GenProps::usage = -"GenProps is a function used by the generic FeynArts model Automatic \ -for constructing the list M$GenericPropagators. It returns predefined standard \ -values for $ScalarHeads, $VectorHeads and $FermionHeads. It is however, \ -possible to use non-standard propagators by modifying this function."; - -$PropagatorMassesStates::usage = -"$PropagatorMassesStates is a variable used by the FeynArts model file \ -Automatic.mod. It is a list specifying the optional arguments of ParticleMass \ -for the particles used. Default value : \ -{Pion[0]->{RenormalizationState[0]},Kaon[0]->{RenormalizationState[0]}}."; - -$MixingFields::usage = -"$MixingFields is a variable used by the FeynArts model file \ -Automatic.mod. It is a list specifying optional mixing fields and their \ -partners, e.g. {PseudoScalar[0][-1]->{Pion[0],PseudoScalar[0][0]},...}. Here \ -PseudoScalar[0][-1] is some intermediate field. Default value : {}."; - -$LastModelRules::usage = -"$LastModelRules is a variable used by the FeynArts model file \ -Automatic.mod. It is merged with M$LastModelRules. Default value : {}."; - -$InsertOnly::usage = -"$InsertOnly is a variable used by the FeynArts model file \ -Automatic.mod. It is a list specifying optional propagator types the \ -particles are to be restricted to. Default value : \ -{Vector[0][0]->{Incoming,Outgoing,External}, - AxialVector[0][0]->{Incoming,Outgoing,External}}."; - -VertexFields::usage = -"VertexFields is one of the quantities of $VerticesSpecifications that \ -must be specified before doing loop calculations with the model 'Automatic'. \ -NOTICE : Any Phi particle-field with argument 0 is interpreted by \ -ParticleMass, DecayConstant and Particle as the particle-field without \ -argument. E.g. ParticleMass[Pion[0]] := ParticleMass[Pion]. Default value \ -{Pion[0],Pion[0],Pion[0],Pion[0]}."; - -IsoSpin::usage = -"IsoSpin is the head for iso-indices used by the model file \ -Automatic.mod. E.g. Index[IsoSpin[J],1] is the first iso-index of the kind \ -J."; - -CreateFCAmp::usage = -"CreateFCAmp[amp,opts] applies -FAToFC to CreateFeynAmp[amp,AmplitudeLevel->Classes,opts] and does a few other \ -adjustings. NOTICE : \ -CreateFCAmp takes the options WFRenormalize, PerturbationOrder, \ -DropOrder and Method and the options of both CreateFeynAmp and FAToFC, \ -WavefunctionRenormalize and DiscardOrders. The options PerturbationOrder, \ -DropOrder and Method are relevant \ -only when WavefunctionRenormalize is set to True. The option Method specifies \ -which method should be used for discarding orders higher than the order \ -specified by DropOrder. It can be either Plus or DiscardOrders. Plus works only \ -for next-to-leading order renormalization."; - -$CouplingIsoIndicesSpecifications::usage = -"$CouplingIsoIndicesSpecifications is a variable used by the models \ -Automatic.gen and Automatic.mod. It is a list specifying the isospin indices \ -of each particle, the range of these indices and the string used as body of \ -the respective indices. If a particle is not in this list, it is assumed \ -that it has no isospin indices. If FieldsSet is used when generating the \ -corresponding classes coupling vector, the setting of the string should agree \ -with that of the option IsoIndicesString of FieldsSet (FieldsSet operates \ -with only one isospin index). Default value : \ -{Pion[0]->{IsoRange->{1,2,3},IsoIndicesString->\"I\"},Kaon[0]->{IsoRange->{1,\ -2},IsoIndicesString->\"J\"}}."; - -IsoRange::usage = -"IsoRange is one of the parameters $CouplingIsoIndicesSpecifications that \ -should be set before doing loop calculations with Phi and FeynArts."; - -$CouplingMomentumVariablesString::usage = -"$CouplingMomentumVariablesString is a variable used by the models \ -Automatic.gen and Automatic.mod. It is a string specifying the variable \ -names used as momentum variables. The setting of \ -$CouplingMomentumVariablesString should usually agree with that of the option \ -MomentumVariablesString of FCToFA and FAToFC. Default value : \"p\"."; - -$CouplingLorentzIndicesString::usage = "$CouplingLorentzIndicesString is a \ -variable used by the models Automatic.gen and Automatic.mod. It is \ -a string specifying the variable names used as Lorentz indices. The setting \ -of $CouplingLorentzIndicesString should \ -usually agree with what one has used in the kinematic coupling vector. \ -Default value : \"\[Mu]\"."; - -DeltaFunctionProducts::usage = -"DeltaFunctionProducts[opts] is the set of all possible products of \ -delta-functions, with each product containing a number of factors determined \ -by ParticlesNumber. The isospin indices given by the setting of the option \ -IsoIndicesString are used."; - -FCToFA::usage = -"FCToFA[m,opts] is the matrix element m calculated with FeynCalc \ -transformed to FeynArts notation. FCToFA collects terms according to the \ -delta functions using the isospin indices given by the setting of the option \ -IsoIndicesString (this is the only thing FCToFA uses this option for)."; - -IsoCollect::usage = -"IsoCollect is an option for FCToFA specifying whether the output should \ -be collected with respect to isospin. Default value : False."; - -FADeltas::usage = -"FADeltas is an option for FCToFA, FAToFC and DeltaFunctionProducts \ -specifying if the FeynCalc SUNDelta functions should be replaced with the \ -value of $FADelta and vice versa. Default value : False."; - -$FADelta::usage = -"$FADelta is an environment variable specifying which symbol should be \ -used for FeynArts Kronecker delta functions. It is consulted by \ -DeltaFunctionProducts, FCToFA, GenericCoupling, FAToFC and \ -DeltaFunctionsCollect. Notice that setting it to the FeynArts built-in \ -function IndexDelta turns on some processing by FeynArts that may be \ -unwanted. Default value : SUNDelta."; - -MomentaCollect::usage = "MomentaCollect[m,opt] collects terms containing \ -the variables given by the setting of the options MomentumVariablesString and \ -ParticlesNumber. If the option ExtendedCollect is set True, it also collects \ -terms containing elements from the environment variable $ExpansionQuantities. \ -NOTICE : When the output of this function is to be used for generating \ -coupling vectors with GenericCoupling or ClassesCoupling, it should be \ -checked that the expansion factors are really overall factors of each term. \ -NOTICE ALSO : When dealing with large expressions, the collection done be \ -MomentaCollect is inefficient because it collects too many redundant \ -patterns. A faster way is to set $VeryVerbose to 3 and collect 'by hand' \ -using only the relevant patterns from the list of patterns displayed."; - -ExtendedCollect::usage = "ExtendedCollect is an option of MomentaCollect \ -specifying whether or not to collect terms containing elements from \ -$ExpansionQuantities. It should usually not be used when the output is for \ -generating coupling vectors with GenericCoupling or ClassesCoupling. Default \ -value : True."; - -HoldMinuses::usage = "HoldMinuses is an option of MomentaCollect specifying \ -whether or not to substitute overall minus signs of a sum with the symbol \ -HoldMinus. Default value : False."; - -HoldMinus::usage = "When the option HoldMinuses of MomentaCollect is set to \ -True, overall minus signs of a sum are substituted with the symbol HoldMinus. \ -Default value : False."; - -GenericCoupling::usage = -"GenericCoupling[mfa] tries to construct the kinematical coupling vector \ -to be used in a generic model file for FeynArts from the matrix element mfa \ -calculated with e.g. FCToFA. GenericCoupling will only work on expressions \ -that have the momenta as overall factors. Such expressions can usually be \ -obtained with MomentaCollect. Notice that GenericCoupling like MomentaCollect \ -depends on the setting of $ExpansionQuantities."; - -ClassesCoupling::usage = -"ClassesCoupling[mfa] tries to construct the coupling vector to be used \ -in a classes model file for FeynArts from the matrix element mfa calculated \ -with e.g. FCToFA. ClassesCoupling will only work on expressions that have \ -the momenta as overall factors. Such expressions can usually be obtained \ -with MomentaCollect."; - -XFileName::usage = -"XFileName is an option for XName and CouplingFilesGenerate, specifying \ -the first part of the names CouplingFilesGenerate uses for saving the \ -FeynArts generic and classes model coupling vectors, the last part is \".Gen\ -\" and \".Mod\" respectively. When XFileName has the default value Automatic, \ -XName generates this last part from Options[XName] or the options (other than \ -XFileName) specified, and so does CouplingFilesGenerate. Default value : \ -Automatic."; - -XName::usage = -"XName[opts] returns the file name given by the setting of XFileName or \ -when XFileName is set to Automatic a name generated from the options (other \ -than XFileName) specified. The generated name uses VertexFields, \ -PerturbationOrder and PhiModel. When XFileName has another value than \ -Automatic, XName[opts] assumes this value. Notice that $ParticleHeads must \ -contain heads of all particles involved."; - -CouplingFilesGenerate::usage = -"CouplingFilesGenerate[m,opts], where m is some amplitude in FeynCalc \ -notation, calculates GenericCoupling[MomentaCollect[FCToFA[m,opts],opts]] and \ -ClassesCoupling[MomentaCollect[FCToFA[m,opts],opts]], and saves them in the \ -directory Phi`CouplingVectors. CouplingFilesGenerate \ -generates the file names using XName and the setting of XFileName or when \ -XFileName is set to Automatic from the options (other than XFileName) \ -specified."; - -CouplingSign::usage = -"CouplingSign is an option for $VerticesSpecifications specifying the \ -sign under interchange of the particles of the kinematical coupling vector. \ -Default value : 1."; - -FAToFC::usage = -"FAToFC[amps,opts] picks out the classes level of the list of amplitudes \ -amps generated by CreateFeynAmp of FeynArts (with PickLevel) and transforms \ -it into a plain list of amplitudes in FeynCalc notation. The momentum \ -variables given by the setting of the option MomentumVariablesString are \ -used. Sum is an option of FAToFC. When set to False, the FeynArts \ -quantities SumOver[i,r], where i is some index and r is the range of this \ -index, are set to 1. This should be ok so long as the usual summation \ -convention applies. With an expression like e.g. SumOver[i,3] (f[i] g[i] / \ -h[i] + a ), the usual summation convention would not apply and Sums should \ -be set to True or Explicit. In the latter case, SumOver[i,r]*exp, where \ -exp is some expression is summed explicitly over i from 1 to r. \ -Default value of Sum : True."; - -IsoToChargedMasses::usage = -"IsoToChargedMasses projects out ParticleMass[p, SUNIndex[i]], where \ -p is a particle name to a ParticleMass of a particle in the charged basis using \\ -$IsoSpinProjectionRules."; - -WFFactor1::usage = -"WFFactor1[prop] is returned by WFFactor when the wave function renormalization \ -factor corresponding to the propagator prop is not found in the directory \"Factors\"."; - -WFFactor::usage = -"WFFactor[prop] searches the directory \"Factors\" and returns the wave \ -function renormalization factor corresponding to the propagator prop. \ -WFFactor is used by WFRenormalize. \ -NOTICE : Wavefunction factors stored in the directory \"Factors\", with \ -a name with \"-0\" preceding the extension \".Fac\" are by convention \ -on-mass-shell."; - -ChargeSymmetry::usage = -"ChargeSymmetry is an option of WFFactor specifying whether the renormalization factor of a \ -particle and its antiparticle are identical."; - -(*WFRenormalize[exp] calculates the wave function renormalization factors \ -for the propagators of exp. Exp must be of the form TopologyList[__][__] as returned \ -by InsertFields.*) - -WFRenormalize::usage = -"WFRenormalize is an option of FAToFC. \ -When set to True, wave function renormalization is performed. WFRenormalize uses \ -the results stored in the directory \"Factors\". The names of the files to load are \ -generated using $Configuration and the option PerturbationOrder. Default value : False."; - -PMRenormalize::usage = -"PMRenormalize[exp] replaces unrenormalized masses of the form \ -ParticleMass[p, RenormalizationState[0]]^2 with renormalized masses of the form \ -ParticleMass[p, RenormalizationState[1]]^2 - c, where p is some particle and \ -c is the higher order correction. It is assumed that all masses occur as positive \ -powers of squared masses. The procedure for obtaining a renormalized \ -expression from a \"raw\" expression with unrenormalized quantities is to \ -first apply DCRenormalize, then PMRenormalize and finally DiscardOrders."; - -DCRenormalize::usage = -"DCRenormalize[exp] replaces unrenormalized decay constants of the form \ -DecayConstant[p, RenormalizationState[0]] with renormalized decay constants of the form \ -DecayConstant[p, RenormalizationState[1]] - c, where p is some particle and \ -c is the higher order correction. It works also for inverse powers of decay constants, \ -in which case it taylor expands the renormalization factor up to the order specified \ -by the option PerturbationOrder. NOTICE : The determination of the powers of the decay \ -constants necessitates expansion of the whole expression exp and the multiplication of \ -each term with a renormalization factor. Therefore the function is slow and returns \ -large expressions, which it, however, should be possible to clean up substantially."; - -DCFactor1::usage = -"DCFactor1[f] is returned by DCFactor when the decay constant renormalization \ -factor corresponding to the decay constant f is not found in the directory \"Factors\"."; - -DCFactor::usage = -"DCFactor[f] searches the directory \"Factors\" and returns the decay \ -constant renormalization factor corresponding to the decay constant f. \ -DCFactor is used by DCRenormalize."; - -PMFactor1::usage = -"PMFactor1[m] is returned by DCFactor when the particle mass renormalization \ -factor corresponding to the mass m is not found in the directory \"Factors\"."; - -PMFactor::usage = -"PMFactor[f] searches the directory \"Factors\" and returns the particle \ -mass renormalization factor corresponding to the particle mass f. \ -PMFactor is used by PMRenormalize."; - -EqualMasses::usage = -"EqualMasses is an option of FAToFC. When set to True, indices are \ -removed from ParticleMass. Default value : True."; - -InternalMomentumVariablesString::usage = -"InternalMomentumVariablesString is an option of FAToFC. When \ -MomentaString is set to \"q\", q1, q2, ... are the internal monemta supplied. \ -Default value : \"q\"."; - -DeltaFunctionsCollect::usage = -"DeltaFunctionsCollect[amp,opts] collects the deltafunctions of the \ -amplitude amp. The isospin indices given by the setting of the option \ -IsoIndicesString are used."; - -DoSumOver::usage = -"DoSumOver[exp] sums factors of SumOver (produced by FeynArts). The option \ -Drop specifies values of the indices to be left out of the sum."; - - -(* -Errors -*) - -GenericCoupling::"nores" = -"Sorry, but I was unable to resolve the expression. Please \ -generate the coupling by hand."; - -ClassesCoupling::"nores" = -"Sorry, but I was unable to resolve the expression. Please \ -generate the coupling by hand."; - -WFFactor::"noprop" = "Unknown propagator type `1`."; - -CreateFCAmp::"nomethod" = "Unknown method `1`."; - -DCRenormalize::"nores" = "Cannot resolve power of `1`. Please renormalize by hand."; - -VerticesSpecifications::"multvert" = -"Error. Bad number of particles `2` matching `1`. Either your \ -\"CouplingVectors\" directory is in disarray or you are giving wrong \ -particles as arguments."; - -VerticesSpecifications::"oddferm" = -"Error. You seem to have an odd number of fermions in your vertex."; - -CheckCouplingSign::"nosym" = -"Warning: There is a problem with the generic coupling vector `1`. It is \ -neither symmetric nor antisymmetric under the following permutations: `2`."; - -DoSumOver::"indleft" = -"Warning: There still seem to be indices `1` left that should have been summed. \ -Please check."; - -CreateFCAmp::"spinormismatch" = -"Error: Cannot resolve spinors."; - -CreateFCAmp::"looprenorm" = -"Warning: Renormalizing loop propagator."; - -Begin["`Package`"] -End[] - - -Begin["`Couplings`Private`"]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* FeynCalc functions *) - -fccombs := - fccombs = MakeFeynCalcPrivateContext["CombinationLists"]; - -(* FeynArts functions *) - -faid := - faid = FeynArts`IndexDelta; -facl := - facl = FeynArts`Classes; -fafm := - fafm = FeynArts`FourMomentum; -faint := - faint = FeynArts`Internal; -faintg := - faintg = FeynArts`Integral; -fafad := - fafad = FeynArts`FAFeynAmpDenominator; -faind := - faind = FeynArts`Index; -fapl := - fapl = FeynArts`PickLevel; -fainc := - fainc = FeynArts`Incoming; -faout := - faout = FeynArts`Outgoing; -fapd := - fapd = FeynArts`FAPropagatorDenominator; -(*Should we keep FAFourVector for FAToFC to work - with old coupling files?*) -fafv := - fafv = Global`FAFourVector; -famt := - famt = Global`FAMetricTensor; -falo := - falo = Global`Lorentz; -facrfa := - facrfa = FeynArts`CreateFeynAmp; -faal := - faal = FeynArts`AmplitudeLevel; -fapolv := - fapolv = Global`FAPolarizationVector; -faext := - faext = FeynArts`External; -fanoncom := - fanoncom = FeynArts`FANonCommutative; -fadm := - fadm = Global`FADiracMatrix; -fachiralp := - fachiralp = Global`FAChiralityProjector; -DiracSpinor := - DiracSpinor = Global`FADiracSpinor; -faferch := - faferch = FeynArts`FermionChain; -fagen := - fagen = System`Generic; -fains := - fains = FeynArts`Insertions; -fatop := - fatop = FeynArts`Topology; -fagr := - fagr = FeynArts`FeynmanGraph; -faloop := - faloop = FeynArts`FALoop; -faprop := - faprop = FeynArts`Propagator; -fadsl := - fadsl = Global`FADiracSlash; -famatr := - famatr = FeynArts`MatrixTrace; -favert := - favert = FeynArts`Vertex; -faso := - faso = FeynArts`SumOver; -fatopl := - fatopl = FeynArts`TopologyList; -faverti := - faverti = FeynArts`Vertices; -facoupmat := - facoupmat = FeynArts`M$CouplingMatrices; -faps := - faps = FeynArts`PSort; -faseens := - faseens = FeynArts`SelfEnergies; -fawfcr := - fawfcr = FeynArts`WFCorrections; -fafi := - fafi = FeynArts`Field; -fatrru := - fatrru = FeynArts`M$TruncationRules; -facol := - facol = Global`Colour; -faanalc := - faanalc = FeynArts`AnalyticalCoupling; -fags := - fags = FeynArts`G; -famass := - famass = FeynArts`Mass; - - -(* Defaults *) - -$VerticesSpecifications = {{VertexFields -> {Pion[0], Pion[0], Pion[0], - Pion[0]}, PerturbationOrder -> {2}, CouplingSign -> 1, - PhiModel -> Phi`Objects`ChPT2, - XFileName -> - Automatic}, {VertexFields -> {Pion[0], Pion[0], Pion[0], Pion[0], - Pion[0], Pion[0]}, PerturbationOrder -> {2}, CouplingSign -> 1, - PhiModel -> Phi`Objects`ChPT2, - XFileName -> Automatic}}; -$PropagatorMassesStates = {Pion[0] -> {RenormalizationState[0]}, - Kaon[0] -> {RenormalizationState[0]}}; -$CouplingLorentzIndicesString = "\[Mu]"; -$CouplingMomentumVariablesString = "p"; -$CouplingIsoIndicesSpecifications = {Pion[ - 0] -> {{IsoRange -> {1, 2, 3}, IsoIndicesString -> "I"}}, - Kaon[0] -> {{IsoRange -> {1, 2}, IsoIndicesString -> "J"}}}; -$MixingFields = {}; -$LastModelRules = {}; -$InsertOnly = {Vector[0][0] -> {fainc, faout, faext}, - AxialVector[0][0] -> {fainc, faout, faext}}; -$FADelta = SUNDelta; -SetAttributes[MomentaScalarProduct, Orderless]; -Options[FCToFA] = {ScalarProductForm -> MomentaScalarProduct, - MomentumVariablesString -> "p", ParticlesNumber -> 4, - IsoIndicesString -> "I", FADeltas -> True, IsoCollect -> False}; -Options[MomentaCollect] = {ParticlesNumber -> 4, PerturbationOrder -> 2, - ScalarProductForm -> (MomentaScalarProduct|Pair), - (*MetricTensor -> Global`FAMetricTensor,*) - MetricTensor -> MetricTensor, - MomentumVariablesString -> "p", ExtendedCollect -> True, - HoldMinuses -> False}; -Options[GenericCoupling] = {ScalarProductForm -> MomentaScalarProduct, -FCToFA->True}; -Options[ClassesCoupling] = {ScalarProductForm -> MomentaScalarProduct, -FCToFA->True}; -Options[XName] = {VertexFields -> {Pion[0], Pion[0], Pion[0], Pion[0]}, - PerturbationOrder -> 2, PhiModel -> Phi`Objects`ChPT2, - XFileName -> Automatic}; -Options[CouplingFilesGenerate] = {VertexFields -> {Pion[0], Pion[0], Pion[0], - Pion[0]}, PerturbationOrder -> 2, - PhiModel -> Phi`Objects`ChPT2, - XFileName -> Automatic}; -Options[FAToFC] = {EqualMasses -> True, ParticlesNumber -> 4, - ScalarProductForm -> MomentaScalarProduct, - MomentumVariablesString -> "p", InternalMomentumVariablesString -> "q", - MomentaSumLeft -> All, DiracTraceEvaluate -> False, Sum -> True, FADeltas -> False}; -Options[DeltaFunctionsCollect] = {ParticlesNumber -> 4, - IsoIndicesString -> "I"}; -Options[DeltaFunctionProducts] = {ParticlesNumber -> 4, - IsoIndicesString -> "I", FADeltas -> False}; -Options[AddExternalLegs] = {ExternalPropagators -> 1, faseens -> False}; -Options[DiscardTopologies] = {PerturbationOrder -> 2, - OrderingPatterns -> {}}; -(*Using :> instead of -> for PhiModel is important*) -(*Options[WFRenormalize] = {PerturbationOrder -> 2, PhiModel :> Global`$Configuration, - OnMassShell -> False, Momentum :> Momentum[Global`p1, D]};*) -Options[PMRenormalize] = {PerturbationOrder -> 2, PhiModel :> Global`$Configuration}; -Options[DCRenormalize] = {PerturbationOrder -> 2, PhiModel :> Global`$Configuration}; -Options[WFFactor] = {PerturbationOrder -> 2, PhiModel :> Global`$Configuration, - ChargeSymmetry -> True, OnMassShell -> False, - Momentum :> Momentum[Global`p1, D]}; -Options[PMFactor] = {PerturbationOrder -> 2, PhiModel :> Global`$Configuration}; -Options[DCFactor] = {PerturbationOrder -> 2, PhiModel :> Global`$Configuration}; -Options[CreateFCAmp] = {WFRenormalize -> False, PerturbationOrder -> 2, - DropOrder -> 4, Method -> Plus, - PhiModel :> Global`$Configuration, - OnMassShell -> False, Momentum :> Momentum[Global`p1, D]}; -Options[DoSumOver] = {Drop -> {0}}; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Change to FeynArts 2 notation *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -(* Terms with the same delta-function factor are collected, and the result is - expressed in FeynArts notation: *) - -SetAttributes[pp, {Orderless}]; - -SetAttributes[pll, {Orderless}]; - -indexsub1 = pp[a__] :> pl /@ {a}; - -indexsub2 = pl[{a__}] :> pll[a]; - -indexsub3[opts___] := - ToExpression[(IsoIndicesString /. Flatten[{opts}] /. - Options[DeltaFunctionProducts]) <> - ToString[(ParticlesNumber + (1 - (-1)^ParticlesNumber)/2) /. - Flatten[{opts}] /. Options[DeltaFunctionProducts]]] -> - ToExpression[(IsoIndicesString /. Flatten[{opts}] /. - Options[DeltaFunctionProducts]) <> - ToString[(ParticlesNumber /. Flatten[{opts}] /. - Options[DeltaFunctionProducts])]]; - -indii[opts___] := - {Permutations[ - Table[ToExpression[(IsoIndicesString /. Flatten[{opts}] /. - Options[DeltaFunctionProducts]) <> - ToString[ - j]], {j, (ParticlesNumber + (1 - (-1)^ParticlesNumber)/2) /. - Flatten[{opts}] /. Options[DeltaFunctionProducts]}]]}; - -indicestemp[opts___] := - Union[Union[MapThread[pp @@ Partition[#1, 2] &, indii[opts] , 1 ]] /. - indexsub1 /. indexsub2 /. indexsub3[opts]]; - -DeltaFunctionProducts[opts___] := - Union[indicestemp[opts] /. (pll -> faid) /. ({faid[a__], b___} -> - faid[a]*b)] /. - If[ (FADeltas /. Flatten[{opts}] /. Options[DeltaFunctionProducts]), - faid -> $FADelta, - faid[a_, b_] :> SUNDelta[SUNIndex[a], SUNIndex[b]] /; - !FreeQ[{a,b}, IsoSpin, Heads -> True] - ]; - - - -(* The vertex in FeynArts notation: *) - -melfeynartstemp[melsimplified_, opts___] :=(**) - (DiracGammaExpand[melsimplified](*/. {SUNN -> Sqrt[2], CA -> Sqrt[2], - CF -> 1/(2*Sqrt[2])}*)/. - - (*Can cause multiple identical pairs of indices. Changed 11/6-2003*) - (*DiracGamma[Momentum[p_,___],___] :> DiracGamma[LorentzIndex[tmpmu=ToExpression[$CouplingLorentzIndicesString<>ToString[p]]]]* - Pair[LorentzIndex[tmpmu],Momentum[p]]*) - DiracGamma[Momentum[p_,___],___] :> fadsl[p] /. - - If[ (FADeltas /. Flatten[{opts}] /. - Options[FCToFA]), - {SUNDelta -> $FADelta, - SU2Delta -> $FADelta, SU3Delta -> $FADelta}, - {} - ] /. - {DOT -> fanoncom, (SUNIndex|ExplicitSUNIndex)[a_] -> a, - Pair[a_Momentum, - b_Momentum] -> - (ScalarProductForm /. Flatten[{opts}] /. Options[FCToFA])[a, b], - Pair[a_LorentzIndex, - b_Momentum] -> fafv[b, a], - Pair[LorentzIndex[li1_, ___], LorentzIndex[li2_, ___]] -> - famt[li1, li2]} /. {LorentzIndex[a_] -> a, Momentum[a_] -> a(*, - DiracGamma -> fadm, ChiralityProjector -> fachiralp*)} /. (*{a__*fadm[b__] -> - a*fanoncom[fadm[b]]}*){a__*DiracGamma[b__] -> - a*fanoncom[DiracGamma[b]], a__*fadsl[b__] -> - a*fanoncom[fadsl[b]]} /. - Flatten[Table[{ToExpression[(MomentumVariablesString /. - Flatten[{opts}] /. Options[FCToFA]) <> - ToString[ - b + (ParticlesNumber/2 /. Flatten[{opts}] /. - Options[FCToFA])]] ->(*-*) - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[FCToFA]) <> - ToString[ - b + (ParticlesNumber/2 /. Flatten[{opts}] /. - Options[FCToFA])]]}, {b, (ParticlesNumber/2 /. - Flatten[{opts}] /. Options[FCToFA])}]]); - -SetAttributes[nonc, Flat]; - -FCToFA[melsimplified_, opts___] := - If[ (IsoCollect /. Flatten[{opts}] /. Options[FCToFA]), - Collect[ExpandAll[ - melfeynartstemp[ - melsimplified (*Commented out 11/5-2003*)(*/. (PhiProjection[pa_, ___][pb_]) :> SUNDelta[pa, pb]*), - opts]], Join[ - DeltaFunctionProducts @@ - Join[Flatten[{opts}], Options[FCToFA]], - {SU2F[___], SU3F[___], SU3D[___], SUNF[___], - SUND[___]}, {UGenerator[__][__]}]], - melfeynartstemp[ - melsimplified (*Commented out 11/5-2003*)(*/. (PhiProjection[pa_, ___][pb_]) :> SUNDelta[pa, pb]*), - opts] - ] /. fanoncom -> nonc /. nonc -> fanoncom; - -negtest[b_] := - Re[b] < 0 || Im[b] < 0; -plus1[a : ((_?negtest*_) ..)] := - -1*plus1 @@ ((-1*#) & /@ {a}); -momprod[pta_, ptab__] := - Union[Flatten[Union @@ Outer[Times, pta, ptab]]]; -momprod[pta_] := - Flatten[pta]; -Head1[Power[a_, b_]] := - Head1[a, b]; -Head1[a_] := - Head[a]; - -MomentaCollect[m_, opts___] := - Block[ {mt = (MetricTensor /. Flatten[{opts}] /. Options[MomentaCollect]), - pc = (ScalarProductForm /. Flatten[{opts}] /. Options[MomentaCollect]), - pcc, j, pp, xf, xff, xfff, tminus, var, Head1, momentaslist, momentaslist1, momentaslist2, - momentaslist3}, - pcc = If[ Head[pc]===Alternatives, - Blank /@ pc, - Blank[pc] - ]; - FCPrint[2, "Scalar product is ", pcc]; - FCPrint[1, "Building list of Collect patterns from momenta"]; - momentaslist1 = - Join[If[ pc === None, - {}, - Join[{Times @@ - Table[(var = ToExpression["a" <> ToString[j]]; - Pattern[Evaluate[var], pcc]), {j, - Ceiling[(PerturbationOrder /. Flatten[{opts}] /. - Options[MomentaCollect])/2]}]}, - {pcc^(Ceiling[(PerturbationOrder /. Flatten[{opts}] /. - Options[MomentaCollect])/2])}] - ], - If[ (ExtendedCollect /. Flatten[{opts}] /. Options[MomentaCollect]), - FCPrint[1, - "Building list of Collect patterns from $ExpansionQuantities"]; - FCPrint[3, " ", $ExpansionQuantities]; - Select[momprod @@ - Table[Join[$ExpansionQuantities, - If[ pc === None, - {}, - {Sqrt[pc[a___]]} - ]](*/.dropnumrules*)/. - {Blank -> xf, BlankSequence -> xff, BlankNullSequence -> xfff} /. - Pattern -> pp /. - {pp[b_, xf[]] -> pp[b, Blank[]], - pp[b_, xff[]] -> pp[b, BlankSequence[]], - pp[b_, xfff[]] -> pp[b, BlankNullSequence[]]} /.pp -> Pattern /. - {xf[] -> ToExpression["a" <> ToString[j] <> "_"], - xff[] -> ToExpression["a" <> ToString[j] <> "__"], - xfff[] -> ToExpression["a" <> ToString[j] <> "___"]}, - {j, (Ceiling[(PerturbationOrder /. Flatten[{opts}] /. Options[MomentaCollect])])}], - FreeQ[#, ___*Power[_, Rational[_, 2]]] &] //. - {a___, b_Times, c___, d_Times, e___} /; - Head1 /@ (b) == Head1 /@ (d) -> {a, b, c, e} //. - {a___, b_, c___} /; OddQ[Count[b, Sqrt[_]]] -> {a, c} //. - Power[a_, Rational[n1_, 2]]*Power[b_, Rational[n2_, 2]] -> - Power[a, Rational[n1 + n2, 2]]*(1 + (-1)^(n1 + n2))/2 /. - Sqrt[_]*__ -> Sequence[], - {} - ](*, $ExpansionQuantities*)]; - momentaslist2 = If[ mt === None, - {}, - mt[__]*momentaslist1 - ]; - (*momentaslist2 = MetricTensor[__]*momentaslist1;*) - momentaslist3 = Join[momentaslist2, momentaslist1](*/. dropnumrules*); - (*Use only patterns that actually occur in the expressions. Added 24/9-2002*) - momentaslist = Select[momentaslist3, !FreeQ[m, #]&]; - FCPrint[3, "I will collect ", StandardForm[momentaslist]]; - FCPrint[1, - "Collecting"];(*We replace numerical functions temporarily*) - Collect[m(*/. dropnumrules*)/. - fafv[-p_, l___]*r_ :> fafv[p, l]*tminus*r, momentaslist] /. - Plus -> plus1 /. plus1 -> Plus /. - fafv[-p_, l___]*r_ :> fafv[p, l]*tminus*r /. tminus -> -1 /. - If[ (HoldMinuses /. Flatten[{opts}] /. Options[MomentaCollect]), - -1*a__* - Plus[b_, bb___] -> a*HoldMinus*Plus[b, bb], - {} - ] - (*/. - setnumrules*)]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Generation of FeynArts 2 couplings *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Here is the kinematical coupling vector to be used in a generic model file - for FeynArts >= 2: *) - -expansionpatterns[opts___] := - Alternatives @@ - Join[$ExpansionQuantities, {(*_Global`FAMetricTensor,*) - _MetricTensor, (*_Global`FADiracMatrix,*) - (*_Global`FAChiralityProjector,*) - _DiracGamma, - _DiracSlash, - _ChiralityProjector, - Blank[ScalarProductForm /. Flatten[{opts}] /. - Options[GenericCoupling]]}]; - - - -GenericCoupling1[a_*m_, opts___] /; -(!FreeQ[a, expansionpatterns[opts]] && FreeQ[m, expansionpatterns[opts]]) := - Flatten[{Select[a*m, !FreeQ[#, Alternatives @@ expansionpatterns[opts]]&] /. - HoldMinus -> 1}]; - - - -llist[a__][opts___] := - Join[{Plus @@ Select[{a}, FreeQ[#, expansionpatterns[opts]] &]}, - Select[{a}, !FreeQ[#, expansionpatterns[opts]]&]] /. - {f___, 0, l___} -> {f, l}; - - - -GenericCoupling1[a_*Plus[m_, n__], opts___] /; - FreeQ[a, expansionpatterns[opts]] := - a*((Plus[m, n] + tempp) /. Plus[aa__, tempp] -> List[aa]) /. - Plus[aa__, tempp] -> - llistt[aa][opts] /. {a1_* m1_ /; (! FreeQ[a1, expansionpatterns[opts]] && - FreeQ[m1, expansionpatterns[opts]]) :> - Sequence @@ Flatten[{Select[ - a1*m1, !FreeQ[#, Alternatives @@ - expansionpatterns[opts]] &]}]} /. - {Plus[_*$FADelta[__], _*$FADelta[__] ..] -> 1, - Plus[$FADelta[__], $FADelta[__] ..] -> 1, - Plus[_*SUNDelta[__], _*SUNDelta[__] ..] -> 1, - Plus[SUNDelta[__], SUNDelta[__] ..] -> - 1,(*Commented out 11/5-2003*)(*Plus[_*PhiProjection[__][_], _*PhiProjection[__][_] ..] -> 1, - Plus[PhiProjection[__][_], PhiProjection[__][_] ..] -> 1,*) - Plus[_*UGenerator[__][_], _*UGenerator[__][_] ..] -> 1, - Plus[UGenerator[__][_], UGenerator[__][_] ..] -> 1, - Plus[_*SUND[__], _*SUND[__] ..] -> 1, - Plus[SUND[__], SUND[__] ..] -> 1, - Plus[_*SUNF[__], _*SUNF[__] ..] -> 1, - Plus[SUNF[__], SUNF[__] ..] -> 1} //. {fac_*$FADelta[__] -> - fac, fac_*SUNDelta[__] -> fac,(*Commented out 11/5-2003*)(*fac_*PhiProjection[__][_] -> fac,*) - fac_*SUND[__] -> fac, fac_*SUNF[__] -> fac} /. - HoldMinus -> 1 /. llistt -> llist; - - - -GenericCoupling1[Plus[m_, mm___],opts___] := - ((m + mm + tempp) /. - Plus[aa__, tempp] -> llistt[aa][opts]) /. - {a1_ * m1_ /; (!FreeQ[a1, expansionpatterns[opts]] && - FreeQ[m1, expansionpatterns[opts]]) :> - Sequence @@ Flatten[{Select[a1*m1, - !FreeQ[#,Alternatives @@ expansionpatterns[opts]]&]}]} /. - {Plus[_*$FADelta[__], _*$FADelta[__] ..] -> 1, - Plus[$FADelta[__], $FADelta[__] ..] -> 1, - Plus[_*SUNDelta[__], _*SUNDelta[__] ..] -> 1, - Plus[SUNDelta[__], SUNDelta[__] ..] -> 1, - (*Commented out 11/5-2003*)(*Plus[_*PhiProjection[__][_], _*PhiProjection[__][_] ..] -> 1, - Plus[PhiProjection[__][_], PhiProjection[__][_] ..] -> 1,*) - Plus[_*UGenerator[__][_], _*UGenerator[__][_] ..] -> 1, - Plus[UGenerator[__][_], UGenerator[__][_] ..] -> 1, - Plus[_*SUND[__], _*SUND[__] ..] -> 1, - Plus[SUND[__], SUND[__] ..] -> 1, - Plus[_*SUNF[__], _*SUNF[__] ..] -> 1, - Plus[SUNF[__], SUNF[__] ..] -> 1} //. {fac_*$FADelta[__] -> - fac, fac_*SUNDelta[__] -> fac,(*Commented out 11/5-2003*)(*fac_*PhiProjection[__][_] -> fac,*) - fac_*SUND[__] -> fac, fac_*SUNF[__] -> fac} /. - HoldMinus -> 1 /. llistt -> llist; - - - -(* Here is the coupling vector to be used in a classes model file for FeynArts 2: *) - -ClassesCoupling1[m_, opts___] := - (numerator = (m + tempp) /. - Plus[aa__, tempp] -> llistt[aa][opts] /. HoldMinus -> -1 /. - llistt -> llist; - classcoupl = numerator/GenericCoupling2[m, opts]; - Table[{classcoupl[[rep]]}, {rep, Length[numerator]}]); - - - -(* Should FCToFA be applied first? *) - -GenericCoupling2[m_,opts___] := - Block[ {fctofa = FCToFA /. Flatten[{opts}] /.Options[GenericCoupling],tmpres, - gencoup1 = GenericCoupling1}, - tmpres = - If[ fctofa, - FCPrint[2,"Applying FCToFA to the expression"]; - GenericCoupling1[FCToFA[m],opts], - FCPrint[1,"FCToFA will not be applied to the expression! Make sure the expression is in FeynArts notation"]; - GenericCoupling1[m,opts] - ]; - If[ Head[tmpres] =!= gencoup1, - tmpres, - Message[GenericCoupling::"nores"]; - ] - ]; - -GenericCoupling[m_,opts___] := - GenericCoupling2[m,opts] //. - {a_*fanoncom[b_] :> fanoncom[a*b], a_*fanoncom[b_,c__] :> fanoncom[a*b,c]} /. - fanoncom -> nonc /. nonc -> fanoncom; - -ClassesCoupling[m_,opts___] := - Block[ {fctofa = FCToFA /. Flatten[{opts}] /.Options[ClassesCoupling],tmpres, - classcoup1 = ClassesCoupling1}, - tmpres = - If[ fctofa, - FCPrint[2,"Applying FCToFA to the expression"]; - ClassesCoupling1[FCToFA[m],opts], - FCPrint[1,"FCToFA will not be applied to the expression! Make sure the expression is in FeynArts notation"]; - ClassesCoupling1[m,opts] - ]; - If[ Head[tmpres] =!= classcoup1, - tmpres, - Message[ClassesCoupling::"nores"]; - ] - ]; - -(* A name is generated for the coupling files: *) - -(*This way we allow higher numbers than 9. E.g. PseudoScalar11 -> 11.*) -(*Notice that the "generation number" must still be <10. E.g. PseudoScalar11[0]*) -pnumber[p_] := - Block[ {char, chars, pchars, i}, - chars = ""; - char = ""; - pchars = Characters[ToString[p]]; - i = 1; - While[StringMatchQ["0123456789", "*" <> pchars[[-i]] <> "*"], - chars = pchars[[-i]] <> chars; - ++i]; - chars - ]; - -xnamerule[opts___] := - XFileName -> - ToString[PhiModel /. Flatten[{opts}] /. - Options[XName]] <> ((VertexFields /. Flatten[{opts}] /. - Options[XName]) /. (p : $ParticleHeads)[ii_] :> - StringTake[ToString[p], {1}] <> (*StringTake[ToString[p], {-1}]*)pnumber[p] <> - ToString[ii]) <> "o" <> - ToString[PerturbationOrder /. Flatten[{opts}] /. Options[XName]]; - -XName[opts___] := - If[ ((XFileName /. Flatten[{opts}] /. Options[XName]) === - Automatic), - (XFileName /. - xnamerule[opts]), - (XFileName /. Flatten[{opts}] /. - Options[XName]) - ]; - - - -(* The complete automatized transformation toFeynArts notations, reduction of -delta-functions, generation of FeynArts 2 couplings and saving of the two -couplings. The two saved coupling vectors can be used for constructing -coupling model files for FeynArts 2. The name is a contraction of all the -option settings in the ordering given by Options[CouplingFilesGenerate] and -with the extension Gen or Mod: *) - - -CouplingFilesGenerate[melsimplified_, opts___] := - (tmp`olddir = Directory[]; - SetDirectory[Phi`$HEPDir]; - SetDirectory["FeynCalc"]; - SetDirectory["Phi"]; - SetDirectory["CouplingVectors"]; - Put[GenericCoupling[MomentaCollect[FCToFA[melsimplified, opts], opts]], - StringTake[XName[opts], - Min[30, StringLength[XName[opts]]]] <> ".Gen"]; - Put[ClassesCoupling[MomentaCollect[FCToFA[melsimplified, opts], opts]], - StringTake[XName[opts], - Min[30, StringLength[XName[opts]]]] <> ".Mod"]; - Print["Two coupling vectors have been saved in files " <> - StringTake[XName[opts], - Min[30, StringLength[XName[opts]]]] <> ".Gen" <> " and " <> - StringTake[XName[opts], - Min[30, StringLength[XName[opts]]]] <> ".Mod"]; - SetDirectory[tmp`olddir];); - - - -(* Construct $VerticesSpecifications from directory listing *) - - -(* Return e.g. {{"A", "0", "0"}, {"P", "1", "0"}, {"o", "2"}} from "A00P10o2" *) - -characterArray[css_] := - Block[ {cs,charArr,i,j}, - cs = Characters[css]; - charArr = {}; - j = 0; - Do[If[ StringMatchQ["0123456789","*"<>cs[[i]]<>"*"]=!=True, - ++j; - charArr = Append[charArr,{cs[[i]]}], - charArr[[j]] = Append[charArr[[j]],cs[[i]]] - ],{i,Length[cs]}]; - charArr - ]; - - -(* Returns a particle name from e.g. toParticle[{"P", "1", "0"}, - $FAParticlesInUse,$ParticleTypes] *) - -toParticle[arr_,pts_,parttps_] := - Block[ {pars,types,parttypes,a}, - parttypes = (ToString/@parttps)/.a_String:> - Sequence[a,"-"<>a]/;StringMatchQ[a,"Fermion"]; - parts = (ToString/@pts)/.a_String:> - Sequence[a,"-"<>a]/;StringMatchQ[a,"Fermion*"]; - pars = Select[ - parts,(StringMatchQ[ToString[#], - arr[[1]]<>"*"<>StringJoin@@Drop[Drop[arr,1],-1]]&& - Length[types = - Select[parttypes, - StringMatchQ[ToString[#],arr[[1]]<>"*"]&]]=== - 1&&(StringLength[types[[1]]]+Length[arr]-2=== - StringLength[ToString[#]]))&]; - If[ Length[pars]===1, - ToExpression[ToString[pars[[1]][arr[[-1]]]]], - Message[VerticesSpecifications::"multvert",arr,pars]; - Return[] - ] - ]; - - -(* Construct fermion vertices, - respecting fermion number conservation. Like e.g. - {{"F","1","0"},{"F","1","0"},{"V","1","0"},{"o","2"}} --> - Sequence[{{"-F","1","0"},{"F","1","0"},{"V","1","0"},{"o","2"}},{{"F","1", - "0"},{"-F","1","0"},{"V","1","0"},{"o","2"}}] *) - -fermionize[v_] := - Block[ {pos,n}, - pos = Position[Drop[v,-1],{"F",__}]//Flatten; - If[ IntegerQ[n = Length[pos]/2]=!=True, - Message[VerticesSpecifications::"oddferm"]; - Return[] - ]; - If[ pos=!={}, - Sequence@@(MapAt[MapAt["-"<>#&,#,{1}]&,v,({#})&/@#]&/@ - fccombs[pos,n]), - v - ] - ]; - -(* Return e.g. {{{"A", "0", "0"}, {"P", "1", "0"}, {"o", "2,4"}}} from - {{{"A", "0", "0"}, {"P", "1", "0"}, {"o", "2"}}, - {{"A", "0", "0"}, {"P", "1", "0"}, {"o", "4"}}} *) - -orderJoin[v_List] := - Block[ {pas,pa,pv}, - pas = Union[Drop[#, -1]&/@v]; - (pa = #; - pv = Select[v, (Drop[#,-1]===pa)& ]; - If[ Length[pv]>1, - Append[pa, {"o", "Sequence["<>StringDrop[StringDrop[ToString[(#[[-1,-1]])&/@pv], -1], 1]<>"]"}], - pv[[1]] - ])& /@ pas - ]; - -(* Construct $VerticesSpecifications. - E.g. - VerticesSpecifications[$Configuration,$FAParticlesInUse,$ParticleTypes] *) - -VerticesSpecifications[conff_,parts_,parttypes_] := - Block[ {fils,verts,verts0,conf,olddir,vecdir}, - conf = ToString[conff]; - vecdir = - ToFileName[{Phi`$HEPDir,"FeynCalc","Phi", - "CouplingVectors"}]; - olddir = Directory[]; - SetDirectory[vecdir]; - filsg = - StringDrop[#,StringLength[conf]]&/@(StringDrop[#,-4]&/@ - FileNames[conf<>"*"<>".Gen"]); - filsm = - StringDrop[#,StringLength[conf]]&/@(StringDrop[#,-4]&/@ - FileNames[conf<>"*"<>".Mod"]); - SetDirectory[olddir]; - fils = Intersection[filsg,filsm]; - verts0 = characterArray/@fils; - verts1 = fermionize/@verts0; - verts = orderJoin[verts1]; - ({VertexFields->(toParticle[#,parts,parttypes]&/@Drop[#,-1]), - PhiModel->ToExpression[conf], - PerturbationOrder->{ToExpression[StringJoin@@(ToString/@ - Drop[#[[-1]],1])]},CouplingSign->1})&/@verts - ]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Symmetry factors for Feynman graphs *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* Below follow two patches to FeynArts which I am not at all sure about: *) - - -(* For n absolutely identical (including signs - e.g. -Fermion7[0]!=Fermion7[0]) -vertices, we get a factor n!: *) - - -(* Added to deal with multiple-graph topologies. - Splits in separate one-graph topologies. *) - -VerticesExtract[top:(fatop[_][__] -> fains[fagen][ - fagr[__][__] -> fains[facl][(fagr[__][__]) ..], - (fagr[__][__] -> fains[facl][(fagr[__][__]) ..]) ..])] := -(*Union @@*) - (VerticesExtract /@ (top /. - ((t : (fatop[_][__])) -> (i:(fains[fagen][ - fagr[__][__] -> fains[facl][(fagr[__][__]) ..], - (fagr[__][__] -> fains[facl][(fagr[__][__]) ..]) ..]))) :> - ((Rule[t, fains[fagen][#]])& /@ (List @@ i)))); - -VerticesExtract[t : (fatop[_][__]) -> fains[fagen][fagr[_, ___][__] -> - fains[facl][fagr[_, ___][classins__],___]]] := - (verts = - Union[Cases[t, favert[_][_], Infinity, Heads -> True]]; - vertsfull = (FullVertex @@ - Cases[t(**)/. p : faprop[_][v_, v_, _] -> Sequence[p, p](**), - faprop[_][___, #, ___], Infinity, Heads -> True]) & /@ - verts; - vertsfull /. {classins} /. - faprop[_][_, _, fi_] -> fi /. (pa : $ParticleHeads)[i_, ___] :> - pa[i]); - -splitinequals[l_] := - Union[Table[Select[l, MatchQ[#, l[[i]]] &], {i, Length[l]}]]; -VerticesSymmetryFactor[ - t : (fatop[_][__]) -> - fains[fagen][ - fagr[n_, r___][genins__] -> - fains[facl][fagr[nn_, rr___][classins__]]]] := - (verts = - Select[VerticesExtract[ - t -> fains[fagen][ - fagr[n, r][genins] -> - fains[facl][fagr[nn, rr][classins]]]], (Length[#] > 1) &]; - symfac = Times @@ (Factorial /@ (Length /@ - Select[splitinequals[verts], (Length[#] > 1) &])); - (t -> - fains[fagen][ - fagr[n/symfac, r][genins] -> - fains[facl][fagr[nn/symfac, rr][classins]]])); - - - -(* Each set of identical progators with scalar, pseudoscalar, vector or -axial-vector fields gives a factor n!, where n is the number of propagators -in the set: *) - -equalprops[ - t : (fatop[_][__]) -> - fains[fagen][ - fagr[__][ - genins__] -> __]] := - ((*Propagators are grouped with head equals[prop]*) - sortedt = - Sort[t] /. - fatop[tn_][f___, faprop[faloop[n_]][vert1_, vert2_, field_], - faprop[faloop[n_]][vert1_, vert2_, fieldd_], l___] :> - fatop[tn][ - f, (equals[faprop[faloop[n]][vert1, vert2, field]][field, - fieldd]), l] //. - fatop[tn_][f___, - equals[faprop[faloop[n_]][vert1_, vert2_, field_]][eqs__], - faprop[faloop[n_]][vert1_, vert2_, fieldd_], l___] :> - fatop[tn][ - f, (equals[faprop[faloop[n]][vert1, vert2, field]][eqs, - fieldd]), - l] /. {genins};(*Finally we select the equals[__][__] and replace equals[prop][ - fields] with the number of identical scalars or vectors in fields*) - Cases[sortedt, equals[__][__], Infinity, - Heads -> - True] /. {equals[faprop[_][_, _, fi_]][ - ff__] /; (! FreeQ[fi, $ScalarHeads | $VectorHeads]) :> - equals[Length[{ff}]], - equals[faprop[_][_, _, fi_]][ - __] /; (FreeQ[fi, $ScalarHeads | $VectorHeads]) :> - equals[1]}); -LoopsSymmetryFactor[ - t : (fatop[_][__]) -> - fains[fagen][ - fagr[n_, r___][genins__] -> - fains[facl][fagr[nn_, rr___][classins__]]]] := - (symfac = - Times @@ (equalprops[ - t -> fains[fagen][ - fagr[n, r][genins] -> - fains[facl][fagr[nn, rr][classins]]]] /. - equals -> Factorial); - (t -> - fains[fagen][ - fagr[n*symfac, r][genins] -> - fains[facl][fagr[nn*symfac, rr][classins]]])); - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Feynman graphs with external sources *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Support functions for DiscardCT, taken from ../FeynArts/Utilities.m: *) - -Renumber[top_] := - Block[ {s}, - s = Sort[(faprop @@ faps[#]) & /@ top]; - s /. MapIndexed[#1 -> Head[#1] @@ #2 &, faverti[s]] - ]; -TopPermute[fatop[_][props__]] := - Block[ {perm}, - perm = Union[Cases[{props}, favert[_][_?Negative], {2}]]; - If[ Length[perm] === 0, - Return[Renumber[{props}]] - ]; - Sort[ - Renumber[{props} /. Thread[perm -> #]] & /@ - Permutations[perm]][[1]] - ]; -Compare1[tops : _[]] = tops; -Compare1[tops_] := - Block[ {perm, p}, - perm = TopPermute /@ (tops/. favert[n_?((# > 1) &), nn___][i_?Positive] :> favert[n,nn][-i] - (*Make all vertices permutable.*)); - (p = Position[perm, #, 1]; - tops[[p[[1,1]]]](*/. fatop[s_][rest__] -> fatop[s/Length[p]][rest]*) - (*Commented out to avoid changing the symmetry factors.*))& /@ - Union[perm] - ]; - - - -(* DiscardCT converts first order conterterm topologies to non-counterterm - topologies: *) - -DiscardCT[tops : fatopl[__]] := - Block[ {maxv, tops1, AAA, AAB}, - maxv = Max[(#[[1]]) & /@ - Cases[tops, favert[_][_], Infinity, Heads -> True]] + 1; - tops1 = Compare1[(RemoveCT[#, maxv] & /@ - Select[tops, ((Length[Union[Cases[#, favert[_, _][_], {2}]]] < - 2 && FreeQ[#, - favert[_, _?((# > 1) &)][_]]) &)])(*/. - favert[a__][b_?((# > 99) &)] -> favert[a][-b]*) - (*Gave problems with Compare1.*) ]; - (*Added 9/6-2003 because InsertFields in FeynArts 3 no longer sorts before inserting; - copied from Insert.m from FeynArts 2.2*) - (Sort[ Sort /@ # /. - {fainc -> AAA, faout -> AAB} ] /. - {AAA -> fainc, AAB -> faout})& /@ tops1 - ]; - -RemoveCT[top_, n_] := - top /. favert[i_, 1][_] -> favert[i][n]; - - - -(* AddCT generates diagrams with one of the vertices of the original diagrams -replaced by a counterterm vertex: *) -(*Changed because FeynArts 3 no longer uses the convention of - numbering internal vertices higher than 99*) -(*Also, FeynArts 3 wants to have Internal propagators last*) - -gs[faprop[fainc][__], faprop[faout][__]] := - True; -gs[faprop[faout][__], faprop[fainc][__]] := - False; -gs[faprop[faout][__], faprop[faint][__]] := - True; -gs[faprop[faint][__], faprop[faout][__]] := - False; - -AddCT[t : fatopl[__]] := - Sort[#, gs] & /@ ((Sequence @@ (# /. ( - List /@ (Rule[#, MapAt[ss[#, 1] &, #, {0, 1}]] & /@ - Union[Union[Cases[Cases[#, faprop[faint | faloop[__]][__], - Infinity], favert[_][_], Infinity, Heads -> True], - Cases[#, favert[_?((Abs[#] > 1) &)][_], Infinity, Heads -> True]]])))) & /@ t /. - ss -> Sequence); - - -(* DropInternalSelfEnergies drops topologies with selfenergy loops on internal legs. *) - -(*Select elements that occur more than once in a list*) -SelectRepeated[s_List] := -(*Added union to deal with more than 2 occurences*) - Union[ - set = {}; - ((If[ FreeQ[set, #], - set = Union[set, {#}]; - seq[], - # - ]) & /@ s) /. - seq -> Sequence]; - -SelectInternalSelfEnergies[fatopl[mesonstop__]] := - Select[fatopl[mesonstop], (selfprops = {}; - (*Added ctverts to account also for CT's on internal lines.*) - ctverts = Alternatives @@ SelectRepeated[Cases[Cases[#, - faprop[faint][_, _], Infinity], favert[2, ___][_], Infinity]]; - loopprops = - List @@ Select[#, MatchQ[#, faprop[faloop[_]][v1_, v2_]]&]; - selfprops = - Union[SelectRepeated[loopprops], - Select[loopprops, MatchQ[#, faprop[faloop[_]][v_, v_]]&]]; - selfverts = Alternatives @@ Union[Flatten[(List @@ #) & /@ selfprops]]; - (Length[Complement[ - Select[List @@ #, - MatchQ[#, faprop[faint][___, selfverts, ___]]&], - selfprops]] === 2 || - FreeQ[#, ctverts] =!= True) && - FreeQ[List @@ #, - faprop[faext|faout|fainc][___, selfverts, ___]])&]; - -DropInternalSelfEnergies[fatopl[mesonstop__]] := - Complement[fatopl[mesonstop],SelectInternalSelfEnergies[fatopl[mesonstop]]]; - - - -(* AddExternalLegs puts on an extra propagator on all external legs (modified - versions of functions from FeynArts): *) - -AddToLeg[faprop[h : (faext | fainc | faout)][from : (favert[1][_]), to_], - n_] := - seq[faprop[h][from, favert[2][n]], - faprop[faint][favert[2][n], to]]; - -AddToLeg[faprop[(faint | faloop[__])][ - from : (favert[__(*Added _ to allow CTs.*)][_]), to_], _] := - faprop[discard][from, to]; - -AddLeg[top_, n_, opts___Rule] := - (exprops = (ExternalPropagators /. Flatten[{opts}] /. - Options[AddExternalLegs]); - posis = fccombs[Range[Length[top]], exprops]; - Map[If[ MatchQ[#, {_, _}], - #[[2]], - # - ] &, - fatopl @@ (MapAt[AddToLeg1[#[[2]], n + #[[1]] - 1] &, - top[[0]] @@ Table[{i, top[[i]]}, {i, Length[top]}], - List /@ #] & /@ posis) /. - fatop[s_][p1___, fatop[snew_][pnew__], p2___] :> - fatop[s snew][p1, pnew, p2] /. AddToLeg1 -> AddToLeg /. - seq -> Sequence, {2}]); - -AddExternalLegs[tops : fatopl[__], opts___Rule] := - Block[ {tops1,maxv,AAA,AAB}, - tops1 = If[ faseens /. Flatten[{opts}] /. Options[AddExternalLegs], - #, - DropInternalSelfEnergies[#] - ]&[ - (maxv = Max[(#[[1]]) & /@ - Cases[tops, favert[__(*Added _ to allow CTs. 10/10-2001*)][_], Infinity, Heads -> True]] + - 1; - Compare1[ - Select[AddLeg[#, maxv, opts] & /@ tops, - FreeQ[#, discard, Infinity, Heads -> True] &]])]; - (*Added 9/6-2003 because InsertFields in FeynArts 3 no longer sorts before inserting; - copied from Insert.m from FeynArts 2.2*) - (Sort[ Sort /@ # /. - {fainc -> AAA, faout -> AAB} ] /. - {AAA -> fainc, AAB -> faout})& /@ tops1 - ]; - - - -(* DiscardTopologies discards topologies with more than a specified number of a -specified type of vertex. *) - -DiscardTopology[ - t : (fatop[_][__] -> fains[fagen][(_[__] -> fains[facl][_[__] ..]) ..]), - opts___] := - Block[ {v }, - ops = (OrderingPatterns /. Flatten[{opts}] /. - Options[DiscardTopologies]); - (If[ ArrayDepth[#] === 2, - Plus @@ Transpose[#], - {Plus @@ #} - ]) &[((v = - VerticesExtract[ - t /.(*Replace external vertex in a propagator with a dummy vertex*) - {faprop[p : (faext | fainc | faout)][a_, favert[1, ___][_], f__] -> - faprop[p][a, favert[dummy], f], - faprop[p : (faext | fainc | faout)][favert[1, ___][_], - a_, f__] -> faprop[p][favert[dummy], a, f]}]); - v /.(*Replace vertices mathing one of the patterns with a 1*) - Alternatives @@ ops -> 1 /. - FullVertex[__] -> 0(*and the rest with 0*))] - ]; - - -DiscardTopologies[tops : (fatopl[___][__]), opts___] := - Block[ {top, dis, i, seq, ins}, - po = (PerturbationOrder /. Flatten[{opts}] /. - Options[DiscardTopologies]); - (top = #; - dis = DiscardTopology[top, opts]; - ins = Table[ - If[ Plus @@ dis[[i]] <= po, - top[[2, i]], - seq[] - ], {i, - Length[dis]}]; - top[[1]] -> (top[[2, 0]] @@ ins) - ) & /@ tops /. - seq -> Sequence /. (fatop[_][__] -> fains[_][]) :> - Sequence[] - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Fixing M$CouplingMatrices and M$GenericCouplings *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* Sometimes classes couplings have dummy indices (to be summed over). If two -such couplings are in the same M$CouplingMatrices, a graph with two vertices -with these two couplings will produce wrong results after application of e.g. -SUNReduce or IndicesCleanup. This function addresses this problem. *) - -(* Added 29/12-2000: Another problem addressed is that for tadpole loops, -e.g. SUND[i1,I1,I1] can occur, where I1 is meant to be summed over explicitly, -but SUND[i1,I1,I1] is set to zero. The solution is to have SUND replaced with -SU3D and have I1,I2,... be in $ConstantIsoIndices. This of only works as long as -FeynArts sticks to using I1,I2,... as dummy indices in the loops. So, in the -coupling vectors, use SU2F or SU3F etc., not SUNF etc. This is easily achieved -by applying SUNReduce *) - -FixCouplingIndices := - Block[ {newinds, tmpcouplmatr, rep, repp, reppp, i, is, - wrap = Phi`Couplings`Wrap}, - Do[FCPrint[2, "Checking M$CouplingMatrices[[", rep, ",", 2, ",", - repp, ",", reppp, "]]"]; - newinds = - Complement[ - Select[Union[ - Flatten[ - Cases[FeynArts`M$CouplingMatrices[[rep, 2, repp, - reppp]], (SU2Delta | SU2F | SU3Delta | SU3F | SU3D | - (*Bug fix. 2/7-2003. SUNDelta, SUND and SUNF can - also contain dummy indices. Fixes problem with - the seventh loop diagram of A7PiPiAmplitude.nb*) - SUNDelta | SUND | SUNF | fasunf | fasund)[__], Infinity, - Heads -> True] /. (SU2Delta | SU2F | SU3Delta | SU3F | SU3D | - SUNDelta | fasunf | fasund | SUNDelta | SUND | SUNF) -> List]], - (!NumberQ[#]) &] /. (SUNIndex|ExplicitSUNIndex)[i_] -> i, - Union[Flatten[ - FeynArts`M$CouplingMatrices[[rep, - 1]] /. (Alternatives @@ $FAParticlesInUse)[__, - is__List] -> is /. C -> List]]]; - If[ newinds =!= {}, - FCPrint[1, "You're using dummy indices, ", newinds, - " in M$CouplingMatrices[[", rep, ",", 2, ",", repp, ",", reppp, - "]]. Wrapping them and the coupling in Wrap. FAToFC will adjust"]; - tmpcouplmatr[rep, repp, reppp] = - wrap[FeynArts`M$CouplingMatrices[[rep, 2, repp, reppp]] /. - Evaluate[(# -> wrap[#]) & /@ newinds]], - tmpcouplmatr[rep, repp, reppp] = - FeynArts`M$CouplingMatrices[[rep, 2, repp, reppp]] - ], {rep, - Length[FeynArts`M$CouplingMatrices]}, {repp, - Length[FeynArts`M$CouplingMatrices[[rep, 2]]]}, {reppp, - Length[FeynArts`M$CouplingMatrices[[rep, 2, repp]]]}]; - FeynArts`M$CouplingMatrices = - Table[FeynArts`M$CouplingMatrices[[rep, 1]] == - Table[tmpcouplmatr[rep, repp, reppp], {repp, - Length[FeynArts`M$CouplingMatrices[[rep, 2]]]}, {reppp, - Length[FeynArts`M$CouplingMatrices[[rep, 2, repp]]]}], {rep, - Length[FeynArts`M$CouplingMatrices]}]; - ]; - - - - -(* Automatic.gen sets G[1] in all couplings. For antisymmetric couplings, it should - be -1. This is fixed by CheckCouplingSign *) - -CheckCouplingSign[coup : (faanalc[__] == fags[__][__]._List)] := - Block[ {parseRuls, mominds, groupedMominds, gmominds, ruls, ruls1, ruls2, - tests, tests2,att}, - att = Attributes[MetricTensor]; - SetAttributes[MetricTensor, Orderless]; - parseRuls = ((_*#[_, f___] :> # @@ - Flatten[{f}])) & /@ (List @@ $ParticleHeads); - mominds = List @@ coup[[1]] /. parseRuls; - groupedMominds = (h = #; - Select[mominds, (Head[#] === - h) &]) & /@ (List @@ $ParticleHeads); - gmominds = Select[groupedMominds, (# =!= {}) &]; - ruls = (sub = #; - ((RuleDelayed @@ #) & /@ Transpose[{sub, #}]) & /@ - Drop[Permutations[sub], 1]) & /@ gmominds; - ruls1 = - ruls /. ($ParticleHeads[f__] :> _[g__]) :> ((RuleDelayed @@ #) & /@ - Transpose[{{f}, {g}}]); - ruls2 = ((Union @@ #) & /@ Flatten[ruls1, 1]) /. RuleDelayed -> rd /. - rd[b_, b_] :> Sequence[] /. rd :> RuleDelayed; - couplings = coup[[-1, -1]]; - (*Check for symmetry*) - tests = (Union[couplings, couplings /. #] === Union[couplings]) & /@ - ruls2; - res = If[ And @@ tests =!= True, - probs = Position[tests, False]; - (*Check for symmetry or antisymmetry*) - tests2 = (Union[couplings, -couplings, couplings /. #] === - Union[couplings, -couplings]) & /@ Extract[ruls2, probs]; - If[ And @@ tests2 =!= True, - probs2 = Position[tests2, False]; - Message[CheckCouplingSign::"nosym", InputForm[coup], - InputForm[Extract[Extract[ruls2, probs], probs2]]]; - False,(*antisymmetric*) - -1 - ],(*symmetric*) - 1 - ]; - Attributes[MetricTensor] = att; - res - ]; - - -FixCouplingSigns := - Block[ {ok, rcouplings, ch, res}, - ok = True; - rcouplings = (res = - ReplacePart[#, ch = CheckCouplingSign[#]; - If[ ch === False, - ok = False - ]; - ch, {-1, 1, 0, 1}]; - If[ #[[-1, 1, 0, 1]] =!= ch && ch =!= False, - FCPrint[1, "Changed ", #[[-1, 1, 0, 1]], " into ", ch, - " for ", #] - ]; - res) & /@ FeynArts`M$GenericCouplings; - If[ ok, - FeynArts`M$GenericCouplings = rcouplings - ]; - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Change from FeynArts 2 to FeynCalc 3 notation *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* Picking out the classes amplitude, substituting some FeynArts heads with -FeynCalc heads, and adding a Hold to FeynAmpDenominator to avoid having it -written out (FeynCalc does not accept it when written out): *) - - -(* A raw amplitude: *) -classesamplitude[amm__ /; FreeQ[amm, facl]][opts___] := - (amm /.PropagatorDenominator1->PropagatorDenominator //. - {famatr[a___, b_, c___] /; UScalarQ[b] -> b*famatr[a, c], - faferch[a___, b_, c___] /; UScalarQ[b] -> b*faferch[a, c]} /. - fafm[faint, a_] :> Momentum[ToExpression[ - (InternalMomentumVariablesString /. Flatten[{opts}] /. Options[FAToFC]) <> ToString[a]], - D] /. - faintg[a_] -> a /. - fafad[a__] -> Hold[fafad[a]] /. - If[ (EqualMasses /. Flatten[{opts}] /. Options[FAToFC]), - ParticleMass[a_, b___][_] -> ParticleMass[a, b], - ParticleMass[a_, b___][c_] -> ParticleMass[a, SUNIndex[c], b] - ]) /. - SUNT[faind[a__], faind[b__], faind[c__]] :> - UGenerator[SUNIndex[faind[a]], SUNN -> 3][UIndex[faind[b]], UIndex[faind[c]]]/. - {faind[(IsoSpin|facol)[i_], b_] :> ToExpression[ToString[i] <> ToString[b]], - faind[falo, b_] :> LorentzIndex[ToExpression[$CouplingLorentzIndicesString <> ToString[b]], - D]}; - - - -(* An amplitude in FeynArts syntax: *) -classesamplitude[amm__ /; !FreeQ[amm, facl]][opts___] := -(**) - (fapl[facl][amm] /.PropagatorDenominator1->PropagatorDenominator //. - {famatr[a___, b_, c___] /; UScalarQ[b] -> b*famatr[a, c], - faferch[a___, b_, c___] /; UScalarQ[b] -> b*faferch[a, c]} /. - fafm[faint, a_] :> Momentum[ToExpression[(InternalMomentumVariablesString /. - Flatten[{opts}] /. Options[FAToFC]) <> ToString[a]], D] /. - faintg[a_] -> a /. - FeynAmpDenominator[a__] -> Hold[FeynAmpDenominator[a]] /. - If[ (EqualMasses /. Flatten[{opts}] /. Options[FAToFC]), - ParticleMass[a_, b___][_] -> ParticleMass[a, b], - ParticleMass[a_, b___][c_] -> ParticleMass[a, SUNIndex[c], b] - ]) /. - SUNT[faind[a__], faind[b__], faind[c__]] :> - UGenerator[SUNIndex[faind[a]], SUNN -> 3][UIndex[faind[b]], UIndex[faind[c]]]/. - {faind[(IsoSpin|facol)[i_], b_] :> ToExpression[ToString[i] <> ToString[b]], - faind[falo, b_] :> LorentzIndex[ToExpression[$CouplingLorentzIndicesString <> ToString[b]], - D]}; - - - -(* The amlitude in standard (FeynCalc) notation. The momenta of outgoing -particles are multiplied by -1, and the particles are thus redefined as -incoming: *) - -amptablefunc[a__ /; FreeQ[a, facl], j_Integer] := - ReleaseHold[Flatten[{a}][[j]]]; -amptablefunc[a__ /; ! FreeQ[a, facl], i_Integer] := - ReleaseHold[a[[i, 3]]]; -amptable[a_] := - Table[amptablefunc[a, i], {i, Length[a]}]; - - -fixindices[ampta_List] := - Block[ {common, rep, repp, wraps, rules, l, inds, newinds, tmpinds, tmpwraps, - amptab1 = ampta}, - (*Products of identical couplings.*) - amptab = ampta /. - Phi`Couplings`Wrap[a_]^n_ :> - (Times @@ (Phi`Couplings`Wrap[dumf[#]*a]& /@ Table[ii, {ii, 1, n}]));(**) - Do[FCPrint[2, "Checking amplitude ", repp]; - If[ (l = Length[wraps = Cases[amptab[[repp]], - HoldPattern[Plus[_Phi`Couplings`Wrap*__ ..]| - _Phi`Couplings`Wrap], {1}]]) > 1 && - Head[amptab[[repp]]] === Times, - FCPrint[1, "Amplitude contains ", l, - " factors with dummy indices. Renaming"]; - inds = {}; - Do[newinds = (#[[1]])& /@ - Union[Cases[wraps[[l]], - Phi`Couplings`Wrap[_?AtomQ], Infinity]]; - tmpinds = newinds; - While[(common = Intersection[inds, tmpinds]) =!= {}, - tmpinds = (If[ FreeQ[common, #], - #, - ToExpression[ - StringTake[ToString[#], 1] <> ToString[#]] - ] &) /@ - tmpinds]; - rules = (((Rule @@ #) &) /@ - Select[Transpose[{newinds, tmpinds}], (#[[1]] =!= #[[2]]) &]); - FCPrint[2, StandardForm[rules]]; - tmpwraps[rep] = (wraps[[rep]] /. rules); - inds = Join[inds, tmpinds];, {rep, l}]; - amptab1 = - ReplacePart[ - amptab1, (((Times @@ (tmpwraps /@ Range[l]))*(amptab1[[repp]] /. - HoldPattern[Plus[_Phi`Couplings`Wrap*__ ..]] -> 1 /. - Phi`Couplings`Wrap[_?(!FreeQ[#,Phi`Couplings`Wrap]&)] -> 1))) /. - Phi`Couplings`Wrap -> Identity, - repp] - ], {repp, Length[amptab1]}]; - amptab1 /. _dumf -> 1 /. Wrap -> Identity - ]; - -(* We put ExplicitSUNIndex on $ConstantIsoIndices to avoid e.g. SUND[I1,I1,a] getting set to 0. - Also necessary to fix the seventh loop diagram of A7PiPiAmplitude.nb (see above). *) -sunind[i_] := - If[ MemberQ[$ConstantIsoIndices, i], - ExplicitSUNIndex[i], - SUNIndex[i] - ]; - -FAToFC[amm_, opts___] := - (traceev = (DiracTraceEvaluate /. Flatten[{opts}] /. Options[FAToFC]); - (*selecting the classes amplitude and transforming - the four momenta and indices*) - FCPrint[2, "Extracting Classes amplitudes\n"]; - tmptable = - amptable[classesamplitude[amm/. - fafv[0, _] -> 0/.(*Workaround because DiracGamma strips - D if not in both DiracGamma and Momentum.*) - DiracGamma->tmpdiga][opts]]; - tmptable1 = fixindices[tmptable]; - FCPrint[2, "\nApplying translation rules"]; - (tmptable1 /. - (*Momenta*){ - fafm[fainc, b_] :> Momentum[ToExpression[(MomentumVariablesString /. - Flatten[{opts}] /. Options[FAToFC]) <> ToString[b]], D], - If[ (MomentaSumLeft /.Flatten[{opts}] /. Options[FAToFC]) === All, - fafm[faout,b_] :>(**)-Momentum[ToExpression[(MomentumVariablesString /. - Flatten[{opts}] /. Options[FAToFC]) <> ToString[b + ((ParticlesNumber/2) /. - Flatten[{opts}] /. Options[FAToFC])]],D], - fafm[faout, b_] :>(**)Momentum[ToExpression[(MomentumVariablesString /. - Flatten[{opts}] /. Options[FAToFC]) <> ToString[b + ((ParticlesNumber/2) /. - Flatten[{opts}] /. Options[FAToFC])]],D] - ] - } /. - (*SU(N) delta function*) If[ (FADeltas /. Flatten[{opts}] /. Options[DeltaFunctionProducts]), - $FADelta[aa_, bb_] :> SUNDelta[SUNIndex[aa],SUNIndex[bb]] /; - !FreeQ[{aa,bb}, IsoSpin, Heads -> True], - {} - ] /. - (*Four-vectors and scalar products*){ - fafv[a_?((!FreeQ[#, fafm | Momentum])&), b_?((Head[#] =!= LorentzIndex)&)] -> Pair[a, LorentzIndex[b]], - fafv[a_?((!FreeQ[#, fafm | Momentum])&), b_?((Head[#] === LorentzIndex)&)] -> Pair[a, b], - (*Added 25/9-2002 in order to have Amplitude work*) - fafv[a_?((FreeQ[#, fafm | Momentum])&), b_?((Head[#] =!= LorentzIndex)&)] -> Pair[LorentzIndex[b], Momentum[a]], - famt[li1_, li2_] /; FreeQ[{li1, li2}, LorentzIndex] -> - Pair[LorentzIndex[li1, D],LorentzIndex[li2, D]], - famt[li1_, li2_] /; !FreeQ[{li1, li2}, LorentzIndex] -> Pair[li1, li2], - - If[ (FADeltas /. Flatten[{opts}] /. Options[DeltaFunctionProducts]), - $FADelta[aa_, bb_] :> SUNDelta[SUNIndex[aa], SUNIndex[bb]] /; - !FreeQ[{aa,bb}, IsoSpin, Heads -> True], - dum->dum - ], - - UGenerator[I5_, op___][J3_, J1_] :> - UGenerator[SUNIndex[I5], op][UIndex[J3],UIndex[J1]] /; - FreeQ[{I5}, SUNIndex|ExplicitSUNIndex, Heads->True] && - FreeQ[{J3,J1}, SUNIndex|ExplicitSUNIndex|UIndex, Heads->True], (*fapd -> PropagatorDenominator, *) - fafad -> FeynAmpDenominator, - (ScalarProductForm /. Flatten[{opts}] /. Options[FAToFC])[ - a_, b_] /; FreeQ[{a, b}, Momentum] -> ScalarProduct[a, b, Dimension -> D], - (ScalarProductForm /. Flatten[{opts}] /. - Options[FAToFC])[a_, b_] /; !FreeQ[{a, b}, Momentum] -> Pair[a, b] - } /. - (*SU(N) stuff*) - { - SUND[ii__] :> SUND @@ (sunind /@ {ii}), - SUNF[ii__] :> SUNF @@ (sunind /@ {ii}), - SUNDelta[ii__] :> SUNDelta @@ (sunind /@ {ii}), - SU2F[ii__] :> SU2F @@ (SUNIndex /@ {ii}), - SU3F[ii__] :> SU3F @@ (SUNIndex /@ {ii}), - SU3D[ii__] :> SU3D @@ (SUNIndex /@ {ii}), - SU2Delta[ii__] :> - SU2Delta @@ (SUNIndex /@ {ii}), - SU3Delta[ii__] :> - SU3Delta @@ (SUNIndex /@ {ii})(*Commented out 11/5-2003*)(*, - PhiProjection[i_Integer][j_] :> PhiProjection[i][SUNIndex[j]]*) - } /. - UGenerator[ii_,op___] :> UGenerator[SUNIndex[ii],op] /. - (*Polarization vectors*) - Pair[a_,b : Plus[-1*_, __]] :> -Pair[a, -b] /. - (*polarization vectors*){ - Conjugate[fapolv][_, f_*Momentum[m_, d___], - LorentzIndex[l_, ___]] -> Pair[LorentzIndex[l], f*Momentum[Polarization[m, -I], d]], - Conjugate[fapolv][_, Momentum[m_, d___], LorentzIndex[l_, ___]] -> - Pair[LorentzIndex[l], Momentum[Polarization[m, -I], d]], - fapolv[_, f_*Momentum[m_, d___], LorentzIndex[l_, ___]] -> - Pair[LorentzIndex[l], f*Momentum[Polarization[m, I], d]], - fapolv[_, Momentum[m_, d___], LorentzIndex[l_, ___]] -> - Pair[LorentzIndex[l], Momentum[Polarization[m, I],d]] - }/. - (*Dirac stuff*){ - tmpdiga[p_?((!FreeQ[{#},Momentum|LorentzIndex])&)] :> DiracGamma[p, D], - tmpdiga[p_?(FreeQ[{#},Momentum|LorentzIndex]&)] :>(DiracGamma[LorentzIndex[p,D], D]) - } /. - {fanoncom[a_, b__] :> (DOT[a, b]/.fanoncom->Identity), - fanoncom[a_] :> (a/.fanoncom->Identity(*Changed 31/1-2002. I have no idea* why mma suddenly screws up here*))} /. - (*famatr[mat__] -> DiracTrace[DOT[mat], DiracTraceEvaluate -> False]*) - If[ traceev =!= (DiracTraceEvaluate /. Options[FAToFC]), - famatr[mat__] -> DiracTrace[DOT[mat], DiracTraceEvaluate -> traceev], - famatr[mat__] -> DiracTrace[DOT[mat]] - ] /. - (*fixing the last momenta without D*) - {Pair -> fcpa1, Momentum -> fcmom1} /. - {fcmom1[a_] -> fcmom1[a, D],LorentzIndex[a_] -> LorentzIndex[a, D]} /. - {fcmom1 -> Momentum, fcpa1 -> Pair} /. - (*Fermions*){DiracSpinor -> Spinor, faferch -> DOT} /. - (DiracTraceEvaluate -> False) -> (DiracTraceEvaluate -> traceev) /. - If[ (Sum /. Flatten[{opts}] /. Options[FAToFC]) === False, - faso[___] -> 1, - faso[i_, r_, ___] :> - faso[SUNIndex[i], r] /; !FreeQ[{i}, IsoSpin, Heads -> True] - ] // - If[ (Sum /. Flatten[{opts}] /. Options[FAToFC]) === Explicit, - (FCPrint[3, "Summing ", StandardForm[#]]; - DoSumOver[#,Sequence@@OptionsSelect[DoSumOver,opts]])&, - Identity - ]) /. - {SUNDelta[a_, b_] /; FreeQ[{a, b}, SUNIndex|ExplicitSUNIndex] -> - SUNDelta[SUNIndex[a], SUNIndex[b]], - SUND[a_, b_, c_] /; FreeQ[{a, b, c}, SUNIndex|ExplicitSUNIndex] -> - SUND[SUNIndex[a], SUNIndex[b], SUNIndex[c]], - SUNF[a_, b_, c_] /; FreeQ[{a, b, c}, SUNIndex|ExplicitSUNIndex] -> - SUNF[SUNIndex[a], SUNIndex[b], SUNIndex[c]], - SU2F[a_, b_, c_] /; FreeQ[{a, b, c}, SUNIndex|ExplicitSUNIndex] -> - SU2F[SUNIndex[a], SUNIndex[b], SUNIndex[c]], - SU3D[a_, b_, c_] /; FreeQ[{a, b, c}, SUNIndex|ExplicitSUNIndex] -> - SU3D[SUNIndex[a], SUNIndex[b], SUNIndex[c]], - SU3F[a_, b_, c_] /; FreeQ[{a, b, c}, SUNIndex|ExplicitSUNIndex] -> - SU3F[SUNIndex[a], SUNIndex[b], SUNIndex[c]]} /. - ExplicitLorentzIndex[a_, ___] -> a) //. - (*Added 13/8-2002 because patching FA model files gives structures like - DiracMatrix[Index[Lorentz, 1]] which is auto-expanded by FC into - DiracGamma[LorentzIndex[Index[Lorentz, 1]]]*) - LorentzIndex[LorentzIndex[mu_, d___],___] :> LorentzIndex[mu, d] /. - (* added Sept. 27 2003 Rolf Mertig*) - tmpdiga :> DiracGamma /. - (* Added 12/4-2004 to allow coupling files to use DiracSlash. - Their momenta will be wrapped in Momentum by the rules above, which is wrong since - DiracSlash is an input function *) - fadsl[a_?(!FreeQ[#, Momentum[__]]&)] :> fadsl[dum + a] //. - {fadsl[dum + a___*Momentum[b__] + c___] :> fadsl[dum + a*{b}[[1]] + c], - fadsl[dum + Momentum[b__] + c___] :> fadsl[dum + {b}[[1]] + c]} /. - dum :> Sequence[]; - -DoSumOver[exp_, opts___Rule] := - Block[ {rr, res, suminds}, - (*Apart is to avoid summing sub-factors and leaving other factors with - SUNIndices untouched. No guarantee however.*) - suminds = Union[(#[[1]])& /@ Cases[exp, faso[__], Infinity, Heads->True]]; - (*F.Orellana, 9/11-2003. Apart factors out e.g. SUNDelta[ExplicitSUNIndex[I1,5] - and leaves a sum of terms with SumOver[...], causing the terms to be summed and - the SUNDelta to be forgotten.*) - res = Factor[Apart[exp]] //. Times[f__, faso[i_, r_, ___]] :> - (If[ Head[r] =!= List, - FCPrint[2, "Summing ", i, " from 1 to ", r]; - rr = Range[1, r], - FCPrint[2, "Summing ", i, " over ", r]; - (*kill off zeros introduced if IsoRange includes 0. 17/6-2003*) - rr = r - ]; - Plus @@ ((Times[f] /. i -> #)& /@ - Select[rr, !MatchQ[(#/.SUNIndex|ExplicitSUNIndex->Identity), - Alternatives @@ (Drop/.{opts}/.Options[DoSumOver])]&])); - If[ FreeQ[res, Alternatives@@suminds], - res, - Message[DoSumOver::"indleft", suminds]; - res - ] - ]; - -DeltaFunctionsCollect[ampf__, opts___] := - Collect[ampf, - Union[Flatten[((DeltaFunctionProducts @@ - Join[Flatten[{opts}], Options[DeltaFunctionsCollect]]) /. - Times -> List)], - Flatten[((DeltaFunctionProducts @@ - Join[Flatten[{opts}], Options[DeltaFunctionsCollect]]) /. - Times -> List)] /. $FADelta -> SUNDelta, - Flatten[((DeltaFunctionProducts @@ - Join[Flatten[{opts}], Options[DeltaFunctionsCollect]]) /. - Times -> List)] /. $FADelta[aa_, bb_] :> - SUNDelta[SUNIndex[aa], SUNIndex[bb]] /; - !FreeQ[{aa,bb}, IsoSpin, Heads -> True]]]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* CreateFCAmp *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Some reshuffling of code to other files might be in place, in order - to minimize the use of giving explicit contexts like - Phi`Utilities` . Some other time...*) - - -(*Useful stuff. Well, not necessary below. Off could just as well -be used. From - -http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&oe=UTF-8&frame=right&th=415f22bd75c86b5c&seekm=CyCoou.8zr%40wri.com#link3 - -Switches message output off and on, but keeps the normal -message-processing mechanisms, so that Check still works. -We could push this up to some context.*) - -DisableMessage[msg_MessageName] := - ( Unprotect[Message]; - Literal[m:Message[msg, ___]] := - Block[ {$Messages = Null}, - m - ] /; $Messages =!= Null; - Protect[Message]; ); - -SetAttributes[EnableMessage, HoldFirst]; - -EnableMessage[msg_MessageName] := - ( Unprotect[Message]; - Literal[m:Message[msg, args___]] =.; - Protect[Message];); - -(*replace isospin with charged masses*) -cruls := - Block[ {parts, part, rul, tmppart}, - (parts = {}; - (part = #[[1]]; - (rul = (tmppart = #[[1]][0, - {#[[2, 1]] | SUNIndex[#[[2, 1]]] | ExplicitSUNIndex[#[[2, 1]]]}]; - tmppart) -> part[0]; - If[ FreeQ[parts /. Alternatives :> (({##}[[1]])&), - tmppart], - parts = Append[parts, tmppart]; - rul, - seq[] - ])& /@ - Cases[{#[[2]]}, _Iso, Infinity])& /@ - Phi`Channels`$IsoSpinProjectionRules /. - seq -> Sequence // Flatten) - ]; - -(* Help functions for mass renormalization *) - -PMFactor[mass_, opts___?OptionQ] := - Block[ {nam, dum, res}, - DisableMessage /@ {List::"string", StringJoin::"string"}; - Off[FeynCalc`CheckDB::"nostring"]; - nam = XName[VertexFields -> {mass[[1]][0]}, - Sequence @@ OptionsSelect[XName, opts, Options[PMFactor]], - XFileName -> Automatic] <> ".Mass"; - res = CheckDB[dum, nam, - NoSave -> True, - ForceSave -> False]; - EnableMessage /@ {List::"string", StringJoin::"string"}; - On[FeynCalc`CheckDB::"nostring"]; - If[ FreeQ[res,dum], - res, - PMFactor1[mass, opts] - ] - ]; - -PMRenormalize[amp_, opts___?OptionQ] := - Block[ {i, p, m, r, rr, pm, por, drru}, - por = (PerturbationOrder /. {opts} /. Options[PMRenormalize]); - (*Should be safe for corrections...*) - drru = {ParticleMass[pp_, RenormalizationState[0]] -> - ParticleMass[pp, RenormalizationState[1]], - (x : (Alternatives @@ $ExpansionQuantities)) :> - (x /. RenormalizationState[0] -> RenormalizationState[1])}; - amp /. (l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> - (l[s] /. ParticleMass -> pm) /. - {PropagatorDenominator[p_, ParticleMass[m_, r___, RenormalizationState[0], rr___]] -> - PropagatorDenominator[p, ParticleMass[m, r, RenormalizationState[1], rr]], - ParticleMass[p_, RenormalizationState[0]]^i_ :> - (ParticleMass[p, RenormalizationState[1]]^2 - - PMFactor[ParticleMass[p, RenormalizationState[0]] /. cruls, - Sequence @@ Complement[ - OptionsSelect[PMFactor, opts, Options[PMRenormalize]], - Options[PMFactor]]] /. drru)^(i/2) - } /. - pm -> ((ParticleMass[##]/.drru)&) - ]; - -(* Help functions for decay constant renormalization *) - -DCFactor[ff_, opts___?OptionQ] := - Block[ {nam, dum, res}, - DisableMessage /@ {List::"string", StringJoin::"string"}; - Off[FeynCalc`CheckDB::"nostring"]; - nam = XName[VertexFields -> {AxialVector[0][0], ff[[1]][0]}, - Sequence @@ OptionsSelect[XName, opts, Options[DCFactor]], - XFileName -> Automatic] <> ".Fac"; - res = CheckDB[dum, nam, - NoSave -> True, - ForceSave -> False]; - EnableMessage /@ {List::"string", StringJoin::"string"}; - On[FeynCalc`CheckDB::"nostring"]; - If[ FreeQ[res,dum], - res, - DCFactor1[ff, opts] - ] - ]; - -DCRenormalize[amp_, opts___?OptionQ] := - Block[ {po, ca, xxs, ex, - $ExpansionQuantities = {ParticleMass[b__], CouplingConstant[QED[1], c___]}, - mms, cou, ruls, ruls1, f, ff, g, x,fac, facinv, pop, len, por}, - por = (PerturbationOrder /. {opts} /. Options[DCRenormalize]); - pop = If[ FreeQ[#, _DCFactor1], - Phi`Utilities`DiscardOrders[#, - PerturbationOrder -> por, DiscardMomenta -> False], - # - ]&; - (*Should be safe for corrections...*) - drru = DecayConstant[pp_, RenormalizationState[0]] -> - DecayConstant[pp, RenormalizationState[1]]; - Plus@@( - Which[(len = Length[ca = Cases[{#}, DecayConstant[_, RenormalizationState[0], ___], - Infinity, Heads->True]])>1, - Message[DCRenormalize::"nores"]; - #, - len === 0, #, - len === 1, - po = Exponent[#, ca[[1]]]; - Which[po==0, Message[DCRenormalize::"nores"]; - #, - po(*>*)<0, fac = DCFactor[ca[[1]] /. cruls, Sequence @@ Complement[ - OptionsSelect[DCFactor, opts, Options[DCRenormalize]], - Options[DCFactor]]]^((**)-po) // pop; - (fac/.drru)*(# /. DecayConstant[pp_, RenormalizationState[0]] -> - DecayConstant[pp, RenormalizationState[1]]), - po(*<*)>0, facinv = DCFactor[ca[[1]] /. cruls, Sequence @@ Complement[ - OptionsSelect[DCFactor, opts, Options[DCRenormalize]], - Options[DCFactor]]]; - If[ FreeQ[facinv, _DCFactor1], - FCPrint[2, "Negative power of decay constant ", ca[[1]]," ", po, - ". Doing Taylor expansion"]; - mms = Union[Cases[facinv, - Alternatives @@ $ExpansionQuantities, Infinity]]; - (*Dummy variables x[1], x[2], ... One for each expansion quantity*) - cou = 0; - xxs = (++cou; - x[cou]) & /@ mms; - (*Substitution rules for switching between x[1], x[2], ... - and the expansion quantities*) - cou = 0; - ruls = ((#^i_ -> (++cou; - x[cou]^(i/2))) & /@ mms); - cou = 0; - ruls1 = (((++cou; - x[cou]) -> #^2) & /@ mms); - (*We can't just throw away the logs ... 13/6-2001*) - f[x_] = facinv (*/. _Log -> 0*) /. ruls; - (*Define the function g[x1_, x2_, ...]*) - Evaluate[g @@ xxs /. - x[a_] :> - Pattern[Evaluate[ToExpression[ToString[x] <> ToString[a]]], - Blank[]]] = f[x] - 1 /. - x[a_] :> ToExpression[ToString[x] <> ToString[a]]; - (*Multi-dimensional Taylor expansion of the inverse - renormalization factor*) - fac = ((Series[1/(1 + (ff @@ xxs)) /. ff :> g, Sequence @@ ({#, 0, 1}& /@ xxs)] (*/. - ff[_?((# === 0)&) ..] -> 0*) // Normal) (*/. ff :> g*) /. ruls1)^((*-*)po) // - pop;, - fac = facinv^((**)-po); - ]; - (fac/.drru)*(# /. DecayConstant[pp_, RenormalizationState[0]] -> - DecayConstant[pp, RenormalizationState[1]]) - ] - - ]& /@ (ex = Expand[amp]; - If[ Head[ex]===Plus, - List@@ex, - {ex} - ])) - ]; - -(* Help functions for wave function renormalization *) - -WFFactor[pro_, opts___?OptionQ] := - Block[ {nam, dum, prop, res, ph, a, rep, wfmomRul, mom, moms, newmom}, - prop = pro /. $LastModelRules /. cruls; - newmom = (Momentum /. Flatten[{opts}] /. - Momentum[a__] :> mom[a] /. Options[WFFactor] /. mom -> Momentum); - DisableMessage /@ {List::"string", StringJoin::"string"}; - Off[FeynCalc`CheckDB::"nostring"]; - nam = XName[VertexFields -> ({prop[[-1]]} /. - If[ ChargeSymmetry /. {opts} /. Options[WFFactor], - -(ph : $ParticleHeads)[a_] -> ph[a], - {} - ]), - Sequence @@ OptionsSelect[XName, opts, Options[WFFactor]], - XFileName -> Automatic] <> - If[ MatchQ[prop[[0, 1]], fainc | faout | faext] && - (OnMassShell/.Flatten[{opts}]/.Options[WFFactor]) === True, - "-0", - "" - ] <> - ".Fac"; - res = Which[(*(Explicit /.Flatten[{opts}]/.Options[WFFactor])=!=True, - WFFactor1[prop, opts],*)(*Explicit -> False causes CreateFCAmp to return rubbish*) - MatchQ[prop[[0, 1]], - fainc | faout | faext], - (*The factor loaded from disk is 1/Z*) - (*External propagators get only the squareroot of a Z-factor*) - (3 - CheckDB[dum, nam, - NoSave -> True, - ForceSave -> False])/2 - 1, - MatchQ[prop[[0, 1]], faint | faloop], - (*Internal propagators get a full Z-factor*) - 1 - CheckDB[dum, nam, - NoSave -> True, - ForceSave -> False], True, - Message[WFFactor::"noprop", prop[[0, 1]]]; - Return[]]; - If[ (moms = Cases[res, Momentum[__], Infinity]) =!= {}, - wfmomRul = moms[[1]] -> newmom, - wfmomRul = {} - ]; - FCPrint[2, "Replacing momenta in loaded factor ", StandardForm[wfmomRul]]; - EnableMessage /@ {List::"string", StringJoin::"string"}; - On[FeynCalc`CheckDB::"nostring"]; - If[ FreeQ[res,dum], - res /. wfmomRul, - WFFactor1[prop(*nam*), opts] - ] - ]; - -nondiracWFRenormalize[exp : fatopl[oo___][tt___], opts___?OptionQ] := - Block[ {props, facs}, - props = List @@ ((List @@ (#[[1]]/. - List @@ #[[2, 1, 2, 1]] /. cruls)) & /@ exp); - FCPrint[3, "Renormalizing non-Dirac propagators ", props]; - facs = (Rule[#, WFFactor[#, - Sequence @@ Complement[ - OptionsSelect[WFFactor, opts, Options[(*WFRenormalize*)CreateFCAmp]], - Options[WFFactor]]]]& /@ #)& /@ props; - FCPrint[2, "with factors ", facs]; - fatopl[oo, fawfcr -> facs][tt] - ]; - -(*Inserts fields and appends the relevant momentum as last argument of each Propagator*) -(*appendMoms[toplist : fatopl[oo___][tt___]] := - Block[{fieldsubs, momtop, oldmom, imom, - FeynArts`Analytic`mc, - FeynArts`Analytic`next, - info = List @@ toplist [[0]], - FeynArts`Analytic`gaugeru = - GaugeRules /. Options[facrfa], -FeynArts`Analytic`truncru = - If[TrueQ[Truncated /. Options[facrfa]], - fatrru, {}], - FeynArts`Analytic`pref = - PreFactor /. Options[facrfa]}, - fieldsubs = (List @@ Take[#, {1, 2}][[2, 1, 1]]) & /@ List @@ toplist; - FeynArts`Analytic`next = - Plus @@ Length /@ (Process /. {info}); - momtop = (Clear[FeynArts`Analytic`c, - FeynArts`Analytic`mc]; - FeynArts`Analytic`c[_] = 0; - FeynArts`Analytic`mc = 0; - FeynArts`Analytic`AppendMomentum /@ #[[1]])& /@ -(fapl[facl][toplist] /. (_ -> fains[_][]) :> - Seq[] /. (fafi[i_] -> fi_?AtomQ) -> (fafi[i] -> - fi[faind[fagen, i]])); - oldmom = Union[ - Cases[momtop, fafm[_FeynArts`Analytic`ZZZ, _], - Infinity]]; -imom = Apply[FeynArts`Analytic`RenumberMom, oldmom, 1]; -momtop[[0]] @@ ((#[[1]] /. #[[2]]) & /@ - Transpose[{(List @@ momtop /. Thread[oldmom -> imom]), - fieldsubs}])];*) - -(*Inserts fields and appends the relevant momentum as last argument of each Propagator*) -(*Notice that topologies with multiple insertions get flattened into multiple - topologies*) -appendMoms[toplist : fatopl[___][___]] := - Block[ {fieldsubs, momtop, oldmom, imom, - FeynArts`Analytic`mc, - FeynArts`Analytic`next, info = List @@ toplist[[0]], - FeynArts`Analytic`gaugeru = - GaugeRules /. Options[facrfa], - FeynArts`Analytic`truncru = - If[ TrueQ[Truncated /. Options[facrfa]], - fatrru, - {} - ], - FeynArts`Analytic`pref = - PreFactor /. Options[facrfa]}, - fieldsubs = (Table[((ll @@ Take[#, {1, 2}][[2, i, 1]])), {i, 1, - Length[#[[2]]]}] & /@ List @@ toplist) /. ll -> List; - FeynArts`Analytic`next = - Plus @@ Length /@ (Process /. {info}); - momtop = (Clear[FeynArts`Analytic`c, - FeynArts`Analytic`mc]; - FeynArts`Analytic`c[_] = 0; - FeynArts`Analytic`mc = 0; - FeynArts`Analytic`AppendMomentum /@ #[[1]]) & /@ - (fapl[facl][toplist] /. (_ -> fains[_][]) :> - Seq[] /. (fafi[i_] -> fi_?AtomQ) -> (fafi[i] -> - fi[faind[fagen, i]])); - oldmom = - Union[Cases[momtop, fafm[_FeynArts`Analytic`ZZZ, _], - Infinity]]; - imom = Apply[FeynArts`Analytic`RenumberMom, oldmom, 1]; - momtop[[0]] @@ - Flatten[((#[[1]] /. #[[2]]) & /@ - Transpose[{(List @@ momtop /. Thread[oldmom -> imom]), - fieldsubs}])] - ]; - - -(* After doing loops with FeynArts, particle masses with SU(N) indices come out. - They can be projected out in charged masses with IsoToChargedMasses *) - -IsoToChargedMasses[exp_] := - Block[ {part, rul, tmppart, parts, subpar, seq}, - parts = {}; - subpar = (part = #[[1]]; - (rul = (tmppart = - ParticleMass[#[[1]], #[[2, 1]] | - SUNIndex[#[[2, 1]]], r___]; - tmppart) -> - ParticleMass[part, r]; - If[ FreeQ[parts /. Alternatives :> (({##}[[1]]) &), - tmppart], - parts = Append[parts, tmppart]; - rul, - seq[] - ]) & /@ - Cases[{#[[2]]}, _Iso, - Infinity]) & /@ $IsoSpinProjectionRules /. - seq -> Sequence // Flatten; - FCPrint[2, "Using iso-spin substitution rules ", StandardForm[subpar]]; - exp /. subpar /. - (subpar /. (ParticleMass -> ((RotateRight[Propagator[Internal][##]])&))) /. - (subpar /. (ParticleMass -> ((RotateRight[Propagator[External][##]])&))) - ]; - -(*Implementation from notebook:*) -(*subpar = (((alt @@ ((ParticleMass[##, ___] & @@ #) & /@ (MapAt[(SUNIndex @@ #)&, -#, {-1}] & /@ Cases[#[[2]], Iso[Alternatives @@ $ParticlesInUse, -{_Integer}], {0, 3}]))) -> (ParticleMass[#[[1]]])) & /@ -$IsoSpinProjectionRules) /. alt[a_] :> a /. alt :> Alternatives*) - -(*Renormalize fermion propagators*) -(*propGamma and propSpinor are used in Automatic.gen*) -(*a product is assumed*) -diracRen1[amp_, opts___?OptionQ] := - Block[ {facsS, facsG, a, b, m, opt, mm, ff, s, ss, v1, v2, p, i}, - If[ FreeQ[amp, _propGamma | _propSpinor], - 0, - facsS = Cases[amp, _propSpinor, Infinity]; - facsG = Cases[amp, _propGamma, Infinity]; - FCPrint[2,"Renormalizing fermion propagators with factors ", - StandardForm[facsS], " : ", StandardForm[facsG]]; - If[ MatchQ[amp, (___*_propSpinor.___._propSpinor) | (___*__._propGamma.__)] =!= True || - Length[facsS] =!= Length[Union[facsS]] || - Length[facsG] =!= Length[Union[facsG]], - Message[CreateFCAmp::"spinormismatch"] - ]; - (Plus @@ ((amp /. - {(# . a__) :> (# . - WFFactor[faprop[faext][favert[1][1], favert[1][1], #[[2]]], - Momentum -> -#[[1]], Sequence @@ Select[OptionsSelect[WFFactor, opts, - Options[(*WFRenormalize*)CreateFCAmp]], !MatchQ[#, (Momentum -> _) | (Momentum :> _)]&]] . a), - (a__ . #) :> (a . - WFFactor[faprop[faext][favert[1][1], favert[1][1], #[[2]]], - Momentum -> -#[[1]], Sequence @@ Select[OptionsSelect[WFFactor, opts, - Options[(*WFRenormalize*)CreateFCAmp]], !MatchQ[#, (Momentum -> _) | (Momentum :> _)]&] - ] . #)})& /@ (facsS))) + - (Plus @@ ((amp /. - # :> (WFFactor[faprop[faint][favert[1][1], favert[1][1], #[[2]]], - Momentum -> -#[[1]], Sequence @@ Select[OptionsSelect[WFFactor, opts, - Options[(*WFRenormalize*)CreateFCAmp]], !MatchQ[#, (Momentum -> _) | (Momentum :> _)]&]] . - #))& /@ (facsG))) /. - WFFactor1[faprop[s_][a_, b_, m_ParticleMass], opt___?OptionQ] :> - If[ FreeQ[mm = IsoToChargedMasses[m], ExplicitSUNIndex|suni, Heads->True]=!=True && - FreeQ[ff = WFFactor[faprop[s][a, b, mm[[1]][0]], opt], WFFactor1, Heads->True], - ff, - WFFactor1[faprop[s][a, b, Sequence@@m], opt] /. - _RenormalizationState|_RenormalizationScheme|_ExpansionState :> Sequence[] /. - faprop[ss_][v1_, v2_, p_, ((ExplicitSUNIndex | SUNIndex)[i_])] :> - faprop[ss][v1, v2, p[0, {i}]] - ] - ] - ]; - -diracRen[amp_, opts___?OptionQ] := - If[ Head[amp]===Plus, - diracRen1[#, opts]&/@amp, - diracRen1[amp, opts] - ]; - -wfren[fac_, amp_, opts___?OptionQ] := - fac*amp + diracRen[amp, opts]; - -CreateFCAmp[amp_, opts___] := - Block[ {(*faopts, me, propmoms, pprops, wffacs, wffac, f, tmp*)}, - -(* need to transport options to CreateFeynAmp, e.g., Truncated -> True, -Rolf Mertig, Sept. 27th. 2003 *) -(*faopts = Sequence@@Select[Join[{opts}, Options@CreateFCAmp], MemberQ[First/@(Options@facrfa), #[[1]]]&];*) -(*Use OptionsSelect, F.Orellana, 1/10-2003*) - faopts = Sequence@@Select[OptionsSelect[facrfa, opts], FreeQ[#, faal]&]; - - (*Wave function renormalization.*) - If[ WFRenormalize /. Flatten[{opts}] /. Options[CreateFCAmp], - FCPrint[2, "Doing wave function renormalization\n"]; - - (*Momenta present in propagator*) - propmoms = - FAToFC /@ ((List @@ #) & /@ - List @@ ( - (*Substitute Internal momenta with sum of vertex momenta*) - ((tmp = #; - tmp /. faprop[faint][v1_, v2_, f_, fafm[faint, i_]] :> - Block[ {mom}, - FCPrint[2, "Fixing internal momenta using momentum conservation"]; - Which[ - Count[tmp, faprop[faint | faloop][___, v1, ___], Infinity] === - 1, - mom = -(Plus @@ ((#[[-1]])& /@ - Cases[tmp, faprop[fainc][___, v1, ___], - Infinity])) - (Plus @@ ((#[[-1]])& /@ - Cases[tmp, faprop[faout][___, v1, ___], - Infinity])), - Count[tmp, Propagator[faint | faloop][___, v2, ___], Infinity] === - 1, - mom = -(Plus @@ ((#[[-1]])& /@ - Cases[tmp, faprop[fainc][___, v2, ___], - Infinity])) - (Plus @@ ((#[[-1]])& /@ - Cases[tmp, faprop[faout][___, v2, ___], - Infinity])), - True, - Message[CreateFCAmp::"looprenorm"]; - mom = fafm[faint, i] - ]; - FCPrint[2, "Replacing ", fafm[faint, i] -> mom]; - faprop[faint][v1, v2, f, mom] - ])& /@ - appendMoms[amp]) /. - (*faprop[a_][b__] :> ({b}[[-1]])*) - (*Take care of fermions separately*) - faprop[_][b__] :> If[ FreeQ[{b}, $FermionHeads], - ({b}[[-1]]), - seq[] - ] /. - seq :> Sequence)); - - (*Renormalization factors*) - (*Take care of fermions separately*) - pprops = ((If[ FreeQ[#[[1]], $FermionHeads], - #[[2]], - seq[] - ] & /@ #)& /@ (fawfcr /. - List @@ nondiracWFRenormalize[amp, opts][[0]])) /. seq :> Sequence; - wffacs = ((#[[1]] /. - - (*Momentum replacement; first, momentum present in renormalization factor*) - (Append[Cases[#, Momentum[___], Infinity], - (*default to replacing q1*) - classesamplitude[{fafm[fainc, 1]}][opts][[1]]][[1]] /. - D :> BlankNullSequence[]) -> - (*next, momentum present in propagator*) - #[[2]] /. - (*remember momenta*) - WFFactor1[f__] :> WFFactor1[f, Momentum -> #[[2]]])& /@ #)& /@ - - (Transpose /@ Transpose[{pprops, propmoms}]); - wffac = Which[(me = Method/.Flatten[{opts}]/.Options[CreateFCAmp]) === - Phi`Utilities`DiscardOrders, - Phi`Utilities`DiscardOrders[ - Times @@ ((1+#)&/@#), Sequence@@OptionsSelect[Phi`Utilities`DiscardOrders, - Flatten[{opts}/.Rule[PerturbationOrder,_]:>Sequence[]/. - DropOrder->PerturbationOrder]]]& /@ wffacs, - me === Plus, - ((1 + Plus @@ #) & /@ wffacs), - True, Message[CreateFCAmp::"nomethod", me]]; - - (*!!! We need to take care of internal propagators... FAToFC should be applied on the products of - wffac and amp !!!*) - - (*(Times@@#)& /@ Transpose[{FAToFC[wffac],FAToFC[facrfa[amp, faal -> facl, faopts], opts]}] /.*) - FAToFC[((wfren[Sequence@@#,opts])& /@ Transpose[{wffac,FAToFC[facrfa[amp, faal -> facl, faopts], Sum->True, opts]}]), - opts] /. - If[ (EqualMasses /. Flatten[{opts}] /. Options[FAToFC]), - (*Not very general :-( But makes life easier for the user...*) - PseudoScalar2[0, {_}] -> PseudoScalar2[0], - {} - ] /. - WFFactor1 -> WFFactor, - FAToFC[facrfa[amp, faal -> facl, faopts], opts] - ] //. - - {propGamma[ mom_, a_] :> DiracGamma[ mom ] + a, - (*Support explicit setting the renormalization state of spinors of - external particles. This should be done by modifying - Phi`Couplings`GenProps in the relevant .conf file. - Suggested by Paul Buettiker July 2004.*) - propSpinor[mom_, a_, b___, i___RenormalizationState, - j___RenormalizationScheme, k___ExpansionState] :> (DiracSpinor[mom, a, b] /. - {ParticleMass[p_, _RenormalizationState, r___] -> - ParticleMass[p, i, r]} /. - ParticleMass[p__, _RenormalizationScheme, r___] -> - ParticleMass[p, j, r] /. - ParticleMass[p__, _ExpansionState, r___] -> - ParticleMass[p, k, r]), - propSpinor[mom_, a_, b___] :> DiracSpinor[mom, a, b]} - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Generation of FeynArts 2 model files *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -$GenObjects = {"M$GenericCouplings", "M$FermionFlipRule", - "M$LastGenericRules"}; -GenSave[modelname_String] := - ( - t = Date[]; - dd = - ToString[t[[3]]] <> "/" <> ToString[t[[2]]] <> "-" <> - ToString[t[[1]]] <> ", " <> ToString[t[[4]]] <> ":" <> - ToString[t[[5]]] <> ":" <> ToString[t[[6]]]; - tmp`olddir = Directory[]; - SetDirectory[Phi`$HEPDir]; - SetDirectory["FeynCalc"]; - SetDirectory["Models"]; - strm = OpenWrite[modelname <> ".gen"]; - WriteString[strm, - "(* ****************************************************************** \ *)\n\n"]; - WriteString[strm, "(* " <> modelname <> ".gen *)\n\n"]; - WriteString[strm, - "(* Coupling definitions generated by Phi, " <> dd <> ". *)\n\n"]; - WriteString[strm, - "(* ****************************************************************** \ *)"]; - Close[strm]; - FCPrint[2, "Will save definitions to file "modelname <> ".gen"]; - strm = OpenAppend[modelname <> ".gen"]; - WriteString[strm, - "\n\n\n(* ****************************************************************** \ *)\n"]; - WriteString[strm, - "(* Definitions for PropagatorType,*)\n(* PropagatorArrow and KinematicIndices *)\n"]; - WriteString[strm, - "(* ****************************************************************** \ *)\n\n"]; - Save[ - modelname <> ".gen", {FeynArts`PropagatorType, - FeynArts`PropagatorArrow, FeynArts`KinematicIndices}]; - WriteString[strm, "\n\n"]; - Close[strm]; - FCPrint[2, - "Saving definition of AnalyticalPropagator to temporary file dum"]; - - (*Save definition of AnalyticalPropagator for reloading later*) - Save["dum", FeynArts`AnalyticalPropagator]; - Clear[FeynArts`AnalyticalPropagator]; - FCPrint[2, "Saving definitions to file "modelname <> ".gen"]; - - (*Now generate the definition lines for M$GenericPropagators*) - genprops = - "M$GenericPropagators = " <> - ToString[ - InputForm[ - Flatten[Phi`Couplings`GenProps /@ \ - (Join[Flatten[{List @@ $ScalarHeads} /. None -> Sequence[]], - Flatten[{List @@ $VectorHeads} /. None -> Sequence[]], - Flatten[{List @@ $FermionHeads} /. - None -> Sequence[]]] /. None -> Sequence[])]]]; - - (*Append the lines to the model file*) - strm = OpenAppend[modelname <> ".gen"]; - WriteString[strm, - "(* ****************************************************************** \ *)\n"]; - WriteString[strm, "(* Definition of M$GenericPropagators *)\n"]; - WriteString[strm, - "(* ****************************************************************** \ *)\n\n"]; - WriteString[strm, genprops <> "\n\n"]; - - (*Append the rest of the definitions*) - Do[ - WriteString[strm, - "(* ****************************************************************** \ *)\n"]; - WriteString[strm, - "(* Definition of " <> $GenObjects[[i]] <> " *)\n"]; - WriteString[strm, - "(* ****************************************************************** \ *)\n\n"]; - WriteString[strm, $GenObjects[[i]] <> " =\n"]; - Write[strm, ToExpression[$GenObjects[[i]]]]; - WriteString[strm, "\n\n"];, - {i, Length[$GenObjects]}]; - Close[strm]; - FCPrint[2, - "Reloading definition of AnalyticalPropagator from - and deleting - file dum"]; - - (*Reestablish defintion of AnalyticalPropagator*) - strm = OpenRead["dum"]; - str = ""; - str1 = ""; - stop = 0; - While[str != "EndOfFile", str = Read[strm, String]; - If[ stop < 2, - If[ StringMatchQ[str, "*AnalyticalPropagator/:*"], - stop = 2 - ] - ]; - If[ stop < 2, - If[ str == " ", - stop = stop + 1; - str1 = str1 <> ";\n\n", - str1 = str1 <> str - ] - ]]; - Close[strm]; - DeleteFile["dum"]; - (*str1 = - StringReplace[str1, - "AnalyticalPropagator" -> "FeynArts`AnalyticalPropagator"];*) - FCPrint[3, "The definition of AnalyticalPropagator: ", str1]; - ToExpression[str1]; - SetDirectory[tmp`olddir]; - - ); -$ModObjects = {"$ScreenSymbolFont", "M$ClassesDescription", - "M$CouplingMatrices", "M$LastModelRules"}; -ModSave[modelname_String] := - ( - t = Date[]; - dd = - ToString[t[[3]]] <> "/" <> ToString[t[[2]]] <> "-" <> - ToString[t[[1]]] <> ", " <> ToString[t[[4]]] <> ":" <> - ToString[t[[5]]] <> ":" <> ToString[t[[6]]]; - tmp`olddir = Directory[]; - SetDirectory[Phi`$HEPDir]; - SetDirectory["FeynCalc"]; - SetDirectory["Models"]; - FCPrint[2, "Will save definitions to file "modelname <> ".mod"]; - strm = OpenWrite[modelname <> ".mod"]; - WriteString[strm, - "(* ****************************************************************** \ *)\n\n"]; - WriteString[strm, "(* " <> modelname <> ".mod *)\n\n"]; - WriteString[strm, - "(* Coupling definitions generated by Phi, " <> dd <> ". *)\n\n"]; - WriteString[strm, - "(* ****************************************************************** \ *)"]; - Close[strm]; - FCPrint[2, - "Using temporary file dum for generating definition of IndexRange"]; - strm = OpenWrite["dum"]; - Save[strm, FeynArts`IndexRange]; - Close[strm]; - strm = OpenRead["dum"]; - str = ""; - str1 = ""; - stop = False; - While[str != "EndOfFile", str = Read[strm, String]; - If[ stop == False, - If[ StringMatchQ[str, "*MakeBoxes*"] || - StringMatchQ[str, "*Attributes*"], - stop = True - ] - ]; - If[ stop == False, - If[ str == " ", - str1 = str1 <> ";\n\n", - str1 = str1 <> str - ] - ]]; - Close[strm]; - DeleteFile["dum"]; - str1 = FixedPoint[StringReplace[#, " " -> " "] &, str1]; - strm = OpenWrite["dum"]; - Save[strm, Phi`Couplings`FAParticleMass]; - Close[strm]; - strm = OpenRead["dum"]; - str = ""; - str2 = ""; - stop = False; - While[str != "EndOfFile", str = Read[strm, String]; - If[ stop == False, - If[ StringMatchQ[str, "*MakeBoxes*"] || - StringMatchQ[str, "*Attributes*"], - stop = True - ] - ]; - If[ stop == False, - If[ str == " ", - str2 = str2 <> ";\n\n", - str2 = str2 <> str - ] - ]]; - Close[strm]; - FCPrint[2, "Deleting file dum"]; - DeleteFile["dum"]; - str2 = FixedPoint[StringReplace[#, " " -> " "] &, str2]; - str2 = str2 <> "\n"; - FCPrint[2, "Saving definitions to file "modelname <> ".mod"]; - strm = OpenAppend[modelname <> ".mod"]; - WriteString[strm, - "\n\n\n(* ****************************************************************** \ *)\n"]; - WriteString[strm, - "(* Definitions for IndexRange and Mass *)\n"]; - WriteString[strm, - "(* ****************************************************************** \ *)\n\n"]; - WriteString[strm, str1]; - WriteString[strm, str2]; - Close[strm]; - strm = OpenAppend[modelname <> ".mod"]; - Do[ - WriteString[strm, - "(* ****************************************************************** \ *)\n"]; - WriteString[strm, - "(* Definition of " <> $ModObjects[[i]] <> " *)\n"]; - WriteString[strm, - "(* ****************************************************************** \ *)\n\n"]; - WriteString[strm, $ModObjects[[i]] <> " =\n"]; - Write[strm, ToExpression[$ModObjects[[i]]]]; - WriteString[strm, "\n\n"];, - {i, Length[$ModObjects]}]; - Close[strm]; - SetDirectory[tmp`olddir]; - - ); - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -FCPrint[1, "Couplings.m loaded"]; -End[]; diff --git a/FeynCalc/Phi/Factors/ChPT2A00P20o2.Fac b/FeynCalc/Phi/Factors/ChPT2A00P20o2.Fac deleted file mode 100644 index d4de224ed..000000000 --- a/FeynCalc/Phi/Factors/ChPT2A00P20o2.Fac +++ /dev/null @@ -1,6 +0,0 @@ -1 + ((32*Pi^2*(4*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]] + - 2*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]] - - LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2)/ -(16*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT2P00P20o2.Fac b/FeynCalc/Phi/Factors/ChPT2P00P20o2.Fac deleted file mode 100644 index f5a312de1..000000000 --- a/FeynCalc/Phi/Factors/ChPT2P00P20o2.Fac +++ /dev/null @@ -1,9 +0,0 @@ -(32*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2 - -(32*Pi^2*(8*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]] + - 4*(CouplingConstant[ChPT2[4], 5, RenormalizationState[0]] - - 4*(2*CouplingConstant[ChPT2[4], 6, RenormalizationState[0]] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[0]])) + - LeutwylerLambda[]) + - Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2)/ -(32*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT2P20o2.Fac b/FeynCalc/Phi/Factors/ChPT2P20o2.Fac deleted file mode 100644 index ef9627e14..000000000 --- a/FeynCalc/Phi/Factors/ChPT2P20o2.Fac +++ /dev/null @@ -1,6 +0,0 @@ -1 + ((384*Pi^2*CouplingConstant[ChPT2[4], 4, RenormalizationState[0]] + - 192*Pi^2*CouplingConstant[ChPT2[4], 5, RenormalizationState[0]] - - 32*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2)/ -(24*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT2P20o2.Mass b/FeynCalc/Phi/Factors/ChPT2P20o2.Mass deleted file mode 100644 index c3bca0bfd..000000000 --- a/FeynCalc/Phi/Factors/ChPT2P20o2.Mass +++ /dev/null @@ -1,7 +0,0 @@ -((-256*Pi^2*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT2[4], 5, RenormalizationState[1]] - - 2*(2*CouplingConstant[ChPT2[4], 6, RenormalizationState[1]] + - CouplingConstant[ChPT2[4], 8, RenormalizationState[1]])) + -Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4)/ -(32*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3A00P110o2.Fac b/FeynCalc/Phi/Factors/ChPT3A00P110o2.Fac deleted file mode 100644 index 35c01ca14..000000000 --- a/FeynCalc/Phi/Factors/ChPT3A00P110o2.Fac +++ /dev/null @@ -1,10 +0,0 @@ -1 + (-128*Pi^2*CouplingConstant[ChPT3[4], 5, RenormalizationState[1]]* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + -512*Pi^2*CouplingConstant[ChPT3[4], 5, RenormalizationState[1]]* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 - -9*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 + -384*Pi^2*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]]* - (ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + - 2*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2))/ -(96*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3A00P20o2.Fac b/FeynCalc/Phi/Factors/ChPT3A00P20o2.Fac deleted file mode 100644 index d9562fe26..000000000 --- a/FeynCalc/Phi/Factors/ChPT3A00P20o2.Fac +++ /dev/null @@ -1,10 +0,0 @@ -1 + (128*Pi^2*CouplingConstant[ChPT3[4], 5, RenormalizationState[1]]* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 - -2*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 - -Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 + -128*Pi^2*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]]* - (ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + - 2*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2))/ -(32*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3A00P60o2.Fac b/FeynCalc/Phi/Factors/ChPT3A00P60o2.Fac deleted file mode 100644 index 611795573..000000000 --- a/FeynCalc/Phi/Factors/ChPT3A00P60o2.Fac +++ /dev/null @@ -1,14 +0,0 @@ -1 + (-3*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2]*ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + -Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + -512*Pi^2*CouplingConstant[ChPT3[4], 5, RenormalizationState[1]]* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 - -6*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 - -4*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 + -512*Pi^2*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]]* - (ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + - 2*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2))/ -(128*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P00P110o2.Fac b/FeynCalc/Phi/Factors/ChPT3P00P110o2.Fac deleted file mode 100644 index d2a0628f8..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P00P110o2.Fac +++ /dev/null @@ -1,17 +0,0 @@ -(96*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -(128*Pi^2*(-3*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]]) - - 3*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2 - -(256*Pi^2*(3*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - 2*(CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] - - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]])) + - Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ScaleMu^2] + - 4*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(96*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P00P20o2.Fac b/FeynCalc/Phi/Factors/ChPT3P00P20o2.Fac deleted file mode 100644 index 506953669..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P00P20o2.Fac +++ /dev/null @@ -1,16 +0,0 @@ -(288*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -(-1152*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] - - 4*(CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 8, RenormalizationState[1]])) - - 9*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2 - -(2304*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]]) + - 9*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ - ScaleMu^2] + - 4*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(288*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P00P60o2.Fac b/FeynCalc/Phi/Factors/ChPT3P00P60o2.Fac deleted file mode 100644 index 9e2c7c2f6..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P00P60o2.Fac +++ /dev/null @@ -1,16 +0,0 @@ -(1152*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -(-4608*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]]) - - 27*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2 - -2*(2304*Pi^2*(2*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] - - 8*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]]) + - 27*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ - ScaleMu^2] + - 2*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(1152*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P011o2.Fac b/FeynCalc/Phi/Factors/ChPT3P011o2.Fac deleted file mode 100644 index 7f18ce912..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P011o2.Fac +++ /dev/null @@ -1,17 +0,0 @@ -(48*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -(128*Pi^2*(-3*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] + - 12*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]]) - - 3*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2 - -(256*Pi^2*(3*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - 2*(CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] - - 6*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]])) + - Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ScaleMu^2] + - 4*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(48*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P02o2.Fac b/FeynCalc/Phi/Factors/ChPT3P02o2.Fac deleted file mode 100644 index 494b131a7..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P02o2.Fac +++ /dev/null @@ -1,16 +0,0 @@ -(144*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -(-1152*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] - - 4*(CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 8, RenormalizationState[1]])) - - 9*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2 - -(2304*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]]) + - 9*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ - ScaleMu^2] + - 4*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(144*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P06o2.Fac b/FeynCalc/Phi/Factors/ChPT3P06o2.Fac deleted file mode 100644 index e4c6b71ee..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P06o2.Fac +++ /dev/null @@ -1,16 +0,0 @@ -(576*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -(-4608*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]]) - - 27*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2 - -2*(2304*Pi^2*(2*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] - - 8*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] - - 4*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]]) + - 27*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ - ScaleMu^2] + - 2*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(576*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P110o2.Fac b/FeynCalc/Phi/Factors/ChPT3P110o2.Fac deleted file mode 100644 index 60833e8ea..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P110o2.Fac +++ /dev/null @@ -1,10 +0,0 @@ -(16*Pi^2*(3*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + - 8*(3*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]] - - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]])* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2) + -(32*Pi^2*(24*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]] + - 16*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]] - - 3*LeutwylerLambda[]) - - 3*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(48*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P110o2.Mass b/FeynCalc/Phi/Factors/ChPT3P110o2.Mass deleted file mode 100644 index 760a6e709..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P110o2.Mass +++ /dev/null @@ -1,38 +0,0 @@ -(36864*Pi^2*CouplingConstant[ChPT3[4], 7, RenormalizationState[1]]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 + -13824*Pi^2*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 - -27*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ScaleMu^2]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 - -7*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ScaleMu^2]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 - -73728*Pi^2*CouplingConstant[ChPT3[4], 7, RenormalizationState[1]]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 - -36864*Pi^2*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 + -44*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ScaleMu^2]* -ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 + -36864*Pi^2*CouplingConstant[ChPT3[4], 7, RenormalizationState[1]]* -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4 + -36864*Pi^2*CouplingConstant[ChPT3[4], 8, RenormalizationState[1]]* -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4 + -72*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ScaleMu^2]* -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4 - -64*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ScaleMu^2]* -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4 + -2304*Pi^2*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]]* -(ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 - - 2*ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 - - 8*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4) - -4608*Pi^2*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]]* -(ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 - - 2*ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 - - 8*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4) - -6912*Pi^2*CouplingConstant[ChPT3[4], 5, RenormalizationState[1]]* -ParticleMass[PseudoScalar[11], RenormalizationState[0]]^4)/ -(864*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P20o2.Fac b/FeynCalc/Phi/Factors/ChPT3P20o2.Fac deleted file mode 100644 index ae97cf835..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P20o2.Fac +++ /dev/null @@ -1,11 +0,0 @@ -1 + -(2*(32*Pi^2*(6*(CouplingConstant[ChPT3[4], 4, RenormalizationState[0]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[0]]) - - LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + -(32*Pi^2*(24*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]] - - LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(48*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P20o2.Mass b/FeynCalc/Phi/Factors/ChPT3P20o2.Mass deleted file mode 100644 index 007f854f8..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P20o2.Mass +++ /dev/null @@ -1,16 +0,0 @@ -((-2304*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] - - 2*(CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 8, RenormalizationState[1]])) + - 9*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2] + - Log[-(ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 - - 4*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ - (3*ScaleMu^2)])*ParticleMass[PseudoScalar[2], RenormalizationState[0]]^ - 4 - 4*(1152*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[ - 1]] - 2*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]]) + - Log[-(ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 - - 4*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ - (3*ScaleMu^2)])*ParticleMass[PseudoScalar[2], RenormalizationState[0]]^ - 2*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)/ -(288*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P60o2.Fac b/FeynCalc/Phi/Factors/ChPT3P60o2.Fac deleted file mode 100644 index 67c29d155..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P60o2.Fac +++ /dev/null @@ -1,14 +0,0 @@ -1 - ((32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + -2*(32*Pi^2*(-8*CouplingConstant[ChPT3[4], 5, RenormalizationState[0]] + - LeutwylerLambda[]) + - Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 - -512*Pi^2*CouplingConstant[ChPT3[4], 4, RenormalizationState[0]]* - (ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 + - 2*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2) + -(32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2)/ -(64*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPT3P60o2.Mass b/FeynCalc/Phi/Factors/ChPT3P60o2.Mass deleted file mode 100644 index c7edfe805..000000000 --- a/FeynCalc/Phi/Factors/ChPT3P60o2.Mass +++ /dev/null @@ -1,12 +0,0 @@ -(-((1152*Pi^2*(CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] - - 2*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]]) + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2) + -4*(-288*Pi^2*(2*CouplingConstant[ChPT3[4], 4, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 5, RenormalizationState[1]] - - 2*(2*CouplingConstant[ChPT3[4], 6, RenormalizationState[1]] + - CouplingConstant[ChPT3[4], 8, RenormalizationState[1]])) + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4)/ -(144*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTEM2P20o2.Fac b/FeynCalc/Phi/Factors/ChPTEM2P20o2.Fac deleted file mode 100644 index 0cc391c90..000000000 --- a/FeynCalc/Phi/Factors/ChPTEM2P20o2.Fac +++ /dev/null @@ -1,151 +0,0 @@ -(3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* -(-64*Pi^2*LeutwylerLambda[]*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^4 + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^4 - - 768*Pi^2*CouplingConstant[ChPT2[4], 4, RenormalizationState[1]]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2 - - 384*Pi^2*CouplingConstant[ChPT2[4], 5, RenormalizationState[1]]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2 - - 64*Pi^2*LeutwylerLambda[]*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2*ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2 + - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2 + - 64*Pi^2*LeutwylerLambda[]*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^4*SU2Delta[ExplicitSUNIndex[3], - SUNIndex[I1]] - - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^4* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] + - 768*Pi^2*CouplingConstant[ChPT2[4], 4, RenormalizationState[1]]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] + - 384*Pi^2*CouplingConstant[ChPT2[4], 5, RenormalizationState[1]]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] - - 64*Pi^2*LeutwylerLambda[]*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2*ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2*SU2Delta[ExplicitSUNIndex[3], - SUNIndex[I1]] + - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] - - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] - - 768*Pi^2*CouplingConstant[ChPT2[4], 4, RenormalizationState[1]]* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^4* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] - - 384*Pi^2*CouplingConstant[ChPT2[4], 5, RenormalizationState[1]]* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^4* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] + - 48*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* - (Pair[Momentum[p1], Momentum[p1]] + - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]) - - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]) + - Pair[Momentum[p1], Momentum[p1]]* - (ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - (768*Pi^2*CouplingConstant[ChPT2[4], 4, RenormalizationState[1]] + - 384*Pi^2*CouplingConstant[ChPT2[4], 5, RenormalizationState[1]] - - (64*Pi^2*LeutwylerLambda[] - Log[ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2/ScaleMu^2])* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]])) + - (64*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2*(1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]))) + -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4* -(ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 - - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2)* -(160*Pi^2*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[1]]* - (Pair[Momentum[p1], Momentum[p1]] + - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]) - - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]) + - 160*Pi^2*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[1]]* - (Pair[Momentum[p1], Momentum[p1]] + - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]) - - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]) - - 9*(-16*Pi^2*LeutwylerJBar[ - -(ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]])) + - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]], - ParticleMass[Vector[1], RenormalizationState[0]]^2, - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + - 8*Pi^2*LeutwylerLambda[]*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2 + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + - 4*Pi^2*LeutwylerJBar[-(ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2*(-1 + SU2Delta[ExplicitSUNIndex[3], - SUNIndex[I1]])) + ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2*SU2Delta[ExplicitSUNIndex[3], - SUNIndex[I1]], ParticleMass[Vector[1], RenormalizationState[0]]^2, - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[1], SUNIndex[I1]] - - 8*Pi^2*LeutwylerJBar[-(ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2*(-1 + SU2Delta[ExplicitSUNIndex[3], - SUNIndex[I1]])) + ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2*SU2Delta[ExplicitSUNIndex[3], - SUNIndex[I1]], ParticleMass[Vector[1], RenormalizationState[0]]^2, - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[2], SUNIndex[I1]] - - 4*Pi^2*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[Vector[1], RenormalizationState[0]]^2, - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2]* - (ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - (SU2Delta[ExplicitSUNIndex[1], SUNIndex[I1]] - - 2*SU2Delta[ExplicitSUNIndex[2], SUNIndex[I1]]) + - 4*Pair[Momentum[p1], Momentum[p1]]* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]])) + - 16*Pi^2*LeutwylerJBar[-(ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2*(-1 + SU2Delta[ExplicitSUNIndex[3], - SUNIndex[I1]])) + ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2*SU2Delta[ExplicitSUNIndex[3], - SUNIndex[I1]], ParticleMass[Vector[1], RenormalizationState[0]]^2, - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] - 8*Pi^2*LeutwylerLambda[]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] - - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] - - 32*Pi^2*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[1]]* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] - - 16*Pi^2*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[1]]* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] + - Pair[Momentum[p1], Momentum[p1]]* - ((8*Pi^2*LeutwylerLambda[] + Log[ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2/ScaleMu^2])* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]) + - 32*Pi^2*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[1]]* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]] + - 16*Pi^2*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[1]]* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]))))/ -(144*Pi^2*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* -(DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* - (Pair[Momentum[p1], Momentum[p1]] - ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2) + -2*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* - CouplingConstant[QED[1], RenormalizationState[0]]^2* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[I1]]))) diff --git a/FeynCalc/Phi/Factors/ChPTEM2P30o2.Fac b/FeynCalc/Phi/Factors/ChPTEM2P30o2.Fac deleted file mode 100644 index f344a4d19..000000000 --- a/FeynCalc/Phi/Factors/ChPTEM2P30o2.Fac +++ /dev/null @@ -1,19 +0,0 @@ -(DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4* -(160*Pi^2*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[1]] + - 160*Pi^2*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[1]] + - 9*(-1 + 8*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2]))*(ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2 - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2) + -3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* -(48*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2 + - (64*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2 + (768*Pi^2*CouplingConstant[ChPT2[4], 4, RenormalizationState[1]] + - 384*Pi^2*CouplingConstant[ChPT2[4], 5, RenormalizationState[1]] + - 64*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2))/(144*Pi^2*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTEM2P40o2.Fac b/FeynCalc/Phi/Factors/ChPTEM2P40o2.Fac deleted file mode 100644 index 27e919a4d..000000000 --- a/FeynCalc/Phi/Factors/ChPTEM2P40o2.Fac +++ /dev/null @@ -1,17 +0,0 @@ -(8*Pi^2*(10*CouplingConstant[ChPTEM2[4], 2, RenormalizationState[1]] - - 18*CouplingConstant[ChPTEM2[4], 3, RenormalizationState[1]] - - 9*CouplingConstant[ChPTEM2[4], 4, RenormalizationState[1]] + - 10*CouplingConstant[ChPTEM2[4], 10, RenormalizationState[1]])* -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4* -(ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 - - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2) + -3*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* -(24*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2 + - (64*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2 + 192*Pi^2*(2*CouplingConstant[ChPT2[4], 4, RenormalizationState[ - 1]] + CouplingConstant[ChPT2[4], 5, RenormalizationState[1]])* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2))/ -(72*Pi^2*CouplingConstant[ChPTEM2[2], RenormalizationState[0]]* -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTEM2V10o2.Fac b/FeynCalc/Phi/Factors/ChPTEM2V10o2.Fac deleted file mode 100644 index 1f4f3533d..000000000 --- a/FeynCalc/Phi/Factors/ChPTEM2V10o2.Fac +++ /dev/null @@ -1,15 +0,0 @@ --((-144*Pi^2 + CouplingConstant[QED[1], RenormalizationState[0]]^2* - (1 + 16*Pi^2*(20*(CouplingConstant[ChPT2[4], 10, RenormalizationState[ - 1]] + 2*CouplingConstant[ChPT2[4], 11, RenormalizationState[ - 1]] + CouplingConstant[ChPTEM2[4], 15, RenormalizationState[ - 1]]) - 3*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2, - LeutwylerJBarEvaluation -> "none"]) + - 3*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2]))*Pair[Momentum[p1], Momentum[p1]] + -192*Pi^2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2, - LeutwylerJBarEvaluation -> "none"]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2)/ -(144*Pi^2*Pair[Momentum[p1], Momentum[p1]]) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2-0.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2-0.Fac deleted file mode 100644 index 98cdf26a5..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2-0.Fac +++ /dev/null @@ -1,2 +0,0 @@ -1 + CouplingConstant[QED[1], RenormalizationState[0]]^2* -CouplingConstant[ChPTPhotonsLeptons3[4], 37, RenormalizationState[0]] diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2.Fac deleted file mode 100644 index 1f8ba1808..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2.Fac +++ /dev/null @@ -1,26 +0,0 @@ -(8*Pi^2*(1 + CouplingConstant[QED[1], RenormalizationState[0]]^2* - CouplingConstant[ChPTPhotonsLeptons3[4], 37, RenormalizationState[0]])* -Pair[Momentum[p1], Momentum[p1]]^2 + -8*Pi^2*CouplingConstant[QED[1], RenormalizationState[0]]^2* -LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[Fermion[7], RenormalizationState[0]]^2, - SmallVariable[ParticleMass[Vector[1], RenormalizationState[0]]]^2, - LeutwylerJBarEvaluation -> "none"]* -ParticleMass[Fermion[7], RenormalizationState[0]]^3* -(DiracGamma[Momentum[p1]] + ParticleMass[Fermion[7], - RenormalizationState[0]]) + Pair[Momentum[p1], Momentum[p1]]* -ParticleMass[Fermion[7], RenormalizationState[0]]* -(-8*Pi^2*ParticleMass[Fermion[7], RenormalizationState[0]] + - CouplingConstant[QED[1], RenormalizationState[0]]^2* - (DiracGamma[Momentum[p1]]*(1 - 24*Pi^2*LeutwylerJBar[ - Pair[Momentum[p1], Momentum[p1]], ParticleMass[Fermion[7], - RenormalizationState[0]]^2, SmallVariable[ParticleMass[Vector[1], - RenormalizationState[0]]]^2, LeutwylerJBarEvaluation -> - "none"]) + (1 - 8*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], - 37, RenormalizationState[0]] + 3*LeutwylerJBar[Pair[Momentum[p1], - Momentum[p1]], ParticleMass[Fermion[7], RenormalizationState[0]]^ - 2, SmallVariable[ParticleMass[Vector[1], RenormalizationState[ - 0]]]^2, LeutwylerJBarEvaluation -> "none"]))* - ParticleMass[Fermion[7], RenormalizationState[0]])))/ -(8*Pi^2*Pair[Momentum[p1], Momentum[p1]]*(Pair[Momentum[p1], Momentum[p1]] - -ParticleMass[Fermion[7], RenormalizationState[0]]^2)) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2.Mass b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2.Mass deleted file mode 100644 index f7ce1690f..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F70o2.Mass +++ /dev/null @@ -1,6 +0,0 @@ --(CouplingConstant[QED[1], RenormalizationState[0]]^2* -(-1 + 16*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[4], 37, - RenormalizationState[1]] + 16*Pi^2*CouplingConstant[ - ChPTPhotonsLeptons3[4], 38, RenormalizationState[1]] + - 3*Log[ParticleMass[Fermion[7], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[Fermion[7], RenormalizationState[0]])/(16*Pi^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2-0.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2-0.Fac deleted file mode 100644 index 98cdf26a5..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2-0.Fac +++ /dev/null @@ -1,2 +0,0 @@ -1 + CouplingConstant[QED[1], RenormalizationState[0]]^2* -CouplingConstant[ChPTPhotonsLeptons3[4], 37, RenormalizationState[0]] diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2.Fac deleted file mode 100644 index 80061b6cf..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2.Fac +++ /dev/null @@ -1,26 +0,0 @@ -(8*Pi^2*(1 + CouplingConstant[QED[1], RenormalizationState[0]]^2* - CouplingConstant[ChPTPhotonsLeptons3[4], 37, RenormalizationState[0]])* -Pair[Momentum[p1], Momentum[p1]]^2 + -8*Pi^2*CouplingConstant[QED[1], RenormalizationState[0]]^2* -LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[Fermion[8], RenormalizationState[0]]^2, - SmallVariable[ParticleMass[Vector[1], RenormalizationState[0]]]^2, - LeutwylerJBarEvaluation -> "none"]* -ParticleMass[Fermion[8], RenormalizationState[0]]^3* -(DiracGamma[Momentum[p1]] + ParticleMass[Fermion[8], - RenormalizationState[0]]) + Pair[Momentum[p1], Momentum[p1]]* -ParticleMass[Fermion[8], RenormalizationState[0]]* -(-8*Pi^2*ParticleMass[Fermion[8], RenormalizationState[0]] + - CouplingConstant[QED[1], RenormalizationState[0]]^2* - (DiracGamma[Momentum[p1]]*(1 - 24*Pi^2*LeutwylerJBar[ - Pair[Momentum[p1], Momentum[p1]], ParticleMass[Fermion[8], - RenormalizationState[0]]^2, SmallVariable[ParticleMass[Vector[1], - RenormalizationState[0]]]^2, LeutwylerJBarEvaluation -> - "none"]) + (1 - 8*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], - 37, RenormalizationState[0]] + 3*LeutwylerJBar[Pair[Momentum[p1], - Momentum[p1]], ParticleMass[Fermion[8], RenormalizationState[0]]^ - 2, SmallVariable[ParticleMass[Vector[1], RenormalizationState[ - 0]]]^2, LeutwylerJBarEvaluation -> "none"]))* - ParticleMass[Fermion[8], RenormalizationState[0]])))/ -(8*Pi^2*Pair[Momentum[p1], Momentum[p1]]*(Pair[Momentum[p1], Momentum[p1]] - -ParticleMass[Fermion[8], RenormalizationState[0]]^2)) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2.Mass b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2.Mass deleted file mode 100644 index 5398895bd..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3F80o2.Mass +++ /dev/null @@ -1,6 +0,0 @@ --(CouplingConstant[QED[1], RenormalizationState[0]]^2* -(-1 + 16*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[4], 37, - RenormalizationState[1]] + 16*Pi^2*CouplingConstant[ - ChPTPhotonsLeptons3[4], 38, RenormalizationState[1]] + - 3*Log[ParticleMass[Fermion[8], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[Fermion[8], RenormalizationState[0]])/(16*Pi^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2-0.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2-0.Fac deleted file mode 100644 index ac97b071e..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2-0.Fac +++ /dev/null @@ -1,29 +0,0 @@ -(64*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2* -(4*CouplingConstant[ChPTPhotonsLeptons3[4], 13, RenormalizationState[1]] + - 4*CouplingConstant[ChPTPhotonsLeptons3[4], 14, RenormalizationState[1]] - - 2*CouplingConstant[ChPTPhotonsLeptons3[4], 15, RenormalizationState[1]] + - CouplingConstant[ChPTPhotonsLeptons3[4], 16, RenormalizationState[1]] + - 2*(CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[ - 1]] + CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[1]]))*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2 + CouplingConstant[ChPTPhotonsLeptons3[2], - RenormalizationState[0]]* -(96*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + - 3*(64*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2 + (64*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - 4*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]] - 3*LeutwylerLambda[]) + - 3*Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + (128*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + 8*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]] + 3*LeutwylerLambda[]) - - 3*(Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[8], RenormalizationState[ - 0]]^2/ScaleMu^2]))*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2))/ -(96*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2.Fac deleted file mode 100644 index 88b53aa91..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2.Fac +++ /dev/null @@ -1,26 +0,0 @@ -(32*Pi^2*(3 + 2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (4*CouplingConstant[ChPTPhotonsLeptons3[4], 13, RenormalizationState[ - 1]] + 4*CouplingConstant[ChPTPhotonsLeptons3[4], 14, - RenormalizationState[1]] - 2*CouplingConstant[ChPTPhotonsLeptons3[4], - 15, RenormalizationState[1]] + CouplingConstant[ - ChPTPhotonsLeptons3[4], 16, RenormalizationState[1]] + - 2*(CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[ - 1]] + CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[1]])))* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -3*(64*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + -(64*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - 4*CouplingConstant[ChPTPhotonsLeptons3[4], - 5, RenormalizationState[1]] - 3*LeutwylerLambda[]) + - 3*Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2 + -(128*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + 8*CouplingConstant[ChPTPhotonsLeptons3[4], - 5, RenormalizationState[1]] + 3*LeutwylerLambda[]) - - 3*(Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[8], RenormalizationState[ - 0]]^2/ScaleMu^2]))*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2)/ -(96*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2.Mass b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2.Mass deleted file mode 100644 index ee75ddca5..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P110o2.Mass +++ /dev/null @@ -1,74 +0,0 @@ -(4*CouplingConstant[QED[1], RenormalizationState[0]]^2* -((16*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] + 12*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 14, RenormalizationState[1]] - - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 15, RenormalizationState[ - 1]] + 3*CouplingConstant[ChPTPhotonsLeptons3[4], 16, - RenormalizationState[1]] + - 2*(3*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[1]] + 3*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 18, RenormalizationState[1]] - - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 19, RenormalizationState[ - 1]] - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 20, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 21, RenormalizationState[1]] + CouplingConstant[ - ChPTPhotonsLeptons3[4], 22, RenormalizationState[1]]))* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 - - 9*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + 2*(-32*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] + 12*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 14, RenormalizationState[1]] - - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 15, RenormalizationState[ - 1]] + 3*CouplingConstant[ChPTPhotonsLeptons3[4], 16, - RenormalizationState[1]] + - 2*(3*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[1]] + 3*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 18, RenormalizationState[1]] - - 2*(3*CouplingConstant[ChPTPhotonsLeptons3[4], 19, - RenormalizationState[1]] + 3*CouplingConstant[ - ChPTPhotonsLeptons3[4], 20, RenormalizationState[1]] + - CouplingConstant[ChPTPhotonsLeptons3[4], 21, RenormalizationState[ - 1]] + CouplingConstant[ChPTPhotonsLeptons3[4], 22, - RenormalizationState[1]])))*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^4 + - 9*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^ - 2) + DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* -((768*Pi^2*(3*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - CouplingConstant[ChPTPhotonsLeptons3[4], - 5, RenormalizationState[1]] - 6*CouplingConstant[ - ChPTPhotonsLeptons3[4], 6, RenormalizationState[1]] + - 48*CouplingConstant[ChPTPhotonsLeptons3[4], 7, RenormalizationState[ - 1]] + 18*CouplingConstant[ChPTPhotonsLeptons3[4], 8, - RenormalizationState[1]]) - - 9*(2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2/ScaleMu^2]) - - 7*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 4 - 4*(384*Pi^2*(3*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - 4*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]] - - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 6, RenormalizationState[ - 1]] + 48*CouplingConstant[ChPTPhotonsLeptons3[4], 7, - RenormalizationState[1]] + 24*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 8, RenormalizationState[1]]) - - 11*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2 - - 4*(1536*Pi^2*(3*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + - 2*(CouplingConstant[ChPTPhotonsLeptons3[4], 5, RenormalizationState[ - 1]] - 3*(CouplingConstant[ChPTPhotonsLeptons3[4], 6, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 7, RenormalizationState[1]] + CouplingConstant[ - ChPTPhotonsLeptons3[4], 8, RenormalizationState[1]]))) - - 9*(Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[8], RenormalizationState[ - 0]]^2/ScaleMu^2]) + - 16*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^ - 4))/(864*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2-0.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2-0.Fac deleted file mode 100644 index 39ece0f53..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2-0.Fac +++ /dev/null @@ -1,33 +0,0 @@ -(4*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* -(8*Pi^2*(24*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] + 24*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 14, RenormalizationState[1]] + - 20*(CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[ - 1]] + CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[1]]) + 9*LeutwylerLambda[]) + - 9*(-1 + Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])) + 3*CouplingConstant[ChPTPhotonsLeptons3[2], - RenormalizationState[0]]* -(96*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + - (192*Pi^2*LeutwylerLambda[] - - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[7], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2 + - (64*Pi^2*(12*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]]) + LeutwylerLambda[]) - - 2*Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[7], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2 + - (128*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[8], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2))/ -(288*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2.Fac deleted file mode 100644 index e00d14ee7..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2.Fac +++ /dev/null @@ -1,40 +0,0 @@ -(-36*CouplingConstant[QED[1], RenormalizationState[0]]^2* -(-1 + 16*Pi^2*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2, - SmallVariable[ParticleMass[Vector[1], RenormalizationState[0]]]^2, - LeutwylerJBarEvaluation -> "none"])*(Pair[Momentum[p1], Momentum[p1]] + - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2) + -((Pair[Momentum[p1], Momentum[p1]] - ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2)* - (4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* - (72*Pi^2 + CouplingConstant[QED[1], RenormalizationState[0]]^2* - (8*Pi^2*(4*(6*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] + 6*CouplingConstant[ - ChPTPhotonsLeptons3[4], 14, RenormalizationState[1]] + - 5*(CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[1]] + CouplingConstant[ - ChPTPhotonsLeptons3[4], 18, RenormalizationState[1]])) + - 9*LeutwylerLambda[]) + - 9*(-1 + Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2]))) + - 3*((192*Pi^2*LeutwylerLambda[] - - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + - (64*Pi^2*(12*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]]) + LeutwylerLambda[]) - - 2*Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2 + - (128*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2)))/ -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2)/ -(288*Pi^2*(Pair[Momentum[p1], Momentum[p1]] - -ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2)) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2.Mass b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2.Mass deleted file mode 100644 index 1d9047358..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P30o2.Mass +++ /dev/null @@ -1,49 +0,0 @@ -(36*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2* -(-2*(64*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 5, RenormalizationState[1]]) + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 - (256*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^ - 2) + DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* -((-2304*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 5, RenormalizationState[1]] - - 2*(CouplingConstant[ChPTPhotonsLeptons3[4], 6, RenormalizationState[ - 1]] + CouplingConstant[ChPTPhotonsLeptons3[4], 8, - RenormalizationState[1]])) + - 9*Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^4 - - 4*(1152*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - 2*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 6, RenormalizationState[1]]) + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2 + - 2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* - ((36 + 64*Pi^2*(-6*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] - 6*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 14, RenormalizationState[1]] - - 5*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[ - 1]] - 5*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[1]] + 6*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 19, RenormalizationState[1]] + - 15*CouplingConstant[ChPTPhotonsLeptons3[4], 20, - RenormalizationState[1]] + 5*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 21, RenormalizationState[1]] + - 23*CouplingConstant[ChPTPhotonsLeptons3[4], 22, - RenormalizationState[1]] + 18*CouplingConstant[ - ChPTPhotonsLeptons3[4], 23, RenormalizationState[1]]) - - 27*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + 1152*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[4], 20, - RenormalizationState[1]]*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2)))/ -(288*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2-0.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2-0.Fac deleted file mode 100644 index 5382785d4..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2-0.Fac +++ /dev/null @@ -1,31 +0,0 @@ -(64*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2* -(12*CouplingConstant[ChPTPhotonsLeptons3[4], 13, RenormalizationState[ - 1]] + 12*CouplingConstant[ChPTPhotonsLeptons3[4], 14, - RenormalizationState[1]] - 18*CouplingConstant[ChPTPhotonsLeptons3[4], - 15, RenormalizationState[1]] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 16, RenormalizationState[1]] + - 10*(CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[ - 1]] + CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[1]]))*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2 + 3*CouplingConstant[ChPTPhotonsLeptons3[2], - RenormalizationState[0]]* -(96*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + - (320*Pi^2*LeutwylerLambda[] - - 4*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[7], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2 + - (64*Pi^2*(12*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]]) - LeutwylerLambda[]) + - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + (128*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[8], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2))/ -(288*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2.Fac deleted file mode 100644 index 711053cf7..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2.Fac +++ /dev/null @@ -1,27 +0,0 @@ -(32*Pi^2*(9 + 2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (12*CouplingConstant[ChPTPhotonsLeptons3[4], 13, RenormalizationState[ - 1]] + 12*CouplingConstant[ChPTPhotonsLeptons3[4], 14, - RenormalizationState[1]] - 18*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 15, RenormalizationState[1]] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 16, RenormalizationState[ - 1]] + 10*(CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[1]])))* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -3*((320*Pi^2*LeutwylerLambda[] - - 4*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[7], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2 + - (64*Pi^2*(12*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]]) - LeutwylerLambda[]) + - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + (128*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[8], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2))/ -(288*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2.Mass b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2.Mass deleted file mode 100644 index 0681433c8..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P40o2.Mass +++ /dev/null @@ -1,38 +0,0 @@ -(ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* -(4*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (-16*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] + 12*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 14, RenormalizationState[1]] - - 18*CouplingConstant[ChPTPhotonsLeptons3[4], 15, RenormalizationState[ - 1]] + 9*CouplingConstant[ChPTPhotonsLeptons3[4], 16, - RenormalizationState[1]] + - 2*(5*CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[ - 1]] + 5*CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[1]] - 6*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 19, RenormalizationState[1]] - - 6*CouplingConstant[ChPTPhotonsLeptons3[4], 20, RenormalizationState[ - 1]] - 5*(CouplingConstant[ChPTPhotonsLeptons3[4], 21, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 22, RenormalizationState[1]])))* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - 9*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2]) + DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 2*((-9*(256*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]] - - 2*(CouplingConstant[ChPTPhotonsLeptons3[4], 6, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 8, RenormalizationState[1]])) - - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2/ScaleMu^2]) + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 - 4*(1152*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - 2*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 6, RenormalizationState[1]]) + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^ - 2)))/(288*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ -4) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2-0.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2-0.Fac deleted file mode 100644 index 18bf1e301..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2-0.Fac +++ /dev/null @@ -1,36 +0,0 @@ -(8*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* -(8*Pi^2*(24*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] + 24*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 14, RenormalizationState[1]] + - 20*(CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[ - 1]] + CouplingConstant[ChPTPhotonsLeptons3[4], 18, - RenormalizationState[1]]) + 9*LeutwylerLambda[]) + - 9*(-1 + Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2])) + 3*CouplingConstant[ChPTPhotonsLeptons3[2], - RenormalizationState[0]]* -(192*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + - (384*Pi^2*LeutwylerLambda[] - - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - 4*Log[ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + - (256*Pi^2*(6*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2] + 4*Log[ParticleMass[PseudoScalar[7], RenormalizationState[ - 0]]^2/ScaleMu^2] + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + 2*(64*Pi^2*(24*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + 12*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]] + 5*LeutwylerLambda[]) - - 2*Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[8], RenormalizationState[ - 0]]^2/ScaleMu^2] - - 2*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^ - 2))/(576*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[2], -RenormalizationState[0]]*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2.Fac deleted file mode 100644 index 474297194..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2.Fac +++ /dev/null @@ -1,43 +0,0 @@ -(-72*CouplingConstant[QED[1], RenormalizationState[0]]^2* -(-1 + 16*Pi^2*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2, - SmallVariable[ParticleMass[Vector[1], RenormalizationState[0]]]^2, - LeutwylerJBarEvaluation -> "none"])*(Pair[Momentum[p1], Momentum[p1]] + - ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2) + -((Pair[Momentum[p1], Momentum[p1]] - ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2)* - (8*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* - (72*Pi^2 + CouplingConstant[QED[1], RenormalizationState[0]]^2* - (8*Pi^2*(4*(6*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] + 6*CouplingConstant[ - ChPTPhotonsLeptons3[4], 14, RenormalizationState[1]] + - 5*(CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[1]] + CouplingConstant[ - ChPTPhotonsLeptons3[4], 18, RenormalizationState[1]])) + - 9*LeutwylerLambda[]) + - 9*(-1 + Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2]))) + - 3*((384*Pi^2*LeutwylerLambda[] - - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - 4*Log[ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + - (256*Pi^2*(6*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2] + 4*Log[ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2/ScaleMu^2] + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + 2*(64*Pi^2*(24*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + 12*CouplingConstant[ - ChPTPhotonsLeptons3[4], 5, RenormalizationState[1]] + - 5*LeutwylerLambda[]) - - 2*Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[8], - RenormalizationState[0]]^2/ScaleMu^2] - - 2*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[8], RenormalizationState[ - 0]]^2)))/DecayConstant[PseudoScalar[1], RenormalizationState[0]]^ - 2)/(576*Pi^2*(Pair[Momentum[p1], Momentum[p1]] - -ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2)) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2.Mass b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2.Mass deleted file mode 100644 index c560ada56..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P70o2.Mass +++ /dev/null @@ -1,51 +0,0 @@ --(6*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (-32*Pi^2*(3*CouplingConstant[ChPTPhotonsLeptons3[4], 20, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 21, RenormalizationState[1]] + CouplingConstant[ - ChPTPhotonsLeptons3[4], 22, RenormalizationState[1]])* - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4 + - 3*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* - (128*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2]))*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + (CouplingConstant[QED[1], RenormalizationState[0]]^2* - (36*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* - (64*Pi^2*(2*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]]) + - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2]) + DecayConstant[PseudoScalar[1], RenormalizationState[ - 0]]^4*(64*Pi^2*(6*CouplingConstant[ChPTPhotonsLeptons3[4], 13, - RenormalizationState[1]] + 6*CouplingConstant[ - ChPTPhotonsLeptons3[4], 14, RenormalizationState[1]] + - 5*CouplingConstant[ChPTPhotonsLeptons3[4], 17, - RenormalizationState[1]] + 5*CouplingConstant[ - ChPTPhotonsLeptons3[4], 18, RenormalizationState[1]] - - 2*(3*CouplingConstant[ChPTPhotonsLeptons3[4], 19, - RenormalizationState[1]] + 12*CouplingConstant[ - ChPTPhotonsLeptons3[4], 20, RenormalizationState[1]] + - CouplingConstant[ChPTPhotonsLeptons3[4], 21, - RenormalizationState[1]] + 10*CouplingConstant[ - ChPTPhotonsLeptons3[4], 22, RenormalizationState[1]] + - 9*CouplingConstant[ChPTPhotonsLeptons3[4], 23, - RenormalizationState[1]])) + - 9*(-4 + 3*Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^ - 2/ScaleMu^2]))) + - DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* - (1152*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - 2*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 6, RenormalizationState[1]]) + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2)*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2 + -4*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* - (288*Pi^2*(2*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 5, RenormalizationState[1]] - - 2*(2*CouplingConstant[ChPTPhotonsLeptons3[4], 6, RenormalizationState[ - 1]] + CouplingConstant[ChPTPhotonsLeptons3[4], 8, - RenormalizationState[1]])) - - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^4)/ -(144*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^4) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2-0.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2-0.Fac deleted file mode 100644 index 0aaf7c9f2..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2-0.Fac +++ /dev/null @@ -1,32 +0,0 @@ -(512*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2* -(3*CouplingConstant[ChPTPhotonsLeptons3[4], 13, RenormalizationState[1]] + - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 14, RenormalizationState[1]] + - CouplingConstant[ChPTPhotonsLeptons3[4], 17, RenormalizationState[1]] + - CouplingConstant[ChPTPhotonsLeptons3[4], 18, RenormalizationState[1]])* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -3*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -(192*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + - (256*Pi^2*LeutwylerLambda[] - - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - 2*Log[ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + - (128*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2] + 2*Log[ParticleMass[PseudoScalar[7], RenormalizationState[ - 0]]^2/ScaleMu^2] + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + 2*(64*Pi^2*(24*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + 12*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]] + 5*LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] - - 2*(Log[ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], - RenormalizationState[0]]^2/ScaleMu^2]))* - ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2))/ -(576*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[2], RenormalizationState[0]]* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2.Fac deleted file mode 100644 index 6a605e270..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2.Fac +++ /dev/null @@ -1,29 +0,0 @@ -(64*Pi^2*(9 + 8*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (3*CouplingConstant[ChPTPhotonsLeptons3[4], 13, RenormalizationState[ - 1]] + 3*CouplingConstant[ChPTPhotonsLeptons3[4], 14, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[1]] + CouplingConstant[ - ChPTPhotonsLeptons3[4], 18, RenormalizationState[1]]))* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + -3*((256*Pi^2*LeutwylerLambda[] - - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - 2*Log[ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + - (128*Pi^2*(12*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2] + 2*Log[ParticleMass[PseudoScalar[7], RenormalizationState[ - 0]]^2/ScaleMu^2] + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2 + 2*(64*Pi^2*(24*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + 12*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 5, RenormalizationState[1]] + 5*LeutwylerLambda[]) - - Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2] - - 2*(Log[ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[11], - RenormalizationState[0]]^2/ScaleMu^2]))* - ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2))/ -(576*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2.Mass b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2.Mass deleted file mode 100644 index 48ac3f080..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3P80o2.Mass +++ /dev/null @@ -1,26 +0,0 @@ -(ParticleMass[PseudoScalar[8], RenormalizationState[0]]^2* -(-128*Pi^2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (3*CouplingConstant[ChPTPhotonsLeptons3[4], 13, RenormalizationState[ - 1]] + 3*CouplingConstant[ChPTPhotonsLeptons3[4], 14, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 17, RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 18, RenormalizationState[1]] - - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 19, RenormalizationState[ - 1]] - 3*CouplingConstant[ChPTPhotonsLeptons3[4], 20, - RenormalizationState[1]] - CouplingConstant[ChPTPhotonsLeptons3[4], - 21, RenormalizationState[1]] - CouplingConstant[ChPTPhotonsLeptons3[4], - 22, RenormalizationState[1]])*DecayConstant[PseudoScalar[1], - RenormalizationState[0]]^2 - -(1152*Pi^2*(CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] - 2*CouplingConstant[ChPTPhotonsLeptons3[4], - 6, RenormalizationState[1]]) + - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2 + -4*(-288*Pi^2*(2*CouplingConstant[ChPTPhotonsLeptons3[4], 4, - RenormalizationState[1]] + CouplingConstant[ChPTPhotonsLeptons3[4], - 5, RenormalizationState[1]] - 4*CouplingConstant[ - ChPTPhotonsLeptons3[4], 6, RenormalizationState[1]] - - 2*CouplingConstant[ChPTPhotonsLeptons3[4], 8, RenormalizationState[ - 1]]) + Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^ - 2/ScaleMu^2])*ParticleMass[PseudoScalar[8], RenormalizationState[0]]^ - 2))/(144*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3V10o2-0.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3V10o2-0.Fac deleted file mode 100644 index aef6d7233..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3V10o2-0.Fac +++ /dev/null @@ -1,12 +0,0 @@ -(144*Pi^2 - CouplingConstant[QED[1], RenormalizationState[0]]^2* -(34 + 384*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[4], 10, - RenormalizationState[0]] + 768*Pi^2*CouplingConstant[ - ChPTPhotonsLeptons3[4], 11, RenormalizationState[0]] + - 384*Pi^2*CouplingConstant[ChPTPhotonsLeptons3[4], 30, - RenormalizationState[0]] + 960*Pi^2*LeutwylerLambda[] + - 12*Log[ParticleMass[Fermion[7], RenormalizationState[0]]^2/ScaleMu^2] + - 12*Log[ParticleMass[Fermion[8], RenormalizationState[0]]^2/ScaleMu^2] + - 3*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] + - 3*Log[ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2/ - ScaleMu^2]))/(144*Pi^2) diff --git a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3V10o2.Fac b/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3V10o2.Fac deleted file mode 100644 index 941ff5f15..000000000 --- a/FeynCalc/Phi/Factors/ChPTPhotonsLeptons3V10o2.Fac +++ /dev/null @@ -1,35 +0,0 @@ --((-144*Pi^2 + CouplingConstant[QED[1], RenormalizationState[0]]^2* - (34 + 48*Pi^2*(8*CouplingConstant[ChPTPhotonsLeptons3[4], 10, - RenormalizationState[0]] + 16*CouplingConstant[ChPTPhotonsLeptons3[ - 4], 11, RenormalizationState[0]] + - 8*CouplingConstant[ChPTPhotonsLeptons3[4], 30, RenormalizationState[ - 0]] - 4*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[Fermion[7], RenormalizationState[0]]^2] - - 4*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[Fermion[8], RenormalizationState[0]]^2] - - LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2] - - LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2] + - 20*LeutwylerLambda[]) + - 12*Log[ParticleMass[Fermion[7], RenormalizationState[0]]^2/ - ScaleMu^2] + 12*Log[ParticleMass[Fermion[8], RenormalizationState[ - 0]]^2/ScaleMu^2] + - 3*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] + 3*Log[ParticleMass[PseudoScalar[7], - RenormalizationState[0]]^2/ScaleMu^2]))* - Pair[Momentum[p1], Momentum[p1]] + -192*Pi^2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (-2*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[Fermion[7], RenormalizationState[0]]^2]* - ParticleMass[Fermion[7], RenormalizationState[0]]^2 - - 2*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[Fermion[8], RenormalizationState[0]]^2]* - ParticleMass[Fermion[8], RenormalizationState[0]]^2 + - LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2]* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 + - LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2]* - ParticleMass[PseudoScalar[7], RenormalizationState[0]]^2))/ -(144*Pi^2*Pair[Momentum[p1], Momentum[p1]]) diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P20o2.Fac b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P20o2.Fac deleted file mode 100644 index bc8208c3c..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P20o2.Fac +++ /dev/null @@ -1,6 +0,0 @@ -1 + (CouplingConstant[ChPTVirtualPhotons2[4], 4, RenormalizationState[1]]* -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2)/ -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2 - -(Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2]* -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2)/ -(16*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P30o2.Fac b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P30o2.Fac deleted file mode 100644 index 6ca092ea7..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P30o2.Fac +++ /dev/null @@ -1,41 +0,0 @@ -(576 - -(18*((64*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2 + (-32*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], 4, - RenormalizationState[0]] + - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2))/(Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) + -(DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* - (ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 - - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2)* - (640*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]] + 640*CouplingConstant[ - ChPTVirtualPhotons2[4], 12, RenormalizationState[0]] + - 576*CouplingConstant[ChPTVirtualPhotons2[4], 19, - RenormalizationState[0]] - - (2*(8*Pi^2*(20*(CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[1]] + CouplingConstant[ChPTVirtualPhotons2[ - 4], 12, RenormalizationState[1]]) + 9*LeutwylerLambda[]) + - 9*(-1 + Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[Vector[1], RenormalizationState[0]]^ - 2/ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2])))/ - Pi^2 - (9*(16*Pi^2*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2, - ParticleMass[Vector[1], RenormalizationState[0]]^2]* - (ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 - - ParticleMass[Vector[1], RenormalizationState[0]]^2)* - (3*Pair[Momentum[p1], Momentum[p1]] + ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2 - ParticleMass[Vector[1], - RenormalizationState[0]]^2) + 3*Pair[Momentum[p1], Momentum[p1]]* - (-((32*Pi^2*LeutwylerLambda[] + Log[ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2) + - (32*Pi^2*LeutwylerLambda[] + Log[ParticleMass[Vector[1], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[Vector[1], RenormalizationState[0]]^2)))/ - (Pi^2*Pair[Momentum[p1], Momentum[p1]]* - (ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 - - ParticleMass[Vector[1], RenormalizationState[0]]^2))))/ -CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]])/576 diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P40o2.Fac b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P40o2.Fac deleted file mode 100644 index 15e9958c3..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2A00P40o2.Fac +++ /dev/null @@ -1,22 +0,0 @@ -1 + ((20*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[0]] - 10*CouplingConstant[ChPTVirtualPhotons2[4], - 11, RenormalizationState[1]] + - 20*CouplingConstant[ChPTVirtualPhotons2[4], 12, RenormalizationState[ - 0]] - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[1]] - - 9*(4*CouplingConstant[ChPTVirtualPhotons2[4], 13, RenormalizationState[ - 0]] - 2*(CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[1]] + CouplingConstant[ChPTVirtualPhotons2[4], - 14, RenormalizationState[0]]) + CouplingConstant[ - ChPTVirtualPhotons2[4], 14, RenormalizationState[1]]))* -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* -(ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 - - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2))/ -(18*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]) + -(-((64*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2) + 16*Pi^2*(CouplingConstant[ChPTVirtualPhotons2[4], 4, - RenormalizationState[0]] + 2*LeutwylerLambda[])* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2)/ -(16*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P20o2.Fac b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P20o2.Fac deleted file mode 100644 index 1113df751..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P20o2.Fac +++ /dev/null @@ -1,102 +0,0 @@ -(576*Pi^2*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2*LeutwylerLambda[]* -(ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]]) - - 2*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]] + - Pair[Momentum[p1], Momentum[p1]]*(1 + SU2Delta[ExplicitSUNIndex[3], - SUNIndex[i1]])) - -3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* -(Pair[Momentum[p1], Momentum[p1]]* - (-((32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2*(-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]])) + - (32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2*(1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]])) + - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ((32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2*(-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]]) - - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - (32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2] + (32*Pi^2*LeutwylerLambda[] + - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2/ScaleMu^2])* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]]))) + -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4* -(-16*Pi^2*(9 + 2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[ - 1]] + 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[1]] - 18*CouplingConstant[ChPTVirtualPhotons2[ - 4], 13, RenormalizationState[1]] + - 9*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[ - 1]]))*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]] + - 2*Pair[Momentum[p1], Momentum[p1]]*(72*Pi^2 + - CouplingConstant[QED[1], RenormalizationState[0]]^2* - (160*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[1]] + 160*Pi^2*CouplingConstant[ - ChPTVirtualPhotons2[4], 12, RenormalizationState[1]] + - 9*(-24*Pi^2*LeutwylerLambda[] + (32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*SU2Delta[ExplicitSUNIndex[1], SUNIndex[i1]] + - 32*Pi^2*LeutwylerLambda[]*SU2Delta[ExplicitSUNIndex[2], - SUNIndex[i1]] + Log[ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2/ScaleMu^2]* - SU2Delta[ExplicitSUNIndex[2], SUNIndex[i1]] + - 16*Pi^2*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2, - ParticleMass[Vector[1], RenormalizationState[0]]^2]* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]]) - - 32*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], 13, - RenormalizationState[1]]*SU2Delta[ExplicitSUNIndex[3], - SUNIndex[i1]] + 16*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], - 14, RenormalizationState[1]]*SU2Delta[ExplicitSUNIndex[3], - SUNIndex[i1]] + 24*Pi^2*LeutwylerLambda[]* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]]))) + - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - (144*Pi^2*(-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]]) + - CouplingConstant[QED[1], RenormalizationState[0]]^2* - (320*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[1]]*(-1 + SU2Delta[ExplicitSUNIndex[3], - SUNIndex[i1]]) + 320*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], - 12, RenormalizationState[1]]*(-1 + SU2Delta[ExplicitSUNIndex[3], - SUNIndex[i1]]) - 9*(48*Pi^2*LeutwylerLambda[] + - 3*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] - 32*Pi^2*LeutwylerLambda[]* - SU2Delta[ExplicitSUNIndex[1], SUNIndex[i1]] - - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2]*SU2Delta[ExplicitSUNIndex[1], SUNIndex[i1]] - - 32*Pi^2*LeutwylerLambda[]*SU2Delta[ExplicitSUNIndex[2], - SUNIndex[i1]] - Log[ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2/ScaleMu^2]* - SU2Delta[ExplicitSUNIndex[2], SUNIndex[i1]] + - 32*Pi^2*LeutwylerJBar[Pair[Momentum[p1], Momentum[p1]], - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2, - ParticleMass[Vector[1], RenormalizationState[0]]^2]* - (SU2Delta[ExplicitSUNIndex[1], SUNIndex[i1]] + - SU2Delta[ExplicitSUNIndex[2], SUNIndex[i1]]) + - 64*Pi^2*LeutwylerJBar[-(ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2*(-1 + SU2Delta[ExplicitSUNIndex[ - 3], SUNIndex[i1]])) + ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2*SU2Delta[ExplicitSUNIndex[3], - SUNIndex[i1]], ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2, ParticleMass[Vector[1], - RenormalizationState[0]]^2]*(-1 + SU2Delta[ExplicitSUNIndex[3], - SUNIndex[i1]]) - 48*Pi^2*LeutwylerLambda[]* - SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]] - - 3*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2]*SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]])))))/ -(144*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* -(DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* - (Pair[Momentum[p1], Momentum[p1]] - ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2) + -2*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - CouplingConstant[QED[1], RenormalizationState[0]]^2* - (-1 + SU2Delta[ExplicitSUNIndex[3], SUNIndex[i1]]))) diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P30o2.Fac b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P30o2.Fac deleted file mode 100644 index 7cde799b9..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P30o2.Fac +++ /dev/null @@ -1,16 +0,0 @@ -(2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* -(72*Pi^2 + CouplingConstant[QED[1], RenormalizationState[0]]^2* - (160*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[1]] + 160*Pi^2*CouplingConstant[ - ChPTVirtualPhotons2[4], 12, RenormalizationState[1]] + - 9*(-1 + 8*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[Vector[1], RenormalizationState[0]]^2/ - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2]))) + -3*(64*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2 - -3*(128*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2)/ -(144*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2) diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P30o2.Mass b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P30o2.Mass deleted file mode 100644 index 350316de6..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P30o2.Mass +++ /dev/null @@ -1,50 +0,0 @@ -(6912*Pi^2*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]^ - 2*CouplingConstant[QED[1], RenormalizationState[0]]^4*LeutwylerLambda[] + -12*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2* -DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* -(48*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* - (1 + 3*CouplingConstant[QED[1], RenormalizationState[0]]^2* - LeutwylerLambda[]) - 8*(44*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 2 + (256*Pi^2*LeutwylerLambda[] - - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 2) + DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4* -(320*Pi^2*CouplingConstant[QED[1], RenormalizationState[0]]^4* - (CouplingConstant[ChPTVirtualPhotons2[4], 23, RenormalizationState[1]] + - 2*CouplingConstant[ChPTVirtualPhotons2[4], 24, RenormalizationState[ - 1]])*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4 + - 2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* - (-((-36 + 320*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], 11, - RenormalizationState[1]] + 320*Pi^2*CouplingConstant[ - ChPTVirtualPhotons2[4], 12, RenormalizationState[1]] + - 432*Pi^2*LeutwylerLambda[] + - 27*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[ - 0]]^2) + 16*Pi^2*(20*CouplingConstant[ChPTVirtualPhotons2[4], 15, - RenormalizationState[1]] + 92*CouplingConstant[ChPTVirtualPhotons2[ - 4], 16, RenormalizationState[1]] + - 4*CouplingConstant[ChPTVirtualPhotons2[4], 17, RenormalizationState[ - 1]] + 72*CouplingConstant[ChPTVirtualPhotons2[4], 18, - RenormalizationState[1]] + 27*LeutwylerLambda[])* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2) + - 3*(-192*Pi^2*CouplingConstant[ChPTVirtualPhotons2[2], - RenormalizationState[0]]*CouplingConstant[QED[1], - RenormalizationState[0]]^2 + 4*(32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^ - 4 + 2*(-32*Pi^2*LeutwylerLambda[] - - 2*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] + Log[ParticleMass[PseudoScalar[4], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2 + - (192*Pi^2*CouplingConstant[ChPTVirtualPhotons2[4], 3, - RenormalizationState[1]] - 64*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[4], RenormalizationState[0]]^ - 4)))/(288*Pi^2*DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^6) diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P40o2.Fac b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P40o2.Fac deleted file mode 100644 index d263a6932..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P40o2.Fac +++ /dev/null @@ -1,14 +0,0 @@ -(8*Pi^2*(9 + 2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - (10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[ - 1]] + 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[1]] - 18*CouplingConstant[ChPTVirtualPhotons2[ - 4], 13, RenormalizationState[1]] + - 9*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[ - 1]]))*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4 + -576*Pi^2*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* -CouplingConstant[QED[1], RenormalizationState[0]]^2*LeutwylerLambda[] - -3*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* -(32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2)/ -(72*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4) diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P40o2.Mass b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P40o2.Mass deleted file mode 100644 index ea993f49b..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2P40o2.Mass +++ /dev/null @@ -1,30 +0,0 @@ -(12*(32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* -(-2*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - CouplingConstant[QED[1], RenormalizationState[0]]^2 + - DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2) + -2*(32*Pi^2*CouplingConstant[QED[1], RenormalizationState[0]]^2* - ((-10*CouplingConstant[ChPTVirtualPhotons2[4], 11, RenormalizationState[ - 1]] - 10*CouplingConstant[ChPTVirtualPhotons2[4], 12, - RenormalizationState[1]] + 18*CouplingConstant[ChPTVirtualPhotons2[ - 4], 13, RenormalizationState[1]] - - 9*CouplingConstant[ChPTVirtualPhotons2[4], 14, RenormalizationState[ - 1]] + 2*(5*(CouplingConstant[ChPTVirtualPhotons2[4], 15, - RenormalizationState[1]] + CouplingConstant[ChPTVirtualPhotons2[ - 4], 16, RenormalizationState[1]]) + CouplingConstant[ - ChPTVirtualPhotons2[4], 17, RenormalizationState[1]]))* - DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4 - - 18*CouplingConstant[ChPTVirtualPhotons2[2], RenormalizationState[0]]* - LeutwylerLambda[]) + 3*DecayConstant[PseudoScalar[2], - RenormalizationState[0]]^2*(32*Pi^2*LeutwylerLambda[] + - Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2])*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2)* -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2 - -9*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^2* -(64*Pi^2*(-CouplingConstant[ChPTVirtualPhotons2[4], 3, - RenormalizationState[1]] + LeutwylerLambda[]) + - Log[ParticleMass[PseudoScalar[4], RenormalizationState[0]]^2/ScaleMu^2])* -ParticleMass[PseudoScalar[4], RenormalizationState[0]]^4)/ -(288*Pi^2*DecayConstant[PseudoScalar[2], RenormalizationState[0]]^4) diff --git a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2V10o2.Fac b/FeynCalc/Phi/Factors/ChPTVirtualPhotons2V10o2.Fac deleted file mode 100644 index 696d638af..000000000 --- a/FeynCalc/Phi/Factors/ChPTVirtualPhotons2V10o2.Fac +++ /dev/null @@ -1,25 +0,0 @@ --(12*CouplingConstant[QED[1], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2* - (2 + - Log[(-1 + Sqrt[1 - (4*ParticleMass[PseudoScalar[3], RenormalizationState[ - 0]]^2)/Pair[Momentum[p1], Momentum[p1]]])/ - (1 + Sqrt[1 - (4*ParticleMass[PseudoScalar[3], RenormalizationState[ - 0]]^2)/Pair[Momentum[p1], Momentum[p1]]])]* - Sqrt[1 - (4*ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2)/ - Pair[Momentum[p1], Momentum[p1]]]) + -Pair[Momentum[p1], Momentum[p1]]*(-144*Pi^2 + - CouplingConstant[QED[1], RenormalizationState[0]]^2* - (1 + 3*Log[ParticleMass[PseudoScalar[3], RenormalizationState[0]]^2/ - ScaleMu^2] + 16*Pi^2*(20*CouplingConstant[ChPTVirtualPhotons2[4], - 5, RenormalizationState[0]] - 40*CouplingConstant[ - ChPTVirtualPhotons2[4], 9, RenormalizationState[0]] + - 20*CouplingConstant[ChPTVirtualPhotons2[4], 25, RenormalizationState[ - 0]] + 6*LeutwylerLambda[] - - (3*(2 + Log[(-1 + Sqrt[1 - (4*ParticleMass[PseudoScalar[3], - RenormalizationState[0]]^2)/Pair[Momentum[p1], - Momentum[p1]]])/(1 + Sqrt[1 - (4*ParticleMass[ - PseudoScalar[3], RenormalizationState[0]]^2)/ - Pair[Momentum[p1], Momentum[p1]]])]* - Sqrt[1 - (4*ParticleMass[PseudoScalar[3], RenormalizationState[ - 0]]^2)/Pair[Momentum[p1], Momentum[p1]]]))/(16*Pi^2)))))/ -(144*Pi^2*Pair[Momentum[p1], Momentum[p1]]) diff --git a/FeynCalc/Phi/Factors/ChPTW3P70S10o2.Fac b/FeynCalc/Phi/Factors/ChPTW3P70S10o2.Fac deleted file mode 100644 index f9378a4e6..000000000 --- a/FeynCalc/Phi/Factors/ChPTW3P70S10o2.Fac +++ /dev/null @@ -1,53 +0,0 @@ -(-2*CouplingConstant[ChPTW3[2], 2]* -(ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 - - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)* -(-288*Pi^2*DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2 + - (256*Pi^2*LeutwylerLambda[] + - 9*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2] - Log[ParticleMass[PseudoScalar[11], RenormalizationState[ - 0]]^2/ScaleMu^2])*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2 + 2*(352*Pi^2*LeutwylerLambda[] + - 9*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ - ScaleMu^2] + 2*Log[ParticleMass[PseudoScalar[11], - RenormalizationState[0]]^2/ScaleMu^2])* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2) + -CouplingConstant[ChPTW3[2], 1]* -(1152*Pi^2*CouplingConstant[ChPTW3[4], 11, RenormalizationState[1]]* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 + - 27*Log[ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2/ - ScaleMu^2]*ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 - - Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ScaleMu^2]* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^4 + - 2304*Pi^2*CouplingConstant[ChPTW3[4], 10, RenormalizationState[1]]* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 + - 1152*Pi^2*CouplingConstant[ChPTW3[4], 11, RenormalizationState[1]]* - ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 + - 960*Pi^2*LeutwylerLambda[]*ParticleMass[PseudoScalar[2], - RenormalizationState[0]]^2*ParticleMass[PseudoScalar[6], - RenormalizationState[0]]^2 + - 8*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2]*ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2 - - 2304*Pi^2*CouplingConstant[ChPTW3[4], 10, RenormalizationState[1]]* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4 - - 2304*Pi^2*CouplingConstant[ChPTW3[4], 11, RenormalizationState[1]]* - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4 - - 960*Pi^2*LeutwylerLambda[]*ParticleMass[PseudoScalar[6], - RenormalizationState[0]]^4 - - 18*Log[ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2/ - ScaleMu^2]*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4 - - 16*Log[ParticleMass[PseudoScalar[11], RenormalizationState[0]]^2/ - ScaleMu^2]*ParticleMass[PseudoScalar[6], RenormalizationState[0]]^4 - - 1152*Pi^2*CouplingConstant[ChPTW3[4], 21, RenormalizationState[1]]* - Pair[Momentum[p1], Momentum[p1]]* - (ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 - - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2) - - 960*Pi^2*LeutwylerLambda[]*Pair[Momentum[p1], Momentum[p1]]* - (ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 - - ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)))/ -(576*Pi^2*CouplingConstant[ChPTW3[2], 2]* -DecayConstant[PseudoScalar[1], RenormalizationState[0]]^2* -(ParticleMass[PseudoScalar[2], RenormalizationState[0]]^2 - -ParticleMass[PseudoScalar[6], RenormalizationState[0]]^2)) diff --git a/FeynCalc/Phi/First.m b/FeynCalc/Phi/First.m deleted file mode 100644 index a0a2e08da..000000000 --- a/FeynCalc/Phi/First.m +++ /dev/null @@ -1,29 +0,0 @@ -(* ************************************************************** *) -(* - -This file is read before anything else. Put here definitions -to be read before the subpackages. - -E.g.: -When using ArgumentsSupply on objects that are defined in a model -file but are in context Phi`Objects`, it is -necessary to define these objects before Objects.m is read. - -*) -(* ************************************************************** *) - -(* Definitions used by the model PiN2 *) - -Phi`Objects`CovariantNucleonFieldDerivative::usage = -"CovariantNucleonFieldDerivative is the nucleon -covariant derivative of J. Gasser, M. E. Sainio and -A. Svarc (1988), Nucl. Phys, B307, 779-853"; - -Phi`Objects`CNDr::usage = -"CNDr is the shorthand notation for -CovariantNucleonFieldDerivative, which is the nucleon -covariant derivative of J. Gasser, M. E. Sainio and -A. Svarc (1988), Nucl. Phys, B307, 779-853"; - -Options[CovariantFieldDerivative] = {Explicit->True, DiagonalToU->True, - SUNN->2, UDimension->Automatic}; diff --git a/FeynCalc/Phi/Lagrangians/BChPT22.m b/FeynCalc/Phi/Lagrangians/BChPT22.m deleted file mode 100644 index a83d1eccc..000000000 --- a/FeynCalc/Phi/Lagrangians/BChPT22.m +++ /dev/null @@ -1,95 +0,0 @@ -(* ****************************************************************** *) -(* *) -(* BChPT22 *) -(* *) -(* ****************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The simplest ChPT lagrangian. - - Taken from J. Gasser, M. E. Sainio and - A. Svarc (1988), Nucl. Phys, B307, 779-853 -*) - - -Begin["Phi`Objects`"]; - -(* ------------------------------------------------------------------ *) - -BChPT22::usage = -"BChPT22.m is the name of the file containing the definitions for -Lagrangian[BChPT2[2]], which is the SU(2) ChPT pion-nucleon -lagrangian. To evaluate use ArgumentsSupply."; - -GAV::usage = -"GAV := CouplingConstant[BChPT2[2]] is axial vector -coupling constant."; - -(* ------------------------------------------------------------------ *) - -End[]; - -(* ------------------------------------------------------------------ *) - -GAV = CouplingConstant[BChPT2[2]]; - -(* ------------------------------------------------------------------ *) - -(* Box definitions *) - -CouplingConstant /: -MakeBoxes[ -CouplingConstant[BChPT2[2],st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["g",FontSlant->"Italic"]][[1]], - MakeBoxes["A"], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* ------------------------------------------------------------------ *) - -(*Lagrangian[BChPT2[2]]:= - -I*(DOT[UVector[DiracBar[QuantumField[Particle[Nucleon]]]], -DiracMatrix[LorentzIndex[\[Mu]]], -CNDr[UVector[QuantumField[Particle[Nucleon]]],{\[Mu]}]])- - - -ParticleMass[Nucleon]* -DOT[UVector[DiracBar[QuantumField[Particle[Nucleon]]]], -UVector[QuantumField[Particle[Nucleon]]]]+ - - -I*CouplingConstant[BChPT2[2],RenormalizationState[0]]* -(DOT[UVector[DiracBar[QuantumField[Particle[Nucleon]]]], -NM[DiracMatrix[LorentzIndex[\[Mu]]],DiracMatrix[5],GasserDelta[\[Mu]]], -UVector[QuantumField[Particle[Nucleon]]]]);*) - -(* Paul's lagrangian. F.Orellana *) -Lagrangian[BChPT2[2]] := - UTrace[NM[USmall[\[Mu]],USmall[\[Nu]]]]* - (UDot[UVector[DiracBar[QuantumField[Particle[Nucleon]]]], - CNDr[CNDr[UVector[QuantumField[Particle[Nucleon]]],{\[Nu]}],{\[Mu]}]]+ - Adjoint[UDot[UVector[DiracBar[QuantumField[Particle[Nucleon]]]], - CNDr[CNDr[UVector[QuantumField[Particle[Nucleon]]],{\[Nu]}],{\[Mu]}]]]); - -(* ------------------------------------------------------------------ *) - -FieldsSet[BChPT2[2]] := - {IsoVector[ - QuantumField[Particle[Pion,RenormalizationState[0]]]], - QuantumField[Particle[Nucleon,RenormalizationState[0]]]}; - -$Lagrangians = Union[$Lagrangians,{BChPT2[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/ChPT22.m b/FeynCalc/Phi/Lagrangians/ChPT22.m deleted file mode 100644 index 60b717d82..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPT22.m +++ /dev/null @@ -1,55 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPT22 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 1997 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The simplest ChPT lagrangian. - - Taken from J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge -*) - - -Begin["Phi`Objects`"]; - -(* --------------------------------------------------------------- *) - -ChPT22::usage = -"ChPT22.m is the name of the file containing the definitions for -Lagrangian[ChPT2[2]], which is the SU(2) lowest order ChPT -lagrangian. To evaluate use ArgumentsSupply."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ChPT2[2]] := - 1/4*DecayConstant[Pion]^2* - - (UTrace[ NM[CDr[MM, {\[Mu]}],Adjoint[CDr[MM, {\[Mu]}]]] ] + - - UTrace[ NM[UChiMatrix, Adjoint[MM]]+NM[MM, Adjoint[UChiMatrix]] ]); - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPT2[2]] := - {IsoVector[ - QuantumField[Particle[Pion, RenormalizationState[0]]] - ]}; - -$Lagrangians = Union[$Lagrangians,{ChPT2[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/ChPT24.m b/FeynCalc/Phi/Lagrangians/ChPT24.m deleted file mode 100644 index c51df8193..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPT24.m +++ /dev/null @@ -1,208 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPT24 *) -(* *) -(* ************************************************************** *) - -(* -Author: Frederik Orellana - -Year: 1997 - -Mathematica Version: 3.0 - -Requirements: Feyncalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The ChPT lagrangian for pion to fourth - order in the energy (mass). - - Taken from J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge - -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPT24::usage = -"ChPT24.m is the name of the file containing the definitions for -Lagrangian[ChPT2[4]], which is the pionic ChPT lagrangian to -fourth order in the energy, first written down by -Gasser and Leutwyler. To evaluate use ArgumentsSupply."; - -L1::usage = -"L1 := CouplingConstant[ChPT2[4],1] is one of the constants of the -fourth order ChPT lagrangian"; - -L2::usage = -"L2 := CouplingConstant[ChPT2[4],2] is one of the constants of the -fourth order ChPT lagrangian"; - -L3::usage = -"L3 := CouplingConstant[ChPT2[4],3] is one of the constants of the -fourth order ChPT lagrangian"; - -L4::usage = -"L4 := CouplingConstant[ChPT2[4],4] is one of the constants of the -fourth order ChPT lagrangian"; - -L5::usage = -"L5 := CouplingConstant[ChPT2[4],5] is one of the constants of the -fourth order ChPT lagrangian"; - -L6::usage = -"L6 := CouplingConstant[ChPT2[4],6] is one of the constants of the -fourth order ChPT lagrangian"; - -L7::usage = -"L7 := CouplingConstant[ChPT2[4],7] is one of the constants of the -fourth order ChPT lagrangian"; - -L8::usage = -"L8 := CouplingConstant[ChPT2[4],8] is one of the constants of the -fourth order ChPT lagrangian"; - -L9::usage = -"L9 := CouplingConstant[ChPT2[4],9] is one of the constants of the -fourth order ChPT lagrangian"; - -L10::usage = -"L10 := CouplingConstant[ChPT2[4],10] is one of the constants of the -fourth order ChPT lagrangian"; - -H1::usage = -"H1 := CouplingConstant[ChPT2[4],11] is one of the constants of the -fourth order ChPT lagrangian"; - -H2::usage = -"H2 := CouplingConstant[ChPT2[4],12] is one of the constants of the -fourth order ChPT lagrangian"; - -(* ---------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Abbreviations *) - -L1 = CouplingConstant[ChPT2[4],1]; -L2 = CouplingConstant[ChPT2[4],2]; -L3 = CouplingConstant[ChPT2[4],3]; -L4 = CouplingConstant[ChPT2[4],4]; -L5 = CouplingConstant[ChPT2[4],5]; -L6 = CouplingConstant[ChPT2[4],6]; -L7 = CouplingConstant[ChPT2[4],7]; -L8 = CouplingConstant[ChPT2[4],8]; -L9 = CouplingConstant[ChPT2[4],9]; -L10 = CouplingConstant[ChPT2[4],10]; -H1 = CouplingConstant[ChPT2[4],11]; -H2 = CouplingConstant[ChPT2[4],12]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPT2[4],11,st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["H",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPT2[4],12,st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["H",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[2]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPT2[4],i_,st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["L",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* ---------------------------------------------------------------- *) - -RenormalizationCoefficients[ChPT2[4]] := - {1/12,1/6,0,1/8,1/4,3/32,0,0,1/6,-1/6,-1/12,0}; - -(* ---------------------------------------------------------------- *) - -Lagrangian[ChPT2[4]] := - L1[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]]], - UTrace[ NM[CDr[MM,{\[Nu]}],Adjoint[CDr[MM,{\[Nu]}]]] ] ]+ - - L2[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]] ], - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]] ] ]+ - - L3[0]* - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]], - CDr[MM,{\[Nu]}],Adjoint[CDr[MM,{\[Nu]}]]] ]+ - - L4[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]]], - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] ]+ - - L5[0]* - UTrace[ NM[NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]], - NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]]] ]+ - - L6[0]* - NM[UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] , - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] ]+ - - L7[0]* - NM[UTrace[ NM[UChiMatrix,Adjoint[MM]]-NM[MM,Adjoint[UChiMatrix]] ] , - UTrace[ NM[UChiMatrix,Adjoint[MM]]-NM[MM,Adjoint[UChiMatrix]] ] ]+ - - L8[0]* - UTrace[ NM[UChiMatrix,Adjoint[MM],UChiMatrix,Adjoint[MM]]+ - NM[MM,Adjoint[UChiMatrix],MM,Adjoint[UChiMatrix]] ]+ - - L9[0]*I* - UTrace[ NM[FST[LeftComponent[0],{\[Mu]},{\[Nu]}], - CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]]+ - NM[FST[RightComponent[0],{\[Mu]},{\[Nu]}], - Adjoint[CDr[MM,{\[Mu]}]],CDr[MM,{\[Nu]}]] ]+ - - L10[0]* - UTrace[ NM[FST[LeftComponent[0],{\[Mu]},{\[Nu]}],MM, - FST[RightComponent[0],{\[Mu]},{\[Nu]}],Adjoint[MM]] ]+ - - H1[0]* - UTrace[ NM[FST[LeftComponent[0],{\[Mu]},{\[Nu]}],FST[LeftComponent[0],{\[Mu]},{\[Nu]}]]+ - NM[FST[RightComponent[0],{\[Mu]},{\[Nu]}],FST[RightComponent[0],{\[Mu]},{\[Nu]}]] ]+ - - H2[0]* - UTrace[ NM[Adjoint[UChiMatrix],UChiMatrix] ]; - -(* ---------------------------------------------------------------- *) - -$Lagrangians = Union[$Lagrangians,{ChPT2[4]}]; - -FieldsSet[ChPT2[4]] := - {IsoVector[ - QuantumField[Particle[Pion,RenormalizationState[0]]] - ]}; diff --git a/FeynCalc/Phi/Lagrangians/ChPT32.m b/FeynCalc/Phi/Lagrangians/ChPT32.m deleted file mode 100644 index a9a843401..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPT32.m +++ /dev/null @@ -1,55 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPT32 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 1997 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The simplest ChPT lagrangian. - - Taken from J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge -*) - - -Begin["Phi`Objects`"]; - -(* --------------------------------------------------------------- *) - -ChPT32::usage = -"ChPT32.m is the name of the file containing the definitions for -Lagrangian[ChPT3[2]], which is the SU(3) lowest order ChPT -lagrangian. To evaluate use ArgumentsSupply."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ChPT3[2]] := - 1/4*DecayConstant[PhiMeson,RenormalizationState[0]]^2* - - (UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]] ] + - - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ]); - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPT3[2]] := - {IsoVector[ - QuantumField[Particle[PhiMeson,RenormalizationState[0]]] - ]}; - -$Lagrangians = Union[$Lagrangians,{ChPT3[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/ChPT34.m b/FeynCalc/Phi/Lagrangians/ChPT34.m deleted file mode 100644 index 84ddbc5af..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPT34.m +++ /dev/null @@ -1,225 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPT34 *) -(* *) -(* ************************************************************** *) - -(* -Author: Frederik Orellana - -Year: 1997 - -Mathematica Version: 3.0 - -Requirements: Feyncalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The ChPT lagrangian for pion to fourth - order in the energy (mass). - - Taken from J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge - -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPT34::usage = -"ChPT34.m is the name of the file containing the definitions for -Lagrangian[ChPT3[4]], which is the mesonic ChPT lagrangian to fourth -order in the energy, first written down by Gasser and Leutwyler. -To evaluate use ArgumentsSupply."; - -L1::usage = -"L1 := CouplingConstant[ChPT3[4],1] is one of the constants of the -fourth order ChPT lagrangian."; - -L2::usage = -"L2 := CouplingConstant[ChPT3[4],2] is one of the constants of the -fourth order ChPT lagrangian."; - -L3::usage = -"L3 := CouplingConstant[ChPT3[4],3] is one of the constants of the -fourth order ChPT lagrangian."; - -L4::usage = -"L4 := CouplingConstant[ChPT3[4],4] is one of the constants of the -fourth order ChPT lagrangian."; - -L5::usage = -"L5 := CouplingConstant[ChPT3[4],5] is one of the constants of the -fourth order ChPT lagrangian."; - -L6::usage = -"L6 := CouplingConstant[ChPT3[4],6] is one of the constants of the -fourth order ChPT lagrangian."; - -L7::usage = -"L7 := CouplingConstant[ChPT3[4],7] is one of the constants of the -fourth order ChPT lagrangian."; - -L8::usage = -"L8 := CouplingConstant[ChPT3[4],8] is one of the constants of the -fourth order ChPT lagrangian."; - -L9::usage = -"L9 := CouplingConstant[ChPT3[4],9] is one of the constants of the -fourth order ChPT lagrangian."; - -L10::usage = -"L10 := CouplingConstant[ChPT3[4],10] is one of the constants of the -fourth order ChPT lagrangian."; - -H1::usage = -"H1 := CouplingConstant[ChPT3[4],11] is one of the constants of the -fourth order ChPT lagrangian."; - -H2::usage = -"H2 := CouplingConstant[ChPT3[4],12] is one of the constants of the -fourth order ChPT lagrangian."; - -(* ---------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Abbreviations *) - -L1 = CouplingConstant[ChPT3[4],1]; -L2 = CouplingConstant[ChPT3[4],2]; -L3 = CouplingConstant[ChPT3[4],3]; -L4 = CouplingConstant[ChPT3[4],4]; -L5 = CouplingConstant[ChPT3[4],5]; -L6 = CouplingConstant[ChPT3[4],6]; -L7 = CouplingConstant[ChPT3[4],7]; -L8 = CouplingConstant[ChPT3[4],8]; -L9 = CouplingConstant[ChPT3[4],9]; -L10 = CouplingConstant[ChPT3[4],10]; -H1 = CouplingConstant[ChPT3[4],11]; -H2 = CouplingConstant[ChPT3[4],12]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPT3[4],11,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["H",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPT3[4],12,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["H",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[2]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPT3[4],i_,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["L",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* ---------------------------------------------------------------- *) - -RenormalizationCoefficients[ChPT3[4]] := - {3/32,3/16,0,1/8,3/8,11/144,0,5/48,1/4,-1/4,-1/8,5/24}; - -(* ---------------------------------------------------------------- *) - -Lagrangian[ChPT3[4]] := - L1[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]]], - UTrace[ NM[CDr[MM,{\[Nu]}],Adjoint[CDr[MM,{\[Nu]}]]] ] ]+ - - L2[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]] ], - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]] ] ]+ - - L3[0]* - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]], - CDr[MM,{\[Nu]}],Adjoint[CDr[MM,{\[Nu]}]]] ]+ - - L4[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]]], - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] ]+ - - L5[0]* - UTrace[ NM[NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]], - NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]]] ]+ - - L6[0]* - NM[UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] , - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] ]+ - - L7[0]* - NM[UTrace[ NM[UChiMatrix,Adjoint[MM]]-NM[MM,Adjoint[UChiMatrix]] ] , - UTrace[ NM[UChiMatrix,Adjoint[MM]]-NM[MM,Adjoint[UChiMatrix]] ] ]+ - - L8[0]* - UTrace[ NM[UChiMatrix,Adjoint[MM],UChiMatrix,Adjoint[MM]]+ - NM[MM,Adjoint[UChiMatrix],MM,Adjoint[UChiMatrix]] ]+ - - (* Electromagnetic case *) - - (*L9[0]*I* - UTrace[ - - NM[FieldStrengthTensor[{\[Mu]},QuantumField[Particle[Photon],{\[Nu]}]], - UQuarkChargeMatrix, - CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]] + - - NM[FieldStrengthTensor[{\[Mu]},QuantumField[Particle[Photon],{\[Nu]}]], - UQuarkChargeMatrix, - Adjoint[CDr[MM,{\[Mu]}]],CDr[MM,{\[Nu]}]] - - ]*) - - (* General case *) - - L9[0]*I* - UTrace[ NM[FST[LeftComponent[0],{\[Mu]},{\[Nu]}], - CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]]+ - NM[FST[RightComponent[0],{\[Mu]},{\[Nu]}], - Adjoint[CDr[MM,{\[Mu]}]],CDr[MM,{\[Nu]}]] ]+ - - L10[0]* - UTrace[ NM[FST[LeftComponent[0],{\[Mu]},{\[Nu]}],MM, - FST[RightComponent[0],{\[Mu]},{\[Nu]}],Adjoint[MM]] ]+ - - H1[0]* - UTrace[ NM[FST[LeftComponent[0],{\[Mu]},{\[Nu]}],FST[LeftComponent[0],{\[Mu]},{\[Nu]}]]+ - NM[FST[RightComponent[0],{\[Mu]},{\[Nu]}],FST[RightComponent[0],{\[Mu]},{\[Nu]}]] ]+ - - H2[0]* - UTrace[ NM[Adjoint[UChiMatrix],UChiMatrix] ]; - -(* ---------------------------------------------------------------- *) - -$Lagrangians = Union[$Lagrangians,{ChPT3[4]}]; - -FieldsSet[ChPT3[4]] := - {IsoVector[ - QuantumField[Particle[PhiMeson,RenormalizationState[0]]] - ]}; diff --git a/FeynCalc/Phi/Lagrangians/ChPTEM22.m b/FeynCalc/Phi/Lagrangians/ChPTEM22.m deleted file mode 100644 index fa19ccab1..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTEM22.m +++ /dev/null @@ -1,85 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPTEM22 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 2001 - -Mathematica Version: 4.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The leading order ChPT lagrangian with - electromagnetic couplings. - - Taken from U. Meissner, G. Mueller, - S. Steininger, hep-ph/9704377 -*) - - -Begin["Phi`Objects`"]; - -ChPTEM22::usage = -"ChPT22 is the name of the file containing the definitions for -Lagrangian[ChPT2EM[2]], which is the leading order pionic -SU(2) ChPT lagrangian with couplings to virtual photons. -To evaluate use ArgumentsSupply."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -pt/:MakeBoxes[pt[a_],TraditionalForm]:=MakeBoxes[TraditionalForm[a]]; -pt/:MakeBoxes[pt[],TraditionalForm]:=""; -pt/:MakeBoxes[pt[RenormalizationState[1]],TraditionalForm]:="r"; -pt/:MakeBoxes[pt[RenormalizationState[0]],TraditionalForm]:=""; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTEM2[2],st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SuperscriptBox[MakeBoxes[StyleForm["C",FontSlant->"Italic"]][[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[pt[st]]]},{ - MakeBoxes[TraditionalForm[pt[sc]]]},{ - MakeBoxes[TraditionalForm[pt[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ChPTEM2[2]] := - 1/4*DecayConstant[Pion]^2* - - (UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]] ] + - - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[Adjoint[UChiMatrix],MM] ]) - - - 1/4* - NM[FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]]]- - - $Gauge/2* - FDr[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]],{\[Mu]}]* - FDr[QuantumField[Particle[Photon],LorentzIndex[\[Nu]]],{\[Nu]}]+ - - CouplingConstant[ChPTEM2[2]]* - UTrace[NM[UMatrix[UChiralSpurionRight],MM, - UMatrix[UChiralSpurionLeft],Adjoint[MM]]]; - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPTEM2[2]] := - {IsoVector[QuantumField[Particle[Pion]]], QuantumField[Particle[Photon]]}; - -$Lagrangians = Union[$Lagrangians,{ChPTEM2[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/ChPTEM24.m b/FeynCalc/Phi/Lagrangians/ChPTEM24.m deleted file mode 100644 index 2b0f1f6fd..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTEM24.m +++ /dev/null @@ -1,244 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTEM24 *) -(* *) -(* ************************************************************** *) - -(* -Author: Frederik Orellana - -Year: 2001 - -Mathematica Version: 4.0 - -Requirements: Feyncalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The next to leading order ChPT lagrangian - with electromagnetic couplings. - - Taken from U. Meissner, G. Mueller, - S. Steininger, hep-ph/9704377 -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPTEM24::usage = -"ChPTEM24.m is the name of the file containing the definitions for -Lagrangian[ChPTEM2[4]], which is the pionic ChPT lagrangian -including virtual photons to fourth order in the energy. -To evaluate use ArgumentsSupply."; - -K1::usage = -"K1 := CouplingConstant[ChPTEM2[4],1] is one of the constants of the -fourth order ChPT lagrangian."; - -K2::usage = -"K2 := CouplingConstant[ChPTEM2[4],2] is one of the constants of the -fourth order ChPT lagrangian."; - -K3::usage = -"K3 := CouplingConstant[ChPTEM2[4],3] is one of the constants of the -fourth order ChPT lagrangian."; - -K4::usage = -"K4 := CouplingConstant[ChPTEM2[4],4] is one of the constants of the -fourth order ChPT lagrangian."; - -K5::usage = -"K5 := CouplingConstant[ChPTEM2[4],5] is one of the constants of the -fourth order ChPT lagrangian."; - -K6::usage = -"K6 := CouplingConstant[ChPTEM2[4],6] is one of the constants of the -fourth order ChPT lagrangian."; - -K7::usage = -"K7 := CouplingConstant[ChPTEM2[4],7] is one of the constants of the -fourth order ChPT lagrangian."; - -K8::usage = -"K8 := CouplingConstant[ChPTEM2[4],8] is one of the constants of the -fourth order ChPT lagrangian."; - -K9::usage = -"K9 := CouplingConstant[ChPTEM2[4],9] is one of the constants of the -fourth order ChPT lagrangian."; - -K10::usage = -"K10 := CouplingConstant[ChPTEM2[4],10] is one of the constants of the -fourth order ChPT lagrangian."; - -K11::usage = -"K11 := CouplingConstant[ChPTEM2[4],11] is one of the constants of the -fourth order ChPT lagrangian."; - -K12::usage = -"K12 := CouplingConstant[ChPTEM2[4],12] is one of the constants of the -fourth order ChPT lagrangian."; - -K13::usage = -"K13 := CouplingConstant[ChPTEM2[4],13] is one of the constants of the -fourth order ChPT lagrangian."; - -K14::usage = -"K14 := CouplingConstant[ChPTEM2[4],14] is one of the constants of the -fourth order ChPT lagrangian."; - -K15::usage = -"K15 := CouplingConstant[ChPTEM2[4],15] is one of the constants of the -fourth order ChPT lagrangian."; - - -(* ---------------------------------------------------------------- *) - -End[]; - - -(* ---------------------------------------------------------------- *) - -(* Abbreviations *) - -K1 = CouplingConstant[ChPTEM2[4],1]; -K2 = CouplingConstant[ChPTEM2[4],2]; -K3 = CouplingConstant[ChPTEM2[4],3]; -K4 = CouplingConstant[ChPTEM2[4],4]; -K5 = CouplingConstant[ChPTEM2[4],5]; -K6 = CouplingConstant[ChPTEM2[4],6]; -K7 = CouplingConstant[ChPTEM2[4],7]; -K8 = CouplingConstant[ChPTEM2[4],8]; -K9 = CouplingConstant[ChPTEM2[4],9]; -K10 = CouplingConstant[ChPTEM2[4],10]; -K11 = CouplingConstant[ChPTEM2[4],11]; -K12 = CouplingConstant[ChPTEM2[4],12]; -K13 = CouplingConstant[ChPTEM2[4],13]; -K14 = CouplingConstant[ChPTEM2[4],14]; -K15 = CouplingConstant[ChPTEM2[4],15]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTEM2[4],i_,st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["k",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* ---------------------------------------------------------------- *) - -RenormalizationCoefficients[ChPTEM2[4]] = -{3/2+3*z+12*z^2, 2*z, -3/4, -2*z, -1/4, 0, 1/4+2*z, -1/8(*-z*)(*I think the -z is a bug?!?*)(*Yes, it's not in the published version*), --3-3*z/5-12*z^2/5, -27/20-z/5, -1/4-z/5, 0, 3/2-12*z/5+84*z^2/25, 0, 1/30} /. -z -> CouplingConstant[ChPTEM2[2],RenormalizationState[0]]/ -DecayConstant[Pion,RenormalizationState[0]]^4; - -(* ---------------------------------------------------------------- *) - -Lagrangian[ChPTEM2[4]] := - K1[0]* - DecayConstant[Pion]^4* - NMPower[UTrace[ NM[UMatrix[UChiralSpurion],MM, - UMatrix[UChiralSpurion],Adjoint[MM]]],2]+ - - K2[0]* - DecayConstant[Pion]^2* - NM[UTrace[ NM[UMatrix[UChiralSpurion],MM, - UMatrix[UChiralSpurion],Adjoint[MM]]], - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]] ]]+ - - K3[0]* - DecayConstant[Pion]^2* - (NMPower[UTrace[ NM[Adjoint[MM],CDr[MM,{\[Mu]}],UMatrix[UChiralSpurion]] ],2] + - NMPower[UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[MM],UMatrix[UChiralSpurion]] ],2])+ - - K4[0]* - DecayConstant[Pion]^2* - NM[UTrace[ NM[Adjoint[MM],CDr[MM,{\[Mu]}],UMatrix[UChiralSpurion]] ], - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[MM],UMatrix[UChiralSpurion]] ]]+ - - K5[0]* - DecayConstant[Pion]^2* - UTrace[NM[(NM[UMatrix[UChiralSpurion], CDr[UMatrix[UChiralSpurion],{\[Mu]}]]- - NM[CDr[UMatrix[UChiralSpurion],{\[Mu]}], UMatrix[UChiralSpurion]]), - Adjoint[MM], CDr[MM,{\[Mu]}]] - - - NM[(NM[UMatrix[UChiralSpurion], CDr[UMatrix[UChiralSpurion],{\[Mu]}]]- - NM[CDr[UMatrix[UChiralSpurion],{\[Mu]}], UMatrix[UChiralSpurion]]), - CDr[MM,{\[Mu]}], Adjoint[MM]] ]+ - - K6[0]* - DecayConstant[Pion]^2* - UTrace[NM[CDr[UMatrix[UChiralSpurion],{\[Mu]}], MM, - CDr[UMatrix[UChiralSpurion],{\[Mu]}], Adjoint[MM]] ]+ - - K7[0]* - DecayConstant[Pion]^2* - NM[UTrace[ NM[UMatrix[UChiralSpurion],MM, - UMatrix[UChiralSpurion],Adjoint[MM]] ], - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[Adjoint[UChiMatrix],MM] ]]+ - - K8[0]* - DecayConstant[Pion]^2* - UTrace[ NM[NM[Adjoint[MM],UChiMatrix]-NM[Adjoint[UChiMatrix],MM], - NM[Adjoint[MM],UMatrix[UChiralSpurion],MM,UMatrix[UChiralSpurion]]- - NM[UMatrix[UChiralSpurion],Adjoint[MM],UMatrix[UChiralSpurion],MM]] ]+ - - K9[0]* - DecayConstant[Pion]^4* - NM[UTrace[ NMPower[UMatrix[UChiralSpurion], 2] ], - UTrace[ NM[UMatrix[UChiralSpurion],MM,UMatrix[UChiralSpurion],Adjoint[MM]] ]]+ - - K10[0]* - DecayConstant[Pion]^2* - NM[UTrace[ NMPower[UMatrix[UChiralSpurion], 2] ], - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]] ]]+ - - K11[0]* - DecayConstant[Pion]^2* - NM[UTrace[ NMPower[UMatrix[UChiralSpurion], 2] ], - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ]]+ - - K12[0]* - DecayConstant[Pion]^2* - UTrace[ NM[CDr[UMatrix[UChiralSpurionRight], {\[Mu]}], - CDr[UMatrix[UChiralSpurionRight], {\[Mu]}] ] + - NM[CDr[UMatrix[UChiralSpurionLeft], {\[Mu]}], - CDr[UMatrix[UChiralSpurionLeft], {\[Mu]}] ] ]+ - - K13[0]* - DecayConstant[Pion]^4* - NMPower[UTrace[ NM[UMatrix[UChiralSpurion],UMatrix[UChiralSpurion]] ],2]+ - - K14[0]* - DecayConstant[Pion]^2* - NM[ - UTrace[ NM[NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]],UMatrix[UChiralSpurion]] + - NM[NM[Adjoint[UChiMatrix],MM]+NM[Adjoint[MM],UChiMatrix],UMatrix[UChiralSpurion]] ], - UTrace[UMatrix[UChiralSpurion] ] - ]+ - - K15[0]* - UTrace[NMPower[UMatrix[UChiralSpurion],2]]* - NM[FieldStrengthTensor[{\[Mu]}, QuantumField[Particle[Photon],{\[Nu]}]], - FieldStrengthTensor[{\[Mu]}, QuantumField[Particle[Photon],{\[Nu]}]]]; - - -(* ---------------------------------------------------------------- *) - -$Lagrangians = Union[$Lagrangians,{ChPTEM2[4]}]; - -FieldsSet[ChPTEM2[4]] := - {IsoVector[QuantumField[Particle[Pion,RenormalizationState[0]]]], - QuantumField[Particle[Photon,RenormalizationState[0]]]}; - diff --git a/FeynCalc/Phi/Lagrangians/ChPTPhoton22.m b/FeynCalc/Phi/Lagrangians/ChPTPhoton22.m deleted file mode 100644 index 098391a74..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTPhoton22.m +++ /dev/null @@ -1,56 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPTPhoton22 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 1997 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The simplest ChPT lagrangian. - - Taken from J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge -*) - - -Begin["Phi`Objects`"]; - -(* --------------------------------------------------------------- *) - -ChPTPhoton22::usage = -"ChPTPhoton22.m is the name of the file containing the definitions for -Lagrangian[ChPT2PhotonPhoton[2]], which is the SU(2) lowest order ChPT -lagrangian with coupling to a photon. To evaluate use ArgumentsSupply."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ChPTPhoton2[2]] := - 1/4*DecayConstant[Pion,RenormalizationState[0]]^2* - - (UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]] ] + - - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ]); - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPTPhoton2[2]] := - {IsoVector[ - QuantumField[Particle[Pion,RenormalizationState[0]]], - QuantumField[Particle[Photon,RenormalizationState[0]],LorentzIndex[\[Mu]]] - ]}; - -$Lagrangians = Union[$Lagrangians,{ChPTPhoton2[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/ChPTPhoton24.m b/FeynCalc/Phi/Lagrangians/ChPTPhoton24.m deleted file mode 100644 index 7fac70790..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTPhoton24.m +++ /dev/null @@ -1,219 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTPhoton24 *) -(* *) -(* ************************************************************** *) - -(* -Author: Frederik Orellana - -Year: 1999 - -Mathematica Version: 3.0 - -Requirements: Feyncalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The ChPT lagrangian for pion to fourth - order in the energy (mass). - - Taken from J.F. Donoghue, E. Golowich - and B.R. Holstein (1992), "Dynamics of - the Standard Model", Cambridge - -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPTPhoton24::usage = -"ChPTPhoton24.m is the name of the file containing the definitions for -Lagrangian[ChPTPhoton2[4]], which is the pionic ChPT lagrangian to -fourth order in the energy, first written down by -Gasser and Leutwyler. To evaluate use ArgumentsSupply."; - -L1::usage = -"L1 := CouplingConstant[ChPTPhoton2[4],1] is one of the constants of the -fourth order ChPT lagrangian."; - -L2::usage = -"L2 := CouplingConstant[ChPTPhoton2[4],2] is one of the constants of the -fourth order ChPT lagrangian."; - -L3::usage = -"L3 := CouplingConstant[ChPTPhoton2[4],3] is one of the constants of the -fourth order ChPT lagrangian."; - -L4::usage = -"L4 := CouplingConstant[ChPTPhoton2[4],4] is one of the constants of the -fourth order ChPT lagrangian."; - -L5::usage = -"L5 := CouplingConstant[ChPTPhoton2[4],5] is one of the constants of the -fourth order ChPT lagrangian."; - -L6::usage = -"L6 := CouplingConstant[ChPTPhoton2[4],6] is one of the constants of the -fourth order ChPT lagrangian."; - -L7::usage = -"L7 := CouplingConstant[ChPTPhoton2[4],7] is one of the constants of the -fourth order ChPT lagrangian."; - -L8::usage = -"L8 := CouplingConstant[ChPTPhoton2[4],8] is one of the constants of the -fourth order ChPT lagrangian."; - -L9::usage = -"L9 := CouplingConstant[ChPTPhoton2[4],9] is one of the constants of the -fourth order ChPT lagrangian."; - -L10::usage = -"L10 := CouplingConstant[ChPTPhoton2[4],10] is one of the constants of the -fourth order ChPT lagrangian."; - -H1::usage = -"H1 := CouplingConstant[ChPTPhoton2[4],11] is one of the constants of the -fourth order ChPT lagrangian."; - -H2::usage = -"H2 := CouplingConstant[ChPTPhoton2[4],12] is one of the constants of the -fourth order ChPT lagrangian."; - -(* ---------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Abbreviations *) - -L1 = CouplingConstant[ChPTPhoton2[4],1]; -L2 = CouplingConstant[ChPTPhoton2[4],2]; -L3 = CouplingConstant[ChPTPhoton2[4],3]; -L4 = CouplingConstant[ChPTPhoton2[4],4]; -L5 = CouplingConstant[ChPTPhoton2[4],5]; -L6 = CouplingConstant[ChPTPhoton2[4],6]; -L7 = CouplingConstant[ChPTPhoton2[4],7]; -L8 = CouplingConstant[ChPTPhoton2[4],8]; -L9 = CouplingConstant[ChPTPhoton2[4],9]; -L10 = CouplingConstant[ChPTPhoton2[4],10]; -H1 = CouplingConstant[ChPTPhoton2[4],11]; -H2 = CouplingConstant[ChPTPhoton2[4],12]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTPhoton2[4],11,st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["H",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTPhoton2[4],12,st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["H",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[2]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTPhoton2[4],i_,st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["L",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* ---------------------------------------------------------------- *) - -RenormalizationCoefficients[ChPTPhoton2[4]] := - {1/12,1/6,0,1/8,1/4,3/32,0,0,1/6,-1/6}; - -(* ---------------------------------------------------------------- *) - -Lagrangian[ChPTPhoton2[4]] := - L1[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]]], - UTrace[ NM[CDr[MM,{\[Nu]}],Adjoint[CDr[MM,{\[Nu]}]]] ] ]+ - - L2[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]] ], - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]] ] ]+ - - L3[0]* - UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]], - CDr[MM,{\[Nu]}],Adjoint[CDr[MM,{\[Nu]}]]] ]+ - - L4[0]* - NM[ UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]]], - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] ]+ - - L5[0]* - UTrace[ NM[NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]], - NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]]] ]+ - - L6[0]* - NM[UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] , - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[MM,Adjoint[UChiMatrix]] ] ]+ - - L7[0]* - NM[UTrace[ NM[Adjoint[UChiMatrix],MM]-NM[Adjoint[MM],UChiMatrix] ] , - UTrace[ NM[Adjoint[UChiMatrix],MM]-NM[Adjoint[MM],UChiMatrix] ] ]+ - - L8[0]* - UTrace[ NM[UChiMatrix,Adjoint[MM],UChiMatrix,Adjoint[MM]]+ - NM[MM,Adjoint[UChiMatrix],MM,Adjoint[UChiMatrix]] ]+ - - L9[0]*I* - UTrace[ - NM[FieldStrengthTensor[{\[Mu]},QuantumField[Particle[Photon],{\[Nu]}]], - UQuarkChargeMatrix, - CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Nu]}]]]+ - - NM[FieldStrengthTensor[{\[Mu]},QuantumField[Particle[Photon],{\[Nu]}]], - UQuarkChargeMatrix, - Adjoint[CDr[MM,{\[Mu]}]],CDr[MM,{\[Nu]}]] ]+ - - L10[0]* - UTrace[ - NM[FieldStrengthTensor[{\[Mu]},QuantumField[Particle[Photon],{\[Nu]}]], - UQuarkChargeMatrix,MM, - FieldStrengthTensor[{\[Mu]},QuantumField[Particle[Photon],{\[Nu]}]], - UQuarkChargeMatrix,Adjoint[MM]] ]+ - - H1[0]* - 2*UTrace[ - NM[FieldStrengthTensor[{\[Mu]},QuantumField[Particle[Photon],{\[Nu]}]], - UQuarkChargeMatrix, - FieldStrengthTensor[{\[Mu]},QuantumField[Particle[Photon],{\[Nu]}]], - UQuarkChargeMatrix] ]+ - - H2[0]* - UTrace[ NM[Adjoint[UChiMatrix],UChiMatrix] ]; - -(* ---------------------------------------------------------------- *) - -$Lagrangians = Union[$Lagrangians,{ChPTPhoton2[4]}]; - -FieldsSet[ChPTPhoton2[4]] := - {IsoVector[ - QuantumField[Particle[Pion,RenormalizationState[0]]], - QuantumField[Particle[Photon,RenormalizationState[0]],LorentzIndex[\[Mu]]] - ]}; diff --git a/FeynCalc/Phi/Lagrangians/ChPTPhotonsLeptons32.m b/FeynCalc/Phi/Lagrangians/ChPTPhotonsLeptons32.m deleted file mode 100644 index 196329d65..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTPhotonsLeptons32.m +++ /dev/null @@ -1,106 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPTPhotonsLeptons32 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 2002 - -Mathematica Version: 4.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The leading order ChPT lagrangian with - electromagnetic couplings. - - Taken from - M. Knecht, H. Neufeld, H. Rupertsberger, P. Talavera - (1999), hep-ph/9909284 -*) - - -Begin["Phi`Objects`"]; - -ChPTPhotonsLeptons32::usage = -"ChPTPhotonsLeptons32 is the name of the file containing the definitions for \ -Lagrangian[ChPTPhotonsLeptons3[2]], which is the leading order mesonic \ -SU(3) ChPT lagrangian with couplings to virtual photons and leptons. \ -To evaluate use ArgumentsSupply."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -pt/:MakeBoxes[pt[a_],TraditionalForm]:=MakeBoxes[TraditionalForm[a]]; -pt/:MakeBoxes[pt[],TraditionalForm]:=""; -pt/:MakeBoxes[pt[RenormalizationState[1]],TraditionalForm]:="r"; -pt/:MakeBoxes[pt[RenormalizationState[0]],TraditionalForm]:=""; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTPhotonsLeptons3[2],st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SuperscriptBox[MakeBoxes[StyleForm["C",FontSlant->"Italic"]][[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[pt[st]]]},{ - MakeBoxes[TraditionalForm[pt[sc]]]},{ - MakeBoxes[TraditionalForm[pt[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ -ChPTPhotonsLeptons3[2]] := - 1/4*DecayConstant[PhiMeson]^2* - - (UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]] ] + - - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[Adjoint[UChiMatrix],MM] ]) - - - 1/4* - NM[FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]]]- - - $Gauge/2* - FDr[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]],{\[Mu]}]* - FDr[QuantumField[Particle[Photon],LorentzIndex[\[Nu]]],{\[Nu]}]+ - - CouplingConstant[ChPTPhotonsLeptons3[2]]* - UTrace[NM[UChiralSpurionRightMatrix,MM, - UChiralSpurionLeftMatrix,Adjoint[MM]]]+ - - DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - (I*QuantumField[FCPartialD[LorentzIndex[\[Mu]]], - Particle[Lepton],SUNIndex[i]]+ - CouplingConstant[QED[1]]* - DOT[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]], - QuantumField[Particle[Lepton],SUNIndex[i]]])]- - - ParticleMass[Lepton,SUNIndex[i]]* - DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - QuantumField[Particle[Lepton],SUNIndex[i]]]+ - - DOT[DiracBar[QuantumField[Particle[Neutrino],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - DiracMatrix[6], - I*QuantumField[FCPartialD[LorentzIndex[\[Mu]]], - Particle[Neutrino],SUNIndex[i]]]; - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPTPhotonsLeptons3[2]] := - {IsoVector[QuantumField[Particle[PhiMeson]]], - QuantumField[Particle[Photon]]}; - -$Lagrangians = Union[$Lagrangians,{ChPTPhotonsLeptons3[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/ChPTPhotonsLeptons34.m b/FeynCalc/Phi/Lagrangians/ChPTPhotonsLeptons34.m deleted file mode 100644 index c3d09c52e..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTPhotonsLeptons34.m +++ /dev/null @@ -1,522 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTPhotonsLeptons34 *) -(* *) -(* ************************************************************** *) - -(* -Author: Frederik Orellana - -Year: 2002 - -Mathematica Version: 4.0 - -Requirements: Feyncalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The next to leading order ChPT lagrangian - with electromagnetic couplings. - - Taken from - M. Knecht, H. Neufeld, H. Rupertsberger, P. Talavera - (1999), hep-ph/9909284 -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPTPhotonsLeptons34::usage = -"ChPTPhotonsLeptons34 is the name of the file containing the definitions for \ -Lagrangian[ChPTPhotonsLeptons3[4]], which is the next-to-leading order mesonic \ -SU(3) ChPT lagrangian with couplings to virtual photons and leptons. \ -To evaluate use ArgumentsSupply."; - -L1::usage = -"L1 := CouplingConstant[ChPTPhotonsLeptons3[4],1] is one of the constants of the -fourth order ChPT lagrangian."; - -L2::usage = -"L2 := CouplingConstant[ChPTPhotonsLeptons3[4],2] is one of the constants of the -fourth order ChPT lagrangian."; - -L3::usage = -"L3 := CouplingConstant[ChPTPhotonsLeptons3[4],3] is one of the constants of the -fourth order ChPT lagrangian."; - -L4::usage = -"L4 := CouplingConstant[ChPTPhotonsLeptons3[4],4] is one of the constants of the -fourth order ChPT lagrangian."; - -L5::usage = -"L5 := CouplingConstant[ChPTPhotonsLeptons3[4],5] is one of the constants of the -fourth order ChPT lagrangian."; - -L6::usage = -"L6 := CouplingConstant[ChPTPhotonsLeptons3[4],6] is one of the constants of the -fourth order ChPT lagrangian."; - -L7::usage = -"L7 := CouplingConstant[ChPTPhotonsLeptons3[4],7] is one of the constants of the -fourth order ChPT lagrangian."; - -L8::usage = -"L8 := CouplingConstant[ChPTPhotonsLeptons3[4],8] is one of the constants of the -fourth order ChPT lagrangian."; - -L9::usage = -"L9 := CouplingConstant[ChPTPhotonsLeptons3[4],9] is one of the constants of the -fourth order ChPT lagrangian."; - -L10::usage = -"L10 := CouplingConstant[ChPTPhotonsLeptons3[4],10] is one of the constants of the -fourth order ChPT lagrangian."; - -H1::usage = -"H1 := CouplingConstant[ChPTPhotonsLeptons3[4],11] is one of the constants of the -fourth order ChPT lagrangian."; - -H2::usage = -"H2 := CouplingConstant[ChPTPhotonsLeptons3[4],12] is one of the constants of the -fourth order ChPT lagrangian."; - -K1::usage = -"K1 := CouplingConstant[ChPTPhotonsLeptons3[4],13] is one of the constants of the -fourth order ChPT lagrangian."; - -K2::usage = -"K2 := CouplingConstant[ChPTPhotonsLeptons3[4],14] is one of the constants of the -fourth order ChPT lagrangian."; - -K3::usage = -"K3 := CouplingConstant[ChPTPhotonsLeptons3[4],15] is one of the constants of the -fourth order ChPT lagrangian."; - -K4::usage = -"K4 := CouplingConstant[ChPTPhotonsLeptons3[4],16] is one of the constants of the -fourth order ChPT lagrangian."; - -K5::usage = -"K5 := CouplingConstant[ChPTPhotonsLeptons3[4],17] is one of the constants of the -fourth order ChPT lagrangian."; - -K6::usage = -"K6 := CouplingConstant[ChPTPhotonsLeptons3[4],18] is one of the constants of the -fourth order ChPT lagrangian."; - -K7::usage = -"K7 := CouplingConstant[ChPTPhotonsLeptons3[4],19] is one of the constants of the -fourth order ChPT lagrangian."; - -K8::usage = -"K8 := CouplingConstant[ChPTPhotonsLeptons3[4],20] is one of the constants of the -fourth order ChPT lagrangian."; - -K9::usage = -"K9 := CouplingConstant[ChPTPhotonsLeptons3[4],21] is one of the constants of the -fourth order ChPT lagrangian."; - -K10::usage = -"K10 := CouplingConstant[ChPTPhotonsLeptons3[4],22] is one of the constants of the -fourth order ChPT lagrangian."; - -K11::usage = -"K11 := CouplingConstant[ChPTPhotonsLeptons3[4],23] is one of the constants of the -fourth order ChPT lagrangian."; - -K12::usage = -"K12 := CouplingConstant[ChPTPhotonsLeptons3[4],24] is one of the constants of the -fourth order ChPT lagrangian."; - -K13::usage = -"K13 := CouplingConstant[ChPTPhotonsLeptons3[4],25] is one of the constants of the -fourth order ChPT lagrangian."; - -K14::usage = -"K14 := CouplingConstant[ChPTPhotonsLeptons3[4],26] is one of the constants of the -fourth order ChPT lagrangian."; - -K15::usage = -"K15 := CouplingConstant[ChPTPhotonsLeptons3[4],27] is one of the constants of the -fourth order ChPT lagrangian."; - -K16::usage = -"K16 := CouplingConstant[ChPTPhotonsLeptons3[4],28] is one of the constants of the -fourth order ChPT lagrangian."; - -K17::usage = -"K17 := CouplingConstant[ChPTPhotonsLeptons3[4],29] is one of the constants of the -fourth order ChPT lagrangian."; - -K18::usage = -"K18 := CouplingConstant[ChPTPhotonsLeptons3[4],30] is one of the constants of the -fourth order ChPT lagrangian."; - -K19::usage = -"K19 := CouplingConstant[ChPTPhotonsLeptons3[4],31] is one of the constants of the -fourth order ChPT lagrangian."; - -(* XX1 etc. is used because FeynArts uses Unique["X"] *) - -XX1::usage = -"XX1 := CouplingConstant[ChPTPhotonsLeptons3[4],32] is one of the constants of the -fourth order ChPT lagrangian."; - -XX2::usage = -"XX2 := CouplingConstant[ChPTPhotonsLeptons3[4],33] is one of the constants of the -fourth order ChPT lagrangian."; - -XX3::usage = -"XX3 := CouplingConstant[ChPTPhotonsLeptons3[4],34] is one of the constants of the -fourth order ChPT lagrangian."; - -XX4::usage = -"XX4 := CouplingConstant[ChPTPhotonsLeptons3[4],35] is one of the constants of the -fourth order ChPT lagrangian."; - -XX5::usage = -"XX5 := CouplingConstant[ChPTPhotonsLeptons3[4],36] is one of the constants of the -fourth order ChPT lagrangian."; - -XX6::usage = -"XX6 := CouplingConstant[ChPTPhotonsLeptons3[4],37] is one of the constants of the -fourth order ChPT lagrangian."; - -XX7::usage = -"XX7 := CouplingConstant[ChPTPhotonsLeptons3[4],38] is one of the constants of the -fourth order ChPT lagrangian."; - -(* ---------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Abbreviations *) - -QQ = UQuarkChargeMatrix; - -L1 = CouplingConstant[ChPTPhotonsLeptons3[4],1]; -L2 = CouplingConstant[ChPTPhotonsLeptons3[4],2]; -L3 = CouplingConstant[ChPTPhotonsLeptons3[4],3]; -L4 = CouplingConstant[ChPTPhotonsLeptons3[4],4]; -L5 = CouplingConstant[ChPTPhotonsLeptons3[4],5]; -L6 = CouplingConstant[ChPTPhotonsLeptons3[4],6]; -L7 = CouplingConstant[ChPTPhotonsLeptons3[4],7]; -L8 = CouplingConstant[ChPTPhotonsLeptons3[4],8]; -L9 = CouplingConstant[ChPTPhotonsLeptons3[4],9]; -L10 = CouplingConstant[ChPTPhotonsLeptons3[4],10]; - -H1 = CouplingConstant[ChPTPhotonsLeptons3[4],11]; -H2 = CouplingConstant[ChPTPhotonsLeptons3[4],12]; - -K1 = CouplingConstant[ChPTPhotonsLeptons3[4],13]; -K2 = CouplingConstant[ChPTPhotonsLeptons3[4],14]; -K3 = CouplingConstant[ChPTPhotonsLeptons3[4],15]; -K4 = CouplingConstant[ChPTPhotonsLeptons3[4],16]; -K5 = CouplingConstant[ChPTPhotonsLeptons3[4],17]; -K6 = CouplingConstant[ChPTPhotonsLeptons3[4],18]; -K7 = CouplingConstant[ChPTPhotonsLeptons3[4],19]; -K8 = CouplingConstant[ChPTPhotonsLeptons3[4],20]; -K9 = CouplingConstant[ChPTPhotonsLeptons3[4],21]; -K10 = CouplingConstant[ChPTPhotonsLeptons3[4],22]; -K11 = CouplingConstant[ChPTPhotonsLeptons3[4],23]; -K12 = CouplingConstant[ChPTPhotonsLeptons3[4],24]; -K13 = CouplingConstant[ChPTPhotonsLeptons3[4],25]; -K14 = CouplingConstant[ChPTPhotonsLeptons3[4],26]; -K15 = CouplingConstant[ChPTPhotonsLeptons3[4],27]; -K16 = CouplingConstant[ChPTPhotonsLeptons3[4],28]; -K17 = CouplingConstant[ChPTPhotonsLeptons3[4],29]; -K18 = CouplingConstant[ChPTPhotonsLeptons3[4],30]; -K19 = CouplingConstant[ChPTPhotonsLeptons3[4],31]; - -XX1 = CouplingConstant[ChPTPhotonsLeptons3[4],32]; -XX2 = CouplingConstant[ChPTPhotonsLeptons3[4],33]; -XX3 = CouplingConstant[ChPTPhotonsLeptons3[4],34]; -XX4 = CouplingConstant[ChPTPhotonsLeptons3[4],35]; -XX5 = CouplingConstant[ChPTPhotonsLeptons3[4],36]; -XX6 = CouplingConstant[ChPTPhotonsLeptons3[4],37]; -XX7 = CouplingConstant[ChPTPhotonsLeptons3[4],38]; - - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTPhotonsLeptons3[4],i_?((#<11)&),st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["L",FontSlant->"Italic"]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant /: MakeBoxes[ - CouplingConstant[ChPTPhotonsLeptons3[4], i_?((10<#<13) &), st___RenormalizationState, - sc___RenormalizationScheme, qs___QuarkMassExpansionState], - TraditionalForm] := - Block[ {ii = i - 10, jj}, - SubsuperscriptBox[MakeBoxes[StyleForm["H", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[jj]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]] /. - "jj" -> ToString[ii] - ]; - -CouplingConstant /: MakeBoxes[ - CouplingConstant[ChPTPhotonsLeptons3[4], i_?((12<#<32)&), st___RenormalizationState, - sc___RenormalizationScheme, qs___QuarkMassExpansionState], - TraditionalForm] := - Block[ {ii = i - 12, jj}, - SubsuperscriptBox[MakeBoxes[StyleForm["K", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[jj]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]] /. - "jj" -> ToString[ii] - ]; - -CouplingConstant /: MakeBoxes[ - CouplingConstant[ChPTPhotonsLeptons3[4], i_?((31<#)&), st___RenormalizationState, - sc___RenormalizationScheme, qs___QuarkMassExpansionState], - TraditionalForm] := - Block[ {ii = i - 31, jj}, - SubsuperscriptBox[MakeBoxes[StyleForm["X", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[jj]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]] /. - "jj" -> ToString[ii] - ]; - - -(* ---------------------------------------------------------------- *) - -RenormalizationCoefficients[ChPTPhotonsLeptons3[4]] = -{3/32,3/16,0,1/8,3/8,11/144,0,5/48,1/4,-1/4,-1/8,5/24, -3/4, z, -3/4, 2 z, -9/4, 3/2 z, 0, z, -1/4, 1/4+3/2 z, 1/8, 1/4, 0, 0, 3/2 + 3 z + 20 z^2, -3 -3/2 z -4 z^2, 3/2 - 3/2 z +2 z^2,-2, urechCorrection (*Fill in!!*), -0,-3/4,-3,-3/2,3/2,-5,-1,-4/3} /. -z -> CouplingConstant[ChPTPhotonsLeptons3[2],RenormalizationState[0]]/ -DecayConstant[PhiMeson,RenormalizationState[0]]^4; - -(* ---------------------------------------------------------------- *) - -Lagrangian[ChPTPhotonsLeptons3[4]] := - -(* p^4 *) - L1[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ] ] + - - L2[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}]] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}]] ] ] + - - L3[0]* - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}], - Adjoint[CDr[MM,{\[Nu]}]], CDr[MM,{\[Nu]}]] ] + - - L4[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NM[Adjoint[UChiMatrix],MM] + NM[UChiMatrix, Adjoint[MM]] ] ] + - - L5[0]* - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}], - NM[ Adjoint[UChiMatrix],MM] + NM[Adjoint[MM], UChiMatrix] ] ] + - - L6[0]* - NM[UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[UChiMatrix, Adjoint[MM]] ], - UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[UChiMatrix, Adjoint[MM]] ] ] + - - L7[0]* - NM[UTrace[ NM[Adjoint[UChiMatrix], MM] - NM[UChiMatrix, Adjoint[MM]] ] , - UTrace[ NM[Adjoint[UChiMatrix], MM] - NM[UChiMatrix, Adjoint[MM]] ] ] + - - L8[0]* - UTrace[ NM[Adjoint[UChiMatrix], MM, Adjoint[UChiMatrix], MM] + - NM[UChiMatrix, Adjoint[MM], UChiMatrix, Adjoint[MM]]] - - - L9[0]*I* - UTrace[ NM[CDr[MM,{\[Mu]}], Adjoint[CDr[MM,{\[Nu]}]], GRight[\[Mu],\[Nu]]] + - NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}], GLeft[\[Mu],\[Nu]]] ] + - - L10[0]* - UTrace[ NM[GRight[\[Mu],\[Nu]], MM, GLeft[\[Mu],\[Nu]], Adjoint[MM]] ] + - - H1[0]* - UTrace[ NM[GRight[\[Mu],\[Nu]], GRight[\[Mu],\[Nu]]] + - NM[GLeft[\[Mu],\[Nu]], GLeft[\[Mu],\[Nu]]] ] + - - H2[0]* - UTrace[ NM[Adjoint[UChiMatrix], UChiMatrix] ] + - - (* e^2 p^2 *) - - DecayConstant[PhiMeson]^2*( - - K1[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NMPower[QQ, 2] ] ] + - - K2[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NM[QQ, MM, QQ, Adjoint[MM]] ] ] + - - K3[0]* - (NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ] ] + - NM[ UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ], - UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ] ])+ - - K4[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ], - UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ] ] + - - K5[0]* - UTrace[ NM[NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]]+ - NM[ CDr[MM,{\[Mu]}], Adjoint[CDr[MM,{\[Mu]}]]], - NMPower[QQ, 2]] ] + - - K6[0]* - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}], QQ, Adjoint[MM], QQ, MM] + - NM[CDr[MM,{\[Mu]}], Adjoint[CDr[MM,{\[Mu]}]], QQ, MM, QQ, Adjoint[MM]]] + - - K7[0]* - NM[ UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix] ], - UTrace[ NMPower[QQ, 2] ] ] + - - K8[0]* - NM[ UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix] ], - UTrace[ NM[QQ, MM, QQ, Adjoint[MM]] ] ] + - - K9[0]* - UTrace[ NM[NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix] + - NM[UChiMatrix, Adjoint[MM]] + NM[MM, Adjoint[UChiMatrix]], - NMPower[QQ, 2]] ] + - - K10[0]* - UTrace[ NM[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix], - QQ, Adjoint[MM], QQ, MM] + - NM[ NM[UChiMatrix, Adjoint[MM]] + NM[MM, Adjoint[UChiMatrix]], - QQ, MM, QQ, Adjoint[MM]] ]+ - - K11[0]* - UTrace[ NM[ NM[Adjoint[UChiMatrix], MM] - NM[Adjoint[MM], UChiMatrix], - QQ, Adjoint[MM], QQ, MM ] + - NM[ NM[UChiMatrix, Adjoint[MM]] - NM[MM, Adjoint[UChiMatrix]], - QQ, MM, QQ,Adjoint[MM] ] ] + - - K12[0]* - UTrace[ NM[ Adjoint[CDr[MM,{\[Mu]}]], - NM[CQRight[\[Mu]], QQ] - - NM[QQ, CQRight[\[Mu]]], MM ] + - NM[ CDr[MM,{\[Mu]}], - NM[CQLeft[\[Mu]], QQ] - - NM[QQ, CQLeft[\[Mu]]], Adjoint[MM] ] ] + - - K13[0]* - UTrace[ NM[ CQRight[\[Mu]], MM, CQLeft[\[Mu]], Adjoint[MM] ] ] + - - K14[0]* - UTrace[ NM[ CQRight[\[Mu]], CQRight[\[Mu]] ] + - NM[ CQLeft[\[Mu]], CQLeft[\[Mu]] ] ]+ - - (*Tentative correction of Urech*) - K19[0]* - UTrace[ NM[ Adjoint[CDr[MM,{\[Mu]}]], - QQ, MM, CQLeft[\[Mu]] ] + - NM[CDr[MM,{\[Mu]}], - QQ, Adjoint[MM], CQRight[\[Mu]] ] ] - - ) + - - (* e^4 *) - - DecayConstant[PhiMeson]^4*( - - K15[0]* - NMPower[UTrace[ NM[QQ, MM, QQ, Adjoint[MM]]], 2]+ - - K16[0]* - NM[ UTrace[ NM[QQ, MM, QQ,Adjoint[MM]] ], - UTrace[ NM[QQ, QQ] ] ] + - - K17[0]* - NMPower[UTrace[ NM[QQ, QQ] ], 2] - - ) + - - (* p^2 e^2 photon propagator counterterm *) - (* corresponds to 3/2 times the X_8 term of Knecht, Neufeld, Rupertsberger and Talavera*) - - K18[0]* - UTrace[NMPower[QQ,2]]* - NM[FieldStrengthTensor[{\[Mu]}, QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[{\[Mu]}, QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]]]+ - - (* Lepton terms *) - CouplingConstant[QED[1]]^2* - ( - XX1[0]*DecayConstant[PhiMeson]^2* - NM[DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - DiracMatrix[7], - QuantumField[Particle[Neutrino],SUNIndex[i]]], - UTrace[NM[USmall[\[Mu]],UAntiCommutator[QQ,UChiralSpurionLeft1Matrix]]]]+ - - XX2[0]*DecayConstant[PhiMeson]^2* - NM[DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - DiracMatrix[7], - QuantumField[Particle[Neutrino],SUNIndex[i]]], - UTrace[NM[USmall[\[Mu]],UCommutator[QQ,UChiralSpurionLeft1Matrix]]]]+ - - XX3[0]*DecayConstant[PhiMeson]^2* - ParticleMass[Lepton,SUNIndex[i]]* - NM[DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[7], - QuantumField[Particle[Neutrino],SUNIndex[i]]], - UTrace[NM[UChiralSpurionLeft1Matrix,QQ]]]+ - - XX4[0]*DecayConstant[PhiMeson]^2* - I*NM[DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - DiracMatrix[7], - QuantumField[Particle[Neutrino],SUNIndex[i]]], - UTrace[NM[UChiralSpurionLeft1Matrix,CQLeft[\[Mu]]]]]+ - - XX5[0]*DecayConstant[PhiMeson]^2* - I*NM[DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - DiracMatrix[7], - QuantumField[Particle[Neutrino],SUNIndex[i]]], - UTrace[NM[UChiralSpurionLeft1Matrix,CQRight[\[Mu]]]]]+ - - XX6[0]* - DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - (I*QuantumField[FCPartialD[LorentzIndex[\[Mu]]], - Particle[Lepton],SUNIndex[i]]+ - CouplingConstant[QED[1]]* - DOT[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]], - QuantumField[Particle[Lepton],SUNIndex[i]]])]+ - - XX7[0]* - ParticleMass[Lepton,SUNIndex[i]]* - DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - QuantumField[Particle[Lepton],SUNIndex[i]]] - ); - -(* ---------------------------------------------------------------- *) - -$Lagrangians = Union[$Lagrangians,{ChPTPhotonsLeptons3[4]}]; - -FieldsSet[ChPTPhotonsLeptons3[4]] := - {IsoVector[QuantumField[Particle[PhiMeson,RenormalizationState[0]]]], - QuantumField[Particle[Photon,RenormalizationState[0]]]}; diff --git a/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons22.m b/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons22.m deleted file mode 100644 index 19e824825..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons22.m +++ /dev/null @@ -1,89 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPTVirtualPhotons22 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 2001 - -Mathematica Version: 4.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The leading order ChPT lagrangian with - electromagnetic couplings. - - Taken from Marc Knecht and Res Urech - (1997), hep-ph/9709348 -*) - - -Begin["Phi`Objects`"]; - -(* --------------------------------------------------------------- *) - -ChPTVirtualPhotons22::usage = -"ChPTVirtualPhotons22.m is the name of the file containing the definitions for \ -Lagrangian[ChPTVirtualPhotons[2]], which is the leading order pionic \ -SU(2) ChPT lagrangian with couplings to virtual photons. \ -To evaluate use ArgumentsSupply."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -pt/:MakeBoxes[pt[a_],TraditionalForm]:=MakeBoxes[TraditionalForm[a]]; -pt/:MakeBoxes[pt[],TraditionalForm]:=""; -pt/:MakeBoxes[pt[RenormalizationState[1]],TraditionalForm]:="r"; -pt/:MakeBoxes[pt[RenormalizationState[0]],TraditionalForm]:=""; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ -ChPTVirtualPhotons2[2],st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SuperscriptBox[MakeBoxes[StyleForm["C",FontSlant->"Italic"]][[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[pt[st]]]},{ - MakeBoxes[TraditionalForm[pt[sc]]]},{ - MakeBoxes[TraditionalForm[pt[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ChPTVirtualPhotons2[2]] := - 1/4*DecayConstant[Pion]^2* - - (UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]] ] + - - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[Adjoint[UChiMatrix],MM] ]) - - - 1/4* - NM[FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]]]- - - $Gauge/2* - FDr[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]],{\[Mu]}]* - FDr[QuantumField[Particle[Photon],LorentzIndex[\[Nu]]],{\[Nu]}]+ - - CouplingConstant[ChPTVirtualPhotons2[2]]* - UTrace[NM[UChiralSpurionRightMatrix, MM, - UChiralSpurionLeftMatrix, Adjoint[MM]]]; - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPTVirtualPhotons2[2]] := - {IsoVector[QuantumField[Particle[Pion]]], - QuantumField[Particle[Photon]]}; - -$Lagrangians = Union[$Lagrangians,{ChPTVirtualPhotons2[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons24.m b/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons24.m deleted file mode 100644 index f432e0188..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons24.m +++ /dev/null @@ -1,364 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTVirtualPhotons24 *) -(* *) -(* ************************************************************** *) - -(* -Author: Frederik Orellana - -Year: 2001 - -Mathematica Version: 4.0 - -Requirements: Feyncalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The next to leading order ChPT lagrangian - with electromagnetic couplings. - - Taken from Marc Knecht and Res Urech - (1997), hep-ph/9709348 -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPTVirtualPhotons24::usage = -"ChPTVirtualPhotons24.m is the name of the file containing the definitions for -Lagrangian[ChPTVirtualPhotons2[4]], which is the pionic ChPT lagrangian -including virtual photons to fourth order in the energy. -To evaluate use ArgumentsSupply."; - -L1::usage = -"L1 := CouplingConstant[ChPTVirtualPhotons2[4],1] is one of the constants of the -fourth order ChPT lagrangian."; - -L2::usage = -"L2 := CouplingConstant[ChPTVirtualPhotons2[4],2] is one of the constants of the -fourth order ChPT lagrangian."; - -L3::usage = -"L3 := CouplingConstant[ChPTVirtualPhotons2[4],3] is one of the constants of the -fourth order ChPT lagrangian."; - -L4::usage = -"L4 := CouplingConstant[ChPTVirtualPhotons2[4],4] is one of the constants of the -fourth order ChPT lagrangian."; - -L5::usage = -"L5 := CouplingConstant[ChPTVirtualPhotons2[4],5] is one of the constants of the -fourth order ChPT lagrangian."; - -L6::usage = -"L6 := CouplingConstant[ChPTVirtualPhotons2[4],6] is one of the constants of the -fourth order ChPT lagrangian."; - -L7::usage = -"L7 := CouplingConstant[ChPTVirtualPhotons2[4],7] is one of the constants of the -fourth order ChPT lagrangian."; - -H1::usage = -"H1 := CouplingConstant[ChPTVirtualPhotons2[4],8] is one of the constants of the -fourth order ChPT lagrangian."; - -H2::usage = -"H2 := CouplingConstant[ChPTVirtualPhotons2[4],9] is one of the constants of the -fourth order ChPT lagrangian."; - -H3::usage = -"H3 := CouplingConstant[ChPTVirtualPhotons2[4],10] is one of the constants of the -fourth order ChPT lagrangian."; - -K1::usage = -"K1 := CouplingConstant[ChPTVirtualPhotons2[4],11] is one of the constants of the -fourth order ChPT lagrangian."; - -K2::usage = -"K2 := CouplingConstant[ChPTVirtualPhotons2[4],12] is one of the constants of the -fourth order ChPT lagrangian."; - -K3::usage = -"K3 := CouplingConstant[ChPTVirtualPhotons2[4],13] is one of the constants of the -fourth order ChPT lagrangian."; - -K4::usage = -"K4 := CouplingConstant[ChPTVirtualPhotons2[4],14] is one of the constants of the -fourth order ChPT lagrangian."; - -K5::usage = -"K5 := CouplingConstant[ChPTVirtualPhotons2[4],15] is one of the constants of the -fourth order ChPT lagrangian."; - -K6::usage = -"K6 := CouplingConstant[ChPTVirtualPhotons2[4],16] is one of the constants of the -fourth order ChPT lagrangian."; - -K7::usage = -"K7 := CouplingConstant[ChPTVirtualPhotons2[4],17] is one of the constants of the -fourth order ChPT lagrangian."; - -K8::usage = -"K8 := CouplingConstant[ChPTVirtualPhotons2[4],18] is one of the constants of the -fourth order ChPT lagrangian."; - -K9::usage = -"K9 := CouplingConstant[ChPTVirtualPhotons2[4],19] is one of the constants of the -fourth order ChPT lagrangian."; - -K10::usage = -"K10 := CouplingConstant[ChPTVirtualPhotons2[4],20] is one of the constants of the -fourth order ChPT lagrangian."; - -K11::usage = -"K11 := CouplingConstant[ChPTVirtualPhotons2[4],21] is one of the constants of the -fourth order ChPT lagrangian."; - -K12::usage = -"K12 := CouplingConstant[ChPTVirtualPhotons2[4],22] is one of the constants of the -fourth order ChPT lagrangian."; - -K13::usage = -"K13 := CouplingConstant[ChPTVirtualPhotons2[4],23] is one of the constants of the -fourth order ChPT lagrangian."; - -K14::usage = -"K14 := CouplingConstant[ChPTVirtualPhotons2[4],24] is one of the constants of the -fourth order ChPT lagrangian."; - -K15::usage = -"K15 := CouplingConstant[ChPTVirtualPhotons2[4],25] is one of the constants of the -fourth order ChPT lagrangian."; - -(* ---------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Abbreviations *) - -QQ = UQuarkChargeMatrix; - -L1 = CouplingConstant[ChPTVirtualPhotons2[4],1]; -L2 = CouplingConstant[ChPTVirtualPhotons2[4],2]; -L3 = CouplingConstant[ChPTVirtualPhotons2[4],3]; -L4 = CouplingConstant[ChPTVirtualPhotons2[4],4]; -L5 = CouplingConstant[ChPTVirtualPhotons2[4],5]; -L6 = CouplingConstant[ChPTVirtualPhotons2[4],6]; -L7 = CouplingConstant[ChPTVirtualPhotons2[4],7]; - -H1 = CouplingConstant[ChPTVirtualPhotons2[4],8]; -H2 = CouplingConstant[ChPTVirtualPhotons2[4],9]; -H3 = CouplingConstant[ChPTVirtualPhotons2[4],10]; - -K1 = CouplingConstant[ChPTVirtualPhotons2[4],11]; -K2 = CouplingConstant[ChPTVirtualPhotons2[4],12]; -K3 = CouplingConstant[ChPTVirtualPhotons2[4],13]; -K4 = CouplingConstant[ChPTVirtualPhotons2[4],14]; -K5 = CouplingConstant[ChPTVirtualPhotons2[4],15]; -K6 = CouplingConstant[ChPTVirtualPhotons2[4],16]; -K7 = CouplingConstant[ChPTVirtualPhotons2[4],17]; -K8 = CouplingConstant[ChPTVirtualPhotons2[4],18]; -K9 = CouplingConstant[ChPTVirtualPhotons2[4],19]; -K10 = CouplingConstant[ChPTVirtualPhotons2[4],20]; -K11 = CouplingConstant[ChPTVirtualPhotons2[4],21]; -K12 = CouplingConstant[ChPTVirtualPhotons2[4],22]; -K13 = CouplingConstant[ChPTVirtualPhotons2[4],23]; -K14 = CouplingConstant[ChPTVirtualPhotons2[4],24]; -K15 = CouplingConstant[ChPTVirtualPhotons2[4],25]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ - ChPTVirtualPhotons2[4],i_?((#<8)&),st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["l",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant /: MakeBoxes[ - CouplingConstant[ - ChPTVirtualPhotons2[4], i_?((7<#<11) &), st___RenormalizationState, - sc___RenormalizationScheme, qs___QuarkMassExpansionState], - TraditionalForm] := - Block[ {ii = i - 7, jj}, - SubsuperscriptBox[MakeBoxes[StyleForm["h", FontSlant -> "Italic"]][[1]], - MakeBoxes[TraditionalForm[jj]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]] /. - "jj" -> ToString[ii] - ]; - -CouplingConstant /: MakeBoxes[ - CouplingConstant[ - ChPTVirtualPhotons2[4], i_?((#>10)&), st___RenormalizationState, - sc___RenormalizationScheme, qs___QuarkMassExpansionState], - TraditionalForm] := - Block[ {ii = i - 10, jj}, - SubsuperscriptBox[MakeBoxes[StyleForm["k", FontSlant -> "Italic"]][[1]], - MakeBoxes[TraditionalForm[jj]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]] /. - "jj" -> ToString[ii] - ]; - -(* ---------------------------------------------------------------- *) - -RenormalizationCoefficients[ChPTVirtualPhotons2[4]] = -{(* p^4 terms *) -1/3, 2/3, -1/2, 2, -1/6, -1/3, 0, 2, 1/12, 0, -(* e^2*p^2 terms *) --27/20-1/5*z, 2*z, -3/4, 2*z, -1/4-1/5*z, -1/4+2*z, 0, 1/8-z, 1/4, 0, 0, -(* e^4 terms *) -3/2-12/5*z+84/25*z^2, -3-3/5*z-12/5*z^2, 3/2+3*z+12*z^2, 1/30} /. -z -> CouplingConstant[ChPTVirtualPhotons2[2],RenormalizationState[0]]/ -DecayConstant[Pion,RenormalizationState[0]]^4; - -(* ---------------------------------------------------------------- *) - -Lagrangian[ChPTVirtualPhotons2[4]] := - -(* p^4 *) - L1[0]/4* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Nu]}]], CDr[MM,{\[Nu]}]] ] ] + - - L2[0]/4* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}]] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}]] ] ] + - - L3[0]/16* - NM[UTrace[ NM[Adjoint[UChiMatrix],MM] + NM[Adjoint[MM],UChiMatrix] ], - UTrace[ NM[Adjoint[UChiMatrix],MM] + NM[Adjoint[MM],UChiMatrix] ] ] + - - L4[0]/4* - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[UChiMatrix,{\[Mu]}]] + - NM[Adjoint[CDr[UChiMatrix,{\[Mu]}]], CDr[MM,{\[Mu]}]] ] + - - L5[0]* - UTrace[ NM[GRight[\[Mu],\[Nu]], Adjoint[GLeft[\[Mu],\[Nu]]]] ] + - - L6[0]*I/2* - UTrace[ NM[GRight[\[Mu],\[Nu]], CDr[MM,{\[Mu]}], Adjoint[CDr[MM,{\[Nu]}]]] + - NM[GLeft[\[Mu],\[Nu]], Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}]] ] - - - L7[0]/16* - NM[UTrace[ NM[Adjoint[UChiMatrix], MM] - NM[Adjoint[MM], UChiMatrix] ] , - UTrace[ NM[Adjoint[UChiMatrix], MM] - NM[Adjoint[MM], UChiMatrix] ] ] + - - (H1[0]+H3[0])/4* - UTrace[ NM[Adjoint[UChiMatrix], UChiMatrix] ] + - - (H1[0]-H3[0])/2* - Re[Det[UChiMatrix]] - - - H2[0]* - UTrace[ NM[GRight[\[Mu],\[Nu]], GRight[\[Mu],\[Nu]]] + - NM[GLeft[\[Mu],\[Nu]], GLeft[\[Mu],\[Nu]]] ] + - - (* e^2 p^2 *) - - DecayConstant[Pion]^2*( - - K1[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NMPower[QQ, 2] ] ] + - - K2[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NM[QQ, MM, QQ, Adjoint[MM]] ] ] + - - K3[0]* - (NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ] ] + - NM[ UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ], - UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ] ])+ - - K4[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ], - UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ] ] + - - K5[0]* - NM[ UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix] ], - UTrace[ NMPower[QQ, 2] ] ] + - - K6[0]* - NM[ UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix] ], - UTrace[ NM[QQ, MM, QQ, Adjoint[MM]] ] ] + - - K7[0]* - NM[UTrace[ NM[ NM[UChiMatrix, Adjoint[MM]] + NM[MM, Adjoint[UChiMatrix]], - QQ ] + - NM[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix], - QQ ] ], - UTrace[ QQ ] - ] + - - K8[0]* - UTrace[ NM[ NM[UChiMatrix, Adjoint[MM]] - NM[MM, Adjoint[UChiMatrix]], - QQ, MM, QQ,Adjoint[MM] ] + - NM[ NM[Adjoint[UChiMatrix], MM] - NM[Adjoint[MM], UChiMatrix], - QQ, Adjoint[MM], QQ, MM ] ] + - - K9[0]* - UTrace[ NM[ Adjoint[CDr[MM,{\[Mu]}]], - NM[CQRight[\[Mu]], QQ] - - NM[QQ, CQRight[\[Mu]]], MM ] + - NM[ CDr[MM,{\[Mu]}], - NM[CQLeft[\[Mu]], QQ] - - NM[QQ, CQLeft[\[Mu]]], Adjoint[MM] ] ] + - - K10[0]* - UTrace[ NM[ CQRight[\[Mu]], MM, CQLeft[\[Mu]], Adjoint[MM] ] ] + - - K11[0]* - UTrace[ NM[ CQRight[\[Mu]], CQRight[\[Mu]] ] + - NM[ CQLeft[\[Mu]], CQLeft[\[Mu]] ] ] - - ) + - - (* e^4 *) - - DecayConstant[Pion]^4*( - - K12[0]* - NMPower[UTrace[ NM[QQ, QQ] ], 2] + - - K13[0]* - NM[ UTrace[ NM[QQ, MM, QQ,Adjoint[MM]] ], - UTrace[ NM[QQ, QQ] ] ] + - - K14[0]* - NMPower[UTrace[ NM[QQ, MM, QQ, Adjoint[MM]]], 2] - - ) + - - (* p^2 e^2 photon propagator counterterm *) - - K15[0]* - UTrace[NMPower[QQ,2]]* - NM[FieldStrengthTensor[{\[Mu]}, QuantumField[Particle[Photon],{\[Nu]}]], - FieldStrengthTensor[{\[Mu]}, QuantumField[Particle[Photon],{\[Nu]}]]]; - -(* ---------------------------------------------------------------- *) - -$Lagrangians = Union[$Lagrangians,{ChPTVirtualPhotons2[4]}]; - -FieldsSet[ChPTVirtualPhotons2[4]] := - {IsoVector[QuantumField[Particle[Pion,RenormalizationState[0]]]], - QuantumField[Particle[Photon,RenormalizationState[0]]]}; - diff --git a/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons32.m b/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons32.m deleted file mode 100644 index 7d3d65843..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons32.m +++ /dev/null @@ -1,87 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPTVirtualPhotons32 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 2001 - -Mathematica Version: 4.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The leading order ChPT lagrangian with - electromagnetic couplings. - - Taken from Res Urech (1994), hep-ph/9405341 -*) - - -Begin["Phi`Objects`"]; - -ChPTVirtualPhotons32::usage = -"ChPTVirtualPhotons32 is the name of the file containing the definitions for \ -Lagrangian[ChPTVirtualPhotons3[2]], which is the leading order mesonic \ -SU(3) ChPT lagrangian with couplings to virtual photons. \ -To evaluate use ArgumentsSupply."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -pt/:MakeBoxes[pt[a_],TraditionalForm]:=MakeBoxes[TraditionalForm[a]]; -pt/:MakeBoxes[pt[],TraditionalForm]:=""; -pt/:MakeBoxes[pt[RenormalizationState[1]],TraditionalForm]:="r"; -pt/:MakeBoxes[pt[RenormalizationState[0]],TraditionalForm]:=""; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTVirtualPhotons3[2],st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SuperscriptBox[MakeBoxes[StyleForm["C",FontSlant->"Italic"]][[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[pt[st]]]},{ - MakeBoxes[TraditionalForm[pt[sc]]]},{ - MakeBoxes[TraditionalForm[pt[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - - -Lagrangian[ChPTVirtualPhotons3[2]] := - 1/4*DecayConstant[PhiMeson]^2* - - (UTrace[ NM[CDr[MM,{\[Mu]}],Adjoint[CDr[MM,{\[Mu]}]]] ] + - - UTrace[ NM[UChiMatrix,Adjoint[MM]]+NM[Adjoint[UChiMatrix],MM] ]) - - - 1/4* - NM[FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]]]- - - $Gauge/2* - FDr[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]],{\[Mu]}]* - FDr[QuantumField[Particle[Photon],LorentzIndex[\[Nu]]],{\[Nu]}]+ - - CouplingConstant[ChPTVirtualPhotons3[2]]* - UTrace[NM[UMatrix[UChiralSpurionRight],MM, - UMatrix[UChiralSpurionLeft],Adjoint[MM]]]; - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPTVirtualPhotons3[2]] := - {IsoVector[QuantumField[Particle[PhiMeson]]], - QuantumField[Particle[Photon]]}; - -$Lagrangians = Union[$Lagrangians,{ChPTVirtualPhotons3[2]}]; - diff --git a/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons34.m b/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons34.m deleted file mode 100644 index b7df45737..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTVirtualPhotons34.m +++ /dev/null @@ -1,416 +0,0 @@ -(* ************************************************************** *) -(* *) -(* ChPTVirtualPhotons34 *) -(* *) -(* ************************************************************** *) - -(* -Author: Frederik Orellana - -Year: 2001 - -Mathematica Version: 4.0 - -Requirements: Feyncalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The next to leading order ChPT lagrangian - with electromagnetic couplings. - - Taken from Res Urech (1994), hep-ph/9405341 -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPTVirtualPhotons34::usage = -"ChPTVirtualPhotons34.m is the name of the file containing the definitions for -Lagrangian[ChPTVirtualPhotons3[4]], which is the mesonic ChPT lagrangian -including virtual photons to fourth order in the energy. -To evaluate use ArgumentsSupply."; - -L1::usage = -"L1 := CouplingConstant[ChPTVirtualPhotons3[4],1] is one of the constants of the -fourth order ChPT lagrangian."; - -L2::usage = -"L2 := CouplingConstant[ChPTVirtualPhotons3[4],2] is one of the constants of the -fourth order ChPT lagrangian."; - -L3::usage = -"L3 := CouplingConstant[ChPTVirtualPhotons3[4],3] is one of the constants of the -fourth order ChPT lagrangian."; - -L4::usage = -"L4 := CouplingConstant[ChPTVirtualPhotons3[4],4] is one of the constants of the -fourth order ChPT lagrangian."; - -L5::usage = -"L5 := CouplingConstant[ChPTVirtualPhotons3[4],5] is one of the constants of the -fourth order ChPT lagrangian."; - -L6::usage = -"L6 := CouplingConstant[ChPTVirtualPhotons3[4],6] is one of the constants of the -fourth order ChPT lagrangian."; - -L7::usage = -"L7 := CouplingConstant[ChPTVirtualPhotons3[4],7] is one of the constants of the -fourth order ChPT lagrangian."; - -L8::usage = -"L8 := CouplingConstant[ChPTVirtualPhotons3[4],8] is one of the constants of the -fourth order ChPT lagrangian."; - -L9::usage = -"L9 := CouplingConstant[ChPTVirtualPhotons3[4],9] is one of the constants of the -fourth order ChPT lagrangian."; - -L10::usage = -"L10 := CouplingConstant[ChPTVirtualPhotons3[4],10] is one of the constants of the -fourth order ChPT lagrangian."; - -H1::usage = -"H1 := CouplingConstant[ChPTVirtualPhotons3[4],11] is one of the constants of the -fourth order ChPT lagrangian."; - -H2::usage = -"H2 := CouplingConstant[ChPTVirtualPhotons3[4],12] is one of the constants of the -fourth order ChPT lagrangian."; - -K1::usage = -"K1 := CouplingConstant[ChPTVirtualPhotons3[4],13] is one of the constants of the -fourth order ChPT lagrangian."; - -K2::usage = -"K2 := CouplingConstant[ChPTVirtualPhotons3[4],14] is one of the constants of the -fourth order ChPT lagrangian."; - -K3::usage = -"K3 := CouplingConstant[ChPTVirtualPhotons3[4],15] is one of the constants of the -fourth order ChPT lagrangian."; - -K4::usage = -"K4 := CouplingConstant[ChPTVirtualPhotons3[4],16] is one of the constants of the -fourth order ChPT lagrangian."; - -K5::usage = -"K5 := CouplingConstant[ChPTVirtualPhotons3[4],17] is one of the constants of the -fourth order ChPT lagrangian."; - -K6::usage = -"K6 := CouplingConstant[ChPTVirtualPhotons3[4],18] is one of the constants of the -fourth order ChPT lagrangian."; - -K7::usage = -"K7 := CouplingConstant[ChPTVirtualPhotons3[4],19] is one of the constants of the -fourth order ChPT lagrangian."; - -K8::usage = -"K8 := CouplingConstant[ChPTVirtualPhotons3[4],20] is one of the constants of the -fourth order ChPT lagrangian."; - -K9::usage = -"K9 := CouplingConstant[ChPTVirtualPhotons3[4],21] is one of the constants of the -fourth order ChPT lagrangian."; - -K10::usage = -"K10 := CouplingConstant[ChPTVirtualPhotons3[4],22] is one of the constants of the -fourth order ChPT lagrangian."; - -K11::usage = -"K11 := CouplingConstant[ChPTVirtualPhotons3[4],23] is one of the constants of the -fourth order ChPT lagrangian."; - -K12::usage = -"K12 := CouplingConstant[ChPTVirtualPhotons3[4],24] is one of the constants of the -fourth order ChPT lagrangian."; - -K13::usage = -"K13 := CouplingConstant[ChPTVirtualPhotons3[4],25] is one of the constants of the -fourth order ChPT lagrangian."; - -K14::usage = -"K14 := CouplingConstant[ChPTVirtualPhotons3[4],26] is one of the constants of the -fourth order ChPT lagrangian."; - -K15::usage = -"K15 := CouplingConstant[ChPTVirtualPhotons3[4],27] is one of the constants of the -fourth order ChPT lagrangian."; - -K16::usage = -"K16 := CouplingConstant[ChPTVirtualPhotons3[4],28] is one of the constants of the -fourth order ChPT lagrangian."; - -K17::usage = -"K17 := CouplingConstant[ChPTVirtualPhotons3[4],29] is one of the constants of the -fourth order ChPT lagrangian."; - -K18::usage = -"K18 := CouplingConstant[ChPTVirtualPhotons3[4],30] is one of the constants of the -fourth order ChPT lagrangian."; - -K19::usage = -"K19 := CouplingConstant[ChPTVirtualPhotons3[4],31] is one of the constants of the -fourth order ChPT lagrangian."; - -(* ---------------------------------------------------------------- *) - -End[]; - -(* ---------------------------------------------------------------- *) - -(* Abbreviations *) - -QQ = UQuarkChargeMatrix; - -L1 = CouplingConstant[ChPTVirtualPhotons3[4],1]; -L2 = CouplingConstant[ChPTVirtualPhotons3[4],2]; -L3 = CouplingConstant[ChPTVirtualPhotons3[4],3]; -L4 = CouplingConstant[ChPTVirtualPhotons3[4],4]; -L5 = CouplingConstant[ChPTVirtualPhotons3[4],5]; -L6 = CouplingConstant[ChPTVirtualPhotons3[4],6]; -L7 = CouplingConstant[ChPTVirtualPhotons3[4],7]; -L8 = CouplingConstant[ChPTVirtualPhotons3[4],8]; -L9 = CouplingConstant[ChPTVirtualPhotons3[4],9]; -L10 = CouplingConstant[ChPTVirtualPhotons3[4],10]; - -H1 = CouplingConstant[ChPTVirtualPhotons3[4],11]; -H2 = CouplingConstant[ChPTVirtualPhotons3[4],12]; - -K1 = CouplingConstant[ChPTVirtualPhotons3[4],13]; -K2 = CouplingConstant[ChPTVirtualPhotons3[4],14]; -K3 = CouplingConstant[ChPTVirtualPhotons3[4],15]; -K4 = CouplingConstant[ChPTVirtualPhotons3[4],16]; -K5 = CouplingConstant[ChPTVirtualPhotons3[4],17]; -K6 = CouplingConstant[ChPTVirtualPhotons3[4],18]; -K7 = CouplingConstant[ChPTVirtualPhotons3[4],19]; -K8 = CouplingConstant[ChPTVirtualPhotons3[4],20]; -K9 = CouplingConstant[ChPTVirtualPhotons3[4],21]; -K10 = CouplingConstant[ChPTVirtualPhotons3[4],22]; -K11 = CouplingConstant[ChPTVirtualPhotons3[4],23]; -K12 = CouplingConstant[ChPTVirtualPhotons3[4],24]; -K13 = CouplingConstant[ChPTVirtualPhotons3[4],25]; -K14 = CouplingConstant[ChPTVirtualPhotons3[4],26]; -K15 = CouplingConstant[ChPTVirtualPhotons3[4],27]; -K16 = CouplingConstant[ChPTVirtualPhotons3[4],28]; -K17 = CouplingConstant[ChPTVirtualPhotons3[4],29]; -K18 = CouplingConstant[ChPTVirtualPhotons3[4],30]; -K19 = CouplingConstant[ChPTVirtualPhotons3[4],31]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTVirtualPhotons3[4],i_?((#<11)&),st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["L",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant /: MakeBoxes[ - CouplingConstant[ChPTVirtualPhotons3[4], i_?((10<#<13) &), st___RenormalizationState, - sc___RenormalizationScheme, qs___QuarkMassExpansionState], - TraditionalForm] := - Block[ {ii = i - 10, jj}, - SubsuperscriptBox[MakeBoxes[StyleForm["H", FontSlant -> "Italic"]][[1]], - MakeBoxes[TraditionalForm[jj]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]] /. - "jj" -> ToString[ii] - ]; - -CouplingConstant /: MakeBoxes[ - CouplingConstant[ChPTVirtualPhotons3[4], i_?((#>12)&), st___RenormalizationState, - sc___RenormalizationScheme, qs___QuarkMassExpansionState], - TraditionalForm] := - Block[ {ii = i - 12, jj}, - SubsuperscriptBox[MakeBoxes[StyleForm["K", FontSlant -> "Italic"]][[1]], - MakeBoxes[TraditionalForm[jj]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]] /. - "jj" -> ToString[ii] - ]; - -(* ---------------------------------------------------------------- *) - -RenormalizationCoefficients[ChPTVirtualPhotons3[4]] = -{3/32,3/16,0,1/8,3/8,11/144,0,5/48,1/4,-1/4,-1/8,5/24, -3/4, z, -3/4, 2 z, -9/4, 3/2 z, 0, z, -1/4, 1/4+3/2 z, 1/8, 1/4, 0, 0, 3/2 + 3 z + 20 z^2} /. -z -> CouplingConstant[ChPTVirtualPhotons3[2],RenormalizationState[0]]/ -DecayConstant[PhiMeson,RenormalizationState[0]]^4; - -(* ---------------------------------------------------------------- *) - - -Lagrangian[ChPTVirtualPhotons3[4]] := - -(* p^4 *) - L1[0]/4* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ] ] + - - L2[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}]] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}]] ] ] + - - L3[0]* - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}], - Adjoint[CDr[MM,{\[Nu]}]], CDr[MM,{\[Nu]}]] ] + - - L4[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}]] ], - UTrace[ NM[Adjoint[UChiMatrix],MM] + NM[UChiMatrix, Adjoint[MM]] ] ] + - - L5[0]* - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}], - NM[ Adjoint[UChiMatrix],MM] + NM[UChiMatrix, Adjoint[MM]] ] ] + - - L6[0]* - NM[UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[UChiMatrix, Adjoint[MM]] ], - UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[UChiMatrix, Adjoint[MM]] ] ] + - - L7[0]* - NM[UTrace[ NM[Adjoint[UChiMatrix], MM] - NM[UChiMatrix, Adjoint[MM]] ] , - UTrace[ NM[Adjoint[UChiMatrix], MM] - NM[UChiMatrix, Adjoint[MM]] ] ] + - - L8[0]* - UTrace[ NM[Adjoint[UChiMatrix], MM, Adjoint[UChiMatrix], MM] + - NM[UChiMatrix, Adjoint[MM], UChiMatrix, Adjoint[MM]]] - - - L9[0]*I* - UTrace[ NM[CDr[MM,{\[Mu]}], Adjoint[CDr[MM,{\[Nu]}]], GRight[\[Mu],\[Nu]]] + - NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Nu]}], GLeft[\[Mu],\[Nu]]] ] + - - L10[0]* - UTrace[ NM[GRight[\[Mu],\[Nu]], Adjoint[GLeft[\[Mu],\[Nu]]]] ] + - - H1[0]* - UTrace[ NM[GRight[\[Mu],\[Nu]], GRight[\[Mu],\[Nu]]] + - NM[GLeft[\[Mu],\[Nu]], GLeft[\[Mu],\[Nu]]] ] + - - H2[0]* - UTrace[ NM[Adjoint[UChiMatrix], UChiMatrix] ] + - - (H1[0]-H3[0])/2* - Re[Det[UChiMatrix]] + - - (* e^2 p^2 *) - - DecayConstant[PhiMeson]^2*( - - K1[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NMPower[QQ, 2] ] ] + - - K2[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ], - UTrace[ NM[QQ, MM, QQ, Adjoint[MM]] ] ] + - - K3[0]* - (NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ], - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ] ] + - NM[ UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ], - UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ] ])+ - - K4[0]* - NM[ UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], QQ, MM] ], - UTrace[ NM[CDr[MM,{\[Mu]}], QQ, Adjoint[MM]] ] ] + - - K5[0]* - UTrace[ NM[NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]]+ - NM[ CDr[MM,{\[Mu]}], Adjoint[CDr[MM,{\[Mu]}]]], - NMPower[QQ, 2]] ] + - - K6[0]* - UTrace[ NM[Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}], QQ, Adjoint[MM], QQ, MM] + - NM[CDr[MM,{\[Mu]}], Adjoint[CDr[MM,{\[Mu]}]], QQ, MM, QQ, Adjoint[MM]]] + - - K7[0]* - NM[ UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix] ], - UTrace[ NMPower[QQ, 2] ] ] + - - K8[0]* - NM[ UTrace[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix] ], - UTrace[ NM[QQ, MM, QQ, Adjoint[MM]] ] ] + - - K9[0]* - UTrace[ NM[NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix] + - NM[UChiMatrix, Adjoint[MM]] + NM[MM, Adjoint[UChiMatrix]], - NMPower[QQ, 2]] ] + - - K10[0]* - UTrace[ NM[ NM[Adjoint[UChiMatrix], MM] + NM[Adjoint[MM], UChiMatrix], - QQ, Adjoint[MM], QQ, MM] + - NM[ NM[UChiMatrix, Adjoint[MM]] + NM[MM, Adjoint[UChiMatrix]], - QQ, MM, QQ, Adjoint[MM]] ]+ - - K11[0]* - UTrace[ NM[ NM[Adjoint[UChiMatrix], MM] - NM[Adjoint[MM], UChiMatrix], - QQ, Adjoint[MM], QQ, MM ] + - NM[ NM[UChiMatrix, Adjoint[MM]] - NM[MM, Adjoint[UChiMatrix]], - QQ, MM, QQ,Adjoint[MM] ] ] + - - K12[0]* - UTrace[ NM[ Adjoint[CDr[MM,{\[Mu]}]], - NM[CQRight[\[Mu]], QQ] - - NM[QQ, CQRight[\[Mu]]], MM ] + - NM[ CDr[MM,{\[Mu]}], - NM[CQLeft[\[Mu]], QQ] - - NM[QQ, CQLeft[\[Mu]]], Adjoint[MM] ] ] + - - K13[0]* - UTrace[ NM[ CQRight[\[Mu]], MM, CQLeft[\[Mu]], Adjoint[MM] ] ] + - - K14[0]* - UTrace[ NM[ CQRight[\[Mu]], CQRight[\[Mu]] ] + - NM[ CQLeft[\[Mu]], CQLeft[\[Mu]] ] ] + - - (*Tentative correction of Urech*) - K19[0]* - UTrace[ NM[ Adjoint[CDr[MM,{\[Mu]}]], - QQ, MM, CQLeft[\[Mu]] ] + - NM[CDr[MM,{\[Mu]}], - QQ, Adjoint[MM], CQRight[\[Mu]] ] ] - - ) + - - (* e^4 *) - - DecayConstant[PhiMeson]^4*( - - K15[0]* - NMPower[UTrace[ NM[QQ, MM, QQ, Adjoint[MM]]], 2]+ - - K16[0]* - NM[ UTrace[ NM[QQ, MM, QQ,Adjoint[MM]] ], - UTrace[ NM[QQ, QQ] ] ] + - - K17[0]* - NMPower[UTrace[ NM[QQ, QQ] ], 2] - - ) + - - (* p^2 e^2 photon propagator counterterm *) - - K18[0]* - UTrace[NMPower[QQ,2]]* - NM[FieldStrengthTensor[{\[Mu]}, QuantumField[Particle[Photon],{\[Nu]}]], - FieldStrengthTensor[{\[Mu]}, QuantumField[Particle[Photon],{\[Nu]}]]]; - -(* ---------------------------------------------------------------- *) - -$Lagrangians = Union[$Lagrangians,{ChPTVirtualPhotons3[4]}]; - -FieldsSet[ChPTVirtualPhotons3[4]] := - {IsoVector[QuantumField[Particle[PhiMeson,RenormalizationState[0]]]], - QuantumField[Particle[Photon,RenormalizationState[0]]]}; diff --git a/FeynCalc/Phi/Lagrangians/ChPTW32.m b/FeynCalc/Phi/Lagrangians/ChPTW32.m deleted file mode 100644 index 3c87bf9ca..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTW32.m +++ /dev/null @@ -1,98 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPTW32 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 2000 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The lowest order CP conserving weak ChPT - lagrangian. - - Taken from Ecker, Kambor and Wyler - Resonances in the weak chiral Lagrangian, - CERN-TH.6610/92 -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPTW32::usage = -"ChPTW32.m is the name of the file containing the definitions for -Lagrangian[ChPTW3[2]] the simplest weak ChPT lagrangian. -To evaluate use ArgumentsSupply."; - -C2::usage = -"C2 := CouplingConstant[ChPTW3[2],1] is one of the constants of the -lowest order weak ChPT lagrangian."; - -C5::usage = -"C5 := CouplingConstant[ChPTW3[2],2] is one of the constants of the -lowest order weak ChPT lagrangian."; - -(* -------------------------------------------------------------- *) - -End[]; - -(* -------------------------------------------------------------- *) - -(* Abbreviations *) - -C2 = CouplingConstant[ChPTW3[2],1]; -C5 = CouplingConstant[ChPTW3[2],2]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTW3[2],1,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["c",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[2]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTW3[2],2,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["c",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[5]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ChPTW3[2]] := - C2*UTrace[ NM[UGeneratorMatrix[6], - Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ] + - - C5*UTrace[ NM[UGeneratorMatrix[6], Adjoint[MM], UChiMatrix]+ - NM[UGeneratorMatrix[6], Adjoint[UChiMatrix], MM] ]; - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPTW3[2]] := - {IsoVector[ - QuantumField[Particle[PhiMeson,RenormalizationState[0]]] - ]}; - -$Lagrangians = Union[$Lagrangians,{ChPTW3[2]}]; - diff --git a/FeynCalc/Phi/Lagrangians/ChPTW34.m b/FeynCalc/Phi/Lagrangians/ChPTW34.m deleted file mode 100644 index 06a4709b6..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTW34.m +++ /dev/null @@ -1,427 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPTW34 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 2000 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The next to leading order CP conserving - delta s = 1 weak ChPT lagrangian. - - Taken from Ecker, Kambor and Wyler - Resonances in the weak chiral Lagrangian, - CERN-TH.6610/92 -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPTW34::usage = -"ChPTW34.m is the name of the file containing the definitions for -Lagrangian[ChPTW3[4]], the lext to leading order CP conserving -weak ChPT lagrangian for delta S = 1. -To evaluate use ArgumentsSupply."; - -N1::usage = -"N1 := CouplingConstant[ChPTW3[4],1] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N2::usage = -"N2 := CouplingConstant[ChPTW3[4],2] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N3::usage = -"N3 := CouplingConstant[ChPTW3[4],3] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N4::usage = -"N4 := CouplingConstant[ChPTW3[4],4] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N5::usage = -"N5 := CouplingConstant[ChPTW3[4],5] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N6::usage = -"L6 := CouplingConstant[ChPTW3[4],6] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N7::usage = -"N7 := CouplingConstant[ChPTW3[4],7] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N8::usage = -"N8 := CouplingConstant[ChPTW3[4],8] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N9::usage = -"N9 := CouplingConstant[ChPTW3[4],9] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N10::usage = -"N10 := CouplingConstant[ChPTW3[4],10] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N11::usage = -"N11 := CouplingConstant[ChPTW3[4],11] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N12::usage = -"N12 := CouplingConstant[ChPTW3[4],12] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N13::usage = -"N13 := CouplingConstant[ChPTW3[4],13] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N14::usage = -"N14 := CouplingConstant[ChPTW3[4],14] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N15::usage = -"N15 := CouplingConstant[ChPTW3[4],15] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N16::usage = -"N16 := CouplingConstant[ChPTW3[4],16] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N17::usage = -"N17 := CouplingConstant[ChPTW3[4],17] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N18::usage = -"N18 := CouplingConstant[ChPTW3[4],18] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N19::usage = -"N19 := CouplingConstant[ChPTW3[4],19] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N20::usage = -"N20 := CouplingConstant[ChPTW3[4],20] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N21::usage = -"N21 := CouplingConstant[ChPTW3[4],21] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N22::usage = -"N22 := CouplingConstant[ChPTW3[4],22] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N23::usage = -"N23 := CouplingConstant[ChPTW3[4],23] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N24::usage = -"N24 := CouplingConstant[ChPTW3[4],24] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N25::usage = -"N25 := CouplingConstant[ChPTW3[4],25] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N26::usage = -"N26 := CouplingConstant[ChPTW3[4],26] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N27::usage = -"N27 := CouplingConstant[ChPTW3[4],27] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N28::usage = -"N28 := CouplingConstant[ChPTW3[4],28] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N29::usage = -"N29 := CouplingConstant[ChPTW3[4],29] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N30::usage = -"N30 := CouplingConstant[ChPTW3[4],30] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N31::usage = -"N31 := CouplingConstant[ChPTW3[4],31] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N32::usage = -"N32 := CouplingConstant[ChPTW3[4],32] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N33::usage = -"N33 := CouplingConstant[ChPTW3[4],33] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N34::usage = -"N34 := CouplingConstant[ChPTW3[4],34] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N35::usage = -"N35 := CouplingConstant[ChPTW3[4],35] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N36::usage = -"N36 := CouplingConstant[ChPTW3[4],36] is one of the constants of the -fourth order weak ChPT lagrangian."; - -N37::usage = -"N37 := CouplingConstant[ChPTW3[4],37] is one of the constants of the -fourth order weak ChPT lagrangian."; - -(* -------------------------------------------------------------- *) - -End[]; - -(* -------------------------------------------------------------- *) - -(* Abbreviations *) - -N1 = CouplingConstant[ChPTW3[4],1]; -N2 = CouplingConstant[ChPTW3[4],2]; -N3 = CouplingConstant[ChPTW3[4],3]; -N4 = CouplingConstant[ChPTW3[4],4]; -N5 = CouplingConstant[ChPTW3[4],5]; -N6 = CouplingConstant[ChPTW3[4],6]; -N7 = CouplingConstant[ChPTW3[4],7]; -N8 = CouplingConstant[ChPTW3[4],8]; -N9 = CouplingConstant[ChPTW3[4],9]; -N10 = CouplingConstant[ChPTW3[4],10]; -N11 = CouplingConstant[ChPTW3[4],11]; -N12 = CouplingConstant[ChPTW3[4],12]; -N13 = CouplingConstant[ChPTW3[4],13]; -N14 = CouplingConstant[ChPTW3[4],14]; -N15 = CouplingConstant[ChPTW3[4],15]; -N16 = CouplingConstant[ChPTW3[4],16]; -N17 = CouplingConstant[ChPTW3[4],17]; -N18 = CouplingConstant[ChPTW3[4],18]; -N19 = CouplingConstant[ChPTW3[4],19]; -N20 = CouplingConstant[ChPTW3[4],20]; -N21 = CouplingConstant[ChPTW3[4],21]; -N22 = CouplingConstant[ChPTW3[4],22]; -N23 = CouplingConstant[ChPTW3[4],23]; -N24 = CouplingConstant[ChPTW3[4],24]; -N25 = CouplingConstant[ChPTW3[4],25]; -N26 = CouplingConstant[ChPTW3[4],26]; -N27 = CouplingConstant[ChPTW3[4],27]; -N28 = CouplingConstant[ChPTW3[4],28]; -N29 = CouplingConstant[ChPTW3[4],29]; -N30 = CouplingConstant[ChPTW3[4],30]; -N31 = CouplingConstant[ChPTW3[4],31]; -N32 = CouplingConstant[ChPTW3[4],32]; -N33 = CouplingConstant[ChPTW3[4],33]; -N34 = CouplingConstant[ChPTW3[4],34]; -N35 = CouplingConstant[ChPTW3[4],35]; -N36 = CouplingConstant[ChPTW3[4],36]; -N37 = CouplingConstant[ChPTW3[4],37]; - -(* ---------------------------------------------------------------- *) - -RenormalizationCoefficients[ChPTW3[4]] := - {2,-1/2,0,1,3/2,-1/4,-9/8,-1/2,3/4,2/3,-13/18,-5/12,0,1/4,1/2,-1/4,0, - -1/8,-5/4,3/4,5/6,5/6,0,0,1/2,-3/4,1/8,0,0,0,0,0,0,0,0,-5/12,-1/8}; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ - ChPTW3[4],i_,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["N",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ChPTW3[4]] := - CouplingConstant[ChPTW3[2],1]/DecayConstant[PhiMeson]^2*( - - (* ............................................................... *) - (* K -> 3 Pi *) - - N1*UTrace[ NM[UDelta, USmall[\[Mu]], USmall[\[Mu]], USmall[\[Nu]], USmall[\[Nu]]] ] + - - N2*UTrace[ NM[UDelta, USmall[\[Mu]], USmall[\[Nu]], USmall[\[Nu]], USmall[\[Mu]]] ] + - - N3*NM[UTrace[ NM[UDelta, USmall[\[Mu]], USmall[\[Nu]]] ], - UTrace[ NM[USmall[\[Mu]], USmall[\[Nu]]] ]] + - - N4*NM[UTrace[ NM[UDelta, USmall[\[Mu]]] ], - UTrace[ NM[USmall[\[Mu]], USmall[\[Nu]], USmall[\[Nu]]] ]] + - - (* ............................................................... *) - (* K -> 2 Pi, 3 Pi *) - - N5*UTrace[ NM[UDelta, UChiPlus, USmall[\[Mu]], USmall[\[Mu]]] + - NM[UDelta, USmall[\[Mu]], USmall[\[Mu]], UChiPlus] ] + - - N6*NM[UTrace[ NM[UDelta, USmall[\[Mu]]] ], - UTrace[ NM[UChiPlus, USmall[\[Mu]]] ]] + - - N7*NM[UTrace[ NM[UDelta, UChiPlus] ], - UTrace[ NM[USmall[\[Mu]], USmall[\[Mu]]] ]] + - - N8*NM[UTrace[ NM[UDelta, USmall[\[Mu]], USmall[\[Mu]]] ], - UTrace[ UChiPlus ]] + - - N9*UTrace[ NM[UDelta, UChiMinus, USmall[\[Mu]], USmall[\[Mu]]] - - NM[UDelta, USmall[\[Mu]], USmall[\[Mu]], UChiMinus] ] + - - N10*UTrace[ NM[UDelta, UChiPlus, UChiPlus] ] + - - N11*NM[UTrace[ NM[UDelta, UChiPlus] ], - UTrace[ UChiPlus ]] + - - N12*UTrace[ NM[UDelta, UChiMinus, UChiMinus] ] + - - N13*NM[UTrace[ NM[UDelta, UChiMinus] ], - UTrace[ UChiMinus ]] + - - (* ............................................................... *) - (* Radiative K decays *) - - N14*I*UTrace[ NM[UDelta, UFPlus[\[Mu],\[Nu]], USmall[\[Mu]], USmall[\[Nu]]] + - NM[UDelta, USmall[\[Mu]], USmall[\[Nu]], UFPlus[\[Mu],\[Nu]]] ] + - - N15*I*UTrace[ NM[UDelta, USmall[\[Mu]], UFPlus[\[Mu],\[Nu]], USmall[\[Nu]]] ] + - - N16*I*UTrace[ NM[UDelta, UFMinus[\[Mu],\[Nu]], USmall[\[Mu]], USmall[\[Nu]]] + - NM[UDelta, USmall[\[Mu]], USmall[\[Nu]], UFMinus[\[Mu],\[Nu]]] ] + - - N17*I*UTrace[ NM[UDelta, USmall[\[Mu]], UFMinus[\[Mu],\[Nu]], USmall[\[Nu]]] ] + - - N18*I*UTrace[ NM[UDelta, UFPlus[\[Mu],\[Nu]], UFPlus[\[Mu],\[Nu]]] - - NM[UDelta, UFMinus[\[Mu],\[Nu]], UFMinus[\[Mu],\[Nu]]] ] + - - (* ............................................................... *) - (* External W bosons*) - - N19*I*UTrace[ NM[UNablaHatDelta[\[Mu]], USmall[\[Mu]], USmall[\[Nu]], USmall[\[Nu]]] - - NM[UNablaHatDelta[\[Mu]], USmall[\[Nu]], USmall[\[Nu]], USmall[\[Mu]]] ] + - - N20*UTrace[ NM[UNablaHatDelta[\[Mu]], UOmega[\[Mu],\[Nu]], USmall[\[Nu]]] + - NM[UNablaHatDelta[\[Mu]], USmall[\[Nu]], UOmega[\[Mu],\[Nu]]] ] + - - N21*I*UTrace[ NM[UNablaHatDelta[\[Mu]], UChiPlus, USmall[\[Mu]]] - - NM[UNablaHatDelta[\[Mu]], USmall[\[Mu]], UChiPlus] ] + - - (*N22*UTrace[ NM[UNablaHatDelta[\[Mu]], CovariantNabla[UChiPlus,{\[Mu]}]] ] +*) - N22*UTrace[ NM[UNablaHatDelta[\[Mu]], NablaChiPlus[\[Mu]]] ] + - - N23*I*UTrace[ NM[UNablaHatDelta[\[Mu]], UChiMinus, USmall[\[Mu]]] + - NM[UNablaHatDelta[\[Mu]], USmall[\[Mu]], UChiMinus] ] + - - N24*I*NM[UTrace[ NM[UNablaHatDelta[\[Mu]], USmall[\[Mu]]] ], - UTrace[ UChiMinus ]] + - - N25*UTrace[ NM[UNablaHatDelta[\[Mu]], UFPlus[\[Mu],\[Nu]], USmall[\[Nu]]] + - NM[UNablaHatDelta[\[Mu]], USmall[\[Nu]], UFPlus[\[Mu],\[Nu]]] ] + - - N26*UTrace[ NM[UNablaHatDelta[\[Mu]], UFMinus[\[Mu],\[Nu]], USmall[\[Nu]]] + - NM[UNablaHatDelta[\[Mu]], USmall[\[Nu]], UFMinus[\[Mu],\[Nu]]] ] + - - N27*UTrace[ NM[2*UFPlus[\[Mu],\[Nu]], UFPlus[\[Mu],\[Nu]]] - - NM[UFPlus[\[Mu],\[Nu]], UFMinus[\[Mu],\[Nu]]] - - NM[UFMinus[\[Mu],\[Nu]], UFPlus[\[Mu],\[Nu]]] ]+ - - (* ............................................................... *) - (* Radiative K decays (anomalous couplings) *) - - N28*I*LC[\[Mu], \[Nu], \[Rho], \[Sigma]]* - NM[UTrace[ NM[UDelta, USmall[\[Mu]]] ], - UTrace[ NM[USmall[\[Nu]], USmall[\[Rho]], USmall[\[Sigma]]] ]]+ - - N29*UTrace[NM[UDelta, - NM[LC[\[Mu], \[Nu], \[Rho], \[Sigma]]* - (UFPlus[\[Rho], \[Sigma]]-UFMinus[\[Rho], \[Sigma]]), - USmall[\[Mu]], USmall[\[Nu]]] - - NM[USmall[\[Mu]], USmall[\[Nu]], - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]* - (UFPlus[\[Rho], \[Sigma]]-UFMinus[\[Rho], \[Sigma]])]] ]+ - - N30*NM[UTrace[ NM[UDelta, USmall[\[Mu]]] ], - UTrace[ NM[LC[\[Mu], \[Nu], \[Rho], \[Sigma]], - UFPlus[\[Rho], \[Sigma]], USmall[\[Nu]]] ]]+ - - N31*NM[UTrace[ NM[UDelta, USmall[\[Mu]]] ], - UTrace[ NM[LC[\[Mu], \[Nu], \[Rho], \[Sigma]], - UFMinus[\[Rho],\[Sigma]], USmall[\[Nu]]] ]]+ - - (* ............................................................... *) - (* External W bosons *) - - N32*I*UTrace[ - NM[UNablaHatDelta[\[Mu]],UDelta, - NM[ - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFPlus[\[Rho], \[Sigma]],USmall[\[Nu]]]- - NM[ - USmall[\[Nu]],LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFPlus[\[Rho], \[Sigma]]]] ]+ - - N32*I*UTrace[ - NM[UNablaHatDelta[\[Mu]],UDelta, - NM[ - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFMinus[\[Rho], \[Sigma]],USmall[\[Nu]]]- - NM[ - USmall[\[Nu]],LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFMinus[\[Rho] ,\[Sigma]]]] ]+ - - N34*UTrace[ - NM[UDelta, - NM[ - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFPlus[\[Rho], \[Sigma]]+ - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFMinus[\[Rho], \[Sigma]], - USmall[\[Mu]], USmall[\[Nu]]]- - NM[ - USmall[\[Mu]], USmall[\[Nu]], - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFPlus[\[Rho], \[Sigma]]+ - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFMinus[\[Rho], \[Sigma]]] - ] ]+ - - N35*I*UTrace[ - NM[UDelta, - NM[ - UFPlus[\[Mu],\[Nu]], - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFMinus[\[Rho], \[Sigma]]]- - NM[ - LC[\[Mu], \[Nu], \[Rho], \[Sigma]]*UFMinus[\[Rho], \[Sigma]], - UFPlus[\[Mu], \[Nu]]]] ]+ - - (* ............................................................... *) - (* Renormalization *) - - N36*UTrace[ NM[UDelta, - NM[UChiPlus, UChiMinus]-NM[UChiMinus, UChiPlus]+ - NM[UChiPlus, UChiPlus]-NM[UChiMinus, UChiMinus]] ] + - - N37*UTrace[ NM[UDelta, - UFPlus[\[Mu],\[Nu]]+UFMinus[\[Mu],\[Nu]], - UFPlus[\[Mu],\[Nu]]+UFMinus[\[Mu],\[Nu]]] ] - - ); - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPTW3[2]] := - {IsoVector[ - QuantumField[Particle[PhiMeson,RenormalizationState[0]]] - ]}; - -$Lagrangians = Union[$Lagrangians,{ChPTW3[4]}]; diff --git a/FeynCalc/Phi/Lagrangians/ChPTWS32.m b/FeynCalc/Phi/Lagrangians/ChPTWS32.m deleted file mode 100644 index d2ab6c2f1..000000000 --- a/FeynCalc/Phi/Lagrangians/ChPTWS32.m +++ /dev/null @@ -1,102 +0,0 @@ -(* *************************************************************** *) -(* *) -(* ChPTWS32 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 2000 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The lowest order CP conserving weak ChPT - lagrangian with coupling to a scalar source. - - Taken from Ecker, Kambor and Wyler - Resonances in the weak chiral Lagrangian, - CERN-TH.6610/92 -*) - - -Begin["Phi`Objects`"]; - -(* -------------------------------------------------------------- *) - -ChPTWS32::usage = -"ChPTWS32 is the name of the file containing the definitions for -Lagrangian[ChPTWS3[2]] the simplest weak ChPT lagrangian. -To evaluate use ArgumentsSupply."; - -C2::usage = -"C2 := CouplingConstant[ChPTW3[2],1] is one of the constants of the -lowest order weak ChPT lagrangian."; - -C5::usage = -"C5 := CouplingConstant[ChPTW3[2],2] is one of the constants of the -lowest order weak ChPT lagrangian."; - -(* -------------------------------------------------------------- *) - -End[]; - -(* -------------------------------------------------------------- *) - -(* Abbreviations *) - -C2 = CouplingConstant[ChPTW3[2],1]; -C5 = CouplingConstant[ChPTW3[2],2]; - -(* ---------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTW3[2], -1,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["c",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[2]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ChPTW3[2], -2,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["c",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[5]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - -Lagrangian[ChPTWS3[2]] := - C2*UTrace[ NM[QuantumField[Particle[Scalar[1]]], - UGeneratorMatrix[6], - Adjoint[CDr[MM,{\[Mu]}]], CDr[MM,{\[Mu]}]] ] + - - C5*UTrace[ NM[QuantumField[Particle[Scalar[1]]], - UGeneratorMatrix[6], Adjoint[MM], UChiMatrix]+ - NM[QuantumField[Particle[Scalar[1]]], - UGeneratorMatrix[6], Adjoint[UChiMatrix], MM] ]; - -(* --------------------------------------------------------------- *) - -FieldsSet[ChPTWS3[2]] := - {IsoVector[ - QuantumField[Particle[PhiMeson,RenormalizationState[0]]] - ]}; - -$Lagrangians = Union[$Lagrangians,{ChPTWS3[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/HBChPT22.m b/FeynCalc/Phi/Lagrangians/HBChPT22.m deleted file mode 100644 index 3eeccdf5e..000000000 --- a/FeynCalc/Phi/Lagrangians/HBChPT22.m +++ /dev/null @@ -1,87 +0,0 @@ -(* ****************************************************************** *) -(* *) -(* HBChPT22 *) -(* *) -(* ****************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The simplest ChPT lagrangian. - - Taken from G.Ecker and M. Mojzis (1995), - hep-ph/9508204 -*) - - -Begin["Phi`Objects`"]; - -(* ------------------------------------------------------------------ *) - -HBChPT22::usage = -"HBChPT22.m is the name of the file containing the definitions for -Lagrangian[HBChPT2[2]], which is the SU(2) ChPT pion-nucleon -lagrangian. To evaluate use ArgumentsSupply."; - -GAV::usage = -"GAV := CouplingConstant[HBChPT2[2]] is axial vector -coupling constant."; - -(* ------------------------------------------------------------------ *) - -End[]; - -(* ------------------------------------------------------------------ *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ -HBChPT2[2],st___RenormalizationState, - sc___RenormalizationScheme,qs___QuarkMassExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["g",FontSlant->"Italic"]][[1]], - MakeBoxes["A"], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* ------------------------------------------------------------------ *) - -GAV = CouplingConstant[HBChPT2[2]]; - -(* ------------------------------------------------------------------ *) - -Lagrangian[HBChPT2[2]] := - I*(UDot[UVector[ - DiracBar[QuantumField[Particle[Nucleon]]]], - DiracMatrix[LorentzIndex[\[Mu]]], - CDr[UVector[QuantumField[Particle[Nucleon]]],{\[Mu]}]])- - - - ParticleMass[Nucleon]* - UDot[UVector[DiracBar[QuantumField[Particle[Nucleon]]]], - UVector[QuantumField[Particle[Nucleon]]]]+ - - - CouplingConstant[ - HBChPT2[2],RenormalizationState[0]]/2* - (UDot[UVector[DiracBar[QuantumField[Particle[Nucleon]]]], - DiracMatrix[LorentzIndex[\[Mu]]],USmall[\[Mu]], - UVector[QuantumField[Particle[Nucleon]]]]); - -(* ------------------------------------------------------------------ *) - -FieldsSet[HBChPT2[2]] := - {IsoVector[ - QuantumField[Particle[Pion,RenormalizationState[0]]]], - UVector[QuantumField[Particle[Nucleon,RenormalizationState[0]]]]}; - -$Lagrangians = Union[$Lagrangians,{HBChPT2[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/QED1.m b/FeynCalc/Phi/Lagrangians/QED1.m deleted file mode 100644 index 22bd734c4..000000000 --- a/FeynCalc/Phi/Lagrangians/QED1.m +++ /dev/null @@ -1,76 +0,0 @@ -(* *************************************************************** *) -(* *) -(* QED1 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The standard QED lagrangian - for the electron. - - Taken from Bjoerken and Drell, - "Relativistic Quantum Fields", - McGraw-Hill 1965 -*) - - -Begin["Phi`Objects`"]; - -(* --------------------------------------------------------------- *) - -QED1::usage = -"QED1.m is the name of the file containing the definitions for -Lagrangian[QED[1]], which is the standard QED lagrangian, -CouplingConstant[QED[1]] is the bare -unit charge (the charge of the positron)."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* --------------------------------------------------------------- *) - -Lagrangian["QED"] := - Lagrangian[QED[1]]; - -(* --------------------------------------------------------------- *) - -Lagrangian[QED[1]] := - -1/4* - DOT[ - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]] - ]+ - - DOT[DiracBar[QuantumField[Particle[Electron]]], - DiracMatrix[LorentzIndex[\[Mu]]], - (I*QuantumField[FCPartialD[LorentzIndex[\[Mu]]],Particle[Electron]]+ - CouplingConstant[QED[1]]* - DOT[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]], - QuantumField[Particle[Electron]]]) - ]- - - ParticleMass[Electron]* - DOT[DiracBar[QuantumField[Particle[Electron]]], - QuantumField[Particle[Electron]]]; - -(* --------------------------------------------------------------- *) - -FieldsSet[QED[1]] := - {QuantumField[Particle[Electron]], - QuantumField[Particle[Photon],LorentzIndex[\[Mu]]]}; - -$Lagrangians = Union[$Lagrangians,{QED[1]}]; - diff --git a/FeynCalc/Phi/Lagrangians/QED2.m b/FeynCalc/Phi/Lagrangians/QED2.m deleted file mode 100644 index 8bcbe1883..000000000 --- a/FeynCalc/Phi/Lagrangians/QED2.m +++ /dev/null @@ -1,137 +0,0 @@ -(* *************************************************************** *) -(* *) -(* QED2 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: Counterterm QED lagrangian - for the electron. - - Taken from S .Weinberg (1995), - "The Quantum Theory of Fields", - Cambridge University Press - - Adapted to the usual space- - time metric (1,-1,-1,-1) -*) - - -Begin["Phi`Objects`"]; - -(* --------------------------------------------------------------- *) - -QED2::usage = -"QED2.m is the name of the file containing the definitions for -Lagrangian[QED[2]], which is the QED counterterm lagrangian."; - -DM::usage = -"DM := CouplingConstant[QED[2],1] is one of the constants of the -counterterm QED lagrangian - the mass counterterm."; - -Z2::usage = -"Z2 := CouplingConstant[QED[2],2] is one of the constants of the -counterterm QED lagrangian - the factor relating the bare to the -physical electron field."; - -Z3::usage = -"Z3 := CouplingConstant[QED[2],3] is one of the constants of the -counterterm QED lagrangian - the factor relating the bare to the -physical photon field."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* --------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ -QED[2],1,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= - SuperscriptBox[ - MakeBoxes[StyleForm["\[Delta]m",FontSlant->"Italic"]][[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ -QED[2],2,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["Z",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[2]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ -QED[2],3,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["Z",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[3]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - -(* Abbreviations *) - -DM = CouplingConstant[QED[2],1]; -Z2 = CouplingConstant[QED[2],2]; -Z3 = CouplingConstant[QED[2],3]; - -(* --------------------------------------------------------------- *) - -Lagrangian[QED[2]] := - -1/4*(Z3[0]-1)* - DOT[FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]]]+ - - (Z2[0]-1)* - (DOT[ - DiracBar[QuantumField[Particle[Electron]]], - DiracMatrix[LorentzIndex[\[Mu]]], - (I*QuantumField[FCPartialD[LorentzIndex[\[Mu]]],Particle[Electron]]+ - CouplingConstant[QED[1]]* - DOT[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]], - QuantumField[Particle[Electron]]]) - ]- - - ParticleMass[Electron]* - DOT[DiracBar[QuantumField[Particle[Electron]]], - QuantumField[Particle[Electron]]])- - - Z2[0]*DM[0]* - DOT[DiracBar[QuantumField[Particle[Electron]]], - QuantumField[Particle[Electron]]]; - -(* --------------------------------------------------------------- *) - -FieldsSet[QED[2]] := - {QuantumField[Particle[Electron,RenormalizationState[0]]], - QuantumField[Particle[Photon,RenormalizationState[0]],LorentzIndex[\[Mu]]]}; - -$Lagrangians = Union[$Lagrangians,{QED[2]}]; diff --git a/FeynCalc/Phi/Lagrangians/QED21.m b/FeynCalc/Phi/Lagrangians/QED21.m deleted file mode 100644 index 32d843e80..000000000 --- a/FeynCalc/Phi/Lagrangians/QED21.m +++ /dev/null @@ -1,73 +0,0 @@ -(* *************************************************************** *) -(* *) -(* QED21 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: The standard QED lagrangian - for three leptons. - - Taken from Bjoerken and Drell, - "Relativistic Quantum Fields", - McGraw-Hill 1965 -*) - - -Begin["Phi`Objects`"]; - -QED21::usage = -"QED21.m is the name of the file containing the definitions for -Lagrangian[QED2[1]], which is the standard QED lagrangian, -CouplingConstant[QED2[1]] is the bare -unit charge (the charge of the positron)."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* --------------------------------------------------------------- *) - -Lagrangian["QED2"] := - Lagrangian[QED2[1]]; - -(* --------------------------------------------------------------- *) - -Lagrangian[QED2[1]] := - -1/4* - DOT[FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]]]+ - - DOT[ - DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - (I*QuantumField[FCPartialD[LorentzIndex[\[Mu]]], - Particle[Lepton],SUNIndex[i]]+ - CouplingConstant[QED[1]]* - DOT[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]], - QuantumField[Particle[Lepton],SUNIndex[i]]]) - ]- - - ParticleMass[Lepton,SUNIndex[i]]* - DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - QuantumField[Particle[Lepton],SUNIndex[i]]]; - -(* --------------------------------------------------------------- *) - -FieldsSet[QED2[1]] := - {QuantumField[Particle[Lepton]], - QuantumField[Particle[Photon],LorentzIndex[\[Mu]]]}; - -$Lagrangians = Union[$Lagrangians,{QED2[1]}]; diff --git a/FeynCalc/Phi/Lagrangians/QED22.m b/FeynCalc/Phi/Lagrangians/QED22.m deleted file mode 100644 index 27b39e3fa..000000000 --- a/FeynCalc/Phi/Lagrangians/QED22.m +++ /dev/null @@ -1,137 +0,0 @@ -(* *************************************************************** *) -(* *) -(* QED22 *) -(* *) -(* *************************************************************** *) - -(* -Author: F.Orellana - -Year: 1998 - -Mathematica Version: 3.0 - -Requirements: FeynCalc > 3, PHI - -Summary: Lagrangian for PHI - -Description: Counterterm QED lagrangian - for three leptons. - - Taken from S .Weinberg (1995), - "The Quantum Theory of Fields", - Cambridge University Press - - Adapted to the usual space- - time metric (1,-1,-1,-1) -*) - - -Begin["Phi`Objects`"]; - -(* --------------------------------------------------------------- *) - -QED22::usage = -"QED22.m is the name of the file containing the definitions for -Lagrangian[QED2[2]], which is the QED counterterm lagrangian."; - -DM::usage = -"DM := CouplingConstant[QED2[2],1] is one of the constants of the -counterterm QED lagrangian - the mass counterterm."; - -Z2::usage = -"Z2 := CouplingConstant[QED2[2],2] is one of the constants of the -counterterm QED lagrangian - the factor relating the bare to the -physical Lepton field."; - -Z3::usage = -"Z3 := CouplingConstant[QED2[2],3] is one of the constants of the -counterterm QED lagrangian - the factor relating the bare to the -physical photon field."; - -(* --------------------------------------------------------------- *) - -End[]; - -(* --------------------------------------------------------------- *) - -(* Box definitions *) - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ -QED[2],1,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= - SuperscriptBox[ - MakeBoxes[StyleForm["\[Delta]m",FontSlant->"Italic"]][[1]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ -QED[2],2,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["Z",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[2]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant/: -MakeBoxes[ - CouplingConstant[ -QED[2],3,st___RenormalizationState, - sc___RenormalizationScheme,qs___ExpansionState], - TraditionalForm]:= -SubsuperscriptBox[MakeBoxes[StyleForm["Z",FontSlant->"Italic"]][[1]], - MakeBoxes[TraditionalForm[3]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]},{ - MakeBoxes[TraditionalForm[IndexBox[sc]]]},{ - MakeBoxes[TraditionalForm[IndexBox[qs]]]}]]]; - -(* --------------------------------------------------------------- *) - -(* Abbreviations *) - -DM = CouplingConstant[QED[2],1]; -Z2 = CouplingConstant[QED[2],2]; -Z3 = CouplingConstant[QED[2],3]; - -(* --------------------------------------------------------------- *) - -Lagrangian[QED2[2]] := - -1/4*(Z3[0]-1)* - DOT[FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]], - FieldStrengthTensor[LorentzIndex[\[Mu]], - QuantumField[Particle[Photon],LorentzIndex[\[Nu]]]]]+ - - (Z2[0]-1)* - (DOT[ - DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - DiracMatrix[LorentzIndex[\[Mu]]], - (I*QuantumField[FCPartialD[LorentzIndex[\[Mu]]],Particle[Lepton],SUNIndex[i]]+ - CouplingConstant[QED[1]]* - DOT[QuantumField[Particle[Photon],LorentzIndex[\[Mu]]], - QuantumField[Particle[Lepton],SUNIndex[i]]]) - ]- - - ParticleMass[Lepton,SUNIndex[i]]* - DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - QuantumField[Particle[Lepton],SUNIndex[i]]])- - - Z2[0]*DM[0]* - DOT[DiracBar[QuantumField[Particle[Lepton],SUNIndex[i]]], - QuantumField[Particle[Lepton],SUNIndex[i]]]; - -(* --------------------------------------------------------------- *) - -FieldsSet[QED2[2]] := - {QuantumField[Particle[Lepton,RenormalizationState[0]]], - QuantumField[Particle[Photon,RenormalizationState[0]],LorentzIndex[\[Mu]]]}; - -$Lagrangians = Union[$Lagrangians,{QED2[2]}]; diff --git a/FeynCalc/Phi/Models/Automatic.gen b/FeynCalc/Phi/Models/Automatic.gen deleted file mode 100644 index 79453038b..000000000 --- a/FeynCalc/Phi/Models/Automatic.gen +++ /dev/null @@ -1,268 +0,0 @@ -(* ****************************************************************** *) -(* *) -(* Automatic.gen *) -(* *) -(* ****************************************************************** *) - -(* -Author: Frederik Orellana 1997 - -Summary: Generic model for FeynArts - -Mathematica Version: 3.0 - -Requirements: FeynArts > 2, PHI, FeynCalc > 3 - -Description: The coupling vector are loaded from files - generated by PHI -*) - -(* ****************************************************************** *) - -$GenericModel = "Automatic"; - -(* ****************************************************************** *) - -(* The minuses for outgoing particles are removed *) - -$VerticesSpecifications1:=($VerticesSpecifications/.-qu_[q__]->qu[q]); - -(* ****************************************************************** *) - -(* Standard definitions for all PHI particle types *) - -PropagatorType[$ScalarHeads]=Straight; -PropagatorType[$VectorHeads]=Sine; -(*PropagatorType[$FermionHeads]=Dashing[{0.003,0.006}];*) -(*FA seems to have lost some flexibility in costumizing the graphics*) -PropagatorType[$FermionHeads]=ScalarDash; - -PropagatorArrow[$ParticleHeads]=None; - -KinematicIndices[$ScalarHeads] := {}; -KinematicIndices[$FermionHeads] := {}; -KinematicIndices[$VectorHeads] := {Lorentz}; - -TheLabel[Index[Lorentz,i_]] := -$CouplingLorentzIndicesString<>ToString[i]; - -(* ****************************************************************** *) - -(* -The function GenProps[p] -gives the propagator description for the particle type p. -Standard definitions are used. -Notice that the setting of $PropagatorMassesStates determines the -renormalization state of the mass used for the propagator of each -particle -*) - -(* The condition added to allow redifining propagators -before loading FeynArts *) -If[And@@((Head[GenProps[#]]===GenProps)&/@ -({$ScalarHeads /. Alternatives -> Sequence})), -GenProps[a:$ScalarHeads]:={ -AnalyticalPropagator[External][ s a[i,p] ] == 1, -AnalyticalPropagator[Internal][ s a[i,p] ] == -I*PropagatorDenominator[p,Mass[a[i]]]}]; - -If[And@@((Head[GenProps[#]]===GenProps)&/@ -({$VectorHeads /. Alternatives -> Sequence})), -GenProps[a:$VectorHeads]:={ -AnalyticalPropagator[External][ s a[i, mom, {li2}] ] == -PolarizationVector[ a[i], mom, li2 ], -AnalyticalPropagator[Internal][ s a[i,mom,{li1}->{li2}] ] == -I*PropagatorDenominator[ mom , Mass[a[i]] ]* -(-MetricTensor[li1, li2])}]; - -If[And@@((Head[GenProps[#]]===GenProps)&/@ -({$FermionHeads /. Alternatives -> Sequence})), -GenProps[a:$FermionHeads]:={ -AnalyticalPropagator[External][ s a[i, mom] ] == -NonCommutative[ -(*Tag, so WFRenormalize can do its thing*) -(*DiracSpinor[ --mom, Mass[ a[i] ], Sequence @@ Drop[{i},1] ]*) -Phi`Couplings`Private`propSpinor[ --mom, Mass[ a[i] ], Sequence @@ Drop[{i},1] ] ], -AnalyticalPropagator[Internal][ s a[i,mom] ] == -NonCommutative[(*DiracGamma[ -mom ] + Mass[a[i]]*) -Phi`Couplings`Private`propGamma[ --mom, Mass[a[i]]] ]* -I*PropagatorDenominator[ mom , Mass[a[i]] ]}]; - -(* ****************************************************************** *) - -(* allfields is all field-types in $VerticesSpecifications -(that is, Pion[0], Pion[1], ... are not distinguished) *) -(* Change 20/3-1999 - mixing fields must also be included in this list *) - -allfields= -Union[Head/@Union[ -Flatten[Transpose[Transpose[ -$VerticesSpecifications1][[1]]/.Rule->List][[2]]], -If[Length[$MixingFields]>0,Transpose[$MixingFields/.Rule->List][[1]],{}]]]; - -(* The function GenProps is used to create propagator definitions -for all particle types *) - -M$GenericPropagators = Flatten[GenProps/@allfields]; - -(* ****************************************************************** *) - -(* Only vector-type particles have Lorentz index *) - -kineindex[a:$VectorHeads,i_]:={ToExpression[ -$CouplingLorentzIndicesString<>ToString[i]]}; -kineindex[a:$ScalarHeads,i_]:=Sequence[]; -kineindex[a:$FermionHeads,i_]:=Sequence[]; - -(* -The coupling vectors are read from the files specified in -$VerticesSpecifications. The left-hand side -(genericfieldsmomenta) of the defintion and the field -configuration (genericfields) are created with the fields -from $VerticesSpecifications. The symmetry sign is also -taken from $VerticesSpecifications -*) - -(* listrepl substitutes the list PerturbationOrder with -one element at a time - to pass it to XName *) - -(*Added 7/6-2000 to allow a list of non-Automatic XFileName's*) -listrepl[{aa___,PerturbationOrder->b_List, -bb___,XFileName->xn_List,cc___},nn_Integer] := -{aa,PerturbationOrder->b[[nn]],bb,XFileName->xn[[nn]],cc}; - -listrepl[{aa___,XFileName->xn_List, -bb___,PerturbationOrder->b_List,cc___},nn_Integer] := -{aa,PerturbationOrder->b[[nn]],bb,XFileName->xn[[nn]],cc}; - -(**) - -listrepl[{aa___,PerturbationOrder->b_List,bb___},nn_Integer] := -{aa,PerturbationOrder->b[[nn]],bb}; - -( -olddir=Directory[]; -SetDirectory[$HEPDir]; -SetDirectory["FeynCalc"]; -SetDirectory["Phi"]; -SetDirectory["CouplingVectors"]; - -Do[ - -Do[ - -(* The coupling vectors are loaded into an array *) - -gloadfile[filenr] = XName[listrepl[ -$VerticesSpecifications1[[repp]],filenr]]<>".Gen"; - -fpath = ToFileName[{$FeynCalcDirectory, "Phi", "CouplingVectors"}, gloadfile[filenr]]; - -VerbosePrint[1,repp," ",filenr, -" Loading generic coupling from ",fpath]; - -genericcouplingvector[repp,filenr] = Get[fpath]; - -VerbosePrint[2, genericcouplingvector[repp,filenr]], - -{filenr,Length[PerturbationOrder/. -$VerticesSpecifications1[[repp]]]}]; - -(* The array is simply joined (flattened) *) - -genericcouplingvector[repp] = -Join@@(Table[genericcouplingvector[repp,filenr], -{filenr,Length[PerturbationOrder/. -$VerticesSpecifications1[[repp]]]}]); - -genericfields[repp] = -Table[ ToExpression["s"<>ToString[rep]]* -$VerticesSpecifications1[[repp,1,2,rep,0]][ -ToExpression["nr"<>ToString[rep]] ], -{rep,1,Length[$VerticesSpecifications1[[repp,1,2]]]} ]; - -genericfieldsmomenta[repp] = -Table[ ToExpression["s"<>ToString[rep]]* -$VerticesSpecifications1[[repp,1,2,rep,0]][ -ToExpression["nr"<>ToString[rep]], -ToExpression[$CouplingMomentumVariablesString<>ToString[rep]], -kineindex[$VerticesSpecifications1[[repp,1,2,rep,0]],rep] ], -{rep,1,Length[$VerticesSpecifications1[[repp,1,2]]]} ];, - -{repp,Length[$VerticesSpecifications1]}]; - -SetDirectory[olddir];); - -csign[rr_]:=CouplingSign/.$VerticesSpecifications1[[rr]]; - -(* ****************************************************************** *) - -(* The loaded coupling vectors and the constructed left-hand sides are -used for constructing the coupling definitions *) - -M$GenericCouplings = -Union[Table[ -AnalyticalCoupling@@(genericfieldsmomenta[repp])== -(G[csign[repp]]@@genericfields[repp]).genericcouplingvector[repp], -{repp,Length[$VerticesSpecifications1]}]]; - -(* Merge coupling vectors belonging to the same vertex *) - -multVertPosG = Position[M$GenericCouplings,#[[1]]]& /@ M$GenericCouplings; - -multVertsG = (Extract[M$GenericCouplings,#[[1]]]& /@ #)& /@ multVertPosG; - -vertsG = Union[(#[[1,1]] == merge @@ ((#[[2]])& /@ #))& /@ multVertsG]; - -M$GenericCouplings= - vertsG /. a:merge[(G[_][__].{__})..] :> a[[1,1]].(Join @@ ((#[[2]])& /@ a)); - -FixCouplingSigns; - -(* ****************************************************************** *) - -(* FermionFlipRules: for a certain mapping of Fermion fields in a coupling -we have to know which operations to perform. -OVERALL minus signs of the flipping are generated by defining G to be -anti-symmetric (G[-1]). -In this model, flip rules are applied for FSS- and FFV-couplings. -FSS contains only omega[+/-], so none of the rules matches. FVV -is antisymmetric and the rules match, resulting in -ga_mu omega[+] -> - ga_mu omega[-] -ga_mu omega[-] -> - ga-mu omega[+]. *) - -M$FermionFlipRule[ 1->2, 2->1, ___ ] = -{ -NonCommutative[ DiracGamma[li_],ChiralityProjector[ 1]] :> -- NonCommutative[ DiracGamma[li], ChiralityProjector[-1] ], -NonCommutative[ DiracGamma[li_],ChiralityProjector[-1]] :> -- NonCommutative[ DiracGamma[li], ChiralityProjector[ 1] ] -}; - -(* This was cleared in a release of FeynArts-3.7. Without it, Dirac traces are not taken *) -$FermionLines = True; -(* This should speed up a bit *) -$SparseCouplings = True; - -(* ****************************************************************** *) - -M$LastGenericRules = { -(* Outgoing vector bosons: throw away signs of momenta *) -PolarizationVector[ -p_, _. k:(FourMomentum[ Outgoing, i_Integer ]), li_ ] :> -Conjugate[PolarizationVector][ p, k, li ] , - -(* for the case of self-energies *) -PolarizationVector[ -p_, k:(- FourMomentum[ Incoming, 1 ]), li_ ] :> -Conjugate[PolarizationVector][ p, k, li ], - -(* relicts of the truncation of spinors: *) - -Dot[ 1, line__, 1 ] :> Dot[ line ], -Dot[ 1, 1 ] :> 1 }; - -(**) diff --git a/FeynCalc/Phi/Models/Automatic.mod b/FeynCalc/Phi/Models/Automatic.mod deleted file mode 100644 index ce77022f1..000000000 --- a/FeynCalc/Phi/Models/Automatic.mod +++ /dev/null @@ -1,357 +0,0 @@ -(* ************************************************************************* *) -(* *) -(* Automatic.mod *) -(* *) -(* ************************************************************************* *) - -(* - Author: Frederik Orellana 1997 - - Summary: Classes model for FeynArts - - Mathematica Version: 3.0 - - Requirements: FeynArts > 2, PHI, FeynCalc > 3 - - Description: The coupling vectors are loaded from - files generated by PHI -*) - -(* ************************************************************************* *) - -(* The minuses for outgoing particles are kept *) - -$VerticesSpecifications2:=($VerticesSpecifications/. - -qu_[q__]->HoldMinus[qu][q]); - -(* ************************************************************************* *) - -$ScreenSymbolFont = "Symbol"; - -(* - A table is generated with settings for the function isoindexx - to be called later on. - isovar[fi,j] is the base j'th iso-spin variable of the field fi - isovarii[fi,j,i] is Index[IsoSpin[isovar[fi,j]],i] - isorange[fi,j] is the range of the j'th iso-spin variable of the - field fi. - The result is that e.g. isoindexx[Pion[0],1,1] returns I1, - isoindexx[Pion[0],1,2] returns I2, ..., because 'I' is set to be - the first (and only) iso-index string of Pion[0] in - $CouplingIsoIndicesSpecifications. - isoindexxx[Pion[0],1] returns {I1}, but had Pion[0] had another - isospin index 'J'( e.g. Pion[0]->{{IsoRange->{1,2,3},IsoIndicesString->"I"}, - {IsoRange->{1,2},IsoIndicesString->"J"}} ), it would have returned {I1,J1} -*) - - -Clear[iistr,iiran,isovar,isovarii,isorange,isovars,isoindexx,isoindexxx]; - -Table[ - -Table[ - - iistr=$CouplingIsoIndicesSpecifications[[rep,2,indexnr,2,2]]; - iiran=$CouplingIsoIndicesSpecifications[[rep,2,indexnr,1,2]]; - - isovar[$CouplingIsoIndicesSpecifications[[rep,1]],indexnr]= - Index[IsoSpin[ToExpression[iistr]]]; - - isovarii[$CouplingIsoIndicesSpecifications[[rep,1]],indexnr,iii_]= - Index[IsoSpin[ToExpression[iistr]],iii]; - - isorange[$CouplingIsoIndicesSpecifications[[rep,1]],indexnr]= - iiran; - - setd[isoindexx[$CouplingIsoIndicesSpecifications[[rep,1]],indexnr,i_], - {stringj[iistr,tostr[i]]}], - -{indexnr,Length[$CouplingIsoIndicesSpecifications[[rep,2]]]}], - -{rep,Length[$CouplingIsoIndicesSpecifications]}]/. - -setd->SetDelayed; - - -isovar[(a:$ParticleHeads)[___],_]:={}; - -isovars[(a:$ParticleHeads)[i_]]:= -Flatten[Table[isovar[a[i],indexnr],{indexnr,Length[ -a[i]/.$CouplingIsoIndicesSpecifications]}]]; - -isovars[(a:$ParticleHeads)[___],_]:={}; - -isoindexx[(a:$ParticleHeads)[___],_,_]:={"seq[]"}; - -isoindexxx[(a:$ParticleHeads)[nr_],i_]:= -Flatten[Table[isoindexx[a[nr],indexnr,i],{indexnr, -Length[a[nr]/.$CouplingIsoIndicesSpecifications]}]]; - -isoindexxx[(a:$ParticleHeads)[___],_,_]:={"seq[]"}; - -(* ************************************************************************* *) - -(* All fields in $VerticesSpecifications *) -(* Change 20/3-1999 - mixing fields must also be included in this list *) - -allfieldstot= -Union[ -Flatten[Transpose[Transpose[ -$VerticesSpecifications1][[1]]/.Rule->List][[2]]], -If[Length[$MixingFields]>0,Transpose[$MixingFields/.Rule->List][[1]],{}]]; - -(* The actual setting of the ranges of the iso-spin variables *) - -Do[ - -Do[ - - IndexRange[ isovar[$CouplingIsoIndicesSpecifications[[reps,1]],indexnr] ] = - - Evaluate[isorange[$CouplingIsoIndicesSpecifications[[reps,1]],indexnr]]; - - TheLabel[ - isovarii[$CouplingIsoIndicesSpecifications[[reps,1]],indexnr,i5_] - ] = "" - (*Uncomment the following and comment '' to have - indices displayed*)(*{((isoindexx[ - $CouplingIsoIndicesSpecifications[[reps,1]],indexnr,reps])/. - tostr->ToString/.stringj->StringJoin)[[1]]," ","("," ", - i5,")"}*);, - -{indexnr,Length[$CouplingIsoIndicesSpecifications[[reps,2]]]}], - -{reps,Length[$CouplingIsoIndicesSpecifications]}]; - -(* ************************************************************************* *) - -(* The appearance for particles in $FAParticlesInUse is set. - FALabel gives the appearance, but is defined only for some particles *) - -TheLabel[iii_] := ToString[iii]; - -(TheLabel[#]=FALabel[Particle[#[0]][[1]],0])&/@$FAParticlesInUse; - -(* ************************************************************************* *) - -(* - The particle mass can have argument RenormalizationState[j], - where j is an integer specifying the order of renormalization. - This must be specified in $PropagatorMassesStates. - Notice that e.g. ParticleMass[PseudoScalar[2][0]] is - ParticleMass[PseudoScalar[2]], whereas ParticleMass[PseudoScalar[2][i]] - is just ParticleMass[PseudoScalar[2][i]] for i!=0. -*) - -FAParticleMass[(a:$ParticleHeads)[i_]]:= - ParticleMass[a[i],##]&@@( - a[i]/.$PropagatorMassesStates/.(aa:$ParticleHeads)[_]->{}); - -(* The particles can have mixing partners. This should be specified - in $MixingFields *) - -mixps[(a:$ParticleHeads)[i_]]/;!FreeQ[$MixingFields,a[i]]:= -a[i]/.$MixingFields; - -mixps[(a:$ParticleHeads)[_]]:={}; - -(* The particle may propagate only on a certain class of propagators. - This should be specified in $InsertOnly *) - -inso[(a:$ParticleHeads)[i_]]/;!FreeQ[$InsertOnly,a[i]]:= -a[i]/.$InsertOnly; - -inso[(a:$ParticleHeads)[_]]:={}; - -(* - descr[p[i]] returns the description for the particle p[i]. - Apart from the iso-spins, standard definitions are used for the - three types of particles. - All three types can have iso-spin indices. - (Only vectors have kinematical indices - see Automatic.gen.) - The propagator label is again given by FALabel. -*) - - (*The Sequence below inserted because of changes - from FA2.1 to FA2.2 - after advise by Thomas Hahn*) - -(* Change 20/3-1999 - allow specification of SelfConjugate *) - -descr[(a:$VectorHeads)[i_]]:= - a[i] == { - SelfConjugate -> - If[MemberQ[ - {True,False},SelfConjugation[a[i]]],SelfConjugation[a[i]],True], - Indices -> isovars[a[i]], - Mass -> FAParticleMass[a[i]], - PropagatorLabel -> (*We use that Particle[aN][0]=Particle[a[N]]. For i=!=0 FALabel definitions must be modified*) - ComposedChar[Sequence@@Join[{FALabel[Particle[a[i]][[1]],i]}, - isovars[a[i]]]], - PropagatorType -> Sine, - PropagatorArrow -> None, - MixingPartners -> mixps[a[i]], - InsertOnly -> inso[a[i]] }; - -descr[(a:$FermionHeads)[i_]]:= - a[i] == { - SelfConjugate -> - If[MemberQ[ - {True,False},SelfConjugation[a[i]]],SelfConjugation[a[i]],False], - Indices -> isovars[a[i]], - Mass -> FAParticleMass[a[i]], - PropagatorLabel -> - ComposedChar[Sequence@@Join[{FALabel[Particle[a[i]][[1]],i]}, - isovars[a[i]]]], - (*PropagatorType -> Dashing[{0.003,0.006}],*) - PropagatorType -> ScalarDash, - PropagatorArrow -> Forward, - MixingPartners -> mixps[a[i]], - InsertOnly -> inso[a[i]] }; - -descr[(a:$ScalarHeads)[i_]]:= - a[i] == { - SelfConjugate -> - If[MemberQ[ - {True,False},SelfConjugation[a[i]]],SelfConjugation[a[i]],True], - Indices -> isovars[a[i]], - Mass -> FAParticleMass[a[i]], - PropagatorLabel -> - ComposedChar[Sequence@@Join[{FALabel[Particle[a[i]][[1]],i]}, - isovars[a[i]]]], - PropagatorType -> Straight, - PropagatorArrow -> None, - MixingPartners -> mixps[a[i]], - InsertOnly -> inso[a[i]] }; - -(* ************************************************************************* *) - -(* The function descr is used to create descriptions for all particles *) - -M$ClassesDescription = (descr/@allfieldstot/. -{(Indices->{}):>Sequence[],(MixingPartners->{}):>Sequence[], -(InsertOnly->{}):>Sequence[]}); - -(* ************************************************************************* *) - -(* - The coupling vectors are read from the files specified in - $VerticesSpecifications. The left-hand side (classesfields) of the - defintion is created with the fields from $VerticesSpecifications -*) - -olddir=Directory[]; -SetDirectory[$HEPDir]; -SetDirectory["FeynCalc"]; -SetDirectory["Phi"]; -SetDirectory["CouplingVectors"]; - -Do[ - -Do[ - -(* The coupling vectors are loaded into an array *) - -cloadfile[filenr] = XName[listrepl[ -$VerticesSpecifications1[[repp]],filenr]]<>".Mod"; - -fpath = ToFileName[{$FeynCalcDirectory, "Phi", "CouplingVectors"}, cloadfile[filenr]]; - -VerbosePrint[1,repp," ",filenr, -" Loading classes coupling from ",fpath]; - -classescouplingvector[repp,filenr] = (Get[fpath]), - -{filenr,Length[PerturbationOrder/. -$VerticesSpecifications1[[repp]]]}]; - -(* - The array is parsed into a list of coupling vectors - with counterterm entries (if there are any couterterms). - Each coupling vector has the length of the flattened - array, and each element of each coupling vector is a - list of length Length[PerturbationOrder]. E.g. for - PerturbationOrder={2,4}, a classes coupling vector - corresponding to e.g. a generic coupling vector of the - form {m^2,p1^2,p1*p2,...,m^4,e^4,p1^4,...} would have the - form {{a1,0},{a2,0},{a3,0},...,{0,b1},{0,b2},...} -*) - -(* The list of zeros into which we will insert the coupling of - the right counterterm order, e.g. {0,0} becomes {a1,0} or - {0,b1} *) - -zerolist=Table[0,{Length[PerturbationOrder/. -$VerticesSpecifications1[[repp]]]}]; - -(* A temporary array of the form outerlist[innerlist[a1,a2,...], - innerlist[b1,b2,...],...] *) - -templist=outerlist@@innerlist/@Table[classescouplingvector[repp,filerep], - {filerep,Length[PerturbationOrder/. -$VerticesSpecifications1[[repp]]]}]/.innerlist[{ga__}]:>innerlist@@Join[ga]; - -(* Transforming the above array into the array we need *) - -(*zeroreplacerules=( - Table[templist[[pos]]->( - ReplacePart[zerolist,#,pos]&/@( - templist[[pos]]/.innerlist->List)),{pos,Length[templist]}]); - -classescouplingvector[repp] = -Join@@(templist/.zeroreplacerules);*) - -classescouplingvector[repp]= - Join@@Table[ - ReplacePart[zerolist,#,pos]&/@( - templist[[pos]]/.innerlist->List),{pos,Length[templist]}]; - -(* The list of in/out fields is extracted from $VerticesSpecifications *) - -classesfields[repp] = Table[ - $VerticesSpecifications2[[repp,1,2,rep,0]][ - $VerticesSpecifications1[[repp,1,2,rep,1]], - ToExpression[ - isoindexxx[$VerticesSpecifications1[[repp,1,2,rep]],rep]/. - tostr->ToString/.stringj->StringJoin]/.{{seq[]}->Sequence[], - {seq[],___}->Sequence[]}], - {rep,1,Length[$VerticesSpecifications1[[repp,1,2]]]} ]/. - HoldMinus[a_][b__]:>-a[b];, - -{repp,Length[$VerticesSpecifications1]}]; - -SetDirectory[olddir]; - -(* ************************************************************************* *) - -(* The coupling vectors and the list of in/out fields are used - for constructing the coupling definitions *) - -M$CouplingMatrices = - -Table[ - - C@@(classesfields[repp])==classescouplingvector[repp], - -{repp,Length[$VerticesSpecifications1]}]; - -(* Merge coupling vectors belonging to the same vertex *) - -multVertPosC = Position[M$CouplingMatrices,#[[1]]]& /@ M$CouplingMatrices; - -multVertsC = (Extract[M$CouplingMatrices, #[[1]]] & /@ #) & /@ multVertPosC; - -M$CouplingMatrices = Union[(#[[1, 1]] == Join @@ ((#[[2]]) & /@ #)) & /@ multVertsC]; - -FixCouplingIndices; - -(* ************************************************************************* *) - -extraLastRuls={HoldPattern[IndexDelta[i_Integer,i_Integer]] -> 1, - IndexDelta[i_Integer,j_Integer] -> 0}; - -M$LastModelRules = If[ListQ[M$LastModelRules ], - Union[M$LastModelRules, extraLastRuls,$LastModelRules ], - Union[extraLastRuls,$LastModelRules ] - ]; - -(**) diff --git a/FeynCalc/Phi/Objects.m b/FeynCalc/Phi/Objects.m deleted file mode 100644 index 9842dd3aa..000000000 --- a/FeynCalc/Phi/Objects.m +++ /dev/null @@ -1,7133 +0,0 @@ -(* Wolfram Language package *) - -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: Objects (Phi) *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Definitions for basic objects and operations of PHI *) - -(* ------------------------------------------------------------------------ *) - -(* SECTIONS: - - 1) UMatrix and UScalar DataTypes - 2) Non-commutative multiplication - 3) Iso-vector products - 4) Power functions - 5) Matrices - 6) Iso-vectors - 7) Explicit objects - 8) Field matrices - 9) Adjoints and conjugates - 10) Traces - 11) SU(2) and SU(3) structure constants - 12) Supplying iso-indices - 13) Transformation to FC notation - 14) Discarding terms - 15) Easy entering of lagrangians - 16) Commutation rules - -*) - -$SUNRules::usage = "$SUNRules is an environment variable used by SUNReduce \ -to (hopefully) simplify expressions involving the functions SU2Delta, \ -SU3Delta, SU2F, SU3F and/or SU3D. After changing it, FixSUN should be \ -evaluated."; - -$SUNDeltaRules::usage = "$SUNDeltaRules is an environment variable used by \ -SUNReduce to (hopefully) simplify expressions involving the functions \ -SU2Delta and/or SU3Delta. After changing it, FixSUN should be evaluated."; - -$SUNDFRules::usage = "$SUNDFRules is an environment variable used by \ -SUNReduce to (hopefully) simplify expressions involving the functions SU2F, \ -SU3F and/or SU3D. After changing it, FixSUN should be evaluated."; - -$SU3FReduceList::usage = "$SU3FReduceList is an environment variable used \ -by SUNReduce to (hopefully) simplify expressions involving the function SU3F. \ -It is regenerated automatically upon evaluating FixSUN and should not be \ -modified by hand."; - -$SU3DReduceList::usage = "$SU3DReduceList is an environment variable used \ -by SUNReduce to (hopefully) simplify expressions involving the function SU3D. \ -It is regenerated automatically upon evaluating FixSUN and should not be \ -modified by hand."; - -$SymSUNDFRUles::usage = "$SymSUNDFRUles is an environment variable used \ -by SUNReduce to (hopefully) simplify expressions involving the functions \ -SU2F, SU3F and SU3D."; - -$ExpansionQuantities::usage = "$ExpansionQuantities is an environment \ -variable used by e.g. MomentaCollect, GenericCoupling and DiscardOrders, \ -specifying which quantites apart from powers of the momenta should be \ -collected. It must be a list of patterns. Notice that the quantities should \ -be given as constants or patterns, but not starting with a blank. That is, \ -e.g. FourVector[__], NOT _FourVector. Naming the blank, e.g. \ -FourVector[a__], will cause collection only according to powers of \ -FourVector[a__], whereas the pure blank will collect only according to \ -FourVector[a__]*FourVector[b__] etc. To have both, both FourVector[__] \ -and FourVector[a__] should be included. Patterns with more than one \ -sequence of blanks like CouplingConstant[model[_],___] should be avoided or \ -the blanks should be named. Default value : \ -{FourVector[__],ParticleMass[Pion,a___],CouplingConstant[QED[1],c___]}."; - -SpaceTimeDimensions::usage = -"SpaceTimeDimensions is a symbol used by DimensionExpand for the \ -default setting of the option Dimension (the number of space-time dimensions)."; - -ScalarProductForm::usage = -"ScalarProductForm is an option for MomentaCollect, FCToFA, FAToFC, \ -GenericCoupling, ClassesCoupling and DiscardOrders, determining which head \ -is used for the scalarproduct of the momenta. One possibility is Pair. \ -ScalarProduct will not work, because \ -ScalarProduct[p1,p2] is immediately replaced with \ -Pair[Momentum[p1], Momentum[p2]], so to generate more readable coupling \ -files, ScalarProductForm can be set to some orderless function like e.g. \ -MomentaScalarProduct, which can then eventually (after generation of \ -amplitudes with FeynArts) be replaced with ScalarProduct. Default value : \ -MomentaScalarProduct|Pair for MomentaCollect MomentaScalarProduct otherwise."; - -Masses::usage = -"Masses is an option for MandelstamReduce and VeltmanExpand, specifying \ -the masses of the scattering process under consideration. For \ -MandelstamReduce there should be four masses. For VeltmanExpand, there can \ -be up to the number of external particles. To have only some of the \ -particles put on-mass-shell, specify e.g. Pair[Momentum[p1],Momentum[p1]] \ -instead of the mass of p1. Default value : \ -{ParticleMass[Pion,RenormalizationsState[0]],ParticleMass[Pion,\ -RenormalizationsState[0]],ParticleMass[Pion,RenormalizationsState[0]],\ -ParticleMass[Pion,RenormalizationsState[0]]}."; - -OnMassShell::usage = -"OnMassShell is an option for MandelstamReduce, AmplitudeProjection, \ -VeltmanExpand, WFFactor and WFRenormalize, specifying whether the 4-momenta \ -of the particles should be put on-mass-shell. MandelstamReduce and VeltmanExpand \ -use the setting of the option Masses, AmplitudeProjection the setting of the \ -option Channel for the numbering of the masses. Default value : False for \ -VeltmanExpand, WFFactor and WFRenormalize, True for the others."; - -PerturbationOrder::usage = -"PerturbationOrder is an option for MomentaCollect, XName, \ -CouplingFilesGenerate, DiscardOrders and FAToFC, specifying the maximum order in the \ -momentum and/or other perturbative expansion parameters from \ -$ExpansionQuantities. It is also and option for DiscardTopology, specifying \ -the order in some additional expansion. Default value : 2. NOTICE: \ -PerturbationOrder is also a setting of $VerticesSpecifications. In this case \ -it should be a list specifying the perturbation (counterterm) orders one \ -wants the model files Automatic.gen and Automatic.mod to include. At \ -present, the list must start at lowest order and have all orders up to the \ -highest order (no 'holes'). So to use only some orders, one has to create \ -coupling files (.Gen and .Mod) containing zero-couplings."; - -(* -End -*) - -(* -Options and environment constants used in this sub-package: -*) - - -MomentaScalarProduct::usage = -"MomentaScalarProduct is the default function of ScalarProductForm, it is \ -simply a wrapper with notational definitions symbolizing a scalar product and \ -has no analytic properties except for being orderless."; - -$StandardSUNBasis::usage = -"$StandardSUNBasis specifies whether or not the standard basis matrices \ -for SU(n) are used. If the basis $SUNBasis[n,j] is changed, it should be set \ -to False (and after that, FixSUN should be evaluated). NOTICE : When not \ -using the standard basis, SUNF is not necessarily antisymmetric in the last \ -two indices and other simplifications are disabled too. Default value : \ -True."; - -SU2Delta::usage = "SU2Delta is the Kronecker delta function of SU(2)."; - -SU3Delta::usage = "SU3Delta is the Kronecker delta function of SU(3)."; - -SU2F::usage = -"SU2F[i,j,k] are the totally antisymmetric structure constants of SU(2). \ -The values returned with integer arguments are determined by the setting of \ -$SUNBasis[n,j]."; - -SU3F::usage = -"SU3F[i,j,k] are the totally antisymmetric structure constants of SU(3). \ -The values returned with integer arguments are determined by the setting of \ -$SUNBasis[n,j]."; - -SU3D::usage = -"SU3D[i,j,k] are the totally symmetric coefficients of SU(3). The values \ -returned with integer arguments are determined by the setting of \ -$SUNBasis[n,j]."; - -FixSUN::usage = -"After changing the setting of $SUNBasis[n,j] and $StandardSUNBasis, \ -FixSUN should be run in order for the change to be effective for the \ -structure constants os SU(2) and/or SU(3)."; - -$ConstantIsoIndices::usage = -"$ConstantIsoIndices are the isospin indices that are not automatically \ -contracted or summed over by SUNReduce. To avoid problems with couplings \ -containing SU3D and tadpoles, these indices should contain the indices \ -FeynArts uses for dummy indices. Default value : {I1,I2,I3,I4,I5,I6}."; - -UIndex::usage = -"UIndex is the head of the indices pertaining to matrices in the space \ -spanned by the generators of the gauge group and the corresponding vectors of \ -dimension given by UDimension, as e.g. supplied by UIndicesSupply. UIndex is \ -by default substituted with SUNIndex by UIndicesSupply."; - -$SUNBasis::usage = -"For general j, $SUNBasis[n,j] are the cartesian basis matrices of \ -dimension 2 j+1 of the group SU(n) acting on spherical vectors. NOTICE: \ -Changing $SUNBasis[n,j], where n is 2 or 3 will affect the values returned by \ -the functions SU2F or SU3F and SU3D."; - -$RenormalizationSuperscripts::usage = -"$RenormalizationSuperscripts is a list of strings specifying the \ -superscripts to be displayed in TraditionalForm for RenormalizatonState[0], \ -RenormalizationState[1], ... Default value : {\"\",\"r\"}."; - -$RSSuperscripts::usage = -"$RSSuperscripts is a list of strings specifying the superscripts to be \ -displayed in TraditionalForm for RenormalizatonScheme[0], \ -RenormalizatonScheme[1], ... Default value : {\"\",\"\"}."; - -$ExpansionSuperscripts::usage = -"$ExpansionSuperscripts is a list of strings specifying the superscripts \ -to be displayed in TraditionalForm for ExpansionState[0], ExpansionState[1], ... \ -Default value : {\"\",\"\"}."; - -$UMatrices::usage = -"$UMatrices is a list of objects which, besides objects with \ -head UMatrix, should be treated as matrices in flavor space. Default value : \ -{UMatrix,MM,SMM,UChiMatrix,USmall,UFPlus,UFMinus,UChiPlus,UChiMinus,UGamma}."; - -IndexBox::usage = -"IndexBox is a head used by for the renormalization superscripts."; - -MM::usage = "MM[x] := -UFieldMatrix[QuantumField[Particle[Pion]][x]]. MM takes three optional \ -arguments with head RenormalizationState, RenormalizationScheme and \ -ExpansionState respectively. MM[i,x] is the i'th power of MM[x]."; - -SMM::usage = "SMM[x] := MM[1/2,x]."; - -MMS::usage = "MMS[x] := -UFieldMatrixSeries[QuantumField[Particle[Pion]][x]]. MMS takes tthree \ -optional arguments with head RenormalizationState, RenormalizationScheme and \ -ExpansionState respectively."; - -NMExpand::usage = -"NMExpand[expr] expands sums in NM products."; - -UDotExpand::usage = -"UDotExpand[expr] expands sums in UDot products."; - -(*DotExpand::usage = -"DotExpand[expr] expands sums in DOT products";*) - -NMSeriesExpand::usage = -"NMSeriesExpand[expr] expands series in NM products."; - -NMFactor::usage = -"NMFactor[expr] factors out overall factors in sums of NM products."; - -(* Commented out because of the different definition below -FieldStrengthTensor::usage = -"FieldStrengthTensor[LorentzIndex[mu],QuantumField[Particle[p],\ -LorentzIndex[nu]][x]] gives the field strength tensor of the particle/source \ -p without the cross product or commutator term. To find the fieldstrength \ -tensor of composed objects, a space-time argument x must be added, i.e. \ -FieldStrengthTensor[obj,LorentzIndex[mu],x] tries to construct the field \ -strength tensor of the object obj.";*) - -FieldStrengthTensorFull::usage = -"FieldStrengthTensorFull[LorentzIndex[mu],IsoVector[obj[LorentzIndex[\ -nu]]][x],c] gives the field strength tensor of the object obj including the cross \ -product term. \ -FieldStrengthTensorFull[LorentzIndex[mu],m[LorentzIndex[nu]],x,c] gives the \ -field strength tensor of the iso-matrix object m including the commutator \ -term. c is an optional parameter specifying the coupling constant \ -multiplying the cross product and commutator term respectively. When not \ -given it is set to 1 and I respectively."; - -FST::usage = "FST is a shortcut for entering a complex object often needed \ -in e.g ChPT. FST[p,mu,nu,x] := \ -FieldStrengthTensor[mu,UGeneratorMatrixIsoDot[QuantumField[Particle[p],nu][x]]\ -,x]+2*I*IsoCross[IsoVector[QuantumField[Particle[p],mu],##][x],IsoVector[\ -QuantumField[Particle[p],nu]][x]]. p is a member of $Particles, mu and nu \ -have head LorentzIndex. FST takes three optional arguments with head \ -RenormalizationState, RenormalizationScheme and ExpansionState respectively \ -and the option SUNN."; - -QED::usage = -"CouplingConstant[QED[1]] is the unit \ -charge."; - -PhiMesonIsoVector::usage = -"PhiMesonIsoVector[x_,opts___] := IsoVector[QuantumField[ -Particle[PhiMeson,RenormalizationState[0]]],opts][x]."; - -PionIsoVector::usage = -"PionIsoVector[x_,opts___] := IsoVector[QuantumField[ -Particle[Pion,RenormalizationState[0]]],opts][x]."; - -Global`$Lagrangians::usage = -"$Lagrangians is a list of the lagrangians loaded (without heads \ -Lagrangian). Setting $Lagrangians to a list of lagrangians in PhiStart.m \ -causes these lagrangians to be loaded at startup."; - -$ParticlesInUse::usage = -"$ParticlesInUse is a variable specifying which PHI-particles are \ -recognized by FeynArts (modified as described in ReadMe.txt) as field names. \ -Default value : {Pion, Kaon, Photon}."; - -$FAParticlesInUse::usage = -"$FAParticlesInUse is $ParticlesInUse in the notation which is actually \ -fed to FeynArts. Default value : {PseudoScalar2,PseudoScalar6,Vector1}."; - -SelfConjugation::usage = -"SelfConjugation is a function taking elements of $FAParticlesInUse as \ -argument and returning True or False. Default values are assigned according \ -to the particle type (scalar, vector or fermion), but these can be changed \ -either also according to the particle type or on a per particle basis. These \ -changes should be made in the relevant configuration (.conf) files."; - -SetFAField::usage = -"SetFAField[f] defines f[i][j] to be fi[j]. E.g. SetFAField[Fermion] \ -defines e.g. Fermion[7][0] to be Fermion7[0]. This truncation of particle \ -heads is a hack to make the pattern matching of FeynArts work with PHI \ -fields."; - -$ParticleHeads::usage = -"$ParticleHeads is a pattern used by the patched version of FeynArts to \ -recognize the particles in $ParticlesInUse."; - -FAUpdate::usage = -"FAUpdate is a command that when issued forces the functions \ -ParticleMass, DecayConstant and Particle to reread $ParticlesInUse."; - -$FermionHeads::usage = -"$FermionHeads is a pattern used by the patched version of FeynArts to \ -recognize the fermions in $ParticlesInUse."; - -$VectorHeads::usage = -"$VectorHeads is a pattern used by the patched version of FeynArts to \ -recognize the vectors and axialvectors in $ParticlesInUse."; - -$ScalarHeads::usage = -"$ScalarHeads is a pattern used by the patched version of FeynArts to \ -recognize the scalars and pseudoscalars in $ParticlesInUse."; - -FALabel::usage = -"To specify a string l to be printed for a particle p[i] by FeynArts, \ -where the index i is an obligatory index of FeynArts specifying that it is \ -the i'th kind of particle p, one should set FALabel[p,i] := l. This can \ -conveniently be done in PhiStart.m or a relevant configuration file."; - -UExp::usage = -"UExp[a,n] returns a power series (in normal form) in a, with \ -coefficients $UExpansionCoefficients truncated at n. UExp[i,a,n] is the i'th \ -power of UExp[a,n]. The non-commutative power NMPower is used. UExp is used \ -by UFieldMatrix."; - -UExpSeries::usage = -"UExpSeries[a,n] returns a power series in a, with coefficients \ -$UExpansionCoefficients truncated at n. The ordinary Power is used. UExp is \ -used by UFieldMatrixSeries. NOTICE: UExpSeries yields a power series - use \ -Normal to get rid of the O[a]^(n+1) term."; - -UFieldMatrix::usage = -"UFieldMatrix[field[x]] is the operator field matrix of the field type \ -field (usually representing the pseudoscalar meson triplet or octet). \ -UFieldMatrix takes an extra argument with head ExpansionState. \ -UFieldMatrix[i,field[x],opts] is the i'th power of \ -UFieldMatrix[field[x],opts]."; - -UFieldMatrixSeries::usage = -"UFieldMatrixSeries[field[x],opts] is the operator field matrix of the \ -field type field (usually representing the pseudoscalar meson triplet or \ -octet). UFieldMatrixSeries takes an extra argument with head ExpansionState. \ -NOTICE: UFieldMatrixSeries yields a power series - use Normal to get rid of \ -the O[a]^(n+1) term."; - -UNMSplit::usage = -"UNMSplit[expr,x,opts] returns the expression expr with NM products of MM \ -and SMM (without arguments) expanded to the order given by the setting of the \ -option DropOrder in the meson fields. DropOrder is the only option of \ -UNMSplit, but other options can be given, which are then passed on to the \ -resulting expressions. Using this function on lagrangians before \ -ArgumentsSupply and DiscardTerms should significantly improve perfomance when \ -working with complicated lagrangians. This is because NM products are \ -decomposed in sums of NM products with each factor containing only the \ -relevant term in the expansion in meson fields. The list of \ -substitution rules $Substitutions is applied before anything else. \ -NOTICE: UNMSplit works only \ -on NM products. Ordinary products should be replaced with NM before applying \ -UNMSplit."; - -Substitute::usage = -"Substitute[expr] applies $Substitutions to expr."; - -USplit::usage = -"USplit is the support function for UNMSplit doing the actual work. \ -USplit[NM[expr],x,opts] returns NM[expr] with MM and SMM (without arguments) \ -expanded to the order given by the setting of the option ExpansionOrder in \ -the meson fields. USplit has no options, but other options can be given, \ -which are then passed on to the resulting expressions."; - -ArgumentsSupply::usage = -"ArgumentsSupply is a function that allows the quick entering of \ -lagrangians. That is, an expression expr can be given without heads for \ -derivatives, Lorentz and isospin arguments and without an extra pairs of \ -empty brackets for scalars. ArgumentsSupply[expr,x,opts] then returns expr \ -with space-time argument x and options specifications and brackets supplied. \ -The relevant option specifications for each function are taken from opts. \ -ArgumentsSupply has no independent options of its own, but the list of \ -substitution rules $Substitutions is applied before anything else. NOTICE: For \ -FieldDerivative and CovariantFieldDerivative, the space-time argument must \ -be ommited and the Lorentz indices must be collected between a pair of curly \ -brackets. NOTICE ALSO: Only standard objects (like MM, SMM, UChiMatrix) are \ -supported by ArgumentsSupply. Non-standard UMatrix, IsoVector, etc. objects \ -must either be entered 'by hand' or be made known by adding rules to $Substitutions."; - -$Substitutions::usage = -"$Substitutions is a list of substitution rules applied repeatedly by \ -ArgumentsSupply."; - -$PreSubstitutions::usage = -"$PreSubstitutions[x] is a list of substitution rules used by ArgumentsSupply."; - -$PostSubstitutions::usage = -"$PostSubstitutions[x] is a list of substitution rules used by ArgumentsSupply."; - -SubX::usage = -"SubX is a variable used in the definitions of $PreSubstitutions and \ -$PostSubstitutions."; - -SubArgs::usage = -"SubArgs is a variable used in the definitions of $PreSubstitutions and \ -$PostSubstitutions."; - -DropOrder::usage = -"DropOrder is an option for UFieldMatrix, UNMSplit and CreateFCAmp. \ -When set to some integer \ -different from Infinity, all iso-vectors of the given field are multiplied \ -with the numeric quantity DropFactor[field] (which is brought out of all \ -non-commutative products). Automatically all powers of DropFactor[] higher \ -than DropOrder are dropped. Notice that when enabling this option, the \ -factor DropFactor[___] should after evaluation of all products be set to 1. \ -This is done automatically by the funtions DiscardTerms and ArgumentsSupply. \ -For CreateFCAmp, DropOrder is only relevant when WaveFunctionRenormalize is set to \ -True, in which case it determines the order above which to drop powers of momenta and \ -objects from $ExpansionQuantities. -Default value : Infinity for UFieldMatrix and 4 for FAToFC."; - -DropFactor::usage = -"DropFactor[field] is the numeric factor used by UFieldMatrix[field,opts] \ -when the option DropOrder is enabled. Notice that the factor DropFactor[___] \ -should after evaluation of all products be set to 1. This is done \ -automatically by the funtions DiscardTerms and ArgumentsSupply."; - -UMatrixProduct::usage = -"UMatrixProduct[a,b] is the matrix product of the two matrices a and b, \ -with non-commutative multiplication NM instead of the usual multiplication \ -between the components."; - -UMatrixPower::usage = -"UMatrixPower[m,n] is the n'th matrix power of the matrix m, with \ -non-commutative multiplication NM instead of the usual multiplication between \ -the components."; - -(*Not used I think. 29/10-2003*) -(*UDotPower::usage = -"UDotPower[v,n] is the n'th power of the U-vector v, with the \ -non-commutative IsoDot instead of the usual multiplication between the \ -components.";*) - -NMPower::usage = -"NMPower[a,n] is the n'th power of the quantity a, with the \ -non-commutative multiplication NM instead of the usual multiplication."; - -CovariantNabla::usage = -"CovariantNabla[f[x],x,{li1,li2,...},opts] is some covariant derivative \ -of f[x] with respect to space-time variables x and with Lorentz indices li1, \ -li2,... By default CovariantNabla is left undefined and should , if needed, \ -be defined in the relevant configuration file. CovariantNabla is recognized \ -by ArgumentsSupply and partly by UNMSplit, that is, for UNMSplit to work, \ -CovariantNabla[f[x],{li1,li2,...},opts] should be defined and return the \ -'extra' part apart from the derivative."; - -Adjoint::usage = -"Adjoint[x] is the adjoint of x, where matrices (with head UMatrix) are \ -transposed and conjugated and scalars (declared with DeclareUScalar) are just \ -conjugated. Adjoint[QuantumField[Particle[p]]] := \ -QuantumField[Adjoint[Particle[p]]]."; - -ChargeConjugate::usage = -"ChargeConjugate[q] is the charge conjugate (anti-particle) of the \ -QuantumField q. ChargeConjugate[QuantumField[Particle[p]]] := \ -QuantumField[Particle[ChargeConjugate[p]]]."; - -DiracBar::usage = -"DiracBar[QuantumField[Particle[p]]] := QuantumField[DiracBar[Particle[p]]],\ -which represents Adjoint[QuantumField[Particle[p]]].DiracMatrix[LorentzIndex[0]]."; - -DeclareUMatrix::usage = -"DeclareUMatrix[m] declares m as a matrix in flavor space for non-commutative \ -functions of PHI. This includes adding m to the list $UMatrices."; - -UndeclareUMatrix::usage = -"UndeclareUMatrix[m] clears m as a matrix in flavor space for non-commutative \ -functions of PHI. This includes removing m from the list $UMatrices."; - -DeclareUScalar::usage = -"DeclareUScalar[s] declares s as a scalar in flavor space for non-commutative \ -functions of PHI. This includes adding s to the list $UScalars."; - -UndeclareUScalar::usage = -"UndeclareUScalar[s] clears s as a scalar in flavor space for non-commutative \ -functions of PHI. This includes removing s from the list $UScalars."; - -$UScalars::usage = -"$UScalars is a list of the scalars known by PHI. Members of this list \ -are function names and they must be Atomic quantities. Apart from the default \ -scalars, others can be added with DeclareUScalar. Default value : \ -{QuarkCondensate, ParticleMass, DecayConstant, CouplingConstant, SU3D, SU3F, \ -SU3Delta, PhiProjection, SUNIndex, SUNF, SUND, SUNDelta}."; - -UScalarQ::usage = -"UScalarQ[x] returns True if x is a scalar as defined with DeclareUScalar \ -or an explicit numerical quantity."; - -UScalar::usage = -"UScalar is a DataType. DataType[x, UScalar] returns True if x is a scalar \ -as defined with DeclareUScalar or an explicit numerical quantity."; - -UMatrixQ::usage = -"UMatrixQ[x] returns True if x is a matrix as defined with DeclareUMatrix \ -or an explicit matrix."; - -UTrace::usage = - "UTrace[ff] gives the trace of expressions involving matrices with defined \ -traces. The option SUNN specifies the trace of UIdentityMatrix: For \ -UTrace[m[opts1],opts2], the setting given in the opts2 overrules the setting \ -of opts1, but when no setting is made in opts2, opts1 is used. When no \ -setting is made in neither opts1 nor opts2, the default of UTrace is used. \ -The option TraceSimplify specifies whether some simplification rules should \ -be implemented. E.g.: UTrace[UGeneratorMatrixIsoVector[opts]^2] is 6 (16) \ -for SUNN 2 (3). For SU(2) UTrace[UGeneratorMatrixIsoVector[opts]^n] is \ -0 for odd n. When UTrace cannot trace a quantity a, UTrace1[a] is returned."; - -CycleUTraces::usage = - "CycleUTraces[ex] rotates the factors in NM or DOT products inside UTrace1 \ -untill the 'lowest' factor is in front. CycleUTraces[ex, f] does the same \ -but using f as the ordering function."; - -HoldUTrace::usage = - "HoldUTrace is an option of UTrace specifying whether or not the trace \ -should be performed."; - -UTrace1::usage = - "UTrace1[a] is what UTrace[a] yields when the trace of a is not known by \ -PHI."; - -TraceSimplify::usage = - "TraceSimplify is an option for UTrace specifying whether some \ -simplification rules should be implemented. E.g.: \ -UTrace[UGeneratorMatrixIsoVector[opts]^2] is 6 (16) for SUNN 2 (3). For \ -SU(2) UTrace[UGeneratorMatrixIsoVector[opts]^n] is 0 for odd n. Default \ -value : True."; - -UTraceToFCTrace::usage = - "UTraceToFCTrace[amp] replaces UTrace of amp with SUNTrace of FeynCalc. \ -This function must be used to do the replacement, a plain substitution will \ -NOT work. Notice that FeynCalc treats all isospin indices as color indices."; - -UChiMatrix::usage = -"UChiMatrix[x,opts] := UMatrix[UChi[opts],opts][x].\ - UChiMatrix takes three optional arguments, with head RenormalizationState, \ -RenormalizationScheme and ExpansionState respectively."; - -UChi::usage = -"UChiMatrix[opts] := UMatrix[UChi[opts],opts]."; - -UGeneratorMatrixIsoDot::usage = -"UGeneratorMatrixIsoDot[a[x],opts] := IsoDot[IsoVector[a,opts][x], \ -UGeneratorMatrixIsoVector[opts]]."; - -UGeneratorMatrixIsoDotFull::usage = -"UGeneratorMatrixIsoDotFull[a[x],opts] := \ -UGeneratorMatrixIsoDot[a[x],opts] + a[x]*UIdentityMatrix[opts], where the \ -last a is assigned SUNIndex[0]."; - -QuarkCondensate::usage = -"QuarkCondensate[opts] (no options recognized as of yet) is the quark \ -antiquark vacuum to vacuum amplitude divided by -DecayConstant[Pion]^2, that \ -is, the low energy constant usually denoted by B0 and given by <0|q qbar|0> = \ --DecayConstant[Pion]^2 B0 and/or ParticleMass[Pion]^2 = \ -(ParticleMass[UpQuark]+ParticleMass[DownQuark]) B0 + (ParticleMass[UpQuark] + \ -ParticleMass[DownQuark])^2 C0 +... QuarkCondensate takes three optional \ -arguments, with head RenormalizationState, RenormalizationScheme and \ -ExpansionState respectively."; - -DiagonalUMatrix::usage = -"DiagonalUMatrix[list,opts] returns the diagonal matrix with diagonal \ -elements list as a linear combination of the generator matrices \ -(UGeneratorMatrix) and the identity matrix (UIdentityMatrix). What is \ -returned depends on the setting of $SUNBasis[n,j] (from which \ -UGeneratorMatrix is derived)."; - -UQuarkMassMatrix::usage = -"UQuarkMassMatrix[opts] := UMatrix[UQuarkMass[opts],opts] is the diagonal \ -quark mass matrix. UQuarkMassMatrix takes three optional arguments, with \ -head RenormalizationState, RenormalizationScheme and ExpansionState \ -respectively. Notice that it depends on the setting of the environment \ -variables $QuarkToPionMassesRules and $QuarkToMesonMassesRules, whose default \ -setting is equivalent to standard ChPT and isospin symmetry in SU(2)."; - -UQuarkMass::usage = -"UMatrix[UQuarkMass[opts],opts] =: UQuarkMassMatrix[opts] is the diagonal \ -quark mass matrix."; - -UQuarkChargeMatrix::usage = -"UQuarkChargeMatrix[opts] := UMatrix[UQuarkCharge[opts],opts] is the \ -diagonal quark charge matrix. UQuarkChargeMatrix takes three optional \ -arguments, with head RenormalizationState, RenormalizationScheme and \ -ExpansionState respectively."; - -UQuarkCharge::usage = -"UMatrix[UQuarkCharge[opts],opts] =: UQuarkChargeMatrix[opts] is the \ -diagonal quark charge matrix."; - -UNucleonChargeMatrix::usage = -""; - -UNucleonCharge::usage = -""; - -UChiralSpurion::usage = -"UMatrix[UChiralSpurion[]][x] represents some \ -spurion. It should be defined in the model configuration files. \ -Usually it is set the the quark charge matrix in the end."; - -UChiralSpurionLeft::usage = -"UMatrix[UChiralSpurionLeft[]][x] represents some lefthanded \ -spurion."; - -UChiralSpurionRight::usage = -"UMatrix[UChiralSpurionRight[]][x] represents some lefthanded \ -spurion."; - -UChiralSpurionMatrix::usage = -"UChiralSpurionMatrix[opts]:=UMatrix[UChiralSpurion[opts]][x]."; - -UChiralSpurionLeftMatrix::usage = -"UChiralSpurionLeftMatrix[opts]:=UMatrix[UChiralSpurionLeft[opts]][x]."; - -UChiralSpurionRightMatrix::usage = -"UChiralSpurionRightMatrix[opts] :=UMatrix[UChiralSpurionRight[]][x]."; - -QuarkToMesonMasses::usage = -"QuarkToMesonMasses is an option for UQuarkMass specifying whether the \ -quark masses in the quark mass matrix should be expressed by the meson masses \ -using the mass relations $QuarkToPionMassesRules (when SUNN is set to \ -2) or $QuarkToMesonMassesRules (when SUNN is set to 3). Default value \ -: True."; - -DiagonalToU::usage = -"DiagonalToU is an option for UQuarkMass and UQuarkCharge specifying \ -whether the diagonal quark mass matrix should be written as a linear \ -combination of the matrices spanning SU(n) (of the form \ -UGeneratorMatrix[SUNIndex[i],opts]) and UIdentityMatrix[opts]. Notice that \ -the transformation depends on the setting of $SUNBasis[n,j]. Default value : \ -False."; - -(*Commented out 11/5-2003*) -(*RemoveIntegerIndices::usage = -"RemoveIntegerIndices is an option for UQuarkMass, UChi, UQuarkCharge, \ -ExpandU, SUNReduce and PhiToFC which determines whether or not isospin \ -functions of integer indices are substituted with a product involving a \ -projection operator (that is, a Kronecker delta function), e.g. \ -UGeneratorMatrix[n,opts] is substituted with \ -IsoDot[ProjectionIsoVector[n,opts],UGeneratorMatrixIsoVector[opts]], where n \ -is an integer. For UQuarkMass and UQuarkCharge it is relevant only when \ -DiagonalToU is enabled. NOTICE: This option does not cause SUNReduce to do \ -the mentioned substitution, it simply causes it not to substitute \ -PhiProjection[m][SUNIndex[n]] with SU2Delta[SUNIndex[m],SUNIndex[n]] or \ -SU3Delta[SUNIndex[m],SUNIndex[n]]. Default value : False. \ -NOTICE : This option really is a hack to make up for the fact that \ -FeynCalc did not like integer valued arguments to SUN functions. It should be \ -completely redundant after version 4.1.0.3 of FeynCalc.";*) - -ProjectionIsoVector::usage = -"ProjectionIsoVector[i_, opts___] := IsoVector[PhiProjection[i], opts]."; - -PhiProjection::usage = -"PhiProjection[i_][j_] := SUNDelta[i, j]."; - -PhiMeson::usage = - "PhiMeson := PseudoScalar[1] represents the pseudoscalar octet of Goldstone \ -bosons."; - -Pion::usage = -"Pion := PseudoScalar[2] represents the triplet of pions. \ -ParticleMass[1,Pion]^2 is the squared renormalized pion mass to first order \ -in the quark masses. ParticleMass[1,Pion,0]^2 is the squared unrenormalized \ -pion mass to first order in the light quark mass. The first integer is \ -optional. When ommited, a 1 is understood. ParticleMass[1,Pion]^2 is thus \ -understood to be equal to (ParticleMass[UpQuark]+ParticleMass[DownQuark]) \ -QuarkCondensate[]. DecayConstant[Pion] is the renormalized pion decay \ -constant. The use of the variable ParticleMass[Pion] for the pion mass is \ -crucial only for the function amplitude[s] when using \ -ScatteringLength[amplitude,m1,m2,ParticleMass[Pion],s,l,opts]. For all other \ -functions whatever symbol may be used."; - -PionPlus::usage = -"PionPlus := PseudoScalar[3] represents the pion of charge +1."; - -PionZero::usage = -"PionZero := PseudoScalar[4] represents the pion of charge 0."; - -PionMinus::usage = -"PionMinus := PseudoScalar[5] represents the pion of charge -1."; - -Kaon::usage = -"Kaon := PseudoScalar[6] is the generic name for the four Kaons."; - -KaonPlus::usage = -"KaonPlus := PseudoScalar[7] represents the kaon of charge +1."; - -KaonZero::usage = -"KaonZero := PseudoScalar[8] represents the kaon of charge 0."; - -KaonZeroBar::usage = -"KaonZeroBar := PseudoScalar[9] represents the anti-particle of the \ -KaonZero of charge 0."; - -KaonMinus::usage = -"KaonMinus := PseudoScalar[10] represents the kaon of charge -1."; - -EtaMeson::usage = "EtaMeson := PseudoScalar[11] represents the eta meson."; - -UPerturbation::usage = "UPerturbation := PseudoScalar[12] represents the \ -perturbation of the meson matrix around the solution of the equation of motion."; - -Lepton::usage = "Lepton := Fermion[1] represents a lepton."; - -Neutrino::usage = "Neutrino := Fermion[2] represents a neutrino."; - -ElectronNeutrino::usage = -"ElectronNeutrino := Fermion[3] represents an electron-neutrino."; - -MuonNeutrino::usage = -"MuonNeutrino := Fermion[4] represents a muon-neutrino."; - -TauonNeutrino::usage = -"TauonNeutrino:= Fermion[5] represents a tauon-neutrino."; - -MassiveLepton::usage = -"MassiveLepton := Fermion[6] represents a massive lepton."; - -Electron::usage = "Electron:=Fermion[7] represents the electron."; - -Muon::usage = "Muon := Fermion[8] represents the muon."; - -Tauon::usage = "Tauon := Fermion[9] represents the tauon."; - -Quark::usage = "Quark := Fermion[10] represents a quark."; - -LightQuark2::usage = -"LightQuark2 := Fermion[11] represents the two lightest quarks."; - -LightQuark3::usage = -"LightQuark3:=Fermion[12] represents the three lightest quarks."; - -DownQuark::usage = "DownQuark := Fermion[13] represents the down-quark."; - -UpQuark::usage = "UpQuark := Fermion[14] represents the up-quark."; - -StrangeQuark::usage = -"StrangeQuark := Fermion[15] represents the strange-quark."; - -CharmQuark::usage = "CharmQuark := Fermion[16] represents the charm-quark."; - -BottomQuark::usage = -"BottomQuark := Fermion[17] represents the beauty-quark."; - -TopQuark::usage = "TopQuark := Fermion[18] represents the truth-quark."; - -BBaryon::usage = -"BBaryon := Fermion[19] represents the octuplet of light baryons."; - -Nucleon::usage = "Nucleon := Fermion[20] represents the two nucleons."; - -Proton::usage = "Proton := Fermion[21] represents the proton."; - -Neutron::usage = "Neutron := Fermion[22] represents the proton."; - -LambdaBaryon::usage = -"LambdaBaryon := Fermion[23] represents the lambda baryon."; - -SigmaPlusBaryon::usage = -"SigmaPlusBaryon := Fermion[24] represents the Sigma-plus baryon."; - -SigmaZeroBaryon::usage = -"SigmaZeroBaryon := Fermion[25] represents the Sigma-zero baryon."; - -SigmaMinusBaryon::usage = -"SigmaMinusBaryon := Fermion[26] represents the Sigma-minus baryon."; - -XiZeroBaryon::usage = -"XiZeroBaryon := Fermion[27] represents the xi-minus baryon."; - -XiMinusBaryon::usage = -"XiMinusBaryon := Fermion[28] represents the xi-minus baryon."; - -Photon::usage = "Photon := Vector[1] represents the photon."; - -Scalar::usage = -"Scalar[i] where i = 1, 2, ... represents a scalar particle or source. \ -Particle[Scalar[i],0]] is an unrenormalized scalar field. \ -Particle[Scalar[i]] is a renormalized scalar field. Scalar[0] is reserved \ -for UChiMatrix."; - -PseudoScalar::usage = -"PseudoScalar[i], where i = 1, 2, ... represents a pseudoscalar particle \ -or source. PseudoScalar[0] is reserved for UChiMatrix. PseudoScalar[1], \ -..., PseudoScalar[11] are reserved for particles."; - -Vector::usage = -"Vector[i], where i = 1, 2, ... represents a vector particle or source. \ -Vector[0] is usually reserved for the CovariantFieldDerivative. Vector[1] is \ -reserved for the photon."; - -AxialVector::usage = -"AxialVector[i], where i = 1, 2, ... represents an axialvector particle \ -or source. AxialVector[0] is usually reserved for the \ -CovariantFieldDerivative."; - -LeftComponent::usage = -"LeftComponent[i], where i = 1, 2, ... represents the left-handed \ -particle or source corresponding to Vector[i] and AxialVector[i]. \ -LeftComponent[0] is usually reserved for the CovariantFieldDerivative."; - -RightComponent::usage = -"RightComponent[i], where i = 1, 2, ... represents the right-handed \ -particle or source corresponding to Vector[i] and AxialVector[i]. \ -RightComponent[0] is usually reserved for the CovariantFieldDerivative."; - -Fermion::usage = -"Fermion[i], where i = 1, 2, ... represents a fermion particle or source. \ -Fermion[1] is reserved for the dublet or octuplet of baryons."; - -Particle::usage = -"Particle[p], where p is some particle or source from $Particles, \ -represents a quantum operator field. Particle takes \ -three optional arguments with head RenormalizationState, \ -RenormalizationScheme and ExpansionState respectively. E.g. \ -QuantumField[Particle[Pion],{},{i1}][x] is the pion field operator with \ -isospin i1."; - -ParticleMass::usage = -"ParticleMass[p] is the mass of the particle p. \ -ParticleMass[p,SUNIndex[i]] is the mass of the particle p with isospin index \ -i. ParticleMass takes three more optional arguments with head \ -RenormalizationState, RenormalizationScheme and ExpansionState respectively. \ -The possible values of p are listed in $Particles."; - -DecayConstant::usage = -"DecayConstant[p] is the decay constant of the particle p. \ -DecayConstant[p,SUNIndex[i]] is the mass of the particle p with isospin \ -index i. DecayConstant takes three optional arguments, with head \ -RenormalizationState, RenormalizationScheme and ExpansionState respectively. \ -The possible values of p are listed in $Particles."; - -RenormalizationState::usage = -"RenormalizationState is the head of an optional arguments of Particle, \ -CouplingConstant, ParticleMass and DecayConstant. Usually the inclusion of \ -the index RenormalizationState[0] means that the quantity is unrenormalized \ -and RenormalizationState[1] that it is renormalized (to one loop). If \ -working with only renormalized or unrenormalized quantities, the argument can \ -simply be ommited. NOTICE: When specifying fields to FeynArts, no \ -specification of RenormalizationState or RenormalizationScheme should be made \ -since it is assumed that the fields are unrenormalized. However, \ -specification of RenormalizationState, RenormalizationScheme and/or \ -ExpansionState may be given to ParticleMass, DecayConstant and/or \ -CouplingConstant in the coupling files generated."; - -RenormalizationScheme::usage = -"RenormalizationScheme is the head of an optional arguments of Particle, \ -CouplingConstant, ParticleMass and DecayConstant. The inclusion of the \ -index RenormalizationScheme[s] means that the quantity is renormalized \ -according to the scheme with code or name s. NOTICE: When specifying fields \ -to FeynArts, no specification of RenormalizationState or \ -RenormalizationScheme should be made since it is assumed that the fields are \ -unrenormalized. However, specification of RenormalizationState, \ -RenormalizationScheme and/or ExpansionState may be given to ParticleMass, \ -DecayConstant and/or CouplingConstant in the coupling files generated."; - -ExpansionState::usage = -"ExpansionState is the head of an optional arguments of \ -CouplingConstant, ParticleMass and DecayConstant. Usually the inclusion of \ -the index ExpansionState[i] means that the quantity is expanded to i\.b4th \ -order in the e.g. the quark mass or the electron charge. NOTICE: When \ -specifying fields to FeynArts, no specification of RenormalizationState or \ -RenormalizationScheme should be made since it is assumed that the fields are \ -unrenormalized. However, specification of RenormalizationState, \ -RenormalizationScheme and/or ExpansionState may be given to ParticleMass, \ -DecayConstant and/or CouplingConstant in the coupling files generated."; - -$ParticleTypes::usage = -"$ParticleTypes is a list of the types of particles and sources \ -defined."; - -$Particles::usage = -"$Particles is a list of the particles and sources defined."; - -FieldStrengthTensor::usage = - "FieldStrengthTensor[der,p[x]], where p is usually of the form \ -QuantumField[___,Particle[_],___], der is a lorentz index with head \ -LorentzIndex, is the field strength tensor of the field p. It can be entered \ -as FieldStrengthTensor[{d},p], where d is a symbol without head."; - -Iso::usage = - "Iso is the head of isovectors like UGeneratorMatrixIsoVector[opts] and \ -PhiMesonIsoVector[x,opts] when these are written out in coordinates, that is, \ -when the function WriteOutIsoVectors has been applied."; - -IsoVector::usage = - "IsoVector[p,opts][x], where p is usually of the form \ -QuantumField[Particle[_]] represents a tuplet of quantities of the type p."; - -UGeneratorMatrixIsoVector::usage = - "UGeneratorMatrixIsoVector[opts] := IsoVector[UGeneratorMatrix[opts],opts]."; - - -UGenerator::usage = -"UGeneratorMatrix[opts] := UMatrix[UGenerator[opts],opts], \ -UGeneratorMatrix[i,opts] := UMatrix[UGenerator[i,opts],opts], where i is some \ -integer represent the matrices that generate SU(n). \ -UGeneratorMatrixIsoVector[opts] := IsoVector[UGeneratorMatrix[opts],opts]. \ -With WriteOutUMatrices explicit matrices can be obtained."; - -UGeneratorMatrix::usage = - "UGeneratorMatrix[opts] := UMatrix[UGenerator], UGeneratorMatrix[i,opts] := \ -UMatrix[UGenerator[i,opts],opts], where i is some integer represent the trace \ -0 matrices that generate SU(n). UGeneratorMatrixIsoVector[opts] := \ -IsoVector[UGeneratorMatrix[opts],opts]. With WriteOutUMatrices explicit \ -matrices can be obtained."; - -WriteOutIsoVectors::usage = -"WriteOutIsoVectors[expr] returns the expression expr with all objects \ -with head IsoVector written as tuplets with head Iso."; - -WriteOutUMatrices::usage = -"WriteOutUMatrices[expr] returns the expression expr with all objects \ -with head UMatrix written as matrices, and objects with head UVector written \ -as vectors. For UGeneratorMatrix, the explicit values are given by \ -$SUNBasis[n,j]. To work with a different basis for SU(n), the definition of \ -$SUNBasis[n,j] can be changed. This will also affect SU2F or SU3F and SU3D. \ -NOTICE: If used in conjunction with WriteOutIsoVectors, WriteOutIsoVectors \ -should be applied before WriteOutUMatrices."; - -UIdentityMatrix::usage = - "UIdentityMatrix[opts] := UMatrix[UIdentity,opts] is the identitymatrix. \ -The trace yielded by UTrace[UIdentityMatrix[opts1],opts] is determined by \ -the setting of SUNN (2 or 3), where opts overrules opts1."; - -UIdentity::usage = - "UIdentityMatrix[opts] := UMatrix[UIdentity,opts] is the identitymatrix. \ -The trace yielded by UTrace[UIdentityMatrix[opts1],opts] is determined by \ -the setting of SUNN (2 or 3), where opts overrules opts1."; - -NM::usage = - "NM is the noncommutative multiplication for multiplying matrices and/or \ -fields."; - -UCommutator::usage = - "UCommutator[a_, b_] := NM[a, b] - NM[b, a]."; - -UAntiCommutator::usage = - "UAntiCommutator[a_, b_] := NM[a, b] + NM[b, a]."; - -IsoDot::usage = - "IsoDot is the dot product used for isospin vectors. IsoDot is neither \ -orderless nor flat."; - -UDot::usage = - "UDot is the dot product used for vectors with head UVector. UDot is neither \ -orderless nor flat."; - -ExpandU::usage = - "ExpandU expands IsoDot products involving UGeneratorMatrixIsoVector[opts] \ -into products containing at most one UGeneratorMatrixIsoVector[opts]. In some \ -cases it may be necessary to apply ExpandU repeatedly, perhaps alternating \ -with NMExpand."; - -ExpandUGenerators::usage = - "ExpandUGenerators expands NM products involving UGeneratorMatrix[opts] \ -into products containing at most one UGeneratorMatrix[opts]."; - -IsoCross::usage = - "IsoCross is a non-commuatative product for isospin vectors with head \ -IsoVector like PhiMesonIsoVector[x,opts], UGeneratorMatrixIsoVector[opts] and \ -tuplets with head Iso. The defining equation is IsoCross[V[a],W[b]][c] = \ -SUNF[a,b,c] Conjugate[V[a]]*W[b], where SUNF[a,b,c] are the antisymmetric \ -structure constants of SU(n) and V[a], W[b] and IsoCross[V[a],W[b]][c] are \ -components of the iso-vectors V, W and IsoCross[V[a],W[b]]."; - -IsoSymmetricCross::usage = - "IsoSymmetricCross is a non-commuatative product for isospin vectors like \ -PhiMesonIsoVector[x,opts], UGeneratorMatrixIsoVector[opts] with head \ -IsoVector and tuplets with head Iso. The defining equation is \ -IsoSymmetricCross[V[a],W[b]][c] = SUND[a,b,c] Conjugate[V[a]]*W[b], where \ -SUND[a,b,c] are the symmetric structure constants of SU(n) and V[a], W[b] and \ -IsoSymmetricCross[V[a],W[b]][c] are components of the iso-vectors V, W and \ -IsoSymmetricCross[V[a],W[b]]."; - -DiscardTerms::usage = - "DiscardTerms[expr,opts] is the expression expr with terms dropped which do \ -not contain a number of fields in accordance with the setting of Retain (and \ -method). Notice that there are two possible settings of the option Method. \ -The default is Coefficient. With this setting, the coefficient of the field \ -product specified with Retain is found. That is, the field product times any \ -other fields will appear. With the setting Expand, only products explicitly \ -matching the product specified with Retain will appear."; - -NoDrop::usage = - "NoDrop is an option for DiscardTerms specifying which fields are to be \ -held out of the dropping algorithm. A possible setting could be NoDrop -> \ -{Vector,AxialVector}. Default value : {}."; - -CommutatorReduce::usage = - "CommutatorReduce is an option for DiscardTerms, ExpandU, \ -ExpandUGenerators, IndicesCleanup, CayleyHamiltonRules, CayleyHamiltonTrick \ -and SUNReduce, specifying whether or \ -not CommutatorReduce should be used for reductions. To \ -speed up things the function SetCommutators can be used. Also, \ -CommutatorReduce is a function which applies certain commutation rules \ -repeatedly to it's argument. Default value : True for ExpandU, False otherwise."; - -FullReduce::usage = - "FullReduce is an option for CommutatorReduce. If set to True, the noncommutative \ -products (NM) involving QuantumField's but not elements from $UNonComm \ -will be replaced with ordinary products and similarly, dotproducts of IsoVector's of \ -QuantumField's will be Sort'ed. Default value : False. - FullReduce is also an option of SUNReduce relevant when Explicit is \ -set to False. When set to True, a set of transformation rules are \ -applied untill the result no longer changes. This can be extremely time \ -consuming for large expressions. When set to False, the same set of \ -transformation rules are applied, but only once. - FullReduce is also an option of UReduce, triggering a slower but more thorough \ -reduction. Default value : True for CommutatorReduce, False for SUNReduce, \ -False for UReduce."; - -SetCommutators::usage = - "SetCommutators causes certain commutators to be set \ -for the current Mathematica session. \ -This should speed up some things, but changes to $UMatrices will then not be \ -detected by e.g. CommutatorReduce."; - -ExpansionOrder::usage = - "ExpansionOrder is an option for UFieldMatrix specifying the order to which \ -the fields are expanded. Default setting : 4."; - -Retain::usage = - "Retain is an option for DiscardTerms specifying which terms should not be \ -discarded. E.g. for Retain -> {Particle[Pion, RenormalizationState[0]] -> \ -2,Particle[Photon, RenormalizationState[0]] -> 1}, all terms but the ones \ -corresponding to a two-pion one-photon vertex will be dropped. Default \ -setting : {Particle[Pion,RenormalizationState[0]] -> 4}."; - -ZPlus::usage = - "ZPlus is a setting for the option ExpansionOrder of DiscardFields implying \ -the retaining of terms to all orders in the meson fields."; - -UDimension::usage = -"UDimension is an option of WriteOutUMatrices, UQuarkMassMatrix, \ -UMatrix, UVector, UFieldMatrix, UGeneratorMatrixIsoDot (not found in \ -Options[UFieldMatrix] or Options[UGeneratorMatrixIsoDot]), ExpandU, \ -ExpandUGenerators, UTrace, UTraceToFCTrace, SUNReduce, UReduce, \ -CharacteristicCoefficient, CayleyHamilton, CayleyHamiltonTrick and \ -CayleyHamiltonRules, specifying the \ -dimension of the representation of the gauge group SU(SUNN), where \ -SUNN is an integer (2 or 3). With the default setting Automatic, \ -UDimension is set equal to SUNN. Default value : Automatic."; - -$UExpansionCoefficients::usage = - "$UExpansionCoefficients is a system variable specifying the representation \ -used for UExp. It is a list of coefficients for the powers of the dot \ -product of the vector of isospin matrices and the vector of meson fields. \ -Default value : {1/0!,1/1!,1/2!,1/3!,1/4!,1/5!,1/6!,1/7!,1/8!,1/9!,1/10!}."; - -$QuarkToPionMassesRules::usage = -"$QuarkToPionMassesRules is a set of rules used by WriteOutUMatrices when \ -the option SUNN is set to 2, and by UQuarkMassMatrix when the option \ -DiagonalToU is enabled and SUNN is set to 2. Notice that the default \ -setting corresponds to lowest order (isospin symmetric) standard ChPT ."; - -$QuarkToMesonMassesRules::usage = -"$QuarkToMesonMassesRules is the set of rules used by WriteOutUMatrices \ -when the option SUNN is set to 3, and by UQuarkMassMatrix when the \ -option DiagonalToU is enabled and the option SUNN is set to 3. Notice \ -that the default setting corresponds to lowest order standard ChPT."; - -$PionToQuarkMassesRule::usage = -"$PionToQuarkMassesRule is a set of rules specifying the transition from \ -pion to quark masses. Notice that the default setting is equivalent to lowest \ -order standard ChPT."; - -$MesonToQuarkMassesRules::usage = -"$MesonToQuarkMassesRules is a set of rules specifying the transition \ -from meson to quark masses. Notice that the default setting is equivalent to \ -lowest order standard ChPT."; - -IsoIndicesList::usage = -"IsoIndicesList[opts] is the set of isospin indices i1, i2, ..., where \ -\"i\" is the setting of IsoIndicesString used by IsoIndicesSupply."; - -IsoIndicesNumber::usage = -"IsoIndicesNumber is an option for IsoIndices specifying the number of \ -isospin indices returned. Default value : $IsoIndicesCounter."; - -ParticlesNumber::usage = -"ParticlesNumber is an option for FieldsSet, MomentumVariables and \ -MomentaSumRule. It specifies the number of particles or sources. Moreover \ -ParticlesNumber is an option for DeltaFunctionProducts, FCToFA and \ -MomentaCollect, specifying the number of lines of the vertex. For FCToFA \ -ParticlesNumber specifies both the number of delta-functions that are used \ -for collecting terms and the number of momentum variables p1,p2,p3,... that \ -are assigned box appearance. Default value : 4."; - -FieldsSet::usage = -"FieldsSet[f,opts] returns a list of the fields f with Lorentz indices \ -mu1, mu2, ..., isospin indices I1, I2, ... and momenta p1, p2, ..., where \ -\"mu\" is the setting of LorentzIndicesString, \"I\" is the setting of \ -IsoIndicesString and \"p\" is the setting of MomentumVariablesString. The \ -number of fields is given by the option ParticlesNumber. When \ -LorentzIndicesString or IsoIndicesString are set to None, the respective \ -indices are not supplied. FieldsSet[lag], where lag is a lagrangian from \ -$Lagrangians returns the field used by this lagrangians (without space-time \ -or momentum dependence and with IsoVector notation instead of SUNIndex \ -notation)."; - -LorentzIndicesString::usage = -"LorentzIndicesString is an option of FieldsSet and LorentzIndicesSupply, \ -specifying the string used as base for the generated Lorentz indices. \ -Default value : None."; - -MomentumVariables::usage = -"MomentumVariables[opt] returns a list {p1,p2,...} of momentum variables, \ -where \"p\" is the setting of MomentumVariablesString. The number of \ -variables is given by the option ParticlesNumber."; - -MomentaSumLeft::usage = -"MomentaSumLeft is an option for MomentaSumRule, FAToFC and \ -MandelstamReduce. For MomentaSumRule and MandelstamReduce it can be given \ -three possible values, All, FirstHalf and Odd. For FAToFC it can be given two \ -possible values, All and FirstHalf. All corresponds to defining all \ -(ParticlesNumber) particles as incoming. This is the convention of FeynCalc. \ -The two remaining values are obviously relevant only for vertices with and \ -even number of legs. FirstHalf corresponds to defining the first half of the \ -ParticlesNumber particles as incoming. This is the convention of FeynArts. \ -Odd corresponds to defining odd-numbered ParticlesNumber particles as \ -incoming. In the case of FAToFC, the setting of MomentaSumLeft simply \ -determines what sign should be put on the outgoing momenta. Default value : \ -All."; - -FirstHalf::usage = -"FirstHalf is a possible assignment of MomentaSumLeft relevant for \ -vertices with and even number of legs. It corresponds to defining the first \ -half of the ParticlesNumber as incoming. This is the convention of FeynArts."; - -Odd::usage = -"Odd is a possible assignment of MomentaSumLeft relevant for vertices \ -with and even number of legs. It corresponds to defining odd-numbered \ -ParticlesNumber as incoming."; - -IsoIndicesSupply::usage = -"IsoIndicesSupply[a,opts] returns the expression a with IsoVector[a][x] \ -replaced by a[SUNIndex[i1]][x], etc., where \"i\" is taken from the setting \ -of IsoIndicesString."; - -IsoIndicesString::usage = -"IsoIndicesString is an option of IsoIndicesSupply, IsoIndicesList, \ -FieldsSet, DeltaFunctionsCollect, DeltaFunctionProducts, ExpandUGenerators \ -and FCToFA. When IsoIndicesString is set to \"i\", the isospin indices used \ -by these functions will be of the form i1, i2, i3, .... Default value : \ -Default value : \"i\" for IsoIndicesSupply, IsoIndicesList, ExpandUGenerators \ -and \"I\" for FieldsSet, DeltaFunctionsCollect, DeltaFunctionProducts and \ -FCToFA."; - -FreeIsoIndexString::usage = -"FreeIsoIndexString is an option of IsoIndicesSupply (PhiToFC) used when \ -NumerateFree is set to False. It specifies the symbol for the free iso-index \ -left after contractions (the dummy index used) in the first round of \ -substitutions. Default value : \"k\"."; - -FreeIsoIndicesString::usage = -"FreeIsoIndicesString is an option of IsoIndicesSupply (PhiToFC) used \ -when NumerateFree is set to True. It specifies the symbols for the free \ -iso-indices left after contractions (the dummy indices used) after the first \ -round of substitutions. Default value : \"I\" (\"k\")."; - -NumerateFree::usage = -"NumerateFree is an option of IsoIndicesSupply (PhiToFC) relevant when \ -there are uncontracted iso-indices (isospin functions with integer indices). \ -When set to True, these indices \ -are numbered, when set to False they are all assigned the same symbol. The \ -symbol(s) used is (are) given by the setting of FreeIsoIndexString \ -(FreeIsoIndicesString). Default value : False (True)."; - -UMatrix::usage = -"UMatrix[m] is a matrix in the space spanned by the generators of SU(n). \ -UIndicesSupply[UMatrix[m]] returns UMatrix[m,UIndex[n1],UIndex[n2]] whereas \ -WriteOutUmatrices[UMatrix[m]] returns \ -Table[m[UIndex[i],UIndex[j]],{i,n},{j,n}], where n is the dimension given by \ -the setting of the option UDimension. UIndex is by default substituted with \ -SUNIndex. UMatrix is also a DataType."; - -UVector::usage = -"UVector[v] is a vector of the dimension of the representation used for \ -the gauge group SU(n). This dimension is given by the setting of the option \ -UDimension. To multiply some UMatrix[m] with UVector[v], use UDot.\ - UIndicesSupply and WriteOutUmatrices will treat a UVector on the first \ -place in a UDot product as horizontal on the last place as vertical."; - -UIndicesSupply::usage = -"UIndicesSupply returns UMatrix[m,UIndex[n1],UIndex[n2]] and \ -UVector[v,UIndex[n3]], where \"n\" is taken from the setting of \ -UIndicesString. When the option UIndexToSUNIndex is set to True, UIndex is \ -substituted with SUNIndex after the indices have been supplied."; - -UIndexToSUNIndex::usage = -"UIndexToSUNIndex is an option of UIndicesSupply. When set to True, \ -UIndex is substituted with SUNIndex after the indices have been supplied. \ -Default value : False."; - -UIndicesString::usage = -"UIndicesString is an option of UIndicesSupply. When UIndicesString is \ -set to e.g. \"n\", the isospin indices used by UIndicesSupply will be of the \ -form n1, n2, n3, .... Notice that usually UIndicesString should be different \ -from IsoIndicesString. Default value : \"n\"."; - -PhiToFC::usage = -"PhiToFC[a] returns the expression a with UGeneratorMatrix[i,opts] \ -replaced with SUNT[SUNIndex[i]], NM replaced with DOT and the space-time \ -dependence stripped of QuantumField. PhiToFC should always be applied to \ -expressions generated with PHI before using FeynRule or FunctionalD."; - -$IsoIndicesCounter::usage = -"$IsoIndicesCounter is a variable which is incremented with one each time \ -IsoIndicesSupply supplies an isospin index. To start with 1, simply set \ -$IsoIndicesCounter = 0."; - -$UIndicesCounter::usage = -"$UIndicesCounter is a variable which is incremented with one each time \ -IsoIndicesSupply supplies a pair of matrix indices. To start with 1, simply \ -set $UIndicesCounter=0."; - -VariableBoxes::usage = -"VariableBoxes[var,opts] declares TraditionalForm (or any other format, \ -specified by the option Format) subscript boxes for \ -var1,var2,...,varp, where var is a string and p is given by the option \ -ParticlesNumber."; - -MomentaSumRule::usage = -"MomentaSumRule[opts] is the momentum conservation rule eliminating the \ -momentum variable for one of the ParticlesNumber participating in the \ -process, e.g. MomentaSumRule[ParticlesNumber->4,MomentaSumLeft->FirstHalf] \ -yields p4->p1+p2-p3, when MomentumVariablesString is set to \"p\"."; - -MomentumVariablesString::usage = -"MomentumVariablesString is an option of FieldsSet, MomentumVariables, \ -MomentaSumRule, MomentaCollect, FAToFC, FAToFC, AmplitudeProjection, \ -MandelstamReduce and VeltmanExpand. When MomentumVariablesString is set to \ -\"p\", the momentum variables used by these functions will be of the form p1, \ -p2, p3, .... Default value : \"p\"."; - -(* -Composed objects for construction of lagrangians -*) - -USmall::usage = -"USmall[mu] is the u-field of WChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -UGamma::usage = -"UGamma[mu] is the gamma-field of BChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -UChiPlus::usage = -"UChiPlus[opts] is the chi_plus-field of WChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -UChiMinus::usage = -"UChiMinus[opts] is the chi_minus-field of WChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -UFMinus::usage = -"UFMinus[mu,nu] is the f_minus-field of WChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -UFPlus::usage = -"UFPlus[mu,nu] is the f_plus-field of WChPT -(Ecker, Kambor and Wyler (1992), CERN-TH.6610/92). -To evaluate use ArgumentsSupply."; - -Begin["`Package`"] -End[] - -Begin["`Objects`Private`"]; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Errors *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -UNMSplit::nores = -"Sorry, but I was unable to resolve some sub-expression(s) `1`. Please \ -check the syntax of your expression."; - -FixSUN::badmatr2 = -"The setting of $SUNBasis[2,1/2] is not a list of 3 2x2 matrices; I \ -cannot handle this."; - -FixSUN::badmatr3 = -"The setting of $SUNBasis[3,1] is not a list of 8 3x3 matrices; I cannot \ -handle this."; - -ExpandU::baddim = -"The gauge group and/or the dimension of the representation do not have \ -valid values or the value(s) could not be determined; `1`, `2`."; - -ExpandUGenerators::baddim = -"The gauge group and/or the dimension of the representation do not have \ -valid values or the value(s) could not be determined; `1`, `2`."; - -DiscardTerms::nomethod = -"Could not determine Method or `1` is not a valid Method."; - -ArgumentsSupply::argxpr = -"Warning : The argument `1` is already in the expression."; - -ArgumentsSupply::noarg = "No space-time argument supplied."; - -Lagrangian::noload = -"The lagrangian `1` is not loaded. Try LoadLagrangian[`1`]."; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Boxes *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* -FeynCalc functions -*) - -fcli = LorentzIndex; -fcpd = ParitalD; -fcsuni = SUNIndex; -fcqf = QuantumField; - -(* -Options and environment constants used in multiple sub-packages: -*) -SpaceTimeDimensions /: Format[SpaceTimeDimensions, TraditionalForm] := - StyleForm["\[GothicCapitalD]", FontSlant -> "Italic"]; - -(* -Options and environment constants used in this sub-package: -*) - -(* -Notational definitions for MomentaScalarProduct: -*) - -MomentaScalarProduct[aua_, -b_] := - -MomentaScalarProduct[aua, b]; -MomentaScalarProduct[-aua_, b_] := - -MomentaScalarProduct[aua, b]; - -(* -Notational box definitions: -*) - -MomentaScalarProduct /: - MakeBoxes[MomentaScalarProduct[aua_, aua_, ___Rule], TraditionalForm] := - SuperscriptBox @@ {MakeBoxes @@ {aua, TraditionalForm}, 2}; - -MomentaScalarProduct /: - MakeBoxes[MomentaScalarProduct[aua_Plus, b_], TraditionalForm] := - RowBox[{"(", MakeBoxes[aua, TraditionalForm], ")", - "\[EmptyVerySmallSquare]", MakeBoxes[b, TraditionalForm]} ] /; - Head[b] =!= Plus; - -MomentaScalarProduct /: - MakeBoxes[MomentaScalarProduct[aua_, b_Plus], TraditionalForm] := - RowBox[{MakeBoxes[aua, TraditionalForm], "\[EmptyVerySmallSquare]", "(", - MakeBoxes[b, TraditionalForm], ")"} ] /; Head[aua] =!= Plus; - -MomentaScalarProduct /: - MakeBoxes[MomentaScalarProduct[aua_Plus, b_Plus], TraditionalForm] := - RowBox[{"(", MakeBoxes[aua, TraditionalForm], ")", - "\[EmptyVerySmallSquare]", "(", MakeBoxes[b, TraditionalForm], ")"}]; - -MomentaScalarProduct /: - MakeBoxes[MomentaScalarProduct[aua_, b_], TraditionalForm] := - RowBox[{MakeBoxes[aua, TraditionalForm], "\[EmptyVerySmallSquare]", - MakeBoxes[b, TraditionalForm]}]; - -SU2Delta /: MakeBoxes[SU2Delta[a_, b_], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["\[Delta]"]], - RowBox[{MakeBoxes[TraditionalForm[a]], MakeBoxes[TraditionalForm[b]]}], - RowBox[{"(", "2", ")"}]]; - -SU3Delta /: MakeBoxes[SU3Delta[a_, b_], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["\[Delta]"]], - RowBox[{MakeBoxes[TraditionalForm[a]], MakeBoxes[TraditionalForm[b]]}], - RowBox[{"(", "3", ")"}]]; - -SU2F /: MakeBoxes[SU2F[a_, b_, c_], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["f"]], - RowBox[{MakeBoxes[TraditionalForm[a]], MakeBoxes[TraditionalForm[b]], - MakeBoxes[TraditionalForm[c]]}], RowBox[{"(", "2", ")"}]]; - -SU3D /: MakeBoxes[SU3D[a_, b_, c_], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["d"]], - RowBox[{MakeBoxes[TraditionalForm[a]], MakeBoxes[TraditionalForm[b]], - MakeBoxes[TraditionalForm[c]]}], RowBox[{"(", "3", ")"}]]; - -SU3F /: MakeBoxes[SU3F[a_, b_, c_], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["f"]], - RowBox[{MakeBoxes[TraditionalForm[a]], MakeBoxes[TraditionalForm[b]], - MakeBoxes[TraditionalForm[c]]}], RowBox[{"(", "3", ")"}]]; - -(* -Functions: -*) - -NM /: - MakeBoxes[NM[aua : (_Plus | _SeriesData)], TraditionalForm] := - RowBox[{"(", MakeBoxes[aua, TraditionalForm], ")"}]; - -NM /: - MakeBoxes[NM[aua_], TraditionalForm] := - MakeBoxes[aua, TraditionalForm]; - -NM /: - MakeBoxes[NM[aua__, b : (_Plus | _SeriesData)], - TraditionalForm] := - RowBox[{MakeBoxes[NM[aua], TraditionalForm], "\[SixPointedStar]", "(", - MakeBoxes[b, TraditionalForm], ")"}]; - -NM /: - MakeBoxes[NM[aua__, b_], - TraditionalForm] := - RowBox[{MakeBoxes[NM[aua], TraditionalForm], "\[SixPointedStar]", - MakeBoxes[b, TraditionalForm]}]; - -UDot /: - MakeBoxes[UDot[aua : (_Plus | _SeriesData)], TraditionalForm] := - RowBox[{"(", MakeBoxes[aua, TraditionalForm], ")"}]; - -UDot /: - MakeBoxes[UDot[aua_], TraditionalForm] := - MakeBoxes[aua, TraditionalForm]; - -UDot /: - MakeBoxes[UDot[aua__, b : (_Plus | _SeriesData)], - TraditionalForm] := - RowBox[{MakeBoxes[UDot[aua], TraditionalForm], "\[Bullet]", "(", - MakeBoxes[b, TraditionalForm], ")"}]; - -UDot /: - MakeBoxes[UDot[aua__, b_], - TraditionalForm] := - RowBox[{MakeBoxes[UDot[aua], TraditionalForm], "\[Bullet]", - MakeBoxes[b, TraditionalForm]}]; - - -IsoDot /: - MakeBoxes[IsoDot[aua : (_Plus | _SeriesData)], TraditionalForm] := - RowBox[{"(", MakeBoxes[aua, TraditionalForm], ")"}]; - -IsoDot /: - MakeBoxes[IsoDot[aua_], TraditionalForm] := - MakeBoxes[aua, TraditionalForm]; - -IsoDot /: - MakeBoxes[IsoDot[aua__, b : (_Plus | _SeriesData)], - TraditionalForm] := - RowBox[{MakeBoxes[IsoDot[aua], TraditionalForm], "\[CenterDot]", "(", - MakeBoxes[b, TraditionalForm], ")"}]; - -IsoDot /: - MakeBoxes[IsoDot[aua__, b_], - TraditionalForm] := - RowBox[{MakeBoxes[IsoDot[aua], TraditionalForm], "\[CenterDot]", - MakeBoxes[b, TraditionalForm]}]; - -IsoCross /: - MakeBoxes[IsoCross[aua : (_Plus | _SeriesData)], TraditionalForm] := - RowBox[{"(", MakeBoxes[aua, TraditionalForm], ")"}]; - -IsoCross /: - MakeBoxes[IsoCross[aua_], TraditionalForm] := - MakeBoxes[aua, TraditionalForm]; - -IsoCross /: - MakeBoxes[IsoCross[aua__, b : (_Plus | _SeriesData)], - TraditionalForm] := - RowBox[{MakeBoxes[IsoCross[aua], TraditionalForm], "\[Times]", "(", - MakeBoxes[b, TraditionalForm], ")"}]; - -IsoCross /: - MakeBoxes[IsoCross[aua__, b_], - TraditionalForm] := - RowBox[{MakeBoxes[IsoCross[aua], TraditionalForm], "\[Times]", - MakeBoxes[b, TraditionalForm]}]; - -IsoSymmetricCross /: - MakeBoxes[IsoSymmetricCross[aua : (_Plus | _SeriesData)], - TraditionalForm] := - RowBox[{"(", MakeBoxes[aua, TraditionalForm], ")"}]; - -IsoSymmetricCross /: - MakeBoxes[IsoSymmetricCross[aua_], TraditionalForm] := - MakeBoxes[aua, TraditionalForm]; - -IsoSymmetricCross /: - MakeBoxes[IsoSymmetricCross[aua__, b : (_Plus | _SeriesData)], - TraditionalForm] := - RowBox[{MakeBoxes[IsoSymmetricCross[aua], TraditionalForm], - "\[CircleTimes]", "(", - MakeBoxes[b, TraditionalForm], ")"}]; - -IsoSymmetricCross /: - MakeBoxes[IsoSymmetricCross[aua__, b_], - TraditionalForm] := - RowBox[{MakeBoxes[IsoSymmetricCross[aua], TraditionalForm], - "\[CircleTimes]", - MakeBoxes[b, TraditionalForm]}]; - -Iso /: - MakeBoxes[Iso[aua___], - TraditionalForm] := - RowBox[{MakeBoxes[AngleBracket[aua], TraditionalForm]}]; - -CovariantNabla /: - MakeBoxes[CovariantNabla[a_, _, lis__FCPartialD, - ___Rule], TraditionalForm] := - RowBox[{SubscriptBox[ - MakeBoxes[ StyleForm["\[Del]", FontSlant -> "Italic"]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {lis}]], "(", - MakeBoxes[TraditionalForm[a]], ")"}]; - -CovariantNabla /: - MakeBoxes[CovariantNabla[a_, _, lis__LorentzIndex, ___Rule], - TraditionalForm] := - RowBox[{SubscriptBox[ - MakeBoxes[ StyleForm["\[Del]", FontSlant -> "Italic"]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {lis}]], "(", - MakeBoxes[TraditionalForm[a]], ")"}]; - -CovariantNabla /: - MakeBoxes[CovariantNabla[a_, {lis___}, ___Rule], - TraditionalForm] := - RowBox[{SubscriptBox[ - MakeBoxes[ StyleForm["\[Del]", FontSlant -> "Italic"]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {lis}]], "(", - MakeBoxes[TraditionalForm[a]], ")"}]; - -FieldStrengthTensor /: - MakeBoxes[ - FieldStrengthTensor[ - li_LorentzIndex, - QuantumField[ - ders___FCPartialD, p_, - iis___SUNIndex| - iis___ExplicitSUNIndex, - lli_LorentzIndex, - lis___LorentzIndex][_], - ___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - QuantumField[ders, p, iis, lis]]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensor /: - MakeBoxes[ - FieldStrengthTensor[ - li_LorentzIndex, - f_[ff___?(FreeQ[{#},LorentzIndex,Heads->True]&), - lli_LorentzIndex, - lis___LorentzIndex, - fff___][_], ___], TraditionalForm] /; {ff,lis,fff}=!={} := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - f[ff, lis, fff]]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensor /: - MakeBoxes[ - FieldStrengthTensor[ - li_LorentzIndex, - f_[ff___?(FreeQ[{#},LorentzIndex,Heads->True]&), - lli_LorentzIndex, - lis___LorentzIndex, - fff___], ___], TraditionalForm] /; {ff,lis,fff}=!={} := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - f[ff, lis, fff]]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensor /: - MakeBoxes[ - FieldStrengthTensor[ - li_LorentzIndex, - f_[ - lli_LorentzIndex - ][_], ___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - f]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensor /: - MakeBoxes[ - FieldStrengthTensor[ - li_LorentzIndex, - f_[ - lli_LorentzIndex - ], ___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - f]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensorFull /: - MakeBoxes[ - FieldStrengthTensorFull[ - li_LorentzIndex, - QuantumField[ - ders___FCPartialD, p_, - iis___SUNIndex| - iis___ExplicitSUNIndex, - lli_LorentzIndex, - lis___LorentzIndex][_], - ___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - QuantumField[ders, p, iis, lis]]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensorFull /: - MakeBoxes[ - FieldStrengthTensorFull[ - li_LorentzIndex, - f_[ff___?(FreeQ[{#},LorentzIndex,Heads->True]&), - lli_LorentzIndex, - lis___LorentzIndex, - fff___][_], ___], TraditionalForm] /; {ff,lis,fff}=!={} := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - f[ff, lis, fff]]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensorFull /: - MakeBoxes[ - FieldStrengthTensorFull[ - li_LorentzIndex, - f_[ff___?(FreeQ[{#},LorentzIndex,Heads->True]&), - lli_LorentzIndex, - lis___LorentzIndex, - fff___], ___], TraditionalForm] /; {ff,lis,fff}=!={} := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - f[ff, lis, fff]]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensorFull /: - MakeBoxes[ - FieldStrengthTensorFull[ - li_LorentzIndex, - f_[ - lli_LorentzIndex - ][_], ___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - f]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -FieldStrengthTensorFull /: - MakeBoxes[ - FieldStrengthTensorFull[ - li_LorentzIndex, - f_[ - lli_LorentzIndex - ], ___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[TraditionalForm[ - f]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {li, lli}]]; - -Unprotect[Conjugate]; - -Conjugate /: - MakeBoxes[Conjugate[aua_], - TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm[TraditionalForm[aua]]], "\[GothicC]"]; - -Conjugate /: - MakeBoxes[Conjugate[Transpose[aua_]], - TraditionalForm] := - RowBox[{MakeBoxes[SuperDagger[TraditionalForm[aua]]]}]; -Protect[Conjugate]; - -Adjoint /: - MakeBoxes[Adjoint[aua_], - TraditionalForm] := - RowBox[{MakeBoxes[SuperDagger[TraditionalForm[aua]]]}]; - -DiracBar /: - MakeBoxes[DiracBar[aua_], - TraditionalForm] := - - RowBox[{MakeBoxes[OverBar[TraditionalForm[aua]]]}]; - -(* UTrace1 /: - - MakeBoxes[UTrace1[aua_, (opts___Rule | opts___List)], - TraditionalForm] := - RowBox[{SubscriptBox[ - MakeBoxes[ "Tr"], MakeBoxes[ "1"]], "(", MakeBoxes[aua, TraditionalForm], - ")"} ]; *) - -UTrace1 /: - MakeBoxes[UTrace1[aua_, (opts___Rule | opts___List)], - TraditionalForm] := - RowBox[{"\[LeftAngleBracket]", MakeBoxes[aua, TraditionalForm], - "\[RightAngleBracket]"} ]; - -(* -Definitions for the "easy entering" part: -*) - -PionIsoVector /: - MakeBoxes[PionIsoVector, - TraditionalForm] := - OverscriptBox[MakeBoxes[StyleForm["\[Pi]", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["\[Rule]"]]]; - -PhiMesonIsoVector /: - MakeBoxes[PhiMesonIsoVector, - TraditionalForm] := - OverscriptBox[MakeBoxes[StyleForm["\[CurlyPhi]", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["\[Rule]"]]]; - -MM /: MakeBoxes[MM[i_,_,___Rule], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[ScriptCapitalU]", FontSlant -> "Italic", - FontWeight -> "Bold"]],MakeBoxes[i]]; - -MM /: MakeBoxes[MM[_,___Rule], TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptCapitalU]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -SMM /: MakeBoxes[SMM[___], TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptU]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -MMS /: MakeBoxes[MMS[___], TraditionalForm] := - MakeBoxes[StyleForm["\[GothicCapitalU]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -MM /: MakeBoxes[MM, TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptCapitalU]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -SMM /: MakeBoxes[SMM, TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptU]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -MMS /: MakeBoxes[MMS, TraditionalForm] := - MakeBoxes[StyleForm["\[GothicCapitalU]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -FST /: MakeBoxes[FST[p_, mu_, nu_], TraditionalForm] := - SubscriptBox[MakeBoxes[ TraditionalForm[p]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {mu, nu}]]; - -FST /: MakeBoxes[FST[p_, {mu_}, {nu_}], TraditionalForm] := - SubscriptBox[MakeBoxes[ TraditionalForm[p]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {mu, nu}]]; - FieldStrengthTensor /: - MakeBoxes[ - FieldStrengthTensor[mu_, - QuantumField[Particle[p__], - nu_]], TraditionalForm] := - SubscriptBox[MakeBoxes[ TraditionalForm[Particle[p]]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {mu, nu}]]; - -UTrace /: MakeBoxes[UTrace[aua_, (opts___Rule | opts___List)], - TraditionalForm] := - - RowBox[{"Tr", "(", MakeBoxes[aua, TraditionalForm], ")"} ]; - -(* -Objects: -*) - -UMatrix /: MakeBoxes[ - UMatrix[um_[lis:(LorentzIndex[_]..)],rr___][x_], TraditionalForm] := - SuperscriptBox[MakeBoxes[TraditionalForm[UMatrix[um, rr][x]]], - MakeBoxes[TraditionalForm[lis]]]; - -UMatrix /: MakeBoxes[ - UMatrix[um_[lis:(LorentzIndex[_]..), r__],rr___], TraditionalForm] := - SuperscriptBox[MakeBoxes[TraditionalForm[UMatrix[um[r], rr][x]]], - MakeBoxes[TraditionalForm[lis]]]; - -UMatrix /: MakeBoxes[ - UMatrix[um_[i_], - (UIndex | SUNIndex | - ExplicitSUNIndex)[mi1_], - (UIndex | SUNIndex | - ExplicitSUNIndex)[mi2_], ___], - TraditionalForm] := - SubsuperscriptBox[MakeBoxes[TraditionalForm[um]][[1, 1]], - RowBox[{"(", MakeBoxes[TraditionalForm[mi1]], - MakeBoxes[TraditionalForm[mi2]], ")"}], - MakeBoxes[TraditionalForm[i]]]; - -UMatrix /: MakeBoxes[ - UMatrix[um_, - (UIndex | SUNIndex | - ExplicitSUNIndex)[mi1_], - (UIndex | SUNIndex | - ExplicitSUNIndex)[mi2_], ___], - TraditionalForm] := - SubscriptBox[MakeBoxes[TraditionalForm[um]][[1, 1]], - RowBox[{"(", MakeBoxes[TraditionalForm[mi1]], - MakeBoxes[TraditionalForm[mi2]], ")"}]]; - -UMatrix /: MakeBoxes[UMatrix[um_[i_ /; FreeQ[i, Rule|fcli], ___Rule], ___Rule], - TraditionalForm] := - SuperscriptBox[(MakeBoxes[ - TraditionalForm[StyleForm[um, FontWeight -> "Bold", SingleLetterItalics -> False]]])[[1, 1, 1]], - MakeBoxes[TraditionalForm[i]]]; - -UMatrix /: MakeBoxes[UMatrix[um_[___Rule], ___Rule], - TraditionalForm] := (MakeBoxes[ - TraditionalForm[StyleForm[um, FontWeight -> "Bold", SingleLetterItalics -> False]]])[[1, 1, 1]]; - -UMatrix /: MakeBoxes[UMatrix[um_ /; AtomQ[um], ___Rule | ___List], - TraditionalForm] := - MakeBoxes[TraditionalForm[StyleForm[um, FontWeight -> "Bold", SingleLetterItalics -> False]]][[1, 1, 1]]; - -(*Added 31/7-2001*) -UMatrix /: MakeBoxes[UMatrix[um_, ___Rule][_], TraditionalForm] := - MakeBoxes[TraditionalForm[StyleForm[um, FontWeight -> "Bold", SingleLetterItalics -> False]]]; - - -UIndex /: MakeBoxes[UIndex[i_], - TraditionalForm] := MakeBoxes[TraditionalForm[i]]; - -UIdentity /: Format[UIdentity, TraditionalForm] := - StyleForm["\[DoubleStruckCapitalI]\[DoubleStruckD]", - FontSlant -> "Italic"]; - -UChiralSpurion /: - MakeBoxes[UChiralSpurion[___], TraditionalForm] := - MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]]; - -UChiralSpurionLeft /: - MakeBoxes[UChiralSpurionLeft[___], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]]; - -UChiralSpurionRight /: - MakeBoxes[UChiralSpurionRight[___], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]]; - -UChiralSpurion /: - MakeBoxes[UChiralSpurion, TraditionalForm] := - MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]]; - -UChiralSpurionLeft /: - MakeBoxes[UChiralSpurionLeft, TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]]; - -UChiralSpurionRight /: - MakeBoxes[UChiralSpurionRight, TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]]; - -UChiralSpurionMatrix /: - MakeBoxes[UChiralSpurionMatrix, - TraditionalForm] := - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -UChiralSpurionLeftMatrix /: - MakeBoxes[UChiralSpurionLeftMatrix, TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["L", FontSlant -> "Plain"]]]; - -UChiralSpurionRightMatrix /: - MakeBoxes[UChiralSpurionRightMatrix, TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["Q", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[StyleForm["R", FontSlant -> "Plain"]]]; - -UMatrix /: - MakeBoxes[UMatrix[UChi[___]][___], - TraditionalForm] := - MakeBoxes[ - StyleForm["\[Chi]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -UChi /: - MakeBoxes[UChi, - TraditionalForm] := - MakeBoxes[StyleForm["\[Chi]", FontSlant -> "Italic"]]; - -UChiMatrix /: - MakeBoxes[UChiMatrix, - TraditionalForm] := - MakeBoxes[ - StyleForm["\[Chi]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -UQuarkChargeMatrix /: - MakeBoxes[UQuarkChargeMatrix, - TraditionalForm] := - MakeBoxes[ - StyleForm["Q", FontSlant -> "Italic", FontWeight -> "Bold"]]; - -UQuarkCharge /: - MakeBoxes[UQuarkCharge, - TraditionalForm] := - MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]]; - -UQuarkCharge /: - MakeBoxes[UQuarkCharge[___], - TraditionalForm] := - MakeBoxes[StyleForm["Q", FontSlant -> "Italic"]]; - -UNucleonChargeMatrix /: - MakeBoxes[UNucleonChargeMatrix, - TraditionalForm] := - MakeBoxes[ - StyleForm["\[ScriptCapitalQ]", FontSlant -> "Italic", FontWeight -> "Bold"]]; - -UNucleonCharge /: - MakeBoxes[UNucleonCharge, - TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptCapitalQ]", FontSlant -> "Italic"]]; - -UNucleonCharge /: - MakeBoxes[UNucleonCharge[___], - TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptCapitalQ]", FontSlant -> "Italic"]]; - -UQuarkMass /: - MakeBoxes[UQuarkMass, - TraditionalForm] := - MakeBoxes[StyleForm["m", FontSlant -> "Italic"]]; - -UQuarkMass /: - MakeBoxes[UQuarkMass[___], - TraditionalForm] := - MakeBoxes[StyleForm["m", FontSlant -> "Italic"]]; - UGenerator /: - MakeBoxes[UGenerator, - TraditionalForm] := - MakeBoxes[StyleForm["\[Sigma]", FontSlant -> "Italic"]]; - -UGenerator /: - MakeBoxes[ - UGenerator[(SUNIndex| - ExplicitSUNIndex)[i_], ___], - TraditionalForm] := - SuperscriptBox[ - MakeBoxes[StyleForm["\[Sigma]", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[i]]]; - -UGenerator /: - MakeBoxes[ - UGenerator[ - (SUNIndex| - ExplicitSUNIndex)[ - i_], ___][(UIndex | SUNIndex | - ExplicitSUNIndex)[ - mi1_], (UIndex | SUNIndex | - ExplicitSUNIndex)[ - mi2_], ___], - TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[StyleForm["\[Sigma]", FontSlant -> "Italic"]], - RowBox[{"(", MakeBoxes[TraditionalForm[mi1]], - MakeBoxes[TraditionalForm[mi2]], ")"}], - MakeBoxes[TraditionalForm[i]]]; - -UGeneratorMatrix /: - MakeBoxes[UGeneratorMatrix, - TraditionalForm] := - MakeBoxes[ - StyleForm["\[Sigma]", FontSlant -> "Italic", - FontWeight -> "Bold"]]; - -IsoVector /: - MakeBoxes[ - IsoVector[ - UGenerator[(UIndex | SUNIndex | - ExplicitSUNIndex)[ - mi1_], (UIndex | SUNIndex | - ExplicitSUNIndex)[ - mi2_], ___], ___], - TraditionalForm] := - SubscriptBox[ - OverscriptBox[ - MakeBoxes[StyleForm["\[Sigma]", FontSlant -> "Italic"]], - MakeBoxes[StyleForm["\[Rule]"]]], - RowBox[{"(", MakeBoxes[TraditionalForm[mi1]], - MakeBoxes[TraditionalForm[mi2]], ")"}]]; - -IsoVector /: - MakeBoxes[ - IsoVector[ - UMatrix[a_, (UIndex | SUNIndex | - ExplicitSUNIndex)[ - mi1_], (UIndex | SUNIndex | - ExplicitSUNIndex)[ - mi2_], ___], ___], - TraditionalForm] := - SubscriptBox[ - OverscriptBox[MakeBoxes[TraditionalForm[a]], - MakeBoxes[StyleForm["\[Rule]"]]], - RowBox[{"(", MakeBoxes[TraditionalForm[mi1]], - MakeBoxes[TraditionalForm[mi2]], ")"}]]; - -IsoVector /: - MakeBoxes[ - IsoVector[ - QuantumField[ - a__FCPartialD, - b__?(FreeQ[#, FCPartialD, - Infinity, Heads -> True] &)], ___][_], - TraditionalForm] := - RowBox[Join[ - MakeBoxes[TraditionalForm[##]] & /@ {a}, {"(", - OverscriptBox[ - MakeBoxes[ - TraditionalForm[ - QuantumField[ - b]]], MakeBoxes[StyleForm["\[Rule]"]]], ")"}]]; - -IsoVector /: - MakeBoxes[ - IsoVector[ - QuantumField[ - a__FCPartialD, - b__?(FreeQ[#, FCPartialD, - Infinity, Heads -> True] &)], ___], - TraditionalForm] := - RowBox[Join[ - MakeBoxes[TraditionalForm[##]] & /@ {a}, {"(", - OverscriptBox[ - MakeBoxes[ - TraditionalForm[ - QuantumField[ - b]]], MakeBoxes[StyleForm["\[Rule]"]]], ")"}]]; - -IsoVector /: - MakeBoxes[IsoVector[a_, (opts___Rule | opts___List)], - TraditionalForm] /; FreeQ[{a}, FCPartialD] := - OverscriptBox[MakeBoxes[TraditionalForm[a]], MakeBoxes[StyleForm["\[Rule]"]]]; - -IsoVector /: - MakeBoxes[IsoVector[a_, (opts___Rule | opts___List)][_], - TraditionalForm] /; FreeQ[{a}, FCPartialD] := - OverscriptBox[MakeBoxes[TraditionalForm[a]], MakeBoxes[StyleForm["\[Rule]"]]]; - -UVector /: - MakeBoxes[ - UVector[QuantumField[ - a__FCPartialD, b__], ___][_], - TraditionalForm] := - RowBox[Join[ - MakeBoxes[TraditionalForm[##]] & /@ {a}, {"(", - OverscriptBox[ - MakeBoxes[ - TraditionalForm[ - QuantumField[ - b]]], MakeBoxes[StyleForm["\[RightVector]"]]], - ")"}]]; - -UVector /: - MakeBoxes[ - UVector[QuantumField[ - a__FCPartialD, b__], ___], - TraditionalForm] := - RowBox[ - Join[MakeBoxes[TraditionalForm[##]] & /@ {a}, {"(", - OverscriptBox[ - MakeBoxes[ - TraditionalForm[ - QuantumField[ - b]]], MakeBoxes[StyleForm["\[RightVector]"]]], - ")"}]]; - -UVector /: - MakeBoxes[UVector[a_, (opts___Rule | opts___List)], - TraditionalForm] /; FreeQ[{a}, FCPartialD] := - OverscriptBox[MakeBoxes[TraditionalForm[a]], - MakeBoxes[StyleForm["\[RightVector]"]]]; - -UVector /: - MakeBoxes[UVector[a_, (opts___Rule | opts___List)][_], - TraditionalForm] /; FreeQ[{a}, FCPartialD] := - OverscriptBox[MakeBoxes[TraditionalForm[a]], - MakeBoxes[StyleForm["\[RightVector]"]]]; - -IndexBox /: MakeBoxes[IndexBox[a_], TraditionalForm] := - MakeBoxes[TraditionalForm[a]]; - -IndexBox /: MakeBoxes[IndexBox[], TraditionalForm] := ""; -RenormalizationState /: MakeBoxes[RenormalizationState[], TraditionalForm] := - Sequence[]; -RenormalizationScheme /: MakeBoxes[RenormalizationScheme[], TraditionalForm] := - Sequence[]; - -ExpansionState /: MakeBoxes[ExpansionState[], TraditionalForm] := Sequence[]; - -RenormalizationState /: - MakeBoxes[RenormalizationState[i_], - TraditionalForm] := $RenormalizationSuperscripts[[i + 1]]; - -RenormalizationScheme /: - MakeBoxes[RenormalizationScheme[i_], - TraditionalForm] := $RSSuperscripts[[i + 1]]; - -ExpansionState /: - MakeBoxes[ExpansionState[i_], - TraditionalForm] := $ExpansionSuperscripts[[i + 1]]; - -IndexBox /: - MakeBoxes[IndexBox[RenormalizationState[i_]], - TraditionalForm] := $RenormalizationSuperscripts[[i + 1]]; - -Particle /: - MakeBoxes[ - Particle[p_, st___RenormalizationState, sc___RenormalizationScheme], - TraditionalForm] /; MemberQ[$ParticleTypes, Head[p]] := - SuperscriptBox[MakeBoxes[TraditionalForm[p]][[1, 1]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}]]]; - -Particle /: - MakeBoxes[ - Particle[p_, st___RenormalizationState, sc___RenormalizationScheme], - TraditionalForm] := - SuperscriptBox[MakeBoxes[TraditionalForm[p]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}]]]; - -Particle /: - MakeBoxes[Particle[p_], - TraditionalForm] := MakeBoxes[TraditionalForm[p]]; - -PhiProjection /: MakeBoxes[PhiProjection, TraditionalForm] := - MakeBoxes[StyleForm["\[DoubleStruckP]"]]; - -PhiProjection /: - MakeBoxes[PhiProjection[i_], - TraditionalForm] := - RowBox[{MakeBoxes[ - StyleForm["\[DoubleStruckP]"]], "(", - MakeBoxes[TraditionalForm[i]], ")"}]; - -PhiProjection /: - MakeBoxes[ - PhiProjection[i_][j_], - TraditionalForm] := - SuperscriptBox[MakeBoxes[TraditionalForm[PhiProjection[i]]], - MakeBoxes[TraditionalForm[j]]]; - -Vector /: MakeBoxes[Vector[1], TraditionalForm] := - MakeBoxes[StyleForm["\[Gamma]"]]; - -Vector /: MakeBoxes[Vector[_], TraditionalForm] := - MakeBoxes[StyleForm["V", FontSlant -> "Italic"]]; - -AxialVector /: MakeBoxes[AxialVector[_], TraditionalForm] := - MakeBoxes[StyleForm["A", FontSlant -> "Italic"]]; - -Scalar /: MakeBoxes[Scalar[_], TraditionalForm] := - MakeBoxes[StyleForm["s", FontSlant -> "Italic"]]; - -PseudoScalar /: MakeBoxes[PseudoScalar[_], TraditionalForm] := - MakeBoxes[StyleForm["p", FontSlant -> "Italic"]]; - -LeftComponent /: MakeBoxes[LeftComponent, TraditionalForm] := - MakeBoxes[StyleForm["L", FontSlant -> "Italic"]]; - -RightComponent /: MakeBoxes[RightComponent, TraditionalForm] := - MakeBoxes[StyleForm["R", FontSlant -> "Italic"]]; - -LeftComponent /: MakeBoxes[LeftComponent[__], TraditionalForm] := - MakeBoxes[StyleForm["L", FontSlant -> "Italic"]]; - -RightComponent /: MakeBoxes[RightComponent[__], TraditionalForm] := - MakeBoxes[StyleForm["R", FontSlant -> "Italic"]]; - -Fermion /: MakeBoxes[Fermion[_], TraditionalForm] := - MakeBoxes[StyleForm["\[Psi]"]]; - -PseudoScalar /: MakeBoxes[PseudoScalar[1], TraditionalForm] := - MakeBoxes[StyleForm["\[CurlyPhi]", FontSlant -> "Italic"]]; - -PseudoScalar /: MakeBoxes[PseudoScalar[2], TraditionalForm] := - MakeBoxes[StyleForm["\[Pi]", FontSlant -> "Italic"]]; - -PseudoScalar /: MakeBoxes[PseudoScalar[3], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[Pi]"]], "+"]; - -PseudoScalar /: MakeBoxes[PseudoScalar[4], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[Pi]"]], "0"]; - -PseudoScalar /: MakeBoxes[PseudoScalar[5], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[Pi]"]], "-"]; - -PseudoScalar /: MakeBoxes[PseudoScalar[6], TraditionalForm] := - MakeBoxes[StyleForm["K"]]; - -PseudoScalar /: MakeBoxes[PseudoScalar[7], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["K"]], "+"]; - -PseudoScalar /: MakeBoxes[PseudoScalar[8], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["K"]], "0"]; - -PseudoScalar /: MakeBoxes[PseudoScalar[9], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm[OverBar[K]]], "0"]; - -PseudoScalar /: MakeBoxes[PseudoScalar[10], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["K"]], "-"]; - -PseudoScalar /: MakeBoxes[PseudoScalar[11], TraditionalForm] := - MakeBoxes[StyleForm["\[Eta]"]]; - -PseudoScalar /: MakeBoxes[PseudoScalar[12], TraditionalForm] := - MakeBoxes[StyleForm["\[Xi]"]]; - -Fermion /: MakeBoxes[Fermion[1], TraditionalForm] := - MakeBoxes[StyleForm["\[ScriptL]"]]; - -Fermion /: MakeBoxes[Fermion[2], TraditionalForm] := - MakeBoxes[StyleForm["\[Nu]"]]; - -Fermion /: MakeBoxes[Fermion[3], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["\[Nu]"]], - MakeBoxes[StyleForm["e"]]]; - -Fermion /: MakeBoxes[Fermion[4], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["\[Nu]"]], - MakeBoxes[StyleForm["\[Mu]"]]]; - -Fermion /: MakeBoxes[Fermion[5], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["\[Nu]"]], - MakeBoxes[StyleForm["\[Tau]"]]]; - -Fermion /: MakeBoxes[Fermion[6], TraditionalForm] := - MakeBoxes[StyleForm["l"]]; - -Fermion /: MakeBoxes[Fermion[7], TraditionalForm] := - MakeBoxes[StyleForm["e"]]; - -Fermion /: MakeBoxes[Fermion[8], TraditionalForm] := - MakeBoxes[StyleForm["\[Mu]"]]; - -Fermion /: MakeBoxes[Fermion[9], TraditionalForm] := - MakeBoxes[StyleForm["\[Tau]"]]; - -Fermion /: MakeBoxes[Fermion[10], TraditionalForm] := - MakeBoxes[StyleForm["\[Psi]"]]; - -Fermion /: MakeBoxes[Fermion[11], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["\[Psi]"]], - MakeBoxes[StyleForm["2"]]]; - -Fermion /: MakeBoxes[Fermion[12], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["\[Psi]"]], - MakeBoxes[StyleForm["3"]]]; - -Fermion /: MakeBoxes[Fermion[13], TraditionalForm] := - MakeBoxes[StyleForm["d"]]; - -Fermion /: MakeBoxes[Fermion[14], TraditionalForm] := - MakeBoxes[StyleForm["u"]]; - -Fermion /: MakeBoxes[Fermion[15], TraditionalForm] := - MakeBoxes[StyleForm["s"]]; - -Fermion /: MakeBoxes[Fermion[16], TraditionalForm] := - MakeBoxes[StyleForm["c"]]; - -Fermion /: MakeBoxes[Fermion[17], TraditionalForm] := - MakeBoxes[StyleForm["b"]]; - -Fermion /: MakeBoxes[Fermion[18], TraditionalForm] := - MakeBoxes[StyleForm["t"]]; - -Fermion /: MakeBoxes[Fermion[19], TraditionalForm] := - MakeBoxes[StyleForm["B"]]; - -Fermion /: MakeBoxes[Fermion[20], TraditionalForm] := - MakeBoxes[StyleForm["N"]]; - -Fermion /: MakeBoxes[Fermion[21], TraditionalForm] := - MakeBoxes[StyleForm["p"]]; - -Fermion /: MakeBoxes[Fermion[22], TraditionalForm] := - MakeBoxes[StyleForm["n"]]; - -Fermion /: MakeBoxes[Fermion[23], TraditionalForm] := - MakeBoxes[StyleForm["\[CapitalLambda]"]]; - -Fermion /: MakeBoxes[Fermion[24], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[CapitalSigma]"]], "+"]; - -Fermion /: MakeBoxes[Fermion[25], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[CapitalSigma]"]], "0"]; - -Fermion /: MakeBoxes[Fermion[26], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[CapitalSigma]"]], "-"]; - -Fermion /: MakeBoxes[Fermion[27], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[CapitalXi]"]], "0"]; - -Fermion /: MakeBoxes[Fermion[28], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["\[CapitalXi]"]], "-"]; - -(* -Contants: -*) - -(*QuarkCondensate /: MakeBoxes[QuarkCondensate[___], TraditionalForm] := - SubscriptBox["\[ScriptCapitalB]", "0"];*) -QuarkCondensate /: - MakeBoxes[ - QuarkCondensate[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState,___Rule], TraditionalForm] := - SubsuperscriptBox[ - MakeBoxes[StyleForm["\[ScriptCapitalB]", FontSlant -> "Italic"]], - MakeBoxes["0"], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]]; - -ParticleMass /: - MakeBoxes[ - ParticleMass[x_, iis___SUNIndex| - iis___ExplicitSUNIndex, - st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["m", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[x]], - RowBox[Join[{TBox @@ {iis}}, {MakeBoxes[ - TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]]; - -DecayConstant /: - MakeBoxes[ - DecayConstant[x_, iis___SUNIndex| - iis___ExplicitSUNIndex, - st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["f", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[x]], - RowBox[Join[{TBox @@ {iis}}, {MakeBoxes[ - TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]]; - -ParticleMass /: - MakeBoxes[ - ParticleMass[x_, st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["m", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[x]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]]; - -DecayConstant /: - MakeBoxes[ - DecayConstant[x_, st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState], TraditionalForm] := - SubsuperscriptBox[MakeBoxes[StyleForm["f", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[x]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant /: - MakeBoxes[ - CouplingConstant[QED[1], ___RenormalizationState, - ___RenormalizationScheme, ___ExpansionState], TraditionalForm] := - MakeBoxes[StyleForm["e", FontSlant -> "Italic"]]; - -CouplingConstant /: - MakeBoxes[ - CouplingConstant[QED[1], st___RenormalizationState, - sc___RenormalizationScheme, qs___ExpansionState], TraditionalForm] := - SuperscriptBox[MakeBoxes[StyleForm["e", FontSlant -> "Italic"]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant /: - MakeBoxes[ - CouplingConstant[x_, st___RenormalizationState, - sc___RenormalizationScheme, qs___ExpansionState], TraditionalForm] /; - MatchQ[x, Alternatives @@ Union[Global`$Lagrangians, {_QED,"QED"[___]}]] =!= True := - SuperscriptBox[MakeBoxes[StyleForm["C", FontSlant -> "Italic"]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]]; - -CouplingConstant /: - MakeBoxes[ - CouplingConstant[x_, i_, st___RenormalizationState, - sc___RenormalizationScheme, qs___ExpansionState], TraditionalForm] /; - MatchQ[x, Alternatives @@ Union[Global`$Lagrangians, {_QED,"QED"[___]}]] =!= True := - SubsuperscriptBox[MakeBoxes[StyleForm["C", FontSlant -> "Italic"]], - MakeBoxes[TraditionalForm[i]], - RowBox[Join[{MakeBoxes[TraditionalForm[IndexBox[st]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[sc]]]}, {MakeBoxes[ - TraditionalForm[IndexBox[qs]]]}]]]; - -(* -Composed objects for construction of lagrangians -*) - -USmall /: MakeBoxes[USmall[{mu_}][_], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["u", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm[mu]]]; - -USmall /: MakeBoxes[USmall[mu_][_], - TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["u", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm[mu]]]; - -USmall /: MakeBoxes[USmall[mu_], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["u", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm[mu]]]; - -UGamma /: MakeBoxes[UGamma[mu_,___][_], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["\[CapitalGamma]", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm[mu]]]; - -UGamma /: MakeBoxes[UGamma[mu_,___], TraditionalForm] := - SubscriptBox[ - MakeBoxes[ - StyleForm["\[CapitalGamma]", FontSlant -> "Italic", - FontWeight -> "Bold"]], - MakeBoxes[TraditionalForm[mu]]]; - -UChiPlus/:MakeBoxes[UChiPlus[_], TraditionalForm] := -SubscriptBox[MakeBoxes[ -StyleForm["\[Chi]",FontSlant->"Italic",FontWeight->"Bold"]], -"+"]; - -UChiMinus/:MakeBoxes[UChiMinus[_], TraditionalForm] := -SubscriptBox[MakeBoxes[ -StyleForm["\[Chi]",FontSlant->"Italic",FontWeight->"Bold"]], -"-"]; - -UChiPlus/:MakeBoxes[UChiPlus, TraditionalForm] := -SubscriptBox[MakeBoxes[ -StyleForm["\[Chi]",FontSlant->"Italic",FontWeight->"Bold"]], -"+"]; - -UChiMinus/:MakeBoxes[UChiMinus, TraditionalForm] := -SubscriptBox[MakeBoxes[ -StyleForm["\[Chi]",FontSlant->"Italic",FontWeight->"Bold"]], -"-"]; - -UFPlus/:MakeBoxes[UFPlus[mu_,nu_][__], TraditionalForm] := -SubscriptBox[SubscriptBox[MakeBoxes[ -StyleForm["f",FontSlant->"Italic",FontWeight->"Bold"]], -"+"],RowBox[{MakeBoxes[TraditionalForm[mu]], - MakeBoxes[TraditionalForm[nu]]}]]; - -UFPlus/:MakeBoxes[UFPlus[mu_,nu_], TraditionalForm] := -SubscriptBox[SubscriptBox[MakeBoxes[ -StyleForm["f",FontSlant->"Italic",FontWeight->"Bold"]], -"+"],RowBox[{MakeBoxes[TraditionalForm[mu]], - MakeBoxes[TraditionalForm[nu]]}]]; - -UFMinus/:MakeBoxes[UFMinus[mu_,nu_][__], TraditionalForm] := -SubscriptBox[SubscriptBox[MakeBoxes[ -StyleForm["f",FontSlant->"Italic",FontWeight->"Bold"]], -"-"],RowBox[{MakeBoxes[TraditionalForm[mu]], - MakeBoxes[TraditionalForm[nu]]}]]; - -UFMinus/:MakeBoxes[UFMinus[mu_,nu_], TraditionalForm] := -SubscriptBox[SubscriptBox[MakeBoxes[ -StyleForm["f",FontSlant->"Italic",FontWeight->"Bold"]], -"-"],RowBox[{MakeBoxes[TraditionalForm[mu]], - MakeBoxes[TraditionalForm[nu]]}]]; - -(* -Notational boxes for isospin indices, momenta, etc.: -*) - -isoindexf[var_, j_] := - {ToExpression[StringJoin[var, Evaluate[ToString[j]]]]}; - -isoindextab[var_, (opts___Rule | opts___List)] := - Table[ isoindexf[var, j] , {j, - 1, (ParticlesNumber /. Flatten[{opts}] /. Options[VariableBoxes])}]; - -isoboxes[var_, (opts___Rule | opts___List)] := - HoldPattern1[MakeBoxes1[Sequence@@##]]& /@ - (seq[#,(Format /. Flatten[{opts}] /. Options[VariableBoxes])]& /@ - Flatten[isoindextab[var, opts]]) /. - seq[a__] :> a /. HoldPattern1 -> HoldPattern /. MakeBoxes1 -> MakeBoxes; - -isoright[var_, (opts___Rule | opts___List)] := - Table[{SubscriptBox[MakeBoxes[StyleForm[var, FontSlant -> "Italic"]], - ToString[j]]}, {j, - 1, (ParticlesNumber /. Flatten[{opts}] /. - Options[VariableBoxes])}] // - Flatten; - -VariableBoxes[var_, (opts___Rule | opts___List)] := - Do[Evaluate[Flatten[isoindextab[var, opts]][[j]]] /: - Evaluate[isoboxes[var, opts][[j]]] := - Evaluate[isoright[var, opts][[j]]], {j, - 1, (ParticlesNumber /. Flatten[{opts}] /. Options[VariableBoxes])}]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Defaults *) - -$Substitutions = {}; -$PreSubstitutions[x_?((# =!= 0) &), ar___] := - ($PreSubstitutions[0] /. {SubX -> x, SubArgs :> Sequence[ar]}); -$PostSubstitutions[x_?((# =!= 0) &), ar___] := - ($PostSubstitutions[0] /. {SubX -> x, SubArgs :> Sequence[ar]}); -$PreSubstitutions[0] = {}; -$PostSubstitutions[0] = {}; -$StandardSUNBasis = True; -$ConstantIsoIndices = -{Global`I1,Global`I2,Global`I3,Global`I4,Global`I5,Global`I6}; -$ExpansionQuantities = {FourVector[__], ParticleMass[Pion, a___], - CouplingConstant[QED[1], c___]}; -UQuarkMassMatrix[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ] := - UMatrix[UQuarkMass[st, sc, qs, ##] & @@ - OptionsSelect[UQuarkMass, opts], ##] & @@ - OptionsSelect[UMatrix, opts]; -UQuarkChargeMatrix[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ] := - UMatrix[UQuarkCharge[st, sc, qs, ##] & @@ - OptionsSelect[UQuarkCharge, opts], ##] & @@ - OptionsSelect[UMatrix, opts]; -(* UNucleonChargeMatrix added by P. Buettiker, 21-Oct-2003 *) -UNucleonChargeMatrix[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ] := - UMatrix[UNucleonCharge[st, sc, qs, ##] & @@ - OptionsSelect[UNucleonCharge, opts], ##] & @@ - OptionsSelect[UMatrix, opts]; -UChiralSpurionMatrix[x_,st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ] := - (UMatrix[UChiralSpurion[st, sc, qs, ##] & @@ - OptionsSelect[UChiralSpurion, opts], ##] & @@ - OptionsSelect[UMatrix, opts])[x]; -UChiralSpurionRightMatrix[x_,st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ] := - (UMatrix[UChiralSpurionRight[st, sc, qs, ##] & @@ - OptionsSelect[UChiralSpurionRight, opts], ##] & @@ - OptionsSelect[UMatrix, opts])[x]; -UChiralSpurionLeftMatrix[x_,st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ] := - (UMatrix[UChiralSpurionLeft[st, sc, qs, ##] & @@ - OptionsSelect[UChiralSpurionLeft, opts], ##] & @@ - OptionsSelect[UMatrix, opts])[x]; -UChiMatrix[x_, st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___] := - UMatrix[UChi[st, sc, qs, opts], - Sequence @@ (OptionsSelect[UMatrix, opts])][x]; -UGeneratorMatrix[i_, opts___] := - UMatrix[UGenerator[i, Sequence @@ OptionsSelect[UGenerator, opts]], - Sequence @@ OptionsSelect[UMatrix, opts]]; -UGeneratorMatrix[opts___Rule | opts___List] := - UMatrix[UGenerator[Sequence @@ OptionsSelect[UGenerator, opts]], - Sequence @@ OptionsSelect[UMatrix, opts]]; -UIdentityMatrix[opts___] := - UMatrix[UIdentity, opts]; -PhiMesonIsoVector[x_, opts___] := - IsoVector[QuantumField[Particle[PhiMeson, RenormalizationState[0]]], opts][x]; -PionIsoVector[x_, opts___] := - IsoVector[QuantumField[Particle[Pion, RenormalizationState[0]]], opts][x]; -UGeneratorMatrixIsoVector[opts___] := - IsoVector[ - UGeneratorMatrix[ - Sequence @@ - Union[OptionsSelect[UMatrix, opts], - OptionsSelect[UGenerator, opts]]], - Sequence @@ OptionsSelect[IsoVector, opts]]; -ProjectionIsoVector[i_, opts___] := - IsoVector[PhiProjection[i], opts]; - -$ParticleTypes = {Scalar, PseudoScalar, Vector, AxialVector, LeftComponent, - RightComponent, Fermion}; - - -(* When a particle-field like e.g. Scalar[3] is fed to FeynArts 2, it is given -like e.g. Scalar[3][1], that is the first kind of Scalar[3] fields. -Automatically Scalar[3][1] is set to Scalar3[1]. This is to make the pattern -matching of FeynArts 2 work. *) - -SetFAField[a_] := - a[aa_][bb__] := - (Begin["Phi`Objects`"]; - Phi`Objects`Private`ParticleName = (ToExpression[ - ToString[a] <> ToString[aa]])[bb]; - End[]; - Phi`Objects`Private`ParticleName); -SetFAField /@ $ParticleTypes; -$Particles = {PhiMeson, Pion, PionPlus, PionMinus, PionZero, Kaon, KaonPlus, - KaonZero, KaonZeroBar, KaonMinus, EtaMeson, DownQuark, UpQuark, - StrangeQuark, CharmQuark, BottomQuark, TopQuark, BBaryon, Nucleon, - Proton, Neutron, LambdaBaryon, SigmaPlusBaryon, SigmaZeroBaryon, - XiZeroBaryon, SigmaMinusBaryon, XiMinusBaryon, Photon}; -(*Dynamic definition*)(*$UAllParticleHeads := - Alternatives @@ Union[Head /@ $Particles];*) -(*Static definition*)$UAllParticleHeads = - Scalar | PseudoScalar | Vector | PseudoVector; -PhiMeson = PseudoScalar[1]; -Pion = PseudoScalar[2]; -PionPlus = -PseudoScalar[3]; -PionMinus = PseudoScalar[5]; -PionZero = -PseudoScalar[4]; -Kaon = PseudoScalar[6]; -KaonPlus = -PseudoScalar[7]; -KaonZero = PseudoScalar[8]; -KaonZeroBar = -PseudoScalar[9]; -KaonMinus = PseudoScalar[10]; -EtaMeson = -PseudoScalar[11]; -UPerturbation = PseudoScalar[12]; -Photon = Vector[1]; -HiggsBoson = Scalar[1]; -Lepton = Fermion[1]; -Neutrino = Fermion[2]; -ElectronNeutrino = -Fermion[3]; -MuonNeutrino = Fermion[4]; -TauonNeutrino = -Fermion[5]; -MassiveLepton = Fermion[6]; -Electron = Fermion[7]; -Muon = -Fermion[8]; -Tauon = Fermion[9]; -Quark = Fermion[10]; -LightQuark2 = -Fermion[11]; -LightQuark3 = Fermion[12]; -DownQuark = Fermion[13]; -UpQuark = -Fermion[14]; -StrangeQuark = Fermion[15]; -CharmQuark = -Fermion[16]; -BottomQuark = Fermion[17]; -TopQuark = Fermion[18]; -BBaryon = -Fermion[19]; -Nucleon = Fermion[20]; -Proton = Fermion[21]; -Neutron = -Fermion[33]; -LambdaBaryon = Fermion[23]; -SigmaPlusBaryon = -Fermion[24]; -SigmaZeroBaryon = Fermion[25]; -SigmaMinusBaryon = -Fermion[26]; -XiZeroBaryon = Fermion[27]; -XiMinusBaryon = Fermion[28]; - - - -(* Interpretation of particlei[0] as particle[i]: *) - -$ParticlesInUse = {PhiMeson, Pion, Kaon, Vector[0], AxialVector[0], - Scalar[0], PseudoScalar[0], Photon, Electron, ElectronNeutrino, BBaryon, - Nucleon}; -$FAParticlesInUse := - Head /@ (#[1] & /@ Evaluate[$ParticlesInUse]); -$ParticleHeads := - $FAParticlesInUse /. {{} :> None, {a_} -> a} /. - List :> Alternatives; -$FermionHeads := - Head /@ (#[1] & /@ - Select[$ParticlesInUse, (Head[#] == Fermion) &]) /. {{} :> - None, {a_} -> a} /. List :> Alternatives; -$VectorHeads := - Head /@ (#[1] & /@ - Select[$ParticlesInUse, (Head[#] == Vector || - Head[#] == AxialVector) &]) /. {{} :> None, {a_} -> - a} /. List :> Alternatives; -$ScalarHeads := - Complement[ - Flatten[{$ParticleHeads /. {{Alternatives -> List, None -> {}}}}], - Flatten[{$VectorHeads /. {Alternatives -> List, None -> {}}}], - Flatten[{$FermionHeads /. {Alternatives -> List, None -> {}}}]] /. - List -> Alternatives; -FeynArts`P$Generic := - (FeynArts`F | FeynArts`S | FeynArts`V | FeynArts`U | - FeynArts`VS | FeynArts`SV | $ParticleHeads); - -fcsuniQ[x_] := - MatchQ[Head[x],(SUNIndex|ExplicitSUNIndex)]; - -dropnumberr[phia_] := - If[ NumberQ[phia], - numr, - phia - ]; -takenumberr[phia_] := - If[ ! NumberQ[phia], - numr, - phia - ]; -dropstringnumbers[phia_] := - ToString /@ (dropnumberr /@ - Flatten[Table[ - ToExpression[StringTake[phia, {phii}]], {phii, - StringLength[phia]}]] /. numr -> Sequence[]) /. - List -> StringJoin; -takestringnumbers[phia_] := - ToString /@ (takenumberr /@ - Flatten[Table[ - ToExpression[StringTake[phia, {phii}]], {phii, - StringLength[phia]}]] /. numr -> Sequence[]) /. - List -> StringJoin; - - - -(* ParticleMass, DecayConstant and Particle recognize e.g. PseudoScalar2[0] as - PseudoScalar[2]: *) -(* And PseudoScalar2[1] as PseudoScalar[2,1].*) - -ParticleMass[(parti0 : $ParticleHeads)[0], rrrest___] := - ParticleMass[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]]], rrrest]; -DecayConstant[(parti0 : $ParticleHeads)[0], rrrest___] := - DecayConstant[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]]], rrrest]; -Particle[(parti0 : $ParticleHeads)[0], rrrest___] := - Particle[ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]]], rrrest]; -ParticleMass[(parti0 : $ParticleHeads)[i_], rrrest___] := - ParticleMass[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]],i], rrrest]; -DecayConstant[(parti0 : $ParticleHeads)[i_], rrrest___] := - DecayConstant[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]],i], rrrest]; -Particle[(parti0 : $ParticleHeads)[i_], rrrest___] := - Particle[ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]],i], rrrest]; - - -FAUpdate := - (ParticleMass[(parti0 : $ParticleHeads)[0], rrrest___] := - ParticleMass[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]]], rrrest]; - DecayConstant[(parti0 : $ParticleHeads)[0], rrrest___] := - DecayConstant[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]]], rrrest]; - Particle[(parti0 : $ParticleHeads)[0], rrrest___] := - Particle[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]]], rrrest]; - ParticleMass[(parti0 : $ParticleHeads)[i_], rrrest___] := - ParticleMass[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]],i], rrrest]; - DecayConstant[(parti0 : $ParticleHeads)[i_], rrrest___] := - DecayConstant[ - ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]],i], rrrest]; - Particle[(parti0 : $ParticleHeads)[i_], rrrest___] := - Particle[ToExpression[dropstringnumbers[ToString[parti0]]][ - ToExpression[takestringnumbers[ToString[parti0]]],i], rrrest]); - -If[ ValueQ[Global`$Lagrangians] =!= True, - Global`$Lagrangians = {} -]; -Lagrangian[l_[ll___]] := - Message[Lagrangian::noload, {l[ll]}[[1]]]; -$RenormalizationSuperscripts = {"", "r"}; -$RSSuperscripts = {"", ""}; -$ExpansionSuperscripts = {"", ""}; -$QuarkToPionMassesRules = {ParticleMass[UpQuark, - rest___] -> (ParticleMass[Pion, rest])^2/(2*QuarkCondensate[rest]), - ParticleMass[DownQuark, - rest___] -> (ParticleMass[Pion, rest])^2/(2* - QuarkCondensate[rest])}; -$PionToQuarkMassesRule = - ParticleMass[Pion, rest___] -> - Sqrt[QuarkCondensate[ - rest]*(ParticleMass[UpQuark, rest] + - ParticleMass[DownQuark, rest])]; -$QuarkToMesonMassesRules = {ParticleMass[UpQuark, - rest___] -> -(ParticleMass[KaonZero, rest]^2 - - ParticleMass[KaonPlus, rest]^2 - - ParticleMass[Pion, rest]^2)/(2*QuarkCondensate[rest]), - ParticleMass[DownQuark, - rest___] -> -(-ParticleMass[KaonZero, rest]^2 + - ParticleMass[KaonPlus, rest]^2 - - ParticleMass[Pion, rest]^2)/(2*QuarkCondensate[rest]), - ParticleMass[StrangeQuark, - rest___] -> -(-ParticleMass[KaonZero, rest]^2 - - ParticleMass[KaonPlus, rest]^2 + - ParticleMass[Pion, rest]^2)/(2*QuarkCondensate[rest])}; -$MesonToQuarkMassesRules = {ParticleMass[Pion, rest___]^2 -> - QuarkCondensate[ - rest]*(ParticleMass[UpQuark, rest] + - ParticleMass[DownQuark, rest]), - ParticleMass[KaonPlus, rest___]^2 -> - QuarkCondensate[ - rest]*(ParticleMass[UpQuark, rest] + - ParticleMass[StrangeQuark, rest]), - ParticleMass[KaonZero, rest___]^2 -> - QuarkCondensate[ - rest]*(ParticleMass[DownQuark, rest] + - ParticleMass[StrangeQuark, rest]), - ParticleMass[EtaMeson, rest___]^2 -> - QuarkCondensate[rest]/ - 3*(4*ParticleMass[StrangeQuark, rest] + - ParticleMass[UpQuark, rest] + ParticleMass[DownQuark, rest])}; -$UExpansionCoefficients = Table[1/(i!), {i, 0, 10}]; - - - -(* SU(2) matrices: *) - - - -(* For general j, T(1) (XMatricesSpherical) acting on x=(x_-j,...,x_j) and - spanning SU(2) are defined (H. F. Jones, Groups, Representations and Physics, - (6.33), but transformed by SUNDelta[m,m']*(-1)^m, that is, Condon-Shortley - convention transformed by SUNDelta[m,m']*(-1)^m). Transforming with - {{-1/Sqrt[2],0,1/Sqrt[2]},{I/Sqrt[2],0,i/Sqrt[2]},{0,1,0}}, one gets the - matrices defined below. *) - -$SUNBasis[2, 1/2] = {{{0, -1}, {-1, 0}}, {{0, -I}, {I, 0}}, {{-1, 0}, {0, 1}}}; - - - -(* SU(3) matrices: *) - - - -(* The 3-dimensional matrices acting on x and spanning SU(3) are defined - (J. F. Donoghue, E. Golowich and B. R. Holstein, Dynamics of the Standard Model, - (2.4) multiplied by 1/2) - (the first 3 refers to the group SU(3), the second to the dimension: *) - -$SUNBasis[3, 1] = {{{0, 1, 0}, {1, 0, 0}, {0, 0, 0}}, {{0, -I, 0}, {I, 0, 0}, {0, 0, - 0}}, {{1, 0, 0}, {0, -1, 0}, {0, 0, 0}}, {{0, 0, 1}, {0, 0, 0}, {1, - 0, 0}}, {{0, 0, -I}, {0, 0, 0}, {I, 0, 0}}, {{0, 0, 0}, {0, 0, - 1}, {0, 1, 0}}, {{0, 0, 0}, {0, 0, -I}, {0, I, 0}}, {{1/Sqrt[3], - 0, 0}, {0, 1/Sqrt[3], 0}, {0, 0, -2/Sqrt[3]}}}; -SelfConjugation[$VectorHeads[_]] := - True; -SelfConjugation[$FermionHeads[_]] := - False; -SelfConjugation[$ScalarHeads[_]] := - True; - -(* --------------------------------------------------------------------- *) -(*Functions in context FeynCalc`Private`*) - -BeginPackage["FeynCalc`"]; - -(*CombinationLists[l, n] returns a list of all possible sets containing n -elements from the list l. (this function is probably in the combinatorics -package, but we have enough in memory already)*) - -Begin["`Private`"]; - -CombinationLists[m_List, n_Integer] := - Union[Select[ - Sort /@ Flatten[Outer[List, Sequence @@ Table[m, {n}]], - n - 1], (Union[#] === #) &]]; - -End[]; -EndPackage[]; - -(* --------------------------------------------------------------------- *) - - -Options[UGenerator] = { SUNN -> 2, UDimension -> Automatic}; -Options[UIdentity] = { SUNN -> 2, UDimension -> Automatic}; -(* Most of this Projection business is no longer necessary. Dropped, 11/5-2003 *) -Options[ExpandU] = { SUNN -> 2, UDimension -> Automatic, - CommutatorReduce -> True(*Commented out 11/5-2003*)(*, RemoveIntegerIndices -> False*)}; -Options[ExpandUGenerators] = { SUNN -> 2, UDimension -> Automatic, - IsoIndicesString -> "i", CommutatorReduce -> False}; -Options[UNMSplit] = { DropOrder -> 4}; -Options[UMatrix] = { SUNN -> 2, UDimension -> Automatic}; -Options[UVector] = { SUNN -> 2, UDimension -> Automatic}; -Options[IsoVector] = { SUNN -> 2}; -Options[UTrace] = {SUNN -> 2, UDimension -> Automatic, - TraceSimplify -> True, HoldUTrace -> False}; -Options[UTraceToFCTrace] = {SUNN -> 2, UDimension -> Automatic}; -Options[DiscardTerms] = {Method -> Coefficient, - Retain -> {Particle[Pion , RenormalizationState[0]] -> 4}, - CommutatorReduce -> False, NoDrop -> {}}; -Options[IsoIndicesSupply] = {IsoIndicesString -> "i", - FreeIsoIndexString -> "k", FreeIsoIndicesString -> "I", - NumerateFree -> False}; -Options[UIndicesSupply] = {UIndicesString -> "n", UIndexToSUNIndex -> False}; -Options[IsoIndicesList] = {IsoIndicesNumber -> $IsoIndicesCounter, - IsoIndicesString -> "i"}; -Options[MomentumVariables] = {ParticlesNumber -> 4, - MomentumVariablesString -> "p"}; -Options[FieldsSet] = {ParticlesNumber -> 4, MomentumVariablesString -> "p", - IsoIndicesString -> "I", LorentzIndicesString -> None}; -Options[MomentaSumRule] = {ParticlesNumber -> 4, MomentaSumLeft -> All, - MomentumVariablesString -> "p"}; -Options[UQuarkMass] = {Explicit -> True, QuarkToMesonMasses -> True, DiagonalToU -> False, - (*Commented out 11/5-2003*)(*RemoveIntegerIndices -> False,*) SUNN -> 2, - UDimension -> Automatic}; -Options[UQuarkCharge] = {Explicit -> True, DiagonalToU -> False, - (*Commented out 11/5-2003*)(* RemoveIntegerIndices -> False,*) - SUNN -> 2, UDimension -> Automatic}; -Options[UChi] = {Explicit -> True, DiagonalToU -> False, SUNN -> 2, - QuarkToMesonMasses -> True(*Commented out 11/5-2003*)(*, RemoveIntegerIndices -> False*), - UDimension -> Automatic}; -(* Options for UNucleonCharge added by P. Buettiker, 21-Oct-2003 *) -Options[UNucleonCharge] = {Explicit -> True, DiagonalToU -> False, - SUNN -> 2, UDimension -> Automatic}; -(* Changed the strings below from "k", "k" to "l", "l" - in order to avoid problems with IndicesCleanup. *) -Options[PhiToFC] = {(*Commented out 11/5-2003*)(*RemoveIntegerIndices -> False,*) FreeIsoIndexString -> "l", - FreeIsoIndicesString -> "l", NumerateFree -> True}; -Options[MM] = {Explicit -> True}; -Options[SMM] = {Explicit -> True}; -Options[MMS] = {Explicit -> True}; -Options[FieldStrengthTensor] = {Explicit -> True}; -Options[FieldStrengthTensorFull] = {Explicit -> True}; -Options[UFieldMatrix] = { ExpansionOrder -> 4, DropOrder -> Infinity, Constant -> Automatic}; -Options[UFieldMatrixSeries] = { ExpansionOrder -> 4, Constant -> Automatic}; -Options[WriteOutUMatrices] = {SUNN -> 2, UDimension -> Automatic, - QuarkToMesonMasses -> True, DiagonalToU -> False(*Commented out 11/5-2003*)(*, - RemoveIntegerIndices -> False*)}; -Options[WriteOutIsoVectors] = {SUNN -> 2}; -Options[VariableBoxes] = {ParticlesNumber -> 4, Format -> TraditionalForm}; -patterns = (BlankSequence | BlankNullSequence | Pattern); -allpatterns = (Blank | BlankSequence | BlankNullSequence | Pattern); -bti[c__] := - (! FreeQ[{c}, UIdentity]); -Options[CommutatorReduce] = {FullReduce -> True}; -Options[LeftComponent] = {Explicit -> True}; -Options[RightComponent] = {Explicit -> True}; -Options[CovariantNabla] = {Explicit -> True}; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* UMatrix and UScalar DataTypes *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -(* UMatrices *) - -(* Check if c contains a matrix. *) - -$UMatrices = {}; - -(*Variables used to avoid loops*) -umset = False; -umdec = False; - -DeclareUMatrix[x_] := - ( - Clear[nbtu,nbtui,btu,btui]; - umdec = True; - If[ umset, - $UMatrices = Append[$UMatrices, x], - $UMatrices = Union[$UMatrices, {x}] - ]; - umdec = False; - nbtu[c__] := - MemSet[nbtu[c], (FreeQ[{c} /. (UTrace1|tr)[ccc_] :> (UTrace1[ccc/.UMatrix->um/. - (Alternatives@@$UMatrices)->um]), - UMatrix[m__ /; FreeQ[{m}, UIdentity]] | (Alternatives@@ - Complement[$UMatrices, {UMatrix}]), - Infinity])] /; FreeQ[{c}, Pattern]; - nbtui[c__] := - MemSet[nbtui[c], FreeQ[{c} /. (UTrace1|tr)[ccc_] :> UTrace1[ccc/.UMatrix->um/. - (Alternatives@@$UMatrices)->um], - UMatrix | (Alternatives@@$UMatrices) , Infinity]] /; FreeQ[{c}, Pattern]; - btu[c__] := - Not[nbtu[c]]; - btui[c__] := - Not[nbtui[c]];); - -DeclareUMatrix[x_,y__] := - DeclareUMatrix /@ {x,y}; - -UndeclareUMatrix[x_] := - ( - Clear[nbtu,nbtui,btu,btui]; - umdec = True; - $UMatrices = Complement[$UMatrices, {x}]; - umdec = False; - nbtu[c__] := - MemSet[nbtu[c], (FreeQ[{c} /. (UTrace1|tr)[ccc_] :> (UTrace1[ccc/.UMatrix->um/. - (Alternatives@@$UMatrices)->um]), - UMatrix[m__ /; FreeQ[{m}, UIdentity]] | (Alternatives@@ - Complement[$UMatrices, {UMatrix}]), - Infinity])] /; FreeQ[{c}, Pattern]; - nbtui[c__] := - MemSet[nbtui[c], FreeQ[{c} /. (UTrace1|tr)[ccc_] :> UTrace1[ccc/.UMatrix->um/. - (Alternatives@@$UMatrices)->um], - UMatrix | (Alternatives@@$UMatrices) , Infinity]] /; FreeQ[{c}, Pattern]; - btu[c__] := - Not[nbtu[c]]; - btui[c__] := - Not[nbtui[c]];); - -UndeclareUMatrix[x_,y__] := - UndeclareUMatrix /@ {x,y}; - -DataType[x_, UMatrix] := - btui[x]; - -UMatrixQ = btui; - -DataType /: -HoldPattern[Set[DataType[x_, UMatrix] , True]] := -(DeclareUMatrix[x]; -True); - -DataType /: -HoldPattern[Set[DataType[x_, UMatrix] , False]] := -(UndeclareUMatrix[x]; -False); - -$UMatrices /: HoldPattern[Set[$UMatrices , m_]] := - (umset = True; - UndeclareUMatrix@@$UMatrices; - DeclareUMatrix@@m; - umset = False; - $UMatrices) /; umdec===False; - - -DeclareUMatrix[UMatrix,MM,SMM,UChiMatrix,USmall,UFPlus,UFMinus,UChiPlus,UChiMinus,UGamma]; - - -(* UScalars *) - - -$UScalars = {}; - -(*Variables used to avoid loops*) -usset = False; -usdec = False; - -DeclareUScalar[x_] := - ( - Clear[UScalarQ,btsbin,btsbin1,btss,btss1,nbts]; - usdec = True; - If[ usset, - $UScalars = Append[$UScalars, x], - $UScalars = Union[$UScalars, {x}] - ]; - usdec = False; - UScalarQ[a_] := - MemSet[UScalarQ[a], (MemberQ[$UScalars, a] || NumericQ[a] || - MemberQ[$UScalars, Head[a]] || - MatchQ[a, (Alternatives @@ $UScalars)] || - MatchQ[a, (Alternatives @@ $UScalars)^_] || - MatchQ[a, (Alternatives @@ $UScalars)[___]^_] || - MemberQ[$UScalars, Head[Head[a]]])] /; FreeQ[{a}, Pattern]; - btsbin[a_] := - MemSet[btsbin[a], If[ UScalarQ[a]&&FreeQ[a, allpatterns], - 1, - 0 - ]] /; FreeQ[{a}, Pattern]; - btsbin1[a_] := - MemSet[btsbin1[a], If[ UScalarQ[a], - 1, - 0 - ]] /; FreeQ[{a}, Pattern]; - - (* btss[a__] is True if {a} contains at least one scalar: *) - btss[a__] := - MemSet[btss[a], Plus @@ btsbin /@ {a} > 0] /; FreeQ[{a}, Pattern]; - btss1[a__] := - MemSet[btss1[a], Plus @@ btsbin1 /@ {a} > 0] /; FreeQ[{a}, Pattern]; - nbts[a_] := - MemSet[nbts[a], ((! (NumericQ[a] || MemberQ[$UScalars, Head[a]] || - MatchQ[a, (Alternatives @@ $UScalars)^_] || - MatchQ[a, (Alternatives @@ $UScalars)[___]^_] || - MemberQ[$UScalars, Head[Head[a]]] || MemberQ[$UScalars, a] || - MatchQ[a, - QuantumField[___, - Particle[(Alternatives @@ $UScalars), ___], ___][_]] || - MatchQ[a, - QuantumField[___, - Particle[(Alternatives @@ $UScalars), ___], ___]])) && - FreeQ[a, allpatterns])] /; FreeQ[{a}, Pattern]; - ); - -DeclareUScalar[x_,y__] := - DeclareUScalar /@ {x,y}; - -UndeclareUScalar[x_] := - ( - Clear[UScalarQ,btsbin,btsbin1,btss,btss1,nbts]; - usdec = True; - $UScalars = Complement[$UScalars, {x}]; - usdec = False; - UScalarQ[a_] := - MemSet[UScalarQ[a], (MemberQ[$UScalars, a] || NumericQ[a] || - MemberQ[$UScalars, Head[a]] || - MatchQ[a, (Alternatives @@ $UScalars)] || - MatchQ[a, (Alternatives @@ $UScalars)^_] || - MatchQ[a, (Alternatives @@ $UScalars)[___]^_] || - MemberQ[$UScalars, Head[Head[a]]])] /; FreeQ[{a}, Pattern]; - btsbin[a_] := - MemSet[btsbin[a], If[ UScalarQ[a]&&FreeQ[a, allpatterns], - 1, - 0 - ]] /; FreeQ[{a}, Pattern]; - btsbin1[a_] := - MemSet[btsbin1[a], If[ UScalarQ[a], - 1, - 0 - ]] /; FreeQ[{a}, Pattern]; - - (* btss[a__] is True if {a} contains at least one scalar: *) - btss[a__] := - MemSet[btss[a], Plus @@ btsbin /@ {a} > 0] /; FreeQ[{a}, Pattern]; - btss1[a__] := - MemSet[btss1[a], Plus @@ btsbin1 /@ {a} > 0] /; FreeQ[{a}, Pattern]; - nbts[a_] := - MemSet[nbts[a], ((! (NumericQ[a] || MemberQ[$UScalars, Head[a]] || - MatchQ[a, (Alternatives @@ $UScalars)^_] || - MatchQ[a, (Alternatives @@ $UScalars)[___]^_] || - MemberQ[$UScalars, Head[Head[a]]] || MemberQ[$UScalars, a] || - MatchQ[a, - QuantumField[___, - Particle[(Alternatives @@ $UScalars), ___], ___][_]] || - MatchQ[a, - QuantumField[___, - Particle[(Alternatives @@ $UScalars), ___], ___]])) && - FreeQ[a, allpatterns])] /; FreeQ[{a}, Pattern]; - ); - -UndeclareUScalar[x_,y__] := - UndeclareUScalar /@ {x,y}; - - -DataType /: -HoldPattern[Set[DataType[x_, UScalar] , True]] := -(DeclareUScalar[x]; -True); - -DataType /: -HoldPattern[Set[DataType[x_, UScalar] , False]] := -(UndeclareUScalar[x]; -False); - -DataType[x_, UScalar] := - UScalarQ[x]; - -$UScalars /: HoldPattern[Set[$UScalars , m_]] := - (usset = True; - UndeclareUScalar@@$UScalars; - DeclareUScalar@@m; - usset = False; - $UScalars) /; usdec===False; - - -DeclareUScalar[QuarkCondensate, ParticleMass, DecayConstant, CouplingConstant, - SU3D, SU3F, SU3Delta, PhiProjection, SUNIndex, SUNF, SUND, SUNDelta, Pair, - SUNN]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Non-commutative multiplication *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -(* Zero and one-elements, etc.: *) - -NM /: NM[] := Sequence[]; -NM[a_] := - a; -NM[f___,a_,Inverse[a_],l___] := - NM[f,UIdentityMatrix[If[ FreeQ[a,SUNN], - Sequence[], - SUNN->gaugedimcheck[UMatrix,a] - ]],l]; -NM[f___,Inverse[a_],a_,l___] := - NM[f,UIdentityMatrix[If[ FreeQ[a,SUNN], - Sequence[], - SUNN->gaugedimcheck[UMatrix,a] - ]],l]; - -UCommutator[a_,b_] := - NM[a,b]-NM[b,a]; -UAntiCommutator[a_,b_] := - NM[a,b]+NM[b,a]; - - -(* Non-commutative product of explicit matrices: *) - -NM[m_ /; MatrixQ[m], n_ /; MatrixQ[n]] /; Length[m] == Length[n] := - Table[Sum[NM[m[[i, k]], n[[k, j]]], {k, 1, Length[m]}], {i, 1, - Length[m]}, {j, 1, Length[m]}]; -NM[m__, n_] := - NM[NM[m], n] /; (Length[{m}] > 1 && And @@ (MatrixQ /@ {m, n})); -NM[m___, n_, mm___] /; (MatrixQ[n] =!= True && nbtui[n] && - MemberQ[MatrixQ /@ {m, mm}, True]) := - NM[m, n*IdentityMatrix[Length[Cases[{m, mm}, _?MatrixQ][[1]]]], mm]; - - - -(* Getting factors out *) - -NM[a___, b_Times, c___] := - NM[a, Sequence @@ b, c]; - - -(* Non-commutative product of non-explicit matrices: *) - -(* Identity matrices are brought left: *) - -NM[aa_, a__] /; MemberQ[{a}, UMatrix[UIdentity, ___]] := - NM[UIdentityMatrix[ - Sequence @@ - OptionsSelect[UMatrix, - List @@ Union @@ Cases[{a}, _UMatrix, Infinity, Heads -> True]]], - Sequence @@ - Select[{aa, a}, ! MemberQ[{#}, UMatrix[UIdentity, ___]] &]]; - -(* The identity matrix is redundant when other matrices are in a product: *) - -NM[a___] /; (MemberQ[{a}, UMatrix[UIdentity, ___]] && btu[a]) := - NM[Sequence @@ Select[{a}, ! MemberQ[{#}, UMatrix[UIdentity, ___]] &]]; - - - -SetAttributes[NM, Flat]; - - -(* Getting scalars out: *) - -NM[a__] /; btss[a] := - (Times @@ Select[{a}, ((UScalarQ[#]&&FreeQ[#,allpatterns])&)])* - (NM[##] & @@ Select[{a}, (! UScalarQ[#] &)]); - - - -(* Expand using distributivity and commutation of identical objects: *) - -NMExpand[expr_] := - expr //. NM[a___, b_ + c_, d___] -> Distribute[NM[a, b + c, d]]; - -(*Moved into fctools`, 26/2-2003*) -(*DotExpand[expr_] := - expr //. {DOT[a___, b_ + c_, d___] :> Distribute[DOT[a, b + c, d]], - DOT[a___, b_*c_, d___] :> b*DOT[a, c, d] /; UScalarQ[b], - DOT[a___, b_, d___] :> b*DOT[a, d] /; UScalarQ[b]};*) - -NMFactor[ex_] := - ex /. {HoldPattern[Plus[r : (((___*NM[___, a_]) | NM[___, a_]) ..)]] :> - NM[Replace[#, b_NM -> dr[b, -1], {0, 1}] & /@ Plus[r], a] /; - Length[{r}] > 1, - HoldPattern[Plus[r : (((___*NM[a_, ___]) | NM[a_, ___]) ..)]] :> - NM[a, Replace[#, b_NM -> dr[b, 1], {0, 1}] & /@ Plus[r]] /; - Length[{r}] > 1} /. dr -> Drop; - -NMFactor[ex_, a_] := - ex /. {HoldPattern[Plus[r : (((___*NM[___, a]) | NM[___, a]) ..)]] :> - NM[Replace[#, b_NM -> dr[b, -1], {0, 1}] & /@ Plus[r], a] /; - Length[{r}] > 1, - HoldPattern[Plus[r : (((___*NM[a, ___]) | NM[a, ___]) ..)]] :> - NM[a, Replace[#, b_NM -> dr[b, 1], {0, 1}] & /@ Plus[r]] /; - Length[{r}] > 1} /. dr -> Drop; - - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Iso-vector products *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* The dot product: *) - - - -(* Notice: The dot product is defined as a.b=Conjugate[a1]b1+Conjugate[a2]b2+... -. This is different from in versions before 1.2, where it was assumed that -the first argument was real. This is the case for the meson fields when -working in the Gell-Mann basis, but not generally. This implies the -redifinition of some definitions to accomodate complex first argument (which -results when working in a different basis than the Gell-Mann matrices). -1/2-2000. *) - - - -(* Zero and one-elements, etc.: *) - -IsoDot[0, _] := - 0; -IsoDot[_, 0] := - 0; -IsoDot[a_] /; FreeQ[a, patterns] := - a; -IsoDot[1, UMatrix[UIdentity, opts___]] := - UMatrix[UIdentity, opts]; -IsoDot[UMatrix[UIdentity, opts___], 1] := - UMatrix[UIdentity, opts]; - - - -(* Distributivity: *) - -$IsoDotDistribute = True; -IsoDot[b__ + c_, d__] /; $IsoDotDistribute := - IsoDot[b, d] + IsoDot[c, d]; -IsoDot[a__, b__ + c_] /; $IsoDotDistribute := - IsoDot[a, b] + IsoDot[a, c]; - - - -(* Commutativity of the iso-vector of matrices UGeneratorMatrixIsoVector[opts] -and any other non-matrix iso-vector (generator iso-vectors are brought to the -right): *) - -IsoDot[a : - IsoVector[(UMatrix[UGenerator[___], ___] | - Conjugate[UMatrix[UGenerator[___], ___]]), ___], - b_ /; FreeQ[b, UMatrix, Infinity, Heads -> True]] := - IsoDot[Conjugate[b], Conjugate[a]]; - - - -(* The reduction formula for products of IsoDots with Pauli and - Gell-Mann matrix iso-vectors. *) - -sigrules[2] = {NM[a___, - IsoDot[aa_, - IsoVector[UMatrix[UGenerator[optsg___Rule], optsm___], - optsv___]], mm___, - IsoDot[cc_, IsoVector[UMatrix[UGenerator[___], ___], ___]], - b___] /; - FreeQ[{a, mm}, UMatrix(*Bug fixed 26/2 - 2000*)(*UGenerator*), - Infinity, Heads -> True] :> - 2/2*NM[a, IsoDot[aa, NM[mm, Conjugate[cc]]], UIdentityMatrix[optsm], - b] + I*NM[a, - IsoDot[IsoCross[Conjugate[aa], NM[mm, cc]], - IsoVector[UMatrix[UGenerator[optsg], optsm], optsv]], b]}; -sigrules[3] = {NM[a___, - IsoDot[aa_, - IsoVector[UMatrix[UGenerator[optsg___Rule], optsm___], - optsv___]], mm___, - IsoDot[cc_, IsoVector[UMatrix[UGenerator[___], ___], ___]], - b___] /; - FreeQ[{a, mm}, UMatrix(*Bug fixed 26/2 - 2000*)(*UGenerator*), - Infinity, Heads -> True] :> - 2/3*NM[a, IsoDot[aa, NM[mm, Conjugate[cc]]], UIdentityMatrix[optsm], - b] + I*NM[a, - IsoDot[IsoCross[Conjugate[aa], NM[mm, cc]], - IsoVector[UMatrix[UGenerator[optsg], optsm], optsv]], b] + - NM[a, IsoDot[IsoSymmetricCross[Conjugate[aa], NM[mm, cc]], - IsoVector[UMatrix[UGenerator[optsg], optsm], optsv]], b]}; - - - -(* Check which dimension is to be used for the representation (e.g. SU(2) can be -represented by 2x2 matrices, 3x3 matrices, etc.). *) - -gaugedimcheck[f_, expr___] := - UDimension /. - Flatten[{Cases[{expr}, _[UDimension, _], Infinity, - Heads -> True]} /. (UDimension -> - Automatic) :> (UDimension -> (SUNN /. - Join[Flatten[ - Cases[{expr}, _[SUNN, _], Infinity, - Heads -> True]], Options[f]]))] /. - Flatten[Options[ - f] /. (UDimension -> - Automatic) -> (UDimension -> (SUNN /. - Join[Flatten[ - Cases[{expr}, _[SUNN, _], Infinity, - Heads -> True]], Options[f]]))]; - - - -(* sigrules2 and sigrules3 could probably be generalized to other than SU(2) and -SU(3) and the standard representations. This will have to wait till some -other time... *) - -(* Change 11/5-2003: Have heads on everything, including Integers *) -removeints = - UMatrix[UGenerator[i:(SUNIndex | ExplicitSUNIndex)[_Integer], opts___], - optst___] :> (IsoDot[ - ProjectionIsoVector[i, - Sequence @@ OptionsSelect[IsoVector, opts, optst]], - UGeneratorMatrixIsoVector[ - Sequence @@ - Union[OptionsSelect[UMatrix, opts, optst], - OptionsSelect[IsoVector, opts, optst], - OptionsSelect[UGenerator, opts, optst]]]]); - -putints = - IsoDot[IsoVector[PhiProjection[i_(*Integer*)], opts___], - IsoVector[UMatrix[UGenerator[ops___], ___], optst___]] :> (UMatrix[ - UGenerator[(*SUNIndex[i]*)i, - Sequence @@ OptionsSelect[UGenerator, ops, opts, optst]], - Sequence @@ OptionsSelect[UMatrix, ops, opts, optst]]); -ExpandU[a_, - opts___] := - (gg = (SUNN /. Flatten[{opts}] /. Options[ExpandU]); - gd = gaugedimcheck[ExpandU, opts, a]; - If[ gg == 2 && gd == 2 || gg == 3 && gd == 3, - FCPrint[2, "The gauge group is SU(", gg, - "); the dimension of the representation is ", gd]; - If[ (CommutatorReduce /. Flatten[{opts}] /. Options[ExpandU]), - FCPrint[2, "Expanding the NM products"]; - NMExpand[ - a /. Power -> NMPower /. removeints] //. (FCPrint[2, - "Applying expansion rules"]; - sigrules[gg]) // (FCPrint[2, - "Applying CommutatorReduce"]; - CommutatorReduce[#,opts])&, - FCPrint[2, "Expanding the NM products"]; - NMExpand[ - a /. Power -> NMPower /. removeints] //. (FCPrint[2, - "Applying expansion rules"]; - sigrules[gg]) - ] /. putints(*Changed 11/5-2003*)(*/. - If[(RemoveIntegerIndices /. Flatten[{opts}] /. Options[ExpandU]), - FCPrint[2, "Removing integer indices"]; removeints, - FCPrint[2, "Putting (back) on integer indices"]; putints]*), - Message[ExpandU::baddim, gg, gd] - ]); - - - -(* Added a new function to expand NM products of generator matrices. Did not -include this functionality in ExpandU, since it's rarely needed. *) - -iixint[opts___] := - (++$IsoIndicesCounter; - ToExpression[(IsoIndicesString /. Flatten[{opts}] /. - Options[ExpandUGenerators]) <> ToString[$IsoIndicesCounter]]); -surules[2, opts___] := - NM[a___, UMatrix[UGenerator[(SUNIndex|ExplicitSUNIndex)[i_], optsg___Rule], optsm___], mm___, - UMatrix[UGenerator[(SUNIndex|ExplicitSUNIndex)[j_], ___], ___], b___] /; - FreeQ[{a, mm}, UMatrix, Infinity, Heads -> True] :> (fi = - SUNIndex[iixint[opts]]; - 2/2*SU2Delta[SUNIndex[i], SUNIndex[j]]* - NM[a, mm, UIdentityMatrix[optsm], b] + - I*SU2F[SUNIndex[i], SUNIndex[j], fi]* - NM[a, mm, UMatrix[UGenerator[fi, optsg], optsm], b]); -surules[3, opts___] := - NM[a___, UMatrix[UGenerator[(SUNIndex|ExplicitSUNIndex)[i_], optsg___Rule], optsm___], mm___, - UMatrix[UGenerator[(SUNIndex|ExplicitSUNIndex)[j_], ___], ___], b___] /; - FreeQ[{a, mm}, UMatrix, Infinity, Heads -> True] :> (fi = - SUNIndex[iixint[opts]]; - 2/3*SU3Delta[SUNIndex[i], SUNIndex[j]]* - NM[a, mm, UIdentityMatrix[optsm], b] + - I*SU3F[SUNIndex[i], SUNIndex[j], SUNIndex[fi]]* - NM[a, mm, UMatrix[UGenerator[SUNIndex[fi], optsg], optsm], b] + - SU3D[SUNIndex[i], SUNIndex[j], fi]* - NM[a, mm, UMatrix[UGenerator[fi, optsg], optsm], b]); - -ExpandUGenerators[a_, - opts___] := - (gg = (SUNN /. Flatten[{opts}] /. Options[ExpandU]); - gd = gaugedimcheck[ExpandU, opts, a]; - If[ gg == 2 && gd == 2 || gg == 3 && gd == 3, - FCPrint[2, "The gauge group is SU(", gg, - "); the dimension of the representation is ", gd]; - If[ (CommutatorReduce /. Flatten[{opts}] /. - Options[ExpandUGenerators]), - FCPrint[2, "Expanding the NM products"]; - NMExpand[ - a /. Power -> NMPower] //. (FCPrint[2, - "Applying expansion rules"]; - surules[gg, opts]) // (FCPrint[2, - "Applying CommutatorReduce"]; - CommutatorReduce[#,opts])&, - FCPrint[2, "Expanding the NM products"]; - NMExpand[ - a /. Power -> NMPower] //. (FCPrint[2, - "Applying expansion rules"]; - surules[gg, opts]) - ], - Message[ExpandU::baddim, gg, gd] - ]); - - - -(* Getting numbers out: *) - -IsoDot[a_*b_, c_] /; UScalarQ[a]&&FreeQ[a,allpatterns] := - Conjugate[a]*IsoDot[b, c]; -IsoDot[a_, b_*c_] /; UScalarQ[b]&&FreeQ[b,allpatterns] := - b*IsoDot[a, c]; - - - -(* Just in case someone would try to IsoDot two scalars... might come in handy -though, - when abusing notation in a mixture of iso-vector and iso-index -notation: *) - -IsoDot[a_, b_] /; btss[a, b] := - Conjugate[a]*b; - - - -(* Getting IsoDots out: *) - -IsoDot[NM[IsoDot[a_, aa_], b_], c_] := - NM[Conjugate[IsoDot[a, aa]], IsoDot[b, c]]; -IsoDot[c_, NM[b_, IsoDot[a_, aa_]]] := - NM[IsoDot[c, b], IsoDot[a, aa]]; - - - -(* Squaring the generator iso-vector: *) - - - -(* These rules could probably be generalized to other than SU(2) and SU(3) and -the standard representations. This will have to wait till some other time... *) - -IsoDot[IsoVector[UMatrix[UGenerator, optsm___], optsv___], - IsoVector[ - UMatrix[UGenerator, ___], ___]] /; ((SUNN /. - Flatten[{optsm, optsv}] /. Options[IsoVector]) == 2 && - gaugedimcheck[UMatrix, optsm, optsv] == 2) :=(*3**) - (*The conjugation on the first argument changes things*) - UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, optsm, optsv]]; -IsoDot[IsoVector[UMatrix[UGenerator, optsm___], optsv___], - IsoVector[ - UMatrix[UGenerator, ___], ___]] /; ((SUNN /. - Flatten[{optsm, optsv}] /. Options[IsoVector]) == 3 && - gaugedimcheck[UMatrix, optsm, optsv] == 3) :=(*16/3*) - 4/3* - UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, optsm, optsv]]; - - - -(* The projection function: *) - -(*Changed 11/5-2003*) -(*Projection[i_Integer][(SUNIndex | ExplicitSUNIndex)[j_Integer]] := If[i == j, 1, 0]; -Projection[i_Integer][j_Integer] := If[i == j, 1, 0];*) -PhiProjection[i_][j_] := - SUNDelta[i, j]; - - - -(* IsoDot of projection iso-vectors: *) - -IsoDot[IsoVector[PhiProjection[i_], opts1___], - IsoVector[PhiProjection[j_], opts2___]] := - If[ !FreeQ[jj[opts1, opts2, Options[IsoVector]], SUNN -> 3], - SU3Delta[i, j], - SU2Delta[i, j] - ]; - - - -(* The cross product: *) - - - -(* Zero and one-elements, etc.: *) - -IsoCross[0, _] := - 0; -IsoCross[_, 0] := - 0; -IsoCross[a_] /; FreeQ[{a}, patterns] := - a; -IsoCross[1, UMatrix[UIdentity, opts___]] := - UMatrix[UIdentity, opts]; -IsoCross[UMatrix[UIdentity, opts___], 1] := - UMatrix[UIdentity, opts]; - - - -(* Distributivity: *) - -IsoCross[b__ + c_, d__] := - IsoCross[b, d] + IsoCross[c, d]; -IsoCross[a__, b__ + c_] := - IsoCross[a, b] + IsoCross[a, c]; - - - -(* Commutativity of the iso-vector of matrices UGeneratorMatrixIsoVector[opts] -and any other non-matrix vector: *) - -IsoCross[IsoVector[UMatrix[UGenerator[a___], optsm___], optsv___], - b_ /; FreeQ[{b}, UMatrix, Infinity, Heads -> True]] := - -IsoCross[ - Conjugate[b], - Conjugate[IsoVector[UMatrix[UGenerator[a], optsm], optsv]]]; - - - -(* Getting numbers out: *) - -IsoCross[a_*b_, c_] /; UScalarQ[a]&&FreeQ[a,allpatterns] := - Conjugate[a]*IsoCross[b, c]; -IsoCross[a_, b_*c_] /; UScalarQ[b]&&FreeQ[b,allpatterns] := - b*IsoCross[a, c]; -IsoCross[a_, b_] /; btss[a, b] := - Conjugate[a]*b; - - -(* IsoCross of projection iso-vectors: *) - -IsoCross[IsoVector[i:(PhiProjection[uindxx[_Integer]]|PhiProjection[_Integer]), opts1___], - IsoVector[j:(PhiProjection[uindxx[_Integer]]|PhiProjection[_Integer]), opts2___]] := - (gg = (SUNN /. Flatten[{opts1, opts2}] /. - Options[IsoVector]); - Sum[Which[gg == 2, SU2F[i, j, k], gg == 3, SU3F[i, j, k], True, - SUNF[i, j, k]]*IsoVector[PhiProjection[SUNIndex[k]], opts1], {k, - gg^2 - 1}]); - - - -(* The symmetric cross product: *) - -(* Zero and one-elements, etc.: *) - -IsoSymmetricCross[0, _] := - 0; -IsoSymmetricCross[_, 0] := - 0; -IsoSymmetricCross[a_] /; FreeQ[a, patterns] := - a; -IsoSymmetricCross[1, UMatrix[UIdentity, opts___]] := - UMatrix[UIdentity, opts]; - -IsoSymmetricCross[UMatrix[UIdentity, opts___], 1] := - UMatrix[UIdentity, opts]; - - - -(* Distributivity: *) - -IsoSymmetricCross[b__ + c_, d__] := - IsoSymmetricCross[b, d] + IsoSymmetricCross[c, d]; -IsoSymmetricCross[a__, b__ + c_] := - IsoSymmetricCross[a, b] + IsoSymmetricCross[a, c]; - - - -(* Commutativity of the iso-vector of matrices UGeneratorMatrixIsoVector[opts] -and any other non-matrix iso-vector?? Are the d-symbols always symmetric in -the first two indices?? *) - -IsoSymmetricCross[IsoVector[UMatrix[UGenerator[___], optsm___], optsv___], - b_ /; FreeQ[{b}, UMatrix, Infinity, Heads -> True]] := - IsoSymmetricCross[Conjugate[b], - Conjugate[IsoVector[UMatrix[UGenerator, optsm], optsv]]]; -IsoSymmetricCross[Iso[b : UMatrix[UGenerator[___], ___] ..], - a_ /; FreeQ[a, UMatrix, Infinity, Heads -> True]] := - IsoSymmetricCross[Conjugate[a], Conjugate[Iso[b]]]; - - - -(* Getting numbers out: *) - -IsoSymmetricCross[a_*b_, c_] /; UScalarQ[a]&&FreeQ[a,allpatterns] := - Conjugate[a]*IsoSymmetricCross[b, c]; -IsoSymmetricCross[a_, b_*c_] /; UScalarQ[b]&&FreeQ[b,allpatterns] := - b*IsoSymmetricCross[a, c]; -IsoSymmetricCross[a_, b_] /; btss[a, b] := - Conjugate[a]*b; - - - -(* IsoSymmetricCross of projection iso-vectors: *) - -IsoSymmetricCross[IsoVector[PhiProjection[i:(PhiProjection[uindxx[_Integer]]|PhiProjection[_Integer])], opts1___], - IsoVector[PhiProjection[j:(PhiProjection[uindxx[_Integer]]|PhiProjection[_Integer])], opts2___]] := - (gg = (SUNN /. Flatten[{opts1, opts2}] /. - Options[IsoVector]); - Sum[Which[gg == 2, SU2D[i, j, k], gg == 3, SU3D[i, j, k], True, - SUND[i, j, k]]*IsoVector[PhiProjection[SUNIndex[k]], opts1], {k, - gg^2 - 1}]); - - - -(* Products of all vectors is zero in SU(2) : *) - -IsoSymmetricCross[a_, - b_] /; (FreeQ[jj[a, b, Options[IsoVector]], SUNN -> 3]) && - (!FreeQ[{a, b}, IsoVector | Iso]) && FreeQ[{a, b}, allpatterns] := - 0; - - - - -(* The UDot product: *) - - -(* Zero and one-elements, etc.: *) - -UDot[0, _] := - 0; -UDot[_, 0] := - 0; -UDot[a_] /; FreeQ[a, patterns] := - a; -UDot[UVector[a__][x_], UMatrix[UIdentity, ___]] := - UVector[a][x]; -UDot[UMatrix[UIdentity, ___], UVector[a__][x_]] := - UVector[a][x]; - - - -(* Distributivity: *) - -$UDotDistribute = True; -(*UDot[a_, b__ + c_, d_] /; $UDotDistribute := UDot[a, b, d] + UDot[a, c, d];*) -UDot[b__ + c_, d__] /; $UDotDistribute := - UDot[b, d] + UDot[c, d]; -UDot[a__, b__ + c_] /; $UDotDistribute := - UDot[a, b] + UDot[a, c]; - - -(* "Inner flatnes" *) - -UDot[a_, aa___, UDot[b__, c_]] := - UDot[a, NM[aa, b], c]; -UDot[UDot[a_, b__], cc___, c_] := - UDot[a, NM[b, cc], c]; - -(*Expanding sums*) - -(* The following was added by P. Buettiker, 13-Nov-03 *) -UDotExpand[expr_] := - Block[ {$UNonComm}, - - (* These non-commuting objects will not be taken out of NM: *) - $UNonComm = Union[$UMatrices, {UMatrix, UVector, DiracBar, - DiracBasis, - DiracGamma, - DiracGammaT, - DiracMatrix, - DiracSlash, - DiracSigma, - FST}]; - expr //. {UDot[a___, b_ + c_, d___] -> Distribute[UDot[a, b + c, d]], - UDot[a___,b_*c_,d___]/;UScalarQ[b] :> b*UDot[a,c,d], - UDot[a___,b_,d___]/;UScalarQ[b] :> b*UDot[a,d], - UDot[a___,b_,c___]/;FreeQ[b, (Alternatives @@ $UNonComm)] && - MatrixQ[c] =!= True:> b*UDot[a,c] } - ]; - - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Power functions *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* The non-commutative power: *) - -NMPower[ff_, n_Integer] /; btui[ff/.UTrace1->utra] && n>0 := - NM @@ Table[ff, {n}]; - -NMPower[ff_, n_Integer] /; btui[ff/.UTrace1->tra] && n<0 := - NM @@ Table[Inverse[ff], {-n}]; - -NMPower[ff_, n_] /; - ((! btui[ff/.UTrace1->tra]) && (! MatrixQ[ff])) := - Power[ff, n]; - -NMPower[ff_, 0] /; MatrixQ[ff] := - IdentityMatrix[Length[ff]]; - -NMPower[ff_, 0] /; btui[ff/.UTrace1->tra] := - UIdentityMatrix[ - Sequence @@ - OptionsSelect[UMatrix, - List @@ Union @@ Cases[{ff}, _UMatrix, Infinity, Heads -> True]]]; - -NMPower[ff_, 0] /; ! btui[ff/.UTrace1->tra] := - 1 - - - -(* Non-commutative matrix product and power: *) - -UMatrixProduct[aa_, bb_] /; MatrixQ[{aa}[[1]]] && MatrixQ[{bb}[[1]]] := - Table[ - Sum[NM[aa[[i, k]], bb[[k, j]]], {k, 1, Length[aa]}], {i, 1, - Length[aa]}, {j, 1, Length[aa]}]; -UMatrixPower[m_ /; MatrixQ[m], 0] := - IdentityMatrix[Length[m]]; -UMatrixPower[m_ /; MatrixQ[m], n_] := - UMatrixProduct[UMatrixPower[m, n - 1], m]; - - - -(* The exponentiation to be used for the U fields: *) - -UExp[m_, n_Integer] := - If[ n >= 0, - $UExpansionCoefficients[[1]]* - UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, m]], - 0 - ] + - If[ n >= 1, - Sum[$UExpansionCoefficients[[i + 1]]*NMPower[m, i], {i, 1, n}], - 0 - ] /. If[ FreeQ[m, UMatrix, Infinity, Heads -> True], - UMatrix[UIdentity, ___] -> 1, - {} - ]; - -UExp[0, m_, (_Integer | _List)] := - UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, m]] /. - If[ FreeQ[m, UMatrix, Infinity, Heads -> True], - UMatrix[UIdentity, ___] -> 1, - {} - ]; - -(*9/7-2003. Fixed bug reported by Paul Buettiker: When zeros were in - $UExpansionCoefficients the thing didn't work*) -(*Having the function remember the values gives problems*) -UExp[ii_, m_, n_Integer] := (*UExp[ii, m, n] =*) - Block[ {ssuu, x, sumstart, pos, zero, uexpCoeffs}, - pos = Position[$UExpansionCoefficients,0,{1}]; - uexpCoeffs = ReplacePart[$UExpansionCoefficients, zero, pos]; - (ssuu = (Sum[uexpCoeffs[[i]]*x^(i - 1), {i, - 1, n + 1}] + O[x]^(n + 1))^ii; - sumstart = Max[ssuu[[4]], 1]; - If[ n >= 0, - ssuu[[3, 1]]* - UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, m]] /. - zero -> 0, - 0 - ] + - If[ n >= 1, - Sum[ssuu[[3, i + 1]]*NMPower[m, i/ssuu[[6]]] /. - zero -> 0, {i, sumstart, ssuu[[5]] - 1}], - 0 - ]) /. - If[ FreeQ[m, UMatrix, Infinity, Heads -> True], - UMatrix[UIdentity, ___] -> 1, - {} - ] - ]; - - -UExp[ii_, m_, l : {_Integer}] := - UExp[ii, m, {l}]; - -UExp[ii_, m_, - l : {__List}] := - (n = Flatten[l]; - sumend = Max[n]; - sumstart = Min[n]; - ssuu = (Sum[$UExpansionCoefficients[[i + 1]]*x^i, {i, 0, sumend}] + - O[x]^(sumend + 1))^ii; - If[ sumend >= 1, - Sum[SeriesCoefficient[ssuu, n[[i]]]*NMPower[m, n[[i]]], {i, 1, - Length[n]}], - UMatrix[UIdentity, Sequence @@ OptionsSelect[UMatrix, m]] - ]) /. - If[ FreeQ[m, UMatrix, Infinity, Heads -> True], - UMatrix[UIdentity, ___] -> 1, - {} - ]; -UExp[ii_, - m_, {fi_Integer, la_Integer}] := - (n = Range[fi, la]; - sumend = Max[n]; - sumstart = Min[n]; - ssuu = (Sum[$UExpansionCoefficients[[i + 1]]*x^i, {i, 0, sumend}] + - O[x]^(sumend + 1))^ii; - If[ sumend >= 1, - Sum[SeriesCoefficient[ssuu, n[[i]]]*NMPower[m, n[[i]]], {i, 1, - Length[n]}], - UMatrix[UIdentity, Sequence @@ OptionsSelect[UMatrix, m]] - ]) /. - If[ FreeQ[m, UMatrix, Infinity, Heads -> True], - UMatrix[UIdentity, ___] -> 1, - {} - ]; - -UExpSeries[a_*m_IsoDot, n_Integer] := - If[ n >= 0, - $UExpansionCoefficients[[1]]* - UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, a*m]], - 0 - ] + - If[ n >= 1, - Sum[$UExpansionCoefficients[[i + 1]]*Power[a, i]*Power[m, i], {i, 1, - n}], - 0 - ] + O[m]^(n + 1); - -UExpSeries[m_, n_Integer] := - If[ n >= 0, - $UExpansionCoefficients[[1]]* - UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, m]], - 0 - ] + - If[ n >= 1, - Sum[$UExpansionCoefficients[[i + 1]]*Power[m, i], {i, 1, n}], - 0 - ] + O[m]^(n + 1); - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Matrices *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Getting the space-time dependence out of UVector: *) - -UVector[QuantumField[a__][x_], opts___] := - UVector[QuantumField[a], opts][x]; - - - -(* Powers of the identity matrix are the identity matrix: *) - -UMatrix /: UMatrix[UIdentity, opts___]^_ := UIdentityMatrix[opts]; -UMatrixPower[UMatrix[UIdentity, opts___], _] := - UIdentityMatrix[opts]; -UMatrix /: UMatrix[UIdentity, opts___]*UMatrix[UIdentity, ___] := - UIdentityMatrix[opts]; -UMatrix /: (UMatrix[UIdentity, ___]*b_ /; btui[b]) := b; - - - -(* The identity matrix dotted with a UVector is the UVector: *) - -(*Changed Dot to UDot for UVectors because the flatness of Dot gives problems. - 29/10-2003.*) -(*Unprotect[Dot];*) -UDot[a___, HoldPattern[Times[b___, UMatrix[UIdentity, ___], bb___]], - c___] /; (!FreeQ[{a}, UMatrix | UVector] || - !FreeQ[{c}, UMatrix | UVector]) := - UDot[a, Times[b, bb], c]; -UDot[a___, HoldPattern[NM[b___, UMatrix[UIdentity, ___], bb___]], - c___] /; (!FreeQ[{a}, UMatrix | UVector] || - !FreeQ[{c}, UMatrix | UVector]) := - UDot[a, NM[b, bb], c]; -UDot[a___, HoldPattern[NM[b___, ba__*UMatrix[UIdentity, ___], bb___]], - c___] /; (!FreeQ[{a}, UMatrix | UVector] || - !FreeQ[{c}, UMatrix | UVector]) := - UDot[a, NM[b, ba, bb], c]; -UDot[a___, UMatrix[UIdentity, ___], - c___] /; (!FreeQ[{a}, UMatrix | UVector] || - !FreeQ[{c}, UMatrix | UVector]) := - UDot[a, c]; -UDot[UMatrix[UIdentity, ___], b_ /; btui[b]] := - b; - - -(* Any matrix to the 0th is the identity matrix: *) - -UMatrixPower[UMatrix[m_, opts___], 0] /; btui[UMatrix[m, opts]] := - UIdentityMatrix[opts]; -UMatrixPower[Adjoint[UMatrix[_, opts___]], 0] := - UIdentityMatrix[opts]; -UMatrixPower[Transpose[UMatrix[_, opts___]], 0] := - UIdentityMatrix[opts]; -UMatrixPower[Conjugate[UMatrix[_, opts___]], 0] := - UIdentityMatrix[opts]; - - - -(* Projection iso-vectors are brought left in dot products: *) - -IsoDot[a_ /; FreeQ[a, PhiProjection], ProjectionIsoVector[i_, b___]] := - IsoDot[ProjectionIsoVector[i, b], Conjugate[a]]; -IsoDot[a_ /; FreeQ[a, PhiProjection], Iso[b : PhiProjection[_][_] ..]] := - IsoDot[Iso[b], Conjugate[a]]; -IsoCross[a_ /; FreeQ[a, PhiProjection], - ProjectionIsoVector[i_, b___]] := - -IsoCross[ProjectionIsoVector[i, b], - Conjugate[a]]; -IsoCross[a_ /; FreeQ[a, PhiProjection], - Iso[b : PhiProjection[_][_] ..]] := - -IsoCross[Iso[b], Conjugate[a]]; -IsoSymmetricCross[a_ /; FreeQ[a, PhiProjection], ProjectionIsoVector[i_, b___]] := - IsoSymmetricCross[ProjectionIsoVector[i, b], Conjugate[a]]; -IsoSymmetricCross[a_ /; FreeQ[a, PhiProjection], Iso[b : PhiProjection[_][_] ..]] := - IsoSymmetricCross[Iso[b], Conjugate[a]]; - - - -(* Resolution of a diagonal matrix over the generator matrices and the identity - matrix: *) - -DiagonalUMatrix[l_List, - opts___] := - (dim = (SUNN /. - Flatten[OptionsSelect[UMatrix, opts]] /. Options[UMatrix] /. - Options[UGenerator]); - gg = WriteOutUMatrices[ - Table[UGeneratorMatrix[SUNIndex[i], - Sequence @@ - Union[OptionsSelect[UGenerator, opts], - OptionsSelect[UMatrix, opts]]], {i, dim^2 - 1}]]; - sol = (((#[[2]]) &) /@ - Sort[Flatten[ - Solve[(Equal @@ #) & /@ - Transpose[{Flatten[ - Sum[gg[[i]]cc[i], {i, dim^2 - 1}] + - cc[0]*IdentityMatrix[ - gaugedimcheck[UMatrix, opts]]], - Flatten[DiagonalMatrix[l]]}], - Table[cc[j], {j, 0, dim^2 - 1}]]]]); - sol.(Join[{UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, opts]]}, - Table[UGeneratorMatrix[SUNIndex[ii], - Sequence @@ - Union[OptionsSelect[UGenerator, opts], - OptionsSelect[UMatrix, opts]]], {ii, dim^2 - 1}]])); - - - -(* The quark charge matrix: *) - -UMatrix[UQuarkCharge[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ], - opts1___] /; (DiagonalToU /. Flatten[{opts}] /. - Options[UQuarkCharge]) && ((SUNN /. - Flatten[OptionsSelect[UMatrix, opts1]] /. - Options[UMatrix]) == - 2) && (gaugedimcheck[UMatrix, opts1, opts] == 2) && (Explicit /. Flatten[{opts}] /. - Options[UQuarkCharge]) := - DiagonalUMatrix[{2/3*CouplingConstant[QED[1],st,sc,qs], -1/3* - CouplingConstant[QED[1],st,sc,qs]}, opts, opts1](*Commented out 11/5-2003*)(*/. - If[(RemoveIntegerIndices /. Flatten[{opts}] /. - Options[UQuarkCharge]), {UMatrix[UGenerator[(SUNIndex | ExplicitSUNIndex)[i_Integer]], - optst___] :> - IsoDot[ProjectionIsoVector[SUNIndex[i], ##] & @@ - OptionsSelect[IsoVector, optst], - UGeneratorMatrixIsoVector[##] & @@ - Union[OptionsSelect[UMatrix, optst], - OptionsSelect[IsoVector, optst], - OptionsSelect[UGenerator, optst]]]}, {}]*); - -UMatrix[UQuarkCharge[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ], - opts1___] /; (DiagonalToU /. Flatten[{opts}] /. - Options[UQuarkCharge]) && ((SUNN /. - Flatten[OptionsSelect[UMatrix, opts1]] /. - Options[UMatrix]) == - 3) && (gaugedimcheck[UMatrix, opts1, opts] == 3) && (Explicit /. Flatten[{opts}] /. - Options[UQuarkCharge]) := - DiagonalUMatrix[{2/3*CouplingConstant[QED[1],st,sc,qs], -1/3* - CouplingConstant[QED[1],st,sc,qs], -1/3*CouplingConstant[QED[1],st,sc,qs]}, opts, - opts1](*Commented out 11/5-2003*)(*/. - If[(RemoveIntegerIndices /. Flatten[{opts}] /. - Options[UQuarkCharge]), {UMatrix[UGenerator[(SUNIndex | ExplicitSUNIndex)[i_Integer]], - optst___] :> - IsoDot[ProjectionIsoVector[SUNIndex[i], ##] & @@ - OptionsSelect[IsoVector, optst], - UGeneratorMatrixIsoVector[##] & @@ - Union[OptionsSelect[UMatrix, optst], - OptionsSelect[IsoVector, optst], - OptionsSelect[UGenerator, optst]]]}, {}]*); - - - -(* The quark mass matrix: *) - -UMatrix[UQuarkMass[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ], - opts1___] /; (DiagonalToU /. Flatten[{opts}] /. - Options[UQuarkMass]) && ((SUNN /. - Flatten[OptionsSelect[UMatrix, opts1]] /. - Options[UMatrix]) == 2) && (gaugedimcheck[UMatrix, opts1] == - 2) && (Explicit /. Flatten[{opts}] /. - Options[UQuarkMass]) := (*ParticleMass[UpQuark, st, sc, - qs]*(-1/2*UGeneratorMatrix[SUNIndex[3], ##] & @@ - OptionsSelect[UMatrix, opts1] + - 1/2*UIdentityMatrix[opts1]) + - ParticleMass[DownQuark, st, sc, - qs]*(1/2*UGeneratorMatrix[SUNIndex[3], ##] & @@ - OptionsSelect[UMatrix, opts1] + - 1/2*UIdentityMatrix[opts1])*) - (*Simpler, more flexible implementation by Paul Buettiker. 19/11-2003*) - DiagonalUMatrix[{ParticleMass[UpQuark, st, sc,qs], - ParticleMass[DownQuark, st, sc,qs]},opts,opts1] /. - If[ (QuarkToMesonMasses /. Flatten[{opts}] /. - Options[UQuarkMass]), - $QuarkToPionMassesRules, - {} - ](*Commented out 11/5-2003*)(*/. - If[(RemoveIntegerIndices /. Flatten[{opts}] /. - Options[UQuarkMass]), {UMatrix[UGenerator[(SUNIndex | ExplicitSUNIndex)[i_Integer]], - optst___] :> - IsoDot[ProjectionIsoVector[SUNIndex[i], ##] & @@ - OptionsSelect[IsoVector, optst], - UGeneratorMatrixIsoVector[##] & @@ - Union[OptionsSelect[UMatrix, optst], - OptionsSelect[IsoVector, optst], - OptionsSelect[UGenerator, optst]]]}, {}]*); - -UMatrix[UQuarkMass[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ], - opts1___] /; (((! DiagonalToU) && QuarkToMesonMasses) /. - Flatten[{opts}] /. - Options[UQuarkMass]) && ((SUNN /. - Flatten[OptionsSelect[UMatrix, opts1]] /. - Options[UMatrix]) == 2) && (gaugedimcheck[UMatrix, opts1] == - 2) && (Explicit /. Flatten[{opts}] /. - Options[UQuarkMass]) := - ParticleMass[Pion, st, sc, qs]^2/(2* - QuarkCondensate[st, sc, qs])*UIdentityMatrix[opts1]; - -UMatrix[UQuarkMass[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ], - opts1___] /; (DiagonalToU /. Flatten[{opts}] /. - Options[UQuarkMass]) && ((SUNN /. - Flatten[OptionsSelect[UMatrix, opts1]] /. - Options[UMatrix]) == 3) && (gaugedimcheck[UMatrix, opts1] == - 3) && (Explicit /. Flatten[{opts}] /. - Options[UQuarkMass]) := (*ParticleMass[UpQuark, st, sc, - qs]*(1/2*UGeneratorMatrix[SUNIndex[3], ##] & @@ - OptionsSelect[UMatrix, opts1] + - 1/(2*Sqrt[3])*UGeneratorMatrix[SUNIndex[8], ##] & @@ - OptionsSelect[UMatrix, opts1] + - 1/3*UIdentityMatrix[opts1]) + - ParticleMass[DownQuark, st, sc, - qs]*(-1/2*UGeneratorMatrix[SUNIndex[3], opts1] + - 1/(2*Sqrt[3])*UGeneratorMatrix[SUNIndex[8], opts1] + - 1/3*UIdentityMatrix[opts1]) + - ParticleMass[StrangeQuark, st, sc, - qs]*(-1/Sqrt[3]*UGeneratorMatrix[SUNIndex[8], ##] & @@ - OptionsSelect[UMatrix, opts1] + - 1/3*UIdentityMatrix[opts1])*) - (*Simpler, more flexible implementation by Paul Buettiker. 19/11-2003*) - DiagonalUMatrix[{ParticleMass[UpQuark, st, sc,qs], - ParticleMass[DownQuark, st, sc,qs], - ParticleMass[StrangeQuark, st, sc,qs]},opts,opts1] /. - If[ (QuarkToMesonMasses /. Flatten[{opts}] /. - Options[UQuarkMass]), - $QuarkToMesonMassesRules, - {} - ](*Commented out 11/5-2003*)(*/. - If[(RemoveIntegerIndices /. Flatten[{opts}] /. - Options[UQuarkMass]), {UMatrix[UGenerator[(SUNIndex | ExplicitSUNIndex)[i_Integer]], - optst___] :> - IsoDot[ProjectionIsoVector[SUNIndex[i], ##] & @@ - OptionsSelect[IsoVector, optst], - UGeneratorMatrixIsoVector[##] & @@ - Union[OptionsSelect[UMatrix, optst], - OptionsSelect[IsoVector, optst], - OptionsSelect[UGenerator, optst]]]}, {}]*); - - - -(* The UChi matrix: *) - -UMatrix[UChi[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ], - opts1 : (__Rule | __List)][x_] /; (Explicit /. Flatten[{opts}] /. - Options[UChi]) := - 2*(QuarkCondensate[st, sc, qs, ##] & @@ - OptionsSelect[QuarkCondensate, opts, - opts1])*((UGeneratorMatrixIsoDotFull[ - QuantumField[Particle[Scalar[0], st, sc, qs, ##]][x], ##] + - I*UGeneratorMatrixIsoDotFull[ - QuantumField[Particle[PseudoScalar[0], st, sc, qs]][ - x], ##]) & @@ - Union[OptionsSelect[UChi, opts, opts1], - OptionsSelect[UMatrix, opts, opts1]]); - -UMatrix[UChi[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ]][x_] /; (Explicit /. Flatten[{opts}] /. - Options[UChi]) := - 2*(QuarkCondensate[st, sc, qs, ##] & @@ - OptionsSelect[QuarkCondensate, - opts])*((UGeneratorMatrixIsoDotFull[ - QuantumField[Particle[Scalar[0], st, sc, qs, ##]][x], ##] + - I*UGeneratorMatrixIsoDotFull[ - QuantumField[Particle[PseudoScalar[0], st, sc, qs]][ - x], ##]) & @@ - Union[OptionsSelect[UChi, opts], OptionsSelect[UMatrix, opts]]); - - -(* The nucleon charge matrix added by P. Buettiker 30-Jul-2003: *) - -UMatrix[UNucleonCharge[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ], - opts1___] /; (DiagonalToU /. Flatten[{opts}] /. - Options[UNucleonCharge]) && ((SUNN /. - Flatten[OptionsSelect[UMatrix, opts1]] /. - Options[UMatrix]) == - 2) && (gaugedimcheck[UMatrix, opts1, opts] == 2) && (Explicit /. Flatten[{opts}] /. - Options[UNucleonCharge]) := - DiagonalUMatrix[{1*CouplingConstant[QED[1],st,sc,qs], 0* - CouplingConstant[QED[1],st,sc,qs]}, opts, opts1]; - -UMatrix[UNucleonCharge[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ], - opts1___] /; (DiagonalToU /. Flatten[{opts}] /. - Options[UNucleonCharge]) && ((SUNN /. - Flatten[OptionsSelect[UMatrix, opts1]] /. - Options[UMatrix]) == - 3) && (gaugedimcheck[UMatrix, opts1, opts] == 3) && (Explicit /. Flatten[{opts}] /. - Options[UNucleonCharge]) := - DiagonalUMatrix[{1*CouplingConstant[QED[1],st,sc,qs], 0* - CouplingConstant[QED[1],st,sc,qs], -1/3*CouplingConstant[QED[1],st,sc,qs]}, opts, - opts1]; - - -(* The vector representation commonly used for external sources: *) - -UGeneratorMatrixIsoDot[a_ + b_, opts___] := - UGeneratorMatrixIsoDot[a, opts] + UGeneratorMatrixIsoDot[b, opts]; - -UGeneratorMatrixIsoDot[a_*b_, opts___] /; UScalarQ[a]&&FreeQ[a,allpatterns] := - a*UGeneratorMatrixIsoDot[b, opts]; - -UGeneratorMatrixIsoDot[0, ___] := - 0; - -UGeneratorMatrixIsoDot[ - a_ /; (Head[a] == IsoVector || Head[a] == IsoCross || - Head[a] == IsoSymmetricCross) && Head[a] =!= Plus, opts___] := - IsoDot[a, - UGeneratorMatrixIsoVector[##] & @@ - Union[OptionsSelect[UMatrix, opts], OptionsSelect[IsoVector, opts], - OptionsSelect[UGenerator, opts]]]; - -UGeneratorMatrixIsoDot[a_ /; Head[a] =!= Plus, opts___] := - IsoDot[IsoVector[a, ##] & @@ OptionsSelect[IsoVector, opts], - UGeneratorMatrixIsoVector[##] & @@ - Union[OptionsSelect[UMatrix, opts], OptionsSelect[IsoVector, opts], - OptionsSelect[UGenerator, opts]]]; - -UGeneratorMatrixIsoDotFull[a_, opts___] := - UGeneratorMatrixIsoDot[a, - opts] + (a /. QuantumField[body__] -> QuantumField[body, SUNIndex[0]])* - UIdentityMatrix[Sequence @@ OptionsSelect[UMatrix, opts]]; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Iso-vectors *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* Linearity: *) - -IsoVector[0] = 0; - -IsoVector[a_*b_, opts___][x_] /; UScalarQ[a]&&FreeQ[a,allpatterns] := - a*IsoVector[b, opts][x]; - -IsoVector[a_*b_, opts___] /; UScalarQ[a] &&FreeQ[a,allpatterns] := - a*IsoVector[b, opts]; - -IsoVector[a_ + b_, opts___][x_] := - IsoVector[a, opts][x] + IsoVector[b, opts][x]; - -IsoVector[a_ + b_, opts___] := - IsoVector[a, opts] + IsoVector[b, opts]; - -IsoVector[0, ___][_] := - 0; - -Iso[a : (b_*_) ..] /; UScalarQ[b]&&FreeQ[b,allpatterns] := - b*Iso @@ ({a}/b); - -Iso[a : (aa_ + bb_) ..] := - Iso @@ (Transpose[{List @@ a}][[1]]) + - Iso @@ (Transpose[{List @@ a}][[2]]); - -Iso /: Plus[isovecs : ((Iso[___Integer, _, ___Integer]) ..)] := - pluss[isovecs] /. Iso[a__] -> {a, temp} /. - pluss -> Plus /. {b__, _*temp} -> Iso[b]; - - - -(* Getting the space-time dependence out: *) - -IsoVector[QuantumField[a__][x_], opts___] := - IsoVector[QuantumField[a], opts][x]; - - - -(* Right- and left-handed fields: *) - -(*Explicit has to be written out. Otherwise later changes (in context Global`) will not work*) -setLeftRightComponents := - ( - IsoVector[QuantumField[aa___, Particle[LeftComponent[a_, opts0___Rule], i___], bb___], opts___][ - x_] /; (Explicit /. {opts0} /. Options[LeftComponent]) := - 1/2*(IsoVector[QuantumField[aa, Particle[Vector[a], i], bb], opts][x] + - IsoVector[QuantumField[aa, Particle[AxialVector[a], i], bb], opts][x]); - IsoVector[QuantumField[aa___, Particle[RightComponent[a_, opts0___Rule], i___], bb___], opts___][ - x_] /; (Explicit /. {opts0} /. Options[RightComponent]) := - 1/2*(IsoVector[QuantumField[aa, Particle[Vector[a], i], bb], opts][x] - - IsoVector[QuantumField[aa, Particle[AxialVector[a], i], bb], opts][x]); - QuantumField[aa___, Particle[LeftComponent[a_, opts0___Rule], i___], bb___][ - x_] /; (Explicit /. {opts0} /. Options[LeftComponent]) := - 1/2*(QuantumField[aa, Particle[Vector[a], i], bb][x] + - QuantumField[aa, Particle[AxialVector[a], i], bb][x]); - QuantumField[aa___, Particle[RightComponent[a_, opts0___Rule], i___], bb___][ - x_] /; (Explicit /. {opts0} /. Options[RightComponent]) := - 1/2*(QuantumField[aa, Particle[Vector[a], i], bb][x] - - QuantumField[aa, Particle[AxialVector[a], i], bb][x]); - ); - -setLeftRightComponents; - - -(* FeynCalc heads are supplied rightaway: *) - -FieldStrengthTensorFull[{der_}, b___] := - FieldStrengthTensorFull[ - LorentzIndex[der], b]; - -FieldStrengthTensor[{der_}, b___] := - FieldStrengthTensor[ - LorentzIndex[der], b]; - - - -(* Field strength tensors: *) - -(* Linearity: *) - -FieldStrengthTensor[der_LorentzIndex, - a_ + b_, r___] := - FieldStrengthTensor[der, a, r] + - FieldStrengthTensor[der, b, r]; -FieldStrengthTensor[der_LorentzIndex, - a_*b_, r___] /; UScalarQ[a] &&FreeQ[a,allpatterns] := - a*FieldStrengthTensor[der, b, r]; - -FieldStrengthTensorFull[der_LorentzIndex, - a_ + b_, r___] := - FieldStrengthTensorFull[der, a, r] + - FieldStrengthTensorFull[der, b, r]; -FieldStrengthTensorFull[der_LorentzIndex, - a_*b_, r___] /; UScalarQ[a] &&FreeQ[a,allpatterns] := - a*FieldStrengthTensorFull[der, b, r]; - - - -(* Without the non-abelian term - the first occuring Lorentz index is used: *) - -(*With a QuantumField as input*) -FieldStrengthTensor[ - der_LorentzIndex, - QuantumField[ders1___FCPartialD, - p_Particle, - lli_LorentzIndex, - lis___LorentzIndex, - iis___?fcsuniQ][x_], opts___Rule] /; - (Explicit/.{opts}/.Options[FieldStrengthTensor]) := - QuantumField[FCPartialD[der], ders1, p, lli, lis, iis][x] - - QuantumField[FCPartialD[lli], ders1, p, der, lis, iis][x]; - -(*With general input*) -FieldStrengthTensor[ - der_LorentzIndex, obj_, x_?AtomQ, opts___Rule] /; - (Explicit/.{opts}/.Options[FieldStrengthTensor]) := - FieldDerivative[obj, x, - der] - (obj /. {(fff_[ - ff_[a___ /; FreeQ[{a}, LorentzIndex|ExplicitLorentzIndex], - b_LorentzIndex, - c___], rest___][x] -> - FieldDerivative[fff[ff[a, der, c], rest][x], x, - b]), (ff_[a___ /; FreeQ[{a}, LorentzIndex|ExplicitLorentzIndex], - b_LorentzIndex, - c___][x] -> FieldDerivative[ff[a, der, c][x], x, b])}); - -(*A field might have been set to zero*) -FieldStrengthTensor[ - _LorentzIndex,0,OptionsPattern[]] := - 0 - - - -(* With the non-abelian term: *) - -(*With an non - matrix iso - vector of QuantumFields as input*) - FieldStrengthTensorFull[ - der_LorentzIndex, - IsoVector[body__][x_], coup_:1, opts___Rule] /; - (Explicit/.{opts}/.Options[FieldStrengthTensorFull]) := - FieldStrengthTensor[der, IsoVector[body][x], x, opts] + - coup*IsoCross[ - IsoVector[body][x] /. - QuantumField[first___, p_Particle, - _LorentzIndex, - rest___] :> QuantumField[first, p, der, rest], IsoVector[body][x]]; - -(*With a matrix of quantum fields as input*) - FieldStrengthTensorFull[ - der_LorentzIndex, obj_, x_, - coup_:I, opts___Rule] /; (!FreeQ[obj,QuantumField,Infinity,Heads->True] && - (Explicit/.{opts}/.Options[FieldStrengthTensorFull])) := - FieldStrengthTensor[der, obj, x, opts] + - coup*(NM[obj /. - QuantumField[first___, p_Particle, - _LorentzIndex, - rest___] :> QuantumField[first, p, der, rest], obj] - - NM[obj, obj /. - QuantumField[first___, p_Particle, - _LorentzIndex, - rest___] :> QuantumField[first, p, der, rest]]); - -(*With general input*) -(*The object must then have only one Lorentz index...*) - FieldStrengthTensorFull[ - der_LorentzIndex, obj_, x_, - coup_?(!MatchQ[#,_Rule]&), opts___Rule] /; (FreeQ[obj,QuantumField,Infinity,Heads->True] && - (Explicit/.{opts}/.Options[FieldStrengthTensorFull])) := - FieldStrengthTensor[der, obj, x, opts] + - coup*(NM[obj /. - _LorentzIndex :> - der, obj] - - NM[obj, obj /. - _LorentzIndex :> - der]); - -FieldStrengthTensorFull[ - der_LorentzIndex, obj_, x_, - opts___Rule] /; (FreeQ[obj,QuantumField,Infinity,Heads->True] && - (Explicit/.{opts}/.Options[FieldStrengthTensorFull])) := - FieldStrengthTensorFull[der,obj,x,I,opts]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Explicit objects *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* Writing out iso-vectors: *) - -WriteOutIsoVectors[aa_, opts___Rule] := - aa /. writeoutivrule1[opts] /. writeoutivrule2[opts] /. - writeoutivrule3[opts]; - - - -(* IsoVectors - general case: *) - -writeoutivrule1[ - opts1___] := - (IsoVector[a_[b__, opts0___Rule], opts___Rule][ - x_] :> (Iso @@ - Table[(a[b, ##] & @@ OptionsSelect[a, opts0, opts1, opts])[ - SUNIndex[isosp]][ - x], {isosp, ((SUNN^2 - 1) /. Flatten[{opts1}] /. - OptionsSelect[IsoVector, opts] /. - Options[IsoVector])}])); - -writeoutivrule2[opts1___] := - IsoVector[a_[b__, opts0___Rule], opts___Rule] :> - Iso @@ Table[(a[b, ##] & @@ OptionsSelect[a, opts0, opts1, opts])[ - SUNIndex[isosp]], {isosp, ((SUNN^2 - 1) /. - Flatten[{opts1}] /. OptionsSelect[IsoVector, opts] /. - Options[IsoVector])}]; - -writeoutivrule3[opts1___] := - IsoVector[a_, OptionsPattern[]] :> - Iso @@ Table[a[SUNIndex[isosp]], {isosp, ((SUNN^2 - 1) /. - Flatten[{opts1}] /. Options[IsoVector])}]; - -(* Dot products. *) - -IsoDot[Iso[aa__], Iso[bb__]] := - Sum[NM[Conjugate[{aa}[[ii]]], {bb}[[ii]]], {ii, 1, Length[{aa}]}] - - -(* Cross products. *) - -IsoCross[Iso[aa__], - Iso[bb__]] := - (ng = (SUNN /. - Join[Flatten[ - Cases[{expr}, _[SUNN, _], Infinity, Heads -> True]], - Options[IsoVector]]); - suf = Which[ng == 2, SU2F, ng == 3, SU3F, True, SUNF]; - Iso @@ Table[ - Sum[suf[ii, jj, kk]*NM[Conjugate[{aa}[[ii]]], {bb}[[jj]]], {ii, 1, - Length[{aa}]}, {jj, 1, Length[{aa}]}], {kk, 1, Length[{aa}]}]); - -IsoSymmetricCross[Iso[aa__], - Iso[bb__]] := - (ng = (SUNN /. - Join[Flatten[ - Cases[{expr}, _[SUNN, _], Infinity, Heads -> True]], - Options[IsoVector]]); - suf = Which[ng == 2, SU2D, ng == 3, SU3D, True, SUND]; - Iso @@ Table[ - Sum[suf[ii, jj, kk]*NM[Conjugate[{aa}[[ii]]], {bb}[[jj]]], {ii, 1, - Length[{aa}]}, {jj, 1, Length[{aa}]}], {kk, 1, Length[{aa}]}]); - - -(* Writing out UMatrices: *) - -uix = UIndex; -(* The tbl stuff: - Don't know why mma messes up when using Table directly *) - -WriteOutUMatrices1[aa_, (optss___Rule | optss___List)] := - aa /. (*UTrace1 checks only for UMatrices not for - explicit matrices when pulling out factors*) - UTrace1 -> tr/. - Power -> NMPower /. {UMatrix[a_[ind___, op___Rule], opts___] :> - tbl[a[ind, Sequence @@ OptionsSelect[a, op, opts, optss]][ - uix[tmp`i], uix[tmp`j]], {tmp`i, - gaugedimcheck[UMatrix, - UMatrix[a[ind, op], opts, optss]]}, {tmp`j, - gaugedimcheck[UMatrix, UMatrix[a[ind, op], opts, optss]]}], - UVector[a_[ind___, op___Rule], opts___] :> - tbl[a[ind, Sequence @@ OptionsSelect[a, op, opts, optss]][ - uix[tmp`i]], {tmp`i, - gaugedimcheck[UVector, UVector[a[ind, op], opts], - optss]}]} /. {UMatrix[a_, opts___] /; AtomQ[a] :> - tbl[a[uix[tmp`i], uix[tmp`j], - Sequence @@ OptionsSelect[a, opts, optss]], {tmp`i, - gaugedimcheck[UMatrix, UMatrix[a, opts], optss]}, {tmp`j, - gaugedimcheck[UMatrix, UMatrix[a, opts], optss]}], - UVector[a_, opts___] /; AtomQ[a] :> - tbl[a[uix[tmp`i], - Sequence @@ OptionsSelect[a, opts, optss]], {tmp`i, - gaugedimcheck[UVector, UVector[a, opts], optss]}]} /. - tbl -> Table /. tr -> UTrace1; -uindxx = (uix | SUNIndex | ExplicitSUNIndex); - -WriteOutUMatrices2[aa_, (optss___Rule | optss___List)] := - aa /. (*UTrace2 checks only for UMatrices not for - explicit matrices when pulling out factors*) - UTrace1 -> tr/. - Power -> NMPower /. {UMatrix[a_[ind___, op___Rule], opts___][x___] :> - tbl[a[ind, Sequence @@ OptionsSelect[a, op, opts, optss]][ - uix[tmp`i], uix[tmp`j]][x], {tmp`i, - gaugedimcheck[UMatrix, - UMatrix[a[ind, op], opts, optss]]}, {tmp`j, - gaugedimcheck[UMatrix, UMatrix[a[ind, op], opts, optss]]}], - UVector[a_[ind___, op___Rule], opts___][x___] :> - tbl[a[ind, Sequence @@ OptionsSelect[a, op, opts, optss]][ - uix[tmp`i]][x], {tmp`i, - gaugedimcheck[UVector, UVector[a[ind, op], opts], - optss]}]} /. {UMatrix[a_, opts___][x___] /; AtomQ[a] :> - tbl[a[uix[tmp`i], uix[tmp`j], - Sequence @@ OptionsSelect[a, opts, optss]][x], {tmp`i, - gaugedimcheck[UMatrix, UMatrix[a, opts], optss]}, {tmp`j, - gaugedimcheck[UMatrix, UMatrix[a, opts], optss]}], - UVector[a_, opts___][x___] /; AtomQ[a] :> - tbl[a[uix[tmp`i], - Sequence @@ OptionsSelect[a, opts, optss]][x], {tmp`i, - gaugedimcheck[UVector, UVector[a, opts], optss]}]} /. - tbl -> Table /. tr -> UTrace1; - -(*Why were the substitutions below necessary? They breake things with e.g. - NM[a[x], UMatrix[b]] + UMatrix[UIdentity] a. This is because e.g. - a+{{b11,b12},{b21,b22}} gives {{a + b11, a + b12}, {a + b21, a + b22}}. - 14/6-2003*) -(*Now we have problems with e.g. - NM[UMatrix[UChiralSpurionLeft1[]][x], UMatrix[UGenerator[ExplicitSUNIndex[1]]]], - so that was the reason: With a product, each factor is written out sequentially - and NM can do it's thing in between. - So let's try another hack: replacing Plus temporarily.*) -(*And now "#% we have problems with e.g - NM[NM[a, UMatrix[aa]] + NM[b, UMatrix[bb]], UMatrix[cc]]. - Fixed by declaring plus a UMatrix.*) -WriteOutUMatrices[aa_, (optss___Rule | optss___List)] := - Block[ {plus, nm, tr, res}, - DeclareUMatrix[plus]; - res = WriteOutUMatrices1[WriteOutUMatrices2[aa/.UTrace1->tr/.NM->nm/.Plus->plus,optss],optss]/. - nm->NM/.plus->Plus/.tr->UTrace1; - UndeclareUMatrix[plus]; - res - ]; - -UIdentity[i : uindxx[_], j : uindxx[_], opts___?OptionQ] := - Which[(SUNN /. Flatten[{opts}] /. Options[UMatrix]) == 2 && - gaugedimcheck[UMatrix, opts] == 2, - SU2Delta[i, - j], (SUNN /. Flatten[{opts}] /. Options[UMatrix]) == 3 && - gaugedimcheck[UMatrix, opts] == 3, SU3Delta[i, j]]; - - -UGenerator[(SUNIndex | ExplicitSUNIndex)[i_Integer], opts___][uindxx[j_Integer], - uindxx[k_Integer]] := - $SUNBasis[ - gaugedimcheck[UGenerator, - opts], ((gaugedimcheck[UGenerator, opts] - 1)/2)][[i, j, k]]; - -UGenerator[(SUNIndex | ExplicitSUNIndex)[i_Integer]][uindxx[j_Integer], - uindxx[k_Integer]] := - $SUNBasis[ - gaugedimcheck[UGenerator, - opts], ((gaugedimcheck[UGenerator, opts] - 1)/2)][[i, j, k]]; - -UGenerator[i_Integer, opts___][uindxx[j_Integer], - uindxx[k_Integer]] := - $SUNBasis[ - gaugedimcheck[UGenerator, - opts], ((gaugedimcheck[UGenerator, opts] - 1)/2)][[i, j, k]]; - -UGenerator[i_Integer][uindxx[j_Integer], - uindxx[k_Integer]] := - $SUNBasis[ - gaugedimcheck[UGenerator, - opts], ((gaugedimcheck[UGenerator, opts] - 1)/2)][[i, j, k]]; - - - -(* UQuarkChargeMatrix is treated as a special case: *) - -UQuarkCharge[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ][uindxx[i_Integer], - uindxx[j_Integer]] /; ((SUNN /. Flatten[{opts}] /. - Options[UQuarkCharge]) == 2 && - gaugedimcheck[UQuarkCharge, opts] == - 2) := - ({{2/3*CouplingConstant[QED[1], st, sc, qs], - 0}, {0, -1/3*CouplingConstant[QED[1], st, sc, qs]}})[[i, j]]; - -UQuarkCharge[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ][ - uindxx[ii_Integer], - uindxx[jj_Integer]] /; ((SUNN /. Flatten[{opts}] /. - Options[UQuarkCharge]) == 3 && - gaugedimcheck[UQuarkCharge, opts] == - 3) := - ({{2/3*CouplingConstant[QED[1], st, sc, qs], 0, - 0}, {0, -1/3*CouplingConstant[QED[1], st, sc, qs], 0}, {0, - 0, -1/3*CouplingConstant[QED[1], st, sc, qs]}})[[ii, jj]]; - - - -(* UQuarkMassMatrix is treated as a special case: *) - -UQuarkMass[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ][uindxx[i_Integer], - uindxx[j_Integer]] /; ((SUNN /. Flatten[{opts}] /. - Options[UQuarkMass]) == 2 && - gaugedimcheck[UQuarkMass, opts] == - 2) := - ({{ParticleMass[UpQuark, st, sc, qs], 0}, {0, - ParticleMass[DownQuark, st, sc, qs]}} /. - If[ (QuarkToMesonMasses /. Flatten[{opts}] /. - Options[UQuarkMass]), - $QuarkToPionMassesRules, - {} - ])[[i, j]]; - -UQuarkMass[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ][ - uindxx[ii_Integer], - uindxx[jj_Integer]] /; ((SUNN /. Flatten[{opts}] /. - Options[UQuarkMass]) == 3 && - gaugedimcheck[UQuarkMass, opts] == - 3) := - ({{ParticleMass[UpQuark, st, sc, qs], 0, 0}, {0, - ParticleMass[DownQuark, st, sc, qs], 0}, {0, 0, - ParticleMass[StrangeQuark, st, sc, qs]}} /. - If[ (QuarkToMesonMasses /. Flatten[{opts}] /. - Options[UQuarkMass]), - $QuarkToMesonMassesRules, - {} - ])[[ii, - jj]]; - -(* UNucleonChargeMatrix added by P. Buettiker 21-Oct-2003 *) -UNucleonCharge[st___RenormalizationState, sc___RenormalizationScheme, - qs___ExpansionState, opts___?OptionQ][uindxx[i_Integer], - uindxx[j_Integer]] /; ((SUNN /. Flatten[{opts}] /. - Options[UQuarkCharge]) == 2 && - gaugedimcheck[UQuarkCharge, opts] == - 2) := - ({{1*CouplingConstant[QED[1], st, sc, qs], - 0}, {0, 0*CouplingConstant[QED[1], st, sc, qs]}})[[i, j]]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Field matrices *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* The U field is expanded in terms of the tuplet of meson fields which we call -PhiMesonIsoVector, assuming the exponential representation for terms of -higher order than 4: *) - -DeclareUScalar[DropFactor]; - -Adjoint[DropFactor[a___]] := - DropFactor[a]; - -Conjugate[DropFactor[a___]] ^:= DropFactor[a]; - -Transpose[DropFactor[a___]] ^:= DropFactor[a]; - - udrop[p_, ar___RenormalizationState, br___RenormalizationScheme, - qs___ExpansionState, opts___Rule | opts___List] := - If[ (DropOrder /. Flatten[{opts}] /. Options[UFieldMatrix]) =!= Infinity, - DropFactor[p, ar, br, qs], - 1 - ]; - -UFieldMatrix[(f_QuantumField)[x_], - opts___?OptionQ] := - UFieldMatrix[1, f[x],opts]; - -UFieldMatrix[ - QuantumField[f__][x_],opts___?OptionQ] := - UFieldMatrix[1, QuantumField[f][x],opts]; - -UFieldMatrix[ii_, - QuantumField[ders___fcpd, - Particle[p_, ar___RenormalizationState, br___RenormalizationScheme, - qs___ExpansionState], - lis___LorentzIndex, - iis___?fcsuniQ], - opts___?OptionQ] := - ( - decon = (Constant /. Flatten[{opts}] /. Options[UFieldMatrix]); - If[ decon==Automatic, - decon = DecayConstant[p, ar, br, qs] - ]; - Clear[DropFactor]; - DropFactor /: MakeBoxes[DropFactor[___], TraditionalForm] := - MakeBoxes[StyleForm["\[Aleph]", FontSlant -> "Italic"]][[1]]; - DropFactor /: - Power[DropFactor[p, ar, br, qs], i_] /; - i > (DropOrder /. Flatten[{opts}] /. Options[UFieldMatrix]) := 0; - expon = IsoDot[((IsoVector[ - QuantumField[ders, Particle[p, ar, br, qs], lis, iis], ##] &) @@ - OptionsSelect[IsoVector, opts]), - UGeneratorMatrixIsoVector @@ - Union[OptionsSelect[UMatrix, opts], - OptionsSelect[IsoVector, opts], - OptionsSelect[UGenerator, opts]]]; - nn = ExpansionOrder /. Flatten[{opts}] /. Options[UFieldMatrix]; - Simplify[UExp[ii, - I*udrop[p, ar, br, qs, opts]*expon/(decon), - nn]]); - -UFieldMatrix[ii_, - QuantumField[ders___fcpd, - Particle[p_, ar___RenormalizationState, br___RenormalizationScheme, - qs___ExpansionState], - lis___LorentzIndex, - iis___?fcsuniQ][x_], - opts___?OptionQ] := - ( - decon = (Constant /. Flatten[{opts}] /. Options[UFieldMatrix]); - If[ decon==Automatic, - decon = DecayConstant[p, ar, br, qs] - ]; - Clear[DropFactor]; - DropFactor /: MakeBoxes[DropFactor[___], TraditionalForm] := - MakeBoxes[StyleForm["\[Aleph]", FontSlant -> "Italic"]][[1]]; - DropFactor /: - Power[DropFactor[p, ar, br, qs], i_] /; - i > (DropOrder /. Flatten[{opts}] /. Options[UFieldMatrix]) := 0; - expon = IsoDot[((IsoVector[ - QuantumField[ders, Particle[p, ar, br, qs], lis, iis], ##] &) @@ - OptionsSelect[IsoVector, opts])[x], - UGeneratorMatrixIsoVector @@ - Union[OptionsSelect[UMatrix, opts], - OptionsSelect[IsoVector, opts], - OptionsSelect[UGenerator, opts]]]; - nn = ExpansionOrder /. Flatten[{opts}] /. Options[UFieldMatrix]; - Simplify[UExp[ii, - I*udrop[p, ar, br, qs, opts]*expon/(decon), - nn]]); - -UFieldMatrixSeries[ - QuantumField[ders___fcpd, - Particle[p_, ar___RenormalizationState, br___RenormalizationScheme, - qs___ExpansionState], - lis___LorentzIndex, - iis___?fcsuniQ], - opts___?OptionQ] := - ( - decon = (Constant /. Flatten[{opts}] /. Options[UFieldMatrixSeries]); - If[ decon==Automatic, - decon = DecayConstant[p, ar, br, qs] - ]; - expon = IsoDot[((IsoVector[ - QuantumField[ders, Particle[p, ar, br, qs], lis, iis], ##] &) @@ - OptionsSelect[IsoVector, opts]), - UGeneratorMatrixIsoVector @@ - Union[OptionsSelect[UMatrix, opts], - OptionsSelect[IsoVector, opts], - OptionsSelect[UGenerator, opts]]]; - nn = ExpansionOrder /. Flatten[{opts}] /. Options[UFieldMatrixSeries]; - Simplify[UExpSeries[I*expon/(decon), nn]]); - -UFieldMatrixSeries[ - QuantumField[ders___fcpd, - Particle[p_, ar___RenormalizationState, br___RenormalizationScheme, - qs___ExpansionState], - lis___LorentzIndex, - iis___?fcsuniQ][x_], - opts___?OptionQ] := - ( - decon = (Constant /. Flatten[{opts}] /. Options[UFieldMatrixSeries]); - If[ decon==Automatic, - decon = DecayConstant[p, ar, br, qs] - ]; - expon = IsoDot[((IsoVector[ - QuantumField[ders, Particle[p, ar, br, qs], lis, iis], ##] &) @@ - OptionsSelect[IsoVector, opts])[x], - UGeneratorMatrixIsoVector @@ - Union[OptionsSelect[UMatrix, opts], - OptionsSelect[IsoVector, opts], - OptionsSelect[UGenerator, opts]]]; - nn = ExpansionOrder /. Flatten[{opts}] /. Options[UFieldMatrixSeries]; - Simplify[UExpSeries[I*expon/(decon), nn]]); - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Adjoints and conjugates *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -(* Anti-particles: *) - -ChargeConjugate[QuantumField[p__][x_]] := - ChargeConjugate[QuantumField[p]][x]; - -ChargeConjugate[QuantumField[ders___, Particle[p_, i___], c___]] := - QuantumField[ders, Particle[ChargeConjugate[p], i], c]; - -ChargeConjugate[IsoVector[a_, b___][x_]] := - IsoVector[ChargeConjugate[a], b][x]; - -Adjoint[IsoVector[a_, b___][x_]] := - IsoVector[Adjoint[a], b][x]; - -Adjoint[IsoVector[a_, b___]] := - IsoVector[Adjoint[a], b]; - -Adjoint[UVector[a_, b___][x_]] := - UVector[Adjoint[a], b][x]; - -Adjoint[UVector[a_, b___]] := - UVector[Adjoint[a], b]; - -Adjoint[PhiProjection[i_]] = PhiProjection[i]; - -(*Commented out 11/5-2003*) -(*Adjoint[Projection[i_][j_]] = Projection[i][j]; - -Projection /: -Conjugate[Projection[i_][j_]] = Projection[i][j];*) - -PhiProjection /: -Conjugate[PhiProjection[i_]] = PhiProjection[i]; - -Adjoint[UMatrix[UGenerator[i___], opts___]] /; $StandardSUNBasis := - UMatrix[UGenerator[i], opts]; - -Adjoint[Adjoint[a_]] := - a; - - - -(* Distributivity of adjungation: *) - -Adjoint[b__ + c_] := - Adjoint[Plus[b]] + Adjoint[c]; - -Adjoint[b__*c_] := - Adjoint[Times[b]]*Adjoint[c]; - -Adjoint[Power[a_, b_]] := - Power[Adjoint[a], b]; - -Adjoint[IsoDot[b_, c_]] := - IsoDot[Conjugate[Adjoint[c]], Conjugate[Adjoint[b]]]; - -Adjoint[IsoCross[b_, c_]] /; $StandardSUNBasis := - -IsoCross[ - Conjugate[Adjoint[c]], Conjugate[Adjoint[b]]]; - -Adjoint[IsoSymmetricCross[b_, c_]] /; $StandardSUNBasis := - IsoSymmetricCross[Conjugate[Adjoint[c]], Adjoint[b]]; - - -(* Operators and matrices are interchanged when adjoined: *) - -(*Adjoint[NM[b__, c_]] := NM[Adjoint[c], Adjoint[NM[b]]];*) -(*Probably faster...*) -Adjoint[NM[a_,b__]] := - NM @@ (Adjoint /@ Reverse[{a,b}]); - -Adjoint[UDot[a_,b__]] := - UDot @@ (Adjoint /@ Reverse[{a,b}]); - -Adjoint[DOT[a_,b__]] := - DOT @@ (Adjoint /@ Reverse[{a,b}]); - -(* Distributivity of conjugation: *) - -Unprotect[Conjugate]; - -Conjugate[b__ + c_] := - Conjugate[Plus[b]] + Conjugate[c]; - -Conjugate[b__*c_] := - Conjugate[Times[b]]*Conjugate[c]; - -Conjugate[Power[a_, b_]]/;Element[b, Reals]===True := - Power[Conjugate[a], b]; - -Conjugate[IsoDot[b_, c_]] := - IsoDot[Conjugate[b], Conjugate[c]]; - -Conjugate[IsoCross[b_, c_]] := - IsoCross[Conjugate[b], Conjugate[c]]; - -Conjugate[IsoSymmetricCross[b_, c_]] := - IsoSymmetricCross[Conjugate[b], Conjugate[c]]; - -Conjugate[NM[b__, c_]] := - NM[Conjugate[b], Conjugate[c]]; - - -(* The generator matrices are self-adjoined - (in the standad representation only). *) - -Adjoint[UMatrix[UGenerator[i_], opts___]] /; $StandardSUNBasis := - UMatrix[UGenerator[i], opts]; - -Adjoint[IsoVector[UMatrix[UGenerator, optsm___], - optsv___]] /; $StandardSUNBasis := - IsoVector[UMatrix[UGenerator, optsm], optsv]; - -Adjoint[UMatrix[UIdentity, opts___]] := - UIdentityMatrix[opts]; - - -Conjugate[a : (SU2F | SU3F | SU3D | SUNF | - SUND)[__]] /; $StandardSUNBasis := - a; - -Conjugate[a : (SU2Delta | SU3Delta | SUNDelta)[__]] := - a; - -Conjugate[UMatrix[UIdentity, opts___]] := - UIdentityMatrix[opts]; - -Conjugate[IsoVector[a_, b___]] := - IsoVector[Conjugate[a], b] /; FreeQ[{a,b}, _sunitemp]; - -Conjugate[IsoVector[a_, b___][x_]] := - IsoVector[Conjugate[a], b][x] /; FreeQ[{a,b,x}, _sunitemp]; - -Protect[Conjugate]; - - -Unprotect[Transpose]; - -(* Scalars are brought out of Transpose: *) - -Transpose[a__Times] /; btss @@ a := - Times[##] & @@ Select[{a}, ((UScalarQ[#]&&FreeQ[#,allpatterns])&)]*Transpose[Times[##]] & @@ - Select[{a}, nbts]; - - -(* The transpose of the diagonal matrices: *) - -Transpose[UMatrix[UIdentity, opts___]] := - UIdentityMatrix[opts]; - -Protect[Transpose]; - - - -(* Scalars are simply conjugated: *) - -Adjoint[a_?((UScalarQ[#]&&FreeQ[#,allpatterns])&)] := - Conjugate[a]; -Adjoint[Conjugate[a_?((UScalarQ[#]&&FreeQ[#,allpatterns])&)]] := - a; -Adjoint[IsoVector[PhiProjection[i_], opts___]] := - IsoVector[PhiProjection[i], opts]; - - - -(* Matrices are transposed and conjugated: *) - -Adjoint[a_?MatrixQ] := - Conjugate[Transpose[a]]; -Adjoint[Conjugate[Transpose[a_]]] := - a; - - -(* Dirac stuff *) - -Adjoint[DiracGamma[ExplicitLorentzIndex[i:(1|2|3)]]] := - -DiracGamma[ExplicitLorentzIndex[i]]; -Adjoint[DiracGamma[i:(1|2|3)]] := - -DiracGamma[i]; -Adjoint[DiracGamma[ExplicitLorentzIndex[i:(0|5|6|7)]]] := - DiracGamma[ExplicitLorentzIndex[i]]; -Adjoint[DiracGamma[i:(0|5|6|7)]] := - DiracGamma[i]; - - -(* The Dirac bar: *) - -DiracBar[QuantumField[p__][x_]] := - DiracBar[QuantumField[p]][x]; -DiracBar[QuantumField[ders___, Particle[p_, i___], c___]] := - QuantumField[ders, DiracBar[Particle[p, i]], c]; -DiracBar[p_][ui_uix] := - DiracBar[p[ui]]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Traces *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* The trace is defined. It should be noted that the trace is performed on -terms proportional to UChiMatrix[opts] only if QuarkMatrixSimplify is true -and on terms proportional to UIdentityMatrix[opts], GeneratorIsoVector[opts] -or Generator[i,opts], which matrices have traces UDimension and 0 -respectively: *) - - -(* Distributivity: *) - -UTrace1[a_ + b_, opts___] := - UTrace1[a, opts] + UTrace1[b, opts]; -UTrace2[a_ + b_, opts___] := - UTrace2[a, opts] + UTrace2[b, opts]; - - - -(* Getting scalars out: *) - -UTrace1[a_Times, opts___] /; (btui[a] && (Union[btui /@ (List @@ a)] =!= {True})) := - Times @@ Select[List @@ a, nbtui]* - UTrace1[Times @@ Select[List @@ a, btui], opts]; - - - -(* Getting scalars out: *) - -UTrace2[a_Times, opts___] /; (btui[a] && (Union[btui /@ (List @@ a)] =!= {True})) := - Times @@ Select[List @@ a, nbtui]* - UTrace2[Times @@ Select[List @@ a, btui], opts]; - - - -(* Traces known by Phi: *) - -UTrace1[0, ___] := - 0; - -UTrace1[a_?NumberQ, ___] := - a; - -UTrace1[IsoVector[UMatrix[UGenerator[___Rule], ___], ___], ___] := - 0; - -UTrace1[UMatrix[UIdentity, opts1___], opts___] := - gaugedimcheck[UTrace, opts, opts1]; - -UTrace1[UMatrix[UGenerator[_, ___Rule], ___], ___] := - 0; - -UTrace1[b_, OptionsPattern[]] /; MatrixQ[b] := - Sum[b[[i, i]], {i, 1, Length[b[[1]]]}]; - - - -(* Products where UIdentityMatrix is the only matrix: *) - -UTrace1[NM[aa__], opts___Rule] /; (nbtu[NM[aa]] && btui[NM[aa]] && - gaugedimcheck[UMatrix, opts, aa] == 2) := - 2*NM[aa (*bug fix by Paul Buettiker; take care of nested traces of sums*) //. - UTrace1[ccc_] :> - UTrace[ccc /. UMatrix[UIdentity, rest___] :> uident[rest]]] /. - UMatrix[UIdentity, ___] -> 1 //. uident[rest___] :> UMatrix[UIdentity, rest]; - -UTrace1[NM[aa__], opts___Rule] /; nbtu[NM[aa]] && btui[NM[aa]] && (gaugedimcheck[UMatrix, - opts, aa] == 3) := - 3*NM[aa] /. UMatrix[UIdentity, ___] -> 1; - - -(* Products with one generator and no other matrices: *) - -HoldPattern[UTrace1[NM[aa__], - opts___Rule]] /; ((TraceSimplify /. Flatten[{opts}] /. - Options[UTrace]) && (Count[NM[aa] /. Power -> NMPower, - UGenerator, Infinity, Heads -> True] == 1) && - FreeQ[NM[aa], UMatrix[a___ /; FreeQ[{a}, UGenerator]], Infinity] && - nbtui[{aa} (*For the case when $UMatrices contain UMatrix*) /. - UMatrix -> tmpUMatrix] && - ((Or@@(MatrixQ/@{aa}))=!=True)) := - 0; - -UTrace1[IsoDot[aa__], - opts___Rule] /; ((TraceSimplify /. Flatten[{opts}] /. - Options[UTrace]) && (Count[IsoDot[aa] /. Power -> NMPower, - UGenerator, Infinity, Heads -> True] == 1) && - FreeQ[IsoDot[aa], UMatrix[a___ /; FreeQ[{a}, UGenerator]], - Infinity] && nbtui[{aa} /. UMatrix -> tmpUMatrix] - ) := - 0; - -UTrace1[IsoCross[aa__], - opts___Rule] /; ((TraceSimplify /. Flatten[{opts}] /. - Options[UTrace]) && (Count[IsoCross[aa] /. Power -> NMPower, - UGenerator, Infinity, Heads -> True] == 1) && - FreeQ[IsoCross[aa], UMatrix[a___ /; FreeQ[{a}, UGenerator]], - Infinity] && nbtui[{aa}UMatrix -> tmpUMatrix] - ) := - 0; - -UTrace1[IsoSymmetricCross[aa__], - opts___Rule] /; ((TraceSimplify /. Flatten[{opts}] /. - Options[UTrace]) && (Count[ - IsoSymmetricCross[aa] /. Power -> NMPower, UGenerator, - Infinity, Heads -> True] == 1) && - FreeQ[IsoSymmetricCross[aa], - UMatrix[a___ /; FreeQ[{a}, UGenerator]], Infinity] && - nbtui[{aa}UMatrix -> tmpUMatrix] - ) := - 0; - - - -(* The final trace function (UTrace of matrices without arguments should not be -evaluated): *) - -UTrace[a_, opts___Rule] /; (! HoldUTrace /. Flatten[{opts}] /. Options[UTrace]) := - UTrace2[a, opts] /. UTrace2 -> UTrace1; - - - -(* Invoking the trace function SUNTrace of FeynCalc: *) - -UTraceToFCTrace[a_, - opts___Rule] /; (gaugedimcheck[UTraceToFCTrace, opts, a] == - 3 && (SUNN /. Flatten[{opts}] /. Options[UTraceToFCTrace]) == - 3) := - (trtemp = (a /. {UTrace1 -> utemp, - UTrace -> utemp}) /. {QuantumField[b___fcpd, field_, - lis___LorentzIndex, - ii__?fcsuniQ] -> - fieldtemp[pdrs[b], qf[field], pdrs[lis]][ii]}; - trtemp1 = trtemp /. utemp[aa_, ___] -> utemp[aa, Explicit -> True]; - trtemp2 = trtemp1 /. utemp -> SUNTrace; - trtemp2 /. {fieldtemp[pdrs[b___], qf[field_], pdrs[lis___]][ii_] -> - QuantumField[b, field, lis, ii]} /. SUNN -> 3); -UTraceToFCTrace[a_, - opts___Rule] /; (gaugedimcheck[UTraceToFCTrace, opts, a] == - 3 && (SUNN /. Flatten[{opts}] /. Options[UTraceToFCTrace]) == - 3) := - (trtemp = (a /. {UTrace1 -> utemp, - UTrace -> utemp}) /. {QuantumField[b___fcpd, field_, - lis___LorentzIndex, - ii__?fcsuniQ] -> - fieldtemp[pdrs[b], qf[field], pdrs[lis]][ii]}; - trtemp1 = trtemp /. utemp[aa_, ___] -> utemp[aa, Explicit -> True]; - trtemp2 = trtemp1 /. utemp -> SUNTrace; - trtemp2 /. {fieldtemp[pdrs[b___], qf[field_], pdrs[lis___]][ii_] -> - QuantumField[b, field, lis, ii]} /. SUNN -> 2); - - - -(* Cyclicity of the trace: *) - -CycleUTraces[expr_, sf___] := - Block[ {a, tmplist, sortlist, smallest}, - expr /. UTrace1[a : ((*DOT*) UDot | NM)[__]] :> (tmplist = List @@ a; - sortlist = Sort[tmplist, sf]; - smallest = sortlist[[1]]; - Do[If[ Count[sortlist, sortlist[[i]]] === 1, - smallest = sortlist[[i]]; - Break[] - ], {i, 1, - Length[sortlist]}]; - While[! (tmplist[[1]] === smallest && tmplist[[-1]] =!= smallest || - tmplist[[1]] === smallest && Length[tmplist] <= 2 || - Length[Union[tmplist]] === 1), - tmplist = RotateLeft[tmplist]]; - UTrace1[a[[0]] @@ tmplist]) - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* SU(2) and SU(3) structure constants *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* The Kronecker delta function: *) - -SetAttributes[SU2Delta, Orderless]; - -(*SU2Delta[a___, uindxx[b_Integer], c___] := SU2Delta[a, b, c];*) -(*This should not be necessary anymore, since now ExplicitSUNIndex - is automatically tagging integers. Commented out 11/5-2003*) - -(*Added 11/5-2003, see above*) - -SU2Delta[uindxx[i_Integer], uindxx[i_Integer]] := - 1; - -SU2Delta[uindxx[_Integer], uindxx[_Integer]] := - 0; - -(**) - -SU2Delta[i_Integer, i_Integer] := - 1; - -SU2Delta[_Integer, _Integer] := - 0; - -SU2Delta[i_Symbol, i_Symbol] /; MemberQ[$ConstantIsoIndices, i] := - 1; - -SU2Delta[SUNIndex[i_Symbol], SUNIndex[i_Symbol]] /; - MemberQ[$ConstantIsoIndices, i] := - 1; - - - -(* The totally antisymmetric structure constants of SU(2) (J. F. Donoghue, E. - Golowich and B. R. Holstein, Dynamics of the Standard Model): *) - -(* We may as well take these directly from the matrices so it is easier to - change basis. *) - -(* This definition is covered by the one below, but I hope it is faster... *) - -(* Commented out 9/6-2003, forgotten 13/5-2003. See below *) - -(*SU2F[a : (uindxx[_Integer]) ..] := SU2F[Sequence @@ (((#[[1]]) &) /@ {a})]; - -SU2F[a___, uindxx[b_Integer], c___] := SU2F[a, b, c];*) - -SU2F[a__] /; (OrderedQ[{a}] != True && $StandardSUNBasis) := - Signature[{a}]*SU2F @@ Sort[{a}]; - -SU2F[a_, b_, c_] /; (!OrderedQ[{a, b}]) := - Signature[{a, b}]*SU2F[##, c] & @@ Sort[{a, b}]; - -SU2F[__Integer] /; $StandardSUNBasis := - 0; - -(*Added 11/5-2003, see above*) -(*Commented out 10/6-2003*) -(*SU2F[uindxx[_Integer]..] /; $StandardSUNBasis := 0;*) -SU2F[uindxx[a_Integer], uindxx[b_Integer], uindxx[c_Integer]] := - SU2F[a, b, c]; -(**) - -SU2F[a_, a_, _] /; $StandardSUNBasis := - 0; - -SU2F[_, b_, b_] /; $StandardSUNBasis := - 0; - -SU2F[a_, _, a_] /; $StandardSUNBasis := - 0; - - - -(* The Kronecker delta function: *) - -SetAttributes[SU3Delta, Orderless]; - -(*SU3Delta[a___, uindxx[b_Integer], c___] := SU3Delta[a, b, c];*) -(*This should not be necessary anymore, since now ExplicitSUNIndex - is automatically tagging integers. Commented out 11/5-2003*) - -(*Added 11/5-2003, see above*) - -SU3Delta[uindxx[i_Integer], uindxx[i_Integer]] := - 1; - -SU3Delta[uindxx[_Integer], uindxx[_Integer]] := - 0; - -(**) - -SU3Delta[i_Integer, i_Integer] := - 1; - -SU3Delta[_Integer, _Integer] := - 0; - -SU3Delta[i_Symbol, i_Symbol] /; MemberQ[$ConstantIsoIndices, i] := - 1; - -SU3Delta[uindxx[i_Symbol], uindxx[i_Symbol]] /; MemberQ[$ConstantIsoIndices, i] := - 1 - - - -(* The totally antisymmetric structure constants and symmetric coefficients of -SU(3) (J. F. Donoghue, E. Golowich and B. R. Holstein, Dynamics of the -Standard Model, (II.2.10)): *) - - - -(* This definition is covered by the one below, but I hope it is faster... *) - -(* Change 13/5-2003. Keep heads on integers, instead SUNIndex -> ExplicitSUNIndex *) -(*SU3F[a : (uindxx[_Integer]) ..] := SU3F[Sequence @@ (((#[[1]]) &) /@ {a})]; - -SU3F[a___, uindxx[b_Integer], c___] := SU3F[a, b, c];*) - - - -(* The totally antisymmetric structure constants of SU(3) (J. F. Donoghue, E. -Golowich and B. R. Holstein, Dynamics of the Standard Model): *) - -pairs[a_] := - Union[Sort /@ Flatten[Outer[List, a, a], 1]] /. {b_, b_} -> Sequence[]; - -pairsd[a_] := - Union[Sort /@ Flatten[Outer[List, a, a], 1]]; - -SU3F[a__] /; (!OrderedQ[{a}] && $StandardSUNBasis) := - Signature[{a}]*SU3F @@ Sort[{a}]; - -SU3F[a_, b_, c_] /; (!OrderedQ[{a, b}]) := - Signature[{a, b}]*SU3F[##, c] & @@ Sort[{a, b}]; - -(*Added 17/6-2003. See below*) -SU3F[___, 0, ___] := - 0; -SU3F[___, uindxx[0], ___] := - 0; - -SU3F[a_Integer, b_Integer, - _] /; (MemberQ[fzeropairlist, Sort[{a, b}]] && $StandardSUNBasis) := - 0; - -(*Added 11/5-2003, see above*) -SU3F[uindxx[a_Integer], uindxx[b_Integer], - _] /; (MemberQ[fzeropairlist, Sort[{a, b}]] && $StandardSUNBasis) := - 0; -SU3F[uindxx[a_Integer], uindxx[b_Integer], uindxx[c_Integer]] := - SU3F[a, b, c]; -(**) - -SU3F[a_, a_, _] /; $StandardSUNBasis := - 0; - -SU3F[_, b_, b_] /; $StandardSUNBasis := - 0; - -SU3F[a_, _, a_] /; $StandardSUNBasis := - 0; - -pairsfunc[a_] := - Rule[(*HoldPattern[*)SU3F[##](*]*)& @@ - Join[#, {i_}], (SU3F[Sequence @@ #, Complement[a, #][[1]]])* - SU3Delta[i, Complement[a, #][[1]]]]& /@ pairs[a]; - - - -(* This definition is covered by the one below, but I hope it is faster... *) - -(* Change 13/5-2003. Keep heads on integers, instead SUNIndex -> ExplicitSUNIndex *) - -(*SU3D[a : (uindxx[_Integer]) ..] := SU3D[Sequence @@ (((#[[1]]) &) /@ {a})]; - -SU3D[a___, uindxx[b_Integer], c___] := SU3D[a, b, c];*) - -SetAttributes[SU3D, Orderless]; - - - -(* The totally symmetric coefficients of SU(3) (J. F. Donoghue, E. Golowich and -B. R. Holstein, Dynamics of the Standard Model): *) - - -(* We may as well take these directly from the matrices so it is easier to - change basis. *) - -(* Added the check for 0. 17/6-2003. SUNIndex[0] is used to indicate SU(N) singlet - QuantumFields and occurs in some Feynman rules. *) - -SU3D[___, 0, ___] := - 0; -SU3D[___, uindxx[0], ___] := - 0; - -SU3D[a_Integer, b_Integer, - _] /; ($StandardSUNBasis && MemberQ[dzeropairlist, Sort[{a, b}]]) := - 0; - -(*Added 11/5-2003, see above*) -SU3D[uindxx[a_Integer], uindxx[b_Integer], - _] /; ($StandardSUNBasis && MemberQ[dzeropairlist, Sort[{a, b}]]) := - 0; - -SU3D[uindxx[a_Integer], uindxx[b_Integer], uindxx[c_Integer]] := - SU3D[a, b, c]; -(**) - -SU3D[___, a : SUNIndex[_?(((!IntegerQ[#]) && - FreeQ[$ConstantIsoIndices, #]) &)], ___, - a_, ___] /; $StandardSUNBasis := - 0; - - - -(* This function drops only as many elements from a as b has - starting from the -left: *) - -ComplementAll[a_List, b_List] := - (listf[0] = a; - Do[listf[l] = listf[l - 1] /. {i___, b[[l]], k___} -> {i, k}, {l, - Length[b]}]; - listf[Length[b]]); - -pairsall[a_] := - Union[Join[Take[#, 2] & /@ Permutations[a]]]; - -pairsfuncd[a_] := - Union[Rule[ - (*HoldPattern[*)SU3D[##](*]*)& @@ Join[#, {i_}], (SU3D @@ a)* - SU3Delta[i, ComplementAll[a, #][[1]]]] & /@ pairsall[a]]; - - - -(* This is to allow changing basis matrices spanning SU(N) and have the change - propagate to the structure constants. Works only when staying in the usual - dimensional representations (2 for SU(2) and 3 for SU(3)). *) - - - -(* fnlist: List of ordered triplets yielding non-zero f. fnonzeropairlist:list -of all pairs of elements which will give f!=0 regardless of the third -argument.. fzeropairlist:list of all pairs of elements which will give f=0 -regardless of the third argument. *) - -FixSUN := - ( - - If[ Phi`$Phi && (Length[$SUNBasis[2, 1/2]] =!= 3 || - Union[MatrixQ /@ $SUNBasis[2, 1/2]] =!= {True} || - Union[Flatten[Dimensions /@ $SUNBasis[2, 1/2]]] =!= {2}), - Message[FixSUN::badmatr2]; - Return[]; - ]; - If[ Phi`$Phi && (Length[$SUNBasis[3, 1]] =!= 8 || - Union[MatrixQ /@ $SUNBasis[3, 1]] =!= {True} || - Union[Flatten[Dimensions /@ $SUNBasis[3, 1]]] =!= {3}), - Message[FixSUN::badmatr2]; - Return[]; - ]; - FCPrint[2, "$StandardSUNBasis is ", $StandardSUNBasis]; - FCPrint[2, "Setting new values of SU2F"]; - tt2 = - Table[WriteOutUMatrices[ - UGeneratorMatrix[SUNIndex[i], SUNN -> 2]], {i, 3}]; - -(*List of (ordered) triplets :*) - trip2f = If[ $StandardSUNBasis, - Flatten[Table[ - Table[Table[hh[k, j, i], {i, j + 1, 3}], {j, k + 1, 3}], {k, - 3}]] /. hh -> List, - Flatten[Table[ - Table[Table[hh[k, j, i], {i, 1, 3}], {j, 1, 3}], {k, 1, - 3}]] /. hh -> List - ]; - Do[SU2F[trip2f[[i, 1]], trip2f[[i, 2]], trip2f[[i, 3]]] = -I/4* - UTrace[Adjoint[ - tt2[[trip2f[[i, - 3]]]]].(tt2[[trip2f[[i, 1]]]].tt2[[trip2f[[i, - 2]]]] - - tt2[[trip2f[[i, 2]]]].tt2[[trip2f[[i, 1]]]])], {i, - Length[trip2f]}]; - FCPrint[2, "Setting new values of SU3F and SU3D"]; - ClearAttributes[SU3D, Orderless]; - If[ $StandardSUNBasis, - SetAttributes[SU3D, Orderless] - ]; - fnlist = {}; - dnlist = {}; - - (*List of (ordered) triplets :*) - tripf = If[ $StandardSUNBasis, - Flatten[Table[ - Table[Table[hh[k, j, i], {i, j + 1, 8}], {j, k + 1, 8}], {k, - 8}]] /. hh -> List, - Flatten[Table[ - Table[Table[hh[k, j, i], {i, 1, 8}], {j, 1, 8}], {k, 8}]] /. - hh -> List - ]; - tripd = - If[ $StandardSUNBasis, - Flatten[Table[ - Table[Table[hh[k, j, i], {i, j, 8}], {j, k, 8}], {k, 8}]] /. - hh -> List, - Flatten[Table[ - Table[Table[hh[k, j, i], {i, 1, 8}], {j, 1, 8}], {k, 8}]] /. - hh -> List - ]; - tt3 = - Table[WriteOutUMatrices[ - UGeneratorMatrix[SUNIndex[i], SUNN -> 3]], {i, 8}]; - Do[If[ (SU3F[tripf[[i, 1]], tripf[[i, 2]], tripf[[i, 3]]] = - Evaluate[-I/4* - UTrace[Adjoint[ - tt3[[tripf[[i, - 3]]]]].(tt3[[tripf[[i, 1]]]].tt3[[tripf[[i, - 2]]]] - - tt3[[tripf[[i, 2]]]].tt3[[tripf[[i, 1]]]])]]) =!= - 0, - fnlist = - Append[fnlist, {tripf[[i, 1]], tripf[[i, 2]], - tripf[[i, 3]]}] - ], {i, Length[tripf]}]; - Do[If[ (SU3D[tripd[[i, 1]], tripd[[i, 2]], tripd[[i, 3]]] = - Evaluate[ - 1/4*UTrace[ - Adjoint[ - tt3[[tripd[[i, - 3]]]]].(tt3[[tripd[[i, 1]]]].tt3[[tripd[[i, - 2]]]] + - tt3[[tripd[[i, 2]]]].tt3[[tripd[[i, 1]]]])]]) =!= - 0, - dnlist = - Append[dnlist, {tripd[[i, 1]], tripd[[i, 2]], - tripd[[i, 3]]}] - ], {i, Length[tripd]}]; - FCPrint[2, - "Building table of reduction rules for SU(2) and SU(3)"]; - fnonzeropairlist = - Union[FlattenAt[pairs /@ fnlist, Table[{i}, {i, Length[fnlist]}]]]; - fzeropairlist = - Complement[ - Union[Sort /@ - Flatten[Outer[ - List, {1, 2, 3, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 6, 7, 8}], - 1]], fnonzeropairlist]; - dnonzeropairlist = - Union[FlattenAt[pairsd /@ dnlist, Table[{i}, {i, Length[dnlist]}]]]; - dzeropairlist = - Complement[ - Union[Sort /@ - Flatten[Outer[ - List, {1, 2, 3, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 5, 6, 7, 8}], - 1]], dnonzeropairlist]; - - (*When two indices are integers, - only some values of the third will give a non - - zero result. $SU3FReduceList is the corresponding list of rules, - substituting SU3F with SU3Delta*) - $SU3FReduceList = - If[ $StandardSUNBasis, - Flatten[Sort[ - Union[FlattenAt[Evaluate[pairsfunc /@ fnlist], - Table[{i}, {i, Length[fnlist]}]]]] //. {a___, b_ -> c_, - b_ -> d_, e___} -> {a, b -> c + d, e}], - {} - ]; - $SU3DReduceList = - If[ $StandardSUNBasis, - Flatten[Sort[ - Union[FlattenAt[Evaluate[pairsfuncd /@ dnlist], - Table[{i}, {i, Length[dnlist]}]]]] //. {a___, b_ -> c_, - b_ -> d_, e___} -> {a, b -> c + d, e}], - {} - ]; - - (* Change 13/5-2003. Keep heads on integers, instead SUNIndex -> ExplicitSUNIndex *) - $SU3FReduceList = $SU3FReduceList //. (f:(SU3F|SU3Delta))[a___, b_Integer, c___] :> - f[a, ExplicitSUNIndex[b], c]; - $SU3DReduceList = $SU3DReduceList //. (f:(SU3D|SU3Delta))[a___, b_Integer, c___] :> - f[a, ExplicitSUNIndex[b], c]; - If[ Phi`$Phi, - $SUNRules = - Join[$SUNDeltaRules, - If[ $StandardSUNBasis, - $SUNDFRules, - {} - ], $SU3FReduceList, - $SU3DReduceList] - ]; - FCPrint[3, "New reduction tables read:\n", $SUNRules]; - - ); - -FixSUN; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Supplying iso-indices *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* Support functions for IsoIndicesSupply. Index numerators, increasing by one -each time applied: *) - -id[x_, OptionsPattern[]] := - x; -$IsoIndicesCounter = 0; -iin[opts___] := - (++$IsoIndicesCounter; - ToExpression[(IsoIndicesString /. Flatten[{opts}] /. - Options[IsoIndicesSupply]) <> ToString[$IsoIndicesCounter]]); -iinintern := - (++iicintern; - ToExpression["internisoindstr" <> ToString[iicintern]]); -iinfree[opts___] := - (++$IsoIndicesCounter; - ToExpression[(FreeIsoIndicesString /. Flatten[{opts}] /. - Options[IsoIndicesSupply]) <> ToString[$IsoIndicesCounter]]); - - - -(* Every object obj ocurring as an argument to IsoDot, IsoCross or -IsoSymmetricCross is substituted with obj[i], where i is an isospin index -generated anew each time. Here follow how the different objects interpret -this additional isospin dependence *) - -IsoVector[a_[ii : uindxx[_], jj : uindxx[_], op___Rule | op___List], opts___][ - i__?fcsuniQ] := - (a[i, ##]& @@ OptionsSelect[a, opts, op])[ii, jj]; -IsoVector[a_[b__, (op___Rule | op___List)], opts___][x_][ - i__?fcsuniQ] := - (a[b, ##]& @@ OptionsSelect[a, op, opts])[i][x]; -IsoVector[a_[b__, (op___Rule | op___List)], opts___][ - i__?fcsuniQ] := - (a[b, ##]& @@ OptionsSelect[a, op, opts])[i]; -(*Added 16/5-2003 to support the simple cases of - IsoDot[IsoVector[a], IsoVector[b]]//IsoIndicesSupply and - IsoDot[IsoVector[a][x], IsoVector[b][]]//IsoIndicesSupply*) -IsoVector[a_Symbol, OptionsPattern[]][i__?fcsuniQ] := - a[i]; -IsoVector[a_Symbol, OptionsPattern[]][x_][i__?fcsuniQ] := - a[x][i]; - - - - -(* IsoVectors - fixing special cases: *) - -QuantumField[ -ders___FCPartialD, a__, - lors___LorentzIndex, - iis___?fcsuniQ][isosp_?fcsuniQ] := - QuantumField[ders, a, lors, isosp, iis]; - -QuantumField[ -ders___FCPartialD, a__, - lors___LorentzIndex, - iis___?fcsuniQ][ui_UIndex] := - QuantumField[ders, a, lors, iis, ui]; - -UMatrix[UGenerator[op___], opts___][ - i_?fcsuniQ] := - UMatrix[UGenerator[i, op], opts]; - -Unprotect[Conjugate]; - Conjugate[UMatrix[UGenerator[op___], opts___]][ - i_?fcsuniQ] := - Conjugate[UMatrix[UGenerator[i, op], opts]]; - -(* Hack to deal with issue with WriteOutIsoVectors. *) -(*Conjugate[Conjugate[a_][(SUNIndex | ExplicitSUNIndex)[i_]]] := a[SUNIndex[i]];*) -(*Added 16/5-2003*) -(*Conjugate[Conjugate[a_][(SUNIndex | ExplicitSUNIndex)[i_]][x_Symbol]] := a[SUNIndex[i]][x];*) -(*Changed 19/5-2003, see below*) - - -Protect[Conjugate]; - - -(* Support function for IsoIndicesSupply. supptemp is a temporary item wrapping -the arguments of IsoCross and IsoSymmetricCross. wrap is a temporary wrapper -for the temporarily free index: *) - -supptemp[a_][sunitemp[wrap[in_]]][in1_] := - supptemp[a] /. sunitemp[wrap[in]] -> sunitemp[in1]; - - - -(* Step two in the supplial of the extra isospin dependence: *) - -indsuppdot[a_, b_, i_] := - NM[Conjugate[a[sunitemp[i]]], b[sunitemp[i]]]; - -indsuppcross[a_, b_, i1_, i2_, i3_] := - supptemp[NM[Conjugate[a[sunitemp[i2]]], b[sunitemp[i3]]]* - SUNF @@ sunitemp /@ {i1, i2, i3}][sunitemp[i1]]; - -indsuppsymmcross[a_, b_, i1_, i2_, i3_] := - supptemp[NM[Conjugate[a[sunitemp[i2]]], b[sunitemp[i3]]]* - SUND @@ sunitemp /@ {i1, i2, i3}][sunitemp[i1]]; - - - -(* Step one in the supplial of the extra isospin dependence: *) - -indicesdotrule[ - optss___] := - (IsoDot[a_, b_] /; - FreeQ[{a, b}, (_IsoDot | _IsoCross | _IsoSymmetricCross)] :> - indsuppdot[a, b, iin[optss]]); - -indicescrossrule[ - optss___] := - (IsoCross[a_, b_] /; - FreeQ[{a, b}, (_IsoDot | _IsoCross | _IsoSymmetricCross)] :> - indsuppcross[a, b, wrap[iinintern], iin[optss], iin[optss]]); - -indicessymmcrossrule[ - optss___] := - (isctemp[a_, b_] /; - FreeQ[{a, b}, (_IsoDot | _IsoCross | _isctemp)] :> - indsuppsymmcross[a, b, wrap[iinintern], iin[optss], iin[optss]]); - - -(* Catching free indices: *) - -(* Catching products in vector products. Added 20/10-2003. - Fixes problem reported by Paul Buettiker. E.g. - IsoDot[NM[IsoVector[d], c], NM[IsoCross[IsoVector[b], IsoVector[bb]], a]] // - IsoIndicesSupply - would not work. - Not really tested... *) -freeindicesrules0 = (t:(NM|Times|UDot(*DOT*)))[a__][SUNIndex[i_]] /; - Count[t[a], _wrap, Infinity, Heads -> True] === 1 :> - (t[a] /. wrap[_] :> SUNIndex[i]) - -freeindicesrules[opts___] := - ( - fi = ToExpression[FreeIsoIndexString /. Flatten[{opts}] /. - Options[IsoIndicesSupply]]; - {f_[SUNIndex[wrap[_]]] -> f, - IsoVector[a__][x_] :> IsoVector[a][x][SUNIndex[fi]], - IsoVector[a__] :> IsoVector[a][SUNIndex[fi]]} - ); - -freeindicesrules1[opts___] := - {f_[SUNIndex[wrap[_]]] -> f, - IsoVector[a__][x_] :> IsoVector[a][x][SUNIndex[iinfree[opts]]], - IsoVector[a__] :> IsoVector[a][SUNIndex[iinfree[opts]]]}; - - - -(* The function that supplies indices to expressions involving IsoDots, - IsoCrosses and IsoSymmetricCrosses of iso-spin vectors: *) - - -IsoIndicesSupply[x_Plus] := - Block[ {tmpic = $IsoIndicesCounter}, - ($IsoIndicesCounter = tmpic; - IsoIndicesSupply[#])& /@ x - ]; - - -IsoIndicesSupply[ - aa_, (optss___Rule | optss___List)] := - (FCPrint[2, - "Starting with number ", $IsoIndicesCounter]; - iicintern = 0; - aa //.(c_?(!FreeQ[{#}, IsoDot[_, _], Infinity] &))^ - n_ :> (FCPrint[2, "Fixing powers"]; - times1 @@ Table[c, {n}]) /. - IsoSymmetricCross -> isctemp //. (FCPrint[2, - "Recursively resolving iso-vector products"]; - {(*Sequence@@proddotrules,*) indicesdotrule[optss], indicescrossrule[optss], - indicessymmcrossrule[optss]}) /. {sunitemp -> SUNIndex, - supptemp -> id, isctemp -> IsoSymmetricCross} //. - freeindicesrules0 /. - If[ NumerateFree /. Flatten[{optss}] /. Options[IsoIndicesSupply], - FCPrint[2, "Non-contracted indices will be numerated"]; - freeindicesrules1[optss], - FCPrint[2, "Non-contracted indices will not be numerated"]; - freeindicesrules[optss] - ] /. - wrap[___] -> - ToExpression[ - FreeIsoIndexString /. Flatten[{optss}] /. - Options[IsoIndicesSupply]] /. times1 -> Times /. - (*Added 19/5-2003, see above*)(*inconsistency; fixed by Paul Buettiker, 11-01-2004*) - {Conjugate[a_Symbol][(SUNIndex | ExplicitSUNIndex)[i_]][x_Symbol] :> Conjugate[a[x][SUNIndex[i]](*[x]*)], - Conjugate[a_Symbol][(SUNIndex | ExplicitSUNIndex)[i_]] :> Conjugate[a[SUNIndex[i]]]}); - - - -(* Support functions for UIndicesSupply: *) - -$UIndicesCounter = 0; -nnn[opts___] := - uix[(++$UIndicesCounter; - ToExpression[(UIndicesString /. Flatten[{opts}] /. - Options[UIndicesSupply]) <> ToString[$UIndicesCounter]])]; - -nnm[opts___] := - uix[(ToExpression[(UIndicesString /. Flatten[{opts}] /. - Options[UIndicesSupply]) <> ToString[$UIndicesCounter + 1]])]; - - - -(* UIndicesSupply: *) - -UIndicesSupply[a_, opts___] := - UIndicesSupply1[a, opts] /. - {UMatrix[m_[ind_, op___], i_uix, j_uix, opt___] :> - m[ind, Sequence @@ OptionsSelect[m, opts, op, opt]][i, j], - UMatrix[m_, i_uix, j_uix, opt___] :> m[i, j, opt]} /. - If[ (UIndexToSUNIndex /. Flatten[{opts}] /. Options[UIndicesSupply]), - uix -> SUNIndex, - {} - ] /. (*DOT*)UDot -> DOT /. nnmm -> NM; - - - -(* Linearity: *) - -UIndicesSupply[a_ + b_, opts___] := - UIndicesSupply[a, opts] + UIndicesSupply[b, opts]; -UIndicesSupply[a_*b_, opts___] /; - FreeQ[a /. UTrace1[aa_] :> UTrace1[aa/. {UMatrix->um, UVector->uv}], UMatrix | UVector] := - a*UIndicesSupply[b, opts]; -UIndicesSupply[a_, ___] /; - FreeQ[a /. UTrace1[aa_] :> UTrace1[aa/. {UMatrix->um, UVector->uv}], UMatrix | UVector] := - a; -UIndicesSupply1[a_ + b_, opts___] := - UIndicesSupply[a, opts] + UIndicesSupply[b, opts]; -UIndicesSupply1[a_*b_, opts___] /; - FreeQ[a /. UTrace1[aa_] :> UTrace1[aa/. {UMatrix->um, UVector->uv}], UMatrix | UVector] := - a*UIndicesSupply[b, opts]; -UIndicesSupply1[a_, ___] /; - FreeQ[a /. UTrace1[aa_] :> UTrace1[aa/. {UMatrix->um, UVector->uv}], UMatrix | UVector] := - a; - - - -(* Supplying matrix indices: *) - - -(* Unnested NMs: *) - -UIndicesSupply1[aa_NM, optss1___] /; - FreeQ[List @@ aa, NM | UDot(*DOT*)] := - (ui1 = - nnmm @@ Table[(If[ ! FreeQ[aa[[rep]], UMatrix], - indexpair = Sequence[nnn[optss1], nnm[optss1]] - ]; - ReplacePart[aa, - aa[[rep]] /. - UMatrix[a_, opts___] :> UMatrix[a, indexpair, opts], - rep][[rep]]), {rep, Length[aa]}] /. nnmm -> NM; - $UIndicesCounter++; - ui1); - - - -(* Nested NMs are NMExpanded: *) - -UIndicesSupply1[a_NM, optss1___] /; (!FreeQ[List @@ a, NM | UDot(*DOT*)]) := - UIndicesSupply1[NMExpand[a], optss1]; - - - -(* A single UMatrix or UVector: *) - -UIndicesSupply1[aa_, optss1___] /; (FreeQ[aa, NM | UDot(*DOT*)] && - !FreeQ[aa, UVector | UMatrix]) := - (indexpair = - Sequence[nnn[optss1], nnm[optss1]]; - $UIndicesCounter++; - aa /. {UMatrix[a_, opts___] :> UMatrix[a, indexpair, opts], - UVector[a_, opts___] :> UVector[a, indexpair[[1]], opts]}); - -UIndicesSupply1[] := - Sequence[]; - -UIndicesSupply[] := - Sequence[]; - - - -(* When supplying indices to a dot product, the enclosed NM product is first -supplied with indices, then the enclosing vectors are supplied with indices: *) - -UIndicesSupply1[(UDot(*DOT*)(* | Dot*))[aa1_, aa2___, - aa3_], optss1___] /; Length[aa1] == 1 && Length[aa3] == 1 := - tempdot[aa1, UIndicesSupply1[NM[aa2]], - aa3] //. {(*vbar.m.v*) - tempdot[a___, b_, c__, d_, - e___] /; (FreeQ[{c}, UVector] && !FreeQ[{b}, UVector] && - !FreeQ[{d}, UVector] && !FreeQ[{c}, UMatrix]) :> - tempdot[a, - b /. UVector[p_] -> - p[Flatten[ - Cases[{c}, _uix, Infinity, Heads -> True]][[1]]], - c, d /. - UVector[p1_] -> - p1[Flatten[ - Cases[{c}, _uix, Infinity, Heads -> True]][[-1]]], - e],(*vbar.v*) - tempdot[a___, b_, c___, d_, - e___] /; (FreeQ[{c}, UVector] && - !FreeQ[{b}, UVector] && ! FreeQ[{d}, UVector] && - FreeQ[{c}, UMatrix]) :> (index = nnn[optss1]; - tempdot[a, b /. UVector[p2_] -> p2[index], c, - d /. UVector[p3_] -> p3[index], e])} //. {(*m.v*) - tempdot[a___, c__, d_, - e___] /; (FreeQ[{c}, UVector] && ! FreeQ[{d}, UVector] && - !FreeQ[{c}, UMatrix]) :> - tempdot[a, c, - d /. UVector[p1_] -> - p1[Flatten[ - Cases[{c}, _uix, Infinity, Heads -> True]][[-1]]], - e],(*v.m*) - tempdot[a___, d_, c__, - e___] /; (FreeQ[{c}, UVector] && ! FreeQ[{d}, UVector] && - !FreeQ[{c}, UMatrix]) :> - tempdot[a, c, - d /. UVector[p1_] -> - p1[Flatten[ - Cases[{c}, _uix, Infinity, Heads -> True]][[1]]], - e]} /. nnmm -> NM /. tempdot -> UDot(*DOT*); - - -UIndicesSupply1[UTrace1[aa_], OptionsPattern[]] := - UIndicesSupply1[ - aa /.(*tracing single matrices*){UTrace[ - UMatrix[a_, ss_uix, _uix, op___]] -> - UMatrix[a, ss, ss, op], - UTrace1[UMatrix[a_, ss_uix, _uix, op___]] -> - UMatrix[a, ss, ss, - op]}] /.(*replacing the last index with the first*)NM -> - nmtemp /. {nmtemp[a___, b_, c___, d_, - e___] /; ((! FreeQ[{b, d}, uix]) && (FreeQ[{a, e}, - uix])) :> (uinds = - Cases[{a, b, c, d, e}, _uix, Infinity, Heads -> True]; - nmtemp[a, b, c, d /. uinds[[-1]] -> uinds[[1]], e])} /. - nmtemp -> NM; - -QuantumField[ders___FCPartialD, a__, uis_uix, - lors___LorentzIndex, - iis___?fcsuniQ][ui_uix] := - QuantumField[ders, a, ui, uis, lors, isosp, iis]; - - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Transformation to FC notation *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -iinint[opts___] := - (++$IsoIndicesCounter; - ToExpression[(FreeIsoIndicesString /. Flatten[{opts}] /. - Options[PhiToFC]) <> ToString[$IsoIndicesCounter]]); - -(*Commented out 11/5-2003*) -(*intindicesrules[ - opts___] := (fi = - ToExpression[ - FreeIsoIndexString /. Flatten[{opts}] /. - Options[IsoIndicesSupply]]; {SUNDelta[a___, b_Integer, c___] :> - Projection[b][a, c], - SUND[a___, b_Integer, c___] :> - SUND[a, SUNIndex[fi], c]*Projection[b][SUNIndex[fi]], - SUNF[a___, b_Integer, c___] :> - SUNF[a, SUNIndex[fi], c]*Projection[b][SUNIndex[fi]]}); - -intindicesrules1[ - opts___] := {SUNDelta[a___, b_Integer, c___] :> Projection[b][a, c], - SUND[a___, b_Integer, c___] :> (fi = SUNIndex[iinint[opts]]; - SUND[a, fi, c]*Projection[b][fi]), - SUNF[a___, b_Integer, c___] :> (fi = SUNIndex[iinint[opts]]; - SUNF[a, fi, c]*Projection[b][fi])}; - -intindicesruleslast[ - opts___] := (fi = - ToExpression[ - FreeIsoIndexString /. Flatten[{opts}] /. Options[IsoIndicesSupply]]; - f_ /; (Count[f, (SUNIndex | ExplicitSUNIndex)[_Integer], Infinity] == 1 && - FreeQ[{f}, - NMPower | Power | NM | Times | Dot | DOT | IsoDot | - IsoCross | IsoSymmetricCross]) :> (ni = - Cases[f, (SUNIndex | ExplicitSUNIndex)[_Integer], Infinity][[1]]; (f /. - ni -> SUNIndex[fi])*Projection[ni[[1]]][SUNIndex[fi]])); - -intindicesruleslast1[opts___] := - f_ /; (Count[f, (SUNIndex | ExplicitSUNIndex)[_Integer], Infinity] == 1 && - FreeQ[{f}, - NMPower | Power | NM | Times | Dot | DOT | IsoDot | IsoCross | - IsoSymmetricCross]) :> (fi = SUNIndex[iinint[opts]]; - ni = Cases[f, SUNIndex[_Integer], Infinity][[1]]; (f /. ni -> fi)* - Projection[ni[[1]]][fi]);*) - -PhiToFC[aa_, OptionsPattern[]] := - aa /. {(*UGenerator[SUNIndex[i_Symbol /; FreeQ[$ConstantIsoIndices, i]], - opts___Rule | opts___List] -> 2*SUNT[SUNIndex[i]],*)NM -> - DOT, QuantumField[pp__][_] :> QuantumField[pp], uix -> SUNIndex, - SU2Delta -> SUNDelta, SU3Delta -> SUNDelta, SU2F -> SUNF, - SU3F -> SUNF, SU3D -> SUND}(*Commented out 11/5-2003*)(*/. (Power | NMPower)[ - p_?(!FreeQ[#, SUNIndex|ExplicitSUNIndex, Infinity, Heads -> True]&), n_] :> - Times @@ MapIndexed[pp, Table[p, {n}]] /. - If[(RemoveIntegerIndices /. Flatten[{opts}] /. Options[PhiToFC]), - If[(NumerateFree /. Flatten[{opts}] /. Options[PhiToFC]), - intindicesrules1[opts], intindicesrules[opts]], {}] /. - If[(RemoveIntegerIndices /. Flatten[{opts}] /. Options[PhiToFC]), - If[(NumerateFree /. Flatten[{opts}] /. Options[PhiToFC]), - intindicesruleslast1[opts], intindicesruleslast[opts]], {}] /. - pp[p_, _] -> p*); - - - -(* The (n-dimensional) isospin indices from 1 to IsoIndicesNumber, used by -IsoIndicesSupply: *) - -IsoIndicesList[opts___?OptionQ] := - (Table[ - ToExpression[(IsoIndicesString /. Flatten[{opts}] /. - Options[IsoIndicesList]) <> ToString[i]], {i, 1, - IsoIndicesNumber /. Flatten[{opts}] /. Options[IsoIndicesList]}]); - - - -(* The momenta of the incoming/outgoing particles: *) - -MomentumVariables[opts___?OptionQ] := - Table[ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentumVariables]) <> ToString[i]], {i, - ParticlesNumber /. Flatten[{opts}] /. Options[MomentumVariables]}]; - - - -(* The fields to be declared to FeynCalc (all are incoming): *) - -FieldsSet[body___fcqf, opts___?OptionQ] /; - VectorQ[ParticlesNumber /. Flatten[{opts}] /. - Options[FieldsSet]] := - (pnr[ - x_] := - (ParticlesNumber /. Flatten[{opts}] /. - Options[FieldsSet])[[x]]; - Table[(QuantumField[##] & @@ - Join[List @@ body, - If[ (LorentzIndicesString /. Flatten[{opts}] /. - Options[FieldsSet]) === - None, - {seq[]}, - {LorentzIndex[ - ToExpression[(LorentzIndicesString /. - Flatten[{opts}] /. Options[FieldsSet]) <> - ToString[pnr[j]]]]} - ], - If[ (IsoIndicesString /. Flatten[{opts}] /. - Options[FieldsSet]) === - None, - {seq[]}, - {SUNIndex[ - ToExpression[(IsoIndicesString /. Flatten[{opts}] /. - Options[FieldsSet]) <> ToString[pnr[j]]]]} - ]])[ - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[FieldsSet]) <> ToString[pnr[j]]]], {j, - Length[ParticlesNumber /. Flatten[{opts}] /. - Options[FieldsSet]]}] /. seq -> Sequence); - -FieldsSet[body___fcqf, opts___?OptionQ] /; - IntegerQ[ParticlesNumber /. Flatten[{opts}] /. Options[FieldsSet]] := - Table[(fcqf1[##] & @@ - Join[List @@ - body, {If[ (LorentzIndicesString /. Flatten[{opts}] /. - Options[FieldsSet]) === - None, - {seq[]}, - {LorentzIndex[ - ToExpression[(LorentzIndicesString /. - Flatten[{opts}] /. Options[FieldsSet]) <> - ToString[j]]]} - ], - If[ (IsoIndicesString /. Flatten[{opts}] /. - Options[FieldsSet]) === - None, - {seq[]}, - {SUNIndex[ - ToExpression[(IsoIndicesString /. - Flatten[{opts}] /. Options[FieldsSet]) <> - ToString[j]]]} - ]}])[ - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[FieldsSet]) <> ToString[j]]], {j, - ParticlesNumber /. Flatten[{opts}] /. Options[FieldsSet]}] /. - seq -> Sequence /. fcqf1 -> QuantumField; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Discarding terms *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* Terms of order different from ExpansionOrder are dropped. For this is used -that terms of order ExpansionOrder in the fields have a factor -tempfac[]^ExpansionOrder. Blank may be used only as e.g. Retain->{_->2}, -that is, alone: *) - -DiscardTerms[l_, opts___Rule] := - Block[ {i, mme, res}, - mme = (Method /. Flatten[{opts}] /. Options[DiscardTerms]); - res = Which[mme === Expand, FCPrint[1, "Using Method->Expand"]; - DiscardTerms1[l, opts], mme === Coefficient, - FCPrint[1, "Using Method->Coefficient"]; - DiscardTerms2[l, opts], True, - Message[DiscardTerms::nomethod, mme]]; - res - ]; - -untugrules = { - (a___.(tempfac[p___]*b_).c___) :> (tempfac[p]*(a.b.c)), - HoldPattern[CovariantFieldDerivative[tempfac[p___]*a_, b__]] -> - tempfac[p]*CovariantFieldDerivative[a, b], - HoldPattern[CovariantNabla[tempfac[p___]*a_, b__]] -> - tempfac[p]*CovariantNabla[a, b], - HoldPattern[CovariantFieldDerivative[tempfac[p___]^n_*a_, b__]] -> - tempfac[p]^n*CovariantFieldDerivative[a, b], - HoldPattern[CovariantNabla[tempfac[p___]^n_*a_, b__]] -> - tempfac[p]^n*CovariantNabla[a, b], - IsoVector[ders___, tempfac[aa__]*pp_, cc___] :> - tempfac[aa]*IsoVector[ders, pp, cc], - UVector[ders___, - tempfac[aa__]*pp_, cc___] :> tempfac[aa]*UVector[ders, pp, cc], - (tempfac[aa__]*bb_[cc__])[x_] -> tempfac[aa]*bb[cc][x]}; - - -DiscardTerms1[l_, opts___Rule] := - Block[ {nodrop, tempfac, tempfacts, retord, rf, ro, ddt1, arg, p, x, ders, - ar, br, qs, ttf, rest, pp, cc, tt, bb, aa, ddt2, ddt3, ddt, tr}, - nodrop = Alternatives @@ (NoDrop /. Flatten[{opts}] /. - Options[DiscardTerms]); - Clear[tempfac, tempfacts, retord, rf,ro]; - SetAttributes[ - tempfac, {NumericFunction, NHoldAll}]; - DeclareUScalar[tempfac, ppf]; - Adjoint[tempfac[a___]] := - tempfac[a]; - Conjugate[tempfac[a___]] ^:= tempfac[a]; - Transpose[tempfac[a___]] ^:= tempfac[a]; - tempfacts = 1; - retord = (Retain /. Flatten[{opts}] /. Options[DiscardTerms]); - Do[rf = retord[[rep, 1]]; - ro = retord[[rep, 2]]; - tempfacts = tempfacts*tempfac @@ rf, {rep, Length[retord]}]; - FCPrint[3, "Putting on overall factor ", tempfacts^2]; - FCPrint[2, - "Putting on dummy factors"]; - ddt1 = - tempfacts^2*l /. - QuantumField[arg__][x_] -> argrec[QuantumField[arg], x] /. - {QuantumField[ders___fcpd, Particle[p_, ar___RenormalizationState, - br___RenormalizationScheme, qs___ExpansionState], rest___] :> - tempfac[p, ar, br, qs]* QuantumField[ders, Particle[p, ar, br, qs], rest], - QuantumField[ders___fcpd, DiracBar[ Particle[p_, ar___RenormalizationState, - br___RenormalizationScheme, qs___ExpansionState]],rest___] :> - tempfac[p, ar, br, qs]*QuantumField[ders, DiracBar[Particle[p, ar, br, qs]],rest]} /. - argrec[tempfac[ttf__]*QuantumField[arg__], x_] -> tempfac[ttf]* - QuantumField[arg][x] //. untugrules /. - If[ Length[retord] === 1 && rf[[1]] === _, - tempfac[tt___] /; FreeQ[{tt}, nodrop] -> tempfac[ppf[]], - {} - ]; - FCPrint[2, "Expanding NM products"]; - ddt2 = NMExpand[ddt1]; - FCPrint[2, "Expanding DOT products"]; - FCPrint[3, ddt2]; - ddt3 = DotExpand[ddt2]; - FCPrint[2, "Expanding"]; - FCPrint[3, ddt3]; - ddt = Expand[ddt3 /. UTrace1 -> tr /. tr -> UTrace1] /. (FCPrint[2, - "Discarding terms"]; - Flatten[ - Table[rf = retord[[rep, 1]]; - ro = retord[[rep, 2]]; - {(tempfac @@ rf)^(ro + 2) -> 1, - tempfac[ppf[]]^(ro + 2) -> 1}, {rep, - Length[retord]}]]) /. - tempfac[tt___] /; FreeQ[{tt}, nodrop] -> 0 /. - DropFactor[___] -> 1; - UndeclareUScalar[tempfac, ppf]; - If[ (CommutatorReduce /. Flatten[{opts}] /. Options[DiscardTerms]), - ddt // (FCPrint[2, - "Applying CommutatorReduce"]; - CommutatorReduce[#,opts])&, - ddt - ] - ]; - - -lpat[i_Integer] := - _?((# > i) &); - -DiscardTerms2[l_, opts___Rule] := - Block[ {nodrop, tempfac, tempfacts, retord, rf, ro, ddt1, arg, p, x, ders, - ar, br, qs, ttf, rest, pp, cc, tt, bb, aa, ddtt, ddt, ddt0}, - Clear[tempfac, tempfacts, tempfactcoeff, retord, rf, ro]; - $UScalars = Union[$UScalars, {tempfac, ppf}]; - Adjoint[tempfac[a___]] := - tempfac[a]; - Conjugate[tempfac[a___]] ^:= tempfac[a]; - Transpose[tempfac[a___]] ^:= tempfac[a]; - tempfacts = 1; - tempfactcoeff = 1; - retord = (Retain /. Flatten[{opts}] /. Options[DiscardTerms]); - Do[rf = retord[[rep, 1]]; - ro := - retord[[rep, 2]]; - tempfacts = tempfacts*tempfac @@ rf; - tempfactcoeff = tempfactcoeff*(tempfac @@ rf)^ro; - FCPrint[3, "Setting ", (tempfac @@ rf)^lpat[ro + 2], ":=0"]; - tempfac /: (tempfac @@ rf)^lpat[ro + 2] := 0, {rep, Length[retord]}]; - FCPrint[2, "Putting on dummy factors"]; - ddt0 = - tempfacts^2*l /. QuantumField[arg__][x_] -> argrec[QuantumField[arg], x] /. - {QuantumField[ders___fcpd, Particle[p_, ar___RenormalizationState, - br___RenormalizationScheme, qs___ExpansionState],rest___] :> - tempfac[p, ar, br, qs]*QuantumField[ders, Particle[p, ar, br, qs], rest], - QuantumField[ders___fcpd, DiracBar[ Particle[p_, ar___RenormalizationState, - br___RenormalizationScheme, qs___ExpansionState]],rest___] :> - tempfac[p, ar, br, qs]*QuantumField[ders, DiracBar[Particle[p, ar, br, qs]],rest]} /. - argrec[tempfac[ttf__]*QuantumField[arg__], x_] -> tempfac[ttf]*QuantumField[arg][x] //. - untugrules /. - If[ Length[retord] === 1 && rf[[1]] === _, - tempfac[tt___] /; FreeQ[{tt}, nodrop] -> tempfac[ppf[]], - {} - ]; - FCPrint[2, "Expanding NM products"]; - ddt1 = NMExpand[ddt0]; - FCPrint[2, "Expand DOT products"]; - ddt0 = DotExpand[ddt1]; - FCPrint[2, "Expanding"]; - ddt = ExpandAll[ddt0]; - FCPrint[2, "Finding the coefficient"]; - FCPrint[3, "of ", - tempfac[ppf[]]^(2*Length[retord] + Plus @@ ((#[[2]]) & /@ retord)), - " in ", ddt /. UTrace1 -> tr /. tr -> UTrace1]; - FCPrint[3, " and of ", tempfacts^2*tempfactcoeff, " in ", ddt]; - ddtt = Coefficient[ddt /. UTrace1 -> tr /. tr -> UTrace1, - tempfac[ - ppf[]]^(2*Length[retord] + - Plus @@ ((#[[2]]) & /@ retord))] + - Coefficient[ddt, tempfacts^2*tempfactcoeff] /. - tempfac[___] -> 1 /. DropFactor[___] -> 1; - $UScalars = - Complement[$UScalars, {tempfac, ppf}]; - If[ (CommutatorReduce /. Flatten[{opts}] /. Options[DiscardTerms]), - ddtt // (FCPrint[2, - "Applying CommutatorReduce"]; - CommutatorReduce[#,opts])&, - ddtt - ] - ]; - -SetCommutators := - ($CommutatorRules /. Rule -> SetDelayed;); - - - -(* Substitution rule to eliminate one of the momentum variables: *) - -MomentaSumRule[opts___?OptionQ] := - Which[(MomentaSumLeft /. Flatten[{opts}] /. Options[MomentaSumRule]) === - FirstHalf, - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentaSumRule]) <> - ToString[ - ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule]]] -> - Sum[ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentaSumRule]) <> ToString[i]], {i, - 1, ((ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule])/2)}] + - Sum[(-ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentaSumRule]) <> - ToString[i]]), {i, (ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule])/2 + - 1, (ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule]) - 1}], (MomentaSumLeft /. - Flatten[{opts}] /. Options[MomentaSumRule]) === All, - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentaSumRule]) <> - ToString[ - ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule]]] -> - Sum[(-ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentaSumRule]) <> ToString[i]]), {i, - 1, (ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule]) - 1}], (MomentaSumLeft /. - Flatten[{opts}] /. Options[MomentaSumRule]) === Odd, - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentaSumRule]) <> - ToString[ - ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule]]] -> - Sum[ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentaSumRule]) <> ToString[i]], {i, - 1, (ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule]), 2}] - - Sum[ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MomentaSumRule]) <> ToString[i]], {i, - 2, (ParticlesNumber /. Flatten[{opts}] /. - Options[MomentaSumRule]) - 2, 2}]]; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Expanding composed objects used in chiral lagrangians *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -(* The u_mu field *) - -$Substitutions = Append[$Substitutions, - USmall[mu_,ar___RenormalizationState,br___RenormalizationScheme, - cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - I*NM[Adjoint[SMM[x,ar,br,cr,opts]], - CDr[MM[x,ar,br,cr,opts],x,{mu}], - Adjoint[SMM[x,ar,br,cr,opts]]]]; - -$Substitutions = Append[$Substitutions, USmall[mu_] :> - -I*NM[Adjoint[SMM],CDr[MM,{mu}],Adjoint[SMM]]]; - -(* ************************************************************** *) - -(* The Gamma_mu field *) - -$Substitutions = Append[$Substitutions, - UGamma[mu_,ar___RenormalizationState,br___RenormalizationScheme, - cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - - 1/2*( - - NM[Adjoint[SMM[x,ar,br,cr,opts]], - FDr[SMM[x,ar,br,cr,opts],x,{mu}]]+ - - I*NM[Adjoint[SMM[x,ar,br,cr,opts]], - UGeneratorMatrixIsoDot[QuantumField[Particle[ - LeftComponent[0],ar,br,cr],{mu}][x]], - SMM[x,ar,br,cr,opts]]+ - - NM[SMM[x,ar,br,cr,opts], - FDr[Adjoint[SMM[x,ar,br,cr,opts]],x,{mu}]]+ - - I*NM[SMM[x,ar,br,cr,opts], - UGeneratorMatrixIsoDot[QuantumField[Particle[ - RightComponent[0],ar,br,cr],{mu}][x]], - Adjoint[SMM[x,ar,br,cr,opts]]] - -)]; - -$Substitutions = Append[$Substitutions, UGamma[mu_] :> - - 1/2*( - - NM[Adjoint[SMM],FDr[SMM,{mu}]]+ - - I*NM[Adjoint[SMM], - UGeneratorMatrixIsoDot[QuantumField[Particle[ - LeftComponent[0]],{mu}]],SMM]+ - - NM[SMM,FDr[Adjoint[SMM],{mu}]]+ - - I*NM[SMM, - UGeneratorMatrixIsoDot[QuantumField[Particle[ - RightComponent[0]],{mu}]],Adjoint[SMM]] - -)]; - -(* ************************************************************** *) - -(* The Chi_plus/Chi_minus fields *) - -$Substitutions = Append[$Substitutions, - UChiPlus[x_,ar___RenormalizationState,br___RenormalizationScheme, - cr___ExpansionState,(opts___Rule|opts___List)] :> - - NM[Adjoint[SMM[x,ar,br,cr,opts]],UChiMatrix[x,ar,br,cr,opts], - Adjoint[SMM[x,ar,br,cr,opts]]]+ - NM[SMM[x,ar,br,cr,opts],Adjoint[UChiMatrix[x,ar,br,cr,opts]], - SMM[x,ar,br,cr,opts]] -]; - -$Substitutions = Append[$Substitutions, - UChiMinus[x_,ar___RenormalizationState,br___RenormalizationScheme, - cr___ExpansionState,(opts___Rule|opts___List)] :> - - NM[Adjoint[SMM[x,ar,br,cr,opts]],UChiMatrix[x,ar,br,cr,opts], - Adjoint[SMM[x,ar,br,cr,opts]]]- - NM[SMM[x,ar,br,cr,opts],Adjoint[UChiMatrix[x,ar,br,cr,opts]], - SMM[x,ar,br,cr,opts]] -]; - -$Substitutions = Append[$Substitutions, UChiPlus :> - NM[Adjoint[SMM],UChiMatrix,Adjoint[SMM]]+NM[SMM,Adjoint[UChiMatrix],SMM]]; - -$Substitutions = Append[$Substitutions, UChiMinus :> - NM[Adjoint[SMM],UChiMatrix,Adjoint[SMM]]-NM[SMM,Adjoint[UChiMatrix],SMM]]; - -(* ************************************************************** *) - -(* The f_plus/f_minus fields. - The fields Vector[0] and AxialVector[0] are used *) - -$Substitutions = Append[$Substitutions, -UFPlus[mu_,nu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -NM[SMM[x,ar,br,cr,opts], - FieldStrengthTensorFull[{mu}, - UGeneratorMatrixIsoDot[ - QuantumField[Particle[ - LeftComponent[0,Sequence@@OptionsSelect[LeftComponent,opts]],ar,br,cr], - {nu}][x]], x, -I,Sequence@@OptionsSelect[FieldStrengthTensorFull,opts]], - Adjoint[SMM[x,ar,br,cr,opts]]]+ - -NM[Adjoint[SMM[x,ar,br,cr,opts]], - FieldStrengthTensorFull[{mu}, - UGeneratorMatrixIsoDot[ - QuantumField[Particle[ - RightComponent[0,Sequence@@OptionsSelect[RightComponent,opts]],ar,br,cr], - {nu}][x]], x, -I,Sequence@@OptionsSelect[FieldStrengthTensorFull,opts]], - SMM[x,ar,br,cr,opts]]]; - -$Substitutions = Append[$Substitutions, UFPlus[mu_,nu_] :> - -NM[SMM,FST[LeftComponent[0],{mu},{nu}],Adjoint[SMM]]+ - -NM[Adjoint[SMM],FST[RightComponent[0],{mu},{nu}],SMM]]; - -$Substitutions = Append[$Substitutions, -UFMinus[mu_,nu_,ar___RenormalizationState,br___RenormalizationScheme, -cr___ExpansionState,(opts___Rule|opts___List)][x_] :> - -NM[SMM[x,ar,br,cr,opts], - FieldStrengthTensorFull[{mu}, - UGeneratorMatrixIsoDot[ - QuantumField[Particle[ - LeftComponent[0,Sequence@@OptionsSelect[LeftComponent,opts]],ar,br,cr], - {nu}][x]], x, -I,Sequence@@OptionsSelect[FieldStrengthTensorFull,opts]], - Adjoint[SMM[x,ar,br,cr,opts]]]- - -NM[Adjoint[SMM[x,ar,br,cr,opts]], - FieldStrengthTensorFull[{mu}, - UGeneratorMatrixIsoDot[ - QuantumField[Particle[ - RightComponent[0,Sequence@@OptionsSelect[RightComponent,opts]],ar,br,cr], - {nu}][x]], x, -I,Sequence@@OptionsSelect[FieldStrengthTensorFull,opts]], - SMM[x,ar,br,cr,opts]]]; - -$Substitutions = Append[$Substitutions, UFMinus[mu_,nu_] :> - -NM[SMM,FST[LeftComponent[0],{mu},{nu}],Adjoint[SMM]]- - -NM[Adjoint[SMM],FST[RightComponent[0],{mu},{nu}],SMM]]; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Easy entering of lagrangians *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -Substitute := - ((# /. $Substitutions)&); - -MM[x_?(! NumberQ[#] &), h___, opts___Rule] /; (Explicit/.Flatten[{opts}]/.Options[MM]) := - UFieldMatrix[QuantumField[(Particle[Pion, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; - -MM[ii_?NumberQ, x_, h___, opts___Rule] /; (Explicit/.Flatten[{opts}]/.Options[MM]) := - UFieldMatrix[ii, QuantumField[(Particle[Pion, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; -SMM[x_, h___, opts___Rule] /; (Explicit/.Flatten[{opts}]/.Options[SMM]) := - MM[1/2, x, h, opts]; - -MMS[x_, h___, opts___Rule] /; (Explicit/.Flatten[{opts}]/.Options[MMS]) := - UFieldMatrixSeries[QuantumField[(Particle[Pion, h])][x], ##] & @@ - Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]; - -FST[p_, {mu_}, {nu_}, x_, a___RenormalizationState, b___RenormalizationScheme, - c___ExpansionState, opts___?OptionQ] := - FST[p, LorentzIndex[mu], LorentzIndex[nu], x, a, b, c, opts]; - - -(* Simpler form: *) - -FST[p_, mu_LorentzIndex, - nu_LorentzIndex, x_, - a___RenormalizationState, b___RenormalizationScheme, - c___ExpansionState, opts___?OptionQ] := - FieldStrengthTensor[mu, - UGeneratorMatrixIsoDotFull[QuantumField[Particle[p, a, b, c], nu][x], opts], x, opts] + - 2*I*UGeneratorMatrixIsoDot[ - IsoCross[(IsoVector[QuantumField[Particle[p, a, b, c], mu], ##] & @@ - OptionsSelect[IsoVector, opts])[ - x], (IsoVector[QuantumField[Particle[p, a, b, c], nu], ##] & @@ - OptionsSelect[IsoVector, opts])[x]], opts]; - -(*Why this??*) -CouplingConstant[a_, b_, rest__][i_] := - CouplingConstant[a, b, RenormalizationState[i], rest]; - -CouplingConstant[a_, b_][i_] := - CouplingConstant[a, b, RenormalizationState[i]]; - - - -(* Splitting products of MMs and SMMs into sums of expanded factors.*) - -(* The help function fdr knows how to do multiple partial derivations and the - product rule: *) - -fdr[(tim : NM | Times | DOT | UDot)[a__, b_], {\[Nu]_}] := - tim[a, fdr[b, {\[Nu]}]] + tim[fdr[tim[a], {\[Nu]}], b]; - -fdr[((ad : (Adjoint | Conjugate | Transpose))[a_]), {\[Mu]__}] := - ad[fdr[a, {\[Mu]}]]; - -fdr[fdr[a_, {\[Mu]__}], {\[Nu]__}] := - fdr[a, Reverse[{\[Mu], \[Nu]}]]; - -fdr[a_Plus, lori : {__}] := - Plus @@ (fdr[#, lori] & /@ (List @@ a)); - - - -(* Help function to get combinations of expansion orders that contribute to the - expansion of a product: *) - -combtab[dummys : List[__], order_Integer] := - (List @@ #) & /@ - Flatten[Table[ - dumfunc @@ - Append[dummys, - order - Sum[dummys[[repp]], {repp, 1, Length[dummys]}]], - Evaluate[ - Sequence @@ - Reverse[Table[{Reverse[dummys][[rep]], 0, - order - - Sum[dummys[[repp]], {repp, 1, - Length[dummys] - rep}]}, {rep, Length[dummys]}]]]]]; - -combtab[{}, n_Integer] := - {{n}}; - -USplit[exp_NM, x_, ar___RenormalizationState, br___RenormalizationScheme, - cr___ExpansionState, - opts___Rule] :=(*Block[{mms, pos, splits, parts, ct, i, ord, ord1, - ad},*) - (ord1 = ExpansionOrder /. Flatten[{opts}]; - If[ Head[ord1] === List, - ord = ord1[[1]], - ord = ord1 - ]; - mms = Select[List @@ exp, ((! FreeQ[{#}, MM | SMM, Infinity]) &)]; - pos = Position[exp, _?((! FreeQ[{#}, MM | SMM, Infinity]) &), {1}]; - splits = Evaluate[(dum @@ #) & /@ pos]; - parts = (ct = combtab[Drop[splits, -1], ord]); - FCPrint[3, "Splitting\n", parts]; - Plus @@ Table[ - ReplacePart[ - exp, (USplit[#[[1]], x, - (*RenormalizationState etc. are no longer in front after Selecting, fixed. 28/9-2000*) - Sequence @@ Join[ - {ar, br, cr}, - Select[{opts}, (MatchQ[#, ExpansionOrder -> _] =!= True) &]], - ExpansionOrder -> {#[[2]]}]) & /@ Transpose[{mms, ct[[i]]}], - pos, ({#}) & /@ Range[Length[pos]]], {i, Length[ct]}](*]*)); - -USplit[fdr[SMM | MM, {_}], ___, ExpansionOrder -> {0}, ___] := - 0; - -USplit1[exp_, x_, ar___RenormalizationState, br___RenormalizationScheme, - cr___ExpansionState, opts___Rule] :=(*Block[{i, n, xx, res, aa, a},*) - (res = - exp //. {CovariantFieldDerivative[ - mm_, {\[Mu]_}] :>(*No x dependence in mm, - so we get the extra part only*) - CovariantFieldDerivative[mm, x, {\[Mu]}, - Sequence @@ - OptionsSelect[CovariantFieldDerivative, opts]] + - fdr[mm, {\[Mu]}], - CovariantNabla[mm_, {\[Mu]_}] :>(*No x dependence in mm, - so we get the extra part only*) - CovariantNabla[mm, x, Sequence @@ (LorentzIndex /@ {\[Mu]}), - Sequence @@ OptionsSelect[CovariantNabla, opts]] + - fdr[mm, {\[Mu]}], FieldDerivative -> fdr, - HoldPattern[USplit[UTrace1[xx_], n__]] :> - UTrace1[USplit[xx, n]], - HoldPattern[ - USplit[(ad : (Adjoint | Conjugate | Transpose))[xx_], - n__]] :> ad[USplit[xx, n]], - USplit[a_ + b_, i__] :> USplit[a, i] + USplit[b, i], - USplit[(Times | NM)[a__], - i__] :> (Times @@ Select[{a}, ((UScalarQ[#]&&FreeQ[#,allpatterns])&)])* - USplit[NM @@ Select[{a}, ((!(UScalarQ[#]&&FreeQ[#,allpatterns]))&)], - i], - USplit[a_, ___, ExpansionOrder -> n_, ___] /; UScalarQ[a] &&FreeQ[a,allpatterns]:> - If[ n === {0}, - a, - 0 - ]} /. - aa_NM /; (! FreeQ[aa, MM | SMM] && - FreeQ[{aa}, USplit, Infinity, Heads -> True]) -> (USplit[aa, - x, - Sequence @@ Join[ - {ar, br, cr},Select[{opts}, (MatchQ[#, ExpansionOrder -> _] =!= True) &]], - ExpansionOrder -> (DropOrder /. Flatten[{opts}] /. Options[UNMSplit])]); - FCPrint[3, "Expanding NM products in ",res]; - NMExpand[res](*]*)); - -UNMSplit[exp_, x_, ar___RenormalizationState, br___RenormalizationScheme, - cr___ExpansionState, - opts___Rule] :=(*Block[{res, errs},*) - (res = - FixedPoint[USplit1[#, x, ar, br, cr, opts] &, - (*Added $PreSubstitutions and $PostSubstitutions for configurability - through configuration files.*) - exp//.$PreSubstitutions[x,ar,br,cr,opts]//. - $Substitutions//.$PostSubstitutions[x,ar,br,cr,opts]]; - res /. - fdr -> FieldDerivative /. - {USplit[mm : (SMM | MM), n__] :> ArgumentsSupply[mm, n], - USplit[mm :FieldDerivative[ - SMM | MM, {__(*_ replaced with __, 18/4 - 2000*)}], - n__] :> ArgumentsSupply[mm, n]} /. - Times -> NM /. - USplit[a_, ___, ExpansionOrder -> n_, ___] /; UScalarQ[a]&&FreeQ[a,allpatterns] :> - If[ n === {0}, - a, - 0 - ](*; - If[(errs = Union[Cases[res, _USplit, Infinity]]) === {}, res, - Message[UNMSplit::nores, errs]]*)(*]*)); - - -(* Hmm... all is very non-general... *) - -ArgumentsSupply1[expr_, x_, ar___RenormalizationState, - br___RenormalizationScheme, cr___ExpansionState, - opts___Rule] := - (FCPrint[3,"Using options ", InputForm[{opts}]]; - - (*Union does not preserve the order. Fixed 28/9-2000*) - o1 = Join[{ar, br, cr},Union[OptionsSelect[UQuarkMass, opts], OptionsSelect[UMatrix, opts]]]; - o2 = Join[{ar, br, cr},Union[OptionsSelect[UFieldMatrix, opts], OptionsSelect[UMatrix, opts]]]; - o22 = Join[{ar, br, cr},Union[OptionsSelect[UFieldMatrixSeries, opts], OptionsSelect[UMatrix, opts]]]; - o3 = OptionsSelect[IsoVector, opts]; - o4 = Join[{ar, br, cr},Union[OptionsSelect[UQuarkCharge, opts], OptionsSelect[UMatrix, opts]]]; - (* o41 added by P. Buettiker on 21-Oct-03 *) - o41 = Join[{ar, br, cr},Union[OptionsSelect[UNucleonCharge, opts], OptionsSelect[UMatrix, opts]]]; - o5 = OptionsSelect[UMatrix, opts]; - o6 = OptionsSelect[UGenerator, opts]; - Block[ { CovariantNabla, - (*CovariantFieldDerivative,*) - CovariantNucleonFieldDerivative, FST, - FieldStrengthTensorFull, - FieldStrengthTensor, MM, MMS, SMM, - IsoVector, PhiMeson, PhiMesonIsoVector, - NM, UTrace1, (*FieldDerivative,*) - IsoDot, IsoCross, IsoSymmetricCross, - UQuarkMassMatrix, UChiMatrix,UChiralSpurionMatrix, - UChiralSpurionRightMatrix,UChiralSpurionLeftMatrix, - UQuarkChargeMatrix, UIdentityMatrix, QCM, - (* UNucleonChargeMatrix added by P. Buettiker on 21-Oct-03: *) - UNucleonChargeMatrix, - a,b,pa,mu,nu,p,i,som,pp,lli,bbb,aa,lisxx}, - NM := - NM5; - CovariantNabla := - CNb2; - (*CovariantFieldDerivative := CDr2;*) - CovariantNucleonFieldDerivative := - CNDr2; - FST[p_[i_], mu_, nu_] := - FST2[p[i], mu, nu, x, ar, br, cr, ##] & @@ o5; - FST[p_, mu_, nu_] := - FST2[p[0], mu, nu, x, ar, br, cr, ##] & @@ o5; - FieldStrengthTensorFull[QuantumField[pp_],lli_LorentzIndex, - opt___Rule] := - fstf[QuantumField[pp][x], lli, opt]; - FieldStrengthTensor[QuantumField[pp_],lli_LorentzIndex, - opt___Rule] := - fst[QuantumField[pp][x], lli, opt]; - UTrace1 := - utr2; - (*FieldDerivative[aa_, {lis__}] := FDr2[aa, {lis}];*) - IsoDot := - IsoDot2; - IsoCross := - IsoCross2; - IsoSymmetricCross := - IsoSymmetricCross2; - PhiMesonIsoVector := - (PV2[x, ##] & @@ o3); - MM[som__] := - MM6[som]; - MM := - (MM2[x, ##] & @@ o2); - SMM[som__] := - SMM6[som]; - SMM := - (SMM2[x, ##] & @@ o2); - MMS[som__] := - MMS6[som]; - MMS := - (MMS2[x, ##] & @@ o22); - UIdentityMatrix := - UIdentityMatrix2[##] & @@ o5; - UQuarkMassMatrix := - QuarkMassMatrix2[##] & @@ o1; - UQuarkChargeMatrix := - UQuarkChargeMatrix2[##] & @@ o4; - (* The following line added by P. Buettiker on 21-Oct-03 *) - UNucleonChargeMatrix := - UNucleonChargeMatrix2[##] & @@ o41; - UChiMatrix := - (Chi2[x, ##] & @@ o1); - UChiralSpurionMatrix := - (UChiSp[x, ##] & @@ o1); - UChiralSpurionRightMatrix := - (UChiSpR[x, ##] & @@ o1); - UChiralSpurionLeftMatrix := - (UChiSpL[x, ##] & @@ o1); - expr - ] ) /. - - {CovariantFieldDerivative :> CDr2, - FieldDerivative[aa_, {lis__}] :> FDr2[aa, {lis}]} /. - - {DropFactor[___] -> 1, - FST2 -> FST, - fstf -> FieldStrengthTensorFull, - fst -> FieldStrengthTensor, MM2 -> MM, - SMM2 -> SMM, - MMS2 ->MMS, - (*utr2 -> UTrace,*)(*moved trace replacement down to avoid non - intentional zeros*) - IsoDot2 -> IsoDot, - IsoCross2 -> IsoCross, - IsoSymmetricCross2 -> IsoSymmetricCross, - PV2 -> PhiMesonIsoVector, - QuarkMassMatrix2 -> UQuarkMassMatrix, - UQuarkChargeMatrix2 -> UQuarkChargeMatrix, - (* Next line added by P. Buettiker, 21-Oct-2003 *) - UNucleonChargeMatrix2 -> UNucleonChargeMatrix, - Chi2 -> UChiMatrix, - UChiSp -> UChiralSpurionMatrix, - UChiSpR -> UChiralSpurionRightMatrix, - UChiSpL -> UChiralSpurionLeftMatrix, - UIdentityMatrix2 -> UIdentityMatrix, - utr2 -> UTrace} //. - - {CNb2[aa_, {lis__}] -> CNb3[aa, x, {lis}, ##] & @@ OptionsSelect[CovariantNabla, opts], - CDr2[aa_, {lis__}] -> CDr3[aa, x, {lis}, ##] & @@ OptionsSelect[CovariantFieldDerivative, opts], - (* Change of P. Buettiker 23-Oct-2003 - Sometimes it is useful to have the possibility of also supplying - RenormalizationState[i] etc. to Covariant(Nucleon)FieldDerivative, - see Configuration/paulBChPT2.conf. - Hence, I modified the definition CNDr2 below. F. Orellana's definition - is the following [commented out]: - CNDr2[aa_, {lis__}] -> CNDr3[aa, x, {lis}, ##] & @@ OptionsSelect[CovariantNucleonFieldDerivative, - opts] - *) - CNDr2[aa_, {lis__}] -> CNDr3[aa, x,{lis},ar,br,cr, ##] & @@ OptionsSelect[CovariantNucleonFieldDerivative, - opts]} /. - - FDr2[aa_, {lis__}] -> FDr3[aa, x, {lis}] /. - - {QuantumField[bbb__][xx_] -> qftemp[bbb][xx], - IsoVector[QuantumField[bbb__], left___][xx_] -> - IsoVector[qftemp[bbb], left][xx], - IsoVector[ffr_[QuantumField[bbb__]], left___][xx_] -> - IsoVector[ffr[qftemp[bbb]], left][xx]} /. - - QuantumField[bbb__] -> QuantumField[bbb][x] /. - - qftemp -> QuantumField /. - - {FDr3 -> FieldDerivative, NM5 -> NM} /. - - {CDr3 -> CovariantFieldDerivative, - CNDr3 -> CovariantNucleonFieldDerivative, - CNb3 -> CovariantNabla} /. - - {Particle[pa_] -> Particle[pa, ar, br, cr], - ParticleMass[pa__?(! MatchQ[#, - _RenormalizationState | _RenormalizationScheme | _ExpansionState] &)] -> - ParticleMass[pa, ar, br, cr], - DecayConstant[pa_] -> DecayConstant[pa, ar, br, cr], - CouplingConstant[pa_] -> CouplingConstant[pa, ar, br, cr]} /. - - {MM6 -> MM, SMM6 -> SMM, MMS6 -> MMS} /. - - UMatrix[UGenerator[i_]] :> - UMatrix[UGenerator[SUNIndex[i], Sequence @@ o6], - Sequence @@ o5] /; FreeQ[i, SUNIndex|ExplicitSUNIndex] /. - - (***************************************************************) - (* The next few lines were added by P. Buettiker, 21-Oct-2003 *) - (* Also the "/." above was a ";" earlier *) - (***************************************************************) - {UMatrix[UQuarkCharge[st___RenormalizationState,sc___RenormalizationScheme, - qs___ExpansionState]]:> - UMatrix[UQuarkCharge[st,sc,qs,Sequence @@ o4],o5], - UMatrix[UNucleonCharge[st___RenormalizationState,sc___RenormalizationScheme, - qs___ExpansionState]]:> - UMatrix[UNucleonCharge[st,sc,qs,Sequence @@ o41],o5]}; - -(******************************************************************) -(*End of the insertion of P. Buettiker, 21-Oct-2003 *) -(******************************************************************) - - - -ArgumentsSupply[expr_, x_, ar___RenormalizationState, - br___RenormalizationScheme,cr___ExpansionState, opts___?OptionQ] := - ( - $UMatrices = Join[$UMatrices, {CDr3, CNDr3, CNb3, CDr2, CNDr2, CNb2}]; - If[ MemberQ[{Rule, RenormalizationState, RenormalizationScheme, - ExpansionState}, Head[x]], - Message[ArgumentsSupply::noarg]; - Return[]; - ]; - If[ !FreeQ[expr, x, Infinity, Heads -> True], - Message[ArgumentsSupply::argxpr, x] - ]; - argres = ArgumentsSupply1[expr//.$PreSubstitutions[x,ar,br,cr,opts]//. - $Substitutions//.$PostSubstitutions[x,ar,br,cr,opts], - x, ar, br, cr, opts]; - $UMatrices = Complement[$UMatrices, {CDr3, CNDr3, CNb3, CDr2, CNDr2, CNb2}]; - argres); - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Commutation rules *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -(* CommutatorReduce: *) - -nsort[{a_, b_}] := - Block[ {s}, - s = Sort[{a, b}]; - If[ s === {a, b}, - {a, b}, - Conjugate /@ s - ] - ]; - -(* Patterns are considered non-scalars by NM, but here we force taking out UTrace1 of patterns *) - patternCommRule = HoldPattern[NM[a__]] :> - (Times @@ Select[{a}, ((UScalarQ[# /. Pattern -> ({##}[[1]] &)] === True)&)])* - (NM @@ Select[{a}, ((UScalarQ[# /. Pattern -> ({##}[[1]] &)] =!= True)&)]) /; btss1[a]; - -checksub[x_List, y_List] := - Block[ {xx, yy}, - xx = StringJoin @@ (ToString /@ x); - yy = StringJoin @@ (ToString /@ y); - StringMatchQ[xx, "*" <> yy <> "*"] || - StringMatchQ[yy, "*" <> xx <> "*"] - ]; - -CommutatorReduce[expr_, op___?OptionQ] := - Block[ {a,b,exp,scq,noncommpatt,$CommutatorRules1,$CommutatorRules2,$CommutatorRules3}, - - - (* These non-commuting objects will not be taken out of NM: *) - $UNonComm = Union[$UMatrices, {UMatrix, UVector, DiracBar, - DiracBasis, - DiracGamma, - DiracGammaT, - DiracMatrix, - DiracSlash, - DiracSigma, - FST}]; - noncommpatt = Alternatives @@ $UNonComm; - - - - (* Some rules are "inverse" of each other and so may leave the object untouched, - but also after the application of one of them something may cancel. Repeated - applications may then cancel something more: *) - $CommutatorRules1 = { - - (*Different field components commute*) - IsoCross[a_, a_] /; FreeQ[a, UMatrix] -> 0, - IsoCross[IsoVector[QuantumField[ders__fcpd, Particle[f__]], body___][x_], - IsoVector[QuantumField[Particle[ff__]], bodyy___][x_]] -> - -IsoCross[Conjugate[IsoVector[QuantumField[Particle[ff]], bodyy][x]], - Conjugate[IsoVector[QuantumField[ders, Particle[f]], body][x]]], - - (*Different field components commute*) - IsoDot[IsoCross[a_, b_],a_] /; (FreeQ[a, UMatrix] || FreeQ[b, UMatrix]) -> 0, - - (*Different field components commute*) - IsoDot[IsoCross[a_, b_], b_] /; (FreeQ[a, UMatrix] || FreeQ[b, UMatrix]) -> 0, - - (*Always valid for cross products*) - IsoDot[a_ /; FreeQ[a, IsoCross], IsoCross[b_, c_]] -> - IsoDot[IsoCross[Conjugate[a], b], c], - - (*Always valid for cross products*) - IsoDot[IsoCross[a_IsoCross, b_], c_] -> - IsoDot[Conjugate[a], IsoCross[b, c]], - - (*Absolutely identical objects commute*) - NM[a___, c_, c_, b___]/; - FreeQ[c, noncommpatt] && MatrixQ[c] =!= True -> - NM[a, c*c, b], - - (*Different field components commute*) - IsoDot[IsoVector[QuantumField[der___, Particle[f_, r___], o___], opts___][x_], - IsoVector[QuantumField[derr___, Particle[ff_, rr___], oo___], optss___][xx_]] /; f =!= ff :> - (res = Sort[IsoDot[IsoVector[QuantumField[der, Particle[f, r], o], opts][x], - IsoVector[QuantumField[derr, Particle[ff, rr], oo], optss][xx]]]; - If[ FreeQ[res[[1]], f], - res, - Conjugate /@ res - ])}; - - - - (* If [the fields of b are different modulo derivatives etc. from the fields of - a and c] or [the fields of b are a subset of the intersection of the fields - of a and c including derivatives etc.] then b is assumed to commute with a - and c. Is this always true?? *) - - (* Changed from using Intersection to using checksub to avoid e.g. - NM[IsoDot[a,b],IsoDot[b,a]] being replaced with Times[...] because - Intersect orders the result *) - $CommutatorRules2 = - {NM[a___, b_, c___] /; ((FreeQ[b, noncommpatt] || FreeQ[{a, c}, noncommpatt])) :> - b*NM[a, c], - - NM[a___, b_, c___] /; - ((FreeQ[b, noncommpatt] || FreeQ[{a, c}, noncommpatt]) && - (Intersection[(#[[1]] &) /@ Cases[b, _Particle, Infinity, Heads -> True], - (#[[1]] &) /@ Cases[{a, c}, _Particle, Infinity, Heads -> True]] === {})) :> - b*NM[a, c], - - NM[a__, b__] /; - ((FreeQ[{b}, noncommpatt] || FreeQ[{a}, noncommpatt]) && - (checksub[ Join[ - Cases[{b},_QuantumField, - Infinity, Heads -> True], - Cases[{a}, _QuantumField, - Infinity, Heads -> True]] ])) :> - NM[b]*NM[a], - - NM[b__,a__] /; - ((FreeQ[{b}, noncommpatt] || FreeQ[{a}, noncommpatt]) && - (checksub[ Join[ - Cases[{b},_QuantumField, - Infinity, Heads -> True], - Cases[{a}, _QuantumField, - Infinity, Heads -> True]] ])) :> - NM[b]*NM[a], - - NM[a___, Times[b_, bb_], c___] /; - ((FreeQ[b, noncommpatt] || FreeQ[{a, c}, noncommpatt]) && - (Intersection[(#[[1]] &) /@ Cases[b, _Particle, Infinity, Heads -> True], - (#[[1]] &) /@ Cases[{a, bb, c}, _Particle, Infinity, Heads -> True]] === {})) :> - b*NM[a, bb, c], - - NM[a___, Times[b_, bb_],c___] /; - ((FreeQ[b, noncommpatt] || FreeQ[{a,c}, noncommpatt]) && - (checksub[ - Join[ - Cases[{a},_QuantumField, - Infinity,Heads -> True], - Cases[{c}, _QuantumField, - Infinity, Heads -> True]], - Cases[{b},_QuantumField, Infinity, - Heads -> True]])) :> - b*NM[a, bb, c], - - (cr:(IsoDot|IsoCross|IsoSymmetricCross))[a_, b_*(bb : (IsoVector[__][_] | IsoVector[__] | IsoCross[__] | - IsoSymmetricCross[__]))] /; - (FreeQ[Head[b], IsoVector] && (FreeQ[b, noncommpatt] || - FreeQ[a,noncommpatt]) && (Intersection[(#[[1]] &) /@ Cases[b, _Particle, Infinity, - Heads -> True], (#[[1]] &) /@ Cases[{a, bb}, _Particle, Infinity, - Heads -> True]] === {} )) -> - b*cr[a, bb], - - (cr:(IsoDot|IsoCross|IsoSymmetricCross))[b_*(bb : (IsoVector[__][_] | IsoVector[__] | IsoCross[__] | - IsoSymmetricCross[__])),a_] /; - (FreeQ[Head[b], IsoVector] && (FreeQ[b, noncommpatt] || - FreeQ[a,noncommpatt]) && (Intersection[(#[[1]] &) /@ Cases[b, _Particle, Infinity, - Heads -> True], (#[[1]] &) /@ Cases[{a, bb}, _Particle, Infinity, - Heads -> True]] === {} )) -> - Conjugate[b]*cr[bb, a], - - (cr:(IsoDot|IsoCross|IsoSymmetricCross))[a_, b_*(bb : (IsoVector[__][_] | IsoVector[__] | IsoCross[__] | - IsoSymmetricCross[__]))] /; - (FreeQ[Head[b], IsoVector] && (FreeQ[b, noncommpatt] || - FreeQ[a,noncommpatt]) && ( - checksub[Cases[a, _QuantumField, Infinity, - Heads -> True], - Cases[b, _QuantumField, Infinity, - Heads -> True]])) -> - b*cr[a, bb] - - }; - $CommutatorRules3 = {UDot[a___, Times[b_, bb_], c___] /; - FreeQ[b, UMatrix, Heads->True] && FreeQ[b, UVector, Heads->True] && FreeQ[b, noncommpatt]:> - b*UDot[a, bb, c]}; - $CommutatorRules = - Join[$CommutatorRules1, $CommutatorRules2, $CommutatorRules3]; - If[ (FullReduce /. Flatten[{op}] /. Options[CommutatorReduce]) =!= True, - expr //. $CommutatorRules, - scq = !UScalarQ[UTrace1]; - DeclareUScalar[UTrace1]; - exp = expr /. patternCommRule //. (*Change 20/10-2003*)($CommutatorRules/._checksub:>True) /. - {(NM | NonCommutativeMultiply)[a__] :> Times[a] /; FreeQ[{a}, noncommpatt], - (p:(IsoDot|IsoCross|IsoSymmetricCross))[a_,b_] :> p@@nsort[{a,b}] /; - (FreeQ[a, noncommpatt] || FreeQ[b, noncommpatt])}; - If[ scq, - UndeclareUScalar[UTrace1] - ]; - exp - ] - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -FCPrint[1, "PHI: Objects.m loaded"]; -End[]; diff --git a/FeynCalc/Phi/Palettes.m b/FeynCalc/Phi/Palettes.m deleted file mode 100644 index 9aadd7354..000000000 --- a/FeynCalc/Phi/Palettes.m +++ /dev/null @@ -1,368 +0,0 @@ -(* Wolfram Language package *) - -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: Palettes (Phi) *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Palettes for PHI *) - -(* ------------------------------------------------------------------------ *) - - -LoadConfiguration::usage = -"LoadConfiguration[c] loads a configuration file c.conf. c must be a string like e.g. \ -\"QED\"."; - -LoadLagrangian::usage = -"LoadLagrangian[l] loads the lagrangian l. l must be a non-string \ -like e.g. QED[1] (or a string like e.g. \"QED1\")."; - -ReloadPhiFA::usage = -"ReloadPhi[conf] reloads Phi with configuration conf, where conf must \ -be given as a string, like e.g. \"QED\", and then reloads FeynArts."; - -RebuildConfigurationsPalette::usage = -"RebuildConfigurationsPalette rebuilds, saves and \ -(re)opens the configurations palette."; - -RebuildLagrangiansPalette::usage = -"RebuildLagrangiansPalette rebuilds, saves and \ -(re)opens the lagrangians palette."; - -Begin["`Package`"] -End[] - -Begin["`Palettes`Private`"]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Configurations *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* LoadConfiguration is called in PhiStart.m *) - -LoadConfiguration["None"] := - Null; -LoadConfiguration[None] := - Null; -LoadConfiguration[conf_] := - Block[ {olddir}, - olddir = Directory[]; - FCPrint[3, "Storing current directory ", olddir]; - SetDirectory[Phi`$HEPDir]; - SetDirectory["FeynCalc"]; - SetDirectory["Phi"]; - SetDirectory["Configurations"]; - FCPrint[3, "Loading configuration ", conf]; - Global`$Configuration = conf; - $PaletteConfiguration = conf; - (* Set context for the name of the configuration *) - Evaluate[ToExpression["Phi`Objects`"<>conf]]; - Get[conf <> ".conf"]; - FCPrint[3, "Resetting to directory ", olddir]; - SetDirectory[olddir]; - ]; - - -ReloadPhiFA[conf_] := - ( - $PaletteConfiguration = conf; - Get["Phi`Phi`"]; - Get["FeynArts`"]); - -RebuildConfigurationsPalette := - Block[ {names, width, height, olddir, nb, bbc}, - - (* Close the clicked notebook *) - NotebookClose[ButtonNotebook[]]; - - (* The directory is set *) - olddir = Directory[]; - SetDirectory[Phi`$HEPDir]; - SetDirectory["FeynCalc"]; - SetDirectory["Phi"]; - SetDirectory["Configurations"]; - - (* A list of the configuration files present: *) - - (*Change 14/5 - 1999, Mac filenames start with colon*) - names = If[ StringMatchQ[#, ":*"] && StringMatchQ[$System, "MacOS*"], - StringDrop[#, 1], - # - ] & /@ (StringDrop[#, -5] & /@ - FileNames["*.conf"]); - - (* The corresponding list of button expressions. For each - configuration, a name is generated and assigned a definition: *) - bbc = List /@ ( - ButtonBox[#, ButtonFunction :> LoadConfiguration[#], - ButtonEvaluator :> Automatic] & /@ names); - width = Ceiling[95/11*Max[Join[StringLength /@ names, {9}]]]; - height = Ceiling[140/7*Length[names] + 100]; - - (* A notebook is created: *) - nb = - Notebook[ - - (* Headline *) - {Cell[BoxData[StyleBox["Load \n configuration:"]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Background -> GrayLevel[0.9], CellFrame -> False, Evaluatable -> False, - CellHorizontalScrolling -> False, LineSpacing -> {1.0, 0}, - FormatType -> InputForm, ScriptMinSize -> 9, - ShowStringCharacters -> False, FontFamily -> "Times", - FontWeight -> "Bold"], - - (* Configuration buttons *) - Cell[BoxData[ - StyleBox[ - GridBox[bbc, RowSpacings -> 0, ColumnSpacings -> 0, - GridDefaultElement :> ButtonBox[ "\[Placeholder]"]], - ButtonBoxOptions -> {ButtonEvaluator -> Automatic, Active -> True, - ButtonStyle -> "Evaluate"}]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Evaluatable -> True, CellGroupingRules -> "InputGrouping", - CellHorizontalScrolling -> True, PageBreakAbove -> True, - PageBreakWithin -> False, GroupPageBreakWithin -> False, - CellLabelMargins -> {{11, Inherited}, {Inherited, Inherited}}, - DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1.25, 0}, - FormatType -> InputForm, ScriptMinSize -> 9, - ShowStringCharacters -> True, NumberMarks -> True, - CounterIncrements -> "Input", StyleMenuListing -> None, - FontFamily -> "Courier", FontWeight -> "Bold"], - - (* Save and reload buttons*) - Cell[BoxData[ - StyleBox[ - GridBox[{{ButtonBox["Rebuild", ButtonFunction :> RebuildConfigurationsPalette, - ButtonEvaluator :> Automatic]}, {ButtonBox["Reload Phi", - ButtonFunction :> ReloadPhiFA[$PaletteConfiguration], - ButtonEvaluator :> Automatic]}}, - RowSpacings -> 0, ColumnSpacings -> 0], - ButtonBoxOptions -> {ButtonEvaluator -> Automatic, Active -> True, - ButtonStyle -> "Evaluate"}]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Evaluatable -> True, CellGroupingRules -> "InputGrouping", - CellHorizontalScrolling -> True, PageBreakAbove -> True, - PageBreakWithin -> False, GroupPageBreakWithin -> False, - CellLabelMargins -> {{11, Inherited}, {Inherited, Inherited}}, - DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1.25, 0}, - AutoItalicWords -> {}, FormatType -> InputForm, ScriptMinSize -> 9, - ShowStringCharacters -> True, NumberMarks -> True, - SingleLetterItalics -> False, CounterIncrements -> "Input", - StyleMenuListing -> None, FontFamily -> "Courier", - FontWeight -> "Bold"]}, - - Background -> GrayLevel[0.9], - WindowTitle -> "Configurations", (*ScreenRectangle -> {{0, 1152}, {0, 850}},*) - Editable -> False, WindowToolbars -> {}, PageWidth -> 342, - WindowSize -> {width, height}, - WindowMargins -> {{0, Automatic}, {Automatic, 0}}, - WindowFrame -> "Palette", WindowElements -> {}, - WindowFrameElements -> "CloseBox", WindowClickSelect -> False, - ScrollingOptions -> {"PagewiseScrolling" -> True}, - ShowCellBracket -> False, CellMargins -> {{0, 0}, {Inherited, 0}}, - Active -> True, CellOpen -> True, ShowCellLabel -> False, - ShowCellTags -> False, - ImageMargins -> {{0, Inherited}, {Inherited, 0}}, - Magnification -> 1]; - - (* The notebook is saved and opened *) - ResetDirectory[]; - SetDirectory["Palettes"]; - Put[nb, "PhiConfigurations.nb"]; - NotebookOpen[ToFileName[{Phi`$HEPDir,"FeynCalc", - "Phi","Palettes"},"PhiConfigurations.nb"]]; - - (* The directory is reset *) - SetDirectory[olddir]; - ]; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Lagrangians *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -LoadLagrangian[] := - None; - -LoadLagrangian[fn_] /; Depth[fn] == 1 := - Block[ {olddir}, - olddir = Directory[]; - FCPrint[3, "Storing current directory ", olddir]; - SetDirectory[Phi`$HEPDir]; - SetDirectory["FeynCalc"]; - SetDirectory["Phi"]; - SetDirectory["Lagrangians"]; - (*Allow using strings. 6/4-2002*) - (*Allow not using strings, keep context Global`. 13/5-2003*) - (*FCPrint[3, - "Putting the following in context Phi`Objects`: ", - Global`$Lagrangians//FullForm]; - Global`$Lagrangians = - Union[ToExpression["Phi`Objects`"<>ToString[#]] & /@ Global`$Lagrangians];*) - Get[ToString[fn] <> ".m"]; - FCPrint[2,"$Lagrangians is now ", Global`$Lagrangians//FullForm]; - FCPrint[3, "Resetting to directory ", olddir]; - SetDirectory[olddir]; - FAUpdate; - ]; - -LoadLagrangian[fn_] /; Depth[fn] == 2 := - Block[ {olddir}, - olddir = Directory[]; - FCPrint[3, "Storing current directory ", olddir]; - SetDirectory[Phi`$HEPDir]; - SetDirectory["FeynCalc"]; - SetDirectory["Phi"]; - SetDirectory["Lagrangians"]; - (*Get[StringDrop[ToString[fn], -3] <> *) (*Change 17/9-2000*) - (*Allow using strings. 6.4.2002*) - (*FCPrint[3, - "Putting the following in context Phi`Objects`: ", - Global`$Lagrangians//FullForm]; - Global`$Lagrangians = - Union[ToExpression["Phi`Objects`"<>ToString[#[[0]]]][#[[1]]] & /@ Global`$Lagrangians];*) - Get[ToString[ToExpression[ToString[fn]][[0]]] <> - ToString[ToExpression[ToString[fn]][[1]]] <> ".m"]; - FCPrint[2,"$Lagrangians is now ", Global`$Lagrangians//FullForm]; - FCPrint[3, "Resetting to directory ", olddir]; - SetDirectory[olddir]; - FAUpdate; - ]; - -LoadLagrangian[fn__] /; Length[{fn}]>1 := - (LoadLagrangian /@ {fn};); - - - -RebuildLagrangiansPalette := - Block[ {names, width, height, olddir, nb, bbc}, - - (* Close the clicked notebook *) - NotebookClose[ButtonNotebook[]]; - - (* The directory is set *) - olddir = Directory[]; - SetDirectory[Phi`$HEPDir]; - SetDirectory["FeynCalc"]; - SetDirectory["Phi"]; - SetDirectory["Lagrangians"]; - - (* A list of the configuration files present: *) - names = If[ StringMatchQ[#, ":*"]&& StringMatchQ[$System, "MacOS*"], - StringDrop[#, 1], - # - ] & /@ (StringDrop[#, -2] & /@ - Select[Select[ - FileNames["*.m"], ! StringMatchQ[#, "d.*"] &], - !StringMatchQ[#, "exp.*"] &]); - - (* The corresponding list of button expressions. For each - configuration, a name is generated and assigned a definition: *) - bbc = List /@ ( - ButtonBox[#, ButtonFunction :> LoadLagrangian[#], - ButtonEvaluator :> Automatic] & /@ names); - width = Ceiling[95/11*Max[Join[StringLength /@ names, {9}]]]; - height = Ceiling[140/7*Length[names] + 70]; - - (* A notebook is created: *) - nb = - Notebook[ - - (* Headline *) - {Cell[BoxData[StyleBox["Load \n lagrangian:"]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Background -> GrayLevel[0.9], CellFrame -> False, Evaluatable -> False, - CellHorizontalScrolling -> False, LineSpacing -> {1.0, 0}, - FormatType -> InputForm, ScriptMinSize -> 9, - ShowStringCharacters -> False, FontFamily -> "Times", - FontWeight -> "Bold"], - - (* Langrangian buttons *) - Cell[BoxData[ - StyleBox[ - GridBox[bbc, RowSpacings -> 0, ColumnSpacings -> 0, - GridDefaultElement :> ButtonBox[ "\\[Placeholder]"]], - ButtonBoxOptions -> {ButtonEvaluator -> Automatic, Active -> True, - ButtonStyle -> "Evaluate"}]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Evaluatable -> True, CellGroupingRules -> "InputGrouping", - CellHorizontalScrolling -> True, PageBreakAbove -> True, - PageBreakWithin -> False, GroupPageBreakWithin -> False, - CellLabelMargins -> {{11, Inherited}, {Inherited, Inherited}}, - DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1.25, 0}, - FormatType -> InputForm, ScriptMinSize -> 9, - ShowStringCharacters -> True, NumberMarks -> True, - CounterIncrements -> "Input", StyleMenuListing -> None, - FontFamily -> "Courier", FontWeight -> "Bold"], - - (* Save and reload buttons*) - Cell[BoxData[ - StyleBox[ - GridBox[{{ButtonBox["Rebuild", ButtonFunction :> RebuildLagrangiansPalette, - ButtonEvaluator :> Automatic]}}, - RowSpacings -> 0, ColumnSpacings -> 0], - ButtonBoxOptions -> {ButtonEvaluator -> Automatic, Active -> True, - ButtonStyle -> "Evaluate"}]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Evaluatable -> True, CellGroupingRules -> "InputGrouping", - CellHorizontalScrolling -> True, PageBreakAbove -> True, - PageBreakWithin -> False, GroupPageBreakWithin -> False, - CellLabelMargins -> {{11, Inherited}, {Inherited, Inherited}}, - DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1.25, 0}, - AutoItalicWords -> {}, FormatType -> InputForm, ScriptMinSize -> 9, - ShowStringCharacters -> True, NumberMarks -> True, - SingleLetterItalics -> False, CounterIncrements -> "Input", - StyleMenuListing -> None, FontFamily -> "Courier", - FontWeight -> "Bold"]}, - - Background -> GrayLevel[0.9], - WindowTitle -> "Load lagrangian", - (*ScreenRectangle -> {{0, 1152}, {0, 850}},*) Editable -> False, - WindowToolbars -> {}, PageWidth -> 342, - WindowSize -> {width, height}, - WindowMargins -> {{147, Automatic}, {Automatic, 0}}, - WindowFrame -> "Palette", WindowElements -> {}, - WindowFrameElements -> "CloseBox", WindowClickSelect -> False, - ScrollingOptions -> {"PagewiseScrolling" -> True}, - ShowCellBracket -> False, CellMargins -> {{0, 0}, {Inherited, 0}}, - Active -> True, CellOpen -> True, ShowCellLabel -> False, - ShowCellTags -> False, - ImageMargins -> {{0, Inherited}, {Inherited, 0}}, - Magnification -> 1]; - - (* The notebook is saved and opened *) - ResetDirectory[]; - SetDirectory["Palettes"]; - Put[nb, "PhiLagrangians.nb"]; - NotebookOpen[ToFileName[{Phi`$HEPDir,"FeynCalc", - "Phi","Palettes"},"PhiLagrangians.nb"]]; - - (* The directory is reset *) - SetDirectory[olddir]; - ]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -FCPrint[1,"Palettes.m loaded"]; -End[]; diff --git a/FeynCalc/Phi/Palettes/PhiConfigurations.nb b/FeynCalc/Phi/Palettes/PhiConfigurations.nb deleted file mode 100644 index 119d3a719..000000000 --- a/FeynCalc/Phi/Palettes/PhiConfigurations.nb +++ /dev/null @@ -1,87 +0,0 @@ -Notebook[{Cell[BoxData[StyleBox["Load \n configuration:"]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Background -> GrayLevel[0.9], CellFrame -> False, Evaluatable -> False, - CellHorizontalScrolling -> False, LineSpacing -> {1., 0}, - FormatType -> InputForm, ScriptMinSize -> 9, ShowStringCharacters -> - False, FontFamily -> "Times", FontWeight -> "Bold"], Cell[ - BoxData[StyleBox[GridBox[{{ButtonBox["BChPT2", - RuleDelayed[ButtonFunction, LoadConfiguration["BChPT2"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPT2", RuleDelayed[ButtonFunction, - LoadConfiguration["ChPT2"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPT3", RuleDelayed[ButtonFunction, - LoadConfiguration["ChPT3"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTEM2", RuleDelayed[ButtonFunction, - LoadConfiguration["ChPTEM2"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTPhoton2", - RuleDelayed[ButtonFunction, LoadConfiguration["ChPTPhoton2"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTPhotonsLeptons3", - RuleDelayed[ButtonFunction, - LoadConfiguration["ChPTPhotonsLeptons3"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTVirtualPhotons2", - RuleDelayed[ButtonFunction, - LoadConfiguration["ChPTVirtualPhotons2"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTVirtualPhotons3", - RuleDelayed[ButtonFunction, - LoadConfiguration["ChPTVirtualPhotons3"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTW3", RuleDelayed[ButtonFunction, - LoadConfiguration["ChPTW3"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["HBChPT2", RuleDelayed[ButtonFunction, - LoadConfiguration["HBChPT2"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["QED2", RuleDelayed[ButtonFunction, - LoadConfiguration["QED2"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["QED", RuleDelayed[ButtonFunction, - LoadConfiguration["QED"]], - RuleDelayed[ButtonEvaluator, Automatic]]}}, RowSpacings -> 0, - ColumnSpacings -> 0, GridDefaultElement :> \ -ButtonBox["\[Placeholder]"]], - Rule[ButtonBoxOptions, List[Rule[ButtonEvaluator, Automatic], - Rule[Active, True], Rule[ButtonStyle, "Evaluate"]]]]], - NotebookDefault, CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Evaluatable -> True, CellGroupingRules -> "InputGrouping", - CellHorizontalScrolling -> True, PageBreakAbove -> True, - PageBreakWithin -> False, GroupPageBreakWithin -> False, - CellLabelMargins -> {{11, Inherited}, {Inherited, Inherited}}, - DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1.25, 0}, - FormatType -> InputForm, ScriptMinSize -> 9, ShowStringCharacters -> True, - NumberMarks -> True, CounterIncrements -> "Input", - StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Bold"], - Cell[ - BoxData[StyleBox[GridBox[{{ButtonBox["Rebuild", - RuleDelayed[ButtonFunction, RebuildConfigurationsPalette], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["Reload Phi", - RuleDelayed[ButtonFunction, ReloadPhiFA[$PaletteConfiguration]], - RuleDelayed[ButtonEvaluator, Automatic]]}}, RowSpacings -> 0, - ColumnSpacings -> 0], Rule[ButtonBoxOptions, - List[Rule[ButtonEvaluator, Automatic], Rule[Active, True], - Rule[ButtonStyle, "Evaluate"]]]]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Evaluatable -> True, CellGroupingRules -> "InputGrouping", - CellHorizontalScrolling -> True, PageBreakAbove -> True, - PageBreakWithin -> False, GroupPageBreakWithin -> False, - CellLabelMargins -> {{11, Inherited}, {Inherited, Inherited}}, - DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1.25, 0}, - AutoItalicWords -> {}, FormatType -> InputForm, ScriptMinSize -> 9, - ShowStringCharacters -> True, NumberMarks -> True, - SingleLetterItalics -> False, CounterIncrements -> "Input", - StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Bold"]}, - Background -> GrayLevel[0.9], WindowTitle -> "Configurations", - Editable -> False, WindowToolbars -> {}, PageWidth -> 342, - WindowSize -> {165, 340}, WindowMargins -> {{0, Automatic}, {Automatic, 0}}, - WindowFrame -> "Palette", WindowElements -> {}, - WindowFrameElements -> "CloseBox", WindowClickSelect -> False, - ScrollingOptions -> {"PagewiseScrolling" -> True}, ShowCellBracket -> False, - CellMargins -> {{0, 0}, {Inherited, 0}}, Active -> True, CellOpen -> True, - ShowCellLabel -> False, ShowCellTags -> False, - ImageMargins -> {{0, Inherited}, {Inherited, 0}}, Magnification -> 1] diff --git a/FeynCalc/Phi/Palettes/PhiLagrangians.nb b/FeynCalc/Phi/Palettes/PhiLagrangians.nb deleted file mode 100644 index 7d2f9c82b..000000000 --- a/FeynCalc/Phi/Palettes/PhiLagrangians.nb +++ /dev/null @@ -1,104 +0,0 @@ -Notebook[{Cell[BoxData[StyleBox["Load \n lagrangian:"]], NotebookDefault, - CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Background -> GrayLevel[0.9], CellFrame -> False, Evaluatable -> False, - CellHorizontalScrolling -> False, LineSpacing -> {1., 0}, - FormatType -> InputForm, ScriptMinSize -> 9, ShowStringCharacters -> - False, FontFamily -> "Times", FontWeight -> "Bold"], Cell[BoxData[ - StyleBox[GridBox[{{ButtonBox["BChPT22", - RuleDelayed[ButtonFunction, LoadLagrangian["BChPT22"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPT22", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPT22"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPT24", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPT24"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPT32", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPT32"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPT34", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPT34"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTEM22", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPTEM22"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTEM24", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPTEM24"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTPhoton22", - RuleDelayed[ButtonFunction, LoadLagrangian["ChPTPhoton22"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTPhoton24", - RuleDelayed[ButtonFunction, LoadLagrangian["ChPTPhoton24"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTVirtualPhotons22", - RuleDelayed[ButtonFunction, - LoadLagrangian["ChPTVirtualPhotons22"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTVirtualPhotons24", - RuleDelayed[ButtonFunction, - LoadLagrangian["ChPTVirtualPhotons24"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTW32", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPTW32"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTW34", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPTW34"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["ChPTWS32", RuleDelayed[ButtonFunction, - LoadLagrangian["ChPTWS32"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["HBChPT22", RuleDelayed[ButtonFunction, - LoadLagrangian["HBChPT22"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["QED1", RuleDelayed[ButtonFunction, - LoadLagrangian["QED1"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["QED21", RuleDelayed[ButtonFunction, - LoadLagrangian["QED21"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["QED22", RuleDelayed[ButtonFunction, - LoadLagrangian["QED22"]], - RuleDelayed[ButtonEvaluator, Automatic]]}, - {ButtonBox["QED2", RuleDelayed[ButtonFunction, - LoadLagrangian["QED2"]], - RuleDelayed[ButtonEvaluator, Automatic]]}}, RowSpacings -> 0, - ColumnSpacings -> 0, GridDefaultElement :> \ -ButtonBox["\\[Placeholder]"]], - Rule[ButtonBoxOptions, List[Rule[ButtonEvaluator, Automatic], - Rule[Active, True], Rule[ButtonStyle, "Evaluate"]]]]], - NotebookDefault, CellMargins -> {{Inherited, Inherited}, {5, Inherited}}, - Evaluatable -> True, CellGroupingRules -> "InputGrouping", - CellHorizontalScrolling -> True, PageBreakAbove -> True, - PageBreakWithin -> False, GroupPageBreakWithin -> False, - CellLabelMargins -> {{11, Inherited}, {Inherited, Inherited}}, - DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1.25, 0}, - 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- Mathematica-Compatible Notebook - -This notebook can be used on any computer system with Mathematica 3.0, -MathReader 3.0, or any compatible application. The data for the notebook -starts with the line of stars above. - -To get the notebook into a Mathematica-compatible application, do one of -the following: - -* Save the data starting with the line of stars above into a file - with a name ending in .nb, then open the file inside the application; - -* Copy the data starting with the line of stars above to the - clipboard, then use the Paste menu command inside the application. - -Data for notebooks contains only printable 7-bit ASCII and can be -sent directly in email or through ftp in text mode. 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CellGroupingRules->"InputGrouping", - PageBreakAbove->True, - PageBreakWithin->False, - CounterIncrements->"Input"], -Cell[29327, 944, 505, 12, 75, NotebookDefault, - PageBreakAbove->True, - CounterIncrements->"Text"], -Cell[29835, 958, 996, 30, 60, NotebookDefault, - CellGroupingRules->"InputGrouping", - PageBreakAbove->True, - PageBreakWithin->False, - CounterIncrements->"Input"], -Cell[30834, 990, 12, 0, 22, InheritFromParent] -}, Closed]] -} -] -*) - - - - -(*********************************************************************** -End of Mathematica Notebook file. -***********************************************************************) - diff --git a/FeynCalc/Phi/Phi.m b/FeynCalc/Phi/Phi.m deleted file mode 100644 index d272295de..000000000 --- a/FeynCalc/Phi/Phi.m +++ /dev/null @@ -1,215 +0,0 @@ -(* ******************************************************** *) -(* *) -(* PHI *) -(* *) -(* Phenomenology of *) -(* Hadronic Interactions *) -(* *) -(* ******************************************************** *) - - -(* ******************************************************** *) - -(* Title: PHI *) - -(* Author: Frederik Orellana (fjob@cabocomm.dk) *) - -(* Summary: Phenomenology of hadronic interactions. - A collection of packages for calculating - transition amplitudes in low energy - hadron physics. - Keywords: ChPT, SU(2), SU(3), effective - lagrangians, coupling vectors, - renormalization, isospin, partial - waves, Mandelstam variables, dispersion - relations. *) - -(* History: Version 1.3 March 2003 - Version 1.2 May 2001 - Version 1.1 February 1999 *) - -(* Contexts: Phi`, - Phi`Objects`, - Phi`Couplings`, - Phi`Renormalization`, - Phi`Channels`, - Phi`Utilities`, - Phi`Palettes`. *) - -(* Package Version 1.3 *) - -(* Mathematica Version >=3 *) - -(* ******************************************************** *) - -(* FeynCalc should be loaded *) - -If[ !ValueQ[FeynCalc`$FeynCalcDirectory], - Phi::nofc = "Before loading Phi, you should load FeynCalc. \ -The kernel will exit now."; - Message[Phi::nofc]; - Exit[0] -] - -(* Get rid of old definitions *) - - tmp`pconf = Null; - tmp`phi = Null; - tmp`vv = Null; - -If[ Phi`$Phi, - tmp`pconf = Phi`$PaletteConfiguration; - tmp`phi = Phi`$Phi; - ClearAll["Phi`*`*`*"]; - ClearAll["Phi`*`*"]; - ClearAll["Phi`*"]; - Unprotect[$Packages]; - $Packages = Complement[$Packages, - {"Phi`Objects`", - "Phi`Palettes`", "Phi`Renormalization`", - "Phi`Channels`", "Phi`Utilities`", - "Phi`Couplings`", "Phi`"}]; - Protect[$Packages]; - $ContextPath = Complement[$ContextPath, - {"Phi`Objects`", - "Phi`Palettes`", "Phi`Renormalization`", - "Phi`Channels`", "Phi`Utilities`", - "Phi`Couplings`", "Phi`"}]; -]; - -(* ************************************************************** *) - -BeginPackage["Phi`"]; - -(* ************************************************************** *) - -(* Usage definitions *) - -$Phi::usage = -"$Phi is a variable indicating whether or not Phi is loaded - it is set \ -to True when loading Phi."; - -Global`$Configuration::usage = -"$Configuration is a string variable determining which configuration is loaded \ -at startup or restart. It can be set before loading FeynCalc, in PhiStart.m or with the \ -configurations palette. If the palette is used for restarting, the setting \ -in PhiStart.m is overruled. Possible values include \"ChPT2\" and \"QED\". Default \ -value : \"None\"."; - -$PaletteConfiguration::usage = -"$PaletteConfiguration is a string variable set when clicking on the \ -configuration palette and overruling the setting of $Configuration. Default \ -value : \"None\"."; - -$HEPDir::usage = -"$HEPDir is a string variable specifying the full path to the parent \ -directory of the directory FeynCalc (containing Phi). It should be set \ -in the startup file First.m. Default value : Directory[]."; - -PhiSymbols::usage = -"PhiSymbols[\"package\"] returns a list of symbols defined in the \ -context package."; - -$PhiVersion::usage= -"contains the version of PHI." - -(* ************************************************************** *) - -Begin["`Private`"]; - -End[]; - -(* ************************************************************** *) - -EndPackage[]; - -(* ************************************************************** *) - -(* Loading of subpackages *) - -Phi`$HEPDir = -ParentDirectory[FeynCalc`$FeynCalcDirectory]; - -(* -$Path = Union[$Path,{Phi`$HEPDir}]; - -(*Give first priority to First.m and PhiStart.m in homedir. Added 28/8-2001*) -$Path = Join[FileNames[$HomeDirectory <> $PathnameSeparator <> - ".Mathematica" <> $PathnameSeparator <> "Applications"], - FileNames[$HomeDirectory <> $PathnameSeparator <> - ".Mathematica" <> $PathnameSeparator <> "*" <> $PathnameSeparator <> - "AddOns" <> $PathnameSeparator <> "Applications"],$Path]; -*) - -Get[FileNameJoin[{$FeynCalcDirectory,"Phi","First.m"}]] - - - -listPhi = Map[ToFileName[{$FeynCalcDirectory,"Phi"}, (# <> ".m")] &, - {"Objects", "Couplings", "Channels", "Utilities", "Renormalization", "Palettes"}]; - -FeynCalc`Private`processDecls/@listPhi; -Get/@listPhi; - - -(* ************************************************************** *) - -(* Defaults *) - -If[ ValueQ[Global`$Configuration] =!= True, - Global`$Configuration = "None" -]; - -If[ tmp`pconf=!=Null, - $PaletteConfiguration = tmp`pconf -]; -If[ tmp`phi=!=Null, - $Phi = tmp`phi -]; - -$PhiVersion = "1.3"; -(* ************************************************************** *) - -(* Loading of user definitions *) - -FCPrint[2,"Loading Phi`PhiStart`"]; - -Get[FileNameJoin[{$FeynCalcDirectory,"Phi","PhiStart.m"}]] - -(*Clean out doubles (strings and non-strings) in $Lagrangians*) -$Lagrangians = Union[(ToExpression[#[[0]]] @@ #) & /@ $Lagrangians]; - -If[ tmp`pconf=!=Null, - $PaletteConfiguration = tmp`pconf -]; -If[ tmp`phi=!=Null, - $Phi = tmp`phi -]; - -(* ************************************************************** *) - -(* Update particles *) - -FAUpdate; - -(* ************************************************************** *) - -(* FeynArts definitions are cleared to avoid error messages *) -(* -If[ NumberQ[FeynArts`$FeynArts], - ClearAll[FeynArts`Greek, FeynArts`UCGreek], - Remove[FeynArts`$FeynArts] -];*) - - -(* ************************************************************** *) - -(* Phi system variables *) - -$Phi = True; - -$PaletteConfiguration = "None"; - -(* ************************************************************** *) - -(**) diff --git a/FeynCalc/Phi/PhiStart.m b/FeynCalc/Phi/PhiStart.m deleted file mode 100644 index 24e56b85f..000000000 --- a/FeynCalc/Phi/PhiStart.m +++ /dev/null @@ -1,611 +0,0 @@ -(* ************************************************************** *) -(* *) -(* PhiStart.m *) -(* *) -(* ************************************************************** *) -(* - -This is the startup file of PHI. - -You'll most likely only need to edit the section -"CHOOSE CONFIGURATION AND LAGRANGIANS" below. - -If you want to customize further, put here model independent -definitions and/or definitions common to all models. - -This file is read after loading the sub-packages. -To have extra definitions read before anything else, put them -in 'First.m'. - -Model specific definitions and usage definitions for classes of -lagrangians are in the relevant configuration file in -the directory 'Configurations'. -You can override these in the present file -(see "EXTRA CONFIGURATION"). -If you are running UNIX (Linux), you can put a copy of -the present file in -~/.Mathematica//AddOns/Applications/FeynCalc/Phi/ -(create the necessary directories) and it will override -the file in the installation directory. - -Coupling files for PHI and FeynArts are in the -directory 'CouplingVectors'. - -Lagrangians for PHI are in the directory -'Lagrangians' and renormalization factors in the -directory 'Factors'. - -*) - -(* ************************************************************** *) - -(* ************************************************************** *) - -(* Abbreviations *) - -Phi`Objects`PMV::usage = -"PMV[x_,opts___] := PhiMesonIsoVector[opts][x]."; - -PMV[x_,opts___] := - PhiMesonIsoVector[opts][x]; - -(* ************************************************************** *) - -(* Adjoints and conjugates *) - -Adjoint[UMatrix[UQuarkMass[a___],b___]] := - UMatrix[UQuarkMass[a],b]; - -DecayConstant/:Conjugate[ax_DecayConstant]=ax; -ParticleMass/:Conjugate[ax_ParticleMass]=ax; -QuarkCondensate/:Conjugate[ax_QuarkCondensate]=ax; -CouplingConstant/:Conjugate[ax_CouplingConstant]=ax; - -(* ************************************************************** *) - -(* Variable boxes *) - -VariableBoxes["p",ParticlesNumber->12]; -VariableBoxes["q",ParticlesNumber->2]; -VariableBoxes["i",ParticlesNumber->12]; -VariableBoxes["I",ParticlesNumber->12]; -VariableBoxes["n",ParticlesNumber->12]; -VariableBoxes["j",ParticlesNumber->12]; -VariableBoxes["k",ParticlesNumber->12]; -VariableBoxes["\[Mu]",ParticlesNumber->12]; - -k/: Format[k,TraditionalForm] := - StyleForm["k",FontSlant->"Italic"]; - -DiracTrace/: -MakeBoxes[ -DiracTrace[a__,DiracTraceEvaluate->False],TraditionalForm]:= -MakeBoxes[DiracTrace[a],TraditionalForm]; - -(* ************************************************************** *) - -(* Change a few FeynArts definitions *) - -(* FeynArts 3 uses CTOrder instead of CountertermOrder *) - -If[ FileNames["*.jar", {ToFileName[$FeynCalcDirectory, "FeynArts"]}]=!= -{}, - CountertermOrder = FeynArts`CTOrder -]; - -(* Labels for lines of Feynman diagrams. - If the FeynArts TeXToPS works on your system, - you can use e.g. "\\phi instead of "\[CurlyPhi]", - so that TeX comes out right too *) - -(*FALabel[_,phii_]:="\[Psi]"<>ToString[phii];*) -FALabel[PhiMeson,0] := - "\[CurlyPhi]"; -FALabel[PhiMeson[0],_] := - "\[CurlyPhi]"; -FeynArts`TheLabel[PseudoScalar1] := - "\[CurlyPhi]"; -FALabel[Pion,0] := - "\[Pi]"; -FALabel[Pion[0],_] := - "\[Pi]"; -FeynArts`TheLabel[PseudoScalar2] := - "\[Pi]"; -FALabel[Kaon,0] := - "K"; -FALabel[Kaon[0],_] := - "K"; -FeynArts`TheLabel[PseudoScalar6] := - "K"; -FALabel[KaonPlus,0] := - "K+"; -FALabel[KaonPlus[0],_] := - "K+"; -FeynArts`TheLabel[PseudoScalar7] := - "K+"; -FALabel[KaonZero,0] := - "K0"; -FALabel[KaonZero[0],_] := - "K0"; -FeynArts`TheLabel[PseudoScalar8] := - "K0"; -FALabel[KaonZeroBar,0] := - "K0_"; -FALabel[KaonZeroBar[0],_] := - "K0_"; -FeynArts`TheLabel[PseudoScalar9] := - "K0_"; -FALabel[KaonMinus,0] := - "K-"; -FALabel[KaonMinus[0],_] := - "K-"; -FeynArts`TheLabel[PseudoScalar10] := - "K-"; -FALabel[Photon,0] := - "\[Gamma]"; -FALabel[Photon[0],_] := - "\[Gamma]"; -FeynArts`TheLabel[Vector1] := - "\[Gamma]"; -FALabel[Vector[0],0] := - "V"; -FALabel[Vector[0][0],_] := - "V"; -FeynArts`TheLabel[Vector0] := - "V"; -FALabel[AxialVector[0],0] := - "A"; -FALabel[AxialVector[0][0],_] := - "A"; -FeynArts`TheLabel[AxialVector0] := - "A"; -FALabel[Fermion[1],0] := - "\[Psi]"; -FALabel[Fermion[1][0],_] := - "\[Psi]"; -FeynArts`TheLabel[Fermion1] := - "\[Psi]"; -FALabel[Fermion[1,1],1] := - "\[Nu]"; -FALabel[Fermion[1,1][1],_] := - "\[Nu]"; -FALabel[Nucleon,0] := - "N"; -FALabel[Nucleon[0],_] := - "N"; -FeynArts`TheLabel[Fermion20] := - "N"; -FALabel[Electron,0] := - "e"; -FALabel[Electron[0],_] := - "e"; -FeynArts`TheLabel[Fermion7] := - "e"; -FALabel[Scalar[0],0] := - "S"; -FALabel[Scalar[0][0],_] := - "S"; -FeynArts`TheLabel[Scalar0] := - "S"; -FALabel[Scalar[1],0] := - "S"; -FALabel[Scalar[1][0],_] := - "S"; -FeynArts`TheLabel[Scalar1] := - "S"; -FALabel[Scalar[2],0] := - "s"; -FALabel[Scalar[2][0],_] := - "s"; -FeynArts`TheLabel[Scalar2] := - "s"; -FALabel[PseudoScalar[0],0] := - "P"; -FALabel[PseudoScalar[0][0],_] := - "P"; -FeynArts`TheLabel[PseudoScalar0] := - "P"; - -(* ************************************************************** *) - -(* Change a few FeynCalc options *) - - $FCS = Union[$FCS, {PMV}]; - FeynCalc`Lagrangian::usage = - "Lagrangian[m[pars]] returns the raw form of the lagrangian of the model \ -m and with parameters pars (e.g. the dimension of the gauge group and the \ -order in the perturbative expansion). To get the full form, use \ -ArgumentsSupply. Lagrangian[\"oqu\"] gives the unpolarized quark operator. \ -Lagrangian[\"oqp\"] gives the polarized quark operator."; - FeynCalc`CouplingConstant::usage = - "CouplingConstant is the head of coupling constants. CouplingConstant \ -takes three extra optional arguments, with head RenormalizationState, \ -RenormalizationScheme and ExpansionState respectively. E.g. \ -CouplingConstant[QED[1]] is the unit charge, CouplingConstant[ChPT2[4],1] \ -is the first of the coupling constants of the lagrangian ChPT2[4]. \ -CouplingConstant[a_,b_,c___][i_] := \ -CouplingConstant[a,b,RenormalizationState[i],c]. \ -CouplingConstant is also an option for several Feynman rule functions and for \ -CovariantD and FieldStrength."; - $Multiplications = Union[$Multiplications,{Times, NM, IsoDot, IsoCross, - IsoSymmetricCross, UDot}]; - $DistributiveFunctions = Union[$DistributiveFunctions, - {Conjugate, ComplexConjugate, Transpose, Adjoint, UTrace, UTrace1, Iso}]; - $Containers = {IsoVector, UVector, UMatrix}; - Options[CovariantFieldDerivative] = {Explicit->True, DiagonalToU->True, - (*RemoveIntegerIndices->False,*) SUNN->2, UDimension->Automatic}; - CovariantFieldDerivative::usage = - "CovariantFieldDerivative[f[x],x,{li1,li2,...},opts] is the covariant \ -derivative of f[x] with respect to space-time variables x and with Lorentz \ -indices li1, li2,... The default CovariantFieldDerivative is taken from \ -mesonic ChPT and includes the external sources Vector and AxialVector, which \ -by default are zero. The definitions of the defaults are in the file \ -PhiStart.m and in the relevant configuration files and should be set \ -according to the process under consideration. Also it may be neccesary to \ -introduce several covariant derivatives (see CovariantNabla). \ -CovariantFieldDerivative is recognized by ArgumentsSupply and partly by \ -UNMSplit, that is, for UNMSplit to work, the 'extra' part apart from the \ -derivative of CovariantFieldDerivative[f[x],x,{li1,li2,...},opts] should not \ -have a meson-field dependence."; - SetOptions[CheckDB, Directory -> - ToFileName[{$FeynCalcDirectory,"Phi"}, "Storage"], - ForceSave -> False, NoSave -> False, Check -> False]; - SetOptions[ILimit, FunctionLimits -> {Log -> Log, - LeutwylerJBar -> (LeutwylerJBar[ - Sequence @@ Select[Expand /@ {##}, ((! MatchQ[#, _Rule | _List]) &)], - LeutwylerJBarEvaluation -> "subthreshold", - ExplicitLeutwylerSigma -> True]&)}]; - SetOptions[B0, - BReduce->False,B0Unique->True,B0Real->False]; - SetOptions[SetMandelstam, - Dimension->{4,D,SpaceTimeDimensions}]; - SetOptions[FeynRule, - InitialFunction->PhiToFC]; - - (*SetOptions[OneLoop, - WriteOutPaVe -> ToFileName[ - {FeynCalc`$FeynCalcDirectory, "Phi"}, "Storage"] <> - $PathnameSeparator]; - - SetOptions[PaVeReduce, - WriteOutPaVe -> ToFileName[ - {FeynCalc`$FeynCalcDirectory, "Phi"}, "Storage"] <> - $PathnameSeparator];*) - - (*Compapatibility with PartialD-operator notation*) - SetOptions[ExpandPartialD, - PartialDRelations -> Union[ - (*Original stuff*)(PartialDRelations /. Options[ExpandPartialD]), - (*Have ExpandPartialD use FieldDerivative for NM products*) - {NM[a___, (FCPartialD|RightPartialD)[x_,LorentzIndex[mu_]], b___] :> - NM[a, FieldDerivative[NM[b], x, LorentzIndex[mu]]], - NM[a___, (FCPartialD|RightPartialD)[LorentzIndex[mu_]], b___] :> - NM[a, FieldDerivative[NM[b], z, LorentzIndex[mu]]] /; (go = - False; - {b} /. ((QuantumField[__][ - y_?AtomQ] | _[___, QuantumField[__], ___][ - y_?AtomQ]) :> (go = True; - z = y)); - go), - NM[a___, LeftPartialD[x_,LorentzIndex[mu_]], b___] :> - NM[FieldDerivative[NM[a], x, LorentzIndex[mu]], b], - NM[a___, LeftPartialD[LorentzIndex[mu_]], b___] :> - NM[FieldDerivative[NM[a], z, LorentzIndex[mu]], b] /; (go = - False; - {a} /. ((QuantumField[__][ - y_?AtomQ] | _[___, QuantumField[__], ___][ - y_?AtomQ]) :> (go = True; - z = y)); - go), - NM[a___, CovariantD[x_,LorentzIndex[mu_]], b___] :> - NM[a, CovariantFieldDerivative[NM[b], x, LorentzIndex[mu]]], - NM[a___, CovariantD[LorentzIndex[mu_]], b___] :> - NM[a, CovariantFieldDerivative[NM[b], z, LorentzIndex[mu]]] /; (go = - False; - {b} /. ((QuantumField[__][ - y_?AtomQ] | _[___, QuantumField[__], ___][ - y_?AtomQ]) :> (go = True; - z = y)); - go), - NM[UMatrix[UIdentity, ___], - (FCPartialD | RightPartialD | LeftPartialD)[__]] :> 0} - ]]; - - (* Not sure why this is necessary, but e.g. the calculation of the electron self energy in - QEDRadiativeCorrections.nb fails without. *) - SetOptions[FourVector, FeynCalcInternal -> False]; - SetOptions[MetricTensor, FeynCalcInternal -> False]; - SetOptions[DiracSlash, FeynCalcInternal -> False]; - - (* A static hack. Not very pretty. Just to have ExpandPartialD work for - a few PHI examples (will have to be reevaluated when changing - $UMatrices if ExpandPartialD is to work for the new UMatrices) *) - DeclareNonCommutative /@ $UMatrices; - - (* Have WFRenormalize work with Dirac matrices *) - DeclareNonCommutative[WFFactor1]; - Phi`Objects`FunctionalDerivative::usage = - "FunctionalDerivative is FunctionalD adapted for use with Phi"; - Phi`Objects`FunctionalDerivative[x_, o__] := - Block[ {tr, r, nm, c, d, i, f}, - i = 0; - f := - (++i); - FunctionalD[ - PhiToFC[x /. HoldPattern[NM[d__]] :> DOT[nm[f], d]] /. - UTrace1 -> ((tr*#) &), o] //. {DOT[nm[_], c__] :> NM[c], - tr*r__ :> UTrace[Times[r]]} - ]; - $Abbreviations = - Union[$Abbreviations, - {"Momentum" -> "", "Pair" -> "", "RenormalizationState" -> "", - "ParticleMass" -> "m", "PseudoScalar" -> "PS", "Scalar" -> "S", - "Vector" -> "V", "AxialVector" -> "AV", "Fermion" -> "F"}]; - - (* Commented out 5/3-2000. - I think its redundant and definitions on SUNIndex slow down everything. *) - (* Well - not quite so. Uncommented again 21/5-2001 *) - NM[a___, b : IsoVector[__][_], c___][SUNIndex[i_]] ^:= NM[a, b[SUNIndex[i]], c]; - NM[a___, b : IsoVector[__], c___][SUNIndex[i_]] ^:= NM[a, b[SUNIndex[i]], c]; - Times[a___, b : IsoVector[__][_], c___][SUNIndex[i_]] ^:= Times[a, b[SUNIndex[i]], c]; - Times[a___, b : IsoVector[__], c___][SUNIndex[i_]] ^:= Times[a, b[SUNIndex[i]], c]; - NM[a___, b : IsoVector[__][_], c___][UIndex[i_]] ^:= NM[a, b[UIndex[i]], c]; - NM[a___, b : IsoVector[__], c___][UIndex[i_]] ^:= NM[a, b[UIndex[i]], c]; - Times[a___, b : IsoVector[__][_], c___][UIndex[i_]] ^:= Times[a, b[UIndex[i]], c]; - Times[a___, b : IsoVector[__], c___][UIndex[i_]] ^:= Times[a, b[UIndex[i]], c]; - - (*Added 3/11-2002 to contract also denominators. F.Orellana. - Unfortunately it slows down things, so we might want to add an option - to disable it...*)(*Moved here from Contract.m, 28/2-2003, - because Rolf commented it out there...*) - Contract[x__, opts___Rule] := - (Contract[x /. Times[a___, b : Pair[_, __]^-1, c___] :> - inv[(1/Times @@ Select[{a, b, c}, MatchQ[#, _^-1] &])](Times @@ - Select[{a, b, c}, ! MatchQ[#, _^-1] &]), opts] /. inv -> ((1/#)&))/; - !FreeQ[{x}, _Pair^-1]; - - -(*Add PHI vertices to Amplitudes database*) -(*First make sure amplist has a value*) -Amplitude[]; -(*Get the PHI amps*) -Block[ {phiAmpList, dum, names, dir}, - dir = ToFileName[{$FeynCalcDirectory, "Phi", "CouplingVectors"}]; - names = - StringReplace[StringReplace[#, dir -> ""], ".Gen" -> ""] & /@ - FileNames["*.Gen", - dir]; - phiAmpList = (# :> - FAToFC[{CheckDB[dum, # <> ".Gen", ForceSave -> False, - NoSave -> True].((#[[1]]) & /@ - CheckDB[dum, # <> ".Mod", ForceSave -> False, - NoSave -> True])}][[1]]) & /@ names; -(*Modify amplist*) - FeynCalc`Amplitude`Private`amplist = - Union[FeynCalc`Amplitude`Private`amplist, - phiAmpList] -]; - - -(* ************************************************************** *) - -(* Recursive definition of multiple derivatives *) - -(* Should usually not be altered *) - -Options[CovariantFieldDerivative] = - {Explicit->True, DiagonalToU->True, - (*RemoveIntegerIndices->True,*) - SUNN->2, UDimension->Automatic}; - -CovariantFieldDerivative[aa_,x_,loris__LorentzIndex,lori1_LorentzIndex] := - (newfuncc[1] = CovariantFieldDerivative[aa,x,lori1]; - Do[newfuncc[rep+1] = CovariantFieldDerivative[ - newfuncc[rep],x,##]&@@Take[{loris},{-rep}], - {rep,1,Length[{loris}]}]; - newfuncc[Length[{loris}]+1]); -(* ************************************************************** *) - -(* (Re-)setting of options and $-variables *) - -(* - Put definitions here you always want different from the - default settings. Model specific definitions should be - put in the relevant configuration file -*) - -(* Check for unpatched FeynArts *) - -$FAPatch = True; - -(* Which representation should be used for the - pion/meson matrix - the default is the exponential *) - -$UExpansionCoefficients = -{1, 1, 1/2, 1/6, 1/24, 1/120, 1/720, 1/5040, 1/40320, - 1/362880, 1/3628800}; - -(* ************************************************************** *) -(* ************ CHOOSE CONFIGURATION AND LAGRANGIANS ************ *) -(* ************************************************************** *) - -(* Which configuration should be used? *) -(* Overridden is set before loading FeynCalc *) - -If[ ValueQ[Global`$Configuration] =!= True || Global`$Configuration === None || - Global`$Configuration === "None", - Global`$Configuration = - "ChPT2"; -(*standard SU(2) ChPT*) - (*"ChPTPhoton2";*)(*standard SU(2) ChPT with coupling to a photon source*) - (*"ChPT3";*) (*Standard SU(3) ChPT*) - (*"ChPTW3";*) (*Weak SU(3) ChPT*) - (*"BChPT2";*) (*Relativistic baryon SU(2) ChPT*) - (*"HBChPT2";*) (*Heavy baryon SU(2) ChPT*) - (*"ChPTEM2";*) (*Standard SU(2) ChPT with virtual photons - Meissner, Steininger*) - (*"ChPTVirtualPhotons2";*) (*Standard SU(2) ChPT with virtual photons - Urech, Knecht*) - (*"ChPTVirtualPhotons3";*) (*Standard SU(2) ChPT with virtual photons - Urech, Knecht*) - (*"QED";*) (*QED with one lepton*) - (*"QED2";*) (*QED with three leptons*) - -] - -(* Actual loading of configuration *) -If[ $PaletteConfiguration=!="None"&&$PaletteConfiguration=!=None&&$Phi===True, - FCPrint[2,"Using ",$PaletteConfiguration," chosen from palette"]; - Global`$Configuration = Evaluate[$PaletteConfiguration] -]; -FCPrint[2,"Loading configuration ",Global`$Configuration]; -tmp`olddir1 = tmp`olddir; -LoadConfiguration[Global`$Configuration]; -tmp`olddir = tmp`olddir1; - -(* Which lagrangians should be loaded? *) - -If[ ValueQ[Global`$Lagrangians] =!= True || Global`$Lagrangians === {}, - Global`$Lagrangians = - {"ChPT2"[2],"ChPT2"[4]}; -(*{"ChPTPhoton2"[2],"ChPTPhoton2"[4]};*) - (*{"ChPT3"[2],"ChPT3"[4]};*) - (*{"ChPTW3"[2],"ChPTW3"[4]};*) - (*{"BChPT2"[2]};*) - (*{"HBChPT2"[2]};*) - (*{"ChPTEM2"[2],"ChPTEM2"[4]};*) - (*{"ChPTVirtualPhotons2"[2],"ChPTVirtualPhotons2"[4]};*) - (*{"ChPTVirtualPhotons3"[2],"ChPTVirtualPhotons3"[4]};*) - (*{"QED"[1],"QED"[2]};*) - (*{"QED2"[1],"QED2"[2]};*) - -] - -(* Actual loading of lagrangians *) -FCPrint[2,"Loading lagrangians ",Global`$Lagrangians]; -LoadLagrangian/@Global`$Lagrangians; - -(* Setting of $VerticesSpecifications using all stored vertices - belonging to the chosen configuration *) -$VerticesSpecifications = - VerticesSpecifications[$Configuration, $FAParticlesInUse, $ParticleTypes]; - -(* ************************************************************** *) -(* ****** END OF CHOOSE CONFIGURATION AND LAGRANGIANS *********** *) -(* ************************************************************** *) - -(* ************************************************************** *) -(* ******************* EXTRA CONFIGURATION ********************** *) -(* ************************************************************** *) - -(* Source fields *) -(* Fields not needed should be set to 0 to speed up things *) - -(* Fields *) -(*QuantumField[___,Particle[Scalar[0],___],___][_]:=0;*) -(*QuantumField[___,Particle[Scalar[1],___],___][_]:=0;*) -(*QuantumField[___,Particle[Scalar[2],___],___][_]:=0;*) -(*QuantumField[___,Particle[PseudoScalar[0],___],___][_]:=0;*) -(*QuantumField[___,Particle[Vector[0],___],___][_]:=0;*) -(*QuantumField[___,Particle[AxialVector[0],___],___][_]:=0;*) - -(* Isovectors *) -(*IsoVector[ -QuantumField[Particle[Scalar[0],___],___],___][_]:=0;*) -(*IsoVector[ -QuantumField[Particle[Scalar[1],___],___],___][_]:=0;*) -(*IsoVector[ -QuantumField[Particle[Scalar[2],___],___],___][_]:=0;*) -(*IsoVector[ -QuantumField[Particle[PseudoScalar[0],___],___],___][_]:=0;*) -(*IsoVector[ -QuantumField[Particle[Vector[0],___],___],___][_]:=0;*) -(*IsoVector[ -QuantumField[Particle[AxialVector[0],___],___],___][_]:=0;*) - -(* Isosinglets *) -(*QuantumField[___,Particle[Scalar[0],___],___, - SUNIndex[0],___][_]:=0;*) -(*QuantumField[___,Particle[Scalar[1],___],___, - SUNIndex[0],___][_]:=0;*) -(*QuantumField[___,Particle[Scalar[2],___],___, - SUNIndex[0],___][_]:=0;*) -(*QuantumField[___,Particle[PseudoScalar[0],___],___, - SUNIndex[0],___][_]:=0;*) -QuantumField[___,Particle[AxialVector[0],___],___, - SUNIndex[0],___][_] := - 0; -QuantumField[___,Particle[Vector[0],___],___, - SUNIndex[0],___][_] := - 0; -QuantumField[___,Particle[LeftComponent[0],___],___, - SUNIndex[0],___][_] := - 0; -QuantumField[___,Particle[RightComponent[0],___],___, - SUNIndex[0],___][_] := - 0; - -(* The setting below expands the zero'th Scalar[0] - source around the quark mass. The Scalar[2] source is - then the perturbation. (- in ChPTW3 we use Scalar[1] for the - hamiltonian source) *) - -IsoVector[QuantumField[Particle[ -Scalar[0],ar___RenormalizationState, -br___RenormalizationScheme,cr___ExpansionState, -opts___Rule|opts___List]],opts1___][x_] := - IsoVector[QuantumField[Particle[Scalar[2],ar,br,cr]],opts1][x]; - -QuantumField[Particle[ -Scalar[0],ar___RenormalizationState, -br___RenormalizationScheme,cr___ExpansionState, -opts___Rule|opts___List], SUNIndex[0]][x_] := - UQuarkMassMatrix[ar,br,cr,opts]+ - QuantumField[Particle[Scalar[2],ar,br,cr, - Sequence@@OptionsSelect[Particle,opts]], - SUNIndex[0]][x]*UIdentityMatrix[opts]; - -(* If you're working with the weak lagrangian; have a momentum - carrying lagrangian or not *) - -$Substitutions = DeleteCases[$Substitutions, -UNablaHatDelta[_] :> _]; - -$Substitutions = Append[$Substitutions, UNablaHatDelta[mu_] :> - -(* The standard definition *) -(*-I*NM[SMM, -UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0]],{mu}]], -UGeneratorMatrix[SUNIndex[6]], -Adjoint[SMM]]+ -I*NM[SMM, -UGeneratorMatrix[SUNIndex[6]], -UGeneratorMatrixIsoDot[QuantumField[Particle[ -LeftComponent[0]],{mu}]], -Adjoint[SMM]]*) - -(* Including a scalar 'source' with momentum *) -NM[SMM,NM[FDr[QuantumField[Particle[Scalar[1]]],{mu}], - UGeneratorMatrix[SUNIndex[6]],Adjoint[SMM]]] -]; - -(* ************************************************************** *) -(* ***************** END OF EXTRA CONFIGURATION ***************** *) -(* ************************************************************** *) - -(* Add the palettes to the palette menu of Mathematica - (Requires a restart of the frontend) and fix red brackets *) - -If[ AtomQ[$FrontEnd]=!=True, - SetOptions[$FrontEnd, PalettePath -> - Append[Select[Options[$FrontEnd, - PalettePath][[1, -1]], ((If[ StringQ[#], - !StringMatchQ[#, "*FeynCalc*Phi*"], - FreeQ[#, "FeynCalc"] && FreeQ[#, "Phi"] - ] === True)&)], - ToFileName[{$FeynCalcDirectory, "Phi"}, "Palettes"]]]; - - (*Under Mathematica 4, the default highlighting unmatched brackets - highlights all right brackets generated by PHI, so we disable it. - This is the default: {"UnmatchedBracketStyle" -> "UnmatchedBracket"}*) - SetOptions[$FrontEnd, AutoStyleOptions -> - {"UnmatchedBracketStyle" -> None}]; -]; diff --git a/FeynCalc/Phi/ReadMe.txt b/FeynCalc/Phi/ReadMe.txt deleted file mode 100644 index 9ef13d840..000000000 --- a/FeynCalc/Phi/ReadMe.txt +++ /dev/null @@ -1,212 +0,0 @@ -PHI (Phenomenology of Hadronic Interactions) is a Mathematica package for -computations in Chiral Perturbation Theory (ChPT). It is meant to be used -in conjunction with the other Mathematica packages FeynArts (version 3 or -higher) and FeynCalc (version 3 or higher). - -PHI is designed for ChPT, but can in principle be adapted for any field -theory. One distinguishing feature of ChPT is that it is not renormalizable -but has a new counterterm lagrangian for each order in the perturbative -expansion and vertices with any number of legs. Also, the perturbative -expansion is not in a coupling constant; instead it is a dual expansion in -the lightest 2 (or 3) quark masses and the external momenta. - -As of version 4.1.1 of FeynCalc, PHI is distributed with FeynCalc. -A changelog and further information than given below can be found at -http://www.feyncalc.org/phi/. Future changelogs will be given in in the -main FeynCalc readme file FCReadme.txt. - - -FEATURES: - -A set of basic objects that can be composed and manipulated to form ChPT -lagrangians. - -Compatibility with FeynArts for automatized generation of -Feynman loop amplitudes including counter terms and starting from a user -defined or built-in lagrangian. The renormalization procedure is partially -automatized for ChPT one-loop processes. - - -GOALS: - -The aim is to ease the computation of amplitudes in ChPT and related effective -models, thereby allowing checks of previous calculations and performing new -calculations. Most standard one-loop amplitudes have been computed, so inevitably -going to two-loops should be attempted. - -The long term goal is to establish a database of amplitudes from phenomenological -effective lagrangians, well checked and easily extensible. - - -PHI QUICKSTART: - -Make sure you have FeynCalc >= 4.1.1; if not, get it at -http://www.feyncalc.org/. -Get the FeynArts tarball from http://www.feynarts.de/ and unpack it in -your "FeynCalc" directory. Set -$LoadPhi=True; $LoadFeynArts=True; -and load FeynCalc with -<<"FeynCalc`". - - -PHI INSTALLATION: - -Mathematica (version 3 or higher) is required. It is recomended not to have -less than 128 MB of RAM and a reasonably fast processor (>300 MHz). - -FeynCalc (version 3 or higher) must be up and running. From version 4.1.1 -of FeynCalc, PHI is distributed with FeynCalc and no further installation of -PHI files is needed. -FeynCalc can be obtained at http://www.feyncalc.org/. - -Furthermore one should get and install FeynArts (version 3 or higher) -according to the description below. -FeynArts can be obtained at http://www.feynarts.de/. - -Finally, the file PhiStart.m should be edited to load the desired model -and lagrangians. Model specific modifications of PHI objects should be -specified in the relevant model configuration file (in Phi/Configurations). - - -FEYNARTS INSTALLATION: - -After downloading the FeynArts tarball (FeynArts3.tar.gz), unpack it in -the FeynCalc installation directory "FeynCalc". -You can check where it is by loading FeynCalc (<<"FeynCalc`") -and evaluating $FeynCalcDirectory. The unpacking must be so that the file -"FeynArts.m" is in "FeynCalc". - -In order to have FeynCalc and FeynArts loaded simultaneously and to be able -to use the PHI fields directly with FeynArts, some changes need to be made to FeynArts. -These changes will be performed the first time you load PHI and FeynArts via FeynCalc. -That is, the first time you load FeynCalc after having evaluated -$LoadPhi=True; $LoadFeynArts=True; -This can be done either directly before evaluating -<<"FeynCalc`" -or you can put the line in your "FCConfig.m" file. - -The automatic modification of the FeynArts files is done by the Mathematica -function FAPatch defined in "Extras/FAPatch.m". The reasons for doing it -this way instead of distributing an alternative version of FeynArts or a true -patch are: 1) To make it clear that FeynArts is a completely separate project -from FeynCalc and have people credit the right authors. 2) We cannot -assume that all users know how to apply a patch. 3) A patch would only -work with one specific version of FeynArts. - -The backdraw is that we cannot be absolutely sure that FAPatch actually -works with future versions of FeynArts. However, attempts will be made -to keep it up to date. If it should not work, it should be possible to -do the changes with a good text editor. Or you can contact fjob@cabocomm.dk -to get a patched version of FeynArts. - - -FEYNARTS CHANGES: - -Below follows a description of the most essential changes needed to be done -to FeynArts. As described above, these will normally be done automatically; -but should this fail, they have to be done manually. - -In the sub-directory "Extras" there are two model files meant to be read by -FeynArts: "Automatic.gen" and "Automatic.mod". These should be placed in the -"Models" directory. - -The names: - -Loop, PolarizationVector, FeynAmp, FeynAmpDenominator, FeynAmpList, -PropagatorDenominator, GaugeXi, NonCommutative, DiracSpinor, DiracTrace - -should be put explicitly in their corresponding FeynCalc context. -That is, e.g. Loop should be replaced with FeynCalc`Loop`Loop - -In Setup.m, the following lines should be added: - -P$Generic = Union[Flatten[P$Generic | $ParticleHeads]]; -P$NonCommuting = Union[Flatten[P$NonCommuting | $FermionHeads]]; -SetOptions[FourVector, FeynCalcInternal -> False]; -SetOptions[MetricTensor, FeynCalcInternal -> False]; -SetOptions[DiracSlash, FeynCalcInternal -> False]; - - -DOCUMENTATION: - -The lists of objects are found in the standard way for each subpackage -(e.g. ?Phi`Channels`*). Also in the standard way, documentation ("man" pages) -can be found for each of the objects: Simply type ?object to get information -on object. It is usually a good idea to start with some of the examples -provided. - -Updates and examples can found on http://www.feyncalc.org/phi/. - - -SUB-PACKAGES: - -The sub-packages are not actually loaded on startup. Instead they are -declared with DeclarePackage, so that when a symbol defined in a package is -used for the first time, the package is loaded. This is similar to FeynCalc, -except FeynCalc has a sub-package for each symbol. The reason for doing this -is of course saving memory. Normally, because of the definitions in -PhiStart.m and/or the configuration file chosen, effectively the -sub-packages Objects, Couplings and Channels will be loaded on startup. - -The sub-packages of PHI are: - -Objects, containing all basic objects, - -Couplings, a package for using the Feynman rules generated from the -lagrangians to generate loop amplitudes, - -Channels, containing utilities for iso-spin reduction and projection -of amplitudes, - -Utilities, containing utilities kinematics and Dirac algebra, - -Renormalization, a package that includes formulas for renormalizing -one-loop amplitudes, - -Palettes, a package generating palettes for loading configurations and -lagrangians. - -The PHI directory also contains the directories Lagrangians (some predefined -lagrangians), Configurations (one configuration file for each family of -lagrangians), Factors (renormalization factors), CouplingVectors (the -coupling vector definitions used by the model files Automatic.gen and -Automatic.mod used by FeynArts) and Storage (for storing intermediate -results), the file First.m where user definitions should be put when they -are to be loaded before anything else, and finally files containing usage, -box, and error definitions for the sub-packages. - -In the PHI directory are also the files Phi.m and PhiStart.m, which are -respectively the startup file and the configuration file. - - -FUTURE PLANS: - -More models, two loops. - - -BUG REPORTS: - -Please report any bugs to the author Frederik Orellana at fjob@cabocomm.dk. -Comments and suggestions are also welcome. - - -LICENSE: - -PHI is covered by the GNU General Public License which can be found -at http://www.feyncalc.org/license.txt. - -This roughly means: - -1. I don't promise that this software works (please report bugs). - -2. It's is free. - -3. If you use this software or parts of it as part of another piece of -software, you must acknowledge it in your documentation. - - - -Have fun. - -Frederik Orellana -CERN, April 1, 2003 diff --git a/FeynCalc/Phi/Renormalization.m b/FeynCalc/Phi/Renormalization.m deleted file mode 100644 index 32dd54c75..000000000 --- a/FeynCalc/Phi/Renormalization.m +++ /dev/null @@ -1,1979 +0,0 @@ -(* Wolfram Language package *) - -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: Renormalization (Phi) *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Dimensional regularization of loop amplitudes *) - -(* ------------------------------------------------------------------------ *) - - -TruncatedGamma::usage = -"TruncatedGamma[x,p,o] is the gamma function of x expanded to order o \ -around p."; - -Spence::usage = -"Spence[x] = PolyLog[2,x] is the Spence integral. \"Spence\" is a \ -possible setting of the option C0Evaluation of VeltmanC0 and VeltmanExpand. \ -This setting will give an evaluation according to formula (5.6) of 't Hooft \ -and Veltman (1979) using the decomposition in Spence functions of the \ -appendix. It is the fastest and most reliable setting."; - -VeltmanB0::usage = -"VeltmanB0[p10,m1^2,m2^2] is the Passarino-Veltman two-point function."; - -VeltmanDelta::usage = -"VeltmanDelta[D-4] is 2/(D-4)-EulerGamma-Log[Pi] with the default \ -options."; - -FeynmanIntegral::usage = -"FeynmanIntegral[p1^2,m1^2,m2^2,n1,n2,d,d1] is the one-loop Feynman \ -integral with integrand 1/((p1-q)^2-m1^2+I*SmallEpsilon)^n1*(p1^2-m2^2+I*SmallEpsilon)^n2). \ -d and d1 are the number of space-time dimensions used for the gamma function \ -and other factors respectively. FeynmanIntegral is used by VeltmanB0 when \ -B0Evaluation is set to \"direct1\"."; - -VeltmanC0::usage = -"***EXPERIMENTAL***\n -VeltmanC0[p10,p20,p12,m1^2,m2^2,m3^2] is the Passarino-Veltman \ -three-point function."; - -VeltmanD0::usage = -"***EXPERIMENTAL***\n -VeltmanD0[p10,p12,p23,p30,p20,m1^2,m2^2,m3^2,m4^2] is the \ -Passarino-Veltman four-point function."; - -VeltmanExpand::usage = -"***EXPERIMENTAL***\n -VeltmanExpand[amp, opts] expands the Passarino-Veltman B0, C0 and D0 \ -functions using the options opts. Besides VeltmanExpand's own options \ -any options of VeltmanB0, VeltmanC0 and VeltmanD0 may be given."; - -B0Evaluation::usage = -"B0Evaluation is an option of VeltmanB0 and VeltmanExpand, specifying how \ -the function should be evaluated. Possible settings are \"none\", \"direct1\" and \ -\"jbar\" for VeltmanB0.\n\n -With the setting B0Evaluation -> \"direct1\" VeltmanB0 will return an expression \ -depending on D and d, where D is the setting of the option Dimension\ and -d is the setting of the option DimensionExpand (d and D may be the same). If \ -DimensionExpand is set to False no expansion of power functions of (d-4) is done.\n\n -Default setting : \"jbar\"."; - -C0Evaluation::usage = -"C0Evaluation is an option of VeltmanC0 and VeltmanExpand, specifying how \ -the function should be evaluated. The fastest and most reliable setting is \ -\"Spence\". the others are provided merely to illustrate e.g. the slow \ -convergence of the integrals. Possible settings are \"none\", \"Spence\", \"infrared\", \"direct1\" \ -and \"direct2\". When \"direct1\", \"direct2\" or \"direct3\" is chosen, the options of \ -NIntegrate may also be specified.\n\n -When C0Evaluation is set to \"direct1\" \ -VeltmanC0 will return what Mathematica makes out of a direct integration of \ -formula (5.2) of 't Hooft and Veltman (1979) using he setting of \ -FCIntegrate.\n\n -When C0Evaluation is set to \"direct2\" VeltmanC0 will return what Mathematica \ -makes out of a direct integration of formula (5.3) of 't Hooft and Veltman \ -(1979) using he setting of FCIntegrate. This setting will in most \ -regions of parameter space give a rather slow and unreliable evaluation, \ -though slightly better than \"direct1\".\n\n -When C0Evaluation is set to \"direct3\" VeltmanC0 will return what Mathematica \ -makes out of a direct integration of formula (5.6) of 't Hooft and Veltman \ -(1979) using he setting of FCIntegrate. This setting will in most \ -regions of parameter space give a rather slow and unreliable evaluation, \ -though slightly better than \"direct1\".\n\n -When C0Evaluation is set to \"direct4\" VeltmanC0 will use a direct symbolic \ -integration of formula (5.6) of 't Hooft and Veltman (1979) made with \ -Integrate. This setting will in most regions of parameter space give a fast \ -and reliable evaluation consistent with \"Spence\", but in some regions it fails \ -because Mathematica does not implement the right cuts.\n\n -When C0Evaluation is set to \"infrared\" an implementation of formulas (E.1-E.3) of 't Hooft and \ -Veltman (1979) is used. The fifth argument of VeltmanC0 is then the (infinitesimal) \ -infrared regulator. The external momenta correponding to the first two arguments \ -must be on-shell.\n\n -When C0Evaluation is set to \"infrared1\" an implementation of formulas (A.22) of Knecht and \ -Urech (1997), valid above threshold, is used. The fifth argument of VeltmanC0 is then the (infinitesimal) \ -infrared regulator. The external momenta correponding to the first two arguments \ -must be on-shell and equal.\n\n -When C0Evaluation is set to \"infrared2\" an implementation of formulas (4.13) of Knecht and \ -Urech (1997), valid below 0, is used. The fifth argument of VeltmanC0 is then the (infinitesimal) \ -infrared regulator. The external momenta correponding to the first two arguments \ -must be on-shell and equal.\n\n -Default setting : \"Spence\" for VeltmanC0 and \ -\"none\" for VeltmanExpand."; - -D0Evaluation::usage = -"D0Evaluation is an option of VeltmanD0 and VeltmanExpand, specifying how \ -the function should be evaluated. The fastest and most reliable setting is \ -VeltmanC0. The others are redundant. Possible settings are \"none\", \ -\"Spence\", \"C0\", and \"direct1\".\n\n -With D0Evaluation -> \"direct1\" VeltmanD0 will return what \ -Mathematica makes out of a direct integration of formula (6.10) of 't Hooft \ -and Veltman (1979) using the setting of FCIntegrate. This setting will \ -in most regions of parameter space give a rather slow and unreliable \ -evaluation.\n\n -Default setting : \"Spence\" for VeltmanD0 and \"none\" for VeltmanExpand."; - -ExpandGammas::usage = -"ExpandGammas[expr] expands the Gamma functions in expr in (dim-4) around fp to \ -order oo, where dim, fp and oo are the setting of the options Dimension, FixPoint and \ -TaylorOrder. ExpandGammas is also an option for VeltmanB0 with default \ -setting True."; - -DimensionExpand::usage = -"DimensionExpand[expr] expands power functions of (D-4), where D is the \ -setting of the option Dimension. DimensionExpand is also an option of \ -VeltmanB0. As such it may be set to either True, False or a symbol. \ -The default is False which implies that no expansion of power functions of (D-4) is done. \ -When set to True, the function DimensionExpand will be applied to the expressions returned \ -by the VeltmanB0's, using the options Options[DimensionExpand] apart from the Dimension, \ -which may be specified or otherwise is taken from Options[VeltmanB0], and expanding in the symbol \ -defined by the setting of the option Dimension. When set to a symbol d expansion of power \ -functions of (d-4) is done"; - -IntegrateHeld::usage = -"IntegrateHeld is a head for unevaluated integrals. Sums are split up \ -and constants are brought out. NOTICE: IntegrateHeld automatically uses the \ -Leibniz rule, so if you differentiating integrals of discontinuous functions, \ -do not use IntegrateHeld.."; - -FixPoint::usage = -"FixPoint is an option for DimensionExpand and VeltmanB0, \ -specifying the point the Taylor series is expanded around. Default setting : \ -0."; - -TaylorOrder::usage = -"TaylorOrder is an option for DimensionExpand and VeltmanB0, \ -specifying the truncation of the relevant Taylor series. \ -Default setting : 2."; - -LeutwylerJ::usage = -"LeutwylerJ is a possible setting of the option B0Evaluation of \ -VeltmanB0 and VeltmanExpand."; - -LeutwylerLambda::usage = -"LeutwylerLambda[opts] represent the infinite quantity in the \ -subtraction scheme used by Gasser and Leutwyler. When \ -ExplicitLeutwylerLambda is set to True an expression containing explicit \ -dimensional infinities is returned."; - -ExplicitLeutwylerLambda::usage = -"ExplicitLeutwylerLambda is an option for LeutwylerLambda, LeutwylerJ0 and \ -VeltmanB0, specifying whether the infinities arising in the \ -D-dimensional integration should be expressed explicitly in terms of D (to \ -order (2-D)/2). Default setting : False."; - -LeutwylerSigma::usage = -"LeutwylerSigma[momentumsquared,pionmasssquared] is the quantity \ -\[Sigma] from J.Gasser and H. Leutwyler (1984), Annals of Physics 158, \ -142-210. It returns an algebraic expression when ExplicitLeutwylerSigma is \ -set to true."; - -ExplicitLeutwylerSigma::usage = -"ExplicitLeutwylerSigma is an option for LeutwylerSigma, LeutwylerJBar and \ -VeltmanB0, specifying whether the function should be \ -evaluated or not. Default setting : False."; - -LeutwylerJ0::usage = -"LeutwylerJ0[m^2] is the quantity J from J.Gasser and H. \ -Leutwyler (1984), Annals of Physics 158, 142-210. LeutwylerJ0[m1^2,m2^2] is \ -the quantity J from J.Gasser and H. Leutwyler (1985), Nuclear Physics \ -B250, 465-516. It returns an algebraic expression involving LeutwylerLambda \ -when ExplicitLeutwylerJ0 is set to True."; - -ExplicitLeutwylerJ0::usage = -"ExplicitLeutwylerJ0 is an option for LeutwylerJ0 and VeltmanB0, \ -specifying whether the function should be evaluated or not. \ -Default setting : False."; - -LeutwylerJBar::usage = -"LeutwylerJBar[s,m^2] is the quantity J-bar from J.Gasser and H. \ -Leutwyler (1984), Annals of Physics 158, 142-210. LeutwylerJBar[s,m1^2,m2^2] \ -is the quantity J-bar from J.Gasser and H. Leutwyler (1985), Nuclear \ -Physics B250, 465-516. It returns an algebraic expression \ -when LeutwylerJBarEvaluation is not set to \"none\"."; - -LeutwylerJBarEvaluation::usage = -"LeutwylerJBarEvaluation is an option for LeutwylerJBar and VeltmanB0, \ -specifying how the function should be evaluated. \ -Possible settings are \"none\", \"general\", \"subthreshold\" and \"physical\". \ -\"subthreshold\" is applicable up to m1^2+m2^2, \"physical\" above m1^2+m2^2. \ -\"general\" is applicable everywhere but yields a somewhat longer expression. \ -Default setting : \"none\"."; - -MassScale::usage = -"MassScale is an option of VeltmanB0, LeutwylerLambda and LeutwylerJ0, \ -specifying the mass scale \ -inserted in the D-dimensional integrals used for dimensional regularization \ -of loop integrals of meson-meson scattering. Default setting : ScaleMu."; - -RenormalizationCoefficients::usage = -"RenormalizationCoefficients[lag] returns the list of renormalization \ -coefficients used for renormalization of the coupling constants of the \ -lagrangian lag. It is used for the default value of \ -RenormalizationCoefficientFunction[lag,i], and should be specified in the \ -file containing the definition of the lagrangian."; - -RenormalizationCoefficientFunction::usage = -"RenormalizationCoefficientFunction is an option of Renormalize, \ -specifying the function f, so that c = c0 - f[c]*l, where c is some \ -renormalized coupling constant, c0 is the unrenormalized equivalent (both \ -with heads CouplingConstant) and f is the infinite quantity specified by the \ -option InfinityFactor. The option actually to be specified is \ -RenormalizationCoefficientFunction[lag,i], which returns the coefficient \ -used in the renormalization of the coupling constant \ -CouplingConstant[lag,i,RenormalizationState[0]]. Default value : \ -RenormalizationCoefficients[lag][[i]]."; - -Renormalize::usage = -"Renormalize[m,opts], where m is a counterterm amplitude, substitutes \ -coupling constants with the renormalized equivalents expressed in terms of \ -the the infinite quantity specified by the option InfinityFactor in opts. \ -The factors specified by the option RenormalizationCoefficientFunction are \ -used. When the renormalized counterterm amplitude is added to the \ -corresponding loop amplitudes, the infinities should cancel."; - -InfinityFactor::usage = -"InfinityFactor is an options of Renormalize specifying the \ -renormalization scheme. Default value : LeutwylerLambda[]."; - -FeynmanParameterize::usage = -"FeynmanParameterize[expr,k(,l(,j))] computes the integral of expr over k \ -(divided by (2 Pi)^d), then computes the integral of the result over l \ -(divided by (2 Pi)^d) if the third argument is provided and, finally, \ -computes the integral of this result over j (divided by (2 Pi)^d), if the \ -fourth argument is given. It uses the algorithm of feynpar by Todd West."; - -FeynmanX::usage = "FeynmanX[1], FeynmanX[2], etc. are Feynman parameters."; - -FeynmanY::usage = "FeynmanY[1], FeynmanY[2], etc. are Feynman parameters."; - -FeynmanZ::usage = "FeynmanZ[1], FeynmanZ[2], etc. are Feynman parameters."; - -(* -Errors -*) - -VeltmanC0::nodef = -"The two first particles are not on-mass-shell."; - -VeltmanC0::nodef1 = -"The two first particles must be on-mass-shell and have identical masses."; - -Begin["`Package`"] -End[] - - -Begin["`Renormalization`Private`"]; - -(* -Boxes -*) - -IntegrateHeld /: MakeBoxes[IntegrateHeld[a__, - b : _List .. ], TraditionalForm] := -RowBox[Join[Table[ - UnderoverscriptBox["\[Integral]", - ToBoxes[TraditionalForm[{b}[[rep, 2]]]], - ToBoxes[TraditionalForm[{b}[[rep, 3]]]]], - {rep,Length[{b}]}], - {MakeBoxes[TraditionalForm[a]]}, - Reverse[Table[RowBox[{"\[DifferentialD]", - ToBoxes[TraditionalForm[{b}[[rep, 1]]]]}], - {rep,Length[{b}]}]]]]; - -FeynmanX /: MakeBoxes[FeynmanX[i_], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["x", FontSlant -> "Italic"]][[1]], - MakeBoxes[TraditionalForm[i]]]; - -FeynmanY /: MakeBoxes[FeynmanY[i_], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["y", FontSlant -> "Italic"]][[1]], - MakeBoxes[TraditionalForm[i]]]; - -FeynmanZ /: MakeBoxes[FeynmanZ[i_], TraditionalForm] := - SubscriptBox[MakeBoxes[StyleForm["z", FontSlant -> "Italic"]][[1]], - MakeBoxes[TraditionalForm[i]]]; - -LeutwylerSigma /: Format[LeutwylerSigma[___], TraditionalForm] := - StyleForm["\[Sigma]", FontSlant -> "Italic"]; - -LeutwylerJBar /: MakeBoxes[LeutwylerJBar[q_, m__, ___Rule], TraditionalForm] := - RowBox[{SubscriptBox[ - MakeBoxes[StyleForm[OverBar["J"], FontSlant -> "Italic"]][[1]], - RowBox[MakeBoxes[TraditionalForm[#]] & /@ {m}]], "(", - MakeBoxes[TraditionalForm[q]], ")"}]; - -LeutwylerJ0 /: MakeBoxes[LeutwylerJ0[___], TraditionalForm] := - RowBox[{MakeBoxes[StyleForm["J", FontSlant -> "Italic"]], "(", "0", ")"}]; - -LeutwylerLambda /: Format[LeutwylerLambda[___], TraditionalForm] := - StyleForm["\[Lambda]", FontSlant -> "Italic"]; - -VeltmanB0 /: MakeBoxes[VeltmanB0, TraditionalForm] := SubscriptBox["B", "0"]; -VeltmanB0 /: MakeBoxes[VeltmanB0[x__, __Rule], TraditionalForm] := - MakeBoxes[TraditionalForm[VeltmanB0[x]]]; - -VeltmanC0 /: MakeBoxes[VeltmanC0, TraditionalForm] := SubscriptBox["C", "0"]; -VeltmanC0 /: MakeBoxes[VeltmanC0[x__, __Rule], TraditionalForm] := - MakeBoxes[TraditionalForm[VeltmanC0[x]]]; - -VeltmanD0 /: MakeBoxes[VeltmanD0, TraditionalForm] := SubscriptBox["D", "0"]; -VeltmanD0 /: MakeBoxes[VeltmanD0[x__, __Rule], TraditionalForm] := - MakeBoxes[TraditionalForm[VeltmanD0[x]]]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Defaults *) - - -Options[VeltmanB0] = { - SmallEpsilon -> SmallEpsilon, - B0Evaluation -> "jbar", - ExpandGammas -> True, - FixPoint -> 0, TaylorOrder -> 2, - Dimension -> D, - MassScale -> ScaleMu, - FCIntegrate -> IntegrateHeld, - DimensionExpand -> SpaceTimeDimensions, - LeutwylerJBarEvaluation -> "none", - ExplicitLeutwylerJ0 -> False, - ExplicitLeutwylerLambda -> False, - ExplicitLeutwylerSigma -> False - }; - -Options[VeltmanC0] = { - SmallEpsilon -> SmallEpsilon, - C0Evaluation -> "Spence", - FCIntegrate -> NIntegrate -}; - -Options[VeltmanD0] = { - SmallEpsilon -> SmallEpsilon, - D0Evaluation -> "Spence", - FCIntegrate -> NIntegrate -}; - -Options[FeynmanIntegral] = {SmallEpsilon -> SmallEpsilon, - FCIntegrate -> IntegrateHeld}; -Options[VeltmanDelta] := - {FixPoint -> 0, TaylorOrder -> 2}; -Options[DimensionExpand] = {Dimension -> SpaceTimeDimensions, FixPoint -> 4, - TaylorOrder -> 1}; -Options[ExpandGammas] = {FixPoint -> 0, TaylorOrder -> 2, Dimension -> D}; -Options[VeltmanExpand] = {(*Dimension -> D, MassScale -> ScaleMu, - ExplicitLeutwylerLambda -> False, LeutwylerJBarEvaluation -> "none", - ExplicitLeutwylerSigma -> False, ExplicitLeutwylerJ0 -> False, - SmallEpsilon -> SmallEpsilon, - ExpandGammas -> True, DimensionExpand -> False, FixPoint -> 0, - TaylorOrder -> 2,*) B0Evaluation -> "jbar", C0Evaluation -> "none", - D0Evaluation -> "none", FCIntegrate -> IntegrateHeld, - OnMassShell -> False, MomentumVariablesString -> "p", - Masses -> {ParticleMass[Pion, RenormalizationState[0]], - ParticleMass[Pion, RenormalizationState[0]], - ParticleMass[Pion, RenormalizationState[0]], - ParticleMass[Pion, RenormalizationState[0]]}}; -Options[LeutwylerLambda] = {Dimension -> D, - MassScale -> ScaleMu, ExplicitLeutwylerLambda -> False}; -Options[LeutwylerJ0] = {MassScale -> ScaleMu, ExplicitLeutwylerJ0 -> False, - ExplicitLeutwylerLambda -> False}; -Options[LeutwylerSigma] = {ExplicitLeutwylerSigma -> False}; -Options[LeutwylerJBar] = {LeutwylerJBarEvaluation -> "none", - ExplicitLeutwylerSigma -> False}; -Options[Renormalize] = {SUNN -> 2, InfinityFactor -> LeutwylerLambda[], - RenormalizationCoefficientFunction[CouplingConstant[lag_, n_, ___]] :> - RenormalizationCoefficients[lag][[n]]}; -Options[FeynmanParameterize] = {Dimension -> D, - FCIntegrate -> - (DOT[Integratedx@@#2, #1] &), - FeynmanParameterNames -> Automatic - (*Compatibility with FeynmanParametrize:*) - (*{Global`x,Global`y,Global`z, Global`\[Alpha]1, - Global`\[Alpha]2, Global`\[Alpha]3}*)}; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* B0 *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -(* Expansion of the gamma function: *) - -TruncatedGamma[dd_, p_, o_] := - Normal[Series[Gamma[d], {d, p, o}]] /. d :> dd; - - -(* The capital delta of the 't Hooft and Veltman article: *) - -VeltmanDelta[d_, opts___] := - TruncatedGamma[ - d/2, (FixPoint /. Flatten[{opts}] /. - Options[VeltmanDelta]), (TaylorOrder /. Flatten[{opts}] /. - Options[VeltmanDelta])] - Log[Pi]; - - -(* Expansion of power functions of (SpaceTimeDimensions-4): *) - -DimensionExpand[a_, opts___] := - Block[ {dim, fixp, oo, b, c, s6}, - dim = Dimension /. Flatten[{opts}] /. Options[DimensionExpand]; - fixp = FixPoint /. Flatten[{opts}] /. Options[DimensionExpand]; - oo = TaylorOrder /. Flatten[{opts}] /. Options[DimensionExpand]; - a /. b_^c_ /; !FreeQ[c, dim] :> Normal[Series[b^c, {dim, fixp, oo}]] - ]; - -(* From Donoghue, Golowich and Holstein: *) - -DenominatorD[m10_, m20_, q0_, x_, opts___] := - m10*x + m20*(1 - x) - q0*x*(1 - x) - - I*(SmallEpsilon /. Flatten[{opts}] /. Options[FeynmanIntegral]); - - -(* Formula (5.4a): *) - -FeynmanIntegral[p10_, m10_, m20_, n1_, n2_, d_, d1_, - opts___] := - ((-1)^(n1 + n2)*I*Pi^(d1/2)* - Gamma[n1 + n2 - d/2]/(Gamma[n1]*Gamma[n2])* - IntegrateHeld[ - Global`x^(n1 - 1)*(1 - Global`x)^(n2 - 1)/ - DenominatorD1[m10, m20, p10, Global`x, - opts]^(*-*)(n1 + n2 - d1/2), {Global`x, 0, 1}]) /. - DenominatorD1 -> DenominatorD /. - IntegrateHeld -> (FCIntegrate /. Flatten[{opts}] /. - Options[FeynmanIntegral]); - -VeltmanB0[p10_, m10_, m20_, - opts___?OptionQ] /; (B0Evaluation /. Flatten[{opts}] /. Options[VeltmanB0]) === - "none" := - B0[p10, m10, m20]; - -VeltmanB0[p10_, m10_, m20_, - opts___?OptionQ] /; (B0Evaluation /. Flatten[{opts}] /. Options[VeltmanB0]) === - "direct1" := - ( - bdi = Dimension /. Flatten[{opts}] /. Options[VeltmanB0]; - dedi = DimensionExpand /. Flatten[{opts}] /. Options[VeltmanB0]; - dedim = If[ dedi, - bdi, - bdi, - dedi - ]; - iib0 =(*-*) - 1/(I*Pi^2)*(MassScale /. Flatten[{opts}] /. - Options[VeltmanB0])^(4 - dedim /. Flatten[{opts}] /. - Options[VeltmanB0])* - FeynmanIntegral[p10, (*Why were they swapped - not correct I think. 5/3-2001*) - (*m20, m10,*)m10, m20, 1, - 1, bdi, dedim, - FCIntegrate -> IntegrateHeld, opts] /. - If[ (ExpandGammas /. Flatten[{opts}] /. Options[VeltmanB0]), - Gamma[x_] -> - TruncatedGamma[ - x, (FixPoint /. Flatten[{opts}] /. - Options[VeltmanB0]), (TaylorOrder /. Flatten[{opts}] /. - Options[VeltmanB0])], - {} - ]; - If[ (DimensionExpand /. Flatten[{opts}] /. Options[VeltmanB0]) =!= False, - Evaluate[DimensionExpand[iib0, Dimension->dedim, opts]], - iib0 - ] /. - IntegrateHeld -> (FCIntegrate /. Flatten[{opts}] /. - Options[VeltmanB0]) (*Why? 26/2-2003*)(*/. - If[dedi =!= False && dedi =!= True, dedim -> bdi, {}]*)); - - -(* Expansion of the Gamma functions of (D-4) around 0 starting with the term -proprotional to the infinite 1/(D-4): *) - -ExpandGammas[a_, opts___] := - Block[ {fixp,oo,dim,eps,test}, - fixp = (FixPoint /. Flatten[{opts}] /. Options[ExpandGammas]); - oo = (TaylorOrder /. Flatten[{opts}] /. Options[ExpandGammas]); - dim = (Dimension /. Flatten[{opts}] /. Options[ExpandGammas]); - (*a /. Gamma[x_] :> TruncatedGamma[x, fixp, oo]*) - a /. Gamma[x_] :> If[ IntegerQ[test = x/.dim->4] && test<1, - Normal[Series[Gamma[x/.dim->4-eps], {eps, fixp, oo}]] /. eps -> 4-dim, - Gamma[test] - ] - ]; - - -(* Splitting up sums and getting constants out: *) - -IntegrateHeld[a_ + b_, {x_, s_, e_}] := - IntegrateHeld[a, {x, s, e}] + IntegrateHeld[b, {x, s, e}]; -IntegrateHeld[a_*b_, {x_, s_, e_}] /; FreeQ[a, x] := - a*IntegrateHeld[b, {x, s, e}]; -IntegrateHeld[a_, {x_, s_, e_}] /; FreeQ[a, x] := - a*(e - s); - - -(* The Leibniz rule: *) - -IntegrateHeld /: HoldPattern[D[IntegrateHeld[ex_, {x_, a_, b_}], d_]] := - - IntegrateHeld[D[ex, d], {x, a, b}]; -HoldPattern[aa_*Derivative[1, _List][IntegrateHeld][_, {b_, c_, d_}]] ^:= - IntegrateHeld[aa, {b, c, d}]; - - -(* The D-dimensional integral B0 from FeynCalc is related to the J function of -Gasser and Leutwyler (1983), "Chiral Perturbation Theory to One Loop", Ann. -Phys. 158, 142-210 by *) - -VeltmanB0[s_, m1s_, m1s_, opts___?OptionQ] /; (B0Evaluation /. Flatten[{opts}] /. - Options[VeltmanB0]) === "jbar" := - (16*Pi^2)*( - LeutwylerJBar[s, m1s, Sequence@@OptionsSelect[LeutwylerJBar, opts]] + - LeutwylerJ0[m1s, Sequence@@OptionsSelect[LeutwylerJ0, opts]]); - - -(* From J.Gasser and H. Leutwyler (1985), Nuclear Physics B250, - 465-516: *) - -VeltmanB0[s_, m1s_, m2s_, opts___?OptionQ] /; (B0Evaluation /. Flatten[{opts}] /. - Options[VeltmanB0]) === "jbar" := - (16*Pi^2)*( - LeutwylerJBar[s, m1s, m2s, Sequence@@OptionsSelect[LeutwylerJBar, opts]] + - LeutwylerJ0[m1s, m2s, Sequence@@OptionsSelect[LeutwylerJ0, opts]]); - - -(* Everything below is taken directly from Gasser and Leutwyler (no additional - factors): *) - -LeutwylerJBar[0, __, OptionsPattern[]] := - 0; - -LeutwylerJBar[s_, m1s_, opts___Rule] /; - (s =!= 0 && MemberQ[{"subthreshold", "physical", "general"}, - (LeutwylerJBarEvaluation /. Flatten[{opts}] /. - Options[LeutwylerJBar])]) := - 1/(16*Pi^2)*(sig*Log[(sig - 1)/(sig + 1)] + 2) /. - sig -> (LeutwylerSigma[s, m1s, ##]& @@ - OptionsSelect[LeutwylerSigma, opts, Options[LeutwylerJBar]]); - -(* Added 3/3-2000. From J.Gasser and H. Leutwyler (1985), Nuclear Physics B250, - 465-516: *) - -LeutwylerJBar[s_, m1s_, m2s_, opts___Rule] /; - (s =!= 0 && ((LeutwylerJBarEvaluation /. Flatten[{opts}] /. - Options[LeutwylerJBar]) === "subthreshold")) := - 1/(32*Pi^2)*(2 + delta/s*Log[m2s/m1s] - sigma/delta*Log[m2s/m1s] - - nu/s*Log[((s + nu)^2 - delta^2)/((s - nu)^2 - delta^2)]) /. - {delta -> m1s - m2s, sigma -> m1s + m2s, - nu -> Sqrt[(s - (Sqrt[m1s] + Sqrt[m2s])^2)(s - (Sqrt[m1s] - - Sqrt[m2s])^2)]}; - -(* JBar is defined by having the imaginary part equal to Pi/16 times the phase space, - see e.g. Knecht&Urech 1997 *) - -LeutwylerJBar[s_, m1s_, m2s_, opts___Rule] /; - (s =!= 0 && ((LeutwylerJBarEvaluation /. Flatten[{opts}] /. - Options[LeutwylerJBar]) === "physical")) := - 1/(32*Pi^2)*(2 + delta/s*Log[m2s/m1s] - sigma/delta*Log[m2s/m1s] + - nu/s*Log[((s - nu)^2 - delta^2)/((s + nu)^2 - delta^2)] + - 2*Pi*I*nu/s) /. - {delta -> m1s - m2s, sigma -> m1s + m2s, - nu -> Sqrt[(s - (Sqrt[m1s] + Sqrt[m2s])^2)(s - (Sqrt[m1s] - - Sqrt[m2s])^2)]}; - -(*Gasser&Leutwyler (A.7) can be integrated explicitly by Mathematica*) -(*g[m12_, m22_, x_, s_] := m12 - s x(1 - x) - (m12 - m22)x; --(16\[Pi]^2)^(-1)Integrate[ - Log[g[m12, m22, x, s]/g[m12, m22, x, 0]], {x, 0, 1}] // FullSimplify*) - -LeutwylerJBar[s_, m1s_, m2s_, opts___Rule] /; - (s =!= 0 && ((LeutwylerJBarEvaluation /. Flatten[{opts}] /. - Options[LeutwylerJBar]) === "general")) := - ((-(m1s - m2s)^2 + (m1s + m2s)*s)*Log[-m1s] + ((m1s - m2s)^2 - (m1s + m2s)*s)*Log[-m2s] + - (m1s - m2s)*(2*s + I*Sqrt[-m1s^2 - (m2s - s)^2 + 2*m1s*(m2s + s)]* - (Log[1 - (I*(m1s - m2s - s))/Sqrt[-m1s^2 - (m2s - s)^2 + 2*m1s*(m2s + s)]] - - Log[1 + (I*(m1s - m2s - s))/Sqrt[-m1s^2 - (m2s - s)^2 + 2*m1s*(m2s + s)]] - - Log[1 - (I*(m1s - m2s + s))/Sqrt[-m1s^2 - (m2s - s)^2 + 2*m1s*(m2s + s)]] + - Log[1 + (I*(m1s - m2s + s))/Sqrt[-m1s^2 - (m2s - s)^2 + 2*m1s*(m2s + s)]])))/ - (32*(m1s - m2s)*Pi^2*s); - - -LeutwylerJ0[s_, opts___Rule] /; - (ExplicitLeutwylerJ0 /. Flatten[{opts}] /. - Options[LeutwylerJ0]) := - -2*LeutwylerLambda[##]& @@ OptionsSelect[LeutwylerLambda, opts] - - 1/(16*Pi^2)*(Log[s/(MassScale /. Flatten[{opts}] /. - Options[LeutwylerJ0])^2] + 1); - - -(* Added 3/3-2000. From J.Gasser and H. Leutwyler (1985), Nuclear Physics B250, - 465-516: *) - -LeutwylerJ0[m1s_, m2s_, opts___Rule] /; (ExplicitLeutwylerJ0 /. Flatten[{opts}] /. - Options[LeutwylerJ0]) := - -2*LeutwylerLambda[##]& @@ OptionsSelect[LeutwylerLambda, opts] - - 1/(16*Pi^2)* - (m1s*Log[m1s/(MassScale /. Flatten[{opts}] /. Options[LeutwylerJ0])^2] - - m2s*Log[m2s/(MassScale /. Flatten[{opts}] /. Options[LeutwylerJ0])^2])/ - (m1s - m2s); - -LeutwylerSigma[s_, m1s_, opts___] /; (ExplicitLeutwylerSigma /. Flatten[{opts}] /. - Options[LeutwylerSigma]) := - Sqrt[1 - 4*m1s/s]; - -LeutwylerLambda[opts___Rule | opts___List] /; - (ExplicitLeutwylerLambda /. Flatten[{opts}] /. - Options[LeutwylerLambda]) := - 1/(16*Pi^2)*(MassScale /. Flatten[{opts}] /. - Options[LeutwylerLambda])^((Dimension /. Flatten[{opts}] /. - Options[LeutwylerLambda]) - - 4)*(1/((Dimension /. Flatten[{opts}] /. Options[LeutwylerLambda]) - - 4) - (Log[4*Pi] - EulerGamma + 1)/2); - - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* C0 *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -VeltmanC0[p10_, p20_, p12_, m10_, m20_, m30_, - opts___] /; (C0Evaluation /. Flatten[{opts}] /. Options[VeltmanC0]) === - "none" := - C0[p10, p20, p12, m10, m20, m30]; - -Spence[x_] := - PolyLog[2, x]; - - -(* VeltmanC0 is taken directly from 't Hooft and Veltman (divided with a factor -I Pi^2 as in Passarino and Veltman): *) - -alpha[a_, b_, c_, - n_] := - (alpsol = Solve[a*\[Alpha]^2 + b*\[Alpha] + c == 0, \[Alpha]]; - If[ alpsol === {}, - (FCPrint[1, "Warning : no roots found, using 0"]; - 0), - \[Alpha] /. alpsol[[3 - 2*n]] - ]); - -alpha1[a_, b_, c_, - n_] := - (alpsol = Solve[a*\[Alpha]^2 + b*\[Alpha] + c == 0, \[Alpha]]; - If[ alpsol === {}, - 0, - \[Alpha] /. alpsol[[3 - 2*n]] - ]); - - -(* 't Hooft and Veltman use the metric (-1,1,1,1), so the definitions from -formulae (5.2) are changed a little: *) - -veaa[p20_] := - p20; -vebb[p10_] := - p10; -vecc[p10_, p20_, p12_] := - p12 - p10 - p20; -vedd[p20_, m20_, m30_] := - m20 - m30 - p20; -veee[p10_, p12_, p20_, m10_, m20_] := - m10 - m20 - p10 - vecc[p10, p20, p12]; -veff[m30_, eps_] := - m30 - I*eps; - - -(* This is formula (5.2): *) - -VeltmanC0[p10_, p20_, p12_, m10_, m20_, m30_, - opts___] /; (C0Evaluation /. Flatten[{opts}] /. Options[VeltmanC0]) === - "direct1" := - Block[ {a = veaa[p20], b = vebb[p10], c = vecc[p10, p20, p12], - d = vedd[p20, m20, m30], e = veee[p10, p12, p20, m10, m20], - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanC0]), - f = veff[m30, eps]}, - IntegrateHeld[(a*x^2 + b*y^2 + c*x*y + d*x + e*y + f)^(-1), {x, 0, - 1}, {y, 0, x}, ##] & @@ - Union[OptionsSelect[NIntegrate, opts], - OptionsSelect[Integrate, opts]] /. - IntegrateHeld -> (FCIntegrate /. Flatten[{opts}] /. - Options[VeltmanC0]) - ]; - - -(* This is formula (5.3): *) - -VeltmanC0[p10_, p20_, p12_, m10_, m20_, m30_, - opts___] /; (C0Evaluation /. Flatten[{opts}] /. Options[VeltmanC0]) === - "direct2" := - Block[ {a = veaa[p20], b = vebb[p10], c = vecc[p10, p20, p12], - d = vedd[p20, m20, m30], e = veee[p10, p12, p20, m10, m20], - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanC0]), - f = veff[m30, eps], alp = alpha[b, c, a, 1]}, - IntegrateHeld[(1 - alp)/((c + 2*alp*b)*(1 - alp)*y + d + e*alp)* - Log[(b*(1 - alp)^2*y^2 + (1 - alp)*(c + 2*alp*b + e)*y + d + - e*alp + - f)/((b*(1 - alp)^2 + (c + 2*alp*b)*(1 - alp))* - y^2 + (e*(1 - alp) + d + e*alp)*y + f)] + - alp/(-(c + 2*alp*b)*alp*y + d + e*alp)* - Log[(b*alp^2*y^2 - alp*(c + 2*alp*b + e)*y + d + e*alp + - f)/((alp^2*b - (c + 2*alp*b)*alp)* - y^2 + (e*alp + d - e*alp)*y + f)], {y, 0, - 1}, ##] & @@ - Union[OptionsSelect[NIntegrate, opts], - OptionsSelect[Integrate, opts]] /. - IntegrateHeld -> (FCIntegrate /. Flatten[{opts}] /. - Options[VeltmanC0]) - ]; - - -(* This is formula (5.6): *) - -VeltmanC0[p10_, p20_, p12_, m10_, m20_, m30_, - opts___] /; (C0Evaluation /. Flatten[{opts}] /. Options[VeltmanC0]) === - "direct3" := - Block[ {a = veaa[p20], b = vebb[p10], c = vecc[p10, p20, p12], - d = vedd[p20, m20, m30], e = veee[p10, p12, p20, m10, m20], - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanC0]), - f = veff[m30, eps], alp = alpha[b, c, a, 1], - y0 = -(d + e*alp)/(c + 2*alp*b), y1 = y0 + alp, y2 = y0/(1 - alp), - y3 = -y0/alp}, - IntegrateHeld[ - 1/((c + 2*alp*b)*y + d + e*alp + 2*a + c*alp)*(Log[ - b*y^2 + (c + e)*y + a + d + f] - - Log[b*y1^2 + (c + e)*y1 + a + d + f]) - (1 - - alp)/((c + 2*alp*b)*(1 - alp)*y + d + - e*alp)*(Log[(a + b + c)*y^2 + (e + d)*y + f] - - Log[(a + b + c)*y2^2 + (e + d)*y2 + f]) - - alp/(-(c + 2*alp*b)*alp*y + d + e*alp)*(Log[a*y^2 + d*y + f] - - Log[a*y3^2 + d*y3 + f]), {y, 0, 1}, ##] & @@ - Union[OptionsSelect[NIntegrate, opts], - OptionsSelect[Integrate, opts]] /. - IntegrateHeld -> (FCIntegrate /. Flatten[{opts}] /. - Options[VeltmanC0]) - ]; -theta[x_] := - If[ x < 0, - 0, - 1 - ]; - - -(* In the 't Hooft and Veltman article, the eta (formula (2.4)) is to enforce -the cut along the negative real axis: *) - -(* The alternative Im (Im1) below is to correct a Mathematica bug causing -Im[...] sometimes to have a small imginary part ... *) - -Im1[x_] := - Sign[Im[x]]*Abs[Im[x]]; -eta[a_, b_] := - 2*Pi*I*(theta[-Im1[a]]*theta[-Im1[b]]*theta[Im1[a*b]] - - theta[Im1[a]]*theta[Im1[b]]*theta[-Im1[a*b]]); -rr[y0_, y1_] := - Spence[y0/(y0 - y1)] - Spence[(y0 - 1)/(y0 - y1)] + - eta[-y1, 1/(y0 - y1)]*Log[y0/(y0 - y1)] - - eta[1 - y1, 1/(y0 - y1)]*Log[(y0 - 1)/(y0 - y1)]; - - -(* The S_3 of appendix B of 't Hooft and Veltman: *) - -s3[a_, b_, c_, yy0_, opts___] := - (epsi = -Sign[Im[c]]; - delta = -Sign[Im[a*yy0^2 + b*yy0 + c]]; - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanC0]); - yy1 = alpha[a, b, c, 1]; - yy2 = alpha[a, b, c, 2]; - imzero1 = alpha1[Im[a], Im[b], Im[c], 1]; - imzero2 = alpha1[Im[a], Im[b], Im[c], 2]; - If[ Im[imzero1] === 0, - If[ (imzero1 < 1 && imzero1 > 0), - FCPrint[1, "Warning : Integral decomposition being used outside range of \ -validity - ", imzero1] - ] - ]; - If[ Im[imzero2] === 0, - If[ (imzero2 < 1 && imzero2 > 0), - FCPrint[1, "Warning : Integral decomposition being used outside range of \ -validity - ", imzero2] - ] - ]; - rr[yy0, yy1] + - rr[yy0, yy2] - (eta[-yy1, -yy2] - eta[yy0 - yy1, yy0 - yy2] - - eta[a - I*epsi*eps, 1/(a - I*delta*eps)])*Log[(yy0 - 1)/yy0]); - - -(* This is formula (5.6) using the above S_3: *) - -VeltmanC0[p10_, p20_, p12_, m10_, m20_, m30_, - opts___] /; (C0Evaluation /. Flatten[{opts}] /. Options[VeltmanC0]) === - "Spence" := - Block[ {a = veaa[p20], b = vebb[p10], c = vecc[p10, p20, p12], - d = vedd[p20, m20, m30], e = veee[p10, p12, p20, m10, m20], - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanC0]), - f = veff[m30, eps], alp = alpha[b, c, a, 1], - y0 = -(d + e*alp)/(c + 2*alp*b), y1 = y0 + alp, y2 = y0/(1 - alp), - y3 = -y0/alp}, - 1/(c + 2*alp*b)* - s3[b, c + e, a + d + f, -(d + e*alp + 2*a + c*alp)/(c + 2*alp*b), - opts] - (1 - alp)/((c + 2*alp*b)*(1 - alp))* - s3[a + b + c, e + d, f, -(d + e*alp)/((c + 2*alp*b)*(1 - alp)), - opts] - alp/(-(c + 2*alp*b)*alp)* - s3[a, d, f, (d + e*alp)/((c + 2*alp*b)*alp), opts] - ]; - - -(* For later use (the D0) we give the three point function in terms of the -a,..,f directly: *) - -vC0[a_, b_, c_, d_, e_, f_, opts___] := - (alp = alpha[b, c, a, 1]; - 1/(c + 2*alp*b)* - s3[b, c + e, a + d + f, -(d + e*alp + 2*a + c*alp)/(c + 2*alp*b), - opts] - (1 - alp)/((c + 2*alp*b)*(1 - alp))* - s3[a + b + c, e + d, f, -(d + e*alp)/((c + 2*alp*b)*(1 - alp)), - opts] - alp/(-(c + 2*alp*b)*alp)* - s3[a, d, f, (d + e*alp)/((c + 2*alp*b)*alp), opts]); - - -(* The S_3 of appendix B of 't Hooft and Veltman using Mathematica's symbolic -integration: *) - -(* (*Integrate[ - 1/(y - y0)*(Log[a*y^2 + b*y + c] - Log[a*y0^2 + b*y0 + c]), {y, 0, 1}] // - InputForm*) *) - -s33[a_, b_, c_, y0_, opts___] := - s33[a, b, c, y0, opts] = - Log[a + b + c]*Log[1 - y0] - Log[(2*a + b - Sqrt[b^2 - 4*a*c])/(2*a)]* - Log[1 - y0] - Log[(2*a + b + Sqrt[b^2 - 4*a*c])/(2*a)]*Log[1 - y0] - - Log[c]*Log[-y0] + Log[(b - Sqrt[b^2 - 4*a*c])/(2*a)]*Log[-y0] + - Log[(b + Sqrt[b^2 - 4*a*c])/(2*a)]*Log[-y0] - - Log[(b - Sqrt[b^2 - 4*a*c])/(2*a)]* - Log[(2*a*y0)/(b - Sqrt[b^2 - 4*a*c] + 2*a*y0)] + - Log[(2*a + b - Sqrt[b^2 - 4*a*c])/(2*a)]* - Log[(2*(-a + a*y0))/(b - Sqrt[b^2 - 4*a*c] + 2*a*y0)] - - Log[(b + Sqrt[b^2 - 4*a*c])/(2*a)]* - Log[(2*a*y0)/(b + Sqrt[b^2 - 4*a*c] + 2*a*y0)] + - Log[(2*a + b + Sqrt[b^2 - 4*a*c])/(2*a)]* - Log[(2*(-a + a*y0))/(b + Sqrt[b^2 - 4*a*c] + 2*a*y0)] - - Log[1 - y0]*Log[c + b*y0 + a*y0^2] + Log[-y0]*Log[c + b*y0 + a*y0^2] - - PolyLog[2, (-b + Sqrt[b^2 - 4*a*c])/(-b + Sqrt[b^2 - 4*a*c] - 2*a*y0)] + - PolyLog[2, (-2*a - b + Sqrt[b^2 - 4*a*c])/ - (-b + Sqrt[b^2 - 4*a*c] - 2*a*y0)] - - PolyLog[2, (b + Sqrt[b^2 - 4*a*c])/(b + Sqrt[b^2 - 4*a*c] + 2*a*y0)] + - PolyLog[2, (2*a + b + Sqrt[b^2 - 4*a*c])/(b + Sqrt[b^2 - 4*a*c] + 2*a*y0)]; - - -(* This is formula (5.6) using the above S_3: *) - -VeltmanC0[p10_, p20_, p12_, m10_, m20_, m30_, - opts___] /; (C0Evaluation /. Flatten[{opts}] /. Options[VeltmanC0]) === - "direct4" := - Block[ {a = veaa[p20], b = vebb[p10], c = vecc[p10, p20, p12], - d = vedd[p20, m20, m30], e = veee[p10, p12, p20, m10, m20], - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanC0]), - f = veff[m30, eps], alp = alpha[b, c, a, 1], - y0 = -(d + e*alp)/(c + 2*alp*b), y1 = y0 + alp, y2 = y0/(1 - alp), - y3 = -y0/alp}, - 1/(c + 2*alp*b)* - s33[b, c + e, a + d + f, -(d + e*alp + 2*a + c*alp)/(c + 2*alp*b), - opts] - (1 - alp)/((c + 2*alp*b)*(1 - alp))* - s33[a + b + c, e + d, f, -(d + e*alp)/((c + 2*alp*b)*(1 - alp)), - opts] - alp/(-(c + 2*alp*b)*alp)* - s33[a, d, f, (d + e*alp)/((c + 2*alp*b)*alp), opts] - ]; - - -(* This is formulas (E.1-E.3) using 2 Spence functions: *) - -VeltmanC0[mmm10_, mmm30_, ss_, m10_, m20_, m30_, - opts___] /; (C0Evaluation /. Flatten[{opts}] /. Options[VeltmanC0]) === - "infrared" := - If[ mmm10=!=m10 || mmm30=!=m30, - Message[VeltmanC0::nodef], - Block[ {s,y1,y2,eps,f1,f2,res,yy1,yy2}, - s = -ss; - yy1 = alpha[-s, (s + m30 - m10), m10, 2]; - yy2 = alpha[-s, (s + m30 - m10), m10, 1]; - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanC0]); - f1 = (-1/(s*(y1 - y2)))*(Log[(y1 - 1)/y1] - Log[(y2 - 1)/y2]); - f2 = (f1*Log[-s - I*eps] - - 1/(s*(y1 - y2))*(1/2*(Log[1 - y1])^2 - 1/2*(Log[-y1])^2 - - 1/2*(Log[1 - y2])^2 + 1/2*(Log[-y2])^2 - - Log[1 - y2]*Log[1 - y1] + Log[-y2]*Log[-y1] + - 2*Log[(y1 - 1)/y1]*Log[y1 - y2] - - 2*Spence[(y1 - 1)/(y1 - y2)] + - 2*Spence[y1/(y1 - y2)])); - res = -1/2*(f1*Log[m20] - f2); - (*Symmetrization seems to be necessary??!?*) - ((res/.{y1->yy1,y2->yy2})+(res/.{y1->yy2,y2->yy1}))/2 - ] - ]; - -(* From Knecht&Urech *) (*Notice that their dilog[x] is -PolyLog[2,1-x]*) - -VeltmanC0[mm10_,mm30_,s_,m10_,m20_,m30_, - opts___?OptionQ]/;(C0Evaluation/.Flatten[{opts}]/.Options[VeltmanC0])=== - "infrared1" := - If[ Union[{mm10,mm30,m10,m30}]=!={m10}, - Message[VeltmanC0::nodef1], - Block[ {sig}, - sig = - LeutwylerSigma[s,m10, - Sequence@@ - OptionsSelect[LeutwylerSigma,opts]]; - (*-*) - 1/(2s sig)(4(-PolyLog[ - 2,1-(1-sig)/(1+sig)])+Pi^2/3+ - Log[(sig-1)/(sig+1)]^2+2(Log[-s/m10]- - Log[m20/m10]+2Log[sig])Log[(sig-1)/(sig+1)]) - ] - ]; - -VeltmanC0[mm10_,mm30_,s_,m10_,m20_,m30_, - opts___?OptionQ]/;(C0Evaluation/.Flatten[{opts}]/.Options[VeltmanC0])=== - "infrared2" := - If[ Union[{mm10,mm30,m10,m30}]=!={m10}, - Message[VeltmanC0::nodef1], - Block[ {sig}, - sig = - LeutwylerSigma[s,m10, - Sequence@@ - OptionsSelect[LeutwylerSigma,opts]]; - (*-*) - 1/(2s sig)(4(-PolyLog[ - 2,-(1-sig)/(1+sig)])+4Pi^2/3+ - Log[(1-sig)/(1+sig)]^2+2(Log[s/m10]- - Log[m20/m10]+2Log[sig])(Log[(1-sig)/(1+sig)]+I Pi)) - ] - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* D0 *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -VeltmanD0[p10_, p20_, p30_, p12_, p13_, p23_, m10_, m20_, m30_, m40_, - opts___] /; (D0Evaluation /. Flatten[{opts}] /. Options[VeltmanD0]) === - "none" := - D0[p10, p20, p30, p12, p13, p23, m10, m20, m30, m40]; - - -(* In the following, p10,... are the p1^2,... appearing in the 't Hooft and -Veltman article (that is, with the Pauli metric (-1,-1,-1,1)). *) - -(* Formulas (6.6) to 6.9): *) - -(* {moms} is to be {p10,p20,p30,p12,p13,p23}. *) - -pp2[i_, j_, moms__] := - (ppl[1, 2] = {moms}[[4]]; - ppl[1, 3] = {moms}[[5]]; - ppl[2, 3] = {moms}[[6]]; - ppl[r_, r_] = 0; - ppsq[1] := - {moms}[[1]]; - ppsq[2] := - {moms}[[2]]; - ppsq[3] := - {moms}[[3]]; - (Sum[ppsq[rep], {rep, i, j - 1}] + - 2*Sum[ppl[rep, rep1], {rep1, i, j - 1}, {rep, i, rep1}])); - - -(* {masses} is to be {m1^2,m2^2,m3^2,m4^2}. *) - -ll[i_, j_, moms__, {masses__}] := - pp2[i, j, moms] + {masses}[[i]] + {masses}[[j]]; -aa[1, moms__, {masses__}] := - (res = - aa[2, moms, {masses}]*(ll[1, 2, moms, {masses}] + - Sqrt[ll[1, 2, moms, {masses}]^2 - - 4*{masses}[[1]]*{masses}[[2]]])/(2*{masses}[[1]]); - If[ ! NumericQ[res] || Im[res] === 0, - res, - FCPrint[1, "Warning: A[1] not real - ", res]; - res - ]); - - -(* The final result is independent of A_2, so we just set it to some value: *) - -aa[2, __, {__}] := - 10000000; -aa[3, moms__, {masses__}] := - (res = ({masses}[[2]]* - aa[2, moms, {masses}]^2 - {masses}[[1]]* - aa[1, moms, {masses}]^2)/(ll[2, 3, moms, {masses}]* - aa[2, moms, {masses}] - - ll[1, 3, moms, {masses}]*aa[1, moms, {masses}]); - If[ ! NumericQ[res] || Im[res] === 0, - res, - FCPrint[1, "Warning: A[3] not real - ", res]; - res - ]); -aa[4, moms__, {masses__}] := - (res = ({masses}[[2]]* - aa[2, moms, {masses}]^2 - {masses}[[1]]* - aa[1, moms, {masses}]^2)/(ll[2, 4, moms, {masses}]* - aa[2, moms, {masses}] - - ll[1, 4, moms, {masses}]*aa[1, moms, {masses}]); - If[ ! NumericQ[res] || Im[res] === 0, - res, - FCPrint[1, "Warning: A[4] not real - ", res]; - res - ]); - - -(* This is formula (6.6): *) - -qq2[i_, j_, p10_, p20_, p30_, p12_, p13_, p23_, m10_, m20_, m30_, - m40_] := - (pp2[i, j, p10, p20, p30, p12, p13, - p23] + {m10, m20, m30, m40}[[i]] + {m10, m20, m30, m40}[[j]])* - aa[i, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[j, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}] - {m10, m20, m30, m40}[[i]]* - aa[i, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2 - {m10, - m20, m30, m40}[[j]]* - aa[j, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2; - - -(* Evaluation using two three point functions: *) - -(* We also put on a minus on the C0 functions due to their definition as the -negative of the 't Hooft and Veltman definition: *) - -(* All in all, I didn't at all achieve to get agreement with FF - the Pi^2 -factor is taken from nowhere - the minuses are not put on after all - just -seems to improve agreement with FF: *) - -VeltmanD0[pf10_, pf20_, pf30_, pp10_, pp20_, pp30_, m10_, m20_, m30_, m40_, - opts___] /; (D0Evaluation /. Flatten[{opts}] /. Options[VeltmanD0]) === - "C0" := - Block[ {$MaxExtraPrecision = - 4000,(*The minus (from the Bjoerken - - Drell metric (-1, -1, -1, 1)) is put on here :*)p10 = pf10, - p20 = pf20, p30 = pf30, p12 = (pp20 - p10 - p20)/2, - p23 = (pp30 - p20 - p30)/2, - p13 = (pp10 - p10 - p20 - p30 - 2*p12 - 2*p23)/2, - mm10 = m10* - aa[1, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm20 = m20* - aa[2, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm30 = - m30*aa[3, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm40 = m40* - aa[4, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - a = -qq2[3, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - b = -qq2[2, 3, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - c = -qq2[2, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] + - qq2[2, 3, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] + - qq2[3, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - d = mm30 - mm40 + - qq2[3, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - e = mm20 - mm30 + - qq2[2, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] - - qq2[3, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanD0]), - f = mm40 - I*eps, - g = -qq2[1, 2, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - h = -qq2[1, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] - - qq2[2, 3, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] + - qq2[1, 3, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] + - qq2[2, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - j = -qq2[1, 3, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] + - qq2[1, 2, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] + - qq2[2, 3, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - k = mm10 - mm20 + - qq2[1, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] - - qq2[2, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40], - optss = Flatten[{opts}]}, - firstc0 = -vC0[a, b, c, d, e, f, ##] & @@ - Join[optss, Options[VeltmanD0]]; - secondc0 = -vC0[a, b, c, d, (e + k), f, ##] & @@ - Join[optss, Options[VeltmanD0]]; - kk = k; - afactors = {aa[1, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}], - aa[2, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}], - aa[3, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}], - aa[4, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]};(*?? ??*) - Pi^2*(Times @@ afactors)/k*(firstc0 - secondc0) - ]; -llaa[i_, j_, - moms__, {masses__}] := - -ll[i, j, moms, {masses}]*aa[i, moms, {masses}]* - aa[j, moms, {masses}] + {masses}[[i]]* - aa[i, moms, {masses}]^2 + {masses}[[j]]*aa[j, moms, {masses}]^2; -laa[i_, j_, moms__, {masses__}] := - ll[i, j, moms, {masses}]*aa[i, moms, {masses}]*aa[j, moms, {masses}] - - 2*{masses}[[j]]*aa[j, moms, {masses}]^2; - - -(* This is formula (6.15): *) - -sss[i_, j_, k_, p10_, p20_, p30_, p12_, p13_, p23_, m10_, m20_, m30_, m40_, - opts___] := - (rootss = - Solve[-qq2[i, j, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40]* - x^2 + (qq2[i, j, p10, p20, p30, p12, p13, p23, m10, m20, m30, - m40] + qq2[k, j, p10, p20, p30, p12, p13, p23, m10, m20, - m30, m40] - - qq2[k, i, p10, p20, p30, p12, p13, p23, m10, m20, m30, - m40])*x - - qq2[k, j, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40] - - I*(SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanC0]) == 0, x]; - x1 = x /. Flatten[rootss][[1]]; - x2 = x /. Flatten[rootss][[-1]]; - -I* - Pi/(-qq2[i, j, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40]*(x1 - - x2))*(Log[(x1 - 1)/x1] - Log[(x2 - 1)/x2])); -ss[p10_, p20_, p30_, p12_, p13_, p23_, {m10_, m20_, m30_, m40_}, opts___] := - Sign[(aa[1, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]/ - aa[2, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}] - - ll[1, 2, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]/(2*m10))]*(theta[ - Re[aa[3, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[4, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]]]* - sss[3, 4, 2, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40, - opts] - theta[ - Re[-aa[3, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]]]*(sss[2, 4, 3, p10, p20, p30, - p12, p13, p23, m10, m20, m30, m40, opts] + - sss[2, 3, 4, p10, p20, p30, p12, p13, p23, m10, m20, m30, m40, - opts])); -yminus[i_, j_, moms__, {masses__}, - ie_] := - (roots = (y /. #) & /@ - Flatten[Solve[ - llaa[i, j, moms, {masses}]*y^2 + - laa[i, j, moms, {masses}]*y + {masses}[[j]]^2* - aa[j, moms, {masses}]^2 - I*ie == 0, y]]; - If[ NumericQ[roots[[1]]] && NumericQ[roots[[-1]]], - If[ Im[roots[[1]]] < 0, - roots[[1]], - roots[[-1]] - ], - roots[[1]] - ]); -yplus[i_, j_, moms__, {masses__}, - ie_] := - (roots = (y /. #) & /@ - Flatten[Solve[ - llaa[i, j, moms, {masses}]*y^2 + - laa[i, j, moms, {masses}]*y + {masses}[[j]]^2* - aa[j, moms, {masses}]^2 - I*ie == 0, y]]; - If[ NumericQ[roots[[1]]] && NumericQ[roots[[-1]]], - If[ Im[roots[[1]]] > 0, - roots[[1]], - roots[[-1]] - ], - roots[[-1]] - ]); - - -(* The S_3 of appendix B of 't Hooft and Veltman: *) - -s3D[a_, b_, c_, yy0_, opts___] := - (epsi = -Sign[Im[c]]; - delta = -Sign[Im[a*yy0^2 + b*yy0 + c]]; - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanD0]); - yy1 = alpha[a, b, c, 1]; - yy2 = alpha[a, b, c, 2]; - imzero1 = alpha1[Im[a], Im[b], Im[c], 1]; - imzero2 = alpha1[Im[a], Im[b], Im[c], 2]; - If[ Im[imzero1] === 0, - If[ (imzero1 < 1 && imzero1 > 0), - FCPrint[1, "Warning : Integral decomposition being used outside range of \ -validity - ", imzero1] - ] - ]; - If[ Im[imzero2] === 0, - If[ (imzero2 < 1 && imzero2 > 0), - FCPrint[1, "Warning : Integral decomposition being used outside range of \ -validity - ", imzero2] - ] - ]; - rr[yy0, yy1] + - rr[yy0, yy2] - (eta[-yy1, -yy2] - eta[yy0 - yy1, yy0 - yy2] - - eta[a - I*epsi*eps, 1/(a - I*delta*eps)])*Log[(yy0 - 1)/yy0]); - - -(* 't Hooft and Veltman use the metric (-1,1,1,1), so the definitions are -changed a little (dot products change sign): *) - -heaa[p30_] := - -p30; -hebb[p20_] := - -p20; -hecc[p23_] := - -2*p23; -hedd[p30_, m30_, m40_] := - m30 - m40 + p30; -heee[p20_, p23_, m20_, m30_] := - m20 - m30 + 2*p23 + p20; -heff[m40_, eps_] := - m40 - I*eps; -hegg[p10_] := - -p10; -hehh[p13_] := - -2*p13; -hejj[p12_] := - -2*p12; -hekk[p10_, p12_, p13_, m10_, m20_] := - m10 - m20 + 2*p12 + 2*p13 + p10; - - -(* This is formula (6.12) using the above S_3: *) - -(* We have to extract the 't Hooft and Veltman external momenta from the -FeynCalc input momenta: *) - -(* p12 is p1*p2 etc. *) - -VeltmanD0[pf10_, pf20_, pf30_, pp10_, pp20_, pp30_, m10_, m20_, m30_, m40_, - opts___] /; (D0Evaluation /. Flatten[{opts}] /. Options[VeltmanD0]) === - "Spence" := - Block[ {(*The minus (from the Bjoerken - - Drell metric (-1, -1, -1, 1)) is put on here :*)p10 = pf10, - p20 = -pf20, p30 = -pf30, p12 = -(pp20 - p10 - p20)/2, - p23 = -(pp30 - p20 - p30)/2, - p13 = -(pp10 - p10 - p20 - p30 - 2*p12 - 2*p23)/2, - mm10 = m10* - aa[1, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm20 = m20* - aa[2, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm30 = m30* - aa[3, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm40 = m40* - aa[4, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - a = heaa[p30], b = hebb[p20], c = hecc[p23], - d = hedd[p30, mm30, mm40], e = heee[p20, p23, mm20, mm30], - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanD0]), - f = heff[mm40, eps], g = hegg[p10], h = hehh[p13], j = hejj[p12], - k = hekk[p10, p12, p13, mm10, mm20], alp = alpha[b, c, a, 1], - y1 = -(d + e*alp)/((c + 2*alp*b)*(1 - alp)), - y2 = (d + e*alp)/((c + 2*alp*b)*alp), - y3 = -(d + e*alp + c*alp + 2*a)/(c + 2*alp*b), - y4 = -(d + e*alp + k*alp)/((c + 2*alp*b)*(1 - alp)), - y5 = (d + e*alp + k*alp)/((c + 2*alp*b)*alp), - y6 = -(d + e*alp + k*alp + c*alp + 2*a)/(c + 2*alp*b)}, - (y[1] = y1; - y[2] = y2; - y[3] = y3; - y[4] = y4; - y[5] = y5; - y[6] = y6; - rr[i_, j_, k_, np10_, np20_, np30_, np12_, np13_, - np23_, {nm10_, nm20_, nm30_, - nm40_}] := - -theta[ - Re[-aa[i, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}]* - aa[j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}]]]/(c + - 2*alp*b)*(Pi^2 + - I*Pi*theta[ - Im[y[k]]]*(2* - Log[y[k] - - yminus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, eps]] - - Log[(y[k] - - yminus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, eps])]*(y[k] - - yplus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, eps])) - - I*Pi*theta[-Im[y[k]]]*(2* - Log[y[k] - - yplus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, eps]] - - Log[y[k] - - yminus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, eps]]*(y[k] - - yplus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, eps]))); - aa[1, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[2, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[3, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[4, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]/ - k*(-1/(c + 2*alp*b)* - s3D[llaa[2, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - laa[2, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - m40*aa[4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]^2 - I*eps, y[1], opts] + - 1/(c + 2*alp*b)* - s3D[llaa[3, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - laa[3, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - m40*aa[4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]^2 - I*eps, y[2], opts] + - 1/(c + 2*alp*b)* - s3D[llaa[2, 3, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - laa[2, 3, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - m30*aa[4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]^2 - I*eps, y[3], opts] + - 1/(c + 2*alp*b)* - s3D[llaa[1, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - laa[1, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - m40*aa[4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]^2 - I*eps, y[4], opts] + - 1/(-c + 2*alp*b)* - s3D[llaa[3, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - laa[3, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - m40*aa[4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]^2 - I*eps, y[5], opts] - - 1/(c + 2*alp*b)* - s3D[llaa[1, 3, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - laa[1, 3, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}], - m30*aa[4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]^2 - I*eps, y[6], opts] - - rr[2, 4, 1, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}] + - rr[3, 4, 2, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}] + - rr[2, 3, 3, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}] + - rr[1, 4, 4, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}] - - rr[3, 4, 5, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}] - - rr[1, 3, 6, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}] + - theta[Re[-aa[1, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]* - aa[2, p10, p20, p30, p12, p13, - p23, {m10, m20, m30, m40}]]]* - ss[p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}, - opts])) - ]; - - -(* This is formula (6.10): *) - -VeltmanD0[pf10_, pf20_, pf30_, pp10_, pp20_, pp30_, m10_, m20_, m30_, m40_, - opts___] /; (D0Evaluation /. Flatten[{opts}] /. Options[VeltmanD0]) === - "direct1" := - Block[ {(*The minus (from the Bjoerken - - Drell metric (-1, -1, -1, 1)) is put on here :*)p10 = pf10, - p20 = -pf20, p30 = -pf30, p12 = -(pp20 - p10 - p20)/2, - p23 = -(pp30 - p20 - p30)/2, - p13 = -(pp10 - p10 - p20 - p30 - 2*p12 - 2*p23)/2, - mm10 = m10* - aa[1, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm20 = m20* - aa[2, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm30 = m30* - aa[3, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - mm40 = m40* - aa[4, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]^2, - a = heaa[p30], b = hebb[p20], c = hecc[p23], - d = hedd[p30, mm30, mm40], e = heee[p20, p23, mm20, mm30], - eps = (SmallEpsilon /. Flatten[{opts}] /. Options[VeltmanD0]), - f = heff[mm40, eps], g = hegg[p10], h = hehh[p13], j = hejj[p12], - k = hekk[p10, p12, p13, mm10, mm20], alp = alpha[b, c, a, 1], - y1 = -(d + e*alp)/((c + 2*alp*b)*(1 - alp)), - y2 = (d + e*alp)/((c + 2*alp*b)*alp), - y3 = (d + e*alp + c*alp + 2*a)/(c + 2*alp*b), - y4 = (d + e*alp + k*alp)/((c + 2*alp*b)*(1 - alp)), - y5 = (d + e*alp + k*alp)/((-c + 2*alp*b)*alp), - y6 = (d + e*alp + k*alp + c*alp + 2*a)/(c + 2*alp*b)}, - (y[1] = y1; - y[2] = y2; - y[3] = y3; - y[4] = y4; - y[5] = y5; - y[6] = y6; - rr[i_, j_, k_, np10_, np20_, np30_, np12_, np13_, - np23_, {nm10_, nm20_, nm30_, - nm40_}] := - -theta[ - Re[-aa[i, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}]* - aa[k, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}]]]/(c + - 2*alp*b)*(Pi^2 + - I*Pi*theta[ - Re[Im[y[k]]*(2* - Log[y[k] - - yminus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, eps]] - - Log[(y[k] - - yminus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, - eps])*(y[k] - - yplus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, - eps])])]] - - I*Pi*theta[ - Re[-Im[y[k]]*(2* - Log[y[k] - - yplus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, eps]] - - Log[(y[k] - - yminus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, - eps])*(y[k] - - yplus[i, j, np10, np20, np30, np12, np13, - np23, {nm10, nm20, nm30, nm40}, - eps])])]]); - aa[1, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[2, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[3, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]* - aa[4, p10, p20, p30, p12, p13, p23, {m10, m20, m30, m40}]/k* - IntegrateHeld[(a*Global`x^2 + b*Global`y^2 + - c*Global`x*Global`y + d*Global`x + e*Global`y + - f)^(-1) - (a*Global`x^2 + b*Global`y^2 + - c*Global`x*Global`y + - d*Global`x + (e + k)*Global`y + f)^(-1), {Global`x, - 0, 1}, {Global`y, 0, Global`x}, ##] & @@ - Union[OptionsSelect[NIntegrate, opts], - OptionsSelect[Integrate, opts]] /. - IntegrateHeld -> (FCIntegrate /. Flatten[{opts}] /. - Options[VeltmanD0])) - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Feynman parameters (taken from feynpar by Todd West) *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - -(* feynpar is the procedure which converts integrals over momentum space into -integrals over Feynman parameters. This procedure calls -privatefeynmanparamter once for each momentum integral to be so converted. *) - -FeynmanParameter1[input1_, input2_, input3_:Null, - input4_:Null, (opts___Rule | opts___List)] := - Block[ {integrator, intermediateresult1, intermediateresult2}, - integrator = If[ FreeQ[input1, FeynmanX], - FeynmanX, - If[ FreeQ[input1, FeynmanY], - FeynmanY, - FeynmanZ - ] - ]; - intermediateresult1 = privatefeyparamter[input1, input2,opts]/. - wrap->Identity/.tmpfad->FeynAmpDenominator; - If[ input3 =!= Null, - FCPrint[3,"First intermediate result: ", intermediateresult1] - ]; - integrator = If[ integrator === FeynmanX, - FeynmanY, - FeynmanZ - ]; - intermediateresult2 = intermediateresult1; - If[ input3 =!= Null, - intermediateresult2 = - intermediateresult1[[0]][privatefeyparamter[ - intermediateresult1[[1]], input3,opts], - Sequence@@Take[List@@intermediateresult1,{2,-1}]] - ]; - If[ input4 =!= Null, - FCPrint[3,"Second intermediate result: ", intermediateresult2] - ]; - integrator = FeynmanZ; - intermediateresult1 = intermediateresult2; - If[ input4 =!= Null, - intermediateresult1 = - intermediateresult2[[0]][privatefeyparamter[ - intermediateresult2[[1]],input4,opts], - Sequence@@Take[List@@intermediateresult2,{2,-1}]] - ]; - intermediateresult1 - (*What was this good for ?? 5/3-2001*) (*/. - vector1_[_]^2 :> - vector1^2 /; - (vector1 =!= m && vector1 =!= FeynmanX && - vector1 =!= FeynmanY && vector1 =!= FeynmanZ)*)]; - -FeynmanParameter1[input1_, input2_, input3_:Null, input4_:Null] := - Block[ {integrator, intermediateresult1, intermediateresult2}, - integrator = If[ FreeQ[input1, FeynmanX], - FeynmanX, - If[ FreeQ[input1, FeynmanY], - FeynmanY, - FeynmanZ - ] - ]; - intermediateresult1 = privatefeyparamter[input1, input2]/.wrap->Identity/.tmpfad->FeynAmpDenominator; - If[ input3 =!= Null, - FCPrint[3,"First intermediate result: ", intermediateresult1] - ]; - integrator = If[ integrator === FeynmanX, - FeynmanY, - FeynmanZ - ]; - intermediateresult2 = intermediateresult1; - If[ input3 =!= Null, - intermediateresult2 = - intermediateresult1[[0]][privatefeyparamter[ - intermediateresult1[[1]], input3],Sequence@@Take[List@@intermediateresult1,{2,-1}]] - ]; - If[ input4 =!= Null, - FCPrint[3,"Second intermediate result: ", intermediateresult2] - ]; - integrator = FeynmanZ; - intermediateresult1 = intermediateresult2; - If[ input4 =!= Null, - intermediateresult1 = - intermediateresult2[[0]][privatefeyparamter[ - intermediateresult2[[1]],input4],Sequence@@Take[List@@intermediateresult2,{2,-1}]] - ]; - intermediateresult1 - (*What was this good for ?? 5/3-2001*) (*/. - vector1_[_]^2 :> - vector1^2 /; - (vector1 =!= m && vector1 =!= FeynmanX && - vector1 =!= FeynmanY && vector1 =!= FeynmanZ)*)]; - -FeynmanParameterize[input1_, rest__, opts___Rule|opts___List] := - Block[ {a,ex,ddiimm,res,momentabacklist,li,fps,len}, - ddiimm = - Dimension /. Flatten[{opts}] /. Options[FeynmanParameterize]; - momentabacklist = {}; - res = input1 /. - {a_*ex_FeynAmpDenominator :> - FeynmanParameter1[a*ex, rest, opts], - ex_FeynAmpDenominator :> - FeynmanParameter1[ex, rest, opts]} /. - IntegrateHeld -> (FCIntegrate /. {opts} /. - Options[FeynmanParameterize]) /. - (((Times @@ #) -> (Pair @@ (Momentum[#,ddiimm] & /@ #))) & /@ - Flatten[Outer[List, momentabacklist, momentabacklist],1]) /. - ((#[li_] -> Pair[LorentzIndex[li, ddiimm], Momentum[#, ddiimm]]) & /@ - momentabacklist)/. - wrap->Identity/.tmpfad->FeynAmpDenominator//Contract; - If[ (len = Length[fps = Union[Cases[res,_FeynmanX|_FeynmanY|_FeynmanZ,Infinity]]]) > - Length[FeynmanParameterNames /. Flatten[{opts}] /. Options[FeynmanParameterize]] || - len===0, - res, - res/.((Rule@@#)&)/@(Transpose[{fps, - Take[FeynmanParameterNames /. Flatten[{opts}] /. Options[FeynmanParameterize],len]}]) - ] - ]; - - -(* The following procedure is called once for each momentum integral that we are -converting. *) - -privatefeyparamter[ex_,kay_, opts___] /; !FreeQ[ex,tmpfad] := - privatefeyparamter[ex/.wrap->Identity/.tmpfad->FeynAmpDenominator, kay, opts]; - -privatefeyparamter[ - ex_FeynAmpDenominator, - kay_, opts___] := - privatefeyparamter[dummy*ex, kay, opts] /. dummy -> 1; - -privatefeyparamter[ - num___*ex_FeynAmpDenominator, kay_, - opts___] := - (ddiimm = - Dimension /. Flatten[{opts}] /. Options[FeynmanParameterize]; - Block[ {g, dimension = ddiimm,(* Fix because we now use - FeynAmpDenominator - in FeynArts too and FeynArts sets FeynAmpDenominator[]=1. 11/2-2001.*) dum, - denom = FeynAmpDenominator[dum], nokay, count, coefofksquared, - enn, finaldenominator, - power, coefficientlist, ell, ellnumerator, elldenominator, msquared, - msquaredminusellsquared, numerator, eyezero, alphaenn}, - Attributes[g] = {Orderless}; - g[x_, y_]*g[x_, z_] ^:= g[y, z] /; ! NumberQ[x]; - g[x_, y_]*(z_)[w___, x_, v___] ^:= - z[w, y, v] /; z =!= m && z =!= Complex && ! NumberQ[x]; - g /: g[x_, _]^2 := dimension /; ! NumberQ[x]; - g[x_, x_] := - dimension /; ! NumberQ[x]; - - - (* Pick out the FeynAmpdenominator and group identical - PropagatorDenominators*) - denominator = ((List @@ ex) //. - List[a___, b_, c___, b_, d___] :> List[a, b^2, c, b, d]) /. - Momentum[mom_, ___] :> (momentabacklist = - Union[momentabacklist, - Cases[MomentumExpand[Momentum[mom]], Momentum[_], Infinity, - Heads -> True] /. Momentum -> Sequence]; - mom); - -(* Pick out factors in the denominator which depend on the momentum -over which we're integrating (kay). *) - nokay = - Times @@ - Map[If[ FreeQ[#1, kay], - #1, - (denom = Join[denom, FeynAmpDenominator[#1]] /. dum -> Sequence[]; - 1) - ] &, - denominator]; - FCPrint[3,"Denominator: ", denom]; - FCPrint[3,"Inverse denominators depending on the integration momentum: ",kay]; - FCPrint[3,"Denominators not depending on the integration momentum: ",nokay]; - enn = Length[denom]; - - -(* Take care of terms in the denominator which are of the form -(kay^2 + 2p kay + M^2)^power , where power is not equal to 1. *) - Block[ {iter}, - Do[If[ Head[denom[[iter]]] === - - Power, - (power[iter] = denom[[iter, 2]]; - denom[[iter]] = - denom[[iter, 1]];), - power[iter] = 1 - ], - {iter, enn} - ] - ]; - FCPrint[3,"Denominator after power fixing: ", denom]; - - -(* Expand each term in the denominator. *) - denom = Map[Expand[#1 //. PropagatorDenominator[a_, b_] :> a^2 - b^2] & , denom, - 2]; - FCPrint[3,"Denominator expanded: ", StandardForm[denom]]; - - -(* If a term in the denominator is of the form (a kay^2 + 2p kay + M^2), -with a not equal to 1, divide this term by a. *) - Block[ {iter}, - Do[If[ (coefofksquared = Coefficient[denom[[iter]], kay, 2]) =!= - 1, - (nokay *= - coefofksquared^power[iter]; - denom[[iter]] = Apart[denom[[iter]]/ - coefofksquared];) - ] , - {iter, enn}] - ]; - FCPrint[3,"Denominator after more power fixing: ", StandardForm[denom]]; - - -(* Introduce Feynman parameters (x[i], y[i], z[i]). *) - finaldenominator = denom[[1]] + Sum[(denom[[iter]] - denom[[iter - 1]])* - integrator[iter - 1], {iter, 2, enn}]; - coefficientlist = CoefficientList[finaldenominator, kay]; - - -(* The new denominator can be written in the form -(kay^2 + 2 ell kay + msquared). *) - ell = Factor[coefficientlist[[2]]/2]; - ellnumerator = Expand[Numerator[ell]]; - elldenominator = Denominator[ell]; - msquared = coefficientlist[[1]]; - msquaredminusellsquared = msquared - Expand[ell ell]; - FCPrint[3,"Masses squared: ", StandardForm[msquared], StandardForm[msquaredminusellsquared]]; - numerator = - Expand[MomentumCombine[Times[num]]/. - Pair[Momentum[mom1_,___],Momentum[mom2_,___]] :> - (lil = Unique[li]; - Pair[LorentzIndex[lil],Momentum[mom1]] Pair[LorentzIndex[lil],Momentum[mom2]])/. - Pair[LorentzIndex[li_, ___], - Momentum[mom_, ___]] :> (momentabacklist = - Union[momentabacklist, - Cases[MomentumExpand[Momentum[mom]], Momentum[_], Infinity, - Heads -> True] /. Momentum -> Sequence]; - MomentumExpand[Momentum[mom]] /. Momentum[momm_, ___] :> momm[li])]; - FCPrint[3,"The numerator: ", numerator]; - - - (* eyezero is approximately equal to the result we get if the - numerator of the expression which we are converting does - not contain any factors of kay. *) - eyezero = ( - I(-1)^(dimension/2)/(2^dimension Pi^(dimension/2)))* - Gamma[(alphaenn = Block[ {iterator, firstletter}, - Sum[power[iterator], {iterator, enn}] - ]) - dimension/2]/ - Block[ {iterator}, - Product[(power[iterator] - 1)!, {iterator, enn}] - ]* - integrator[enn - 1]^(power[enn] - 1)* - Block[ {iterator}, - Product[(integrator[iterator - 1] - - integrator[iterator])^(power[iterator] - 1), - {iterator, 2, enn - 1}] - ] (1 - integrator[1])^ - (power[1] - 1) msquaredminusellsquared^(dimension/2 - alphaenn); - FCPrint[3,"eyezero: ", eyezero]; - - - (* The rest of this procedure handles any factors of kay which - may appear in the numerator (up to terms of the form kay^5). *) - numerator = numerator //. kay^2 :> kay[Unique["dumb$"]]^2; - numerator = numerator //. kay mom_Symbol xxxxxx___ :> - kay[dumb = Unique["dumb$"]] mom[dumb] xxxxxx; - numerator = - numerator /. kay[xx1_] kay[yy2_] kay[zz3_] kay[ww4_] kay[vv5_] :> - -(privateel[xx1] privateel[yy2] privateel[zz3] privateel[ww4]privateel[ - vv5] + - (g[xx1, yy2]privateel[zz3]privateel[ww4]privateel[vv5] + - g[xx1, zz3]privateel[yy2]privateel[ww4]privateel[vv5] + - g[yy2, zz3]privateel[xx1]privateel[ww4]privateel[vv5] + - g[xx1, ww4]privateel[zz3]privateel[yy2]privateel[vv5] + - g[yy2, ww4]privateel[xx1]privateel[zz3]privateel[vv5] + - g[zz3, ww4]privateel[xx1]privateel[yy2]privateel[vv5] + - g[xx1, vv5]privateel[zz3]privateel[ww4]privateel[yy2] + - g[yy2, vv5]privateel[xx1]privateel[ww4]privateel[zz3] + - g[zz3, vv5]privateel[xx1]privateel[yy2]privateel[ww4] + - g[ww4, vv5]privateel[xx1]privateel[yy2]privateel[zz3])* - msquaredminusellsquared/(2 alphaenn - 2 - dimension) + - (g[xx1, yy2]g[zz3, ww4]privateel[vv5] + - g[xx1, zz3]g[yy2, ww4]privateel[vv5] + - g[xx1, ww4]g[yy2, zz3]privateel[vv5] + - g[xx1, yy2]g[zz3, vv5]privateel[ww4] + - g[xx1, yy2]g[ww4, vv5]privateel[zz3] + - g[xx1, zz3]g[yy2, vv5]privateel[ww4] + - g[xx1, zz3]g[ww4, vv5]privateel[yy2] + - g[yy2, zz3]g[xx1, vv5]privateel[ww4] + - g[yy2, zz3]g[ww4, vv5]privateel[xx1] + - g[xx1, ww4]g[yy2, vv5]privateel[zz3] + - g[xx1, ww4]g[zz3, vv5]privateel[yy2] + - g[yy2, ww4]g[xx1, vv5]privateel[zz3] + - g[yy2, ww4]g[zz3, vv5]privateel[xx1] + - g[zz3, ww4]g[xx1, vv5]privateel[yy2] + - g[zz3, ww4]g[yy2, vv5]privateel[xx1])msquaredminusellsquared^2/ - ((2 alphaenn - 2 - dimension)(2 alphaenn - 4 - dimension))); - numerator = numerator /. kay[xx1_] kay[yy2_] kay[zz3_] kay[ww4_]^2 :> - -(privateel[xx1] privateel[yy2] privateel[zz3] privateel[ww4]* - privateel[ww4] + (g[xx1, yy2]privateel[zz3]privateel[ww4]privateel[ww4] + - g[xx1, zz3]privateel[yy2]privateel[ww4]privateel[ww4] + - g[yy2, zz3]privateel[xx1]privateel[ww4]privateel[ww4] + - g[xx1, ww4]privateel[zz3]privateel[yy2]privateel[ww4] + - g[yy2, ww4]privateel[xx1]privateel[zz3]privateel[ww4] + - g[zz3, ww4]privateel[xx1]privateel[yy2]privateel[ww4] + - g[xx1, ww4]privateel[zz3]privateel[ww4]privateel[yy2] + - g[yy2, ww4]privateel[xx1]privateel[ww4]privateel[zz3] + - g[zz3, ww4]privateel[xx1]privateel[yy2]privateel[ww4] + - g[ww4, ww4]privateel[xx1]privateel[yy2]privateel[zz3])* - msquaredminusellsquared/(2 alphaenn - 2 - dimension) + - (g[xx1, yy2]g[zz3, ww4]privateel[ww4] + - g[xx1, zz3]g[yy2, ww4]privateel[ww4] + - g[xx1, ww4]g[yy2, zz3]privateel[ww4] + - g[xx1, yy2]g[zz3, ww4]privateel[ww4] + - g[xx1, yy2]g[ww4, ww4]privateel[zz3] + - g[xx1, zz3]g[yy2, ww4]privateel[ww4] + - g[xx1, zz3]g[ww4, ww4]privateel[yy2] + - g[yy2, zz3]g[xx1, ww4]privateel[ww4] + - g[yy2, zz3]g[ww4, ww4]privateel[xx1] + - g[xx1, ww4]g[yy2, ww4]privateel[zz3] + - g[xx1, ww4]g[zz3, ww4]privateel[yy2] + - g[yy2, ww4]g[xx1, ww4]privateel[zz3] + - g[yy2, ww4]g[zz3, ww4]privateel[xx1] + - g[zz3, ww4]g[xx1, ww4]privateel[yy2] + - g[zz3, ww4]g[yy2, ww4]privateel[xx1])msquaredminusellsquared^2/ - ((2 alphaenn - 2 - dimension)(2 alphaenn - 4 - dimension))); - numerator = numerator /. kay[xx1_] kay[yy2_]^2 kay[ww4_]^2 :> - -(privateel[xx1] privateel[yy2] privateel[yy2] privateel[ww4]privateel[ww4] + - (g[xx1, yy2]privateel[yy2]privateel[ww4]privateel[ww4] + - g[xx1, yy2]privateel[yy2]privateel[ww4]privateel[ww4] + - g[yy2, yy2]privateel[xx1]privateel[ww4]privateel[ww4] + - g[xx1, ww4]privateel[yy2]privateel[yy2]privateel[ww4] + - g[yy2, ww4]privateel[xx1]privateel[yy2]privateel[ww4] + - g[yy2, ww4]privateel[xx1]privateel[yy2]privateel[ww4] + - g[xx1, ww4]privateel[yy2]privateel[ww4]privateel[yy2] + - g[yy2, ww4]privateel[xx1]privateel[ww4]privateel[yy2] + - g[yy2, ww4]privateel[xx1]privateel[yy2]privateel[ww4] + - g[ww4, ww4]privateel[xx1]privateel[yy2]privateel[yy2])* - msquaredminusellsquared/(2 alphaenn - 2 - dimension) + - (g[xx1, yy2]g[yy2, ww4]privateel[ww4] + - g[xx1, yy2]g[yy2, ww4]privateel[ww4] + - g[xx1, ww4]g[yy2, yy2]privateel[ww4] + - g[xx1, yy2]g[yy2, ww4]privateel[ww4] + - g[xx1, yy2]g[ww4, ww4]privateel[yy2] + - g[xx1, yy2]g[yy2, ww4]privateel[ww4] + - g[xx1, yy2]g[ww4, ww4]privateel[yy2] + - g[yy2, yy2]g[xx1, ww4]privateel[ww4] + - g[yy2, yy2]g[ww4, ww4]privateel[xx1] + - g[xx1, ww4]g[yy2, ww4]privateel[yy2] + - g[xx1, ww4]g[yy2, ww4]privateel[yy2] + - g[yy2, ww4]g[xx1, ww4]privateel[yy2] + - g[yy2, ww4]g[yy2, ww4]privateel[xx1] + - g[yy2, ww4]g[xx1, ww4]privateel[yy2] + - g[yy2, ww4]g[yy2, ww4]privateel[xx1])*msquaredminusellsquared^2/ - ((2 alphaenn - 2 - dimension)(2 alphaenn - 4 - dimension))); - numerator = - numerator /. - kay[xx1_] kay[yy2_] kay[zz3_] kay[ - ww4_] :> - (privateel[xx1] privateel[yy2] privateel[ - zz3] privateel[ww4] + - (g[xx1, yy2]privateel[zz3]privateel[ww4] + - g[xx1, zz3]privateel[yy2]privateel[ww4] + - g[yy2, zz3]privateel[xx1]privateel[ww4] + - g[xx1, ww4]privateel[zz3]privateel[yy2] + - g[yy2, ww4]privateel[xx1]privateel[zz3] + - g[zz3, ww4]privateel[xx1]privateel[yy2])* - msquaredminusellsquared/(2 alphaenn - 2 - dimension) + - (g[xx1, yy2]g[zz3, ww4] + g[xx1, zz3]g[yy2, ww4] + g[xx1, ww4]g[yy2, zz3])* - msquaredminusellsquared^2/((2 alphaenn - 2 - dimension)* - (2 alphaenn - 4 - dimension))); - numerator = - numerator /. - kay[xx1_] kay[ - yy2_] kay[ - zz3_]^2 :> - (privateel[xx1] privateel[yy2] privateel[ - zz3] privateel[zz3] + - (g[xx1, yy2]privateel[zz3]privateel[zz3] + - g[xx1, zz3]privateel[yy2]privateel[zz3] + - g[yy2, zz3]privateel[xx1]privateel[zz3] + - g[xx1, zz3]privateel[zz3]privateel[yy2] + - g[yy2, zz3]privateel[xx1]privateel[zz3] + - g[zz3, zz3]privateel[xx1]privateel[yy2])* - msquaredminusellsquared/(2 alphaenn - 2 - dimension) + - (g[xx1, yy2]g[zz3, zz3] + g[xx1, zz3]g[yy2, zz3] + g[xx1, zz3]g[yy2, zz3])* - msquaredminusellsquared^2/((2 alphaenn - 2 - dimension)* - (2 alphaenn - 4 - dimension))); - numerator = numerator /. kay[xx1_]^2 kay[zz3_]^2 :> - (privateel[xx1] privateel[xx1] privateel[zz3]privateel[zz3] + - (g[xx1, xx1]privateel[zz3]privateel[zz3] + - g[xx1, zz3]privateel[xx1]privateel[zz3] + - g[xx1, zz3]privateel[xx1]privateel[zz3] + - g[xx1, zz3]privateel[zz3]privateel[xx1] + - g[xx1, zz3]privateel[xx1]privateel[zz3] + - g[zz3, zz3]privateel[xx1]privateel[xx1])msquaredminusellsquared/ - (2 alphaenn - 2 - dimension) + - (g[xx1, xx1]g[zz3, zz3] + g[xx1, zz3]g[xx1, zz3] + g[xx1, zz3]g[xx1, zz3])* - msquaredminusellsquared^2/((2 alphaenn - 2 - dimension)* - (2 alphaenn - 4 - dimension))); - numerator = numerator /. kay[xx1_] kay[yy2_] kay[zz3_] :> - -(privateel[xx1] privateel[yy2] privateel[zz3] + - (1/2)(g[xx1, yy2]privateel[zz3] + g[xx1, zz3]privateel[yy2] + - g[yy2, zz3]privateel[xx1])msquaredminusellsquared/(alphaenn - 1 - - dimension/2)); - numerator = numerator /. kay[xx1_]^2 kay[zz3_] :> - -(privateel[xx1]^2privateel[zz3] + (1/2)(g[xx1, xx1]privateel[zz3] + - privateel[zz3] + privateel[zz3])msquaredminusellsquared/ - (alphaenn - 1 - dimension/2)); - numerator = - numerator /. kay[xx1_] kay[yy2_] :> (privateel[xx1] privateel[yy2] + - g[xx1, yy2] msquaredminusellsquared/(2(alphaenn - 1 - dimension/2))); - numerator = numerator /. kay[xx1_]^2 :> (privateel[xx1]^2 + g[xx1, xx1]* - msquaredminusellsquared/(2(alphaenn - 1 - dimension/2))); - numerator = numerator /. kay[xx1_] -> -privateel[xx1]; - integrators = - If[ enn == 2, - {integrator[1], 0, 1}, - Sequence @@ (Join[{{integrator[1], 0, 1}}, - Table[{integrator[iterator], 0, - integrator[iterator - 1]}, {iterator, 2, enn - 1}]]) - ]; - FCPrint[3,"The final eyezero: ",eyezero]; - FCPrint[3,"The final numerator: ",numerator]; - FCPrint[3,"The final nokay: ",nokay]; - IntegrateHeld[((2*Pi)^dimension)*numerator*wrap[eyezero]* - If[ Head[nokay]===Times, - tmpfad@@nokay, - If[ nokay===1, - 1, - tmpfad[nokay] - ] - ], - integrators] /. - g[a_, b_] :> Pair[LorentzIndex[a], LorentzIndex[b]] - ]); - -privateel[xxx2_] := - Block[ {temporary}, - temporary = ellnumerator /. - xxx3___ yyy3_Symbol :> xxx3 yyy3[xxx2]; - Map[If[ Head[#] === Symbol, - #[xxx2], - # - ] &, temporary, {1}]/ - elldenominator - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Dimensional expansion of integrals *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* The pole terms are isolated: *) - -VeltmanExpand[amp_, opts___?OptionQ] := - ( - a0opts = Options[A0]; - SetOptions[A0, A0ToB0->True]; - mv[i_] := - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MandelstamReduce]) <> ToString[i]]; - masses1[i_] := - Masses[[i]]; - res = amp /. ParticleMass[a__]^2 -> ParticleMass[a]^2 /. - {B0[p10_, m10_, m20_] :> VeltmanB0[p10, m10, m20, ##]& @@ - OptionsSelect[VeltmanB0, opts, Sequence @@ - Select[Options[VeltmanExpand], FreeQ[#,FCIntegrate]&]], - C0[p10_, p12_, p20_, m10_, m20_, m30_] :> - VeltmanC0[p10, p12, p20, m10, m20, m30, ##]& @@ - OptionsSelect[VeltmanC0, opts, Sequence @@ - Select[Options[VeltmanExpand], FreeQ[#,FCIntegrate]&]], - D0[p10_, p12_, p23_, p30_, p20_, p13_, m10_, m20_, m30_, m40_] :> - VeltmanD0[p10, p12, p23, p30, p20, p13, m10, m20, m30, m40, ##]& @@ - OptionsSelect[VeltmanD0, opts, Sequence @@ - Select[Options[VeltmanExpand], FreeQ[#,FCIntegrate]&]]} /. - (B0Evaluation -> "jbar") :> (B0Evaluation -> "direct1") /. - If[ (OnMassShell /. Flatten[{opts}] /. Options[VeltmanExpand]), - Table[Pair[Momentum[mv[irep], ___], Momentum[mv[irep], ___]] -> - masses1[irep]^2, {irep, Length[(Masses /. Flatten[{opts}] /. - Options[VeltmanExpand])]}], - {} - ] /. - IntegrateHeld -> (FCIntegrate /. Flatten[{opts}] /. Options[VeltmanExpand]) /. - LeutwylerLambda[oopp__] :> (LeutwylerLambda[##]& @@ - Complement[Flatten[{oopp}], Options[LeutwylerLambda]]); - SetOptions[A0,Sequence@@a0opts]; - res); - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Renormalization *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Wavefuntion and decay constant renormalization of the lowest order amplitudes -and two loop renormalization should be added.... *) - -Renormalize[m_, opts___] := - m /. CouplingConstant[a_[l_], n_, aaa___, RenormalizationState[0], - b___] :> (CouplingConstant[a[l], n, aaa, RenormalizationState[1], - b] + (RenormalizationCoefficientFunction[ - CouplingConstant[a[l], n]] /. Flatten[{opts}] /. - Options[Renormalize])*(InfinityFactor /. Flatten[{opts}] /. - Options[Renormalize])); - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -FCPrint[1,"PHI: Renormalization.m loaded"]; -End[]; diff --git a/FeynCalc/Phi/Storage/ReadMe.txt b/FeynCalc/Phi/Storage/ReadMe.txt deleted file mode 100644 index 1da6b13f8..000000000 --- a/FeynCalc/Phi/Storage/ReadMe.txt +++ /dev/null @@ -1,4 +0,0 @@ -This file is here in order to have a non-empty storage directory. -If the directory is empty it cannot be in CVS and we are likely to -forget it when creating the distribution tarball. -Without the directory, CheckDB will not work properly. \ No newline at end of file diff --git a/FeynCalc/Phi/Utilities.m b/FeynCalc/Phi/Utilities.m deleted file mode 100644 index c25e82dc8..000000000 --- a/FeynCalc/Phi/Utilities.m +++ /dev/null @@ -1,1909 +0,0 @@ -(* Wolfram Language package *) - -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: Utilities (Phi) *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Utilities for kinematics and Dirac algebra *) - -(* ------------------------------------------------------------------------ *) - -MandelstamReduce::usage = -"MandelstamReduce[amp,opts] gives the amplitude amp with all momenta \ -variables given by the option MomentumVariablesString substituted by \ -Mandelstam variables MandelstamS, MandelstamT and MandelstamU. When the \ -option OnMassShell is set to True, the masses specified in the option Masses \ -are used. The substituted Mandelstam variables depend on the value of the \ -option MomentaSumLeft. E.g. For MomentaSumLeft set to All, the following \ -convention is used: s=(p1+p2)^2, t=(p2+p3)^2, u=(p1+p3)^2 with all particles \ -incoming.\n -When the option Cancel is set to one of \ -MandelstamS, MandelstamT or MandelstamU, this variable is cancelled using the \ -Mandelstam relation. The cancellation is disabled by setting \ -Cancel to None. Default value of Cancel : MandelstamU"; - -MandelstamS::usage = "MandelstamS is the Mandelstam s-variable"; - -MandelstamT::usage = "MandelstamT is the Mandelstam t-variable"; - -MandelstamU::usage = "MandelstamU is the Mandelstam u-variable"; - -$LorentzIndicesCounter::usage = -"$LorentzIndicesCounter is a variable numbering the indices supplied by \ -LorentzIndicesSupply. To start at 1 simply set $LorentzIndicesCounter = 0"; - -LorentzIndicesSupply::usage = -"LorentzIndicesSupply replaces ScalarProduct's and Pair's of momenta and \ -gamma matrices with products with written out Lorentz indices"; - -FourPoint::usage = -"FourPoint[q,exp] expresses a rank four tensor integral (exp is the \ -integrand, q is the four-momentum to be integrated with respect to) in terms \ -of lower rank PaVe's according to the formula on page 22 in the FeynCalc 1.0 \ -manual. Any lower rank subexpressions resulting from the expansion of exp or \ -already in exp are passed to OneLoop, and FourPoint accepts the options \ -of OneLoop and passes them on"; - -GammaSort::usage = -"GammaSort[exp] returns the expression with DOT products of gamma \ -matrices sorted according to the ordering function specified"; - -Gamma5AntiCommute::usage = -"Gamma5AntiCommute is an option of GammaSort specifying whether or not \ -the gamma-5 matrix should be taken to anticommute with the other gamma \ -matrices. Default value : False"; - -OrderingFunction::usage = -"OrderingFunction is an option of GammaSort specifying which function \ -should be used for the ordering of the gamma matrices. Default value : \ -OrderedQ"; - -DiscardMomenta::usage = -"DiscardMomenta is an option for DiscardOrders. When set to True, any \ -ocurring momentum will be considered an expansion quantity, and higher powers \ -will be discarded. Default value : True"; - -DiscardOrders::usage = -"DiscardOrders[m,opts] discards products with the total order of momenta \ -and/or any other quantities from $ExpansionQuantities higher than the \ -PerturbationOrder specified in opts or Options[DiscardOrders]."; - -FCToTracer::usage = -"FCToTracer[exp] translates the expression exp involving unevaluated \ -FeynCalc DiracTrace's to Tracer notation with the Tracer line indices set to \ -variable names determined by the setting of the option TracerIndicesString."; - -$TracerIndicesCounter::usage = -"$TracerIndicesCounter is a variable used by FCToTracer for generating \ -fermion line indices."; - -TracerIndicesString::usage = -"TracerIndicesString is an option of FCToTracer specifying the index used \ -for the fermion line index of Tracer. Default value : \"l\"."; - -TracerToFC::usage = -"TracerToFC[exp] translates the expression exp traced with Tracer to \ -FeynCalc notation."; - -CharacteristicCoefficient::usage = -"CharacteristicCoefficient[a,opts][i] returns the i'th coefficient of the \ -characteristic polynomial of the square matrix a expressed in terms of traces of powers \ -of a. The dimension of a is specified by the option UDimension."; - -CayleyHamilton::usage = -"CayleyHamilton[m1,m2, ...] returns the Cayley-Hamilton identity applied to the sum of \ -the square matrices m1, m2, ... If the option Eliminate is set to True and the number of \ -matrices agrees with the dimension of the matrices (specified by the option UDimension), \ -terms with products of identical matrices are recursively eliminated."; - -CayleyHamiltonTrick::usage = -"CayleyHamiltonTrick[exp] applies Cayley-Hamilton identities obtained with the matrices \ -specified by the setting of the option UMatrices to exp."; - -CayleyHamiltonRules::usage = -"CayleyHamiltonRules[mats] returns rules usable for reduction using Cayley-Hamilton and \ -the matrices mats. mats must be a list of lists of matrices."; - -UMatrices::usage = -"UMatrices is an option of CayleyHamiltonTrick."; - -UReduce::usage = -"UReduce[exp] applies different matrix identities for MM[x] and SMM[x] to the expression \ -exp attempting to bring exp into a more compact form. Notice that MM[x] and SMM[x] should \ -be given without options, that is, it is assumed that SetOptions[MM, Explicit->False] \ -and SetOptions[SMM, Explicit->False] have been evaluated. UReduce is also an option for \ -CayleyHamiltonRules and CayleyHamiltonTrick with default value False And True respectively."; - -UOrder::usage = -"UOrder arranges products of U and d_mu U to have U first."; - -UOrder1::usage = -"UOrde1r arranges products of U and d_mu U to have U last."; - -UGammaTrick::usage = -"UGammaTrick[exp] applies the identity (7.14) and (7.20) from Gasser and Leutwyler \ -(1985) to FieldDerivative's of UGamma[_][_] in exp."; - -SMMToMM::usage = -"SMMToMM[expr] replaces NM[SMM[x],SMM[x]] with MM[x]. SMMToMM is also an option \ -of UReduce which can be either True of False. The better use is as an option of UReduce \ -because UReduce also tries several reduction rules for getting SMM[x]'s next to each other."; - -SurfaceReduce::usage = -"SurfaceReduce[exp] reduces NM products involving FieldDerivative in exp using \ -that total derivatives vanish upon integration. The option DifferenceOrder controls \ -at which difference in differentation order reduction will be attempted. Setting \ -DifferenceOrder smaller than 2 will result in a transformation that do not close."; - -EOMTrick::usage = -"EOMTrick[exp] applies the equations of motion as given by $EOMRules to the \ -expression exp."; - -$EOMRules::usage = -"$EOMRules are equation of motion reduction rules specified in the model \ -specific configuration files."; - -UPerturb::usage = -"UPerturb[exp] expands instances of MM and some composed objects around the \ -solution to the equations of motion up to the order specified by the option ExpansionOrder. \ -The field used for the perturbation is UPerturbation. The expansion is done using the \ -convention of Bijnens, Colangelo and Ecker 1999, u^2 = u e^(i xi Sqrt[2]/f) u."; - -UFields::usage = -"UFields is an option of UPerturb specifying which fields will be expanded. \ -UFields is also an option of SurfaceReduce restricting the reduction of derivatives to \ -terms containing this pattern. The pattern can be e.g. _ or UPerturbation (doing NMExpand and \ -Expand first is then a good idea). \ -Default value : {USmall, UChiPlus, UChiMinus, UFPLus, UFMinus, MM} for UPerturb. \ -UPerturbation for SurfaceReduce."; - -UCoefficient::usage = -"UCoefficient[q][i][args_] is the i'th coefficient of the expansion of the quantity \ -q in the perturbation field around the solution to the equations of motion used by UPerturb. \ -If new quantities are introduced (functions of SMM), the corresponding UCoefficient's need to \ -be defined in order to get the expansion using UPerturb."; - -$GellmannOkubo::usage = -"$GellmannOkubo is a substitution rule for the eta-meson mass using the Gell-mann-Okubo \ -mass formula."; - -GellmannOkubo::usage = -"GellmannOkubo[exp] applies $GellmannOkubo to exp."; - -$GellmannOkuboInv::usage = -"$GellmannOkubo is a substitution rule putting back the eta-meson mass using the \ -Gell-mann-Okubo mass formula."; - -PhiToLaTeX::usage = -"PhiToLaTeX[expr] constructs LaTeX from the expression expr."; - -FixFermionAdjoints::usage = -"FixFermionAdjoints[expr] substitutes DiracBars in expr with Adjoints, applies \ -DiracSimplify and substitutes back."; - -Begin["`Package`"] -End[] - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -Begin["`Utilities`Private`"]; - -(* Errors *) - -CayleyHamilton::baddim = -"Warning: You are requesting using Cayley-Hamilton on a sum with \ -a number of terms that does not agree with the dimension of the matrices. The \ -result may not be very useful."; -UPerturb::"nocoeff" = -"Warning: Yor are requesting expanding in UPerturbation to order `1`. \ -Only up to order 2 is implemented in terms of USmall and CovariantNabla. (If \ -you have the energy, please do work out the expansion and send it to \ -feyncalc@feyncalc.org)."; -UPerturb::"badlim" = "Error: `1` is not a valid summation limit."; -DiscardOrders::wffac = "Warning: Expression contains unknown renormalization factor(s)."; - - -(* -Boxes -*) - - -MandelstamS /: MakeBoxes[MandelstamS, TraditionalForm] := - MakeBoxes[StyleForm["s", FontSlant -> "Italic"]][[1]]; -MandelstamT /: MakeBoxes[MandelstamT, TraditionalForm] := - MakeBoxes[StyleForm["t", FontSlant -> "Italic"]][[1]]; -MandelstamU /: MakeBoxes[MandelstamU, TraditionalForm] := - MakeBoxes[StyleForm["u", FontSlant -> "Italic"]][[1]]; - - -(* FeynCalc functions *) -fccombs := - fccombs = MakeFeynCalcPrivateContext["CombinationLists"]; - -(* Tracer functions *) - -trtr := - trtr = Tracer`GammaTrace; -trid = Tracer`TrU; -trsp := - trsp = Tracer`Spur; -trdot := - trdot = Tracer`TrS; -vecd := - vecd = Tracer`VectorDimension; -trsig := - trsig = Tracer`Sigma; -treps := - treps = Tracer`TrEps; - - - -(* Defaults *) - -Options[MandelstamReduce] = {MomentaSumLeft -> All, OnMassShell -> True, - Cancel -> MandelstamU, MomentumVariablesString -> "p", - MomentaSumRule -> True, - Masses -> {ParticleMass[Pion, RenormalizationState[1]], - ParticleMass[Pion, RenormalizationState[1]], - ParticleMass[Pion, RenormalizationState[1]], - ParticleMass[Pion, RenormalizationState[1]]}}; -DeclareUScalar[MandelstamS]; -DeclareUScalar[MandelstamT]; -DeclareUScalar[MandelstamU]; -Options[LorentzIndicesSupply] = {LorentzIndicesString -> "\[Nu]"}; -Options[GammaSort] = {Gamma5AntiCommute -> False, - OrderingFunction -> OrderedQ}; -Options[DiscardOrders] = {PerturbationOrder -> 4, DiscardMomenta -> True, - ScalarProductForm -> MomentaScalarProduct}; -Options[FCToTracer] := - {TracerIndicesString -> "l"}; -Options[SurfaceReduce] = {DifferenceOrder -> 2, UFields -> UPerturbation}; -Options[UReduce] = {SMMToMM -> False, FullReduce -> True, SUNN -> 2, UDimension -> Automatic}; -Options[SMMToMM] = {SUNN -> 2}; -Options[UPerturb] = {ExpansionOrder -> {1}, SUNN -> 2, -UFields -> {USmall, UChiPlus, UChiMinus, UFPlus, UFMinus, MM}}; -Options[CharacteristicCoefficient] = {UDimension -> 2}; -Options[CayleyHamilton] = {UDimension -> 2, Eliminate -> True}; -Options[CayleyHamiltonRules] = {SUNN -> 2, UDimension -> 2, - CommutatorReduce->True, UReduce -> False}; -tmpoptscdr = Options[CovariantFieldDerivative]; -tmpoptscn = Options[CovariantNabla]; -tmpoptsmm = Options[MM]; -tmpoptssmm = Options[SMM]; -SetOptions[CovariantFieldDerivative, Explicit -> False]; -SetOptions[MM, Explicit -> False]; -Options[CayleyHamiltonTrick] = {SUNN -> 2, UDimension -> 2, - CommutatorReduce -> True, UReduce -> True, - UMatrices :> {{I NM[Adjoint[CovariantFieldDerivative[MM[Global`x_], - Global`x_, {Global`\[Rho]1_}]], MM[Global`x_]], - I NM[Adjoint[MM[Global`x_]], CovariantFieldDerivative[MM[Global`x_], - Global`x_, {Global`\[Rho]2_}]], - NM[Adjoint[CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]1_}]], - CovariantFieldDerivative[MM[Global`x_], Global`x_, {Global`\[Rho]2_}]]}}}; -SetOptions[CovariantFieldDerivative, Sequence@@tmpoptscdr]; -SetOptions[MM, Sequence@@tmpoptsmm]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Mandelstam simplification *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -mv[opts___][i_] := - ToExpression[(MomentumVariablesString /. Flatten[{opts}] /. - Options[MandelstamReduce]) <> ToString[i]]; -mss[opts___][i_] := - Pair[Momentum[mv[opts][i]], Momentum[mv[opts][i]]]; -masses1[opts___][i_] := - (Masses /. Flatten[{opts}] /. - Options[MandelstamReduce])[[i]]; - -manrul[opts___] := - {MandelstamS + MandelstamU + MandelstamT -> Sum[mss[opts][i], {i,1,4}], - -MandelstamS - MandelstamU - MandelstamT -> -Sum[mss[opts][i], {i,1,4}], - MandelstamU + MandelstamT -> -MandelstamS + Sum[mss[opts][i], {i,1,4}], - -MandelstamU - MandelstamT -> MandelstamS - Sum[mss[opts][i], {i,1,4}], - MandelstamS + MandelstamT -> -MandelstamU + Sum[mss[opts][i], {i,1,4}], - -MandelstamS - MandelstamT -> MandelstamU - Sum[mss[opts][i], {i,1,4}], - MandelstamS + MandelstamU -> -MandelstamT + Sum[mss[opts][i], {i,1,4}], - -MandelstamS - MandelstamU -> MandelstamT - Sum[mss[opts][i], {i,1,4}], - a_*MandelstamS + b_*MandelstamT + b_*MandelstamU -> - (a - b)*MandelstamS + b*Sum[mss[opts][i], {i,1,4}], - b_*MandelstamS + a_*MandelstamT + b_*MandelstamU -> - (a - b)*MandelstamT + b*Sum[mss[opts][i], {i,1,4}], - b_*MandelstamS + b_*MandelstamT + a_*MandelstamU -> - (a - b)*MandelstamU + b*Sum[mss[opts][i], {i,1,4}]}; - -(* The convention used is: s=(p1+p2)^2, t=(p2+p3)^2, u=(p1+p3)^2 with all \ -particles incoming (All) as in FeynCalc, that is s=(p1+p2)^2, t=(p2-p3)^2, \ -u=(p1-p3)^2 (FirstHalf) where particles 1 and 2 are incoming and p3 and p4 \ -are outgoing: *) - -sturules[opts___] /; ((MomentaSumLeft /. Flatten[{opts}] /. - Options[MandelstamReduce]) === All) := - {Pair[ - Momentum[mv[opts][1], ___], Momentum[mv[opts][2], ___]] -> - MandelstamS/ - 2 - (Pair[Momentum[mv[opts][1]], Momentum[mv[opts][1]]] + - Pair[Momentum[mv[opts][2]], Momentum[mv[opts][2]]])/2, - Pair[Momentum[mv[opts][2], ___], Momentum[mv[opts][3], ___]] -> - MandelstamT/ - 2 - (Pair[Momentum[mv[opts][2]], Momentum[mv[opts][2]]] + - Pair[Momentum[mv[opts][3]], Momentum[mv[opts][3]]])/2, - Pair[Momentum[mv[opts][1], ___], Momentum[mv[opts][3], ___]] -> - MandelstamU/ - 2 - (Pair[Momentum[mv[opts][1]], Momentum[mv[opts][1]]] + - Pair[Momentum[mv[opts][3]], Momentum[mv[opts][3]]])/2}; - -sturules[opts___] /; (MomentaSumLeft /. Flatten[{opts}] /. - Options[MandelstamReduce]) === - Phi`Objects`FirstHalf := - {Pair[ - Momentum[mv[opts][1], ___], Momentum[mv[opts][2], ___]] -> - MandelstamS/ - 2 - (Pair[Momentum[mv[opts][1]], Momentum[mv[opts][1]]] + - Pair[Momentum[mv[opts][2]], Momentum[mv[opts][2]]])/2, - Pair[Momentum[mv[opts][2], ___], - Momentum[mv[opts][3], ___]] -> -MandelstamT/ - 2 + (Pair[Momentum[mv[opts][2]], Momentum[mv[opts][2]]] + - Pair[Momentum[mv[opts][3]], Momentum[mv[opts][3]]])/2, - Pair[Momentum[mv[opts][1], ___], - Momentum[mv[opts][3], ___]] -> -MandelstamU/ - 2 + (Pair[Momentum[mv[opts][1]], Momentum[mv[opts][1]]] + - Pair[Momentum[mv[opts][3]], Momentum[mv[opts][3]]])/2}; - -sturules[opts___] /; (MomentaSumLeft /. Flatten[{opts}] /. - Options[MandelstamReduce]) === - Phi`Objects`Odd := - {Pair[ - Momentum[mv[opts][1], ___], - Momentum[mv[opts][2], ___]] -> -MandelstamS/ - 2 + (Pair[Momentum[mv[opts][1]], Momentum[mv[opts][1]]] + - Pair[Momentum[mv[opts][2]], Momentum[mv[opts][2]]])/2, - Pair[Momentum[mv[opts][2], ___], - Momentum[mv[opts][3], ___]] -> -MandelstamT/ - 2 + (Pair[Momentum[mv[opts][2]], Momentum[mv[opts][2]]] + - Pair[Momentum[mv[opts][3]], Momentum[mv[opts][3]]])/2, - Pair[Momentum[mv[opts][1], ___], Momentum[mv[opts][3], ___]] -> - MandelstamU/ - 2 - (Pair[Momentum[mv[opts][1]], Momentum[mv[opts][1]]] + - Pair[Momentum[mv[opts][3]], Momentum[mv[opts][3]]])/2}; - -strules[opts___] := - (Cancel /. Flatten[{opts}] /. - Options[MandelstamReduce]) -> - mss[opts][1] + mss[opts][2] + mss[opts][3] + mss[opts][4] - - Complement[{MandelstamS, MandelstamT, - MandelstamU}, {(Cancel /. Flatten[{opts}] /. - Options[MandelstamReduce])}][[1]] - - Complement[{MandelstamS, MandelstamT, - MandelstamU}, {(Cancel /. Flatten[{opts}] /. - Options[MandelstamReduce])}][[2]]; - -MandelstamReduce1[amp_, opts___Rule] := - ExpandScalarProduct[ - amp /. - (*We don't want a polarization vector Polarization[p1] to - be replaced with Polarization[-p2-p3-p4]*) - Polarization[a__] :> ToString/@Polarization[a] /. - If[ MomentaSumRule /. Flatten[{opts}] /. Options[MandelstamReduce], - MomentaSumRule@@ - OptionsSelect[MomentaSumRule,opts,Options[MandelstamReduce]], - {} - ] /. - Polarization[a__] :> ToExpression/@Polarization[a]] /. - sturules[opts] /. - If[ (OnMassShell /. Flatten[{opts}] /. - Options[MandelstamReduce]), - Table[Pair[Momentum[mv[opts][irep], ___], Momentum[mv[opts][irep], ___]] -> - masses1[opts][irep]^2, {irep, 4}], - {} - ] /. - If[ !(Cancel /. Flatten[{opts}] /. - Options[MandelstamReduce]) === None, - strules[opts], - {} - ] /. - If[ (OnMassShell /. Flatten[{opts}] /. Options[MandelstamReduce]), - Table[Pair[Momentum[mv[opts][irep], ___], Momentum[mv[opts][irep], ___]] -> - masses1[opts][irep]^2, {irep, 4}], - {} - ]; - -MandelstamReduce[amp_, opts___Rule] := - MandelstamReduce1[ - MandelstamReduce1[amp, opts] /. - manrul[opts], MomentaSumRule->False, opts]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Lorentz indices *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* Support functions for LorentzIndicesSupply. Index numerators, increasing by \ -one each time applied: *) - -id[x_, OptionsPattern[]] := - x; -$LorentzIndicesCounter = 0; -lin[opts___] := - (++$LorentzIndicesCounter; - ToExpression[(LorentzIndicesString /. Flatten[{opts}] /. - Options[LorentzIndicesSupply]) <> - ToString[$LorentzIndicesCounter]]); - - - -(* Step one in the supplial of the extra Lorentz index dependence: *) - -indicesdotrule1[optss___] := - ((Pair | ScalarProduct)[a_, - b_] /; (! FreeQ[a, Momentum] && ! FreeQ[b, Momentum]) :> - indsuppdot[a, b, lin[optss]]); -indicesdotrule2[optss___] := - (DiracGamma[ - a : Momentum[_, ___] | ___*Momentum[_, ___] | - HoldPattern[Plus[((___* - Momentum[_,___]) | - Momentum[_, ___]) ..]], dim___] :> - indsuppdot[a, fcdiga1[lorentzdummy, dim], lin[optss]]); - - - -(* Step two in the supplial of the extra Lorentz index dependence: *) - -indsuppdot[a_, b_, i_] /; (! FreeQ[a, Momentum] && ! FreeQ[b, Momentum]) := - a*b /. Momentum[c_, dim___] -> Pair[Momentum[c, dim], loritemp[i, dim]]; -indsuppdot[ - a : Momentum[_, ___] | ___*Momentum[_, ___] | - HoldPattern[ - Plus[((___*Momentum[_, ___]) | - Momentum[_, ___])..]], - fcdiga1[lorentzdummy, dim___], i_] := - a*DiracGamma[loritemp[i, dim], dim] /. - Momentum[c_, dimm___] -> Pair[Momentum[c, dimm], loritemp[i, dimm]]; - - - -(* The function that supplies indices to expressions involving IsoDots, -IsoCrosses and IsoSymmetricCrosses of iso-spin vectors: *) - -LorentzIndicesSupply[aa_, (optss___Rule | optss___List)] := - (aa /. - (Pair | ScalarProduct)[a_, b_]^n_ :> times1 @@ Table[DOT[a, b], {rep, n}] /. - Power[a_, b_ /; b > 0 && IntegerQ[b]] :> - times1 @@ Table[a, {ddum, 1, b}]/. - {indicesdotrule1[optss], indicesdotrule2[optss]} /. - loritemp -> LorentzIndex /. - times1 -> Times); - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Rank four tensor integrals *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* A four point tensor integral of rank four can not be handled by FeynCalc. We - reduce it to lower rank PaVe's. *) - - - -(* The stuff below is just to have constants taken out and sums expanded: *) - - - -(* Clear[FourPoint]; *) - -FourPoint[q_, a_Plus, opts___] := - (FourPoint[q, #, opts] & /@ a); -FourPoint[q_, a_*b_, opts___] /; FreeQ[a, q | PropagatorDenominator] := - a*FourPoint[q, b, opts]; - - -FourPoint[q_, aa_*FeynAmpDenominator[f___, PropagatorDenominator[Momentum[q1_, d___] + Momentum[q2_, - d___] + m___, m1_], l___], opts___] := - FourPoint[q, aa*MomentumCombine[FeynAmpDenominator[f, PropagatorDenominator[Momentum[q1, d] + - Momentum[q2, d] + m, m1], l]], opts]; - -FourPoint[q_, - FeynAmpDenominator[PropagatorDenominator[Momentum[q1_, d___], m1_], PropagatorDenominator[Momentum[q2_, d___], m2_], - PropagatorDenominator[Momentum[q3_, d___], m3_], PropagatorDenominator[Momentum[q4_, d___], m4_]]* - Pair[LorentzIndex[l1_, d___], Momentum[qq1_, d___]]* - Pair[LorentzIndex[l2_, d___], Momentum[qq2_, d___]]* - Pair[LorentzIndex[l3_, d___], Momentum[qq3_, d___]]* - Pair[LorentzIndex[l4_, d___], Momentum[qq4_, d___]], - opts___] /; (!FreeQ[qq1, q] && ! FreeQ[qq2, q] && - !FreeQ[qq3, q] && ! FreeQ[qq4, q]) && (Head[qq1] == Plus || - Head[qq2] == Plus || Head[qq3] == Plus || Head[qq4] == Plus) := - FourPoint[q, - Expand[FeynAmpDenominator[PropagatorDenominator[Momentum[q1, d], m1], PropagatorDenominator[Momentum[q2, d], m2], - PropagatorDenominator[Momentum[q3, d], m3], PropagatorDenominator[Momentum[q4, d], m4]]* - MomentumExpand[Pair[LorentzIndex[l1, d], Momentum[qq1, d]]* - Pair[LorentzIndex[l2, d], Momentum[qq2, d]]* - Pair[LorentzIndex[l3, d], Momentum[qq3, d]]* - Pair[LorentzIndex[l4, d], Momentum[qq4, d]]]], opts]; - -FourPoint[q_, aa : HoldPattern[Times[___, (_[ - PropagatorDenominator[ - Momentum[_, ___], _] ..]), a_]], opts___] /; - !FreeQ[{a},q] && Head[a]===Times && !FreeQ[Head/@List@@a, Plus] := - FourPoint[q, Times[aa]//ExpandAll, opts]; - - - -(* Formula taken from the FeynCalc1.0 manual (don't know why Rolf didn't - implement it himself...): *) - -FourPoint[q_, - FeynAmpDenominator[PropagatorDenominator[Momentum[q_, d___], m0_], PropagatorDenominator[Momentum[q_ + _, d___], m1_], - PropagatorDenominator[Momentum[q_ + _, d___], m2_], - PropagatorDenominator[Momentum[q_ + _, d___], m3_]]* - Pair[LorentzIndex[l1_, d___], Momentum[q_, d___]]*Pair[LorentzIndex[l2_, d___], - Momentum[q_, d___]]*Pair[LorentzIndex[l3_, d___], Momentum[q_, d___]]* - Pair[LorentzIndex[l4_, d___], Momentum[q_, d___]], OptionsPattern[]] := - (pp[1] = p1; - pp[2] = p2; - pp[3] = p3; - pp[4] = p4; - I*Pi^2*((Pair[LorentzIndex[l1], LorentzIndex[l2]]*Pair[LorentzIndex[l3], LorentzIndex[l4]] + - Pair[LorentzIndex[l1], LorentzIndex[l3]]*Pair[LorentzIndex[l2], LorentzIndex[l4]] + - Pair[LorentzIndex[l1], LorentzIndex[l4]]*Pair[LorentzIndex[l2], LorentzIndex[l3]])* - PaVe[0, 0, 0, - 0, {Pair[Momentum[p1, d], Momentum[p1, d]], - Pair[Momentum[p1 + p2, d], Momentum[p1 + p2, d]], - Pair[Momentum[p2 + p3, d], Momentum[p2 + p3, d]], - Pair[Momentum[p3, d], Momentum[p3, d]], - Pair[Momentum[p2, d], Momentum[p2, d]], - Pair[Momentum[p1 + p3, d], Momentum[p1 + p3, d]]}, {m0^2, m1^2, - m2^2, m3^2}] + - Sum[(Pair[LorentzIndex[l1], LorentzIndex[l2]]*Pair[Momentum[pp[i]], LorentzIndex[l3]]* - Pair[Momentum[pp[j]], LorentzIndex[l4]] + - Pair[LorentzIndex[l1], LorentzIndex[l3]]*Pair[Momentum[pp[i]], LorentzIndex[l2]]* - Pair[Momentum[pp[j]], LorentzIndex[l4]] + - Pair[LorentzIndex[l1], LorentzIndex[l4]]*Pair[Momentum[pp[i]], LorentzIndex[l2]]* - Pair[Momentum[pp[j]], LorentzIndex[l3]] + - Pair[LorentzIndex[l2], LorentzIndex[l3]]*Pair[Momentum[pp[i]], LorentzIndex[l1]]* - Pair[Momentum[pp[j]], LorentzIndex[l4]] + - Pair[LorentzIndex[l2], LorentzIndex[l4]]*Pair[Momentum[pp[i]], LorentzIndex[l1]]* - Pair[Momentum[pp[j]], LorentzIndex[l3]] + - Pair[LorentzIndex[l3], LorentzIndex[l4]]*Pair[Momentum[pp[i]], LorentzIndex[l1]]* - Pair[Momentum[pp[j]], LorentzIndex[l2]])* - PaVe[0, 0, i, - j, {Pair[Momentum[p1, d], Momentum[p1, d]], - Pair[Momentum[p1 + p2, d], Momentum[p1 + p2, d]], - Pair[Momentum[p2 + p3, d], Momentum[p2 + p3, d]], - Pair[Momentum[p3, d], Momentum[p3, d]], - Pair[Momentum[p2, d], Momentum[p2, d]], - Pair[Momentum[p1 + p3, d], Momentum[p1 + p3, d]]}, {m0^2, m1^2, - m2^2, m3^2}], {i, 3}, {j, 3}] + - Sum[(Pair[Momentum[pp[i]], LorentzIndex[l1]]*Pair[Momentum[pp[j]], LorentzIndex[l3]]* - Pair[Momentum[pp[k]], LorentzIndex[l1]]* - Pair[Momentum[pp[l]], LorentzIndex[l3]])* - PaVe[i, j, k, - l, {Pair[Momentum[p1, d], Momentum[p1, d]], - Pair[Momentum[p1 + p2, d], Momentum[p1 + p2, d]], - Pair[Momentum[p2 + p3, d], Momentum[p2 + p3, d]], - Pair[Momentum[p3, d], Momentum[p3, d]], - Pair[Momentum[p2, d], Momentum[p2, d]], - Pair[Momentum[p1 + p3, d], Momentum[p1 + p3, d]]}, {m0^2, m1^2, - m2^2, m3^2}], {i, 3}, {j, 3}, {k, 3}, {l, 3}])); - - - -(* Tensor integrals of rank lower than four are simply handed to OneLoop: *) - -FourPoint[q_, aa : HoldPattern[Times[___, (_[ - PropagatorDenominator[ - Momentum[_, d___], _] ..]), a___, - b:((Pair[ - _[_, d___], Momentum[q_, - d___]]|Pair[ - Momentum[q_, - d___], _[_, d___]]) ..), ___]], opts___] := - OneLoop[q, Times[aa], opts] /; - Length[{b}] < 4 && FreeQ[{a},q]; - -FourPoint[q_, aa : HoldPattern[Times[___, (_[ - PropagatorDenominator[ - Momentum[_, ___], _] ..]), a___]], opts___] /; - FreeQ[{a},q] := - OneLoop[q, Times[aa], opts]; - -FourPoint[q_, aa : HoldPattern[_[ - PropagatorDenominator[ - Momentum[_, ___], _] ..]], opts___] := - OneLoop[q, Times[aa], opts]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Ordering gamma matrices *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -gaso[DiracGamma[LorentzIndex[mu_, r1___], rr1___], DiracGamma[LorentzIndex[nu_, r2___], rr2___], - opts___] := - (orderfkt = (OrderingFunction /. Flatten[{opts}] /. - Options[GammaSort]); - If[ orderfkt[{DiracGamma[LorentzIndex[mu, r1], rr1], DiracGamma[LorentzIndex[nu, r2], rr2]}], - tl[DiracGamma[LorentzIndex[mu, r1], rr1], DiracGamma[LorentzIndex[nu, r2], rr2]], - tl[DiracGamma[LorentzIndex[nu, r2], rr2], DiracGamma[LorentzIndex[mu, r1], rr1]] - - 2*Pair[LorentzIndex[mu, r1], LorentzIndex[nu, r2]] - ]); -par[x_, i_] := - (pp = Cases[x, DiracGamma[__], Infinity, Heads -> True]; - If[ pp === 0, - 0, - pp[[i]] - ]); -sortrules[ - opts___] := - (orderfkt = (OrderingFunction /. Flatten[{opts}] /. - Options[GammaSort]); - {tl[f___, fi_, red[fii_], fiii___] /; - Head[fi] =!= Plus :> (iso = gaso[fi, fii, opts]; - fiso = iso /. Pair[__] -> 0; - giso = iso - fiso; - If[ Sort[{f, fi, fii}][[-1]] =!= fii, - tl[f, red[par[fiso, 1]], par[fiso, 2], fiii] + - tl[f, giso, fiii], - tl[f, red[fi], fii, fiii] - ]), - tl[a___, b_, c__] /; FreeQ[b, DiracGamma] -> b*tl[a, c], - tl[a__, b_, c___] /; FreeQ[b, DiracGamma] -> b*tl[a, c], - tl[a___, Plus[b_, bb__], c__] :> Plus @@ (tl[a, #, c] & /@ {b, bb}), - tl[f___, fi_, - fii_] /; (! orderfkt[{f, fi, fii}] && - FreeQ[{f, fi, fii}, red]) -> tl[f, fi, red[fii]], - tl[red[f_], fi___, fii_] /; (! orderfkt[{f, fi, fii}]) -> - tl[f, fi, red[fii]]}); -gammasort[xx__, opts___Rule | opts___List] := - tl[xx] //. sortrules[opts] /. tl -> DOT /. red[x_] -> x; -GammaSort[DOT[exp_, ex__], - opts___] := - (exp1 = - If[ (Gamma5AntiCommute /. Flatten[{opts}] /. Options[GammaSort]) && - !FreeQ[tl[exp, ex], DiracGamma[LorentzIndex[5, ___], ___]], - pos = Position[ - tl[exp, ex], _?(!FreeQ[#, DiracGamma[LorentzIndex[5, ___], __]] &), {1}]; - (-1)^pos* - Delete[DOT @@ Join[{tl[exp, ex][[pos]]}, {exp}], pos + 1], - tl[exp, ex] - ]; - exp2 = exp1 /. {tl[aa___, a_, b__, c_, - cc___] /; (!FreeQ[a, DiracGamma[LorentzIndex[5, ___], __] | gsort] && - !FreeQ[c, DiracGamma[LorentzIndex[5, ___], __] | gsort] && - FreeQ[{b}, DiracGamma[LorentzIndex[5, ___], __] | gsort]) -> - tl[aa, a, gsort[b], c, cc], - tl[aa___, c_, - cc___] /; (! FreeQ[c, DiracGamma[LorentzIndex[5, ___], __] | gsort] && - FreeQ[{aa}, DiracGamma[LorentzIndex[5, ___], __] | gsort]) -> - tl[gsort[aa], c, cc], - tl[aa___, c_, - cc___] /; (! FreeQ[c, DiracGamma[LorentzIndex[5, ___], __] | gsort] && - FreeQ[{cc}, DiracGamma[LorentzIndex[5, ___], __] | gsort]) -> - tl[aa, c, gsort[cc]], - tl[a__] /; FreeQ[{a}, DiracGamma[LorentzIndex[5, ___], __] | gsort] :> - tl[gsort[a]]}; - DOT @@ Flatten[{exp2} /. {gsort -> gammasort, tl -> Sequence}]); -GammaSort[Plus[x_, y__], OptionsPattern[]] := - Plus @@ GammaSort /@ {x, y}; -GammaSort[x_, OptionsPattern[]] /; FreeQ[x, DiracGamma] := - x; -GammaSort[DiracGamma[x__], OptionsPattern[]] := - DiracGamma[x]; -GammaSort[DiracTrace[x_, op___], opts___] := - DiracTrace[GammaSort[x, opts], op]; -GammaSort[Times[x_, y__], OptionsPattern[]] := - Times @@ GammaSort /@ {x, y}; - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Gamma traces with Tracer *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - - - -(* FeynCalc's \ -DiracTrace[DOT[DiracGamma[momentum[p,D],D],DiracGamma[LorentzIndex[mu,D],D],..\ -.]], DiracSigma[DiracGamma[LorentzIndex[mu]],DiracGamma[LorentzIndex[nu]]] \ -are substituted with Tracer's GammaTrace[l1,p,{mu},...], Sigma[{mu},{nu}] \ -etc. *) - -$TracerIndicesCounter = 0; -tin[opts___] := - (++$TracerIndicesCounter; - ToExpression[(TracerIndicesString /. Flatten[{opts}] /. - Options[FCToTracer]) <> ToString[$TracerIndicesCounter]]); -FCToTracer[exp_, - opts___] := - (res1 = - exp /. DiracTrace[DOT[a__], ___] :> - trtr[tin[opts], - DOT[a] /. {DOT[LorentzIndex[mu_, ___], LorentzIndex[nu_, ___]] -> - trdot[{LorentzIndex[mu]}, {LorentzIndex[nu]}], fcsig -> trsig, - DiracGamma[LorentzIndex[mu_, ___], ___] -> {LorentzIndex[mu]}, - Plus[aa___, b_, c___] /; FreeQ[b, DiracGamma] -> - Plus[aa, trid*b, c], - Eps[aa__] -> (treps[aa] /. - LorentzIndex[mu_] -> {LorentzIndex[mu]})} /. - DOT -> Sequence] /. - DiracGamma[p_, ___] /; (! FreeQ[p, Momentum]) :> (p /. - Momentum[pp_, ___] -> pp)); -TracerToFC[ - exp_] := - (If[ Tracer`Private`d === 4, - curdim = Sequence[], - curdim = SpaceDimensions - ]; - trsp /@ Table[trl[i], {i, $TracerIndicesCounter}]; - res2 = exp /. - Table[ToExpression[(TracerIndicesString /. Flatten[{opts}] /. - Options[FCToTracer]) <> ToString[i]] -> - trl[i], {i, $TracerIndicesCounter}]; - If[ ! FreeQ[res2, trtr], - Print["Expression not traced"]; - Abort[] - ]; - res2 /. {Momentum[p_] -> Momentum[p, curdim], {LorentzIndex[mu_]} -> LorentzIndex[mu], - trdot -> Pair, trsig :> fcsig, - treps[a__] :> (Eps[a] /. {LorentzIndex[mu_]} -> LorentzIndex[mu, curdim])}); - - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Discarding higher orders *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(*Commented out 16/9-2002. Will look at DOT instead*) -(*SetAttributes[ditchmom, NumericFunction];*) -DiscardOrders[am_, opts___] := - (If[ !FreeQ[am, Phi`Couplings`WFFactor1], - Message[DiscardOrders::wffac] - ]; - (spf = (Phi`Objects`ScalarProductForm /. - Flatten[{opts}] /. Options[DiscardOrders]); - Cancel[ExpandAll[ - ditchmom[]^2*am /. - If[ (DiscardMomenta /. Flatten[{opts}] /. - Options[DiscardOrders]), - {ParticleMass[a__] -> - ditchmom[]*ParticleMass[a, temprec], - MandelstamS -> ditchmom[]^2*MandelstamS[temprec], - MandelstamT -> ditchmom[]^2*MandelstamT[temprec], - MandelstamU -> ditchmom[]^2*MandelstamU[temprec], - Momentum[a__] /; FreeQ[{a}, Polarization] -> - ditchmom[]*Momentum[a, temprec]}, - {} - ] /. (Rule[ - at : # /; FreeQ[at, temprec], - ditchmom[]* - at] & /@ $ExpansionQuantities) //. {Pair[ - ditchmom[]*a_, b_] -> ditchmom[]*Pair[a, b], - spf[ditchmom[]*a_, b_] -> ditchmom[]*spf[a, b]} /. - ff_[temprec] -> ff /. temprec -> Sequence[]]] /. - ditchmom[]^i_ /; - i > (PerturbationOrder + 2 /. Flatten[{opts}] /. - Options[DiscardOrders]) -> 0 /. ditchmom[] -> 1)); - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Characteristic polynomial and Cayley-Hamilton *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(*Se Karakteristisk polynomium og Newtonformler i H.A. Nielsen*) - -CharacteristicCoefficient[a_, opts___Rule][i_] /; - Phi`Objects`Private`gaugedimcheck[ - CharacteristicCoefficient, opts, a] === i := - (-1)^(Phi`Objects`Private`gaugedimcheck[ - CharacteristicCoefficient, opts, a])(*Bug fixed 19/2-2002*); - -CharacteristicCoefficient[a_, opts___Rule][i_] := - Block[ {n = - Phi`Objects`Private`gaugedimcheck[ - CharacteristicCoefficient, opts, a]}, - 1/(i - n)Sum[ - UTrace[NMPower[a, k]]CharacteristicCoefficient[a, opts][i + k], {k, - 1, n - i}] - ]; - -CayleyHamilton[m__, opts___Rule] := - CayleyHamilton[m, opts] = - Block[ {n = Phi`Objects`Private`gaugedimcheck[ - CharacteristicCoefficient, opts, a], coms, len = Length[{m}], - ch, el, submat}, - If[ len =!= n || (Eliminate /. {opts} /. Options[CayleyHamilton]) =!= - True, - If[ len =!= n, - Message[CayleyHamilton::baddim] - ]; - Sum[CharacteristicCoefficient[UMatrix[b], opts][i] NMPower[ - UMatrix[b], i], {i, 0, n}] /. - UMatrix[b] -> Plus[m] // CycleUTraces // NMExpand // - Expand // CycleUTraces, - Do[coms = fccombs[{m}, k]; - ch[k] = Sum[ - Sum[CharacteristicCoefficient[UMatrix[b], opts][i]NMPower[ - UMatrix[b], i], {i, 0, n}] /. - UMatrix[b] -> (Plus @@ coms[[l]]) // CycleUTraces // - NMExpand // Expand, {l, Length[coms]}] // CycleUTraces; - FCPrint[2, "Doing ", k, "-term Cayley-Hamilton"]; - el[k] = ch[k] - - If[ k === 1, - 0, - Plus @@ - Table[submat = - NM[Sequence @@ - Table[{m}[[1]], {dum, 1, len - sp + 1}], - Sequence @@ Drop[{m}, len - sp + 1]]; - FCPrint[2, "Eliminating ", submat, - " with coefficients", " ", - Coefficient[ch[k], submat], " ", - Coefficient[el[sp], submat]]; - Coefficient[ch[k], submat]/ - Coefficient[el[sp], submat]el[sp], {sp, 1, - k - 1}] - ] // Expand, {k, 1, len}]; - el[len] - ] - ]; - -(*Support function for calhamSort*) -(*Count number of adjacent Lorentz vectors*) -licount = (Count[# /. UTrace1 -> tr /. Power -> NMPower /. - NM -> nm //. - {nm[a___, l_?((!FreeQ[#, LorentzIndex[__]] && FreeQ[#, _nm]) &), - ll_?((!FreeQ[#, LorentzIndex[__]] && FreeQ[#, _nm]) &), b___] :> - nm[a, pp[Unique[pp]], b] /; - Cases[l, LorentzIndex[__], Infinity] === Cases[ll, LorentzIndex[__], Infinity], - nm[l_?((!FreeQ[#, LorentzIndex[__]] && FreeQ[#, _nm]) &), a__, - ll_?((!FreeQ[#, LorentzIndex[__]] && FreeQ[#, _nm]) &)] :> - nm[a, pp[Unique[pp]]] /; - Cases[l, LorentzIndex[__], Infinity] === - Cases[ll, LorentzIndex[__], Infinity]}, _pp, Infinity] &); - -(*Function to sort matrices to find left-hand side*) -calhamSort = Block[ {tmp = # . UTrace1 -> tr}, - (Count[#1, _tr, Infinity] < Count[#2, _tr, Infinity] || - Count[#1, _tr, Infinity] === Count[#2, _tr, Infinity] && - licount[#1] < licount[#2] || - Count[#1, _tr, Infinity] === Count[#2, _tr, Infinity] && - licount[#1] == licount[#2] && - LeafCount[#1] > LeafCount[#2] - ) - ]&; - -CayleyHamiltonRules[mats_List, opts___Rule] := - Block[ {(*calham, fac, scalham, rightside, a, len, i, tr, submats, j, - calhamrules, subres*)}, - calhamrules = {}; - FCPrint[3, Length[mats], " sets of matrices"]; - Do[FCPrint[2, j]; - len = Length[mats[[j]]]; - submats = Table[UMatrix[a[i]], {i, 1, len - 1}]; - calham = (subres = (UTrace[ - NM[CayleyHamilton[ - If[ j===1, - FCPrint[2, "Calling CayleyHamilton on ", submats, - " (first time only)"] - ]; - Sequence @@ submats, - Sequence @@ - OptionsSelect[CayleyHamilton, Eliminate -> True, - opts, Options[CayleyHamiltonRules]]], - UMatrix[a[len]]]] // - (FCPrint[3, "Expanding"]; - #)& // - NMExpand // Expand // CycleUTraces) /. - (FCPrint[3, "Substituting matrices"]; - (Rule @@ #) & /@ - Transpose[{Append[submats, UMatrix[a[len]]], mats[[j]]}]) /. - (*Get scalars out of UTrace1*)Pattern -> pat /. pat -> Pattern)// - (FCPrint[3, "Reducing ", subres]; - #)& // - If[ (UReduce /. {opts} /. Options[CayleyHamiltonRules])=!=False, - FCPrint[1, "Doing UReduce"]; - UReduce[#, Sequence@@OptionsSelect[UReduce, - Options[CayleyHamiltonRules],opts]] // CommutatorReduce // CycleUTraces, - If[ (CommutatorReduce/.{opts}/.Options[CayleyHamiltonRules])=!=False, - # //NMExpand // CommutatorReduce // CycleUTraces, - # - ] - ]&; - FCPrint[2, "Finding left-hand side of ", calham]; - scalham = - Sort[List @@ Expand[calham /. UTrace1 -> tr /. - Power -> NMPower], calhamSort ]; - fac = scalham[[1]] /. _tr -> 1; - rightside = (-(Plus @@ Drop[scalham/fac, 1]) /. - Pattern -> (({##}[[1]]) &)); - leftside = Cancel[scalham[[1]]/fac]; - FCPrint[2, "Left-hand side is ", leftside]; - calhamrules = - Append[calhamrules, leftside -> rightside], {j, 1, Length[mats]}]; - If[ (CommutatorReduce/.{opts}/.Options[CayleyHamiltonRules])=!=False, - calhamrules /. tr -> UTrace // CommutatorReduce, - calhamrules /. tr -> UTrace - ] - ]; - - -CayleyHamiltonTrick[exp_, opts___Rule] := - Block[ {ruls}, - ruls = - CayleyHamiltonRules[FCPrint[1, "Building Cayley-Hamilton rules..."]; - UMatrices /. {opts} /. Options[CayleyHamiltonTrick], - Sequence@@OptionsSelect[CayleyHamiltonRules, opts, Options[CayleyHamiltonTrick]]]; - FCPrint[1, "Applying rules"]; - exp /. ruls - ]; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Reduction of lagrangians *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Here we deal symbolically with SMM[x] and MM[x], which should thus not - be expanded *) -SetOptions[MM, Explicit -> False]; -SetOptions[SMM, Explicit -> False]; -SetOptions[CovariantFieldDerivative, Explicit -> False]; - -(* With no scalar and pseudo-scalar sources, \[Chi] is self-adjoined: *) - -idRules = {nm[ff___, SMM[x_], Adjoint[SMM[x_]], ll___] -> nm[ff, ll], - nm[ff___, Adjoint[SMM[x_]], SMM[x_], ll___] -> nm[ff, ll], - nm[ff___, MM[x_], Adjoint[MM[x_]], ll___] -> nm[ff, ll], - nm[ff___, Adjoint[MM[x_]], MM[x_], ll___] -> nm[ff, ll], - nm[ff___, SMM[x_], Adjoint[MM[x_]], ll___] -> nm[ff, Adjoint[SMM[x]], ll], - nm[ff___, Adjoint[SMM[x_]], MM[x_], ll___] -> nm[ff, SMM[x], ll], - nm[ff___, Adjoint[MM[x_]], SMM[x_], ll___] -> nm[ff, Adjoint[SMM[x]], ll], - nm[ff___, MM[x_], Adjoint[SMM[x_]], ll___] -> nm[ff, SMM[x], ll], - UTrace1[nm[SMM[x_], ff___, Adjoint[SMM[x_]]]] :> UTrace1[nm[ff]], - UTrace1[nm[Adjoint[SMM[x_]], ff___, SMM[x_]]] :> UTrace1[nm[ff]], - UTrace1[nm[MM[x_], ff___, Adjoint[MM[x_]]]] :> UTrace1[nm[ff]], - UTrace1[nm[Adjoint[MM[x_]], ff___, MM[x_]]] :> UTrace1[nm[ff]], - Trace1[nm[SMM[x_], ff___, Adjoint[MM[x_]]]] :> - UTrace1[nm[ff, Adjoint[SMM[x]]]], - Trace1[nm[MM[x_], ff___, Adjoint[SMM[x_]]]] :> UTrace1[nm[ff, SMM[x]]], - UTrace1[nm[Adjoint[MM[x_]], ff___, SMM[x_]]] :> - UTrace1[nm[ff, Adjoint[SMM[x]]]], - UTrace1[nm[Adjoint[SMM[x_]], ff___, MM[x_]]] :> UTrace1[nm[ff, SMM[x]]]}; - - -UIdTrick[expr_,opts___Rule] := - expr /. NM -> nm /. idRules /. nm -> NM /. - UTrace1[] :> (Phi`Objects`Private`gaugedimcheck[UReduce,opts,expr]); - -(* At least with the exponential representation these traces are 0. Follows also - from det u =1. *) - -traceRules0 = {UTrace1[ - NM[SMM[x_], Adjoint[FieldDerivative[SMM[x_], _, LorentzIndex[_]]]]] -> 0, - UTrace1[ - NM[Adjoint[SMM[x_]], FieldDerivative[SMM[x_], _, LorentzIndex[_]]]] -> 0, - UTrace1[ - NM[Adjoint[FieldDerivative[SMM[x_], _, LorentzIndex[_]]], SMM[x_]]] -> 0, - UTrace1[ - NM[FieldDerivative[SMM[x_], _, LorentzIndex[_]], Adjoint[SMM[x_]]]] -> 0, - UTrace1[ - NM[SMM[x_], - Adjoint[CovariantFieldDerivative[SMM[x_], _, LorentzIndex[_]]]]] -> 0, - UTrace1[ - NM[Adjoint[SMM[x_]], - CovariantFieldDerivative[SMM[x_], _, LorentzIndex[_]]]] -> 0, - UTrace1[NM[ - Adjoint[CovariantFieldDerivative[SMM[x_], _, LorentzIndex[_]]], - SMM[x_]]] -> 0, - UTrace1[NM[CovariantFieldDerivative[SMM[x_], _, LorentzIndex[_]], - Adjoint[SMM[x_]]]] -> 0, - UTrace1[NM[ - FieldDerivative[FieldDerivative[SMM[x_], x_, LorentzIndex[li2_]], - x_, LorentzIndex[li1_]], Adjoint[SMM[x_]]]] -> -UTrace1[ - NM[FieldDerivative[SMM[x], x, LorentzIndex[li1]], - Adjoint[FieldDerivative[SMM[x], x, LorentzIndex[li2]]]]], - UTrace1[NM[SMM[x_], - Adjoint[FieldDerivative[ - FieldDerivative[SMM[x_], x_, LorentzIndex[li2_]], x_, - LorentzIndex[li1_]]]]] -> -UTrace1[ - NM[FieldDerivative[SMM[x], x, LorentzIndex[li2]], - Adjoint[FieldDerivative[SMM[x], x, LorentzIndex[li1]]]]]}; - -traceRules = Join[traceRules0, traceRules0 /. SMM -> MM]; - -UTraceTrick := - ((# /. traceRules) &); - -(* We will need to simplify using that total derivatives vanish: *) - -uDagRul = - NM[SMM[x_], Adjoint[FieldDerivative[ - FieldDerivative[SMM[x_], x_, LorentzIndex[li2_]], x_, LorentzIndex[li1_]]]] :> - -(NM[FieldDerivative[SMM[x], x, LorentzIndex[li2]], - Adjoint[FieldDerivative[SMM[x], x, LorentzIndex[li1]]]] + - NM[FieldDerivative[ - FieldDerivative[SMM[x], x, LorentzIndex[li2]], x, - LorentzIndex[li1]], Adjoint[SMM[x]]] + - NM[FieldDerivative[SMM[x], x, LorentzIndex[li1]], - Adjoint[FieldDerivative[SMM[x], x, LorentzIndex[li2]]]])(*/; - Sort[{li1,li2}]=!={li1,li2}*); - -UDagRul = uDagRul /. SMM -> MM; - -(* The derivative of the product of U and Adjoint[U] is 0. And the derived rules works -also for the covariant derivative. -That is, NM[CovariantFieldDerivative[U],Adjoint[U]] = - -NM[U,Adjoint[CovariantFieldDerivative[U]]] *) - -du[li1_][x_] = FieldDerivative[SMM[x], x, LorentzIndex[li1]]; -dua[li1_][x_] = Adjoint[FieldDerivative[SMM[x], x, LorentzIndex[li1]]]; - - -ddu[li1_][x_] = CovariantFieldDerivative[SMM[x], x, LorentzIndex[li1]]; -ddua[li1_][x_] = - Adjoint[CovariantFieldDerivative[SMM[x], x, LorentzIndex[li1]]]; - -uRules10 = {rul[nm[f___, duu[li1_][x_], Adjoint[SMM[x_]], g___], - cond[-nm[f, SMM[x], duaa[li1][x], g], (mq[pt[{dum, f}, -1], - SMM[_] | Adjoint[SMM[_]]] || mq[pt[{dum, dum, f}, {-2, -1}], - {duu[_][_] | duaa[_][_] | SMM[_] | Adjoint[SMM[_]], - duu[_][_] | duaa[_][_] | SMM[_] | Adjoint[SMM[_]]}] || - eq[{f}, {}] && (mq[pt[{dum, g}, -1], SMM[_] | Adjoint[SMM[_]]] || - mq[pt[{dum, dum, g}, {-2, -1}], {duu[_][_] | - duaa[_][_] | SMM[_] | Adjoint[SMM[_]], duu[_][_] | duaa[_][_] | SMM[_] | - Adjoint[SMM[_]]}]))]], rul[nm[f___, duaa[li1_][x_], SMM[x_], g___], - cond[-nm[f, Adjoint[SMM[x]], duu[li1][x], g], (mq[pt[{dum, f}, -1], - SMM[_] | Adjoint[SMM[_]]] || mq[pt[{dum, dum, f}, {-2, -1}], - {duu[_][_] | duaa[_][_] | SMM[_] | Adjoint[SMM[_]], - duu[_][_] | duaa[_][_] | SMM[_] | Adjoint[SMM[_]]}] || eq[{f}, {}] && - (mq[pt[{dum, g}, -1], SMM[_] | Adjoint[SMM[_]]] || - mq[pt[{dum, dum, g}, {-2, -1}], {duu[_][_] | duaa[_][_] | SMM[_] | - Adjoint[SMM[_]], duu[_][_] | duaa[_][_] | SMM[_] | - Adjoint[SMM[_]]}]))]]} /. {{duu -> du, duaa -> dua}, - {duu -> ddu, duaa -> ddua}} /. - rul -> RuleDelayed /. cond -> Condition /. {mq -> MatchQ, - eq -> SameQ} /. pt -> Part // Flatten; - -uRules1 = Join[uRules10, uRules10 /. SMM -> MM]; - -applyuRules1 = (# /. NM -> nm /. uRules1 /. nm -> NM) &; -UOrder = (# /. NM -> nm /. (uRules1 /. Condition -> cc /. cc[a_, _] -> a) /. nm -> NM) &; - -uRules20 = {rul[nm[f___, SMM[x_], duaa[li1_][x_], g___], - cond[-nm[f, duu[li1][x], Adjoint[SMM[x]], g], - (mq[pt[{g, dum}, 1], SMM[_] | Adjoint[SMM[_]]] || - mq[pt[{g, dum, dum}, {1, 2}], {duu[_][_] | duaa[_][_] | - SMM[_] | Adjoint[SMM[_]], duu[_][_] | duaa[_][_] | SMM[_] | - Adjoint[SMM[_]]}] || eq[{g}, {}] && (mq[pt[{f, dum}, 1], - SMM[_] | Adjoint[SMM[_]]] || mq[pt[{f, dum, dum}, {1, 2}], {duu[_][_] | - duaa[_][_] | SMM[_] | Adjoint[SMM[_]], duu[_][_] | duaa[_][_] | SMM[_] | - Adjoint[SMM[_]]}]))]], rul[nm[f___, Adjoint[SMM[x_]], duu[li1_][x_], g___], - cond[-nm[f, duaa[li1][x], SMM[x], g], (mq[pt[{g, dum}, 1], SMM[_] | Adjoint[SMM[_]]] || - mq[pt[{g, dum, dum}, {1, 2}], {duu[_][_] | duaa[_][_] | - SMM[_] | Adjoint[SMM[_]], duu[_][_] | duaa[_][_] | SMM[_] | Adjoint[SMM[_]]}] || - eq[{g}, {}] && (mq[pt[{f, dum}, 1], SMM[_] | Adjoint[SMM[_]]] || - mq[pt[{f, dum, dum}, {1, 2}], {duu[_][_] | duaa[_][_] | SMM[_] | Adjoint[SMM[_]], - duu[_][_] | duaa[_][_] | SMM[_] | Adjoint[SMM[_]]}]))]]} /. - {{duu -> du, duaa -> dua}, {duu -> ddu, duaa -> ddua}} /. - rul -> RuleDelayed /. cond -> Condition /. - {mq -> MatchQ, eq -> SameQ} /. pt -> Part // Flatten; - -uRules2 = Join[uRules20, uRules20 /. SMM -> MM]; - -applyuRules2 = (# /. NM -> nm /. uRules2 /. nm -> NM) &; -UOrder1 = (# /. NM -> nm /. (uRules2 /. Condition -> cc /. cc[a_, _] -> a) /. nm -> NM) &; - -applyuRules12 = (# /. NM -> nm /. uRules1 /. uRules2 /. nm -> NM) &; -applyuRules12n = (# /. NM -> nm /. (uRules1 /. Condition -> cc /. cc[a_, _] -> a) /. - (uRules2 /. Condition -> cc /. cc[a_, _] -> a) /. nm -> NM) &; - -applyuRules21 = (# /. NM -> nm /. uRules2 /. uRules1 /. nm -> NM) &; -applyuRules21n = (# /. NM -> nm /. (uRules2 /. Condition -> cc /. cc[a_, _] -> a) /. - (uRules1 /. Condition -> cc /. cc[a_, _] -> a) /. nm -> NM) &; - -(* Use this to get u's side by side: *) - -usurules = {(NM[f___, SMM[x_] | Adjoint[SMM[x_]], SMM[x_] | Adjoint[SMM[x_]], - l___] | NM[f___, MM[x_] | Adjoint[MM[x_]], - MM[x_] | Adjoint[MM[x_]], l___]) -> - NM[f, usu, l], (UTrace1[NM[SMM[x_] | Adjoint[SMM[x_]], f__, - SMM[x_] | Adjoint[SMM[x_]]]] | - UTrace1[NM[MM[x_] | Adjoint[MM[x_]], f__, - MM[x_] | Adjoint[MM[x_]]]]) -> NM[f, usu]}; - -UPair[exp_, opts___Rule] := - (exp /. (a : HoldPattern[NM[__]]) :> (tmpa = a // applyuRules1; - If[ Count[a /. usurules, usu, Infinity] > - Count[tmpa /. usurules, usu, Infinity], - a, - tmpa - ]) /. (a : HoldPattern[NM[__]]) :> (tmpa = - a // applyuRules2; - If[ Count[a /. usurules, usu, Infinity] > - Count[tmpa /. usurules, usu, Infinity], - a, - tmpa - ]) /. (a : HoldPattern[NM[__]]) :> (tmpa = - a // applyuRules12; - If[ Count[a /. usurules, usu, Infinity] > - Count[tmpa /. usurules, usu, Infinity], - a, - tmpa - ]) /. (a : - HoldPattern[NM[__]]) :> (tmpa = a // applyuRules21; - If[ Count[a /. usurules, usu, Infinity] > - Count[tmpa /. usurules, usu, Infinity], - a, - tmpa - ]) // - UIdTrick[#,opts]&); - -UDrop[exp_, opts___Rule] := - Block[ {(*tmpexp,tmpexp1,res*)}, - tmpexp = exp // UOrder // UIdTrick[#,opts]& // CycleUTraces; - tmpexp1 = exp /. UTrace1 -> (UTrace[RotateLeft[#]] &) // UOrder // UIdTrick[#,opts]& // CycleUTraces; - res = {exp,tmpexp,tmpexp1}[[Ordering[LeafCount/@{exp,tmpexp,tmpexp1}][[1]]]]; - tmpexp = res // UOrder1 // UIdTrick[#,opts]& // CycleUTraces; - tmpexp1 = res /. UTrace1 -> (UTrace[RotateLeft[#]] &) // UOrder1 // UIdTrick[#,opts]& // CycleUTraces; - res = {exp,tmpexp,tmpexp1}[[Ordering[LeafCount/@{exp,tmpexp,tmpexp1}][[1]]]]; - tmpexp = res // applyuRules12n // UIdTrick[#,opts]& // CycleUTraces; - tmpexp1 = res /. UTrace1 -> (UTrace[RotateLeft[#]] &) // applyuRules12n // UIdTrick[#,opts]& // CycleUTraces; - res = {exp,tmpexp,tmpexp1}[[Ordering[LeafCount/@{exp,tmpexp,tmpexp1}][[1]]]]; - tmpexp = res // applyuRules21n // UIdTrick[#,opts]& // CycleUTraces; - tmpexp1 = res /. UTrace1 -> (UTrace[RotateLeft[#]] &) // applyuRules21n // UIdTrick[#,opts]& // CycleUTraces; - res = {exp,tmpexp,tmpexp1}[[Ordering[LeafCount/@{exp,tmpexp,tmpexp1}][[1]]]]; - res - ]; - - -(*SU(2) rules for tr(d_mu U d_mu U^(+) d_nu U d_nu U^(+)) - not Cayley-Hamilton, but follow from -writing out the exponentials and using sigma.dphi sigma.dphi = dphi.dphi in SU(2) (no SU2D) -- or from inserting U U^(+) and decomposing the traceless matrices dU U^(+) in Pauli matrices*) -(*See Dobado,Gomez-Nicola,Maroto,Pelaez p. 149*) - -SUNURules[2] := - If[ (Explicit/.Options[MM])===False && (Explicit/.Options[SMM])===False, - {UTrace1[ - NM[Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu1_]]], - CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu2_]], - Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu2_]]], - CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu1_]]]] -> - 1/2*UTrace[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]], - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]]]UTrace[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu2]]], - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu2]]]], - UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu1_]]], - CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu1_]], - Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu2_]]], - CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu2_]]]] -> - 1/2*UTrace[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]], - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]]]UTrace[ - NM[Adjoint[ - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu2]]], - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu2]]]]}, - {} - ]; - - -SUNURules[_] := - {}; - - -(*Going from u to U *) - -(*WRONG?!*) -(*SU(2) rules like above*) -(* diffBigURules[2] := - {NM[CovariantFieldDerivative[SMM[x_], x_, LorentzIndex[mu1_]], - Adjoint[CovariantFieldDerivative[SMM[x_], x_, LorentzIndex[mu1_]]]] :> - 1/4 NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]], - Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]]], - UTrace1[NM[Adjoint[CovariantFieldDerivative[SMM[x_], x_, LorentzIndex[mu1_]]], - m__,CovariantFieldDerivative[SMM[x_], x_, LorentzIndex[mu1_]]]] :> - 1/4 UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]], - m,CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]]], - NM[Adjoint[CovariantFieldDerivative[SMM[x_], x_, LorentzIndex[mu1_]]], - CovariantFieldDerivative[SMM[x_], x_, LorentzIndex[mu1_]]] :> - 1/4 NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]], - CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]], - UTrace1[NM[CovariantFieldDerivative[SMM[x_], x_, LorentzIndex[mu1_]], - m__,Adjoint[CovariantFieldDerivative[SMM[x_], x_, LorentzIndex[mu1_]]]]] :> - 1/4 UTrace1[NM[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]], - m,Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu1]]]]]}; *) - -diffBigURules[_] := - {}; - - -diffURules = {NM[FieldDerivative[SMM[x_], x_, LorentzIndex[li1_]], SMM[x_]] -> - FieldDerivative[MM[x], x, LorentzIndex[li1]] - - NM[SMM[x], FieldDerivative[SMM[x], x, LorentzIndex[li1]]], - NM[Adjoint[FieldDerivative[SMM[x_], x_, LorentzIndex[li1_]]], - Adjoint[SMM[x_]]] -> - Adjoint[FieldDerivative[MM[x], x, LorentzIndex[li1]]] - - NM[Adjoint[SMM[x]], - Adjoint[FieldDerivative[SMM[x], x, LorentzIndex[li1]]]]}; - -bigURules = {nm[f___, SMM[x_], SMM[x_], l___] -> nm[f, MM[x], l], - nm[f___, Adjoint[SMM[x_]], Adjoint[SMM[x_]], l___] -> - nm[f, Adjoint[MM[x]], l], - nm[SMM[x_], m__, SMM[x_]] -> nm[MM[x], m], - nm[Adjoint[SMM[x_]], m__, Adjoint[SMM[x_]]] -> - nm[m, Adjoint[MM[x]]]}; - -SMMToMM[exp_,opts___Rule] := - (max = Max[(Length /@ Cases[exp, _NM, Infinity])]; - FixedPoint[(# /. bigURules /. diffURules /. - diffBigURules[(SUNN /. {opts} /. - Options[UReduce])]// NMExpand) &, - exp /. NM -> nm, max] /. nm -> NM); - -(* Have tr(d_mu U d_mu U^(+) d_nu U d_nu U^(+)) replaced with - tr(d_mu U^(+) d_mu Ud_nu U^(+) d_nu U). - Follows from writing in terms of u_mu's. If anyone should want to do higher order - calculations than p^8, well change the 8 below accordingly :-)*) - -ddURules = Table[(ex = (cut[UTrace1[ - nm@@Table[ - seq[idd[ - CovariantFieldDerivative[MM[pat[x,_]],pat[x,_], - LorentzIndex[mu[i]]]], - adj[CovariantFieldDerivative[MM[pat[x,_]],pat[x,_], - LorentzIndex[mu[i+1]]]]],{i,1,n,2}]]]/.seq->Sequence); - rull[(ex/.mu:>(pat[ToExpression["mu"<>ToString[#]], - Blank[]]&)/.pat->Pattern/.{idd-> - Identity,adj->Adjoint}), - condd[(ex/.mu:>(ToExpression[ - "mu"<>ToString[#]]&)/.{idd->Adjoint, - adj->Identity}/.pat[_,_]->x), - usq[sor[{mu1,mu2}],{mu1,mu2}]]]),{n,2,8,2}]/.{nm->NM, - rull->RuleDelayed,condd->Condition,usq->SameQ, - sor->Sort, cut->CycleUTraces}; - -ddURules1 = - Table[(ex = (cut[UTrace1[ - nm@@Table[ - seq[idd[ - CovariantFieldDerivative[MM[pat[x,_]],pat[x,_], - LorentzIndex[mu[i]]]], - adj[CovariantFieldDerivative[MM[pat[x,_]],pat[x,_], - LorentzIndex[mu[i+1]]]]],{i,1,n,2}]]]/.seq->Sequence); - rull[(ex/.mu:>(pat[ToExpression["mu"<>ToString[#]], - Blank[]]&)/.pat->Pattern/.{idd->Adjoint, - adj->Identity}), - condd[(ex/.mu:>(ToExpression[ - "mu"<>ToString[#]]&)/.{idd->Identity, - adj->Adjoint}/.pat[_,_]->x), - usq[sor[{mu1,mu2}],{mu1,mu2}]]]),{n,2,8,2}]/.{nm->NM, - rull->RuleDelayed,condd->Condition,usq->SameQ, - sor->Sort, cut->CycleUTraces}; - -UReduce[exp_, opts___Rule] := - Block[ {res,opsMM,opsSMM,end}, - opsMM = Options[MM]; - opsSMM = Options[SMM]; - SetOptions[MM, Explicit -> False]; - SetOptions[SMM, Explicit -> False]; - res = If[ (SMMToMM /. {opts} /. Options[UReduce]) =!= True, - (*Added inner UPair in order to force cancellation in SU(3) CayleyHamiltonRules*) - FixedPoint[CycleUTraces[UPair[ - UTraceTrick[UIdTrick[UPair[NMExpand[# /. uDagRul /. UDagRul /. ddURules /. ddURules1]],opts] /. - SUNURules[(SUNN /. {opts} /. - Options[UReduce])]],opts]]&, - exp, 10], - FixedPoint[CycleUTraces[SMMToMM[UPair[ - UTraceTrick[UIdTrick[UPair[NMExpand[# /. uDagRul /. UDagRul /. ddURules /. ddURules1]],opts] /. - SUNURules[(SUNN /. {opts} /. - Options[UReduce])]],opts],opts]]&, - exp, 10] - ]; - end = If[ (FullReduce /. {opts} /. Options[UReduce]) === True, - FixedPoint[CycleUTraces[UDrop[UTraceTrick[UIdTrick[NMExpand[# /. uDagRul /. UDagRul],opts]],opts]]&, - res, 10], - res - ]; - Options[MM] = opsMM; - Options[SMM] = opsSMM; - end - ]; - - - -(* Total derivatives vanish upon integration *) - -(* Should be cleaned up and generalized to traces of products - involving covariant derivatives *) - -(*Disables checks for differentation orders all together*) -(*surfaceRules[0]:=(surfaceRules[1]/. Condition -> cond /. -cond[a_, __] -> (*a*) Condition[a,usq[fq[dd, ufis, Heads -> True],True]]); - -surfaceRules1[0]:=(surfaceRules1[1]/. Condition -> cond /. -cond[a_, __] -> (*a*) Condition[a,usq[fq[dd, ufis, Heads -> True],True]]);*) - -surfaceRules[0] := - (surfaceRules[1] /. sr0 -> True); -surfaceRules1[0] := - (surfaceRules1[1] /. sr0 -> True); - -surfaceRules[n_] := - { - surdum + nm[f___,FieldDerivative[dd_,x_,LorentzIndex[li1_]],r___] :> - surdum + idd[-nm[fdr[nm[f,r],x,LorentzIndex[li1]],dd]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& - (sr0 || Length[{f,r}]>0&&((m1 = Max[Depth/@ - Union[Cases[{f,r},_FCPartialD| - _FieldDerivative,Infinity,Heads->True]]])< - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity,Heads->True]]])+n || m1==-Infinity&&m2==-Infinity&&n<=1)), - - surdum + nm[uo___,NM[f___,FieldDerivative[dd_,x_,LorentzIndex[li1_]],r___], - ou___] :> surdum + idd[nm[ - nm[uo,ou,-nm[NM[fdr[NM[f],x,LorentzIndex[li1]],dd,r]]- - nm[NM[f,dd,fdr[NM[r],x,LorentzIndex[li1]]]]]- - nm[fdr[nm[uo,ou],x,LorentzIndex[li1]],NM[f,dd,r]]]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& (sr0 || (m1 = Max[Depth/@ - Union[Cases[{f,r,ou},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])< - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])+n || m1==-Infinity&&m2==-Infinity&&n<=1), - - surdum + nm[uo___, - utr[NM[f___,FieldDerivative[dd_,x_, - LorentzIndex[li1_]], - r___]],ou___]:> - surdum + idd[-nm[uo,ou,utr[ - NM[fdr[NM[f],x,LorentzIndex[li1]],dd,r]+ - NM[f,dd,fdr[NM[r],x,LorentzIndex[li1]]]]]- - nm[fdr[nm[uo,ou],x,LorentzIndex[li1]], - utr[NM[f,dd,r]]]]/; - ( (FreeQ[dd, ufis, Heads->True] =!=True))&& (sr0 || (m1 = Max[Depth/@ - Union[Cases[{f,r,ou},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])< - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])+n || m1==-Infinity&&m2==-Infinity&&n<=1), - - surdum + nm[uo___,NM[f___,Adjoint[FieldDerivative[dd_,x_,LorentzIndex[li1_]]],r___], - ou___] :> - surdum + idd[nm[ - nm[uo,ou,-NM[fdr[NM[f],x,LorentzIndex[li1]],Adjoint[dd],r]- - NM[f,Adjoint[dd],fdr[NM[r],x,LorentzIndex[li1]]]]- - nm[fdr[nm[uo,ou],x,LorentzIndex[li1]],NM[f,Adjoint[dd],r]]]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& (sr0 || (m1 = Max[Depth/@ - Union[Cases[{f,r,ou},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])< - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])+n || m1==-Infinity&&m2==-Infinity&&n<=1), - - surdum + - nm[uo___,utr[NM[f___,Adjoint[FieldDerivative[dd_,x_, - LorentzIndex[li1_]]], - r___]],ou___]:> - surdum + idd[-nm[uo,ou, - utr[NM[fdr[NM[f],x,LorentzIndex[li1]],Adjoint[dd],r] - +NM[f,Adjoint[dd],fdr[NM[r],x,LorentzIndex[li1]]]]]- - nm[fdr[nm[uo,ou],x,LorentzIndex[li1]], - utr[NM[f,Adjoint[dd],r]]]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& (sr0 || (m1 = Max[Depth/@ - Union[Cases[{f,r,ou},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])<= - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])+n-1 || m1==-Infinity&&m2==-Infinity&&n<=1)}; - -surfaceRules1[n_] := - { - surdum + nm[f___,dd:(QuantumField[FCPartialD[li1_,___], - _, ___][x_] | (IsoVector | UVector | UMatrix)[ - QuantumField[FCPartialD[li1_,___], __]][x_] | - IsoDot[IsoVector[QuantumField[FCPartialD[li1_,___], __]][x_], - IsoVector[UMatrix[UGenerator[___], ___], ___]]),r___] :> - surdum + idd[-nm[fdr[nm[f,r],x,LorentzIndex[li1]],dd/.FCPartialD[__]->Sequence[]]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& - (sr0 || Length[{f,r}]>0&&((m1 = Max[Depth/@ - Union[Cases[{f,r},_FCPartialD| - _FieldDerivative,Infinity,Heads->True]]])< - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity,Heads->True]]])+n || m1==-Infinity&&m2==-Infinity&&n<=1)), - - surdum + nm[uo___,NM[f___,dd:(QuantumField[FCPartialD[li1_,___], - _, ___][x_] | (IsoVector | UVector | UMatrix)[ - QuantumField[FCPartialD[li1_,___], __]][x_] | - IsoDot[IsoVector[QuantumField[FCPartialD[li1_,___], __]][x_], - IsoVector[UMatrix[UGenerator[___], ___], ___]]),r___], - ou___] :> surdum + idd[nm[ - nm[uo,ou,-nm[NM[fdr[NM[f],x,LorentzIndex[li1]],dd/.FCPartialD[__]->Sequence[],r]]- - nm[NM[f,dd,fdr[NM[r],x,LorentzIndex[li1]]]]]- - nm[fdr[nm[uo,ou],x,LorentzIndex[li1]],NM[f,dd/.FCPartialD[__]->Sequence[],r]]]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& (sr0 || (m1 = Max[Depth/@ - Union[Cases[{f,r,ou},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])< - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])+n || m1==-Infinity&&m2==-Infinity&&n<=1), - - surdum + nm[uo___, - utr[NM[f___,dd:(QuantumField[FCPartialD[li1_,___], - _, ___][x_] | (IsoVector | UVector | UMatrix)[ - QuantumField[FCPartialD[li1_,___], __]][x_] | - IsoDot[IsoVector[QuantumField[FCPartialD[li1_,___], __]][x_], - IsoVector[UMatrix[UGenerator[___], ___], ___]]), - r___]],ou___]:> - surdum + idd[-nm[uo,ou,utr[ - NM[fdr[NM[f],x,LorentzIndex[li1]],dd/.FCPartialD[__]->Sequence[],r]+ - NM[f,dd/.FCPartialD[__]->Sequence[],fdr[NM[r],x,LorentzIndex[li1]]]]]- - nm[fdr[nm[uo,ou],x,LorentzIndex[li1]], - utr[NM[f,dd/.FCPartialD[__]->Sequence[],r]]]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& (sr0 || (m1 = Max[Depth/@ - Union[Cases[{f,r,ou},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])< - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])+n || m1==-Infinity&&m2==-Infinity&&n<=1), - - surdum + nm[uo___,NM[f___,Adjoint[dd:(QuantumField[FCPartialD[li1_,___], - _, ___][x_] | (IsoVector | UVector | UMatrix)[ - QuantumField[FCPartialD[li1_,___], __]][x_] | - IsoDot[IsoVector[QuantumField[FCPartialD[li1_,___], __]][x_], - IsoVector[UMatrix[UGenerator[___], ___], ___]])],r___], - ou___] :> - surdum + idd[nm[ - nm[uo,ou,-NM[fdr[NM[f],x,LorentzIndex[li1]],Adjoint[dd/.FCPartialD[__]->Sequence[]],r]- - NM[f,Adjoint[dd/.FCPartialD[__]->Sequence[]],fdr[NM[r],x,LorentzIndex[li1]]]]- - nm[fdr[nm[uo,ou],x,LorentzIndex[li1]],NM[f,Adjoint[dd/.FCPartialD[__]->Sequence[]],r]]]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& (sr0 || (m1 = Max[Depth/@ - Union[Cases[{f,r,ou},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])< - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])+n || m1==-Infinity&&m2==-Infinity&&n<=1), - - surdum + - nm[uo___,utr[NM[f___,Adjoint[dd:(QuantumField[FCPartialD[li1_,___], - _, ___][x_] | (IsoVector | UVector | UMatrix)[ - QuantumField[FCPartialD[li1_,___], __]][x_] | - IsoDot[IsoVector[QuantumField[FCPartialD[li1_,___], __]][x_], - IsoVector[UMatrix[UGenerator[___], ___], ___]])], - r___]],ou___]:> - surdum + idd[-nm[uo,ou, - utr[NM[fdr[NM[f],x,LorentzIndex[li1]],Adjoint[dd/.FCPartialD[__]->Sequence[]],r] - +NM[f,Adjoint[dd/.FCPartialD[__]->Sequence[]],fdr[NM[r],x,LorentzIndex[li1]]]]]- - nm[fdr[nm[uo,ou],x,LorentzIndex[li1]], - utr[NM[f,Adjoint[dd/.FCPartialD[__]->Sequence[]],r]]]]/; - (FreeQ[dd, ufis, Heads->True] =!=True)&& (sr0 || (m1 = Max[Depth/@ - Union[Cases[{f,r,ou},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])<= - (m2 = Max[Depth/@ - Union[Cases[{dd},_FCPartialD| - _FieldDerivative,Infinity, - Heads->True]]])+n-1 || m1==-Infinity&&m2==-Infinity&&n<=1)}; - -SurfaceReduce[expr_,opts___Rule] := - Block[ {n = DifferenceOrder/.{opts}/.Options[SurfaceReduce],re,res,qf,pd,r,x,isod}, - ufis = UFields/.{opts}/.Options[SurfaceReduce]; - re = Expand[surdum + expr](*//. - {QuantumField[pd:(FCPartialD[_]..), r__?(FreeQ[#, {FCPartialD}, Heads -> True] &)][x_] :> - FieldDerivative[qf[r][x], x, (LorentzIndex @@ #) & /@ {pd}], - IsoDot[IsoVector[ - QuantumField[pd : (FCPartialD[_] ..), r__?(FreeQ[#, {FCPartialD}, Heads -> True] &)]][x_], - l_] :> FieldDerivative[ - isod[IsoVector[qf[r]][x], l], x, (LorentzIndex @@ #) & /@ {pd}] /; - FreeQ[l, FCPartialD | FieldDerivative | CovariantFieldDerivative | - CovariantNabla, Heads -> True]}*); - res = surdum + Expand[NMExpand[If[ Head[#]===Times, - nm@@#, - nm[#] - ]&/@re]] /. UTrace1[a_]^n_ :> - (Sequence@@Table[utr[a],{n}]) /. UTrace1->utr //. - (surfaceRules1[n]/.sr0->False/.fq->FreeQ/.usq->UnsameQ) //. - (surfaceRules[n]/.sr0->False/.fq->FreeQ/.usq->UnsameQ) /. idd -> Identity /. nm -> Times /. surdum -> 0/. - qf -> QuantumField /.isod -> IsoDot /. fdr -> FieldDerivative /. - utr -> UTrace/. FieldDerivative[_,LorentzIndex[_]]->0 // - UTraceTrick - ]; - -(* Return to defaults *) -SetOptions[MM, Sequence@@tmpoptsmm]; -SetOptions[SMM, Sequence@@tmpoptssmm]; -SetOptions[CovariantFieldDerivative, Sequence@@tmpoptscdr]; - - -(* (7.14) and (7.20) from Gasser and Leutwyler (1985) *) - -gammaRule = - FieldDerivative[UGamma[LorentzIndex[li1_],opts___Rule][x_], x_, LorentzIndex[li2_]] /; - Sort[{li1,li2}] =!= {li1,li2} :> - FieldDerivative[UGamma[LorentzIndex[li2],opts][x], x, - LorentzIndex[li1]] + - UCommutator[UGamma[LorentzIndex[li1],opts][x], - UGamma[LorentzIndex[li2],opts][x]] - - 1/4 UCommutator[USmall[LorentzIndex[li1],Sequence@@OptionsSelect[USmall,opts]][x], - USmall[LorentzIndex[li2],Sequence@@OptionsSelect[USmall,opts]][x]] - - 1/2 I NM[Adjoint[SMM[x,Sequence@@OptionsSelect[SMM,opts]]], - FieldStrengthTensorFull[{li1}, - UGeneratorMatrixIsoDotFull[ - QuantumField[Particle[ - LeftComponent[0,Sequence@@OptionsSelect[RightComponent,opts]]], - {li2}][x]], x, I,Sequence@@OptionsSelect[FieldStrengthTensorFull,opts]], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]] - - 1/2 I NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - FieldStrengthTensorFull[{li1}, - UGeneratorMatrixIsoDotFull[ - QuantumField[Particle[ - RightComponent[0,Sequence@@OptionsSelect[LeftComponent,opts]]], - {li2}][x]], x, I,Sequence@@OptionsSelect[FieldStrengthTensorFull,opts]], - Adjoint[SMM[x,Sequence@@OptionsSelect[SMM,opts]]]]; - - -UGammaTrick[exp_] := - exp /. gammaRule; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Reduction using equations of motion *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -$EOMRules := - {UTrace1[NM[Adjoint[MM[x_]], CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], - Adjoint[UMatrix[UChi[chopts___]][x_]], CovariantFieldDerivative[MM[x_], x_, - LorentzIndex[mu_]]]] -> - -UTrace1[NM[MM[x], Adjoint[CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[chopts]][x], - Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]]]- - Det[Adjoint[UMatrix[UChi[chopts]][x]]]/2 - Det[UMatrix[UChi[chopts]][x]]/2 - - UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, LorentzIndex[mu]]]] - - UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, - LorentzIndex[mu]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]] + - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]^2/4 + - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]])/2 + - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]]^2/4 - - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], UMatrix[UChi[chopts]][x]]], - - UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]]], - CovariantFieldDerivative[MM[x_], x_, LorentzIndex[mu_]], - Adjoint[UMatrix[UChi[chopts___]][x_]], MM[x_]]] -> - -(-UTrace1[NM[MM[x], Adjoint[CovariantFieldDerivative[MM[x], x, - LorentzIndex[mu]]], UMatrix[UChi[chopts]][x], - Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]]]- - Det[Adjoint[UMatrix[UChi[chopts]][x]]]/2 - Det[UMatrix[UChi[chopts]][x]]/2 - - UTrace1[NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]], - CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, LorentzIndex[mu]]]] - - UTrace1[NM[Adjoint[CovariantFieldDerivative[UMatrix[UChi[chopts]][x], x, - LorentzIndex[mu]]], CovariantFieldDerivative[MM[x], x, LorentzIndex[mu]]]] + - UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]^2/4 + - (UTrace1[NM[Adjoint[MM[x]], UMatrix[UChi[chopts]][x]]]* - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]])/2 + - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], MM[x]]]^2/4 - - UTrace1[NM[Adjoint[UMatrix[UChi[chopts]][x]], UMatrix[UChi[chopts]][x]]])}; - - -EOMTrick[expr_] := - expr /. - Join[$EOMRules, (Expand[a_ * #[[1]]] -> a * #[[2]])& /@ $EOMRules]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Expansion of the fields around the solution to the equations of motion *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* Auxiliary functions*) - -xi[x_] := - IsoDot[IsoVector[QuantumField[Particle[PseudoScalar[12]]]][x], - IsoVector[UMatrix[UGenerator[]]]]; - -(*See Ecker 1992, CERN-TH-6660/92*) - -uExpRight[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule] := - NM[SMM[x,Sequence@@OptionsSelect[SMM,opts]], - UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[pm,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]]]; - -uExpLeftAdj[x_,a___RenormalizationState,b___RenormalizationScheme, - c___ExpansionState,opts___Rule] := - NM[UFieldMatrix[ - DecayConstant[UPerturbation,a,b,c]/DecayConstant[pm,a,b,c]/ - Sqrt[2],QuantumField[Particle[UPerturbation,a,b,c]][x], - Sequence@@OptionsSelect[UFieldMatrix,opts]], - SMM[x,Sequence@@OptionsSelect[SMM,opts]]]; - -(* The u_mu field *) - -(*Keep things compact*) -SetOptions[CovariantNabla, Explicit -> False]; - -UCoefficient[USmall][0][li_, x_] = USmall[li][x]; -UCoefficient[USmall][1][li_, x_] = - -Sqrt[2]/DecayConstant[pm] CovariantNabla[xi[x], x, {li}]; -UCoefficient[USmall][2][li_, x_] = - 1/4/DecayConstant[pm]^2 UCommutator[xi[x], - UCommutator[USmall[li][x], xi[x]]]; -UCoefficient[USmall][do_?((# > 2) &)][li_, x_] := - UCoefficient[USmall][do][li, x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - I*NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - CDr[NM[uExpRight[x, ExpansionOrder -> do], - uExpLeftAdj[x, ExpansionOrder -> do]], x, {li}, - Explicit -> True], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // - NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}](* // UReduce*)); - -(*Return to defaults*) -SetOptions[CovariantNabla, Sequence@@tmpoptscn]; - - -(* The chi_+ field*) - -UCoefficient[UChiPlus][0][x_] = UChiPlus[x]; -UCoefficient[UChiPlus][1][x_] = - -I/Sqrt[2]/DecayConstant[pm]UAntiCommutator[xi[x], - UChiMinus[x]]; -UCoefficient[UChiPlus][2][x_] = - -1/4/DecayConstant[pm]^2UAntiCommutator[xi[x], - UAntiCommutator[xi[x], UChiPlus[x]]]; -UCoefficient[UChiPlus][do_?((# > 2) &)][x_] := - UCoefficient[UChiPlus][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChi[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] + - NM[uExpLeftAdj[x, ExpansionOrder -> do], - Adjoint[UMatrix[UChi[]][x]], - uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] (*// UReduce*)); - -(* The chi_- field*) - -UCoefficient[UChiMinus][0][x_] = UChiMinus[x]; -UCoefficient[UChiMinus][1][x_] = - -I/Sqrt[2]/DecayConstant[pm]UAntiCommutator[xi[x], - UChiPlus[x]]; -UCoefficient[UChiMinus][2][x_] = -1/4/DecayConstant[pm]^2 UAntiCommutator[xi[x], - UAntiCommutator[xi[x], UChiMinus[x]]]; -UCoefficient[UChiMinus][do_?((# > 2) &)][x_] := - UCoefficient[UChiMinus][do][x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - UMatrix[UChi[]][x], - Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] - - NM[uExpLeftAdj[x, ExpansionOrder -> do], - Adjoint[UMatrix[UChi[]][x]], - uExpRight[x, ExpansionOrder -> do]] // NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] (*// UReduce*)); - -(* The f_+ field*) - -UCoefficient[UFPlus][0][li1_, li2_, x_] = UFPlus[li1, li2][x]; -UCoefficient[UFPlus][1][li1_, li2_, x_] = - I/Sqrt[2]/DecayConstant[pm]UCommutator[xi[x], UFMinus[li1, li2][x]]; -UCoefficient[UFPlus][2][li1_, li2_, x_] = -1/4/DecayConstant[pm]^2 UCommutator[xi[x], - UCommutator[xi[x], UFPlus[li1, li2][x]]]; -UCoefficient[UFPlus][do_?((# > 2) &)][li1_, li2_, x_] := - UCoefficient[UChiPlus][do][li1, li2, x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - NM[uExpLeftAdj[x, ExpansionOrder -> do], - FieldStrengthTensorFull[{li1}, - UGeneratorMatrixIsoDot[ - QuantumField[Particle[LeftComponent[0]], {li2}][x]], - x, -I], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] + - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - FieldStrengthTensorFull[{li1}, - UGeneratorMatrixIsoDot[ - QuantumField[Particle[RightComponent[0]], {li2}][x]], - x, -I], uExpRight[x, ExpansionOrder -> do]] // - NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] (*// UReduce*)); - -(* The f_- field*) - -UCoefficient[UFMinus][0][li1_, li2_, x_] = UFMinus[li1, li2][x]; -UCoefficient[UFMinus][1][li1_, li2_, x_] = - I/Sqrt[2]/DecayConstant[pm]UCommutator[xi[x], UFPlus[li1, li2][x]]; -UCoefficient[UFMinus][2][li1_, li2_, x_] = - -1/4/DecayConstant[pm]^2UCommutator[xi[x], - UCommutator[xi[x], UFMinus[li1, li2][x]]]; -UCoefficient[UFPlus][do_?((# > 2) &)][li1_, li2_, x_] := - UCoefficient[UFMinus][do][li1, li2, x] = (Message[UPerturb::"nocoeff", do]; - DiscardTerms[ - NM[uExpLeftAdj[x, ExpansionOrder -> do], - FieldStrengthTensorFull[{li1}, - UGeneratorMatrixIsoDot[ - QuantumField[Particle[LeftComponent[0]], {li2}][x]], - x, -I], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] - - NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], - FieldStrengthTensorFull[{li1}, - UGeneratorMatrixIsoDot[ - QuantumField[Particle[RightComponent[0]], {li2}][x]], - x, -I], uExpRight[x, ExpansionOrder -> do]] // - NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] (*// UReduce*)); - -(* The U-field*) - -UCoefficient[MM][do_][x_] := - UCoefficient[MM][do][x] = ( - DiscardTerms[ - NM[uExpRight[x, ExpansionOrder -> do], - uExpLeftAdj[x, ExpansionOrder -> do]]// - NMExpand // Expand, - Retain -> {Particle[UPerturbation] -> do}] (*// UReduce*)); - -UPerturb[exp_, opts___Rule] := - Block[ {or, lim, quants, ruls, subs, a, b, i, summ, UCoeff}, - or = ExpansionOrder /. {opts} /. Options[UPerturb]; - lim = Which[NumericQ[or], {i, 0, or}, - Head[or] === - List && (Length[or] === 1 || - Length[or] === 2) && (And @@ (NumericQ /@ or)), {i, - Sequence @@ or}, True, Message[UPerturb::"badlim", or]; - Return[]]; - quants = UFields /. {opts} /. Options[UPerturb]; - subs = (#[a__][b__] :> #[a, b]) & /@ quants; - ruls = ((#[a__] -> ((summ[UCoeff[#][i][a], lim])) & /@ quants) /. - summ -> Sum); - exp /. subs /. ruls /. UCoeff -> UCoefficient /. - pm -> If[ (SUNN /. {opts} /. Options[UPerturb]) === 2, - Pion, - PhiMeson - ] - ]; - - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Conversion to LaTeX *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -removeBlankSpace[x_String] := - FixedPoint[StringReplace[#, " " -> " "] &, x]; - -(*First sketch of a LaTeX output functions; - should be abstracted*) -PhiToLaTeX[x_] := - StringReplace[ - ToString[ - x /. _RenormalizationState -> Sequence[] /. - SUNIndex | ExplicitSUNIndex -> Identity /. - (SU2Delta|SU3Delta|SUNDelta)[a_, b_] :> - "\\delta_{" <> ToString[a] <> ToString[b] <> "}" /. - Pair[Momentum[p2], Momentum[p2]]^i_ :> - "q^" <> ToString[2i] //. - - (*Phi`Renormalization` is not in $ContextPath *) - {Phi`Renormalization`LeutwylerJBar[a__, __Rule] :> - Phi`Renormalization`LeutwylerJBar[a], - QuarkCondensate[___] -> "B_0", Pi -> "\\pi", Log -> "\\log", - Pair[_LorentzIndex, ___] -> Sequence[], - _DecayConstant -> "f", - CouplingConstant[Phi`Objects`ChPTW3[2], 1] -> "c_2", - CouplingConstant[Phi`Objects`ChPTW3[2], 2] -> "c_5", - CouplingConstant[Phi`Objects`ChPT2[4], i_, ___] :> "L_{" <> ToString[i] <> "}", - CouplingConstant[Phi`Objects`ChPT3[4], i_, ___] :> "L_{" <> ToString[i] <> "}", - CouplingConstant[Phi`Objects`ChPTW3[4], i_, ___] :> "n_{" <> ToString[i] <> "}", - MandelstamT -> "t", MandelstamS -> "s", MandelstamU -> "u", - ParticleMass[Pion] -> "m_{\\rm \\pi}", - ParticleMass[Kaon] -> "m_{\\rm K}", - ParticleMass[EtaMeson] -> "m_{\\rm \\eta}", - ScaleMu -> "\\mu", - Pair[Momentum[p2], Momentum[p2]] -> "q^2"}, - - FormatType -> InputForm, PageWidth -> 120], - {"\"" -> "", - "I" -> "i", - "[" -> "(", "]" -> ")", "*" -> " ", - "\n" -> "", "LeutwylerJBar" -> "\\overline{J}"} - ] // removeBlankSpace // StandardForm // InputForm; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -(********************************************************************************) -(* Miscellaneous *) -(********************************************************************************) -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) - -(* The Gell-mann Okubo mass formula *) - -$GellmannOkubo = {ParticleMass[EtaMeson, r___]^ - n_ -> ((-ParticleMass[PionZero, r]^2 + 4ParticleMass[KaonZero, r]^2)/ - 3)^(n/2)}; - -GellmannOkubo[exp_] := - Block[ {l, s, pm}, - exp /. - (l : (Phi`Renormalization`LeutwylerJBar | Log))[s__] :> - (l[s] /. ParticleMass -> pm) /. $GellmannOkubo /. - pm -> ParticleMass - ]; - -$GellmannOkuboInv = {ParticleMass[PseudoScalar[2], r___]^2 - - 4 ParticleMass[PseudoScalar[6], r___]^2 :> -3* - ParticleMass[PseudoScalar[11], - r]^2, -ParticleMass[PseudoScalar[2], r___]^2 + - 4 ParticleMass[PseudoScalar[6], r___]^2 :> - 3*ParticleMass[PseudoScalar[11], r]^2, - 4/3 - ParticleMass[Pion]^2/(3 ParticleMass[Kaon]^2) :> - ParticleMass[EtaMeson]^2/(ParticleMass[Kaon]^2)}; - - -(* Substitute DiracBars with Adjoints, permute and substitute back *) -(*First implementation - should be improved...*) -FixFermionAdjoints[ex_] := - ((ex /. - {QuantumField[d___, DiracBar[Particle[Fermion[f_], r___]], rr___][x_] :> - DOT[Adjoint[QuantumField[d, Particle[Fermion[f], r], rr][x]], - DiracGamma[ExplicitLorentzIndex[0]]], QuantumField[d___, - Adjoint[DiracBar[Particle[Fermion[f_], r___]]], rr___][x_] :> - DOT[DiracGamma[ExplicitLorentzIndex[0]], - QuantumField[d, Particle[Fermion[f], r], rr][x]]} // - DiracSimplify) /. - DOT[Adjoint[DiracGamma[LorentzIndex[mu_]]], - DiracGamma[ExplicitLorentzIndex[0]]] :> - DOT[DiracGamma[ExplicitLorentzIndex[0]], - DiracGamma[LorentzIndex[mu]]] // DiracSimplify) /. - DOT[Adjoint[QuantumField[d___, Particle[Fermion[f_], r___], rr___][x_]], - DiracGamma[ExplicitLorentzIndex[0]]] :> - QuantumField[d, DiracBar[Particle[Fermion[f], r]], rr][x] // - DiracSimplify; - -(*XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX*) -FCPrint[1,"PHI: Utilities.m loaded"]; -End[]; diff --git a/FeynCalc/QCD/CalculateCounterTerm.m b/FeynCalc/QCD/CalculateCounterTerm.m index a13cdd6d4..cfa3d508e 100755 --- a/FeynCalc/QCD/CalculateCounterTerm.m +++ b/FeynCalc/QCD/CalculateCounterTerm.m @@ -21,8 +21,10 @@ Begin["`CalculateCounterTerm`Private`"] -Options[CalculateCounterTerm] = {Chisholm -> False, - FinalSubstitutions -> {D -> 4}}; +Options[CalculateCounterTerm] = { + Chisholm -> False, + FinalSubstitutions -> {D -> 4} +}; mapart[y_Plus] := @@ -97,7 +99,8 @@ CalculateCounterTerm[exp_, k_, saveit_:D, opt___Rule] := Block[ {t0 = exp, chish, ta, sunt,pow2,opvar,finsub, - lt, t1,t2,t3,t4,t5,t6,t7,ht7,t8,t9,t10,t11,t12,t13,nt7,lnt7}, + lt, t1,t2,t3,t4,t5,t6,t7,ht7,t8,t9,t10,t11,t12,t13,nt7,lnt7, pr, sut8, + fsut8, fa1, fa2}, chish = Chisholm /. {opt} /. Options[CalculateCounterTerm]; t1 = Collect2[ChangeDimension[t0, 4] // Trick, SUNIndex,Factoring->False]; @@ -174,15 +177,15 @@ If[ Head[t7] =!= Plus, nt7 = ChangeDimension[TID[t7, k, Isolate -> True], 4], lnt7 = Length[t7]; - For[ijn = 1, ijn <= lnt7, ijn++, - FCPrint[2,"ijn = ",ijn," out of", lnt7, - " ", InputForm[SelectNotFree[t7[[ijn]], k]]]; - nt7 = nt7 + (( ( SelectFree[dummy t7[[ijn]],k] + For[r = 1, r <= lnt7, r++, + FCPrint[2,"ijn = ",r," out of", lnt7, + " ", InputForm[SelectNotFree[t7[[r]], k]]]; + nt7 = nt7 + (( ( SelectFree[dummy t7[[r]],k] ) /.dummy -> 1 ) * ChangeDimension[ FixedPoint[ReleaseHold, - TID[SelectNotFree[dummy t7[[ijn]],k], k, + TID[SelectNotFree[dummy t7[[r]],k], k, Contract -> True, Isolate -> True ] ], 4] @@ -277,7 +280,7 @@ LorentzIndex[mu3_], Momentum[OPEDelta]] ) :> FeynCalcInternal[ - DiracMatrix[mu1,mu2,mu3]* + GA[mu1,mu2,mu3]* LC[mu1,mu2,mu3][OPEDelta] ] } diff --git a/FeynCalc/QCD/FC2RHI.m b/FeynCalc/QCD/FC2RHI.m index e1f73c4f1..e9ae161df 100644 --- a/FeynCalc/QCD/FC2RHI.m +++ b/FeynCalc/QCD/FC2RHI.m @@ -28,8 +28,11 @@ Begin["`FC2RHI`Private`"] -Options[FC2RHI] = {Dimension -> D, IncludePair -> True, - Do -> True}; +Options[FC2RHI] = { + Dimension -> D, + IncludePair -> True, + Do -> True +}; FC2RHI[exp_, opt___Rule] := FC2RHI[exp, FCGV["q1"], FCGV["q2"], opt]; @@ -44,16 +47,17 @@ y; FC2RHI[x_Plus, b__] := Map[FC2RHI[#, b]&, x] /; - !FreeQ[x,FeynAmpDenominator]; + !FreeQ[x,FeynAmpDenominator]; FC2RHI[xy_ /; Head[xy]=!=Plus, k1_, k2_, opts___Rule] := If[ !FreeQ[xy, FeynAmpDenominator] && FreeQ[xy, PropagatorDenominator[_, ma_ /; ma=!=0]], MemSet[FC2RHI[xy, k1,k2,opts], Block[ {x, xx,nx, ne,fa, dim, fd, dp, dk1, dk2, dpk1, dpk2, dk1k2,p, - nk12, nk22, k12,k22,k1k2,k1p,k2p, pk12,pk22,k1k22, - fad, inc, a, b, c, d, e, doheuristics,power2sub,(*dof,*) - vV,wW,xX,yY,zZ, al, be, ga, de, ep, result, check,dummyp}, + nk12, nk22, k12,k22,k1k2,k1p,k2p, pk12,pk22,k1k22, pru, + fad, inc, c, d, e, doheuristics,power2sub,(*dof,*) + vV,wW,xX,yY,zZ, al, be, ga, de, ep, result, check,dummyp, qch, + int, iall, rhi, ncheck}, dim = Dimension /. {opts} /. Options[FC2RHI]; inc = IncludePair /. {opts} /. Options[FC2RHI]; doheuristics = Do /. {opts} /. Options[FC2RHI]; @@ -106,9 +110,9 @@ xx = x; If[ !FreeQ[xx, Power2], power2sub = Cases2[xx, Power2]; - power2sub = Table[power2sub[[ij]] -> - (power2sub[[ij]]/.Power2->Power), - {ij,Length[power2sub]} + power2sub = Table[power2sub[[r]] -> + (power2sub[[r]]/.Power2->Power), + {r,Length[power2sub]} ]; xx = xx /. power2sub;, power2sub = {} @@ -260,13 +264,13 @@ int = nx iall; se[y_] := (If[ #===1, - 0, - If[ Head[#] === Power, - #[[2]], - y - ] - ]& - )[SelectNotFree[int, y^h_]]; + 0, + If[ Head[#] === Power, + #[[2]], + y + ] + ]& + )[SelectNotFree[int, y^h_]]; rhi = Map[se, {nk12,nk22,k1p,k2p,k1k2, dk1, dk2, dpk1, dpk2, dk1k2, k12, k22, pk12, pk22, k1k22} diff --git a/FeynCalc/QCD/FC2TLI.m b/FeynCalc/QCD/FC2TLI.m index 00c811b51..a2b93d421 100644 --- a/FeynCalc/QCD/FC2TLI.m +++ b/FeynCalc/QCD/FC2TLI.m @@ -41,16 +41,17 @@ y; FC2TLI[x_Plus, b__] := Map[FC2TLI[#, b]&, x] /; - !FreeQ2[x,{FAD,FeynAmpDenominator}]; + !FreeQ2[x,{FAD,FeynAmpDenominator}]; FC2TLI[xy_ /; Head[xy]=!=Plus, k1_, k2_, opts___Rule] := If[ !FreeQ2[xy, {FeynAmpDenominator,FAD}], MemSet[FC2TLI[xy, k1,k2,opts], Block[ {x, xx,nx, onx, ne,fa, dim, fd, dp, dk1, dk2, dpk1, dpk2, dk1k2,p, nk12, nk22, k12,k22,k1k2,k1p,k2p, pk12,pk22,k1k22,mf, mfm, - fad, inc, a, b, c, d, e, doheuristics,power2sub,(*dof,*)pfix, + fad, inc, c, d, e, doheuristics,power2sub,(*dof,*)pfix, vV,wW,xX,yY,zZ, al, be, ga, de, ep, result, check,dummyp, - lr1, lr2, lork1,lork2, lorfa, lorcheck}, + lr1, lr2, lork1,lork2, lorfa, lorcheck, qch, pru, anx, mass, + iall, int, rhi, ncheck}, dim = Dimension /. {opts} /. Options[FC2TLI]; inc = IncludePair /. {opts} /. Options[FC2TLI]; doheuristics = Do /. {opts} /. Options[FC2TLI]; @@ -107,15 +108,14 @@ xx = x; If[ !FreeQ[xx, Power2], power2sub = Cases2[xx, Power2]; - power2sub = Table[power2sub[[ij]] -> - (power2sub[[ij]]/.Power2->Power), - {ij,Length[power2sub]} + power2sub = Table[power2sub[[r]] -> + (power2sub[[r]]/.Power2->Power), + {r,Length[power2sub]} ]; xx = xx /. power2sub;, power2sub = {} ]; - pru = (a_)^(w_ /; Head[w] =!= Integer) :> - (PowerExpand[Factor2[one*a]^w] /. one -> 1); + pru = (a_)^(w_ /; Head[w] =!= Integer) :> (PowerExpand[Factor2[one*a]^w] /. one -> 1); xx = xx //. pru; xx = xx /. { (-dp + dk1)^w_ :> ( (-1)^w (dp - dk1)^w ), (-dp + dk2)^w_ :> ( (-1)^w (dp - dk2)^w ), @@ -288,13 +288,13 @@ (*NN*) If[ Length[mass] === 1, mass = mass[[1]]; - (*NN*) + (*NN*) mf[aa_] := If[ !FreeQ[onx,aa[mass]], aa[mass], aa[0] ]; - (*NN*) + (*NN*) mfm[aa_] := If[ !FreeQ[onx,aa[mass]], {aa[mass],mass}, @@ -306,18 +306,18 @@ mfm[aa_] := {aa[0],0}, mf[aa_] := - Catch[Do[If[ !FreeQ[onx,aa[mass[[ij]]]], - Throw[aa[mass[[ij]]]] - ], - {ij, Length[mass]}]; - aa[0] - ]; + Catch[Do[If[ !FreeQ[onx,aa[mass[[j]]]], + Throw[aa[mass[[j]]]] + ], + {j, Length[mass]}]; + aa[0] + ]; mfm[aa_] := - Catch[Do[If[ !FreeQ[onx,aa[mass[[ij]]]], - Throw[{aa[mass[[ij]]],mass[[ij]]}] - ], - {ij, Length[mass]}]; - {aa[0],0} + Catch[Do[If[ !FreeQ[onx,aa[mass[[j]]]], + Throw[{aa[mass[[j]]],mass[[j]]}] + ], + {j, Length[mass]}]; + {aa[0],0} ]; ]; ]; @@ -334,16 +334,16 @@ int = nx iall; se[y_] := (If[ #===1, - 0, - If[ Head[#] === Power, - If[ Length[#[[1]]]===1, - {#[[2]],#[[1,1]]}, - #[[2]] - ], - y - ] - ]& - )[ SelectNotFree[int, y^h_] ]; + 0, + If[ Head[#] === Power, + If[ Length[#[[1]]]===1, + {#[[2]],#[[1,1]]}, + #[[2]] + ], + y + ] + ]& + )[ SelectNotFree[int, y^h_] ]; rhi = Map[se, {nk12,nk22,k1p,k2p,k1k2, dk1, dk2, dpk1, dpk2, dk1k2, diff --git a/FeynCalc/QCD/FromTFI.m b/FeynCalc/QCD/FromTFI.m index 01a562142..d040c4a36 100644 --- a/FeynCalc/QCD/FromTFI.m +++ b/FeynCalc/QCD/FromTFI.m @@ -26,24 +26,24 @@ Options[FromTFI] = { TLI2FC -> True }; FromTFI[exp_, opts___Rule] := FromTFI[exp, FCGV["q1"],FCGV["q2"], FCGV["p"],opts]; -FromTFI[exp_, q1_, q2_, p_, opts___Rule] := +FromTFI[exp_, (*q1*)_, (*q2*)_, (*p*)_, opts___Rule] := Block[ {t}, t = exp /. { - TFI[d_Symbol, pp_, props_List] :> TLI[{0,0,0,0,0}, props], - TFI[d_Symbol, pp_, {x_,y_,z_,v_,w_}, props_List] :> + TFI[(*d*)_Symbol, (*pp*)_, props_List] :> TLI[{0,0,0,0,0}, props], + TFI[(*d*)_Symbol, (*pp*)_, {x_,y_,z_,v_,w_}, props_List] :> TLI[{x,y,z,v,w}, {0,0,0,0,0}, props], - TFI[d_Symbol, pp_, dp_, {a_,b_}, props_List] :> + TFI[(*d*)_Symbol, (*pp*)_, (*dp*)_, {a_,b_}, props_List] :> TLI[{a,b,0,0,0}, props], - TFI[d_Symbol, pp_, dp_, {a_,b_}, {x_,y_,z_,v_,w_}, props_List] :> + TFI[(*d*)_Symbol, (*pp*)_, (*dp*)_, {a_,b_}, {x_,y_,z_,v_,w_}, props_List] :> TLI[{x,y,z,v,w}, {a,b,0,0,0}, props], - TVi[d_Symbol, pp_, {nm1_,nm2_,nm3_,nm4_}] :> + TVi[(*d*)_Symbol, (*pp*)_, {nm1_,nm2_,nm3_,nm4_}] :> TLI[{0,0,0,0,0},{0,nm2,nm3,nm4,nm1}], - TVi[d_Symbol, pp_, {x_,y_,z_,v_,w_}, {nm1_,nm2_,nm3_,nm4_}] :> + TVi[(*d*)_Symbol, (*pp*)_, {x_,y_,z_,v_,w_}, {nm1_,nm2_,nm3_,nm4_}] :> TLI[{x,y,z,v,w}, {0,0,0,0,0},{0,nm2,nm3,nm4,nm1}], - TVi[d_Symbol, pp_, {a_,b_}, {x_,y_,z_,v_,w_}, + TVi[(*d*)_Symbol, (*pp*)_, {a_,b_}, {x_,y_,z_,v_,w_}, {nm1_,nm2_,nm3_,nm4_}] :> TLI[{x,y,z,v,w}, {a,b,0,0,0},{0,nm2,nm3,nm4,nm1}], - TJi[d_Symbol, pp_, {nm1_,nm2_,nm3_}] :> + TJi[(*d*)_Symbol, (*pp*)_, {nm1_,nm2_,nm3_}] :> TLI[{0,0,0,0,0},{nm1,0,0,nm3,nm2}] }; If[ (TLI2FC /. {opts} /. Options[FromTFI]) === True, diff --git a/FeynCalc/QCD/OPE1Loop.m b/FeynCalc/QCD/OPE1Loop.m index 6e90ad04a..c6ed52737 100755 --- a/FeynCalc/QCD/OPE1Loop.m +++ b/FeynCalc/QCD/OPE1Loop.m @@ -28,6 +28,10 @@ Begin["`OPE1Loop`Private`"] +dim::usage=""; +dummy::usage=""; +muUUu::usage=""; + Options[OPE1Loop] = { Collecting -> True, Dimension -> D, @@ -66,9 +70,9 @@ ]; PairFix[exp_, {ka__}] := - Block[ {tt}, + Block[ {tt, pf}, FCPrint[3,"entering PairFix"]; - pf = Table[Pair[Momentum[{ka}[[j]], di___], Momentum[{ka}[[j]], di___] + pf = Table[Pair[Momentum[{ka}[[j]], d___], Momentum[{ka}[[j]], d___] ]^n_Integer?Negative, {j, Length[{ka}]} ]; If[ FreeQ2[exp, pf], @@ -85,22 +89,20 @@ ]; -OPE1Loop[grname_,k_ /; Head[k] =!= List, - integ_ /; Head[integ] =!= Plus,opts___Rule - ] := - Block[ {collecting, contrac,amp,dim,powexp,feyncan, feyncanon, subloop, fsc, +OPE1Loop[(*grname*)_,k_ /; Head[k] =!= List, integ_ /; Head[integ] =!= Plus,opts___Rule] := + Block[ {collecting, contrac,amp,powexp,feyncan, feyncanon, subloop, fsc, opsumdoit, qp1, subfactor = 1, ampp, fad, fap, trf = {}, - sunntocacf, sunftotraces, fds1, fscrule + sunntocacf, sunftotraces, fds1, fscrule, null1, null2, nn, lamp }, If[ FreeQ[integ,k](* || (!FreeQ[integ, (_. +_. Pair[Momentum[k,___], _] )^(hw_/;Head[hw] =!=Integer) ] )*) || (!FreeQ2[integ, {(_. +_. Pair[Momentum[k,___], _] - )^(hw_Integer?Negative), + )^((*hw*)_Integer?Negative), Power2[ (_. +_. Pair[Momentum[k,___], _] - ), (hw_Integer?Negative) + ), ((*hw*)_Integer?Negative) ] } ] @@ -165,11 +167,10 @@ amp = ChangeDimension[integ//FeynCalcInternal, dim]//Trick; amp = amp /. DiracTrace -> Tr2; amp = FeynAmpDenominatorCombine[amp]; - amp0 = amp; + If[ !FreeQ[amp,OPE], amp = Coefficient[ Expand2[amp, OPE], OPE] ]; - amp1 = amp; contrac[yy_] := Contract[yy, EpsContract->False]; FCPrint[1,"sunsimplifying"]; @@ -215,7 +216,7 @@ If[ !MatchQ[SelectNotFree[a,k] /. Power2->Power, (_. Pair[Momentum[OPEDelta,dim], Momentum[k,dim]])^ (w_/;Head[w]=!=Integer) * - (_. Pair[Momentum[OPEDelta,dim], Momentum[pe_,dim]] + + (_. Pair[Momentum[OPEDelta,dim], Momentum[(*pe*)_,dim]] + _. Pair[Momentum[OPEDelta,dim], Momentum[k,dim]])^ (v_/;Head[v]=!=Integer) ], @@ -223,12 +224,12 @@ ( PowerSimplify[ Apart[SelectFree[a, {OPEi, OPEj}] * Sum[((a/SelectFree[a,{OPEi,OPEj}])/.Power2->Power) //. - {(-1)^(n_Integer?EvenQ m_. + aa_) :> (-1)^aa + {(-1)^(_Integer?EvenQ _. + aa_) :> (-1)^aa }, b ] ] ]/. ((pl_Plus)^(w_/;Head[w] =!= Integer) :> Power2[pl,w]) - )/.(-1)^(n_Integer?EvenQ m_. + aa_.) :> (-1)^aa + )/.(-1)^(_Integer?EvenQ _. + aa_.) :> (-1)^aa ]; (* @@ -236,7 +237,7 @@ *) ops[null1] = ops[null2] = 0; ops[a_ OPESum[xa_,xb_]] := - a/(SelectNotFree[a dUM, k]) OPESum[xa SelectNotFree[a dUM,k],xb]; + a/(SelectNotFree[a dummy, k]) OPESum[xa SelectNotFree[a dummy,k],xb]; amp = Map[ops, amp + null1 + null2] /. ops -> Identity; amp = fds1[amp]//PowerSimplify; ]; @@ -249,7 +250,7 @@ ]; qp1[x_] := fds1[ ApartFF[x,{k}]]; - rli = {}; + (*rli = {};*) nn = 0; nn = qup1[amp]; amp = nn; @@ -298,7 +299,7 @@ ] ]; amp = EpsEvaluate[nn]; - amp4 = amp; + If[ collecting === False, amp = Expand[amp], If[ collecting === True, diff --git a/FeynCalc/QCD/OPE2TID.m b/FeynCalc/QCD/OPE2TID.m index 1fc06af4b..36adb5e27 100755 --- a/FeynCalc/QCD/OPE2TID.m +++ b/FeynCalc/QCD/OPE2TID.m @@ -24,6 +24,10 @@ Begin["`OPE2TID`Private`"] +mU::usage=""; +nu::usage=""; +rho::usage=""; + diracsimp[a_] := If[ !FreeQ[a, DiracGamma], DiracSimplify[a], @@ -67,7 +71,7 @@ temp0, n, alL, beT,checkd,muu,k12shift = {},dumi,diramp, alpha = FCGV[ToString[Unique["lI"]]], beta = FCGV[ToString[Unique["lI"]]], delfactor, temp2, temp3, tempf, temp4, qQQ,epscontract, - sccon, eeeps,eepcsa, rho,rhoo,phead,fake,mem, + sccon, eeeps,eepcsa, rhoo,phead,fake,mem, epscos, epscont, epsc, decrules, decrulespv, checkk, fcheck, decrulesspecial, speciallabel = False, dirrramp,contractlabel,kape }, @@ -300,12 +304,9 @@ (* "amputate" a special Eps... *) If[ FreeQ[temp, Eps[__]^2] && - (!FreeQ[temp, Eps[a___, Momentum[k1, en___], Momentum[k2, en___], b___]] - ) && (FreeQ[temp, - Eps[a___, Momentum[k1, en___], Momentum[k2, en___], b___] * - Eps[c__] - ] - ), + (!FreeQ[temp, Eps[a___, Momentum[k1, e___], Momentum[k2, e___], b___]] + ) && (FreeQ[temp, Eps[a___, Momentum[k1, e___], Momentum[k2, e___], b___] * Eps[c__] + ]), alL = FCGV[ToString[Unique["lI"]]]; beT = FCGV[ToString[Unique["lI"]]]; FCPrint[1,"AMPuTATe EPs"]; @@ -319,20 +320,19 @@ (* another special case ... *) If[ MatchQ[temp, _. Pair[Momentum[k1,___],LorentzIndex[__]] * Pair[Momentum[k2,___],LorentzIndex[__]] * - Eps[aaa___, Momentum[k1,didi___], b___] - ], + Eps[(*aaa*)___, Momentum[k1,(*didi*)___], b___]], rhoo = Unique[dumi]; - temp = temp /. Eps[aaa___, Momentum[k1,didi___], b___] :> + temp = temp /. Eps[aaa___, Momentum[k1,(*didi*)___], b___] :> (Eps[aaa,LorentzIndex[rhoo,n],b] * Pair[Momentum[k1,n], LorentzIndex[rhoo,n]] ) ]; If[ MatchQ[temp, _. Pair[Momentum[k1,___],LorentzIndex[__]] * Pair[Momentum[k2,___],LorentzIndex[__]] * - Eps[aaa___, Momentum[k2,didi___], b___] + Eps[(*aaa*)___, Momentum[k2,(*didi*)___], b___] ], rhoo = Unique[dumi]; - temp = temp /. Eps[aaa___,Momentum[k2,didi___], b___] :> + temp = temp /. Eps[aaa___,Momentum[k2,(*didi*)___], b___] :> (Eps[aaa,LorentzIndex[rhoo,n],b] * Pair[Momentum[k2,n], LorentzIndex[rhoo,n]] ) @@ -726,7 +726,7 @@ ) ] /; (Sort[Union[{qi,qj,k1,k2}]] === {k1,k2}) && FreeQ2[{r, s, t, u}, {k1, k2}] && - (checkd[k1] || check[k2]) && mem[T1,T2], + (checkd[k1] (*|| check[k2]*)) && mem[T1,T2], (* checkd[qi,qj] && mem[T1,T2], *) @@ -2263,17 +2263,17 @@ temp = temp /. fake[OPEm]->1 ]; If[ (contractlabel === True) && (!FreeQ[temp, LorentzIndex]), - For[ijji = 1, ijji < 6, ijji++, - If[ (EvenQ[#] && (Length[#]>0))&[Position[temp,$MU[ijji]]], - temp = temp /. $MU[ijji] -> muu[ijji]; + For[i = 1, i < 6, i++, + If[ (EvenQ[#] && (Length[#]>0))&[Position[temp,$MU[i]]], + temp = temp /. $MU[i] -> muu[i]; ] ]; temp = Expand2[temp, LorentzIndex]; If[ Head[temp] === Plus, ntemp = 0; - For[int = 1, int <=Length[temp], int++, - FCPrint[2,"int = ",int, " out of",Length[temp]]; - ntemp = ntemp + Contract[temp[[int]], Expanding -> True, + For[j = 1, j <=Length[temp], j++, + FCPrint[2,"int = ",j, " out of",Length[temp]]; + ntemp = ntemp + Contract[temp[[j]], Expanding -> True, EpsContract -> False, Rename -> True] ]; @@ -2302,18 +2302,18 @@ PairContract -> Pair; FCPrint[1,"PairContract done"]; If[ !FreeQ[temp, LorentzIndex], - For[ijji = 1, ijji < 6, ijji++, - If[ (EvenQ[#] && (Length[#]>0))&[Position[temp,$MU[ijji]]], - temp = temp /. $MU[ijji] -> muu[ijji]; + For[j = 1, j < 6, j++, + If[ (EvenQ[#] && (Length[#]>0))&[Position[temp,$MU[j]]], + temp = temp /. $MU[j] -> muu[j]; ] ]; FCPrint[1,"contracting agaaaaaaaaaain in OPE2TID"]; temp = Expand2[temp,LorentzIndex]; If[ Head[temp] === Plus, ntemp = 0; - For[int = 1, int <=Length[temp], int++, - FCPrint[2,"int = ",int, " out of",Length[temp]]; - ntemp = ntemp + Contract[temp[[int]], Expanding -> True, + For[r = 1, r <=Length[temp], r++, + FCPrint[2,"int = ",r, " out of",Length[temp]]; + ntemp = ntemp + Contract[temp[[r]], Expanding -> True, EpsContract -> False, Rename -> True] ]; diff --git a/FeynCalc/QCD/OPEInt.m b/FeynCalc/QCD/OPEInt.m index e16433dbd..e24ff0241 100755 --- a/FeynCalc/QCD/OPEInt.m +++ b/FeynCalc/QCD/OPEInt.m @@ -36,11 +36,12 @@ }; OPEInt[exp_, kk_, pp_, x_, opt___Rule] := - Block[ {facout,nex, nex0, epsc, epscc,factorout, divout, - epscdi, - n, k, ka, p, p2, sumk, sumk0, sumk1,de, dufa, powsub, opgeom, qqq, - null1, null2, qse, dUMMYM, mUuU, nUuU, finsu,flowerpower,delcol, - locepsilon, floweps, epsorder, nfa, noflow, opm, apa, dE, xXx, qqqk}, + Block[{ facout,nex, nex0, epsc, epscc,factorout, divout, + epscdi, n, k, ka, p, p2, sumk, sumk0, sumk1,de, dufa, powsub, opgeom, qqq, + null1, null2, qse, dUMMYM, mUuU, nUuU, finsu,flowerpower,delcol, + locepsilon, floweps, epsorder, nfa, noflow, opm, apa, dE, xXx, qqqk, nex1, null, + muUU, irules0, irules1, irules2, irules3, nfax + }, facout = 1; n = Dimension /. {opt} /. Options[OPEInt]; k = Momentum[kk, n]; @@ -83,7 +84,7 @@ (* amputate *) mUuU = LorentzIndex[FCGV[ToString[Unique["li"]]], n]; nUuU = LorentzIndex[FCGV[ToString[Unique["lI"]]], n]; - nex = nex /. Eps[a___, Momentum[kk,dii___], b___]^2 :> + nex = nex /. Eps[a___, Momentum[kk,(*dii*)___], b___]^2 :> (Eps[a, mUuU, b] * Pair[Momentum[kk, n], mUuU] * Eps[a, nUuU, b] * Pair[Momentum[kk, n], nUuU] ); @@ -116,8 +117,8 @@ nex = dufa nex ]; irules0 = { - anynonsense_. FeynAmpDenominator[PropagatorDenominator[k, 0]..]:>0, - anynonsense_. FeynAmpDenominator[PropagatorDenominator[k-p, 0]..]:>0, + _. FeynAmpDenominator[PropagatorDenominator[k, 0]..]:>0, + _. FeynAmpDenominator[PropagatorDenominator[k-p, 0]..]:>0, (* i1munu *) qqq[ Pair[de, k]^m_ fun1_[a___, ka, b___Momentum] * fun2_[aa___,ka,bb___Momentum] * @@ -127,17 +128,17 @@ ] ]:> (muUU = LorentzIndex[Unique[$MU], n]; - ( Pair[de, p]^m x^(m-1) (x (1-x))^(n/2-2) * - (*g_munu*) - ( Contract[fun1[a, muUU, b] fun2[aa, muUU, bb]] (1/2) Gamma[2-n/2] x* - (1-x) + - (*p_mu p_nu*) - EpsEvaluate[fun1[a,p,b] fun2[aa,p,bb]] Gamma[3-n/2] x^2/p2 + - EpsEvaluate[(fun1[a,p,b] fun2[aa,de,bb] + fun1[a,de,b] fun2[aa,p,bb] - ) / Pair[de, p]] (1/2) (Gamma[2-n/2]-Gamma[3-n/2]) (2x^2-x)+ - 1/4 (Gamma[3-n/2] (1-4 x + 4 x^2) + Gamma[2-n/2] (4 x - 6 x^2)) * - fun1[a,de,b] fun2[aa,de,bb] p2/Pair[de,p]^2) - )) /; ( ((fun1 === Eps) || (fun1 === Pair)) && + ( Pair[de, p]^m x^(m-1) (x (1-x))^(n/2-2) * + (*g_munu*) + ( Contract[fun1[a, muUU, b] fun2[aa, muUU, bb]] (1/2) Gamma[2-n/2] x* + (1-x) + + (*p_mu p_nu*) + EpsEvaluate[fun1[a,p,b] fun2[aa,p,bb]] Gamma[3-n/2] x^2/p2 + + EpsEvaluate[(fun1[a,p,b] fun2[aa,de,bb] + fun1[a,de,b] fun2[aa,p,bb] + ) / Pair[de, p]] (1/2) (Gamma[2-n/2]-Gamma[3-n/2]) (2x^2-x)+ + 1/4 (Gamma[3-n/2] (1-4 x + 4 x^2) + Gamma[2-n/2] (4 x - 6 x^2)) * + fun1[a,de,b] fun2[aa,de,bb] p2/Pair[de,p]^2) + )) /; ( ((fun1 === Eps) || (fun1 === Pair)) && ((fun2 === Eps) || (fun2 === Pair)) ), @@ -153,41 +154,41 @@ (muUU = LorentzIndex[Unique[$MU], n]; (*i6munu*) - EpsEvaluate[ - ( ((2 - n)*x^(-3 + m)*((1 - x)*x)^(n/2)* - (4 - n - 12*x + 4*n*x + 12*x^2 - 4*n*x^2)* - (* - FourVector[OPEDelta, MU]* FourVector[OPEDelta, NU]* + EpsEvaluate[ + ( ((2 - n)*x^(-3 + m)*((1 - x)*x)^(n/2)* + (4 - n - 12*x + 4*n*x + 12*x^2 - 4*n*x^2)* + (* + FV[OPEDelta, MU]* FV[OPEDelta, NU]* *) - fun1[a, de, b] fun2[aa, de, bb] * - Gamma[2 - n/2]* - Pair[de, p]^(-2 + m))/(16*(1 - x)^3) + - ((4 - n)*(6 - n)*x^(-1 + m)*((1 - x)*x)^(n/2)* - Gamma[2 - n/2]* - (* - FourVector[p, MU]* FourVector[p, NU]* + fun1[a, de, b] fun2[aa, de, bb] * + Gamma[2 - n/2]* + Pair[de, p]^(-2 + m))/(16*(1 - x)^3) + + ((4 - n)*(6 - n)*x^(-1 + m)*((1 - x)*x)^(n/2)* + Gamma[2 - n/2]* + (* + FV[p, MU]* FV[p, NU]* *) - fun1[a, p, b] fun2[aa, p, bb] * - Pair[de, p]^m)/ - (4*(1 - x)^3*Pair[p, p]^2) + - ((4 - n)*x^(-2 + m)*((1 - x)*x)^(n/2)*(2 - n - 6*x + 2*n*x)* - (* - (FourVector[OPEDelta, NU]*FourVector[p, MU] + - FourVector[OPEDelta, MU]*FourVector[p, NU])* + fun1[a, p, b] fun2[aa, p, bb] * + Pair[de, p]^m)/ + (4*(1 - x)^3*Pair[p, p]^2) + + ((4 - n)*x^(-2 + m)*((1 - x)*x)^(n/2)*(2 - n - 6*x + 2*n*x)* + (* + (FV[OPEDelta, NU]*FV[p, MU] + + FV[OPEDelta, MU]*FV[p, NU])* *) - (fun1[a,p,b] fun2[aa,de,bb] + fun1[a,de,b] fun2[aa,p,bb] - )* - Gamma[2 - n/2]* - Pair[de, p]^(-1 + m))/ - (8*(1 - x)^3*Pair[p, p]) + - ((4 - n)*x^(-2 + m)*((1 - x)*x)^(n/2)*Gamma[2 - n/2]* - (* - MetricTensor[MU, NU]* + (fun1[a,p,b] fun2[aa,de,bb] + fun1[a,de,b] fun2[aa,p,bb] + )* + Gamma[2 - n/2]* + Pair[de, p]^(-1 + m))/ + (8*(1 - x)^3*Pair[p, p]) + + ((4 - n)*x^(-2 + m)*((1 - x)*x)^(n/2)*Gamma[2 - n/2]* + (* + MT[MU, NU]* *) - Contract[fun1[a,muUU,b] fun2[aa, muUU, bb]]* - Pair[de, p]^m)/ - (4*(1 - x)^2*Pair[p, p]) - )] + Contract[fun1[a,muUU,b] fun2[aa, muUU, bb]]* + Pair[de, p]^m)/ + (4*(1 - x)^2*Pair[p, p]) + )] ) }; irules1 = { diff --git a/FeynCalc/QCD/OPEIntegrate.m b/FeynCalc/QCD/OPEIntegrate.m index 745f434d5..54a2214d2 100755 --- a/FeynCalc/QCD/OPEIntegrate.m +++ b/FeynCalc/QCD/OPEIntegrate.m @@ -41,7 +41,7 @@ n, k, ka, p2, fp, sumk, sumk0, sumk1,de, dufa, powsub, opgeom, qqq, null1, null2, qse, dUMMYM, mUuU, nUuU, finsu,flowerpower,delcol, locepsilon, floweps, epsorder, nfa, noflow, opm, apa, dE, xXx, qqqk, - sumbinom, sumbinomback + sumbinom, sumbinomback, ki, null, nex1, muUU, nfax }, facout = 1; n = Dimension /. {opt} /. Options[OPEIntegrate]; @@ -58,52 +58,52 @@ sumk0 /: (y_ /; !FreeQ[y, kk]) sumk0[aaa_, b_] := sumk0[aaa y, b]; sumk1[a_Times, b_] := sumk[qqq[SelectNotFree[a, kk]],b - ] (a/SelectNotFree[a,kk]); + ] (a/SelectNotFree[a,kk]); (* ( * *) powsub[xx_] := xx /. (a_/;(Head[a]===Plus) && (Length[a]>2) - )^(w_/;Head[w]=!=Integer) :> - (Isolate[Collect2[a,kk],kk, IsolateNames->loc - ]^w) /. - { - (((nok_/;FreeQ[nok,k]) - Pair[de,k])^ - a_Integer?Negative - ) :> - (sumk0[Pair[de,k]^(-a OPEk) / - nok^(-a (OPEk+1)), {OPEk,0,Infinity} - ] - )^(-a), - ( (n_. Pair[de, k] + (nok_ /; FreeQ[nok,k]) - )^a_Integer?Negative - ) :> - (-sumk0[n^(-a OPEk) Pair[de,k]^(-a OPEk) / - (-nok)^(-a (OPEk+1)), {OPEk,0,Infinity} - ] - ), + )^(w_/;Head[w]=!=Integer) :> + (Isolate[Collect2[a,kk],kk, IsolateNames->loc + ]^w) /. + { + (((nok_/;FreeQ[nok,k]) - Pair[de,k])^ + a_Integer?Negative + ) :> + (sumk0[Pair[de,k]^(-a OPEk) / + nok^(-a (OPEk+1)), {OPEk,0,Infinity} + ] + )^(-a), + ( (p_. Pair[de, k] + (nok_ /; FreeQ[nok,k]) + )^a_Integer?Negative + ) :> + (-sumk0[p^(-a OPEk) Pair[de,k]^(-a OPEk) / + (-nok)^(-a (OPEk+1)), {OPEk,0,Infinity} + ] + ), (* NEW 08/95 *) - ((n_. Pair[de,k] + m_ )^a_/;Head[a] =!= Integer - ) :> - (ki = Unique[OPEi]; - n^a sumbinom[a,OPEk[ki]] Pair[de,k]^OPEk[ki] * - PowerSimplify[(m/n)^(a-OPEk[ki])] - ) + ((p_. Pair[de,k] + m_ )^a_/;Head[a] =!= Integer + ) :> + (ki = Unique[OPEi]; + p^a sumbinom[a,OPEk[ki]] Pair[de,k]^OPEk[ki] * + PowerSimplify[(m/p)^(a-OPEk[ki])] + ) (* ueberfluessig (01/95) , - (Pair[de,k]^m_ (Pair[de,p_] - Pair[de,k])^a_) :> - (sumk0[Pair[de,k]^(OPEk+m/(-a)) / - Pair[de,p]^(OPEk+1), {OPEk,0,Infinity} - ] - )^(-a), - (Pair[de,k]^m_ (Pair[de,k] - Pair[de,p_])^a_) :> - (-sumk0[Pair[de,k]^(OPEk+m/(-a)) / - Pair[de,p]^(OPEk+1), {OPEk,0,Infinity} - ] - )^(-a) + (Pair[de,k]^m_ (Pair[de,p_] - Pair[de,k])^a_) :> + (sumk0[Pair[de,k]^(OPEk+m/(-a)) / + Pair[de,p]^(OPEk+1), {OPEk,0,Infinity} + ] + )^(-a), + (Pair[de,k]^m_ (Pair[de,k] - Pair[de,p_])^a_) :> + (-sumk0[Pair[de,k]^(OPEk+m/(-a)) / + Pair[de,p]^(OPEk+1), {OPEk,0,Infinity} + ] + )^(-a) *) - } /. sumk0 -> sumk; + } /. sumk0 -> sumk; opgeom[xy_,aa_] := sumk[powsub[xy], aa]; (* @@ -116,7 +116,7 @@ (* amputate *) mUuU = LorentzIndex[FCGV[ToString[Unique["li"]]], n]; nUuU = LorentzIndex[FCGV[ToString[Unique["li"]]], n]; - nex = nex /. Eps[a___, Momentum[kk,dii___], b___]^2 :> + nex = nex /. Eps[a___, Momentum[kk,(*dii*)___], b___]^2 :> (Eps[a, mUuU, b] * Pair[Momentum[kk, n], mUuU] * Eps[a, nUuU, b] * Pair[Momentum[kk, n], nUuU] ); @@ -154,8 +154,8 @@ fp[pe_] := fp[pe] = (-p2[pe]/ScaleMu^2)^Expand[(n/2 - 2)]; irules0 = { - anynonsense_. FeynAmpDenominator[PropagatorDenominator[k, 0]..]:>0, - anynonsense_. FeynAmpDenominator[PropagatorDenominator[k+ y_, 0]]:>0, + _. FeynAmpDenominator[PropagatorDenominator[k, 0]..]:>0, + _. FeynAmpDenominator[PropagatorDenominator[k+ _, 0]]:>0, (* i1munu *) qqq[ Pair[de, k]^m_ fun1_[a___, ka, b___Momentum] * fun2_[aa___,ka,bb___Momentum] * @@ -165,17 +165,17 @@ ] ]:> (muUU = LorentzIndex[Unique[$MU], n]; - fp[p] ( Pair[de, p]^m x^(m-1) (x (1-x))^(n/2-2) * - (*g_munu*) - ( Contract[fun1[a, muUU, b] fun2[aa, muUU, bb]] (1/2) Gamma[2-n/2] x* - (1-x) + - (*p_mu p_nu*) - EpsEvaluate[fun1[a,p,b] fun2[aa,p,bb]] Gamma[3-n/2] x^2/p2[p] + - EpsEvaluate[(fun1[a,p,b] fun2[aa,de,bb] + fun1[a,de,b] fun2[aa,p,bb] - ) / Pair[de, p]] (1/2) (Gamma[2-n/2]-Gamma[3-n/2]) (2x^2-x)+ - 1/4 (Gamma[3-n/2] (1-4 x + 4 x^2) + Gamma[2-n/2] (4 x - 6 x^2)) * - fun1[a,de,b] fun2[aa,de,bb] p2[p]/Pair[de,p]^2) - )) /; ( ((fun1 === Eps) || (fun1 === Pair)) && + fp[p] ( Pair[de, p]^m x^(m-1) (x (1-x))^(n/2-2) * + (*g_munu*) + ( Contract[fun1[a, muUU, b] fun2[aa, muUU, bb]] (1/2) Gamma[2-n/2] x* + (1-x) + + (*p_mu p_nu*) + EpsEvaluate[fun1[a,p,b] fun2[aa,p,bb]] Gamma[3-n/2] x^2/p2[p] + + EpsEvaluate[(fun1[a,p,b] fun2[aa,de,bb] + fun1[a,de,b] fun2[aa,p,bb] + ) / Pair[de, p]] (1/2) (Gamma[2-n/2]-Gamma[3-n/2]) (2x^2-x)+ + 1/4 (Gamma[3-n/2] (1-4 x + 4 x^2) + Gamma[2-n/2] (4 x - 6 x^2)) * + fun1[a,de,b] fun2[aa,de,bb] p2[p]/Pair[de,p]^2) + )) /; ( ((fun1 === Eps) || (fun1 === Pair)) && ((fun2 === Eps) || (fun2 === Pair)) ), @@ -191,41 +191,41 @@ (muUU = LorentzIndex[Unique[$MU], n]; (*i6munu*) - fp[p] EpsEvaluate[ - ( ((2 - n)*x^(-3 + m)*((1 - x)*x)^(n/2)* - (4 - n - 12*x + 4*n*x + 12*x^2 - 4*n*x^2)* - (* - FourVector[OPEDelta, MU]* FourVector[OPEDelta, NU]* + fp[p] EpsEvaluate[ + ( ((2 - n)*x^(-3 + m)*((1 - x)*x)^(n/2)* + (4 - n - 12*x + 4*n*x + 12*x^2 - 4*n*x^2)* + (* + FV[OPEDelta, MU]* FV[OPEDelta, NU]* *) - fun1[a, de, b] fun2[aa, de, bb] * - Gamma[2 - n/2]* - Pair[de, p]^(-2 + m))/(16*(1 - x)^3) + - ((4 - n)*(6 - n)*x^(-1 + m)*((1 - x)*x)^(n/2)* - Gamma[2 - n/2]* - (* - FourVector[p, MU]* FourVector[p, NU]* + fun1[a, de, b] fun2[aa, de, bb] * + Gamma[2 - n/2]* + Pair[de, p]^(-2 + m))/(16*(1 - x)^3) + + ((4 - n)*(6 - n)*x^(-1 + m)*((1 - x)*x)^(n/2)* + Gamma[2 - n/2]* + (* + FV[p, MU]* FV[p, NU]* *) - fun1[a, p, b] fun2[aa, p, bb] * - Pair[de, p]^m)/ - (4*(1 - x)^3*Pair[p, p]^2) + - ((4 - n)*x^(-2 + m)*((1 - x)*x)^(n/2)*(2 - n - 6*x + 2*n*x)* - (* - (FourVector[OPEDelta, NU]*FourVector[p, MU] + - FourVector[OPEDelta, MU]*FourVector[p, NU])* + fun1[a, p, b] fun2[aa, p, bb] * + Pair[de, p]^m)/ + (4*(1 - x)^3*Pair[p, p]^2) + + ((4 - n)*x^(-2 + m)*((1 - x)*x)^(n/2)*(2 - n - 6*x + 2*n*x)* + (* + (FV[OPEDelta, NU]*FV[p, MU] + + FV[OPEDelta, MU]*FV[p, NU])* *) - (fun1[a,p,b] fun2[aa,de,bb] + fun1[a,de,b] fun2[aa,p,bb] - )* - Gamma[2 - n/2]* - Pair[de, p]^(-1 + m))/ - (8*(1 - x)^3*Pair[p, p]) + - ((4 - n)*x^(-2 + m)*((1 - x)*x)^(n/2)*Gamma[2 - n/2]* - (* - MetricTensor[MU, NU]* + (fun1[a,p,b] fun2[aa,de,bb] + fun1[a,de,b] fun2[aa,p,bb] + )* + Gamma[2 - n/2]* + Pair[de, p]^(-1 + m))/ + (8*(1 - x)^3*Pair[p, p]) + + ((4 - n)*x^(-2 + m)*((1 - x)*x)^(n/2)*Gamma[2 - n/2]* + (* + MT[MU, NU]* *) - Contract[fun1[a,muUU,b] fun2[aa, muUU, bb]]* - Pair[de, p]^m)/ - (4*(1 - x)^2*Pair[p, p]) - )] + Contract[fun1[a,muUU,b] fun2[aa, muUU, bb]]* + Pair[de, p]^m)/ + (4*(1 - x)^2*Pair[p, p]) + )] ) }; irules1 = { @@ -338,17 +338,11 @@ True ]; irulesmassive = { - qqq[ - Pair[de, ka]^m_ FeynAmpDenominator[ - PropagatorDenominator[k, em_ /; nos[em]], - PropagatorDenominator[k - p_, 0] - ] - ] :> (- - I fp[p] em^(Epsilon/2) ( 2/Epsilon Pair[de, p]^m Gamma[1-Epsilon/2] x^m * - (1-x)^Epsilon - )) /. p2[p] -> em^2 /. ScaleMu -> (-I em), - qqq[ - Pair[de, ka]^m_ FeynAmpDenominator[ + qqq[Pair[de, ka]^m_ FeynAmpDenominator[PropagatorDenominator[k, e_ /; nos[e]], PropagatorDenominator[k - p_, 0]]] :> + (- I fp[p] e^(Epsilon/2) ( 2/Epsilon Pair[de, p]^m Gamma[1-Epsilon/2] x^m * + (1-x)^Epsilon)) /. p2[p] -> e^2 /. ScaleMu -> (-I e), + + qqq[Pair[de, ka]^m_ FeynAmpDenominator[ PropagatorDenominator[k, em_ /; nos[em]], PropagatorDenominator[k, em_ /; nos[em]], PropagatorDenominator[k - p_, 0] @@ -406,21 +400,21 @@ ] ]:> (muUU = LorentzIndex[Unique[$MU], n]; - (I fp[p] * ( - x^m Pair[de,p]^m (1-x)^(n-4) * - ( - -Gamma[3-n/2] x^2/(1-x) fun1[a,p,b] fun2[aa,p,bb]/em^2 + - 1/2 Gamma[2-n/2] * - Contract[fun1[a,muUU,b] fun2[aa, muUU, bb]] (1-x) + - + Contract[ fun1[a,de,b] fun2[aa,p,bb] + - fun1[a,p,b] fun2[aa,de,bb] - ]/Pair[de,p] * - (-Gamma[3-n/2] x + Gamma[2-n/2] (x-1/2) ) + - Contract[fun1[a,de,b] fun2[aa,de,bb]]/Pair[de,p]^2 em^2 * - (-Gamma[3-n/2] (1-x) + 3/2 (1-x) Gamma[2-n/2]) - ) - ) - )) + (I fp[p] * ( + x^m Pair[de,p]^m (1-x)^(n-4) * + ( + -Gamma[3-n/2] x^2/(1-x) fun1[a,p,b] fun2[aa,p,bb]/em^2 + + 1/2 Gamma[2-n/2] * + Contract[fun1[a,muUU,b] fun2[aa, muUU, bb]] (1-x) + + + Contract[ fun1[a,de,b] fun2[aa,p,bb] + + fun1[a,p,b] fun2[aa,de,bb] + ]/Pair[de,p] * + (-Gamma[3-n/2] x + Gamma[2-n/2] (x-1/2) ) + + Contract[fun1[a,de,b] fun2[aa,de,bb]]/Pair[de,p]^2 em^2 * + (-Gamma[3-n/2] (1-x) + 3/2 (1-x) Gamma[2-n/2]) + ) + ) + )) }; nex = nex//.irules0 //. irules1 //. irules2 /. irulesmassive /. diff --git a/FeynCalc/QCD/OPEIntegrate2.m b/FeynCalc/QCD/OPEIntegrate2.m index 0b98443b0..a200141b0 100755 --- a/FeynCalc/QCD/OPEIntegrate2.m +++ b/FeynCalc/QCD/OPEIntegrate2.m @@ -21,6 +21,10 @@ Begin["`OPEIntegrate2`Private`"] +kli::usage=""; +dummy::usage=""; +sumgeom::usage=""; + Options[OPEIntegrate2] = { Collecting -> False, FeynmanParameterNames -> {FCGV["x"], FCGV["y"], FCGV["z"]}, @@ -111,24 +115,24 @@ isol[ka_][y_] := Isolate[y,Append[SelectFree[Variables[Flatten[ - Cases2[y,Power2]/. Power2->List]],Pair], - ka], IsolateNames->ll, IsolateSplit->5555I]; + Cases2[y,Power2]/. Power2->List]],Pair], + ka], IsolateNames->KK, IsolateSplit->5555I]; gpowsub[xx_,k_] := xx /. { - (((nok_ /; FreeQ[nok,k]) - - Pair[de_, Momentum[k,D]])^a_Integer?Negative - ) :> - (sumgeom[ {OPEl,0,Infinity} ]* - Pair[de, Momentum[k,D]]^(-a OPEl)/ - nok^(-a (OPEl+1)) - )^(-a), - ((Pair[de_, Momentum[k,D]] + - (nok_/;FreeQ[nok,k]))^ a_Integer?Negative - ) :> - (-sumgeom[ {OPEl,0,Infinity} ] * - Pair[de, Momentum[k,D] - ]^(-a OPEl)/(-nok)^(-a (OPEl+1)) - ) }; + (((nok_ /; FreeQ[nok,k]) - + Pair[de_, Momentum[k,D]])^a_Integer?Negative + ) :> + (sumgeom[ {OPEl,0,Infinity} ]* + Pair[de, Momentum[k,D]]^(-a OPEl)/ + nok^(-a (OPEl+1)) + )^(-a), + ((Pair[de_, Momentum[k,D]] + + (nok_/;FreeQ[nok,k]))^ a_Integer?Negative + ) :> + (-sumgeom[ {OPEl,0,Infinity} ] * + Pair[de, Momentum[k,D] + ]^(-a OPEl)/(-nok)^(-a (OPEl+1)) + ) }; opsu[a_Plus,b__] := Map[opsu[#,b]&,a]; @@ -169,7 +173,7 @@ FeynCalcExternal[ PowerSimplify[ ExpandScalarProduct[FeynCalcInternal[ z (pe-SO[k])^em]/. k-> -k+(pe/.SO->Identity) - ]] ] /. FAD -> fadk /. + ]] ] /. FAD -> fadk /. fadk -> fado /. fado -> FAD; If[ Head[exp] === Times, exp = FeynCalcExternal[exp] /.SO->SOD/.SP->SPD; @@ -184,7 +188,7 @@ exp = FeynCalcExternal[FeynAmpDenominatorSimplify[ FeynCalcInternal[exp]] ] /. FAD-> fadk /. fadk->fado/.fado->FAD; - If[ MatchQ[exp, any_ (SOD[k]-bla_)^(em_/;Head[em]=!=Integer)], + If[ MatchQ[exp, _ (SOD[k]-_)^(em_/;Head[em]=!=Integer)], exp = exp /. (SOD[k]-bla_)^pow_ :> ( PowerSimplify[(-1)^pow]*(bla-SOD[k])^pow) ]; @@ -238,10 +242,10 @@ ] ]; -denmatch[Power[den_,mm_], ka_ /; Length[ka]===2] := +denmatch[Power[den_,(*mm*)_], ka_ /; Length[ka]===2] := True /; FreeQ[FourDivergence[Expand[ExpandScalarProduct[den]] - Pair[ka,ka], - Pair[ka,LorentzIndex[any,ka[[2]]]] + Pair[ka,LorentzIndex[dummy,ka[[2]]]] ], ka[[1]] ]; @@ -251,7 +255,7 @@ False ]; getl[h_,ka_Momentum] := - Block[ {tg,ll}, + Block[ {tg,ll, check}, If[ !MatchQ[SelectFree[h,{Power2,LorentzIndex}], _^_], False, (*else*) @@ -279,13 +283,13 @@ ]; getopem[h_] := (If[ Head[#]===Pair, - 1, - If[ Head[#]===Power || Head[#]===Power2, - #[[2]], - False - ] - ]& - )@SelectNotFree[h, Power2]; + 1, + If[ Head[#]===Power || Head[#]===Power2, + #[[2]], + False + ] + ]& + )@SelectNotFree[h, Power2]; getmu[h_] := Cases2[h, LorentzIndex]; @@ -313,7 +317,7 @@ MatchQ[h//Numerator, Power2[Pair[Momentum[OPEDelta,___], km], _]* Pair[km, LorentzIndex[aa_,___]]* - Pair[km, LorentzIndex[bb_,___]] + Pair[km, LorentzIndex[bb_,___]]/;(aa=!=bb)(*VS*) ]&& denmatch[SelectFree[h,Power2]//Denominator,km] && MatchQ[SelectNotFree[h, Power2], Power2[Pair[Momentum[OPEDelta,___],km ],_]]; @@ -324,14 +328,14 @@ Power2[Pair[Momentum[OPEDelta,___],km ],_]* Pair[km, LorentzIndex[aa_,___]]* Pair[km, LorentzIndex[bb_,___]]* - Pair[km, LorentzIndex[cc_,___]] + Pair[km, LorentzIndex[cc_,___]]/;(aa=!=bb && bb=!=cc)(*VS*) ]&& denmatch[SelectFree[h,Power2]//Denominator,km] && MatchQ[SelectNotFree[h,Power2], Power2[Pair[Momentum[OPEDelta,___],km ],_]]; (* I^(m)_alpha *) ilist[ih_, Momentum[k_,n_], od_Integer] := - Block[ {al,m2,l,de,m,mu,h,fake}, + Block[ {al,m2,l,de,m,mu,h,fake,lmu,nu,la,lnu,lla,dmu,dnu,dla,del,l2}, h = ih /. (a_ /; !FreeQ[a,k])^(w_ /;Head[w]=!=Integer) :> Power2[a, w]; de = Momentum[OPEDelta, n]; @@ -403,24 +407,24 @@ dmu dnu dla/del^3 ) , True, Print["MISTTTTTTTTTTTTTTTTT"]; - Dialog[]; - h + Dialog[]; + h ]/.fake->0 /. Power[aa_,bb_] :> Power[aa,Expand[bb]] ]; opeinttable = { -kli[k_,FAD[k_,k_Symbol.., (k_)+(p1_),___] (_. + _. SOD[k_])^(OPEm+_.)] :>0 +kli[k_,FAD[k_,k_Symbol.., (k_)+((*p1*)_),___] (_. + _. SOD[k_])^(OPEm+_.)] :>0 , -kli[k_,FAD[k_Symbol.., (k_)+(p1_), (k_)+(p2_),___] * +kli[k_,FAD[k_Symbol.., (k_)+((*p1*)_), (k_)+((*p2*)_),___] * (_. + _. SOD[k_])^(OPEm+_.)] :>0 , -kli[k_,FAD[k_Symbol.., (k_)+(p1_), (k_)+(p2_),___] * +kli[k_,FAD[k_Symbol.., (k_)+((*p1*)_), (k_)+((*p2*)_),___] * (_. + _. SOD[k_])^(OPEm+_.) SOD[k_]^_. ] :>0 , -kli[k_,FAD[k_,(k_)-(p1_),(k_)-(p3_)] (_. + _. SOD[k_])^(OPEm+_.)] :>0 +kli[k_,FAD[k_,(k_)-((*p1*)_),(k_)-((*p3*)_)] (_. + _. SOD[k_])^(OPEm+_.)] :>0 , -kli[k_,FAD[k_,k_,(k_)-(p1_),(k_)-(p3_)] (_. + _. SOD[k_])^(OPEm+_.)]:>0 +kli[k_,FAD[k_,k_,(k_)-((*p1*)_),(k_)-((*p3*)_)] (_. + _. SOD[k_])^(OPEm+_.)]:>0 , kli[k_,FAD[(k_)-(p3_),(k_)-(p1_)]*SOD[k_]^(OPEm+en_.) SPD[k_,k_]]:> (-2*I*Sn*SO[p3]^(1 + en + OPEm)* @@ -548,17 +552,17 @@ kli[k_,FAD[k_,(k_)-(p3_)]*SOD[k_]^(-2+OPEm)]:> (-2*I*Sn*SO[p3]^(-2+OPEm))/(Epsilon*(-1+OPEm)) , -kli[k_,FAD[k_,(k_)-(p3_),(k_)-(p1_)]* SOD[k_]^(-2+OPEm)]:>0 +kli[k_,FAD[k_,(k_)-((*p3*)_),(k_)-((*p1*)_)]* SOD[k_]^(-2+OPEm)]:>0 , kli[k_,FAD[k_,(k_)-(p1_)]*SOD[k_]^(-1+OPEm)]:> (-2*I*Sn*SO[p1]^(-1+OPEm))/(Epsilon*OPEm) , -kli[k_,FAD[k_,k_,(k_)-(p1_)]*SOD[k_]^(-1+OPEm)]:>0 +kli[k_,FAD[k_,k_,(k_)-((*p1*)_)]*SOD[k_]^(-1+OPEm)]:>0 , kli[k_,FAD[k_,(k_)-(p3_)]*SOD[k_]^(-1+OPEm)]:> (-2*I*Sn*SO[p3]^(-1+OPEm))/(Epsilon*OPEm) , -kli[k_,FAD[k_,k_,(k_)-(p3_)]*SOD[k_]^(-1+OPEm)]:>0 +kli[k_,FAD[k_,k_,(k_)-((*p3*)_)]*SOD[k_]^(-1+OPEm)]:>0 , kli[k_,FAD[(k_)-(p3_),(k_)-(p1_)]*SOD[k_]^(-1+OPEm)]:> (2*I*Sn*SO[p1]^OPEm)/(Epsilon*OPEm*(-SO[p1]+SO[p3]))- @@ -581,17 +585,17 @@ (2*I*Sn*SO[p1]^(1+en+OPEm))/(Epsilon*(1+en+OPEm)*(-SO[p1]+SO[p3])) , -kli[k_,FAD[k_,k_,(k_)-(p1_)]*SOD[k_]^(1+OPEm)]:>0, -kli[k_,FAD[k_,k_,(k_)-(p3_)]*SOD[k_]^(1+OPEm)]:>0, -kli[k_,FAD[k_,(k_)-(p3_),(k_)-(p1_)]* SOD[k_]^(1+OPEm)]:>0, -kli[k_,FAD[k_,k_,(k_)-(p3_),(k_)-(p1_)]* SOD[k_]^(2+OPEm)]:>0, -kli[k_,FAD[k_,(k_)-(p3_),(k_)-(p1_)]* SOD[k_]^(-1+OPEm)]:>0, -kli[k_,FAD[k_,k_,(k_)-(p3_),(k_)-(p1_)]* SOD[k_]^(-1+OPEm)]:>0, -kli[k_,FAD[k_,k_,(k_)-(p1_)]*SOD[k_]^OPEm]:>0, -kli[k_,FAD[k_,k_,(k_)-(p3_)]*SOD[k_]^OPEm]:>0, -kli[k_,FAD[k_,(k_)-(p3_),(k_)-(p1_)]*SOD[k_]^OPEm]:>0, -kli[k_,FAD[k_,k_,(k_)-(p3_),(k_)-(p1_)]* SOD[k_]^(1+OPEm)]:>0, -kli[k_,FAD[k_,k_,(k_)-(p3_),(k_)-(p1_)]*SOD[k_]^OPEm]:> 0, +kli[k_,FAD[k_,k_,(k_)-((*p1*)_)]*SOD[k_]^(1+OPEm)]:>0, +kli[k_,FAD[k_,k_,(k_)-((*p3*)_)]*SOD[k_]^(1+OPEm)]:>0, +kli[k_,FAD[k_,(k_)-((*p3*)_),(k_)-((*p1*)_)]* SOD[k_]^(1+OPEm)]:>0, +kli[k_,FAD[k_,k_,(k_)-((*p3*)_),(k_)-((*p1*)_)]* SOD[k_]^(2+OPEm)]:>0, +kli[k_,FAD[k_,(k_)-((*p3*)_),(k_)-((*p1*)_)]* SOD[k_]^(-1+OPEm)]:>0, +kli[k_,FAD[k_,k_,(k_)-((*p3*)_),(k_)-((*p1*)_)]* SOD[k_]^(-1+OPEm)]:>0, +kli[k_,FAD[k_,k_,(k_)-((*p1*)_)]*SOD[k_]^OPEm]:>0, +kli[k_,FAD[k_,k_,(k_)-((*p3*)_)]*SOD[k_]^OPEm]:>0, +kli[k_,FAD[k_,(k_)-((*p3*)_),(k_)-((*p1*)_)]*SOD[k_]^OPEm]:>0, +kli[k_,FAD[k_,k_,(k_)-((*p3*)_),(k_)-((*p1*)_)]* SOD[k_]^(1+OPEm)]:>0, +kli[k_,FAD[k_,k_,(k_)-((*p3*)_),(k_)-((*p1*)_)]*SOD[k_]^OPEm]:> 0, (* newW*) kli[k_,FAD[k_, -p1_ + p2_ + k_]*(SOD[p2_] + SOD[k_])^(OPEm + en_.)]:> @@ -626,13 +630,13 @@ (SO[p1] - SO[p2])^(1 + en + OPEm)/((1 + en + OPEm)*SO[p2])))/ Epsilon , -kli[k_, FAD[k_, -p1_ + (k_), -p2_ + (k_)]* - (SOD[p1_] - SOD[k_])^(OPEm + (en_.))] :> 0 +kli[k_, FAD[k_, -p1_ + (k_), -(*p2*)_ + (k_)]* + (SOD[p1_] - SOD[k_])^(OPEm + ((*en*)_.))] :> 0 , -kli[k_, FAD[k_, -p1_ + (k_), -p1_ + (k_), -p2_ + (k_)]* - (SOD[p1_] - SOD[k_])^(OPEm + (en_.))] :> 0 +kli[k_, FAD[k_, -p1_ + (k_), -p1_ + (k_), -(*p2*)_ + (k_)]* + (SOD[p1_] - SOD[k_])^(OPEm + ((*en*)_.))] :> 0 , -kli[k_, FAD[k_, k_, -p1_ + p2_ + (k_)]*SOD[k_]^(OPEm + (en_.))] :> 0 +kli[k_, FAD[k_, k_, -(*p1*)_ + (*p2*)_ + (k_)]*SOD[k_]^(OPEm + ((*en*)_.))] :> 0 , kli[k_, FAD[k_, k_, -p1_ + p2_ + (k_)]*SOD[k_]^(OPEm + (en_.))* SPD[p1_, k_]] :> @@ -658,27 +662,27 @@ (-SO[p1] + SO[p2])^(1 + en + OPEm)*((1 + en + OPEm)*SO[p1] + SO[p2])))/ (Epsilon*(1 + en + OPEm)*(2 + en + OPEm)*SO[p1]) , -kli[k_, FAD[k_, -p2_ + (k_)]*(SOD[p2_] - SOD[k_])^(en_. + OPEm)*SOD[k_] - ] :> +kli[k_, FAD[k_, -p2_ + (k_)]*(SOD[p2_] - SOD[k_])^(en_. + OPEm)*SOD[k_]] :> (-2*I*Sn*SO[p2]^(1 + en + OPEm))/(Epsilon*(1 + en + OPEm)*(2 + OPEm+en)) , -kli[k_, FAD[(k_) - (p2_), (k_) - (p1_)]*SOD[k_]* - (-SOD[k_] + SOD[p2_])^(en + OPEm)] :> -(2*I*(-1)^(1 + en + OPEm)*Sn* - ((SO[p1] - SO[p2])^(1 + en + OPEm)/(1 + en + OPEm) - - (SO[p1] - SO[p2])^(1 + en + OPEm)/((1 + en + OPEm)*(2 + en + OPEm)) + - ((SO[p1] - SO[p2])^(en + OPEm)*SO[p2])/(1 + en + OPEm)))/Epsilon +kli[k_, FAD[(k_) - (p2_), (k_) - (p1_)]*SOD[k_]*(-SOD[k_] + SOD[p2_])^(e + OPEm)] :> +(2*I*(-1)^(1 + e + OPEm)*Sn* + ((SO[p1] - SO[p2])^(1 + e + OPEm)/(1 + e + OPEm) - + (SO[p1] - SO[p2])^(1 + e + OPEm)/((1 + e + OPEm)*(2 + e + OPEm)) + + ((SO[p1] - SO[p2])^(e + OPEm)*SO[p2])/(1 + e + OPEm)))/Epsilon }; +(*TODO This is simply not right! One should never mess up with such + low-level functions as If!!!*) Unprotect[If]; If[ -Re[OPEi - OPEm] > 1, aa_, - bb_ + (*bb*)_ ] := aa; If[ -Re[OPEi - OPEm] > 2, aa_, - bb_ + (*bb*)_ ] := aa; diff --git a/FeynCalc/QCD/OPEIntegrateDelta.m b/FeynCalc/QCD/OPEIntegrateDelta.m index 9f56ffe9d..ec3375650 100755 --- a/FeynCalc/QCD/OPEIntegrateDelta.m +++ b/FeynCalc/QCD/OPEIntegrateDelta.m @@ -51,7 +51,7 @@ recorded for reference (and bug-checking) in the global list OPEIntegrateDelta[expr_, x_, m_, ops___Rule] := Block[ {tt, locdim, null, xmpart, fypart, lpa, new, dim, reg, nonreg, mint, ppi, kernel, rkern, f1, kfa, intsave, eporder, res,ttii, - ttx, finsub}, + ttx, finsub, fy, ttnox, ttp}, eporder = EpsilonOrder /. {ops} /. Options[OPEIntegrateDelta]; dim = Dimension /. {ops} /. Options[OPEIntegrateDelta]; finsub = FinalSubstitutions /. {ops} /. Options[OPEIntegrateDelta]; diff --git a/FeynCalc/QCD/OPESum.m b/FeynCalc/QCD/OPESum.m index 7deb30123..819b1164e 100755 --- a/FeynCalc/QCD/OPESum.m +++ b/FeynCalc/QCD/OPESum.m @@ -31,7 +31,7 @@ 0; -OPESum[__, {_,0,m_Integer?Negative},___List] := +OPESum[__, {_,0,_Integer?Negative},___List] := 0; OPESum[a_, {i_, j_, n_Integer/; n>=0}, any___] := diff --git a/FeynCalc/QCD/OPESumSimplify.m b/FeynCalc/QCD/OPESumSimplify.m index e9d6fd55c..9ec7e4644 100755 --- a/FeynCalc/QCD/OPESumSimplify.m +++ b/FeynCalc/QCD/OPESumSimplify.m @@ -44,7 +44,7 @@ moreind, {i,c,d}] /. lsum4s -> OPESum; powsu7[a_] := a; - powsu7[b_, mor___List, {i_, c_, d_}] := + powsu7[b_, mor___List, {i_, _, _}] := powsu7[b /. Power2[(-1),any_] :> Expand[(-1)^any] /. { (-1)^i pow_[a_,i] :> pow[-a,i] /; pow === Power || pow===Power2, diff --git a/FeynCalc/QCD/RHI.m b/FeynCalc/QCD/RHI.m index 63dd48c97..3acb12082 100755 --- a/FeynCalc/QCD/RHI.m +++ b/FeynCalc/QCD/RHI.m @@ -40,14 +40,15 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n End[] Begin["`RHI`Private`"] +est::usage=""; -Options[RHI] = {Directory -> "rh/ope/diagrams/", - (*nosaveDir -> False["rhisave"],*) - EpsilonOrder -> 0, - FORM -> False, - Momentum -> FCGV["p"]}; - - +Options[RHI] = { + Directory -> "rh/ope/diagrams/", + (*nosaveDir -> False["rhisave"],*) + EpsilonOrder -> 0, + FORM -> False, + Momentum -> FCGV["p"] +}; RHI[{v_,w_,x_,y_,z_},{a_,b_,c_,d_,e_}, {al_,be_,ga_,de_,ep_}, {k1_, k2_},o___Rule ] := @@ -142,13 +143,13 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n {al_, (be_Integer)?Positive, ga_, 0, (ep_Integer)?Positive},o___Rule ] := (Block[ {sop,p}, - p = Momentum /. {o} /. Options[RHI]; - sop = Pair[Momentum[OPEDelta,D], Momentum[p,D]]; - (rRHI[{0, 0, 1, 0, 0}, {-1 + a, 1 + b, c, d, e}, {al, be, ga, 0, ep},o] - - rRHI[{-2 + a, 1 + b, c, d, e}, {-1 + al, be, ga, 0, ep},o]*sop + - rRHI[{0, 0, 0, 0, 1}, {-1 + a, b, c, d, e}, {al, be, ga, 0, ep},o]*sop - )//Expand - ]/.rRHI->RHI) /; ((b =!= 0) || (d =!= 0) || (e =!= 0)); + p = Momentum /. {o} /. Options[RHI]; + sop = Pair[Momentum[OPEDelta,D], Momentum[p,D]]; + (rRHI[{0, 0, 1, 0, 0}, {-1 + a, 1 + b, c, d, e}, {al, be, ga, 0, ep},o] - + rRHI[{-2 + a, 1 + b, c, d, e}, {-1 + al, be, ga, 0, ep},o]*sop + + rRHI[{0, 0, 0, 0, 1}, {-1 + a, b, c, d, e}, {al, be, ga, 0, ep},o]*sop + )//Expand + ]/.rRHI->RHI) /; ((b =!= 0) || (d =!= 0) || (e =!= 0)); RHI[{0, 0, 1, 0, 0}, {a_, b_, c_, d_, e_}, {(al_Integer)?Positive, be_, 0, de_, (ep_Integer)?Positive}, @@ -313,7 +314,7 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n *) -RHI[{a_,b_,c_,d_,e_},{al_,0,ga_,de_ /; de =!= 0,ep_}, opt___Rule] := +RHI[{a_,b_,c_,d_,e_},{al_,0,ga_,de_ /; de =!= 0,ep_}, (*opt*)___Rule] := (-1)^e RHI[{c,d,a,b,e}, {ga,de,al,0,ep}]; (* q1 -> -q1+p; q2 -> -q2+p *) @@ -339,13 +340,13 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n {dd__}, opt___Rule ] := - RHI[{-1, b-1,c,d,e+1}, {dd}, opt] + - RHI[{0,b-1,c,d,e}, {dd}, opt]; + RHI[{0,b-1,c,d,e}, {dd}, opt]; RHI[{a_Integer?Positive,-1,c_Integer,d_Integer,e_/;Head[e]=!=Integer}, {dd__}, opt___Rule ] := RHI[{a-1,-1,c,d,e+1}, {dd}, opt] + - RHI[{a-1,0,c,d,e}, {dd}, opt]; + RHI[{a-1,0,c,d,e}, {dd}, opt]; RHI[{0,-1,0,0,e_/;Head[e]=!=Integer}, {1,1,1,1,1}, opt___Rule @@ -353,8 +354,7 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n PowerSimplify[(-1)^e] RHI[{-1,0,0,0,e},{1,1,1,1,1},opt]; RHI[{a_,b_,c_,d_,e_Integer?Positive},{bla__}, opt___Rule] := - Sum[Binomial[e,ii] (-1)^(e-ii) RHI[{a+ii, b+e-ii,c,d,0}, {bla}, opt - ], {ii,0,e}]//Expand; + Sum[Binomial[e,i] (-1)^(e-i) RHI[{a+i, b+e-i,c,d,0}, {bla}, opt], {i,0,e}]//Expand; RHI[{a_,n_Integer?Positive,c_,d_,-1},{bla__}, opt___Rule] := -RHI[{a,n-1,c,d,0},{bla},opt] + RHI[{a+1,n-1,c,d,-1},{bla},opt]; @@ -374,9 +374,7 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n (-1)^e RHI[{b, a, d, c, e}, {be, al, de, -1, ep}, opt]; (* f442*) -RHI[{a_,b_Integer,c_,0,e_ /; Head[e]=!=Integer}, - {al_,be_,ga_,0, ep_},opt___Rule - ] := +RHI[{a_,b_Integer,c_,0,e_ /; Head[e]=!=Integer}, {al_,be_,ga_,0, ep_}, (*opt*)___Rule] := RHI[{a,e,c,0,b},{al,ep,ga,0,be}]; @@ -417,7 +415,7 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n opt___Rule ] := 0 /; (EpsilonOrder /. {opt} /. Options[RHI]) < 0 && - (Apply[Plus, SelectFree[ll,OPEm]]>=0); + (Apply[Plus, SelectFree[ll,OPEm]]>=0); RHI[snum___List, {a_,b_,c_,d_,e_,f_,g_},{al_,be_,ga_,de_,ep_}, opt___Rule] := loadrhi[snum,{a,b,c,d,e,f,g},{al,be,ga,de,ep}, nosaveDir /. {opt} /. @@ -453,10 +451,10 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n (* shortdef *) short[x_] := StringReplace[ToString[x /. - { Times :> est, Plus :> est, - Pair :> est, Power :> est - } /. {est :> st}], {"[" -> "", "]" -> "", ", " -> ""} - ]; + { Times :> est, Plus :> est, + Pair :> est, Power :> est + } /. {est :> st}], {"[" -> "", "]" -> "", ", " -> ""} + ]; (*XXX*) frh = FixedPoint[ReleaseHold, #]&; loadrhi[indi___List, save_String, opt___Rule] := @@ -594,8 +592,9 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n }; fromform[y_String,opt___Rule] := - Block[ {formprog, fil,new1,newm,new,fac}, -(* construct the form program *) + Block[{ formprog, fil,new1,newm,new,fac, ww, myflag, rhd0, + mmm, null1, null2}, + (* construct the form program *) If[ (EpsilonOrder /. {opt} /. Options[RHI]) < 0, formprog = Join[form1, {y}, form2], If[ (EpsilonOrder /. {opt} /. Options[RHI]) === 1, @@ -640,9 +639,9 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n ]; new = Join[{"("}, new, {")"}]; OpenWrite[HomeDirectory[]<>"/rh/ope/diagrams/doit.m"]; - For[ij = 1, ij <= Length[new], ij++, + For[r = 1, r <= Length[new], r++, WriteString[HomeDirectory[]<>"/rh/ope/diagrams/doit.m", - new[[ij]], "\n"]; + new[[r]], "\n"]; ]; Close[HomeDirectory[]<>"/rh/ope/diagrams/doit.m"]; new = Get[HomeDirectory[]<>"/rh/ope/diagrams/doit.m"]; @@ -665,15 +664,15 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n newm = SelectNotFree[new, FCGV["MINUSONE"]]; clo[yy__] := If[ !FreeQ2[{yy}, {Epsilon, - DeltaFunction}], + DeltaFunction}], Plus[yy], Collect2[Plus[yy], {PolyLog,Log},Factoring->False] ]; coled[xx_] := Collect2[xx /. DeltaFunction[_]->0, Epsilon, - Factoring->False] + - DeltaFunction[1-FCGV["x"]] Collect2[D[xx, - DeltaFunction[1-FCGV["x"]]], Epsilon,Factoring->False]; + Factoring->False] + + DeltaFunction[1-FCGV["x"]] Collect2[D[xx, + DeltaFunction[1-FCGV["x"]]], Epsilon,Factoring->False]; new1 = coled[new1] /. Plus -> clo; If[ newm =!= 0, mmm = SelectNotFree[newm, FCGV["MINUSONE"]]; @@ -692,28 +691,28 @@ The exponents of the numerator scalar product are (dl = OPEDelta): \n\n str[y_] := StringReplace[y, {"[" -> "(", - "]" -> ")", - "d_(1-x)" -> "DeltaFunction[1-x]", - "(-)^m" -> "(MINUSONE)^m", - "p.p" -> "ScalarProduct[p,p]", - "zeta2" -> "Zeta2", - "zeta3" -> "Zeta[3]", - "s12(1-x)" -> "Nielsen[1,2][1-x]", - "li2(1-x)" -> "PolyLog[2,1-x]", - "li3(1-x)" -> "PolyLog[3,1-x]", - "li3(-x)" -> "PolyLog[3,-x]", - "li3(-(1-x)/(1+x))" -> - "PolyLog[3,-(1-x)/(1+x)]", - "li3((1-x)/(1+x))" -> - "PolyLog[3,(1-x)/(1+x)]", - "li2(-x)" -> "PolyLog[2,-x]", - "log(x)" -> "Log[x]", - "log(x,1 - 1/2*x)" -> "LOG[x,1-x/2]", - "li2(x,1/2*x)" -> "LI2[x,1/2 x]", - "log(1+x)" -> "Log[1+x]", - "log(1-x)" -> "Log[1-x]" - } - ]; + "]" -> ")", + "d_(1-x)" -> "DeltaFunction[1-x]", + "(-)^m" -> "(MINUSONE)^m", + "p.p" -> "ScalarProduct[p,p]", + "zeta2" -> "Zeta2", + "zeta3" -> "Zeta[3]", + "s12(1-x)" -> "Nielsen[1,2][1-x]", + "li2(1-x)" -> "PolyLog[2,1-x]", + "li3(1-x)" -> "PolyLog[3,1-x]", + "li3(-x)" -> "PolyLog[3,-x]", + "li3(-(1-x)/(1+x))" -> + "PolyLog[3,-(1-x)/(1+x)]", + "li3((1-x)/(1+x))" -> + "PolyLog[3,(1-x)/(1+x)]", + "li2(-x)" -> "PolyLog[2,-x]", + "log(x)" -> "Log[x]", + "log(x,1 - 1/2*x)" -> "LOG[x,1-x/2]", + "li2(x,1/2*x)" -> "LI2[x,1/2 x]", + "log(1+x)" -> "Log[1+x]", + "log(1-x)" -> "Log[1-x]" + } + ]; diff --git a/FeynCalc/QCD/RHM.m b/FeynCalc/QCD/RHM.m index c43e96438..1b4a912d6 100755 --- a/FeynCalc/QCD/RHM.m +++ b/FeynCalc/QCD/RHM.m @@ -66,15 +66,15 @@ }, opt___Rule ] := Block[{p}, p = Momentum /. {opt} /. Options[RHM]; -Sum[-(((-1)^ie*Binomial[e, ie]*Gamma[-2 + be + de - Epsilon/2]* +Sum[-(((-1)^r*Binomial[e, r]*Gamma[-2 + be + de - Epsilon/2]* Gamma[2 + d - de + Epsilon/2]*Gamma[2 + c + Epsilon/2 - ga]* Gamma[-2 + al - Epsilon/2 + ga]* - Gamma[2 + a - al + e + Epsilon/2 - ie]* - Gamma[2 + b - be + Epsilon/2 + ie]*Power2[SO[p], a + b + c + d + e]* + Gamma[2 + a - al + e + Epsilon/2 - r]* + Gamma[2 + b - be + Epsilon/2 + r]*Power2[SO[p], a + b + c + d + e]* Power2[-SP[p, p], Epsilon2]*Power2[SP[p, p], 4 - al - be - de - ga])/ (Gamma[al]*Gamma[be]*Gamma[de]*Gamma[ga]* - Gamma[4 + a - al + c + e + Epsilon - ga - ie]* - Gamma[4 + b - be + d - de + Epsilon + ie])), {ie, 0, e}] + Gamma[4 + a - al + c + e + Epsilon - ga - r]* + Gamma[4 + b - be + d - de + Epsilon + r])), {r, 0, e}] ]; RHM[{a_Integer, b_Integer, c_Integer, d_Integer, 0}, diff --git a/FeynCalc/QCD/RHO.m b/FeynCalc/QCD/RHO.m index 1908434bb..b10d37b26 100755 --- a/FeynCalc/QCD/RHO.m +++ b/FeynCalc/QCD/RHO.m @@ -28,11 +28,11 @@ RHO[i_Integer, mu_, nu_, p_, opt___Rule] := Block[ {gmn, pm, dm, pn, dn, dp, p2, re}, - gmn = MetricTensor[mu,nu]; - pm = FourVector[p, mu]; - pn = FourVector[p, nu]; - dm = FourVector[OPEDelta, mu]; - dn = FourVector[OPEDelta, nu]; + gmn = MT[mu,nu]; + pm = FV[p, mu]; + pn = FV[p, nu]; + dm = FV[OPEDelta, mu]; + dn = FV[OPEDelta, nu]; dp = ScalarProduct[OPEDelta, p]; p2 = ScalarProduct[p]; re = diff --git a/FeynCalc/QCD/Simplify2.m b/FeynCalc/QCD/Simplify2.m index 09adf9f87..884f9eed5 100755 --- a/FeynCalc/QCD/Simplify2.m +++ b/FeynCalc/QCD/Simplify2.m @@ -20,7 +20,7 @@ Begin["`Simplify2`Private`"] Simplify2[y_] := - Block[ {t1,t2,t3,null1, null2, cct, col,min}, + Block[ {t1,t2,t3,null1, null2, cct, col,min, llt, ll, dd, cc}, col = Collect2[##, Factoring->False]; cct = {CA, CF, Tf}; llt = {Log, PlusDistribution, PolyLog, Zeta2}; diff --git a/FeynCalc/QCD/SimplifyGTI.m b/FeynCalc/QCD/SimplifyGTI.m index d846bfe34..cadcd9662 100755 --- a/FeynCalc/QCD/SimplifyGTI.m +++ b/FeynCalc/QCD/SimplifyGTI.m @@ -21,8 +21,9 @@ Options[SimplifyGTI] = {Negative -> False}; -negflag := - Negative /. Options[SimplifyGTI]; +(*negflag := + Negative /. Options[SimplifyGTI];*) + eExpand = Identity; (* @@ -1003,39 +1004,29 @@ , *) -gti[{0,-1,0,0,e_/;Head[e]=!=Integer}, - {1,1,1,1,1} - ] :> PowerSimplify[(-1)^e] gti[{-1,0,0,0,e},{1,1,1,1,1}] -, +gti[{0,-1,0,0,e_/;Head[e]=!=Integer}, {1,1,1,1,1}] :> + PowerSimplify[(-1)^e] gti[{-1,0,0,0,e},{1,1,1,1,1}], gti[{a_,b_,c_,d_,e_Integer?Positive},{bla__}] :> -Sum[Binomial[e,ii] (-1)^(e-ii) gti[{a+ii, b+e-ii,c,d,0}, {bla} - ], {ii,0,e}]//eExpand -, + Sum[Binomial[e,i] (-1)^(e-i) gti[{a+i, b+e-i,c,d,0}, {bla}], {i,0,e}]//eExpand, + gti[{a_,b_,1,d_,e_},{bla__}] :> -Dp gti[{a,b,0,d,e},{bla}] - gti[{a+1,b,0,d,e},{bla}] -, + Dp gti[{a,b,0,d,e},{bla}] - gti[{a+1,b,0,d,e},{bla}], gti[{a_,b_,c_,1,e_},{bla__}] :> -Dp gti[{a,b,c,0,e},{bla}] - gti[{a,b+1,c,0,e},{bla}] -, + Dp gti[{a,b,c,0,e},{bla}] - gti[{a,b+1,c,0,e},{bla}], gti[{a_,b_Integer?Positive,c_,d_/;Head[d]=!=Integer,e_},{bla__}] :> -Dp gti[{a,b-1,c,d,e},{bla}] - gti[{a,b-1,c,d+1,e},{bla}] -, + Dp gti[{a,b-1,c,d,e},{bla}] - gti[{a,b-1,c,d+1,e},{bla}], gti[{a_Integer?Positive,b_,c_/;Head[c]=!=Integer,d_,e_},{bla__}] :> -Dp gti[{a-1,b,c,d,e},{bla}] - gti[{a-1,b,c+1,d,e},{bla}] -, + Dp gti[{a-1,b,c,d,e},{bla}] - gti[{a-1,b,c+1,d,e},{bla}], gti[{a_,b_,c_Integer?Positive,d_,e_},{bla__}] :> -Sum[Binomial[c,ii] (-1)^(c-ii) Dp^ii * - gti[{a+c-ii,b,0,d,e}, {bla}], {ii,0,c}] // eExpand -, + Sum[Binomial[c,i] (-1)^(c-i) Dp^i * gti[{a+c-i,b,0,d,e}, {bla}], {i,0,c}] // eExpand, gti[{a_,b_,c_,d_Integer?Positive,e_},{bla__}] :> -Sum[Binomial[d,ii] (-1)^(d-ii) Dp^ii * - gti[{a,b+d-ii,c,0,e}, {bla}], {ii,0,d}] // eExpand + Sum[Binomial[d,i] (-1)^(d-i) Dp^i * gti[{a,b+d-i,c,0,e}, {bla}], {i,0,d}] // eExpand }; (* diff --git a/FeynCalc/QCD/SymbolicSum.m b/FeynCalc/QCD/SymbolicSum.m index 3c507d30a..18efd53d6 100755 --- a/FeynCalc/QCD/SymbolicSum.m +++ b/FeynCalc/QCD/SymbolicSum.m @@ -154,7 +154,7 @@ (a^(opem4+2)/((a-(1/b)) (a-c)) + b^(-opem4-2)/( ((1/b)-a) ((1/b)-c)) + c^(opem4+2)/((c-a) (c-(1/b))) ) - ) /; FreeQ2[{any,opem4},{OPEi,OPEj}]; + ) /; FreeQ2[{(*any,*)opem4},{OPEi,OPEj}]; SymbolicSum3[a_^OPEj b_^(any_. + OPEi - OPEj) c_^(opem4_ -OPEi), {OPEi, 0, opem4_}, {OPEj, 0, OPEi} diff --git a/FeynCalc/QCD/TLI.m b/FeynCalc/QCD/TLI.m index 9e98cb6cd..f7f0b6ec0 100755 --- a/FeynCalc/QCD/TLI.m +++ b/FeynCalc/QCD/TLI.m @@ -75,26 +75,26 @@ The exponents of the numerator scalar product are (dl = OPEDelta): (* true 0's *) -TLI[{a_,b_,0,d_,0}, {n1_Integer, nm2_,0,nm4_,0}, ___Rule] := +TLI[{_,_,0,_,0}, {_Integer, _,0,_,0}, ___Rule] := 0; (*NEW0997*) -TLI[{a_,b_,c_,0,0}, {nm1_, 0, nm3_, n4_Integer,0}, ___Rule] := +TLI[{_,_,_,0,0}, {_, 0, _, _Integer,0}, ___Rule] := 0; TLI[{a_ /; !MatchQ[a, _Integer?Negative], b_ /; !MatchQ[b, _Integer?Negative],0,0,0}, - {{n1_,m1_},{n2_,m2_}, 0,0,0}, ___Rule] := + {{_,_},{_,_}, 0,0,0}, ___Rule] := 0 /; (a + b) > 0; (* this assumes that m is generic; thus: don't use this for m=0 *) -TLI[{a_, b_, 0,0,e_}, {x_, y_, 0, 0, z_}, opt___Rule] := +TLI[{a_, b_, 0,0,e_}, {_, _, 0, 0, _}, ___Rule] := 0 /; (Head[a]=!=Integer) || (Head[b]=!=Integer) || (Head[e]=!=Integer); -TLI[{0,0,a_, b_, e_}, {0, 0, x_, y_, z_}, opt___Rule] := +TLI[{0,0,a_, b_, e_}, {0, 0, _, _, _}, ___Rule] := 0 /; (Head[a]=!=Integer) || (Head[b]=!=Integer) || (Head[e]=!=Integer); @@ -102,8 +102,7 @@ The exponents of the numerator scalar product are (dl = OPEDelta): (* special cases ; all checked by TARCER *) -TLI[{0, 0, 0, 1, 0}, {m_, 0, 0, 0, 0}, {{2, M_}, {1, M_}, 1, 0, 1}, -opt___Rule] := +TLI[{0, 0, 0, 1, 0}, {m_, 0, 0, 0, 0}, {{2, M_}, {1, M_}, 1, 0, 1}, ___Rule] := -TLI[{m, 0, 0, 0, 0}, {1, 0, 1, 0, {1, M}}]/(4*M^2) + TLI[{m, 0, 0, 0, 0}, {1, 1, 1, 0, {1, M}}]/4 + TLI[{m, 0, 0, 0, 0}, {{1, M}, 0, 1, 0, {1, M}}]/(4*M^2) - @@ -111,19 +110,19 @@ The exponents of the numerator scalar product are (dl = OPEDelta): TLI[{m, 0, 0, 0, 0}, {{2, M}, 1, 1, 0, 0}]/4 + M^2*TLI[{m, 0, 0, 0, 0}, {{2, M}, 1, 1, 0, {1, M}}]; -TLI[{1, m_, 0, 0, 0}, {{1, M_}, {1, M_}, 0, 1, 1}, opt___Rule] := +TLI[{1, m_, 0, 0, 0}, {{1, M_}, {1, M_}, 0, 1, 1}, ___Rule] := TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, 1, 0, 1, 0}]/(2*M^2) - TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, 1, 0, 1, 1}]/2 - TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, {1, M}, 0, 1, 0}]/(2*M^2) + TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, {1, M}, 0, 1, 1}]; - TLI[{1, m_, 0, 0, 0}, {{1, M_}, {2, M_}, 0, 0, 1}, opt___Rule] := + TLI[{1, m_, 0, 0, 0}, {{1, M_}, {2, M_}, 0, 0, 1}, ___Rule] := TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, 1, 0, 0, 1}]/(2*M^2) - TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, {1, M}, 0, 0, 1}]/(2*M^2) - TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, {2, M}, 0, 0, 0}]/(2*M^2) + TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, {2, M}, 0, 0, 1}]; - TLI[{1, m_, 0, 0, 0}, {{1, M_}, {2, M_}, 0, 1, 1}, opt___Rule] := + TLI[{1, m_, 0, 0, 0}, {{1, M_}, {2, M_}, 0, 1, 1}, ___Rule] := -TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, 1, 0, 1, 0}]/(2*M^4) + TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, 1, 0, 1, 1}]/(2*M^2) + TLI[{0, 1 + m, 0, 0, 0}, {{1, M}, {1, M}, 0, 1, 0}]/(2*M^4) - @@ -231,13 +230,13 @@ The exponents of the numerator scalar product are (dl = OPEDelta): (* this generates Delta.p *) sod[rul___Rule] := FeynCalcInternal[SOD[Momentum /. {rul} /. - Options[TLI]]]; + Options[TLI]]]; ma[i_] := StyleBox[i//ToString, - FontColor -> RGBColor[0,0,1] - ]; + FontColor -> RGBColor[0,0,1] + ]; - ma[{i_, m_}] := + ma[{i_, _}] := StyleBox[ToString[i], FontWeight -> "Bold", FontColor -> RGBColor[1,0,0] diff --git a/FeynCalc/QCD/TLIFP.m b/FeynCalc/QCD/TLIFP.m index e6a4d1d81..6f816fbf4 100755 --- a/FeynCalc/QCD/TLIFP.m +++ b/FeynCalc/QCD/TLIFP.m @@ -19,6 +19,8 @@ Begin["`TLIFP`Private`"] +rule2F1::usage=""; +tli::usage=""; (* 15. Feb 1996; *) (* General parametrizations for graph #1, #2, #3, #4 *) @@ -28,13 +30,18 @@ (* Map[Integrate[#, {t, 0, 1}, {u, 0, 1}], ...] is understood *) -Options[TLIFP] = { FeynmanParameterNames -> - {FCGV["x"], FCGV["t"], FCGV["u"], FCGV["s"], - FCGV["y"]}, - GammaExpand -> True, - Momentum -> FCGV["p"], - Print -> True - }; +Options[TLIFP] = { + FeynmanParameterNames -> { + FCGV["x"], + FCGV["t"], + FCGV["u"], + FCGV["s"], + FCGV["y"] + }, + GammaExpand -> True, + Momentum -> FCGV["p"], + Print -> True +}; TLIFP[exp_, opt___Rule] := Block[ {tlifp, so,x,t,u,s,y,p, r1,r2,r3,gaex, simp, comment, MCH, integ, pinteg}, @@ -59,7 +66,7 @@ integ[yy_] := True /; DataType[yy, PositiveInteger] === True; (* check for integer*) - pinteg[yy_Integer?Positive] := + pinteg[_Integer?Positive] := True; (* check for positive integer*) pinteg[yy_ /; DataType[yy, PositiveInteger] === True] := True; @@ -92,7 +99,7 @@ (1 - t*u)^(4 - a1 - a2 - a4 - a5 + Epsilon) ) ) /. {Dot :> Times, EulerGamma :> 0, y :> 1 - x} - ) /; 2 - a2 - a4 > 0; + ) /; 2 - a2 - a4 > 0; (* ************************ tlifp, RFP1ende ************************ *) @@ -124,7 +131,7 @@ (1 - t*u)^(-2 + a4 - Epsilon/2) ) ) /. {Dot :> Times, EulerGamma :> 0, y :> 1 - x} - ) /; 2 - a2 - a4 <= 0; + ) /; 2 - a2 - a4 <= 0; (************************* tlifp, RFP2ende ************************ *) @@ -150,7 +157,7 @@ (t^(-1 + a2)*(1 - t)^(-3 + a1 + a5 - Epsilon/2)* (1 - t*u)^(4 - a1 - a2 - a4 - a5 + Epsilon)) ) /. {Dot :> Times, EulerGamma :> 0} - ) /; 2 - a2 - a4 + Epsilon/2 > 0; + ) /; 2 - a2 - a4 + Epsilon/2 > 0; (* ************************ tlifp, RFP3prime *********************** *) @@ -175,7 +182,7 @@ (t^(-3 + a1 + a5 - Epsilon/2)*(1 - t)^(-1 + a2)* (1 - t*u)^(-2 + a4 - Epsilon/2)) ) /. {Dot :> Times, EulerGamma :> 0} - ) /; 2 - a2 - a4 <= 0; + ) /; 2 - a2 - a4 <= 0; (* ************************ tlifp, RFP4 prime ******************** *) (* ************************ tlifp, RFP5 ************************ *) @@ -195,7 +202,7 @@ Gamma[4 - a2 - a4 + Epsilon + g2 + g4])) . (x^a3 (1 - x)^(3 - a1 - 2 a3 + Epsilon + g3)) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP5 ************************ *) @@ -218,7 +225,7 @@ E^(Epsilon*EulerGamma) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP5b ************************ *) @@ -249,7 +256,7 @@ via Hamberg (3C.31) the expression (1 - u)^(-1 + a4 + g2) * (1 - (1 - x) u)^(-1) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP6 *********************** *) (* ************************ tlifp, RFP7 ************************ *) @@ -281,7 +288,7 @@ via Hamberg (3C.31) the expression ((1 - u)*u*(1 - x)^2 + t*x)^(4 - a1 - a3 - a4 - a5 + Epsilon) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP7 ************************ *) @@ -314,7 +321,7 @@ via Hamberg (3C.31) the expression (t*u + (1 - u)*x)^(4 - a1 - a2 - a4 - a5 + Epsilon) ) ) /. {Dot :> Times, EulerGamma :> 0} - ) /; a2 =!= 0; + ) /; a2 =!= 0; (* ************************ tlifp, RFP8 ************************ *) (* ************************ tlifp, RFP8b ************************ *) @@ -341,7 +348,7 @@ via Hamberg (3C.31) the expression (1 - u*(1 - 1/x))^(4 - a1 - a4 - a5 + Epsilon) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP8b ************************ *) (* ************************ tlifp, RFP8c ************************ *) (* Caution: Handle the x -> 1 behaviour with care ******************* *) @@ -376,7 +383,7 @@ via Hamberg (3C.31) the expression (t*u + x - u*x)^(4 - a1 - a3 - a4 - a5 + Epsilon) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP8c ************************ *) @@ -407,7 +414,7 @@ via Hamberg (3C.31) the expression (t*(1 - x) + (1 - u)*u*x^2)^(4 - a2 - a3 - a4 - a5 + Epsilon) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP9 ************************ *) @@ -463,7 +470,7 @@ via Hamberg (3C.31) the expression ) ) ) /. {Dot :> Times, EulerGamma :> 0, y :> 1 - x} - ); + ); (* ************************ tlifp, RFP12 ************************ *) (* ************************ tlifp, RFP13 ************************ *) tlifp[tLI[{g1_?integ, g2_?integ, g3_?integ, g4_?integ, m_}, @@ -520,7 +527,7 @@ via Hamberg (3C.31) the expression ) ) ) /. {Dot :> Times, EulerGamma :> 0, y :> 1 - x} - ); + ); (* ************************ tlifp, RFP13 ************************ *) (* ************************ tlifp, RFP14 ************************ *) tlifp[tLI[{g1_?integ, g2_?integ, g3_?integ, g4_?integ, m_}, @@ -558,7 +565,7 @@ via Hamberg (3C.31) the expression ) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP14 ************************ *) (* ************************ tlifp, RFP15 ************************ *) tlifp[tLI[{g1_?integ, g2_?integ, g3_?integ, g4_?integ, m_}, @@ -582,7 +589,7 @@ via Hamberg (3C.31) the expression (u + x - u*x)^g1*(1 - u + u*x)^g4 ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* For g1 = g4 = 0 integrable in closed Form *********************** *) (* ************************ tlifp, RFP15 ************************ *) @@ -682,7 +689,7 @@ via Hamberg (3C.31) the expression ) ) ) /. {Dot :> Times, EulerGamma :> 0} - ) /; integ[g5] && integ[g1]; + ) /; integ[g5] && integ[g1]; (* ************************ tlifp, RFP17 ************************ *) (* ************************ tlifp, RFP18 ************************ *) tlifp[tLI[{g1_ /; MCH[g1], g2_ /; MCH[g2], g3_?integ, g4_?integ, g5_?integ}, @@ -715,7 +722,7 @@ via Hamberg (3C.31) the expression -((1 - y)/((1 - x)*y))] ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP18 ************************ *) (* ************************ tlifp, RFP19 ************************ *) tlifp[tLI[{g1_ /; MCH[g1], g2_?integ, g3_?integ, g4_?integ, g5_ /;MCH[g5]}, @@ -742,7 +749,7 @@ via Hamberg (3C.31) the expression -2 + a3 + a5 - Epsilon/2, -2 + a3 + a4 + a5 - Epsilon/2, -(y/(x*(1 - y)))])/Gamma[-2 + a3 + a4 + a5 - Epsilon/2] ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP19 ************************ *) (* ************************ tlifp, RFP21 ************************ *) @@ -777,7 +784,7 @@ via Hamberg (3C.31) the expression (4 - a1 - a2 - a3 - a4 - a5 + Epsilon) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP21 ************************ *) (* ************************ tlifp, RFP22 ************************ *) @@ -804,7 +811,7 @@ via Hamberg (3C.31) the expression (1 - s*t*x)^(-4 + a2 + a4 + a5 - Epsilon - g2 - g4 - g5) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP22 ************************ *) @@ -832,7 +839,7 @@ via Hamberg (3C.31) the expression Gamma[4 - a2 - a4 + Epsilon + g2 + g4]) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP23 ************************ *) (* ************************ tlifp, RFP24 ************************ *) @@ -858,7 +865,7 @@ via Hamberg (3C.31) the expression (Gamma[-2 + a3 + a4 + a5 - Epsilon/2]*Gamma[4 - a4 - a5 + Epsilon + g4 + g5]) ) ) /. {Dot :> Times, EulerGamma :> 0} - ); + ); (* ************************ tlifp, RFP24 ************************ *) @@ -875,8 +882,8 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR1"]; - tlifp[tLI[{m, g4, g3, g2, 0}, {{a1, M}, {a4, M}, a3, a2, 0}]] - ); + tlifp[tLI[{m, g4, g3, g2, 0}, {{a1, M}, {a4, M}, a3, a2, 0}]] + ); (* PR2 *) (* 1 <--> 3, 2 <--> 4 ALLGEMEIN *) @@ -887,11 +894,11 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR2"]; - (-1)^g5 tlifp[tLI[{g3, g4, g1, g2, g5}, - {{a3, M}, a4, a1, {a2, M}, {a5, M}} - ] - ] - ); + (-1)^g5 tlifp[tLI[{g3, g4, g1, g2, g5}, + {{a3, M}, a4, a1, {a2, M}, {a5, M}} + ] + ] + ); (* PR3 *) (* 1 <--> 4, 2 <--> 3 ALLGEMEIN *) @@ -903,10 +910,10 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR3"]; - tlifp[tLI[{m, g3, g2, g1, g5}, - {{a4, M}, a3, a2, {a1, M}, {a5,M}}] - ] - ); + tlifp[tLI[{m, g3, g2, g1, g5}, + {{a4, M}, a3, a2, {a1, M}, {a5,M}}] + ] + ); (* PR4 *) tlifp[tLI[{m_ /; MCH[m], g2_, g3_, g4_, g5_}, @@ -914,10 +921,10 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR4"]; - tlifp[tLI[{m, g5, g3, g4, g2}, - {{a1, M}, {a5, M}, a3, 0, a2}] - ] - ); + tlifp[tLI[{m, g5, g3, g4, g2}, + {{a1, M}, {a5, M}, a3, 0, a2}] + ] + ); (* PR5 *) tlifp[tLI[{m_ /; MCH[m], g2_, g3_, g4_, g5_}, @@ -926,11 +933,11 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR5"]; - (-1)^g5 tlifp[ tLI[{g2, m, g4, g3, g5}, - {{a2, M}, {a1, M}, 0, a3, a5} - ] - ] - ); + (-1)^g5 tlifp[ tLI[{g2, m, g4, g3, g5}, + {{a2, M}, {a1, M}, 0, a3, a5} + ] + ] + ); (* PR6 *) tlifp[ tLI[{0, g2_?integ, g3_?integ, g4_?integ, m_ /; MCH[m]}, @@ -940,11 +947,11 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR6"]; - (-1)^g3 tlifp[tLI[{m, g4, 0, g2, g3}, - {{a5, M}, {a4, M}, 0, a2, a3} - ] - ] - ); + (-1)^g3 tlifp[tLI[{m, g4, 0, g2, g3}, + {{a5, M}, {a4, M}, 0, a2, a3} + ] + ] + ); (* PR7 *) tlifp[ tLI[{m_, g2_?integ, g3_?integ, g4_?integ, 0}, @@ -955,8 +962,8 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR7"]; - tlifp[tLI[{m, g4, g3, g2, 0}, {{a1,M}, {a4,M}, a3, a2, 0}]] - ); + tlifp[tLI[{m, g4, g3, g2, 0}, {{a1,M}, {a4,M}, a3, a2, 0}]] + ); (* PR8 *) tlifp[ tLI[{m_, g2_?integ, g3_?integ, g4_?integ, 0}, @@ -967,8 +974,8 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR8"]; - tlifp[tLI[{m, g4, g3, g2, 0}, {{a1,M}, {a4,M}, a3, a2, 0}]] - ); + tlifp[tLI[{m, g4, g3, g2, 0}, {{a1,M}, {a4,M}, a3, a2, 0}]] + ); (* PR9 *) tlifp[ tLI[{g1_, g2_, g3_, g4_, g5_}, @@ -977,8 +984,8 @@ via Hamberg (3C.31) the expression }] ] := (comment["using PR9"]; - tlifp[tLI[{g4, g3, g2, g1, g5}, {{a4, M}, {a3, M}, a2, a1, 0}]] - ); + tlifp[tLI[{g4, g3, g2, g1, g5}, {{a4, M}, {a3, M}, a2, a1, 0}]] + ); (* PR10 *) tlifp[tLI[{g1_, 0, g3_, g4_, m_ /; MCH[m]}, @@ -987,9 +994,9 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR10"]; - (-1)^(m) (-1)^g4 * - tLI[{m, g3, 0, g1, g4}, {{a5, M}, a3, 0, {a1, M}, {a4, M}}] - ); + (-1)^(m) (-1)^g4 * + tLI[{m, g3, 0, g1, g4}, {{a5, M}, a3, 0, {a1, M}, {a4, M}}] + ); (* PR11 *) tlifp[tLI[{g1_, g2_, 0, g4_, g5_}, @@ -997,10 +1004,10 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR11"]; - (-1)^g5 tlifp[tLI[{g2, g5, g4, 0, g1}, - {0, a5, a4, 0, {a1, M}}] - ] - ); + (-1)^g5 tlifp[tLI[{g2, g5, g4, 0, g1}, + {0, a5, a4, 0, {a1, M}}] + ] + ); (* PR12 *) tlifp[tLI[{g1_, g2_, 0_, g4_, g5_}, @@ -1008,8 +1015,8 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR12"]; - tlifp[(-1)^g5 * tLI[{g3, g4, g1, g2, g5}, {0, a4, a1, 0, {a5, M}}]] - ); + tlifp[(-1)^g5 * tLI[{(*g3*)0(*?? VS*), g4, g1, g2, g5}, {0, a4, a1, 0, {a5, M}}]] + ); (* PR13 *) tlifp[tLI[{g1_, m_ /; MCH[m], g3_, g4_, 0}, @@ -1019,8 +1026,8 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR13"]; - tlifp[ tLI[{m, g1, g4, g3, 0}, { {a2,M}, {a1,M}, a4, a3, 0}]] - ); + tlifp[ tLI[{m, g1, g4, g3, 0}, { {a2,M}, {a1,M}, a4, a3, 0}]] + ); (* PR14 *) tlifp[tLI[{g1_, m_ /; MCH[m], g3_, g4_, g5_}, @@ -1030,11 +1037,11 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR14"]; - (-1)^g5 tlifp[ tLI[{m, g1, g4, g3, g5}, - {0, a1, a4, {a3, M}, {a5, M}} - ] - ] - ); + (-1)^g5 tlifp[ tLI[{m, g1, g4, g3, g5}, + {0, a1, a4, {a3, M}, {a5, M}} + ] + ] + ); (* PR15 *) tlifp[tLI[{g1_, g2_, g3_, g4_, m_ /; MCH[m]}, @@ -1044,11 +1051,11 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR15"]; - tlifp[ tLI[{g4, g3, g2, g1, m}, - {{a4, M}, 0, a2, {a1, M}, {a5, M}} - ] - ] - ); + tlifp[ tLI[{g4, g3, g2, g1, m}, + {{a4, M}, 0, a2, {a1, M}, {a5, M}} + ] + ] + ); (* PR16 *) (* correction 04/15 *) tlifp[tLI[{g1_?NonNegative, m_, 0, g4_?integ, g5_?integ}, @@ -1058,14 +1065,14 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR16"]; - (-1)^g5 Sum[Binomial[g1, i] (-1)^(g1-i) * - tlifp[ tLI[{m+i, g5+g1-i, g4, 0, 0}, - {{a2, M}, {a5, M}, a4, 0, 0} - ] - ], - {i, 0, g1} - ] - ); + (-1)^g5 Sum[Binomial[g1, i] (-1)^(g1-i) * + tlifp[ tLI[{m+i, g5+g1-i, g4, 0, 0}, + {{a2, M}, {a5, M}, a4, 0, 0} + ] + ], + {i, 0, g1} + ] + ); (* PR17 *) tlifp[tLI[{0, m_, 1, g4_?integ, g5_?integ}, @@ -1075,14 +1082,14 @@ via Hamberg (3C.31) the expression ] ] := (comment["using PR17"]; - tlifp[ tLI[{0, m, 0, g4 + 1, g5}, - {0, {a2, M}, 0, a4, {a5, M}} - ] - - tLI[{0, m, 0, g4 , g5 + 1}, - {0, {a2, M}, 0, a4, {a5, M}} - ] - ] - ); + tlifp[ tLI[{0, m, 0, g4 + 1, g5}, + {0, {a2, M}, 0, a4, {a5, M}} + ] - + tLI[{0, m, 0, g4 , g5 + 1}, + {0, {a2, M}, 0, a4, {a5, M}} + ] + ] + ); (* ********************************************************************* *) @@ -1099,9 +1106,9 @@ via Hamberg (3C.31) the expression ] := so[r] * tlihyp[tLI[{m, 1, g3, g4, g5}, {{a1, M}, 0, a3, {a4, M}, {a5,M}}] - ] - + ] - tlihyp[tLI[{m, 1, g3, g4+1,g5}, {{a1, M}, 0, a3, {a4, M}, {a5,M}}] - ]; + ]; tlihyp[tLI[{m_, 1, g3_?integ, g4_?integ, g5_?integ}, {{a1_?integ, M_Symbol}, 0, a3_?integ, {a4_?integ, M_Symbol}, {a5_?integ, M_Symbol}} @@ -1109,9 +1116,9 @@ via Hamberg (3C.31) the expression ] := so[r] * tlihyp[tLI[{m, 0, g3, g4, g5}, {{a1, M}, 0, a3, {a4, M}, {a5,M}}] - ] - + ] - tlihyp[tLI[{m, 0, g3, g4+1,g5}, {{a1, M}, 0, a3, {a4, M}, {a5,M}}] - ]; + ]; tlihyp[tLI[{m_ , 0, g3_?integ, g4_?integ, g5_?integ}, {{a1_?integ, M_Symbol}, 0, a3_?integ, {a4_?integ, M_Symbol}, {a5_?integ, M_Symbol}} @@ -1151,7 +1158,7 @@ via Hamberg (3C.31) the expression - y^2/(4 x (x+y))] ) ) /. {Dot :> Times, EulerGamma :> 0, y :> 1 - x} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP5 ************************ *) @@ -1209,9 +1216,9 @@ via Hamberg (3C.31) the expression ] ] := so[r] tlihyp[tLI[{g1, m, 0, g4, g5}, {{a1, M}, {a2, M}, 0, a4, a5}] - ] - - tlihyp[tLI[{g1+1, m, 0, g4, g5}, {{a1, M}, {a2, M}, 0, a4, a5}] - ]; + ] - + tlihyp[tLI[{g1+1, m, 0, g4, g5}, {{a1, M}, {a2, M}, 0, a4, a5}] + ]; tlihyp[tLI[{g1_?integ, m_ , 0, g4_?integ, g5_?integ}, {{a1_?pinteg, M_Symbol}, {a2_?pinteg, M_Symbol}, 0, a4_?pinteg, a5_?pinteg} @@ -1257,7 +1264,7 @@ via Hamberg (3C.31) the expression Gamma[-4 + a1 + a2 + 2*a5 - Epsilon - g5]) ) ) /. {Dot :> Times, EulerGamma :> 0, y :> 1 - x} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP3ende ************************ *) @@ -1296,7 +1303,7 @@ via Hamberg (3C.31) the expression Gamma[a2 + a4 + g1 + g5]) ) )/.{Dot :> Times, EulerGamma :> 0} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP6ende ************************ *) @@ -1322,7 +1329,7 @@ via Hamberg (3C.31) the expression Exp[-I Pi Epsilon/2] ) )/.{Dot :> Times, EulerGamma :> 0} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP7ende ************************ *) @@ -1345,7 +1352,7 @@ via Hamberg (3C.31) the expression (1 - x)^(4+Epsilon-a2-2*a4+g4-1) ) )/.{Dot :> Times, EulerGamma :> 0} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP8ende ************************ *) @@ -1356,18 +1363,18 @@ via Hamberg (3C.31) the expression ] := so[r] * tlihyp[tLI[{m, 1, g3, g4, g5}, {{a1, M}, 0, a3, a4, a5}] - ] - + ] - tlihyp[tLI[{m, 1, g3, g4+1,g5}, {{a1, M}, 0, a3, a4, a5}] - ]; + ]; tlihyp[tLI[{m_, 1, g3_, g4_, g5_}, {{a1_?pinteg, M_Symbol}, 0, a3_?integ, a4_?pinteg, a5_?pinteg} ] ] := so[r] * tlihyp[tLI[{m, 0, g3, g4, g5}, {{a1, M}, 0, a3, a4, a5}] - ] - + ] - tlihyp[tLI[{m, 0, g3, g4+1,g5}, {{a1, M}, 0, a3, a4, a5}] - ]; + ]; tlihyp[tLI[{m_, 0, g3_, g4_, g5_}, {{a1_?pinteg, M_Symbol}, 0, a3_?integ, a4_?pinteg, a5_?pinteg} ] @@ -1388,7 +1395,7 @@ via Hamberg (3C.31) the expression (1 - x)^(8+2*Epsilon-a1-2*a3-2*a4-2*a5+g3+g4+g5-1) ) )/.{Dot :> Times, EulerGamma :> 0} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP9ende ************************ *) (* FORMER TLIHYP end*) r1 = exp /. {TLI :> tli, TLI2 :> tli}; diff --git a/FeynCalc/QCD/TLIHYP.m b/FeynCalc/QCD/TLIHYP.m index 445e93682..c5babcbea 100755 --- a/FeynCalc/QCD/TLIHYP.m +++ b/FeynCalc/QCD/TLIHYP.m @@ -20,6 +20,8 @@ Begin["`TLIHYP`Private`"] +tli::usage=""; + (* Fri Feb 16 04:09:29 MET 1996 *) (* By R. Scharf *) @@ -31,7 +33,7 @@ True; (* the m of the spin *) integ[y_ /; Head[y] === Integer] := True; (* check for integer*) -pinteg[y_Integer?Positive] := +pinteg[_Integer?Positive] := True; (* check for positive integer*) pinteg[y_ /; DataType[y, PositiveInteger] === True] := True; @@ -46,7 +48,7 @@ }; TLIHYP[exp_, opt___Rule] := - Block[ {tlihyp, so, x, p}, + Block[{ tlihyp, so, x, p, rule2F1}, x = FeynmanParameterNames /. {opt} /. Options[TLIHYP]; p = Momentum /. {opt} /. Options[TLIHYP]; so[r] = ScalarProduct[OPEDelta, p]; @@ -61,9 +63,9 @@ ] := so[r] * tlihyp[tLI[{m, 0, g3, g4, g5}, {{a1, M}, 0, a3, {a4, M}, {a5,M}}] - ] - + ] - tlihyp[tLI[{m, 0, g3, g4+1,g5}, {{a1, M}, 0, a3, {a4, M}, {a5,M}}] - ]; + ]; tlihyp[tLI[{m_ , 0, g3_?integ, g4_?integ, g5_?integ}, {{a1_?integ, M_Symbol}, 0, a3_?integ, {a4_?integ, M_Symbol}, {a5_?integ, M_Symbol}} @@ -103,7 +105,7 @@ - y^2/(4 x (x+y))] ) ) /. {Dot :> Times, EulerGamma :> 0, y :> 1 - x} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP5 ************************ *) @@ -150,7 +152,7 @@ (Gamma[2 - a4 + Epsilon/2]*Gamma[-4 + a1 + a2 + 2*a5 - Epsilon - g5]) ) ) /. {Dot :> Times, EulerGamma :> 0} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP1ende ************************ *) (* ************************ tlihyp, RHYP3 ************************ *) @@ -160,9 +162,9 @@ ] ] := so[r] tlihyp[tLI[{g1, m, 0, g4, g5}, {{a1, M}, {a2, M}, 0, a4, a5}] - ] - - tlihyp[tLI[{g1+1, m, 0, g4, g5}, {{a1, M}, {a2, M}, 0, a4, a5}] - ]; + ] - + tlihyp[tLI[{g1+1, m, 0, g4, g5}, {{a1, M}, {a2, M}, 0, a4, a5}] + ]; tlihyp[tLI[{g1_?integ, m_ , 0, g4_?integ, g5_?integ}, {{a1_?integ, M_Symbol}, {a2_?integ, M_Symbol}, 0, a4_?integ, a5_?integ} @@ -208,7 +210,7 @@ Gamma[-4 + a1 + a2 + 2*a5 - Epsilon - g5]) ) ) /. {Dot :> Times, EulerGamma :> 0, y :> 1 - x} - )/.rule2F1; + )/.rule2F1; (* ************************ tlihyp, RHYP3 ************************ *) exp /. TLI -> tli /. tli[ww__] :> tlihyp[tLI[ww]] /. tlihyp -> Identity /. tLI -> TLI diff --git a/FeynCalc/QCD/Twist2AlienOperator.m b/FeynCalc/QCD/Twist2AlienOperator.m index 60eaca677..0d3a6817f 100755 --- a/FeynCalc/QCD/Twist2AlienOperator.m +++ b/FeynCalc/QCD/Twist2AlienOperator.m @@ -29,7 +29,7 @@ Options[Twist2AlienOperator] = { CouplingConstant -> SMP["g_s"], Dimension -> D, Polarization -> 0}; Twist2AlienOperator[pi_, 0, opt___Rule] := - Block[ {dim, p, re, pol, del}, + Block[ {dim, p, re, pol, del, coup, li1,li2,li3}, coup = CouplingConstant /. {opt} /. Options[Twist2AlienOperator]; dim = Dimension /. {opt} /. Options[Twist2AlienOperator]; pol = Polarization /. {opt} /. Options[Twist2AlienOperator]; @@ -69,7 +69,7 @@ (* count1 *) Twist2AlienOperator[p1_, _, {p3_, mu_, a_}, 0, opt___Rule] := - Block[ {dim, re, pol, del}, + Block[ {dim, re, pol, del, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2AlienOperator]; dim = Dimension /. {opt} /. Options[Twist2AlienOperator]; pol = Polarization /. {opt} /. Options[Twist2AlienOperator]; diff --git a/FeynCalc/QCD/Twist2CounterOperator.m b/FeynCalc/QCD/Twist2CounterOperator.m index f8a9d8ac6..5f7c593bd 100755 --- a/FeynCalc/QCD/Twist2CounterOperator.m +++ b/FeynCalc/QCD/Twist2CounterOperator.m @@ -40,7 +40,7 @@ (* C7 *) Twist2CounterOperator[pi_, 7, opt___Rule] := - Block[ {dim, p, re, pol, del}, + Block[ {dim, p, re, pol, del, coup, li1,li2,li3}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; @@ -81,7 +81,7 @@ (* C1 *) (* COUNT1 *) Twist2CounterOperator[p1_, pe3_, {_, mu_, a_}, 1, opt___Rule] := - Block[ {dim, re, pol, del, oex, p3 = -pe3}, + Block[ {dim, re, pol, del, oex, p3 = -pe3, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; @@ -125,7 +125,7 @@ (* C2 *) (* Count2 *) Twist2CounterOperator[p1_, _, {p3_, mu_, a_}, 2, opt___Rule] := - Block[ {dim, re, pol, del, oex, dp1, dp3}, + Block[ {dim, re, pol, del, oex, dp1, dp3, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; @@ -199,7 +199,7 @@ (* C3 *) (* Count3 *) Twist2CounterOperator[p1_, _, {p3_, mu_, a_}, 3, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; @@ -243,7 +243,7 @@ (* C13 *) (* Count13 *) Twist2CounterOperator[p_, mu_, nu_, a_, b_, 13, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; @@ -272,7 +272,7 @@ (* C4 *) (* Count4 *) Twist2CounterOperator[p1_, _, {p3_, mu_, a_}, 4, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; @@ -403,11 +403,9 @@ (*C11 *) (* Count11 *) -Twist2CounterOperator[p1_, mu1_, a1_, p2_, mu2_, a2_, pe3_, mu3_, a3_, - 11, x_, opt___Rule - ] := - Block[ {dim, re, pol, p3}, - (* p3 = p1+p2 *) +Twist2CounterOperator[p1_, mu1_, a1_, (*p2*)_, mu2_, a2_, pe3_, mu3_, a3_, 11, x_, opt___Rule] := + Block[ {dim, re, pol, p3, coup}, + (* p3 = p1+p2 *) p3 = -pe3; coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; @@ -1269,10 +1267,8 @@ (* C12 *) (* Count12 *) -Twist2CounterOperator[p1_, mu1_, a1_, p2_, mu2_, a2_, p3_, mu3_, a3_, - 12, opt___Rule - ] := - Block[ {dim, re, pol, del, oex, dp1, dp3}, +Twist2CounterOperator[p1_, mu1_, a1_, (*p2*)_, mu2_, a2_, (*p3*)_, mu3_, a3_, _(*s12*), opt___Rule] := + Block[ {dim, re, pol, del, oex, dp1, dp3, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; @@ -1293,7 +1289,7 @@ (Epsilon*(-1 + OPEm)*OPEm) ) , - nochnich + "Not ready yet!" ]; ChangeDimension[FeynCalcInternal[re],dim] ]; @@ -1306,7 +1302,7 @@ (* C30 *) Twist2CounterOperator[mu_,a_, 30, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; ChangeDimension[uc30[mu, a, coup],dim] @@ -1318,7 +1314,7 @@ (* C31 *) Twist2CounterOperator[mu_,a_, 31, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; ChangeDimension[uc31[mu, a, coup],dim] @@ -1332,14 +1328,15 @@ (* C40 *) (* Count40 *) Twist2CounterOperator[p1_, 40, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; Which[pol === 0, ChangeDimension[uc40[p1, coup],dim], pol === 1, - ChangeDimension[pc40[p1,coup],dim] + "Not available!" + (*ChangeDimension[pc40[p1,coup],dim]*) ] ]; @@ -1351,63 +1348,67 @@ (* C41 *) (* Count41 *) Twist2CounterOperator[p1_, 41, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; Which[pol === 0, ChangeDimension[uc41[p1, coup],dim], pol === 1, - ChangeDimension[pc41[p1, coup],dim] + "Not available!" + (*ChangeDimension[pc41[p1, coup],dim]*) + ] ]; (* NEW *) (* C42 *) (* Count42; p1, p2, p3 incoming; p1: fermion*) -uc42[p1_, p2_, p3_, mu_, a_, coup_] := +uc42[p1_, p2_, (*p3*)_, mu_, a_, (*coup*)_] := -( (-2*CA*SMP["g_s"]^3*Sn*SUNT[a]*FV[OPEDelta, mu]*GS[OPEDelta]* (SO[p1]^OPEm*SO[p2] + (-1)^OPEm*SO[p1]*SO[p2]^OPEm))/ (Epsilon*OPEm*(1 + OPEm)*SO[p1]*SO[p2]*(SO[p1] + SO[p2])) ); Twist2CounterOperator[p1_, p2_, p3_, mu_, a_, 42, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; Which[pol === 0, ChangeDimension[uc42[p1, p2, p3, mu, a, coup],dim], pol === 1, - ChangeDimension[pc42[p1, -p2, p3, coup],dim] + "Not available!" + (*ChangeDimension[pc42[p1, -p2, p3, coup],dim]*) ] ]; (* NEW *) (* C43 *) (* Count43 p2 outgoing *) -uc43[p1_, p2_, p3_, mu_, a_, coup_] := +uc43[p1_, p2_, (*p3*)_, mu_, a_, (*coup*)_] := -(-2*(CA - 2*CF)*SMP["g_s"]^3*Sn*FV[OPEDelta, mu]*GS[OPEDelta]* (SO[p1]^(1 + OPEm) - SO[p1]*(SO[p1] - SO[p2])^OPEm - SO[p1]^OPEm*SO[p2])*SUNT[a])/ (Epsilon*OPEm*(1 + OPEm)*SO[p1]*(SO[p1] - SO[p2])*SO[p2]); Twist2CounterOperator[p1_, p2_, p3_, mu_, a_, 43, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; Which[pol === 0, ChangeDimension[uc43[p1, -p2, p3, mu, a, coup],dim], pol === 1, - ChangeDimension[pc43[p1, -p2, p3, mu, a, coup],dim] + "Not available!" + (*ChangeDimension[pc43[p1, -p2, p3, mu, a, coup],dim]*) ] ]; (* C44 *) (* Count44 p2 outgoing *) -uc44[p1_, p2_, p3_, mu_, a_, coup_] := +uc44[p1_, p2_, (*p3*)_, mu_, a_, (*coup*)_] := -( -2*(CA - 2*CF)*SMP["g_s"]^3*(1 - OPEm)*Sn*FV[OPEDelta, mu]* GS[OPEDelta]*((-1)^OPEm*(SO[p1] - SO[p2])^OPEm*SO[p2] + SO[p1]*SO[p2]^OPEm - SO[p2]^(1 + OPEm))*SUNT[a])/ @@ -1415,21 +1416,22 @@ (* Count44 p2 incoming*) Twist2CounterOperator[p1_, p2_, p3_, mu_, a_, 44, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; Which[pol === 0, ChangeDimension[uc44[p1, -p2, p3, mu, a, coup],dim], pol === 1, - ChangeDimension[pc44[p1, -p2, p3, mu, a, coup],dim] + "Not available!" + (*ChangeDimension[pc44[p1, -p2, p3, mu, a, coup],dim]*) ] ]; (* C45 *) (* Count45 p2 outgoing *) (*for some reson there always is a global sign wrong ....*) -uc45[p1_, p2_, p3_, mu_, a_, coup_] := +uc45[p1_, p2_, (*p3*)_, mu_, a_, (*coup*)_] := -Block[ {j = OPEl}, (CA*SMP["g_s"]^3*Sn*DOT[SUNT[a] , GS[OPEDelta]]*FV[OPEDelta, mu]* (2*SO[p1]^OPEm*SO[p2] - 2*SO[p1]*SO[p2]^OPEm - @@ -1443,20 +1445,21 @@ Twist2CounterOperator[p1_, p2_, p3_, mu_, a_, 45, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; Which[pol === 0, ChangeDimension[uc45[p1, -p2, p3, mu, a, coup],dim], pol === 1, - ChangeDimension[pc45[p1, -p2, p3, mu, a, coup],dim] + "Not available!" + (*ChangeDimension[pc45[p1, -p2, p3, mu, a, coup],dim]*) ] ]; (* C46 *) (* Count46 p2 outgoing *) -uc46[p1_, p2_, p3_, mu_, a_, coup_] := +uc46[p1_, p2_, (*p3*)_, mu_, a_, (*coup*)_] := -Block[ {j = OPEl}, -((CA*SMP["g_s"]^3*Sn*DOT[SUNT[a] , GS[OPEDelta]]*FV[OPEDelta, mu]* (OPEm*OPESum[(SO[p1]^(j - OPEm)*SO[p2]^(-j + OPEm))/j, @@ -1468,14 +1471,15 @@ ]; Twist2CounterOperator[p1_, p2_, p3_, mu_, a_, 46, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; Which[pol === 0, ChangeDimension[uc46[p1, -p2, p3, mu, a, coup],dim], pol === 1, - ChangeDimension[pc46[p1, -p2, p3, mu, a, coup],dim] + "Not available!" + (*ChangeDimension[pc46[p1, -p2, p3, mu, a, coup],dim]*) ] ]; @@ -1503,7 +1507,7 @@ *) (* Count47 p2 outgoing *) -uc47[p1_, _, p3_, mu_, a_, coup_] := +uc47[p1_, _, p3_, mu_, a_, (*coup*)_] := - (2*(CA - 2*CF)*SMP["g_s"]^3*Sn*FV[OPEDelta, mu]*GS[OPEDelta]* ((-1)^OPEm*SO[p1]^(1 + OPEm) - (-1)^OPEm*SO[p1]*(SO[p1] - SO[p3])^OPEm + @@ -1512,14 +1516,15 @@ (Epsilon*OPEm*(1 + OPEm)*SO[p1]*(SO[p1] - SO[p3])*SO[p3]); Twist2CounterOperator[p1_, p2_, p3_, mu_, a_, 47, opt___Rule] := - Block[ {dim, re, pol, del, oex}, + Block[ {dim, re, pol, del, oex, coup}, coup = CouplingConstant /. {opt} /. Options[Twist2CounterOperator]; dim = Dimension /. {opt} /. Options[Twist2CounterOperator]; pol = Polarization /. {opt} /. Options[Twist2CounterOperator]; Which[pol === 0, ChangeDimension[uc47[p1, p2, p3, mu, a, coup],dim], pol === 1, - ChangeDimension[pc47[p1, p2, p3, mu, a, coup],dim] + "Not available!" + (*ChangeDimension[pc47[p1, p2, p3, mu, a, coup],dim]*) ] ]; diff --git a/FeynCalc/QCD/Twist2GluonOperator.m b/FeynCalc/QCD/Twist2GluonOperator.m index 30708639e..b8c4106a7 100755 --- a/FeynCalc/QCD/Twist2GluonOperator.m +++ b/FeynCalc/QCD/Twist2GluonOperator.m @@ -42,6 +42,8 @@ Begin["`Twist2GluonOperator`Private`"] +del::usage=""; + Options[Twist2GluonOperator] = { CouplingConstant -> SMP["g_s"], Dimension -> D, @@ -49,14 +51,11 @@ Explicit -> False, ZeroMomentumInsertion -> True }; +(*Used to be $AchmedRoss=False *) +AchmedRoss=False; GO = Twist2GluonOperator; -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - -Twist2GluonOperator[x___, i_Integer, y___] := - Twist2GluonOperator[x, l[i], c[i], y]; - Twist2GluonOperator[a1_, a2_, a3_, a4_, a5_, opt:OptionsPattern[]] := Twist2GluonOperator[a1, {a2, a3}, {a4,a5}, opt] /; FreeQ2[Map[Head, {a1, a2, a3, a4, a5}], {Integer, Rule}]; @@ -184,7 +183,7 @@ psi[opt] Twist2GluonOperator[pi, {nui}, {mui},opt] /; !OrderedQ[{mui,nui}]; Twist2GluonOperator[pi_ /; Head[pi] =!= List, {mui_}, {nui_}, OptionsPattern[]] := - Block[ {dim, p, mu, nu, re, pol, del}, + Block[ {dim, p, mu, nu, re, pol}, dim = OptionValue[Dimension]; pol = OptionValue[Polarization]; p = Mo[pi, dim]; @@ -510,7 +509,7 @@ IntegerQ[m] && $OPEWard =!= False; Twist2GluonOperator[{pi_, mui_, ai_}, {qi_, nui_, bi_}, {ki_, lai_, ci_}, opt:OptionsPattern[]] := - Block[ {coup, dim, pol, p, q, k, mu, nu, la, a, b, c, re, del, threegluon, m,l}, + Block[ {coup, dim, pol, p, q, k, mu, nu, la, a, b, c, re, threegluon, m,l}, coup = OptionValue[CouplingConstant]; dim = OptionValue[Dimension]; pol = OptionValue[Polarization]; @@ -524,7 +523,7 @@ re = -I coup ((1 + Power2[(-1),OPEm])/2) SUNF[a,b,c] * Twist2GluonOperator[{pi//m, mui//l}, {qi//m, nui//l}, {ki//m, lai//l}, opt], - If[ !$AchmedRoss, + If[ !AchmedRoss, re = coup (1 - Power2[(-1),OPEm]) SUNF[a,b,c] * Twist2GluonOperator[{pi//m, mui//l}, {qi//m, nui//l}, {ki//m, lai//l}, opt], @@ -546,7 +545,7 @@ },{LorentzIndex,Momentum}]; Twist2GluonOperator[{pi_, mui_}, {qi_, nui_}, {ki_, lai_}, OptionsPattern[]] := - Block[ {coup, dim, pol, p, q, k, mu, nu, la, re, del, mm,ll, threegluon, threegluonar}, + Block[ {coup, dim, pol, p, q, k, mu, nu, la, re, mm,ll, threegluon, threegluonar}, coup = OptionValue[CouplingConstant]; dim = OptionValue[Dimension]; pol = OptionValue[Polarization]; @@ -561,8 +560,103 @@ re = (o3[mu,nu,la, p,q,k, del] + o3[nu,la,mu, q,k,p, del] + o3[la,mu,nu, k,p,q, del]), - (*This is Achmed & Ross ... ; really ...*) - threegluonar[{m_, k1_}, {n_, k2_}, {l_, k3_}] := + + (*threegluon stuff*) + + + If[ AchmedRoss, + re = ACHMED (-1) threegluonar[{mu,p},{nu,q},{la,k}], + re = threegluon[OptionValue[Explicit]][{mu,p},{nu,q},{la,k}] + ]; + ]; + re//simp[OptionValue[Explicit]] + ] /; OptionValue[Explicit]; + +(* 4-gluon operator *) + +Twist2GluonOperator[a1_, a2_, a3_, a4_, a5_, a6_, a7_, a8_, a9_, + a10_, a11_, a12_, opt___Rule] := + Twist2GluonOperator[{a1,a2,a3}, {a4,a5,a6}, {a7,a8,a9}, {a10,a11,a12}, opt]; + +Twist2GluonOperator[{p_,mu_}, {q_,nu_}, + {k_,la_}, {s_,si_}, opt___Rule + ] := + Block[ {dlt, dim, m, l, pol}, + dim = Dimension /. {opt} /. Options[Twist2GluonOperator]; + pol = Polarization /. {opt} /. Options[Twist2GluonOperator]; + dlt = Momentum[OPEDelta, dim]; + m[y_] := + Mo[y,dim]; + l[y_] := + Li[y,dim]; + dlt = Momentum[OPEDelta, Dimension /. {opt} /. + Options[Twist2GluonOperator]]; + If[ pol === 0, + o415[mu//l,nu//l,la//l,si//l, p//m,q//m,k//m,s//m,dlt], + pol4p[mu//l,nu//l,la//l,si//l, p//m,q//m,k//m,s//m,dlt] + ]//simp[Explicit /. {opt} /. Options[Twist2GluonOperator]] + ]/; + (Explicit /. {opt} /. Options[Twist2GluonOperator]) =!= False; + + + + (* with the sums *) + threegluon[True][{l1_,p1_}, {l2_,p2_}, {l3_,p3_}] := + -(OPESum[(-1)^OPEi*Pair[p3, del]^OPEi* + Pair[del, p2]^(-3 - OPEi + OPEm), {OPEi, 0, -3 + OPEm}]* + (Eps[l3, l2, del, p2]*Pair[p3, del] + + Eps[l2, p3, del, p2]*Pair[l3, del])*Pair[l1, del] - + OPESum[(-1)^OPEi*Pair[p3, del]^OPEi* + Pair[del, p1]^(-3 - OPEi + OPEm), {OPEi, 0, -3 + OPEm}]* + (Eps[l3, l1, del, p1]*Pair[p3, del] + + Eps[l1, p3, del, p1]*Pair[l3, del])*Pair[l2, del] + + Pair[p3, del]^(-2 + OPEm)* + (Eps[l3, l2, p3, del]*Pair[l1, del] - + Eps[l3, l1, p3, del]*Pair[l2, del]) + + (Eps[l1, l2, del, p1]*Pair[l3, del] + + Eps[l3, l1, del, p1]*Pair[l2, del])* + Pair[del, p1]^(-2 + OPEm) + + OPESum[(-1)^OPEi*Pair[del, p1]^OPEi* + Pair[del, p2]^(-3 - OPEi + OPEm), {OPEi, 0, -3 + OPEm}]* + Pair[l3, del]*(Eps[l2, del, p1, p2]*Pair[l1, del] - + Eps[l1, l2, del, p2]*Pair[del, p1]) + + (Eps[l1, l2, del, p2]*Pair[l3, del] - + Eps[l3, l2, del, p2]*Pair[l1, del])* + Pair[del, p2]^(-2 + OPEm)); + +(* the sums done *) + threegluon[All][{l1_,p1_}, {l2_,p2_}, {l3_,p3_}] := + EpsEvaluate[ + -(Eps[l1, l2, del, p1]*Pair[del, l3]*Power2[Pair[del, p1], -2 + OPEm]) + + (Eps[l2, del, p1, p2]*Pair[del, l1]*Pair[del, l3]* + (Power2[-1, OPEm]*Power2[Pair[del, p1], -2 + OPEm] - + Power2[Pair[del, p2], -2 + OPEm]))/(Pair[del, p1] + Pair[del, p2]) - + (Eps[l1, l2, del, p2]*Pair[del, l3]* + (Pair[del, p1]*Power2[-1, OPEm]*Power2[Pair[del, p1], -2 + OPEm] + + Pair[del, p2]*Power2[Pair[del, p2], -2 + OPEm]))/ + (Pair[del, p1] + Pair[del, p2]) - + Eps[l3, l2, p3, del]*Pair[del, l1]*Power2[Pair[del, p3], -2 + OPEm] + + Eps[l3, l1, p3, del]*Pair[del, l2]*Power2[Pair[del, p3], -2 + OPEm] - + (Eps[l1, p3, del, p1]*Pair[del, l2]*Pair[del, l3]* + (-Power2[Pair[del, p1], -2 + OPEm] + + Power2[-1, OPEm]*Power2[Pair[del, p3], -2 + OPEm]))/ + (Pair[del, p1] + Pair[del, p3]) + + (Eps[l2, p3, del, p2]*Pair[del, l1]*Pair[del, l3]* + (-Power2[Pair[del, p2], -2 + OPEm] + + Power2[-1, OPEm]*Power2[Pair[del, p3], -2 + OPEm]))/ + (Pair[del, p2] + Pair[del, p3]) - + (Eps[l3, l1, del, p1]*Pair[del, l2]* + (Pair[del, p1]*Power2[Pair[del, p1], -2 + OPEm] + + Pair[del, p3]*Power2[-1, OPEm]*Power2[Pair[del, p3], -2 + OPEm]))/ + (Pair[del, p1] + Pair[del, p3]) + + (Eps[l3, l2, del, p2]*Pair[del, l1]* + (Pair[del, p2]*Power2[Pair[del, p2], -2 + OPEm] + + Pair[del, p3]*Power2[-1, OPEm]*Power2[Pair[del, p3], -2 + OPEm]))/ + (Pair[del, p2] + Pair[del, p3]) + ]; + +(*This is Achmed & Ross ... ; really ...*) +threegluonar[{m_, k1_}, {n_, k2_}, {l_, k3_}] := ( Eps[m, n, del, k1]*Pair[del, l]*Power2[Pair[del, k1], -2 + OPEm] + Eps[l, n, del, k1]*Pair[del, m]*Power2[Pair[del, k1], -2 + OPEm] + @@ -625,93 +719,6 @@ Power2[Pair[del, k2], -1 + OPEm] + Power2[Pair[del, k3], -1 + OPEm]) ); - (* the sums done *) - threegluon[All][{l1_,p1_}, {l2_,p2_}, {l3_,p3_}] := - EpsEvaluate[ - -(Eps[l1, l2, del, p1]*Pair[del, l3]*Power2[Pair[del, p1], -2 + OPEm]) + - (Eps[l2, del, p1, p2]*Pair[del, l1]*Pair[del, l3]* - (Power2[-1, OPEm]*Power2[Pair[del, p1], -2 + OPEm] - - Power2[Pair[del, p2], -2 + OPEm]))/(Pair[del, p1] + Pair[del, p2]) - - (Eps[l1, l2, del, p2]*Pair[del, l3]* - (Pair[del, p1]*Power2[-1, OPEm]*Power2[Pair[del, p1], -2 + OPEm] + - Pair[del, p2]*Power2[Pair[del, p2], -2 + OPEm]))/ - (Pair[del, p1] + Pair[del, p2]) - - Eps[l3, l2, p3, del]*Pair[del, l1]*Power2[Pair[del, p3], -2 + OPEm] + - Eps[l3, l1, p3, del]*Pair[del, l2]*Power2[Pair[del, p3], -2 + OPEm] - - (Eps[l1, p3, del, p1]*Pair[del, l2]*Pair[del, l3]* - (-Power2[Pair[del, p1], -2 + OPEm] + - Power2[-1, OPEm]*Power2[Pair[del, p3], -2 + OPEm]))/ - (Pair[del, p1] + Pair[del, p3]) + - (Eps[l2, p3, del, p2]*Pair[del, l1]*Pair[del, l3]* - (-Power2[Pair[del, p2], -2 + OPEm] + - Power2[-1, OPEm]*Power2[Pair[del, p3], -2 + OPEm]))/ - (Pair[del, p2] + Pair[del, p3]) - - (Eps[l3, l1, del, p1]*Pair[del, l2]* - (Pair[del, p1]*Power2[Pair[del, p1], -2 + OPEm] + - Pair[del, p3]*Power2[-1, OPEm]*Power2[Pair[del, p3], -2 + OPEm]))/ - (Pair[del, p1] + Pair[del, p3]) + - (Eps[l3, l2, del, p2]*Pair[del, l1]* - (Pair[del, p2]*Power2[Pair[del, p2], -2 + OPEm] + - Pair[del, p3]*Power2[-1, OPEm]*Power2[Pair[del, p3], -2 + OPEm]))/ - (Pair[del, p2] + Pair[del, p3]) - ]; - - (* with the sums *) - threegluon[True][{l1_,p1_}, {l2_,p2_}, {l3_,p3_}] := - -(OPESum[(-1)^OPEi*Pair[p3, del]^OPEi* - Pair[del, p2]^(-3 - OPEi + OPEm), {OPEi, 0, -3 + OPEm}]* - (Eps[l3, l2, del, p2]*Pair[p3, del] + - Eps[l2, p3, del, p2]*Pair[l3, del])*Pair[l1, del] - - OPESum[(-1)^OPEi*Pair[p3, del]^OPEi* - Pair[del, p1]^(-3 - OPEi + OPEm), {OPEi, 0, -3 + OPEm}]* - (Eps[l3, l1, del, p1]*Pair[p3, del] + - Eps[l1, p3, del, p1]*Pair[l3, del])*Pair[l2, del] + - Pair[p3, del]^(-2 + OPEm)* - (Eps[l3, l2, p3, del]*Pair[l1, del] - - Eps[l3, l1, p3, del]*Pair[l2, del]) + - (Eps[l1, l2, del, p1]*Pair[l3, del] + - Eps[l3, l1, del, p1]*Pair[l2, del])* - Pair[del, p1]^(-2 + OPEm) + - OPESum[(-1)^OPEi*Pair[del, p1]^OPEi* - Pair[del, p2]^(-3 - OPEi + OPEm), {OPEi, 0, -3 + OPEm}]* - Pair[l3, del]*(Eps[l2, del, p1, p2]*Pair[l1, del] - - Eps[l1, l2, del, p2]*Pair[del, p1]) + - (Eps[l1, l2, del, p2]*Pair[l3, del] - - Eps[l3, l2, del, p2]*Pair[l1, del])* - Pair[del, p2]^(-2 + OPEm)); - If[ $AchmedRoss, - re = ACHMED (-1) threegluonar[{mu,p},{nu,q},{la,k}], - re = threegluon[OptionValue[Explicit]][{mu,p},{nu,q},{la,k}] - ]; - ]; - re//simp[OptionValue[Explicit]] - ] /; OptionValue[Explicit]; - -(* 4-gluon operator *) - -Twist2GluonOperator[a1_, a2_, a3_, a4_, a5_, a6_, a7_, a8_, a9_, - a10_, a11_, a12_, opt___Rule] := - Twist2GluonOperator[{a1,a2,a3}, {a4,a5,a6}, {a7,a8,a9}, {a10,a11,a12}, opt]; - -Twist2GluonOperator[{p_,mu_}, {q_,nu_}, - {k_,la_}, {s_,si_}, opt___Rule - ] := - Block[ {dlt, dim, m, l, pol}, - dim = Dimension /. {opt} /. Options[Twist2GluonOperator]; - pol = Polarization /. {opt} /. Options[Twist2GluonOperator]; - dlt = Momentum[OPEDelta, dim]; - m[y_] := - Mo[y,dim]; - l[y_] := - Li[y,dim]; - dlt = Momentum[OPEDelta, Dimension /. {opt} /. - Options[Twist2GluonOperator]]; - If[ pol === 0, - o415[mu//l,nu//l,la//l,si//l, p//m,q//m,k//m,s//m,dlt], - pol4p[mu//l,nu//l,la//l,si//l, p//m,q//m,k//m,s//m,dlt] - ]//simp[Explicit /. {opt} /. Options[Twist2GluonOperator]] - ]/; - (Explicit /. {opt} /. Options[Twist2GluonOperator]) =!= False; (* calculated by FC *) diff --git a/FeynCalc/QCD/Twist2QuarkOperator.m b/FeynCalc/QCD/Twist2QuarkOperator.m index c673392d2..da66ad9de 100755 --- a/FeynCalc/QCD/Twist2QuarkOperator.m +++ b/FeynCalc/QCD/Twist2QuarkOperator.m @@ -44,8 +44,6 @@ Begin["`Twist2QuarkOperator`Private`"] -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - DeclareNonCommutative[Twist2QuarkOperator]; Options[Twist2QuarkOperator] = { @@ -100,9 +98,6 @@ Twist2QuarkOperator[p_, _Integer, _Integer] := Twist2QuarkOperator[p]; -Twist2QuarkOperator[x___, i_Integer, y___] := - Twist2QuarkOperator[x, l[i], c[i], y]; - (* Quark - Quark - Gluon *) Twist2QuarkOperator[{p1_,__} {p2_,__}, {p3_,mu_,a_ /; Head[a] =!= Rule}, opt:OptionsPattern[]] := diff --git a/FeynCalc/QCD/Twist3QuarkOperator.m b/FeynCalc/QCD/Twist3QuarkOperator.m index 54c6a6e40..9cbfd5994 100755 --- a/FeynCalc/QCD/Twist3QuarkOperator.m +++ b/FeynCalc/QCD/Twist3QuarkOperator.m @@ -36,12 +36,13 @@ p3 denotes the (incoming) gluon momentum. Begin["`Twist3QuarkOperator`Private`"] -Options[Twist3QuarkOperator] = { CouplingConstant -> SMP["g_s"], - Dimension -> D, Polarization -> 1}; +Options[Twist3QuarkOperator] = { + CouplingConstant -> SMP["g_s"], + Dimension -> D, + Polarization -> 1 +}; -Twist3QuarkOperator[a1_/;Head[a1] =!= List, v_/;Head[v] =!=Integer, - w_/;Head[w] =!= Integer, - opt___Rule] := +Twist3QuarkOperator[a1_/;Head[a1] =!= List, v_/;Head[v] =!=Integer, w_/;Head[w] =!= Integer, opt___Rule] := Twist3QuarkOperator[a1, opt]; (* 2 - Quark operator; unpolarized : RH (3A.8); (3A.9) *) @@ -59,26 +60,19 @@ p3 denotes the (incoming) gluon momentum. re ]; -{l, c} = MakeFeynCalcPrivateContext /@ {"l", "c"}; - -Twist3QuarkOperator[p_, i_Integer, j_Integer] := +Twist3QuarkOperator[p_, _Integer, _Integer] := QuarkOperator[p]; -Twist3QuarkOperator[x___, i_Integer, y___] := - QuarkOperator[x, l[i], c[i], y]; - (* Quark - Quark - Gluon *) -Twist3QuarkOperator[{p1_,__} {p2_,__}, {p3_,mu_,a_ /; Head[a] =!= Rule}, - opt___Rule] := +Twist3QuarkOperator[{p1_,__} {p2_,__}, {p3_,mu_,a_ /; Head[a] =!= Rule}, opt___Rule] := Twist3QuarkOperator[{p1}, {p2}, {p3, mu, a}, opt]; -Twist3QuarkOperator[p1_,_,_, p2_,_,_, p3_,mu_,a_ /; Head[a] =!= Rule, - opt___Rule] := +Twist3QuarkOperator[p1_,_,_, p2_,_,_, p3_,mu_,a_ /; Head[a] =!= Rule, opt___Rule] := Twist3QuarkOperator[{p1}, {p2}, {p3, mu, a}, opt]; -Twist3QuarkOperator[{p2_}, {p1_}, {p3_, mu_, a_}, opt___Rule] := - Block[ {dim, pe1, pe2, pol, del, muu, coup}, +Twist3QuarkOperator[{p2_}, {p1_}, {_, mu_, a_}, opt___Rule] := + Block[ {dim, pe1, pe2, pol, del, muu, coup, re}, coup = CouplingConstant /. {opt} /. Options[Twist3QuarkOperator]; dim = Dimension /. {opt} /. Options[Twist3QuarkOperator]; pol = Polarization /. {opt} /. Options[Twist3QuarkOperator]; @@ -88,37 +82,28 @@ p3 denotes the (incoming) gluon momentum. muu = LorentzIndex[mu, dim]; If[ pol === 0, re = -coup SUNT[SUNIndex[a]] Pair[del,muu] * - OPESum[(-1)^OPEi Pair[del, pe1]^OPEi * - Pair[del, pe2]^(OPEm-OPEi-2), - {OPEi, 0, OPEm-2}], + OPESum[(-1)^OPEi Pair[del, pe1]^OPEi * + Pair[del, pe2]^(OPEm-OPEi-2), {OPEi, 0, OPEm-2}], re = -coup (*((1-(-1)^OPEm)/2)*) * - DOT[DiracGamma[del,dim], DiracGamma[5], - SUNT[SUNIndex[a]]] Pair[del,muu] * - OPESum[(-1)^OPEi Pair[del, pe1]^OPEi * - Pair[del, pe2]^(OPEm-OPEi-2), - {OPEi, 0, OPEm-2}] + DOT[DiracGamma[del,dim], DiracGamma[5], SUNT[SUNIndex[a]]] Pair[del,muu] * + OPESum[(-1)^OPEi Pair[del, pe1]^OPEi * Pair[del, pe2]^(OPEm-OPEi-2), {OPEi, 0, OPEm-2}] ]; re ]; (* Quark - Quark - Gluon - Gluon *) -Twist3QuarkOperator[{p1_,__} {p2_,__}, {p3_,mu_,a_ /; Head[a] =!= Rule}, - {p4_,nu_,b_ /; Head[b] =!= Rule}, - opt___Rule] := +Twist3QuarkOperator[{p1_,__} {p2_,__}, {p3_,mu_,a_ /; Head[a] =!= Rule}, {p4_,nu_,b_ /; Head[b] =!= Rule}, opt___Rule] := Twist3QuarkOperator[{p1}, {p2}, {p3, mu, a}, {p4, nu, b}, opt]; -Twist3QuarkOperator[p1_,_,_, p2_,_,_, p3_,mu_,a_ /; Head[a] =!= Rule, - p4_,nu_,b_, - opt___Rule] := +Twist3QuarkOperator[p1_,_,_, p2_,_,_, p3_,mu_,a_ /; Head[a] =!= Rule, p4_,nu_,b_, opt___Rule] := Twist3QuarkOperator[{p1}, {p2}, {p3, mu, a}, {p4, nu, b}, opt]; -Twist3QuarkOperator[{p2_}, {p1_}, {p3_, mu_, c_},{p4_, nu_, d_}, - opt___Rule] := - Block[ {dim, pe1, pe2, pe3, pe4, pol, del, muu, coup}, - coup = CouplingConstant /. {opt} /. Options[Twist3QuarkOperator]; - dim = Dimension /. {opt} /. Options[Twist3QuarkOperator]; - pol = Polarization /. {opt} /. Options[Twist3QuarkOperator]; +Twist3QuarkOperator[{p2_}, {p1_}, {p3_, mu_, c_},{p4_, nu_, d_}, opt___Rule] := + Block[{ dim, pe1, pe2, pe3, pe4, pol, del, muu, nuu, coup, re}, + coup= CouplingConstant /. {opt} /. Options[Twist3QuarkOperator]; + dim = Dimension /. {opt} /. Options[Twist3QuarkOperator]; + pol = Polarization /. {opt} /. Options[Twist3QuarkOperator]; pe1 = Momentum[p1, dim]; pe2 = Momentum[p2, dim]; pe3 = Momentum[p3, dim]; @@ -126,8 +111,9 @@ p3 denotes the (incoming) gluon momentum. del = Momentum[OPEDelta, dim]; muu = LorentzIndex[mu, dim]; nuu = LorentzIndex[nu, dim]; + If[ pol === 0, - re = notyet, + re = "Not ready yet!", re = (-coup^2 (*((1-(-1)^OPEm)/2)*) * DOT[DiracGamma[del], DiracGamma[5], (DOT[SUNT[SUNIndex[d]], SUNT[SUNIndex[c]]]* diff --git a/FeynCalc/SUN/CalcColorFactor.m b/FeynCalc/SUN/CalcColorFactor.m index 98ec65848..d8a06aa20 100644 --- a/FeynCalc/SUN/CalcColorFactor.m +++ b/FeynCalc/SUN/CalcColorFactor.m @@ -14,12 +14,8 @@ CalcColorFactor::usage = -"CalcColorFactor[expr] calculates the color factor of expr. \ -CalcColorFactor is useful for application on FeynArts produced amplitudes. \ -CalcColorFactor is just a macro function for \ -CalcColorFactor[x_] := If[FreeQ2[FeynCalcInternal[x], SUNIndex], x, \ -SUNSimplify[SUNSimplify[(If[ !FreeQ[#1, DiracGamma], DiracTrick[#1], #1] & )[ \ -SUNSimplify[x]], Explicit -> False], Explicit -> True]]."; +"CalcColorFactor[exp] calculates the color factor of exp. \n +CalcColorFactor is useful for application on FeynArts produced amplitudes."; (* ------------------------------------------------------------------------ *) @@ -30,14 +26,16 @@ SetAttributes[CalcColorFactor, Listable]; -Options[CalcColorFactor] = {SUNNToCACF -> True}; +Options[CalcColorFactor] = { + SUNNToCACF -> True +}; SetAttributes[CalcColorFactor, Listable]; CalcColorFactor[x_Plus, opts:OptionsPattern[]] := CalcColorFactor[#, opts]& /@ x; CalcColorFactor[x_, OptionsPattern[]] := - Module[{tmp = FeynCalcInternal[x]}, + Module[{tmp = FeynCalcInternal[x], fac}, If[FreeQ[tmp, SUNIndex], tmp, If[Head[tmp]=!=Times, diff --git a/FeynCalc/SUN/FCColorIsolate.m b/FeynCalc/SUN/FCColorIsolate.m index 46b9f63cb..ebe8e5bad 100755 --- a/FeynCalc/SUN/FCColorIsolate.m +++ b/FeynCalc/SUN/FCColorIsolate.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Isolates colored objects *) @@ -16,10 +16,8 @@ (* ------------------------------------------------------------------------ *) FCColorIsolate::usage = -"FCColorIsolate[expr,{q1,q2,...}] wraps colored objetcts (SUNT,SUNF,...) into heads \ -specified by the user " <> ToString[ -Hyperlink[Style["\[RightSkeleton]", "SR"], "paclet:FeynCalc/ref/FCColorIsolate"], -StandardForm]; +"FCColorIsolate[exp] wraps colored objects (SUNT,SUNF etc.) into heads \ +specified by the user."; FCColorIsolate::fail = "FCColorIsolate failed to isolate colored objects in `1`!"; @@ -30,27 +28,42 @@ Begin["`FCColorIsolate`Private`"] Options[FCColorIsolate] = { - ClearHeads -> {FCGV["ColorObject"]}, - Collecting -> True, - DotSimplify -> True, - ExceptHeads -> {}, - Expanding -> True, - FCI -> False, - Factoring -> Factor, - Head -> FCGV["ColorObject"], - Isolate -> False, - IsolateNames -> KK, - IsolateFast -> False, - SUNT -> True, - SUNF -> True, - SUND -> True, - SUNTrace -> True + ClearHeads -> {FCGV["ColorObject"]}, + Collecting -> True, + DotSimplify -> True, + ExceptHeads -> {}, + Expanding -> True, + FCE -> False, + FCI -> False, + Factoring -> Factor, + Head -> FCGV["ColorObject"], + Isolate -> False, + IsolateFast -> False, + IsolateNames -> KK, + SUND -> True, + SUNF -> True, + SUNT -> True, + SUNTrace -> True, + TimeConstrained -> 3 }; -FCColorIsolate[expr_, OptionsPattern[]] := - Block[ {res, null1, null2, ex,tmp, head, restHead}, - head = OptionValue[Head]; +FCColorIsolate[expr_List, opts:OptionsPattern[]]:= + FCColorIsolate[#, opts]&/@expr; + +FCColorIsolate[expr_/; Head[expr]=!=List, OptionsPattern[]] := + Block[ {res, null1, null2, ex,tmp, head, optHead, headR, relevantHeads}, + + optHead = OptionValue[Head]; + + relevantHeads = Complement[FeynCalc`Package`SUNHeadsList, OptionValue[ExceptHeads]]; + + If[MatchQ[optHead,{_,_}], + {head, headR} = optHead, + + head = optHead; + headR = Identity + ]; If[OptionValue[FCI], ex = expr/. (Map[Rule[#, Identity] &, OptionValue[ClearHeads]]), @@ -58,26 +71,26 @@ ]; - If[ FreeQ2[ex,SUNHeadsList], - Return[ex] + If[ FreeQ2[ex,relevantHeads], + Return[restHead[ex] /. restHead -> headR] ]; If[ OptionValue[Expanding], - ex = Expand2[ex, SUNHeadsList]; + ex = Expand2[ex, relevantHeads]; ]; (* and out of the DOTs *) If[ OptionValue[DotSimplify] && !FreeQ[ex,DOT], - tmp = FCSplit[ex, SUNHeadsList, Expanding->OptionValue[Expanding]]; + tmp = FCSplit[ex, relevantHeads, Expanding->OptionValue[Expanding]]; ex = tmp[[1]]+ DotSimplify[tmp[[2]],Expanding->False] ]; If[ OptionValue[Collecting], - ex = Collect2[ex,SUNHeadsList,Factoring->OptionValue[Factoring]]; + ex = Collect2[ex,relevantHeads,Factoring->OptionValue[Factoring],TimeConstrained->OptionValue[TimeConstrained]]; ]; - res = (Map[(restHead[SelectFree[#, SUNHeadsList]]* - head[SelectNotFree[#, SUNHeadsList]]) &, + res = (Map[(restHead[SelectFree[#, relevantHeads]]* + head[SelectNotFree[#, relevantHeads]]) &, ex + null1 + null2] /. {null1 | null2 -> 0} /. head[1] -> 1); res = res /. {head[x_] /; !FreeQ2[x, OptionValue[ExceptHeads]] :> x}; @@ -105,20 +118,27 @@ res = res //. head[(x_SUND)^n_. y_.] :> x^n head[y]; ]; - res = res //. head[x_]/; FreeQ2[x,SUNHeadsList] :> x; + res = res //. head[x_]/; FreeQ2[x,relevantHeads] :> x; If[ OptionValue[Isolate], res = res/. restHead[x_]:> Isolate[x,IsolateNames->OptionValue[IsolateNames],IsolateFast->OptionValue[IsolateFast]], - res = res /. restHead -> Identity + res = res /. restHead[0]->0 /. restHead -> headR; ]; - If [ !FreeQ[res/. head[__] :> 1, SUNHeadsList] & , + If [ !FreeQ[res/. head[__] :> 1, relevantHeads] & , Message[FCColorIsolate::fail, ex]; Abort[] ]; + If[ OptionValue[FCE], + res = FCE[res] + ]; + res ]; +restHead[0]= + 0; + FCPrint[1,"FCColorIsolate.m loaded."]; End[] diff --git a/FeynCalc/SUN/SUNDeltaContract.m b/FeynCalc/SUN/SUNDeltaContract.m index bf27041cc..75e079d18 100644 --- a/FeynCalc/SUN/SUNDeltaContract.m +++ b/FeynCalc/SUN/SUNDeltaContract.m @@ -6,12 +6,12 @@ (* ------------------------------------------------------------------------ *) SUNDeltaContract::usage= -"SUNDeltaContract[expr] substitues for all SUNDelta in expr \ -SUNDeltaContract, contracts the SUN(N) indices and resubstitutes SUNDelta. \ -\n -SUNDeltaContract[i, j] is the Kronecker-delta for SU(N) \ -with contraction properties. SUNDeltaContract wraps also the \ -head SUNIndex around its arguments."; +"SUNDeltaContract[exp] substitues for all SUNDelta in exp \ +SUNDeltaContract, contracts the adjoint SU(N) indices and resubstitutes \ +SUNDelta. \n +SUNDeltaContract[i, j] is the Kronecker-delta for SU(N) in the adjoint \ +representation with contraction properties. It wraps the head SUNIndex \ +around its arguments."; (* ------------------------------------------------------------------------ *) diff --git a/FeynCalc/SUN/SUNFDeltaContract.m b/FeynCalc/SUN/SUNFDeltaContract.m index b5dd4d6e3..1634f80be 100644 --- a/FeynCalc/SUN/SUNFDeltaContract.m +++ b/FeynCalc/SUN/SUNFDeltaContract.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Kronecker delta for SU(N) in the fundamental representation *) @@ -16,13 +16,12 @@ (* ------------------------------------------------------------------------ *) SUNFDeltaContract::usage= -"SUNFDeltaContract[expr] substitues for all \ -SUNFDelta in expr SUNFDeltaContract, contracts \ -the SU(N) fundamental indices and resubstitutes SUNFDelta. \ -\n -SUNFDeltaContract[i, j] is the Kronecker-delta for SU(N) in the \ -fundamental representation with contraction properties. \ -SUNFDeltaContract wraps also the head SUNFIndex around its arguments."; +"SUNFDeltaContract[exp] substitues for all SUNFDelta in exp with \ +SUNFDeltaContract, contracts the fundamental SU(N) indices and resubstitutes \ +SUNFDelta. \n +SUNFDeltaContract[i, j] is the Kronecker-delta for SU(N) in the fundamental \ +representation with contraction properties. It wraps the head SUNFIndex \ +around its arguments."; (* ------------------------------------------------------------------------ *) diff --git a/FeynCalc/SUN/SUNFSimplify.m b/FeynCalc/SUN/SUNFSimplify.m index 2f278a497..c98562f93 100644 --- a/FeynCalc/SUN/SUNFSimplify.m +++ b/FeynCalc/SUN/SUNFSimplify.m @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Simplifies expressions that contain SU(N) indices in the @@ -15,8 +15,8 @@ (* ------------------------------------------------------------------------ *) SUNFSimplify::usage = " -SUNFSimplify[expr] simplifies expression that contain SU(N) indices in the \ -fundamental representation"; +SUNFSimplify[exp] is an auxiliary function that simplifies expressions \ +containing SU(N) indices in the fundamental representation."; (* ------------------------------------------------------------------------ *) @@ -29,7 +29,10 @@ fci[z_ /; FreeQ[z, Pattern]] := (fci[z] = FCI[z]); -Options[SUNFSimplify] = {SUNNToCACF->True ,Explicit->False}; +Options[SUNFSimplify] = { + Explicit -> False, + SUNNToCACF -> True +}; SUNFSimplify[expr_, OptionsPattern[]] := Block[ {temp = fci[expr],simplify}, diff --git a/FeynCalc/SUN/SUNSimplify.m b/FeynCalc/SUN/SUNSimplify.m index ebd04f456..92360cbb9 100644 --- a/FeynCalc/SUN/SUNSimplify.m +++ b/FeynCalc/SUN/SUNSimplify.m @@ -15,12 +15,8 @@ (* ------------------------------------------------------------------------ *) SUNSimplify::usage = -"SUNSimplify simplifies products of SUNT (and complex conjugated) -matrices. Renaming of dummy indices may be performed. -If the option SUNTrace is set to False, then any SUNT-matrices are -taken out of DiracTrace[...]; otherwise a color-trace is taken (by -SUNTrace) before taking the SUN-objects in front of DiracTrace[...]. -Whether SUNF is replaced by traces is determined by the option Explicit."; +"SUNSimplify[exp] simplifies products of SUNT and SUNTF \ +matrices in the expression."; SUNFJacobi::usage="SUNFJacobi is an option for SUNSimplify, indicating whether the Jacobi identity should be used."; @@ -42,6 +38,9 @@ (* *********************************************************************** *) +suntrace::usage=""; +sunt::usage=""; + fcis[z_ /; FreeQ[z, Pattern]] := (fcis[z] = FeynCalcInternal[z]); (* change SUNT' which are multiplied with each other to lambdaT's *) @@ -396,12 +395,16 @@ SUNF[xx_SUNIndex, yy_SUNIndex, zz_SUNIndex] * dotT[aa___, SUNT[yy_SUNIndex], SUNT[zz_SUNIndex], bb___] :> I/2 SUNN dotT[aa,SUNT[xx],bb] /; noint[yy,zz], - SUNF[xx_SUNIndex, yy_SUNIndex, zz_SUNIndex] * - SUNT[xx_SUNIndex] :> - I DOT[SUNT[zz] , SUNT[yy]] - I DOT[SUNT[yy] , SUNT[zz]] /; noint[xx], - SUNF[xx_SUNIndex, yy_SUNIndex, zz_SUNIndex] * - SUNT[zz_SUNIndex] :> - I DOT[SUNT[yy] , SUNT[xx]] - I DOT[SUNT[xx] , SUNT[yy]] /; noint[zz] + + SUNF[xx_SUNIndex, yy_SUNIndex, zz_SUNIndex] SUNT[xx_SUNIndex] :> + I DOT[SUNT[zz] , SUNT[yy]] - I DOT[SUNT[yy] , SUNT[zz]] /; noint[xx], + + SUNF[xx_SUNIndex, yy_SUNIndex, zz_SUNIndex] SUNT[zz_SUNIndex] :> + I DOT[SUNT[yy] , SUNT[xx]] - I DOT[SUNT[xx] , SUNT[yy]] /; noint[zz], + + SUNF[xx_SUNIndex, yy_SUNIndex, zz_SUNIndex] SUNT[yy_SUNIndex] :> + I DOT[SUNT[xx] , SUNT[zz]] - I DOT[SUNT[zz] , SUNT[xx]] /; noint[yy] + } /. dotT[] -> 1 //. {dotT[a___,1,b___] :> dotT[a,b]} /. dotT[] -> 1 /. dotT -> DOT; If[ sft === True, @@ -507,27 +510,7 @@ } /. sUNF -> SUNF; ]; - (*Dropped ComplexIndex. F.Orellana, 20/2-2003*) - (*If[!FreeQ[temp, ComplexIndex], - temp = temp /. DOT -> dooot /. - { - (SUNT[SUNIndex[a_]] /; FreeQ[{a}, ComplexIndex]) * - SUNT[SUNIndex[ComplexIndex[b_]]] :> - DOT[SUNTrace[SUNT[SUNIndex[a]] , SUNT[SUNIndex[b]]] ], - - (SUNT[SUNIndex[ComplexIndex[a_]]] ) * - dooot[(b:SUNT[SUNIndex[_]]..) /; FreeQ[{b}, ComplexIndex]] :> - DOT[SUNTrace[SUNT[SUNIndex[a]] , b] ], - - (SUNT[SUNIndex[a_ /; FreeQ[{a}, ComplexIndex]] ]) * - dooot[b:SUNT[SUNIndex[ComplexIndex[_]]]..] :> - DOT[SUNTrace[SUNT[SUNIndex[a]] , b] ], - - dooot[(a:SUNT[SUNIndex[_]]..) /; FreeQ[{a}, ComplexIndex]] * - dooot[b:SUNT[SUNIndex[ComplexIndex[_]]]..] :> - SUNTrace[dooot @@ Join[{a}, Reverse[{b}]/.ComplexIndex -> Identity]] - } /. dooot -> DOT; - ];*) + If[ !FreeQ[temp, SUNIndex], temp = temp /. sunsi; ]; diff --git a/FeynCalc/SUN/SUNTrace.m b/FeynCalc/SUN/SUNTrace.m index 40df1a618..eb3bbb2fc 100644 --- a/FeynCalc/SUN/SUNTrace.m +++ b/FeynCalc/SUN/SUNTrace.m @@ -13,7 +13,7 @@ (* ------------------------------------------------------------------------ *) SUNTrace::usage= -"SUNTrace[expr] calculates the color-trace."; +"SUNTrace[exp] calculates the color-trace."; (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -21,10 +21,12 @@ Begin["`SUNTrace`Private`"] -Options[SUNTrace] = {Explicit -> False}; +Options[SUNTrace] = { + Explicit -> False +}; HoldPattern[SUNTrace[n_, ___Rule]] := - SUNN n /; FreeQ2[n, {SUNT, Pattern, Blank, BlankSequence, BlankNullSequence}]; + SUNN n /; FCPatternFreeQ[{n}, {SUNT}]; (* this is the function which puts everything together ********* *) SUNTrace[expr_Plus, op___Rule] := @@ -99,7 +101,7 @@ SUNTrace[ expr_, OptionsPattern[] ] := (fixgell[expr]/. gellm2->SUNTrace)/; ((Head[expr] =!= Times) || (Select[expr, !FreeQ[#, SUNT]&] ===1 )) && - (expr=!=(fixgell[expr] /. gellm2->Identity)) && FreeQ2[expr,{Pattern, Blank, BlankSequence, BlankNullSequence}] && + (expr=!=(fixgell[expr] /. gellm2->Identity)) && FCPatternFreeQ[{expr}] && (fcis[expr]===expr); SUNTrace[x_?externQ] := diff --git a/FeynCalc/Shared/CacheManagement.m b/FeynCalc/Shared/CacheManagement.m index a18bb954f..b1e940c1c 100755 --- a/FeynCalc/Shared/CacheManagement.m +++ b/FeynCalc/Shared/CacheManagement.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Functions for managing memoization in FeynCalc *) @@ -54,11 +54,14 @@ whiteListNames = { ExpandScalarProduct, PairContract, - FCFastContract + FCFastContract, + FeynCalc`NPointTo4Point`Private`getDet, + FeynCalc`SimplifyPolyLog`Private`simplifyArgument, + FeynCalc`FCApart`Private`pfracRaw }; FCUseCache[fcFunc_, args_List, opts_List: {}] := - Block[{fullOpts, cachedHead,depArgs}, + Block[{fullOpts, cachedHead,depArgs, standardSet}, fullOpts = Sort[Flatten[Join[opts, FilterRules[Options[fcFunc], Except[opts]]]]]; cachedHead=ToExpression["cacheFunc"<>ToString[fcFunc]]; @@ -69,31 +72,25 @@ Abort[] ]; + standardSet = DownValues[#]&/@{ + Pair, CartesianPair, TemporalPair, ScalarProduct, CartesianScalarProduct, + Momentum, CartesianMomentum, TemporalMomentum, SP, SPD, SPE, CSP, CSPD, CSPE, TC + }; + standardSet = Join[standardSet,{FeynCalc`Package`DiracGammaScheme, FeynCalc`Package`PauliSigmaScheme}]; + Which[ fcFunc === ExpandScalarProduct, - depArgs = cachedToString[{ DownValues[Pair], - DownValues[ScalarProduct], - DownValues[SP], - DownValues[SPD], - DownValues[SPE], - $BreitMaison, - $Larin}], + depArgs = cachedToString[standardSet], fcFunc === PairContract, - depArgs = cachedToString[{ DownValues[Pair], - DownValues[ScalarProduct], - DownValues[SP], - DownValues[SPD], - DownValues[SPE], - $BreitMaison, - $Larin}], + depArgs = cachedToString[standardSet], fcFunc === FCFastContract, - depArgs = cachedToString[{ DownValues[Pair], - DownValues[ScalarProduct], - DownValues[SP], - DownValues[SPD], - DownValues[SPE], - $BreitMaison, - $Larin}], + depArgs = cachedToString[standardSet], + fcFunc === FeynCalc`NPointTo4Point`Private`getDet, + depArgs = cachedToString[standardSet], + fcFunc === FeynCalc`SimplifyPolyLog`Private`simplifyArgument, + depArgs = cachedToString[standardSet], + fcFunc === FeynCalc`FCApart`Private`pfracRaw, + depArgs = cachedToString[standardSet], True, Message[FCUseCache::blacklist,fcFunc]; Abort[] diff --git a/FeynCalc/Shared/Collect.m b/FeynCalc/Shared/Collect.m index 42246f53b..0147651f2 100755 --- a/FeynCalc/Shared/Collect.m +++ b/FeynCalc/Shared/Collect.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Expansion of the Mathematica Collect *) @@ -36,6 +36,12 @@ the latter two of these cause the coefficients to be factored. The option Head (default Plus) \ specified the function applied to the list of monomials multiplied by their coefficients."; +FactoringDenominator::usage = "FactoringDenominator is an option for Collect2. \ +It is taken into account only when the option numerator is set to True. \ +If FactoringDenominator is set to any function f, this function will be applied to \ +the denominator of the fraction. The default value is False, i.e. the denominator \ +will be left unchanged."; + Collect2::failmsg = "Error! Collect2 has encountered a fatal problem and must abort the computation. \ The problem reads: `1`" @@ -51,44 +57,54 @@ Options[Collect2] = { - Denominator -> False, - Dot -> False, - FCFactorOut -> 1, - FCVerbose -> False, - Expanding -> True, - Factoring -> Factor, - IsolateFast -> False, - IsolateNames -> False, - Head->Identity + Denominator -> False, + Dot -> False, + Expanding -> True, + FCFactorOut -> 1, + FCVerbose -> False, + Factoring -> Factor, + FactoringDenominator -> False, + Head -> Identity, + InitialFunction -> Identity, + IntermediateSubstitutions -> {}, + IsolateFast -> False, + IsolateNames -> False, + Numerator -> False, + TimeConstrained -> Infinity }; Options[Collect3] = { Factoring -> False, Head -> Plus }; - +(* SetAttributes[holdForm,HoldAll]; - +*) Collect2[a_ == b_, y__] := Collect2[a,y] == Collect2[b,y]; +Collect2[(h:Rule|RuleDelayed)[a_,b_], y__] := + With[{zz=Collect2[b,y]}, h[a,zz]]; + Collect2[x_List, y__] := Collect2[#, y]& /@ x; Collect2[x_, y_, opts:OptionsPattern[]] := - Collect2[x, {y}, opts] /; (Head[y]=!=List && !OptionQ[y]); + Collect2[x, {y}, opts] /; (Head[y]=!=List && !OptionQ[y] && Head[x]=!=List && !OptionQ[x]); Collect2[x_, z__, y_, opts:OptionsPattern[]] := - Collect2[x, {z,y}, opts] /; (Head[y]=!=List && !OptionQ[y]); + Collect2[x, {z,y}, opts] /; (Head[y]=!=List && !OptionQ[y] && Head[x]=!=List && !OptionQ[x]); -Collect2[ expr_, vv_List/; (!OptionQ[vv] || vv==={}), opts:OptionsPattern[]] := - Block[{monomList,ru,nx,lk,factoring,optIsolateNames,tog,fr0,frx,lin,tv={},mp,mp2,cd,co,dde, +Collect2[expr_, vv_List/; (!OptionQ[vv] || vv==={}), opts:OptionsPattern[]] := + Block[{monomList,ru,nx,lk,factoring,optIsolateNames,tog,fr0,frx,lin,tv={},mp,monomialHead,cd,co,dde, new = 0, unity,re,compCON,ccflag = False, factor,expanding, times,time, - null1,null2,coeffArray,tvm,coeffHead,optIsolateFast,tempIso,factorOut}, + null1,null2,coeffArray,tvm,coeffHead,optIsolateFast,tempIso,factorOut, monomRepRule={}, + nonAtomicMonomials,optHead,firstHead,secondHead=Null,optInitialFunction,numerator,denominator, + optNumerator, optFactoringDenominator, optTimeConstrained}, If [OptionValue[FCVerbose]===False, cl2Verbose=$VeryVerbose, - If[MatchQ[OptionValue[FCVerbose], _Integer?Positive | 0], + If[MatchQ[OptionValue[FCVerbose], _Integer], cl2Verbose=OptionValue[FCVerbose] ]; ]; @@ -98,6 +114,19 @@ OptionValue[Expanding], OptionValue[Denominator], OptionValue[IsolateFast] }; + + optHead = OptionValue[Head]; + optInitialFunction = OptionValue[InitialFunction]; + optNumerator = OptionValue[Numerator]; + optFactoringDenominator = OptionValue[FactoringDenominator]; + optTimeConstrained = OptionValue[TimeConstrained]; + + If[ Head[optHead]===List, + firstHead = optHead[[1]]; + secondHead = optHead[[2]], + firstHead = optHead + ]; + factorOut = OptionValue[FCFactorOut]; Which[ @@ -109,12 +138,20 @@ times = OptionValue[Dot] ]; - If[factoring === True || factoring === Factor2, - factor = Factor2, - If[factoring =!= False, - factor = factoring; factoring = True, - factor = Identity - ]; + Switch[factoring, + False, + factor = Identity, + True|Factor2, + factor = Function[fuArg,TimeConstrained[Factor2[fuArg],optTimeConstrained,fuArg]], + {_,_Integer}, + factor = Function[fuArg, + If[ TrueQ[LeafCount[fuArg]cl2Verbose]; @@ -122,19 +159,54 @@ nx = expr; + If[ !FreeQ[nx,SeriesData], + Message[Collect2::failmsg,"Collect2 cannot work on expressions that contain SeriesData!"]; + Abort[] + ]; + + If[ optNumerator && Head[nx]===Times, + numerator=Numerator[nx]; + If[ optFactoringDenominator===False, + denominator=Denominator[nx], + denominator=optFactoringDenominator[Denominator[nx]] + ]; + nx = numerator, + denominator = 1 + ]; + + nx = nx /. OptionValue[IntermediateSubstitutions]; + nx = nx/factorOut; FCPrint[2,"Collect2: After factoring out ", factorOut, " :", nx, FCDoControl->cl2Verbose]; + + + FCPrint[1,"Collect2: Applying initial function.", FCDoControl->cl2Verbose]; + If[ Head[optInitialFunction]===List, + nx = (Composition@@optInitialFunction)[nx], + nx = optInitialFunction[nx] + ]; + FCPrint[3,"Collect2: After initial function ", nx, FCDoControl->cl2Verbose]; + monomList = Union[Select[ vv, ((Head[#] =!= Plus) && (Head[#] =!= Times) && (!NumberQ[#]))& ]]; monomList = Select[ monomList, !FreeQ[nx, #]&]; + (*If the monomials are not atomic, we should better mask them beforehand *) + nonAtomicMonomials = Select[monomList, ! AtomQ[#] &]; + If[nonAtomicMonomials=!={} && FCPatternFreeQ[nonAtomicMonomials], + monomRepRule = Thread[Rule[nonAtomicMonomials,Table[Unique["monom"], {r,1,Length[nonAtomicMonomials]} ]]]; + monomList = monomList/.monomRepRule; + nx = nx/.monomRepRule; + monomRepRule = Reverse/@monomRepRule + ]; + FCPrint[1,"Collect2: Monomials w.r.t which we will collect: ", monomList, FCDoControl->cl2Verbose]; If[Length[monomList] === 0, - (* The expression is free of terms in momomList*) + FCPrint[1,"Collect2: The input expression contains no relevant monomials, leaving.", FCDoControl->cl2Verbose]; unity = 1; - Return[factorOut nx] + Return[factorOut factor[nx]/denominator] ]; @@ -147,6 +219,7 @@ nx = nx/. holdForm[k_[ii_]] -> lk[k][ii]; + time=AbsoluteTime[]; If[ factoring === False, FCPrint[1,"Collect2: No factoring.", FCDoControl->cl2Verbose]; (* This can speed things up, if the expression contains very large sums free of @@ -164,6 +237,7 @@ holdForm[Plus[x]]; nx = nx /. Plus -> fr0 /. fr0 -> frx ]; + FCPrint[1,"Collect2: Factoring part done, timing: ", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; If[ expanding =!= False, time=AbsoluteTime[]; @@ -177,7 +251,8 @@ (* lin denotes the part free of monomList *) {lin,nx} = FCSplit[nx,monomList,Expanding->False]; FCPrint[1,"Collect2: Separation done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cl2Verbose]; - FCPrint[2,"Collect2: Part that contains the monomials: ", nx, FCDoControl->cl2Verbose]; + FCPrint[3,"Collect2: Part that contains the monomials: ", nx, FCDoControl->cl2Verbose]; + FCPrint[3,"Collect2: Linear part: ", lin, FCDoControl->cl2Verbose]; If[factoring =!= False && lin=!=0, time=AbsoluteTime[]; @@ -190,9 +265,9 @@ time=AbsoluteTime[]; FCPrint[1,"Collect2: Wrapping the momomials with special heads.", FCDoControl->cl2Verbose]; - nx = (Map[(SelectFree[#, monomList] mp2[SelectNotFree[#, monomList]]) &, + nx = (Map[(SelectFree[#, monomList] monomialHead[SelectNotFree[#, monomList]]) &, nx + null1 + null2] /. {null1 | null2 -> 0}) ; - tv = Cases2[nx,mp2]; + tv = Cases2[nx,monomialHead]; FCPrint[1,"Collect2: Wrapping done, timing: ", N[AbsoluteTime[] - time, 4] , FCDoControl->cl2Verbose]; FCPrint[3,"Collect2: nx: ", nx , FCDoControl->cl2Verbose]; @@ -211,11 +286,12 @@ FCPrint[1,"Collect2: Computing CoefficientArrays.", FCDoControl->cl2Verbose]; coeffArray = CoefficientArrays[nx,tv]; FCPrint[1,"Collect2: CoefficientArrays ready, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; + FCPrint[3,"Collect2: CoefficientArrays:", coeffArray, FCDoControl->cl2Verbose]; time=AbsoluteTime[]; FCPrint[1,"Collect2: Collecting the monomials.", FCDoControl->cl2Verbose]; - tvm = (FRH[# /.holdForm->Identity, IsolateNames->{optIsolateNames,tempIso}] /. mp2 -> cd /. cd -> OptionValue[Head])&/@tv; + tvm = (FRH[# /.holdForm->Identity, IsolateNames->{optIsolateNames,tempIso}] /. monomialHead -> cd /. cd -> firstHead)&/@tv; FCPrint[3,"Collect2: tvm: ", tvm, FCDoControl->cl2Verbose]; @@ -224,34 +300,63 @@ Abort[] ]; - new = Sum[Dot[coeffHead[coeffArray[[i]]] , Sequence @@ Table[tvm, {i - 1}]], {i, 2, Length[coeffArray]}]; + new = Sum[dotHold[coeffHead[coeffArray[[i]]] , Sequence @@ Table[tvm, {i - 1}]], {i, 2, Length[coeffArray]}]; + + FCPrint[1,"Collect2: Done collecting the monomials, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; + FCPrint[3,"Collect2: prelminiary new: ", new, FCDoControl->cl2Verbose]; + time=AbsoluteTime[]; + FCPrint[1,"Collect2: Obtaining the final result.", FCDoControl->cl2Verbose]; - coeffHead[li_SparseArray]:= - (tog[unity*#])&/@li /; optIsolateNames===False; + If[ optIsolateNames===False, - coeffHead[li_SparseArray]:= - Isolate[tog[unity*#]/. {unity:>1, lk[ka_][j_] :> holdForm[ka[j]]}, - IsolateNames -> optIsolateNames, IsolateFast-> optIsolateFast]&/@li /;optIsolateNames=!=False; + coeffHead[li_SparseArray]:= + tog[unity*#]&/@li, - FCPrint[1,"Collect2: Done collecting the monomials, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; + coeffHead[li_SparseArray]:= + Isolate[tog[unity*#]/. {unity:>1, lk[ka_][j_] :> holdForm[ka[j]]}, + IsolateNames -> optIsolateNames, IsolateFast-> optIsolateFast]&/@li; + ]; + + new = new/.dotHold-> Dot; + + FCPrint[1,"Collect2: The final result is ready, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; + FCPrint[3,"Collect2: new: ", new, FCDoControl->cl2Verbose]; If[ !FreeQ2[lin,monomList], Message[Collect2::failmsg,"Linear part contains monomials!"]; + Print[lin]; Abort[] ]; + time=AbsoluteTime[]; + + FCPrint[1,"Collect2: Releasing tempIso.", FCDoControl->cl2Verbose]; If[ optIsolateNames =!= False, lin = Isolate[ FRH[lin/.holdForm->Identity, IsolateNames->{tempIso,optIsolateNames}], IsolateNames->optIsolateNames, IsolateFast->optIsolateFast], lin = FRH[lin/.holdForm->Identity, IsolateNames->{tempIso,optIsolateNames}] ]; + FCPrint[1,"Collect2: Done releasing tempIso, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; - (*If[ factoring === False, - new = FRH[new,IsolateNames->{optIsolateNames,tempIso}] - ];*) - - re = ((new + lin) /. lk[ka_][j_] -> holdForm[ka[j]] /. frx->Plus); + If[ secondHead=!=Null, + time=AbsoluteTime[]; + FCPrint[1,"Collect2: Applying secondHead.", FCDoControl->cl2Verbose]; + lin = secondHead[lin,1] /. secondHead[0,_] -> 0; + new = secondHead/@(new + null1 + null2) /. secondHead[null1|null2]->0 /. secondHead[a_firstHead b_]:> secondHead[b,a]; + FCPrint[1,"Collect2: Done applying secondHead, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; + ]; time=AbsoluteTime[]; + FCPrint[1,"Collect2: Putting re togehter.", FCDoControl->cl2Verbose]; + re = ((new + lin) /. lk[ka_][j_] -> holdForm[ka[j]] /. frx->Plus); + FCPrint[1,"Collect2: Done putting re togehter, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; + + (*Just a small consistency check *) + If[ optIsolateNames =!= False, + If[ !FreeQ2[FRH[Cases[re,_HoldForm,Infinity]//Sort//DeleteDuplicates,IsolateNames->{optIsolateNames}], monomList], + Message[Collect2::failmsg,"Isolated prefactors contain monomials!"]; + Abort[] + ] + ]; FCPrint[1,"Collect2: Done releasing tempIso, timing:", N[AbsoluteTime[] - time, 4], FCDoControl->cl2Verbose]; @@ -262,7 +367,7 @@ unity=1; - re = factorOut*re; + re = (factorOut (re/denominator))/.monomRepRule; FCPrint[1,"Collect2: Leaving.", FCDoControl->cl2Verbose]; FCPrint[3,"Collect2: Leaving with", re, FCDoControl->cl2Verbose]; diff --git a/FeynCalc/Shared/DataType.m b/FeynCalc/Shared/DataType.m index ee05913b4..8cfb43da7 100644 --- a/FeynCalc/Shared/DataType.m +++ b/FeynCalc/Shared/DataType.m @@ -26,7 +26,10 @@ "PositiveNumber is a data type. E.g. DataType[Epsilon, PositiveNumber] = True (by default). "; FCTensor::usage = -"FCTensor is a data type. E.g. DataType[R, FCTensor] = True. "; +"FCTensor is a data type. E.g. DataType[R, FCTensor] = True."; + +FCVariable::usage = +"FCVariable is a data type. E.g. DataType[z, FCVariable] = True."; DataType::usage = "DataType[exp, type] = True defines the object exp to have datatype type. \ @@ -41,6 +44,8 @@ Begin["`DataType`Private`"] +set::usage=""; + DataType[_] := (Message[DataType::argrx, DataType, 1, "2 or more"]; Abort[]); @@ -63,56 +68,79 @@ updates $NonComm and NonCommFreeQ *) DataType /: - HoldPattern[Set[DataType[exp_, NonCommutative], True]] := - Block[{ndt, ndf, dt, ncq, nnn, nnt, set, downvalues, hp}, - If[!MemberQ[$NonComm, exp], - AppendTo[$NonComm, exp] + HoldPattern[Set[DataType[exp_, NonCommutative], (bool:True|False)]] := + Block[{ndt, ndf, dt, ncq, nnt, nnf, downvalues, hp, dvals, tmp}, + + If[ bool, + (* True *) + If[!MemberQ[$NonComm, exp], + AppendTo[$NonComm, exp] + ], + (* False *) + If[MemberQ[$NonComm, exp], + $NonComm = SelectFree[$NonComm, exp]; + ]; + ]; - ndt = (RuleDelayed @@ {HoldPattern @@ {dt[exp, NonCommutative]}, True}) /. dt -> DataType; - ndf = (RuleDelayed @@ {HoldPattern @@ {dt[exp, NonCommutative]}, False}) /. dt -> DataType; - If[FreeQ[DownValues[DataType], ndt], - DownValues[DataType] = Prepend[SelectFree[DownValues[DataType]/.{DataType->dt,HoldPattern->hp}, - ndf/.{DataType->dt,HoldPattern->hp}]/.{dt->DataType,hp->HoldPattern}, ndt] + + dvals = DownValues[DataType]/.{DataType->dt,HoldPattern->hp}; + ndt = (RuleDelayed @@ {hp @@ {dt[exp, NonCommutative]}, True}); + ndf = (RuleDelayed @@ {hp @@ {dt[exp, NonCommutative]}, False}); + + If[ bool, + (* True *) + If[ FreeQ[dvals, ndt], + If[ !FreeQ[dvals, ndf], + tmp = SelectFree[dvals, ndf], + tmp = dvals + ]; + DownValues[DataType] = (Flatten[{tmp, ndt}] /. hp->HoldPattern /. dt -> DataType); + + ], + + (* False *) + If[ FreeQ[dvals, ndf], + If[ !FreeQ[dvals, ndt], + tmp = SelectFree[dvals, ndt], + tmp = dvals + ]; + DownValues[DataType] = (Flatten[{tmp, ndf}] /. hp->HoldPattern /. dt -> DataType); + ] ]; - (* Update NonCommFreeQ *) - nnt = (RuleDelayed @@ {HoldPattern @@ {ncq[exp]}, False}) /. ncq -> NonCommFreeQ; - set[downvalues[NonCommFreeQ],Prepend[SelectFree[DownValues@@{NonCommFreeQ}, exp], - nnt]] /. {set :> Set, downvalues :> DownValues}; - (* Update NonCommQ *) - nnt = (RuleDelayed @@ {HoldPattern @@ {ncq[exp]}, True}) /. ncq -> NonCommQ; - set[downvalues[NonCommQ],Prepend[SelectFree[DownValues@@{NonCommQ}, exp], - nnt]] /. {set :> Set, downvalues :> DownValues}; - True - ]; + nnt = (RuleDelayed @@ {hp[ncq[exp]], True}) /. ncq -> NonCommFreeQ; + nnf = (RuleDelayed @@ {HoldPattern @@ {ncq[exp]}, False}) /. ncq -> NonCommQ; + + (* Careful, the downvalues of NonCommFreeQ and NonCommQ swell up a lot due to + the memoization of those function. So one should avoid modifying them unless + absolutely necessary. *) -DataType /: - HoldPattern[Set[DataType[exp_, NonCommutative], False]] := - Block[{ndt, ndf, dt, ncq, nnn, nnt, set, downvalues,hp}, - If[MemberQ[$NonComm, exp], - $NonComm = SelectFree[$NonComm, exp]; - ]; - ndt = (RuleDelayed @@ {HoldPattern @@{dt[exp, NonCommutative]}, True}) /. dt -> DataType; - ndf = (RuleDelayed @@ {HoldPattern @@{dt[exp, NonCommutative]}, False}) /. dt -> DataType; - If[FreeQ[DownValues[DataType], ndf], - DownValues[DataType] = Prepend[SelectFree[DownValues[DataType]/.{DataType->dt,HoldPattern->hp}, - ndt/.{DataType->dt,HoldPattern->hp}]/.{dt->DataType,hp->HoldPattern}, ndf] - ]; (* Update NonCommFreeQ *) - nnn = (RuleDelayed @@ {HoldPattern @@{ncq[exp]}, _}) /. ncq -> NonCommFreeQ; - If[!FreeQ[DownValues[NonCommFreeQ], nnn], - DownValues[NonCommFreeQ] = SelectFree[DownValues[NonCommFreeQ], nnn] + If[ !FreeQ[DownValues[NonCommFreeQ],exp], + dvals = DownValues[NonCommFreeQ]; + If[ bool, + (*True*) + set[downvalues[NonCommFreeQ],Prepend[SelectFree[dvals, exp], nnf]] /. {set :> Set, downvalues :> DownValues}, + + (*False*) + set[downvalues[NonCommFreeQ],Prepend[SelectFree[dvals, exp], nnt]] /. {set :> Set, downvalues :> DownValues} + ] ]; - nnt = (RuleDelayed @@ {HoldPattern @@ {ncq[exp]}, True}) /. ncq -> NonCommFreeQ; - set[downvalues[NonCommFreeQ],Prepend[SelectFree[DownValues@@{NonCommFreeQ}, exp], - nnt]] /. {set :> Set, downvalues :> DownValues}; + (* Update NonCommQ *) - nnt = (RuleDelayed @@ {HoldPattern @@ {ncq[exp]}, False}) /. ncq -> NonCommQ; - set[downvalues[NonCommQ],Prepend[SelectFree[DownValues@@{NonCommQ}, exp], - nnt]] /. {set :> Set, downvalues :> DownValues}; - False - ]; + If[ !FreeQ[DownValues[NonCommQ],exp], + dvals = DownValues[NonCommQ]; + If[ bool, + (*True*) + set[downvalues[NonCommQ],Prepend[SelectFree[dvals, exp], nnt]] /. {set :> Set, downvalues :> DownValues}, + + (*False*) + set[downvalues[NonCommQ],Prepend[SelectFree[dvals, exp], nnf]] /. {set :> Set, downvalues :> DownValues} + ] + ]; + bool + ]; (* Special rules for FCTensor *) (* Setting DataType[x,FCTensor]=True or DataType[x,FCTensor]=False diff --git a/FeynCalc/Shared/Explicit.m b/FeynCalc/Shared/Explicit.m index aae83b0e5..1ae7d228e 100644 --- a/FeynCalc/Shared/Explicit.m +++ b/FeynCalc/Shared/Explicit.m @@ -23,15 +23,18 @@ Begin["`Explicit`Private`"] Options[Explicit] = { - CouplingConstant -> SMP["g_s"], - Dimension -> D, - Gauge -> 1, - OPE -> False + CouplingConstant -> SMP["g_s"], + Dimension -> D, + Gauge -> 1, + OPE -> False }; -Explicit[y_, opts:OptionsPattern[]] := - Block[{dim, gh, gp, gvv, ghv, gv, qp, qgv, t2g, t2q, fis, pr, r = y}, - dim = OptionValue[Explicit,{opts},Dimension]; +Explicit[expr_, opts:OptionsPattern[]] := + Block[{gh, gp, gvv, ghv, gv, qp, qgv, t2g, t2q, fis, ex}, + + + ex = expr; + gv[x__] := ExpandScalarProduct[ GluonVertex[x, Explicit -> True, FilterRules[{opts}, Options[GluonVertex]]]]; gp[x__] := ExpandScalarProduct[GluonPropagator[x, Explicit -> True, @@ -50,7 +53,8 @@ FilterRules[{opts}, Options[Twist2QuarkOperator]]]; fis[x__] := FieldStrength[x, Explicit->True, FilterRules[{opts}, Options[FieldStrength]]]; - r = r /. { + + ex = ex /. { GluonVertex :> gv, GluonPropagator :> gp, GhostPropagator :> gh, @@ -59,13 +63,12 @@ QuarkGluonVertex :> qgv, Twist2GluonOperator :> t2g, Twist2QuarkOperator :> t2q, - FieldStrength :> fis + FieldStrength :> fis, + FCChargeConjugateTransposed[xx_, op:OptionsPattern[]] :> FCChargeConjugateTransposed[xx, Explicit->True, + Sequence@@FilterRules[{op}, Except[Explicit]]] }; - (* use ChangeDimension only if there have been changes *) - If[r =!= y, - r = ChangeDimension[r, dim] - ]; - r + + ex ]; FCPrint[1,"Explicit.m loaded"]; diff --git a/FeynCalc/Shared/FCCheckSyntax.m b/FeynCalc/Shared/FCCheckSyntax.m new file mode 100755 index 000000000..6fd55ea6d --- /dev/null +++ b/FeynCalc/Shared/FCCheckSyntax.m @@ -0,0 +1,193 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCCheckSyntax *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Checks if the expression contains dummy indices *) + +(* ------------------------------------------------------------------------ *) + + + +FCCheckSyntax::usage = +"FCCheckSyntax[exp] attempts to detect mistakes and inconsistencies \ +in the user input. The function returns the original expression but \ +will abort the evaluation if it thinks that the input is incorrect. \n +Notice that false positives are possible and it is not guaranteed \ +that the input which passes FCCheckSyntax is indeed fully correct. \n +FCCheckSyntax is also an option for several FeynCalc routines \ +If set to True, those functions will try to check the syntax of the input \ +expressions to detect possible inconsistencies. \ +However, on large expressions such checks may cost a lot of performance, \ +which is why this option is set to False by default."; + +FCCheckSyntax::failmsg = +"Error! FCCheckSyntax has found an inconsistency in your input expression \ +and must abort the evaluation. The problem reads: `1` `2`" + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCCheckSyntax`Private`"] + +indexHeads = {LorentzIndex, CartesianIndex, SUNIndex, SUNFIndex}; +nonCommHeads = {DiracGamma, PauliSigma, SUNT}; + +Options[FCCheckSyntax] = { + DotSimplify -> True, + FCI -> False +}; + + +getFreeIndices[ex_, head_]:= + Cases[ex, Blank[head], Infinity]//ReplaceAll[#, head[z_, ___] :> z] & // Tally // Cases[#, {z_, 1} :> z] & // Sort; + +getMoreThanTwoIndices[ex_, head_]:= + Cases[ex, Blank[head], Infinity]//ReplaceAll[#, head[z_, ___] :> z] & // Tally // Cases[#, {z_, n_}/;(n>2) :> z] &; + +getAllIndices[ex_, head_]:= + Cases[ex, Blank[head], Infinity] // DeleteDuplicates // Sort // ReplaceAll[#, head[z_, ___] :> z] & // DeleteDuplicates // Sort + +checkEinsteinSummation[expr0_, head_]:= + Block[{expr=expr0, ex,times,freeLiList,fullLiList,dummyLiList,null1,null2,listExpr}, + + If[ !FreeQ[expr, Power], + expr = expr /. Power[a_, b_Integer?Positive] /; !FreeQ[a, LorentzIndex] :> + Apply[times, Table[a, {b}]]; + ]; + + If[Head[expr]===Plus, + ex=First[expr]; + listExpr = List@@expr, + ex=expr; + listExpr = {expr} + ]; + + + + (* List of the free indices *) + freeLiList = getFreeIndices[ex,head]; + + (* List of all indices that appear in the expression *) + fullLiList = getAllIndices[ex,head]; + + (* List of all dummy Lorentz indices that appear in the expression *) + dummyLiList = Complement[fullLiList, freeLiList]; + + (* Check that there is only one dsHead per term and no nested dsHeads *) + + Scan[ + ( + + + Which[ + + freeLiList=!=getFreeIndices[#,head], + Message[FCCheckSyntax::failmsg, "Different number of free indices in ", ex]; + Abort[], + + getMoreThanTwoIndices[#,head]=!={}, + Message[FCCheckSyntax::failmsg, "More than two repeating indices in ", ToString[#,InputForm]]; + Abort[], + + True, + Null + ])&, listExpr]; + + ]; + +checkIndices[ex_,head_]:= + If[!FreeQ[ex,head], + checkEinsteinSummation[ex,head] + ]; + +nonComRulePrep[head_,dotHead_,powerHead_,timesHead_]:= + { + a_head b_head -> timesHead[a b], + a_head b_powerHead/; !FreeQ[b,head] -> timesHead[a b], + a_head (b: dotHead[_head,___]) -> timesHead[a b], + a_head (b: dotHead[___,_head]) -> timesHead[a b], + (a: dotHead[_head,___]) (b: dotHead[_head,___]) -> timesHead[a b], + (a: dotHead[_head,___]) (b: dotHead[___,_head]) -> timesHead[a b], + (a: dotHead[___,_head]) (b: dotHead[_head,___]) -> timesHead[a b], + (a: dotHead[___,_head]) (b: dotHead[___,_head]) -> timesHead[a b] + }; + +nonComCheck[ex_,head_,powerHead_,timesHead_]:= + If[ !FreeQ[ex,timesHead], + Message[FCCheckSyntax::failmsg, "Commutative products of "<> ToString[head] <> " in ", + SelectNotFree2[ex,timesHead]/.timesHead->Identity/.powerHead->Times]; + Abort[] + ]; + +FCCheckSyntax[expr_, OptionsPattern[]] := + Block[{fullLiList, freeLiList, ex, times, i, sel, sel2, tmp, timesGamma, timesSUNT, + timesSigma,dotHold}, + + + FCPrint[1, "FCCheckSyntax: Entering."]; + FCPrint[3, "FCCheckSyntax: Entering with: ", expr]; + + If[ !OptionValue[FCI], + ex = FCI[expr], + ex = expr + ]; + (* + If[ !FreeQ[expr,DOT] && OptionValue[DotExpand], + ex = DotExpand[ex] + ];*) + + If[ !FreeQ[expr,DOT] && OptionValue[DotSimplify], + ex = DotSimplify[ex] + ]; + + ex = Expand2[ex,indexHeads]; + + + + (* Check Einstein summation for the relevant indices *) + Scan[checkIndices[ex,#]&,indexHeads]; + + + + (* Syntax errors for noncommutative objects *) + If[!FreeQ2[ex,nonCommHeads], + + If[ !FreeQ[ex, Power], + ex = ex /. Power[a_, b_Integer?Positive] /; !FreeQ2[a, nonCommHeads] :> + Apply[times, Table[a, {b}]]; + ]; + + ex = ex /. DOT -> dotHold; + + ex = ex /. Dispatch[nonComRulePrep[DiracGamma,dotHold,times,timesGamma]]; + + ex = ex /. Dispatch[nonComRulePrep[PauliSigma,dotHold,times,timesSigma]]; + ex = ex /. Dispatch[nonComRulePrep[SUNT,dotHold,times,timesSUNT]]; + + nonComCheck[ex,DiracGamma,times,timesGamma]; + nonComCheck[ex,PauliSigma,times,timesSigma]; + + nonComCheck[ex,SUNT,times,timesSUNT]; + + + ]; + + + + expr + + ]; + +FCPrint[1,"FCCheckSyntax.m loaded."]; +End[] diff --git a/FeynCalc/Shared/FCCompareResults.m b/FeynCalc/Shared/FCCompareResults.m new file mode 100755 index 000000000..0c57dba2c --- /dev/null +++ b/FeynCalc/Shared/FCCompareResults.m @@ -0,0 +1,125 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCCompareResults *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Compare given results to the known values *) + +(* ------------------------------------------------------------------------ *) + +FCCompareResults::usage = +"FCCompareResults[{res1,res2,...},{res1Known,res2Known,...}] compares \ +the given list of expression {res1,res2,...} to the list of expressions \ +{res1Known,res2Known,...} that represenet the correct results. This is \ +handy for checking both intermediate and final results of calculations, \ +where you know what should come out at the end."; + +FCCompareResults::failmsg = +"Error! FCCompareResults has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`"; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCCompareResults`Private`"] + +Options[FCCompareResults] = { + Differences -> False, + ExpandScalarProduct -> True, + Factoring -> Factor, + FCI -> False, + Function -> { + Function[Print[Style[#1,"Text",Bold], " ", If[TrueQ[#4],Style[#2,"Text",Darker[Green],Bold],Style[#3,"Text",Red,Bold]]]], + Function[WriteString["stdout","\033[1m"<>#1<>"\033[0m "<> If[TrueQ[#4], + "\033[1m \033[32m"<>#2<>"\033[0m \033[0;39m","\033[1m \033[31m"<>#3<>"\033[0m \033[0;39m"]<>"\n"]] + }, + Interrupt -> {Hold[Abort[]], Automatic}, + Text -> {"Check of the results:", "The results agree.", "The results disagree."} +}; + +FCCompareResults[r1_, r2:Except[_?OptionQ], opts:OptionsPattern[]]:= + FCCompareResults[{r1}, {r2}, opts]/; Head[r1]=!=List && Head[r2]=!=List; + +FCCompareResults[obtainedResult_List, knownResult_List/;(knownResult==={} || !OptionQ[knownResult]), OptionsPattern[]]:= + Block[{ res1, res2, diff, factoring, match=False, text, function, interrupt, + interruptCommand, noFrontEnd, tmp, set}, + + noFrontEnd = TrueQ[$FrontEnd===Null]; + + factoring = OptionValue[Factoring]; + text = OptionValue[Text]; + {interruptCommand, interrupt} = OptionValue[Interrupt]; + + If[ TrueQ[interrupt===Automatic] && noFrontEnd, + interrupt=True, + + If[ TrueQ[interrupt], + interrupt=True, + interrupt=False + ] + ]; + + If[ OptionValue[Function]=!=False, + If[ noFrontEnd, + function = OptionValue[Function][[2]], + function = OptionValue[Function][[1]] + ] + ]; + + If[ Length[res1]=!=Length[res2], + Message[FCCompareResults::failmsg, "The list of the obtained and the list of the known results are of different lengths."]; + Abort[] + ]; + + If[ !MatchQ[text, {_String,_String,_String}], + Message[FCCompareResults::failmsg, "The supplied text messages are not strings."]; + Abort[] + ]; + + If[!OptionValue[FCI], + {res1,res2} = FCI[{obtainedResult, knownResult}], + {res1,res2} = {obtainedResult, knownResult} + ]; + + If[ OptionValue[ExpandScalarProduct], + {res1,res2} = ExpandScalarProduct[#,FCI->True]&/@{res1, res2} + ]; + + diff = res1 - res2; + + If[ factoring=!=False, + diff = factoring/@diff + ]; + + If[ TrueQ[MatchQ[diff, {0..}] || MatchQ[diff, {{0}..}] || diff==={} || Union[Flatten[diff]]==={0} ], + match = True + ]; + + If[ OptionValue[Function]=!=False, + function[text[[1]],text[[2]],text[[3]],match]; + ]; + + If[ interrupt && match=!=True, + ReleaseHold[interruptCommand] + ]; + + If[ TrueQ[OptionValue[Differences]], + match = diff + ]; + + match + + ]; + +FCPrint[1,"FCCompareResults.m loaded."]; +End[] diff --git a/FeynCalc/Shared/Factor.m b/FeynCalc/Shared/Factor.m index 5ab29c642..ce27a2a38 100755 --- a/FeynCalc/Shared/Factor.m +++ b/FeynCalc/Shared/Factor.m @@ -37,9 +37,9 @@ There are four possible settings of the option Method (0,1,2,3). Begin["`Factor`Private`"] Options[Factor2] = { - FactorFull -> False, - Method -> 3 - }; + FactorFull -> False, + Method -> 3 +}; Factor1[x_] := Block[{factor1t1,factor1t2,factor1t3,mt,mi,m1,mp1,nx=x,iIii}, diff --git a/FeynCalc/Shared/FeynCalcExternal.m b/FeynCalc/Shared/FeynCalcExternal.m index b8b3df9e0..3a1672b9f 100755 --- a/FeynCalc/Shared/FeynCalcExternal.m +++ b/FeynCalc/Shared/FeynCalcExternal.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Changes certain objects ("Symbols") from the FeynCalc @@ -37,6 +37,8 @@ Begin["`FeynCalcExternal`Private`"] FCE = FeynCalcExternal; +dimS::usage=""; +fermtmp::usage=""; Options[FeynCalcExternal] = { FinalSubstitutions -> {} @@ -49,7 +51,7 @@ FeynCalcExternal[x_,opts___Rule] := - Block[{ru, ti, r, vv, rv, uru}, + Block[{ru, ti, r, vv, rv, uru, revru}, sundeltanoi[y__] := SD@@({y} /. SUNIndex -> Identity); sunfdeltanoi[y__] := @@ -58,12 +60,16 @@ uru = FinalSubstitutions /. {opts} /. Options[FeynCalcExternal]; ru = { + DiracIndexDelta :> diracdelta, + DiracChain :> diracchain, + PauliSigma :> sigmaback, DiracGamma :> diracback, DiracSigma :> dirsig, Eps :> eps, FeynAmpDenominator :> feynampback, - MetricTensor :> metricmul, Pair :> pairback, + CartesianPair :> cpairback, + TemporalPair :> tpairback, SUND :> sundback, SUNDelta :> sundeltanoi, SUNFDelta :> sunfdeltanoi, @@ -76,13 +82,16 @@ Power2 :> Power} /. LorentzIndex -> iDent /. SUNIndex -> iDent /. SUNFIndex -> iDent; ru = Join[ru, Flatten[{uru}]]; vv = Cases2[x, { + DiracChain, + DiracIndexDelta, + CartesianPair, DiracGamma, DiracSigma, Eps, FeynAmpDenominator, - MetricTensor, Pair, PropagatorDenominator, + PauliSigma, SUND, SUNDelta, SUNFDelta, @@ -92,13 +101,27 @@ SUNDeltaContract, SUNFDeltaContract, ScalarProduct, + TemporalPair, Power2 } /. sequence -> Sequence]; - rv = Map[(# -> ((MomentumCombine[#])/.ru ) )&, vv]//Dispatch; - x /. rv + revru = Map[Reverse, SelectFree[ru,Power]]; + + x /. rv /. Dispatch[revru] ]; +diracdelta[i_,j_]:= + DIDelta[i,j] /. (DiracIndex|ExplicitDiracIndex) -> iDent; + +diracchain[a_,b_]:= + DCHN[FCE[a],b] /. (DiracIndex|ExplicitDiracIndex) -> iDent; + +diracchain[a_,b_,c_]:= + ( + fermtmp=FCE[{a,b,c}]; + (DCHN@@fermtmp) /. (DiracIndex|ExplicitDiracIndex) -> iDent + ) + dirsig[a__] := DiracSigma[DOT[a]]; @@ -111,16 +134,12 @@ SUNFback[a_, b_, c_] := SUNF[a, b, c] /; FreeQ[{a,b,c},SUNIndex]; -metricmul[a_ b_,dim__] := - MetricTensor[a,b,dim]; -metricmul[a_, b_,dim___] := - MetricTensor[a,b,dim]; - scalarmul[a_ b_,dim__] := ScalarProduct[a,b,dim]; scalarmul[a_, b_,dim___] := ScalarProduct[a,b,dim]; + pairback[ExplicitLorentzIndex[a_?NumberQ], ExplicitLorentzIndex[b_?NumberQ]] := MT[a,b]; pairback[ExplicitLorentzIndex[a_?NumberQ], LorentzIndex[b_]] := @@ -132,7 +151,7 @@ pairback[LorentzIndex[a_,D-4], LorentzIndex[b_,D-4]] := MTE[a,b]; pairback[LorentzIndex[a_,d_], LorentzIndex[b_,d_]] := - MetricTensor[a,b,Dimension->d] /;(d=!=D && d=!= D-4); + Pair[LorentzIndex[a,d], LorentzIndex[b,d]] /;(d=!=D && d=!= D-4); pairback[ExplicitLorentzIndex[a_?NumberQ], Momentum[b_]] := @@ -144,7 +163,7 @@ pairback[LorentzIndex[a_, D-4], Momentum[b_, D-4]] := FVE[b,a]; pairback[LorentzIndex[a_,d_], Momentum[b_,d_]] := - FourVector[b,a,Dimension->d] /;(d=!=D && d=!= D-4); + Pair[LorentzIndex[a,d], Momentum[b,d]] /;(d=!=D && d=!= D-4); pairback[Momentum[OPEDelta], Momentum[b_]] := SO[b]; @@ -168,21 +187,65 @@ pairback[Momentum[a_, d_], Momentum[b_, d_]] := ScalarProduct[a, b, Dimension -> d]/;(d=!=D && d=!= D-4); +cpairback[CartesianIndex[a_], CartesianMomentum[b_]] := + CV[b,a]; +cpairback[CartesianIndex[a_, D-1], CartesianMomentum[b_, D-1]] := + CVD[b,a]; +cpairback[CartesianIndex[a_, D-4], CartesianMomentum[b_, D-4]] := + CVE[b,a]; + +cpairback[CartesianIndex[a_], CartesianIndex[b_]] := + KD[a,b]; +cpairback[CartesianIndex[a_,D-1], CartesianIndex[b_,D-1]] := + KDD[a,b]; +cpairback[CartesianIndex[a_,D-4], CartesianIndex[b_,D-4]] := + KDE[a,b]; + +cpairback[CartesianMomentum[a_], CartesianMomentum[b_]] := + CSP[a, b]; +cpairback[CartesianMomentum[a_, D-1], CartesianMomentum[b_, D-1]] := + CSPD[a, b]; +cpairback[CartesianMomentum[a_, D-4], CartesianMomentum[b_, D-4]] := + CSPE[a, b]; + +tpairback[ExplicitLorentzIndex[0],TemporalMomentum[a_]]:= + TC[a]; + +diracback[ExplicitLorentzIndex[0]]:= + TGA[]; + diracback[LorentzIndex[a_]] := GA[a]; diracback[LorentzIndex[a_,D],D] := GAD[a]; diracback[LorentzIndex[a_,D-4],D-4] := GAE[a]; -diracback[lm_[a_,n_/;(n=!=D && n=!=D-4)],en___] := + +diracback[CartesianIndex[a_]] := + CGA[a]; +diracback[CartesianIndex[a_, D-1], D] := + CGAD[a]; +diracback[CartesianIndex[a_, D-4], D-4] := + CGAE[a]; + + +diracback[lm_[a_,n_/;(n=!=D && n=!=D-4 && n=!=D-1)],en___] := DiracGamma[lm[a,n],en]; diracback[Momentum[a_]] := GS[a]; -diracback[Momentum[a_, n_Symbol], n_Symbol] := +diracback[Momentum[a_, D], D] := GSD[a]; -diracback[Momentum[a_, n_Symbol-4], n_Symbol-4] := +diracback[Momentum[a_, D-4], D-4] := GSE[a]; + +diracback[CartesianMomentum[a_]] := + CGS[a]; +diracback[CartesianMomentum[a_, D-1], D] := + CGSD[a]; +diracback[CartesianMomentum[a_, D-4], D-4] := + CGSE[a]; + diracback[5] := GA[5]; diracback[6] := @@ -193,6 +256,35 @@ GA[x]; diracback[x_?NumberQ] := GA[x]; + +sigmaback[LorentzIndex[a_]] := + SI[a]; +sigmaback[LorentzIndex[a_,D],D-1] := + SID[a]; +sigmaback[LorentzIndex[a_,D-4],D-4] := + SIE[a]; + +sigmaback[CartesianIndex[a_]] := + CSI[a]; +sigmaback[CartesianIndex[a_, D-1], D-1] := + CSID[a]; +sigmaback[CartesianIndex[a_, D-4], D-4] := + CSIE[a]; + +sigmaback[Momentum[a_]] := + SIS[a]; +sigmaback[Momentum[a_, D], D-1] := + SISD[a]; +sigmaback[Momentum[a_, D-4], D-4] := + SISE[a]; + +sigmaback[CartesianMomentum[a_]] := + CSIS[a]; +sigmaback[CartesianMomentum[a_, D-1], D-1] := + CSISD[a]; +sigmaback[CartesianMomentum[a_, D-4], D-4] := + CSISE[a]; + suntback[(SUNIndex|ExplicitSUNIndex)[a_]] := SUNT[a]; suntback[a__Symbol] := @@ -207,88 +299,149 @@ propd[a_, b_/;b=!=0] := {a/.Momentum->iDent, b}; -feynampback[a__] := +cpropd[ex1_, ex2_, m2_, {n_, etasign_}] := + {{ex1 /. CartesianMomentum -> iDent, ex2 //. { + CartesianPair[CartesianMomentum[x_, ___], CartesianMomentum[y_, ___]] :> + DOT[x, y], (CSPD | CSP | CSPE)[x_, y_] :> DOT[x, y]}}, {m2, etasign}, n}; + +spropd[ex1_, ex2_, m2_, {n_, etasign_}] := + {{ex1 /. Momentum -> iDent, ex2 //. { + Pair[Momentum[x_, ___], Momentum[y_, ___]] :> + DOT[x, y], (SPD | SP | SPE)[x_, y_] :> DOT[x, y]}}, {-m2, etasign}, n}; + +feynampback[a__]/; !FreeQ[{a},GenericPropagatorDenominator] && !MatchQ[{a},{__GenericPropagatorDenominator}] := + feynampback@@(SelectNotFree[{a}, GenericPropagatorDenominator]) feynampback@@(SelectFree[{a}, GenericPropagatorDenominator]); + + +feynampback[a__]/; !MatchQ[Union[Head/@{a}],{_}] := + feynampback@@(SelectNotFree[{a}, GenericPropagatorDenominator]) * + feynampback@@(SelectNotFree[{a}, CartesianPropagatorDenominator]) * + feynampback@@(SelectNotFree[{a}, PropagatorDenominator])* + feynampback@@(SelectNotFree[{a}, StandardPropagatorDenominator])* + feynampback@@(SelectFree[{a}, {GenericPropagatorDenominator,CartesianPropagatorDenominator,PropagatorDenominator,StandardPropagatorDenominator}]); + +feynampback[]:= + 1; + +feynampback[a__PropagatorDenominator] := Switch [ - Union[Cases[{a}, Momentum[_, dim_: 4] :> dim, Infinity]], + dimS=Union[Cases[{a}, Momentum[_, dim_: 4] :> dim, Infinity]]; + dimS, {D}, FAD @@ ({a} /. PropagatorDenominator -> propd), + {4}, FAD[Sequence @@ ({a} /. PropagatorDenominator -> propd),Dimension->4], + (* special case for PD[0,_] *) + ({} && !FreeQ[{a},PD[0,_]]), + FAD @@ ({a} /. PropagatorDenominator -> propd), + + {_}, + FAD[Sequence @@ ({a} /. PropagatorDenominator -> propd),Dimension->First[dimS]], + + _, + Message[FCE::feynamp,ToString[{a},InputForm]]; + Abort[] + ]; + +feynampback[a__CartesianPropagatorDenominator] := + Switch [ + dimS=FCGetDimensions[{a},FCI->True]; + dimS, + {D-1} | {}, + CFAD @@ ({a} /. CartesianPropagatorDenominator -> cpropd), + + {3}, + CFAD[Sequence @@ ({a} /. CartesianPropagatorDenominator -> cpropd),Dimension->3], + + {_}, + CFAD[Sequence @@ ({a} /. CartesianPropagatorDenominator -> cpropd),Dimension->First[dimS]], + _, Message[FCE::feynamp,ToString[{a},InputForm]]; - FeynAmpDenominator[a] + Abort[] ]; +feynampback[a__StandardPropagatorDenominator] := + Switch [ + dimS=FCGetDimensions[{a},FCI->True]; + dimS, + {D} | {}, + SFAD @@ ({a} /. StandardPropagatorDenominator -> spropd), + + {4}, + SFAD[Sequence @@ ({a} /. StandardPropagatorDenominator -> spropd),Dimension->4], + + {_}, + SFAD[Sequence @@ ({a} /. StandardPropagatorDenominator -> spropd),Dimension->First[dimS]], + + _, + Message[FCE::feynamp,ToString[{a},InputForm]]; + Abort[] + ]; + +feynampback[a__GenericPropagatorDenominator] := + GFAD[Sequence@@({a}/. GenericPropagatorDenominator[ex_,{n_,s_}]:> {{FCE[ex],s},n} )] + +eps[a_, b_, c_, d_] := + Signature[{a,b,c,d}] eps@@Sort[{a,b,c,d}]/; !OrderedQ[{a,b,c,d}]; +eps[Momentum[a_],Momentum[b_],Momentum[c_],Momentum[d_]]:= + LC[][a,b,c,d]; +eps[(LorentzIndex|ExplicitLorentzIndex)[a_],Momentum[b_],Momentum[c_],Momentum[d_]]:= + LC[a][b,c,d]; +eps[(LorentzIndex|ExplicitLorentzIndex)[a_],(LorentzIndex|ExplicitLorentzIndex)[b_],Momentum[c_],Momentum[d_]]:= + LC[a,b][c,d]; -eps[a_, b_, c_, d_, opts:OptionsPattern[Eps]] := - Signature[{a,b,c,d}] eps@@ Join[Sort[{a,b,c,d}],{opts}] /; !OrderedQ[{a,b,c,d}]; +eps[(LorentzIndex|ExplicitLorentzIndex)[a_],(LorentzIndex|ExplicitLorentzIndex)[b_],(LorentzIndex|ExplicitLorentzIndex)[c_],Momentum[d_]]:= + LC[a,b,c][d]; -eps[Momentum[a_],Momentum[b_],Momentum[c_],Momentum[d_], -opt:OptionsPattern[Eps]]:= - LC[][a,b,c,d]/; OptionValue[Eps,{opt},Dimension]===4; +eps[(LorentzIndex|ExplicitLorentzIndex)[a_],(LorentzIndex|ExplicitLorentzIndex)[b_],(LorentzIndex|ExplicitLorentzIndex)[c_],(LorentzIndex|ExplicitLorentzIndex)[d_]]:= + LC[a,b,c,d]; -eps[(LorentzIndex|ExplicitLorentzIndex)[a_],Momentum[b_],Momentum[c_],Momentum[d_], -opt:OptionsPattern[Eps]]:= - LC[a][b,c,d]/; OptionValue[Eps,{opt},Dimension]===4; +eps[Momentum[a_,D],Momentum[b_,D],Momentum[c_,D],Momentum[d_,D]]:= + LCD[][a,b,c,d]; -eps[(LorentzIndex|ExplicitLorentzIndex)[a_],(LorentzIndex|ExplicitLorentzIndex)[b_],Momentum[c_],Momentum[d_], -opt:OptionsPattern[Eps]]:= - LC[a,b][c,d]/; OptionValue[Eps,{opt},Dimension]===4; +eps[LorentzIndex[a_,D],Momentum[b_,D], Momentum[c_,D],Momentum[d_,D]]:= + LCD[a][b,c,d]; -eps[(LorentzIndex|ExplicitLorentzIndex)[a_],(LorentzIndex|ExplicitLorentzIndex)[b_],(LorentzIndex|ExplicitLorentzIndex)[c_],Momentum[d_], -opt:OptionsPattern[Eps]]:= - LC[a,b,c][d]/; OptionValue[Eps,{opt},Dimension]===4; +eps[LorentzIndex[a_,D],LorentzIndex[b_,D], Momentum[c_,D],Momentum[d_,D]]:= + LCD[a,b][c,d]; -eps[(LorentzIndex|ExplicitLorentzIndex)[a_],(LorentzIndex|ExplicitLorentzIndex)[b_],(LorentzIndex|ExplicitLorentzIndex)[c_],(LorentzIndex|ExplicitLorentzIndex)[d_], -opt:OptionsPattern[Eps]]:= - LC[a,b,c,d]/; OptionValue[Eps,{opt},Dimension]===4; +eps[LorentzIndex[a_,D], LorentzIndex[b_,D], LorentzIndex[c_,D], Momentum[d_,D]]:= + LCD[a,b,c][d]; -eps[Momentum[a_,D],Momentum[b_,D],Momentum[c_,D],Momentum[d_,D], -opt:OptionsPattern[Eps]]:= - LCD[][a,b,c,d]/; OptionValue[Eps,{opt},Dimension]===D; +eps[LorentzIndex[a_,D],LorentzIndex[b_,D], LorentzIndex[c_,D],LorentzIndex[d_,D]]:= + LCD[a,b,c,d]; -eps[LorentzIndex[a_,D],Momentum[b_,D], Momentum[c_,D],Momentum[d_,D], -opt:OptionsPattern[Eps]]:= - LCD[a][b,c,d]/; OptionValue[Eps,{opt},Dimension]===D; +eps[(h1:Momentum|LorentzIndex)[a_,dd_], (h2:Momentum|LorentzIndex)[b_,dd_], (h3:Momentum|LorentzIndex)[c_,dd_], (h4:Momentum|LorentzIndex)[d_,dd_]]:= + Eps[h1[a,dd], h2[b,dd], h3[c,dd], h4[d,dd]]/;dd=!=D; -eps[LorentzIndex[a_,D],LorentzIndex[b_,D], Momentum[c_,D],Momentum[d_,D], -opt:OptionsPattern[Eps]]:= - LCD[a,b][c,d]/; OptionValue[Eps,{opt},Dimension]===D; +eps[CartesianMomentum[a_],CartesianMomentum[b_],CartesianMomentum[c_]]:= + CLC[][a,b,c]; -eps[LorentzIndex[a_,D], LorentzIndex[b_,D], LorentzIndex[c_,D], Momentum[d_,D], -opt:OptionsPattern[Eps]]:= - LCD[a,b,c][d]/; OptionValue[Eps,{opt},Dimension]===D; +eps[CartesianIndex[a_], CartesianMomentum[b_], CartesianMomentum[c_]]:= + CLC[a][b,c]; -eps[LorentzIndex[a_,D],LorentzIndex[b_,D], LorentzIndex[c_,D],LorentzIndex[d_,D], -opt:OptionsPattern[Eps]]:= - LCD[a,b,c,d]/; OptionValue[Eps,{opt},Dimension]===D; +eps[CartesianIndex[a_], CartesianIndex[b_], CartesianMomentum[c_]]:= + CLC[a,b][c]; -eps[Momentum[a_,dd_],Momentum[b_,dd_],Momentum[c_,dd_],Momentum[d_,dd_], -opt:OptionsPattern[Eps]]:= - LeviCivita[Dimension->dd][a,b,c,d, - Dimension->dd]/;dd=!=D && OptionValue[Eps,{opt},Dimension]===dd; +eps[CartesianIndex[a_], CartesianIndex[b_], CartesianIndex[c_]]:= + CLC[a,b,c]; -eps[LorentzIndex[a_,dd_],Momentum[b_,dd_], Momentum[c_,dd_],Momentum[d_,dd_], -opt:OptionsPattern[Eps]]:= - LeviCivita[a,Dimension->dd][b,c,d, - Dimension->dd]/;dd=!=D && OptionValue[Eps,{opt},Dimension]===dd; +eps[CartesianMomentum[a_, D-1],CartesianMomentum[b_, D-1],CartesianMomentum[c_, D-1]]:= + CLCD[][a,b,c]; -eps[LorentzIndex[a_, dd_],LorentzIndex[b_, dd_], Momentum[c_,dd_],Momentum[d_,dd_], -opt:OptionsPattern[Eps]]:= - LeviCivita[a,b,Dimension->dd][c, - d,Dimension->dd]/;dd=!=D && OptionValue[Eps,{opt},Dimension]===dd; +eps[CartesianIndex[a_, D-1], CartesianMomentum[b_, D-1], CartesianMomentum[c_, D-1]]:= + CLCD[a][b,c]; -eps[LorentzIndex[a_,dd_], LorentzIndex[b_,dd_], LorentzIndex[c_,dd_], Momentum[d_,dd_], -opt:OptionsPattern[Eps]]:= - LeviCivita[a,b,c,Dimension->dd][d, - Dimension->dd]/;dd=!=D && OptionValue[Eps,{opt},Dimension]===dd; +eps[CartesianIndex[a_, D-1], CartesianIndex[b_, D-1], CartesianMomentum[c_, D-1]]:= + CLCD[a,b][c]; -eps[LorentzIndex[a_,dd_],LorentzIndex[b_,dd_], LorentzIndex[c_,dd_],LorentzIndex[d_,dd_], -opt:OptionsPattern[Eps]]:= - LeviCivita[a,b,c,d,Dimension->dd]/;dd=!=D && OptionValue[Eps,{opt},Dimension]===dd; +eps[CartesianIndex[a_, D-1], CartesianIndex[b_, D-1], CartesianIndex[c_, D-1]]:= + CLCD[a,b,c]; FCPrint[1,"FeynCalcExternal.m loaded"]; End[] diff --git a/FeynCalc/Shared/FeynCalcForm.m b/FeynCalc/Shared/FeynCalcForm.m index 24a579540..955acba90 100644 --- a/FeynCalc/Shared/FeynCalcForm.m +++ b/FeynCalc/Shared/FeynCalcForm.m @@ -9,10 +9,10 @@ (* ------------------------------------------------------------------------ *) FCF::usage= -"FCF is a short form for FeynCalcForm."; +"FCF[exp] is a short form for FeynCalcForm[exp]."; FeynCalcForm::usage= -"FeynCalcForm[expr] changes the printed output to an easy to read \ +"FeynCalcForm[exp] changes the printed output to an easy to read \ form. Whether the result of FeynCalcForm[expr] is displayed \ or not, depends on the setting of $PrePrint. \ $PrePrint = FeynCalcForm forces displaying everything \ @@ -26,6 +26,9 @@ Begin["`FeynCalcForm`Private`"] +fcdot2::usage=""; +hold::usage=""; + FCF = FeynCalcForm; bra = "("; @@ -121,7 +124,7 @@ Format[fcdot2[a_,b__]] := Infix[fcdot2[a,b], " "]; (* ??? *) -fcdot2[x-y,x-rd]; +(*fcdot2[x-y,x-rd];*) Format[fcdot2[a_]] := a; diF[x_-4]:= @@ -157,7 +160,7 @@ "tr"[x]; fdprop[a__] := - 1 / denfa[dudu[a]]; + 1 / denfa[hold[a]]; compind[a_] := If[Head[a] === Symbol, StringJoin[ToString[a],"*"], a "*"]; @@ -191,15 +194,13 @@ Subscript[SequenceForm["(", a, ")"], " + "]; feynCalcForm[x_,opt___Rule]:= - Block[{xxxx = Evaluate[x], subs}, + Block[{xxxx = Evaluate[x], subs, fcdot, diracsldid}, subs = FinalSubstitutions /. {opt} /. Options[FeynCalcForm]; xxxx = xxxx /. subs; xxxx = xxxx/.(n_Real Second)->timefix[n]; xxxx = (xxxx/. DOT:>fcdot /. SUNN :> "N"/. SUNTrace :> "tr" /. LeviCivita[lv__] :> epsd[lv] /. Eps[vl__] :> epsd[vl] /. MetricTensor[v_, w_, OptionsPattern[]] :> "g"[v, w] /. - (* FourVector[Subscript[p_,s_], mu_] :> - (SequenceForm@@Flatten[ {sumst[p[s]],"[",mu,"]"}])/.*) ScalarProduct[ v_,v_ ] :> v^2 /. ScalarProduct[v_ w_] :> (SequenceForm@@Flatten[ {v//sumst ,{"."},w//sumst} ]) /. (* PolarizationVector[ka_, mu_, ___] :> "ep"[ka, mu] /. *) @@ -242,8 +243,6 @@ DiracGamma[Momentum[v_,di_],di_] :> DiracSlash[v, Dimension -> 4] } /. - DiracGammaT[aa_,___]:> - "gat"[aa] /. { DiracGamma[5] :> "ga[5]", DiracGamma[6] :> "ga[6]", @@ -267,8 +266,7 @@ If[(Dimension /. Options[DiracSlash]) =!= 4, DiracSlash[v__]:> diracsldid[(Dimension /. Options[DiracSlash])][v]/. - diracsldid :> - diracsldi, + diracsldid :> diracsldi, {} ]/. DiracSlash[aa_] :> @@ -364,10 +362,6 @@ feynden[v]/. PropagatorDenominator[v__] :> fdprop[v]/. - Lower[v_,___] :> - v /. - Upper[v_,___] :> - v /. Momentum[v__] :> didm[v] /. LorentzIndex[v__] :> diff --git a/FeynCalc/Shared/FeynCalcInternal.m b/FeynCalc/Shared/FeynCalcInternal.m index 76cc14f81..5412e636f 100755 --- a/FeynCalc/Shared/FeynCalcInternal.m +++ b/FeynCalc/Shared/FeynCalcInternal.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Changes certain objects ("Symbols") into the FeynCalc @@ -31,12 +31,25 @@ Begin["`FeynCalcInternal`Private`"] +sfadim::usage=""; +cfadim::usage=""; fadim::usage=""; repeated::usage=""; +fchntmp::usage=""; +cfadEtaSign::usage=""; +gfadEtaSign::usage=""; +sfadEtaSign::usage=""; +head::usage=""; + +tmp1::usage=""; +tmp2::usage=""; +holdDOT::usage=""; FCI = FeynCalcInternal; -Options[FeynCalcInternal] = {FinalSubstitutions -> {}}; +Options[FeynCalcInternal] = { + FinalSubstitutions -> {} +}; SetAttributes[FeynCalcInternal, HoldFirst]; @@ -77,6 +90,7 @@ MetricTensor :> metricT, DiracMatrix :> diracM, DiracSlash :> diracS, + DIDelta :> didelta, FourVector :> fourV, SD :> sdeltacont, SDF :> sfdeltacont, @@ -87,10 +101,14 @@ SUNFDeltaContract :> sfdeltacontr, SUNT :> sunTint, SUNTF :> sunTFint, + SFAD :> sfadint, FAD :> fadint, + GFAD :> gfadint, + CFAD :> cfadint, FVD :> fvd, FVE :> fve, FV :> fv, + DCHN :> fchn, LeviCivita :> levicivita, LC :> lc, LCD :> lcd, @@ -107,8 +125,51 @@ SPD :> spd, SPE :> spe, SO :> so, - SOD :> sod}, - {PropagatorDenominator :> propagatorD}, + SOD :> sod, + + TC :> tc, + CV :> cv, + CVD :> cvd, + CVE :> cve, + + KD :> kd, + KDD :> kdd, + KDE :> kde, + + CSP :> csp, + CSPD :> cspd, + CSPE :> cspe, + + CLC :> clc, + CLCD :> clcd, + + TGA :> tga, + CGA :> cga, + CGAD :> cgad, + CGAE :> cgae, + + CGS :> cgs, + CGSD :> cgsd, + CGSE :> cgse, + + SI :> si, + SID :> sid, + SIE :> sie, + + SIS :> sis, + SISD :> sisd, + SISE :> sise, + + CSI :> csi, + CSID :> csid, + CSIE :> csie, + + CSIS :> csis, + CSISD :> csisd, + CSISE :> csise + + + }, {ScalarProduct :> scalarP}, {Dot -> DOT}, {ChiralityProjector[1] :> DiracGamma[6]}, @@ -124,6 +185,8 @@ If[ru =!={}, ReplaceRepeated[x//.{ LC[a___][b___] :> lcl[{a},{b}], LCD[a___][b___] :> lcdl[{a},{b}], + CLC[a___][b___] :> clcl[{a},{b}], + CLCD[a___][b___] :> clcdl[{a},{b}], LeviCivita[a___][b___] :> levicivital[{a},{b}]}, Dispatch[ru], MaxIterations -> 20] /. {mt :> MT, fv :> FV} /. Dispatch[revru], x @@ -149,6 +212,9 @@ metricT[x_, x_,op_:{}] := (Dimension/.op/.Options[MetricTensor]); +didelta[i_,j_]:= + DiracIndexDelta[DiracIndex[i],DiracIndex[j]]; + Options[diracM] = {Dimension -> 4, FCI -> True}; diracM[n_?NumberQ y:Except[_?OptionQ], opts:OptionsPattern[]] := @@ -219,17 +285,37 @@ Pair[LorentzIndex[y,OptionValue[Dimension]], Momentum[x,OptionValue[Dimension]]]/; FreeQ[x, Plus]; -propagatorD[x_] := - propagatorD[x, 0] /; FreeQ2[x, {Pattern, Pair, ScalarProduct}]; +dirIndex[a_Spinor]:= + a; + +dirIndex[a_]/;Head[a]=!=Spinor:= + DiracIndex[a/.DiracIndex->Identity]; + +fchn[a: (_Spinor | _SpinorUBar | _SpinorVBar),b_]:= + ( + fchntmp=FCI[{a,b}]; + DiracChain[fchntmp[[1]],dirIndex[fchntmp[[2]]]] + )/; !MemberQ[{Spinor,SpinorU,SpinorV,SpinorUBar,SpinorVBar},Head[b]]; + -propagatorD[x_, y_] := (propagatorD[x, y] = - PropagatorDenominator[MomentumExpand[ Momentum[x,D] ],y]) /;FreeQ2[x,{Momentum, Pattern,HoldForm}]; +fchn[a_,b : (_Spinor | _SpinorU | _SpinorV)]:= + ( + fchntmp=FCI[{a,b}]; + DiracChain[dirIndex[fchntmp[[1]]],fchntmp[[2]]] + )/; !MemberQ[{Spinor,SpinorU,SpinorV,SpinorUBar,SpinorVBar},Head[a]]; -propagatorD[x_, y_] := (propagatorD[x, y] = - PropagatorDenominator[x//MomentumExpand, y]) /; (FreeQ[{x,y}, Pattern] ) && (MomentumExpand[x] =!= x); +fchn[a : (_Spinor | _SpinorUBar | _SpinorVBar), b : (_Spinor | _SpinorU | _SpinorV)]:= + ( + fchntmp=FCI[{a,b}]; + DiracChain[fchntmp[[1]],fchntmp[[2]]] + ); -propagatorD[x_, y_] := - PropagatorDenominator[x, y] /; (MomentumExpand[x] === x); + +fchn[a_,b_,c_]:= + ( + fchntmp=FCI[{a,b,c}]; + DiracChain[fchntmp[[1]],dirIndex[fchntmp[[2]]],dirIndex[fchntmp[[3]]]] + ); sunTint[x__] := sunT[x] /. sunT -> SUNT; @@ -274,13 +360,67 @@ Pair[x, y] ]; +cfadint[a___, b_, opts:OptionsPattern[]] := + ( + cfadint[Sequence@@(head [a,b] //. head[x___, y_, z___]/; Head[y]=!=List :> head[x,{y,0},z]),opts] + )/;!MatchQ[{a,b},{__List}] && !OptionQ[b]; + +cfadint[a___List, b_List/; !OptionQ[b], opts:OptionsPattern[]] := + ( + cfadim = OptionValue[CFAD,{opts},Dimension]; + cfadEtaSign = OptionValue[CFAD,{opts},EtaSign]; + cfadint2 @@ Map[#&, {a,b}] + ); + +gfadint[a___, b_, opts:OptionsPattern[]] := + ( + gfadint[Sequence@@(head [a,b] //. head[x___, y_, z___]/; Head[y]=!=List :> head[x,{{y,1},1},z]),opts] + )/;!MatchQ[{a,b},{__List}] && !OptionQ[b]; + +gfadint[a___List, b_List/; !OptionQ[b], opts:OptionsPattern[]] := + ( + gfadEtaSign = OptionValue[GFAD,{opts},EtaSign]; + FeynAmpDenominator @@ Map[gpropp, FCI[{a,b}]] + ); + +sfadint[a___, b_, opts:OptionsPattern[]] := + ( + sfadint[Sequence@@(head [a,b] //. head[x___, y_, z___]/; Head[y]=!=List :> head[x,{y,0},z]),opts] + )/;!MatchQ[{a,b},{__List}] && !OptionQ[b]; + +sfadint[a___List, b_List/; !OptionQ[b], opts:OptionsPattern[]] := + ( + sfadim = OptionValue[SFAD,{opts},Dimension]; + sfadEtaSign = OptionValue[SFAD,{opts},EtaSign]; + sfadint2 @@ Map[#&, {a,b}] + ); + +gpropp[{ex_, n_:1}]:= + GenericPropagatorDenominator[ex, {n, gfadEtaSign}]; + +gpropp[{{ex_}, n_:1}]:= + GenericPropagatorDenominator[ex, {n, gfadEtaSign}]; + +gpropp[{{ex_, s_}, n_:1}]:= + GenericPropagatorDenominator[ex, {n,s}]; + fadint[a__, opts:OptionsPattern[]] := (fadim = OptionValue[FAD,{opts},Dimension]; fadint2 @@ Map[Flatten[{#}]&, {a}]); +fadint2[b__List] := + FeynAmpDenominator @@ Map[propp, {b}/.Repeated->repeated]; + +cfadint2[b__List] := + FeynAmpDenominator @@ Map[cpropp[#,cfadim,cfadEtaSign]&, {b}/. Repeated->repeated]; + +sfadint2[b__List] := + FeynAmpDenominator @@ Map[spropp[#,sfadim,sfadEtaSign]&, {b}/. Repeated->repeated]; + propp[{x_}]:= PropagatorDenominator[Momentum[x, fadim],0]//MomentumExpand; +(* Pattern matching related *) propp[{repeated[{x_, m_}]}]:= Repeated[PropagatorDenominator[Momentum[x, fadim], m] // MomentumExpand]; @@ -289,8 +429,65 @@ PropagatorDenominator[Momentum[x, fadim], m] // MomentumExpand; -fadint2[b__List] := - FeynAmpDenominator @@ Map[propp, {b}/.Repeated->repeated]; + +cproppMomPart[{ex1_,ex2_}, dim_]:= + {CartesianMomentum[ex1, dim], ex2}//MomentumExpand; + +cproppMomPart[ex_/;Head[ex]=!=List, dim_]:= + {CartesianMomentum[ex, dim],0}//MomentumExpand; + + +cproppMassPart[{m2_, etasign_}, _]:= + {m2,etasign}; + +(*If the sign of I*eta is not specified, we take the default option! *) +cproppMassPart[m2_/;Head[m2]=!=List, etaOpt_]:= + {m2, etaOpt}; + +cproppMassPart[{m2_/;Head[m2]=!=List}, etaOpt_]:= + {m2, etaOpt}; + + +cpropp[{a_}, dim_, etaOpt_]:= + cpropp[{a, 0 , 1}, dim, etaOpt]; + +cpropp[{a_, b_ , n_:1}, dim_, etaOpt_]:= + ( + tmp1= cproppMomPart[a/. DOT->holdDOT /. holdDOT[x_,y_]:> CartesianPair[CartesianMomentum[x,dim],CartesianMomentum[y,dim]],dim]; + tmp2= cproppMassPart[b, etaOpt]; + CartesianPropagatorDenominator[tmp1[[1]], tmp1[[2]], tmp2[[1]],{n, tmp2[[2]]}] + ); + + +sproppMomPart[{ex1_,ex2_}, dim_]:= + {Momentum[ex1, dim], ex2}//MomentumExpand; + +sproppMomPart[ex_/;Head[ex]=!=List, dim_]:= + {Momentum[ex, dim],0}//MomentumExpand; + +(*Notice that m^2 has the minus sign by default!*) +sproppMassPart[{m2_, etasign_}, _]:= + {-m2,etasign}; + +(*If the sign of I*eta is not specified, we take the default option! *) +sproppMassPart[m2_/;Head[m2]=!=List, etaOpt_]:= + {-m2, etaOpt}; + +sproppMassPart[{m2_/;Head[m2]=!=List}, etaOpt_]:= + {-m2, etaOpt}; + + +spropp[{a_}, dim_, etaOpt_]:= + spropp[{a, 0 , 1}, dim, etaOpt]; + +spropp[{a_, b_ , n_:1}, dim_, etaOpt_]:= + ( + tmp1= sproppMomPart[a/. DOT->holdDOT /. holdDOT[x_,y_]:> Pair[Momentum[x,dim],Momentum[y,dim]],dim]; + tmp2= sproppMassPart[b, etaOpt]; + StandardPropagatorDenominator[tmp1[[1]], tmp1[[2]], tmp2[[1]],{n, tmp2[[2]]}] + ); + + sp[a_,b_] := Pair[Momentum[a], Momentum[b]]; @@ -298,6 +495,14 @@ Pair[Momentum[a, D], Momentum[b,D]]; spe[a_,b_] := Pair[Momentum[a, D-4], Momentum[b,D-4]]; + +csp[a_,b_] := + CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]; +cspd[a_,b_] := + CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b,D-1]]; +cspe[a_,b_] := + CartesianPair[CartesianMomentum[a, D-4], CartesianMomentum[b,D-4]]; + so[a_] := Pair[Momentum[a], Momentum[OPEDelta]]; sod[a_] := @@ -309,6 +514,17 @@ Pair[Momentum[a, D-4], LorentzIndex[b,D-4]]; fv[a_,b_] := Pair[Momentum[a], LorentzIndex[b]]; + +tc[a_]:= + TemporalPair[TemporalMomentum[a],ExplicitLorentzIndex[0]]; +cvd[a_,b_] := + CartesianPair[CartesianMomentum[a, D-1], CartesianIndex[b, D-1]]; +cve[a_,b_] := + CartesianPair[CartesianMomentum[a, D-4], CartesianIndex[b,D-4]]; +cv[a_,b_] := + CartesianPair[CartesianMomentum[a], CartesianIndex[b]]; + + mt[a_,b_] := Pair[LorentzIndex[a], LorentzIndex[b]]; mtd[a_,b_] := @@ -316,6 +532,13 @@ mte[a_,b_] := Pair[LorentzIndex[a, D-4], LorentzIndex[b, D-4]]; +kd[a_,b_] := + CartesianPair[CartesianIndex[a], CartesianIndex[b]]; +kdd[a_,b_] := + CartesianPair[CartesianIndex[a, D-1], CartesianIndex[b, D-1]]; +kde[a_,b_] := + CartesianPair[CartesianIndex[a, D-4], CartesianIndex[b, D-4]]; + gs[a_] := DiracGamma[Momentum[a]]; gsd[a_] := @@ -343,26 +566,90 @@ DiracGamma[ExplicitLorentzIndex[a,D-4],D-4]/; (a=!=5 && a=!=6 && a=!=7); -lc[a__] := (Eps@@Join[(LorentzIndex/@{a}),{Dimension->4}])/; - FreeQ[{a},Rule] && (Length[{a}] === 4); +tga[] := + DiracGamma[ExplicitLorentzIndex[0]]; + +cga[a_] := + DiracGamma[CartesianIndex[a]]/; !IntegerQ[a]; +cgad[a_] := + DiracGamma[CartesianIndex[a,D-1],D]/; !IntegerQ[a]; +cgae[a_] := + DiracGamma[CartesianIndex[a,D-4],D-4]/; !IntegerQ[a]; + +cgs[a_] := + DiracGamma[CartesianMomentum[a]]/; !IntegerQ[a]; +cgsd[a_] := + DiracGamma[CartesianMomentum[a,D-1],D]/; !IntegerQ[a]; +cgse[a_] := + DiracGamma[CartesianMomentum[a,D-4],D-4]/; !IntegerQ[a]; + +si[a_] := + PauliSigma[LorentzIndex[a]]/; !IntegerQ[a]; +sid[a_] := + PauliSigma[LorentzIndex[a, D],D-1]/; !IntegerQ[a]; +sie[a_] := + PauliSigma[LorentzIndex[a, D-4],D-4]/; !IntegerQ[a]; + +sis[a_] := + PauliSigma[Momentum[a]]/; !IntegerQ[a]; +sisd[a_] := + PauliSigma[Momentum[a, D],D-1]/; !IntegerQ[a]; +sise[a_] := + PauliSigma[Momentum[a, D-4],D-4]/; !IntegerQ[a]; + + +csi[a_] := + PauliSigma[CartesianIndex[a]]/; !IntegerQ[a]; +csid[a_] := + PauliSigma[CartesianIndex[a, D-1],D-1]/; !IntegerQ[a]; +csie[a_] := + PauliSigma[CartesianIndex[a, D-4],D-4]/; !IntegerQ[a]; + +csis[a_] := + PauliSigma[CartesianMomentum[a]]/; !IntegerQ[a]; +csisd[a_] := + PauliSigma[CartesianMomentum[a, D-1],D-1]/; !IntegerQ[a]; +csise[a_] := + PauliSigma[CartesianMomentum[a, D-4],D-4]/; !IntegerQ[a]; + +lc[a__]:= + Eps@@(LorentzIndex/@{a})/; FreeQ[{a},Rule] && (Length[{a}] === 4); + +lcd[a__]:= + Eps@@(LorentzIndex[#,D]&/@{a})/;FreeQ[{a},Rule] && (Length[{a}] === 4); + +clc[a__]:= + Eps@@(CartesianIndex/@{a})/; FreeQ[{a},Rule] && (Length[{a}] === 3); + +clcd[a__]:= + Eps@@(CartesianIndex[#,D-1]&/@{a})/;FreeQ[{a},Rule] && (Length[{a}] === 3); + +lcl[{x___},{y___}]:= + (Eps@@Join[LorentzIndex/@{x}, Momentum/@{y}]/; Length[Join[{x},{y}]]===4); + +lcdl[{x___},{y___}]:= + (Eps@@Join[Map[LorentzIndex[#, D]& ,{x}], Map[Momentum[#, D]& ,{y}]]/; Length[Join[{x},{y}]]===4); + +clcl[{x___},{y___}]:= + (Eps@@Join[CartesianIndex/@{x}, CartesianMomentum/@{y}]/; Length[Join[{x},{y}]]===3); + +clcdl[{x___},{y___}]:= + (Eps@@Join[Map[CartesianIndex[#, D-1]& ,{x}], Map[CartesianMomentum[#, D-1]& ,{y}]]/; Length[Join[{x},{y}]]===3); + -lcd[a__] := (Eps@@Join[(LorentzIndex[#,D]&/@{a}),{Dimension->D}])/; - FreeQ[{a},Rule] && (Length[{a}] === 4); +clcl[{x___},{y___}]:= + (Eps@@Join[CartesianIndex/@{x}, CartesianMomentum/@{y}]/; Length[Join[{x},{y}]]===3); -lcl[{x___},{y___}]:= (Eps@@Join[LorentzIndex/@{x}, - Momentum/@{y},{Dimension->4}]/; Length[Join[{x},{y}]]===4); +clcdl[{x___},{y___}]:= + (Eps@@Join[Map[CartesianIndex[#, D-1]& ,{x}], Map[CartesianMomentum[#, D-1]& ,{y}]]/; Length[Join[{x},{y}]]===3); -lcdl[{x___},{y___}]:= (Eps@@Join[Map[LorentzIndex[#, D]& ,{x}], - Map[Momentum[#, D]& ,{y}],{Dimension->D}]/; Length[Join[{x},{y}]]===4); levicivita[x:Except[_?OptionQ].., opts:OptionsPattern[LeviCivita]] := - Eps@@Join[(LorentzIndex[#,OptionValue[LeviCivita,{opts},Dimension]]&/@{x}), - {Dimension->OptionValue[LeviCivita,{opts},Dimension]}]/; Length[{x}]===4; + Eps@@Join[(LorentzIndex[#,OptionValue[LeviCivita,{opts},Dimension]]&/@{x})]/; Length[{x}]===4; levicivital[{x:Except[_?OptionQ]..., opts1:OptionsPattern[LeviCivita]},{y:Except[_?OptionQ]..., opts2:OptionsPattern[LeviCivita]}] := Eps@@Join[Map[LorentzIndex[#, OptionValue[LeviCivita,{opts1},Dimension]]& ,{x}], - Map[Momentum[#, OptionValue[LeviCivita,{opts1},Dimension]]& ,{y}], - {Dimension->OptionValue[LeviCivita,{opts1},Dimension]}]/; Length[{x,y}]===4 && + Map[Momentum[#, OptionValue[LeviCivita,{opts1},Dimension]]& ,{y}]]/; Length[{x,y}]===4 && OptionValue[LeviCivita,{opts1},Dimension]===OptionValue[LeviCivita,{opts2},Dimension]; tosunf[a_, b_, c_] := diff --git a/FeynCalc/Shared/Isolate.m b/FeynCalc/Shared/Isolate.m index aae8a9e8c..7baade173 100755 --- a/FeynCalc/Shared/Isolate.m +++ b/FeynCalc/Shared/Isolate.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Isolate introduces abbreviations for common @@ -67,19 +67,19 @@ Begin["`Isolate`Private`"] Options[Isolate] = { - IsolateNames -> KK, - IsolatePrint -> False, - IsolateFast -> False, - IsolateSplit -> Infinity, - IsolateTimes -> False, - IsolatePlus -> False + IsolateFast -> False, + IsolateNames -> KK, + IsolatePlus -> False, + IsolatePrint -> False, + IsolateSplit -> Infinity, + IsolateTimes -> False }; Isolate[OptionsPattern[]] := (Message[Isolate::argt, Isolate, 0, 1, 2]; Abort[]); Isolate[_,_,a___,z:Except[_?OptionQ], OptionsPattern[]] := - (Message[Isolate::argt, Isolate, Length[{a}]+3, 1, 2]; Abort[]); + (Message[Isolate::argt, Isolate, Length[{a}]+3, 1, 2]; Abort[])/; !OptionQ[z] Isolate[y_HoldForm^n_., _, OptionsPattern[]] := y^n; @@ -243,7 +243,7 @@ ]; remIsolate[x_, abb_ /; Head[abb] =!= List] := - Block[{re, h}, + Block[{re, h, temp}, If[Length[(re = Select[DownValues @@ {abb}, (#[[2]]===x) &])] > 0, re = re[[1,1]] /. {Literal :> HoldForm, HoldPattern :> HoldForm}, If[ Head[abb]===Symbol, diff --git a/FeynCalc/Shared/LegacyObjects.m b/FeynCalc/Shared/LegacyObjects.m new file mode 100644 index 000000000..08438d2a8 --- /dev/null +++ b/FeynCalc/Shared/LegacyObjects.m @@ -0,0 +1,285 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: LegacyObjects *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Legacy symbols scheduled for removal somewhere in the future *) + +(* ------------------------------------------------------------------------ *) + +ChiralityProjector::usage = +"ChiralityProjector[+1] denotes DiracGamma[6] (=1/2(1 + DiracMatrix[5])). \ +ChiralityProjector[-1] denotes DiracGamma[7] (=1/2(1 - DiracMatrix[5])). \ +ChiralityProjector is a legacy symbol that might be removed in a future FeynCalc \ +version. For the user input shortcuts use GA[6] and GA[7] instead."; + +DiracSpinor::usage = +"DiracSpinor is the same as Spinor. DiracSpinor is a legacy symbol that might be \ +removed in a future FeynCalc version.."; + +DiracMatrix::usage = +"DiracMatrix[m] denotes a Dirac gamma matrix with Lorentz index m. \ +DiracMatrix[m1, m2, ..] is a product of gamma matrices with Lorentz \ +indices m1, m2, etc. DiracMatrix[5] is g^5. \ +DiracMatrix is a legacy symbol that might be removed in a future FeynCalc \ +version. For the user input shortcuts use GA or GAD instead."; + +DiracSlash::usage = +"DiracSlash[p] is the contraction FourVector[p, mu]*DiracSlash[mu]. \ +A product of those can be entered in the form DiracSlash[p1, p2, ..]. \ +DiracSlash is a legacy symbol that might be removed in a future FeynCalc \ +version. For the user input shortcuts use GS or GSD instead."; + +FourVector::usage = +"FourVector[p, mu] is the four dimensional vector p with Lorentz index m. \ +A vector with space-time Dimension d is obtained by supplying the option \ +Dimension->d. FourVector is a legacy symbol that might be removed in a future FeynCalc \ +version. For the user input shortcuts use FV or FVD instead. " + +IFPD::usage = "IFPD[p, m] denotes (p^2 - m^2)." + +LeviCivita::usage = +"LeviCivita[mu, nu, ro, si] is an input function for the \ +totally antisymmetric Levi-Civita tensor. \ +It evaluates automatically \ +to the internal representation Eps[ LorentzIndex[mu], LorentzIndex[nu], \ +LorentzIndex[ro], LorentzIndex[si] ] \ +(or with a second argument in LorentzIndex for the Dimension, \ +if the option Dimension of LeviCivita is changed). \ +LeviCivita[mu, nu ...][ p, ...] evaluates to \ +Eps[LorentzIndex[mu], LorentzIndex[nu], ..., Momentum[p], ...]. \ +LeviCivita is a legacy symbol that might be removed in a future FeynCalc \ +version. For the user input shortcuts use LC or LCD instead."; + +MetricTensor::usage = +"MetricTensor[mu, nu] is the metric tensor in 4 dimensions. \ +The metric tensor in d dimensions is obtained by supplying the +option Dimension->d.\ +MetricTensor is a legacy symbol that might be removed in a future FeynCalc \ +version. For the user input shortcuts use MT or MTD instead."; + +MetricTensor::usage = +"MetricTensor[mu, nu] is the metric tensor in 4 dimensions. \ +The metric tensor in d dimensions is obtained by supplying the +option Dimension->d.\ +MetricTensor is a legacy symbol that might be removed in a future FeynCalc \ +version. For the user input shortcuts use MT or MTD instead."; + +$BreitMaison::usage = +"$BreitMaison is a legacy switch for the Breitenlohner-Maison-t'Hooft-Veltman \ +scheme. The modern way is to use FCSetDiracGammaScheme to specify \ +a scheme for handling Dirac matrices in dimensional regularization and \ +FCGetDiracGammaScheme to check the current setting."; + +$Larin::usage = +"$Larin is a legacy switch for the Larin-Gorishny-Atkyampo-DelBurgo \ +scheme. The modern way is to use FCSetDiracGammaScheme to specify \ +a scheme for handling Dirac matrices in dimensional regularization and \ +FCGetDiracGammaScheme to check the current setting."; + +DiracMatrix::noint = +"DiracMatrix[`1`] is forbidden in FeynCalc. For consistency reasons, the only allowed integer \ +arguments can be 0, 1, 2, 3, 5, 6 and 7. Evaluation aborted!"; + +DiracSlash::noint = +"DiracSlash[`1`] is forbidden in FeynCalc. For consistency reasons, the only allowed integer \ +argument can be 0. Evaluation aborted!"; + + +(* ------------------------------------------------------------------------ *) +Begin["`Package`"] + + + +End[] + +Begin["`LegacyObjects`Private`"] + +DeclareNonCommutative[ChiralityProjector]; +DeclareNonCommutative[DiracSpinor]; +DeclareNonCommutative[DiracMatrix]; +DeclareNonCommutative[DiracSlash]; + +$BreitMaison = False; +$Larin = False; + +Options[ChiralityProjector] = {FCI -> True}; +Options[DiracMatrix] = {Dimension -> 4, FCI -> True}; +Options[DiracSlash] = {Dimension -> 4, FCI -> True}; +Options[FourVector] = {Dimension -> 4, FCI -> True}; +Options[LeviCivita] = {Dimension -> 4, FCI->True}; +Options[MetricTensor] = {Dimension -> 4, FCI -> True}; + +FeynCalc`Package`TrFeynCalcObjects = Join[FeynCalc`Package`TrFeynCalcObjects, DiracMatrix | DiracSlash]; + + +ChiralityProjector[1, OptionsPattern[]] := + DiracGamma[6]/; OptionValue[FCI]; + +ChiralityProjector[-1, OptionsPattern[]] := + DiracGamma[7]/; OptionValue[FCI]; + +DiracMatrix[(a:5|6|7), OptionsPattern[]] := + DiracGamma[a]/; OptionValue[FCI] && MatchQ[OptionValue[Dimension],_]; + +DiracMatrix[a_, OptionsPattern[]] := + DiracGamma[LorentzIndex[a, OptionValue[Dimension]], + OptionValue[Dimension]]/; OptionValue[FCI] && Head[a]=!=DOT && !StringQ[a] && !NumberQ[a]; + +DiracMatrix[(a:0|1|2|3), OptionsPattern[]] := + DiracGamma[ExplicitLorentzIndex[a, OptionValue[Dimension]], + OptionValue[Dimension]]/; OptionValue[FCI] && Head[a]=!=DOT && !StringQ[a]; + +DiracMatrix[x_?NumberQ, OptionsPattern[]] := + (Message[DiracMatrix::noint, x]; Abort[])/; !MemberQ[{0, 1, 2, 3, 5, 6, 7}, x]; + +DiracMatrix[DOT[a_,b__], opts:OptionsPattern[]] := + DOT@@(DiracMatrix[#,opts]& /@ {a,b}); + +DiracMatrix[a_,b:Except[_?OptionQ].., opts:OptionsPattern[]] := + DOT@@(DiracMatrix[#,opts]& /@ {a,b}); + +DiracSlash[DOT[a_,b__], opts:OptionsPattern[]] := + DOT@@(DiracSlash[#,opts]& /@ {a,b}); + +DiracSlash[a_,b:Except[_?OptionQ].., opts:OptionsPattern[]] := + DOT@@(DiracSlash[#,opts]& /@ {a,b}); + +DiracSlash[a_, OptionsPattern[]] := + DiracGamma[Momentum[a, OptionValue[Dimension]], + OptionValue[Dimension]]/; OptionValue[FCI] && !NumberQ[a]; + +DiracSlash[0, OptionsPattern[]] := + 0; + +DiracSlash[x_?NumberQ, OptionsPattern[]] := + (Message[DiracSlash::noint, x]; Abort[])/; x=!=0; + +DiracSpinor = Spinor; + +FourVector[a_,b_, OptionsPattern[]] := + Pair[Momentum[a, OptionValue[Dimension]], + LorentzIndex[b, OptionValue[Dimension]]]/; OptionValue[FCI]; + + +IFPD[Momentum[OPEDelta,___],0] := + 0; + +LeviCivita[x:Except[_?OptionQ].., opts:OptionsPattern[LeviCivita]][y:Except[_?OptionQ].., + opts:OptionsPattern[LeviCivita]]/; (Length[{x,y}] =!= 4) && (FCPatternFreeQ[{x,y,opts}]) := + Message[LeviCivita::argrx, "LeviCivita["<>ToString[{x,opts}]<>"]["<>ToString[{y,opts}]<>"]", Length[{x,y}], 4]; + +LeviCivita[x:Except[_?OptionQ] ..., opts:OptionsPattern[]]/; (Length[{x}] > 4) && (FCPatternFreeQ[{x,opts}]) := + Message[LeviCivita::argrx, "LeviCivita["<>ToString[{x,opts}]<>"]", Length[{x}], 4]; + +LeviCivita[ a:Except[_?OptionQ].., opts:OptionsPattern[]] := + FCI[LeviCivita[a,Join[{FCI->False},FilterRules[{opts},Except[FCI]]]]]/; Length[{a}] === 4 && OptionValue[FCI]; + +LeviCivita[x:Except[_?OptionQ]..., opts1:OptionsPattern[LeviCivita]][y:Except[_?OptionQ]..., opts2:OptionsPattern[LeviCivita]] := + FCI[LeviCivita[x,Join[{FCI->False},FilterRules[{opts1},Except[FCI]]]][y,Join[{FCI->False},FilterRules[{opts2},Except[FCI]]]]]/; + Length[{x,y}] === 4 && OptionValue[LeviCivita,{opts1},FCI] && OptionValue[LeviCivita,{opts2},FCI]; + +MetricTensor[a_, b_, OptionsPattern[]] := + Pair[LorentzIndex[a, OptionValue[Dimension]], LorentzIndex[b, OptionValue[Dimension]]]/; OptionValue[FCI]; + + +FourVector /: + MakeBoxes[FourVector[a_,b_, opts:OptionsPattern[]], TraditionalForm]:= + ToBoxes[Pair[Momentum[a, OptionValue[FourVector, {opts},Dimension]], LorentzIndex[b, OptionValue[FourVector, {opts},Dimension]]],TraditionalForm]/; + !OptionValue[FourVector, {opts},FCI]; + + +MetricTensor /: + MakeBoxes[MetricTensor[a_, b_, opts:OptionsPattern[]], TraditionalForm]:= + ToBoxes[Pair[LorentzIndex[a,OptionValue[{opts},Dimension]],LorentzIndex[b,OptionValue[{opts},Dimension]]], TraditionalForm]/; !OptionValue[{opts},FCI]; + +ChiralityProjector /: + MakeBoxes[ChiralityProjector[1,OptionsPattern[]], TraditionalForm]:= + ToBoxes[DiracGamma[6],TraditionalForm]; + +ChiralityProjector /: + MakeBoxes[ChiralityProjector[-1,OptionsPattern[]], TraditionalForm]:= + ToBoxes[DiracGamma[7],TraditionalForm]; + +DiracMatrix /: + MakeBoxes[DiracMatrix[x_/;!MemberQ[{5,6,7},x], opts:OptionsPattern[]], TraditionalForm]:= + ToBoxes[DiracGamma[LorentzIndex[x,OptionValue[DiracMatrix, {opts},Dimension]], + OptionValue[DiracMatrix, {opts},Dimension]],TraditionalForm]/; !OptionValue[{opts},FCI]; + +DiracMatrix /: + MakeBoxes[DiracMatrix[(x:5|6|7), opts:OptionsPattern[]], TraditionalForm]:= + ToBoxes[DiracGamma[x],TraditionalForm]/; !OptionValue[{opts},FCI]; + + +DiracSlash /: + MakeBoxes[DiracSlash[x_, opts:OptionsPattern[]], TraditionalForm]:= + ToBoxes[DiracGamma[Momentum[x,OptionValue[DiracSlash, {opts},Dimension]], + OptionValue[DiracSlash, {opts},Dimension]],TraditionalForm]/; !OptionValue[{opts},FCI]; + +IFPD /: + MakeBoxes[IFPD[a_,c_], TraditionalForm]:= + If[ c === 0, + TBox[a^2], + TBox["(", a^2," - ", c^2, ")"] + ]; + +LeviCivita /: + MakeBoxes[LeviCivita[(a:Except[_?OptionQ]..)/; Length[{a}] === 4, opts:OptionsPattern[LeviCivita]/;!OptionValue[LeviCivita,{opts},FCI]], + TraditionalForm]:= + ToBoxes[Eps[Sequence@@(LorentzIndex[#,OptionValue[LeviCivita,{opts},Dimension]]&/@{a})],TraditionalForm]; + +LeviCivita /: + MakeBoxes[LeviCivita[x:Except[_?OptionQ]..., opts1:OptionsPattern[LeviCivita]][y:Except[_?OptionQ]..., opts2:OptionsPattern[LeviCivita]], TraditionalForm]:= + ToBoxes[Eps[Sequence@@(LorentzIndex[#,OptionValue[LeviCivita,{opts1},Dimension]]&/@{x}), + Sequence@@(Momentum[#,OptionValue[LeviCivita,{opts2},Dimension]]&/@{y})],TraditionalForm]/; + Length[{x,y}] === 4 && !OptionValue[LeviCivita,{opts1,opts2},FCI]; + + +$BreitMaison /: Set[$BreitMaison, True] := + ( + OwnValues[$BreitMaison] = {HoldPattern[$BreitMaison] :> True}; + OwnValues[$Larin] = {HoldPattern[$Larin] :> False}; + FCSetDiracGammaScheme["BMHV"]; + True + ); + +$BreitMaison /: Set[$BreitMaison, False] := + ( + OwnValues[$BreitMaison] = {HoldPattern[$BreitMaison] :> False}; + If[ TrueQ[$Larin === False], + FCSetDiracGammaScheme["NDR"], + FCSetDiracGammaScheme["Larin"] + ]; + False + ); + +$Larin /: Set[$Larin, True] := + ( + OwnValues[$Larin] = {HoldPattern[$Larin] :> True}; + OwnValues[$BreitMaison] = {HoldPattern[$BreitMaison] :> False}; + FCSetDiracGammaScheme["Larin"]; + True + ); + +$Larin /: Set[$Larin, False] := + ( + OwnValues[$Larin] = {HoldPattern[$Larin] :> False}; + If[TrueQ[$BreitMaison === False], + FCSetDiracGammaScheme["NDR"], + FCSetDiracGammaScheme["BMHV"] + ]; + False + ); + + +FCPrint[1,"LegacyObjects loaded."]; +End[] + diff --git a/FeynCalc/Shared/Series2.m b/FeynCalc/Shared/Series2.m index 0f0b2dca4..c774f59a9 100755 --- a/FeynCalc/Shared/Series2.m +++ b/FeynCalc/Shared/Series2.m @@ -29,10 +29,10 @@ Begin["`Series2`Private`"] Options[Series2] = { - Collecting -> False, - Factoring -> True, - FinalSubstitutions -> {EulerGamma -> 0}, - SimplifyPolyLog -> True + Collecting -> False, + Factoring -> True, + FinalSubstitutions -> {EulerGamma -> 0}, + SimplifyPolyLog -> True }; Series2[a_, e_, n_Integer, ops___Rule] := @@ -43,7 +43,7 @@ Series2[a_, {x_, 0, nn_}, ops___Rule] := Block[{re, rec, polysub, polysimp, finsub, res, n=nn, ll, hypfix, - hyp, hyb, hyphyp, gamspec}, + hyp, hyb, hyphyp, gamspec, hypex, hyback}, gammas[y_] := If[FreeQ[y, Gamma], diff --git a/FeynCalc/Shared/Series3.m b/FeynCalc/Shared/Series3.m index b8ce67102..bfe0de176 100755 --- a/FeynCalc/Shared/Series3.m +++ b/FeynCalc/Shared/Series3.m @@ -30,8 +30,8 @@ Begin["`Private`"] Options[Series3] = { - Factoring -> True, - FinalSubstitutions -> {} + Factoring -> True, + FinalSubstitutions -> {} }; Series3[a_, e_, n_Integer, ops___Rule] := @@ -42,7 +42,7 @@ Series3[a_, {x_, 0, nn_}, ops___Rule] := Block[{re, rec, polysub, polysimp, finsub, res, n=nn, - hypfix, hyp, hyb, hyphyp}, + hypfix, hyp, hyb, hyphyp, hyback, hypex}, hypex = {Hypergeometric2F1[p1_,p2_,p3_,z_] :> Apply[Hypergeometric2F1, Append[Expand/@{p1,p2,p3},Factor2[z]]]}; diff --git a/FeynCalc/Shared/SharedObjects.m b/FeynCalc/Shared/SharedObjects.m index e3f8b3306..36211a6f7 100644 --- a/FeynCalc/Shared/SharedObjects.m +++ b/FeynCalc/Shared/SharedObjects.m @@ -2,13 +2,13 @@ (* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Title: CoreObjects *) +(* :Title: SharedObjects *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Basic FeynCalc objects *) @@ -28,9 +28,34 @@ CF::usage = "CF is one of the Casimir operator eigenvalues of SU(N); CF = (N^2-1)/(2 N)"; -ChiralityProjector::usage = -"ChiralityProjector[+1] denotes DiracGamma[6] (=1/2(1 + DiracMatrix[5])). \ -ChiralityProjector[-1] denotes DiracGamma[7] (=1/2(1 - DiracMatrix[5]))."; +CFAD::usage = +"CFAD[{{q1+ ..., p1.q2 + ...,} {m^2, s}, n}, ...] denotes a Cartesian propagator \ +given by 1/[(q1+...)^2 + p1.q2 ... + m^2 + sign*I*eta]^n, where \ +q1^2 and p1.q2 are Cartesian sclar products in D-1 dimensions. \ +For brevity one can also use shorter forms \ +such as CFAD[{q1+ ..., m^2}, ...], CFAD[{q1+ ..., m^2 , n}, ...], \ +CFAD[{q1+ ..., {m^2, -1}}, ...], CFAD[q1,...] etc. If s is not explicitly specified, \ +then its value is determined by the \ +option EtaSign, which has the default value +1. If n is not explicitly \ +specified, then the default value 1 is assumed. Translation into FeynCalc \ +internal form is performed by FeynCalcInternal, where a CFAD is encoded \ +using the special head CartesianPropagatorDenominator."; + +CartesianPropagatorDenominator::usage = +"CartesianPropagatorDenominator[CartesianMomentum[q1,D-1]+..., \ +CartesianPair[CartesianMomentum[q1,D-1],CartesianMomentum[p1,D-1] + ...,m^2, \ +{n,s}] encodes a generic Cartesian propagator denominator \ +1/[(q1+...)^2 + q1.p1 + ... + m^2 + s*I eta]^n. \ +CartesianPropagatorDenominator is an internal object. To enter such propagators \ +in FeynCalc you should use CFAD."; + +PropagatorDenominator::usage = +"PropagatorDenominator[Momentum[q], m] is a factor of the denominator of a \ +propagator. If q is supposed to be D-dimensional enter: \ +PropagatorDenominator[Momentum[q, D], m]. What is meant is \ +1/(q^2-m^2). PropagatorDenominator[p] evaluates to PropagatorDenominator[p,0]. +PropagatorDenominator is an internal object. To enter such propagators \ +in FeynCalc you should use FAD."; CounterT::usage = "CounterT is a factor used by GluonPropagator and \ QuarkPropagator when CounterTerm is set to All."; @@ -45,49 +70,44 @@ "DeltaFunctionPrime denotes the derivative of the Dirac delta-function."; DiracBasis::usage = -"DiracBasis[any] is a head which is wrapped around Dirac structures \ -(and the 1) as a result of the function DiracReduce. \ -Eventually you want to substitute DiracBasis by Identity (or \ -set: DiracBasis[1] = S; DiracBasis[DiracMatrix[mu]] = P; etc.)."; +"DiracBasis[exp] is a head which is wrapped around Dirac structures \ +(and the 1) as a result of the function DiracReduce."; DiracGamma::usage = "DiracGamma[x, dim] is the way all Dirac \ matrices and slashes are represented (in the internal representation). \ -Use DiracMatrix (or GA, GAD) and DiracSlash (or GS, GSD) \ -for manual (short) input. \ +Use GA or GAD and GS or GSD for manual (short) input. \ DiraGamma[x, 4] simplifies to DiracGamma[x]."; -DiracGammaT::usage = -"DiracGammaT[x] denotes the transpose of DiracGamma. \ -Transpose[DiracGammaT[x]] gives DiracGamma[x]. \ -Note that x must have Head LorentzIndex or Momentum."; -(* :Comments: still experimental !!! check SUSY-calculations *) - -DiracMatrix::usage = -"DiracMatrix[m] denotes a Dirac gamma matrix with Lorentz index m. \ -DiracMatrix[m1, m2, ..] is a product of gamma matrices with Lorentz \ -indices m1, m2, etc. DiracMatrix[5] is gamma5."; +DiracIndex::usage = +"DiracIndex is the head of Dirac indices. \ +The internal representation of a four-dimensional \ +spinorial index i is DiracIndex[i]. If the first \ +argument is an integer, DiracIndex[i] turns into \ +ExplicitDiracIndex[i]. \n +Dirac indices are the indices that denote the components \ +of Dirac matrices or spinors. They should not be confused with \ +the Lorentz indices attached to the Dirac matrices. For example \ +in case of g^mu_ij, mu is a Lorentz index, while i and j are \ +spinorial indices."; + +DiracIndexDelta::usage = +"DiracIndexDelta[DiracIndex[i],DiracIndex[j]] is the Kronecker-delta \ +in the Dirac space with two explicit Dirac indices i and j."; + +DIDelta::usage = +"DIDelta[i,j] is the Kronecker-delta in the Dirac space. DIDelta[i,j] is \ +transformed into DiracDelta[DiracIndex[i],DiracIndex[j]] by FeynCalcInternal."; DiracSigma::usage = "DiracSigma[a, b] stands for I/2*(a . b - b . a) in 4 dimensions. \ -a and b must have Head DiracGamma, DiracMatrix or DiracSlash. \ -Only antisymmetry is implemented."; - -DiracSlash::usage = -"DiracSlash[p] is the contraction FourVector[p, mu]*DiracSlash[mu]. \ -A product of those can be entered in the form DiracSlash[p1, p2, ..]." - -DiracSpinor::usage = -"DiracSpinor[p, m, ind] is a Dirac spinor for a fermion with momentum p \ -and mass m and indices ind. DiracSpinor is the same as Spinor."; +a and b must have Head DiracGamma. Only antisymmetry is implemented."; Eps::usage = "Eps[a, b, c, d] represents the totally antisymmetric epsilon \ (Levi-Civita) tensor. The \"a,b, ...\" should have head \ LorentzIndex or Momentum or Integer. \ -In case of integers the Levi-Civita tensor is evaluated immediately. \ -Eps has an option Dimension (default 4). \ -As alternative input LeviCivita[mu,nu, ...][p,q,...] can be used."; +As alternative input LC[mu,nu, ...][p,q,...] can be used."; Epsilon::usage = "Epsilon is (D-4), where D is the number of space-time dimensions. Epsilon \ @@ -101,25 +121,50 @@ Eps has an option Dimension (default 4). \ "EpsilonIR denotes (D-4), where D is the number of space-time dimensions. EpsilonIR \ stands for a small negative number that explicitly regulates only IR divergences."; +ExplicitDiracIndex::usage = +"ExplicitDiracIndex[ind] is an explicit Dirac index, i.e., ind is \ +an integer."; + ExplicitLorentzIndex::usage = "ExplicitLorentzIndex[ind] is an explicit Lorentz index, i.e., ind is \ an integer."; ExplicitSUNIndex::usage = "ExplicitSUNIndex[ind] is a specific SU(N) index in the adjoint \ -representation, i.e., ind is an integer."; +representation, i.e. ind is an integer."; ExplicitSUNFIndex::usage = "ExplicitSUNIndex[ind] is a specific SU(N) index in the fundamental \ -representation, i.e., ind is an integer."; +representation, i.e. ind is an integer."; FAD::usage = "FAD[q, q-p, ...] denotes 1/(q^2 (q-p)^2 ...). \ FAD[{q1,m}, {q1-p,m}, q2, ...] is \ 1/( (q1^2 - m^2) ( (q1-p)^2 - m^2 ) q2^2 ... ). -(Translation into FeynCalc internal form is performed by +(Translation into FeynCalc internal form is performed by \ FeynCalcInternal.)"; +DCHN::usage = +"DCHN[x,i,j] is a chain of Dirac matrices x and is transformed \ +into DiracChain[FCI[x],DiracIndex[i],DiracIndex[j]] by \ +FeynCalcInternal."; + +FCTopology::usage= +"FCTopology[id, {prop1, prop2, ...}] denotes a topology with the identifier id \ +that is characterized by the propagators {prop1, prop2, ...}. The propagators \ +in the list do not necessarily have to form a valid basis, i.e. the basis may also \ +be incomplete or overdetermined."; + +DiracChain::usage = +"DiracChain[x,i,j] denotes a chain of Dirac \ +matrices x, where the Dirac indices i and j \ +are explicit. For example, \ +DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],DiracIndex[j]] \ +denotes a standalone Dirac matrix g^mu_ij. A DiracChain with only two \ +arguments denotes a spinor component, e.g. \ +DiracChain[Spinor[Momentum[p],m],DiracIndex[i]] stands for the i-th \ +component of Spinor[Momentum[p],m]"; + FeynAmp::usage = "FeynAmp[q, amp] denotes a Feynman amplitude. \ amp denotes the analytical expression for the amplitude, \ @@ -127,22 +172,18 @@ Eps has an option Dimension (default 4). \ FeynAmp[q1, q2, amp] denotes a two-loop amplitude."; FeynAmpDenominator::usage = -"FeynAmpDenominator[ PropagatorDenominator[ ... ], \ -PropagatorDenominator[ ... ], ... ] represents \ +"FeynAmpDenominator[...] represents \ the inverse denominators of the propagators, i.e. FeynAmpDenominator[x] \ -is 1/x ."; +is 1/x. Different propagator denominators are represented using special \ +heads such as PropagatorDenominator, StandardPropagatorDenominator, \ +CartesianPropagatorDenominator etc. "; FeynAmpList::usage = "FeynAmpList[info][FeynAmp[...], FeynAmp[...], ...] is a head of a list of \ Feynman amplitudes." -FourVector::usage = -"FourVector[p, mu] is the four Dimensional vector p with Lorentz index m. \ -A vector with space-time Dimension d is obtained by supplying the option \ -Dimension->d." - FV::usage = -"FV[p,mu] is a fourvector and is transformed into \ +"FV[p,mu] is a 4-vector and is transformed into \ Pair[Momentum[p], LorentzIndex[mu]] by FeynCalcInternal."; FVD::usage = @@ -168,19 +209,35 @@ Eps has an option Dimension (default 4). \ ""; GA::usage = -"GA[mu] can be used as input for gamma_mu and is \ -transformed into DiracMatrix[mu] by FeynCalcInternal."; +"GA[mu] can be used as input for gamma^mu and is \ +transformed into DiracGamma[LorentzIndex[mu]] by FeynCalcInternal."; GA5::usage = "GA5 is equivalent to DiracGamma[5] and denotes gamma5."; GAD::usage = -"GAD[mu] can be used as input for a D-dimensional gamma_mu and is \ -transformed into DiracMatrix[mu, Dimension->D] by FeynCalcInternal."; +"GAD[mu] can be used as input for a D-dimensional gamma^mu and is \ +transformed into DiracGamma[LorentzIndex[mu, D], D] by FeynCalcInternal."; GAE::usage = -"GAE[mu] can be used as input for a D-4-dimensional gamma_mu and is \ -transformed into DiracMatrix[mu, Dimension->D-4] by FeynCalcInternal."; +"GAE[mu] can be used as input for a D-4-dimensional gamma^mu and is \ +transformed into DiracGamma[LorentzIndex[mu, D-4], D-4] by FeynCalcInternal."; + +GFAD::usage = +"GFAD[{expr,n,sign},...] denotes 1/(expr + sign I eta)^n. \ +(Translation into FeynCalc internal form is performed by \ +FeynCalcInternal.)"; + +GFAD::usage = +"GFAD[{{{x, s}, n}, ...] denotes a generic propagator \ +given by 1/[x + s*I*eta]^n, where x can be an arbitray expression. \ +For brevity one can also use shorter forms \ +such as GFAD[{x, n}, ...], GFAD[{x}, ...] or GFAD[x, ...]. \ +If s is not explicitly specified, then its value is determined by the \ +option EtaSign, which has the default value +1. If n is not explicitly \ +specified, then the default value 1 is assumed. Translation into FeynCalc \ +internal form is performed by FeynCalcInternal, where a GFAD is encoded \ +using the special head GenericPropagatorDenominator."; GaugeField::usage = "GaugeField is a name of a gauge field."; @@ -188,36 +245,43 @@ Eps has an option Dimension (default 4). \ GaugeXi::usage = "GaugeXi is a head for gauge parameters."; +GenericPropagatorDenominator::usage = +"GenericPropagatorDenominator[expr, {n,s}] is a generic factor of the denominator of a \ +propagator. Unlike PropagatorDenominator that is supposed to mean 1/(q^2-m^2), \ +expr in GenericPropagatorDenominator can be an arbitrary combination of Pair, \ +CartesianPair and TemporalPair objects. Using n one can specify the power of the \ +propagator, while s (+1 or -1) fixes the sign of I*eta. GenericPropagatorDenominator \ +is an internal object. To enter such propagators in FeynCalc you should use GFAD."; + GluonField::usage = "GluonField is a name of a gauge field."; GS::usage = -"GS[p] is transformed into DiracSlash[p] by FeynCalcInternal. \ +"GS[p] is transformed into DiracGamma[Momentum[p]] by FeynCalcInternal. \ GS[p,q, ...] is equivalent to GS[p].GS[q]. ..."; GSD::usage = -"GSD[p] is transformed into DiracSlash[p,Dimension->D] by FeynCalcInternal."; +"GSD[p] is transformed into DiracGamma[Momentum[p, D], D] by FeynCalcInternal. \ +GSD[p,q, ...] is equivalent to GSD[p].GSD[q]. ..."; GSE::usage = -"GSE[p] is transformed into DiracSlash[p,Dimension->D-4] by FeynCalcInternal."; - -IFPD::usage = "IFPD[p, m] denotes (p^2 - m^2)." +"GSE[p] is transformed into DiracGamma[Momentum[p, D-4], D-4] by FeynCalcInternal. \ +GSE[p,q, ...] is equivalent to GSE[p].GSE[q]. ..."; Integratedx::usage = "Integratedx[x, low, up] is a variable representing the integration \ operator Integrate[#, {x,low,up}]&."; LC::usage = -"LC[m,n,r,s] evaluates to LeviCivita[m,n,r,s] applying \ -FeynCalcInternal. \ -LC[m,...][p, ...] evaluates to LeviCivita[m,...][p,...] \ +"LC[m,n,r,s] evaluates to Eps[LorentzIndex[m], LorentzIndex[n], \ +LorentzIndex[r], LorentzIndex[s]] applying FeynCalcInternal. \ +LC[m,...][p, ...] evaluates to Eps[LorentzIndex[m], ..., Momentum[p], ...] \ applying FeynCalcInternal."; LCD::usage = -"LCD[m,n,r,s] evaluates to LeviCivita[m,n,r,s,Dimension->D] \ -applying FeynCalcInternal. \ -LCD[m,...][p, ...] evaluates to \ -LeviCivita[m,...,Dimension->D][p,...,Dimension->D] \ +"LCD[m,n,r,s] evaluates to Eps[LorentzIndex[m,D], LorentzIndex[n,D], \ +LorentzIndex[r,D], LorentzIndex[s,D]] applying FeynCalcInternal. \ +LCD[m,...][p, ...] evaluates to Eps[LorentzIndex[m, D], ..., Momentum[p, D], ...] \ applying FeynCalcInternal."; LeftPartialD::usage = @@ -233,23 +297,15 @@ Eps has an option Dimension (default 4). \ right. ExplicitPartialD[LeftRightPartialD2[mu]] gives \ (RightPartialD[mu] + LeftPartialD[mu])."; -LeviCivita::usage = -"LeviCivita[mu, nu, ro, si] is an input function for the \ -totally antisymmetric Levi-Civita tensor. \ -It evaluates automatically \ -to the internal representation Eps[ LorentzIndex[mu], LorentzIndex[nu], \ -LorentzIndex[ro], LorentzIndex[si] ] \ -(or with a second argument in LorentzIndex for the Dimension, \ -if the option Dimension of LeviCivita is changed). \ -LeviCivita[mu, nu ...][ p, ...] evaluates to \ -Eps[LorentzIndex[mu], LorentzIndex[nu], ..., Momentum[p], ...]."; - Li2::usage = "Li2 is an abbreviation for the dilog function, i.e., Li2 = PolyLog[2,#]&."; Li3::usage = "Li3 is an abbreviation for the trilog function, i.e., Li3 = PolyLog[3,#]&."; +Li4::usage = +"Li4 is an abbreviation for the PolyLog[4,x] function, i.e., Li4 = PolyLog[4,#]&."; + LorentzIndex::usage = "LorentzIndex is the head of Lorentz indices. \ The internal representation of a four-dimensional mu is \ @@ -259,14 +315,6 @@ Eps has an option Dimension (default 4). \ If the first argument is an integer, LorentzIndex[i] turns into \ ExplicitLorentzIndex[i]."; -Lower::usage = -"Lower may be used inside LorentzIndex to indicate a covariant LorentzIndex."; - -MetricTensor::usage = -"MetricTensor[mu, nu] is the metric tensor in 4 dimensions. \ -The metric tensor in d dimensions is obtained by supplying the -option Dimension->d."; - Momentum::usage = "Momentum is the head of a four momentum (p). \ The internal representation of a four-dimensional p is \ @@ -298,12 +346,6 @@ Eps has an option Dimension (default 4). \ The first one acts on QuantumField[f], the second on QuantumField[f][x], \ where f is some field name and x is a space-time variable."; -PauliSigma::usage = -"PauliSigma denotes the vector of the 3 Pauli matrices. \ -PauliSigma[1], PauliSigma[2], PauliSigma[3] give the \ -explicit Pauli matrices. PauliSigma[] yields \ -{PauliSigma[1], PauliSigma[2], PauliSigma[3]}."; - PlusDistribution::usage = "PlusDistribution[1/(1-x)] denotes the distribution (1/(1-x))_+. \n PlusDistribution[Log[1-x]/(1-x)] denotes the distribution \ @@ -315,7 +357,7 @@ Eps has an option Dimension (default 4). \ "Polarization[k] = Polarization[k, I] represents a \ polarization momentum with (incoming) momentum k. \ A slashed polarization vector (e1(k) slash) has to be entered -as DiracSlash[Polarization[k]]. \ +as GS[Polarization[k]]. \ The internal representation for a polarization vector e1 \ corresponding to a boson with four momentum k is: \ Momentum[ Polarization[ k, I ] ]. \ @@ -332,17 +374,14 @@ A slashed polarization vector (e1(k) slash) has to be entered PropagatorDenominator::usage = "PropagatorDenominator[Momentum[q], m] is a factor of the denominator of a \ -propagator. If q is supposed to be D-dimensional enter: \ -PropagatorDenominator[Momentum[q, D], m]. What is meant is \ -1/(q^2-m^2). PropagatorDenominator[p] evaluates to PropagatorDenominator[p,0]."; +propagator. If q is supposed to be D-dimensional, use \ +PropagatorDenominator[Momentum[q, D], m]. What is meant is \ +1/(q^2-m^2). PropagatorDenominator must appear inside FeynAmpDenominator, it \ +is not a standalone object."; PD::usage = "PD is an abbreviation for PropagatorDenominator."; -$PairBrackets::usage = -"$PairBrackets determines whether brackets are drawn around \ -scalar products in the notebook interface."; - QuantumField::usage = "QuantumField[par1, par2, ..., ftype, {lorind}, {sunind}] \ denotes a quantum field of type ftype with (possible) \ @@ -372,17 +411,41 @@ denotes a quantum field of type ftype with (possible) \ "ScaleMu is the mass scale used for dimensional regularization \ of loop integrals"; +SFAD::usage = +"SFAD[{{q1+ ..., p1.q2 + ...,} {m^2, s}, n}, ...] denotes a Lorentzian propagator \ +given by 1/[(q1+...)^2 + p1.q2 ... + m^2 + sign*I*eta]^n, where \ +q1^2 and p1.q2 are scalar products of Lorentz vectors in D dimensions. \ +For brevity one can also use shorter forms \ +such as SFAD[{q1+ ..., m^2}, ...], SFAD[{q1+ ..., m^2 , n}, ...], \ +SFAD[{q1+ ..., {m^2, -1}}, ...], SFAD[q1,...] etc. If s is not explicitly specified, \ +then its value is determined by the \ +option EtaSign, which has the default value +1. If n is not explicitly \ +specified, then the default value 1 is assumed. Translation into FeynCalc \ +internal form is performed by FeynCalcInternal, where a SFAD is encoded \ +using the special head StandardPropagatorDenominator."; + +StandardPropagatorDenominator::usage = +"StandardPropagatorDenominator[Momentum[q1,D]+..., \ +Pair[Momentum[q1,D],Momentum[p1,D] + ...,m^2, \ +{n,s}] encodes a generic Lorentzian propagator denominator \ +1/[(q1+...)^2 + q1.p1 + ... + m^2 + s*I eta]^n. \ +This allows to accomodate for standard propagators of the type \ +1/(p^2-m^2) but also for propagators encountered in manifestly \ +Lorentz covariant effective field theories such as HQET or SCET. \ +StandardPropagatorDenominator is an internal object. To enter such propagators \ +in FeynCalc you should use SFAD."; + OPE::usage = "OPE is a convenience variable to separate OPE insertions. OPE is also \ an option of several input functions like GluonPropagator."; SD::usage = -"SD[i, j] is the (FeynCalc-external) Kronecker-delta for SU(N) with color \ +"SD[i, j] denotes the SU(N) Kronecker delta with color \ indices i and j in the adjoint represnetation. SD[i,j] is transformed into \ SUNDelta[SUNIndex[i],SUNIndex[j]] by FeynCalcInternal."; SDF::usage = -"SDF[i, j] is the (FeynCalc-external) Kronecker-delta for SU(N) with color \ +"SDF[i, j] denotes the SU(N) Kronecker delta with color \ indices i and j in the fundamental represnetation. SDF[i,j] is transformed into \ SUNFDelta[SUNFIndex[i],SUNFIndex[j]] by FeynCalcInternal."; @@ -427,7 +490,7 @@ denotes a quantum field of type ftype with (possible) \ "Spinor[p, m] represents a Dirac spinor. \ Which of the spinors u, v,u_bar or v_bar \ is understood, depends on the sign of the momentum (p) \ -argument and the relative position of DiracSlash[p]: \ +argument and the relative position of GS[p]: \ Spinor[sign p, mass] is that spinor which yields \ sign*mass*Spinor[p, mass] if the Dirac equation is applied ."; @@ -463,6 +526,9 @@ denotes a quantum field of type ftype with (possible) \ "SpinorVBarD[p, m] denotes a vbar-spinor that depends on the \ D-dimensional momentum p"; +StandardMatrixElement::usage = +"StandardMatrixElement[ ... ] is the head for matrix element abbreviations."; + SUND::usage = "SUND[a, b, c] is the symmetric SU(N) d_{a,b,c}."; @@ -480,22 +546,22 @@ denotes a quantum field of type ftype with (possible) \ SUNIndex::usage = "SUNIndex[a] is an SU(N) index in the adjoint representation. \ -If the argument is an integer SUNIndex[a] turns into ExplicitSUNIndex[a]."; +If the argument is an integer, SUNIndex[a] turns into ExplicitSUNIndex[a]."; SUNFIndex::usage = "SUNFIndex[a] is an SU(N) index in the fundamental representation. \ -If the argument is an integer SUNIndex[a] turns into ExplicitSUNFIndex[a]."; +If the argument is an integer, SUNFIndex[a] turns into ExplicitSUNFIndex[a]."; SUNN::usage = "SUNN denotes the number of colors. Trick[SUNDelta[a, a]] yields (SUNN^2 -1)."; SUNT::usage = "SUNT[a] is the SU(N) T^a generator in the fundamental representation. \ -The fundamental indices are implicit" +The fundamental indices are implicit." SUNTF::usage = "SUNTF[{a},i,j] is the SU(N) T^a_ij generator in the fundamental representation. \ -The fundamental indices i and j are explicit" +The fundamental indices i and j are explicit." Tf::usage = "Tf is a group constant (sometimes called TR, as in eq. (2.5.133) in T. Muta, \ @@ -527,18 +593,25 @@ denotes a quantum field of type ftype with (possible) \ This is concerns only typesetting in the TraditionalForm output and doesn't change \ the physical behavior of those objects." -Upper::usage = "Upper may be used inside LorentzIndex to indicate an \ -contravariant LorentzIndex."; +TypesettingExplicitLorentzIndex::usage = +"TypesettingExplicitLorentzIndex determines the TraditionalForm typesetting of \ +explicit Lorentz indices." Zeta2::usage = "Zeta2 denotes Zeta[2]. For convenience every Pi^2 occuring in \ OPEIntegrateDelta is replaced by (6 Zeta2)."; -$FCMomentumSubHeads::usage = "$FCMomentumSubHeads is a pattern that \ -contains Heads which may appear inside Momentum and need special treatment." +Zeta4::usage = +"Zeta4 denotes Zeta[4]"; -$FCLorentzIndexSubHeads::usage = "$FCLorentzIndexSubHeads is a pattern that \ -contains Heads which may appear inside LorentzIndex and need special treatment." +Zeta6::usage = +"Zeta6 denotes Zeta[6]"; + +Zeta8::usage = +"Zeta8 denotes Zeta[8]"; + +Zeta10::usage = +"Zeta10 denotes Zeta[10]"; DiracGamma::gamma5fail = "`1` is forbidden in FeynCalc. You should always use 4-dimensional Gamma^5 or chiral projectors. \ @@ -549,34 +622,260 @@ denotes a quantum field of type ftype with (possible) \ "DiracGamma[`1`] is forbidden in FeynCalc. If you want to specify an explicit Lorentz index, \ please use DiracGamma[ExplicitLorentzIndex[`1`]]. Evaluation aborted!"; +GA::noint = +"GA[`1`] is forbidden in FeynCalc. For consistency reasons, the only allowed integer \ +arguments can be 0, 1, 2, 3, 5, 6 and 7. Evaluation aborted!"; + +GAD::noint = +"GAD[`1`] is forbidden in FeynCalc. For consistency reasons, the only allowed integer \ +arguments can be 0, 1, 2 and 3. Evaluation aborted!"; + +GAE::noint = +"GAE[`1`] is forbidden in FeynCalc. For consistency reasons, the only allowed integer \ +arguments can be 0, 1, 2 and 3. Evaluation aborted!"; + +GS::noint = +"GS[`1`] is forbidden in FeynCalc. For consistency reasons, the only allowed integer \ +argument can be 0. Evaluation aborted!"; + +GSD::noint = +"GSD[`1`] is forbidden in FeynCalc. For consistency reasons, the only allowed integer \ +argument can be 0. Evaluation aborted!"; + +GSE::noint = +"GSE[`1`] is forbidden in FeynCalc. For consistency reasons, the only allowed integer \ +argument can be 0. Evaluation aborted!"; + Momentum::lorentzhead = "`1` is forbidden in FeynCalc. Momentum cannot be the head of a LorentzIndex!"; LorentzIndex::momentumhead = "`1` is forbidden in FeynCalc. LorentzIndex cannot be the head of a Momentum !"; +LorentzIndex::explicitlorentzhead = +"`1` is forbidden in FeynCalc. LorentzIndex cannot be the head of an ExplicitLorentzIndex!"; + +Pair::invalid = +"`1` does not represent a valid Pair object!"; + +CartesianPair::invalid = +"`1` does not represent a valid CartesianPair object!"; + +TemporalPair::invalid = +"`1` does not represent a valid TemporalPair object!"; + +SharedObjects::failmsg = +"Error! FeynCalc has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + +(* ------------------------------------------------------------------------ *) +(* New NR objects *) +(* ------------------------------------------------------------------------ *) + +CartesianIndex::usage = +"CartesianIndex is the head of Cartesian indices. \ +The internal representation of a three-dimensional i is \ +CartesianIndex[i]. For other than three dimensions: \ +CartesianIndex[i, Dimension]. \ +CartesianIndex[i, 3] simplifies to CartesianIndex[i]. \ +The first argument cannot be an integer."; + +CartesianMomentum::usage = +"CartesianMomentum is the head of a three momentum (p). \ +The internal representation of a three-dimensional p is \ +CartesianMomentum[p]. For other than three dimensions: CartesianMomentum[p, Dimension]. \n +CartesianMomentum[p, 3] simplifies to CartesianMomentum[p]."; + +CartesianPair::usage = +"CartesianPair[a , b] is a special pairing used in the internal \ +representation: a and b may have heads CartesianIndex or CartesianMomentum. \ +If both a and b have head CartesianIndex, the Kronecker delta is \ +understood. If a and b have head CartesianMomentum, a scalar product is \ +meant. If one of a and b has head CartesianIndex and the other \ +CartesianMomentum, a Cartesian vector (p^i) is understood."; + +TC::usage = +"TC[p] is the temporal component of a 4-vector and is transformed into \ +TemporalPair[TemporalMomentum[p], ExplicitLorentzIndex[0]] by FeynCalcInternal."; + +CV::usage = +"CV[p,i] is a 3-dimensional Cartesian vector and is transformed into \ +CartesianPair[CartesianMomentum[p], CartesianIndex[i]] by FeynCalcInternal."; + +CVD::usage = +"CVD[p,i] is a D-1-dimensional Cartesian vector and is transformed into \ +CartesianPair[CartesianMomentum[p,D], CartesianIndex[i,D]] by FeynCalcInternal."; + +CVE::usage = +"CVE[p,i] is a D-4-dimensional Cartesian vector and is transformed into \ +CartesianPair[CartesianMomentum[p,D-4], CartesianIndex[i,D-4]] by FeynCalcInternal."; + +KD::usage = +"KD[i,j] is the Kronecker delta in 3 dimensions."; + +KDD::usage = +"KDD[i,j] is the Kronecker delta in D-1 dimensions."; + +KDE::usage = +"KDE[i,j] is the Kronecker delta in D-4 dimensions."; + +CSP::usage = +"CSP[p,q] is the 3-dimensional scalar product of p with q and is \ +transformed into CartesianPair[CartesianMomentum[p],CartesianMomentum[q]] by FeynCalcInternal. \ +CSP[p] is the same as CSP[p,p] (=p^2)."; + +CSPD::usage = +"CSPD[p,q] is the D-1-dimensional scalar product of p with q and is \ +transformed into CartesianPair[CartesianMomentum[p, D-1],CartesianMomentum[q, D-1]] by FeynCalcInternal. \ +CSPD[p] is the same as CSPD[p,p] (=p^2)."; + +CSPE::usage = +"CSPE[p,q] is the D-4-dimensional scalar product of p with q and is \ +transformed into CartesianPair[CartesianMomentum[p, D-4],CartesianMomentum[q, D-4]] by FeynCalcInternal. \ +CSPE[p] is the same as CSPE[p,p] (=p^2)."; + +CLC::usage = +"CLC[m,n,r] evaluates to Eps[CartesianIndex[m], CartesianIndex[n], \ +CartesianIndex[r]] applying FeynCalcInternal. \ +CLC[m,...][p, ...] evaluates to Eps[CartesianIndex[m], ..., CartesianMomentum[p], ...] \ +applying FeynCalcInternal."; + +CLCD::usage = +"CLCD[m,n,r] evaluates to Eps[CartesianIndex[m, D-1], CartesianIndex[n, D-1], \ +CartesianIndex[r,D-1]] applying FeynCalcInternal. \ +CLC[m,...][p, ...] evaluates to Eps[CartesianIndex[m, D-1], ..., CartesianMomentum[p, D-1], ...] \ +applying FeynCalcInternal."; + +TGA::usage = +"TGA[] can be used as input for gamma^0 in 4 dimensions and is \ +transformed into DiracGamma[ExplicitLorentzIndex[0]] by FeynCalcInternal."; + +CGA::usage = +"CGA[i] can be used as input for gamma^i in 4 dimensions, where i is a Cartesian index, and is \ +transformed into DiracGamma[CartesianIndex[i]] by FeynCalcInternal."; + +CGAD::usage = +"CGAD[i] can be used as input for gamma^i in D dimensions, where i is a Cartesian index, and is \ +transformed into DiracGamma[CartesianIndex[i,D-1],D] by FeynCalcInternal."; + +CGAE::usage = +"CGAE[i] can be used as input for gamma^i in D-4 dimensions, where i is a Cartesian index, and is \ +transformed into DiracGamma[CartesianIndex[i,D-4],D-4] by FeynCalcInternal."; + +CGS::usage = +"CGS[p] is transformed into DiracGamma[CartesianMomentum[p]] by FeynCalcInternal. \ +CGS[p,q, ...] is equivalent to CGS[p].CGS[q]. ..."; + +CGSD::usage = +"CGSD[p] is transformed into DiracGamma[CartesianMomentum[p, D-1], D] by FeynCalcInternal. \ +CGSD[p,q, ...] is equivalent to CGSD[p].CGSD[q]. ..."; + +CGSE::usage = +"CGSE[p] is transformed into DiracGamma[CartesianMomentum[p, D-4], D-4] by FeynCalcInternal. \ +CGSE[p,q, ...] is equivalent to CGSE[p].CGSE[q]. ..."; + +SI::usage = +"SI[mu] can be used as input for 3-dimensional sigma^mu with 4-dimensional Lorentz +index mu and is transformed into PauliSigma[LorentzIndex[mu]] by FeynCalcInternal."; + +SID::usage = +"SID[mu] can be used as input for D-1-dimensional sigma^mu with D-dimensional Lorentz +index mu and is transformed into PauliSigma[LorentzIndex[mu,D],D-1] by FeynCalcInternal."; + +SIE::usage = +"SIE[mu] can be used as input for D-4-dimensional sigma^mu with D-4-dimensional Lorentz +index mu and is transformed into PauliSigma[LorentzIndex[mu,D-4],D-4] by FeynCalcInternal."; + +SIS::usage = +"SIS[p] can be used as input for 3-dimensional sigma^mu p_mu with 4-dimensional Lorentz +vector p and is transformed into PauliSigma[Momentum[p]] by FeynCalcInternal."; + +SISD::usage = +"SISD[p] can be used as input for D-1-dimensional sigma^mu p_mu with D-dimensional Lorentz +vector p and is transformed into PauliSigma[Momentum[p, D], D-1] by FeynCalcInternal."; + +SISE::usage = +"SISE[p] can be used as input for D-4-dimensional sigma^mu p_mu with D-4-dimensional Lorentz +vector p and is transformed into PauliSigma[Momentum[p, D-4], D-4] by FeynCalcInternal."; + +CSI::usage = +"CSI[i] can be used as input for 3-dimensional sigma^i with 3-dimensional Cartesian +index i and is transformed into PauliSigma[CartesianIndex[i]] by FeynCalcInternal."; + +CSID::usage = +"CSID[i] can be used as input for D-1-dimensional sigma^i with D-1-dimensional Cartesian +index i and is transformed into PauliSigma[CartesianIndex[i, D-1], D-1] by FeynCalcInternal."; + +CSIE::usage = +"CSIE[i] can be used as input for D-4-dimensional sigma^i with D-4-dimensional Cartesian +index i and is transformed into PauliSigma[CartesianIndex[i, D-4], D-4] by FeynCalcInternal."; + +CSIS::usage = +"CSIS[p] can be used as input for 3-dimensional sigma^i p_i with 3-dimensional Cartesian +vector p and is transformed into PauliSigma[CartesianMomentum[p]] by FeynCalcInternal."; + +CSISD::usage = +"CSISD[p] can be used as input for D-1-dimensional sigma^i p_i with D-1-dimensional Cartesian +vector p and is transformed into PauliSigma[CartesianMomentum[p, D-1], D-1] by FeynCalcInternal."; + +CSISE::usage = +"CSISE[p] can be used as input for D-4-dimensional sigma^i p_i with D-4-dimensional Cartesian +vector p and is transformed into PauliSigma[CartesianMomentum[p, D-4], D-4] by FeynCalcInternal."; + +PauliSigma::usage = +"PauliSigma[x,dim] is the internal representation of a Pauli matrix \ +with a Lorentz or Cartesian index or a contraction of a Pauli matrix and a Lorentz \ +or Cartesian vector. PauliSigma[x,3] simplifies to PauliSigma[x]."; + +PauliXi::usage = +"PauliXi[I] represents a two-component Pauli spinor \[Xi], while PauliXi[-I] stands for \ +\[Xi]^\[Dagger]."; + +PauliEta::usage = +"PauliEta[I] represents a two-component Pauli spinor \[Eta], while PauliEta[-I] stands for \ +\[Eta]^\[Dagger]."; + +TemporalMomentum::usage = +"TemporalMomentum[p] is the head of the temporal component of a four momentum p^0. \ +The internal representation of the temporal component p^0 is \ +TemporalMomentum[p]. TemporalMomentum may appear only inside TemporalPair."; + +TemporalPair::usage = +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]] is a special pairing used in the internal \ +representation to denote p^0, the temporal components of a four momentum p."; + + (* ------------------------------------------------------------------------ *) Begin["`Package`"] initialPairDownValues; +initialCartesianPairDownValues; +initialTemporalPairDownValues; initialSPDownValues; initialSPDDownValues; +initialSPEDownValues; +initialCSPDownValues; +initialCSPDDownValues; +initialCSPEDownValues; +initialTCDownValues; initialScalarProducts; +initialMomentumDownValues; +initialCartesianMomentumDownValues; +initialTemporalMomentumDownValues; + DiracHeadsList; SUNHeadsList; TensorArgsList; +NRStuff; +PauliHeadsList; +TrFeynCalcObjects; End[] Begin["`SharedObjects`Private`"] -DeclareNonCommutative[ChiralityProjector]; DeclareNonCommutative[DiracGamma]; -DeclareNonCommutative[DiracGammaT]; -DeclareNonCommutative[DiracMatrix]; DeclareNonCommutative[DiracSigma]; -DeclareNonCommutative[DiracSlash]; -DeclareNonCommutative[DiracSpinor]; DeclareNonCommutative[GA]; DeclareNonCommutative[GA5]; DeclareNonCommutative[GAD]; @@ -588,7 +887,7 @@ denotes a quantum field of type ftype with (possible) \ DeclareNonCommutative[LeftRightPartialD]; DeclareNonCommutative[LeftRightPartialD2]; DeclareNonCommutative[FCPartialD]; -DeclareNonCommutative[PauliSigma]; +DeclareNonCommutative[OPESum]; DeclareNonCommutative[QuantumField]; DeclareNonCommutative[RightPartialD]; DeclareNonCommutative[Spinor]; @@ -598,17 +897,35 @@ denotes a quantum field of type ftype with (possible) \ DeclareNonCommutative[SpinorVBar]; DeclareNonCommutative[SUNT]; +(* NRStuff *) +DeclareNonCommutative[PauliSigma]; +DeclareNonCommutative[PauliXi]; +DeclareNonCommutative[PauliEta]; +DeclareNonCommutative[TGA]; +DeclareNonCommutative[CGA]; +DeclareNonCommutative[CGAD]; +DeclareNonCommutative[CGAE]; +DeclareNonCommutative[CGS]; +DeclareNonCommutative[CGSD]; +DeclareNonCommutative[CGSE]; +DeclareNonCommutative[SI]; +DeclareNonCommutative[SID]; +DeclareNonCommutative[SIE] +DeclareNonCommutative[CSI]; +DeclareNonCommutative[CSID]; +DeclareNonCommutative[CSIE] + DeclareFCTensor[Pair]; DeclareFCTensor[Eps]; - -$FCLorentzIndexSubHeads = _Upper | _Lower; +(* NRStuff *) +DeclareFCTensor[CartesianPair]; $TypesettingDim4 = "_"; $TypesettingDimE = "^"; $TypesettingDimD = ""; +TypesettingExplicitLorentzIndex = Function[x,x]; DataType[Epsilon, PositiveNumber] = True; -$PairBrackets = False; Unprotect[Greater]; Greater[Re[Epsilon],-4] = True; @@ -621,14 +938,20 @@ denotes a quantum field of type ftype with (possible) \ Unprotect[Conjugate]; Conjugate[x_Pair] := (x /. - {Polarization[k_, a:Except[_?OptionQ], opts:OptionsPattern[]] :> - Polarization[k, Conjugate[a], opts]} ) /;!FreeQ[x, Polarization]; + {Polarization[k_, a:Except[_?OptionQ], o:OptionsPattern[]] :> + Polarization[k, Conjugate[a], o]} ) /;!FreeQ[x, Polarization]; Protect[Conjugate]; +SetAttributes[DIDelta, Orderless]; +SetAttributes[DiracIndexDelta, Orderless]; SetAttributes[ExplicitLorentzIndex, Constant]; +SetAttributes[ExplicitDiracIndex, Constant]; SetAttributes[ExplicitSUNIndex, {Constant, Flat, OneIdentity}]; SetAttributes[ExplicitSUNFIndex, {Constant, Flat, OneIdentity}]; SetAttributes[LorentzIndex, Constant]; +SetAttributes[KD, Orderless]; +SetAttributes[KDD, Orderless]; +SetAttributes[KDE, Orderless]; SetAttributes[MT, Orderless]; SetAttributes[MTD, Orderless]; SetAttributes[MTE, Orderless]; @@ -638,211 +961,374 @@ denotes a quantum field of type ftype with (possible) \ SetAttributes[SP, Orderless]; SetAttributes[SPE, Orderless]; SetAttributes[SPD, Orderless]; +SetAttributes[CSP, Orderless]; +SetAttributes[CSPE, Orderless]; +SetAttributes[CSPD, Orderless]; SetAttributes[SUND, Orderless]; SetAttributes[SUNDelta, Orderless]; SetAttributes[SUNFDelta, Orderless]; SetAttributes[SUNIndex, {Constant, Flat, OneIdentity}]; SetAttributes[SUNFIndex, {Constant, Flat, OneIdentity}]; - -Options[ChiralityProjector] = {FCI -> True}; -Options[DiracMatrix] = {Dimension -> 4, FCI -> True}; -Options[DiracSlash] = {Dimension -> 4, FCI -> True}; -Options[Eps] = {Dimension -> 4}; +(* NRStuff *) +SetAttributes[CartesianPair, Orderless]; +SetAttributes[TemporalPair, Orderless]; + +(* Here we define the default I*eta prescription to be -I*eta! + for Cartesian propagators *) +Options[CFAD] = {Dimension -> D-1, EtaSign -> -1}; +Options[GFAD] = {EtaSign -> 1}; Options[FAD] = {Dimension -> D}; Options[FCGV] = {SilentTypeSetting -> False, EvaluateFCGV -> False}; -Options[FourVector] = {Dimension -> 4, FCI -> True}; -Options[LeviCivita] = {Dimension -> 4, FCI->True}; -Options[MetricTensor] = {Dimension -> 4, FCI -> True}; +Options[SFAD] = {Dimension -> D, EtaSign -> 1}; Options[SUND] = {Explicit -> False}; Options[SUNF] = {Explicit -> False}; Options[Polarization] = {Transversality -> False}; -DiracHeadsList = {DiracGamma,DiracGammaT,Spinor,DiracSigma}; + +(* TODO Explicit syntax checks in the definitions of core objects are too expensive :( + Instead we should use a syntax checker function that will be applied to the given expression *) +DiracHeadsList = {DiracGamma,Spinor,DiracSigma,DiracChain, DiracIndexDelta, DiracTrace}; + +PauliHeadsList = {PauliSigma,PauliXi,PauliEta}; SUNHeadsList = {SUNT,SUNTF,SUNF,SUNIndex,SUNFIndex,SUNDelta,SUNN,CA,CF}; -TensorArgsList = {LorentzIndex, ExplicitLorentzIndex, Momentum}; +TrFeynCalcObjects = DiracGamma | DiracChain | GA | GAD | GAE | GS | GSD | GSE | Pair | CGA | CGAD | CGAE | CGS | CGSD | CGSE | DCHN; -CA /: - MakeBoxes[CA, TraditionalForm]:= - SubscriptBox["C", "A"]; -CF /: - MakeBoxes[CF, TraditionalForm]:= - SubscriptBox["C", "F"]; +TensorArgsList = { + LorentzIndex, ExplicitLorentzIndex, Momentum, + CartesianIndex, CartesianMomentum, TemporalMomentum +}; -AntiQuarkField /: - MakeBoxes[AntiQuarkField, TraditionalForm]:= - OverscriptBox["\[Psi]","_"]; +CHeadsList = { + CartesianIndex, CartesianMomentum, CartesianPair, TemporalMomentum, TemporalPair +}; -ChiralityProjector[1, OptionsPattern[]] := - DiracGamma[6]/; OptionValue[FCI]; -ChiralityProjector[-1, OptionsPattern[]] := - DiracGamma[7]/; OptionValue[FCI]; -ChiralityProjector /: - MakeBoxes[ChiralityProjector[1,OptionsPattern[]], TraditionalForm]:= - ToBoxes[DiracGamma[6],TraditionalForm]; +NRStuff={ + CartesianPair, CartesianMomentum, CartesianIndex, TemporalMomentum, TemporalPair, -ChiralityProjector /: - MakeBoxes[ChiralityProjector[-1,OptionsPattern[]], TraditionalForm]:= - ToBoxes[DiracGamma[7],TraditionalForm]; + CV, CVD, CVE, TC, + KD, KDD, KDE, + CSP, CSPD, CSPE, -(*Added 18 April 2001, Frederik Orellana*) -DeltaFunction[_?((NumericQ[#]===True&&(Positive[#]===True||Negative[#]===True))&)] := + CLC, CLCD, + CGA, CGAD, CGAE, TGA, + CGS, CGSD, CGSE, + + SI, SID, SIE, + SIS, SISD, SISE, + + CSI, CSID, CSIE, + CSIS, CSISD, CSISE +}; + +CSP/: + Set[CSP[a_, b_] , c_]:= + (CartesianScalarProduct[a,b,Dimension->3,SetDimensions->{3}]=c) + +CSP/: + Set[CSP[a_] , c_]:= + (CartesianScalarProduct[a,a,Dimension->3,SetDimensions->{3}]=c) + +CSPD/: + Set[CSPD[a_, b_] , c_]:= + (CartesianScalarProduct[a,b,Dimension->D-1,SetDimensions->{D-1}]=c) + +CSPD/: + Set[CSPD[a_] , c_]:= + (CartesianScalarProduct[a,a,Dimension->D-1,SetDimensions->{D-1}]=c) + +CSPE/: + Set[CSPE[a_, b_] , c_]:= + (CartesianScalarProduct[a,b,Dimension->D-4,SetDimensions->{D-4}]=c) + +CSPE/: + Set[CSPE[a_] , c_]:= + (CartesianScalarProduct[a,a,Dimension->D-4,SetDimensions->{D-4}]=c) + +CSP[0,_]:= 0; -DeltaFunction[0] := - 1; +CSPD[0,_]:= + 0; -DeltaFunction /: - MakeBoxes[ DeltaFunction[y_], TraditionalForm]:= - RowBox[{"\[Delta]", "(", TBox[y], ")"}]; +CSPE[0,_]:= + 0; -DeltaFunctionDoublePrime /: - MakeBoxes[ DeltaFunctionDoublePrime[y_], TraditionalForm]:= - RowBox[{SuperscriptBox["\[Delta]","\[DoublePrime]"], - "(", TBox[y], ")"}]; +CSP[a_] := + CSP[a,a]; -DeltaFunctionPrime /: - MakeBoxes[ DeltaFunctionPrime[y_], TraditionalForm]:= - RowBox[{SuperscriptBox["\[Delta]","\[Prime]"], - "(", TBox[y], ")"}]; +CSPD[a_] := + CSPD[a,a]; -DiracGamma /: - Transpose[DiracGamma[a__]]:= DiracGammaT[a]; +CSPE[a_] := + CSPE[a,a]; -DiracGamma[] = 1; +CV[0,_] := + 0; -DiracGamma[x_ (h: LorentzIndex|ExplicitLorentzIndex|Momentum)[p_, dim1_:4], dim2_:4] := - x DiracGamma[h[p, dim1], dim2]; +CVD[0,_] := + 0; -DiracGamma[(x: LorentzIndex|ExplicitLorentzIndex|Momentum)[y_, dim_:4], 4] := - DiracGamma[x[y,dim]]; +CVE[0,_] := + 0; -DiracGamma[x_Integer, ___] := - (Message[DiracGamma::noint, x]; Abort[])/; (x=!=0 && x=!=5 && x=!=6 && x=!=7); +CV[-a_Symbol,b_]:= + -CV[a,b]; -DiracGamma[(n:5|6|7), 4] := - DiracGamma[n]; +CVD[-a_Symbol,b_]:= + -CVD[a,b]; -DiracGamma[(n:5|6|7), dim_] := - Message[DiracGamma::gamma5fail, ToString[DiracGamma[ToString[n],ToString[dim]]]]; +CVE[-a_Symbol,b_]:= + -CVE[a,b]; + +TC[0] = + 0; + +CGA[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CGAD[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CGAE[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CGS[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CGSD[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CGSE[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CGA[x_, y__] := + DOT @@ Map[CGA,{x,y}]; + +CGAD[x_, y__] := + DOT @@ Map[CGAD,{x,y}]; + +CGAE[x_, y__] := + DOT @@ Map[CGAE,{x,y}]; + +CGS[x_, y__] := + DOT @@ Map[CGS,{x,y}]; + +CGSD[x_, y__] := + DOT @@ Map[CGSD,{x,y}]; + +CGSE[x_, y__] := + DOT @@ Map[CGSE,{x,y}]; + +CGS[0] = + 0; + +CGSD[0] = + 0; + +CGSE[0] = + 0; + +(* ------------------------------------------------------------------------ *) + +CSI[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CSID[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CSIE[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CSIS[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CSISD[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CSISE[_?NumberQ]:= + ( + Message[SharedObjects::failmsg, "Explicit indices are not supported inside Cartesian objects."]; + Abort[] + ); + +CSI[x_, y__] := + DOT @@ Map[CSI,{x,y}]; + +CSID[x_, y__] := + DOT @@ Map[CSID,{x,y}]; + +CSIE[x_, y__] := + DOT @@ Map[CSIE,{x,y}]; + +CSIS[x_, y__] := + DOT @@ Map[CSIS,{x,y}]; + +CSISD[x_, y__] := + DOT @@ Map[CSISD,{x,y}]; + +CSISE[x_, y__] := + DOT @@ Map[CSISE,{x,y}]; + +CSIS[0] = + 0; + +CSISD[0] = + 0; + +CSISE[0] = + 0; + +DeltaFunction[_?((NumericQ[#]===True&&(Positive[#]===True||Negative[#]===True))&)] := + 0; + +DeltaFunction[0] := + 1; + +(* ------------------------------------------------------------------------ *) DiracGamma[_, 0] := 0; -DiracGamma[0,___]:= +DiracGamma[0, ___]:= 0; +DiracGamma[x_,y_, z__]/; !MemberQ[{1, 2}, Length[{x,y,z}]] && FCPatternFreeQ[{x,y,z}] := + ( + Message[DiracGamma::argrx, "DiracGamma[" <> ToString[{x,y,z}] <> "]", Length[{x,y,z}], "1 or 2"]; + Abort[] + ); + + DiracGamma[a_Plus, dim_:4] := Map[DiracGamma[#,dim]&, a]; -DiracGamma[(h1:LorentzIndex|Momentum)[x_,dim1_:4], (h2:LorentzIndex|Momentum)[y_,dim2_:4]] := - DOT[DiracGamma[h1[x,dim1], dim1], - DiracGamma[h2[y,dim2], dim2]]; +DiracGamma[x_, 4] := + DiracGamma[x]; -DiracGamma[(h1:LorentzIndex|Momentum)[x_,dim1_:4], (h2:LorentzIndex|Momentum)[y_,dim2_:4], z__] := - DOT[DiracGamma[h1[x,dim1], dim1], - DiracGamma[h2[y,dim2], dim2], - DiracGamma[z]]; +DiracGamma[x_ (h:TemporalMomentum|CartesianMomentum|Momentum)[p_, dim1___], dim2___] := + x DiracGamma[h[p, dim1], dim2]; + +DiracGamma[(LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[_], _Symbol-4 ] := + 0; (* 4 or 3, D-4 *) -DiracGamma[(LorentzIndex|Momentum)[_], _Symbol-4 ] := - 0; (* 4, D-4 *) +DiracGamma[_TemporalMomentum, _Symbol-4]:= + 0; -DiracGamma[(LorentzIndex|Momentum)[_, _Symbol-4]] := - 0; (* 4, D-4 *) +DiracGamma[(LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[_, _Symbol-4]] := + 0; (* D-4, 4 *) -DiracGamma[(h:LorentzIndex|Momentum)[x_, dim_Symbol], dim_Symbol-4] := +DiracGamma[(h:LorentzIndex|ExplicitLorentzIndex|Momentum)[x_, dim_Symbol], dim_Symbol-4] := DiracGamma[h[x, dim-4], dim-4]; (* D, D-4 *) -DiracGamma[(h:LorentzIndex|Momentum)[x_, dim_Symbol-4], dim_Symbol] := +DiracGamma[(h:CartesianIndex|CartesianMomentum)[i_, dim_Symbol-1], dim_Symbol-4]:= + DiracGamma[h[i, dim-4], dim-4]; (* D, D-4 *) + +DiracGamma[(h:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[x_, dim_Symbol-4], dim_Symbol] := DiracGamma[h[x, dim-4], dim-4]; (* D-4, D *) -DiracGamma[(h:LorentzIndex|Momentum)[x_], _Symbol] := - DiracGamma[h[x]]; (* 4, D *) +DiracGamma[(h:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[x_], _Symbol] := + DiracGamma[h[x]]; (* 4 or 3, D *) -DiracGamma[(h:LorentzIndex|Momentum)[x_,_Symbol]] := +DiracGamma[(h:LorentzIndex|ExplicitLorentzIndex|Momentum)[x_,_Symbol]] := DiracGamma[h[x]]; (* D, 4 *) -(* Typesetting for Dirac slashes. *) -(* ------------------------------------------------------------------------ *) +DiracGamma[(h:CartesianIndex|CartesianMomentum)[i_,_Symbol -1]]:= + DiracGamma[h[i]]; (* D-1, 4 *) -dgammaRep[dim1_,dim2_] := - Which[ - dim1===4 && dim1===dim2, - OverscriptBox["\[Gamma]", $TypesettingDim4], - MatchQ[dim1,_Symbol] && dim1===dim2, - If[ $TypesettingDimD==="", - "\[Gamma]", - OverscriptBox["\[Gamma]", $TypesettingDimD] - ], - MatchQ[dim1,_Symbol-4] && dim1===dim2, - OverscriptBox["\[Gamma]", $TypesettingDimE], - True, - SubscriptBox["\[Gamma]", ToBoxes[dim1,TraditionalForm]] - ]; +DiracGamma[m_TemporalMomentum, _Symbol]:= + DiracGamma[m]; -DiracGamma /: - MakeBoxes[ DiracGamma[ Momentum[x_,dim1_:4],dim2_:4], TraditionalForm ]:= - If[ Head[x]===Plus, - RowBox[{dgammaRep[dim2,dim1], "\[CenterDot]","(", TBox[Momentum[x,dim1]],")"}], - RowBox[{dgammaRep[dim2,dim1], "\[CenterDot]", TBox[Momentum[x,dim1]]}] - ]/; !MatchQ[x,$FCMomentumSubHeads]; +DiracGamma[m_TemporalMomentum]:= + FeynCalc`Package`MetricT DiracGamma[ExplicitLorentzIndex[0]] TemporalPair[m, ExplicitLorentzIndex[0]]; +DiracGamma[x_ n_ /; DataType[n, FCVariable], dim_: 4] := + n DiracGamma[x, dim]; -(* Typesetting for Dirac matrices. *) -(* ------------------------------------------------------------------------ *) +(* Explicit indices and gamma^5*) -DiracGamma /: - MakeBoxes[ DiracGamma[(lo: LorentzIndex | ExplicitLorentzIndex)[in_, dim1_:4], dim2_:4], TraditionalForm ]:= - If[ $Covariant===False, - SuperscriptBox[RowBox[{dgammaRep[dim2,dim1]}], TBox[lo[in,dim1]]], - SubscriptBox[RowBox[{dgammaRep[dim2,dim1]}], TBox[lo[in,dim1]]] - ]/;!MatchQ[in,$FCLorentzIndexSubHeads]; - -DiracGamma /: - MakeBoxes[ DiracGamma[(lo: LorentzIndex | ExplicitLorentzIndex)[(in: Upper| Lower)[x_], - dim1_:4], dim2_:4], TraditionalForm ]:= - If[ in===Upper, - SuperscriptBox[RowBox[{dgammaRep[dim2,dim1]}], TBox[lo[in[x],dim1]]], - SubscriptBox[RowBox[{dgammaRep[dim2,dim1]}], TBox[lo[in[x],dim1]]] - ]/;!MatchQ[x,$FCLorentzIndexSubHeads]; - -DiracGamma /: - MakeBoxes[ DiracGamma[(a : (5 | 6 | 7))], TraditionalForm ]:= - SuperscriptBox[RowBox[{dgammaRep[4,4]}], TBox[a]]; - -(* Typesetting for transposed Dirac matrices. *) -(* ------------------------------------------------------------------------ *) +DiracGamma[x_?NumberQ, ___] := + (Message[DiracGamma::noint, x]; Abort[])/; (x=!=0 && x=!=5 && x=!=6 && x=!=7); + +DiracGamma[(n:5|6|7), _Symbol] := + DiracGamma[n]; + +DiracGamma[(5|6|7), _Symbol - 4] := + ( + Message[SharedObjects::failmsg, "D-4 dimensional g^5 or chiral projectors do not exist!"]; + Abort[] + ) + +(* Explicit Dirac indices *) -DiracGammaT /: - Transpose[DiracGammaT[a__]]:= DiracGamma[a]; +DiracChain[0,__]:= + 0; + +DiracChain[_,0]:= + 0; + +DiracChain[1, i_Spinor, j : (_DiracIndex | _ExplicitDiracIndex)]:= + DiracChain[i,j]; -DiracGammaT /: - MakeBoxes[DiracGammaT[a_,dim_:4], TraditionalForm]:= - SuperscriptBox[RowBox[{"(",ToBoxes[DiracGamma[a,dim],TraditionalForm],")"}],"T"]; +DiracChain[x_/;x=!=1, i_,j_]/; FreeQ2[{FCI[x]},DiracHeadsList] && FCPatternFreeQ[{x,i,j}]:= + x DiracChain[1, i,j]; -DiracMatrix[(a:5|6|7), opts:OptionsPattern[]] := - Message[DiracGamma::gamma5fail, ToString[DiracGamma[ToString[a],ToString[opts]]]]/; - OptionValue[Dimension]=!=4; +DiracChain[1, a_Spinor, b_Spinor]:= + DiracChain[a,b]; -DiracMatrix[(a:5|6|7), OptionsPattern[]] := - DiracGamma[a]/; OptionValue[FCI] && OptionValue[Dimension]===4; +DiracChain[a_?NumberQ b_DOT, i_, j_]:= + a DiracChain[b,i,j]; -DiracMatrix[(a:Except[5|6|7]), OptionsPattern[]] := - DiracGamma[LorentzIndex[a, OptionValue[Dimension]], - OptionValue[Dimension]]/; OptionValue[FCI] && Head[a]=!=DOT && !StringQ[a]; +DCHN[0,__]:= + 0; + +DCHN[_,0]:= + 0; -DiracMatrix[DOT[a_,b__], opts:OptionsPattern[]] := - DOT@@(DiracMatrix[#,opts]& /@ {a,b}); +DCHN[1,a_Spinor,b_Spinor]:= + DCHN[a,b]; -DiracMatrix[a_,b:Except[_?OptionQ].., opts:OptionsPattern[]] := - DOT@@(DiracMatrix[#,opts]& /@ {a,b}); -DiracMatrix /: - MakeBoxes[DiracMatrix[x_, opts:OptionsPattern[]], TraditionalForm]:= - ToBoxes[FCI[DiracMatrix[x,opts]],TraditionalForm]/; !OptionValue[{opts},FCI]; +DiracIndex[i_Integer] := + ExplicitDiracIndex[i]; + +(* ------------------------------------------------------------------------ *) DiracSigma[DOT[a_,b_]] := DiracSigma[a,b]; @@ -850,14 +1336,11 @@ denotes a quantum field of type ftype with (possible) \ DiracSigma[___, 0, ___] = 0; -DiracSigma[a_, b_] := - -DiracSigma[b, a] /; !OrderedQ[{a,b}]; - -DiracSigma[DiracMatrix[a_, b_]] := - -DiracSigma[DiracMatrix[b, a]] /; !OrderedQ[{a,b}]; +DiracSigma[a_, a_] := + 0/; FCPatternFreeQ[{a}]; -DiracSigma[DiracSlash[a_, b_]] := - -DiracSigma[DiracSlash[b, a]] /; !OrderedQ[{a,b}]; +DiracSigma[a_, b_] := + -DiracSigma[b, a] /; !OrderedQ[{a,b}] && FCPatternFreeQ[{a,b}]; DiracSigma[a_ DiracGamma[b__], c_. DiracGamma[d__]] := a c DiracSigma[DiracGamma[b], DiracGamma[d]]; @@ -865,81 +1348,73 @@ denotes a quantum field of type ftype with (possible) \ DiracSigma[a_. DiracGamma[b__], c_ DiracGamma[d__]] := a c DiracSigma[DiracGamma[b], DiracGamma[d]]; -DiracSigma /: - MakeBoxes[DiracSigma[(DiracGamma | DiracMatrix | DiracSlash | GA | GAD | GS | GSD)[x_,___], - (DiracGamma | DiracMatrix | DiracSlash | GA | GAD | GS | GSD)[y_,___]], TraditionalForm]:= - SuperscriptBox["\[Sigma]", TBox[x,y]]; - -DiracSlash[DOT[a_,b__], opts:OptionsPattern[]] := - DOT@@(DiracSlash[#,opts]& /@ {a,b}); +(* ------------------------------------------------------------------------ *) -DiracSlash[a_,b:Except[_?OptionQ].., opts:OptionsPattern[]] := - DOT@@(DiracSlash[#,opts]& /@ {a,b}); +Eps[___, 0, ___]:= + 0; -DiracSlash[a_, OptionsPattern[]] := - DiracGamma[Momentum[a, OptionValue[Dimension]], - OptionValue[Dimension]]/; OptionValue[FCI]; +Eps[x__] := + 0/; Signature[{x}]===0 && FCPatternFreeQ[{x}]; -DiracSlash /: - MakeBoxes[DiracSlash[x_, opts:OptionsPattern[]], TraditionalForm]:= - ToBoxes[FCI[DiracSlash[x,opts]],TraditionalForm]/; !OptionValue[{opts},FCI]; +Eps[x___, a:(CartesianMomentum|Momentum|LorentzIndex|CartesianIndex)[_,_Symbol-4], y___]:= + 0/; FCPatternFreeQ[{x,a,y}]; -DiracSpinor = Spinor; +Eps[x___, ExplicitLorentzIndex[0] | _TemporalMomentum, y___]:= + 0/; Length[{x,y}]===2; -Eps[x__, Dimension->4] := - Eps[x]/; OptionValue[Eps,Dimension]===4 && Length[{x}]===4; +Eps[(_CartesianMomentum | _CartesianIndex),(_CartesianMomentum | _CartesianIndex),(_CartesianMomentum | _CartesianIndex),(_CartesianMomentum | _CartesianIndex)]:= + 0; -Eps[x:Except[_?OptionQ] ..., opts:OptionsPattern[]]/; (Length[{x}] =!= 4) && (FreeQ2[{x,opts},{Pattern, -Blank,BlankSequence,BlankNullSequence}]) := - Message[Eps::argrx, "Eps["<>ToString[{x,opts}]<>"]", Length[{x}], 4]; +Eps[x__]/; !MemberQ[{3, 4}, Length[{x}]] && FCPatternFreeQ[{x}] := + ( + Message[Eps::argrx, "Eps[" <> ToString[{x}] <> "]", Length[{x}], "3 or 4"]; + Abort[] + ); -Eps[x__Symbol | x__FCGV, OptionsPattern[]] := - 0/; Signature[{x}]===0 && Length[{x}]===4; +Eps[x___, n_ a:( _Momentum| _CartesianMomentum),y___]:= + n Eps[x,a,y]; -Eps[a___, n1_. (LorentzIndex|ExplicitLorentzIndex|Momentum)[mu_,dim_:4], b___, - n2_. (LorentzIndex|ExplicitLorentzIndex|Momentum)[mu_,dim_:4], c___, OptionsPattern[]] := - 0 /; NumberQ[n1 n2] && - Length[{a,n1,b,n2,c}]===4; +Eps[x___, (h1:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[a_], y___, (h2:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[b_, _Symbol] ,z___]:= + Eps@@(Take[#,1]&/@{x,h1[a],y,h2[b],z})/; FCPatternFreeQ[{x,h1[a],y,h2[b],z}] && h1[a]=!=ExplicitLorentzIndex[0]; -Eps[x__] := - 0 /; ((!FreeQ[{x}, LorentzIndex[_,_Symbol -4]]) || (!FreeQ[{x}, Momentum[_,_Symbol -4]])) && - Length[{x}]===4; +Eps[x___, (h1:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[a_], y___, (h2:CartesianIndex|CartesianMomentum)[b_, _Symbol -1] ,z___]:= + Eps@@(Take[#,1]&/@{x,h1[a],y,h2[b],z})/; FCPatternFreeQ[{x,h1[a],y,h2[b],z}] && h1[a]=!=ExplicitLorentzIndex[0] ; -Eps[a___, (c: LorentzIndex | Momentum)[mu_,_Symbol], b:Except[_?OptionQ]..., opts:OptionsPattern[]] := - (Eps[a, c[mu], b, opts]) /; OptionValue[Dimension]===4 && Length[{a, c[mu], b}]===4; +Eps[x___, m_TemporalMomentum, y___]:= + TemporalPair[ExplicitLorentzIndex[0],m]Eps[x,ExplicitLorentzIndex[0],y]; -Eps /: - MakeBoxes[Eps[x__, OptionsPattern[]] ,TraditionalForm]:= - SuperscriptBox["\[Epsilon]", TBox[x]]/; - FreeQ2[{x}, Join[(List @@ ($FCLorentzIndexSubHeads /. Blank -> Identity)), - (List @@ ($FCMomentumSubHeads /. Blank -> Identity))]] && Length[{x}]===4; +Eps[x___, Momentum[p_], y___]:= + FeynCalc`Package`MetricS Eps[x,CartesianMomentum[p],y]/; Length[{x,y}]===2; -Epsilon /: - MakeBoxes[Epsilon, TraditionalForm]:= - TagBox["\[CurlyEpsilon]", TraditionalForm]; +Eps[x___, Momentum[p_, dim_Symbol], y___]:= + FeynCalc`Package`MetricS Eps[x,CartesianMomentum[p,dim-1],y]/; Length[{x,y}]===2; -EpsilonUV /: - MakeBoxes[EpsilonUV, TraditionalForm] := - SubscriptBox["\[CurlyEpsilon]", "UV"]; +(* Do not get confused, our $LeviCivitaSign is -eps^{0123} = eps^{1230}. This is why + it is correct to have $LeviCivitaSign and not -$LeviCivitaSign here. *) +Eps[x1 : (_Momentum | _CartesianMomentum | _CartesianIndex), + x2 : (_Momentum | _CartesianMomentum | _CartesianIndex), + x3 : (_Momentum | _CartesianMomentum | _CartesianIndex), ExplicitLorentzIndex[0]]:= + $LeviCivitaSign Eps[x1,x2,x3]; -EpsilonIR /: - MakeBoxes[EpsilonIR, TraditionalForm] := - SubscriptBox["\[CurlyEpsilon]", "IR"]; +Eps[ExplicitLorentzIndex[0], x1 : (_Momentum | _CartesianMomentum | _CartesianIndex), + x2 : (_Momentum | _CartesianMomentum | _CartesianIndex), + x3 : (_Momentum | _CartesianMomentum | _CartesianIndex)]:= + -$LeviCivitaSign Eps[x1,x2,x3]; ExplicitLorentzIndex[x_, 4] := ExplicitLorentzIndex[x, 4] = ExplicitLorentzIndex[x]; -ExplicitLorentzIndex /: - MakeBoxes[ ExplicitLorentzIndex[p_, dim_ : 4], TraditionalForm]:= - If[ $LorentzIndices =!= True, - ToBoxes[p,TraditionalForm], - SubscriptBox[ToBoxes[p, TraditionalForm], ToBoxes[dim, TraditionalForm]] - ]/; !MatchQ[p,$FCLorentzIndexSubHeads]; +ExplicitLorentzIndex[x: (1|2|3), dim_Symbol] := + ExplicitLorentzIndex[x, dim] = ExplicitLorentzIndex[x]; + +ExplicitLorentzIndex[x: (1|2|3), dim_Symbol-4] := + ExplicitLorentzIndex[x, dim-4] = 0; -ExplicitLorentzIndex /: - MakeBoxes[ ExplicitLorentzIndex[p_, dim_ : 4], TraditionalForm]:= - ToBoxes[ExplicitLorentzIndex[Identity@@p,dim], - TraditionalForm]/; MatchQ[p,$FCLorentzIndexSubHeads]; +ExplicitLorentzIndex[0, _Symbol]:= + ExplicitLorentzIndex[0]; + +ExplicitLorentzIndex[0, _Symbol-4]:= + 0; ExplicitSUNIndex/: SUNIndex[i_ExplicitSUNIndex]:= ExplicitSUNIndex[i]; @@ -947,26 +1422,6 @@ denotes a quantum field of type ftype with (possible) \ ExplicitSUNFIndex/: SUNFIndex[i_ExplicitSUNFIndex]:= ExplicitSUNFIndex[i]; -ExplicitSUNIndex /: - MakeBoxes[ ExplicitSUNIndex[p_], TraditionalForm]:= - ToBoxes[p, TraditionalForm]; - -ExplicitSUNFIndex /: - MakeBoxes[ ExplicitSUNFIndex[p_], TraditionalForm]:= - ToBoxes[p, TraditionalForm]; - -ff[{y_,z_}] := - SequenceForm["[",y^2, "-", z^2,"]"]; - -ff[{y_,0}] := - ff[y]; - -ff[{y_}] := - ff[y]; - -ff[y_/;Head[y]=!=List] := - SequenceForm["[",y^2,"]"]; - FAD[-p_, opts:OptionsPattern[]] := FAD[p,opts]; @@ -981,48 +1436,9 @@ denotes a quantum field of type ftype with (possible) \ FAD[{_,_,0}, OptionsPattern[]]:= 1; -FAD/: - MakeBoxes[FAD[a__,OptionsPattern[]], TraditionalForm]/; !MemberQ[{a},{_,_,_}]:= - ToBoxes[1/ (Apply[Dot,Map[ff, {a}]]/. Dot -> dootpow /. dootpow -> DOT), TraditionalForm]; - -FCGV /: MakeBoxes[FCGV[a_String, opts:OptionsPattern[]], TraditionalForm]/; OptionValue[FCGV,{opts},SilentTypeSetting] := - ToBoxes[a, TraditionalForm]; - FCGV[a_String, OptionsPattern[]] := ToExpression[a]/; OptionValue[EvaluateFCGV]; -FeynAmp /: - MakeBoxes[FeynAmp[q__Symbol, amp_], TraditionalForm ]:= - RowBox[Join[Map[RowBox[{"\[Integral]", - RowBox[{SuperscriptBox["\[DifferentialD]", "D"], - TBox[#]}]}] &, {q}], {"(", TBox[amp], ")"}]]; - -FeynAmp /: - MakeBoxes[FeynAmp[_[__], q__Symbol, amp_], TraditionalForm]:= - ToBoxes[FeynAmp[q,amp], TraditionalForm]; - - -FeynAmpDenominator[ar__List] := - FeynAmpDenominator[ar] = FCI[FAD[ar]]; - -MakeBoxes[f_. FeynAmpDenominator[a__], TraditionalForm ] := - ((MakeBoxes[#,TraditionalForm]&)@@{f/ Apply[DOT, Map[( #[[1]]^2 - - #[[2]]^2)&, {a}]]}); - -FourVector[a_,b_, OptionsPattern[]] := - Pair[Momentum[a, OptionValue[Dimension]], - LorentzIndex[b, OptionValue[Dimension]]]/; OptionValue[FCI]; - -FourVector /: - MakeBoxes[FourVector[a_,b_, opts:OptionsPattern[]], TraditionalForm]:= - ToBoxes[FCI[FourVector[a,b,opts]],TraditionalForm]/; !OptionValue[{opts},FCI]; - -FV[p_ /; Head[p]=!=Momentum, Momentum[b_]] := - SP[p,b]; - -FV[Momentum[p_], Momentum[b_]] := - SP[p,b]; - FV[0,_] := 0; @@ -1032,40 +1448,35 @@ denotes a quantum field of type ftype with (possible) \ FVE[0,_] := 0; -(* Typesetting for vectors in the FCE notation. *) -(* ------------------------------------------------------------------------ *) +FV[-a_Symbol,b_]:= + -FV[a,b]; -FV /: - MakeBoxes[FV[a_, b_], TraditionalForm]:= - ToBoxes[FCI[FV[a,b]], TraditionalForm]; +FVD[-a_Symbol,b_]:= + -FVD[a,b]; -MakeBoxes[Power[FV[a_, b_], n_], TraditionalForm] := - ToBoxes[Power[FCI[FV[a, b]], n], TraditionalForm]; +FVE[-a_Symbol,b_]:= + -FVE[a,b]; -FVD /: - MakeBoxes[FVD[a_, b_], TraditionalForm]:= - ToBoxes[FCI[FVD[a,b]], TraditionalForm]; - -MakeBoxes[Power[FVD[a_, b_], n_], TraditionalForm] := - ToBoxes[Power[FCI[FVD[a, b]], n], TraditionalForm]; +GA5 = + DiracGamma[5]; -FVE /: - MakeBoxes[FVE[a_, b_], TraditionalForm]:= - ToBoxes[FCI[FVE[a,b]], TraditionalForm]; +GA[x_?NumberQ] := + (Message[GA::noint, x]; Abort[])/; !MemberQ[{0, 1, 2, 3, 5, 6, 7}, x]; -MakeBoxes[Power[FVE[a_, b_], n_], TraditionalForm] := - ToBoxes[Power[FCI[FVE[a, b]], n], TraditionalForm]; +GAD[x_?NumberQ] := + (Message[GAD::noint, x]; Abort[])/; !MemberQ[{0, 1, 2, 3, 5, 6, 7}, x]; -(* ------------------------------------------------------------------------ *) - -GA5 = - DiracGamma[5]; +GAE[x_?NumberQ] := + (Message[GAE::noint, x]; Abort[])/; !MemberQ[{0, 1, 2, 3, 5, 6, 7}, x]; GAD[(n:5|6|7)] := - Message[DiracGamma::gamma5fail, ToString[GAD[ToString[n]]]]; + GA[n]; -GAE[(n:5|6|7)] := - Message[DiracGamma::gamma5fail, ToString[GAE[ToString[n]]]]; +GAE[(5|6|7)] := + ( + Message[SharedObjects::failmsg, "D-4 dimensional g^5 or chiral projectors do not exist!"]; + Abort[] + ) GA[DOT[x_,y__]] := Map[GA,DOT[x,y]]; @@ -1085,35 +1496,23 @@ denotes a quantum field of type ftype with (possible) \ GAE[x_, y__] := DOT @@ Map[GAE,{x,y}]; -(* TraditionalForm of the Dirac matrices in the FCE notation *) -(* ------------------------------------------------------------------------ *) - -GA /: - MakeBoxes[ GA[x_], TraditionalForm ]:= ToBoxes[FCI[GA[x]], TraditionalForm]; - -GAD /: - MakeBoxes[ GAD[x_], TraditionalForm ]:= ToBoxes[FCI[GAD[x]], TraditionalForm]; - -GAE /: - MakeBoxes[ GAE[x_], TraditionalForm ]:= ToBoxes[FCI[GAE[x]], TraditionalForm]; +GS[0] := + 0; -(* ------------------------------------------------------------------------ *) +GSD[0] := + 0; -GaugeField /: - MakeBoxes[GaugeField, TraditionalForm]:= - "A"; +GSE[0] := + 0; -GaugeXi /: - MakeBoxes[GaugeXi[a_], TraditionalForm]:= - SubscriptBox["\[Xi]", TBox[a]]; +GS[x_?NumberQ] := + (Message[GS::noint, x]; Abort[])/; x=!=0; -GaugeXi /: - MakeBoxes[GaugeXi, TraditionalForm]:= - TagBox["\[Xi]", TraditionalForm] +GSD[x_?NumberQ] := + (Message[GSD::noint, x]; Abort[])/; x=!=0; -GluonField /: - MakeBoxes[GluonField, TraditionalForm]:= - "A"; +GSE[x_?NumberQ] := + (Message[GSE::noint, x]; Abort[])/; x=!=0; GS[DOT[x_,y__]] := Map[GS,DOT[x,y]]; @@ -1133,72 +1532,20 @@ denotes a quantum field of type ftype with (possible) \ GSE[x_, y__] := DOT @@ Map[GSE, {x, y}]; - -(* TraditionalForm typesetting of the Dirac slashes in the FCE notation. *) -(* ------------------------------------------------------------------------ *) - -GS/: - MakeBoxes[GS[a_], TraditionalForm ]:= - ToBoxes[FCI[GS[a]], TraditionalForm]; - -GSD/: - MakeBoxes[GSD[a_], TraditionalForm ]:= - ToBoxes[FCI[GSD[a]], TraditionalForm]; - -GSE/: - MakeBoxes[GSE[a_], TraditionalForm ]:= - ToBoxes[FCI[GSE[a]], TraditionalForm]; - (* ------------------------------------------------------------------------ *) -IFPD[Momentum[OPEDelta,___],0] := - 0; - -IFPD /: - MakeBoxes[IFPD[a_,c_], TraditionalForm]:= - If[ c === 0, - TBox[a^2], - TBox["(", a^2," - ", c^2, ")"] - ]; - -Integratedx /: - MakeBoxes[Integratedx[x_, low_, up_], TraditionalForm]:= - RowBox[{SubsuperscriptBox["\[Integral]", TBox[low], - TBox[up]], "\[DifferentialD]", - MakeBoxes[TraditionalForm[x]], "\[VeryThinSpace]" }]; - -LC[x___][y___]/; (Length[{x,y}] =!= 4) && (FreeQ2[{x,y},{Pattern, - Blank,BlankSequence,BlankNullSequence}]) := +LC[x___][y___]/; (Length[{x,y}] =!= 4) && (FCPatternFreeQ[{x,y}]) := Message[LC::argrx, "LC["<>ToString[{x}]<>"]["<>ToString[{y}]<>"]", Length[{x,y}], 4]; -LCD[x___][y___]/; (Length[{x,y}] =!= 4) && (FreeQ2[{x,y},{Pattern, - Blank,BlankSequence,BlankNullSequence}]) := +LCD[x___][y___]/; (Length[{x,y}] =!= 4) && (FCPatternFreeQ[{x,y}]) := Message[LCD::argrx, "LCD["<>ToString[{x}]<>"]["<>ToString[{y}]<>"]", Length[{x,y}], 4]; -LC[x___]/; (Length[{x}] > 4) && (FreeQ2[{x},{Pattern, -Blank,BlankSequence,BlankNullSequence}]) := +LC[x___]/; (Length[{x}] > 4) && (FCPatternFreeQ[{x}]) := Message[LC::argrx, "LC["<>ToString[{x}]<>"]", Length[{x}], 4]; -LCD[x___]/; (Length[{x}] > 4) && (FreeQ2[{x},{Pattern, -Blank,BlankSequence,BlankNullSequence}]) := +LCD[x___]/; (Length[{x}] > 4) && (FCPatternFreeQ[{x}]) := Message[LCD::argrx, "LCD["<>ToString[{x}]<>"]", Length[{x}], 4]; -LC/: - MakeBoxes[LC[x___][y___] ,TraditionalForm]:= - ToBoxes[FCI[LC[x][y]],TraditionalForm]/; Length[{x,y}]===4; - -LC/: - MakeBoxes[LC[x__] ,TraditionalForm]:= - ToBoxes[FCI[LC[x]],TraditionalForm]/; Length[{x}]===4; - -LCD /: - MakeBoxes[LCD [x___][y___] ,TraditionalForm]:= - ToBoxes[FCI[LCD[x][y]],TraditionalForm]/; Length[{x,y}]===4; - -LCD /: - MakeBoxes[LCD [x__] ,TraditionalForm]:= - ToBoxes[FCI[LCD[x]],TraditionalForm]/; Length[{x}]===4; - LeftPartialD[x__] := LeftPartialD @@ (LorentzIndex /@ {x}) /;FreeQ2[{x}, {LorentzIndex, Momentum, OPEDelta, RowBox, @@ -1217,19 +1564,9 @@ denotes a quantum field of type ftype with (possible) \ DOT @@ Map[LeftPartialD, {x, y}]; (* Here one must use named blanks, since otherwise DotSimplify - is not able to convert this into rules... *) -Commutator[RightPartialD[x_], LeftPartialD[y_]] = - 0; - -LeftPartialD/: - MakeBoxes[LeftPartialD[x_ ^n_],TraditionalForm]:= - SubsuperscriptBox[RowBox[{OverscriptBox["\[PartialD]", - "\[LeftArrow]"]}], TBox[" ",x],TBox[n]] /; Head[x] === Momentum; - -LeftPartialD /: - MakeBoxes[LeftPartialD[x_], TraditionalForm]:= - SubscriptBox[OverscriptBox["\[PartialD]", - "\[LeftArrow]"], TBox[x]]; + is not able to convert this into rules. But I also don't want + WWB to complain about unused variables here. So... *) +ToExpression["Commutator[RightPartialD[x_], LeftPartialD[y_]] = 0;"] LeftRightPartialD[xx__] := LeftRightPartialD@@ (LorentzIndex /@ {xx}) /; @@ -1247,11 +1584,6 @@ denotes a quantum field of type ftype with (possible) \ LeftRightPartialD[x_Momentum, y__Momentum] := DOT @@ Map[LeftRightPartialD, {x, y}]; -LeftRightPartialD /: - MakeBoxes[LeftRightPartialD[x_] , TraditionalForm]:= - SubscriptBox[OverscriptBox["\[PartialD]", - "\[LeftRightArrow]"], TBox[x]]; - LeftRightPartialD2[xx__] := LeftRightPartialD2@@ (LorentzIndex /@ {xx}) /; FreeQ2[{xx}, {LorentzIndex, Momentum, OPEDelta, RowBox, @@ -1271,38 +1603,8 @@ denotes a quantum field of type ftype with (possible) \ LeftRightPartialD2[Momentum[OPEDelta]^n_Integer?Positive] := DOT @@ Map[LeftRightPartialD2, Table[Momentum[OPEDelta],{n}]]; -LeftRightPartialD2 /: - MakeBoxes[LeftRightPartialD2[x_], TraditionalForm]:= - ToBoxes[LeftRightPartialD[x],TraditionalForm]; - -LeviCivita[x:Except[_?OptionQ].., opts:OptionsPattern[LeviCivita]][y:Except[_?OptionQ].., - opts:OptionsPattern[LeviCivita]]/; (Length[{x,y}] =!= 4) && (FreeQ2[{x,y,opts},{Pattern, - Blank,BlankSequence,BlankNullSequence}]) := - Message[LeviCivita::argrx, "LeviCivita["<>ToString[{x,opts}]<>"]["<>ToString[{y,opts}]<>"]", Length[{x,y}], 4]; - -LeviCivita[x:Except[_?OptionQ] ..., opts:OptionsPattern[]]/; (Length[{x}] > 4) && (FreeQ2[{x,opts},{Pattern, -Blank,BlankSequence,BlankNullSequence}]) := - Message[LeviCivita::argrx, "LeviCivita["<>ToString[{x,opts}]<>"]", Length[{x}], 4]; - -LeviCivita[ a:Except[_?OptionQ].., opts:OptionsPattern[]] := - FCI[LeviCivita[a,Join[{FCI->False},FilterRules[{opts},Except[FCI]]]]]/; Length[{a}] === 4 && OptionValue[FCI]; - -LeviCivita[x:Except[_?OptionQ]..., opts1:OptionsPattern[LeviCivita]][y:Except[_?OptionQ]..., opts2:OptionsPattern[LeviCivita]] := - FCI[LeviCivita[x,Join[{FCI->False},FilterRules[{opts1},Except[FCI]]]][y,Join[{FCI->False},FilterRules[{opts2},Except[FCI]]]]]/; - Length[{x,y}] === 4 && OptionValue[LeviCivita,{opts1},FCI] && OptionValue[LeviCivita,{opts2},FCI]; - -LeviCivita /: - MakeBoxes[LeviCivita[(a:Except[_?OptionQ]..)/; Length[{a}] === 4, opts:OptionsPattern[LeviCivita]/;!OptionValue[LeviCivita,{opts},FCI]], - TraditionalForm]:= - ToBoxes[FCI[LeviCivita[a,Join[{FCI->False},FilterRules[{opts},Except[FCI]]]]],TraditionalForm]; - -LeviCivita /: - MakeBoxes[LeviCivita[x:Except[_?OptionQ]..., - opts1:OptionsPattern[LeviCivita]][y:Except[_?OptionQ]..., - opts2:OptionsPattern[LeviCivita]], TraditionalForm]:= - ToBoxes[FCI[LeviCivita[x,Join[{FCI->False},FilterRules[{opts1},Except[FCI]]]][y,Join[{FCI->False},FilterRules[{opts2},Except[FCI]]]]],TraditionalForm]/; - Length[{x,y}] === 4 && !OptionValue[LeviCivita,{opts1,opts2},FCI]; - +Li4 = + PolyLog[4,#]&; Li3 = PolyLog[3,#]&; Li2 = @@ -1312,7 +1614,11 @@ denotes a quantum field of type ftype with (possible) \ (Message[LorentzIndex::momentumhead,ToString[LorentzIndex[FCGV["Momentum"][x],dim],InputForm]]; LorentzIndex[FCGV["Momentum"][x],dim]); -(* expanded because of CreateFCAmp's strange results ... *) +LorentzIndex[ExplicitLorentzIndex[x_], dim_:4]:= + (Message[LorentzIndex::explicitlorentzhead,ToString[LorentzIndex[FCGV["ExplicitLorentzIndex"][x],dim],InputForm]]; + LorentzIndex[FCGV["ExplicitLorentzIndex"][x],dim]); + +(* To allow things like FVD[p,LorentzIndex[mu,D]] ... *) LorentzIndex[LorentzIndex[in_, dim_ :4], dim_ :4] := LorentzIndex[in,dim]; @@ -1325,33 +1631,15 @@ denotes a quantum field of type ftype with (possible) \ LorentzIndex[in_Integer?NonNegative,dim_ :4] := ExplicitLorentzIndex[in,dim]; -LorentzIndex /: - MakeBoxes[ LorentzIndex[p_, dim_ : 4], TraditionalForm]:= - If[ $LorentzIndices =!= True, - ToBoxes[p,TraditionalForm], - SubscriptBox[ToBoxes[p, TraditionalForm], - ToBoxes[dim, TraditionalForm]] - ]/; !MatchQ[p,$FCLorentzIndexSubHeads]; - -LorentzIndex /: - MakeBoxes[ LorentzIndex[p_, dim_ : 4], TraditionalForm]:= - ToBoxes[LorentzIndex[Identity@@p,dim], - TraditionalForm]/; MatchQ[p,$FCLorentzIndexSubHeads]; - -MetricTensor[a_, b_, OptionsPattern[]] := - Pair[LorentzIndex[a, OptionValue[Dimension]], - LorentzIndex[b, OptionValue[Dimension]]]/; OptionValue[FCI]; - -MetricTensor /: - MakeBoxes[MetricTensor[a_, b_, opts:OptionsPattern[]], TraditionalForm]:= - ToBoxes[FCI[MetricTensor[a,b,opts]], TraditionalForm]/; !OptionValue[{opts},FCI]; - Momentum[x_ GaugeXi[y_], dim_:4] := GaugeXi[y] Momentum[x,dim]; Momentum[x_ n_?NumberQ, dim_ :4] := n Momentum[x, dim]; +Momentum[x_ n_/;DataType[n,FCVariable], dim_ :4] := + n Momentum[x, dim]; + Momentum[x:Except[_Pattern], 4] := Momentum[x, 4] = Momentum[x]; @@ -1370,82 +1658,10 @@ denotes a quantum field of type ftype with (possible) \ Momentum[x, dim1], Momentum[x, {dim1,dim2}] ]; -(* Typesetting for momenta. *) -(* ------------------------------------------------------------------------ *) - -momentumRep[p_,dim_] := - Which[ - dim===4, - OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDim4], - MatchQ[dim,_Symbol], - If[ $TypesettingDimD==="", - ToBoxes[p,TraditionalForm], - OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDimD] - ], - MatchQ[dim,_Symbol-4], - OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDimE], - True, - SubscriptBox[ToBoxes[p,TraditionalForm], ToBoxes[dim,TraditionalForm]] - ]; - -Momentum /: - MakeBoxes[ Momentum[Polarization[a_, b:Except[_?OptionQ],OptionsPattern[]], dim_:4], - TraditionalForm ]:= - RowBox[{polarizationRep[b,dim],"(",TBox[a],")"}]/; !MatchQ[a, $FCMomentumSubHeads]; - -Momentum /: - MakeBoxes[ Momentum[ OPEDelta, _:4 ], TraditionalForm]:= - TBox[OPEDelta]; - -Momentum /: - MakeBoxes[ Momentum[p:Except[_Subscript | _Superscript | _Plus],dim_:4], TraditionalForm]:= - momentumRep[p,dim]/; p=!=OPEDelta && !MatchQ[p,$FCMomentumSubHeads]; - -Momentum /: - MakeBoxes[Momentum[(p:Subscript|Superscript)[x_,y_], dim_: 4], TraditionalForm] := - If[ p===Subscript, - SubscriptBox[TBox[Momentum[x, dim]], ToBoxes[y,TraditionalForm]], - SuperscriptBox[TBox[Momentum[x, dim]], ToBoxes[y,TraditionalForm]] - ]; - -Momentum /: - MakeBoxes[ Momentum[p_Plus,dim_: 4], TraditionalForm]:= - TBox[MomentumExpand[Momentum[p,dim]]]/; FreeQ2[p,$FCMomentumSubHeads]; - -(* ------------------------------------------------------------------------ *) - -MT[Momentum[a_], Momentum[b_]] := - SP[a,b]; - -MT[Momentum[a_, D], Momentum[b_, D]] := - SPD[a,b]; - -MT[Momentum[a_, D-4], Momentum[b_, D-4]] := - SPE[a,b]; - -MT /: - MakeBoxes[ MT[x_,y_], TraditionalForm ]:= - ToBoxes[FCI[MT[x,y]], TraditionalForm]; - -MTE /: - MakeBoxes[ MTE[x_,y_], TraditionalForm ]:= - ToBoxes[FCI[MTE[x,y]], TraditionalForm]; - -MTD /: - MakeBoxes[ MTD[x_,y_], TraditionalForm ]:= - ToBoxes[FCI[MTD[x,y]], TraditionalForm]; - -Nf /: - MakeBoxes[Nf, TraditionalForm]:= - SubscriptBox["N", "f"]; OPE /: OPE^_Integer?Positive := 0; -OPE /: - MakeBoxes[OPE, TraditionalForm]:= - "\[CapitalOmega]" - Pair[0,_] := 0; @@ -1467,8 +1683,7 @@ denotes a quantum field of type ftype with (possible) \ scalar product where one momentum lives in D and the other in 4 dimensions. *) -Pair[(a : LorentzIndex | Momentum)[x_, _Symbol], - (b : LorentzIndex | Momentum)[y_]] := +Pair[(a : LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, _Symbol], (b : LorentzIndex | ExplicitLorentzIndex | Momentum | CartesianIndex | CartesianMomentum)[y_]] := Pair[a[x], b[y]]; (* A momentum vector with 4 components and the Lorentz index in @@ -1477,8 +1692,7 @@ denotes a quantum field of type ftype with (possible) \ in D-4 dimensions and for a scalar product where one momentum lives in 4 and the other in D-4 dimensions. *) -Pair[(LorentzIndex | Momentum)[_, _Symbol-4], - (LorentzIndex | Momentum)[_]] := +Pair[(LorentzIndex | Momentum | CartesianIndex | CartesianMomentum)[_, _Symbol-4], (LorentzIndex | ExplicitLorentzIndex | Momentum | CartesianIndex | CartesianMomentum)[_]] := 0; (* A momentum vector with D components and the Lorentz index in @@ -1488,247 +1702,86 @@ denotes a quantum field of type ftype with (possible) \ product where one momentum lives in D and the other in D-4 dimensions. *) -Pair[(a : LorentzIndex | Momentum)[x_, dim_Symbol], - (b : LorentzIndex | Momentum)[y_, dim_Symbol-4]] := +Pair[(a : LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, dim_Symbol], (b : LorentzIndex | ExplicitLorentzIndex | Momentum | CartesianIndex | CartesianMomentum)[y_, dim_Symbol-4]] := Pair[a[x, dim-4], b[y, dim-4]]; +Pair[(a : LorentzIndex | ExplicitLorentzIndex | Momentum | CartesianIndex | CartesianMomentum)[x_], CartesianIndex[y_, _Symbol-1]] := + Pair[a[x], CartesianIndex[y]]; +Pair[(a : LorentzIndex | ExplicitLorentzIndex | Momentum)[x_, dim_Symbol-4], (h: CartesianIndex | CartesianMomentum)[y_, dim_Symbol-1]] := + Pair[a[x,dim-4], h[y,dim-4]]; -Pair[Momentum[x_, ___], Momentum[Polarization[x_, y:Except[_?OptionQ]..., - OptionsPattern[Polarization]],___]] := - 0/; OptionValue[Polarization,Transversality]; -Pair[Momentum[x_,___], Momentum[Polarization[_?NumberQ x_, - y:Except[_?OptionQ]..., OptionsPattern[Polarization]],___]] := - 0/; OptionValue[Polarization,Transversality]; +Pair[Momentum[x_, ___], Momentum[Polarization[x_, y:Except[_?OptionQ]..., OptionsPattern[Polarization]],___]] := + 0/; OptionValue[Polarization,Transversality] && !OptionQ[{y}]; -(* Typesetting for the metric tensor. *) -(* ------------------------------------------------------------------------ *) +Pair[Momentum[x_,___], Momentum[Polarization[_?NumberQ x_, y:Except[_?OptionQ]..., OptionsPattern[Polarization]],___]] := + 0/; OptionValue[Polarization,Transversality] && !OptionQ[{y}]; -metricRep[dim_] := - Which[ - dim==={4,4}, - OverscriptBox["g", $TypesettingDim4], - MatchQ[dim,{_Symbol,_Symbol}] && dim[[1]]===dim[[2]], - If[ $TypesettingDimD==="", - "g", - OverscriptBox["g", $TypesettingDimD] - ], - MatchQ[dim,{_Symbol-4, _Symbol-4}] && dim[[1]]===dim[[2]], - OverscriptBox["g", $TypesettingDimE], - True, - SubscriptBox["g", ToBoxes[dim,TraditionalForm]] - ]; +Pair[ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]]:= + FeynCalc`Package`MetricT; +Pair[ExplicitLorentzIndex[0], Momentum[p_]]:= + TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]; -Pair /: - MakeBoxes[Pair[ (LorentzIndex|ExplicitLorentzIndex)[(a : Upper | Lower)[x_], dim1_:4], - (LorentzIndex|ExplicitLorentzIndex)[(b : Upper | Lower)[y_], dim2_:4]], - TraditionalForm]:= - Which[ - a===Upper && b===Upper, - SuperscriptBox[RowBox[{metricRep[{dim1,dim2}]}], - TBox[LorentzIndex[a[x],dim1], LorentzIndex[b[y],dim2]]], - a===Lower && b===Lower, - SubscriptBox[RowBox[{metricRep[{dim1,dim2}]}], - TBox[LorentzIndex[a[x],dim1], LorentzIndex[b[y],dim2]] ], - a===Lower && b===Upper, - SubsuperscriptBox[RowBox[{metricRep[{dim1,dim2}]}], - TBox[LorentzIndex[a[x],dim1]], TBox[LorentzIndex[b[y],dim2]] ], - a===Upper && b===Lower, - SubsuperscriptBox[RowBox[{metricRep[{dim1,dim2}]}], - TBox[LorentzIndex[b[y],dim2]], TBox[LorentzIndex[a[x],dim1]] ] - ]; +(* g^0i is zero by definition *) +Pair[ExplicitLorentzIndex[0], _CartesianIndex]:= + 0; -Pair /: - MakeBoxes[Pair[(LorentzIndex|ExplicitLorentzIndex)[a_, dim1_:4], - (LorentzIndex|ExplicitLorentzIndex)[b_, dim2_:4] ], TraditionalForm]:= - If[ $Covariant===False, - ToBoxes[Pair[LorentzIndex[Upper[a],dim1],LorentzIndex[Upper[b],dim2]],TraditionalForm], - ToBoxes[Pair[LorentzIndex[Lower[a],dim1],LorentzIndex[Lower[b],dim2]],TraditionalForm] - ]/; !MatchQ[a, $FCLorentzIndexSubHeads] && !MatchQ[b, $FCLorentzIndexSubHeads]; +Pair[ExplicitLorentzIndex[0], _CartesianMomentum]:= + 0; -(* Typesetting for scalar products. *) -(* ------------------------------------------------------------------------ *) +Pair[i_CartesianIndex, j_CartesianIndex]:= + FeynCalc`Package`MetricS CartesianPair[i, j]; -MakeBoxes[Pair[c1_. Momentum[a_, dim1_ : 4], c2_.Momentum[b_, dim2_ : 4]]^n_Integer?Positive, - TraditionalForm] := - If[ $PairBrackets === True, - RowBox[{SuperscriptBox[TBox[Pair[c1 Momentum[a,dim1],c2 Momentum[b,dim2]]],n]}], - RowBox[{SuperscriptBox[TBox["(",Pair[c1 Momentum[a,dim1],c2 Momentum[b,dim2]],")"],n]}] - ] /; a=!=b; - -Pair /: - MakeBoxes[Pair[c_. Momentum[a_, dim_ : 4],c_. Momentum[a_, dim_ : 4]], - TraditionalForm]:= - If[ Head[a]===Plus, - RowBox[{SuperscriptBox[TBox["(",c Momentum[a,dim],")"],2]}], - SuperscriptBox[TBox[c Momentum[a,dim]],2] - ]; - -MakeBoxes[Power[Pair[c_. Momentum[a_, dim_ : 4], c_. Momentum[a_, dim_ : 4]],n_Integer?Positive], -TraditionalForm] := - If[ Head[a]===Plus, - RowBox[{SuperscriptBox[TBox["(",c Momentum[a,dim],")"],2 n]}], - SuperscriptBox[TBox[c Momentum[a,dim]],2 n] - ]; +Pair[CartesianIndex[i_], Momentum[p_]]:= + CartesianPair[CartesianIndex[i], CartesianMomentum[p]]; -Pair /: - MakeBoxes[Pair[c1_. Momentum[a_, dim1_ : 4]+a1_:0, c2_. Momentum[b_, dim2_ : 4]+b1_:0],TraditionalForm]:= - Block[ { m1 = MomentumExpand[c1 Momentum[a,dim1]+a1], - m2 = MomentumExpand[c2 Momentum[b,dim2]+b1]}, - Which[ - Head[m1]=!=Plus && Head[m2]=!=Plus, - If[ $PairBrackets === True && (m1)=!=(m2), - TBox["(", m1, "\[CenterDot]", m2, ")"], - TBox[m1, "\[CenterDot]", m2] - ], - Head[m1]=!=Plus && Head[m2]===Plus, - If[ $PairBrackets === True && (m1)=!=(m2), - TBox["(",m1,"\[CenterDot]", "(",m2,")",")"], - TBox[m1,"\[CenterDot]", "(",m2,")"] - ], - Head[m1]===Plus && Head[m2]=!=Plus, - If[ $PairBrackets === True && (m1)=!=(m2), - TBox["(","(",m1,")","\[CenterDot]", m2,")"], - TBox["(",m1,")","\[CenterDot]", m2] - ], - Head[m1]===Plus && Head[m2]===Plus, - If[ $PairBrackets === True && (m1)=!=(m2), - TBox["(","(",m1,")","\[CenterDot]", "(",m2,")",")"], - TBox["(",m1,")","\[CenterDot]", "(",m2,")"] - ] - ] - ]/; !MatchQ[a,$FCMomentumSubHeads] && !MatchQ[b,$FCMomentumSubHeads]; - -(* Typesetting for polarization vectors. *) -(* ------------------------------------------------------------------------ *) +Pair[CartesianIndex[i_, dim_Symbol-4], Momentum[p_, dim_Symbol-4]]:= + CartesianPair[CartesianIndex[i,dim-4], CartesianMomentum[p,dim-4]]; -polarizationRep[pol_,dim_] := - Which[ - pol===Complex[0,1] && dim===4, - OverscriptBox["\[CurlyEpsilon]", $TypesettingDim4], - pol===Complex[0,1] && MatchQ[dim,_Symbol], - If[ $TypesettingDimD==="", - ToBoxes["\[CurlyEpsilon]",TraditionalForm], - OverscriptBox["\[CurlyEpsilon]", $TypesettingDimD] - ], - pol===Complex[0,1] && MatchQ[dim,_Symbol-4], - OverscriptBox["\[CurlyEpsilon]", $TypesettingDimE], - pol===Complex[0,-1] && dim===4, - SuperscriptBox[OverscriptBox["\[CurlyEpsilon]", $TypesettingDim4],"*"], - pol===Complex[0,-1] && MatchQ[dim,_Symbol], - If[ $TypesettingDimD==="", - SuperscriptBox[ToBoxes["\[CurlyEpsilon]",TraditionalForm],"*"], - SuperscriptBox[OverscriptBox["\[CurlyEpsilon]", $TypesettingDimD],"*"] - ], - pol===Complex[0,-1] && MatchQ[dim,_Symbol-4], - SuperscriptBox[OverscriptBox["\[CurlyEpsilon]", $TypesettingDimE],"*"], - True, - SuperscriptBox["\[CurlyEpsilon]", TBox[pol,dim]] - ]; +Pair[CartesianIndex[i_, dim_Symbol-1], Momentum[p_, dim_Symbol]]:= + CartesianPair[CartesianIndex[i,dim-1], CartesianMomentum[p,dim-1]]; -Pair /: - MakeBoxes[Pair[ - (LorentzIndex| - ExplicitLorentzIndex)[(x: Upper | Lower)[a_], dim_ : 4], - Momentum[Polarization[b_, c:Except[_?OptionQ], OptionsPattern[]], dim_: 4]], TraditionalForm]:= - If[ x===Upper, - RowBox[{SuperscriptBox[polarizationRep[c,dim], TBox[LorentzIndex[x[a]]]], "(",TBox[b],")"}], - RowBox[{SubscriptBox[polarizationRep[c,dim], TBox[LorentzIndex[x[a]]]], "(",TBox[b],")"}] - ]; /!MatchQ[a,$FCLorentzIndexSubHeads] && !MatchQ[b,$FCMomentumSubHeads]; - -Pair /: - MakeBoxes[Pair[ - (l : LorentzIndex| - ExplicitLorentzIndex)[a_, dim_ : 4], - Momentum[Polarization[b_, c_, opts:OptionsPattern[]], dim_: 4]], TraditionalForm]:= - If[ $Covariant===False, - ToBoxes[Pair[l[Upper[a],dim],Momentum[Polarization[b, c, opts],dim]],TraditionalForm], - ToBoxes[Pair[l[Lower[a],dim],Momentum[Polarization[b, c, opts],dim]],TraditionalForm] - ]/; !MatchQ[a,$FCLorentzIndexSubHeads] && !MatchQ[b,$FCMomentumSubHeads]; - -(* Typesetting for momentum vectors. *) -(* ------------------------------------------------------------------------ *) +Pair[i_CartesianIndex, p_CartesianMomentum]:= + FeynCalc`Package`MetricS CartesianPair[i, p]; -Pair /: - MakeBoxes[Pair[(LorentzIndex| ExplicitLorentzIndex)[(x: Upper | Lower)[a_],dim1_ : 4], - Momentum[b_ ,dim2_ : 4]+c_:0], TraditionalForm]:= - If[ Head[b]===Plus || c=!=0, - If[ x===Upper, - SuperscriptBox[ RowBox[{"(",TBox[Momentum[b+c,dim1]],")"}], TBox[LorentzIndex[x[a],dim2]]], - SubscriptBox[ RowBox[{"(",TBox[Momentum[b+c,dim1]],")"}], TBox[LorentzIndex[x[a],dim2]]] - ], - If[ x===Upper, - SuperscriptBox[ RowBox[{TBox[Momentum[b+c,dim1]]}], TBox[LorentzIndex[x[a],dim2]]], - SubscriptBox[ RowBox[{TBox[Momentum[b+c,dim1]]}], TBox[LorentzIndex[x[a],dim2]]] - ] - ]/; !MatchQ[a,$FCLorentzIndexSubHeads] && - !MatchQ[b,Flatten[_Polarization | $FCMomentumSubHeads]] && - FreeQ2[b, List @@ ($FCMomentumSubHeads /. Blank -> Identity)]; - -Pair /: - MakeBoxes[Pair[(LorentzIndex| ExplicitLorentzIndex)[a_, dim1_ : 4], - Momentum[b_, dim2_ : 4]+c_:0], TraditionalForm]:= - If[ $Covariant===False, - ToBoxes[Pair[LorentzIndex[Upper[a],dim1],Momentum[b,dim2]+c],TraditionalForm], - ToBoxes[Pair[LorentzIndex[Lower[a],dim1],Momentum[b,dim2]+c],TraditionalForm] - ]/; (!MatchQ[a,$FCLorentzIndexSubHeads] && !MatchQ[b,Flatten[_Polarization | $FCMomentumSubHeads]]); - -MakeBoxes[Power[Pair[(h : LorentzIndex | ExplicitLorentzIndex)[a___], b_Momentum + c_: 0], n_], TraditionalForm] := - SuperscriptBox[RowBox[{"(", ToBoxes[Pair[h[a], b + c], TraditionalForm], ")"}],ToBoxes[n]]; +Pair[p_CartesianMomentum, q_CartesianMomentum]:= + FeynCalc`Package`MetricS CartesianPair[p, q]; -(* ------------------------------------------------------------------------ *) +Pair[Momentum[q_], CartesianMomentum[p_]]:= + CartesianPair[CartesianMomentum[q], CartesianMomentum[p]]; -FCPartialD[x__] := - FCPartialD@@(LorentzIndex /@ {x})/; - FreeQ2[{x},{LorentzIndex, Momentum, OPEDelta, - RowBox, Pattern, Blank}] && (Union[{x}]=!={1}); +Pair[Momentum[q_, dim_Symbol-4], CartesianMomentum[p_, dim_Symbol-4]]:= + CartesianPair[CartesianMomentum[q,dim-4], CartesianMomentum[p,dim-4]]; -FCPartialD[(1)..] = 1; -FCPartialD[c:OPEDelta..] := - FCPartialD @@ (Momentum /@ {c}); -FCPartialD[x_LorentzIndex, y__LorentzIndex] := - DOT @@ Map[FCPartialD, {x, y}]; -FCPartialD[x_Momentum, y__Momentum] := - DOT @@ Map[FCPartialD, {x, y}]; +Pair[Momentum[q_, dim_Symbol], CartesianMomentum[p_, dim_Symbol-1]]:= + CartesianPair[CartesianMomentum[q,dim-1], CartesianMomentum[p,dim-1]]; -FCPartialD /: - MakeBoxes[FCPartialD[x_ ^n_], TraditionalForm]:= - SubsuperscriptBox["\[PartialD]", TBox[x], - TBox[n]] /; Head[x] === Momentum; +Pair[p_Momentum, q_CartesianMomentum]:= + CartesianPair[p, q]; -FCPartialD /: - MakeBoxes[ FCPartialD[x_], TraditionalForm]:= - SubscriptBox["\[PartialD]", ToBoxes[x,TraditionalForm]]; -FCPartialD /: - MakeBoxes[ FCPartialD[x_, LorentzIndex[mu__]], TraditionalForm]:= - RowBox[{"\[PartialD]", "/", "\[PartialD]", SuperscriptBox[ToBoxes[x,TraditionalForm], - ToBoxes[LorentzIndex[mu],TraditionalForm]]}]; +FCPartialD[x__] := + FCPartialD@@(LorentzIndex /@ {x})/; FreeQ2[{x},{LorentzIndex, Momentum, OPEDelta, RowBox, Pattern, Blank}] && (Union[{x}]=!={1}); -PauliSigma[1] = - { {0, 1}, {1,0} }; +FCPartialD[(1)..] = + 1; -PauliSigma[2] = - { {0,-I}, {I,0} }; +FCPartialD[c:OPEDelta..] := + FCPartialD @@ (Momentum /@ {c}); -PauliSigma[3] = - { {1, 0}, {0,-1}}; +FCPartialD[x_LorentzIndex, y__LorentzIndex] := + DOT @@ Map[FCPartialD, {x, y}]; -PauliSigma[] = - {PauliSigma[1], PauliSigma[2], PauliSigma[3]}; +FCPartialD[x_Momentum, y__Momentum] := + DOT @@ Map[FCPartialD, {x, y}]; PlusDistribution[Log[x_ (1-x_)]/(1-x_)] := Log[x] /(1-x) + PlusDistribution[Log[1-x]/(1-x)]; -PlusDistribution /: - MakeBoxes[PlusDistribution[ a_ ], TraditionalForm]:= - SubscriptBox[RowBox[{"(", MakeBoxes[a, - TraditionalForm],")"}],"+"]; - (* by convention *) -Polarization[k_, opts:OptionsPattern[]] /; FreeQ[k,Blank|BlankSequence|BlankNullSequence] := +Polarization[k_, opts:OptionsPattern[]] /; FCPatternFreeQ[{k}] := Polarization[k,Flatten[Join[FilterRules[Options[Polarization],Except[{opts}]],{opts}]]] = Polarization[k, I, opts]; Polarization[-x_, I, opts:OptionsPattern[]] := @@ -1736,11 +1789,7 @@ denotes a quantum field of type ftype with (possible) \ Polarization[-x_,-I, opts:OptionsPattern[]] := -Polarization[x,-I, opts]; -(* -Polarization /: - MakeBoxes[Polarization[a_, b:Except[_?OptionQ], OptionsPattern[]], TraditionalForm]:= - RowBox[{polarizationRep[b,4],"(",TBox[a],")"}]/; !MatchQ[a, $FCMomentumSubHeads]; -*) + PolarizationVector[x_,{y_,z_}] := PolarizationVector[x, y, z]; @@ -1754,38 +1803,25 @@ denotes a quantum field of type ftype with (possible) \ AtomQ[{x}[[1]]] || Head[{x}[[-1]]===SUNIndex]); -fourv[x__] := - FCI[FourVector[x]]; - polVec[Polarization[k__], mu_, opts:OptionsPattern[]] := - fourv[Polarization[k, opts], mu, Dimension -> 4 ]; - + Pair[Momentum[Polarization[k, opts]], LorentzIndex[mu]]; polVec[Polarization[k__],mu_, glu_, opts:OptionsPattern[]] := - fourv[Polarization[k, I, SUNIndex[glu/.SUNIndex->Identity], - opts], mu, Dimension->4 ]; + Pair[Momentum[Polarization[k, I, SUNIndex[glu], opts]], LorentzIndex[mu]]; polVec[k_,mu_ , opts:OptionsPattern[]] := - fourv[Polarization[k, I, opts], mu, Dimension->4 ]; + Pair[Momentum[Polarization[k, I, opts]], LorentzIndex[mu]]; polVec[k_,mu_,glu_, opts:OptionsPattern[]] := If[ FreeQ[glu, Blank], - fourv[Polarization[k, I, SUNIndex[glu/.SUNIndex->Identity],opts], mu, Dimension->4 ], - fourv[Polarization[k, I, glu], mu, Dimension -> 4] + Pair[Momentum[Polarization[k, I, SUNIndex[glu/.SUNIndex->Identity],opts]], LorentzIndex[mu]], + Pair[Momentum[Polarization[k, I, glu]], LorentzIndex[mu]] ]; -PropagatorDenominator[a_ /; FreeQ2[a, {BlankNullSequence,Pattern}] - ] := +PropagatorDenominator[a_ /; FCPatternFreeQ[{a}]] := PropagatorDenominator[a, 0]; -PropagatorDenominator/: - MakeBoxes[PropagatorDenominator[a_, 0], TraditionalForm]:= - ToBoxes[1/a^2, TraditionalForm]; - -MakeBoxes[f_. PropagatorDenominator[a_, b_/;b=!=0], TraditionalForm] := - ToBoxes[f/(a^2-b^2), TraditionalForm]; - PD = PropagatorDenominator; lori[OPEDelta] := @@ -1806,107 +1842,11 @@ denotes a quantum field of type ftype with (possible) \ QuantumField[f1_QuantumField] := f1; -QuantumField /: - MakeBoxes[ QuantumField[a_/;Head[a]=!=FCPartialD][p_], TraditionalForm]:= - TBox[a,"(",p,")"]; - -QuantumField /: - MakeBoxes[ QuantumField[a_/;Head[a]=!=FCPartialD], TraditionalForm]:= - TBox[a]; - -QuantumField /: - MakeBoxes[ QuantumField[f_/;Head[f]=!=FCPartialD, (LorentzIndex|ExplicitLorentzIndex|Momentum)[mu_,_:4]], TraditionalForm]:= - SubscriptBox[TBox[f], TBox[mu]]; - -QuantumField /: - MakeBoxes[QuantumField[f_/;Head[f]=!=FCPartialD, lori : (LorentzIndex | ExplicitLorentzIndex | Momentum)[_, _ : 4]..., - otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___], TraditionalForm] := - If[ {lori}=!={}, - SubsuperscriptBox[TBox[f], TBox[lori], TBox[otherIndices1, otherIndices2]], - SuperscriptBox[TBox[f], TBox[otherIndices1, otherIndices2]] - ]; - -QuantumField /: - MakeBoxes[ QuantumField[f_/;Head[f]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex| Momentum)[_,_ : 4]..., - otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___][p_], - TraditionalForm]:= - If[ {lori}=!={}, - RowBox[{SubsuperscriptBox[TBox[f], TBox[lori], TBox[otherIndices1, otherIndices2]], "(", TBox[p], ")"}], - RowBox[{SuperscriptBox[TBox[f], TBox[otherIndices1, otherIndices2]], "(", TBox[p], ")"}] - ]; - -QuantumField /: - MakeBoxes[ QuantumField[FCPartialD[pa_], a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex| Momentum)[_,_ : 4]..., - otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___], TraditionalForm]:= - If[ {lori}=!={}, - RowBox[{SubscriptBox["(\[PartialD]", TBox[pa]], SubsuperscriptBox[TBox[a], TBox[lori], TBox[otherIndices1, otherIndices2]],")"}], - RowBox[{SubscriptBox["(\[PartialD]", TBox[pa]], SuperscriptBox[TBox[a], TBox[otherIndices1, otherIndices2]],")"}] - ]; - -QuantumField /: - MakeBoxes[ QuantumField[FCPartialD[pa_], a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex| Momentum)[_,_ : 4]...], TraditionalForm]:= - If[ {lori}=!={}, - RowBox[{SubscriptBox["(\[PartialD]", TBox[pa]], SubscriptBox[TBox[a], TBox[lori]],")"}], - RowBox[{SubscriptBox["(\[PartialD]", TBox[pa]], TBox[a],")"}] - ]; - - -QuantumField /: - MakeBoxes[ QuantumField[FCPartialD[pa_]^m_, a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex| Momentum)[_,_ : 4]..., - otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___], - TraditionalForm]:= - If[ {lori}=!={}, - RowBox[{"(",SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]], SubsuperscriptBox[TBox[a], TBox[lori], TBox[otherIndices1, otherIndices2]],")"}], - RowBox[{"(",SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]], SuperscriptBox[TBox[a], TBox[otherIndices1, otherIndices2]],")"}] - ]; - -QuantumField /: - MakeBoxes[ QuantumField[FCPartialD[pa_]^m_, a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex | Momentum)[_,_ : 4]...], - TraditionalForm]:= - If[ {lori}=!={}, - RowBox[{"(",SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]], SubscriptBox[TBox[a], TBox[lori]],")"}], - RowBox[{"(",SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]],TBox[a],")"}] - ]; - -QuantumField /: - MakeBoxes[ QuantumField[pa__FCPartialD, a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex | Momentum)[_,_ : 4]...], - TraditionalForm]:= - If[ {lori}=!={}, - RowBox[{"(",TBox[pa], SubscriptBox[TBox[a], TBox[lori]],")"}], - RowBox[{"(",TBox[pa], TBox[a],")"}] - ]; - -QuantumField /: - MakeBoxes[ QuantumField[pa__FCPartialD, a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex | Momentum)[_,_ : 4]..., - otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___], TraditionalForm]:= - If[ {lori}=!={}, - RowBox[{"(",TBox[pa], SubsuperscriptBox[TBox[a], TBox[lori], TBox[otherIndices1, otherIndices2]],")"}], - RowBox[{"(",TBox[pa], SuperscriptBox[TBox[a], TBox[otherIndices1, otherIndices2]],")"}] - ]; - - - -QuarkField /: - MakeBoxes[QuarkField, TraditionalForm]:= "\[Psi]"; - -QuarkFieldPsi /: - MakeBoxes[QuarkFieldPsi, TraditionalForm]:= "\[Psi]"; - -QuarkFieldChi /: - MakeBoxes[QuarkFieldChi, TraditionalForm]:= "\[Chi]"; - -QuarkFieldPsiDagger /: - MakeBoxes[QuarkFieldPsiDagger, TraditionalForm]:= SuperscriptBox["\[Psi]","\[Dagger]"]; - -QuarkFieldChiDagger /: - MakeBoxes[QuarkFieldChiDagger, TraditionalForm]:= SuperscriptBox["\[Chi]","\[Dagger]"]; - RightPartialD[xx__] := - RightPartialD @@ (LorentzIndex /@ {xx}) /; - FreeQ2[{xx}, {LorentzIndex, Momentum, OPEDelta, RowBox, - Pattern, Blank}] && (Union[{xx}]=!={1}); + RightPartialD @@ (LorentzIndex /@ {xx}) /; FreeQ2[{xx}, {LorentzIndex, Momentum, OPEDelta, RowBox, Pattern, Blank}] && (Union[{xx}]=!={1}); -RightPartialD[(1)..] = 1; +RightPartialD[(1)..] = + 1; RightPartialD[c:OPEDelta..] := RightPartialD @@ (Momentum /@ {c}); @@ -1917,40 +1857,32 @@ denotes a quantum field of type ftype with (possible) \ RightPartialD[x_Momentum, y__Momentum] := DOT @@ Map[RightPartialD, {x, y}]; +SI[x_, y__] := + DOT @@ Map[SI,{x,y}]; -RightPartialD /: - MakeBoxes[RightPartialD[x_ ^n_],TraditionalForm]:= - SubsuperscriptBox[RowBox[{OverscriptBox["\[PartialD]", - "\[RightArrow]"]}], TBox[" ",x],TBox[n]] /; Head[x] === Momentum; +SID[x_, y__] := + DOT @@ Map[SID,{x,y}]; -RightPartialD /: - MakeBoxes[RightPartialD[x_] ,TraditionalForm]:= - SubscriptBox[RowBox[{OverscriptBox["\[PartialD]", - "\[RightArrow]"]}], TBox[x]]; +SIE[x_, y__] := + DOT @@ Map[SIE,{x,y}]; -ScaleMu /: - MakeBoxes[ScaleMu, TraditionalForm]:= - "\[Mu]"; +SIS[x_, y__] := + DOT @@ Map[SIS,{x,y}]; -Tf /: - MakeBoxes[Tf, TraditionalForm]:= - SubscriptBox["T","f"]; +SISD[x_, y__] := + DOT @@ Map[SISD,{x,y}]; -SD /: - MakeBoxes[SD[a_, b_], TraditionalForm]:= - SuperscriptBox["\[Delta]", TBox[a,b]]; +SISE[x_, y__] := + DOT @@ Map[SISE,{x,y}]; -SDF /: - MakeBoxes[SDF[a_, b_], TraditionalForm]:= - SubscriptBox["\[Delta]", TBox[a,b]]; +SIS[0] = + 0; -SmallDelta /: - MakeBoxes[SmallDelta, TraditionalForm]:= - "\[Delta]"; +SISD[0] = + 0; -SmallEpsilon /: - MakeBoxes[SmallEpsilon, TraditionalForm]:= - "\[Epsilon]"; +SISE[0] = + 0; SmallVariable[0] = 0; @@ -1958,26 +1890,6 @@ denotes a quantum field of type ftype with (possible) \ SmallVariable[x_^pow_] := SmallVariable[x]^pow; -SmallVariable /: - MakeBoxes[SmallVariable[a_], TraditionalForm]:= - MakeBoxes[a, TraditionalForm]; - -SO /: - MakeBoxes[SO[x_],TraditionalForm]:= - If[ Head[x] =!= Plus, - TBox["\[CapitalDelta]", "\[CenterDot]", x], - TBox["\[CapitalDelta]", "\[CenterDot]", "(",x,")"] - ]; - - -SOD /: - MakeBoxes[SOD[x_],TraditionalForm]:= - If[ Head[x] =!= Plus, - TBox["\[CapitalDelta]", "\[CenterDot]",x], - TBox["\[CapitalDelta]", "\[CenterDot]", "(",x,")"] - ]; - - SP/: Set[SP[a_, b_] , c_]:= (ScalarProduct[a,b,Dimension->4,SetDimensions->{4}]=c) @@ -2013,123 +1925,53 @@ denotes a quantum field of type ftype with (possible) \ SP[a_] := SP[a,a]; + SPD[a_] := SPD[a,a]; + SPE[a_] := SPE[a,a]; - -(* Typesetting for scalar products in the FCE notation. *) -(* ------------------------------------------------------------------------ *) - -SP /: - MakeBoxes[SP[a_, b_], TraditionalForm]:= - ToBoxes[FCI[SP[a,b]], TraditionalForm]; - -SPD /: - MakeBoxes[SPD[a_, b_], TraditionalForm]:= - ToBoxes[FCI[SPD[a,b]], TraditionalForm]; - -SPE /: - MakeBoxes[SPE[a_, b_], TraditionalForm]:= - ToBoxes[FCI[SPE[a,b]], TraditionalForm]; - -(* ------------------------------------------------------------------------ *) - HoldPattern[Spinor[a__,{1}]] := Spinor[a]; -frp[y___] := - FreeQ2[{y}, {Pattern, Blank,BlankSequence, BlankNullSequence,HoldForm}]; - -Spinor[n_. x_/; (frp[x]&&FreeQ[x, Momentum]), y___/;frp[y]] := +Spinor[n_. x_/; (FCPatternFreeQ[{x}]&&FreeQ2[x, {Momentum, Hold, HoldForm}]), y___/;FCPatternFreeQ[{y}]] := (Spinor[n x, y] = Spinor[n Momentum[x], y]) /; - (frp[{n, x, y}] && (n^2)===1); - + (FCPatternFreeQ[{n, x, y}] && (n^2)===1); +(* Spinor[kk_.+ n_. Momentum[ a_Plus, dim_ : 4], m_, y___] := Spinor[kk+ n Momentum[a, dim], m, y] = (Spinor[MomentumExpand[kk + n Momentum[a, dim]] ,m,y] ); +*) Spinor[p_ , _. SmallVariable[_], in___] := - Spinor[p, 0, in] /; frp[p]; + Spinor[p, 0, in]/; FCPatternFreeQ[{p}]; Spinor[p_ ] := - Spinor[p,0,1] /; frp[p]; + Spinor[p,0,1]/; FCPatternFreeQ[{p}]; Spinor[p_, m_ /; FreeQ[m, Pattern]] := - Spinor[p, m, 1] /; frp[p]; - -Spinor /: - MakeBoxes[Spinor[p_,0,___], TraditionalForm]:= - TBox["\[CurlyPhi]","(",p,")"]; -Spinor /: - MakeBoxes[Spinor[p_,m_ /; m=!=0,___], TraditionalForm]:= - TBox["\[CurlyPhi]","(",p, ",", m, ")"]; - -SpinorU /: - MakeBoxes[SpinorU[p_], TraditionalForm]:= - TBox["u","(",p,")"]; -SpinorU /: - MakeBoxes[SpinorU[p_,m_,___], TraditionalForm]:= - TBox["u","(",p,",",m,")"]; -SpinorU /: - MakeBoxes[SpinorU[p_,0,___], TraditionalForm]:= - TBox["u","(",p,")"]; -SpinorUBar /: - MakeBoxes[SpinorUBar[p_], TraditionalForm]:= - RowBox[{OverscriptBox["u", "_"],"(",TBox[p],")"}]; -SpinorUBar /: - MakeBoxes[SpinorUBar[p_,m_,___], TraditionalForm]:= - RowBox[{OverscriptBox["u", "_"],"(",TBox[p],",",TBox[m],")"}]; -SpinorUBar /: - MakeBoxes[SpinorUBar[p_,0,___], TraditionalForm]:= - RowBox[{OverscriptBox["u", "_"],"(",TBox[p],")"}]; -SpinorV /: - MakeBoxes[SpinorV[p__], TraditionalForm]:= - TBox["v","(",p,")"]; -SpinorV /: - MakeBoxes[SpinorV[p_,m_,___], TraditionalForm]:= - TBox["v","(",p,",",m,")"]; -SpinorV /: - MakeBoxes[SpinorV[p_,0,___], TraditionalForm]:= - TBox["v","(",p,")"]; -SpinorVBar /: - MakeBoxes[SpinorVBar[p__], TraditionalForm]:= - RowBox[{OverscriptBox["v", "_"],"(",TBox[p],")"}]; -SpinorVBar /: - MakeBoxes[SpinorVBar[p_,m_,___], TraditionalForm]:= - RowBox[{OverscriptBox["v", "_"],"(",TBox[p],",",TBox[m],")"}]; -SpinorVBar /: - MakeBoxes[SpinorVBar[p_,0,___], TraditionalForm]:= - RowBox[{OverscriptBox["v", "_"],"(",TBox[p],")"}]; + Spinor[p, m, 1]/; FCPatternFreeQ[{p}]; -SUND[a_SUNIndex,a_SUNIndex, b:Except[_?OptionQ], OptionsPattern[]] := +StandardMatrixElement[0] := 0; -SUND[a_,b_,c:Except[_?OptionQ], OptionsPattern[]] := - 2 SUNTrace[SUNT[a,b,c]] + 2 SUNTrace[SUNT[b,a,c]] /; OptionValue[Explicit]; - -SUND /: - MakeBoxes[SUND[a_, b_,c:Except[_?OptionQ], OptionsPattern[]], TraditionalForm]:= - SuperscriptBox["d", TBox[a,b,c]] +StandardMatrixElement[x_Plus] := + Map[StandardMatrixElement,x]; -SUNDelta /: - MakeBoxes[SUNDelta[a_, b_], TraditionalForm ]:= - SuperscriptBox["\[Delta]", TBox[a,b]] +SUND[a_SUNIndex,a_SUNIndex, b:Except[_?OptionQ], OptionsPattern[]] := + 0 && !OptionQ[b]; -SUNFDelta /: - MakeBoxes[SUNFDelta[a_, b_], TraditionalForm ]:= - SubscriptBox["\[Delta]", TBox[a,b]] +SUND[a_,b_,c:Except[_?OptionQ], OptionsPattern[]] := + 2 SUNTrace[SUNT[a,b,c]] + 2 SUNTrace[SUNT[b,a,c]] /; OptionValue[Explicit]; HoldPattern[SUNF[a___, x_, b___, x_, c___, ___Rule]] := 0 /; (Head[x] === SUNIndex) && FreeQ[x, Pattern] && Length[{a,x,b,x,c}] == 3; - HoldPattern[SUNF[a___, x_, y_, b___, ___Rule]] := - -SUNF[a, y, x, b] /; FreeQ[{a,x,y,b}, Pattern] && - Length[{a,x,y,b}] === 3 && (!OrderedQ[{x, y}]) && + -SUNF[a, y, x, b] /; FreeQ[{a,x,y,b}, Pattern] && Length[{a,x,y,b}] === 3 && (!OrderedQ[{x, y}]) && Head[x] === SUNIndex && Head[y] === SUNIndex; @@ -2142,15 +1984,7 @@ denotes a quantum field of type ftype with (possible) \ HoldPattern[SUNF[i_,j_,k_,l_, OptionsPattern[]]] := - (With[ {sui = FCGV[ToString[Unique["s"]]]}, - SUNF[i,j,SUNIndex[sui]] * - SUNF[SUNIndex[sui],k,l] - ])/; OptionValue[Explicit]; - -SUNF /: - MakeBoxes[SUNF[a_, b_,c:Except[_?OptionQ], - OptionsPattern[]], TraditionalForm]:= - SuperscriptBox["f", TBox[a,b,c]] + (With[ {sui = FCGV[ToString[Unique["s"]]]}, SUNF[i,j,SUNIndex[sui]] SUNF[SUNIndex[sui],k,l]])/; OptionValue[Explicit]; SUNIndex[i_Integer] := ExplicitSUNIndex[i]; @@ -2158,55 +1992,252 @@ denotes a quantum field of type ftype with (possible) \ SUNFIndex[i_Integer] := ExplicitSUNFIndex[i]; -SUNIndex /: - MakeBoxes[SUNIndex[p_], TraditionalForm]:= - ToBoxes[p, TraditionalForm]; - -SUNFIndex /: - MakeBoxes[SUNFIndex[p_], TraditionalForm]:= - ToBoxes[p, TraditionalForm]; - -(* add maybe later something to convert SUNN^2 -> CA, CF *) -SUNN /: - MakeBoxes[ SUNN, TraditionalForm ]:= "N"; - -SUNT /: - MakeBoxes[SUNT[a_], TraditionalForm]:= - SuperscriptBox["T", ToBoxes[a, TraditionalForm]]; - -SUNT /: - MakeBoxes[SUNT[a_,b__], TraditionalForm]:= - ToBoxes[FCI[SUNT[a,b]],TraditionalForm]; - -SUNTF /: - MakeBoxes[SUNTF[{a_}, b_, c_], TraditionalForm]:= - SubsuperscriptBox["T", TBox[b, c], - ToBoxes[a, TraditionalForm]]; - -SUNTF /: - MakeBoxes[SUNTF[{a1_, a2__}, b_, c_], TraditionalForm]:= - SubscriptBox[RowBox[Join[{"("},Map[SuperscriptBox["T", - ToBoxes[#, TraditionalForm]] &, {a1,a2}], {")"}]], TBox[b, c]]; - SUNTF[a_,b_,c_] := - SUNTF[{a},b,c]/;Head[a]=!=List; + SUNTF[{a},b,c]/;Head[a]=!=List && FCPatternFreeQ[{a,b,c}]; (* Tr[T^a] = 0 *) SUNTF[{_},i_SUNFIndex,i_SUNFIndex]:= 0; +SUNIndex[SUNFIndex[___]]:= + (Message[SharedObjects::failmsg,"SUNFIndex is not allowed inside SUNIndex"]; + Abort[]); + +SUNFIndex[SUNIndex[___]]:= + (Message[SharedObjects::failmsg,"SUNIndex is not allowed inside SUNFIndex"]; + Abort[]); + + +(* ------------------------------------------------------------------------ *) + Zeta2 /: N[Zeta2] = N[Zeta[2]]; + Zeta2 /: N[Zeta2, prec_] := N[Zeta[2], prec]; Zeta2 /: - MakeBoxes[Zeta2, TraditionalForm] := - RowBox[{"\[Zeta]","(",2,")"}]; + Conjugate[Zeta2] := Zeta2; + +Zeta4 /: + N[Zeta4] = N[Zeta[4]]; + +Zeta4 /: + N[Zeta4, prec_] := N[Zeta[4], prec]; + +Zeta4 /: + Conjugate[Zeta4] := Zeta4; + +Zeta6 /: + N[Zeta6] = N[Zeta[6]]; + +Zeta6 /: + N[Zeta6, prec_] := N[Zeta[6], prec]; + +Zeta6 /: + Conjugate[Zeta6] := Zeta6; + +Zeta8 /: + N[Zeta8] = N[Zeta[8]]; + +Zeta8 /: + N[Zeta8, prec_] := N[Zeta[8], prec]; + +Zeta8 /: + Conjugate[Zeta8] := Zeta8; + +Zeta10 /: + N[Zeta10] = N[Zeta[10]]; + +Zeta10 /: + N[Zeta10, prec_] := N[Zeta[10], prec]; + +Zeta10 /: + Conjugate[Zeta10] := Zeta10; + + +(* ------------------------------------------------------------------------ *) +(* New NR objects *) +(* ------------------------------------------------------------------------ *) + +CartesianIndex[x_/;FCPatternFreeQ[{x}], 3] := + CartesianIndex[x, 3] = CartesianIndex[x]; + +CartesianIndex[_, 0] := + 0; + +CartesianIndex[_Integer, ___] := + ( + Message[SharedObjects::failmsg,"Explicit cartesian indices are not supported"]; + Abort[] + ); + +CartesianMomentum[x_ n_?NumberQ, dim_ :3] := + n CartesianMomentum[x, dim]; + +CartesianMomentum[x_ n_/;DataType[n,FCVariable], dim_ :3] := + n CartesianMomentum[x, dim]; + +CartesianMomentum[x:Except[_Pattern], 3] := + CartesianMomentum[x, 3] = CartesianMomentum[x]; + +CartesianMomentum[0, _:3] := + 0; + +CartesianMomentum[_, 0] := + 0; + +CartesianMomentum[(h:LorentzIndex|ExplicitLorentzIndex|CartesianIndex|Momentum|TemporalMomentum)[___], _:3]:= + (Message[SharedObjects::failmsg,ToString[h,InputForm]<>" is not allowed inside CartesianMomentum"]; + Abort[]) + +CartesianMomentum[CartesianMomentum[x_, dim1_:3], dim2_:3] := + If[ dim1===dim2, + CartesianMomentum[x, dim1], + CartesianMomentum[x, {dim1,dim2}] + ]; + +(* ------------------------------------------------------------------------ *) + +CartesianPair[0,_] := + 0; + + +CartesianPair[(CartesianIndex | CartesianMomentum)[_, _Symbol-4], (CartesianIndex | CartesianMomentum)[_]] := + 0; + +CartesianPair[(h:LorentzIndex|ExplicitLorentzIndex|Momentum|TemporalMomentum)[___], _]:= + (Message[SharedObjects::failmsg,ToString[h,InputForm]<>" is not allowed inside CartesianPair"]; + Abort[]); + +CartesianPair[n_ x_CartesianMomentum, y_] := + n CartesianPair[x, y]; + +CartesianPair[(a : CartesianIndex | CartesianMomentum)[x_, _Symbol-1], (b : CartesianIndex | CartesianMomentum)[y_]] := + CartesianPair[a[x], b[y]]; + + +CartesianPair[(a : CartesianIndex | CartesianMomentum)[x_, dim_Symbol-1], (b : CartesianIndex | CartesianMomentum)[y_, dim_Symbol-4]] := + CartesianPair[a[x, dim-4], b[y, dim-4]]; +(* +CartesianPair[CartesianMomentum[x_, ___], CartesianMomentum[Polarization[x_, y:Except[_?OptionQ]..., OptionsPattern[Polarization]],___]] := + 0/; OptionValue[Polarization,Transversality]; + +CartesianPair[CartesianMomentum[x_,___], CartesianMomentum[Polarization[_?NumberQ x_, y:Except[_?OptionQ]..., OptionsPattern[Polarization]],___]] := + 0/; OptionValue[Polarization,Transversality];*) + +PauliSigma[_, 0] := + 0; + +PauliSigma[0, ___]:= + 0; + +PauliSigma[x_,y_, z__]/; !MemberQ[{1, 2}, Length[{x,y,z}]] && FCPatternFreeQ[{x,y,z}] := + ( + Message[PauliSigma::argrx, "PauliSigma[" <> ToString[{x,y,z}] <> "]", Length[{x,y,z}], "1 or 2"]; + Abort[] + ); + + +PauliSigma[a_Plus, dim___] := + Map[PauliSigma[#,dim]&, a]; + +PauliSigma[x_, 3] := + PauliSigma[x]; + +PauliSigma[x_ (h:TemporalMomentum|CartesianMomentum|Momentum)[p_, dim1___], dim2___] := + x PauliSigma[h[p, dim1], dim2]; + +PauliSigma[(LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[_], _Symbol-4 ] := + 0; (* 4 or 3, D-4 *) + +PauliSigma[_TemporalMomentum | ExplicitLorentzIndex[0], _Symbol-4]:= + 0; + +PauliSigma[(LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[_, _Symbol-4]] := + 0; (* D-4, 3 *) + +PauliSigma[(h:LorentzIndex|ExplicitLorentzIndex|Momentum)[x_, dim_Symbol], dim_Symbol-4] := + PauliSigma[h[x, dim-4], dim-4]; (* D, D-4 *) + +PauliSigma[(h:CartesianIndex|CartesianMomentum)[i_, dim_Symbol-1], dim_Symbol-4]:= + PauliSigma[h[i, dim-4], dim-4]; (* D, D-4 *) + +PauliSigma[(h:LorentzIndex|ExplicitLorentzIndex|Momentum|CartesianIndex|CartesianMomentum)[x_, dim_Symbol-4], dim_Symbol-1] := + PauliSigma[h[x, dim-4], dim-4]; (* D-4, D-1 *) + +PauliSigma[(h:LorentzIndex|ExplicitLorentzIndex|Momentum|TemporalMomentum|CartesianIndex|CartesianMomentum)[x_], _Symbol-1] := + PauliSigma[h[x]]; (* 4 or 3, D-1 *) + +PauliSigma[(h:LorentzIndex|ExplicitLorentzIndex|Momentum)[x_,_Symbol]] := + PauliSigma[h[x]]; (* D, 3 *) + +PauliSigma[(h:CartesianIndex|CartesianMomentum)[i_,_Symbol -1]]:= + PauliSigma[h[i]]; (* D-1, 3 *) + +PauliSigma[m_TemporalMomentum]:= + FeynCalc`Package`MetricT TemporalPair[m,ExplicitLorentzIndex[0]]; + +PauliSigma[ExplicitLorentzIndex[0]]= + 1; + +PauliSigma[x_ n_ /; DataType[n, FCVariable], dim_: 3] := + n PauliSigma[x, dim]; + +TemporalPair[0,_] := + 0; + +TemporalPair[(h:CartesianMomentum|Momentum|LorentzIndex|CartesianIndex)[__], _]:= + (Message[SharedObjects::failmsg,ToString[h,InputForm]<>" is not allowed inside TemporalPair"]; + Abort[]); + +TemporalPair[ExplicitLorentzIndex[x_/;x=!=0], _]:= + (Message[SharedObjects::failmsg,ToString[ExplicitLorentzIndex[x],InputForm]<>" is not allowed inside TemporalPair"]; + Abort[]); + +TemporalPair[n_ x_TemporalMomentum, y_] := + n TemporalPair[x, y]; + +TemporalMomentum[x_, 4] := + TemporalMomentum[x, 4] = TemporalMomentum[x]; + +TemporalMomentum[x_, dim_Symbol] := + TemporalMomentum[x, dim] = TemporalMomentum[x]; + +TemporalMomentum[x_, dim_Symbol-4] := + TemporalMomentum[x, dim-4] = 0; + +TemporalMomentum[x_ n_?NumberQ] := + n TemporalMomentum[x]; + +TemporalMomentum[x_ n_/;DataType[n,FCVariable]] := + n TemporalMomentum[x]; + +TemporalMomentum[0] := + 0; + +TC/: + Set[TC[a_] , b_]:= + SetTemporalComponent[a,b]; + +initialPairDownValues = DownValues[Pair]; +initialCartesianPairDownValues = DownValues[CartesianPair]; +initialTemporalPairDownValues = DownValues[TemporalPair]; + +initialSPDownValues = DownValues[SP]; +initialSPDDownValues = DownValues[SPD]; +initialSPEDownValues = DownValues[SPE]; + +initialCSPDownValues = DownValues[CSP]; +initialCSPDDownValues = DownValues[CSPD]; +initialCSPEDownValues = DownValues[CSPE]; + +initialTCDownValues = DownValues[TC]; + +initialMomentumDownValues = DownValues[Momentum]; +initialCartesianMomentumDownValues = DownValues[CartesianMomentum]; +initialTemporalMomentumDownValues = DownValues[TemporalMomentum]; -initialPairDownValues = DownValues[Pair]; -initialSPDownValues = DownValues[SP]; -initialSPDDownValues = DownValues[SPD]; initialScalarProducts = $ScalarProducts; diff --git a/FeynCalc/Shared/SharedObjectsTypesetting.m b/FeynCalc/Shared/SharedObjectsTypesetting.m new file mode 100644 index 000000000..a216dd6e7 --- /dev/null +++ b/FeynCalc/Shared/SharedObjectsTypesetting.m @@ -0,0 +1,1722 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: SharedObjectsTypesetting *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Typesetting for basic FeynCalc objects *) + +(* ------------------------------------------------------------------------ *) + + +(* ------------------------------------------------------------------------ *) +Begin["`Package`"] + +End[] + +Begin["`SharedObjectsTypesetting`Private`"] + +dootpow::usage=""; +csp::usage=""; +sp::usage=""; +m2Exp::usage=""; +m2ExpFirst::usage=""; + +CartesianIndex /: + MakeBoxes[ CartesianIndex[p_, ___], TraditionalForm]:= + ToBoxes[Style[p,Bold],TraditionalForm]; + +(* Typesetting for cartesian momenta. *) +(* ------------------------------------------------------------------------ *) + +CartesianMomentum /: + MakeBoxes[ CartesianMomentum[Polarization[a_, b:Except[_?OptionQ],OptionsPattern[]], dim_:3], TraditionalForm]:= + RowBox[{cpolarizationRep[b,dim],"(",TBox[a],")"}]; + +CartesianMomentum /: + MakeBoxes[ CartesianMomentum[p:Except[_Subscript | _Superscript | _Plus],dim_:3], TraditionalForm]:= + CartesianMomentumRep[Style[p,Bold],dim]; + +CartesianMomentum /: + MakeBoxes[CartesianMomentum[(p:Subscript|Superscript)[x_,y_], dim_: 3], TraditionalForm] := + If[ p===Subscript, + SubscriptBox[TBox[CartesianMomentum[Style[x,Bold], dim]], ToBoxes[y,TraditionalForm]], + SuperscriptBox[TBox[CartesianMomentum[Style[x,Bold], dim]], ToBoxes[y,TraditionalForm]] + ]; + +CartesianMomentum /: + MakeBoxes[CartesianMomentum[p_Plus,dim_: 3], TraditionalForm]:= + TBox[CartesianMomentum[#,dim]&/@Expand[p]]; + +CartesianMomentumRep[p_,dim_] := + Which[ + dim===3, + OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDim4], + MatchQ[dim,_Symbol-1], + If[ $TypesettingDimD==="", + ToBoxes[p,TraditionalForm], + OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDimD] + ], + MatchQ[dim,_Symbol-4], + OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDimE], + True, + SubscriptBox[ToBoxes[p,TraditionalForm], ToBoxes[dim,TraditionalForm]] + ]; + + +(* Typesetting for the Kronecker delta. *) +(* ------------------------------------------------------------------------ *) + +kroneckerRep[dim_] := + Which[ + dim==={3,3}, + OverscriptBox["\[Delta]", $TypesettingDim4], + MatchQ[dim,{_Symbol-1,_Symbol-1}] && dim[[1]]===dim[[2]], + If[ $TypesettingDimD==="", + "\[Delta]", + OverscriptBox["\[Delta]", $TypesettingDimD] + ], + MatchQ[dim,{_Symbol-4, _Symbol-4}] && dim[[1]]===dim[[2]], + OverscriptBox["\[Delta]", $TypesettingDimE], + True, + SubscriptBox["\[Delta]", ToBoxes[dim,TraditionalForm]] + ]; + + +CartesianPair /: + MakeBoxes[CartesianPair[CartesianIndex[a_, dim1_:3], CartesianIndex[b_, dim2_:3] ], TraditionalForm]:= + SuperscriptBox[RowBox[{kroneckerRep[{dim1,dim2}]}], TBox[CartesianIndex[a,dim1], CartesianIndex[b,dim2]]]; + +(* Typesetting for scalar products. *) +(* ------------------------------------------------------------------------ *) + +MakeBoxes[CartesianPair[c1_. CartesianMomentum[a_, dim1_ : 3], c2_. CartesianMomentum[b_, dim2_ : 3]]^n_Integer?Positive, + TraditionalForm] := + RowBox[{SuperscriptBox[TBox["(",CartesianPair[c1 CartesianMomentum[a,dim1],c2 CartesianMomentum[b,dim2]],")"],n]}]/; a=!=b; + +MakeBoxes[Power[CartesianPair[c_. CartesianMomentum[a_, dim_ : 3], c_. CartesianMomentum[a_, dim_ : 3]],n_Integer?Positive], +TraditionalForm] := + If[ Head[a]===Plus, + RowBox[{SuperscriptBox[TBox["(",c CartesianMomentum[a,dim],")"],2 n]}], + SuperscriptBox[TBox[c CartesianMomentum[a,dim]],2 n] + ]; + +CartesianPair /: + MakeBoxes[CartesianPair[c1_. CartesianMomentum[a_, dim1_ : 3]+a1_:0, c2_. CartesianMomentum[b_, dim2_ : 3]+b1_:0],TraditionalForm]:= + Block[{ m1 = Expand[(c1*a +a1)/.CartesianMomentum[z_,___]:>z], + m2 = Expand[(c2*b +b1)/.CartesianMomentum[z_,___]:>z]}, + Which[ + + m1===m2, + If[ Head[m1]===Plus, + RowBox[{SuperscriptBox[TBox["(",CartesianMomentum[m1,dim1],")"],2]}], + SuperscriptBox[TBox[CartesianMomentum[m1,dim1]],2] + ], + + Head[m1]=!=Plus && Head[m2]=!=Plus, + TBox[CartesianMomentum[m1,dim1], "\[CenterDot]", CartesianMomentum[m2,dim2]], + Head[m1]=!=Plus && Head[m2]===Plus, + TBox[CartesianMomentum[m1,dim1],"\[CenterDot]", "(",CartesianMomentum[m2,dim2],")"], + Head[m1]===Plus && Head[m2]=!=Plus, + TBox["(",CartesianMomentum[m1,dim1],")","\[CenterDot]", CartesianMomentum[m2,dim2]], + Head[m1]===Plus && Head[m2]===Plus, + TBox["(",CartesianMomentum[m1,dim1],")","\[CenterDot]", "(",CartesianMomentum[m2,dim2],")"] + ] + ]; + +(* Typesetting for polarization vectors. *) +(* ------------------------------------------------------------------------ *) + +cpolarizationRep[pol_,dim_] := + Which[ + pol===Complex[0,1] && dim===3, + OverscriptBox[TBox[Style["\[CurlyEpsilon]",Bold]], $TypesettingDim4], + pol===Complex[0,1] && MatchQ[dim,_Symbol-1], + If[ $TypesettingDimD==="", + TBox[Style["\[CurlyEpsilon]",Bold]], + OverscriptBox[TBox[Style["\[CurlyEpsilon]",Bold]], $TypesettingDimD] + ], + pol===Complex[0,1] && MatchQ[dim,_Symbol-4], + OverscriptBox[TBox[Style["\[CurlyEpsilon]",Bold]], $TypesettingDimE], + pol===Complex[0,-1] && dim===3, + SuperscriptBox[OverscriptBox[TBox[Style["\[CurlyEpsilon]",Bold]], $TypesettingDim4],"*"], + pol===Complex[0,-1] && MatchQ[dim,_Symbol-1], + If[ $TypesettingDimD==="", + SuperscriptBox[TBox[Style["\[CurlyEpsilon]",Bold]],"*"], + SuperscriptBox[OverscriptBox[TBox[Style["\[CurlyEpsilon]",Bold]], $TypesettingDimD],"*"] + ], + pol===Complex[0,-1] && MatchQ[dim,_Symbol-4], + SuperscriptBox[OverscriptBox[TBox[Style["\[CurlyEpsilon]",Bold]], $TypesettingDimE],"*"], + True, + SuperscriptBox[TBox[Style["\[CurlyEpsilon]",Bold]], TBox[pol,dim]] + ]; + +CartesianPair /: + MakeBoxes[CartesianPair[ + CartesianIndex[a_, dim_ : 3],CartesianMomentum[Polarization[b_, c:Except[_?OptionQ], OptionsPattern[]], dim_: 3]], TraditionalForm]:= + RowBox[{SuperscriptBox[cpolarizationRep[c,dim], TBox[CartesianIndex[a]]], "(",TBox[b],")"}]; + +(* Typesetting for Cartesian momentum vectors. *) +(* ------------------------------------------------------------------------ *) + +CartesianPair /: + MakeBoxes[CartesianPair[CartesianIndex[a_,dim_ : 3], + (c0: _. CartesianMomentum[_, dim_ : 3])+ c1_:0], TraditionalForm]:= + If[ !FreeQ2[{(c0+c1)/.dim->Identity},{Plus,Times}], + SuperscriptBox[ RowBox[{"(",TBox[c0 + c1],")"}], TBox[CartesianIndex[a,dim]]], + SuperscriptBox[ RowBox[{TBox[c0 + c1]}], TBox[CartesianIndex[a,dim]]] + ]; + +MakeBoxes[Power[CartesianPair[h_CartesianIndex, c0_. b_CartesianMomentum + c1_: 0], n_], TraditionalForm] := + SuperscriptBox[RowBox[{"(", ToBoxes[CartesianPair[h, c0 b + c1], TraditionalForm], ")"}],ToBoxes[n]]; + + +(* FCE typesetting*) + +TGA /: + MakeBoxes[ TGA[], TraditionalForm ]:= + ToBoxes[DiracGamma[ExplicitLorentzIndex[0]], TraditionalForm]; + +CGA /: + MakeBoxes[ CGA[x_], TraditionalForm ]:= + ToBoxes[DiracGamma[CartesianIndex[x]], TraditionalForm]; + +CGAD /: + MakeBoxes[ CGAD[x_], TraditionalForm ]:= + ToBoxes[DiracGamma[CartesianIndex[x, D-1],D], TraditionalForm]; + +CGAE /: + MakeBoxes[ CGAE[x_], TraditionalForm ]:= + ToBoxes[DiracGamma[CartesianIndex[x, D-4], D-4], TraditionalForm]; + +CGS /: + MakeBoxes[ CGS[x_], TraditionalForm ]:= + ToBoxes[DiracGamma[CartesianMomentum[x]], TraditionalForm]; + +CGSD /: + MakeBoxes[ CGSD[x_], TraditionalForm ]:= + ToBoxes[DiracGamma[CartesianMomentum[x, D-1],D], TraditionalForm]; + +CGSE /: + MakeBoxes[ CGSE[x_], TraditionalForm ]:= + ToBoxes[DiracGamma[CartesianMomentum[x, D-4],D-4], TraditionalForm]; + + +SI /: + MakeBoxes[ SI[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[LorentzIndex[x]], TraditionalForm]; + +SID /: + MakeBoxes[ SID[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[LorentzIndex[x,D],D-1], TraditionalForm]; + +SIE /: + MakeBoxes[ SIE[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[LorentzIndex[x,D-4],D-4], TraditionalForm]; + + +SIS /: + MakeBoxes[ SIS[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[Momentum[x]], TraditionalForm]; + +SISD /: + MakeBoxes[ SISD[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[Momentum[x,D],D-1], TraditionalForm]; + +SISE /: + MakeBoxes[ SISE[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[Momentum[x,D-4],D-4], TraditionalForm]; + + + +CSI /: + MakeBoxes[ CSI[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[CartesianIndex[x]], TraditionalForm]; + +CSID /: + MakeBoxes[ CSID[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[CartesianIndex[x,D-1],D-1], TraditionalForm]; + +CSIE /: + MakeBoxes[ CSIE[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[CartesianIndex[x,D-4],D-4], TraditionalForm]; + + +CSIS /: + MakeBoxes[ CSIS[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[CartesianMomentum[x]], TraditionalForm]; + +CSISD /: + MakeBoxes[ CSISD[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[CartesianMomentum[x,D-1],D-1], TraditionalForm]; + +CSISE /: + MakeBoxes[ CSISE[x_], TraditionalForm ]:= + ToBoxes[PauliSigma[CartesianMomentum[x,D-4],D-4], TraditionalForm]; + +TC /: + MakeBoxes[TC[a_], TraditionalForm]:= + ToBoxes[TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[a]], TraditionalForm]; + +MakeBoxes[Power[TC[a_], n_], TraditionalForm] := + ToBoxes[Power[TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[a]], n], TraditionalForm]; + +CV /: + MakeBoxes[CV[a_, b_], TraditionalForm]:= + ToBoxes[CartesianPair[CartesianMomentum[a],CartesianIndex[b]], TraditionalForm]; + +MakeBoxes[Power[CV[a_, b_], n_], TraditionalForm] := + ToBoxes[Power[CartesianPair[CartesianMomentum[a],CartesianIndex[b]], n], TraditionalForm]; + +CVD /: + MakeBoxes[CVD[a_, b_], TraditionalForm]:= + ToBoxes[CartesianPair[CartesianMomentum[a,D-1],CartesianIndex[b,D-1]], TraditionalForm]; + +MakeBoxes[Power[CVD[a_, b_], n_], TraditionalForm] := + ToBoxes[Power[CartesianPair[CartesianMomentum[a,D-1],CartesianIndex[b,D-1]], n], TraditionalForm]; + +CVE /: + MakeBoxes[CVE[a_, b_], TraditionalForm]:= + ToBoxes[CartesianPair[CartesianMomentum[a,D-4],CartesianIndex[b,D-4]], TraditionalForm]; + +MakeBoxes[Power[CVE[a_, b_], n_], TraditionalForm] := + ToBoxes[Power[CartesianPair[CartesianMomentum[a,D-4],CartesianIndex[b,D-4]], n], TraditionalForm]; + +KD /: + MakeBoxes[ KD[x_,y_], TraditionalForm ]:= + ToBoxes[CartesianPair[CartesianIndex[x],CartesianIndex[y]], TraditionalForm]; + +KDE /: + MakeBoxes[ KDE[x_,y_], TraditionalForm ]:= + ToBoxes[CartesianPair[CartesianIndex[x,D-4],CartesianIndex[y,D-4]], TraditionalForm]; + +KDD /: + MakeBoxes[ KDD[x_,y_], TraditionalForm ]:= + ToBoxes[CartesianPair[CartesianIndex[x,D-1],CartesianIndex[y,D-1]], TraditionalForm]; + + +CSP /: + MakeBoxes[CSP[a_, b_], TraditionalForm]:= + ToBoxes[CartesianPair[CartesianMomentum[a],CartesianMomentum[b]], TraditionalForm]; + +CSPD /: + MakeBoxes[CSPD[a_, b_], TraditionalForm]:= + ToBoxes[CartesianPair[CartesianMomentum[a,D-1],CartesianMomentum[b,D-1]], TraditionalForm]; + +CSPE /: + MakeBoxes[CSPE[a_, b_], TraditionalForm]:= + ToBoxes[CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[b,D-4]], TraditionalForm]; +CLC/: + MakeBoxes[CLC[x___][y___] ,TraditionalForm]:= + ToBoxes[Eps[Sequence@@(CartesianIndex/@{x}),Sequence@@(CartesianMomentum/@{y})],TraditionalForm]/; Length[{x,y}]===3; + +CLC/: + MakeBoxes[CLC[a_,b_,c_] ,TraditionalForm]:= + ToBoxes[Eps[CartesianIndex[a],CartesianIndex[b],CartesianIndex[c]],TraditionalForm]; + + +CLCD/: + MakeBoxes[CLCD[x___][y___] ,TraditionalForm]:= + ToBoxes[Eps[Sequence@@(CartesianIndex[#,D-1]&/@{x}),Sequence@@(CartesianMomentum[#,D-1]&/@{y})],TraditionalForm]/; Length[{x,y}]===3; + +CLCD /: + MakeBoxes[CLCD [a_,b_,c_] ,TraditionalForm]:= + ToBoxes[Eps[CartesianIndex[a,D-1],CartesianIndex[b,D-1],CartesianIndex[c,D-1]],TraditionalForm]; + + +(* Typesetting for matrices and slashes. *) +(* ------------------------------------------------------------------------ *) + +CA /: + MakeBoxes[CA, TraditionalForm]:= + SubscriptBox["C", "A"]; +CF /: + MakeBoxes[CF, TraditionalForm]:= + SubscriptBox["C", "F"]; + +AntiQuarkField /: + MakeBoxes[AntiQuarkField, TraditionalForm]:= + OverscriptBox["\[Psi]","_"]; + +DeltaFunction /: + MakeBoxes[ DeltaFunction[y_], TraditionalForm]:= + RowBox[{"\[Delta]", "(", TBox[y], ")"}]; + +DeltaFunctionDoublePrime /: + MakeBoxes[ DeltaFunctionDoublePrime[y_], TraditionalForm]:= + RowBox[{SuperscriptBox["\[Delta]","\[DoublePrime]"], + "(", TBox[y], ")"}]; + +DeltaFunctionPrime /: + MakeBoxes[ DeltaFunctionPrime[y_], TraditionalForm]:= + RowBox[{SuperscriptBox["\[Delta]","\[Prime]"], + "(", TBox[y], ")"}]; + + +(* Typesetting for Dirac matrices and slashes. *) +(* ------------------------------------------------------------------------ *) + + +cgammaSigmaRep[dim1_,dim2_,sym_] := + Which[ + dim1===3 && dim2===4, + OverscriptBox[TBox[Style[sym,Bold]], $TypesettingDim4], + MatchQ[{dim1,dim2},{dim_Symbol-1,dim_Symbol}], + If[ $TypesettingDimD==="", + TBox[Style[sym,Bold]], + OverscriptBox[TBox[Style[sym,Bold]], $TypesettingDimD] + ], + MatchQ[dim1,_Symbol-4] && dim1===dim2, + OverscriptBox[TBox[Style[sym,Bold]], $TypesettingDimE], + True, + SubscriptBox[TBox[Style[sym,Bold]], ToBoxes[dim1,TraditionalForm]] + ]; + +gammaRep[dim1_,dim2_, sym_] := + Which[ + dim1===4 && dim1===dim2, + OverscriptBox[sym, $TypesettingDim4], + MatchQ[dim1,_Symbol] && dim1===dim2, + If[ $TypesettingDimD==="", + sym, + OverscriptBox[sym, $TypesettingDimD] + ], + MatchQ[dim1,_Symbol-4] && dim1===dim2, + OverscriptBox[sym, $TypesettingDimE], + True, + SubscriptBox[sym, ToBoxes[dim1,TraditionalForm]] + ]; + +DiracGamma /: + MakeBoxes[ DiracGamma[(h:Momentum|TemporalMomentum)[x_,dim1_:4],dim2_:4], TraditionalForm ]:= + If[ Head[x]===Plus, + RowBox[{gammaRep[dim2,dim1,"\[Gamma]"], "\[CenterDot]","(", TBox[h[x,dim1]],")"}], + RowBox[{gammaRep[dim2,dim1,"\[Gamma]"], "\[CenterDot]", TBox[h[x,dim1]]}] + ]; + +DiracGamma /: + MakeBoxes[ DiracGamma[ CartesianMomentum[x_,dim1_:3],dim2_:4], TraditionalForm ]:= + If[ Head[x]===Plus, + RowBox[{cgammaSigmaRep[dim1,dim2,"\[Gamma]"], "\[CenterDot]","(", TBox[CartesianMomentum[x,dim1]],")"}], + RowBox[{cgammaSigmaRep[dim1,dim2,"\[Gamma]"], "\[CenterDot]", TBox[CartesianMomentum[x,dim1]]}] + ]; + +DiracGamma /: + MakeBoxes[ DiracGamma[(lo: LorentzIndex | ExplicitLorentzIndex)[in_, dim1_:4], dim2_:4], TraditionalForm ]:= + SuperscriptBox[RowBox[{gammaRep[dim2,dim1,"\[Gamma]"]}], TBox[lo[in,dim1]]]; + +DiracGamma /: + MakeBoxes[ DiracGamma[CartesianIndex[in_, dim1_:3], dim2_:4], TraditionalForm ]:= + SuperscriptBox[RowBox[{cgammaSigmaRep[dim1,dim2,"\[Gamma]"]}], TBox[CartesianIndex[in,dim1]]]; + +DiracGamma /: + MakeBoxes[ DiracGamma[(a : (5 | 6 | 7))], TraditionalForm ]:= + SuperscriptBox[RowBox[{gammaRep[4,4,"\[Gamma]"]}], TBox[a]]; + +(* Fermionic chains with 3 arguments *) + +(* (UBar.X)_i or (VBar.X)_j *) +DiracChain /: + MakeBoxes[ DiracChain[a_, b : (_Spinor | _SpinorUBar | _SpinorVBar | _SpinorUBarD | _SpinorVBarD), ind : (_DiracIndex | _ExplicitDiracIndex)], TraditionalForm ]:= + SubscriptBox[RowBox[{"(",ToBoxes[b,TraditionalForm],".",ToBoxes[a,TraditionalForm],")"}],TBox[ind]]; + +DCHN /: + MakeBoxes[ DCHN[a_, b : (_Spinor | _SpinorUBar | _SpinorVBar | _SpinorUBarD | _SpinorVBarD), + ind_/; !MemberQ[{Spinor,SpinorU,SpinorV,SpinorUD,SpinorVD,SpinorUBar,SpinorVBar,SpinorUBarD,SpinorVBarD},Head[ind]]], TraditionalForm ]:= + ToBoxes[DiracChain[a,b,DiracIndex[ind]], TraditionalForm]; + +(* (X.U)_i or (X.V)_j *) +DiracChain /: + MakeBoxes[ DiracChain[a_, ind : (_DiracIndex | _ExplicitDiracIndex), b : (_Spinor | _SpinorU | _SpinorV| _SpinorUD | _SpinorVD)], TraditionalForm ]:= + SubscriptBox[RowBox[{"(",ToBoxes[a,TraditionalForm],".",ToBoxes[b,TraditionalForm],")"}],TBox[ind]]; + +DCHN /: + MakeBoxes[ DCHN[a_, ind_/; !MemberQ[{Spinor,SpinorU,SpinorV,SpinorUD,SpinorVD,SpinorUBar,SpinorVBar,SpinorUBarD,SpinorVBarD},Head[ind]], + b : (_Spinor | _SpinorU | _SpinorV | _SpinorUD | _SpinorVD)], TraditionalForm ]:= + ToBoxes[DiracChain[a,DiracIndex[ind],b], TraditionalForm]; + +(* UBar.X.U, UBar.X.V, VBar.X.U or VBar.X.V *) +DiracChain /: + MakeBoxes[ DiracChain[a_,b : (_Spinor | _SpinorUBar | _SpinorVBar | _SpinorUBarD | _SpinorVBarD), c : (_Spinor | _SpinorU | _SpinorV | _SpinorUD | _SpinorVD)], TraditionalForm ]:= + RowBox[{"(",ToBoxes[b,TraditionalForm],".",ToBoxes[a,TraditionalForm],".",ToBoxes[c,TraditionalForm],")"}]; + +DCHN /: + MakeBoxes[ DCHN[a_, b : (_Spinor | _SpinorUBar | _SpinorVBar | _SpinorUBarD | _SpinorVBarD), c : (_Spinor | _SpinorU | _SpinorV | _SpinorUD | _SpinorVD)], TraditionalForm ]:= + ToBoxes[DiracChain[a,b,c], TraditionalForm]; + +(* X_ij *) +DiracChain /: + MakeBoxes[ DiracChain[a_, ind1 : (_DiracIndex | _ExplicitDiracIndex), ind2 : (_DiracIndex | _ExplicitDiracIndex)], TraditionalForm ]:= + SubscriptBox[RowBox[{"(",ToBoxes[a,TraditionalForm],")"}],TBox[ind1,ind2]]; + +DCHN /: + MakeBoxes[ DCHN[a_, + ind1_/; !MemberQ[{Spinor,SpinorU,SpinorV,SpinorUD,SpinorVD,SpinorUBar,SpinorVBar,SpinorUBarD,SpinorVBarD},Head[ind1]], + ind2_/; !MemberQ[{Spinor,SpinorU,SpinorV,SpinorUD,SpinorVD,SpinorUBar,SpinorVBar,SpinorUBarD,SpinorVBarD},Head[ind2]]], TraditionalForm ]:= + ToBoxes[DiracChain[a,DiracIndex[ind1],DiracIndex[ind2]], TraditionalForm]; + +(* Fermionic chains with 2 arguments *) + +(* UBar_i or VBar_i *) +DiracChain /: + MakeBoxes[ DiracChain[a : (_Spinor | _SpinorUBar | _SpinorVBar| _SpinorUBarD | _SpinorVBarD), ind : (_DiracIndex | _ExplicitDiracIndex)], TraditionalForm ]:= + SubscriptBox[RowBox[{"(",ToBoxes[a,TraditionalForm],")"}],TBox[ind]]; +DCHN /: + MakeBoxes[ DCHN[a : (_Spinor | _SpinorUBar | _SpinorVBar| _SpinorUBarD | _SpinorVBarD),b_/; + !MemberQ[{Spinor,SpinorU,SpinorV,SpinorUD,SpinorVD,SpinorUBar,SpinorVBar,SpinorUBarD,SpinorVBarD},Head[b]]], TraditionalForm ]:= + ToBoxes[DiracChain[a,DiracIndex[b]], TraditionalForm]; + +(* U_i or V_i *) +DiracChain /: + MakeBoxes[ DiracChain[ind : (_DiracIndex | _ExplicitDiracIndex), a : (_Spinor | _SpinorU | _SpinorV | _SpinorUD | _SpinorVD)], TraditionalForm ]:= + SubscriptBox[RowBox[{"(",ToBoxes[a,TraditionalForm],")"}],TBox[ind]]; + +DCHN /: + MakeBoxes[ DCHN[a_/; !MemberQ[{Spinor,SpinorU,SpinorV,SpinorUD,SpinorVD,SpinorUBar,SpinorVBar,SpinorUBarD,SpinorVBarD},Head[a]], b_], TraditionalForm ]:= + ToBoxes[DiracChain[DiracIndex[a],b], TraditionalForm]; + +(* UBar.U, UBar.V, VBar.U or VBar.V *) +DiracChain /: + MakeBoxes[ DiracChain[a : (_Spinor | _SpinorUBar | _SpinorVBar| _SpinorUBarD | _SpinorVBarD),b: (_Spinor | _SpinorU | _SpinorV | _SpinorUD | _SpinorVD)], TraditionalForm ]:= + RowBox[{"(",ToBoxes[a,TraditionalForm],".",ToBoxes[b,TraditionalForm],")"}]; + +DCHN /: + MakeBoxes[ DCHN[a : (_Spinor | _SpinorUBar | _SpinorVBar| _SpinorUBarD | _SpinorVBarD), b : (_Spinor | _SpinorU | _SpinorV | _SpinorUD | _SpinorVD)], TraditionalForm ]:= + ToBoxes[DiracChain[a,b], TraditionalForm]; + +DiracIndex /: + MakeBoxes[DiracIndex[p_], TraditionalForm]:= + ToBoxes[p, TraditionalForm]; + + +DiracSigma /: + MakeBoxes[DiracSigma[(DiracGamma | GA | GAD | GS | GSD | CGA | CGAD | CGS | CGSD | TGA )[x_,___], + (DiracGamma | GA | GAD | GS | GSD | CGA | CGAD | CGS | CGSD | TGA)[y_,___]], TraditionalForm]:= + SuperscriptBox["\[Sigma]", TBox[x,y]]; + +DiracIndexDelta /: + MakeBoxes[ DiracIndexDelta[(ind1: DiracIndex | ExplicitDiracIndex)[i_],(ind2: DiracIndex | ExplicitDiracIndex)[j_]], TraditionalForm ]:= + SubscriptBox["\[Delta]",TBox[ind1[i],ind2[j]]]; + +DIDelta /: + MakeBoxes[ DIDelta[i_,j_], TraditionalForm ]:= + SubscriptBox["\[Delta]",TBox[i,j]]; + +Eps /: + MakeBoxes[Eps[a__],TraditionalForm]:= + SuperscriptBox[OverscriptBox["\[Epsilon]",$TypesettingDimD], TBox[a]]/; Length[First[{a}]]===2; + +Eps /: + MakeBoxes[Eps[a__],TraditionalForm]:= + SuperscriptBox[OverscriptBox["\[Epsilon]",$TypesettingDim4], TBox[a]]/; MatchQ[Length[First[{a}]],1|0]; + +Epsilon /: + MakeBoxes[Epsilon, TraditionalForm]:= + TagBox["\[CurlyEpsilon]", TraditionalForm]; + +EpsilonUV /: + MakeBoxes[EpsilonUV, TraditionalForm] := + SubscriptBox["\[CurlyEpsilon]", "UV"]; + +EpsilonIR /: + MakeBoxes[EpsilonIR, TraditionalForm] := + SubscriptBox["\[CurlyEpsilon]", "IR"]; + +ExplicitDiracIndex /: + MakeBoxes[ ExplicitDiracIndex[p_], TraditionalForm]:= + ToBoxes[p, TraditionalForm]; + +ExplicitLorentzIndex /: + MakeBoxes[ ExplicitLorentzIndex[p_, dim_ : 4], TraditionalForm]:= + ToBoxes[TypesettingExplicitLorentzIndex[p, dim],TraditionalForm]; + +ExplicitSUNIndex /: + MakeBoxes[ ExplicitSUNIndex[p_], TraditionalForm]:= + ToBoxes[p, TraditionalForm]; + +ExplicitSUNFIndex /: + MakeBoxes[ ExplicitSUNFIndex[p_], TraditionalForm]:= + ToBoxes[p, TraditionalForm]; + +fadTypeset[{y_,z_/;z=!=0}, dim_] := + SequenceForm[Pair[Momentum[y,dim],Momentum[y,dim]], "-", z^2]; + +fadTypeset[{y_,0}, dim_] := + fadTypeset[y, dim]; + +fadTypeset[{y_}, dim_] := + fadTypeset[y, dim]; + +fadTypeset[y_/;Head[y]=!=List, dim_] := + SequenceForm[Pair[Momentum[y,dim],Momentum[y,dim]]]; + + + +gfadTypeset[ex_/;Head[ex]=!=List, etaOpt_] := + gfadTypeset[{{ex,etaOpt}, 1}, etaOpt]; + +gfadTypeset[{ex_/;Head[ex]=!=List, rest___}, etaOpt_] := + gfadTypeset[{{ex,etaOpt},rest}, etaOpt]; + +gfadTypeset[{{ex_}, rest___}, etaOpt_] := + gfadTypeset[{{ex,etaOpt},rest}, etaOpt]; + +gfadTypeset[{a_List}, etaOpt_] := + gfadTypeset[{a, 1}, etaOpt]; + +gfadTypeset[{{ex_,s_},n_}, _] := + Row[{"(",ex, + If[$FCShowIEta, + + Sequence@@{If[s===1, + "+", + "-" + ], + I "\[Eta]"}, + Unevaluated[Sequence[]] + ],")"}]^n; + +cfadTypeset[ex_/;Head[ex]=!=List, dim_, etaOpt_] := + cfadTypeset[{{ex,0},{0,etaOpt}}, dim, etaOpt]; + +cfadTypeset[{ex_/;Head[ex]=!=List, rest__}, dim_, etaOpt_] := + cfadTypeset[{{ex,0},rest}, dim, etaOpt]; + +cfadTypeset[{a_List, m2_/;Head[m2]=!=List, rest___}, dim_, etaOpt_] := + cfadTypeset[{a,{m2,etaOpt},rest}, dim, etaOpt]; + +cfadTypeset[{a_List}, dim_, etaOpt_] := + cfadTypeset[{a,{0,etaOpt},1}, dim, etaOpt]; + + +(* When updating cfadTypeset, please check that + +{CFAD[{{0, 0}, m}], +CFAD[{{0, 0}, -m}], +CFAD[{{0, 0}, m1 + m2}], +CFAD[{{0, 0}, m1 - m2}], +CFAD[{{0, 0}, -m1 + m2}], +CFAD[{{0, 0}, -m1 - m2}], +CFAD[{{0, p.q}, m}], +CFAD[{{0, p.q}, -m}], +CFAD[{{0, p.q}, m1 + m2}], +CFAD[{{0, p.q}, m1 - m2}], +CFAD[{{0, p.q}, -m1 + m2}], +CFAD[{{0, p.q}, -m1 - m2}], + +CFAD[{{p, 0}, m}], +CFAD[{{p, 0}, -m}], +CFAD[{{p, 0}, m1 + m2}], +CFAD[{{p, 0}, m1 - m2}], +CFAD[{{p, 0}, -m1 + m2}], +CFAD[{{p, 0}, -m1 - m2}], + +CFAD[{{p, p.q}, m}], +CFAD[{{p, p.q}, -m}], +CFAD[{{p, p.q}, m1 + m2}], +CFAD[{{p, p.q}, m1 - m2}], +CFAD[{{p, p.q}, -m1 + m2}], +CFAD[{{p, p.q}, -m1 - m2}] +} + +is displayed correctly! + +*) + +cfadTypeset[{{ex1_, ex2_}, {m2_,etasign_}, n_: (1)}, dim_, _] := + ( + m2Exp=Expand[m2]; + Row[{"(", + + If[ ex1=!=0, + CartesianPair[CartesianMomentum[ex1,dim],CartesianMomentum[ex1,dim]], + Unevaluated[Sequence[]] + ], + + If[ex2=!=0, + + If[ ((Abs[ex2] /. Abs -> Identity) =!= ex2), + Unevaluated@Sequence["-", Expand[-ex2 /. csp[x_,y_] :> CartesianPair[CartesianMomentum[x,dim],CartesianMomentum[y,dim]]]], + If[ ex1===0, + ex2 /. csp[x_,y_] :> CartesianPair[CartesianMomentum[x,dim],CartesianMomentum[y,dim]], + Unevaluated@Sequence["+", ex2 /. csp[x_,y_] :> CartesianPair[CartesianMomentum[x,dim],CartesianMomentum[y,dim]]] + ] + ], + + Unevaluated[Sequence[]] + ], + + + + + If[ m2Exp=!=0, + + Sequence@@{ + If[ (ex1===0 && ex2===0), + (* ex1 and ex2 are both zero -> no extra sign *) + Unevaluated[Sequence[]], + + (* at least one of the two is not zero -> extra sign might be needed *) + If[ Head[m2Exp]===Plus, + (* we have a sum *) + m2ExpFirst = With[{xx = m2Exp}, ToExpression[First[First[MakeBoxes[xx, TraditionalForm]]]]]; + If[ + (Abs[m2ExpFirst]/.Abs->Identity) =!= m2ExpFirst, + (*there is a relative minus sign! *) + Unevaluated[Sequence[]], + (*there is no relative minus sign! *) + "+" + ], + (* we have a single term *) + If[ ((Abs[m2Exp] /. Abs -> Identity) =!= (m2Exp)), + (*there is a relative minus sign! *) + Unevaluated[Sequence[]], + (*there is no relative minus sign! *) + "+" + ] + ] + ], + m2Exp + }, + Unevaluated[Sequence[]] + ], + + + + + + If[$FCShowIEta, + + Sequence@@{If[etasign===1, + "+", + "-" + ], + I "\[Eta]"}, + Unevaluated[Sequence[]] + ], + + ")"}]^(n) + ); + + + +sfadTypeset[ex_/;Head[ex]=!=List, dim_, etaOpt_] := + sfadTypeset[{{ex,0},{0,etaOpt}}, dim, etaOpt]; + +sfadTypeset[{ex_/;Head[ex]=!=List, rest__}, dim_, etaOpt_] := + sfadTypeset[{{ex,0},rest}, dim, etaOpt]; + +sfadTypeset[{a_List, m2_/;Head[m2]=!=List, rest___}, dim_, etaOpt_] := + sfadTypeset[{a,{m2,etaOpt},rest}, dim, etaOpt]; + +sfadTypeset[{a_List}, dim_, etaOpt_] := + sfadTypeset[{a,{0,etaOpt},1}, dim, etaOpt]; + +(* When updating sfadTypeset, please check that + +{SFAD[{{0, 0}, m}], +SFAD[{{0, 0}, -m}], +SFAD[{{0, 0}, m1 + m2}], +SFAD[{{0, 0}, m1 - m2}], +SFAD[{{0, 0}, -m1 + m2}], +SFAD[{{0, 0}, -m1 - m2}], +SFAD[{{0, p.q}, m}], +SFAD[{{0, p.q}, -m}], +SFAD[{{0, p.q}, m1 + m2}], +SFAD[{{0, p.q}, m1 - m2}], +SFAD[{{0, p.q}, -m1 + m2}], +SFAD[{{0, p.q}, -m1 - m2}], + +SFAD[{{p, 0}, m}], +SFAD[{{p, 0}, -m}], +SFAD[{{p, 0}, m1 + m2}], +SFAD[{{p, 0}, m1 - m2}], +SFAD[{{p, 0}, -m1 + m2}], +SFAD[{{p, 0}, -m1 - m2}], + +SFAD[{{p, p.q}, m}], +SFAD[{{p, p.q}, -m}], +SFAD[{{p, p.q}, m1 + m2}], +SFAD[{{p, p.q}, m1 - m2}], +SFAD[{{p, p.q}, -m1 + m2}], +SFAD[{{p, p.q}, -m1 - m2}] + + +} +is displayed correctly! + +*) + +sfadTypeset[{{ex1_, ex2_}, {m2_,etasign_}, n_: (1)}, dim_, _] := + ( + m2Exp=Expand[-m2]; + Row[{"(", + + If[ ex1=!=0, + Pair[Momentum[ex1,dim],Momentum[ex1,dim]], + Unevaluated[Sequence[]] + ], + + If[ex2=!=0, + + If[ ((Abs[ex2] /. Abs -> Identity) =!= ex2), + Unevaluated@Sequence["-", Expand[-ex2 /. sp[x_,y_] :> Pair[Momentum[x,dim],Momentum[y,dim]]]], + If[ ex1===0, + ex2 /. sp[x_,y_] :> Pair[Momentum[x,dim],Momentum[y,dim]], + Unevaluated@Sequence["+", ex2 /. sp[x_,y_] :> Pair[Momentum[x,dim],Momentum[y,dim]]] + ] + ], + + Unevaluated[Sequence[]] + ], + + If[ m2Exp=!=0, + + Sequence@@{ + If[ (ex1===0 && ex2===0), + (* ex1 and ex2 are both zero -> no extra sign *) + Unevaluated[Sequence[]], + + (* at least one of the two is not zero -> extra sign might be needed *) + If[ Head[m2Exp]===Plus, + (* we have a sum *) + m2ExpFirst = With[{xx = m2Exp}, ToExpression[First[First[MakeBoxes[xx, TraditionalForm]]]]]; + If[ + (Abs[m2ExpFirst]/.Abs->Identity) =!= m2ExpFirst, + (*there is a relative minus sign! *) + Unevaluated[Sequence[]], + (*there is no relative minus sign! *) + "+" + ], + (* we have a single term *) + If[ ((Abs[m2Exp] /. Abs -> Identity) =!= (m2Exp)), + (*there is a relative minus sign! *) + Unevaluated[Sequence[]], + (*there is no relative minus sign! *) + "+" + ] + ] + ], + m2Exp + }, + Unevaluated[Sequence[]] + ], + + If[$FCShowIEta, + + Sequence@@{If[etasign===1, + "+", + "-" + ], + I "\[Eta]"}, + Unevaluated[Sequence[]] + ], + + ")"}]^(n) +); + +MakeBoxes[pref_. FAD[a__, opts:OptionsPattern[]], TraditionalForm]:= + ToBoxes[pref/(Apply[DOT,Map[fadTypeset[#,OptionValue[FAD,{opts},Dimension]]&, {a}]]/. DOT -> dootpow), TraditionalForm]/; !MemberQ[{a},{_,_,_}] && !MemberQ[{a},{_,_,_,_,_}] && FCPatternFreeQ[{a,opts}]; + +MakeBoxes[pref_. GFAD[a__, opts:OptionsPattern[]], TraditionalForm]:= + ToBoxes[pref/(Apply[DOT,Map[gfadTypeset[#,OptionValue[GFAD,{opts},EtaSign]]&, {a}]]/. DOT -> dootpow), TraditionalForm]/; FCPatternFreeQ[{a,opts}]; + +MakeBoxes[pref_. CFAD[a__, opts:OptionsPattern[]], TraditionalForm] := + ToBoxes[pref/(Apply[DOT, Map[cfadTypeset[# /. DOT[x_,y_]:> csp[x,y], OptionValue[CFAD,{opts},Dimension], OptionValue[CFAD,{opts},EtaSign]]&, {a}]] /. DOT -> dootpow), TraditionalForm]/; FCPatternFreeQ[{a,opts}]; + +MakeBoxes[pref_. SFAD[a__, opts:OptionsPattern[]], TraditionalForm] := + ToBoxes[pref/(Apply[DOT, Map[sfadTypeset[# /. DOT[x_,y_]:> sp[x,y], OptionValue[SFAD,{opts},Dimension], OptionValue[SFAD,{opts},EtaSign]]&, {a}]] /. DOT -> dootpow), TraditionalForm]/; FCPatternFreeQ[{a,opts}]; + + +FCGV /: MakeBoxes[FCGV[a_String, opts:OptionsPattern[]], TraditionalForm]/; OptionValue[FCGV,{opts},SilentTypeSetting] := + ToBoxes[a, TraditionalForm]; + +FeynAmp /: + MakeBoxes[FeynAmp[q__Symbol, amp_], TraditionalForm ]:= + RowBox[Join[Map[RowBox[{"\[Integral]", + RowBox[{SuperscriptBox["\[DifferentialD]", "D"], + TBox[#]}]}] &, {q}], {"(", TBox[amp], ")"}]]; + +FeynAmp /: + MakeBoxes[FeynAmp[_[__], q__Symbol, amp_], TraditionalForm]:= + ToBoxes[FeynAmp[q,amp], TraditionalForm]; + +MakeBoxes[pref_. FeynAmpDenominator[a__], TraditionalForm]:= + ToBoxes[pref / (Apply[DOT, (feynAmpDenominatorTypeset/@{a})]/. DOT -> dootpow), TraditionalForm]/; FCPatternFreeQ[{a}]; + +feynAmpDenominatorTypeset[PropagatorDenominator[p_,0]]:= + SequenceForm[Pair[p,p]]; + +feynAmpDenominatorTypeset[PropagatorDenominator[p_,m_]]:= + SequenceForm[Pair[p,p], "-", m^2]; + +feynAmpDenominatorTypeset[StandardPropagatorDenominator[ex1_,ex2_,m2_,{n_,s_}]]:= + Row[{"(", + + If[ ex1=!=0, + Pair[ex1,ex1], + Unevaluated[Sequence[]] + ], + + If[ex2=!=0, + + If[ ((Abs[ex2] /. Abs -> Identity) =!= ex2), + Unevaluated@Sequence["-", Expand[-ex2]], + If[ ex1===0, + ex2, + Unevaluated@Sequence["+", ex2] + ] + ], + + Unevaluated[Sequence[]] + ], + + If[m2=!=0, + (*If m2 is negative *) + Sequence@@{If[((Abs[m2] /. Abs -> Identity) =!= (-m2)), + If[ (ex1===0 && ex2===0), + Unevaluated[Sequence[]], + "+" + ], + Unevaluated[Sequence[]] + ], + Expand[m2]}, + Unevaluated[Sequence[]] + ], + + If[$FCShowIEta, + + Sequence@@{If[s===1, + "+", + "-" + ], + I "\[Eta]"}, + Unevaluated[Sequence[]] + ], + + ")"}]^(n); + +feynAmpDenominatorTypeset[CartesianPropagatorDenominator[ex1_,ex2_,m2_,{n_,s_}]]:= + Row[{"(", + + If[ ex1=!=0, + CartesianPair[ex1,ex1], + Unevaluated[Sequence[]] + ], + + If[ex2=!=0, + + If[ ((Abs[ex2] /. Abs -> Identity) =!= ex2), + Unevaluated@Sequence["-", Expand[-ex2]], + If[ ex1===0, + ex2, + Unevaluated@Sequence["+", ex2] + ] + ], + + Unevaluated[Sequence[]] + ], + + If[m2=!=0, + + Sequence@@{If[((Abs[m2] /. Abs -> Identity) =!= m2) || (ex1===0 && ex2===0), + Unevaluated[Sequence[]], + "+" + ], + m2}, + Unevaluated[Sequence[]] + ], + + If[$FCShowIEta, + + Sequence@@{If[s===1, + "+", + "-" + ], + I "\[Eta]"}, + Unevaluated[Sequence[]] + ], + + ")"}]^(n); + + + +feynAmpDenominatorTypeset[GenericPropagatorDenominator[ex1_,{n_,s_}]]:= + Row[{"(", + + If[ ex1=!=0, + ex1, + Unevaluated[Sequence[]] + ], + + If[$FCShowIEta, + + Sequence@@{If[s===1, + "+", + "-" + ], + I "\[Eta]"}, + Unevaluated[Sequence[]] + ], + + ")"}]^(n); + + +(* Typesetting for vectors in the FCE notation. *) +(* ------------------------------------------------------------------------ *) + +FV /: + MakeBoxes[FV[a_, b_], TraditionalForm]:= + ToBoxes[Pair[Momentum[a],LorentzIndex[b]], TraditionalForm]; + +MakeBoxes[Power[FV[a_, b_], n_], TraditionalForm] := + ToBoxes[Power[Pair[Momentum[a],LorentzIndex[b]], n], TraditionalForm]; + +FVD /: + MakeBoxes[FVD[a_, b_], TraditionalForm]:= + ToBoxes[Pair[Momentum[a, D],LorentzIndex[b, D]], TraditionalForm]; + +MakeBoxes[Power[FVD[a_, b_], n_], TraditionalForm] := + ToBoxes[Power[Pair[Momentum[a, D],LorentzIndex[b, D]], n], TraditionalForm]; + +FVE /: + MakeBoxes[FVE[a_, b_], TraditionalForm]:= + ToBoxes[Pair[Momentum[a, D-4],LorentzIndex[b, D-4]], TraditionalForm]; + +MakeBoxes[Power[FVE[a_, b_], n_], TraditionalForm] := + ToBoxes[Power[Pair[Momentum[a, D-4],LorentzIndex[b, D-4]], n], TraditionalForm]; + +(* ------------------------------------------------------------------------ *) + + +(* TraditionalForm of the Dirac matrices in the FCE notation *) +(* ------------------------------------------------------------------------ *) + +GA /: + MakeBoxes[GA[x_/;!MemberQ[{5,6,7},x]], TraditionalForm ]:= + ToBoxes[DiracGamma[LorentzIndex[x]], TraditionalForm]; + +GA /: + MakeBoxes[GA[x_/;MemberQ[{5,6,7},x]], TraditionalForm ]:= + ToBoxes[DiracGamma[x], TraditionalForm]; + +GAD /: + MakeBoxes[GAD[x_], TraditionalForm ]:= + ToBoxes[DiracGamma[LorentzIndex[x, D], D], TraditionalForm]; + +GAE /: + MakeBoxes[GAE[x_], TraditionalForm ]:= + ToBoxes[DiracGamma[LorentzIndex[x, D-4], D-4], TraditionalForm]; + +(* ------------------------------------------------------------------------ *) + +GaugeField /: + MakeBoxes[GaugeField, TraditionalForm]:= + "A"; + +GaugeXi /: + MakeBoxes[GaugeXi[a_], TraditionalForm]:= + SubscriptBox["\[Xi]", TBox[a]]; + +GaugeXi /: + MakeBoxes[GaugeXi, TraditionalForm]:= + TagBox["\[Xi]", TraditionalForm] + +GluonField /: + MakeBoxes[GluonField, TraditionalForm]:= + "A"; + +(* TraditionalForm typesetting of the Dirac slashes in the FCE notation. *) +(* ------------------------------------------------------------------------ *) + +GS/: + MakeBoxes[GS[a_], TraditionalForm ]:= + ToBoxes[DiracGamma[Momentum[a]], TraditionalForm]; + +GSD/: + MakeBoxes[GSD[a_], TraditionalForm ]:= + ToBoxes[DiracGamma[Momentum[a,D],D], TraditionalForm]; + +GSE/: + MakeBoxes[GSE[a_], TraditionalForm ]:= + ToBoxes[DiracGamma[Momentum[a,D-4],D-4], TraditionalForm]; + +(* ------------------------------------------------------------------------ *) + +Integratedx /: + MakeBoxes[Integratedx[x_, low_, up_], TraditionalForm]:= + RowBox[{SubsuperscriptBox["\[Integral]", TBox[low], + TBox[up]], "\[DifferentialD]", + MakeBoxes[TraditionalForm[x]], "\[VeryThinSpace]" }]; + +LC/: + MakeBoxes[LC[x___][y___] ,TraditionalForm]:= + ToBoxes[Eps[Sequence@@(LorentzIndex/@{x}),Sequence@@(Momentum/@{y})],TraditionalForm]/; Length[{x,y}]===4; + +LC/: + MakeBoxes[LC[a_,b_,c_,d_] ,TraditionalForm]:= + ToBoxes[Eps[LorentzIndex[a],LorentzIndex[b],LorentzIndex[c],LorentzIndex[d]],TraditionalForm]; + +LCD /: + MakeBoxes[LCD [x___][y___] ,TraditionalForm]:= + ToBoxes[Eps[Sequence@@(LorentzIndex[#,D]&/@{x}),Sequence@@(Momentum[#,D]&/@{y})],TraditionalForm]/; Length[{x,y}]===4; + +LCD /: + MakeBoxes[LCD [a_,b_,c_,d_] ,TraditionalForm]:= + ToBoxes[Eps[LorentzIndex[a,D],LorentzIndex[b,D],LorentzIndex[c,D],LorentzIndex[d,D]],TraditionalForm]; + +LeftPartialD/: + MakeBoxes[LeftPartialD[x_ ^n_],TraditionalForm]:= + SubsuperscriptBox[RowBox[{OverscriptBox["\[PartialD]", + "\[LeftArrow]"]}], TBox[" ",x],TBox[n]] /; Head[x] === Momentum; + +LeftPartialD /: + MakeBoxes[LeftPartialD[x_], TraditionalForm]:= + SubscriptBox[OverscriptBox["\[PartialD]", + "\[LeftArrow]"], TBox[x]]; + +LeftRightPartialD /: + MakeBoxes[LeftRightPartialD[x_] , TraditionalForm]:= + SubscriptBox[OverscriptBox["\[PartialD]", + "\[LeftRightArrow]"], TBox[x]]; + +LeftRightPartialD2 /: + MakeBoxes[LeftRightPartialD2[x_], TraditionalForm]:= + ToBoxes[LeftRightPartialD[x],TraditionalForm]; + +LorentzIndex /: + MakeBoxes[ LorentzIndex[p_, ___], TraditionalForm]:= + ToBoxes[p,TraditionalForm]; + +(* Typesetting for momenta. *) +(* ------------------------------------------------------------------------ *) + +momentumRep[p_,dim_] := + Which[ + dim===4, + OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDim4], + MatchQ[dim,_Symbol], + If[ $TypesettingDimD==="", + ToBoxes[p,TraditionalForm], + OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDimD] + ], + MatchQ[dim,_Symbol-4], + OverscriptBox[ToBoxes[p,TraditionalForm], $TypesettingDimE], + True, + SubscriptBox[ToBoxes[p,TraditionalForm], ToBoxes[dim,TraditionalForm]] + ]; + +Momentum /: + MakeBoxes[ Momentum[Polarization[a_, b:Except[_?OptionQ],OptionsPattern[]], dim_:4], + TraditionalForm ]:= + RowBox[{polarizationRep[b,dim],"(",TBox[a],")"}]; + +Momentum /: + MakeBoxes[ Momentum[ OPEDelta, _:4 ], TraditionalForm]:= + TBox[OPEDelta]; + +Momentum /: + MakeBoxes[ Momentum[p:Except[_Subscript | _Superscript | _Plus],dim_:4], TraditionalForm]:= + momentumRep[p,dim]/; p=!=OPEDelta; + +Momentum /: + MakeBoxes[Momentum[(p:Subscript|Superscript)[x_,y_], dim_: 4], TraditionalForm] := + If[ p===Subscript, + SubscriptBox[TBox[Momentum[x, dim]], ToBoxes[y,TraditionalForm]], + SuperscriptBox[TBox[Momentum[x, dim]], ToBoxes[y,TraditionalForm]] + ]; + +Momentum /: + MakeBoxes[Momentum[p_Plus,dim_: 4], TraditionalForm]:= + TBox[Momentum[#,dim]&/@Expand[p]]; + +(* ------------------------------------------------------------------------ *) + +MT /: + MakeBoxes[MT[x_,y_], TraditionalForm ]:= + ToBoxes[Pair[LorentzIndex[x],LorentzIndex[y]], TraditionalForm]; + +MTE /: + MakeBoxes[MTE[x_,y_], TraditionalForm ]:= + ToBoxes[Pair[LorentzIndex[x, D-4],LorentzIndex[y, D-4]], TraditionalForm]; + +MTD /: + MakeBoxes[MTD[x_,y_], TraditionalForm ]:= + ToBoxes[Pair[LorentzIndex[x, D],LorentzIndex[y, D]], TraditionalForm]; + +Nf /: + MakeBoxes[Nf, TraditionalForm]:= + SubscriptBox["N", "f"]; + +OPE /: + MakeBoxes[OPE, TraditionalForm]:= + "\[CapitalOmega]" + +(* Typesetting for the metric tensor. *) +(* ------------------------------------------------------------------------ *) + +metricRep[dim_] := + Which[ + dim==={4,4}, + OverscriptBox["g", $TypesettingDim4], + MatchQ[dim,{_Symbol,_Symbol}] && dim[[1]]===dim[[2]], + If[ $TypesettingDimD==="", + "g", + OverscriptBox["g", $TypesettingDimD] + ], + MatchQ[dim,{_Symbol-4, _Symbol-4}] && dim[[1]]===dim[[2]], + OverscriptBox["g", $TypesettingDimE], + True, + SubscriptBox["g", ToBoxes[dim,TraditionalForm]] + ]; + + +Pair /: + MakeBoxes[Pair[CartesianIndex[i_], LorentzIndex[l_,dim2_:4]],TraditionalForm]:= + SuperscriptBox[RowBox[{metricRep[{4,dim2}]}], + TBox[CartesianIndex[i], LorentzIndex[l,dim2]]]; + +Pair /: + MakeBoxes[Pair[CartesianIndex[i_,dim1_Symbol-1], LorentzIndex[l_,dim2_:4]],TraditionalForm]:= + SuperscriptBox[RowBox[{metricRep[{dim1,dim2}]}], + TBox[CartesianIndex[i,dim1-1], LorentzIndex[l,dim2]]]; + +Pair /: + MakeBoxes[Pair[CartesianIndex[i_,dim1_Symbol-4], LorentzIndex[l_,dim2_:4]],TraditionalForm]:= + SuperscriptBox[RowBox[{metricRep[{dim1-4,dim2}]}], + TBox[CartesianIndex[i,dim1-4], LorentzIndex[l,dim2]]]; +Pair /: + MakeBoxes[Pair[(LorentzIndex|ExplicitLorentzIndex)[a_, dim1_:4], (LorentzIndex|ExplicitLorentzIndex)[b_, dim2_:4] ], TraditionalForm]:= + SuperscriptBox[RowBox[{metricRep[{dim1,dim2}]}], TBox[LorentzIndex[a,dim1], LorentzIndex[b,dim2]]]; + +(* Typesetting for scalar products. *) +(* ------------------------------------------------------------------------ *) + +MakeBoxes[Pair[c1_. Momentum[a_, dim1_ : 4], c2_. Momentum[b_, dim2_ : 4]]^n_Integer?Positive, TraditionalForm] := + RowBox[{SuperscriptBox[TBox["(",Pair[c1 Momentum[a,dim1],c2 Momentum[b,dim2]],")"],n]}]/; a=!=b; + +MakeBoxes[Power[Pair[c_. Momentum[a_, dim_ : 4], c_. Momentum[a_, dim_ : 4]],n_Integer?Positive], TraditionalForm] := + If[ Head[a]===Plus, + RowBox[{SuperscriptBox[TBox["(",c Momentum[a,dim],")"],2 n]}], + SuperscriptBox[TBox[c Momentum[a,dim]],2 n] + ]; + +Pair /: + MakeBoxes[Pair[c1_. Momentum[a_, dim1_ : 4]+a1_:0, c2_. Momentum[b_, dim2_ : 4]+b1_:0],TraditionalForm]:= + Block[ { m1 = Expand[(c1*a +a1)/.Momentum[z_,___]:>z], + m2 = Expand[(c2*b +b1)/.Momentum[z_,___]:>z]}, + Which[ + m1===m2, + If[ Head[m1]===Plus, + RowBox[{SuperscriptBox[TBox["(",Momentum[m1,dim1],")"],2]}], + SuperscriptBox[TBox[Momentum[m1,dim1]],2] + ], + + Head[m1]=!=Plus && Head[m2]=!=Plus, + TBox[Momentum[m1,dim1], "\[CenterDot]", Momentum[m2,dim2]], + Head[m1]=!=Plus && Head[m2]===Plus, + TBox[Momentum[m1,dim1],"\[CenterDot]", "(",Momentum[m2,dim2],")"], + Head[m1]===Plus && Head[m2]=!=Plus, + TBox["(",Momentum[m1,dim1],")","\[CenterDot]", Momentum[m2,dim2]], + Head[m1]===Plus && Head[m2]===Plus, + TBox["(",Momentum[m1,dim1],")","\[CenterDot]", "(",Momentum[m2,dim2],")"] + + ] + ]; + +(* Typesetting for polarization vectors. *) +(* ------------------------------------------------------------------------ *) + +polarizationRep[pol_,dim_] := + Which[ + pol===Complex[0,1] && dim===4, + OverscriptBox["\[CurlyEpsilon]", $TypesettingDim4], + pol===Complex[0,1] && MatchQ[dim,_Symbol], + If[ $TypesettingDimD==="", + ToBoxes["\[CurlyEpsilon]",TraditionalForm], + OverscriptBox["\[CurlyEpsilon]", $TypesettingDimD] + ], + pol===Complex[0,1] && MatchQ[dim,_Symbol-4], + OverscriptBox["\[CurlyEpsilon]", $TypesettingDimE], + pol===Complex[0,-1] && dim===4, + SuperscriptBox[OverscriptBox["\[CurlyEpsilon]", $TypesettingDim4],"*"], + pol===Complex[0,-1] && MatchQ[dim,_Symbol], + If[ $TypesettingDimD==="", + SuperscriptBox[ToBoxes["\[CurlyEpsilon]",TraditionalForm],"*"], + SuperscriptBox[OverscriptBox["\[CurlyEpsilon]", $TypesettingDimD],"*"] + ], + pol===Complex[0,-1] && MatchQ[dim,_Symbol-4], + SuperscriptBox[OverscriptBox["\[CurlyEpsilon]", $TypesettingDimE],"*"], + True, + SuperscriptBox["\[CurlyEpsilon]", TBox[pol,dim]] + ]; + +Pair /: + MakeBoxes[Pair[ + (LorentzIndex| ExplicitLorentzIndex)[a_, dim_ : 4], + Momentum[Polarization[b_, c:Except[_?OptionQ], OptionsPattern[]], dim_: 4]], TraditionalForm]:= + RowBox[{SuperscriptBox[polarizationRep[c,dim], TBox[LorentzIndex[a]]], "(",TBox[b],")"}]; + +(* Typesetting for momentum vectors. *) +(* ------------------------------------------------------------------------ *) + +Pair /: + MakeBoxes[Pair[(h : LorentzIndex| ExplicitLorentzIndex)[a_, dim_ : 4], (c0: _. Momentum[_, dim_ : 4])+ c1_:0], TraditionalForm]:= + If[ !FreeQ2[{(c0+c1)/.dim->Identity},{Plus,Times}], + SuperscriptBox[ RowBox[{"(",TBox[c0 + c1],")"}], TBox[h[a,dim]]], + SuperscriptBox[ RowBox[{TBox[c0 + c1]}], TBox[h[a,dim]]] + ]; + + + +MakeBoxes[Power[Pair[(h : LorentzIndex | ExplicitLorentzIndex)[a___], c0_. b_Momentum + c1_: 0], n_], TraditionalForm] := + SuperscriptBox[RowBox[{"(", ToBoxes[Pair[h[a], c0 b + c1], TraditionalForm], ")"}],ToBoxes[n]]; + +Pair /: + MakeBoxes[Pair[(h : LorentzIndex| ExplicitLorentzIndex)[a_], (c0: _. _CartesianMomentum)+ c1_:0], TraditionalForm]:= + ToBoxes[Pair[h[a], CartesianIndex["$"]] CartesianPair[CartesianIndex["$"], c0+c1] , TraditionalForm]; + +Pair /: + MakeBoxes[Pair[(h : LorentzIndex| ExplicitLorentzIndex)[a_, dim_Symbol], (c0: _. _CartesianMomentum)+ c1_:0], TraditionalForm]:= + ToBoxes[Pair[h[a,dim], CartesianIndex["$",dim-1]] CartesianPair[CartesianIndex["$",dim-1], c0+c1] , TraditionalForm]; + +Pair /: + MakeBoxes[Pair[(h : LorentzIndex| ExplicitLorentzIndex)[a_, dim_Symbol-4], (c0: _. _CartesianMomentum)+ c1_:0], TraditionalForm]:= + ToBoxes[Pair[h[a,dim-4], CartesianIndex["$",dim-4]] CartesianPair[CartesianIndex["$",dim-4], c0+c1] , TraditionalForm]; + +(* ------------------------------------------------------------------------ *) + + + +(* Typesetting for Pauli matrices and slashes. *) +(* ------------------------------------------------------------------------ *) + +sigmaRep[dim1_,dim2_, sym_] := + Which[ + dim1===3 && dim2===4, + OverscriptBox[sym, $TypesettingDim4], + MatchQ[{dim1,dim2},{dim_Symbol-1,dim_Symbol}], + If[ $TypesettingDimD==="", + sym, + OverscriptBox[sym, $TypesettingDimD] + ], + MatchQ[dim1,_Symbol-4] && dim1===dim2, + OverscriptBox[sym, $TypesettingDimE], + True, + SubscriptBox[sym, ToBoxes[dim1,TraditionalForm]] + ]; + + + +cSigmaRep[dim1_,dim2_,sym_] := + Which[ + dim1===3 && dim2===3, + OverscriptBox[TBox[Style[sym,Bold]], $TypesettingDim4], + MatchQ[dim1,_Symbol-1] && dim1===dim2, + If[ $TypesettingDimD==="", + TBox[Style[sym,Bold]], + OverscriptBox[TBox[Style[sym,Bold]], $TypesettingDimD] + ], + MatchQ[dim1,_Symbol-4] && dim1===dim2, + OverscriptBox[TBox[Style[sym,Bold]], $TypesettingDimE], + True, + SubscriptBox[TBox[Style[sym,Bold]], ToBoxes[dim1,TraditionalForm]] + ]; + + +PauliSigma /: + MakeBoxes[ PauliSigma[ Momentum[x_,dim1_:4],dim2_:3], TraditionalForm ]:= + If[ Head[x]===Plus, + RowBox[{sigmaRep[dim2,dim1,"\[Sigma]"], "\[CenterDot]","(", TBox[Momentum[x,dim1]],")"}], + RowBox[{sigmaRep[dim2,dim1,"\[Sigma]"], "\[CenterDot]", TBox[Momentum[x,dim1]]}] + ]; + +PauliSigma /: + MakeBoxes[ PauliSigma[ CartesianMomentum[x_,dim1_:3],dim2_:3], TraditionalForm ]:= + If[ Head[x]===Plus, + RowBox[{cSigmaRep[dim1,dim2,"\[Sigma]"], "\[CenterDot]","(", TBox[CartesianMomentum[x,dim1]],")"}], + RowBox[{cSigmaRep[dim1,dim2,"\[Sigma]"], "\[CenterDot]", TBox[CartesianMomentum[x,dim1]]}] + ]; + +PauliSigma /: + MakeBoxes[ PauliSigma[LorentzIndex[in_, dim1_:4], dim2_:3], TraditionalForm ]:= + SuperscriptBox[RowBox[{sigmaRep[dim2,dim1,"\[Sigma]"]}], TBox[LorentzIndex[in,dim1]]]; + +PauliSigma /: + MakeBoxes[ PauliSigma[CartesianIndex[in_, dim1_:3], dim2_:3], TraditionalForm ]:= + SuperscriptBox[RowBox[{cSigmaRep[dim1,dim2,"\[Sigma]"]}], TBox[CartesianIndex[in,dim1]]]; + +PauliXi/: + MakeBoxes[PauliXi[Complex[0, 1]], TraditionalForm] := + "\[Xi]"; + +PauliXi/: + MakeBoxes[PauliXi[Complex[0, -1]], TraditionalForm] := + SuperscriptBox["\[Xi]", "\[Dagger]"]; + +PauliEta/: + MakeBoxes[PauliEta[Complex[0, 1]], TraditionalForm] := + "\[Eta]"; + +PauliEta/: + MakeBoxes[PauliEta[Complex[0, -1]], TraditionalForm] := + SuperscriptBox["\[Eta]", "\[Dagger]"]; + +(* ------------------------------------------------------------------------ *) + +FCPartialD /: + MakeBoxes[FCPartialD[x_ ^n_], TraditionalForm]:= + SubsuperscriptBox["\[PartialD]", TBox[x], + TBox[n]] /; Head[x] === Momentum; + +FCPartialD /: + MakeBoxes[ FCPartialD[x_], TraditionalForm]:= + SubscriptBox["\[PartialD]", ToBoxes[x,TraditionalForm]]; + +FCPartialD /: + MakeBoxes[ FCPartialD[x_, LorentzIndex[mu__]], TraditionalForm]:= + RowBox[{"\[PartialD]", "/", "\[PartialD]", SuperscriptBox[ToBoxes[x,TraditionalForm], + ToBoxes[LorentzIndex[mu],TraditionalForm]]}]; + +PlusDistribution /: + MakeBoxes[PlusDistribution[ a_ ], TraditionalForm]:= + SubscriptBox[RowBox[{"(", MakeBoxes[a, + TraditionalForm],")"}],"+"]; + +QuantumField /: + MakeBoxes[ QuantumField[a_/;Head[a]=!=FCPartialD][p_], TraditionalForm]:= + TBox[a,"(",p,")"]; + +QuantumField /: + MakeBoxes[ QuantumField[a_/;Head[a]=!=FCPartialD], TraditionalForm]:= + TBox[a]; + +QuantumField /: + MakeBoxes[ QuantumField[f_/;Head[f]=!=FCPartialD, (LorentzIndex|ExplicitLorentzIndex|Momentum)[mu_,_:4]], TraditionalForm]:= + SubscriptBox[TBox[f], TBox[mu]]; + +QuantumField /: + MakeBoxes[QuantumField[f_/;Head[f]=!=FCPartialD, lori : (LorentzIndex | ExplicitLorentzIndex | Momentum)[_, _ : 4]..., + otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___], TraditionalForm] := + If[ {lori}=!={}, + SubsuperscriptBox[TBox[f], TBox[lori], TBox[otherIndices1, otherIndices2]], + SuperscriptBox[TBox[f], TBox[otherIndices1, otherIndices2]] + ]; + +QuantumField /: + MakeBoxes[ QuantumField[f_/;Head[f]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex| Momentum)[_,_ : 4]..., + otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___][p_], + TraditionalForm]:= + If[ {lori}=!={}, + RowBox[{SubsuperscriptBox[TBox[f], TBox[lori], TBox[otherIndices1, otherIndices2]], "(", TBox[p], ")"}], + RowBox[{SuperscriptBox[TBox[f], TBox[otherIndices1, otherIndices2]], "(", TBox[p], ")"}] + ]; + +QuantumField /: + MakeBoxes[ QuantumField[FCPartialD[pa_], a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex| Momentum)[_,_ : 4]..., + otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___], TraditionalForm]:= + If[ {lori}=!={}, + RowBox[{SubscriptBox["(\[PartialD]", TBox[pa]], SubsuperscriptBox[TBox[a], TBox[lori], TBox[otherIndices1, otherIndices2]],")"}], + RowBox[{SubscriptBox["(\[PartialD]", TBox[pa]], SuperscriptBox[TBox[a], TBox[otherIndices1, otherIndices2]],")"}] + ]; + +QuantumField /: + MakeBoxes[ QuantumField[FCPartialD[pa_], a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex| Momentum)[_,_ : 4]...], TraditionalForm]:= + If[ {lori}=!={}, + RowBox[{SubscriptBox["(\[PartialD]", TBox[pa]], SubscriptBox[TBox[a], TBox[lori]],")"}], + RowBox[{SubscriptBox["(\[PartialD]", TBox[pa]], TBox[a],")"}] + ]; + + +QuantumField /: + MakeBoxes[ QuantumField[FCPartialD[pa_]^m_, a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex| Momentum)[_,_ : 4]..., + otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___], + TraditionalForm]:= + If[ {lori}=!={}, + RowBox[{"(",SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]], SubsuperscriptBox[TBox[a], TBox[lori], TBox[otherIndices1, otherIndices2]],")"}], + RowBox[{"(",SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]], SuperscriptBox[TBox[a], TBox[otherIndices1, otherIndices2]],")"}] + ]; + +QuantumField /: + MakeBoxes[ QuantumField[FCPartialD[pa_]^m_, a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex | Momentum)[_,_ : 4]...], + TraditionalForm]:= + If[ {lori}=!={}, + RowBox[{"(",SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]], SubscriptBox[TBox[a], TBox[lori]],")"}], + RowBox[{"(",SuperscriptBox[TBox[FCPartialD[pa]],TBox[m]],TBox[a],")"}] + ]; + +QuantumField /: + MakeBoxes[ QuantumField[pa__FCPartialD, a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex | Momentum)[_,_ : 4]...], + TraditionalForm]:= + If[ {lori}=!={}, + RowBox[{"(",TBox[pa], SubscriptBox[TBox[a], TBox[lori]],")"}], + RowBox[{"(",TBox[pa], TBox[a],")"}] + ]; + +QuantumField /: + MakeBoxes[ QuantumField[pa__FCPartialD, a_/;Head[a]=!=FCPartialD, lori: (LorentzIndex | ExplicitLorentzIndex | Momentum)[_,_ : 4]..., + otherIndices1_/;!MatchQ[Head[otherIndices1],LorentzIndex|ExplicitLorentzIndex|Momentum], otherIndices2___], TraditionalForm]:= + If[ {lori}=!={}, + RowBox[{"(",TBox[pa], SubsuperscriptBox[TBox[a], TBox[lori], TBox[otherIndices1, otherIndices2]],")"}], + RowBox[{"(",TBox[pa], SuperscriptBox[TBox[a], TBox[otherIndices1, otherIndices2]],")"}] + ]; + +QuarkField /: + MakeBoxes[QuarkField, TraditionalForm]:= "\[Psi]"; + +QuarkFieldPsi /: + MakeBoxes[QuarkFieldPsi, TraditionalForm]:= "\[Psi]"; + +QuarkFieldChi /: + MakeBoxes[QuarkFieldChi, TraditionalForm]:= "\[Chi]"; + +QuarkFieldPsiDagger /: + MakeBoxes[QuarkFieldPsiDagger, TraditionalForm]:= SuperscriptBox["\[Psi]","\[Dagger]"]; + +QuarkFieldChiDagger /: + MakeBoxes[QuarkFieldChiDagger, TraditionalForm]:= SuperscriptBox["\[Chi]","\[Dagger]"]; + +RightPartialD /: + MakeBoxes[RightPartialD[x_ ^n_],TraditionalForm]:= + SubsuperscriptBox[RowBox[{OverscriptBox["\[PartialD]", + "\[RightArrow]"]}], TBox[" ",x],TBox[n]] /; Head[x] === Momentum; + +RightPartialD /: + MakeBoxes[RightPartialD[x_] ,TraditionalForm]:= + SubscriptBox[RowBox[{OverscriptBox["\[PartialD]", + "\[RightArrow]"]}], TBox[x]]; + +ScaleMu /: + MakeBoxes[ScaleMu, TraditionalForm]:= + "\[Mu]"; + +Tf /: + MakeBoxes[Tf, TraditionalForm]:= + SubscriptBox["T","f"]; + +SD /: + MakeBoxes[SD[a_, b_], TraditionalForm]:= + SuperscriptBox["\[Delta]", TBox[a,b]]; + +SDF /: + MakeBoxes[SDF[a_, b_], TraditionalForm]:= + SubscriptBox["\[Delta]", TBox[a,b]]; + +SmallDelta /: + MakeBoxes[SmallDelta, TraditionalForm]:= + "\[Delta]"; + +SmallEpsilon /: + MakeBoxes[SmallEpsilon, TraditionalForm]:= + "\[Epsilon]"; + +SmallVariable /: + MakeBoxes[SmallVariable[a_], TraditionalForm]:= + MakeBoxes[a, TraditionalForm]; + +SO /: + MakeBoxes[SO[x_],TraditionalForm]:= + If[ Head[x] =!= Plus, + TBox["\[CapitalDelta]", "\[CenterDot]", x], + TBox["\[CapitalDelta]", "\[CenterDot]", "(",x,")"] + ]; + + +SOD /: + MakeBoxes[SOD[x_],TraditionalForm]:= + If[ Head[x] =!= Plus, + TBox["\[CapitalDelta]", "\[CenterDot]",x], + TBox["\[CapitalDelta]", "\[CenterDot]", "(",x,")"] + ]; + +(* Typesetting for scalar products in the FCE notation. *) +(* ------------------------------------------------------------------------ *) + +SP /: + MakeBoxes[SP[a_, b_], TraditionalForm]:= + ToBoxes[Pair[Momentum[a],Momentum[b]], TraditionalForm]; + +SPD /: + MakeBoxes[SPD[a_, b_], TraditionalForm]:= + ToBoxes[Pair[Momentum[a,D],Momentum[b,D]], TraditionalForm]; + +SPE /: + MakeBoxes[SPE[a_, b_], TraditionalForm]:= + ToBoxes[Pair[Momentum[a,D-4],Momentum[b,D-4]], TraditionalForm]; + +(* ------------------------------------------------------------------------ *) + +Spinor /: + MakeBoxes[Spinor[p_,0,___], TraditionalForm]:= + TBox["\[CurlyPhi]","(",p,")"]; + +Spinor /: + MakeBoxes[Spinor[p_,m_ /; m=!=0,___], TraditionalForm]:= + TBox["\[CurlyPhi]","(",p, ",", m, ")"]; + +SpinorU /: + MakeBoxes[SpinorU[p_], TraditionalForm]:= + RowBox[{"u","(",TBox[p],")"}]; + +SpinorU /: + MakeBoxes[SpinorU[p_,m_,___], TraditionalForm]:= + RowBox[{"u","(",TBox[p],",",TBox[m],")"}]; + +SpinorU /: + MakeBoxes[SpinorU[p_,0,___], TraditionalForm]:= + RowBox[{"u","(",TBox[p],")"}]; + +SpinorUBar /: + MakeBoxes[SpinorUBar[p_], TraditionalForm]:= + RowBox[{OverscriptBox["u", "_"],"(",TBox[p],")"}]; + +SpinorUBar /: + MakeBoxes[SpinorUBar[p_,m_,___], TraditionalForm]:= + RowBox[{OverscriptBox["u", "_"],"(",TBox[p],",",TBox[m],")"}]; + +SpinorUBar /: + MakeBoxes[SpinorUBar[p_,0,___], TraditionalForm]:= + RowBox[{OverscriptBox["u", "_"],"(",TBox[p],")"}]; + +SpinorV /: + MakeBoxes[SpinorV[p__], TraditionalForm]:= + RowBox[{"v","(",TBox[p],")"}]; + + +SpinorV /: + MakeBoxes[SpinorV[p_,m_,___], TraditionalForm]:= + RowBox[{"v","(",TBox[p],",",TBox[m],")"}]; + +SpinorV /: + MakeBoxes[SpinorV[p_,0,___], TraditionalForm]:= + RowBox[{"v","(",TBox[p],")"}]; + +SpinorVBar /: + MakeBoxes[SpinorVBar[p__], TraditionalForm]:= + RowBox[{OverscriptBox["v", "_"],"(",TBox[p],")"}]; + +SpinorVBar /: + MakeBoxes[SpinorVBar[p_,m_,___], TraditionalForm]:= + RowBox[{OverscriptBox["v", "_"],"(",TBox[p],",",TBox[m],")"}]; + +SpinorVBar /: + MakeBoxes[SpinorVBar[p_,0,___], TraditionalForm]:= + RowBox[{OverscriptBox["v", "_"],"(",TBox[p],")"}]; + + +SpinorUBarD /: + MakeBoxes[SpinorUBarD[p_,m___], TraditionalForm]:= + ToBoxes[SpinorUBar[p,m],TraditionalForm]; + +SpinorVBarD /: + MakeBoxes[SpinorVBarD[p_,m___], TraditionalForm]:= + ToBoxes[SpinorVBar[p,m],TraditionalForm]; + +SpinorUD /: + MakeBoxes[SpinorUD[p_,m___], TraditionalForm]:= + ToBoxes[SpinorU[p,m],TraditionalForm]; + +SpinorVD /: + MakeBoxes[SpinorVD[p_,m___], TraditionalForm]:= + ToBoxes[SpinorV[p,m],TraditionalForm]; + +StandardMatrixElement /: + MakeBoxes[StandardMatrixElement[x_], TraditionalForm] := + RowBox[{"\[LeftDoubleBracketingBar]",TBox[x],"\[RightDoubleBracketingBar]"}]; + +SUND /: + MakeBoxes[SUND[a_, b_,c:Except[_?OptionQ], OptionsPattern[]], TraditionalForm]:= + SuperscriptBox["d", TBox[a,b,c]] + +SUNDelta /: + MakeBoxes[SUNDelta[a_, b_], TraditionalForm ]:= + SuperscriptBox["\[Delta]", TBox[a,b]] + +SUNFDelta /: + MakeBoxes[SUNFDelta[a_, b_], TraditionalForm ]:= + SubscriptBox["\[Delta]", TBox[a,b]] + +SUNF /: + MakeBoxes[SUNF[a_, b_,c:Except[_?OptionQ], OptionsPattern[]], TraditionalForm]:= + SuperscriptBox["f", TBox[a,b,c]] + +SUNIndex /: + MakeBoxes[SUNIndex[p_], TraditionalForm]:= + ToBoxes[p, TraditionalForm]; + +SUNFIndex /: + MakeBoxes[SUNFIndex[p_], TraditionalForm]:= + ToBoxes[p, TraditionalForm]; + +(* add maybe later something to convert SUNN^2 -> CA, CF *) +SUNN /: + MakeBoxes[ SUNN, TraditionalForm ]:= "N"; + +SUNT /: + MakeBoxes[SUNT[a_], TraditionalForm]:= + SuperscriptBox["T", ToBoxes[a, TraditionalForm]]; + +SUNT /: + MakeBoxes[SUNT[a_,b__], TraditionalForm]:= + ToBoxes[DOT@@(SUNT/@{a, b}),TraditionalForm]; + +SUNTF /: + MakeBoxes[SUNTF[{a_}, b_, c_], TraditionalForm]:= + SubsuperscriptBox["T", TBox[b, c], ToBoxes[a, TraditionalForm]]; + +SUNTF /: + MakeBoxes[SUNTF[{a1_, a2__}, b_, c_], TraditionalForm]:= + SubscriptBox[RowBox[Join[{"("},Map[SuperscriptBox["T", + ToBoxes[#, TraditionalForm]] &, {a1,a2}], {")"}]], TBox[b, c]]; + + +TemporalPair /: + MakeBoxes[TemporalPair[ExplicitLorentzIndex[0], (c0: _. TemporalMomentum[b_]) + c1_:0], TraditionalForm]:= + If[ Head[b]===Plus || c1=!=0, + SuperscriptBox[ RowBox[{"(",TBox[TemporalMomentum[c0+c1]],")"}], + 0], + SuperscriptBox[ RowBox[{TBox[c0+c1]}], + 0] + ]; + + + +(* Typesetting for momenta. *) +(* ------------------------------------------------------------------------ *) + +TemporalMomentum /: + MakeBoxes[TemporalMomentum[x_], TraditionalForm]:= + ToBoxes[Momentum[x,D],TraditionalForm]; + +Zeta2 /: + MakeBoxes[Zeta2, TraditionalForm] := + RowBox[{"\[Zeta]","(",2,")"}]; + +Zeta4 /: + MakeBoxes[Zeta4, TraditionalForm] := + RowBox[{"\[Zeta]","(",4,")"}]; + +Zeta6 /: + MakeBoxes[Zeta6, TraditionalForm] := + RowBox[{"\[Zeta]","(",6,")"}]; + +Zeta8 /: + MakeBoxes[Zeta8, TraditionalForm] := + RowBox[{"\[Zeta]","(",8,")"}]; + +Zeta10 /: + MakeBoxes[Zeta10, TraditionalForm] := + RowBox[{"\[Zeta]","(",10,")"}]; + + + +FCPrint[1,"SharedObjectsTypesetting loaded."]; +End[] + diff --git a/FeynCalc/Shared/SharedOptions.m b/FeynCalc/Shared/SharedOptions.m index e2fb58edf..b89aac5f5 100644 --- a/FeynCalc/Shared/SharedOptions.m +++ b/FeynCalc/Shared/SharedOptions.m @@ -6,15 +6,20 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Options shared by various FeynCalc objects and functions *) (* ------------------------------------------------------------------------ *) +CartesianIndexNames::usage = +"CartesianIndexNames is an option for FCCanonicalizeDummyIndices \ +and other functions. It renames the generic dummy Cartesian indices to the indices \ +in the supplied list."; + ClearHeads::usage = "ClearHeads is an option of FCLoopIsolate, FCDiracIsolate \ and other functions. It takes a list of heads that will be replaced by Identity in \ the isolating function. This is useful for cases when we first apply \ @@ -23,8 +28,7 @@ out of the old heads."; Collecting::usage = -"Collecting is an option of Contract2, ApartFF, SquareAmplitude, \ -Series2, TID and related functions. Setting it to True will trigger \ +"Collecting is an option of multiple functions. Setting it to True will trigger \ some kind of collecting of the result."; CouplingConstant::usage = @@ -32,36 +36,37 @@ for CovariantD and FieldStrength."; Dimension::usage = -"Dimension is an option for DiracMatrix, DiracSlash, FourVector, \ -LeviCivita, MetricTensor, SetMandelstam, OneLoop and ScalarProduct. \ -The default setting is sometimes 4, sometimes D. \ +"Dimension is an option for SetMandelstam, ScalarProduct, FAD \ +and other symbols or functions. The default setting is sometimes 4, sometimes D. \ The setting should always be 4, a symbol (D, n, ...), or \ (D-4), (n-4), ... ."; -DimensionalReduction::usage= -"DimensionalReduction is an option for TID and OneLoopSimplify."; +DiracIndexNames::usage = +"DiracIndexNames is an option for FCFAConvert, FCCanonicalizeDummyIndices \ +and other functions. It renames the generic dummy Dirac indices to the indices \ +in the supplied list."; DiracTraceEvaluate::usage = -"DiracTraceEvaluate is an option for DiracTrace and TR. \ -If set to False, DiracTrace remains unevaluated."; +"DiracTraceEvaluate is an option for DiracTrace, DiracSimplify and \ +some other functions. If set to False, Dirac traces remain unevaluated."; Divideout::usage = "Divideout is an option for OPEInt and OPEInsert. \ The setting is divided out at the end."; -EpsContract::usage= -"EpsContract is an option of Contract specifying whether Levi-Civita \ -tensors Eps[...] will be contracted, i.e., products \ -of two Eps are replaced via the determinant formula."; - -EpsDiscard::usage= -"EpsDiscard is an option for FeynCalc2FORM and SquareAmplitude. \ -If set to True all Levi-Civita tensors are replaced by 0 after contraction."; - EpsilonOrder::usage = "EpsilonOrder is an option of OPEIntegrateDelta and RHI. The setting \ determines the order n (Epsilon^n) which should be kept."; +EtaSign::usage = +"EtaSign is an option for SFAD, GFAD, CFAD and other objects representing \ +propagators. It specifies the default sign of the I \[Eta] prescription in the \ +propagators, e.g. for standard Feynman propagators the value 1 corresponds to \ +1/( p^2-m^2 + I \[Eta]), while the value -1 sets 1/( p^2-m^2 - I \[Eta]). \ +Notice that if the sign of I \[Eta] is already specified in the propagator, \ +e.g. CFAD[{q,{m^2,1}}], then this specification always overrides the EtaSign \ +option. Hence CFAD[{q,{m^2,1}}, EtaSign->-1] still has the positive I \[Eta]."; + ExceptHeads::usage = "ExceptHeads is an option of FCLoopIsolate, \ FCDiracIsolate and other functions. It takes a list of heads that \ are not allowed to appear inside isolated expression. For example, \ @@ -79,27 +84,24 @@ performed. For DotSimplity, it determines \ whether noncommutative expansion is done."; -FCCheckSyntax::usage = "FCCheckSyntax is an option for several FeynCalc \ -functions that require correct syntax in order to produce sensible results. \ -If set to True, those functions will try to check the syntax of the input -expressions to detect possible inconsistencies (which mostly come from the -users not familiar with FeynCalc). However, on large expressions such checks -may cost a lot of performance, which is why this option is set to False \ -by default."; - Factoring::usage = "Factoring is an option for Collect2, Contract, \ Tr and more functions. If set to True, the result will be \ factored, using Factor2. If set to any function f, this function \ will be used."; ExtraFactor::usage= -"ExtraFactor is an option for SquareAmplitude, FermionSpinSum and \ +"ExtraFactor is an option for FermionSpinSum and \ DoPolarizationSums. The setting ExtraFactor -> fa \ multiplies the whole amplitude with the factor fa before squaring."; Factorout::usage = "Factorout is an option for OPEInt and OPEIntegrate."; +FCJoinDOTs::usage = +"FCJoinDOTs is an option for DotSimplify and other functions that use \ +DotSimplify internally. When set to True, DotSimplify will try to rewrite \ +expressions like A.X.B + A.Y.B as A.(X+Y).B."; + FCVerbose::usage = "FCVerbose is an option for several functions that allows to specify \ a local value of $VeryVerbose inside those functions. When set to a positive \ @@ -149,10 +151,16 @@ expressions to detect possible inconsistencies (which mostly come from the {FCIntegral[ ... ] :> bla, ...}."; IntermediateSubstitutions::usage = -"IntermediateSubstitutions is an option for OneLoop and \ -and SquareAmplitude. All substitutions indicated hereby are done at \ +"IntermediateSubstitutions is an option of various FeynCalc functions. \ +All substitutions indicated hereby are done at \ an intermediate stage of the calculation."; +InsideDiracTrace::usage = +"InsideDiracTrace is an option of DiracSimplify and some other functions \ +dealing with Dirac algebra. If set to True, the function assumes to operate \ +inside a Dirac trace, i.e., products of an odd number \ +of Dirac matrices are discarded."; + IsolateNames::usage = "IsolateNames is an option for Isolate and Collect2. \ Its default setting is KK. Instead of a symbol the \ @@ -176,6 +184,11 @@ expressions to detect possible inconsistencies (which mostly come from the "PaVeIntegralHeads is an option for FCLoopIsolate, FCLoopSplit and other \ functions. It gives a list of heads that denote Passarino-Veltman integrals"; +PauliReduce::usage= +"PauliReduce is an option for PauliTrick and other functions. It specifies \ +whether a chain of Pauli matrices should be reduced to at most one matrix by +rewriting every pair of matrices in terms of commutator and anticommutator."; + Mandelstam::usage = "Mandelstam is an option for DiracTrace, OneLoop, OneLoopSum, Tr \ and TrickMandelstam. A typical setting is \ @@ -206,9 +219,30 @@ expressions to detect possible inconsistencies (which mostly come from the QuarkMass::usage= "QuarkMass is an option of Amplitude."; -SpinPolarizationSum::usage= -"SpinPolarizationSum is an option for SquareAmplitude and \ -FermionSpinSum. The set (pure) function acts on the usual spin sum."; +SchoutenAllowZeroGain::usage= +"SchoutenAllowZeroGain is an option for FCSchoutenBruteForce and other \ +functions that attempt to simplify the input expression by applying Schouten's \ +identity. When set to True, the algorithm would apply Schouten's identity \ +to the given expression even if this does not decrease the total number of terms \ +in the expression. This is sometimes useful when the algorithm gets stuck and +cannot find further transformation that would make the expression shorter."; + +SchoutenAllowNegativeGain::usage= +"SchoutenAllowZeroGain is an option for FCSchoutenBruteForce and other \ +functions that attempt to simplify the input expression by applying Schouten's \ +identity. It is similar to SchoutenAllowZeroGain with the difference that even \ +transformations that increase the total number of terms might be applied in an \ +attempt to arrive to shorter expressions at a later stage."; + +SetDimensions::usage = +"SetDimensions is an option for ScalarProduct, CartesianScalarProduct and \ +various FCLoopBasis* functions. For scalar products it specifies the dimensions \ +for which the scalar products will be set when ScalarProduct or CartesianScalarProduct \ +are used with the equality sign, e.g. in ScalarProduct[a, b] = m^2. By default, the \ +scalar products are set for 4 and D dimensions. By changing this option \ +the user can add other dimensions or delete the exising ones. In case of the FCLoopBasis* +functions this option specifies the dimensions of the loop and external momenta to be taken \ +into account when extracting the propagator basis."; SUNIndexNames::usage = "SUNIndexNames is an option for FCFAConvert, FCCanonicalizeDummyIndices \ @@ -225,7 +259,7 @@ expressions to detect possible inconsistencies (which mostly come from the operator eigenvalues CA (=N) and CF (=(N^2-1)/(2 N)) are introduced."; TraceOfOne::usage = -"TraceOfOne is an option for Tr and DiracTrace. \ +"TraceOfOne is an option for Tr, DiracTrace and DiracChainJoin \ Its setting determines the value of the unit trace."; VirtualBoson::usage = @@ -236,17 +270,16 @@ expressions to detect possible inconsistencies (which mostly come from the that involve a virtual photon as an external state." West::usage = -"West is an option for DiracTrace, TR and other functions that deal \ -with traces of Dirac matrices. It applies only to the computation of \ -D-dimensional chiral traces (i.e. those that involve one gamma5) in the \ -Breitenlohner-Maison-t'Hooft-Veltman (BMHV) scheme. If set to True, such \ -traces will be computed according to formula (A.5) from \ -Comp. Phys. Comm 77 (1993) 286-298, which is also known as West's formula."; +"West is an option for DiracTrace and several other functions that deal \ +with traces of Dirac matrices. The option applies only to the computation \ +of D-dimensional traces with an odd number of \[Gamma]^5 in the \ +Breitenlohner-Maison-t'Hooft-Veltman (BMHV) scheme. With West->True (default setting), \ +such traces are computed according to formula (A.5) from Comp. Phys. Comm 77 (1993) \ +286-298, which is also known as West's formula."; WriteOut::usage = -"WriteOut is an option for OneLoop and SquareAmplitude. \ -If set to True, the result of OneLoop will be written to a \ -file called \"name.res\", where name is the first argument of OneLoop."; +"WriteOut is an option for OneLoop and several other functions. It is responsible \ +for saving the results to a file ."; WriteOutPaVe::usage= "WriteOutPaVe is an option for PaVeReduce and OneLoopSum. \ diff --git a/FeynCalc/Shared/SharedTools.m b/FeynCalc/Shared/SharedTools.m index 3e1bef8bf..2aaa56292 100644 --- a/FeynCalc/Shared/SharedTools.m +++ b/FeynCalc/Shared/SharedTools.m @@ -6,9 +6,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Small helper tools extensively used in FeynCalc *) @@ -39,25 +39,94 @@ "Expand2[exp, x] expands all sums containing x. \ Expand2[exp, {x1, x2, ...}] expands all sums containing x1, x2, ...."; -FCFactorOut::usage= -"FCFactorOut[exp, pref] factors out pref out of exp. This is often need to \ -bring exp into a particular form that Mathematica refuses to give"; +ExpandAll2::usage= +"ExpandAll2[exp] is similar to ExpandAll, but much faster on simple structures."; FCAntiSymmetrize::usage= "FCAntiSymmetrize[expr, {a1, a2, ...}] antisymmetrizes expr with respect \ to the variables a1, a2, ... "; +FCCheckVersion::usage= +"FCCheckVersion[major,minor,build] checks if the current version of FeynCalc \ +is larger or equal than marjor.minor.build. For example, FCCheckVersion[9,3,0] \ +will generate a warning (when running with the frontend) or quit kernel (when \ +running without the frontend) if the loaded FeynCalc version is older than 9.3.0. \n +Notice that this function is available only since FeynCalc 9.3."; + +FCDuplicateFreeQ::usage= +"FCDuplicateFreeQ[list] yields True if list contains no duplicates and False otherwise. \n +FCDuplicateFreeQ[list,test] uses test to determine whether two objects should be considered \ +duplicates.\n +FCDuplicateFreeQ returns the same results as the standard DuplicateFreeQ. \ +The only reason for introducing FCDuplicateFreeQ is that DuplicateFreeQ is not available \ +in Mathematica 8 and 9, which are still supported by FeynCalc."; + +FCGetNotebookDirectory::usage= +"FCGetNotebookDirectory[] is a convenience function that returns the directory \ +in which the current notebook or .m file is located. It also works when the FrontEnd \ +is not available."; + +FCFactorOut::usage= +"FCFactorOut[exp, pref] factors out pref out of exp. This is often need to \ +bring exp into a particular form that Mathematica refuses to give."; + +FCMakeIndex::usage= +"FCMakeIndex[str1, str2, head] generates an index with the given head out \ +of the string str1 and str2. For example, FCMakeIndex[\"Lor\",\"1\",LorentzIndex] \ +yields LorentzIndex[Lor1]. The second argument can also be an integer. FCMakeIndex \ +is useful for converting the output of different diagram generators such as \ +FeynArts or QGAF into the FeynCalc notation. It uses memoization to improve the \ +performance." + FCPatternFreeQ::usage = -"FCPatternFreeQ[{expr}] yields True if {expr} does not contain any \ +"FCPatternFreeQ[{exp}] yields True if {exp} does not contain any \ pattern objects, e.g. Pattern, Blank, BlankSequence and BlankNullSequence. \n -FCPatternFreeQ[{expr},{h1,h2,...}] checks that in addition to the pattern \ +FCPatternFreeQ[{exp},{h1,h2,...}] checks that in addition to the pattern \ objects, no heads h1, h2, ... are present."; -FCSplit::usage = "FCSplit[expr,{v1, v2, ...}] splits expr into pieces \ +FCProgressBar::usage = +"FCProgressBar[text, i, total] is a simple auxiliary function that can \ +be used to display the progress of a certain evaluation, e.g. mapping a list \ +of integrals to some function. Here i is the number of the current step \ +while total denotes the overall number of steps. A simple usage example \ +is Table[FCProgressBar[\"Calculating integral \", i, 10], {i, 1, 10}]."; + +FCReloadFunctionFromFile::usage = +"FCReloadFunctionFromFile[function, path] is an auxiliary function that \ +attempts to remove all the definitions of the given FeynCalc function and \ +then reload them from the specified file. It is intended to be a helper tool \ +for FeynCalc developers, which allows one to debug/improve internal functions \ +and test the results without restarting the kernel. Depending on the complexity \ +of the given function, there might also be unknown side effects. The function is \ +not meant to be invoked by the normal users. "; + +FCReplaceAll::usage= +"FCReplaceAll[exp, ru1, ...] is like ReplaceAll, but it also allows to apply multiple \ +replacement rules sequentially. Instead of doing exp /. ru1 /. ru2 /. ru3 one can just \ +write FCReplaceAll[exp, ru1, ru2, ru3]."; + +FCReplaceRepeated::usage= +"FCReplaceRepeated[exp, ru1, ...] is like ReplaceRepeated, but it also allows to apply multiple \ +replacement rules sequentially. Instead of doing exp //. ru1 //. ru2 //. ru3 one can just \ +write FCReplaceRepeated[exp, ru1, ru2, ru3]."; + +FCSplit::usage = "FCSplit[exp,{v1, v2, ...}] splits expr into pieces \ that are free of any occurence of v1, v2, ... and pieces that contain \ those variables. This works both on sums and products. The output \ is provided in the form of a two element list. One can recover the \ -original expression by applying Total to that list"; +original expression by applying Total to that list."; + +FCProductSplit::usage = "FCProductSplit[exp,{v1, v2, ...}] splits exp \ +into two products, where the first one is free of \ +v1, v2, ... and the second one contains those variables. \ +The output is provided in the form of a two element list. One can recover the \ +original expression by multiplying both elements with each other."; + +FCSubsetQ::usage= +"FCSubsetQ[list1,list2] yields True if list2 is a subset of list1 and \ +False otherwise. It returns the same results as the standard SubsetQ. \ +The only reason for introducing FCSubsetQ is that SubsetQ is not available \ +in Mathematica 8 and 9, which are still supported by FeynCalc."; FCSymmetrize::usage= "FCSymmetrize[expr, {a1, a2, ...}] symmetrizes expr with respect \ @@ -90,14 +159,14 @@ MemSet::usage = "MemSet[f[x_], body] is like f[x_] := f[x] = body, \ -but dependend on the value of the setting of MemoryAvailable -> \ +but dependend on the value of the setting of FCMemoryAvailable -> \ memorycut (memorycut - MemoryInUse[]/10.^6) \ MemSet[f[x_], body] may evaluate as f[x_] := body." -MemoryAvailable::usage = -"MemoryAvailable is an option of MemSet. It can be set to an integer n, \ +FCMemoryAvailable::usage = +"FCMemoryAvailable is an option of MemSet. It can be set to an integer n, \ where n is the available amount of main memory in Mega Byte. \ -The default setting is $MemoryAvailable."; +The default setting is $FCMemoryAvailable."; MLimit::usage= "MLimit[expr, {lims}] takes multiple limits of expr using the limits lims."; @@ -135,8 +204,8 @@ an integer (even if it is symbolic). Furthermore \ (-1)^(-n) -> (-1)^n and Exp[I m Pi] -> (-1)^m."; SelectFree2::usage= -"SelectFree2[expr, a, b, ...] is like SelectFree but -it first expands the expression w.r.t to the arguments via +"SelectFree2[expr, a, b, ...] is like SelectFree but \ +it first expands the expression w.r.t to the arguments via \ Expand2"; SelectFree::usage= @@ -154,8 +223,8 @@ an integer (even if it is symbolic). Furthermore \ a sum)."; SelectNotFree2::usage= -"SelectNotFree2[expr, a, b, ...] is like SelectNotFree but -it first expands the expression w.r.t to the arguments via +"SelectNotFree2[expr, a, b, ...] is like SelectNotFree but \ +it first expands the expression w.r.t to the arguments via \ Expand2"; SelectSplit::usage= @@ -166,7 +235,17 @@ an integer (even if it is symbolic). Furthermore \ XYT::usage= "XYT[exp, x,y] transforms (x y)^m away ..." -FCSplit::fail = "Error! Splitting `1` w.r.t `2` failed!"; +FCProductSplit::failmsg = "Error! FCProductSplit has encountered a fatal problem and must abort the computation. \n +The problem reads: `1`"; + +FCSplit::failmsg = "Error! FCSplit has encountered a fatal problem and must abort the computation. \n +The problem reads: `1`"; + +FCReloadFunctionFromFile::failmsg = "Error! FCReloadFunctionFromFile has encountered a fatal problem and must abort the computation. \n +The problem reads: `1`"; + +FCDuplicateFreeQ::failmsg = "Error! FCDuplicateFreeQ has encountered a fatal problem and must abort the computation. \n +The problem reads: `1`"; Begin["`Package`"] End[] @@ -180,45 +259,55 @@ an integer (even if it is symbolic). Furthermore \ Options[Cases2] = { Heads -> False }; + Options[Combine] = { Expanding -> False }; + Options[SelectSplit] = { Heads -> None }; - Options[FCFactorOut] = { - Factoring -> Simplify + Factoring -> Simplify, + Head -> Identity }; - - Options[ILimit] = { FunctionLimits -> {Log -> Log} }; + Options[MemSet] = { - MemoryAvailable -> $MemoryAvailable + FCMemoryAvailable -> $FCMemoryAvailable }; + Options[MLimit] = { Limit -> Limit }; +Options[NTerms] = { + Expand -> True +}; + Options[FCSplit] = { Expanding -> True }; +Options[FCProductSplit] = { + Abort -> False +}; + Options[FRH] = { - IsolateNames->All + IsolateNames -> All }; Options[PowerSimplify] = { - Assumptions->True, - PowerExpand->True + Assumptions -> True, + PowerExpand -> True }; Options[Power2] = { - Assumptions->True + Assumptions -> True }; Cases2[expr_, {f___}, opts:OptionsPattern[]] := @@ -228,7 +317,7 @@ an integer (even if it is symbolic). Furthermore \ Union[Cases[{expr}, HoldPattern[f[___]], Infinity,opts]]; Cases2[expr_, f_, g__, opts:OptionsPattern[]] := - Union[Cases[{expr}, Alternatives@@(#[___]&/@{f,g}), + Union[Cases[{expr}, Alternatives@@(HoldPattern[#[___]]&/@{f,g}), Infinity, FilterRules[{opts}, Options[Cases]]]]; @@ -306,14 +395,186 @@ an integer (even if it is symbolic). Furthermore \ ] ]; + +ExpandAll2[expr_] := + FixedPoint[ + Switch[ Head[#], + Times, + Distribute[#], + Plus, + If[ !FreeQ[List@@#,Plus], + (ExpandAll2 /@ #), + # + ], + _, + # + ] &, expr]; + FCAntiSymmetrize[x_,v_List] := Block[{su}, su[y_, {a__}, {b__}] := y /. Thread[{a} -> {b}]; 1 / Factorial[Length[v]] Plus@@Map[(Signature[#] su[x,v,#])&, Permutations[v]] ]; +FCCheckVersion[major_Integer?NonNegative, minor_Integer?NonNegative, build_Integer?NonNegative, OptionsPattern[]]:= + Block[{str}, + str = "Your FeynCalc version is too old. The following code requires at least FeynCalc "<> + ToString[major]<>"."<> ToString[minor]<>"."<> ToString[build]<>"."; + If[ !MatchQ[ToExpression[StringSplit[$FeynCalcVersion, "."]],{a_/;a>=major,b_/;b>=minor,c_/; c>=build}], + If[ ($FrontEnd === Null || $Notebooks===False), + Print[str]; + Quit[], + CreateDialog[{TextCell[str], DefaultButton[]}, Modal->True]; + ] + ] + ]; + + +FCDuplicateFreeQ[ex_/; Head[ex] =!= List, ___] := + ( + Message[FCDuplicateFreeQ::failmsg, "The input expression is not a list."]; + Abort[] + ); + +FCDuplicateFreeQ[{}, ___] := + True; + +FCDuplicateFreeQ[ex_List, test_ : FCGV[""]] := + Block[{tmp, num}, + + If[ test === FCGV[""], + tmp = Last[SortBy[Tally[ex], Last]], + tmp = Check[Last[SortBy[Tally[ex, test], Last]], $Failed, Tally::smtst] + ]; + + If[ Head[tmp] =!= List || tmp === {}, + Message[FCDuplicateFreeQ::failmsg, "Failed to count the elements in the list."]; + Abort[] + ]; + + num = Last[tmp]; + + If[ !MatchQ[num, _Integer?NonNegative], + Message[FCDuplicateFreeQ::failmsg, "Failed to count the elements in the list."]; + Abort[] + ]; + + num < 2 + ]; + + +FCMakeIndex[x_String, y_List, head_: Identity] := + MemSet[ FCMakeIndex[x, y, head], + FCMakeIndex[x,#,head]&/@y + ]; + +FCMakeIndex[x_String, y_String, head_: Identity] := + MemSet[ FCMakeIndex[x, y, head], + head[ToExpression[x <> y]] + ]; + +FCMakeIndex[x_String, y_Integer, head_: Identity] := + MemSet[ FCMakeIndex[x, y, head], + head[ToExpression[x <> ToString[y]]] + ]/; y >= 0; + +FCMakeIndex[x_String, y_Integer, head_: Identity] := + MemSet[ FCMakeIndex[x, y, head], + head[ToExpression[x <> "Minus" <> ToString[-y]]] + ]/; y < 0; + FCFactorOut[expr_,pref_,OptionsPattern[]]:= - pref OptionValue[Factoring][expr/pref]; + pref OptionValue[Head][OptionValue[Factoring][expr/pref]]; + +FCGetNotebookDirectory[]:= + Block[{dir}, + If[$FrontEnd===Null, + dir=DirectoryName[$InputFileName], + dir=NotebookDirectory[] + ]; + dir + ]; + +FCPatternFreeQ[expr_List]:= + FreeQ2[expr, {Pattern, Blank,BlankSequence,BlankNullSequence, Alternatives}]; + +FCPatternFreeQ[expr_List ,objs_List]:= + FreeQ2[expr, Join[ {Pattern, Blank,BlankSequence,BlankNullSequence, Alternatives}, objs]]; + +FCProgressBar[text_String, i_Integer, tot_Integer] := + FCPrint[0, text <> ToString[i] <> " / " <> ToString[tot] <> "\n", UseWriteString -> True]; + + +FCReloadFunctionFromFile[fun_, file_String] := + Block[{names, names1, names2, str1, str2}, + + If[! TrueQ[FileExistsQ[file]], + Message[FCReloadFunctionFromFile::failmsg, "The file " <> file <> " does not exist."]; + Abort[] + ]; + + str1 = "FeynCalc`" <> ToString[fun] <> "`*"; + str2 = "FeynCalc`" <> ToString[fun] <> "`Private`*"; + names = Join[Names[str1], Names[str2]]; + + With[{x = str1}, ClearAll[x]]; + With[{x = str2}, ClearAll[x]]; + + If[ names =!= {}, + Quiet[Remove /@ names, Remove::rmnsm] + ]; + + ClearAll[fun]; + Quiet[Remove[fun], Remove::rmnsm]; + + BeginPackage["FeynCalc`"]; + FCDeclareHeader[file]; + Get[file]; + EndPackage[]; + Null +]; + +FCProductSplit[expr_, vars_List /; vars =!= {}, OptionsPattern[]] := + Block[{dummy,exprAsList,pow,free,notfree}, + If[ NTerms[expr,Expand->False] > 1, + Message[FCProductSplit::failmsg,"The input expression is not a product"]; + Abort[] + ]; + + exprAsList = List@@(expr*dummy); + If[ !FreeQ[exprAsList,Power], + exprAsList /. Power -> pow //. { + {a___,pow[b_,n_Integer?Positive],c___} :> {a,Sequence@@ConstantArray[b,n],c}, + {a___,pow[b_,n_Integer?Negative],c___} :> {a,Sequence@@ConstantArray[1/b,-n],c} + } /. pow -> Power + ]; + + free = SelectFree[exprAsList,vars] /. dummy :> Unevaluated[Sequence[]]; + notfree = SelectNotFree[exprAsList,vars]; + + free = Times@@free; + notfree = Times@@notfree; + + If[ free*notfree =!= expr || ! FreeQ2[free, vars], + Message[FCProductSplit::failmsg, "Error! Splitting" <>ToString[expr,InputForm]<> " w.r.t " <>ToString[vars,InputForm]<> " failed!"]; + Abort[] + ]; + + {free,notfree} + ]; + + +FCReplaceAll[ex_, ru_] := + ReplaceAll[ex, ru]; + +FCReplaceAll[ex_, ru1_, ru2__] := + Fold[ReplaceAll, ex, {ru1, ru2}]; + +FCReplaceRepeated[ex_, ru_] := + ReplaceRepeated[ex, ru]; + +FCReplaceRepeated[ex_, ru1_, ru2__] := + Fold[ReplaceRepeated, ex, {ru1, ru2}]; FCPatternFreeQ[expr_List]:= FreeQ2[expr, {Pattern, Blank,BlankSequence,BlankNullSequence}]; @@ -322,16 +583,30 @@ an integer (even if it is symbolic). Furthermore \ FreeQ2[expr, Join[ {Pattern, Blank,BlankSequence,BlankNullSequence}, objs]]; FCSplit[expr_, vars_List /; vars =!= {}, OptionsPattern[]] := - Block[ {free, notfree, tmp, null1, null2}, + Block[ {free, notfree, tmp, time}, If[ OptionValue[Expanding], tmp = Expand2[expr, vars], tmp = expr ]; - free = SelectFree[tmp + null1 + null2, vars] /. null1 | null2 -> 0; - notfree = - SelectNotFree[tmp + null1 + null2, vars] /. null1 | null2 -> 0; + + time=AbsoluteTime[]; + + If[Head[tmp]===Plus, + free = SelectFree[tmp, vars]; + notfree = SelectNotFree[tmp, vars], + + If[ FreeQ2[tmp,vars], + free = tmp; + notfree = 0, + + notfree = tmp; + free = 0 + ] + ]; + FCPrint[1,"FCSplit: Splitting, timing: ", N[AbsoluteTime[] - time, 4]]; + If[ free + notfree =!= tmp || ! FreeQ2[free, vars], - Message[FCSplit::fail, expr, vars]; + Message[FCSplit::failmsg, "Error! Splitting" <>ToString[expr,InputForm]<> " w.r.t " <>ToString[vars,InputForm]<> " failed!"]; Abort[] ]; {free, notfree} @@ -340,6 +615,11 @@ an integer (even if it is symbolic). Furthermore \ FCSplit[expr_List, vars_List /; vars =!= {}, opts:OptionsPattern[]]:= Map[FCSplit[#, vars, opts]&, expr]; +FCSplit[_, vars_, OptionsPattern[]]:= + ( + Message[FCSplit::failmsg, "The second argument must be a list."]; + Abort[] + )/; Head[vars]=!=List; FCSymmetrize[x_,v_List] := Block[{su}, @@ -347,6 +627,13 @@ an integer (even if it is symbolic). Furthermore \ 1 / Factorial[Length[v]] Plus@@Map[su[x, v, #]&, Permutations[v]] ]; + +FCSubsetQ[l1_List, l2_List] := +(DeleteDuplicates[Sort[MemberQ[l1, #] & /@ l2]] === {True}) /; l2 =!= {}; + +FCSubsetQ[_List, {}] := + True; + FreeQ2[_,{}] := True; @@ -429,20 +716,32 @@ an integer (even if it is symbolic). Furthermore \ ]; MemSet[x_,y_, OptionsPattern[]] := - If[(OptionValue[MemoryAvailable] - MemoryInUse[]/1000000.) <1. || $DisableMemSet, + If[(OptionValue[FCMemoryAvailable] - MemoryInUse[]/1000000.) <1. || $DisableMemSet, y, Set[x, y] - ]; + ]/; MatchQ[OptionValue[FCMemoryAvailable],_Integer?Positive]; + +MemSet[_,_, OptionsPattern[]]:= + ( + Message[FeynCalc::failmsg,"The value of FCMemoryAvailable is not a positive integer."]; + Abort[] + )/; !MatchQ[OptionValue[FCMemoryAvailable],_Integer?Positive]; MLimit[x_, l_List, OptionsPattern[]] := Fold[OptionValue[Limit][#1, Flatten[{##2}][[1]]]&, x, l]; -NTerms[x_Plus] := +NTerms[x_Plus, OptionsPattern[]] := Length[x]; -NTerms[x_] := - Block[{ntermslex = Expand[x]}, +NTerms[x_, OptionsPattern[]] := + Block[{ntermslex}, + + If[ OptionValue[Expand], + ntermslex = Expand[x], + ntermslex = x + ]; + If[ Head[ntermslex]===Plus, ntermslex = Length[ntermslex], If[x===0, diff --git a/FeynCalc/Shared/Solve.m b/FeynCalc/Shared/Solve.m index 70681a234..2f071a394 100755 --- a/FeynCalc/Shared/Solve.m +++ b/FeynCalc/Shared/Solve.m @@ -28,8 +28,19 @@ Begin["`Solve`Private`"] -Options[Solve2] = {Factoring -> Factor2, FinalSubstitutions -> {}}; -Options[Solve3] = {Factoring -> False, FinalSubstitutions -> {}, ParallelMap -> False}; +sol3Verbose::usage=""; + +Options[Solve2] = { + Factoring -> Factor2, + FinalSubstitutions -> {} +}; + +Options[Solve3] = { + FCVerbose -> False, + Factoring -> False, + FinalSubstitutions -> {}, + ParallelMap -> False +}; Solve2[a_/;Head[a]=!=List, b__] := Solve2[{a}, b]; @@ -39,7 +50,7 @@ Solve2[ai_List, bii_, ops___Rule] := Block[{fixeq, temp, re, factor , finsub, a, b, bi,dumsub, dum}, bi = Flatten[{bii}]; - dumsub = Table[bi[[ij]] -> dum[ij],{ij,Length[bi]}]; + dumsub = Table[bi[[r]] -> dum[r],{r,Length[bi]}]; a = Flatten[{ai}] /. dumsub; b = Last/@dumsub; factor = Factoring /. {ops} /. Options[Solve2]; @@ -63,12 +74,36 @@ Solve3[a_/;Head[a]=!=List, b__] := Solve3[{a}, b]; -Solve3[eqq_List, clii_List, ops___Rule] := - Block[{cli = clii, factor , finsub,newel, lneq, neqh,isol, neq, newneq, - col, new, res = {}, parmap, pmap, starttime = AbsoluteTime[]}, - factor = Factoring /. {ops} /. Options[Solve3]; - finsub = FinalSubstitutions/. {ops} /. Options[Solve3]; - parmap = ParallelMap /. {ops} /. Options[Solve3]; +Solve3[eqq_List, clii_List, OptionsPattern[]] := + Block[{cli = clii, factor, factorSpecial, optFactoring, finsub,newel, lneq, neqh,isol, neq, newneq, + col, new, res = {}, parmap, pmap, starttime = AbsoluteTime[], neq1}, + + optFactoring = OptionValue[Factoring]; + finsub = OptionValue[FinalSubstitutions]; + parmap = OptionValue[ParallelMap]; + + If [OptionValue[FCVerbose]===False, + sol3Verbose=$VeryVerbose, + If[MatchQ[OptionValue[FCVerbose], _Integer], + sol3Verbose=OptionValue[FCVerbose] + ]; + ]; + + Switch[optFactoring, + False, + factor = Identity; + factorSpecial = Identity, + True|Factor2, + factor = Factor2; + factorSpecial = Identity, + {_, _}, + factor = optFactoring[[1]]; + factorSpecial = optFactoring[[2]], + _, + factor = optFactoring; + factorSpecial = optFactoring + ]; + (* High - school algorithm *) isol[xy__] := @@ -78,8 +113,8 @@ ]; With[{cli = cli}, - col = ( FCPrint[2," Collect with Factor "]; - Collect[#, cli, Factor] ) & + col = ( FCPrint[2," Collect with ", factorSpecial]; + Collect[#, cli, factorSpecial] ) & ]; If[TrueQ[parmap], @@ -100,16 +135,27 @@ neq = eqq /. Equal[a_, b_] :> (a-b); For[i = 1, i <= Length[eqq], i++, + If[ i>Length[cli], + Break[]; + ]; If[!FreeQ[neq, cli[[i]]], - FCPrint[1,"solve3 i = ",i," time used : ", - Round[(starttime-AbsoluteTime[])/60], " minutes" ]; + FCPrint[1,"solve3 i = ",i," time used : ", Round[(starttime-AbsoluteTime[])/60], " minutes", FCDoControl->sol3Verbose]; While[FreeQ[neq1 = (*col[*)neq[[1]] /. res(*]*), cli[[i]]], - FCPrint[2,"rotating ", i]; + FCPrint[2,"rotating ", i, FCDoControl->sol3Verbose]; neq = RotateLeft[neq = Prepend[Rest[neq],neq1]] ]; - FCPrint[2,"solving for ",cli[[i]]]; + FCPrint[2,"solving for ",cli[[i]], FCDoControl->sol3Verbose]; (*{neq1,cli[[i]]}>>"neq1.s";*) - new = Solve2[neq1, cli[[i]], Factoring -> False][[1]]; + + + FCPrint[1,"Solve3: Calling Solve2.", FCDoControl->sol3Verbose]; + new = Solve2[neq1, cli[[i]], Factoring -> factor][[1]]; + + (*new = Solve[neq1, cli[[i]]];*) + FCPrint[1,"Solve3: Solve2 done.", FCDoControl->sol3Verbose]; + FCPrint[3,"Solve3: new:", new, FCDoControl->sol3Verbose]; + + (* FCPrint[3,"solution = ",new//InputForm]; new >>"new.s"; @@ -118,18 +164,23 @@ CHANGE 20100110 new = new[[1]] -> Collect2[new[[2]], cli, Factoring -> Factor2]; *) - new = new[[1]] -> Collect[new[[2]], cli, Factor]; + + FCPrint[3,"Solve3: Calling Collect.", FCDoControl->sol3Verbose]; + new = new[[1]] -> Collect[new[[2]], cli, factorSpecial]; + FCPrint[3,"Solve3: Collect done.", FCDoControl->sol3Verbose]; + If[!FreeQ2[new[[2]], cli], + FCPrint[3,"Solve3: Applying Cancel.", FCDoControl->sol3Verbose]; new = new[[1]] -> Map[Cancel, new[[2]]]; ]; - FCPrint[3,"solution = ",new//InputForm]; + FCPrint[3,"solution = ",new//InputForm, FCDoControl->sol3Verbose]; neq = Rest[neq]; If[i>1, res = Append[specsimp[res, new], new], res = {new} ]; If[isol3Verbose]; newneq = {}; (* neqh = Hold@@{neq}; @@ -150,10 +201,11 @@ Clear[newel]; ]; neq = newneq; *) - FCPrint[1,"leafcount neq = ", LeafCount[neq]]; + FCPrint[1,"leafcount neq = ", LeafCount[neq], FCDoControl->sol3Verbose]; ]; ]; ]; + FCPrint[1,"Solve3: Main loop done.", FCDoControl->sol3Verbose]; res = res /. finsub; If[factor =!= False, res = pmap[(#[[1]] -> factor[#[[2]]])&, res] diff --git a/FeynCalc/Shared/TimedIntegrate.m b/FeynCalc/Shared/TimedIntegrate.m index c5580515b..420086441 100644 --- a/FeynCalc/Shared/TimedIntegrate.m +++ b/FeynCalc/Shared/TimedIntegrate.m @@ -29,10 +29,10 @@ "Manual abort"; Options[TimedIntegrate] = { - Timing -> 10, Assumptions -> Epsilon > 0, - Integrate -> Integrate, - Expand -> True + Expand -> True, + Integrate -> Integrate, + Timing -> 10 }; TimedIntegrate[exp_,vars__List,opts___Rule] := diff --git a/FeynCalc/Tables/Amplitude.m b/FeynCalc/Tables/Amplitude.m index c1a822898..6a80761e3 100755 --- a/FeynCalc/Tables/Amplitude.m +++ b/FeynCalc/Tables/Amplitude.m @@ -24,78 +24,140 @@ Begin["`Amplitude`Private`"] -Options[Amplitude] = {Dimension->D, -Gauge -> 1, QuarkMass -> 0, Polarization -> 1 }; + +(* TODO For later one would need to find a better solution (FCGV?), for now + just put all this stuff into the `Private` context*) + +nochnich::usage=""; +ampswitch::usage=""; + +mu::usage=""; +nu::usage=""; +al::usage=""; +be::usage=""; +li1::usage=""; + +alpha::usage=""; +beta::usage=""; +delta::usage=""; +kappa::usage=""; +ka::usage=""; +gamma::usage=""; +rho::usage=""; +ro::usage=""; +lambda::usage=""; +tau::usage=""; +xi::usage=""; +si::usage=""; + +q1::usage=""; +q2::usage=""; +p1::usage=""; +p2::usage=""; +ci1::usage=""; +ci2::usage=""; +ci3::usage=""; +ci4::usage=""; + +c5::usage=""; +c6::usage=""; +de::usage=""; + +nice::usage=""; + + + + +Options[Amplitude] = { + Dimension -> D, + Gauge -> 1, + QuarkMass -> 0, + Polarization -> 1 +}; abbs = { - alpha :> FCGV["\[Alpha]"], beta :> FCGV["\[Beta]"], - al :> FCGV["\[Alpha]"], be :> FCGV["\[Beta]"], - delta :> FCGV["\[Delta]"], - kappa :> FCGV["\[Kappa]"], - ka :> FCGV["\[Kappa]"], - gamma :> FCGV["\[Gamma]"], - mu :> FCGV["\[Mu]"], nu :> FCGV["\[Nu]"], - rho:> FCGV["\[Rho]"], sigma:> FCGV["\[Sigma]"], - ro:> FCGV["\[Rho]"], si:> FCGV["\[Sigma]"], - lambda:> FCGV["\[Lambda]"], tau:> FCGV["\[Tau]"], - xi :> FCGV["\[Xi]"], - a :> FCGV["a"], b :> FCGV["b"], c :> FCGV["c"], - d :> FCGV["d"], e :> FCGV["e"], f :> FCGV["f"], - i :> FCGV["i"], j :> FCGV["j"], h :> FCGV["h"], - r :> FCGV["r"], - s :> FCGV["s"], v :> FCGV["v"], w :> FCGV["w"] - }; + alpha :> FCGV["\[Alpha]"], + beta :> FCGV["\[Beta]"], + al :> FCGV["\[Alpha]"], + be :> FCGV["\[Beta]"], + delta :> FCGV["\[Delta]"], + kappa :> FCGV["\[Kappa]"], + ka :> FCGV["\[Kappa]"], + gamma :> FCGV["\[Gamma]"], + mu :> FCGV["\[Mu]"], + nu :> FCGV["\[Nu]"], + rho :> FCGV["\[Rho]"], +(* sigma :> FCGV["\[Sigma]"],*) + ro :> FCGV["\[Rho]"], + si :> FCGV["\[Sigma]"], + lambda :> FCGV["\[Lambda]"], + tau :> FCGV["\[Tau]"], + xi :> FCGV["\[Xi]"], + a :> FCGV["a"], + b :> FCGV["b"], + c :> FCGV["c"], + d :> FCGV["d"], + e :> FCGV["e"], + f :> FCGV["f"], + i :> FCGV["i"], + j :> FCGV["j"], + h :> FCGV["h"], + r :> FCGV["r"], + s :> FCGV["s"], + v :> FCGV["v"], + w :> FCGV["w"] +}; -If[$Notebooks === True, - nice = Join[abbs, - {p :> FCGV["p"], - q :> FCGV["q"], - k :> FCGV["k"], - q1 :> FCGV["q1"], - q2 :> FCGV["q2"], - p1 :> FCGV["p1"], - p2 :> FCGV["p2"], - u5 :> Subscript["u",5], - li1:> Subscript[FCGV["\[Lambda]"], 1], - li2:> Subscript[FCGV["\[Lambda]"], 2], - li3:> Subscript[FCGV["\[Lambda]"], 3], - li4:> Subscript[FCGV["\[Lambda]"], 4], - li5:> Subscript[FCGV["\[Lambda]"], 5], - li6:> Subscript[FCGV["\[Lambda]"], 6], - li7:> Subscript[FCGV["\[Lambda]"], 7], - li8:> Subscript[FCGV["\[Lambda]"], 8], - li9:> Subscript[FCGV["\[Lambda]"], 9], - li10:> Subscript[FCGV["\[Lambda]"], 10], - li11:> Subscript[FCGV["\[Lambda]"], 11], - li12:> Subscript[FCGV["\[Lambda]"], 12], - li13:> Subscript[FCGV["\[Lambda]"], 13], - li14:> Subscript[FCGV["\[Lambda]"], 14], - li15:> Subscript[FCGV["\[Lambda]"], 15], - li16:> Subscript[FCGV["\[Lambda]"], 16], - li17:> Subscript[FCGV["\[Lambda]"], 17], - ci1:> Subscript["c", 1], - ci2:> Subscript["c", 2], - ci3:> Subscript["c", 3], - ci4:> Subscript["c", 4], - ci5:> Subscript["c", 5], - ci6:> Subscript["c", 6], - ci7:> Subscript["c", 7], - ci8:> Subscript["c", 8], - ci9:> Subscript["c", 9], - ci10:> Subscript["c", 10], - ci11:> Subscript["c", 11], - ci12:> Subscript["c", 12], - ci13:> Subscript["c", 13], - ci14:> Subscript["c", 14], - ci15:> Subscript["c", 15], - ci16:> Subscript["c", 16], - ci17:> Subscript["c", 17], - u1:> Subscript["u",1], - u2:> Subscript["u",2], - u3:> Subscript["u",3], - u4:> Subscript["u",4], - u5:> Subscript["u",5] - } ] +If[ $Notebooks === True, + nice = Join[abbs, { + p :> FCGV["p"], + q :> FCGV["q"], + k :> FCGV["k"], + q1 :> FCGV["q1"], + q2 :> FCGV["q2"], + p1 :> FCGV["p1"], + p2 :> FCGV["p2"](*, + u5 :> Subscript["u",5], + li1:> Subscript[FCGV["\[Lambda]"], 1], + li2:> Subscript[FCGV["\[Lambda]"], 2], + li3:> Subscript[FCGV["\[Lambda]"], 3], + li4:> Subscript[FCGV["\[Lambda]"], 4], + li5:> Subscript[FCGV["\[Lambda]"], 5], + li6:> Subscript[FCGV["\[Lambda]"], 6], + li7:> Subscript[FCGV["\[Lambda]"], 7], + li8:> Subscript[FCGV["\[Lambda]"], 8], + li9:> Subscript[FCGV["\[Lambda]"], 9], + li10:> Subscript[FCGV["\[Lambda]"], 10], + li11:> Subscript[FCGV["\[Lambda]"], 11], + li12:> Subscript[FCGV["\[Lambda]"], 12], + li13:> Subscript[FCGV["\[Lambda]"], 13], + li14:> Subscript[FCGV["\[Lambda]"], 14], + li15:> Subscript[FCGV["\[Lambda]"], 15], + li16:> Subscript[FCGV["\[Lambda]"], 16], + li17:> Subscript[FCGV["\[Lambda]"], 17], + ci1:> Subscript["c", 1], + ci2:> Subscript["c", 2], + ci3:> Subscript["c", 3], + ci4:> Subscript["c", 4], + ci5:> Subscript["c", 5], + ci6:> Subscript["c", 6], + ci7:> Subscript["c", 7], + ci8:> Subscript["c", 8], + ci9:> Subscript["c", 9], + ci10:> Subscript["c", 10], + ci11:> Subscript["c", 11], + ci12:> Subscript["c", 12], + ci13:> Subscript["c", 13], + ci14:> Subscript["c", 14], + ci15:> Subscript["c", 15], + ci16:> Subscript["c", 16], + ci17:> Subscript["c", 17], + u1:> Subscript["u",1], + u2:> Subscript["u",2], + u3:> Subscript["u",3], + u4:> Subscript["u",4], + u5:> Subscript["u",5]*) + }] , nice = Join[abbs, {p :> FCGV["p"], @@ -106,1486 +168,1482 @@ p1 :> FCGV["p1"], p2 :> FCGV["p2"] } ] - ]; +]; -Amplitude[nam___, opt___Rule] := Block[{ -qo, go, gv, qgv,gp,qp,qpm,qpmi, -ghp, gi, pol, gauge, nonz, mass, ggv, pro - }, -pol = Polarization /. {opt} /. Options[Amplitude]; -mass = QuarkMass /. {opt} /. Options[Amplitude]; -gauge = Gauge /. {opt} /. Options[Amplitude]; -qo[y__] := qo[y] = Twist2QuarkOperator[y, Polarization -> pol]; -go[y__] := go[y] = Twist2GluonOperator[y, Polarization -> pol]; -gi[a__, b1_,b2_, c1_,c2_] := ggv[a, c1,c2, b1,b2]; -gv = GluonVertex; -nonz = ZeroMomentumInsertion -> False; -qgv = QuarkGluonVertex; -ggv = GluonGhostVertex; -ghp = GhostPropagator; -pro = -I/4 LC[mu, nu][OPEDelta, p]; -gp[y__] := gp[y] = GluonPropagator[y, Gauge -> gauge]; -qp = QuarkPropagator; -qpm[a_,__]:= qpm[a]; -qpmi[a_,__]:= qpmi[a]; -(*NN*)If[Head[mass] =!= List, -(*NN*) qpm[a_] := (*qpm[a] = *)QuarkPropagator[{a,mass}]; -(*NN*) qpmi[a_]:= (*qpmi[a] =*) QuarkPropagator[{a,mass}] -(*NN*) , -(*NN*) qpm[a_] := (*qpm[a] =*) QuarkPropagator[{a,mass[[1]]}]; -(*NN*) qpmi[a_]:= (*qpmi[a]=*) QuarkPropagator[{a,mass[[2]]}] -(*NN*) ]; +Amplitude[nam___, opt___Rule] := + Block[{ qo, go, gv, qgv,gp,qp,qpm,qpmi, + ghp, gi, pol, gauge, nonz, mass, ggv, pro, + ampswitch, amplist}, + pol = Polarization /. {opt} /. Options[Amplitude]; + mass = QuarkMass /. {opt} /. Options[Amplitude]; + gauge = Gauge /. {opt} /. Options[Amplitude]; + qo[y__] := qo[y] = Twist2QuarkOperator[y, Polarization -> pol]; + go[y__] := go[y] = Twist2GluonOperator[y, Polarization -> pol]; + gi[aa__, b1_,b2_, c1_,c2_] := ggv[aa, c1,c2, b1,b2]; + gv = GluonVertex; + nonz = ZeroMomentumInsertion -> False; + qgv = QuarkGluonVertex; + ggv = GluonGhostVertex; + ghp = GhostPropagator; + pro = -I/4 LC[mu, nu][OPEDelta, p]; + gp[y__] := gp[y] = GluonPropagator[y, Gauge -> gauge]; + qp = QuarkPropagator; + qpm[aa_,__]:= qpm[aa]; + qpmi[aa_,__]:= qpmi[aa]; + (*NN*)If[Head[mass] =!= List, + (*NN*) qpm[aa_] := (*qpm[a] = *)QuarkPropagator[{aa,mass}]; + (*NN*) qpmi[aa_]:= (*qpmi[a] =*) QuarkPropagator[{aa,mass}] + (*NN*) , + (*NN*) qpm[aa_] := (*qpm[a] =*) QuarkPropagator[{aa,mass[[1]]}]; + (*NN*) qpmi[aa_]:= (*qpmi[a]=*) QuarkPropagator[{aa,mass[[2]]}] + (*NN*) ]; -ghp = GhostPropagator; + ghp = GhostPropagator; -(*To allow adding stuff to amplist later. F.Orellana, 25/9-2002*) -If[ampswitch=!=True, + (*To allow adding stuff to amplist later. F.Orellana, 25/9-2002*) + If[ ampswitch=!=True, -amplist = { -(* the five graphs for the onshell calculation *) -"onop1" :> -PolarizationVector[p1,mu] PolarizationVector[p2,nu] * -go[{k-p1,p2-k}, {al,ci1}, {be,ci2}, nonz] * - gp[k-p1, {al,ci1}, {de,c6}] gp[k-p2, {be,ci2},{ka,ci3}] * - gp[k, {si,c5},{ro,ci4}] * - gv[-p1,mu,a, k,si,c5, p1-k,de,c6] * - gv[p2,nu,b, k-p2,ka,ci3, -k,ro,ci4] -, -"onop2" :> -(1/2)* -PolarizationVector[p1,mu] PolarizationVector[p2,nu] * -go[{k-p1,p2-k}, {al,ci1}, {be,ci2}, nonz] * - gp[k-p1, {al,ci1}, {ro,ci3}] gp[k-p2, {be,ci2}, {si,ci4}] * - gv[-p1,mu,a, p2,nu,b, p1-k,ro,ci3, k-p2,si,ci4] -, -"onop3" :> -- PolarizationVector[p1,mu] PolarizationVector[p2,nu] * -SUNDelta[a,b] * Tf * -( -DiracTrace[DOT[ - qo[{k-p1,p2-k}, nonz] , - qp[k-p1] , (I SMP["g_s"] GA[mu]) , qp[k] , (I SMP["g_s"] GA[nu]) , - qp[k-p2] - ]] + -DiracTrace[DOT[ - qo[{p2-k,k-p1}, nonz] , - qp[-k+p2] , (I SMP["g_s"] GA[nu]) , qp[-k] , (I SMP["g_s"] GA[mu]) , - qp[-k+p1] - ]] -), -"onop4" :> -CF * - DOT[Spinor[p2] , (I GA[al]) , qp[k-p2] , - qo[{k-p1,p2-k}, nonz] , - qp[k-p1] , (I GA[be]) , Spinor[-p1]] gp[k,al,be] -, -"onop5" :> -CF * - DOT[Spinor[p2] , (I GA[al]) , qp[k-p2] , - qo[{k-p1,p2-k}, nonz] , - qp[k-p1] , (I GA[be]) , Spinor[-p1]] gp[k,al,be] -, -"onec" :> -DOT[qgv[al,a] , qp[k - p] , qo[k] , - qp[k - p] , qgv[be,b]] gp[k,al,be] -, -"oned" :> --DiracTrace[2 Tf DOT[qo[k] , qp[k] , qgv[mu,a] , qp[k-p] , - qgv[nu,b] , qp[k]] - ] - -DiracTrace[2 Tf DOT[qo[-k] , qp[-k] , qgv[nu,b] , qp[p-k] , - qgv[mu,a] , qp[-k]] - ] -, -(*psqq*) -"q2se2" :> -1 * -DiracTrace[2 Tf * -DOT[qpmi[-q1,7,8] , qgv[9] , -qpmi[-(q1-q2),10,5] , qgv[3] (*, qpm[-q1,4,6] , qo[-q1,6,7] *) - ]] * -gp[q2,1,3] * gp[q2,9,11] * -DOT[qgv[11] , qpm[p-q2,2,12] , qgv[1]] -, -"nsqq1" :> - 1* ( - DOT[qgv[4] , qpm[p-q2] , qgv[3] , qpm[p-q1] , - qo[p-q1] , qpm[p-q1] , qgv[2] , qpm[p-q2] , qgv[1]] * - gp[q1-q2,2,3] gp[q2,1,4] - ) -, -(* the 2-loop quark selfenergy graph similar to nsqq1 *) -"q2se1" :> 1 * ( -DOT[qgv[4] , qpm[p-q2] , qgv[3] , qpm[p-q1] , -(*qo[p-q1] , qpm[p-q1] , *)qgv[2] , qpm[p-q2] , qgv[1]] * -gp[q1-q2,2,3] gp[q2,1,4] - ) -, -"nsqq2" :> 2 * ( -DOT[qgv[4],qpm[q1],qgv[3],qpm[q2],gp[q1-q2,2,3], -qo[q1,0,-q2,0,q2-q1,2],qpm[q1].qgv[1]] * -gp[p-q1,1,4] - ) -, -"nsqq3" :> 2 * ( -DOT[qgv[2],qpm[q2],qgv[3],qpm[q1],qgv[4], -qpm[q2],qo[q2],qpm[q2],qgv[1]] gp[q2-p,1,2] gp[q1-q2,3,4] + amplist = { + (* the five graphs for the onshell calculation *) + "onop1" :> + PolarizationVector[p1,mu] PolarizationVector[p2,nu] * + go[{k-p1,p2-k}, {al,ci1}, {be,ci2}, nonz] * + gp[k-p1, {al,ci1}, {de,c6}] gp[k-p2, {be,ci2},{ka,ci3}] * + gp[k, {si,c5},{ro,ci4}] * + gv[-p1,mu,a, k,si,c5, p1-k,de,c6] * + gv[p2,nu,b, k-p2,ka,ci3, -k,ro,ci4] + , + "onop2" :> + (1/2)* + PolarizationVector[p1,mu] PolarizationVector[p2,nu] * + go[{k-p1,p2-k}, {al,ci1}, {be,ci2}, nonz] * + gp[k-p1, {al,ci1}, {ro,ci3}] gp[k-p2, {be,ci2}, {si,ci4}] * + gv[-p1,mu,a, p2,nu,b, p1-k,ro,ci3, k-p2,si,ci4] + , + "onop3" :> + - PolarizationVector[p1,mu] PolarizationVector[p2,nu] * + SUNDelta[a,b] * Tf * + ( + DiracTrace[DOT[ + qo[{k-p1,p2-k}, nonz] , + qp[k-p1] , (I SMP["g_s"] GA[mu]) , qp[k] , (I SMP["g_s"] GA[nu]) , + qp[k-p2] + ]] + + DiracTrace[DOT[ + qo[{p2-k,k-p1}, nonz] , + qp[-k+p2] , (I SMP["g_s"] GA[nu]) , qp[-k] , (I SMP["g_s"] GA[mu]) , + qp[-k+p1] + ]] + ), + "onop4" :> + CF * + DOT[Spinor[p2] , (I GA[al]) , qp[k-p2] , + qo[{k-p1,p2-k}, nonz] , + qp[k-p1] , (I GA[be]) , Spinor[-p1]] gp[k,al,be] + , + "onop5" :> + CF * + DOT[Spinor[p2] , (I GA[al]) , qp[k-p2] , + qo[{k-p1,p2-k}, nonz] , + qp[k-p1] , (I GA[be]) , Spinor[-p1]] gp[k,al,be] + , + "onec" :> + DOT[qgv[al,a] , qp[k - p] , qo[k] , + qp[k - p] , qgv[be,b]] gp[k,al,be] + , + "oned" :> + -DiracTrace[2 Tf DOT[qo[k] , qp[k] , qgv[mu,a] , qp[k-p] , + qgv[nu,b] , qp[k]] + ] - + DiracTrace[2 Tf DOT[qo[-k] , qp[-k] , qgv[nu,b] , qp[p-k] , + qgv[mu,a] , qp[-k]] + ] + , + (*psqq*) + "q2se2" :> -1 * + DiracTrace[2 Tf * + DOT[qpmi[-q1,7,8] , qgv[9] , + qpmi[-(q1-q2),10,5] , qgv[3] (*, qpm[-q1,4,6] , qo[-q1,6,7] *) + ]] * + gp[q2,1,3] * gp[q2,9,11] * + DOT[qgv[11] , qpm[p-q2,2,12] , qgv[1]] + , + "nsqq1" :> + 1* ( + DOT[qgv[4] , qpm[p-q2] , qgv[3] , qpm[p-q1] , + qo[p-q1] , qpm[p-q1] , qgv[2] , qpm[p-q2] , qgv[1]] * + gp[q1-q2,2,3] gp[q2,1,4] ) -, -"nsqq4" :> 2 * ( -DOT[qgv[1],qpm[q1],qgv[2],gp[q2,2,3],qpm[q1-q2], -qgv[3],qpm[q1],qo[p,0,-q1,0,q1-p,4]] gp[q1-p,1,4] - ) -, -"nsqq5" :> -1 * ( -DOT[qgv[4],qpm[p-q1],qo[p-q1],qpm[p-q1],qgv[1], -gp[q1,1,6] , DiracTrace[DOT[qgv[6],qpmi[q2-q1], -qgv[5],qpmi[q2] 2 Tf Nf]] , -gp[q1,4,5]] ) -(*NEW*) -, -"nsqq6" :> 1/2 * ( -DOT[qgv[4],qpm[p-q1],qo[p-q1],qpm[p-q1],qgv[1]] * -gp[q1,1,2] gp[q1,3,4] gv[q1,2, -q2,8, q2-q1,6] * -gv[-q1,3, q2,5, q1-q2, 7] gp[q2,8,5] gp[q1-q2,6,7] - ) -, -"nsqq7" :> -1* ( -DOT[qgv[4],qpm[p-q1],qo[p-q1],qpm[p-q1],qgv[1] , -gp[q1,1,2],gp[q1,3,4],ggv[q1,2, q2-q1,6, -q2,8], -ggv[q1,3, q2,5, q1-q2,7]] * -ghp[q2,5,8] ghp[q2-q1, 6,7] - ) -, -"nsqq8" :> -2 * ( -DOT[qgv[4],qpm[p-q1],qo[p,0, -p+q1, 0, -q1,1]] * -DiracTrace[2 Tf Nf DOT[qgv[2],qpmi[q2-q1],qgv[3],qpmi[q2]]]* -gp[q1,1,2] gp[q1,3,4] - ) -, -"nsqq9" :> 1 * ( -DOT[qgv[4],qpm[p-q1],qo[p,0,q1-p,0, -q1,1]] * -gp[q1,1,2] gp[q1,3,4] gp[q2,6,8] gp[q2-q1,5,7] * -gv[q1,2, q2-q1,5, -q2,6] gv[q2,8, -q1,3, q1-q2,7] - ) -, -(* similar to graph 9 *) -"q2se3" :> 1/2 * ( -DOT[qgv[4],qpm[p-q1],(*qo[p,0,q1-p,0, -q1,1],*) qgv[1]] * -gp[q1,1,2] gp[q1,3,4] gp[q2,6,8] gp[q2-q1,5,7] * -gv[q1,2, q2-q1,5, -q2,6] gv[q2,8, -q1,3, q1-q2,7] - ) -, -"qg1" :> -If[pol === 1, - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[q2,1,3] , - qgv[mu,a] , - qp[(q2-p)] , - qgv[10] , - gp[(q1-p), 9, 10] , - gv[-p,nu,b, q1,8, p-q1, 9] , - gp[q1,7,8] , - qp[(q2-q1),6,12] , - qgv[7] , - qp[q2,4,5] , - qo[q2,3,4]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[-q2,4,5] , - qgv[7] , - qp[-(q2-q1),6,12] , - qgv[10] , - gp[q1,7,8] , - gv[-p,nu,b, q1,8, p-q1, 9] , - gp[q1-p, 9, 10] , - qp[-(q2-p)] , - qgv[mu,a] , - qp[-q2,1,3] , - qo[-q2,3,4]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[q2] , - qgv[3] , - qp[(q2-q1)] , - gp[q1,1,3] , - gv[p,mu,a, q1-p,2, -q1,1] , - gp[q1-p,2,12] , - qgv[12] , - qp[(q2-p)] , - qgv[nu,b] , - qp[q2] , - qo[q2,6,7]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[-q2] , - qgv[nu,b] , - qp[-(q2-p)] , - qgv[12] , - gp[q1-p,2,12] , - gv[p,mu,a, q1-p,2, -q1,1] , - gp[q1,1,3] , - qp[-(q2-q1)] , - qgv[3] , - qp[-q2] , - qo[-q2,6,7]] - ] -, -nochnich -] -, -"qg2" :> -If[pol === 1, --1 * DiracTrace[2 Tf pro * - DOT[qp[q2,1,3] , - qgv[mu,a] , - qp[q2-p,2,10] , - qgv[9] , - gp[q1-q2, 4, 9] , - qp[q1-p,7,8] , - qgv[nu, b] , - qp[q1] , - qo[q2, 3, -q1, 5, q1-q2, 4]] - ] + + , + (* the 2-loop quark selfenergy graph similar to nsqq1 *) + "q2se1" :> 1 * ( + DOT[qgv[4] , qpm[p-q2] , qgv[3] , qpm[p-q1] , + (*qo[p-q1] , qpm[p-q1] , *)qgv[2] , qpm[p-q2] , qgv[1]] * + gp[q1-q2,2,3] gp[q2,1,4] + ) + , + "nsqq2" :> 2 * ( + DOT[qgv[4],qpm[q1],qgv[3],qpm[q2],gp[q1-q2,2,3], + qo[q1,0,-q2,0,q2-q1,2],qpm[q1].qgv[1]] * + gp[p-q1,1,4] + ) + , + "nsqq3" :> 2 * ( + DOT[qgv[2],qpm[q2],qgv[3],qpm[q1],qgv[4], + qpm[q2],qo[q2],qpm[q2],qgv[1]] gp[q2-p,1,2] gp[q1-q2,3,4] + ) + , + "nsqq4" :> 2 * ( + DOT[qgv[1],qpm[q1],qgv[2],gp[q2,2,3],qpm[q1-q2], + qgv[3],qpm[q1],qo[p,0,-q1,0,q1-p,4]] gp[q1-p,1,4] + ) + , + "nsqq5" :> -1 * ( + DOT[qgv[4],qpm[p-q1],qo[p-q1],qpm[p-q1],qgv[1], + gp[q1,1,6] , DiracTrace[DOT[qgv[6],qpmi[q2-q1], + qgv[5],qpmi[q2] 2 Tf Nf]] , + gp[q1,4,5]] ) + (*NEW*) + , + "nsqq6" :> 1/2 * ( + DOT[qgv[4],qpm[p-q1],qo[p-q1],qpm[p-q1],qgv[1]] * + gp[q1,1,2] gp[q1,3,4] gv[q1,2, -q2,8, q2-q1,6] * + gv[-q1,3, q2,5, q1-q2, 7] gp[q2,8,5] gp[q1-q2,6,7] + ) + , + "nsqq7" :> -1* ( + DOT[qgv[4],qpm[p-q1],qo[p-q1],qpm[p-q1],qgv[1] , + gp[q1,1,2],gp[q1,3,4],ggv[q1,2, q2-q1,6, -q2,8], + ggv[q1,3, q2,5, q1-q2,7]] * + ghp[q2,5,8] ghp[q2-q1, 6,7] + ) + , + "nsqq8" :> -2 * ( + DOT[qgv[4],qpm[p-q1],qo[p,0, -p+q1, 0, -q1,1]] * + DiracTrace[2 Tf Nf DOT[qgv[2],qpmi[q2-q1],qgv[3],qpmi[q2]]]* + gp[q1,1,2] gp[q1,3,4] + ) + , + "nsqq9" :> 1 * ( + DOT[qgv[4],qpm[p-q1],qo[p,0,q1-p,0, -q1,1]] * + gp[q1,1,2] gp[q1,3,4] gp[q2,6,8] gp[q2-q1,5,7] * + gv[q1,2, q2-q1,5, -q2,6] gv[q2,8, -q1,3, q1-q2,7] + ) + , + (* similar to graph 9 *) + "q2se3" :> 1/2 * ( + DOT[qgv[4],qpm[p-q1],(*qo[p,0,q1-p,0, -q1,1],*) qgv[1]] * + gp[q1,1,2] gp[q1,3,4] gp[q2,6,8] gp[q2-q1,5,7] * + gv[q1,2, q2-q1,5, -q2,6] gv[q2,8, -q1,3, q1-q2,7] + ) + , + "qg1" :> + If[pol === 1, + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[q2,1,3] , + qgv[mu,a] , + qp[(q2-p)] , + qgv[10] , + gp[(q1-p), 9, 10] , + gv[-p,nu,b, q1,8, p-q1, 9] , + gp[q1,7,8] , + qp[(q2-q1),6,12] , + qgv[7] , + qp[q2,4,5] , + qo[q2,3,4]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[-q2,4,5] , + qgv[7] , + qp[-(q2-q1),6,12] , + qgv[10] , + gp[q1,7,8] , + gv[-p,nu,b, q1,8, p-q1, 9] , + gp[q1-p, 9, 10] , + qp[-(q2-p)] , + qgv[mu,a] , + qp[-q2,1,3] , + qo[-q2,3,4]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[q2] , + qgv[3] , + qp[(q2-q1)] , + gp[q1,1,3] , + gv[p,mu,a, q1-p,2, -q1,1] , + gp[q1-p,2,12] , + qgv[12] , + qp[(q2-p)] , + qgv[nu,b] , + qp[q2] , + qo[q2,6,7]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[-q2] , + qgv[nu,b] , + qp[-(q2-p)] , + qgv[12] , + gp[q1-p,2,12] , + gv[p,mu,a, q1-p,2, -q1,1] , + gp[q1,1,3] , + qp[-(q2-q1)] , + qgv[3] , + qp[-q2] , + qo[-q2,6,7]] + ] + , + nochnich + ] + , + "qg2" :> + If[pol === 1, + -1 * DiracTrace[2 Tf pro * + DOT[qp[q2,1,3] , + qgv[mu,a] , + qp[q2-p,2,10] , + qgv[9] , + gp[q1-q2, 4, 9] , + qp[q1-p,7,8] , + qgv[nu, b] , + qp[q1] , + qo[q2, 3, -q1, 5, q1-q2, 4]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[-q1] , + qgv[nu, b] , + qp[-(q1-p),7,8] , + gp[q1-q2, 4, 9] , + qgv[9] , + qp[-(q2-p), 2, 10] , + qgv[mu,a] , + qp[-q2,1,3] , + qo[-q1, 5, q2, 3, q1-q2, 4]] + ] + , + nochnich + ] + , + "qg3" :> + If[pol === 1, + (* fermion loop at the left , anti clockwise *) + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[q2,1,3] , + qgv[mu,a] , + qp[q2-p] , + qgv[8] , + qp[q2-q1,4,9] , + gp[q1-p,8,7] , + gv[-p,nu,b,p-q1,7,q1,6] , + gp[q1,5,6] , + qo[q2,3, q1-q2,4, -q1,5]] + ] + + (-1) * (* fermion loop at the left, anti - clockwise *) + DiracTrace[2 Tf pro * + DOT[qp[-(q2-q1),4,9] , + qgv[8] , + qp[-(q2-p)] , + qgv[mu,a] , + qp[-q2,1,3] , + gp[q1,5,6] , + gv[-p,nu,b,p-q1,7,q1,6] , + gp[(q1-p),8,7] , + qo[q1-q2,4, q2,3, -q1,5]] + ] + + (* fermion loop at the right, anti-clockwise *) + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[-q1,5,6] , + qgv[nu,b] , + qp[-(q1-p)] , + qgv[10] , + qp[-(q1-q2)] , + qo[-q1,5, q1-q2,4, q2,3] , + gp[q2-p,2,10] , + gv[p,mu,a, -q2,1, q2-p,2] , + gp[q2,1,3]] + ] + + (* fermion loop at the right, clockwise *) + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[(q1-q2)] , + qgv[10] , + qp[(q1-p)] , + qgv[nu,b] , + qp[q1,5,6] , + qo[q1-q2,4, -q1,5, q2,3] , + gp[q2-p,2,10] , + gv[p,mu,a, -q2,1, q2-p,2] , + gp[q2,1,3]] + ] + , + nochnich + ] + , + "qg4" :> + If[pol === 1, (-1) * - DiracTrace[2 Tf pro * - DOT[qp[-q1] , - qgv[nu, b] , - qp[-(q1-p),7,8] , - gp[q1-q2, 4, 9] , - qgv[9] , - qp[-(q2-p), 2, 10] , - qgv[mu,a] , - qp[-q2,1,3] , - qo[-q1, 5, q2, 3, q1-q2, 4]] - ] -, -nochnich -] -, -"qg3" :> -If[pol === 1, -(* fermion loop at the left , anti clockwise *) + DiracTrace[2 Tf pro * + DOT[qp[-(q2-q1),7,8] , + qgv[10] , + gp[q1-p,10,11] , + gv[-p,nu,b, p-q1,11, q1,12] , + gp[q1,5,12] , + qp[-(q2-p),9,2] , + qgv[mu,a] , + qp[-q2] , + qgv[5] , + qp[-(q2-q1)] , + qo[-(q2-q1),6,7]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[(q2-q1)] , + qgv[5] , + qp[q2] , + qgv[mu,a] , + qp[(q2-p),9,2] , + gp[-q1,5,12] , + gv[-p,nu,b, p-q1,11, q1,12] , + gp[q1-p,10,11] , + qgv[10] , + qp[q2-q1,7,8] , + qo[q2-q1,6,7]] + ] + , + nochnich + ] + , + "qg5" :> + If[pol === 1, + -1* + DiracTrace[2 Tf pro * + DOT[qp[-q1,2,3] , + qgv[4] , + gp[q2-q1,4,8] , + qp[-q2,5,6] , + qgv[8] , + qp[-q1,7,9] , + qgv[nu,b] , + qp[-(q1-p),10,1] , + qo[-(q1-p),1, -q1,2, p,mu,a]] + ] + + -1* + DiracTrace[2 Tf pro * + DOT[qp[(q1-p),10,1] , + qgv[nu,b] , + qp[q1,7,9] , + qgv[8] , + qp[q2,5,6] , + gp[q2-q1,4,8] , + qgv[4] , + qp[q1,2,3] , + qo[(q1-p),1, q1,2, p,mu,a]] + ] + , + nochnich + ] + , + "qg6" :> + If[pol === 1, (-1) * - DiracTrace[2 Tf pro * - DOT[qp[q2,1,3] , - qgv[mu,a] , - qp[q2-p] , - qgv[8] , - qp[q2-q1,4,9] , - gp[q1-p,8,7] , - gv[-p,nu,b,p-q1,7,q1,6] , - gp[q1,5,6] , - qo[q2,3, q1-q2,4, -q1,5]] - ] + - (-1) * (* fermion loop at the left, anti - clockwise *) - DiracTrace[2 Tf pro * - DOT[qp[-(q2-q1),4,9] , + DiracTrace[2 Tf pro * + DOT[qp[-q2,4,5] , + qgv[6] , + gp[q1-q2,6,10] , + qp[-q1,7,8] , + qgv[10] , + qp[-q2,9,11] , + qgv[nu,b] , + qp[-(q2-p),12,2] , + qgv[mu,a] , + qp[-q2,1,3], + qo[-q2, 3,4]] + ] + + (-1)* + DiracTrace[2 Tf pro * + DOT[qp[q2,1,3], + qgv[mu,a] , + qp[(q2-p),12,2] , + qgv[nu,b] , + qp[q2,9,11] , + qgv[10] , + qp[q1,7,8] , + gp[-(q1-q2),6,10] , + qgv[6] , + qp[q2,4,5] , + qo[q2, 3,4]] + ] + + (-1)* + DiracTrace[2 Tf pro * + DOT[qp[q2] , + qgv[6] , + gp[q2-q1, 6,9] , + qp[q1,7,8] , + qgv[9] , + qp[q2] , + qgv[mu,a] , + qp[-(p-q2)] , + qgv[nu,b] , + qp[q2] , + qo[q2,3,4]] + ] + + (-1)* + DiracTrace[2 Tf pro * + DOT[qp[-q2] , + qgv[nu,b] , + qp[(p-q2)] , + qgv[mu,a] , + qp[-q2] , + qgv[9] , + qp[-q1,7,8] , + gp[q2-q1, 6,9] , + qgv[6] , + qp[-q2] , + qo[-q2,3,4]] + ] + , + nochnich + ] + , + "qg7" :> + If[pol === 1, + (-1)* + DiracTrace[2 Tf pro * + DOT[qp[-(q2-q1), 4, 8] , qgv[8] , - qp[-(q2-p)] , - qgv[mu,a] , - qp[-q2,1,3] , - gp[q1,5,6] , - gv[-p,nu,b,p-q1,7,q1,6] , - gp[(q1-p),8,7] , - qo[q1-q2,4, q2,3, -q1,5]] - ] + - (* fermion loop at the right, anti-clockwise *) - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[-q1,5,6] , - qgv[nu,b] , - qp[-(q1-p)] , - qgv[10] , - qp[-(q1-q2)] , - qo[-q1,5, q1-q2,4, q2,3] , - gp[q2-p,2,10] , - gv[p,mu,a, -q2,1, q2-p,2] , - gp[q2,1,3]] - ] + - (* fermion loop at the right, clockwise *) + qp[q1, 6, 5] , + qo[q1-q2, 4, -q1,5, q2,3] , + gp[q2,8,9] , + gv[q2,9, p-q2,10, -p, nu,b] , + gp[q2-p, 2, 10] , + gv[p,mu,a, -q2, 1, q2-p, 2] , + gp[q2, 1, 3]] + ] + + (-1)* + DiracTrace[2 Tf pro * + DOT[qp[-q1, 6, 5] , + qgv[8] , + qp[(q2-q1), 4, 8] , + qo[-q1,5, q1-q2,4, q2,3] , + gp[q2,8,9] , + gv[q2,9, p-q2,10, -p, nu,b] , + gp[q2-p, 2, 10] , + gv[p,mu,a, -q2, 1, q2-p, 2] , + gp[q2, 1, 3]] + ] + , + nochnich + ] + , + "qg8" :> + If[pol === 1, (-1) * - DiracTrace[2 Tf pro * - DOT[qp[(q1-q2)] , - qgv[10] , - qp[(q1-p)] , - qgv[nu,b] , - qp[q1,5,6] , - qo[q1-q2,4, -q1,5, q2,3] , - gp[q2-p,2,10] , - gv[p,mu,a, -q2,1, q2-p,2] , - gp[q2,1,3]] - ] -, -nochnich -] -, -"qg4" :> -If[pol === 1, -(-1) * - DiracTrace[2 Tf pro * - DOT[qp[-(q2-q1),7,8] , - qgv[10] , - gp[q1-p,10,11] , - gv[-p,nu,b, p-q1,11, q1,12] , - gp[q1,5,12] , - qp[-(q2-p),9,2] , - qgv[mu,a] , - qp[-q2] , - qgv[5] , - qp[-(q2-q1)] , - qo[-(q2-q1),6,7]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[(q2-q1)] , - qgv[5] , - qp[q2] , - qgv[mu,a] , - qp[(q2-p),9,2] , - gp[-q1,5,12] , - gv[-p,nu,b, p-q1,11, q1,12] , - gp[q1-p,10,11] , - qgv[10] , - qp[q2-q1,7,8] , - qo[q2-q1,6,7]] - ] -, -nochnich -] -, -"qg5" :> -If[pol === 1, --1* - DiracTrace[2 Tf pro * - DOT[qp[-q1,2,3] , - qgv[4] , - gp[q2-q1,4,8] , - qp[-q2,5,6] , - qgv[8] , - qp[-q1,7,9] , - qgv[nu,b] , - qp[-(q1-p),10,1] , - qo[-(q1-p),1, -q1,2, p,mu,a]] - ] + + DiracTrace[2 Tf pro * + DOT[qp[q1-q2] , + qgv[7] , + gp[q1,4,7] , + qp[-q2,8,9] , + qgv[nu,b] , + qp[-(q2-p),2,10] , + qgv[mu,a] , + qp[-q2, 1,3] , + qo[q1-q2,5, q2,3, -q1,4]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[q2, 1,3] , + qgv[mu,a] , + qp[(q2-p),2,10] , + qgv[nu,b] , + qp[q2,8,9] , + gp[q1,4,7] , + qgv[7] , + qp[-(q1-q2)] , + qo[q2,3, q1-q2,5, -q1,4]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[-(q1-q2)] , + qgv[7] , + gp[q1,4,7] , + qp[q2] , + qgv[mu,a] , + qp[-(p-q2)] , + qgv[nu,b] , + qp[q2] , + qo[q2-q1,5, -q2,3, q1,4]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[-q2] , + qgv[nu,b] , + qp[-(q2-p)] , + qgv[mu,a] , + qp[-q2] , + gp[q1,4,7] , + qgv[7] , + qp[q1-q2] , + qo[-q2,3, q2-q1,5, q1,4]] + ] + , + nochnich + ] + , + "qg9" :> + If[pol === 1, -1* - DiracTrace[2 Tf pro * - DOT[qp[(q1-p),10,1] , - qgv[nu,b] , - qp[q1,7,9] , - qgv[8] , - qp[q2,5,6] , - gp[q2-q1,4,8] , - qgv[4] , - qp[q1,2,3] , - qo[(q1-p),1, q1,2, p,mu,a]] - ] -, -nochnich -] -, -"qg6" :> -If[pol === 1, -(-1) * - DiracTrace[2 Tf pro * - DOT[qp[-q2,4,5] , - qgv[6] , - gp[q1-q2,6,10] , - qp[-q1,7,8] , - qgv[10] , - qp[-q2,9,11] , - qgv[nu,b] , - qp[-(q2-p),12,2] , - qgv[mu,a] , - qp[-q2,1,3], - qo[-q2, 3,4]] - ] + - (-1)* - DiracTrace[2 Tf pro * - DOT[qp[q2,1,3], - qgv[mu,a] , - qp[(q2-p),12,2] , - qgv[nu,b] , - qp[q2,9,11] , - qgv[10] , - qp[q1,7,8] , - gp[-(q1-q2),6,10] , - qgv[6] , - qp[q2,4,5] , - qo[q2, 3,4]] - ] + - (-1)* - DiracTrace[2 Tf pro * - DOT[qp[q2] , - qgv[6] , - gp[q2-q1, 6,9] , - qp[q1,7,8] , - qgv[9] , - qp[q2] , - qgv[mu,a] , - qp[-(p-q2)] , - qgv[nu,b] , - qp[q2] , - qo[q2,3,4]] - ] + - (-1)* - DiracTrace[2 Tf pro * - DOT[qp[-q2] , - qgv[nu,b] , - qp[(p-q2)] , - qgv[mu,a] , - qp[-q2] , - qgv[9] , - qp[-q1,7,8] , - gp[q2-q1, 6,9] , - qgv[6] , - qp[-q2] , - qo[-q2,3,4]] - ] -, -nochnich -] -, -"qg7" :> -If[pol === 1, -(-1)* - DiracTrace[2 Tf pro * - DOT[qp[-(q2-q1), 4, 8] , - qgv[8] , - qp[q1, 6, 5] , - qo[q1-q2, 4, -q1,5, q2,3] , - gp[q2,8,9] , - gv[q2,9, p-q2,10, -p, nu,b] , - gp[q2-p, 2, 10] , - gv[p,mu,a, -q2, 1, q2-p, 2] , - gp[q2, 1, 3]] - ] + - (-1)* - DiracTrace[2 Tf pro * - DOT[qp[-q1, 6, 5] , - qgv[8] , - qp[(q2-q1), 4, 8] , - qo[-q1,5, q1-q2,4, q2,3] , - gp[q2,8,9] , - gv[q2,9, p-q2,10, -p, nu,b] , - gp[q2-p, 2, 10] , - gv[p,mu,a, -q2, 1, q2-p, 2] , - gp[q2, 1, 3]] - ] -, -nochnich -] -, -"qg8" :> -If[pol === 1, -(-1) * - DiracTrace[2 Tf pro * - DOT[qp[q1-q2] , - qgv[7] , - gp[q1,4,7] , - qp[-q2,8,9] , - qgv[nu,b] , - qp[-(q2-p),2,10] , - qgv[mu,a] , - qp[-q2, 1,3] , - qo[q1-q2,5, q2,3, -q1,4]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[q2, 1,3] , - qgv[mu,a] , - qp[(q2-p),2,10] , - qgv[nu,b] , - qp[q2,8,9] , - gp[q1,4,7] , - qgv[7] , - qp[-(q1-q2)] , - qo[q2,3, q1-q2,5, -q1,4]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[-(q1-q2)] , - qgv[7] , - gp[q1,4,7] , - qp[q2] , - qgv[mu,a] , - qp[-(p-q2)] , - qgv[nu,b] , - qp[q2] , - qo[q2-q1,5, -q2,3, q1,4]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[-q2] , - qgv[nu,b] , - qp[-(q2-p)] , - qgv[mu,a] , - qp[-q2] , - gp[q1,4,7] , - qgv[7] , - qp[q1-q2] , - qo[-q2,3, q2-q1,5, q1,4]] - ] -, -nochnich -] -, -"qg9" :> -If[pol === 1, --1* - DiracTrace[2 Tf pro * - DOT[qp[-q1,7,9] , - gp[q2,9,11] , - gv[-p,nu,b, q2,11, -q2+p,12] , - gp[q2-p,2,12] , - gv[p,mu,a, -q2,1, q2-p,2] , - gp[q2,1,3] , - qgv[9] , - qp[-(q1-q2)] , - qgv[3] , - qp[-q1] , - qo[-q1,6,7]]] + - -1* - DiracTrace[2 Tf pro * - DOT[qp[q1] , - qgv[3] , - qp[(q1-q2)] , - qgv[9] , - gp[q2,1,3] , - gv[p,mu,a, -q2,1, q2-p,2] , - gp[q2-p,2,12] , - gv[-p,nu,b, q2,11, -q2+p,12] , - gp[q2,9,11] , - qp[q1,7,9] , - qo[q1,6,7]]] -, -nochnich -] -, -"qg10" :> -If[pol === 1, -(-1)* DiracTrace[2 Tf * pro * - DOT[qp[-q1,7,9] , - qgv[10] , - gp[q1-q2,5,10] , - qp[-q2,9,11] , - qgv[nu,b] , - qp[-(q2-p),2,12] , - qgv[mu,a] , - qp[-q2,1,3] , - qgv[5] , - qp[-q1,4,6] , - qo[-q1,6,7]] - ] + - (-1)* - DiracTrace[2 Tf * pro * - DOT[qp[q1,6,4] , - qgv[5] , - qp[q2,1,3] , - qgv[mu,a] , - qp[(q2-p),2,12] , - qgv[nu,b] , - qp[q2,9,11] , - gp[q1-q2,5,10] , - qgv[10] , - qp[q1,7,9] , - qo[q1,6,7]] - ] -, -nochnich -] -, -"qg11" :> -If[pol === 1, -(-1) *DiracTrace[ 2 Tf pro * - DOT[qp[-q2,4,5] , - qgv[nu,b] , - qp[(p-q2),6,7] , - qgv[8] , - qp[-(q1-p),9,10] , - gp[q2 - q1, 8, 12] , - qgv[12] , - qp[-(q2-p),11,2] , - qgv[mu,a] , - qp[-q2,1,3] , - qo[-q2,3,4]] ] + - (-1) DiracTrace[ 2 Tf pro * - DOT[qp[q2,1,3] , - qgv[mu,a] , - qp[(q2-p),11,2] , - qgv[12] , - gp[-(q2 - q1), 8, 12] , - qp[(q1-p),9,10] , - qgv[8] , - qp[-(p-q2),6,7] , - qgv[nu,b] , - qp[q2,4,5] , - qo[q2,3,4]] ] -, -nochnich -] -, -"qg12" :> 0 -, -"qg13" :> 0 -, -"qg14" :> -If[pol === 1, -(* amp16 *) -DiracTrace[FeynAmpDenominatorSimplify[FeynAmpDenominatorCombine[ -SUNSimplify[Trick[ -(-1) * - DiracTrace[2 Tf pro * - DOT[qp[-q2,4,5] , - qgv[6] , - gp[q1-q2,6,12] , - qp[-q1,7,8] , - qgv[nu,b] , - qp[-(q1-p),9,10] , - qgv[12] , - qp[-(q2-p), 2, 11] , - qgv[mu,a] , - qp[-q2,1,3] , - qo[-q2,3,4]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[q2,1,3] , - qgv[mu,a] , - qp[(q2-p), 2, 11] , - qgv[12] , - qp[(q1-p),9,10] , - qgv[nu,b] , - qp[q1,7,8] , - gp[q1-q2,6,12] , - qgv[6] , - qp[q2,4,5] , - qo[q2,3,4]] - ] + -(-1) * - DiracTrace[2 Tf pro * - DOT[qp[-q1] , - qgv[nu,b] , - qp[-(q1-p)] , - qgv[12] , - gp[q1-q2,5,12] , - qp[-(q2-p)] , - qgv[mu,a] , - qp[-q2] , - qgv[5] , - qp[-q1] , - qo[-q1,6,7]] - ] + - (-1) * - DiracTrace[2 Tf pro * - DOT[qp[q1] , - qgv[5] , - qp[q2] , - qgv[mu, a] , - qp[(q2-p)] , - gp[q1-q2,5,12] , - qgv[12] , - qp[(q1-p)] , - qgv[nu,b] , - qp[q1] , - qo[q1,6,7]] - ] -], SUNTrace->True]/.DiracTrace->FeynAmpDenominatorSimplify - ], q1, q2]//Factor2 - ] -, -nochnich -] -, -(*NEW*) -"nsqq10" :> -2 * ( -DOT[qgv[4] , qpm[p-q1] , qo[p,0,q1-p,0, -q1,1]] * -gp[q1,1,2] gp[q1,3,4] ggv[q1,2, q2-q1,5, -q2,6] * -ggv[-q1,3, q2,8, q1-q2,7] * -ghp[q2,6,8] ghp[q2-q1, 5,7] + DiracTrace[2 Tf pro * + DOT[qp[-q1,7,9] , + gp[q2,9,11] , + gv[-p,nu,b, q2,11, -q2+p,12] , + gp[q2-p,2,12] , + gv[p,mu,a, -q2,1, q2-p,2] , + gp[q2,1,3] , + qgv[9] , + qp[-(q1-q2)] , + qgv[3] , + qp[-q1] , + qo[-q1,6,7]]] + + -1* + DiracTrace[2 Tf pro * + DOT[qp[q1] , + qgv[3] , + qp[(q1-q2)] , + qgv[9] , + gp[q2,1,3] , + gv[p,mu,a, -q2,1, q2-p,2] , + gp[q2-p,2,12] , + gv[-p,nu,b, q2,11, -q2+p,12] , + gp[q2,9,11] , + qp[q1,7,9] , + qo[q1,6,7]]] + , + nochnich + ] + , + "qg10" :> + If[pol === 1, + (-1)* DiracTrace[2 Tf * pro * + DOT[qp[-q1,7,9] , + qgv[10] , + gp[q1-q2,5,10] , + qp[-q2,9,11] , + qgv[nu,b] , + qp[-(q2-p),2,12] , + qgv[mu,a] , + qp[-q2,1,3] , + qgv[5] , + qp[-q1,4,6] , + qo[-q1,6,7]] + ] + + (-1)* + DiracTrace[2 Tf * pro * + DOT[qp[q1,6,4] , + qgv[5] , + qp[q2,1,3] , + qgv[mu,a] , + qp[(q2-p),2,12] , + qgv[nu,b] , + qp[q2,9,11] , + gp[q1-q2,5,10] , + qgv[10] , + qp[q1,7,9] , + qo[q1,6,7]] + ] + , + nochnich + ] + , + "qg11" :> + If[pol === 1, + (-1) *DiracTrace[ 2 Tf pro * + DOT[qp[-q2,4,5] , + qgv[nu,b] , + qp[(p-q2),6,7] , + qgv[8] , + qp[-(q1-p),9,10] , + gp[q2 - q1, 8, 12] , + qgv[12] , + qp[-(q2-p),11,2] , + qgv[mu,a] , + qp[-q2,1,3] , + qo[-q2,3,4]] ] + + (-1) DiracTrace[ 2 Tf pro * + DOT[qp[q2,1,3] , + qgv[mu,a] , + qp[(q2-p),11,2] , + qgv[12] , + gp[-(q2 - q1), 8, 12] , + qp[(q1-p),9,10] , + qgv[8] , + qp[-(p-q2),6,7] , + qgv[nu,b] , + qp[q2,4,5] , + qo[q2,3,4]] ] + , + nochnich + ] + , + "qg12" :> 0 + , + "qg13" :> 0 + , + "qg14" :> + If[pol === 1, + (* amp16 *) + DiracTrace[FeynAmpDenominatorSimplify[FeynAmpDenominatorCombine[ + SUNSimplify[Trick[ + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[-q2,4,5] , + qgv[6] , + gp[q1-q2,6,12] , + qp[-q1,7,8] , + qgv[nu,b] , + qp[-(q1-p),9,10] , + qgv[12] , + qp[-(q2-p), 2, 11] , + qgv[mu,a] , + qp[-q2,1,3] , + qo[-q2,3,4]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[q2,1,3] , + qgv[mu,a] , + qp[(q2-p), 2, 11] , + qgv[12] , + qp[(q1-p),9,10] , + qgv[nu,b] , + qp[q1,7,8] , + gp[q1-q2,6,12] , + qgv[6] , + qp[q2,4,5] , + qo[q2,3,4]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[-q1] , + qgv[nu,b] , + qp[-(q1-p)] , + qgv[12] , + gp[q1-q2,5,12] , + qp[-(q2-p)] , + qgv[mu,a] , + qp[-q2] , + qgv[5] , + qp[-q1] , + qo[-q1,6,7]] + ] + + (-1) * + DiracTrace[2 Tf pro * + DOT[qp[q1] , + qgv[5] , + qp[q2] , + qgv[mu, a] , + qp[(q2-p)] , + gp[q1-q2,5,12] , + qgv[12] , + qp[(q1-p)] , + qgv[nu,b] , + qp[q1] , + qo[q1,6,7]] + ] + ], SUNTrace->True]/.DiracTrace->FeynAmpDenominatorSimplify + ], q1, q2]//Factor2 + ] + , + nochnich + ] + , + (*NEW*) + "nsqq10" :> -2 * ( + DOT[qgv[4] , qpm[p-q1] , qo[p,0,q1-p,0, -q1,1]] * + gp[q1,1,2] gp[q1,3,4] ggv[q1,2, q2-q1,5, -q2,6] * + ggv[-q1,3, q2,8, q1-q2,7] * + ghp[q2,6,8] ghp[q2-q1, 5,7] + ) + , + (* similar to graph 10 *) + "q2se4" :> -1 * ( + DOT[qgv[4] , qpm[p-q1] , qgv[1](*, qo[p,0,q1-p,0, -q1,1]*)] * + gp[q1,1,2] gp[q1,3,4] ggv[q1,2, q2-q1,5, -q2,6] * + ggv[q1,3, q2,8, q1-q2,7] * + ghp[q2,6,8] ghp[q2-q1, 5,7] + ) + , + "nsqq11" :> 2 * ( + DOT[qgv[3],qpm[p-q1],qgv[4],qpm[q2-q1], + qgv[2],qpm[q2],qo[q2],qpm[q2],qgv[1]] * + gp[q2-p,1,4] gp[q1,2,3] + ) + , + (* the 2-loop quark selfenergy dervived from nsqq11 *) + "q2se5" :> 1 * ( + DOT[qgv[3],qpm[p-q1],qgv[4],qpm[q2-q1], + qgv[2],(*qpm[q2],qo[q2],*)qpm[q2],qgv[1]] * + gp[q2-p,1,4] gp[q1,2,3] + ) + , + "nsqq12" :> 2 * ( + DOT[qgv[3],qpm[q2],qgv[2],qpm[q1],qo[q1], + qpm[q1],qgv[1] gp[p-q1,1,4] gp[q1-q2,5,2]] * + gp[p-q2,6,3] gv[p-q1,4, q1-q2,5, q2-p,6] + ) + , + "nsqq13" :> 1 * ( + DOT[qgv[4],qpm[p-q1],qgv[3],qpm[q2-q1], + qo[q2-q1],qpm[q2-q1],qgv[2],qpm[q2], + qgv[1]] gp[q2-p,1,3] gp[q1,2,4] + ) + (*gives just the same as above*) + (*+ + 1 * ( + DOT[qgv[4] , qpm[q1] , qgv[2] , qpm[q1-q2] , + qo[q1-q2] , qpm[q1-q2] , qgv[3] , qpm[p-q2] , + qgv[1]] * gp[p-q1,4,3] gp[q2,2,1]) + *) + , + (* the 2-loop quark selfenergy dervived from nsqq13 *) + "q2se7" :> 1 * ( + DOT[qgv[4],qpm[p-q1],qgv[3] , (*qpm[q2-q1], + qo[q2-q1],*) qpm[q2-q1],qgv[2],qpm[q2], + qgv[1]] gp[q2-p,1,3] gp[q1,2,4] + ) + , + "nsqq14" :> 2 * ( + DOT[qgv[4],qpm[q2],qgv[3],qpm[q2-q1],qgv[2],qpm[p-q1], + qo[p,0, q1-p,0, -q1,1]] gp[q1,1,3] gp[q2-p,2,4] + ) + , + "nsqq15" :> 2 * ( + DOT[qgv[4],qpm[-q2+p],qgv[2],qpm[p-q1], + qo[p,0, q1-p,0, -q1,1]] gp[q1,1,3] gp[q1-q2,2,5] * + gp[q2,4,6] gv[q1,3, -q1+q2,5, -q2,6] + ) + , + "nsqq16" :> 1 * ( + DOT[qgv[3],qpm[q2],qo[q1,0,-q2,0,q2-q1,2],qpm[q1]] * + DOT[qgv[1] gp[p-q1,1,5],gp[q2-q1,2,6] gp[p-q2,3,4]] * + gv[p-q1,5, q1-q2,6, q2-p,4] + ) + , + "q2se6" :> 1 * ( + DOT[qgv[3],qpm[q2],(*qo[q1,0,-q2,0,q2-q1,2]*)qgv[2],qpm[q1], + qgv[1]] DOT[gp[p-q1,1,5],gp[q2-q1,2,6]] gp[p-q2,3,4] * + gv[p-q1,5, q1-q2,6, q2-p,4] + ) + , + "nsqq17" :> 2 * ( + DOT[qgv[4],qpm[p-q1],qgv[3],qpm[q2-q1], + qo[q2,0,q1-q2,0,-q1,2] , qpm[q2],qgv[1]] * + gp[q2-p,1,3] gp[q1,2,4] + ) + (* + + + 1 ( + DOT[qgv[4],qpm[q1],qo[q1-q2,0,-q1,0,q2,1] , + qpm[q1-q2] , qgv[3] , qpm[p-q2] , qgv[2]] + gp[q2,1,2] gp[q1-p,3,4] + ) + *) + , + "nsqq18" :> + 1* ( + DOT[qgv[4],qpm[p-q2],qo[p-q1,_,_,q2-p,_,_,q1,2,-q2,3], + qpm[p-q1],qgv[1]] * + gp[q1,1,2] gp[q2,3,4] + ) + , + "nsqq19" :> 1 * ( + DOT[qgv[6],qpm[p-q1],qo[p,_,_, q1-p,_,_, q2-q1,2, -q2,1]] * + gp[q2-q1,2,4] gp[q2,1,3] gp[q1,5,6] * + gv[-q1,5, q2,3, q1-q2,4] + ) + , + "nsqq20" :> 2 * ( + DOT[qgv[4],qpm[p-q2],qgv[3],qpm[q1-q2], + qo[p,_,_, q2-q1,_,_, q1-p,1, -q2,2]] * + gp[q1-p,1,3] gp[q2,2,4] + ) + (* + , + "qg10" :> + 1 * go[q2-q1, 6, 7] * + gp[q1-q2, 4, 6] * + gp[q1-q2, 7, 8] * + gp[q2, 1, 3] * + gp[q1, 5, 12] * + gv[q2,3, q1-q2,4, -q1,5] * + DiracTrace[ + DOT[qgv[12] , + qp[p-q1, 10, 11] , + qgv[8] , + qp[p-q2, 2, 9] , + qgv[1] , + (GS[p]/4) , DiracGamma[5]] + ] + *) + , + "gq1" :> ( 1 * + go[q2, 3,4] * + gp[q1,7,8] * + gp[q2,1,3] * + gp[q2,4,5] * + gp[q2,9,11] * + gp[q1-q2,6,10] * + gv[q1,8, -q2,9, q2-q1,10] * + gv[q2,5, q1-q2,6, -q1,7] * + DOT[qgv[11] , qp[p-q2,2,12] , qgv[1]] ) -, -(* similar to graph 10 *) -"q2se4" :> -1 * ( -DOT[qgv[4] , qpm[p-q1] , qgv[1](*, qo[p,0,q1-p,0, -q1,1]*)] * -gp[q1,1,2] gp[q1,3,4] ggv[q1,2, q2-q1,5, -q2,6] * -ggv[q1,3, q2,8, q1-q2,7] * -ghp[q2,6,8] ghp[q2-q1, 5,7] + , + "gq2" :> (-2 * + go[q2, 3,4] * + ghp[q1,7,8] * + gp[q2,1,3] * + gp[q2,4,5] * + gp[q2,9,11] * + ghp[q1-q2,6,10] * + ggv[-q2,9,q1,8, q2-q1,10] * + ggv[q2,5, q1-q2,6, -q1,7] * + DOT[qgv[11] , qp[p-q2,2,12] , qgv[1]] ) -, -"nsqq11" :> 2 * ( -DOT[qgv[3],qpm[p-q1],qgv[4],qpm[q2-q1], -qgv[2],qpm[q2],qo[q2],qpm[q2],qgv[1]] * -gp[q2-p,1,4] gp[q1,2,3] + , + "gq3" :> (-2 * + go[q2, 3,4] * + gp[q2,1,3] * + gp[q2,4,5] * gp[q2,9,11] * + DiracTrace[ (2 Tf) Nf * + DOT[qgv[5] , + qp[q1] , + qgv[9] , + qp[q1-q2]] + ] * + DOT[qgv[11] , qp[p-q2,2,12] , qgv[1]] ) -, -(* the 2-loop quark selfenergy dervived from nsqq11 *) -"q2se5" :> 1 * ( -DOT[qgv[3],qpm[p-q1],qgv[4],qpm[q2-q1], -qgv[2],(*qpm[q2],qo[q2],*)qpm[q2],qgv[1]] * -gp[q2-p,1,4] gp[q1,2,3] + , + "gq4" :> (1 * + go[q2,3,4] * + gp[q2,1,3] * + gp[q2,4,5] * + DOT[qgv[5] , qp[p-q2] , qgv[8] , + gp[q2 - q1, 8, 12] , + qp[p-q1] , + qgv[12] , qp[p-q2] , qgv[1]] ) -, -"nsqq12" :> 2 * ( -DOT[qgv[3],qpm[q2],qgv[2],qpm[q1],qo[q1], -qpm[q1],qgv[1] gp[p-q1,1,4] gp[q1-q2,5,2]] * -gp[p-q2,6,3] gv[p-q1,4, q1-q2,5, q2-p,6] + , + "gq5" :> (go[q1,6,7] * + gp[q1,4,6] * + gp[q1,7,8] * + gp[q2,1,3] * + gp[q2,9,11] * + gp[q1-q2,5,10] * + gv[q2,3, -q1,4, q1-q2,5] * + gv[q1,8, -q2,9, q2-q1,10] * + DOT[qgv[11] , qp[p-q2,2,12] , qgv[1]] ) -, -"nsqq13" :> 1 * ( -DOT[qgv[4],qpm[p-q1],qgv[3],qpm[q2-q1], -qo[q2-q1],qpm[q2-q1],qgv[2],qpm[q2], -qgv[1]] gp[q2-p,1,3] gp[q1,2,4] + , + "gq6" :> (1 * + go[q2,3, q1-q2,4, -q1,5] * + gp[q2,1,3] * + gp[q1,5,6] * + gp[q2,8,9] * + gp[q1-q2,4,7]* + gv[q1,6, q2-q1,7, -q2,8] * + DOT[qgv[9] , qp[p-q2,2,12] , qgv[1]] ) -(*gives just the same as above*) -(*+ -1 * ( -DOT[qgv[4] , qpm[q1] , qgv[2] , qpm[q1-q2] , -qo[q1-q2] , qpm[q1-q2] , qgv[3] , qpm[p-q2] , -qgv[1]] * gp[p-q1,4,3] gp[q2,2,1]) - *) -, -(* the 2-loop quark selfenergy dervived from nsqq13 *) -"q2se7" :> 1 * ( -DOT[qgv[4],qpm[p-q1],qgv[3] , (*qpm[q2-q1], -qo[q2-q1],*) qpm[q2-q1],qgv[2],qpm[q2], -qgv[1]] gp[q2-p,1,3] gp[q1,2,4] - ) -, -"nsqq14" :> 2 * ( -DOT[qgv[4],qpm[q2],qgv[3],qpm[q2-q1],qgv[2],qpm[p-q1], -qo[p,0, q1-p,0, -q1,1]] gp[q1,1,3] gp[q2-p,2,4] + , + "gq7" :> ( 1 * + go[q1,6,7] * + gp[q1,4,6] * + gp[q1,7,8] * + DOT[qgv[12] , qp[q2,9,11] , + gp[q2-p,2,12] , + qgv[8] , qp[q2-q1] , + qgv[4] , qp[q2,1,3] , + qgv[2]] ) -, -"nsqq15" :> 2 * ( -DOT[qgv[4],qpm[-q2+p],qgv[2],qpm[p-q1], -qo[p,0, q1-p,0, -q1,1]] gp[q1,1,3] gp[q1-q2,2,5] * -gp[q2,4,6] gv[q1,3, -q1+q2,5, -q2,6] + , + "gq8" :> ( 2 * + go[q2,3,4] * + gp[q2,1,3] * + gp[q2,4,5] * + gp[q1-q2,6,12] * + gp[q1,7,8] * + gv[q2,5, q1-q2,6, -q1, 7] * + DOT[qgv[8] , + qp[p - q1, 9, 10] , + qgv[12] , + qp[p - q2, 2, 12] , + qgv[1]] ) -, -"nsqq16" :> 1 * ( -DOT[qgv[3],qpm[q2],qo[q1,0,-q2,0,q2-q1,2],qpm[q1]] * -DOT[qgv[1] gp[p-q1,1,5],gp[q2-q1,2,6] gp[p-q2,3,4]] * -gv[p-q1,5, q1-q2,6, q2-p,4] + , + "gq9" :> (2 * + go[q2,3,4] * + gp[q2,1,3] * + gp[q2,4,5] * + DOT[gp[p - q1, 9, 10] , + qgv[9] , + qp[q1,7,8] , + qgv[5] , + qp[q1-q2,6,12] , + qgv[10] , + qp[p - q2, 2, 11] , + qgv[1]] ) -, -"q2se6" :> 1 * ( -DOT[qgv[3],qpm[q2],(*qo[q1,0,-q2,0,q2-q1,2]*)qgv[2],qpm[q1], -qgv[1]] DOT[gp[p-q1,1,5],gp[q2-q1,2,6]] gp[p-q2,3,4] * -gv[p-q1,5, q1-q2,6, q2-p,4] + , + "gq10" :> (1 * + go[q2-q1, 6, 7] * + gp[q1-q2, 4, 6] * + gp[q1-q2, 7, 8] * + gp[q2, 1, 3] * + gp[q1, 5, 12] * + gv[q2,3, q1-q2,4, -q1,5] * + DOT[qgv[12] , + qp[p-q1, 10, 11] , + qgv[8] , + qp[p-q2, 2, 9] , + qgv[1]] + ) + , + "gq11" :> (go[q2,3, q1-q2,4, -q1,5] * + gp[q2,1,3] * gp[q1-q2,4,9] * gp[q1,5,6] * + DOT[qgv[6] , qp[p-q1] , qgv[9] , + qp[p-q2] , qgv[1]] + ) + , + "gg1" :> go[p,mu,a, -q1,1, q1-p,2] * + gp[q1-p, 2, 3] gp[q1, 1, 10] * + gp[q1-q2, 4, 9] gp[q2-p, 5, 6] * + gp[q2, 7, 8] * + gv[ p-q1, 3, q1-q2,4, q2-p, 5 ] * + gv[ p-q2,6, q2,7, -p,nu,b ] * + gv[ -q2,8, q2-q1,9, q1,10] + , + "gg2" :> 2 * + go[q2, 3, 4] * + gp[q2, 1, 3] * + gp[q2-p, 2, 11] * + gp[q2, 4, 5] * + gp[q1-q2, 6, 12] * + gp[q1, 7, 8] * + gp[q1-p, 9, 10] * + gv[p,mu,a, -q2,1, q2-p, 2] * + gv[q2,5, -q1,7, q1-q2,6] * + gv[q2-q1,12, p-q2,11, q1-p,10]* + gv[q1,8, p-q1,9, -p,nu,b] + , + "gg3" :> go[q2,3, q1-q2,4, -q1,5] * + gp[q2, 1, 3] * + gp[q2-p, 2, 10] * + gp[q1-q2, 4, 9] * + gp[-q1, 5, 6] * + gp[q1-p, 8, 7] * + gv[p,mu,a, -q2,1, q2-p, 2] * + gv[p-q2, 10, q2-q1,9, q1-p,8] * + gv[-p,nu,b, q1,6, p-q1,7] + , + "gg4" :> ( + 1/2 * + go[q2-q1, 6, 7] * + gp[q2, 1, 3] * + gp[q2-p, 2, 9] * + gp[q1-q2, 4, 6] * + gp[q1, 5, 12] * + gp[q1-q2, 7, 8] * + gp[p-q1, 10, 11] * + gv[p,mu,a, -q2,1, q2-p, 2] * + gv[q2,3, q1-q2,4, -q1,5] * + gv[q2-q1,8, p-q2,9, -p+q1,10] * + gv[-p,nu,b, q1,12, -q1+p,11] ) -, -"nsqq17" :> 2 * ( -DOT[qgv[4],qpm[p-q1],qgv[3],qpm[q2-q1], -qo[q2,0,q1-q2,0,-q1,2] , qpm[q2],qgv[1]] * -gp[q2-p,1,3] gp[q1,2,4] + , + "gg5" :> ( + 1/3 * + go[p,mu,a, -q1,1, q2-p,2, q1-q2,3] * + gp[q1, 1, 4] * + gp[q2-p, 2, 5] * + gp[q1-q2, 3, 6] * + gv[-p,nu,b, q1,4, p-q2,5, q2-q1,6] ) -(* -+ - 1 ( -DOT[qgv[4],qpm[q1],qo[q1-q2,0,-q1,0,q2,1] , -qpm[q1-q2] , qgv[3] , qpm[p-q2] , qgv[2]] -gp[q2,1,2] gp[q1-p,3,4] + , + "gg6" :> ( + 1/2 * + go[q1, 4, 5] * + gp[q1, 1, 4] * + gp[q1, 5, 6] * + gp[q1-q2, 2, 7] * + gp[q2-p, 3, 8] * + gv[ p,mu,a, -q1,1, q1-q2,2, q2-p,3] * + gv[-p,nu,b, q1,6, q2-q1,7, p-q2,8] ) -*) -, -"nsqq18" :> -1* ( -DOT[qgv[4],qpm[p-q2],qo[p-q1,_,_,q2-p,_,_,q1,2,-q2,3], -qpm[p-q1],qgv[1]] * -gp[q1,1,2] gp[q2,3,4] -) -, -"nsqq19" :> 1 * ( -DOT[qgv[6],qpm[p-q1],qo[p,_,_, q1-p,_,_, q2-q1,2, -q2,1]] * -gp[q2-q1,2,4] gp[q2,1,3] gp[q1,5,6] * -gv[-q1,5, q2,3, q1-q2,4] + , + "gg7" :> ( + 1/2 * + go[p,mu,a, q2-p,1, -q2,2] * + gp[q2-p, 1, 4] * + gp[q2, 2, 3] * + gp[q1, 6, 8] * + gp[q1-p, 5, 7] * + gv[q2,3, p-q2,4, q1-p,5, -q1,6] * + gv[-p,nu,b, -q1+p,7, q1,8] ) -, -"nsqq20" :> 2 * ( -DOT[qgv[4],qpm[p-q2],qgv[3],qpm[q1-q2], -qo[p,_,_, q2-q1,_,_, q1-p,1, -q2,2]] * -gp[q1-p,1,3] gp[q2,2,4] + , + "gg8" :> ( + 1 * + go[q2, 3, 4] * + gp[q2, 1, 3] * + gp[q2, 4, 5] * + gp[q2-p, 2, 6] * + gp[q1-p, 7, 10] * + gp[q1, 8, 9] * + gv[p,mu,a, -q2,1, q2-p,2] * + gv[q2,5, p-q2,6, q1-p,7, -q1,8] * + gv[-p,nu,b, p-q1,10, q1,9] ) -(* -, -"qg10" :> -1 * go[q2-q1, 6, 7] * - gp[q1-q2, 4, 6] * - gp[q1-q2, 7, 8] * - gp[q2, 1, 3] * - gp[q1, 5, 12] * - gv[q2,3, q1-q2,4, -q1,5] * - DiracTrace[ - DOT[qgv[12] , - qp[p-q1, 10, 11] , - qgv[8] , - qp[p-q2, 2, 9] , - qgv[1] , - (DiracSlash[p]/4) , DiracGamma[5]] - ] -*) -, -"gq1" :> ( 1 * - go[q2, 3,4] * - gp[q1,7,8] * - gp[q2,1,3] * - gp[q2,4,5] * - gp[q2,9,11] * - gp[q1-q2,6,10] * - gv[q1,8, -q2,9, q2-q1,10] * - gv[q2,5, q1-q2,6, -q1,7] * - DOT[qgv[11] , qp[p-q2,2,12] , qgv[1]] - ) -, -"gq2" :> (-2 * - go[q2, 3,4] * - ghp[q1,7,8] * - gp[q2,1,3] * - gp[q2,4,5] * - gp[q2,9,11] * - ghp[q1-q2,6,10] * - ggv[-q2,9,q1,8, q2-q1,10] * - ggv[q2,5, q1-q2,6, -q1,7] * - DOT[qgv[11] , qp[p-q2,2,12] , qgv[1]] - ) -, -"gq3" :> (-2 * - go[q2, 3,4] * - gp[q2,1,3] * - gp[q2,4,5] * gp[q2,9,11] * - DiracTrace[ (2 Tf) Nf * - DOT[qgv[5] , - qp[q1] , - qgv[9] , - qp[q1-q2]] - ] * - DOT[qgv[11] , qp[p-q2,2,12] , qgv[1]] - ) -, -"gq4" :> (1 * - go[q2,3,4] * - gp[q2,1,3] * - gp[q2,4,5] * - DOT[qgv[5] , qp[p-q2] , qgv[8] , - gp[q2 - q1, 8, 12] , - qp[p-q1] , - qgv[12] , qp[p-q2] , qgv[1]] - ) -, -"gq5" :> (go[q1,6,7] * - gp[q1,4,6] * - gp[q1,7,8] * - gp[q2,1,3] * - gp[q2,9,11] * - gp[q1-q2,5,10] * - gv[q2,3, -q1,4, q1-q2,5] * - gv[q1,8, -q2,9, q2-q1,10] * - DOT[qgv[11] , qp[p-q2,2,12] , qgv[1]] - ) -, -"gq6" :> (1 * - go[q2,3, q1-q2,4, -q1,5] * - gp[q2,1,3] * - gp[q1,5,6] * - gp[q2,8,9] * - gp[q1-q2,4,7]* - gv[q1,6, q2-q1,7, -q2,8] * - DOT[qgv[9] , qp[p-q2,2,12] , qgv[1]] - ) -, -"gq7" :> ( 1 * - go[q1,6,7] * - gp[q1,4,6] * - gp[q1,7,8] * - DOT[qgv[12] , qp[q2,9,11] , - gp[q2-p,2,12] , - qgv[8] , qp[q2-q1] , - qgv[4] , qp[q2,1,3] , - qgv[2]] - ) -, -"gq8" :> ( 2 * - go[q2,3,4] * - gp[q2,1,3] * - gp[q2,4,5] * - gp[q1-q2,6,12] * - gp[q1,7,8] * - gv[q2,5, q1-q2,6, -q1, 7] * - DOT[qgv[8] , - qp[p - q1, 9, 10] , - qgv[12] , - qp[p - q2, 2, 12] , - qgv[1]] - ) -, -"gq9" :> (2 * - go[q2,3,4] * - gp[q2,1,3] * - gp[q2,4,5] * - DOT[gp[p - q1, 9, 10] , - qgv[9] , - qp[q1,7,8] , - qgv[5] , - qp[q1-q2,6,12] , - qgv[10] , - qp[p - q2, 2, 11] , - qgv[1]] - ) -, -"gq10" :> (1 * - go[q2-q1, 6, 7] * - gp[q1-q2, 4, 6] * - gp[q1-q2, 7, 8] * - gp[q2, 1, 3] * - gp[q1, 5, 12] * - gv[q2,3, q1-q2,4, -q1,5] * - DOT[qgv[12] , - qp[p-q1, 10, 11] , + , + "gg9" :> ( + 1/4 * + go[q2,3, p-q2,4, -q1,5, q1-p,6] * + gp[q2, 3, 1] * + gp[q2-p, 2, 4] * + gp[q1-p, 6, 7] * + gp[q1, 5, 8] * + gv[ p,mu,a, -q2,1, q2-p,2] * + gv[-p,nu,b, q1,8, p-q1,7] + ) + , + "gg10" :> ( + 1 * + go[p,mu,a, -q1,2, q1-q2,3, q2-p,4] * + gp[q1, 2, 9] * + gp[q1-q2, 3, 6] * + gp[q2-p, 4, 5] * + gp[q1-p, 7, 8] * + gv[p-q2,5, q2-q1,6, q1-p,7] * + gv[-p,nu,b, q1,9, p-q1,8] + ) + , + "gg11" :> ( + 2 * + go[q2, 4, 5] * + gp[q2, 4, 1] * + gp[q2, 5, 6] * + gp[q1, 8, 9] * + gp[q2-q1, 2, 7] * + gp[p-q1, 3, 10] * + gv[p,mu,a, -q2,1, q2-q1,2, q1-p,3] * + gv[q2,6, q1-q2,7, -q1,8] * + gv[-p,nu,b, q1,9, p-q1,10] + ) + , + "gg12" :> ( + 1 * + go[q2,3, q1-q2,4, -q1,5] * + gp[q2,1,3] * + gp[q1,5,6] * + gp[q1-q2,4,7]* + gp[q2-p,2,8] * + gv[p,mu,a, -q2,1, q2-p,2] * + gv[-p,nu,b, q1,6, q2-q1,7, p-q2,8] + ) + , + "gg13" :> ( + 1 * + go[q2,3,4] * + gp[q2,1,3] * + gp[q2,4,5] * + gp[q1,7,9] * + gp[q1-q2,6,8] * + gp[q2-p,2,10] * + gv[q2,5, q1-q2,6, -q1,7] * + gv[p,mu,a, -q2,1, q2-p,2] * + gv[-p,nu,b, q2-q1,8, q1,9, p-q2,10] + ) + , + "gg14" :> ( + 1 * + go[p,mu,a, q2-p,1, -q2,2] * + gp[q2, 2,3] * + gp[q2-p,1,8] * + gp[q1,5,6] * + gp[q1-q2,4,7] * + gv[q2,3, -q1,5, q1-q2,4] * + gv[-p,nu,b, q1,6, q2-q1,7, p-q2,8] + ) + , + "gg15" :> ( + 1 * + go[q2,3,4] * + gp[q2,3,1] * + gp[q2,4,5] * + gp[q2-p,2,9] * + gp[q1-p,8,7] * + gp[q2-q1,10,6] * + gv[p,mu,a, -q2,1, q2-p,2] * + gv[q1-p,8, p-q2,9, q2-q1,10] * + gv[-p,nu,b, q2,5, q1-q2,6, p-q1,7] + ) + , + "gg16" :> ( + 1 * + go[p,mu,a, q1-p,1 ,-q1,2] * + gp[q1,2,3] * + gp[q1,7,9] * + gp[q1-p,1,10] * + gp[q2,5,6] * + gp[q2-q1,4,8] * + gv[q1,3, q2-q1,4, -q2,5] * + gv[q2,6, -q1,7, q1-q2,8] * + gv[-p,nu,b, q1,9, p-q1,10] + ) + , + "gg17" :> ( + 1 * + go[q2, 3,4] * + gp[q1,7,8] * + gp[q2,1,3] * + gp[q2,4,5] * + gp[q2,9,11] * + gp[q2-p,2,12] * + gp[q1-q2,6,10] * + gv[p,mu,a, -q2,1, q2-p,2] * + gv[q2,5, q1-q2,6, -q1,7] * + gv[q1,8, -q2,9, q2-q1,10] * + gv[-p,nu,b, q2,11, p-q2,12] + ) + , + "gg18" :> ( + 1 * + go[q2,3, -q1,5, q1-q2,4] * + gp[q2,1,3] * + gp[q2,8,9] * + gp[q1,5,6] * + gp[q1-q2,4,7] * + gp[p-q2,2,10] * + gv[p,mu,a, -q2,1, q2-p,2] * + gv[q1,6, q2-q1,7, -q2,8] * + gv[-p,nu,b, q2,9, p-q2,10] + ) + , + "gg19" :> ( + 1 * + go[q1,6,7] * + gp[q1,4,6] * + gp[q1,7,8] * + gp[q2,1,3] * + gp[q2,9,11] * + gp[q1-q2,5,10] * + gp[q2-p,2,12] * + gv[p,mu,a, -q2,1, q2-p,2] * + gv[q2,3, -q1,4, q1-q2,5] * + gv[q1,8, -q2,9, q2-q1,10] * + gv[-p,nu,b, q2,11, p-q2,12] + ) + , + "gg20" :> ( + 1/2 * + go[q2,3,4] * + gp[q2,1,3] * + gp[q2,4,5] * + gp[q2-p,2,11] * + gp[q2-p,7,6] * + gp[q1-p,9,10] * + gp[q2-q1,8,12] * + gv[p,mu,a, -q2,1, q2-p,2] * + gv[q1-p,10, p-q2,11, q2-q1,12] * + gv[q2-p,7, q1-q2,8, p-q1,9] * + gv[-p,nu,b, q2,5, p-q2,6] + ) + , + "gg21" :> ( + -2* + go[p,mu,a, -q1,1, q1-p,2] * + gp[q1-p, 2, 3] gp[q1, 1, 10] * + ghp[q1-q2, 4, 9] ghp[q2-p, 5, 6] * + ghp[q2, 7, 8] * + ggv[p-q1, 3, q1-q2,4, q2-p, 5 ] * + ggv[-p,nu,b, p-q2, 6, q2, 7 ] * + ggv[q1,10, -q2,8, q2-q1,9] + ) + , + "gg22" :> ( + -2 * + go[q2, 3, 4] * + gp[q2, 1, 3] * + gp[q2-p, 2, 11] * + gp[q2, 4, 5] * + ghp[q1-q2, 6, 12] * + ghp[q1, 7, 8] * + ghp[q1-p, 9, 10] * + gv[p,mu,a, -q2,1, q2-p, 2] * + ggv[q2,5, -q1,7, q1-q2,6] * + ggv[p-q2,11, q2-q1,12, q1-p,10]* + ggv[-p,nu,b, p-q1,9, q1,8] + ) + , + "gg23" :> ( + -2 * + go[q2, 3, 4] * + gp[q2, 1, 3] * + gp[q2-p, 2, 11] * + gp[q2, 4, 5] * + ghp[q1-q2, 6, 12] * + ghp[q1, 7, 8] * + ghp[q1-p, 9, 10] * + gv[p,mu,a, -q2,1, q2-p, 2] * + ggv[q2,5, q1-q2,6, -q1,7] * + ggv[p-q2,11, q1-p,10, q2-q1,12]* + ggv[-p,nu,b, q1,8, p-q1,9] + ) + , + "gg24" :> ( + -1 * + go[q2-q1, 6, 7] * + ghp[q2, 1, 3] * + ghp[q2-p, 2, 9] * + gp[q1-q2, 4, 6] * + ghp[q1, 5, 12] * + gp[q1-q2, 7, 8] * + ghp[p-q1, 10, 11] * + ggv[p,mu,a, q2-p,2, -q2,1] * + ggv[q1-q2,4, q2,3, -q1,5] * + ggv[q2-q1,8, -p+q1,10, p-q2,9] * + ggv[-p,nu,b, q1,12, -q1+p,11] + ) + , + "gg25" :> ( + -2 * + go[q1,6,7] * + gp[q1,4,6] * + gp[q1,7,8] * + ghp[q2,1,3] * + ghp[q2,9,11] * + ghp[q1-q2,5,10] * + ghp[q2-p,2,12] * + ggv[p,mu,a, q2-p,2, -q2,1] * + ggv[-q1,4, q2,3, q1-q2,5] * + ggv[q1,8, q2-q1,10, -q2,9] * + ggv[-p,nu,b, q2,11, p-q2,12] + ) + , + "gg26" :> ( + -1 * + go[q1,6,7] * + gp[q1,4,6] * + gp[q1,7,8] * + ghp[q2,1,3] * + ghp[q2,9,11] * + ghp[q1-q2,5,10] * + ghp[q2-p,2,12] * + gi[p,mu,a, q2-p,2, -q2,1] * + gi[-q1,4, q2,3, q1-q2,5] * + gi[q1,8, q2-q1,10, -q2,9] * + gi[-p,nu,b, q2,11, p-q2,12] + ) + , + "gg27" :> ( + -2 * + go[p,mu,a, q1-p,1 ,-q1,2] * + gp[q1,2,3] * + gp[q1,7,9] * + gp[q1-p,1,10] * + ghp[q2,5,6] * + ghp[q2-q1,4,8] * + ggv[q1,3, q2-q1,4, -q2,5] * + ggv[-q1,7, q2,6, q1-q2,8] * + gv[-p,nu,b, q1,9, p-q1,10] + ) + , + "gg28" :> ( + -2 * + go[q2, 3,4] * + ghp[q1,7,8] * + gp[q2,1,3] * + gp[q2,4,5] * + gp[q2,9,11] * + gp[q2-p,2,12] * + ghp[q1-q2,6,10] * + gv[p,mu,a, -q2,1, q2-p,2] * + ggv[q2,5, q1-q2,6, -q1,7] * + ggv[-q2,9, q1,8, q2-q1,10] * + gv[-p,nu,b, q2,11, p-q2,12] + ) + , + "gg29" :> ( + -1 * + go[q2,3,4] * + gp[q2,1,3] * + gp[q2,4,5] * + gp[q2-p,2,11] * + gp[q2-p,7,6] * + ghp[q1-p,9,10] * + ghp[q2-q1,8,12] * + gv[p,mu,a, -q2,1, q2-p,2] * + ggv[p-q2,11, q1-p,10, q2-q1,12] * + ggv[q2-p,7, q1-q2,8, p-q1,9] * + gv[-p,nu,b, q2,5, p-q2,6] + ) + , + "gg30" :> ( + -2* DiracTrace[2 Tf * + DOT[go[p,mu,a, -q1,1, q1-p,2] , + gp[q1-p, 2, 3] gp[q1, 1, 10] , + qgv[10] , qp[-q2] , + qgv[nu,b] , + qp[p-q2] , + qgv[3] , + qp[q1-q2]] + ] + ) + , + "gg31" :> ( + -2* DiracTrace[2 Tf * + DOT[go[q2, 3, 4] , + gp[q2, 1, 3] , + gp[q2-p, 2, 11] , + gp[q2, 4, 5] , + qgv[11] , + qp[q2-q1, 6, 12] , + qgv[5] , + qp[-q1, 8, 7] , + qgv[nu,b], + qp[p-q1, 10, 9] , + gv[p,mu,a, -q2,1, q2-p, 2]] + ] + ) + , + "gg32" :> ( + -2* + DiracTrace[2 Tf * + DOT[go[q2, 3, 4] , + gp[q2, 1, 3] , + gp[q2-p, 2, 11] , + gp[q2, 4, 5] , + qgv[11] , + qp[-(p-q1), 10, 9] , + qgv[nu,b], + qp[q1, 8, 7] , + qgv[5] , + qp[q1-q2, 6, 12] , + gv[p,mu,a, -q2,1, q2-p, 2]] + ] + ) + , + "gg33" :> ( + -1* + DiracTrace[2 Tf * + DOT[go[q2-q1, 6, 7] , + gp[q1-q2, 4, 6] , + gp[q1-q2, 7, 8] , + qp[q2, 1, 3] , + qgv[mu,a] , + qp[q2-p, 2, 9] , + qgv[8] , + qp[q1-p, 10, 11] , + qgv[nu,b], + qp[q1, 5, 12] , + qgv[4]] + ] + ) + , + "gg34" :> ( + -2* + DiracTrace[2 Tf * + DOT[go[q1,6,7] , + gp[q1,4,6] , + gp[q1,7,8] , + qp[-q2,1,3] , + qgv[4] , + qp[q1-q2,5,10] , qgv[8] , - qp[p-q2, 2, 9] , - qgv[1]] - ) -, -"gq11" :> (go[q2,3, q1-q2,4, -q1,5] * - gp[q2,1,3] * gp[q1-q2,4,9] * gp[q1,5,6] * - DOT[qgv[6] , qp[p-q1] , qgv[9] , - qp[p-q2] , qgv[1]] - ) -, -"gg1" :> go[p,mu,a, -q1,1, q1-p,2] * - gp[q1-p, 2, 3] gp[q1, 1, 10] * - gp[q1-q2, 4, 9] gp[q2-p, 5, 6] * - gp[q2, 7, 8] * - gv[ p-q1, 3, q1-q2,4, q2-p, 5 ] * - gv[ p-q2,6, q2,7, -p,nu,b ] * - gv[ -q2,8, q2-q1,9, q1,10] -, -"gg2" :> 2 * - go[q2, 3, 4] * - gp[q2, 1, 3] * - gp[q2-p, 2, 11] * - gp[q2, 4, 5] * - gp[q1-q2, 6, 12] * - gp[q1, 7, 8] * - gp[q1-p, 9, 10] * - gv[p,mu,a, -q2,1, q2-p, 2] * - gv[q2,5, -q1,7, q1-q2,6] * - gv[q2-q1,12, p-q2,11, q1-p,10]* - gv[q1,8, p-q1,9, -p,nu,b] -, -"gg3" :> go[q2,3, q1-q2,4, -q1,5] * - gp[q2, 1, 3] * - gp[q2-p, 2, 10] * - gp[q1-q2, 4, 9] * - gp[-q1, 5, 6] * - gp[q1-p, 8, 7] * - gv[p,mu,a, -q2,1, q2-p, 2] * - gv[p-q2, 10, q2-q1,9, q1-p,8] * - gv[-p,nu,b, q1,6, p-q1,7] -, -"gg4" :> ( -1/2 * - go[q2-q1, 6, 7] * - gp[q2, 1, 3] * - gp[q2-p, 2, 9] * - gp[q1-q2, 4, 6] * - gp[q1, 5, 12] * - gp[q1-q2, 7, 8] * - gp[p-q1, 10, 11] * - gv[p,mu,a, -q2,1, q2-p, 2] * - gv[q2,3, q1-q2,4, -q1,5] * - gv[q2-q1,8, p-q2,9, -p+q1,10] * - gv[-p,nu,b, q1,12, -q1+p,11] - ) -, -"gg5" :> ( -1/3 * - go[p,mu,a, -q1,1, q2-p,2, q1-q2,3] * - gp[q1, 1, 4] * - gp[q2-p, 2, 5] * - gp[q1-q2, 3, 6] * - gv[-p,nu,b, q1,4, p-q2,5, q2-q1,6] - ) -, -"gg6" :> ( -1/2 * - go[q1, 4, 5] * - gp[q1, 1, 4] * - gp[q1, 5, 6] * - gp[q1-q2, 2, 7] * - gp[q2-p, 3, 8] * - gv[ p,mu,a, -q1,1, q1-q2,2, q2-p,3] * - gv[-p,nu,b, q1,6, q2-q1,7, p-q2,8] - ) -, -"gg7" :> ( -1/2 * - go[p,mu,a, q2-p,1, -q2,2] * - gp[q2-p, 1, 4] * - gp[q2, 2, 3] * - gp[q1, 6, 8] * - gp[q1-p, 5, 7] * - gv[q2,3, p-q2,4, q1-p,5, -q1,6] * - gv[-p,nu,b, -q1+p,7, q1,8] - ) -, -"gg8" :> ( -1 * - go[q2, 3, 4] * - gp[q2, 1, 3] * - gp[q2, 4, 5] * - gp[q2-p, 2, 6] * - gp[q1-p, 7, 10] * - gp[q1, 8, 9] * - gv[p,mu,a, -q2,1, q2-p,2] * - gv[q2,5, p-q2,6, q1-p,7, -q1,8] * - gv[-p,nu,b, p-q1,10, q1,9] - ) -, -"gg9" :> ( -1/4 * - go[q2,3, p-q2,4, -q1,5, q1-p,6] * - gp[q2, 3, 1] * - gp[q2-p, 2, 4] * - gp[q1-p, 6, 7] * - gp[q1, 5, 8] * - gv[ p,mu,a, -q2,1, q2-p,2] * - gv[-p,nu,b, q1,8, p-q1,7] - ) -, -"gg10" :> ( -1 * - go[p,mu,a, -q1,2, q1-q2,3, q2-p,4] * - gp[q1, 2, 9] * - gp[q1-q2, 3, 6] * - gp[q2-p, 4, 5] * - gp[q1-p, 7, 8] * - gv[p-q2,5, q2-q1,6, q1-p,7] * - gv[-p,nu,b, q1,9, p-q1,8] - ) -, -"gg11" :> ( -2 * - go[q2, 4, 5] * - gp[q2, 4, 1] * - gp[q2, 5, 6] * - gp[q1, 8, 9] * - gp[q2-q1, 2, 7] * - gp[p-q1, 3, 10] * - gv[p,mu,a, -q2,1, q2-q1,2, q1-p,3] * - gv[q2,6, q1-q2,7, -q1,8] * - gv[-p,nu,b, q1,9, p-q1,10] - ) -, -"gg12" :> ( -1 * - go[q2,3, q1-q2,4, -q1,5] * - gp[q2,1,3] * - gp[q1,5,6] * - gp[q1-q2,4,7]* - gp[q2-p,2,8] * - gv[p,mu,a, -q2,1, q2-p,2] * - gv[-p,nu,b, q1,6, q2-q1,7, p-q2,8] - ) -, -"gg13" :> ( -1 * - go[q2,3,4] * - gp[q2,1,3] * - gp[q2,4,5] * - gp[q1,7,9] * - gp[q1-q2,6,8] * - gp[q2-p,2,10] * - gv[q2,5, q1-q2,6, -q1,7] * - gv[p,mu,a, -q2,1, q2-p,2] * - gv[-p,nu,b, q2-q1,8, q1,9, p-q2,10] - ) -, -"gg14" :> ( -1 * - go[p,mu,a, q2-p,1, -q2,2] * - gp[q2, 2,3] * - gp[q2-p,1,8] * - gp[q1,5,6] * - gp[q1-q2,4,7] * - gv[q2,3, -q1,5, q1-q2,4] * - gv[-p,nu,b, q1,6, q2-q1,7, p-q2,8] - ) -, -"gg15" :> ( -1 * - go[q2,3,4] * - gp[q2,3,1] * - gp[q2,4,5] * - gp[q2-p,2,9] * - gp[q1-p,8,7] * - gp[q2-q1,10,6] * - gv[p,mu,a, -q2,1, q2-p,2] * - gv[q1-p,8, p-q2,9, q2-q1,10] * - gv[-p,nu,b, q2,5, q1-q2,6, p-q1,7] - ) -, -"gg16" :> ( -1 * - go[p,mu,a, q1-p,1 ,-q1,2] * - gp[q1,2,3] * - gp[q1,7,9] * - gp[q1-p,1,10] * - gp[q2,5,6] * - gp[q2-q1,4,8] * - gv[q1,3, q2-q1,4, -q2,5] * - gv[q2,6, -q1,7, q1-q2,8] * - gv[-p,nu,b, q1,9, p-q1,10] - ) -, -"gg17" :> ( -1 * - go[q2, 3,4] * - gp[q1,7,8] * - gp[q2,1,3] * - gp[q2,4,5] * - gp[q2,9,11] * - gp[q2-p,2,12] * - gp[q1-q2,6,10] * - gv[p,mu,a, -q2,1, q2-p,2] * - gv[q2,5, q1-q2,6, -q1,7] * - gv[q1,8, -q2,9, q2-q1,10] * - gv[-p,nu,b, q2,11, p-q2,12] - ) -, -"gg18" :> ( -1 * - go[q2,3, -q1,5, q1-q2,4] * - gp[q2,1,3] * - gp[q2,8,9] * - gp[q1,5,6] * - gp[q1-q2,4,7] * - gp[p-q2,2,10] * - gv[p,mu,a, -q2,1, q2-p,2] * - gv[q1,6, q2-q1,7, -q2,8] * - gv[-p,nu,b, q2,9, p-q2,10] - ) -, -"gg19" :> ( -1 * - go[q1,6,7] * - gp[q1,4,6] * - gp[q1,7,8] * - gp[q2,1,3] * - gp[q2,9,11] * - gp[q1-q2,5,10] * - gp[q2-p,2,12] * - gv[p,mu,a, -q2,1, q2-p,2] * - gv[q2,3, -q1,4, q1-q2,5] * - gv[q1,8, -q2,9, q2-q1,10] * - gv[-p,nu,b, q2,11, p-q2,12] - ) -, -"gg20" :> ( -1/2 * - go[q2,3,4] * - gp[q2,1,3] * - gp[q2,4,5] * - gp[q2-p,2,11] * - gp[q2-p,7,6] * - gp[q1-p,9,10] * - gp[q2-q1,8,12] * - gv[p,mu,a, -q2,1, q2-p,2] * - gv[q1-p,10, p-q2,11, q2-q1,12] * - gv[q2-p,7, q1-q2,8, p-q1,9] * - gv[-p,nu,b, q2,5, p-q2,6] - ) -, -"gg21" :> ( --2* - go[p,mu,a, -q1,1, q1-p,2] * - gp[q1-p, 2, 3] gp[q1, 1, 10] * - ghp[q1-q2, 4, 9] ghp[q2-p, 5, 6] * - ghp[q2, 7, 8] * - ggv[p-q1, 3, q1-q2,4, q2-p, 5 ] * - ggv[-p,nu,b, p-q2, 6, q2, 7 ] * - ggv[q1,10, -q2,8, q2-q1,9] - ) -, -"gg22" :> ( --2 * - go[q2, 3, 4] * - gp[q2, 1, 3] * - gp[q2-p, 2, 11] * - gp[q2, 4, 5] * - ghp[q1-q2, 6, 12] * - ghp[q1, 7, 8] * - ghp[q1-p, 9, 10] * - gv[p,mu,a, -q2,1, q2-p, 2] * - ggv[q2,5, -q1,7, q1-q2,6] * - ggv[p-q2,11, q2-q1,12, q1-p,10]* - ggv[-p,nu,b, p-q1,9, q1,8] - ) -, -"gg23" :> ( --2 * - go[q2, 3, 4] * - gp[q2, 1, 3] * - gp[q2-p, 2, 11] * - gp[q2, 4, 5] * - ghp[q1-q2, 6, 12] * - ghp[q1, 7, 8] * - ghp[q1-p, 9, 10] * - gv[p,mu,a, -q2,1, q2-p, 2] * - ggv[q2,5, q1-q2,6, -q1,7] * - ggv[p-q2,11, q1-p,10, q2-q1,12]* - ggv[-p,nu,b, q1,8, p-q1,9] - ) -, -"gg24" :> ( --1 * - go[q2-q1, 6, 7] * - ghp[q2, 1, 3] * - ghp[q2-p, 2, 9] * - gp[q1-q2, 4, 6] * - ghp[q1, 5, 12] * - gp[q1-q2, 7, 8] * - ghp[p-q1, 10, 11] * - ggv[p,mu,a, q2-p,2, -q2,1] * - ggv[q1-q2,4, q2,3, -q1,5] * - ggv[q2-q1,8, -p+q1,10, p-q2,9] * - ggv[-p,nu,b, q1,12, -q1+p,11] - ) -, -"gg25" :> ( --2 * - go[q1,6,7] * - gp[q1,4,6] * - gp[q1,7,8] * - ghp[q2,1,3] * - ghp[q2,9,11] * - ghp[q1-q2,5,10] * - ghp[q2-p,2,12] * - ggv[p,mu,a, q2-p,2, -q2,1] * - ggv[-q1,4, q2,3, q1-q2,5] * - ggv[q1,8, q2-q1,10, -q2,9] * - ggv[-p,nu,b, q2,11, p-q2,12] - ) -, -"gg26" :> ( --1 * - go[q1,6,7] * - gp[q1,4,6] * - gp[q1,7,8] * - ghp[q2,1,3] * - ghp[q2,9,11] * - ghp[q1-q2,5,10] * - ghp[q2-p,2,12] * - gi[p,mu,a, q2-p,2, -q2,1] * - gi[-q1,4, q2,3, q1-q2,5] * - gi[q1,8, q2-q1,10, -q2,9] * - gi[-p,nu,b, q2,11, p-q2,12] - ) -, -"gg27" :> ( --2 * - go[p,mu,a, q1-p,1 ,-q1,2] * - gp[q1,2,3] * - gp[q1,7,9] * - gp[q1-p,1,10] * - ghp[q2,5,6] * - ghp[q2-q1,4,8] * - ggv[q1,3, q2-q1,4, -q2,5] * - ggv[-q1,7, q2,6, q1-q2,8] * - gv[-p,nu,b, q1,9, p-q1,10] - ) -, -"gg28" :> ( --2 * - go[q2, 3,4] * - ghp[q1,7,8] * - gp[q2,1,3] * - gp[q2,4,5] * - gp[q2,9,11] * - gp[q2-p,2,12] * - ghp[q1-q2,6,10] * - gv[p,mu,a, -q2,1, q2-p,2] * - ggv[q2,5, q1-q2,6, -q1,7] * - ggv[-q2,9, q1,8, q2-q1,10] * - gv[-p,nu,b, q2,11, p-q2,12] - ) -, -"gg29" :> ( --1 * - go[q2,3,4] * - gp[q2,1,3] * - gp[q2,4,5] * - gp[q2-p,2,11] * - gp[q2-p,7,6] * - ghp[q1-p,9,10] * - ghp[q2-q1,8,12] * - gv[p,mu,a, -q2,1, q2-p,2] * - ggv[p-q2,11, q1-p,10, q2-q1,12] * - ggv[q2-p,7, q1-q2,8, p-q1,9] * - gv[-p,nu,b, q2,5, p-q2,6] - ) -, -"gg30" :> ( --2* DiracTrace[2 Tf * - DOT[go[p,mu,a, -q1,1, q1-p,2] , - gp[q1-p, 2, 3] gp[q1, 1, 10] , - qgv[10] , qp[-q2] , - qgv[nu,b] , - qp[p-q2] , - qgv[3] , - qp[q1-q2]] - ] - ) -, -"gg31" :> ( --2* DiracTrace[2 Tf * - DOT[go[q2, 3, 4] , - gp[q2, 1, 3] , - gp[q2-p, 2, 11] , - gp[q2, 4, 5] , - qgv[11] , - qp[q2-q1, 6, 12] , - qgv[5] , - qp[-q1, 8, 7] , - qgv[nu,b], - qp[p-q1, 10, 9] , - gv[p,mu,a, -q2,1, q2-p, 2]] - ] - ) -, -"gg32" :> ( --2* - DiracTrace[2 Tf * - DOT[go[q2, 3, 4] , - gp[q2, 1, 3] , - gp[q2-p, 2, 11] , - gp[q2, 4, 5] , - qgv[11] , - qp[-(p-q1), 10, 9] , - qgv[nu,b], - qp[q1, 8, 7] , - qgv[5] , - qp[q1-q2, 6, 12] , - gv[p,mu,a, -q2,1, q2-p, 2]] - ] - ) -, -"gg33" :> ( --1* - DiracTrace[2 Tf * - DOT[go[q2-q1, 6, 7] , - gp[q1-q2, 4, 6] , - gp[q1-q2, 7, 8] , - qp[q2, 1, 3] , - qgv[mu,a] , - qp[q2-p, 2, 9] , - qgv[8] , - qp[q1-p, 10, 11] , - qgv[nu,b], - qp[q1, 5, 12] , - qgv[4]] - ] - ) -, -"gg34" :> ( --2* - DiracTrace[2 Tf * - DOT[go[q1,6,7] , - gp[q1,4,6] , - gp[q1,7,8] , - qp[-q2,1,3] , - qgv[4] , - qp[q1-q2,5,10] , - qgv[8] , - qp[-q2,9,11] , - qgv[nu,b] , - qp[p-q2,2,12] , - qgv[mu,a]] - ] - ) -, -"gg35" :> ( --2* - DiracTrace[2 Tf * - DOT[go[p,mu,a, q1-p,1 ,-q1,2] , - gp[q1,2,3] , - gp[q1,7,9] , - gp[q1-p,1,10] , - qpm[-q2,5,6] , - qgv[7] , - qpm[q1-q2,4,8] , - qgv[3] , - gv[-p,nu,b, q1,9, p-q1,10]] - ] - ) -, -"gg36" :> ( --2 * - DiracTrace[2 Tf * - DOT[go[q2, 3,4] , - gp[q2,1,3] , - gp[q2,4,5] , - gp[q2,9,11] , - gp[q2-p,2,12] , - qp[q1-q2,6,10] , - qgv[9] , - qp[q1,7,8] , - qgv[5] , - gv[p,mu,a, -q2,1, q2-p,2] , - gv[-p,nu,b, q2,11, p-q2,12]] - ] - ) -, -"gg37" :> ( --1 * - DiracTrace[ 2 Tf * - DOT[go[q2,3,4] , - gp[q2,1,3] , - gp[q2,4,5] , - gp[q2-p,2,11] , - gp[q2-p,7,6] , - qp[q1-p,9,10] , - qgv[7] , - qp[q1-q2,8,12] , - qgv[11] , - gv[p,mu,a, -q2,1, q2-p,2] , - gv[-p,nu,b, q2,5, p-q2,6]] - ] - ) -, -"se1g1" :> (gv[p,mu,a, q-p,alpha,c, -q,beta,e] * - gp[p-q, alpha,c, rho,d] * - gv[-p,nu,b, p-q,rho,d, q,sigma,f] * - gp[q, beta,e, sigma,f] - ) -, -"se2g1" :> (gv[p,mu,a, -q1,alpha,c, q1-p,beta,i] * - gp[q1, alpha,c, delta,d] * - gv[q1,delta,d, -q2,kappa,r, q2-q1,lambda,e] * - gp[q1-q2, lambda,e, rho,h] * - gv[p-q1,xi,j, q2-p,sigma,w, q1-q2,rho,h] * - gp[q2, kappa,r, gamma,s] * - gv[-p,nu,b, q2,gamma,s, p-q2,tau,v] * - gp[q2-p, tau,v, sigma,w] * - gp[q1-p, xi,j, beta,i] - ) -} -]; - -ampswitch = True; - -(* AMPLIST = amplist; *) -If[{nam} == {opt} == {}, -(#[[1]])&/@amplist, -SUNDeltaContract@ -DotSimplify[ChangeDimension[ToString[nam] /. amplist /. nice, - Dimension /. {opt}/.Options[Amplitude]],Expanding->False] + qp[-q2,9,11] , + qgv[nu,b] , + qp[p-q2,2,12] , + qgv[mu,a]] + ] + ) + , + "gg35" :> ( + -2* + DiracTrace[2 Tf * + DOT[go[p,mu,a, q1-p,1 ,-q1,2] , + gp[q1,2,3] , + gp[q1,7,9] , + gp[q1-p,1,10] , + qpm[-q2,5,6] , + qgv[7] , + qpm[q1-q2,4,8] , + qgv[3] , + gv[-p,nu,b, q1,9, p-q1,10]] + ] + ) + , + "gg36" :> ( + -2 * + DiracTrace[2 Tf * + DOT[go[q2, 3,4] , + gp[q2,1,3] , + gp[q2,4,5] , + gp[q2,9,11] , + gp[q2-p,2,12] , + qp[q1-q2,6,10] , + qgv[9] , + qp[q1,7,8] , + qgv[5] , + gv[p,mu,a, -q2,1, q2-p,2] , + gv[-p,nu,b, q2,11, p-q2,12]] + ] + ) + , + "gg37" :> ( + -1 * + DiracTrace[ 2 Tf * + DOT[go[q2,3,4] , + gp[q2,1,3] , + gp[q2,4,5] , + gp[q2-p,2,11] , + gp[q2-p,7,6] , + qp[q1-p,9,10] , + qgv[7] , + qp[q1-q2,8,12] , + qgv[11] , + gv[p,mu,a, -q2,1, q2-p,2] , + gv[-p,nu,b, q2,5, p-q2,6]] + ] + ) + , + "se1g1" :> (gv[p,mu,a, q-p,alpha,c, -q,beta,e] * + gp[p-q, alpha,c, rho,d] * + gv[-p,nu,b, p-q,rho,d, q,si,f] * + gp[q, beta,e, si,f] + ) + , + "se2g1" :> (gv[p,mu,a, -q1,alpha,c, q1-p,beta,i] * + gp[q1, alpha,c, delta,d] * + gv[q1,delta,d, -q2,kappa,r, q2-q1,lambda,e] * + gp[q1-q2, lambda,e, rho,h] * + gv[p-q1,xi,j, q2-p,si,w, q1-q2,rho,h] * + gp[q2, kappa,r, gamma,s] * + gv[-p,nu,b, q2,gamma,s, p-q2,tau,v] * + gp[q2-p, tau,v, si,w] * + gp[q1-p, xi,j, beta,i] + ) + } + ]; + ampswitch = True; + (* AMPLIST = amplist; *) + If[ {nam} == {opt} == {}, + (#[[1]])&/@amplist, + SUNDeltaContract@DotSimplify[ChangeDimension[ToString[nam] /. amplist /. nice, Dimension /. {opt}/.Options[Amplitude]],Expanding->False] ] -]; + ]; FCPrint[1,"Amplitude.m loaded"]; End[] diff --git a/FeynCalc/Tables/AnomalousDimension.m b/FeynCalc/Tables/AnomalousDimension.m index 2b607e6bc..ee508a108 100755 --- a/FeynCalc/Tables/AnomalousDimension.m +++ b/FeynCalc/Tables/AnomalousDimension.m @@ -25,7 +25,7 @@ AnomalousDimension[es_, opt___Rule] := AnomalousDimension[es, OPEm, opt]; AnomalousDimension[es_, m_Symbol, opt___Rule] := -Block[{pol, s, s1, s2, s1t, s2t, s12,s21,s12t,d3,s3t, +Block[{pol, s, s1, s2, s1t, s2t, s12,s21,s12t,d3,s3t,s3, S1,S2,S12,S12t,S21,S3,S3t,S1t,S2t,ST,sim,simfun,n=m}, simfun = Simplify /. {opt} /. Options[AnomalousDimension]; If[simfun === FullSimplify, @@ -44,7 +44,7 @@ sim[3n^4+6n^3+16n^2+13n-3] = -3 + n*(1 + n)*(13 + 3*n*(1 + n)); sim[n^6+3n^5+5n^4+n^3-8n^2+2n+4] = 4 + n*(2 + n*(-8 + n*(1 + n*(5 + n*(3 + n))))); - sim[zz_] := FullSimplify[z] + sim[z_] := FullSimplify[z] ]; s = ToString[es]; s1 = SumS[1, m-1]; S1 = SumS[1, m]; diff --git a/FeynCalc/Tables/ConvoluteTable.m b/FeynCalc/Tables/ConvoluteTable.m index 6e555e497..bae13425c 100755 --- a/FeynCalc/Tables/ConvoluteTable.m +++ b/FeynCalc/Tables/ConvoluteTable.m @@ -22,8 +22,11 @@ Begin["`ConvoluteTable`Private`"] +cT::usage=""; +cTcT::usage=""; + ConvoluteTable[f_, g_, opt___Rule] := -ConvoluteTable[f, g, FCGV[ToString[Unique["x"]]], opt]; +ConvoluteTable[f, g, FCGV["x"], opt]; ConvoluteTable[if_, ig_, x_,___Rule] := cTab[if,ig,x]; diff --git a/FeynCalc/Tables/FCShowReferenceCard.m b/FeynCalc/Tables/FCShowReferenceCard.m new file mode 100644 index 000000000..9a0245d9e --- /dev/null +++ b/FeynCalc/Tables/FCShowReferenceCard.m @@ -0,0 +1,56 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: FCShowReferenceCard *) + +(* +This software is covered by the GNU General Public License 3. +Copyright (C) 1990-2018 Rolf Mertig +Copyright (C) 1997-2018 Frederik Orellana +Copyright (C) 2014-2018 Vladyslav Shtabovenko +*) + +(* :Summary: Shows reference cards. +*) + +(* ------------------------------------------------------------------------ *) + + + +FCShowReferenceCard::usage = "FCShowReferenceCard[{\"name\"}] shows the \ +reference card that corresponds to \"name\". Reference cards are stored \ +in Tables/ReferenceCards inside the FeynCalc main directory. \n +FCShowReferenceCard[] lists available reference cards."; + +FCShowReferenceCard::nav = "The reference card you requested is not available."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`FCShowReferenceCard`Private`"] + +FCShowReferenceCard[l_List] := +Block[{res = l}, + + res = res /. refCards; + If[ Head[res]===List, + Message[FCShowReferenceCard::nav], + Print[res] + ]; + + +]; + +FCShowReferenceCard[]:= + First[Transpose[refCards/. Rule -> List]]; + +refFiles = FileNames["*.ref", FileNameJoin[{$FeynCalcDirectory, "Tables", "ReferenceCards"}]] +refCards = {} +Scan[(refCards = Join[refCards, Get[#]];) &, refFiles] + + +FCPrint[1,"FCShowReferenceCard.m loaded."]; +End[] diff --git a/FeynCalc/Tables/Gamma1.m b/FeynCalc/Tables/Gamma1.m index 10a7ae311..3f1f2fa30 100755 --- a/FeynCalc/Tables/Gamma1.m +++ b/FeynCalc/Tables/Gamma1.m @@ -61,7 +61,7 @@ 2*PolyGamma[2, -2 + be + de] + 4*Zeta[3]))/(48*Gamma[be]*Gamma[de]) ), (be === 1) && (de === 1) && (al+ga>2), -bd1 = ( (-2*Gamma[-2 + al + ga])/(Epsilon*Gamma[al]*Gamma[ga]) - +(*bd1 = *)( (-2*Gamma[-2 + al + ga])/(Epsilon*Gamma[al]*Gamma[ga]) - (Gamma[-2 + al + ga]*(EulerGamma - PolyGamma[0, -2 + al + ga]))/ (Gamma[al]*Gamma[ga]) - (Epsilon*Gamma[-2 + al + ga]* (6*EulerGamma^2 + Pi^2 - 12*EulerGamma*PolyGamma[0, -2 + al + ga] + @@ -77,7 +77,7 @@ 2*PolyGamma[2, -2 + al + ga] + 4*Zeta[3]))/(48*Gamma[al]*Gamma[ga]) ), (al===1) && (be===1) && (ga===1) && (de===1), -ag1bd1 = ( 4/Epsilon^2 + (4*EulerGamma)/Epsilon + +(*ag1bd1 = *)( 4/Epsilon^2 + (4*EulerGamma)/Epsilon + (12*EulerGamma^2 + Pi^2)/6 + (Epsilon*(4*EulerGamma^3 + EulerGamma*Pi^2 + 2*Zeta[3]))/6 + (Epsilon^2*(240*EulerGamma^4 + 120*EulerGamma^2*Pi^2 + 7*Pi^4 + diff --git a/FeynCalc/Tables/Gamma3.m b/FeynCalc/Tables/Gamma3.m index d5539eb0c..d4f178a6c 100755 --- a/FeynCalc/Tables/Gamma3.m +++ b/FeynCalc/Tables/Gamma3.m @@ -22,7 +22,11 @@ Begin["`Gamma3`Private`"] -Options[Gamma3] = {EpsilonOrder -> 3}; +gamma3::usage=""; + +Options[Gamma3] = { + EpsilonOrder -> 3 +}; Gamma3[al_ /;Head[al]=!=Integer, be_, ga_, ep_,___Rule] := Gamma[al+be+ga+ep-4-Epsilon]/Gamma[al+be+ep-2-Epsilon/2]/Gamma[ga] * diff --git a/FeynCalc/Tables/Hill.m b/FeynCalc/Tables/Hill.m new file mode 100755 index 000000000..f4d2a5212 --- /dev/null +++ b/FeynCalc/Tables/Hill.m @@ -0,0 +1,43 @@ +(* ::Package:: *) + +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) + +(* :Title: Hill *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Hill's identity *) + +(* ------------------------------------------------------------------------ *) + + +Hill::usage = "Hill[x,y] gives the Hill identity with arguments x and y. \ +The returned object is 0."; + +(* ------------------------------------------------------------------------ *) + +Begin["`Package`"] +End[] + +Begin["`Hill`Private`"] + +Hill[x_, y_] := + Block[ {t0, t1,t2,t3,t4, t5}, + + t0 = Factor2[1-x]; + t1 = Factor2[1-y]; + t2 = Factor2[(x-y)/x]; + t4 = Factor2[t0/t1]; + t3 = Factor2[y/x t4]; + t5 = Factor2[(x-y)/t1]; + + PolyLog[2,x] - PolyLog[2,y] + PolyLog[2,Factor2[y/x]] + PolyLog[2, t4] - PolyLog[2, t3] - Pi^2/6 + Log[x] (Log[t0] - Log[t1]) + + Log[t4] ( Log[t5]-Log[x]- Log[t2] + Log[t1]) - Log[t3] (Log[Factor2[(x-y)/(x (1-y))]] - Log[t2] + Log[t1]) + ] +FCPrint[1,"Hill.m loaded."]; +End[] diff --git a/FeynCalc/Tables/Integrate3.m b/FeynCalc/Tables/Integrate3.m index 23f5d5f34..07c15c1d8 100755 --- a/FeynCalc/Tables/Integrate3.m +++ b/FeynCalc/Tables/Integrate3.m @@ -27,7 +27,7 @@ Begin["`Integrate3`Private`"] -mcheck[y_Integer?Positive] := True; +mcheck[_Integer?Positive] := True; mcheck[y_] := If[Variables[y] === {}, False, DataType[First[Variables[y]], PositiveInteger] ]; @@ -101,7 +101,7 @@ iT[DeltaFunctionDoublePrime[1-x_] f_., {x_, 0, 1}] :> (D[f, x, x]/.x->1), *) -iT[en_Integer,{x_,0,1}] :> en, +iT[en_Integer,{_,0,1}] :> en, iT[PolyLog[2,1-x_] / (1-x_)^2,{x_,0,1}] :> (FCPrint[3,"DISTRIBUTION sense "]; @@ -771,7 +771,7 @@ (* w1 *) (*I137I*) -(*X*)iT[(x_^n_?mcheck) DeltaFunction[1-x_], +(*X*)iT[(x_^_?mcheck) DeltaFunction[1-x_], {x_,0,1}] :> 1, (* w2 *) @@ -2368,7 +2368,7 @@ (*X*)iT[(Log[1-x_]^2)/x_, {x_,0,1}] :>2*Zeta[3] , (*RX34*) -(*X*)iT[Log[1-x]^2*x^-1, {x_,0,1}] :> 2*Zeta[3] +(*X*)iT[Log[1-x_]^2*x_^-1, {x_,0,1}] :> 2*Zeta[3] , (*RX39*) (*X*)iT[ Log[1 + (x_)]^2/(x_), {x_,0,1}] :> 1/4*Zeta[3] diff --git a/FeynCalc/Tables/Integrate5.m b/FeynCalc/Tables/Integrate5.m index 26ca25101..6d1b5c071 100755 --- a/FeynCalc/Tables/Integrate5.m +++ b/FeynCalc/Tables/Integrate5.m @@ -22,6 +22,8 @@ Begin["`Integrate5`Private`"] +sing::usage=""; + Integrate5[a_, b_List, c__List, opts___?OptionQ] := Integrate5[Integrate5[a,b, opts], c, opts] /; FreeQ[SelectNotFree[a, b[[1]]], DeltaFunction]; @@ -45,28 +47,31 @@ Integrate -> Integrate3 /. Integrate3 -> Integrate *); -integrateD[a_, b_, c___] := Block[{i3, tt, nop, n1, n2}, -If[Head[i3 = Integrate3[a, b, c]] =!= Integrate3, i3, - If[FreeQ[a, PlusDistribution], -(* -Dialog[a]; -*) - integrate2[a, b, c], -(* -Dialog[a]; -*) - tt = Collect2[a, PlusDistribution, Factoring -> True]; -FCPrint[2,"integrating ",tt//InputForm]; - nop = SelectFree[n1 + n2 + tt, PlusDistribution]/.{n1:>0, n2:>0}; - pd = tt - nop; - pd = Collect2[ - If[Head[pd] === Plus, - Map[intDistribution[#, b, c]&, pd], - intDistribution[pd,b,c] - ] + integrate2[nop, b, c], - {Log, PolyLog}]; - pd - ]]]; +integrateD[a_, b_, c___] := + Block[{ i3, tt, nop, n1, n2,pd}, + If[Head[i3 = Integrate3[a, b, c]] =!= Integrate3, + i3, + If[ FreeQ[a, PlusDistribution], + (* + Dialog[a]; + *) + integrate2[a, b, c], + (* + Dialog[a]; + *) + tt = Collect2[a, PlusDistribution, Factoring -> True]; + FCPrint[2,"integrating ",tt//InputForm]; + nop = SelectFree[n1 + n2 + tt, PlusDistribution]/.{n1:>0, n2:>0}; + pd = tt - nop; + pd = Collect2[ + If[ Head[pd] === Plus, + Map[intDistribution[#, b, c]&, pd], + intDistribution[pd,b,c] + ] + integrate2[nop, b, c], {Log, PolyLog}]; + pd + ] + ] + ]; (* 10 *) intDistribution[ PlusDistribution[1/(1-x2_)] * @@ -150,7 +155,7 @@ Zeta2 DeltaFunction[1 - x] ) /; FreeQ2[f, {x1, x2}]; -intDistribution[f_. PlusDistribution[1/(1-x1_)] * +intDistribution[_. PlusDistribution[1/(1-x1_)] * PlusDistribution[Log[1-x2_]/(1-x2_)] * DeltaFunction[x_ - (x1_ x2_)], {x1_,0,1},{x2_,0,1} ] := -Log[x] Log[1-x]/(1-x) + 3/2 Log[1-x]^2/(1-x) - @@ -164,7 +169,7 @@ ], {x1,0,1} ]; -integrate1[f_. PlusDistribution[Log[y_] / (1-x1_)], {x1_,0,1} +integrate1[f_. PlusDistribution[Log[_] / (1-x1_)], {x1_,0,1} ] := 0 /; FreeQ[f, x1]; integrate1[Log[1 - z_ / x1_] PlusDistribution[1/(1 - x1_)], diff --git a/FeynCalc/Tables/Kummer.m b/FeynCalc/Tables/Kummer.m index 6d548e416..032a399bd 100755 --- a/FeynCalc/Tables/Kummer.m +++ b/FeynCalc/Tables/Kummer.m @@ -24,111 +24,123 @@ Begin["`Kummer`Private`"] gm=Gamma; -Kummer[i_Integer /; MemberQ[Range[96],i] && - !MemberQ[Range[25,90], i] - ][exp_] := -Block[{F, u}, - u = exp /. Hypergeometric2F1 -> F; -Which[i === 1, u /. F[a_,b_,c_,z_] :> - Factor2[1-z]^(c-a-b) F[c-a, c-b,c,z] - , - i === 2, u /. F[a_,b_,c_,z_] :> - Factor2[1-z]^(c-a-b) F[c-a, c-b,c,z] - , - i === 3, u /. F[a_,b_,c_,z_] :> - Factor2[1-z]^(-a) F[a,c-b,c,Factor2[z/(z-1)]] - , - i === 4, u /. F[a_,b_,c_,z_] :> - Factor2[1-z]^(-b) F[c-a,b,c,Factor2[z/(z-1)]] - , - i === 5, u /. F[a_,b_,cc_,zz_] :> (*c=a+b+1-cc; z = 1-zz *) - Factor2[1-zz]^(-a-b+cc) F[-b + cc,-a + cc,cc,Factor2[zz]] - , - i === 6, u /. F[a_,b_,cc_,zz_] :> (*c=a+b+1-cc; z=1-zz*) - Factor2[1-zz]^(-a-b+cc) F[-b + cc,-a + cc,cc,Factor2[zz]] - , - i === 7, u /. F[a_,b_,cc_,zz_] :> (*c=a+b+1-cc; z = 1-zz*) - Factor2[1-zz]^(-a) F[a, -b + cc, cc,Factor2[1-1/(1-zz)]] - , - i === 8, u /. F[a_,b_,cc_,zz_] :> (*c=a+b+1-cc; z=1-zz*) - Factor2[1-zz]^(-b) F[-a + cc,b,cc,Factor2[1-1/(1-zz)]] - , - i === 9, u /. F[a_,bb_,cc_,zz_] :> (* z = 1/zz *) - Factor2[-1/zz]^(a+bb-cc) Factor2[1-1/zz]^(-a-bb+cc) * - F[-a + cc, -bb + cc, cc, Factor2[zz]] - , - i === 10, u /. F[a_,bb_,cc_,zz_] :> (* z = 1/zz *) - Factor2[-1/zz]^(a+bb-cc) Factor2[1-1/zz]^(-a-bb+cc) * - F[-a + cc, -bb + cc, cc, Factor2[zz]] - , - i === 11, u /. F[a_,bb_,cc_,zz_] :> (* z = 1/zz *) - Factor2[-1/zz]^a (Factor2[1-zz])^(-a) * - F[a, -bb + cc, cc, Factor2[1/(1-1/zz)]] - , - i === 12, u /. F[a_,bb_,cc_,zz_] :> (* z = 1/zz *) - Factor2[-1/zz]^(bb-a) Factor2[1-1/zz]^(-bb) * - F[bb, -a + cc, cc, Factor2[1/(1-1/zz)]] - , - i === 13, u /. F[aa_,b_,cc_,zz_] :> (* z = 1/zz *) - Factor2[-1/zz]^(aa + b - cc) Factor2[1-1/zz]^(-aa - b + cc)* - F[-b + cc, -aa + cc, cc, Factor2[zz]] - , - i === 14, u /. F[aa_,b_,cc_,zz_] :> (* z = 1/zz *) - Factor2[-1/zz]^(aa + b - cc) Factor2[1-1/zz]^(-aa - b + cc)* - F[-b + cc, -aa + cc, cc, Factor2[zz]] - , - i === 15, u /. F[aa_,b_,cc_,zz_] :> (* z = 1/zz *) - Factor2[-1/zz]^b Factor2[1-1/zz]^(-b) * - F[b,-aa + cc,cc,Factor2[1/(1-1/zz)]] - , - i === 16, u /. F[aa_,b_,cc_,zz_] :> (* z = 1/zz *) - Factor2[-1/zz]^aa Factor2[1-1/zz]^(-aa) * - F[aa,cc-b,cc,Factor2[1/(1-1/zz)]] - , - i === 17, u /. F[aa_,bb_,cc_,z_] :> - (1-z)^(-aa - bb + cc) F[-aa + cc,-bb + cc,cc,z] - , - i === 18, u /. F[aa_,bb_,cc_,z_] :> - (1-z)^(-aa - bb + cc) F[-aa + cc,-bb + cc,cc,z] - , - i === 19, u /. F[aa_,bb_,cc_,z_] :> - (1-z)^(-aa) F[aa, -bb + cc, cc, z/(z - 1)] - , - i === 20, u /. F[aa_,bb_,cc_,z_] :> - (1-z)^(-bb) F[bb, -aa + cc, cc, z/(-1 + z)] - , - i === 21, u /. F[aa_,bb_,cc_,zz_] :> - (1-zz)^(-aa - bb + cc) F[-bb + cc, -aa + cc, cc, zz] - , - i === 22, u /. F[aa_,bb_,cc_,zz_] :> - (1-zz)^(-aa - bb + cc) F[-bb + cc, -aa + cc, cc, zz] - , - i === 23, u /. F[aa_,bb_,cc_,zz_] :> - zz^(-aa) F[aa, -bb + cc, cc, 1 - zz^(-1)] - , - i === 24, u /. F[aa_,bb_,cc_,zz_] :> - (1-zz)^(-bb) F[bb, -aa + cc, cc, Factor2[1 - (1-zz)^(-1)]] - , - i === 94, u /. F[a_,b_,g_,z_] :> - gm[g] gm[g-a-b]/gm[g-a]/gm[g-b] * - F[a,b,a+b-g+1,Factor2[1-z]] + - Factor2[1-z]^(g-a-b) gm[g] gm[a+b-g]/gm[a]/gm[b]* - F[g-a,g-b,g-a-b+1,Factor2[1-z]] - , - i === 95, u /. F[a_,b_,g_,z_] :> - Factor2[1-z]^(-a) gm[g] gm[b-a]/gm[b]/gm[g-a] * - F[a,g-b,a-b+1,Factor2[1/(1-z)]] + - Factor2[1-z]^(-b) gm[g] gm[a-b]/gm[a]/gm[g-b] * - F[b,g-a,b-a+1,Factor2[1/(1-z)]] - , - i === 96, u /. F[a_,b_,g_,z_] :> - gm[g] gm[b-a]/gm[b]/gm[g-a] PowerSimplify[(-1)^a] * - Factor2[z]^(-a) F[a,a+1-g,a+1-b, Factor2[1/z]] + - gm[g] gm[a-b]/gm[a]/gm[g-b] PowerSimplify[(-1)^b] * - Factor2[z]^(-b) F[b,b+1-g,b+1-a, Factor2[1/z]] - - ] /. F -> Hypergeometric2F1 - ]; +Kummer[i_Integer /; MemberQ[Range[96],i] && !MemberQ[Range[25,90], i]][exp_] := + Block[{F, u}, + u = exp /. Hypergeometric2F1 -> F; + Which[ + i === 1, + u /. F[a_,b_,c_,z_] :> + Factor2[1-z]^(c-a-b) F[c-a, c-b,c,z], + + i === 2, + u /. F[a_,b_,c_,z_] :> + Factor2[1-z]^(c-a-b) F[c-a, c-b,c,z], + + i === 3, + u /. F[a_,b_,c_,z_] :> + Factor2[1-z]^(-a) F[a,c-b,c,Factor2[z/(z-1)]], + + i === 4, + u /. F[a_,b_,c_,z_] :> + Factor2[1-z]^(-b) F[c-a,b,c,Factor2[z/(z-1)]], + + i === 5, + u /. F[a_,b_,cc_,zz_] :> (*c=a+b+1-cc; z = 1-zz *) + Factor2[1-zz]^(-a-b+cc) F[-b + cc,-a + cc,cc,Factor2[zz]], + + i === 6, + u /. F[a_,b_,cc_,zz_] :> (*c=a+b+1-cc; z=1-zz*) + Factor2[1-zz]^(-a-b+cc) F[-b + cc,-a + cc,cc,Factor2[zz]], + + i === 7, + u /. F[a_,b_,cc_,zz_] :> (*c=a+b+1-cc; z = 1-zz*) + Factor2[1-zz]^(-a) F[a, -b + cc, cc,Factor2[1-1/(1-zz)]], + + i === 8, + u /. F[a_,b_,cc_,zz_] :> (*c=a+b+1-cc; z=1-zz*) + Factor2[1-zz]^(-b) F[-a + cc,b,cc,Factor2[1-1/(1-zz)]], + + i === 9, + u /. F[a_,bb_,cc_,zz_] :> (* z = 1/zz *) + Factor2[-1/zz]^(a+bb-cc) Factor2[1-1/zz]^(-a-bb+cc) F[-a + cc, -bb + cc, cc, Factor2[zz]], + + i === 10, + u /. F[a_,bb_,cc_,zz_] :> (* z = 1/zz *) + Factor2[-1/zz]^(a+bb-cc) Factor2[1-1/zz]^(-a-bb+cc) F[-a + cc, -bb + cc, cc, Factor2[zz]], + + i === 11, + u /. F[a_,bb_,cc_,zz_] :> (* z = 1/zz *) + Factor2[-1/zz]^a (Factor2[1-zz])^(-a) F[a, -bb + cc, cc, Factor2[1/(1-1/zz)]], + + i === 12, + u /. F[a_,bb_,cc_,zz_] :> (* z = 1/zz *) + Factor2[-1/zz]^(bb-a) Factor2[1-1/zz]^(-bb) F[bb, -a + cc, cc, Factor2[1/(1-1/zz)]], + + i === 13, + u /. F[aa_,b_,cc_,zz_] :> (* z = 1/zz *) + Factor2[-1/zz]^(aa + b - cc) Factor2[1-1/zz]^(-aa - b + cc) F[-b + cc, -aa + cc, cc, Factor2[zz]], + + i === 14, + u /. F[aa_,b_,cc_,zz_] :> (* z = 1/zz *) + Factor2[-1/zz]^(aa + b - cc) Factor2[1-1/zz]^(-aa - b + cc)F[-b + cc, -aa + cc, cc, Factor2[zz]], + + i === 15, + u /. F[aa_,b_,cc_,zz_] :> (* z = 1/zz *) + Factor2[-1/zz]^b Factor2[1-1/zz]^(-b) F[b,-aa + cc,cc,Factor2[1/(1-1/zz)]], + + i === 16, + u /. F[aa_,b_,cc_,zz_] :> (* z = 1/zz *) + Factor2[-1/zz]^aa Factor2[1-1/zz]^(-aa) F[aa,cc-b,cc,Factor2[1/(1-1/zz)]], + + i === 17, + u /. F[aa_,bb_,cc_,z_] :> + (1-z)^(-aa - bb + cc) F[-aa + cc,-bb + cc,cc,z], + + i === 18, + u /. F[aa_,bb_,cc_,z_] :> + (1-z)^(-aa - bb + cc) F[-aa + cc,-bb + cc,cc,z], + + i === 19, + u /. F[aa_,bb_,cc_,z_] :> + (1-z)^(-aa) F[aa, -bb + cc, cc, z/(z - 1)], + + i === 20, + u /. F[aa_,bb_,cc_,z_] :> + (1-z)^(-bb) F[bb, -aa + cc, cc, z/(-1 + z)], + + i === 21, + u /. F[aa_,bb_,cc_,zz_] :> + (1-zz)^(-aa - bb + cc) F[-bb + cc, -aa + cc, cc, zz], + + i === 22, + u /. F[aa_,bb_,cc_,zz_] :> + (1-zz)^(-aa - bb + cc) F[-bb + cc, -aa + cc, cc, zz], + + i === 23, + u /. F[aa_,bb_,cc_,zz_] :> + zz^(-aa) F[aa, -bb + cc, cc, 1 - zz^(-1)], + + i === 24, + u /. F[aa_,bb_,cc_,zz_] :> + (1-zz)^(-bb) F[bb, -aa + cc, cc, Factor2[1 - (1-zz)^(-1)]], + + i === 94, + u /. F[a_,b_,g_,z_] :> + gm[g] gm[g-a-b]/gm[g-a]/gm[g-b] F[a,b,a+b-g+1,Factor2[1-z]] + + Factor2[1-z]^(g-a-b) gm[g] gm[a+b-g]/gm[a]/gm[b] F[g-a,g-b,g-a-b+1,Factor2[1-z]], + + i === 95, + u /. F[a_,b_,g_,z_] :> + Factor2[1-z]^(-a) gm[g] gm[b-a]/gm[b]/gm[g-a] F[a,g-b,a-b+1,Factor2[1/(1-z)]] + + Factor2[1-z]^(-b) gm[g] gm[a-b]/gm[a]/gm[g-b] F[b,g-a,b-a+1,Factor2[1/(1-z)]], + + i === 96, + u /. F[a_,b_,g_,z_] :> + gm[g] gm[b-a]/gm[b]/gm[g-a] PowerSimplify[(-1)^a] Factor2[z]^(-a) F[a,a+1-g,a+1-b, Factor2[1/z]] + + gm[g] gm[a-b]/gm[a]/gm[g-b] PowerSimplify[(-1)^b] Factor2[z]^(-b) F[b,b+1-g,b+1-a, Factor2[1/z]] + + ] /. F -> Hypergeometric2F1 + ]; FCPrint[1,"Kummer.m loaded."]; End[] diff --git a/FeynCalc/Tables/Nielsen.m b/FeynCalc/Tables/Nielsen.m index a39d5934d..f2b25004f 100755 --- a/FeynCalc/Tables/Nielsen.m +++ b/FeynCalc/Tables/Nielsen.m @@ -19,51 +19,59 @@ Begin["`Nielsen`Private`"] -Options[Nielsen] = {PolyLog -> False}; +Options[Nielsen] = { + PolyLog -> False +}; -Nielsen[3,1,y_] := PolyLog[4, y] /; (PolyLog /. Options[Nielsen]); -Nielsen[3,1,y_,PolyLog->True] := PolyLog[4, y]; +Nielsen[3,1,y_, OptionsPattern[]] := + PolyLog[4, y] /; OptionValue[PolyLog]; +Nielsen[1,2,0, OptionsPattern[]] = + 0; -Nielsen[1,2,0] = 0; -Nielsen[1,2,-1] = Zeta[3]/8; -Nielsen[1,2,1/2] = Zeta[3]/8; -Nielsen[1,2,1] = Zeta[3]; +Nielsen[1,2,-1, OptionsPattern[]] = + Zeta[3]/8; -Nielsen /: N[Nielsen[n_,p_,x_]] := -(-1)^(n+p-1)/(n-1)!/p! NIntegrate[Log[1-x t]^p Log[t]^(n-1)/t,{t,0,1}]; +Nielsen[1,2,1/2, OptionsPattern[]] = + Zeta[3]/8; + +Nielsen[1,2,1, OptionsPattern[]] = + Zeta[3]; + +Nielsen /: + N[Nielsen[n_,p_,x_, OptionsPattern[]]] := + (-1)^(n+p-1)/(n-1)!/p! NIntegrate[Log[1-x t]^p Log[t]^(n-1)/t,{t,0,1}]; niel[n_,p_,x_] := -(-1)^(n+p-1)/(n-1)!/p! Integrate[Log[1-x t]^p Log[t]^(n-1)/t,{t,0,1}]; - -Nielsen[1,2,x_, opt___Rule] := - Expand[( -(Log[1 - x]^2*Log[x])/2 + Log[1 - x]*PolyLog[2, 1 - x] - - PolyLog[3, 1 - x] + Zeta[3] - )/. PolyLog[2,y_Symbol] :> - Zeta2 - Log[1 - y] Log[y] - PolyLog[2, 1 - y] - ] /; (PolyLog /. {opt} /. Options[Nielsen]); - -Nielsen[1,3,x_, opt___Rule] := - Expand[ (Pi^4/15 - Log[1 - x]^3*Log[x] - - 3*Log[1 - x]^2*PolyLog[2, 1 - x] + + (-1)^(n+p-1)/(n-1)!/p! Integrate[Log[1-x t]^p Log[t]^(n-1)/t,{t,0,1}]; + +Nielsen[1,2,x_, OptionsPattern[]] := + Expand[ + ((Log[1 - x]^2*Log[x])/2 + Log[1 - x]*PolyLog[2, 1 - x] - PolyLog[3, 1 - x] + Zeta[3] + )/. PolyLog[2,y_Symbol] :> Zeta2 - Log[1 - y] Log[y] - PolyLog[2, 1 - y] + ]/; OptionValue[PolyLog]; + +Nielsen[1,3,x_, OptionsPattern[]] := + Expand[ + (Pi^4/15 - Log[1 - x]^3*Log[x] - + 3*Log[1 - x]^2*PolyLog[2, 1 - x] + 6*Log[1 - x]*PolyLog[3, 1 - x] - 6*PolyLog[4, 1 - x])/6 - ] /; (PolyLog /. {opt} /. Options[Nielsen]); + ]/; OptionValue[PolyLog]; -Nielsen[2,2,s_, opt___Rule] := - Expand[ -Pi^4/90 + (Zeta2*Log[1 - s]^2)/2 + Log[1 - s]^4/24 - - (Log[1 - s]^3*Log[s])/6 - Log[1 - s]*PolyLog[3, s] - PolyLog[4, 1 - s] + - PolyLog[4, s] + PolyLog[4, s/(-1 + s)] + Log[1 - s]*Zeta[3] - ] /; (PolyLog /. {opt} /. Options[Nielsen]); +Nielsen[2,2,s_, OptionsPattern[]] := + Expand[ + Pi^4/90 + (Zeta2*Log[1 - s]^2)/2 + Log[1 - s]^4/24 - + (Log[1 - s]^3*Log[s])/6 - Log[1 - s]*PolyLog[3, s] - PolyLog[4, 1 - s] + + PolyLog[4, s] + PolyLog[4, s/(-1 + s)] + Log[1 - s]*Zeta[3] + ]/; OptionValue[PolyLog]; (* Nielsen[3,1,y] := -1/2 Integrate[Log[t]^2 Log[1-y t]/t, {t,0,1}] *) - Nielsen /: MakeBoxes[Nielsen[i_,j_,exp_], TraditionalForm] := - RowBox[{SubscriptBox["S",TBox[i,j]],"(", - TBox[exp],")"}] +Nielsen /: + MakeBoxes[Nielsen[i_,j_,exp_, OptionsPattern[]], TraditionalForm] := + RowBox[{SubscriptBox["S",TBox[i,j]],"(", TBox[exp],")"}]; FCPrint[1,"Nielsen.m loaded."]; End[] diff --git a/FeynCalc/Tables/RTL.m b/FeynCalc/Tables/RTL.m index 31a406a94..1396ac922 100755 --- a/FeynCalc/Tables/RTL.m +++ b/FeynCalc/Tables/RTL.m @@ -20,52 +20,89 @@ Begin["`RTL`Private`"] -Options[RTL] = {Dimension -> D, - FeynmanParameterNames -> FCGV["x"], - Momentum -> FCGV["p"], - QuarkMass -> FCGV["M"] - }; +so::usage=""; +dum::usage=""; -RTL[exp_, opt___Rule] := Block[{lsimp, MCH, so, p, x, M, dim, res}, -dim = Dimension /. {opt} /. Options[RTL]; -x = FeynmanParameterNames /. {opt} /. Options[RTL]; -p = Momentum /. {opt} /. Options[RTL]; -M = QuarkMass /. {opt} /. Options[RTL]; +Options[RTL] = { + Dimension -> D, + FeynmanParameterNames -> FCGV["x"], + Momentum -> FCGV["p"], + QuarkMass -> FCGV["M"] +}; + +RTL[exp_, opt___Rule] := + Block[{p, x, M, dim, res}, + + dim = Dimension /. {opt} /. Options[RTL]; + x = FeynmanParameterNames /. {opt} /. Options[RTL]; + p = Momentum /. {opt} /. Options[RTL]; + M = QuarkMass /. {opt} /. Options[RTL]; + + so[] = Pair[Momentum[p], Momentum[OPEDelta]]; + + (* + RTLI[{1, 0, 0, 0, m_}, {a_, b_, b_, a_, c_},oot___Rule] := + 1/2 RTLI[{0, 0, 0, 0, m}, {a, b, b, a, c}] so[oot] + + 1/2 RTLI[{0, 0, 0, 0, m+1}, {a, b, b, a, c}]; + *) -lsimp[0]=0; -lsimp[a_Plus] := Map[lsimp, a]; -lsimp[t_Times] := Block[{mm}, - If[FreeQ[t, OPEm], mm = 1, mm = OPEm]; - ((SelectNotFree[t, {Epsilon,p,Smu,CA,CF,Tf,SMP["g_s"]}] * - x^(mm-1))/.dum[Epsilon]->1) * - Collect2[SimplifyDeltaFunction[Expand[Apart3[ - SelectFree[t, {Epsilon,p,Smu,CA,CF,Tf,SMP["g_s"]}]/x^(mm-1),x] - ]](* /. {DeltaFunction[1-x] f_ :> - (f/.x->1) DeltaFunction[1-x] - } *) , - {Log, PolyLog, Zeta,Zeta2,DeltaFunction,DeltaFunctionPrime}, - Factoring->False - ] ]; + (* + tlist = + tlist/.(a_ :> b_) :> (ruledel[a/. {M:> (M_/;M=!=0), OPEi:> OPEi_}, b] /. + ruledel:>RuleDelayed); + *) + + res = + ((Collect[Expand[dum[Epsilon] Series2[FCI[ChangeDimension[exp /. TLI -> RTLI, 4] /. tlilist] /. dim -> (4 + Epsilon), + Epsilon, 0]],Epsilon, Factor]) // lsimp) /. RTLI -> TLI; + + (* + If[Head[res] =!= Plus, pref = 1, + pref = SelectNotFree[dummy First[res]/. (-1)^OPEm:>bla , + {M,p,Smu,CA,CF,Tf,SMP["g_s"], OPEm}]; + res = pref . Map[(#/pref)&, res] + ]; + *) + res]; (*?? MCH[y_] := If[Head[y] =!= Integer, If[FreeQ[y,OPEi],True,False], False]; *) -MCH[y_] := If[Head[y] =!= Integer, True, False]; +MCH[y_] := + If[ Head[y] =!= Integer, + True, + False + ]; (* MCH[_]:=True; *) -so[] = Pair[Momentum[p], Momentum[OPEDelta]]; +lsimp[0]= + 0; + +lsimp[a_Plus] := + Map[lsimp, a]; + +lsimp[t_Times] := + Block[{mm}, + If[ FreeQ[t, OPEm], + mm = 1, + mm = OPEm + ]; + + ((SelectNotFree[t, {Epsilon,p,Smu,CA,CF,Tf,SMP["g_s"]}] x^(mm-1))/.dum[Epsilon]->1) * + Collect2[SimplifyDeltaFunction[Expand[Apart3[ + SelectFree[t, {Epsilon,p,Smu,CA,CF,Tf,SMP["g_s"]}]/x^(mm-1),x] + ]](* /. {DeltaFunction[1-x] f_ :> + (f/.x->1) DeltaFunction[1-x] + } *) , + {Log, PolyLog, Zeta,Zeta2,DeltaFunction,DeltaFunctionPrime}, Factoring->False] + ]; -(* - RTLI[{1, 0, 0, 0, m_}, {a_, b_, b_, a_, c_},oot___Rule] := -1/2 RTLI[{0, 0, 0, 0, m}, {a, b, b, a, c}] so[oot] + -1/2 RTLI[{0, 0, 0, 0, m+1}, {a, b, b, a, c}]; -*) tlilist = { (* r1i1.r *) -RTLI[{m_ /; MCH[m], -2, 0, 0, 0}, {{2, M_}, 0, 0, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], -2, 0, 0, 0}, {{2, _}, 0, 0, 1, 1}, r___] :> Smu^2*x^(-1 + m)*((-1 + x^(-1))/Epsilon - 2*Log[1 - x] + (2*Log[1 - x])/x + Log[x])*so[r]^(-2 + m) , @@ -83,7 +120,7 @@ so[r]^(-1 + m) , (* r1i4.r *) -RTLI[{m_ /; MCH[m], -1, 0, 0, 0}, {{2, M_}, 0, 0, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], -1, 0, 0, 0}, {{2, _}, 0, 0, 1, 1}, r___] :> Smu^2*x^(-1 + m)*(-(Log[x]/Epsilon) - 2*Log[1 - x]*Log[x] + Log[x]^2/4 - PolyLog[2, 1 - x])*so[r]^(-1 + m) , @@ -109,7 +146,7 @@ 2*x*PolyLog[2, 1 - x])*so[r]^m)/M^2 , (* r1i9.r *) -RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{2, M_}, 0, 0, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{2, _}, 0, 0, 1, 1}, r___] :> Smu^2*x^(-1 + m)*(-1 + (1 - x)/Epsilon + x + 2*Log[1 - x] - 2*x*Log[1 - x] - Log[x]/2 + (x*Log[x])/2)*so[r]^m , @@ -272,7 +309,7 @@ x*PolyLog[2, 1 - x])*so[r]^m , (*r3i4.r*) -RTLI[{0, m_ /; MCH[m], 0, 0, 0}, {{1, M_}, 1, 0, 1, 1}, r___] :> +RTLI[{0, m_ /; MCH[m], 0, 0, 0}, {{1, _}, 1, 0, 1, 1}, r___] :> Smu^2*x^(-1 + m)*(-2*x - (2*x)/Epsilon^2 - I*Pi*x + (9*x*Zeta2)/2 - Log[1 - x] + 2*x*Log[1 - x] + I*Pi*x*Log[1 - x] - (x*Log[1 - x]^2)/4 + x*Log[x] + I*Pi*x*Log[x] - 2*x*Log[1 - x]*Log[x] - (x*Log[x]^2)/2 + @@ -325,7 +362,7 @@ r4end *) , (* r7i1.r *) -RTLI[{m_ /; MCH[m], 2, -1, 0, 0}, {{1, M_}, 0, 1, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 2, -1, 0, 0}, {{1, _}, 0, 1, 1, 1}, r___] :> Smu^2*x^(-1 + m)*so[r]^(1 + m)* (2 - 2/(1 - x) + (34*x)/27 + (20*x^2)/27 + Zeta2/2 - Zeta2/(2*(1 - x)) + (x*Zeta2)/3 + (x^2*Zeta2)/6 + DeltaFunction[1 - x] - @@ -345,7 +382,7 @@ (x^2*Log[x])/3)/Epsilon - (7*DeltaFunction[1 - x]*Zeta[3])/12) , (* r7i2.r *) -RTLI[{m_ /; MCH[m], 2, -2, 0, 0}, {{1, M_}, 0, 1, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 2, -2, 0, 0}, {{1, _}, 0, 1, 1, 1}, r___] :> Smu^2*x^(-1 + m)*so[r]^m*(-2 - 2/(1 - x)^2 + 4/(1 - x) - (20*x)/27 - Zeta2/2 - Zeta2/(2*(1 - x)^2) + Zeta2/(1 - x) - (x*Zeta2)/6 - 3*DeltaFunction[1 - x] - (3*Zeta2*DeltaFunction[1 - x])/4 + @@ -370,7 +407,7 @@ (7*DeltaFunctionPrime[1 - x]*Zeta[3])/6) , (* r7i3.r *) -RTLI[{m_ /; MCH[m], 1, 0, 0, 0}, {{1, M_}, 0, 1, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 1, 0, 0, 0}, {{1, _}, 0, 1, 1, 1}, r___] :> Smu^2*x^(-1 + m)*(-x - x^2 + (-x - x^2)/Epsilon^2 - (x*Zeta2)/4 - (x^2*Zeta2)/4 + 2*x*Log[1 - x] + 2*x^2*Log[1 - x] - 2*x*Log[1 - x]^2 - 2*x^2*Log[1 - x]^2 - (x*Log[x])/2 - (x^2*Log[x])/2 + @@ -379,7 +416,7 @@ (x*Log[x])/2 + (x^2*Log[x])/2)/Epsilon)*so[r]^(1 + m) , (* r7i4.r *) -RTLI[{m_ /; MCH[m], 1, -1, 0, 0}, {{1, M_}, 0, 1, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 1, -1, 0, 0}, {{1, _}, 0, 1, 1, 1}, r___] :> Smu^2*x^(-1 + m)*so[r]^m*(2 - 2/(1 - x) + x + Zeta2/2 - Zeta2/(2*(1 - x)) + (x*Zeta2)/4 + DeltaFunction[1 - x] - DeltaFunction[1 - x]/Epsilon^3 + (Zeta2*DeltaFunction[1 - x])/4 + @@ -394,7 +431,7 @@ (x*Log[x])/2)/Epsilon - (7*DeltaFunction[1 - x]*Zeta[3])/12) , (* r7i5.r *) -RTLI[{m_ /; MCH[m], 1, -2, 0, 0}, {{1, M_}, 0, 1, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 1, -2, 0, 0}, {{1, _}, 0, 1, 1, 1}, r___] :> Smu^2*x^(-1 + m)*so[r]^(-1 + m)* (-1 - 2/(1 - x)^2 + 3/(1 - x) - Zeta2/4 - Zeta2/(2*(1 - x)^2) + (3*Zeta2)/(4*(1 - x)) - (5*DeltaFunction[1 - x])/2 - @@ -425,13 +462,13 @@ (4*Log[1 - x])/(1 - x) - Log[x] + Log[x]/(1 - x))*so[r]^m)/M^2 , (* r7i7.r *) -RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{1, M_}, 0, 1, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{1, _}, 0, 1, 1, 1}, r___] :> Smu^2*x^(-1 + m)*(-2*x - (2*x)/Epsilon^2 - (x*Zeta2)/2 + 4*x*Log[1 - x] - 4*x*Log[1 - x]^2 - x*Log[x] + 2*x*Log[1 - x]*Log[x] - (x*Log[x]^2)/4 + (2*x - 4*x*Log[1 - x] + x*Log[x])/Epsilon)*so[r]^m , (* r7i8.r *) -RTLI[{m_ /; MCH[m], 0, -1, 0, 0}, {{1, M_}, 0, 1, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 0, -1, 0, 0}, {{1, _}, 0, 1, 1, 1}, r___] :> Smu^2*x^(-1 + m)*so[r]^(-1 + m)* (2 - 2/(1 - x) + Zeta2/2 - Zeta2/(2*(1 - x)) + DeltaFunction[1 - x] - DeltaFunction[1 - x]/Epsilon^3 + (Zeta2*DeltaFunction[1 - x])/4 + @@ -445,7 +482,7 @@ (7*DeltaFunction[1 - x]*Zeta[3])/12) , (* r7i9.r *) -RTLI[{m_ /; MCH[m], 0, -2, 0, 0}, {{1, M_}, 0, 1, 1, 1}, r___] :> +RTLI[{m_ /; MCH[m], 0, -2, 0, 0}, {{1, _}, 0, 1, 1, 1}, r___] :> Smu^2*x^(-1 + m)*so[r]^(-2 + m)* (-2/(1 - x)^2 + 2/(1 - x) - Zeta2/(2*(1 - x)^2) + Zeta2/(2*(1 - x)) - 2*DeltaFunction[1 - x] - (Zeta2*DeltaFunction[1 - x])/2 + @@ -466,7 +503,7 @@ (7*DeltaFunctionPrime[1 - x]*Zeta[3])/6) , (* r7i10.r *) -RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{1, M_}, 0, 2, 1, 0}, r___] :> 0 +RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{1, _}, 0, 2, 1, 0}, ___] :> 0 , (* r11i1.r *) RTLI[{m_ /; MCH[m], 1, 0, 0, 0}, {{1, M_}, 1, 1, {1, M_}, {1, M_}}, r___] :> @@ -510,7 +547,7 @@ 2*PolyLog[2, -x] + 2*x*PolyLog[2, -x])*so[r]^(-1 + m) , (* r11i15.r *) -RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{2, M_}, 1, 0, {1, M_}, 0}, r___] :> 0 +RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{2, M_}, 1, 0, {1, M_}, 0}, ___] :> 0 , (* r11i16.r *) RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{2, M_}, 0, 1, {1, M_}, 0}, r___] :> @@ -535,7 +572,7 @@ 2*Log[1 - x] - (2*Log[1 - x])/(1 - x)^2 + (4*Log[1 - x])/(1 - x))*so[r]^m , (* r11i19.r *) -RTLI[{m_ /; MCH[m], -1, 0, 0, 0}, {{2, M_}, 1, 0, {1, M_}, 0}, r___] :> 0 +RTLI[{m_ /; MCH[m], -1, 0, 0, 0}, {{2, M_}, 1, 0, {1, M_}, 0}, ___] :> 0 , (* r11i2.r *) RTLI[{m_ /; MCH[m], 0, 0, 0, 0}, {{2, M_}, 1, 1, {1, M_}, {1, M_}}, r___] :> @@ -1358,7 +1395,7 @@ (DeltaFunction[1 - x]*Zeta[3])/3))/so[r] , (* r18i10.r *) -RTLI[{0, 0, 0, 0, 0}, {{1, M_}, {1, M_}, 1, 1, 0}, r___] :> +RTLI[{0, 0, 0, 0, 0}, {{1, M_}, {1, M_}, 1, 1, 0}, ___] :> Smu^2*x^(-1 + OPEm)*(-12*DeltaFunction[1 - x] - (4*DeltaFunction[1 - x])/Epsilon^2 + (8*DeltaFunction[1 - x])/Epsilon - Zeta2*DeltaFunction[1 - x]) @@ -1458,30 +1495,6 @@ Epsilon) }; -(* -tlist = -tlist/.(a_ :> b_) :> (ruledel[a/. {M:> (M_/;M=!=0), OPEi:> OPEi_}, b] /. - ruledel:>RuleDelayed); -*) - -res = -( -(rere = - Collect[Expand[dum[Epsilon] Series2[ -FeynCalcInternal[ChangeDimension[exp /. TLI -> RTLI, 4] /.tlilist - ] /. dim -> (4 + Epsilon), - Epsilon, 0]],Epsilon, Factor - ]) // lsimp -) /. RTLI -> TLI; - -(* -If[Head[res] =!= Plus, pref = 1, - pref = SelectNotFree[dummy First[res]/. (-1)^OPEm:>bla , - {M,p,Smu,CA,CF,Tf,SMP["g_s"], OPEm}]; - res = pref . Map[(#/pref)&, res] - ]; -*) - res]; FCPrint[1,"RTL.m loaded."]; End[] diff --git a/FeynCalc/Tables/ReferenceCards/FeynArts.ref b/FeynCalc/Tables/ReferenceCards/FeynArts.ref new file mode 100644 index 000000000..b81e1755d --- /dev/null +++ b/FeynCalc/Tables/ReferenceCards/FeynArts.ref @@ -0,0 +1,116 @@ +{ +Rule[ +{"FeynArts"}, + +Grid[{ + {"\!\(\* +StyleBox[\"class\",\nFontSlant->\"Italic\"]\)", "\!\(\* +StyleBox[\"self\",\nFontSlant->\"Italic\"]\)\!\(\* +StyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\* +StyleBox[\"conj\",\nFontSlant->\"Italic\"]\)\!\(\* +StyleBox[\".\",\nFontSlant->\"Italic\"]\)", "\!\(\* +StyleBox[\"indices\",\nFontSlant->\"Italic\"]\)", "\!\(\* +StyleBox[\"members\",\nFontSlant->\"Italic\"]\)", "\!\(\* +StyleBox[\"mass\",\nFontSlant->\"Italic\"]\)"}, + + {Column[{"F[1]", "(neutrinos)", ""}], Column[{"no", "", ""}], + Column[{"Generation", "", ""}], + Column[{"F[1, {1}] \!\(\*SubscriptBox[\(\[Nu]\), \(e\)]\) ", + "F[1, {2}] \!\(\*SubscriptBox[\(\[Nu]\), \(\[Mu]\)]\) ", + "F[1, {3}] \!\(\*SubscriptBox[\(\[Nu]\), \(\[Tau]\)]\) "}], + Column[{"0", "0", "0"}]}, + + {Column[{"F[2]", "(massive leptons)", ""}], + Column[{"no", "", ""}], Column[{"Generation", "", ""}], + Column[{"F[2, {1}] \!\(\* +StyleBox[\"e\",\nFontSlant->\"Italic\"]\) ", "F[2, {2}] \[Mu] ", + "F[2, {3}] \[Tau] "}], Column[{"ME", "MM", "ML"}]}, + + {Column[{"F[3]", "(up-type quarks)", ""}], Column[{"no", "", ""}], + Column[{"Generation", "Color", ""}], Column[{"F[3, {1, \!\(\* +StyleBox[\"o\",\nFontSlant->\"Italic\"]\)}] \!\(\* +StyleBox[\"u\",\nFontSlant->\"Italic\"]\) ", "F[3, {2, \!\(\* +StyleBox[\"o\",\nFontSlant->\"Italic\"]\)}] \!\(\* +StyleBox[\"c\",\nFontSlant->\"Italic\"]\) ", "F[3, {3, \!\(\* +StyleBox[\"o\",\nFontSlant->\"Italic\"]\)}] \!\(\* +StyleBox[\"t\",\nFontSlant->\"Italic\"]\) "}], + Column[{"MU", "MC", "MT"}]}, + + {Column[{"F[4]", "(down-type quarks)", ""}], + Column[{"no", "", ""}], Column[{"Generation", "Color", ""}], + Column[{"F[4, {1, \!\(\* +StyleBox[\"o\",\nFontSlant->\"Italic\"]\)}] \!\(\* +StyleBox[\"d\",\nFontSlant->\"Italic\"]\) ", "F[4, {2, \!\(\* +StyleBox[\"o\",\nFontSlant->\"Italic\"]\)}] \!\(\* +StyleBox[\"s\",\nFontSlant->\"Italic\"]\) ", "F[4, {3, \!\(\* +StyleBox[\"o\",\nFontSlant->\"Italic\"]\)}] \!\(\* +StyleBox[\"b\",\nFontSlant->\"Italic\"]\) "}], + Column[{"MD", "MS", "MB"}]}, + + {Column[{"V[1]", "V[2]", "V[3]", "V[4] (mixing field)"}], + Column[{"yes", "yes", "no", "yes"}], Column[{"", "", ""}], + Column[{"V[1] \[Gamma] ", "V[2] \!\(\* +StyleBox[\"Z\",\nFontSlant->\"Italic\"]\) ", "V[3] \!\(\* +StyleBox[SuperscriptBox[\"W\", \"-\"],\nFontSlant->\"Italic\"]\) ", + "V[4] \!\(\* +StyleBox[\"\[Gamma]\",\nFontSlant->\"Italic\"]\)\!\(\* +StyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\* +StyleBox[\"Z\",\nFontSlant->\"Italic\"]\) "}], + Column[{"0", "MZ", "MW", "MAZ"}]}, + + {Column[{"S[1]", "S[2]", "S[3]"}], Column[{"yes", "yes", "no"}], + Column[{"", "", ""}], Column[{"S[1] \!\(\* +StyleBox[\"H\",\nFontSlant->\"Italic\"]\) ", "S[2] \!\(\* +StyleBox[SuperscriptBox[ +StyleBox[\"G\",\nFontSlant->\"Italic\"], \"0\"],\nFontSlant->\"Italic\ +\"]\) ", "S[3] \!\(\* +StyleBox[SuperscriptBox[\"G\", \"-\"],\nFontSlant->\"Italic\"]\) "}], + Column[{"MH", "MG0", "MGp"}]}, + + {Column[{"U[1]", "U[2]", "U[3]", "U[4]"}], + Column[{"no", "no", "no", "no"}], Column[{"", "", "", ""}], + Column[{"U[1] \!\(\*SubscriptBox[ +StyleBox[\"u\",\nFontSlant->\"Italic\"], \(\[Gamma]\)]\) ", + "U[2] \!\(\* +StyleBox[SubscriptBox[ +StyleBox[\"u\",\nFontSlant->\"Italic\"], \"Z\"],\nFontSlant->\"Italic\ +\"]\) ", "U[3] \!\(\*SubscriptBox[ +StyleBox[\"u\",\nFontSlant->\"Italic\"], \(-\)]\) ", "U[4] \!\(\* +StyleBox[SubscriptBox[\"u\", \"+\"],\nFontSlant->\"Italic\"]\) "}], + Column[{"0", "MZ", "MW", "MW"}]}, + + + {Column[{"SV[2] (mixing field)", "SV[3] (mixing field)"}], + Column[{"yes", "no"}], Column[{"", ""}], Column[{"SV[2] \!\(\* +StyleBox[SuperscriptBox[ +StyleBox[\"G\",\nFontSlant->\"Italic\"], \"0\"],\nFontSlant->\"Italic\ +\"]\)\!\(\* +StyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\* +StyleBox[\"Z\",\nFontSlant->\"Italic\"]\) ", "SV[3] \!\(\* +StyleBox[SuperscriptBox[ +StyleBox[\"G\",\nFontSlant->\"Italic\"], \"-\"],\nFontSlant->\"Italic\ +\"]\)\!\(\* +StyleBox[\"-\",\nFontSlant->\"Italic\"]\)\!\(\*SuperscriptBox[ +StyleBox[\"W\",\nFontSlant->\"Italic\"], \(-\)]\) "}], + Column[{"MZ", "MW"}]}, + {"The following fields are avaialble via the SMQCD extension:", + SpanFromLeft}, + + {Column[{"V[5]", "U[5]"}], Column[{"yes", "no"}], + Column[{"Gluon", "Gluon"}], Column[{"V[5, {i}] \!\(\* +StyleBox[SubscriptBox[\"g\", \"i\"],\nFontSlant->\"Italic\"]\) ", + "U[5, {i}] \!\(\*SubscriptBox[ +StyleBox[\"u\",\nFontSlant->\"Italic\"], +StyleBox[SubscriptBox[\"g\", +StyleBox[\"i\",\nFontSlant->\"Italic\"]],\nFontSlant->\"Italic\"]]\) \ +"}], Column[{"0", "0"}]}, + + + {"Comments: V[4] is commented out by default in SM.mod; + SV[2] and SV[3] must be enabled with $SVMixing = True.", + SpanFromLeft} + + }, Frame -> All, Alignment -> {Left, Top}, +Spacings -> {1.5, 1.5}] +] +} diff --git a/FeynCalc/Tables/SimplifyPolyLog.m b/FeynCalc/Tables/SimplifyPolyLog.m index 6918db132..14c92377a 100755 --- a/FeynCalc/Tables/SimplifyPolyLog.m +++ b/FeynCalc/Tables/SimplifyPolyLog.m @@ -1,19 +1,21 @@ -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) +(* ::Package:: *) -(* :Title: SimplifyPolyLog *) +(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) -(* :Author: Rolf Mertig *) +(* :Title: SimplifyPolyLog *) -(* ------------------------------------------------------------------------ *) -(* :History: clarified usage message in answer to -http://www.feyncalc.org/forum/0013.html +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) -(* ------------------------------------------------------------------------ *) -(* :Summary: SimplifyPolyLog *) +(* :Summary: Simplifies expressions containing polylogarithms *) (* ------------------------------------------------------------------------ *) + SimplifyPolyLog::usage = "SimplifyPolyLog[y] performs several simplifications assuming \ that the variables occuring in the Log and PolyLog functions \ @@ -23,6 +25,10 @@ SPL::usage= "SPL is an abbreviation for SimplifyPolyLog."; +SimplifyPolyLog::failmsg = +"Error! SimplifyPolyLog has encountered a fatal problem and must abort the computation. \ +The problem reads: `1`" + (* ------------------------------------------------------------------------ *) Begin["`Package`"] @@ -32,88 +38,197 @@ SPL=SimplifyPolyLog; -SimplifyPolyLog[y_] := Block[{logf, li2f, loli}, -loli = {Log :> logf, PolyLog :> li2f}; -logf[su_] := logf[su] = - If[FreeQ[su,Plus], Log[su], Log[Factor2[Cancel[Factor2[su]]]]]; -li2f[n_,su_] := li2f[n,su] = - If[FreeQ[su,Plus], PolyLog[n,su], - PolyLog[n,Factor2[Cancel[Factor2[su]]]]]; -Expand2[y/.Zeta2->(Pi^2/6)/.loli/.simptab/.simptab/. - simptab/.simptab/.simptab/.simptab/.loli/.Pi^2->6Zeta2 , {Log,Pi}]/. - {Pi^2 :> 6 Zeta2 , Pi^3 :> Pi 6 Zeta2, - Log[4]:> 2 Log[2],Log[8] :> 3 Log[2] , Log[16] :> 4 Log[2], - Log[32]:> 5 Log[2], Log[64]:>6 Log[2], - Log[128]:> 7 Log[2], Log[256]:>8 Log[2], Log[512]:>9 Log[2], - Log[1024] :> 10 Log[2]} - ]; - -funex[PolyGamma[2,2]] :> 2 - 2 Zeta[3]; -funex[PolyGamma[a_,b_]] := funex[PolyGamma[a,b]] = -Expand[FunctionExpand[PolyGamma[a,b]] /. EulerGamma->0]; +optEulerGamma::usage=""; +optLog::usage=""; +optPolyLog::usage=""; +optSqrt::usage=""; +optTrig::usage=""; + +Options[SimplifyPolyLog] = { + EulerGamma -> True, + Log -> True, + Nielsen -> True, + PolyLog -> True, + Sqrt -> True, + Trig -> True +}; + +SimplifyPolyLog[expr_, OptionsPattern[]]/; FCPatternFreeQ[{expr}] := + Block[{logSimp, tmp, repRule={}, var}, + + logSimp = {Log :> simplifyArgumentLog, PolyLog :> simplifyArgumentPolyLog}; + + optEulerGamma = OptionValue[EulerGamma]; + optLog = OptionValue[Log]; + optPolyLog = OptionValue[PolyLog]; + optSqrt = OptionValue[Sqrt]; + optTrig = OptionValue[Trig]; + + + tmp = expr; + + tmp = tmp/.Zeta2->(Pi^2/6)/.logSimp/.simptab/.simptab/.simptab/.simptab/.simptab/.simptab/.logSimp/.Pi^2->6 Zeta2; + + If[ !FreeQ2[tmp,{simplifyArgument,simplifyArgumentPolyLog}], + Message[SimplifyPolyLog::failmsg, "Simplification of the arguments of Polylogs failed."]; + Abort[] + ]; + + + tmp = tmp/. PolyLog[a_,b_,c_]:> Nielsen[a,b,c]; + + If[ !OptionValue[Nielsen], + tmp = tmp/. Nielsen[z__]:> Nielsen[z,PolyLog->True] + ]; + + tmp = Expand2[tmp,{Log,Pi,Zeta2,Zeta4,Zeta6}]; + + tmp = tmp /. { + Pi^2 :> 6 Zeta2, + Pi^3 :> 6 Pi Zeta2, + Pi^4 :> 90 Zeta4, + Pi^5 :> 90 Pi Zeta4, + Pi^6 :> 945 Zeta6, + Pi^7 :> 945 Pi Zeta6, + Pi^8 :> 9450 Zeta8, + Pi^9 :> 9450 Pi Zeta8, + Pi^10 :> 93555 Zeta10, + Pi^11 :> 93555 Pi Zeta10, + Log[x_Integer?EvenQ] :> PowerExpand[Log[x]] + }; + + tmp = tmp //. { + Zeta2^2 -> 5 Zeta4/2, + Zeta2^3 -> 35 Zeta6/8, + Zeta2^4 -> 175 Zeta8/24, + Zeta2^5 -> 385 Zeta10/32, + + Zeta4^2 -> 7 Zeta8/6, + Zeta2*Zeta4 -> 7 Zeta6/4, + Zeta2*Zeta6 -> 5 Zeta8/3, + Zeta2*Zeta8 -> 33 Zeta10/20, + Zeta4*Zeta6 -> 11 Zeta10/10, + + Zeta2^n_/; n>5 -> Zeta[2]^n, + Zeta4^n_/; n>2 -> Zeta[4]^n, + Zeta6^n_/; n>1 -> Zeta[6]^n, + Zeta8^n_/; n>1 -> Zeta[8]^n, + Zeta10^n_/; n>1 -> Zeta[10]^n + }; + + tmp + + ]; + +(*The arguments of logs and polylogs might contain scalar products, so a naive memoization is not safe here! *) + +simplifyArgument[su_, head_, {}] := + If[ FreeQ[su,Plus], + head[su], + head[Factor2[Cancel[Factor2[su]]]] + ]; + +simplifyArgument[su1_, su2_, head_, {}] := + If[ FreeQ[su2,Plus], + head[su1,su2], + head[su1,Factor2[Cancel[Factor2[su2]]]] + ]; + +simplifyArgumentLog[su_, OptionsPattern[]] := + FCUseCache[simplifyArgument,{su, Log}]; + +simplifyArgumentPolyLog[su1_,su2_] := + FCUseCache[simplifyArgument,{su1, su2, PolyLog}]; + +(*Currently no simplifications for Nielsen's polylogs*) +simplifyArgumentPolyLog[su1_,su2_, su3_] := + PolyLog[su1,su2,su3]; + +polyGammaExpand[PolyGamma[a_,b_]]:= + Expand[FunctionExpand[PolyGamma[a,b]] /. EulerGamma->0]/; !optEulerGamma; + +polyGammaExpand[PolyGamma[a_,b_]]:= + Expand[FunctionExpand[PolyGamma[a,b]]]/; optEulerGamma; + +(* + These relations follow from the basic properties of polylogs. + Many of them can be found in L. Lewin's "Polylogarithms and Associated Functions" + and "Table of Integrals and Formulae for Feynman Diagram Calculations" by Devoto and Duke. + Furthermore, new relations can be easily derived by differentiating the given polylog + w.r.t x and then integrating in x from 0 to t or from 1 to z (whatever converges better). + For example + + Integrate[D[PolyLog[2, 1 - x], x], {x, 0, t}, Assumptions -> {t > 0, t < 1}] + + and so on. The correctness of the expression can be then checked via + Plot[exp1-exp2,{x,0,1}]. This is the only way, as Mathematica will not recognize most + of these transformations. +*) simptab = { -PolyGamma[a_Integer, b_?NumberQ] :> funex[PolyGamma[a,b]], -(*NEW0897*) -PolyLog[2, -((1 - 2*t_Symbol)/t_Symbol)] :> - (-Zeta2 + + PolyGamma[a_Integer, b_?NumberQ] :> + polyGammaExpand[PolyGamma[a,b]], + + (*The duplication formula *) + PolyLog[s_, -Sqrt[x_Symbol]]/; optSqrt && optPolyLog :> + 2^(1-s) PolyLog[s, x] - PolyLog[s, Sqrt[x]],(*, + + PolyLog[s_, -x_Symbol] :> + 2^(1-s) PolyLog[s, x^2] - PolyLog[s, x], + *) + + PolyLog[2, -((1 - 2*t_Symbol)/t_Symbol)]/; optPolyLog :> + ( + -Zeta2 + 2*Log[2]*Log[1 - 2*t] + 2*Log[1 - 2*t]*Log[t] + 2*Log[1 - t]*Log[t] - Log[t]^2 - - 2*Log[2]* - Log[-1 + 2*t] - - 2*Log[1 - t]* - Log[-1 + 2*t] + + 2*Log[2]*Log[-1 + 2*t] - + 2*Log[1 - t]*Log[-1 + 2*t] + 2*PolyLog[2, 1 - t] - - 2*PolyLog[2, - 2*(1 - t)] + - 2*PolyLog[2, 2*t])/2 -, -PolyLog[2, (2*(1 - t_Symbol))/ - (1 - 2*t_Symbol)] :> - (6*Zeta2 - - 2*Log[2]* - Log[-(1 - 2*t)^(-1)] + + 2*PolyLog[2, 2*(1 - t)] + + 2*PolyLog[2, 2*t] + )/2, + + PolyLog[2, (2*(1 - t_Symbol))/(1 - 2*t_Symbol)]/; optPolyLog :> + ( + 6*Zeta2 - + 2*Log[2]*Log[-(1 - 2*t)^(-1)] + 2*I*Pi*Log[1 - 2*t] - Log[1 - 2*t]^2 - 2*I*Pi*Log[1 - t] + - 2*Log[1 - 2*t]* - Log[1 - t] - - 2*Log[-(1 - 2*t)^(-1)]* - Log[(1 - t)/(1 - 2*t)] - 2*Log[(1 - t)/(1 - 2*t)]* - Log[t] + - 2*Log[(1 - t)/ - (1 - 2*t)]* - Log[-(t/(1 - 2*t))] - - 2*Log[2]* - Log[-1 + 2*t] - - 2*Log[1 - t]* - Log[-1 + 2*t] - - 2*PolyLog[2, 2*(1 - t)])/ 2 -, -PolyLog[2, (1 - t_Symbol)^2/ - (1 - 2*t_Symbol)] :> - (2*I*Pi*Log[1 - 2*t] + + 2*Log[1 - 2*t]*Log[1 - t] - + 2*Log[-(1 - 2*t)^(-1)]*Log[(1 - t)/(1 - 2*t)] - + 2*Log[(1 - t)/(1 - 2*t)]*Log[t] + + 2*Log[(1 - t)/(1 - 2*t)]*Log[-(t/(1 - 2*t))] - + 2*Log[2]*Log[-1 + 2*t] - + 2*Log[1 - t]*Log[-1 + 2*t] - + 2*PolyLog[2, 2*(1 - t)] + )/ 2, + + PolyLog[2, (1 - t_Symbol)^2/(1 - 2*t_Symbol)]/; optPolyLog :> + ( + 2*I*Pi*Log[1 - 2*t] + 4*Log[2]*Log[1 - 2*t] - Log[1 - 2*t]^2 - 4*I*Pi*Log[1 - t] + - 4*Log[1 - 2*t]* - Log[1 - t] + + 4*Log[1 - 2*t]*Log[1 - t] + 4*Log[1 - 2*t]*Log[t] - - 4*Log[2]* - Log[-1 + 2*t] - - 4*Log[1 - t]* - Log[-1 + 2*t] + + 4*Log[2]*Log[-1 + 2*t] - + 4*Log[1 - t]*Log[-1 + 2*t] + 8*PolyLog[2, 1 - t] - - 4*PolyLog[2, - 2*(1 - t)] + - 4*PolyLog[2, 2*t])/2 -, -PolyLog[2, (1 - t_Symbol)/(1 - 2*t_Symbol)] :> - (3*Zeta2 + 2*I*Pi*Log[1 - 2*t] + - 2*Log[2]*Log[1 - 2*t] - Log[1 - 2*t]^2 - + 4*PolyLog[2,2*(1 - t)] + + 4*PolyLog[2, 2*t] + )/2, + + PolyLog[2, (1 - t_Symbol)/(1 - 2*t_Symbol)]/; optPolyLog :> + ( + 3*Zeta2 + + 2*I*Pi*Log[1 - 2*t] + + 2*Log[2]*Log[1 - 2*t] - + Log[1 - 2*t]^2 - 2*I*Pi*Log[1 - t] + 2*Log[1 - 2*t]*Log[1 - t] + 2*Log[1 - 2*t]*Log[t] - @@ -121,419 +236,938 @@ 2*Log[1 - t]*Log[-1 + 2*t] + 2*PolyLog[2, 1 - t] - 2*PolyLog[2, 2*(1 - t)] + - 2*PolyLog[2, 2*t])/2 -, -Log[-(t_Symbol^2/(1 - 2*t_Symbol))] :> - Log[t] + Log[-(t/(1 - 2*t))] -, - -PolyLog[2, -(t_Symbol/(1 - 2*t_Symbol))] :> - Zeta2 - Log[(1 - t)/(1 - 2*t)]* - Log[-(t/(1 - 2*t))] - + 2*PolyLog[2, 2*t] + )/2, + + Log[-(t_Symbol^2/(1 - 2*t_Symbol))] :> + Log[t] + Log[-(t/(1 - 2*t))], + + PolyLog[2, -(t_Symbol/(1 - 2*t_Symbol))]/; optPolyLog :> + ( + Zeta2 - + Log[(1 - t)/(1 - 2*t)]*Log[-(t/(1 - 2*t))] - PolyLog[2, (1 - t)/(1 - 2*t)] -, - PolyLog[2, -(t_Symbol^2/(1 - 2*t_Symbol))] :> - Zeta2 - Log[(1 - t)^2/(1 - 2*t)]* - Log[-(t^2/(1 - 2*t))] - + ), + + PolyLog[2, -(t_Symbol^2/(1 - 2*t_Symbol))]/; optPolyLog :> + ( + Zeta2 - + Log[(1 - t)^2/(1 - 2*t)]*Log[-(t^2/(1 - 2*t))] - PolyLog[2, (1 - t)^2/(1 - 2*t)] -, + ), -PolyLog[3, (1 - t_Symbol)^2/t_Symbol^2] :> - (2*Pi^2*Log[1 - t])/3 - 4*Log[1 - t]^2*Log[-((1 - 2*t)/t)] + - 8*Log[1 - t]*Log[-((1 - 2*t)/t)]*Log[t] - 2*Log[1 - t]*Log[t]^2 - - 4*Log[-((1 - 2*t)/t)]*Log[t]^2 + (2*Log[t]^3)/3 - + PolyLog[3, (1 - t_Symbol)^2/t_Symbol^2]/; optPolyLog :> + ( + 2*Pi^2*Log[1 - t]/3 - + 4*Log[1 - t]^2*Log[-((1 - 2*t)/t)] + + 8*Log[1 - t]*Log[-((1 - 2*t)/t)]*Log[t] - + 2*Log[1 - t]*Log[t]^2 - + 4*Log[-((1 - 2*t)/t)]*Log[t]^2 + + (2*Log[t]^3)/3 - 4*Log[1 - t]*PolyLog[2, -((1 - 2*t)/t)] + 4*Log[t]*PolyLog[2, -((1 - 2*t)/t)] - 4*Log[1 - t]*PolyLog[2, (1 - t)/t] + 4*Log[t]*PolyLog[2, (1 - t)/t] - 4*PolyLog[3, 1 - t] + 4*PolyLog[3, (1 - t)/t] - 4*PolyLog[3, t] + 4*Zeta[3] -, -PolyLog[2, 2 - x_Symbol] :> -Zeta2 - I*Pi*Log[2 - x] - Log[1 - x]*Log[2 - x] - PolyLog[2, -1 + x] -, -PolyLog[2, (1 + x_Symbol)/x_Symbol] :> -2*Zeta2 + I*Pi*Log[x] - Log[x]^2/2 - -I*Pi*Log[1 + x] + Log[x]*Log[1 + x] + - PolyLog[2, -x] -, -PolyLog[2, (1 - x_Symbol)/2] :> -(Zeta2 - Log[2]^2 + 2*Log[2]*Log[1 + x] + 2*Log[x]*Log[1 + x] - + ), + + PolyLog[2, 2 - x_Symbol]/; optPolyLog :> + ( + Zeta2 - + I*Pi*Log[2 - x] - + Log[1 - x]*Log[2 - x] - + PolyLog[2, -1 + x] + ), + + PolyLog[2, (1 + x_Symbol)/x_Symbol]/; optPolyLog :> + ( + 2*Zeta2 + + I*Pi*Log[x] - + Log[x]^2/2 - + I*Pi*Log[1 + x] + + Log[x]*Log[1 + x] + + PolyLog[2, -x] + ), + + PolyLog[2, (1 - x_Symbol)/2]/; optPolyLog :> + ( + Zeta2 - + Log[2]^2 + 2*Log[2]*Log[1 + x] + 2*Log[x]*Log[1 + x] - Log[1 + x]^2 + 2*PolyLog[2, 1 - x] + 2*PolyLog[2, -x] - - 2*PolyLog[2, (1 - x)/(1 + x)])/2 -, -PolyLog[2, -(1 - x_Symbol)/(2*x_Symbol)] :> - (4*Zeta2 + 4*I*Pi*Log[2] - 3*Log[2]^2 + 4*Log[2]*Log[1 - x] + -4*I*Pi*Log[x] - 6*Log[2]*Log[x] + 4*Log[1 - x]*Log[x] - 3*Log[x]^2 - -4*I*Pi*Log[1 + x] + 2*Log[2]*Log[1 + x] - 4*Log[1 - x]*Log[1 + x] + -2*Log[x]*Log[1 + x] + Log[1 + x]^2 + 2*PolyLog[2, (1 - x)/(1 + x)] - - 4*PolyLog[2, (1 + x)/(2*x)])/2 - -, -PolyLog[3, -(x_^2/(1 - x_^2))] :> - 7*Zeta2*Log[1 - x] + I*Pi*Log[1 - x]^2 + Log[1 - x]^3/6 - - Log[1 - x]^2*Log[x] + Zeta2*Log[1 + x] - 2*I*Pi*Log[1 - x]*Log[1 + x] + - (Log[1 - x]^2*Log[1 + x])/2 - 2*Log[1 - x]*Log[x]*Log[1 + x] - - I*Pi*Log[1 + x]^2 + (Log[1 - x]*Log[1 + x]^2)/2 - Log[x]*Log[1 + x]^2 + - Log[1 + x]^3/6 - 4*PolyLog[3, 1 - x] - 4*PolyLog[3, -x] - -4*PolyLog[3, x] - 4*PolyLog[3, 1 + x] - 2*PolyLog[3, -((1 + x)/(1 - x))] + - 2*PolyLog[3, (1 + x)/(1 - x)] + (9*Zeta[3])/2 -, -PolyLog[2, -(x_^2/(1 - x_^2))] :> --2*Zeta2 - Log[1 - x]^2/2 + 2*Log[1 - x]*Log[x] - Log[1 - x]*Log[1 + x] - - Log[1 + x]^2/2 + 2*PolyLog[2, 1 - x] - 2*PolyLog[2, -x] -, -PolyLog[3, -(1 - x_Symbol)^(-1)] :> - Log[1 - x]^3/6 + Zeta2*Log[1 - x] + PolyLog[3, -1 + x] -, -PolyLog[3, (1 - x_Symbol)^2] :> - 4*PolyLog[3, 1 - x] + 4*PolyLog[3, -1 + x] -, -PolyLog[2, -1 + 2*x_Symbol] :> -Zeta2 - Log[2]*Log[-1 + 2*x] - Log[1 - x]*Log[-1 + 2*x] - - PolyLog[2, 2*(1 - x)] -, -PolyLog[2, (1 - 2*x_Symbol)/(1 - x_Symbol)] :> - -Log[1 - x]^2/2 + Log[1 - x]*Log[x] - Log[x]^2/2 - - PolyLog[2, -((1 - 2*x)/x)] -, -PolyLog[2, (1 - 2*x_Symbol)/(2*(1 - x_Symbol))] :> - -Log[2]^2/2 - Log[2]*Log[1 - x] - Log[1 - x]^2/2 - + 2*PolyLog[2, (1 - x)/(1 + x)] + )/2, + + PolyLog[2, (1 - Sqrt[x_Symbol])/2]/; optSqrt && optPolyLog :> + ( + -Log[2]^2/2 + Log[2]*Log[1 + Sqrt[x]] - Log[1 + Sqrt[x]]^2/2 + + 2*PolyLog[2, 1 - Sqrt[x]] - PolyLog[2, (1 - Sqrt[x])/(1 + Sqrt[x])] - + PolyLog[2, 1 - x]/2 + ), + + PolyLog[2, (1 - Sqrt[x_Symbol])/2]/; optSqrt && optPolyLog :> + ( + - PolyLog[2, (1 + Sqrt[x])/2] + + Zeta2 - + Log[2]^2 + Log[1 + Sqrt[x]]^2 + Log[2] Log[1 - x] - + Log[1 + Sqrt[x]] Log[1 - x] + ), + + PolyLog[2, -(1 - x_Symbol)/(2*x_Symbol)]/; optPolyLog :> + ( + 4*Zeta2 + + 4*I*Pi*Log[2] - + 3*Log[2]^2 + + 4*Log[2]*Log[1 - x] + + 4*I*Pi*Log[x] - + 6*Log[2]*Log[x] + + 4*Log[1 - x]*Log[x] - + 3*Log[x]^2 - + 4*I*Pi*Log[1 + x] + + 2*Log[2]*Log[1 + x] - + 4*Log[1 - x]*Log[1 + x] + + 2*Log[x]*Log[1 + x] + + Log[1 + x]^2 + + 2*PolyLog[2, (1 - x)/(1 + x)] - + 4*PolyLog[2, (1 + x)/(2*x)] + )/2, + + PolyLog[3, -(x_^2/(1 - x_^2))]/; optPolyLog :> + ( + 7*Zeta2*Log[1 - x] + + I*Pi*Log[1 - x]^2 + + Log[1 - x]^3/6 - + Log[1 - x]^2*Log[x] + + Zeta2*Log[1 + x] - + 2*I*Pi*Log[1 - x]*Log[1 + x] + + (Log[1 - x]^2*Log[1 + x])/2 - + 2*Log[1 - x]*Log[x]*Log[1 + x] - + I*Pi*Log[1 + x]^2 + + (Log[1 - x]*Log[1 + x]^2)/2 - + Log[x]*Log[1 + x]^2 + + Log[1 + x]^3/6 - + 4*PolyLog[3, 1 - x] - + 4*PolyLog[3, -x] - + 4*PolyLog[3, x] - + 4*PolyLog[3, 1 + x] - + 2*PolyLog[3, -((1 + x)/(1 - x))] + + 2*PolyLog[3, (1 + x)/(1 - x)] + + (9*Zeta[3])/2 + ), + + PolyLog[2, -(x_^2/(1 - x_^2))]/; optPolyLog :> + ( + -2*Zeta2 - + Log[1 - x]^2/2 + + 2*Log[1 - x]*Log[x] - + Log[1 - x]*Log[1 + x] - + Log[1 + x]^2/2 + + 2*PolyLog[2, 1 - x] - + 2*PolyLog[2, -x] + ), + + PolyLog[3, -(1 - x_Symbol)^(-1)]/; optPolyLog :> + Log[1 - x]^3/6 + Zeta2*Log[1 - x] + PolyLog[3, -1 + x], + + PolyLog[3, (1 - x_Symbol)^2]/; optPolyLog :> + 4*PolyLog[3, 1 - x] + 4*PolyLog[3, -1 + x], + + PolyLog[2, -1 + 2*x_Symbol]/; optPolyLog :> + Zeta2 - Log[2]*Log[-1 + 2*x] - Log[1 - x]*Log[-1 + 2*x] - PolyLog[2, 2*(1 - x)], + + PolyLog[2, (1 - 2*x_Symbol)/(1 - x_Symbol)]/; optPolyLog :> + -Log[1 - x]^2/2 + Log[1 - x]*Log[x] - Log[x]^2/2 - PolyLog[2, -((1 - 2*x)/x)], + + PolyLog[2, (1 - 2*x_Symbol)/(2*(1 - x_Symbol))]/; optPolyLog :> + -Log[2]^2/2 - Log[2]*Log[1 - x] - Log[1 - x]^2/2 - PolyLog[2, -1 + 2*x], + + PolyLog[2, (1 - x_Symbol)/x_Symbol]/; optPolyLog :> + ( + Zeta2 - + I*Pi*Log[1 - x] - + Log[1 - 2*x]*Log[1 - x] + + I*Pi*Log[x] + + Log[1 - 2*x]*Log[x] + + Log[1 - x]*Log[x] - + Log[x]^2 - + PolyLog[2, -((1 - 2*x)/x)] + ), + + PolyLog[2, 1/(2*(1 - x_Symbol))]/; optPolyLog :> + ( + Zeta2 - + Log[2]^2/2 + + Log[2]*Log[1 - 2*x] - + Log[2]*Log[1 - x] + + Log[1 - 2*x]*Log[1 - x] - + Log[1 - x]^2/2 + PolyLog[2, -1 + 2*x] -, -PolyLog[2, (1 - x_Symbol)/x_Symbol] :> - Zeta2 - I*Pi*Log[1 - x] - Log[1 - 2*x]*Log[1 - x] + I*Pi*Log[x] + - Log[1 - 2*x]*Log[x] + Log[1 - x]*Log[x] - Log[x]^2 - - PolyLog[2, -((1 - 2*x)/x)] -, - -PolyLog[2, 1/(2*(1 - x_Symbol))] :> - Zeta2 - Log[2]^2/2 + Log[2]*Log[1 - 2*x] - Log[2]*Log[1 - x] + -Log[1 - 2*x]*Log[1 - x] - Log[1 - x]^2/2 + PolyLog[2, -1 + 2*x] -, -PolyLog[2, x_Symbol/(1 + x_Symbol)] :> - -Pi^2/6 + I*Pi*Log[1 + x] + Log[x]*Log[1 + x] - Log[1 + x]^2/2 + - PolyLog[2, 1 + x] -, -PolyLog[3, x_^(-2)] :> -2*Pi^2*Log[x] - 12*Zeta2*Log[x] - 2*I*Pi*Log[x]^2 - 4*Log[1 - x]*Log[x]^2 + - (4*Log[x]^3)/3 - 4*Log[x]*PolyLog[2, 1 - x] - 4*Log[x]*PolyLog[2, x] + - 4*PolyLog[3, -x] + 4*PolyLog[3, x] -, -PolyLog[3, (1 - x_Symbol^2)^(-1)] :> - -8*Zeta2*Log[1 - x] - (3*I)/2*Pi*Log[1 - x]^2 + Log[1 - x]^3/6 - - 2*Zeta2*Log[1 + x] + I*Pi*Log[1 - x]*Log[1 + x] + - (Log[1 - x]^2*Log[1 + x])/2 + I/2*Pi*Log[1 + x]^2 + - (Log[1 - x]*Log[1 + x]^2)/2 + Log[1 + x]^3/6 + 4*PolyLog[3, 1 - x] + - 4*PolyLog[3, 1 + x] + 2*PolyLog[3, -((1 + x)/(1 - x))] - - 2*PolyLog[3, (1 + x)/(1 - x)] - (7*Zeta[3])/2 -, -PolyLog[3, 1 - x_Symbol^2] :> --6*Zeta2*Log[1 - x] - I*Pi*Log[1 - x]^2 + 2*I*Pi*Log[1 - x]*Log[1 + x] + - I*Pi*Log[1 + x]^2 + 4*PolyLog[3, 1 - x] + 4*PolyLog[3, 1 + x] + - 2*PolyLog[3, -((1 + x)/(1 - x))] - 2*PolyLog[3, (1 + x)/(1 - x)] - - (7*Zeta[3])/2 -, -PolyLog[2, 2/(1 - x_Symbol)] :> - (7*Zeta2 - 2*I*Pi*Log[2] + 4*I*Pi*Log[1 - x] + 2*Log[2]*Log[1 - x] - - 2*Log[1 - x]^2 - 2*I*Pi*Log[1 + x] - 2*Log[2]*Log[1 + x] + -2*Log[1 - x]*Log[1 + x] - 2*Log[x]*Log[1 + x] - 2*PolyLog[2, 1 - x] - - 2*PolyLog[2, -x] - 2*PolyLog[2, (1 + x)/(1 - x)])/2 -, - PolyLog[2, -((1 + x_Symbol)/(1 - x_Symbol))] :> - (-5*Pi^2 - 12*I*Pi*Log[1 - x] + 12*I*Pi*Log[1 + x] + -12*Log[x]*Log[1 + x] + 12*PolyLog[2, 1 - x] + 12*PolyLog[2, -x] + - 12*PolyLog[2, (1 + x)/(1 - x)])/12 -, - PolyLog[2, (1 + x_Symbol)/(-1 + x_Symbol)] :> - (-5*Pi^2 - 12*I*Pi*Log[1 - x] + 12*I*Pi*Log[1 + x] + -12*Log[x]*Log[1 + x] + 12*PolyLog[2, 1 - x] + 12*PolyLog[2, -x] + - 12*PolyLog[2, (1 + x)/(1 - x)])/12 -, -PolyLog[2, 1 + x_Symbol] :> - Zeta2 - I*Pi*Log[1 + x] - Log[x]*Log[1 + x] - PolyLog[2, -x] -, - PolyLog[2,1/x_(*/;FreeQ[x,Plus]*)] :> (Log[(x-1)/x] Log[x] + Pi^2/3 - - PolyLog[2,x] - Log[x] Log[1-x] + - 1/2 Log[x]^2 - ) -, - PolyLog[2,-1/x_(*/;FreeQ[x,Plus]*)] :> (Log[(+x+1)/x] Log[-x] + Pi^2/3 - - PolyLog[2,-x] - Log[-x] Log[1+x] + - 1/2 Log[-x]^2 - ) -, - -(* a matter of taste -PolyLog[2, 1 - x_] -> Zeta2 - Log[1 - x] Log[x] - PolyLog[2, x], -*) -PolyLog[2, x_ /; FreeQ2[x,{Plus,Times,Power}]] :> - Zeta2 - Log[1 - x] Log[x] - PolyLog[2, 1 - x] -, -PolyLog[2, x_^(-2)] :> -2*Zeta2 + 2*I*Pi*Log[x] + 2*Log[1 - x]*Log[x] - Log[x]^2 + -2*PolyLog[2, 1 - x] + 2*PolyLog[2, -x^(-1)] -, -PolyLog[2, (1 + x_Symbol)/(1 - x_Symbol^2)] :> -2*Zeta2 + I*Pi*Log[1 - x] - Log[1 - x]^2/2 - PolyLog[2, 1 - x] - -, -PolyLog[2,1-x_^2] :> -PolyLog[2,1-x] - PolyLog[2,x]-2 PolyLog[2,-x]- -Log[x] Log[1-x] - 2 Log[x] Log[1+x] -, -PolyLog[2, -((1 - x_Symbol)/(1 + x_Symbol))] :> -(-3*Zeta2)/2 - Log[x]*(-Log[1 - x] + Log[1 + x]) - PolyLog[2, -x] + -PolyLog[2, x] + PolyLog[2, (1 - x)/(1 + x)] -, -PolyLog[2, ((x_Symbol -1)/(1 + x_Symbol))] :> -(-3*Zeta2)/2 - Log[x]*(-Log[1 - x] + Log[1 + x]) - PolyLog[2, -x] + -PolyLog[2, x] + PolyLog[2, (1 - x)/(1 + x)] -, -PolyLog[2, (1 + x_Symbol)/2] :> -Zeta2/2 - Log[2]^2/2 + Log[2]*Log[1 - x] - Log[1 - x]*Log[1 + x] - -Log[x]*Log[1 + x] + Log[1 + x]^2/2 - PolyLog[2, 1 - x] - PolyLog[2, -x] + -PolyLog[2, (1 - x)/(1 + x)] -, -PolyLog[2, (1 + x_Symbol)/(1 - x_Symbol)] :> -2*Zeta2 + I*Pi*Log[1 - x] - Log[1 - x]^2/2 - I*Pi*Log[1 + x] + -Log[1 - x]*Log[1 + x] - Log[1 + x]^2/2 - -PolyLog[2, (1 - x)/(1 + x)] -, -PolyLog[2, (-2*x_Symbol)/(1 - x_Symbol)] :> -Zeta2 + I*Pi*Log[1 - x] + Log[2]*Log[1 - x] - Log[1 - x]^2 + -Log[1 - x]*Log[x] - I*Pi*Log[1 + x] - Log[2]*Log[1 + x] + -Log[1 - x]*Log[1 + x] - Log[x]*Log[1 + x] - -PolyLog[2, (1 + x)/(1 - x)] -, -PolyLog[2, x_^2] :> - Zeta2 - Log[1 - x]*Log[x] - PolyLog[2, 1 - x] + 2*PolyLog[2, -x] + - PolyLog[2, x] -, -PolyLog[2, (1 + x_Symbol)/(2*x_Symbol)] :> - (2*Zeta2 + 2*I*Pi*Log[2] - Log[2]^2 + 2*Log[2]*Log[1 - x] + - 2*I*Pi*Log[x] - 2*Log[2]*Log[x] + 2*Log[1 - x]*Log[x] - Log[x]^2 - - 2*I*Pi*Log[1 + x] - 2*Log[1 - x]*Log[1 + x] + Log[1 + x]^2 + - 2*PolyLog[2, (1 - x)/(1 + x)])/2 -, -PolyLog[2, x_Symbol/(1 + x_Symbol)] :> - (-Log[1 + x]^2 - 2*PolyLog[2, -x])/2 -, - PolyLog[2, -x_Symbol/(1-x_Symbol)] :> -1/2 Log[1-x]^2 - PolyLog[2, x] -, - PolyLog[2, 1 - 1/x_Symbol] :> -Log[x]^2/2 - PolyLog[2, 1 - x] -, - PolyLog[2, (x_Symbol - 1)/x_Symbol] :> -Log[x]^2/2 - PolyLog[2, 1 - x] -, - PolyLog[2, -(1 - x_Symbol)/x_Symbol]:> -Log[x]^2/2 - PolyLog[2, 1 - x] -, - PolyLog[2, x_Symbol/(x_Symbol -1)] :> -1/2 Log[1-x]^2 - PolyLog[2, x] -, - PolyLog[3, x_Symbol] :> - (2*Zeta2*Log[x] - Log[1 - x]*Log[x]^2 - 2*Nielsen[1, 2, 1 - x] - - 2*Log[x]*PolyLog[2, 1 - x] + 2*Zeta[3])/2 -, -(* + ), + + PolyLog[2, x_Symbol/(1 + x_Symbol)]/; optPolyLog :> + -Pi^2/6 + I*Pi*Log[1 + x] + Log[x]*Log[1 + x] - Log[1 + x]^2/2 + PolyLog[2, 1 + x], + + PolyLog[3, x_^(-2)]/; optPolyLog :> + ( + 2*Pi^2*Log[x] - + 12*Zeta2*Log[x] - + 2*I*Pi*Log[x]^2 - + 4*Log[1 - x]*Log[x]^2 + + (4*Log[x]^3)/3 - + 4*Log[x]*PolyLog[2, 1 - x] - + 4*Log[x]*PolyLog[2, x] + + 4*PolyLog[3, -x] + + 4*PolyLog[3, x] + ), + + PolyLog[3, (1 - x_Symbol^2)^(-1)]/; optPolyLog :> + ( + -8*Zeta2*Log[1 - x] - + (3*I)/2*Pi*Log[1 - x]^2 + + Log[1 - x]^3/6 - + 2*Zeta2*Log[1 + x] + + I*Pi*Log[1 - x]*Log[1 + x] + + (Log[1 - x]^2*Log[1 + x])/2 + + I/2*Pi*Log[1 + x]^2 + + (Log[1 - x]*Log[1 + x]^2)/2 + + Log[1 + x]^3/6 + + 4*PolyLog[3, 1 - x] + + 4*PolyLog[3, 1 + x] + + 2*PolyLog[3, -((1 + x)/(1 - x))] - + 2*PolyLog[3, (1 + x)/(1 - x)] - + (7*Zeta[3])/2 + ), + + PolyLog[3, 1 - x_Symbol^2]/; optPolyLog :> + ( + -6*Zeta2*Log[1 - x] - + I*Pi*Log[1 - x]^2 + + 2*I*Pi*Log[1 - x]*Log[1 + x] + + I*Pi*Log[1 + x]^2 + + 4*PolyLog[3, 1 - x] + + 4*PolyLog[3, 1 + x] + + 2*PolyLog[3, -((1 + x)/(1 - x))] - + 2*PolyLog[3, (1 + x)/(1 - x)] - + (7*Zeta[3])/2 + ), + + PolyLog[2, 2/(1 - x_Symbol)]/; optPolyLog :> + ( + 7*Zeta2 - + 2*I*Pi*Log[2] + + 4*I*Pi*Log[1 - x] + + 2*Log[2]*Log[1 - x] - + 2*Log[1 - x]^2 - + 2*I*Pi*Log[1 + x] - + 2*Log[2]*Log[1 + x] + + 2*Log[1 - x]*Log[1 + x] - + 2*Log[x]*Log[1 + x] - + 2*PolyLog[2, 1 - x] - + 2*PolyLog[2, -x] - + 2*PolyLog[2, (1 + x)/(1 - x)] + )/2, + + PolyLog[2, 2/(1 + x_Symbol)]/; optPolyLog :> + ( + -(Log[-1 + x]*Log[2/(1 + x)]) + + (Log[2/(1 + x)]*Log[2*(1 + x)])/2 + + PolyLog[2, (1 - x)/2] + Zeta2 + ), + + PolyLog[2, -((1 + x_Symbol)/(1 - x_Symbol))]/; optPolyLog :> + ( + -5*Pi^2 - + 12*I*Pi*Log[1 - x] + + 12*I*Pi*Log[1 + x] + + 12*Log[x]*Log[1 + x] + + 12*PolyLog[2, 1 - x] + + 12*PolyLog[2, -x] + + 12*PolyLog[2, (1 + x)/(1 - x)] + )/12, + + PolyLog[2, (1 + x_Symbol)/(-1 + x_Symbol)]/; optPolyLog :> + ( + -5*Pi^2 - + 12*I*Pi*Log[1 - x] + + 12*I*Pi*Log[1 + x] + + 12*Log[x]*Log[1 + x] + + 12*PolyLog[2, 1 - x] + + 12*PolyLog[2, -x] + + 12*PolyLog[2, (1 + x)/(1 - x)] + )/12, + + PolyLog[2, 1 + x_Symbol]/; optPolyLog :> + Zeta2 - I*Pi*Log[1 + x] - Log[x]*Log[1 + x] - PolyLog[2, -x], + + PolyLog[2, 1 + Sqrt[x_Symbol]] /; optSqrt && optPolyLog :> + ( + - PolyLog[2, -Sqrt[x]] + + Zeta2 - I Pi Log[1 + Sqrt[x]] - 1/2 Log[1 + Sqrt[x]] Log[x] + ), + + + PolyLog[2,1/x_]/; optPolyLog :> + Log[(x-1)/x] Log[x] + Pi^2/3 - PolyLog[2,x] - Log[x] Log[1-x] + 1/2 Log[x]^2, + + PolyLog[2,-1/x_]/; optPolyLog :> + Log[(+x+1)/x] Log[-x] + Pi^2/3 - PolyLog[2,-x] - Log[-x] Log[1+x] + 1/2 Log[-x]^2, + + (* a matter of taste + PolyLog[2, 1 - x_] -> Zeta2 - Log[1 - x] Log[x] - PolyLog[2, x], *) + + PolyLog[2, x_ /; FreeQ2[x,{Plus,Times,Power}]] && optPolyLog :> + Zeta2 - Log[1 - x] Log[x] - PolyLog[2, 1 - x], + + PolyLog[2, Sqrt[x_Symbol]]/; optSqrt && optPolyLog :> + ( + - PolyLog[2, 1 - Sqrt[x]] + + Zeta2 + 1/2 Log[1 + Sqrt[x]] Log[x] - 1/2 Log[1 - x] Log[x] + ), + + PolyLog[2, x_^(-2)]/; optPolyLog :> + 2*Zeta2 + 2*I*Pi*Log[x] + 2*Log[1 - x]*Log[x] - Log[x]^2 + 2*PolyLog[2, 1 - x] + 2*PolyLog[2, -x^(-1)], + + PolyLog[2, (1 + x_Symbol)/(1 - x_Symbol^2)]/; optPolyLog :> + 2*Zeta2 + I*Pi*Log[1 - x] - Log[1 - x]^2/2 - PolyLog[2, 1 - x], + + PolyLog[2,1-x_^2]/; optPolyLog :> + PolyLog[2,1-x] - PolyLog[2,x]-2 PolyLog[2,-x]- Log[x] Log[1-x] - 2 Log[x] Log[1+x], + + PolyLog[2, -((1 - x_Symbol)/(1 + x_Symbol))]/; optPolyLog :> + (-3*Zeta2)/2 - Log[x]*(-Log[1 - x] + Log[1 + x]) - PolyLog[2, -x] + PolyLog[2, x] + PolyLog[2, (1 - x)/(1 + x)], + + PolyLog[2, ((x_Symbol -1)/(1 + x_Symbol))]/; optPolyLog :> + (-3*Zeta2)/2 - Log[x]*(-Log[1 - x] + Log[1 + x]) - PolyLog[2, -x] + PolyLog[2, x] + PolyLog[2, (1 - x)/(1 + x)], + + PolyLog[2, (1 + x_Symbol)/2]/; optPolyLog :> + ( + Zeta2/2 - + Log[2]^2/2 + + Log[2]*Log[1 - x] - + Log[1 - x]*Log[1 + x] - + Log[x]*Log[1 + x] + + Log[1 + x]^2/2 - + PolyLog[2, 1 - x] - + PolyLog[2, -x] + + PolyLog[2, (1 - x)/(1 + x)] + ), + + PolyLog[2, (1 + Sqrt[x_Symbol])/2]/; optSqrt && optPolyLog :> + ( + Zeta2 - Log[2]^2/2 - Log[2] Log[1 + Sqrt[x]] + + 3/2 Log[1 + Sqrt[x]]^2 + Log[2] Log[1 - x] - + Log[1 + Sqrt[x]] Log[1 - x] - 2 PolyLog[2, 1 - Sqrt[x]] + + PolyLog[2, (1 - Sqrt[x])/(1 + Sqrt[x])] + 1/2 PolyLog[2, 1 - x] + ), + + PolyLog[2, (1 + x_Symbol)/(1 - x_Symbol)]/; optPolyLog :> + ( + 2*Zeta2 + + I*Pi*Log[1 - x] - + Log[1 - x]^2/2 - + I*Pi*Log[1 + x] + + Log[1 - x]*Log[1 + x] - + Log[1 + x]^2/2 - + PolyLog[2, (1 - x)/(1 + x)] + ), + + PolyLog[2, (-2*x_Symbol)/(1 - x_Symbol)]/; optPolyLog :> + ( + Zeta2 + + I*Pi*Log[1 - x] + + Log[2]*Log[1 - x] - + Log[1 - x]^2 + + Log[1 - x]*Log[x] - + I*Pi*Log[1 + x] - + Log[2]*Log[1 + x] + + Log[1 - x]*Log[1 + x] - + Log[x]*Log[1 + x] - + PolyLog[2, (1 + x)/(1 - x)] + ), + + PolyLog[2, x_^2]/; optPolyLog :> + Zeta2 - Log[1 - x]*Log[x] - PolyLog[2, 1 - x] + 2*PolyLog[2, -x] + PolyLog[2, x], + + PolyLog[2, (1 + x_Symbol)/(2*x_Symbol)]/; optPolyLog :> + ( + 2*Zeta2 + + 2*I*Pi*Log[2] - + Log[2]^2 + + 2*Log[2]*Log[1 - x] + + 2*I*Pi*Log[x] - + 2*Log[2]*Log[x] + + 2*Log[1 - x]*Log[x] - + Log[x]^2 - + 2*I*Pi*Log[1 + x] - + 2*Log[1 - x]*Log[1 + x] + + Log[1 + x]^2 + + 2*PolyLog[2, (1 - x)/(1 + x)] + )/2, + + + PolyLog[2, x_Symbol/(1 + x_Symbol)]/; optPolyLog :> + (-Log[1 + x]^2 - 2*PolyLog[2, -x])/2, + + PolyLog[2, 2 x_Symbol/(1 + x_Symbol)]/; optPolyLog :> + ( + -Pi^2/12 + Log[2]^2/2 - Log[1 - x]*Log[2/(1 + x)] - Log[1 + x]^2/2 + PolyLog[2, (1 - x)/2] - PolyLog[2, -x] + PolyLog[2, x] + ), + + PolyLog[2, -x_Symbol/(1-x_Symbol)]/; optPolyLog :> + -1/2 Log[1-x]^2 - PolyLog[2, x], + + PolyLog[2, 1 - 1/x_Symbol]/; optPolyLog :> + -Log[x]^2/2 - PolyLog[2, 1 - x], + + PolyLog[2, (x_Symbol - 1)/x_Symbol]/; optPolyLog :> + -Log[x]^2/2 - PolyLog[2, 1 - x], + + PolyLog[2, -(1 - x_Symbol)/x_Symbol]/; optPolyLog :> + -Log[x]^2/2 - PolyLog[2, 1 - x], + + PolyLog[2, x_Symbol/(x_Symbol -1)]/; optPolyLog :> + -1/2 Log[1-x]^2 - PolyLog[2, x], + + PolyLog[3, x_Symbol]/; optPolyLog :> + (2*Zeta2*Log[x] - Log[1 - x]*Log[x]^2 - 2*Nielsen[1, 2, 1 - x] - 2*Log[x]*PolyLog[2, 1 - x] + 2*Zeta[3])/2, + + (* Nielsen[1, 2, x_Symbol] :> (Log[1 - x]^2*Log[x])/2 + - Log[1 - x]*PolyLog[2, 1 - x] - PolyLog[3, 1 - x] + Zeta[3] -, -*) - Nielsen[1,2, -x_/(1-x_)] :> -1/6 Log[1-x]^3 + Nielsen[1,2,x] -, -PolyLog[2, -(x_^2/(1 - x_^2))] :> --2*Zeta2 - Log[1 - x]^2/2 + 2*Log[1 - x]*Log[x] - Log[1 - x]*Log[1 + x] - - Log[1 + x]^2/2 + 2*PolyLog[2, 1 - x] - 2*PolyLog[2, -x] -, -PolyLog[2, 1 - 2*x_Symbol] :> --Zeta2/2 + Log[1 - x]*Log[x] - Log[x]^2/2 + -PolyLog[2, 1 - x] + PolyLog[2, -1 + 2*x] - PolyLog[2, (-1 + 2*x)/x] -, -PolyLog[3, x_Symbol^(-1)] :> - (-2*Pi^2*Log[x] - 3*I*Pi*Log[x]^2 + Log[x]^3 + 6*PolyLog[3, x])/6 -, -PolyLog[3, (1 - x_Symbol)^(-1)] :> - -2*Zeta2*Log[1 - x] - I/2*Pi*Log[1 - x]^2 + Log[1 - x]^3/6 + - PolyLog[3, 1 - x] -, -PolyLog[3, (1 + x_Symbol)/x_Symbol] :> -(-12*Zeta2*Log[x] - 3*I*Pi*Log[x]^2 + Log[x]^3 + 18*Zeta2*Log[1 + x] + - 6*I*Pi*Log[x]*Log[1 + x] - 3*Log[x]^2*Log[1 + x] - - 6*I*Pi*Log[1 + x]^2 - 6*PolyLog[3, -x] - 6*PolyLog[3, 1 + x] + - 6*Zeta[3])/6 -, -(* do it the other way round -PolyLog[3, (1 + x_Symbol)^(-1)] :> - (-9*I*Pi*Log[1 + x]^2 - 12*Log[x]*Log[1 + x]^2 + Log[1 + x]^3 - -12*Log[1 + x]*PolyLog[2, -x] - 12*Log[1 + x]*PolyLog[2, 1 + x] + - 6*PolyLog[3, 1 + x])/6 -, -*) -PolyLog[3, 1 + x_Symbol] :> - (12*Zeta2*Log[1 + x] - 3*I*Pi*Log[1 + x]^2 - Log[1 + x]^3 + - 6*PolyLog[3, (1 + x)^(-1)])/6 -, -PolyLog[3, - (x_/;FreeQ[x,Plus])^(-1)] :> - Zeta2*Log[x] + Log[x]^3/6 + PolyLog[3, -x] -(* -, -PolyLog[3,1-x_Symbol] :> - (Log[1 - x]^2*Log[x] - 2*Nielsen[1, 2, x] + - 2*Log[1 - x]*PolyLog[2, 1 - x] + 2*Zeta[3])/2 -*) -, - -PolyLog[3, z_Symbol^2] :> - -4*((Log[1 - z]*Log[z]^2)/8 + (Log[z]^2*Log[1 + z])/8 - - (Log[z]^2*Log[1 - z^2])/8 - PolyLog[3, -z] - PolyLog[3, z]) -, - PolyLog[3, -x_Symbol/(1-x_Symbol)] :> - -PolyLog[3, x] - PolyLog[3,1-x] + 1/6 Log[1-x]^3 - - 1/2 Log[x] Log[1-x]^2 + Zeta2 Log[1-x] + Zeta[3] -(* -, - PolyLog[3, x_/(1+x_)] :> -Nielsen[1,2,-x] + PolyLog[2,-x] Log[1-x] - PolyLog[3,-x] + 1/6 Log[1+x]^3 -Li3(x/(1+x)) = S12(-x) + Li2(-x) ln(1-x) - Li3(-x) + 1/6 ln(1+x)^3 -*) -, - PolyLog[3,1 - 1/(x_/;FreeQ[x,Plus])] :> - Nielsen[1,2,x] - PolyLog[3,x] + Log[1-x] PolyLog[2,x] + - 1/6 Log[x]^3 + Zeta2 (Log[x]-Log[1-x])+ - 1/2Log[x] Log[1-x] (Log[1-x] - Log[x]) -, - PolyLog[3,-(1 - x_Symbol)/x_Symbol] :> - Nielsen[1,2,x] - PolyLog[3,x] + Log[1-x] PolyLog[2,x] + - 1/6 Log[x]^3 + Zeta2 (Log[x]-Log[1-x])+ - 1/2Log[x] Log[1-x] (Log[1-x] - Log[x]) -, -PolyLog[3,(x_Symbol-1)/x_Symbol] :> - Nielsen[1,2,x] - PolyLog[3,x] + Log[1-x] PolyLog[2,x] + - 1/6 Log[x]^3 + Zeta2 (Log[x]-Log[1-x])+ - 1/2Log[x] Log[1-x] (Log[1-x] - Log[x]) -, -PolyLog[3, (1 + x_Symbol)/(2*x_Symbol)] :> - (3*I*Pi*Log[2]^2 - 4*Log[2]^3 + 3*Log[2]^2*Log[1 - x] + - 6*I*Pi*Log[2]*Log[x] - 12*Log[2]^2*Log[x] + -6*Log[2]*Log[1 - x]*Log[x] + 3*I*Pi*Log[x]^2 - 12*Log[2]*Log[x]^2 + - 3*Log[1 - x]*Log[x]^2 - 4*Log[x]^3 - 6*I*Pi*Log[2]*Log[1 + x] + - 9*Log[2]^2*Log[1 + x] - 6*Log[2]*Log[1 - x]*Log[1 + x] - - 6*I*Pi*Log[x]*Log[1 + x] + 18*Log[2]*Log[x]*Log[1 + x] - - 6*Log[1 - x]*Log[x]*Log[1 + x] + 9*Log[x]^2*Log[1 + x] + - 3*I*Pi*Log[1 + x]^2 - 6*Log[2]*Log[1 + x]^2 + - 3*Log[1 - x]*Log[1 + x]^2 - 6*Log[x]*Log[1 + x]^2 + Log[1 + x]^3 - + Log[1 - x]*PolyLog[2, 1 - x] - PolyLog[3, 1 - x] + Zeta[3], *) + Nielsen[1,2, -x_/(1-x_)] :> + -1/6 Log[1-x]^3 + Nielsen[1,2,x], + + PolyLog[2, -(x_^2/(1 - x_^2))]/; optPolyLog :> + -2*Zeta2 - Log[1 - x]^2/2 + 2*Log[1 - x]*Log[x] - Log[1 - x]*Log[1 + x] - Log[1 + x]^2/2 + 2*PolyLog[2, 1 - x] - 2*PolyLog[2, -x], + + PolyLog[2, 1 - 2*x_Symbol]/; optPolyLog :> + -Zeta2/2 + Log[1 - x]*Log[x] - Log[x]^2/2 + PolyLog[2, 1 - x] + PolyLog[2, -1 + 2*x] - PolyLog[2, (-1 + 2*x)/x], + + PolyLog[3, x_Symbol^(-1)]/; optPolyLog :> + (-2*Pi^2*Log[x] - 3*I*Pi*Log[x]^2 + Log[x]^3 + 6*PolyLog[3, x])/6, + + PolyLog[3, (1 - x_Symbol)^(-1)]/; optPolyLog :> + -2*Zeta2*Log[1 - x] - I/2*Pi*Log[1 - x]^2 + Log[1 - x]^3/6 + PolyLog[3, 1 - x], + + PolyLog[3, (1 + x_Symbol)/x_Symbol]/; optPolyLog :> + ( + -12*Zeta2*Log[x] - + 3*I*Pi*Log[x]^2 + + Log[x]^3 + + 18*Zeta2*Log[1 + x] + + 6*I*Pi*Log[x]*Log[1 + x] - + 3*Log[x]^2*Log[1 + x] - + 6*I*Pi*Log[1 + x]^2 - + 6*PolyLog[3, -x] - + 6*PolyLog[3, 1 + x] + + 6*Zeta[3] + )/6, + + (* do it the other way round + PolyLog[3, (1 + x_Symbol)^(-1)] :> + (-9*I*Pi*Log[1 + x]^2 - 12*Log[x]*Log[1 + x]^2 + Log[1 + x]^3 - + 12*Log[1 + x]*PolyLog[2, -x] - 12*Log[1 + x]*PolyLog[2, 1 + x] + + 6*PolyLog[3, 1 + x])/6 + ,*) + PolyLog[3, 1 + x_Symbol]/; optPolyLog :> + ( + 12*Zeta2*Log[1 + x] - + 3*I*Pi*Log[1 + x]^2 - + Log[1 + x]^3 + + 6*PolyLog[3, (1 + x)^(-1)] + )/6, + + PolyLog[3, 1 + Sqrt[x_Symbol]]/; optSqrt && optPolyLog :> + ( + 2*Zeta2*Log[1 + Sqrt[x]] - + (I/2)*Pi*Log[1 + Sqrt[x]]^2 - + Log[1 + Sqrt[x]]^3/6 + + PolyLog[3, (1 + Sqrt[x])^(-1)] + ), + + PolyLog[3, - (x_/;FreeQ[x,Plus])^(-1)]/; optPolyLog :> + Zeta2*Log[x] + Log[x]^3/6 + PolyLog[3, -x], + (* + , + PolyLog[3,1-x_Symbol] :> + (Log[1 - x]^2*Log[x] - 2*Nielsen[1, 2, x] + + 2*Log[1 - x]*PolyLog[2, 1 - x] + 2*Zeta[3])/2 + *) + + PolyLog[3, 2/(1 + x_Symbol)]/; optPolyLog :> + ( + (Zeta2*Log[2])/2 - + Log[2]^3/6 - + 2*Zeta2*Log[1 + x] + + I*Pi*Log[2]*Log[1 + x] + + (Log[2]^2*Log[1 + x])/2 - + (I/2)*Pi*Log[1 + x]^2 - + (Log[2]*Log[1 + x]^2)/2 + + Log[1 + x]^3/6 + + PolyLog[3, 2] + + PolyLog[3, (1 + x)/2] - + (7*Zeta[3])/8 + ), + + PolyLog[3, z_Symbol^2]/; optPolyLog :> + ( + -4*((Log[1 - z]*Log[z]^2)/8 + + (Log[z]^2*Log[1 + z])/8 - + (Log[z]^2*Log[1 - z^2])/8 - + PolyLog[3, -z] - PolyLog[3, z]) + ), + + PolyLog[3, -x_Symbol/(1-x_Symbol)]/; optPolyLog :> + -PolyLog[3, x] - PolyLog[3,1-x] + 1/6 Log[1-x]^3 - 1/2 Log[x] Log[1-x]^2 + Zeta2 Log[1-x] + Zeta[3], + + PolyLog[3,1 - 1/(x_/;FreeQ[x,Plus])]/; optPolyLog :> + ( + Nielsen[1,2,x] - + PolyLog[3,x] + + Log[1-x] PolyLog[2,x] + + 1/6 Log[x]^3 + + Zeta2 (Log[x]-Log[1-x])+ + 1/2Log[x] Log[1-x] (Log[1-x] - Log[x]) + ), + + PolyLog[3,-(1 - x_Symbol)/x_Symbol]/; optPolyLog :> + ( + Nielsen[1,2,x] - + PolyLog[3,x] + + Log[1-x] PolyLog[2,x] + + 1/6 Log[x]^3 + + Zeta2 (Log[x]-Log[1-x])+ + 1/2Log[x] Log[1-x] (Log[1-x] - Log[x]) + ), + + PolyLog[3,(x_Symbol-1)/x_Symbol]/; optPolyLog :> + ( + Nielsen[1,2,x] - + PolyLog[3,x] + + Log[1-x] PolyLog[2,x] + + 1/6 Log[x]^3 + + Zeta2 (Log[x]-Log[1-x])+ + 1/2Log[x] Log[1-x] (Log[1-x] - Log[x]) + ), + + PolyLog[3, (1 + x_Symbol)/(2*x_Symbol)]/; optPolyLog :> + ( + 3*I*Pi*Log[2]^2 - + 4*Log[2]^3 + + 3*Log[2]^2*Log[1 - x] + + 6*I*Pi*Log[2]*Log[x] - + 12*Log[2]^2*Log[x] + + 6*Log[2]*Log[1 - x]*Log[x] + + 3*I*Pi*Log[x]^2 - + 12*Log[2]*Log[x]^2 + + 3*Log[1 - x]*Log[x]^2 - + 4*Log[x]^3 - + 6*I*Pi*Log[2]*Log[1 + x] + + 9*Log[2]^2*Log[1 + x] - + 6*Log[2]*Log[1 - x]*Log[1 + x] - + 6*I*Pi*Log[x]*Log[1 + x] + + 18*Log[2]*Log[x]*Log[1 + x] - + 6*Log[1 - x]*Log[x]*Log[1 + x] + + 9*Log[x]^2*Log[1 + x] + + 3*I*Pi*Log[1 + x]^2 - + 6*Log[2]*Log[1 + x]^2 + + 3*Log[1 - x]*Log[1 + x]^2 - + 6*Log[x]*Log[1 + x]^2 + Log[1 + x]^3 - 6*Log[2]*PolyLog[2, -(1 - x)/(2*x)] - 6*Log[x]*PolyLog[2, -(1 - x)/(2*x)] + 6*Log[1 + x]*PolyLog[2, -(1 - x)/(2*x)] - 6*Log[2]*PolyLog[2, (1 + x)/(2*x)] - 6*Log[x]*PolyLog[2, (1 + x)/(2*x)] + -6*Log[1 + x]*PolyLog[2, (1 + x)/(2*x)] - 6*PolyLog[3, -(1 - x)/(2*x)] - - 6*PolyLog[3, (1 - x)/(1 + x)] + 6*Zeta[3])/6 -, -PolyLog[3, (-2*x_Symbol)/(1 - x_Symbol)] :> -(-6*Zeta2*Log[2] - Log[2]^3 + 6*Zeta2*Log[1 - x] + 3*Log[2]^2*Log[1 - x] - - 3*Log[2]*Log[1 - x]^2 + Log[1 - x]^3 - 6*Zeta2*Log[x] - - 3*Log[2]^2*Log[x] + 6*Log[2]*Log[1 - x]*Log[x] - -3*Log[1 - x]^2*Log[x] - 3*Log[2]*Log[x]^2 + 3*Log[1 - x]*Log[x]^2 - - Log[x]^3 + 6*PolyLog[3, -(1 - x)/(2*x)])/6 -, -PolyLog[3, -((1 + x_Symbol)/ (1 - x_Symbol))] :> -Zeta2*Log[1 - x] + Log[1 - x]^3/6 - - Zeta2*Log[1 + x] - (Log[1 - x]^2*Log[1 + x])/ - 2 + (Log[1 - x]*Log[1 + x]^ 2)/2 - Log[1 + x]^3/6 + - PolyLog[3, -((1 - x)/ (1 + x))] -, - -PolyLog[3, (1 + x_Symbol)/(1 - x_Symbol)] :> -+I/6*(12*I*Zeta2*Log[1 - x] - 3*Pi*Log[1 - x]^2 - I*Log[1 - x]^3 - - 12*I*Zeta2*Log[1 + x] + 6*Pi*Log[1 - x]*Log[1 + x] + - 3*I*Log[1 - x]^2*Log[1 + x] - 3*Pi*Log[1 + x]^2 - - 3*I*Log[1 - x]*Log[1 + x]^2 + I*Log[1 + x]^3 - - 6*I*PolyLog[3, (1 - x)/(1 + x)]) - - -(*XY*) -(* -PolyLog[3, (1 - x_Symbol)/(1 + x_Symbol)] :> --I/6*(12*I*Zeta2*Log[1 - x] - 3*Pi*Log[1 - x]^2 - I*Log[1 - x]^3 - - 12*I*Zeta2*Log[1 + x] + 6*Pi*Log[1 - x]*Log[1 + x] + - 3*I*Log[1 - x]^2*Log[1 + x] - 3*Pi*Log[1 + x]^2 - - 3*I*Log[1 - x]*Log[1 + x]^2 + I*Log[1 + x]^3 + - 6*I*PolyLog[3, (1 + x)/(1 - x)]) -*) -, - PolyLog[2, (1 + x_Symbol)/(2*x_Symbol)] -> -Pi^2/6 + I*Pi*Log[2] - Log[2]^2/2 + Log[2]*Log[1 - x] + I*Pi*Log[x] - -Log[2]*Log[x] + Log[1 - x]*Log[x] - Log[x]^2/2 - I*Pi*Log[1 + x] - -Log[1 - x]*Log[1 + x] + Log[1 + x]^2/2 + PolyLog[2, (1 - x)/(1 + x)] - -, - -PolyLog[3, 2/(1 - x_Symbol)] :> -(Pi^2*Log[2] - 3*I*Pi*Log[2]^2 + Log[2]^3 - Pi^2*Log[1 - x] + - 6*I*Pi*Log[2]*Log[1 - x] - 3*I*Pi*Log[1 - x]^2 - -3*Log[2]*Log[1 - x]^2 + 2*Log[1 - x]^3 - 3*Log[2]^2*Log[1 + x] + -6*Log[2]*Log[1 - x]*Log[1 + x] - 3*Log[1 - x]^2*Log[1 + x] - -6*PolyLog[3, (1 + x)/2] - 6*PolyLog[3, -((1 + x)/(1 - x))] + 6*Zeta[3])/ - 6 -, - -(* some weird formala ... *) - - PolyLog[3, x_Symbol/(1 + x_Symbol)] :> - 3*Zeta2*Log[1 + x] - Log[-x]*Log[1 + x]^2 + Log[x]*Log[1 + x]^2 + - Log[x]*PolyLog[2, -x] + Log[x]*PolyLog[2, x/(1 + x)] - PolyLog[3, -x] + - PolyLog[3, (1 + x)^(-1)] - 2*PolyLog[3, 1 + x] + Zeta[3] -, - PolyLog[4, -x_/(1-x_)] :> --Log[1 - x]^4/24 - Nielsen[1, 3, x] + Nielsen[2, 2, x] - - (Log[1 - x]^2*PolyLog[2, x])/2 + - Log[1 - x]*(-Nielsen[1, 2, x] + PolyLog[3, x]) - PolyLog[4, x] -,Log[1/x_Symbol] :> -Log[x] -,Log[1/x_Symbol^2] :> - 2 Log[x] -,Log[1/(x_Symbol+1)] :> -Log[x+1] -,Log[x_Symbol/(x_Symbol+1)] :> Log[x]-Log[x+1] -,Log[1/(1-x_Symbol)] :> -Log[1-x] -,Log[-1/x_Symbol] :> -Log[x] + I Pi -,Log[-1/(1-x_Symbol)] :> -Log[1-x] + I Pi -,Log[-x_Symbol] :> Log[x] + I Pi -,Log[(x_Symbol)^2] :> 2 Log[x] -,Log[-x_Symbol^2] :> 2 Log[x] + I Pi -,Log[x_Symbol-1] :> Log[1-x] + I Pi -,Log[(x_Symbol-1)/x_Symbol] :> Log[1-x]-Log[x]+I Pi -,Log[-(1-x_Symbol)/x_Symbol] :> Log[1-x]-Log[x]+I Pi -, -Log[-1-x_Symbol] :> Log[1 + x] + I Pi -, -Log[1-x_Symbol^2] :> Log[1-x] + Log[1+x] -, -Log[(1-x_Symbol) x_Symbol] :> Log[1-x] + Log[x] -, -Log[(1-x_Symbol)/x_Symbol] :> Log[1-x] - Log[x] -, -Log[(1-x_Symbol)/(1+x_Symbol)] :> Log[1-x] - Log[1+x] -, -Log[(1+x_Symbol)/(1-x_Symbol)] :> Log[1+x] - Log[1-x] -, -Log[(x_Symbol + 1)/x_Symbol] :> Log[x+1] - Log[x] -, -Log[x_Symbol/(1-x_Symbol)] :> Log[x] -Log[1-x] -, -Log[x_Symbol/(x_Symbol-1)] :> Log[x] -Log[1-x] + I Pi -, -Log[x_Symbol/(x_Symbol+1)] :> Log[x] -Log[1+x] -, -Log[-x_Symbol/(1-x_Symbol)] :> Log[x] -Log[1-x] + I Pi -, -Log[r_?NumberQ x_]:> Log[r] + Log[x] /;r>0 -, -Pi^2 :> 6 Zeta2 -, -Pi^3 :> Pi 6 Zeta2 -, -ArcSinh[z_] :> Log[z + Sqrt[z^2 + 1]] -, -ArcCosh[z_] :> Log[z + Sqrt[z^2 - 1]] -, -ArcTanh[z_] :> 1/2 Log[(z+1)/(z-1)] + 6*Log[1 + x]*PolyLog[2, (1 + x)/(2*x)] - + 6*PolyLog[3, -(1 - x)/(2*x)] - + 6*PolyLog[3, (1 - x)/(1 + x)] + + 6*Zeta[3] + )/6, + + PolyLog[3, (-2*x_Symbol)/(1 - x_Symbol)]/; optPolyLog :> + ( + -6*Zeta2*Log[2] - + Log[2]^3 + + 6*Zeta2*Log[1 - x] + + 3*Log[2]^2*Log[1 - x] - + 3*Log[2]*Log[1 - x]^2 + + Log[1 - x]^3 - + 6*Zeta2*Log[x] - + 3*Log[2]^2*Log[x] + + 6*Log[2]*Log[1 - x]*Log[x] - + 3*Log[1 - x]^2*Log[x] - + 3*Log[2]*Log[x]^2 + 3*Log[1 - x]*Log[x]^2 - + Log[x]^3 + + 6*PolyLog[3, -(1 - x)/(2*x)] + )/6, + + + PolyLog[3, (-2*Sqrt[x_Symbol])/(1 - Sqrt[x_Symbol])]/; optSqrt && optPolyLog :> + ( + -(Zeta2*Log[2]) - Log[2]^3/6 + Zeta2*Log[1 - Sqrt[x]] + (Log[2]^2*Log[1 - Sqrt[x]])/2 - (Log[2]*Log[1 - Sqrt[x]]^2)/2 + Log[1 - Sqrt[x]]^3/6 - + Zeta2*Log[Sqrt[x]] - (Log[2]^2*Log[Sqrt[x]])/2 + Log[2]*Log[1 - Sqrt[x]]*Log[Sqrt[x]] - (Log[1 - Sqrt[x]]^2*Log[Sqrt[x]])/2 - (Log[2]*Log[Sqrt[x]]^2)/2 + + (Log[1 - Sqrt[x]]*Log[Sqrt[x]]^2)/2 - Log[Sqrt[x]]^3/6 + PolyLog[3, -(1 - Sqrt[x])/(2*Sqrt[x])] + ), + + + PolyLog[3, -((1 + x_Symbol)/ (1 - x_Symbol))]/; optPolyLog :> + ( + Zeta2*Log[1 - x] + + Log[1 - x]^3/6 - + Zeta2*Log[1 + x] - + (Log[1 - x]^2*Log[1 + x])/2 + + (Log[1 - x]*Log[1 + x]^ 2)/2 - + Log[1 + x]^3/6 + + PolyLog[3, -((1 - x)/ (1 + x))] + ), + + PolyLog[3, (1 + x_Symbol)/(1 - x_Symbol)]/; optPolyLog :> + +I/6*( + 12*I*Zeta2*Log[1 - x] - + 3*Pi*Log[1 - x]^2 - I*Log[1 - x]^3 - + 12*I*Zeta2*Log[1 + x] + + 6*Pi*Log[1 - x]*Log[1 + x] + + 3*I*Log[1 - x]^2*Log[1 + x] - + 3*Pi*Log[1 + x]^2 - + 3*I*Log[1 - x]*Log[1 + x]^2 + + I*Log[1 + x]^3 - + 6*I*PolyLog[3, (1 - x)/(1 + x)] + ), + + + PolyLog[3, -(1 - x_Symbol)/(1 + x_Symbol)]/; optPolyLog :> + ( + -(Zeta2*Log[2]) + Log[2]^3/3 - (Log[2]^2*Log[1 - x])/2 + Zeta2*Log[1 + x] - (Log[2]^2*Log[1 + x])/2 + Log[2]*Log[1 - x]*Log[1 + x] - + (Log[1 - x]*Log[1 + x]^2)/2 + Log[1 + x]^3/6 - PolyLog[3, (1 - x)/2] - PolyLog[3, (1 + x)/2] + Zeta[3] + ), + + PolyLog[3, -(1 - Sqrt[x_Symbol])/(1 + Sqrt[x_Symbol])]/; optSqrt && optPolyLog :> + ( + -(Zeta2*Log[2]) + Log[2]^3/3 - (Log[2]^2*Log[1 - Sqrt[x]])/2 + Zeta2*Log[1 + Sqrt[x]] - (Log[2]^2*Log[1 + Sqrt[x]])/2 + + Log[2]*Log[1 - Sqrt[x]]*Log[1 + Sqrt[x]] - (Log[1 - Sqrt[x]]*Log[1 + Sqrt[x]]^2)/2 + Log[1 + Sqrt[x]]^3/6 - PolyLog[3, (1 - Sqrt[x])/2] - + PolyLog[3, (1 + Sqrt[x])/2] + Zeta[3] + ), + + (*XY*) + (* + PolyLog[3, (1 - x_Symbol)/(1 + x_Symbol)] :> + -I/6*(12*I*Zeta2*Log[1 - x] - 3*Pi*Log[1 - x]^2 - I*Log[1 - x]^3 - + 12*I*Zeta2*Log[1 + x] + 6*Pi*Log[1 - x]*Log[1 + x] + + 3*I*Log[1 - x]^2*Log[1 + x] - 3*Pi*Log[1 + x]^2 - + 3*I*Log[1 - x]*Log[1 + x]^2 + I*Log[1 + x]^3 + + 6*I*PolyLog[3, (1 + x)/(1 - x)]) + *) + + PolyLog[2, (1 + x_Symbol)/(2*x_Symbol)]/; optPolyLog :> + ( + Pi^2/6 + + I*Pi*Log[2] - + Log[2]^2/2 + + Log[2]*Log[1 - x] + + I*Pi*Log[x] - + Log[2]*Log[x] + + Log[1 - x]*Log[x] - + Log[x]^2/2 - + I*Pi*Log[1 + x] - + Log[1 - x]*Log[1 + x] + + Log[1 + x]^2/2 + + PolyLog[2, (1 - x)/(1 + x)] + ), + + PolyLog[3, 2/(1 - x_Symbol)]/; optPolyLog :> + ( + Pi^2*Log[2] - + 3*I*Pi*Log[2]^2 + + Log[2]^3 - + Pi^2*Log[1 - x] + + 6*I*Pi*Log[2]*Log[1 - x] - + 3*I*Pi*Log[1 - x]^2 - + 3*Log[2]*Log[1 - x]^2 + + 2*Log[1 - x]^3 - + 3*Log[2]^2*Log[1 + x] + + 6*Log[2]*Log[1 - x]*Log[1 + x] - + 3*Log[1 - x]^2*Log[1 + x] - + 6*PolyLog[3, (1 + x)/2] - + 6*PolyLog[3, -((1 + x)/(1 - x))] + + 6*Zeta[3] + )/6, + + (* some weird formula, a shorter version below ... *) + + PolyLog[3, x_Symbol/(1 + x_Symbol)]/; optPolyLog :> + ( + 3*Zeta2*Log[1 + x] - + Log[-x]*Log[1 + x]^2 + + Log[x]*Log[1 + x]^2 + + Log[x]*PolyLog[2, -x] + + Log[x]*PolyLog[2, x/(1 + x)] - + PolyLog[3, -x] + + PolyLog[3, (1 + x)^(-1)] - + 2*PolyLog[3, 1 + x] + + Zeta[3] + ), + + PolyLog[3, Sqrt[x_Symbol]/(1 + Sqrt[x_Symbol])]/; optSqrt && optPolyLog :> + ( + -(Zeta2*Log[1 + Sqrt[x]]) + + Log[1 + Sqrt[x]]^3/3 - + (Log[1 + Sqrt[x]]^2*Log[Sqrt[x]])/2 - + PolyLog[3, (1 + Sqrt[x])^(-1)] - + PolyLog[3, -Sqrt[x]] + Zeta[3] + ), + + + PolyLog[3, 2 x_Symbol/(1 + x_Symbol)]/; optPolyLog :> + ( + 2*Zeta2*Log[2] - Log[2]^3/6 + (Log[2]^2*Log[x])/2 + (Log[2]*Log[x]^2)/2 + (Log[1 - x]*Log[x]^2)/2 + Log[x]^3/6 - Zeta2*Log[1 + x] + (Log[2]^2*Log[1 + x])/2 - + Log[2]*Log[1 - x]*Log[1 + x] - Log[2]*Log[x]*Log[1 + x] - Log[1 - x]*Log[x]*Log[1 + x] - Log[x]^2*Log[1 + x] + (Log[2]*Log[1 + x]^2)/2 + + Log[1 - x]*Log[1 + x]^2 + (3*Log[x]*Log[1 + x]^2)/2 - (5*Log[1 + x]^3)/6 + Log[x]*PolyLog[2, (1 - x)/(1 + x)] - Log[1 + x]*PolyLog[2, (1 - x)/(1 + x)] + + Log[x]*PolyLog[2, (2*x)/(1 + x)] - Log[1 + x]*PolyLog[2, (2*x)/(1 + x)] + PolyLog[3, (1 - x)/2] - PolyLog[3, -(1 - x)/(2*x)] + PolyLog[3, -((1 - x)/(1 + x))] - + PolyLog[3, (1 - x)/(1 + x)] + PolyLog[3, (1 + x)/2] + ), + + + PolyLog[3, 2 Sqrt[x_Symbol]/(1 + Sqrt[x_Symbol])]/; optSqrt && optPolyLog :> + ( + 2*Zeta2*Log[2] - Log[2]^3/6 - 2*Zeta2*Log[1 + Sqrt[x]] + (Log[2]^2*Log[1 + Sqrt[x]])/2 - (Log[2]*Log[1 + Sqrt[x]]^2)/2 + Log[1 + Sqrt[x]]^3/6 + + Zeta2*Log[Sqrt[x]] + (Log[2]^2*Log[Sqrt[x]])/2 - Log[2]*Log[1 - Sqrt[x]]*Log[Sqrt[x]] + Log[1 - Sqrt[x]]*Log[1 + Sqrt[x]]*Log[Sqrt[x]] - + (Log[1 + Sqrt[x]]^2*Log[Sqrt[x]])/2 + (Log[2]*Log[Sqrt[x]]^2)/2 - (Log[1 - Sqrt[x]]*Log[Sqrt[x]]^2)/2 + Log[Sqrt[x]]^3/6 + PolyLog[3, (1 - Sqrt[x])/2] + + PolyLog[3, -((1 - Sqrt[x])/(1 + Sqrt[x]))] - PolyLog[3, (1 - Sqrt[x])/(1 + Sqrt[x])] + PolyLog[3, (1 + Sqrt[x])/2] - PolyLog[3, -(1 - Sqrt[x])/(2*Sqrt[x])] + ), + + + PolyLog[3, (1-Sqrt[z_Symbol])/(1 + Sqrt[z_Symbol])]/; optSqrt && optPolyLog :> + ( + -(Zeta2*Log[2]) + Log[2]^3/3 + 2*Zeta2*Log[1 + Sqrt[z]] - Log[2]*Log[1 + Sqrt[z]]^2 + Log[1 + Sqrt[z]]^3/3 - (Log[2]^2*Log[1 - z])/2 + + Log[2]*Log[1 + Sqrt[z]]*Log[1 - z] - (Log[1 + Sqrt[z]]^2*Log[1 - z])/2 - PolyLog[3, (1 - Sqrt[z])/2] + 2*PolyLog[3, 1 - Sqrt[z]] + + 2*PolyLog[3, (1 + Sqrt[z])^(-1)] - PolyLog[3, (1 + Sqrt[z])/2] - PolyLog[3, 1 - z]/2 - (3*Zeta[3])/4 + ), + + PolyLog[3, x_Symbol/(1 + x_Symbol)]/; optPolyLog :> + ( + -Zeta2 Log[1 + x] - 1/2 Log[x] Log[1 + x]^2 + 1/3 Log[1 + x]^3 - + PolyLog[3, -x] - PolyLog[3, 1/(1 + x)] + Zeta[3] + ), + + PolyLog[4, -x_/(1-x_)]/; optPolyLog :> + ( + -Log[1 - x]^4/24 - + Nielsen[1, 3, x] + + Nielsen[2, 2, x] - + (Log[1 - x]^2*PolyLog[2, x])/2 + + Log[1 - x]*(-Nielsen[1, 2, x] + PolyLog[3, x]) - + PolyLog[4, x] + ), + + Log[1/x_Symbol]/; optLog :> + -Log[x], + + Log[1/x_Symbol^2]/; optLog :> + - 2 Log[x], + + Log[1/(x_Symbol+1)]/; optLog :> + -Log[x+1], + + Log[n_Integer?Positive/(x_Symbol+1)]/; optLog :> + Log[n]-Log[x+1], + + Log[Power[(x_Symbol+1),n_Integer]]/; n<0 && optLog :> + - n Log[x+1], + + Log[Power[(x_Symbol^2+1),n_Integer]]/; n<0 && optLog :> + - n Log[x^2+1], + + Log[x_Symbol/(x_Symbol+1)]/; optLog :> + Log[x]-Log[x+1], + + Log[1/(1-x_Symbol)]/; optLog :> + -Log[1-x], + + Log[n_Integer?Positive/(1-x_Symbol)]/; optLog :> + Log[n]-Log[1-x], + + Log[Power[(1-x_Symbol),n_Integer]]/; n<0 && optLog :> + - n Log[1-x], + + Log[Power[(1-x_Symbol^2),n_Integer]]/; n<0 && optLog :> + - n Log[1-x^2], + + Log[(n1_Integer?Positive - x_Symbol)/(n2_Integer?Positive - x_Symbol)] /; n1 >= 1 && n2 >= 1 && optLog :> + Log[n1 - x] - Log[n2 - x], + + Log[-1/x_Symbol]/; optLog :> + -Log[x] + I Pi, + + Log[-1/(1-x_Symbol)]/; optLog :> + -Log[1-x] + I Pi, + + Log[-x_Symbol]/; optLog :> + Log[x] + I Pi, + + Log[n_Integer?Negative x_Symbol]/; optLog :> + Log[-n] + Log[x] + I Pi, + + Log[-Sqrt[x_Symbol]]/; optSqrt :> + 1/2 Log[x] + I Pi, + + Log[(x_Symbol)^n_Integer?Positive]/; optLog :> + n Log[x], + + Log[-x_Symbol^2]/; optLog :> + 2 Log[x] + I Pi, + + Log[x_Symbol-1]/; optLog :> + Log[1-x] + I Pi, + + Log[(x_Symbol-1)/x_Symbol]/; optLog :> + Log[1-x]-Log[x]+I Pi, + + Log[-(1-x_Symbol)/x_Symbol]/; optLog :> + Log[1-x]-Log[x]+I Pi, + + Log[-1-x_Symbol]/; optLog :> + Log[1 + x] + I Pi, + + Log[1-x_Symbol^2]/; optLog :> + Log[1-x] + Log[1+x], + + Log[(1-x_Symbol) x_Symbol]/; optLog :> + Log[1-x] + Log[x], + + Log[(1-x_Symbol)/x_Symbol]/; optLog :> + Log[1-x] - Log[x], + + Log[(1-x_Symbol)/(1+x_Symbol)]/; optLog :> + Log[1-x] - Log[1+x], + + Log[(1+x_Symbol)/(1-x_Symbol)]/; optLog :> + Log[1+x] - Log[1-x], + + Log[(x_Symbol + 1)/x_Symbol]/; optLog :> + Log[x+1] - Log[x], + + Log[x_Symbol/(1-x_Symbol)]/; optLog :> + Log[x] -Log[1-x], + + Log[x_Symbol/(x_Symbol-1)]/; optLog :> + Log[x] -Log[1-x] + I Pi, + + Log[x_Symbol/(x_Symbol+1)]/; optLog :> + Log[x] -Log[1+x], + + Log[-x_Symbol/(1-x_Symbol)]/; optLog :> + Log[x] -Log[1-x] + I Pi, + + Log[(r_?NumberQ/; FreeQ[r, Complex]) x_]/; r>0 && optLog :> + Log[r] + Log[x] , + + Log[1-Sqrt[x_Symbol]]/; optSqrt && optLog :> + Log[1-x] - Log[1+Sqrt[x]], + + Log[Sqrt[x_Symbol]]/; optSqrt && optLog :> + 1/2 Log[x], + + Log[-((Sqrt[1 - x_Symbol] - Sqrt[-x_Symbol]) Power[-x_Symbol,-1/2])]/; optSqrt && optLog :> + Log[-(Sqrt[1 - x] - Sqrt[-x])] - Log[Sqrt[-x]], + + Log[Rational[-1, n_Integer?Positive] ((Sqrt[1 - x_Symbol] - Sqrt[-x_Symbol]) Power[-x_Symbol, -1/2])]/; optSqrt && optLog :> + Log[-(Sqrt[1 - x] - Sqrt[-x])] - Log[n Sqrt[-x]], + + Log[(Sqrt[1 - x_Symbol] + Sqrt[-x_Symbol]) Power[-x_Symbol,-1/2]]/; optSqrt && optLog :> + Log[(Sqrt[1 - x] + Sqrt[-x])] - Log[Sqrt[-x]], + + Log[(Sqrt[-x_Symbol] - Sqrt[1 - x_Symbol])]/; optSqrt && optLog :> + -Log[(Sqrt[-x] + Sqrt[1 - x])] + I Pi, + + Log[(Sqrt[1 - x_Symbol] - Sqrt[-x_Symbol])]/; optSqrt && optLog :> + -Log[Sqrt[1 - x] + Sqrt[-x]], + + Log[Sqrt[1 - x_Symbol] Power[-x_Symbol,-1/2]]/; optSqrt && optLog :> + Log[Sqrt[1 - x]] - Log[Sqrt[-x]], + + Log[Sqrt[1 - x_Symbol]/(Sqrt[1 - x_Symbol] + Sqrt[-x_Symbol])]/; optSqrt && optLog :> + 1/2 Log[1-x]- Log[Sqrt[1 - x] + Sqrt[-x]], + + Log[Sqrt[-x_Symbol]/(Sqrt[1 - x_Symbol] + Sqrt[-x_Symbol])]/; optSqrt && optLog :> + Log[Sqrt[-x]] - Log[Sqrt[1 - x] + Sqrt[-x]], + + Log[((Sqrt[1 - x_Symbol] - Sqrt[-x_Symbol]) Power[1-x_Symbol,-1/2])]/; optSqrt && optLog :> + Log[Sqrt[1-x]-Sqrt[-x]]-Log[Sqrt[1-x]], + + + Log[((Sqrt[1 - x_Symbol] + Sqrt[-x_Symbol]) Power[1-x_Symbol,-1/2])]/; optSqrt && optLog :> + Log[Sqrt[1-x]+Sqrt[-x]]-Log[Sqrt[1-x]], + + Log[Sqrt[- x_Symbol] Power[1-x_Symbol,-1/2]]/; optSqrt && optLog :> + Log[Sqrt[- x]] - Log[Sqrt[1-x]], + + + Log[Sqrt[-x_Symbol]]/; optSqrt && optLog :> + (I/2)*Pi + Log[x]/2, + + Log[-Sqrt[-x_Symbol]]/; optSqrt && optLog :> + -I Pi/2 + Log[x]/2, + + Log[Sqrt[1 - x_Symbol]]/; optSqrt && optLog :> + 1/2 Log[1 - x], + + Log[-Sqrt[1 - x_Symbol] Power[-x_Symbol,-1/2]]/; optSqrt && optLog :> + Log[-Sqrt[1 - x]] - Log[Sqrt[-x]], + + Log[-Sqrt[1 - x_Symbol]]/; optSqrt && optLog :> + Log[Sqrt[1 - x]] + I Pi, + + Log[Sqrt[x_Symbol]/(1 + Sqrt[x_Symbol])]/; optSqrt && optLog :> + Log[Sqrt[x]] - Log[1 + Sqrt[x]], + + Log[(1 - Sqrt[x_Symbol])/(1 + Sqrt[x_Symbol])]/; optSqrt && optLog :> + Log[1-Sqrt[x]] - Log[1+Sqrt[x]], + + Log[(1 + Sqrt[x_Symbol])/(1 - Sqrt[x_Symbol])]/; optSqrt && optLog :> + Log[1+Sqrt[x]] - Log[1-Sqrt[x]], + + Log[1/(1 - Sqrt[x_Symbol])]/; optSqrt && optLog :> + - Log[1-Sqrt[x]], + + Log[1/(1 + Sqrt[x_Symbol])]/; optSqrt && optLog :> + - Log[1+Sqrt[x]], + + Log[-(Sqrt[x_Symbol]/(1-Sqrt[x_Symbol]))]/; optSqrt && optLog :> + Log[-Sqrt[x]]-Log[1-Sqrt[x]], + + Log[(1 - 2 Sqrt[x_Symbol])/(1 - Sqrt[x_Symbol])]/; optSqrt && optLog :> + Log[1 - 2 Sqrt[x]] - Log[1 - Sqrt[x]], + + + Pi^2 :> + 6 Zeta2, + + Pi^3 :> + Pi 6 Zeta2, + + ArcSinh[z_Symbol]/; optTrig :> + Log[z + Sqrt[z^2 + 1]], + + ArcCosh[z_Symbol]/; optTrig :> + Log[z + Sqrt[z^2 - 1]], + + ArcTanh[z_Symbol]/; optTrig :> + 1/2 Log[(z+1)/(z-1)], + + Log[1-Complex[0,1]]/; optLog :> + (-I/4)*Pi + Log[2]/2, + + Log[1+Complex[0,1]]/; optLog :> + (I/4)*Pi + Log[2]/2, + + PolyLog[3,Complex[Rational[1,2],Rational[1,2]]]/; optPolyLog :> + ((21*I)/64)*Pi*Zeta2 + (Zeta2*Log[2])/32 + ((3*I)/32)*Pi*Log[2]^2 + Log[2]^3/48 - PolyLog[3, 1 + I] + (35*Zeta[3])/32, + + PolyLog[3,Complex[1,-1]]/; optPolyLog :> + (3*Zeta2*Log[2])/8 - PolyLog[3, 1 + I] + (35*Zeta[3])/32, + + PolyLog[3,Complex[0,1]]/; optPolyLog :> + ((3*I)/16)*Pi*Zeta2 - (3*Zeta[3])/32 + }; FCPrint[1,"SimplifyPolyLog.m loaded."]; diff --git a/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q1Q2ExtMom0To2.tid b/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q1Q2ExtMom0To2.tid new file mode 100644 index 000000000..a016be683 --- /dev/null +++ b/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q1Q2ExtMom0To2.tid @@ -0,0 +1,294 @@ +{ +tidl[{{q1_,mu_},{q1_,nu_},{q1_,rho_},{q2_,si_}},{},n_]/; q1=!=q2 :> + Block[{encli, m1, m2, m3, m4, m5, m6, s1, t1, t2}, + encli={(m3*m4*t1*t2)/(n*s1)+(m2*m5*t1*t2)/(n*s1)+(m1*m6*t1*t2)/(n*s1), + {s1->2+n},{t1->SP[q1,q1],t2->SP[q1,q2],m1->MT[mu,nu], + m2->MT[mu,rho],m3->MT[mu,si],m4->MT[nu,rho],m5->MT[nu,si], + m6->MT[rho,si]}}; + scpexp[encli,n]], +tidl[{{q1_,mu_},{q1_,nu_},{q1_,rho_},{q2_,si_}},{p1_},n_]/; q1=!=q2 :> + Block[{encli, m1, m2, m3, m4, m5, m6, s1, s2, s3, s4, s5, s6, s7, t1, t2, t3, t4, t5, v1, v2, v3, v4}, + encli={(m3*m4*s3*s6)/(s1*s2*t1^2)+(m2*m5*s3*s6)/(s1*s2*t1^2)+ + (m1*m6*s3*s6)/(s1*s2*t1^2)+(m6*s5*s6*v1*v2)/(s1*s2*t1^3)+ + (m5*s5*s6*v1*v3)/(s1*s2*t1^3)+(m3*s5*s6*v2*v3)/(s1*s2*t1^3)+ + (m4*s3*s4*v1*v4)/(s1*s2*t1^3)+(m2*s3*s4*v2*v4)/(s1*s2*t1^3)+ + (m1*s3*s4*v3*v4)/(s1*s2*t1^3)+(s7*v1*v2*v3*v4)/(s1*s2*t1^4), + {s1->-1+n,s2->1+n,s3->-t2^2+t1*t4, + s4->2*t2*t3+n*t2*t3-t1*t5,s5->2*t2^2+n*t2^2-t1*t4, + s6->-(t2*t3)+t1*t5,s7->8*t2^3*t3+6*n*t2^3*t3+n^2*t2^3*t3- + 6*t1*t2*t3*t4-3*n*t1*t2*t3*t4-6*t1*t2^2*t5-3*n*t1*t2^2*t5+ + 3*t1^2*t4*t5},{t1->SP[p1,p1],t2->SP[p1,q1],t3->SP[p1,q2], + t4->SP[q1,q1],t5->SP[q1,q2],t1->SP[p1,p1],v1->FV[p1,mu], + v2->FV[p1,nu],v3->FV[p1,rho],v4->FV[p1,si],m1->MT[mu,nu], + m2->MT[mu,rho],m3->MT[mu,si],m4->MT[nu,rho],m5->MT[nu,si], + m6->MT[rho,si]}}; + scpexp[encli,n]], +tidl[{{q1_,mu_},{q1_,nu_},{q1_,rho_},{q2_,si_}},{p1_, p2_},n_]/; q1=!=q2 :> + Block[{encli, m1, m2, m3, m4, m5, m6, s1, s10, s11, s12, s13, s14, s15, s16, s17, s18, s19, s2, s3, s4, s5, s6, s7, s8, s9, t1, t2, t3, t4, t5, t6, t7, t8, t9, v1, v2, v3, v4, v5, v6, v7, v8}, +encli={(m3*m4*s3*s4)/(n*s1*s2^2)+(m2*m5*s3*s4)/(n*s1*s2^2)+ +(m1*m6*s3*s4)/(n*s1*s2^2)+(m6*s4*s7*v1*v2)/(n*s1*s2^3)+ +(m5*s4*s7*v1*v3)/(n*s1*s2^3)+(m3*s4*s7*v2*v3)/(n*s1*s2^3)+ +(m4*s11*s3*v1*v4)/(n*s1*s2^3)+(m2*s11*s3*v2*v4)/(n*s1*s2^3)+ +(m1*s11*s3*v3*v4)/(n*s1*s2^3)+(s19*v1*v2*v3*v4)/(n*s1*s2^4)+ +(m6*s4*s6*v2*v5)/(n*s1*s2^3)+(m5*s4*s6*v3*v5)/(n*s1*s2^3)+ +(m4*s3*s9*v4*v5)/(n*s1*s2^3)+(s18*v2*v3*v4*v5)/(n*s1*s2^4)+ +(m6*s4*s6*v1*v6)/(n*s1*s2^3)+(m3*s4*s6*v3*v6)/(n*s1*s2^3)+ +(m2*s3*s9*v4*v6)/(n*s1*s2^3)+(s18*v1*v3*v4*v6)/(n*s1*s2^4)+ +(m6*s4*s5*v5*v6)/(n*s1*s2^3)+(s16*v3*v4*v5*v6)/(n*s1*s2^4)+ +(m5*s4*s6*v1*v7)/(n*s1*s2^3)+(m3*s4*s6*v2*v7)/(n*s1*s2^3)+ +(m1*s3*s9*v4*v7)/(n*s1*s2^3)+(s18*v1*v2*v4*v7)/(n*s1*s2^4)+ +(m5*s4*s5*v5*v7)/(n*s1*s2^3)+(s16*v2*v4*v5*v7)/(n*s1*s2^4)+ +(m3*s4*s5*v6*v7)/(n*s1*s2^3)+(s16*v1*v4*v6*v7)/(n*s1*s2^4)+ +(s13*v4*v5*v6*v7)/(n*s1*s2^4)+(m4*s10*s3*v1*v8)/(n*s1*s2^3)+ +(m2*s10*s3*v2*v8)/(n*s1*s2^3)+(m1*s10*s3*v3*v8)/(n*s1*s2^3)+ +(s17*v1*v2*v3*v8)/(n*s1*s2^4)+(m4*s3*s8*v5*v8)/(n*s1*s2^3)+ +(s15*v2*v3*v5*v8)/(n*s1*s2^4)+(m2*s3*s8*v6*v8)/(n*s1*s2^3)+ +(s15*v1*v3*v6*v8)/(n*s1*s2^4)+(s14*v3*v5*v6*v8)/(n*s1*s2^4)+ +(m1*s3*s8*v7*v8)/(n*s1*s2^3)+(s15*v1*v2*v7*v8)/(n*s1*s2^4)+ +(s14*v2*v5*v7*v8)/(n*s1*s2^4)+(s14*v1*v6*v7*v8)/(n*s1*s2^4)+ +(s12*v5*v6*v7*v8)/(n*s1*s2^4),{s1->-2+n,s2->t2^2-t1*t5, +s3->t3^2*t5-2*t2*t3*t6+t1*t6^2+t2^2*t8-t1*t5*t8, +s4->t3*t4*t5-t2*t4*t6-t2*t3*t7+t1*t6*t7+t2^2*t9-t1*t5*t9, +s5->n*t2^2*t3^2+t1*t3^2*t5-2*t1*t2*t3*t6-2*n*t1*t2*t3*t6+ +t1^2*t6^2+n*t1^2*t6^2+t1*t2^2*t8-t1^2*t5*t8, +s6->-(t2*t3^2*t5)-n*t2*t3^2*t5+2*t2^2*t3*t6+n*t2^2*t3*t6+ +n*t1*t3*t5*t6-t1*t2*t6^2-n*t1*t2*t6^2-t2^3*t8+t1*t2*t5*t8, +s7->t3^2*t5^2+n*t3^2*t5^2-2*t2*t3*t5*t6-2*n*t2*t3*t5*t6+ +n*t2^2*t6^2+t1*t5*t6^2+t2^2*t5*t8-t1*t5^2*t8, +s8->n*t2^2*t3*t4+t1*t3*t4*t5-t1*t2*t4*t6-n*t1*t2*t4*t6- +t1*t2*t3*t7-n*t1*t2*t3*t7+t1^2*t6*t7+n*t1^2*t6*t7+t1*t2^2*t9- +t1^2*t5*t9,s9->-(t2*t3*t4*t5)-n*t2*t3*t4*t5+t2^2*t4*t6+ +n*t1*t4*t5*t6+t2^2*t3*t7+n*t2^2*t3*t7-t1*t2*t6*t7-n*t1*t2*t6*t7- +t2^3*t9+t1*t2*t5*t9,s10->-(t2*t3*t4*t5)-n*t2*t3*t4*t5+ +t2^2*t4*t6+n*t2^2*t4*t6+t2^2*t3*t7+n*t1*t3*t5*t7-t1*t2*t6*t7- +n*t1*t2*t6*t7-t2^3*t9+t1*t2*t5*t9, +s11->t3*t4*t5^2+n*t3*t4*t5^2-t2*t4*t5*t6-n*t2*t4*t5*t6- +t2*t3*t5*t7-n*t2*t3*t5*t7+n*t2^2*t6*t7+t1*t5*t6*t7+t2^2*t5*t9- +t1*t5^2*t9,s12->-2*n*t2^4*t3^3*t4+n^2*t2^4*t3^3*t4+ +6*n*t1*t2^2*t3^3*t4*t5+3*t1^2*t3^3*t4*t5^2-3*n*t1*t2^3*t3^2*t4*t6- +3*n^2*t1*t2^3*t3^2*t4*t6-9*t1^2*t2*t3^2*t4*t5*t6- +9*n*t1^2*t2*t3^2*t4*t5*t6+6*t1^2*t2^2*t3*t4*t6^2+ +9*n*t1^2*t2^2*t3*t4*t6^2+3*n^2*t1^2*t2^2*t3*t4*t6^2+ +3*t1^3*t3*t4*t5*t6^2+3*n*t1^3*t3*t4*t5*t6^2-3*t1^3*t2*t4*t6^3- +4*n*t1^3*t2*t4*t6^3-n^2*t1^3*t2*t4*t6^3-n*t1*t2^3*t3^3*t7- +n^2*t1*t2^3*t3^3*t7-3*t1^2*t2*t3^3*t5*t7-3*n*t1^2*t2*t3^3*t5*t7+ +6*t1^2*t2^2*t3^2*t6*t7+9*n*t1^2*t2^2*t3^2*t6*t7+ +3*n^2*t1^2*t2^2*t3^2*t6*t7+3*t1^3*t3^2*t5*t6*t7+ +3*n*t1^3*t3^2*t5*t6*t7-9*t1^3*t2*t3*t6^2*t7-12*n*t1^3*t2*t3*t6^2*t7- +3*n^2*t1^3*t2*t3*t6^2*t7+3*t1^4*t6^3*t7+4*n*t1^4*t6^3*t7+ +n^2*t1^4*t6^3*t7+3*n*t1*t2^4*t3*t4*t8+3*t1^2*t2^2*t3*t4*t5*t8- +3*n*t1^2*t2^2*t3*t4*t5*t8-3*t1^3*t3*t4*t5^2*t8-3*t1^2*t2^3*t4*t6*t8- +3*n*t1^2*t2^3*t4*t6*t8+3*t1^3*t2*t4*t5*t6*t8+ +3*n*t1^3*t2*t4*t5*t6*t8-3*t1^2*t2^3*t3*t7*t8-3*n*t1^2*t2^3*t3*t7*t8+ +3*t1^3*t2*t3*t5*t7*t8+3*n*t1^3*t2*t3*t5*t7*t8+3*t1^3*t2^2*t6*t7*t8+ +3*n*t1^3*t2^2*t6*t7*t8-3*t1^4*t5*t6*t7*t8-3*n*t1^4*t5*t6*t7*t8+ +3*n*t1*t2^4*t3^2*t9+3*t1^2*t2^2*t3^2*t5*t9-3*n*t1^2*t2^2*t3^2*t5*t9- +3*t1^3*t3^2*t5^2*t9-6*t1^2*t2^3*t3*t6*t9-6*n*t1^2*t2^3*t3*t6*t9+ +6*t1^3*t2*t3*t5*t6*t9+6*n*t1^3*t2*t3*t5*t6*t9+3*t1^3*t2^2*t6^2*t9+ +3*n*t1^3*t2^2*t6^2*t9-3*t1^4*t5*t6^2*t9-3*n*t1^4*t5*t6^2*t9+ +3*t1^2*t2^4*t8*t9-6*t1^3*t2^2*t5*t8*t9+3*t1^4*t5^2*t8*t9, +s13->-(n*t2^3*t3^3*t4*t5)-n^2*t2^3*t3^3*t4*t5-3*t1*t2*t3^3*t4*t5^2- +3*n*t1*t2*t3^3*t4*t5^2+3*n*t2^4*t3^2*t4*t6+9*t1*t2^2*t3^2*t4*t5*t6+ +6*n*t1*t2^2*t3^2*t4*t5*t6+3*n^2*t1*t2^2*t3^2*t4*t5*t6+ +3*n*t1^2*t3^2*t4*t5^2*t6-6*t1*t2^3*t3*t4*t6^2- +6*n*t1*t2^3*t3*t4*t6^2-3*t1^2*t2*t3*t4*t5*t6^2- +6*n*t1^2*t2*t3*t4*t5*t6^2-3*n^2*t1^2*t2*t3*t4*t5*t6^2+ +3*t1^2*t2^2*t4*t6^3+3*n*t1^2*t2^2*t4*t6^3+n*t1^3*t4*t5*t6^3+ +n^2*t1^3*t4*t5*t6^3+n*t2^4*t3^3*t7+n^2*t2^4*t3^3*t7+ +3*t1*t2^2*t3^3*t5*t7+3*n*t1*t2^2*t3^3*t5*t7-6*t1*t2^3*t3^2*t6*t7- +9*n*t1*t2^3*t3^2*t6*t7-3*n^2*t1*t2^3*t3^2*t6*t7- +3*t1^2*t2*t3^2*t5*t6*t7-3*n*t1^2*t2*t3^2*t5*t6*t7+ +9*t1^2*t2^2*t3*t6^2*t7+12*n*t1^2*t2^2*t3*t6^2*t7+ +3*n^2*t1^2*t2^2*t3*t6^2*t7-3*t1^3*t2*t6^3*t7-4*n*t1^3*t2*t6^3*t7- +n^2*t1^3*t2*t6^3*t7-3*t1*t2^3*t3*t4*t5*t8-3*n*t1*t2^3*t3*t4*t5*t8+ +3*t1^2*t2*t3*t4*t5^2*t8+3*n*t1^2*t2*t3*t4*t5^2*t8+ +3*t1*t2^4*t4*t6*t8-3*t1^2*t2^2*t4*t5*t6*t8+ +3*n*t1^2*t2^2*t4*t5*t6*t8-3*n*t1^3*t4*t5^2*t6*t8+3*t1*t2^4*t3*t7*t8+ +3*n*t1*t2^4*t3*t7*t8-3*t1^2*t2^2*t3*t5*t7*t8- +3*n*t1^2*t2^2*t3*t5*t7*t8-3*t1^2*t2^3*t6*t7*t8- +3*n*t1^2*t2^3*t6*t7*t8+3*t1^3*t2*t5*t6*t7*t8+ +3*n*t1^3*t2*t5*t6*t7*t8-3*n*t2^5*t3^2*t9-3*t1*t2^3*t3^2*t5*t9+ +3*n*t1*t2^3*t3^2*t5*t9+3*t1^2*t2*t3^2*t5^2*t9+6*t1*t2^4*t3*t6*t9+ +6*n*t1*t2^4*t3*t6*t9-6*t1^2*t2^2*t3*t5*t6*t9- +6*n*t1^2*t2^2*t3*t5*t6*t9-3*t1^2*t2^3*t6^2*t9-3*n*t1^2*t2^3*t6^2*t9+ +3*t1^3*t2*t5*t6^2*t9+3*n*t1^3*t2*t5*t6^2*t9-3*t1*t2^5*t8*t9+ +6*t1^2*t2^3*t5*t8*t9-3*t1^3*t2*t5^2*t8*t9, +s14->-(n*t2^3*t3^3*t4*t5)-n^2*t2^3*t3^3*t4*t5-3*t1*t2*t3^3*t4*t5^2- +3*n*t1*t2*t3^3*t4*t5^2+3*n*t2^4*t3^2*t4*t6+n^2*t2^4*t3^2*t4*t6+ +9*t1*t2^2*t3^2*t4*t5*t6+7*n*t1*t2^2*t3^2*t4*t5*t6+ +2*n^2*t1*t2^2*t3^2*t4*t5*t6+2*n*t1^2*t3^2*t4*t5^2*t6- +6*t1*t2^3*t3*t4*t6^2-8*n*t1*t2^3*t3*t4*t6^2- +2*n^2*t1*t2^3*t3*t4*t6^2-3*t1^2*t2*t3*t4*t5*t6^2- +4*n*t1^2*t2*t3*t4*t5*t6^2-n^2*t1^2*t2*t3*t4*t5*t6^2+ +3*t1^2*t2^2*t4*t6^3+4*n*t1^2*t2^2*t4*t6^3+n^2*t1^2*t2^2*t4*t6^3+ +n*t2^4*t3^3*t7+3*t1*t2^2*t3^3*t5*t7+2*n*t1*t2^2*t3^3*t5*t7+ +n^2*t1*t2^2*t3^3*t5*t7+n*t1^2*t3^3*t5^2*t7-6*t1*t2^3*t3^2*t6*t7- +7*n*t1*t2^3*t3^2*t6*t7-n^2*t1*t2^3*t3^2*t6*t7- +3*t1^2*t2*t3^2*t5*t6*t7-5*n*t1^2*t2*t3^2*t5*t6*t7- +2*n^2*t1^2*t2*t3^2*t5*t6*t7+9*t1^2*t2^2*t3*t6^2*t7+ +11*n*t1^2*t2^2*t3*t6^2*t7+2*n^2*t1^2*t2^2*t3*t6^2*t7+ +n*t1^3*t3*t5*t6^2*t7+n^2*t1^3*t3*t5*t6^2*t7-3*t1^3*t2*t6^3*t7- +4*n*t1^3*t2*t6^3*t7-n^2*t1^3*t2*t6^3*t7-2*n*t2^5*t3*t4*t8- +3*t1*t2^3*t3*t4*t5*t8+n*t1*t2^3*t3*t4*t5*t8+3*t1^2*t2*t3*t4*t5^2*t8+ +n*t1^2*t2*t3*t4*t5^2*t8+3*t1*t2^4*t4*t6*t8+3*n*t1*t2^4*t4*t6*t8- +3*t1^2*t2^2*t4*t5*t6*t8-3*n*t1^2*t2^2*t4*t5*t6*t8+ +3*t1*t2^4*t3*t7*t8+2*n*t1*t2^4*t3*t7*t8-3*t1^2*t2^2*t3*t5*t7*t8- +n*t1^2*t2^2*t3*t5*t7*t8-n*t1^3*t3*t5^2*t7*t8-3*t1^2*t2^3*t6*t7*t8- +3*n*t1^2*t2^3*t6*t7*t8+3*t1^3*t2*t5*t6*t7*t8+ +3*n*t1^3*t2*t5*t6*t7*t8-n*t2^5*t3^2*t9-3*t1*t2^3*t3^2*t5*t9- +n*t1*t2^3*t3^2*t5*t9+3*t1^2*t2*t3^2*t5^2*t9+ +2*n*t1^2*t2*t3^2*t5^2*t9+6*t1*t2^4*t3*t6*t9+4*n*t1*t2^4*t3*t6*t9- +6*t1^2*t2^2*t3*t5*t6*t9-2*n*t1^2*t2^2*t3*t5*t6*t9- +2*n*t1^3*t3*t5^2*t6*t9-3*t1^2*t2^3*t6^2*t9-3*n*t1^2*t2^3*t6^2*t9+ +3*t1^3*t2*t5*t6^2*t9+3*n*t1^3*t2*t5*t6^2*t9-3*t1*t2^5*t8*t9+ +6*t1^2*t2^3*t5*t8*t9-3*t1^3*t2*t5^2*t8*t9, +s15->2*t2^2*t3^3*t4*t5^2+3*n*t2^2*t3^3*t4*t5^2+ +n^2*t2^2*t3^3*t4*t5^2+t1*t3^3*t4*t5^3+n*t1*t3^3*t4*t5^3- +6*t2^3*t3^2*t4*t5*t6-8*n*t2^3*t3^2*t4*t5*t6- +2*n^2*t2^3*t3^2*t4*t5*t6-3*t1*t2*t3^2*t4*t5^2*t6- +4*n*t1*t2*t3^2*t4*t5^2*t6-n^2*t1*t2*t3^2*t4*t5^2*t6+ +4*t2^4*t3*t4*t6^2+4*n*t2^4*t3*t4*t6^2+n^2*t2^4*t3*t4*t6^2+ +4*t1*t2^2*t3*t4*t5*t6^2+8*n*t1*t2^2*t3*t4*t5*t6^2+ +2*n^2*t1*t2^2*t3*t4*t5*t6^2+t1^2*t3*t4*t5^2*t6^2-2*t1*t2^3*t4*t6^3- +3*n*t1*t2^3*t4*t6^3-n^2*t1*t2^3*t4*t6^3-t1^2*t2*t4*t5*t6^3- +n*t1^2*t2*t4*t5*t6^3-2*t2^3*t3^3*t5*t7-2*n*t2^3*t3^3*t5*t7- +t1*t2*t3^3*t5^2*t7-2*n*t1*t2*t3^3*t5^2*t7-n^2*t1*t2*t3^3*t5^2*t7+ +4*t2^4*t3^2*t6*t7+2*n*t2^4*t3^2*t6*t7+4*t1*t2^2*t3^2*t5*t6*t7+ +10*n*t1*t2^2*t3^2*t5*t6*t7+2*n^2*t1*t2^2*t3^2*t5*t6*t7+ +t1^2*t3^2*t5^2*t6*t7+n^2*t1^2*t3^2*t5^2*t6*t7-6*t1*t2^3*t3*t6^2*t7- +7*n*t1*t2^3*t3*t6^2*t7-n^2*t1*t2^3*t3*t6^2*t7- +3*t1^2*t2*t3*t5*t6^2*t7-5*n*t1^2*t2*t3*t5*t6^2*t7- +2*n^2*t1^2*t2*t3*t5*t6^2*t7+2*t1^2*t2^2*t6^3*t7+ +3*n*t1^2*t2^2*t6^3*t7+n^2*t1^2*t2^2*t6^3*t7+t1^3*t5*t6^3*t7+ +n*t1^3*t5*t6^3*t7+2*t2^4*t3*t4*t5*t8+3*n*t2^4*t3*t4*t5*t8- +t1*t2^2*t3*t4*t5^2*t8-3*n*t1*t2^2*t3*t4*t5^2*t8-t1^2*t3*t4*t5^3*t8- +2*t2^5*t4*t6*t8-2*n*t2^5*t4*t6*t8+t1*t2^3*t4*t5*t6*t8+ +n*t1*t2^3*t4*t5*t6*t8+t1^2*t2*t4*t5^2*t6*t8+n*t1^2*t2*t4*t5^2*t6*t8- +2*t2^5*t3*t7*t8+t1*t2^3*t3*t5*t7*t8-3*n*t1*t2^3*t3*t5*t7*t8+ +t1^2*t2*t3*t5^2*t7*t8+3*n*t1^2*t2*t3*t5^2*t7*t8+2*t1*t2^4*t6*t7*t8+ +2*n*t1*t2^4*t6*t7*t8-t1^2*t2^2*t5*t6*t7*t8-n*t1^2*t2^2*t5*t6*t7*t8- +t1^3*t5^2*t6*t7*t8-n*t1^3*t5^2*t6*t7*t8+2*t2^4*t3^2*t5*t9+ +2*n*t2^4*t3^2*t5*t9-t1*t2^2*t3^2*t5^2*t9-n*t1*t2^2*t3^2*t5^2*t9- +t1^2*t3^2*t5^3*t9-n*t1^2*t3^2*t5^3*t9-4*t2^5*t3*t6*t9- +2*n*t2^5*t3*t6*t9+2*t1*t2^3*t3*t5*t6*t9-2*n*t1*t2^3*t3*t5*t6*t9+ +2*t1^2*t2*t3*t5^2*t6*t9+4*n*t1^2*t2*t3*t5^2*t6*t9+2*t1*t2^4*t6^2*t9+ +3*n*t1*t2^4*t6^2*t9-t1^2*t2^2*t5*t6^2*t9-3*n*t1^2*t2^2*t5*t6^2*t9- +t1^3*t5^2*t6^2*t9+2*t2^6*t8*t9-3*t1*t2^4*t5*t8*t9+t1^3*t5^3*t8*t9, +s16->2*t2^2*t3^3*t4*t5^2+3*n*t2^2*t3^3*t4*t5^2+ +n^2*t2^2*t3^3*t4*t5^2+t1*t3^3*t4*t5^3+n*t1*t3^3*t4*t5^3- +6*t2^3*t3^2*t4*t5*t6-7*n*t2^3*t3^2*t4*t5*t6-n^2*t2^3*t3^2*t4*t5*t6- +3*t1*t2*t3^2*t4*t5^2*t6-5*n*t1*t2*t3^2*t4*t5^2*t6- +2*n^2*t1*t2*t3^2*t4*t5^2*t6+4*t2^4*t3*t4*t6^2+2*n*t2^4*t3*t4*t6^2+ +4*t1*t2^2*t3*t4*t5*t6^2+10*n*t1*t2^2*t3*t4*t5*t6^2+ +2*n^2*t1*t2^2*t3*t4*t5*t6^2+t1^2*t3*t4*t5^2*t6^2+ +n^2*t1^2*t3*t4*t5^2*t6^2-2*t1*t2^3*t4*t6^3-2*n*t1*t2^3*t4*t6^3- +t1^2*t2*t4*t5*t6^3-2*n*t1^2*t2*t4*t5*t6^3-n^2*t1^2*t2*t4*t5*t6^3- +2*t2^3*t3^3*t5*t7-3*n*t2^3*t3^3*t5*t7-n^2*t2^3*t3^3*t5*t7- +t1*t2*t3^3*t5^2*t7-n*t1*t2*t3^3*t5^2*t7+4*t2^4*t3^2*t6*t7+ +4*n*t2^4*t3^2*t6*t7+n^2*t2^4*t3^2*t6*t7+4*t1*t2^2*t3^2*t5*t6*t7+ +8*n*t1*t2^2*t3^2*t5*t6*t7+2*n^2*t1*t2^2*t3^2*t5*t6*t7+ +t1^2*t3^2*t5^2*t6*t7-6*t1*t2^3*t3*t6^2*t7-8*n*t1*t2^3*t3*t6^2*t7- +2*n^2*t1*t2^3*t3*t6^2*t7-3*t1^2*t2*t3*t5*t6^2*t7- +4*n*t1^2*t2*t3*t5*t6^2*t7-n^2*t1^2*t2*t3*t5*t6^2*t7+ +2*t1^2*t2^2*t6^3*t7+3*n*t1^2*t2^2*t6^3*t7+n^2*t1^2*t2^2*t6^3*t7+ +t1^3*t5*t6^3*t7+n*t1^3*t5*t6^3*t7+2*t2^4*t3*t4*t5*t8+ +2*n*t2^4*t3*t4*t5*t8-t1*t2^2*t3*t4*t5^2*t8-n*t1*t2^2*t3*t4*t5^2*t8- +t1^2*t3*t4*t5^3*t8-n*t1^2*t3*t4*t5^3*t8-2*t2^5*t4*t6*t8+ +t1*t2^3*t4*t5*t6*t8-3*n*t1*t2^3*t4*t5*t6*t8+t1^2*t2*t4*t5^2*t6*t8+ +3*n*t1^2*t2*t4*t5^2*t6*t8-2*t2^5*t3*t7*t8-2*n*t2^5*t3*t7*t8+ +t1*t2^3*t3*t5*t7*t8+n*t1*t2^3*t3*t5*t7*t8+t1^2*t2*t3*t5^2*t7*t8+ +n*t1^2*t2*t3*t5^2*t7*t8+2*t1*t2^4*t6*t7*t8+3*n*t1*t2^4*t6*t7*t8- +t1^2*t2^2*t5*t6*t7*t8-3*n*t1^2*t2^2*t5*t6*t7*t8-t1^3*t5^2*t6*t7*t8+ +2*t2^4*t3^2*t5*t9+3*n*t2^4*t3^2*t5*t9-t1*t2^2*t3^2*t5^2*t9- +3*n*t1*t2^2*t3^2*t5^2*t9-t1^2*t3^2*t5^3*t9-4*t2^5*t3*t6*t9- +2*n*t2^5*t3*t6*t9+2*t1*t2^3*t3*t5*t6*t9-2*n*t1*t2^3*t3*t5*t6*t9+ +2*t1^2*t2*t3*t5^2*t6*t9+4*n*t1^2*t2*t3*t5^2*t6*t9+2*t1*t2^4*t6^2*t9+ +2*n*t1*t2^4*t6^2*t9-t1^2*t2^2*t5*t6^2*t9-n*t1^2*t2^2*t5*t6^2*t9- +t1^3*t5^2*t6^2*t9-n*t1^3*t5^2*t6^2*t9+2*t2^6*t8*t9- +3*t1*t2^4*t5*t8*t9+t1^3*t5^3*t8*t9, +s17->-3*t2*t3^3*t4*t5^3-4*n*t2*t3^3*t4*t5^3-n^2*t2*t3^3*t4*t5^3+ +9*t2^2*t3^2*t4*t5^2*t6+12*n*t2^2*t3^2*t4*t5^2*t6+ +3*n^2*t2^2*t3^2*t4*t5^2*t6-6*t2^3*t3*t4*t5*t6^2- +9*n*t2^3*t3*t4*t5*t6^2-3*n^2*t2^3*t3*t4*t5*t6^2- +3*t1*t2*t3*t4*t5^2*t6^2-3*n*t1*t2*t3*t4*t5^2*t6^2+n*t2^4*t4*t6^3+ +n^2*t2^4*t4*t6^3+3*t1*t2^2*t4*t5*t6^3+3*n*t1*t2^2*t4*t5*t6^3+ +3*t2^2*t3^3*t5^2*t7+3*n*t2^2*t3^3*t5^2*t7+n*t1*t3^3*t5^3*t7+ +n^2*t1*t3^3*t5^3*t7-6*t2^3*t3^2*t5*t6*t7-6*n*t2^3*t3^2*t5*t6*t7- +3*t1*t2*t3^2*t5^2*t6*t7-6*n*t1*t2*t3^2*t5^2*t6*t7- +3*n^2*t1*t2*t3^2*t5^2*t6*t7+3*n*t2^4*t3*t6^2*t7+ +9*t1*t2^2*t3*t5*t6^2*t7+6*n*t1*t2^2*t3*t5*t6^2*t7+ +3*n^2*t1*t2^2*t3*t5*t6^2*t7+3*n*t1^2*t3*t5^2*t6^2*t7- +n*t1*t2^3*t6^3*t7-n^2*t1*t2^3*t6^3*t7-3*t1^2*t2*t5*t6^3*t7- +3*n*t1^2*t2*t5*t6^3*t7-3*t2^3*t3*t4*t5^2*t8-3*n*t2^3*t3*t4*t5^2*t8+ +3*t1*t2*t3*t4*t5^3*t8+3*n*t1*t2*t3*t4*t5^3*t8+3*t2^4*t4*t5*t6*t8+ +3*n*t2^4*t4*t5*t6*t8-3*t1*t2^2*t4*t5^2*t6*t8- +3*n*t1*t2^2*t4*t5^2*t6*t8+3*t2^4*t3*t5*t7*t8- +3*t1*t2^2*t3*t5^2*t7*t8+3*n*t1*t2^2*t3*t5^2*t7*t8- +3*n*t1^2*t3*t5^3*t7*t8-3*t1*t2^3*t5*t6*t7*t8- +3*n*t1*t2^3*t5*t6*t7*t8+3*t1^2*t2*t5^2*t6*t7*t8+ +3*n*t1^2*t2*t5^2*t6*t7*t8-3*t2^3*t3^2*t5^2*t9-3*n*t2^3*t3^2*t5^2*t9+ +3*t1*t2*t3^2*t5^3*t9+3*n*t1*t2*t3^2*t5^3*t9+6*t2^4*t3*t5*t6*t9+ +6*n*t2^4*t3*t5*t6*t9-6*t1*t2^2*t3*t5^2*t6*t9- +6*n*t1*t2^2*t3*t5^2*t6*t9-3*n*t2^5*t6^2*t9-3*t1*t2^3*t5*t6^2*t9+ +3*n*t1*t2^3*t5*t6^2*t9+3*t1^2*t2*t5^2*t6^2*t9-3*t2^5*t5*t8*t9+ +6*t1*t2^3*t5^2*t8*t9-3*t1^2*t2*t5^3*t8*t9, +s18->-3*t2*t3^3*t4*t5^3-4*n*t2*t3^3*t4*t5^3-n^2*t2*t3^3*t4*t5^3+ +9*t2^2*t3^2*t4*t5^2*t6+11*n*t2^2*t3^2*t4*t5^2*t6+ +2*n^2*t2^2*t3^2*t4*t5^2*t6+n*t1*t3^2*t4*t5^3*t6+ +n^2*t1*t3^2*t4*t5^3*t6-6*t2^3*t3*t4*t5*t6^2-7*n*t2^3*t3*t4*t5*t6^2- +n^2*t2^3*t3*t4*t5*t6^2-3*t1*t2*t3*t4*t5^2*t6^2- +5*n*t1*t2*t3*t4*t5^2*t6^2-2*n^2*t1*t2*t3*t4*t5^2*t6^2+ +n*t2^4*t4*t6^3+3*t1*t2^2*t4*t5*t6^3+2*n*t1*t2^2*t4*t5*t6^3+ +n^2*t1*t2^2*t4*t5*t6^3+n*t1^2*t4*t5^2*t6^3+3*t2^2*t3^3*t5^2*t7+ +4*n*t2^2*t3^3*t5^2*t7+n^2*t2^2*t3^3*t5^2*t7-6*t2^3*t3^2*t5*t6*t7- +8*n*t2^3*t3^2*t5*t6*t7-2*n^2*t2^3*t3^2*t5*t6*t7- +3*t1*t2*t3^2*t5^2*t6*t7-4*n*t1*t2*t3^2*t5^2*t6*t7- +n^2*t1*t2*t3^2*t5^2*t6*t7+3*n*t2^4*t3*t6^2*t7+n^2*t2^4*t3*t6^2*t7+ +9*t1*t2^2*t3*t5*t6^2*t7+7*n*t1*t2^2*t3*t5*t6^2*t7+ +2*n^2*t1*t2^2*t3*t5*t6^2*t7+2*n*t1^2*t3*t5^2*t6^2*t7- +n*t1*t2^3*t6^3*t7-n^2*t1*t2^3*t6^3*t7-3*t1^2*t2*t5*t6^3*t7- +3*n*t1^2*t2*t5*t6^3*t7-3*t2^3*t3*t4*t5^2*t8-3*n*t2^3*t3*t4*t5^2*t8+ +3*t1*t2*t3*t4*t5^3*t8+3*n*t1*t2*t3*t4*t5^3*t8+3*t2^4*t4*t5*t6*t8+ +2*n*t2^4*t4*t5*t6*t8-3*t1*t2^2*t4*t5^2*t6*t8- +n*t1*t2^2*t4*t5^2*t6*t8-n*t1^2*t4*t5^3*t6*t8+3*t2^4*t3*t5*t7*t8+ +3*n*t2^4*t3*t5*t7*t8-3*t1*t2^2*t3*t5^2*t7*t8- +3*n*t1*t2^2*t3*t5^2*t7*t8-2*n*t2^5*t6*t7*t8-3*t1*t2^3*t5*t6*t7*t8+ +n*t1*t2^3*t5*t6*t7*t8+3*t1^2*t2*t5^2*t6*t7*t8+ +n*t1^2*t2*t5^2*t6*t7*t8-3*t2^3*t3^2*t5^2*t9-3*n*t2^3*t3^2*t5^2*t9+ +3*t1*t2*t3^2*t5^3*t9+3*n*t1*t2*t3^2*t5^3*t9+6*t2^4*t3*t5*t6*t9+ +4*n*t2^4*t3*t5*t6*t9-6*t1*t2^2*t3*t5^2*t6*t9- +2*n*t1*t2^2*t3*t5^2*t6*t9-2*n*t1^2*t3*t5^3*t6*t9-n*t2^5*t6^2*t9- +3*t1*t2^3*t5*t6^2*t9-n*t1*t2^3*t5*t6^2*t9+3*t1^2*t2*t5^2*t6^2*t9+ +2*n*t1^2*t2*t5^2*t6^2*t9-3*t2^5*t5*t8*t9+6*t1*t2^3*t5^2*t8*t9- +3*t1^2*t2*t5^3*t8*t9,s19->3*t3^3*t4*t5^4+4*n*t3^3*t4*t5^4+ +n^2*t3^3*t4*t5^4-9*t2*t3^2*t4*t5^3*t6-12*n*t2*t3^2*t4*t5^3*t6- +3*n^2*t2*t3^2*t4*t5^3*t6+6*t2^2*t3*t4*t5^2*t6^2+ +9*n*t2^2*t3*t4*t5^2*t6^2+3*n^2*t2^2*t3*t4*t5^2*t6^2+ +3*t1*t3*t4*t5^3*t6^2+3*n*t1*t3*t4*t5^3*t6^2-n*t2^3*t4*t5*t6^3- +n^2*t2^3*t4*t5*t6^3-3*t1*t2*t4*t5^2*t6^3-3*n*t1*t2*t4*t5^2*t6^3- +3*t2*t3^3*t5^3*t7-4*n*t2*t3^3*t5^3*t7-n^2*t2*t3^3*t5^3*t7+ +6*t2^2*t3^2*t5^2*t6*t7+9*n*t2^2*t3^2*t5^2*t6*t7+ +3*n^2*t2^2*t3^2*t5^2*t6*t7+3*t1*t3^2*t5^3*t6*t7+ +3*n*t1*t3^2*t5^3*t6*t7-3*n*t2^3*t3*t5*t6^2*t7- +3*n^2*t2^3*t3*t5*t6^2*t7-9*t1*t2*t3*t5^2*t6^2*t7- +9*n*t1*t2*t3*t5^2*t6^2*t7-2*n*t2^4*t6^3*t7+n^2*t2^4*t6^3*t7+ +6*n*t1*t2^2*t5*t6^3*t7+3*t1^2*t5^2*t6^3*t7+3*t2^2*t3*t4*t5^3*t8+ +3*n*t2^2*t3*t4*t5^3*t8-3*t1*t3*t4*t5^4*t8-3*n*t1*t3*t4*t5^4*t8- +3*t2^3*t4*t5^2*t6*t8-3*n*t2^3*t4*t5^2*t6*t8+3*t1*t2*t4*t5^3*t6*t8+ +3*n*t1*t2*t4*t5^3*t6*t8-3*t2^3*t3*t5^2*t7*t8-3*n*t2^3*t3*t5^2*t7*t8+ +3*t1*t2*t3*t5^3*t7*t8+3*n*t1*t2*t3*t5^3*t7*t8+3*n*t2^4*t5*t6*t7*t8+ +3*t1*t2^2*t5^2*t6*t7*t8-3*n*t1*t2^2*t5^2*t6*t7*t8- +3*t1^2*t5^3*t6*t7*t8+3*t2^2*t3^2*t5^3*t9+3*n*t2^2*t3^2*t5^3*t9- +3*t1*t3^2*t5^4*t9-3*n*t1*t3^2*t5^4*t9-6*t2^3*t3*t5^2*t6*t9- +6*n*t2^3*t3*t5^2*t6*t9+6*t1*t2*t3*t5^3*t6*t9+ +6*n*t1*t2*t3*t5^3*t6*t9+3*n*t2^4*t5*t6^2*t9+3*t1*t2^2*t5^2*t6^2*t9- +3*n*t1*t2^2*t5^2*t6^2*t9-3*t1^2*t5^3*t6^2*t9+3*t2^4*t5^2*t8*t9- +6*t1*t2^2*t5^3*t8*t9+3*t1^2*t5^4*t8*t9}, +{t1->SP[p1,p1],t2->SP[p1,p2],t3->SP[p1,q1],t4->SP[p1,q2], +t5->SP[p2,p2],t6->SP[p2,q1],t7->SP[p2,q2],t8->SP[q1,q1], +t9->SP[q1,q2],v1->FV[p1,mu],v2->FV[p1,nu],v3->FV[p1,rho], +v4->FV[p1,si],v5->FV[p2,mu],v6->FV[p2,nu],v7->FV[p2,rho], +v8->FV[p2,si],m1->MT[mu,nu],m2->MT[mu,rho],m3->MT[mu,si], +m4->MT[nu,rho],m5->MT[nu,si],m6->MT[rho,si]}}; +scpexp[encli,n]] +} diff --git a/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q1Q2ExtMom0To3.tid b/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q1Q2ExtMom0To3.tid deleted file mode 100644 index 318f91e7f..000000000 --- a/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q1Q2ExtMom0To3.tid +++ /dev/null @@ -1,297 +0,0 @@ -{ -tidl[{{q1_,mu_},{q1_,nu_},{q1_,rho_},{q2_,si_}},{},n_]/; q1=!=q2 :> - Block[{s1,m1,m2,m3,m4,m5,m6,encli}, - encli={(m3*m4*SP[q1,q1]*SP[q1,q2])/(n*s1)+(m2*m5*SP[q1,q1]*SP[q1,q2])/ - (n*s1)+(m1*m6*SP[q1,q1]*SP[q1,q2])/(n*s1),{s1->2+n}, - {m1->MT[mu,nu],m2->MT[mu,rho],m3->MT[mu,si],m4->MT[nu,rho], - m5->MT[nu,si],m6->MT[rho,si]}}; - scpexp[encli,n] - ], -tidl[{{q1_,mu_},{q1_,nu_},{q1_,rho_},{q2_,si_}},{p1_},n_]/; q1=!=q2 :> - Block[{s1,s2,s3,s4,s5,s6,t1,t2,t3,t4,t5,v1,v2,v3,v4,m1,m2,m3,m4,m5,m6,encli}, - encli={-((m3*m4*s2*s3)/(s1*t1^2))-(m2*m5*s2*s3)/(s1*t1^2)- - (m1*m6*s2*s3)/(s1*t1^2)+(m6*s3*s4*v1*v2)/(s1*t1^3)+ - (m5*s3*s4*v1*v3)/(s1*t1^3)+(m3*s3*s4*v2*v3)/(s1*t1^3)+ - (m4*s2*s5*v1*v4)/(s1*t1^3)+(m2*s2*s5*v2*v4)/(s1*t1^3)+ - (m1*s2*s5*v3*v4)/(s1*t1^3)-(s6*v1*v2*v3*v4)/(s1*t1^4), - {s1->1-n^2,s2->t2^2-t1*t4,s3->t2*t3-t1*t5, - s4->2*t2^2+n*t2^2-t1*t4,s5->2*t2*t3+n*t2*t3-t1*t5, - s6->8*t2^3*t3+6*n*t2^3*t3+n^2*t2^3*t3-6*t1*t2*t3*t4- - 3*n*t1*t2*t3*t4-6*t1*t2^2*t5-3*n*t1*t2^2*t5+3*t1^2*t4*t5}, - {t1->SP[p1,p1],t2->SP[p1,q1],t3->SP[p1,q2],t4->SP[q1,q1], - t5->SP[q1,q2],v1->FV[p1,mu],v2->FV[p1,nu],v3->FV[p1,rho], - v4->FV[p1,si],m1->MT[mu,nu],m2->MT[mu,rho],m3->MT[mu,si], - m4->MT[nu,rho],m5->MT[nu,si],m6->MT[rho,si]}}; - scpexp[encli,n] - ], -tidl[{{q1_,mu_},{q1_,nu_},{q1_,rho_},{q2_,si_}},{p1_, p2_},n_]/; q1=!=q2 :> - Block[{s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,s11,s12,s13,s14,s15,s16,s17,s18, - s19,t1,t2,t3,t4,t5,t6,t7,t8,t9,v1,v2,v3,v4,v5,v6,v7,v8,m1,m2,m3,m4,m5,m6,encli}, - encli={-((m3*m4*s3*s4)/(n*s1*s2^2))-(m2*m5*s3*s4)/(n*s1*s2^2)- - (m1*m6*s3*s4)/(n*s1*s2^2)-(m6*s4*s7*v1*v2)/(n*s1*s2^3)- - (m5*s4*s7*v1*v3)/(n*s1*s2^3)-(m3*s4*s7*v2*v3)/(n*s1*s2^3)- - (m4*s11*s3*v1*v4)/(n*s1*s2^3)-(m2*s11*s3*v2*v4)/(n*s1*s2^3)- - (m1*s11*s3*v3*v4)/(n*s1*s2^3)-(s19*v1*v2*v3*v4)/(n*s1*s2^4)+ - (m6*s4*s6*v2*v5)/(n*s1*s2^3)+(m5*s4*s6*v3*v5)/(n*s1*s2^3)+ - (m4*s3*s9*v4*v5)/(n*s1*s2^3)+(s18*v2*v3*v4*v5)/(n*s1*s2^4)+ - (m6*s4*s6*v1*v6)/(n*s1*s2^3)+(m3*s4*s6*v3*v6)/(n*s1*s2^3)+ - (m2*s3*s9*v4*v6)/(n*s1*s2^3)+(s18*v1*v3*v4*v6)/(n*s1*s2^4)- - (m6*s4*s5*v5*v6)/(n*s1*s2^3)-(s16*v3*v4*v5*v6)/(n*s1*s2^4)+ - (m5*s4*s6*v1*v7)/(n*s1*s2^3)+(m3*s4*s6*v2*v7)/(n*s1*s2^3)+ - (m1*s3*s9*v4*v7)/(n*s1*s2^3)+(s18*v1*v2*v4*v7)/(n*s1*s2^4)- - (m5*s4*s5*v5*v7)/(n*s1*s2^3)-(s16*v2*v4*v5*v7)/(n*s1*s2^4)- - (m3*s4*s5*v6*v7)/(n*s1*s2^3)-(s16*v1*v4*v6*v7)/(n*s1*s2^4)+ - (s13*v4*v5*v6*v7)/(n*s1*s2^4)+(m4*s10*s3*v1*v8)/(n*s1*s2^3)+ - (m2*s10*s3*v2*v8)/(n*s1*s2^3)+(m1*s10*s3*v3*v8)/(n*s1*s2^3)+ - (s17*v1*v2*v3*v8)/(n*s1*s2^4)-(m4*s3*s8*v5*v8)/(n*s1*s2^3)- - (s15*v2*v3*v5*v8)/(n*s1*s2^4)-(m2*s3*s8*v6*v8)/(n*s1*s2^3)- - (s15*v1*v3*v6*v8)/(n*s1*s2^4)+(s14*v3*v5*v6*v8)/(n*s1*s2^4)- - (m1*s3*s8*v7*v8)/(n*s1*s2^3)-(s15*v1*v2*v7*v8)/(n*s1*s2^4)+ - (s14*v2*v5*v7*v8)/(n*s1*s2^4)+(s14*v1*v6*v7*v8)/(n*s1*s2^4)- - (s12*v5*v6*v7*v8)/(n*s1*s2^4),{s1->2-n,s2->t2^2-t1*t5, - s3->t3^2*t5-2*t2*t3*t6+t1*t6^2+t2^2*t8-t1*t5*t8, - s4->t3*t4*t5-t2*t4*t6-t2*t3*t7+t1*t6*t7+t2^2*t9-t1*t5*t9, - s5->n*t2^2*t3^2+t1*t3^2*t5-2*t1*t2*t3*t6-2*n*t1*t2*t3*t6+ - t1^2*t6^2+n*t1^2*t6^2+t1*t2^2*t8-t1^2*t5*t8, - s6->t2*t3^2*t5+n*t2*t3^2*t5-2*t2^2*t3*t6-n*t2^2*t3*t6- - n*t1*t3*t5*t6+t1*t2*t6^2+n*t1*t2*t6^2+t2^3*t8-t1*t2*t5*t8, - s7->t3^2*t5^2+n*t3^2*t5^2-2*t2*t3*t5*t6-2*n*t2*t3*t5*t6+ - n*t2^2*t6^2+t1*t5*t6^2+t2^2*t5*t8-t1*t5^2*t8, - s8->n*t2^2*t3*t4+t1*t3*t4*t5-t1*t2*t4*t6-n*t1*t2*t4*t6- - t1*t2*t3*t7-n*t1*t2*t3*t7+t1^2*t6*t7+n*t1^2*t6*t7+t1*t2^2*t9- - t1^2*t5*t9,s9->t2*t3*t4*t5+n*t2*t3*t4*t5-t2^2*t4*t6- - n*t1*t4*t5*t6-t2^2*t3*t7-n*t2^2*t3*t7+t1*t2*t6*t7+n*t1*t2*t6*t7+ - t2^3*t9-t1*t2*t5*t9,s10->t2*t3*t4*t5+n*t2*t3*t4*t5-t2^2*t4*t6- - n*t2^2*t4*t6-t2^2*t3*t7-n*t1*t3*t5*t7+t1*t2*t6*t7+n*t1*t2*t6*t7+ - t2^3*t9-t1*t2*t5*t9,s11->t3*t4*t5^2+n*t3*t4*t5^2-t2*t4*t5*t6- - n*t2*t4*t5*t6-t2*t3*t5*t7-n*t2*t3*t5*t7+n*t2^2*t6*t7+ - t1*t5*t6*t7+t2^2*t5*t9-t1*t5^2*t9, - s12->-2*n*t2^4*t3^3*t4+n^2*t2^4*t3^3*t4+6*n*t1*t2^2*t3^3*t4*t5+ - 3*t1^2*t3^3*t4*t5^2-3*n*t1*t2^3*t3^2*t4*t6-3*n^2*t1*t2^3*t3^2*t4*t6- - 9*t1^2*t2*t3^2*t4*t5*t6-9*n*t1^2*t2*t3^2*t4*t5*t6+ - 6*t1^2*t2^2*t3*t4*t6^2+9*n*t1^2*t2^2*t3*t4*t6^2+ - 3*n^2*t1^2*t2^2*t3*t4*t6^2+3*t1^3*t3*t4*t5*t6^2+ - 3*n*t1^3*t3*t4*t5*t6^2-3*t1^3*t2*t4*t6^3-4*n*t1^3*t2*t4*t6^3- - n^2*t1^3*t2*t4*t6^3-n*t1*t2^3*t3^3*t7-n^2*t1*t2^3*t3^3*t7- - 3*t1^2*t2*t3^3*t5*t7-3*n*t1^2*t2*t3^3*t5*t7+6*t1^2*t2^2*t3^2*t6*t7+ - 9*n*t1^2*t2^2*t3^2*t6*t7+3*n^2*t1^2*t2^2*t3^2*t6*t7+ - 3*t1^3*t3^2*t5*t6*t7+3*n*t1^3*t3^2*t5*t6*t7-9*t1^3*t2*t3*t6^2*t7- - 12*n*t1^3*t2*t3*t6^2*t7-3*n^2*t1^3*t2*t3*t6^2*t7+3*t1^4*t6^3*t7+ - 4*n*t1^4*t6^3*t7+n^2*t1^4*t6^3*t7+3*n*t1*t2^4*t3*t4*t8+ - 3*t1^2*t2^2*t3*t4*t5*t8-3*n*t1^2*t2^2*t3*t4*t5*t8- - 3*t1^3*t3*t4*t5^2*t8-3*t1^2*t2^3*t4*t6*t8-3*n*t1^2*t2^3*t4*t6*t8+ - 3*t1^3*t2*t4*t5*t6*t8+3*n*t1^3*t2*t4*t5*t6*t8-3*t1^2*t2^3*t3*t7*t8- - 3*n*t1^2*t2^3*t3*t7*t8+3*t1^3*t2*t3*t5*t7*t8+ - 3*n*t1^3*t2*t3*t5*t7*t8+3*t1^3*t2^2*t6*t7*t8+3*n*t1^3*t2^2*t6*t7*t8- - 3*t1^4*t5*t6*t7*t8-3*n*t1^4*t5*t6*t7*t8+3*n*t1*t2^4*t3^2*t9+ - 3*t1^2*t2^2*t3^2*t5*t9-3*n*t1^2*t2^2*t3^2*t5*t9-3*t1^3*t3^2*t5^2*t9- - 6*t1^2*t2^3*t3*t6*t9-6*n*t1^2*t2^3*t3*t6*t9+6*t1^3*t2*t3*t5*t6*t9+ - 6*n*t1^3*t2*t3*t5*t6*t9+3*t1^3*t2^2*t6^2*t9+3*n*t1^3*t2^2*t6^2*t9- - 3*t1^4*t5*t6^2*t9-3*n*t1^4*t5*t6^2*t9+3*t1^2*t2^4*t8*t9- - 6*t1^3*t2^2*t5*t8*t9+3*t1^4*t5^2*t8*t9, - s13->n*t2^3*t3^3*t4*t5+n^2*t2^3*t3^3*t4*t5+3*t1*t2*t3^3*t4*t5^2+ - 3*n*t1*t2*t3^3*t4*t5^2-3*n*t2^4*t3^2*t4*t6-9*t1*t2^2*t3^2*t4*t5*t6- - 6*n*t1*t2^2*t3^2*t4*t5*t6-3*n^2*t1*t2^2*t3^2*t4*t5*t6- - 3*n*t1^2*t3^2*t4*t5^2*t6+6*t1*t2^3*t3*t4*t6^2+ - 6*n*t1*t2^3*t3*t4*t6^2+3*t1^2*t2*t3*t4*t5*t6^2+ - 6*n*t1^2*t2*t3*t4*t5*t6^2+3*n^2*t1^2*t2*t3*t4*t5*t6^2- - 3*t1^2*t2^2*t4*t6^3-3*n*t1^2*t2^2*t4*t6^3-n*t1^3*t4*t5*t6^3- - n^2*t1^3*t4*t5*t6^3-n*t2^4*t3^3*t7-n^2*t2^4*t3^3*t7- - 3*t1*t2^2*t3^3*t5*t7-3*n*t1*t2^2*t3^3*t5*t7+6*t1*t2^3*t3^2*t6*t7+ - 9*n*t1*t2^3*t3^2*t6*t7+3*n^2*t1*t2^3*t3^2*t6*t7+ - 3*t1^2*t2*t3^2*t5*t6*t7+3*n*t1^2*t2*t3^2*t5*t6*t7- - 9*t1^2*t2^2*t3*t6^2*t7-12*n*t1^2*t2^2*t3*t6^2*t7- - 3*n^2*t1^2*t2^2*t3*t6^2*t7+3*t1^3*t2*t6^3*t7+4*n*t1^3*t2*t6^3*t7+ - n^2*t1^3*t2*t6^3*t7+3*t1*t2^3*t3*t4*t5*t8+3*n*t1*t2^3*t3*t4*t5*t8- - 3*t1^2*t2*t3*t4*t5^2*t8-3*n*t1^2*t2*t3*t4*t5^2*t8- - 3*t1*t2^4*t4*t6*t8+3*t1^2*t2^2*t4*t5*t6*t8- - 3*n*t1^2*t2^2*t4*t5*t6*t8+3*n*t1^3*t4*t5^2*t6*t8-3*t1*t2^4*t3*t7*t8- - 3*n*t1*t2^4*t3*t7*t8+3*t1^2*t2^2*t3*t5*t7*t8+ - 3*n*t1^2*t2^2*t3*t5*t7*t8+3*t1^2*t2^3*t6*t7*t8+ - 3*n*t1^2*t2^3*t6*t7*t8-3*t1^3*t2*t5*t6*t7*t8- - 3*n*t1^3*t2*t5*t6*t7*t8+3*n*t2^5*t3^2*t9+3*t1*t2^3*t3^2*t5*t9- - 3*n*t1*t2^3*t3^2*t5*t9-3*t1^2*t2*t3^2*t5^2*t9-6*t1*t2^4*t3*t6*t9- - 6*n*t1*t2^4*t3*t6*t9+6*t1^2*t2^2*t3*t5*t6*t9+ - 6*n*t1^2*t2^2*t3*t5*t6*t9+3*t1^2*t2^3*t6^2*t9+3*n*t1^2*t2^3*t6^2*t9- - 3*t1^3*t2*t5*t6^2*t9-3*n*t1^3*t2*t5*t6^2*t9+3*t1*t2^5*t8*t9- - 6*t1^2*t2^3*t5*t8*t9+3*t1^3*t2*t5^2*t8*t9, - s14->n*t2^3*t3^3*t4*t5+n^2*t2^3*t3^3*t4*t5+3*t1*t2*t3^3*t4*t5^2+ - 3*n*t1*t2*t3^3*t4*t5^2-3*n*t2^4*t3^2*t4*t6-n^2*t2^4*t3^2*t4*t6- - 9*t1*t2^2*t3^2*t4*t5*t6-7*n*t1*t2^2*t3^2*t4*t5*t6- - 2*n^2*t1*t2^2*t3^2*t4*t5*t6-2*n*t1^2*t3^2*t4*t5^2*t6+ - 6*t1*t2^3*t3*t4*t6^2+8*n*t1*t2^3*t3*t4*t6^2+ - 2*n^2*t1*t2^3*t3*t4*t6^2+3*t1^2*t2*t3*t4*t5*t6^2+ - 4*n*t1^2*t2*t3*t4*t5*t6^2+n^2*t1^2*t2*t3*t4*t5*t6^2- - 3*t1^2*t2^2*t4*t6^3-4*n*t1^2*t2^2*t4*t6^3-n^2*t1^2*t2^2*t4*t6^3- - n*t2^4*t3^3*t7-3*t1*t2^2*t3^3*t5*t7-2*n*t1*t2^2*t3^3*t5*t7- - n^2*t1*t2^2*t3^3*t5*t7-n*t1^2*t3^3*t5^2*t7+6*t1*t2^3*t3^2*t6*t7+ - 7*n*t1*t2^3*t3^2*t6*t7+n^2*t1*t2^3*t3^2*t6*t7+ - 3*t1^2*t2*t3^2*t5*t6*t7+5*n*t1^2*t2*t3^2*t5*t6*t7+ - 2*n^2*t1^2*t2*t3^2*t5*t6*t7-9*t1^2*t2^2*t3*t6^2*t7- - 11*n*t1^2*t2^2*t3*t6^2*t7-2*n^2*t1^2*t2^2*t3*t6^2*t7- - n*t1^3*t3*t5*t6^2*t7-n^2*t1^3*t3*t5*t6^2*t7+3*t1^3*t2*t6^3*t7+ - 4*n*t1^3*t2*t6^3*t7+n^2*t1^3*t2*t6^3*t7+2*n*t2^5*t3*t4*t8+ - 3*t1*t2^3*t3*t4*t5*t8-n*t1*t2^3*t3*t4*t5*t8-3*t1^2*t2*t3*t4*t5^2*t8- - n*t1^2*t2*t3*t4*t5^2*t8-3*t1*t2^4*t4*t6*t8-3*n*t1*t2^4*t4*t6*t8+ - 3*t1^2*t2^2*t4*t5*t6*t8+3*n*t1^2*t2^2*t4*t5*t6*t8- - 3*t1*t2^4*t3*t7*t8-2*n*t1*t2^4*t3*t7*t8+3*t1^2*t2^2*t3*t5*t7*t8+ - n*t1^2*t2^2*t3*t5*t7*t8+n*t1^3*t3*t5^2*t7*t8+3*t1^2*t2^3*t6*t7*t8+ - 3*n*t1^2*t2^3*t6*t7*t8-3*t1^3*t2*t5*t6*t7*t8- - 3*n*t1^3*t2*t5*t6*t7*t8+n*t2^5*t3^2*t9+3*t1*t2^3*t3^2*t5*t9+ - n*t1*t2^3*t3^2*t5*t9-3*t1^2*t2*t3^2*t5^2*t9- - 2*n*t1^2*t2*t3^2*t5^2*t9-6*t1*t2^4*t3*t6*t9-4*n*t1*t2^4*t3*t6*t9+ - 6*t1^2*t2^2*t3*t5*t6*t9+2*n*t1^2*t2^2*t3*t5*t6*t9+ - 2*n*t1^3*t3*t5^2*t6*t9+3*t1^2*t2^3*t6^2*t9+3*n*t1^2*t2^3*t6^2*t9- - 3*t1^3*t2*t5*t6^2*t9-3*n*t1^3*t2*t5*t6^2*t9+3*t1*t2^5*t8*t9- - 6*t1^2*t2^3*t5*t8*t9+3*t1^3*t2*t5^2*t8*t9, - s15->2*t2^2*t3^3*t4*t5^2+3*n*t2^2*t3^3*t4*t5^2+ - n^2*t2^2*t3^3*t4*t5^2+t1*t3^3*t4*t5^3+n*t1*t3^3*t4*t5^3- - 6*t2^3*t3^2*t4*t5*t6-8*n*t2^3*t3^2*t4*t5*t6- - 2*n^2*t2^3*t3^2*t4*t5*t6-3*t1*t2*t3^2*t4*t5^2*t6- - 4*n*t1*t2*t3^2*t4*t5^2*t6-n^2*t1*t2*t3^2*t4*t5^2*t6+ - 4*t2^4*t3*t4*t6^2+4*n*t2^4*t3*t4*t6^2+n^2*t2^4*t3*t4*t6^2+ - 4*t1*t2^2*t3*t4*t5*t6^2+8*n*t1*t2^2*t3*t4*t5*t6^2+ - 2*n^2*t1*t2^2*t3*t4*t5*t6^2+t1^2*t3*t4*t5^2*t6^2-2*t1*t2^3*t4*t6^3- - 3*n*t1*t2^3*t4*t6^3-n^2*t1*t2^3*t4*t6^3-t1^2*t2*t4*t5*t6^3- - n*t1^2*t2*t4*t5*t6^3-2*t2^3*t3^3*t5*t7-2*n*t2^3*t3^3*t5*t7- - t1*t2*t3^3*t5^2*t7-2*n*t1*t2*t3^3*t5^2*t7-n^2*t1*t2*t3^3*t5^2*t7+ - 4*t2^4*t3^2*t6*t7+2*n*t2^4*t3^2*t6*t7+4*t1*t2^2*t3^2*t5*t6*t7+ - 10*n*t1*t2^2*t3^2*t5*t6*t7+2*n^2*t1*t2^2*t3^2*t5*t6*t7+ - t1^2*t3^2*t5^2*t6*t7+n^2*t1^2*t3^2*t5^2*t6*t7-6*t1*t2^3*t3*t6^2*t7- - 7*n*t1*t2^3*t3*t6^2*t7-n^2*t1*t2^3*t3*t6^2*t7- - 3*t1^2*t2*t3*t5*t6^2*t7-5*n*t1^2*t2*t3*t5*t6^2*t7- - 2*n^2*t1^2*t2*t3*t5*t6^2*t7+2*t1^2*t2^2*t6^3*t7+ - 3*n*t1^2*t2^2*t6^3*t7+n^2*t1^2*t2^2*t6^3*t7+t1^3*t5*t6^3*t7+ - n*t1^3*t5*t6^3*t7+2*t2^4*t3*t4*t5*t8+3*n*t2^4*t3*t4*t5*t8- - t1*t2^2*t3*t4*t5^2*t8-3*n*t1*t2^2*t3*t4*t5^2*t8-t1^2*t3*t4*t5^3*t8- - 2*t2^5*t4*t6*t8-2*n*t2^5*t4*t6*t8+t1*t2^3*t4*t5*t6*t8+ - n*t1*t2^3*t4*t5*t6*t8+t1^2*t2*t4*t5^2*t6*t8+n*t1^2*t2*t4*t5^2*t6*t8- - 2*t2^5*t3*t7*t8+t1*t2^3*t3*t5*t7*t8-3*n*t1*t2^3*t3*t5*t7*t8+ - t1^2*t2*t3*t5^2*t7*t8+3*n*t1^2*t2*t3*t5^2*t7*t8+2*t1*t2^4*t6*t7*t8+ - 2*n*t1*t2^4*t6*t7*t8-t1^2*t2^2*t5*t6*t7*t8-n*t1^2*t2^2*t5*t6*t7*t8- - t1^3*t5^2*t6*t7*t8-n*t1^3*t5^2*t6*t7*t8+2*t2^4*t3^2*t5*t9+ - 2*n*t2^4*t3^2*t5*t9-t1*t2^2*t3^2*t5^2*t9-n*t1*t2^2*t3^2*t5^2*t9- - t1^2*t3^2*t5^3*t9-n*t1^2*t3^2*t5^3*t9-4*t2^5*t3*t6*t9- - 2*n*t2^5*t3*t6*t9+2*t1*t2^3*t3*t5*t6*t9-2*n*t1*t2^3*t3*t5*t6*t9+ - 2*t1^2*t2*t3*t5^2*t6*t9+4*n*t1^2*t2*t3*t5^2*t6*t9+2*t1*t2^4*t6^2*t9+ - 3*n*t1*t2^4*t6^2*t9-t1^2*t2^2*t5*t6^2*t9-3*n*t1^2*t2^2*t5*t6^2*t9- - t1^3*t5^2*t6^2*t9+2*t2^6*t8*t9-3*t1*t2^4*t5*t8*t9+t1^3*t5^3*t8*t9, - s16->2*t2^2*t3^3*t4*t5^2+3*n*t2^2*t3^3*t4*t5^2+ - n^2*t2^2*t3^3*t4*t5^2+t1*t3^3*t4*t5^3+n*t1*t3^3*t4*t5^3- - 6*t2^3*t3^2*t4*t5*t6-7*n*t2^3*t3^2*t4*t5*t6-n^2*t2^3*t3^2*t4*t5*t6- - 3*t1*t2*t3^2*t4*t5^2*t6-5*n*t1*t2*t3^2*t4*t5^2*t6- - 2*n^2*t1*t2*t3^2*t4*t5^2*t6+4*t2^4*t3*t4*t6^2+2*n*t2^4*t3*t4*t6^2+ - 4*t1*t2^2*t3*t4*t5*t6^2+10*n*t1*t2^2*t3*t4*t5*t6^2+ - 2*n^2*t1*t2^2*t3*t4*t5*t6^2+t1^2*t3*t4*t5^2*t6^2+ - n^2*t1^2*t3*t4*t5^2*t6^2-2*t1*t2^3*t4*t6^3-2*n*t1*t2^3*t4*t6^3- - t1^2*t2*t4*t5*t6^3-2*n*t1^2*t2*t4*t5*t6^3-n^2*t1^2*t2*t4*t5*t6^3- - 2*t2^3*t3^3*t5*t7-3*n*t2^3*t3^3*t5*t7-n^2*t2^3*t3^3*t5*t7- - t1*t2*t3^3*t5^2*t7-n*t1*t2*t3^3*t5^2*t7+4*t2^4*t3^2*t6*t7+ - 4*n*t2^4*t3^2*t6*t7+n^2*t2^4*t3^2*t6*t7+4*t1*t2^2*t3^2*t5*t6*t7+ - 8*n*t1*t2^2*t3^2*t5*t6*t7+2*n^2*t1*t2^2*t3^2*t5*t6*t7+ - t1^2*t3^2*t5^2*t6*t7-6*t1*t2^3*t3*t6^2*t7-8*n*t1*t2^3*t3*t6^2*t7- - 2*n^2*t1*t2^3*t3*t6^2*t7-3*t1^2*t2*t3*t5*t6^2*t7- - 4*n*t1^2*t2*t3*t5*t6^2*t7-n^2*t1^2*t2*t3*t5*t6^2*t7+ - 2*t1^2*t2^2*t6^3*t7+3*n*t1^2*t2^2*t6^3*t7+n^2*t1^2*t2^2*t6^3*t7+ - t1^3*t5*t6^3*t7+n*t1^3*t5*t6^3*t7+2*t2^4*t3*t4*t5*t8+ - 2*n*t2^4*t3*t4*t5*t8-t1*t2^2*t3*t4*t5^2*t8-n*t1*t2^2*t3*t4*t5^2*t8- - t1^2*t3*t4*t5^3*t8-n*t1^2*t3*t4*t5^3*t8-2*t2^5*t4*t6*t8+ - t1*t2^3*t4*t5*t6*t8-3*n*t1*t2^3*t4*t5*t6*t8+t1^2*t2*t4*t5^2*t6*t8+ - 3*n*t1^2*t2*t4*t5^2*t6*t8-2*t2^5*t3*t7*t8-2*n*t2^5*t3*t7*t8+ - t1*t2^3*t3*t5*t7*t8+n*t1*t2^3*t3*t5*t7*t8+t1^2*t2*t3*t5^2*t7*t8+ - n*t1^2*t2*t3*t5^2*t7*t8+2*t1*t2^4*t6*t7*t8+3*n*t1*t2^4*t6*t7*t8- - t1^2*t2^2*t5*t6*t7*t8-3*n*t1^2*t2^2*t5*t6*t7*t8-t1^3*t5^2*t6*t7*t8+ - 2*t2^4*t3^2*t5*t9+3*n*t2^4*t3^2*t5*t9-t1*t2^2*t3^2*t5^2*t9- - 3*n*t1*t2^2*t3^2*t5^2*t9-t1^2*t3^2*t5^3*t9-4*t2^5*t3*t6*t9- - 2*n*t2^5*t3*t6*t9+2*t1*t2^3*t3*t5*t6*t9-2*n*t1*t2^3*t3*t5*t6*t9+ - 2*t1^2*t2*t3*t5^2*t6*t9+4*n*t1^2*t2*t3*t5^2*t6*t9+2*t1*t2^4*t6^2*t9+ - 2*n*t1*t2^4*t6^2*t9-t1^2*t2^2*t5*t6^2*t9-n*t1^2*t2^2*t5*t6^2*t9- - t1^3*t5^2*t6^2*t9-n*t1^3*t5^2*t6^2*t9+2*t2^6*t8*t9- - 3*t1*t2^4*t5*t8*t9+t1^3*t5^3*t8*t9, - s17->3*t2*t3^3*t4*t5^3+4*n*t2*t3^3*t4*t5^3+n^2*t2*t3^3*t4*t5^3- - 9*t2^2*t3^2*t4*t5^2*t6-12*n*t2^2*t3^2*t4*t5^2*t6- - 3*n^2*t2^2*t3^2*t4*t5^2*t6+6*t2^3*t3*t4*t5*t6^2+ - 9*n*t2^3*t3*t4*t5*t6^2+3*n^2*t2^3*t3*t4*t5*t6^2+ - 3*t1*t2*t3*t4*t5^2*t6^2+3*n*t1*t2*t3*t4*t5^2*t6^2-n*t2^4*t4*t6^3- - n^2*t2^4*t4*t6^3-3*t1*t2^2*t4*t5*t6^3-3*n*t1*t2^2*t4*t5*t6^3- - 3*t2^2*t3^3*t5^2*t7-3*n*t2^2*t3^3*t5^2*t7-n*t1*t3^3*t5^3*t7- - n^2*t1*t3^3*t5^3*t7+6*t2^3*t3^2*t5*t6*t7+6*n*t2^3*t3^2*t5*t6*t7+ - 3*t1*t2*t3^2*t5^2*t6*t7+6*n*t1*t2*t3^2*t5^2*t6*t7+ - 3*n^2*t1*t2*t3^2*t5^2*t6*t7-3*n*t2^4*t3*t6^2*t7- - 9*t1*t2^2*t3*t5*t6^2*t7-6*n*t1*t2^2*t3*t5*t6^2*t7- - 3*n^2*t1*t2^2*t3*t5*t6^2*t7-3*n*t1^2*t3*t5^2*t6^2*t7+ - n*t1*t2^3*t6^3*t7+n^2*t1*t2^3*t6^3*t7+3*t1^2*t2*t5*t6^3*t7+ - 3*n*t1^2*t2*t5*t6^3*t7+3*t2^3*t3*t4*t5^2*t8+3*n*t2^3*t3*t4*t5^2*t8- - 3*t1*t2*t3*t4*t5^3*t8-3*n*t1*t2*t3*t4*t5^3*t8-3*t2^4*t4*t5*t6*t8- - 3*n*t2^4*t4*t5*t6*t8+3*t1*t2^2*t4*t5^2*t6*t8+ - 3*n*t1*t2^2*t4*t5^2*t6*t8-3*t2^4*t3*t5*t7*t8+ - 3*t1*t2^2*t3*t5^2*t7*t8-3*n*t1*t2^2*t3*t5^2*t7*t8+ - 3*n*t1^2*t3*t5^3*t7*t8+3*t1*t2^3*t5*t6*t7*t8+ - 3*n*t1*t2^3*t5*t6*t7*t8-3*t1^2*t2*t5^2*t6*t7*t8- - 3*n*t1^2*t2*t5^2*t6*t7*t8+3*t2^3*t3^2*t5^2*t9+3*n*t2^3*t3^2*t5^2*t9- - 3*t1*t2*t3^2*t5^3*t9-3*n*t1*t2*t3^2*t5^3*t9-6*t2^4*t3*t5*t6*t9- - 6*n*t2^4*t3*t5*t6*t9+6*t1*t2^2*t3*t5^2*t6*t9+ - 6*n*t1*t2^2*t3*t5^2*t6*t9+3*n*t2^5*t6^2*t9+3*t1*t2^3*t5*t6^2*t9- - 3*n*t1*t2^3*t5*t6^2*t9-3*t1^2*t2*t5^2*t6^2*t9+3*t2^5*t5*t8*t9- - 6*t1*t2^3*t5^2*t8*t9+3*t1^2*t2*t5^3*t8*t9, - s18->3*t2*t3^3*t4*t5^3+4*n*t2*t3^3*t4*t5^3+n^2*t2*t3^3*t4*t5^3- - 9*t2^2*t3^2*t4*t5^2*t6-11*n*t2^2*t3^2*t4*t5^2*t6- - 2*n^2*t2^2*t3^2*t4*t5^2*t6-n*t1*t3^2*t4*t5^3*t6- - n^2*t1*t3^2*t4*t5^3*t6+6*t2^3*t3*t4*t5*t6^2+7*n*t2^3*t3*t4*t5*t6^2+ - n^2*t2^3*t3*t4*t5*t6^2+3*t1*t2*t3*t4*t5^2*t6^2+ - 5*n*t1*t2*t3*t4*t5^2*t6^2+2*n^2*t1*t2*t3*t4*t5^2*t6^2- - n*t2^4*t4*t6^3-3*t1*t2^2*t4*t5*t6^3-2*n*t1*t2^2*t4*t5*t6^3- - n^2*t1*t2^2*t4*t5*t6^3-n*t1^2*t4*t5^2*t6^3-3*t2^2*t3^3*t5^2*t7- - 4*n*t2^2*t3^3*t5^2*t7-n^2*t2^2*t3^3*t5^2*t7+6*t2^3*t3^2*t5*t6*t7+ - 8*n*t2^3*t3^2*t5*t6*t7+2*n^2*t2^3*t3^2*t5*t6*t7+ - 3*t1*t2*t3^2*t5^2*t6*t7+4*n*t1*t2*t3^2*t5^2*t6*t7+ - n^2*t1*t2*t3^2*t5^2*t6*t7-3*n*t2^4*t3*t6^2*t7-n^2*t2^4*t3*t6^2*t7- - 9*t1*t2^2*t3*t5*t6^2*t7-7*n*t1*t2^2*t3*t5*t6^2*t7- - 2*n^2*t1*t2^2*t3*t5*t6^2*t7-2*n*t1^2*t3*t5^2*t6^2*t7+ - n*t1*t2^3*t6^3*t7+n^2*t1*t2^3*t6^3*t7+3*t1^2*t2*t5*t6^3*t7+ - 3*n*t1^2*t2*t5*t6^3*t7+3*t2^3*t3*t4*t5^2*t8+3*n*t2^3*t3*t4*t5^2*t8- - 3*t1*t2*t3*t4*t5^3*t8-3*n*t1*t2*t3*t4*t5^3*t8-3*t2^4*t4*t5*t6*t8- - 2*n*t2^4*t4*t5*t6*t8+3*t1*t2^2*t4*t5^2*t6*t8+ - n*t1*t2^2*t4*t5^2*t6*t8+n*t1^2*t4*t5^3*t6*t8-3*t2^4*t3*t5*t7*t8- - 3*n*t2^4*t3*t5*t7*t8+3*t1*t2^2*t3*t5^2*t7*t8+ - 3*n*t1*t2^2*t3*t5^2*t7*t8+2*n*t2^5*t6*t7*t8+3*t1*t2^3*t5*t6*t7*t8- - n*t1*t2^3*t5*t6*t7*t8-3*t1^2*t2*t5^2*t6*t7*t8- - n*t1^2*t2*t5^2*t6*t7*t8+3*t2^3*t3^2*t5^2*t9+3*n*t2^3*t3^2*t5^2*t9- - 3*t1*t2*t3^2*t5^3*t9-3*n*t1*t2*t3^2*t5^3*t9-6*t2^4*t3*t5*t6*t9- - 4*n*t2^4*t3*t5*t6*t9+6*t1*t2^2*t3*t5^2*t6*t9+ - 2*n*t1*t2^2*t3*t5^2*t6*t9+2*n*t1^2*t3*t5^3*t6*t9+n*t2^5*t6^2*t9+ - 3*t1*t2^3*t5*t6^2*t9+n*t1*t2^3*t5*t6^2*t9-3*t1^2*t2*t5^2*t6^2*t9- - 2*n*t1^2*t2*t5^2*t6^2*t9+3*t2^5*t5*t8*t9-6*t1*t2^3*t5^2*t8*t9+ - 3*t1^2*t2*t5^3*t8*t9,s19->3*t3^3*t4*t5^4+4*n*t3^3*t4*t5^4+ - n^2*t3^3*t4*t5^4-9*t2*t3^2*t4*t5^3*t6-12*n*t2*t3^2*t4*t5^3*t6- - 3*n^2*t2*t3^2*t4*t5^3*t6+6*t2^2*t3*t4*t5^2*t6^2+ - 9*n*t2^2*t3*t4*t5^2*t6^2+3*n^2*t2^2*t3*t4*t5^2*t6^2+ - 3*t1*t3*t4*t5^3*t6^2+3*n*t1*t3*t4*t5^3*t6^2-n*t2^3*t4*t5*t6^3- - n^2*t2^3*t4*t5*t6^3-3*t1*t2*t4*t5^2*t6^3-3*n*t1*t2*t4*t5^2*t6^3- - 3*t2*t3^3*t5^3*t7-4*n*t2*t3^3*t5^3*t7-n^2*t2*t3^3*t5^3*t7+ - 6*t2^2*t3^2*t5^2*t6*t7+9*n*t2^2*t3^2*t5^2*t6*t7+ - 3*n^2*t2^2*t3^2*t5^2*t6*t7+3*t1*t3^2*t5^3*t6*t7+ - 3*n*t1*t3^2*t5^3*t6*t7-3*n*t2^3*t3*t5*t6^2*t7- - 3*n^2*t2^3*t3*t5*t6^2*t7-9*t1*t2*t3*t5^2*t6^2*t7- - 9*n*t1*t2*t3*t5^2*t6^2*t7-2*n*t2^4*t6^3*t7+n^2*t2^4*t6^3*t7+ - 6*n*t1*t2^2*t5*t6^3*t7+3*t1^2*t5^2*t6^3*t7+3*t2^2*t3*t4*t5^3*t8+ - 3*n*t2^2*t3*t4*t5^3*t8-3*t1*t3*t4*t5^4*t8-3*n*t1*t3*t4*t5^4*t8- - 3*t2^3*t4*t5^2*t6*t8-3*n*t2^3*t4*t5^2*t6*t8+3*t1*t2*t4*t5^3*t6*t8+ - 3*n*t1*t2*t4*t5^3*t6*t8-3*t2^3*t3*t5^2*t7*t8-3*n*t2^3*t3*t5^2*t7*t8+ - 3*t1*t2*t3*t5^3*t7*t8+3*n*t1*t2*t3*t5^3*t7*t8+3*n*t2^4*t5*t6*t7*t8+ - 3*t1*t2^2*t5^2*t6*t7*t8-3*n*t1*t2^2*t5^2*t6*t7*t8- - 3*t1^2*t5^3*t6*t7*t8+3*t2^2*t3^2*t5^3*t9+3*n*t2^2*t3^2*t5^3*t9- - 3*t1*t3^2*t5^4*t9-3*n*t1*t3^2*t5^4*t9-6*t2^3*t3*t5^2*t6*t9- - 6*n*t2^3*t3*t5^2*t6*t9+6*t1*t2*t3*t5^3*t6*t9+ - 6*n*t1*t2*t3*t5^3*t6*t9+3*n*t2^4*t5*t6^2*t9+3*t1*t2^2*t5^2*t6^2*t9- - 3*n*t1*t2^2*t5^2*t6^2*t9-3*t1^2*t5^3*t6^2*t9+3*t2^4*t5^2*t8*t9- - 6*t1*t2^2*t5^3*t8*t9+3*t1^2*t5^4*t8*t9}, - {t1->SP[p1,p1],t2->SP[p1,p2],t3->SP[p1,q1],t4->SP[p1,q2], - t5->SP[p2,p2],t6->SP[p2,q1],t7->SP[p2,q2],t8->SP[q1,q1], - t9->SP[q1,q2],v1->FV[p1,mu],v2->FV[p1,nu],v3->FV[p1,rho], - v4->FV[p1,si],v5->FV[p2,mu],v6->FV[p2,nu],v7->FV[p2,rho], - v8->FV[p2,si],m1->MT[mu,nu],m2->MT[mu,rho],m3->MT[mu,si], - m4->MT[nu,rho],m5->MT[nu,si],m6->MT[rho,si]}}; - scpexp[encli,n] - ] -} diff --git a/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2ExtMom0To2.tid b/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2ExtMom0To2.tid new file mode 100644 index 000000000..4992344de --- /dev/null +++ b/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2ExtMom0To2.tid @@ -0,0 +1,78 @@ +{ +tidl[{{q1_,mu_},{q1_,nu_},{q2_,rho_}},{},n_]/; q1=!=q2 :> + 0, + +tidl[{{q1_,mu_},{q1_,nu_},{q2_,rho_}},{p1_},n_]/; q1=!=q2 :> + Block[{encli, m1, m2, m3, s1, s2, s3, s4, t1, t2, t3, t4, t5, v1, v2, v3}, + encli={(m3*s3*t2*v1)/(s1*t1^2)+(m2*s3*t2*v2)/(s1*t1^2)+ + (m1*s2*t3*v3)/(s1*t1^2)+(s4*v1*v2*v3)/(s1*t1^3), + {s1->-1+n,s2->-t2^2+t1*t4,s3->-(t2*t3)+t1*t5, + s4->2*t2^2*t3+n*t2^2*t3-t1*t3*t4-2*t1*t2*t5}, + {t1->SP[p1,p1],t2->SP[p1,q1],t3->SP[p1,q2],t4->SP[q1,q1], + t5->SP[q1,q2],t1->SP[p1,p1],t2->SP[p1,q1],t3->SP[p1,q2], + v1->FV[p1,mu],v2->FV[p1,nu],v3->FV[p1,rho],m1->MT[mu,nu], + m2->MT[mu,rho],m3->MT[nu,rho]}}; + scpexp[encli,n]], + +tidl[{{q1_,mu_},{q1_,nu_},{q2_,rho_}},{p1_, p2_},n_]/; q1=!=q2 :> + Block[{encli, m1, m2, m3, s1, s10, s11, s12, s13, s14, s2, s3, s4, s5, s6, s7, s8, + s9, t1, t2, t3, t4, t5, t6, t7, t8, t9, v1, v2, v3, v4, v5, v6}, + encli={(m3*s4*s8*v1)/(s1*s2^2)+(m2*s4*s8*v2)/(s1*s2^2)+ + (m1*s3*s6*v3)/(s1*s2^2)+(s14*v1*v2*v3)/(s1*s2^3)+ + (m3*s4*s7*v4)/(s1*s2^2)+(s13*v2*v3*v4)/(s1*s2^3)+ + (m2*s4*s7*v5)/(s1*s2^2)+(s13*v1*v3*v5)/(s1*s2^3)+ + (s10*v3*v4*v5)/(s1*s2^3)+(m1*s3*s5*v6)/(s1*s2^2)+ + (s12*v1*v2*v6)/(s1*s2^3)+(s11*v2*v4*v6)/(s1*s2^3)+ + (s11*v1*v5*v6)/(s1*s2^3)+(s9*v4*v5*v6)/(s1*s2^3), + {s1->-2+n,s2->t2^2-t1*t5,s3->t3^2*t5-2*t2*t3*t6+t1*t6^2+ + t2^2*t8-t1*t5*t8,s4->t3*t4*t5-t2*t4*t6-t2*t3*t7+t1*t6*t7+ + t2^2*t9-t1*t5*t9,s5->t2*t4-t1*t7,s6->-(t4*t5)+t2*t7, + s7->t2*t3-t1*t6,s8->-(t3*t5)+t2*t6, + s9->-2*t2^3*t3^2*t4+n*t2^3*t3^2*t4+3*t1*t2*t3^2*t4*t5- + 2*n*t1*t2^2*t3*t4*t6-2*t1^2*t3*t4*t5*t6+t1^2*t2*t4*t6^2+ + n*t1^2*t2*t4*t6^2-n*t1*t2^2*t3^2*t7-t1^2*t3^2*t5*t7+ + 2*t1^2*t2*t3*t6*t7+2*n*t1^2*t2*t3*t6*t7-t1^3*t6^2*t7- + n*t1^3*t6^2*t7+t1*t2^3*t4*t8-t1^2*t2*t4*t5*t8-t1^2*t2^2*t7*t8+ + t1^3*t5*t7*t8+2*t1*t2^3*t3*t9-2*t1^2*t2*t3*t5*t9- + 2*t1^2*t2^2*t6*t9+2*t1^3*t5*t6*t9, + s10->-(n*t2^2*t3^2*t4*t5)-t1*t3^2*t4*t5^2+2*t2^3*t3*t4*t6+ + 2*n*t1*t2*t3*t4*t5*t6-2*t1*t2^2*t4*t6^2+t1^2*t4*t5*t6^2- + n*t1^2*t4*t5*t6^2+n*t2^3*t3^2*t7+t1*t2*t3^2*t5*t7- + 2*t1*t2^2*t3*t6*t7-2*n*t1*t2^2*t3*t6*t7+t1^2*t2*t6^2*t7+ + n*t1^2*t2*t6^2*t7-t1*t2^2*t4*t5*t8+t1^2*t4*t5^2*t8+t1*t2^3*t7*t8- + t1^2*t2*t5*t7*t8-2*t2^4*t3*t9+2*t1*t2^2*t3*t5*t9+2*t1*t2^3*t6*t9- + 2*t1^2*t2*t5*t6*t9,s11->-(n*t2^2*t3^2*t4*t5)-t1*t3^2*t4*t5^2+ + t2^3*t3*t4*t6+n*t2^3*t3*t4*t6+t1*t2*t3*t4*t5*t6+ + n*t1*t2*t3*t4*t5*t6-t1*t2^2*t4*t6^2-n*t1*t2^2*t4*t6^2+ + t2^3*t3^2*t7+n*t1*t2*t3^2*t5*t7-3*t1*t2^2*t3*t6*t7- + n*t1*t2^2*t3*t6*t7+t1^2*t3*t5*t6*t7-n*t1^2*t3*t5*t6*t7+ + t1^2*t2*t6^2*t7+n*t1^2*t2*t6^2*t7-t2^4*t4*t8+t1*t2^2*t4*t5*t8+ + t1*t2^3*t7*t8-t1^2*t2*t5*t7*t8-t2^4*t3*t9+t1^2*t3*t5^2*t9+ + 2*t1*t2^3*t6*t9-2*t1^2*t2*t5*t6*t9, + s12->t2*t3^2*t4*t5^2+n*t2*t3^2*t4*t5^2-2*t2^2*t3*t4*t5*t6- + 2*n*t2^2*t3*t4*t5*t6+n*t2^3*t4*t6^2+t1*t2*t4*t5*t6^2- + 2*t2^2*t3^2*t5*t7+t1*t3^2*t5^2*t7-n*t1*t3^2*t5^2*t7+ + 2*t2^3*t3*t6*t7+2*n*t1*t2*t3*t5*t6*t7-n*t1*t2^2*t6^2*t7- + t1^2*t5*t6^2*t7+t2^3*t4*t5*t8-t1*t2*t4*t5^2*t8-t1*t2^2*t5*t7*t8+ + t1^2*t5^2*t7*t8+2*t2^3*t3*t5*t9-2*t1*t2*t3*t5^2*t9-2*t2^4*t6*t9+ + 2*t1*t2^2*t5*t6*t9,s13->t2*t3^2*t4*t5^2+n*t2*t3^2*t4*t5^2- + 3*t2^2*t3*t4*t5*t6-n*t2^2*t3*t4*t5*t6+t1*t3*t4*t5^2*t6- + n*t1*t3*t4*t5^2*t6+t2^3*t4*t6^2+n*t1*t2*t4*t5*t6^2- + t2^2*t3^2*t5*t7-n*t2^2*t3^2*t5*t7+t2^3*t3*t6*t7+n*t2^3*t3*t6*t7+ + t1*t2*t3*t5*t6*t7+n*t1*t2*t3*t5*t6*t7-n*t1*t2^2*t6^2*t7- + t1^2*t5*t6^2*t7+t2^3*t4*t5*t8-t1*t2*t4*t5^2*t8-t2^4*t7*t8+ + t1*t2^2*t5*t7*t8+2*t2^3*t3*t5*t9-2*t1*t2*t3*t5^2*t9-t2^4*t6*t9+ + t1^2*t5^2*t6*t9,s14->-(t3^2*t4*t5^3)-n*t3^2*t4*t5^3+ + 2*t2*t3*t4*t5^2*t6+2*n*t2*t3*t4*t5^2*t6-n*t2^2*t4*t5*t6^2- + t1*t4*t5^2*t6^2+t2*t3^2*t5^2*t7+n*t2*t3^2*t5^2*t7- + 2*n*t2^2*t3*t5*t6*t7-2*t1*t3*t5^2*t6*t7-2*t2^3*t6^2*t7+ + n*t2^3*t6^2*t7+3*t1*t2*t5*t6^2*t7-t2^2*t4*t5^2*t8+t1*t4*t5^3*t8+ + t2^3*t5*t7*t8-t1*t2*t5^2*t7*t8-2*t2^2*t3*t5^2*t9+2*t1*t3*t5^3*t9+ + 2*t2^3*t5*t6*t9-2*t1*t2*t5^2*t6*t9}, + {t1->SP[p1,p1],t2->SP[p1,p2],t3->SP[p1,q1],t4->SP[p1,q2], + t5->SP[p2,p2],t6->SP[p2,q1],t7->SP[p2,q2],t8->SP[q1,q1], + t9->SP[q1,q2],v1->FV[p1,mu],v2->FV[p1,nu],v3->FV[p1,rho], + v4->FV[p2,mu],v5->FV[p2,nu],v6->FV[p2,rho],m1->MT[mu,nu], + m2->MT[mu,rho],m3->MT[nu,rho]}}; + scpexp[encli,n]] +} diff --git a/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2ExtMom1To2.tid b/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2ExtMom1To2.tid deleted file mode 100644 index 70f443ece..000000000 --- a/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2ExtMom1To2.tid +++ /dev/null @@ -1,77 +0,0 @@ -{ - -tidl[{{q1_,mu_},{q1_,nu_},{q2_,rho_}},{p1_},n_]/; q1=!=q2 :> - Block[{s1,s2,s3,s4,t1,t2,t3,t4,t5,v1,v2,v3,m1,m2,m3,encli}, - encli={(m3*s3*t2*v1)/(s1*t1^2)+(m2*s3*t2*v2)/(s1*t1^2)+ - (m1*s2*t3*v3)/(s1*t1^2)-(s4*v1*v2*v3)/(s1*t1^3), - {s1->1-n,s2->t2^2-t1*t4,s3->t2*t3-t1*t5, - s4->2*t2^2*t3+n*t2^2*t3-t1*t3*t4-2*t1*t2*t5}, - {t1->SP[p1,p1],t2->SP[p1,q1],t3->SP[p1,q2],t4->SP[q1,q1], - t5->SP[q1,q2],v1->FV[p1,mu],v2->FV[p1,nu],v3->FV[p1,rho], - m1->MT[mu,nu],m2->MT[mu,rho],m3->MT[nu,rho]}}; - scpexp[encli,n] - ], - -tidl[{{q1_,mu_},{q1_,nu_},{q2_,rho_}},{p1_, p2_},n_]/; q1=!=q2 :> - Block[{s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,s11,s12,s13,s14,t1, - t2,t3,t4,t5,t6,t7,t8,t9,v1,v2,v3,v4,v5,v6,m1,m2,m3,encli}, - encli={(m3*s7*s8*v1)/(s1*s2^2)+(m2*s7*s8*v2)/(s1*s2^2)+ - (m1*s4*s5*v3)/(s1*s2^2)+(s14*v1*v2*v3)/(s1*s2^3)- - (m3*s6*s7*v4)/(s1*s2^2)-(s13*v2*v3*v4)/(s1*s2^3)- - (m2*s6*s7*v5)/(s1*s2^2)-(s13*v1*v3*v5)/(s1*s2^3)+ - (s10*v3*v4*v5)/(s1*s2^3)-(m1*s3*s4*v6)/(s1*s2^2)- - (s12*v1*v2*v6)/(s1*s2^3)+(s11*v2*v4*v6)/(s1*s2^3)+ - (s11*v1*v5*v6)/(s1*s2^3)-(s9*v4*v5*v6)/(s1*s2^3), - {s1->2-n,s2->t2^2-t1*t5,s3->t2*t4-t1*t7, - s4->t3^2*t5-2*t2*t3*t6+t1*t6^2+t2^2*t8-t1*t5*t8, - s5->t4*t5-t2*t7,s6->t2*t3-t1*t6, - s7->t3*t4*t5-t2*t4*t6-t2*t3*t7+t1*t6*t7+t2^2*t9-t1*t5*t9, - s8->t3*t5-t2*t6,s9->-2*t2^3*t3^2*t4+n*t2^3*t3^2*t4+ - 3*t1*t2*t3^2*t4*t5-2*n*t1*t2^2*t3*t4*t6-2*t1^2*t3*t4*t5*t6+ - t1^2*t2*t4*t6^2+n*t1^2*t2*t4*t6^2-n*t1*t2^2*t3^2*t7- - t1^2*t3^2*t5*t7+2*t1^2*t2*t3*t6*t7+2*n*t1^2*t2*t3*t6*t7- - t1^3*t6^2*t7-n*t1^3*t6^2*t7+t1*t2^3*t4*t8-t1^2*t2*t4*t5*t8- - t1^2*t2^2*t7*t8+t1^3*t5*t7*t8+2*t1*t2^3*t3*t9-2*t1^2*t2*t3*t5*t9- - 2*t1^2*t2^2*t6*t9+2*t1^3*t5*t6*t9, - s10->n*t2^2*t3^2*t4*t5+t1*t3^2*t4*t5^2-2*t2^3*t3*t4*t6- - 2*n*t1*t2*t3*t4*t5*t6+2*t1*t2^2*t4*t6^2-t1^2*t4*t5*t6^2+ - n*t1^2*t4*t5*t6^2-n*t2^3*t3^2*t7-t1*t2*t3^2*t5*t7+ - 2*t1*t2^2*t3*t6*t7+2*n*t1*t2^2*t3*t6*t7-t1^2*t2*t6^2*t7- - n*t1^2*t2*t6^2*t7+t1*t2^2*t4*t5*t8-t1^2*t4*t5^2*t8-t1*t2^3*t7*t8+ - t1^2*t2*t5*t7*t8+2*t2^4*t3*t9-2*t1*t2^2*t3*t5*t9-2*t1*t2^3*t6*t9+ - 2*t1^2*t2*t5*t6*t9,s11->n*t2^2*t3^2*t4*t5+t1*t3^2*t4*t5^2- - t2^3*t3*t4*t6-n*t2^3*t3*t4*t6-t1*t2*t3*t4*t5*t6- - n*t1*t2*t3*t4*t5*t6+t1*t2^2*t4*t6^2+n*t1*t2^2*t4*t6^2- - t2^3*t3^2*t7-n*t1*t2*t3^2*t5*t7+3*t1*t2^2*t3*t6*t7+ - n*t1*t2^2*t3*t6*t7-t1^2*t3*t5*t6*t7+n*t1^2*t3*t5*t6*t7- - t1^2*t2*t6^2*t7-n*t1^2*t2*t6^2*t7+t2^4*t4*t8-t1*t2^2*t4*t5*t8- - t1*t2^3*t7*t8+t1^2*t2*t5*t7*t8+t2^4*t3*t9-t1^2*t3*t5^2*t9- - 2*t1*t2^3*t6*t9+2*t1^2*t2*t5*t6*t9, - s12->t2*t3^2*t4*t5^2+n*t2*t3^2*t4*t5^2-2*t2^2*t3*t4*t5*t6- - 2*n*t2^2*t3*t4*t5*t6+n*t2^3*t4*t6^2+t1*t2*t4*t5*t6^2- - 2*t2^2*t3^2*t5*t7+t1*t3^2*t5^2*t7-n*t1*t3^2*t5^2*t7+ - 2*t2^3*t3*t6*t7+2*n*t1*t2*t3*t5*t6*t7-n*t1*t2^2*t6^2*t7- - t1^2*t5*t6^2*t7+t2^3*t4*t5*t8-t1*t2*t4*t5^2*t8-t1*t2^2*t5*t7*t8+ - t1^2*t5^2*t7*t8+2*t2^3*t3*t5*t9-2*t1*t2*t3*t5^2*t9-2*t2^4*t6*t9+ - 2*t1*t2^2*t5*t6*t9,s13->t2*t3^2*t4*t5^2+n*t2*t3^2*t4*t5^2- - 3*t2^2*t3*t4*t5*t6-n*t2^2*t3*t4*t5*t6+t1*t3*t4*t5^2*t6- - n*t1*t3*t4*t5^2*t6+t2^3*t4*t6^2+n*t1*t2*t4*t5*t6^2- - t2^2*t3^2*t5*t7-n*t2^2*t3^2*t5*t7+t2^3*t3*t6*t7+n*t2^3*t3*t6*t7+ - t1*t2*t3*t5*t6*t7+n*t1*t2*t3*t5*t6*t7-n*t1*t2^2*t6^2*t7- - t1^2*t5*t6^2*t7+t2^3*t4*t5*t8-t1*t2*t4*t5^2*t8-t2^4*t7*t8+ - t1*t2^2*t5*t7*t8+2*t2^3*t3*t5*t9-2*t1*t2*t3*t5^2*t9-t2^4*t6*t9+ - t1^2*t5^2*t6*t9,s14->t3^2*t4*t5^3+n*t3^2*t4*t5^3- - 2*t2*t3*t4*t5^2*t6-2*n*t2*t3*t4*t5^2*t6+n*t2^2*t4*t5*t6^2+ - t1*t4*t5^2*t6^2-t2*t3^2*t5^2*t7-n*t2*t3^2*t5^2*t7+ - 2*n*t2^2*t3*t5*t6*t7+2*t1*t3*t5^2*t6*t7+2*t2^3*t6^2*t7- - n*t2^3*t6^2*t7-3*t1*t2*t5*t6^2*t7+t2^2*t4*t5^2*t8-t1*t4*t5^3*t8- - t2^3*t5*t7*t8+t1*t2*t5^2*t7*t8+2*t2^2*t3*t5^2*t9-2*t1*t3*t5^3*t9- - 2*t2^3*t5*t6*t9+2*t1*t2*t5^2*t6*t9}, - {t1->SP[p1,p1],t2->SP[p1,p2],t3->SP[p1,q1],t4->SP[p1,q2], - t5->SP[p2,p2],t6->SP[p2,q1],t7->SP[p2,q2],t8->SP[q1,q1], - t9->SP[q1,q2],v1->FV[p1,mu],v2->FV[p1,nu],v3->FV[p1,rho], - v4->FV[p2,mu],v5->FV[p2,nu],v6->FV[p2,rho],m1->MT[mu,nu], - m2->MT[mu,rho],m3->MT[nu,rho]}}; - scpexp[encli,n] - ] -} diff --git a/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2Q2ExtMom0To2.tid b/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2Q2ExtMom0To2.tid new file mode 100644 index 000000000..aed2aa7fa --- /dev/null +++ b/FeynCalc/Tables/TIDL/TwoLoopQ1Q1Q2Q2ExtMom0To2.tid @@ -0,0 +1,792 @@ +{ +tidl[{{q1_, mu_}, {q1_, nu_}, {q2_, rho_}, {q2_, si_}},{},n_]/; q1=!=q2 :> + Block[{encli, m1, m2, m3, m4, m5, m6, s1, s2, s3, s4, t1, t2, t3}, + encli={(m3*m4*s3)/(n*s1*s2)+(m2*m5*s3)/(n*s1*s2)+(m1*m6*s4)/(n*s1*s2), + {s1->-1+n,s2->2+n,s3->n*t2^2-t1*t3, + s4->-2*t2^2+t1*t3+n*t1*t3},{t1->SP[q1,q1],t2->SP[q1,q2], + t3->SP[q2,q2],m1->MT[mu,nu],m2->MT[mu,rho],m3->MT[mu,si], + m4->MT[nu,rho],m5->MT[nu,si],m6->MT[rho,si]}}; + scpexp[encli,n]], + + +tidl[{{q1_, mu_}, {q1_, nu_}, {q2_, rho_}, {q2_, si_}},{p1_},n_]/; q1=!=q2 :> + Block[{encli, m1, m2, m3, m4, m5, m6, s1, s2, s3, s4, s5, s6, s7, s8, s9, t1, t2, t3, t4, t5, t6, v1, v2, v3, v4}, + encli={(m3*m4*s4)/(s1*s2*s3*t1^2)+(m2*m5*s4)/(s1*s2*s3*t1^2)+ + (m1*m6*s9)/(s1*s2*s3*t1^2)+(m6*s8*v1*v2)/(s1*s2*s3*t1^3)+ + (m5*s5*v1*v3)/(s1*s2*s3*t1^3)+(m3*s5*v2*v3)/(s1*s2*s3*t1^3)+ + (m4*s5*v1*v4)/(s1*s2*s3*t1^3)+(m2*s5*v2*v4)/(s1*s2*s3*t1^3)+ + (m1*s7*v3*v4)/(s1*s2*s3*t1^3)+(s6*v1*v2*v3*v4)/(s2*s3*t1^4), + {s1->-2+n,s2->-1+n,s3->1+n, + s4->-2*t2^2*t3^2+n*t2^2*t3^2+t1*t3^2*t4+2*t1*t2*t3*t5- + 2*n*t1*t2*t3*t5-t1^2*t5^2+n*t1^2*t5^2+t1*t2^2*t6-t1^2*t4*t6, + s5->4*t2^2*t3^2-n^2*t2^2*t3^2-t1*t3^2*t4-4*t1*t2*t3*t5+ + n*t1*t2*t3*t5+n^2*t1*t2*t3*t5+t1^2*t5^2-n*t1^2*t5^2-t1*t2^2*t6+ + t1^2*t4*t6,s6->8*t2^2*t3^2+6*n*t2^2*t3^2+n^2*t2^2*t3^2- + 2*t1*t3^2*t4-n*t1*t3^2*t4-8*t1*t2*t3*t5-4*n*t1*t2*t3*t5+ + 2*t1^2*t5^2-2*t1*t2^2*t6-n*t1*t2^2*t6+t1^2*t4*t6, + s7->4*t2^2*t3^2-n^2*t2^2*t3^2-2*t1*t3^2*t4+n^2*t1*t3^2*t4- + 4*t1*t2*t3*t5+2*t1^2*t5^2+n*t1*t2^2*t6-n*t1^2*t4*t6, + s8->4*t2^2*t3^2-n^2*t2^2*t3^2+n*t1*t3^2*t4-4*t1*t2*t3*t5+ + 2*t1^2*t5^2-2*t1*t2^2*t6+n^2*t1*t2^2*t6-n*t1^2*t4*t6, + s9->-2*t2^2*t3^2+n*t2^2*t3^2-n*t1*t3^2*t4+4*t1*t2*t3*t5- + 2*t1^2*t5^2-n*t1*t2^2*t6+n*t1^2*t4*t6}, + {t1->SP[p1,p1],t2->SP[p1,q1],t3->SP[p1,q2],t4->SP[q1,q1], + t5->SP[q1,q2],t6->SP[q2,q2],t1->SP[p1,p1],v1->FV[p1,mu], + v2->FV[p1,nu],v3->FV[p1,rho],v4->FV[p1,si],m1->MT[mu,nu], + m2->MT[mu,rho],m3->MT[mu,si],m4->MT[nu,rho],m5->MT[nu,si], + m6->MT[rho,si]}}; + scpexp[encli,n]], +tidl[{{q1_, mu_}, {q1_, nu_}, {q2_, rho_}, {q2_, si_}},{p1_, p2_},n_]/; q1=!=q2 :> + Block[{encli, m1, m2, m3, m4, m5, m6, s1, s10, s11, s12, s13, s14, s15, s16, s17, s18, s19, s2, + s20, s21, s22, s23, s24, s3, s4, s5, s6, s7, s8, s9, t1, t10, t2, t3, t4, t5, t6, t7, t8, t9, v1, v2, v3, v4, v5, v6, v7, v8}, + encli={(m3*m4*s4)/(n*s1*s2^2*s3)+(m2*m5*s4)/(n*s1*s2^2*s3)+ + (m1*m6*s5)/(n*s1*s2^2*s3)+(m6*s18*v1*v2)/(n*s1*s2^3*s3)+ + (m5*s16*v1*v3)/(n*s1*s2^3*s3)+(m3*s16*v2*v3)/(n*s1*s2^3*s3)+ + (m4*s16*v1*v4)/(n*s1*s2^3*s3)+(m2*s16*v2*v4)/(n*s1*s2^3*s3)+ + (m1*s17*v3*v4)/(n*s1*s2^3*s3)+(s24*v1*v2*v3*v4)/(n*s1*s2^4)+ + (m6*s13*v2*v5)/(n*s1*s2^3*s3)+(m5*s10*v3*v5)/(n*s1*s2^3*s3)+ + (m4*s10*v4*v5)/(n*s1*s2^3*s3)+(s23*v2*v3*v4*v5)/(n*s1*s2^4)+ + (m6*s13*v1*v6)/(n*s1*s2^3*s3)+(m3*s10*v3*v6)/(n*s1*s2^3*s3)+ + (m2*s10*v4*v6)/(n*s1*s2^3*s3)+(s23*v1*v3*v4*v6)/(n*s1*s2^4)+ + (m6*s8*v5*v6)/(n*s1*s2^3*s3)+(s21*v3*v4*v5*v6)/(n*s1*s2^4*s3)+ + (m5*s11*v1*v7)/(n*s1*s2^3*s3)+(m3*s11*v2*v7)/(n*s1*s2^3*s3)+ + (m1*s12*v4*v7)/(n*s1*s2^3*s3)+(s22*v1*v2*v4*v7)/(n*s1*s2^4)+ + (m5*s6*v5*v7)/(n*s1*s2^3*s3)+(s19*v2*v4*v5*v7)/(n*s1*s2^4*s3)+ + (m3*s6*v6*v7)/(n*s1*s2^3*s3)+(s19*v1*v4*v6*v7)/(n*s1*s2^4*s3)+ + (s14*v4*v5*v6*v7)/(n*s1*s2^4)+(m4*s11*v1*v8)/(n*s1*s2^3*s3)+ + (m2*s11*v2*v8)/(n*s1*s2^3*s3)+(m1*s12*v3*v8)/(n*s1*s2^3*s3)+ + (s22*v1*v2*v3*v8)/(n*s1*s2^4)+(m4*s6*v5*v8)/(n*s1*s2^3*s3)+ + (s19*v2*v3*v5*v8)/(n*s1*s2^4*s3)+(m2*s6*v6*v8)/(n*s1*s2^3*s3)+ + (s19*v1*v3*v6*v8)/(n*s1*s2^4*s3)+(s14*v3*v5*v6*v8)/(n*s1*s2^4)+ + (m1*s7*v7*v8)/(n*s1*s2^3*s3)+(s20*v1*v2*v7*v8)/(n*s1*s2^4*s3)+ + (s15*v2*v5*v7*v8)/(n*s1*s2^4)+(s15*v1*v6*v7*v8)/(n*s1*s2^4)+ + (s9*v5*v6*v7*v8)/(n*s1*s2^4),{s1->-2+n,s2->t2^2-t1*t5, + s3->-3+n,s4->-(t10*t2^2*t3^2*t5)+t1*t10*t3^2*t5^2- + 3*t3^2*t4^2*t5^2+n*t3^2*t4^2*t5^2+2*t10*t2^3*t3*t6- + 2*t1*t10*t2*t3*t5*t6+6*t2*t3*t4^2*t5*t6-2*n*t2*t3*t4^2*t5*t6- + t1*t10*t2^2*t6^2-2*t2^2*t4^2*t6^2+n*t2^2*t4^2*t6^2+ + t1^2*t10*t5*t6^2-t1*t4^2*t5*t6^2+6*t2*t3^2*t4*t5*t7- + 2*n*t2*t3^2*t4*t5*t7-8*t2^2*t3*t4*t6*t7+2*n*t2^2*t3*t4*t6*t7- + 4*t1*t3*t4*t5*t6*t7+2*n*t1*t3*t4*t5*t6*t7+6*t1*t2*t4*t6^2*t7- + 2*n*t1*t2*t4*t6^2*t7-2*t2^2*t3^2*t7^2+n*t2^2*t3^2*t7^2- + t1*t3^2*t5*t7^2+6*t1*t2*t3*t6*t7^2-2*n*t1*t2*t3*t6*t7^2- + 3*t1^2*t6^2*t7^2+n*t1^2*t6^2*t7^2-t10*t2^4*t8+2*t1*t10*t2^2*t5*t8- + t2^2*t4^2*t5*t8-t1^2*t10*t5^2*t8+t1*t4^2*t5^2*t8+2*t2^3*t4*t7*t8- + 2*t1*t2*t4*t5*t7*t8-t1*t2^2*t7^2*t8+t1^2*t5*t7^2*t8- + 4*t2^2*t3*t4*t5*t9+2*n*t2^2*t3*t4*t5*t9+4*t1*t3*t4*t5^2*t9- + 2*n*t1*t3*t4*t5^2*t9+4*t2^3*t4*t6*t9-2*n*t2^3*t4*t6*t9- + 4*t1*t2*t4*t5*t6*t9+2*n*t1*t2*t4*t5*t6*t9+4*t2^3*t3*t7*t9- + 2*n*t2^3*t3*t7*t9-4*t1*t2*t3*t5*t7*t9+2*n*t1*t2*t3*t5*t7*t9- + 4*t1*t2^2*t6*t7*t9+2*n*t1*t2^2*t6*t7*t9+4*t1^2*t5*t6*t7*t9- + 2*n*t1^2*t5*t6*t7*t9-2*t2^4*t9^2+n*t2^4*t9^2+4*t1*t2^2*t5*t9^2- + 2*n*t1*t2^2*t5*t9^2-2*t1^2*t5^2*t9^2+n*t1^2*t5^2*t9^2, + s5->-(t10*t2^2*t3^2*t5)+n*t10*t2^2*t3^2*t5+t1*t10*t3^2*t5^2- + n*t1*t10*t3^2*t5^2-3*t3^2*t4^2*t5^2+n*t3^2*t4^2*t5^2+ + 2*t10*t2^3*t3*t6-2*n*t10*t2^3*t3*t6-2*t1*t10*t2*t3*t5*t6+ + 2*n*t1*t10*t2*t3*t5*t6+6*t2*t3*t4^2*t5*t6-2*n*t2*t3*t4^2*t5*t6- + t1*t10*t2^2*t6^2+n*t1*t10*t2^2*t6^2-2*t2^2*t4^2*t6^2+ + t1^2*t10*t5*t6^2-n*t1^2*t10*t5*t6^2-t1*t4^2*t5*t6^2+ + n*t1*t4^2*t5*t6^2+6*t2*t3^2*t4*t5*t7-2*n*t2*t3^2*t4*t5*t7- + 8*t2^2*t3*t4*t6*t7+4*n*t2^2*t3*t4*t6*t7-4*t1*t3*t4*t5*t6*t7+ + 6*t1*t2*t4*t6^2*t7-2*n*t1*t2*t4*t6^2*t7-2*t2^2*t3^2*t7^2- + t1*t3^2*t5*t7^2+n*t1*t3^2*t5*t7^2+6*t1*t2*t3*t6*t7^2- + 2*n*t1*t2*t3*t6*t7^2-3*t1^2*t6^2*t7^2+n*t1^2*t6^2*t7^2- + t10*t2^4*t8+n*t10*t2^4*t8+2*t1*t10*t2^2*t5*t8- + 2*n*t1*t10*t2^2*t5*t8-t2^2*t4^2*t5*t8+n*t2^2*t4^2*t5*t8- + t1^2*t10*t5^2*t8+n*t1^2*t10*t5^2*t8+t1*t4^2*t5^2*t8- + n*t1*t4^2*t5^2*t8+2*t2^3*t4*t7*t8-2*n*t2^3*t4*t7*t8- + 2*t1*t2*t4*t5*t7*t8+2*n*t1*t2*t4*t5*t7*t8-t1*t2^2*t7^2*t8+ + n*t1*t2^2*t7^2*t8+t1^2*t5*t7^2*t8-n*t1^2*t5*t7^2*t8- + 4*t2^2*t3*t4*t5*t9+4*t1*t3*t4*t5^2*t9+4*t2^3*t4*t6*t9- + 4*t1*t2*t4*t5*t6*t9+4*t2^3*t3*t7*t9-4*t1*t2*t3*t5*t7*t9- + 4*t1*t2^2*t6*t7*t9+4*t1^2*t5*t6*t7*t9-2*t2^4*t9^2+ + 4*t1*t2^2*t5*t9^2-2*t1^2*t5^2*t9^2, + s6->-(t1*t10*t2^2*t3^2*t5)-3*n*t2^2*t3^2*t4^2*t5+ + n^2*t2^2*t3^2*t4^2*t5+t1^2*t10*t3^2*t5^2-3*t1*t3^2*t4^2*t5^2+ + n*t1*t3^2*t4^2*t5^2+2*t1*t10*t2^3*t3*t6+3*n*t2^3*t3*t4^2*t6- + n^2*t2^3*t3*t4^2*t6-2*t1^2*t10*t2*t3*t5*t6+6*t1*t2*t3*t4^2*t5*t6+ + n*t1*t2*t3*t4^2*t5*t6-n^2*t1*t2*t3*t4^2*t5*t6-t1^2*t10*t2^2*t6^2- + 2*t1*t2^2*t4^2*t6^2-2*n*t1*t2^2*t4^2*t6^2+n^2*t1*t2^2*t4^2*t6^2+ + t1^3*t10*t5*t6^2-t1^2*t4^2*t5*t6^2+3*n*t2^3*t3^2*t4*t7- + n^2*t2^3*t3^2*t4*t7+6*t1*t2*t3^2*t4*t5*t7+n*t1*t2*t3^2*t4*t5*t7- + n^2*t1*t2*t3^2*t4*t5*t7-8*t1*t2^2*t3*t4*t6*t7- + 7*n*t1*t2^2*t3*t4*t6*t7+3*n^2*t1*t2^2*t3*t4*t6*t7- + 4*t1^2*t3*t4*t5*t6*t7-n*t1^2*t3*t4*t5*t6*t7+n^2*t1^2*t3*t4*t5*t6*t7+ + 6*t1^2*t2*t4*t6^2*t7+4*n*t1^2*t2*t4*t6^2*t7- + 2*n^2*t1^2*t2*t4*t6^2*t7-2*t1*t2^2*t3^2*t7^2-2*n*t1*t2^2*t3^2*t7^2+ + n^2*t1*t2^2*t3^2*t7^2-t1^2*t3^2*t5*t7^2+6*t1^2*t2*t3*t6*t7^2+ + 4*n*t1^2*t2*t3*t6*t7^2-2*n^2*t1^2*t2*t3*t6*t7^2-3*t1^3*t6^2*t7^2- + 2*n*t1^3*t6^2*t7^2+n^2*t1^3*t6^2*t7^2-t1*t10*t2^4*t8+ + 2*t1^2*t10*t2^2*t5*t8-t1*t2^2*t4^2*t5*t8-t1^3*t10*t5^2*t8+ + t1^2*t4^2*t5^2*t8+2*t1*t2^3*t4*t7*t8-2*t1^2*t2*t4*t5*t7*t8- + t1^2*t2^2*t7^2*t8+t1^3*t5*t7^2*t8-3*n*t2^4*t3*t4*t9+ + n^2*t2^4*t3*t4*t9-4*t1*t2^2*t3*t4*t5*t9+5*n*t1*t2^2*t3*t4*t5*t9- + n^2*t1*t2^2*t3*t4*t5*t9+4*t1^2*t3*t4*t5^2*t9-2*n*t1^2*t3*t4*t5^2*t9+ + 4*t1*t2^3*t4*t6*t9+n*t1*t2^3*t4*t6*t9-n^2*t1*t2^3*t4*t6*t9- + 4*t1^2*t2*t4*t5*t6*t9-n*t1^2*t2*t4*t5*t6*t9+n^2*t1^2*t2*t4*t5*t6*t9+ + 4*t1*t2^3*t3*t7*t9+n*t1*t2^3*t3*t7*t9-n^2*t1*t2^3*t3*t7*t9- + 4*t1^2*t2*t3*t5*t7*t9-n*t1^2*t2*t3*t5*t7*t9+n^2*t1^2*t2*t3*t5*t7*t9- + 4*t1^2*t2^2*t6*t7*t9-n*t1^2*t2^2*t6*t7*t9+n^2*t1^2*t2^2*t6*t7*t9+ + 4*t1^3*t5*t6*t7*t9+n*t1^3*t5*t6*t7*t9-n^2*t1^3*t5*t6*t7*t9- + 2*t1*t2^4*t9^2+n*t1*t2^4*t9^2+4*t1^2*t2^2*t5*t9^2- + 2*n*t1^2*t2^2*t5*t9^2-2*t1^3*t5^2*t9^2+n*t1^3*t5^2*t9^2, + s7->-(t1*t10*t2^2*t3^2*t5)+n*t1*t10*t2^2*t3^2*t5- + 3*n*t2^2*t3^2*t4^2*t5+n^2*t2^2*t3^2*t4^2*t5+t1^2*t10*t3^2*t5^2- + n*t1^2*t10*t3^2*t5^2-3*t1*t3^2*t4^2*t5^2+n*t1*t3^2*t4^2*t5^2+ + 2*t1*t10*t2^3*t3*t6-2*n*t1*t10*t2^3*t3*t6+6*n*t2^3*t3*t4^2*t6- + 2*n^2*t2^3*t3*t4^2*t6-2*t1^2*t10*t2*t3*t5*t6+ + 2*n*t1^2*t10*t2*t3*t5*t6+6*t1*t2*t3*t4^2*t5*t6- + 2*n*t1*t2*t3*t4^2*t5*t6-t1^2*t10*t2^2*t6^2+n*t1^2*t10*t2^2*t6^2- + 2*t1*t2^2*t4^2*t6^2-3*n*t1*t2^2*t4^2*t6^2+n^2*t1*t2^2*t4^2*t6^2+ + t1^3*t10*t5*t6^2-n*t1^3*t10*t5*t6^2-t1^2*t4^2*t5*t6^2+ + n*t1^2*t4^2*t5*t6^2+6*t1*t2*t3^2*t4*t5*t7+4*n*t1*t2*t3^2*t4*t5*t7- + 2*n^2*t1*t2*t3^2*t4*t5*t7-8*t1*t2^2*t3*t4*t6*t7- + 8*n*t1*t2^2*t3*t4*t6*t7+4*n^2*t1*t2^2*t3*t4*t6*t7- + 4*t1^2*t3*t4*t5*t6*t7+6*t1^2*t2*t4*t6^2*t7+4*n*t1^2*t2*t4*t6^2*t7- + 2*n^2*t1^2*t2*t4*t6^2*t7-2*t1*t2^2*t3^2*t7^2-t1^2*t3^2*t5*t7^2- + 2*n*t1^2*t3^2*t5*t7^2+n^2*t1^2*t3^2*t5*t7^2+6*t1^2*t2*t3*t6*t7^2+ + 4*n*t1^2*t2*t3*t6*t7^2-2*n^2*t1^2*t2*t3*t6*t7^2-3*t1^3*t6^2*t7^2- + 2*n*t1^3*t6^2*t7^2+n^2*t1^3*t6^2*t7^2-t1*t10*t2^4*t8+ + n*t1*t10*t2^4*t8-3*n*t2^4*t4^2*t8+n^2*t2^4*t4^2*t8+ + 2*t1^2*t10*t2^2*t5*t8-2*n*t1^2*t10*t2^2*t5*t8-t1*t2^2*t4^2*t5*t8+ + 4*n*t1*t2^2*t4^2*t5*t8-n^2*t1*t2^2*t4^2*t5*t8-t1^3*t10*t5^2*t8+ + n*t1^3*t10*t5^2*t8+t1^2*t4^2*t5^2*t8-n*t1^2*t4^2*t5^2*t8+ + 2*t1*t2^3*t4*t7*t8+4*n*t1*t2^3*t4*t7*t8-2*n^2*t1*t2^3*t4*t7*t8- + 2*t1^2*t2*t4*t5*t7*t8-4*n*t1^2*t2*t4*t5*t7*t8+ + 2*n^2*t1^2*t2*t4*t5*t7*t8-t1^2*t2^2*t7^2*t8-2*n*t1^2*t2^2*t7^2*t8+ + n^2*t1^2*t2^2*t7^2*t8+t1^3*t5*t7^2*t8+2*n*t1^3*t5*t7^2*t8- + n^2*t1^3*t5*t7^2*t8-4*t1*t2^2*t3*t4*t5*t9+4*t1^2*t3*t4*t5^2*t9+ + 4*t1*t2^3*t4*t6*t9-4*t1^2*t2*t4*t5*t6*t9+4*t1*t2^3*t3*t7*t9- + 4*t1^2*t2*t3*t5*t7*t9-4*t1^2*t2^2*t6*t7*t9+4*t1^3*t5*t6*t7*t9- + 2*t1*t2^4*t9^2+4*t1^2*t2^2*t5*t9^2-2*t1^3*t5^2*t9^2, + s8->-3*n*t10*t2^4*t3^2+n^2*t10*t2^4*t3^2-t1*t10*t2^2*t3^2*t5+ + 4*n*t1*t10*t2^2*t3^2*t5-n^2*t1*t10*t2^2*t3^2*t5- + 3*n*t2^2*t3^2*t4^2*t5+n^2*t2^2*t3^2*t4^2*t5+t1^2*t10*t3^2*t5^2- + n*t1^2*t10*t3^2*t5^2-3*t1*t3^2*t4^2*t5^2+n*t1*t3^2*t4^2*t5^2+ + 2*t1*t10*t2^3*t3*t6+4*n*t1*t10*t2^3*t3*t6-2*n^2*t1*t10*t2^3*t3*t6- + 2*t1^2*t10*t2*t3*t5*t6-4*n*t1^2*t10*t2*t3*t5*t6+ + 2*n^2*t1^2*t10*t2*t3*t5*t6+6*t1*t2*t3*t4^2*t5*t6+ + 4*n*t1*t2*t3*t4^2*t5*t6-2*n^2*t1*t2*t3*t4^2*t5*t6- + t1^2*t10*t2^2*t6^2-2*n*t1^2*t10*t2^2*t6^2+n^2*t1^2*t10*t2^2*t6^2- + 2*t1*t2^2*t4^2*t6^2+t1^3*t10*t5*t6^2+2*n*t1^3*t10*t5*t6^2- + n^2*t1^3*t10*t5*t6^2-t1^2*t4^2*t5*t6^2-2*n*t1^2*t4^2*t5*t6^2+ + n^2*t1^2*t4^2*t5*t6^2+6*n*t2^3*t3^2*t4*t7-2*n^2*t2^3*t3^2*t4*t7+ + 6*t1*t2*t3^2*t4*t5*t7-2*n*t1*t2*t3^2*t4*t5*t7-8*t1*t2^2*t3*t4*t6*t7- + 8*n*t1*t2^2*t3*t4*t6*t7+4*n^2*t1*t2^2*t3*t4*t6*t7- + 4*t1^2*t3*t4*t5*t6*t7+6*t1^2*t2*t4*t6^2*t7+4*n*t1^2*t2*t4*t6^2*t7- + 2*n^2*t1^2*t2*t4*t6^2*t7-2*t1*t2^2*t3^2*t7^2-3*n*t1*t2^2*t3^2*t7^2+ + n^2*t1*t2^2*t3^2*t7^2-t1^2*t3^2*t5*t7^2+n*t1^2*t3^2*t5*t7^2+ + 6*t1^2*t2*t3*t6*t7^2+4*n*t1^2*t2*t3*t6*t7^2- + 2*n^2*t1^2*t2*t3*t6*t7^2-3*t1^3*t6^2*t7^2-2*n*t1^3*t6^2*t7^2+ + n^2*t1^3*t6^2*t7^2-t1*t10*t2^4*t8+n*t1*t10*t2^4*t8+ + 2*t1^2*t10*t2^2*t5*t8-2*n*t1^2*t10*t2^2*t5*t8-t1*t2^2*t4^2*t5*t8+ + n*t1*t2^2*t4^2*t5*t8-t1^3*t10*t5^2*t8+n*t1^3*t10*t5^2*t8+ + t1^2*t4^2*t5^2*t8-n*t1^2*t4^2*t5^2*t8+2*t1*t2^3*t4*t7*t8- + 2*n*t1*t2^3*t4*t7*t8-2*t1^2*t2*t4*t5*t7*t8+2*n*t1^2*t2*t4*t5*t7*t8- + t1^2*t2^2*t7^2*t8+n*t1^2*t2^2*t7^2*t8+t1^3*t5*t7^2*t8- + n*t1^3*t5*t7^2*t8-4*t1*t2^2*t3*t4*t5*t9+4*t1^2*t3*t4*t5^2*t9+ + 4*t1*t2^3*t4*t6*t9-4*t1^2*t2*t4*t5*t6*t9+4*t1*t2^3*t3*t7*t9- + 4*t1^2*t2*t3*t5*t7*t9-4*t1^2*t2^2*t6*t7*t9+4*t1^3*t5*t6*t7*t9- + 2*t1*t2^4*t9^2+4*t1^2*t2^2*t5*t9^2-2*t1^3*t5^2*t9^2, + s9->n*t1*t10*t2^4*t3^2-2*n*t2^4*t3^2*t4^2+n^2*t2^4*t3^2*t4^2+ + t1^2*t10*t2^2*t3^2*t5-n*t1^2*t10*t2^2*t3^2*t5+ + 6*n*t1*t2^2*t3^2*t4^2*t5-t1^3*t10*t3^2*t5^2+3*t1^2*t3^2*t4^2*t5^2- + 2*t1^2*t10*t2^3*t3*t6-2*n*t1^2*t10*t2^3*t3*t6- + 2*n*t1*t2^3*t3*t4^2*t6-2*n^2*t1*t2^3*t3*t4^2*t6+ + 2*t1^3*t10*t2*t3*t5*t6+2*n*t1^3*t10*t2*t3*t5*t6- + 6*t1^2*t2*t3*t4^2*t5*t6-6*n*t1^2*t2*t3*t4^2*t5*t6+ + t1^3*t10*t2^2*t6^2+n*t1^3*t10*t2^2*t6^2+2*t1^2*t2^2*t4^2*t6^2+ + 3*n*t1^2*t2^2*t4^2*t6^2+n^2*t1^2*t2^2*t4^2*t6^2-t1^4*t10*t5*t6^2- + n*t1^4*t10*t5*t6^2+t1^3*t4^2*t5*t6^2+n*t1^3*t4^2*t5*t6^2- + 2*n*t1*t2^3*t3^2*t4*t7-2*n^2*t1*t2^3*t3^2*t4*t7- + 6*t1^2*t2*t3^2*t4*t5*t7-6*n*t1^2*t2*t3^2*t4*t5*t7+ + 8*t1^2*t2^2*t3*t4*t6*t7+12*n*t1^2*t2^2*t3*t4*t6*t7+ + 4*n^2*t1^2*t2^2*t3*t4*t6*t7+4*t1^3*t3*t4*t5*t6*t7+ + 4*n*t1^3*t3*t4*t5*t6*t7-6*t1^3*t2*t4*t6^2*t7-8*n*t1^3*t2*t4*t6^2*t7- + 2*n^2*t1^3*t2*t4*t6^2*t7+2*t1^2*t2^2*t3^2*t7^2+ + 3*n*t1^2*t2^2*t3^2*t7^2+n^2*t1^2*t2^2*t3^2*t7^2+t1^3*t3^2*t5*t7^2+ + n*t1^3*t3^2*t5*t7^2-6*t1^3*t2*t3*t6*t7^2-8*n*t1^3*t2*t3*t6*t7^2- + 2*n^2*t1^3*t2*t3*t6*t7^2+3*t1^4*t6^2*t7^2+4*n*t1^4*t6^2*t7^2+ + n^2*t1^4*t6^2*t7^2+t1^2*t10*t2^4*t8+n*t1*t2^4*t4^2*t8- + 2*t1^3*t10*t2^2*t5*t8+t1^2*t2^2*t4^2*t5*t8-n*t1^2*t2^2*t4^2*t5*t8+ + t1^4*t10*t5^2*t8-t1^3*t4^2*t5^2*t8-2*t1^2*t2^3*t4*t7*t8- + 2*n*t1^2*t2^3*t4*t7*t8+2*t1^3*t2*t4*t5*t7*t8+ + 2*n*t1^3*t2*t4*t5*t7*t8+t1^3*t2^2*t7^2*t8+n*t1^3*t2^2*t7^2*t8- + t1^4*t5*t7^2*t8-n*t1^4*t5*t7^2*t8+4*n*t1*t2^4*t3*t4*t9+ + 4*t1^2*t2^2*t3*t4*t5*t9-4*n*t1^2*t2^2*t3*t4*t5*t9- + 4*t1^3*t3*t4*t5^2*t9-4*t1^2*t2^3*t4*t6*t9-4*n*t1^2*t2^3*t4*t6*t9+ + 4*t1^3*t2*t4*t5*t6*t9+4*n*t1^3*t2*t4*t5*t6*t9-4*t1^2*t2^3*t3*t7*t9- + 4*n*t1^2*t2^3*t3*t7*t9+4*t1^3*t2*t3*t5*t7*t9+ + 4*n*t1^3*t2*t3*t5*t7*t9+4*t1^3*t2^2*t6*t7*t9+4*n*t1^3*t2^2*t6*t7*t9- + 4*t1^4*t5*t6*t7*t9-4*n*t1^4*t5*t6*t7*t9+2*t1^2*t2^4*t9^2- + 4*t1^3*t2^2*t5*t9^2+2*t1^4*t5^2*t9^2, + s10->t10*t2^3*t3^2*t5-t1*t10*t2*t3^2*t5^2+3*t2*t3^2*t4^2*t5^2+ + 2*n*t2*t3^2*t4^2*t5^2-n^2*t2*t3^2*t4^2*t5^2-2*t10*t2^4*t3*t6+ + 2*t1*t10*t2^2*t3*t5*t6-6*t2^2*t3*t4^2*t5*t6-n*t2^2*t3*t4^2*t5*t6+ + n^2*t2^2*t3*t4^2*t5*t6-3*n*t1*t3*t4^2*t5^2*t6+ + n^2*t1*t3*t4^2*t5^2*t6+t1*t10*t2^3*t6^2+2*t2^3*t4^2*t6^2- + n*t2^3*t4^2*t6^2-t1^2*t10*t2*t5*t6^2+t1*t2*t4^2*t5*t6^2+ + 3*n*t1*t2*t4^2*t5*t6^2-n^2*t1*t2*t4^2*t5*t6^2-6*t2^2*t3^2*t4*t5*t7- + 4*n*t2^2*t3^2*t4*t5*t7+2*n^2*t2^2*t3^2*t4*t5*t7+8*t2^3*t3*t4*t6*t7+ + n*t2^3*t3*t4*t6*t7-n^2*t2^3*t3*t4*t6*t7+4*t1*t2*t3*t4*t5*t6*t7+ + 7*n*t1*t2*t3*t4*t5*t6*t7-3*n^2*t1*t2*t3*t4*t5*t6*t7- + 6*t1*t2^2*t4*t6^2*t7-n*t1*t2^2*t4*t6^2*t7+n^2*t1*t2^2*t4*t6^2*t7- + 3*n*t1^2*t4*t5*t6^2*t7+n^2*t1^2*t4*t5*t6^2*t7+2*t2^3*t3^2*t7^2+ + 2*n*t2^3*t3^2*t7^2-n^2*t2^3*t3^2*t7^2+t1*t2*t3^2*t5*t7^2- + 6*t1*t2^2*t3*t6*t7^2-4*n*t1*t2^2*t3*t6*t7^2+ + 2*n^2*t1*t2^2*t3*t6*t7^2+3*t1^2*t2*t6^2*t7^2+2*n*t1^2*t2*t6^2*t7^2- + n^2*t1^2*t2*t6^2*t7^2+t10*t2^5*t8-2*t1*t10*t2^3*t5*t8+ + t2^3*t4^2*t5*t8+t1^2*t10*t2*t5^2*t8-t1*t2*t4^2*t5^2*t8- + 2*t2^4*t4*t7*t8+2*t1*t2^2*t4*t5*t7*t8+t1*t2^3*t7^2*t8- + t1^2*t2*t5*t7^2*t8+4*t2^3*t3*t4*t5*t9+n*t2^3*t3*t4*t5*t9- + n^2*t2^3*t3*t4*t5*t9-4*t1*t2*t3*t4*t5^2*t9-n*t1*t2*t3*t4*t5^2*t9+ + n^2*t1*t2*t3*t4*t5^2*t9-4*t2^4*t4*t6*t9+2*n*t2^4*t4*t6*t9+ + 4*t1*t2^2*t4*t5*t6*t9-5*n*t1*t2^2*t4*t5*t6*t9+ + n^2*t1*t2^2*t4*t5*t6*t9+3*n*t1^2*t4*t5^2*t6*t9- + n^2*t1^2*t4*t5^2*t6*t9-4*t2^4*t3*t7*t9-n*t2^4*t3*t7*t9+ + n^2*t2^4*t3*t7*t9+4*t1*t2^2*t3*t5*t7*t9+n*t1*t2^2*t3*t5*t7*t9- + n^2*t1*t2^2*t3*t5*t7*t9+4*t1*t2^3*t6*t7*t9+n*t1*t2^3*t6*t7*t9- + n^2*t1*t2^3*t6*t7*t9-4*t1^2*t2*t5*t6*t7*t9-n*t1^2*t2*t5*t6*t7*t9+ + n^2*t1^2*t2*t5*t6*t7*t9+2*t2^5*t9^2-n*t2^5*t9^2-4*t1*t2^3*t5*t9^2+ + 2*n*t1*t2^3*t5*t9^2+2*t1^2*t2*t5^2*t9^2-n*t1^2*t2*t5^2*t9^2, + s11->t10*t2^3*t3^2*t5-t1*t10*t2*t3^2*t5^2+3*t2*t3^2*t4^2*t5^2+ + 2*n*t2*t3^2*t4^2*t5^2-n^2*t2*t3^2*t4^2*t5^2-2*t10*t2^4*t3*t6+ + 2*t1*t10*t2^2*t3*t5*t6-6*t2^2*t3*t4^2*t5*t6-4*n*t2^2*t3*t4^2*t5*t6+ + 2*n^2*t2^2*t3*t4^2*t5*t6+t1*t10*t2^3*t6^2+2*t2^3*t4^2*t6^2+ + 2*n*t2^3*t4^2*t6^2-n^2*t2^3*t4^2*t6^2-t1^2*t10*t2*t5*t6^2+ + t1*t2*t4^2*t5*t6^2-6*t2^2*t3^2*t4*t5*t7-n*t2^2*t3^2*t4*t5*t7+ + n^2*t2^2*t3^2*t4*t5*t7-3*n*t1*t3^2*t4*t5^2*t7+ + n^2*t1*t3^2*t4*t5^2*t7+8*t2^3*t3*t4*t6*t7+n*t2^3*t3*t4*t6*t7- + n^2*t2^3*t3*t4*t6*t7+4*t1*t2*t3*t4*t5*t6*t7+ + 7*n*t1*t2*t3*t4*t5*t6*t7-3*n^2*t1*t2*t3*t4*t5*t6*t7- + 6*t1*t2^2*t4*t6^2*t7-4*n*t1*t2^2*t4*t6^2*t7+ + 2*n^2*t1*t2^2*t4*t6^2*t7+2*t2^3*t3^2*t7^2-n*t2^3*t3^2*t7^2+ + t1*t2*t3^2*t5*t7^2+3*n*t1*t2*t3^2*t5*t7^2-n^2*t1*t2*t3^2*t5*t7^2- + 6*t1*t2^2*t3*t6*t7^2-n*t1*t2^2*t3*t6*t7^2+n^2*t1*t2^2*t3*t6*t7^2- + 3*n*t1^2*t3*t5*t6*t7^2+n^2*t1^2*t3*t5*t6*t7^2+3*t1^2*t2*t6^2*t7^2+ + 2*n*t1^2*t2*t6^2*t7^2-n^2*t1^2*t2*t6^2*t7^2+t10*t2^5*t8- + 2*t1*t10*t2^3*t5*t8+t2^3*t4^2*t5*t8+t1^2*t10*t2*t5^2*t8- + t1*t2*t4^2*t5^2*t8-2*t2^4*t4*t7*t8+2*t1*t2^2*t4*t5*t7*t8+ + t1*t2^3*t7^2*t8-t1^2*t2*t5*t7^2*t8+4*t2^3*t3*t4*t5*t9+ + n*t2^3*t3*t4*t5*t9-n^2*t2^3*t3*t4*t5*t9-4*t1*t2*t3*t4*t5^2*t9- + n*t1*t2*t3*t4*t5^2*t9+n^2*t1*t2*t3*t4*t5^2*t9-4*t2^4*t4*t6*t9- + n*t2^4*t4*t6*t9+n^2*t2^4*t4*t6*t9+4*t1*t2^2*t4*t5*t6*t9+ + n*t1*t2^2*t4*t5*t6*t9-n^2*t1*t2^2*t4*t5*t6*t9-4*t2^4*t3*t7*t9+ + 2*n*t2^4*t3*t7*t9+4*t1*t2^2*t3*t5*t7*t9-5*n*t1*t2^2*t3*t5*t7*t9+ + n^2*t1*t2^2*t3*t5*t7*t9+3*n*t1^2*t3*t5^2*t7*t9- + n^2*t1^2*t3*t5^2*t7*t9+4*t1*t2^3*t6*t7*t9+n*t1*t2^3*t6*t7*t9- + n^2*t1*t2^3*t6*t7*t9-4*t1^2*t2*t5*t6*t7*t9-n*t1^2*t2*t5*t6*t7*t9+ + n^2*t1^2*t2*t5*t6*t7*t9+2*t2^5*t9^2-n*t2^5*t9^2-4*t1*t2^3*t5*t9^2+ + 2*n*t1*t2^3*t5*t9^2+2*t1^2*t2*t5^2*t9^2-n*t1^2*t2*t5^2*t9^2, + s12->t10*t2^3*t3^2*t5-n*t10*t2^3*t3^2*t5-t1*t10*t2*t3^2*t5^2+ + n*t1*t10*t2*t3^2*t5^2+3*t2*t3^2*t4^2*t5^2+2*n*t2*t3^2*t4^2*t5^2- + n^2*t2*t3^2*t4^2*t5^2-2*t10*t2^4*t3*t6+2*n*t10*t2^4*t3*t6+ + 2*t1*t10*t2^2*t3*t5*t6-2*n*t1*t10*t2^2*t3*t5*t6- + 6*t2^2*t3*t4^2*t5*t6-4*n*t2^2*t3*t4^2*t5*t6+ + 2*n^2*t2^2*t3*t4^2*t5*t6+t1*t10*t2^3*t6^2-n*t1*t10*t2^3*t6^2+ + 2*t2^3*t4^2*t6^2-t1^2*t10*t2*t5*t6^2+n*t1^2*t10*t2*t5*t6^2+ + t1*t2*t4^2*t5*t6^2+2*n*t1*t2*t4^2*t5*t6^2-n^2*t1*t2*t4^2*t5*t6^2- + 6*t2^2*t3^2*t4*t5*t7-n*t2^2*t3^2*t4*t5*t7+n^2*t2^2*t3^2*t4*t5*t7- + 3*n*t1*t3^2*t4*t5^2*t7+n^2*t1*t3^2*t4*t5^2*t7+8*t2^3*t3*t4*t6*t7+ + 2*n*t2^3*t3*t4*t6*t7-2*n^2*t2^3*t3*t4*t6*t7+4*t1*t2*t3*t4*t5*t6*t7+ + 6*n*t1*t2*t3*t4*t5*t6*t7-2*n^2*t1*t2*t3*t4*t5*t6*t7- + 6*t1*t2^2*t4*t6^2*t7-n*t1*t2^2*t4*t6^2*t7+n^2*t1*t2^2*t4*t6^2*t7- + 3*n*t1^2*t4*t5*t6^2*t7+n^2*t1^2*t4*t5*t6^2*t7+2*t2^3*t3^2*t7^2+ + t1*t2*t3^2*t5*t7^2+2*n*t1*t2*t3^2*t5*t7^2-n^2*t1*t2*t3^2*t5*t7^2- + 6*t1*t2^2*t3*t6*t7^2-4*n*t1*t2^2*t3*t6*t7^2+ + 2*n^2*t1*t2^2*t3*t6*t7^2+3*t1^2*t2*t6^2*t7^2+2*n*t1^2*t2*t6^2*t7^2- + n^2*t1^2*t2*t6^2*t7^2+t10*t2^5*t8-n*t10*t2^5*t8- + 2*t1*t10*t2^3*t5*t8+2*n*t1*t10*t2^3*t5*t8+t2^3*t4^2*t5*t8+ + 2*n*t2^3*t4^2*t5*t8-n^2*t2^3*t4^2*t5*t8+t1^2*t10*t2*t5^2*t8- + n*t1^2*t10*t2*t5^2*t8-t1*t2*t4^2*t5^2*t8-2*n*t1*t2*t4^2*t5^2*t8+ + n^2*t1*t2*t4^2*t5^2*t8-2*t2^4*t4*t7*t8-n*t2^4*t4*t7*t8+ + n^2*t2^4*t4*t7*t8+2*t1*t2^2*t4*t5*t7*t8-2*n*t1*t2^2*t4*t5*t7*t8+ + 3*n*t1^2*t4*t5^2*t7*t8-n^2*t1^2*t4*t5^2*t7*t8+t1*t2^3*t7^2*t8+ + 2*n*t1*t2^3*t7^2*t8-n^2*t1*t2^3*t7^2*t8-t1^2*t2*t5*t7^2*t8- + 2*n*t1^2*t2*t5*t7^2*t8+n^2*t1^2*t2*t5*t7^2*t8+4*t2^3*t3*t4*t5*t9- + 4*t1*t2*t3*t4*t5^2*t9-4*t2^4*t4*t6*t9+4*t1*t2^2*t4*t5*t6*t9- + 4*t2^4*t3*t7*t9+4*t1*t2^2*t3*t5*t7*t9+4*t1*t2^3*t6*t7*t9- + 4*t1^2*t2*t5*t6*t7*t9+2*t2^5*t9^2-4*t1*t2^3*t5*t9^2+ + 2*t1^2*t2*t5^2*t9^2,s13->t10*t2^3*t3^2*t5+2*n*t10*t2^3*t3^2*t5- + n^2*t10*t2^3*t3^2*t5-t1*t10*t2*t3^2*t5^2-2*n*t1*t10*t2*t3^2*t5^2+ + n^2*t1*t10*t2*t3^2*t5^2+3*t2*t3^2*t4^2*t5^2+2*n*t2*t3^2*t4^2*t5^2- + n^2*t2*t3^2*t4^2*t5^2-2*t10*t2^4*t3*t6-n*t10*t2^4*t3*t6+ + n^2*t10*t2^4*t3*t6+2*t1*t10*t2^2*t3*t5*t6-2*n*t1*t10*t2^2*t3*t5*t6- + 6*t2^2*t3*t4^2*t5*t6-n*t2^2*t3*t4^2*t5*t6+n^2*t2^2*t3*t4^2*t5*t6+ + 3*n*t1^2*t10*t3*t5^2*t6-n^2*t1^2*t10*t3*t5^2*t6- + 3*n*t1*t3*t4^2*t5^2*t6+n^2*t1*t3*t4^2*t5^2*t6+t1*t10*t2^3*t6^2+ + 2*n*t1*t10*t2^3*t6^2-n^2*t1*t10*t2^3*t6^2+2*t2^3*t4^2*t6^2- + t1^2*t10*t2*t5*t6^2-2*n*t1^2*t10*t2*t5*t6^2+n^2*t1^2*t10*t2*t5*t6^2+ + t1*t2*t4^2*t5*t6^2+2*n*t1*t2*t4^2*t5*t6^2-n^2*t1*t2*t4^2*t5*t6^2- + 6*t2^2*t3^2*t4*t5*t7-4*n*t2^2*t3^2*t4*t5*t7+ + 2*n^2*t2^2*t3^2*t4*t5*t7+8*t2^3*t3*t4*t6*t7+2*n*t2^3*t3*t4*t6*t7- + 2*n^2*t2^3*t3*t4*t6*t7+4*t1*t2*t3*t4*t5*t6*t7+ + 6*n*t1*t2*t3*t4*t5*t6*t7-2*n^2*t1*t2*t3*t4*t5*t6*t7- + 6*t1*t2^2*t4*t6^2*t7-4*n*t1*t2^2*t4*t6^2*t7+ + 2*n^2*t1*t2^2*t4*t6^2*t7+2*t2^3*t3^2*t7^2+t1*t2*t3^2*t5*t7^2+ + 2*n*t1*t2*t3^2*t5*t7^2-n^2*t1*t2*t3^2*t5*t7^2-6*t1*t2^2*t3*t6*t7^2- + n*t1*t2^2*t3*t6*t7^2+n^2*t1*t2^2*t3*t6*t7^2-3*n*t1^2*t3*t5*t6*t7^2+ + n^2*t1^2*t3*t5*t6*t7^2+3*t1^2*t2*t6^2*t7^2+2*n*t1^2*t2*t6^2*t7^2- + n^2*t1^2*t2*t6^2*t7^2+t10*t2^5*t8-n*t10*t2^5*t8- + 2*t1*t10*t2^3*t5*t8+2*n*t1*t10*t2^3*t5*t8+t2^3*t4^2*t5*t8- + n*t2^3*t4^2*t5*t8+t1^2*t10*t2*t5^2*t8-n*t1^2*t10*t2*t5^2*t8- + t1*t2*t4^2*t5^2*t8+n*t1*t2*t4^2*t5^2*t8-2*t2^4*t4*t7*t8+ + 2*n*t2^4*t4*t7*t8+2*t1*t2^2*t4*t5*t7*t8-2*n*t1*t2^2*t4*t5*t7*t8+ + t1*t2^3*t7^2*t8-n*t1*t2^3*t7^2*t8-t1^2*t2*t5*t7^2*t8+ + n*t1^2*t2*t5*t7^2*t8+4*t2^3*t3*t4*t5*t9-4*t1*t2*t3*t4*t5^2*t9- + 4*t2^4*t4*t6*t9+4*t1*t2^2*t4*t5*t6*t9-4*t2^4*t3*t7*t9+ + 4*t1*t2^2*t3*t5*t7*t9+4*t1*t2^3*t6*t7*t9-4*t1^2*t2*t5*t6*t7*t9+ + 2*t2^5*t9^2-4*t1*t2^3*t5*t9^2+2*t1^2*t2*t5^2*t9^2, + s14->-(n*t10*t2^5*t3^2)-t1*t10*t2^3*t3^2*t5+n*t1*t10*t2^3*t3^2*t5- + n*t2^3*t3^2*t4^2*t5-n^2*t2^3*t3^2*t4^2*t5+t1^2*t10*t2*t3^2*t5^2- + 3*t1*t2*t3^2*t4^2*t5^2-3*n*t1*t2*t3^2*t4^2*t5^2+2*t1*t10*t2^4*t3*t6+ + 2*n*t1*t10*t2^4*t3*t6+2*n*t2^4*t3*t4^2*t6-2*t1^2*t10*t2^2*t3*t5*t6- + 2*n*t1^2*t10*t2^2*t3*t5*t6+6*t1*t2^2*t3*t4^2*t5*t6+ + 4*n*t1*t2^2*t3*t4^2*t5*t6+2*n^2*t1*t2^2*t3*t4^2*t5*t6+ + 2*n*t1^2*t3*t4^2*t5^2*t6-t1^2*t10*t2^3*t6^2-n*t1^2*t10*t2^3*t6^2- + 2*t1*t2^3*t4^2*t6^2-2*n*t1*t2^3*t4^2*t6^2+t1^3*t10*t2*t5*t6^2+ + n*t1^3*t10*t2*t5*t6^2-t1^2*t2*t4^2*t5*t6^2-2*n*t1^2*t2*t4^2*t5*t6^2- + n^2*t1^2*t2*t4^2*t5*t6^2+2*n*t2^4*t3^2*t4*t7+n^2*t2^4*t3^2*t4*t7+ + 6*t1*t2^2*t3^2*t4*t5*t7+5*n*t1*t2^2*t3^2*t4*t5*t7+ + n^2*t1*t2^2*t3^2*t4*t5*t7+n*t1^2*t3^2*t4*t5^2*t7- + 8*t1*t2^3*t3*t4*t6*t7-10*n*t1*t2^3*t3*t4*t6*t7- + 2*n^2*t1*t2^3*t3*t4*t6*t7-4*t1^2*t2*t3*t4*t5*t6*t7- + 6*n*t1^2*t2*t3*t4*t5*t6*t7-2*n^2*t1^2*t2*t3*t4*t5*t6*t7+ + 6*t1^2*t2^2*t4*t6^2*t7+7*n*t1^2*t2^2*t4*t6^2*t7+ + n^2*t1^2*t2^2*t4*t6^2*t7+n*t1^3*t4*t5*t6^2*t7+ + n^2*t1^3*t4*t5*t6^2*t7-2*t1*t2^3*t3^2*t7^2-3*n*t1*t2^3*t3^2*t7^2- + n^2*t1*t2^3*t3^2*t7^2-t1^2*t2*t3^2*t5*t7^2-n*t1^2*t2*t3^2*t5*t7^2+ + 6*t1^2*t2^2*t3*t6*t7^2+8*n*t1^2*t2^2*t3*t6*t7^2+ + 2*n^2*t1^2*t2^2*t3*t6*t7^2-3*t1^3*t2*t6^2*t7^2- + 4*n*t1^3*t2*t6^2*t7^2-n^2*t1^3*t2*t6^2*t7^2-t1*t10*t2^5*t8+ + 2*t1^2*t10*t2^3*t5*t8-t1*t2^3*t4^2*t5*t8-n*t1*t2^3*t4^2*t5*t8- + t1^3*t10*t2*t5^2*t8+t1^2*t2*t4^2*t5^2*t8+n*t1^2*t2*t4^2*t5^2*t8+ + 2*t1*t2^4*t4*t7*t8+n*t1*t2^4*t4*t7*t8-2*t1^2*t2^2*t4*t5*t7*t8- + n*t1^3*t4*t5^2*t7*t8-t1^2*t2^3*t7^2*t8-n*t1^2*t2^3*t7^2*t8+ + t1^3*t2*t5*t7^2*t8+n*t1^3*t2*t5*t7^2*t8-2*n*t2^5*t3*t4*t9- + 4*t1*t2^3*t3*t4*t5*t9+4*t1^2*t2*t3*t4*t5^2*t9+ + 2*n*t1^2*t2*t3*t4*t5^2*t9+4*t1*t2^4*t4*t6*t9+2*n*t1*t2^4*t4*t6*t9- + 4*t1^2*t2^2*t4*t5*t6*t9-2*n*t1^3*t4*t5^2*t6*t9+4*t1*t2^4*t3*t7*t9+ + 4*n*t1*t2^4*t3*t7*t9-4*t1^2*t2^2*t3*t5*t7*t9- + 4*n*t1^2*t2^2*t3*t5*t7*t9-4*t1^2*t2^3*t6*t7*t9- + 4*n*t1^2*t2^3*t6*t7*t9+4*t1^3*t2*t5*t6*t7*t9+ + 4*n*t1^3*t2*t5*t6*t7*t9-2*t1*t2^5*t9^2+4*t1^2*t2^3*t5*t9^2- + 2*t1^3*t2*t5^2*t9^2,s15->-(t1*t10*t2^3*t3^2*t5)- + n*t1*t10*t2^3*t3^2*t5-n*t2^3*t3^2*t4^2*t5-n^2*t2^3*t3^2*t4^2*t5+ + t1^2*t10*t2*t3^2*t5^2+n*t1^2*t10*t2*t3^2*t5^2- + 3*t1*t2*t3^2*t4^2*t5^2-3*n*t1*t2*t3^2*t4^2*t5^2+2*t1*t10*t2^4*t3*t6+ + n*t1*t10*t2^4*t3*t6+2*n*t2^4*t3*t4^2*t6+n^2*t2^4*t3*t4^2*t6- + 2*t1^2*t10*t2^2*t3*t5*t6+6*t1*t2^2*t3*t4^2*t5*t6+ + 5*n*t1*t2^2*t3*t4^2*t5*t6+n^2*t1*t2^2*t3*t4^2*t5*t6- + n*t1^3*t10*t3*t5^2*t6+n*t1^2*t3*t4^2*t5^2*t6-t1^2*t10*t2^3*t6^2- + n*t1^2*t10*t2^3*t6^2-2*t1*t2^3*t4^2*t6^2-3*n*t1*t2^3*t4^2*t6^2- + n^2*t1*t2^3*t4^2*t6^2+t1^3*t10*t2*t5*t6^2+n*t1^3*t10*t2*t5*t6^2- + t1^2*t2*t4^2*t5*t6^2-n*t1^2*t2*t4^2*t5*t6^2+2*n*t2^4*t3^2*t4*t7+ + 6*t1*t2^2*t3^2*t4*t5*t7+4*n*t1*t2^2*t3^2*t4*t5*t7+ + 2*n^2*t1*t2^2*t3^2*t4*t5*t7+2*n*t1^2*t3^2*t4*t5^2*t7- + 8*t1*t2^3*t3*t4*t6*t7-10*n*t1*t2^3*t3*t4*t6*t7- + 2*n^2*t1*t2^3*t3*t4*t6*t7-4*t1^2*t2*t3*t4*t5*t6*t7- + 6*n*t1^2*t2*t3*t4*t5*t6*t7-2*n^2*t1^2*t2*t3*t4*t5*t6*t7+ + 6*t1^2*t2^2*t4*t6^2*t7+8*n*t1^2*t2^2*t4*t6^2*t7+ + 2*n^2*t1^2*t2^2*t4*t6^2*t7-2*t1*t2^3*t3^2*t7^2- + 2*n*t1*t2^3*t3^2*t7^2-t1^2*t2*t3^2*t5*t7^2-2*n*t1^2*t2*t3^2*t5*t7^2- + n^2*t1^2*t2*t3^2*t5*t7^2+6*t1^2*t2^2*t3*t6*t7^2+ + 7*n*t1^2*t2^2*t3*t6*t7^2+n^2*t1^2*t2^2*t3*t6*t7^2+ + n*t1^3*t3*t5*t6*t7^2+n^2*t1^3*t3*t5*t6*t7^2-3*t1^3*t2*t6^2*t7^2- + 4*n*t1^3*t2*t6^2*t7^2-n^2*t1^3*t2*t6^2*t7^2-t1*t10*t2^5*t8- + n*t2^5*t4^2*t8+2*t1^2*t10*t2^3*t5*t8-t1*t2^3*t4^2*t5*t8+ + n*t1*t2^3*t4^2*t5*t8-t1^3*t10*t2*t5^2*t8+t1^2*t2*t4^2*t5^2*t8+ + 2*t1*t2^4*t4*t7*t8+2*n*t1*t2^4*t4*t7*t8-2*t1^2*t2^2*t4*t5*t7*t8- + 2*n*t1^2*t2^2*t4*t5*t7*t8-t1^2*t2^3*t7^2*t8-n*t1^2*t2^3*t7^2*t8+ + t1^3*t2*t5*t7^2*t8+n*t1^3*t2*t5*t7^2*t8-2*n*t2^5*t3*t4*t9- + 4*t1*t2^3*t3*t4*t5*t9+4*t1^2*t2*t3*t4*t5^2*t9+ + 2*n*t1^2*t2*t3*t4*t5^2*t9+4*t1*t2^4*t4*t6*t9+4*n*t1*t2^4*t4*t6*t9- + 4*t1^2*t2^2*t4*t5*t6*t9-4*n*t1^2*t2^2*t4*t5*t6*t9+ + 4*t1*t2^4*t3*t7*t9+2*n*t1*t2^4*t3*t7*t9-4*t1^2*t2^2*t3*t5*t7*t9- + 2*n*t1^3*t3*t5^2*t7*t9-4*t1^2*t2^3*t6*t7*t9-4*n*t1^2*t2^3*t6*t7*t9+ + 4*t1^3*t2*t5*t6*t7*t9+4*n*t1^3*t2*t5*t6*t7*t9-2*t1*t2^5*t9^2+ + 4*t1^2*t2^3*t5*t9^2-2*t1^3*t2*t5^2*t9^2, + s16->-(t10*t2^2*t3^2*t5^2)+t1*t10*t3^2*t5^3-3*t3^2*t4^2*t5^3- + 2*n*t3^2*t4^2*t5^3+n^2*t3^2*t4^2*t5^3+2*t10*t2^3*t3*t5*t6- + 2*t1*t10*t2*t3*t5^2*t6+6*t2*t3*t4^2*t5^2*t6+4*n*t2*t3*t4^2*t5^2*t6- + 2*n^2*t2*t3*t4^2*t5^2*t6-t1*t10*t2^2*t5*t6^2-2*t2^2*t4^2*t5*t6^2- + 2*n*t2^2*t4^2*t5*t6^2+n^2*t2^2*t4^2*t5*t6^2+t1^2*t10*t5^2*t6^2- + t1*t4^2*t5^2*t6^2+6*t2*t3^2*t4*t5^2*t7+4*n*t2*t3^2*t4*t5^2*t7- + 2*n^2*t2*t3^2*t4*t5^2*t7-8*t2^2*t3*t4*t5*t6*t7- + 7*n*t2^2*t3*t4*t5*t6*t7+3*n^2*t2^2*t3*t4*t5*t6*t7- + 4*t1*t3*t4*t5^2*t6*t7-n*t1*t3*t4*t5^2*t6*t7+n^2*t1*t3*t4*t5^2*t6*t7+ + 3*n*t2^3*t4*t6^2*t7-n^2*t2^3*t4*t6^2*t7+6*t1*t2*t4*t5*t6^2*t7+ + n*t1*t2*t4*t5*t6^2*t7-n^2*t1*t2*t4*t5*t6^2*t7-2*t2^2*t3^2*t5*t7^2- + 2*n*t2^2*t3^2*t5*t7^2+n^2*t2^2*t3^2*t5*t7^2-t1*t3^2*t5^2*t7^2+ + 3*n*t2^3*t3*t6*t7^2-n^2*t2^3*t3*t6*t7^2+6*t1*t2*t3*t5*t6*t7^2+ + n*t1*t2*t3*t5*t6*t7^2-n^2*t1*t2*t3*t5*t6*t7^2-3*n*t1*t2^2*t6^2*t7^2+ + n^2*t1*t2^2*t6^2*t7^2-3*t1^2*t5*t6^2*t7^2+n*t1^2*t5*t6^2*t7^2- + t10*t2^4*t5*t8+2*t1*t10*t2^2*t5^2*t8-t2^2*t4^2*t5^2*t8- + t1^2*t10*t5^3*t8+t1*t4^2*t5^3*t8+2*t2^3*t4*t5*t7*t8- + 2*t1*t2*t4*t5^2*t7*t8-t1*t2^2*t5*t7^2*t8+t1^2*t5^2*t7^2*t8- + 4*t2^2*t3*t4*t5^2*t9-n*t2^2*t3*t4*t5^2*t9+n^2*t2^2*t3*t4*t5^2*t9+ + 4*t1*t3*t4*t5^3*t9+n*t1*t3*t4*t5^3*t9-n^2*t1*t3*t4*t5^3*t9+ + 4*t2^3*t4*t5*t6*t9+n*t2^3*t4*t5*t6*t9-n^2*t2^3*t4*t5*t6*t9- + 4*t1*t2*t4*t5^2*t6*t9-n*t1*t2*t4*t5^2*t6*t9+n^2*t1*t2*t4*t5^2*t6*t9+ + 4*t2^3*t3*t5*t7*t9+n*t2^3*t3*t5*t7*t9-n^2*t2^3*t3*t5*t7*t9- + 4*t1*t2*t3*t5^2*t7*t9-n*t1*t2*t3*t5^2*t7*t9+n^2*t1*t2*t3*t5^2*t7*t9- + 3*n*t2^4*t6*t7*t9+n^2*t2^4*t6*t7*t9-4*t1*t2^2*t5*t6*t7*t9+ + 5*n*t1*t2^2*t5*t6*t7*t9-n^2*t1*t2^2*t5*t6*t7*t9+ + 4*t1^2*t5^2*t6*t7*t9-2*n*t1^2*t5^2*t6*t7*t9-2*t2^4*t5*t9^2+ + n*t2^4*t5*t9^2+4*t1*t2^2*t5^2*t9^2-2*n*t1*t2^2*t5^2*t9^2- + 2*t1^2*t5^3*t9^2+n*t1^2*t5^3*t9^2, + s17->-(t10*t2^2*t3^2*t5^2)+n*t10*t2^2*t3^2*t5^2+t1*t10*t3^2*t5^3- + n*t1*t10*t3^2*t5^3-3*t3^2*t4^2*t5^3-2*n*t3^2*t4^2*t5^3+ + n^2*t3^2*t4^2*t5^3+2*t10*t2^3*t3*t5*t6-2*n*t10*t2^3*t3*t5*t6- + 2*t1*t10*t2*t3*t5^2*t6+2*n*t1*t10*t2*t3*t5^2*t6+ + 6*t2*t3*t4^2*t5^2*t6+4*n*t2*t3*t4^2*t5^2*t6- + 2*n^2*t2*t3*t4^2*t5^2*t6-t1*t10*t2^2*t5*t6^2+n*t1*t10*t2^2*t5*t6^2- + 2*t2^2*t4^2*t5*t6^2+t1^2*t10*t5^2*t6^2-n*t1^2*t10*t5^2*t6^2- + t1*t4^2*t5^2*t6^2-2*n*t1*t4^2*t5^2*t6^2+n^2*t1*t4^2*t5^2*t6^2+ + 6*t2*t3^2*t4*t5^2*t7+4*n*t2*t3^2*t4*t5^2*t7- + 2*n^2*t2*t3^2*t4*t5^2*t7-8*t2^2*t3*t4*t5*t6*t7- + 8*n*t2^2*t3*t4*t5*t6*t7+4*n^2*t2^2*t3*t4*t5*t6*t7- + 4*t1*t3*t4*t5^2*t6*t7+6*t1*t2*t4*t5*t6^2*t7+4*n*t1*t2*t4*t5*t6^2*t7- + 2*n^2*t1*t2*t4*t5*t6^2*t7-2*t2^2*t3^2*t5*t7^2-3*n*t2^2*t3^2*t5*t7^2+ + n^2*t2^2*t3^2*t5*t7^2-t1*t3^2*t5^2*t7^2+n*t1*t3^2*t5^2*t7^2+ + 6*n*t2^3*t3*t6*t7^2-2*n^2*t2^3*t3*t6*t7^2+6*t1*t2*t3*t5*t6*t7^2- + 2*n*t1*t2*t3*t5*t6*t7^2-3*n*t1*t2^2*t6^2*t7^2+n^2*t1*t2^2*t6^2*t7^2- + 3*t1^2*t5*t6^2*t7^2+n*t1^2*t5*t6^2*t7^2-t10*t2^4*t5*t8+ + n*t10*t2^4*t5*t8+2*t1*t10*t2^2*t5^2*t8-2*n*t1*t10*t2^2*t5^2*t8- + t2^2*t4^2*t5^2*t8-2*n*t2^2*t4^2*t5^2*t8+n^2*t2^2*t4^2*t5^2*t8- + t1^2*t10*t5^3*t8+n*t1^2*t10*t5^3*t8+t1*t4^2*t5^3*t8+ + 2*n*t1*t4^2*t5^3*t8-n^2*t1*t4^2*t5^3*t8+2*t2^3*t4*t5*t7*t8+ + 4*n*t2^3*t4*t5*t7*t8-2*n^2*t2^3*t4*t5*t7*t8-2*t1*t2*t4*t5^2*t7*t8- + 4*n*t1*t2*t4*t5^2*t7*t8+2*n^2*t1*t2*t4*t5^2*t7*t8-3*n*t2^4*t7^2*t8+ + n^2*t2^4*t7^2*t8-t1*t2^2*t5*t7^2*t8+4*n*t1*t2^2*t5*t7^2*t8- + n^2*t1*t2^2*t5*t7^2*t8+t1^2*t5^2*t7^2*t8-n*t1^2*t5^2*t7^2*t8- + 4*t2^2*t3*t4*t5^2*t9+4*t1*t3*t4*t5^3*t9+4*t2^3*t4*t5*t6*t9- + 4*t1*t2*t4*t5^2*t6*t9+4*t2^3*t3*t5*t7*t9-4*t1*t2*t3*t5^2*t7*t9- + 4*t1*t2^2*t5*t6*t7*t9+4*t1^2*t5^2*t6*t7*t9-2*t2^4*t5*t9^2+ + 4*t1*t2^2*t5^2*t9^2-2*t1^2*t5^3*t9^2, + s18->-(t10*t2^2*t3^2*t5^2)-2*n*t10*t2^2*t3^2*t5^2+ + n^2*t10*t2^2*t3^2*t5^2+t1*t10*t3^2*t5^3+2*n*t1*t10*t3^2*t5^3- + n^2*t1*t10*t3^2*t5^3-3*t3^2*t4^2*t5^3-2*n*t3^2*t4^2*t5^3+ + n^2*t3^2*t4^2*t5^3+2*t10*t2^3*t3*t5*t6+4*n*t10*t2^3*t3*t5*t6- + 2*n^2*t10*t2^3*t3*t5*t6-2*t1*t10*t2*t3*t5^2*t6- + 4*n*t1*t10*t2*t3*t5^2*t6+2*n^2*t1*t10*t2*t3*t5^2*t6+ + 6*t2*t3*t4^2*t5^2*t6+4*n*t2*t3*t4^2*t5^2*t6- + 2*n^2*t2*t3*t4^2*t5^2*t6-3*n*t10*t2^4*t6^2+n^2*t10*t2^4*t6^2- + t1*t10*t2^2*t5*t6^2+4*n*t1*t10*t2^2*t5*t6^2-n^2*t1*t10*t2^2*t5*t6^2- + 2*t2^2*t4^2*t5*t6^2-3*n*t2^2*t4^2*t5*t6^2+n^2*t2^2*t4^2*t5*t6^2+ + t1^2*t10*t5^2*t6^2-n*t1^2*t10*t5^2*t6^2-t1*t4^2*t5^2*t6^2+ + n*t1*t4^2*t5^2*t6^2+6*t2*t3^2*t4*t5^2*t7+4*n*t2*t3^2*t4*t5^2*t7- + 2*n^2*t2*t3^2*t4*t5^2*t7-8*t2^2*t3*t4*t5*t6*t7- + 8*n*t2^2*t3*t4*t5*t6*t7+4*n^2*t2^2*t3*t4*t5*t6*t7- + 4*t1*t3*t4*t5^2*t6*t7+6*n*t2^3*t4*t6^2*t7-2*n^2*t2^3*t4*t6^2*t7+ + 6*t1*t2*t4*t5*t6^2*t7-2*n*t1*t2*t4*t5*t6^2*t7-2*t2^2*t3^2*t5*t7^2- + t1*t3^2*t5^2*t7^2-2*n*t1*t3^2*t5^2*t7^2+n^2*t1*t3^2*t5^2*t7^2+ + 6*t1*t2*t3*t5*t6*t7^2+4*n*t1*t2*t3*t5*t6*t7^2- + 2*n^2*t1*t2*t3*t5*t6*t7^2-3*n*t1*t2^2*t6^2*t7^2+ + n^2*t1*t2^2*t6^2*t7^2-3*t1^2*t5*t6^2*t7^2+n*t1^2*t5*t6^2*t7^2- + t10*t2^4*t5*t8+n*t10*t2^4*t5*t8+2*t1*t10*t2^2*t5^2*t8- + 2*n*t1*t10*t2^2*t5^2*t8-t2^2*t4^2*t5^2*t8+n*t2^2*t4^2*t5^2*t8- + t1^2*t10*t5^3*t8+n*t1^2*t10*t5^3*t8+t1*t4^2*t5^3*t8- + n*t1*t4^2*t5^3*t8+2*t2^3*t4*t5*t7*t8-2*n*t2^3*t4*t5*t7*t8- + 2*t1*t2*t4*t5^2*t7*t8+2*n*t1*t2*t4*t5^2*t7*t8-t1*t2^2*t5*t7^2*t8+ + n*t1*t2^2*t5*t7^2*t8+t1^2*t5^2*t7^2*t8-n*t1^2*t5^2*t7^2*t8- + 4*t2^2*t3*t4*t5^2*t9+4*t1*t3*t4*t5^3*t9+4*t2^3*t4*t5*t6*t9- + 4*t1*t2*t4*t5^2*t6*t9+4*t2^3*t3*t5*t7*t9-4*t1*t2*t3*t5^2*t7*t9- + 4*t1*t2^2*t5*t6*t7*t9+4*t1^2*t5^2*t6*t7*t9-2*t2^4*t5*t9^2+ + 4*t1*t2^2*t5^2*t9^2-2*t1^2*t5^3*t9^2, + s19->-2*t10*t2^4*t3^2*t5-2*n*t10*t2^4*t3^2*t5+n^2*t10*t2^4*t3^2*t5+ + t1*t10*t2^2*t3^2*t5^2+2*n*t1*t10*t2^2*t3^2*t5^2- + n^2*t1*t10*t2^2*t3^2*t5^2-6*t2^2*t3^2*t4^2*t5^2- + 7*n*t2^2*t3^2*t4^2*t5^2+n^3*t2^2*t3^2*t4^2*t5^2+t1^2*t10*t3^2*t5^3- + 3*t1*t3^2*t4^2*t5^3-2*n*t1*t3^2*t4^2*t5^3+n^2*t1*t3^2*t4^2*t5^3+ + 4*t10*t2^5*t3*t6+n*t10*t2^5*t3*t6-n^2*t10*t2^5*t3*t6- + 2*t1*t10*t2^3*t3*t5*t6+2*n*t1*t10*t2^3*t3*t5*t6+ + 12*t2^3*t3*t4^2*t5*t6+11*n*t2^3*t3*t4^2*t5*t6- + 2*n^2*t2^3*t3*t4^2*t5*t6-n^3*t2^3*t3*t4^2*t5*t6- + 2*t1^2*t10*t2*t3*t5^2*t6-3*n*t1^2*t10*t2*t3*t5^2*t6+ + n^2*t1^2*t10*t2*t3*t5^2*t6+6*t1*t2*t3*t4^2*t5^2*t6+ + 7*n*t1*t2*t3*t4^2*t5^2*t6-n^3*t1*t2*t3*t4^2*t5^2*t6- + 2*t1*t10*t2^4*t6^2-2*n*t1*t10*t2^4*t6^2+n^2*t1*t10*t2^4*t6^2- + 4*t2^4*t4^2*t6^2-2*n*t2^4*t4^2*t6^2+n^2*t2^4*t4^2*t6^2+ + t1^2*t10*t2^2*t5*t6^2+2*n*t1^2*t10*t2^2*t5*t6^2- + n^2*t1^2*t10*t2^2*t5*t6^2-4*t1*t2^2*t4^2*t5*t6^2- + 7*n*t1*t2^2*t4^2*t5*t6^2+n^3*t1*t2^2*t4^2*t5*t6^2+ + t1^3*t10*t5^2*t6^2-t1^2*t4^2*t5^2*t6^2+12*t2^3*t3^2*t4*t5*t7+ + 11*n*t2^3*t3^2*t4*t5*t7-2*n^2*t2^3*t3^2*t4*t5*t7- + n^3*t2^3*t3^2*t4*t5*t7+6*t1*t2*t3^2*t4*t5^2*t7+ + 7*n*t1*t2*t3^2*t4*t5^2*t7-n^3*t1*t2*t3^2*t4*t5^2*t7- + 16*t2^4*t3*t4*t6*t7-6*n*t2^4*t3*t4*t6*t7+n^2*t2^4*t3*t4*t6*t7+ + n^3*t2^4*t3*t4*t6*t7-16*t1*t2^2*t3*t4*t5*t6*t7- + 32*n*t1*t2^2*t3*t4*t5*t6*t7+6*n^2*t1*t2^2*t3*t4*t5*t6*t7+ + 2*n^3*t1*t2^2*t3*t4*t5*t6*t7-4*t1^2*t3*t4*t5^2*t6*t7+ + 2*n*t1^2*t3*t4*t5^2*t6*t7-3*n^2*t1^2*t3*t4*t5^2*t6*t7+ + n^3*t1^2*t3*t4*t5^2*t6*t7+12*t1*t2^3*t4*t6^2*t7+ + 11*n*t1*t2^3*t4*t6^2*t7-2*n^2*t1*t2^3*t4*t6^2*t7- + n^3*t1*t2^3*t4*t6^2*t7+6*t1^2*t2*t4*t5*t6^2*t7+ + 7*n*t1^2*t2*t4*t5*t6^2*t7-n^3*t1^2*t2*t4*t5*t6^2*t7- + 4*t2^4*t3^2*t7^2-2*n*t2^4*t3^2*t7^2+n^2*t2^4*t3^2*t7^2- + 4*t1*t2^2*t3^2*t5*t7^2-7*n*t1*t2^2*t3^2*t5*t7^2+ + n^3*t1*t2^2*t3^2*t5*t7^2-t1^2*t3^2*t5^2*t7^2+12*t1*t2^3*t3*t6*t7^2+ + 11*n*t1*t2^3*t3*t6*t7^2-2*n^2*t1*t2^3*t3*t6*t7^2- + n^3*t1*t2^3*t3*t6*t7^2+6*t1^2*t2*t3*t5*t6*t7^2+ + 7*n*t1^2*t2*t3*t5*t6*t7^2-n^3*t1^2*t2*t3*t5*t6*t7^2- + 6*t1^2*t2^2*t6^2*t7^2-7*n*t1^2*t2^2*t6^2*t7^2+ + n^3*t1^2*t2^2*t6^2*t7^2-3*t1^3*t5*t6^2*t7^2-2*n*t1^3*t5*t6^2*t7^2+ + n^2*t1^3*t5*t6^2*t7^2-2*t10*t2^6*t8+n*t10*t2^6*t8+ + 3*t1*t10*t2^4*t5*t8-2*n*t1*t10*t2^4*t5*t8-2*t2^4*t4^2*t5*t8- + 2*n*t2^4*t4^2*t5*t8+n^2*t2^4*t4^2*t5*t8+n*t1^2*t10*t2^2*t5^2*t8+ + t1*t2^2*t4^2*t5^2*t8+2*n*t1*t2^2*t4^2*t5^2*t8- + n^2*t1*t2^2*t4^2*t5^2*t8-t1^3*t10*t5^3*t8+t1^2*t4^2*t5^3*t8+ + 4*t2^5*t4*t7*t8+n*t2^5*t4*t7*t8-n^2*t2^5*t4*t7*t8- + 2*t1*t2^3*t4*t5*t7*t8+2*n*t1*t2^3*t4*t5*t7*t8- + 2*t1^2*t2*t4*t5^2*t7*t8-3*n*t1^2*t2*t4*t5^2*t7*t8+ + n^2*t1^2*t2*t4*t5^2*t7*t8-2*t1*t2^4*t7^2*t8-2*n*t1*t2^4*t7^2*t8+ + n^2*t1*t2^4*t7^2*t8+t1^2*t2^2*t5*t7^2*t8+2*n*t1^2*t2^2*t5*t7^2*t8- + n^2*t1^2*t2^2*t5*t7^2*t8+t1^3*t5^2*t7^2*t8-8*t2^4*t3*t4*t5*t9- + 7*n*t2^4*t3*t4*t5*t9+3*n^2*t2^4*t3*t4*t5*t9+4*t1*t2^2*t3*t4*t5^2*t9+ + 6*n*t1*t2^2*t3*t4*t5^2*t9-2*n^2*t1*t2^2*t3*t4*t5^2*t9+ + 4*t1^2*t3*t4*t5^3*t9+n*t1^2*t3*t4*t5^3*t9-n^2*t1^2*t3*t4*t5^3*t9+ + 8*t2^5*t4*t6*t9+n*t2^5*t4*t6*t9-n^2*t2^5*t4*t6*t9- + 4*t1*t2^3*t4*t5*t6*t9+6*n*t1*t2^3*t4*t5*t6*t9- + 2*n^2*t1*t2^3*t4*t5*t6*t9-4*t1^2*t2*t4*t5^2*t6*t9- + 7*n*t1^2*t2*t4*t5^2*t6*t9+3*n^2*t1^2*t2*t4*t5^2*t6*t9+ + 8*t2^5*t3*t7*t9+n*t2^5*t3*t7*t9-n^2*t2^5*t3*t7*t9- + 4*t1*t2^3*t3*t5*t7*t9+6*n*t1*t2^3*t3*t5*t7*t9- + 2*n^2*t1*t2^3*t3*t5*t7*t9-4*t1^2*t2*t3*t5^2*t7*t9- + 7*n*t1^2*t2*t3*t5^2*t7*t9+3*n^2*t1^2*t2*t3*t5^2*t7*t9- + 8*t1*t2^4*t6*t7*t9-7*n*t1*t2^4*t6*t7*t9+3*n^2*t1*t2^4*t6*t7*t9+ + 4*t1^2*t2^2*t5*t6*t7*t9+6*n*t1^2*t2^2*t5*t6*t7*t9- + 2*n^2*t1^2*t2^2*t5*t6*t7*t9+4*t1^3*t5^2*t6*t7*t9+ + n*t1^3*t5^2*t6*t7*t9-n^2*t1^3*t5^2*t6*t7*t9-4*t2^6*t9^2+ + n*t2^6*t9^2+6*t1*t2^4*t5*t9^2-n*t1*t2^4*t5*t9^2- + n*t1^2*t2^2*t5^2*t9^2-2*t1^3*t5^3*t9^2+n*t1^3*t5^3*t9^2, + s20->-2*t10*t2^4*t3^2*t5+t1*t10*t2^2*t3^2*t5^2- + 2*n*t1*t10*t2^2*t3^2*t5^2+n^2*t1*t10*t2^2*t3^2*t5^2- + 6*t2^2*t3^2*t4^2*t5^2-7*n*t2^2*t3^2*t4^2*t5^2+ + n^3*t2^2*t3^2*t4^2*t5^2+t1^2*t10*t3^2*t5^3+2*n*t1^2*t10*t3^2*t5^3- + n^2*t1^2*t10*t3^2*t5^3-3*t1*t3^2*t4^2*t5^3-2*n*t1*t3^2*t4^2*t5^3+ + n^2*t1*t3^2*t4^2*t5^3+4*t10*t2^5*t3*t6-2*t1*t10*t2^3*t3*t5*t6+ + 4*n*t1*t10*t2^3*t3*t5*t6-2*n^2*t1*t10*t2^3*t3*t5*t6+ + 12*t2^3*t3*t4^2*t5*t6+14*n*t2^3*t3*t4^2*t5*t6- + 2*n^3*t2^3*t3*t4^2*t5*t6-2*t1^2*t10*t2*t3*t5^2*t6- + 4*n*t1^2*t10*t2*t3*t5^2*t6+2*n^2*t1^2*t10*t2*t3*t5^2*t6+ + 6*t1*t2*t3*t4^2*t5^2*t6+4*n*t1*t2*t3*t4^2*t5^2*t6- + 2*n^2*t1*t2*t3*t4^2*t5^2*t6-2*t1*t10*t2^4*t6^2-3*n*t1*t10*t2^4*t6^2+ + n^2*t1*t10*t2^4*t6^2-4*t2^4*t4^2*t6^2-4*n*t2^4*t4^2*t6^2- + n^2*t2^4*t4^2*t6^2+n^3*t2^4*t4^2*t6^2+t1^2*t10*t2^2*t5*t6^2+ + 4*n*t1^2*t10*t2^2*t5*t6^2-n^2*t1^2*t10*t2^2*t5*t6^2- + 4*t1*t2^2*t4^2*t5*t6^2-6*n*t1*t2^2*t4^2*t5*t6^2+ + 2*n^2*t1*t2^2*t4^2*t5*t6^2+t1^3*t10*t5^2*t6^2-n*t1^3*t10*t5^2*t6^2- + t1^2*t4^2*t5^2*t6^2+n*t1^2*t4^2*t5^2*t6^2+12*t2^3*t3^2*t4*t5*t7+ + 8*n*t2^3*t3^2*t4*t5*t7-4*n^2*t2^3*t3^2*t4*t5*t7+ + 6*t1*t2*t3^2*t4*t5^2*t7+10*n*t1*t2*t3^2*t4*t5^2*t7+ + 2*n^2*t1*t2*t3^2*t4*t5^2*t7-2*n^3*t1*t2*t3^2*t4*t5^2*t7- + 16*t2^4*t3*t4*t6*t7-8*n*t2^4*t3*t4*t6*t7+4*n^2*t2^4*t3*t4*t6*t7- + 16*t1*t2^2*t3*t4*t5*t6*t7-28*n*t1*t2^2*t3*t4*t5*t6*t7+ + 4*n^3*t1*t2^2*t3*t4*t5*t6*t7-4*t1^2*t3*t4*t5^2*t6*t7+ + 12*t1*t2^3*t4*t6^2*t7+14*n*t1*t2^3*t4*t6^2*t7- + 2*n^3*t1*t2^3*t4*t6^2*t7+6*t1^2*t2*t4*t5*t6^2*t7+ + 4*n*t1^2*t2*t4*t5*t6^2*t7-2*n^2*t1^2*t2*t4*t5*t6^2*t7- + 4*t2^4*t3^2*t7^2+2*n*t2^4*t3^2*t7^2-4*t1*t2^2*t3^2*t5*t7^2- + 12*n*t1*t2^2*t3^2*t5*t7^2+4*n^2*t1*t2^2*t3^2*t5*t7^2- + t1^2*t3^2*t5^2*t7^2+n*t1^2*t3^2*t5^2*t7^2-3*n^2*t1^2*t3^2*t5^2*t7^2+ + n^3*t1^2*t3^2*t5^2*t7^2+12*t1*t2^3*t3*t6*t7^2+ + 8*n*t1*t2^3*t3*t6*t7^2-4*n^2*t1*t2^3*t3*t6*t7^2+ + 6*t1^2*t2*t3*t5*t6*t7^2+10*n*t1^2*t2*t3*t5*t6*t7^2+ + 2*n^2*t1^2*t2*t3*t5*t6*t7^2-2*n^3*t1^2*t2*t3*t5*t6*t7^2- + 6*t1^2*t2^2*t6^2*t7^2-7*n*t1^2*t2^2*t6^2*t7^2+ + n^3*t1^2*t2^2*t6^2*t7^2-3*t1^3*t5*t6^2*t7^2-2*n*t1^3*t5*t6^2*t7^2+ + n^2*t1^3*t5*t6^2*t7^2-2*t10*t2^6*t8+3*t1*t10*t2^4*t5*t8+ + n*t1*t10*t2^4*t5*t8-2*t2^4*t4^2*t5*t8-3*n*t2^4*t4^2*t5*t8+ + n^2*t2^4*t4^2*t5*t8-2*n*t1^2*t10*t2^2*t5^2*t8+t1*t2^2*t4^2*t5^2*t8+ + 4*n*t1*t2^2*t4^2*t5^2*t8-n^2*t1*t2^2*t4^2*t5^2*t8-t1^3*t10*t5^3*t8+ + n*t1^3*t10*t5^3*t8+t1^2*t4^2*t5^3*t8-n*t1^2*t4^2*t5^3*t8+ + 4*t2^5*t4*t7*t8-2*t1*t2^3*t4*t5*t7*t8+4*n*t1*t2^3*t4*t5*t7*t8- + 2*n^2*t1*t2^3*t4*t5*t7*t8-2*t1^2*t2*t4*t5^2*t7*t8- + 4*n*t1^2*t2*t4*t5^2*t7*t8+2*n^2*t1^2*t2*t4*t5^2*t7*t8- + 2*t1*t2^4*t7^2*t8+t1^2*t2^2*t5*t7^2*t8-2*n*t1^2*t2^2*t5*t7^2*t8+ + n^2*t1^2*t2^2*t5*t7^2*t8+t1^3*t5^2*t7^2*t8+2*n*t1^3*t5^2*t7^2*t8- + n^2*t1^3*t5^2*t7^2*t8-8*t2^4*t3*t4*t5*t9-8*n*t2^4*t3*t4*t5*t9+ + 4*n^2*t2^4*t3*t4*t5*t9+4*t1*t2^2*t3*t4*t5^2*t9+ + 8*n*t1*t2^2*t3*t4*t5^2*t9-4*n^2*t1*t2^2*t3*t4*t5^2*t9+ + 4*t1^2*t3*t4*t5^3*t9+8*t2^5*t4*t6*t9+8*n*t2^5*t4*t6*t9- + 4*n^2*t2^5*t4*t6*t9-4*t1*t2^3*t4*t5*t6*t9-8*n*t1*t2^3*t4*t5*t6*t9+ + 4*n^2*t1*t2^3*t4*t5*t6*t9-4*t1^2*t2*t4*t5^2*t6*t9+8*t2^5*t3*t7*t9- + 4*n*t2^5*t3*t7*t9-4*t1*t2^3*t3*t5*t7*t9+16*n*t1*t2^3*t3*t5*t7*t9- + 4*n^2*t1*t2^3*t3*t5*t7*t9-4*t1^2*t2*t3*t5^2*t7*t9- + 12*n*t1^2*t2*t3*t5^2*t7*t9+4*n^2*t1^2*t2*t3*t5^2*t7*t9- + 8*t1*t2^4*t6*t7*t9-8*n*t1*t2^4*t6*t7*t9+4*n^2*t1*t2^4*t6*t7*t9+ + 4*t1^2*t2^2*t5*t6*t7*t9+8*n*t1^2*t2^2*t5*t6*t7*t9- + 4*n^2*t1^2*t2^2*t5*t6*t7*t9+4*t1^3*t5^2*t6*t7*t9-4*t2^6*t9^2+ + 2*n*t2^6*t9^2+6*t1*t2^4*t5*t9^2-4*n*t1*t2^4*t5*t9^2+ + 2*n*t1^2*t2^2*t5^2*t9^2-2*t1^3*t5^3*t9^2, + s21->-2*t10*t2^4*t3^2*t5-3*n*t10*t2^4*t3^2*t5+n^2*t10*t2^4*t3^2*t5+ + t1*t10*t2^2*t3^2*t5^2+4*n*t1*t10*t2^2*t3^2*t5^2- + n^2*t1*t10*t2^2*t3^2*t5^2-6*t2^2*t3^2*t4^2*t5^2- + 7*n*t2^2*t3^2*t4^2*t5^2+n^3*t2^2*t3^2*t4^2*t5^2+t1^2*t10*t3^2*t5^3- + n*t1^2*t10*t3^2*t5^3-3*t1*t3^2*t4^2*t5^3-2*n*t1*t3^2*t4^2*t5^3+ + n^2*t1*t3^2*t4^2*t5^3+4*t10*t2^5*t3*t6-2*t1*t10*t2^3*t3*t5*t6+ + 4*n*t1*t10*t2^3*t3*t5*t6-2*n^2*t1*t10*t2^3*t3*t5*t6+ + 12*t2^3*t3*t4^2*t5*t6+8*n*t2^3*t3*t4^2*t5*t6- + 4*n^2*t2^3*t3*t4^2*t5*t6-2*t1^2*t10*t2*t3*t5^2*t6- + 4*n*t1^2*t10*t2*t3*t5^2*t6+2*n^2*t1^2*t10*t2*t3*t5^2*t6+ + 6*t1*t2*t3*t4^2*t5^2*t6+10*n*t1*t2*t3*t4^2*t5^2*t6+ + 2*n^2*t1*t2*t3*t4^2*t5^2*t6-2*n^3*t1*t2*t3*t4^2*t5^2*t6- + 2*t1*t10*t2^4*t6^2-4*t2^4*t4^2*t6^2+2*n*t2^4*t4^2*t6^2+ + t1^2*t10*t2^2*t5*t6^2-2*n*t1^2*t10*t2^2*t5*t6^2+ + n^2*t1^2*t10*t2^2*t5*t6^2-4*t1*t2^2*t4^2*t5*t6^2- + 12*n*t1*t2^2*t4^2*t5*t6^2+4*n^2*t1*t2^2*t4^2*t5*t6^2+ + t1^3*t10*t5^2*t6^2+2*n*t1^3*t10*t5^2*t6^2-n^2*t1^3*t10*t5^2*t6^2- + t1^2*t4^2*t5^2*t6^2+n*t1^2*t4^2*t5^2*t6^2-3*n^2*t1^2*t4^2*t5^2*t6^2+ + n^3*t1^2*t4^2*t5^2*t6^2+12*t2^3*t3^2*t4*t5*t7+ + 14*n*t2^3*t3^2*t4*t5*t7-2*n^3*t2^3*t3^2*t4*t5*t7+ + 6*t1*t2*t3^2*t4*t5^2*t7+4*n*t1*t2*t3^2*t4*t5^2*t7- + 2*n^2*t1*t2*t3^2*t4*t5^2*t7-16*t2^4*t3*t4*t6*t7- + 8*n*t2^4*t3*t4*t6*t7+4*n^2*t2^4*t3*t4*t6*t7- + 16*t1*t2^2*t3*t4*t5*t6*t7-28*n*t1*t2^2*t3*t4*t5*t6*t7+ + 4*n^3*t1*t2^2*t3*t4*t5*t6*t7-4*t1^2*t3*t4*t5^2*t6*t7+ + 12*t1*t2^3*t4*t6^2*t7+8*n*t1*t2^3*t4*t6^2*t7- + 4*n^2*t1*t2^3*t4*t6^2*t7+6*t1^2*t2*t4*t5*t6^2*t7+ + 10*n*t1^2*t2*t4*t5*t6^2*t7+2*n^2*t1^2*t2*t4*t5*t6^2*t7- + 2*n^3*t1^2*t2*t4*t5*t6^2*t7-4*t2^4*t3^2*t7^2-4*n*t2^4*t3^2*t7^2- + n^2*t2^4*t3^2*t7^2+n^3*t2^4*t3^2*t7^2-4*t1*t2^2*t3^2*t5*t7^2- + 6*n*t1*t2^2*t3^2*t5*t7^2+2*n^2*t1*t2^2*t3^2*t5*t7^2- + t1^2*t3^2*t5^2*t7^2+n*t1^2*t3^2*t5^2*t7^2+12*t1*t2^3*t3*t6*t7^2+ + 14*n*t1*t2^3*t3*t6*t7^2-2*n^3*t1*t2^3*t3*t6*t7^2+ + 6*t1^2*t2*t3*t5*t6*t7^2+4*n*t1^2*t2*t3*t5*t6*t7^2- + 2*n^2*t1^2*t2*t3*t5*t6*t7^2-6*t1^2*t2^2*t6^2*t7^2- + 7*n*t1^2*t2^2*t6^2*t7^2+n^3*t1^2*t2^2*t6^2*t7^2-3*t1^3*t5*t6^2*t7^2- + 2*n*t1^3*t5*t6^2*t7^2+n^2*t1^3*t5*t6^2*t7^2-2*t10*t2^6*t8+ + 3*t1*t10*t2^4*t5*t8+n*t1*t10*t2^4*t5*t8-2*t2^4*t4^2*t5*t8- + 2*n*t1^2*t10*t2^2*t5^2*t8+t1*t2^2*t4^2*t5^2*t8- + 2*n*t1*t2^2*t4^2*t5^2*t8+n^2*t1*t2^2*t4^2*t5^2*t8-t1^3*t10*t5^3*t8+ + n*t1^3*t10*t5^3*t8+t1^2*t4^2*t5^3*t8+2*n*t1^2*t4^2*t5^3*t8- + n^2*t1^2*t4^2*t5^3*t8+4*t2^5*t4*t7*t8-2*t1*t2^3*t4*t5*t7*t8+ + 4*n*t1*t2^3*t4*t5*t7*t8-2*n^2*t1*t2^3*t4*t5*t7*t8- + 2*t1^2*t2*t4*t5^2*t7*t8-4*n*t1^2*t2*t4*t5^2*t7*t8+ + 2*n^2*t1^2*t2*t4*t5^2*t7*t8-2*t1*t2^4*t7^2*t8-3*n*t1*t2^4*t7^2*t8+ + n^2*t1*t2^4*t7^2*t8+t1^2*t2^2*t5*t7^2*t8+4*n*t1^2*t2^2*t5*t7^2*t8- + n^2*t1^2*t2^2*t5*t7^2*t8+t1^3*t5^2*t7^2*t8-n*t1^3*t5^2*t7^2*t8- + 8*t2^4*t3*t4*t5*t9-8*n*t2^4*t3*t4*t5*t9+4*n^2*t2^4*t3*t4*t5*t9+ + 4*t1*t2^2*t3*t4*t5^2*t9+8*n*t1*t2^2*t3*t4*t5^2*t9- + 4*n^2*t1*t2^2*t3*t4*t5^2*t9+4*t1^2*t3*t4*t5^3*t9+8*t2^5*t4*t6*t9- + 4*n*t2^5*t4*t6*t9-4*t1*t2^3*t4*t5*t6*t9+16*n*t1*t2^3*t4*t5*t6*t9- + 4*n^2*t1*t2^3*t4*t5*t6*t9-4*t1^2*t2*t4*t5^2*t6*t9- + 12*n*t1^2*t2*t4*t5^2*t6*t9+4*n^2*t1^2*t2*t4*t5^2*t6*t9+ + 8*t2^5*t3*t7*t9+8*n*t2^5*t3*t7*t9-4*n^2*t2^5*t3*t7*t9- + 4*t1*t2^3*t3*t5*t7*t9-8*n*t1*t2^3*t3*t5*t7*t9+ + 4*n^2*t1*t2^3*t3*t5*t7*t9-4*t1^2*t2*t3*t5^2*t7*t9- + 8*t1*t2^4*t6*t7*t9-8*n*t1*t2^4*t6*t7*t9+4*n^2*t1*t2^4*t6*t7*t9+ + 4*t1^2*t2^2*t5*t6*t7*t9+8*n*t1^2*t2^2*t5*t6*t7*t9- + 4*n^2*t1^2*t2^2*t5*t6*t7*t9+4*t1^3*t5^2*t6*t7*t9-4*t2^6*t9^2+ + 2*n*t2^6*t9^2+6*t1*t2^4*t5*t9^2-4*n*t1*t2^4*t5*t9^2+ + 2*n*t1^2*t2^2*t5^2*t9^2-2*t1^3*t5^3*t9^2, + s22->-(t10*t2^3*t3^2*t5^2)-n*t10*t2^3*t3^2*t5^2+t1*t10*t2*t3^2*t5^3+ + n*t1*t10*t2*t3^2*t5^3-3*t2*t3^2*t4^2*t5^3-4*n*t2*t3^2*t4^2*t5^3- + n^2*t2*t3^2*t4^2*t5^3+2*t10*t2^4*t3*t5*t6+2*n*t10*t2^4*t3*t5*t6- + 2*t1*t10*t2^2*t3*t5^2*t6-2*n*t1*t10*t2^2*t3*t5^2*t6+ + 6*t2^2*t3*t4^2*t5^2*t6+8*n*t2^2*t3*t4^2*t5^2*t6+ + 2*n^2*t2^2*t3*t4^2*t5^2*t6-n*t10*t2^5*t6^2-t1*t10*t2^3*t5*t6^2+ + n*t1*t10*t2^3*t5*t6^2-2*t2^3*t4^2*t5*t6^2-3*n*t2^3*t4^2*t5*t6^2- + n^2*t2^3*t4^2*t5*t6^2+t1^2*t10*t2*t5^2*t6^2-t1*t2*t4^2*t5^2*t6^2- + n*t1*t2*t4^2*t5^2*t6^2+6*t2^2*t3^2*t4*t5^2*t7+ + 7*n*t2^2*t3^2*t4*t5^2*t7+n^2*t2^2*t3^2*t4*t5^2*t7+ + n*t1*t3^2*t4*t5^3*t7+n^2*t1*t3^2*t4*t5^3*t7-8*t2^3*t3*t4*t5*t6*t7- + 10*n*t2^3*t3*t4*t5*t6*t7-2*n^2*t2^3*t3*t4*t5*t6*t7- + 4*t1*t2*t3*t4*t5^2*t6*t7-6*n*t1*t2*t3*t4*t5^2*t6*t7- + 2*n^2*t1*t2*t3*t4*t5^2*t6*t7+2*n*t2^4*t4*t6^2*t7+ + n^2*t2^4*t4*t6^2*t7+6*t1*t2^2*t4*t5*t6^2*t7+ + 5*n*t1*t2^2*t4*t5*t6^2*t7+n^2*t1*t2^2*t4*t5*t6^2*t7+ + n*t1^2*t4*t5^2*t6^2*t7-2*t2^3*t3^2*t5*t7^2-2*n*t2^3*t3^2*t5*t7^2- + t1*t2*t3^2*t5^2*t7^2-2*n*t1*t2*t3^2*t5^2*t7^2- + n^2*t1*t2*t3^2*t5^2*t7^2+2*n*t2^4*t3*t6*t7^2+ + 6*t1*t2^2*t3*t5*t6*t7^2+4*n*t1*t2^2*t3*t5*t6*t7^2+ + 2*n^2*t1*t2^2*t3*t5*t6*t7^2+2*n*t1^2*t3*t5^2*t6*t7^2- + n*t1*t2^3*t6^2*t7^2-n^2*t1*t2^3*t6^2*t7^2-3*t1^2*t2*t5*t6^2*t7^2- + 3*n*t1^2*t2*t5*t6^2*t7^2-t10*t2^5*t5*t8+2*t1*t10*t2^3*t5^2*t8- + t2^3*t4^2*t5^2*t8-n*t2^3*t4^2*t5^2*t8-t1^2*t10*t2*t5^3*t8+ + t1*t2*t4^2*t5^3*t8+n*t1*t2*t4^2*t5^3*t8+2*t2^4*t4*t5*t7*t8+ + n*t2^4*t4*t5*t7*t8-2*t1*t2^2*t4*t5^2*t7*t8-n*t1^2*t4*t5^3*t7*t8- + t1*t2^3*t5*t7^2*t8-n*t1*t2^3*t5*t7^2*t8+t1^2*t2*t5^2*t7^2*t8+ + n*t1^2*t2*t5^2*t7^2*t8-4*t2^3*t3*t4*t5^2*t9-4*n*t2^3*t3*t4*t5^2*t9+ + 4*t1*t2*t3*t4*t5^3*t9+4*n*t1*t2*t3*t4*t5^3*t9+4*t2^4*t4*t5*t6*t9+ + 4*n*t2^4*t4*t5*t6*t9-4*t1*t2^2*t4*t5^2*t6*t9- + 4*n*t1*t2^2*t4*t5^2*t6*t9+4*t2^4*t3*t5*t7*t9+2*n*t2^4*t3*t5*t7*t9- + 4*t1*t2^2*t3*t5^2*t7*t9-2*n*t1^2*t3*t5^3*t7*t9-2*n*t2^5*t6*t7*t9- + 4*t1*t2^3*t5*t6*t7*t9+4*t1^2*t2*t5^2*t6*t7*t9+ + 2*n*t1^2*t2*t5^2*t6*t7*t9-2*t2^5*t5*t9^2+4*t1*t2^3*t5^2*t9^2- + 2*t1^2*t2*t5^3*t9^2,s23->-(t10*t2^3*t3^2*t5^2)- + n*t10*t2^3*t3^2*t5^2+t1*t10*t2*t3^2*t5^3+n*t1*t10*t2*t3^2*t5^3- + 3*t2*t3^2*t4^2*t5^3-4*n*t2*t3^2*t4^2*t5^3-n^2*t2*t3^2*t4^2*t5^3+ + 2*t10*t2^4*t3*t5*t6+n*t10*t2^4*t3*t5*t6-2*t1*t10*t2^2*t3*t5^2*t6+ + 6*t2^2*t3*t4^2*t5^2*t6+7*n*t2^2*t3*t4^2*t5^2*t6+ + n^2*t2^2*t3*t4^2*t5^2*t6-n*t1^2*t10*t3*t5^3*t6+n*t1*t3*t4^2*t5^3*t6+ + n^2*t1*t3*t4^2*t5^3*t6-t1*t10*t2^3*t5*t6^2-n*t1*t10*t2^3*t5*t6^2- + 2*t2^3*t4^2*t5*t6^2-2*n*t2^3*t4^2*t5*t6^2+t1^2*t10*t2*t5^2*t6^2+ + n*t1^2*t10*t2*t5^2*t6^2-t1*t2*t4^2*t5^2*t6^2- + 2*n*t1*t2*t4^2*t5^2*t6^2-n^2*t1*t2*t4^2*t5^2*t6^2+ + 6*t2^2*t3^2*t4*t5^2*t7+8*n*t2^2*t3^2*t4*t5^2*t7+ + 2*n^2*t2^2*t3^2*t4*t5^2*t7-8*t2^3*t3*t4*t5*t6*t7- + 10*n*t2^3*t3*t4*t5*t6*t7-2*n^2*t2^3*t3*t4*t5*t6*t7- + 4*t1*t2*t3*t4*t5^2*t6*t7-6*n*t1*t2*t3*t4*t5^2*t6*t7- + 2*n^2*t1*t2*t3*t4*t5^2*t6*t7+2*n*t2^4*t4*t6^2*t7+ + 6*t1*t2^2*t4*t5*t6^2*t7+4*n*t1*t2^2*t4*t5*t6^2*t7+ + 2*n^2*t1*t2^2*t4*t5*t6^2*t7+2*n*t1^2*t4*t5^2*t6^2*t7- + 2*t2^3*t3^2*t5*t7^2-3*n*t2^3*t3^2*t5*t7^2-n^2*t2^3*t3^2*t5*t7^2- + t1*t2*t3^2*t5^2*t7^2-n*t1*t2*t3^2*t5^2*t7^2+2*n*t2^4*t3*t6*t7^2+ + n^2*t2^4*t3*t6*t7^2+6*t1*t2^2*t3*t5*t6*t7^2+ + 5*n*t1*t2^2*t3*t5*t6*t7^2+n^2*t1*t2^2*t3*t5*t6*t7^2+ + n*t1^2*t3*t5^2*t6*t7^2-n*t1*t2^3*t6^2*t7^2-n^2*t1*t2^3*t6^2*t7^2- + 3*t1^2*t2*t5*t6^2*t7^2-3*n*t1^2*t2*t5*t6^2*t7^2-t10*t2^5*t5*t8+ + 2*t1*t10*t2^3*t5^2*t8-t2^3*t4^2*t5^2*t8-n*t2^3*t4^2*t5^2*t8- + t1^2*t10*t2*t5^3*t8+t1*t2*t4^2*t5^3*t8+n*t1*t2*t4^2*t5^3*t8+ + 2*t2^4*t4*t5*t7*t8+2*n*t2^4*t4*t5*t7*t8-2*t1*t2^2*t4*t5^2*t7*t8- + 2*n*t1*t2^2*t4*t5^2*t7*t8-n*t2^5*t7^2*t8-t1*t2^3*t5*t7^2*t8+ + n*t1*t2^3*t5*t7^2*t8+t1^2*t2*t5^2*t7^2*t8-4*t2^3*t3*t4*t5^2*t9- + 4*n*t2^3*t3*t4*t5^2*t9+4*t1*t2*t3*t4*t5^3*t9+ + 4*n*t1*t2*t3*t4*t5^3*t9+4*t2^4*t4*t5*t6*t9+2*n*t2^4*t4*t5*t6*t9- + 4*t1*t2^2*t4*t5^2*t6*t9-2*n*t1^2*t4*t5^3*t6*t9+4*t2^4*t3*t5*t7*t9+ + 4*n*t2^4*t3*t5*t7*t9-4*t1*t2^2*t3*t5^2*t7*t9- + 4*n*t1*t2^2*t3*t5^2*t7*t9-2*n*t2^5*t6*t7*t9-4*t1*t2^3*t5*t6*t7*t9+ + 4*t1^2*t2*t5^2*t6*t7*t9+2*n*t1^2*t2*t5^2*t6*t7*t9-2*t2^5*t5*t9^2+ + 4*t1*t2^3*t5^2*t9^2-2*t1^2*t2*t5^3*t9^2, + s24->t10*t2^2*t3^2*t5^3+n*t10*t2^2*t3^2*t5^3-t1*t10*t3^2*t5^4- + n*t1*t10*t3^2*t5^4+3*t3^2*t4^2*t5^4+4*n*t3^2*t4^2*t5^4+ + n^2*t3^2*t4^2*t5^4-2*t10*t2^3*t3*t5^2*t6-2*n*t10*t2^3*t3*t5^2*t6+ + 2*t1*t10*t2*t3*t5^3*t6+2*n*t1*t10*t2*t3*t5^3*t6- + 6*t2*t3*t4^2*t5^3*t6-8*n*t2*t3*t4^2*t5^3*t6- + 2*n^2*t2*t3*t4^2*t5^3*t6+n*t10*t2^4*t5*t6^2+t1*t10*t2^2*t5^2*t6^2- + n*t1*t10*t2^2*t5^2*t6^2+2*t2^2*t4^2*t5^2*t6^2+ + 3*n*t2^2*t4^2*t5^2*t6^2+n^2*t2^2*t4^2*t5^2*t6^2-t1^2*t10*t5^3*t6^2+ + t1*t4^2*t5^3*t6^2+n*t1*t4^2*t5^3*t6^2-6*t2*t3^2*t4*t5^3*t7- + 8*n*t2*t3^2*t4*t5^3*t7-2*n^2*t2*t3^2*t4*t5^3*t7+ + 8*t2^2*t3*t4*t5^2*t6*t7+12*n*t2^2*t3*t4*t5^2*t6*t7+ + 4*n^2*t2^2*t3*t4*t5^2*t6*t7+4*t1*t3*t4*t5^3*t6*t7+ + 4*n*t1*t3*t4*t5^3*t6*t7-2*n*t2^3*t4*t5*t6^2*t7- + 2*n^2*t2^3*t4*t5*t6^2*t7-6*t1*t2*t4*t5^2*t6^2*t7- + 6*n*t1*t2*t4*t5^2*t6^2*t7+2*t2^2*t3^2*t5^2*t7^2+ + 3*n*t2^2*t3^2*t5^2*t7^2+n^2*t2^2*t3^2*t5^2*t7^2+t1*t3^2*t5^3*t7^2+ + n*t1*t3^2*t5^3*t7^2-2*n*t2^3*t3*t5*t6*t7^2-2*n^2*t2^3*t3*t5*t6*t7^2- + 6*t1*t2*t3*t5^2*t6*t7^2-6*n*t1*t2*t3*t5^2*t6*t7^2- + 2*n*t2^4*t6^2*t7^2+n^2*t2^4*t6^2*t7^2+6*n*t1*t2^2*t5*t6^2*t7^2+ + 3*t1^2*t5^2*t6^2*t7^2+t10*t2^4*t5^2*t8-2*t1*t10*t2^2*t5^3*t8+ + t2^2*t4^2*t5^3*t8+n*t2^2*t4^2*t5^3*t8+t1^2*t10*t5^4*t8- + t1*t4^2*t5^4*t8-n*t1*t4^2*t5^4*t8-2*t2^3*t4*t5^2*t7*t8- + 2*n*t2^3*t4*t5^2*t7*t8+2*t1*t2*t4*t5^3*t7*t8+ + 2*n*t1*t2*t4*t5^3*t7*t8+n*t2^4*t5*t7^2*t8+t1*t2^2*t5^2*t7^2*t8- + n*t1*t2^2*t5^2*t7^2*t8-t1^2*t5^3*t7^2*t8+4*t2^2*t3*t4*t5^3*t9+ + 4*n*t2^2*t3*t4*t5^3*t9-4*t1*t3*t4*t5^4*t9-4*n*t1*t3*t4*t5^4*t9- + 4*t2^3*t4*t5^2*t6*t9-4*n*t2^3*t4*t5^2*t6*t9+4*t1*t2*t4*t5^3*t6*t9+ + 4*n*t1*t2*t4*t5^3*t6*t9-4*t2^3*t3*t5^2*t7*t9-4*n*t2^3*t3*t5^2*t7*t9+ + 4*t1*t2*t3*t5^3*t7*t9+4*n*t1*t2*t3*t5^3*t7*t9+4*n*t2^4*t5*t6*t7*t9+ + 4*t1*t2^2*t5^2*t6*t7*t9-4*n*t1*t2^2*t5^2*t6*t7*t9- + 4*t1^2*t5^3*t6*t7*t9+2*t2^4*t5^2*t9^2-4*t1*t2^2*t5^3*t9^2+ + 2*t1^2*t5^4*t9^2},{t1->SP[p1,p1],t2->SP[p1,p2],t3->SP[p1,q1], + t4->SP[p1,q2],t5->SP[p2,p2],t6->SP[p2,q1],t7->SP[p2,q2], + t8->SP[q1,q1],t9->SP[q1,q2],t10->SP[q2,q2],v1->FV[p1,mu], + v2->FV[p1,nu],v3->FV[p1,rho],v4->FV[p1,si],v5->FV[p2,mu], + v6->FV[p2,nu],v7->FV[p2,rho],v8->FV[p2,si],m1->MT[mu,nu], + m2->MT[mu,rho],m3->MT[mu,si],m4->MT[nu,rho],m5->MT[nu,si], + m6->MT[rho,si]}}; + scpexp[encli,n]] +} diff --git a/FeynCalc/Tarcer/TARCER.m b/FeynCalc/Tarcer/TARCER.m deleted file mode 100644 index 4dd641dd9..000000000 --- a/FeynCalc/Tarcer/TARCER.m +++ /dev/null @@ -1,4191 +0,0 @@ -(* ::Package:: *) - -(* ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *) - -(* :Title: TARCER *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1998-2015 Rolf Mertig - Copyright (C) 1998-2015 Rainer Scharf - Copyright (C) 1998-2015 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: TARCER is a Mathematica program for the reduction - of two-loop propagator integrals *) - -(* ------------------------------------------------------------------------ *) - -(* - -COMMENTS (VS 04.8.2011) changed typsetting for SEpsilon -COMMENTS (RM 19.8.2011) changed typsetting for SEpsilon -COMMENTS (RM 20.7.2011) changed the way .mx files are named -COMMENTS (RM 14.3..2004) uncommented a global variable assignement.changed default setting of $RankLimit to {2,5}. -COMMENTS (RM 31.10.2003) Change default settings of TarcerExpand, modify $BasisIntegras for massless integrals, -changed default setting of $RankLimit to {1,6}. -COMMENTS (RM 28.10.2003) Fixed a bug in TarcerExpand (only introduced recently), -changed default setting of $RankLimit to {1,5}. -COMMENTS (RM 24.9.2003) Relaxed a condition in equation (61) and (6153) -COMMENTS (RM 18.9.2003): Fixed things for 5.0, eliminated a TVI symmetry (causing infinite recursion) and added -TFI decomposition into products of TAI's (was somehow missing but shows up in, e.g., the 2-loop Higss selfenergy). -Putting TFI back into the Tarcer context, because the fcloops context created trouble ... -Changed default of $Comment to False. -COMMENTS (FO 8.9.2002.): Changed context of TFI to HighEnergyPhysics`fcloops`TFI` and updated other HighEnergyPhysics`* - contexts. -COMMENTS (FO 15.3.2001.): Changed PreFactor into Prefactor1 to avoid conflict with FeynArts and FeynCalc. -COMMENTS (FO 15.3.2001.): Changed context of Zeta2 and made definition dependent on not having loaded FeynCalc. -COMMENTS (RM 25.4.): TFISimplify (like TFIRecurse, but without trule[9]). -COMMENTS (RM 23.4.): bug fixed in tlrule[17]. -COMMENTS (RM 6.4.): special TVR relations added to TVR. -COMMENTS (RM 22.3.): TVI Symmetry added to TVR. -COMMENTS (RM 18.3.): More rules added to $TTable. -COMMENTS (RM 18.2.): More rules added to $TTable. -COMMENTS (RM 21.2.): Included $TTable. added tlrule[25] -COMMENTS (RM 20.2.): $RankLimit = {0,6} ; Changed TarcerRecurse such that special TJR and TVR - (reducing D -> D-2) are used first. -COMMENTS (RM 15.2.): $RankLimit = {0,8} ; -The following test now works: - - Print["test 1 : TFI[D, pp, {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1,MW}}] = ", - Timing[t1 =TarcerRecurse[TFI[D, pp, {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1,MW}}]] - ] // InputForm - ] - - Print["test 2 : TFI[d, pp, 0, {0, 0, 0, 0, 4},{{1, m1}, {1, m2}, 0, 0, 0}] = ", - Timing[t2 =TarcerRecurse[TFI[D, pp, 0, {0, 0, 0, 0, 4},{{1, m1}, {1, m2}, 0, 0, 0}]]; - ] // InputForm - ] - -COMMENTS (RM 13.2.): tlrule[11] and trule[12] made more restrictive: inhibiting thus a recursion if {n5,m5} equals {0,0}. -COMMENTS (RM 12.2.): tlrule[15] made safer (in order to not get 0 :> 0 ); - TFIRecurse made safer (to not get into a recursion); - There is still something wrong with the tlrule's ; since - TFIRecurse[TFI[D, pp, {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1, MW}}]] - doesn't work .. -COMMENTS (RM 5.2.): tlrule[10] slightly changed to cover more cases. -COMMENTS (RM 2.2.): FunctionExpand added in tlrule[9]. Option TimeConstraint added to - TarcerRecurse (because TimeConstrained is buggy under Linux). -COMMENTS (RM 1.2.): Changed TarcerRecurse. New TLR definition. - default $RankLimit={0,6}; -$Remember=True; -COMMENTS (RM 19.1.): changes are: tlrule[22] and tlrule[23], minor efficiency changes (Expand3 = Identity) - and other small programming optimizations. -COMMENTS (RM 22.1.): changes are: bug in tlrule[23] fixed, new tlrule[24], new option Factor to - TarcerReduce (doesn't change anything by default, but allows for improved Factoring). - -See also: hep-ph/9801383, published in Comput. Phys. Commun. 111 (1998) 265-273 *) - - -Unset[$Post]; -$Post = (#;) &; -If[$Notebooks =!= True, $Post = (#;) &]; - -$HistoryLength = 0; - -BeginPackage["Tarcer`",{"FeynCalc`"}]; - -TarcerRecurse::usage = -"TarcerRecurse[expr] applies recurrence relations for all TFI's \ -(and TVI, TJI, TBI, TAI) in expr. For evaluation and Laurent \ -expansion of the resulting basis integrals use TarcerExpand."; - -TarcerExpand::usage = -"TarcerExpand[expr, d -> (4+e), order] or TarcerExpand[epxr, d -> \ -(4-e), order] or TarcerExpand[expr, d -> (4 - 2 om)substitutes \ -integrals as specified by the option TarcerRules, and does a Laurent \ -expansion in the variable around 0 at the right hand side of the \ -second argument (i.e., you can use whatever convention you like ...). \ -The same effect as TarcerExpand[TarcerRecurse[expr], ...] can be \ -achieved by setting the option TarcerRecurse of TarcerExpand to True. \ -TarcerExpand[expr, d -> (4+e)] is equivalent to TarcerExpand[expr, d -> \ -(4+e), 0]."; - -TarcerReduce::usage = -"TarcerReduce is an option to TarcerExpand. It should be set to a \ -list of basic integrals."; - -Cayley::usage = -"Cayley[m1,m2,m3,m4,m5,Sqrt[pp]] is the Cayley determinant."; - -Cayleyu::usage = -"Cayleyu are the sub-Cayley-determinants as described in Tarasov's \ -paper."; - -CayleyD::usage = -"CayleyD are the sub-Cayley-determinants as described in Tarasov's \ -paper."; - -Prefactor1::usage = -"Prefactor1[expr] may be used to prohibit TarcerExpand from \ -Taylor-expanding expr."; - -SEpsilon::usage = -"Sepsilon[d] is an abbreviation for Exp[(d-4)/2 EulerGamma]."; - -TFI::usage = -"TFI[d, pp, {{n1,m1},{n2,m2},{n3,m3},{n4,m4},{n5,m5}}] is - the 2-loop d-dimensional integral - 1/( (q1^2 - m1^2)^n1 (q2^2 - m2^2)^n2 ((q1-p)^2 - m3^2)^n3 * - ((q2-p)^2 - m4^2)^n4 ((q1-q2)^2 - m5^2)^n5 ) . - - TFI[d, pp, {x,y,z,v,w}, {{n1,m1},{n2,m2},{n3,m3},{n4,m4},{n5,m5}}] - has as additional factors in the numerator \ -(q1^2)^x*(q2^2)^y*(q1.p)^z* - (q2.p)^v*(q1.q2)^w . - - TFI[d, pp, dp, {a,b}, {{n1,m1},{n2,m2},{n3,m3},{n4,m4},{n5,m5}}] - has as additional factors in the numerator (OPEDelta.q1)^a * \ -(OPEDelta.q2)^b; - dp is (OPEDelta.p)."; - -TFIRecurse::usage = -"TFIRecurse[expr] applies the recursion algorithm implemented in \ -TARCER.nb (following Tarasov) to TFI's (and TVI's, TJI's, TBI's, \ -TAI's in expr."; - -TFISimplify::usage = -"TFISimplify[expr] applies the recursion algorithm implemented in \ -TARCER.nb (following Tarasov) to TFI's (and TVI's, TJI's, TBI's, \ -TAI's in expr, except k1.k2."; - -TVI::usage = -"TVI[d,pp,{ {n1,m1},{n2,m2},{n3,m3},{n4,m4}}] is the massive 2-loop \ -integral with four propagators in d dimensions. "; - -TJI::usage = -"TJI[d, pp, { {n1,m1},{n2,m2},{n3,m3} }] is the massive 2-loop \ -integral with three propagators in d dimensions. "; - -TKI::usage = -"TKI[d, 0, { {n1,m1},{n2,m2},{n3,m3} }] is the bubble massive \ -2-loop selfenergy type integral with three propagators in d \ -dimensions. "; - -TBI::usage = -"TBI[d, pp, { {n1,m1},{n2,m2} }] is the massive 1-loop selfenergy \ -type integral with two propagators in d dimensions."; - -TAI::usage = -"TAI[d, pp, { {n1,m1} }] is the massive 1-loop selfenergy type \ -integral with one propagator in d dimensions."; - -TFR::usage = -"TFR is similar in syntax to TFI but applies once the recurrence \ -relations derived for TFI."; - -TVR::usage = -"TVR is similar in syntax to TVI but applies once the recurrence \ -relations derived for TVI."; - -TJR::usage = -"TJR is similar in syntax to TJI but applies once the recurrence \ -relations derived for TJI."; - -TBR::usage = -"TBR is similar in syntax to TBI but applies once the recurrence \ -relations derived for TBI."; - -TAR::usage = -"TAR is similar in syntax to TAI but applies once the recurrence \ -relations derived for TAI."; - -$RankLimit::usage = -"$RankLimit is the list of integers specifying the highest possible \ -sums of exponents of scalar products; i.e., {a+b, r+s} means that at \ -most (Delta.k1)^a * (Delta.k2)^2 * (p.k1)^r * (p.k2)^s in the \ -numerator will be calculated (a,b,r,s have to be non-negative \ -integares). $RankLimit has to be set in the TARCER.nb notebook. In \ -the tarcer.mx file this is not possible anymore."; - -$TarcerRecursed::usage = -"If $Comment is set to True all integrals\n\t\twhich are reduced \ -are collected in the global variable $TarcerRecured."; - -$BasisIntegrals::usage = -"$BasisIntegrals is a list of some basis integrals. It is the \ -default setting of TarcerReduce of TarcerExpand."; - -$Comment::usage = -"$Comment can be set to True or False. If set to False no comments \ -are generated."; - -$CommentNotebook::usage = -"$Comment can be set to True or False. Setting it to True will \ -generate a separate notebook (if and only if $Comment is True) where \ -the used recursion relations are displayed."; - -$RecursionStop::usage = -"$RecursionStop sets an upper limit on the total number of \ -recursion levels. Its purpose is to inhibit erroneous infinite \ -recursions."; - -$TTable::usage = -"$TTable is a list of precomputed reductions. $TTable is the \ -default setting of the option Table of TarcerRecurse. "; - -$TarcerVersion::usage= -"contains the version of TARCER." - -Begin["`Private`"]; - -pal1::usage=""; -pal2::usage=""; - -m1::usage=""; -m2::usage=""; -m3::usage=""; -m4::usage=""; -m5::usage=""; -hCayley::usage=""; -hCayleyD::usage=""; -cD::usage=""; -cu::usage=""; -setd::usage=""; -notnecessaryf::usage=""; -gamma::usage=""; -test::usage=""; -ia::usage=""; -ib::usage=""; -ir::usage=""; -es::usage=""; -top::usage=""; -set::usage=""; -factor::usage=""; - -$TarcerVersion = "2.0"; -Expand3 = Identity; -$RankLimit = {0, 6}; -$RankLimit = {1, 6}; -$RankLimit = {2, 5}; -$CheckRecursion = False; -$PutPalettes = False; -atime = AbsoluteTime[]; - - -SEpsilon /: - MakeBoxes[SEpsilon[d_], fmt_] := - InterpretationBox @@ {StyleBox[SubscriptBox["S", ToBoxes[First[Variables[d]], fmt]], FontWeight -> "Bold"], SEpsilon[d], Editable -> False} - -MakeBoxes[SEpsilon[d_]^n_, fmt_] := - InterpretationBox @@ {StyleBox[SubsuperscriptBox["S", ToBoxes[First[Variables[d]], fmt], n], FontWeight -> "Bold"], SEpsilon[d], Editable -> False} - -Prefactor1 /: - MakeBoxes[Prefactor1[d_], fmt_] := - InterpretationBox @@ {MakeBoxes[d, fmt], Prefactor1[d], Editable -> False} - -MakeBoxes[Schiebe[i_, pm_String] , _] := - InterpretationBox[StyleBox[SuperscriptBox[i, pm], FontWeight -> "Bold"], Schiebe[i, pm], Editable -> True] - -CayleyD /: - MakeBoxes[CayleyD[i_Integer][_], _] := - FractionBox[SubscriptBox["\[CapitalDelta]", i], "\[CapitalDelta]"]; - -CayleyD /: - MakeBoxes[CayleyD[i_Integer, j_Integer][_], _] := - FractionBox[SubscriptBox["\[CapitalDelta]", 10 i + j], "\[CapitalDelta]"]; - -CayleyD /: - MakeBoxes[CayleyD[i_Integer, j_Integer, k_Integer][_], _] := - FractionBox[SubscriptBox["\[CapitalDelta]", 100 i + 10 j + k], "\[CapitalDelta]"]; - -Cayley /: - MakeBoxes[Cayley[i_Integer][_], _] := - SubscriptBox["\[CapitalDelta]", i]; - -Cayley /: - MakeBoxes[Cayley[i_Integer, j_Integer][_], _] := - SubscriptBox["\[CapitalDelta]", 10 i + j]; - -Cayley /: - MakeBoxes[Cayley[i_Integer, j_Integer, k_Integer][_], _] := - SubscriptBox["\[CapitalDelta]", 100 i + 10 j + k]; - -Cayleyu /: - MakeBoxes[Cayleyu[i_Integer, j_Integer, k_Integer][_], _] := - SubscriptBox["u", 100 i + 10 j + k]; - -MakeBoxes[PP, _] := - InterpretationBox[SuperscriptBox[p, 2], PP]; - -MakeBoxes[m1^(p_), _] := - InterpretationBox[SubsuperscriptBox[m, 1, p], m1^p]; - -MakeBoxes[m2^(p_), _] := - InterpretationBox[SubsuperscriptBox[m, 2, p], m2^p]; - -MakeBoxes[m3^(p_), _] := - InterpretationBox[SubsuperscriptBox[m, 3, p], m3^p]; - -MakeBoxes[m4^(p_), _] := - InterpretationBox[SubsuperscriptBox[m, 4, p], m4^p]; - -MakeBoxes[m5^(p_), _] := - InterpretationBox[SubsuperscriptBox[m, 5, p], m5^p]; - -m6 = Sqrt[PP]; - -MakeBoxes[m1, _] := - InterpretationBox[SubscriptBox[m, 1], m1]; - -MakeBoxes[m2, _] := - InterpretationBox[SubscriptBox[m, 2], m2]; - -MakeBoxes[m3, _] := - InterpretationBox[SubscriptBox[m, 3], m3]; - -MakeBoxes[m4, _] := - InterpretationBox[SubscriptBox[m, 4], m4]; - -MakeBoxes[m5, _] := - InterpretationBox[SubscriptBox[m, 5], m5]; - -mbt[z_] := - ToBoxes[z, TraditionalForm]; - -redblue[z_ /; Head[z] =!= Plus] := - mbt[z]; - -redblue[z_ - 1] := - StyleBox[mbt[z], FontColor -> RGBColor[1, 0, 0]]; - -redblue[z_Subscript - 2] := - StyleBox[SubscriptBox[OverscriptBox[z[[1]], "_"], z[[2]]], FontColor -> RGBColor[1, 0, 0]]; - -redblue[z_ - 2] := - StyleBox[OverscriptBox[mbt[z], "_"], FontColor -> RGBColor[1, 0, 0]]; -redblue[z_ - 3] := - StyleBox[UnderscriptBox[OverscriptBox[mbt[z], "_"], "_"], FontColor -> RGBColor[1, 0, 0]]; - -redblue[z_ + 1] := - StyleBox[mbt[z], FontColor -> RGBColor[0, 0, 1]]; - -redblue[z_ + 2] := - StyleBox[OverscriptBox[mbt[z], "_"], FontColor -> RGBColor[0, 0, 1]]; - -redblue[z_Subscript + 2] := - StyleBox[SubscriptBox[OverscriptBox[z[[1]], "_"], z[[2]]], FontColor -> RGBColor[0, 0, 1]]; - -TFI /: - MakeBoxes[TFI[d_, pp_, {ur__}, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", ur}]], TFI[d, pp, {ur}, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TFI /: - MakeBoxes[TFI[d_, pp_, dp_, any__, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", Apply[Sequence, Flatten[{any}]]}]], TFI[d, pp, dp, any, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] /; Head[dp] =!= List; - -TFI /: - MakeBoxes[TFI[dpp__, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[First[{dpp}], TraditionalForm], ")"}]], TFI[dpp, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; - -TVI /: - MakeBoxes[TVI[dpp__, {den__}], fmt_] := - ( - (InterpretationBox @@ {SubsuperscriptBox[StyleBox["V", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TVI][dpp, {den}], Editable -> True}) /. Hold[TVI] -> TVI - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; - -TJI /: - MakeBoxes[TJI[d_, 0, {den__}], fmt_] := - ( - (InterpretationBox @@ {SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], Hold[TJI][d, 0, {den}], Editable -> True}) /. Hold[TJI] -> TJI - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TJI /: - MakeBoxes[TJI[dpp__, {den__}], fmt_] := - ( - (InterpretationBox @@ {SubsuperscriptBox[StyleBox["J", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TJI][dpp, {den}], Editable -> True}) /. Hold[TJI] -> TJI - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TKI /: - MakeBoxes[TKI[d_, ___, {den__}], fmt_] := - ( - SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]] - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TKI /: - MakeBoxes[TKI[dpp__, {den__}], fmt_] := - ( - (InterpretationBox @@ {SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TKI][dpp, {den}], Editable -> True}) /. Hold[TKI] -> TKI - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TBI /: - MakeBoxes[TBI[d_, ___, {den__}], fmt_] := - ( - SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]] - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TBI /: - MakeBoxes[TBI[d_, pp___, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TBI[d, pp, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TAI /: - MakeBoxes[TAI[d_, ___, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["A", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TAI[d, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TFIC /: - MakeBoxes[TFIC[d_, pp_, {0, 0, i_, 0, 0}, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", i, "0"}]], TFIC[d, pp, {0, 0, i, 0, 0}, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TFIC /: - MakeBoxes[TFIC[d_, pp_, {0, 0, 0, i_, 0}, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", "0", i}]], TFIC[d, pp, {0, 0, 0, i, 0}, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TFIC /: - MakeBoxes[TFIC[dpp__, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[First[{dpp}], TraditionalForm], ")"}]], TFIC[dpp, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; - -TVIC /: - MakeBoxes[TVIC[dpp__, {den__}], fmt_] := - ( - (InterpretationBox @@ {SubsuperscriptBox[StyleBox["V", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TVIC][dpp, {den}], Editable -> True}) /. Hold[TVIC] -> TVIC - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; - -TJIC /: - MakeBoxes[TJIC[d_, 0, {den__}], fmt_] := - ((InterpretationBox @@ {SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], Hold[TJIC][d, 0, {den}], Editable -> True}) /. Hold[TJIC] -> TJIC - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] - -TJIC /: - MakeBoxes[TJIC[dpp__, {den__}], fmt_] := - ((InterpretationBox @@ {SubsuperscriptBox[StyleBox["J", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TJIC][dpp, {den}], Editable -> True}) /. Hold[TJIC] -> TJIC - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] - -TBIC /: - MakeBoxes[TBIC[d_, ___, {den__}], fmt_] := - ( - SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]] - ) /;MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TBIC /: - MakeBoxes[TBIC[d_, pp___, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TBIC[d, pp, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TAIC /: - MakeBoxes[TAIC[d_, ___, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["A", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TAIC[d, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TFR /: - MakeBoxes[TFR[d_, pp_, {0, 0, i_, 0, 0}, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", i, "0"}]], TFR[d, pp, {0, 0, i, 0, 0}, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TFR /: - MakeBoxes[TFR[d_, pp_, {0, 0, 0, i_, 0}, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", "0", i}]], TFR[d, pp, {0, 0, 0, i, 0}, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TFR /: - MakeBoxes[TFR[dpp__, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[First[{dpp}], TraditionalForm], ")"}]], TFR[dpp, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; - -TVR /: - MakeBoxes[TVR[dpp__, {den__}], fmt_] := - ( - (InterpretationBox @@ {SubsuperscriptBox[StyleBox["V", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TVR][dpp, {den}], Editable -> True}) /. Hold[TVR] -> TVR - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; - -TJR /: - MakeBoxes[TJR[d_, 0, {den__}], fmt_] := - ( - (InterpretationBox @@ {SubsuperscriptBox[StyleBox["K", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], Hold[TJR][d, 0, {den}], Editable -> True}) /. Hold[TJR] -> TJR - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt] - -TJR /: - MakeBoxes[TJR[dpp__, {den__}], fmt_] := - ( - (InterpretationBox @@ {SubsuperscriptBox[StyleBox["J", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[{dpp}[[1]], TraditionalForm], ")"}]], Hold[TJR][dpp, {den}], Editable -> True}) /. Hold[TJR] -> TJR - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TBR /: - MakeBoxes[TBR[d_, ___, {den__}], fmt_] := - ( - SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]] - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TBR /: - MakeBoxes[TBR[d_, pp___, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["B", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TBR[d, pp, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -TAR /: - MakeBoxes[TAR[d_, ___, {den__}], fmt_] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["A", SingleLetterItalics -> False, FontWeight -> "Bold"], RowBox @@ {(redblue /@ {den})}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")"}]], TAR[d, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; - -n1 /: - MakeBoxes[n1, TraditionalForm] := - SubscriptBox["\[Nu]", 1]; -n2 /: - MakeBoxes[n2, TraditionalForm] := - SubscriptBox["\[Nu]", 2]; -n3 /: - MakeBoxes[n3, TraditionalForm] := - SubscriptBox["\[Nu]", 3]; -n4 /: - MakeBoxes[n4, TraditionalForm] := - SubscriptBox["\[Nu]", 4]; -n5 /: - MakeBoxes[n5, TraditionalForm] := - SubscriptBox["\[Nu]", 5]; - -MakeBoxes[ParD[i_]^j_, TraditionalForm] := - SubsuperscriptBox["\[PartialD]", i, j]; - -MakeBoxes[ParD[i_], TraditionalForm] ^= - SubscriptBox["\[PartialD]", i]; - -MakeBoxes[DPlus, TraditionalForm] := - StyleBox[SuperscriptBox["d", "+"], FontWeight -> "Bold", SingleLetterItalics -> False]; - -MakeBoxes[TpD[_, b_], TraditionalForm] := - MakeBoxes[b, TraditionalForm] - -If[ $PutPalettes === True, - tobut[a_] := - ButtonBox[ToBoxes[a, StandardForm], ButtonStyle -> "Paste"]; - If[ Head[pal1] === NotebookObject, - NotebookClose[pal1]]; - pal1 = NotebookPut[ - Notebook[{Cell[BoxData[GridBox[Join[Transpose@{ - Table[tobut@(Subscript[m, j]^2), {j, 5}], - Table[tobut@Subscript[\[Nu], j], {j, 5}], - Table[tobut@Schiebe[i, "+"], {i, 5}], - Table[tobut@Schiebe[i, "-"], {i, 5}]}, { - tobut /@ {PP, Subscript[\[CapitalDelta], \[Placeholder]], Subscript[u, \[Placeholder]], \[ScriptCapitalC] }}], - RowSpacings -> 0, ColumnSpacings -> 0]], NotebookDefault]}, - Editable -> True, - WindowToolbars -> {}, - WindowSize -> {Fit, Fit}, - WindowMargins -> {{0, Automatic}, {0, Automatic}}, - WindowFrame -> "Palette", - WindowElements -> {}, - WindowFrameElements -> "CloseBox", - WindowClickSelect -> False, - ScrollingOptions -> {"PagewiseScrolling" -> True}, - ShowCellBracket -> False, - CellMargins -> {{0, 0}, {0, 0}}, - Active -> True, - CellOpen -> True, - ShowCellLabel -> False, - ShowCellTags -> False, - ImageMargins -> {{0, 0}, {0, 0}}, - Magnification -> 2, Visible -> True] - ]; - SetOptions[pal1, WindowMargins -> {{0, Automatic}, {Automatic, 0}}]; - SetOptions[pal1, Visible -> True, WindowSize -> {Fit, Fit}]; - - If[ Head[pal2] === NotebookObject, - NotebookClose[pal2] - ]; - - pal2 = NotebookPut[Notebook[{Cell[BoxData[GridBox[ - - JJJ = Join[ - {tobut /@ { - TFI[d + 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}], - TVI[d + 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}], - TJI[d + 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}], - TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}], - TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}], - TAI[d, {Subscript[\[Nu], 1]}]}}, - {tobut /@ { - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}], - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}], - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}], - TKI[d - 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}], - TBI[d - 2, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}], - TAI[d - 2, {Subscript[\[Nu], 1]}]}} - ], RowSpacings -> 0, ColumnSpacings -> 0]], NotebookDefault]}, - - Editable -> True, - WindowToolbars -> {}, - WindowSize -> {FitAll, FitAll}, - WindowMargins -> {{0, Automatic}, {0, Automatic}}, - WindowFrame -> "Palette", - WindowElements -> {}, - WindowFrameElements -> "CloseBox", - WindowClickSelect -> False, - ScrollingOptions -> {"PagewiseScrolling" -> True}, - ShowCellBracket -> False, - CellMargins -> {{0, 0}, {0, 0}}, - Active -> True, - CellOpen -> True, - ShowCellLabel -> False, - ShowCellTags -> False, - ImageMargins -> {{0, 0}, {0, 0}}, - Magnification -> 2, Visible -> True] - ]; - SetOptions[pal2, WindowMargins -> {{Automatic, 15}, {Automatic, 4}}]; - SetOptions[pal2, Visible -> True, WindowSize -> {Fit, Fit}]; - SetOptions[pal2, WindowSize -> {Fit, Fit}] -]; - -OperatorApplyF[x_ == y_] := - Block[{sch}, - sch = { - Schiebe[i_, "+"]^ni_. TFI[d_, {n15__}] :> - TFI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], - Schiebe[i_, "-"]^ni_. TFI[d_, {n15__}] :> - TFI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] - }; - Map[Collect[Expand[#] //. sch, TFI[__], Factor] &, x == y] - ]; - -OperatorApplyV[x_ == y_] := - Block[{sch}, - sch = { - Schiebe[i_, "+"]^ni_. TVI[d_, {n15__}] :> - TVI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], - Schiebe[i_, "-"]^ni_. TVI[d_, {n15__}] :> - TVI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] - }; - Map[Collect[Expand[#] //. sch, TVI[__], Factor] &, x == y] - ]; - -OperatorApplyJ[x_ == y_] := - Block[{sch}, - sch = { - Schiebe[i_, "+"]^ni_. TJI[d_, {n15__}] :> - TJI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], - Schiebe[i_, "-"]^ni_. TJI[d_, {n15__}] :> - TJI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] - }; - Map[Collect[Expand[#] //. sch, TJI[__], Factor] &, x == y] - ]; - -OperatorApplyK[x_ == y_] := - Block[{sch}, - sch = { - Schiebe[i_, "+"]^ni_. TKI[d_, {n15__}] :> - TKI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], - Schiebe[i_, "-"]^ni_. TKI[d_, {n15__}] :> - TKI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] - }; - Map[Collect[Expand[#] //. sch, TKI[__], Factor] &, x == y] - ]; - -OperatorApplyK[x_ == y_] := - Block[{sch}, - sch = { - Schiebe[i_, "+"]^ni_. TKI[d_, {n15__}] :> - TKI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], - Schiebe[i_, "-"]^ni_. TKI[d_, {n15__}] :> - TKI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] - }; - Map[Collect[Expand[#] //. sch, TKI[__], Factor] &, x == y] - ]; - -OperatorApplyB[x_ == y_] := - Block[{sch}, - sch = { - Schiebe[i_, "+"]^ni_. TBI[d_, {n15__}] :> - TBI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], - Schiebe[i_, "-"]^ni_. TBI[d_, {n15__}] :> - TBI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] - }; - Map[Collect[Expand[#] //. sch, TBI[__], Factor] &, x == y] - ]; - -OperatorApplyA[x_ == y_] := - Block[{sch}, - sch = { - Schiebe[i_, "+"]^ni_. TAI[d_, {n15__}] :> - TAI[d, ReplacePart[{n15}, {n15}[[i]] + ni, i]], - Schiebe[i_, "-"]^ni_. TAI[d_, {n15__}] :> - TAI[d, ReplacePart[{n15}, {n15}[[i]] - ni, i]] - }; - Map[Collect[Expand[#] //. sch, TAI[__], Factor] &, x == y] - ]; - -MassDerivative[STLI[any__, { {al_, m1_}, {be_, m2_}, {ga_, m3_}, {de_, m4_}, {ep_, m5_}}], {{0, d1_}, {0, d2_}, {0, d3_}, {0, d4_}, {0, d5_}}] := - Pochhammer[al, d1] Pochhammer[be, d2] Pochhammer[ga, d3] Pochhammer[de, d4] Pochhammer[ep, d5] * - STLI[any, {{al + d1, m1}, {be + d2, m2}, {ga + d3, m3}, {de + d4, m4}, {ep + d5, m5}}]; - -TarasovT[abrs__, qq_ /; Head[qq] =!= List] := - TarasovT[abrs, qq, {"g", "g", "g", "g", "g"}] - -TarasovT[r_, s_, qq_, {alp1_, alp2_, alp3_, alp4_, alp5_}] := - Block[{ al1, al2, al3, al4, al5, alrul, new, Q1, Q11, Q12, Q2, Q22, dum1, dum2, be1, be2, ga1, ga2, rho}, - - If[ alp1 === 0, - al1 = 0 - ]; - - If[ alp2 === 0, - al2 = 0 - ]; - - If[ alp3 === 0, - al3 = 0 - ]; - - If[ alp4 === 0, - al4 = 0 - ]; - - If[ alp5 === 0, - al5 = 0 - ]; - - alrul = Select[{ al1 :> I ParD[1], al2 :> I ParD[2], al3 :> I ParD[3], al4 :> I ParD[4], al5 :> I ParD[5]}, ! MatchQ[#, 0 :> _] &]; - - Q1 = al3 al5 + al4 al5 + al2 al3 + al3 al4; - Q2 = al4 al5 + al3 al5 + al1 al4 + al3 al4; - Q11 = 1/(-4) ( al2 + al4 + al5 ); - Q22 = 1/(-4) ( al1 + al3 + al5 ); - Q12 = 1/(-2) al5; - new = - I^(-r-s) ( D[ Exp[ I qq ( be1 Q1 + be2 Q2 + be1^2 Q11 + be2^2 Q22 + be1 be2 Q12 ) rho ], {be1, r}, {be2, s}] ) /. - Join[alrul, {be1 :> 0, be2 :> 0, rho :> -Pi^2/Pi^2 DPlus}]; - - Map[(Select[#, (FreeQ[#, ParD] && FreeQ[#, DPlus]) &] TpD[qq, Select[#, (! (FreeQ[#, ParD] && FreeQ[#, DPlus])) &]]) &, - (Expand[new, ParD] + dum1 dum2)] /. {dum1 :> 0, dum2 :> 0} - ]; - -TarasovT[r_, s_, pp_, dp_ /; Head[dp] =!= List] := - TarasovT[r, s, pp, dp, {"g", "g", "g", "g", "g"}] - -TarasovT[a_, b_, r_, s_, pp_, dp_, {alp1_, alp2_, alp3_, alp4_, alp5_}] := - Block[{al1, al2, al3, al4, al5, alrul, new, Q1, Q11, Q12, Q2, Q22, dum1, dum2, be1, be2, ga1, ga2, rho}, - - If[alp1 === 0, al1 = 0]; If[alp2 === 0, al2 = 0]; - If[alp3 === 0, al3 = 0]; If[alp4 === 0, al4 = 0]; - If[alp5 === 0, al5 = 0]; - - alrul = Select[{al1 :> I ParD[1], al2 :> I ParD[2], al3 :> I ParD[3], al4 :> I ParD[4], al5 :> I ParD[5]}, !(MatchQ[#1, 0 :> _]) &]; - - Q1 = al3 al5 + al4 al5 + al2 al3 + al3 al4; - Q2 = al4 al5 + al3 al5 + al1 al4 + al3 al4; - Q11 = -(1/4) (al2 + al4 + al5); Q22 = -(1/4) (al1 + al3 + al5); - Q12 = -(al5/2); - new = - I^(-r - s - a - b) * - D[Exp[I ((be1 pp + ga1 dp) Q1 + (be2 pp + ga2 dp) Q2 + be1 (be1 pp + 2 ga1 dp) Q11 + be2 (be2 pp + 2 ga2 dp) Q22 + (be1 be2 pp + (be1 ga2 + be2 ga1) dp) Q12) rho], - {be1, r}, {be2, s}, {ga1, a}, {ga2, b}] /. Join[alrul, {be1 :> 0, be2 :> 0, ga1 :> 0, ga2 :> 0, rho :> -((Pi^2 DPlus)/Pi^2)}]; - - (Select[#1, FreeQ[#1, ParD] && FreeQ[#1, DPlus] &] TpD[pp, Select[#1, ! (FreeQ[#1, ParD] && FreeQ[#1, DPlus]) &]] &) /@ (Expand[new] + dum1 dum2) /. - {dum1 :> 0, dum2 :> 0} - ]; - -ApplyTarasovT[tij_, exp_] := - Block[{dump}, - dump = Product[ParD[j]^dummy, {j, 5}]; - - Expand[tij exp] /. (STLI[de_, pp_, pe__List] TpD[_, DPlus^i_. t_]) :> - MassDerivative[STLI[ de /. de :> (de + 2 i), pp, pe], t dump /. Times -> List /. Power[_, n_] :> {0, n} /. dummy -> 0] - ]; - -Prefactor1 /: - Prefactor1[a_]^n_ := - Prefactor1[a^n]; - -MakeBoxes[Block, StandardForm] := - StyleBox["Block", FontSize -> 16, FontWeight -> "Bold", FontColor -> RGBColor[1, 0.2, 0.2]]; - -MakeBoxes[Cayley, StandardForm] := - StyleBox["Cayley", FontColor -> RGBColor[1, 0, 0.4]]; - -MakeBoxes[CayleyD, StandardForm] := - StyleBox["CayleyD", FontColor -> RGBColor[1, 0.2, 1]]; - -MakeBoxes[Cayleyu, StandardForm] := - StyleBox["Cayleyu", FontColor -> RGBColor[0.8, 0.8, 0.4]]; - -MakeBoxes[IFF, StandardForm] := - StyleBox["IFF", FontColor -> RGBColor[0.6, 0.4, 1]]; - -MakeBoxes[MakeFun, StandardForm] := - StyleBox["MakeFun", FontColor -> RGBColor[1, 0.6, 0.6]]; - -MakeBoxes[TFI, StandardForm] := - StyleBox["TFI", FontColor -> RGBColor[1, 0.6, 0]]; - -MakeBoxes[TFR, StandardForm] := - StyleBox["TFR", FontColor -> RGBColor[0, 0.6, 0]]; - -MakeBoxes[ToArgs, StandardForm] := - StyleBox["ToArgs", FontColor -> RGBColor[0.2, 0.6, 1]]; - -MakeBoxes[TVI, StandardForm] := - StyleBox["TVI", FontColor -> RGBColor[0.2, 0.4, 0.8]]; - -MakeBoxes[TVR, StandardForm] := - StyleBox["TVR", FontColor -> RGBColor[0.2, 0.8, 1]]; - -PQ[_Integer?Positive] := - True; - -PNQ[0] = - True; - -PNQ[_Integer?Positive] := - True; - -FactorC[z_] := - FactorC[z] = Factor[z] - -TFI[depp__, {a___, b_Integer, c___}] := - TFI[depp, {a, {b, 0}, c}]; - -TFI[depp__, {a___, {0, m_ /; m =!= 0}, b___}] := - TFI[depp, {a, {0, 0}, b}]; - -TFI[a__, {0, 0}, b__List] := TFI[a, b]; - -TFI[d_, pp_, _, {0, 0}, {x1_, x2_, x3_, x4_, x5_}, list_List] := - TFI[d, pp, {x1, x2, x3, x4, x5}, list]; - -TFI[d_, pp_, dp_, {a_, b_}, {0, 0, 0, 0, 0}, list_List] := - TFI[d, pp, dp, {a, b}, list]; - -TFI[d_, pp_, dp_ /; Head[dp] =!= List, {0, 0, 0, 0, 0}, list_List] := - TFI[d, pp, list]; - -TFI[d_, pp_, dp_ /; Head[dp] =!= List, list_List] := - TFI[d, pp, list]; - -TFI[d_, pp_, dp_ /; Head[dp] =!= List, {x1_, x2_, x3_, x4_, x5_}, list_List] := - TFI[d, pp, {x1, x2, x3, x4, x5}, list]; - -TFI[__, {{_, _}, {0, 0}, {_, _}, {0, 0}, {_, 0}}] := - 0; - -TFI[__, {{0, 0}, {_, _}, {0, 0}, {_, _}, {_, 0}}] := - 0; - -TFI[__, {{0, 0}, {_, _}, {_, 0}, {_, _}, {0, 0}}] := - 0; - -TFI[__, {{_, 0}, {_, _}, {0, 0}, {_, _}, {0, 0}}] := - 0; - -TFI[__, {{_, _}, {_, 0}, {_, _}, {0, 0}, {0, 0}}] := - 0; - -TFI[__, {{_, _}, {0, 0}, {_, _}, {_, 0}, {0, 0}}] := - 0; - -TFI[__, {{0, 0}, {0, 0}, {0, 0}, {_, 0}, {_, _}}] := - 0; - -TFI[__, {{0, 0}, {0, 0}, {_, 0}, {0, 0}, {_, _}}] := - 0; - -TFI[__, {{0, 0}, {_, 0}, {0, 0}, {0, 0}, {_, _}}] := - 0; - -TFI[__, {{_, 0}, {0, 0}, {0, 0}, {0, 0}, {_, _}}] := - 0; - -TFI[__, {{_, _}, {_, 0}, {0, 0}, {0, 0}, {0, 0}}] := - 0; - -TFI[__, {{_, 0}, {_, _}, {0, 0}, {0, 0}, {0, 0}}] := - 0; - -TFI[__, {{_, _}, {0, 0}, {0, 0}, {_, 0}, {0, 0}}] := - 0; - -TFI[__, {{_, 0}, {0, 0}, {0, 0}, {_, _}, {0, 0}}] := - 0; - -TFI[__, {{0, 0}, {_, 0}, {_, _}, {0, 0}, {0, 0}}] := - 0; - -TFI[__, {{0, 0}, {_, _}, {_, 0}, {0, 0}, {0, 0}}] := - 0; - -TFI[__, {{0, 0}, {0, 0}, {_, _}, {_, 0}, {0, 0}}] := - 0; - -TFI[__, {{0, 0}, {0, 0}, {_, 0}, {_, _}, {0, 0}}] := - 0; - -If[ $Notebooks, - - mbt[z_] := - ToBoxes[z, TraditionalForm]; - - redblue[z_ /; Head[z] =!= Plus] := - mbt[z]; - - redblue[(z_) - 1] := - StyleBox[mbt[z], FontColor -> RGBColor[1, 0, 0]]; - - redblue[(z_Subscript) - 2] := - StyleBox[SubscriptBox[OverscriptBox[z[[1]], "_"], z[[2]]], FontColor -> RGBColor[1, 0, 0]]; - - redblue[(z_) - 2] := - StyleBox[OverscriptBox[mbt[z], "_"], FontColor -> RGBColor[1, 0, 0]]; - - redblue[(z_) - 3] := - StyleBox[UnderscriptBox[OverscriptBox[mbt[z], "_"], "_"], FontColor -> RGBColor[1, 0, 0]]; - - redblue[(z_) + 1] := - StyleBox[mbt[z], FontColor -> RGBColor[0, 0, 1]]; - - redblue[(z_) + 2] := - StyleBox[OverscriptBox[mbt[z], "_"], FontColor -> RGBColor[0, 0, 1]]; - - redblue[(z_Subscript) + 2] := - StyleBox[SubscriptBox[OverscriptBox[z[[1]], "_"], z[[2]]], FontColor -> RGBColor[0, 0, 1]]; - - TFI /: - MakeBoxes[TFI[d_, pp_, {ur__}, {den__}], TraditionalForm] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", Rule[SingleLetterItalics, False], - Rule[FontWeight, "Bold"]], RowBox @@ {redblue /@ {den}}, - RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", ur}]], TFI[d, pp, {ur}, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, TraditionalForm]; - - TFI /: - MakeBoxes[TFI[d_, pp_, dp_, any__, {den__}], TraditionalForm] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", Rule[SingleLetterItalics, False], - Rule[FontWeight, "Bold"]], RowBox @@ {redblue /@ {den}}, RowBox[{"(", ToBoxes[d, TraditionalForm], ")", " ", - Sequence @@ Flatten[{any}]}]], TFI[d, pp, dp, any, {den}], Editable -> True} - ) /; Head[dp] =!= List; - - TFI /: - MakeBoxes[TFI[dpp__, {den__}], TraditionalForm] := - ( - InterpretationBox @@ {SubsuperscriptBox[StyleBox["F", Rule[SingleLetterItalics, False], Rule[FontWeight, "Bold"]], - RowBox @@ {redblue /@ {den}}, RowBox[{"(", ToBoxes[First[{dpp}], TraditionalForm], ")"}]], TFI[dpp, {den}], Editable -> True} - ) /; MemberQ[{StandardForm, TraditionalForm}, TraditionalForm] && Head[Last[{dpp}]] =!= List; -]; - - -TJI[de_, pp_, {{n1_Integer, m1_}, {n2_Integer, m2_}, {n3_Integer, m3_}}] := - ( - TJI[de, pp, {{n1, m1}, {n2, m2}, {n3, m3}}] = - TJI[de, pp, Reverse[Sort[{{n1, m1}, {n2, m2}, {n3, m3}}]]] - ) /; !OrderedQ[{{n3, m3}, {n2, m2}, {n1, m1}}]; - -TJI[_, 0, {{_, 0}, {_, 0}, {_, 0}}] := - 0 - -TBI[de_, pp_, {{n1_Integer, m1_}, {n2_Integer, m2_}}] := - ( - TJI[de, pp, {{n1, m1}, {n2, m2}}] = - TBI[de, pp, Reverse[Sort[{{n1, m1}, {n2, m2}}]]] - ) /; !OrderedQ[{{n2, m2}, {n1, m1}}]; - -TBI[_, 0, {{_, 0}, {_, 0}}] := - 0; - -TAI[_, _, {{_Integer, 0}}] := - 0; - -\[CapitalDelta]\[ScriptCapitalC] = - (-(1/2)) Det[{ - {0, 1, 1, 1, 1}, - {1, 0, Subscript[\[Mu], 6], Subscript[\[Mu], 4], Subscript[\[Mu], 3]}, - {1, Subscript[\[Mu], 6], 0, Subscript[\[Mu], 2], Subscript[\[Mu], 1]}, - {1, Subscript[\[Mu], 4], Subscript[\[Mu], 2], 0, Subscript[\[Mu], 5]}, - {1, Subscript[\[Mu], 3], Subscript[\[Mu], 1], Subscript[\[Mu], 5], 0}} -]; - -checkli = { - \[ScriptCapitalC] -> - \[CapitalDelta]\[ScriptCapitalC], - - Subscript[\[CapitalDelta], i_] :> - D[\[CapitalDelta]\[ScriptCapitalC], Subscript[\[Mu], i]], - - Subscript[\[Mu], 6] :> PP, - Subscript[\[Mu], i_] :> ToExpression[StringJoin["m", ToString[i]]]^2, - Subscript[m, 1] :> Sqrt[m1^2], - Subscript[m, 2] :> Sqrt[m2^2], Subscript[m, 3] :> Sqrt[m3^2], - Subscript[m, 4] :> Sqrt[m4^2], - Subscript[m, 5] :> Sqrt[m5^2], - - Subscript[\[CapitalDelta], i_, j_, k_] :> - Subscript[\[Mu], i]^2 + Subscript[\[Mu], j]^2 + Subscript[\[Mu], k]^2 - 2*(Subscript[\[Mu], i]*Subscript[\[Mu], j] + - Subscript[\[Mu], j]*Subscript[\[Mu], k] + Subscript[\[Mu], k]*Subscript[\[Mu], i]), - - Subscript[u, i_, j_, k_] :> - Subscript[\[Mu], i] - Subscript[\[Mu], j] - Subscript[\[Mu], k], - - Subscript[\[CapitalSigma], i_] :> - 3*d - 2*Sum[Subscript[\[Nu], j], {j, 1, i}] - 2, - - Subscript[\[Nu], 1] :> n1, - Subscript[\[Nu], 2] :> n2, - Subscript[\[Nu], 3] :> n3, - Subscript[\[Nu], 4] :> n4, - Subscript[\[Nu], 5] :> n5 -}; - - -Subscript[\[CapitalDelta], i_, j_, k_] := - Subscript[\[CapitalDelta], Sequence @@ Sort[{i, j, k}]] /; !OrderedQ[{i, j, k}]; - -ToArgs[z_] := - Expand[z //. checkli]; - -setd[hCayley[m1_, m2_, m3_, m4_, m5_, p_], set[hCayley[m1, m2, m3, m4, m5, p], - factor[ToArgs[\[ScriptCapitalC]] /. PP -> p^2]] -] /. { hCayley :> Cayley, setd :> SetDelayed, set :> Set, factor :> Factor}; - -Do[ setd[hCayley[i][{m1_, m2_, m3_, m4_, m5_, p_}], - set[hCayley[i][{m1, m2, m3, m4, m5, p}], - factor[ToArgs[Subscript[\[CapitalDelta], i]] /. PP -> p^2]]] /. { - hCayley :> Cayley, setd :> SetDelayed, set :> Set, factor :> Factor}, {i, 6} -]; - - -Cayley[i_, j_, k_][m_List] := - Cayley[i, j, k][m] = - Block[{mm = m}, - While[ - Length[mm] < 7, - AppendTo[mm, Last[mm]] - ]; - - FactorC[mm[[i]]^4 - 2*mm[[j]]^2*mm[[i]]^2 - 2*mm[[k]]^2*mm[[i]]^2 + mm[[j]]^4 + mm[[k]]^4 - 2*mm[[j]]^2*mm[[k]]^2] - ]; - -Cayleyu[i_, j_, k_][m_List] := - Cayleyu[i, j, k][mm] = - Block[{mm = m}, - While[ - Length[mm] < 7, - AppendTo[mm, Last[mm]] - ]; - - FactorC[mm[[i]]^2 - mm[[j]]^2 - mm[[k]]^2] - ]; - -Do[setd[hCayleyD[i][{m1_, m2_, m3_, m4_, m5_, p_}], - set[hCayleyD[i][{m1, m2, m3, m4, m5, p}], - factor[(ToArgs[Subscript[\[CapitalDelta], i]] /. PP -> p^2)/\[ScriptCapitalC][m1, m2, m3, m4, m5, p]]]] /. - {hCayleyD :> CayleyD, setd :> SetDelayed, set :> Set, factor :> Factor, \[ScriptCapitalC] :> Cayley}, {i, 6} -]; - -setd[hCayleyD[1, 2, 5][{m1_, m2_, m3_, m4_, m5_, p_}], - set[hCayleyD[1, 2, 5][{m1, m2, m3, m4, m5, p}], - factor[(ToArgs[Subscript[\[CapitalDelta], 1, 2, 5]] /. PP -> p^2)/\[ScriptCapitalC][m1, m2, m3, m4, m5, p]]] -] /. {hCayleyD :> CayleyD, setd :> SetDelayed, set :> Set, factor :> Factor, \[ScriptCapitalC] :> Cayley}; - -setd[hCayleyD[1, 3, 6][{m1_, m2_, m3_, m4_, m5_, p_}], - set[hCayleyD[1, 3, 6][{m1, m2, m3, m4, m5, p}], - factor[(ToArgs[Subscript[\[CapitalDelta], 1, 3, 6]] /. PP -> p^2)/\[ScriptCapitalC][m1, m2, m3, m4, m5, p]]] -] /. {hCayleyD :> CayleyD, setd :> SetDelayed, set :> Set, factor :> Factor, \[ScriptCapitalC] :> Cayley}; - -setd[hCayleyD[3, 4, 5][{m1_, m2_, m3_, m4_, m5_, p_}], - set[hCayleyD[3, 4, 5][{m1, m2, m3, m4, m5, p}], - factor[(ToArgs[Subscript[\[CapitalDelta], 3, 4, 5]] /. PP -> p^2)/\[ScriptCapitalC][m1, m2, m3, m4, m5, p]]] -] /. {hCayleyD :> CayleyD, setd :> SetDelayed, set :> Set, factor :> Factor, \[ScriptCapitalC] :> Cayley}; - -nutonandDelta[w_, 5] := - w /. { - Subscript[\[Nu], 1] :> n1, - Subscript[\[Nu], 2] :> n2, - Subscript[\[Nu], 3] :> n3, - Subscript[\[Nu], 4] :> n4, - Subscript[\[Nu], 5] :> n5, - Subscript[\[CapitalDelta], ijk__] :> \[ScriptCapitalC]*cD[ijk], - Subscript[u, ijk__] :> cu[ijk], - Subscript[D, ijk__] :> TA[D, ijk], - Subscript[\[Rho], ijk__] :> TA[\[Rho], ijk], - Subscript[\[Phi], ijk__] :> TA[\[Phi], ijk], - Subscript[\[Sigma], i_, j_, k_] :> TA[\[Sigma], d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], Subscript[\[Nu], k]], - Subscript[h, i_, j_, k_] :> TA[h, d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], Subscript[\[Nu], k]], - Subscript[S, i_, j_, k_] :> TA[S, d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], Subscript[\[Nu], k]], - Subscript[\[CapitalSigma], i_] :> ToArgs[Subscript[\[CapitalSigma], i]]} /. { - - Subscript[\[Nu], 1] :> n1, - Subscript[\[Nu], 2] :> n2, - Subscript[\[Nu], 3] :> n3, - Subscript[\[Nu], 4] :> n4, - Subscript[\[Nu], 5] :> n5, - Subscript[m, 1] :> m1, - Subscript[m, 2] :> m2, - Subscript[m, 3] :> m3, - Subscript[m, 4] :> m4, - Subscript[m, 5] :> m5 - }; - -nutonandDelta[w_] := - w /. { - Subscript[\[Nu], 1] :> n1, - Subscript[\[Nu], 2] :> n2, - Subscript[\[Nu], 3] :> n3, - Subscript[\[Nu], 4] :> n4, - Subscript[\[Nu], 5] :> n5, - Subscript[\[CapitalDelta], ijk__] :> cD[ijk], - Subscript[u, ijk__] :> cu[ijk], - Subscript[D, ijk__] :> TA[D, ijk], - Subscript[\[Rho], ijk__] :> TA[\[Rho], ijk], - Subscript[\[Phi], ijk__] :> TA[\[Phi], ijk], - Subscript[\[Sigma], i_, j_, k_] :> TA[\[Sigma], d, i, j, k, Subscript[\[Nu], i], - Subscript[\[Nu], j], Subscript[\[Nu], k]], - Subscript[h, i_, j_, k_] :> TA[h, d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], Subscript[\[Nu], k]], - Subscript[S, i_, j_, k_] :> TA[S, d, i, j, k, Subscript[\[Nu], i], Subscript[\[Nu], j], - Subscript[\[Nu], k]], - Subscript[\[CapitalSigma], i_] :> ToArgs[Subscript[\[CapitalSigma], i]]} /. { - - Subscript[\[Nu], 1] :> n1, - Subscript[\[Nu], 2] :> n2, - Subscript[\[Nu], 3] :> n3, - Subscript[\[Nu], 4] :> n4, - Subscript[\[Nu], 5] :> n5, - Subscript[m, 1] :> m1, - Subscript[m, 2] :> m2, - Subscript[m, 3] :> m3, - Subscript[m, 4] :> m4, - Subscript[m, 5] :> m5 - }; - -addPeP[TFR[d_, pp_, li1_, rest_]] := - TFR[d, pp, li1, rest]; - -addPeP[TFI[d_, pp_, li1_List]] := - TFI[d, pp, li1]; - -addPeP[TFR[d_, pp_, dp_Symbol, li1_, rest_]] := - TFR[d, pp, dp, li1, rest]; - -addPeP[TFI[d_, pp_, dp_Symbol, li1_List]] := - TFI[d, pp, dp, li1]; - -addPeP[TVI[d_, pp_, li1_List]] := - TVI[d, pp, li1]; - -(* TODO ??? *) -nnnnnaddPeP[(any_)[d_, pp_, li1_List, rest__List]] := - any[d, pp, li1, rest] /; any =!= List - -addPeP[z_List] := Append[z, Sqrt[PP]]; - -addPeP[TFI[d_, z_List]] := - TFI[d, PP, z]; - -addPeP[TVI[d_, z_List]] := - TVI[d, PP, z]; - -addPeP[TJI[d_, z_List]] := - TJI[d, PP, z]; - -addPeP[TFR[d_, z_List]] := - TFR[d, PP_, z]; - -addPeP[TFR[d_, pl_List, z_List]] := - TFR[d, PP_, pl, z]; - -addPeP[TVR[d_, z__List]] := - TVR[d, PP_, z]; - -addPeP[TJR[d_, z__List]] := - TJR[d, PP_, z]; - -nutomass[w_] := - w /. { - Subscript[\[Nu], 1] + (i1_.) :> {n1 + i1, m1}, - Subscript[\[Nu], 2] + (i2_.) :> {n2 + i2, m2}, - Subscript[\[Nu], 3] + (i3_.) :> {n3 + i3, m3}, - Subscript[\[Nu], 4] + (i4_.) :> {n4 + i4, m4}, - Subscript[\[Nu], 5] + (i5_.) :> {n5 + i5, m5}} /. - {in1_Integer, in2_Integer, in3_Integer, in4_Integer} :> {{in1, m1}, {in2, m2}, {in3, m3}, {in4, m4}} /. - {in1_Integer, in2_Integer, in3_Integer} :> {{in1, m1}, {in2, m2}, {in3, m3}}; - -Clear[maybeF]; - -maybeF[z_Times] := - FactorC[z] /; FreeQ[z, TFI] && FreeQ[z, TVI] && FreeQ[z, TJI] && Length[Cases[z, cD[__], -1]] > 1; - -maybeF[z_] := z; - -SetAttributes[top, Listable]; -SetAttributes[IFF, HoldAll]; - -Clear[MakeFun]; - -MakeFun[(c_.) TFI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := - Block[{nm, nmrel, setdel, pat, blank, pattern, patternTest, identitL}, - nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; - HoldForm @@ {setdel[ - addPeP[TFR @@ top /@ nutomass[{t}]] /. nmrel, - Hold[Condition][Hold[CompoundExpression][ - Hold[TComment][eqn, addPeP[nutomass[TFR[t]]] /. - TFR -> TFIC /. {Pattern :> pat, Blank :> blank} /. pat[PP, blank[]] :> PP /. nmrel], - - Collect[ TT = Expand3[nutonandDelta[(1/c) (rhs /. TFI[te__] :> addPeP[nutomass[TFI[te]]]), 5]], - TFI[__], maybeF[(Collect[Numerator[#1], cD[__], Factor]/Collect[Denominator[#1], cD[__], Factor] & ) /@ - Factor[#1]] & ] /. nmrel - ], - - nutonandDelta[IFF[conds], 5]]] /. top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. - patternTest[pattern[dm_ /; MemberQ[{d, PP, DP, m1, m2, m3, m4, m5}, dm], blank[]], _] :> - pattern[dm, blank[]] /. {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. - cD[ijk__] -> Hold[CayleyD[ijk]][addPeP[BLA = nutomass[Last[{t}]] /. nmrel /. {_, ma_} :> ma]] /. - addPeP -> Identity /. Hold[CompoundExpression] -> CompoundExpression /. Hold[Condition][a_, IFF[b_]] -> a /; b /. - Hold[Set] -> Set /. Hold[TComment] -> TComment /. Hold[CayleyD[ijk__]] -> CayleyD[ijk] /. {setdel :> SetDelayed} /. - Identity -> identit /. identit[a_] -> a - ]; - -MakeFun[(c_.) TFI[t__] == (rhs_), eqn_String, mrel_: {}] := - Block[{nm, nmrel, setdel, pat, blank, pattern, patternTest, identit}, - nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; - - HoldForm @@ {setdel[ - addPeP[TFR @@ top /@ nutomass[{t}]] /. nmrel, - - Hold[CompoundExpression][Hold[TComment][eqn, addPeP[nutomass[TFR[t]]] /. TFR -> TFIC /. {Pattern :> pat, Blank :> blank} /. - pat[PP, blank[]] :> PP /. nmrel], - Collect[TT = Expand3[nutonandDelta[(1/c)*(rhs /. TFI[te__] :> addPeP[nutomass[TFI[te]]])]], TFI[__], - maybeF[(Collect[Numerator[#1], cD[__], Factor] / Collect[Denominator[#1], cD[__], Factor] & ) /@ Factor[#1]] & ] /. nmrel] - ] /. top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. - patternTest[ pattern[dm_ /; MemberQ[{d, PP, DP, m1, m2, m3, m4, m5}, dm], blank[]], _] :> pattern[dm, blank[]] /. - {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. - cD[ijk__] -> Hold[CayleyD[ijk]][addPeP[nutomass[Last[{t}]] /. addPeP -> Identity /. nmrel /. - {nuu_, ma_} :> ma]] /. Hold[CompoundExpression] -> CompoundExpression /. Hold[Condition][a_, IFF[b_]] -> a /; b /. - Hold[Set] -> Set /. Hold[TComment] -> TComment /. Hold[CayleyD[ijk__]] -> CayleyD[ijk] /. {setdel :> SetDelayed} /. - addPeP -> Identity /. Identity -> identit /. identit[a_] -> a - ] /; Head[mrel] =!= IFF; - -MakeFun[(c_.) TVI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := - Block[{nm, nmrel, setdel, pat, blank, pattern, patternTest, identit}, - nmrel = - Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; - - nmrel = - Join[nmrel, { - Subscript[m, 1] :> m1, - Subscript[m, 2] :> m2, - Subscript[m, 3] :> m3, - Subscript[m, 4] :> m4, - Subscript[\[CapitalSigma], i_] :> - ToArgs[Subscript[\[CapitalSigma], i]]} - ]; - HoldForm @@ {setdel[ - addPeP[TVR @@ top /@ nutomass[{t}]] /. nmrel, - - Hold[Condition][Hold[CompoundExpression][Hold[TComment][eqn, addPeP[nutomass[TVR[t]]] /. - TVR -> TVIC /. {Pattern :> pat, Blank :> blank} /. pat[PP, blank[]] :> PP /. nmrel], - - Collect[TT = Expand3[nutonandDelta[(1/c) (rhs /. TVI[te__] :> addPeP[nutomass[TVI[te]]])]], - TVI[__], maybeF[(Collect[Numerator[#1], cu[__], Factor]/ Collect[Denominator[#1], cu[__], Factor] & ) /@ - Factor[#1]] & ] /. \[ScriptCapitalC] -> 1 /. nmrel], nutonandDelta[IFF[conds]]] - ] /. - top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. - patternTest[pattern[dm_ /; MemberQ[{d, PP, m1, m2, m3, m4}, dm], blank[]], _] :> - pattern[dm, blank[]] /. {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. - HoldPattern[TA[aijk__]] -> Hold[TA[aijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_} :> ma]] /. - cD[ijk__] -> Hold[Cayley[ijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_} :> ma]] /. cu[ijk__] -> - Hold[Cayleyu[ijk]][addPeP[nutomass[Last[{t}]] /. addPeP -> Identity /. nmrel /. {_, ma_} :> ma]] /. - Hold[CompoundExpression] -> CompoundExpression /. Hold[Condition][a_, IFF[b_]] -> a /; b /. Hold[Set] -> Set /. - Hold[TComment] -> TComment /. addPeP -> Identity /. Hold[Cayleyu[ijk__]] -> Cayleyu[ijk] /. - Hold[Cayley[ijk__]] -> Cayley[ijk] /. Hold[TA] -> TA /. {setdel :> SetDelayed} /. Identity -> identit /. identit[a_] -> a - ]; - -MakeFun[(c_.) TVI[t__] == (rhs_), eqn_String, mrel_: {}] := - Block[{nm, nmrel, setdel, pat, blank, pattern, patternTest}, - nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; - - nmrel = Join[nmrel, { - Subscript[m, 1] :> m1, - Subscript[m, 2] :> m2, - Subscript[m, 3] :> m3, - Subscript[m, 4] :> m4, - Subscript[\[CapitalSigma], i_] :> ToArgs[Subscript[\[CapitalSigma], i]]}]; - - HoldForm @@ {setdel[ - addPeP[TVR @@ top /@ nutomass[{t}]] /. nmrel, - - Hold[CompoundExpression][Hold[TComment][eqn, addPeP[nutomass[TVR[t]]] /. - TVR -> TVIC /. {Pattern :> pat, Blank :> blank} /. pat[PP, blank[]] :> PP /. nmrel], - - Collect[TT = Expand3[nutonandDelta[(1/c)*(rhs /. TVI[te__] :> addPeP[nutomass[TVI[te]]])]], - TVI[__], maybeF[(Collect[Numerator[#1], cu[__], Factor]/ Collect[Denominator[#1], cu[__], Factor] & ) /@ - Factor[#1]] & ] /. nmrel /. \[ScriptCapitalC] -> 1] - ] /. - top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. - patternTest[pattern[dm_ /; MemberQ[{d, PP, m1, m2, m3, m4}, dm], blank[]], _] :> pattern[dm, blank[]] /. - {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. cD[ijk__] -> - Hold[Cayley[ijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {nuu_, ma_Symbol} :> ma]] /. - cu[ijk__] -> Hold[Cayleyu[ijk]][addPeP[nutomass[Last[{t}]] /. - nmrel /. {nuu_, ma_Symbol} :> ma]] /. Hold[CompoundExpression] -> CompoundExpression /. - Hold[Set] -> Set /. Hold[TComment] -> TComment /. addPeP -> Identity /. Hold[Cayleyu[ijk__]] -> Cayleyu[ijk] /. - Hold[Cayley[ijk__]] -> Cayley[ijk] /. {setdel :> SetDelayed} /. Identity -> identit /. identit[a_] -> a - ] /; Head[mrel] =!= IFF; - -MakeFun[(c_.) TJI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := - Block[{nm, nmrel, result, setdel, pat, blank, pattern, patternTest, tT}, - - \[ScriptCapitalC] = 1; - - nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor] & ]; - - nmrel = - Join[nmrel, { - Subscript[m, 1] :> m1, - Subscript[m, 2] :> m2, - Subscript[m, 3] :> m3, - Subscript[m, 4] :> m4, - Subscript[\[CapitalSigma], i_] :> - ToArgs[Subscript[\[CapitalSigma], i]]} - ]; - - result = - HoldForm @@ {setdel[ - addPeP[TJR @@ top /@ nutomass[{tT = t}]] /. nmrel, - - Hold[Condition][Hold[CompoundExpression][Hold[TComment][eqn, addPeP[nutomass[TJR[t]]] /. TJR -> TJIC /. - {Pattern :> pat, Blank :> blank} /. pat[PP, blank[]] :> PP /. nmrel], - TJ = Collect[ TT = Expand3[nutonandDelta[(1/c) (rhs /. TJI[te__] :> addPeP[nutomass[TJI[te]]])]], TJI[__], - maybeF[(Collect[Numerator[#1], cu[__], Factor]/Collect[Denominator[#1], cu[__], Factor] & ) /@ Factor[#1]] & ] /. - \[ScriptCapitalC] -> 1 /. nmrel], nutonandDelta[IFF[conds]]] - ] /. - top[i_Integer] -> i /. top :> (patternTest[pattern[#1, blank[]], PQ] & ) /. - patternTest[pattern[dm_ /; MemberQ[{d, PP, m1, m2, m3, m4}, dm], blank[]], _] :> - pattern[dm, blank[]] /. {blank :> Blank, pattern :> Pattern, patternTest :> PatternTest}} /. - HoldPattern[TA[aijk__]] -> Hold[TA][aijk][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_} :> ma]] /. cD[ijk__] -> - Hold[Cayley[ijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_Symbol} :> ma]] /. cu[ijk__] -> - Hold[Cayleyu[ijk]][addPeP[nutomass[Last[{t}]] /. nmrel /. {_, ma_Symbol} :> ma]] /. - Hold[CompoundExpression] -> CompoundExpression /. Hold[Condition][a_, IFF[b_]] -> a /; b /. - Hold[Set] -> Set /. Hold[TComment] -> TComment /. Hold[Cayleyu[ijk__]] -> Cayleyu[ijk] /. - Hold[Cayley[ijk__]] -> Cayley[ijk] /. Hold[TA] -> TA /. {setdel :> SetDelayed}; \[ScriptCapitalC] =. ; - - result - ]; - -SetAttributes[paTT, HoldFirst]; - -MakeFun[(c_.) TKI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := - MakeFun[c TJI[t] == rhs /. TKI -> TJI, eqn, IFF[conds], mrel] /. - {PP :> 0, Sqrt[PP] :> 0, Pattern :> paTT} /. paTT[0, _] -> 0 /. paTT -> Pattern /. TJIC[d_, li_List] :> TJIC[d, 0, li]; - -MakeFun[(c_.) TBI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := - MakeFun[c TJI[t] == rhs /. TBI -> TJI, eqn, IFF[conds], mrel] /. - {TJI :> TBI, TJR :> TBR, TJIC :> TBIC}; - -MakeFun[(c_.) TAI[t__] == (rhs_), eqn_String, IFF[conds_], mrel_: {}] := - MakeFun[c TJI[t] == rhs /. TAI -> TJI, eqn, IFF[conds], mrel] /. {TJI :> TAI, TJR :> TAR, TJIC :> TAIC}; - -Interchange[z_, (i_) \[LeftRightArrow] (j_)] := - nuExplicit[z] /. { - - Subscript[\[Nu], i] :> Subscript[\[Nu], j], - Subscript[\[Nu], j] :> Subscript[\[Nu], i], - Subscript[m, i] :> Subscript[m, j], - Subscript[m, j] :> Subscript[m, i], - Subscript[\[CapitalDelta], ij__] :> - Subscript[\[CapitalDelta], ij] /. {i :> j, j :> i}, - Subscript[u, ij__] :> (Subscript[u, ij] /. {i :> j, j :> i}), - Subscript[h, ij__] :> (Subscript[h, ij] /. {i :> j, j :> i}), - Subscript[\[Phi], ij__] :> (Subscript[\[Phi], ij] /. {i :> j, j :> i}), - Subscript[\[Rho], ij__] :> (Subscript[\[Rho], ij] /. {i :> j, j :> i}), - Subscript[\[Sigma], ij__] :> (Subscript[\[Sigma], ij] /. {i :> j, j :> i}), - Subscript[D, ij__] :> (Subscript[D, ij] /. {i :> j, j :> i})} /. { - - TFI[depp__, args_List] :> TFI[depp, Sort[args]] /; ! OrderedQ[args], - TVI[depp__, args_List] :> TVI[depp, Sort[args]] /; ! OrderedQ[args], - TJI[depp__, args_List] :> TJI[depp, Sort[args]] /; ! OrderedQ[args], - TBI[depp__, args_List] :> TBI[depp, Sort[args]] /; ! OrderedQ[args] - }; - -Interchange[z_, (i_) \[LeftRightArrow] (j_), vw__] := - Interchange[Interchange[z, i \[LeftRightArrow] j], vw]; - -Interchange[z_, {(i_) \[LeftRightArrow] (j_)}] := - Interchange[Interchange[z, i \[LeftRightArrow] j]]; - -Interchange[z_, {(i_) \[LeftRightArrow] (j_), vw__}] := - Interchange[Interchange[z, i \[LeftRightArrow] j], vw]; - - -nuExplicit[z_] := - z /. - Subscript[\[CapitalSigma], i_] :> - Expand[3*d - 2 - 2*Sum[Subscript[\[Nu], j], {j, 1, i}]] /. { - - Subscript[\[Sigma], i_, j_, k_] :> - (-(1/4))*(d - Subscript[\[Nu], i] - 2*Subscript[\[Nu], j])*Subscript[\[Phi], i, j, k] - - (1/4)*(d - 2*Subscript[\[Nu], i] - Subscript[\[Nu], j])*Subscript[\[Phi], j, i, k] - - (1/4)*(2*d - 2*Subscript[\[Nu], i] - 2*Subscript[\[Nu], j] - Subscript[\[Nu], k] - 1)*Subscript[\[Phi], k, i, j], - - Subscript[h, i_, j_, k_] :> - (-(1/2))*(d - 2*Subscript[\[Nu], j] - Subscript[\[Nu], k])*Subscript[m, k]^2* - Subscript[\[Phi], i, j, k] - (1/2)*(2*d - Subscript[\[Nu], i] - 2*Subscript[\[Nu], j] - - 2*Subscript[\[Nu], k] - 1)*Subscript[m, i]^2*Subscript[\[Phi], k, i, j] + (d - Subscript[\[Nu], j] - - 2*Subscript[\[Nu], k]) Subscript[\[Rho], i, j, k], - Subscript[S, i_, j_, k_] :> - (-(d - 2*Subscript[\[Nu], j] - Subscript[\[Nu], k])) Subscript[m, k]^2* - Subscript[\[Phi], j, i, k] - (d - Subscript[\[Nu], j] - 2*Subscript[\[Nu], k])* - Subscript[m, j]^2 Subscript[\[Phi], k, i, j] + 2*(2*d - Subscript[\[Nu], i] - 2*Subscript[\[Nu], j] - - 2*Subscript[\[Nu], k] - 1)*Subscript[\[Rho], i, j, k] - }; - -MakeBoxes[TA[a_, ___Symbol, ijk___Integer][__], _] := - SubscriptBox[a, RowBox[{ijk}]] - -MakeBoxes[TA[a_, ___Symbol, ijk___Integer, ___Symbol][__], _] := - SubscriptBox[a, RowBox[{ijk}]] - -TA[args__][mar_List] := - TA[args][mar] = ta[args][mar]; - -ta[D, i_Integer, j_Integer, k_Integer][{em__}] := - With[ - {q = Last[{em}], mi = {em}[[i]], mj = {em}[[j]], mk = {em}[[k]]}, - - Factor[ - q^8 - 4*q^6*(mi^2 + mj^2 + mk^2) + q^4*(6*(mi^4 + mj^4 + mk^4) + 4*(mi^2*mj^2 + mk^2*mi^2 + mk^2*mj^2)) - - 4*q^2*(mi^6 + mj^6 + mk^6 - mi^2*(mj^4 + mk^4) - mj^2*(mi^4 + mk^4) - mk^2*(mi^4 + mj^4) + - 10*mi^2*mj^2*mk^2) + Cayley[i, j, k][{em}]^2 - ] - ]; - -ta[\[Rho], i_Integer, j_Integer, k_Integer][{em__}] := - With[ - {q = Last[{em}], mi = {em}[[i]], mj = {em}[[j]], mk = {em}[[k]]}, - - Factor[ - -q^6 + 3*q^4*(mi^2 + mj^2 + mk^2) - q^2*(3*(mi^4 + mj^4 + mk^4) + - 2*(mi^2*mj^2 + mk^2*mi^2 + mk^2*mj^2)) + (mi^6 + mj^6 + - mk^6 - mi^2*(mj^4 + mk^4) - mj^2*(mi^4 + mk^4) - mk^2*(mi^4 + mj^4) + 10*mi^2*mj^2*mk^2)] - ]; - -ta[\[Phi], i_Integer, j_Integer, k_Integer][{em__}] := - With[ - {q = Last[{em}], mi = {em}[[i]], mj = {em}[[j]], mk = {em}[[k]]}, - - 4*Factor[q^4 + 2*q^2*(mi^2 - mj^2 - mk^2) + (mj^2 - mk^2)^2 + mi^2*(2*mj^2 + 2*mk^2 - 3*mi^2)] - ]; - -ta[\[Sigma], d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer][{em__}] := - Factor[ - (-(1/4))*(d - \[Nu]i - 2*\[Nu]j)* - TA[\[Phi], i, j, k][{em}] - (1/4)*(d - 2*\[Nu]i - \[Nu]j)* - TA[\[Phi], j, i, k][{em}] - (1/4)*(2*d - 2*\[Nu]i - 2*\[Nu]j - \[Nu]k - 1)*TA[\[Phi], k, i, j][{em}] - ]; - -ta[h, d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer][{em__}] := - With[ - {mk = {em}[[k]]}, - - Factor[ - (-(1/2))*(d - 2*\[Nu]j - \[Nu]k)*mk^2* - TA[\[Phi], i, j, k][{em}] - (1/2)*(2*d - \[Nu]i - 2*\[Nu]j - 2*\[Nu]k - 1)*mi^2* - TA[\[Phi], k, i, j][{em}] + (d - \[Nu]j - 2 \[Nu]k) TA[\[Rho], i, j, k][{em}] - ] - ]; - -ta[S, d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer][{em__}] := - With[ - {mj = {em}[[j]], mk = {em}[[k]]}, - - Factor[ - (-(d - 2*\[Nu]j - \[Nu]k))*mk^2* TA[\[Phi], j, i, k][{em}] - (d - \[Nu]j - 2*\[Nu]k)*mj^2* - TA[\[Phi], k, i, j][{em}]*test* - test*2*(2*d - \[Nu]i - 2*\[Nu]j - 2*\[Nu]k - 1)* - TA[\[Rho], i, j, k][{em}] - ] - ]; - -TVIKernel[d_, PP, lis_] := - (-PP)^(d - n1 - n2 - n3 - n4)*(m1^2/(-PP))^s1*(m2^2/(-PP))^s2*(m3^2/(-PP))^s3*(m4^2/(-PP))^s4*TVIpsi[d, lis /. {m1 -> s1, m2 -> s2, m3 -> s3, m4 -> s4}]; - -TVIPsi[d_, {{n1_, s1_}, {n2_, s2_}, {n3_, s3_}, {n4_, s4_}}] := - (-1)^(n1 + n2 + n3 + n4 + 1)*((gamma[-s1]*gamma[d/2 - n1 - s1])/gamma[n1])* - ((gamma[-s2]*gamma[d/2 - n2 - s2])/gamma[n2])* - ((gamma[-s3]*gamma[d/2 - n3 - s3])/gamma[n3])* - ((gamma[-s4]*gamma[n4 + s4])/gamma[n4])* - (gamma[n1 + n2 + n3 + n4 + s1 + s2 + s3 + s4 - d]/gamma[3*(d/2) - n1 - n2 - n3 - n4 - s1 - s2 - s3 - s4])* - (gamma[n1 + n3 + s1 + s3 - d/2]/gamma[n1 + n3 + n4 + s1 + s3 + s4 - d/2])* - (gamma[d - n1 - n3 - n4 - s1 - s3 - s4]/gamma[d - n1 - n3 - s1 - s3]); - -CheckTVIRecursion[expr_] := - If[ $CheckRecursion === True, - - Block[{rel, kern, nkern, z1, z2, z3, z4}, - rel = Extract[expr /. TVIC -> TVIkernel, {1, 2, 1, 1, 2}] - - Extract[expr /. TVI -> TVIkernel, {1, 2, 1, 2}]; - - If[ {TVIkernel} === Union[Head /@ Cases[rel, (ff_)[__] /; Context[ff] =!= "System`", 4]], - rel = Collect[Numerator[Together[rel]], TVI[__], Factor]; - kern = rel /. TVIkernel -> TVIKernel; - - kern = kern /. {PP -> -1, m1 -> Sqrt[z1], m2 -> Sqrt[z2], m3 -> Sqrt[z3], m4 -> Sqrt[z4]}; kern = PowerExpand[kern]; - kern = Expand[kern]; - - kern = kern /. {z1^(s1 + (w1_.))*z2^(s2 + (w2_.))*z3^(s3 + (w3_.))*z4^(s4 + (w4_.))*(fac_) :> (fac /. { - s1 -> s1 - w1, s2 -> s2 - w2, s3 -> s3 - w3, s4 -> s4 - w4})}; - - kern = kern /. TVIpsi -> TVIPsi /. {gamma[zz_] :> gamma[Expand[zz]]} /. {gamma[(zz_) + (nn_Integer)] :> - gamma[zz] Pochhammer[zz, nn]}; - - kern = kern /. {gamma[_] :> 1}; - - kern = kern /. {(-1)^((_) + (ww_Integer)) :> (-1)^ww} /. {(-1)^(_) :> 1}; - - nkern = Table[kern /. Thread[{d, n1, n2, n3, n4, s1, s2, s3, s4} -> Table[Random[], {9}]], {3}]; - nkern, - - Print["Matching Error"] - ] - ], - - If[$Notebooks, FCPrint[1,"Off"]] - ]; - -TJIKernel[d_, PP, lis_] := - (-PP)^(d - n1 - n2 - n3) (m1^2/(-PP))^s1 (m2^2/(-PP))^s2*(m3^2/(-PP))^s3 TJIpsi[d, lis /. {m1 -> s1, m2 -> s2, m3 -> s3}]; - -TJIPsi[d_, {{n1_, s1_}, {n2_, s2_}, {n3_, s3_}}] := - Evaluate[TVIPsi[d, {{n1, s1}, {n2, s2}, {n3, s3}, {0, 0}}]/gamma[0]]; - -Clear[CheckTJIRecursion]; - -CheckTJIRecursion[expr_] := - If[$CheckRecursion === True, - Block[ {rel, kern, nkern, z1, z2, z3}, - rel = Extract[expr /. TJIC -> TJIkernel, {1, 2, 1, 1, 2}] - Extract[expr /. TJI -> TJIkernel, {1, 2, 1, 2}]; - REL = rel; - If[{TJIkernel} === Union[Head /@ Cases[rel, (ff_)[__] /; Context[ff] =!= "System`", 4]], - rel = Collect[Numerator[Together[rel]], TJI[__], Factor]; - kern = rel /. TJIkernel -> TJIKernel; - kern = kern /. {PP -> -1, m1 -> Sqrt[z1], m2 -> Sqrt[z2], m3 -> Sqrt[z3]}; - kern = PowerExpand[kern]; - kern = Expand[kern]; - kern = kern /. {z1^(s1 + (w1_.)) z2^(s2 + (w2_.))*z3^(s3 + (w3_.)) (fac_) :> (fac /. {s1 -> s1 - w1, s2 -> s2 - w2, s3 -> s3 - w3})}; - kern = kern /. TJIpsi -> TJIPsi /. {gamma[zz_] :> gamma[Expand[zz]]} /. {gamma[(zz_) + (nn_Integer)] :> gamma[zz] Pochhammer[zz, nn]}; - kern = kern /. {gamma[_] :> 1}; - kern = kern /. {(-1)^((_) + (ww_Integer)) :> (-1)^ww} /. {(-1)^(_) :> 1}; - nkern = Table[ kern /. Thread[{d, n1, n2, n3, s1, s2, s3} -> Table[Random[], {7}]], {3}]; - nkern, - - Print["Matching Error"]] - ], - - If[$Notebooks, FCPrint[1,"Off"]] - ]; - -TFR[d_, pp_, {{n1_, m1_}, {n2_, m2_}, {0, 0}, {0, 0}, {0, 0}}] := - TAI[d, pp, {{n1, m1}}]*TAI[d, {{n2, m2}}]; - -Subscript[e, 35] = - 2*Subscript[\[Nu], 1]*\[ScriptCapitalC]*Schiebe[1, "+"]* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == - ( - (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - Subscript[\[Nu], 5])*Subscript[\[CapitalDelta], 1] + - Subscript[\[CapitalDelta], 3, 4, 5]*(Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[2, "-"] - Schiebe[1, "-"]) - - Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"]) + Subscript[\[CapitalDelta], 2]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*(Schiebe[5, "-"] - Schiebe[2, "-"]) + - Subscript[\[Nu], 3]*Schiebe[3, "+"]*(Schiebe[5, "-"] - Schiebe[4, "-"]) + Subscript[\[Nu], 5] - Subscript[\[Nu], 1]) + - Subscript[\[CapitalDelta], 6]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*Schiebe[3, "-"] + - Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"]) + Subscript[\[Nu], 3] - Subscript[\[Nu], 1]) - ) * TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; - -Subscript[s, 35] = - OperatorApplyF[Subscript[e, 35]]; - -Subscript[h, 351] = - Subscript[s, 35] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 351] = -MakeFun[Subscript[h, 351], "(35_1)", IFF[Subscript[\[Nu], 1] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; - -Subscript[f, 352] = -MakeFun[Interchange[Subscript[h, 351], 1 \[LeftRightArrow] 2, 3 \[LeftRightArrow] 4], "(35_2)", - IFF[Subscript[\[Nu], 2] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; - -Subscript[f, 353] = -MakeFun[Interchange[Subscript[h, 351], 1 \[LeftRightArrow] 3, 2 \[LeftRightArrow] 4], "(35_3)", - IFF[Subscript[\[Nu], 3] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; - -Subscript[f, 354] = -MakeFun[Interchange[Subscript[h, 351], 1 \[LeftRightArrow] 4, 2 \[LeftRightArrow] 3], "(35_4)", - IFF[Subscript[\[Nu], 4] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; - -Subscript[e, 3501] = - (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - Subscript[\[Nu], 5])* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == - (Subscript[\[Nu], 5]*(Schiebe[1, "-"] - Schiebe[2, "-"]) Schiebe[5, "+"] + - Subscript[\[Nu], 3]*Schiebe[1, "-"]*Schiebe[3, "+"])*TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], - Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; - -Subscript[s, 3501] = - OperatorApplyF[Subscript[e, 3501]]; - -Subscript[h, 3501] = - Subscript[s, 3501]; - -Subscript[f, 3501] = - MakeFun[Subscript[s, 3501], "(3501)", IFF[PP === m5^2], {m1 :> 0, m2 :> m5, m3 :> m5}] - -Subscript[e, 3502] = - (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - Subscript[\[Nu], 5])* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == - (Subscript[\[Nu], 5]*(Schiebe[1, "-"] - Schiebe[2, "-"])*Schiebe[5, "+"] + Subscript[\[Nu], 3]*Schiebe[1, "-"]*Schiebe[3, "+"])* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; - -Subscript[s, 3502] = - OperatorApplyF[Subscript[e, 3502]]; - -Subscript[h, 3502] = - Subscript[s, 3502]; - -Subscript[f, 3502] = - MakeFun[Subscript[h, 3502], "(3502)", IFF[PP === m5^2], {m4 :> 0, m2 :> m5, m3 :> m5}]; - -Subscript[h, 3503] = - Interchange[Subscript[s, 3502], 1 \[LeftRightArrow] 2, 3 \[LeftRightArrow] 4]; - -Subscript[f, 3503] = - MakeFun[Subscript[h, 3503], "(3503)", IFF[PP === m5^2], {m2 :> 0, m1 :> m5, m4 :> m5}]; - - -Subscript[h, 3504] = -Interchange[Subscript[s, 3502], 1 \[LeftRightArrow] 3, 2 \[LeftRightArrow] 4]; - -Subscript[f, 3504] = -MakeFun[Subscript[h, 3504], "(3504)", IFF[PP === m5^2], {m3 :> 0, m1 :> m5, m4 :> m5}]; - -Subscript[e, 41] = - 2*Subscript[\[Nu], 5]*\[ScriptCapitalC]*Schiebe[5, "+"]* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == - (Subscript[\[CapitalDelta], 1, 3, 6]*(Subscript[\[Nu], 3] Schiebe[3, "+"]*(Schiebe[4, "-"] - Schiebe[5, "-"]) + - Subscript[\[Nu], 1] Schiebe[1, "+"]*(Schiebe[2, "-"] - Schiebe[5, "-"])) + - (d - Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - 2 Subscript[\[Nu], 5])*Subscript[\[CapitalDelta], 5] + - Subscript[\[CapitalDelta], 2]*(Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[1, "-"] - Schiebe[2, "-"]) + - Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + Subscript[\[Nu], 1] - Subscript[\[Nu], 5]) + - Subscript[\[CapitalDelta], 4]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*Schiebe[3, "-"] + - Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"]) + - Subscript[\[Nu], 3] - Subscript[\[Nu], 5]))* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; - -Subscript[s, 41] = - OperatorApplyF[Subscript[e, 41]]; - -Subscript[h, 41] = - Subscript[s, 41] /. Subscript[\[Nu], 5] -> Subscript[\[Nu], 5] - 1; - -Subscript[f, 41] = - MakeFun[Subscript[h, 41], "(41)", IFF[Subscript[\[Nu], 5] > 1 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]]; - -Subscript[e, 43] = (d - Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - 2*Subscript[\[Nu], 5])* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == - (Subscript[\[Nu], 1] Schiebe[1, "+"]*(Schiebe[5, "-"] - Schiebe[2, "-"]) + - Subscript[\[Nu], 3] Schiebe[3, "+"]*(Schiebe[5, "-"] - Schiebe[4, "-"]))* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; - -Subscript[s, 43] = - OperatorApplyF[Subscript[e, 43]]; - -Subscript[e,44] = - (d - Subscript[\[Nu], 2] - Subscript[\[Nu], 4] - 2*Subscript[\[Nu], 5])* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == - (Subscript[\[Nu], 2] Schiebe[2, "+"]*(Schiebe[5, "-"] - Schiebe[1, "-"]) + Subscript[\[Nu], 4]* - Schiebe[4, "+"]*(Schiebe[5, "-"] - Schiebe[3, "-"]))* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; - -Subscript[s, 44] = - OperatorApplyF[Subscript[e, 44]]; - -Subscript[e, 45] = - Subscript[\[CapitalDelta], 1, 3, 6]* - Schiebe[1, "+"] TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}] == - (Subscript[u, 6, 1, 3]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*Schiebe[3, "-"] + Subscript[\[Nu], 5]*Schiebe[5, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"])) - - - 2*Subscript[u, 1, 3, 6]*(Subscript[\[Nu], 2]* Schiebe[2, "+"]*(Schiebe[5, "-"] - Schiebe[1, "-"]) + - Subscript[\[Nu], 4] Schiebe[4, "+"]*(Schiebe[5, "-"] - Schiebe[3, "-"]) - - Subscript[\[CapitalSigma], 5] - Subscript[\[Nu], 1] + 3*Subscript[\[Nu], 3]) + - 2*Subscript[m, 3]^2*(Subscript[\[Nu], 5] Schiebe[5, "+"]*(Schiebe[1, "-"] - Schiebe[2, "-"]) + - Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + Subscript[\[Nu], 1] - Subscript[\[Nu], 3]))* - TFI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4], Subscript[\[Nu], 5]}]; - -Subscript[s, 45] = - OperatorApplyF[Subscript[e, 45]]; - -Subscript[f, 43] = -MakeFun[Subscript[s, 43], "(43)", IFF[Subscript[\[Nu], 1] + Subscript[\[Nu], 3] + 2*Subscript[\[Nu], 5] - (d /. _Symbol :> 4) =!= 0], - {m5 :> 0, m4 :> m3, m2 :> m1}]; - -Subscript[f, 44] = - MakeFun[Subscript[s, 44], "(44)", {m5 :> 0, m4 :> m3, m2 :> m1}]; - -Subscript[f, 50] = - HoldForm[TFR[d_, PP_, {{(n1_)?PQ, m1_}, {(n2_)?PQ, m2_}, {(n3_)?PQ, m3_}, {(n4_)?PQ, m4_}, {(n5_)?PQ, m5_}}] := - ( - TComment["(50)", TFIC[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {n4, m4}, {n5, m5}}]]; - Block[{ - - r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11, r12, r13, r14, r15, - r16, r17, r18, r19, r20, r21, r22, r23, r24, r25, r26, r27, r28, r29, - r30, r31, r32, r33, r34, r35, r36, r37, r38, r39, r40, r41, r42, r43, - r44, r45, r46, r47, r48, r49, r50, r51, r52, r53, r54, r55, r56, r57, - r58, r59, r60, r61, r62, r63, r64, r65, r66, r67, r68, r69, r70, r71, - r72, r73, r74, r75, r76, r77, r78, r79, r80, r81, r82, r83, r84, r85, - r86, r87, r88, r89, r90, r91, r92, r93, r94, r95, r96, r97, r98, r99, - r100, r101, r102, r103, r104, r105, r106, r107, r108, r109, r110, - r111, r112, r113, r114, r115, r116, r117, r118, r119, r120, r121, - r122, r123, r124, r125, r126, r127, r128, r129, r130, r131, r132, - r133, r134, r135, r136, r137, r138, r139, r140, r141, r142, r143, - r144, r145, r146, r147, r148, r149, r150, r151, r152, r153, r154, - r155, r156, r157, r158, r159, r160, r161, r162, r163, r164, r165, - r166, r167, r168, r169, r170, r171, r172, r173, r174, r175, r176, - r177, r178, r179, r180, r181, r182, r183, r184, r185, r186, r187, - r188, r189, r190, r191, r192, r193, r194, r195, r196, r197, r198, - r199, r200, r201, r202, r203, r204, r205, r206, r207, r208, r209, - r210, r211, r212, r213, r214, r215, r216, r217, r218, r219, r220, - r221, r222, r223, r224, r225, r226, r227, r228, r229, r230, r231, - r232, r233, r234, r235, r236, r237, r238, r239, r240, r241, r242, - r243, r244, r245, r246, r247, r248, r249, r250, r251, r252, r253, - r254, r255, r256, r257, r258, r259, r260, r261, r262, r263, r264, - r265, r266, r267, r268, r269, r270, r271, r272, r273, r274, r275, - r276, r277, r278, r279, r280, r281, r282, r283, r284, r285, r286, - r287, r288, r289, r290, r291, r292, r293, r294, r295, r296, r297, - r298, r299, r300, r301, r302, r303, r304, r305, r306}, - - - r1 = 3 - d; - r2 = 4 - d; - r3 = -(m1^2*m2^2*m3^2) + m2^4*m3^2 + m2^2*m3^4 + m1^4*m4^2 - m1^2*m2^2*m4^2 - m1^2*m3^2*m4^2 - m2^2*m3^2*m4^2 + - m1^2*m4^4 + m1^2*m2^2*m5^2 - m2^2*m3^2*m5^2 - m1^2*m4^2*m5^2 + m3^2*m4^2*m5^2 + m1^2*m3^2*PP - - m2^2*m3^2*PP - m1^2*m4^2*PP + m2^2*m4^2*PP - m1^2*m5^2*PP - m2^2*m5^2*PP - m3^2*m5^2*PP - m4^2*m5^2*PP + m5^4*PP + - m5^2*PP^2; - r4 = -4 + d; - r5 = -3 + d; - r6 = -7 + 2*d; - r7 = -(m2^2*r4) + m3^2*r5 - m5^2*r5 + m4^2*r6; - r8 = -10 + 3*d; - r9 = -m3^2 + m4^2; - r10 = -11 + 3*d; - r11 = -(m4^2*r10) - 3*m5^2*r5 + m3^2*r6; - r12 = m2^2*r11 + m5^4*r5 + m2^4*r8 + m4^2*r4*r9 + m5^2*r5*r9; - r13 = -6 + d; - r14 = -(m4^2*r13) + m5^2*r5; - r15 = -3*m3^2 - m4^2*r10 + m5^2*r5; - r16 = m3^2*r14 + m2^2*r15 + m2^4*r4 - 2*m3^4*r5 - 3*m4^2*m5^2*r5 + m5^4*r5 + m4^4*r8; - r17 = m3^2 + 2*m4^2; - r18 = -1 + d; - r19 = -(m3^2*r13) - 2*m4^2*r18 + 2*m5^2*r5; - r20 = 2*m2^4 - 3*m3^4 + d*m3^4 - 3*m3^2*m4^2 + 2*m4^4 + m2^2*r19 - 2*m5^4*r5 + m5^2*r17*r5; - r21 = 2 + d; - r22 = 2*m5^2 - m4^2*r21 + m2^2*r4 - m3^2*r4; - r23 = -7 + d; - r24 = 6*m4^2 - 4*m5^2; - r25 = 3*m3^2 + m4^2*r18 + m5^2*r23; - r26 = -6*m4^4 - 2*m4^2*m5^2*r23 + m3^2*r24 + 2*m2^2*r25 - 2*m2^4*r4 - m3^4*r4; - r27 = m3^4 + m3^2*m4^2 - 2*m4^4; - r28 = m3^2 + m4^2*r23; - r29 = -2*m4^2*r18 + m3^2*r21 + 2*m5^2*r23; - r30 = -6*m2^4 + 2*m5^2*r28 - m2^2*r29 + r27*r4; - r31 = m1^4*r22 + m1^2*r26 + m3^2*r30 + m1^6*r4; - r32 = m3 - m4; - r33 = m3 + m4; - r34 = 2*m3^2 + m4^2; - r35 = -17 + 3*d; - r36 = m3^2*r23 + m4^2*r35; - r37 = -9 + d; - r38 = 17 - 3*d; - r39 = 5*m3^2 + m4^2*r37 + m5^2*r38; - r40 = 1 + d; - r41 = 5*m4^2 - m5^2*r23 + m2^2*r4 - m3^2*r40; - r42 = m5^4*r35 - m5^2*r36 + m2^2*r39 - 2*m1^4*r4 + m2^4*r4 - r32*r33*r34*r4 + m1^2*r41; - r43 = m1^2 - m2^2 + m3^2 - m4^2; - r44 = 2*m5^2*r13 + r4*r43; - r45 = m3^4*r12 + m1^4*r16 + m1^2*m3^2*r20 + PP*r31 + PP^2*r42 + PP^3*r44 + m1^6*r7; - r46 = m2^2 + m4^2; - r47 = 13 - 3*d; - r48 = m4^2*r47 - m5^2*r5 + m3^2*r6; - r49 = m5^4*r5 + m5^2*r32*r33*r5 + m4^2*r4*r9; - r50 = -18 + 4*d; - r51 = -(m4^2*r13) - 3*m5^2*r5; - r52 = 2*m3^4*r5 + m4^2*m5^2*r5 + m5^4*r5 + m4^4*r50 + m3^2*r51; - r53 = -3*m4^2 + 2*m5^2*r5; - r54 = m4^4*r47 + 2*m3^4*r5 + m4^2*m5^2*r5 - 2*m5^4*r5 + m3^2*r53; - r55 = m4^2*r13 + 6*m3^2*r5 - 2*m5^2*r5; - r56 = 3*m4^2 + m3^2*r5 - m5^2*r5; - r57 = 7 - 2*d; - r58 = m3^2*r5 + 3*m5^2*r5 + m4^2*r57; - r59 = m2^6*r4 + m2^2*m4^2*r55 + m2^4*r56 + m4^4*r58; - r60 = m4^2 - m3^2*r5; - r61 = 10 - 3*d; - r62 = 2*m5^2 + 3*m4^2*r4 + m3^2*r61; - r63 = m4^2 + m5^2*r5; - r64 = -4*m4^2*m5^2 + 3*m4^4*r4 - 2*m3^4*r5 + 2*m3^2*r63; - r65 = m4^2 + m3^2*r5 - m5^2*r5; - r66 = 2*m3^2*r5 + 2*m5^2*r5 + m4^2*r61; - r67 = 3*m2^4*r4 + 2*m2^2*r65 + m4^2*r66; - r68 = -3*m2^6*r4 - 2*m1^4*m4^2*r5 + 2*m4^2*m5^2*r60 + m2^4*r62 + m2^2*r64 + m1^2*r67 - 3*m4^4*r4*r9; - r69 = -13 + 3*d; - r70 = m3^2*r5 + m4^2*r69; - r71 = m4^2 - 3*m2^2*r4 - m3^2*r5 + m5^2*r5; - r72 = -5 + d; - r73 = m3^2 + m5^2*r69 + m4^2*r72; - r74 = 3*m2^4*r4 - m5^4*r5 + m5^2*r70 + m1^2*r71 + m2^2*r73 + 3*m4^2*r4*r9; - r75 = m1^2 - m2^2 + m3^2 - m4^2 - 2*m5^2; - r76 = m2^8*r4 + m2^6*r48 + m4^4*r49 + 2*m1^4*m4^2*r46*r5 + m2^4*r52 + m2^2*m4^2*r54 - m1^2*r59 + PP*r68 + PP^2*r74 + PP^3*r4*r75; - r77 = m3^2 - m4^2 + m5^2; - r78 = -2*m2^2 + m4^2 + m5^2; - r79 = -2*m1^2 - m3^2 - m4^2 + m5^2; - r80 = m1^4 + PP^2 - m1^2*r77 + m3^2*r78 + PP*r79; - r81 = m3^2 + m4^2; - r82 = m3^2 + m4^2 + m5^2; - r83 = m1^2 + m3^2 - m5^2; - r84 = m1^4 + 2*m3^2*m4^2 - m4^4 + PP^2 - m2^2*r77 + m5^2*r81 - m1^2*r82 - 2*PP*r83; - r85 = m1 - m3; - r86 = -PP + r85^2; - r87 = m1 + m3; - r88 = -PP + r87^2; - r89 = m2 - m4; - r90 = m2 + m4; - r91 = -m1^2 - m2^2 - m3^2 - m4^2 + 2*m5^2; - r92 = PP^2 + r85*r87*r89*r90 + PP*r91; - r93 = m2^2 - 3*m4^2; - r94 = m4 - m5; - r95 = m4 + m5; - r96 = 2*m3^2 - m4^2 + m5^2; - r97 = -m1^2 - m2^2 - 2*m3^2 + 3*m5^2; - r98 = PP^2 + m1^2*r93 + m2^2*r94*r95 + m4^2*r96 + PP*r97; - r99 = -2 + d; - r100 = -m1^2 + m2^2; - r101 = m2^2 + m1^2*r72; - r102 = m3^2*r101 - 2*m3^4*r4 + m2^2*r100*r4; - r103 = 9 - 2*d; - r104 = m2^2*r23 + m3^2*r72; - r105 = 2*m1^4 + m2^4*r103 + m1^2*r104 + m2^2*m3^2*r5; - r106 = -9 + 2*d; - r107 = m1 - m2; - r108 = m1 + m2; - r109 = -(r106*r107*r108) + m3^2*r4; - r110 = m2^2*r102 + m4^2*r105 + m4^4*r109 - m4^6*r4; - r111 = m1^2 + m2^2; - r112 = m2^2*r4 - 2*m1^2*r72; - r113 = -19 + 5*d; - r114 = m3^2*r112 + m3^4*r113 + m2^2*r111*r4; - r115 = m3^2*r5 + m2^2*r6; - r116 = 2*m1^4 + 2*m1^2*r115 + m2^4*r13 + m3^4*r72 - 2*m2^2*m3^2*r99; - r117 = m2^2*r106 + m3^2*r4 - m1^2*r99; - r118 = m2^2*r114 - m4^2*r116 + m4^4*r117 - m4^6*r6; - r119 = -(m2^2*r5) + 2*m3^2*r57 + m1^2*r72; - r120 = m1^2*r18 + 2*m3^2*r4 - m2^2*r5; - r121 = m2^2*r119 + m4^2*r120 + 2*m4^4*r5; - r122 = m3^2*r5 + m4^2*r72; - r123 = -2*m2^2*r4 - m4^2*r69 + m3^2*r72; - r124 = m2^2*r122 + m1^2*r123 + 2*m2^4*r4 + 2*m4^2*r32*r33*r4; - r125 = -3*m4^2 + m2^2*r4 - m3^2*r72; - r126 = m3^2 - m4^2*r72; - r127 = -2*m3^2*m4^2 - 2*m1^2*r125 - 2*m2^2*r126 + m4^4*r18 - 4*m2^4*r4 + m3^4*r72; - r128 = -(m2^2*r18) + 2*m4^2*r5 + m1^2*r72 + 2*m3^2*r72; - r129 = m5^2*r127 - m5^4*r128 - r124*r32*r33 + m5^6*r72; - r130 = -m1^2 + m2^2 + m3^2 - m4^2; - r131 = -14 + 3*d; - r132 = -(m3^2*r13) + m4^2*r131 + m1^2*r4 + 5*m2^2*r4; - r133 = -2*m5^4 + m5^2*r132 + r130*r32*r33*r4; - r134 = m5^2*r118 + m5^4*r121 + PP*r129 + PP^2*r133 + r110*r32*r33 - 2*m5^2*PP^3*r4 + m5^6*r5*r89*r90; - r135 = m3 - m4 - m5; - r136 = m3 + m4 - m5; - r137 = m3 - m4 + m5; - r138 = m3 + m4 + m5; - r139 = -10 + d; - r140 = 13 - 2*d; - r141 = d*m4^2 + 2*m3^2*r5; - r142 = -8 + d; - r143 = m4^2*r142 - m3^2*r99 + m5^2*r99; - r144 = m3^2*m4^2*r139 + m4^4*r140 - m5^2*r141 + m2^2*r143 + m3^4*r5 + m5^4*r5; - r145 = 3*m3^4 - 12*m3^2*m4^2 + 7*m4^4; - r146 = 3*m3^2 + 4*m4^2; - r147 = m3^2 - 11*m4^2; - r148 = 7*m3^4 + 10*m3^2*m4^2 - 17*m4^4 - 5*m5^4 - 2*m5^2*r147; - r149 = m2^2 + 2*m3^2 + m4^2; - r150 = -m2^4 + m2^2*m3^2 + m3^4 + 3*m2^2*m4^2 + m3^2*m4^2 - m4^4 + m5^4 - m5^2*r149; - r151 = 3*m3^6 + 6*m3^4*m4^2 - 17*m3^2*m4^4 + 8*m4^6 + 3*m5^6 - m5^2*r145 - m5^4*r146 + m2^2*r148 - d*r150*r77 + 6*m2^4*r94*r95; - r152 = -(m3^2*m4) + m4^3; - r153 = 11 - 2*d; - r154 = -(d*m3^2*m4^2) + m4^4*r153 + m3^4*r5; - r155 = m4^2 + m3^2*r5; - r156 = r142*r32*r33 + m5^2*r99; - r157 = 11 - 3*d; - r158 = -8 + 3*d; - r159 = m5^2*r158 + m4^2*r21; - r160 = -3*m3^4 + 2*m4^2*m5^2*r106 + m5^4*r157 + m3^2*r159 - m4^4*r18; - r161 = -2*m2^6 + m5^2*r154 - 2*m5^4*r155 + m2^4*r156 + m2^2*r160 + r152^2*r4 + m5^6*r5; - r162 = m4^2*r23 - 3*m3^2*r72; - r163 = -4*m2^2 + m4^2*r18 + m3^2*r23; - r164 = -m3^4 + m4^4; - r165 = -(m2^4*r13) + m2^2*r162 + m1^2*r163 + r164*r4 + m1^4*r99; - r166 = -19 + 4*d; - r167 = m4^2 + m3^2*r72; - r168 = m3^2 + m4^2*r69; - r169 = -2*r168 + 4*m2^2*r4; - r170 = -m3^4 + m2^4*r13 - m4^4*r166 + 2*m2^2*r167 + m1^2*r169 + 2*m3^2*m4^2*r72 + m1^4*r99; - r171 = m1^2 - m2^2 + 4*m4^2; - r172 = -(m5^2*r170) + r165*r32*r33 + m5^6*r72 - m5^4*r171*r72; - r173 = m2^2 + m3^2; - r174 = -(m4^2*r13) + r131*r173 + m1^2*r8; - r175 = m5^2*r174 - 2*m5^4*r4 + r130*r32*r33*r4; - r176 = 2*m1^6*m4^2 + m1^4*r144 + m1^2*r151 + m3^2*r161 + PP*r172 + PP^2*r175 - 2*m5^2*PP^3*r4; - r177 = m3^2 + m4^2 - m5^2; - r178 = -2*m1^2 + m3^2 - m4^2 + m5^2; - r179 = -m3^2 + m4^2 + m5^2; - r180 = m2^2*r177 + m4^2*r178 + PP*r179; - r181 = -2*m2^2 - m3^2 + m4^2 + m5^2; - r182 = m1^2*r177 + m3^2*r181 + PP*r77; - r183 = -(m2^2*r13) - 2*m3^2*r5; - r184 = m1^2*r183 - 2*m3^4*r4 + m2^4*r57 + m1^4*r72 - m2^2*m3^2*r99; - r185 = 3*m2^2*r4 + m3^2*r72; - r186 = m2^4*r106 + 2*m1^2*r185 + m1^4*r40 - 2*m2^2*m3^2*r6; - r187 = r111*r13 - m3^2*r4; - r188 = m2^2*r184 + m4^2*r186 - m4^4*r187 + m4^6*r4; - r189 = 2*m1^2 + m3^2*r10 + 2*m2^2*r5; - r190 = m2^2*r5 + m3^2*r72 + 2*m1^2*r99; - r191 = m2^2*r189 - m4^2*r190 - m4^4*r5; - r192 = -(m3^2*r5) - m4^2*r72; - r193 = 2*m2^2*r4 + m4^2*r69 - m3^2*r72; - r194 = m2^2*r192 + m1^2*r193 - 2*m2^4*r4 + 2*m4^2*r4*r9; - r195 = m2^2 + m4^2 + m3^2*r72; - r196 = -(m3^2*r6) - m4^2*r72; - r197 = m2^4*r157 + 2*m1^2*r195 + 2*m2^2*r196 + 2*m4^2*r17*r4 + m1^4*r72; - r198 = m4^2*r10 - 2*m2^2*r5 + 2*m1^2*r72 + m3^2*r72; - r199 = r107*r108*r194 + m5^2*r197 - m5^4*r198 + m5^6*r72; - r200 = m1^2 - m2^2 - m3^2 + m4^2; - r201 = m1^2 + m2^2 + m3^2 + 5*m4^2; - r202 = 2*m5^4 - r107*r108*r200 - m5^2*r201; - r203 = r107*r108*r110 - m5^2*r188 - m5^4*r191 + PP*r199 + 2*m5^2*PP^3*r4 + PP^2*r202*r4 + m5^6*r5*r89*r90; - r204 = m4^2 + m5^2; - r205 = -2*m5^2*r5 + m4^2*r99; - r206 = 18 - 5*d; - r207 = m4^2*r206 + m5^2*r8 - 2*m3^2*r99; - r208 = m2^2*r207 + 2*m2^4*r4 - m3^4*r5 - m3^2*r204*r5 + r205*r94*r95; - r209 = 2*m3^2*m4^2 + m4^4*r142 + 2*m3^4*r5; - r210 = -(m4^2*r18) + m3^2*r5; - r211 = 3 - 2*d; - r212 = m5^2 + m4^2*r157 + m3^2*r211; - r213 = m4^2*r106 + m3^2*r4; - r214 = -(d*m3^4) + 10*m3^2*m4^2 - 2*d*m3^2*m4^2 - 2*m4^4 + d*m4^4 + 2*m5^2*r213 - 2*m5^4*r4; - r215 = d*m3^2*m4^4 - 2*m4^6 - m5^2*r209 + m5^4*r210 + m2^4*r212 + m2^2*r214 + m2^6*r4 + m5^6*r5 - m3^4*m4^2*r99; - r216 = m4^2*r13 + m3^2*r99; - r217 = m3^2*r5 - m4^2*r72; - r218 = 13 - 4*d; - r219 = 3*m3^2 + m5^2*r218 + m4^2*r23; - r220 = m4^2*r142 + m5^2*r61; - r221 = 2*m3^4 + 2*m4^2*m5^2 - m4^4*r13 + m3^2*r220 + 2*m5^4*r6; - r222 = m4^2*m5^2*r216 + m5^4*r217 + m2^4*r219 + m2^2*r221 - m5^6*r5 + m2^6*r99; - r223 = -(m3^2*r10) + m4^2*r5; - r224 = 4*m3^2*m4^2 + m1^2*r122 + m4^4*r13 + m2^2*r223 + m1^4*r4 - m2^4*r4 - m3^4*r99; - r225 = -m3^2 + m2^2*r72 - m4^2*r72; - r226 = -2*m4^2*r106 + 2*m3^2*r69; - r227 = m1^4*r106 + m2^4*r106 - m4^4*r13 - 2*m1^2*r225 + m2^2*r226 - 4*m3^2*m4^2*r4 - m3^4*r99; - r228 = m3^2 + 3*m4^2; - r229 = r107*r108*r224 - m5^2*r227 + m5^6*r72 - m5^4*r228*r72; - r230 = m4^2*r131 + m1^2*r4 + m2^2*r4 + m3^2*r8; - r231 = 2*m5^4*r106 - m5^2*r230 - r107*r108*r200*r4; - r232 = m1^4*r208 - m1^2*r215 - m3^2*r222 + PP*r229 + PP^2*r231 + 2*m5^2*PP^3*r4 + m1^6*r7; - r233 = -2*m3^2 + m4^2; - r234 = -m2^2 + m4^2 - 2*m5^2; - r235 = -m1^2 + m2^2 + m5^2; - r236 = m1^4 + m5^4 + m2^2*r233 + m1^2*r234 + PP*r235 - m5^2*r46; - r237 = -m2^2 + m5^2; - r238 = m2^2 + m3^2 - 2*m4^2 + m5^2; - r239 = -m1^2 + m2^2 - m5^2; - r240 = m1^4 + m3^2*r237 - m1^2*r238 + PP*r239; - r241 = m3^2 + 3*m4^2 - m5^2; r242 = -3*m3^2 - m4^2 + m5^2; - r243 = m5^4 - m5^2*r228 + m1^2*r241 + m2^2*r242 + 2*PP*r32*r33 + 2*m4^2*r9; - r244 = 2*m1^2 + m2^2 + m4^2; - r245 = -2*m1^2 - m3^2 - m4^2 + 3*m5^2; - r246 = m1^4 - 3*m2^2*m3^2 + m5^4 + PP^2 + m4^2*r173 - m5^2*r244 + PP*r245; - r247 = -2*m3^2 + m4^2 + m5^2; - r248 = -m2^4 - m4^2*m5^2 + PP*r235 + m2^2*r247 + m1^2*r46; - r249 = m2^2*r153 + m1^2*r5; r250 = 2*m1^2 + m2^2*r4; - r251 = m2^2*r13 + m1^2*r139; - r252 = r107*r108*r250 + m3^2*r251 - m3^4*r4; - r253 = m1^2*r140 + 2*m3^2*r4 + m2^2*r72; - r254 = m3^4*r249 + m4^2*r252 + m4^4*r253 - m4^6*r4 + m2^2*m3^2*r100*r99; - r255 = 2*m3^2 + m4^2*r13; - r256 = -2*m3^2*r5 + m2^2*r99 - m4^2*r99; - r257 = -11 + 2*d; - r258 = -(m4^4*r106) + 2*m3^2*m4^2*r23 - m3^4*r257; - r259 = 4*m4^2 + m3^2*r13; - r260 = -2*m2^4 + 6*m3^2*m4^2 + 2*m2^2*r259 + m4^4*r37 + m3^4*r5; - r261 = -5*m3^4*m4^2 + m2^4*r255 + m1^4*r256 + m2^2*r258 + m1^2*r260 - m2^6*r4 + m3^6*r5 + m4^6*r6 - 3*m3^2*m4^4*r72; - r262 = m3^4 + m3^2*m4^2 + m4^4; - r263 = m1^4 + m2^4 - 2*r262 + m1^2*r81 + m2^2*r81; - r264 = m1^2 + m2^2 - m3^2 - m4^2; - r265 = -(r13*r32*r33) + m2^2*r99; - r266 = -2*m1^2*r265 - r32^2*r33^2*r4 + 2*m2^2*r13*r9 + m1^4*r99 + m2^4*r99; - r267 = m3^2*r13 + m4^2*r4; - r268 = -16 + 3*d; - r269 = m3^2*r13 - m4^2*r268 + m2^2*r4; - r270 = 2*m2^2*r267 + 2*m1^2*r269 + r13*r228*r32*r33 + m2^4*r61 + m1^4*r99; - r271 = 2*m2^2 + m4^2*r23 - m3^2*r72; - r272 = -(m5^2*r270) - 2*m5^4*r271 + r266*r32*r33; - r273 = 2*m3^2 - 2*m4^2 - m5^2; - r274 = m1^2*r5 - m2^2*r5 + r273*r72; - r275 = r200*r254 + m5^2*r261 + PP*r272 + 2*m5^2*PP^2*r274 + m5^4*r263*r5 - m5^6*r264*r5; - r276 = -2*m2^2*m3^2 - 2*m3^4 + 3*m3^2*m4^2 - m4^4 + 3*m3^2*m5^2 + 2*m4^2*m5^2 - m5^4 + m1^2*r177 + PP*r77; - r277 = -(m4^2*r106) + m2^2*r4 - m3^2*r5; - r278 = -2*m3^4 - m3^2*m4^2*r13 + m2^2*r196 + m2^4*r4 + m4^4*r4; - r279 = m4^2*r131 + m3^2*r8; - r280 = m2^2*r279 - 2*m2^4*r4 + m4^2*r32*r33*r99; - r281 = m1^4*r277 + m2^2*r278 + m1^2*r280; - r282 = 11*m3^2 - 3*d*m3^2 + 9*m4^2 - 2*d*m4^2; - r283 = 15 - 4*d; - r284 = m4^2*r106 + m2^2*r283 + m3^2*r5; - r285 = m4^4*r13 + 4*m3^2*m4^2*r5 - m3^4*r99; - r286 = -m4^2 + m3^2*r5; - r287 = -(m4^2*r5) + m3^2*r6; - r288 = 2*m2^2*r287 + m2^4*r72 - 2*r286*r81; - r289 = -2*m3^2*m4^4 + m2^4*r282 + m1^4*r284 + m2^2*r285 + m1^2*r288 - m4^6*r4 + m1^6*r5 + m2^6*r6 + m3^4*m4^2*r99; - r290 = 2*m2^2 - m3^2 - m4^2; - r291 = 2*m1^4 + 2*m2^4 - m3^4 - m4^4 + m1^2*r290 - m2^2*r81; - r292 = m2^2 - m3^2 + m4^2; - r293 = m1^4*r4 + m2^4*r4 - 2*m1^2*r292*r4 + 2*m2^2*r4*r9 - r32^2*r33^2*r99; r294 = m3^2*r13 - m4^2*r131; - r295 = m2^2*r13 - r4*r81; - r296 = m1^4*r131 + 2*m2^2*r294 - 2*m1^2*r295 - 2*m3^2*m4^2*r4 + m4^4*r8 - m2^4*r99 - m3^4*r99; - r297 = 2*m4^2 - m2^2*r5 + m1^2*r72; - r298 = r107*r108*r293 - m5^2*r296 + 2*m5^4*r297; - r299 = -2*m5^2*r32*r33*r5 + 2*m5^4*r72; - r300 = r130*r281 - m5^2*r289 + PP*r298 + PP^2*r299 - m5^6*r264*r5 + m5^4*r291*r5; - r301 = -2*m2^2*m3^2 - m3^2*m4^2 + m4^4 + m5^4 - m5^2*r17 + m1^2*r177 + PP*r77; - r302 = m2^2 + 2*m3^2 - 3*m4^2; - r303 = -m1^2 + m2^2 - 3*m5^2; - r304 = m1^4 - m2^2*m4^2 - m5^4 + m5^2*r149 - m1^2*r302 + PP*r303; - r305 = -( - (r45 TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{2, m1}, {1, m3}}])/(4*r3)) + - (r76 TBI[d, PP, {{1, m3}, {1, m1}}] TBI[d, PP, {{2, m2}, {1, m4}}])/(4*r3) - - (r80 TBI[d, PP, {{2, m1}, {1, m3}}] TBI[d, PP, {{2, m2}, {1, m4}}])/2 - - (r45 TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{2, m3}, {1, m1}}])/(4*r3) - - (r84 TBI[d, PP, {{2, m2}, {1, m4}}] TBI[d, PP, {{2, m3}, {1, m1}}])/2 - - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{2, m3}, {2, m1}}] + - (r76 TBI[d, PP, {{1, m3}, {1, m1}}] TBI[d, PP, {{2, m4}, {1, m2}}])/(4*r3) - - (r92*TBI[d, PP, {{2, m1}, {1, m3}}] TBI[d, PP, {{2, m4}, {1, m2}}])/2 - - (r98*TBI[d, PP, {{2, m3}, {1, m1}}] TBI[d, PP, {{2, m4}, {1, m2}}])/2 - - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{3, m1}, {1, m3}}] - - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}] TBI[d, PP, {{3, m3}, {1, m1}}] - - r3*TFI[r99, PP, {{1, m1}, {1, m2}, {1, m3}, {1, m4}, {1, m5}}] - - (r134*TVI[d, PP, {{1, m5}, {1, m1}, {2, m4}, {1, m3}}])/(4*r3) - - (r135*r136*r137*r138*TVI[d, PP, {{1, m5}, {1, m1}, {2, m4}, {2, m3}}])/2 - - (r176*TVI[d, PP, {{1, m5}, {1, m2}, {2, m3}, {1, m4}}])/(4*r3) + - (r180*TVI[d, PP, {{1, m5}, {1, m2}, {2, m3}, {2, m4}}])/2 - - r182*TVI[d, PP, {{1, m5}, {1, m2}, {3, m3}, {1, m4}}] + - (r203 TVI[d, PP, {{1, m5}, {1, m3}, {2, m2}, {1, m1}}])/(4*r3) + - (r232*TVI[d, PP, {{1, m5}, {1, m4}, {2, m1}, {1, m2}}])/(4*r3) + - (r236*TVI[d, PP, {{1, m5}, {1, m4}, {2, m1}, {2, m2}}])/2 + - r240*TVI[d, PP, {{1, m5}, {1, m4}, {3, m1}, {1, m2}}] + - (r45*TVI[d, PP, {{1, m5}, {2, m1}, {1, m4}, {1, m3}}])/(4*r3) + - (r86*r88*TVI[d, PP, {{1, m5}, {2, m1}, {1, m4}, {2, m3}}])/2 + - (r92*TVI[d, PP, {{1, m5}, {2, m1}, {2, m4}, {1, m3}}])/2 - - (r76*TVI[d, PP, {{1, m5}, {2, m2}, {1, m3}, {1, m4}}])/(4*r3) - - (r243*TVI[d, PP, {{1, m5}, {2, m2}, {2, m3}, {1, m4}}])/2 + - (r45*TVI[d, PP, {{1, m5}, {2, m3}, {1, m2}, {1, m1}}])/(4*r3) + - (r86*r88*TVI[d, PP, {{1, m5}, {2, m3}, {1, m2}, {2, m1}}])/2 + - (r246*TVI[d, PP, {{1, m5}, {2, m3}, {2, m2}, {1, m1}}])/2 - - (r76*TVI[d, PP, {{1, m5}, {2, m4}, {1, m1}, {1, m2}}])/(4*r3) + - (r248*TVI[d, PP, {{1, m5}, {2, m4}, {2, m1}, {1, m2}}])/2 + - r86*r88*TVI[d, PP, {{1, m5}, {3, m1}, {1, m4}, {1, m3}}] + - r86*r88*TVI[d, PP, {{1, m5}, {3, m3}, {1, m2}, {1, m1}}] + - (r275*TVI[d, PP, {{2, m5}, {1, m1}, {1, m4}, {1, m3}}])/(4*r3) + - (r276*TVI[d, PP, {{2, m5}, {1, m1}, {1, m4}, {2, m3}}])/2 - - (r180*TVI[d, PP, {{2, m5}, {1, m1}, {2, m4}, {1, m3}}])/2 - - (r275*TVI[d, PP, {{2, m5}, {1, m2}, {1, m3}, {1, m4}}])/(4*r3) + - (r180*TVI[d, PP, {{2, m5}, {1, m2}, {1, m3}, {2, m4}}])/2 - - (r276*TVI[d, PP, {{2, m5}, {1, m2}, {2, m3}, {1, m4}}])/2 - - (r300*TVI[d, PP, {{2, m5}, {1, m3}, {1, m2}, {1, m1}}])/(4*r3) - - (r240*TVI[d, PP, {{2, m5}, {1, m3}, {1, m2}, {2, m1}}])/2 - - (r236*TVI[d, PP, {{2, m5}, {1, m3}, {2, m2}, {1, m1}}])/2 + - (r300*TVI[d, PP, {{2, m5}, {1, m4}, {1, m1}, {1, m2}}])/(4*r3) + - (r236*TVI[d, PP, {{2, m5}, {1, m4}, {1, m1}, {2, m2}}])/2 + - (r240*TVI[d, PP, {{2, m5}, {1, m4}, {2, m1}, {1, m2}}])/2 + - (r182*TVI[d, PP, {{2, m5}, {2, m1}, {1, m4}, {1, m3}}])/2 - - (r301*TVI[d, PP, {{2, m5}, {2, m2}, {1, m3}, {1, m4}}])/2 - - (r304*TVI[d, PP, {{2, m5}, {2, m3}, {1, m2}, {1, m1}}])/2 + - (r248*TVI[d, PP, {{2, m5}, {2, m4}, {1, m1}, {1, m2}}])/2; - - - - r306 = Factor /@ r305/(PP*r1*r2); r306]) /; - n1 === 1 && n2 === 1 && n3 === 1 && n4 === 1 && n5 === 1 && MatchQ[d, _Symbol + _Integer?Positive] && PP =!= 0 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0 - ]; - -Subscript[e, 51] = - Subscript[\[CapitalDelta], 1, 3, 4]*Subscript[\[Nu], 1]* - Schiebe[1, "+"] TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (2*Subscript[m, 3]^2*Subscript[\[Nu], 3]* - Schiebe[3, "+"]*(Schiebe[1, "-"] - Schiebe[4, "-"]) + Subscript[u, 4, 1, 3]*Subscript[\[Nu], 1]* - Schiebe[1, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"]) + Subscript[u, 1, 3, 4]*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3]) + - 2*Subscript[m, 3]^2*(Subscript[\[Nu], 1] - Subscript[\[Nu], 3]))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2],Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 51] = - OperatorApplyV[Subscript[e, 51]]; - -Subscript[h, 51] = - Subscript[s, 51] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 - -Subscript[f, 51] = - MakeFun[Subscript[h, 51], "(51)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[\[CapitalDelta], 1, 3, 4] =!= 0]]; - -CheckTVIRecursion[Subscript[f, 51]] - -Subscript[e, 52] = - Subscript[\[CapitalDelta], 2, 4, 6]*Subscript[\[Nu], 2]* - Schiebe[2, "+"]* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (2*Subscript[m, 1]^2*Subscript[\[Nu], 1] Schiebe[1, "+"]*(Schiebe[4, "-"] - Schiebe[2, "-"]) + - 2*Subscript[m, 3]^2*Subscript[\[Nu], 3]* Schiebe[3, "+"]*(Schiebe[4, "-"] - Schiebe[2, "-"]) - - 2*Subscript[m, 4]^2*Subscript[\[Nu], 4]*Schiebe[4, "+"]*Schiebe[2, "-"] + - (2*Subscript[m, 2]^2 - Subscript[u, 4, 2, 6])*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[4, "-"] - - (Subscript[\[CapitalSigma], 4] + 2)*(Schiebe[4, "-"] - Schiebe[2, "-"]) + - Subscript[u, 2, 4, 6]*(d - 3*Subscript[\[Nu], 2]) + 2*Subscript[m, 4]^2*(Subscript[\[Nu], 4] - Subscript[\[Nu], 2]))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 52] = - OperatorApplyV[Subscript[e, 52]] - -Subscript[h, 52] = - nuExplicit[Subscript[s, 52]] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1; - -Subscript[f, 52] = - MakeFun[Subscript[h, 52], "(52)", IFF[Subscript[\[Nu], 2] > 1 && Subscript[\[CapitalDelta], 2, 4, 6] =!= 0]]; - - -Subscript[h, 53] = - Interchange[Subscript[s, 51], 1 \[LeftRightArrow] 3] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; - -Subscript[f, 53] = - MakeFun[Subscript[h, 53], "(53)", IFF[Subscript[\[Nu], 3] > 1 && Subscript[\[CapitalDelta], 3, 1, 4] =!= 0]]; - - -Subscript[e, 54] = - 2*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"]* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (Subscript[u, 4, 1, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + Subscript[\[Nu], 1]* - Schiebe[1, "+"]*(Schiebe[4, "-"] - Schiebe[3, "-"]) + (d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3]))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 54] = - OperatorApplyV[Subscript[e, 54]]; - -Subscript[h, 54] = - Subscript[s, 54] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; - -Subscript[f, 54] = -MakeFun[Subscript[h, 54], "(54)", IFF[Subscript[\[Nu], 3] > 1 && m3 =!= 0]]; - -Subscript[e, 55] = - 2*Subscript[m, 4]^2*Subscript[\[Nu], 4]*Schiebe[4, "+"]* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (Subscript[u, 3, 1, 4]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + Subscript[u, 6, 2, 4]*Subscript[\[Nu], 2]*Schiebe[2, "+"] + - Subscript[\[Nu], 1]*Schiebe[1, "+"]*(Schiebe[3, "-"] - Schiebe[4, "-"]) - - Subscript[\[Nu], 2]*Schiebe[2, "+"] Schiebe[4, "-"] + (d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 4]))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 55] = - OperatorApplyV[Subscript[e, 55]]; - -Subscript[h, 55] = - Subscript[s, 55] /. Subscript[\[Nu], 4] -> Subscript[\[Nu], 4] - 1; - -Subscript[f, 55] = - MakeFun[Subscript[h, 55], "(55)", IFF[Subscript[\[Nu], 4] > 1 && m4 =!= 0 && Subscript[\[Nu], 3] > 1]]; - -Subscript[e, 56] = - 2*Subscript[m, 4]^2*Subscript[\[Nu], 4]*Schiebe[4, "+"]* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (-2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] + Subscript[u, 6, 2, 4]*Subscript[\[Nu], 2]*Schiebe[2, "+"] - - 2*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] - Subscript[\[Nu], 2]*Schiebe[2, "+"]* - Schiebe[4, "-"] + (2*d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3] - - 2*Subscript[\[Nu], 4]))*TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 56] = - OperatorApplyV[Subscript[e, 56]]; - -Subscript[h, 56] = - Subscript[s, 56] /. Subscript[\[Nu], 4] -> Subscript[\[Nu], 4] - 1; - -Subscript[f, 56] = - MakeFun[Subscript[h, 56], "(56)", IFF[Subscript[\[Nu], 4] > 1 && m4 =!= 0 && Subscript[\[Nu], 3] === 1]]; - -Subscript[e, 59] = - (2*Subscript[m, 1]^2*Subscript[u, 1, 3, 4]*(d - Subscript[\[Nu], 1] - - 2*Subscript[\[Nu], 3]) + (Subscript[\[Nu], 3] - 1)*Subscript[u, 4, 1, 3]^2 + 4*Subscript[m, 1]^2* - Subscript[m, 3]^2*(Subscript[\[Nu], 1] - Subscript[\[Nu], 3]))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (Subscript[u, 4, 1, 3]*Subscript[\[Nu], 3]*Schiebe[3, "+"]* - Schiebe[4, "-"]*(Schiebe[4, "-"] - Schiebe[1, "-"]) - - 4*Subscript[m, 1]^2*Subscript[m, 3]^2*Subscript[\[Nu], 3] Schiebe[3, "+"]* - Schiebe[1, "-"] + (4*Subscript[m, 1]^2*Subscript[m, 3]^2 + - Subscript[u, 4, 1, 3]^2)*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[4, "-"] + - Subscript[u, 4, 1, 3]*(Subscript[\[Nu], 3] - 1)*Schiebe[1, "-"] - - (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] + 1)*Subscript[u, 4, 1, 3]*Schiebe[3, "-"] + - (d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3] + 1)*Subscript[u, 4, 1, 3]*Schiebe[4, "-"])* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 59] = - OperatorApplyV[Subscript[e, 59]]; - -Subscript[h, 59] = - Subscript[s, 59]; - -Subscript[f, 59] = - MakeFun[Subscript[h, 59], "(59)", - IFF[Subscript[\[CapitalDelta], 1, 3, 4] == 0 && 4*Subscript[m, 3]^2*Subscript[m, 1]^2 - 4*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Subscript[m, 1]^2 + - 2*d*Subscript[u, 1, 3, 4]*Subscript[m, 1]^2 - 4*Subscript[\[Nu], 3]*Subscript[u, 1, 3, 4]*Subscript[m, 1]^2 - - 2*Subscript[u, 1, 3, 4]*Subscript[m, 1]^2 + Subscript[\[Nu], 3]*Subscript[u, 4, 1, 3]^2 - Subscript[u, 4, 1, 3]^2 =!= 0 && - n1 === 1 && n2 === 1 && n4 === 1 && MatchQ[d, _Integer]]]; - -Subscript[e, 60] = - 2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"]* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (Subscript[u, 4, 1, 3]*Subscript[\[Nu], 3]*Schiebe[3, "+"] + Subscript[\[Nu], 3]*Schiebe[3, "+"]*(Schiebe[4, "-"] - Schiebe[1, "-"]) + - (d - Subscript[\[Nu], 3] - 2*Subscript[\[Nu], 1]))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 60] = - OperatorApplyV[Subscript[e, 60]]; - -Subscript[h, 60] = - Subscript[s, 60] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[notnecessaryf, 60] = - MakeFun[Subscript[h, 60], "(60)", IFF[Subscript[\[Nu], 1] > 1 && m1 =!= 0]]; - -Subscript[e, 61] = - (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3])* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - Subscript[\[Nu], 3]* Schiebe[3, "+"]*(Schiebe[1, "-"] - Schiebe[4, "-"])* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 61] = - OperatorApplyV[Subscript[e, 61]]; - -Subscript[h, 61] = - Subscript[s, 61]; - -Subscript[f, 61] = - MakeFun[Subscript[h, 61], "(61)", IFF[m1 === 0 && m3 === m4]]; - -Subscript[h, 6153] = - Interchange[Subscript[s, 61], 1 \[LeftRightArrow] 3]; - -Subscript[f, 6153] = - MakeFun[Subscript[h, 6153], "(6153)", IFF[m3 === 0 && m1 === m4]]; - -Subscript[e, 62] = - (PP - Subscript[m, 2]^2)*(Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] + 2*Subscript[\[Nu], 4] + 2)* - Schiebe[4, "+"]* TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - ((Subscript[m, 1]^2 - Subscript[u, 6, 1, 2])*Subscript[\[Nu], 1]*Schiebe[1, "+"] + - 4*Subscript[m, 2]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"] + - 2*Subscript[m, 1]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + - (Subscript[\[CapitalSigma], 4] - 2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] - - 2*Subscript[m, 1]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"])* - Schiebe[2, "-"]*Schiebe[4, "+"] + (PP - Subscript[m, 2]^2)*Subscript[\[Nu], 1]* Schiebe[1, "+"]*Schiebe[4, "+"]*Schiebe[3, "-"] - - Subscript[\[CapitalSigma], 4])* TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 62] = - OperatorApplyV[Subscript[e, 62]]; - -Subscript[h, 62] = - nuExplicit[Subscript[s, 62]] /. Subscript[\[Nu], 4] -> Subscript[\[Nu], 4] - 1; - -Subscript[f, 62] = - MakeFun[Subscript[h, 62], "(62)", IFF[PP =!= m2^2 && Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] + 2*Subscript[\[Nu], 4] =!= 0], {m4 :> 0, m3 :> m1, n2 :> 1}]; -Subscript[e, 63] = - (PP - Subscript[m, 2]^2)*((Subscript[m, 3]^2 - Subscript[m, 1]^2)*(d - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3] + - 2*Subscript[\[Nu], 4]) + 2*Subscript[m, 3]^2*(Subscript[\[Nu], 3] - Subscript[\[Nu], 1]))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - ((Subscript[m, 1]^2 - Subscript[m, 3]^2)*((2*Subscript[m, 1]^2*Subscript[\[Nu], 1] Schiebe[1, "+"] + - 2*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] - Subscript[\[CapitalSigma], 4] - 2)* - (Schiebe[2, "-"] - Schiebe[4, "-"]) - 4*Subscript[m, 2]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"] Schiebe[4, "-"]) + - - 2*(PP - Subscript[m, 2]^2)*(Subscript[m, 3]^2*Subscript[\[Nu], 3]* - Schiebe[3, "+"]*(Schiebe[1, "-"] - Schiebe[4, "-"]) + Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"]* - (Schiebe[4, "-"] - Schiebe[3, "-"])))* TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 63] = - OperatorApplyV[Subscript[e, 63]]; - -Subscript[h, 63] = - nuExplicit[Subscript[s, 63]]; - -Subscript[f, 63] = - MakeFun[Subscript[h, 63], "(63)", IFF[PP =!= m2^2 && Cayley[1, 3, 4][{m1, m2, m3, m4}] =!= 0], {m4 :>0}]; - -Subscript[f, 63] = - MakeFun[Subscript[h, 63], "(63)", IFF[PP =!= m2^2 && Cayley[1, 3, 4][{m1, m2, m3, m4}] =!= 0], {m4 :> 0, n1 :> 1, n3 :> 1}]; - -Subscript[r, 6552] = - nuExplicit[Subscript[e, 52]] /. Subscript[\[CapitalDelta], 2, 4, 6] -> 0; - -formal = - Solve[Subscript[e, 55] /. TVI[__] -> 1, Schiebe[4, "+"]][[1, 1]] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1; - -Subscript[n, 6552] = - OperatorApplyV[Subscript[r, 6552] /. formal]; - -Subscript[s, 6552] = - -Subscript[n, 6552][[2, 4]] == Subscript[n, 6552][[2]] - Subscript[n, 6552][[2, 4]]; - -Subscript[f, 6552] = - MakeFun[Subscript[s, 6552], "(6552)", IFF[Subscript[\[CapitalDelta], 2, 4, 6] === 0 && - Expand[2*(Subscript[\[Nu], 2] - Subscript[\[Nu], 4])* m4^2 + (3*Subscript[\[Nu], 2] - d)* - Subscript[u, 2, 4, 6] + Subscript[\[Nu], 2]*Subscript[u, 6, 2, 4]] =!= 0] - ]; - -Subscript[r, 6552] = - nuExplicit[Subscript[e, 52]] /. Subscript[\[CapitalDelta], 2, 4, 6] -> 0; - -Subscript[n, 6552] = - OperatorApplyV[Subscript[r, 6552]]; - - -Subscript[s, 6552] = - -Subscript[n, 6552][[2, 5]] == Subscript[n, 6552][[2]] - Subscript[n, 6552][[2, 5]]; - -Subscript[f, 6552] = - MakeFun[Subscript[s, 6552], "(6552)", IFF[Subscript[\[CapitalDelta], 2, 4, 6] === 0 && - Expand[-2*Subscript[\[Nu], 2]*Subscript[m, 4]^2 + 2*Subscript[\[Nu], 4]*Subscript[m, 4]^2 + d*Subscript[u, 2, 4, 6] - - 3*Subscript[\[Nu], 2]*Subscript[u, 2, 4, 6]] =!= 0]]; - -Subscript[r, 6553] = - nuExplicit[Subscript[s, 55]] /. Subscript[u, 3, 1, 4] -> 0 /. Subscript[u, 6, 2, 4] -> 0 /. Subscript[m, 4] -> 0; - -Subscript[h, 6553] = - -Subscript[r, 6553][[2, 1]] == Subscript[r, 6553][[2]] - Subscript[r, 6553][[2, 1]]; - -Subscript[f, 6553] = - MakeFun[Subscript[h, 6553], "(6553)", IFF[Subscript[u, 6, 2, 4] === 0 && Subscript[u, 1, 3, 4] === 0], m4 :> 0]; - -Subscript[e, 66] = - 4*PP*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]* - TVI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (-((6*d - 6*Subscript[\[Nu], 1] - 5*Subscript[\[Nu], 2] - 6*Subscript[\[Nu], 3] - 4*Subscript[\[Nu], 4] - - 6*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"]) + (Subscript[u, 6, 2, 4] - 4*Subscript[m, 2]^2)* - Subscript[\[Nu], 2]*Schiebe[2, "+"] - 6*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + - 2*(Subscript[u, 6, 2, 4] - Subscript[m, 4]^2)*Subscript[\[Nu], 4]*Schiebe[4, "+"] - - Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[4, "-"] - 2*Subscript[\[Nu], 4]*Schiebe[4, "+"]*Schiebe[2, "-"]))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 66] = - OperatorApplyV[Subscript[e, 66]]; - -Subscript[h, 66] = - Subscript[s, 66] /. { - Subscript[\[Nu], 1] :> Subscript[\[Nu], 1] - 1, - Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 1, - Subscript[\[Nu], 3] :> Subscript[\[Nu], 3] - 1, d :> d - 2 - }; - -Subscript[f, 66] = - MakeFun[Subscript[h, 66], "(66)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 2] > 1 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 67] = - 4*PP*Subscript[\[Nu], 1]*(Subscript[\[Nu], 1] + 1)*Schiebe[1, "+"] Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]* - TVI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - ((6*d - 6*Subscript[\[Nu], 1] - 5*Subscript[\[Nu], 2] - 6*Subscript[\[Nu], 3] - 4*Subscript[\[Nu], 4]) - - 2*(Subscript[u, 2, 4, 6] + 3*Subscript[m, 1]^2)*Subscript[\[Nu], 1] Schiebe[1, "+"] + - (Subscript[u, 6, 2, 4] - 4*Subscript[m, 2]^2) Subscript[\[Nu], 2]*Schiebe[2, "+"] - - 6*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + 2*(Subscript[u, 6, 2, 4] - Subscript[m, 4]^2) Subscript[\[Nu], 4]*Schiebe[4, "+"] + - 2*Subscript[\[Nu], 1] Schiebe[1, "+"]*(Schiebe[4, "-"] - Schiebe[2, "-"]) - - Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[4, "-"] - 2*Subscript[\[Nu], 4]*Schiebe[4, "+"]*Schiebe[2, "-"])* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 67] = - OperatorApplyV[Subscript[e, 67]]; - -Subscript[e, 67] = - 4*PP*Subscript[\[Nu], 1]*(Subscript[\[Nu], 1] + 1)*Schiebe[1, "+"] Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]* - TVI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (2*(2*d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3] - Subscript[\[Nu], 4]) - - 2*(Subscript[u, 2, 4, 6] + 2*Subscript[m, 1]^2)*Subscript[\[Nu], 1]*Schiebe[1, "+"] - - 4*Subscript[m, 2]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"] - 4*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + - 2*Subscript[u, 6, 2, 4]*Subscript[\[Nu], 4]*Schiebe[4, "+"] + 2*Subscript[\[Nu], 1]* - Schiebe[1, "+"]*(Schiebe[4, "-"] - Schiebe[2, "-"]) - 2*Subscript[\[Nu], 4]*Schiebe[4, "+"]*Schiebe[2, "-"])* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 67] = - OperatorApplyV[Subscript[e, 67]]; - -Subscript[h, 67] = - Subscript[s, 67] /. {Subscript[\[Nu], 1] :> Subscript[\[Nu], 1] - 2, Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 1, d :> d - 2}; - -Subscript[f, 67] = - MakeFun[Subscript[h, 67], "(67)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 2 && Subscript[\[Nu], 2] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[h, 6713] = - Interchange[Subscript[s, 67], 1 \[LeftRightArrow] 3] /. {Subscript[\[Nu], 3] :> Subscript[\[Nu], 3] - 2, Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 1, d :> d - 2}; - -Subscript[f, 6713] = - MakeFun[Subscript[h, 6713], "(6713)", IFF[PP =!= 0 && Subscript[\[Nu], 3] > 2 && Subscript[\[Nu], 2] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 68] = - 4*PP*Subscript[m, 4]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*(Subscript[\[Nu], 2] + 1)*Schiebe[2, "+"]* - Schiebe[2, "+"]*TVI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}] == - (-(((Subscript[m, 1]^2 - Subscript[m, 3]^2)*(2*d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - - 2*Subscript[\[Nu], 3] - 2*Subscript[\[Nu], 4]) + Subscript[m, 4]^2*(2*Subscript[\[Nu], 1] + - Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3])) - Subscript[u, 1, 3, 4]*(2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] + - Subscript[u, 2, 4, 6]*Subscript[\[Nu], 2]*Schiebe[2, "+"]) + - Subscript[u, 3, 1, 4]*(2*Subscript[m, 3]^2*Subscript[\[Nu], 3]*Schiebe[3, "+"] + Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[4, "-"]) - - 2*Subscript[m, 4]^2*(Subscript[\[Nu], 2]*Schiebe[2, "+"] + Subscript[\[Nu], 4]*Schiebe[4, "+"])*(Schiebe[3, "-"] - Schiebe[1, "-"])))* - TVI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3], Subscript[\[Nu], 4]}]; - -Subscript[s, 68] = - OperatorApplyV[Subscript[e, 68]]; - -Subscript[h, 68] = - Subscript[s, 68] /. {Subscript[\[Nu], 1] :> Subscript[\[Nu], 1] - 1, Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 2, d :> d - 2}; - -Subscript[f, 68] = - MakeFun[Subscript[h, 68], "(68)", IFF[PP =!= 0 && m4 =!= 0 && Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 2] > 2 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[h, 6813] = - Interchange[Subscript[s, 68], 1 \[LeftRightArrow] 3] /. {Subscript[\[Nu], 2] :> Subscript[\[Nu], 2] - 2, Subscript[\[Nu], 3] :> Subscript[\[Nu], 3] - 1, d :> d - 2}; - -Subscript[f, 6813] = - MakeFun[Subscript[h, 6813], "(6813)", IFF[PP =!= 0 && m4 =!= 0 && Subscript[\[Nu], 2] > 2 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 70] = - (3*d - 10)*(d - 3)^2*Subscript[m, 4]^2 TVI[d, {1, 1, 1, 1}] == - (1/(4*PP))*((3*d - 10)*Subscript[\[CapitalDelta], 1, 3, 4]*(Subscript[\[CapitalDelta], 2, 4, 6] + Subscript[u, 2, 4, 6]*(Schiebe[2, "-"] - Schiebe[4, "-"])) - - 8*(d - 4)^2*PP*Subscript[m, 3]^2*Subscript[m, 4]^2*Schiebe[4, "-"])*TVI[-2 + d, {1, 1, 1,1}] + ((d - 3)* - Subscript[m, 4]^2*(4*Subscript[m, 1]^2*(d - 4)*Schiebe[1, "+"]* - Schiebe[1, "+"] - 8*(d - 3)*Subscript[m, 2]^2*Schiebe[2, "+"] Schiebe[2, "+"] + (3*d - 10)*(d - 3)*Schiebe[2, "+"]) + - Subscript[u, 6, 2, 4]*((1/2)*(3*d - 10)* Subscript[u, 1, 3, 4]*(Schiebe[1, "+"] - Schiebe[3, "+"]) + (d - 2)*(d - 3)* - Subscript[m, 4]^2*Schiebe[1, "+"])*Schiebe[2, "+"] - Subscript[m, 4]^2*((d - 4)^2*Subscript[u, 1, 3, 4]* Schiebe[2, "+"] + - (3*d - 10)*Subscript[u, 4, 1, 3]* Schiebe[3, "+"])*Schiebe[1, "+"])*Schiebe[4, "-"]* - TVI[d, {1, 1, 1, 1}] - (d - 3)* Subscript[m, 4]^2*(4*(d - 4)*Subscript[m, 1]^2*Schiebe[1, "+"] + (d - 2)*(Subscript[u, 6, 2, 4]*Schiebe[2, "+"] - - 2*Subscript[m, 4]^2*Schiebe[4, "+"]))*Schiebe[1, "+"]* Schiebe[3, "-"]* TVI[d, {1, 1, 1, 1}] + (1/2)*(3*d - 10)* - Subscript[u, 1, 3, 4]*(Subscript[u, 6, 2, 4]*Schiebe[2, "+"] - 2*Subscript[m, 4]^2*Schiebe[4, "+"])* - (Schiebe[3, "+"]*Schiebe[1, "-"] - Schiebe[1, "+"]*Schiebe[3, "-"])*TVI[d, {1, 1, 1, 1}]; - -Subscript[s, 70] = - OperatorApplyV[Subscript[e, 70]]; - -Subscript[h, 70] = - Subscript[s, 70]; - -Subscript[f, 70] = - MakeFun[Subscript[h, 70], "(70)", IFF[m4 =!= 0 && PP =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 71] = - 2*Subscript[D, 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (2*Subscript[h, 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + - 2*Subscript[h, 2, 1, 3]*Subscript[\[Nu], 2]*Schiebe[2, "+"] + - 4*Subscript[m, 3]^2*Subscript[\[Sigma], 1, 2, 3]*Subscript[\[Nu], 3]* Schiebe[3, "+"] + - Subscript[m, 3]^2*Subscript[\[Phi], 2, 1, 3]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + - Subscript[m, 3]^2*Subscript[\[Phi], 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[2, "-"] - - 2*Subscript[\[Rho], 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[3, "-"] + - (1/2)*Subscript[\[CapitalSigma], 3]*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])*Subscript[\[Phi], 3, 2, 1])* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 71] = - OperatorApplyJ[Subscript[e, 71]]; - -Subscript[h, 71] = - nuExplicit[Subscript[s, 71]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1; - -Subscript[f, 71] = - MakeFun[Subscript[h, 71], "(71)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 2] > 1 && Subscript[D, 1, 2, 3] =!= 0]]; - - -Subscript[h, 7123] = - Interchange[Subscript[s, 71], 2 \[LeftRightArrow] 3] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; - -Subscript[f, 7123] = - MakeFun[Subscript[h, 7123], "(7123)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 3] > 1 && Subscript[D, 1, 3, 2] =!= 0]]; - - -Subscript[h, 7113] = - Interchange[Subscript[s, 71], 1 \[LeftRightArrow] 3] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; - -Subscript[f, 7113] = - MakeFun[Subscript[h, 7113], "(7113)", IFF[Subscript[\[Nu], 2] > 1 && Subscript[\[Nu], 3] > 1 && Subscript[D, 3, 2, 1] =!= 0]]; - -Subscript[e, 78] = - 2*Subscript[m, 1]^2*Subscript[D, 1, 2, 3]* - Subscript[\[Nu], 1]*(Subscript[\[Nu], 1] + 1)*Schiebe[1, "+"]* - Schiebe[1, "+"]* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - ((-Subscript[\[CapitalSigma], 3])*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])*Subscript[\[Rho], 1, 2, 3] + - Subscript[m, 2]^2*Subscript[m, 3]^2*Subscript[\[Phi], 1, 2, 3]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + - Subscript[m, 1]^2*Subscript[m, 3]^2*Subscript[\[Phi], 2, 1, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[2, "-"] + - Subscript[m, 1]^2*Subscript[m, 2]^2*Subscript[\[Phi], 3, 1, 2]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[3, "-"] + - (d - 2 - 2*Subscript[\[Nu], 1])*Subscript[D, 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + - Subscript[m, 1]^2*Subscript[S, 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] + Subscript[m, 2]^2*Subscript[S, 2, 1, 3]*Subscript[\[Nu], 2]*Schiebe[2, "+"] + - Subscript[m, 3]^2*Subscript[S, 3, 1, 2]*Subscript[\[Nu], 3]*Schiebe[3, "+"])* TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 78] = - OperatorApplyJ[Subscript[e, 78]]; - -Subscript[h, 78] = - nuExplicit[Subscript[s, 78]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 2; - -Subscript[f, 78] = - MakeFun[Subscript[h, 78], "(78)", IFF[Subscript[\[Nu], 1] > 2 && m1 =!= 0 && Subscript[D, 1, 2, 3] =!= 0]]; - -Subscript[e, 80] = - Subscript[\[Nu], 1]*(d - 2*Subscript[\[Nu], 1] - 2)* - Subscript[\[CapitalDelta], 2, 3, 6]*Schiebe[1, "+"]* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], - Subscript[\[Nu], 3]}] == - (-4*Subscript[m, 2]^2*Subscript[m, 3]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]*Schiebe[1, "-"] + - 2*Subscript[m, 2]^2*((PP - Subscript[m, 2]^2)*(2*d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - - 2*Subscript[\[Nu], 3] - 1) - Subscript[m, 3]^2*(2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 1))*Subscript[\[Nu], 2]*Schiebe[2, "+"] + - 2*Subscript[m, 3]^2*((PP - Subscript[m, 3]^2)*(2*d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - Subscript[\[Nu], 3] - 1) - - Subscript[m, 2]^2*(2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3] - 1))*Subscript[\[Nu], 3]*Schiebe[3, "+"] - - Subscript[\[CapitalSigma], 3]*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - - Subscript[\[Nu], 3])*Subscript[u, 6, 2, 3])*TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 80] = - OperatorApplyJ[Subscript[e, 80]]; - -Subscript[h, 80] = - nuExplicit[Subscript[s, 80]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 80] = - MakeFun[Subscript[h, 80], "(80)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[\[CapitalDelta], 2, 3, 6] =!= 0], m1 :> 0]; - -Subscript[e, 81] = - PP*(Subscript[\[CapitalSigma], 3] + 2)*Subscript[\[Nu], 1]* - Schiebe[1, "+"]*Subscript[\[Nu], 2]*Schiebe[2, "+"]*TJI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (PP*(d - 2*Subscript[\[Nu], 3]) + Subscript[m, 1]^2*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2]) + - Subscript[m, 2]^2*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2]) - - 2*Subscript[m, 3]^2*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3]) - - 2*Subscript[m, 3]^2*(PP - Subscript[m, 3]^2)*Subscript[\[Nu], 3]*Schiebe[3, "+"] + - Subscript[m, 1]^2*(PP - Subscript[m, 1]^2 - - 3*Subscript[m, 2]^2 + 3*Subscript[m, 3]^2 - - Schiebe[2, "-"] + Schiebe[3, "-"])*Subscript[\[Nu], 1]*Schiebe[1, "+"] + - Subscript[m, 2]^2*(PP - 3*Subscript[m, 1]^2 - Subscript[m, 2]^2 + 3*Subscript[m, 3]^2 - Schiebe[1, "-"] + - Schiebe[3, "-"])*Subscript[\[Nu], 2]*Schiebe[2, "+"])* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 81] = - OperatorApplyJ[Subscript[e, 81]]; - -Subscript[h, 81] = - nuExplicit[Subscript[s, 81]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1 /. d -> d - 2; - -Subscript[f, 81] = - MakeFun[Subscript[h, 81], "(81)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 2] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - - -Subscript[h, 8123] = - Interchange[Subscript[s, 81], 2 \[LeftRightArrow] 3] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1 /. d -> d - 2; - -Subscript[f, 8123] = - MakeFun[Subscript[h, 8123], "(8123)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 1 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[h, 8113] = - Interchange[Subscript[s, 81], 1 \[LeftRightArrow] 3] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1 /. d -> d - 2; - -Subscript[f, 8113] = - MakeFun[Subscript[h, 8113], "(8113)", IFF[PP =!= 0 && Subscript[\[Nu], 2] > 1 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - - -Subscript[e, 82] = - (-PP)*Subscript[m, 1]^2*(Subscript[\[CapitalSigma], 3] + 2)* - Subscript[\[Nu], 1]*(Subscript[\[Nu], 1] + 1)*Schiebe[1, "+"]*Schiebe[1, "+"]*TJI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] + - (1/2)*PP*(Subscript[\[CapitalSigma], 3] + 2)*(Subscript[\[CapitalSigma], 3] + 4)*Subscript[\[Nu], 1]*Schiebe[1, "+"]* - TJI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - ((-(1/2))*PP^2*(d + 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3]) + - (1/2)* - PP*(Subscript[m, 1]^2*(6*Subscript[\[Nu], 1] + 6*Subscript[\[Nu], 2] + 6*Subscript[\[Nu], 3] - 7*d) + - Subscript[m, 2]^2*(7*d - 2*Subscript[\[Nu], 1] - 4*Subscript[\[Nu], 2] - 10*Subscript[\[Nu], 3]) + - Subscript[m, 3]^2*(7*d - 2*Subscript[\[Nu], 1] - 10*Subscript[\[Nu], 2] - 4*Subscript[\[Nu], 3])) + - (Subscript[m, 2]^2)^2*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2]) + (Subscript[m, 3]^2)^2* - (d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3]) + - Subscript[m, 1]^2* Subscript[m, 2]^2*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2]) + - - Subscript[m, 1]^2*Subscript[m, 3]^2*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3]) - 4*Subscript[m, 2]^2* - Subscript[m, 3]^2*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3]) - - Subscript[m, 1]^2*(2*PP^2 - PP*(2*Subscript[m, 1]^2 + Subscript[m, 2]^2 + Subscript[m, 3]^2) + - Subscript[m, 1]^2*(Subscript[m, 2]^2 + Subscript[m, 3]^2) + 3*(Subscript[m, 2]^2 - Subscript[m, 3]^2)^2)*Subscript[\[Nu], 1]*Schiebe[1, "+"] + - - Subscript[m, 2]^2*(PP^2 + (PP - Subscript[m, 2]^2)*(3*Subscript[m, 1]^2 - 5*Subscript[m, 3]^2 + Schiebe[1, "-"] - - Schiebe[3, "-"]) - (Subscript[m, 2]^2)^2)*Subscript[\[Nu], 2]*Schiebe[2, "+"] + - - Subscript[m, 3]^2*(PP^2 + (PP - Subscript[m, 3]^2)*(3*Subscript[m, 1]^2 - 5*Subscript[m, 2]^2 + Schiebe[1, "-"] - - Schiebe[2, "-"]) - (Subscript[m, 3]^2)^2)*Subscript[\[Nu], 3]*Schiebe[3, "+"] - - (1/2)*PP*(Subscript[\[CapitalSigma], 3] + 2)*(Schiebe[1, "-"] - Schiebe[2, "-"] - Schiebe[3, "-"]) - - Subscript[m, 1]^2*(Subscript[m, 2]^2 - Subscript[m, 3]^2)*Subscript[\[Nu], 1]*Schiebe[1, "+"]*(Schiebe[2, "-"] - Schiebe[3, "-"]))* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[r, 82] = - OperatorApplyJ[Subscript[e, 82]]; - -Subscript[s, 82] = - Subscript[r, 82][[1, 2]] == -Subscript[r, 82][[1, 1]] + Subscript[r, 82][[2]]; - -Subscript[h, 82] = nuExplicit[Subscript[s, 82]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 2 /. d -> d - 2; - -Subscript[f, 82] = - MakeFun[Subscript[h, 82], "(82)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 2 && m1 =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; - - -Subscript[h, 8213] = - Interchange[Subscript[s, 82], 1 \[LeftRightArrow] 3] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 2 /. d -> d - 2; - -Subscript[f, 8213] = - MakeFun[Subscript[h, 8213], "(8213)", IFF[PP =!= 0 && m3 =!= 0 && Subscript[\[Nu], 3] > 2 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[h, 8212] = - Interchange[Subscript[s, 82], 1 \[LeftRightArrow] 2] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 2 /. d -> d - 2; - -Subscript[f, 8212] = - MakeFun[Subscript[h, 8212], "(8212)", IFF[PP =!= 0 && Subscript[\[Nu], 2] > 2 && m2 =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 83] = - PP*(Subscript[\[CapitalSigma], 3] + 2)*(Subscript[\[CapitalSigma], 3] + 4)*Subscript[\[Nu], 1]* - Schiebe[1, "+"]*TJI[2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - ((-PP^2)*(d + 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3]) + - PP*(Subscript[m, 2]^2*(7*d - 2*Subscript[\[Nu], 1] - 4*Subscript[\[Nu], 2] - 10*Subscript[\[Nu], 3]) + - Subscript[m, 3]^2*(7*d - 2*Subscript[\[Nu], 1] - 10*Subscript[\[Nu], 2] - 4*Subscript[\[Nu], 3])) + - 2*(Subscript[m, 2]^2)^2*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2]) + - 2*(Subscript[m, 3]^2)^2*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 3]) - - 8*Subscript[m, 2]^2*Subscript[m, 3]^2*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3]) + - 2*Subscript[m, 2]^2*(PP^2 - (PP - Subscript[m, 2]^2)*(5*Subscript[m, 3]^2 - - Schiebe[1, "-"] + Schiebe[3, "-"]) - (Subscript[m, 2]^2)^2)*Subscript[\[Nu], 2]*Schiebe[2, "+"] + - 2*Subscript[m, 3]^2*(PP^2 - (PP - Subscript[m, 3]^2)*(5*Subscript[m, 2]^2 - Schiebe[1, "-"] + Schiebe[2, "-"]) - - (Subscript[m, 3]^2)^2)*Subscript[\[Nu], 3]*Schiebe[3, "+"] - - PP*(Subscript[\[CapitalSigma], 3] + 2)*(Schiebe[1, "-"] - Schiebe[2, "-"] - Schiebe[3, "-"]))* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 83] = - OperatorApplyJ[Subscript[e, 83]]; - -Subscript[h, 83] = - nuExplicit[Subscript[s, 83]] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 /. d -> d - 2; - -Subscript[f, 83] = - MakeFun[Subscript[h, 83], "(83)", IFF[PP =!= 0 && Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol + _Integer?Positive]], m1 :> 0]; - -Subscript[t, 1] = - Subscript[m, 1]^2 + Subscript[m, 2]^2 + Subscript[m, 3]^2; - -Subscript[t, 2] = - 3*(Subscript[m, 1]^4 + Subscript[m, 2]^4 + Subscript[m, 3]^4) + - 2*(Subscript[m, 1]^2*Subscript[m, 2]^2 + Subscript[m, 1]^2*Subscript[m, 3]^2 + - Subscript[m, 2]^2*Subscript[m, 3]^2); - -Subscript[t, 3] = - Subscript[m, 1]^2*(Subscript[m, 1]^4 - Subscript[m, 2]^4 - Subscript[m, 3]^4) + - Subscript[m, 2]^2*(Subscript[m, 2]^4 - Subscript[m, 1]^4 - Subscript[m, 3]^4) + - Subscript[m, 3]^2*(Subscript[m, 3]^4 - Subscript[m, 1]^4 - Subscript[m, 2]^4) + - 10*Subscript[m, 1]^2*Subscript[m, 2]^2*Subscript[m, 3]^2; - -f[\[Mu]1_, \[Mu]2_, \[Mu]3_] := - \[Mu]1*(PP - \[Mu]1)*(-2*(d - 4)*PP^2 + PP*(4*Subscript[t, 1]*(5*d - 18) - 24*\[Mu]1*(2*d - 7)) - - 2*(4*d - 13)*Subscript[t, 1]^2 + 2*(9*d - 31)*Subscript[t, 2] - 24*\[Mu]2*\[Mu]3*(4*d - 13) - 24*\[Mu]1^2*(2*d - 7)); - -Subscript[f, 1, 2, 3] = - f[Subscript[m, 1]^2, Subscript[m, 2]^2, Subscript[m, 3]^2]; - -Subscript[f, 2, 1, 3] = - f[Subscript[m, 2]^2, Subscript[m, 1]^2, Subscript[m, 3]^2]; - -Subscript[f, 3, 2, 1] = - f[Subscript[m, 3]^2, Subscript[m, 2]^2, Subscript[m, 1]^2]; - -g[\[Mu]1_, \[Mu]2_, \[Mu]3_] := - ((\[Mu]1*\[Mu]2)/(d - 4))*(4*(d - 4)*PP^2 - 4*(7*d - 24)*PP*(3*\[Mu]3 - 2*Subscript[t, 1]) - - Subscript[t, 1]^2*(23*d - 80) + Subscript[t, 2]*(9*d - 32) - 12*\[Mu]3^2*(d - 4) + 12*\[Mu]1*\[Mu]2*(7*d - 24)); - -Subscript[g, 1, 2, 3] = - g[Subscript[m, 1]^2, Subscript[m, 2]^2, Subscript[m, 3]^2]; - -Subscript[g, 1, 3, 2] = - g[Subscript[m, 1]^2, Subscript[m, 3]^2, Subscript[m, 2]^2]; - -Subscript[g, 2, 3, 1] = - g[Subscript[m, 2]^2, Subscript[m, 3]^2, Subscript[m, 1]^2]; - - -Subscript[e, 87] = - 3*PP*(d - 3)*(d - 4)*(3*d - 8)*(3*d - 10)*TJI[d, {1, 1, 1}] == - ((d - 4)^2*PP^3 - 2*PP^2*Subscript[t, 1]*(d - 4)*(6*d - 23) + - PP*(5*Subscript[t, 1]^2*(15*d^2 - 117*d + 224) - - Subscript[t, 2]*(42*d^2 - 331*d + 640)) - (1/4)*(d - 5)*(Subscript[t, 3]*(27*d - 90) - - Subscript[t, 1]*Subscript[t, 2]*(3*d - 2) - 2*Subscript[t, 1]^3*(5*d - 26)) + - Subscript[f, 1, 2, 3]*Schiebe[1, "+"] + - Subscript[f, 2, 1, 3]*Schiebe[2, "+"] + - Subscript[f, 3, 2, 1]*Schiebe[3, "+"] + - Subscript[g, 1, 2, 3]*Schiebe[1, "+"]*Schiebe[2, "+"]*Schiebe[3, "-"] + - Subscript[g, 1, 3, 2]*Schiebe[1, "+"]*Schiebe[2, "-"]*Schiebe[3, "+"] + - Subscript[g, 2, 3, 1]*Schiebe[1, "-"]*Schiebe[2, "+"]*Schiebe[3, "+"])*TJI[-2 + d, {1, 1, 1}]; - -Subscript[s, 87] = - OperatorApplyJ[Subscript[e, 87]]; - -Subscript[h, 87] = - Subscript[s, 87]; - -Subscript[f, 87] = - MakeFun[Subscript[h, 87], "(87)", IFF[PP =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 90] = - 3*PP*(d - 3)*(d - 4)*(3*d - 10)*Schiebe[1, "+"]*TJI[d, {1, 1, 1}] == - ((-Subscript[m, 1]^2)*(PP^2*(7*d - 24) - 2*PP*((4*d - 15)*Subscript[t, 1] - (d - 5)* - Subscript[m, 1]^2) + (3/2)*(d - 5)*Subscript[t, 1]^2 + (5/2)*(d - 3)*Subscript[t, 2] - - 2*(5*d - 17)*(Subscript[m, 1]^2)^2 - 2*(13*d - 45)*Subscript[m, 2]^2*Subscript[m, 3]^2)* - Schiebe[1, "+"] + 2*Subscript[m, 2]^2*(PP - Subscript[m, 2]^2)*((d - 3)*(PP + Subscript[m, 2]^2 - - 5*Subscript[m, 3]^2) + (7*d - 25)*Subscript[m, 1]^2)*Schiebe[2, "+"] + - 2*Subscript[m, 3]^2*(PP - Subscript[m, 3]^2)*((d - 3)*(PP - 5*Subscript[m, 2]^2 + - Subscript[m, 3]^2) + (7*d - 25)*Subscript[m, 1]^2)*Schiebe[3, "+"] - (d - 3)*(d - 4)*PP^2 + - - PP*((7*d - 30)*(d - 3)*Subscript[t, 1] - (7*d - 31)*(3*d - 10)*Subscript[m, 1]^2) + - (1/4)*(d - 5)*((17*d - 66)*Subscript[t, 1]^2 - (3*d - 14)*Subscript[t, 2] - - 4*(3*d - 10)*((Subscript[m, 1]^2)^2 + 5*Subscript[m, 2]^2*Subscript[m, 3]^2)) + - (2/(d - 4))*(((PP + Subscript[m, 2]^2)*(7*d - 24) + (d - 4)*Subscript[m, 1]^2 - - (5*d - 18)*Subscript[m, 3]^2)*Subscript[m, 1]^2*Subscript[m, 2]^2*Schiebe[1, "+"]*Schiebe[2, "+"]*Schiebe[3,"-"] + - ((PP + Subscript[m, 3]^2)*(7*d - 24) + (d - 4)*Subscript[m, 1]^2 - - (5*d - 18)*Subscript[m, 2]^2)*Subscript[m, 1]^2*Subscript[m, 3]^2*Schiebe[1, "+"]*Schiebe[2, "-"]*Schiebe[3, "+"] - - 2*((PP + Subscript[m, 2]^2 + Subscript[m, 3]^2)*(d - 3) + - (d - 4)*Subscript[m, 1]^2)*Subscript[m, 2]^2*Subscript[m, 3]^2*Schiebe[1, "-"]*Schiebe[2, "+"]*Schiebe[3, "+"]))*TJI[-2 + d, {1, 1, 1}]; - -Subscript[s, 90] = - OperatorApplyJ[Subscript[e, 90]]; - -Subscript[h, 90] = - Subscript[s, 90]; - -Subscript[f, 90] = - MakeFun[Subscript[h, 90], "(90)", IFF[PP =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 91.1] = - (d - 2)*Subscript[\[Nu], 1]*Schiebe[1, "+"]*TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (-Subscript[u, 1, 2, 3] - Schiebe[1, "-"] + Schiebe[2, "-"] + Schiebe[3, "-"])* - TKI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 91.1] = - OperatorApplyK[Subscript[e, 91.1]]; - -Subscript[e, 91.2] = - (d - 2)*Subscript[\[Nu], 2]*Schiebe[2, "+"]*Subscript[\[Nu], 3]*Schiebe[3, "+"]* - TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2],Subscript[\[Nu], 3]}] == - (-2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] + (d - 2 - 2*Subscript[\[Nu], 1]))* - TKI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 91.2] = - OperatorApplyK[Subscript[e, 91.2]]; - -Subscript[e, 91.3] = - (d - 2)*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])* - TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (-(Subscript[\[CapitalDelta], 1, 2, 3] + Subscript[u, 1, 2, 3]*Schiebe[1, "-"] + Subscript[u, 2, 1, 3]*Schiebe[2, "-"] + - Subscript[u, 3, 1, 2]*Schiebe[3, "-"])) TKI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 91.3] = - OperatorApplyK[Subscript[e, 91.3]]; - -Subscript[e, 91.4] = - Subscript[\[CapitalDelta], 1, 2, 3]*Subscript[\[Nu], 1]*Schiebe[1, "+"] TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (Subscript[u, 1, 2, 3]*(d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2]) + - 2*Subscript[m, 2]^2*(Subscript[\[Nu], 1] - Subscript[\[Nu], 2]) + - Subscript[u, 3, 1, 2]*Subscript[\[Nu], 1]*Schiebe[1, "+"] (Schiebe[2, "-"] - Schiebe[3, "-"]) + - 2*Subscript[m, 2]^2*Subscript[\[Nu], 2]*Schiebe[2, "+"]*(Schiebe[1, "-"] - Schiebe[3, "-"]))* - TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 91.4] = - OperatorApplyK[Subscript[e, 91.4]]; - -Subscript[h, 911] = - Subscript[s, 91.1] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 911] = - MakeFun[Subscript[h, 911], "(911)", IFF[Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[h, 912] = - Subscript[s, 91.2] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1 /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1; - -Subscript[f, 912] = - MakeFun[Subscript[h, 912], "(912)", IFF[Subscript[\[Nu], 2] > 1 && Subscript[\[Nu], 3] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[h, 913] = - Subscript[s, 91.3]; - -Subscript[f, 913] = - MakeFun[Subscript[h, 913], "(913)", IFF[(n2 === 1 || n3 === 1) && MatchQ[d, _Symbol + _Integer?Positive]], n1 :> 1]; - -Subscript[h, 914] = - Subscript[s, 91.4] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 914] = - MakeFun[Subscript[h, 914], "(914)", IFF[Subscript[\[CapitalDelta], 1, 2, 3] =!= 0 && Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol]]]; - - -Subscript[e, 92] = - 2*Subscript[m, 2]*Subscript[m,3]*(Subscript[m, 2] + Subscript[m, 3])*(d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - - 2*Subscript[\[Nu], 3] - 1)*Schiebe[1, "+"] TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (Subscript[m, 2]*((d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3] - 1)*(Schiebe[1, "+"]*Schiebe[2, "-"] -1) + - (Subscript[\[Nu], 1] - Subscript[\[Nu], 2] + 1)*Schiebe[1, "+"]*Schiebe[3, "-"]) + - Subscript[m, 3]*((d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2] - Subscript[\[Nu], 3] - 1)*(Schiebe[1, "+"]*Schiebe[3, "-"] - 1) + - (Subscript[\[Nu], 1] - Subscript[\[Nu], 3] + 1)*Schiebe[1, "+"]*Schiebe[2, "-"]))* - TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 92] = - OperatorApplyK[Subscript[e, 92]]; - -Subscript[e, 93] = - 2*Subscript[m, 2]^2*(d - 2*Subscript[\[Nu], 1] - 2)*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - - Subscript[\[Nu], 3] - 1)*(d - 2*Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])*Schiebe[1, "+"]* - TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (d - 2*Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3])*(d - 2*Subscript[\[Nu], 1] - - 2*Subscript[\[Nu], 2])*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - Subscript[\[Nu], 3])* - TKI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 93] = - OperatorApplyK[Subscript[e, 93]]; - -Subscript[h, 93] = - Subscript[s, 93] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 93] = - MakeFun[Subscript[h, 93], "(93)", IFF[Subscript[\[Nu], 1] > 1 && Subscript[m, 2] =!= 0], {m1 :> 0, m3 :> m2}]; - -Subscript[e, 94] = - Subscript[\[CapitalDelta], 1, 2, 6]*Subscript[\[Nu], 1]*Schiebe[1, "+"]*TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}] == - (Subscript[u, 6, 1, 2]*(Subscript[\[Nu], 1]*Schiebe[1, "+"]*Schiebe[2, "-"] - d + Subscript[\[Nu], 1] + 2*Subscript[\[Nu], 2]) + - 2*Subscript[m, 2]^2*(Subscript[\[Nu], 2]*Schiebe[2, "+"]*Schiebe[1, "-"] - d + 2*Subscript[\[Nu], 1] + Subscript[\[Nu], 2]))* - TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}]; - -Subscript[s, 94] = - OperatorApplyB[Subscript[e, 94]]; - -Subscript[h, 94] = - Subscript[s, 94] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 94] = - MakeFun[Subscript[h, 94], "(94)", IFF[Subscript[\[CapitalDelta], 1, 2, 6] =!= 0 && Subscript[\[Nu], 1] > 1]]; - -Subscript[n, 9401] = - Subscript[s, 94] /. Subscript[\[CapitalDelta], 1, 2, 6] -> 0 /. Subscript[u, 6, 1, 2] -> 0; - -Subscript[h, 9401] = - -Subscript[n, 9401][[2, 2]] == Subscript[n, 9401][[2, 1]]; - -Subscript[f, 9401] = - MakeFun[Subscript[h, 9401], "(9401)", IFF[Subscript[\[CapitalDelta], 1, 2, 6] === 0 && Subscript[u, 6, 1, 2] === 0 && m2 =!= 0]]; - -Subscript[n, 9402] = -Interchange[Subscript[s, 94] /. Subscript[\[CapitalDelta], 1, 2, 6] -> 0 /. Subscript[u, 6, 1, 2] -> 0, 1 \[LeftRightArrow] 2]; - -Subscript[h, 9402] = - -Subscript[n, 9402][[2, 1]] == Subscript[n, 9402][[2, 2]]; - -Subscript[f, 9402] = - MakeFun[Subscript[h, 9402], "(9402)", IFF[Subscript[\[CapitalDelta], 1, 2, 6] === 0 && Subscript[u, 6, 1, 2] === 0 && m1 =!= 0]]; - -Subscript[e, 95] = - 2*PP*Subscript[\[Nu], 1]*Schiebe[1, "+"] TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}] == (Subscript[u, 1, 2, 6] + - Schiebe[1, "-"] - Schiebe[2, "-"])*TBI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}]; - -Subscript[s, 95] = - OperatorApplyB[Subscript[e, 95]]; - -Subscript[h, 95] = - Subscript[s, 95] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 95] = - MakeFun[Subscript[h, 95], "(95)", IFF[Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 96] = - 2*PP*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - 1)*TBI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}] == - (Subscript[\[CapitalDelta], 1, 2, 6] + Subscript[u, 1, 2, 6]*Schiebe[1, "-"] + Subscript[u, 2, 1, 6]*Schiebe[2, "-"])* - TBI[-2 + d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2]}]; - -Subscript[s, 96] = - OperatorApplyB[Subscript[e, 96]]; - -Subscript[h, 96] = - Subscript[s, 96]; - -Subscript[f, 96] = - MakeFun[Subscript[h, 96], "(96)", IFF[MatchQ[d, _Symbol + _Integer?Positive]], n1 :> 1]; - -Subscript[e, 97] = - 2*Subscript[m, 1]^2*Subscript[\[Nu], 1]*Schiebe[1, "+"] TAI[d, {Subscript[\[Nu], 1]}] == - (d - 2*Subscript[\[Nu], 1]) TAI[d, {Subscript[\[Nu], 1]}]; - -Subscript[s, 97] = - OperatorApplyA[Subscript[e, 97]]; - -Subscript[h, 97] = - Subscript[s, 97] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 97] = - MakeFun[Subscript[h, 97], "(97)", IFF[Subscript[\[Nu], 1] > 1 && MatchQ[d, _Symbol]]]; - -Subscript[e, 98] = - (d - 2*Subscript[\[Nu], 1])*TAI[d, {Subscript[\[Nu], 1]}] == -2*Subscript[m, 1]^2* - TAI[-2 + d, {Subscript[\[Nu], 1]}]; - -Subscript[s, 98] = - OperatorApplyA[Subscript[e, 98]]; - -Subscript[h, 98] = - Subscript[s, 98]; - -Subscript[f, 98] = - MakeFun[Subscript[h, 98], "(98)", IFF[MatchQ[d, _Symbol + _Integer?Positive]]]; - -Subscript[e, 99] = - Subscript[\[Nu], 1]*(d - 2*Subscript[\[Nu], 2] - 2*Subscript[\[Nu], 3])*(d - Subscript[\[Nu], 2] - - Subscript[\[Nu], 3] - 1)*Schiebe[1, "+"]*TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (-Subscript[\[Nu], 2])*(-d + 2*Subscript[\[Nu], 2] + 2)*(-2*d + Subscript[\[Nu], 1] + 2*Subscript[\[Nu], 2] + 2*Subscript[\[Nu], 3] + 2)* - Schiebe[2, "+"]*TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 99] = - OperatorApplyJ[Subscript[e, 99]]; - -Subscript[h, 99] = - Subscript[s, 99] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1; - -Subscript[f, 99] = - MakeFun[Subscript[h, 99], "(99)", IFF[m1^2 === PP && Subscript[\[Nu], 1] > 1], {m2 :> 0, m3 :> 0}]; - -Subscript[h, 9912] = - Interchange[ Subscript[s, 99] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1, 1 \[LeftRightArrow] 2]; - -Subscript[f, 9912] = - MakeFun[Subscript[h, 9912], "(9912)", IFF[m2^2 === PP && Subscript[\[Nu], 2] > 1], {m1 :> 0, m3 :> 0}]; - -Subscript[h, 9913] = - Interchange[Subscript[s, 99] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1, 1 \[LeftRightArrow] 3]; - -Subscript[f, 9913] = - MakeFun[Subscript[h, 9913], "(9913)", IFF[m3^2 === PP && Subscript[\[Nu], 3] > 1], {m1 :> 0, m2 :> 0}]; - -Subscript[e, 100] = - 2*Subscript[m, 2]^2*(1 - Subscript[\[Nu], 2])*Subscript[\[Nu], 2]*Schiebe[2, "+"]* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] == - (d - 2*Subscript[\[Nu], 2])*(1 - Subscript[\[Nu], 2])*TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}] - - Subscript[\[Nu], 1]*(-d + 2*Subscript[\[Nu], 1] + 2)*Schiebe[1, "+"]*Schiebe[2, "-"]* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], Subscript[\[Nu], 3]}]; - -Subscript[s, 100] = - OperatorApplyJ[Subscript[e, 100]]; - -Subscript[h, 100] = - Subscript[s, 100]; - -Subscript[f, 100] = - MakeFun[Subscript[h, 100] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1, "(100)", IFF[Subscript[\[Nu], 2] > 2 && m2 =!= 0], m1 :> 0]; - -Subscript[h, 1002] = - Interchange[Subscript[s, 100], 1 \[LeftRightArrow] 3]; - -Subscript[f, 1002] = - MakeFun[Subscript[h, 1002] /. Subscript[\[Nu], 2] -> Subscript[\[Nu], 2] - 1, "(1002)", IFF[Subscript[\[Nu], 2] > 2 && m2 =!= 0], m3 :> 0]; - -Subscript[h, 1003] = - Interchange[Subscript[s, 100], 1 \[LeftRightArrow] 3, 1 \[LeftRightArrow] 2]; - -Subscript[f, 1003] = - MakeFun[Subscript[h, 1003] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1, "(1003)", IFF[Subscript[\[Nu], 1] > 2 && m1 =!= 0], m3 :> 0]; - -Subscript[h, 1004] = - Interchange[Subscript[s, 100], 1 \[LeftRightArrow] 2]; - -Subscript[f, 1004] = - MakeFun[Subscript[h, 1004] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1, "(1004)", IFF[Subscript[\[Nu], 1] > 2 && m1 =!= 0], m2 :> 0]; - -Subscript[h, 1005] = - Interchange[Subscript[s, 100], 2 \[LeftRightArrow] 3]; - -Subscript[f, 1005] = - MakeFun[Subscript[h, 1005] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1, "(1005)", - IFF[Subscript[\[Nu], 3] > 2 && m3 =!= 0], m1 :> 0]; - -Subscript[h, 1006] = - Interchange[Subscript[s, 100], 2 \[LeftRightArrow] 3, 1 \[LeftRightArrow] 2]; - -Subscript[f, 1006] = - MakeFun[Subscript[h, 1006] /. Subscript[\[Nu], 3] -> Subscript[\[Nu], 3] - 1, "(1006)", IFF[Subscript[\[Nu], 3] > 2 && m3 =!= 0], m2 :> 0]; - -Subscript[s, 150] = - TFI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {-1, m4}, {n5, m5}}] == - TFI[d, PP, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}, {n5, m5}}] - - 2*TFI[d, PP, {0, 0, 0, 1, 0}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}] + (PP + m2^2 - m4^2)* - TFI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}]; - -Subscript[h, 150] = - Subscript[s, 150]; - -Subscript[f, 150] = - MakeFun[Subscript[h, 150], "(150)"]; - -Subscript[s, 151] = - TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2, m2}, {n3, m3}, {-1, m4}, {n5, m5}}] == - TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}, {n5, m5}}] - - 2*TFI[d, PP, DP, {a, b}, {0, 0, 0, 1, 0}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}] + - (PP + m2^2 - m4^2)*TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}]; - -Subscript[h, 151] = - Subscript[s, 151]; - -Subscript[f, 151] = - ReplacePart[MakeFun[Subscript[h, 151], "(151)"], {a_, b_}, {1, 1, 4}]; - -Subscript[s, 152] = - TVI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {-1, m4}}] == - TVI[d, PP, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}}] - - 2*TFI[d, PP, {0, 0, 0, 1, 0}, {{0, 0}, {n2, m2}, {n3, m3}, {0, 0}, {n1, m1}}] + - (PP + m2^2 - m4^2)*TVI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}}]; - -Subscript[h, 152] = - Subscript[s, 152]; - -Subscript[f, 152] = - MakeFun[Subscript[h, 152], "(152)"]; - -Subscript[s, 153] = - TVI[d, PP, {{n1, m1}, {-1, m2}, {n3, m3}, {n4, m4}}] == - TFI[d, PP, {0, 1, 0, 0, 0}, {{0, 0}, {0, 0}, {n3, m3}, {n4, m4}, {n1, m1}}] + - m2^2*TVI[d, PP, {{n1, m1}, {0, 0}, {n3, m3}, {n4, m4}}]; - -Subscript[h, 153] = - Subscript[s, 153]; - -Subscript[f, 153] = - MakeFun[Subscript[h, 153], "(153)"]; - -Subscript[s, 200] = - 16*Subscript[m, 1]^2* - Subscript[\[Nu], - 1]*(d - Subscript[\[Nu], 1] - Subscript[\[Nu], 2] - - Subscript[\[Nu], 3])* - TJI[d, {1 + Subscript[\[Nu], 1], Subscript[\[Nu], 2], - Subscript[\[Nu], 3]}] == - (-(1 + 3*d - 3*Subscript[\[Nu], 1] - 4*Subscript[\[Nu], 2]))* - Subscript[\[Nu], 3]* - TJI[d, {-1 + Subscript[\[Nu], 1], Subscript[\[Nu], 2], - 1 + Subscript[\[Nu], 3]}] - - Subscript[\[Nu], - 2]*(1 + 3*d - 3*Subscript[\[Nu], 1] - 4*Subscript[\[Nu], 3])* - TJI[d, {-1 + Subscript[\[Nu], 1], 1 + Subscript[\[Nu], 2], - Subscript[\[Nu], 3]}] + - (-1 + 2*d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 2])* - Subscript[\[Nu], 3]* - TJI[d, {Subscript[\[Nu], 1], -1 + Subscript[\[Nu], 2], - 1 + Subscript[\[Nu], 3]}] - - (-6*d^2 + 22*d*Subscript[\[Nu], 1] - - 16*Subscript[\[Nu], 1]^2 - Subscript[\[Nu], 2] + - 6*d*Subscript[\[Nu], 2] - - 13*Subscript[\[Nu], 1]*Subscript[\[Nu], 2] - - Subscript[\[Nu], 3] + 6*d*Subscript[\[Nu], 3] - - 13*Subscript[\[Nu], 1]*Subscript[\[Nu], 3] - - 4*Subscript[\[Nu], 2]*Subscript[\[Nu], 3])* - TJI[d, {Subscript[\[Nu], 1], Subscript[\[Nu], 2], - Subscript[\[Nu], 3]}] + - Subscript[\[Nu], - 2]*(-1 + 2*d - Subscript[\[Nu], 1] - 2*Subscript[\[Nu], 3])* - TJI[d, {Subscript[\[Nu], 1], - 1 + Subscript[\[Nu], 2], -1 + Subscript[\[Nu], 3]}]; -Subscript[h, 200] = -Subscript[s, 200] /. Subscript[\[Nu], 1] -> Subscript[\[Nu], 1] - 1 -Subscript[f, 200] = -MakeFun[Subscript[h, 200], "(200)", - IFF[Subscript[\[Nu], 1] > 1 && m1 =!= 0 && PP === m1^2], {m2 :> m1, m3 :> m1}]; - -Subscript[f, 201] = - HoldForm[TJR[d_, PP_, {{(n1_)?PQ, 0}, {(n2_)?PQ, 0}, {(n3_)?PQ, m3_}}] := - ( - TComment["(201)", TJIC[d, {{n1, 0}, {n2, 0}, {n3, m3}}]]; - -(((d - n1 - n2)*(-2 - d + 2*n1 + 2*n2)*(3*d - 2*n1 - 2*n2 - 2*n3)*(-1 - d + n1 + n2 + n3)* - TJI[d, PP, {{-1 + n1, 0}, {n2, 0}, {n3, m3}}])/(2*m3^2*(d - 2*n1)*(-1 + n1)*(2*d - 2*n1 - 2*n2 - n3)*(1 + - 2*d - 2*n1 - 2*n2 - n3))) - ) /; n1 > 1 && m3 =!= 0 && PP === m3^2]; - -Subscript[f, 202] = - HoldForm[TJR[d_, PP_, {{(n1_)?PQ, 0}, {(n3_)?PQ, m3_}, {(n2_)?PQ, 0}}] := - ( - TComment["(202)", TJIC[d, {{n1, 0}, {n2, 0}, {n3, m3}}]]; - -(((d - n1 - n2)*(-2 - d + 2*n1 + 2*n2)*(3*d - 2*n1 - 2*n2 - 2*n3)*(-1 - d + n1 + n2 + n3)* - TJI[d, m3^2, {{-1 + n1, 0}, {n2, 0}, {n3, m3}}])/(2*m3^2*(d - 2*n1)*(-1 + n1)*(2*d - 2*n1 - 2*n2 - n3)*(1 + - 2*d - 2*n1 - 2*n2 - n3)))) /; n1 > 1 && m3 =!= 0 && PP === m3^2]; - -Subscript[f, 203] = - HoldForm[TJR[d_, 0, {{(n1_)?PQ, 0}, {(n2_)?PQ, m2_}, {(n3_)?PQ, m2_}}] := - ( - TComment["(203)", TJIC[d, 0, {{n1, 0}, {n2, m2}, {n3, m2}}]]; - ((d - 2*(-1 + n1 + n2))*(1 + d - n1 - n2 - n3)*(d - 2*(-1 + n1 + n3))* - TJR[d, 0, {{-1 + n1, 0}, {n2, m2}, {n3, m2}}])/(2*m2^2*(d - 2*n1)*(1 + d - 2*n1 - n2 - n3)*(2 + d - 2*n1 - n2 - n3)))]; - - -Subscript[f, 204] = - HoldForm[TJR[d_, 0, {{(n2_)?PQ, m2_}, {(n1_)?PQ, 0}, {(n3_)?PQ, m2_}}] := - ( - TComment["(204)", TJIC[d, 0, {{n2, m2}, {n1, 0}, {n3, m2}}]]; - ((d - 2*(-1 + n1 + n2))*(1 + d - n1 - n2 - n3)*(d - 2*(-1 + n1 + n3))* - TJR[d, 0, {{-1 + n1, 0}, {n2, m2}, {n3, m2}}])/(2*m2^2*(d - 2*n1)*(1 + d - 2*n1 - n2 - n3)*(2 + d - 2*n1 - n2 - n3)))]; - -Subscript[f, 205] = - HoldForm[TJR[d_, - 0, {{(n2_)?PQ, m2_}, {(n3_)?PQ, m2_}, {(n1_)?PQ, 0}}] := - ( - TComment["(205)", TJIC[d, 0, {{n2, m2}, {n3, m2}, {n1, 0}}]]; - ((d - 2*(-1 + n1 + n2))*(1 + d - n1 - n2 - n3)*(d - 2*(-1 + n1 + n3))* - TJR[d, 0, {{-1 + n1, 0}, {n2, m2}, {n3, m2}}])/(2* m2^2*(d - 2*n1)*(1 + d - 2*n1 - n2 - n3)*(2 + d - 2*n1 - n2 - n3)))]; - -If[ MatchQ[$RankLimit, {_Integer?NonNegative, _Integer? NonNegative}], - $TarasovTdeltaplimit = $RankLimit[[1]]; - $TarasovTplimit = $RankLimit[[2]], - - $TarasovTdeltaplimit = 2; - $TarasovTplimit = 2 -]; - -tarti = - Timing[ - ia = 0; - ib = 0; - ir = 0; - es = 0; - Do[ - If[ 0 < ia + ib + ir + es, - WriteString["stdout", {ia, ib, ir, es}]; - Set @@ {Subscript[s, 10^4 + 1000*ia + 100*ib + 10*ir + es], - - TFI[d, PP, DP, {ia, ib}, {0, 0, ir, es, 0}, {{n1, m1}, {n2, m2}, {n3, m3}, {n4, m4}, {n5, m5}}] == - ApplyTarasovT[TarasovT[ia, ib, ir, es, PP, DP], - - STLI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {n4, m4}, {n5, m5}}]] /. STLI -> TFI} - ], - {ia, 0, $TarasovTdeltaplimit}, {ib, 0, $TarasovTdeltaplimit - ia}, {ir, 0, $TarasovTplimit}, {es, 0, $TarasovTplimit - ir} - ] - ]; - -matarti = - Timing[ - ia = 0; - ib = 0; - ir = 0; - es = 0; - Do[ - If[0 < ia + ib + ir + es, - WriteString["stdout", {ia, ib, ir, es}]; - Subscript[f, 10^4 + 1000*ia + 100*ib + 10*ir + es] = - MakeFun[Subscript[s, 10^4 + 1000*ia + 100*ib + 10*ir + es], - StringJoin["(1", ToString[ia], ToString[ib], ToString[ir], ToString[es], ")"]] /. PQ :> PNQ - ], - {ia, 0, $TarasovTdeltaplimit}, {ib, 0, $TarasovTdeltaplimit - ia}, {ir, 0, $TarasovTplimit}, {es, 0, $TarasovTplimit - ir} - ] - ] - -(*TODO ...*) -Share[] - -TVR[2 + (d_Symbol), pp_, {{1, m1_}, {1, m1_}, {2, 0}, {1, m1_}}] := - ((-6*m1^2 + 2*d*m1^2 + 3*pp)*TAI[d, 0, {{1, m1}}]^2)/(12*(-3 + d)*(-1 + d)*m1^2*pp) + - ((4*m1^2 - pp)*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/(4*(-3 + d)*(-1 + d)* m1^2) - - ((6*m1^2 - 2*d*m1^2 - 7*pp + 2*d*pp)*TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(6*(-2 + d)*(-1 + d)*pp) + - ((-4*m1^2 + pp)*(-6*m1^2 + 2*d*m1^2 + 3*pp)*TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(6*(-3 + d)*(-2 + d)*(-1 + d)*pp) /; m1 =!= 0 && pp =!= 0; - -TVR[4 + (d_Symbol), pp_, {{1, m1_}, {1, m1_}, {2, 0}, {1, m1_}}] := - -((-96*d*m1^6 + 352*d^2*m1^6 - 384*d^3*m1^6 + 128*d^4*m1^6 - - 192*m1^4*pp + 1008*d*m1^4*pp - 1632*d^2*m1^4*pp + - 912*d^3*m1^4*pp - 144*d^4*m1^4*pp + 288*m1^2*pp^2 - - 1536*d*m1^2*pp^2 + 2316*d^2*m1^2*pp^2 - 1086*d^3*m1^2*pp^2 + 66*d^4*m1^2*pp^2 + 72*d*pp^3 - 166*d^2*pp^3 + 81*d^3*pp^3 + - 4*d^4*pp^3)*TAI[d, 0, {{1, m1}}]^2)/ (36*(-1 + d)^2*d^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)* pp^2) + - ((4*m1^2 - pp)^2*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/(4*(-1 + d)^2*d*(1 + d)) - - ((288*m1^8 - 1152*d*m1^8 + 1504*d^2*m1^8 - 768*d^3*m1^8 + 128*d^4*m1^8 - 816*m1^6*pp + 2480*d*m1^6*pp - - 2224*d^2*m1^6*pp + 736*d^3*m1^6*pp - 80*d^4*m1^6*pp + 864*m1^4*pp^2 - 2196*d*m1^4*pp^2 + - 1446*d^2*m1^4*pp^2 - 252*d^3*m1^4*pp^2 - 6*d^4*m1^4*pp^2 - 432*m1^2*pp^3 + 1086*d*m1^2*pp^3 - - 895*d^2*m1^2*pp^3 + 315*d^3*m1^2*pp^3 - 44*d^4*m1^2*pp^3 + 4*d*pp^4 - 2*d^2*pp^4 - 4*d^3*pp^4 + 2*d^4*pp^4)* - TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(18*(-2 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) + - (m1^2*(4*m1^2 - pp)*(-96*m1^6 + 352*d*m1^6 - 384*d^2*m1^6 + 128*d^3*m1^6 + 240*m1^4*pp - 624*d*m1^4*pp + - 384*d^2*m1^4*pp - 48*d^3*m1^4*pp - 192*m1^2*pp^2 + 420*d*m1^2*pp^2 - 162*d^2*m1^2*pp^2 - - 18*d^3*m1^2*pp^2 + 72*pp^3 - 154*d*pp^3 + 81*d^2*pp^3 - 8*d^3*pp^3)* - TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(18*(-2 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) /; m1 =!= 0 && pp =!= 0; - -TVR[4 + (d_Symbol), pp_, {{1, m1_}, {1, m1_}, {3, 0}, {1, m1_}}] := - ((-72*d^2*m1^6 + 144*d^3*m1^6 - 88*d^4*m1^6 + 16*d^5*m1^6 - - 240*d*m1^4*pp + 572*d^2*m1^4*pp - 398*d^3*m1^4*pp + - 84*d^4*m1^4*pp - 2*d^5*m1^4*pp - 96*m1^2*pp^2 + 480*d*m1^2*pp^2 - - 744*d^2*m1^2*pp^2 + 390*d^3*m1^2*pp^2 - 50*d^4*m1^2*pp^2 + 4*d^5*m1^2*pp^2 - 24*d*pp^3 + - 54*d^2*pp^3 - 27*d^3*pp^3)*TAI[d, 0, {{1, m1}}]^2)/ (24*(-3 + d)*(-1 + d)^2*d*(1 + d)*(-4 + 3*d)*(-2 + 3*d)* - m1^2*pp^2) + ((4*m1^2 - pp)^2*TAI[d, 0, {{1, m1}}]* TBI[d, pp, {{1, m1}, {1, m1}}])/(8*(-3 + d)*(-1 + d)^2*(1 + d)* m1^2) + - ((-72*d*m1^6 + 144*d^2*m1^6 - 88*d^3*m1^6 + 16*d^4*m1^6 - 96*m1^4*pp + 260*d*m1^4*pp - 166*d^2*m1^4*pp + - 12*d^3*m1^4*pp + 6*d^4*m1^4*pp + 160*m1^2*pp^2 - 300*d*m1^2*pp^2 + 50*d^2*m1^2*pp^2 + - 90*d^3*m1^2*pp^2 - 24*d^4*m1^2*pp^2 - 48*pp^3 + 114*d*pp^3 - 67*d^2*pp^3 + 4*d^3*pp^3 + 2*d^4*pp^3)* - TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ (12*(-2 + d)*(-1 + d)^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)* pp^2) - - ((-4*m1^2 + pp)*(72*d*m1^6 - 144*d^2*m1^6 + 88*d^3*m1^6 - 16*d^4*m1^6 + 96*m1^4*pp - 236*d*m1^4*pp + - 122*d^2*m1^4*pp + 12*d^3*m1^4*pp - 10*d^4*m1^4*pp - 96*m1^2*pp^2 + - 180*d*m1^2*pp^2 - 30*d^2*m1^2*pp^2 - 46*d^3*m1^2*pp^2 + 8*d^4*m1^2*pp^2 + 24*pp^3 - 54*d*pp^3 + 27*d^2*pp^3)* - TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(12*(-3 + d)*(-2 + d)*(-1 + d)^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) /; m1 =!= 0 && pp =!= 0; - -TVR[6 + (d_Symbol), pp_, {{1, m1_}, {1, m1_}, {4, 0}, {1, m1_}}] := - ((2304*d*m1^10 - 4608*d^2*m1^10 - 3520*d^3*m1^10 + 6976*d^4*m1^10 + 1472*d^5*m1^10 - 2624*d^6*m1^10 - - 256*d^7*m1^10 + 256*d^8*m1^10 + 4608*m1^8*pp - - 9600*d*m1^8*pp - 7680*d^2*m1^8*pp + 9312*d^3*m1^8*pp + 11680*d^4*m1^8*pp - - 6560*d^5*m1^8*pp - 2880*d^6*m1^8*pp + 1088*d^7*m1^8*pp + - 32*d^8*m1^8*pp + 6912*m1^6*pp^2 - 35712*d*m1^6*pp^2 + 1056*d^2*m1^6*pp^2 + - 85296*d^3*m1^6*pp^2 - 37032*d^4*m1^6*pp^2 - 20484*d^5*m1^6*pp^2 + 8700*d^6*m1^6*pp^2 - - 12*d^7*m1^6*pp^2 - 84*d^8*m1^6*pp^2 - 20736*m1^4*pp^3 + 58752*d*m1^4*pp^3 + 40560*d^2*m1^4*pp^3 - - 150536*d^3*m1^4*pp^3 + 18980*d^4*m1^4*pp^3 + 48946*d^5*m1^4*pp^3 - 6748*d^6*m1^4*pp^3 - - 146*d^7*m1^4*pp^3 + 128*d^8*m1^4*pp^3 + 3456*m1^2*pp^4 - 13824*d*m1^2*pp^4 - 4176*d^2*m1^2*pp^4 + - 35784*d^3*m1^2*pp^4 - 8332*d^4*m1^2*pp^4 - 10162*d^5*m1^2*pp^4 + 1122*d^6*m1^2*pp^4 - - 80*d^7*m1^2*pp^4 - 8*d^8*m1^2*pp^4 + 864*d*pp^5 - 216*d^2*pp^5 - 2268*d^3*pp^5 + 486*d^4*pp^5 + 729*d^5*pp^5)* - TAI[d, 0, {{1, m1}}]^2)/(432*(-3 + d)*(-1 + d)^2* d^2*(1 + d)*(2 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)* m1^2*pp^3) + - ((4*m1^2 - pp)^3*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/(16*(-3 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*m1^2) - - ((-1152*m1^10 + 2880*d*m1^10 + 320*d^2*m1^10 - 3648*d^3*m1^10 + 1088*d^4*m1^10 + 768*d^5*m1^10 - - 256*d^6*m1^10 - 192*m1^8*pp + 1312*d*m1^8*pp + 2080*d^2*m1^8*pp - 6880*d^3*m1^8*pp + 4032*d^4*m1^8*pp - 192*d^5*m1^8*pp - - 160*d^6*m1^8*pp + 6336*m1^6*pp^2 - 6960*d*m1^6*pp^2 - 16960*d^2*m1^6*pp^2 + 17292*d^3*m1^6*pp^2 - - 1828*d^4*m1^6*pp^2 - 828*d^5*m1^6*pp^2 + 68*d^6*m1^6*pp^2 - 9504*m1^4*pp^3 + - 3624*d*m1^4*pp^3 + 26104*d^2*m1^4*pp^3 - 10938*d^3*m1^4*pp^3 - 4976*d^4*m1^4*pp^3 + - 330*d^5*m1^4*pp^3 + 400*d^6*m1^4*pp^3 + 6336*m1^2*pp^4 - 3640*d*m1^2*pp^4 - 14584*d^2*m1^2*pp^4 + - 9190*d^3*m1^2*pp^4 + 1374*d^4*m1^2*pp^4 - 600*d^5*m1^2*pp^4 - 56*d^6*m1^2*pp^4 - 864*pp^5 + - 732*d*pp^5 + 1864*d^2*pp^5 - 1695*d^3*pp^5 + 148*d^4*pp^5 + 36*d^5*pp^5 + 4*d^6*pp^5)* - TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(216*(-2 + d)*(-1 + d)^2* - d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)*pp^3) + - ((-4*m1^2 + pp)*(1152*m1^10 - 2880*d*m1^10 - 320*d^2*m1^10 + - 3648*d^3*m1^10 - 1088*d^4*m1^10 - 768*d^5*m1^10 + - 256*d^6*m1^10 + 576*m1^8*pp - 2208*d*m1^8*pp - 2304*d^2*m1^8*pp + - 8000*d^3*m1^8*pp - 4256*d^4*m1^8*pp - 32*d^5*m1^8*pp + 224*d^6*m1^8*pp - 6336*m1^6*pp^2 + - 6288*d*m1^6*pp^2 + 16320*d^2*m1^6*pp^2 - 14868*d^3*m1^6*pp^2 + 684*d^4*m1^6*pp^2 + - 804*d^5*m1^6*pp^2 - 12*d^6*m1^6*pp^2 + 6912*m1^4*pp^3 - 3192*d*m1^4*pp^3 - 18160*d^2*m1^4*pp^3 + - 7950*d^3*m1^4*pp^3 + 3128*d^4*m1^4*pp^3 - 78*d^5*m1^4*pp^3 - 160*d^6*m1^4*pp^3 - - 3456*m1^2*pp^4 + 1800*d*m1^2*pp^4 + 8136*d^2*m1^2*pp^4 - 4322*d^3*m1^2*pp^4 - - 1042*d^4*m1^2*pp^4 + 128*d^5*m1^2*pp^4 + 16*d^6*m1^2*pp^4 + 432*pp^5 - 324*d*pp^5 - 972*d^2*pp^5 + 729*d^3*pp^5)* - TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(216*(-3 + d)*(-2 + d)*(-1 + d)^2* - d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)*pp^3) /; m1 =!= 0 && pp =!= 0; - -TVR[6 + (d_Symbol), pp_, {{2, m1_}, {1, m1_}, {3, 0}, {1, m1_}}] := - -((-1536*d*m1^10 + 2560*d^2*m1^10 + 3200*d^3*m1^10 - - 3584*d^4*m1^10 - 2176*d^5*m1^10 + 1024*d^6*m1^10 + - 512*d^7*m1^10 - 3072*m1^8*pp + 6528*d*m1^8*pp + 5376*d^2*m1^8*pp - 7520*d^3*m1^8*pp - - 5568*d^4*m1^8*pp + 3232*d^5*m1^8*pp + 1344*d^6*m1^8*pp - 320*d^7*m1^8*pp - 2304*m1^6*pp^2 + - 13824*d*m1^6*pp^2 + 192*d^2*m1^6*pp^2 - 31584*d^3*m1^6*pp^2 + 11232*d^4*m1^6*pp^2 + - 8088*d^5*m1^6*pp^2 - 2304*d^6*m1^6*pp^2 - 24*d^7*m1^6*pp^2 + 6912*m1^4*pp^3 - 19584*d*m1^4*pp^3 - - 12688*d^2*m1^4*pp^3 + 50584*d^3*m1^4*pp^3 - 7516*d^4*m1^4*pp^3 - 16982*d^5*m1^4*pp^3 + - 2564*d^6*m1^4*pp^3 + 310*d^7*m1^4*pp^3 - 1152*m1^2*pp^4 + 4608*d*m1^2*pp^4 + 1392*d^2*m1^2*pp^4 - - 11896*d^3*m1^2*pp^4 + 2820*d^4*m1^2*pp^4 + 3374*d^5*m1^2*pp^4 - 414*d^6*m1^2*pp^4 + - 8*d^7*m1^2*pp^4 - 288*d*pp^5 + 72*d^2*pp^5 + 756*d^3*pp^5 - 162*d^4*pp^5 - 243*d^5*pp^5)* - TAI[d, 0, {{1, m1}}]^2)/(144*(-1 + d)^2*d^2*(1 + d)*(2 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)* - m1^2*pp^3) + ((4*m1^2 - pp)^3*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/(16*(-1 + d)^2* - d*(1 + d)*(3 + d)*m1^2) - ((2304*m1^10 - 5760*d*m1^10 - 640*d^2*m1^10 + 7296*d^3*m1^10 - 2176*d^4*m1^10 - 1536*d^5*m1^10 + - 512*d^6*m1^10 - 1344*m1^8*pp + 1120*d*m1^8*pp - 1376*d^2*m1^8*pp + 5280*d^3*m1^8*pp - 4896*d^4*m1^8*pp + 1280*d^5*m1^8*pp - - 64*d^6*m1^8*pp - 5184*m1^6*pp^2 + 7584*d*m1^6*pp^2 + 14800*d^2*m1^6*pp^2 - 21496*d^3*m1^6*pp^2 + - 6120*d^4*m1^6*pp^2 + 280*d^5*m1^6*pp^2 - 184*d^6*m1^6*pp^2 + 9504*m1^4*pp^3 - - 3720*d*m1^4*pp^3 - 27296*d^2*m1^4*pp^3 + 15378*d^3*m1^4*pp^3 + 4114*d^4*m1^4*pp^3 - - 666*d^5*m1^4*pp^3 - 674*d^6*m1^4*pp^3 - 6336*m1^2*pp^4 + 5720*d*m1^2*pp^4 + 13712*d^2*m1^2*pp^4 - - 13926*d^3*m1^2*pp^4 + 1284*d^4*m1^2*pp^4 + 946*d^5*m1^2*pp^4 - 80*d^6*m1^2*pp^4 + 864*pp^5 - - 1020*d*pp^5 - 1636*d^2*pp^5 + 2311*d^3*pp^5 - 693*d^4*pp^5 + 20*d^5*pp^5 + 4*d^6*pp^5)* - TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/(72*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)*pp^3) + - ((4*m1^2 - pp)*(-768*m1^10 + 1664*d*m1^10 + 768*d^2*m1^10 - 2176*d^3*m1^10 + 512*d^5*m1^10 + 192*m1^8*pp + - 288*d*m1^8*pp + 704*d^2*m1^8*pp - 2272*d^3*m1^8*pp + 1024*d^4*m1^8*pp + - 64*d^5*m1^8*pp + 1920*m1^6*pp^2 - 1824*d*m1^6*pp^2 - 5472*d^2*m1^6*pp^2 + 4584*d^3*m1^6*pp^2 - - 168*d^5*m1^6*pp^2 - 2304*m1^4*pp^3 + 616*d*m1^4*pp^3 + 6192*d^2*m1^4*pp^3 - - 1946*d^3*m1^4*pp^3 - 1128*d^4*m1^4*pp^3 - 230*d^5*m1^4*pp^3 + 1152*m1^2*pp^4 - 600*d*m1^2*pp^4 - - 2744*d^2*m1^2*pp^4 + 1414*d^3*m1^2*pp^4 + 374*d^4*m1^2*pp^4 - 16*d^5*m1^2*pp^4 - 144*pp^5 + - 108*d*pp^5 + 324*d^2*pp^5 - 243*d^3*pp^5)*TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/(72*(-2 + d)*(-1 + d)^2* - d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)*(2 + 3*d)*pp^3) /; m1 =!= 0 && pp =!= 0; - -TFR[d_, PP_ /; Head[PP] =!= List, {{0, _}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] := - TVI[d, PP, {{n5, m5}, {n2, m2}, {n3, m3}, {n4, m4}}]; - -TFR[d_, PP_ /; Head[PP] =!= List, {{n2_, m2_}, {0, _}, {n4_, m4_}, {n3_, m3_}, {n5_, m5_}}] := - TVI[d, PP, {{n5, m5}, {n2, m2}, {n3, m3}, {n4, m4}}]; - -TFR[d_, PP_ /; Head[PP] =!= List, {{n3_, m3_}, {n4_, m4_}, {0, _}, {n2_, m2_}, {n5_, m5_}}] := - TVI[d, PP, {{n5, m5}, {n2, m2}, {n3, m3}, {n4, m4}}]; - -TFR[d_, PP_ /; Head[PP] =!= List, {{n4_, m4_}, {n3_, m3_}, {n2_, m2_}, {0, _}, {n5_, m5_}}] := - TVI[d, PP, {{n5, m5}, {n2, m2}, {n3, m3}, {n4, m4}}]; - -TFR[d_, PP_ /; Head[PP] =!= List, {{n1_, m1_}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}, {0, _}}] := - TBI[d, PP, {{n1, m1}, {n3, m3}}]*TBI[d, PP, {{n2, m2}, {n4, m4}}]; - -TVI[d_, PP_, {{0, _}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}}] := - TAI[d, 0, {{n3, m3}}]*TBI[d, PP, {{n2, m2}, {n4, m4}}]; - -TVI[d_, PP_, {{n1_, m1_}, {n2_, m2_}, {0, _}, {n4_, m4_}}] := - TAI[d, 0, {{n1, m1}}]*TBI[d, PP, {{n2, m2}, {n4, m4}}]; - -TVI[d_, _, {{n1_, m1_}, {0, _}, {n3_, m3_}, {n4_, m4_}}] := - TJI[d, 0, {{n1, m1}, {n3, m3}, {n4, m4}}]; - -TVI[d_, PP_, {{n1_, m1_}, {n2_, m2_}, {n3_, m3_}, {0, _}}] := - TJI[d, PP, {{n2, m2}, {n1, m1}, {n3, m3}}]; - -TJI[d_, _, {{0, _}, {n2_, m2_}, {n3_, m3_}}] := - TAI[d, 0, {{n2, m2}}]*TAI[d, 0, {{n3, m3}}]; - -TJI[d_, _, {{n1_, m1_}, {0, _}, {n3_, m3_}}] := - TAI[d, 0, {{n1, m1}}]*TAI[d, 0, {{n3, m3}}]; - -TJI[d_, _, {{n1_, m1_}, {n2_, m2_}, {0, _}}] := - TAI[d, 0, {{n1, m1}}]*TAI[d, 0, {{n2, m2}}]; - -TBI[d_, _, {{0, _}, {n2_, m2_}}] := - TAI[d, 0, {{n2, m2}}]; - -TBI[d_, _, {{n1_, m1_}, {0, _}}] := - TAI[d, 0, {{n1, m1}}]; - -TAI[d_, {{n_Integer, m_}}] := - TAI[d, 0, {{n, m}}]; - -TAI[d_, {n_Integer, m_}] := - TAI[d, 0, {{n, m}}]; - -TAI[d_, 0, {n_Integer, m_}] := - TAI[d, 0, {{n, m}}]; - -$TLRComment = False; -TLRComment[s_String] := - WriteString["stdout", s, " "] /; $TLRComment === True; - -applytlrules[y_, fun_] := - fun[y /. TFI -> TLR /. TLRules /. TLR -> TFI]; - -TFIRecurse[z_, f_: Identity] := - (FixedPoint[(applytlrules[#1, f] ) & , z, 1000] /. TAI[dim_, pp_, list_List]/;pp=!=0:>TAI[dim,0,list]); - -applytlrules2[y_, fun_] := - fun[y /. TFI -> TLR /. TLRules2 /. TLR -> TFI]; - -TFISimplify[z_, f_: Identity] := - (FixedPoint[applytlrules2[#1, f] & , z, 1000]/. TAI[dim_, pp_, list_List]/;pp=!=0:>TAI[dim,0,list]); - -ExpandMaybe = - Identity; - -fN[li_List] := fN[li] = li /. {0, _} :> {0, 0}; -TLR[depp__, {a___, b_Integer, c___}] := TLR[depp, {a, {b, 0}, c}]; - -tlrule[1] = - TLR[d_, pp_, {0, 0, 0, 0, 0}, pr_] :> (NoTLRComment["tlrule1"]; TFI[d, pp, pr /. {0, _} :> {0, 0}] ); - -tlrule[2] = - TLR[dpp__, {(v_)?PQ, w_, x_, y_, z_}, {{(n1_)?PQ, m1_}, nm2_, nm3_, nm4_, nm5_}] :> - ( - TLRComment["tlrule2"]; - ExpandMaybe[ - If[ v <= n1, - If[ m1 === 0, - TLR[dpp, {0, w, x, y, z}, {{n1 - v, 0}, nm2, nm3, nm4, nm5}], - Sum[Binomial[v, i] TLR[dpp, {0, w, x, y, z}, {fN[{n1 - i, m1}], nm2, nm3, nm4, nm5}]*(m1^2)^(v - i), {i, 0, v}] - ], - If[ m1 === 0, - TLR[dpp, {v - n1, w, x, y, z}, {{0, 0}, nm2, nm3, nm4, nm5}], - Sum[Binomial[n1, i] TLR[dpp, {v - n1, w, x, y, z}, {fN[{n1 - i, m1}], nm2, nm3, nm4, nm5}]*(m1^2)^(n1 - i), {i, 0, n1}] - ] - ] - ] - ); - -tlrule[3] = - TLR[dpp__, {v_, (w_)?PQ, x_, y_, z_}, {nm1_, {(n2_)?PQ, m2_}, nm3_, nm4_, nm5_}] :> - ( - TLRComment["tlrule3"]; - ExpandMaybe[ - If[ w <= n2, - If[ m2 === 0, - TLR[dpp, {v, 0, x, y, z}, {nm1, {n2 - w, 0}, nm3, nm4, nm5}], - Sum[Binomial[w, i] TLR[dpp, {v, 0, x, y, z}, {nm1, fN[{n2 - i, m2}], nm3, nm4, nm5}]*(m2^2)^(w - i), {i, 0, w}] - ], - If[ m2 === 0, - TLR[dpp, {v, w - n2, x, y, z}, {nm1, {0, 0}, nm3, nm4, nm5}], - Sum[Binomial[n2, i] TLR[dpp, {v, w - n2, x, y, z}, {nm1, fN[{n2 - i, m2}], nm3, nm4, nm5}]*(m2^2)^(n2 - i), {i, 0, n2}]]]] - ); - -tlrule[4] = - TLR[dpp__, {v_, w_, (x_)?PQ, y_, z_}, {{(n1_)?PQ, m1_}, nm2_, {(n3_)?PQ, m3_}, nm4_, nm5_}] :> - ( - TLRComment["tlrule4"]; - ExpandMaybe[ - (1/2)*TLR[dpp, {v + 1, w, x - 1, y, z}, {{n1, m1}, nm2, {n3, m3}, nm4, nm5}] - - (1/2)*TLR[dpp, {v, w, x - 1, y, z}, {{n1, m1}, nm2, fN[{n3 - 1, m3}], nm4, nm5}] + - (1/2)*({dpp}[[2]] - m3^2)*TLR[dpp, {v, w, x - 1, y, z}, {{n1, m1}, nm2, {n3, m3}, nm4, nm5}]] - ); - -tlrule[5] = - TLR[dpp__, {v_, w_, x_, (y_)?PQ, z_}, {{n1_, m1_}, {(n2_)?PQ, m2_}, nm3_, {(n4_)?PQ, m4_}, nm5_}] :> - ( - TLRComment["tlrule5"]; - ExpandMaybe[ - (1/2)*TLR[dpp, {v, w + 1, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, {n4, m4}, nm5}] - - (1/2)*TLR[dpp, {v, w, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, fN[{n4 - 1, m4}], nm5}] + - (1/2)*({dpp}[[2]] - m4^2) TLR[dpp, {v, w, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, {n4, m4}, nm5}]] - ); - -tlrule[6] = - TLR[dpp__, {v_, w_, x_, y_, (z_)?PQ}, {{n1_, m1_}, {n2_, m2_}, nm3_, nm4_, {(n5_)?PQ, m5_}}] :> - ( - TLRComment["tlrule6"]; - ExpandMaybe[ - (1/2)*TLR[dpp, {v + 1, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}] - - (1/2)*TLR[dpp, {v, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, fN[{n5 - 1, m5}]}] + - (1/2)*TLR[dpp, {v, w + 1, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}] - - (1/2)*m5^2*TLR[dpp, {v, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}]] - ); - -tlrule[7] = - TLR[d_, pp_, dp___, {(v_)?PQ, w_, x_, y_, z_}, {{0, _}, nm2_, {(n3_)?PQ, m3_}, nm4_, nm5_}] :> - ( - TLRComment["tlrule7"]; - ExpandMaybe[ - TLR[d, pp, dp, {v - 1, w, x, y, z}, {{0, 0}, nm2, fN[{n3 - 1, m3}], nm4, nm5}] + - 2*TLR[d, pp, dp, {v - 1, w, x + 1, y, z}, {{0, 0}, nm2, {n3, m3}, nm4, nm5}] - - (pp - m3^2)*TLR[d, pp, dp, {v - 1, w, x, y, z}, {{0, 0}, nm2, {n3, m3}, nm4, nm5}] - ] - ); - -tlrule[8] = - TLR[d_, pp_, dp___, {v_, (w_)?PQ, x_, y_, z_}, {nm1_, {0, _}, nm3_, {(n4_)?PQ, m4_}, nm5_}] :> - ( - TLRComment["tlrule8"]; - ExpandMaybe[ - TLR[d, pp, dp, {v, w - 1, x, y, z}, {nm1, {0, 0}, nm3, fN[{n4 - 1, m4}], nm5}] + - 2*TLR[d, pp, dp, {v, w - 1, x, y + 1, z}, {nm1, {0, 0}, nm3, {n4, m4}, nm5}] - (pp - m4^2)* - TLR[d, pp, dp, {v, w - 1, x, y, z}, {nm1, {0, 0}, nm3, {n4, m4}, nm5}] - ] - ); - -tlrule[9] = - TLR[d_, pp_, {v_, w_, x_, y_, (z_)?PQ}, {nm1_, nm2_, nm3_, nm4_, {0, _}}] :> - ( - TLRComment["tlrule9"]; - FunctionExpand[ - ExpandMaybe[ - Sum[(Gamma[k + 1/2]*Gamma[d/2 - 1/2]*Binomial[z, 2*k]*Binomial[k, i]*Binomial[k, j]*(-1)^(i + j)*pp^(i + j - z)* - TLR[d, pp, {v + i, w + j, x + z - 2*i, y + z - 2*j, 0}, {nm1, nm2, nm3, nm4, {0, 0}}])/(Gamma[1/2]* - Gamma[k + d/2 - 1/2]), {k, 0, Floor[z/2]}, {i, 0, k}, {j, 0, k}] - ] - ] - ); - -tlrule[10] = - TLR[_, _, {_, _, (x_)?PNQ, (y_)?PNQ, _}, {{(_)?PQ, _}, {(_)?PQ, _}, {0, _}, {0, _}, _}] :> (TLRComment["tlrule10"]; 0 /; OddQ[x + y]); - -tlrule[11] = - TLR[d_, pp_, {v_, w_, (x_)?PQ, (y_)?PQ, z_}, {nm1_, nm2_, {0, _}, {0, _}, {(n5_)?PQ, m5_}}] :> - ( - TLRComment["tlrule11"]; - ExpandMaybe[(pp/(d + x + y - 2))*((x - 1)*TLR[d, pp, {v + 1, w, x - 2, y, z}, {nm1, nm2, {0, 0}, {0, 0}, {n5, m5}}] + - y*TLR[d, pp, {v, w, x - 1, y - 1, z + 1}, {nm1, nm2, {0, 0}, {0, 0}, {n5, m5}}])] /; EvenQ[x + y] && x > 1); - -tlrule[12] = - TLR[d_, pp_, {v_, w_, (x_)?PQ, (y_)?PQ, z_}, {nm1_, nm2_, {0, _}, {0, _}, {(n5_)?PQ, m5_}}] :> - ( - TLRComment["tlrule12"]; - ExpandMaybe[ - (pp/(d + x + y - 2))*((y - 1)*TLR[d, pp, {v, w + 1, x, y - 2, z}, {nm1, nm2, {0, 0}, {0, 0}, {n5, m5}}] + - x*TLR[d, pp, {v, w, x - 1, y - 1, z + 1}, {nm1, nm2, {0, 0}, {0, 0}, {n5, m5}}])] /; EvenQ[x + y] && y > 1 - ); - -tlrule[13] = - TLR[d_, pp_, {0, 0, 0, (y_)?PQ, 0}, {nm1_, {0, 0}, nm3_, {(n4_)?PQ, m4_}, nm5_}] :> - ( - TLRComment["tlrule13"]; - Sum[Binomial[y, i]*pp^(y - i)*(-1)^i*TLR[d, pp, {0, 0, 0, i, 0}, {nm3, {n4, m4}, nm1, {0, 0}, nm5}], {i, 0, y}] - ); - -tlrule[14] = - TLR[d_, pp_, {0, 0, (x_)?PQ, 0, 0}, {{0, 0}, nm2_, {(n3_)?PQ, m3_}, nm4_, nm5_}] :> - ( - TLRComment["tlrule14"]; - Sum[Binomial[x, i]*pp^(x - i)*(-1)^i* TLR[d, pp, {0, 0, i, 0, 0}, {{n3, m3}, nm4, {0, 0}, nm2, nm5}], {i, 0, x}]); - -tlrule[15] = - HoldPattern[TLR[_, _, {_, _, _, _, _}, {{_, 0}, {_, 0}, {0, _}, {0, _}, {0, _}}]] :> (TLRComment["tlrule15"]; 0); - -tlrule[16] = - TLR[_, _, {0, 0, (x_)?PQ, (y_)?PQ, 0}, {{_, _}, {_, _}, {0, _}, {0, _}, {0, _}}] :> (TLRComment["tlrule16"]; 0 /; OddQ[x] || OddQ[y]); - -tlrule[17] = - TLR[d_, pp_, {(a_)?PQ, b_, 0, de_, 0}, {{0, _}, {n2_, m2_}, {0, _}, {n4_, m4_}, {n5_, m5_}}] :> - ( - TLRComment["tlrule17"]; - Sum[Binomial[a, i]*Binomial[i, j]*(1 + (-1)^j)*2^(j - 1)* - TLR[d, pp, {a - i, b + i - j, 0, de,j}, {{n5, m5}, {n2, m2}, {0, 0}, {n4, m4}, {0, 0}}], {i, 0, a}, {j, 0, i}] - ); - -tlrule[18] = - TLR[d_, pp_, dp_, {(a_)?PNQ, (b_)?PNQ}, {1, 0, 0, 0, 0}, {{0, 0}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] :> - ( - TLRComment["tlrule18"]; - Sum[Binomial[a, i]*Binomial[b,j]*((pp + m3^2)*TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}] + - TLR[d, pp, dp, {i, j}, {{n3 - 1, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}] - - 2*TLR[d, pp, dp, {i, j}, {0, 0, 1, 0, 0}, {{n3, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}])*(-1)^(i + j)*dp^(a + b - i - j), {i, 0, a}, {j, 0, b}] - ); - -tlrule[19] = - TLR[d_, pp_, dp_, {(a_)?PNQ, (b_)?PNQ}, {0, 1, 0, 0, 0}, {{n1_, m1_}, {0, 0}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] :> - ( - TLRComment["tlrule18"]; - Sum[Binomial[a, i]*Binomial[b, j]*((pp + m4^2)* TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4, m4}, {n1, m1}, {0, 0}, {n5, m5}}] + - TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4 - 1, m4}, {n1, m1}, {0, 0}, {n5, m5}}] - - 2*TLR[d, pp, dp, {i, j}, {0, 0, 0, 1, 0}, {{n3, m3}, {n4, m4}, {n1, m1}, {0, 0}, {n5, m5}}])*(-1)^(i + j)*dp^(a + b - i - j), {i, 0, a}, {j, 0, b}] - ); - -tlrule[20] = - TLR[d_, pp_, {(v_)?PQ, w_, x_, y_, 0}, {{0, _}, nm2_, {0, _}, nm4_, {(n5_)?PQ, m5_}}] :> - ( - TLRComment["tlrule20"]; - Sum[Binomial[i, r]*Binomial[v, i]*Binomial[x, j]*2^r*TLR[d, pp, {v - i, -r + i + w, j, x - j + y, r}, {{n5, m5}, nm2, 0, nm4, 0}], {j, 0, x}, {i, 0, v}, {r, 0, i}] - ); - -tlrule[21] = - TLR[d_, pp_, {v_, (w_)?PQ, x_, y_, 0}, {nm1_, {0, _}, nm3_, {0, _}, nm5_}] :> - ( - TLRComment["tlrule21"]; - TLR[d, pp, {w, v, y, x, 0}, {{0, 0}, nm1, {0, 0}, nm3, nm5}] - ); - -tlrule[22] = - TLR[d_, pp_, dp_, {0, (b_)?PNQ}, {0, (w_)?PNQ, 0, (y_)?PNQ, 1}, {nm1_, nm2_, nm3_, nm4_, {0, 0}}] :> - ( - TLRComment["tlrule22"]; (1/pp)* - TLR[d, pp, dp, {0, b}, {0, w, 1, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - ); - -tlrule[23] = - TLR[d_, pp_, dp_, {1, (b_)?PNQ}, {0, (w_)?PNQ, 0, (y_)?PNQ, 1}, {nm1_, nm2_, nm3_, nm4_, {0, 0}}] :> - ( - TLRComment["tlrule23"]; - (1/((1 - d)*pp))*TLR[d, pp, dp, {0, b + 1}, {0, w, 2, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - - ((d*dp)/((1 - d)*pp^2))*TLR[d, pp, dp, {0, b}, {0, w, 2, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - (1/(1 - d))* - TLR[d, pp, dp, {0, b + 1}, {1, w, 0, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] + (dp/((1 - d)*pp))* - TLR[d, pp, dp, {0, b}, {1, w, 0, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - ); - -tlrule[24] = - TLR[d_, pp_, dp_, {2, (b_)?PNQ}, {0, (w_)?PNQ, 0, (y_)?PNQ, 1}, {nm1_, nm2_, nm3_, nm4_, {0, 0}}] :> - ( - TLRComment["tlrule24"]; - 2*dp*(1/((1 - d)*pp^2))* TLR[d, pp, dp, {0, b + 1}, {0, w, 3, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - - (((d + 2)*dp^2)/((1 - d)*pp^3))*TLR[d, pp, dp, {0, b}, {0, w, 3, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - - ((2*dp)/((1 - d)*pp))*TLR[d, pp, dp, {0, b + 1}, {1, w, 1, y, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] + ((3*dp^2)/((1 - d)*pp^2))* - TLR[d, pp, dp, {0, b}, {1, w, 1, y + 1, 0}, {nm1, nm2, nm3, nm4, {0, 0}}] - ); - -tlrule[25] = - TLR[dim_, pp_, {a_, b_, (c_)?PNQ, (d_)?PQ, 0}, {nm1_, nm2_, nm3_, {0, _}, nm5_}] :> - ( - TLRComment["tlrule25"]; - TLR[dim, pp, {b, a, d, c, 0}, {nm2, nm1, {0, 0}, nm3, nm5}] - ) /; d > c; - -TLRules = Array[tlrule, 25]; - -TLRules2 = Drop[TLRules, {9, 9}]; - -TLR[__, {{_, _}, {0, _}, {_, _}, {0, _}, {_, 0}}] := - 0; -TLR[__, {{0, _}, {_, _}, {0, _}, {_, _}, {_, 0}}] := - 0; -TLR[__, {{0, _}, {_, _}, {_, 0}, {_, _}, {0, _}}] := - 0; -TLR[__, {{_, 0}, {_, _}, {0, _}, {_, _}, {0, _}}] := - 0; -TLR[__, {{_, _}, {_, 0}, {_, _}, {0, _}, {0, _}}] := - 0; -TLR[__, {{_, _}, {0, _}, {_, _}, {_, 0}, {0, _}}] := - 0; - -SetAttributes[seeetDelayed, HoldAll]; - -seeetDelayed[TLR[a__], b_] := - SetDelayed @@ {TLR[a], b}; - -lis1 = - Permutations[{{0, _}, {0, _}, {0, _}, {_, _}, {_, 0}}]; - -lis2 = - Table[TLR[__, lis1[[i]]] :> 0, {i, Length[lis1]}] /. RuleDelayed -> seeetDelayed; - -Clear[lis1, lis2]; - -TJIS[d_, (M_)^2, {{\[Alpha]_, 0}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := - SMu^2*(((-1)^(\[Alpha] + \[Beta] + \[Gamma] + 1)/(-M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4))* - Exp[(-I)*Pi*(d - 4)]*(Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]/Gamma[(3/2)*d - \[Alpha] - \[Beta] - \[Gamma]])* - (Gamma[d/2 - \[Alpha]]/Gamma[\[Alpha]])*(Gamma[d/2 - \[Beta]]/ Gamma[\[Beta]])*(Gamma[d/2 - \[Gamma]]/Gamma[\[Gamma]])); - -TJIS[d_, (M_)^2, {{\[Beta]_, 0}, {\[Gamma]_, 0}, {\[Alpha]_, M_}}] := - TJIS[d, M^2, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]; - -TJIS[d_, (M_)^2, {{\[Beta]_, 0}, {\[Alpha]_, M_}, {\[Gamma]_, 0}}] := - TJIS[d, M^2, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]; - -TJIS[d_, (M_)^2, {{\[Alpha]_, M_}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := - (SMu^2/(M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4))*(-1)^(\[Alpha] + \[Beta] + \[Gamma] +1)* - (Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]/(Gamma[\[Alpha]]* Gamma[\[Beta]]*Gamma[\[Gamma]]))* - ((Gamma[d/2 - \[Gamma]]*Gamma[d/2 - \[Beta]])/ Gamma[d - \[Beta] - \[Gamma]])*((Gamma[\[Beta] + \[Gamma] - d/2]* - Gamma[2*d - \[Alpha] - 2*\[Beta] - 2*\[Gamma]])/ Gamma[(3*d)/2 - \[Alpha] - \[Beta] - \[Gamma]]); - -TJIS[d_, 0, {{\[Beta]_, 0}, {\[Alpha]_, M_}, {\[Gamma]_, 0}}] := - TJIS[d, 0, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]; - -TJIS[d_, 0, {{\[Beta]_, 0}, {\[Gamma]_, 0}, {\[Alpha]_, M_}}] := - TJIS[d, 0, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]; - -TJIS[d_, 0, {{\[Alpha]_, M_}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := - (SMu^2/(M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4))*(-1)^(\[Alpha] + \[Beta] + \[Gamma] + 1)* - (Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]/(Gamma[\[Alpha]]* Gamma[\[Beta]]*Gamma[\[Gamma]]))* - ((Gamma[\[Beta] + \[Gamma] - d/2]*Gamma[d/2 - \[Beta]]* Gamma[d/2 - \[Gamma]])/Gamma[d/2]); - -TJIS[d_, 0, {{\[Beta]_, M_}, {\[Alpha]_, 0}, {\[Gamma]_, M_}}] := - TJIS[d, 0, {{\[Alpha], 0}, {\[Beta], M}, {\[Gamma], M}}]; - -TJIS[d_, 0, {{\[Beta]_, M_}, {\[Gamma]_, M_}, {\[Alpha]_, 0}}] := - TJIS[d, 0, {{\[Alpha], 0}, {\[Beta], M}, {\[Gamma], M}}]; - -TJIS[d_, 0, {{\[Alpha]_, 0}, {\[Beta]_, M_}, {\[Gamma]_, M_}}] := - (SMu^2/(M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4))*(-1)^(\[Alpha] + \[Beta] + \[Gamma] + 1)* - (Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]/(Gamma[\[Beta]]* Gamma[\[Gamma]]))*(Gamma[d/2 - \[Alpha]]/Gamma[d/2])* - ((Gamma[\[Alpha] + \[Gamma] - d/2]*Gamma[\[Alpha] + \[Beta] - d/2])/ Gamma[2*\[Alpha] + \[Beta] + \[Gamma] - d]); - -TJIS[d_, 0, {{\[Alpha]_, 0}, {\[Beta]_, M_}, {\[Gamma]_, M_}}] := - (SMu^2*(-1)^(\[Alpha] + \[Beta] + \[Gamma] + 1)*Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]*Gamma[d/2 - \[Alpha]]* - (Gamma[\[Alpha] + \[Gamma] - d/2]*Gamma[\[Alpha] + \[Beta] - d/2]))/((M^2)^(\[Alpha] + \[Beta] + \[Gamma] - 4)*(Gamma[\[Beta]]* - Gamma[\[Gamma]])*Gamma[d/2]*Gamma[2*\[Alpha] + \[Beta] + \[Gamma] - d]); - -TAIS[d_, 0, {{1, M_}}] := - (-I)*M^2*SMu*Gamma[(4 - d)/2 - 1] - -TBIS[_, 0, {{_, 0}, {_, 0}}] := - 0; - -TBIS[d_, (M_)^2, {{\[Alpha]_, 0}, {\[Beta]_, 0}}] := - I*SMu*(((-1)^(\[Alpha] + \[Beta])/(-M^2)^(\[Alpha] + \[Beta] - 2))* - Exp[(-I)*Pi*((d - 4)/2)]*(Gamma[\[Alpha] + \[Beta] - d/2]/(Gamma[\[Alpha]]*Gamma[\[Beta]]))* - ((Gamma[d/2 - \[Alpha]]*Gamma[d/2 - \[Beta]])/ Gamma[d - \[Alpha] - \[Beta]])); - -TJIS[d_Symbol, (M_)^2, {{1, M_}, {1, M_}, {1, M_}}] := - M^2*SMu^2*(-(6/(-4 + d)^2) + 17/(2*(-4 + d)) + (1/8)*(-59 - 2*Pi^2) + (-4 + d)^3*TJI111e + - (1/ 1920)*((-4 + d)^2*(16755 - 4750*Pi^2 - 14*Pi^4 + 3840*Pi^2*Log[2] - 12080*Zeta[3])) + - (1/96)*(-4 + d)*(195 + 98*Pi^2 - 48*Zeta[3])); - -$CommentNotebook = True; - -TComment[s_String, b_] := - If[ - If[ !ValueQ[$TarcerRecursed], $TarcerRecursed = {}]; !MemberQ[$TarcerRecursed, {s, b}], - AppendTo[$TarcerRecursed, {s, b}]; - - If[ $Notebooks && $CommentNotebook === True, - - If[ $commentnb === False, - $commentnb = True; - $cnb = NotebookCreate[StyleDefinitions -> "NaturalColor.nb", Magnification -> 1.5]; - SetOptions[$cnb, WindowMargins -> {{0, Automatic}, {Automatic, 0}}]; SetOptions[$cnb, WindowSize -> {500, 300}]; - NotebookWrite[$cnb, Cell[BoxData[ToBoxes[b /. Rule[TFIC, TFI], StandardForm]], "Input", CellDingbat -> StringJoin[s, " "]]], - - NotebookWrite[$cnb, Cell[BoxData[ToBoxes[b /. Rule[TFIC, TFI], StandardForm]], "Input", CellDingbat -> StringJoin[s, " "]]] - ], - - Print[s, b /. {TFIC :> TFI, TVIC :> TVI, TJIC :> TJI, TBIC :> TBI, TAIC :> TAI}] - ] - ] /; $Comment === True; - -$TTable = {}; - -FEPrint[a__String] := - Print[a] /; $Notebooks === False; - -FEPrint[a__String] := - If[ Head[$cnb] === NotebookObject, - NotebookWrite[$cnb, Cell[StringJoin @@ {a}, "SmallText"]]; - SelectionMove[$cnb, After, Cell] - ] /; $Notebooks === True; - -Options[TarcerRecurse] = { - Factor -> Factor, - TimeConstraint -> Infinity, - Table :> $TTable, - Together -> Together, - Replace -> {} -}; - -TarcerRecurse[z_, opts___] := - Catch[ - Block[{ basisdone, factorfun, fertig, dummm1, dummm2, getvars, - te, time, cutoff, tog, ttable, facfun, nexp, oldexpr, rec, - special, sti, tl, tcheck, tjrd, tvrd, together, vars, $cc = 0, $cv, t0, tvars}, - - time = AbsoluteTime[]; - ttable = Table /. {opts} /. Options[TarcerRecurse]; - - If[ !MatchQ[ttable, - {__RuleDelayed}], - ttable = {} - ]; - - special = Replace /. {opts} /. Options[TarcerRecurse]; - cutoff = TimeConstraint /. {opts} /. Options[TarcerRecurse]; - together = Together /. {opts} /. Options[TarcerRecurse]; - factorfun = Factor /. {opts} /. Options[TarcerRecurse]; $commentnb = False; - - tog = - ((If[ #1 > 1001, - If[ $Comment, - FEPrint[ - StringJoin[ - "coefficient # ", - If[ ValueQ[$cv], - ToString[$cc], - "" - ], - If[ ValueQ[$cv], - StringJoin[" (", ToString[$cv], ")"], - "" - ], - " simplified, " - ], ToString[#1]]]]; #2) & - )[LeafCount[#1], $cc++; together[#1]]&; - - If[ !ValueQ[$TarcerRecursed], - $TarcerRecursed = {} - ]; - - $TarcerRecursed = {}; - - t0 = ToTFi[z] /. {TFi :> TFI, ToTFi :> Identity}; - - If[ - ttable =!= {}, - t0 = t0 /. ttable - ]; - - getvars = - Select[Variables[#1], MatchQ[#1, TFI[__] | TVI[__] | TJI[__] | TBI[__] | TAI[__]] & ] & ; - - If[ !FreeQ[t0, TFI], - t0 = Collect[t0 = TFIRecurse[t0] /. ttable, getvars[t0], tog] - ]; - - If[ !FreeQ[t0, TVI[_Plus, __]], - - tvrd = Select[DownValues[TVR], ! FreeQ[#1, TVI[_ - 2, __]] & ] /. TVR -> TVI; - t0 = Collect[t0 = t0 /. tvrd /. tvrd /. tvrd /. tvrd, getvars[t0], tog]; - - If[ !FreeQ[t0, TVI[_Plus, __]], - t0 = Collect[t0 = t0 //. tvrd, getvars[t0], tog] - ] - ]; - - - tjrd = Select[DownValues[TJR], ! FreeQ[#1, TJI[_ - 2, __]] & ] /. TJR -> TJI; - - If[ !FreeQ[t0, TJI[_Plus, __]], - tjrd = Select[DownValues[TJR], ! FreeQ[#1, TJI[_ - 2, __]] & ] /. TJR -> TJI; - t0 = Collect[t0 = t0 /. tjrd /. tjrd /. tjrd /. tjrd, getvars[t0], tog]; - - If[ !FreeQ[t0, TJI[_Plus, __]], - t0 = Collect[t0 = t0 //. tjrd, getvars[t0], tog] - ] - ]; - - rec[expr_, {ti_, tr_}] := - ( - sti = ToString[ti]; - - If[ FreeQ[expr, ti], - expr, - nexp = expr; - - If[ $Comment, - ( - If[ #1 === 1, - FEPrint[StringJoin[sti, " level, there is 1 ", sti]], - FEPrint[StringJoin[sti, " level, there are "], ToString[#1], StringJoin[" ", sti, "'s "]]] & ) - [Count[nexp, ti[__], -1]] - ]; - - nexp = nexp /. ti -> tr /. tr -> ti; - - If[ !FreeQ[nexp, TJI[_Plus, __]], - nexp = nexp //. tjrd - ]; - - tvars = getvars[nexp]; $cc = 0; $cv = Length[tvars]; - nexp = Collect[nexp, tvars, tog]; - - If[ cutoff =!= Infinity, - If[ AbsoluteTime[] - time > cutoff, - Throw[$Failed]] - ]; - nexp - ] - ); - basisdone = 0; - - tl = {{TFI, TFR}, {TVI, TVR}, {TJI, TJR}, {TBI, TBR}, {TAI, TAR}}; - - Do[ - t0 = FixedPoint[rec[#1, tl[[i]]] & , t0, 100]; - - If[ Head[t0] === Plus, - fertig = Select[t0, ! FreeQ[#1, tl[[i, 1]]]]; - basisdone = basisdone + fertig; t0 = t0 - fertig - ], {i, Length[tl]} - ]; - - t0 = t0 + basisdone; - $cv =. ; - - t0 = Collect[t0, {TAI[__], TAI[a1__]*TAI[a2__], TAI[__], TBI[__], TJI[__], TVI[__], TFI[__]}, factorfun]; - - If[ $Comment, - FEPrint["the result has ", ToString[Length[t0 + dummm1 + dummm2] - 2], " terms"] - ]; - - If[ $Notebooks, - SetSelectedNotebook[EvaluationNotebook[]] - ]; - - t0 = t0 /. TAI[dim_, pp_, list_List]/;pp=!=0:>TAI[dim,0,list]; - - t0 - ] - ]; - -Options[TarcerExpand] = { - TarcerReduce :> $BasisIntegrals, - TarcerRecurse -> False, Zeta -> True, - Replace -> {Prefactor1 -> Identity, EulerGamma -> 0} -}; - -TarcerExpand[expr_, d_Symbol -> fe_ /; Length[Variables[fe]] === 1, ru___Rule] := - TarcerExpand[expr, d -> fe, 0, ru]; - -TarcerExpand[expr_, d_Symbol -> fe_, (order_Integer)?NonNegative, opts___Rule] := - Block[{ - t1, t2, t3, t4, numfa, z2rule, restfa, ta0, tarcNumericalFactor, tarcFactor1, eeps, ints, vars, - t0, recurse, zeta2replace}, - - eeps = Variables[fe][[1]]; - tarcNumericalFactor[x_] := - If[ NumberQ[x], - x, - If[ Head[x] === Times, - If[ NumberQ[First[x]], - First[x], - 1 - ], - 1 - ] - ]; - - tarcFactor1[x_] := - Block[{factor1t1, factor1t2, factor1t3, mt, mi, m1, mp1, nx = x, iIii}, - - mt = #1 /. Plus -> mi /. mi -> Plus /. m1 -> -1 /. mp1 -> (-(Plus[##1]) & ) /. iIii -> I &; - - mi[y_, z__] := - m1*mp1[y, z] /; ( - If[ Head[#1] === Complex, - False, - If[ #1 < 0, - True, - False] - ]&)[tarcNumericalFactor[y]]; - - nx = x /. Complex[0, b_] -> b*iIii; - - If[ Head[nx] =!= Plus, - mt[nx /. Plus -> (Factor1[Plus[##1]] & )], - - factor1t1 = List @@ (#1 /. Plus -> factor1t3 & ) /@ nx; - factor1t2 = PolynomialGCD @@ factor1t1 /. factor1t3 -> Plus; - mt[factor1t2 Plus @@ ((#1 /. factor1t3 -> Plus)/factor1t2 & ) /@ factor1t1] - ] - ]; - - - Catch[ - e = eeps; - {ints, recurse, zeta2replace} = {TarcerReduce, TarcerRecurse, Zeta} /. Flatten[{opts, Options[TarcerExpand]}]; - - If[ zeta2replace =!= True, - z2rule = {}, - z2rule = Pi^2 :> 6*ToExpression["Zeta2"] - ]; - - ints = Flatten[ints]; - - If[ recurse =!= True, - ta0 = expr, - ta0 = TarcerRecurse[expr] - ]; - - t1 = ta0 /. ints /. { - SEpsilon[de_] :> SEpsilon[ToString[d]], - Prefactor1[de_] :> Prefactor1[ToString[de, InputForm]] - }; - - vars = Select[Variables[t1], Length[#1] > 0 & ]; - - If[ !FreeQ[vars, TFI | TVI | TJI | TKI | TBI | TAI], - Print["Returning the list of remaining integrals."]; - Throw[Select[vars, !FreeQ[#1, TFI | TVI | TJI | TKI | TBI | TAI] & ]] - ]; - - t1 = t1 /. d -> fe; polygafu[2, 1] = -2*Zeta[3]; - - polygafu[2, 2] = 2 - 2*Zeta[3]; - - polygafu[x_, y_] := - polygafu[x, y] = FunctionExpand[PolyGamma[x, y]]; - - t2 = Normal[t1 + O[e]^(order + 1)] /. PolyGamma -> polygafu /. (Replace /. {opts} /. Options[TarcerExpand]); - - t3 = Collect[t2, e, Expand[#1] /. z2rule & ]; - t3 = t2 /. ToString[d] :> fe; - - t4 = tarcFactor1[Expand[t3]] //. pre : (Prefactor1 | SEpsilon)[a_]*Prefactor1[b_] :> Prefactor1[a*b] /. Prefactor1[1] :> - 1 /. Prefactor1[xy_] :> Prefactor1[xy /. st_String :> ToExpression[st]] /. Prefactor1[(m_)^e*(xx_)]*(m_)^(any_) :> - Prefactor1[m^(e + any)*xx] /. z2rule; - - - If[ Head[t4] === Times, - numfa = tarcNumericalFactor[t4]; - restfa = Select[t4, FreeQ[#1, eeps | Log | Zeta] & ]; - - extracoll[z_, e] := - Block[{}, - If[ Head[z] === Plus, - (extracoll[#1, e] & ) /@ z, - z /. xy_Plus :> - If[ Length[Variables[xy]] === 0, - xy, - Collect[xy, Complement[Variables[xy], {e}]] - ] - ] - ]; - - (Select[t4, !FreeQ[#1, Prefactor1] & ]*(restfa/numfa)) . extracoll[Collect[Expand[(numfa*Select[t4, FreeQ[#1, Prefactor1] & ])/restfa], e], e], - - t4 - ] /. s_String :> ToExpression[s] /. d -> fe /. (Replace /. {opts} /. Options[TarcerExpand])]] /; Length[Variables[fe]] === 1; - -tfch = { - TFR :> Hold[TFR], - TVR :> Hold[TVR], - TJR :> Hold[TJR], - TBR :> Hold[TBR], - TAR :> Hold[TAR], - TComment :> Hold[TComment] -}; - -rtfch = - Reverse /@ tfch; - -SetAttributes[condrest, HoldRest]; - -Clear[remember]; -remember[zi_HoldForm] := - Block[{z = zi /. tfch}, - If[ !FreeQ[z, Condition], - Hold[HoldForm][ - Hold[SetDelayed][z[[1, 1]], ReplacePart[z[[1, 2]], Prepend[Extract[z, {1, 2, 1}, Hold], - z[[1, 1]] /. PatternTest -> pt /. pt[a_, _] :> a /. Pattern -> pat /. pat[a_, _] :> a], 1]] - ] /. Hold[HoldForm] -> HoldForm /. rtfch /. Hold[SetDelayed] -> SetDelayed /. Hold -> Set, - Hold[HoldForm][ - Hold[SetDelayed][z[[1, 1]], Prepend[Extract[z, {1, 2}, Hold], z[[1, 1]] /. PatternTest -> pt /. - pt[a_, _] :> a /. Pattern -> pat /. pat[a_, _] :> a]] - ] /. - Hold[HoldForm] -> HoldForm /. rtfch /. Hold[SetDelayed] -> SetDelayed /. Hold -> Set] - ]; - -$TarasovTdeltaplimit - -aa2 = Array[Subscript[f, #1] &, 10000 + ($TarasovTdeltaplimit + 1)*1000]; - -bb12 = Select[aa2, Head[#1] =!= Subscript &]; -Clear[aa2]; - -Print["there are ", Length[bb12], " recursion equations for $RankLimit = ", $RankLimit]; - -If[ $Remember === True, - - RCHECK = True; - nb = remember /@ bb12, - nb = bb12 -]; - -Clear[bb12]; - - -(* Checks of the recursion relations *) -CheckTVIRecursion[Subscript[f, 52]]; -CheckTVIRecursion[Subscript[f, 53]]; -CheckTVIRecursion[Subscript[f, 51]]; -CheckTVIRecursion[Subscript[f, 54]]; -CheckTVIRecursion[Subscript[f, 55]]; -CheckTVIRecursion[Subscript[f, 56]] -CheckTVIRecursion[Subscript[notnecessaryf, 60]]; -CheckTVIRecursion[Subscript[f, 63]]; -CheckTVIRecursion[Subscript[f, 66]]; -CheckTVIRecursion[Subscript[f, 67]]; -CheckTVIRecursion[Subscript[f, 6713]]; -CheckTVIRecursion[Subscript[f, 68]]; -CheckTVIRecursion[Subscript[f, 6813]]; -CheckTJIRecursion[Subscript[f, 7113]]; -CheckTJIRecursion[Subscript[f, 71]]; -CheckTJIRecursion[Subscript[f, 7123]]; -CheckTJIRecursion[Subscript[f, 78]]; -CheckTJIRecursion[Subscript[f, 80]]; -CheckTJIRecursion[Subscript[f, 81]]; -CheckTJIRecursion[Subscript[f, 8113]]; -CheckTJIRecursion[Subscript[f, 8123]]; -CheckTJIRecursion[Subscript[f, 82]]; -CheckTJIRecursion[Subscript[f, 8213]]; -CheckTJIRecursion[Subscript[f, 8212]]; -CheckTJIRecursion[Subscript[f, 83]]; -CheckTJIRecursion[Subscript[f, 100]]; -CheckTJIRecursion[Subscript[f, 1002]]; -CheckTJIRecursion[Subscript[f, 1003]]; -CheckTJIRecursion[Subscript[f, 1004]]; -CheckTJIRecursion[Subscript[f, 1005]]; -CheckTJIRecursion[Subscript[f, 1006]]; - - - -$Post =. -ReleaseHold[nb]; -$Comment = False; -End[]; -EndPackage[]; - - -$BasisIntegrals = { - TAI[d_, 0, {{1, M_}}] -> - -I*E^(1/2*(4 - d)*EulerGamma)*M^2*Gamma[-1 + (4 - d)/2]*Prefactor1[(M^2)^(1/2*(-4 + d))*SEpsilon[d]], - - TBI[d_, pp_, {{1, 0},{1, 0}}] -> - (I*E^(((4 - d)*EulerGamma)/2)*Gamma[2 - d/2]*Gamma[-1 + d/2]^2*Prefactor1[ (-pp)^((-4 + d)/2)*SEpsilon[d]])/Gamma[-2 + d], - - TJI[d_, pp_, {{1,0},{1,0},{1,0}}] -> - -((pp*Gamma[3 - d]*Gamma[-1 + d/2]^3*E^((4 - d)*EulerGamma)*Prefactor1[(-pp)^(-4 + d)*SEpsilon[d]^2])/(Gamma[-3 + (3*d)/2] )), - - TJI[d_, M_^2, {{1,M_},{1,0},{1,0}}] -> - (M^2*Gamma[3 - d]*Gamma[2 - d/2]*Gamma[-1 + d/2]^2*Gamma[-5 + 2*d]*E^((4 - d)*EulerGamma) Prefactor1[(M^2)^(-4 + d)*SEpsilon[d]^2])/(Gamma[-2 + d]*Gamma[-3 + (3*d)/2]), - - TJI[d_Symbol, (M_)^2, {{1, M_}, {1, M_}, {1, M_}}]-> - M^2*Prefactor1[(M^2)^(-4 + d)*SEpsilon[d]^2]*(-6/(-4 + d)^2 + 17/(2*(-4 + d)) + (-59 - 2*Pi^2)/8 + (-4 + d)^3*TJI111e + - ((-4 + d)^2*(16755 - 4750*Pi^2 - 14*Pi^4 + 3840*Pi^2*Log[2] - 12080*Zeta[3]))/1920 + ((-4 + d)*(195 + 98*Pi^2 - 48*Zeta[3]))/96), - - TJI[d_, 0, {{1, M_}, {1, M_}, {1, 0}}]->(M^2*Gamma[3 - d]*Gamma[2 - d/2]^2*Gamma[-1 + d/2]*E^((4 - d)*EulerGamma)* - Prefactor1[(M^2)^(-4 + d)*SEpsilon[d]^2])/(Gamma[4 - d]*Gamma[d/2]), - - TJI[d_, 0, {{1,M_},{1,0},{1,0}}] ->(M^2*Gamma[3 - d]*Gamma[2 - d/2]*Gamma[-1 + d/2]^2*E^((4 - d)*EulerGamma)*Prefactor1[(M^2)^(-4 + d)*SEpsilon[d]^2])/Gamma[d/2] -}; - -filename= ToFileName[{$FeynCalcDirectory,"Tarcer"},StringJoin["tarcer", StringReplace[$System,{"-"->"","Microsoft"->"","("->"",")"->""," "->""}], StringJoin @@ - ToString /@ $RankLimit, ".mx"]]; - -DumpSave[filename, { - Tarcer`Cayley, - Tarcer`CayleyD, - Tarcer`Cayleyu, - Tarcer`Prefactor1, - Tarcer`TarcerRecurse, - Tarcer`TFIRecurse, - Tarcer`TFISimplify, - Tarcer`SEpsilon, - Tarcer`TarcerExpand, - Tarcer`TarcerReduce, - Tarcer`TAI, - Tarcer`TAR, - Tarcer`TBI, - Tarcer`TBR, - Tarcer`TFI, - Tarcer`TFR, - Tarcer`TJI, - Tarcer`TJR, - Tarcer`TKI, - Tarcer`TVI, - Tarcer`TVR, - Tarcer`$BasisIntegrals, - Tarcer`$Comment, - Tarcer`$CommentNotebook, - Tarcer`$RankLimit, - Tarcer`$RecursionStop, - Tarcer`$TTable, - Tarcer`Private`applytlrules, - Tarcer`Private`applytlrules2, - Tarcer`Private`ExpandMaybe, - Tarcer`Private`FactorC, - Tarcer`Private`FEPrint, - Tarcer`Private`fN, - Tarcer`Private`mbt, - Tarcer`Private`PNQ, - Tarcer`Private`PQ, - Tarcer`Private`ta, - Tarcer`Private`TA, - Tarcer`Private`TAIC, - Tarcer`Private`TBIC, - Tarcer`Private`TComment, - Tarcer`Private`TLRComment, - Tarcer`Private`TFIC, - Tarcer`Private`TJIC, - Tarcer`Private`TLR, - Tarcer`Private`tlrule, - Tarcer`Private`redblue, - Tarcer`Private`TLRules, - Tarcer`Private`TLRules2, - Tarcer`Private`TVIC, - Tarcer`Private`$TLRComment, - Tarcer`$TarcerVersion -}]; - - - - -$HistoryLength = \[Infinity]; - -Print["Elapsed time: ", Round[AbsoluteTime[] - Tarcer`Private`atime]/60. min]; -Print["File size: ", Round[FileByteCount[filename]/1024.^2], "MB"]; diff --git a/FeynCalc/Tarcer/TARCER.nb b/FeynCalc/Tarcer/TARCER.nb deleted file mode 100755 index 8c663dd9c..000000000 --- a/FeynCalc/Tarcer/TARCER.nb +++ /dev/null @@ -1,32437 +0,0 @@ -(* Content-type: application/vnd.wolfram.mathematica *) - -(*** Wolfram Notebook File ***) -(* http://www.wolfram.com/nb *) - -(* CreatedBy='Mathematica 10.0' *) - -(*CacheID: 234*) -(* Internal cache information: -NotebookFileLineBreakTest -NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 1005293, 32427] -NotebookOptionsPosition[ 920265, 29843] -NotebookOutlinePosition[ 942518, 30583] -CellTagsIndexPosition[ 936924, 30399] -WindowFrame->Normal*) - -(* Beginning of Notebook Content *) -Notebook[{ - -Cell[CellGroupData[{ -Cell["TARCER 2.0", "Title", - TextAlignment->Center, - CellTags->"T1.1"], - -Cell[TextData[{ - "A ", - StyleBox["Mathematica", - FontSlant->"Italic"], - " program for the reduction of two-loop propagator integrals " -}], "Text", - TextAlignment->Center], - -Cell[TextData[{ - "Rolf Mertig\n", - ButtonBox["GluonVision GmbH\n", - BaseStyle->"Hyperlink", - ButtonData:>{ - URL["http://www.mertig.com"], None}], - "and\nRainer Scharf\n", - ButtonBox["Universit\[ADoubleDot]t Leipzig", - BaseStyle->"Hyperlink", - ButtonData:>{ - URL["http://www.physik.uni-leipzig.de/~scharf/"], None}] -}], "Text", - Editable->False, - TextAlignment->Center, - CellTags->"T1.2"], - -Cell["19.8.2011", "Text", - TextAlignment->Center], - -Cell["COMMENTS (VS 04.8.2011) changed typsetting for SEpsilon", "Text"], - -Cell["COMMENTS (RM 19.8.2011) changed typsetting for SEpsilon", "Text"], - -Cell["COMMENTS (RM 20.7.2011) changed the way .mx files are named", "Text", - CellChangeTimes->{{3.522785415984375*^9, 3.522785425109375*^9}}], - -Cell["\<\ -COMMENTS (RM 14.3..2004) uncommented a global variable assignement.changed \ -default setting of $RankLimit to {2,5}.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 31.10.2003) Change default settings of TarcerExpand, modify \ -$BasisIntegras for massless integrals, -changed default setting of $RankLimit to {1,6}.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 28.10.2003) Fixed a bug in TarcerExpand (only introduced \ -recently), -changed default setting of $RankLimit to {1,5}.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 24.9.2003) Relaxed a condition in equation (61) and (6153)\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 18.9.2003): Fixed things for 5.0, eliminated a TVI symmetry \ -(causing infinite recursion) and added -TFI decomposition into products of TAI's (was somehow missing but shows up \ -in, e.g., the 2-loop Higss selfenergy). -Putting TFI back into the Tarcer context, because the fcloops context created \ -trouble ... -Changed default of $Comment to False.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (FO 8.9.2002.): Changed context of TFI to \ -HighEnergyPhysics`fcloops`TFI` and updated other HighEnergyPhysics`* contexts.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (FO 15.3.2001.): Changed PreFactor into Prefactor1 to avoid conflict \ -with FeynArts and FeynCalc.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (FO 15.3.2001.): Changed context of Zeta2 and made definition \ -dependent on not having loaded FeynCalc.\ -\>", "Text"], - -Cell[TextData[{ - "COMMENTS (RM 25.4.): ", - ButtonBox["TFISimplify", - BaseStyle->"Hyperlink", - ButtonData:>"T1.7.1.1"], - " (like TFIRecurse, but without trule[9])." -}], "Text"], - -Cell[TextData[{ - "COMMENTS (RM 23.4.): bug fixed in ", - ButtonBox["tlrule[17]", - BaseStyle->"Hyperlink", - ButtonData:>"tlrule17"], - "." -}], "Text"], - -Cell[TextData[{ - "COMMENTS (RM 6.4.): ", - ButtonBox["special TVR relations", - BaseStyle->"Hyperlink", - ButtonData:>"specialTVR"], - " added to TVR." -}], "Text"], - -Cell[TextData[{ - "COMMENTS (RM 22.3.): ", - ButtonBox["TVI Symmetry", - BaseStyle->"Hyperlink", - ButtonData:>"Tsymmetry"], - " added to TVR." -}], "Text"], - -Cell[TextData[{ - "COMMENTS (RM 18.3.): More rules added to ", - ButtonBox["$TTable", - BaseStyle->"Hyperlink", - ButtonData:>"$TTable"], - ". " -}], "Text"], - -Cell[TextData[{ - "COMMENTS (RM 18.2.): More rules added to ", - ButtonBox["$TTable", - BaseStyle->"Hyperlink", - ButtonData:>"$TTable"], - ". " -}], "Text"], - -Cell[TextData[{ - "COMMENTS (RM 21.2.): Included ", - ButtonBox["$TTable", - BaseStyle->"Hyperlink", - ButtonData:>"$TTable"], - ". added tlrule[25]" -}], "Text"], - -Cell["\<\ -COMMENTS (RM 20.2.): $RankLimit = {0,6} ; Changed TarcerRecurse such that \ -special TJR and TVR (reducing D -> D-2) are used first.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 15.2.): $RankLimit = {0,8} ; - The following test now works: - - Print[\"test 1 : TFI[D, pp, \ -{0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1,MW}}] = \", - Timing[t1 \ -=TarcerRecurse[TFI[D, pp, {0, 0, 0, 1, 3}, {{1, MW}, {1, MZ}, {0, 0}, {1, \ -MZ}, {1,MW}}]] - ] // \ -InputForm - ] - - Print[\"test 2 : TFI[d, \ -pp, 0, {0, 0, 0, 0, 4},{{1, m1}, {1, m2}, 0, 0, 0}] = \", - Timing[t2 \ -=TarcerRecurse[TFI[D, pp, 0, {0, 0, 0, 0, 4},{{1, m1}, {1, m2}, 0, 0, 0}]]; - ] // \ -InputForm - ] -\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 13.2.): tlrule[11] and trule[12] made more restrictive: \ -inhibiting thus a recursion if {n5,m5} equals {0,0}.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 12.2.): tlrule[15] made safer (in order to not get 0 :> 0 ); - TFIRecurse made safer (to not \ -get into a recursion); - There is still something \ -wrong with the tlrule's ; since - TFIRecurse[TFI[D, pp, {0, 0, 0, 1, \ -3}, {{1, MW}, {1, MZ}, {0, 0}, {1, MZ}, {1, MW}}]] - doesn't work ..\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 5.2.): tlrule[10] slightly changed to cover more cases.\ -\>", "Text"], - -Cell["\<\ -COMMENTS (RM 2.2.): FunctionExpand added in tlrule[9]. 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The same effect as \ -TarcerExpand[TarcerRecurse[expr], ...] can be achieved by setting the option \ -TarcerRecurse of TarcerExpand to True. 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m4^2*r10 + m5^2*r5, - r16 = - m3^2*r14 + m2^2*r15 + m2^4*r4 - 2*m3^4*r5 - - 3*m4^2*m5^2*r5 + m5^4*r5 + m4^4*r8, - r17 = m3^2 + 2*m4^2, r18 = -1 + d, - r19 = -(m3^2*r13) - 2*m4^2*r18 + 2*m5^2*r5, - r20 = - 2*m2^4 - 3*m3^4 + d*m3^4 - 3*m3^2*m4^2 + - 2*m4^4 + m2^2*r19 - 2*m5^4*r5 + m5^2*r17*r5, - r21 = 2 + d, r22 = - 2*m5^2 - m4^2*r21 + m2^2*r4 - m3^2*r4, - r23 = -7 + d, r24 = 6*m4^2 - 4*m5^2, - r25 = 3*m3^2 + m4^2*r18 + m5^2*r23, - r26 = - -6*m4^4 - 2*m4^2*m5^2*r23 + m3^2*r24 + - 2*m2^2*r25 - 2*m2^4*r4 - m3^4*r4, - r27 = m3^4 + m3^2*m4^2 - 2*m4^4, - r28 = m3^2 + m4^2*r23, - r29 = -2*m4^2*r18 + m3^2*r21 + 2*m5^2*r23, - r30 = -6*m2^4 + 2*m5^2*r28 - m2^2*r29 + r27*r4, - r31 = m1^4*r22 + m1^2*r26 + m3^2*r30 + m1^6*r4, - r32 = m3 - m4, r33 = m3 + m4, - r34 = 2*m3^2 + m4^2, r35 = -17 + 3*d, - r36 = m3^2*r23 + m4^2*r35, r37 = -9 + d, - r38 = 17 - 3*d, - r39 = 5*m3^2 + m4^2*r37 + m5^2*r38, - r40 = 1 + d, r41 = - 5*m4^2 - m5^2*r23 + m2^2*r4 - m3^2*r40, - r42 = - m5^4*r35 - m5^2*r36 + m2^2*r39 - 2*m1^4*r4 + - m2^4*r4 - r32*r33*r34*r4 + m1^2*r41, - r43 = m1^2 - m2^2 + m3^2 - m4^2, - r44 = 2*m5^2*r13 + r4*r43, - r45 = - m3^4*r12 + m1^4*r16 + m1^2*m3^2*r20 + - PP*r31 + PP^2*r42 + PP^3*r44 + m1^6*r7, - r46 = m2^2 + m4^2, r47 = 13 - 3*d, - r48 = m4^2*r47 - m5^2*r5 + m3^2*r6, - r49 = m5^4*r5 + m5^2*r32*r33*r5 + m4^2*r4*r9, - r50 = -18 + 4*d, r51 = -(m4^2*r13) - 3*m5^2*r5, - r52 = - 2*m3^4*r5 + m4^2*m5^2*r5 + m5^4*r5 + - m4^4*r50 + m3^2*r51, - r53 = -3*m4^2 + 2*m5^2*r5, - r54 = - m4^4*r47 + 2*m3^4*r5 + m4^2*m5^2*r5 - - 2*m5^4*r5 + m3^2*r53, - r55 = m4^2*r13 + 6*m3^2*r5 - 2*m5^2*r5, - r56 = 3*m4^2 + m3^2*r5 - m5^2*r5, - r57 = 7 - 2*d, - r58 = m3^2*r5 + 3*m5^2*r5 + m4^2*r57, - r59 = - m2^6*r4 + m2^2*m4^2*r55 + m2^4*r56 + m4^4*r58, - r60 = m4^2 - m3^2*r5, r61 = 10 - 3*d, - r62 = 2*m5^2 + 3*m4^2*r4 + m3^2*r61, - r63 = m4^2 + m5^2*r5, - r64 = - -4*m4^2*m5^2 + 3*m4^4*r4 - 2*m3^4*r5 + - 2*m3^2*r63, r65 = m4^2 + m3^2*r5 - m5^2*r5, - r66 = 2*m3^2*r5 + 2*m5^2*r5 + m4^2*r61, - r67 = 3*m2^4*r4 + 2*m2^2*r65 + m4^2*r66, - 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r93 = m2^2 - 3*m4^2, r94 = m4 - m5, - r95 = m4 + m5, r96 = 2*m3^2 - m4^2 + m5^2, - r97 = -m1^2 - m2^2 - 2*m3^2 + 3*m5^2, - r98 = - PP^2 + m1^2*r93 + m2^2*r94*r95 + m4^2*r96 + - PP*r97, r99 = -2 + d, r100 = -m1^2 + m2^2, - r101 = m2^2 + m1^2*r72, - r102 = m3^2*r101 - 2*m3^4*r4 + m2^2*r100*r4, - r103 = 9 - 2*d, r104 = m2^2*r23 + m3^2*r72, - r105 = - 2*m1^4 + m2^4*r103 + m1^2*r104 + m2^2*m3^2*r5, - r106 = -9 + 2*d, r107 = m1 - m2, - r108 = m1 + m2, - r109 = -(r106*r107*r108) + m3^2*r4, - r110 = - m2^2*r102 + m4^2*r105 + m4^4*r109 - m4^6*r4, - r111 = m1^2 + m2^2, - r112 = m2^2*r4 - 2*m1^2*r72, r113 = -19 + 5*d, - r114 = m3^2*r112 + m3^4*r113 + m2^2*r111*r4, - r115 = m3^2*r5 + m2^2*r6, - r116 = - 2*m1^4 + 2*m1^2*r115 + m2^4*r13 + m3^4*r72 - - 2*m2^2*m3^2*r99, - r117 = m2^2*r106 + m3^2*r4 - m1^2*r99, - r118 = - m2^2*r114 - m4^2*r116 + m4^4*r117 - m4^6*r6, - r119 = -(m2^2*r5) + 2*m3^2*r57 + m1^2*r72, - r120 = m1^2*r18 + 2*m3^2*r4 - m2^2*r5, - r121 = m2^2*r119 + m4^2*r120 + 2*m4^4*r5, - r122 = m3^2*r5 + m4^2*r72, - r123 = -2*m2^2*r4 - m4^2*r69 + m3^2*r72, - r124 = - m2^2*r122 + m1^2*r123 + 2*m2^4*r4 + - 2*m4^2*r32*r33*r4, - r125 = -3*m4^2 + m2^2*r4 - m3^2*r72, - r126 = m3^2 - m4^2*r72, - r127 = - -2*m3^2*m4^2 - 2*m1^2*r125 - 2*m2^2*r126 + - m4^4*r18 - 4*m2^4*r4 + m3^4*r72, - r128 = - -(m2^2*r18) + 2*m4^2*r5 + m1^2*r72 + - 2*m3^2*r72, - r129 = - m5^2*r127 - m5^4*r128 - r124*r32*r33 + - m5^6*r72, r130 = -m1^2 + m2^2 + m3^2 - m4^2, - r131 = -14 + 3*d, - r132 = - -(m3^2*r13) + m4^2*r131 + m1^2*r4 + 5*m2^2*r4, - r133 = -2*m5^4 + m5^2*r132 + r130*r32*r33*r4, - r134 = - m5^2*r118 + m5^4*r121 + PP*r129 + PP^2*r133 + - r110*r32*r33 - 2*m5^2*PP^3*r4 + - m5^6*r5*r89*r90, r135 = m3 - m4 - m5, - r136 = m3 + m4 - m5, r137 = m3 - m4 + m5, - r138 = m3 + m4 + m5, r139 = -10 + d, - r140 = 13 - 2*d, r141 = d*m4^2 + 2*m3^2*r5, - r142 = -8 + d, - r143 = m4^2*r142 - m3^2*r99 + m5^2*r99, - r144 = - m3^2*m4^2*r139 + m4^4*r140 - m5^2*r141 + - m2^2*r143 + m3^4*r5 + m5^4*r5, - r145 = 3*m3^4 - 12*m3^2*m4^2 + 7*m4^4, - r146 = 3*m3^2 + 4*m4^2, r147 = m3^2 - 11*m4^2, - r148 = - 7*m3^4 + 10*m3^2*m4^2 - 17*m4^4 - 5*m5^4 - - 2*m5^2*r147, r149 = m2^2 + 2*m3^2 + m4^2, - r150 = - -m2^4 + m2^2*m3^2 + m3^4 + 3*m2^2*m4^2 + - m3^2*m4^2 - m4^4 + m5^4 - m5^2*r149, - r151 = - 3*m3^6 + 6*m3^4*m4^2 - 17*m3^2*m4^4 + - 8*m4^6 + 3*m5^6 - m5^2*r145 - m5^4*r146 + - m2^2*r148 - d*r150*r77 + 6*m2^4*r94*r95, - r152 = -(m3^2*m4) + m4^3, r153 = 11 - 2*d, - r154 = -(d*m3^2*m4^2) + m4^4*r153 + m3^4*r5, - r155 = m4^2 + m3^2*r5, - r156 = r142*r32*r33 + m5^2*r99, - r157 = 11 - 3*d, r158 = -8 + 3*d, - r159 = m5^2*r158 + m4^2*r21, - r160 = - -3*m3^4 + 2*m4^2*m5^2*r106 + m5^4*r157 + - m3^2*r159 - m4^4*r18, - r161 = - -2*m2^6 + m5^2*r154 - 2*m5^4*r155 + - m2^4*r156 + m2^2*r160 + r152^2*r4 + m5^6*r5, - r162 = m4^2*r23 - 3*m3^2*r72, - r163 = -4*m2^2 + m4^2*r18 + m3^2*r23, - r164 = -m3^4 + m4^4, - r165 = - -(m2^4*r13) + m2^2*r162 + m1^2*r163 + - r164*r4 + m1^4*r99, r166 = -19 + 4*d, - r167 = m4^2 + m3^2*r72, r168 = m3^2 + m4^2*r69, - r169 = -2*r168 + 4*m2^2*r4, - r170 = - -m3^4 + m2^4*r13 - m4^4*r166 + 2*m2^2*r167 + - m1^2*r169 + 2*m3^2*m4^2*r72 + m1^4*r99, - r171 = m1^2 - m2^2 + 4*m4^2, - r172 = - -(m5^2*r170) + r165*r32*r33 + m5^6*r72 - - m5^4*r171*r72, r173 = m2^2 + m3^2, - r174 = -(m4^2*r13) + r131*r173 + m1^2*r8, - r175 = m5^2*r174 - 2*m5^4*r4 + r130*r32*r33*r4, - r176 = - 2*m1^6*m4^2 + m1^4*r144 + m1^2*r151 + - m3^2*r161 + PP*r172 + PP^2*r175 - - 2*m5^2*PP^3*r4, r177 = m3^2 + m4^2 - m5^2, - r178 = -2*m1^2 + m3^2 - m4^2 + m5^2, - r179 = -m3^2 + m4^2 + m5^2, - r180 = m2^2*r177 + m4^2*r178 + PP*r179, - r181 = -2*m2^2 - m3^2 + m4^2 + m5^2, - r182 = m1^2*r177 + m3^2*r181 + PP*r77, - r183 = -(m2^2*r13) - 2*m3^2*r5, - r184 = - m1^2*r183 - 2*m3^4*r4 + m2^4*r57 + m1^4*r72 - - m2^2*m3^2*r99, r185 = 3*m2^2*r4 + m3^2*r72, - r186 = - m2^4*r106 + 2*m1^2*r185 + m1^4*r40 - - 2*m2^2*m3^2*r6, r187 = r111*r13 - m3^2*r4, - r188 = - m2^2*r184 + m4^2*r186 - m4^4*r187 + m4^6*r4, - r189 = 2*m1^2 + m3^2*r10 + 2*m2^2*r5, - r190 = m2^2*r5 + m3^2*r72 + 2*m1^2*r99, - r191 = m2^2*r189 - m4^2*r190 - m4^4*r5, - r192 = -(m3^2*r5) - m4^2*r72, - r193 = 2*m2^2*r4 + m4^2*r69 - m3^2*r72, - r194 = - m2^2*r192 + m1^2*r193 - 2*m2^4*r4 + - 2*m4^2*r4*r9, r195 = m2^2 + m4^2 + m3^2*r72, - r196 = -(m3^2*r6) - m4^2*r72, - r197 = - m2^4*r157 + 2*m1^2*r195 + 2*m2^2*r196 + - 2*m4^2*r17*r4 + m1^4*r72, - r198 = - m4^2*r10 - 2*m2^2*r5 + 2*m1^2*r72 + m3^2*r72, - r199 = - r107*r108*r194 + m5^2*r197 - m5^4*r198 + - m5^6*r72, r200 = m1^2 - m2^2 - m3^2 + m4^2, - r201 = m1^2 + m2^2 + m3^2 + 5*m4^2, - r202 = 2*m5^4 - r107*r108*r200 - m5^2*r201, - r203 = - r107*r108*r110 - m5^2*r188 - m5^4*r191 + - PP*r199 + 2*m5^2*PP^3*r4 + PP^2*r202*r4 + - m5^6*r5*r89*r90, r204 = m4^2 + m5^2, - r205 = -2*m5^2*r5 + m4^2*r99, r206 = 18 - 5*d, - r207 = m4^2*r206 + m5^2*r8 - 2*m3^2*r99, - r208 = - m2^2*r207 + 2*m2^4*r4 - m3^4*r5 - - m3^2*r204*r5 + r205*r94*r95, - r209 = 2*m3^2*m4^2 + m4^4*r142 + 2*m3^4*r5, - r210 = -(m4^2*r18) + m3^2*r5, r211 = 3 - 2*d, - r212 = m5^2 + m4^2*r157 + m3^2*r211, - r213 = m4^2*r106 + m3^2*r4, - r214 = - -(d*m3^4) + 10*m3^2*m4^2 - 2*d*m3^2*m4^2 - - 2*m4^4 + d*m4^4 + 2*m5^2*r213 - 2*m5^4*r4, - r215 = - d*m3^2*m4^4 - 2*m4^6 - m5^2*r209 + - m5^4*r210 + m2^4*r212 + m2^2*r214 + - m2^6*r4 + m5^6*r5 - m3^4*m4^2*r99, - r216 = m4^2*r13 + m3^2*r99, - r217 = m3^2*r5 - m4^2*r72, r218 = 13 - 4*d, - r219 = 3*m3^2 + m5^2*r218 + m4^2*r23, - r220 = m4^2*r142 + m5^2*r61, - r221 = - 2*m3^4 + 2*m4^2*m5^2 - m4^4*r13 + m3^2*r220 + - 2*m5^4*r6, r222 = - m4^2*m5^2*r216 + m5^4*r217 + m2^4*r219 + - m2^2*r221 - m5^6*r5 + m2^6*r99, - r223 = -(m3^2*r10) + m4^2*r5, - r224 = - 4*m3^2*m4^2 + m1^2*r122 + m4^4*r13 + - m2^2*r223 + m1^4*r4 - m2^4*r4 - m3^4*r99, - r225 = -m3^2 + m2^2*r72 - m4^2*r72, - r226 = -2*m4^2*r106 + 2*m3^2*r69, - r227 = - m1^4*r106 + m2^4*r106 - m4^4*r13 - - 2*m1^2*r225 + m2^2*r226 - 4*m3^2*m4^2*r4 - - m3^4*r99, r228 = m3^2 + 3*m4^2, - r229 = - r107*r108*r224 - m5^2*r227 + m5^6*r72 - - m5^4*r228*r72, - r230 = m4^2*r131 + m1^2*r4 + m2^2*r4 + m3^2*r8, - r231 = - 2*m5^4*r106 - m5^2*r230 - r107*r108*r200*r4, - r232 = - m1^4*r208 - m1^2*r215 - m3^2*r222 + PP*r229 + - PP^2*r231 + 2*m5^2*PP^3*r4 + m1^6*r7, - r233 = -2*m3^2 + m4^2, - r234 = -m2^2 + m4^2 - 2*m5^2, - r235 = -m1^2 + m2^2 + m5^2, - r236 = - m1^4 + m5^4 + m2^2*r233 + m1^2*r234 + - PP*r235 - m5^2*r46, r237 = -m2^2 + m5^2, - r238 = m2^2 + m3^2 - 2*m4^2 + m5^2, - r239 = -m1^2 + m2^2 - m5^2, - r240 = m1^4 + m3^2*r237 - m1^2*r238 + PP*r239, - r241 = m3^2 + 3*m4^2 - m5^2, - r242 = -3*m3^2 - m4^2 + m5^2, - r243 = - m5^4 - m5^2*r228 + m1^2*r241 + m2^2*r242 + - 2*PP*r32*r33 + 2*m4^2*r9, - r244 = 2*m1^2 + m2^2 + m4^2, - r245 = -2*m1^2 - m3^2 - m4^2 + 3*m5^2, - r246 = - m1^4 - 3*m2^2*m3^2 + m5^4 + PP^2 + - m4^2*r173 - m5^2*r244 + PP*r245, - r247 = -2*m3^2 + m4^2 + m5^2, - r248 = - -m2^4 - m4^2*m5^2 + PP*r235 + m2^2*r247 + - m1^2*r46, r249 = m2^2*r153 + m1^2*r5, - r250 = 2*m1^2 + m2^2*r4, - r251 = m2^2*r13 + m1^2*r139, - r252 = r107*r108*r250 + m3^2*r251 - m3^4*r4, - r253 = m1^2*r140 + 2*m3^2*r4 + m2^2*r72, - r254 = - m3^4*r249 + m4^2*r252 + m4^4*r253 - m4^6*r4 + - m2^2*m3^2*r100*r99, r255 = 2*m3^2 + m4^2*r13, - r256 = -2*m3^2*r5 + m2^2*r99 - m4^2*r99, - r257 = -11 + 2*d, - r258 = - -(m4^4*r106) + 2*m3^2*m4^2*r23 - m3^4*r257, - r259 = 4*m4^2 + m3^2*r13, - r260 = - -2*m2^4 + 6*m3^2*m4^2 + 2*m2^2*r259 + - m4^4*r37 + m3^4*r5, - r261 = - -5*m3^4*m4^2 + m2^4*r255 + m1^4*r256 + - m2^2*r258 + m1^2*r260 - m2^6*r4 + m3^6*r5 + - m4^6*r6 - 3*m3^2*m4^4*r72, - r262 = m3^4 + m3^2*m4^2 + m4^4, - r263 = - m1^4 + m2^4 - 2*r262 + m1^2*r81 + m2^2*r81, - r264 = m1^2 + m2^2 - m3^2 - m4^2, - r265 = -(r13*r32*r33) + m2^2*r99, - r266 = - -2*m1^2*r265 - r32^2*r33^2*r4 + - 2*m2^2*r13*r9 + m1^4*r99 + m2^4*r99, - r267 = m3^2*r13 + m4^2*r4, r268 = -16 + 3*d, - r269 = m3^2*r13 - m4^2*r268 + m2^2*r4, - r270 = - 2*m2^2*r267 + 2*m1^2*r269 + - r13*r228*r32*r33 + m2^4*r61 + m1^4*r99, - r271 = 2*m2^2 + m4^2*r23 - m3^2*r72, - r272 = - -(m5^2*r270) - 2*m5^4*r271 + r266*r32*r33, - r273 = 2*m3^2 - 2*m4^2 - m5^2, - r274 = m1^2*r5 - m2^2*r5 + r273*r72, - r275 = - r200*r254 + m5^2*r261 + PP*r272 + - 2*m5^2*PP^2*r274 + m5^4*r263*r5 - - m5^6*r264*r5, - r276 = - -2*m2^2*m3^2 - 2*m3^4 + 3*m3^2*m4^2 - m4^4 + - 3*m3^2*m5^2 + 2*m4^2*m5^2 - m5^4 + - m1^2*r177 + PP*r77, - r277 = -(m4^2*r106) + m2^2*r4 - m3^2*r5, - r278 = - -2*m3^4 - m3^2*m4^2*r13 + m2^2*r196 + - m2^4*r4 + m4^4*r4, - r279 = m4^2*r131 + m3^2*r8, - r280 = - m2^2*r279 - 2*m2^4*r4 + m4^2*r32*r33*r99, - r281 = m1^4*r277 + m2^2*r278 + m1^2*r280, - r282 = 11*m3^2 - 3*d*m3^2 + 9*m4^2 - 2*d*m4^2, - r283 = 15 - 4*d, - r284 = m4^2*r106 + m2^2*r283 + m3^2*r5, - r285 = m4^4*r13 + 4*m3^2*m4^2*r5 - m3^4*r99, - r286 = -m4^2 + m3^2*r5, - r287 = -(m4^2*r5) + m3^2*r6, - r288 = 2*m2^2*r287 + m2^4*r72 - 2*r286*r81, - r289 = - -2*m3^2*m4^4 + m2^4*r282 + m1^4*r284 + - m2^2*r285 + m1^2*r288 - m4^6*r4 + m1^6*r5 + - m2^6*r6 + m3^4*m4^2*r99, - r290 = 2*m2^2 - m3^2 - m4^2, - r291 = - 2*m1^4 + 2*m2^4 - m3^4 - m4^4 + m1^2*r290 - - m2^2*r81, r292 = m2^2 - m3^2 + m4^2, - r293 = - m1^4*r4 + m2^4*r4 - 2*m1^2*r292*r4 + - 2*m2^2*r4*r9 - r32^2*r33^2*r99, - r294 = m3^2*r13 - m4^2*r131, - r295 = m2^2*r13 - r4*r81, - r296 = - m1^4*r131 + 2*m2^2*r294 - 2*m1^2*r295 - - 2*m3^2*m4^2*r4 + m4^4*r8 - m2^4*r99 - - m3^4*r99, r297 = 2*m4^2 - m2^2*r5 + m1^2*r72, - r298 = - r107*r108*r293 - m5^2*r296 + 2*m5^4*r297, - r299 = -2*m5^2*r32*r33*r5 + 2*m5^4*r72, - r300 = - r130*r281 - m5^2*r289 + PP*r298 + PP^2*r299 - - m5^6*r264*r5 + m5^4*r291*r5, - r301 = - -2*m2^2*m3^2 - m3^2*m4^2 + m4^4 + m5^4 - - m5^2*r17 + m1^2*r177 + PP*r77, - r302 = m2^2 + 2*m3^2 - 3*m4^2, - r303 = -m1^2 + m2^2 - 3*m5^2, - r304 = - m1^4 - m2^2*m4^2 - m5^4 + m5^2*r149 - - m1^2*r302 + PP*r303, - r305 = - -((r45*TBI[d, PP, {{1, m4}, {1, m2}}]* - TBI[d, PP, {{2, m1}, {1, m3}}])/(4*r3)) -+ (r76*TBI[d, PP, {{1, m3}, {1, m1}}]* - TBI[d, PP, {{2, m2}, {1, m4}}])/(4*r3) - - (r80*TBI[d, PP, {{2, m1}, {1, m3}}]* - TBI[d, PP, {{2, m2}, {1, m4}}])/2 - - (r45*TBI[d, PP, {{1, m4}, {1, m2}}]* - TBI[d, PP, {{2, m3}, {1, m1}}])/(4*r3) - - (r84*TBI[d, PP, {{2, m2}, {1, m4}}]* - TBI[d, PP, {{2, m3}, {1, m1}}])/2 - - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}]* - TBI[d, PP, {{2, m3}, {2, m1}}] + - (r76*TBI[d, PP, {{1, m3}, {1, m1}}]* - TBI[d, PP, {{2, m4}, {1, m2}}])/(4*r3) - - (r92*TBI[d, PP, {{2, m1}, {1, m3}}]* - TBI[d, PP, {{2, m4}, {1, m2}}])/2 - - (r98*TBI[d, PP, {{2, m3}, {1, m1}}]* - TBI[d, PP, {{2, m4}, {1, m2}}])/2 - - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}]* - TBI[d, PP, {{3, m1}, {1, m3}}] - - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}]* - TBI[d, PP, {{3, m3}, {1, m1}}] - - r3*TFI[r99, PP, - {{1, m1}, {1, m2}, {1, m3}, {1, m4}, - {1, m5}}] - - (r134*TVI[d, PP, - {{1, m5}, {1, m1}, {2, m4}, {1, m3}}])/ - (4*r3) - (r135*r136*r137*r138* - TVI[d, PP, - {{1, m5}, {1, m1}, {2, m4}, {2, m3}}])/2 -- (r176*TVI[d, PP, {{1, m5}, {1, m2}, {2, m3}, - {1, m4}}])/(4*r3) + - (r180*TVI[d, PP, - {{1, m5}, {1, m2}, {2, m3}, {2, m4}}])/2 -- r182*TVI[d, PP, {{1, m5}, {1, m2}, {3, m3}, - {1, m4}}] + - (r203*TVI[d, PP, - {{1, m5}, {1, m3}, {2, m2}, {1, m1}}])/ - (4*r3) + (r232* - TVI[d, PP, - {{1, m5}, {1, m4}, {2, m1}, {1, m2}}])/ - (4*r3) + (r236* - TVI[d, PP, - 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((-72*d*m1^6 + 144*d^2*m1^6 - 88*d^3*m1^6 + 16*d^4*m1^6 - - 96*m1^4*pp + 260*d*m1^4*pp - 166*d^2*m1^4*pp + - 12*d^3*m1^4*pp + 6*d^4*m1^4*pp + 160*m1^2*pp^2 - - 300*d*m1^2*pp^2 + 50*d^2*m1^2*pp^2 + 90*d^3*m1^2*pp^2 - - 24*d^4*m1^2*pp^2 - 48*pp^3 + 114*d*pp^3 - 67*d^2*pp^3 + - 4*d^3*pp^3 + 2*d^4*pp^3)*TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ - (12*(-2 + d)*(-1 + d)^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) - - ((-4*m1^2 + pp)*(72*d*m1^6 - 144*d^2*m1^6 + 88*d^3*m1^6 - - 16*d^4*m1^6 + 96*m1^4*pp - 236*d*m1^4*pp + 122*d^2*m1^4*pp + - 12*d^3*m1^4*pp - 10*d^4*m1^4*pp - 96*m1^2*pp^2 + - 180*d*m1^2*pp^2 - 30*d^2*m1^2*pp^2 - 46*d^3*m1^2*pp^2 + - 8*d^4*m1^2*pp^2 + 24*pp^3 - 54*d*pp^3 + 27*d^2*pp^3)* - TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/ -(12*(-3 + d)*(-2 + d)*(-1 + d)^2*(1 + d)*(-4 + 3*d)*(-2 + 3*d)*pp^2) /; \ -(m1=!=0)&&(pp=!=0);\ -\>", "Input"], - -Cell["\<\ -TVR[6 + d_Symbol, pp_, - {{1, m1_}, {1, m1_}, {4, 0}, {1, m1_}}] := - ((2304*d*m1^10 - 4608*d^2*m1^10 - 3520*d^3*m1^10 + 6976*d^4*m1^10 + - 1472*d^5*m1^10 - 2624*d^6*m1^10 - 256*d^7*m1^10 + - 256*d^8*m1^10 + 4608*m1^8*pp - 9600*d*m1^8*pp - - 7680*d^2*m1^8*pp + 9312*d^3*m1^8*pp + 11680*d^4*m1^8*pp - - 6560*d^5*m1^8*pp - 2880*d^6*m1^8*pp + 1088*d^7*m1^8*pp + - 32*d^8*m1^8*pp + 6912*m1^6*pp^2 - 35712*d*m1^6*pp^2 + - 1056*d^2*m1^6*pp^2 + 85296*d^3*m1^6*pp^2 - - 37032*d^4*m1^6*pp^2 - 20484*d^5*m1^6*pp^2 + - 8700*d^6*m1^6*pp^2 - 12*d^7*m1^6*pp^2 - 84*d^8*m1^6*pp^2 - - 20736*m1^4*pp^3 + 58752*d*m1^4*pp^3 + 40560*d^2*m1^4*pp^3 - - 150536*d^3*m1^4*pp^3 + 18980*d^4*m1^4*pp^3 + - 48946*d^5*m1^4*pp^3 - 6748*d^6*m1^4*pp^3 - 146*d^7*m1^4*pp^3 + - 128*d^8*m1^4*pp^3 + 3456*m1^2*pp^4 - 13824*d*m1^2*pp^4 - - 4176*d^2*m1^2*pp^4 + 35784*d^3*m1^2*pp^4 - - 8332*d^4*m1^2*pp^4 - 10162*d^5*m1^2*pp^4 + - 1122*d^6*m1^2*pp^4 - 80*d^7*m1^2*pp^4 - 8*d^8*m1^2*pp^4 + - 864*d*pp^5 - 216*d^2*pp^5 - 2268*d^3*pp^5 + 486*d^4*pp^5 + - 729*d^5*pp^5)*TAI[d, 0, {{1, m1}}]^2)/ - (432*(-3 + d)*(-1 + d)^2*d^2*(1 + d)*(2 + d)*(3 + d)*(-4 + 3*d)* - (-2 + 3*d)*(2 + 3*d)*m1^2*pp^3) + - ((4*m1^2 - pp)^3*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/ - (16*(-3 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*m1^2) - - ((-1152*m1^10 + 2880*d*m1^10 + 320*d^2*m1^10 - 3648*d^3*m1^10 + - 1088*d^4*m1^10 + 768*d^5*m1^10 - 256*d^6*m1^10 - 192*m1^8*pp + - 1312*d*m1^8*pp + 2080*d^2*m1^8*pp - 6880*d^3*m1^8*pp + - 4032*d^4*m1^8*pp - 192*d^5*m1^8*pp - 160*d^6*m1^8*pp + - 6336*m1^6*pp^2 - 6960*d*m1^6*pp^2 - 16960*d^2*m1^6*pp^2 + - 17292*d^3*m1^6*pp^2 - 1828*d^4*m1^6*pp^2 - 828*d^5*m1^6*pp^2 + - 68*d^6*m1^6*pp^2 - 9504*m1^4*pp^3 + 3624*d*m1^4*pp^3 + - 26104*d^2*m1^4*pp^3 - 10938*d^3*m1^4*pp^3 - - 4976*d^4*m1^4*pp^3 + 330*d^5*m1^4*pp^3 + 400*d^6*m1^4*pp^3 + - 6336*m1^2*pp^4 - 3640*d*m1^2*pp^4 - 14584*d^2*m1^2*pp^4 + - 9190*d^3*m1^2*pp^4 + 1374*d^4*m1^2*pp^4 - 600*d^5*m1^2*pp^4 - - 56*d^6*m1^2*pp^4 - 864*pp^5 + 732*d*pp^5 + 1864*d^2*pp^5 - - 1695*d^3*pp^5 + 148*d^4*pp^5 + 36*d^5*pp^5 + 4*d^6*pp^5)* - TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ - (216*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)* - (2 + 3*d)*pp^3) + ((-4*m1^2 + pp)* - (1152*m1^10 - 2880*d*m1^10 - 320*d^2*m1^10 + 3648*d^3*m1^10 - - 1088*d^4*m1^10 - 768*d^5*m1^10 + 256*d^6*m1^10 + 576*m1^8*pp - - 2208*d*m1^8*pp - 2304*d^2*m1^8*pp + 8000*d^3*m1^8*pp - - 4256*d^4*m1^8*pp - 32*d^5*m1^8*pp + 224*d^6*m1^8*pp - - 6336*m1^6*pp^2 + 6288*d*m1^6*pp^2 + 16320*d^2*m1^6*pp^2 - - 14868*d^3*m1^6*pp^2 + 684*d^4*m1^6*pp^2 + 804*d^5*m1^6*pp^2 - - 12*d^6*m1^6*pp^2 + 6912*m1^4*pp^3 - 3192*d*m1^4*pp^3 - - 18160*d^2*m1^4*pp^3 + 7950*d^3*m1^4*pp^3 + 3128*d^4*m1^4*pp^3 - - 78*d^5*m1^4*pp^3 - 160*d^6*m1^4*pp^3 - 3456*m1^2*pp^4 + - 1800*d*m1^2*pp^4 + 8136*d^2*m1^2*pp^4 - 4322*d^3*m1^2*pp^4 - - 1042*d^4*m1^2*pp^4 + 128*d^5*m1^2*pp^4 + 16*d^6*m1^2*pp^4 + - 432*pp^5 - 324*d*pp^5 - 972*d^2*pp^5 + 729*d^3*pp^5)* - TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/ - (216*(-3 + d)*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)* - (-2 + 3*d)*(2 + 3*d)*pp^3) /; (m1=!=0)&&(pp=!=0);\ -\>", "Input"], - -Cell["\<\ - TVR[6 + d_Symbol, pp_, {{2, m1_}, {1, m1_}, {3, 0}, {1, m1_}}] := - -((-1536*d*m1^10 + 2560*d^2*m1^10 + 3200*d^3*m1^10 - 3584*d^4*m1^10 - - 2176*d^5*m1^10 + 1024*d^6*m1^10 + 512*d^7*m1^10 - - 3072*m1^8*pp + 6528*d*m1^8*pp + 5376*d^2*m1^8*pp - - 7520*d^3*m1^8*pp - 5568*d^4*m1^8*pp + 3232*d^5*m1^8*pp + - 1344*d^6*m1^8*pp - 320*d^7*m1^8*pp - 2304*m1^6*pp^2 + - 13824*d*m1^6*pp^2 + 192*d^2*m1^6*pp^2 - 31584*d^3*m1^6*pp^2 + - 11232*d^4*m1^6*pp^2 + 8088*d^5*m1^6*pp^2 - - 2304*d^6*m1^6*pp^2 - 24*d^7*m1^6*pp^2 + 6912*m1^4*pp^3 - - 19584*d*m1^4*pp^3 - 12688*d^2*m1^4*pp^3 + - 50584*d^3*m1^4*pp^3 - 7516*d^4*m1^4*pp^3 - - 16982*d^5*m1^4*pp^3 + 2564*d^6*m1^4*pp^3 + 310*d^7*m1^4*pp^3 - - 1152*m1^2*pp^4 + 4608*d*m1^2*pp^4 + 1392*d^2*m1^2*pp^4 - - 11896*d^3*m1^2*pp^4 + 2820*d^4*m1^2*pp^4 + - 3374*d^5*m1^2*pp^4 - 414*d^6*m1^2*pp^4 + 8*d^7*m1^2*pp^4 - - 288*d*pp^5 + 72*d^2*pp^5 + 756*d^3*pp^5 - 162*d^4*pp^5 - - 243*d^5*pp^5)*TAI[d, 0, {{1, m1}}]^2)/ - (144*(-1 + d)^2*d^2*(1 + d)*(2 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)* - (2 + 3*d)*m1^2*pp^3) + - ((4*m1^2 - pp)^3*TAI[d, 0, {{1, m1}}]*TBI[d, pp, {{1, m1}, {1, m1}}])/ - (16*(-1 + d)^2*d*(1 + d)*(3 + d)*m1^2) - - ((2304*m1^10 - 5760*d*m1^10 - 640*d^2*m1^10 + 7296*d^3*m1^10 - - 2176*d^4*m1^10 - 1536*d^5*m1^10 + 512*d^6*m1^10 - - 1344*m1^8*pp + 1120*d*m1^8*pp - 1376*d^2*m1^8*pp + - 5280*d^3*m1^8*pp - 4896*d^4*m1^8*pp + 1280*d^5*m1^8*pp - - 64*d^6*m1^8*pp - 5184*m1^6*pp^2 + 7584*d*m1^6*pp^2 + - 14800*d^2*m1^6*pp^2 - 21496*d^3*m1^6*pp^2 + - 6120*d^4*m1^6*pp^2 + 280*d^5*m1^6*pp^2 - 184*d^6*m1^6*pp^2 + - 9504*m1^4*pp^3 - 3720*d*m1^4*pp^3 - 27296*d^2*m1^4*pp^3 + - 15378*d^3*m1^4*pp^3 + 4114*d^4*m1^4*pp^3 - 666*d^5*m1^4*pp^3 - - 674*d^6*m1^4*pp^3 - 6336*m1^2*pp^4 + 5720*d*m1^2*pp^4 + - 13712*d^2*m1^2*pp^4 - 13926*d^3*m1^2*pp^4 + - 1284*d^4*m1^2*pp^4 + 946*d^5*m1^2*pp^4 - 80*d^6*m1^2*pp^4 + - 864*pp^5 - 1020*d*pp^5 - 1636*d^2*pp^5 + 2311*d^3*pp^5 - - 693*d^4*pp^5 + 20*d^5*pp^5 + 4*d^6*pp^5)* - TJI[d, pp, {{1, m1}, {1, m1}, {1, 0}}])/ - (72*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)* - (2 + 3*d)*pp^3) + ((4*m1^2 - pp)* - (-768*m1^10 + 1664*d*m1^10 + 768*d^2*m1^10 - 2176*d^3*m1^10 + - 512*d^5*m1^10 + 192*m1^8*pp + 288*d*m1^8*pp + 704*d^2*m1^8*pp - - 2272*d^3*m1^8*pp + 1024*d^4*m1^8*pp + 64*d^5*m1^8*pp + - 1920*m1^6*pp^2 - 1824*d*m1^6*pp^2 - 5472*d^2*m1^6*pp^2 + - 4584*d^3*m1^6*pp^2 - 168*d^5*m1^6*pp^2 - 2304*m1^4*pp^3 + - 616*d*m1^4*pp^3 + 6192*d^2*m1^4*pp^3 - 1946*d^3*m1^4*pp^3 - - 1128*d^4*m1^4*pp^3 - 230*d^5*m1^4*pp^3 + 1152*m1^2*pp^4 - - 600*d*m1^2*pp^4 - 2744*d^2*m1^2*pp^4 + 1414*d^3*m1^2*pp^4 + - 374*d^4*m1^2*pp^4 - 16*d^5*m1^2*pp^4 - 144*pp^5 + 108*d*pp^5 + - 324*d^2*pp^5 - 243*d^3*pp^5)* - TJI[d, pp, {{2, m1}, {1, m1}, {1, 0}}])/ - (72*(-2 + d)*(-1 + d)^2*d*(1 + d)*(3 + d)*(-4 + 3*d)*(-2 + 3*d)* - (2 + 3*d)*pp^3) /; (m1=!=0)&&(pp=!=0);\ -\>", "Input"] -}, Open ]], - -Cell[CellGroupData[{ - -Cell["five -> four", "Subsection", - CellTags->"T1.6.121.1"], - -Cell["\<\ -TFI[d_, PP_/;Head[PP]=!=List,{ {0, m1_}, {n2_, m2_}, - {n3_, m3_}, {n4_, m4_}, - {n5_, m5_} }] := -TVI[d,PP, {{n5,m5}, {n2,m2}, {n3,m3}, {n4,m4}}]\ -\>", "Text"], - -Cell[BoxData[ - 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Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/LICENSE.md b/LICENSE.md deleted file mode 100644 index 536cfcae1..000000000 --- a/LICENSE.md +++ /dev/null @@ -1 +0,0 @@ -[GNU General Public License Version 3](http://www.gnu.org/licenses/gpl-3.0.txt) diff --git a/README.MD b/README.MD index f00aa001e..e1a9bbbba 100644 --- a/README.MD +++ b/README.MD @@ -1,6 +1,6 @@ # FeynCalc -[![license: GPLv3](https://img.shields.io/badge/license-GPLv3-brightgreen.svg)](https://github.com/FeynCalc/feyncalc/LICENSE.md) +[![license: GPLv3](https://img.shields.io/badge/license-GPLv3-brightgreen.svg)](https://github.com/FeynCalc/feyncalc/blob/master/LICENSE) [![latest release](https://img.shields.io/github/release/FeynCalc/feyncalc.svg)](https://github.com/FeynCalc/feyncalc/releases) ![compatibility](https://img.shields.io/badge/Mathematica-8.x_9.x_10.x_11.x-brightgreen.svg) @@ -12,13 +12,13 @@ Visit our [wiki](https://github.com/FeynCalc/feyncalc/wiki) to learn more about # Using FeynCalc in your research -Development of FeynCalc costs of a lot of effort and is done on a largely voluntarily basis. +Development of FeynCalc costs a lot of effort and is done on a largely voluntarily basis. To support the developers and increase their academic visibility, please acknowledge our work when you use FeynCalc in your research. You can do so by citing the two FeynCalc papers: * V. Shtabovenko, R. Mertig and F. Orellana, "New Developments in FeynCalc 9.0", -Comput. Phys. Commun., 207C, 432-444, 2016, arXiv:1601.01167. +Comput. Phys. Commun., 207, 432--444, 2016, arXiv:1601.01167. * R. Mertig, M. Böhm, and A. Denner, "Feyn Calc - Computer-algebraic calculation of Feynman amplitudes", Comput. Phys. Commun., 64, 345--359, 1991. @@ -27,11 +27,11 @@ Comput. Phys. Commun., 64, 345--359, 1991. FeynCalc is covered by the GNU General Public License 3. -Copyright (C) 1990-2016 Rolf Mertig +Copyright (C) 1990-2018 Rolf Mertig -Copyright (C) 1997-2016 Frederik Orellana +Copyright (C) 1997-2018 Frederik Orellana -Copyright (C) 2014-2016 Vladyslav Shtabovenko +Copyright (C) 2014-2018 Vladyslav Shtabovenko FeynCalc is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as diff --git a/SUPPORT.md b/SUPPORT.md new file mode 100644 index 000000000..bbb25d6db --- /dev/null +++ b/SUPPORT.md @@ -0,0 +1 @@ +Before you submit an issue, please read the FeynCalc [support guidelines](https://github.com/FeynCalc/feyncalc/wiki/Support) first. diff --git a/Tests/Checks/CheckToTFI.m b/Tests/Checks/CheckToTFI.m index c8b6c0b41..1e2e1e222 100644 --- a/Tests/Checks/CheckToTFI.m +++ b/Tests/Checks/CheckToTFI.m @@ -1,14 +1,12 @@ (* ::Package:: *) - - (* :Title: CheckToTFI *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Checks that ToTFI is able to correctly convert all @@ -25,8 +23,8 @@ Print["Checking ToTFI"]; $FeynCalcStartupMessages = False; -$LoadFeynArts=True; -$LoadTARCER=True; +$LoadAddOns={"TARCER","FeynArts"}; + < False, Numbering -> None]; -amps = Map[ReplaceAll[#, FeynAmp[_, _, amp_, ___] :> amp] &,Apply[List, - FCPrepareFAAmp[CreateFeynAmp[inserts, Truncated -> True, - GaugeRules -> {}, PreFactor -> 1/((2^D)*(Pi)^(D/2))], - UndoChiralSplittings -> True]]] /. {SumOver[__] :> 1, - MQU[Index[Generation, 3]] -> MQ, - GaugeXi[_] -> GaugeXi} /. {InMom1 -> p, OutMom1 -> p, - LoopMom1 -> q1, LoopMom2 -> q2}; +amps = FCFAConvert[CreateFeynAmp[inserts, Truncated -> True, +GaugeRules -> {}, PreFactor -> 1/((2^D)*(Pi)^(D/2))],IncomingMomenta->{p}, +OutgoingMomenta->{p},LoopMomenta->{q1,q2},DropSumOver->True, +FinalSubstitutions->{MQU[Index[Generation, 3]] -> MQ},List->False,ChangeDimension->D]; + -xx = ApartFF[Total[amps], {q1, q2}]; -yy = Isolate[Collect2[xx, FeynAmpDenominator], FeynAmpDenominator] /. +xx = ApartFF[amps, {q1, q2},Collecting->False]; +yy=Collect2[xx,FeynAmpDenominator,Factoring->False,IsolateNames->KK] /. FeynAmpDenominator[x__] :> FRH[FeynAmpDenominator[x]]; zz = ToTFI[#, q1, q2, p] & /@ Cases[yy, FeynAmpDenominator[__], Infinity] // Union; -a = Cases[zz, FAD[__], Infinity] // Union; -b = Cases[zz, TFI[__], Infinity] // Union; +a = Cases2[zz, FAD]; +b = Cases2[zz, TFI]; On[Assert]; Assert[a === {FAD[p]}] -Assert[b === {TFI[D, - SPD[p, p], {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {0, 0}}], -TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {1, 0}, {0, 0}}], -TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {1, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {1, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {2, 0}, {0, 0}}], -TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {2, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {2, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {0, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {0, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {1, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {2, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {2, 0}, {0, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {2, 0}, {0, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{2, 0}, {1, MQ}, {1, 0}, {0, 0}, {1, MQ}}], -TFI[D, SPD[p, - p], {{2, 0}, {1, MQD[Index[Generation, 3]]}, {1, 0}, {0, 0}, {1, - MQD[Index[Generation, 3]]}}], -TFI[D, SPD[p, p], {{2, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{2, 0}, {2, 0}, {1, 0}, {0, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{3, 0}, {1, 0}, {1, 0}, {0, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{3, 0}, {1, 0}, {1, 0}, {0, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{3, 0}, {1, MQ}, {1, 0}, {0, 0}, {1, MQ}}], -TFI[D, SPD[p, - p], {{3, 0}, {1, MQD[Index[Generation, 3]]}, {1, 0}, {0, 0}, {1, - MQD[Index[Generation, 3]]}}], -TFI[D, SPD[p, p], {{3, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{3, 0}, {2, 0}, {1, 0}, {0, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{4, 0}, {1, 0}, {1, 0}, {0, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{4, 0}, {1, 0}, {1, 0}, {0, 0}, {2, 0}}], -TFI[D, SPD[p, p], {{4, 0}, {1, MQ}, {1, 0}, {0, 0}, {1, MQ}}], -TFI[D, SPD[p, - p], {{4, 0}, {1, MQD[Index[Generation, 3]]}, {1, 0}, {0, 0}, {1, - MQD[Index[Generation, 3]]}}], -TFI[D, SPD[p, p], {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}], -TFI[D, SPD[p, p], {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {2, 0}}]}]; +Assert[b === {TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {0, 0}}], TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {1, 0}}], TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {2, 0}}], +TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {1, 0}, {1, 0}}], TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {1, 0}, {2, 0}}], TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {2, 0}, {1, 0}}], +TFI[D, SPD[p, p], {{1, 0}, {1, 0}, {2, 0}, {2, 0}, {2, 0}}], TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {0, 0}, {1, 0}}], TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {0, 0}, {2, 0}}], +TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {1, 0}, {0, 0}}], TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {1, 0}, {1, 0}}], TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {1, 0}, {2, 0}, {1, 0}}], +TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {2, 0}, {0, 0}, {1, 0}}], TFI[D, SPD[p, p], {{2, 0}, {1, 0}, {2, 0}, {0, 0}, {2, 0}}], TFI[D, SPD[p, p], {{2, 0}, {1, MQ}, {1, 0}, {0, 0}, {1, MQ}}], +TFI[D, SPD[p, p], {{2, 0}, {1, MQD[Index[Generation, 3]]}, {1, 0}, {0, 0}, {1, MQD[Index[Generation, 3]]}}], TFI[D, SPD[p, p], {{2, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}], +TFI[D, SPD[p, p], {{2, 0}, {2, 0}, {1, 0}, {0, 0}, {2, 0}}], TFI[D, SPD[p, p], {{2, 0}, {2, 0}, {1, 0}, {1, 0}, {0, 0}}], TFI[D, SPD[p, p], {{3, 0}, {1, 0}, {1, 0}, {0, 0}, {1, 0}}], +TFI[D, SPD[p, p], {{3, 0}, {1, 0}, {1, 0}, {0, 0}, {2, 0}}], TFI[D, SPD[p, p], {{3, 0}, {1, MQ}, {1, 0}, {0, 0}, {1, MQ}}], +TFI[D, SPD[p, p], {{3, 0}, {1, MQD[Index[Generation, 3]]}, {1, 0}, {0, 0}, {1, MQD[Index[Generation, 3]]}}], TFI[D, SPD[p, p], {{3, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}], +TFI[D, SPD[p, p], {{3, 0}, {2, 0}, {1, 0}, {0, 0}, {2, 0}}], TFI[D, SPD[p, p], {{4, 0}, {1, 0}, {1, 0}, {0, 0}, {1, 0}}], TFI[D, SPD[p, p], {{4, 0}, {1, 0}, {1, 0}, {0, 0}, {2, 0}}], +TFI[D, SPD[p, p], {{4, 0}, {1, MQ}, {1, 0}, {0, 0}, {1, MQ}}], TFI[D, SPD[p, p], {{4, 0}, {1, MQD[Index[Generation, 3]]}, {1, 0}, {0, 0}, {1, MQD[Index[Generation, 3]]}}], +TFI[D, SPD[p, p], {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {1, 0}}], TFI[D, SPD[p, p], {{4, 0}, {2, 0}, {1, 0}, {0, 0}, {2, 0}}]}]; diff --git a/Tests/Dirac/Anti5.test b/Tests/Dirac/Anti5.test index 7461e742f..487276408 100644 --- a/Tests/Dirac/Anti5.test +++ b/Tests/Dirac/Anti5.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Anti5 *) @@ -15,7 +15,7 @@ Tests`Dirac`fcstAnti5ToTheRight = { -{"fcstAnti5ToTheRight-ID1","$BreitMaison=False;\n $Larin=False;\n Anti5[GA[5].GA[mu]]", +{"fcstAnti5ToTheRight-ID1","FCSetDiracGammaScheme[\"NDR\"];\n Anti5[GA[5].GA[mu]]", "-DiracGamma[LorentzIndex[mu]] . DiracGamma[5]"}, {"fcstAnti5ToTheRight-ID2","Anti5[GA[5].GA[mu], 1]", "-DiracGamma[LorentzIndex[mu]] . DiracGamma[5]"}, @@ -48,7 +48,13 @@ Tests`Dirac`fcstAnti5ToTheRight = { {"fcstAnti5ToTheRight-ID15","Anti5[GA[5].GAE[mu].GAE[nu].GAE[rho], Infinity]", "DiracGamma[5] . DiracGamma[LorentzIndex[mu, -4 + D], -4 + D] . DiracGamma[LorentzIndex[nu, -4 + D], -4 + D] . DiracGamma[LorentzIndex[rho, -4 + D], -4 + D]"}, -{"fcstAnti5ToTheRight-ID16","$BreitMaison=True;\nAnti5[GA[5].GA[mu]]", +{"fcstAnti5ToTheRight-ID15.1","Anti5[GA[5].CGA[i], 1] // FCE", "-CGA[i].GA[5]"}, +{"fcstAnti5ToTheRight-ID15.2","Anti5[GA[5].CGA[i, j, k]] // FCE", "-CGA[i].GA[5].CGA[j].CGA[k]"}, +{"fcstAnti5ToTheRight-ID15.3","Anti5[GA[5].CGA[i, j, k], Infinity] // FCE", "-CGA[i].CGA[j].CGA[k].GA[5]"}, +{"fcstAnti5ToTheRight-ID15.4","Anti5[GA[5].CGAD[i], 1] // FCE", "-CGAD[i].GA[5]"}, +{"fcstAnti5ToTheRight-ID15.5","Anti5[GA[5].CGAD[i, j, k]] // FCE", "-CGAD[i].GA[5].CGAD[j].CGAD[k]"}, +{"fcstAnti5ToTheRight-ID15.6","Anti5[GA[5].CGAD[i, j, k], Infinity] // FCE", "-CGAD[i].CGAD[j].CGAD[k].GA[5]"}, +{"fcstAnti5ToTheRight-ID16","FCSetDiracGammaScheme[\"BMHV\"];\nAnti5[GA[5].GA[mu]]", "-DiracGamma[LorentzIndex[mu]] . DiracGamma[5]"}, {"fcstAnti5ToTheRight-ID17","Anti5[GA[5].GA[mu], 1]", "-DiracGamma[LorentzIndex[mu]] . DiracGamma[5]"}, @@ -98,12 +104,23 @@ Tests`Dirac`fcstAnti5ToTheRight = { DiracGamma[LorentzIndex[rho, -4 + D], -4 + D]"}, {"fcstAnti5ToTheRight-ID30","Anti5[GA[5].GAE[mu].GAE[nu].GAE[rho], Infinity]", "DiracGamma[LorentzIndex[mu, -4 + D], -4 + D] . DiracGamma[LorentzIndex[nu, -4 + D], -4 + D] . - DiracGamma[LorentzIndex[rho, -4 + D], -4 + D] . DiracGamma[5]"} + DiracGamma[LorentzIndex[rho, -4 + D], -4 + D] . DiracGamma[5]"}, +{"fcstAnti5ToTheRight-ID30.1","Anti5[GA[5].CGAD[i], 1] // FCE", "-CGAD[i].GA[5] + 2 CGAE[i].GA[5]"}, +{"fcstAnti5ToTheRight-ID30.2","Anti5[GA[5].CGAD[i, j, k]] // FCE", "-CGAD[i].GA[5].CGAD[j].CGAD[k] + 2 CGAE[i].GA[5].CGAD[j].CGAD[k]"}, +{"fcstAnti5ToTheRight-ID30.3","Anti5[GA[5].CGAD[i, j, k], Infinity] // FCE", "-CGAD[i].CGAD[j].CGAD[k].GA[5] + 2 CGAD[i].CGAD[j].CGAE[k].GA[5] - +2 (-CGAD[i].CGAE[j].CGAD[k].GA[5] + + 2 CGAD[i].CGAE[j].CGAE[k].GA[5]) + +2 (CGAE[i].CGAD[j].CGAD[k].GA[5] - 2 CGAE[i].CGAD[j].CGAE[k].GA[5] + + 2 (-CGAE[i].CGAE[j].CGAD[k].GA[5] + + 2 CGAE[i].CGAE[j].CGAE[k].GA[5]))"}, +{"fcstAnti5ToTheRight-ID30.4","Anti5[GA[5].CGAE[i], 1] // FCE", "CGAE[i].GA[5]"}, +{"fcstAnti5ToTheRight-ID30.5","Anti5[GA[5].CGAE[i, j, k]] // FCE", "CGAE[i].GA[5].CGAE[j].CGAE[k]"}, +{"fcstAnti5ToTheRight-ID30.6","Anti5[GA[5].CGAE[i, j, k], Infinity] // FCE", "CGAE[i].CGAE[j].CGAE[k].GA[5]"} }; Tests`Dirac`fcstAnti5ToTheLeft = { -{"fcstAnti5ToTheLeft-ID1","$BreitMaison=False;\n $Larin=False;\n Anti5[GA[mu].GA[5]]", +{"fcstAnti5ToTheLeft-ID1","FCSetDiracGammaScheme[\"NDR\"]\n Anti5[GA[mu].GA[5]]", "DiracGamma[LorentzIndex[mu]] . DiracGamma[5]"}, {"fcstAnti5ToTheLeft-ID2","Anti5[GA[mu].GA[5], -1]", "-DiracGamma[5] . DiracGamma[LorentzIndex[mu]]"}, @@ -148,7 +165,14 @@ Tests`Dirac`fcstAnti5ToTheLeft = { "DiracGamma[LorentzIndex[mu, -4 + D], -4 + D] . DiracGamma[LorentzIndex[nu, -4 + D], -4 + D] . DiracGamma[LorentzIndex[rho, -4 + D], -4 + D] . DiracGamma[5]"}, -{"fcstAnti5ToTheLeft-ID16","$BreitMaison=True;\nAnti5[GA[mu].GA[5]]", +{"fcstAnti5ToTheLeft-ID15.1","Anti5[CGA[i].GA[5], -1] // FCE", "-GA[5].CGA[i]"}, +{"fcstAnti5ToTheLeft-ID15.2","Anti5[CGA[i, j, k].GA[5],-2] // FCE", "CGA[i].GA[5].CGA[j].CGA[k]"}, +{"fcstAnti5ToTheLeft-ID15.3","Anti5[CGA[i, j, k].GA[5], -Infinity] // FCE", "-GA[5].CGA[i].CGA[j].CGA[k]"}, +{"fcstAnti5ToTheLeft-ID15.4","Anti5[CGAD[i].GA[5], -1] // FCE", "-GA[5].CGAD[i]"}, +{"fcstAnti5ToTheLeft-ID15.5","Anti5[CGAD[i, j, k].GA[5],-2] // FCE", "CGAD[i].GA[5].CGAD[j].CGAD[k]"}, +{"fcstAnti5ToTheLeft-ID15.6","Anti5[CGAD[i, j, k].GA[5], -Infinity] // FCE", "-GA[5].CGAD[i].CGAD[j].CGAD[k]"}, + +{"fcstAnti5ToTheLeft-ID16","FCSetDiracGammaScheme[\"BMHV\"];\nAnti5[GA[mu].GA[5]]", "DiracGamma[LorentzIndex[mu]] . DiracGamma[5]"}, {"fcstAnti5ToTheLeft-ID17","Anti5[GA[mu].GA[5], -1]", "-DiracGamma[5] . DiracGamma[LorentzIndex[mu]]"}, @@ -210,11 +234,24 @@ DiracGamma[LorentzIndex[rho, -4 + D], -4 + D]"}, {"fcstAnti5ToTheLeft-ID30","Anti5[GAE[mu].GAE[nu].GAE[rho].GA[5], -Infinity]", "DiracGamma[5] . DiracGamma[LorentzIndex[mu, -4 + D], -4 + D] . DiracGamma[LorentzIndex[nu, -4 + D], -4 + D] . -DiracGamma[LorentzIndex[rho, -4 + D], -4 + D]"} +DiracGamma[LorentzIndex[rho, -4 + D], -4 + D]"}, +{"fcstAnti5ToTheLeft-ID30.1","Anti5[CGAD[i].GA[5], -1] // FCE", "-GA[5].CGAD[i] + 2 GA[5].CGAE[i]"}, +{"fcstAnti5ToTheLeft-ID30.2","Anti5[CGAD[i, j, k].GA[5],-2] // FCE", "CGAD[i].GA[5].CGAD[j].CGAD[k] - 2 CGAD[i].GA[5].CGAE[j].CGAD[k] + +2 (-CGAD[i].GA[5].CGAD[j].CGAE[k] + 2 CGAD[i].GA[5].CGAE[j].CGAE[k])"}, +{"fcstAnti5ToTheLeft-ID30.3","Anti5[CGAD[i, j, k].GA[5], -Infinity] // FCE", +"-GA[5].CGAD[i].CGAD[j].CGAD[k] + 2 GA[5].CGAE[i].CGAD[j].CGAD[k] - +2 (-GA[5].CGAD[i].CGAE[j].CGAD[k] + + 2 GA[5].CGAE[i].CGAE[j].CGAD[k]) + +2 (GA[5].CGAD[i].CGAD[j].CGAE[k] - 2 GA[5].CGAE[i].CGAD[j].CGAE[k] + + 2 (-GA[5].CGAD[i].CGAE[j].CGAE[k] + + 2 GA[5].CGAE[i].CGAE[j].CGAE[k]))"}, +{"fcstAnti5ToTheLeft-ID30.4","Anti5[CGAE[i].GA[5], -1] // FCE", "GA[5].CGAE[i]"}, +{"fcstAnti5ToTheLeft-ID30.5","Anti5[CGAE[i, j, k].GA[5],-2] // FCE", "CGAE[i].GA[5].CGAE[j].CGAE[k]"}, +{"fcstAnti5ToTheLeft-ID30.6","Anti5[CGAE[i, j, k].GA[5], -Infinity] // FCE", "GA[5].CGAE[i].CGAE[j].CGAE[k]"} }; Tests`Dirac`fcstAnti5EvenGamma5 = { -{"fcstAnti5EvenGamma5-ID1","$BreitMaison=False;\n $Larin=False;\n Anti5[GA[5].GA[5]]","1"}, +{"fcstAnti5EvenGamma5-ID1","FCSetDiracGammaScheme[\"NDR\"]\n Anti5[GA[5].GA[5]]","1"}, {"fcstAnti5EvenGamma5-ID2","Anti5[GA[5].GA[5].GA[5]]","DiracGamma[5]"}, {"fcstAnti5EvenGamma5-ID3","Anti5[GA[5].GA[5].GA[5].GA[5]]","1"}, {"fcstAnti5EvenGamma5-ID4","Anti5[GA[5].GA[i].GA[5].GA[j].GA[5].GA[k].GA[5],Infinity]", @@ -224,46 +261,44 @@ Tests`Dirac`fcstAnti5EvenGamma5 = { Tests`Dirac`fcstAnti5Gamma567 = { -{"fcstAnti5Gamma567-ID1","$BreitMaison=False; \n $Larin=False; \nAnti5[x.GA[5].GA[6].GA[i]]//FCE","x . GA[i]/2 - x . GA[i] . GA[5]/2"}, -{"fcstAnti5Gamma567-ID2","Anti5[x.GA[5].GA[7].GA[i]] // FCE","-x . GA[i]/2 - x . GA[i] . GA[5]/2"}, -{"fcstAnti5Gamma567-ID3","Anti5[x.GA[6].GA[5].GA[i]] // FCE","(1/2) x.GA[i] - 1/2 x.GA[i].GA[5]"}, -{"fcstAnti5Gamma567-ID4","Anti5[x.GA[6].GA[6].GA[i]] // FCE","1/2 x.GA[i] - 1/2 x.GA[i].GA[5]"}, +{"fcstAnti5Gamma567-ID1","FCSetDiracGammaScheme[\"NDR\"]; \nAnti5[x.GA[5].GA[6].GA[i]]//FCE","x*GA[i] . GA[7]"}, +{"fcstAnti5Gamma567-ID2","Anti5[x.GA[5].GA[7].GA[i]] // FCE","-(x*GA[i] . GA[6])"}, +{"fcstAnti5Gamma567-ID3","Anti5[x.GA[6].GA[5].GA[i]] // FCE","x*GA[i] . GA[7]"}, +{"fcstAnti5Gamma567-ID4","Anti5[x.GA[6].GA[6].GA[i]] // FCE","x*GA[i] . GA[7]"}, {"fcstAnti5Gamma567-ID5","Anti5[x.GA[6].GA[7].GA[i]] // FCE","0"}, -{"fcstAnti5Gamma567-ID6","Anti5[x.GA[7].GA[5].GA[i]] // FCE","x.GA[i].GA[5]"}, +{"fcstAnti5Gamma567-ID6","Anti5[x.GA[7].GA[5].GA[i]] // FCE","-(x*GA[i] . GA[6])"}, {"fcstAnti5Gamma567-ID7","Anti5[x.GA[7].GA[6].GA[i]] // FCE","0"}, -{"fcstAnti5Gamma567-ID8","Anti5[x.GA[7].GA[7].GA[i]] // FCE","(1/2) x.GA[i] + 1/2 x.GA[i].GA[5]"}, -{"fcstAnti5Gamma567-ID9","Anti5[GA[i].GA[5].GA[6].y] // FCE","1/2 GA[i].y + 1/2 GA[i].GA[5].y"}, -{"fcstAnti5Gamma567-ID10","Anti5[GA[i].GA[5].GA[7].y] // FCE","-1/2 GA[i].y + 1/2 GA[i].GA[5].y"}, -{"fcstAnti5Gamma567-ID11","Anti5[GA[i].GA[6].GA[5].y] // FCE","(1/2) GA[i].y + 1/2 GA[i].GA[5].y"}, -{"fcstAnti5Gamma567-ID12","Anti5[GA[i].GA[6].GA[6].y] // FCE","1/2 GA[i].y + 1/2 GA[i].GA[5].y"}, +{"fcstAnti5Gamma567-ID8","Anti5[x.GA[7].GA[7].GA[i]] // FCE","x*GA[i] . GA[6]"}, +{"fcstAnti5Gamma567-ID9","Anti5[GA[i].GA[5].GA[6].y] // FCE","y*GA[i] . GA[6]"}, +{"fcstAnti5Gamma567-ID10","Anti5[GA[i].GA[5].GA[7].y] // FCE","-(y*GA[i] . GA[7])"}, +{"fcstAnti5Gamma567-ID11","Anti5[GA[i].GA[6].GA[5].y] // FCE","y*GA[i] . GA[6]"}, +{"fcstAnti5Gamma567-ID12","Anti5[GA[i].GA[6].GA[6].y] // FCE","y*GA[i] . GA[6]"}, {"fcstAnti5Gamma567-ID13","Anti5[GA[i].GA[6].GA[7].y] // FCE","0"}, -{"fcstAnti5Gamma567-ID14","Anti5[GA[i].GA[7].GA[5].y] // FCE","-GA[i].GA[5].y"}, +{"fcstAnti5Gamma567-ID14","Anti5[GA[i].GA[7].GA[5].y] // FCE","-(y*GA[i] . GA[7])"}, {"fcstAnti5Gamma567-ID15","Anti5[GA[i].GA[7].GA[6].y] // FCE","0"}, -{"fcstAnti5Gamma567-ID16","Anti5[GA[i].GA[7].GA[7].y] // FCE","+(1/2) GA[i].y - 1/2 GA[i].GA[5].y"}, -{"fcstAnti5Gamma567-ID17","$BreitMaison=True;\n $Larin=False; \n Anti5[x.GA[5].GA[6].GA[i]]//FCE","1/2 x.GA[i] - 1/2 x.GA[i].GA[5]"}, -{"fcstAnti5Gamma567-ID18","Anti5[x.GA[5].GA[7].GA[i]] // FCE","-1/2 x.GA[i] - 1/2 x.GA[i].GA[5]"}, -{"fcstAnti5Gamma567-ID19","Anti5[x.GA[6].GA[5].GA[i]] // FCE","(1/2) x.GA[i] - 1/2 x.GA[i].GA[5]"}, -{"fcstAnti5Gamma567-ID20","Anti5[x.GA[6].GA[6].GA[i]] // FCE","1/2 x.GA[i] - 1/2 x.GA[i].GA[5]"}, +{"fcstAnti5Gamma567-ID16","Anti5[GA[i].GA[7].GA[7].y] // FCE","y*GA[i] . GA[7]"}, +{"fcstAnti5Gamma567-ID17","FCSetDiracGammaScheme[\"BMHV\"]; \n Anti5[x.GA[5].GA[6].GA[i]]//FCE","x*GA[i] . GA[7]"}, +{"fcstAnti5Gamma567-ID18","Anti5[x.GA[5].GA[7].GA[i]] // FCE","-(x*GA[i] . GA[6])"}, +{"fcstAnti5Gamma567-ID19","Anti5[x.GA[6].GA[5].GA[i]] // FCE","x*GA[i] . GA[7]"}, +{"fcstAnti5Gamma567-ID20","Anti5[x.GA[6].GA[6].GA[i]] // FCE","x*GA[i] . GA[7]"}, {"fcstAnti5Gamma567-ID21","Anti5[x.GA[6].GA[7].GA[i]] // FCE","0"}, -{"fcstAnti5Gamma567-ID22","Anti5[x.GA[7].GA[5].GA[i]] // FCE","x.GA[i].GA[5]"}, +{"fcstAnti5Gamma567-ID22","Anti5[x.GA[7].GA[5].GA[i]] // FCE","-(x*GA[i] . GA[6])"}, {"fcstAnti5Gamma567-ID23","Anti5[x.GA[7].GA[6].GA[i]] // FCE","0"}, -{"fcstAnti5Gamma567-ID24","Anti5[x.GA[7].GA[7].GA[i]] // FCE","(1/2) x.GA[i] + 1/2 x.GA[i].GA[5]"}, -{"fcstAnti5Gamma567-ID25","Anti5[GA[i].GA[5].GA[6].y] // FCE","1/2 GA[i].y + 1/2 GA[i].GA[5].y"}, -{"fcstAnti5Gamma567-ID26","Anti5[GA[i].GA[5].GA[7].y] // FCE","-1/2 GA[i].y + 1/2 GA[i].GA[5].y"}, -{"fcstAnti5Gamma567-ID27","Anti5[GA[i].GA[6].GA[5].y] // FCE","(1/2) GA[i].y + 1/2 GA[i].GA[5].y"}, -{"fcstAnti5Gamma567-ID28","Anti5[GA[i].GA[6].GA[6].y] // FCE","1/2 GA[i].y + 1/2 GA[i].GA[5].y"}, +{"fcstAnti5Gamma567-ID24","Anti5[x.GA[7].GA[7].GA[i]] // FCE","x*GA[i] . GA[6]"}, +{"fcstAnti5Gamma567-ID25","Anti5[GA[i].GA[5].GA[6].y] // FCE","y*GA[i] . GA[6]"}, +{"fcstAnti5Gamma567-ID26","Anti5[GA[i].GA[5].GA[7].y] // FCE","-(y*GA[i] . GA[7])"}, +{"fcstAnti5Gamma567-ID27","Anti5[GA[i].GA[6].GA[5].y] // FCE","y*GA[i] . GA[6]"}, +{"fcstAnti5Gamma567-ID28","Anti5[GA[i].GA[6].GA[6].y] // FCE","y*GA[i] . GA[6]"}, {"fcstAnti5Gamma567-ID29","Anti5[GA[i].GA[6].GA[7].y] // FCE","0"}, -{"fcstAnti5Gamma567-ID30","Anti5[GA[i].GA[7].GA[5].y] // FCE","-GA[i].GA[5].y"}, +{"fcstAnti5Gamma567-ID30","Anti5[GA[i].GA[7].GA[5].y] // FCE","-(y*GA[i] . GA[7])"}, {"fcstAnti5Gamma567-ID31","Anti5[GA[i].GA[7].GA[6].y] // FCE","0"}, -{"fcstAnti5Gamma567-ID32","Anti5[GA[i].GA[7].GA[7].y] // FCE","(1/2) GA[i].y - 1/2 GA[i].GA[5].y"} +{"fcstAnti5Gamma567-ID32","Anti5[GA[i].GA[7].GA[7].y] // FCE","y*GA[i] . GA[7]"} }; Tests`Dirac`fcstAnti5ToTheRightLarin = ({ -{"fcstAnti5ToTheRightLarin-ID1", "$BreitMaison=False; - $Larin=True; - Anti5[GA[5].GA[mu]]//FCE", "-GA[mu] . GA[5]"}, +{"fcstAnti5ToTheRightLarin-ID1", "FCSetDiracGammaScheme[\"Larin\"]; \n Anti5[GA[5].GA[mu]]//FCE", "-GA[mu] . GA[5]"}, {"fcstAnti5ToTheRightLarin-ID2", "Anti5[GA[5].GA[mu], 1]//FCE", "-GA[mu] . GA[5]"}, {"fcstAnti5ToTheRightLarin-ID3", @@ -307,9 +342,7 @@ Tests`Dirac`fcstAnti5ToTheRightLarin = Tests`Dirac`fcstAnti5ToTheLeftLarin = ({ -{"fcstAnti5ToTheLeftLarin-ID1", "$BreitMaison=False; - $Larin=True; - Anti5[GA[mu].GA[5]]//FCE", "GA[mu] . GA[5]"}, +{"fcstAnti5ToTheLeftLarin-ID1", "FCSetDiracGammaScheme[\"Larin\"]; \n Anti5[GA[mu].GA[5]]//FCE", "GA[mu] . GA[5]"}, {"fcstAnti5ToTheLeftLarin-ID2", "Anti5[GA[mu].GA[5], -1]//FCE", "-GA[5] . GA[mu]"}, {"fcstAnti5ToTheLeftLarin-ID3", @@ -351,10 +384,59 @@ Tests`Dirac`fcstAnti5ToTheLeftLarin = +Tests`Dirac`fcstAnti5ToTheRightLarin = +({ +{"fcstAnti5ToTheRightLarin-ID1", "FCSetDiracGammaScheme[\"Larin\"]; \n Anti5[GA[5].GA[mu]]//FCE", "-GA[mu] . GA[5]"}, +{"fcstAnti5ToTheRightLarin-ID2", "Anti5[GA[5].GA[mu], 1]//FCE", +"-GA[mu] . GA[5]"}, +{"fcstAnti5ToTheRightLarin-ID3", +"Anti5[GA[5].GA[mu, nu, rho]]//FCE", +"-GA[mu] . GA[5] . GA[nu] . GA[rho]"}, +{"fcstAnti5ToTheRightLarin-ID4", +"Anti5[GA[5].GA[mu, nu, rho], 2]//FCE", +"GA[mu] . GA[nu] . GA[5] . GA[rho]"}, +{"fcstAnti5ToTheRightLarin-ID5", +"Anti5[GA[5].GA[mu, nu, rho], Infinity]//FCE", +"-GA[mu] . GA[nu] . GA[rho] . GA[5]"}, +{"fcstAnti5ToTheRightLarin-ID6", "Anti5[GA[5].GAD[mu]]//FCE", +"GA[5] . GAD[mu]"}, +{"fcstAnti5ToTheRightLarin-ID7", "Anti5[GA[5].GAD[mu], 1]//FCE", +"GA[5] . GAD[mu]"}, +{"fcstAnti5ToTheRightLarin-ID8", +"Anti5[GA[5].GAD[mu, nu, rho]]//FCE", +"GA[5] . GAD[mu] . GAD[nu] . GAD[rho]"}, +{"fcstAnti5ToTheRightLarin-ID9", +"Anti5[GA[5].GAD[mu, nu, rho], 2]//FCE", +"GA[5] . GAD[mu] . GAD[nu] . GAD[rho]"}, +{"fcstAnti5ToTheRightLarin-ID10", +"Anti5[GA[5].GAD[mu, nu, rho], Infinity]//FCE", +"GA[5] . GAD[mu] . GAD[nu] . GAD[rho]"}, +{"fcstAnti5ToTheRightLarin-ID11", "Anti5[GA[5].GAE[i]]//FCE", +"GA[5] . GAE[i]"}, +{"fcstAnti5ToTheRightLarin-ID12", "Anti5[GA[5].GAE[i], 1]//FCE", +"GA[5] . GAE[i]"}, +{"fcstAnti5ToTheRightLarin-ID13", +"Anti5[GA[5].GAE[mu].GAE[nu].GAE[rho]]//FCE", +"GA[5] . GAE[mu] . GAE[nu] . GAE[rho]"}, +{"fcstAnti5ToTheRightLarin-ID14", +"Anti5[GA[5].GAE[mu].GAE[nu].GAE[rho],2]//FCE", +"GA[5] . GAE[mu] . GAE[nu] . GAE[rho]"}, +{"fcstAnti5ToTheRightLarin-ID15", +"Anti5[GA[5].GAE[mu].GAE[nu].GAE[rho], Infinity]//FCE", +"GA[5] . GAE[mu] . GAE[nu] . GAE[rho]"} +}); +Tests`Dirac`fcstAnti5DiracChain = +({ +{"fcstAnti5DiracChain-ID1", "Anti5[DCHN[GA[5, mu, nu, rho], i, j], FCE -> True]", + "-DCHN[GA[mu].GA[5].GA[nu].GA[rho], i, j]"}, +{"fcstAnti5DiracChain-ID2", "Anti5[DCHN[GAD[5, mu, nu, rho], i, j], 2, FCE -> True]", + "DCHN[GAD[mu].GAD[nu].GA[5].GAD[rho], i, j]"}, - +{"fcstAnti5DiracChain-ID3", "Anti5[DCHN[GAD[mu, nu, 5, rho], i, j], -1, FCE -> True]", + "-DCHN[GAD[mu].GA[5].GAD[nu].GAD[rho], i, j]"} +}); diff --git a/Tests/Dirac/Chisholm.test b/Tests/Dirac/Chisholm.test index 25b77c00b..cec01e097 100644 --- a/Tests/Dirac/Chisholm.test +++ b/Tests/Dirac/Chisholm.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Chisholm *) @@ -15,23 +15,213 @@ -Tests`Dirac`fcstChisholm = { -{"fcstChisholm-ID1", "(Chisholm[DiracMatrix[mu, nu, rho]]// FCRenameDummyIndices) /. {$AL[x_] -> tau}", -"I DiracGamma[LorentzIndex[tau]].DiracGamma[5] Eps[ - LorentzIndex[mu], LorentzIndex[nu], LorentzIndex[rho], - LorentzIndex[tau]] + - DiracGamma[LorentzIndex[rho]] Pair[LorentzIndex[mu], - LorentzIndex[nu]] - - DiracGamma[LorentzIndex[nu]] Pair[LorentzIndex[mu], - LorentzIndex[rho]] + - DiracGamma[LorentzIndex[mu]] Pair[LorentzIndex[nu], - LorentzIndex[rho]]"}, -{"fcstChisholm-ID2", "(Chisholm[GA[alpha, beta, mu, nu]] //FCRenameDummyIndices) /. {$AL[x_] -> rho}", -"(-I)*DiracGamma[LorentzIndex[rho]] . DiracGamma[LorentzIndex[nu]] . DiracGamma[5]* - Eps[LorentzIndex[alpha], LorentzIndex[beta], LorentzIndex[mu], LorentzIndex[rho]] + -DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[nu]]*Pair[LorentzIndex[alpha], LorentzIndex[beta]] - -DiracGamma[LorentzIndex[beta]] . DiracGamma[LorentzIndex[nu]]*Pair[LorentzIndex[alpha], LorentzIndex[mu]] + -DiracGamma[LorentzIndex[alpha]] . DiracGamma[LorentzIndex[nu]]*Pair[LorentzIndex[beta], LorentzIndex[mu]]"}, -{"fcstChisholm-ID3", "MatchQ[$LeviCivitaSign = I; tmp = Chisholm[GA[i1, i2, i3]]; $LeviCivitaSign = -1; FCE[tmp], -GA[a_].GA[5] LC[i1, i2, i3, a_] + GA[i3] MT[i1, i2] - GA[i2] MT[i1, i3] + GA[i1] MT[i2, i3]]", "True"} -}; +Tests`Dirac`fcstChisholm = +({ +{"fcstChisholm-ID1", "Chisholm[GAD[mu,nu,rho]]", +"DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[LorentzIndex[nu, \ +D], D] . DiracGamma[LorentzIndex[rho, D], D]"}, +{"fcstChisholm-ID2", +"Chisholm[GA[mu,nu,rho],FCE\[Rule]True]/.{$MU[x_]\[Rule]tau}", +"I*GA[tau] . GA[5]*LC[mu, nu, rho, tau] + GA[rho]*MT[mu, nu] - \ +GA[nu]*MT[mu, rho] + GA[mu]*MT[nu, rho]"}, +{"fcstChisholm-ID3", +"Chisholm[GA[alpha,beta,mu,nu],FCE\[Rule]True]/.{$MU[x_]\[Rule]tau}\ +", "I*GA[alpha] . GA[tau] . GA[5]*LC[beta, mu, nu, tau] + GA[alpha] . GA[nu]*MT[beta, mu] - +GA[alpha] . GA[mu]*MT[beta, nu] + GA[alpha] . GA[beta]*MT[mu, nu]"}, +{"fcstChisholm-ID4", +"MatchQ[$LeviCivitaSign=I;tmp=Chisholm[GA[i1,i2,i3]];$\ +LeviCivitaSign=-1;FCE[tmp],GA[a_].GA[5] LC[i1,i2,i3,a_]+GA[i3] \ +MT[i1,i2]-GA[i2] MT[i1,i3]+GA[i1] MT[i2,i3]]", "True"}, +{"fcstChisholm-ID5", "Chisholm[0]", "0"}, +{"fcstChisholm-ID6", "Chisholm[x]", "x"}, +{"fcstChisholm-ID7", +"Chisholm[x+GA[mu,nu,rho],FCE\[Rule]True]/.{$MU[x_]\[Rule]tau}", +"x + I*GA[tau] . GA[5]*LC[mu, nu, rho, tau] + GA[rho]*MT[mu, nu] - \ +GA[nu]*MT[mu, rho] + GA[mu]*MT[nu, rho]"}, +{"fcstChisholm-ID8", +"Chisholm[GA[mu,nu,rho],FCE\[Rule]True,FCDiracIsolate\[Rule]False]/.{\ +$MU[x_]\[Rule]tau}", +"I*GA[tau] . GA[5]*LC[mu, nu, rho, tau] + GA[rho]*MT[mu, nu] - \ +GA[nu]*MT[mu, rho] + GA[mu]*MT[nu, rho]"}, +{"fcstChisholm-ID9", +"MatchQ[Chisholm[GA[i,j,5],Mode\[Rule]2,FCE\[Rule]True],1/\ +2DiracSigma[GA[a_],GA[b_]] LC[i,j,a_,b_]+GA[5] MT[i,j]]", "True"}, +{"fcstChisholm-ID10", +"MatchQ[Chisholm[(x+GA[i,j,5]),FCE\[Rule]True,Mode\[Rule]2],x+1/2 \ +DiracSigma[GA[a_],GA[b_]] LC[i,j,a_,b_]+GA[5] MT[i,j]]", "True"}, +{"fcstChisholm-ID11", +"MatchQ[Chisholm[GA[k,i,j,5,g],FCE\[Rule]True,Mode\[Rule]2],1/2 \ +GA[k].DiracSigma[GA[a_],GA[b_]].GA[g] LC[i,j,a_,b_]-GA[k].GA[g].GA[5] \ +MT[i,j]]", "True"}, +{"fcstChisholm-ID12", +"MatchQ[Chisholm[GA[k,i,j,5,g],DiracSigmaExplicit\[Rule]True,FCE\ +\[Rule]True,Mode\[Rule]2],1/4 I GA[k].GA[a_].GA[b_].GA[g] \ +LC[i,j,a_,b_]-1/4 I GA[k].GA[b_].GA[a_].GA[g] \ +LC[i,j,a_,b_]-GA[k].GA[g].GA[5] MT[i,j]]", "True"}, +{"fcstChisholm-ID13", +"MatchQ[Chisholm[GA[i,j,5],Mode\[Rule]2,FCE\[Rule]True,\ +FCDiracIsolate\[Rule]False],1/2DiracSigma[GA[a_],GA[b_]] \ +LC[i,j,a_,b_]+GA[5] MT[i,j]]", "True"}, +{"fcstChisholm-ID14", +"MatchQ[Chisholm[(x+GA[i,j,5]),FCE\[Rule]True,Mode\[Rule]2,\ +FCDiracIsolate\[Rule]False],x+1/2 DiracSigma[GA[a_],GA[b_]] \ +LC[i,j,a_,b_]+GA[5] MT[i,j]]", "True"}, +{"fcstChisholm-ID15", +"MatchQ[Chisholm[GA[k,i,j,5,g],FCE\[Rule]True,Mode\[Rule]2,\ +FCDiracIsolate\[Rule]False],1/2 GA[k].DiracSigma[GA[a_],GA[b_]].GA[g] \ +LC[i,j,a_,b_]-GA[k].GA[g].GA[5] MT[i,j]]", "True"}, +{"fcstChisholm-ID16", +"MatchQ[Chisholm[GA[k,i,j,5,g],DiracSigmaExplicit\[Rule]True,FCE\ +\[Rule]True,Mode\[Rule]2,FCDiracIsolate\[Rule]False],1/4 I \ +GA[k].GA[a_].GA[b_].GA[g] LC[i,j,a_,b_]-1/4 I \ +GA[k].GA[b_].GA[a_].GA[g] LC[i,j,a_,b_]-GA[k].GA[g].GA[5] MT[i,j]]", +"True"}, +{"fcstChisholm-ID17", "Chisholm[CGA[i, j, k]]", +"DiracGamma[CartesianIndex[i]].DiracGamma[CartesianIndex[j]].DiracGamma[CartesianIndex[k]]"}, +{"fcstChisholm-ID18", +"MatchQ[$LeviCivitaSign=I; \ +Chisholm[DiracSigma[GA[mu],GA[nu]].GA[5],Mode\[Rule]2,FCE\[Rule]True],\ +\[IndentingNewLine]\!\(\*FractionBox[\(1\), \(2\)]\) \ +DiracSigma[GA[a_],GA[b_]] LC[mu,nu,a_,b_]]", "True"}, +{"fcstChisholm-ID19", +"MatchQ[$LeviCivitaSign=-1; \ +Chisholm[DiracSigma[GA[mu],GA[nu]].GA[5],Mode\[Rule]2,FCE\[Rule]True],\ +\[IndentingNewLine]I\!\(\*FractionBox[\(1\), \(2\)]\) \ +DiracSigma[GA[a_],GA[b_]] LC[mu,nu,a_,b_]]", "True"}, +{"fcstChisholm-ID20", +"MatchQ[$LeviCivitaSign=-I; \ +Chisholm[DiracSigma[GA[mu],GA[nu]].GA[5],Mode\[Rule]2,FCE\[Rule]True],\ +\[IndentingNewLine]-\!\(\*FractionBox[\(1\), \(2\)]\) \ +DiracSigma[GA[a_],GA[b_]] LC[mu,nu,a_,b_]]", "True"}, +{"fcstChisholm-ID21", +"MatchQ[$LeviCivitaSign=1; \ +Chisholm[DiracSigma[GA[mu],GA[nu]].GA[5],Mode\[Rule]2,FCE\[Rule]True],\ +\[IndentingNewLine]-I\!\(\*FractionBox[\(1\), \(2\)]\) \ +DiracSigma[GA[a_],GA[b_]] LC[mu,nu,a_,b_]]", "True"}, +{"fcstChisholm-ID22", +"MatchQ[$LeviCivitaSign=I; \ +Chisholm[GS[p].DiracSigma[GA[mu],GA[nu]].GA[5].GS[q],Mode\[Rule]2,FCE\ +\[Rule]True],\[IndentingNewLine]\!\(\*FractionBox[\(1\), \(2\)]\) \ +GS[p].DiracSigma[GA[a_],GA[b_]].GS[q] LC[mu,nu,a_,b_]]", "True"}, +{"fcstChisholm-ID23", +"MatchQ[$LeviCivitaSign=-I; \ +Chisholm[GS[p].DiracSigma[GA[mu],GA[nu]].GA[5].GS[q],Mode\[Rule]2,FCE\ +\[Rule]True],\[IndentingNewLine]-\!\(\*FractionBox[\(1\), \(2\)]\) \ +GS[p].DiracSigma[GA[a_],GA[b_]].GS[q] LC[mu,nu,a_,b_]]", "True"}, +{"fcstChisholm-ID24", +"MatchQ[$LeviCivitaSign=1; \ +Chisholm[GS[p].DiracSigma[GA[mu],GA[nu]].GA[5].GS[q],Mode\[Rule]2,FCE\ +\[Rule]True],\[IndentingNewLine]-I\!\(\*FractionBox[\(1\), \(2\)]\) \ +GS[p].DiracSigma[GA[a_],GA[b_]].GS[q] LC[mu,nu,a_,b_]]", "True"}, +{"fcstChisholm-ID25", +"MatchQ[$LeviCivitaSign=-1; \ +Chisholm[GS[p].DiracSigma[GA[mu],GA[nu]].GA[5].GS[q],Mode\[Rule]2,FCE\ +\[Rule]True],\[IndentingNewLine]I\!\(\*FractionBox[\(1\), \(2\)]\) \ +GS[p].DiracSigma[GA[a_],GA[b_]].GS[q] LC[mu,nu,a_,b_]]", "True"}, +{"fcstChisholm-ID26", +"FCCanonicalizeDummyIndices[ +Chisholm[SpinorUBar[p1].GA[a, b, c, d, e].SpinorU[p2], FCE -> True], +LorentzIndexNames -> {mu}]", +"I Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[b]].DiracGamma[ + 5].Spinor[Momentum[p2], 0, 1] Eps[LorentzIndex[a], +LorentzIndex[c], LorentzIndex[d], LorentzIndex[e]] - +I Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[a]].DiracGamma[ + 5].Spinor[Momentum[p2], 0, 1] Eps[LorentzIndex[b], +LorentzIndex[c], LorentzIndex[d], LorentzIndex[e]] + +I Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 5].Spinor[Momentum[p2], 0, 1] Eps[LorentzIndex[c], +LorentzIndex[d], LorentzIndex[e], LorentzIndex[mu]] Pair[ +LorentzIndex[a], LorentzIndex[b]] + +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[e]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[d]] Pair[ +LorentzIndex[b], LorentzIndex[c]] - +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[d]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[e]] Pair[ +LorentzIndex[b], LorentzIndex[c]] - +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[e]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[c]] Pair[ +LorentzIndex[b], LorentzIndex[d]] + +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[c]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[e]] Pair[ +LorentzIndex[b], LorentzIndex[d]] + +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[d]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[c]] Pair[ +LorentzIndex[b], LorentzIndex[e]] - +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[c]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[d]] Pair[ +LorentzIndex[b], LorentzIndex[e]] + +I Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 5].Spinor[Momentum[p2], 0, 1] Eps[LorentzIndex[a], +LorentzIndex[b], LorentzIndex[e], LorentzIndex[mu]] Pair[ +LorentzIndex[c], LorentzIndex[d]] + +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[e]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[b]] Pair[ +LorentzIndex[c], LorentzIndex[d]] - +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[b]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[e]] Pair[ +LorentzIndex[c], LorentzIndex[d]] + +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[a]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[b], LorentzIndex[e]] Pair[ +LorentzIndex[c], LorentzIndex[d]] - +I Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 5].Spinor[Momentum[p2], 0, 1] Eps[LorentzIndex[a], +LorentzIndex[b], LorentzIndex[d], LorentzIndex[mu]] Pair[ +LorentzIndex[c], LorentzIndex[e]] - +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[d]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[b]] Pair[ +LorentzIndex[c], LorentzIndex[e]] + +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[b]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[d]] Pair[ +LorentzIndex[c], LorentzIndex[e]] - +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[a]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[b], LorentzIndex[d]] Pair[ +LorentzIndex[c], LorentzIndex[e]] + +I Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 5].Spinor[Momentum[p2], 0, 1] Eps[LorentzIndex[a], +LorentzIndex[b], LorentzIndex[c], LorentzIndex[mu]] Pair[ +LorentzIndex[d], LorentzIndex[e]] + +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[c]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[b]] Pair[ +LorentzIndex[d], LorentzIndex[e]] - +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[b]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[a], LorentzIndex[c]] Pair[ +LorentzIndex[d], LorentzIndex[e]] + +Spinor[Momentum[p1], 0, 1].DiracGamma[LorentzIndex[a]].Spinor[ + Momentum[p2], 0, 1] Pair[LorentzIndex[b], LorentzIndex[c]] Pair[ +LorentzIndex[d], LorentzIndex[e]]"}, +{"fcstChisholm-ID27","Chisholm[DCHN[GA[i, j, k], a, b], FCDiracIsolate -> False] // +FCCanonicalizeDummyIndices[#, LorentzIndexNames -> {mu}, +FCE -> True] &", +"I DCHN[GA[mu].GA[5], a, b] LC[i, j, k, mu] + +DCHN[GA[k], a, b] MT[i, j] - DCHN[GA[j], a, b] MT[i, k] + +DCHN[GA[i], a, b] MT[j, k]"}, +{"fcstChisholm-ID28","Chisholm[DCHN[GA[i, j, k], a, b]] // +FCCanonicalizeDummyIndices[#, LorentzIndexNames -> {mu}, +FCE -> True] &","I DCHN[GA[mu].GA[5], a, b] LC[i, j, k, mu] + +DCHN[GA[k], a, b] MT[i, j] - DCHN[GA[j], a, b] MT[i, k] + +DCHN[GA[i], a, b] MT[j, k]"}, +{"fcstChisholm-ID29","Chisholm[DCHN[GA[i, j, k] + GA[i].GS[p].GA[j].GS[q].GA[k], a, b]] // +FCCanonicalizeDummyIndices[#, LorentzIndexNames -> {mu}, +FCE -> True] &","DCHN[GA[k], a, b] FV[p, j] FV[q, i] - +DCHN[GA[j], a, b] FV[p, k] FV[q, i] + +DCHN[GA[k], a, b] FV[p, i] FV[q, j] + +DCHN[GA[i], a, b] FV[p, k] FV[q, j] + +DCHN[GA[j], a, b] FV[p, i] FV[q, k] + +DCHN[GA[i], a, b] FV[p, j] FV[q, k] + +I DCHN[GA[mu].GA[5], a, b] LC[i, j, k, mu] + +DCHN[GA[k], a, b] MT[i, j] + DCHN[GS[q], a, b] FV[p, k] MT[i, j] - +DCHN[GS[p], a, b] FV[q, k] MT[i, j] - DCHN[GA[j], a, b] MT[i, k] - +DCHN[GS[q], a, b] FV[p, j] MT[i, k] - +DCHN[GS[p], a, b] FV[q, j] MT[i, k] + DCHN[GA[i], a, b] MT[j, k] - +DCHN[GS[q], a, b] FV[p, i] MT[j, k] + +DCHN[GS[p], a, b] FV[q, i] MT[j, k] - +DCHN[GA[k], a, b] MT[i, j] SP[p, q] + +DCHN[GA[j], a, b] MT[i, k] SP[p, q] - +DCHN[GA[i], a, b] MT[j, k] SP[p, q] - +I DCHN[GA[mu].GA[5], a, b] MT[j, k] LC[i, mu][p, q] + +I DCHN[GA[i].GA[5], a, b] LC[j, k][p, q] - +I DCHN[GS[p].GA[5], a, b] LC[i, j, k][q] + +I DCHN[GA[mu].GA[5], a, b] FV[q, k] LC[i, j, mu][p] + +I DCHN[GA[mu].GA[5], a, b] FV[q, j] LC[i, k, mu][p] + +I DCHN[GA[mu].GA[5], a, b] FV[p, i] LC[j, k, mu][q]"} +}) diff --git a/Tests/Dirac/Chisholm2.test b/Tests/Dirac/Chisholm2.test deleted file mode 100644 index d8cd8f191..000000000 --- a/Tests/Dirac/Chisholm2.test +++ /dev/null @@ -1,36 +0,0 @@ - - -(* :Title: Chisholm2.test *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Framework independent unit tests for Chisholm2 *) - -(* ------------------------------------------------------------------------ *) - - - -Tests`Dirac`fcstChisholm2 = -({ -{"fcstChisholm2-ID1", "Chisholm2[x]", "x"}, -{"fcstChisholm2-ID2", -"MatchQ[tmp=Chisholm2[GA[i,j,5]];FCE[tmp],1/2DiracSigma[GA[a_],GA[\ -b_]] LC[i,j,a_,b_]+GA[5] MT[i,j]]", "True"}, -{"fcstChisholm2-ID3", -"MatchQ[tmp=Chisholm2[(x+GA[i,j,5])];FCE[tmp],x+1/2 \ -DiracSigma[GA[a_],GA[b_]] LC[i,j,a_,b_]+GA[5] MT[i,j]]", "True"}, -{"fcstChisholm2-ID4", -"MatchQ[tmp=Chisholm2[GA[k,i,j,5,g]];FCE[tmp],1/2 \ -GA[k].DiracSigma[GA[a_],GA[b_]].GA[g] LC[i,j,a_,b_]-GA[k].GA[g].GA[5] \ -MT[i,j]]", "True"}, -{"fcstChisholm2-ID5", -"MatchQ[tmp=Chisholm2[GA[k,i,j,5,g],DiracSigmaExplicit\[Rule]True];\ -FCE[tmp],1/4 I GA[k].GA[a_].GA[b_].GA[g] LC[i,j,a_,b_]-1/4 I \ -GA[k].GA[b_].GA[a_].GA[g] LC[i,j,a_,b_]-GA[k].GA[g].GA[5] MT[i,j]]", -"True"} -}) diff --git a/Tests/Dirac/Dirac.mt b/Tests/Dirac/Dirac.mt index a7de5893b..125a9b469 100644 --- a/Tests/Dirac/Dirac.mt +++ b/Tests/Dirac/Dirac.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "Dirac" directory *) @@ -17,85 +17,243 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "Dirac"}]] Get/@tests; -stingCompare[a_,b_]:=If[ToString[a]===ToString[b],True,False]; - -DeclareNonCommutative[FCNCA,FCNCB,FCNCC]; +If[ $OnlySubTest=!="", + testNames = "Tests`Dirac`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + + + +stringCompare[a_,b_]:=If[ToString[a]===ToString[b],True,False]; + +stringCompareIgnore[_,_]:= + True; +DeclareNonCommutative[FCNCA,FCNCB,FCNCC,nc1,nc2,nc3,nc4]; + +If[ Names["Tests`Dirac`fcstAnti5*"]=!={}, + FCSetDiracGammaScheme["NDR"]; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstAnti5*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + FCSetDiracGammaScheme["NDR"] +]; + +If[ Names["Tests`Dirac`fcstFCChargeConjugateTransposed*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstFCChargeConjugateTransposed*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracSubstitute67*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracSubstitute67*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracSubstitute5*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracSubstitute5*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstSpinorChainTranspose*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstSpinorChainTranspose*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstSpinorChainTrick*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstSpinorChainTrick*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstSpinorChainChiralSplit*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstSpinorChainChiralSplit*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstSirlinSimplify*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstSirlinSimplify*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstChisholm*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstChisholm*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; -$BreitMaison = False; -$Larin = False; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`Dirac`fcstAnti5*"])]; -$BreitMaison = False; -$Larin = False; +If[ Names["Tests`Dirac`fcstDiracSigmaExplicit*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracSigmaExplicit*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`Dirac`fcstChisholm*"])]; +If[ Names["Tests`Dirac`fcstDiracSubstitute67*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracSubstitute67*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`Dirac`fcstChisholm2*"])]; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, +If[ Names["Tests`Dirac`fcstEpsChisholm*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstEpsChisholm*"])]; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracChainJoin*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracChainJoin*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracChainCombine*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracChainCombine*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracChainExpand*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracChainExpand*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracChainFactor*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracChainFactor*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstToDiracSigma*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstToDiracSigma*"])]; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstToDiracGamma67*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstToDiracGamma67*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracGammaCombine*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracGammaCombine*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracGammaExpand*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracGammaExpand*"])]; - -$BreitMaison = False; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracEquation*"])]; -$BreitMaison = False; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracSigmaExpand*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracSigmaExpand*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracEquation*"]=!={}, + FCSetDiracGammaScheme["NDR"]; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracEquation*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + FCSetDiracGammaScheme["NDR"] +]; + +If[ Names["Tests`Dirac`fcstDiracOrder*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracOrder*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, +If[ Names["Tests`Dirac`fcstFCDiracIsolate*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstFCDiracIsolate*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, +If[ Names["Tests`Dirac`fcstDiracReduce*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracReduce*"])]; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join[Tests`Dirac`fcstDiracSimplify]]; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],(#[[4]]),TestID->#[[1]], - MessagesEquivalenceFunction->stingCompare]&, - Join[Tests`Dirac`fcstDiracSimplifyDotWarnings]]; - - -$BreitMaison=False; -$Larin=False; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracTrick*"])]; - -$BreitMaison=False; -$Larin=False; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join[ Tests`Dirac`fcstTr, - Tests`Dirac`fcstTr4AllFreeNoGamma5, - Tests`Dirac`fcstTrDAllFreeNoGamma5, - Tests`Dirac`fcstTr4AllFreeOneGamma5]]; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracSimplify"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracSimplify"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracSimplifySirlin"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracSimplifySirlin"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Dirac`fcstDiracSimplifyDotWarnings*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],(#[[4]]),testID->#[[1]], + MessagesEquivalenceFunction->stringCompareIgnore]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracSimplifyDotWarnings"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + +If[ Names["Tests`Dirac`fcstDiracTrick*"]=!={}, + FCSetDiracGammaScheme["NDR"]; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracTrick*"])]; + FCSetDiracGammaScheme["NDR"]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + +If[ Names["Tests`Dirac`fcstTr"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstTr"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + +If[ Names["Tests`Dirac`fcstTr4AllFreeNoGamma5"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstTr4AllFreeNoGamma5"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + +If[ Names["Tests`Dirac`fcstTrDAllFreeNoGamma5"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstTrDAllFreeNoGamma5"])];\ + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + +If[ Names["Tests`Dirac`fcstTr4AllFreeOneGamma5"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Dirac`fcstTr4AllFreeOneGamma5"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + +If[ Names["Tests`Dirac`fcstDiracTrace*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstDiracTrace*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; - -$BreitMaison=False; -$Larin=True; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join[ Tests`Dirac`fcstTrLarin]]; +If[ Names["Tests`Dirac`fcstTrLarin*"]=!={}, + FCSetDiracGammaScheme["Larin"]; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstTrLarin*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + FCSetDiracGammaScheme["NDR"] +]; -$Larin=False; -$BreitMaison=False; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, +If[ Names["Tests`Dirac`fcstToLarin*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Dirac`fcstToLarin*"])]; - + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; diff --git a/Tests/Dirac/DiracChainCombine.test b/Tests/Dirac/DiracChainCombine.test new file mode 100644 index 000000000..8b15d3d36 --- /dev/null +++ b/Tests/Dirac/DiracChainCombine.test @@ -0,0 +1,50 @@ + + +(* :Title: DiracChainCombine.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracChainCombine *) + +(* ------------------------------------------------------------------------ *) + +Tests`Dirac`fcstDiracChainCombine = +({ +{"fcstDiracChainCombine-ID1", +"DiracChainCombine[DCHN[GS[p],i,j]+DCHN[GS[q],i,j],FCE\[Rule]True]\ +", "DCHN[GS[p] + GS[q], i, j]"}, +{"fcstDiracChainCombine-ID2", +"DiracChainCombine[DCHN[GS[p],SpinorUBar[p1,m],j]+DCHN[GS[q],\ +SpinorUBar[p1,m],j],FCE\[Rule]True]", +"DCHN[GS[p] + GS[q], Spinor[Momentum[p1], m, 1], j]"}, +{"fcstDiracChainCombine-ID3", +"DiracChainCombine[DCHN[GS[p],i,SpinorU[p1,m]]+DCHN[GS[q],i,\ +SpinorU[p1,m]],FCE\[Rule]True]", +"DCHN[GS[p] + GS[q], i, Spinor[Momentum[p1], m, 1]]"}, +{"fcstDiracChainCombine-ID4", +"DiracChainCombine[DCHN[GS[p],SpinorVBar[p2,m2],SpinorU[p1,m1]]+\ +DCHN[GS[q],SpinorVBar[p2,m2],SpinorU[p1,m1]],FCE\[Rule]True]", +"DCHN[GS[p] + GS[q], Spinor[-Momentum[p2], m2, 1], \ +Spinor[Momentum[p1], m1, 1]]"}, +{"fcstDiracChainCombine-ID5", +"DiracChainCombine[DCHN[GS[p],i,j]+DCHN[GS[q],i,j],\ +DiracGammaCombine\[Rule]True,FCE\[Rule]True]", "DCHN[GS[p + q], i, j]"}, +{"fcstDiracChainCombine-ID6", +"DiracChainCombine[(DCHN[GSD[q], Dir3, Dir4] FAD[{k, me}])/( +2 SPD[q, q]) + 1/(2 SPD[q, q]) FAD[k, {k - q, me}] (-2 DCHN[GSD[q], Dir3, Dir4] SPD[q, q] + +2 DCHN[1, Dir3, Dir4] me SPD[q, q] + DCHN[GSD[q], Dir3, Dir4] (-me^2 + SPD[q, q])), FCE -> True]", + "(DCHN[GSD[q], Dir3, Dir4] FAD[{k, me}])/(2 SPD[q, q]) + ( +DCHN[2 me SPD[q, q] - 2 GSD[q] SPD[q, q] + + GSD[q] (-me^2 + SPD[q, q]), Dir3, Dir4] FAD[k, {k - q, me}])/( +2 SPD[q, q])"}, +{"fcstDiracChainCombine-ID7", +"DiracChainCombine[ +DCHN[1, i, j] DCHN[1, k, l] + DCHN[1, k, l] DCHN[GA[5], i, j] + +DCHN[1, i, j] DCHN[GA[5], k, l] + +DCHN[GA[5], i, j] DCHN[GA[5], k, l], FCE->True]", "DCHN[1 + GA[5], i, j] DCHN[1 + GA[5], k, l]"} +}) diff --git a/Tests/Dirac/DiracChainExpand.test b/Tests/Dirac/DiracChainExpand.test new file mode 100644 index 000000000..7afe45a6a --- /dev/null +++ b/Tests/Dirac/DiracChainExpand.test @@ -0,0 +1,75 @@ + + +(* :Title: DiracChainExpand.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracChainExpand *) + +(* ------------------------------------------------------------------------ *) + +Tests`Dirac`fcstDiracChainExpand = +({ +{"fcstDiracChainExpand-ID1", +"DiracChainExpand[DCHN[1,i,j],FCE\[Rule]True, DiracChainFactor -> False]", "DCHN[1, i, j]"}, +{"fcstDiracChainExpand-ID2", +"DiracChainExpand[DCHN[GS[p]+m,i,j],FCE\[Rule]True, DiracChainFactor -> False]", +"m*DCHN[1, i, j] + DCHN[GS[p], i, j]"}, +{"fcstDiracChainExpand-ID3", +"DiracChainExpand[DCHN[(GS[p]+m).GA[mu],i,j],FCE\[Rule]True, DiracChainFactor -> False]", +"DCHN[GS[p] . GA[mu], i, j] + DCHN[m*GA[mu], i, j]"}, +{"fcstDiracChainExpand-ID4", +"DiracChainExpand[DCHN[GA[nu].(GS[p]+m).GA[mu],i,j],FCE\[Rule]True, DiracChainFactor -> False]\ +", "DCHN[m*GA[nu] . GA[mu], i, j] + DCHN[GA[nu] . GS[p] . GA[mu], i, \ +j]"}, +{"fcstDiracChainExpand-ID5", +"DiracChainExpand[DCHN[GA[nu].(GS[p]+m).GA[mu],SpinorUBar[p1,m1],j]\ +,FCE\[Rule]True, DiracChainFactor -> False]", +"DCHN[m*GA[nu] . GA[mu], Spinor[Momentum[p1], m1, 1], j] + \ +DCHN[GA[nu] . GS[p] . GA[mu], Spinor[Momentum[p1], m1, 1], j]"}, +{"fcstDiracChainExpand-ID6", +"DiracChainExpand[DCHN[GA[nu].(GS[p]+m).GA[mu],i,SpinorV[p2,m2]],\ +FCE\[Rule]True, DiracChainFactor -> False]", +"DCHN[m*GA[nu] . GA[mu], i, Spinor[-Momentum[p2], m2, 1]] + \ +DCHN[GA[nu] . GS[p] . GA[mu], i, Spinor[-Momentum[p2], m2, 1]]"}, +{"fcstDiracChainExpand-ID7", +"DiracChainExpand[DCHN[GA[nu].(GS[p]+m).GA[mu],SpinorUBar[p1,m1],\ +SpinorV[p2,m2]],FCE\[Rule]True, DiracChainFactor -> False]", +"DCHN[m*GA[nu] . GA[mu], Spinor[Momentum[p1], m1, 1], \ +Spinor[-Momentum[p2], m2, 1]] + DCHN[GA[nu] . GS[p] . GA[mu], \ +Spinor[Momentum[p1], m1, 1], Spinor[-Momentum[p2], m2, 1]]"}, +{"fcstDiracChainExpand-ID8", +"DiracChainExpand[DCHN[GS[p1]+m,i,j]DCHN[GA[mu],j,k]DCHN[GS[p2]+m,\ +k,l],FCE\[Rule]True]", +"DCHN[GA[mu], j, k]*(m*DCHN[1, i, j] + DCHN[GS[p1], i, \ +j])*(m*DCHN[1, k, l] + DCHN[GS[p2], k, l])"}, +{"fcstDiracChainExpand-ID9", +"DiracChainExpand[DCHN[GS[p1]+m,i,j]DCHN[GA[mu],j,k]\ +\[IndentingNewLine]DCHN[GS[p2]+m,k,l],Momentum\[Rule]{p1},FCE\[Rule]\ +True]", "DCHN[GA[mu], j, k]*(m*DCHN[1, i, j] + DCHN[GS[p1], i, \ +j])*DCHN[m + GS[p2], k, l]"}, +{"fcstDiracChainExpand-ID10", +"DiracChainExpand[DCHN[(GS[p1+p2]+m).GS[p3+p4],i,j]DCHN[GA[mu],j,k]\ +DCHN[(GS[p2+p3]+m),k,l],Momentum\[Rule]{p1},FCE\[Rule]True, DiracChainFactor -> False]", +"DCHN[GA[mu], j, k]*DCHN[m + GS[p2 + p3], k, l]*(DCHN[GS[p1] . \ +GS[p3 + p4], i, j] + DCHN[GS[p2] . GS[p3 + p4], i, j] + DCHN[m*GS[p3 \ ++ p4], i, j])"}, +{"fcstDiracChainExpand-ID11", +"DiracChainExpand[DCHN[SpinorUBar[p1], i] DCHN[SpinorV[p1], j] DIDelta[i, j], +FCE -> True]", +"DCHN[Spinor[-Momentum[p1], 0, 1], j] DCHN[Spinor[Momentum[p1], 0, 1], +i] DIDelta[i, j]"}, +{"fcstDiracChainExpand-ID12", +"DiracChainExpand[DCHN[-FVD[p, mu] GA[mu] + m, Dir3, Dir4], +FCE -> True]", +"m DCHN[1, Dir3, Dir4] - DCHN[GA[mu], Dir3, Dir4] FVD[p, mu]"}, +{"fcstDiracChainExpand-ID13", +"DiracChainExpand[DCHN[-FVD[p, mu] GA[mu] + m, Dir3, Dir4], +FCE -> True, DiracChainFactor -> False]", +"m DCHN[1, Dir3, Dir4] + DCHN[-FVD[p, mu] GA[mu], Dir3, Dir4]"} +}) diff --git a/Tests/Dirac/DiracChainFactor.test b/Tests/Dirac/DiracChainFactor.test new file mode 100644 index 000000000..097ad919e --- /dev/null +++ b/Tests/Dirac/DiracChainFactor.test @@ -0,0 +1,37 @@ + + +(* :Title: DiracChainFactor.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracChainFactor *) + +(* ------------------------------------------------------------------------ *) + +Tests`Dirac`fcstDiracChainFactor = +({ +{"fcstDiracChainFactor-ID1", +"DiracChainFactor[DCHN[GA[mu].GA[$AL[$31]].GA[mu] \ +FV[p,$AL[$31]],i,j]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[LorentzIndex[$AL[$31]]] . DiracGamma[LorentzIndex[mu]], \ +DiracIndex[i], DiracIndex[j]]*Pair[LorentzIndex[$AL[$31]], \ +Momentum[p]]"}, +{"fcstDiracChainFactor-ID2", +"DiracChainFactor[DCHN[GA[mu].GA[$AL[$31]].GA[mu]x,i,j]]", +"x*DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[LorentzIndex[$AL[$31]]] . DiracGamma[LorentzIndex[mu]], \ +DiracIndex[i], DiracIndex[j]]"}, +{"fcstDiracChainFactor-ID3", +"DiracChainFactor[DCHN[GA[mu].z.GA[$AL[$31]].GA[mu]x,i,j]]", +"x*z*DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[LorentzIndex[$AL[$31]]] . DiracGamma[LorentzIndex[mu]], \ +DiracIndex[i], DiracIndex[j]]"}, +{"fcstDiracChainFactor-ID4", "DiracChainFactor[DCHN[(x.y.z),i,j]]", +"DiracChain[1, DiracIndex[i], DiracIndex[j]]*x . y . z"} +}); diff --git a/Tests/Dirac/DiracChainJoin.test b/Tests/Dirac/DiracChainJoin.test new file mode 100644 index 000000000..df99c7e98 --- /dev/null +++ b/Tests/Dirac/DiracChainJoin.test @@ -0,0 +1,115 @@ + + +(* :Title: DiracChainJoin.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracChainJoin *) + +(* ------------------------------------------------------------------------ *) + +Tests`Dirac`fcstDiracChainJoin = +({ +{"fcstDiracChainJoin-ID1", "DiracChainJoin[0]", "0"}, +{"fcstDiracChainJoin-ID2", +"DiracChainJoin[GA[i],FCE\[Rule]True]", +"DiracGamma[LorentzIndex[i]]"}, +{"fcstDiracChainJoin-ID3", +"DiracChainJoin[GAD[mu,mu],FCE\[Rule]True]", +"DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[LorentzIndex[mu, \ +D], D]"}, +{"fcstDiracChainJoin-ID4", +"DiracChainJoin[DCHN[GA[i],Spinor[Momentum[p1],m1,1],\ +Spinor[Momentum[p2],m1,1]],FCE\[Rule]True]", +"Spinor[Momentum[p1], m1, 1] . GA[i] . Spinor[Momentum[p2], m1, \ +1]"}, +{"fcstDiracChainJoin-ID5", +"DiracChainJoin[DCHN[Spinor[Momentum[p1],m1,1],i]DCHN[j, +Spinor[Momentum[p2],m1,1]]DIDelta[i,j],FCE\[Rule]True]", +"Spinor[Momentum[p1], m1, 1] . Spinor[Momentum[p2], m1, 1]"}, +{"fcstDiracChainJoin-ID6", +"DiracChainJoin[DCHN[Spinor[Momentum[p1],m1,1],i]DCHN[i, +Spinor[Momentum[p2],m1,1]],FCE\[Rule]True]", +"Spinor[Momentum[p1], m1, 1] . Spinor[Momentum[p2], m1, 1]"}, +{"fcstDiracChainJoin-ID7", +"DiracChainJoin[DCHN[i,Spinor[Momentum[p1],m1,1]]DCHN[GS[p]\ ++m,Spinor[Momentum[p2],m1,1],j]DIDelta[i,j],FCE\[Rule]True]", +"Spinor[Momentum[p2], m1, 1] . (m + GS[p]) . Spinor[Momentum[p1], \ +m1, 1]"}, +{"fcstDiracChainJoin-ID8", +"DiracChainJoin[DCHN[i,Spinor[Momentum[p1],m1,1]]DCHN[GS[p]\ ++m,Spinor[Momentum[p2],m1,1],i],FCE\[Rule]True]", +"Spinor[Momentum[p2], m1, 1] . (m + GS[p]) . Spinor[Momentum[p1], \ +m1, 1]"}, +{"fcstDiracChainJoin-ID9", +"DiracChainJoin[DIDelta[i,i]]", "4"}, +{"fcstDiracChainJoin-ID10", +"DiracChainJoin[DIDelta[i,j]^2]", "4"}, +{"fcstDiracChainJoin-ID11", +"DiracChainJoin[DCHN[GA[i],i,i]]", +"DiracTrace[DiracGamma[LorentzIndex[i]]]"}, +{"fcstDiracChainJoin-ID12", +"DiracChainJoin[ +DCHN[GSD[-k1 + p1], Dir1, Dir2] DCHN[GSD[Polarization[k1, -I]], Dir2, + Spinor[Momentum[p1, D], QGMassQ, 1]] DCHN[ +GSD[Polarization[k2, -I]], Spinor[-Momentum[p2, D], QGMassQ, 1], +Dir1], FCE -> True]", +"Spinor[-Momentum[p2, D], QGMassQ, 1].GSD[ +Polarization[k2, -I]].GSD[-k1 + p1].GSD[ +Polarization[k1, -I]].Spinor[Momentum[p1, D], QGMassQ, 1]"}, +{"fcstDiracChainJoin-ID13", +"DiracChainJoin[DiracIndexDelta[DiracIndex[i], DiracIndex[i]], +TraceOfOne -> D]", "D"}, +{"fcstDiracChainJoin-ID14", +"DiracChainJoin[ +DiracIndexDelta[DiracIndex[i], DiracIndex[j]] DiracIndexDelta[ +DiracIndex[j], DiracIndex[k]], FCE -> True]", "DIDelta[i,k]"}, +{"fcstDiracChainJoin-ID15", +"DiracChainJoin[DCHN[SpinorUBar[p1,m1],i]DCHN[j,SpinorV[p2,m2]]\ +DCHN[1,i,j],FCE\[Rule]True]", +"Spinor[Momentum[p1], m1, 1] . Spinor[-Momentum[p2], m2, 1]"}, +{"fcstDiracChainJoin-ID16", +"DiracChainJoin[DCHN[Spinor[p1,m1],i]DCHN[j,Spinor[p2,m2]]DCHN[\ +1,i,j],FCE\[Rule]True]", +"Spinor[Momentum[p1], m1, 1] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracChainJoin-ID17", +"DiracChainJoin[DCHN[SpinorUBar[p1,m1],i]DCHN[j,SpinorV[p2,m2]]\ +DIDelta[i,j],FCE\[Rule]True]", +"Spinor[Momentum[p1], m1, 1] . Spinor[-Momentum[p2], m2, 1]"}, +{"fcstDiracChainJoin-ID18", +"DiracChainJoin[DCHN[Spinor[p1,m1],i]DCHN[j,Spinor[p2,m2]]\ +DIDelta[i,j],FCE\[Rule]True]", +"Spinor[Momentum[p1], m1, 1] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracChainJoin-ID19", +"DiracChainJoin[DCHN[Spinor[p1,m1],i]DCHN[Spinor[p2,m2],j]\ +DIDelta[i,j],FCE\[Rule]True]", +"DCHN[Spinor[Momentum[p1], m1, 1], j]*DCHN[Spinor[Momentum[p2], \ +m2, 1], j]"}, +{"fcstDiracChainJoin-ID20", +"DiracChainJoin[DCHN[Spinor[p1, m], j] DCHN[GA[mu], i, j], +FCE -> True]", +"DCHN[Spinor[p1, m], j] DCHN[GA[mu], i, j]"}, +{"fcstDiracChainJoin-ID21", +"DiracChainJoin[DCHN[Spinor[p1, m], j] DCHN[Spinor[p2, m], i], +FCE -> True]", +"DCHN[Spinor[Momentum[p1], m, 1], j] DCHN[Spinor[Momentum[p2], m, 1], +i]"}, +{"fcstDiracChainJoin-ID22", +"DiracChainJoin[ +DCHN[GA[Lor2].GA[6].(me + GS[LoopMom1]).GA[Lor1].GA[6], +Spinor[Momentum[OutMom1], me, 1], Dir1] DCHN[ +Spinor[Momentum[InMom1], me, 1], Dir1], FCE -> True]", +"DCHN[Spinor[Momentum[InMom1], me, 1], Dir1] DCHN[ +GA[Lor2].GA[6].(me + GS[LoopMom1]).GA[Lor1].GA[6], +Spinor[Momentum[OutMom1], me, 1], Dir1]"}, +{"fcstDiracChainJoin-ID23", +"DiracChainJoin[ +DCHN[GA[nu], h, i] DCHN[GS[p] + m, i, j] DCHN[GA[mu], j, k], +FCDiracIsolate -> False, FCE -> True]", +"DCHN[GA[nu].(m + GS[p]).GA[mu], h, k]"} +}); diff --git a/Tests/Dirac/DiracEquation.test b/Tests/Dirac/DiracEquation.test index 8fe599031..87555650c 100644 --- a/Tests/Dirac/DiracEquation.test +++ b/Tests/Dirac/DiracEquation.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DiracEquation *) @@ -38,7 +38,7 @@ Tests`Dirac`fcstDiracEquation = { "DiracEquation[SpinorUBar[p, m].GSD[p]]"}, {"fcstDiracEquation-ID12","DiracEquation[SpinorVBar[p, m].GSD[p]]", "DiracEquation[SpinorVBar[p, m].GSD[p]]"}, -{"fcstDiracEquation-ID13","$BreitMaison=False \n DiracEquation[GSD[p].GSD[q].GA[i].SpinorUD[Momentum[p, D], m]] // FCE", +{"fcstDiracEquation-ID13","FCSetDiracGammaScheme[\"NDR\"] \n DiracEquation[GSD[p].GSD[q].GA[i].SpinorUD[Momentum[p, D], m]] // FCE", "m GSD[q].GA[i].Spinor[Momentum[p, D], m, 1] - 2 GSD[q].Spinor[Momentum[p, D], m, 1] FV[p, i] + 2 GA[i].Spinor[Momentum[p, D], m, 1] SPD[p, q]"}, @@ -115,7 +115,7 @@ Tests`Dirac`fcstDiracEquation = { SpinorVBarD[Momentum[p, D], m].GSD[q].GA[i, 5].GAD[j].GSD[p]] // FCE", "Spinor[-Momentum[p, D], m, 1] . GSD[q] . GA[i] . GSD[p] . GA[5] . GAD[j] + 2*Spinor[-Momentum[p, D], m, 1] . GSD[q] . GA[i] . GA[5]*FVD[p, j]"}, -{"fcstDiracEquation-ID29","$BreitMaison=True \n DiracEquation[ +{"fcstDiracEquation-ID29","FCSetDiracGammaScheme[\"BMHV\"] \n DiracEquation[ GSD[p].GSD[q].GA[i, 5].SpinorUD[Momentum[p, D], m]] // FCE", "-m GSD[q].GA[i].GA[5].Spinor[Momentum[p, D], m, 1] + 2 GSD[q].GA[i].GA[5].GSE[p].Spinor[Momentum[p, D], m, 1] - @@ -157,5 +157,115 @@ Tests`Dirac`fcstDiracEquation = { SpinorVBarD[Momentum[p, D], m].GSD[q].GA[i, 5].GAD[j].GSD[p]] // FCE", "Spinor[-Momentum[p, D], m, 1].GSD[q].GA[i].GSD[p].GA[5].GAD[j] - 2 Spinor[-Momentum[p, D], m, 1].GSD[q].GA[i].GSE[p].GA[5].GAD[j] + - 2 Spinor[-Momentum[p, D], m, 1].GSD[q].GA[i].GA[5] FVD[p, j]"} + 2 Spinor[-Momentum[p, D], m, 1].GSD[q].GA[i].GA[5] FVD[p, j]"}, +{"fcstDiracEquation-ID37", +"DiracEquation[GS[p].CGA[i].SpinorU[p,m]]", +"-(m*DiracGamma[CartesianIndex[i]] . Spinor[Momentum[p], m, 1]) + \ +2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*Spinor[Momentum[p], m, 1]"}, +{"fcstDiracEquation-ID38", +"DiracEquation[GSD[p].CGA[i].SpinorUD[p,m]]", +"-(m*DiracGamma[CartesianIndex[i]] . Spinor[Momentum[p, D], m, 1]) + \ +2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*Spinor[Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID39", +"DiracEquation[GSD[p].CGS[r].SpinorUD[p,m]]", +"-(m*DiracGamma[CartesianMomentum[r]] . Spinor[Momentum[p, D], m, 1]) + \ +2*CartesianPair[CartesianMomentum[p], CartesianMomentum[r]]*Spinor[Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID40", +"DiracEquation[GSD[p].CGAD[i].SpinorUD[p,m]]", +"-(m*DiracGamma[CartesianIndex[i, -1 + D], D] . Spinor[Momentum[p, D], m, \ +1]) + 2*CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + \ +D]]*Spinor[Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID41", +"DiracEquation[GSD[p].CGSD[r].SpinorUD[p,m]]", +"-(m*DiracGamma[CartesianMomentum[r, -1 + D], D] . Spinor[Momentum[p, D], \ +m, 1]) + 2*CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[r, -1 + \ +D]]*Spinor[Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID42", +"DiracEquation[GS[p].CGA[i].SpinorV[p,m]]", +"m*DiracGamma[CartesianIndex[i]] . Spinor[-Momentum[p], m, 1] + \ +2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*Spinor[-Momentum[p], m, 1]"}, +{"fcstDiracEquation-ID43", +"DiracEquation[GSD[p].CGA[i].SpinorVD[p,m]]", +"m*DiracGamma[CartesianIndex[i]] . Spinor[-Momentum[p, D], m, 1] + \ +2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*Spinor[-Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID44", +"DiracEquation[GSD[p].CGS[r].SpinorVD[p,m]]", +"m*DiracGamma[CartesianMomentum[r]] . Spinor[-Momentum[p, D], m, 1] + \ +2*CartesianPair[CartesianMomentum[p], CartesianMomentum[r]]*Spinor[-Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID45", +"DiracEquation[GSD[p].CGAD[i].SpinorVD[p,m]]", +"m*DiracGamma[CartesianIndex[i, -1 + D], D] . Spinor[-Momentum[p, D], m, \ +1] + 2*CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + \ +D]]*Spinor[-Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID46", +"DiracEquation[GSD[p].CGSD[r].SpinorVD[p,m]]", +"m*DiracGamma[CartesianMomentum[r, -1 + D], D] . Spinor[-Momentum[p, D], \ +m, 1] + 2*CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[r, -1 + \ +D]]*Spinor[-Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID47", +"DiracEquation[SpinorU[p,m].CGA[i].GS[p]]", +"-(m*Spinor[Momentum[p], m, 1] . DiracGamma[CartesianIndex[i]]) + \ +2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*Spinor[Momentum[p], m, 1]"}, +{"fcstDiracEquation-ID48", +"DiracEquation[SpinorUD[p,m].CGA[i].GSD[p]]", +"-(m*Spinor[Momentum[p, D], m, 1] . DiracGamma[CartesianIndex[i]]) + \ +2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*Spinor[Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID49", +"DiracEquation[SpinorUD[p,m].CGS[r].GSD[p]]", +"-(m*Spinor[Momentum[p, D], m, 1] . DiracGamma[CartesianMomentum[r]]) + \ +2*CartesianPair[CartesianMomentum[p], CartesianMomentum[r]]*Spinor[Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID50", +"DiracEquation[SpinorUD[p,m].CGAD[i].GSD[p]]", +"-(m*Spinor[Momentum[p, D], m, 1] . DiracGamma[CartesianIndex[i, -1 + D], \ +D]) + 2*CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + \ +D]]*Spinor[Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID51", +"DiracEquation[SpinorUD[p,m].CGSD[r].GSD[p]]", +"-(m*Spinor[Momentum[p, D], m, 1] . DiracGamma[CartesianMomentum[r, -1 + \ +D], D]) + 2*CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[r, -1 + \ +D]]*Spinor[Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID52", +"DiracEquation[SpinorV[p,m].CGA[i].GS[p]]", +"m*Spinor[-Momentum[p], m, 1] . DiracGamma[CartesianIndex[i]] + \ +2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*Spinor[-Momentum[p], m, 1]"}, +{"fcstDiracEquation-ID53", +"DiracEquation[SpinorVD[p,m].CGA[i].GSD[p]]", +"m*Spinor[-Momentum[p, D], m, 1] . DiracGamma[CartesianIndex[i]] + \ +2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*Spinor[-Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID54", +"DiracEquation[SpinorVD[p,m].CGS[r].GSD[p]]", +"m*Spinor[-Momentum[p, D], m, 1] . DiracGamma[CartesianMomentum[r]] + \ +2*CartesianPair[CartesianMomentum[p], CartesianMomentum[r]]*Spinor[-Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID55", +"DiracEquation[SpinorVD[p,m].CGAD[i].GSD[p]]", +"m*Spinor[-Momentum[p, D], m, 1] . DiracGamma[CartesianIndex[i, -1 + D], \ +D] + 2*CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + \ +D]]*Spinor[-Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID56", +"DiracEquation[SpinorVD[p,m].CGSD[r].GSD[p]]", +"m*Spinor[-Momentum[p, D], m, 1] . DiracGamma[CartesianMomentum[r, -1 + \ +D], D] + 2*CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[r, -1 + \ +D]]*Spinor[-Momentum[p, D], m, 1]"}, +{"fcstDiracEquation-ID57", +"DiracEquation[ +Spinor[Momentum[pE2, D], 0, 1].GAD[mu].GA[ + 7].Spinor[-Momentum[pE1, D], 0, 1] Spinor[ + Momentum[pB, D] - Momentum[pE1, D] - Momentum[pE2, D], 0, 1].GSD[ + pE1].GSD[pE1].GAD[mu].GA[7].Spinor[Momentum[pB, D], mB, 1]]", +"Spinor[Momentum[pB, D] - Momentum[pE1, D] - Momentum[pE2, D], 0, +1].DiracGamma[LorentzIndex[mu, D], D].DiracGamma[7].Spinor[ +Momentum[pB, D], mB, 1] Spinor[Momentum[pE2, D], 0, 1].DiracGamma[ +LorentzIndex[mu, D], D].DiracGamma[7].Spinor[-Momentum[pE1, D], 0, +1] Pair[Momentum[pE1, D], Momentum[pE1, D]]"}, +{"fcstDiracEquation-ID58", +"DiracEquation[ +Spinor[Momentum[p1, D], m1, 1].GAD[mu].GA[7].Spinor[Momentum[p2, D], + m2, 1] Spinor[-Momentum[p1, D], m1, 1].GAD[mu].GSD[p1].GA[ + 7].Spinor[-Momentum[p3, D], m2, 1], FCE -> True]", +"2 m1 Spinor[-Momentum[p1, D], m1, 1].GA[7].Spinor[-Momentum[p3, D], + m2, 1] Spinor[Momentum[p1, D], m1, 1].GA[7].Spinor[ + Momentum[p2, D], m2, 1] + +m1 Spinor[-Momentum[p1, D], m1, 1].GAD[mu].GA[ + 7].Spinor[-Momentum[p3, D], m2, 1] Spinor[Momentum[p1, D], m1, + 1].GAD[mu].GA[7].Spinor[Momentum[p2, D], m2, 1]"} } diff --git a/Tests/Dirac/DiracGammaCombine.test b/Tests/Dirac/DiracGammaCombine.test new file mode 100644 index 000000000..aaeee7087 --- /dev/null +++ b/Tests/Dirac/DiracGammaCombine.test @@ -0,0 +1,47 @@ + + +(* :Title: DiracGammaCombine.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracGammaCombine *) + +(* ------------------------------------------------------------------------ *) + +Tests`Dirac`fcstDiracGammaCombine = +({ +{"fcstDiracGammaCombine-ID1", +"DiracGammaCombine[GS[p]+GS[q],FCE\[Rule]True]", "GS[p + q]"}, +{"fcstDiracGammaCombine-ID2", +"DiracGammaCombine[GS[p]+GSD[q],FCE\[Rule]True]", "GS[p] + GSD[q]"}, +{"fcstDiracGammaCombine-ID3", +"DiracGammaCombine[GS[p]+GS[q]+m,FCE\[Rule]True]", "m + GS[p + q]"}, +{"fcstDiracGammaCombine-ID4", +"DiracGammaCombine[GA[i].(GS[p]+GS[q]+m).GA[j],FCE\[Rule]True]", +"GA[i] . (m + GS[p + q]) . GA[j]"}, +{"fcstDiracGammaCombine-ID5", +"DiracGammaCombine[GA[i].(2GS[p]+3GS[q]+m).GA[j],FCE\[Rule]True]", +"GA[i] . (m + GS[2*p + 3*q]) . GA[j]"}, +{"fcstDiracGammaCombine-ID6", +"DiracGammaCombine[GA[i].(2GS[p]+3GS[p]+m).GA[j],FCE\[Rule]True]", +"GA[i] . (m + 5*GS[p]) . GA[j]"}, +{"fcstDiracGammaCombine-ID7", +"DiracGammaCombine[CGS[p] + CGS[q], FCE -> True]", "CGS[p + q]"}, +{"fcstDiracGammaCombine-ID8", +"DiracGammaCombine[CGS[p] + CGSD[q], FCE -> True]", "CGS[p] + CGSD[q]"}, +{"fcstDiracGammaCombine-ID9", +"DiracGammaCombine[CGS[p] + CGS[q] + m, FCE -> True]", "m + CGS[p + q]"}, +{"fcstDiracGammaCombine-ID10", +"DiracGammaCombine[CGA[i].(CGS[p] + CGS[q] + m).CGA[j], FCE -> True]", "CGA[i].(m + CGS[p + q]).CGA[j]"}, +{"fcstDiracGammaCombine-ID11", +"DiracGammaCombine[CGA[i].(2 CGS[p] + 3 CGS[q] + m).CGA[j], +FCE -> True]", "CGA[i].(m + CGS[2 p + 3 q]).CGA[j]"}, +{"fcstDiracGammaCombine-ID12", +"DiracGammaCombine[CGA[i].(2 CGS[p] + 3 CGS[p] + m).CGA[j], +FCE -> True]", "CGA[i].(m + 5 CGS[p]).CGA[j]"} +}); diff --git a/Tests/Dirac/DiracGammaExpand.test b/Tests/Dirac/DiracGammaExpand.test index ce819a597..5c5c429ab 100644 --- a/Tests/Dirac/DiracGammaExpand.test +++ b/Tests/Dirac/DiracGammaExpand.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DiracGammaExpand *) @@ -26,5 +26,23 @@ Tests`Dirac`fcstDiracGammaExpand = { DiracGamma[5 Momentum[a] + c Momentum[b + d] + Momentum[e]]] // FCE","5 GS[a] + c (GS[b] + GS[d]) + GS[e]"}, {"fcstDiracGammaExpand-ID6","DiracGammaExpand[DiracGamma[5 Momentum[a, D] + c Momentum[b + d, D] + Momentum[e, D], D]] // FCE", - "5*GSD[a] + c*(GSD[b] + GSD[d]) + GSD[e]"} + "5*GSD[a] + c*(GSD[b] + GSD[d]) + GSD[e]"}, +{"fcstDiracGammaExpand-ID7","DiracGammaExpand[CGS[q].CGS[p - q]] // FCE", + "CGS[q].(CGS[p] - CGS[q])"}, +{"fcstDiracGammaExpand-ID8","DiracGammaExpand[CGS[a + b].CGS[c + d], Momentum -> {a}] // FCE", + "(CGS[a] + CGS[b]).CGS[c + d]"}, +{"fcstDiracGammaExpand-ID9","DiracGammaExpand[CGS[a + b].CGS[c + d], Momentum -> {c}] // FCE", + "CGS[a + b].(CGS[c] + CGS[d])"}, +{"fcstDiracGammaExpand-ID10","DiracGammaExpand[CGS[a + b].CGS[c + d], Momentum -> All] // FCE", + "(CGS[a] + CGS[b]).(CGS[c] + CGS[d])"}, +{"fcstDiracGammaExpand-ID11","DiracGammaExpand[DiracGamma[5 CartesianMomentum[a] + c CartesianMomentum[b + d] + CartesianMomentum[e]]] // FCE", + "5 CGS[a] + c (CGS[b] + CGS[d]) + CGS[e]"}, +{"fcstDiracGammaExpand-ID12","DiracGammaExpand[ +DiracGamma[ +5 CartesianMomentum[a, D - 1] + c CartesianMomentum[b + d, D - 1] + + CartesianMomentum[e, D - 1], D]] // FCE", + "5 CGSD[a] + c (CGSD[b] + CGSD[d]) + CGSD[e]"}, +{"fcstDiracGammaExpand-ID13","DiracGammaExpand[DiracSigma[x GSD[p + q], 3 GSD[r + s]], FCE -> True]", + "3 x (DiracSigma[GSD[p], GSD[r]] + DiracSigma[GSD[p], GSD[s]] + +DiracSigma[GSD[q], GSD[r]] + DiracSigma[GSD[q], GSD[s]])"} }; diff --git a/Tests/Dirac/DiracOrder.test b/Tests/Dirac/DiracOrder.test index 2d1eec661..5da12fa2b 100644 --- a/Tests/Dirac/DiracOrder.test +++ b/Tests/Dirac/DiracOrder.test @@ -4,20 +4,168 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DiracOrder *) (* ------------------------------------------------------------------------ *) -Tests`Dirac`fcstDiracOrder = { -{"fcstDiracOrder-ID1","DiracOrder[DiracMatrix[b, a]]","-DiracGamma[LorentzIndex[a]] . DiracGamma[LorentzIndex[b]] + 2*Pair[LorentzIndex[a], LorentzIndex[b]]"}, -{"fcstDiracOrder-ID2","DiracOrder[-DiracGamma[LorentzIndex[a]].DiracGamma[LorentzIndex[b]] + - 2*Pair[LorentzIndex[a], LorentzIndex[b]], {b, a}]","DiracGamma[LorentzIndex[b]] . DiracGamma[LorentzIndex[a]]"}, -{"fcstDiracOrder-ID3","DiracOrder[DiracMatrix[mu, mu].DiracSlash[p, p]]","4*Pair[Momentum[p], Momentum[p]]"}, -{"fcstDiracOrder-ID4","DiracOrder[DiracMatrix[a, mu, a, Dimension -> D]]","2*DiracGamma[LorentzIndex[mu, D], D] - D*DiracGamma[LorentzIndex[mu, D], D]"}, -{"fcstDiracOrder-ID5","DiracOrder[DiracSlash[-p, q, p]]","DiracGamma[Momentum[q]]*Pair[Momentum[p], Momentum[p]] - 2*DiracGamma[Momentum[p]]*Pair[Momentum[p], Momentum[q]]"} -} +Tests`Dirac`fcstDiracOrder = +({ +{"fcstDiracOrder-ID1", "FCSetDiracGammaScheme[\"BMHV\"]; \n DiracOrder[0]", "0"}, +{"fcstDiracOrder-ID2", +"ClearAll[tmp]; \n MatchQ[DiracOrder[Sum[tmp[i],{i,1,10000}]],Sum[tmp[i],{i,1,10000}]\ +]", "True"}, +{"fcstDiracOrder-ID3", "DiracOrder[GA[a],FCE\[Rule]True]", +"GA[a]"}, +{"fcstDiracOrder-ID4", "DiracOrder[GA[b,a],FCE\[Rule]True]", +"-GA[a] . GA[b] + 2*MT[a, b]"}, +{"fcstDiracOrder-ID5", "DiracOrder[GAD[b,a],FCE\[Rule]True]", +"-GAD[a] . GAD[b] + 2*MTD[a, b]"}, +{"fcstDiracOrder-ID6", "DiracOrder[GAE[b,a],FCE\[Rule]True]", +"-GAE[a] . GAE[b] + 2*MTE[a, b]"}, +{"fcstDiracOrder-ID7", "DiracOrder[GA[a,b],{b,a},FCE\[Rule]True]", +"-GA[b] . GA[a] + 2*MT[a, b]"}, +{"fcstDiracOrder-ID8", "DiracOrder[GAD[a,b],{b,a},FCE\[Rule]True]", +"-GAD[b] . GAD[a] + 2*MTD[a, b]"}, +{"fcstDiracOrder-ID9", "DiracOrder[GAE[a,b],{b,a},FCE\[Rule]True]", +"-GAE[b] . GAE[a] + 2*MTE[a, b]"}, +{"fcstDiracOrder-ID10", +"DiracOrder[-GA[a].GA[b]+2 MT[a,b],{b,a},FCE\[Rule]True]", +"GA[b] . GA[a]"}, +{"fcstDiracOrder-ID11", +"DiracOrder[-GAD[a].GAD[b]+2 MTD[a,b],{b,a},FCE\[Rule]True]", +"GAD[b] . GAD[a]"}, +{"fcstDiracOrder-ID12", +"DiracOrder[-GAE[a].GAE[b]+2 MTE[a,b],{b,a},FCE\[Rule]True]", +"GAE[b] . GAE[a]"}, +{"fcstDiracOrder-ID13", +"DiracOrder[GA[mu,mu].GS[p,p],FCE\[Rule]True]", "4*SP[p, p]"}, +{"fcstDiracOrder-ID14", +"DiracOrder[GAD[mu,mu].GSD[p,p],FCE\[Rule]True]", "D*SPD[p, p]"}, +{"fcstDiracOrder-ID15", +"DiracOrder[GAD[mu,mu].GS[p,p],FCE\[Rule]True]", "D*SP[p, p]"}, +{"fcstDiracOrder-ID16", +"DiracOrder[GAD[nu,mu].GA[nu,mu],FCE\[Rule]True]", "-8"}, +{"fcstDiracOrder-ID17", "DiracOrder[GAD[a,mu,a],FCE\[Rule]True]", +"(2 - D)*GAD[mu]"}, +{"fcstDiracOrder-ID18", "DiracOrder[GS[-p,q,p],FCE\[Rule]True]", +"GS[q]*SP[p, p] - 2*GS[p]*SP[p, q]"}, +{"fcstDiracOrder-ID19", "DiracOrder[GSD[-p,q,p],FCE\[Rule]True]", +"GSD[q]*SPD[p, p] - 2*GSD[p]*SPD[p, q]"}, +{"fcstDiracOrder-ID20", +"DiracOrder[-GA[a].GA[b]+2 \ +MT[a,b],{b,a},FCDiracIsolate\[Rule]False,FCE\[Rule]True]", +"GA[b] . GA[a]"}, +{"fcstDiracOrder-ID21", +"DiracOrder[-GAD[a].GAD[b]+2 \ +MTD[a,b],{b,a},FCDiracIsolate\[Rule]False,FCE\[Rule]True]", +"GAD[b] . GAD[a]"}, +{"fcstDiracOrder-ID22", +"DiracOrder[-GAE[a].GAE[b]+2 \ +MTE[a,b],{b,a},FCDiracIsolate\[Rule]False,FCE\[Rule]True]", +"GAE[b] . GAE[a]"}, +{"fcstDiracOrder-ID23", +"DiracOrder[GAD[nu,mu].GA[nu,mu],DiracTrick\[Rule]False,FCE\[Rule]\ +True]", "-8*(8 - GA[mu] . GAD[mu]) + 2*(8 - GA[nu] . GAD[nu]) + \ +6*GA[nu] . GAD[nu] + GA[mu] . GA[nu] . GAD[mu] . GAD[nu]"}, +{"fcstDiracOrder-ID24", +"DiracOrder[GA[i1,i2,i3,i4],{i4,i3,i2,i1},FCE\ +\[Rule]True]", +"GA[i4] . GA[i3] . GA[i2] . GA[i1] - 2*GA[i4] . GA[i3]*MT[i1, i2] \ ++ 2*GA[i4] . GA[i2]*MT[i1, i3] - 2*GA[i3] . GA[i2]*MT[i1, i4] - \ +2*GA[i4] . GA[i1]*MT[i2, i3] + 2*GA[i3] . GA[i1]*MT[i2, i4] - \ +2*GA[i2] . GA[i1]*MT[i3, i4] + 4*(MT[i1, i4]*MT[i2, i3] - MT[i1, \ +i3]*MT[i2, i4] + MT[i1, i2]*MT[i3, i4])"}, + +{"fcstDiracOrder-ID25", "DiracOrder[CGA[a],FCE\[Rule]True]", +"CGA[a]"}, +{"fcstDiracOrder-ID26", "DiracOrder[CGA[b,a],FCE\[Rule]True]", +"-CGA[a] . CGA[b] - 2*KD[a, b]"}, +{"fcstDiracOrder-ID27", "DiracOrder[CGAD[b,a],FCE\[Rule]True]", +"-CGAD[a] . CGAD[b] - 2*KDD[a, b]"}, +{"fcstDiracOrder-ID28", "DiracOrder[CGAE[b,a],FCE\[Rule]True]", +"-CGAE[a] . CGAE[b] - 2*KDE[a, b]"}, +{"fcstDiracOrder-ID29", "DiracOrder[CGA[a,b],{b,a},FCE\[Rule]True]", + "-CGA[b] . CGA[a] - 2*KD[a, b]"}, +{"fcstDiracOrder-ID30", +"DiracOrder[CGAD[a,b],{b,a},FCE\[Rule]True]", +"-CGAD[b] . CGAD[a] - 2*KDD[a, b]"}, +{"fcstDiracOrder-ID31", +"DiracOrder[CGAE[a,b],{b,a},FCE\[Rule]True]", +"-CGAE[b] . CGAE[a] - 2*KDE[a, b]"}, +{"fcstDiracOrder-ID32", +"DiracOrder[-CGA[a].CGA[b]-2 KD[a,b],{b,a},FCE\[Rule]True]", +"CGA[b] . CGA[a]"}, +{"fcstDiracOrder-ID33", +"DiracOrder[-CGAD[a].CGAD[b]-2 KDD[a,b],{b,a},FCE\[Rule]True]", +"CGAD[b] . CGAD[a]"}, +{"fcstDiracOrder-ID34", +"DiracOrder[-CGAE[a].CGAE[b]-2 KDE[a,b],{b,a},FCE\[Rule]True]", +"CGAE[b] . CGAE[a]"}, +{"fcstDiracOrder-ID35", +"DiracOrder[CGA[mu,mu].CGS[p,p],FCE\[Rule]True]", "3*CSP[p, p]"}, +{"fcstDiracOrder-ID36", +"DiracOrder[CGAD[mu,mu].CGSD[p,p],FCE\[Rule]True]", +"-((1 - D)*CSPD[p, p])"}, +{"fcstDiracOrder-ID37", +"DiracOrder[CGAD[mu,mu].CGS[p,p],FCE\[Rule]True]", +"-((1 - D)*CSP[p, p])"}, +{"fcstDiracOrder-ID38", +"DiracOrder[CGAD[nu,mu].CGA[nu,mu],FCE\[Rule]True]", "-3"}, +{"fcstDiracOrder-ID39", "DiracOrder[CGAD[a,mu,a],FCE\[Rule]True]", +"(-3 + D)*CGAD[mu]"}, +{"fcstDiracOrder-ID40", "DiracOrder[CGS[-p,q,p],FCE\[Rule]True]", +"-(CGS[q]*CSP[p, p]) + 2*CGS[p]*CSP[p, q]"}, +{"fcstDiracOrder-ID41", "DiracOrder[CGSD[-p,q,p],FCE\[Rule]True]", +"-(CGSD[q]*CSPD[p, p]) + 2*CGSD[p]*CSPD[p, q]"}, +{"fcstDiracOrder-ID42", +"DiracOrder[-CGA[a].CGA[b]-2 \ +KD[a,b],{b,a},FCDiracIsolate\[Rule]False,FCE\[Rule]True]", +"CGA[b] . CGA[a]"}, +{"fcstDiracOrder-ID43", +"DiracOrder[-CGAD[a].CGAD[b]-2 \ +KDD[a,b],{b,a},FCDiracIsolate\[Rule]False,FCE\[Rule]True]", +"CGAD[b] . CGAD[a]"}, +{"fcstDiracOrder-ID44", +"DiracOrder[-CGAE[a].CGAE[b]-2 \ +KDE[a,b],{b,a},FCDiracIsolate\[Rule]False,FCE\[Rule]True]", +"CGAE[b] . CGAE[a]"}, +{"fcstDiracOrder-ID45", +"DiracOrder[CGAD[nu,mu].CGA[nu,mu],DiracTrick\[Rule]False,FCE\ +\[Rule]True]", +"6*(-6 - CGA[mu] . CGAD[mu]) - 2*(-6 - CGA[nu] . CGA[nu]) - \ +2*CGA[nu] . CGA[nu] - 4*CGA[nu] . CGAD[nu] - CGA[mu] . CGAD[mu] . \ +CGA[nu] . CGAD[nu]"}, +{"fcstDiracOrder-ID46", +"FCSetDiracGammaScheme[\"NDR\"]; DiracOrder[CGA[i1,i2,i3,i4],{i4,i3,i2,i1},FCE\ +\[Rule]True]", +"CGA[i4] . CGA[i3] . CGA[i2] . CGA[i1] + 2*CGA[i4] . \ +CGA[i3]*KD[i1, i2] - 2*CGA[i4] . CGA[i2]*KD[i1, i3] + 2*CGA[i3] . \ +CGA[i2]*KD[i1, i4] + 2*CGA[i4] . CGA[i1]*KD[i2, i3] - 2*CGA[i3] . \ +CGA[i1]*KD[i2, i4] + 2*CGA[i2] . CGA[i1]*KD[i3, i4] + 4*(KD[i1, \ +i4]*KD[i2, i3] - KD[i1, i3]*KD[i2, i4] + KD[i1, i2]*KD[i3, i4])"}, +{"fcstDiracOrder-ID47", "DiracOrder[TGA[].CGA[i],FCE\[Rule]True]", +"-CGA[i] . TGA[]"}, +{"fcstDiracOrder-ID48", "FCSetDiracGammaScheme[\"BMHV\"]; \n tmp=DiracOrder[TGA[].CGAD[i],FCE\[Rule]True]; +FCSetDiracGammaScheme[\"NDR\"]; \n tmp", +"-CGAD[i] . TGA[]"}, +{"fcstDiracOrder-ID49", "DiracOrder[TGA[].GA[mu],FCE\[Rule]True]", +"-GA[mu] . TGA[] + 2*MT[0, mu]"}, +{"fcstDiracOrder-ID50", +"DiracOrder[CGA[j].TGA[].CGA[i],FCE\[Rule]True]", +"CGA[i] . CGA[j] . TGA[] + 2*KD[i, j]*TGA[]"}, +{"fcstDiracOrder-ID51", +"DiracOrder[TGA[].CGA[i]-CGA[i].TGA[],{ExplicitLorentzIndex[0],i},FCE\ +\[Rule]True]", "2*TGA[] . CGA[i]"}, +{"fcstDiracOrder-ID52", +"DiracOrder[CGA[i].TGA[]-TGA[].CGA[i],FCE\[Rule]True]", +"2*CGA[i] . TGA[]"}, +{"fcstDiracOrder-ID53", +"DiracOrder[DCHN[GA[j, i, l, k], a, b],FCE->True]", +"DCHN[GA[i].GA[j].GA[k].GA[l] - 2 GA[k].GA[l] MT[i, j] - +2 GA[i].GA[j] MT[k, l] + 4 MT[i, j] MT[k, l], a, b]"} +}); diff --git a/Tests/Dirac/DiracReduce.test b/Tests/Dirac/DiracReduce.test index 1d510417c..65e342268 100644 --- a/Tests/Dirac/DiracReduce.test +++ b/Tests/Dirac/DiracReduce.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DiracReduce *) @@ -15,11 +15,11 @@ Tests`Dirac`fcstDiracReduce = { -{"fcstDiracReduce-ID1","DiracReduce[DiracMatrix[mu, nu]]", +{"fcstDiracReduce-ID1","DiracReduce[DiracMatrix[mu, nu],FCE->True]", "(-I)*DiracSigma[GA[mu], GA[nu]] + MT[mu, nu]"}, {"fcstDiracReduce-ID2","FCI[DiracReduce[DiracMatrix[mu, nu]]]", "FCI[(-I)*DiracSigma[DiracGamma[LorentzIndex[mu]], DiracGamma[LorentzIndex[nu]]] + Pair[LorentzIndex[mu], LorentzIndex[nu]]]"}, -{"fcstDiracReduce-ID3","MatchQ[DiracReduce[DiracMatrix[mu, nu, rho]], +{"fcstDiracReduce-ID3","MatchQ[DiracReduce[DiracMatrix[mu, nu, rho],FCE->True], I*GA[a_].GA[5]*LC[mu, nu, rho, a_] + GA[rho]*MT[mu, nu] - GA[nu]*MT[mu, rho] + GA[mu]*MT[nu, rho]]","True"}, {"fcstDiracReduce-ID4","MatchQ[FCI[DiracReduce[DiracMatrix[mu, nu, rho]]], @@ -28,7 +28,7 @@ Tests`Dirac`fcstDiracReduce = { DiracGamma[LorentzIndex[rho]]*Pair[LorentzIndex[mu], LorentzIndex[nu]] - DiracGamma[LorentzIndex[nu]]*Pair[LorentzIndex[mu], LorentzIndex[rho]] + DiracGamma[LorentzIndex[mu]]*Pair[LorentzIndex[nu], LorentzIndex[rho]]]","True"}, -{"fcstDiracReduce-ID5","DiracReduce[DiracMatrix[mu, nu, rho, sigma]]","(-I)*GA[5]*LC[mu, nu, rho, sigma] - I*DiracSigma[GA[rho], GA[sigma]]*MT[mu, nu] + +{"fcstDiracReduce-ID5","DiracReduce[DiracMatrix[mu, nu, rho, sigma],FCE->True]","(-I)*GA[5]*LC[mu, nu, rho, sigma] - I*DiracSigma[GA[rho], GA[sigma]]*MT[mu, nu] + I*DiracSigma[GA[nu], GA[sigma]]*MT[mu, rho] - I*DiracSigma[GA[nu], GA[rho]]*MT[mu, sigma] - I*DiracSigma[GA[mu], GA[sigma]]*MT[nu, rho] + MT[mu, sigma]*MT[nu, rho] + I*DiracSigma[GA[mu], GA[rho]]*MT[nu, sigma] - MT[mu, rho]*MT[nu, sigma] - @@ -45,13 +45,13 @@ I*DiracSigma[GA[mu], GA[nu]]*MT[rho, sigma] + MT[mu, nu]*MT[rho, sigma]"}, Pair[LorentzIndex[rho], LorentzIndex[sigma]]"}, {"fcstDiracReduce-ID7", "MatchQ[DiracReduce[(SpinorUBar[p, m].DiracMatrix[i].DiracMatrix[j].DiracMatrix[k].SpinorU[p, m]) * - (SpinorUBar[k, m].DiracMatrix[i].DiracMatrix[j].DiracMatrix[k].SpinorU[k, m])], + (SpinorUBar[k, m].DiracMatrix[i].DiracMatrix[j].DiracMatrix[k].SpinorU[k, m]),DiracSimplify->True,FCE->True], 10*Spinor[Momentum[k], m, 1].GA[a_].Spinor[Momentum[k], m, 1]* Spinor[Momentum[p], m, 1].GA[a_].Spinor[Momentum[p], m, 1] + 6*Spinor[Momentum[k], m, 1].GA[a_].GA[5].Spinor[Momentum[k], m, 1]* Spinor[Momentum[p], m, 1].GA[a_].GA[5].Spinor[Momentum[p], m, 1]]","True"}, {"fcstDiracReduce-ID8", - "MatchQ[$LeviCivitaSign = -I; \n tmp = DiracReduce[GA[i1, i2, 5]] // FCE; \n $LeviCivitaSign = -1; \n + "MatchQ[$LeviCivitaSign = -I; \n tmp = DiracReduce[GA[i1, i2, 5],FCE->True]; \n $LeviCivitaSign = -1; \n tmp, 1/2 I DiracSigma[GA[a_], GA[b_]] LC[i1, i2, a_, b_] + GA[5] MT[i1, i2]]","True"}, {"fcstDiracReduce-ID9", "GA[i0, i, j] // DiracReduce // FCI // EpsChisholm // @@ -59,9 +59,238 @@ DiracOrder[#, {i0, i, j}] & // FCE","GA[i0].GA[i].GA[j]"}, {"fcstDiracReduce-ID10", "(GA[i, j, k, l] // DiracReduce // FCI) - (GA[i, j, k, l] // Chisholm // - ToDiracSigma[#, GA[k], GA[l]] & // - ToDiracSigma[#, GA[j], GA[l]] & // + ToDiracSigma[#, GA[i], GA[k]] & // + ToDiracSigma[#, GA[i], GA[j]] & // ToDiracSigma[#, GA[i], GA[l]] & // Expand // DiracOrder // -Chisholm2)","0"} - +Chisholm[#, Mode -> 2] &)","0"}, +{"fcstDiracReduce-ID11", + "FCCanonicalizeDummyIndices[ +DiracReduce[(I*EL^3* + Spinor[Momentum[p1], QMass, 1].DiracGamma[ + Momentum[ + Polarization[kg, -I, Transversality -> True]]].DiracGamma[ + Momentum[kg]].DiracGamma[Momentum[{L, I}]].DiracGamma[ + Momentum[kp]].DiracGamma[ + Momentum[Polarization[kp, -I]]].Spinor[-Momentum[p2], QMass, + 1]*FeynAmpDenominator[ + PropagatorDenominator[-Momentum[kg] - Momentum[p1], QMass], + PropagatorDenominator[Momentum[kp] + Momentum[p2], QMass]]* + SUNTF[{SUNIndex[cg]}, SUNFIndex[cq], SUNFIndex[cqbar]])/s], +LorentzIndexNames -> {mu}]//FCE", +"(I*EL^3*Spinor[Momentum[p1], QMass, 1] . GS[Polarization[kg, -I, Transversality -> True]] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]* +(SP[kg, Polarization[kp, -I]]*SP[kp, {L, I}] + SP[kg, {L, I}]*SP[kp, Polarization[kp, -I]] - SP[kg, kp]*SP[{L, I}, Polarization[kp, -I]])*SUNTF[{cg}, cq, cqbar])/s + +(I*EL^3*Spinor[Momentum[p1], QMass, 1] . GS[Polarization[kp, -I]] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]* +(SP[kg, {L, I}]*SP[kp, Polarization[kg, -I, Transversality -> True]] - SP[kg, kp]*SP[{L, I}, Polarization[kg, -I, Transversality -> True]])*SUNTF[{cg}, cq, cqbar])/s - +(I*EL^3*Spinor[Momentum[p1], QMass, 1] . GS[{L, I}] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]* +(SP[kg, Polarization[kp, -I]]*SP[kp, Polarization[kg, -I, Transversality -> True]] - SP[kg, kp]*SP[Polarization[kp, -I], Polarization[kg, -I, Transversality -> True]])*SUNTF[{cg}, cq, cqbar])/s + +(I*EL^3*Spinor[Momentum[p1], QMass, 1] . GS[kp] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]* +(SP[kg, Polarization[kp, -I]]*SP[{L, I}, Polarization[kg, -I, Transversality -> True]] - SP[kg, {L, I}]*SP[Polarization[kp, -I], Polarization[kg, -I, Transversality -> True]])*SUNTF[{cg}, cq, cqbar])/s + +(I*EL^3*Spinor[Momentum[p1], QMass, 1] . GS[kg] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]* +(SP[kp, Polarization[kg, -I, Transversality -> True]]*SP[{L, I}, Polarization[kp, -I]] - SP[kp, Polarization[kp, -I]]*SP[{L, I}, Polarization[kg, -I, Transversality -> True]] - + SP[kp, {L, I}]*SP[Polarization[kp, -I], Polarization[kg, -I, Transversality -> True]])*SUNTF[{cg}, cq, cqbar])/s - +(EL^3*Spinor[Momentum[p1], QMass, 1] . GS[Polarization[kg, -I, Transversality -> True]] . GA[5] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]*SUNTF[{cg}, cq, cqbar]* +LC[][kg, kp, {L, I}, Polarization[kp, -I]])/s - (EL^3*Spinor[Momentum[p1], QMass, 1] . GS[kg] . GA[5] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]* +SUNTF[{cg}, cq, cqbar]*LC[][kp, {L, I}, Polarization[kp, -I], Polarization[kg, -I, Transversality -> True]])/s - +(EL^3*Spinor[Momentum[p1], QMass, 1] . GA[mu] . GA[5] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]*SP[{L, I}, Polarization[kp, -I]]*SUNTF[{cg}, cq, cqbar]* +LC[mu][kg, kp, Polarization[kg, -I, Transversality -> True]])/s + (EL^3*Spinor[Momentum[p1], QMass, 1] . GA[mu] . GA[5] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]* +SP[kp, Polarization[kp, -I]]*SUNTF[{cg}, cq, cqbar]*LC[mu][kg, {L, I}, Polarization[kg, -I, Transversality -> True]])/s + +(EL^3*Spinor[Momentum[p1], QMass, 1] . GA[mu] . GA[5] . Spinor[-Momentum[p2], QMass, 1]*FAD[{-kg - p1, QMass}, {kp + p2, QMass}, Dimension -> 4]*SP[kp, {L, I}]*SUNTF[{cg}, cq, cqbar]* +LC[mu][kg, Polarization[kp, -I], Polarization[kg, -I, Transversality -> True]])/s"}, +{"fcstDiracReduce-ID12", + "FCCanonicalizeDummyIndices[ +DiracReduce[ +DiracGamma[ + Momentum[Polarization[kg, -I]]].(m + + DiracGamma[Momentum[p1]]).DiracGamma[ + Momentum[{L, I}]].(m + DiracGamma[Momentum[p2]]).DiracGamma[ + Momentum[Polarization[kp, -I]]], FCVerbose -> 0], +LorentzIndexNames -> {mu}] // FCE", +"(-I)*m*DiracSigma[GS[Polarization[kg, -I]], GS[Polarization[kp, -I]]]*(SP[p1, {L, I}] + SP[p2, {L, I}]) + DiracSigma[GS[{L, I}], GS[Polarization[kp, -I]]]* +((-I)*m*SP[p1, Polarization[kg, -I]] + I*m*SP[p2, Polarization[kg, -I]]) - I*m*DiracSigma[GS[{L, I}], GS[Polarization[kg, -I]]]*(SP[p1, Polarization[kp, -I]] - SP[p2, Polarization[kp, -I]]) + +I*m*DiracSigma[GS[p1], GS[Polarization[kp, -I]]]*SP[{L, I}, Polarization[kg, -I]] - I*m*DiracSigma[GS[p2], GS[Polarization[kp, -I]]]*SP[{L, I}, Polarization[kg, -I]] - +m*SP[p1, Polarization[kp, -I]]*SP[{L, I}, Polarization[kg, -I]] + m*SP[p2, Polarization[kp, -I]]*SP[{L, I}, Polarization[kg, -I]] + +GS[Polarization[kp, -I]]*(SP[p1, Polarization[kg, -I]]*SP[p2, {L, I}] + SP[p1, {L, I}]*SP[p2, Polarization[kg, -I]] + m^2*SP[{L, I}, Polarization[kg, -I]] - SP[p1, p2]*SP[{L, I}, Polarization[kg, -I]]) + +I*m*DiracSigma[GS[p1], GS[Polarization[kg, -I]]]*SP[{L, I}, Polarization[kp, -I]] - I*m*DiracSigma[GS[p2], GS[Polarization[kg, -I]]]*SP[{L, I}, Polarization[kp, -I]] + +m*SP[p1, Polarization[kg, -I]]*SP[{L, I}, Polarization[kp, -I]] - m*SP[p2, Polarization[kg, -I]]*SP[{L, I}, Polarization[kp, -I]] + +GS[Polarization[kg, -I]]*(SP[p1, Polarization[kp, -I]]*SP[p2, {L, I}] + SP[p1, {L, I}]*SP[p2, Polarization[kp, -I]] + m^2*SP[{L, I}, Polarization[kp, -I]] - SP[p1, p2]*SP[{L, I}, Polarization[kp, -I]]) - +I*m*DiracSigma[GS[p1], GS[{L, I}]]*SP[Polarization[kg, -I], Polarization[kp, -I]] + I*m*DiracSigma[GS[p2], GS[{L, I}]]*SP[Polarization[kg, -I], Polarization[kp, -I]] + +m*SP[p1, {L, I}]*SP[Polarization[kg, -I], Polarization[kp, -I]] + m*SP[p2, {L, I}]*SP[Polarization[kg, -I], Polarization[kp, -I]] + +GS[{L, I}]*(-(SP[p1, Polarization[kp, -I]]*SP[p2, Polarization[kg, -I]]) + SP[p1, Polarization[kg, -I]]*SP[p2, Polarization[kp, -I]] - m^2*SP[Polarization[kg, -I], Polarization[kp, -I]] + +SP[p1, p2]*SP[Polarization[kg, -I], Polarization[kp, -I]]) + GS[p2]*(SP[p1, Polarization[kp, -I]]*SP[{L, I}, Polarization[kg, -I]] - SP[p1, Polarization[kg, -I]]*SP[{L, I}, Polarization[kp, -I]] - +SP[p1, {L, I}]*SP[Polarization[kg, -I], Polarization[kp, -I]]) + GS[p1]*(-(SP[p2, Polarization[kp, -I]]*SP[{L, I}, Polarization[kg, -I]]) + SP[p2, Polarization[kg, -I]]*SP[{L, I}, Polarization[kp, -I]] - +SP[p2, {L, I}]*SP[Polarization[kg, -I], Polarization[kp, -I]]) + I*GS[Polarization[kg, -I]] . GA[5]*LC[][p1, p2, {L, I}, Polarization[kp, -I]] - +I*m*GA[5]*LC[][p1, {L, I}, Polarization[kg, -I], Polarization[kp, -I]] - I*GS[p1] . GA[5]*LC[][p2, {L, I}, Polarization[kg, -I], Polarization[kp, -I]] + +I*m*GA[5]*LC[][p2, {L, I}, Polarization[kg, -I], Polarization[kp, -I]] + I*GA[mu] . GA[5]*SP[{L, I}, Polarization[kp, -I]]*LC[mu][p1, p2, Polarization[kg, -I]] - +I*GA[mu] . GA[5]*SP[p2, Polarization[kp, -I]]*LC[mu][p1, {L, I}, Polarization[kg, -I]] + I*GA[mu] . GA[5]*SP[p2, {L, I}]*LC[mu][p1, Polarization[kg, -I], Polarization[kp, -I]] + +I*GA[mu] . GA[5]*SP[p1, Polarization[kg, -I]]*LC[mu][p2, {L, I}, Polarization[kp, -I]] + I*m^2*GA[mu] . GA[5]*LC[mu][{L, I}, Polarization[kg, -I], Polarization[kp, -I]]"}, +{"fcstDiracReduce-ID13","DiracReduce[ +DiracGamma[ + Momentum[Polarization[kg, -I]]].(QMass + + DiracGamma[Momentum[kg + p1]]).DiracGamma[ + Momentum[{L, I}]].(QMass + + DiracGamma[Momentum[-kp - p2]]).DiracGamma[ + Momentum[Polarization[kp, -I]]]] // +FCCanonicalizeDummyIndices[#, LorentzIndexNames -> {mu}, +FCE -> True] &","-I QMass DiracSigma[GS[Polarization[kg, -I]], +GS[Polarization[kp, -I]]] (SP[kg, {L, I}] - SP[kp, {L, I}] + + SP[p1, {L, I}] - SP[p2, {L, I}]) + +DiracSigma[GS[{L, I}], +GS[Polarization[kp, -I]]] (-I QMass SP[kg, Polarization[kg, -I]] - + I QMass SP[kp, Polarization[kg, -I]] - + I QMass SP[p1, Polarization[kg, -I]] - + I QMass SP[p2, Polarization[kg, -I]]) - +I QMass DiracSigma[GS[{L, I}], +GS[Polarization[kg, -I]]] (SP[kg, Polarization[kp, -I]] + + SP[kp, Polarization[kp, -I]] + SP[p1, Polarization[kp, -I]] + + SP[p2, Polarization[kp, -I]]) + +I QMass DiracSigma[GS[kg], GS[Polarization[kp, -I]]] SP[{L, I}, +Polarization[kg, -I]] + +I QMass DiracSigma[GS[kp], GS[Polarization[kp, -I]]] SP[{L, I}, +Polarization[kg, -I]] + +I QMass DiracSigma[GS[p1], GS[Polarization[kp, -I]]] SP[{L, I}, +Polarization[kg, -I]] + +I QMass DiracSigma[GS[p2], GS[Polarization[kp, -I]]] SP[{L, I}, +Polarization[kg, -I]] - +QMass SP[kg, Polarization[kp, -I]] SP[{L, I}, Polarization[kg, -I]] - +QMass SP[kp, Polarization[kp, -I]] SP[{L, I}, +Polarization[kg, -I]] - +QMass SP[p1, Polarization[kp, -I]] SP[{L, I}, Polarization[kg, -I]] - +QMass SP[p2, Polarization[kp, -I]] SP[{L, I}, +Polarization[kg, -I]] + +GS[Polarization[ + kp, -I]] (-SP[kg, Polarization[kg, -I]] SP[kp, {L, I}] - + SP[kg, {L, I}] SP[kp, Polarization[kg, -I]] - + SP[kp, Polarization[kg, -I]] SP[p1, {L, I}] - + SP[kp, {L, I}] SP[p1, Polarization[kg, -I]] - + SP[kg, Polarization[kg, -I]] SP[p2, {L, I}] - + SP[p1, Polarization[kg, -I]] SP[p2, {L, I}] - + SP[kg, {L, I}] SP[p2, Polarization[kg, -I]] - + SP[p1, {L, I}] SP[p2, Polarization[kg, -I]] + + QMass^2 SP[{L, I}, Polarization[kg, -I]] + + SP[kg, kp] SP[{L, I}, Polarization[kg, -I]] + + SP[kg, p2] SP[{L, I}, Polarization[kg, -I]] + + SP[kp, p1] SP[{L, I}, Polarization[kg, -I]] + + SP[p1, p2] SP[{L, I}, Polarization[kg, -I]]) + +I QMass DiracSigma[GS[kg + p1], GS[Polarization[kg, -I]]] SP[{L, I}, +Polarization[kp, -I]] - +I QMass DiracSigma[GS[-kp - p2], GS[Polarization[kg, -I]]] SP[{L, I}, + Polarization[kp, -I]] - +GS[-kp - p2] (SP[kg, Polarization[kg, -I]] + + SP[p1, Polarization[kg, -I]]) SP[{L, I}, Polarization[kp, -I]] + +QMass SP[kg + p1, Polarization[kg, -I]] SP[{L, I}, +Polarization[kp, -I]] + +QMass SP[-kp - p2, Polarization[kg, -I]] SP[{L, I}, +Polarization[kp, -I]] + +2 QMass SP[kp + p2, Polarization[kg, -I]] SP[{L, I}, +Polarization[kp, -I]] + +GS[Polarization[ + kg, -I]] (-SP[kg, Polarization[kp, -I]] SP[kp, {L, I}] - + SP[kg, {L, I}] SP[kp, Polarization[kp, -I]] - + SP[kp, Polarization[kp, -I]] SP[p1, {L, I}] - + SP[kp, {L, I}] SP[p1, Polarization[kp, -I]] - + SP[kg, Polarization[kp, -I]] SP[p2, {L, I}] - + SP[p1, Polarization[kp, -I]] SP[p2, {L, I}] - + SP[kg, {L, I}] SP[p2, Polarization[kp, -I]] - + SP[p1, {L, I}] SP[p2, Polarization[kp, -I]] + + QMass^2 SP[{L, I}, Polarization[kp, -I]] + + SP[kg, kp] SP[{L, I}, Polarization[kp, -I]] + + SP[kg, p2] SP[{L, I}, Polarization[kp, -I]] + + SP[kp, p1] SP[{L, I}, Polarization[kp, -I]] + + SP[p1, p2] SP[{L, I}, Polarization[kp, -I]]) - +I QMass DiracSigma[GS[kg], GS[{L, I}]] SP[Polarization[kg, -I], +Polarization[kp, -I]] - +I QMass DiracSigma[GS[kp], GS[{L, I}]] SP[Polarization[kg, -I], +Polarization[kp, -I]] - +I QMass DiracSigma[GS[p1], GS[{L, I}]] SP[Polarization[kg, -I], +Polarization[kp, -I]] - +I QMass DiracSigma[GS[p2], GS[{L, I}]] SP[Polarization[kg, -I], +Polarization[kp, -I]] + +QMass SP[kg, {L, I}] SP[Polarization[kg, -I], Polarization[kp, -I]] - +QMass SP[kp, {L, I}] SP[Polarization[kg, -I], +Polarization[kp, -I]] + +QMass SP[p1, {L, I}] SP[Polarization[kg, -I], Polarization[kp, -I]] - +QMass SP[p2, {L, I}] SP[Polarization[kg, -I], +Polarization[kp, -I]] + +GS[{L, I}] (SP[kg, Polarization[kp, -I]] SP[kp, + Polarization[kg, -I]] - + SP[kg, Polarization[kg, -I]] SP[kp, Polarization[kp, -I]] - + SP[kp, Polarization[kp, -I]] SP[p1, Polarization[kg, -I]] + + SP[kp, Polarization[kg, -I]] SP[p1, Polarization[kp, -I]] + + SP[kg, Polarization[kp, -I]] SP[p2, Polarization[kg, -I]] + + SP[p1, Polarization[kp, -I]] SP[p2, Polarization[kg, -I]] - + SP[kg, Polarization[kg, -I]] SP[p2, Polarization[kp, -I]] - + SP[p1, Polarization[kg, -I]] SP[p2, Polarization[kp, -I]] - + QMass^2 SP[Polarization[kg, -I], Polarization[kp, -I]] - + SP[kg, kp] SP[Polarization[kg, -I], Polarization[kp, -I]] - + SP[kg, p2] SP[Polarization[kg, -I], Polarization[kp, -I]] - + SP[kp, p1] SP[Polarization[kg, -I], Polarization[kp, -I]] - + SP[p1, p2] SP[Polarization[kg, -I], Polarization[kp, -I]]) + +GS[kp] (-SP[kg, Polarization[kp, -I]] SP[{L, I}, + Polarization[kg, -I]] - + SP[p1, Polarization[kp, -I]] SP[{L, I}, Polarization[kg, -I]] + + SP[kg, {L, I}] SP[Polarization[kg, -I], Polarization[kp, -I]] + + SP[p1, {L, I}] SP[Polarization[kg, -I], Polarization[kp, -I]]) + +GS[p2] (-SP[kg, Polarization[kp, -I]] SP[{L, I}, + Polarization[kg, -I]] - + SP[p1, Polarization[kp, -I]] SP[{L, I}, Polarization[kg, -I]] + + SP[kg, {L, I}] SP[Polarization[kg, -I], Polarization[kp, -I]] + + SP[p1, {L, I}] SP[Polarization[kg, -I], Polarization[kp, -I]]) + +GS[kg + p1] (SP[kp, Polarization[kp, -I]] SP[{L, I}, + Polarization[kg, -I]] + + SP[p2, Polarization[kp, -I]] SP[{L, I}, Polarization[kg, -I]] - + SP[kp, Polarization[kg, -I]] SP[{L, I}, Polarization[kp, -I]] - + SP[p2, Polarization[kg, -I]] SP[{L, I}, Polarization[kp, -I]] + + SP[kp, {L, I}] SP[Polarization[kg, -I], Polarization[kp, -I]] + + SP[p2, {L, I}] SP[Polarization[kg, -I], Polarization[kp, -I]]) - +I GS[Polarization[kg, -I]].GA[5] LC[][kg, kp, {L, I}, +Polarization[kp, -I]] - +I GS[Polarization[kg, -I]].GA[5] LC[][kg, p2, {L, I}, +Polarization[kp, -I]] - +I QMass GA[5] LC[][kg, {L, I}, Polarization[kg, -I], +Polarization[kp, -I]] + +I GS[Polarization[kg, -I]].GA[5] LC[][kp, p1, {L, I}, +Polarization[kp, -I]] + +I GS[kg + p1].GA[5] LC[][kp, {L, I}, Polarization[kg, -I], +Polarization[kp, -I]] - +I QMass GA[5] LC[][kp, {L, I}, Polarization[kg, -I], +Polarization[kp, -I]] - +I GS[Polarization[kg, -I]].GA[5] LC[][p1, p2, {L, I}, +Polarization[kp, -I]] - +I QMass GA[5] LC[][p1, {L, I}, Polarization[kg, -I], +Polarization[kp, -I]] + +I GS[kg + p1].GA[5] LC[][p2, {L, I}, Polarization[kg, -I], +Polarization[kp, -I]] - +I QMass GA[5] LC[][p2, {L, I}, Polarization[kg, -I], +Polarization[kp, -I]] - +I GA[mu].GA[5] SP[{L, I}, Polarization[kp, -I]] LC[mu][kg, kp, +Polarization[kg, -I]] - +I GA[mu].GA[5] SP[{L, I}, Polarization[kp, -I]] LC[mu][kg, p2, +Polarization[kg, -I]] + +GA[mu].GA[5] (I SP[kp, Polarization[kp, -I]] + + I SP[p2, Polarization[kp, -I]]) LC[mu][kg, {L, I}, +Polarization[kg, -I]] + +GA[mu].GA[5] (-I SP[kp, {L, I}] - I SP[p2, {L, I}]) LC[mu][kg, +Polarization[kg, -I], Polarization[kp, -I]] + +I GA[mu].GA[5] SP[{L, I}, Polarization[kp, -I]] LC[mu][kp, p1, +Polarization[kg, -I]] + +GA[mu].GA[5] (-I SP[kg, Polarization[kg, -I]] - + I SP[p1, Polarization[kg, -I]]) LC[mu][kp, {L, I}, +Polarization[kp, -I]] - +I GA[mu].GA[5] SP[{L, I}, Polarization[kp, -I]] LC[mu][p1, p2, +Polarization[kg, -I]] + +GA[mu].GA[5] (I SP[kp, Polarization[kp, -I]] + + I SP[p2, Polarization[kp, -I]]) LC[mu][p1, {L, I}, +Polarization[kg, -I]] + +GA[mu].GA[5] (-I SP[kp, {L, I}] - I SP[p2, {L, I}]) LC[mu][p1, +Polarization[kg, -I], Polarization[kp, -I]] + +GA[mu].GA[5] (-I SP[kg, Polarization[kg, -I]] - + I SP[p1, Polarization[kg, -I]]) LC[mu][p2, {L, I}, +Polarization[kp, -I]] + +I QMass^2 GA[mu].GA[5] LC[mu][{L, I}, Polarization[kg, -I], +Polarization[kp, -I]]"}, +{"fcstDiracReduce-ID14","DiracReduce[DCHN[GA[i, j, k], a, b]] // +FCCanonicalizeDummyIndices[#, LorentzIndexNames -> {mu}, +FCE -> True] &","I DCHN[GA[mu].GA[5], a, b] LC[i, j, k, mu] + +DCHN[GA[k], a, b] MT[i, j] - DCHN[GA[j], a, b] MT[i, k] + +DCHN[GA[i], a, b] MT[j, k]"} } diff --git a/Tests/Dirac/DiracSigmaExpand.test b/Tests/Dirac/DiracSigmaExpand.test new file mode 100644 index 000000000..68c7041a7 --- /dev/null +++ b/Tests/Dirac/DiracSigmaExpand.test @@ -0,0 +1,55 @@ + + +(* :Title: DiracSigmaExpand.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracSigmaExpand *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstDiracSigmaExpand = +({ +{"fcstDiracSigmaExpand-ID1", "DiracSigmaExpand[0,FCE\[Rule]True]", +"0"}, +{"fcstDiracSigmaExpand-ID2", +"DiracSigmaExpand[DiracSigma[GSD[p],GSD[r]],FCE\[Rule]True]", +"DiracSigma[GSD[p], GSD[r]]"}, +{"fcstDiracSigmaExpand-ID3", +"DiracSigmaExpand[DiracSigma[GSD[p]+GSD[q],GSD[r]+GSD[s]],FCE\ +\[Rule]True]", +"DiracSigma[GSD[p], GSD[r]] + DiracSigma[GSD[p], GSD[s]] + \ +DiracSigma[GSD[q], GSD[r]] + DiracSigma[GSD[q], GSD[s]]"}, +{"fcstDiracSigmaExpand-ID4", +"DiracSigmaExpand[DiracSigma[GSD[p],GSD[r]+GSD[s]],FCE\[Rule]True]\ +", "DiracSigma[GSD[p], GSD[r]] + DiracSigma[GSD[p], GSD[s]]"}, +{"fcstDiracSigmaExpand-ID5", +"DiracSigmaExpand[DiracSigma[GSD[p]+GSD[q],GSD[r]],FCE\[Rule]True]\ +", "DiracSigma[GSD[p], GSD[r]] + DiracSigma[GSD[q], GSD[r]]"}, +{"fcstDiracSigmaExpand-ID6", +"DiracSigmaExpand[DiracSigma[GSD[p]+GSD[q],3GSD[r]],FCE\[Rule]True]\ +", "3*DiracSigma[GSD[p], GSD[r]] + 3*DiracSigma[GSD[q], GSD[r]]"}, +{"fcstDiracSigmaExpand-ID7", +"DiracSigmaExpand[DiracSigma[x \ +GSD[p]+GSD[q],3GSD[r]],FCE\[Rule]True]", +"3*x*DiracSigma[GSD[p], GSD[r]] + 3*DiracSigma[GSD[q], GSD[r]]"}, +{"fcstDiracSigmaExpand-ID8", +"DiracSigmaExpand[DiracSigma[x \ +GSD[p+q],3GSD[r+s]],FCE\[Rule]True]", +"3*x*DiracSigma[GSD[p + q], GSD[r + s]]"}, +{"fcstDiracSigmaExpand-ID9", +"DiracSigmaExpand[DiracSigma[x \ +GSD[p+q],3GSD[r+s]],DiracGammaExpand\[Rule]True,FCE\[Rule]True]", +"3*x*(DiracSigma[GSD[p], GSD[r]] + DiracSigma[GSD[p], GSD[s]] + \ +DiracSigma[GSD[q], GSD[r]] + DiracSigma[GSD[q], GSD[s]])"}, +{"fcstDiracSigmaExpand-ID10", +"DiracSigmaExpand[DiracSigma[GSD[p]+GSD[q],GAD[mu]],FCE\[Rule]True]\ +", "-DiracSigma[GAD[mu], GSD[p]] - DiracSigma[GAD[mu], GSD[q]]"} +}); diff --git a/Tests/Dirac/DiracSigmaExplicit.test b/Tests/Dirac/DiracSigmaExplicit.test new file mode 100644 index 000000000..bd648444b --- /dev/null +++ b/Tests/Dirac/DiracSigmaExplicit.test @@ -0,0 +1,61 @@ + + +(* :Title: DiracSigmaExplicit.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracSigmaExplicit *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstDiracSigmaExplicit = +({ +{"fcstDiracSigmaExplicit-ID1", +"DiracSigmaExplicit[DiracSigma[GA[i],GA[j]],FCE\[Rule]True]", +"(I/2)*(GA[i] . GA[j] - GA[j] . GA[i])"}, +{"fcstDiracSigmaExplicit-ID2", +"DiracSigmaExplicit[GS[p].DiracSigma[GA[i],GA[j]].GS[q],FCE\[Rule]\ +True]", "(I/2)*(GS[p] . GA[i] . GA[j] . GS[q] - GS[p] . GA[j] . GA[i] \ +. GS[q])"}, +{"fcstDiracSigmaExplicit-ID3", +"DiracSigmaExplicit[GS[p].(4DiracSigma[GA[i],GA[j]]).GS[q],FCE\ +\[Rule]True]", +"(2*I)*(GS[p] . GA[i] . GA[j] . GS[q] - GS[p] . GA[j] . GA[i] . \ +GS[q])"}, +{"fcstDiracSigmaExplicit-ID4", +"DiracSigmaExplicit[GS[p].(3SUNT[a].DiracSigma[GA[i],GA[j]]).GS[q],\ +FCE\[Rule]True]", +"GS[p] . (((3*I)/2)*(SUNT[a] . GA[i] . GA[j] - SUNT[a] . GA[j] . \ +GA[i])) . GS[q]"}, +{"fcstDiracSigmaExplicit-ID5", +"DiracSigmaExplicit[DiracSigma[GAD[i],GAD[j]],FCE\[Rule]True]", +"(I/2)*(GAD[i] . GAD[j] - GAD[j] . GAD[i])"}, +{"fcstDiracSigmaExplicit-ID6", +"DiracSigmaExplicit[DiracSigma[GAD[i],GA[j]],FCE\[Rule]True]", +"(-I/2)*(GA[j] . GAD[i] - GAD[i] . GA[j])"}, +{"fcstDiracSigma-ID7", +"DiracSigmaExplicit[DiracSigma[TGA[],CGA[i]],FCE\[Rule]True]", +"I*TGA[] . CGA[i]"}, +{"fcstDiracSigma-ID8", +"DiracSigmaExplicit[DiracSigma[TGA[],CGAD[i]],FCE\[Rule]True]", +"I*TGA[] . CGAD[i]"}, +{"fcstDiracSigma-ID9", +"DiracSigmaExplicit[DiracSigma[CGA[i],TGA[]],FCE\[Rule]True]", +"(-I)*TGA[] . CGA[i]"}, +{"fcstDiracSigma-ID10", +"DiracSigmaExplicit[DiracSigma[CGAD[i],TGA[]],FCE\[Rule]True]", +"(-I)*TGA[] . CGAD[i]"}, +{"fcstDiracSigma-ID11", +"DiracSigmaExplicit[DiracSigma[CGA[i],CGA[j]],FCE\[Rule]True]", +"I*(CGA[i] . CGA[j] + KD[i, j])"}, +{"fcstDiracSigma-ID12", +"DiracSigmaExplicit[DiracSigma[CGAD[i],CGAD[j]],FCE\[Rule]True]", +"I*(CGAD[i] . CGAD[j] + KDD[i, j])"} +}); diff --git a/Tests/Dirac/DiracSimplify.test b/Tests/Dirac/DiracSimplify.test index ced66d64d..77178c140 100644 --- a/Tests/Dirac/DiracSimplify.test +++ b/Tests/Dirac/DiracSimplify.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DiracSimplify *) @@ -19,9 +19,9 @@ Tests`Dirac`fcstDiracSimplify = { {"fcstDiracSimplify-ID2","DiracSimplify[DiracMatrix[mu, nu, rho, sigma, mu]]","-2*DiracGamma[LorentzIndex[sigma]] . DiracGamma[LorentzIndex[rho]] . DiracGamma[LorentzIndex[nu]]"}, {"fcstDiracSimplify-ID3","DiracSimplify[1/2 DiracMatrix[mu, a, b, c, d, mu]]","DiracGamma[LorentzIndex[c]] . DiracGamma[LorentzIndex[b]] . DiracGamma[LorentzIndex[a]] . DiracGamma[LorentzIndex[d]] + DiracGamma[LorentzIndex[d]] . DiracGamma[LorentzIndex[a]] . DiracGamma[LorentzIndex[b]] . DiracGamma[LorentzIndex[c]]"}, -{"fcstDiracSimplify-ID4","DiracSimplify[DiracSlash[p], DiracSlash[-q] + m, DiracSlash[p]]","m*Pair[Momentum[p], Momentum[p]] + DiracGamma[Momentum[q]]*Pair[Momentum[p], Momentum[p]] - +{"fcstDiracSimplify-ID4","DiracSimplify[GS[p].(GS[-q] + m).GS[p]]","m*Pair[Momentum[p], Momentum[p]] + DiracGamma[Momentum[q]]*Pair[Momentum[p], Momentum[p]] - 2*DiracGamma[Momentum[p]]*Pair[Momentum[p], Momentum[q]]"}, -{"fcstDiracSimplify-ID5","DiracSimplify[DiracMatrix[5], DiracMatrix[mu]]","-DiracGamma[LorentzIndex[mu]] . DiracGamma[5]"}, +{"fcstDiracSimplify-ID5","DiracSimplify[GA[5,mu]]","-DiracGamma[LorentzIndex[mu]] . DiracGamma[5]"}, {"fcstDiracSimplify-ID6","DiracSimplify[DiracMatrix[6, nu, 7, mu]]","DiracGamma[LorentzIndex[nu]] . DiracGamma[LorentzIndex[mu]] . DiracGamma[6]"}, {"fcstDiracSimplify-ID7","DiracSimplify[(DiracSlash[p] - m).SpinorU[p, m]]","0"}, {"fcstDiracSimplify-ID8","DiracSimplify[(DiracSlash[p] + m).SpinorV[p, m]]","0"}, @@ -29,12 +29,12 @@ DiracGamma[LorentzIndex[d]] . DiracGamma[LorentzIndex[a]] . DiracGamma[LorentzIn {"fcstDiracSimplify-ID10","DiracSimplify[SpinorVBar[p, m].DiracSlash[q].(DiracSlash[p] - m)]","2*Pair[Momentum[p], Momentum[q]]*Spinor[-Momentum[p], m, 1]"}, {"fcstDiracSimplify-ID11","DiracSimplify[SpinorVBar[p, m1].DiracSlash[q, p].SpinorU[q, m2]]","m1*m2*Spinor[-Momentum[p], m1, 1] . Spinor[Momentum[q], m2, 1] + 2*Spinor[-Momentum[p], m1, 1] . Spinor[Momentum[q], m2, 1]* Pair[Momentum[p], Momentum[q]]"}, -{"fcstDiracSimplify-ID11","$BreitMaison = True;\nDiracSimplify[DiracGamma[5] . DiracGamma[LorentzIndex[mu, D], D]]","2*DiracGamma[LorentzIndex[mu, -4 + D], -4 + D] . DiracGamma[5] - DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[5]"}, -{"fcstDiracSimplify-ID12","DiracSimplify[DiracMatrix[6] .DiracMatrix[mu, Dimension -> D]]","DiracGamma[LorentzIndex[mu, -4 + D], -4 + D] . DiracGamma[5] + DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[7]"}, -{"fcstDiracSimplify-ID13","$BreitMaison = False;\nDiracSimplify[DiracMatrix[6] .DiracMatrix[mu, Dimension -> D]]","DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[7]"}, +{"fcstDiracSimplify-ID11","FCSetDiracGammaScheme[\"BMHV\"];\nDiracSimplify[DiracGamma[5] . DiracGamma[LorentzIndex[mu, D], D]]","2*DiracGamma[LorentzIndex[mu, -4 + D], -4 + D] . DiracGamma[5] - DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[5]"}, +{"fcstDiracSimplify-ID12","DiracSimplify[DiracMatrix[6] .DiracMatrix[mu, Dimension -> D]]", +"DiracGamma[LorentzIndex[mu]] . DiracGamma[7] + DiracGamma[LorentzIndex[mu, -4 + D], -4 + D] . DiracGamma[6]"}, +{"fcstDiracSimplify-ID13","FCSetDiracGammaScheme[\"NDR\"];\nDiracSimplify[DiracMatrix[6] .DiracMatrix[mu, Dimension -> D]]","DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[7]"}, {"fcstDiracSimplify-ID14","DiracSimplify[Spinor[p1, m1].(DiracSlash[p2]).DiracMatrix[7].Spinor[p2,m2]] // FCE", -"1/2 m2 Spinor[Momentum[p1], m1, 1].Spinor[Momentum[p2], m2, 1] + -1/2 m2 Spinor[Momentum[p1], m1, 1].GA[5].Spinor[Momentum[p2], m2, 1]"}, +"m2*Spinor[Momentum[p1], m1, 1].GA[6].Spinor[Momentum[p2], m2, 1]"}, {"fcstDiracSimplify-ID15", "DiracSimplify[Spinor[-Momentum[p2],0,1].GS[Polarization[k1,-I]].GS[k1].GS[Polarization[k2,-I]].GA[7].Spinor[Momentum[p1],0,1],DiracSubstitute67->True]//FCE", "1/2 Spinor[-Momentum[p2], 0, 1].GS[Polarization[k1, -I]].GS[k1].GS[ @@ -45,8 +45,21 @@ DiracGamma[LorentzIndex[d]] . DiracGamma[LorentzIndex[a]] . DiracGamma[LorentzIn "DiracSimplify[GA[i].(GS[p] + M).GA[j].GA[6].GA[k].GA[j], InsideDiracTrace -> True] // FCE", "-M MT[i, k]"}, {"fcstDiracSimplify-ID17", -"DiracSimplify[(1/2 - GA[5]/2).(-((a + GS[p + q])/b)).(1/2 + GA[5]/2)] // FCE", +"DiracSimplify[(1/2 - GA[5]/2).(-((a + GS[p + q])/b)).(1/2 + GA[5]/2), ToDiracGamma67 -> False, FCE -> True]", "-(GS[p].GA[5]/(2 b)) - GS[q].GA[5]/(2 b) - GS[p]/(2 b) - GS[q]/(2 b)"}, + + +{"fcstDiracSimplify-ID18","DiracSimplify[ +Spinor[-Momentum[p2, D], m, 1].GAD[Lor1].(m + GSD[-l - p2]).GAD[Lor3].Spinor[-Momentum[p4, D], m, 1]] // FCE","-Spinor[-Momentum[p2, D], m, 1].GAD[Lor1].GSD[l].GAD[Lor3].Spinor[-Momentum[p4, D], m, 1] - +2 Spinor[-Momentum[p2, D], m, 1].GAD[Lor3].Spinor[-Momentum[p4, D], m, 1] FVD[p2, Lor1]"}, +{"fcstDiracSimplify-ID19","DiracSimplify[ +Spinor[Momentum[p3, D], m, 1].GAD[Lor3].(m + GSD[-l + p1]).GAD[Lor1].Spinor[Momentum[p1, D], m, 1]] // FCE","-Spinor[Momentum[p3, D], m, 1].GAD[Lor3].GSD[l].GAD[Lor1].Spinor[ +Momentum[p1, D], m, 1] + 2 Spinor[Momentum[p3, D], m, 1].GAD[Lor3].Spinor[Momentum[p1, D], m, 1] FVD[p1, Lor1]"}, +{"fcstDiracSimplify-ID20","DiracSimplify[ +Spinor[-Momentum[p2, D], m, 1].GAD[Lor4].(m + GSD[-l - p2]).GAD[Lor1].Spinor[-Momentum[p4, D], m, 1]] // FCE","-Spinor[-Momentum[p2, D], m, 1].GAD[Lor4].GSD[l].GAD[Lor1].Spinor[-Momentum[p4, D], m, 1] - 2 Spinor[-Momentum[p2, D], m, 1].GAD[Lor1].Spinor[-Momentum[p4, D], m, 1] FVD[p2, Lor4]"}, +{"fcstDiracSimplify-ID21","DiracSimplify[Spinor[Momentum[p3, D], m, 1].GAD[Lor4].(m + GSD[l + p3]).GAD[Lor1].Spinor[Momentum[p1, D], m, 1]] // FCE","Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[l].GAD[Lor1].Spinor[ +Momentum[p1, D], m, 1] + 2 Spinor[Momentum[p3, D], m, 1].GAD[Lor1].Spinor[Momentum[p1, D], m, 1] FVD[p3, Lor4]"}, +{"fcstDiracSimplify-ID21","DiracSimplify[CGA[i].CGS[p].CGA[j].CGA[i]]//FCE","4 CV[p, j] + CGS[p].CGA[j]"}, {"fcstDiracSimplify-ID22","DiracSimplify[-(1/SPD[p, p]) 8 (2 - D) Spinor[Momentum[p, D], M, 1].GSD[p].Spinor[ Momentum[p, D], M, 1] FAD[{k1, M}] + (1/SPD[p, p]) @@ -58,25 +71,370 @@ DiracGamma[LorentzIndex[d]] . DiracGamma[LorentzIndex[a]] . DiracGamma[LorentzIn 1] (M^2 - ma^2 + SPD[p, p]) - D Spinor[Momentum[p, D], M, 1].GSD[p].Spinor[Momentum[p, D], M, 1] (M^2 - ma^2 + SPD[p, p]))]//FCE", - "32 D M^2 FAD[{k1, M}, {k1 - p, ma}] + (1/SPD[p, p]) 16 (-2 + D) M^2 (FAD[{k1, M}] - FAD[{k1, ma}] - - M^2 FAD[{k1, M}, {k1 - p, ma}] + ma^2 FAD[{k1, M}, {k1 - p, ma}] - - FAD[{k1, M}, {k1 - p, ma}] SPD[p, p])"} -} + "32*M^2*FAD[{k1, M}, {k1 - p, ma}] + 16*D*M^2*FAD[{k1, M}, {k1 - p, ma}] - + (32*M^2*FAD[{k1, M}])/SPD[p, p] + (16*D*M^2*FAD[{k1, M}])/SPD[p, p] + + (32*M^2*FAD[{k1, ma}])/SPD[p, p] - (16*D*M^2*FAD[{k1, ma}])/SPD[p, p] + + (32*M^4*FAD[{k1, M}, {k1 - p, ma}])/SPD[p, p] - + (16*D*M^4*FAD[{k1, M}, {k1 - p, ma}])/SPD[p, p] - + (32*M^2*ma^2*FAD[{k1, M}, {k1 - p, ma}])/SPD[p, p] + + (16*D*M^2*ma^2*FAD[{k1, M}, {k1 - p, ma}])/SPD[p, p]"}, +{"fcstDiracSimplify-ID23","DiracSimplify[DiracTrace[GA[a, b, a]] + GA[a, a], DiracTrace -> False, FCE -> True]","4 + DiracTrace[GA[a].GA[b].GA[a]]"}, +{"fcstDiracSimplify-ID24","DiracSimplify[DiracTrace[GA[a, b, a]] + GA[a, b], +DiracTraceEvaluate -> True, FCE -> True]","GA[a].GA[b]"}, +{"fcstDiracSimplify-ID25","DiracSimplify[DiracTrace[GA[a, b, c, d]] + GA[a, b, c, d], +DiracTraceEvaluate -> True, FCE -> True]","GA[a].GA[b].GA[c].GA[d] + 4 MT[a, d] MT[b, c] - 4 MT[a, c] MT[b, d] + 4 MT[a, b] MT[c, d]"}, +{"fcstDiracSimplify-ID26", +"DiracSimplify[(1/2 - GA[5]/2).(-((a + GS[p + q])/b)).(1/2 + GA[5]/2), FCE -> True]", +"-(GS[p].GA[6]/b) - GS[q].GA[6]/b"}, +{"fcstDiracSimplify-ID27", +"DiracSimplify[GA[i, 5, j, i], DiracSubstitute5 -> True, FCE -> True]", +"-2 GA[j].GA[6] + 2 GA[j].GA[7]"}, +{"fcstDiracSimplify-ID28", +"DiracSimplify[DiracTrace[(m + GS[k1]).GA[6].GA[nu]. +(m + GS[k2]).GA[mu].GA[7]], DiracTraceEvaluate -> True, +FCE -> True]", +"2 FV[k1, nu] FV[k2, mu] + 2 FV[k1, mu] FV[k2, nu] - +2 MT[mu, nu] SP[k1, k2] + 2 I LC[mu, nu][k1, k2]"}, + + +{"fcstDiracSimplify-ID29", +"(I GA[al].GA[5] LC[\[Mu], \[Nu], \[Rho], al] + +GA[\[Rho]] MT[\[Mu], \[Nu]] - GA[\[Nu]] MT[\[Mu], \[Rho]] + +GA[\[Mu]] MT[\[Nu], \[Rho]]).(I GA[be].GA[ + 5] LC[\[Mu], \[Nu], \[Rho], be] + GA[\[Rho]] MT[\[Mu], \[Nu]] - +GA[\[Nu]] MT[\[Mu], \[Rho]] + GA[\[Mu]] MT[\[Nu], \[Rho]])//DiracSimplify", +"16"}, +{"fcstDiracSimplify-ID30", +"DiracSimplify[(GA[nu].GS[p] + GS[p].GA[nu] - 2 FV[p, nu]),DiracOrder -> True]", +"0"}, +{"fcstDiracSimplify-ID31", +"DiracSimplify[ +DiracTrace[(m2 + GSD[l - p1 - p2 - p3]).(I EL GAD[Lor3]).(m2 + + GSD[l - p3]).(I EL GAD[Lor1]).(m2 + + GSD[l]).(-((I EL m2)/(4 m1)))] Spinor[Momentum[p1, D], 0, + 1].(I EL GAD[Lor2]).Spinor[-Momentum[p2, D], 0, 1] FVD[ +Polarization[p3, -I, Transversality -> True], Lor1] MTD[Lor2, +Lor3],FCE->True]", +"-((EL^4 m2^4 Spinor[Momentum[p1, D], 0, 1].GSD[ + Polarization[p3, -I, + Transversality -> True]].Spinor[-Momentum[p2, D], 0, 1])/m1) + ( +EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + Polarization[p3, -I, + Transversality -> True]].Spinor[-Momentum[p2, D], 0, 1] SPD[l, +l])/m1 - ( +2 EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + Polarization[p3, -I, + Transversality -> True]].Spinor[-Momentum[p2, D], 0, 1] SPD[l, +p3])/m1 - ( +4 EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + l].Spinor[-Momentum[p2, D], 0, 1] SPD[l, +Polarization[p3, -I, Transversality -> True]])/m1 + ( +4 EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + p3].Spinor[-Momentum[p2, D], 0, 1] SPD[l, +Polarization[p3, -I, Transversality -> True]])/m1 + ( +EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + Polarization[p3, -I, + Transversality -> True]].Spinor[-Momentum[p2, D], 0, 1] SPD[p1, +p3])/m1 - ( +EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + p3].Spinor[-Momentum[p2, D], 0, 1] SPD[p1, +Polarization[p3, -I, Transversality -> True]])/m1 + ( +EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + Polarization[p3, -I, + Transversality -> True]].Spinor[-Momentum[p2, D], 0, 1] SPD[p2, +p3])/m1 - ( +EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + p3].Spinor[-Momentum[p2, D], 0, 1] SPD[p2, +Polarization[p3, -I, Transversality -> True]])/m1 + ( +EL^4 m2^2 Spinor[Momentum[p1, D], 0, 1].GSD[ + Polarization[p3, -I, + Transversality -> True]].Spinor[-Momentum[p2, D], 0, 1] SPD[p3, +p3])/m1"}, +{"fcstDiracSimplify-ID32","DiracSimplify[TGA[].CGA[i].TGA[].CGA[i]]","3"}, +{"fcstDiracSimplify-ID33","DiracSimplify[TGA[].CGA[i].CGA[i].TGA[]]","-3"}, +{"fcstDiracSimplify-ID34","DiracSimplify[-1/2 GA[5].(GAD[mu].GSD[v] - FVD[v, mu]) FVD[v, mu]]","0"}, +{"fcstDiracSimplify-ID35","DiracSimplify[CGA[i].CGS[p].CGA[j].CGS[p + q] KD[i, j], FCE -> True]","-CSP[p, p] + CGS[p].CGS[q]"}, +{"fcstDiracSimplify-ID36","DiracSimplify[DiracTrace[1]]","4"}, +{"fcstDiracSimplify-ID37","DiracSimplify[ +DCHN[GSD[-k1 + p1], Dir1, Dir2] DCHN[GSD[Polarization[k1, -I]], Dir2, + Spinor[Momentum[p1, D], QGMassQ, 1]] DCHN[ +GSD[Polarization[k2, -I]], Spinor[-Momentum[p2, D], QGMassQ, 1], +Dir1], FCE -> True]","-(QGMassQ*Spinor[-Momentum[p2, D], QGMassQ, 1] . + GSD[Polarization[k2, -I]] . GSD[Polarization[k1, -I]] . + Spinor[Momentum[p1, D], QGMassQ, 1]) - +Spinor[-Momentum[p2, D], QGMassQ, 1] . GSD[Polarization[k2, -I]] . +GSD[k1] . GSD[Polarization[k1, -I]] . Spinor[Momentum[p1, D], QGMassQ, +1] + 2*Spinor[-Momentum[p2, D], QGMassQ, 1] . +GSD[Polarization[k2, -I]] . Spinor[Momentum[p1, D], QGMassQ, 1]* +SPD[p1, Polarization[k1, -I]]"}, +{"fcstDiracSimplify-ID38","DiracSimplify[DiracTrace[GAD[al, be].GA[5].GAD[mu, nu]] DiracTrace[ +GAD[al, be, mu, nu]]]","0"}, +{"fcstDiracSimplify-ID39","DiracSimplify[ +Spinor[-Momentum[p1, D], mb, 1].GAD[mu].GAD[nu].GA[7].Spinor[ + Momentum[p3, D], ms, 1] Spinor[Momentum[p1, D], mb, 1].GAD[ + nu].GAD[mu].GA[7].Spinor[-Momentum[p2, D], ms, 1], +DiracOrder -> True] // +FCCanonicalizeDummyIndices[#, LorentzIndexNames -> {mu, nu}, +FCE -> True] &","2 D Spinor[-Momentum[p1, D], mb, 1].GA[7].Spinor[Momentum[p3, D], ms, + 1] Spinor[Momentum[p1, D], mb, 1].GA[7].Spinor[-Momentum[p2, D], + ms, 1] - +Spinor[-Momentum[p1, D], mb, 1].GAD[mu].GAD[nu].GA[7].Spinor[ + Momentum[p3, D], ms, 1] Spinor[Momentum[p1, D], mb, 1].GAD[ + mu].GAD[nu].GA[7].Spinor[-Momentum[p2, D], ms, 1]"}, +{"fcstDiracSimplify-ID40","DiracSimplify[{c1 GA[mu].(GS[p] + m).GA[mu], +c2 DiracTrace[GA[mu, nu]]},FCE->True]","{4 c1 m - 2 c1 GS[p], 4 c2 MT[mu, nu]}"}, +{"fcstDiracSimplify-ID41","Total[DiracSimplify[{SpinorUBar[p].GA[mu, nu].SpinorV[q] SpinorUBar[ + p2].DiracSigma[GA[mu], GA[nu]].SpinorV[q2], +-SpinorUBar[p].GA[mu, nu].SpinorV[q] SpinorUBar[p2].DiracSigma[ + GA[mu], GA[nu]].SpinorV[q2]}, +LorentzIndexNames -> Table[mu[i], {i, 1, 10}]]]","0"} +}; + + + + +Tests`Dirac`fcstDiracSimplifySirlin = +({ +{"fcstDiracSimplifySirlin-ID1", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,nu,6].SpinorU[p1,\ +m1]SpinorUBar[p4,m4].GA[mu,tau,nu,6].SpinorU[p2,m2],FCE\[Rule]True],\ +\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[6].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[6].Spinor[Momentum[p2],m2,1] \ +MT[rho,tau]]", "True"}, +{"fcstDiracSimplifySirlin-ID2", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,nu,7].SpinorU[p1,\ +m1]SpinorUBar[p4,m4].GA[mu,tau,nu,7].SpinorU[p2,m2],FCE\[Rule]True],\ +\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[7].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[7].Spinor[Momentum[p2],m2,1] \ +MT[rho,tau]]", "True"}, +{"fcstDiracSimplifySirlin-ID3", +"DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,nu,6].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,tau,nu,7].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[tau] . GA[6] . \ +Spinor[Momentum[p1], m1, 1]*Spinor[Momentum[p4], m4, 1] . GA[rho] . \ +GA[7] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracSimplifySirlin-ID4", +"DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,nu,7].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,tau,nu,6].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[tau] . GA[7] . \ +Spinor[Momentum[p1], m1, 1]*Spinor[Momentum[p4], m4, 1] . GA[rho] . \ +GA[6] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracSimplifySirlin-ID5", +"DiracSimplify[SpinorUBar[p3,m3].GA[nu,rho,mu,7].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,tau,nu,7].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[tau] . GA[7] . \ +Spinor[Momentum[p1], m1, 1]*Spinor[Momentum[p4], m4, 1] . GA[rho] . \ +GA[7] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracSimplifySirlin-ID6", +"DiracSimplify[SpinorUBar[p3,m3].GA[nu,rho,mu,6].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,tau,nu,6].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[tau] . GA[6] . \ +Spinor[Momentum[p1], m1, 1]*Spinor[Momentum[p4], m4, 1] . GA[rho] . \ +GA[6] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracSimplifySirlin-ID7", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[nu,rho,mu,6].SpinorU[p1,\ +m1]SpinorUBar[p2,m2].GA[mu,tau,nu,7].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[6].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p2],m2,1].GA[a_].GA[7].Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]]", "True"}, +{"fcstDiracSimplifySirlin-ID8", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[nu,rho,mu,7].SpinorU[p1,\ +m1]SpinorUBar[p2,m2].GA[mu,tau,nu,6].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[7].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p2],m2,1].GA[a_].GA[6].Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]]", "True"}, +{"fcstDiracSimplifySirlin-ID9", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].nc1.GA[mu,rho,nu].nc2.\ +SpinorU[p1,m1]SpinorUBar[p4,m4].nc3.GA[mu,tau,nu].nc4.SpinorU[p4,m4],\ +FCE\[Rule]True],\[IndentingNewLine]2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[tau].nc2.Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].nc3.GA[rho].nc4.Spinor[Momentum[p4],m4,1]-2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[tau].nc2.GA[5].Spinor[Momentum[p1],\ +m1,1] Spinor[Momentum[p4],m4,1].nc3.GA[rho].nc4.GA[5].Spinor[Momentum[\ +p4],m4,1]+2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[a_].nc2.Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].nc3.GA[a_].nc4.Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]+2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[a_].nc2.GA[5].Spinor[Momentum[p1],m1,\ +1] Spinor[Momentum[p4],m4,1].nc3.GA[a_].nc4.GA[5].Spinor[Momentum[p4],\ +m4,1] MT[rho,tau]]", "True"}, +{"fcstDiracSimplifySirlin-ID10", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].nc1.GA[nu,rho,mu].nc2.\ +SpinorU[p1,m1]SpinorUBar[p4,m4].nc3.GA[mu,tau,nu].nc4.SpinorU[p4,m4],\ +FCE\[Rule]True],\[IndentingNewLine]2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[tau].nc2.Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].nc3.GA[rho].nc4.Spinor[Momentum[p4],m4,1]+2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[tau].nc2.GA[5].Spinor[Momentum[p1],\ +m1,1] Spinor[Momentum[p4],m4,1].nc3.GA[rho].nc4.GA[5].Spinor[Momentum[\ +p4],m4,1]+2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[a_].nc2.Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].nc3.GA[a_].nc4.Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]-2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[a_].nc2.GA[5].Spinor[Momentum[p1],m1,\ +1] Spinor[Momentum[p4],m4,1].nc3.GA[a_].nc4.GA[5].Spinor[Momentum[p4],\ +m4,1] MT[rho,tau]]", "True"}, +{"fcstDiracSimplifySirlin-ID11", +"DiracSimplify[SpinorUBar[p3,m3].GA[mu,nu,6].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,nu,7].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[6] . Spinor[Momentum[p1], m1, \ +1]*Spinor[Momentum[p4], m4, 1] . GA[7] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracSimplifySirlin-ID12", +"DiracSimplify[SpinorUBar[p3,m3].GA[mu,nu,7].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,nu,6].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[7] . Spinor[Momentum[p1], m1, \ +1]*Spinor[Momentum[p4], m4, 1] . GA[6] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracSimplifySirlin-ID13", +"DiracSimplify[SpinorUBar[p3,m3].GA[mu,nu,6].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[nu,mu,7].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[6] . Spinor[Momentum[p1], m1, \ +1]*Spinor[Momentum[p4], m4, 1] . GA[7] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracSimplifySirlin-ID14", +"DiracSimplify[SpinorUBar[p3,m3].GA[mu,nu,7].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[nu,mu,6].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[7] . Spinor[Momentum[p1], m1, \ +1]*Spinor[Momentum[p4], m4, 1] . GA[6] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstDiracSimplifySirlin-ID15", +"MatchQ[DiracSimplify[SpinorUBar[p1,m1].GA[mu,nu,6].SpinorU[p2,m2]\ +SpinorUBar[p3,m3].GA[mu,nu,6].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]-\!\(\*FractionBox[\(1\), \(2\)]\) \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p4],m4,1]+4 \ +Spinor[Momentum[p1],m1,1].GA[6].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[6].Spinor[Momentum[p4],m4,1]-\!\(\*\ +FractionBox[\(1\), \(4\)]\) \[ImaginaryI] \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS283_],GA[liS284_]].Spinor[\ +Momentum[p4],m4,1] LC[liS281_,liS282_,liS283_,liS284_]]", "True"}, +{"fcstDiracSimplifySirlin-ID16", +"MatchQ[DiracSimplify[SpinorUBar[p1,m1].GA[mu,nu,7].SpinorU[p2,m2]\ +SpinorUBar[p3,m3].GA[mu,nu,7].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]-\!\(\*FractionBox[\(1\), \(2\)]\) \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p4],m4,1]+4 \ +Spinor[Momentum[p1],m1,1].GA[7].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[7].Spinor[Momentum[p4],m4,1]+\!\(\*\ +FractionBox[\(1\), \(4\)]\) \[ImaginaryI] \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS283_],GA[liS284_]].Spinor[\ +Momentum[p4],m4,1] LC[liS281_,liS282_,liS283_,liS284_]]", "True"}, +{"fcstDiracSimplifySirlin-ID17", +"MatchQ[DiracSimplify[SpinorUBar[p1,m1].GA[mu,nu,6].SpinorU[p2,m2]\ +SpinorUBar[p3,m3].GA[nu,mu,6].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]\!\(\*FractionBox[\(1\), \(2\)]\) \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p4],m4,1]+4 \ +Spinor[Momentum[p1],m1,1].GA[6].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[6].Spinor[Momentum[p4],m4,1]+\!\(\*\ +FractionBox[\(1\), \(4\)]\) \[ImaginaryI] \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS283_],GA[liS284_]].Spinor[\ +Momentum[p4],m4,1] LC[liS281_,liS282_,liS283_,liS284_]]", "True"}, +{"fcstDiracSimplifySirlin-ID18", +"MatchQ[DiracSimplify[SpinorUBar[p1,m1].GA[mu,nu,7].SpinorU[p2,m2]\ +SpinorUBar[p3,m3].GA[nu,mu,7].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]\!\(\*FractionBox[\(1\), \(2\)]\) \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p4],m4,1]+4 \ +Spinor[Momentum[p1],m1,1].GA[7].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[7].Spinor[Momentum[p4],m4,1]-\!\(\*\ +FractionBox[\(1\), \(4\)]\) \[ImaginaryI] \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS283_],GA[liS284_]].Spinor[\ +Momentum[p4],m4,1] LC[liS281_,liS282_,liS283_,liS284_]]", "True"}, +{"fcstDiracSimplifySirlin-ID19", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[6].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[mu,al,si,be,nu].GA[6].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]16 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[6].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[6].Spinor[Momentum[p4],m4,1] \ +MT[al,rho] MT[be,tau]]", "True"}, +{"fcstDiracSimplifySirlin-ID20", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[7].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[mu,al,si,be,nu].GA[7].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]16 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[7].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[7].Spinor[Momentum[p4],m4,1] \ +MT[al,rho] MT[be,tau]]", "True"}, +{"fcstDiracSimplifySirlin-ID21", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[6].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[mu,al,si,be,nu].GA[7].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[rho].GA[be].GA[6].Spinor[Momentum[\ +p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[al].GA[tau].GA[7].Spinor[Momentum[\ +p4],m4,1]]", "True"}, +{"fcstDiracSimplifySirlin-ID22", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[7].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[mu,al,si,be,nu].GA[6].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[rho].GA[be].GA[7].Spinor[Momentum[\ +p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[al].GA[tau].GA[6].Spinor[Momentum[\ +p4],m4,1]]", "True"}, +{"fcstDiracSimplifySirlin-ID23", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[6].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[nu,al,si,be,mu].GA[6].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[be].GA[tau].GA[a_].GA[6].Spinor[Momentum[\ +p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[al].GA[rho].GA[6].Spinor[Momentum[\ +p4],m4,1]]", "True"}, +{"fcstDiracSimplifySirlin-ID24", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[7].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[nu,al,si,be,mu].GA[7].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[be].GA[tau].GA[a_].GA[7].Spinor[Momentum[\ +p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[al].GA[rho].GA[7].Spinor[Momentum[\ +p4],m4,1]]", "True"}, +{"fcstDiracSimplifySirlin-ID25", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[6].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[nu,al,si,be,mu].GA[7].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]16 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[6].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[7].Spinor[Momentum[p4],m4,1] \ +MT[al,tau] MT[be,rho]]", "True"}, +{"fcstDiracSimplifySirlin-ID26", +"MatchQ[DiracSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[7].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[nu,al,si,be,mu].GA[6].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]16 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[7].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[6].Spinor[Momentum[p4],m4,1] \ +MT[al,tau] MT[be,rho]]", "True"} +}); + + Tests`Dirac`fcstDiracSimplifyDotWarnings = { {"fcstDiracSimplifyDotWarnings-ID1","CheckAbort[DiracSimplify[GA[a] GA[b],FCCheckSyntax->True],True]", - "True","{Message[DiracSimplify::noncom, GA[a]*GA[b]]}"}, + "True"}, {"fcstDiracSimplifyDotWarnings-ID2","CheckAbort[DiracSimplify[GA[a, b] GA[c],FCCheckSyntax->True],True]", - "True","{Message[DiracSimplify::noncom, GA[a] . GA[b]*GA[c]]}"}, + "True"}, {"fcstDiracSimplifyDotWarnings-ID3","CheckAbort[DiracSimplify[GA[a, b] GA[c, d],FCCheckSyntax->True],True]", - "True","{Message[DiracSimplify::noncom, GA[a] . GA[b]*GA[c] . GA[d]]}"}, + "True"}, {"fcstDiracSimplifyDotWarnings-ID4","CheckAbort[DiracSimplify[SUNT[a] SUNT[b],FCCheckSyntax->True],True]", - "True","{Message[DiracSimplify::noncom, SUNT[a]*SUNT[b]]}"}, + "True"}, {"fcstDiracSimplifyDotWarnings-ID5","CheckAbort[DiracSimplify[SUNT[a, b] SUNT[c],FCCheckSyntax->True],True]", - "True","{Message[DiracSimplify::noncom, SUNT[c]*SUNT[a, b]]}"}, + "True"}, {"fcstDiracSimplifyDotWarnings-ID6","CheckAbort[DiracSimplify[SUNT[a, b] SUNT[c, d],FCCheckSyntax->True],True]", - "True","{Message[DiracSimplify::noncom, SUNT[a, b]*SUNT[c, d]]}"}, + "True"}, {"fcstDiracSimplifyDotWarnings-ID7","CheckAbort[DiracSimplify[(GA[a] + M) GA[b],FCCheckSyntax->True],True]", - "True","{Message[DiracSimplify::noncom, (M + GA[a])*GA[b]]}"} + "True"} } diff --git a/Tests/Dirac/DiracSubstitute5.test b/Tests/Dirac/DiracSubstitute5.test new file mode 100644 index 000000000..fa6a27e68 --- /dev/null +++ b/Tests/Dirac/DiracSubstitute5.test @@ -0,0 +1,31 @@ + + +(* :Title: DiracSubstitute5.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracSubstitute5 *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstDiracSubstitute5 = +({ +{"fcstDiracSubstitute5-ID1", +"DiracSubstitute5[GA[5],FCE\[Rule]True]", "GA[6] - GA[7]"}, +{"fcstDiracSubstitute5-ID2", +"DiracSubstitute67[DiracSubstitute5[GA[5]],FCE\[Rule]True]", +"GA[5]"}, +{"fcstDiracSubstitute5-ID3", +"DiracSubstitute5[SpinorUBar[p1,m1].GSD[p].GA[5].SpinorV[p2,m2]]\ +//DotSimplify//FCE", +"Spinor[Momentum[p1], m1, 1] . GSD[p] . GA[6] . \ +Spinor[-Momentum[p2], m2, 1] - Spinor[Momentum[p1], m1, 1] . GSD[p] . \ +GA[7] . Spinor[-Momentum[p2], m2, 1]"} +}); diff --git a/Tests/Dirac/DiracSubstitute67.test b/Tests/Dirac/DiracSubstitute67.test new file mode 100644 index 000000000..d1963b6d5 --- /dev/null +++ b/Tests/Dirac/DiracSubstitute67.test @@ -0,0 +1,30 @@ + + +(* :Title: DiracSubstitute67.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DiracSubstitute67 *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstDiracSubstitute67 = +({ +{"fcstDiracSubstitute67-ID1", +"DiracSubstitute67[GA[6],FCE\[Rule]True]", "1/2 + GA[5]/2"}, +{"fcstDiracSubstitute67-ID2", +"DiracSubstitute67[GA[7],FCE\[Rule]True]", "1/2 - GA[5]/2"}, +{"fcstDiracSubstitute67-ID3", +"DiracSubstitute67[GA[mu,6,nu],FCE\[Rule]True]", +"GA[mu] . (1/2 + GA[5]/2) . GA[nu]"}, +{"fcstDiracSubstitute67-ID4", +"DiracSubstitute67[GA[mu,7,nu],FCE\[Rule]True]", +"GA[mu] . (1/2 - GA[5]/2) . GA[nu]"} +}); diff --git a/Tests/Dirac/DiracTrace.test b/Tests/Dirac/DiracTrace.test index 056d769ad..9043f33f0 100644 --- a/Tests/Dirac/DiracTrace.test +++ b/Tests/Dirac/DiracTrace.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DiracTrace *) @@ -75,12 +75,12 @@ Momentum[q2]])"}, {"fcstDiracTrace-ID28", "DiracTrace[GA[i,j,k,7,l,m],DiracTraceEvaluate\[Rule]True]", "0"}, {"fcstDiracTrace-ID29", -"$BreitMaison = True; (DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], +"FCSetDiracGammaScheme[\"BMHV\"]; (DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True] - DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], DiracTraceEvaluate -> True, West -> False]) // Simplify", "0"}, {"fcstDiracTrace-ID30", -"$BreitMaison = False; \n DeclareNonCommutative[ncA]; \n Tr[GA[i, j].ncA.GA[k, l], FCVerbose -> 0] // FCE", +"FCSetDiracGammaScheme[\"NDR\"]; \n DeclareNonCommutative[ncA]; \n Tr[GA[i, j].ncA.GA[k, l], FCVerbose -> 0] // FCE", "DiracTrace[GA[i].GA[j].ncA.GA[k].GA[l]]"}, {"fcstDiracTrace-ID31", "DiracTrace[DiracTrace[GA[i, j]], DiracTraceEvaluate -> True] // FCE", @@ -91,6 +91,170 @@ DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5], {"fcstDiracTrace-ID33", "DiracTrace[DiracSigma[GA[a], GA[b]].GA[a].GA[b], DiracTraceEvaluate -> True]", -"-48 I"} -} -); +"-48 I"}, +{"fcstDiracTrace-ID34", +"DiracTrace[CGA[i, j], DiracTraceEvaluate -> True]", +"-4 CartesianPair[CartesianIndex[i], CartesianIndex[j]]"}, +{"fcstDiracTrace-ID35", +"DiracTrace[CGA[i, j, k, l].GA[5], DiracTraceEvaluate -> True]", +"0"}, +{"fcstDiracTrace-ID36", +"DiracTrace[CGS[i, j, k, l].GA[5], DiracTraceEvaluate -> True]", +"0"}, +{"fcstDiracTrace-ID37", +"DiracTrace[CGA[i, j, k, l], DiracTraceEvaluate -> True] // FCE", +"4 (KD[i, l] KD[j, k] - KD[i, k] KD[j, l] + KD[i, j] KD[k, l])"}, +{"fcstDiracTrace-ID38", +"DiracTrace[CGAD[i, j, k, l], DiracTraceEvaluate -> True] // FCE", +"4 (KDD[i, l] KDD[j, k] - KDD[i, k] KDD[j, l] + KDD[i, j] KDD[k, l])"}, +{"fcstDiracTrace-ID39", +"DiracTrace[CGA[i].GA[mu], DiracTraceEvaluate -> True]", +"4 Pair[CartesianIndex[i], LorentzIndex[mu]]"}, +{"fcstDiracTrace-ID40", +"DiracTrace[GSD[q].GSD[p1] + GSD[q].GSD[p2], DiracTraceEvaluate -> True]", +"4 (Pair[Momentum[p1, D], Momentum[q, D]] + +Pair[Momentum[p2, D], Momentum[q, D]])"}, +{"fcstDiracTrace-ID41", +"DiracTrace[GS[a + i, b, c, d, e, f, g, h], DiracTraceEvaluate -> True, FCE -> True]", +"4*(SP[a, h]*SP[b, g]*SP[c, f]*SP[d, e] - SP[a, g]*SP[b, h]*SP[c, f]*SP[d, e] - SP[a, h]*SP[b, f]*SP[c, g]*SP[d, e] + SP[a, f]*SP[b, h]*SP[c, g]*SP[d, e] + +SP[a, g]*SP[b, f]*SP[c, h]*SP[d, e] - SP[a, f]*SP[b, g]*SP[c, h]*SP[d, e] - SP[a, h]*SP[b, g]*SP[c, e]*SP[d, f] + SP[a, g]*SP[b, h]*SP[c, e]*SP[d, f] + +SP[a, h]*SP[b, e]*SP[c, g]*SP[d, f] - SP[a, e]*SP[b, h]*SP[c, g]*SP[d, f] - SP[a, g]*SP[b, e]*SP[c, h]*SP[d, f] + SP[a, e]*SP[b, g]*SP[c, h]*SP[d, f] + +SP[a, h]*SP[b, f]*SP[c, e]*SP[d, g] - SP[a, f]*SP[b, h]*SP[c, e]*SP[d, g] - SP[a, h]*SP[b, e]*SP[c, f]*SP[d, g] + SP[a, e]*SP[b, h]*SP[c, f]*SP[d, g] + +SP[a, f]*SP[b, e]*SP[c, h]*SP[d, g] - SP[a, e]*SP[b, f]*SP[c, h]*SP[d, g] - SP[a, g]*SP[b, f]*SP[c, e]*SP[d, h] + SP[a, f]*SP[b, g]*SP[c, e]*SP[d, h] + +SP[a, g]*SP[b, e]*SP[c, f]*SP[d, h] - SP[a, e]*SP[b, g]*SP[c, f]*SP[d, h] - SP[a, f]*SP[b, e]*SP[c, g]*SP[d, h] + SP[a, e]*SP[b, f]*SP[c, g]*SP[d, h] + +SP[a, h]*SP[b, g]*SP[c, d]*SP[e, f] - SP[a, g]*SP[b, h]*SP[c, d]*SP[e, f] - SP[a, h]*SP[b, d]*SP[c, g]*SP[e, f] + SP[a, d]*SP[b, h]*SP[c, g]*SP[e, f] + +SP[a, g]*SP[b, d]*SP[c, h]*SP[e, f] - SP[a, d]*SP[b, g]*SP[c, h]*SP[e, f] + SP[a, h]*SP[b, c]*SP[d, g]*SP[e, f] - SP[a, c]*SP[b, h]*SP[d, g]*SP[e, f] + +SP[a, b]*SP[c, h]*SP[d, g]*SP[e, f] + SP[b, i]*SP[c, h]*SP[d, g]*SP[e, f] - SP[b, h]*SP[c, i]*SP[d, g]*SP[e, f] - SP[a, g]*SP[b, c]*SP[d, h]*SP[e, f] + +SP[a, c]*SP[b, g]*SP[d, h]*SP[e, f] - SP[a, b]*SP[c, g]*SP[d, h]*SP[e, f] - SP[b, i]*SP[c, g]*SP[d, h]*SP[e, f] + SP[b, g]*SP[c, i]*SP[d, h]*SP[e, f] + +SP[b, h]*SP[c, g]*SP[d, i]*SP[e, f] - SP[b, g]*SP[c, h]*SP[d, i]*SP[e, f] - SP[a, h]*SP[b, f]*SP[c, d]*SP[e, g] + SP[a, f]*SP[b, h]*SP[c, d]*SP[e, g] + +SP[a, h]*SP[b, d]*SP[c, f]*SP[e, g] - SP[a, d]*SP[b, h]*SP[c, f]*SP[e, g] - SP[a, f]*SP[b, d]*SP[c, h]*SP[e, g] + SP[a, d]*SP[b, f]*SP[c, h]*SP[e, g] - +SP[a, h]*SP[b, c]*SP[d, f]*SP[e, g] + SP[a, c]*SP[b, h]*SP[d, f]*SP[e, g] - SP[a, b]*SP[c, h]*SP[d, f]*SP[e, g] - SP[b, i]*SP[c, h]*SP[d, f]*SP[e, g] + +SP[b, h]*SP[c, i]*SP[d, f]*SP[e, g] + SP[a, f]*SP[b, c]*SP[d, h]*SP[e, g] - SP[a, c]*SP[b, f]*SP[d, h]*SP[e, g] + SP[a, b]*SP[c, f]*SP[d, h]*SP[e, g] + +SP[b, i]*SP[c, f]*SP[d, h]*SP[e, g] - SP[b, f]*SP[c, i]*SP[d, h]*SP[e, g] - SP[b, h]*SP[c, f]*SP[d, i]*SP[e, g] + SP[b, f]*SP[c, h]*SP[d, i]*SP[e, g] + +SP[a, g]*SP[b, f]*SP[c, d]*SP[e, h] - SP[a, f]*SP[b, g]*SP[c, d]*SP[e, h] - SP[a, g]*SP[b, d]*SP[c, f]*SP[e, h] + SP[a, d]*SP[b, g]*SP[c, f]*SP[e, h] + +SP[a, f]*SP[b, d]*SP[c, g]*SP[e, h] - SP[a, d]*SP[b, f]*SP[c, g]*SP[e, h] + SP[a, g]*SP[b, c]*SP[d, f]*SP[e, h] - SP[a, c]*SP[b, g]*SP[d, f]*SP[e, h] + +SP[a, b]*SP[c, g]*SP[d, f]*SP[e, h] + SP[b, i]*SP[c, g]*SP[d, f]*SP[e, h] - SP[b, g]*SP[c, i]*SP[d, f]*SP[e, h] - SP[a, f]*SP[b, c]*SP[d, g]*SP[e, h] + +SP[a, c]*SP[b, f]*SP[d, g]*SP[e, h] - SP[a, b]*SP[c, f]*SP[d, g]*SP[e, h] - SP[b, i]*SP[c, f]*SP[d, g]*SP[e, h] + SP[b, f]*SP[c, i]*SP[d, g]*SP[e, h] + +SP[b, g]*SP[c, f]*SP[d, i]*SP[e, h] - SP[b, f]*SP[c, g]*SP[d, i]*SP[e, h] - SP[b, h]*SP[c, g]*SP[d, f]*SP[e, i] + SP[b, g]*SP[c, h]*SP[d, f]*SP[e, i] + +SP[b, h]*SP[c, f]*SP[d, g]*SP[e, i] - SP[b, f]*SP[c, h]*SP[d, g]*SP[e, i] - SP[b, g]*SP[c, f]*SP[d, h]*SP[e, i] + SP[b, f]*SP[c, g]*SP[d, h]*SP[e, i] + +SP[a, h]*SP[b, e]*SP[c, d]*SP[f, g] - SP[a, e]*SP[b, h]*SP[c, d]*SP[f, g] - SP[a, h]*SP[b, d]*SP[c, e]*SP[f, g] + SP[a, d]*SP[b, h]*SP[c, e]*SP[f, g] + +SP[a, e]*SP[b, d]*SP[c, h]*SP[f, g] - SP[a, d]*SP[b, e]*SP[c, h]*SP[f, g] + SP[a, h]*SP[b, c]*SP[d, e]*SP[f, g] - SP[a, c]*SP[b, h]*SP[d, e]*SP[f, g] + +SP[a, b]*SP[c, h]*SP[d, e]*SP[f, g] + SP[b, i]*SP[c, h]*SP[d, e]*SP[f, g] - SP[b, h]*SP[c, i]*SP[d, e]*SP[f, g] - SP[a, e]*SP[b, c]*SP[d, h]*SP[f, g] + +SP[a, c]*SP[b, e]*SP[d, h]*SP[f, g] - SP[a, b]*SP[c, e]*SP[d, h]*SP[f, g] - SP[b, i]*SP[c, e]*SP[d, h]*SP[f, g] + SP[b, e]*SP[c, i]*SP[d, h]*SP[f, g] + +SP[b, h]*SP[c, e]*SP[d, i]*SP[f, g] - SP[b, e]*SP[c, h]*SP[d, i]*SP[f, g] + SP[a, d]*SP[b, c]*SP[e, h]*SP[f, g] - SP[a, c]*SP[b, d]*SP[e, h]*SP[f, g] + +SP[a, b]*SP[c, d]*SP[e, h]*SP[f, g] + SP[b, i]*SP[c, d]*SP[e, h]*SP[f, g] - SP[b, d]*SP[c, i]*SP[e, h]*SP[f, g] + SP[b, c]*SP[d, i]*SP[e, h]*SP[f, g] - +SP[b, h]*SP[c, d]*SP[e, i]*SP[f, g] + SP[b, d]*SP[c, h]*SP[e, i]*SP[f, g] - SP[b, c]*SP[d, h]*SP[e, i]*SP[f, g] - SP[a, g]*SP[b, e]*SP[c, d]*SP[f, h] + +SP[a, e]*SP[b, g]*SP[c, d]*SP[f, h] + SP[a, g]*SP[b, d]*SP[c, e]*SP[f, h] - SP[a, d]*SP[b, g]*SP[c, e]*SP[f, h] - SP[a, e]*SP[b, d]*SP[c, g]*SP[f, h] + +SP[a, d]*SP[b, e]*SP[c, g]*SP[f, h] - SP[a, g]*SP[b, c]*SP[d, e]*SP[f, h] + SP[a, c]*SP[b, g]*SP[d, e]*SP[f, h] - SP[a, b]*SP[c, g]*SP[d, e]*SP[f, h] - +SP[b, i]*SP[c, g]*SP[d, e]*SP[f, h] + SP[b, g]*SP[c, i]*SP[d, e]*SP[f, h] + SP[a, e]*SP[b, c]*SP[d, g]*SP[f, h] - SP[a, c]*SP[b, e]*SP[d, g]*SP[f, h] + +SP[a, b]*SP[c, e]*SP[d, g]*SP[f, h] + SP[b, i]*SP[c, e]*SP[d, g]*SP[f, h] - SP[b, e]*SP[c, i]*SP[d, g]*SP[f, h] - SP[b, g]*SP[c, e]*SP[d, i]*SP[f, h] + +SP[b, e]*SP[c, g]*SP[d, i]*SP[f, h] - SP[a, d]*SP[b, c]*SP[e, g]*SP[f, h] + SP[a, c]*SP[b, d]*SP[e, g]*SP[f, h] - SP[a, b]*SP[c, d]*SP[e, g]*SP[f, h] - +SP[b, i]*SP[c, d]*SP[e, g]*SP[f, h] + SP[b, d]*SP[c, i]*SP[e, g]*SP[f, h] - SP[b, c]*SP[d, i]*SP[e, g]*SP[f, h] + SP[b, g]*SP[c, d]*SP[e, i]*SP[f, h] - +SP[b, d]*SP[c, g]*SP[e, i]*SP[f, h] + SP[b, c]*SP[d, g]*SP[e, i]*SP[f, h] + SP[b, h]*SP[c, g]*SP[d, e]*SP[f, i] - SP[b, g]*SP[c, h]*SP[d, e]*SP[f, i] - +SP[b, h]*SP[c, e]*SP[d, g]*SP[f, i] + SP[b, e]*SP[c, h]*SP[d, g]*SP[f, i] + SP[b, g]*SP[c, e]*SP[d, h]*SP[f, i] - SP[b, e]*SP[c, g]*SP[d, h]*SP[f, i] + +SP[b, h]*SP[c, d]*SP[e, g]*SP[f, i] - SP[b, d]*SP[c, h]*SP[e, g]*SP[f, i] + SP[b, c]*SP[d, h]*SP[e, g]*SP[f, i] - SP[b, g]*SP[c, d]*SP[e, h]*SP[f, i] + +SP[b, d]*SP[c, g]*SP[e, h]*SP[f, i] - SP[b, c]*SP[d, g]*SP[e, h]*SP[f, i] + SP[a, f]*SP[b, e]*SP[c, d]*SP[g, h] - SP[a, e]*SP[b, f]*SP[c, d]*SP[g, h] - +SP[a, f]*SP[b, d]*SP[c, e]*SP[g, h] + SP[a, d]*SP[b, f]*SP[c, e]*SP[g, h] + SP[a, e]*SP[b, d]*SP[c, f]*SP[g, h] - SP[a, d]*SP[b, e]*SP[c, f]*SP[g, h] + +SP[a, f]*SP[b, c]*SP[d, e]*SP[g, h] - SP[a, c]*SP[b, f]*SP[d, e]*SP[g, h] + SP[a, b]*SP[c, f]*SP[d, e]*SP[g, h] + SP[b, i]*SP[c, f]*SP[d, e]*SP[g, h] - +SP[b, f]*SP[c, i]*SP[d, e]*SP[g, h] - SP[a, e]*SP[b, c]*SP[d, f]*SP[g, h] + SP[a, c]*SP[b, e]*SP[d, f]*SP[g, h] - SP[a, b]*SP[c, e]*SP[d, f]*SP[g, h] - +SP[b, i]*SP[c, e]*SP[d, f]*SP[g, h] + SP[b, e]*SP[c, i]*SP[d, f]*SP[g, h] + SP[b, f]*SP[c, e]*SP[d, i]*SP[g, h] - SP[b, e]*SP[c, f]*SP[d, i]*SP[g, h] + +SP[a, d]*SP[b, c]*SP[e, f]*SP[g, h] - SP[a, c]*SP[b, d]*SP[e, f]*SP[g, h] + SP[a, b]*SP[c, d]*SP[e, f]*SP[g, h] + SP[b, i]*SP[c, d]*SP[e, f]*SP[g, h] - +SP[b, d]*SP[c, i]*SP[e, f]*SP[g, h] + SP[b, c]*SP[d, i]*SP[e, f]*SP[g, h] - SP[b, f]*SP[c, d]*SP[e, i]*SP[g, h] + SP[b, d]*SP[c, f]*SP[e, i]*SP[g, h] - +SP[b, c]*SP[d, f]*SP[e, i]*SP[g, h] + SP[b, e]*SP[c, d]*SP[f, i]*SP[g, h] - SP[b, d]*SP[c, e]*SP[f, i]*SP[g, h] + SP[b, c]*SP[d, e]*SP[f, i]*SP[g, h] - +SP[b, h]*SP[c, f]*SP[d, e]*SP[g, i] + SP[b, f]*SP[c, h]*SP[d, e]*SP[g, i] + SP[b, h]*SP[c, e]*SP[d, f]*SP[g, i] - SP[b, e]*SP[c, h]*SP[d, f]*SP[g, i] - +SP[b, f]*SP[c, e]*SP[d, h]*SP[g, i] + SP[b, e]*SP[c, f]*SP[d, h]*SP[g, i] - SP[b, h]*SP[c, d]*SP[e, f]*SP[g, i] + SP[b, d]*SP[c, h]*SP[e, f]*SP[g, i] - +SP[b, c]*SP[d, h]*SP[e, f]*SP[g, i] + SP[b, f]*SP[c, d]*SP[e, h]*SP[g, i] - SP[b, d]*SP[c, f]*SP[e, h]*SP[g, i] + SP[b, c]*SP[d, f]*SP[e, h]*SP[g, i] - +SP[b, e]*SP[c, d]*SP[f, h]*SP[g, i] + SP[b, d]*SP[c, e]*SP[f, h]*SP[g, i] - SP[b, c]*SP[d, e]*SP[f, h]*SP[g, i] + SP[b, g]*SP[c, f]*SP[d, e]*SP[h, i] - +SP[b, f]*SP[c, g]*SP[d, e]*SP[h, i] - SP[b, g]*SP[c, e]*SP[d, f]*SP[h, i] + SP[b, e]*SP[c, g]*SP[d, f]*SP[h, i] + SP[b, f]*SP[c, e]*SP[d, g]*SP[h, i] - +SP[b, e]*SP[c, f]*SP[d, g]*SP[h, i] + SP[b, g]*SP[c, d]*SP[e, f]*SP[h, i] - SP[b, d]*SP[c, g]*SP[e, f]*SP[h, i] + SP[b, c]*SP[d, g]*SP[e, f]*SP[h, i] - +SP[b, f]*SP[c, d]*SP[e, g]*SP[h, i] + SP[b, d]*SP[c, f]*SP[e, g]*SP[h, i] - SP[b, c]*SP[d, f]*SP[e, g]*SP[h, i] + SP[b, e]*SP[c, d]*SP[f, g]*SP[h, i] - +SP[b, d]*SP[c, e]*SP[f, g]*SP[h, i] + SP[b, c]*SP[d, e]*SP[f, g]*SP[h, i])"}, +{"fcstDiracTrace-ID42", +"DiracTrace[GS[a, b, c, d, e, f, g, h + i], DiracTraceEvaluate -> True, FCE -> True]", +"4*(SP[a, h]*SP[b, g]*SP[c, f]*SP[d, e] + SP[a, i]*SP[b, g]*SP[c, f]*SP[d, e] - SP[a, g]*SP[b, h]*SP[c, f]*SP[d, e] - SP[a, g]*SP[b, i]*SP[c, f]*SP[d, e] - +SP[a, h]*SP[b, f]*SP[c, g]*SP[d, e] - SP[a, i]*SP[b, f]*SP[c, g]*SP[d, e] + SP[a, f]*SP[b, h]*SP[c, g]*SP[d, e] + SP[a, f]*SP[b, i]*SP[c, g]*SP[d, e] + +SP[a, g]*SP[b, f]*SP[c, h]*SP[d, e] - SP[a, f]*SP[b, g]*SP[c, h]*SP[d, e] + SP[a, g]*SP[b, f]*SP[c, i]*SP[d, e] - SP[a, f]*SP[b, g]*SP[c, i]*SP[d, e] - +SP[a, h]*SP[b, g]*SP[c, e]*SP[d, f] - SP[a, i]*SP[b, g]*SP[c, e]*SP[d, f] + SP[a, g]*SP[b, h]*SP[c, e]*SP[d, f] + SP[a, g]*SP[b, i]*SP[c, e]*SP[d, f] + +SP[a, h]*SP[b, e]*SP[c, g]*SP[d, f] + SP[a, i]*SP[b, e]*SP[c, g]*SP[d, f] - SP[a, e]*SP[b, h]*SP[c, g]*SP[d, f] - SP[a, e]*SP[b, i]*SP[c, g]*SP[d, f] - +SP[a, g]*SP[b, e]*SP[c, h]*SP[d, f] + SP[a, e]*SP[b, g]*SP[c, h]*SP[d, f] - SP[a, g]*SP[b, e]*SP[c, i]*SP[d, f] + SP[a, e]*SP[b, g]*SP[c, i]*SP[d, f] + +SP[a, h]*SP[b, f]*SP[c, e]*SP[d, g] + SP[a, i]*SP[b, f]*SP[c, e]*SP[d, g] - SP[a, f]*SP[b, h]*SP[c, e]*SP[d, g] - SP[a, f]*SP[b, i]*SP[c, e]*SP[d, g] - +SP[a, h]*SP[b, e]*SP[c, f]*SP[d, g] - SP[a, i]*SP[b, e]*SP[c, f]*SP[d, g] + SP[a, e]*SP[b, h]*SP[c, f]*SP[d, g] + SP[a, e]*SP[b, i]*SP[c, f]*SP[d, g] + +SP[a, f]*SP[b, e]*SP[c, h]*SP[d, g] - SP[a, e]*SP[b, f]*SP[c, h]*SP[d, g] + SP[a, f]*SP[b, e]*SP[c, i]*SP[d, g] - SP[a, e]*SP[b, f]*SP[c, i]*SP[d, g] - +SP[a, g]*SP[b, f]*SP[c, e]*SP[d, h] + SP[a, f]*SP[b, g]*SP[c, e]*SP[d, h] + SP[a, g]*SP[b, e]*SP[c, f]*SP[d, h] - SP[a, e]*SP[b, g]*SP[c, f]*SP[d, h] - +SP[a, f]*SP[b, e]*SP[c, g]*SP[d, h] + SP[a, e]*SP[b, f]*SP[c, g]*SP[d, h] - SP[a, g]*SP[b, f]*SP[c, e]*SP[d, i] + SP[a, f]*SP[b, g]*SP[c, e]*SP[d, i] + +SP[a, g]*SP[b, e]*SP[c, f]*SP[d, i] - SP[a, e]*SP[b, g]*SP[c, f]*SP[d, i] - SP[a, f]*SP[b, e]*SP[c, g]*SP[d, i] + SP[a, e]*SP[b, f]*SP[c, g]*SP[d, i] + +SP[a, h]*SP[b, g]*SP[c, d]*SP[e, f] + SP[a, i]*SP[b, g]*SP[c, d]*SP[e, f] - SP[a, g]*SP[b, h]*SP[c, d]*SP[e, f] - SP[a, g]*SP[b, i]*SP[c, d]*SP[e, f] - +SP[a, h]*SP[b, d]*SP[c, g]*SP[e, f] - SP[a, i]*SP[b, d]*SP[c, g]*SP[e, f] + SP[a, d]*SP[b, h]*SP[c, g]*SP[e, f] + SP[a, d]*SP[b, i]*SP[c, g]*SP[e, f] + +SP[a, g]*SP[b, d]*SP[c, h]*SP[e, f] - SP[a, d]*SP[b, g]*SP[c, h]*SP[e, f] + SP[a, g]*SP[b, d]*SP[c, i]*SP[e, f] - SP[a, d]*SP[b, g]*SP[c, i]*SP[e, f] + +SP[a, h]*SP[b, c]*SP[d, g]*SP[e, f] + SP[a, i]*SP[b, c]*SP[d, g]*SP[e, f] - SP[a, c]*SP[b, h]*SP[d, g]*SP[e, f] - SP[a, c]*SP[b, i]*SP[d, g]*SP[e, f] + +SP[a, b]*SP[c, h]*SP[d, g]*SP[e, f] + SP[a, b]*SP[c, i]*SP[d, g]*SP[e, f] - SP[a, g]*SP[b, c]*SP[d, h]*SP[e, f] + SP[a, c]*SP[b, g]*SP[d, h]*SP[e, f] - +SP[a, b]*SP[c, g]*SP[d, h]*SP[e, f] - SP[a, g]*SP[b, c]*SP[d, i]*SP[e, f] + SP[a, c]*SP[b, g]*SP[d, i]*SP[e, f] - SP[a, b]*SP[c, g]*SP[d, i]*SP[e, f] - +SP[a, h]*SP[b, f]*SP[c, d]*SP[e, g] - SP[a, i]*SP[b, f]*SP[c, d]*SP[e, g] + SP[a, f]*SP[b, h]*SP[c, d]*SP[e, g] + SP[a, f]*SP[b, i]*SP[c, d]*SP[e, g] + +SP[a, h]*SP[b, d]*SP[c, f]*SP[e, g] + SP[a, i]*SP[b, d]*SP[c, f]*SP[e, g] - SP[a, d]*SP[b, h]*SP[c, f]*SP[e, g] - SP[a, d]*SP[b, i]*SP[c, f]*SP[e, g] - +SP[a, f]*SP[b, d]*SP[c, h]*SP[e, g] + SP[a, d]*SP[b, f]*SP[c, h]*SP[e, g] - SP[a, f]*SP[b, d]*SP[c, i]*SP[e, g] + SP[a, d]*SP[b, f]*SP[c, i]*SP[e, g] - +SP[a, h]*SP[b, c]*SP[d, f]*SP[e, g] - SP[a, i]*SP[b, c]*SP[d, f]*SP[e, g] + SP[a, c]*SP[b, h]*SP[d, f]*SP[e, g] + SP[a, c]*SP[b, i]*SP[d, f]*SP[e, g] - +SP[a, b]*SP[c, h]*SP[d, f]*SP[e, g] - SP[a, b]*SP[c, i]*SP[d, f]*SP[e, g] + SP[a, f]*SP[b, c]*SP[d, h]*SP[e, g] - SP[a, c]*SP[b, f]*SP[d, h]*SP[e, g] + +SP[a, b]*SP[c, f]*SP[d, h]*SP[e, g] + SP[a, f]*SP[b, c]*SP[d, i]*SP[e, g] - SP[a, c]*SP[b, f]*SP[d, i]*SP[e, g] + SP[a, b]*SP[c, f]*SP[d, i]*SP[e, g] + +SP[a, g]*SP[b, f]*SP[c, d]*SP[e, h] - SP[a, f]*SP[b, g]*SP[c, d]*SP[e, h] - SP[a, g]*SP[b, d]*SP[c, f]*SP[e, h] + SP[a, d]*SP[b, g]*SP[c, f]*SP[e, h] + +SP[a, f]*SP[b, d]*SP[c, g]*SP[e, h] - SP[a, d]*SP[b, f]*SP[c, g]*SP[e, h] + SP[a, g]*SP[b, c]*SP[d, f]*SP[e, h] - SP[a, c]*SP[b, g]*SP[d, f]*SP[e, h] + +SP[a, b]*SP[c, g]*SP[d, f]*SP[e, h] - SP[a, f]*SP[b, c]*SP[d, g]*SP[e, h] + SP[a, c]*SP[b, f]*SP[d, g]*SP[e, h] - SP[a, b]*SP[c, f]*SP[d, g]*SP[e, h] + +SP[a, g]*SP[b, f]*SP[c, d]*SP[e, i] - SP[a, f]*SP[b, g]*SP[c, d]*SP[e, i] - SP[a, g]*SP[b, d]*SP[c, f]*SP[e, i] + SP[a, d]*SP[b, g]*SP[c, f]*SP[e, i] + +SP[a, f]*SP[b, d]*SP[c, g]*SP[e, i] - SP[a, d]*SP[b, f]*SP[c, g]*SP[e, i] + SP[a, g]*SP[b, c]*SP[d, f]*SP[e, i] - SP[a, c]*SP[b, g]*SP[d, f]*SP[e, i] + +SP[a, b]*SP[c, g]*SP[d, f]*SP[e, i] - SP[a, f]*SP[b, c]*SP[d, g]*SP[e, i] + SP[a, c]*SP[b, f]*SP[d, g]*SP[e, i] - SP[a, b]*SP[c, f]*SP[d, g]*SP[e, i] + +SP[a, h]*SP[b, e]*SP[c, d]*SP[f, g] + SP[a, i]*SP[b, e]*SP[c, d]*SP[f, g] - SP[a, e]*SP[b, h]*SP[c, d]*SP[f, g] - SP[a, e]*SP[b, i]*SP[c, d]*SP[f, g] - +SP[a, h]*SP[b, d]*SP[c, e]*SP[f, g] - SP[a, i]*SP[b, d]*SP[c, e]*SP[f, g] + SP[a, d]*SP[b, h]*SP[c, e]*SP[f, g] + SP[a, d]*SP[b, i]*SP[c, e]*SP[f, g] + +SP[a, e]*SP[b, d]*SP[c, h]*SP[f, g] - SP[a, d]*SP[b, e]*SP[c, h]*SP[f, g] + SP[a, e]*SP[b, d]*SP[c, i]*SP[f, g] - SP[a, d]*SP[b, e]*SP[c, i]*SP[f, g] + +SP[a, h]*SP[b, c]*SP[d, e]*SP[f, g] + SP[a, i]*SP[b, c]*SP[d, e]*SP[f, g] - SP[a, c]*SP[b, h]*SP[d, e]*SP[f, g] - SP[a, c]*SP[b, i]*SP[d, e]*SP[f, g] + +SP[a, b]*SP[c, h]*SP[d, e]*SP[f, g] + SP[a, b]*SP[c, i]*SP[d, e]*SP[f, g] - SP[a, e]*SP[b, c]*SP[d, h]*SP[f, g] + SP[a, c]*SP[b, e]*SP[d, h]*SP[f, g] - +SP[a, b]*SP[c, e]*SP[d, h]*SP[f, g] - SP[a, e]*SP[b, c]*SP[d, i]*SP[f, g] + SP[a, c]*SP[b, e]*SP[d, i]*SP[f, g] - SP[a, b]*SP[c, e]*SP[d, i]*SP[f, g] + +SP[a, d]*SP[b, c]*SP[e, h]*SP[f, g] - SP[a, c]*SP[b, d]*SP[e, h]*SP[f, g] + SP[a, b]*SP[c, d]*SP[e, h]*SP[f, g] + SP[a, d]*SP[b, c]*SP[e, i]*SP[f, g] - +SP[a, c]*SP[b, d]*SP[e, i]*SP[f, g] + SP[a, b]*SP[c, d]*SP[e, i]*SP[f, g] - SP[a, g]*SP[b, e]*SP[c, d]*SP[f, h] + SP[a, e]*SP[b, g]*SP[c, d]*SP[f, h] + +SP[a, g]*SP[b, d]*SP[c, e]*SP[f, h] - SP[a, d]*SP[b, g]*SP[c, e]*SP[f, h] - SP[a, e]*SP[b, d]*SP[c, g]*SP[f, h] + SP[a, d]*SP[b, e]*SP[c, g]*SP[f, h] - +SP[a, g]*SP[b, c]*SP[d, e]*SP[f, h] + SP[a, c]*SP[b, g]*SP[d, e]*SP[f, h] - SP[a, b]*SP[c, g]*SP[d, e]*SP[f, h] + SP[a, e]*SP[b, c]*SP[d, g]*SP[f, h] - +SP[a, c]*SP[b, e]*SP[d, g]*SP[f, h] + SP[a, b]*SP[c, e]*SP[d, g]*SP[f, h] - SP[a, d]*SP[b, c]*SP[e, g]*SP[f, h] + SP[a, c]*SP[b, d]*SP[e, g]*SP[f, h] - +SP[a, b]*SP[c, d]*SP[e, g]*SP[f, h] - SP[a, g]*SP[b, e]*SP[c, d]*SP[f, i] + SP[a, e]*SP[b, g]*SP[c, d]*SP[f, i] + SP[a, g]*SP[b, d]*SP[c, e]*SP[f, i] - +SP[a, d]*SP[b, g]*SP[c, e]*SP[f, i] - SP[a, e]*SP[b, d]*SP[c, g]*SP[f, i] + SP[a, d]*SP[b, e]*SP[c, g]*SP[f, i] - SP[a, g]*SP[b, c]*SP[d, e]*SP[f, i] + +SP[a, c]*SP[b, g]*SP[d, e]*SP[f, i] - SP[a, b]*SP[c, g]*SP[d, e]*SP[f, i] + SP[a, e]*SP[b, c]*SP[d, g]*SP[f, i] - SP[a, c]*SP[b, e]*SP[d, g]*SP[f, i] + +SP[a, b]*SP[c, e]*SP[d, g]*SP[f, i] - SP[a, d]*SP[b, c]*SP[e, g]*SP[f, i] + SP[a, c]*SP[b, d]*SP[e, g]*SP[f, i] - SP[a, b]*SP[c, d]*SP[e, g]*SP[f, i] + +SP[a, f]*SP[b, e]*SP[c, d]*SP[g, h] - SP[a, e]*SP[b, f]*SP[c, d]*SP[g, h] - SP[a, f]*SP[b, d]*SP[c, e]*SP[g, h] + SP[a, d]*SP[b, f]*SP[c, e]*SP[g, h] + +SP[a, e]*SP[b, d]*SP[c, f]*SP[g, h] - SP[a, d]*SP[b, e]*SP[c, f]*SP[g, h] + SP[a, f]*SP[b, c]*SP[d, e]*SP[g, h] - SP[a, c]*SP[b, f]*SP[d, e]*SP[g, h] + +SP[a, b]*SP[c, f]*SP[d, e]*SP[g, h] - SP[a, e]*SP[b, c]*SP[d, f]*SP[g, h] + SP[a, c]*SP[b, e]*SP[d, f]*SP[g, h] - SP[a, b]*SP[c, e]*SP[d, f]*SP[g, h] + +SP[a, d]*SP[b, c]*SP[e, f]*SP[g, h] - SP[a, c]*SP[b, d]*SP[e, f]*SP[g, h] + SP[a, b]*SP[c, d]*SP[e, f]*SP[g, h] + SP[a, f]*SP[b, e]*SP[c, d]*SP[g, i] - +SP[a, e]*SP[b, f]*SP[c, d]*SP[g, i] - SP[a, f]*SP[b, d]*SP[c, e]*SP[g, i] + SP[a, d]*SP[b, f]*SP[c, e]*SP[g, i] + SP[a, e]*SP[b, d]*SP[c, f]*SP[g, i] - +SP[a, d]*SP[b, e]*SP[c, f]*SP[g, i] + SP[a, f]*SP[b, c]*SP[d, e]*SP[g, i] - SP[a, c]*SP[b, f]*SP[d, e]*SP[g, i] + SP[a, b]*SP[c, f]*SP[d, e]*SP[g, i] - +SP[a, e]*SP[b, c]*SP[d, f]*SP[g, i] + SP[a, c]*SP[b, e]*SP[d, f]*SP[g, i] - SP[a, b]*SP[c, e]*SP[d, f]*SP[g, i] + SP[a, d]*SP[b, c]*SP[e, f]*SP[g, i] - +SP[a, c]*SP[b, d]*SP[e, f]*SP[g, i] + SP[a, b]*SP[c, d]*SP[e, f]*SP[g, i])"}, +{"fcstDiracTrace-ID43", +"DiracTrace[GS[p, k, d, c].GA[5].GS[t, z], DiracTraceEvaluate -> True, FCE -> True]", +"(4*I)*(-(SP[t, z]*LC[][c, d, k, p]) + SP[k, p]*LC[][c, d, t, z] - SP[d, p]*LC[][c, k, t, z] + SP[d, k]*LC[][c, p, t, z] - +SP[c, z]*LC[][d, k, p, t] + SP[c, t]*LC[][d, k, p, z])"}, +{"fcstDiracTrace-ID44", +"DiracTrace[GA[5].GS[t, z].GS[p, k, d, c], DiracTraceEvaluate -> True, FCE -> True]", +"(4*I)*(-(SP[t, z]*LC[][c, d, k, p]) + SP[k, p]*LC[][c, d, t, z] - SP[d, p]*LC[][c, k, t, z] + SP[d, k]*LC[][c, p, t, z] - +SP[c, z]*LC[][d, k, p, t] + SP[c, t]*LC[][d, k, p, z])"}, +{"fcstDiracTrace-ID45", +"DiracTrace[(GS[p2] + m).(GS[a, pp] - GS[pp, a]).(GS[p1] + m),DiracTraceEvaluate -> True, FCE -> True]", +"8 (SP[a, p2] SP[p1, pp] - SP[a, p1] SP[p2, pp])"}, +{"fcstDiracTrace-ID46", +"FCSetDiracGammaScheme[\"BMHV\"]; +tmp = (DiracTrace[GAD[i1, i2, i3].GA[6].GAD[i5, i6, i7].GA[6], + DiracTraceEvaluate -> True] - +DiracTrace[GAD[i1, i2, i3].((1 + GA[5])/2).GAD[i5, i6, i7].((1 + GA[5])/2), + DiracTraceEvaluate -> True]); FCSetDiracGammaScheme[\"NDR\"];\n tmp","0"}, +{"fcstDiracTrace-ID46", +"FCSetDiracGammaScheme[\"NDR-Drop\"]; +tmp = (DiracTrace[GAD[i1, i2, i3,5,i5, i6, i7], + DiracTraceEvaluate -> True]); FCSetDiracGammaScheme[\"NDR\"];\n tmp","0"}, +{"fcstDiracTrace-ID47", "DiracTrace[DOT[1, 0], DiracTraceEvaluate -> True]","0"}, +{"fcstDiracTrace-ID48", "DiracTrace[DOT[1, 1], DiracTraceEvaluate -> True]","4"}, +{"fcstDiracTrace-ID49", "DiracTrace[DOT[a, b], DiracTraceEvaluate -> True]","4 a b"}, +{"fcstDiracTrace-ID50", "DiracTrace[DOT[3,1,2,1], DiracTraceEvaluate -> True]","24"}, +{"fcstDiracTrace-ID51", "DiracTrace[DOT[1, 1], DiracTraceEvaluate -> True, +FCDiracIsolate -> False]", "4"}, +{"fcstDiracTrace-ID52", "DiracTrace[GA[mu, nu], DiracTraceEvaluate -> True, +FCDiracIsolate -> False]", "4 Pair[LorentzIndex[mu], LorentzIndex[nu]]"}, +{"fcstDiracTrace-ID53", "DiracTrace[DiracSigma[GA[mu], GA[nu]].GA[rho, si], +DiracTraceEvaluate -> True, FCDiracIsolate -> False]", "4 I (Pair[LorentzIndex[mu], LorentzIndex[si]] Pair[LorentzIndex[nu], + LorentzIndex[rho]] - Pair[LorentzIndex[mu], LorentzIndex[rho]] Pair[LorentzIndex[nu], + LorentzIndex[si]])"} +}); diff --git a/Tests/Dirac/DiracTrick.test b/Tests/Dirac/DiracTrick.test index fac1c42b2..13dc8ca1c 100644 --- a/Tests/Dirac/DiracTrick.test +++ b/Tests/Dirac/DiracTrick.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DiracTrick *) @@ -59,17 +59,17 @@ m3].GA[j].Spinor[p4,m4]]//FCE", "DiracTrick[GA[7].GA[mu]]//FCE", "GA[mu] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID17", "DiracTrick[GA[7].GAD[mu]]//FCE", "GAD[mu] . GA[6]"}, -{"fcstDiracTrickCoreProperties-ID18", "$BreitMaison=True; +{"fcstDiracTrickCoreProperties-ID18", "FCSetDiracGammaScheme[\"BMHV\"]; \n DiracTrick[GA[6].GA[mu]]//FCE", "GA[mu] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID19", "DiracTrick[GA[6].GAD[mu]]//FCE", -"GAD[mu] . GA[7] + GAE[mu] . GA[5]"}, +"GA[mu] . GA[7] + GAE[mu] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID20", "DiracTrick[GA[7].GA[mu]]//FCE", "GA[mu] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID21", "DiracTrick[GA[7].GAD[mu]]//FCE", -"GAD[mu] . GA[6] - GAE[mu] . GA[5]"}, -{"fcstDiracTrickCoreProperties-ID22", "$BreitMaison=False; +"GA[mu] . GA[6] + GAE[mu] . GA[7]"}, +{"fcstDiracTrickCoreProperties-ID22", "FCSetDiracGammaScheme[\"NDR\"]; \n DiracTrick[GA[5].GA[i, j, k]]//FCE", "-GA[i] . GA[j] . GA[k] . GA[5]"}, {"fcstDiracTrickCoreProperties-ID23", @@ -81,7 +81,7 @@ DiracTrick[GA[5].GA[i, j, k]]//FCE", {"fcstDiracTrickCoreProperties-ID25", "DiracTrick[GA[5].GAD[i, j, k,l]]//FCE", "GAD[i] . GAD[j] . GAD[k] . GAD[l] . GA[5]"}, -{"fcstDiracTrickCoreProperties-ID26", "$BreitMaison=True; +{"fcstDiracTrickCoreProperties-ID26", "FCSetDiracGammaScheme[\"BMHV\"]; \n DiracTrick[GA[5].GA[i]]//FCE", "-GA[i] . GA[5]"}, {"fcstDiracTrickCoreProperties-ID27", "DiracTrick[GA[5].GAD[i]]//FCE", @@ -113,8 +113,7 @@ GAE[k] . GAE[l] . GA[5]) + 2*(GAE[i] . GAE[j] . GAD[k] . GAD[l] . \ GA[5] - 2*GAE[i] . GAE[j] . GAD[k] . GAE[l] . GA[5] + 2*(-GAE[i] . \ GAE[j] . GAE[k] . GAD[l] . GA[5] + 2*GAE[i] . GAE[j] . GAE[k] . \ GAE[l] . GA[5])))"}, -{"fcstDiracTrickCoreProperties-ID32", "$BreitMaison=False; - $Larin=False; +{"fcstDiracTrickCoreProperties-ID32", "FCSetDiracGammaScheme[\"NDR\"]; \n DiracTrick[GA[7].(GA[mu] + 2 m).GA[nu, rho, si, 6]]//FCE", "2*m*GA[nu] . GA[rho] . GA[si] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID33", @@ -183,265 +182,175 @@ DiracTrick[GA[7].(GA[mu] + 2 m).GA[nu, rho, si, 6]]//FCE", {"fcstDiracTrickCoreProperties-ID56", "DiracTrick[GA[7].(GAD[mu] + 2 m).GAD[nu, rho, si].GA[7]]//FCE", "GAD[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[7]"}, -{"fcstDiracTrickCoreProperties-ID57", "$BreitMaison=True; +{"fcstDiracTrickCoreProperties-ID57", "FCSetDiracGammaScheme[\"BMHV\"]; \n DiracTrick[GA[7].(GA[mu] + 2 m).GA[nu, rho, si, 6]]//FCE", "2*m*GA[nu] . GA[rho] . GA[si] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID58", "DiracTrick[GA[7].(GAD[mu] + 2 m).GAD[nu, rho, si].GA[6]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GAD[si] . GA[6] - GAD[nu] . GAD[rho] . \ -GAE[si] . GA[6] - GAD[nu] . GAE[rho] . GAD[si] . GA[6] + 2*GAD[nu] . \ -GAE[rho] . GAE[si] . GA[6] - GAE[nu] . GAD[rho] . GAD[si] . GA[6] + \ -2*GAE[nu] . GAD[rho] . GAE[si] . GA[6] - 2*(-GAE[nu] . GAE[rho] . \ -GAD[si] . GA[6] + 2*GAE[nu] . GAE[rho] . GAE[si] . GA[6])) + GAD[mu] \ -. GAD[nu] . GAD[rho] . GAE[si] . GA[6] + GAD[mu] . GAD[nu] . GAE[rho] \ -. GAD[si] . GA[6] - 2*GAD[mu] . GAD[nu] . GAE[rho] . GAE[si] . GA[6] \ -+ GAD[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[6] - 2*GAD[mu] . \ -GAE[nu] . GAD[rho] . GAE[si] . GA[6] + 2*(-GAD[mu] . GAE[nu] . \ -GAE[rho] . GAD[si] . GA[6] + 2*GAD[mu] . GAE[nu] . GAE[rho] . GAE[si] \ -. GA[6]) + GAE[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[6] - 2*GAE[mu] \ -. GAD[nu] . GAD[rho] . GAE[si] . GA[6] + 2*(-GAE[mu] . GAD[nu] . \ -GAE[rho] . GAD[si] . GA[6] + 2*GAE[mu] . GAD[nu] . GAE[rho] . GAE[si] \ -. GA[6]) - 2*(GAE[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[6] - \ -2*GAE[mu] . GAE[nu] . GAD[rho] . GAE[si] . GA[6] + 2*(-GAE[mu] . \ -GAE[nu] . GAE[rho] . GAD[si] . GA[6] + 2*GAE[mu] . GAE[nu] . GAE[rho] \ -. GAE[si] . GA[6]))"}, +"GA[mu] . GA[nu] . GA[rho] . GAE[si] . GA[6] + GA[mu] . GA[nu] . GAE[rho] . GA[si] . GA[6] + +GA[mu] . GAE[nu] . GA[rho] . GA[si] . GA[6] + GA[mu] . GAE[nu] . GAE[rho] . GAE[si] . GA[6] + +(2*m + GAE[mu]) . GA[nu] . GA[rho] . GA[si] . GA[6] + (2*m + +GAE[mu]) . GA[nu] . GAE[rho] . GAE[si] . GA[6] + (2*m + +GAE[mu]) . GAE[nu] . GA[rho] . GAE[si] . GA[6] + (2*m + +GAE[mu]) . GAE[nu] . GAE[rho] . GA[si] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID59", "DiracTrick[GA[7].(GA[mu] + 2 m).GAD[nu, rho, si].GA[6]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GAD[si] . GA[6] - GAD[nu] . GAD[rho] . \ -GAE[si] . GA[6] - GAD[nu] . GAE[rho] . GAD[si] . GA[6] + 2*GAD[nu] . \ -GAE[rho] . GAE[si] . GA[6] - GAE[nu] . GAD[rho] . GAD[si] . GA[6] + \ -2*GAE[nu] . GAD[rho] . GAE[si] . GA[6] - 2*(-GAE[nu] . GAE[rho] . \ -GAD[si] . GA[6] + 2*GAE[nu] . GAE[rho] . GAE[si] . GA[6])) + GA[mu] . \ -GAD[nu] . GAD[rho] . GAE[si] . GA[6] + GA[mu] . GAD[nu] . GAE[rho] . \ -GAD[si] . GA[6] - 2*GA[mu] . GAD[nu] . GAE[rho] . GAE[si] . GA[6] + \ -GA[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[6] - 2*GA[mu] . GAE[nu] . \ -GAD[rho] . GAE[si] . GA[6] + 2*(-GA[mu] . GAE[nu] . GAE[rho] . \ -GAD[si] . GA[6] + 2*GA[mu] . GAE[nu] . GAE[rho] . GAE[si] . GA[6])"}, +"2*m*(GA[nu] . GA[rho] . GA[si] . GA[6] + GA[nu] . GAE[rho] . GAE[si] . GA[6] + +GAE[nu] . GA[rho] . GAE[si] . GA[6] + GAE[nu] . GAE[rho] . GA[si] . GA[6]) + +GA[mu] . GA[nu] . GA[rho] . GAE[si] . GA[6] + GA[mu] . GA[nu] . GAE[rho] . GA[si] . GA[6] + +GA[mu] . GAE[nu] . GA[rho] . GA[si] . GA[6] + GA[mu] . GAE[nu] . GAE[rho] . GAE[si] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID60", "DiracTrick[GA[7].(GAD[mu] + 2 m).GA[nu, rho, si, 6]]//FCE", -"2*m*GA[nu] . GA[rho] . GA[si] . GA[6] + GAE[mu] . GA[nu] . \ -GA[rho] . GA[si] . GA[6]"}, +"(2*m + GAE[mu]) . GA[nu] . GA[rho] . GA[si] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID61", "DiracTrick[GA[6].(GA[mu] + 2 m).GA[nu, rho, si, 7]]//FCE", "2*m*GA[nu] . GA[rho] . GA[si] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID62", "DiracTrick[GA[6].(GAD[mu] + 2 m).GAD[nu, rho, si].GA[7]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GAD[si] . GA[7] - GAD[nu] . GAD[rho] . \ -GAE[si] . GA[7] - GAD[nu] . GAE[rho] . GAD[si] . GA[7] + 2*GAD[nu] . \ -GAE[rho] . GAE[si] . GA[7] - GAE[nu] . GAD[rho] . GAD[si] . GA[7] + \ -2*GAE[nu] . GAD[rho] . GAE[si] . GA[7] + 2*(GAE[nu] . GAE[rho] . \ -GAD[si] . GA[7] - 2*GAE[nu] . GAE[rho] . GAE[si] . GA[7])) + GAD[mu] \ -. GAD[nu] . GAD[rho] . GAE[si] . GA[7] + GAD[mu] . GAD[nu] . GAE[rho] \ -. GAD[si] . GA[7] - 2*GAD[mu] . GAD[nu] . GAE[rho] . GAE[si] . GA[7] \ -+ GAD[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[7] - 2*GAD[mu] . \ -GAE[nu] . GAD[rho] . GAE[si] . GA[7] - 2*(GAD[mu] . GAE[nu] . \ -GAE[rho] . GAD[si] . GA[7] - 2*GAD[mu] . GAE[nu] . GAE[rho] . GAE[si] \ -. GA[7]) + GAE[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[7] - 2*GAE[mu] \ -. GAD[nu] . GAD[rho] . GAE[si] . GA[7] - 2*(GAE[mu] . GAD[nu] . \ -GAE[rho] . GAD[si] . GA[7] - 2*GAE[mu] . GAD[nu] . GAE[rho] . GAE[si] \ -. GA[7]) + 2*(-GAE[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[7] + \ -2*GAE[mu] . GAE[nu] . GAD[rho] . GAE[si] . GA[7] + 2*(GAE[mu] . \ -GAE[nu] . GAE[rho] . GAD[si] . GA[7] - 2*GAE[mu] . GAE[nu] . GAE[rho] \ -. GAE[si] . GA[7]))"}, +"GA[mu].GA[nu].GA[rho].GAE[si].GA[7] + +GA[mu].GA[nu].GAE[rho].GA[si].GA[7] + +GA[mu].GAE[nu].GA[rho].GA[si].GA[7] + +GA[mu].GAE[nu].GAE[rho].GAE[si].GA[7] + (2*m + GAE[mu]).GA[nu].GA[ +rho].GA[si].GA[7] + (2*m + GAE[mu]).GA[nu].GAE[rho].GAE[si].GA[ +7] + (2*m + GAE[mu]).GAE[nu].GA[rho].GAE[si].GA[ +7] + (2*m + GAE[mu]).GAE[nu].GAE[rho].GA[si].GA[7]"}, {"fcstDiracTrickCoreProperties-ID63", "DiracTrick[GA[6].(GA[mu] + 2 m).GAD[nu, rho, si].GA[7]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GAD[si] . GA[7] - GAD[nu] . GAD[rho] . \ -GAE[si] . GA[7] - GAD[nu] . GAE[rho] . GAD[si] . GA[7] + 2*GAD[nu] . \ -GAE[rho] . GAE[si] . GA[7] - GAE[nu] . GAD[rho] . GAD[si] . GA[7] + \ -2*GAE[nu] . GAD[rho] . GAE[si] . GA[7] + 2*(GAE[nu] . GAE[rho] . \ -GAD[si] . GA[7] - 2*GAE[nu] . GAE[rho] . GAE[si] . GA[7])) + GA[mu] . \ -GAD[nu] . GAD[rho] . GAE[si] . GA[7] + GA[mu] . GAD[nu] . GAE[rho] . \ -GAD[si] . GA[7] - 2*GA[mu] . GAD[nu] . GAE[rho] . GAE[si] . GA[7] + \ -GA[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[7] - 2*GA[mu] . GAE[nu] . \ -GAD[rho] . GAE[si] . GA[7] - 2*(GA[mu] . GAE[nu] . GAE[rho] . GAD[si] \ -. GA[7] - 2*GA[mu] . GAE[nu] . GAE[rho] . GAE[si] . GA[7])"}, +"2*m*(GA[nu].GA[rho].GA[si].GA[7] + GA[nu].GAE[rho].GAE[si].GA[7] + + GAE[nu].GA[rho].GAE[si].GA[7] + GAE[nu].GAE[rho].GA[si].GA[7]) + +GA[mu].GA[nu].GA[rho].GAE[si].GA[7] + +GA[mu].GA[nu].GAE[rho].GA[si].GA[7] + +GA[mu].GAE[nu].GA[rho].GA[si].GA[7] + +GA[mu].GAE[nu].GAE[rho].GAE[si].GA[7]"}, {"fcstDiracTrickCoreProperties-ID64", "DiracTrick[GA[6].(GAD[mu] + 2 m).GA[nu, rho, si, 7]]//FCE", -"2*m*GA[nu] . GA[rho] . GA[si] . GA[7] + GAE[mu] . GA[nu] . \ -GA[rho] . GA[si] . GA[7]"}, +"(2*m + GAE[mu]).GA[nu].GA[rho].GA[si].GA[7]"}, {"fcstDiracTrickCoreProperties-ID65", "DiracTrick[GA[6].(GA[mu] + 2 m).GA[nu, rho, 6]]//FCE", "2*m*GA[nu] . GA[rho] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID66", "DiracTrick[GA[6].(GAD[mu] + 2 m).GAD[nu, rho].GA[6]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GA[6] - GAD[nu] . GAE[rho] . GA[6] - \ -GAE[nu] . GAD[rho] . GA[6] + 2*GAE[nu] . GAE[rho] . GA[6]) + GAD[mu] \ -. GAD[nu] . GAE[rho] . GA[6] + GAD[mu] . GAE[nu] . GAD[rho] . GA[6] - \ -2*GAD[mu] . GAE[nu] . GAE[rho] . GA[6] + GAE[mu] . GAD[nu] . GAD[rho] \ -. GA[6] - 2*GAE[mu] . GAD[nu] . GAE[rho] . GA[6] + 2*(-GAE[mu] . \ -GAE[nu] . GAD[rho] . GA[6] + 2*GAE[mu] . GAE[nu] . GAE[rho] . GA[6])"}, +"GA[mu].GA[nu].GAE[rho].GA[6] + +GA[mu].GAE[nu].GA[rho].GA[6] + (2*m + GAE[mu]).GA[nu].GA[rho].GA[ +6] + (2*m + GAE[mu]).GAE[nu].GAE[rho].GA[6]"}, {"fcstDiracTrickCoreProperties-ID67", "DiracTrick[GA[6].(GA[mu] + 2 m).GAD[nu, rho].GA[6]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GA[6] - GAD[nu] . GAE[rho] . GA[6] - \ -GAE[nu] . GAD[rho] . GA[6] + 2*GAE[nu] . GAE[rho] . GA[6]) + GA[mu] . \ -GAD[nu] . GAE[rho] . GA[6] + GA[mu] . GAE[nu] . GAD[rho] . GA[6] - \ -2*GA[mu] . GAE[nu] . GAE[rho] . GA[6]"}, +"2*m*(GA[nu].GA[rho].GA[6] + GAE[nu].GAE[rho].GA[6]) + +GA[mu].GA[nu].GAE[rho].GA[6] + GA[mu].GAE[nu].GA[rho].GA[6]"}, {"fcstDiracTrickCoreProperties-ID68", "DiracTrick[GA[6].(GAD[mu] + 2 m).GA[nu, rho, 6]]//FCE", -"2*m*GA[nu] . GA[rho] . GA[6] + GAE[mu] . GA[nu] . GA[rho] . \ -GA[6]"}, +"(2*m + GAE[mu]).GA[nu].GA[rho].GA[6]"}, {"fcstDiracTrickCoreProperties-ID69", "DiracTrick[GA[7].(GA[mu] + 2 m).GA[nu, rho, 7]]//FCE", "2*m*GA[nu] . GA[rho] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID70", "DiracTrick[GA[7].(GAD[mu] + 2 m).GAD[nu, rho].GA[7]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GA[7] - GAD[nu] . GAE[rho] . GA[7] - \ -GAE[nu] . GAD[rho] . GA[7] + 2*GAE[nu] . GAE[rho] . GA[7]) + GAD[mu] \ -. GAD[nu] . GAE[rho] . GA[7] + GAD[mu] . GAE[nu] . GAD[rho] . GA[7] - \ -2*GAD[mu] . GAE[nu] . GAE[rho] . GA[7] + GAE[mu] . GAD[nu] . GAD[rho] \ -. GA[7] - 2*GAE[mu] . GAD[nu] . GAE[rho] . GA[7] - 2*(GAE[mu] . \ -GAE[nu] . GAD[rho] . GA[7] - 2*GAE[mu] . GAE[nu] . GAE[rho] . GA[7])"}, +"GA[mu].GA[nu].GAE[rho].GA[7] + +GA[mu].GAE[nu].GA[rho].GA[7] + (2*m + GAE[mu]).GA[nu].GA[rho].GA[ +7] + (2*m + GAE[mu]).GAE[nu].GAE[rho].GA[7]"}, {"fcstDiracTrickCoreProperties-ID71", "DiracTrick[GA[7].(GA[mu] + 2 m).GAD[nu, rho].GA[7]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GA[7] - GAD[nu] . GAE[rho] . GA[7] - \ -GAE[nu] . GAD[rho] . GA[7] + 2*GAE[nu] . GAE[rho] . GA[7]) + GA[mu] . \ -GAD[nu] . GAE[rho] . GA[7] + GA[mu] . GAE[nu] . GAD[rho] . GA[7] - \ -2*GA[mu] . GAE[nu] . GAE[rho] . GA[7]"}, +"2*m*(GA[nu].GA[rho].GA[7] + GAE[nu].GAE[rho].GA[7]) + +GA[mu].GA[nu].GAE[rho].GA[7] + GA[mu].GAE[nu].GA[rho].GA[7]"}, {"fcstDiracTrickCoreProperties-ID72", "DiracTrick[GA[7].(GAD[mu] + 2 m).GA[nu, rho, 7]]//FCE", -"2*m*GA[nu] . GA[rho] . GA[7] + GAE[mu] . GA[nu] . GA[rho] . \ -GA[7]"}, +"(2*m + GAE[mu]).GA[nu].GA[rho].GA[7]"}, {"fcstDiracTrickCoreProperties-ID73", "DiracTrick[GA[6].(GA[mu] + 2 m).GA[6]]//FCE", "2*m*GA[6]"}, {"fcstDiracTrickCoreProperties-ID74", "DiracTrick[GA[6].(GAD[mu] + 2 m).GA[6]]//FCE", -"GAE[mu] . GA[6] + 2*m*GA[6]"}, +"(2*m + GAE[mu]).GA[6]"}, {"fcstDiracTrickCoreProperties-ID75", "DiracTrick[GA[7].(GA[mu] + 2 m).GA[7]]//FCE", "2*m*GA[7]"}, {"fcstDiracTrickCoreProperties-ID76", "DiracTrick[GA[7].(GAD[mu] + 2 m).GA[7]]//FCE", -"GAE[mu] . GA[7] + 2*m*GA[7]"}, +"(2*m + GAE[mu]) . GA[7]"}, {"fcstDiracTrickCoreProperties-ID77", "DiracTrick[GA[6].(GA[mu] + 2 m).GA[7]]//FCE", "GA[mu] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID78", "DiracTrick[GA[6].(GAD[mu] + 2 m).GA[7]]//FCE", -"GAD[mu] . GA[7] - GAE[mu] . GA[7]"}, +"GA[mu] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID79", "DiracTrick[GA[7].(GA[mu] + 2 m).GA[6]]//FCE", "GA[mu] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID80", "DiracTrick[GA[7].(GAD[mu] + 2 m).GA[6]]//FCE", -"GAD[mu] . GA[6] - GAE[mu] . GA[6]"}, +"GA[mu] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID81", "DiracTrick[GA[6].(GA[mu] + 2 m).GA[nu, rho, 7]]//FCE", "GA[mu] . GA[nu] . GA[rho] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID82", "DiracTrick[GA[6].(GAD[mu] + 2 m).GAD[nu, rho].GA[7]]//FCE", -"2*m*(GAD[nu] . GAE[rho] . GA[7] + GAE[nu] . GAD[rho] . GA[7] - \ -2*GAE[nu] . GAE[rho] . GA[7]) + GAD[mu] . GAD[nu] . GAD[rho] . GA[7] \ -- GAD[mu] . GAD[nu] . GAE[rho] . GA[7] - GAD[mu] . GAE[nu] . GAD[rho] \ -. GA[7] + 2*GAD[mu] . GAE[nu] . GAE[rho] . GA[7] - GAE[mu] . GAD[nu] \ -. GAD[rho] . GA[7] + 2*GAE[mu] . GAD[nu] . GAE[rho] . GA[7] + \ -2*(GAE[mu] . GAE[nu] . GAD[rho] . GA[7] - 2*GAE[mu] . GAE[nu] . \ -GAE[rho] . GA[7])"}, +"GA[mu].GA[nu].GA[rho].GA[7] + +GA[mu].GAE[nu].GAE[rho].GA[7] + (2*m + GAE[mu]).GA[nu].GAE[rho].GA[ +7] + (2*m + GAE[mu]).GAE[nu].GA[rho].GA[7]"}, {"fcstDiracTrickCoreProperties-ID83", "DiracTrick[GA[6].(GA[mu] + 2 m).GAD[nu, rho].GA[7]]//FCE", -"2*m*(GAD[nu] . GAE[rho] . GA[7] + GAE[nu] . GAD[rho] . GA[7] - \ -2*GAE[nu] . GAE[rho] . GA[7]) + GA[mu] . GAD[nu] . GAD[rho] . GA[7] - \ -GA[mu] . GAD[nu] . GAE[rho] . GA[7] - GA[mu] . GAE[nu] . GAD[rho] . \ -GA[7] + 2*GA[mu] . GAE[nu] . GAE[rho] . GA[7]"}, +"2*m*(GA[nu].GAE[rho].GA[7] + GAE[nu].GA[rho].GA[7]) + +GA[mu].GA[nu].GA[rho].GA[7] + GA[mu].GAE[nu].GAE[rho].GA[7]"}, {"fcstDiracTrickCoreProperties-ID84", "DiracTrick[GA[6].(GAD[mu] + 2 m).GA[nu, rho, 7]]//FCE", -"GAD[mu] . GA[nu] . GA[rho] . GA[7] - GAE[mu] . GA[nu] . GA[rho] . \ -GA[7]"}, +"GA[mu] . GA[nu] . GA[rho] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID85", "DiracTrick[GA[7].(GA[mu] + 2 m).GA[nu, rho, 6]]//FCE", "GA[mu] . GA[nu] . GA[rho] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID86", "DiracTrick[GA[7].(GAD[mu] + 2 m).GAD[nu, rho].GA[6]]//FCE", -"2*m*(GAD[nu] . GAE[rho] . GA[6] + GAE[nu] . GAD[rho] . GA[6] - \ -2*GAE[nu] . GAE[rho] . GA[6]) + GAD[mu] . GAD[nu] . GAD[rho] . GA[6] \ -- GAD[mu] . GAD[nu] . GAE[rho] . GA[6] - GAD[mu] . GAE[nu] . GAD[rho] \ -. GA[6] + 2*GAD[mu] . GAE[nu] . GAE[rho] . GA[6] - GAE[mu] . GAD[nu] \ -. GAD[rho] . GA[6] + 2*GAE[mu] . GAD[nu] . GAE[rho] . GA[6] - \ -2*(-GAE[mu] . GAE[nu] . GAD[rho] . GA[6] + 2*GAE[mu] . GAE[nu] . \ -GAE[rho] . GA[6])"}, +"GA[mu].GA[nu].GA[rho].GA[6] + +GA[mu].GAE[nu].GAE[rho].GA[6] + (2*m + GAE[mu]).GA[nu].GAE[rho].GA[ +6] + (2*m + GAE[mu]).GAE[nu].GA[rho].GA[6]"}, {"fcstDiracTrickCoreProperties-ID87", "DiracTrick[GA[7].(GA[mu] + 2 m).GAD[nu, rho].GA[6]]//FCE", -"2*m*(GAD[nu] . GAE[rho] . GA[6] + GAE[nu] . GAD[rho] . GA[6] - \ -2*GAE[nu] . GAE[rho] . GA[6]) + GA[mu] . GAD[nu] . GAD[rho] . GA[6] - \ -GA[mu] . GAD[nu] . GAE[rho] . GA[6] - GA[mu] . GAE[nu] . GAD[rho] . \ -GA[6] + 2*GA[mu] . GAE[nu] . GAE[rho] . GA[6]"}, +"2*m*(GA[nu].GAE[rho].GA[6] + GAE[nu].GA[rho].GA[6]) + +GA[mu].GA[nu].GA[rho].GA[6] + GA[mu].GAE[nu].GAE[rho].GA[6]"}, {"fcstDiracTrickCoreProperties-ID88", "DiracTrick[GA[7].(GAD[mu] + 2 m).GA[nu, rho, 6]]//FCE", -"GAD[mu] . GA[nu] . GA[rho] . GA[6] - GAE[mu] . GA[nu] . GA[rho] . \ -GA[6]"}, +"GA[mu] . GA[nu] . GA[rho] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID89", "DiracTrick[GA[6].(GA[mu] + 2 m).GA[nu, rho, si, 6]]//FCE", "GA[mu] . GA[nu] . GA[rho] . GA[si] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID90", "DiracTrick[GA[6].(GAD[mu] + 2 m).GAD[nu, rho, si].GA[6]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GAE[si] . GA[6] + GAD[nu] . GAE[rho] . \ -GAD[si] . GA[6] - 2*GAD[nu] . GAE[rho] . GAE[si] . GA[6] + GAE[nu] . \ -GAD[rho] . GAD[si] . GA[6] - 2*GAE[nu] . GAD[rho] . GAE[si] . GA[6] + \ -2*(-GAE[nu] . GAE[rho] . GAD[si] . GA[6] + 2*GAE[nu] . GAE[rho] . \ -GAE[si] . GA[6])) + GAD[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[6] - \ -GAD[mu] . GAD[nu] . GAD[rho] . GAE[si] . GA[6] - GAD[mu] . GAD[nu] . \ -GAE[rho] . GAD[si] . GA[6] + 2*GAD[mu] . GAD[nu] . GAE[rho] . GAE[si] \ -. GA[6] - GAD[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[6] + 2*GAD[mu] \ -. GAE[nu] . GAD[rho] . GAE[si] . GA[6] - 2*(-GAD[mu] . GAE[nu] . \ -GAE[rho] . GAD[si] . GA[6] + 2*GAD[mu] . GAE[nu] . GAE[rho] . GAE[si] \ -. GA[6]) - GAE[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[6] + 2*GAE[mu] \ -. GAD[nu] . GAD[rho] . GAE[si] . GA[6] - 2*(-GAE[mu] . GAD[nu] . \ -GAE[rho] . GAD[si] . GA[6] + 2*GAE[mu] . GAD[nu] . GAE[rho] . GAE[si] \ -. GA[6]) + 2*(GAE[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[6] - \ -2*GAE[mu] . GAE[nu] . GAD[rho] . GAE[si] . GA[6] + 2*(-GAE[mu] . \ -GAE[nu] . GAE[rho] . GAD[si] . GA[6] + 2*GAE[mu] . GAE[nu] . GAE[rho] \ -. GAE[si] . GA[6]))"}, +"GA[mu].GA[nu].GA[rho].GA[si].GA[6] + +GA[mu].GA[nu].GAE[rho].GAE[si].GA[6] + +GA[mu].GAE[nu].GA[rho].GAE[si].GA[6] + +GA[mu].GAE[nu].GAE[rho].GA[si].GA[6] + (2*m + GAE[mu]).GA[nu].GA[ +rho].GAE[si].GA[6] + (2*m + GAE[mu]).GA[nu].GAE[rho].GA[si].GA[ +6] + (2*m + GAE[mu]).GAE[nu].GA[rho].GA[si].GA[ +6] + (2*m + GAE[mu]).GAE[nu].GAE[rho].GAE[si].GA[6]"}, {"fcstDiracTrickCoreProperties-ID91", "DiracTrick[GA[6].(GA[mu] + 2 m).GAD[nu, rho, si].GA[6]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GAE[si] . GA[6] + GAD[nu] . GAE[rho] . \ -GAD[si] . GA[6] - 2*GAD[nu] . GAE[rho] . GAE[si] . GA[6] + GAE[nu] . \ -GAD[rho] . GAD[si] . GA[6] - 2*GAE[nu] . GAD[rho] . GAE[si] . GA[6] + \ -2*(-GAE[nu] . GAE[rho] . GAD[si] . GA[6] + 2*GAE[nu] . GAE[rho] . \ -GAE[si] . GA[6])) + GA[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[6] - \ -GA[mu] . GAD[nu] . GAD[rho] . GAE[si] . GA[6] - GA[mu] . GAD[nu] . \ -GAE[rho] . GAD[si] . GA[6] + 2*GA[mu] . GAD[nu] . GAE[rho] . GAE[si] \ -. GA[6] - GA[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[6] + 2*GA[mu] . \ -GAE[nu] . GAD[rho] . GAE[si] . GA[6] - 2*(-GA[mu] . GAE[nu] . \ -GAE[rho] . GAD[si] . GA[6] + 2*GA[mu] . GAE[nu] . GAE[rho] . GAE[si] \ -. GA[6])"}, +"2*m*(GA[nu].GA[rho].GAE[si].GA[6] + GA[nu].GAE[rho].GA[si].GA[6] + + GAE[nu].GA[rho].GA[si].GA[6] + GAE[nu].GAE[rho].GAE[si].GA[6]) + +GA[mu].GA[nu].GA[rho].GA[si].GA[6] + +GA[mu].GA[nu].GAE[rho].GAE[si].GA[6] + +GA[mu].GAE[nu].GA[rho].GAE[si].GA[6] + +GA[mu].GAE[nu].GAE[rho].GA[si].GA[6]"}, {"fcstDiracTrickCoreProperties-ID92", "DiracTrick[GA[6].(GAD[mu] + 2 m).GA[nu, rho, si, 6]]//FCE", -"GAD[mu] . GA[nu] . GA[rho] . GA[si] . GA[6] - GAE[mu] . GA[nu] . \ -GA[rho] . GA[si] . GA[6]"}, +"GA[mu] . GA[nu] . GA[rho] . GA[si] . GA[6]"}, {"fcstDiracTrickCoreProperties-ID93", "DiracTrick[GA[7].(GA[mu] + 2 m).GA[nu, rho, si, 7]]//FCE", "GA[mu] . GA[nu] . GA[rho] . GA[si] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID94", "DiracTrick[GA[7].(GAD[mu] + 2 m).GAD[nu, rho, si].GA[7]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GAE[si] . GA[7] + GAD[nu] . GAE[rho] . \ -GAD[si] . GA[7] - 2*GAD[nu] . GAE[rho] . GAE[si] . GA[7] + GAE[nu] . \ -GAD[rho] . GAD[si] . GA[7] - 2*GAE[nu] . GAD[rho] . GAE[si] . GA[7] - \ -2*(GAE[nu] . GAE[rho] . GAD[si] . GA[7] - 2*GAE[nu] . GAE[rho] . \ -GAE[si] . GA[7])) + GAD[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[7] - \ -GAD[mu] . GAD[nu] . GAD[rho] . GAE[si] . GA[7] - GAD[mu] . GAD[nu] . \ -GAE[rho] . GAD[si] . GA[7] + 2*GAD[mu] . GAD[nu] . GAE[rho] . GAE[si] \ -. GA[7] - GAD[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[7] + 2*GAD[mu] \ -. GAE[nu] . GAD[rho] . GAE[si] . GA[7] + 2*(GAD[mu] . GAE[nu] . \ -GAE[rho] . GAD[si] . GA[7] - 2*GAD[mu] . GAE[nu] . GAE[rho] . GAE[si] \ -. GA[7]) - GAE[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[7] + 2*GAE[mu] \ -. GAD[nu] . GAD[rho] . GAE[si] . GA[7] + 2*(GAE[mu] . GAD[nu] . \ -GAE[rho] . GAD[si] . GA[7] - 2*GAE[mu] . GAD[nu] . GAE[rho] . GAE[si] \ -. GA[7]) - 2*(-GAE[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[7] + \ -2*GAE[mu] . GAE[nu] . GAD[rho] . GAE[si] . GA[7] + 2*(GAE[mu] . \ -GAE[nu] . GAE[rho] . GAD[si] . GA[7] - 2*GAE[mu] . GAE[nu] . GAE[rho] \ -. GAE[si] . GA[7]))"}, +"GA[mu].GA[nu].GA[rho].GA[si].GA[7] + +GA[mu].GA[nu].GAE[rho].GAE[si].GA[7] + +GA[mu].GAE[nu].GA[rho].GAE[si].GA[7] + +GA[mu].GAE[nu].GAE[rho].GA[si].GA[7] + (2*m + GAE[mu]).GA[nu].GA[ +rho].GAE[si].GA[7] + (2*m + GAE[mu]).GA[nu].GAE[rho].GA[si].GA[ +7] + (2*m + GAE[mu]).GAE[nu].GA[rho].GA[si].GA[ +7] + (2*m + GAE[mu]).GAE[nu].GAE[rho].GAE[si].GA[7]"}, {"fcstDiracTrickCoreProperties-ID95", "DiracTrick[GA[7].(GA[mu] + 2 m).GAD[nu, rho, si].GA[7]]//FCE", -"2*m*(GAD[nu] . GAD[rho] . GAE[si] . GA[7] + GAD[nu] . GAE[rho] . \ -GAD[si] . GA[7] - 2*GAD[nu] . GAE[rho] . GAE[si] . GA[7] + GAE[nu] . \ -GAD[rho] . GAD[si] . GA[7] - 2*GAE[nu] . GAD[rho] . GAE[si] . GA[7] - \ -2*(GAE[nu] . GAE[rho] . GAD[si] . GA[7] - 2*GAE[nu] . GAE[rho] . \ -GAE[si] . GA[7])) + GA[mu] . GAD[nu] . GAD[rho] . GAD[si] . GA[7] - \ -GA[mu] . GAD[nu] . GAD[rho] . GAE[si] . GA[7] - GA[mu] . GAD[nu] . \ -GAE[rho] . GAD[si] . GA[7] + 2*GA[mu] . GAD[nu] . GAE[rho] . GAE[si] \ -. GA[7] - GA[mu] . GAE[nu] . GAD[rho] . GAD[si] . GA[7] + 2*GA[mu] . \ -GAE[nu] . GAD[rho] . GAE[si] . GA[7] + 2*(GA[mu] . GAE[nu] . GAE[rho] \ -. GAD[si] . GA[7] - 2*GA[mu] . GAE[nu] . GAE[rho] . GAE[si] . GA[7])"}, +"2*m*(GA[nu].GA[rho].GAE[si].GA[7] + GA[nu].GAE[rho].GA[si].GA[7] + + GAE[nu].GA[rho].GA[si].GA[7] + GAE[nu].GAE[rho].GAE[si].GA[7]) + +GA[mu].GA[nu].GA[rho].GA[si].GA[7] + +GA[mu].GA[nu].GAE[rho].GAE[si].GA[7] + +GA[mu].GAE[nu].GA[rho].GAE[si].GA[7] + +GA[mu].GAE[nu].GAE[rho].GA[si].GA[7]"}, {"fcstDiracTrickCoreProperties-ID96", "DiracTrick[GA[7].(GAD[mu] + 2 m).GA[nu, rho, si, 7]]//FCE", -"GAD[mu] . GA[nu] . GA[rho] . GA[si] . GA[7] - GAE[mu] . GA[nu] . \ -GA[rho] . GA[si] . GA[7]"}, +"GA[mu] . GA[nu] . GA[rho] . GA[si] . GA[7]"}, {"fcstDiracTrickCoreProperties-ID97", "DiracTrick[GA[mu].GA[i].GA[i].GA[nu]]//FCE", "4*GA[mu] . GA[nu]"}, @@ -953,7 +862,7 @@ i10].GAD[mu]] + i10].GAE[mu]]) // FCE // ReplaceAll[#, GAE[i_] -> GAD[i] - \ GA[i]] & // - DiracSimplify[#, DiracCanonical -> True] &", "0"}, + DiracSimplify[#, DiracOrder -> True] &", "0"}, {"fcstDiracTrickCoreProperties-ID111", "(DiracTrick[ GA[mu].GAD[i1, i2, i3, i4, i5, i6, i7, i8, i9, i11].GA[mu]] - DiracTrick[GAD[mu].GAD[i1, i2, i3, i4, i5, i6, i7, i8, i9, \ @@ -962,7 +871,7 @@ i11].GAD[mu]] + i11].GAE[mu]]) // FCE // ReplaceAll[#, GAE[i_] -> GAD[i] - \ GA[i]] & // - DiracSimplify[#, DiracCanonical -> True] &", "0"}, + DiracSimplify[#, DiracOrder -> True] &", "0"}, {"fcstDiracTrickCoreProperties-ID112", "(DiracTrick[GSD[p].GAD[i1, i2, i3, i4, i5, i6, i7].GSD[p]] /. {D -> \ D - 4})", @@ -1196,11 +1105,35 @@ GAE[i9] . GAE[i10] . GAE[i11]*SP[p, p] - GAE[i1] . GAE[i2] . GAE[i3] \ . GAE[i4] . GAE[i5] . GAE[i6] . GAE[i7] . GAE[i8] . GAE[i9] . \ GAE[i10] . GAE[i11]*SPE[p, p]"}, {"fcstDiracTrickCoreProperties-ID118", -"DiracTrick[GA[i, j].FCNCA.GA[i, j]] // FCE", "GA[i] . GA[j] . FCNCA . GA[i] . GA[j]"} +"DiracTrick[GA[i, j].FCNCA.GA[i, j]] // FCE", "GA[i] . GA[j] . FCNCA . GA[i] . GA[j]"}, +{"fcstDiracTrickCoreProperties-ID119", +"MatchQ[DiracTrick[#, FCDiracIsolate -> False, FCI -> True] & /@ +Table[DiracGamma[LorentzIndex[mu]].DiracGamma[LorentzIndex[mu]], {i, 1, 10000}], {4 ..}]", "True"}, +{"fcstDiracTrickCoreProperties-ID120", +"DiracTrick[(aa GA[7] + bb GA[6]).(GS[p] + m)] // FCE", "GS[p].(aa GA[6] + bb GA[7]) + m (bb GA[6] + aa GA[7])"}, +{"fcstDiracTrickCoreProperties-ID121", +"DiracTrick[(aa GA[7] + bb GA[6]).(GS[p] + m).GA[mu, nu, rho]] // FCE", "m GA[mu].GA[nu].GA[rho].(aa GA[6] + bb GA[7]) + +GS[p].GA[mu].GA[nu].GA[rho].(bb GA[6] + aa GA[7])"}, +{"fcstDiracTrickCoreProperties-ID122", +"Spinor[Momentum[p3, D], m, 1].GAD[Lor4].(m + GSD[l + p3]).GAD[ + Lor1].Spinor[Momentum[p1, D]] // DiracGammaExpand // +DotSimplify // DiracTrick[#, FCJoinDOTs -> False, FCE -> True] &", "m Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1] + Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[l].GAD[Lor1].Spinor[ +Momentum[p1, D], 0, 1] + Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[p3].GAD[Lor1].Spinor[Momentum[p1, D], 0, 1]"}, +{"fcstDiracTrickCoreProperties-ID119", +"DiracTrick[GA[mu].(1/2 + GA[5]/2).GA[mu]]", "4 DiracGamma[7]"}, +{"fcstDiracTrickCoreProperties-ID120", +"DiracTrick[GA[mu].(1 + GA[5]/2).GA[mu], FCE -> True]", "4 - 2 GA[5]"}, +{"fcstDiracTrickCoreProperties-ID121", +"DiracTrick[GA[mu].(cc1 + cc2 GA[5]).(GS[p] + m).GA[rho], FCE -> True]", "cc1 GA[mu].(m + GS[p]).GA[rho] + cc2 GA[mu].(-m + GS[p]).GA[rho].GA[5]"}, +{"fcstDiracTrickCoreProperties-ID122", +"FCSetDiracGammaScheme[\"NDR\"]\n DiracTrick[GAD[mu].(cc1 + cc2 GA[5]).(GSD[p] + m).GAD[rho], FCE -> True]", "cc1 GAD[mu].(m + GSD[p]).GAD[rho] + cc2 GAD[mu].(-m + GSD[p]).GAD[rho].GA[5]"}, +{"fcstDiracTrickCoreProperties-ID123", +"DiracTrick[GAD[mu].DiracGamma[ExplicitLorentzIndex[i, D], D].GAD[mu]]", "(2 - D) DiracGamma[ExplicitLorentzIndex[i, D], D]"} }); Tests`Dirac`fcstDiracTrick = { -{"fcstDiracTrick-ID1","$BreitMaison=False;\nDiracTrick[GA[mu,nu,mu]]","-2*DiracGamma[LorentzIndex[nu]]"}, +{"fcstDiracTrick-ID1","FCSetDiracGammaScheme[\"NDR\"];\n DiracTrick[GA[mu,nu,mu]]","-2*DiracGamma[LorentzIndex[nu]]"}, {"fcstDiracTrick-ID2","DiracTrick[GAD[mu,nu,mu]]","(2 - D)*DiracGamma[LorentzIndex[nu, D], D]"}, {"fcstDiracTrick-ID3","DiracTrick[GA[5,mu,nu]]","DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[nu]]. DiracGamma[5]"}, {"fcstDiracTrick-ID4","DiracTrick[GA[6,mu,7]]","DiracGamma[LorentzIndex[mu]] . DiracGamma[7]"}, @@ -1283,11 +1216,28 @@ Tests`Dirac`fcstDiracTrick = { {"fcstDiracTrick-ID24","DiracTrick[GAD[i1,i2,i3,i4,i5,i6,i7,i8,i9,i1,i2,i3,i4,i5,i6,i7,i8,i9]]//Expand", "D^9-72 D^8+1848 D^7-22176 D^6+139440 D^5-486528 D^4+940672 D^3-927744 D^2+354560 D"}, {"fcstDiracTrick-ID25","DiracTrick[GAD[i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i1,i2,i3,i4,i5,i6,i7,i8,i9,i10]]//Expand", - "-D^10+90 D^9-3000 D^8+48720 D^7-431760 D^6+2220960 D^5-6776320 D^4+11957760 D^3-11079680 D^2+4063232 D"} + "-D^10+90 D^9-3000 D^8+48720 D^7-431760 D^6+2220960 D^5-6776320 D^4+11957760 D^3-11079680 D^2+4063232 D"}, +{"fcstDiracTrick-ID26","DiracTrick[GAD[rho, mu, nu], InsideDiracTrace -> True, Evaluate -> False]", "0"}, +{"fcstDiracTrick-ID27","DiracTrick[GAD[rho, mu, 7, nu, 6], InsideDiracTrace -> True, Evaluate -> False]", "0"}, +{"fcstDiracTrick-ID28","DiracTrick[GAD[mu, 7].GSD[p1 - q].GAD[nu, rho, 6], +InsideDiracTrace -> True, Evaluate -> False, +FCE -> True]", "GAD[mu].GSD[p1 - q].GAD[nu].GAD[rho].GA[6]"}, +{"fcstDiracTrick-ID29","FCSetDiracGammaScheme[\"NDR-Drop\"]; \n +tmp = DiracTrick[GAD[mu, nu, rho, si, 5], InsideDiracTrace -> True, +Evaluate -> False]; \n +FCSetDiracGammaScheme[\"NDR\"]; \n tmp", "0"}, +{"fcstDiracTrick-ID30","FCSetDiracGammaScheme[\"NDR-Drop\"]; \n +tmp = DiracTrick[GAD[mu, nu, rho, si, 6], InsideDiracTrace -> True, +Evaluate -> False, FCE -> True]; \n +FCSetDiracGammaScheme[\"NDR\"]; \n tmp", "1/2 GAD[mu].GAD[nu].GAD[rho].GAD[si]"}, +{"fcstDiracTrick-ID31","FCSetDiracGammaScheme[\"NDR-Drop\"]; \n +tmp = DiracTrick[GAD[mu, nu, rho, si, 6], InsideDiracTrace -> True, +Evaluate -> False, FCE -> True]; \n +FCSetDiracGammaScheme[\"NDR\"]; \n tmp", "1/2 GAD[mu].GAD[nu].GAD[rho].GAD[si]"} }; Tests`Dirac`fcstDiracTrickBMHV = ({ -{"fcstDiracTrickBMHV-ID1", "$BreitMaison=True; +{"fcstDiracTrickBMHV-ID1", "FCSetDiracGammaScheme[\"BMHV\"]; \n DiracTrick[GA[5].GAD[mu]]//FCE", "-GAD[mu] . GA[5] + 2*GAE[mu] . GA[5]"}, {"fcstDiracTrickBMHV-ID2", "DiracTrick[GA[5].GA[mu]]//FCE", @@ -1333,11 +1283,21 @@ DiracTrick[GA[5].GAD[mu]]//FCE", {"fcstDiracTrickBMHV-ID23", "DiracTrick[GSE[p].GS[p]]//FCE", "GSE[p] . GS[p]"}, {"fcstDiracTrickBMHV-ID24", "DiracTrick[GSE[p].GSE[p]]//FCE", -"SPE[p, p]"} +"SPE[p, p]"}, +{"fcstDiracTrickBMHV-ID25", "DiracTrick[GSD[l1].GAD[mu].GSD[p].GAD[mu].GSD[l2], FCE -> True]", +"(2 - D) GSD[l1].GSD[p].GSD[l2]"}, +{"fcstDiracTrickBMHV-ID26", "DiracTrick[GS[l1].GA[mu].GS[p].GA[mu].GS[l2], FCE -> True]", +"-2 GS[l1].GS[p].GS[l2]"}, +{"fcstDiracTrickBMHV-ID27", "DiracTrick[GSE[l1].GAE[mu].GSE[p].GAE[mu].GSE[l2], FCE -> True]", +"(6 - D) GSE[l1].GSE[p].GSE[l2]"}, +{"fcstDiracTrickBMHV-ID28", +"DiracTrick[GAE[mu].TGA[].GA[x, 0, y].GAE[mu], FCE -> True]", "(-4 + D) TGA[].GA[x].TGA[].GA[y]"}, +{"fcstDiracTrickBMHV-ID29", +"DiracTrick[FCI[GAE[mu].TGA[].GAE[mu]], FCE -> True]", "-(-4 + D) TGA[]"} }); Tests`Dirac`fcstDiracTrickOneFreeIndex = { -{"fcstDiracTrickOneFreeIndex-ID1","$BreitMaison=True; \n $Larin=False; \n DiracTrick[GAD[mu, nu, mu]]", +{"fcstDiracTrickOneFreeIndex-ID1","FCSetDiracGammaScheme[\"BMHV\"]; \n DiracTrick[GAD[mu, nu, mu]]", "(2 - D)*DiracGamma[LorentzIndex[nu, D], D]"}, {"fcstDiracTrickOneFreeIndex-ID2","DiracTrick[GAD[mu].GA[nu].GAD[mu]]", "(2 - D)*DiracGamma[LorentzIndex[nu]]"}, @@ -1690,14 +1650,17 @@ Tests`Dirac`fcstDiracTrickFiveFreeIndices = { }; Tests`Dirac`fcstDiracTrickLarin = { -{"fcstDiracTrickLarin-ID1","$BreitMaison=False;\n$Larin=True;\nDiracTrick[GAD[a, b, c].GA[5].GAD[b, a, m]] // FCE", - "GAD[a].GAD[b].GAD[c].GA[5].GAD[b].GAD[a].GAD[m]"} +{"fcstDiracTrickLarin-ID1","FCSetDiracGammaScheme[\"Larin\"];\nDiracTrick[GAD[a, b, c].GA[5].GAD[b, a, m]] // FCE", + "GAD[a].GAD[b].GAD[c].GA[5].GAD[b].GAD[a].GAD[m]"}, +{"fcstDiracTrickLarin-ID2","MatchQ[DiracTrick[DiracTrace[GSD[p1].GA[6].GSD[p2].GA[6]], +FCE -> True], DiracTrace[1/2 GSD[p1].GSD[p2].GA[6] + 1/12 I GAD[dtlarLia656_].GAD[dtlarLib657_].GAD[dtlarLic658_].GSD[p2].GA[6] +LCD[dtlarLia656_, dtlarLib657_, dtlarLic658_][p1]]]", "True"} }; Tests`Dirac`fcstDiracTrickInsideDiracTrace = ({ {"fcstDiracTrickInsideDiracTrace-ID1", -"$BreitMaison=False; \n DiracTrick[GA[i],InsideDiracTrace\[Rule]True]//FCE", "0"}, +"FCSetDiracGammaScheme[\"NDR\"]; \n \n DiracTrick[GA[i],InsideDiracTrace\[Rule]True]//FCE", "0"}, {"fcstDiracTrickInsideDiracTrace-ID2", "DiracTrick[GA[i,5],InsideDiracTrace\[Rule]True]//FCE", "0"}, {"fcstDiracTrickInsideDiracTrace-ID3", @@ -1708,18 +1671,33 @@ Tests`Dirac`fcstDiracTrickInsideDiracTrace = "DiracTrick[GA[i,5,5],InsideDiracTrace\[Rule]True]//FCE", "0"}, {"fcstDiracTrickInsideDiracTrace-ID6", "DiracTrick[GA[i,j],InsideDiracTrace\[Rule]True]//FCE", -"GA[i] . GA[j]"}, +"MT[i,j]"}, +{"fcstDiracTrickInsideDiracTrace-ID6.1", +"DiracTrick[GAD[i,j],InsideDiracTrace\[Rule]True]//FCE", +"MTD[i,j]"}, +{"fcstDiracTrickInsideDiracTrace-ID6.2", +"DiracTrick[GAE[i,j],InsideDiracTrace\[Rule]True]//FCE", +"MTE[i,j]"}, +{"fcstDiracTrickInsideDiracTrace-ID6.3", +"DiracTrick[GS[p,q],InsideDiracTrace\[Rule]True]//FCE", +"SP[p,q]"}, +{"fcstDiracTrickInsideDiracTrace-ID6.3", +"DiracTrick[GSD[p,q],InsideDiracTrace\[Rule]True]//FCE", +"SPD[p,q]"}, +{"fcstDiracTrickInsideDiracTrace-ID6.4", +"DiracTrick[GSE[p,q],InsideDiracTrace\[Rule]True]//FCE", +"SPE[p,q]"}, {"fcstDiracTrickInsideDiracTrace-ID7", "DiracTrick[GA[i,j,5],InsideDiracTrace\[Rule]True]//FCE", "0"}, {"fcstDiracTrickInsideDiracTrace-ID8", "DiracTrick[GA[i,j,6],InsideDiracTrace\[Rule]True]//FCE", -"GA[i] . GA[j]/2"}, +"MT[i,j]/2"}, {"fcstDiracTrickInsideDiracTrace-ID9", "DiracTrick[GA[i,j,7],InsideDiracTrace\[Rule]True]//FCE", -"GA[i] . GA[j]/2"}, +"MT[i,j]/2"}, {"fcstDiracTrickInsideDiracTrace-ID10", "DiracTrick[GA[i,j,5,5],InsideDiracTrace\[Rule]True]//FCE", -"GA[i] . GA[j]"}, +"MT[i,j]"}, {"fcstDiracTrickInsideDiracTrace-ID11", "DiracTrick[GA[i,j,k],InsideDiracTrace\[Rule]True]//FCE", "0"}, {"fcstDiracTrickInsideDiracTrace-ID12", @@ -1783,12 +1761,15 @@ GA[mu].GA[5]+f1 GA[mu]),InsideDiracTrace\[Rule]True]//FCE", "DiracTrick[ GS[p2].GA[si].GS[k1].GS[p1].GS[k2].GS[k1].GA[si].GS[p2].GA[7], InsideDiracTrace -> True] // FCE", -"GS[k2].GS[p1] SP[k1, k1] SP[p2, p2] + -GS[p1].GS[k2] SP[k1, k1] SP[p2, p2]"}, +"2 SP[k1, k1] SP[k2, p1] SP[p2, p2]"}, {"fcstDiracTrickInsideDiracTrace-ID32", "DiracTrick[GA[i].GS[q].GA[j].GA[i] FV[2 p + q, j], InsideDiracTrace -> True] // FCE", -"4 SP[q, 2 p + q]"} +"4 SP[q, 2 p + q]"}, +{"fcstDiracTrickInsideDiracTrace-ID32", +"FCSetDiracGammaScheme[\"NDR-Drop\"]; \n +tmp = DiracTrick[GA[5].GS[pp1].GA[5], InsideDiracTrace -> True]; \n +FCSetDiracGammaScheme[\"NDR\"]; \n tmp","0"} }); fcstDiracTrickChiralTricks = @@ -1855,3 +1836,334 @@ DiracGamma[5]"}, "6*DiracGamma[LorentzIndex[i]] . DiracGamma[7]"} }); +Tests`Dirac`fcstDiracTrickCartesianFourDimNoGamma5 = +({ +{"fcstDiracTrickCartesianFourDimNoGamma5-ID1", +"DiracTrick[TGA[].TGA[]]", "1"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID2", +"DiracTrick[TGA[].CGA[i]]", +"-DiracGamma[CartesianIndex[i]] . DiracGamma[ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID3", +"DiracTrick[TGA[].CGA[i,j,k,l]]", +"DiracGamma[CartesianIndex[i]] . DiracGamma[CartesianIndex[j]] . \ +DiracGamma[CartesianIndex[k]] . DiracGamma[CartesianIndex[l]] . DiracGamma[ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID4", +"DiracTrick[TGA[].CGA[i,j,k,l,m]]", +"-DiracGamma[CartesianIndex[i]] . DiracGamma[CartesianIndex[j]] . \ +DiracGamma[CartesianIndex[k]] . DiracGamma[CartesianIndex[l]] . DiracGamma[CartesianIndex[m]] \ +. DiracGamma[ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID5", +"DiracTrick[CGA[i].CGA[i]]", "-3"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID6", +"DiracTrick[CGS[p].CGS[p]]", +"-CartesianPair[CartesianMomentum[p], CartesianMomentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID7", +"DiracTrick[GA[mu].CGA[i].GA[mu]]", "-2*DiracGamma[CartesianIndex[i]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID8", +"DiracTrick[GA[mu].CGA[i,j].GA[mu]]", +"-4*CartesianPair[CartesianIndex[i], CartesianIndex[j]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID9", +"DiracTrick[GA[mu].CGA[i,j,k].GA[mu]]", +"-2*DiracGamma[CartesianIndex[k]] . DiracGamma[CartesianIndex[j]] . \ +DiracGamma[CartesianIndex[i]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID10", +"DiracTrick[GA[mu].CGS[p].GA[mu]]", +"-2*DiracGamma[CartesianMomentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID11", +"DiracTrick[GA[mu].CGS[p,q].GA[mu]]", +"-4*CartesianPair[CartesianMomentum[p], CartesianMomentum[q]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID12", +"DiracTrick[GA[mu].CGS[p,q,r].GA[mu]]", +"-2*DiracGamma[CartesianMomentum[r]] . DiracGamma[CartesianMomentum[q]] . \ +DiracGamma[CartesianMomentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID13", +"DiracTrick[GS[p].CGA[i].GS[p]]", +"2*CartesianPair[CartesianIndex[i], CartesianMomentum[p]]*DiracGamma[Momentum[p]] - \ +DiracGamma[CartesianIndex[i]]*Pair[Momentum[p], Momentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID14", +"DiracTrick[GS[p].CGA[i,j].GS[p]]", +"2*(-(CartesianPair[CartesianIndex[j], CartesianMomentum[p]]*DiracGamma[CartesianIndex[i]] . \ +DiracGamma[Momentum[p]]) + CartesianPair[CartesianIndex[i], \ +CartesianMomentum[p]]*DiracGamma[CartesianIndex[j]] . DiracGamma[Momentum[p]]) + \ +DiracGamma[CartesianIndex[i]] . DiracGamma[CartesianIndex[j]]*Pair[Momentum[p], \ +Momentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID15", +"DiracTrick[GS[p].CGA[i,j,k].GS[p]]", +"2*(CartesianPair[CartesianIndex[k], CartesianMomentum[p]]*DiracGamma[CartesianIndex[i]] . \ +DiracGamma[CartesianIndex[j]] . DiracGamma[Momentum[p]] - CartesianPair[CartesianIndex[j], \ +CartesianMomentum[p]]*DiracGamma[CartesianIndex[i]] . DiracGamma[CartesianIndex[k]] . \ +DiracGamma[Momentum[p]] + CartesianPair[CartesianIndex[i], \ +CartesianMomentum[p]]*DiracGamma[CartesianIndex[j]] . DiracGamma[CartesianIndex[k]] . \ +DiracGamma[Momentum[p]]) - DiracGamma[CartesianIndex[i]] . \ +DiracGamma[CartesianIndex[j]] . DiracGamma[CartesianIndex[k]]*Pair[Momentum[p], \ +Momentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID16", +"DiracTrick[TGA[].GA[mu].TGA[]]", +"-DiracGamma[LorentzIndex[mu]] + \ +2*DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID17", +"DiracTrick[TGA[].GA[mu,nu].TGA[]]", +"DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[nu]] + \ +2*DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]] - \ +2*DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[nu], ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID18", +"DiracTrick[TGA[].GA[mu,nu,rho].TGA[]]", +"-DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[LorentzIndex[rho]] + 2*DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[LorentzIndex[rho]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]] - \ +2*DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[rho]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[nu], ExplicitLorentzIndex[0]] + \ +2*DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[rho], ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID19", +"DiracTrick[TGA[].GS[p].TGA[]]", +"-DiracGamma[Momentum[p]] + 2*DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID20", +"DiracTrick[TGA[].GS[p,q].TGA[]]", +"DiracGamma[Momentum[p]] . DiracGamma[Momentum[q]] + \ +2*DiracGamma[Momentum[q]] . DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]] - 2*DiracGamma[Momentum[p]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID21", +"DiracTrick[TGA[].GS[p,q,r].TGA[]]", +"-DiracGamma[Momentum[p]] . DiracGamma[Momentum[q]] . \ +DiracGamma[Momentum[r]] + 2*DiracGamma[Momentum[q]] . \ +DiracGamma[Momentum[r]] . DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]] - 2*DiracGamma[Momentum[p]] . DiracGamma[Momentum[r]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]] + \ +2*DiracGamma[Momentum[p]] . DiracGamma[Momentum[q]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[r]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID22", +"DiracTrick[TGA[].CGA[i].TGA[]]", "-DiracGamma[CartesianIndex[i]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID23", +"DiracTrick[TGA[].CGA[i,j].TGA[]]", +"DiracGamma[CartesianIndex[i]] . DiracGamma[CartesianIndex[j]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID24", +"DiracTrick[TGA[].CGA[i,j,k].TGA[]]", +"-DiracGamma[CartesianIndex[i]] . DiracGamma[CartesianIndex[j]] . \ +DiracGamma[CartesianIndex[k]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID25", +"DiracTrick[TGA[].CGS[p].TGA[]]", "-DiracGamma[CartesianMomentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID26", +"DiracTrick[TGA[].CGS[p,q].TGA[]]", +"DiracGamma[CartesianMomentum[p]] . DiracGamma[CartesianMomentum[q]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID27", +"DiracTrick[TGA[].CGS[p,q,r].TGA[]]", +"-DiracGamma[CartesianMomentum[p]] . DiracGamma[CartesianMomentum[q]] . \ +DiracGamma[CartesianMomentum[r]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID28", +"DiracTrick[CGA[ii].GA[mu].CGA[ii]]", +"DiracGamma[LorentzIndex[mu]] + \ +2*DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID29", +"DiracTrick[CGA[ii].GA[mu,nu].CGA[ii]]", +"DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[nu]] - \ +4*Pair[LorentzIndex[mu], LorentzIndex[nu]] + \ +2*DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]] - \ +2*DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[nu], ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID30", +"DiracTrick[CGA[ii].GA[mu,nu,rho].CGA[ii]]", +"-DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[LorentzIndex[rho]] + 2*DiracGamma[LorentzIndex[rho]] . \ +DiracGamma[LorentzIndex[nu]] . DiracGamma[LorentzIndex[mu]] + \ +2*DiracGamma[LorentzIndex[nu]] . DiracGamma[LorentzIndex[rho]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]] - \ +2*DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[rho]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[nu], ExplicitLorentzIndex[0]] + \ +2*DiracGamma[LorentzIndex[mu]] . DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*Pair[LorentzIndex[rho], ExplicitLorentzIndex[0]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID31", +"DiracTrick[CGA[ii].GS[p].CGA[ii]]", +"DiracGamma[Momentum[p]] + 2*DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID32", +"DiracTrick[CGA[ii].GS[p,q].CGA[ii]]", +"DiracGamma[Momentum[p]] . DiracGamma[Momentum[q]] - \ +4*Pair[Momentum[p], Momentum[q]] + 2*DiracGamma[Momentum[q]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]] - \ +2*DiracGamma[Momentum[p]] . DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[q]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID33", +"DiracTrick[CGA[ii].GS[p,q,r].CGA[ii]]", +"-DiracGamma[Momentum[p]] . DiracGamma[Momentum[q]] . \ +DiracGamma[Momentum[r]] + 2*DiracGamma[Momentum[r]] . \ +DiracGamma[Momentum[q]] . DiracGamma[Momentum[p]] + \ +2*DiracGamma[Momentum[q]] . DiracGamma[Momentum[r]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]] - \ +2*DiracGamma[Momentum[p]] . DiracGamma[Momentum[r]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]] + \ +2*DiracGamma[Momentum[p]] . DiracGamma[Momentum[q]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[r]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID34", +"DiracTrick[CGA[ii].CGA[i].CGA[ii]]", "DiracGamma[CartesianIndex[i]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID35", +"DiracTrick[CGA[ii].CGA[i,j].CGA[ii]]", +"4*CartesianPair[CartesianIndex[i], CartesianIndex[j]] + DiracGamma[CartesianIndex[i]] . \ +DiracGamma[CartesianIndex[j]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID36", +"DiracTrick[CGA[ii].CGA[i,j,k].CGA[ii]]", +"-DiracGamma[CartesianIndex[i]] . DiracGamma[CartesianIndex[j]] . \ +DiracGamma[CartesianIndex[k]] + 2*DiracGamma[CartesianIndex[k]] . \ +DiracGamma[CartesianIndex[j]] . DiracGamma[CartesianIndex[i]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID37", +"DiracTrick[CGA[ii].CGS[p].CGA[ii]]", "DiracGamma[CartesianMomentum[p]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID38", +"DiracTrick[CGA[ii].CGS[p,q].CGA[ii]]", +"4*CartesianPair[CartesianMomentum[p], CartesianMomentum[q]] + DiracGamma[CartesianMomentum[p]] . \ +DiracGamma[CartesianMomentum[q]]"}, +{"fcstDiracTrickCartesianFourDimNoGamma5-ID39", +"DiracTrick[CGA[ii].CGS[p,q,r].CGA[ii]]", +"-DiracGamma[CartesianMomentum[p]] . DiracGamma[CartesianMomentum[q]] . \ +DiracGamma[CartesianMomentum[r]] + 2*DiracGamma[CartesianMomentum[r]] . \ +DiracGamma[CartesianMomentum[q]] . DiracGamma[CartesianMomentum[p]]"} +}); + +Tests`Dirac`fcstDiracTrickCartesianChiralTricks = +({ +{"fcstDiracTrickCartesianChiralTricks-ID1", +"DiracTrick[CGA[i].GA[5].(2 GA[5]+4)]", +"2*DiracGamma[CartesianIndex[i]] + 4*DiracGamma[CartesianIndex[i]] . \ +DiracGamma[5]"}, +{"fcstDiracTrickCartesianChiralTricks-ID2", +"DiracTrick[CGA[i].(2 GA[5]+4).GA[5]]", +"2*DiracGamma[CartesianIndex[i]] + 4*DiracGamma[CartesianIndex[i]] . \ +DiracGamma[5]"}, +{"fcstDiracTrickCartesianChiralTricks-ID3", +"DiracTrick[CGA[i].GA[5].(2 GA[6]+4)]", +"4*DiracGamma[CartesianIndex[i]] . DiracGamma[5] + 2*DiracGamma[CartesianIndex[i]] \ +. DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID4", +"DiracTrick[CGA[i].(2 GA[6]+4).GA[5]]", +"4*DiracGamma[CartesianIndex[i]] . DiracGamma[5] + 2*DiracGamma[CartesianIndex[i]] \ +. DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID5", +"DiracTrick[CGA[i].GA[5].(2 GA[7]+4)]", +"4*DiracGamma[CartesianIndex[i]] . DiracGamma[5] - 2*DiracGamma[CartesianIndex[i]] \ +. DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID6", +"DiracTrick[CGA[i].(2 GA[7]+4).GA[5]]", +"4*DiracGamma[CartesianIndex[i]] . DiracGamma[5] - 2*DiracGamma[CartesianIndex[i]] \ +. DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID7", +"DiracTrick[CGA[i].GA[6].(2 GA[5]+4)]", +"6*DiracGamma[CartesianIndex[i]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID8", +"DiracTrick[CGA[i].(2 GA[5]+4).GA[6]]", +"6*DiracGamma[CartesianIndex[i]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID9", +"DiracTrick[CGA[i].GA[6].(2 GA[6]+4)]", +"6*DiracGamma[CartesianIndex[i]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID10", +"DiracTrick[CGA[i].(2 GA[6]+4).GA[6]]", +"6*DiracGamma[CartesianIndex[i]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID11", +"DiracTrick[CGA[i].GA[6].(2 GA[7]+4)]", +"4*DiracGamma[CartesianIndex[i]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID12", +"DiracTrick[CGA[i].(2 GA[7]+4).GA[6]]", +"4*DiracGamma[CartesianIndex[i]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID13", +"DiracTrick[CGA[i].GA[7].(2 GA[5]+4)]", +"2*DiracGamma[CartesianIndex[i]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID14", +"DiracTrick[CGA[i].(2 GA[5]+4).GA[7]]", +"2*DiracGamma[CartesianIndex[i]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID15", +"DiracTrick[CGA[i].GA[7].(2 GA[6]+4)]", +"4*DiracGamma[CartesianIndex[i]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID16", +"DiracTrick[CGA[i].(2 GA[6]+4).GA[7]]", +"4*DiracGamma[CartesianIndex[i]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID17", +"DiracTrick[CGA[i].GA[7].(2 GA[7]+4)]", +"6*DiracGamma[CartesianIndex[i]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID18", +"DiracTrick[CGA[i].(2 GA[7]+4).GA[7]]", +"6*DiracGamma[CartesianIndex[i]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID19", +"DiracTrick[TGA[].GA[5].(2 GA[5]+4)]", +"2*DiracGamma[ExplicitLorentzIndex[0]] + 4*DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[5]"}, +{"fcstDiracTrickCartesianChiralTricks-ID20", +"DiracTrick[TGA[].(2 GA[5]+4).GA[5]]", +"2*DiracGamma[ExplicitLorentzIndex[0]] + 4*DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[5]"}, +{"fcstDiracTrickCartesianChiralTricks-ID21", +"DiracTrick[TGA[].GA[5].(2 GA[6]+4)]", +"4*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[5] + 2*DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID22", +"DiracTrick[TGA[].(2 GA[6]+4).GA[5]]", +"4*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[5] + 2*DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID23", +"DiracTrick[TGA[].GA[5].(2 GA[7]+4)]", +"4*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[5] - 2*DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID24", +"DiracTrick[TGA[].(2 GA[7]+4).GA[5]]", +"4*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[5] - 2*DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID25", +"DiracTrick[TGA[].GA[6].(2 GA[5]+4)]", +"6*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID26", +"DiracTrick[TGA[].(2 GA[5]+4).GA[6]]", +"6*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID27", +"DiracTrick[TGA[].GA[6].(2 GA[6]+4)]", +"6*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID28", +"DiracTrick[TGA[].(2 GA[6]+4).GA[6]]", +"6*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID29", +"DiracTrick[TGA[].GA[6].(2 GA[7]+4)]", +"4*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID30", +"DiracTrick[TGA[].(2 GA[7]+4).GA[6]]", +"4*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[6]"}, +{"fcstDiracTrickCartesianChiralTricks-ID31", +"DiracTrick[TGA[].GA[7].(2 GA[5]+4)]", +"2*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID32", +"DiracTrick[TGA[].(2 GA[5]+4).GA[7]]", +"2*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID33", +"DiracTrick[TGA[].GA[7].(2 GA[6]+4)]", +"4*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID34", +"DiracTrick[TGA[].(2 GA[6]+4).GA[7]]", +"4*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID35", +"DiracTrick[TGA[].GA[7].(2 GA[7]+4)]", +"6*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[7]"}, +{"fcstDiracTrickCartesianChiralTricks-ID36", +"DiracTrick[TGA[].(2 GA[7]+4).GA[7]]", +"6*DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[7]"} +}); + +Tests`Dirac`fcstDiracTrickDiracChain = +({ +{"fcstDiracTrickDiracChain-ID1", +"DiracTrick[DCHN[GS[p].GS[q].GS[p],i,j],FCE\[Rule]True]", +"DCHN[-(GS[q]*SP[p, p]) + 2*GS[p]*SP[p, q], i, j]"}, +{"fcstDiracTrickDiracChain-ID2", +"DiracTrick[DCHN[GS[p].GS[q].GS[p],i,j],DiracChain\[Rule]False,FCE\ +\[Rule]True]", "DCHN[GS[p] . GS[q] . GS[p], i, j]"}, +{"fcstDiracTrickDiracChain-ID3", +"DiracTrick[DCHN[GS[p].GS[q].GS[p],i,j]+DCHN[GS[q].GS[p].GS[q],i,j]\ +,FCE\[Rule]True]", +"DCHN[-(GS[q]*SP[p, p]) + 2*GS[p]*SP[p, q], i, j] + \ +DCHN[2*GS[q]*SP[p, q] - GS[p]*SP[q, q], i, j]"}, +{"fcstDiracTrickDiracChain-ID4", +"DiracTrick[DCHN[GS[p].GS[q].GS[p],i,j]+DCHN[GS[q].GS[p].GS[q],i,j]\ +,DiracChain\[Rule]False,FCE\[Rule]True]", +"DCHN[GS[p] . GS[q] . GS[p], i, j] + DCHN[GS[q] . GS[p] . GS[q], \ +i, j]"} +}) diff --git a/Tests/Dirac/EpsChisholm.test b/Tests/Dirac/EpsChisholm.test index b7d2677be..063b76918 100644 --- a/Tests/Dirac/EpsChisholm.test +++ b/Tests/Dirac/EpsChisholm.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for EpsChisholm *) @@ -110,5 +110,22 @@ GA[i9] . GA[jj1]*MT[j2, j3]*MT[jj2, jj3]"}, "EpsChisholm[(SpinorUBar[p1, m1].SpinorV[p2, m2] + SpinorUBar[p1, m1].GS[k].SpinorV[p2, m2])] // FCE", "Spinor[Momentum[p1], m1, 1].Spinor[-Momentum[p2], m2, 1] + -Spinor[Momentum[p1], m1, 1].GS[k].Spinor[-Momentum[p2], m2, 1]"} +Spinor[Momentum[p1], m1, 1].GS[k].Spinor[-Momentum[p2], m2, 1]"}, +{"fcstEpsChisholm-ID8", +"EpsChisholm[GA[i1].CGA[k] LC[j1, i1, j2, j3]] // FCE", +"-I GA[j1].GA[j2].GA[j3].CGA[k].GA[5] + +I GA[j3].CGA[k].GA[5] MT[j1, j2] - I GA[j2].CGA[k].GA[5] MT[j1, j3] + +I GA[j1].CGA[k].GA[5] MT[j2, j3]"}, +{"fcstEpsChisholm-ID9", +"EpsChisholm[ +GA[i1].CGA[k] Eps[CartesianIndex[a], LorentzIndex[i1], CartesianIndex[b], + CartesianIndex[c]]] // FCE", +"-I CGA[a].CGA[b].CGA[c].CGA[k].GA[5] - +I CGA[c].CGA[k].GA[5] KD[a, b] + I CGA[b].CGA[k].GA[5] KD[a, c] - +I CGA[a].CGA[k].GA[5] KD[b, c]"}, +{"fcstEpsChisholm-ID10","EpsChisholm[DCHN[GA[i1, mu], a, b] LC[j1, i1, j2, j3],FCE->True]", +"-I DCHN[GA[j1].GA[j2].GA[j3].GA[mu].GA[5], a, b] + +I DCHN[GA[j3].GA[mu].GA[5], a, b] MT[j1, j2] - +I DCHN[GA[j2].GA[mu].GA[5], a, b] MT[j1, j3] + +I DCHN[GA[j1].GA[mu].GA[5], a, b] MT[j2, j3]"} }); diff --git a/Tests/Dirac/FCChargeConjugateTransposed.test b/Tests/Dirac/FCChargeConjugateTransposed.test new file mode 100644 index 000000000..d785212ea --- /dev/null +++ b/Tests/Dirac/FCChargeConjugateTransposed.test @@ -0,0 +1,104 @@ + + +(* :Title: FCChargeConjugateTransposed.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCChargeConjugateTransposed *) + +(* ------------------------------------------------------------------------ *) + +Tests`Dirac`fcstFCChargeConjugateTransposed = +({ +{"fcstFCChargeConjugateTransposed-ID1", "FCCCT[0]", "0"}, +{"fcstFCChargeConjugateTransposed-ID2", "FCCCT[1]", "1"}, +{"fcstFCChargeConjugateTransposed-ID3", +"FCCCT[GA[i],Explicit\[Rule]True]", "-DiracGamma[LorentzIndex[i]]"}, +{"fcstFCChargeConjugateTransposed-ID4", +"FCCCT[GAD[i],Explicit\[Rule]True]", +"-DiracGamma[LorentzIndex[i, D], D]"}, +{"fcstFCChargeConjugateTransposed-ID5", +"FCCCT[GAD[i],Explicit\[Rule]True,FCDiracIsolate\[Rule]False]", +"-DiracGamma[LorentzIndex[i, D], D]"}, +{"fcstFCChargeConjugateTransposed-ID6", +"FCCCT[GS[p],Explicit\[Rule]True]", "-DiracGamma[Momentum[p]]"}, +{"fcstFCChargeConjugateTransposed-ID7", +"FCCCT[GSD[p],Explicit\[Rule]True]", +"-DiracGamma[Momentum[p, D], D]"}, +{"fcstFCChargeConjugateTransposed-ID8", +"FCCCT[GA[5],Explicit\[Rule]True]", "DiracGamma[5]"}, +{"fcstFCChargeConjugateTransposed-ID9", +"FCCCT[GA[6],Explicit\[Rule]True]", "DiracGamma[6]"}, +{"fcstFCChargeConjugateTransposed-ID10", +"FCCCT[GA[7],Explicit\[Rule]True]", "DiracGamma[7]"}, +{"fcstFCChargeConjugateTransposed-ID11", +"FCCCT[1/2(1+GA[5]),Explicit\[Rule]True]", "1/2 + DiracGamma[5]/2"}, +{"fcstFCChargeConjugateTransposed-ID12", +"FCCCT[1/2(1+GA[mu,5]),Explicit\[Rule]True]", +"1/2 - DiracGamma[5] . DiracGamma[LorentzIndex[mu]]/2"}, +{"fcstFCChargeConjugateTransposed-ID13", +"FCCCT[GS[p]+m,Explicit\[Rule]True]", +"m - DiracGamma[Momentum[p]]"}, +{"fcstFCChargeConjugateTransposed-ID14", +"FCCCT[GSD[p]+m,Explicit\[Rule]True]", +"m - DiracGamma[Momentum[p, D], D]"}, +{"fcstFCChargeConjugateTransposed-ID15", +"FCCCT[GA[mu].(GS[p]+m).GA[nu],Explicit\[Rule]True]", +"DiracGamma[LorentzIndex[nu]] . (m - DiracGamma[Momentum[p]]) . \ +DiracGamma[LorentzIndex[mu]]"}, +{"fcstFCChargeConjugateTransposed-ID16", +"FCCCT[GA[6].GS[l].GA[7],Explicit\[Rule]True]", +"-DiracGamma[7] . DiracGamma[Momentum[l]] . DiracGamma[6]"}, +{"fcstFCChargeConjugateTransposed-ID17", +"FCCCT[GA[6].GS[l].SUNT[a].GA[7].SUNT[b],Explicit\[Rule]True]", +"-(DiracGamma[7] . DiracGamma[Momentum[l]] . \ +DiracGamma[6]*FCChargeConjugateTransposed[SUNT[SUNIndex[a]] . \ +SUNT[SUNIndex[b]], Explicit -> False])"}, +{"fcstFCChargeConjugateTransposed-ID18", +"FCCCT[DiracSigma[GAD[a],GAD[b]],Explicit\[Rule]True]", +"-DiracSigma[DiracGamma[LorentzIndex[a, D], D], \ +DiracGamma[LorentzIndex[b, D], D]]"}, +{"fcstFCChargeConjugateTransposed-ID19", +"FCCCT[DiracSigma[GAD[a],GA[5]],Explicit\[Rule]True]", +"(-I/2)*DiracGamma[5] . DiracGamma[LorentzIndex[a, D], D] + \ +(I/2)*DiracGamma[LorentzIndex[a, D], D] . DiracGamma[5]"}, +{"fcstFCChargeConjugateTransposed-ID20", +"FCCCT[DiracSigma[GA[5],GA[6]],Explicit\[Rule]True]", +"(-I/2)*DiracGamma[5] . DiracGamma[6] + (I/2)*DiracGamma[6] . \ +DiracGamma[5]"}, +{"fcstFCChargeConjugateTransposed-ID21", +"DeclareNonCommutative[AAA1]; + FCCCT[GA[mu].AAA1.(GS[p]+m).GA[nu],Explicit\[Rule]True]", +"DiracGamma[LorentzIndex[nu]] . (m - DiracGamma[Momentum[p]]) . \ +FCChargeConjugateTransposed[AAA1, Explicit -> False] . \ +DiracGamma[LorentzIndex[mu]]"}, +{"fcstFCChargeConjugateTransposed-ID22", +"UnDeclareNonCommutative[AAA1]; + FCCCT[SpinorUBar[p1].GA[mu].(GS[p]+m).GA[nu].SpinorU[p2],Explicit\ +\[Rule]True]", +"FCChargeConjugateTransposed[Spinor[Momentum[p1], 0, 1] . \ +DiracGamma[LorentzIndex[mu]] . (m + DiracGamma[Momentum[p]]) . \ +DiracGamma[LorentzIndex[nu]] . Spinor[Momentum[p2], 0, 1], Explicit -> \ +False]"}, +{"fcstFCChargeConjugateTransposed-ID23", +"FCCCT[SpinorUBar[p1].GA[mu].(GS[p]+m).GA[nu].SpinorU[p2],Explicit\ +\[Rule]True,FCDiracIsolate\[Rule]False]", +"FCChargeConjugateTransposed[Spinor[Momentum[p1], 0, 1] . \ +DiracGamma[LorentzIndex[mu]] . (m + DiracGamma[Momentum[p]]) . \ +DiracGamma[LorentzIndex[nu]] . Spinor[Momentum[p2], 0, 1], Explicit -> \ +False, FCDiracIsolate -> False]"}, +{"fcstFCChargeConjugateTransposed-ID24", +"FCChargeConjugateTransposed[DCHN[GA[mu, 5, nu], i, j], +Explicit -> True, FCE -> True]","DCHN[GA[nu].GA[5].GA[mu], j, i]"}, +{"fcstFCChargeConjugateTransposed-ID25", +"FCChargeConjugateTransposed[DCHN[GA[mu, 5, nu], SpinorUBar[p], i], +Explicit -> True, FCE -> True]","FCChargeConjugateTransposed[ +DCHN[GA[mu].GA[5].GA[nu], Spinor[Momentum[p], 0, 1], i], +Explicit -> False, FeynCalcExternal -> True]"} +}); + diff --git a/Tests/Dirac/FCDiracIsolate.test b/Tests/Dirac/FCDiracIsolate.test index 1307eec68..309226b7f 100644 --- a/Tests/Dirac/FCDiracIsolate.test +++ b/Tests/Dirac/FCDiracIsolate.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCDiracIsolate *) @@ -31,13 +31,12 @@ SpinorUBar[p1,m1].GA[5].SpinorVBar[p2,m2]+zz]", xx*FCGV[\"DiracChain\"][Spinor[Momentum[p1], m1, 1] . DiracGamma[5] . \ Spinor[-Momentum[p2], m2, 1]]"}, {"fcstFCDiracIsolate-ID8", -"FCDiracIsolate[yy GA[i]+xx \ -SpinorUBar[p1,m1].GA[5].SpinorVBar[p2,m2]+zz+DiracTrace[GA[i,j]],\ -DiracGamma\[Rule]False]", -"zz + yy*DiracGamma[LorentzIndex[i]] + \ -DiracTrace[DiracGamma[LorentzIndex[i]] . DiracGamma[LorentzIndex[j]]] \ -+ xx*FCGV[\"DiracChain\"][Spinor[Momentum[p1], m1, 1] . DiracGamma[5] \ -. Spinor[-Momentum[p2], m2, 1]]"}, +"FCDiracIsolate[ +yy GA[i] + xx SpinorUBar[p1, m1].GA[5].SpinorVBar[p2, m2] + zz + +DiracTrace[GA[i, j]], DiracGamma -> False]", +"zz + yy*DiracGamma[LorentzIndex[i]] + +FCGV[\"DiracChain\"][DiracTrace[DiracGamma[LorentzIndex[i]] . DiracGamma[LorentzIndex[j]]]] + +xx*FCGV[\"DiracChain\"][Spinor[Momentum[p1], m1, 1] . DiracGamma[5] . Spinor[-Momentum[p2], m2, 1]]"}, {"fcstFCDiracIsolate-ID9", "FCDiracIsolate[yy GA[i]+xx \ SpinorUBar[p1,m1].GA[5].SpinorVBar[p2,m2]+zz+DiracTrace[GA[i,j]],\ @@ -97,6 +96,197 @@ LorentzIndex -> True, Head -> dch] // FCE", "1/2 I dsHead[GA[i].GA[j]] - 1/2 I dsHead[GA[j].GA[i]]"}, {"fcstFCDiracIsolate-ID19", "FCDiracIsolate[DiracSigma[GA[i], GA[j]], Head -> dsHead]//FCE", -"dsHead[DiracSigma[GA[i], GA[j]]]"} +"dsHead[DiracSigma[GA[i], GA[j]]]"}, +{"fcstFCDiracIsolate-ID20", +"FCDiracIsolate[SI[i].GA[mu, nu, rho].SI[j], Head -> dsHead] // FCE", +"SI[i].SI[j] dsHead[GA[mu].GA[nu].GA[rho]]"}, +{"fcstFCDiracIsolate-ID21", +"Spinor[Momentum[p3, D], m, 1].GAD[Lor4].(m + GSD[l + p3]).GAD[Lor1].Spinor[Momentum[p1, D]] // DiracGammaExpand // +DotSimplify //FCDiracIsolate[#, DiracGammaCombine -> False, Head -> dsHead,FCE->True] &", +"m dsHead[Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GAD[Lor1].Spinor[Momentum[p1, D], 0, 1]] + +dsHead[Spinor[Momentum[p3, D], m, 1].GAD[Lor4].(GSD[l] + GSD[p3]).GAD[Lor1].Spinor[Momentum[p1, D], 0, 1]]"}, +{"fcstFCDiracIsolate-ID22", +"Spinor[Momentum[p3, D], m, 1].GAD[Lor4].(m + GSD[l + p3]).GAD[Lor1].Spinor[Momentum[p1, D]] // DiracGammaExpand // +DotSimplify // FCDiracIsolate[#, DiracGammaCombine -> False, Head -> dch, +FCJoinDOTs -> False, FCE -> True] &", +"m dch[Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GAD[Lor1].Spinor[Momentum[p1, D], 0, 1]] + +dch[Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[l].GAD[Lor1].Spinor[Momentum[p1, D], 0, 1]] + +dch[Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[p3].GAD[Lor1].Spinor[Momentum[p1, D], 0, 1]]"}, +{"fcstFCDiracIsolate-ID23", +"FCDiracIsolate[ +4 Spinor[Momentum[k], m, 1].GA[i].Spinor[Momentum[k], m, 1] Spinor[ + Momentum[p], m, 1].GA[i].Spinor[Momentum[p], m, 1] + +2 Spinor[Momentum[k], m, 1].GA[j].Spinor[Momentum[k], m, 1] Spinor[ + Momentum[p], m, 1].GA[j].Spinor[Momentum[p], m, 1] + +4 Spinor[Momentum[k], m, 1].GA[k].Spinor[Momentum[k], m, 1] Spinor[ + Momentum[p], m, 1].GA[k].Spinor[Momentum[p], m, 1] + +6 Spinor[Momentum[k], m, 1].GA[$MU[$39]].GA[5].Spinor[Momentum[k], + m, 1] Spinor[Momentum[p], m, 1].GA[$MU[$39]].GA[5].Spinor[ + Momentum[p], m, 1], Spinor -> Join, Head -> dch,FCE->True]", +"4 dch[Spinor[Momentum[k], m, 1].GA[i].Spinor[Momentum[k], m, + 1] Spinor[Momentum[p], m, 1].GA[i].Spinor[Momentum[p], m, 1]] + +2 dch[Spinor[Momentum[k], m, 1].GA[j].Spinor[Momentum[k], m, + 1] Spinor[Momentum[p], m, 1].GA[j].Spinor[Momentum[p], m, 1]] + +4 dch[Spinor[Momentum[k], m, 1].GA[k].Spinor[Momentum[k], m, + 1] Spinor[Momentum[p], m, 1].GA[k].Spinor[Momentum[p], m, 1]] + +6 dch[Spinor[Momentum[k], m, 1].GA[$MU[$39]].GA[5].Spinor[ + Momentum[k], m, 1] Spinor[Momentum[p], m, 1].GA[$MU[$39]].GA[ + 5].Spinor[Momentum[p], m, 1]]"}, +{"fcstFCDiracIsolate-ID24", +"FCDiracIsolate[GA[mu].(1 + GA[5]).GA[nu], Head -> dsHead, ToDiracGamma67 -> True]//FCE", +"2 dsHead[GA[mu].GA[6].GA[nu]]"}, +{"fcstFCDiracIsolate-ID25", +"FCDiracIsolate[ +PolarizationVector[p, mu] SP[p1, + p2] SpinorUBar[p, m].GA[i].SpinorV[p, m] + -Eps[LorentzIndex[nu], + LorentzIndex[rho], LorentzIndex[si], + Momentum[Polarization[p, I]]] SP[p1, + p2] SpinorUBar[p2, m].GA[i].SpinorV[p2, m] + g, +Polarization -> True, FCE -> True,Head->di]", +"g + di[Spinor[Momentum[p], m, 1] . GA[i] . Spinor[-Momentum[p], m, 1]* + FV[Polarization[p, I], mu]]*SP[p1, p2] - +di[Spinor[Momentum[p2], m, 1] . GA[i] . Spinor[-Momentum[p2], m, 1]* + LC[nu, rho, si][Polarization[p, I]]]*SP[p1, p2]"}, +{"fcstFCDiracIsolate-ID26", +"FCDiracIsolate[ +a (2 Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] (2 FV[p, a] - FV[q, a]) + + 2 Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] (2 FV[p, b] - FV[q, b]) + + 2 Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, + 1] MT[a, + b]) (4 Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], + m2, 1] (2 FV[p, a] + FV[q, a]) + + 4 Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] (2 FV[p, b] + FV[q, b]) - + m2 Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1] MT[ + a, b] + 4 Spinor[Momentum[p + q], m2, 1].GS[q].Spinor[ + Momentum[p], m2, 1] MT[a, b]), LorentzIndex -> All, +FCJoinDOTs -> True, Spinor -> Join, Head -> dsHead] // FCE", +"32 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], m2, + 1] FV[p, a]^2] + +32 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] FV[p, a] FV[p, b]] + +32 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], m2, + 1] FV[p, a] FV[p, b]] + +32 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] FV[p, b]^2] - +16 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] FV[p, b] FV[q, a]] + +16 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], m2, + 1] FV[p, b] FV[q, a]] - +8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], m2, + 1] FV[q, a]^2] + +16 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] FV[p, a] FV[q, b]] - +16 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], m2, + 1] FV[p, a] FV[q, b]] - +8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] FV[q, a] FV[q, b]] - +8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], m2, + 1] FV[q, a] FV[q, b]] - +8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] FV[q, b]^2] - +4 a m2 dsHead[ +Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1] Spinor[ + Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, 1] FV[p, + a] MT[a, b]] + +16 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], m2, + 1] FV[p, a] MT[a, b]] + +16 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GS[q].Spinor[Momentum[p], m2, + 1] FV[p, a] MT[a, b]] - +4 a m2 dsHead[ +Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1] Spinor[ + Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, 1] FV[p, + b] MT[a, b]] + +16 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] FV[p, b] MT[a, b]] + +16 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GS[q].Spinor[Momentum[p], m2, + 1] FV[p, b] MT[a, b]] + +2 a m2 dsHead[ +Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1] Spinor[ + Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, 1] FV[q, + a] MT[a, b]] + +8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[Momentum[p], m2, + 1] FV[q, a] MT[a, b]] - +8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GS[q].Spinor[Momentum[p], m2, + 1] FV[q, a] MT[a, b]] + +2 a m2 dsHead[ +Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1] Spinor[ + Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, 1] FV[q, + b] MT[a, b]] + +8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] FV[q, b] MT[a, b]] - +8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GS[q].Spinor[Momentum[p], m2, + 1] FV[q, b] MT[a, b]] - +2 a m2 dsHead[ +Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1] Spinor[ + Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, 1] MT[a, + b]^2] + 8 a dsHead[ +Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, + 1] Spinor[Momentum[p + q], m2, 1].GS[q].Spinor[Momentum[p], m2, + 1] MT[a, b]^2]"}, +{"fcstFCDiracIsolate-ID27", "FCDiracIsolate[ +DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], +DiracIndex[j]], FCE -> True]", "DCHN[GA[mu], i, j]"}, +{"fcstFCDiracIsolate-ID28", "FCDiracIsolate[ +DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], +DiracIndex[j]], DiracChain -> True, Head -> dirac, FCE -> True]", "dirac[DCHN[GA[mu], i, j]]"}, +{"fcstFCDiracIsolate-ID29", "FCDiracIsolate[DiracChain[1, DiracIndex[i], DiracIndex[j]] GA[mu], +DiracGamma -> False, DiracChain -> True, Head -> dirac, +FCE -> True]", "dirac[DCHN[1, i, j]]*GA[mu]"}, +{"fcstFCDiracIsolate-ID30", "FCDiracIsolate[CGA[i].CGS[p].CGA[j].CGS[p + q] KD[i, j], +CartesianIndex -> True, Head -> dch, FCE -> True]", "dch[CGA[i].CGS[p].CGA[j].CGS[p + q] KD[i, j]]"}, +{"fcstFCDiracIsolate-ID31", "Spinor[Momentum[p3, D], m, 1].GAD[Lor4].(m + GSD[l + p3]).GAD[ +Lor1].Spinor[Momentum[p1, D]] // DiracGammaExpand // DotSimplify // +FCDiracIsolate[#, DiracGammaCombine -> False, Head -> {dch, re}, + FCJoinDOTs -> False, FCE -> True] &", "Spinor[Momentum[p3, D], m, 1].GAD[Lor4].(m + GSD[l + p3]).GAD[ + Lor1].Spinor[Momentum[p1, D]] // DiracGammaExpand // +DotSimplify // +FCDiracIsolate[#, DiracGammaCombine -> False, Head -> {dch, re}, +FCJoinDOTs -> False, FCE -> True] &"}, +{"fcstFCDiracIsolate-ID32", "FCDiracIsolate[x,Head->{di,re}]", "re[x]"}, +{"fcstFCDiracIsolate-ID33", "FCDiracIsolate[{GA[i], GS[p]}, Head -> di, FCE -> True]", +"{di[GA[i]], di[GS[p]]}"} }); diff --git a/Tests/Dirac/IntegrationTests/DiracSimplify.test b/Tests/Dirac/IntegrationTests/DiracSimplify.test new file mode 100644 index 000000000..68eab660e --- /dev/null +++ b/Tests/Dirac/IntegrationTests/DiracSimplify.test @@ -0,0 +1,25 @@ +Tests`Dirac`fcitDiracSimplify = +({ +{"fcitDiracSimplify-ID1", +"TimeConstrained[ +FCClearScalarProducts[]; {SP[p] = m^2, SP[p1] = m^2, SP[p2] = m^2, +SP[k1] = 0, SP[k2] = 0, SP[q] = u^2, SP[q, s] = 0}; +Line13 := (GS[p2] - m).GA[be1].(GS[p1] + m).GA[be].(GS[p] - m).GA[ + al1].GS[k2].GA[al].(1 - GA[5]); +Line14 := +GS[k1].GA[al1].(GS[q] - GS[p1] - GS[p2] - u).GA[ + be1].(GS[q] - u).(1 + GA[5].GS[s]).GA[ + be].(GS[q] - GS[p1] - GS[p] - u).GA[al].(1 - GA[5]); +Line15 := (GS[p] - m).GA[be1].(GS[p1] + m).GA[be].(GS[p2] - m).GA[ + al1].GS[k2].GA[al].(1 - GA[5]); +Line16 := +GS[k1].GA[al1].(GS[q] - GS[p1] - GS[p] - u).GA[ + be1].(GS[q] - u).(1 + GA[5].GS[s]).GA[ + be].(GS[q] - GS[p1] - GS[p2] - u).GA[al].(1 - GA[5]); +Tr13 = DiracTrace[Line13]; +Tr14 = DiracTrace[Line14]; +Tr15 = DiracTrace[Line15]; +Tr16 = DiracTrace[Line16]; +res = DiracSimplify[Tr13 Tr14 + Tr15 Tr16];, If[$VersionNumber>=9,80,160]]; +LeafCount[res] > 13000", "True"} +}); diff --git a/Tests/Dirac/IntegrationTests/DiracTrace.test b/Tests/Dirac/IntegrationTests/DiracTrace.test new file mode 100644 index 000000000..6066ab7d8 --- /dev/null +++ b/Tests/Dirac/IntegrationTests/DiracTrace.test @@ -0,0 +1,20 @@ +Tests`Dirac`fcitDiracTrace = +({ +{"fcitDiracTrace-ID1", +"TimeConstrained[ +res = DiracTrace[(mc + GSD[k1]).GAD[ + c[li3]].(mc + GSD[k1 + k2 + p - q]).GAD[ + c[ga]].(-mc + GSD[p] - GSD[q]).GA[ + 5].(mc + GSD[p] + GSD[q]).GAD[c[li2]].(-mc + GSD[k2]).GAD[ + li2].(mc + GSD[p] + GSD[q]).GA[5].(-mc + GSD[p] - GSD[q]).GAD[ + ga].(mc - GSD[k2 + 2 p]).GAD[li3], + DiracTraceEvaluate -> True];, If[$VersionNumber>=9,30,60], $Failed]; +LeafCount[res] > 17000000", "True"}, +{"fcitDiracTrace-ID2", +"TimeConstrained[ +res = DiracTrace[ + Dot[GSD[i1],GSD[i2],GSD[i3],GSD[i4],GSD[i5],GSD[i6],GSD[i7], + GSD[i8],GSD[i9],GSD[i10],GSD[i11],GSD[i12],GSD[i13],GSD[i14]], + DiracTraceEvaluate -> True];, If[$VersionNumber>=9,16,32], $Failed]; +LeafCount[res] > 6500000", "True"} +}); diff --git a/Tests/Dirac/IntegrationTests/iTestsDirac.mt b/Tests/Dirac/IntegrationTests/iTestsDirac.mt new file mode 100644 index 000000000..ee8541973 --- /dev/null +++ b/Tests/Dirac/IntegrationTests/iTestsDirac.mt @@ -0,0 +1,30 @@ +(* :Title: iTestsDirac.mt *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Integration tests for functions in the "Dirac" directory *) + +(* ------------------------------------------------------------------------ *) + +Needs["FeynCalc`"]; + +(*$FCAdvice = False;*) + +ClearAll[itestsLorentz]; +itestsLorentz = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "Dirac", "IntegrationTests"}]] +Get/@itestsLorentz; + +FCClearScalarProducts[]; + + + +Map[Test[ExpandAll[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],0,TestID->#[[1]]]&, + Join[ + Tests`Dirac`fcitDiracTrace, + Tests`Dirac`fcitDiracSimplify + ]]; diff --git a/Tests/Dirac/SirlinSimplify.test b/Tests/Dirac/SirlinSimplify.test new file mode 100644 index 000000000..a765044fc --- /dev/null +++ b/Tests/Dirac/SirlinSimplify.test @@ -0,0 +1,274 @@ + + +(* :Title: SirlinSimplify.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for SirlinSimplify *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstSirlinSimplify = +({ +{"fcstSirlinSimplify-ID1", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,nu,6].SpinorU[\ +p1,m1]SpinorUBar[p4,m4].GA[mu,tau,nu,6].SpinorU[p2,m2],FCE\[Rule]True]\ +,\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[6].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[6].Spinor[Momentum[p2],m2,1] \ +MT[rho,tau]]", "True"}, +{"fcstSirlinSimplify-ID2", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,nu,7].SpinorU[\ +p1,m1]SpinorUBar[p4,m4].GA[mu,tau,nu,7].SpinorU[p2,m2],FCE\[Rule]True]\ +,\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[7].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[7].Spinor[Momentum[p2],m2,1] \ +MT[rho,tau]]", "True"}, +{"fcstSirlinSimplify-ID3", +"SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,nu,6].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,tau,nu,7].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[tau] . GA[6] . \ +Spinor[Momentum[p1], m1, 1]*Spinor[Momentum[p4], m4, 1] . GA[rho] . \ +GA[7] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSirlinSimplify-ID4", +"SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,nu,7].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,tau,nu,6].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[tau] . GA[7] . \ +Spinor[Momentum[p1], m1, 1]*Spinor[Momentum[p4], m4, 1] . GA[rho] . \ +GA[6] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSirlinSimplify-ID5", +"SirlinSimplify[SpinorUBar[p3,m3].GA[nu,rho,mu,7].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,tau,nu,7].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[tau] . GA[7] . \ +Spinor[Momentum[p1], m1, 1]*Spinor[Momentum[p4], m4, 1] . GA[rho] . \ +GA[7] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSirlinSimplify-ID6", +"SirlinSimplify[SpinorUBar[p3,m3].GA[nu,rho,mu,6].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,tau,nu,6].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[tau] . GA[6] . \ +Spinor[Momentum[p1], m1, 1]*Spinor[Momentum[p4], m4, 1] . GA[rho] . \ +GA[6] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSirlinSimplify-ID7", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[nu,rho,mu,6].SpinorU[\ +p1,m1]SpinorUBar[p2,m2].GA[mu,tau,nu,7].SpinorU[p4,m4],FCE\[Rule]True]\ +,\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[6].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p2],m2,1].GA[a_].GA[7].Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]]", "True"}, +{"fcstSirlinSimplify-ID8", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[nu,rho,mu,7].SpinorU[\ +p1,m1]SpinorUBar[p2,m2].GA[mu,tau,nu,6].SpinorU[p4,m4],FCE\[Rule]True]\ +,\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[7].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p2],m2,1].GA[a_].GA[6].Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]]", "True"}, +{"fcstSirlinSimplify-ID9", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].nc1.GA[mu,rho,nu].nc2.\ +SpinorU[p1,m1]SpinorUBar[p4,m4].nc3.GA[mu,tau,nu].nc4.SpinorU[p4,m4],\ +FCE\[Rule]True],\[IndentingNewLine]2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[tau].nc2.Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].nc3.GA[rho].nc4.Spinor[Momentum[p4],m4,1]-2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[tau].nc2.GA[5].Spinor[Momentum[p1],\ +m1,1] Spinor[Momentum[p4],m4,1].nc3.GA[rho].nc4.GA[5].Spinor[Momentum[\ +p4],m4,1]+2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[a_].nc2.Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].nc3.GA[a_].nc4.Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]+2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[a_].nc2.GA[5].Spinor[Momentum[p1],m1,\ +1] Spinor[Momentum[p4],m4,1].nc3.GA[a_].nc4.GA[5].Spinor[Momentum[p4],\ +m4,1] MT[rho,tau]]", "True"}, +{"fcstSirlinSimplify-ID10", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].nc1.GA[nu,rho,mu].nc2.\ +SpinorU[p1,m1]SpinorUBar[p4,m4].nc3.GA[mu,tau,nu].nc4.SpinorU[p4,m4],\ +FCE\[Rule]True],\[IndentingNewLine]2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[tau].nc2.Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].nc3.GA[rho].nc4.Spinor[Momentum[p4],m4,1]+2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[tau].nc2.GA[5].Spinor[Momentum[p1],\ +m1,1] Spinor[Momentum[p4],m4,1].nc3.GA[rho].nc4.GA[5].Spinor[Momentum[\ +p4],m4,1]+2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[a_].nc2.Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].nc3.GA[a_].nc4.Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]-2 \ +Spinor[Momentum[p3],m3,1].nc1.GA[a_].nc2.GA[5].Spinor[Momentum[p1],m1,\ +1] Spinor[Momentum[p4],m4,1].nc3.GA[a_].nc4.GA[5].Spinor[Momentum[p4],\ +m4,1] MT[rho,tau]]", "True"}, +{"fcstSirlinSimplify-ID11", +"SirlinSimplify[SpinorUBar[p3,m3].GA[mu,nu,6].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,nu,7].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[6] . Spinor[Momentum[p1], m1, \ +1]*Spinor[Momentum[p4], m4, 1] . GA[7] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSirlinSimplify-ID12", +"SirlinSimplify[SpinorUBar[p3,m3].GA[mu,nu,7].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[mu,nu,6].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[7] . Spinor[Momentum[p1], m1, \ +1]*Spinor[Momentum[p4], m4, 1] . GA[6] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSirlinSimplify-ID13", +"SirlinSimplify[SpinorUBar[p3,m3].GA[mu,nu,6].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[nu,mu,7].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[6] . Spinor[Momentum[p1], m1, \ +1]*Spinor[Momentum[p4], m4, 1] . GA[7] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSirlinSimplify-ID14", +"SirlinSimplify[SpinorUBar[p3,m3].GA[mu,nu,7].SpinorU[p1,m1]\ +SpinorUBar[p4,m4].GA[nu,mu,6].SpinorU[p2,m2],FCE\[Rule]True]", +"4*Spinor[Momentum[p3], m3, 1] . GA[7] . Spinor[Momentum[p1], m1, \ +1]*Spinor[Momentum[p4], m4, 1] . GA[6] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSirlinSimplify-ID15", +"MatchQ[SirlinSimplify[SpinorUBar[p1,m1].GA[mu,nu,6].SpinorU[p2,m2]\ +SpinorUBar[p3,m3].GA[mu,nu,6].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]-\!\(\*FractionBox[\(1\), \(2\)]\) \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p4],m4,1]+4 \ +Spinor[Momentum[p1],m1,1].GA[6].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[6].Spinor[Momentum[p4],m4,1]-\!\(\*\ +FractionBox[\(1\), \(4\)]\) \[ImaginaryI] \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS283_],GA[liS284_]].Spinor[\ +Momentum[p4],m4,1] LC[liS281_,liS282_,liS283_,liS284_]]", "True"}, +{"fcstSirlinSimplify-ID16", +"MatchQ[SirlinSimplify[SpinorUBar[p1,m1].GA[mu,nu,7].SpinorU[p2,m2]\ +SpinorUBar[p3,m3].GA[mu,nu,7].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]-\!\(\*FractionBox[\(1\), \(2\)]\) \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p4],m4,1]+4 \ +Spinor[Momentum[p1],m1,1].GA[7].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[7].Spinor[Momentum[p4],m4,1]+\!\(\*\ +FractionBox[\(1\), \(4\)]\) \[ImaginaryI] \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS283_],GA[liS284_]].Spinor[\ +Momentum[p4],m4,1] LC[liS281_,liS282_,liS283_,liS284_]]", "True"}, +{"fcstSirlinSimplify-ID17", +"MatchQ[SirlinSimplify[SpinorUBar[p1,m1].GA[mu,nu,6].SpinorU[p2,m2]\ +SpinorUBar[p3,m3].GA[nu,mu,6].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]\!\(\*FractionBox[\(1\), \(2\)]\) \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p4],m4,1]+4 \ +Spinor[Momentum[p1],m1,1].GA[6].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[6].Spinor[Momentum[p4],m4,1]+\!\(\*\ +FractionBox[\(1\), \(4\)]\) \[ImaginaryI] \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS283_],GA[liS284_]].Spinor[\ +Momentum[p4],m4,1] LC[liS281_,liS282_,liS283_,liS284_]]", "True"}, +{"fcstSirlinSimplify-ID18", +"MatchQ[SirlinSimplify[SpinorUBar[p1,m1].GA[mu,nu,7].SpinorU[p2,m2]\ +SpinorUBar[p3,m3].GA[nu,mu,7].SpinorU[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]\!\(\*FractionBox[\(1\), \(2\)]\) \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p4],m4,1]+4 \ +Spinor[Momentum[p1],m1,1].GA[7].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[7].Spinor[Momentum[p4],m4,1]-\!\(\*\ +FractionBox[\(1\), \(4\)]\) \[ImaginaryI] \ +Spinor[Momentum[p1],m1,1].DiracSigma[GA[liS281_],GA[liS282_]].Spinor[\ +Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].DiracSigma[GA[liS283_],GA[liS284_]].Spinor[\ +Momentum[p4],m4,1] LC[liS281_,liS282_,liS283_,liS284_]]", "True"}, +{"fcstSirlinSimplify-ID19", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[6].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[mu,al,si,be,nu].GA[6].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]16 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[6].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[6].Spinor[Momentum[p4],m4,1] \ +MT[al,rho] MT[be,tau]]", "True"}, +{"fcstSirlinSimplify-ID20", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[7].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[mu,al,si,be,nu].GA[7].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]16 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[7].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[7].Spinor[Momentum[p4],m4,1] \ +MT[al,rho] MT[be,tau]]", "True"}, +{"fcstSirlinSimplify-ID21", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[6].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[mu,al,si,be,nu].GA[7].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[rho].GA[be].GA[6].Spinor[Momentum[\ +p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[al].GA[tau].GA[7].Spinor[Momentum[\ +p4],m4,1]]", "True"}, +{"fcstSirlinSimplify-ID22", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[7].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[mu,al,si,be,nu].GA[6].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[rho].GA[be].GA[7].Spinor[Momentum[\ +p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[al].GA[tau].GA[6].Spinor[Momentum[\ +p4],m4,1]]", "True"}, +{"fcstSirlinSimplify-ID23", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[6].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[nu,al,si,be,mu].GA[6].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[be].GA[tau].GA[a_].GA[6].Spinor[Momentum[\ +p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[al].GA[rho].GA[6].Spinor[Momentum[\ +p4],m4,1]]", "True"}, +{"fcstSirlinSimplify-ID24", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[7].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[nu,al,si,be,mu].GA[7].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]4 \ +Spinor[Momentum[p3],m3,1].GA[be].GA[tau].GA[a_].GA[7].Spinor[Momentum[\ +p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[al].GA[rho].GA[7].Spinor[Momentum[\ +p4],m4,1]]", "True"}, +{"fcstSirlinSimplify-ID25", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[6].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[nu,al,si,be,mu].GA[7].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]16 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[6].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[7].Spinor[Momentum[p4],m4,1] \ +MT[al,tau] MT[be,rho]]", "True"}, +{"fcstSirlinSimplify-ID26", +"MatchQ[SirlinSimplify[SpinorUBar[p3,m3].GA[mu,rho,si,tau \ +,nu].GA[7].SpinorU[p1,m1]SpinorUBar[p4,m4].GA[nu,al,si,be,mu].GA[6].\ +SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine]16 \ +Spinor[Momentum[p3],m3,1].GA[a_].GA[7].Spinor[Momentum[p1],m1,1] \ +Spinor[Momentum[p4],m4,1].GA[a_].GA[6].Spinor[Momentum[p4],m4,1] \ +MT[al,tau] MT[be,rho]]", "True"}, +{"fcstSirlinSimplify-ID27", +"MatchQ[SirlinSimplify[SpinorUBar[p1,m1].GA[mu,rho,nu].(1/2+la1/2 \ +GA[5]).SpinorU[p2,m2]SpinorUBar[p3,m3].GA[mu,tau,nu].(1/2+la2/2 \ +GA[5]).SpinorU[p4,m4],FCE\[Rule]True],\[IndentingNewLine](1-la1) \ +(1+la2) Spinor[Momentum[p1],m1,1].GA[tau].GA[7].Spinor[Momentum[p2],\ +m2,1] Spinor[Momentum[p3],m3,1].GA[rho].GA[6].Spinor[Momentum[p4],m4,\ +1]+(1+la1) (1-la2) \ +Spinor[Momentum[p1],m1,1].GA[tau].GA[6].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[rho].GA[7].Spinor[Momentum[p4],m4,1]+(1+\ +la1) (1+la2) \ +Spinor[Momentum[p1],m1,1].GA[liS428_].GA[6].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[liS428_].GA[6].Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]+(1-la1) (1-la2) \ +Spinor[Momentum[p1],m1,1].GA[liS428_].GA[7].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[liS428_].GA[7].Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]]", "True"}, +{"fcstSirlinSimplify-ID28", +"MatchQ[SirlinSimplify[SpinorUBar[p1,m1].GA[nu,rho,mu].(1/2+la1/2 \ +GA[5]).SpinorU[p2,m2]SpinorUBar[p3,m3].GA[mu,tau,nu].(1/2+la2/2 \ +GA[5]).SpinorU[p4,m4],FCE\[Rule]True],(1+la1) (1+la2) \ +Spinor[Momentum[p1],m1,1].GA[tau].GA[6].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[rho].GA[6].Spinor[Momentum[p4],m4,1]+(1-\ +la1) (1-la2) \ +Spinor[Momentum[p1],m1,1].GA[tau].GA[7].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[rho].GA[7].Spinor[Momentum[p4],m4,1]+(1-\ +la1) (1+la2) \ +Spinor[Momentum[p1],m1,1].GA[liS463_].GA[7].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[liS463_].GA[6].Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]+(1+la1) (1-la2) \ +Spinor[Momentum[p1],m1,1].GA[liS463_].GA[6].Spinor[Momentum[p2],m2,1] \ +Spinor[Momentum[p3],m3,1].GA[liS463_].GA[7].Spinor[Momentum[p4],m4,1] \ +MT[rho,tau]]", "True"} +}); diff --git a/Tests/Dirac/SpinorChainChiralSplit.test b/Tests/Dirac/SpinorChainChiralSplit.test new file mode 100644 index 000000000..a0229031d --- /dev/null +++ b/Tests/Dirac/SpinorChainChiralSplit.test @@ -0,0 +1,52 @@ + + +(* :Title: SpinorChainChiralSplit.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for SpinorChainChiralSplit *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstSpinorChainChiralSplit = +({ +{"fcstSpinorChainChiralSplit-ID1", "SpinorChainChiralSplit[GA[5]]", +"DiracGamma[5]"}, +{"fcstSpinorChainChiralSplit-ID2", +"SpinorChainChiralSplit[SpinorUBar[p1,m1].GSD[p].SpinorV[p2,m2]]", +"Spinor[Momentum[p1], m1, 1] . DiracGamma[Momentum[p, D], D] . \ +DiracGamma[6] . Spinor[-Momentum[p2], m2, 1] + Spinor[Momentum[p1], \ +m1, 1] . DiracGamma[Momentum[p, D], D] . DiracGamma[7] . \ +Spinor[-Momentum[p2], m2, 1]"}, +{"fcstSpinorChainChiralSplit-ID3", +"SpinorChainChiralSplit[SpinorUBar[p1,m1].GSD[p].SpinorV[p2,m2]+x]\ +", "x + Spinor[Momentum[p1], m1, 1] . DiracGamma[Momentum[p, D], D] . \ +DiracGamma[6] . Spinor[-Momentum[p2], m2, 1] + Spinor[Momentum[p1], \ +m1, 1] . DiracGamma[Momentum[p, D], D] . DiracGamma[7] . \ +Spinor[-Momentum[p2], m2, 1]"}, +{"fcstSpinorChainChiralSplit-ID4", +"SpinorChainChiralSplit[SpinorUBar[p1,m1].GSD[p].GA[5].SpinorV[p2,\ +m2]]", "Spinor[Momentum[p1], m1, 1] . DiracGamma[Momentum[p, D], D] . \ +DiracGamma[6] . Spinor[-Momentum[p2], m2, 1] - Spinor[Momentum[p1], \ +m1, 1] . DiracGamma[Momentum[p, D], D] . DiracGamma[7] . \ +Spinor[-Momentum[p2], m2, 1]"}, +{"fcstSpinorChainChiralSplit-ID5", +"SpinorChainChiralSplit[SpinorUBar[p1,m1].GSD[p].GA[5].SpinorV[p2,\ +m2],DiracSubstitute5\[Rule]False]", +"Spinor[Momentum[p1], m1, 1] . DiracGamma[Momentum[p, D], D] . \ +DiracGamma[5] . Spinor[-Momentum[p2], m2, 1]"}, +{"fcstSpinorChainChiralSplit-ID6", +"SpinorChainChiralSplit[SpinorUBar[p1,m1].GSD[p].GA[5].SpinorV[p2,\ +m2],Head\[Rule]dhead]", +"dhead[Spinor[Momentum[p1], m1, 1] . DiracGamma[Momentum[p, D], D] \ +. DiracGamma[6] . Spinor[-Momentum[p2], m2, 1]] - \ +dhead[Spinor[Momentum[p1], m1, 1] . DiracGamma[Momentum[p, D], D] . \ +DiracGamma[7] . Spinor[-Momentum[p2], m2, 1]]"} +}); diff --git a/Tests/Dirac/SpinorChainTranspose.test b/Tests/Dirac/SpinorChainTranspose.test new file mode 100644 index 000000000..ee361b10f --- /dev/null +++ b/Tests/Dirac/SpinorChainTranspose.test @@ -0,0 +1,98 @@ + + +(* :Title: SpinorChainTranspose.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for SpinorChainTranspose *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstSpinorChainTranspose = +({ +{"fcstSpinorChainTranspose-ID1", "SpinorChainTranspose[1]", "1"}, +{"fcstSpinorChainTranspose-ID2", "SpinorChainTranspose[GA[mu]]", +"DiracGamma[LorentzIndex[mu]]"}, +{"fcstSpinorChainTranspose-ID3", +"SpinorChainTranspose[SpinorUBar[p1,m1].SpinorU[p2,m2]]", +"Spinor[Momentum[p1], m1, 1] . Spinor[Momentum[p2], m2, 1]"}, +{"fcstSpinorChainTranspose-ID4", +"SpinorChainTranspose[SpinorUBar[p1,m1].SpinorV[p2,m2]]", +"Spinor[Momentum[p1], m1, 1] . Spinor[-Momentum[p2], m2, 1]"}, +{"fcstSpinorChainTranspose-ID5", +"SpinorChainTranspose[SpinorUBarD[p1,m1].SpinorUD[p2,m2]]", +"Spinor[Momentum[p1, D], m1, 1] . Spinor[Momentum[p2, D], m2, \ +1]"}, +{"fcstSpinorChainTranspose-ID6", +"SpinorChainTranspose[SpinorUBarD[p1,m1].SpinorVD[p2,m2]]", +"Spinor[Momentum[p1, D], m1, 1] . Spinor[-Momentum[p2, D], m2, 1]"}, +{"fcstSpinorChainTranspose-ID7", +"SpinorChainTranspose[SpinorVBar[p1,m1].SpinorU[p2,m2]]", +"-Spinor[-Momentum[p2], m2, 1] . Spinor[Momentum[p1], m1, 1]"}, +{"fcstSpinorChainTranspose-ID8", +"SpinorChainTranspose[SpinorVBar[p1,m1].SpinorV[p2,m2]]", +"-Spinor[Momentum[p2], m2, 1] . Spinor[Momentum[p1], m1, 1]"}, +{"fcstSpinorChainTranspose-ID9", +"SpinorChainTranspose[SpinorVBarD[p1,m1].SpinorUD[p2,m2]]", +"-Spinor[-Momentum[p2, D], m2, 1] . Spinor[Momentum[p1, D], m1, \ +1]"}, +{"fcstSpinorChainTranspose-ID10", +"SpinorChainTranspose[SpinorVBarD[p1,m1].SpinorVD[p2,m2]]", +"-Spinor[Momentum[p2, D], m2, 1] . Spinor[Momentum[p1, D], m1, 1]"}, +{"fcstSpinorChainTranspose-ID11", +"SpinorChainTranspose[SpinorVBar[p1,m1].GA[mu,nu].SpinorU[p2,m2]]", + "-Spinor[-Momentum[p2], m2, 1] . DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[LorentzIndex[mu]] . Spinor[Momentum[p1], m1, 1]"}, +{"fcstSpinorChainTranspose-ID12", +"SpinorChainTranspose[SpinorVBar[p1,m1].GA[mu,nu].SpinorV[p2,m2]]", + "-Spinor[Momentum[p2], m2, 1] . DiracGamma[LorentzIndex[nu]] . \ +DiracGamma[LorentzIndex[mu]] . Spinor[Momentum[p1], m1, 1]"}, +{"fcstSpinorChainTranspose-ID13", +"SpinorChainTranspose[SpinorVBarD[p1,m1].GAD[mu,nu].SpinorUD[p2,m2]\ +]", "-Spinor[-Momentum[p2, D], m2, 1] . DiracGamma[LorentzIndex[nu, \ +D], D] . DiracGamma[LorentzIndex[mu, D], D] . Spinor[Momentum[p1, D], \ +m1, 1]"}, +{"fcstSpinorChainTranspose-ID14", +"SpinorChainTranspose[SpinorVBarD[p1,m1].GAD[mu,nu].SpinorVD[p2,m2]\ +]", "-Spinor[Momentum[p2, D], m2, 1] . DiracGamma[LorentzIndex[nu, \ +D], D] . DiracGamma[LorentzIndex[mu, D], D] . Spinor[Momentum[p1, D], \ +m1, 1]"}, +{"fcstSpinorChainTranspose-ID15", +"SpinorChainTranspose[SpinorVBarD[p1,m1].GAD[mu,nu].FCNCA.SpinorVD[\ +p2,m2]]", +"-Spinor[Momentum[p2, D], m2, 1] . \ +FCChargeConjugateTransposed[FCNCA, Explicit -> False, \ +FeynCalcInternal -> True, DotSimplify -> False] . \ +DiracGamma[LorentzIndex[nu, D], D] . DiracGamma[LorentzIndex[mu, D], \ +D] . Spinor[Momentum[p1, D], m1, 1]"}, +{"fcstSpinorChainTranspose-ID16", +"SpinorChainTranspose[Spinor[Momentum[k],m,1].GA[6].GS[l].GA[7].\ +Spinor[-Momentum[l],m,1]+Spinor[Momentum[l],m,1].GA[6].GS[l].GA[7].\ +Spinor[-Momentum[k],m,1]]", +"Spinor[Momentum[k], m, 1] . DiracGamma[6] . \ +DiracGamma[Momentum[l]] . DiracGamma[7] . Spinor[-Momentum[l], m, 1] \ ++ Spinor[Momentum[l], m, 1] . DiracGamma[6] . DiracGamma[Momentum[l]] \ +. DiracGamma[7] . Spinor[-Momentum[k], m, 1]"}, +{"fcstSpinorChainTranspose-ID17", +"SpinorChainTranspose[Spinor[Momentum[k],m,1].GA[6].GS[l].GA[7].\ +Spinor[-Momentum[l],m,1]+Spinor[Momentum[l],m,1].GA[6].GS[l].GA[7].\ +Spinor[-Momentum[k],m,1],Select\[Rule]{{SpinorUBar[k,m],SpinorV[l,m]}}\ +]", "Spinor[Momentum[l], m, 1] . DiracGamma[6] . \ +DiracGamma[Momentum[l]] . DiracGamma[7] . Spinor[-Momentum[k], m, 1] \ ++ Spinor[Momentum[l], m, 1] . DiracGamma[7] . DiracGamma[Momentum[l]] \ +. DiracGamma[6] . Spinor[-Momentum[k], m, 1]"}, +{"fcstSpinorChainTranspose-ID18","SpinorChainTranspose[DCHN[GA[mu, 5, nu], SpinorVBar[p], SpinorU[q]], +FCE -> True]","-Spinor[-Momentum[q], 0, 1].GA[nu].GA[5].GA[mu].Spinor[Momentum[p], 0, + 1]"}, +{"fcstSpinorChainTranspose-ID19","SpinorChainTranspose[DCHN[SpinorVBar[p], SpinorU[q]], FCE -> True]", + "-Spinor[-Momentum[q], 0, 1].Spinor[Momentum[p], 0, 1]"}, +{"fcstSpinorChainTranspose-ID20","SpinorChainTranspose[DCHN[1, SpinorVBar[p], SpinorU[q]], FCE -> True]", + "-Spinor[-Momentum[q], 0, 1].Spinor[Momentum[p], 0, 1]"} +}); diff --git a/Tests/Dirac/SpinorChainTrick.test b/Tests/Dirac/SpinorChainTrick.test new file mode 100644 index 000000000..2a296f395 --- /dev/null +++ b/Tests/Dirac/SpinorChainTrick.test @@ -0,0 +1,132 @@ + + +(* :Title: SpinorChainTrick.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for SpinorChainTrick *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstSpinorChainTrick = +({ +{"fcstSpinorChainTrick-ID1", "SpinorChainTrick[0]", "0"}, +{"fcstSpinorChainTrick-ID2", "SpinorChainTrick[a]", "a"}, +{"fcstSpinorChainTrick-ID3", +"SpinorChainTrick[SpinorUBar[p1,m1].GA[mu].SpinorU[p2,m2],FCE\ +\[Rule]True]", +"Spinor[Momentum[p1], m1, 1] . GA[mu] . Spinor[Momentum[p2], m2, \ +1]"}, +{"fcstSpinorChainTrick-ID4", +"MatchQ[SpinorChainTrick[SpinorUBar[p1,m1].GA[mu].SpinorU[p2,m2]\ +SpinorVBar[p1,m1].GA[mu].SpinorV[p4,m4],FCE\[Rule]True],\ +\[IndentingNewLine]Spinor[-Momentum[p1],m1,1].GA[FCGV[x_]].Spinor[-\ +Momentum[p4],m4,1] \ +Spinor[Momentum[p1],m1,1].GA[FCGV[x_]].Spinor[Momentum[p2],m2,1]]", +"True"}, +{"fcstSpinorChainTrick-ID5", +"MatchQ[\[IndentingNewLine]SpinorChainTrick[a \ +SpinorUBar[p1,m1].GA[mu].SpinorU[p2,m2]SpinorVBar[p1,m1].GA[mu].\ +SpinorV[p4,m4]+\[IndentingNewLine]b \ +SpinorUBar[p1,m1].GA[nu].SpinorU[p2,m2]SpinorVBar[p1,m1].GA[nu].\ +SpinorV[p4,m4],FCE\[Rule]True],\[IndentingNewLine](a+b) \ +Spinor[-Momentum[p1],m1,1].GA[FCGV[x_]].Spinor[-Momentum[p4],m4,1] \ +Spinor[Momentum[p1],m1,1].GA[FCGV[x_]].Spinor[Momentum[p2],m2,1]]", +"True"}, +{"fcstSpinorChainTrick-ID6", +"SpinorChainTrick[ +a SpinorUBar[p1, m1].GA[mu].SpinorU[p2, m2] SpinorVBar[p1, m1].GAE[ + mu].SpinorV[p4, m4] + +b SpinorUBar[p1, m1].GAE[nu].SpinorU[p2, m2] SpinorVBar[p1, m1].GA[ + nu].SpinorV[p4, m4], FCE -> True]", +"0"}, +{"fcstSpinorChainTrick-ID7", +"MatchQ[SpinorChainTrick[ +a SpinorUBar[p1, m1].GA[mu].SpinorU[p2, m2] SpinorVBar[p1, m1].GAD[ + mu].SpinorV[p4, m4] + +b SpinorUBar[p1, m1].GA[nu].SpinorU[p2, m2] SpinorVBar[p1, m1].GAD[ + nu].SpinorV[p4, m4], +FCE -> True], (a + b) Spinor[-Momentum[p1], m1, 1].GA[ + FCGV[x_]].Spinor[-Momentum[p4], m4, 1] Spinor[Momentum[p1], m1, + 1].GA[FCGV[x_]].Spinor[Momentum[p2], m2, 1]]", +"True"}, +{"fcstSpinorChainTrick-ID8", +"FCSetDiracGammaScheme[\"BMHV\"]; \n tmp=MatchQ[SpinorChainTrick[ +a SpinorUBar[p1, m1].GAE[mu].SpinorU[p2, m2] SpinorVBar[p1, m1].GAD[ + mu].SpinorV[p4, m4] + +b SpinorUBar[p1, m1].GAE[nu].SpinorU[p2, m2] SpinorVBar[p1, + m1].GAD[nu].SpinorV[p4, m4], +FCE -> True], (a + b) Spinor[-Momentum[p1], m1, 1].GAE[ + FCGV[x_]].Spinor[-Momentum[p4], m4, 1] Spinor[Momentum[p1], m1, + 1].GAE[FCGV[x_]].Spinor[Momentum[p2], m2, 1]]; \n +FCSetDiracGammaScheme[\"NDR\"]; \n tmp", +"True"}, +{"fcstSpinorChainTrick-ID9", +"MatchQ[SpinorChainTrick[ +SpinorUBar[p1, m1].GA[mu, rho, nu].(1/2 + la1/2 GA[5]).SpinorU[p2, + m2] SpinorUBar[p3, m3].GA[mu, tau, + nu].(1/2 + la2/2 GA[5]).SpinorU[p4, m4], FCE -> True], +Spinor[Momentum[p1], m1, 1].GA[l1_].GA[rho].GA[ + l2_].(1/2 + 1/2 la1 GA[5]).Spinor[Momentum[p2], m2, 1] Spinor[ + Momentum[p3], m3, 1].GA[l1_].GA[tau].GA[ + l2_].(1/2 + 1/2 la2 GA[5]).Spinor[Momentum[p4], m4, 1] +]", +"True"}, +{"fcstSpinorChainTrick-ID10", +"SpinorChainTrick[ +z (8 Spinor[Momentum[p - q], m1, 1].GA[b].Spinor[Momentum[p], m1, + 1] (2 FV[p, a] - FV[q, a]) + + 8 Spinor[Momentum[p - q], m1, 1].GA[a].Spinor[Momentum[p], m1, + 1] (2 FV[p, b] - FV[q, b]) + + 8 Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, + 1] MT[a, + b]) (4 Spinor[Momentum[p + q], m2, 1].GA[b].Spinor[ + Momentum[p], m2, 1] (2 FV[p, a] + FV[q, a]) + + 4 Spinor[Momentum[p + q], m2, 1].GA[a].Spinor[Momentum[p], m2, + 1] (2 FV[p, b] + FV[q, b]) - + m2 Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1] MT[ + a, b] + 4 Spinor[Momentum[p + q], m2, 1].GS[q].Spinor[ + Momentum[p], m2, 1] MT[a, b])] // +FCCanonicalizeDummyIndices[#, + LorentzIndexNames -> {mu, nu}] & // FCE", +"224*m1*m2*z*Spinor[Momentum[p - q], m1, 1].Spinor[Momentum[p], m1, 1]* +Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1] + +240*m2*z*Spinor[Momentum[p + q], m2, 1].Spinor[Momentum[p], m2, 1]* +Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, 1] + +64*z*Spinor[Momentum[p - q], m1, 1].GS[q].Spinor[Momentum[p], m1, 1]* +Spinor[Momentum[p + q], m2, 1].GS[q].Spinor[Momentum[p], m2, 1] + +64*z*Spinor[Momentum[p - q], m1, 1].GA[mu].Spinor[Momentum[p], m1, + 1]*Spinor[Momentum[p + q], m2, 1].GA[mu].Spinor[Momentum[p], m2, + 1]*(4*SP[p, p] - SP[q, q])"}, +{"fcstSpinorChainTrick-ID11", +"MatchQ[SpinorChainTrick[ +SpinorUBar[p].GA[mu, nu].SpinorV[q] DiracTrace[ + x1 GA[mu, nu] + x2 GA[nu, mu]]], +x1 DiracTrace[ + DiracGamma[LorentzIndex[a_FCGV]].DiracGamma[ + LorentzIndex[b_FCGV]]] Spinor[Momentum[p], 0, 1].DiracGamma[ + LorentzIndex[a_FCGV]].DiracGamma[ + LorentzIndex[b_FCGV]].Spinor[-Momentum[q], 0, 1] + +x2 DiracTrace[ + DiracGamma[LorentzIndex[a_FCGV]].DiracGamma[ + LorentzIndex[b_FCGV]]] Spinor[Momentum[p], 0, 1].DiracGamma[ + LorentzIndex[b_FCGV]].DiracGamma[ + LorentzIndex[a_FCGV]].Spinor[-Momentum[q], 0, 1]]","True"}, +{"fcstSpinorChainTrick-ID12","SpinorChainTrick[ +SpinorUBar[p].GA[mu, nu].SpinorV[q] DiracTrace[ +x1 GA[mu, nu] + x2 GA[nu, mu]], +LorentzIndexNames -> Table[mu[i], {i, 1, 10}], FCE -> True]", +"x1 DiracTrace[ +GA[mu[1]].GA[mu[2]]] Spinor[Momentum[p], 0, 1].GA[mu[1]].GA[ + mu[2]].Spinor[-Momentum[q], 0, 1] + +x2 DiracTrace[ +GA[mu[1]].GA[mu[2]]] Spinor[Momentum[p], 0, 1].GA[mu[2]].GA[ + mu[1]].Spinor[-Momentum[q], 0, 1]"} +}); diff --git a/Tests/Dirac/ToDiracGamma67.test b/Tests/Dirac/ToDiracGamma67.test new file mode 100644 index 000000000..9945e23b1 --- /dev/null +++ b/Tests/Dirac/ToDiracGamma67.test @@ -0,0 +1,61 @@ + + +(* :Title: ToDiracGamma67.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for ToDiracGamma67 *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Dirac`fcstToDiracGamma67 = +({ +{"fcstToDiracGamma67-ID1", +"ToDiracGamma67[(1/2+GA[5]/2),FCE\[Rule]True]", "GA[6]"}, +{"fcstToDiracGamma67-ID2", +"ToDiracGamma67[(1/2-GA[5]/2),FCE\[Rule]True]", "GA[7]"}, +{"fcstToDiracGamma67-ID3", +"ToDiracGamma67[1/2(1+GA[5]),FCE\[Rule]True]", "GA[6]"}, +{"fcstToDiracGamma67-ID4", +"ToDiracGamma67[1/2(1-GA[5]),FCE\[Rule]True]", "GA[7]"}, +{"fcstToDiracGamma67-ID5", +"ToDiracGamma67[4(1+GA[5]),FCE\[Rule]True]", "8*GA[6]"}, +{"fcstToDiracGamma67-ID6", +"ToDiracGamma67[3(1+GA[5]),FCE\[Rule]True]", "6*GA[6]"}, +{"fcstToDiracGamma67-ID7", +"ToDiracGamma67[GA[mu].(1/2+GA[5]/2).GA[nu],FCE\[Rule]True]", +"GA[mu] . GA[6] . GA[nu]"}, +{"fcstToDiracGamma67-ID8", +"ToDiracGamma67[GA[mu].(1/2-GA[5]/2).GA[nu],FCE\[Rule]True]", +"GA[mu] . GA[7] . GA[nu]"}, +{"fcstToDiracGamma67-ID9", +"ToDiracGamma67[GA[mu].(1/2(1+GA[5])).GA[nu],FCE\[Rule]True]", +"GA[mu] . GA[6] . GA[nu]"}, +{"fcstToDiracGamma67-ID10", +"ToDiracGamma67[GA[mu].(1/2(1-GA[5])).GA[nu],FCE\[Rule]True]", +"GA[mu] . GA[7] . GA[nu]"}, +{"fcstToDiracGamma67-ID11", +"ToDiracGamma67[GA[mu].(4(1+GA[5])).GA[nu],FCE\[Rule]True]", +"GA[mu] . (8*GA[6]) . GA[nu]"}, +{"fcstToDiracGamma67-ID12", +"ToDiracGamma67[GA[mu].(3(1-GA[5])).GA[nu],FCE\[Rule]True]", +"GA[mu] . (6*GA[7]) . GA[nu]"}, +{"fcstToDiracGamma67-ID13", "ToDiracGamma67[GA[5],FCE\[Rule]True]", +"GA[5]"}, +{"fcstToDiracGamma67-ID14", +"ToDiracGamma67[GA[5],All\[Rule]True,FCE\[Rule]True]", +"GA[6] - GA[7]"}, +{"fcstToDiracGamma67-ID15", +"ToDiracGamma67[GA[mu,5,nu],FCE\[Rule]True]", +"GA[mu] . GA[5] . GA[nu]"}, +{"fcstToDiracGamma67-ID16", +"ToDiracGamma67[GA[mu,5,nu],All\[Rule]True,FCE\[Rule]True]", +"GA[mu] . (GA[6] - GA[7]) . GA[nu]"} +}); diff --git a/Tests/Dirac/ToDiracSigma.test b/Tests/Dirac/ToDiracSigma.test index 7a4030a7a..fc361b97a 100644 --- a/Tests/Dirac/ToDiracSigma.test +++ b/Tests/Dirac/ToDiracSigma.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ToDiracSigma *) @@ -26,5 +26,13 @@ Tests`Dirac`fcstToDiracSigma = {"fcstToDiracSigma-ID4", "DiracSigmaExplicit[DiracSigma[DiracGamma[LorentzIndex[i]],\ DiracGamma[LorentzIndex[j]]]]//ToDiracSigma[#,GA[i],GA[j]]&\ -//ToDiracSigma[#,GA[j],GA[i]]&//FCE", "DiracSigma[GA[i], GA[j]]"} +//ToDiracSigma[#,GA[j],GA[i]]&//FCE", "DiracSigma[GA[i], GA[j]]"}, + +{"fcstToDiracSigma-ID5", "ToDiracSigma[CGA[i, j], CGA[i], CGA[j]] // FCE","-I DiracSigma[CGA[i], CGA[j]] - KD[i, j]"}, +{"fcstToDiracSigma-ID6", "ToDiracSigma[CGA[i, j], CGA[m], CGA[j]] // FCE","CGA[i].CGA[j]"}, +{"fcstToDiracSigma-ID7", "ToDiracSigma[CGA[i, j, k], CGA[i], CGA[j]] // FCE","-I DiracSigma[CGA[i], CGA[j]].CGA[k] - CGA[k] KD[i, j]"}, +{"fcstToDiracSigma-ID8", "DiracSigmaExplicit[ + DiracSigma[DiracGamma[CartesianIndex[i]], DiracGamma[CartesianIndex[j]]]] // +ToDiracSigma[#, CGA[i], CGA[j]] & // +ToDiracSigma[#, CGA[j], CGA[i]] & // FCE","DiracSigma[CGA[i], CGA[j]]"} }) diff --git a/Tests/Dirac/ToLarin.test b/Tests/Dirac/ToLarin.test index 404b7305f..f3a42612a 100644 --- a/Tests/Dirac/ToLarin.test +++ b/Tests/Dirac/ToLarin.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ToLarin *) @@ -17,12 +17,15 @@ Tests`Dirac`fcstToLarin = { {"fcstToLarin-ID1","MatchQ[(tmp = ToLarin[GAD[i1, i2, i3, i4, i5, i6].GA[5]]; FCE[tmp]), 1/6 I GAD[i1].GAD[i2].GAD[i3].GAD[i4].GAD[i5].GAD[x_].GAD[y_].GAD[ z_] LCD[x_, y_, z_, i6]]","True"}, -{"fcstToLarin-ID2","MatchQ[(tmp = +{"fcstToLarin-ID2","FCE[EpsEvaluate[ +FCCanonicalizeDummyIndices[ ToLarin[DiracTrace[GAD[i1, i2, i3, i4, i5, i6].GA[5]] DiracTrace[ - GAD[i1, j2, j3, j4, j5, j6].GA[5]]]; FCE[tmp]), -DiracTrace[ -1/6 I GAD[i1].GAD[i2].GAD[i3].GAD[i4].GAD[i5].GAD[a_].GAD[b_].GAD[ - c_] LCD[a_, b_, c_, i6]] DiracTrace[ -1/6 I GAD[i1].GAD[j2].GAD[j3].GAD[j4].GAD[j5].GAD[d_].GAD[e_].GAD[ - f_] LCD[d_, e_, f_, j6]]]","True"} + GAD[i1, j2, j3, j4, j5, j6].GA[5]]], +LorentzIndexNames -> {al, be, ga, mu, nu, rho, si}]]]","-(1/36) DiracTrace[ +GAD[al].GAD[i2].GAD[i3].GAD[i4].GAD[i5].GAD[be].GAD[ga].GAD[ + mu]] DiracTrace[ +GAD[al].GAD[j2].GAD[j3].GAD[j4].GAD[j5].GAD[nu].GAD[rho].GAD[ + si]] LCD[be, ga, i6, mu] LCD[j6, nu, rho, si]"}, +{"fcstToLarin-ID3","FCE[ToLarin[GAD[i1, i2, i3, i4, i5].CGA[i6].GA[5]]]", +"GAD[i1].GAD[i2].GAD[i3].GAD[i4].GAD[i5].CGA[i6].GA[5]"} } diff --git a/Tests/Dirac/Tr.test b/Tests/Dirac/Tr.test index cd5c1eab9..4d81de53d 100644 --- a/Tests/Dirac/Tr.test +++ b/Tests/Dirac/Tr.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for TR *) @@ -46,14 +46,14 @@ Tests`Dirac`fcstTr = { Pair[Momentum[p], Momentum[p]]*Pair[Momentum[p], Momentum[Derivative[1][p]]]"}, {"fcstTr-ID6", - "$BreitMaison=True; \n tmp = Tr[DiracMatrix[b, Dimension -> D].DiracMatrix[a, + "FCSetDiracGammaScheme[\"BMHV\"]; \n tmp = Tr[DiracMatrix[b, Dimension -> D].DiracMatrix[a, Dimension -> D].DiracGamma[Momentum[p1]].DiracGamma[ Momentum[p2]].DiracMatrix[nu, Dimension -> D].DiracMatrix[b, Dimension -> D].DiracGamma[Momentum[p2]].DiracGamma[ Momentum[p3]].DiracMatrix[a, Dimension -> D].DiracGamma[ Momentum[p1]].DiracMatrix[nu, Dimension -> D].DiracGamma[ Momentum[p3]].DiracGamma[Momentum[p1]].DiracGamma[Momentum[p2]], - PairCollect -> True]; \n $BreitMaison=False; \n tmp", + PairCollect -> True]; \n FCSetDiracGammaScheme[\"NDR\"]; \n tmp", "-4*((288 - 224*D + 56*D^2 - 4*D^3)*Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], Momentum[p3]]^2*Pair[Momentum[p2], Momentum[p2]] + (-256 + 128*D - 16*D^2)*Pair[Momentum[p1], Momentum[p2]]^2*Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p2], Momentum[p3]] + @@ -99,8 +99,8 @@ Tests`Dirac`fcstTr = { 4*Pair[LorentzIndex[rho], Momentum[p1]]*Pair[LorentzIndex[sigma], Momentum[p1]] - 2*Pair[LorentzIndex[rho], Momentum[k1]]*Pair[LorentzIndex[sigma], Momentum[p2]] + 4*Pair[LorentzIndex[rho], Momentum[p1]]*Pair[LorentzIndex[sigma], Momentum[p2]])"}, -{"fcST-TR-ID11", - "$BreitMaison=True; \n FCClearScalarProducts[]; \n Tr[DiracMatrix[a[1], Dimension -> (d - 4)].DiracMatrix[a[2], +{"fcstTr-ID11", + "FCSetDiracGammaScheme[\"BMHV\"]; \n FCClearScalarProducts[]; \n Tr[DiracMatrix[a[1], Dimension -> (d - 4)].DiracMatrix[a[2], Dimension -> (d - 4)].DiracMatrix[a[3], Dimension -> (d - 4)]. DiracMatrix[a[4], Dimension -> (d - 4)].DiracMatrix[a[5], Dimension -> (d - 4)].DiracMatrix[a[6], @@ -116,7 +116,7 @@ Tests`Dirac`fcstTr = { Dimension -> (d - 4)]] // Expand","123469824 - 135962624*d + 63224832*d^2 - 16145920*d^3 + 2461760*d^4 - 227584*d^5 + 12320*d^6 - 352*d^7 + 4*d^8"}, -{"fcST-TR-ID12","Tr[DiracMatrix[a[1], Dimension -> (d - 4)].DiracMatrix[a[2], +{"fcstTr-ID12","Tr[DiracMatrix[a[1], Dimension -> (d - 4)].DiracMatrix[a[2], Dimension -> (d - 4)].DiracMatrix[a[3], Dimension -> (d - 4)]. DiracMatrix[a[4], Dimension -> (d - 4)].DiracMatrix[a[5], Dimension -> (d - 4)].DiracMatrix[a[6], @@ -135,7 +135,7 @@ Tests`Dirac`fcstTr = { "-1879576576 + 2220901376*d - 1127626752*d^2 + 321806848*d^3 - 56625408*d^4 + 6331584*d^5 - 446208*d^6 + 18912*d^7 - 432*d^8 + 4*d^9"}, -{"fcST-TR-ID13", +{"fcstTr-ID13", "Tr[DiracMatrix[a[1], Dimension -> (d - 4)].DiracMatrix[a[2], Dimension -> (d - 4)].DiracMatrix[a[3], Dimension -> (d - 4)]. DiracMatrix[a[4], Dimension -> (d - 4)].DiracMatrix[a[5], @@ -157,7 +157,7 @@ Tests`Dirac`fcstTr = { "-31023169536 + 38971179008*d - 21328977920*d^2 + 6679521280*d^3 - 1320732160*d^4 + 171464832*d^5 - 14710080*d^6 + 816960*d^7 - 27840*d^8 + 520*d^9 - 4*d^10"}, -{"fcST-TR-ID14", +{"fcstTr-ID14", "Tr[DiracMatrix[a[1], Dimension -> (d - 4)].DiracMatrix[a[2], Dimension -> (d - 4)].DiracMatrix[a[3], Dimension -> (d - 4)]. DiracMatrix[a[4], Dimension -> (d - 4)].DiracMatrix[a[5], @@ -184,6 +184,7 @@ Tests`Dirac`fcstTr = { {"fcstTr-ID15","Tr[DiracTrace[GA[i, j]]] // FCE","16 MT[i, j]"}, {"fcstTr-ID16","Tr[GSD[pv3].GAD[n2].GSD[pv4].GAE[i1].GA[5]]","0"}, {"fcstTr-ID17","Tr[GSD[pv3, pv4, pv5].GAD[n2].GSD[pv4].GAE[i1].GA[5]]","0"}, +{"fcstTr-ID18","Tr[CGA[i, j]]","-4 CartesianPair[CartesianIndex[i], CartesianIndex[j]]"}, {"fcstTr-ID19"," {$LeviCivitaSign = 1;\n FCE[Tr[GA[i1, i2, i3, i4, 5]]], $LeviCivitaSign = -1;\n FCE[Tr[GA[i1, i2, i3, i4, 5]]], $LeviCivitaSign = 1;\n FCE[Tr[GA[i1, i2, i3, i4, 5]]], @@ -273,8 +274,63 @@ tmp", mc2 (mc2^2 + ms2^2 - s - u) (YiPR Ys1CC Ys2 + YiPRCC Ys1 Ys2CC) - mb (mc1^2 (YiPRCC Ys1 Ys2 + YiPR Ys1CC Ys2CC) + (mc2^2 - s) * (YiPRCC Ys1 Ys2 + YiPR Ys1CC Ys2CC) + -2 mc1 mc2 (YiPR Ys1 Ys2 + YiPRCC Ys1CC Ys2CC))"} +2 mc1 mc2 (YiPR Ys1 Ys2 + YiPRCC Ys1CC Ys2CC))"}, +{"fcstTr-ID27", + "FCSetDiracGammaScheme[\"BMHV\"]; \n tmp = FCE[Simplify[Tr[GAD[al].GA[5].GAD[al, la, mu, nu, rho]] + + Tr[GA[5].GAD[al].GAD[al, la, mu, nu, rho]]]]; \n tmp", + "-8 I (-4 + D) LC[la, mu, nu, rho]"}, +{"fcstTr-ID28", "Tr[GS[p].GS[p].GS[r]]", "0"}, +{"fcstTr-ID29", "Tr[GS[p].GS[q].GS[r]]", "0"}, +{"fcstTr-ID30", + "FCSetDiracGammaScheme[\"BMHV\"]; \n FCClearScalarProducts[]; \n ScalarProduct[p, p, SetDimensions -> {4, D, D - 4}] = 0; \n ScalarProduct[l, l, SetDimensions -> {4, D, D - 4}] = 0; \n + ScalarProduct[o, o, SetDimensions -> {4, D, D - 4}] = 0; \n + tmp = (SelectFree[ + Expand[Contract[ + (-1)Tr[GAD[rho].GSD[o].GAD[rho].(GSD[l] + GSD[o]).GAD[ + mu].(1 - GA[5]).GSD[p].GAD[ + nu].(1 - GA[5]).(GSD[l] + GSD[o])]*I* + LCD[mu, nu, al, bet] FVD[p, al] FVD[o + l - p, + bet]] /. + Pair[h1_[a1_, d_Symbol], h2_[a2_, d_Symbol]] :> + Pair[h1[a1], h2[a2]] - + Pair[h1[a1, d - 4], h2[a2, d - 4]]], D - 4]/4/2/ + SP[l, o]/2/SP[l, o]) /. D -> 4 + 2*eps // +ExpandScalarProduct // Expand // FCE; \n FCClearScalarProducts[]; \n tmp", + "-((4 SP[l, p]^2)/SP[l, o]) - (4 eps SP[l, p]^2)/SP[l, o] - (4 SP[l, p] SP[o, p])/SP[l, o] - (4 eps SP[l, p] SP[o, p])/SP[l, o]"}, +{"fcstTr-ID31", + "FCSetDiracGammaScheme[\"BMHV\"]; \n FCClearScalarProducts[]; \n ScalarProduct[p, p, SetDimensions -> {4, D, D - 4}] = 0; \n ScalarProduct[l, l, SetDimensions -> {4, D, D - 4}] = 0; \n + ScalarProduct[o, o, SetDimensions -> {4, D, D - 4}] = 0; \n + tmp = (SelectFree[ + Expand[Contract[(-1) Tr[ + GSD[o].GAD[rho].(GSD[l] + GSD[o]).GAD[ + mu].(1 - GA[5]).GSD[p].GAD[ + nu].(1 - GA[5]).(GSD[l] + GSD[o]).GAD[rho]]*I* + LCD[mu, nu, al, bet] FVD[p, al] FVD[o + l - p, + bet]] /. + Pair[h1_[a1_, d_Symbol], h2_[a2_, d_Symbol]] :> + Pair[h1[a1], h2[a2]] - + Pair[h1[a1, d - 4], h2[a2, d - 4]]], D - 4]/4/2/ + SP[l, o]/2/SP[l, o]) /. D -> 4 + 2*eps // + ExpandScalarProduct // Expand // FCE; \n FCClearScalarProducts[]; \n tmp", + "-((4 SP[l, p]^2)/SP[l, o]) - (4 eps SP[l, p]^2)/SP[l, o] - (4 SP[l, p] SP[o, p])/SP[l, o] - (4 eps SP[l, p] SP[o, p])/SP[l, o]"}, +{"fcstTr-ID32", "Tr[FV[k1 + k2, mu] (GA[al] FV[k1, al] + m).(GA[mu] f1 - 1/2 I/m 1/2 I (GA[mu, nu] - GA[nu, mu]) FV[k1 - k2, nu] f2).(GS[k1] + m)]//FCE", +"8 f1 m (SP[k1, k1] + SP[k1, k2])"}, +{"fcstTr-ID33", "Tr[1/32 GA[m].(1 - GA[5]).GS[k].(1 + GA[5]).GA[n].(1 - GA[5]).GS[p].(1 + GA[5])] // FCE", +"FV[k, n] FV[p, m] + FV[k, m] FV[p, n] - MT[m, n] SP[k, p] +I LC[m, n][k, p]"}, +{"fcstTr-ID34", "Tr[GA[5].(GA[5] + GS[p]).GA[5].GS[q]]//FCE", "-4 SP[p, q]"}, +{"fcstTr-ID35", "Tr[(1 + GA[5].GS[p]).GA[5].GS[q]]//FCE", "-4 SP[p, q]"}, +{"fcstTr-ID36", "Tr[(GA[j].GS[q] - GS[q].GA[j]).(GA[i].GS[q] - GS[q].GA[i])] // FCE", "16*(FV[q, i]*FV[q, j] - MT[i, j]*SP[q, q])"}, +{"fcstTr-ID37", "Tr[DiracSimplify[(GA[j].GS[q] - GS[q].GA[j]).(GA[i].GS[q] - +GS[q].GA[i])]] // FCE", "16*FV[q, i]*FV[q, j] - 16*MT[i, j]*SP[q, q]"}, +{"fcstTr-ID38", "Tr[(GS[p1] + m).(GA[mu].GS[k].GA[nu] + 2 GA[mu] FV[p2, nu]).(GS[p2] + + m).(GA[nu].GS[k].GA[mu] + + 2 GA[mu] FV[p2, nu]), FCE -> True]", "16 (4 m^2 SP[k, k] + 4 m^2 SP[k, p2] + 2 SP[k, p1] SP[k, p2] - +SP[k, k] SP[p1, p2] + 4 m^2 SP[p2, p2] - 2 SP[k, p1] SP[p2, p2] - +2 SP[p1, p2] SP[p2, p2])"}, +{"fcstTr-ID39", "Tr[GA[m].(GA[n].GA[6] + GA[n].GA[7])] // FCE", "4 MT[m, n]"}, +{"fcstTr-ID40", "Tr[GA[i1, i2, 5, i3, i4, i5, i6]] - Tr[GA[i1, i2, i3, i4, i5, i6, 5]]", "0"} }; + (*--------------------------------------------------------------------------------------------------*) Tests`Dirac`fcstTr4AllFreeNoGamma5 = ({ @@ -1264,210 +1320,7 @@ i8])"}, "Tr[GA[i1,i2,i3,i4,i5,i6,i7,i8,i9,5]]//FCE", "0"}, {"fcstTr4AllFreeOneGamma5-ID9", "Tr[GA[i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,5]]//FCE", -"(4*I)*(LC[i5, i6, i7, i9]*MT[i1, i4]*MT[i10, i8]*MT[i2, i3] - -LC[i4, i6, i7, i9]*MT[i1, i5]*MT[i10, i8]*MT[i2, i3] - -LC[i5, i6, i7, i8]*MT[i1, i4]*MT[i10, i9]*MT[i2, i3] + -LC[i4, i6, i7, i8]*MT[i1, i5]*MT[i10, i9]*MT[i2, i3] - -LC[i5, i6, i7, i9]*MT[i1, i3]*MT[i10, i8]*MT[i2, i4] + -LC[i3, i6, i7, i9]*MT[i1, i5]*MT[i10, i8]*MT[i2, i4] + -LC[i5, i6, i7, i8]*MT[i1, i3]*MT[i10, i9]*MT[i2, i4] - -LC[i3, i6, i7, i8]*MT[i1, i5]*MT[i10, i9]*MT[i2, i4] + -LC[i4, i6, i7, i9]*MT[i1, i3]*MT[i10, i8]*MT[i2, i5] - -LC[i3, i6, i7, i9]*MT[i1, i4]*MT[i10, i8]*MT[i2, i5] - -LC[i4, i6, i7, i8]*MT[i1, i3]*MT[i10, i9]*MT[i2, i5] + -LC[i3, i6, i7, i8]*MT[i1, i4]*MT[i10, i9]*MT[i2, i5] + -LC[i5, i6, i7, i9]*MT[i1, i2]*MT[i10, i8]*MT[i3, i4] - -LC[i2, i6, i7, i9]*MT[i1, i5]*MT[i10, i8]*MT[i3, i4] - -LC[i5, i6, i7, i8]*MT[i1, i2]*MT[i10, i9]*MT[i3, i4] + -LC[i2, i6, i7, i8]*MT[i1, i5]*MT[i10, i9]*MT[i3, i4] + -LC[i10, i7, i8, i9]*MT[i1, i6]*MT[i2, i5]*MT[i3, i4] - -LC[i10, i6, i8, i9]*MT[i1, i7]*MT[i2, i5]*MT[i3, i4] + -LC[i1, i6, i7, i9]*MT[i10, i8]*MT[i2, i5]*MT[i3, i4] - -LC[i1, i6, i7, i8]*MT[i10, i9]*MT[i2, i5]*MT[i3, i4] - -LC[i10, i7, i8, i9]*MT[i1, i5]*MT[i2, i6]*MT[i3, i4] + -LC[i10, i5, i8, i9]*MT[i1, i7]*MT[i2, i6]*MT[i3, i4] + -LC[i10, i6, i8, i9]*MT[i1, i5]*MT[i2, i7]*MT[i3, i4] - -LC[i10, i5, i8, i9]*MT[i1, i6]*MT[i2, i7]*MT[i3, i4] - -LC[i4, i6, i7, i9]*MT[i1, i2]*MT[i10, i8]*MT[i3, i5] + -LC[i2, i6, i7, i9]*MT[i1, i4]*MT[i10, i8]*MT[i3, i5] + -LC[i4, i6, i7, i8]*MT[i1, i2]*MT[i10, i9]*MT[i3, i5] - -LC[i2, i6, i7, i8]*MT[i1, i4]*MT[i10, i9]*MT[i3, i5] - -LC[i10, i7, i8, i9]*MT[i1, i6]*MT[i2, i4]*MT[i3, i5] + -LC[i10, i6, i8, i9]*MT[i1, i7]*MT[i2, i4]*MT[i3, i5] - -LC[i1, i6, i7, i9]*MT[i10, i8]*MT[i2, i4]*MT[i3, i5] + -LC[i1, i6, i7, i8]*MT[i10, i9]*MT[i2, i4]*MT[i3, i5] + -LC[i10, i7, i8, i9]*MT[i1, i4]*MT[i2, i6]*MT[i3, i5] - -LC[i10, i4, i8, i9]*MT[i1, i7]*MT[i2, i6]*MT[i3, i5] - -LC[i10, i6, i8, i9]*MT[i1, i4]*MT[i2, i7]*MT[i3, i5] + -LC[i10, i4, i8, i9]*MT[i1, i6]*MT[i2, i7]*MT[i3, i5] + -LC[i10, i7, i8, i9]*MT[i1, i5]*MT[i2, i4]*MT[i3, i6] - -LC[i10, i5, i8, i9]*MT[i1, i7]*MT[i2, i4]*MT[i3, i6] - -LC[i10, i7, i8, i9]*MT[i1, i4]*MT[i2, i5]*MT[i3, i6] + -LC[i10, i4, i8, i9]*MT[i1, i7]*MT[i2, i5]*MT[i3, i6] + -LC[i10, i5, i8, i9]*MT[i1, i4]*MT[i2, i7]*MT[i3, i6] - -LC[i10, i4, i8, i9]*MT[i1, i5]*MT[i2, i7]*MT[i3, i6] - -LC[i10, i6, i8, i9]*MT[i1, i5]*MT[i2, i4]*MT[i3, i7] + -LC[i10, i5, i8, i9]*MT[i1, i6]*MT[i2, i4]*MT[i3, i7] + -LC[i10, i6, i8, i9]*MT[i1, i4]*MT[i2, i5]*MT[i3, i7] - -LC[i10, i4, i8, i9]*MT[i1, i6]*MT[i2, i5]*MT[i3, i7] - -LC[i10, i5, i8, i9]*MT[i1, i4]*MT[i2, i6]*MT[i3, i7] + -LC[i10, i4, i8, i9]*MT[i1, i5]*MT[i2, i6]*MT[i3, i7] + -LC[i3, i6, i7, i9]*MT[i1, i2]*MT[i10, i8]*MT[i4, i5] - -LC[i2, i6, i7, i9]*MT[i1, i3]*MT[i10, i8]*MT[i4, i5] - -LC[i3, i6, i7, i8]*MT[i1, i2]*MT[i10, i9]*MT[i4, i5] + -LC[i2, i6, i7, i8]*MT[i1, i3]*MT[i10, i9]*MT[i4, i5] + -LC[i10, i7, i8, i9]*MT[i1, i6]*MT[i2, i3]*MT[i4, i5] - -LC[i10, i6, i8, i9]*MT[i1, i7]*MT[i2, i3]*MT[i4, i5] + -LC[i1, i6, i7, i9]*MT[i10, i8]*MT[i2, i3]*MT[i4, i5] - -LC[i1, i6, i7, i8]*MT[i10, i9]*MT[i2, i3]*MT[i4, i5] - -LC[i10, i7, i8, i9]*MT[i1, i3]*MT[i2, i6]*MT[i4, i5] + -LC[i10, i3, i8, i9]*MT[i1, i7]*MT[i2, i6]*MT[i4, i5] + -LC[i10, i6, i8, i9]*MT[i1, i3]*MT[i2, i7]*MT[i4, i5] - -LC[i10, i3, i8, i9]*MT[i1, i6]*MT[i2, i7]*MT[i4, i5] + -LC[i10, i7, i8, i9]*MT[i1, i2]*MT[i3, i6]*MT[i4, i5] - -LC[i10, i2, i8, i9]*MT[i1, i7]*MT[i3, i6]*MT[i4, i5] - -LC[i1, i10, i8, i9]*MT[i2, i7]*MT[i3, i6]*MT[i4, i5] - -LC[i10, i6, i8, i9]*MT[i1, i2]*MT[i3, i7]*MT[i4, i5] + -LC[i10, i2, i8, i9]*MT[i1, i6]*MT[i3, i7]*MT[i4, i5] + -LC[i1, i10, i8, i9]*MT[i2, i6]*MT[i3, i7]*MT[i4, i5] - -LC[i10, i7, i8, i9]*MT[i1, i5]*MT[i2, i3]*MT[i4, i6] + -LC[i10, i5, i8, i9]*MT[i1, i7]*MT[i2, i3]*MT[i4, i6] + -LC[i10, i7, i8, i9]*MT[i1, i3]*MT[i2, i5]*MT[i4, i6] - -LC[i10, i3, i8, i9]*MT[i1, i7]*MT[i2, i5]*MT[i4, i6] - -LC[i10, i5, i8, i9]*MT[i1, i3]*MT[i2, i7]*MT[i4, i6] + -LC[i10, i3, i8, i9]*MT[i1, i5]*MT[i2, i7]*MT[i4, i6] - -LC[i10, i7, i8, i9]*MT[i1, i2]*MT[i3, i5]*MT[i4, i6] + -LC[i10, i2, i8, i9]*MT[i1, i7]*MT[i3, i5]*MT[i4, i6] + -LC[i1, i10, i8, i9]*MT[i2, i7]*MT[i3, i5]*MT[i4, i6] + -LC[i10, i5, i8, i9]*MT[i1, i2]*MT[i3, i7]*MT[i4, i6] - -LC[i10, i2, i8, i9]*MT[i1, i5]*MT[i3, i7]*MT[i4, i6] - -LC[i1, i10, i8, i9]*MT[i2, i5]*MT[i3, i7]*MT[i4, i6] + -LC[i10, i6, i8, i9]*MT[i1, i5]*MT[i2, i3]*MT[i4, i7] - -LC[i10, i5, i8, i9]*MT[i1, i6]*MT[i2, i3]*MT[i4, i7] - -LC[i10, i6, i8, i9]*MT[i1, i3]*MT[i2, i5]*MT[i4, i7] + -LC[i10, i3, i8, i9]*MT[i1, i6]*MT[i2, i5]*MT[i4, i7] + -LC[i10, i5, i8, i9]*MT[i1, i3]*MT[i2, i6]*MT[i4, i7] - -LC[i10, i3, i8, i9]*MT[i1, i5]*MT[i2, i6]*MT[i4, i7] + -LC[i10, i6, i8, i9]*MT[i1, i2]*MT[i3, i5]*MT[i4, i7] - -LC[i10, i2, i8, i9]*MT[i1, i6]*MT[i3, i5]*MT[i4, i7] - -LC[i1, i10, i8, i9]*MT[i2, i6]*MT[i3, i5]*MT[i4, i7] - -LC[i10, i5, i8, i9]*MT[i1, i2]*MT[i3, i6]*MT[i4, i7] + -LC[i10, i2, i8, i9]*MT[i1, i5]*MT[i3, i6]*MT[i4, i7] + -LC[i1, i10, i8, i9]*MT[i2, i5]*MT[i3, i6]*MT[i4, i7] + -LC[i10, i7, i8, i9]*MT[i1, i4]*MT[i2, i3]*MT[i5, i6] - -LC[i10, i4, i8, i9]*MT[i1, i7]*MT[i2, i3]*MT[i5, i6] - -LC[i10, i7, i8, i9]*MT[i1, i3]*MT[i2, i4]*MT[i5, i6] + -LC[i10, i3, i8, i9]*MT[i1, i7]*MT[i2, i4]*MT[i5, i6] + -LC[i10, i4, i8, i9]*MT[i1, i3]*MT[i2, i7]*MT[i5, i6] - -LC[i10, i3, i8, i9]*MT[i1, i4]*MT[i2, i7]*MT[i5, i6] + -LC[i10, i7, i8, i9]*MT[i1, i2]*MT[i3, i4]*MT[i5, i6] - -LC[i10, i2, i8, i9]*MT[i1, i7]*MT[i3, i4]*MT[i5, i6] - -LC[i1, i10, i8, i9]*MT[i2, i7]*MT[i3, i4]*MT[i5, i6] - -LC[i10, i4, i8, i9]*MT[i1, i2]*MT[i3, i7]*MT[i5, i6] + -LC[i10, i2, i8, i9]*MT[i1, i4]*MT[i3, i7]*MT[i5, i6] + -LC[i1, i10, i8, i9]*MT[i2, i4]*MT[i3, i7]*MT[i5, i6] + -LC[i10, i3, i8, i9]*MT[i1, i2]*MT[i4, i7]*MT[i5, i6] - -LC[i10, i2, i8, i9]*MT[i1, i3]*MT[i4, i7]*MT[i5, i6] - -LC[i1, i10, i8, i9]*MT[i2, i3]*MT[i4, i7]*MT[i5, i6] - -LC[i10, i6, i8, i9]*MT[i1, i4]*MT[i2, i3]*MT[i5, i7] + -LC[i10, i4, i8, i9]*MT[i1, i6]*MT[i2, i3]*MT[i5, i7] + -LC[i10, i6, i8, i9]*MT[i1, i3]*MT[i2, i4]*MT[i5, i7] - -LC[i10, i3, i8, i9]*MT[i1, i6]*MT[i2, i4]*MT[i5, i7] - -LC[i10, i4, i8, i9]*MT[i1, i3]*MT[i2, i6]*MT[i5, i7] + -LC[i10, i3, i8, i9]*MT[i1, i4]*MT[i2, i6]*MT[i5, i7] - -LC[i10, i6, i8, i9]*MT[i1, i2]*MT[i3, i4]*MT[i5, i7] + -LC[i10, i2, i8, i9]*MT[i1, i6]*MT[i3, i4]*MT[i5, i7] + -LC[i1, i10, i8, i9]*MT[i2, i6]*MT[i3, i4]*MT[i5, i7] + -LC[i10, i4, i8, i9]*MT[i1, i2]*MT[i3, i6]*MT[i5, i7] - -LC[i10, i2, i8, i9]*MT[i1, i4]*MT[i3, i6]*MT[i5, i7] - -LC[i1, i10, i8, i9]*MT[i2, i4]*MT[i3, i6]*MT[i5, i7] - -LC[i10, i3, i8, i9]*MT[i1, i2]*MT[i4, i6]*MT[i5, i7] + -LC[i10, i2, i8, i9]*MT[i1, i3]*MT[i4, i6]*MT[i5, i7] + -LC[i1, i10, i8, i9]*MT[i2, i3]*MT[i4, i6]*MT[i5, i7] + -LC[i3, i4, i5, i9]*MT[i1, i2]*MT[i10, i8]*MT[i6, i7] - -LC[i2, i4, i5, i9]*MT[i1, i3]*MT[i10, i8]*MT[i6, i7] - -LC[i3, i4, i5, i8]*MT[i1, i2]*MT[i10, i9]*MT[i6, i7] + -LC[i2, i4, i5, i8]*MT[i1, i3]*MT[i10, i9]*MT[i6, i7] + -LC[i10, i5, i8, i9]*MT[i1, i4]*MT[i2, i3]*MT[i6, i7] - -LC[i10, i4, i8, i9]*MT[i1, i5]*MT[i2, i3]*MT[i6, i7] + -LC[i1, i4, i5, i9]*MT[i10, i8]*MT[i2, i3]*MT[i6, i7] - -LC[i1, i4, i5, i8]*MT[i10, i9]*MT[i2, i3]*MT[i6, i7] - -LC[i10, i5, i8, i9]*MT[i1, i3]*MT[i2, i4]*MT[i6, i7] + -LC[i10, i3, i8, i9]*MT[i1, i5]*MT[i2, i4]*MT[i6, i7] + -LC[i10, i4, i8, i9]*MT[i1, i3]*MT[i2, i5]*MT[i6, i7] - -LC[i10, i3, i8, i9]*MT[i1, i4]*MT[i2, i5]*MT[i6, i7] + -LC[i10, i5, i8, i9]*MT[i1, i2]*MT[i3, i4]*MT[i6, i7] - -LC[i10, i2, i8, i9]*MT[i1, i5]*MT[i3, i4]*MT[i6, i7] - -LC[i1, i10, i8, i9]*MT[i2, i5]*MT[i3, i4]*MT[i6, i7] - -LC[i10, i4, i8, i9]*MT[i1, i2]*MT[i3, i5]*MT[i6, i7] + -LC[i10, i2, i8, i9]*MT[i1, i4]*MT[i3, i5]*MT[i6, i7] + -LC[i1, i10, i8, i9]*MT[i2, i4]*MT[i3, i5]*MT[i6, i7] + -LC[i10, i3, i8, i9]*MT[i1, i2]*MT[i4, i5]*MT[i6, i7] - -LC[i10, i2, i8, i9]*MT[i1, i3]*MT[i4, i5]*MT[i6, i7] + -LC[i1, i2, i3, i9]*MT[i10, i8]*MT[i4, i5]*MT[i6, i7] - -LC[i1, i2, i3, i8]*MT[i10, i9]*MT[i4, i5]*MT[i6, i7] - -LC[i1, i10, i8, i9]*MT[i2, i3]*MT[i4, i5]*MT[i6, i7] + -LC[i1, i2, i3, i5]*MT[i10, i9]*MT[i4, i8]*MT[i6, i7] - -LC[i1, i2, i3, i5]*MT[i10, i8]*MT[i4, i9]*MT[i6, i7] - -LC[i1, i2, i3, i4]*MT[i10, i9]*MT[i5, i8]*MT[i6, i7] + -LC[i1, i2, i3, i4]*MT[i10, i8]*MT[i5, i9]*MT[i6, i7] + -LC[i3, i4, i5, i7]*MT[i1, i2]*MT[i10, i9]*MT[i6, i8] - -LC[i2, i4, i5, i7]*MT[i1, i3]*MT[i10, i9]*MT[i6, i8] + -LC[i1, i4, i5, i7]*MT[i10, i9]*MT[i2, i3]*MT[i6, i8] + -LC[i1, i2, i3, i7]*MT[i10, i9]*MT[i4, i5]*MT[i6, i8] - -LC[i1, i2, i3, i5]*MT[i10, i9]*MT[i4, i7]*MT[i6, i8] + -LC[i1, i2, i3, i4]*MT[i10, i9]*MT[i5, i7]*MT[i6, i8] - -LC[i3, i4, i5, i7]*MT[i1, i2]*MT[i10, i8]*MT[i6, i9] + -LC[i2, i4, i5, i7]*MT[i1, i3]*MT[i10, i8]*MT[i6, i9] - -LC[i1, i4, i5, i7]*MT[i10, i8]*MT[i2, i3]*MT[i6, i9] - -LC[i1, i2, i3, i7]*MT[i10, i8]*MT[i4, i5]*MT[i6, i9] + -LC[i1, i2, i3, i5]*MT[i10, i8]*MT[i4, i7]*MT[i6, i9] - -LC[i1, i2, i3, i4]*MT[i10, i8]*MT[i5, i7]*MT[i6, i9] - -LC[i3, i4, i5, i6]*MT[i1, i2]*MT[i10, i9]*MT[i7, i8] + -LC[i2, i4, i5, i6]*MT[i1, i3]*MT[i10, i9]*MT[i7, i8] - -LC[i1, i4, i5, i6]*MT[i10, i9]*MT[i2, i3]*MT[i7, i8] - -LC[i1, i2, i3, i6]*MT[i10, i9]*MT[i4, i5]*MT[i7, i8] + -LC[i1, i2, i3, i5]*MT[i10, i9]*MT[i4, i6]*MT[i7, i8] - -LC[i1, i2, i3, i4]*MT[i10, i9]*MT[i5, i6]*MT[i7, i8] + -LC[i3, i4, i5, i6]*MT[i1, i2]*MT[i10, i8]*MT[i7, i9] - -LC[i2, i4, i5, i6]*MT[i1, i3]*MT[i10, i8]*MT[i7, i9] + -LC[i1, i4, i5, i6]*MT[i10, i8]*MT[i2, i3]*MT[i7, i9] + -LC[i1, i2, i3, i6]*MT[i10, i8]*MT[i4, i5]*MT[i7, i9] - -LC[i1, i2, i3, i5]*MT[i10, i8]*MT[i4, i6]*MT[i7, i9] + -LC[i1, i2, i3, i4]*MT[i10, i8]*MT[i5, i6]*MT[i7, i9] + -LC[i3, i4, i5, i7]*MT[i1, i2]*MT[i10, i6]*MT[i8, i9] - -LC[i2, i4, i5, i7]*MT[i1, i3]*MT[i10, i6]*MT[i8, i9] - -LC[i3, i4, i5, i6]*MT[i1, i2]*MT[i10, i7]*MT[i8, i9] + -LC[i2, i4, i5, i6]*MT[i1, i3]*MT[i10, i7]*MT[i8, i9] + -LC[i10, i5, i6, i7]*MT[i1, i4]*MT[i2, i3]*MT[i8, i9] - -LC[i10, i4, i6, i7]*MT[i1, i5]*MT[i2, i3]*MT[i8, i9] + -LC[i1, i4, i5, i7]*MT[i10, i6]*MT[i2, i3]*MT[i8, i9] - -LC[i1, i4, i5, i6]*MT[i10, i7]*MT[i2, i3]*MT[i8, i9] - -LC[i10, i5, i6, i7]*MT[i1, i3]*MT[i2, i4]*MT[i8, i9] + -LC[i10, i3, i6, i7]*MT[i1, i5]*MT[i2, i4]*MT[i8, i9] + -LC[i10, i4, i6, i7]*MT[i1, i3]*MT[i2, i5]*MT[i8, i9] - -LC[i10, i3, i6, i7]*MT[i1, i4]*MT[i2, i5]*MT[i8, i9] + -LC[i10, i5, i6, i7]*MT[i1, i2]*MT[i3, i4]*MT[i8, i9] - -LC[i10, i2, i6, i7]*MT[i1, i5]*MT[i3, i4]*MT[i8, i9] - -LC[i1, i10, i6, i7]*MT[i2, i5]*MT[i3, i4]*MT[i8, i9] - -LC[i10, i4, i6, i7]*MT[i1, i2]*MT[i3, i5]*MT[i8, i9] + -LC[i10, i2, i6, i7]*MT[i1, i4]*MT[i3, i5]*MT[i8, i9] + -LC[i1, i10, i6, i7]*MT[i2, i4]*MT[i3, i5]*MT[i8, i9] + -LC[i10, i3, i6, i7]*MT[i1, i2]*MT[i4, i5]*MT[i8, i9] - -LC[i10, i2, i6, i7]*MT[i1, i3]*MT[i4, i5]*MT[i8, i9] + -LC[i1, i2, i3, i7]*MT[i10, i6]*MT[i4, i5]*MT[i8, i9] - -LC[i1, i2, i3, i6]*MT[i10, i7]*MT[i4, i5]*MT[i8, i9] - -LC[i1, i10, i6, i7]*MT[i2, i3]*MT[i4, i5]*MT[i8, i9] + -LC[i1, i2, i3, i5]*MT[i10, i7]*MT[i4, i6]*MT[i8, i9] - -LC[i1, i2, i3, i5]*MT[i10, i6]*MT[i4, i7]*MT[i8, i9] - -LC[i1, i2, i3, i4]*MT[i10, i7]*MT[i5, i6]*MT[i8, i9] + -LC[i1, i2, i3, i4]*MT[i10, i6]*MT[i5, i7]*MT[i8, i9] + -LC[i10, i3, i4, i5]*MT[i1, i2]*MT[i6, i7]*MT[i8, i9] - -LC[i10, i2, i4, i5]*MT[i1, i3]*MT[i6, i7]*MT[i8, i9] + -LC[i1, i2, i3, i5]*MT[i10, i4]*MT[i6, i7]*MT[i8, i9] - -LC[i1, i2, i3, i4]*MT[i10, i5]*MT[i6, i7]*MT[i8, i9] - -LC[i1, i10, i4, i5]*MT[i2, i3]*MT[i6, i7]*MT[i8, i9] - -LC[i1, i10, i2, i3]*MT[i4, i5]*MT[i6, i7]*MT[i8, i9])"} +"4*(I*LC[i5, i6, i7, i9]*MT[i1, i4]*MT[i10, i8]*MT[i2, i3] - I*LC[i4, i6, i7, i9]*MT[i1, i5]*MT[i10, i8]*MT[i2, i3] - I*LC[i5, i6, i7, i8]*MT[i1, i4]*MT[i10, i9]*MT[i2, i3] + I*LC[i4, i6, i7, i8]*MT[i1, i5]*MT[i10, i9]*MT[i2, i3] - I*LC[i5, i6, i7, i9]*MT[i1, i3]*MT[i10, i8]*MT[i2, i4] + I*LC[i3, i6, i7, i9]*MT[i1, i5]*MT[i10, i8]*MT[i2, i4] + I*LC[i5, i6, i7, i8]*MT[i1, i3]*MT[i10, i9]*MT[i2, i4] - I*LC[i3, i6, i7, i8]*MT[i1, i5]*MT[i10, i9]*MT[i2, i4] + I*LC[i4, i6, i7, i9]*MT[i1, i3]*MT[i10, i8]*MT[i2, i5] - I*LC[i3, i6, i7, i9]*MT[i1, i4]*MT[i10, i8]*MT[i2, i5] - I*LC[i4, i6, i7, i8]*MT[i1, i3]*MT[i10, i9]*MT[i2, i5] + I*LC[i3, i6, i7, i8]*MT[i1, i4]*MT[i10, i9]*MT[i2, i5] + I*LC[i5, i6, i7, i9]*MT[i1, i2]*MT[i10, i8]*MT[i3, i4] - I*LC[i2, i6, i7, i9]*MT[i1, i5]*MT[i10, i8]*MT[i3, i4] - I*LC[i5, i6, i7, i8]*MT[i1, i2]*MT[i10, i9]*MT[i3, i4] + I*LC[i2, i6, i7, i8]*MT[i1, i5]*MT[i10, i9]*MT[i3, i4] + I*LC[i10, i7, i8, i9]*MT[i1, i6]*MT[i2, i5]*MT[i3, i4] - I*LC[i10, i6, i8, i9]*MT[i1, i7]*MT[i2, i5]*MT[i3, i4] + I*LC[i1, i6, i7, i9]*MT[i10, i8]*MT[i2, i5]*MT[i3, i4] - I*LC[i1, i6, i7, i8]*MT[i10, i9]*MT[i2, i5]*MT[i3, i4] - I*LC[i10, i7, i8, i9]*MT[i1, i5]*MT[i2, i6]*MT[i3, i4] + I*LC[i10, i5, i8, i9]*MT[i1, i7]*MT[i2, i6]*MT[i3, i4] + I*LC[i10, i6, i8, i9]*MT[i1, i5]*MT[i2, i7]*MT[i3, i4] - I*LC[i10, i5, i8, i9]*MT[i1, i6]*MT[i2, i7]*MT[i3, i4] - I*LC[i4, i6, i7, i9]*MT[i1, i2]*MT[i10, i8]*MT[i3, i5] + I*LC[i2, i6, i7, i9]*MT[i1, i4]*MT[i10, i8]*MT[i3, i5] + I*LC[i4, i6, i7, i8]*MT[i1, i2]*MT[i10, i9]*MT[i3, i5] - I*LC[i2, i6, i7, i8]*MT[i1, i4]*MT[i10, i9]*MT[i3, i5] - I*LC[i10, i7, i8, i9]*MT[i1, i6]*MT[i2, i4]*MT[i3, i5] + I*LC[i10, i6, i8, i9]*MT[i1, i7]*MT[i2, i4]*MT[i3, i5] - I*LC[i1, i6, i7, i9]*MT[i10, i8]*MT[i2, i4]*MT[i3, i5] + I*LC[i1, i6, i7, i8]*MT[i10, i9]*MT[i2, i4]*MT[i3, i5] + I*LC[i10, i7, i8, i9]*MT[i1, i4]*MT[i2, i6]*MT[i3, i5] - I*LC[i10, i4, i8, i9]*MT[i1, i7]*MT[i2, i6]*MT[i3, i5] - I*LC[i10, i6, i8, i9]*MT[i1, i4]*MT[i2, i7]*MT[i3, i5] + I*LC[i10, i4, i8, i9]*MT[i1, i6]*MT[i2, i7]*MT[i3, i5] + I*LC[i10, i7, i8, i9]*MT[i1, i5]*MT[i2, i4]*MT[i3, i6] - I*LC[i10, i5, i8, i9]*MT[i1, i7]*MT[i2, i4]*MT[i3, i6] - I*LC[i10, i7, i8, i9]*MT[i1, i4]*MT[i2, i5]*MT[i3, i6] + I*LC[i10, i4, i8, i9]*MT[i1, i7]*MT[i2, i5]*MT[i3, i6] + I*LC[i10, i5, i8, i9]*MT[i1, i4]*MT[i2, i7]*MT[i3, i6] - I*LC[i10, i4, i8, i9]*MT[i1, i5]*MT[i2, i7]*MT[i3, i6] - I*LC[i10, i6, i8, i9]*MT[i1, i5]*MT[i2, i4]*MT[i3, i7] + I*LC[i10, i5, i8, i9]*MT[i1, i6]*MT[i2, i4]*MT[i3, i7] + I*LC[i10, i6, i8, i9]*MT[i1, i4]*MT[i2, i5]*MT[i3, i7] - I*LC[i10, i4, i8, i9]*MT[i1, i6]*MT[i2, i5]*MT[i3, i7] - I*LC[i10, i5, i8, i9]*MT[i1, i4]*MT[i2, i6]*MT[i3, i7] + I*LC[i10, i4, i8, i9]*MT[i1, i5]*MT[i2, i6]*MT[i3, i7] + I*LC[i3, i6, i7, i9]*MT[i1, i2]*MT[i10, i8]*MT[i4, i5] - I*LC[i2, i6, i7, i9]*MT[i1, i3]*MT[i10, i8]*MT[i4, i5] - I*LC[i3, i6, i7, i8]*MT[i1, i2]*MT[i10, i9]*MT[i4, i5] + I*LC[i2, i6, i7, i8]*MT[i1, i3]*MT[i10, i9]*MT[i4, i5] + I*LC[i10, i7, i8, i9]*MT[i1, i6]*MT[i2, i3]*MT[i4, i5] - I*LC[i10, i6, i8, i9]*MT[i1, i7]*MT[i2, i3]*MT[i4, i5] + I*LC[i1, i6, i7, i9]*MT[i10, i8]*MT[i2, i3]*MT[i4, i5] - I*LC[i1, i6, i7, i8]*MT[i10, i9]*MT[i2, i3]*MT[i4, i5] - I*LC[i10, i7, i8, i9]*MT[i1, i3]*MT[i2, i6]*MT[i4, i5] + I*LC[i10, i3, i8, i9]*MT[i1, i7]*MT[i2, i6]*MT[i4, i5] + I*LC[i10, i6, i8, i9]*MT[i1, i3]*MT[i2, i7]*MT[i4, i5] - I*LC[i10, i3, i8, i9]*MT[i1, i6]*MT[i2, i7]*MT[i4, i5] + I*LC[i10, i7, i8, i9]*MT[i1, i2]*MT[i3, i6]*MT[i4, i5] - I*LC[i10, i2, i8, i9]*MT[i1, i7]*MT[i3, i6]*MT[i4, i5] - I*LC[i1, i10, i8, i9]*MT[i2, i7]*MT[i3, i6]*MT[i4, i5] - I*LC[i10, i6, i8, i9]*MT[i1, i2]*MT[i3, i7]*MT[i4, i5] + I*LC[i10, i2, i8, i9]*MT[i1, i6]*MT[i3, i7]*MT[i4, i5] + I*LC[i1, i10, i8, i9]*MT[i2, i6]*MT[i3, i7]*MT[i4, i5] - I*LC[i10, i7, i8, i9]*MT[i1, i5]*MT[i2, i3]*MT[i4, i6] + I*LC[i10, i5, i8, i9]*MT[i1, i7]*MT[i2, i3]*MT[i4, i6] + I*LC[i10, i7, i8, i9]*MT[i1, i3]*MT[i2, i5]*MT[i4, i6] - I*LC[i10, i3, i8, i9]*MT[i1, i7]*MT[i2, i5]*MT[i4, i6] - I*LC[i10, i5, i8, i9]*MT[i1, i3]*MT[i2, i7]*MT[i4, i6] + I*LC[i10, i3, i8, i9]*MT[i1, i5]*MT[i2, i7]*MT[i4, i6] - I*LC[i10, i7, i8, i9]*MT[i1, i2]*MT[i3, i5]*MT[i4, i6] + I*LC[i10, i2, i8, i9]*MT[i1, i7]*MT[i3, i5]*MT[i4, i6] + I*LC[i1, i10, i8, i9]*MT[i2, i7]*MT[i3, i5]*MT[i4, i6] + I*LC[i10, i5, i8, i9]*MT[i1, i2]*MT[i3, i7]*MT[i4, i6] - I*LC[i10, i2, i8, i9]*MT[i1, i5]*MT[i3, i7]*MT[i4, i6] - I*LC[i1, i10, i8, i9]*MT[i2, i5]*MT[i3, i7]*MT[i4, i6] + I*LC[i10, i6, i8, i9]*MT[i1, i5]*MT[i2, i3]*MT[i4, i7] - I*LC[i10, i5, i8, i9]*MT[i1, i6]*MT[i2, i3]*MT[i4, i7] - I*LC[i10, i6, i8, i9]*MT[i1, i3]*MT[i2, i5]*MT[i4, i7] + I*LC[i10, i3, i8, i9]*MT[i1, i6]*MT[i2, i5]*MT[i4, i7] + I*LC[i10, i5, i8, i9]*MT[i1, i3]*MT[i2, i6]*MT[i4, i7] - I*LC[i10, i3, i8, i9]*MT[i1, i5]*MT[i2, i6]*MT[i4, i7] + I*LC[i10, i6, i8, i9]*MT[i1, i2]*MT[i3, i5]*MT[i4, i7] - I*LC[i10, i2, i8, i9]*MT[i1, i6]*MT[i3, i5]*MT[i4, i7] - I*LC[i1, i10, i8, i9]*MT[i2, i6]*MT[i3, i5]*MT[i4, i7] - I*LC[i10, i5, i8, i9]*MT[i1, i2]*MT[i3, i6]*MT[i4, i7] + I*LC[i10, i2, i8, i9]*MT[i1, i5]*MT[i3, i6]*MT[i4, i7] + I*LC[i1, i10, i8, i9]*MT[i2, i5]*MT[i3, i6]*MT[i4, i7] + I*LC[i10, i7, i8, i9]*MT[i1, i4]*MT[i2, i3]*MT[i5, i6] - I*LC[i10, i4, i8, i9]*MT[i1, i7]*MT[i2, i3]*MT[i5, i6] - I*LC[i10, i7, i8, i9]*MT[i1, i3]*MT[i2, i4]*MT[i5, i6] + I*LC[i10, i3, i8, i9]*MT[i1, i7]*MT[i2, i4]*MT[i5, i6] + I*LC[i10, i4, i8, i9]*MT[i1, i3]*MT[i2, i7]*MT[i5, i6] - I*LC[i10, i3, i8, i9]*MT[i1, i4]*MT[i2, i7]*MT[i5, i6] + I*LC[i10, i7, i8, i9]*MT[i1, i2]*MT[i3, i4]*MT[i5, i6] - I*LC[i10, i2, i8, i9]*MT[i1, i7]*MT[i3, i4]*MT[i5, i6] - I*LC[i1, i10, i8, i9]*MT[i2, i7]*MT[i3, i4]*MT[i5, i6] - I*LC[i10, i4, i8, i9]*MT[i1, i2]*MT[i3, i7]*MT[i5, i6] + I*LC[i10, i2, i8, i9]*MT[i1, i4]*MT[i3, i7]*MT[i5, i6] + I*LC[i1, i10, i8, i9]*MT[i2, i4]*MT[i3, i7]*MT[i5, i6] + I*LC[i10, i3, i8, i9]*MT[i1, i2]*MT[i4, i7]*MT[i5, i6] - I*LC[i10, i2, i8, i9]*MT[i1, i3]*MT[i4, i7]*MT[i5, i6] - I*LC[i1, i10, i8, i9]*MT[i2, i3]*MT[i4, i7]*MT[i5, i6] - I*LC[i10, i6, i8, i9]*MT[i1, i4]*MT[i2, i3]*MT[i5, i7] + I*LC[i10, i4, i8, i9]*MT[i1, i6]*MT[i2, i3]*MT[i5, i7] + I*LC[i10, i6, i8, i9]*MT[i1, i3]*MT[i2, i4]*MT[i5, i7] - I*LC[i10, i3, i8, i9]*MT[i1, i6]*MT[i2, i4]*MT[i5, i7] - I*LC[i10, i4, i8, i9]*MT[i1, i3]*MT[i2, i6]*MT[i5, i7] + I*LC[i10, i3, i8, i9]*MT[i1, i4]*MT[i2, i6]*MT[i5, i7] - I*LC[i10, i6, i8, i9]*MT[i1, i2]*MT[i3, i4]*MT[i5, i7] + I*LC[i10, i2, i8, i9]*MT[i1, i6]*MT[i3, i4]*MT[i5, i7] + I*LC[i1, i10, i8, i9]*MT[i2, i6]*MT[i3, i4]*MT[i5, i7] + I*LC[i10, i4, i8, i9]*MT[i1, i2]*MT[i3, i6]*MT[i5, i7] - I*LC[i10, i2, i8, i9]*MT[i1, i4]*MT[i3, i6]*MT[i5, i7] - I*LC[i1, i10, i8, i9]*MT[i2, i4]*MT[i3, i6]*MT[i5, i7] - I*LC[i10, i3, i8, i9]*MT[i1, i2]*MT[i4, i6]*MT[i5, i7] + I*LC[i10, i2, i8, i9]*MT[i1, i3]*MT[i4, i6]*MT[i5, i7] + I*LC[i1, i10, i8, i9]*MT[i2, i3]*MT[i4, i6]*MT[i5, i7] + I*LC[i3, i4, i5, i9]*MT[i1, i2]*MT[i10, i8]*MT[i6, i7] - I*LC[i2, i4, i5, i9]*MT[i1, i3]*MT[i10, i8]*MT[i6, i7] - I*LC[i3, i4, i5, i8]*MT[i1, i2]*MT[i10, i9]*MT[i6, i7] + I*LC[i2, i4, i5, i8]*MT[i1, i3]*MT[i10, i9]*MT[i6, i7] + I*LC[i10, i5, i8, i9]*MT[i1, i4]*MT[i2, i3]*MT[i6, i7] - I*LC[i10, i4, i8, i9]*MT[i1, i5]*MT[i2, i3]*MT[i6, i7] + I*LC[i1, i4, i5, i9]*MT[i10, i8]*MT[i2, i3]*MT[i6, i7] - I*LC[i1, i4, i5, i8]*MT[i10, i9]*MT[i2, i3]*MT[i6, i7] - I*LC[i10, i5, i8, i9]*MT[i1, i3]*MT[i2, i4]*MT[i6, i7] + I*LC[i10, i3, i8, i9]*MT[i1, i5]*MT[i2, i4]*MT[i6, i7] + I*LC[i10, i4, i8, i9]*MT[i1, i3]*MT[i2, i5]*MT[i6, i7] - I*LC[i10, i3, i8, i9]*MT[i1, i4]*MT[i2, i5]*MT[i6, i7] + I*LC[i10, i5, i8, i9]*MT[i1, i2]*MT[i3, i4]*MT[i6, i7] - I*LC[i10, i2, i8, i9]*MT[i1, i5]*MT[i3, i4]*MT[i6, i7] - I*LC[i1, i10, i8, i9]*MT[i2, i5]*MT[i3, i4]*MT[i6, i7] - I*LC[i10, i4, i8, i9]*MT[i1, i2]*MT[i3, i5]*MT[i6, i7] + I*LC[i10, i2, i8, i9]*MT[i1, i4]*MT[i3, i5]*MT[i6, i7] + I*LC[i1, i10, i8, i9]*MT[i2, i4]*MT[i3, i5]*MT[i6, i7] + I*LC[i10, i3, i8, i9]*MT[i1, i2]*MT[i4, i5]*MT[i6, i7] - I*LC[i10, i2, i8, i9]*MT[i1, i3]*MT[i4, i5]*MT[i6, i7] + I*LC[i1, i2, i3, i9]*MT[i10, i8]*MT[i4, i5]*MT[i6, i7] - I*LC[i1, i2, i3, i8]*MT[i10, i9]*MT[i4, i5]*MT[i6, i7] - I*LC[i1, i10, i8, i9]*MT[i2, i3]*MT[i4, i5]*MT[i6, i7] + I*LC[i1, i2, i3, i5]*MT[i10, i9]*MT[i4, i8]*MT[i6, i7] - I*LC[i1, i2, i3, i5]*MT[i10, i8]*MT[i4, i9]*MT[i6, i7] - I*LC[i1, i2, i3, i4]*MT[i10, i9]*MT[i5, i8]*MT[i6, i7] + I*LC[i1, i2, i3, i4]*MT[i10, i8]*MT[i5, i9]*MT[i6, i7] + I*LC[i3, i4, i5, i7]*MT[i1, i2]*MT[i10, i9]*MT[i6, i8] - I*LC[i2, i4, i5, i7]*MT[i1, i3]*MT[i10, i9]*MT[i6, i8] + I*LC[i1, i4, i5, i7]*MT[i10, i9]*MT[i2, i3]*MT[i6, i8] + I*LC[i1, i2, i3, i7]*MT[i10, i9]*MT[i4, i5]*MT[i6, i8] - I*LC[i1, i2, i3, i5]*MT[i10, i9]*MT[i4, i7]*MT[i6, i8] + I*LC[i1, i2, i3, i4]*MT[i10, i9]*MT[i5, i7]*MT[i6, i8] - I*LC[i3, i4, i5, i7]*MT[i1, i2]*MT[i10, i8]*MT[i6, i9] + I*LC[i2, i4, i5, i7]*MT[i1, i3]*MT[i10, i8]*MT[i6, i9] - I*LC[i1, i4, i5, i7]*MT[i10, i8]*MT[i2, i3]*MT[i6, i9] - I*LC[i1, i2, i3, i7]*MT[i10, i8]*MT[i4, i5]*MT[i6, i9] + I*LC[i1, i2, i3, i5]*MT[i10, i8]*MT[i4, i7]*MT[i6, i9] - I*LC[i1, i2, i3, i4]*MT[i10, i8]*MT[i5, i7]*MT[i6, i9] - I*LC[i3, i4, i5, i6]*MT[i1, i2]*MT[i10, i9]*MT[i7, i8] + I*LC[i2, i4, i5, i6]*MT[i1, i3]*MT[i10, i9]*MT[i7, i8] - I*LC[i1, i4, i5, i6]*MT[i10, i9]*MT[i2, i3]*MT[i7, i8] - I*LC[i1, i2, i3, i6]*MT[i10, i9]*MT[i4, i5]*MT[i7, i8] + I*LC[i1, i2, i3, i5]*MT[i10, i9]*MT[i4, i6]*MT[i7, i8] - I*LC[i1, i2, i3, i4]*MT[i10, i9]*MT[i5, i6]*MT[i7, i8] + I*LC[i3, i4, i5, i6]*MT[i1, i2]*MT[i10, i8]*MT[i7, i9] - I*LC[i2, i4, i5, i6]*MT[i1, i3]*MT[i10, i8]*MT[i7, i9] + I*LC[i1, i4, i5, i6]*MT[i10, i8]*MT[i2, i3]*MT[i7, i9] + I*LC[i1, i2, i3, i6]*MT[i10, i8]*MT[i4, i5]*MT[i7, i9] - I*LC[i1, i2, i3, i5]*MT[i10, i8]*MT[i4, i6]*MT[i7, i9] + I*LC[i1, i2, i3, i4]*MT[i10, i8]*MT[i5, i6]*MT[i7, i9] + I*LC[i3, i4, i5, i7]*MT[i1, i2]*MT[i10, i6]*MT[i8, i9] - I*LC[i2, i4, i5, i7]*MT[i1, i3]*MT[i10, i6]*MT[i8, i9] - I*LC[i3, i4, i5, i6]*MT[i1, i2]*MT[i10, i7]*MT[i8, i9] + I*LC[i2, i4, i5, i6]*MT[i1, i3]*MT[i10, i7]*MT[i8, i9] + I*LC[i10, i5, i6, i7]*MT[i1, i4]*MT[i2, i3]*MT[i8, i9] - I*LC[i10, i4, i6, i7]*MT[i1, i5]*MT[i2, i3]*MT[i8, i9] + I*LC[i1, i4, i5, i7]*MT[i10, i6]*MT[i2, i3]*MT[i8, i9] - I*LC[i1, i4, i5, i6]*MT[i10, i7]*MT[i2, i3]*MT[i8, i9] - I*LC[i10, i5, i6, i7]*MT[i1, i3]*MT[i2, i4]*MT[i8, i9] + I*LC[i10, i3, i6, i7]*MT[i1, i5]*MT[i2, i4]*MT[i8, i9] + I*LC[i10, i4, i6, i7]*MT[i1, i3]*MT[i2, i5]*MT[i8, i9] - I*LC[i10, i3, i6, i7]*MT[i1, i4]*MT[i2, i5]*MT[i8, i9] + I*LC[i10, i5, i6, i7]*MT[i1, i2]*MT[i3, i4]*MT[i8, i9] - I*LC[i10, i2, i6, i7]*MT[i1, i5]*MT[i3, i4]*MT[i8, i9] - I*LC[i1, i10, i6, i7]*MT[i2, i5]*MT[i3, i4]*MT[i8, i9] - I*LC[i10, i4, i6, i7]*MT[i1, i2]*MT[i3, i5]*MT[i8, i9] + I*LC[i10, i2, i6, i7]*MT[i1, i4]*MT[i3, i5]*MT[i8, i9] + I*LC[i1, i10, i6, i7]*MT[i2, i4]*MT[i3, i5]*MT[i8, i9] + I*LC[i10, i3, i6, i7]*MT[i1, i2]*MT[i4, i5]*MT[i8, i9] - I*LC[i10, i2, i6, i7]*MT[i1, i3]*MT[i4, i5]*MT[i8, i9] + I*LC[i1, i2, i3, i7]*MT[i10, i6]*MT[i4, i5]*MT[i8, i9] - I*LC[i1, i2, i3, i6]*MT[i10, i7]*MT[i4, i5]*MT[i8, i9] - I*LC[i1, i10, i6, i7]*MT[i2, i3]*MT[i4, i5]*MT[i8, i9] + I*LC[i1, i2, i3, i5]*MT[i10, i7]*MT[i4, i6]*MT[i8, i9] - I*LC[i1, i2, i3, i5]*MT[i10, i6]*MT[i4, i7]*MT[i8, i9] - I*LC[i1, i2, i3, i4]*MT[i10, i7]*MT[i5, i6]*MT[i8, i9] + I*LC[i1, i2, i3, i4]*MT[i10, i6]*MT[i5, i7]*MT[i8, i9] + I*LC[i10, i3, i4, i5]*MT[i1, i2]*MT[i6, i7]*MT[i8, i9] - I*LC[i10, i2, i4, i5]*MT[i1, i3]*MT[i6, i7]*MT[i8, i9] + I*LC[i1, i2, i3, i5]*MT[i10, i4]*MT[i6, i7]*MT[i8, i9] - I*LC[i1, i2, i3, i4]*MT[i10, i5]*MT[i6, i7]*MT[i8, i9] - I*LC[i1, i10, i4, i5]*MT[i2, i3]*MT[i6, i7]*MT[i8, i9] - I*LC[i1, i10, i2, i3]*MT[i4, i5]*MT[i6, i7]*MT[i8, i9])"} }) Tests`Dirac`fcstTrLarin = { diff --git a/Tests/ExportImport/ExportImport.mt b/Tests/ExportImport/ExportImport.mt index 1d8dbbd9e..16f84d9f3 100644 --- a/Tests/ExportImport/ExportImport.mt +++ b/Tests/ExportImport/ExportImport.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "Feynman" directory *) @@ -17,6 +17,14 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "ExportImport"}]] Get/@tests; +If[ $OnlySubTest=!="", + testNames = "Tests`ExportImport`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + FCClearScalarProducts[]; Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, diff --git a/Tests/ExportImport/FCAbbreviate.test b/Tests/ExportImport/FCAbbreviate.test index 4ba3e2f71..875fdc8e1 100644 --- a/Tests/ExportImport/FCAbbreviate.test +++ b/Tests/ExportImport/FCAbbreviate.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCAbbreviate *) @@ -14,13 +14,13 @@ (* ------------------------------------------------------------------------ *) Tests`ExportImport`fcstFCAbbreviate = ({ -{"fcstCompleteSquare-ID1", "FCAbbreviate[(a + I b)^2, {}, {}]", +{"fcstFCAbbreviate-ID1", "FCAbbreviate[(a + I b)^2, {}, {}]", "{{}, {}, {a -> var1, b -> var2}}"}, -{"fcstCompleteSquare-ID2", "FCAbbreviate[SPD[p, k] FAD[{q, SMP[\"m_e\"]}, {q + p, m}], {q}, {p, k}, +{"fcstFCAbbreviate-ID2", "FCAbbreviate[SPD[p, k] FAD[{q, SMP[\"m_e\"]}, {q + p, m}], {q}, {p, k}, Head -> spd]", "{{spd[k, k] -> sp1, spd[k, p] -> sp2, spd[p, p] -> sp3}, {SMP[\"m_e\"] -> sm1}, {m -> var1}}"}, -{"fcstCompleteSquare-ID3", "FCClearScalarProducts[]; \n SPD[p1, p1] = 0; \n SPD[p2, p2] = 0; \n SPD[p3, p3] = 0; \n +{"fcstFCAbbreviate-ID3", "FCClearScalarProducts[]; \n SPD[p1, p1] = 0; \n SPD[p2, p2] = 0; \n SPD[p3, p3] = 0; \n SPD[p1, p2] = s/2; \n SPD[p1, p3] = -(s + t)/2; \n SPD[p2, p3] = t/2; \n FCAbbreviate[ SPD[p2, p3] FAD[q, q - p1 - p2, q - p1 - p2 - p3], {q}, {p1, p2, p3},Head -> spd]", "{{spd[p1, p1] -> 0, spd[p1, p2] -> var1/2, spd[p1, p3] -> (-var1 - var2)/2, diff --git a/Tests/ExportImport/SMPToSymbol.test b/Tests/ExportImport/SMPToSymbol.test new file mode 100644 index 000000000..b1a41c514 --- /dev/null +++ b/Tests/ExportImport/SMPToSymbol.test @@ -0,0 +1,21 @@ + + +(* :Title: SMPToSymbol.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for SMPToSymbol *) + +(* ------------------------------------------------------------------------ *) + +Tests`ExportImport`fcstSMPToSymbol = ({ +{"fcstSMPToSymbol-ID1", "SMPToSymbol[a + b]", "a+b"}, +{"fcstSMPToSymbol-ID2", "SMPToSymbol[SMP[\"m_e\"]^2 + SMP[\"m_mu\"]^2 + c SMP[\"s_w\"]]", +"me^2 + mmu^2 + c sw"}, +{"fcstSMPToSymbol-ID3", "SMPToSymbol[SMP[{\"V_cb\", I}] SMP[{\"V_cb\", -I}]]", "Vcb VcbCC"} +}) diff --git a/Tests/ExportImport/Write2.test b/Tests/ExportImport/Write2.test index 1ed1655b9..703169ffd 100644 --- a/Tests/ExportImport/Write2.test +++ b/Tests/ExportImport/Write2.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2018 Rolf Mertig - Copyright (C) 1997-2018 Frederik Orellana - Copyright (C) 2014-2018 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Write2 *) diff --git a/Tests/Feynman/BackgroundGluonVertex.test b/Tests/Feynman/BackgroundGluonVertex.test index 7c37e6aed..e43da908d 100644 --- a/Tests/Feynman/BackgroundGluonVertex.test +++ b/Tests/Feynman/BackgroundGluonVertex.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for BackgroundGluonVertex *) diff --git a/Tests/Feynman/CompleteSquare.test b/Tests/Feynman/CompleteSquare.test index ee0b18d37..7e35a376d 100644 --- a/Tests/Feynman/CompleteSquare.test +++ b/Tests/Feynman/CompleteSquare.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for CompleteSquare *) diff --git a/Tests/Feynman/ComplexConjugate.test b/Tests/Feynman/ComplexConjugate.test index 305c0fe75..43b367a5a 100644 --- a/Tests/Feynman/ComplexConjugate.test +++ b/Tests/Feynman/ComplexConjugate.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ComplexConjugate *) @@ -19,5 +19,119 @@ Tests`Feynman`fcstComplexConjugate = { {"fcstComplexConjugate-ID2","ComplexConjugate[SUNTF[a,b,c]]", "SUNTF[{SUNIndex[a]}, SUNFIndex[c], SUNFIndex[b]]"}, {"fcstComplexConjugate-ID3","ComplexConjugate[SUNTF[{a1,a2,a3},b,c]]", - "SUNTF[{SUNIndex[a3], SUNIndex[a2], SUNIndex[a1]}, SUNFIndex[c], SUNFIndex[b]]"} + "SUNTF[{SUNIndex[a3], SUNIndex[a2], SUNIndex[a1]}, SUNFIndex[c], SUNFIndex[b]]"}, +{"fcstComplexConjugate-ID4","MatchQ[ComplexConjugate[GA[a].GA[5].GA[a]], +-DiracGamma[LorentzIndex[x_]].DiracGamma[5].DiracGamma[LorentzIndex[x_]] /; x =!= a]", + "True"}, +{"fcstComplexConjugate-ID5","ComplexConjugate[PauliXi[-I].CSI[i].PauliEta[I], FCE -> True]", + "PauliEta[-I].CSI[i].PauliXi[I]"}, +{"fcstComplexConjugate-ID6","ComplexConjugate[PauliXi[-I].CSI[i, j, k].PauliEta[I], FCE -> True]", + "PauliEta[-I].CSI[k].CSI[j].CSI[i].PauliXi[I]"}, +{"fcstComplexConjugate-ID7","ComplexConjugate[PauliXi[-I].CSIS[p, q, r].PauliEta[I], FCE -> True]", + "PauliEta[-I].CSIS[r].CSIS[q].CSIS[p].PauliXi[I]"}, +{"fcstComplexConjugate-ID8","ComplexConjugate[SpinorUBar[p1, m1].GA[mu, nu, rho].SpinorV[p2, m2], FCE -> True]", + "Spinor[-Momentum[p2], m2, 1].GA[rho].GA[nu].GA[mu].Spinor[Momentum[p1], m1, 1]"}, +{"fcstComplexConjugate-ID9","ComplexConjugate[SpinorUBar[p1, m1].CGA[i, j, k].SpinorV[p2, m2], FCE -> True]", + "Spinor[-Momentum[p2], m2, 1].CGA[k].CGA[j].CGA[i].Spinor[Momentum[p1], m1, 1]"}, +{"fcstComplexConjugate-ID10","ComplexConjugate[aaa]", + "aaa"}, +{"fcstComplexConjugate-ID11","ComplexConjugate[aaa,Conjugate->{aaa}]", + "Conjugate[aaa]"}, +{"fcstComplexConjugate-ID12","ComplexConjugate[SUNDelta[SUNIndex[Glu3], SUNIndex[Glu4]]]", + "SUNDelta[SUNIndex[Glu3], SUNIndex[Glu4]]"}, +{"fcstComplexConjugate-ID13","ComplexConjugate[SpinorUBar[k].GA[mu].(1 - la GA[5]).SpinorU[p, m], FCE -> True]", +"Spinor[Momentum[p], m, 1].(1 + la GA[5]).GA[mu].Spinor[Momentum[k], 0, 1]"}, +{"fcstComplexConjugate-ID14","ComplexConjugate[Spinor[-Momentum[p1], 0, 1].GA[al].(CRE GA[6] + CLE GA[7]).Spinor[Momentum[p2], 0, 1], FCE -> True]", +"Spinor[Momentum[p2], 0, 1] . (CLE*GA[6] + CRE*GA[7]) . GA[al] . Spinor[-Momentum[p1], 0, 1]"}, +{"fcstComplexConjugate-ID15","ComplexConjugate[Spinor[Momentum[p4], M4, 1].GA[ +be].(OR GA[6] + OL GA[7]).(-MGJ + GS[p3] + GS[p5]).(CA1 FMIX1A (A2 GA[6] + A1 GA[7]) + CA2 FMIX2A (A4 GA[6] + A3 GA[7])).Spinor[-Momentum[p5], M5, 1], FCE -> True]", +"Spinor[-Momentum[p5], M5, 1] . (CA1*FMIX1A*(A1*GA[6] + A2*GA[7]) + CA2*FMIX2A*(A3*GA[6] + A4*GA[7])) . (-MGJ + GS[p3] + GS[p5]) . (OL*GA[6] + OR*GA[7]) . GA[be] . +Spinor[Momentum[p4], M4, 1]"}, +{"fcstComplexConjugate-ID16","ComplexConjugate[Spinor[Momentum[k2], mb, 1].(mb GA[6] + GA[7] mt), FCE -> True]", + "(mt*GA[6] + mb*GA[7]) . Spinor[Momentum[k2], mb, 1]"}, +{"fcstComplexConjugate-ID17","ComplexConjugate[(mb GA[6] + GA[7] mt), FCE -> True]", + "(mt*GA[6] + mb*GA[7])"}, +{"fcstComplexConjugate-ID18","ComplexConjugate[FCChargeConjugateTransposed[GA[\[Mu], 5, \[Nu]]], +FCE -> True]", "-GA[\[Mu]] . GA[5] . GA[\[Nu]]"}, +{"fcstComplexConjugate-ID19", +"ComplexConjugate[SpinorUBar[p1,m1].FCCCT[GA[mu]].SpinorV[p2,m2],\ +FCE->True]", +"-Spinor[-Momentum[p2], m2, 1] . GA[mu] . Spinor[Momentum[p1], m1, \ +1]"}, +{"fcstComplexConjugate-ID20", +"ComplexConjugate[SpinorUBar[p1,m1].FCCCT[GA[5]].SpinorV[p2,m2],\ +FCE->True]", +"-Spinor[-Momentum[p2], m2, 1] . GA[5] . Spinor[Momentum[p1], m1, \ +1]"}, +{"fcstComplexConjugate-ID21", +"ComplexConjugate[SpinorUBar[p1,m1].FCCCT[GA[mu,nu]].SpinorV[p2,m2]\ +,FCE->True]", +"Spinor[-Momentum[p2], m2, 1] . GA[mu] . GA[nu] . \ +Spinor[Momentum[p1], m1, 1]"}, +{"fcstComplexConjugate-ID22", +"ComplexConjugate[SpinorUBar[p1,m1].FCCCT[GA[mu,5,nu]].SpinorV[p2,\ +m2],FCE->True]", +"-Spinor[-Momentum[p2], m2, 1] . GA[mu] . GA[5] . GA[nu] . \ +Spinor[Momentum[p1], m1, 1]"}, +{"fcstComplexConjugate-ID23", +"ComplexConjugate[SpinorUBar[p1,m1].FCCCT[GA[mu,nu,rho]].SpinorV[\ +p2,m2],FCE->True]", +"-Spinor[-Momentum[p2], m2, 1] . GA[mu] . GA[nu] . GA[rho] . \ +Spinor[Momentum[p1], m1, 1]"}, +{"fcstComplexConjugate-ID24", +"ComplexConjugate[SpinorUBar[p1,m1].FCCCT[GA[mu,nu,rho,5]].SpinorV[\ +p2,m2],FCE->True]", +"Spinor[-Momentum[p2], m2, 1] . GA[mu] . GA[nu] . GA[rho] . GA[5] \ +. Spinor[Momentum[p1], m1, 1]"}, +{"fcstComplexConjugate-ID25", +"ComplexConjugate[SpinorUBar[p1,m1].FCCCT[GS[p]+m].SpinorV[p2,m2],\ +FCE->True]", +"Spinor[-Momentum[p2], m2, 1] . (m - GS[p]) . Spinor[Momentum[p1], \ +m1, 1]"}, +{"fcstComplexConjugate-ID26", +"ComplexConjugate[SpinorUBar[p1,m1].FCCCT[GA[mu].(GS[p]+m).GA[nu]].\ +SpinorV[p2,m2],FCE->True]", +"Spinor[-Momentum[p2], m2, 1] . GA[mu] . (m - GS[p]) . GA[nu] . \ +Spinor[Momentum[p1], m1, 1]"}, +{"fcstComplexConjugate-ID27", "ComplexConjugate[SpinorUBar[p1, m1].FCCCT[GA[mu]].SpinorV[p2, m2], +FCE -> True]","-Spinor[-Momentum[p2], m2, 1].GA[mu].Spinor[Momentum[p1], m1, 1]"}, +{"fcstComplexConjugate-ID28", "FCCanonicalizeDummyIndices[ +DCHN[Spinor[-Momentum[p1], m1, 1], $AL[$42]] DCHN[ +Spinor[Momentum[p2], m2, 1], $AL[$43]] DCHN[ +GA[5].GA[nu].GA[mu], $AL[$42], $AL[$43]], +DiracIndexNames -> {i, j}, FCE -> True]","DCHN[Spinor[-Momentum[p1], m1, 1], i] DCHN[ +Spinor[Momentum[p2], m2, 1], j] DCHN[GA[5].GA[nu].GA[mu], i, j]"}, +{"fcstComplexConjugate-ID29", "ComplexConjugate[ +I*Spinor[Momentum[k1], mq, 1].((((-4*I)/3)*2^(1/4)*sinW*Sqrt[cosW^2*GF*mZ^2*sinW^2]* +GS[Polarization[p, I]].GA[6]*SDF[Col2, Col3])/cosW + ((2*I)*2^(1/4)* +Sqrt[cosW^2*GF*mZ^2*sinW^2]*(1/2 - (2*sinW^2)/3)* +GS[Polarization[p, I]].GA[7]*SDF[Col2, Col3])/(cosW*sinW)).Spinor[-Momentum[k2], mq, 1],FCE->True]", +"-I ((I 2^(1/4) Sqrt[ + cosW^2 GF mZ^2 sinW^2] (-3 + 4 sinW^2) Spinor[-Momentum[k2], mq, + 1].GA[6].GS[Polarization[p, -I]].Spinor[Momentum[k1], mq, + 1] SDF[Col2, Col3])/(3 cosW sinW) + ( +4 I 2^(1/4) sinW Sqrt[cosW^2 GF mZ^2 sinW^2] + Spinor[-Momentum[k2], mq, 1].GA[7].GS[ + Polarization[p, -I]].Spinor[Momentum[k1], mq, 1] SDF[Col2, + Col3])/(3 cosW))"}, +{"fcstComplexConjugate-ID30", +"ComplexConjugate[foo*y[a,b]*h[k,l]*z*rest,Conjugate\[Rule]{foo}]", + "rest*z*Conjugate[foo]*h[k, l]*y[a, b]"}, +{"fcstComplexConjugate-ID31", +"ComplexConjugate[foo*y[a,b]*h[k,l]*z*rest,Conjugate\[Rule]{y[i_,j_\ +]\[RuleDelayed]yCC[i,j]}]", "foo*rest*z*h[k, l]*yCC[a, b]"}, +{"fcstComplexConjugate-ID32", +"ComplexConjugate[foo*y[a,b]*h[k,l]*z*rest,Conjugate\[Rule]{z\ +\[Rule]-z}]", "-(foo*rest*z*h[k, l]*y[a, b])"}, +{"fcstComplexConjugate-ID33", +"ComplexConjugate[foo*y[a,b]*h[k,l]*z*rest,Conjugate\[Rule]{foo,y[\ +i_,j_]\[RuleDelayed]yCC[i,j],z\[Rule]-z}]", +"-(rest*z*Conjugate[foo]*h[k, l]*yCC[a, b])"}, +{"fcstComplexConjugate-ID34", +"Quiet[ComplexConjugate[(Spinor[-Momentum[p2],MassFu[Index[I3Gen, 2], +SUNFIndex[Col2]], 1].DiracGamma[7].Spinor[Momentum[p3], +MassFQ[Index[I3Gen, 3], SUNFIndex[Col3]],1])]]", +"Spinor[Momentum[p3], MassFQ[Index[I3Gen, 3], SUNFIndex[Col3]], +1].DiracGamma[6].Spinor[-Momentum[p2], +MassFu[Index[I3Gen, 2], SUNFIndex[Col2]], 1]"} }; diff --git a/Tests/Feynman/CovariantD.test b/Tests/Feynman/CovariantD.test index 06cd3b39d..852939c2a 100644 --- a/Tests/Feynman/CovariantD.test +++ b/Tests/Feynman/CovariantD.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for CovariantD *) diff --git a/Tests/Feynman/DoPolarizationSums.test b/Tests/Feynman/DoPolarizationSums.test index 44cb1932c..66a768117 100644 --- a/Tests/Feynman/DoPolarizationSums.test +++ b/Tests/Feynman/DoPolarizationSums.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DoPolarizationSums *) @@ -25,14 +25,11 @@ Tests`Feynman`fcstDoPolarizationSums = { Pair[LorentzIndex[b_], Momentum[k2]]* Pair[Momentum[k1], Momentum[k2]])]","True"}, {"fcstDoPolarizationSums-ID3","MatchQ[Contract[ - SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[ +SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[ k1, mu] FV[k2, nu] Pair[LorentzIndex[nu], - Momentum[Polarization[p, I]]]] // DoPolarizationSums[#, p, 0, Contract->False] &, - Pair[LorentzIndex[a_], Momentum[k1]]* - Pair[LorentzIndex[a_], Momentum[Polarization[p, I]]]* - Pair[LorentzIndex[b_], Momentum[k2]]* - Pair[LorentzIndex[b_], Momentum[Polarization[p, I]]]* - Pair[Momentum[k1], Momentum[k2]]]","True"}, + Momentum[Polarization[p, -I]]]] // +DoPolarizationSums[#, p, 0, Contract -> False, FCE -> True] &, +-FV[k1, a_] FV[k2, b_] MT[a_, b_] SP[k1, k2]]","True"}, {"fcstDoPolarizationSums-ID4","MatchQ[Contract[ SP[p, p] (SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[k1, mu] FV[k2, nu] Pair[ @@ -60,15 +57,11 @@ Tests`Feynman`fcstDoPolarizationSums = { Pair[LorentzIndex[b_, D], Momentum[k2, D]]* Pair[Momentum[k1, D], Momentum[k2, D]])]","True"}, {"fcstDoPolarizationSums-ID7","MatchQ[Contract[ - SPD[k1, k2] Pair[LorentzIndex[mu, D], +SPD[k1, k2] Pair[LorentzIndex[mu, D], Momentum[Polarization[p, I], D]] FVD[k1, mu] FVD[k2, nu] Pair[ - LorentzIndex[nu, D], Momentum[Polarization[p, I], D]]] // - DoPolarizationSums[#, p, 0,Contract->False] &, - Pair[LorentzIndex[a_, D], Momentum[k1, D]]* - Pair[LorentzIndex[a_, D], Momentum[Polarization[p, I], D]]* - Pair[LorentzIndex[b_, D], Momentum[k2, D]]* - Pair[LorentzIndex[b_, D], Momentum[Polarization[p, I], D]]* - Pair[Momentum[k1, D], Momentum[k2, D]]]","True"}, + LorentzIndex[nu, D], Momentum[Polarization[p, -I], D]]] // +DoPolarizationSums[#, p, 0, Contract -> False, FCE -> True] &, +-FVD[k1, a_] FVD[k2, b_] MTD[a_, b_] SPD[k1, k2]]","True"}, {"fcstDoPolarizationSums-ID8","MatchQ[Contract[ SPD[p, p] (SPD[k1, k2] Pair[LorentzIndex[mu, D], Momentum[Polarization[p, I], D]] FVD[k1, mu] FVD[k2, nu] Pair[ @@ -103,14 +96,12 @@ Tests`Feynman`fcstDoPolarizationSums = { Pair[LorentzIndex[b_], Momentum[p]])/ Pair[Momentum[n], Momentum[p]])]","True"}, {"fcstDoPolarizationSums-ID11","MatchQ[Contract[ - SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[ +SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[ k1, mu] FV[k2, nu] Pair[LorentzIndex[nu], - Momentum[Polarization[p, I]]]] // DoPolarizationSums[#, p, n,Contract->False] &, - Pair[LorentzIndex[a_], Momentum[k1]]* - Pair[LorentzIndex[a_], Momentum[Polarization[p, I]]]* - Pair[LorentzIndex[b_], Momentum[k2]]* - Pair[LorentzIndex[b_], Momentum[Polarization[p, I]]]* - Pair[Momentum[k1], Momentum[k2]]]","True"}, + Momentum[Polarization[p, -I]]]] // +DoPolarizationSums[#, p, n, Contract -> False, FCE -> True] &, +FV[k1, a_] FV[k2, b_] SP[k1,k2] (-MT[a_, b_] - (FV[p, a_] FV[p, b_] SP[n, n])/SP[n, p]^2 + ( + FV[n, b_] FV[p, a_])/SP[n, p] + (FV[n, a_] FV[p, b_])/SP[n, p])]","True"}, {"fcstDoPolarizationSums-ID12","MatchQ[Contract[ SP[p, p] (SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[k1, mu] FV[k2, nu] Pair[ @@ -162,15 +153,13 @@ Tests`Feynman`fcstDoPolarizationSums = { Pair[LorentzIndex[b_, D], Momentum[p, D]])/ Pair[Momentum[n, D], Momentum[p, D]])]","True"}, {"fcstDoPolarizationSums-ID14","MatchQ[Contract[ - SPD[k1, k2] Pair[LorentzIndex[mu, D], +SPD[k1, k2] Pair[LorentzIndex[mu, D], Momentum[Polarization[p, I], D]] FVD[k1, mu] FVD[k2, nu] Pair[ - LorentzIndex[nu, D], Momentum[Polarization[p, I], D]]] // - DoPolarizationSums[#, p, n,Contract->False] &, - Pair[LorentzIndex[a_, D], Momentum[k1, D]]* - Pair[LorentzIndex[a_, D], Momentum[Polarization[p, I], D]]* - Pair[LorentzIndex[b_, D], Momentum[k2, D]]* - Pair[LorentzIndex[b_, D], Momentum[Polarization[p, I], D]]* - Pair[Momentum[k1, D], Momentum[k2, D]]]","True"}, + LorentzIndex[nu, D], Momentum[Polarization[p, -I], D]]] // +DoPolarizationSums[#, p, n, Contract -> False, FCE -> True] &, +FVD[k1, a_] FVD[k2, b_] SPD[k1,k2] (-MTD[a_, b_] - (FVD[p, a_] FVD[p, b_] SPD[n, n])/ + SPD[n, p]^2 + (FVD[n, b_] FVD[p, a_])/SPD[n, p] + ( + FVD[n, a_] FVD[p, b_])/SPD[n, p])]","True"}, {"fcstDoPolarizationSums-ID16","MatchQ[Contract[ SPD[p, p] (SPD[k1, k2] Pair[LorentzIndex[mu, D], Momentum[Polarization[p, I], D]] FVD[k1, mu] FVD[k2, nu] Pair[ @@ -216,31 +205,20 @@ Tests`Feynman`fcstDoPolarizationSums = { Pair[LorentzIndex[b_], Momentum[p]])/ Pair[Momentum[p], Momentum[p]])]","True"}, {"fcstDoPolarizationSums-ID19","MatchQ[Contract[ - SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[ +SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[ k1, mu] FV[k2, nu] Pair[LorentzIndex[nu], - Momentum[Polarization[p, I]]]] // DoPolarizationSums[#, p,Contract->False] &, - Pair[LorentzIndex[a_], Momentum[k1]]* - Pair[LorentzIndex[a_], Momentum[Polarization[p, I]]]* - Pair[LorentzIndex[b_], Momentum[k2]]* - Pair[LorentzIndex[b_], Momentum[Polarization[p, I]]]* - Pair[Momentum[k1], Momentum[k2]]]","True"}, -{"fcstDoPolarizationSums-ID20","MatchQ [Contract[ - SP[p, p] (SP[k1, k2] Pair[LorentzIndex[mu], - Momentum[Polarization[p, I]]] FV[k1, mu] FV[k2, nu] Pair[ - LorentzIndex[nu], Momentum[Polarization[p, -I]]] + - DiracGamma[Momentum[Polarization[p, I]]]. DiracGamma[ - Momentum[Polarization[p, -I]]] )] // DoPolarizationSums[#, p,Contract->False] &, - DiracGamma[LorentzIndex[a_]]. DiracGamma[ LorentzIndex[ - b_]]*(-Pair[LorentzIndex[a_], - LorentzIndex[b_]] + (Pair[LorentzIndex[a_], Momentum[p]]* - Pair[LorentzIndex[b_], Momentum[p]])/ - Pair[Momentum[p], Momentum[p]])*Pair[Momentum[p], Momentum[p]] + - Pair[LorentzIndex[c_], Momentum[k2]]* - Pair[LorentzIndex[d_], Momentum[k1]]* - Pair[Momentum[k1], Momentum[k2]]*(-Pair[LorentzIndex[c_], - LorentzIndex[d_]] + (Pair[LorentzIndex[c_], Momentum[p]]* - Pair[LorentzIndex[d_], Momentum[p]])/ - Pair[Momentum[p], Momentum[p]])*Pair[Momentum[p], Momentum[p]]]","True"}, + Momentum[Polarization[p, -I]]]] // +DoPolarizationSums[#, p, Contract -> False, FCE -> True] &, +FV[k1, a_] FV[k2, b_] ((FV[p, a_] FV[p, b_])/M - MT[a_, b_]) SP[k1,k2]]","True"}, +{"fcstDoPolarizationSums-ID20","MatchQ[Contract[ +SP[p, p] (SP[k1, k2] Pair[LorentzIndex[mu], + Momentum[Polarization[p, I]]] FV[k1, mu] FV[k2, nu] Pair[ + LorentzIndex[nu], Momentum[Polarization[p, -I]]] + + DiracGamma[Momentum[Polarization[p, I]]].DiracGamma[ + Momentum[Polarization[p, -I]]])] // +DoPolarizationSums[#, p, Contract -> False, FCE -> True] &, +((FV[p, a_] FV[p, b_])/M - MT[a_, b_]) (M GA[a_].GA[b_] + + M FV[k1, a_] FV[k2, b_] SP[k1, k2])]","True"}, {"fcstDoPolarizationSums-ID21","Contract[SPD[k1, k2] FVD[p, mu] Pair[LorentzIndex[mu, D], Momentum[Polarization[k1, I], D]]] // DoPolarizationSums[#, p,Contract->False] &","3*Pair[Momentum[k1, D], Momentum[k2, D]]*Pair[Momentum[p, D], Momentum[Polarization[k1, I], D]]"}, {"fcstDoPolarizationSums-ID22","MatchQ[Contract[ @@ -256,31 +234,21 @@ Tests`Feynman`fcstDoPolarizationSums = { Pair[LorentzIndex[b_, D], Momentum[p, D]])/ Pair[Momentum[p, D], Momentum[p, D]])]","True"}, {"fcstDoPolarizationSums-ID23","MatchQ[Contract[ - SPD[k1, k2] Pair[LorentzIndex[mu, D], +SPD[k1, k2] Pair[LorentzIndex[mu, D], Momentum[Polarization[p, I], D]] FVD[k1, mu] FVD[k2, nu] Pair[ - LorentzIndex[nu, D], Momentum[Polarization[p, I], D]]] // - DoPolarizationSums[#, p,Contract->False] &, - Pair[LorentzIndex[a_, D], Momentum[k1, D]]* - Pair[LorentzIndex[a_, D], Momentum[Polarization[p, I], D]]* - Pair[LorentzIndex[b_, D], Momentum[k2, D]]* - Pair[LorentzIndex[b_, D], Momentum[Polarization[p, I], D]]* - Pair[Momentum[k1, D], Momentum[k2, D]]]","True"}, + LorentzIndex[nu, D], Momentum[Polarization[p, -I], D]]] // +DoPolarizationSums[#, p, Contract -> False, FCE -> True] &, +FVD[k1, a_] FVD[k2, b_] SPD[k1,k2] (-MTD[a_, b_] + (FVD[p, a_] FVD[p, b_])/SPD[p, p])]","True"}, {"fcstDoPolarizationSums-ID24","MatchQ[Contract[ - SPD[p, p] (SPD[k1, k2] Pair[LorentzIndex[mu, D], - Momentum[Polarization[p, I], D]] FVD[k1, mu] FVD[k2, nu] Pair[ - LorentzIndex[nu, D], Momentum[Polarization[p, -I], D]] + - DiracGamma[Momentum[Polarization[p, I], D], D]. DiracGamma[ - Momentum[Polarization[p, -I], D], D] )] // DoPolarizationSums[#, p,Contract->False] &, - DiracGamma[LorentzIndex[a_, D], D]. DiracGamma[LorentzIndex[b_, D], D]* - (-Pair[LorentzIndex[a_, D], LorentzIndex[b_, D]] + - (Pair[LorentzIndex[a_, D], Momentum[p, D]]*Pair[LorentzIndex[b_, D], Momentum[p, D]])/ - Pair[Momentum[p, D], Momentum[p, D]])* Pair[Momentum[p, D], Momentum[p, D]] + - Pair[LorentzIndex[c_, D], Momentum[k2, D]]* - Pair[LorentzIndex[d_, D], Momentum[k1, D]]* - Pair[Momentum[k1, D], Momentum[k2, D]]*(-Pair[LorentzIndex[c_, D], - LorentzIndex[d_, D]] + (Pair[LorentzIndex[c_, D], Momentum[p, D]]* - Pair[LorentzIndex[d_, D], Momentum[p, D]])/ Pair[Momentum[p, D], Momentum[p, D]])* - Pair[Momentum[p, D], Momentum[p, D]]]","True"}, +SPD[p, p] (SPD[k1, k2] Pair[LorentzIndex[mu, D], + Momentum[Polarization[p, I], D]] FVD[k1, mu] FVD[k2, nu] Pair[ + LorentzIndex[nu, D], Momentum[Polarization[p, -I], D]] + + DiracGamma[Momentum[Polarization[p, I], D], D].DiracGamma[ + Momentum[Polarization[p, -I], D], D])] // +DoPolarizationSums[#, p, Contract -> False, FCE -> True] &, +(-MTD[a_, b_] + (FVD[p, a_] FVD[p, b_])/ + SPD[p, p]) (GAD[a_].GAD[b_] SPD[p, p] + + FVD[k1, a_] FVD[k2, b_] SPD[k1, k2] SPD[p, p])]","True"}, {"fcstDoPolarizationSums-ID25","Contract[SP[k1, k2] FV[p, mu] Pair[LorentzIndex[mu], Momentum[Polarization[k1, I]]]] // DoPolarizationSums[#, p, 0, ExtraFactor->1/2,Contract->False] &", "Pair[Momentum[k1], Momentum[k2]]*Pair[Momentum[p], Momentum[Polarization[k1, I]]]"}, @@ -322,43 +290,37 @@ Tests`Feynman`fcstDoPolarizationSums = { {"fcstDoPolarizationSums-ID31","FCClearScalarProducts[]; ScalarProduct[p,p]= M; \n MatchQ[SP[k1, k2] Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[k1, mu] FV[k2, nu] Pair[ LorentzIndex[nu], Momentum[Polarization[p, -I]]] // - DoPolarizationSums[#, p] &, Expand[Pair[Momentum[k1], - Momentum[k2]] (-Pair[Momentum[k1], Momentum[k2]] + ( - Pair[Momentum[k1], Momentum[p]] Pair[Momentum[k2], Momentum[p]])/ - Pair[Momentum[p], Momentum[p]])]]", "True"}, -{"fcstDoPolarizationSums-ID32","MatchQ[SP[p,p] (SP[k1, k2] - Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]] FV[k1, mu] FV[k2, nu] - Pair[LorentzIndex[nu], Momentum[Polarization[p, -I]]] + - DiracGamma[Momentum[Polarization[p, I]]].DiracGamma[Momentum[Polarization[p, - -I]]]) // DoPolarizationSums[#, p] &, Expand[DiracGamma[Momentum[p]].DiracGamma[Momentum[p]] - - DiracGamma[LorentzIndex[a_]].DiracGamma[LorentzIndex[a_]] Pair[ Momentum[p], Momentum[p]] + - Pair[Momentum[k1], Momentum[k2]] (-Pair[Momentum[k1], Momentum[k2]] + ( - Pair[Momentum[k1], Momentum[p]] Pair[Momentum[k2], Momentum[p]])/ - Pair[Momentum[p], Momentum[p]]) Pair[Momentum[p], Momentum[p]]]]","True"}, -{"fcstDoPolarizationSums-ID33","MatchQ[SP[p,p] (SP[k1, k2] Pair[LorentzIndex[mu], - Momentum[Polarization[p, I, Transversality -> True]]] FV[k1,mu] - FV[k2, nu] Pair[LorentzIndex[nu],Momentum[Polarization[p, -I, - Transversality -> True]]] + DiracGamma[Momentum[Polarization[p, - I, Transversality -> True]]].DiracGamma[Momentum[Polarization[p, - -I, Transversality -> True]]]) // DoPolarizationSums[#, p] &, - Expand[DiracGamma[Momentum[p]].DiracGamma[Momentum[p]] - - DiracGamma[LorentzIndex[a_]].DiracGamma[LorentzIndex[a_]] Pair[ - Momentum[p], Momentum[p]] + Pair[Momentum[k1], + DoPolarizationSums[#, p] &, Pair[Momentum[k1], Momentum[k2]] (-Pair[Momentum[k1], Momentum[k2]] + ( Pair[Momentum[k1], Momentum[p]] Pair[Momentum[k2], Momentum[p]])/ - Pair[Momentum[p], Momentum[p]]) Pair[Momentum[p], Momentum[p]]]]","True"}, -{"fcstDoPolarizationSums-ID34","MatchQ[SP[p, p] (SP[k1, k2] Pair[LorentzIndex[mu], - Momentum[Polarization[p, I, Transversality -> True]]] FV[k1, mu] - FV[k2, nu] Pair[LorentzIndex[nu], Momentum[Polarization[p, -I, - Transversality -> True]]] + DiracGamma[Momentum[ - Polarization[p, I, Transversality -> True]]].DiracGamma[ + Pair[Momentum[p], Momentum[p]])]", "True"}, +{"fcstDoPolarizationSums-ID32","MatchQ[SP[p,p] (SP[k1, k2] Pair[LorentzIndex[mu], + Momentum[Polarization[p, I]]] FV[k1, mu] FV[k2, nu] Pair[ + LorentzIndex[nu], Momentum[Polarization[p, -I]]] + + DiracGamma[Momentum[Polarization[p, I]]].DiracGamma[ + Momentum[Polarization[p, -I]]]) // +DoPolarizationSums[#, p, FCE -> True] &, -M GA[a_].GA[a_] + +GS[p].GS[p] - M SP[k1, k2]^2 + SP[k1, k2] SP[k1, p] SP[k2, p]]","True"}, +{"fcstDoPolarizationSums-ID33","MatchQ[SP[p, + p] (SP[k1, k2] Pair[LorentzIndex[mu], + Momentum[Polarization[p, I, Transversality -> True]]] FV[k1, + mu] FV[k2, nu] Pair[LorentzIndex[nu], + Momentum[Polarization[p, -I, Transversality -> True]]] + + DiracGamma[Momentum[Polarization[p, I, Transversality -> True]]].DiracGamma[ Momentum[Polarization[p, -I, Transversality -> True]]]) // - DoPolarizationSums[#, p] &, Expand[DiracGamma[Momentum[p]].DiracGamma[Momentum[p]] - - DiracGamma[LorentzIndex[a_]].DiracGamma[LorentzIndex[a_]] Pair[ - Momentum[p], Momentum[p]] + Pair[Momentum[k1], - Momentum[k2]] (-Pair[Momentum[k1], Momentum[k2]] + ( - Pair[Momentum[k1], Momentum[p]] Pair[Momentum[k2], Momentum[p]])/ - Pair[Momentum[p], Momentum[p]]) Pair[Momentum[p], Momentum[p]]]]","True"}, +DoPolarizationSums[#, p, FCE -> True] &, -M GA[a_].GA[a_] + +GS[p].GS[p] - M SP[k1, k2]^2 + SP[k1, k2] SP[k1, p] SP[k2, p]]","True"}, +{"fcstDoPolarizationSums-ID34","MatchQ[SP[p1, + p2] (SP[k1, k2] Pair[LorentzIndex[mu], + Momentum[Polarization[p, I, Transversality -> True]]] FV[k1, + mu] FV[k2, nu] Pair[LorentzIndex[nu], + Momentum[Polarization[p, -I, Transversality -> True]]] + + DiracGamma[Momentum[Polarization[p, I, Transversality -> True]]].DiracGamma[ + Momentum[Polarization[p, -I, Transversality -> True]]]) // + DoPolarizationSums[#, p, FCE -> True] &, + -GA[a_].GA[a_] SP[p1, p2] + (GS[p].GS[p] SP[p1, p2])/M - + SP[k1, k2]^2 SP[p1, p2] + ( + SP[k1, k2] SP[k1, p] SP[k2, p] SP[p1, p2])/M]","True"}, {"fcstDoPolarizationSums-ID35", "DoPolarizationSums[Pair[Momentum[p1],Momentum[Polarization[x1,I]]]Pair[Momentum[p2], Momentum[Polarization[x1,-I]]]+1,x1,0,GaugeTrickN->4,VirtualBoson->True]//FCE", @@ -382,7 +344,7 @@ DoPolarizationSums[#, k] & // DoPolarizationSums[#, p] & // FCE", FV[p, ka] FV[p, la] MT[mu, nu])/SP[p, p] + ( FV[k, mu] FV[k, nu] FV[p, ka] FV[p, la])/(SP[k, k] SP[p, p])"}, {"fcstDoPolarizationSums-ID38", - "FCClearScalarProduct[]; \n ScalarProduct[p1, p1] = 0; \n + "FCClearScalarProducts[]; \n ScalarProduct[p1, p1] = 0; \n ScalarProduct[p2, p2] = 0; \n Pair[LorentzIndex[Subscript[\[Alpha], 1], D], Momentum[Polarization[p1, I, Transversality -> True], D]] Pair[ @@ -393,7 +355,7 @@ FV[k, mu] FV[k, nu] FV[p, ka] FV[p, la])/(SP[k, k] SP[p, p])"}, LorentzIndex[Subscript[\[Alpha], 2], D], Momentum[Polarization[p2, -I, Transversality -> True], D]] // DoPolarizationSums[#, p1, n] & // DoPolarizationSums[#, p2, n] &", - "2*(2 - D) - (2 - D)*D"}, + "(2 - D)^2"}, {"fcstDoPolarizationSums-ID39", "Pair[LorentzIndex[Subscript[\[Alpha], 1], D], Momentum[Polarization[p1, I, Transversality -> True], D]] Pair[ @@ -405,11 +367,30 @@ FV[k, mu] FV[k, nu] FV[p, ka] FV[p, la])/(SP[k, k] SP[p, p])"}, Momentum[Polarization[p2, -I, Transversality -> True], D]] // DoPolarizationSums[#, p1, n, Contract -> False] & // DoPolarizationSums[#, p2, n, Contract -> False] & // Contract", - "D^2 - 4 D + 4"}, + "(2 - D)^2"}, {"fcstDoPolarizationSums-ID40", "DoPolarizationSums[Pair[Momentum[Polarization[p1, -I]],Momentum[Polarization[p1, I]]], p1, 0]", "-4"}, {"fcstDoPolarizationSums-ID41", "DoPolarizationSums[Pair[Momentum[Polarization[p1, -I],D],Momentum[Polarization[p1, I],D]], p1, 0]", - "-D"} + "-D"}, +{"fcstDoPolarizationSums-ID42", + "tmp=DoPolarizationSums[DiracTrace[ + GS[p1].GS[Polarization[k1, -I, Transversality -> True]].GS[p2].GS[ + k3]] SP[k3, Polarization[k1, I, Transversality -> True]],k1] // FCE; \n + FCClearScalarProducts[]; \n tmp", + "-DiracTrace[GS[p1].GS[k3].GS[p2].GS[k3]] + (DiracTrace[GS[p1].GS[k1].GS[p2].GS[k3]] SP[k1, k3])/SP[k1, k1]"}, +{"fcstDoPolarizationSums-ID43", "CartesianPair[CartesianIndex[i], +CartesianMomentum[Polarization[k, -I]]] CartesianPair[ +CartesianIndex[j], CartesianMomentum[Polarization[k, I]]] // +DoPolarizationSums[#, k, FCE -> True] &", "KD[i, j] + (CV[k, i] CV[k, j])/SP[k, k]"}, +{"fcstDoPolarizationSums-ID44", "CartesianPair[CartesianMomentum[p], +CartesianMomentum[Polarization[k, -I]]] CartesianPair[ +CartesianMomentum[q], CartesianMomentum[Polarization[k, I]]] // +DoPolarizationSums[#, k, FCE -> True] &", "CSP[p, q] + (CSP[k, p] CSP[k, q])/SP[k, k]"}, +{"fcstDoPolarizationSums-ID45", "CartesianPair[CartesianMomentum[p, D - 1], +CartesianMomentum[Polarization[k, -I], D - 1]] CartesianPair[ +CartesianMomentum[q, D - 1], +CartesianMomentum[Polarization[k, I], D - 1]] // +DoPolarizationSums[#, k, FCE -> True] &", "CSPD[p, q] + (CSPD[k, p] CSPD[k, q])/SPD[k, k]"} }; diff --git a/Tests/Feynman/ExpandPartialD.test b/Tests/Feynman/ExpandPartialD.test index 5f85a1251..12574d831 100644 --- a/Tests/Feynman/ExpandPartialD.test +++ b/Tests/Feynman/ExpandPartialD.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ExpandPartialD *) diff --git a/Tests/Feynman/ExplicitPartialD.test b/Tests/Feynman/ExplicitPartialD.test index 2aa1f66fb..bd56d39a1 100644 --- a/Tests/Feynman/ExplicitPartialD.test +++ b/Tests/Feynman/ExplicitPartialD.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ExplicitPartialD *) diff --git a/Tests/Feynman/FCFADiracChainJoin.test b/Tests/Feynman/FCFADiracChainJoin.test new file mode 100644 index 000000000..43ffd46b8 --- /dev/null +++ b/Tests/Feynman/FCFADiracChainJoin.test @@ -0,0 +1,182 @@ + + +(* :Title: FCFADiracChainJoin.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCFADiracChainJoin *) + +(* ------------------------------------------------------------------------ *) + +Tests`Feynman`fcstFCFADiracChainJoin = { + +{"fcstFCFADiracChainJoin-ID1","FCFADiracChainJoin[-(1/(16 \[Pi]^4)) I el^2 DCHN[ +Spinor[-Momentum[p, D], me, 1], Dir1] DCHN[ +Spinor[Momentum[q, D], me, 1], Dir2] DCHN[GAD[Lor1], Dir1, +Dir3] DCHN[GAD[Lor2], Dir2, Dir4] DCHN[me - GSD[k], Dir3, +Dir4] FAD[{k, me}, k - q] MTD[Lor1, Lor2], FCE -> True]", +"-(1/(16 \[Pi]^4))*I el^2 Spinor[Momentum[q, D], me, 1].GAD[ + Lor2].(-(me + GSD[k]).GAD[Lor1]).Spinor[Momentum[p, D], me, + 1] FAD[{k, me}, k - q] MTD[Lor1, Lor2]"}, + +{"fcstFCFADiracChainJoin-ID2","FCFADiracChainJoin[{DCHN[Spinor[-Momentum[p1, D], mb, 1], Dir1] DCHN[ + Spinor[-Momentum[p2, D], ms, 1], Dir2] DCHN[ + Spinor[Momentum[p3, D], ms, 1], Dir3] DCHN[ + Spinor[Momentum[p4, D], mb, 1], + Dir4] (8 I DiracChain[ + DiracGamma[LorentzIndex[Ind404, D], D].GA[7], DiracIndex[Dir1], + DiracIndex[Dir2]] DiracChain[ + DiracGamma[LorentzIndex[Ind404, D], D].GA[7], DiracIndex[Dir4], + DiracIndex[ + Dir3]] (F1T SDF[colInB, colOutS] SDF[colInS, colOutB] + + F1 SDF[colInB, colInS] SDF[colOutB, colOutS]) + + 8 I DiracChain[DiracGamma[LorentzIndex[Ind403, D], D].GA[7], + DiracIndex[Dir1], DiracIndex[Dir3]] DiracChain[ + DiracGamma[LorentzIndex[Ind403, D], D].GA[7], DiracIndex[Dir4], + DiracIndex[ + Dir2]] (F1 SDF[colInB, colOutS] SDF[colInS, colOutB] + + F1T SDF[colInB, colInS] SDF[colOutB, colOutS]) + + 8 I tauPref DCHN[GA[7], Dir1, Dir2] DCHN[GA[7], Dir4, + Dir3] (F2T SDF[colInB, colOutS] SDF[colInS, colOutB] + + F2 SDF[colInB, colInS] SDF[colOutB, colOutS]) + + 8 I DCHN[GA[7], Dir1, Dir3] DCHN[GA[7], Dir4, + Dir2] (F2 SDF[colInB, colOutS] SDF[colInS, colOutB] + + F2T SDF[colInB, colInS] SDF[colOutB, colOutS]))}, FCE -> True]", +"{-8 I Spinor[-Momentum[p1, D], mb, 1].GAD[Ind404].GA[7].Spinor[ + Momentum[p2, D], ms, 1] Spinor[Momentum[p4, D], mb, 1].GAD[ + Ind404].GA[7].Spinor[-Momentum[p3, D], ms, + 1] (F1T SDF[colInB, colOutS] SDF[colInS, colOutB] + + F1 SDF[colInB, colInS] SDF[colOutB, colOutS]) + +8 I Spinor[-Momentum[p1, D], mb, 1].GAD[Ind403].GA[ + 7].Spinor[-Momentum[p3, D], ms, 1] Spinor[Momentum[p4, D], mb, + 1].GAD[Ind403].GA[7].Spinor[Momentum[p2, D], ms, + 1] (F1 SDF[colInB, colOutS] SDF[colInS, colOutB] + + F1T SDF[colInB, colInS] SDF[colOutB, colOutS]) - +8 I tauPref Spinor[-Momentum[p1, D], mb, 1].GA[7].Spinor[ + Momentum[p2, D], ms, 1] Spinor[Momentum[p4, D], mb, 1].GA[ + 7].Spinor[-Momentum[p3, D], ms, + 1] (F2T SDF[colInB, colOutS] SDF[colInS, colOutB] + + F2 SDF[colInB, colInS] SDF[colOutB, colOutS]) + +8 I Spinor[-Momentum[p1, D], mb, 1].GA[7].Spinor[-Momentum[p3, D], + ms, 1] Spinor[Momentum[p4, D], mb, 1].GA[7].Spinor[ + Momentum[p2, D], ms, + 1] (F2 SDF[colInB, colOutS] SDF[colInS, colOutB] + + F2T SDF[colInB, colInS] SDF[colOutB, colOutS])}"}, +{"fcstFCFADiracChainJoin-ID3", +"FCFADiracChainJoin[e^2 DCHN[Spinor[-Momentum[p1],me,1],Dir1] +DCHN[Spinor[-Momentum[p2],me,1],Dir2] DCHN[me+GS[-k1+p2],Dir3,Dir4] +DCHN[GS[Polarization[k1,-I,Transversality->True]],Dir2,Dir4] +DCHN[GS[Polarization[k2,-I,Transversality->True]],Dir1,Dir3] +FAD[{k1-p2,me},Dimension->4]+e^2 DCHN[Spinor[-Momentum[p1],me,1],Dir1] +DCHN[Spinor[-Momentum[p2],me,1],Dir2] DCHN[me+GS[-k2+p2],Dir3,Dir4] +DCHN[GS[Polarization[k1,-I,Transversality->True]],Dir1,Dir3] +DCHN[GS[Polarization[k2,-I,Transversality->True]],Dir2,Dir4] FAD[{k2-p2,me},Dimension->4],FCE->True]", +"e^2 Spinor[-Momentum[p2], me, 1].GS[ + Polarization[k1, -I, + Transversality -> + True]].(-(me - GS[-k1 + p2]).GS[ + Polarization[k2, -I, Transversality -> True]]).Spinor[ + Momentum[p1], me, 1] FAD[{k1 - p2, me}, Dimension -> 4] + +e^2 Spinor[-Momentum[p2], me, 1].GS[ + Polarization[k2, -I, + Transversality -> + True]].(-(me - GS[-k2 + p2]).GS[ + Polarization[k1, -I, Transversality -> True]]).Spinor[ + Momentum[p1], me, 1] FAD[{k2 - p2, me}, Dimension -> 4]"}, +{"fcstFCFADiracChainJoin-ID4","FCFADiracChainJoin[e^2 DCHN[Spinor[Momentum[k1],me,1],Dir3] +DCHN[Spinor[Momentum[k2],me,1],Dir4] DCHN[Spinor[-Momentum[p1],me,1],Dir1] +DCHN[Spinor[-Momentum[p2],me,1],Dir2] DCHN[GA[Lor2],Dir1,Dir4] +DCHN[GA[Lor2],Dir2,Dir3] FAD[k1-p2,Dimension->4]+ +e^2 DCHN[Spinor[Momentum[k1],me,1],Dir3] DCHN[Spinor[Momentum[k2],me,1],Dir4] +DCHN[Spinor[-Momentum[p1],me,1],Dir1] DCHN[Spinor[-Momentum[p2],me,1],Dir2] +DCHN[GA[Lor2],Dir1,Dir3] DCHN[GA[Lor2],Dir2,Dir4] FAD[k2-p2,Dimension->4],FCE->True]", +"e^2 Spinor[-Momentum[p1], me, 1].GA[Lor2].Spinor[-Momentum[k2], me, + 1] Spinor[-Momentum[p2], me, 1].GA[Lor2].Spinor[-Momentum[k1], me, + 1] FAD[k1 - p2, Dimension -> 4] - +e^2 Spinor[-Momentum[p1], me, 1].GA[Lor2].Spinor[-Momentum[k1], me, + 1] Spinor[-Momentum[p2], me, 1].GA[Lor2].Spinor[-Momentum[k2], me, + 1] FAD[k2 - p2, Dimension -> 4]"}, +{"fcstFCFADiracChainJoin-ID5","FCFADiracChainJoin[ +I gs^2 DCHN[Spinor[-Momentum[p1, D], mb, 1], Dir1] DCHN[ +Spinor[-Momentum[p2, D], ms, 1], Dir2] DCHN[ +Spinor[Momentum[p3, D], ms, 1], Dir3] DCHN[ +Spinor[Momentum[p4, D], mb, 1], Dir4] DCHN[GAD[Lor1], Dir5, +Dir7] DCHN[GAD[Lor2], Dir1, Dir9] DCHN[mb + GSD[p2 - p3 - p4 - q1], + Dir9, Dir10] DCHN[mc + GSD[-p3 - p4 - q1 - q2], Dir11, +Dir12] DCHN[mc - GSD[q2], Dir5, Dir6] DCHN[mc + GSD[q1 + q2], Dir7, + Dir8] FAD[{q1, MGl}, {q2, mc}, {q1 + q2, mc}, {-p2 + p3 + p4 + q1, + mb}, {p3 + p4 + q1 + q2, mc}] MTD[Lor1, +Lor2] (4 I heffPref ORIG DCHN[GAD[Ind26].GA[7], Dir10, Dir6] DCHN[ + GAD[Ind26].GA[7], Dir11, + Dir2] (C1 SDF[Col5, Col8] SDF[Col7, colInS] + + C2 SDF[Col5, Col7] SDF[Col8, colInS]) + + 4 I FIERZ heffPref DCHN[GAD[Ind27].GA[7], Dir10, Dir2] DCHN[ + GAD[Ind27].GA[7], Dir11, + Dir6] (C1 SDF[Col5, Col8] SDF[Col7, colInS] + + C2 SDF[Col5, Col7] SDF[Col8, colInS])) (4 I heffPref ORIG DCHN[ + GAD[Ind24].GA[7], Dir4, Dir12] DCHN[GAD[Ind24].GA[7], Dir8, + Dir3] (C2 SDF[Col6, colOutS] SDF[Col8, colOutB] + + C1 SDF[Col6, Col8] SDF[colOutB, colOutS]) + + 4 I FIERZ heffPref DCHN[GAD[Ind25].GA[7], Dir4, Dir3] DCHN[ + GAD[Ind25].GA[7], Dir8, + Dir12] (C2 SDF[Col6, colOutS] SDF[Col8, colOutB] + + C1 SDF[Col6, Col8] SDF[colOutB, colOutS])) SUNTF[{Glu5}, Col5, +Col6] SUNTF[{Glu5}, colInB, Col7], FCE -> True]", +"16 I FIERZ^2 gs^2 heffPref^2 DiracTrace[ +GAD[Ind27].GA[7].(mc + GSD[q2]).GAD[Lor1].(mc + GSD[q1 + q2]).GAD[ + Ind25].GA[7].(mc - GSD[-p3 - p4 - q1 - q2])] Spinor[ + Momentum[p4, D], mb, 1].GAD[Ind25].GA[7].Spinor[-Momentum[p3, D], + ms, 1] Spinor[-Momentum[p1, D], mb, 1].GAD[ + Lor2].(mb + GSD[p2 - p3 - p4 - q1]).GAD[Ind27].GA[7].Spinor[ + Momentum[p2, D], ms, 1] FAD[{q1, MGl}, {q2, mc}, {q1 + q2, + mc}, {-p2 + p3 + p4 + q1, mb}, {p3 + p4 + q1 + q2, mc}] MTD[Lor1, +Lor2] (C1 SDF[Col5, Col8] SDF[Col7, colInS] + + C2 SDF[Col5, Col7] SDF[Col8, colInS]) (C2 SDF[Col6, colOutS] SDF[ + Col8, colOutB] + + C1 SDF[Col6, Col8] SDF[colOutB, colOutS]) SUNTF[{Glu5}, Col5, +Col6] SUNTF[{Glu5}, colInB, Col7] - +16 I FIERZ gs^2 heffPref^2 ORIG Spinor[-Momentum[p1, D], mb, 1].GAD[ + Lor2].(mb + GSD[p2 - p3 - p4 - q1]).GAD[Ind27].GA[7].Spinor[ + Momentum[p2, D], ms, 1] Spinor[Momentum[p3, D], ms, 1].GA[7].GAD[ + Ind24].(mc - GSD[q1 + q2]).GAD[ + Lor1].(mc - GSD[q2]).(-GA[7].GAD[Ind27]).(mc + + GSD[-p3 - p4 - q1 - q2]).(-GA[7].GAD[Ind24]).Spinor[-Momentum[p4, + D], mb, 1] FAD[{q1, MGl}, {q2, mc}, {q1 + q2, + mc}, {-p2 + p3 + p4 + q1, mb}, {p3 + p4 + q1 + q2, mc}] MTD[Lor1, +Lor2] (C1 SDF[Col5, Col8] SDF[Col7, colInS] + + C2 SDF[Col5, Col7] SDF[Col8, colInS]) (C2 SDF[Col6, colOutS] SDF[ + Col8, colOutB] + + C1 SDF[Col6, Col8] SDF[colOutB, colOutS]) SUNTF[{Glu5}, Col5, +Col6] SUNTF[{Glu5}, colInB, Col7] - +16 I gs^2 heffPref^2 ORIG^2 Spinor[-Momentum[p2, D], ms, + 1].(-GA[7].GAD[Ind26]).(mc + + GSD[-p3 - p4 - q1 - q2]).(-GA[7].GAD[Ind24]).Spinor[-Momentum[p4, + D], mb, 1] Spinor[Momentum[p3, D], ms, 1].GA[7].GAD[ + Ind24].(mc - GSD[q1 + q2]).GAD[Lor1].(mc - GSD[q2]).GA[7].GAD[ + Ind26].(mb - GSD[p2 - p3 - p4 - q1]).GAD[Lor2].Spinor[ + Momentum[p1, D], mb, 1] FAD[{q1, MGl}, {q2, mc}, {q1 + q2, + mc}, {-p2 + p3 + p4 + q1, mb}, {p3 + p4 + q1 + q2, mc}] MTD[Lor1, +Lor2] (C1 SDF[Col5, Col8] SDF[Col7, colInS] + + C2 SDF[Col5, Col7] SDF[Col8, colInS]) (C2 SDF[Col6, colOutS] SDF[ + Col8, colOutB] + + C1 SDF[Col6, Col8] SDF[colOutB, colOutS]) SUNTF[{Glu5}, Col5, +Col6] SUNTF[{Glu5}, colInB, Col7] + +16 I FIERZ gs^2 heffPref^2 ORIG Spinor[Momentum[p4, D], mb, 1].GAD[ + Ind25].GA[7].Spinor[-Momentum[p3, D], ms, + 1] Spinor[-Momentum[p1, D], mb, 1].GAD[ + Lor2].(mb + GSD[p2 - p3 - p4 - q1]).GAD[Ind26].GA[ + 7].(mc + GSD[q2]).GAD[Lor1].(mc + GSD[q1 + q2]).GAD[Ind25].GA[ + 7].(mc - GSD[-p3 - p4 - q1 - q2]).GAD[Ind26].GA[7].Spinor[ + Momentum[p2, D], ms, 1] FAD[{q1, MGl}, {q2, mc}, {q1 + q2, + mc}, {-p2 + p3 + p4 + q1, mb}, {p3 + p4 + q1 + q2, mc}] MTD[Lor1, +Lor2] (C1 SDF[Col5, Col8] SDF[Col7, colInS] + + C2 SDF[Col5, Col7] SDF[Col8, colInS]) (C2 SDF[Col6, colOutS] SDF[ + Col8, colOutB] + + C1 SDF[Col6, Col8] SDF[colOutB, colOutS]) SUNTF[{Glu5}, Col5, +Col6] SUNTF[{Glu5}, colInB, Col7]"} +}; diff --git a/Tests/Feynman/FCPrepareFAAmp.test b/Tests/Feynman/FCPrepareFAAmp.test index 3e758da50..1e3c9f349 100644 --- a/Tests/Feynman/FCPrepareFAAmp.test +++ b/Tests/Feynman/FCPrepareFAAmp.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCPrepareFAAmp *) @@ -23,5 +23,78 @@ m]] // FCPrepareFAAmp","FeynAmpDenominator[ PropagatorDenominator[Momentum[P], MW Sqrt[GaugeXi[W]]], PropagatorDenominator[Momentum[k], m]]"}, {"fcstFCPrepareFAAmp-ID2","FCPrepareFAAmp[FeynArts`IndexDelta[FeynArts`Index[Global`Gluon, 1], -FeynArts`Index[Global`Gluon, 2]]]","SUNDelta[SUNIndex[Glu1], SUNIndex[Glu2]]"} +FeynArts`Index[Global`Gluon, 2]]]","SUNDelta[SUNIndex[Glu1], SUNIndex[Glu2]]"}, +{"fcstFCPrepareFAAmp-ID2","FCPrepareFAAmp[Spinor[-Momentum[InMom2], m, 1] . + (I*(-1 + Zpsi)*(-DiracGamma[Momentum[InMom2]]) . + DiracGamma[6] + + I*(-1 + Zpsi)*(-DiracGamma[Momentum[InMom2]]) . + DiracGamma[7] - + I*(-1 + Zm*Zpsi)*m) . (-DiracGamma[Momentum[InMom2]] + + m) . ((-I)*DiracGamma[LorentzIndex[Lor2]]*gs* + SUNTF[{SUNIndex[Glu4]}, cqbar, SUNFIndex[Col5]]) . + (DiracGamma[Momentum[-InMom2 + OutMom2]] + m) . + ((-I)*DiracGamma[LorentzIndex[Lor1]]*gs* + SUNTF[{SUNIndex[Glu3]}, SUNFIndex[Col5], cq]) . + Spinor[Momentum[InMom1], m, 1], UndoChiralSplittings -> True]", + "Spinor[-Momentum[InMom2], m, 1] . ((-I)*m*(-1 + Zm*Zpsi) - I*(-1 + Zpsi)*DiracGamma[Momentum[InMom2]]) . (m - DiracGamma[Momentum[InMom2]]) . +((-I)*gs*DiracGamma[LorentzIndex[Lor2]]*SUNTF[{SUNIndex[Glu4]}, cqbar, SUNFIndex[Col5]]) . (m + DiracGamma[Momentum[-InMom2 + OutMom2]]) . +((-I)*gs*DiracGamma[LorentzIndex[Lor1]]*SUNTF[{SUNIndex[Glu3]}, SUNFIndex[Col5], cq]) . Spinor[Momentum[InMom1], m, 1]"}, +{"fcstFCPrepareFAAmp-ID2","FCPrepareFAAmp[ +FeynArts`FAPropagatorDenominator[ +FeynArts`FourMomentum[FeynArts`Incoming, 2] - +FeynArts`FourMomentum[FeynArts`Outgoing, 1], MU, 2]]","FeynAmpDenominator[PropagatorDenominator[Momentum[InMom2 - OutMom1], MU], PropagatorDenominator[Momentum[InMom2 - OutMom1], MU]]"}, +{"fcstFCPrepareFAAmp-ID3","FCPrepareFAAmp[ +FeynArts`FAPropagatorDenominator[ +FeynArts`FourMomentum[FeynArts`Incoming, 2] - +FeynArts`FourMomentum[FeynArts`Outgoing, 1], MU, 2], +FeynAmpDenominatorCombine -> False]","FeynAmpDenominator[ +PropagatorDenominator[Momentum[InMom2 - OutMom1], MU]]^2"}, +{"fcstFCPrepareFAAmp-ID3","FCPrepareFAAmp[((-I/16)* + FeynArts`FAFeynAmpDenominator[ + FeynArts`FAPropagatorDenominator[FeynArts`FourMomentum[FeynArts`Internal, 1], ME], + FeynArts`FAPropagatorDenominator[ + FeynArts`FourMomentum[FeynArts`Internal, 1] - FeynArts`FourMomentum[FeynArts`Outgoing, 1], 0]]* + FAMetricTensor[FeynArts`Index[Lorentz, 1], FeynArts`Index[Lorentz, 2]]* + FeynArts`DiracObject[FADiracSpinor[FeynArts`FourMomentum[FeynArts`Incoming, 1], ME]][ + FeynArts`Index[Dirac, 1]]* + FeynArts`DiracObject[FADiracSpinor[FeynArts`FourMomentum[FeynArts`Outgoing, 1], ME]][ + FeynArts`Index[Dirac, 2]]* + FeynArts`DiracObject[FADiracSlash[FeynArts`FourMomentum[FeynArts`Internal, 1]] + ME][ + FeynArts`Index[Dirac, 3], FeynArts`Index[Dirac, 4]]* + (I*EL* + FeynArts`DiracObject[FADiracMatrix[FeynArts`Index[Lorentz, 1]], + FAChiralityProjector[-1]][FeynArts`Index[Dirac, 4], FeynArts`Index[Dirac, 1]] + + I*EL* + FeynArts`DiracObject[FADiracMatrix[FeynArts`Index[Lorentz, 1]], + FAChiralityProjector[1]][FeynArts`Index[Dirac, 4], FeynArts`Index[Dirac, 1]])* + (I*EL* + FeynArts`DiracObject[FADiracMatrix[FeynArts`Index[Lorentz, 2]], + FAChiralityProjector[-1]][FeynArts`Index[Dirac, 2], FeynArts`Index[Dirac, 3]] + + I*EL* + FeynArts`DiracObject[FADiracMatrix[FeynArts`Index[Lorentz, 2]], + FAChiralityProjector[1]][FeynArts`Index[Dirac, 2], FeynArts`Index[Dirac, 3]]))/ +Pi^4]","((-I/16)*DiracChain[Spinor[Momentum[InMom1], ME, 1], DiracIndex[Dir1]]*DiracChain[Spinor[Momentum[OutMom1], ME, 1], DiracIndex[Dir2]]* +DiracChain[ME + DiracGamma[Momentum[LoopMom1]], DiracIndex[Dir3], DiracIndex[Dir4]]*(I*EL*DiracChain[DiracGamma[LorentzIndex[Lor1]] . DiracGamma[6], DiracIndex[Dir4], DiracIndex[Dir1]] + +I*EL*DiracChain[DiracGamma[LorentzIndex[Lor1]] . DiracGamma[7], DiracIndex[Dir4], DiracIndex[Dir1]])* +(I*EL*DiracChain[DiracGamma[LorentzIndex[Lor2]] . DiracGamma[6], DiracIndex[Dir2], DiracIndex[Dir3]] + +I*EL*DiracChain[DiracGamma[LorentzIndex[Lor2]] . DiracGamma[7], DiracIndex[Dir2], DiracIndex[Dir3]])*FeynAmpDenominator[PropagatorDenominator[Momentum[LoopMom1], ME], +PropagatorDenominator[Momentum[LoopMom1 - OutMom1], 0]]*Pair[LorentzIndex[Lor1], LorentzIndex[Lor2]])/Pi^4"}, +{"fcstFCPrepareFAAmp-ID4","FCPrepareFAAmp[FeynArts`IndexDelta[SUNIndex[a],SUNIndex[b]]]","SUNDelta[SUNIndex[a], SUNIndex[b]]"}, +{"fcstFCPrepareFAAmp-ID5","FCPrepareFAAmp[FeynArts`IndexDelta[ExplicitSUNIndex[a],ExplicitSUNIndex[b]]]","SUNDelta[ExplicitSUNIndex[a], ExplicitSUNIndex[b]]"}, +{"fcstFCPrepareFAAmp-ID6","FCPrepareFAAmp[FeynArts`IndexDelta[SUNFIndex[a],SUNFIndex[b]]]","SUNFDelta[SUNFIndex[a], SUNFIndex[b]]"}, +{"fcstFCPrepareFAAmp-ID7","FCPrepareFAAmp[FeynArts`IndexDelta[ExplicitSUNFIndex[a],ExplicitSUNFIndex[b]]]","SUNFDelta[ExplicitSUNFIndex[a], ExplicitSUNFIndex[b]]"}, +{"fcstFCPrepareFAAmp-ID8","MatchQ[FCPrepareFAAmp[ +Times[FeynArts`IndexSum[ + Times[FeynArts`DiracObject[Global`FADiracMatrix[a], + Global`FAChiralityProjector[-1]][ + FeynArts`Index[Global`Dirac, 1], + FeynArts`Index[Global`Dirac, 3]], + FeynArts`DiracObject[Global`FADiracMatrix[a], + Global`FAChiralityProjector[-1]][ + FeynArts`Index[Global`Dirac, 4], + FeynArts`Index[Global`Dirac, 2]]], List[a, 1, 4]]]], +DiracChain[DiracGamma[z_LorentzIndex].DiracGamma[7], +DiracIndex[Dir1], DiracIndex[Dir3]] DiracChain[ +DiracGamma[z_LorentzIndex].DiracGamma[7], DiracIndex[Dir4], +DiracIndex[Dir2]]]","True"} }; diff --git a/Tests/Feynman/FermionSpinSum.test b/Tests/Feynman/FermionSpinSum.test index 0922931a3..a7cd7c4e6 100644 --- a/Tests/Feynman/FermionSpinSum.test +++ b/Tests/Feynman/FermionSpinSum.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FermionSpinSum *) @@ -92,5 +92,126 @@ m2].GA[5].GA[i].Spinor[p1, m1],m],Momentum\[Rule]{p1,p2}]//FCE", "DiracTrace[(m1 + DiracGamma[Momentum[p1, m], m]) . \ DiracGamma[LorentzIndex[i, m], m] . GA[5] . (m2 + \ DiracGamma[Momentum[p2, m], m]) . GA[5] . DiracGamma[LorentzIndex[i, \ -m], m]]"} +m], m]]"}, +{"fcstFermionSpinSum-ID15", +"FermionSpinSum[ +Spinor[Momentum[l1], 0, 1].CGA[aa].Spinor[-Momentum[l2], 0, + 1] SpinorVBar[l2].CGA[bb].SpinorU[l1] Eps[ +CartesianMomentum[kphat], CartesianIndex[aa], +CartesianMomentum[Polarization[kp, I]]] Eps[ +CartesianMomentum[kphat], CartesianIndex[bb], +CartesianMomentum[Polarization[kp, -I]]], FCE -> True]", +"DiracTrace[GS[l1].CGA[aa].GS[l2].CGA[bb]] Eps[ +CartesianMomentum[kphat], CartesianIndex[aa], +CartesianMomentum[Polarization[kp, I]]] Eps[ +CartesianMomentum[kphat], CartesianIndex[bb], +CartesianMomentum[Polarization[kp, -I]]]"}, +{"fcstFermionSpinSum-ID16", +"FermionSpinSum[SpinorUBar[p1,m1].SpinorU[p2,m2] \ +SpinorVBar[p1,m1].SpinorV[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(-m2 + GS[p2]) . (-m1 + GS[p1])]"}, +{"fcstFermionSpinSum-ID17", +"FermionSpinSum[SpinorUBarD[p1,m1].SpinorUD[p2,m2] \ +SpinorVBarD[p1,m1].SpinorVD[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(-m2 + GSD[p2]) . (-m1 + GSD[p1])]"}, +{"fcstFermionSpinSum-ID18", +"FermionSpinSum[SpinorUBar[p1,m1].GA[mu].SpinorU[p2,m2] \ +SpinorVBar[p1,m1].GA[mu].SpinorV[p2,m2],FCE\[Rule]True]", +"DiracTrace[(-m2 + GS[p2]) . GA[mu] . (-m1 + GS[p1]) . GA[mu]]"}, +{"fcstFermionSpinSum-ID19", +"FermionSpinSum[SpinorUBarD[p1,m1].GAD[mu].SpinorUD[p2,m2] \ +SpinorVBarD[p1,m1].GAD[mu].SpinorVD[p2,m2],FCE\[Rule]True]", +"DiracTrace[(-m2 + GSD[p2]) . GAD[mu] . (-m1 + GSD[p1]) . \ +GAD[mu]]"}, +{"fcstFermionSpinSum-ID20", +"FermionSpinSum[SpinorUBar[p1,m1].GA[mu,nu].SpinorU[p2,m2] \ +SpinorVBar[p1,m1].GA[mu,nu].SpinorV[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(-m2 + GS[p2]) . GA[nu] . GA[mu] . (-m1 + GS[p1]) . \ +GA[mu] . GA[nu]]"}, +{"fcstFermionSpinSum-ID21", +"FermionSpinSum[SpinorUBarD[p1,m1].GAD[mu,nu].SpinorUD[p2,m2] \ +SpinorVBarD[p1,m1].GAD[mu,nu].SpinorVD[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(-m2 + GSD[p2]) . GAD[nu] . GAD[mu] . (-m1 + GSD[p1]) \ +. GAD[mu] . GAD[nu]]"}, +{"fcstFermionSpinSum-ID22", +"FermionSpinSum[SpinorUBar[p1,m1].GA[mu,5,nu].SpinorU[p2,m2] \ +SpinorVBar[p1,m1].GA[mu,5,nu].SpinorV[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(-m2 + GS[p2]) . GA[nu] . GA[5] . GA[mu] . (-m1 + \ +GS[p1]) . GA[mu] . GA[5] . GA[nu]]"}, +{"fcstFermionSpinSum-ID23", +"FermionSpinSum[SpinorUBar[p1,m1].SpinorV[p2,m2] \ +SpinorVBar[p1,m1].SpinorU[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(m2 + GS[p2]) . (-m1 + GS[p1])]"}, +{"fcstFermionSpinSum-ID24", +"FermionSpinSum[SpinorUBarD[p1,m1].SpinorVD[p2,m2] \ +SpinorVBarD[p1,m1].SpinorUD[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(m2 + GSD[p2]) . (-m1 + GSD[p1])]"}, +{"fcstFermionSpinSum-ID25", +"FermionSpinSum[SpinorUBar[p1,m1].GA[mu].SpinorV[p2,m2] \ +SpinorVBar[p1,m1].GA[mu].SpinorU[p2,m2],FCE\[Rule]True]", +"DiracTrace[(m2 + GS[p2]) . GA[mu] . (-m1 + GS[p1]) . GA[mu]]"}, +{"fcstFermionSpinSum-ID26", +"FermionSpinSum[SpinorUBarD[p1,m1].GAD[mu].SpinorVD[p2,m2] \ +SpinorVBarD[p1,m1].GAD[mu].SpinorUD[p2,m2],FCE\[Rule]True]", +"DiracTrace[(m2 + GSD[p2]) . GAD[mu] . (-m1 + GSD[p1]) . GAD[mu]]"}, +{"fcstFermionSpinSum-ID27", +"FermionSpinSum[SpinorUBar[p1,m1].GA[mu,nu].SpinorV[p2,m2] \ +SpinorVBar[p1,m1].GA[mu,nu].SpinorU[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(m2 + GS[p2]) . GA[nu] . GA[mu] . (-m1 + GS[p1]) . \ +GA[mu] . GA[nu]]"}, +{"fcstFermionSpinSum-ID28", +"FermionSpinSum[SpinorUBarD[p1,m1].GAD[mu,nu].SpinorVD[p2,m2] \ +SpinorVBarD[p1,m1].GAD[mu,nu].SpinorUD[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(m2 + GSD[p2]) . GAD[nu] . GAD[mu] . (-m1 + GSD[p1]) \ +. GAD[mu] . GAD[nu]]"}, +{"fcstFermionSpinSum-ID29", +"FermionSpinSum[SpinorUBar[p1,m1].GA[mu,5,nu].SpinorV[p2,m2] \ +SpinorVBar[p1,m1].GA[mu,5,nu].SpinorU[p2,m2],FCE\[Rule]True]", +"-DiracTrace[(m2 + GS[p2]) . GA[nu] . GA[5] . GA[mu] . (-m1 + \ +GS[p1]) . GA[mu] . GA[5] . GA[nu]]"}, +{"fcstFermionSpinSum-ID30", +"FermionSpinSum[-Spinor[-Momentum[k],m,1].Spinor[Momentum[l],m,1] \ +Spinor[Momentum[k],m,1].Spinor[-Momentum[l],m,1]-Spinor[Momentum[k],m,\ +1].Spinor[-Momentum[l],m,1] \ +Spinor[-Momentum[k],m,1].GA[5].Spinor[Momentum[l],m,1]-Spinor[-\ +Momentum[k],m,1].Spinor[Momentum[l],m,1] \ +Spinor[Momentum[k],m,1].GA[5].Spinor[-Momentum[l],m,1]-Spinor[-\ +Momentum[k],m,1].GA[5].Spinor[Momentum[l],m,1] \ +Spinor[Momentum[k],m,1].GA[5].Spinor[-Momentum[l],m,1]+2 \ +Spinor[Momentum[k],m,1].Spinor[-Momentum[l],m,1] \ +Spinor[-Momentum[l],m,1].GA[7].Spinor[Momentum[k],m,1]+2 \ +Spinor[Momentum[k],m,1].GA[5].Spinor[-Momentum[l],m,1] \ +Spinor[-Momentum[l],m,1].GA[7].Spinor[Momentum[k],m,1]+2 \ +Spinor[-Momentum[k],m,1].Spinor[Momentum[l],m,1] \ +Spinor[Momentum[l],m,1].GA[7].Spinor[-Momentum[k],m,1]+2 \ +Spinor[-Momentum[k],m,1].GA[5].Spinor[Momentum[l],m,1] \ +Spinor[Momentum[l],m,1].GA[7].Spinor[-Momentum[k],m,1]-4 \ +Spinor[-Momentum[l],m,1].GA[7].Spinor[Momentum[k],m,1] \ +Spinor[Momentum[l],m,1].GA[7].Spinor[-Momentum[k],m,1],FCE\[Rule]True]\ +", "DiracTrace[(m + GS[l]) . (-m + GS[k])] + 2*DiracTrace[(-m + \ +GS[k]) . (m + GS[l]) . GA[7]] + 2*DiracTrace[(m + GS[k]) . (-m + \ +GS[l]) . GA[7]] + DiracTrace[(-m + GS[l]) . GA[5] . (m + GS[k])] + \ +DiracTrace[(m + GS[l]) . GA[5] . (-m + GS[k])] + 2*DiracTrace[(-m + \ +GS[k]) . GA[5] . (m + GS[l]) . GA[7]] + 2*DiracTrace[(m + GS[k]) . \ +GA[5] . (-m + GS[l]) . GA[7]] + 4*DiracTrace[(m + GS[k]) . GA[7] . \ +(-m + GS[l]) . GA[7]] + DiracTrace[(m + GS[l]) . GA[5] . (-m + GS[k]) \ +. GA[5]]"}, +{"fcstFermionSpinSum-ID31", "FermionSpinSum[ +Spinor[Momentum[k2], me, 1].GA[6].Spinor[-Momentum[k1], MNeu[1], 1]* +Spinor[-Momentum[p1], MNeu[1], 1].GA[7].Spinor[Momentum[p2], me, 1]* +Spinor[Momentum[p1], MNeu[1], 1].GA[7].Spinor[Momentum[k2], me, \ +1]* +Spinor[Momentum[p2], me, 1].GA[6].Spinor[Momentum[k1], MNeu[1], \ +1], +FCE -> True]", +"-DiracTrace[(GS[k1] + MNeu[1]) . GA[6] . (me - GS[k2]) . GA[7] . \ +(GS[p1] - MNeu[1]) . GA[7] . (me + GS[p2]) . GA[6]]"}, +{"fcstFermionSpinSum-ID32", "FermionSpinSum[ +Spinor[p1, m1].GA[i].GA[5].Spinor[p2, m2] Spinor[k1, m3].GA[j].GA[ + 5].Spinor[k2, m4] Spinor[k2, m4].GA[5].GA[j].Spinor[k1, m3]* +Spinor[p2, m2].GA[5].GA[i].Spinor[p1, m1], Head -> spSum, +FCE -> True]", +"DiracTrace[ +spSum[m3 + GS[k1]].GA[j].GA[5].spSum[m4 + GS[k2]].GA[5].GA[j]] DiracTrace[ +spSum[m1 + GS[p1]].GA[i].GA[5].spSum[m2 + GS[p2]].GA[5].GA[i]]"} }); diff --git a/Tests/Feynman/FeynRule.test b/Tests/Feynman/FeynRule.test index 09bfd294c..297240f71 100644 --- a/Tests/Feynman/FeynRule.test +++ b/Tests/Feynman/FeynRule.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FeynRule *) diff --git a/Tests/Feynman/Feynman.mt b/Tests/Feynman/Feynman.mt index 3c33bdd05..febbd3e06 100644 --- a/Tests/Feynman/Feynman.mt +++ b/Tests/Feynman/Feynman.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "Feynman" directory *) @@ -17,6 +17,14 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "Feynman"}]] Get/@tests; +If[ $OnlySubTest=!="", + testNames = "Tests`Feynman`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + FCClearScalarProducts[]; ClearAll[M]; diff --git a/Tests/Feynman/FieldDerivative.test b/Tests/Feynman/FieldDerivative.test index 114dbd902..55f856433 100644 --- a/Tests/Feynman/FieldDerivative.test +++ b/Tests/Feynman/FieldDerivative.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FieldDerivative *) diff --git a/Tests/Feynman/FieldStrength.test b/Tests/Feynman/FieldStrength.test index 2810a39bf..53bc2d996 100644 --- a/Tests/Feynman/FieldStrength.test +++ b/Tests/Feynman/FieldStrength.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FieldStrength *) diff --git a/Tests/Feynman/FunctionalD.test b/Tests/Feynman/FunctionalD.test index a0b8343c9..3300e38d7 100644 --- a/Tests/Feynman/FunctionalD.test +++ b/Tests/Feynman/FunctionalD.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FunctionalD *) diff --git a/Tests/Feynman/GhostPropagator.test b/Tests/Feynman/GhostPropagator.test index 724e9dd41..b813dc1c8 100644 --- a/Tests/Feynman/GhostPropagator.test +++ b/Tests/Feynman/GhostPropagator.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for GhostPropagator *) @@ -22,5 +22,5 @@ Tests`Feynman`fcstGhostPropagator = ({ 0]]*SUNDelta[SUNIndex[a], SUNIndex[b]]"}, {"fcstGhostPropagator-ID3", "GhostPropagator[p,1,2]//Explicit", "I*FeynAmpDenominator[PropagatorDenominator[Momentum[p, D], \ -0]]*SUNDelta[SUNIndex[ci1], SUNIndex[ci2]]"} +0]]*SUNDelta[ExplicitSUNIndex[1], ExplicitSUNIndex[2]]"} }); diff --git a/Tests/Feynman/GluonGhostVertex.test b/Tests/Feynman/GluonGhostVertex.test index 04b94a0a3..419a9df89 100644 --- a/Tests/Feynman/GluonGhostVertex.test +++ b/Tests/Feynman/GluonGhostVertex.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for GluonGhostVertex *) diff --git a/Tests/Feynman/GluonPropagator.test b/Tests/Feynman/GluonPropagator.test index d154b02a3..2fdb93152 100644 --- a/Tests/Feynman/GluonPropagator.test +++ b/Tests/Feynman/GluonPropagator.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for GluonPropagator *) @@ -19,7 +19,7 @@ Tests`Feynman`fcstGluonPropagator = ({ "I*FAD[p]*((1 - al)*FAD[p]*FVD[p, mu]*FVD[p, nu] - MTD[mu, \ nu])*SD[a, b]"}, {"fcstGluonPropagator-ID2", -"GluonPropagator[p,mu,a,nu,b,Gauge\[Rule]{Momentum[n],1}]\ +"GluonPropagator[p,mu,a,nu,b,Gauge\[Rule]{Momentum[n,D],1}]\ //Explicit//FCE", "I*FAD[p]*SD[a, b]*(-MTD[mu, nu] + (FVD[n, nu]*FVD[p, mu] + FVD[n, \ mu]*FVD[p, nu])/SPD[n, p] - (FVD[p, mu]*FVD[p, nu]*SPD[n, n] - FVD[n, \ @@ -28,9 +28,9 @@ mu]*FVD[n, nu]*SPD[p, p])/SPD[n, p]^2)"}, "GluonPropagator[p,mu,nu]//Explicit//FCE", "(-I)*FAD[p]*MTD[mu, nu]"}, {"fcstGluonPropagator-ID4", -"Explicit[GP[p,1,2],Gauge\[Rule]xi]//FCE", +"Explicit[GP[p,li1,li2],Gauge\[Rule]xi]//FCE", "I*FAD[p]*((1 - xi)*FAD[p]*FVD[p, li1]*FVD[p, li2] - MTD[li1, \ -li2])*SD[ci1, ci2]"}, +li2])"}, {"fcstGluonPropagator-ID5", "GluonPropagator[p,mu,a,nu,b,CounterTerm\[Rule] 1]//Explicit//FCE", "((-I)*CA*Gstrong^2*Sn*SD[a, b]*((11*FVD[p, mu]*FVD[p, nu])/3 - \ diff --git a/Tests/Feynman/GluonSelfEnergy.test b/Tests/Feynman/GluonSelfEnergy.test index 9b7b03370..1affe334c 100644 --- a/Tests/Feynman/GluonSelfEnergy.test +++ b/Tests/Feynman/GluonSelfEnergy.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for GluonSelfEnergy *) diff --git a/Tests/Feynman/GluonVertex.test b/Tests/Feynman/GluonVertex.test index fde4893ec..0f74541a4 100644 --- a/Tests/Feynman/GluonVertex.test +++ b/Tests/Feynman/GluonVertex.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Twist2GluonOperator *) @@ -21,7 +21,7 @@ Momentum[p, D], {LorentzIndex[mu, D]}, {LorentzIndex[nu, D]}]"}, {"fcstTwist2GluonOperator-ID2","Twist2GluonOperator[p, {mu, a}, {nu, b}, Explicit -> True]// FCE", "1/2 (1 + (-1)^OPEm) SD[a, b] SOD[p]^(-2 + OPEm) (-(FVD[OPEDelta, nu] FVD[p, mu] + - FVD[OPEDelta, mu] FVD[p, nu]) SOD[p] + MTD[mu, nu] SOD[p]^2 + + FVD[OPEDelta, mu] FVD[p, nu]) SOD[p] + MTD[mu, nu] SOD[p]^2 + FVD[OPEDelta, mu] FVD[OPEDelta, nu] SPD[p, p])"} }; diff --git a/Tests/Feynman/Lagrangian.test b/Tests/Feynman/Lagrangian.test index 89637d121..f2eb74b2d 100644 --- a/Tests/Feynman/Lagrangian.test +++ b/Tests/Feynman/Lagrangian.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Lagrangian *) diff --git a/Tests/Feynman/PolarizationSum.test b/Tests/Feynman/PolarizationSum.test index 7057af9c2..62bf22449 100644 --- a/Tests/Feynman/PolarizationSum.test +++ b/Tests/Feynman/PolarizationSum.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for PolarizationSum *) @@ -58,5 +58,74 @@ Tests`Feynman`fcstPolarizationSum = { Momentum[n2]])^2 - (Pair[LorentzIndex[mu], Momentum[k1 + k2]]*Pair[LorentzIndex[nu], Momentum[k1 + k2]]* Pair[Momentum[n2], Momentum[n2]])/(Pair[Momentum[k1], Momentum[n1]] + Pair[Momentum[k1], Momentum[n2]] + Pair[Momentum[k2], Momentum[n1]] + Pair[Momentum[k2], Momentum[n2]])^2"}, -{"fcstPolarizationSum-ID8","PolarizationSum[mu, nu, x1,0,VirtualBoson->True]//FCE","-MT[mu, nu]"} +{"fcstPolarizationSum-ID8","PolarizationSum[mu, nu, x1,0,VirtualBoson->True]//FCE","-MT[mu, nu]"}, +{"fcstPolarizationSum-ID9", +"PolarizationSum[mu,nu,Heads\[Rule]{LorentzIndex,CartesianIndex}]", + "-Pair[CartesianIndex[nu], LorentzIndex[mu]]"}, +{"fcstPolarizationSum-ID10", +"PolarizationSum[mu,nu,Heads\[Rule]{CartesianIndex,LorentzIndex}]", + "-Pair[CartesianIndex[mu], LorentzIndex[nu]]"}, +{"fcstPolarizationSum-ID11", +"PolarizationSum[mu,nu,Heads\[Rule]{CartesianIndex,CartesianIndex}]\ +", "CartesianPair[CartesianIndex[mu], CartesianIndex[nu]]"}, +{"fcstPolarizationSum-ID12", +"PolarizationSum[mu,nu,k,Heads\[Rule]{LorentzIndex,CartesianIndex}]\ +", "-Pair[CartesianIndex[nu], LorentzIndex[mu]] + \ +(CartesianPair[CartesianIndex[nu], \ +CartesianMomentum[k]]*Pair[LorentzIndex[mu], \ +Momentum[k]])/Pair[Momentum[k], Momentum[k]]"}, +{"fcstPolarizationSum-ID13", +"PolarizationSum[mu,nu,k,Heads\[Rule]{CartesianIndex,LorentzIndex}]\ +", "-Pair[CartesianIndex[mu], LorentzIndex[nu]] + \ +(CartesianPair[CartesianIndex[mu], \ +CartesianMomentum[k]]*Pair[LorentzIndex[nu], \ +Momentum[k]])/Pair[Momentum[k], Momentum[k]]"}, +{"fcstPolarizationSum-ID14", +"PolarizationSum[mu,nu,k,Heads\[Rule]{CartesianIndex,\ +CartesianIndex}]", +"CartesianPair[CartesianIndex[mu], CartesianIndex[nu]] + \ +(CartesianPair[CartesianIndex[mu], \ +CartesianMomentum[k]]*CartesianPair[CartesianIndex[nu], \ +CartesianMomentum[k]])/Pair[Momentum[k], Momentum[k]]"}, +{"fcstPolarizationSum-ID15", +"PolarizationSum[mu,nu,k,n,Heads\[Rule]{LorentzIndex,\ +CartesianIndex},VirtualBoson\[Rule]True]", +"-Pair[CartesianIndex[nu], LorentzIndex[mu]] + \ +(CartesianPair[CartesianIndex[nu], \ +CartesianMomentum[n]]*Pair[LorentzIndex[mu], \ +Momentum[k]])/Pair[Momentum[k], Momentum[n]] + \ +(CartesianPair[CartesianIndex[nu], \ +CartesianMomentum[k]]*Pair[LorentzIndex[mu], \ +Momentum[n]])/Pair[Momentum[k], Momentum[n]] - \ +(CartesianPair[CartesianIndex[nu], \ +CartesianMomentum[k]]*Pair[LorentzIndex[mu], \ +Momentum[k]]*Pair[Momentum[n], Momentum[n]])/Pair[Momentum[k], \ +Momentum[n]]^2"}, +{"fcstPolarizationSum-ID16", +"PolarizationSum[mu,nu,k,n,Heads\[Rule]{CartesianIndex,\ +LorentzIndex},VirtualBoson\[Rule]True]", +"-Pair[CartesianIndex[mu], LorentzIndex[nu]] + \ +(CartesianPair[CartesianIndex[mu], \ +CartesianMomentum[n]]*Pair[LorentzIndex[nu], \ +Momentum[k]])/Pair[Momentum[k], Momentum[n]] + \ +(CartesianPair[CartesianIndex[mu], \ +CartesianMomentum[k]]*Pair[LorentzIndex[nu], \ +Momentum[n]])/Pair[Momentum[k], Momentum[n]] - \ +(CartesianPair[CartesianIndex[mu], \ +CartesianMomentum[k]]*Pair[LorentzIndex[nu], \ +Momentum[k]]*Pair[Momentum[n], Momentum[n]])/Pair[Momentum[k], \ +Momentum[n]]^2"}, +{"fcstPolarizationSum-ID17", +"PolarizationSum[mu,nu,k,n,Heads\[Rule]{CartesianIndex,\ +CartesianIndex},VirtualBoson\[Rule]True]", +"CartesianPair[CartesianIndex[mu], CartesianIndex[nu]] + \ +(CartesianPair[CartesianIndex[mu], \ +CartesianMomentum[n]]*CartesianPair[CartesianIndex[nu], \ +CartesianMomentum[k]] + CartesianPair[CartesianIndex[mu], \ +CartesianMomentum[k]]*CartesianPair[CartesianIndex[nu], \ +CartesianMomentum[n]])/Pair[Momentum[k], Momentum[n]] - \ +(CartesianPair[CartesianIndex[mu], \ +CartesianMomentum[k]]*CartesianPair[CartesianIndex[nu], \ +CartesianMomentum[k]]*Pair[Momentum[n], \ +Momentum[n]])/Pair[Momentum[k], Momentum[n]]^2"} }; diff --git a/Tests/Feynman/QuarkGluonVertex.test b/Tests/Feynman/QuarkGluonVertex.test index 3d3d94ac4..700932546 100644 --- a/Tests/Feynman/QuarkGluonVertex.test +++ b/Tests/Feynman/QuarkGluonVertex.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for QuarkGluonVertex *) diff --git a/Tests/Feynman/QuarkPropagator.test b/Tests/Feynman/QuarkPropagator.test index c35c5859b..9b7d885f5 100644 --- a/Tests/Feynman/QuarkPropagator.test +++ b/Tests/Feynman/QuarkPropagator.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for QuarkPropagator *) diff --git a/Tests/Feynman/SMP.test b/Tests/Feynman/SMP.test index e3c8a3ba1..4bfca55a1 100644 --- a/Tests/Feynman/SMP.test +++ b/Tests/Feynman/SMP.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for SMP *) diff --git a/Tests/Feynman/SMVertex.test b/Tests/Feynman/SMVertex.test index 92208ab50..f37d3164a 100644 --- a/Tests/Feynman/SMVertex.test +++ b/Tests/Feynman/SMVertex.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for SMVertex *) diff --git a/Tests/Feynman/ScalarGluonVertex.test b/Tests/Feynman/ScalarGluonVertex.test index 50874d633..5b9ce7e34 100644 --- a/Tests/Feynman/ScalarGluonVertex.test +++ b/Tests/Feynman/ScalarGluonVertex.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ScalarGluonVertex *) diff --git a/Tests/Feynman/SquareAmplitude.test b/Tests/Feynman/SquareAmplitude.test new file mode 100644 index 000000000..9f1c502ac --- /dev/null +++ b/Tests/Feynman/SquareAmplitude.test @@ -0,0 +1,56 @@ + + +(* :Title: SquareAmplitude.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for SquareAmplitude *) + +(* ------------------------------------------------------------------------ *) + +Tests`Feynman`fcstSquareAmplitude = +({ +{"fcstSquareAmplitude-ID1", "SquareAmplitude[{a},{b}]", "{a*b}"}, +{"fcstSquareAmplitude-ID2", "SquareAmplitude[{a1,a2},{b1,b2}]", +"{a1*b1, a1*b2, a2*b1, a2*b2}"}, +{"fcstSquareAmplitude-ID3", +"SquareAmplitude[{a1,a2,a3},{b1,b2,b3}]", +"{a1*b1, a1*b2, a1*b3, a2*b1, a2*b2, a2*b3, a3*b1, a3*b2, \ +a3*b3}"}, +{"fcstSquareAmplitude-ID4", +"SquareAmplitude[{a1,a2,a3},{b1,b2,b3},List\[Rule]False]", +"a1*b1 + a2*b1 + a3*b1 + a1*b2 + a2*b2 + a3*b2 + a1*b3 + a2*b3 + \ +a3*b3"}, +{"fcstSquareAmplitude-ID5", +"SquareAmplitude[{a1,a2,a3},{b1,b2,b3},Real\[Rule]True]", +"{a1*b1, 2*a2*b1, a2*b2, 2*a3*b1, 2*a3*b2, a3*b3}"}, +{"fcstSquareAmplitude-ID6", +"SquareAmplitude[{a1,a2,a3},{b1,b2,b3},Real\[Rule]True,List\[Rule]\ +False]", "a1*b1 + 2*a2*b1 + 2*a3*b1 + a2*b2 + 2*a3*b2 + a3*b3"}, +{"fcstSquareAmplitude-ID7", +"SquareAmplitude[{a1,a2,a3},{b1,b2,b3},Indexed\[Rule]mark]", +"{a1*b1*mark[1, 1], a1*b2*mark[1, 2], a1*b3*mark[1, 3], \ +a2*b1*mark[2, 1], a2*b2*mark[2, 2], a2*b3*mark[2, 3], a3*b1*mark[3, \ +1], a3*b2*mark[3, 2], a3*b3*mark[3, 3]}"}, +{"fcstSquareAmplitude-ID8", +"SquareAmplitude[{a1,a2,a3},{b1,b2,b3},List\[Rule]False,Indexed\ +\[Rule]mark]", +"a1*b1*mark[1, 1] + a1*b2*mark[1, 2] + a1*b3*mark[1, 3] + \ +a2*b1*mark[2, 1] + a2*b2*mark[2, 2] + a2*b3*mark[2, 3] + \ +a3*b1*mark[3, 1] + a3*b2*mark[3, 2] + a3*b3*mark[3, 3]"}, +{"fcstSquareAmplitude-ID9", +"SquareAmplitude[{a1,a2,a3},{b1,b2,b3},Real\[Rule]True,Indexed\ +\[Rule]mark]", +"{a1*b1*mark[1, 1], 2*a2*b1*mark[2, 1], a2*b2*mark[2, 2], \ +2*a3*b1*mark[3, 1], 2*a3*b2*mark[3, 2], a3*b3*mark[3, 3]}"}, +{"fcstSquareAmplitude-ID10", +"SquareAmplitude[{a1,a2,a3},{b1,b2,b3},Real\[Rule]True,List\[Rule]\ +False,Indexed\[Rule]mark]", +"a1*b1*mark[1, 1] + 2*a2*b1*mark[2, 1] + a2*b2*mark[2, 2] + \ +2*a3*b1*mark[3, 1] + 2*a3*b2*mark[3, 2] + a3*b3*mark[3, 3]"} +}); diff --git a/Tests/Feynman/ToStandardMatrixElement.test b/Tests/Feynman/ToStandardMatrixElement.test new file mode 100644 index 000000000..2080f7345 --- /dev/null +++ b/Tests/Feynman/ToStandardMatrixElement.test @@ -0,0 +1,409 @@ + + +(* :Title: ToStandardMatrixElement.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for ToStandardMatrixElement *) + +(* ------------------------------------------------------------------------ *) + +Tests`Feynman`fcstToStandardMatrixElement = +({ +{"fcstToStandardMatrixElement-ID1", "ToStandardMatrixElement[1]", +"1"}, +{"fcstToStandardMatrixElement-ID2", +"ToStandardMatrixElement[GA[i,k]]", +"StandardMatrixElement[DiracGamma[LorentzIndex[i]] . \ +DiracGamma[LorentzIndex[k]]]"}, +{"fcstToStandardMatrixElement-ID3", +"ToStandardMatrixElement[SUNT[a]]", +"StandardMatrixElement[SUNT[SUNIndex[a]]]"}, +{"fcstToStandardMatrixElement-ID4", +"ToStandardMatrixElement[SUNT[a]GA[i,k]+x]", +"x + StandardMatrixElement[DiracGamma[LorentzIndex[i]] . \ +DiracGamma[LorentzIndex[k]]*SUNT[SUNIndex[a]]]"}, +{"fcstToStandardMatrixElement-ID5", +"ToStandardMatrixElement[x \ +SpinorUBar[p2,m2].GA[6].SpinorV[p1,m1]+y \ +SpinorUBar[p2,m2].GA[7].SpinorV[p1,m1]]", +"x*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . \ +DiracGamma[6] . Spinor[-Momentum[p1], m1, 1]] + \ +y*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . DiracGamma[7] . \ +Spinor[-Momentum[p1], m1, 1]]"}, +{"fcstToStandardMatrixElement-ID6", +"ToStandardMatrixElement[x \ +SpinorUBar[p2,m2].GA[6].SpinorV[p1,m1]+y \ +SpinorUBar[p2,m2].GA[7].SpinorV[p1,m1],DiracSubstitute67\[Rule]True]", + "x*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . \ +DiracGamma[6] . Spinor[-Momentum[p1], m1, 1]] + \ +y*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . DiracGamma[7] . \ +Spinor[-Momentum[p1], m1, 1]]"}, +{"fcstToStandardMatrixElement-ID7", +"ToStandardMatrixElement[-\!\(\*SuperscriptBox[\(gs\), \(2\)]\) \ +Spinor[Momentum[p2],m,1].GS[Polarization[k2,-\[ImaginaryI],\ +Transversality\[Rule]True]].(m+GS[k2+p2]).GS[Polarization[k1,\ +\[ImaginaryI],Transversality\[Rule]True]].Spinor[Momentum[p1],m,1] \ +FAD[{-k2-p2,m},Dimension\[Rule]4] SUNTF[{Glu2},Col5,Col1] \ +SUNTF[{Glu4},Col3,Col5]-\!\(\*SuperscriptBox[\(gs\), \(2\)]\) \ +Spinor[Momentum[p2],m,1].GS[Polarization[k1,\[ImaginaryI],\ +Transversality\[Rule]True]].(m+GS[-k1+p2]).GS[Polarization[k2,-\ +\[ImaginaryI],Transversality\[Rule]True]].Spinor[Momentum[p1],m,1] \ +FAD[{k1-p2,m},Dimension\[Rule]4] SUNTF[{Glu2},Col3,Col5] \ +SUNTF[{Glu4},Col5,Col1]+2 \[ImaginaryI] \!\(\*SuperscriptBox[\(gs\), \ +\(2\)]\) Spinor[Momentum[p2],m,1].GS[Polarization[k1,\[ImaginaryI],\ +Transversality\[Rule]True]].Spinor[Momentum[p1],m,1] \ +FAD[-k1+k2,Dimension\[Rule]4] \ +SP[k1,Polarization[k2,-\[ImaginaryI],Transversality\[Rule]True]] \ +SUNF[Glu2,Glu4,Glu5] SUNTF[{Glu5},Col3,Col1]+2 \[ImaginaryI] \ +\!\(\*SuperscriptBox[\(gs\), \(2\)]\) \ +Spinor[Momentum[p2],m,1].GS[Polarization[k2,-\[ImaginaryI],\ +Transversality\[Rule]True]].Spinor[Momentum[p1],m,1] \ +FAD[-k1+k2,Dimension\[Rule]4] \ +SP[k2,Polarization[k1,\[ImaginaryI],Transversality\[Rule]True]] \ +SUNF[Glu2,Glu4,Glu5] SUNTF[{Glu5},Col3,Col1]+\[ImaginaryI] \ +\!\(\*SuperscriptBox[\(gs\), \(2\)]\) \ +Spinor[Momentum[p2],m,1].GS[-k1-k2].Spinor[Momentum[p1],m,1] \ +FAD[-k1+k2,Dimension\[Rule]4] \ +SP[Polarization[k1,\[ImaginaryI],Transversality\[Rule]True],\ +Polarization[k2,-\[ImaginaryI],Transversality\[Rule]True]] \ +SUNF[Glu2,Glu4,Glu5] SUNTF[{Glu5},Col3,Col1]]", +"-(gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k2] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k2]] . DiracGamma[Momentum[Polarization[k1, I, \ +Transversality -> True]]] . DiracGamma[Momentum[Polarization[k2, -I, \ +Transversality -> True]]] . DiracGamma[6] . Spinor[Momentum[p1], m, \ +1]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]]) - \ +gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k2] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k2]] . DiracGamma[Momentum[Polarization[k1, I, \ +Transversality -> True]]] . DiracGamma[Momentum[Polarization[k2, -I, \ +Transversality -> True]]] . DiracGamma[7] . Spinor[Momentum[p1], m, \ +1]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]] - \ +2*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k2] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[Polarization[k1, I, Transversality -> True]]] . \ +DiracGamma[6] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[p2], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]] - \ +2*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k2] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[Polarization[k1, I, Transversality -> True]]] . \ +DiracGamma[7] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[p2], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]] + \ +2*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k2] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k2]] . DiracGamma[6] . Spinor[Momentum[p1], m, \ +1]*Pair[Momentum[Polarization[k1, I, Transversality -> True]], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]] + \ +2*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k2] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k2]] . DiracGamma[7] . Spinor[Momentum[p1], m, \ +1]*Pair[Momentum[Polarization[k1, I, Transversality -> True]], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]] - \ +gs^2*FeynAmpDenominator[PropagatorDenominator[Momentum[k1] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k1]] . DiracGamma[Momentum[Polarization[k1, I, \ +Transversality -> True]]] . DiracGamma[Momentum[Polarization[k2, -I, \ +Transversality -> True]]] . DiracGamma[6] . Spinor[Momentum[p1], m, \ +1]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]] - \ +gs^2*FeynAmpDenominator[PropagatorDenominator[Momentum[k1] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k1]] . DiracGamma[Momentum[Polarization[k1, I, \ +Transversality -> True]]] . DiracGamma[Momentum[Polarization[k2, -I, \ +Transversality -> True]]] . DiracGamma[7] . Spinor[Momentum[p1], m, \ +1]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]] - \ +2*gs^2*FeynAmpDenominator[PropagatorDenominator[Momentum[k1] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[Polarization[k2, -I, Transversality -> True]]] . \ +DiracGamma[6] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[p2], \ +Momentum[Polarization[k1, I, Transversality -> \ +True]]]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]] - \ +2*gs^2*FeynAmpDenominator[PropagatorDenominator[Momentum[k1] - \ +Momentum[p2], m]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[Polarization[k2, -I, Transversality -> True]]] . \ +DiracGamma[7] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[p2], \ +Momentum[Polarization[k1, I, Transversality -> \ +True]]]*SUNTF[{SUNIndex[Glu2]}, SUNFIndex[Col3], \ +SUNFIndex[Col5]]*SUNTF[{SUNIndex[Glu4]}, SUNFIndex[Col5], \ +SUNFIndex[Col1]]] + \ +(2*I)*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k1] + \ +Momentum[k2], 0]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[Polarization[k1, I, Transversality -> True]]] . \ +DiracGamma[6] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[k1], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNF[SUNIndex[Glu2], SUNIndex[Glu4], \ +SUNIndex[Glu5]]*SUNTF[{SUNIndex[Glu5]}, SUNFIndex[Col3], \ +SUNFIndex[Col1]]] + \ +(2*I)*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k1] + \ +Momentum[k2], 0]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[Polarization[k1, I, Transversality -> True]]] . \ +DiracGamma[7] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[k1], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNF[SUNIndex[Glu2], SUNIndex[Glu4], \ +SUNIndex[Glu5]]*SUNTF[{SUNIndex[Glu5]}, SUNFIndex[Col3], \ +SUNFIndex[Col1]]] + \ +(2*I)*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k1] + \ +Momentum[k2], 0]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[Polarization[k2, -I, Transversality -> True]]] . \ +DiracGamma[6] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[k2], \ +Momentum[Polarization[k1, I, Transversality -> \ +True]]]*SUNF[SUNIndex[Glu2], SUNIndex[Glu4], \ +SUNIndex[Glu5]]*SUNTF[{SUNIndex[Glu5]}, SUNFIndex[Col3], \ +SUNFIndex[Col1]]] + \ +(2*I)*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k1] + \ +Momentum[k2], 0]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[Polarization[k2, -I, Transversality -> True]]] . \ +DiracGamma[7] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[k2], \ +Momentum[Polarization[k1, I, Transversality -> \ +True]]]*SUNF[SUNIndex[Glu2], SUNIndex[Glu4], \ +SUNIndex[Glu5]]*SUNTF[{SUNIndex[Glu5]}, SUNFIndex[Col3], \ +SUNFIndex[Col1]]] - \ +I*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k1] + \ +Momentum[k2], 0]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k1]] . DiracGamma[6] . Spinor[Momentum[p1], m, \ +1]*Pair[Momentum[Polarization[k1, I, Transversality -> True]], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNF[SUNIndex[Glu2], SUNIndex[Glu4], \ +SUNIndex[Glu5]]*SUNTF[{SUNIndex[Glu5]}, SUNFIndex[Col3], \ +SUNFIndex[Col1]]] - \ +I*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k1] + \ +Momentum[k2], 0]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k1]] . DiracGamma[7] . Spinor[Momentum[p1], m, \ +1]*Pair[Momentum[Polarization[k1, I, Transversality -> True]], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNF[SUNIndex[Glu2], SUNIndex[Glu4], \ +SUNIndex[Glu5]]*SUNTF[{SUNIndex[Glu5]}, SUNFIndex[Col3], \ +SUNFIndex[Col1]]] - \ +I*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k1] + \ +Momentum[k2], 0]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k2]] . DiracGamma[6] . Spinor[Momentum[p1], m, \ +1]*Pair[Momentum[Polarization[k1, I, Transversality -> True]], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNF[SUNIndex[Glu2], SUNIndex[Glu4], \ +SUNIndex[Glu5]]*SUNTF[{SUNIndex[Glu5]}, SUNFIndex[Col3], \ +SUNFIndex[Col1]]] - \ +I*gs^2*FeynAmpDenominator[PropagatorDenominator[-Momentum[k1] + \ +Momentum[k2], 0]]*StandardMatrixElement[Spinor[Momentum[p2], m, 1] . \ +DiracGamma[Momentum[k2]] . DiracGamma[7] . Spinor[Momentum[p1], m, \ +1]*Pair[Momentum[Polarization[k1, I, Transversality -> True]], \ +Momentum[Polarization[k2, -I, Transversality -> \ +True]]]*SUNF[SUNIndex[Glu2], SUNIndex[Glu4], \ +SUNIndex[Glu5]]*SUNTF[{SUNIndex[Glu5]}, SUNFIndex[Col3], \ +SUNFIndex[Col1]]]"}, +{"fcstToStandardMatrixElement-ID8", +"ToStandardMatrixElement[x SpinorUBar[p2,m2].SpinorV[p1,m1]+y \ +SpinorUBar[p2,m2].GA[7].SpinorV[p1,m1]]", +"x*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . \ +DiracGamma[6] . Spinor[-Momentum[p1], m1, 1]] + (x + \ +y)*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . DiracGamma[7] \ +. Spinor[-Momentum[p1], m1, 1]]"}, +{"fcstToStandardMatrixElement-ID9", +"ToStandardMatrixElement[x SpinorUBar[p2,m2].SpinorV[p1,m1]+y \ +SpinorUBar[p2,m2].GA[7].SpinorV[p1,m1],SpinorChainChiralSplit->False]\ +", "x*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . \ +Spinor[-Momentum[p1], m1, 1]] + \ +y*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . DiracGamma[7] . \ +Spinor[-Momentum[p1], m1, 1]]"}, +{"fcstToStandardMatrixElement-ID10", +"ToStandardMatrixElement[x \ +SpinorUBar[p2,m2].GA[5].SpinorV[p1,m1]+y \ +SpinorUBar[p2,m2].GA[7].SpinorV[p1,m1],DiracSubstitute5\[Rule]False]", + "x*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . \ +DiracGamma[5] . Spinor[-Momentum[p1], m1, 1]] + \ +y*StandardMatrixElement[Spinor[Momentum[p2], m2, 1] . DiracGamma[7] . \ +Spinor[-Momentum[p1], m1, 1]]"}, +{"fcstToStandardMatrixElement-ID11", +"ToStandardMatrixElement[GA[nu], Spinor -> True,FCE->True]", + "GA[nu]"}, +{"fcstToStandardMatrixElement-ID12", +"ToStandardMatrixElement[-(1/\[Pi]^2) + I (2 I \[Pi]^2 Spinor[Momentum[p3], ms, 1].GS[ + Polarization[p2, I]].GA[7].Spinor[Momentum[p1], mb, 1] PaVe[0, + 0, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] + + 2 I \[Pi]^2 Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[ + Momentum[p1], mb, 1] PaVe[1, + 1, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] SP[p1, Polarization[p2, I]] + + I \[Pi]^2 Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[ + Momentum[p1], mb, 1] PaVe[ + 1, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] (2 SP[p1, Polarization[p2, I]] - + SP[p2, Polarization[p2, I]]) - + I \[Pi]^2 C0[SPD[p1, p1], SPD[p2, p2], + SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], mt^2, mh^2, + mh^2] Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[ + Momentum[p1], mb, 1] SP[p2, Polarization[p2, I]] - + I \[Pi]^2 (2 Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[ + Momentum[p1], mb, 1] - + Spinor[Momentum[p3], ms, 1].GS[p2].GA[7].Spinor[Momentum[p1], + mb, 1]) PaVe[ + 2, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] SP[p2, Polarization[p2, I]] + + 2 I \[Pi]^2 Spinor[Momentum[p3], ms, 1].GS[p2].GA[7].Spinor[ + Momentum[p1], mb, 1] PaVe[2, + 2, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] SP[p2, Polarization[p2, I]] - + 2 I \[Pi]^2 PaVe[1, + 2, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> + True] (Spinor[Momentum[p3], ms, 1].GS[p2].GA[7].Spinor[ + Momentum[p1], mb, 1] SP[p1, Polarization[p2, I]] + + Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[Momentum[p1], + mb, 1] SP[p2, Polarization[p2, I]])),FCE->True]", + "2*PaVe[0, 0, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GS[Polarization[p2, I]] . GA[7] . Spinor[Momentum[p1], mb, 1]] + +2*mb*(PaVe[1, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] + +PaVe[1, 1, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True])* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GA[6] . Spinor[Momentum[p1], mb, 1]*SP[p1, Polarization[p2, I]]] - +2*PaVe[1, 2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GS[p2] . GA[7] . Spinor[Momentum[p1], mb, 1]*SP[p1, Polarization[p2, I]]] - +mb*(C0[SPD[p1, p1], SPD[p2, p2], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], mt^2, mh^2, mh^2] + PaVe[1, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, + {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] + 2*PaVe[2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True] + 2*PaVe[1, 2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True])*StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GA[6] . Spinor[Momentum[p1], mb, 1]*SP[p2, Polarization[p2, I]]] + +(PaVe[2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] + +2*PaVe[2, 2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True])* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GS[p2] . GA[7] . Spinor[Momentum[p1], mb, 1]*SP[p2, Polarization[p2, I]]]"}, + + + + + +{"fcstToStandardMatrixElement-ID12", +"ToStandardMatrixElement[-(1/\[Pi]^2) + I (2 I \[Pi]^2 Spinor[Momentum[p3], ms, 1].GS[ + Polarization[p2, I]].GA[7].Spinor[Momentum[p1], mb, 1] PaVe[0, + 0, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] + + 2 I \[Pi]^2 Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[ + Momentum[p1], mb, 1] PaVe[1, + 1, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] SP[p1, Polarization[p2, I]] + + I \[Pi]^2 Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[ + Momentum[p1], mb, 1] PaVe[ + 1, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] (2 SP[p1, Polarization[p2, I]] - + SP[p2, Polarization[p2, I]]) - + I \[Pi]^2 C0[SPD[p1, p1], SPD[p2, p2], + SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], mt^2, mh^2, + mh^2] Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[ + Momentum[p1], mb, 1] SP[p2, Polarization[p2, I]] - + I \[Pi]^2 (2 Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[ + Momentum[p1], mb, 1] - + Spinor[Momentum[p3], ms, 1].GS[p2].GA[7].Spinor[Momentum[p1], + mb, 1]) PaVe[ + 2, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] SP[p2, Polarization[p2, I]] + + 2 I \[Pi]^2 Spinor[Momentum[p3], ms, 1].GS[p2].GA[7].Spinor[ + Momentum[p1], mb, 1] PaVe[2, + 2, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] SP[p2, Polarization[p2, I]] - + 2 I \[Pi]^2 PaVe[1, + 2, {SPD[p1, p1], SPD[p1, p1] + 2 SPD[p1, p2] + SPD[p2, p2], + SPD[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> + True] (Spinor[Momentum[p3], ms, 1].GS[p2].GA[7].Spinor[ + Momentum[p1], mb, 1] SP[p1, Polarization[p2, I]] + + Spinor[Momentum[p3], ms, 1].GS[p1].GA[7].Spinor[Momentum[p1], + mb, 1] SP[p2, Polarization[p2, I]])),FCE->True,ChangeDimension->D]", + "2*PaVe[0, 0, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, +PaVeAutoOrder -> True, PaVeAutoReduce -> True]*StandardMatrixElement[ +Spinor[Momentum[p3, D], ms, 1] . GSD[Polarization[p2, I]] . GA[7] . Spinor[Momentum[p1, D], mb, 1]] + +2*mb*(PaVe[1, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True] + +PaVe[1, 1, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True])*StandardMatrixElement[ +Spinor[Momentum[p3, D], ms, 1] . GA[6] . Spinor[Momentum[p1, D], mb, 1]*SPD[p1, Polarization[p2, I]]] - +2*PaVe[1, 2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, +PaVeAutoOrder -> True, PaVeAutoReduce -> True]*StandardMatrixElement[ +Spinor[Momentum[p3, D], ms, 1] . GSD[p2] . GA[7] . Spinor[Momentum[p1, D], mb, 1]* + SPD[p1, Polarization[p2, I]]] - +mb*(C0[SPD[p1, p1], SPD[p2, p2], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], mt^2, mh^2, mh^2] + +PaVe[1, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True] + +2*PaVe[2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True] + +2*PaVe[1, 2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True])*StandardMatrixElement[ +Spinor[Momentum[p3, D], ms, 1] . GA[6] . Spinor[Momentum[p1, D], mb, 1]*SPD[p2, Polarization[p2, I]]] + +(PaVe[2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True] + +2*PaVe[2, 2, {SPD[p1, p1], SPD[p1, p1] + 2*SPD[p1, p2] + SPD[p2, p2], SPD[p2, p2]}, {mh^2, mt^2, mh^2}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True])*StandardMatrixElement[ +Spinor[Momentum[p3, D], ms, 1] . GSD[p2] . GA[7] . Spinor[Momentum[p1, D], mb, 1]* + SPD[p2, Polarization[p2, I]]]"}, +{"fcstToStandardMatrixElement-ID13", +"ToStandardMatrixElement[ +Spinor[-Momentum[p1, D], mb, 1].GAD[mu].GAD[nu].GA[7].Spinor[ + Momentum[p3, D], ms, 1] Spinor[Momentum[p1, D], mb, 1].GAD[ + nu].GAD[mu].GA[7].Spinor[-Momentum[p2, D], ms, 1]] // +FCCanonicalizeDummyIndices[#, LorentzIndexNames -> {mu, nu}, +FCE -> True] &","2 D StandardMatrixElement[ +Spinor[-Momentum[p1, D], mb, 1].GA[7].Spinor[Momentum[p3, D], ms, + 1] Spinor[Momentum[p1, D], mb, 1].GA[7].Spinor[-Momentum[p2, D], + ms, 1]] - +StandardMatrixElement[ +Spinor[-Momentum[p1, D], mb, 1].GAD[mu].GAD[nu].GA[7].Spinor[ + Momentum[p3, D], ms, 1] Spinor[Momentum[p1, D], mb, 1].GAD[ + mu].GAD[nu].GA[7].Spinor[-Momentum[p2, D], ms, 1]]"}, +{"fcstToStandardMatrixElement-ID14", "ToStandardMatrixElement[ +SpinorUBar[p1].GA[mu, nu].SpinorV[p2] SpinorVBar[p3].GA[mu, + nu].SpinorU[p4] + +SpinorUBar[p1].GA[al, be].SpinorV[p2] SpinorVBar[p3].GA[al, + be].SpinorU[p4], LorentzIndexNames -> {i1, i2}, FCE -> True]", +"2 StandardMatrixElement[ +Spinor[Momentum[p1], 0, 1].GA[i1].GA[i2].GA[ + 6].Spinor[-Momentum[p2], 0, 1] Spinor[-Momentum[p3], 0, 1].GA[ + i1].GA[i2].GA[6].Spinor[Momentum[p4], 0, 1]] + +2 StandardMatrixElement[ +Spinor[Momentum[p1], 0, 1].GA[i1].GA[i2].GA[ + 7].Spinor[-Momentum[p2], 0, 1] Spinor[-Momentum[p3], 0, 1].GA[ + i1].GA[i2].GA[6].Spinor[Momentum[p4], 0, 1]] + +2 StandardMatrixElement[ +Spinor[Momentum[p1], 0, 1].GA[i1].GA[i2].GA[ + 6].Spinor[-Momentum[p2], 0, 1] Spinor[-Momentum[p3], 0, 1].GA[ + i1].GA[i2].GA[7].Spinor[Momentum[p4], 0, 1]] + +2 StandardMatrixElement[ +Spinor[Momentum[p1], 0, 1].GA[i1].GA[i2].GA[ + 7].Spinor[-Momentum[p2], 0, 1] Spinor[-Momentum[p3], 0, 1].GA[ + i1].GA[i2].GA[7].Spinor[Momentum[p4], 0, 1]]"} +}); diff --git a/Tests/LoopIntegrals/Apart2.test b/Tests/LoopIntegrals/Apart2.test index d909844bd..e6c2aec3d 100644 --- a/Tests/LoopIntegrals/Apart2.test +++ b/Tests/LoopIntegrals/Apart2.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Apart2 *) diff --git a/Tests/LoopIntegrals/ApartFF.test b/Tests/LoopIntegrals/ApartFF.test index d039f3cd2..1c4a5afbc 100644 --- a/Tests/LoopIntegrals/ApartFF.test +++ b/Tests/LoopIntegrals/ApartFF.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ApartFF *) @@ -35,7 +35,7 @@ Tests`LoopIntegrals`fcstApartFF = {"fcstApartFF-ID11", "ApartFF[SPD[q2,p]SPD[q1,p]FAD[{q1,m},{q2,m},q1-p,q2-p,q2-q1],{q1,\ q2}]//FCE", -"-FAD[{q1, m}, -p + q2, q1 - q2]/2 + FAD[{q1, m}, {q2, m}, -q1 + q2]/4 + +"-FAD[{q1, m}, -p + q2, q1 - q2]/2 + FAD[{q1, m}, {q2, m}, q1 - q2]/4 + (FAD[q2, q1, {-p + q1, m}, q1 - q2]*(m^2 + SPD[p, p]))/2 - (FAD[{q1, m}, {q2, m}, q1 - q2, -p + q1]*(m^2 + SPD[p, p]))/2 + (FAD[{q1, m}, {q2, m}, -p + q2, q1 - q2, -p + q1]*(m^2 + SPD[p, p])^2)/4"}, @@ -76,5 +76,90 @@ tmp = ApartFF[FAD[q, {-(p/2) + q, m}, {p/2 + q, m}, {p/2 + q, m}], {q}]//FCE; \n {"fcstApartFF-ID23","FCClearScalarProducts[]; \n SPD[p, p] = 4 m^2; \n tmp = ApartFF[FAD[{k1 - p/2 + q, m}, {k1 - p/2 + q, m}, {p/2 + q, m}, q, {-(p/2) + q, m}], {q}]//FCE; \n FCClearScalarProducts[]; \n tmp ","-FAD[q, {-(p/2) + q, m}, {-(p/2) + q, m}, {-k1 + p/2 + q, m}, {-k1 + p/2 + q, m}] + 2 FAD[{q, m}, {-k1 + q, m}, {-k1 + q, m}, -{-p + q, m}, {-p + q, m}]"} +{-p + q, m}, {-p + q, m}]"}, +{"fcstApartFF-ID24","ApartFF[SPD[k1, p] SPD[p, p] FAD[{p, m0}], {p}, MaxIterations -> 1, FDS -> False] // FCE", +"FAD[{p, m0}] SPD[k1, p] SPD[p, p]"}, +{"fcstApartFF-ID25","ApartFF[SPD[k1, p] SPD[p, p] FAD[{p, m0}], {p}, MaxIterations -> 2, FDS -> False] // FCE", +"m0^2 FAD[{p, m0}] SPD[k1, p]"}, +{"fcstApartFF-ID26", +"ApartFF[SPD[l,-p1+p3+p2]SFAD[{l,m1^2},{l-p1+p3+p2,m3^2},l-p1+p2,l-\ +k1],{l},FDS\[Rule]False,FCE\[Rule]True]", +"1/2 SFAD[{{l, 0}, {m1^2, 1}, 1}, {{-k1 + l, 0}, {0, 1}, + 1}, {{l - p1 + p2, 0}, {0, 1}, 1}] - +1/2 SFAD[{{-k1 + l, 0}, {0, 1}, 1}, {{l - p1 + p2, 0}, {0, 1}, + 1}, {{l - p1 + p2 + p3, 0}, {m3^2, 1}, 1}] - +1/2 SFAD[{{l, 0}, {m1^2, 1}, 1}, {{-k1 + l, 0}, {0, 1}, + 1}, {{l - p1 + p2, 0}, {0, 1}, + 1}, {{l - p1 + p2 + p3, 0}, {m3^2, 1}, 1}] (m1^2 - m3^2 + + SPD[p1, p1] - 2 SPD[p1, p2] - 2 SPD[p1, p3] + SPD[p2, p2] + + 2 SPD[p2, p3] + SPD[p3, p3])"}, +{"fcstApartFF-ID27", +"ApartFF[SPD[l,-p1+p3+p2]SFAD[{l,-m1^2},{l-p1+p3+p2,-m3^2},l-p1+p2,\ +l-k1],{l},FDS\[Rule]False,FCE\[Rule]True]", +"SFAD[{{l, 0}, {-m1^2, 1}, 1}, {{-k1 + l, 0}, {0, 1}, 1}, +{{l - p1 + p2, 0}, {0, 1}, 1}]/2 - +SFAD[{{-k1 + l, 0}, {0, 1}, 1}, {{l - p1 + p2, 0}, {0, 1}, 1}, +{{l - p1 + p2 + p3, 0}, {-m3^2, 1}, 1}]/2 + +(SFAD[{{l, 0}, {-m1^2, 1}, 1}, {{-k1 + l, 0}, {0, 1}, 1}, + {{l - p1 + p2, 0}, {0, 1}, 1}, {{l - p1 + p2 + p3, 0}, {-m3^2, 1}, 1}]* +(m1^2 - m3^2 - SPD[p1, p1] + 2*SPD[p1, p2] + 2*SPD[p1, p3] - + SPD[p2, p2] - 2*SPD[p2, p3] - SPD[p3, p3]))/2"}, +{"fcstApartFF-ID28", +"ApartFF[CSPD[l,-p1+p3+p2]CFAD[{l,m1^2},{l-p1+p3+p2,m3^2},l-p1+p2,\ +l-k1],{l},FDS\[Rule]False,FCE\[Rule]True]", +"CFAD[{{l, 0}, {m1^2, -1}, 1}, {{-k1 + l, 0}, {0, -1}, 1}, +{{l - p1 + p2, 0}, {0, -1}, 1}]/2 - +CFAD[{{-k1 + l, 0}, {0, -1}, 1}, {{l - p1 + p2, 0}, {0, -1}, 1}, +{{l - p1 + p2 + p3, 0}, {m3^2, -1}, 1}]/2 + +(CFAD[{{l, 0}, {m1^2, -1}, 1}, {{-k1 + l, 0}, {0, -1}, 1}, + {{l - p1 + p2, 0}, {0, -1}, 1}, {{l - p1 + p2 + p3, 0}, {m3^2, -1}, 1}]* +(m1^2 - m3^2 - CSPD[p1, p1] + 2*CSPD[p1, p2] + 2*CSPD[p1, p3] - + CSPD[p2, p2] - 2*CSPD[p2, p3] - CSPD[p3, p3]))/2"}, +{"fcstApartFF-ID29", +"ApartFF[FAD[l,{k1+k2+l-p2,MC},{k1+l,MC}]SPD[k1,l],{l},FDS\[Rule]\ +False,FCE\[Rule]True]", +"FAD[l, {k1 + k2 + l - p2, MC}]/2 - FAD[{k1 + l, MC}, {k1 + k2 + l \ +- p2, MC}]/2 + (FAD[{k1 + k2 + l - p2, MC}, l, {k1 + l, MC}]*(MC^2 - \ +SPD[k1, k1]))/2"}, +{"fcstApartFF-ID30", +"ApartFF[SFAD[l,{k1+k2+l-p2,MC^2},{k1+l,MC^2}]SPD[k1,l],{l},FDS\ +\[Rule]False,FCE\[Rule]True]", +"SFAD[{{l, 0}, {0, 1}, 1}, {{k1 + k2 + l - p2, 0}, {MC^2, 1}, 1}]/2 - +SFAD[{{k1 + l, 0}, {MC^2, 1}, 1}, {{k1 + k2 + l - p2, 0}, {MC^2, 1}, 1}]/ +2 + (SFAD[{{l, 0}, {0, 1}, 1}, {{k1 + l, 0}, {MC^2, 1}, 1}, + {{k1 + k2 + l - p2, 0}, {MC^2, 1}, 1}]*(MC^2 - SPD[k1, k1]))/2"}, +{"fcstApartFF-ID31", +"ApartFF[SFAD[l,{k1+k2+l-p2,-MC^2},{k1+l,-MC^2}]SPD[k1,l],{l},FDS\ +\[Rule]False,FCE\[Rule]True]", +"SFAD[{{l, 0}, {0, 1}, 1}, {{k1 + k2 + l - p2, 0}, {-MC^2, 1}, 1}]/2 - +SFAD[{{k1 + l, 0}, {-MC^2, 1}, 1}, {{k1 + k2 + l - p2, 0}, {-MC^2, 1}, 1}]/ +2 - (SFAD[{{l, 0}, {0, 1}, 1}, {{k1 + l, 0}, {-MC^2, 1}, 1}, + {{k1 + k2 + l - p2, 0}, {-MC^2, 1}, 1}]*(MC^2 + SPD[k1, k1]))/2"}, +{"fcstApartFF-ID32", +"ApartFF[CFAD[l,{k1+k2+l-p2,MC^2},{k1+l,MC^2}]CSPD[k1,l],{l},FDS\ +\[Rule]False,FCE\[Rule]True]", +"CFAD[{{l, 0}, {0, -1}, 1}, {{k1 + k2 + l - p2, 0}, {MC^2, -1}, 1}]/2 - +CFAD[{{k1 + l, 0}, {MC^2, -1}, 1}, {{k1 + k2 + l - p2, 0}, {MC^2, -1}, 1}]/ +2 - (CFAD[{{l, 0}, {0, -1}, 1}, {{k1 + l, 0}, {MC^2, -1}, 1}, + {{k1 + k2 + l - p2, 0}, {MC^2, -1}, 1}]*(MC^2 + CSPD[k1, k1]))/2"}, +{"fcstApartFF-ID33", +"ApartFF[SPD[q2, p] SPD[q1, p] FAD[{q1, m}, {q2, m}, q1 - p, q2 - p, +q2 - q1, q1], {q1, q2}, Numerator -> False, FCE -> True]", +"-((FAD[q1, {q2, m}, -p + q2, q1 - q2, -p + q1] SPD[p, q1] SPD[p, q2])/ +m^2) + (FAD[{q1, m}, {q2, m}, -p + q2, q1 - q2, -p + q1] SPD[p, +q1] SPD[p, q2])/m^2"}, +{"fcstApartFF-ID34", "ApartFF[FVD[q, i] FVD[q, j], {q}]","0"}, +{"fcstApartFF-ID35", "ApartFF[FVD[q, i] FVD[q, j] SFAD[{q, m, -1}], {q}]","0"}, +{"fcstApartFF-ID36", "ApartFF[CVD[q, i] CVD[q, j] CFAD[{q, mm}, {q, m, -1}], {q}, +FCE -> True]","(m - mm) CFAD[{{q, 0}, {mm, -1}, 1}] CVD[q, i] CVD[q, j]"}, +{"fcstApartFF-ID34", +"ApartFF[CTdec[{{q, i}, {q, j}}, {p}, List -> False] CFAD[q,q + p], {q}, FCE -> True]", +"(CFAD[{{q, 0}, {0, -1}, 1}, {{p + q, 0}, {0, -1}, +1}] (-CVD[p, i] CVD[p, j] + D CVD[p, i] CVD[p, j] - +CSPD[p, p] KDD[i, j]))/(4 (-2 + D))"}, +{"fcstApartFF-ID35", "ApartFF[TC[q] GFAD[(TC[q] - x)] SFAD[{{0, p.q}, x}], {q}, FCE -> True]", +"GFAD[{{-x + TC[q], 1}, 1}] SFAD[{{0, p.q}, {x, 1}, 1}] TC[q]"}, +{"fcstApartFF-ID36", "ApartFF[TC[q] GFAD[(TC[q] - x)] SFAD[{{0, p.q}, x}], {q}, +TemporalMomentum -> True, FCE -> True]", +"x GFAD[{{-x + TC[q], 1}, 1}] SFAD[{{0, p.q}, {x, 1}, 1}]"} }) diff --git a/Tests/LoopIntegrals/CTdec.test b/Tests/LoopIntegrals/CTdec.test new file mode 100644 index 000000000..b355b5343 --- /dev/null +++ b/Tests/LoopIntegrals/CTdec.test @@ -0,0 +1,427 @@ + + +(* :Title: Tdec.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for CTdec *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstCTdec = +({ +{"fcstCTdec-ID1", "CTdec[{{l,i1},{l,i2}},{p1}]", +"{{X1 -> -1 + D, X2 -> CSPD[l, l], X3 -> CSPD[l, p1], X4 -> \ +CSPD[p1, p1]}, -(((X1*X3^2 - X2*X4)*CVD[p1, i1]*CVD[p1, i2])/((1 - \ +X1)*X4^2)) + ((X3^2 - X2*X4)*KDD[i1, i2])/((1 - X1)*X4)}"}, +{"fcstCTdec-ID2", "CTdec[{{l,i1},{l,i2}},{p1},UseTIDL\[Rule]False]", + "{{X1 -> -1 + D, X2 -> CSPD[l, l], X3 -> CSPD[l, p1], X4 -> \ +CSPD[p1, p1]}, -(((X1*X3^2 - X2*X4)*CVD[p1, i1]*CVD[p1, i2])/((1 - \ +X1)*X4^2)) + ((X3^2 - X2*X4)*KDD[i1, i2])/((1 - X1)*X4)}"}, +{"fcstCTdec-ID3", "CTdec[{{l,i1},{l,i2}},{p1},List\[Rule]False]", +"-((((-1 + D)*CSPD[l, p1]^2 - CSPD[l, l]*CSPD[p1, p1])*CVD[p1, \ +i1]*CVD[p1, i2])/((2 - D)*CSPD[p1, p1]^2)) + ((CSPD[l, p1]^2 - \ +CSPD[l, l]*CSPD[p1, p1])*KDD[i1, i2])/((2 - D)*CSPD[p1, p1])"}, +{"fcstCTdec-ID4", +"CTdec[{{l,i1},{l,i2}},{p1},UseTIDL\[Rule]False,List\[Rule]False]", + "-((((-1 + D)*CSPD[l, p1]^2 - CSPD[l, l]*CSPD[p1, p1])*CVD[p1, \ +i1]*CVD[p1, i2])/((2 - D)*CSPD[p1, p1]^2)) + ((CSPD[l, p1]^2 - \ +CSPD[l, l]*CSPD[p1, p1])*KDD[i1, i2])/((2 - D)*CSPD[p1, p1])"}, +{"fcstCTdec-ID5", +"CTdec[{{l,i1},{l,i2}},{p1},List\[Rule]False,FeynCalcExternal\ +\[Rule]False]", +"(CartesianPair[CartesianIndex[i1, -1 + D], CartesianIndex[i2, -1 \ ++ D]]*(CartesianPair[CartesianMomentum[l, -1 + D], \ +CartesianMomentum[p1, -1 + D]]^2 - CartesianPair[CartesianMomentum[l, \ +-1 + D], CartesianMomentum[l, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], \ +CartesianMomentum[p1, -1 + D]]))/((2 - \ +D)*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, \ +-1 + D]]) - (CartesianPair[CartesianIndex[i1, -1 + D], \ +CartesianMomentum[p1, -1 + D]]*CartesianPair[CartesianIndex[i2, -1 + \ +D], CartesianMomentum[p1, -1 + D]]*((-1 + \ +D)*CartesianPair[CartesianMomentum[l, -1 + D], CartesianMomentum[p1, \ +-1 + D]]^2 - CartesianPair[CartesianMomentum[l, -1 + D], \ +CartesianMomentum[l, -1 + D]]*CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p1, -1 + D]]))/((2 - \ +D)*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, \ +-1 + D]]^2)"}, +{"fcstCTdec-ID6", +"CTdec[{{l,i1},{l,i2}},{p1},UseTIDL\[Rule]False,List\[Rule]False,\ +FeynCalcExternal\[Rule]False]", +"(CartesianPair[CartesianIndex[i1, -1 + D], CartesianIndex[i2, -1 \ ++ D]]*(CartesianPair[CartesianMomentum[l, -1 + D], \ +CartesianMomentum[p1, -1 + D]]^2 - CartesianPair[CartesianMomentum[l, \ +-1 + D], CartesianMomentum[l, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], \ +CartesianMomentum[p1, -1 + D]]))/((2 - \ +D)*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, \ +-1 + D]]) - (CartesianPair[CartesianIndex[i1, -1 + D], \ +CartesianMomentum[p1, -1 + D]]*CartesianPair[CartesianIndex[i2, -1 + \ +D], CartesianMomentum[p1, -1 + D]]*((-1 + \ +D)*CartesianPair[CartesianMomentum[l, -1 + D], CartesianMomentum[p1, \ +-1 + D]]^2 - CartesianPair[CartesianMomentum[l, -1 + D], \ +CartesianMomentum[l, -1 + D]]*CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p1, -1 + D]]))/((2 - \ +D)*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, \ +-1 + D]]^2)"}, +{"fcstCTdec-ID7", +"CTdec[{{l,i1},{l,i2}},{p1},List\[Rule]False,Dimension\[Rule]3]", +"((3*CSP[l, p1]^2 - CSP[l, l]*CSP[p1, p1])*CV[p1, i1]*CV[p1, \ +i2])/(2*CSP[p1, p1]^2) - ((CSP[l, p1]^2 - CSP[l, l]*CSP[p1, \ +p1])*KD[i1, i2])/(2*CSP[p1, p1])"}, +{"fcstCTdec-ID8", +"CTdec[{{l,i1},{l,i2}},{p1},UseTIDL\[Rule]False,List\[Rule]False,\ +Dimension\[Rule]3]", +"((3*CSP[l, p1]^2 - CSP[l, l]*CSP[p1, p1])*CV[p1, i1]*CV[p1, \ +i2])/(2*CSP[p1, p1]^2) - ((CSP[l, p1]^2 - CSP[l, l]*CSP[p1, \ +p1])*KD[i1, i2])/(2*CSP[p1, p1])"}, +{"fcstCTdec-ID9", +"CTdec[{{l,i1},{l,i2}},{p1},List\[Rule]False,Dimension\[Rule]3,\ +FeynCalcExternal\[Rule]False]", +"-(CartesianPair[CartesianIndex[i1], \ +CartesianIndex[i2]]*(CartesianPair[CartesianMomentum[l], \ +CartesianMomentum[p1]]^2 - CartesianPair[CartesianMomentum[l], \ +CartesianMomentum[l]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p1]]))/(2*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p1]]) + (CartesianPair[CartesianIndex[i1], \ +CartesianMomentum[p1]]*CartesianPair[CartesianIndex[i2], \ +CartesianMomentum[p1]]*(3*CartesianPair[CartesianMomentum[l], \ +CartesianMomentum[p1]]^2 - CartesianPair[CartesianMomentum[l], \ +CartesianMomentum[l]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p1]]))/(2*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p1]]^2)"}, +{"fcstCTdec-ID10", +"CTdec[{{l,i1},{l,i2},{l,i3}},{},UseTIDL\[Rule]False]", "{0, 0}"}, +{"fcstCTdec-ID11", +"CTdec[{{q1,$3050},{q1,$3489},{q2,$3047},{q2,$3488}},{k1},\ +Dimension\[Rule]D-1,List\[Rule]True,UseTIDL\[Rule]False,FCE\[Rule]\ +True]", "{{X1 -> -1 + D, X2 -> CSPD[q1, q1], X3 -> CSPD[q1, q2], X4 -> \ +CSPD[k1, q1], X5 -> CSPD[q2, q2], X6 -> CSPD[k1, q2], X7 -> CSPD[k1, \ +k1]}, -(((8*X4^2*X6^2 + 6*X1*X4^2*X6^2 + X1^2*X4^2*X6^2 - \ +2*X4^2*X5*X7 - X1*X4^2*X5*X7 - 8*X3*X4*X6*X7 - 4*X1*X3*X4*X6*X7 - \ +2*X2*X6^2*X7 - X1*X2*X6^2*X7 + 2*X3^2*X7^2 + X2*X5*X7^2)*CVD[k1, \ +$3047]*CVD[k1, $3050]*CVD[k1, $3488]*CVD[k1, $3489])/((1 - \ +X1^2)*X7^4)) + ((4*X4^2*X6^2 - X1^2*X4^2*X6^2 - 2*X4^2*X5*X7 + \ +X1^2*X4^2*X5*X7 - 4*X3*X4*X6*X7 + X1*X2*X6^2*X7 + 2*X3^2*X7^2 - \ +X1*X2*X5*X7^2)*CVD[k1, $3050]*CVD[k1, $3489]*KDD[$3047, $3488])/((2 - \ +X1)*(1 - X1^2)*X7^3) + ((4*X4^2*X6^2 - X1^2*X4^2*X6^2 - X4^2*X5*X7 - \ +4*X3*X4*X6*X7 + X1*X3*X4*X6*X7 + X1^2*X3*X4*X6*X7 - X2*X6^2*X7 + \ +X3^2*X7^2 - X1*X3^2*X7^2 + X2*X5*X7^2)*(CVD[k1, $3488]*CVD[k1, \ +$3489]*KDD[$3047, $3050] + CVD[k1, $3050]*CVD[k1, $3488]*KDD[$3047, \ +$3489]))/((2 - X1)*(1 - X1^2)*X7^3) + ((4*X4^2*X6^2 - X1^2*X4^2*X6^2 \ ++ X1*X4^2*X5*X7 - 4*X3*X4*X6*X7 - 2*X2*X6^2*X7 + X1^2*X2*X6^2*X7 + \ +2*X3^2*X7^2 - X1*X2*X5*X7^2)*CVD[k1, $3047]*CVD[k1, $3488]*KDD[$3050, \ +$3489])/((2 - X1)*(1 - X1^2)*X7^3) - ((2*X4^2*X6^2 - X1*X4^2*X6^2 + \ +X1*X4^2*X5*X7 - 4*X3*X4*X6*X7 + X1*X2*X6^2*X7 + 2*X3^2*X7^2 - \ +X1*X2*X5*X7^2)*KDD[$3047, $3488]*KDD[$3050, $3489])/((2 - X1)*(1 - \ +X1^2)*X7^2) + ((4*X4^2*X6^2 - X1^2*X4^2*X6^2 - X4^2*X5*X7 - \ +4*X3*X4*X6*X7 + X1*X3*X4*X6*X7 + X1^2*X3*X4*X6*X7 - X2*X6^2*X7 + \ +X3^2*X7^2 - X1*X3^2*X7^2 + X2*X5*X7^2)*(CVD[k1, $3047]*CVD[k1, \ +$3489]*KDD[$3050, $3488] + CVD[k1, $3047]*CVD[k1, $3050]*KDD[$3488, \ +$3489]))/((2 - X1)*(1 - X1^2)*X7^3) - ((2*X4^2*X6^2 - X1*X4^2*X6^2 - \ +X4^2*X5*X7 - 2*X3*X4*X6*X7 + 2*X1*X3*X4*X6*X7 - X2*X6^2*X7 + \ +X3^2*X7^2 - X1*X3^2*X7^2 + X2*X5*X7^2)*(KDD[$3047, $3489]*KDD[$3050, \ +$3488] + KDD[$3047, $3050]*KDD[$3488, $3489]))/((2 - X1)*(1 - \ +X1^2)*X7^2)}"}, +{"fcstCTdec-ID12", +"CTdec[{{l,i1},{l,i2},{l,i3}},{},UseTIDL\[Rule]False,List\[Rule]\ +False]", "0"}, +{"fcstCTdec-ID13", +"CTdec[{{l1,i1},{l1,i2},{l2,i3}},{},UseTIDL\[Rule]False]", +"{0, 0}"}, +{"fcstCTdec-ID14", +"CTdec[{{l1,i1},{l1,i2},{l2,i3}},{},UseTIDL\[Rule]False,List\[Rule]\ +False]", "0"}, +{"fcstCTdec-ID15", +"CTdec[{{q2, mu1}, {q1, mu2}, {q1, mu3}, {q1, mu4}, {q1, mu5}}, \ +{k1}, +UseParallelization -> False, List -> False]", +"-(((24*CSPD[k1, q1]^4*CSPD[k1, q2] + 10*(-1 + D)*CSPD[k1, \ +q1]^4*CSPD[k1, q2] + (-1 + D)^2*CSPD[k1, q1]^4*CSPD[k1, q2] - \ +24*CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[k1, q2]*CSPD[q1, q1] - 6*(-1 + \ +D)*CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[k1, q2]*CSPD[q1, q1] + 3*CSPD[k1, \ +k1]^2*CSPD[k1, q2]*CSPD[q1, q1]^2 - 16*CSPD[k1, k1]*CSPD[k1, \ +q1]^3*CSPD[q1, q2] - 4*(-1 + D)*CSPD[k1, k1]*CSPD[k1, q1]^3*CSPD[q1, \ +q2] + 12*CSPD[k1, k1]^2*CSPD[k1, q1]*CSPD[q1, q1]*CSPD[q1, \ +q2])*CVD[k1, mu1]*CVD[k1, mu2]*CVD[k1, mu3]*CVD[k1, mu4]*CVD[k1, \ +mu5])/((1 - (-1 + D)^2)*CSPD[k1, k1]^5)) + (CSPD[k1, q1]*(4*CSPD[k1, \ +q1]^2 + (-1 + D)*CSPD[k1, q1]^2 - 3*CSPD[k1, k1]*CSPD[q1, \ +q1])*(CSPD[k1, q1]*CSPD[k1, q2] - CSPD[k1, k1]*CSPD[q1, q2])*(CVD[k1, \ +mu3]*CVD[k1, mu4]*CVD[k1, mu5]*KDD[mu1, mu2] + CVD[k1, mu2]*CVD[k1, \ +mu4]*CVD[k1, mu5]*KDD[mu1, mu3] + CVD[k1, mu2]*CVD[k1, mu3]*CVD[k1, \ +mu5]*KDD[mu1, mu4] + CVD[k1, mu2]*CVD[k1, mu3]*CVD[k1, mu4]*KDD[mu1, \ +mu5]))/((1 - (-1 + D)^2)*CSPD[k1, k1]^4) + ((CSPD[k1, q1]^2 - \ +CSPD[k1, k1]*CSPD[q1, q1])*(4*CSPD[k1, q1]^2*CSPD[k1, q2] + (-1 + \ +D)*CSPD[k1, q1]^2*CSPD[k1, q2] - CSPD[k1, k1]*CSPD[k1, q2]*CSPD[q1, \ +q1] - 2*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[q1, q2])*(CVD[k1, mu1]*CVD[k1, \ +mu4]*CVD[k1, mu5]*KDD[mu2, mu3] + CVD[k1, mu1]*CVD[k1, mu3]*CVD[k1, \ +mu5]*KDD[mu2, mu4] + CVD[k1, mu1]*CVD[k1, mu3]*CVD[k1, mu4]*KDD[mu2, \ +mu5] + CVD[k1, mu1]*CVD[k1, mu2]*CVD[k1, mu5]*KDD[mu3, mu4] + CVD[k1, \ +mu1]*CVD[k1, mu2]*CVD[k1, mu4]*KDD[mu3, mu5] + CVD[k1, mu1]*CVD[k1, \ +mu2]*CVD[k1, mu3]*KDD[mu4, mu5]))/((1 - (-1 + D)^2)*CSPD[k1, k1]^4) - \ +(CSPD[k1, q1]*(CSPD[k1, q1]^2 - CSPD[k1, k1]*CSPD[q1, q1])*(CSPD[k1, \ +q1]*CSPD[k1, q2] - CSPD[k1, k1]*CSPD[q1, q2])*(CVD[k1, mu5]*KDD[mu1, \ +mu4]*KDD[mu2, mu3] + CVD[k1, mu4]*KDD[mu1, mu5]*KDD[mu2, mu3] + \ +CVD[k1, mu5]*KDD[mu1, mu3]*KDD[mu2, mu4] + CVD[k1, mu3]*KDD[mu1, \ +mu5]*KDD[mu2, mu4] + CVD[k1, mu4]*KDD[mu1, mu3]*KDD[mu2, mu5] + \ +CVD[k1, mu3]*KDD[mu1, mu4]*KDD[mu2, mu5] + CVD[k1, mu5]*KDD[mu1, \ +mu2]*KDD[mu3, mu4] + CVD[k1, mu2]*KDD[mu1, mu5]*KDD[mu3, mu4] + \ +CVD[k1, mu4]*KDD[mu1, mu2]*KDD[mu3, mu5] + CVD[k1, mu2]*KDD[mu1, \ +mu4]*KDD[mu3, mu5] + CVD[k1, mu3]*KDD[mu1, mu2]*KDD[mu4, mu5] + \ +CVD[k1, mu2]*KDD[mu1, mu3]*KDD[mu4, mu5]))/((1 - (-1 + D)^2)*CSPD[k1, \ +k1]^3) - (CSPD[k1, q2]*(CSPD[k1, q1]^2 - CSPD[k1, k1]*CSPD[q1, \ +q1])^2*(CVD[k1, mu1]*KDD[mu2, mu5]*KDD[mu3, mu4] + CVD[k1, \ +mu1]*KDD[mu2, mu4]*KDD[mu3, mu5] + CVD[k1, mu1]*KDD[mu2, \ +mu3]*KDD[mu4, mu5]))/((1 - (-1 + D)^2)*CSPD[k1, k1]^3)"}, +{"fcstCTdec-ID16", +"CTdec[{{q1,$3050},{q1,$3489},{q2,$3047},{q2,$3488}},{k1},\ +Dimension\[Rule]D-1,List\[Rule]False,UseTIDL\[Rule]False,FCE\[Rule]\ +True]", "-(((8*CSPD[k1, q1]^2*CSPD[k1, q2]^2 + 6*(-1 + D)*CSPD[k1, \ +q1]^2*CSPD[k1, q2]^2 + (-1 + D)^2*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - \ +2*CSPD[k1, k1]*CSPD[k1, q2]^2*CSPD[q1, q1] - (-1 + D)*CSPD[k1, \ +k1]*CSPD[k1, q2]^2*CSPD[q1, q1] - 8*CSPD[k1, k1]*CSPD[k1, \ +q1]*CSPD[k1, q2]*CSPD[q1, q2] - 4*(-1 + D)*CSPD[k1, k1]*CSPD[k1, \ +q1]*CSPD[k1, q2]*CSPD[q1, q2] + 2*CSPD[k1, k1]^2*CSPD[q1, q2]^2 - \ +2*CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[q2, q2] - (-1 + D)*CSPD[k1, \ +k1]*CSPD[k1, q1]^2*CSPD[q2, q2] + CSPD[k1, k1]^2*CSPD[q1, \ +q1]*CSPD[q2, q2])*CVD[k1, $3047]*CVD[k1, $3050]*CVD[k1, \ +$3488]*CVD[k1, $3489])/((1 - (-1 + D)^2)*CSPD[k1, k1]^4)) + \ +((4*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - (-1 + D)^2*CSPD[k1, \ +q1]^2*CSPD[k1, q2]^2 + (-1 + D)*CSPD[k1, k1]*CSPD[k1, q2]^2*CSPD[q1, \ +q1] - 4*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, q2]*CSPD[q1, q2] + \ +2*CSPD[k1, k1]^2*CSPD[q1, q2]^2 - 2*CSPD[k1, k1]*CSPD[k1, \ +q1]^2*CSPD[q2, q2] + (-1 + D)^2*CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[q2, \ +q2] - (-1 + D)*CSPD[k1, k1]^2*CSPD[q1, q1]*CSPD[q2, q2])*CVD[k1, \ +$3050]*CVD[k1, $3489]*KDD[$3047, $3488])/((1 - (-1 + D)^2)*(3 - \ +D)*CSPD[k1, k1]^3) + ((4*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - (-1 + \ +D)^2*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - CSPD[k1, k1]*CSPD[k1, \ +q2]^2*CSPD[q1, q1] - 4*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, \ +q2]*CSPD[q1, q2] + (-1 + D)*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, \ +q2]*CSPD[q1, q2] + (-1 + D)^2*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, \ +q2]*CSPD[q1, q2] + CSPD[k1, k1]^2*CSPD[q1, q2]^2 - (-1 + D)*CSPD[k1, \ +k1]^2*CSPD[q1, q2]^2 - CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[q2, q2] + \ +CSPD[k1, k1]^2*CSPD[q1, q1]*CSPD[q2, q2])*(CVD[k1, $3488]*CVD[k1, \ +$3489]*KDD[$3047, $3050] + CVD[k1, $3050]*CVD[k1, $3488]*KDD[$3047, \ +$3489]))/((1 - (-1 + D)^2)*(3 - D)*CSPD[k1, k1]^3) + ((4*CSPD[k1, \ +q1]^2*CSPD[k1, q2]^2 - (-1 + D)^2*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - \ +2*CSPD[k1, k1]*CSPD[k1, q2]^2*CSPD[q1, q1] + (-1 + D)^2*CSPD[k1, \ +k1]*CSPD[k1, q2]^2*CSPD[q1, q1] - 4*CSPD[k1, k1]*CSPD[k1, \ +q1]*CSPD[k1, q2]*CSPD[q1, q2] + 2*CSPD[k1, k1]^2*CSPD[q1, q2]^2 + (-1 \ ++ D)*CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[q2, q2] - (-1 + D)*CSPD[k1, \ +k1]^2*CSPD[q1, q1]*CSPD[q2, q2])*CVD[k1, $3047]*CVD[k1, \ +$3488]*KDD[$3050, $3489])/((1 - (-1 + D)^2)*(3 - D)*CSPD[k1, k1]^3) - \ +((2*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - (-1 + D)*CSPD[k1, q1]^2*CSPD[k1, \ +q2]^2 + (-1 + D)*CSPD[k1, k1]*CSPD[k1, q2]^2*CSPD[q1, q1] - \ +4*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, q2]*CSPD[q1, q2] + 2*CSPD[k1, \ +k1]^2*CSPD[q1, q2]^2 + (-1 + D)*CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[q2, \ +q2] - (-1 + D)*CSPD[k1, k1]^2*CSPD[q1, q1]*CSPD[q2, q2])*KDD[$3047, \ +$3488]*KDD[$3050, $3489])/((1 - (-1 + D)^2)*(3 - D)*CSPD[k1, k1]^2) + \ +((4*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - (-1 + D)^2*CSPD[k1, \ +q1]^2*CSPD[k1, q2]^2 - CSPD[k1, k1]*CSPD[k1, q2]^2*CSPD[q1, q1] - \ +4*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, q2]*CSPD[q1, q2] + (-1 + \ +D)*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, q2]*CSPD[q1, q2] + (-1 + \ +D)^2*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, q2]*CSPD[q1, q2] + CSPD[k1, \ +k1]^2*CSPD[q1, q2]^2 - (-1 + D)*CSPD[k1, k1]^2*CSPD[q1, q2]^2 - \ +CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[q2, q2] + CSPD[k1, k1]^2*CSPD[q1, \ +q1]*CSPD[q2, q2])*(CVD[k1, $3047]*CVD[k1, $3489]*KDD[$3050, $3488] + \ +CVD[k1, $3047]*CVD[k1, $3050]*KDD[$3488, $3489]))/((1 - (-1 + \ +D)^2)*(3 - D)*CSPD[k1, k1]^3) - ((2*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - \ +(-1 + D)*CSPD[k1, q1]^2*CSPD[k1, q2]^2 - CSPD[k1, k1]*CSPD[k1, \ +q2]^2*CSPD[q1, q1] - 2*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, \ +q2]*CSPD[q1, q2] + 2*(-1 + D)*CSPD[k1, k1]*CSPD[k1, q1]*CSPD[k1, \ +q2]*CSPD[q1, q2] + CSPD[k1, k1]^2*CSPD[q1, q2]^2 - (-1 + D)*CSPD[k1, \ +k1]^2*CSPD[q1, q2]^2 - CSPD[k1, k1]*CSPD[k1, q1]^2*CSPD[q2, q2] + \ +CSPD[k1, k1]^2*CSPD[q1, q1]*CSPD[q2, q2])*(KDD[$3047, \ +$3489]*KDD[$3050, $3488] + KDD[$3047, $3050]*KDD[$3488, $3489]))/((1 \ +- (-1 + D)^2)*(3 - D)*CSPD[k1, k1]^2)"} +}); + + +Tests`LoopIntegrals`fcstCTdecNegativeMomenta = +({ +{"fcstCTdecNegativeMomenta-ID1", +"ExpandScalarProduct[(CTdec[{{q,mu}},{-p1}]/.{p1\[Rule]-p1})]\ +===FCI[CTdec[{{q,mu}},{p1}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID2", +"ExpandScalarProduct[(CTdec[{{q,mu}},{-p1,p2}]/.{p1\[Rule]-p1})]\ +===FCI[CTdec[{{q,mu}},{p1,p2}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID3", +"ExpandScalarProduct[(CTdec[{{q,mu}},{-p1,-p2}]/.{p1\[Rule]-p1,p2\ +\[Rule]-p2})]===FCI[CTdec[{{q,mu}},{p1,p2}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID4", +"ExpandScalarProduct[(CTdec[{{q,mu}},{-p1,-p2,p3}]/.{p1\[Rule]-p1,\ +p2\[Rule]-p2})]===FCI[CTdec[{{q,mu}},{p1,p2,p3}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID5", +"ExpandScalarProduct[(CTdec[{{q,mu}},{p1,-p2,p3}]/.{p2\[Rule]-p2})]\ +===FCI[CTdec[{{q,mu}},{p1,p2,p3}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID6", +"ExpandScalarProduct[(CTdec[{{q,mu}},{-p1,-p2,-p3}]/.{p1\[Rule]-p1,\ +p2\[Rule]-p2,p3\[Rule]-p3})]===FCI[CTdec[{{q,mu}},{p1,p2,p3}]]", +"True"}, +{"fcstCTdecNegativeMomenta-ID7", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu}},{-p1}]/.{p1\[Rule]-p1})\ +]===FCI[CTdec[{{q,mu},{q,nu}},{p1}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID8", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu}},{-p1,p2}]/.{p1\[Rule]-\ +p1})]===FCI[CTdec[{{q,mu},{q,nu}},{p1,p2}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID9", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu}},{-p1,-p2}]/.{p1\[Rule]-\ +p1,p2\[Rule]-p2})]===FCI[CTdec[{{q,mu},{q,nu}},{p1,p2}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID10", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu}},{-p1,-p2,p3}]/.{p1\ +\[Rule]-p1,p2\[Rule]-p2})]===FCI[CTdec[{{q,mu},{q,nu}},{p1,p2,p3}]]", +"True"}, +{"fcstCTdecNegativeMomenta-ID11", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu}},{p1,-p2,p3}]/.{p2\ +\[Rule]-p2})]===FCI[CTdec[{{q,mu},{q,nu}},{p1,p2,p3}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID12", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu}},{-p1,-p2,-p3}]/.{p1\ +\[Rule]-p1,p2\[Rule]-p2,p3\[Rule]-p3})]===FCI[CTdec[{{q,mu},{q,nu}},{\ +p1,p2,p3}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID13", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu},{q,rho}},{-p1}]/.{p1\ +\[Rule]-p1})]===FCI[CTdec[{{q,mu},{q,nu},{q,rho}},{p1}]]", "True"}, +{"fcstCTdecNegativeMomenta-ID14", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu},{q,rho}},{-p1,p2}]/.{p1\ +\[Rule]-p1})]===FCI[CTdec[{{q,mu},{q,nu},{q,rho}},{p1,p2}]]", +"True"}, +{"fcstCTdecNegativeMomenta-ID15", +"ExpandScalarProduct[(CTdec[{{q,mu},{q,nu},{q,rho}},{-p1,-p2}]/.{\ +p1\[Rule]-p1,p2\[Rule]-p2})]===FCI[CTdec[{{q,mu},{q,nu},{q,rho}},{p1,\ +p2}]]", "True"} +}) + +Tests`LoopIntegrals`fcstCTdecVanishingGD = +({ +{"fcstCTdecVanishingGD-ID1", +"FCClearScalarProducts[];CartesianScalarProduct[p1,p1]=0;\ +CartesianScalarProduct[p2,p2]=0;CartesianScalarProduct[p1,p2]=0;CTdec[\ +{{q,mu}},{p1}]", "{{}, CVD[q, mu]}"}, +{"fcstCTdecVanishingGD-ID2", +"CTdec[{{q,mu}},{p1},List\[Rule]False]", "CVD[q, mu]"}, +{"fcstCTdecVanishingGD-ID3", "CTdec[{{q,mu},{q,nu}},{p1}]", +"{{}, CVD[q, mu]*CVD[q, nu]}"}, +{"fcstCTdecVanishingGD-ID4", +"CTdec[{{q,mu},{q,nu}},{p1},List\[Rule]False]", +"CVD[q, mu]*CVD[q, nu]"}, +{"fcstCTdecVanishingGD-ID5", "CTdec[{{q,mu}},{p1,p2}]", +"{{}, CVD[q, mu]}"}, +{"fcstCTdecVanishingGD-ID6", +"CTdec[{{q,mu}},{p1,p2},List\[Rule]False]", "CVD[q, mu]"}, +{"fcstCTdecVanishingGD-ID7", "CTdec[{{q,mu},{q,nu}},{p1,p2}]", +"{{}, CVD[q, mu]*CVD[q, nu]}"}, +{"fcstCTdecVanishingGD-ID8", +"CTdec[{{q,mu},{q,nu}},{p1,p2},List\[Rule]False]", +"CVD[q, mu]*CVD[q, nu]"}, +{"fcstCTdecVanishingGD-ID9", +"FCClearScalarProducts[]; CartesianScalarProduct[p3,p3]=m^2; \ +CartesianScalarProduct[p4,p4]=m^2; CartesianScalarProduct[p3,p4]=m^2; \ +CTdec[{{q,mu}},{p3,p4}]", "{{}, CVD[q, mu]}"}, +{"fcstCTdecVanishingGD-ID10", +"CTdec[{{q,mu}},{p3,p4},List\[Rule]False]", "CVD[q, mu]"}, +{"fcstCTdecVanishingGD-ID11", +"tmp = CTdec[{{q,mu}},{p,p},List\[Rule]False]; FCClearScalarProducts[]; tmp", "CVD[q, mu]"} +}); + +Tests`LoopIntegrals`fcstCTdecVanishingMultiLoop = +({ +{"fcstCTdecVanishingMultiLoop-ID1", +"CTdec[{{q1,mu},{q2,nu},{q2,rho}},{p},List\[Rule]False,UseTIDL\ +\[Rule]False]//FCE", +"-(((2*CSPD[p, q1]*CSPD[p, q2]^2 + (-1 + D)*CSPD[p, q1]*CSPD[p, \ +q2]^2 - 2*CSPD[p, p]*CSPD[p, q2]*CSPD[q1, q2] - CSPD[p, p]*CSPD[p, \ +q1]*CSPD[q2, q2])*CVD[p, mu]*CVD[p, nu]*CVD[p, rho])/((2 - D)*CSPD[p, \ +p]^3)) + (CSPD[p, q2]*(CSPD[p, q1]*CSPD[p, q2] - CSPD[p, p]*CSPD[q1, \ +q2])*(CVD[p, rho]*KDD[mu, nu] + CVD[p, nu]*KDD[mu, rho]))/((2 - \ +D)*CSPD[p, p]^2) + (CSPD[p, q1]*(CSPD[p, q2]^2 - CSPD[p, p]*CSPD[q2, \ +q2])*CVD[p, mu]*KDD[nu, rho])/((2 - D)*CSPD[p, p]^2)"}, +{"fcstCTdecVanishingMultiLoop-ID2", +"CTdec[{{q1,mu},{q2,nu},{q3,rho}},{p},List\[Rule]False,UseTIDL\ +\[Rule]False]//FCE", +"-(((2*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, q3] + (-1 + D)*CSPD[p, \ +q1]*CSPD[p, q2]*CSPD[p, q3] - CSPD[p, p]*CSPD[p, q3]*CSPD[q1, q2] - \ +CSPD[p, p]*CSPD[p, q2]*CSPD[q1, q3] - CSPD[p, p]*CSPD[p, q1]*CSPD[q2, \ +q3])*CVD[p, mu]*CVD[p, nu]*CVD[p, rho])/((2 - D)*CSPD[p, p]^3)) + \ +(CSPD[p, q3]*(CSPD[p, q1]*CSPD[p, q2] - CSPD[p, p]*CSPD[q1, \ +q2])*CVD[p, rho]*KDD[mu, nu])/((2 - D)*CSPD[p, p]^2) + (CSPD[p, \ +q2]*(CSPD[p, q1]*CSPD[p, q3] - CSPD[p, p]*CSPD[q1, q3])*CVD[p, \ +nu]*KDD[mu, rho])/((2 - D)*CSPD[p, p]^2) + (CSPD[p, q1]*(CSPD[p, \ +q2]*CSPD[p, q3] - CSPD[p, p]*CSPD[q2, q3])*CVD[p, mu]*KDD[nu, \ +rho])/((2 - D)*CSPD[p, p]^2)"}, +{"fcstCTdecVanishingMultiLoop-ID3", +"CTdec[{{q1,mu},{q2,nu},{q3,rho},{q3,si}},{p},List\[Rule]False,\ +UseTIDL\[Rule]False]//FCE", +"-(((8*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, q3]^2 + 6*(-1 + D)*CSPD[p, \ +q1]*CSPD[p, q2]*CSPD[p, q3]^2 + (-1 + D)^2*CSPD[p, q1]*CSPD[p, \ +q2]*CSPD[p, q3]^2 - 2*CSPD[p, p]*CSPD[p, q3]^2*CSPD[q1, q2] - (-1 + \ +D)*CSPD[p, p]*CSPD[p, q3]^2*CSPD[q1, q2] - 4*CSPD[p, p]*CSPD[p, \ +q2]*CSPD[p, q3]*CSPD[q1, q3] - 2*(-1 + D)*CSPD[p, p]*CSPD[p, \ +q2]*CSPD[p, q3]*CSPD[q1, q3] - 4*CSPD[p, p]*CSPD[p, q1]*CSPD[p, \ +q3]*CSPD[q2, q3] - 2*(-1 + D)*CSPD[p, p]*CSPD[p, q1]*CSPD[p, \ +q3]*CSPD[q2, q3] + 2*CSPD[p, p]^2*CSPD[q1, q3]*CSPD[q2, q3] - \ +2*CSPD[p, p]*CSPD[p, q1]*CSPD[p, q2]*CSPD[q3, q3] - (-1 + D)*CSPD[p, \ +p]*CSPD[p, q1]*CSPD[p, q2]*CSPD[q3, q3] + CSPD[p, p]^2*CSPD[q1, \ +q2]*CSPD[q3, q3])*CVD[p, mu]*CVD[p, nu]*CVD[p, rho]*CVD[p, si])/((1 - \ +(-1 + D)^2)*CSPD[p, p]^4)) + ((4*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, \ +q3]^2 - (-1 + D)^2*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, q3]^2 - 2*CSPD[p, \ +p]*CSPD[p, q3]^2*CSPD[q1, q2] + (-1 + D)^2*CSPD[p, p]*CSPD[p, \ +q3]^2*CSPD[q1, q2] - 2*CSPD[p, p]*CSPD[p, q2]*CSPD[p, q3]*CSPD[q1, \ +q3] - 2*CSPD[p, p]*CSPD[p, q1]*CSPD[p, q3]*CSPD[q2, q3] + 2*CSPD[p, \ +p]^2*CSPD[q1, q3]*CSPD[q2, q3] + (-1 + D)*CSPD[p, p]*CSPD[p, \ +q1]*CSPD[p, q2]*CSPD[q3, q3] - (-1 + D)*CSPD[p, p]^2*CSPD[q1, \ +q2]*CSPD[q3, q3])*CVD[p, rho]*CVD[p, si]*KDD[mu, nu])/((1 - (-1 + \ +D)^2)*(3 - D)*CSPD[p, p]^3) + ((4*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, \ +q3]^2 - (-1 + D)^2*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, q3]^2 - CSPD[p, \ +p]*CSPD[p, q3]^2*CSPD[q1, q2] - 3*CSPD[p, p]*CSPD[p, q2]*CSPD[p, \ +q3]*CSPD[q1, q3] + (-1 + D)^2*CSPD[p, p]*CSPD[p, q2]*CSPD[p, \ +q3]*CSPD[q1, q3] - CSPD[p, p]*CSPD[p, q1]*CSPD[p, q3]*CSPD[q2, q3] + \ +(-1 + D)*CSPD[p, p]*CSPD[p, q1]*CSPD[p, q3]*CSPD[q2, q3] + CSPD[p, \ +p]^2*CSPD[q1, q3]*CSPD[q2, q3] - (-1 + D)*CSPD[p, p]^2*CSPD[q1, \ +q3]*CSPD[q2, q3] - CSPD[p, p]*CSPD[p, q1]*CSPD[p, q2]*CSPD[q3, q3] + \ +CSPD[p, p]^2*CSPD[q1, q2]*CSPD[q3, q3])*(CVD[p, nu]*CVD[p, \ +si]*KDD[mu, rho] + CVD[p, nu]*CVD[p, rho]*KDD[mu, si]))/((1 - (-1 + \ +D)^2)*(3 - D)*CSPD[p, p]^3) + ((4*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, \ +q3]^2 - (-1 + D)^2*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, q3]^2 - CSPD[p, \ +p]*CSPD[p, q3]^2*CSPD[q1, q2] - CSPD[p, p]*CSPD[p, q2]*CSPD[p, \ +q3]*CSPD[q1, q3] + (-1 + D)*CSPD[p, p]*CSPD[p, q2]*CSPD[p, \ +q3]*CSPD[q1, q3] - 3*CSPD[p, p]*CSPD[p, q1]*CSPD[p, q3]*CSPD[q2, q3] \ ++ (-1 + D)^2*CSPD[p, p]*CSPD[p, q1]*CSPD[p, q3]*CSPD[q2, q3] + \ +CSPD[p, p]^2*CSPD[q1, q3]*CSPD[q2, q3] - (-1 + D)*CSPD[p, \ +p]^2*CSPD[q1, q3]*CSPD[q2, q3] - CSPD[p, p]*CSPD[p, q1]*CSPD[p, \ +q2]*CSPD[q3, q3] + CSPD[p, p]^2*CSPD[q1, q2]*CSPD[q3, q3])*(CVD[p, \ +mu]*CVD[p, si]*KDD[nu, rho] + CVD[p, mu]*CVD[p, rho]*KDD[nu, \ +si]))/((1 - (-1 + D)^2)*(3 - D)*CSPD[p, p]^3) - ((2*CSPD[p, \ +q1]*CSPD[p, q2]*CSPD[p, q3]^2 - (-1 + D)*CSPD[p, q1]*CSPD[p, \ +q2]*CSPD[p, q3]^2 - CSPD[p, p]*CSPD[p, q3]^2*CSPD[q1, q2] - CSPD[p, \ +p]*CSPD[p, q2]*CSPD[p, q3]*CSPD[q1, q3] + (-1 + D)*CSPD[p, p]*CSPD[p, \ +q2]*CSPD[p, q3]*CSPD[q1, q3] - CSPD[p, p]*CSPD[p, q1]*CSPD[p, \ +q3]*CSPD[q2, q3] + (-1 + D)*CSPD[p, p]*CSPD[p, q1]*CSPD[p, \ +q3]*CSPD[q2, q3] + CSPD[p, p]^2*CSPD[q1, q3]*CSPD[q2, q3] - (-1 + \ +D)*CSPD[p, p]^2*CSPD[q1, q3]*CSPD[q2, q3] - CSPD[p, p]*CSPD[p, \ +q1]*CSPD[p, q2]*CSPD[q3, q3] + CSPD[p, p]^2*CSPD[q1, q2]*CSPD[q3, \ +q3])*(KDD[mu, si]*KDD[nu, rho] + KDD[mu, rho]*KDD[nu, si]))/((1 - (-1 \ ++ D)^2)*(3 - D)*CSPD[p, p]^2) + ((4*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, \ +q3]^2 - (-1 + D)^2*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, q3]^2 + (-1 + \ +D)*CSPD[p, p]*CSPD[p, q3]^2*CSPD[q1, q2] - 2*CSPD[p, p]*CSPD[p, \ +q2]*CSPD[p, q3]*CSPD[q1, q3] - 2*CSPD[p, p]*CSPD[p, q1]*CSPD[p, \ +q3]*CSPD[q2, q3] + 2*CSPD[p, p]^2*CSPD[q1, q3]*CSPD[q2, q3] - \ +2*CSPD[p, p]*CSPD[p, q1]*CSPD[p, q2]*CSPD[q3, q3] + (-1 + \ +D)^2*CSPD[p, p]*CSPD[p, q1]*CSPD[p, q2]*CSPD[q3, q3] - (-1 + \ +D)*CSPD[p, p]^2*CSPD[q1, q2]*CSPD[q3, q3])*CVD[p, mu]*CVD[p, \ +nu]*KDD[rho, si])/((1 - (-1 + D)^2)*(3 - D)*CSPD[p, p]^3) - \ +((2*CSPD[p, q1]*CSPD[p, q2]*CSPD[p, q3]^2 - (-1 + D)*CSPD[p, \ +q1]*CSPD[p, q2]*CSPD[p, q3]^2 + (-1 + D)*CSPD[p, p]*CSPD[p, \ +q3]^2*CSPD[q1, q2] - 2*CSPD[p, p]*CSPD[p, q2]*CSPD[p, q3]*CSPD[q1, \ +q3] - 2*CSPD[p, p]*CSPD[p, q1]*CSPD[p, q3]*CSPD[q2, q3] + 2*CSPD[p, \ +p]^2*CSPD[q1, q3]*CSPD[q2, q3] + (-1 + D)*CSPD[p, p]*CSPD[p, \ +q1]*CSPD[p, q2]*CSPD[q3, q3] - (-1 + D)*CSPD[p, p]^2*CSPD[q1, \ +q2]*CSPD[q3, q3])*KDD[mu, nu]*KDD[rho, si])/((1 - (-1 + D)^2)*(3 - \ +D)*CSPD[p, p]^2)"} +}); + diff --git a/Tests/LoopIntegrals/FCApart.test b/Tests/LoopIntegrals/FCApart.test index 0968239d3..6037f0d3f 100644 --- a/Tests/LoopIntegrals/FCApart.test +++ b/Tests/LoopIntegrals/FCApart.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCApart *) @@ -61,14 +61,13 @@ m}]*(m^2 - SPD[p1, p1] - 2*SPD[p2, p2]))/4 + (FAD[k, {k - p2, m}, {k \ {"fcstFCApart-ID12", "FCApart[ \ (SPD[q1,p1]SPD[q2,p2])FAD[q1,q2,{q1+p1,m},{q2+p2,m},{q2+p2,m}],{q1,q2}\ -]//FCE", "-FAD[q1, {-p2 + q1, m}, {-p1 + q2, m}]/4 + FAD[{-p1 + q1, \ -m}, {-p2 + q2, m}, {-p2 + q2, m}]/4 + (FAD[q1, q2, {-p1 + q1, m}, \ -{-p2 + q2, m}]*(m^2 - SPD[p1, p1]))/4 - (FAD[q1, {-p1 + q1, m}, {-p2 \ -+ q2, m}, {-p2 + q2, m}]*(m^2 - SPD[p1, p1]))/4 + (FAD[q1, q2, {-p2 + \ -q1, m}, {-p2 + q1, m}]*(m^2 - SPD[p2, p2]))/4 - (FAD[q1, {-p2 + q1, \ -m}, {-p2 + q1, m}, {-p1 + q2, m}]*(m^2 - SPD[p2, p2]))/4 + (FAD[q1, \ -q2, {-p1 + q1, m}, {-p2 + q2, m}, {-p2 + q2, m}]*(m^2 - SPD[p1, \ -p1])*(m^2 - SPD[p2, p2]))/4"}, +]//FCE", +"-FAD[q1, {q2, m}, {-p2 + q1, m}]/4 + FAD[{q1, m}, {q1, m}, {q2, m}]/4 + +(FAD[q1, q2, {-p1 + q1, m}, {-p2 + q2, m}]*(m^2 - SPD[p1, p1]))/4 - +(FAD[q1, {q2, m}, {q2, m}, {-p1 + q1, m}]*(m^2 - SPD[p1, p1]))/4 - +(FAD[q1, {q2, m}, {-p2 + q1, m}, {-p2 + q1, m}]*(m^2 - SPD[p2, p2]))/4 + +(FAD[q1, q2, {-p1 + q1, m}, {-p2 + q2, m}, {-p2 + q2, m}]*(m^2 - +SPD[p1, p1])*(m^2 - SPD[p2, p2]))/4"}, {"fcstFCApart-ID13", "ApartFF[FVD[q1, mu] FVD[q2, nu] FAD[q1, q2, {p1 - q2}, {q1 - p1}, {q2 - p1}], {q1, q2}] // FCE", "FAD[q1, q2, -p1 + q2, -p1 + q1, -p1 + q2]*FVD[q1, mu]*FVD[q2, \ @@ -127,7 +126,7 @@ k1])^2)/4 + (m0^2*FAD[{p, m0}, {-k1 + p, m1}]*(m0^2 - m1^2 + SPD[k1, \ k1])^2)/4 - SPD[k1, p]/2 - (m0^2*FAD[{p, m0}]*SPD[k1, p])/2 \ + (FAD[{-k1 + p, m1}]*(m0^2 - 2*m1^2 + 2*SPD[k1, k1])*SPD[p, \ p])/4 + (FAD[{-k1 + p, m1}]*SPD[p, p]^2)/4- SPD[p,p]/4"}, -{"fcstFCApart-ID20.1", +{"fcstFCApart-ID21", "FCApart[FAD[{p,m0},{-k1+p,m1}] SPD[k1,p] \ ^2SPD[p,p],{p},MaxIterations\[Rule]Infinity,FDS\[Rule]False]//FCE", "- (m0^2*FAD[{p, m0}]*(m0^2 - m1^2 \ @@ -135,5 +134,314 @@ p])/4 + (FAD[{-k1 + p, m1}]*SPD[p, p]^2)/4- SPD[p,p]/4"}, k1])^2)/4 + (m0^2*FAD[{p, m0}, {-k1 + p, m1}]*(m0^2 - m1^2 + SPD[k1, \ k1])^2)/4 - (m0^2*FAD[{p, m0}]*SPD[k1, p])/2 \ + (FAD[{-k1 + p, m1}]*(m0^2 - 2*m1^2 + 2*SPD[k1, k1])*SPD[p, \ -p])/4 + (FAD[{-k1 + p, m1}]*SPD[p, p]^2)/4"} +p])/4 + (FAD[{-k1 + p, m1}]*SPD[p, p]^2)/4"}, +{"fcstFCApart-ID22", +"FCApart[CFAD[-q+x,{{0,q.p}}],{q},FCE\[Rule]True,FDS\[Rule]False]", + "CFAD[{{-q + x, 0}, {0, -1}, 1}, {{0, p . q}, {0, -1}, 1}]"}, +{"fcstFCApart-ID23", +"FCApart[CFAD[-q+x,{{q,q.p}}],{q},FCE\[Rule]True,FDS\[Rule]False]", + "CFAD[{{-q + x, 0}, {0, -1}, 1}, {{q, p.q}, {0, -1}, 1}]"}, +{"fcstFCApart-ID24", +"FCApart[CVD[q,i]CVD[q,j]CFAD[q,q+l,q-l],{q},FDS\[Rule]False,FCE\ +\[Rule]True]", +"(CFAD[{{q, 0}, {0, -1}, 1}, {{-l + q, 0}, {0, -1}, 1}]*CVD[q, \ +i]*CVD[q, j])/(2*CSPD[l, l]) + (CFAD[{{q, 0}, {0, -1}, 1}, {{l + q, \ +0}, {0, -1}, 1}]*CVD[q, i]*CVD[q, j])/(2*CSPD[l, l]) - (CFAD[{{-l + \ +q, 0}, {0, -1}, 1}, {{l + q, 0}, {0, -1}, 1}]*CVD[q, i]*CVD[q, \ +j])/CSPD[l, l]"}, +{"fcstFCApart-ID25", +"FCApart[CFAD[q,q+l,q-l],{q},FDS\[Rule]False,FCE\[Rule]True]", +"CFAD[{{q, 0}, {0, -1}, 1}, {{-l + q, 0}, {0, -1}, 1}]/(2*CSPD[l, \ +l]) + CFAD[{{q, 0}, {0, -1}, 1}, {{l + q, 0}, {0, -1}, 1}]/(2*CSPD[l, \ +l]) - CFAD[{{-l + q, 0}, {0, -1}, 1}, {{l + q, 0}, {0, -1}, \ +1}]/CSPD[l, l]"}, +{"fcstFCApart-ID26", +"FCApart[CSPD[q,r]^2*CFAD[q,{q+l,m^2},{q-l,m^2}],{q},FDS\[Rule]\ +False,FCE\[Rule]True]", +"(CFAD[{{q, 0}, {0, -1}, 1}, {{-l + q, 0}, {m^2, -1}, 1}]*CSPD[q, \ +r]^2)/(2*(m^2 + CSPD[l, l])) + (CFAD[{{q, 0}, {0, -1}, 1}, {{l + q, \ +0}, {m^2, -1}, 1}]*CSPD[q, r]^2)/(2*(m^2 + CSPD[l, l])) - (CFAD[{{-l \ ++ q, 0}, {m^2, -1}, 1}, {{l + q, 0}, {m^2, -1}, 1}]*CSPD[q, \ +r]^2)/(m^2 + CSPD[l, l])"}, +{"fcstFCApart-ID27", +"FCApart[CSPD[q,l]^2CFAD[q,{q+l,m^2},{q-l,m^2}],{q},FDS\[Rule]\ +False,FCE\[Rule]True]", +"-CFAD[{{q, 0}, {0, -1}, 1}]/4 + CFAD[{{-l + q, 0}, {m^2, -1}, \ +1}]/8 + CFAD[{{l + q, 0}, {m^2, -1}, 1}]/8 + (CFAD[{{q, 0}, {0, -1}, \ +1}, {{-l + q, 0}, {m^2, -1}, 1}]*(m^2 + CSPD[l, l]))/8 + (CFAD[{{q, \ +0}, {0, -1}, 1}, {{l + q, 0}, {m^2, -1}, 1}]*(m^2 + CSPD[l, l]))/8"}, +{"fcstFCApart-ID28", +"FCApart[CSPD[q,l]^2CSPD[q,r]^2CFAD[q,{q+l,m^2},{q-l,m^2}],{q},FDS\ +\[Rule]False,FCE\[Rule]True]", +"-(CFAD[{{q, 0}, {0, -1}, 1}]*CSPD[q, r]^2)/4 + (CFAD[{{-l + q, \ +0}, {m^2, -1}, 1}]*CSPD[q, r]^2)/8 + (CFAD[{{l + q, 0}, {m^2, -1}, \ +1}]*CSPD[q, r]^2)/8 + (CFAD[{{q, 0}, {0, -1}, 1}, {{-l + q, 0}, {m^2, \ +-1}, 1}]*(m^2 + CSPD[l, l])*CSPD[q, r]^2)/8 + (CFAD[{{q, 0}, {0, -1}, \ +1}, {{l + q, 0}, {m^2, -1}, 1}]*(m^2 + CSPD[l, l])*CSPD[q, r]^2)/8"}, +{"fcstFCApart-ID29", +"FCApart[(CSPD[k,p1]CSPD[k,p2])CFAD[k,{k+p1,m^2},{k+p2,m^2},{k+p2,\ +m^2}],{k},FDS\[Rule]False,FCE\[Rule]True]", +"CFAD[{{k, 0}, {0, -1}, 1}, {{k + p2, 0}, {m^2, -1}, 1}]/4 - +CFAD[{{k + p2, 0}, {m^2, -1}, 1}, {{k + p2, 0}, {m^2, -1}, 1}]/4 - +(CFAD[{{k + p1, 0}, {m^2, -1}, 1}, {{k + p2, 0}, {m^2, -1}, 1}, + {{k + p2, 0}, {m^2, -1}, 1}]*CSPD[k, p2])/2 - +(CFAD[{{k, 0}, {0, -1}, 1}, {{k + p1, 0}, {m^2, -1}, 1}, + {{k + p2, 0}, {m^2, -1}, 1}]*(m^2 + CSPD[p1, p1]))/4 + +(CFAD[{{k + p1, 0}, {m^2, -1}, 1}, {{k + p2, 0}, {m^2, -1}, 1}, + {{k + p2, 0}, {m^2, -1}, 1}]*(m^2 + CSPD[p1, p1]))/4 - +(CFAD[{{k, 0}, {0, -1}, 1}, {{k + p2, 0}, {m^2, -1}, 1}, + {{k + p2, 0}, {m^2, -1}, 1}]*(m^2 + CSPD[p2, p2]))/4 + +(CFAD[{{k, 0}, {0, -1}, 1}, {{k + p1, 0}, {m^2, -1}, 1}, + {{k + p2, 0}, {m^2, -1}, 1}, {{k + p2, 0}, {m^2, -1}, 1}]* +(m^2 + CSPD[p1, p1])*(m^2 + CSPD[p2, p2]))/4"}, +{"fcstFCApart-ID30", +"FCApart[(CSPD[q1,p1]CSPD[q2,p2])CFAD[q1,q2,{q1+p1,-m^2},{q2+p2,-m^\ +2},{q2+p2,-m^2}],{q1,q2},FDS\[Rule]False,FCE\[Rule]True]", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, +{{p2 + q2, 0}, {-m^2, -1}, 1}]/4 - +CFAD[{{q1, 0}, {0, -1}, 1}, {{p2 + q2, 0}, {-m^2, -1}, 1}, +{{p2 + q2, 0}, {-m^2, -1}, 1}]/4 + +CFAD[{{p1 + q1, 0}, {-m^2, -1}, 1}, {{p2 + q2, 0}, {-m^2, -1}, 1}, +{{p2 + q2, 0}, {-m^2, -1}, 1}]/4 - +CFAD[{{q2, 0}, {0, -1}, 1}, {{p1 + q1, 0}, {-m^2, -1}, 1}, +{{p2 + q2, 0}, {-m^2, -1}, 1}]/4 - +(CFAD[{{q1, 0}, {0, -1}, 1}, {{p1 + q1, 0}, {-m^2, -1}, 1}, + {{p2 + q2, 0}, {-m^2, -1}, 1}, {{p2 + q2, 0}, {-m^2, -1}, 1}]* +(m^2 - CSPD[p1, p1]))/4 + +(CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, + {{p1 + q1, 0}, {-m^2, -1}, 1}, {{p2 + q2, 0}, {-m^2, -1}, 1}]* +(m^2 - CSPD[p1, p1]))/4 + +(CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, + {{p2 + q2, 0}, {-m^2, -1}, 1}, {{p2 + q2, 0}, {-m^2, -1}, 1}]* +(m^2 - CSPD[p2, p2]))/4 - +(CFAD[{{q2, 0}, {0, -1}, 1}, {{p1 + q1, 0}, {-m^2, -1}, 1}, + {{p2 + q2, 0}, {-m^2, -1}, 1}, {{p2 + q2, 0}, {-m^2, -1}, 1}]* +(m^2 - CSPD[p2, p2]))/4 + +(CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, + {{p1 + q1, 0}, {-m^2, -1}, 1}, {{p2 + q2, 0}, {-m^2, -1}, 1}, + {{p2 + q2, 0}, {-m^2, -1}, 1}]*(m^2 - CSPD[p1, p1])* +(m^2 - CSPD[p2, p2]))/4"}, +{"fcstFCApart-ID31", +"FCApart[SFAD[-q+x,{{0,q.p}}],{q},FCE\[Rule]True,FDS\[Rule]False]", + "SFAD[{{-q + x, 0}, {0, 1}, 1}, {{0, p.q}, {0, 1}, 1}]"}, +{"fcstFCApart-ID32", +"FCApart[SFAD[-q+x,{{q,q.p}}],{q},FCE\[Rule]True,FDS\[Rule]False]", + "SFAD[{{-q + x, 0}, {0, 1}, 1}, {{q, p.q}, {0, 1}, 1}]"}, +{"fcstFCApart-ID33", +"FCApart[FVD[q,mu]FVD[q,nu]SFAD[q,q+l,q-l],{q},FDS\[Rule]False,FCE\ +\[Rule]True]", +"(FVD[q, mu]*FVD[q, nu]*SFAD[{{q, 0}, {0, 1}, 1}, {{-l + q, 0}, \ +{0, 1}, 1}])/(2*SPD[l, l]) + (FVD[q, mu]*FVD[q, nu]*SFAD[{{q, 0}, {0, \ +1}, 1}, {{l + q, 0}, {0, 1}, 1}])/(2*SPD[l, l]) - (FVD[q, mu]*FVD[q, \ +nu]*SFAD[{{-l + q, 0}, {0, 1}, 1}, {{l + q, 0}, {0, 1}, 1}])/SPD[l, \ +l]"}, +{"fcstFCApart-ID34", +"FCApart[SFAD[q,q+l,q-l],{q},FDS\[Rule]False,FCE\[Rule]True]", +"SFAD[{{q, 0}, {0, 1}, 1}, {{-l + q, 0}, {0, 1}, 1}]/(2*SPD[l, l]) \ ++ SFAD[{{q, 0}, {0, 1}, 1}, {{l + q, 0}, {0, 1}, 1}]/(2*SPD[l, l]) - \ +SFAD[{{-l + q, 0}, {0, 1}, 1}, {{l + q, 0}, {0, 1}, 1}]/SPD[l, l]"}, +{"fcstFCApart-ID35", +"FCApart[SPD[q,r]^2*SFAD[q,{q+l,m^2},{q-l,m^2}],{q},FDS\[Rule]\ +False,FCE\[Rule]True]", +"-(SFAD[{{q, 0}, {0, 1}, 1}, {{-l + q, 0}, {m^2, 1}, 1}]*SPD[q, \ +r]^2)/(2*(m^2 - SPD[l, l])) - (SFAD[{{q, 0}, {0, 1}, 1}, {{l + q, 0}, \ +{m^2, 1}, 1}]*SPD[q, r]^2)/(2*(m^2 - SPD[l, l])) + (SFAD[{{-l + q, \ +0}, {m^2, 1}, 1}, {{l + q, 0}, {m^2, 1}, 1}]*SPD[q, r]^2)/(m^2 - \ +SPD[l, l])"}, +{"fcstFCApart-ID36", +"FCApart[SPD[q,r]^2*SFAD[q,{q+l,-m^2},{q-l,-m^2}],{q},FDS\[Rule]\ +False,FCE\[Rule]True]", +"(SFAD[{{q, 0}, {0, 1}, 1}, {{-l + q, 0}, {-m^2, 1}, 1}]*SPD[q, \ +r]^2)/(2*(m^2 + SPD[l, l])) + (SFAD[{{q, 0}, {0, 1}, 1}, {{l + q, 0}, \ +{-m^2, 1}, 1}]*SPD[q, r]^2)/(2*(m^2 + SPD[l, l])) - (SFAD[{{-l + q, \ +0}, {-m^2, 1}, 1}, {{l + q, 0}, {-m^2, 1}, 1}]*SPD[q, r]^2)/(m^2 + \ +SPD[l, l])"}, +{"fcstFCApart-ID37", +"FCApart[SPD[q,l]^2SFAD[q,{q+l,m^2},{q-l,m^2}],{q},FDS\[Rule]False,\ +FCE\[Rule]True]", +"-SFAD[{{q, 0}, {0, 1}, 1}]/4 + SFAD[{{-l + q, 0}, {m^2, 1}, 1}]/8 \ ++ SFAD[{{l + q, 0}, {m^2, 1}, 1}]/8 - (SFAD[{{q, 0}, {0, 1}, 1}, {{-l \ ++ q, 0}, {m^2, 1}, 1}]*(m^2 - SPD[l, l]))/8 - (SFAD[{{q, 0}, {0, 1}, \ +1}, {{l + q, 0}, {m^2, 1}, 1}]*(m^2 - SPD[l, l]))/8"}, +{"fcstFCApart-ID38", +"FCApart[SPD[q,l]^2SFAD[q,{q+l,-m^2},{q-l,-m^2}],{q},FDS\[Rule]\ +False,FCE\[Rule]True]", +"-SFAD[{{q, 0}, {0, 1}, 1}]/4 + SFAD[{{-l + q, 0}, {-m^2, 1}, \ +1}]/8 + SFAD[{{l + q, 0}, {-m^2, 1}, 1}]/8 + (SFAD[{{q, 0}, {0, 1}, \ +1}, {{-l + q, 0}, {-m^2, 1}, 1}]*(m^2 + SPD[l, l]))/8 + (SFAD[{{q, \ +0}, {0, 1}, 1}, {{l + q, 0}, {-m^2, 1}, 1}]*(m^2 + SPD[l, l]))/8"}, +{"fcstFCApart-ID39", +"FCApart[SPD[q,l]^2SPD[q,r]^2SFAD[q,{q+l,m^2},{q-l,m^2}],{q},FDS\ +\[Rule]False,FCE\[Rule]True]", +"-(SFAD[{{q, 0}, {0, 1}, 1}]*SPD[q, r]^2)/4 + (SFAD[{{-l + q, 0}, \ +{m^2, 1}, 1}]*SPD[q, r]^2)/8 + (SFAD[{{l + q, 0}, {m^2, 1}, \ +1}]*SPD[q, r]^2)/8 - (SFAD[{{q, 0}, {0, 1}, 1}, {{-l + q, 0}, {m^2, \ +1}, 1}]*(m^2 - SPD[l, l])*SPD[q, r]^2)/8 - (SFAD[{{q, 0}, {0, 1}, 1}, \ +{{l + q, 0}, {m^2, 1}, 1}]*(m^2 - SPD[l, l])*SPD[q, r]^2)/8"}, +{"fcstFCApart-ID40", +"FCApart[SPD[q,l]^2SPD[q,r]^2SFAD[q,{q+l,-m^2},{q-l,-m^2}],{q},FDS\ +\[Rule]False,FCE\[Rule]True]", +"-(SFAD[{{q, 0}, {0, 1}, 1}]*SPD[q, r]^2)/4 + (SFAD[{{-l + q, 0}, \ +{-m^2, 1}, 1}]*SPD[q, r]^2)/8 + (SFAD[{{l + q, 0}, {-m^2, 1}, \ +1}]*SPD[q, r]^2)/8 + (SFAD[{{q, 0}, {0, 1}, 1}, {{-l + q, 0}, {-m^2, \ +1}, 1}]*(m^2 + SPD[l, l])*SPD[q, r]^2)/8 + (SFAD[{{q, 0}, {0, 1}, 1}, \ +{{l + q, 0}, {-m^2, 1}, 1}]*(m^2 + SPD[l, l])*SPD[q, r]^2)/8"}, +{"fcstFCApart-ID41", +"FCApart[(SPD[k,p1]SPD[k,p2])SFAD[k,{k+p1,m^2},{k+p2,m^2},{k+p2,m^\ +2}],{k},FDS\[Rule]False,FCE\[Rule]True]", +"SFAD[{{k, 0}, {0, 1}, 1}, {{k + p2, 0}, {m^2, 1}, 1}]/4 - +SFAD[{{k + p2, 0}, {m^2, 1}, 1}, {{k + p2, 0}, {m^2, 1}, 1}]/4 - +(SFAD[{{k + p1, 0}, {m^2, 1}, 1}, {{k + p2, 0}, {m^2, 1}, 1}, + {{k + p2, 0}, {m^2, 1}, 1}]*SPD[k, p2])/2 + +(SFAD[{{k, 0}, {0, 1}, 1}, {{k + p1, 0}, {m^2, 1}, 1}, + {{k + p2, 0}, {m^2, 1}, 1}]*(m^2 - SPD[p1, p1]))/4 - +(SFAD[{{k + p1, 0}, {m^2, 1}, 1}, {{k + p2, 0}, {m^2, 1}, 1}, + {{k + p2, 0}, {m^2, 1}, 1}]*(m^2 - SPD[p1, p1]))/4 + +(SFAD[{{k, 0}, {0, 1}, 1}, {{k + p2, 0}, {m^2, 1}, 1}, + {{k + p2, 0}, {m^2, 1}, 1}]*(m^2 - SPD[p2, p2]))/4 + +(SFAD[{{k, 0}, {0, 1}, 1}, {{k + p1, 0}, {m^2, 1}, 1}, + {{k + p2, 0}, {m^2, 1}, 1}, {{k + p2, 0}, {m^2, 1}, 1}]* +(m^2 - SPD[p1, p1])*(m^2 - SPD[p2, p2]))/4"}, +{"fcstFCApart-ID42", +"FCApart[(SPD[k,p1]SPD[k,p2])SFAD[k,{k+p1,-m^2},{k+p2,-m^2},{k+p2,-\ +m^2}],{k},FDS\[Rule]False,FCE\[Rule]True]", +"SFAD[{{k, 0}, {0, 1}, 1}, {{k + p2, 0}, {-m^2, 1}, 1}]/4 - +SFAD[{{k + p2, 0}, {-m^2, 1}, 1}, {{k + p2, 0}, {-m^2, 1}, 1}]/4 - +(SFAD[{{k + p1, 0}, {-m^2, 1}, 1}, {{k + p2, 0}, {-m^2, 1}, 1}, + {{k + p2, 0}, {-m^2, 1}, 1}]*SPD[k, p2])/2 - +(SFAD[{{k, 0}, {0, 1}, 1}, {{k + p1, 0}, {-m^2, 1}, 1}, + {{k + p2, 0}, {-m^2, 1}, 1}]*(m^2 + SPD[p1, p1]))/4 + +(SFAD[{{k + p1, 0}, {-m^2, 1}, 1}, {{k + p2, 0}, {-m^2, 1}, 1}, + {{k + p2, 0}, {-m^2, 1}, 1}]*(m^2 + SPD[p1, p1]))/4 - +(SFAD[{{k, 0}, {0, 1}, 1}, {{k + p2, 0}, {-m^2, 1}, 1}, + {{k + p2, 0}, {-m^2, 1}, 1}]*(m^2 + SPD[p2, p2]))/4 + +(SFAD[{{k, 0}, {0, 1}, 1}, {{k + p1, 0}, {-m^2, 1}, 1}, + {{k + p2, 0}, {-m^2, 1}, 1}, {{k + p2, 0}, {-m^2, 1}, 1}]* +(m^2 + SPD[p1, p1])*(m^2 + SPD[p2, p2]))/4"}, +{"fcstFCApart-ID43", +"FCApart[(SPD[q1,p1]SPD[q2,p2])SFAD[q1,q2,{q1+p1,m^2},{q2+p2,m^2},{\ +q2+p2,m^2}],{q1,q2},FDS\[Rule]False,FCE\[Rule]True]", +"SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, +{{p2 + q2, 0}, {m^2, 1}, 1}]/4 - +SFAD[{{q1, 0}, {0, 1}, 1}, {{p2 + q2, 0}, {m^2, 1}, 1}, +{{p2 + q2, 0}, {m^2, 1}, 1}]/4 + +SFAD[{{p1 + q1, 0}, {m^2, 1}, 1}, {{p2 + q2, 0}, {m^2, 1}, 1}, +{{p2 + q2, 0}, {m^2, 1}, 1}]/4 - +SFAD[{{q2, 0}, {0, 1}, 1}, {{p1 + q1, 0}, {m^2, 1}, 1}, +{{p2 + q2, 0}, {m^2, 1}, 1}]/4 - +(SFAD[{{q1, 0}, {0, 1}, 1}, {{p1 + q1, 0}, {m^2, 1}, 1}, + {{p2 + q2, 0}, {m^2, 1}, 1}, {{p2 + q2, 0}, {m^2, 1}, 1}]* +(m^2 - SPD[p1, p1]))/4 + +(SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{p1 + q1, 0}, {m^2, 1}, 1}, {{p2 + q2, 0}, {m^2, 1}, 1}]* +(m^2 - SPD[p1, p1]))/4 + +(SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{p2 + q2, 0}, {m^2, 1}, 1}, {{p2 + q2, 0}, {m^2, 1}, 1}]* +(m^2 - SPD[p2, p2]))/4 - +(SFAD[{{q2, 0}, {0, 1}, 1}, {{p1 + q1, 0}, {m^2, 1}, 1}, + {{p2 + q2, 0}, {m^2, 1}, 1}, {{p2 + q2, 0}, {m^2, 1}, 1}]* +(m^2 - SPD[p2, p2]))/4 + +(SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{p1 + q1, 0}, {m^2, 1}, 1}, {{p2 + q2, 0}, {m^2, 1}, 1}, + {{p2 + q2, 0}, {m^2, 1}, 1}]*(m^2 - SPD[p1, p1])*(m^2 - SPD[p2, p2]))/4"}, +{"fcstFCApart-ID44", +"FCApart[(SPD[q1,p1]SPD[q2,p2])SFAD[q1,q2,{q1+p1,-m^2},{q2+p2,-m^2}\ +,{q2+p2,-m^2}],{q1,q2},FDS\[Rule]False,FCE\[Rule]True]", +"SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, +{{p2 + q2, 0}, {-m^2, 1}, 1}]/4 - +SFAD[{{q1, 0}, {0, 1}, 1}, {{p2 + q2, 0}, {-m^2, 1}, 1}, +{{p2 + q2, 0}, {-m^2, 1}, 1}]/4 + +SFAD[{{p1 + q1, 0}, {-m^2, 1}, 1}, {{p2 + q2, 0}, {-m^2, 1}, 1}, +{{p2 + q2, 0}, {-m^2, 1}, 1}]/4 - +SFAD[{{q2, 0}, {0, 1}, 1}, {{p1 + q1, 0}, {-m^2, 1}, 1}, +{{p2 + q2, 0}, {-m^2, 1}, 1}]/4 + +(SFAD[{{q1, 0}, {0, 1}, 1}, {{p1 + q1, 0}, {-m^2, 1}, 1}, + {{p2 + q2, 0}, {-m^2, 1}, 1}, {{p2 + q2, 0}, {-m^2, 1}, 1}]* +(m^2 + SPD[p1, p1]))/4 - +(SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{p1 + q1, 0}, {-m^2, 1}, 1}, {{p2 + q2, 0}, {-m^2, 1}, 1}]* +(m^2 + SPD[p1, p1]))/4 - +(SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{p2 + q2, 0}, {-m^2, 1}, 1}, {{p2 + q2, 0}, {-m^2, 1}, 1}]* +(m^2 + SPD[p2, p2]))/4 + +(SFAD[{{q2, 0}, {0, 1}, 1}, {{p1 + q1, 0}, {-m^2, 1}, 1}, + {{p2 + q2, 0}, {-m^2, 1}, 1}, {{p2 + q2, 0}, {-m^2, 1}, 1}]* +(m^2 + SPD[p2, p2]))/4 + +(SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{p1 + q1, 0}, {-m^2, 1}, 1}, {{p2 + q2, 0}, {-m^2, 1}, 1}, + {{p2 + q2, 0}, {-m^2, 1}, 1}]*(m^2 + SPD[p1, p1])*(m^2 + SPD[p2, p2]))/ +4"}, +{"fcstFCApart-ID45", +"FCApart[FCI[ +SFAD[{{-p2 + p4, 0}, {0, 1}, 1}, {{-p2 - p3 + p4, 0}, {0, 1}, + 1}, {{0, -p2.p3 + a b p3.p4}, {0, 1}, 1}, {{p2, 0}, {0, 1}, + 1}, {{p3, 0}, {0, 1}, 1}, {{p2 + p3, 0}, {0, 1}, 1}]], {p2, p3}, +FDS -> False, FCE -> True]", +"-(a*b*SFAD[{{p2, 0}, {0, 1}, 1}, {{p3, 0}, {0, 1}, 1}, + {{p2 + p3, 0}, {0, 1}, 1}, {{-p2 + p4, 0}, {0, 1}, 1}, + {{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, 1}, + {{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, 1}])/2 + +(a*b*SFAD[{{p2, 0}, {0, 1}, 1}, {{p3, 0}, {0, 1}, 1}, + {{p2 + p3, 0}, {0, 1}, 1}, {{-p2 - p3 + p4, 0}, {0, 1}, 1}, + {{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, 1}, + {{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, 1}])/2 + +((-1 + a*b)*SFAD[{{p2, 0}, {0, 1}, 1}, {{p3, 0}, {0, 1}, 1}, + {{-p2 + p4, 0}, {0, 1}, 1}, {{-p2 - p3 + p4, 0}, {0, 1}, 1}, + {{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, 1}, + {{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, 1}])/2 + +SFAD[{{p2, 0}, {0, 1}, 1}, {{p2 + p3, 0}, {0, 1}, 1}, +{{-p2 + p4, 0}, {0, 1}, 1}, {{-p2 - p3 + p4, 0}, {0, 1}, 1}, +{{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, 1}, {{0, -p2 . p3 + a*b*p3 . p4}, + {0, 1}, 1}]/2 - ((-1 + a*b)*SFAD[{{p3, 0}, {0, 1}, 1}, + {{p2 + p3, 0}, {0, 1}, 1}, {{-p2 + p4, 0}, {0, 1}, 1}, + {{-p2 - p3 + p4, 0}, {0, 1}, 1}, {{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, + 1}, {{0, -p2 . p3 + a*b*p3 . p4}, {0, 1}, 1}])/2"}, +{"fcstFCApart-ID46", +"FCApart[SFAD[p1, p2, p3, -p1 - p2 - p3 + Q, -p2 + Q, -p1 - p2 + Q, +p1 + p3], {p1, p2, p3}, FDS -> False, FCE -> True]", +"SFAD[{{p1, 0}, {0, 1}, 1}, {{p2, 0}, {0, 1}, 1}, {{p3, 0}, {0, 1}, +1}, {{-p1 - p2 - p3 + Q, 0}, {0, 1}, 1}, {{-p2 + Q, 0}, {0, 1}, +1}, {{-p1 - p2 + Q, 0}, {0, 1}, 1}, {{p1 + p3, 0}, {0, 1}, 1}]"}, +{"fcstFCApart-ID47", +"FCApart[SFAD[{{0,k.l},{0,1},1},{{k,0},{0,1},1}] SPD[k,l],{k},FCE\ +\[Rule]True]", "SFAD[{{k, 0}, {0, 1}, 1}]"}, +{"fcstFCApart-ID48", +"FCApart[CFAD[{{0,k.l},{0,1},1},{{k,0},{0,1},1}] CSPD[k,l],{k},FCE\ +\[Rule]True]", "CFAD[{{k, 0}, {0, 1}, 1}]"}, +{"fcstFCApart-ID49", +"FCApart[SFAD[{{0,k.l},{0,1},3},{{k,0},{0,1},1}] \ +SPD[k,l]^2,{k},FCE\[Rule]True]", +"SFAD[{{0, k . l}, {0, 1}, 1}, {{k, 0}, {0, 1}, 1}]"}, +{"fcstFCApart-ID50", +"FCApart[SFAD[{{0,k.l},{0,1},1},{{k,0},{0,1},1}] \ +SPD[k,l]^2,{k},FCE\[Rule]True]", "SFAD[{{k, 0}, {0, 1}, 1}]*SPD[k, l]"}, +{"fcstFCApart-ID51", +"FCApart[FCI[SPD[p, q]^2 SFAD[{{0, p.q}, x}]], {q},FCE->True]", +"0"}, +{"fcstFCApart-ID52", +"FCApart[FCI[CSPD[p, q]^2 CFAD[q, {{0, p.q}, x}]], {q}, FCE -> True]", +"x^2 CFAD[{{q, 0}, {0, -1}, 1}, {{0, p.q}, {x, -1}, 1}]"}, +{"fcstFCApart-ID53", +"(AbsoluteTiming[ +FCApart[SFAD[{{0, c1 + p1.Q}}] SFAD[{{0, c2 + p1.Q}}] SFAD[{{p1, + 0}, {0, 1}, 1}] SFAD[{{p2, 0}, {0, 1}, + 1}] SFAD[{{p3, 0}, {0, 1}, 1}] SFAD[{{-p1 + Q, 0}, {0, 1}, + 1}] SFAD[{{-p2 + Q, 0}, {0, 1}, + 1}] SFAD[{{-p1 - p2 + Q, 0}, {0, 1}, + 1}] SFAD[{{-p1 - p2 - p3 + Q, 0}, {0, 1}, 1}], {p1, p2, p3}, + FDS -> False]][[1]] < 1.5) || $VersionNumber < 10.", +"True"}, +{"fcstFCApart-ID54", +"FCApart[CFAD[{{k, 0}, {0, -1}, 1}, {{k - P, 0}, {0, -1}, 1}] CSPD[k, +P]^2 GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}], {k}, FCE -> True]", +"-(1/2) CFAD[{{k, 0}, {0, -1}, 1}] CSPD[k, +P] GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}] + +1/2 CFAD[{{k - P, 0}, {0, -1}, 1}] CSPD[k, +P] GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}] - +1/4 CFAD[{{k, 0}, {0, -1}, 1}] CSPD[P, +P] GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}] + +1/4 CFAD[{{k - P, 0}, {0, -1}, 1}] CSPD[P, +P] GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}] + +1/4 CFAD[{{k, 0}, {0, -1}, 1}, {{k - P, 0}, {0, -1}, 1}] CSPD[P, +P]^2 GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}]"} }) diff --git a/Tests/LoopIntegrals/FCGram.test b/Tests/LoopIntegrals/FCGram.test new file mode 100644 index 000000000..6d645db86 --- /dev/null +++ b/Tests/LoopIntegrals/FCGram.test @@ -0,0 +1,34 @@ + + +(* :Title: FCGram.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCGram *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCGramMatrix = { +{"fcstFCGram-ID1","FCGramMatrix[{p1, p2}, FCE -> True]", "{{2 SPD[p1, p1], 2 SPD[p1, p2]}, {2 SPD[p1, p2], 2 SPD[p2, p2]}}"}, +{"fcstFCGram-ID2","FCGramMatrix[{p1, p2}, Dimension -> 4, FCE -> True]", "{{2 SP[p1, p1], 2 SP[p1, p2]}, {2 SP[p1, p2], 2 SP[p2, p2]}}"}, +{"fcstFCGram-ID3","FCGramMatrix[{p1, 0}, FCE -> True]", "{{2 SPD[p1, p1], 0}, {0, 0}}"}, +{"fcstFCGram-ID4","FCGramMatrix[{0, 0}, FCE -> True]", "{{0, 0}, {0, 0}}"}, +{"fcstFCGram-ID5","FCGramMatrix[{p1, p2}, FCE -> True, +Head -> {CartesianPair, CartesianMomentum}, Dimension -> D - 1]", "{{2 CSPD[p1, p1], 2 CSPD[p1, p2]}, {2 CSPD[p1, p2], 2 CSPD[p2, p2]}}"}, +{"fcstFCGram-ID6","FCGramMatrix[{p1, 0}, FCE -> True, +Head -> {CartesianPair, CartesianMomentum}, Dimension -> D - 1]", "{{2 CSPD[p1, p1], 0}, {0, 0}}"} +}; + +Tests`LoopIntegrals`fcstFCGramDeterminant = { +{"fcstFCGramDeterminant-ID1","FCGramDeterminant[{p1, p2}, FCE -> True]", "-4 SPD[p1, p2]^2 + 4 SPD[p1, p1] SPD[p2, p2]"}, +{"fcstFCGramDeterminant-ID2","FCGramDeterminant[{p1, 0}]", "0"}, +{"fcstFCGramDeterminant-ID3","FCGramDeterminant[{p1, p2}, FCE -> True, +Head -> {CartesianPair, CartesianMomentum}, Dimension -> D - 1]", "-4 CSPD[p1, p2]^2 + 4 CSPD[p1, p1] CSPD[p2, p2]"}, +{"fcstFCGramDeterminant-ID4","FCGramDeterminant[{p1, 0}, FCE -> True, +Head -> {CartesianPair, CartesianMomentum}, Dimension -> D - 1]", "0"} +}; diff --git a/Tests/LoopIntegrals/FCHideShowEpsilon.test b/Tests/LoopIntegrals/FCHideShowEpsilon.test index c7663dd94..219398723 100644 --- a/Tests/LoopIntegrals/FCHideShowEpsilon.test +++ b/Tests/LoopIntegrals/FCHideShowEpsilon.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCHideEpsilon and @@ -44,7 +44,11 @@ b + b^2) Log[4Pi]]", "(a + b)^2*SMP[\"Delta\"]"}, "SMP[\"Delta_UV\"]"}, {"fcstFCEpsilonHide-ID10", "FCHideEpsilon[2/EpsilonIR - EulerGamma + Log[4 Pi], D -> 4 - Epsilon]", -"SMP[\"Delta_IR\"]"} +"SMP[\"Delta_IR\"]"}, +{"fcstFCEpsilonHide-ID11", +"FCHideEpsilon[1/Epsilon - EulerGamma + Log[4 Pi] + Log[ScaleMu^2/m^2], +D -> 4 - 2 Epsilon, Subtract -> EulerGamma - Log[4 Pi] - Log[ScaleMu^2/m^2]]", +"SMP[\"Delta\"]"} }); Tests`LoopIntegrals`fcstFCShowEpsilon = @@ -55,10 +59,12 @@ Tests`LoopIntegrals`fcstFCShowEpsilon = "EpsilonUV^(-1) - EulerGamma + Log[4*Pi]"}, {"fcstFCEpsilonShow-ID3", "FCShowEpsilon[SMP[\"Delta_IR\"]]", "EpsilonIR^(-1) - EulerGamma + Log[4*Pi]"}, -{"fcstFCEpsilonShow-ID1", "FCShowEpsilon[SMP[\"Delta\"],D->4- Epsilon]", +{"fcstFCEpsilonShow-ID4", "FCShowEpsilon[SMP[\"Delta\"],D->4- Epsilon]", "2 Epsilon^(-1) - EulerGamma + Log[4*Pi]"}, -{"fcstFCEpsilonShow-ID2", "FCShowEpsilon[SMP[\"Delta_UV\"],D->4- Epsilon]", +{"fcstFCEpsilonShow-ID5", "FCShowEpsilon[SMP[\"Delta_UV\"],D->4- Epsilon]", "2 EpsilonUV^(-1) - EulerGamma + Log[4*Pi]"}, -{"fcstFCEpsilonShow-ID3", "FCShowEpsilon[SMP[\"Delta_IR\"],D->4- Epsilon]", -"2 EpsilonIR^(-1) - EulerGamma + Log[4*Pi]"} +{"fcstFCEpsilonShow-ID6", "FCShowEpsilon[SMP[\"Delta_IR\"],D->4- Epsilon]", +"2 EpsilonIR^(-1) - EulerGamma + Log[4*Pi]"}, +{"fcstFCEpsilonShow-ID7", "FCShowEpsilon[SMP[\"Delta\"],Subtract -> EulerGamma - Log[4 Pi] - Log[ScaleMu^2/m^2]]", +"Epsilon^(-1) - EulerGamma + Log[4*Pi]+Log[ScaleMu^2/m^2]"} }); diff --git a/Tests/LoopIntegrals/FCLoopBasis.test b/Tests/LoopIntegrals/FCLoopBasis.test index bcc5097bc..bc60447fb 100644 --- a/Tests/LoopIntegrals/FCLoopBasis.test +++ b/Tests/LoopIntegrals/FCLoopBasis.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCLoopBasis *) @@ -37,7 +37,59 @@ Tests`LoopIntegrals`fcstFCLoopBasisIncompleteQ = "FCLoopBasisIncompleteQ[FAD[q1,q2,{q1-l1,m1},{q2-l2,m2}],{q1,q2}]", "True"}, {"fcstFCLoopBasisIncompleteQ-ID9", "FCLoopBasisIncompleteQ[SPD[q1,q2]SPD[q1,l2]SPD[q2,l1]FAD[q1,q2,{\ -q1-l1,m1},{q2-l2,m2}],{q1,q2}]", "False"} +q1-l1,m1},{q2-l2,m2}],{q1,q2}]", "False"}, +{"fcstFCLoopBasisIncompleteQ-ID10", +"FCLoopBasisIncompleteQ[CFAD[{q1,m1}],{q1}]", "False"}, +{"fcstFCLoopBasisIncompleteQ-ID11", +"FCLoopBasisIncompleteQ[CFAD[q1,{q1,m1}],{q1}]", "False"}, +{"fcstFCLoopBasisIncompleteQ-ID12", +"FCLoopBasisIncompleteQ[CFAD[{q1,m1},{q1-l+p,m}],{q1}]", "True"}, +{"fcstFCLoopBasisIncompleteQ-ID13", +"FCLoopBasisIncompleteQ[CSPD[q1,l]CFAD[{q1,m1},{q1-l+p,m}],{q1}]", +"False"}, +{"fcstFCLoopBasisIncompleteQ-ID14", +"FCLoopBasisIncompleteQ[CFAD[{q1,m1},{q2,m2}],{q1,q2}]", "True"}, +{"fcstFCLoopBasisIncompleteQ-ID15", +"FCLoopBasisIncompleteQ[CSPD[q1,q2]CFAD[{q1,m1},{q2,m2}],{q1,q2}]", + "False"}, +{"fcstFCLoopBasisIncompleteQ-ID16", +"FCLoopBasisIncompleteQ[CFAD[{q1,m1},{q2,m2},q1-q2],{q1,q2}]", +"False"}, +{"fcstFCLoopBasisIncompleteQ-ID17", +"FCLoopBasisIncompleteQ[CFAD[q1,q2,{q1-l1,m1},{q2-l2,m2}],{q1,q2}]\ +", "True"}, +{"fcstFCLoopBasisIncompleteQ-ID18", +"FCLoopBasisIncompleteQ[CSPD[q1,q2]CSPD[q1,l2]CSPD[q2,l1]CFAD[q1,\ +q2,{q1-l1,m1},{q2-l2,m2}],{q1,q2}]", "False"}, +{"FCLoopBasisIncompleteQ-ID19", +"FCLoopBasisIncompleteQ[SFAD[{q1,m1}],{q1}]", "False"}, +{"FCLoopBasisIncompleteQ-ID20", +"FCLoopBasisIncompleteQ[SFAD[q1,{q1,m1}],{q1}]", "False"}, +{"FCLoopBasisIncompleteQ-ID21", +"FCLoopBasisIncompleteQ[SFAD[{q1,m1},{q1-l+p,m}],{q1}]", "True"}, +{"FCLoopBasisIncompleteQ-ID22", +"FCLoopBasisIncompleteQ[SPD[q1,l]SFAD[{q1,m1},{q1-l+p,m}],{q1}]", +"False"}, +{"FCLoopBasisIncompleteQ-ID23", +"FCLoopBasisIncompleteQ[SFAD[{q1,m1},{q2,m2}],{q1,q2}]", "True"}, +{"FCLoopBasisIncompleteQ-ID24", +"FCLoopBasisIncompleteQ[SPD[q1,q2]SFAD[{q1,m1},{q2,m2}] ,{q1,q2}]", + "False"}, +{"FCLoopBasisIncompleteQ-ID25", +"FCLoopBasisIncompleteQ[SFAD[{q1,m1},{q2,m2},q1-q2],{q1,q2} ]", +"False"}, +{"FCLoopBasisIncompleteQ-ID26", +"FCLoopBasisIncompleteQ[SFAD[q1,q2,{q1-l1,m1},{q2-l2,m2}] \ +,{q1,q2}]", "True"}, +{"FCLoopBasisIncompleteQ-ID27", +"FCLoopBasisIncompleteQ[SPD[q1,q2]SPD[q1,l2]SPD[q2,l1]SFAD[q1,q2,{\ +q1-l1,m1},{q2-l2,m2}],{q1,q2}]", "False"}, +{"FCLoopBasisIncompleteQ-ID28", +"FCLoopBasisIncompleteQ[ +FCTopology[top1, {SFAD[p1], SFAD[p2], SFAD[p1 - p2]}], {p1, p2}]", "False"}, +{"FCLoopBasisIncompleteQ-ID29", +"FCLoopBasisIncompleteQ[ +FCTopology[top1, {SFAD[p1], SFAD[p2]}], {p1, p2}]", "True"} }); Tests`LoopIntegrals`fcstFCLoopBasisOverdeterminedQ = @@ -73,7 +125,108 @@ q2,{q1-l1,m1},{q2-l2,m2}],{q1,q2}]", "False"}, "True"}, {"fcstFCLoopBasisOverdeterminedQ-ID12", "FCLoopBasisOverdeterminedQ[FAD[q1,q2,{q1+l,m1},{q1-l,m1},{q2+l,m1}\ -,{q2-l,m1}],{q1,q2}]", "True"} +,{q2-l,m1}],{q1,q2}]", "True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID13", +"FCLoopBasisOverdeterminedQ[CFAD[{q1,m1}],{q1},{}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID14", +"FCLoopBasisOverdeterminedQ[CFAD[{q1,m1},{q1-l+p,m}],{q1}]", +"False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID15", +"FCLoopBasisOverdeterminedQ[CSPD[q1,l]CFAD[{q1,m1},{q1-l+p,m}],{q1}\ +]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID16", +"FCLoopBasisOverdeterminedQ[CFAD[{q1,m1},{q2,m2}],{q1,q2}]", +"False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID17", +"FCLoopBasisOverdeterminedQ[CSPD[q1,q2]CFAD[{q1,m1},{q2,m2}],{q1,\ +q2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID18", +"FCLoopBasisOverdeterminedQ[CFAD[{q1,m1},{q2,m2},q1-q2],{q1,q2}]", +"False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID19", +"FCLoopBasisOverdeterminedQ[CFAD[q1,q2,{q1-l1,m1},{q2-l2,m2}],{q1,\ +q2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID20", +"FCLoopBasisOverdeterminedQ[CSPD[q1,q2]CSPD[q1,l2]CSPD[q2,l1]CFAD[\ +q1,q2,{q1-l1,m1},{q2-l2,m2}],{q1,q2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID21", +"FCLoopBasisOverdeterminedQ[CFAD[q1,{q1,m1}],{q1}]", "True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID22", +"FCLoopBasisOverdeterminedQ[CFAD[q1,{q1+l,m1},{q1-l,m2}],{q1}]", +"True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID23", +"FCLoopBasisOverdeterminedQ[CSPD[q1,l]CFAD[q1,{q1+l,m1}],{q1}]", +"True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID24", +"FCLoopBasisOverdeterminedQ[CFAD[q1,q2,{q1+l,m1},{q1-l,m1},{q2+l,\ +m1},{q2-l,m1}],{q1,q2}]", "True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID25", +"FCLoopBasisOverdeterminedQ[SFAD[{q1,m1}],{q1},{}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID26", +"FCLoopBasisOverdeterminedQ[SFAD[{q1,m1},{q1-l+p,m}],{q1}]", +"False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID27", +"FCLoopBasisOverdeterminedQ[SPD[q1,l]SFAD[{q1,m1},{q1-l+p,m}],{q1}]\ +", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID28", +"FCLoopBasisOverdeterminedQ[SFAD[{q1,m1},{q2,m2}],{q1,q2}]", +"False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID29", +"FCLoopBasisOverdeterminedQ[SPD[q1,q2]SFAD[{q1,m1},{q2,m2}],{q1,q2}\ +]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID30", +"FCLoopBasisOverdeterminedQ[SFAD[{q1,m1},{q2,m2},q1-q2],{q1,q2}]", +"False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID31", +"FCLoopBasisOverdeterminedQ[SFAD[q1,q2,{q1-l1,m1},{q2-l2,m2}],{q1,\ +q2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID32", +"FCLoopBasisOverdeterminedQ[SPD[q1,q2]SPD[q1,l2]SPD[q2,l1]SFAD[q1,\ +q2,{q1-l1,m1},{q2-l2,m2}],{q1,q2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID33", +"FCLoopBasisOverdeterminedQ[SFAD[q1,{q1,m1}],{q1}]", "True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID34", +"FCLoopBasisOverdeterminedQ[SFAD[q1,{q1+l,m1},{q1-l,m2}],{q1}]", +"True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID35", +"FCLoopBasisOverdeterminedQ[SPD[q1,l]SFAD[q1,{q1+l,m1}],{q1}]", +"True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID36", +"FCLoopBasisOverdeterminedQ[SFAD[q1,q2,{q1+l,m1},{q1-l,m1},{q2+l,\ +m1},{q2-l,m1}],{q1,q2}]", "True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID37", +"FCLoopBasisOverdeterminedQ[ +SFAD[p1, p2, Q - p1 - p2, {{0, p2.Q - p1.p2}}], {p1, p2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID38", +"FCLoopBasisOverdeterminedQ[ +SFAD[p1, p2, Q - p1 - p2] GFAD[SPD[p2, Q] - SPD[p1, p2]], {p1, p2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID39", +"FCLoopBasisOverdeterminedQ[ +FCTopology[top1, {SFAD[p1], SFAD[p2], SFAD[p1 - p2]}], {p1, p2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID40", +"FCLoopBasisOverdeterminedQ[ +FCTopology[ +top1, {SFAD[p1], SFAD[p2], SFAD[p1 - p2], SFAD[{{0, p1.p2}}]}], {p1, +p2}]", "True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID41", +"FCLoopBasisOverdeterminedQ[ +ExpandScalarProduct[ +SPD[l, -p1 - p2 - p3]^3 FAD[l, l - p2, l - p1 - p2 - p3]], {l}]", "True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID42", +"FCLoopBasisOverdeterminedQ[ +ExpandScalarProduct[ +SPD[l, -p1 - p2 - p3]^3 FAD[l, l - p2, l - p1 - p2 - p3]], {l}]", "True"}, +{"fcstFCLoopBasisOverdeterminedQ-ID43", +"FCLoopBasisOverdeterminedQ[ +GFAD[{p1.q p2.q + x}] SFAD[p1] SPD[p2, r]^2, {p1, p2}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID44", +"FCLoopBasisOverdeterminedQ[ +CFAD[{{-k + P, 0}, {0, -1}, +1}] GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}], {k}]", "False"}, +{"fcstFCLoopBasisOverdeterminedQ-ID45", +"FCLoopBasisOverdeterminedQ[ +CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{-k + P, 0}, {0, -1}, + 1}] GFAD[{{EN - V0 - TC[k], 1}, 1}] TC[k], {k}]", "True"} }); Tests`LoopIntegrals`fcstFCLoopBasisFindCompletion = @@ -111,5 +264,804 @@ SPD[l2, q1], SPD[q1, q2]}}"}, q2 - k] SPD[q1, q2], {q1, q2}, Method -> { FAD[{q2 + k, m}], FAD[{q1 - p, m}], SPD[p, q2], SPD[k, q1]}]//FCE", "{FAD[p + q1, -k + q2] SPD[q1, q2], {FAD[{k + q2, m}], -FAD[{-p + q1, m}], SPD[p, q2], SPD[k, q1]}}"} +FAD[{-p + q1, m}], SPD[p, q2], SPD[k, q1]}}"}, +{"fcstFCLoopBasisFindCompletion-ID9","FCLoopBasisFindCompletion[CFAD[q1 + p, q2 - k] CSPD[q1, q2], {q1, q2}, +Method -> {CFAD[{q2 + k, m}], CFAD[{q1 - p, m}], CSPD[p, q2], +CSPD[k, q1]}, FCE -> True]","{CFAD[{{p + q1, 0}, {0, -1}, 1}, {{-k + q2, 0}, {0, -1}, 1}] CSPD[q1, +q2], {CFAD[{{k + q2, 0}, {m, -1}, 1}], +CFAD[{{-p + q1, 0}, {m, -1}, 1}], CSPD[p, q2], CSPD[k, q1]}}"}, +{"fcstFCLoopBasisFindCompletion-ID10","FCLoopBasisFindCompletion[ +CFAD[q1, q2, {q1 - l1, m1}, {q2 - l2, m2}], {q1, q2}, FCE -> True]","{CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, +1}, {{-l1 + q1, 0}, {m1, -1}, 1}, {{-l2 + q2, 0}, {m2, -1}, +1}], {CSPD[l1, q2], CSPD[l2, q1], CSPD[q1, q2]}}"}, +{"fcstFCLoopBasisFindCompletion-ID11","FCLoopBasisFindCompletion[CFAD[{q1, m1}, {q2, m2}], {q1, q2}, +FCE -> True]","{CFAD[{{q1, 0}, {m1, -1}, 1}, {{q2, 0}, {m2, -1}, 1}], {CSPD[q1, q2]}}"}, +{"fcstFCLoopBasisFindCompletion-ID12","FCLoopBasisFindCompletion[CFAD[{q1, m1}, {q1 - l + p, m}], {q1}, +FCE -> True]","{CFAD[{{q1, 0}, {m1, -1}, 1}, {{-l + p + q1, 0}, {m, -1}, 1}], {CSPD[l, q1]}}"}, +{"fcstFCLoopBasisFindCompletion-ID13", +"FCLoopBasisFindCompletion[SFAD[q1+p,q2-k] \ +SPD[q1,q2],{q1,q2},Method\[Rule]{SFAD[{q2+k,m}],SFAD[{q1-p,m}],SPD[p,\ +q2],SPD[k,q1]},FCE\[Rule]True]", +"{SFAD[{{p + q1, 0}, {0, 1}, 1}, {{-k + q2, 0}, {0, 1}, \ +1}]*SPD[q1, q2], {SFAD[{{k + q2, 0}, {m, 1}, 1}], SFAD[{{-p + q1, 0}, \ +{m, 1}, 1}], SPD[p, q2], SPD[k, q1]}}"}, +{"fcstFCLoopBasisFindCompletion-ID14", +"FCLoopBasisFindCompletion[SFAD[q1,q2,{q1-l1,m1},{q2-l2,m2}],{q1,\ +q2},FCE\[Rule]True]", +"{SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, {{-l1 + q1, 0}, \ +{m1, 1}, 1}, {{-l2 + q2, 0}, {m2, 1}, 1}], {SPD[l1, q2], SPD[l2, q1], \ +SPD[q1, q2]}}"}, +{"fcstFCLoopBasisFindCompletion-ID15", +"FCLoopBasisFindCompletion[SFAD[{q1,m1},{q2,m2}],{q1,q2},FCE\[Rule]\ +True]", "{SFAD[{{q1, 0}, {m1, 1}, 1}, {{q2, 0}, {m2, 1}, 1}], \ +{SPD[q1, q2]}}"}, +{"fcstFCLoopBasisFindCompletion-ID16", +"FCLoopBasisFindCompletion[SFAD[{q1,m1},{q1-l+p,m}],{q1},FCE\[Rule]\ +True]", "{SFAD[{{q1, 0}, {m1, 1}, 1}, {{-l + p + q1, 0}, {m, 1}, 1}], \ +{SPD[l, q1]}}"}, + + +{"fcstFCLoopBasisFindCompletion-ID17", +"FCLoopBasisFindCompletion[ +FCI@SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, + 1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, + 1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, + 1}, {{0, (k1 - k2).r1}, {0, 1}, 1}, {{0, (k2 + k3).r2}, {0, 1}, + 1}, {{0, (-k1 + k2 + q).r2}, {0, 1}, 1}, {{k1, 0}, {0, 1}, + 1}], {k1, k2, k3}, Method -> {SPD[k1, k3], SPD[k1, r1]}, +Check -> False, FCE -> True]", "{SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, +1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, +1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, +1}, {{0, (k1 - k2).r1}, {0, 1}, 1}, {{0, (k2 + k3).r2}, {0, 1}, +1}, {{0, (-k1 + k2 + q).r2}, {0, 1}, 1}, {{k1, 0}, {0, 1}, +1}], {SPD[k1, k3], SPD[k1, r1]}}"}, +{"fcstFCLoopBasisFindCompletion-ID18", +"FCLoopBasisFindCompletion[ +FCI@SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, + 1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, + 1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, + 1}, {{0, (k1 - k2).r1}, {0, 1}, 1}, {{0, (k2 + k3).r2}, {0, 1}, + 1}, {{0, (-k1 + k2 + q).r2}, {0, 1}, 1}, {{k1, 0}, {0, 1}, + 1}], {k1, k2, k3}, Method -> {SPD[k1, k3]}, Check -> False, +FCE -> True]", "{SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, +1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, +1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, +1}, {{0, (k1 - k2).r1}, {0, 1}, 1}, {{0, (k2 + k3).r2}, {0, 1}, +1}, {{0, (-k1 + k2 + q).r2}, {0, 1}, 1}, {{k1, 0}, {0, 1}, +1}], {SPD[k1, k3]}}"}, + +{"fcstFCLoopBasisFindCompletion-ID19", +"FCLoopBasisFindCompletion[ +FCI@SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, + 1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, + 1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, + 1}, {{0, (k1 - k2).r1}, {0, 1}, 1}, {{0, (k2 + k3).r2}, {0, 1}, + 1}, {{0, (-k1 + k2 + q).r2}, {0, 1}, 1}, {{k1, 0}, {0, 1}, + 1}], {k1, k2, k3}, Method -> {SFAD[{{0, (k1 + k2).k3}}]}, +Check -> False, ExpandScalarProduct -> False]", "{FeynAmpDenominator[ +StandardPropagatorDenominator[Momentum[k2, D], 0, 0, {1, 1}], +StandardPropagatorDenominator[-Momentum[k1, D] + Momentum[k2, D], 0, + 0, {1, 1}], +StandardPropagatorDenominator[Momentum[k3, D], 0, 0, {1, 1}], +StandardPropagatorDenominator[Momentum[k2, D] + Momentum[k3, D], 0, +0, {1, 1}], +StandardPropagatorDenominator[ +Momentum[k1, D] + Momentum[k3, D] - Momentum[q, D], 0, 0, {1, 1}], +StandardPropagatorDenominator[-Momentum[k1, D] + Momentum[q, D], 0, +0, {1, 1}], +StandardPropagatorDenominator[0, +Pair[Momentum[k1, D] - Momentum[k2, D], Momentum[r1, D]], +0, {1, 1}], +StandardPropagatorDenominator[0, +Pair[Momentum[k2, D] + Momentum[k3, D], Momentum[r2, D]], +0, {1, 1}], +StandardPropagatorDenominator[0, +Pair[-Momentum[k1, D] + Momentum[k2, D] + Momentum[q, D], + Momentum[r2, D]], 0, {1, 1}], +StandardPropagatorDenominator[Momentum[k1, D], 0, +0, {1, 1}]], {SFAD[{{0, (k1 + k2).k3}}]}}"}, +{"fcstFCLoopBasisFindCompletion-ID20,"FCLoopBasisFindCompletion[ +SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, +1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, +1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, +1}, {{0, (k1 - k2).n}, {0, 1}, 1}, {{0, (k1 + k3).n}, {0, 1}, +1}, {{0, nb.(-k1 - k3 + q)}, {0, 1}, 1}, {{k1, 0}, {0, 1}, +1}], {k1, k2, k3}, +Method -> {SPD[k1, k3], SPD[k2, k3], SPD[k1, nb], SPD[k2, nb], +SPD[k2, q]}, Check -> False, FCE -> True]","{SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, +1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, +1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, +1}, {{0, (k1 - k2).n}, {0, 1}, 1}, {{0, (k1 + k3).n}, {0, 1}, +1}, {{0, nb.(-k1 - k3 + q)}, {0, 1}, 1}, {{k1, 0}, {0, 1}, +1}], {SPD[k1, k3], SPD[k1, nb], SPD[k2, nb], SPD[k2, q]}}"}, +{"fcstFCLoopBasisFindCompletion-ID21,"FCLoopBasisFindCompletion[ +SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, +1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, +1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, +1}, {{0, (k1 - k2).n}, {0, 1}, 1}, {{0, (k1 + k3).n}, {0, 1}, +1}, {{0, nb.(-k1 - k3 + q)}, {0, 1}, 1}, {{k1, 0}, {0, 1}, +1}], {k1, k2, k3}, +Method -> {SPD[k1, k3], SPD[k2, k3], SPD[k1, nb], SPD[k2, nb], +SPD[k2, q]}, Check -> False, Abort -> True, FCE -> True]","{SFAD[{{k2, 0}, {0, 1}, 1}, {{-k1 + k2, 0}, {0, 1}, +1}, {{k3, 0}, {0, 1}, 1}, {{k2 + k3, 0}, {0, 1}, +1}, {{k1 + k3 - q, 0}, {0, 1}, 1}, {{-k1 + q, 0}, {0, 1}, +1}, {{0, (k1 - k2).n}, {0, 1}, 1}, {{0, (k1 + k3).n}, {0, 1}, +1}, {{0, nb.(-k1 - k3 + q)}, {0, 1}, 1}, {{k1, 0}, {0, 1}, 1}], {}}"} +}); + +Tests`LoopIntegrals`fcstFCLoopBasisSplit = +({ +{"fcstFCLoopBasisSplit-ID1", +"FCLoopBasisSplit[FCI@FAD[{q,m}],{q1,q2},Head\[Rule]loopInt,FCE\ +\[Rule]True]", +"loopInt[FeynAmpDenominator[PropagatorDenominator[Momentum[q, D], \ +m]], 0]"}, +{"fcstFCLoopBasisSplit-ID2", +"FCLoopBasisSplit[FCI@FAD[{q1,m}],{q1,q2},Head\[Rule]loopInt,FCE\ +\[Rule]True]", "{loopInt[FAD[{q1, m}], {q1}]}"}, +{"fcstFCLoopBasisSplit-ID3", +"FCLoopBasisSplit[FCI@FAD[{q1,m},{q2,m},{p1-p2,0}],{q1,q2},Head\ +\[Rule]loopInt,FCE\[Rule]True]", +"{loopInt[FAD[{q1, m}], {q1}], loopInt[FAD[{q2, m}], {q2}], \ +loopInt[FAD[p1 - p2], 0]}"}, +{"fcstFCLoopBasisSplit-ID4", +"FCLoopBasisSplit[FCI@FAD[{q1,m},{q2,m}],{q1,q2},Head\[Rule]\ +loopInt,FCE\[Rule]True]", +"{loopInt[FAD[{q1, m}], {q1}], loopInt[FAD[{q2, m}], {q2}]}"}, +{"fcstFCLoopBasisSplit-ID5", +"FCLoopBasisSplit[FCI@FAD[{q1,m},{q2-q3,m}],{q1,q2},Head\[Rule]\ +loopInt,FCE\[Rule]True]", +"{loopInt[FAD[{q1, m}], {q1}], loopInt[FAD[{q2 - q3, m}], \ +{q2}]}"}, +{"fcstFCLoopBasisSplit-ID6", +"FCLoopBasisSplit[FCI@FAD[{q1,m},{q2,m},{q3-q4,0},{q3-p,m},{q5}],{\ +q1,q2,q3,q4,q5},Head\[Rule]loopInt,FCE\[Rule]True]", +"{loopInt[FAD[{q1, m}], {q1}], loopInt[FAD[{q2, m}], {q2}], \ +loopInt[FAD[q5], {q5}], loopInt[FAD[{-p + q3, m}, q3 - q4], {q3, \ +q4}]}"}, +{"fcstFCLoopBasisSplit-ID7", +"FCLoopBasisSplit[FCI@FAD[{q1,m},{q2,m},{q3-q4,0},{q3-p,m},{q5}],{\ +q1,q2,q3,q4,q5},Head\[Rule]loopInt,List\[Rule]False,FCE\[Rule]True]", +"loopInt[FAD[q5], {q5}]*loopInt[FAD[{q1, m}], \ +{q1}]*loopInt[FAD[{q2, m}], {q2}]*loopInt[FAD[{-p + q3, m}, q3 - q4], \ +{q3, q4}]"}, +{"fcstFCLoopBasisSplit-ID8", +"FCLoopBasisSplit[FCI[CFAD[q1, q1 - q2, q2, {q3, m^2}]], {q1, q2, q3}, +Head -> loop, FCE -> True]", +"{loop[CFAD[{{q3, 0}, {m^2, -1}, 1}], {q3}], +loop[CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, +{{q1 - q2, 0}, {0, -1}, 1}], {q1, q2}]}"}, +{"fcstFCLoopBasisSplit-ID9", +"FCLoopBasisSplit[FCI[SFAD[q1, q1 - q2, q2, {q3, m^2}]], {q1, q2, q3}, +Head -> loop, FCE -> True]", +"{loop[SFAD[{{q3, 0}, {m^2, 1}, 1}], {q3}], +loop[SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, +{{q1 - q2, 0}, {0, 1}, 1}], {q1, q2}]}"} +}); + +Tests`LoopIntegrals`fcstFCLoopBasisExtract = +{{"fcstFCLoopBasisExtract-ID1", +"FCLoopBasisExtract[FCI[CFAD[q,q-p,q-p]],{q},SetDimensions->{D-1}]", +"{{CartesianPair[CartesianMomentum[q, -1 + D], CartesianMomentum[q, \ +-1 + D]], CartesianPair[CartesianMomentum[p, -1 + D], \ +CartesianMomentum[p, -1 + D]] - 2*CartesianPair[CartesianMomentum[p, \ +-1 + D], CartesianMomentum[q, -1 + D]] + \ +CartesianPair[CartesianMomentum[q, -1 + D], CartesianMomentum[q, -1 + \ +D]]}, {CartesianPair[CartesianMomentum[p, -1 + D], \ +CartesianMomentum[q, -1 + D]], CartesianPair[CartesianMomentum[q, -1 \ ++ D], CartesianMomentum[q, -1 + D]]}, {1, 2}, \ +{FeynAmpDenominator[CartesianPropagatorDenominator[CartesianMomentum[\ +q, -1 + D], 0, 0, {1, -1}]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[-CartesianMomentum[\ +p, -1 + D] + CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]}}"}, \ +{"fcstFCLoopBasisExtract-ID2", +"FCLoopBasisExtract[FCI[CSP[q,p]CFAD[q,q-p,q-p]],{q},SetDimensions->{3,D-1}]", +"{{CartesianPair[CartesianMomentum[p], CartesianMomentum[q]], \ +CartesianPair[CartesianMomentum[q, -1 + D], CartesianMomentum[q, -1 + \ +D]], CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[p, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p, -1 + D], \ +CartesianMomentum[q, -1 + D]] + CartesianPair[CartesianMomentum[q, -1 \ ++ D], CartesianMomentum[q, -1 + D]]}, \ +{CartesianPair[CartesianMomentum[p], CartesianMomentum[q]], \ +CartesianPair[CartesianMomentum[q], CartesianMomentum[q]], \ +CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + \ +D]], CartesianPair[CartesianMomentum[q, -1 + D], CartesianMomentum[q, \ +-1 + D]]}, {-1, 1, 2}, {CartesianPair[CartesianMomentum[p], \ +CartesianMomentum[q]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[CartesianMomentum[q,\ +-1 + D], 0, 0, {1, -1}]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[-CartesianMomentum[\ +p, -1 + D] + CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]}}"}, \ +{"fcstFCLoopBasisExtract-ID3", +"FCLoopBasisExtract[FCI[CSPD[q,p]CFAD[q,q-p,q-p]],{q},SetDimensions->{3,D-1}]", +"{{CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[q, \ +-1 + D]], CartesianPair[CartesianMomentum[q, -1 + D], \ +CartesianMomentum[q, -1 + D]], CartesianPair[CartesianMomentum[p, -1 \ ++ D], CartesianMomentum[p, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 \ ++ D]] + CartesianPair[CartesianMomentum[q, -1 + D], \ +CartesianMomentum[q, -1 + D]]}, {CartesianPair[CartesianMomentum[p, \ +-1 + D], CartesianMomentum[q, -1 + D]], \ +CartesianPair[CartesianMomentum[q, -1 + D], CartesianMomentum[q, -1 + \ +D]]}, {-1, 1, 2}, {CartesianPair[CartesianMomentum[p, -1 + D], \ +CartesianMomentum[q, -1 + D]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[CartesianMomentum[q,\ +-1 + D], 0, 0, {1, -1}]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[-CartesianMomentum[\ +p, -1 + D] + CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]}}"}, +{"fcstFCLoopBasisExtract-ID4","FCLoopBasisExtract[FCI[SFAD[q, q - p, q - p]], {q}, SetDimensions->{D}]", +"{{Pair[Momentum[q, D], Momentum[q, D]], +Pair[Momentum[p, D], Momentum[p, D]] - +2 Pair[Momentum[p, D], Momentum[q, D]] + +Pair[Momentum[q, D], Momentum[q, D]]}, {Pair[Momentum[p, D], +Momentum[q, D]], Pair[Momentum[q, D], Momentum[q, D]]}, {1, +2}, {FeynAmpDenominator[ +StandardPropagatorDenominator[Momentum[q, D], 0, 0, {1, 1}]], +FeynAmpDenominator[ +StandardPropagatorDenominator[-Momentum[p, D] + Momentum[q, D], 0, + 0, {1, 1}]]}}"}, +{"fcstFCLoopBasisExtract-ID5","FCLoopBasisExtract[FCI[SPD[q, p] SFAD[q, q - p, q - p]], {q}, SetDimensions->{4, D}]", +"{{Pair[Momentum[p, D], Momentum[q, D]], +Pair[Momentum[q, D], Momentum[q, D]], +Pair[Momentum[p, D], Momentum[p, D]] - +2 Pair[Momentum[p, D], Momentum[q, D]] + +Pair[Momentum[q, D], Momentum[q, D]]}, {Pair[Momentum[p, D], +Momentum[q, D]], Pair[Momentum[q, D], Momentum[q, D]]}, {-1, 1, +2}, {Pair[Momentum[p, D], Momentum[q, D]], +FeynAmpDenominator[ +StandardPropagatorDenominator[Momentum[q, D], 0, 0, {1, 1}]], +FeynAmpDenominator[ +StandardPropagatorDenominator[-Momentum[p, D] + Momentum[q, D], 0, + 0, {1, 1}]]}}"}, +{"fcstFCLoopBasisExtract-ID6","FCLoopBasisExtract[FCI[SPD[q, p] SFAD[q, q - p, q - p]], {q}, SetDimensions->{4, D}]", +"{{Pair[Momentum[p, D], Momentum[q, D]], +Pair[Momentum[q, D], Momentum[q, D]], +Pair[Momentum[p, D], Momentum[p, D]] - +2 Pair[Momentum[p, D], Momentum[q, D]] + +Pair[Momentum[q, D], Momentum[q, D]]}, {Pair[Momentum[p, D], +Momentum[q, D]], Pair[Momentum[q, D], Momentum[q, D]]}, {-1, 1, +2}, {Pair[Momentum[p, D], Momentum[q, D]], +FeynAmpDenominator[ +StandardPropagatorDenominator[Momentum[q, D], 0, 0, {1, 1}]], +FeynAmpDenominator[ +StandardPropagatorDenominator[-Momentum[p, D] + Momentum[q, D], 0, + 0, {1, 1}]]}}"}, +{"fcstFCLoopBasisExtract-ID7","FCLoopBasisExtract[FCI@CFAD[{k, 0, 4}, l - k], {k}, SetDimensions->{D - 1}]", +"{{CartesianPair[CartesianMomentum[k, -1 + D], +CartesianMomentum[k, -1 + D]], +CartesianPair[CartesianMomentum[k, -1 + D], + CartesianMomentum[k, -1 + D]] - +2 CartesianPair[CartesianMomentum[k, -1 + D], + CartesianMomentum[l, -1 + D]] + +CartesianPair[CartesianMomentum[l, -1 + D], + CartesianMomentum[l, -1 + D]]}, {CartesianPair[ +CartesianMomentum[k, -1 + D], CartesianMomentum[k, -1 + D]], +CartesianPair[CartesianMomentum[k, -1 + D], +CartesianMomentum[l, -1 + D]]}, {4, +1}, {FeynAmpDenominator[ +CartesianPropagatorDenominator[CartesianMomentum[k, -1 + D], 0, + 0, {1, -1}]], +FeynAmpDenominator[ +CartesianPropagatorDenominator[-CartesianMomentum[k, -1 + D] + + CartesianMomentum[l, -1 + D], 0, 0, {1, -1}]]}}"}, +{"fcstFCLoopBasisExtract-ID8","FCLoopBasisExtract[FCI@SFAD[{k, 0, 4}, l - k], {k}, SetDimensions->{D}]", +"{{Pair[Momentum[k, D], Momentum[k, D]], +Pair[Momentum[k, D], Momentum[k, D]] - +2 Pair[Momentum[k, D], Momentum[l, D]] + +Pair[Momentum[l, D], Momentum[l, D]]}, {Pair[Momentum[k, D], +Momentum[k, D]], Pair[Momentum[k, D], Momentum[l, D]]}, {4, +1}, {FeynAmpDenominator[ +StandardPropagatorDenominator[Momentum[k, D], 0, 0, {1, 1}]], +FeynAmpDenominator[ +StandardPropagatorDenominator[-Momentum[k, D] + Momentum[l, D], 0, + 0, {1, 1}]]}}"}, +{"fcstFCLoopBasisExtract-ID9","FCLoopBasisExtract[FCI[SFAD[p1]], {p1, p2}, FCTopology -> True, +FCE -> True]", +"{{SPD[p1, p1]}, {SPD[p1, p1], SPD[p1, p2], +SPD[p2, p2]}, {1}, {SFAD[{{p1, 0}, {0, 1}, 1}]}}"}, +{"fcstFCLoopBasisExtract-ID10","FCLoopBasisExtract[FCI[SFAD[p1]], {p1, p2, p3}, FCTopology -> True, +FCE -> True]", +"{{SPD[p1, p1]}, {SPD[p1, p1], SPD[p1, p2], SPD[p1, p3], SPD[p2, p2], +SPD[p2, p3], SPD[p3, p3]}, {1}, {SFAD[{{p1, 0}, {0, 1}, 1}]}}"}, +{"fcstFCLoopBasisExtract-ID11","FCLoopBasisExtract[ +GFAD[{p1.q p2.q + x}] SFAD[p1] SPD[p2, r]^2, {p1, p2}, FCE -> True]", +"{{SPD[p2, r], x + p1 . q*p2 . q, SPD[p1, p1]}, {SPD[p1, p1], SPD[p1, p2], +SPD[p1, r], SPD[p2, p2], SPD[p2, r], p1 . q*p2 . q}, {-2, 1, 1}, {SPD[p2, r], +GFAD[{{x + p1 . q*p2 . q, 1}, 1}], SFAD[{{p1, 0}, {0, 1}, 1}]}}"}, +{"fcstFCLoopBasisExtract-ID12","FCLoopBasisExtract[ +FAD[q1, -k1 + q1, -k1 + q1, -k1 + q1, +q2] (SPD[k1, k1] - SPD[q1, q1]) (-SPD[k1, k1] + SPD[q1, q1]), {q1, +q2}, FCE -> True]", +"{{SPD[k1, k1] - SPD[q1, q1], -SPD[k1, k1] + SPD[q1, q1], SPD[q1, q1], +SPD[k1, k1] - 2 SPD[k1, q1] + SPD[q1, q1], +SPD[q2, q2]}, {SPD[k1, q1], SPD[k1, q2], SPD[q1, q1], SPD[q1, q2], +SPD[q2, q2]}, {-1, -1, 1, 3, +1}, {GFAD[{{SPD[k1, k1] - SPD[q1, q1], 1}, -1}], +GFAD[{{-SPD[k1, k1] + SPD[q1, q1], 1}, -1}], FAD[q1], FAD[-k1 + q1], +FAD[q2]}}"}, +{"fcstFCLoopBasisExtract-ID13","FCLoopBasisExtract[ +FAD[q1, q1 - k1, q2, q1 + q2] SPD[2 k1 - q1, q1 + 2 q2], {q1, q2}, +FCE -> True]", +"{{2 SPD[k1, q1] + 4 SPD[k1, q2] - SPD[q1, q1] - 2 SPD[q1, q2], +SPD[q1, q1], SPD[k1, k1] - 2 SPD[k1, q1] + SPD[q1, q1], SPD[q2, q2], +SPD[q1, q1] + 2 SPD[q1, q2] + SPD[q2, q2]}, {SPD[k1, q1], +SPD[k1, q2], SPD[q1, q1], SPD[q1, q2], SPD[q2, q2]}, {-1, 1, 1, 1, +1}, {2 SPD[k1, q1] + 4 SPD[k1, q2] - SPD[q1, q1] - 2 SPD[q1, q2], +FAD[q1], FAD[-k1 + q1], FAD[q2], FAD[q1 + q2]}}"}, +{"fcstFCLoopBasisExtract-ID14","FCLoopBasisExtract[GFAD[(TC[q] - x)] * +SFAD[{{0, p.q}, x}], {q}, FCE -> True]", +"{{-x + SPD[p, q], -x + TC[q]}, {SP[p, q], SP[q, q], SPD[p, q], +SPD[q, q], TC[q]}, {1, 1}, {SFAD[{{0, p.q}, {x, 1}, 1}], +GFAD[{{-x + TC[q], 1}, 1}]}}"}, +{"fcstFCLoopBasisExtract-ID15","FCLoopBasisExtract[TC[q] GFAD[(TC[q] - +x)] SFAD[{{0, p.q}, x}], {q}, FCE -> True]", +"{{-x + SPD[p, q], -x + TC[q], TC[q]}, {SP[p, q], SP[q, q], SPD[p, q], +SPD[q, q], TC[q]}, {1, 1, -1}, {SFAD[{{0, p.q}, {x, 1}, 1}], +GFAD[{{-x + TC[q], 1}, 1}], GFAD[{{TC[q], 1}, -1}]}}"}, +{"fcstFCLoopBasisExtract-ID16","FCLoopBasisExtract[ +CFAD[{{-k + P, 0}, {0, -1}, 1}] GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}], {k}, FCE -> True]", +"{{EN - V0 + Sqrt[CSPD[k, k]], +CSPD[k, k] - 2*CSPD[k, P] + CSPD[P, P]}, {CSPD[k, k], CSPD[k, P], +Sqrt[CSPD[k, k]]}, {1, +1}, {GFAD[{{EN - V0 + Sqrt[CSPD[k, k]], 1}, 1}], +CFAD[{{-k + P, 0}, {0, -1}, 1}]}}"}, +{"fcstFCLoopBasisExtract-ID17","FCLoopBasisExtract[ +CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{-k + P, 0}, {0, -1}, + 1}] GFAD[{{EN - V0 - TC[k], 1}, 1}] TC[k], {k}, FCE -> True]", +"{{EN - V0 - TC[k], CSPD[k, k] - TC[k]^2, +CSPD[k, k] - 2 CSPD[k, P] + CSPD[P, P], TC[k]}, {CSPD[k, k], +CSPD[k, P], TC[k], TC[k]^2}, {1, 1, +1, -1}, {GFAD[{{EN - V0 - TC[k], 1}, 1}], +CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}], CFAD[{{-k + P, 0}, {0, -1}, 1}], +GFAD[{{TC[k], 1}, -1}]}}"}, +{"fcstFCLoopBasisExtract-ID17", +"FCLoopBasisExtract[{FAD[q1-p1],SPD[q1,p]},{q1},SetDimensions\ +\[Rule]{D},FCE\[Rule]True]", +"{{SPD[p, q1], SPD[p1, p1] - 2*SPD[p1, q1] + SPD[q1, q1]}, {SPD[p, \ +q1], SPD[p1, q1], SPD[q1, q1]}, {-1, 1}, {SPD[p, q1], FAD[-p1 + \ +q1]}}"}, +{"fcstFCLoopBasisExtract-ID18", +"FCLoopBasisExtract[{FAD[q1-p1],FAD[{q1,m1}],SPD[q1,p]},{q1},\ +SetDimensions\[Rule]{D},FCE\[Rule]True]", +"{{SPD[p, q1], SPD[p1, p1] - 2*SPD[p1, q1] + SPD[q1, q1], -m1^2 + \ +SPD[q1, q1]}, {SPD[p, q1], SPD[p1, q1], SPD[q1, q1]}, {-1, 1, 1}, \ +{SPD[p, q1], FAD[-p1 + q1], FAD[{q1, m1}]}}"}, +{"fcstFCLoopBasisExtract-ID19", +"FCLoopBasisExtract[{FAD[q1],FAD[q1-k1,q2,q1+q2], SPD[2 k1-q1,q1+2 \ +q2]},{q1,q2},FCE\[Rule]True]", +"{{2*SPD[k1, q1] + 4*SPD[k1, q2] - SPD[q1, q1] - 2*SPD[q1, q2], \ +SPD[q1, q1], SPD[k1, k1] - 2*SPD[k1, q1] + SPD[q1, q1], SPD[q2, q2], \ +SPD[q1, q1] + 2*SPD[q1, q2] + SPD[q2, q2]}, {SPD[k1, q1], SPD[k1, \ +q2], SPD[q1, q1], SPD[q1, q2], SPD[q2, q2]}, {-1, 1, 1, 1, 1}, \ +{2*SPD[k1, q1] + 4*SPD[k1, q2] - SPD[q1, q1] - 2*SPD[q1, q2], \ +FAD[q1], FAD[-k1 + q1], FAD[q2], FAD[q1 + q2]}}"}, +{"fcstFCLoopBasisExtract-ID20", +"FCLoopBasisExtract[{FAD[q1-p1],SPD[q1,p]},{q1},SetDimensions\ +\[Rule]{D},FCE\[Rule]True]", +"{{SPD[p, q1], SPD[p1, p1] - 2*SPD[p1, q1] + SPD[q1, q1]}, {SPD[p, \ +q1], SPD[p1, q1], SPD[q1, q1]}, {-1, 1}, {SPD[p, q1], FAD[-p1 + \ +q1]}}"}, +{"fcstFCLoopBasisExtract-ID21", +"FCLoopBasisExtract[{FAD[q1-p1],FAD[{q1,m1}],SPD[q1,p]},{q1},\ +SetDimensions\[Rule]{D},FCE\[Rule]True]", +"{{SPD[p, q1], SPD[p1, p1] - 2*SPD[p1, q1] + SPD[q1, q1], -m1^2 + \ +SPD[q1, q1]}, {SPD[p, q1], SPD[p1, q1], SPD[q1, q1]}, {-1, 1, 1}, \ +{SPD[p, q1], FAD[-p1 + q1], FAD[{q1, m1}]}}"}, +{"fcstFCLoopBasisExtract-ID22", +"FCLoopBasisExtract[{FAD[q1],FAD[q1-k1,q2,q1+q2], SPD[2 k1-q1,q1+2 \ +q2]},{q1,q2},FCE\[Rule]True]", +"{{2*SPD[k1, q1] + 4*SPD[k1, q2] - SPD[q1, q1] - 2*SPD[q1, q2], \ +SPD[q1, q1], SPD[k1, k1] - 2*SPD[k1, q1] + SPD[q1, q1], SPD[q2, q2], \ +SPD[q1, q1] + 2*SPD[q1, q2] + SPD[q2, q2]}, {SPD[k1, q1], SPD[k1, \ +q2], SPD[q1, q1], SPD[q1, q2], SPD[q2, q2]}, {-1, 1, 1, 1, 1}, \ +{2*SPD[k1, q1] + 4*SPD[k1, q2] - SPD[q1, q1] - 2*SPD[q1, q2], \ +FAD[q1], FAD[-k1 + q1], FAD[q2], FAD[q1 + q2]}}"} +}; + +Tests`LoopIntegrals`fcstFCLoopBasisGetSize = +({ +{"fcstFCLoopBasisGetSize-ID1", "FCLoopBasisGetSize[1,0]", "1"}, +{"fcstFCLoopBasisGetSize-ID2", "FCLoopBasisGetSize[1,1]", "2"}, +{"fcstFCLoopBasisGetSize-ID3", "FCLoopBasisGetSize[1,2]", "3"}, +{"fcstFCLoopBasisGetSize-ID4", "FCLoopBasisGetSize[1,3]", "4"}, +{"fcstFCLoopBasisGetSize-ID5", "FCLoopBasisGetSize[2,1]", "5"}, +{"fcstFCLoopBasisGetSize-ID6", "FCLoopBasisGetSize[3,1]", "9"}, +{"fcstFCLoopBasisGetSize-ID7", "FCLoopBasisGetSize[3,1,1]", "10"}, +{"fcstFCLoopBasisGetSize-ID8", "FCLoopBasisGetSize[4,1,1]", "15"}, +{"fcstFCLoopBasisGetSize-ID9", "FCLoopBasisGetSize[3,3]", "15"} +}) + +Tests`LoopIntegrals`fcstFCLoopBasisIntegralToPropagators = +({ +{"fcstFCLoopBasisIntegralToPropagators-ID1", +"FCLoopBasisIntegralToPropagators[FCI[SFAD[p1]],{p1}]", +"{FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p1, \ +D], 0, 0, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID2", +"FCLoopBasisIntegralToPropagators[x FCI[SFAD[p1]],{p1}]", +"{FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p1, \ +D], 0, 0, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID3", +"FCLoopBasisIntegralToPropagators[FCI[SFAD[p1,p2]],{p1,p2}]", +"{FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p1, \ +D], 0, 0, {1, 1}]], \ +FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p2, D], 0, \ +0, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID4", +"FCLoopBasisIntegralToPropagators[FCI[SFAD[p1,p2]],{p2}]", +"{FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p2, \ +D], 0, 0, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID5", +"FCLoopBasisIntegralToPropagators[FCI[SPD[p1,p2]],{p2}]", +"{FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], 0, {-1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID6", +"FCLoopBasisIntegralToPropagators[FCI[ty CFAD[q,q-p,q-p]],{q}]", +"{FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[-CartesianMomentum[\ +p, -1 + D] + CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID7", +"FCLoopBasisIntegralToPropagators[FCI[CSP[q,p]CFAD[q,q-p,q-p]],{q}]", +"{FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p], CartesianMomentum[q]], 0, {-1, \ +-1}]], FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[-CartesianMomentum[\ +p, -1 + D] + CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID8", +"FCLoopBasisIntegralToPropagators[FCI[CSPD[q,p]CFAD[q,q-p,q-p]],{q}]", + "{FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + \ +D]], 0, {-1, -1}]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[CartesianMomentum[q,\ +-1 + D], 0, 0, {1, -1}]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[-CartesianMomentum[\ +p, -1 + D] + CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID9", +"FCLoopBasisIntegralToPropagators[FCI[SFAD[q,q-p,q-p]],{q}]", +"{FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]], \ +FeynAmpDenominator[StandardPropagatorDenominator[-Momentum[p, D] + \ +Momentum[q, D], 0, 0, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID10", +"FCLoopBasisIntegralToPropagators[FCI[SPD[q,p] SFAD[q,q-p,q-p]],{q}]", + "{FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p, D], Momentum[q, D]], 0, {-1, 1}]], \ +FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], 0, \ +0, {1, 1}]], \ +FeynAmpDenominator[StandardPropagatorDenominator[-Momentum[p, D] + \ +Momentum[q, D], 0, 0, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID11", +"FCLoopBasisIntegralToPropagators[FCI@CFAD[{k,0,4},l-k],{k}]", +"{FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[k, -1 + D], 0, 0, {1, -1}]], \ +FeynAmpDenominator[CartesianPropagatorDenominator[-CartesianMomentum[\ +k, -1 + D] + CartesianMomentum[l, -1 + D], 0, 0, {1, -1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID12", +"FCLoopBasisIntegralToPropagators[FCI[FAD[q,{q,0,3}]],{q}]", +"{FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], 0, 0, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID13", +"FCLoopBasisIntegralToPropagators[FCI[SPD[q,p] SFAD[q,q-p,q-p] \ +SFAD[q-p]],{q},Tally\[Rule]True]", +"{{FeynAmpDenominator[StandardPropagatorDenominator[-Momentum[p, \ +D] + Momentum[q, D], 0, 0, {1, 1}]], 3}, \ +{FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], 0, \ +0, {1, 1}]], 1}, {FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p, D], Momentum[q, D]], 0, {-1, 1}]], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID14", +"FCLoopBasisIntegralToPropagators[FCI[SPD[q,p] SFAD[q,q-p,q-p] \ +SFAD[q-p]],{q},Tally\[Rule]True,FCE->True]", +"{{SFAD[{{-p + q, 0}, {0, 1}, 1}], 3}, {SFAD[{{q, 0}, {0, 1}, 1}], \ +1}, {SFAD[{{0, p . q}, {0, 1}, -1}], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID15", +"FCLoopBasisIntegralToPropagators[FCI[SPD[q,p] FAD[q,q-p,q-p] \ +FAD[q-p]],{q},Tally\[Rule]True,FCE\[Rule]True]", +"{{SFAD[{{-p + q, 0}, {0, 1}, 1}], 3}, {SFAD[{{q, 0}, {0, 1}, 1}], \ +1}, {SFAD[{{0, p . q}, {0, 1}, -1}], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID16", +"FCLoopBasisIntegralToPropagators[FCI[SPD[q,p] FAD[q,q-p,q-p] \ +FAD[q-p]],{q},Tally\[Rule]True,FCE\[Rule]True]", +"{{SFAD[{{-p + q, 0}, {0, 1}, 1}], 3}, {SFAD[{{q, 0}, {0, 1}, 1}], \ +1}, {SFAD[{{0, p . q}, {0, 1}, -1}], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID17", +"FCLoopBasisIntegralToPropagators[FCI[SPD[q,p] FAD[q,q-p,q-p] \ +SFAD[q-p]],{q},Tally\[Rule]True,FCE\[Rule]True]", +"{{SFAD[{{-p + q, 0}, {0, 1}, 1}], 3}, {SFAD[{{q, 0}, {0, 1}, 1}], \ +1}, {SFAD[{{0, p . q}, {0, 1}, -1}], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID18", +"FCLoopBasisIntegralToPropagators[FCI[SPD[q,p]FAD[q,q-p,q-p] \ +SFAD[q-p]],{q},Tally\[Rule]True,FCE\[Rule]True]", +"{{SFAD[{{-p + q, 0}, {0, 1}, 1}], 3}, {SFAD[{{q, 0}, {0, 1}, 1}], \ +1}, {SFAD[{{0, p . q}, {0, 1}, -1}], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID19", +"FCLoopBasisIntegralToPropagators[FAD[p]SFAD[p],{p},FCE\[Rule]True]", +"{SFAD[{{p, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID20", +"FCLoopBasisIntegralToPropagators[SPD[p,q]^2 \ +FCI[SPD[p,q]]SFAD[q,p-q],{q},FCE->True]", +"{SFAD[{{0, p . q}, {0, 1}, -1}], SFAD[{{p - q, 0}, {0, 1}, 1}], \ +SFAD[{{q, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID21", +"FCLoopBasisIntegralToPropagators[SPD[p,q]^2 \ +FCI[SPD[p,q]]SFAD[q,p-q]^6,{q},FCE->True]", +"{SFAD[{{0, p . q}, {0, 1}, -1}], SFAD[{{p - q, 0}, {0, 1}, 1}], \ +SFAD[{{q, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID22", +"FCLoopBasisIntegralToPropagators[SPD[p,q]^2 \ +FCI[SPD[p,q]]SFAD[q,p-q],{q},Tally\[Rule]True,FCE->True]", +"{{SFAD[{{q, 0}, {0, 1}, 1}], 1}, {SFAD[{{p - q, 0}, {0, 1}, 1}], \ +1}, {SFAD[{{0, p . q}, {0, 1}, -1}], 3}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID23", +"FCLoopBasisIntegralToPropagators[SPD[p,q]^2 \ +FCI[SPD[p,q]]SFAD[q,p-q]^6,{q},Tally\[Rule]True,FCE->True]", +"{{SFAD[{{q, 0}, {0, 1}, 1}], 6}, {SFAD[{{p - q, 0}, {0, 1}, 1}], \ +6}, {SFAD[{{0, p . q}, {0, 1}, -1}], 3}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID24", +"FCLoopBasisIntegralToPropagators[x FCI[SFAD[p1]], {p1}, Rest -> True, +FCE -> True]", +"{{SFAD[{{p1, 0}, {0, 1}, 1}]}, x}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID25", +"FCLoopBasisIntegralToPropagators[x*t FCI[SFAD[p1]], {p1}, Rest -> True, +FCE -> True]", +"{{SFAD[{{p1, 0}, {0, 1}, 1}]}, x*t}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID26", +"FCLoopBasisIntegralToPropagators[SPD[p, q]^2 FCI[SPD[p, q]] SFAD[q, p - q], {q}, + Tally -> True, FCE -> True, Negative -> True]", +"{{SFAD[{{q, 0}, {0, 1}, 1}], 1}, {SFAD[{{p - q, 0}, {0, 1}, 1}], +1}, {SFAD[{{0, p.q}, {0, 1}, -1}], -3}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID27", +"FCLoopBasisIntegralToPropagators[SPD[p, q]^2 FCI[SPD[p, q]] SFAD[q, p - q], {q}, Tally -> True, +FCE -> True, Negative -> True, Pair -> True]", +"{{SFAD[{{q, 0}, {0, 1}, 1}], 1}, {SFAD[{{p - q, 0}, {0, 1}, 1}], +1}, {SPD[p, q], -3}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID28", +"FCLoopBasisIntegralToPropagators[ +CSPD[p, q]^2 FCI[CSPD[p, q]] CFAD[q, p - q], {q}, Tally -> True, +FCE -> True, Negative -> True, CartesianPair -> True]", +"{{CSPD[p, q], -3}, {CFAD[{{q, 0}, {0, -1}, 1}], +1}, {CFAD[{{p - q, 0}, {0, -1}, 1}], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID29", +"FCLoopBasisIntegralToPropagators[CFAD[{k, 0, 4}, l - k], {k}, +Tally -> True, FCE -> True]", +"{{CFAD[{{k, 0}, {0, -1}, 1}], 4}, {CFAD[{{-k + l, 0}, {0, -1}, 1}], +1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID30", +"FCLoopBasisIntegralToPropagators[SFAD[{k, 0, 4}, l - k], {k}, +Tally -> True, FCE -> True]", +"{{SFAD[{{k, 0}, {0, 1}, 1}], 4}, {SFAD[{{-k + l, 0}, {0, 1}, 1}], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID31", +"FCLoopBasisIntegralToPropagators[(Pair[Momentum[-k1/2, D], + Momentum[l, D]] + + Pair[Momentum[-k2/2, D], Momentum[l, D]]) FAD[{l, 0, + 2}, {-k1/2 - k2/2 + l, m}, {k1/2 - k2/2 + l, m}], {l}, +MomentumCombine -> True, Tally -> False]", +"{FeynAmpDenominator[StandardPropagatorDenominator[0, -Pair[Momentum[k1 + k2, D], Momentum[l, D]]/2, 0, {-1, 1}]], +FeynAmpDenominator[StandardPropagatorDenominator[Momentum[l, D], 0, 0, {1, 1}]], FeynAmpDenominator[StandardPropagatorDenominator[-Momentum[k1, D]/2 - Momentum[k2, D]/2 + Momentum[l, D], +0, m^2, {1, 1}]], FeynAmpDenominator[StandardPropagatorDenominator[Momentum[k1, D]/2 - Momentum[k2, D]/2 + Momentum[l, D], 0, m^2, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID32", +"FCLoopBasisIntegralToPropagators[GFAD[{p1.q p2.q + x}] SFAD[p1], {p1, p2}, FCE -> True]", +"{GFAD[{{x + p1.q p2.q, 1}, 1}], SFAD[{{p1, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID33", +"FCLoopBasisIntegralToPropagators[GFAD[{p1.q p2.q + x, 2}] SFAD[p1], {p1, p2}, Tally -> True,FCE -> True]", +"{{GFAD[{{x + p1.q p2.q, 1}, 1}], 2}, {SFAD[{{p1, 0}, {0, 1}, 1}], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID34", +"FCLoopBasisIntegralToPropagators[FeynAmpDenominator[ +StandardPropagatorDenominator[-Momentum[p2, D] + Momentum[Q, D], 0, +0, {1, 1}]]^2, {p1, p2, p3}, FCE -> True]", +"{SFAD[{{-p2 + Q, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID35", +"FCLoopBasisIntegralToPropagators[FeynAmpDenominator[ +StandardPropagatorDenominator[-Momentum[p2, D] + Momentum[Q, D], 0, +0, {1, 1}]]^2, {p1, p2, p3}, FCE -> True, Tally->True]", +"{{SFAD[{{-p2 + Q, 0}, {0, 1}, 1}], 2}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID36", +"FCLoopBasisIntegralToPropagators[ +ExpandScalarProduct[SPD[l, -p1 - p2 - p3]^3 FAD[l, l - p2, l - p1 - p2 - p3]], {l}, +FCE -> True]", +"{GFAD[{{-SPD[l, p1 + p2 + p3], 1}, -1}], SFAD[{{l, 0}, {0, 1}, 1}], +SFAD[{{l - p2, 0}, {0, 1}, 1}], +SFAD[{{l - p1 - p2 - p3, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID37", +"FCLoopBasisIntegralToPropagators[ +ExpandScalarProduct[SPD[l, -p1 - p2 - p3]^3 FAD[l, l - p2, l - p1 - p2 - p3]], {l}, +FCE -> True, MomentumCombine->True]", +"{SFAD[{{0, -l.(p1 + p2 + p3)}, {0, 1}, -1}], +SFAD[{{l, 0}, {0, 1}, 1}], SFAD[{{l - p2, 0}, {0, 1}, 1}], +SFAD[{{l - p1 - p2 - p3, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID38", +"FCLoopBasisIntegralToPropagators[ +ExpandScalarProduct[ +CSPD[l, -p1 - p2 - p3]^3 FAD[l, l - p2, l - p1 - p2 - p3]], {l}, +MomentumCombine -> True, FCE -> True]", +"{CFAD[{{0, -l.(p1 + p2 + p3)}, {0, -1}, -1}], +SFAD[{{l, 0}, {0, 1}, 1}], SFAD[{{l - p2, 0}, {0, 1}, 1}], +SFAD[{{l - p1 - p2 - p3, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID40", +"FCLoopBasisIntegralToPropagators[ +ExpandScalarProduct[ +CSPD[l, -p1 - p2 - p3]^3 FAD[l, l - p2, l - p1 - p2 - p3]], {l}, +MomentumCombine -> True, FCE -> True]", +"{CFAD[{{0, -l.(p1 + p2 + p3)}, {0, -1}, -1}], +SFAD[{{l, 0}, {0, 1}, 1}], SFAD[{{l - p2, 0}, {0, 1}, 1}], +SFAD[{{l - p1 - p2 - p3, 0}, {0, 1}, 1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID41", +"FCLoopBasisIntegralToPropagators[GFAD[(TC[q]-x)]SFAD[{{0,p.q},x}],\ +{q}]", "{FeynAmpDenominator[GenericPropagatorDenominator[-x + \ +TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]], {1, 1}]], \ +FeynAmpDenominator[StandardPropagatorDenominator[0, Pair[Momentum[p, \ +D], Momentum[q, D]], -x, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID42", +"FCLoopBasisIntegralToPropagators[GFAD[(TC[q]-x)]SFAD[{{0,p.q},x}],\ +{q},Tally\[Rule]True]", +"{{FeynAmpDenominator[GenericPropagatorDenominator[-x + \ +TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]], {1, 1}]], 1}, \ +{FeynAmpDenominator[StandardPropagatorDenominator[0, Pair[Momentum[p, \ +D], Momentum[q, D]], -x, {1, 1}]], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID43", +"FCLoopBasisIntegralToPropagators[TC[q]GFAD[(TC[q]-x)]SFAD[{{0,p.q}\ +,x}],{q}]", +"{FeynAmpDenominator[GenericPropagatorDenominator[TemporalPair[\ +ExplicitLorentzIndex[0], TemporalMomentum[q]], {-1, 1}]], \ +FeynAmpDenominator[GenericPropagatorDenominator[-x + \ +TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]], {1, 1}]], \ +FeynAmpDenominator[StandardPropagatorDenominator[0, Pair[Momentum[p, \ +D], Momentum[q, D]], -x, {1, 1}]]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID44", +"FCLoopBasisIntegralToPropagators[TC[q]GFAD[(TC[q]-x)]SFAD[{{0,p.q}\ +,x}],{q},Tally\[Rule]True]", +"{{FeynAmpDenominator[GenericPropagatorDenominator[-x + \ +TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]], {1, 1}]], 1}, \ +{FeynAmpDenominator[StandardPropagatorDenominator[0, Pair[Momentum[p, \ +D], Momentum[q, D]], -x, {1, 1}]], 1}, \ +{FeynAmpDenominator[GenericPropagatorDenominator[TemporalPair[\ +ExplicitLorentzIndex[0], TemporalMomentum[q]], {-1, 1}]], 1}}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID45", +"FCLoopBasisIntegralToPropagators[{SPD[p1]},{p1},FCE->True]", +"{SFAD[{{0, p1 . p1}, {0, 1}, -1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID46", +"FCLoopBasisIntegralToPropagators[{SPD[p1]-m1^2},{p1},FCE->True]", +"{GFAD[{{-m1^2 + SPD[p1, p1], 1}, -1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID47", +"FCLoopBasisIntegralToPropagators[{SPD[p1]-m1^2,SPD[p1,q]},{p1},\ +FCE->True]", +"{GFAD[{{-m1^2 + SPD[p1, p1], 1}, -1}], SFAD[{{0, p1 . q}, {0, 1}, \ +-1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID48", +"FCLoopBasisIntegralToPropagators[{SPD[p3],SPD[p1]-m1^2,SPD[p1,q],\ +SPD[p1-p3]},{p1,p3},FCE->True]", +"{GFAD[{{-m1^2 + SPD[p1, p1], 1}, -1}], SFAD[{{0, p1 . q}, {0, 1}, \ +-1}], SFAD[{{0, (p1 - p3) . (p1 - p3)}, {0, 1}, -1}], SFAD[{{0, p3 . \ +p3}, {0, 1}, -1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID49", +"FCLoopBasisIntegralToPropagators[{SPD[p3],SPD[p1]-m1^2,SPD[p1,q],\ +SPD[p1-p3]},{p1,p3},Sort\[Rule]False,FCE->True]", +"{SFAD[{{0, p3 . p3}, {0, 1}, -1}], GFAD[{{-m1^2 + SPD[p1, p1], \ +1}, -1}], SFAD[{{0, p1 . q}, {0, 1}, -1}], SFAD[{{0, (p1 - p3) . (p1 \ +- p3)}, {0, 1}, -1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID50", +"FCLoopBasisIntegralToPropagators[{CSPD[p1]},{p1},FCE->True]", +"{CFAD[{{0, p1 . p1}, {0, -1}, -1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID51", +"FCLoopBasisIntegralToPropagators[{CSPD[p1]+m1^2},{p1},FCE->True]", + "{GFAD[{{m1^2 + CSPD[p1, p1], 1}, -1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID52", +"FCLoopBasisIntegralToPropagators[{CSPD[p1]+m1^2,CSPD[p1,q]},{p1},\ +FCE->True]", +"{CFAD[{{0, p1 . q}, {0, -1}, -1}], GFAD[{{m1^2 + CSPD[p1, p1], \ +1}, -1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID53", +"FCLoopBasisIntegralToPropagators[{CSPD[p3],SPD[p1]+m1^2,SPD[p1,q],\ +SPD[p1-p3]},{p1,p3},FCE->True]", +"{CFAD[{{0, p3 . p3}, {0, -1}, -1}], GFAD[{{m1^2 + SPD[p1, p1], \ +1}, -1}], SFAD[{{0, p1 . q}, {0, 1}, -1}], SFAD[{{0, (p1 - p3) . (p1 \ +- p3)}, {0, 1}, -1}]}"}, +{"fcstFCLoopBasisIntegralToPropagators-ID54", +"FCLoopBasisIntegralToPropagators[{CSPD[p3],CSPD[p1]+m1^2,SPD[p1,q]\ +,SPD[p1-p3]},{p1,p3},Sort\[Rule]False,FCE->True]", +"{CFAD[{{0, p3 . p3}, {0, -1}, -1}], GFAD[{{m1^2 + CSPD[p1, p1], \ +1}, -1}], SFAD[{{0, p1 . q}, {0, 1}, -1}], SFAD[{{0, (p1 - p3) . (p1 \ +- p3)}, {0, 1}, -1}]}"} }); + +Tests`LoopIntegrals`fcstFCLoopBasisCreateScalarProducts = +({ +{"fcstFCLoopBasisCreateScalarProducts-ID1", +"FCLoopBasisCreateScalarProducts[{l},{},{D},Pair]", +"{Pair[Momentum[l, D], Momentum[l, D]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID2", +"FCLoopBasisCreateScalarProducts[{l},{},{d1,d2},Pair]", +"{Pair[Momentum[l, d1], Momentum[l, d1]], Pair[Momentum[l, d2], \ +Momentum[l, d2]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID3", +"FCLoopBasisCreateScalarProducts[{l},{p1,p2},{4},Pair]", +"{Pair[Momentum[l], Momentum[l]], Pair[Momentum[l], Momentum[p1]], \ +Pair[Momentum[l], Momentum[p2]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID4", +"FCLoopBasisCreateScalarProducts[{l},{p1,p2},{d1,d2},Pair]", +"{Pair[Momentum[l, d1], Momentum[l, d1]], Pair[Momentum[l, d1], \ +Momentum[p1, d1]], Pair[Momentum[l, d1], Momentum[p2, d1]], \ +Pair[Momentum[l, d2], Momentum[l, d2]], Pair[Momentum[l, d2], \ +Momentum[p1, d2]], Pair[Momentum[l, d2], Momentum[p2, d2]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID5", +"FCLoopBasisCreateScalarProducts[{l1,l2},{p1,p2},{D},Pair]", +"{Pair[Momentum[l1, D], Momentum[l1, D]], Pair[Momentum[l2, D], \ +Momentum[l2, D]], Pair[Momentum[l1, D], Momentum[l2, D]], \ +Pair[Momentum[l1, D], Momentum[p1, D]], Pair[Momentum[l1, D], \ +Momentum[p2, D]], Pair[Momentum[l2, D], Momentum[p1, D]], \ +Pair[Momentum[l2, D], Momentum[p2, D]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID6", +"FCLoopBasisCreateScalarProducts[{l},{},{D-1},CartesianPair]", +"{CartesianPair[CartesianMomentum[l, -1 + D], CartesianMomentum[l, \ +-1 + D]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID7", +"FCLoopBasisCreateScalarProducts[{l},{},{d1,d2},CartesianPair]", +"{CartesianPair[CartesianMomentum[l, d1], CartesianMomentum[l, \ +d1]], CartesianPair[CartesianMomentum[l, d2], CartesianMomentum[l, \ +d2]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID8", +"FCLoopBasisCreateScalarProducts[{l},{p1,p2},{3},CartesianPair]", +"{CartesianPair[CartesianMomentum[l], CartesianMomentum[l]], \ +CartesianPair[CartesianMomentum[l], CartesianMomentum[p1]], \ +CartesianPair[CartesianMomentum[l], CartesianMomentum[p2]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID9", +"FCLoopBasisCreateScalarProducts[{l},{p1,p2},{d1,d2},CartesianPair]\ +", "{CartesianPair[CartesianMomentum[l, d1], CartesianMomentum[l, \ +d1]], CartesianPair[CartesianMomentum[l, d1], CartesianMomentum[p1, \ +d1]], CartesianPair[CartesianMomentum[l, d1], CartesianMomentum[p2, \ +d1]], CartesianPair[CartesianMomentum[l, d2], CartesianMomentum[l, \ +d2]], CartesianPair[CartesianMomentum[l, d2], CartesianMomentum[p1, \ +d2]], CartesianPair[CartesianMomentum[l, d2], CartesianMomentum[p2, \ +d2]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID10", +"FCLoopBasisCreateScalarProducts[{l1,l2},{p1,p2},{D-1},\ +CartesianPair]", +"{CartesianPair[CartesianMomentum[l1, -1 + D], \ +CartesianMomentum[l1, -1 + D]], CartesianPair[CartesianMomentum[l2, \ +-1 + D], CartesianMomentum[l2, -1 + D]], \ +CartesianPair[CartesianMomentum[l1, -1 + D], CartesianMomentum[l2, -1 \ ++ D]], CartesianPair[CartesianMomentum[l1, -1 + D], \ +CartesianMomentum[p1, -1 + D]], CartesianPair[CartesianMomentum[l1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], \ +CartesianPair[CartesianMomentum[l2, -1 + D], CartesianMomentum[p1, -1 \ ++ D]], CartesianPair[CartesianMomentum[l2, -1 + D], \ +CartesianMomentum[p2, -1 + D]]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID11", +"FCLoopBasisCreateScalarProducts[{l1,l2,l3},{p1,p2},{D},Pair,FCE\ +\[Rule]True]", +"{SPD[l1, l1], SPD[l2, l2], SPD[l3, l3], SPD[l1, l2], SPD[l1, l3], \ +SPD[l2, l3], SPD[l1, p1], SPD[l1, p2], SPD[l2, p1], SPD[l2, p2], \ +SPD[l3, p1], SPD[l3, p2]}"}, +{"fcstFCLoopBasisCreateScalarProducts-ID12", +"FCLoopBasisCreateScalarProducts[{l1,l2,l3},{p1,p2},{D-1},\ +CartesianPair,FCE\[Rule]True]", +"{CSPD[l1, l1], CSPD[l2, l2], CSPD[l3, l3], CSPD[l1, l2], CSPD[l1, \ +l3], CSPD[l2, l3], CSPD[l1, p1], CSPD[l1, p2], CSPD[l2, p1], CSPD[l2, \ +p2], CSPD[l3, p1], CSPD[l3, p2]}"} +}) + + +Tests`LoopIntegrals`fcstFCLoopBasisPropagatorsToTopology = +({ +{"fcstFCLoopBasisPropagatorsToTopology-ID1", +"FCLoopBasisPropagatorsToTopology[{SPD[q]},FCE\[Rule]True]", +"{SPD[q, q]}"}, +{"fcstFCLoopBasisPropagatorsToTopology-ID2", +"FCLoopBasisPropagatorsToTopology[{2SPD[q]},FCE\[Rule]True]", +"{2*SPD[q, q]}"}, +{"fcstFCLoopBasisPropagatorsToTopology-ID3", +"FCLoopBasisPropagatorsToTopology[{FAD[q]},FCE\[Rule]True]", +"{SPD[q, q]}"}, +{"fcstFCLoopBasisPropagatorsToTopology-ID4", +"FCLoopBasisPropagatorsToTopology[{FAD[{q,m}]},FCE\[Rule]True]", +"{-m^2 + SPD[q, q]}"}, +{"fcstFCLoopBasisPropagatorsToTopology-ID5", +"FCLoopBasisPropagatorsToTopology[{FAD[{q,m}],SPD[q,p]},FCE\[Rule]\ +True]", "{-m^2 + SPD[q, q], SPD[p, q]}"}, +{"fcstFCLoopBasisPropagatorsToTopology-ID6", +"FCLoopBasisPropagatorsToTopology[{SFAD[{q,m}],SPD[q,p]},FCE\[Rule]\ +True]", "{-m + SPD[q, q], SPD[p, q]}"}, +{"fcstFCLoopBasisPropagatorsToTopology-ID7", +"FCLoopBasisPropagatorsToTopology[{CFAD[{q,m}],SPD[q,p]},FCE\[Rule]\ +True]", "{m + CSPD[q, q], SPD[p, q]}"} +}) diff --git a/Tests/LoopIntegrals/FCLoopCanonicalize.test b/Tests/LoopIntegrals/FCLoopCanonicalize.test index 0e5001c09..86c278aa6 100644 --- a/Tests/LoopIntegrals/FCLoopCanonicalize.test +++ b/Tests/LoopIntegrals/FCLoopCanonicalize.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCLoopCanonicalize *) @@ -98,5 +98,82 @@ Tests`LoopIntegrals`fcstFCLoopCanonicalize = { FeynAmpDenominator[PropagatorDenominator[Momentum[q, D], 0], PropagatorDenominator[Momentum[p, D] + Momentum[q, D], m]] Pair[ LorentzIndex[x_FCGV, D], Momentum[q, D]] Pair[ - LorentzIndex[y_FCGV, D], Momentum[q, D]]]}}]","True"} + LorentzIndex[y_FCGV, D], Momentum[q, D]]]}}]","True"}, +{"fcstFCLoopCanonicalize-ID12","MatchQ[FCLoopCanonicalize[FCL[CVD[q, mu]], q, + FCL], {{FCL[ + CartesianPair[CartesianIndex[mu, D - 1], + CartesianMomentum[q, D - 1]]]}, {{CartesianIndex[x_FCGV, + D - 1] -> CartesianIndex[mu, D - 1]}}, {FCL[ + CartesianPair[CartesianIndex[x_FCGV, D - 1], + CartesianMomentum[q, D - 1]]]}, {FCL[ + CartesianPair[CartesianIndex[x_FCGV, D - 1], + CartesianMomentum[q, D - 1]]]}}]","True"}, +{"fcstFCLoopCanonicalize-ID13","MatchQ[FCLoopCanonicalize[ + FCL[CVD[q, mu]] + FCL[CVD[q, nu]] + FCL[CVD[q, rho]], q, + FCL], {{FCL[ + CartesianPair[CartesianIndex[mu, D - 1], + CartesianMomentum[q, D - 1]]], + FCL[CartesianPair[CartesianIndex[nu, D - 1], + CartesianMomentum[q, D - 1]]], + FCL[CartesianPair[CartesianIndex[rho, D - 1], + CartesianMomentum[q, D - 1]]]}, {{CartesianIndex[x_FCGV, + D - 1] -> + CartesianIndex[mu, D - 1]}, {CartesianIndex[x_FCGV, D - 1] -> + CartesianIndex[nu, D - 1]}, {CartesianIndex[x_FCGV, D - 1] -> + CartesianIndex[rho, D - 1]}}, {FCL[ + CartesianPair[CartesianIndex[x_FCGV, D - 1], + CartesianMomentum[q, D - 1]]], + FCL[CartesianPair[CartesianIndex[x_FCGV, D - 1], + CartesianMomentum[q, D - 1]]], + FCL[CartesianPair[CartesianIndex[x_FCGV, D - 1], + CartesianMomentum[q, D - 1]]]}, {FCL[ + CartesianPair[CartesianIndex[x_FCGV, D - 1], + CartesianMomentum[q, D - 1]]]}}]","True"}, +{"fcstFCLoopCanonicalize-ID14","MatchQ[FCLoopCanonicalize[a + FCL[CartesianPair[CartesianMomentum[q], CartesianIndex[mu]]], + q, FCL], {{FCL[ + CartesianPair[CartesianIndex[mu], CartesianMomentum[q]]]}, + {{CartesianIndex[x_FCGV] -> CartesianIndex[mu]}}, {FCL[ + CartesianPair[CartesianIndex[x_FCGV], + CartesianMomentum[q]]]}, {FCL[ + CartesianPair[CartesianIndex[x_FCGV], CartesianMomentum[q]]]}}]","True"}, +{"fcstFCLoopCanonicalize-ID15","MatchQ[FCLoopCanonicalize[FCL[FVD[q, mu]] + FCL[CVD[q, i]], q, +FCL], {{FCL[ + CartesianPair[CartesianIndex[i, -1 + D], + CartesianMomentum[q, -1 + D]]], +FCL[Pair[LorentzIndex[mu, D], + Momentum[q, D]]]}, {{CartesianIndex[a_FCGV, -1 + D] -> + CartesianIndex[i, -1 + D]}, {LorentzIndex[a_FCGV, D] -> + LorentzIndex[mu, D]}}, {FCL[ + CartesianPair[CartesianIndex[a_FCGV, -1 + D], + CartesianMomentum[q, -1 + D]]], +FCL[Pair[LorentzIndex[a_FCGV, D], Momentum[q, D]]]}, {FCL[ + CartesianPair[CartesianIndex[a_FCGV, -1 + D], + CartesianMomentum[q, -1 + D]]], +FCL[Pair[LorentzIndex[a_FCGV, D], Momentum[q, D]]]}}]","True"}, +{"fcstFCLoopCanonicalize-ID16","MatchQ[FCLoopCanonicalize[ +a FCL[FVD[q, mu]] + b FCL[CVD[q, i]] + c FCL[FVD[q, rho]] + +d FCL[CVD[q, j]], q, +FCL], {{FCL[ + CartesianPair[CartesianIndex[i, -1 + D], + CartesianMomentum[q, -1 + D]]], +FCL[CartesianPair[CartesianIndex[j, -1 + D], + CartesianMomentum[q, -1 + D]]], +FCL[Pair[LorentzIndex[mu, D], Momentum[q, D]]], +FCL[Pair[LorentzIndex[rho, D], + Momentum[q, D]]]}, {{CartesianIndex[a_FCGV, -1 + D] -> + CartesianIndex[i, -1 + D]}, {CartesianIndex[a_FCGV, -1 + D] -> + CartesianIndex[j, -1 + D]}, {LorentzIndex[a_FCGV, D] -> + LorentzIndex[mu, D]}, {LorentzIndex[a_FCGV, D] -> + LorentzIndex[rho, D]}}, {FCL[ + CartesianPair[CartesianIndex[a_FCGV, -1 + D], + CartesianMomentum[q, -1 + D]]], +FCL[CartesianPair[CartesianIndex[a_FCGV, -1 + D], + CartesianMomentum[q, -1 + D]]], +FCL[Pair[LorentzIndex[a_FCGV, D], Momentum[q, D]]], +FCL[Pair[LorentzIndex[a_FCGV, D], Momentum[q, D]]]}, {FCL[ + CartesianPair[CartesianIndex[a_FCGV, -1 + D], + CartesianMomentum[q, -1 + D]]], +FCL[Pair[LorentzIndex[a_FCGV, D], Momentum[q, D]]]}}]","True"} }; + diff --git a/Tests/LoopIntegrals/FCLoopEikonalPropagatorFreeQ.test b/Tests/LoopIntegrals/FCLoopEikonalPropagatorFreeQ.test new file mode 100644 index 000000000..a30518993 --- /dev/null +++ b/Tests/LoopIntegrals/FCLoopEikonalPropagatorFreeQ.test @@ -0,0 +1,37 @@ + + +(* :Title: fcstFCLoopEikonalPropagatorFreeQ.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + fcstFCLoopEikonalPropagatorFreeQ *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCLoopEikonalPropagatorFreeQ = +({ +{"fcstFCLoopEikonalPropagatorFreeQ-ID1", +"FCLoopEikonalPropagatorFreeQ[FCI@SFAD[p,p-q]]", "True"}, +{"fcstFCLoopEikonalPropagatorFreeQ-ID2", +"FCLoopEikonalPropagatorFreeQ[FCI@SFAD[{{0,p.q}}]]", "False"}, +{"fcstFCLoopEikonalPropagatorFreeQ-ID3", +"FCLoopEikonalPropagatorFreeQ[FCI@CFAD[p,p-q]]", "True"}, +{"fcstFCLoopEikonalPropagatorFreeQ-ID4", +"FCLoopEikonalPropagatorFreeQ[FCI@CFAD[{{0,p.q}}]]", "False"}, +{"fcstFCLoopEikonalPropagatorFreeQ-ID5", +"FCLoopEikonalPropagatorFreeQ[FCI@CFAD[{{0,p.q}}],Momentum\[Rule]{\ +q}]", "False"}, +{"fcstFCLoopEikonalPropagatorFreeQ-ID6", +"FCLoopEikonalPropagatorFreeQ[FCI@CFAD[{{0,p.q}}],Momentum\[Rule]{\ +r}]", "True"}, +{"fcstFCLoopEikonalPropagatorFreeQ-ID7", +"FCLoopEikonalPropagatorFreeQ[FCI@SFAD[{{q, q.p}}]]", "True"}, +{"fcstFCLoopEikonalPropagatorFreeQ-ID8", +"FCLoopEikonalPropagatorFreeQ[FCI@SFAD[{{q, q.p}}], First -> False]", "False"} +}); diff --git a/Tests/LoopIntegrals/FCLoopExtract.test b/Tests/LoopIntegrals/FCLoopExtract.test index 071c839e8..b4d0b6d11 100644 --- a/Tests/LoopIntegrals/FCLoopExtract.test +++ b/Tests/LoopIntegrals/FCLoopExtract.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCLoopExtract *) @@ -56,5 +56,247 @@ m}]*FVD[q1, mu]]}}"}, {"fcstFCLoopExtract-ID10", "FCLoopExtract[a FCI[FAD[{q, 0, 2}]] + b FCI[FAD[{q, 0, 1}]], {q}, loop, FCLoopIBPReducableQ -> True] // FCE", -"{0, b FAD[q] + a loop[FAD[q, q]], {loop[FAD[q, q]]}}"} +"{0, b FAD[q] + a loop[FAD[q, q]], {loop[FAD[q, q]]}}"}, +{"fcstFCLoopExtract-ID11", +"FCLoopExtract[FAD[{q1,m0}],{q1},loopInt,FCLoopBasisSplit\[Rule]\ +True,FCE\[Rule]True]", +"{0, loopInt[FAD[{q1, m0}], {q1}], {loopInt[FAD[{q1, m0}], \ +{q1}]}}"}, +{"fcstFCLoopExtract-ID12", +"FCLoopExtract[FAD[{q1,m0},{p1+p2}],{q1},loopInt,FCLoopBasisSplit\ +\[Rule]True,FCE\[Rule]True]", +"{0, FAD[p1 + p2]*loopInt[FAD[{q1, m0}], {q1}], {loopInt[FAD[{q1, \ +m0}], {q1}]}}"}, +{"fcstFCLoopExtract-ID13", +"FCLoopExtract[FAD[{q1,m0},{p1+p2}],{q2},loopInt,FCLoopBasisSplit\ +\[Rule]True,FCE\[Rule]True]", "{FAD[{q1, m0}, p1 + p2], 0, {}}"}, +{"fcstFCLoopExtract-ID14", +"FCLoopExtract[FAD[{q1,0},{q2,0},{q1-p,0},{q1-q2}],{q1,q2},loopInt,\ +FCLoopBasisSplit\[Rule]True,FCE\[Rule]True]", +"{0, loopInt[FAD[q2, q1, q1 - q2, -p + q1], {q1, q2}], \ +{loopInt[FAD[q2, q1, q1 - q2, -p + q1], {q1, q2}]}}"}, +{"fcstFCLoopExtract-ID15", +"FCLoopExtract[FAD[{q3,0},{q1,0},{q2,0},{q1-p,0},{q1-q2}],{q1,q2,\ +q3},loopInt,FCLoopBasisSplit\[Rule]True,FCE\[Rule]True]", +"{0, loopInt[FAD[q3], {q3}]*loopInt[FAD[q2, q1, q1 - q2, -p + q1], \ +{q1, q2}], {loopInt[FAD[q3], {q3}], loopInt[FAD[q2, q1, q1 - q2, -p + \ +q1], {q1, q2}]}}"}, +{"fcstFCLoopExtract-ID16", +"FCLoopExtract[GFAD[{SPD[q1,p]SPD[q2,p],n}],{q1,q2},loopInt]\ +//FCE", "{0, loopInt[ +GFAD[{{SPD[p, q1] SPD[p, q2], 1}, n}]], {loopInt[ +GFAD[{{SPD[p, q1] SPD[p, q2], 1}, n}]]}}"}, +{"fcstFCLoopExtract-ID17", +"FCLoopExtract[GFAD[{SPD[q1,p]SPD[q2,p],2}],{q1,q2},loopInt]\ +//FCE", "{0, loopInt[ +GFAD[{{SPD[p, q1] SPD[p, q2], 1}, 2}]], {loopInt[ +GFAD[{{SPD[p, q1] SPD[p, q2], 1}, 2}]]}}"}, +{"fcstFCLoopExtract-ID18", +"FCLoopExtract[FAD[{q2,m}]GFAD[{SPD[q1,p]SPD[q2,p],2}],{q1,q2},\ +loopInt]//FCE", +"{0, loopInt[ +FAD[{q2, m}] GFAD[{{SPD[p, q1] SPD[p, q2], 1}, 2}]], {loopInt[ +FAD[{q2, m}] GFAD[{{SPD[p, q1] SPD[p, q2], 1}, 2}]]}}"}, +{"fcstFCLoopExtract-ID19", +"FCLoopExtract[FAD[{q2, m}] GFAD[{SPD[q1, p] SPD[q2, p], 2}], {q1, q2}, loopInt, +GFAD -> False] // FCE", +"{0, FAD[{q2, m}] GFAD[{{SPD[p, q1] SPD[p, q2], 1}, 2}], {}}"}, +{"fcstFCLoopExtract-ID19", +"FCLoopExtract[CFAD[{q3,0},{q1,0},{q2,0},{q1-p,0},{q1-q2}],{q1,q2,\ +q3},loopInt,FCLoopBasisSplit\[Rule]True,FCE\[Rule]True]", +"{0, loopInt[CFAD[{{q3, 0}, {0, -1}, 1}], {q3}]* +loopInt[CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, + {{-p + q1, 0}, {0, -1}, 1}, {{q1 - q2, 0}, {0, -1}, 1}], {q1, q2}], +{loopInt[CFAD[{{q3, 0}, {0, -1}, 1}], {q3}], +loopInt[CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, + {{-p + q1, 0}, {0, -1}, 1}, {{q1 - q2, 0}, {0, -1}, 1}], {q1, q2}]}}"}, +{"fcstFCLoopExtract-ID20", +"FCLoopExtract[CFAD[{q1,0},{q2,0},{q1-p,0},{q1-q2}],{q1,q2},\ +loopInt,FCLoopBasisSplit\[Rule]True,FCE\[Rule]True]", +"{0, loopInt[CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, +{{-p + q1, 0}, {0, -1}, 1}, {{q1 - q2, 0}, {0, -1}, 1}], {q1, q2}], +{loopInt[CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, + {{-p + q1, 0}, {0, -1}, 1}, {{q1 - q2, 0}, {0, -1}, 1}], {q1, q2}]}}"}, +{"fcstFCLoopExtract-ID21", +"FCLoopExtract[CFAD[{q1,m0},{p1+p2}],{q2},loopInt,FCLoopBasisSplit\ +\[Rule]True,FCE\[Rule]True]", +"{CFAD[{{q1, 0}, {m0, -1}, 1}, {{p1 + p2, 0}, {0, -1}, 1}], 0, \ +{}}"}, +{"fcstFCLoopExtract-ID22", +"FCLoopExtract[CFAD[{q1,m0},{p1+p2}],{q1},loopInt,FCLoopBasisSplit\ +\[Rule]True,FCE\[Rule]True]", +"{0, CFAD[{{p1 + p2, 0}, {0, -1}, 1}]*loopInt[CFAD[{{q1, 0}, {m0, \ +-1}, 1}], {q1}], {loopInt[CFAD[{{q1, 0}, {m0, -1}, 1}], {q1}]}}"}, +{"fcstFCLoopExtract-ID23", +"FCLoopExtract[CFAD[{q1,m0}],{q1},loopInt,FCLoopBasisSplit\[Rule]\ +True,FCE\[Rule]True]", +"{0, loopInt[CFAD[{{q1, 0}, {m0, -1}, 1}], {q1}], \ +{loopInt[CFAD[{{q1, 0}, {m0, -1}, 1}], {q1}]}}"}, +{"fcstFCLoopExtract-ID24", +"FCLoopExtract[a FCI[CFAD[{q,0,2}]]+b \ +FCI[CFAD[{q,0,1}]],{q},loop,FCLoopIBPReducableQ\[Rule]True,FCE\[Rule]\ +True]", "{0, b*CFAD[{{q, 0}, {0, -1}, 1}] + a*loop[CFAD[{{q, 0}, {0, -1}, 2}]], +{loop[CFAD[{{q, 0}, {0, -1}, 2}]]}}"}, +{"fcstFCLoopExtract-ID25", +"FCLoopExtract[CVD[q1,mu]CFAD[{q1,m}]+A0[m],{q1,q2},loopInt,\ +DropScaleless\[Rule]True,FCLoopSplit\[Rule]{3,4},FCE\[Rule]True]", +"{A0[m], loopInt[CFAD[{{q1, 0}, {m, -1}, 1}]*CVD[q1, mu]], \ +{loopInt[CFAD[{{q1, 0}, {m, -1}, 1}]*CVD[q1, mu]]}}"}, +{"fcstFCLoopExtract-ID26", +"FCLoopExtract[CFAD[{q1,m}]+CSPD[q1,q2],{q1,q2},loopInt,\ +DropScaleless\[Rule]True]", +"{0, loopInt[FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]], \ +{loopInt[FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]]}}"}, +{"fcstFCLoopExtract-ID27", +"FCLoopExtract[CVD[q1,mu]CVD[q2,nu]CFAD[{q1,m}]+CGAD[mu].(CGSD[q1]+\ +M).CGAD[nu]CFAD[q1,{q1+p,m}],{q1,q2},loopInt]", +"{0, loopInt[CartesianPair[CartesianIndex[mu, -1 + D], \ +CartesianMomentum[q1, -1 + D]]*CartesianPair[CartesianIndex[nu, -1 + \ +D], CartesianMomentum[q2, -1 + \ +D]]*FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]] + \ +M*DiracGamma[CartesianIndex[mu, -1 + D], D] . \ +DiracGamma[CartesianIndex[nu, -1 + D], \ +D]*loopInt[FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[p, -1 + D] + \ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]] + \ +loopInt[DiracGamma[CartesianIndex[mu, -1 + D], D] . \ +DiracGamma[CartesianMomentum[q1, -1 + D], D] . \ +DiracGamma[CartesianIndex[nu, -1 + D], \ +D]*FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[p, -1 + D] + \ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]], \ +{loopInt[CartesianPair[CartesianIndex[mu, -1 + D], \ +CartesianMomentum[q1, -1 + D]]*CartesianPair[CartesianIndex[nu, -1 + \ +D], CartesianMomentum[q2, -1 + \ +D]]*FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]], \ +loopInt[FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[p, -1 + D] + \ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]], \ +loopInt[DiracGamma[CartesianIndex[mu, -1 + D], D] . \ +DiracGamma[CartesianMomentum[q1, -1 + D], D] . \ +DiracGamma[CartesianIndex[nu, -1 + D], \ +D]*FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[p, -1 + D] + \ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]]}}"}, +{"fcstFCLoopExtract-ID28", +"FCLoopExtract[CVD[q1,mu]CFAD[{q1,m}]+CVD[p,mu]CFAD[q1,{q1+p,m}],{\ +q1,q2},loopInt]", +"{0, loopInt[CartesianPair[CartesianIndex[mu, -1 + D], \ +CartesianMomentum[q1, -1 + \ +D]]*FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]] + \ +CartesianPair[CartesianIndex[mu, -1 + D], CartesianMomentum[p, -1 + \ +D]]*loopInt[FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[p, -1 + D] + \ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]], \ +{loopInt[CartesianPair[CartesianIndex[mu, -1 + D], \ +CartesianMomentum[q1, -1 + \ +D]]*FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]], \ +loopInt[FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[p, -1 + D] + \ +CartesianMomentum[q1, -1 + D], 0, m, {1, -1}]]]}}"}, +{"fcstFCLoopExtract-ID29", +"FCLoopExtract[SFAD[{q3,0},{q1,0},{q2,0},{q1-p,0},{q1-q2}],{q1,q2,\ +q3},loopInt,FCLoopBasisSplit\[Rule]True,FCE\[Rule]True]", +"{0, loopInt[SFAD[{{q3, 0}, {0, 1}, 1}], {q3}]* +loopInt[SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{-p + q1, 0}, {0, 1}, 1}, {{q1 - q2, 0}, {0, 1}, 1}], {q1, q2}], +{loopInt[SFAD[{{q3, 0}, {0, 1}, 1}], {q3}], +loopInt[SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{-p + q1, 0}, {0, 1}, 1}, {{q1 - q2, 0}, {0, 1}, 1}], {q1, q2}]}}"}, +{"fcstFCLoopExtract-ID30", +"FCLoopExtract[SFAD[{q1,0},{q2,0},{q1-p,0},{q1-q2}],{q1,q2},\ +loopInt,FCLoopBasisSplit\[Rule]True,FCE\[Rule]True]", +"{0, loopInt[SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, +{{-p + q1, 0}, {0, 1}, 1}, {{q1 - q2, 0}, {0, 1}, 1}], {q1, q2}], +{loopInt[SFAD[{{q1, 0}, {0, 1}, 1}, {{q2, 0}, {0, 1}, 1}, + {{-p + q1, 0}, {0, 1}, 1}, {{q1 - q2, 0}, {0, 1}, 1}], {q1, q2}]}}"}, +{"fcstFCLoopExtract-ID31", +"FCLoopExtract[SFAD[{q1,m0},{p1+p2}],{q1},loopInt,FCLoopBasisSplit\ +\[Rule]True,FCE\[Rule]True]", +"{0, loopInt[SFAD[{{q1, 0}, {m0, 1}, 1}], {q1}]*SFAD[{{p1 + p2, \ +0}, {0, 1}, 1}], {loopInt[SFAD[{{q1, 0}, {m0, 1}, 1}], {q1}]}}"}, +{"fcstFCLoopExtract-ID32", +"FCLoopExtract[SFAD[{q1,m0}],{q1},loopInt,FCLoopBasisSplit\[Rule]\ +True,FCE\[Rule]True]", +"{0, loopInt[SFAD[{{q1, 0}, {m0, 1}, 1}], {q1}], \ +{loopInt[SFAD[{{q1, 0}, {m0, 1}, 1}], {q1}]}}"}, +{"fcstFCLoopExtract-ID33", +"FCLoopExtract[a FCI[SFAD[{q,0,2}]]+b \ +FCI[SFAD[{q,0,1}]],{q},loop,FCLoopIBPReducableQ\[Rule]True,FCE\[Rule]\ +True]", "{0, a*loop[SFAD[{{q, 0}, {0, 1}, 2}]] + b*SFAD[{{q, 0}, {0, \ +1}, 1}], {loop[SFAD[{{q, 0}, {0, 1}, 2}]]}}"}, +{"fcstFCLoopExtract-ID34", +"FCLoopExtract[FVD[q1,mu]SFAD[{q1,m}]+A0[m],{q1,q2},loopInt,\ +DropScaleless\[Rule]True,FCLoopSplit\[Rule]{3,4},FCE\[Rule]True]", +"{A0[m], loopInt[FVD[q1, mu]*SFAD[{{q1, 0}, {m, 1}, 1}]], \ +{loopInt[FVD[q1, mu]*SFAD[{{q1, 0}, {m, 1}, 1}]]}}"}, +{"fcstFCLoopExtract-ID35", +"FCLoopExtract[SFAD[{q1,m}]+SPD[q1,q2],{q1,q2},loopInt,\ +DropScaleless\[Rule]True]", +"{0, loopInt[FeynAmpDenominator[StandardPropagatorDenominator[\ +Momentum[q1, D], 0, -m, {1, 1}]]], \ +{loopInt[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1,\ +D], 0, -m, {1, 1}]]]}}"}, +{"fcstFCLoopExtract-ID36", +"FCLoopExtract[FVD[q1,mu]FVD[q2,nu]SFAD[{q1,m}]+GAD[mu].(GSD[q1]+M)\ +.GAD[nu]SFAD[q1,{q1+p,m}],{q1,q2},loopInt]", +"{0, M*DiracGamma[LorentzIndex[mu, D], D] . \ +DiracGamma[LorentzIndex[nu, D], \ +D]*loopInt[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[\ +q1, D], 0, 0, {1, 1}], StandardPropagatorDenominator[Momentum[p, D] + \ +Momentum[q1, D], 0, -m, {1, 1}]]] + \ +loopInt[DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[Momentum[q1, \ +D], D] . DiracGamma[LorentzIndex[nu, D], \ +D]*FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1, D], \ +0, 0, {1, 1}], StandardPropagatorDenominator[Momentum[p, D] + \ +Momentum[q1, D], 0, -m, {1, 1}]]] + \ +loopInt[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1, \ +D], 0, -m, {1, 1}]]*Pair[LorentzIndex[mu, D], Momentum[q1, \ +D]]*Pair[LorentzIndex[nu, D], Momentum[q2, D]]], \ +{loopInt[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1,\ +D], 0, 0, {1, 1}], StandardPropagatorDenominator[Momentum[p, D] + \ +Momentum[q1, D], 0, -m, {1, 1}]]], \ +loopInt[DiracGamma[LorentzIndex[mu, D], D] . DiracGamma[Momentum[q1, \ +D], D] . DiracGamma[LorentzIndex[nu, D], \ +D]*FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1, D], \ +0, 0, {1, 1}], StandardPropagatorDenominator[Momentum[p, D] + \ +Momentum[q1, D], 0, -m, {1, 1}]]], \ +loopInt[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1, \ +D], 0, -m, {1, 1}]]*Pair[LorentzIndex[mu, D], Momentum[q1, \ +D]]*Pair[LorentzIndex[nu, D], Momentum[q2, D]]]}}"}, +{"fcstFCLoopExtract-ID37", +"FCLoopExtract[FVD[q1,mu]SFAD[{q1,m}]+FVD[p,mu]SFAD[q1,{q1+p,m}],{\ +q1,q2},loopInt]", +"{0, loopInt[FeynAmpDenominator[StandardPropagatorDenominator[\ +Momentum[q1, D], 0, -m, {1, 1}]]*Pair[LorentzIndex[mu, D], \ +Momentum[q1, D]]] + \ +loopInt[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1, \ +D], 0, 0, {1, 1}], StandardPropagatorDenominator[Momentum[p, D] + \ +Momentum[q1, D], 0, -m, {1, 1}]]]*Pair[LorentzIndex[mu, D], \ +Momentum[p, D]], \ +{loopInt[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1,\ +D], 0, 0, {1, 1}], StandardPropagatorDenominator[Momentum[p, D] + \ +Momentum[q1, D], 0, -m, {1, 1}]]], \ +loopInt[FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q1, \ +D], 0, -m, {1, 1}]]*Pair[LorentzIndex[mu, D], Momentum[q1, D]]]}}"}, +{"fcstFCLoopExtract-ID38", +"FCLoopExtract[ +FVD[q1, mu] FVD[q2, nu] FAD[{q1, m}] + +GAD[mu].(GSD[q1] + M).GAD[nu] FAD[q1, {q1 + p, m}], {q1, +q2}, loopInt, Numerator -> False, FCE -> True]", +"{0, FVD[q1, mu]*FVD[q2, nu]*loopInt[FAD[{q1, m}]] + (M*GAD[mu] . GAD[nu] + +GAD[mu] . GSD[q1] . GAD[nu])*loopInt[FAD[q1, {p + q1, m}]], + {loopInt[FAD[{q1, m}]], loopInt[FAD[q1, {p + q1, m}]]}}"} }); diff --git a/Tests/LoopIntegrals/FCLoopIBPReducableQ.test b/Tests/LoopIntegrals/FCLoopIBPReducableQ.test index 2e684f0e6..52b5bf3f7 100644 --- a/Tests/LoopIntegrals/FCLoopIBPReducableQ.test +++ b/Tests/LoopIntegrals/FCLoopIBPReducableQ.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for fcstFCLoopIBPReducableQ *) @@ -29,5 +29,41 @@ Tests`LoopIntegrals`fcstFCLoopIBPReducableQ = "FCLoopIBPReducableQ[FCI[SPD[q,q]^2FAD[{q,0,1},{q+p,m,2}]]]", "True"}, {"fcstFCLoopIBPReducableQ-ID7", -"FCLoopIBPReducableQ[FCI[SPD[q,r]FAD[{q,0,1},{q+p,m,2}]]]", "True"} +"FCLoopIBPReducableQ[FCI[SPD[q,r]FAD[{q,0,1},{q+p,m,2}]]]", "True"}, +{"fcstFCLoopIBPReducableQ-ID8", +"FCLoopIBPReducableQ[FCI[CFAD[{q,0,1}]]]", "False"}, +{"fcstFCLoopIBPReducableQ-ID9", +"FCLoopIBPReducableQ[FCI[CFAD[{q,0,2}]]]", "True"}, +{"fcstFCLoopIBPReducableQ-ID10", +"FCLoopIBPReducableQ[FCI[CSPD[q,q]CFAD[{q,0,1}]]]", "False"}, +{"fcstFCLoopIBPReducableQ-ID11", +"FCLoopIBPReducableQ[FCI[CSPD[q,q]^2CFAD[{q,0,1}]]]", "True"}, +{"fcstFCLoopIBPReducableQ-ID12", +"FCLoopIBPReducableQ[FCI[CSPD[q,q]^2CFAD[{q,0,1},{q+p,m,2}]]]", +"True"}, +{"fcstFCLoopIBPReducableQ-ID13", +"FCLoopIBPReducableQ[FCI[CSPD[q,r]CFAD[{q,0,1},{q+p,m,2}]]]", +"True"}, +{"fcstFCLoopIBPReducableQ-ID14", +"FCLoopIBPReducableQ[FCI[GFAD[{q,1}]]]", "False"}, +{"fcstFCLoopIBPReducableQ-ID15", +"FCLoopIBPReducableQ[FCI[GFAD[{q,2}]]]", "True"}, +{"FCLoopIBPReducableQ-ID16", +"FCLoopIBPReducableQ[FCI[SFAD[{q,0,1}]]]", "False"}, +{"FCLoopIBPReducableQ-ID17", +"FCLoopIBPReducableQ[FCI[SFAD[{q,0,2}]]]", "True"}, +{"FCLoopIBPReducableQ-ID18", +"FCLoopIBPReducableQ[FCI[SPD[q,q]SFAD[{q,0,1}]]]", "False"}, +{"FCLoopIBPReducableQ-ID19", +"FCLoopIBPReducableQ[FCI[SPD[q,q]^2SFAD[{q,0,1}]]]", "True"}, +{"FCLoopIBPReducableQ-ID20", +"FCLoopIBPReducableQ[FCI[SPD[q,q]^2SFAD[{q,0,1},{q+p,m,2}]]]", +"True"}, +{"FCLoopIBPReducableQ-ID21", +"FCLoopIBPReducableQ[FCI[SPD[q,r]SFAD[{q,0,1},{q+p,m,2}]]]", +"True"}, +{"FCLoopIBPReducableQ-ID22", +"FCLoopIBPReducableQ[FCI[SFAD[{q,1}]]]", "False"}, +{"FCLoopIBPReducableQ-ID23", +"FCLoopIBPReducableQ[FCI[SFAD[{q,2}]]]", "False"} }); diff --git a/Tests/LoopIntegrals/FCLoopIsolate.test b/Tests/LoopIntegrals/FCLoopIsolate.test index 855c6aa11..6606e4dca 100644 --- a/Tests/LoopIntegrals/FCLoopIsolate.test +++ b/Tests/LoopIntegrals/FCLoopIsolate.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCLoopIsolate *) @@ -68,5 +68,95 @@ GA[j] . GSD[i] . GA[5]*SUNT[a]*FCGV[\"LoopInt\"][FAD[{q, m}]*FVD[q, i]]"}, Head -> loop, FCLoopIBPReducableQ -> True] // FCE","b FAD[q] + a loop[FAD[q, q]]"}, {"fcstFCLoopIsolate-ID20","FCLoopIsolate[Foobar[x], {}, PaVeIntegralHeads -> Join[OptionValue[FCLoopIsolate, PaVeIntegralHeads], {Foobar}],Head -> loop]","loop[Foobar[x]]"}, -{"fcstFCLoopIsolate-ID21","FCLoopIsolate[0, {}, PaVe -> False, ExpandScalarProduct -> True]","0"} +{"fcstFCLoopIsolate-ID21","FCLoopIsolate[CSP[q, p] x + z (q + y) + CGS[q], {q}, Head -> loop]","y z + z loop[q] + x loop[CartesianPair[CartesianMomentum[p], CartesianMomentum[q]]] + +loop[DiracGamma[CartesianMomentum[q]]]"}, +{"fcstFCLoopIsolate-ID22","FCLoopIsolate[0, {}, PaVe -> False, ExpandScalarProduct -> True]","0"}, +{"fcstFCLoopIsolate-ID23","FCLoopIsolate[xx FAD[l, l + p2, l + p2 - p3 - p4] FVD[l, +nu] (FVD[p1, Lor4] + FVD[-l - p2 + p3 + p4, Lor4]) MTD[Lor3,mu] , {l}, Full -> False, ExpandScalarProduct -> True, +Head -> loopInt] // FCE", +"xx (FVD[p1, Lor4] - FVD[p2 - p3 - p4, Lor4]) loopInt[ +FAD[l, l + p2, l + p2 - p3 - p4] FVD[l, nu]] MTD[Lor3, mu] - +xx loopInt[FAD[l, l + p2, l + p2 - p3 - p4] FVD[l, Lor4] FVD[l, nu]] MTD[Lor3, mu]"}, +{"fcstFCLoopIsolate-ID24","FCLoopIsolate[xx FAD[l, l + p2, l + p2 - p3 - p4] FVD[l, +nu] (FVD[p1, Lor4] + FVD[-l - p2 + p3 + p4, Lor4]) MTD[Lor3,mu] , {l}, ExpandScalarProduct -> True, Head -> loopInt] // +FCE", +"xx (FVD[p1, Lor4] - FVD[p2, Lor4] + FVD[p3, Lor4] + FVD[p4, Lor4]) loopInt[FAD[l, l + p2, l + +p2 - p3 - p4] FVD[l, nu]] MTD[Lor3, mu] -xx loopInt[FAD[l, l + p2, l + p2 - p3 - +p4] FVD[l, Lor4] FVD[l, nu]] MTD[Lor3, mu]"}, +{"fcstFCLoopIsolate-ID25", +"FCLoopIsolate[GFAD[{SPD[q1,p]SPD[q2,p],n}],{q1,q2},\ +Head->loopInt]//FCE", +"loopInt[GFAD[{{SPD[p, q1]*SPD[p, q2], 1}, n}]]"}, +{"fcstFCLoopIsolate-ID26", +"FCLoopIsolate[GFAD[{SPD[q1,p]SPD[q2,p],2}],{q1,q2},\ +Head->loopInt]//FCE", +"loopInt[GFAD[{{SPD[p, q1]*SPD[p, q2], 1}, 2}]]"}, +{"fcstFCLoopIsolate-ID27", +"FCLoopIsolate[FAD[{q2,m}]GFAD[{SPD[q1,p]SPD[q2,p],2}],{q1,q2},\ +Head->loopInt]//FCE", +"loopInt[FAD[{q2, m}]*GFAD[{{SPD[p, q1]*SPD[p, q2], 1}, 2}]]"}, +{"fcstFCLoopIsolate-ID28", +"FCLoopIsolate[ +FAD[{q2, m}] GFAD[{SPD[q1, p] SPD[q2, p], 2}], {q1, q2}, +Head -> loopInt, GFAD -> False] // FCE", +"FAD[{q2, m}]*GFAD[{{SPD[p, q1]*SPD[p, q2], 1}, 2}]"}, +{"fcstFCLoopIsolate-ID29", +"FCLoopIsolate[SUNT[i].(x+y).SUNT[j]+(CGS[x]+CGA[j].(CGSD[i] \ +CVD[q,i]+CGSD[p]).GA[5]).SUNT[a]CFAD[{q,m}],{q},FCE\[Rule]True]", +"SUNT[i] . (x + y) . SUNT[j] + (CGS[x] + CGA[j] . CGSD[p] . \ +GA[5])*SUNT[a]*FCGV[\"LoopInt\"][CFAD[{{q, 0}, {m, -1}, 1}]] + CGA[j] \ +. CGSD[i] . GA[5]*SUNT[a]*FCGV[\"LoopInt\"][CFAD[{{q, 0}, {m, -1}, \ +1}]*CVD[q, i]]"}, +{"fcstFCLoopIsolate-ID30", +"FCLoopIsolate[CGSD[p+q] CFAD[{q,m}],{q},FCE\[Rule]True]", +"CGSD[p]*FCGV[\"LoopInt\"][CFAD[{{q, 0}, {m, -1}, 1}]] + \ +FCGV[\"LoopInt\"][CFAD[{{q, 0}, {m, -1}, 1}]*CGSD[q]]"}, +{"fcstFCLoopIsolate-ID31", +"FCLoopIsolate[a CFAD[{q1,m},{q3,m}]+b CFAD[{q1,m1},{q1-q2,m2}]+c \ +CFAD[{q1,m}]+d \ +CFAD[{q2,m}],{q1,q2},MultiLoop\[Rule]True,Head\[Rule]TT,FCE\[Rule]\ +True]", "c*CFAD[{{q1, 0}, {m, -1}, 1}] + d*CFAD[{{q2, 0}, {m, -1}, \ +1}] + a*CFAD[{{q1, 0}, {m, -1}, 1}]*CFAD[{{q3, 0}, {m, -1}, 1}] + \ +b*TT[CFAD[{{q1, 0}, {m1, -1}, 1}, {{q1 - q2, 0}, {m2, -1}, 1}]]"}, +{"fcstFCLoopIsolate-ID32", +"FCLoopIsolate[FCLoopIsolate[a CFAD[{q1,m},{q3,m}]+b \ +CFAD[{q1,m1},{q1-q2,m2}]+c CFAD[{q1,m}]+d \ +CFAD[{q2,m}],{q1,q2},MultiLoop\[Rule]True,Head\[Rule]TT],{q1,q3},\ +MultiLoop\[Rule]True,Head\[Rule]TT2,FCE\[Rule]True]", +"c*CFAD[{{q1, 0}, {m, -1}, 1}] + d*CFAD[{{q2, 0}, {m, -1}, 1}] + \ +b*TT[CFAD[{{q1, 0}, {m1, -1}, 1}, {{q1 - q2, 0}, {m2, -1}, 1}]] + \ +a*TT2[CFAD[{{q1, 0}, {m, -1}, 1}]*CFAD[{{q3, 0}, {m, -1}, 1}]]"}, +{"fcstFCLoopIsolate-ID33", +"FCLoopIsolate[CSPD[q+k,p+l] CFAD[{q,m}],{q},FCE\[Rule]True]", +"FCGV[\"LoopInt\"][CFAD[{{q, 0}, {m, -1}, 1}]*CSPD[l + p, k + q]]"}, +{"fcstFCLoopIsolate-ID34", +"FCLoopIsolate[CSPD[q+k,p+l] CFAD[{q,m}],{q},ExpandScalarProduct\ +\[Rule]True,FCE\[Rule]True]", +"(CSPD[k, l] + CSPD[k, p])*FCGV[\"LoopInt\"][CFAD[{{q, 0}, {m, \ +-1}, 1}]] + FCGV[\"LoopInt\"][CFAD[{{q, 0}, {m, -1}, 1}]*CSPD[l, q]] \ ++ FCGV[\"LoopInt\"][CFAD[{{q, 0}, {m, -1}, 1}]*CSPD[p, q]]"}, +{"fcstFCLoopIsolate-ID35", +"FCLoopIsolate[a FCI[CFAD[{q,0,2}]]+b FCI[CFAD[{q,0,1}]],{q},Head\ +\[Rule]loop,FCLoopIBPReducableQ\[Rule]True,FCE\[Rule]True]", +"b*CFAD[{{q, 0}, {0, -1}, 1}] + a*loop[CFAD[{{q, 0}, {0, -1}, \ +2}]]"}, +{"fcstFCLoopIsolate-ID36", +"FCLoopIsolate[xx CFAD[l,l+p2,l+p2-p3-p4] CVD[l,nu] \ +(CVD[p1,Lor4]+CVD[-l-p2+p3+p4,Lor4]) \ +KDD[Lor3,mu],{l},ExpandScalarProduct\[Rule]True,Head\[Rule]loopInt,\ +FCE\[Rule]True]", +"xx*(CVD[p1, Lor4] - CVD[p2, Lor4] + CVD[p3, Lor4] + CVD[p4, \ +Lor4])*KDD[Lor3, mu]*loopInt[CFAD[{{l, 0}, {0, -1}, 1}, {{l + p2, 0}, \ +{0, -1}, 1}, {{l + p2 - p3 - p4, 0}, {0, -1}, 1}]*CVD[l, nu]] - \ +xx*KDD[Lor3, mu]*loopInt[CFAD[{{l, 0}, {0, -1}, 1}, {{l + p2, 0}, {0, \ +-1}, 1}, {{l + p2 - p3 - p4, 0}, {0, -1}, 1}]*CVD[l, Lor4]*CVD[l, \ +nu]]"}, +{"fcstFCLoopIsolate-ID37", +"FCLoopIsolate[SPD[q + k, p + l] FAD[{q, m}], {q}, Numerator -> False, +Head -> loop, FCE -> True]", +"loop[FAD[{q, m}]] SPD[l + p, k + q]"}, +{"fcstFCLoopIsolate-ID38", +"FCLoopIsolate[FAD[q1] GFAD[{SPD[q1, p] SPD[q2, p], 2}], {q1, q2}, +Head -> loopInt, FAD -> False, FCE -> True]", +"FAD[q1] GFAD[{{SPD[p, q1] SPD[p, q2], 1}, 2}]"} }; diff --git a/Tests/LoopIntegrals/FCLoopMixedIntegralQ.test b/Tests/LoopIntegrals/FCLoopMixedIntegralQ.test new file mode 100644 index 000000000..630f1f5e8 --- /dev/null +++ b/Tests/LoopIntegrals/FCLoopMixedIntegralQ.test @@ -0,0 +1,33 @@ + + +(* :Title: fcstFCLoopMixedIntegralQ.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + fcstFCLoopMixedIntegralQ *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCLoopMixedIntegralQ = +({ +{"fcstFCLoopMixedIntegralQ-ID1", +"FCLoopMixedIntegralQ[FCI[FVD[p, mu] CFAD[q, q - p]]]", "True"}, +{"fcstFCLoopMixedIntegralQ-ID2", +"FCLoopMixedIntegralQ[FCI[FVD[p, mu] FAD[q, q - p]]]", "False"}, +{"fcstFCLoopMixedIntegralQ-ID3", +"FCLoopMixedIntegralQ[FCI[FVD[p, mu] SFAD[q, q - p]]]", "False"}, +{"fcstFCLoopMixedIntegralQ-ID4", +"FCLoopMixedIntegralQ[FCI[CVD[p, mu] SFAD[q, q - p]]]", "True"}, +{"fcstFCLoopMixedIntegralQ-ID5", +"FCLoopMixedIntegralQ[ +FeynAmpDenominatorCombine[GFAD[TC[q] + EN] SFAD[q]]]", "True"}, +{"fcstFCLoopMixedIntegralQ-ID6", +"FCLoopMixedIntegralQ[ +FeynAmpDenominatorCombine[GFAD[TC[q] + EN] CFAD[q]]]", "True"} +}); diff --git a/Tests/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.test b/Tests/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.test new file mode 100644 index 000000000..f3ac49a23 --- /dev/null +++ b/Tests/LoopIntegrals/FCLoopMixedToCartesianAndTemporal.test @@ -0,0 +1,99 @@ + + +(* :Title: fcstFCLoopMixedToCartesianAndTemporal.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + FCLoopMixedToCartesianAndTemporal *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCLoopMixedToCartesianAndTemporal = +({ +{"fcstFCLoopMixedToCartesianAndTemporal-ID1", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[q],{q},FCE->True]", +"-CFAD[{{q, 0}, {-TC[q]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID2", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[q+p],{q},FCE->True]", +"-CFAD[{{p + q, 0}, {-TC[p + q]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID3", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[q1+q2+p],{q1,q2},\ +FCE->True]", "-CFAD[{{p + q1 + q2, 0}, {-TC[p + q1 + q2]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID4", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{q,m^2}],{q},FCE->True]\ +", "-CFAD[{{q, 0}, {m^2 - TC[q]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID5", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{q+p,m^2}],{q},\ +FCE->True]", "-CFAD[{{p + q, 0}, {m^2 - TC[p + q]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID6", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{q1+q2+p,m^2}],{q1,q2},\ +FCE->True]", +"-CFAD[{{p + q1 + q2, 0}, {m^2 - TC[p + q1 + q2]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID7", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{q,q.p},m^2}],{q},\ +FCE->True]", +"-CFAD[{{q, p . q}, {m^2 - TC[p]*TC[q] - TC[q]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID8", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{q,q.p},m^2,2}],{q},\ +FCE->True]", +"CFAD[{{q, p . q}, {m^2 - TC[p]*TC[q] - TC[q]^2, -1}, 2}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID9", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{q,q.p},m^2,3}],{q},\ +FCE->True]", +"-CFAD[{{q, p . q}, {m^2 - TC[p]*TC[q] - TC[q]^2, -1}, 3}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID10", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{q,q.p},0}],{q},\ +FCE->True]", "-CFAD[{{q, p . q}, {-(TC[p]*TC[q]) - TC[q]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID11", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{q,q.p},0,2}],{q},\ +FCE->True]", +"CFAD[{{q, p . q}, {-(TC[p]*TC[q]) - TC[q]^2, -1}, 2}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID12", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{q,q.p},0,3}],{q},\ +FCE->True]", "-CFAD[{{q, p . q}, {-(TC[p]*TC[q]) - TC[q]^2, -1}, 3}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID13", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{q,0}],{q},FCE->True]", + "-CFAD[{{q, 0}, {-TC[q]^2, -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID14", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{q,0,2}],{q},FCE->True]\ +", "CFAD[{{q, 0}, {-TC[q]^2, -1}, 2}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID15", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{q,0,3}],{q},FCE->True]\ +", "-CFAD[{{q, 0}, {-TC[q]^2, -1}, 3}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID16", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{0,q.p},0}],{q},\ +FCE->True]", "-CFAD[{{0, p . q}, {-(TC[p]*TC[q]), -1}, 1}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID17", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{0,q.p},0,2}],{q},\ +FCE->True]", "CFAD[{{0, p . q}, {-(TC[p]*TC[q]), -1}, 2}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID18", +"FCLoopMixedToCartesianAndTemporal[FCI@SFAD[{{0,q.p},0,3}],{q},\ +FCE->True]", "-CFAD[{{0, p . q}, {-(TC[p]*TC[q]), -1}, 3}]"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID19", +"FCLoopMixedToCartesianAndTemporal[ \ +FCI[TC[k]FAD[{k,m3},{k-pH,m2},{k-pE1,pPH}]],{k},FCE\[Rule]True]", +"-(CFAD[{{k, 0}, {-m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - \ +TC[k - pH]^2, -1}, 1}, {{k - pE1, 0}, {-pPH^2 - TC[k - pE1]^2, -1}, \ +1}]*TC[k])"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID20", +"FCLoopMixedToCartesianAndTemporal[FCI[TC[k] FVD[k,mu] \ +FAD[k,k+p]],{k},FCE\[Rule]True]", +"CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k + p, 0}, {-TC[k + p]^2, \ +-1}, 1}]*TC[k]*(-Pair[CartesianMomentum[k, -1 + D], LorentzIndex[mu, \ +D]] + MT[0, mu]*TC[k])"}, +{"fcstFCLoopMixedToCartesianAndTemporal-ID21", +"FCLoopMixedToCartesianAndTemporal[ +FCI[TC[k] FVD[k, mu] FAD[k, k + p]], {k}, Uncontract -> True, +FCE -> True] // FCCanonicalizeDummyIndices[#, CartesianIndexNames -> {i}] &//FCE", +"-CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k + p, 0}, {-TC[k + p]^2, -1}, + 1}] CVD[k, i] Pair[CartesianIndex[i, -1 + D], +LorentzIndex[mu, D]] TC[k] + +CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k + p, 0}, {-TC[k + p]^2, -1}, + 1}] MT[0, mu] TC[k]^2"} +}); diff --git a/Tests/LoopIntegrals/FCLoopNonIntegerPropagatorPowersFreeQ.test b/Tests/LoopIntegrals/FCLoopNonIntegerPropagatorPowersFreeQ.test new file mode 100644 index 000000000..2199b9c5e --- /dev/null +++ b/Tests/LoopIntegrals/FCLoopNonIntegerPropagatorPowersFreeQ.test @@ -0,0 +1,37 @@ + + +(* :Title: fcstFCLoopNonIntegerPropagatorPowersFreeQ.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + FCLoopNonIntegerPropagatorPowersFreeQ *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCLoopNonIntegerPropagatorPowersFreeQ = +({ +{"fcstFCLoopNonIntegerPropagatorPowersFreeQ-ID1", +"FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q+p,mm}]]", +"True"}, +{"fcstFCLoopNonIntegerPropagatorPowersFreeQ-ID2", +"FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q+p,mm,2}]]", +"True"}, +{"fcstFCLoopNonIntegerPropagatorPowersFreeQ-ID3", +"FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q+p,mm,-1}]]", +"True"}, +{"fcstFCLoopNonIntegerPropagatorPowersFreeQ-ID4", +"FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q+p,mm,1/2}]]", +"False"}, +{"fcstFCLoopNonIntegerPropagatorPowersFreeQ-ID5", +"FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q+p,mm,n}]]", +"False"}, +{"fcstFCLoopNonIntegerPropagatorPowersFreeQ-ID6", +"FCLoopNonIntegerPropagatorPowersFreeQ[FCI@CFAD[{q+p,mm,0.5}]]", +"False"} +}); diff --git a/Tests/LoopIntegrals/FCLoopPropagatorPowersCombine.test b/Tests/LoopIntegrals/FCLoopPropagatorPowersCombine.test new file mode 100644 index 000000000..ec09dd5b7 --- /dev/null +++ b/Tests/LoopIntegrals/FCLoopPropagatorPowersCombine.test @@ -0,0 +1,47 @@ + + +(* :Title: fcstFCLoopPropagatorPowersCombine.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + fcstFCLoopPropagatorPowersCombine *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCLoopPropagatorPowersCombine = +({ +{"fcstFCLoopPropagatorPowersCombine-ID1", +"FCLoopPropagatorPowersCombine[SFAD[{{q,0},{m,1},1},{{q,0},{m,1},1}\ +],FCE->True]", "SFAD[{{q, 0}, {m, 1}, 2}]"}, +{"fcstFCLoopPropagatorPowersCombine-ID2", +"FCLoopPropagatorPowersCombine[SFAD[{{q,0},{m,1},1},{{q+p,0},{mm,1}\ +,1},{{q,0},{m,1},1}],FCE->True]", +"SFAD[{{q, 0}, {m, 1}, 2}, {{p + q, 0}, {mm, 1}, 1}]"}, +{"fcstFCLoopPropagatorPowersCombine-ID3", +"FCLoopPropagatorPowersCombine[SFAD[{{q,0},{m,1},-1},{{q+p,0},{mm,\ +1},1},{{q,0},{m,1},1}],FCE->True]", +"SFAD[{{p + q, 0}, {mm, 1}, 1}]"}, +{"fcstFCLoopPropagatorPowersCombine-ID4", +"FCLoopPropagatorPowersCombine[SFAD[{{q,0},{m,1},-1},{{q,0},{m,1},\ +1}],FCE->True]", "1"}, +{"fcstFCLoopPropagatorPowersCombine-ID5", +"FCLoopPropagatorPowersCombine[CFAD[{{q,0},{m,1},1},{{q,0},{m,1},1}\ +],FCE->True]", "CFAD[{{q, 0}, {m, 1}, 2}]"}, +{"fcstFCLoopPropagatorPowersCombine-ID6", +"FCLoopPropagatorPowersCombine[CFAD[{{q,0},{m,1},1},{{q+p,0},{mm,1}\ +,1},{{q,0},{m,1},1}],FCE->True]", +"CFAD[{{q, 0}, {m, 1}, 2}, {{p + q, 0}, {mm, 1}, 1}]"}, +{"fcstFCLoopPropagatorPowersCombine-ID7", +"FCLoopPropagatorPowersCombine[CFAD[{{q,0},{m,1},-1},{{q+p,0},{mm,\ +1},1},{{q,0},{m,1},1}],FCE->True]", +"CFAD[{{p + q, 0}, {mm, 1}, 1}]"}, +{"fcstFCLoopPropagatorPowersCombine-ID8", +"FCLoopPropagatorPowersCombine[CFAD[{{q,0},{m,1},-1},{{q,0},{m,1},\ +1}],FCE->True]", "1"} +}); diff --git a/Tests/LoopIntegrals/FCLoopPropagatorPowersExpand.test b/Tests/LoopIntegrals/FCLoopPropagatorPowersExpand.test new file mode 100644 index 000000000..c98f70f82 --- /dev/null +++ b/Tests/LoopIntegrals/FCLoopPropagatorPowersExpand.test @@ -0,0 +1,33 @@ + + +(* :Title: fcstFCLoopPropagatorPowersExpand.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + fcstFCLoopPropagatorPowersExpand *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCLoopPropagatorPowersExpand = +({ +{"fcstFCLoopPropagatorPowersExpand-ID1", +"FCLoopPropagatorPowersExpand[FCI[SFAD[{q,m,2}]],FCE\[Rule]True]", +"SFAD[{{q, 0}, {m, 1}, 1}, {{q, 0}, {m, 1}, 1}]"}, +{"fcstFCLoopPropagatorPowersExpand-ID2", +"FCLoopPropagatorPowersExpand[FCI[CFAD[{q,m,2}]],FCE\[Rule]True]", +"CFAD[{{q, 0}, {m, -1}, 1}, {{q, 0}, {m, -1}, 1}]"}, +{"fcstFCLoopPropagatorPowersExpand-ID3", +"FCLoopPropagatorPowersExpand[FCI[SFAD[q,{q,m,2}]],FCE\[Rule]True]\ +", "SFAD[{{q, 0}, {0, 1}, 1}, {{q, 0}, {m, 1}, 1}, {{q, 0}, {m, 1}, \ +1}]"}, +{"fcstFCLoopPropagatorPowersExpand-ID4", +"FCLoopPropagatorPowersExpand[FCI[SFAD[{q,m,2},q+p]],FCE\[Rule]\ +True]", "SFAD[{{q, 0}, {m, 1}, 1}, {{q, 0}, {m, 1}, 1}, {{p + q, 0}, \ +{0, 1}, 1}]"} +}); diff --git a/Tests/LoopIntegrals/FCLoopRemoveNegativePropagatorPowers.test b/Tests/LoopIntegrals/FCLoopRemoveNegativePropagatorPowers.test new file mode 100644 index 000000000..11b40c9eb --- /dev/null +++ b/Tests/LoopIntegrals/FCLoopRemoveNegativePropagatorPowers.test @@ -0,0 +1,43 @@ + + +(* :Title: FCLoopRemoveNegativePropagatorPowers.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + FCLoopRemoveNegativePropagatorPowers *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCLoopRemoveNegativePropagatorPowers = +({ +{"fcstFCLoopRemoveNegativePropagatorPowers-ID1", +"FCLoopRemoveNegativePropagatorPowers[SFAD[{q,m,2}],FCE->True]", +"SFAD[{{q, 0}, {m, 1}, 2}]"}, +{"fcstFCLoopRemoveNegativePropagatorPowers-ID2", +"FCLoopRemoveNegativePropagatorPowers[SFAD[{q,m,-1}],FCE->True]", +"-m + SPD[q, q]"}, +{"fcstFCLoopRemoveNegativePropagatorPowers-ID3", +"FCLoopRemoveNegativePropagatorPowers[SFAD[{q,m},{q,m,-2}],\ +FCE->True]", "-m + SPD[q, q]"}, +{"fcstFCLoopRemoveNegativePropagatorPowers-ID4", +"FCLoopRemoveNegativePropagatorPowers[SFAD[{q,m},q+p,{q,m,-2}],\ +FCE->True]", "SFAD[{{p + q, 0}, {0, 1}, 1}]*(-m + SPD[q, q])"}, +{"fcstFCLoopRemoveNegativePropagatorPowers-ID5", +"FCLoopRemoveNegativePropagatorPowers[CFAD[{q,m,2}],FCE->True]", +"CFAD[{{q, 0}, {m, -1}, 2}]"}, +{"fcstFCLoopRemoveNegativePropagatorPowers-ID6", +"FCLoopRemoveNegativePropagatorPowers[CFAD[{q,m,-1}],FCE->True]", +"m + CSPD[q, q]"}, +{"fcstFCLoopRemoveNegativePropagatorPowers-ID7", +"FCLoopRemoveNegativePropagatorPowers[CFAD[{q,m},{q,m,-2}],\ +FCE->True]", "m + CSPD[q, q]"}, +{"fcstFCLoopRemoveNegativePropagatorPowers-ID8", +"FCLoopRemoveNegativePropagatorPowers[CFAD[{q,m},q+p,{q,m,-2}],\ +FCE->True]", "CFAD[{{p + q, 0}, {0, -1}, 1}]*(m + CSPD[q, q])"} +}); diff --git a/Tests/LoopIntegrals/FCLoopSamePropagatorHeadsQ.test b/Tests/LoopIntegrals/FCLoopSamePropagatorHeadsQ.test new file mode 100644 index 000000000..3f381257c --- /dev/null +++ b/Tests/LoopIntegrals/FCLoopSamePropagatorHeadsQ.test @@ -0,0 +1,34 @@ + + +(* :Title: fcstFCLoopSamePropagatorHeadsQ.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + fcstFCLoopSamePropagatorHeadsQ *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFCLoopSamePropagatorHeadsQ = +({ +{"fcstFCLoopSamePropagatorHeadsQ-ID1", +"FCLoopSamePropagatorHeadsQ[FCI[FAD[q,q-p]]]", "True"}, +{"fcstFCLoopSamePropagatorHeadsQ-ID2", +"FCLoopSamePropagatorHeadsQ[FCI[SFAD[q,q-p]]]", "True"}, +{"fcstFCLoopSamePropagatorHeadsQ-ID3", +"FCLoopSamePropagatorHeadsQ[FCI[CFAD[q,q-p]]]", "True"}, +{"fcstFCLoopSamePropagatorHeadsQ-ID4", +"FCLoopSamePropagatorHeadsQ[FeynAmpDenominatorCombine[FAD[q,q-p]\ +FAD[l,l+k]]]", "True"}, +{"fcstFCLoopSamePropagatorHeadsQ-ID5", +"FCLoopSamePropagatorHeadsQ[FeynAmpDenominatorCombine[CFAD[q,q-p]\ +SFAD[l,l+k]]]", "False"}, +{"fcstFCLoopSamePropagatorHeadsQ-ID6", +"FCLoopSamePropagatorHeadsQ[FeynAmpDenominatorCombine[FAD[q,q-p]\ +SFAD[l,l+k]]]", "False"} +}); diff --git a/Tests/LoopIntegrals/FCLoopSolutionList.test b/Tests/LoopIntegrals/FCLoopSolutionList.test index 350d50e1d..252105cee 100644 --- a/Tests/LoopIntegrals/FCLoopSolutionList.test +++ b/Tests/LoopIntegrals/FCLoopSolutionList.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCLoopSolutionList *) diff --git a/Tests/LoopIntegrals/FCLoopSplit.test b/Tests/LoopIntegrals/FCLoopSplit.test index a117f9106..2bfad8525 100644 --- a/Tests/LoopIntegrals/FCLoopSplit.test +++ b/Tests/LoopIntegrals/FCLoopSplit.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCLoopSplit *) @@ -51,10 +51,39 @@ FVD[q, i]*SUNT[a]}"}, {"fcstFCLoopSplit-ID12","FCLoopSplit[ 1/6 (m1^2 + m2^2) + A0[m2^2]/6 + 1/3 m1^2 B0[0, m1^2, m2^2] + 1/6 (m1^2 - m2^2) B1[0, m1^2, m2^2], {}]", -"{1/6 (m1^2 + m2^2), -A0[m2^2]/6 + 1/3 m1^2 B0[0, m1^2, m2^2] + -1/6 (m1^2 - m2^2) B1[0, m1^2, m2^2], 0, 0}"}, +"{(m1^2 + m2^2)/6, A0[m2^2]/6 + (m1^2*B0[0, m1^2, m2^2])/3 + ((m1^2 - m2^2)*B1[0, m1^2, m2^2])/6, 0, 0}"}, {"fcstFCLoopSplit-ID13","FCLoopSplit[Foobar[x], {}, PaVeIntegralHeads -> Join[OptionValue[FCLoopIsolate, PaVeIntegralHeads], {Foobar}]]", -"{0, Foobar[x], 0, 0}"} +"{0, Foobar[x], 0, 0}"}, +{"fcstFCLoopSplit-ID14", +"FCLoopSplit[c CSPD[q,p] CFAD[{q,m}],{q},FCE\[Rule]True]", +"{0, 0, c*CFAD[{{q, 0}, {m, -1}, 1}]*CSPD[p, q], 0}"}, +{"fcstFCLoopSplit-ID15", +"FCLoopSplit[CVD[q,mu] CFAD[{q,m}],{q},FCE\[Rule]True]", +"{0, 0, 0, CFAD[{{q, 0}, {m, -1}, 1}]*CVD[q, mu]}"}, +{"fcstFCLoopSplit-ID16", +"FCLoopSplit[c CVD[q,mu] CFAD[{q,m}],{q},FCE->True]", +"{0, 0, 0, c*CFAD[{{q, 0}, {m, -1}, 1}]*CVD[q, mu]}"}, +{"fcstFCLoopSplit-ID17", +"FCLoopSplit[c+b CFAD[{q,mu}]+CSPD[q,k] CSPD[q,l] CFAD[{q,m}]+b \ +CVD[q,mu] CSPD[q,l] CFAD[{q,m}],{q},FCE\[Rule]True]", +"{c, b*CFAD[{{q, 0}, {mu, -1}, 1}], CFAD[{{q, 0}, {m, -1}, \ +1}]*CSPD[k, q]*CSPD[l, q], b*CFAD[{{q, 0}, {m, -1}, 1}]*CSPD[l, \ +q]*CVD[q, mu]}"}, +{"fcstFCLoopSplit-ID18", +"FCLoopSplit[c SPD[q,p] SFAD[{q,m}],{q},FCE\[Rule]True]", +"{0, 0, c*SFAD[{{q, 0}, {m, 1}, 1}]*SPD[p, q], 0}"}, +{"fcstFCLoopSplit-ID19", +"FCLoopSplit[FVD[q,mu] SFAD[{q,m}],{q},FCE\[Rule]True]", +"{0, 0, 0, FVD[q, mu]*SFAD[{{q, 0}, {m, 1}, 1}]}"}, +{"fcstFCLoopSplit-ID20", +"FCLoopSplit[c FVD[q,mu] SFAD[{q,m}],{q},FCE->True]", +"{0, 0, 0, c*FVD[q, mu]*SFAD[{{q, 0}, {m, 1}, 1}]}"}, +{"fcstFCLoopSplit-ID21", +"FCLoopSplit[c+b SFAD[{q,mu}]+SPD[q,k] SPD[q,l] SFAD[{q,m}]+b \ +FVD[q,mu] SPD[q,l]SFAD[{q,m}],{q},FCE\[Rule]True]", +"{c, b*SFAD[{{q, 0}, {mu, 1}, 1}], SFAD[{{q, 0}, {m, 1}, \ +1}]*SPD[k, q]*SPD[l, q], b*FVD[q, mu]*SFAD[{{q, 0}, {m, 1}, \ +1}]*SPD[l, q]}"} + }; diff --git a/Tests/LoopIntegrals/FCMultiLoopTID.test b/Tests/LoopIntegrals/FCMultiLoopTID.test index c10c4eda4..dec91a32f 100644 --- a/Tests/LoopIntegrals/FCMultiLoopTID.test +++ b/Tests/LoopIntegrals/FCMultiLoopTID.test @@ -2,12 +2,12 @@ Tests`LoopIntegrals`fcstFCMultiLoopTID = ({ {"fcstFCMultiLoopTID-ID1", "FCMultiLoopTID[0,{q1,q2},FCE->True]", "0"}, {"fcstFCMultiLoopTID-ID2", -"$BreitMaison=True; \n tmp= FCMultiLoopTID[FVE[q1, mu] FVE[q2, nu] FAD[{q1, m}], {q1, q2},FCE->True]; -\n $BreitMaison=False; tmp", -"(FAD[{q1, m}] MTE[mu, nu] SPD[q1, q2])/D"}, +"FCSetDiracGammaScheme[\"BMHV\"]; \n tmp= FCMultiLoopTID[FVE[q1, mu] FAD[{q1 + p1, m}, {q2 + p2, m}], {q1, q2}, +FCE -> True]; \n FCSetDiracGammaScheme[\"NDR\"]; tmp", +"-FAD[{q1, m}, {q2, m}] FVE[p1, mu]"}, {"fcstFCMultiLoopTID-ID3", -"FCMultiLoopTID[FVD[q1,mu]FVD[q2,nu]FAD[{q1,m}],{q1,q2},FCE->True]", -"(FAD[{q1, m}]*MTD[mu, nu]*SPD[q1, q2])/D"}, +"FCMultiLoopTID[FVD[q1, mu] FAD[{q1 + p1, m}, {q2 + p2, m}], {q1, q2}, FCE -> True]", +"-FAD[{q1, m}, {q2, m}] FVD[p1, mu]"}, {"fcstFCMultiLoopTID-ID4", "FCMultiLoopTID[FVD[q1,mu]SPD[q1,q2]FVD[q2,nu]FAD[{q1,m}],{q1},FCE->True]", "(FAD[{q1, m}]*FVD[q2, mu]*FVD[q2, nu]*SPD[q1, q2]^2)/SPD[q2, \ @@ -15,175 +15,279 @@ q2]"}, {"fcstFCMultiLoopTID-ID5", "FCMultiLoopTID[FVD[q1,mu]FVD[q2,nu]SPD[q1,q2]FAD[{q1,m1},{q2,m2},{\ q1-q2}],{q1,q2},FCE->True]", -"-((m1^2 + m2^2)*FAD[{q1, m1}, {q2, m2}]*MTD[mu, nu])/(4*D) + \ -((m1^2 + m2^2)^2*FAD[{q1, m1}, {q2, m2}, -q1 + q2]*MTD[mu, nu])/(4*D) \ -- (FAD[{q1, m2}, {q2, m1}]*MTD[mu, nu]*SPD[q1, q2])/(2*D)"}, +"-((m1^2 + m2^2)*FAD[{q1, m1}, {q2, m2}]*MTD[mu, nu])/(4*D) + +((m1^2 + m2^2)^2*FAD[{q1, m1}, {q2, m2}, q1 - q2]*MTD[mu, nu])/(4*D)"}, {"fcstFCMultiLoopTID-ID6", "FCMultiLoopTID[FVD[q1,mu]FVD[q2,nu]SPD[q1,q2]FAD[{q1+p2,m},{q2-p1,\ m},{q1-q2}],{q1,q2},FCE->True]", -"(FAD[{p2 + q1, m}, {-p1 + q2, m}, q1 - q2]*SPD[p1, q1]*SPD[p1, \ -q2]*(-2*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + D*FVD[p2, mu]*FVD[p2, \ -nu]*SPD[p1, p2]^2 + FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p2, p2] + \ -FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]*SPD[p2, p2] - D*FVD[p1, \ -nu]*FVD[p2, mu]*SPD[p1, p2]*SPD[p2, p2] + FVD[p1, mu]*FVD[p2, \ -nu]*SPD[p1, p2]*SPD[p2, p2] - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, \ -p2]*SPD[p2, p2] + MTD[mu, nu]*SPD[p1, p2]^2*SPD[p2, p2] - FVD[p1, \ -mu]*FVD[p1, nu]*SPD[p2, p2]^2 + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p2, \ -p2]^2 - MTD[mu, nu]*SPD[p1, p1]*SPD[p2, p2]^2)*SPD[q1, q2])/((-2 + \ -D)*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])^2) - (FAD[{-p2 + q1, m}, \ -{-p1 + q2, m}]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2]) + \ -D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] - FVD[p1, \ -nu]*FVD[p2, mu]*SPD[p1, p2]^2 + FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 \ -- D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, p2]^3 \ -+ 2*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - D*FVD[p1, \ -nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, \ -nu]*SPD[p1, p2]*SPD[p2, p2] + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, \ -p2]*SPD[p2, p2] - MTD[mu, nu]*SPD[p1, p1]*SPD[p1, p2]*SPD[p2, \ -p2])*SPD[p2, q1]*SPD[q1, q2])/(2*(-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, \ -p1]*SPD[p2, p2])^2) - (FAD[{-p2 + q1, m}, {p1 + q2, m}, -q1 + \ -q2]*(2*m^2 - SPD[p1, p1] - SPD[p2, p2])*(-(FVD[p2, mu]*FVD[p2, \ -nu]*SPD[p1, p1]*SPD[p1, p2]) + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, \ -p1]*SPD[p1, p2] - FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 + FVD[p1, \ -mu]*FVD[p2, nu]*SPD[p1, p2]^2 - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, \ -p2]^2 + MTD[mu, nu]*SPD[p1, p2]^3 + 2*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, \ -p1]*SPD[p2, p2] - D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - \ -FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] + D*FVD[p1, \ -mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] - MTD[mu, nu]*SPD[p1, \ -p1]*SPD[p1, p2]*SPD[p2, p2])*SPD[p2, q1]*SPD[q1, q2])/(2*(-2 + \ -D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])^2) - (FAD[{-p2 + q1, \ -m}, {p1 + q2, m}, -q1 + q2]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, \ -p1]*SPD[p1, p2]) + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] \ -- FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 + FVD[p1, mu]*FVD[p2, \ -nu]*SPD[p1, p2]^2 - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + MTD[mu, \ -nu]*SPD[p1, p2]^3 + 2*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] \ -- D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - FVD[p1, \ -mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] + D*FVD[p1, mu]*FVD[p1, \ -nu]*SPD[p1, p2]*SPD[p2, p2] - MTD[mu, nu]*SPD[p1, p1]*SPD[p1, \ -p2]*SPD[p2, p2])*SPD[p2, q1]^2*SPD[q1, q2])/((-2 + D)*(-SPD[p1, p2]^2 \ -+ SPD[p1, p1]*SPD[p2, p2])^2) - (FAD[{p2 + q1, m}, {-p1 + q2, m}, q1 \ -- q2]*SPD[p1, q1]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2]) \ -+ D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] + FVD[p1, \ -nu]*FVD[p2, mu]*SPD[p1, p2]^2 - D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, \ -p2]^2 - FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, \ -p2]^3 + 2*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p2, p2] - D*FVD[p1, \ -mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, \ -nu]*SPD[p1, p2]*SPD[p2, p2] + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, \ -p2]*SPD[p2, p2] - MTD[mu, nu]*SPD[p1, p1]*SPD[p1, p2]*SPD[p2, \ -p2])*SPD[p2, q2]*SPD[q1, q2])/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, \ -p1]*SPD[p2, p2])^2) + (FAD[{p2 + q1, m}, {-p1 + q2, m}, q1 - \ -q2]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]^2) + D*FVD[p2, mu]*FVD[p2, \ -nu]*SPD[p1, p1]^2 + FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p1, p2] - \ -D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p1, p2] + FVD[p1, \ -mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] - D*FVD[p1, mu]*FVD[p2, \ -nu]*SPD[p1, p1]*SPD[p1, p2] - 2*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]^2 \ -+ D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, \ -p1]*SPD[p1, p2]^2 + FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p1]*SPD[p2, p2] - \ -MTD[mu, nu]*SPD[p1, p1]^2*SPD[p2, p2])*SPD[p2, q1]*SPD[p2, \ -q2]*SPD[q1, q2])/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, \ -p2])^2) - (FAD[{p2 + q1, m}, {-p1 + q2, m}, q1 - q2]*(FVD[p2, \ -mu]*FVD[p2, nu]*SPD[p1, p1] - FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2] - \ -FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2] + MTD[mu, nu]*SPD[p1, p2]^2 + \ -FVD[p1, mu]*FVD[p1, nu]*SPD[p2, p2] - MTD[mu, nu]*SPD[p1, p1]*SPD[p2, \ -p2])*SPD[q1, q2]^2)/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, \ -p2])) + (FAD[{-p2 + q1, m}, {p1 + q2, m}, -q1 + q2]*(-(FVD[p2, \ -mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2]) + D*FVD[p2, mu]*FVD[p2, \ -nu]*SPD[p1, p1]*SPD[p1, p2] - FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 + \ -FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 - D*FVD[p1, mu]*FVD[p2, \ -nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, p2]^3 + 2*FVD[p1, nu]*FVD[p2, \ -mu]*SPD[p1, p1]*SPD[p2, p2] - D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, \ -p1]*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] + \ -D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] - MTD[mu, \ -nu]*SPD[p1, p1]*SPD[p1, p2]*SPD[p2, p2])*SPD[p2, q1]*SPD[q1, \ -q2]^2)/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])^2)"}, +"(FAD[{-p1 + q1, m}, q1 - q2, {p2 + q2, m}]*SPD[p1, q1]*SPD[p1, q2]*(-2*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + + FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p2, p2] + FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]*SPD[p2, p2] - D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]*SPD[p2, p2] + + FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]*SPD[p2, p2] - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]*SPD[p2, p2] + MTD[mu, nu]*SPD[p1, p2]^2*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, nu]*SPD[p2, p2]^2 + + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p2, p2]^2 - MTD[mu, nu]*SPD[p1, p1]*SPD[p2, p2]^2)*SPD[q1, q2])/((-2 + D)*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])^2) - +(FAD[{-p2 + q1, m}, {-p1 + q2, m}]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2]) + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] - FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 + + FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, p2]^3 + 2*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - + D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] - + MTD[mu, nu]*SPD[p1, p1]*SPD[p1, p2]*SPD[p2, p2])*SPD[p2, q1]*SPD[q1, q2])/(2*(-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])^2) - +(FAD[{-p2 + q1, m}, q1 - q2, {p1 + q2, m}]*(2*m^2 - SPD[p1, p1] - SPD[p2, p2])*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2]) + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] - + FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 + FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, p2]^3 + + 2*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] + + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] - MTD[mu, nu]*SPD[p1, p1]*SPD[p1, p2]*SPD[p2, p2])*SPD[p2, q1]*SPD[q1, q2])/(2*(-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])^2) - +(FAD[{-p1 + q1, m}, q1 - q2, {p2 + q2, m}]*SPD[p1, q2]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2]) + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] + + FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 - D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 - FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, p2]^3 + + 2*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p2, p2] - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] + + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] - MTD[mu, nu]*SPD[p1, p1]*SPD[p1, p2]*SPD[p2, p2])*SPD[p2, q1]*SPD[q1, q2])/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])^2) - +(FAD[{-p2 + q1, m}, q1 - q2, {p1 + q2, m}]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2]) + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] - FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 + + FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, p2]^3 + 2*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - + D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] - + MTD[mu, nu]*SPD[p1, p1]*SPD[p1, p2]*SPD[p2, p2])*SPD[p2, q1]^2*SPD[q1, q2])/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])^2) + +(FAD[{-p1 + q1, m}, q1 - q2, {p2 + q2, m}]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]^2) + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]^2 + FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p1, p2] - + D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p1, p2] + FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] - + 2*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]^2 + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, p1]*SPD[p1, p2]^2 + FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p1]*SPD[p2, p2] - + MTD[mu, nu]*SPD[p1, p1]^2*SPD[p2, p2])*SPD[p2, q1]*SPD[p2, q2]*SPD[q1, q2])/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])^2) - +(FAD[{-p1 + q1, m}, q1 - q2, {p2 + q2, m}]*(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1] - FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2] - FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2] + MTD[mu, nu]*SPD[p1, p2]^2 + + FVD[p1, mu]*FVD[p1, nu]*SPD[p2, p2] - MTD[mu, nu]*SPD[p1, p1]*SPD[p2, p2])*SPD[q1, q2]^2)/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])) + +(FAD[{-p2 + q1, m}, q1 - q2, {p1 + q2, m}]*(-(FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2]) + D*FVD[p2, mu]*FVD[p2, nu]*SPD[p1, p1]*SPD[p1, p2] - FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p2]^2 + + FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 - D*FVD[p1, mu]*FVD[p2, nu]*SPD[p1, p2]^2 + MTD[mu, nu]*SPD[p1, p2]^3 + 2*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - + D*FVD[p1, nu]*FVD[p2, mu]*SPD[p1, p1]*SPD[p2, p2] - FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] + D*FVD[p1, mu]*FVD[p1, nu]*SPD[p1, p2]*SPD[p2, p2] - + MTD[mu, nu]*SPD[p1, p1]*SPD[p1, p2]*SPD[p2, p2])*SPD[p2, q1]*SPD[q1, q2]^2)/((-2 + D)*(-SPD[p1, p2]^2 + SPD[p1, p1]*SPD[p2, p2])^2)"}, {"fcstFCMultiLoopTID-ID7", "FCMultiLoopTID[SPD[q1,q2]FAD[{q1,m1},{q2,m2},{q1-q2}],{q1,q2},FCE->True]", -"-FAD[{q1, m1}, {q2, m2}]/2 + ((m1^2 + m2^2)*FAD[{q1, m1}, \ -{q2, m2}, -q1 + q2])/2"}, +"-FAD[{q1, m1}, {q2, m2}]/2 + ((m1^2 + m2^2)*FAD[{q1, m1}, {q2, m2}, q1 - q2])/2"}, {"fcstFCMultiLoopTID-ID8", "FCMultiLoopTID[GSD[q1]SPD[q1,q2]FAD[{q1,m1},{q2,m2},{q1-q2}],{q1,\ q2},FCE->True]", "0"}, {"fcstFCMultiLoopTID-ID9", "FCMultiLoopTID[GSD[q1].GSD[q2]SPD[q1,q2]FAD[{q1,m1},{q2,m2},{q1-\ q2}],{q1,q2}]//DiracTrick//FCE", -"((m1^2 + m2^2)*(-FAD[{q1, m1}, {q2, m2}] + m1^2*FAD[{q1, m1}, {q2, m2}, --q1 + q2] + m2^2*FAD[{q1, m1}, {q2, m2}, -q1 + q2]))/4 - -(FAD[{q1, m1}, {q2, m2}]*SPD[q1, q2])/2"}, -{"fcstFCMultiLoopTID-ID10", -"FCMultiLoopTID[GSD[q1].GSD[q2]SPD[q1,q2]FAD[{q1,m1},{q2,m2},{q1-q2}]\ -,{q1,q2}]//DiracTrick//FCE", -"1/4 (m1^2 + m2^2) (-FAD[{q1, m1}, {q2, m2}] + - m1^2 FAD[{q1, m1}, {q2, m2}, -q1 + q2] + - m2^2 FAD[{q1, m1}, {q2, m2}, -q1 + q2]) - -1/2 FAD[{q1, m1}, {q2, m2}] SPD[q1, q2]"}, +"-((m1^2 + m2^2)*(FAD[{q1, m1}, {q2, m2}] - + m1^2*FAD[{q1, m1}, {q2, m2}, q1 - q2] - + m2^2*FAD[{q1, m1}, {q2, m2}, q1 - q2]))/4"}, {"fcstFCMultiLoopTID-ID11", "FCMultiLoopTID[LCD[][q1,q2,a,b]SPD[q1,q2]FAD[{q1-p1,m1},{q2-p2,m2},\ {q1-q2}],{q1,q2},FCE->True]", -"-(FAD[{-p2 + q1, m2}, {-p1 + q2, m1}]*SPD[p2, q1]*SPD[q1, \ -q2]*LCD[][a, b, p1, p2])/(2*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])) \ -+ (FAD[{-p1 + q1, m1}, {-p2 + q2, m2}, q1 - q2]*SPD[p1, q2]*SPD[p2, \ -q1]*SPD[q1, q2]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, \ -p1]*SPD[p2, p2]) + (FAD[{-p2 + q1, m2}, {-p1 + q2, m1}, -q1 + \ -q2]*(m1^2 + m2^2 - SPD[p1, p1] - SPD[p2, p2])*SPD[p2, q1]*SPD[q1, \ -q2]*LCD[][a, b, p1, p2])/(2*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])) \ -+ (FAD[{-p2 + q1, m2}, {-p1 + q2, m1}, -q1 + q2]*SPD[p2, \ -q1]^2*SPD[q1, q2]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, \ -p1]*SPD[p2, p2]) - (FAD[{-p2 + q1, m2}, {-p1 + q2, m1}, -q1 + \ -q2]*SPD[p2, q1]*SPD[q1, q2]^2*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - \ -SPD[p1, p1]*SPD[p2, p2])"}, +"-(FAD[{-p2 + q1, m2}, {-p1 + q2, m1}]*SPD[p2, q1]*SPD[q1, q2]*LCD[][a, b, p1, p2])/(2*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])) + +(FAD[{-p1 + q1, m1}, q1 - q2, {-p2 + q2, m2}]*SPD[p1, q2]*SPD[p2, q1]*SPD[q1, q2]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2]) + +(FAD[{-p2 + q1, m2}, q1 - q2, {-p1 + q2, m1}]*(m1^2 + m2^2 - SPD[p1, p1] - SPD[p2, p2])*SPD[p2, q1]*SPD[q1, q2]*LCD[][a, b, p1, p2])/(2*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])) + +(FAD[{-p2 + q1, m2}, q1 - q2, {-p1 + q2, m1}]*SPD[p2, q1]^2*SPD[q1, q2]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2]) - +(FAD[{-p2 + q1, m2}, q1 - q2, {-p1 + q2, m1}]*SPD[p2, q1]*SPD[q1, q2]^2*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])"}, {"fcstFCMultiLoopTID-ID12", "FCMultiLoopTID[LCD[][q1,q2,a,b]SPD[q1,q2]FAD[{q1-p1,m1},{q2-p2,m2}\ ,{q1-q2}],{q1,q2},FCE->True]", -"-(FAD[{-p2 + q1, m2}, {-p1 + q2, m1}]*SPD[p2, q1]*SPD[q1, \ -q2]*LCD[][a, b, p1, p2])/(2*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, \ -p2])) + (FAD[{-p1 + q1, m1}, {-p2 + q2, m2}, q1 - q2]*SPD[p1, \ -q2]*SPD[p2, q1]*SPD[q1, q2]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - \ -SPD[p1, p1]*SPD[p2, p2]) + (FAD[{-p2 + q1, m2}, {-p1 + q2, m1}, -q1 + \ -q2]*(m1^2 + m2^2 - SPD[p1, p1] - SPD[p2, p2])*SPD[p2, q1]*SPD[q1, \ -q2]*LCD[][a, b, p1, p2])/(2*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, \ -p2])) + (FAD[{-p2 + q1, m2}, {-p1 + q2, m1}, -q1 + q2]*SPD[p2, \ -q1]^2*SPD[q1, q2]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, \ -p1]*SPD[p2, p2]) - (FAD[{-p2 + q1, m2}, {-p1 + q2, m1}, -q1 + \ -q2]*SPD[p2, q1]*SPD[q1, q2]^2*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - \ -SPD[p1, p1]*SPD[p2, p2])"}, +"-(FAD[{-p2 + q1, m2}, {-p1 + q2, m1}]*SPD[p2, q1]*SPD[q1, q2]*LCD[][a, b, p1, p2])/(2*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])) + +(FAD[{-p1 + q1, m1}, q1 - q2, {-p2 + q2, m2}]*SPD[p1, q2]*SPD[p2, q1]*SPD[q1, q2]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2]) + +(FAD[{-p2 + q1, m2}, q1 - q2, {-p1 + q2, m1}]*(m1^2 + m2^2 - SPD[p1, p1] - SPD[p2, p2])*SPD[p2, q1]*SPD[q1, q2]*LCD[][a, b, p1, p2])/(2*(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])) + +(FAD[{-p2 + q1, m2}, q1 - q2, {-p1 + q2, m1}]*SPD[p2, q1]^2*SPD[q1, q2]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2]) - +(FAD[{-p2 + q1, m2}, q1 - q2, {-p1 + q2, m1}]*SPD[p2, q1]*SPD[q1, q2]^2*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])"}, {"fcstFCMultiLoopTID-ID13", "FCMultiLoopTID[FVD[q1, mu] FVD[q2, nu] FAD[q1, q2, {p1 - q2}, {q1 - p1}, {q2 - p1}], {q1, q2},FCE->True]", -"(FAD[q2, q1, -p1 + q2, -p1 + q1, -p1 + q1]*(D*FVD[p1, mu]*FVD[p1, nu] - -MTD[mu, nu]*SPD[p1, p1]))/(4*(-1 + D)) - (FAD[q2, q1, -p1 + q2, -p1 + q1]*(D*FVD[p1, mu]*FVD[p1, nu] - -MTD[mu, nu]*SPD[p1, p1]))/(4*(-1 + D)*SPD[p1, p1]) + (FAD[q2, q1, -p1 + q2, -p1 + q1, -p1 + q2]*(-(FVD[p1, mu]*FVD[p1, nu]) + -MTD[mu, nu]*SPD[p1, p1])*SPD[q1, q2])/((-1 + D)*SPD[p1, p1])"}, +"(FAD[q1, q1, q2, -p1 + q1, -p1 + q2]*(D*FVD[p1, mu]*FVD[p1, nu] - MTD[mu, nu]*SPD[p1, p1]))/(4*(-1 + D)) - (FAD[q1, q2, -p1 + q1, -p1 + q2]*(D*FVD[p1, mu]*FVD[p1, nu] - MTD[mu, nu]*SPD[p1, p1]))/ +(4*(-1 + D)*SPD[p1, p1]) + (FAD[q1, q2, -p1 + q1, -p1 + q1, -p1 + q2]*(-(FVD[p1, mu]*FVD[p1, nu]) + MTD[mu, nu]*SPD[p1, p1])*SPD[q1, q2])/((-1 + D)*SPD[p1, p1])"}, {"fcstFCMultiLoopTID-ID14", "FCMultiLoopTID[ FVD[q1, mu] FVD[q2, nu] LCD[mu, nu][a, b] FAD[{q1 - p1, m1}, {q2 - p2, m2}, {q1 - q2}], {q1, q2}, FCE->True]", -"(FAD[{-p1 + q1, m1}, {-p2 + q2, m2}, q1 - q2] SPD[p1, q2] SPD[p2, - q1] LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - - SPD[p1, p1] SPD[p2, p2]) - (FAD[{-p1 + q1, m1}, {-p2 + q2, m2}, - q1 - q2] SPD[p1, q1] SPD[p2, q2] LCD[][a, b, p1, p2])/(SPD[p1, - p2]^2 - SPD[p1, p1] SPD[p2, p2])"}, +"(FAD[{-p1 + q1, m1}, q1 - q2, {-p2 + q2, m2}]*SPD[p1, q2]*SPD[p2, q1]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2]) - +(FAD[{-p2 + q1, m2}, q1 - q2, {-p1 + q2, m1}]*SPD[p1, q2]*SPD[p2, q1]*LCD[][a, b, p1, p2])/(SPD[p1, p2]^2 - SPD[p1, p1]*SPD[p2, p2])"}, {"fcstFCMultiLoopTID-ID15", "FCMultiLoopTID[ FAD[p1, {p2, m}, {p3, m}, p1, p1, p1, {-p1 + p2, m}, {-p1 + p3, m}] FVD[p1, Lor1] FVD[p1, Lor2] (SPD[p1, p1] - 2 (SPD[p1, p2] + SPD[p1, p3] - 2 SPD[p2, p3]))^2, {p1, p2, p3},FCE -> True]", - "(2*FAD[p1, p1, p1, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D - (FAD[p1, p1, p1, {p2, m}, {-p1 + p2, m}]*MTD[Lor1, Lor2])/D - -(2*FAD[p1, p1, p1, {p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D + (2*FAD[p1, p1, {p2, m}, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D - -(2*FAD[{p3, m}, p1, p1, p1, {-p1 + p2, m}]*MTD[Lor1, Lor2])/D + (FAD[{p3, m}, p1, p1, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D - -(FAD[{p3, m}, p1, p1, {p2, m}, {-p1 + p2, m}]*MTD[Lor1, Lor2])/D - (FAD[{p3, m}, p1, p1, {p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D + -(FAD[{p3, m}, p1, {p2, m}, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D - (m^2*FAD[p1, p1, p1, {p2, m}, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D + -(2*FAD[{p3, m}, p1, p1, p1, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p2])/D - -(8*FAD[{p1, m}, p2, p2, p2, {p1 - p2, m}, {p2 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p3])/D - -(2*FAD[{p3, m}, p1, p1, p1, {p2, m}, {-p1 + p2, m}]*MTD[Lor1, Lor2]*SPD[p1, p3])/D - -(8*FAD[{p3, m}, p2, p2, p2, {p1 - p2, m}, {p2 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p3])/D + -(8*FAD[{p3, m}, {p1, m}, p2, p2, p2, {-p1 + p2, m}]*MTD[Lor1, Lor2]*SPD[p1, p3])/D - -(8*FAD[{p3, m}, {p1, m}, p2, p2, {p1 - p2, m}, {p2 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p3])/D + -(16*FAD[{p3, m}, {p1, m}, p2, p2, p2, {p1 - p2, m}, {p2 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p3]^2)/D + -(FAD[p1, p1, p1, {p2, m}, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2]*SPD[p3, p3])/D"}, + "(2*FAD[p1, p1, p1, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D - + (4*FAD[p1, p1, p1, {p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D + (2*FAD[p1, p1, {p2, m}, {p1 - p2, m}, + {p1 - p3, m}]*MTD[Lor1, Lor2])/D - (2*FAD[p1, p1, {p2, m}, {p3, m}, {p1 - p2, m}]*MTD[Lor1, Lor2])/D + + (FAD[p1, {p2, m}, {p3, m}, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2])/D + + (4*FAD[p1, p1, p1, {p3, m}, {p1 - p2, m}, {p1 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p2])/D - + (16*FAD[{p1, m}, p3, p3, p3, {p1 - p3, m}, {p2 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p2])/D - + (8*FAD[{p1, m}, {p2, m}, p3, p3, {p1 - p3, m}, {p2 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p2])/D + + (16*FAD[{p1, m}, {p2, m}, p3, p3, p3, {p1 - p3, m}, {p2 - p3, m}]*MTD[Lor1, Lor2]*SPD[p1, p2]^2)/D"}, {"fcstFCMultiLoopTID-ID16", "FCMultiLoopTID[(GSD[l] + m) SPD[l, p2] FAD[{l, m1}, {l + p, m2}], {l}, FCE -> True]", -"m*FAD[{l, m1}, {l + p, m2}]*SPD[l, p2] + -(FAD[{l, m2}]*SPD[p, p2]*(GSD[p2]*SPD[p, p2] - -GSD[p]*SPD[p2, p2]))/(2*(SPD[p, p2]^2 - SPD[p, p]*SPD[p2, p2])) + -(FAD[{l, m1}, {l + p, m2}]*SPD[l, p2]^2*(GSD[p2]*SPD[p, p] - -GSD[p]*SPD[p, p2]))/(-SPD[p, p2]^2 + SPD[p, p]*SPD[p2, p2]) - -(FAD[{l, m1}, {l - p, m2}]*SPD[l, p2]*(m1^2 - m2^2 + -SPD[p, p])*(GSD[p2]*SPD[p, p2] - -GSD[p]*SPD[p2, p2]))/(2*(-SPD[p, p2]^2 + SPD[p, p]*SPD[p2, p2]))"} +"m*FAD[{l, m1}, {l + p, m2}]*SPD[l, p2] + (FAD[{l, m1}, {l - p, m2}]*SPD[l, p2]*(m1^2 - m2^2 + SPD[p, p])*(GSD[p2]*SPD[p, p2] - GSD[p]*SPD[p2, p2]))/(2*(SPD[p, p2]^2 - SPD[p, p]*SPD[p2, p2])) + +(FAD[{l, m2}]*SPD[p, p2]*(GSD[p2]*SPD[p, p2] - GSD[p]*SPD[p2, p2]))/(2*(SPD[p, p2]^2 - SPD[p, p]*SPD[p2, p2])) + (FAD[{l, m1}, {l - p, m2}]*SPD[l, p2]^2*(GSD[p2]*SPD[p, p] - GSD[p]*SPD[p, p2]))/ +(-SPD[p, p2]^2 + SPD[p, p]*SPD[p2, p2])", +"-(FAD[l, l - p]*SPD[p, Polarization[k, I]])/2"}, +{"fcstFCMultiLoopTID-ID17", "FCMultiLoopTID[FVD[k, mu] SFAD[k, k + l, {{0, k.l}}], {k}, +FCE -> True]","(FVD[l, mu] SFAD[{{k, 0}, {0, 1}, 1}, {{k + l, 0}, {0, 1}, 1}])/SPD[l, +l]"}, +{"fcstFCMultiLoopTID-ID18", "FCMultiLoopTID[FVD[k, mu] FVD[k, nu] SFAD[k, k + l, {{0, k.l}}], {k}, +FCE -> True]","-(SFAD[{{k, 0}, {0, 1}, 1}, {{k + l, 0}, {0, 1}, 1}]*(D*FVD[l, mu]*FVD[l, nu] - MTD[mu, nu]*SPD[l, l]))/(2*(-1 + D)*SPD[l, l]) + +(SFAD[{{0, k . l}, {0, 1}, 1}, {{k + l, 0}, {0, 1}, 1}]*(-(FVD[l, mu]*FVD[l, nu]) + MTD[mu, nu]*SPD[l, l]))/((-1 + D)*SPD[l, l])"}, +{"fcstFCMultiLoopTID-ID19", "FCMultiLoopTID[ +SFAD[{p1, -mE^2}, {p2, - mE^2}, {p1 + p2, 0, + 2}, {p3, -mE^2}, {-p1 - p2 + p3, - + mE^2}, {p2, -mE^2}, {p1, -mE^2}] FVD[p1, Lor1] FVD[p2, +Lor2] (SPD[p1, p1] - 2 SPD[p1, p3] - SPD[p2, p2] + + 2 SPD[p2, p3])^2, {p1, p2, p3}, FDS -> False, FCE -> True]", +"-((MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}])/D) + +(MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}])/D + +(MTD[Lor1, Lor2]*SFAD[{{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}])/D - +(2*mE^2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}])/D + +(MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, {{p1, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p1, p2])/D + (MTD[Lor1, Lor2]*SFAD[{{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p1, p2])/D + +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p1, p3])/D - +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p1, p3])/D - +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p1, p3])/D + +(2*MTD[Lor1, Lor2]*SFAD[{{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p1, p3])/D + +(4*mE^2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p1, p3])/D - (4*mE^2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p1, p3])/D + (2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p1, p3]^2)/D - (2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p1, p3]^2)/D - (2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p1, p3]^2)/D + (4*mE^2*MTD[Lor1, Lor2]* +SFAD[{{p1, 0}, {-mE^2, 1}, 1}, {{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p1, p3]^2)/D - (2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p2, p3])/D + +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}]*SPD[p2, p3])/D - +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p2, p3])/D + +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p2, p3])/D - +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}]*SPD[p2, p3])/D + +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p2, p3])/D + +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p2, p3])/D - +(2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}]*SPD[p2, p3])/D + +(4*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p2, p3])/D - +(2*MTD[Lor1, Lor2]*SFAD[{{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]*SPD[p2, p3])/D - +(4*mE^2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p2, p3])/D + (4*mE^2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}]*SPD[p2, p3])/D - +(4*mE^2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p2, p3])/D - (4*mE^2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p2, p3])/D + (4*mE^2*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p2, p3])/D + (6*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p3, 0}, {-mE^2, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p2, p3]^2)/D - (6*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p1, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p2, p3]^2)/D - (6*MTD[Lor1, Lor2]*SFAD[{{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p2, p3]^2)/D + (12*mE^2*MTD[Lor1, Lor2]* +SFAD[{{p1, 0}, {-mE^2, 1}, 1}, {{p1, 0}, {-mE^2, 1}, 1}, + {{p2, 0}, {-mE^2, 1}, 1}, {{p2, 0}, {-mE^2, 1}, 1}, + {{p3, 0}, {-mE^2, 1}, 1}, {{p1 + p2, 0}, {0, 1}, 1}, + {{p1 + p2, 0}, {0, 1}, 1}, {{-p1 - p2 + p3, 0}, {-mE^2, 1}, 1}]* +SPD[p2, p3]^2)/D"}, +{"fcstFCMultiLoopTID-ID20", "FCMultiLoopTID[ +FAD[q1, q1 - k1, q1 - k1, q1 - k1, q2] SPD[k1 - q1, k1 + q1] SPD[ +q1 - k1, q1 + k1], {q1, q2}]","0"}, +{"fcstFCMultiLoopTID-ID21", "FCMultiLoopTID[ +FAD[q1, q1 - k1, q2, q1 + q2] SPD[2 k1 - q1, q1 + 2 q2], {q1, q2}, +FCE -> True]","2 FAD[q2, q1, q1 + q2, -k1 + q1] SPD[k1, q1] + +4 FAD[q2, q1, q1 + q2, -k1 + q1] SPD[k1, q2] - +FAD[q2, q1, q1 + q2, -k1 + q1] SPD[q1, q1] - +2 FAD[q2, q1, q1 + q2, -k1 + q1] SPD[q1, q2]"}, +{"fcstFCMultiLoopTID-ID22", "FCMultiLoopTID[FVD[q, i] FVD[q, j] SFAD[{{0, p.q}, x}], {q}, +FCE -> True]","0"}, +{"fcstFCMultiLoopTID-ID23", "FCMultiLoopTID[FVD[q, i] FVD[q, j] SFAD[{{0, p.q}, x}, q + p], {q}, +FCE -> True]", +"(1/((-1 + D) SPD[p, p]^2))*SFAD[{{q, 0}, {0, 1}, 1}, {{0, p.(-p + q)}, {x, 1}, +1}] (D x^2 FVD[p, i] FVD[p, j] + +2 x FVD[p, i] FVD[p, j] SPD[p, p] - x^2 MTD[i, j] SPD[p, p] + +FVD[p, i] FVD[p, j] SPD[p, p]^2 - 2 x MTD[i, j] SPD[p, p]^2 - +MTD[i, j] SPD[p, p]^3)"}, +{"fcstFCMultiLoopTID-ID24", "FCMultiLoopTID[ +DCHN[-GSD[k] + me, Dir3, Dir4] FAD[{k, me}, k - q], {k},FCE->True]","me DCHN[1, Dir3, Dir4] FAD[{k, me}, k - q] + ( +DCHN[GSD[q], Dir3, Dir4] FAD[{k, me}])/(2 SPD[q, q]) - (DCHN[GSD[q], Dir3, Dir4] FAD[k, {k - q, me}] (me^2 + SPD[q, q]))/( +2 SPD[q, q])"}, +{"fcstFCMultiLoopTID-ID25", "FCMultiLoopTID[ +DCHN[GAD[mu].(-GSD[k] + me).GAD[nu], Dir3, Dir4] FAD[{k, me}, +k - q], {k}, FCE -> True]","me DCHN[GAD[mu].GAD[nu], Dir3, Dir4] FAD[{k, me}, k - q] + ( +DCHN[GAD[mu].GSD[q].GAD[nu], Dir3, Dir4] FAD[{k, me}])/(2 SPD[q, q]) - (DCHN[GAD[mu].GSD[q].GAD[nu], Dir3, Dir4] FAD[ +k, {k - q, me}] (me^2 + SPD[q, q]))/(2 SPD[q, q])"}, +{"fcstFCMultiLoopTID-ID26", "FCMultiLoopTID[ +DiracTrace[GAD[mu].(GSD[q]).GAD[nu, rho, 5]] FAD[q, q - p], {q}, +DiracSimplify -> False, FCE -> True]","1/2 DiracTrace[GAD[mu].GSD[p].GAD[nu].GAD[rho].GA[5]] FAD[q, -p + q]"}, +{"fcstFCMultiLoopTID-ID27", "FCMultiLoopTID[ +DiracTrace[GAD[mu].(GSD[q] + m).GAD[nu, rho, 5]] FAD[q, q - p], {q}, +DiracSimplify -> False, FCE -> True]","m DiracTrace[GAD[mu].GAD[nu].GAD[rho].GA[5]] FAD[q, -p + q] + +1/2 DiracTrace[GAD[mu].GSD[p].GAD[nu].GAD[rho].GA[5]] FAD[q, -p + q]"} }) diff --git a/Tests/LoopIntegrals/FCReplaceD.test b/Tests/LoopIntegrals/FCReplaceD.test index 86296b89f..ab505f72a 100644 --- a/Tests/LoopIntegrals/FCReplaceD.test +++ b/Tests/LoopIntegrals/FCReplaceD.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCReplaceD *) @@ -14,13 +14,45 @@ (* ------------------------------------------------------------------------ *) Tests`LoopIntegrals`fcstFCReplaceD = { -{"fcstFCReplaceD-ID1","FCReplaceD[SPD[p, p], D -> 4 - 2 Epsilon]","Pair[Momentum[p, D], Momentum[p, D]]"}, -{"fcstFCReplaceD-ID2","FCReplaceD[ScaleMu^(D - 4) SPD[p, p]*D, D -> 4 - 2 Epsilon]", -"(4 - 2 Epsilon) ScaleMu^(-2 Epsilon)*Pair[Momentum[p, D], Momentum[p, D]]"}, -{"fcstFCReplaceD-ID3","FCReplaceD[MTD[mu, nu]*D, D -> 4 - 2 Epsilon]", -"(4 - 2 Epsilon) Pair[LorentzIndex[mu, D], LorentzIndex[nu, D]]"}, -{"fcstFCReplaceD-ID4","FCReplaceD[GAD[i] D, D -> 4 - 2 Eps] // FCE","(4 - 2 Eps) GAD[i]"}, -{"fcstFCReplaceD-ID5","FCReplaceD[GSD[p] D, D -> 4 - 2 Eps] // FCE","(4 - 2 Eps) GSD[p]"}, -{"fcstFCReplaceD-ID6","FCReplaceD[GA[x], D -> 4 - 2 Epsilon] // FCE","GA[x]"}, -{"fcstFCReplaceD-ID7","FCReplaceD[FV[x, i], D -> 4 - 2 Eps] // FCE","FV[x, i]"} +{"fcstFCReplaceD-ID1","FCReplaceD[SPD[p, p], D -> 4 - 2 Epsilon, FCE->True]","SPD[p, p]"}, +{"fcstFCReplaceD-ID2","FCReplaceD[ScaleMu^(D - 4) SPD[p, p]*D, D -> 4 - 2 Epsilon, FCE->True]", +"(4 - 2 Epsilon) ScaleMu^(-2 Epsilon)*SPD[p, p]"}, +{"fcstFCReplaceD-ID3","FCReplaceD[MTD[mu, nu]*D, D -> 4 - 2 Epsilon,FCE->True]", +"(4 - 2 Epsilon) MTD[mu,nu]"}, +{"fcstFCReplaceD-ID4","FCReplaceD[GAD[i] D, D -> 4 - 2 Eps,FCE->True]","(4 - 2 Eps) GAD[i]"}, +{"fcstFCReplaceD-ID5","FCReplaceD[GSD[p] D, D -> 4 - 2 Eps,FCE->True]","(4 - 2 Eps) GSD[p]"}, +{"fcstFCReplaceD-ID6","FCReplaceD[GA[x], D -> 4 - 2 Epsilon,FCE->True]","GA[x]"}, +{"fcstFCReplaceD-ID7","FCReplaceD[FV[x, i], D -> 4 - 2 Eps,FCE->True] ","FV[x, i]"}, +{"fcstFCReplaceD-ID8", "FCReplaceD[CSP[p,p],D\[Rule]4-2 Epsilon]", +"CartesianPair[CartesianMomentum[p], CartesianMomentum[p]]"}, +{"fcstFCReplaceD-ID9", +"FCReplaceD[ScaleMu^(D-4) CSP[p,p]*D,D\[Rule]4-2 Epsilon]", +"((4 - 2*Epsilon)*CartesianPair[CartesianMomentum[p], \ +CartesianMomentum[p]])/ScaleMu^(2*Epsilon)"}, +{"fcstFCReplaceD-ID10", +"FCReplaceD[KD[mu,nu]*(D-1),D\[Rule]4-2 Epsilon]", +"(3 - 2*Epsilon)*CartesianPair[CartesianIndex[mu], CartesianIndex[nu]]"}, +{"fcstFCReplaceD-ID11", +"FCReplaceD[CGAD[i] D,D\[Rule]4-2 Eps,FCE\[Rule]True]", +"(4 - 2*Eps)*CGAD[i]"}, +{"fcstFCReplaceD-ID12", +"FCReplaceD[CGSD[p] D,D\[Rule]4-2 Eps,FCE\[Rule]True]", +"(4 - 2*Eps)*CGSD[p]"}, +{"fcstFCReplaceD-ID13", +"FCReplaceD[SID[i] D,D\[Rule]4-2 Eps,FCE\[Rule]True]", +"(4 - 2*Eps)*SID[i]"}, +{"fcstFCReplaceD-ID14", +"FCReplaceD[SISD[p] D,D\[Rule]4-2 Eps,FCE\[Rule]True]", +"(4 - 2*Eps)*SISD[p]"}, +{"fcstFCReplaceD-ID15", +"FCReplaceD[CSID[i] D,D\[Rule]4-2 Eps,FCE\[Rule]True]", +"(4 - 2*Eps)*CSID[i]"}, +{"fcstFCReplaceD-ID16", +"FCReplaceD[CSISD[p] D,D\[Rule]4-2 Eps,FCE\[Rule]True]", +"(4 - 2*Eps)*CSISD[p]"}, +{"fcstFCReplaceD-ID17", +"FCReplaceD[CGA[x],D\[Rule]4-2 Epsilon,FCE\[Rule]True]", +"CGA[x]"}, +{"fcstFCReplaceD-ID18", +"FCReplaceD[CV[x,i],D\[Rule]4-2 Eps,FCE\[Rule]True]", "CV[x, i]"} } diff --git a/Tests/LoopIntegrals/FeynAmpDenominatorCombine.test b/Tests/LoopIntegrals/FeynAmpDenominatorCombine.test index 778b1e2e3..abf10a77d 100644 --- a/Tests/LoopIntegrals/FeynAmpDenominatorCombine.test +++ b/Tests/LoopIntegrals/FeynAmpDenominatorCombine.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for @@ -17,5 +17,51 @@ Tests`LoopIntegrals`fcstFeynAmpDenominatorCombine = { {"fcstFeynAmpDenominatorCombine-ID1", "FeynAmpDenominatorCombine[FAD[q] FAD[q - p]] // FCE", - "FAD[q, -p + q]"} + "FAD[q, -p + q]"}, +{"fcstFeynAmpDenominatorCombine-ID2", + "FeynAmpDenominatorCombine[GFAD[{SPD[q1, p] SPD[q2, p], 2}] FAD[{p, m}]]", + "FeynAmpDenominator[GenericPropagatorDenominator[ +Pair[Momentum[p, D], Momentum[q1, D]] Pair[Momentum[p, D], + Momentum[q2, D]], {2, 1}], +PropagatorDenominator[Momentum[p, D], m]]"}, +{"fcstFeynAmpDenominatorCombine-ID3", + "FeynAmpDenominatorCombine[ SFAD[{SPD[q1, p] SPD[q2, p], 2}] FAD[{p, m}]]", + "FeynAmpDenominator[PropagatorDenominator[Momentum[p, D], m], +StandardPropagatorDenominator[ +Momentum[Pair[Momentum[p, D], Momentum[q1, D]] Pair[Momentum[p, D], + Momentum[q2, D]], D], 0, -2, {1, 1}]]"}, +{"fcstFeynAmpDenominatorCombine-ID4", + "FeynAmpDenominatorCombine[ +FeynAmpDenominator[CartesianPropagatorDenominator[ +CartesianMomentum[p, -1 + D] - CartesianMomentum[q, -1 + D],0, 0, +{1, -1}]]*FeynAmpDenominator[CartesianPropagatorDenominator[ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]], FCE -> True]", + "CFAD[{{q, 0}, {0, -1}, 1}, {{p - q, 0}, {0, -1}, 1}]"}, +{"fcstFeynAmpDenominatorCombine-ID5", + "FeynAmpDenominatorCombine[ +FeynAmpDenominator[StandardPropagatorDenominator[ + Momentum[p, D] - Momentum[q, D], 0, 0, + {1, -1}]]*FeynAmpDenominator[StandardPropagatorDenominator[ + Momentum[q, D], 0, 0, {1, -1}]], FCE -> True]", +"SFAD[{{q, 0}, {0, -1}, 1}, {{p - q, 0}, {0, -1}, 1}]"}, +{"fcstFeynAmpDenominatorCombine-ID6", + "FeynAmpDenominatorCombine[ +SFAD[{{q1, 0}, {0, -1}, 1}] SFAD[{{-p + q1, 0}, {0, -1}, + 1}] SFAD[{{q1 - q2, 0}, {0, -1}, 1}] SFAD[{{q2, 0}, {0, -1}, 1}], +FCE -> True]", +"SFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, +1}, {{-p + q1, 0}, {0, -1}, 1}, {{q1 - q2, 0}, {0, -1}, 1}]"}, + +{"fcstFeynAmpDenominatorCombine-ID7", + "FeynAmpDenominatorCombine[ +CFAD[{{q1, 0}, {0, -1}, 1}] CFAD[{{-p + q1, 0}, {0, -1}, + 1}] CFAD[{{q1 - q2, 0}, {0, -1}, 1}] CFAD[{{q2, 0}, {0, -1}, 1}], +FCE -> True]", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, +1}, {{-p + q1, 0}, {0, -1}, 1}, {{q1 - q2, 0}, {0, -1}, 1}]"}, +{"fcstFeynAmpDenominatorCombine-ID8", + "FeynAmpDenominatorCombine[ +FAD[p3] FAD[p1 + p2] FAD[q + p2] FAD[q, q + p1], Momentum -> {q}, +FCE -> True]", +"FAD[p1 + p2] FAD[p3] FAD[p2 + q] FAD[q, p1 + q]"} } diff --git a/Tests/LoopIntegrals/FeynAmpDenominatorExplicit.test b/Tests/LoopIntegrals/FeynAmpDenominatorExplicit.test new file mode 100644 index 000000000..afd52ceba --- /dev/null +++ b/Tests/LoopIntegrals/FeynAmpDenominatorExplicit.test @@ -0,0 +1,190 @@ + + +(* :Title: FeynAmpDenominatorExplicit.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for + FeynAmpDenominatorExplicit *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`fcstFeynAmpDenominatorExplicit = { + +{"fcstFeynAmpDenominatorExplicit-ID1", + "FeynAmpDenominatorExplicit[FAD[{q, m}, {q - p, 0}] // FCI] // FCE", + "1/((-m^2 + SPD[q, q]) (SPD[p, p] - 2 SPD[p, q] + SPD[q, q]))"}, +{"fcstFeynAmpDenominatorExplicit-ID2","FeynAmpDenominatorExplicit[FAD[{q, m}, {q - p, 0}] // FCI, + Head -> dummy] // FCE","dummy[1/((-m^2 + SPD[q, q]) (SPD[p, p] - 2 SPD[p, q] + SPD[q, q]))]"}, +{"fcstFeynAmpDenominatorExplicit-ID3","FeynAmpDenominatorExplicit[ + FAD[{q, m}, {q - p, 0}] // FCI // FeynAmpDenominatorSplit, + Head -> dummy] // FCE","dummy[1/(-m^2 + SPD[q, q])] dummy[1/( + SPD[p, p] - 2 SPD[p, q] + SPD[q, q])]"}, +{"fcstFeynAmpDenominatorExplicit-ID4", + "FeynAmpDenominatorExplicit[FAD[{q, m}, {q + p}]] // FCE", + "1/((-m^2 + SPD[q, q]) (SPD[p, p] + 2 SPD[p, q] + SPD[q, q]))" +}, +{"fcstFeynAmpDenominatorExplicit-ID5", + "FeynAmpDenominatorExplicit[FAD[{q, m}, {q + p}], Dimension -> 4]//FCE", + "1/((-m^2 + SP[q, q]) (SP[p, p] + 2 SP[p, q] + SP[q, q]))" +}, +{"fcstFeynAmpDenominatorExplicit-ID6", + "FCClearScalarProducts[]; \n SPD[p, p] = s; FeynAmpDenominatorExplicit[FAD[{p + q, m}], Mandelstam -> {s, t, u, m^2}, FCE->True]", + "1/(-t - u + 2 SPD[p, q] + SPD[q, q])"}, +{"fcstFeynAmpDenominatorExplicit-ID7", + "tmp = FeynAmpDenominatorExplicit[FAD[{p + q, m}], FCE -> True]; \n FCClearScalarProducts[]; \n tmp", + "1/(-m^2 + s + 2 SPD[p, q] + SPD[q, q])"}, +{"fcstFeynAmpDenominatorExplicit-ID8", + "FeynAmpDenominatorExplicit[FAD[{p, SmallVariable[m]}], FCE -> True]", + "1/(-SmallVariable[m]^2 + SPD[p, p])"}, +{"fcstFeynAmpDenominatorExplicit-ID9", + "FeynAmpDenominatorExplicit[FAD[{p, SmallVariable[m]}], FCE -> True, SmallVariable->True]", + "1/(SPD[p, p])"}, +{"fcstFeynAmpDenominatorExplicit-ID10", + "FeynAmpDenominatorExplicit[aa FAD[{q, m}], Denominator -> True, Head -> hd, FCE -> True]", + "aa/hd[-m^2 + SPD[q, q]]"}, +{"fcstFeynAmpDenominatorExplicit-ID11", + "FeynAmpDenominatorExplicit[GFAD[{{SPD[q1, p] SPD[q2, p], 1}, 2}], FCE -> True]", + "1/(SPD[p, q1]^2 SPD[p, q2]^2)"}, +{"fcstFeynAmpDenominatorExplicit-ID12", + "FeynAmpDenominatorExplicit[FAD[{p1 + p2, 0}], ExpandScalarProduct -> False]", + "1/Pair[Momentum[p1, D] + Momentum[p2, D], Momentum[p1, D] + Momentum[p2, D]]"}, +{"fcstFeynAmpDenominatorExplicit-ID13", + "FeynAmpDenominatorExplicit[FAD[{p1 + p2, 0}], ExpandScalarProduct -> False, MomentumCombine -> True]", + "1/Pair[Momentum[p1 + p2, D], Momentum[p1 + p2, D]]"}, +{"fcstFeynAmpDenominatorExplicit-ID14", +"FeynAmpDenominatorExplicit[CFAD[p1],FCE\[Rule]True]", +"CSPD[p1, p1]^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID15", +"FeynAmpDenominatorExplicit[CFAD[p1,p2],FCE\[Rule]True]", +"1/(CSPD[p1, p1]*CSPD[p2, p2])"}, +{"fcstFeynAmpDenominatorExplicit-ID16", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2}}],FCE\[Rule]True]", + "(CSPD[p1, p1] + CSPD[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID17", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},0}],FCE\[Rule]True]\ +", "(CSPD[p1, p1] + CSPD[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID18", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},0,0}],FCE\[Rule]\ +True]", "1"}, +{"fcstFeynAmpDenominatorExplicit-ID19", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},m2}],FCE\[Rule]\ +True]", "(m2 + CSPD[p1, p1] + CSPD[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID20", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},m2,2}],FCE\[Rule]\ +True]", "(m2 + CSPD[p1, p1] + CSPD[p1, p2])^(-2)"}, +{"fcstFeynAmpDenominatorExplicit-ID21", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},m2,n}],FCE\[Rule]\ +True]", "((m2 + CSPD[p1, p1] + CSPD[p1, p2])^(-1))^n"}, +{"fcstFeynAmpDenominatorExplicit-ID22", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},{m2,-1},2}],FCE\ +\[Rule]True]", "(m2 + CSPD[p1, p1] + CSPD[p1, p2])^(-2)"}, +{"fcstFeynAmpDenominatorExplicit-ID23", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},{m2,-1},n}],FCE\ +\[Rule]True]", "((m2 + CSPD[p1, p1] + CSPD[p1, p2])^(-1))^n"}, +{"fcstFeynAmpDenominatorExplicit-ID24", +"FeynAmpDenominatorExplicit[CFAD[p1,Dimension->3],FCE\[Rule]\ +True]", "CSP[p1, p1]^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID25", +"FeynAmpDenominatorExplicit[CFAD[p1,p2,Dimension->3],FCE\[Rule]\ +True]", "1/(CSP[p1, p1]*CSP[p2, p2])"}, +{"fcstFeynAmpDenominatorExplicit-ID26", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2}},Dimension->3],FCE\ +\[Rule]True]", "(CSP[p1, p1] + CSP[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID27", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},0},Dimension->3],\ +FCE\[Rule]True]", "(CSP[p1, p1] + CSP[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID28", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},0,0},Dimension->3],\ +FCE\[Rule]True]", "1"}, +{"fcstFeynAmpDenominatorExplicit-ID29", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},m2},Dimension->3],\ +FCE\[Rule]True]", "(m2 + CSP[p1, p1] + CSP[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID30", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},m2,2},Dimension->3]\ +,FCE\[Rule]True]", "(m2 + CSP[p1, p1] + CSP[p1, p2])^(-2)"}, +{"fcstFeynAmpDenominatorExplicit-ID31", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},m2,n},Dimension->3]\ +,FCE\[Rule]True]", "((m2 + CSP[p1, p1] + CSP[p1, p2])^(-1))^n"}, +{"fcstFeynAmpDenominatorExplicit-ID32", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},{m2,-1},2},\ +Dimension->3],FCE\[Rule]True]", +"(m2 + CSP[p1, p1] + CSP[p1, p2])^(-2)"}, +{"fcstFeynAmpDenominatorExplicit-ID33", +"FeynAmpDenominatorExplicit[CFAD[{{p1,p1.p2},{m2,-1},n},\ +Dimension->3],FCE\[Rule]True]", +"((m2 + CSP[p1, p1] + CSP[p1, p2])^(-1))^n"}, +{"fcstFeynAmpDenominatorExplicit-ID34", +"FeynAmpDenominatorExplicit[SFAD[p1],FCE\[Rule]True]", +"SPD[p1, p1]^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID35", +"FeynAmpDenominatorExplicit[SFAD[p1,p2],FCE\[Rule]True]", +"1/(SPD[p1, p1]*SPD[p2, p2])"}, +{"fcstFeynAmpDenominatorExplicit-ID36", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2}}],FCE\[Rule]True]", + "(SPD[p1, p1] + SPD[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID37", +"FeynAmpDenominatorExplicit[SFAD[{{0,p1.p2}}],FCE\[Rule]True]", +"SPD[p1, p2]^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID38", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},0}],FCE\[Rule]True]\ +", "(SPD[p1, p1] + SPD[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID39", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},0,0}],FCE\[Rule]\ +True]", "1"}, +{"fcstFeynAmpDenominatorExplicit-ID40", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},m2}],FCE\[Rule]\ +True]", "(-m2 + SPD[p1, p1] + SPD[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID41", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},m2,2}],FCE\[Rule]\ +True]", "(-m2 + SPD[p1, p1] + SPD[p1, p2])^(-2)"}, +{"fcstFeynAmpDenominatorExplicit-ID42", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},m2,n}],FCE\[Rule]\ +True]", "((-m2 + SPD[p1, p1] + SPD[p1, p2])^(-1))^n"}, +{"fcstFeynAmpDenominatorExplicit-ID43", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},{m2,-1},2}],FCE\ +\[Rule]True]", "(-m2 + SPD[p1, p1] + SPD[p1, p2])^(-2)"}, +{"fcstFeynAmpDenominatorExplicit-ID44", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},{m2,-1},n}],FCE\ +\[Rule]True]", "((-m2 + SPD[p1, p1] + SPD[p1, p2])^(-1))^n"}, +{"fcstFeynAmpDenominatorExplicit-ID45", +"FeynAmpDenominatorExplicit[SFAD[p1,Dimension->4],FCE\[Rule]\ +True]", "SP[p1, p1]^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID46", +"FeynAmpDenominatorExplicit[SFAD[p1,p2,Dimension->4],FCE\[Rule]\ +True]", "1/(SP[p1, p1]*SP[p2, p2])"}, +{"fcstFeynAmpDenominatorExplicit-ID47", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2}},Dimension->4],FCE\ +\[Rule]True]", "(SP[p1, p1] + SP[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID48", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},0},Dimension->4],\ +FCE\[Rule]True]", "(SP[p1, p1] + SP[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID49", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},0,0},Dimension->4],\ +FCE\[Rule]True]", "1"}, +{"fcstFeynAmpDenominatorExplicit-ID50", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},m2},Dimension->4],\ +FCE\[Rule]True]", "(-m2 + SP[p1, p1] + SP[p1, p2])^(-1)"}, +{"fcstFeynAmpDenominatorExplicit-ID51", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},m2,2},Dimension->4]\ +,FCE\[Rule]True]", "(-m2 + SP[p1, p1] + SP[p1, p2])^(-2)"}, +{"fcstFeynAmpDenominatorExplicit-ID52", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},m2,n},Dimension->4]\ +,FCE\[Rule]True]", "((-m2 + SP[p1, p1] + SP[p1, p2])^(-1))^n"}, +{"fcstFeynAmpDenominatorExplicit-ID53", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},{m2,-1},2},\ +Dimension->4],FCE\[Rule]True]", +"(-m2 + SP[p1, p1] + SP[p1, p2])^(-2)"}, +{"fcstFeynAmpDenominatorExplicit-ID54", +"FeynAmpDenominatorExplicit[SFAD[{{p1,p1.p2},{m2,-1},n},\ +Dimension->4],FCE\[Rule]True]", +"((-m2 + SP[p1, p1] + SP[p1, p2])^(-1))^n"}, +{"fcstFeynAmpDenominatorExplicit-ID55", +"PropagatorDenominatorExplicit[FAD[{q, m}, {q - p, 0}], FCE -> True]", +"1/((-m^2 + SPD[q, q]) (SPD[p, p] - 2 SPD[p, q] + SPD[q, q]))"} +} diff --git a/Tests/LoopIntegrals/FeynAmpDenominatorSimplify.test b/Tests/LoopIntegrals/FeynAmpDenominatorSimplify.test index e2406a06e..c342fb597 100644 --- a/Tests/LoopIntegrals/FeynAmpDenominatorSimplify.test +++ b/Tests/LoopIntegrals/FeynAmpDenominatorSimplify.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for @@ -54,5 +54,123 @@ ApartFF[FAD[{qp, m}, {qp - q}, {qp, M, 2}, {qp - q, M, 2}], {qp}], qp]", "FAD[{qp, M}, {qp, M}, {-q + qp, M}]"}, {"fcstFeynAmpDenominatorSimplify-ID15", "FDS[FAD[{qp, M}, {-q + qp, M, 2}], qp] // FCE", - "FAD[{qp, M}, {qp, M}, {-q + qp, M}]"} + "FAD[{qp, M}, {qp, M}, {-q + qp, M}]"}, +{"fcstFeynAmpDenominatorSimplify-ID16", + "FDS[FAD[p1, p4, p3, p2]] // FCE", + "FAD[p1, p2, p3, p4]"}, +{"fcstFeynAmpDenominatorSimplify-ID17", + "FCE[FDS[x1 FAD[{q1 + p, m}, {q2, m}, {q1 + p - q2}, {q1}] + x2 FAD[{q1 + p, m}, {q1 + p}, {q2, m}], q1, q2]]", + "x2*FAD[q1, {q1, m}, {q2, m}] + x1*FAD[{q1, m}, {q2, m}, -p + q1, q1 - q2]"}, +{"fcstFeynAmpDenominatorSimplify-ID18", + "FDS[SPD[q1, p] SPD[q2, p] SPD[q3, p] FAD[{q1, m}, {q2, m}, {q3,m}, {q1 - q2}, {q2 - q3}, {q1 - q3}], q1, q2, q3]", + "0"}, +{"fcstFeynAmpDenominatorSimplify-ID19", +"FDS[FAD[{q1,m2},{q2,m1}],q1,q2,FCE\[Rule]True]", +"FAD[{q1, m1}, {q2, m2}]"}, +{"fcstFeynAmpDenominatorSimplify-ID20", +"FDS[FAD[{q1,m2},{q2,m1}]-FAD[{q2,m2},{q1,m1}],q1,q2,FCE\[Rule]\ +True]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID21", +"FDS[FAD[{q2,m}] FAD[q1,{-p2+q1,m}]-FAD[{q1,m}] \ +FAD[q2,{-p2+q2,m}],q1,q2]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID22", +"FDS[(1/(4 (1-D)))FAD[q2,-p1+q2] FAD[q1,q1,-p1+q1] (D FVD[p1,mu] \ +FVD[p1,nu]-MTD[mu,nu] SPD[p1,p1])-(1/(4 (1-D)))FAD[q1,-p1+q1] \ +FAD[q2,q2,-p1+q2] (D FVD[p1,mu] FVD[p1,nu]-MTD[mu,nu] \ +SPD[p1,p1]),q1,q2]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID13", +"FDS[FeynAmpDenominator[ + PropagatorDenominator[Momentum[p1] + Momentum[p2], 0]]^3] // FCE", +"FAD[p1 + p2, p1 + p2, p1 + p2, Dimension -> 4]"}, +{"fcstFeynAmpDenominatorSimplify-ID14", +"FDS[(FeynAmpDenominator[ + PropagatorDenominator[Momentum[p1] + Momentum[p2], 0]]^2 - +FeynAmpDenominator[ + PropagatorDenominator[Momentum[p1] + Momentum[p2], 0], + PropagatorDenominator[Momentum[p1] + Momentum[p2], 0]])]", +"0"}, + +{"fcstFeynAmpDenominatorSimplify-ID15", +"FDS[-FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], + PropagatorDenominator[ + 1/2 (-Momentum[k1, D] - Momentum[k2, D]) + Momentum[l, D], m]] - +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], +PropagatorDenominator[-Momentum[k1, D] - Momentum[k2, D] + + 1/2 (Momentum[k1, D] + Momentum[k2, D]) + Momentum[l, D], + m]] , l, FCE -> True]", +"-2*FAD[l, {-k1/2 - k2/2 + l, m}]"}, +{"fcstFeynAmpDenominatorSimplify-ID16", +"FDS[FVD[l, mu] FAD[{l, m}, {l + p, m}] GFAD[{SPD[l, p], 1}], l, +FCE -> True]", +"FAD[{l, m}, {l + p, m}] FVD[l, mu] GFAD[{{SPD[l, p], 1}, 1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID17", +"FDS[FAD[q1, q1 + p, q2, q2 + p], q1, q2, +FeynAmpDenominatorCombine -> False, FCE -> True]", +"FAD[q1, -p + q1] FAD[q2, -p + q2]"}, +{"fcstFeynAmpDenominatorSimplify-ID18","FDS[CFAD[q, {q - p, 0, 2}], q, FCE -> True]", + "CFAD[{{q, 0}, {0, -1}, 1}, {{-p + q, 0}, {0, -1}, 2}]"}, +{"fcstFeynAmpDenominatorSimplify-ID19","FDS[SFAD[q, {q - p, 0, 2}], q, FCE -> True]", + "SFAD[{{q, 0}, {0, 1}, 1}, {{-p + q, 0}, {0, 1}, 2}]"}, +{"fcstFeynAmpDenominatorSimplify-ID20","FDS[SFAD[{{0, (k1 + k3).n}, {0, 1}, 1}], k1, k2, FCE->True]", + "0"}, +{"fcstFeynAmpDenominatorSimplify-ID21", +"FDS[SFAD[-k2-k3-k1],k1,k2,k3,Rename\[Rule]False,\ +DetectLoopTopologies\[Rule]False,FCE\[Rule]True]", +"SFAD[{{k1 + k2 + k3, 0}, {0, 1}, 1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID22", +"FDS[CFAD[-k2-k3-k1],k1,k2,k3,Rename\[Rule]False,\ +DetectLoopTopologies\[Rule]False,FCE\[Rule]True]", +"CFAD[{{k1 + k2 + k3, 0}, {0, -1}, 1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID23", +"FDS[SFAD[-k2-k3-k1],k1,k2,Rename\[Rule]False,DetectLoopTopologies\ +\[Rule]False,FCE\[Rule]True]", "SFAD[{{k1 + k2 + k3, 0}, {0, 1}, 1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID24", +"FDS[CFAD[-k2-k3-k1],k1,k2,Rename\[Rule]False,DetectLoopTopologies\ +\[Rule]False,FCE\[Rule]True]", "CFAD[{{k1 + k2 + k3, 0}, {0, -1}, 1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID25", +"FDS[SFAD[q, q - p, {{0, q.k}}], q, FCE -> True]", "SFAD[{{q, 0}, +{0, 1}, 1}, {{0, k.q}, {0, 1}, 1}, {{p - q, 0}, {0, 1}, +1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID26", +"FDS[SFAD[q, q - p, {{0, q.k}}], q, FCE -> True]", +"SFAD[{{q, 0}, {0, 1}, 1}, {{0, k.q}, {0, 1}, 1}, {{p - q, 0}, {0, 1},1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID27", +"FDS[SFAD[q, q - p, {{q, q.k}}], q, FCE -> True]", +"SFAD[{{q, 0}, {0, 1}, 1}, {{-p + q, 0}, {0, 1}, 1}, {{q, k.q}, {0, 1},1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID28", +"FDS[SFAD[{{0, p.q}}], q]","0"}, +{"fcstFeynAmpDenominatorSimplify-ID29", +"FDS[SFAD[{{p, p.q}}], q, FCE -> True]","SFAD[{{p, p.q}, {0, 1}, 1}]"}, +{"fcstFeynAmpDenominatorSimplify-ID30", +"FDS[SFAD[{{0, p.q}, m^2}], q]","0"}, +{"fcstFeynAmpDenominatorSimplify-ID31", +"FDS[TC[q]^2 SFAD[q] CVD[q, i] CVD[q, j], q,FCE->True]", +"CVD[q, i] CVD[q, j] SFAD[{{q, 0}, {0, 1}, 1}] TC[q]^2"}, +{"fcstFeynAmpDenominatorSimplify-ID32", +"FDS[SFAD[{{0,2q.(p+r)},0,2}],q,FCE->True]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID33", +"FDS[SFAD[{{0,2q.(p+r)}},{{0,2q.(p+b)}}],q,FCE->True]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID34", +"FDS[SFAD[q,{{0,2q.(p+r)},0,2}],q,FCE->True]", +"SFAD[{{q, 0}, {0, 1}, 1}, {{0, 2*q . (p + r)}, {0, 1}, 2}]"}, +{"fcstFeynAmpDenominatorSimplify-ID35", +"FDS[CFAD[{{0,2q.(p+r)},0,2}],q,FCE->True]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID36", +"FDS[CFAD[{{0,2q.(p+r)}},{{0,2q.(p+b)}}],q]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID37", +"FDS[CFAD[q,{{0,2q.(p+r)},0,2}],q,FCE->True]", +"CFAD[{{q, 0}, {0, -1}, 1}, {{0, 2*q . (p + r)}, {0, -1}, 2}]"}, +{"fcstFeynAmpDenominatorSimplify-ID38", +"FDS[TC[q]SFAD[q],q,FCE->True]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID39", +"FDS[TC[q]^2SFAD[q],q,FCE->True]", +"SFAD[{{q, 0}, {0, 1}, 1}]*TC[q]^2"}, +{"fcstFeynAmpDenominatorSimplify-ID40", +"FDS[CFAD[{q,0,2}],q,FCE->True]", "0"}, +{"fcstFeynAmpDenominatorSimplify-ID41", +"FDS[(FAD[{l, m1}, {l - p, m2}] SPD[l, p2]^2 (GSD[p2] SPD[p, p] - +GSD[p] SPD[p, p2]))/(-SPD[p, p2]^2 + +SPD[p, p] SPD[p2, p2]) - (FAD[{l, m1}, {l + p, m2}] SPD[l, +p2]^2 (GSD[p2] SPD[p, p] - GSD[p] SPD[p, p2]))/(-SPD[p, p2]^2 + +SPD[p, p] SPD[p2, p2]), l]", "0"} } diff --git a/Tests/LoopIntegrals/FeynAmpDenominatorSplit.test b/Tests/LoopIntegrals/FeynAmpDenominatorSplit.test index d3276fab2..e77c6220d 100644 --- a/Tests/LoopIntegrals/FeynAmpDenominatorSplit.test +++ b/Tests/LoopIntegrals/FeynAmpDenominatorSplit.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for @@ -23,5 +23,44 @@ Tests`LoopIntegrals`fcstFeynAmpDenominatorSplit = { {"fcstFeynAmpDenominatorSplit-ID3", "FeynAmpDenominatorSplit[FAD[q1, q2, p + k, q1 - p, p - k, q1, l, q3],Momentum -> {q1, q2, q3}] // FCE", "FAD[k + p, -k + p, l] FAD[q1, q2, -p + q1, q1, q3]" -} +}, +{"fcstFeynAmpDenominatorSplit-ID4", + "FeynAmpDenominatorSplit[FeynAmpDenominator[PropagatorDenominator[Momentum[p + r + l, D], m1], PropagatorDenominator[Momentum[q, D], m2]]]", + "FeynAmpDenominator[PropagatorDenominator[Momentum[q, D], m2]] FeynAmpDenominator[PropagatorDenominator[Momentum[l, D] + Momentum[p, D] + Momentum[r, D], m1]]" +}, +{"fcstFeynAmpDenominatorSplit-ID5", + "FeynAmpDenominatorSplit[FeynAmpDenominator[PropagatorDenominator[Momentum[p + r + l, D], m1], PropagatorDenominator[Momentum[q, D], m2]], MomentumExpand -> False]", + "FeynAmpDenominator[PropagatorDenominator[Momentum[q, D], m2]] FeynAmpDenominator[PropagatorDenominator[Momentum[l + p + r, D], m1]]" +}, +{"fcstFeynAmpDenominatorSplit-ID6", + "FeynAmpDenominatorSplit[ +FeynAmpDenominator[myPD[CartesianMomentum[q1], m1], myPD[CartesianMomentum[q2], m2], myPD[CartesianMomentum[q3], m3]]]", + "FeynAmpDenominator[myPD[CartesianMomentum[q1], m1]] FeynAmpDenominator[myPD[CartesianMomentum[q2], m2]] FeynAmpDenominator[myPD[CartesianMomentum[q3], m3]]" +}, +{"fcstFeynAmpDenominatorSplit-ID7", + "FeynAmpDenominatorSplit[FeynAmpDenominator[myPD[CartesianMomentum[q1], m1], myPD[CartesianMomentum[q2], m2],myPD[CartesianMomentum[q3], m3]], Momentum -> {q1}]", + "FeynAmpDenominator[myPD[CartesianMomentum[q1], m1]] FeynAmpDenominator[myPD[CartesianMomentum[q2], m2], myPD[CartesianMomentum[q3], m3]]" +}, +{"fcstFeynAmpDenominatorSplit-ID8", + "FeynAmpDenominatorSplit[FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[p, D], Momentum[q1, D]] Pair[Momentum[p, D], Momentum[q2, D]], {2, 1}], + PropagatorDenominator[Momentum[p, D], m]], FCE -> True]", + "FAD[{p, m}] GFAD[{{SPD[p, q1] SPD[p, q2], 1}, 2}]" +}, +{"fcstFeynAmpDenominatorSplit-ID9", + "FeynAmpDenominatorSplit[FAD[q, q + p, q - a, q2], List -> True, FCE -> True]", + "{FAD[q], FAD[p + q], FAD[-a + q], FAD[q2]}" +}, +{"fcstFeynAmpDenominatorSplit-ID10", + "FeynAmpDenominatorSplit[CFAD[q, q + p, q2 - p, q - a, q2], +List -> True, Momentum -> {q}, FCE -> True]", + "{CFAD[{{-p + q2, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}], +CFAD[{{q, 0}, {0, -1}, 1}, {{p + q, 0}, {0, -1}, +1}, {{-a + q, 0}, {0, -1}, 1}]}" +}, +{"fcstFeynAmpDenominatorSplit-ID11", + "FeynAmpDenominatorSplit[SFAD[q, q + p, q - a, q2], List -> True, FCE -> True]", + "{SFAD[{{q, 0}, {0, 1}, 1}], SFAD[{{p + q, 0}, {0, 1}, 1}], +SFAD[{{-a + q, 0}, {0, 1}, 1}], SFAD[{{q2, 0}, {0, 1}, 1}]}"} + + } diff --git a/Tests/LoopIntegrals/IntegrationTests/OneLoopMisc.test b/Tests/LoopIntegrals/IntegrationTests/OneLoopMisc.test new file mode 100644 index 000000000..e15345205 --- /dev/null +++ b/Tests/LoopIntegrals/IntegrationTests/OneLoopMisc.test @@ -0,0 +1,9 @@ +Tests`LoopIntegrals`fcitOneLoopMiscTests = +({ +{"fcitOneLoopMiscTests-ID1","Simplify[PaVeReduce[(OneLoop[k, +FVD[k, i] SPD[k, p] SPD[k] FAD[{k + p - q, mw}, {k + p + q, mw}, {k, my}]] - +OneLoop[k, FVD[k, i] SPD[k, p] SPD[k] FAD[{k + p - q, mw}, {k + p + q, mw}, {k, mu}]]) /. mu -> my]]", "0"}, +{"fcitOneLoopMiscTests-ID2","Simplify[PaVeReduce[OneLoop[k, ChangeDimension[ FCI[SP[k] SP[k, p] FourVector[k, +a] FAD[{k + p - q, mw}, {k + p + q, mw}, {k, my}]], D]]] -PaVeReduce[OneLoop[k, ChangeDimension[FCI[SP[k] SP[k, +p] FourVector[k, a] FAD[{k + p - q, mw}, {k + p + q, mw}, {k, my}]], D]]]]", "0"} +}) diff --git a/Tests/LoopIntegrals/IntegrationTests/TIDL.test b/Tests/LoopIntegrals/IntegrationTests/TIDL.test new file mode 100644 index 000000000..139869613 --- /dev/null +++ b/Tests/LoopIntegrals/IntegrationTests/TIDL.test @@ -0,0 +1,84 @@ +Tests`LoopIntegrals`fcitTIDL = +({ +{"fcitTIDL-ID1", +"Together[Contract[MTD[mu1,mu2]Tdec[{{p1,mu1},{p2,mu2}},{},List\ +\[Rule]False]]]", "Pair[Momentum[p1, D], Momentum[p2, D]]"}, +{"fcitTIDL-ID2", +"Together[Contract[MTD[mu1,mu2]Tdec[{{p1,mu1},{p2,mu2}},{q1},List\ +\[Rule]False]]]", "Pair[Momentum[p1, D], Momentum[p2, D]]"}, +{"fcitTIDL-ID3", +"Together[Contract[MTD[mu1,mu2]Tdec[{{p1,mu1},{p2,mu2}},{q1,q2},\ +List\[Rule]False]]]", "Pair[Momentum[p1, D], Momentum[p2, D]]"}, +{"fcitTIDL-ID4", +"Together[Contract[MTD[mu1,mu2]Tdec[{{p1,mu1},{p2,mu2}},{q1,q2,q3},\ +List\[Rule]False]]]", "Pair[Momentum[p1, D], Momentum[p2, D]]"}, +{"fcitTIDL-ID5", +"Together[Contract[MTD[mu1,mu2]Tdec[{{p1,mu1},{p2,mu2}},{q1,q2,q3,\ +q4},List\[Rule]False]]]", "Pair[Momentum[p1, D], Momentum[p2, D]]"}, +{"fcitTIDL-ID6", +"Together[Contract[MTD[mu1,mu2]FVD[q1,mu3]Tdec[{{p1,mu1},{p1,mu2},{\ +p2,mu3}},{},List\[Rule]False]]]", "0"}, +{"fcitTIDL-ID7", +"Together[Contract[MTD[mu1,mu2]FVD[q1,mu3]Tdec[{{p1,mu1},{p1,mu2},{\ +p2,mu3}},{q1},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[q1, D]]"}, +{"fcitTIDL-ID8", +"Together[Contract[MTD[mu1,mu2]FVD[q1,mu3]Tdec[{{p1,mu1},{p1,mu2},{\ +p2,mu3}},{q1,q2},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[q1, D]]"}, +{"fcitTIDL-ID9", +"Together[Contract[MTD[mu1,mu2]FVD[q1,mu3]Tdec[{{p1,mu1},{p1,mu2},{\ +p2,mu3}},{q1,q2,q3},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[q1, D]]"}, +{"fcitTIDL-ID10", +"Together[Contract[MTD[mu1,mu2]MTD[mu3,mu4]Tdec[{{p1,mu1},{p1,mu2},\ +{p1,mu3},{p2,mu4}},{},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p1, D], \ +Momentum[p2, D]]"}, +{"fcitTIDL-ID11", +"Together[Contract[MTD[mu1,mu2]MTD[mu3,mu4]Tdec[{{p1,mu1},{p1,mu2},\ +{p1,mu3},{p2,mu4}},{q1},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p1, D], \ +Momentum[p2, D]]"}, +{"fcitTIDL-ID12", +"Together[Contract[MTD[mu1,mu2]MTD[mu3,mu4]Tdec[{{p1,mu1},{p1,mu2},\ +{p1,mu3},{p2,mu4}},{q1,q2},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p1, D], \ +Momentum[p2, D]]"}, +{"fcitTIDL-ID13", +"Together[Contract[MTD[mu1,mu2]MTD[mu3,mu4]Tdec[{{p1,mu1},{p1,mu2},\ +{p2,mu3},{p2,mu4}},{},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]]"}, +{"fcitTIDL-ID14", +"Together[Contract[MTD[mu1,mu2]MTD[mu3,mu4]Tdec[{{p1,mu1},{p1,mu2},\ +{p2,mu3},{p2,mu4}},{q1},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]]"}, +{"fcitTIDL-ID15", +"Together[Contract[MTD[mu1,mu2]MTD[mu3,mu4]Tdec[{{p1,mu1},{p1,mu2},\ +{p2,mu3},{p2,mu4}},{q1,q2},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]]"}, +{"fcitTIDL-ID16", +"Together[Contract[MTD[mu1,mu2]FVD[q1,mu3]Tdec[{{p1,mu1},{p2,mu2},{\ +p3,mu3}},{},List\[Rule]False]]]", "0"}, +{"fcitTIDL-ID17", +"Together[Contract[MTD[mu1,mu2]FVD[q1,mu3]Tdec[{{p1,mu1},{p2,mu2},{\ +p3,mu3}},{q1},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p3, D], \ +Momentum[q1, D]]"}, +{"fcitTIDL-ID18", +"Together[Contract[MTD[mu1,mu2]FVD[q1,mu3]Tdec[{{p1,mu1},{p2,mu2},{\ +p3,mu3}},{q1,q2},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p3, D], \ +Momentum[q1, D]]"}, +{"fcitTIDL-ID19", +"Together[Contract[MTD[mu1,mu2]MTD[mu3,mu4]Tdec[{{p1,mu1},{p2,mu2},\ +{p3,mu3},{p4,mu4}},{},List\[Rule]False]]]", +"Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p3, D], \ +Momentum[p4, D]]"} +}) diff --git a/Tests/LoopIntegrals/IntegrationTests/TIDMTests.test b/Tests/LoopIntegrals/IntegrationTests/TIDMTests.test index 30125d442..6c716471b 100644 --- a/Tests/LoopIntegrals/IntegrationTests/TIDMTests.test +++ b/Tests/LoopIntegrals/IntegrationTests/TIDMTests.test @@ -3,168 +3,96 @@ Tests`LoopIntegrals`fcitTIDMTests = {"fcitTIDMTests-ID1", "TID[FAD[{z,M},{k+z,M},{-k+pp-z,MD},{p-z,m}] GSD[z] \ SPD[k,z],z]//FCE", -"(FAD[{z, M}, {-k - p + z, m}]*(-(GSD[pp]*(SPD[k, k] + 2*SPD[k, p] \ -+ SPD[p, p])) + GSD[-k - p]*(-SPD[k, pp] - SPD[p, pp])))/(4*((-SPD[k, \ -pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, \ -pp])) + (FAD[{z, M}, {-pp + z, MD}]*(-(GSD[pp]*(-SPD[k, pp] - SPD[p, \ -pp])) + GSD[-k - p]*SPD[pp, pp]))/(4*((-SPD[k, pp] - SPD[p, pp])^2 - \ -(SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])) + (FAD[{z, m}, \ -{-p + z, M}]*(GSD[-k + pp]*SPD[p, p] - GSD[p]*(-SPD[k, p] + SPD[p, \ -pp])))/(4*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]))) - (FAD[{z, MD}, {-k + pp + z, \ -M}]*(GSD[-k + pp]*(-SPD[k, p] + SPD[p, pp]) - GSD[p]*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp])))/(4*((-SPD[k, p] + SPD[p, pp])^2 - \ -SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) + (FAD[{z, M}, \ -{k + z, M}, {-p + z, m}]*SPD[k, k]*(GSD[-k + pp]*(SPD[k, p]^2 - \ -SPD[k, k]*SPD[p, p]) - GSD[p]*(SPD[k, p]*(-SPD[k, k] + SPD[k, pp]) - \ -SPD[k, k]*(-SPD[k, p] + SPD[p, pp])) - GSD[k]*(-((-SPD[k, k] + SPD[k, \ -pp])*SPD[p, p]) + SPD[k, p]*(-SPD[k, p] + SPD[p, pp]))))/(4*((-SPD[k, \ -k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, \ -pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, \ -pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - \ -SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) + \ -(FAD[{z, M}, {-k + z, M}, {-pp + z, MD}]*SPD[k, k]*(GSD[-k + \ -pp]*(-(SPD[k, p]*(-SPD[k, k] + SPD[k, pp])) + SPD[k, k]*(-SPD[k, p] + \ -SPD[p, pp])) - GSD[p]*(-(-SPD[k, k] + SPD[k, pp])^2 + SPD[k, \ -k]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - GSD[k]*((-SPD[k, k] + \ -SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) - SPD[k, p]*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]))))/(4*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, \ -p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) \ -+ SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]))) - (FAD[{z, MD}, {-k - p + pp + z, \ -m}]*(GSD[-k + pp]*SPD[p, p]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, \ -k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) - GSD[p]*(-SPD[k, p] + \ -SPD[p, pp])*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] \ -+ SPD[p, p])*SPD[pp, pp]) - GSD[-k + pp]*(-SPD[k, p] + SPD[p, \ -pp])*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + \ -SPD[p, p])*SPD[pp, pp]) + GSD[p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, \ -pp])*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + \ -SPD[p, p])*SPD[pp, pp]) - GSD[pp]*(SPD[k, k] + 2*SPD[k, p] + SPD[p, \ -p])*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, \ -pp] + SPD[pp, pp])) + GSD[-k - p]*(-SPD[k, pp] - SPD[p, \ -pp])*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, \ -pp] + SPD[pp, pp])) - GSD[pp]*(-SPD[k, pp] - SPD[p, pp])*((-SPD[k, p] \ -+ SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) \ -+ GSD[-k - p]*SPD[pp, pp]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, \ -p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))))/(4*((-SPD[k, pp] - \ -SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, \ -pp])*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, \ -pp] + SPD[pp, pp]))) - (FAD[{z, M}, {-k + z, M}, {p + z, m}, {-k + pp \ -+ z, MD}]*SPD[k, k]*(-(GSD[-k + pp]*(m^2 - M^2 - SPD[p, p])*(-(SPD[k, \ -p]*(-SPD[k, k] + SPD[k, pp])) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp]))) \ -- GSD[-k + pp]*SPD[k, k]*((-SPD[k, k] + SPD[k, pp])*SPD[p, p] - \ -SPD[k, p]*(-SPD[k, p] + SPD[p, pp])) + GSD[-k + pp]*(SPD[k, p]^2 - \ -SPD[k, k]*SPD[p, p])*(M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] + SPD[pp, \ -pp]) - GSD[p]*(SPD[k, p]*(-SPD[k, k] + SPD[k, pp]) - SPD[k, \ -k]*(-SPD[k, p] + SPD[p, pp]))*(M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] \ -+ SPD[pp, pp]) - GSD[k]*(-((-SPD[k, k] + SPD[k, pp])*SPD[p, p]) + \ -SPD[k, p]*(-SPD[k, p] + SPD[p, pp]))*(M^2 - MD^2 + SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]) + GSD[p]*(m^2 - M^2 - SPD[p, \ -p])*(-(-SPD[k, k] + SPD[k, pp])^2 + SPD[k, k]*(SPD[k, k] - 2*SPD[k, \ -pp] + SPD[pp, pp])) + GSD[p]*SPD[k, k]*((-SPD[k, k] + SPD[k, \ -pp])*(-SPD[k, p] + SPD[p, pp]) - SPD[k, p]*(SPD[k, k] - 2*SPD[k, pp] \ -+ SPD[pp, pp])) + GSD[k]*(m^2 - M^2 - SPD[p, p])*((-SPD[k, k] + \ -SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) - SPD[k, p]*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp])) + GSD[k]*SPD[k, k]*(-(-SPD[k, p] + \ -SPD[p, pp])^2 + SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, \ -pp]))))/(4*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, \ -p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, \ -k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, \ -pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + \ -SPD[pp, pp]))) - (FAD[{z, M}, {p + z, m}, {-k + pp + z, MD}]*(GSD[-k \ -+ pp]*SPD[k, k]*((-SPD[k, k] + SPD[k, pp])*SPD[p, p] - SPD[k, \ -p]*(-SPD[k, p] + SPD[p, pp]))*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, \ -p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - GSD[p]*SPD[k, \ -k]*((-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) - SPD[k, \ -p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))*((-SPD[k, p] + SPD[p, \ -pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - \ -GSD[k]*SPD[k, k]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] \ -- 2*SPD[k, pp] + SPD[pp, pp]))*(-(-SPD[k, p] + SPD[p, pp])^2 + SPD[p, \ -p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + GSD[-k + pp]*(m^2 - \ -M^2 - SPD[p, p])*(-SPD[k, p] + SPD[p, pp])*((-SPD[k, k] + SPD[k, \ -pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] \ -+ SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, \ -p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, \ -p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - GSD[p]*(m^2 - M^2 - \ -SPD[p, p])*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])*((-SPD[k, k] + \ -SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, \ -pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, \ -pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - \ -SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + \ -GSD[-k + pp]*SPD[p, p]*(M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] + \ -SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, \ -p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, \ -k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, \ -pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + \ -SPD[pp, pp])) - GSD[p]*(-SPD[k, p] + SPD[p, pp])*(M^2 - MD^2 + SPD[k, \ -k] - 2*SPD[k, pp] + SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, \ -p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) \ -+ SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]))))/(4*((-SPD[k, p] + SPD[p, pp])^2 - \ -SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))*((-SPD[k, k] + \ -SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, \ -pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, \ -pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - \ -SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) + \ -(FAD[{z, M}, {-pp + z, MD}, {-k - p + z, m}]*(-(GSD[-k + pp]*SPD[k, \ -k]*(SPD[k, p]^2 - SPD[k, k]*SPD[p, p])*((-SPD[k, pp] - SPD[p, pp])^2 \ -- (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])) + GSD[p]*SPD[k, \ -k]*(SPD[k, p]*(-SPD[k, k] + SPD[k, pp]) - SPD[k, k]*(-SPD[k, p] + \ -SPD[p, pp]))*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] \ -+ SPD[p, p])*SPD[pp, pp]) - GSD[-k + pp]*SPD[k, k]*(-(SPD[k, \ -p]*(-SPD[k, k] + SPD[k, pp])) + SPD[k, k]*(-SPD[k, p] + SPD[p, \ -pp]))*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + \ -SPD[p, p])*SPD[pp, pp]) + GSD[-k + pp]*SPD[k, k]*((-SPD[k, k] + \ -SPD[k, pp])*SPD[p, p] - SPD[k, p]*(-SPD[k, p] + SPD[p, \ -pp]))*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + \ -SPD[p, p])*SPD[pp, pp]) + GSD[k]*SPD[k, k]*(-((-SPD[k, k] + SPD[k, \ -pp])*SPD[p, p]) + SPD[k, p]*(-SPD[k, p] + SPD[p, pp]))*((-SPD[k, pp] \ -- SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) \ -+ GSD[p]*SPD[k, k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + \ -2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])*(-(-SPD[k, k] + SPD[k, pp])^2 + \ -SPD[k, k]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + GSD[k]*SPD[k, \ -k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, \ -p])*SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) \ -- SPD[k, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - GSD[p]*SPD[k, \ -k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, \ -p])*SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) \ -- SPD[k, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - GSD[k]*SPD[k, \ -k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, \ -p])*SPD[pp, pp])*(-(-SPD[k, p] + SPD[p, pp])^2 + SPD[p, p]*(SPD[k, k] \ -- 2*SPD[k, pp] + SPD[pp, pp])) - GSD[pp]*(m^2 - M^2 - SPD[k, k] - \ -2*SPD[k, p] - SPD[p, p])*(-SPD[k, pp] - SPD[p, pp])*((-SPD[k, k] + \ -SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, \ -pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, \ -pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - \ -SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + \ -GSD[-k - p]*(m^2 - M^2 - SPD[k, k] - 2*SPD[k, p] - SPD[p, p])*SPD[pp, \ -pp]*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] \ -+ SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + \ -SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) \ -- SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + \ -GSD[pp]*(SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*(M^2 - MD^2 + SPD[pp, \ -pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] \ -+ SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + \ -SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) \ -- SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - \ -GSD[-k - p]*(-SPD[k, pp] - SPD[p, pp])*(M^2 - MD^2 + SPD[pp, \ -pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] \ -+ SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + \ -SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) \ -- SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + \ -2*GSD[k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + \ -SPD[p, p])*SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - \ -2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + \ -SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - \ -2*SPD[k, pp] + SPD[pp, pp]))))/(4*((-SPD[k, pp] - SPD[p, pp])^2 - \ -(SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])*((-SPD[k, k] + \ -SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, \ -pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, \ -pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - \ -SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])))"}, +"-(FAD[{z, M}, {-k - p + z, m}]*(GSD[pp]*SPD[k, k] + 2*GSD[pp]*SPD[k, p] + GSD[-k - p]*SPD[k, pp] + GSD[pp]*SPD[p, p] + GSD[-k - p]*SPD[p, pp]))/ +(4*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])) + (FAD[{z, M}, {-pp + z, MD}]*(GSD[pp]*SPD[k, pp] + GSD[pp]*SPD[p, pp] + GSD[-k - p]*SPD[pp, pp]))/ +(4*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])) + (FAD[{z, m}, {-p + z, M}]*(GSD[p]*SPD[k, p] + GSD[-k + pp]*SPD[p, p] - GSD[p]*SPD[p, pp]))/ +(4*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) + +(FAD[{z, MD}, {-k + pp + z, M}]*(GSD[p]*SPD[k, k] + GSD[-k + pp]*SPD[k, p] - 2*GSD[p]*SPD[k, pp] - GSD[-k + pp]*SPD[p, pp] + GSD[p]*SPD[pp, pp]))/ +(4*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) + +(FAD[{z, M}, {k + z, M}, {-p + z, m}]*SPD[k, k]*(GSD[-k + pp]*(SPD[k, p]^2 - SPD[k, k]*SPD[p, p]) - GSD[p]*(SPD[k, p]*(-SPD[k, k] + SPD[k, pp]) - SPD[k, k]*(-SPD[k, p] + SPD[p, pp])) - + GSD[k]*(-((-SPD[k, k] + SPD[k, pp])*SPD[p, p]) + SPD[k, p]*(-SPD[k, p] + SPD[p, pp]))))/ +(4*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) + +(FAD[{z, M}, {-k + z, M}, {-pp + z, MD}]*SPD[k, k]*(GSD[-k + pp]*(-(SPD[k, p]*(-SPD[k, k] + SPD[k, pp])) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])) - + GSD[p]*(-(-SPD[k, k] + SPD[k, pp])^2 + SPD[k, k]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[k]*((-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) - SPD[k, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))))/ +(4*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) + +(FAD[{z, MD}, {-k - p + pp + z, m}]*(-(GSD[p]*SPD[k, k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])) - + GSD[-k + p + pp]*SPD[k, p]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) + + 2*GSD[p]*SPD[k, pp]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) - + GSD[-k + pp]*SPD[p, p]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) + + GSD[-k + p + pp]*SPD[p, pp]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) - + GSD[p]*SPD[pp, pp]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) + + GSD[pp]*SPD[k, k]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + 2*GSD[pp]*SPD[k, p]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[k + p + pp]*SPD[k, pp]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[pp]*SPD[p, p]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[k + p + pp]*SPD[p, pp]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[-k - p]*SPD[pp, pp]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))))/(4*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])* +((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) - +(FAD[{z, M}, {-k + z, M}, {p + z, m}, {-k + pp + z, MD}]*SPD[k, k]*(-(GSD[-k + pp]*(m^2 - M^2 - SPD[p, p])*(-(SPD[k, p]*(-SPD[k, k] + SPD[k, pp])) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp]))) - + GSD[-k + pp]*SPD[k, k]*((-SPD[k, k] + SPD[k, pp])*SPD[p, p] - SPD[k, p]*(-SPD[k, p] + SPD[p, pp])) + GSD[-k + pp]*(SPD[k, p]^2 - SPD[k, k]*SPD[p, p])* + (M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - GSD[p]*(SPD[k, p]*(-SPD[k, k] + SPD[k, pp]) - SPD[k, k]*(-SPD[k, p] + SPD[p, pp]))* + (M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - GSD[k]*(-((-SPD[k, k] + SPD[k, pp])*SPD[p, p]) + SPD[k, p]*(-SPD[k, p] + SPD[p, pp]))* + (M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) + GSD[p]*(m^2 - M^2 - SPD[p, p])*(-(-SPD[k, k] + SPD[k, pp])^2 + SPD[k, k]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[p]*SPD[k, k]*((-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) - SPD[k, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[k]*(m^2 - M^2 - SPD[p, p])*((-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) - SPD[k, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[k]*SPD[k, k]*(-(-SPD[k, p] + SPD[p, pp])^2 + SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))))/ +(4*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) - +(FAD[{z, M}, {p + z, m}, {-k + pp + z, MD}]*(GSD[-k + pp]*SPD[k, k]*((-SPD[k, k] + SPD[k, pp])*SPD[p, p] - SPD[k, p]*(-SPD[k, p] + SPD[p, pp]))* + ((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - GSD[p]*SPD[k, k]*((-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) - + SPD[k, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[k]*SPD[k, k]*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))*(-(-SPD[k, p] + SPD[p, pp])^2 + SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[p]*SPD[k, k]*(m^2 - M^2 - SPD[p, p])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[-k + pp]*SPD[k, p]*(m^2 - M^2 - SPD[p, p])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + 2*GSD[p]*SPD[k, pp]*(m^2 - M^2 - SPD[p, p])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[-k + pp]*(m^2 - M^2 - SPD[p, p])*SPD[p, pp]*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[p]*(m^2 - M^2 - SPD[p, p])*SPD[pp, pp]*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + GSD[p]*SPD[k, p]*(M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])* + ((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[-k + pp]*SPD[p, p]*(M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - + GSD[p]*SPD[p, pp]*(M^2 - MD^2 + SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))))/ +(4*((-SPD[k, p] + SPD[p, pp])^2 - SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))) + +(FAD[{z, M}, {-pp + z, MD}, {-k - p + z, m}]*(-(GSD[-k + pp]*SPD[k, k]*(SPD[k, p]^2 - SPD[k, k]*SPD[p, p])*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])) + + GSD[p]*SPD[k, k]*(SPD[k, p]*(-SPD[k, k] + SPD[k, pp]) - SPD[k, k]*(-SPD[k, p] + SPD[p, pp]))*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) - + GSD[-k + pp]*SPD[k, k]*(-(SPD[k, p]*(-SPD[k, k] + SPD[k, pp])) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp]))*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) + + GSD[-k + pp]*SPD[k, k]*((-SPD[k, k] + SPD[k, pp])*SPD[p, p] - SPD[k, p]*(-SPD[k, p] + SPD[p, pp]))*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) + + GSD[k]*SPD[k, k]*(-((-SPD[k, k] + SPD[k, pp])*SPD[p, p]) + SPD[k, p]*(-SPD[k, p] + SPD[p, pp]))*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp]) + + GSD[p]*SPD[k, k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])*(-(-SPD[k, k] + SPD[k, pp])^2 + SPD[k, k]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[k - p]*SPD[k, k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) - + SPD[k, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) - GSD[k]*SPD[k, k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])* + (-(-SPD[k, p] + SPD[p, pp])^2 + SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + GSD[pp]*SPD[k, pp]*(m^2 - M^2 - SPD[k, k] - 2*SPD[k, p] - SPD[p, p])* + ((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + GSD[pp]*(m^2 - M^2 - SPD[k, k] - 2*SPD[k, p] - SPD[p, p])*SPD[p, pp]* + ((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + GSD[-k - p]*(m^2 - M^2 - SPD[k, k] - 2*SPD[k, p] - SPD[p, p])*SPD[pp, pp]* + ((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[pp]*SPD[k, k]*(M^2 - MD^2 + SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + 2*GSD[pp]*SPD[k, p]*(M^2 - MD^2 + SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[-k - p]*SPD[k, pp]*(M^2 - MD^2 + SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[pp]*SPD[p, p]*(M^2 - MD^2 + SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + GSD[-k - p]*SPD[p, pp]*(M^2 - MD^2 + SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])) + + 2*GSD[k]*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])*((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - + 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - + SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]))))/(4*((-SPD[k, pp] - SPD[p, pp])^2 - (SPD[k, k] + 2*SPD[k, p] + SPD[p, p])*SPD[pp, pp])* +((-SPD[k, k] + SPD[k, pp])^2*SPD[p, p] - 2*SPD[k, p]*(-SPD[k, k] + SPD[k, pp])*(-SPD[k, p] + SPD[p, pp]) + SPD[k, k]*(-SPD[k, p] + SPD[p, pp])^2 + + SPD[k, p]^2*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp]) - SPD[k, k]*SPD[p, p]*(SPD[k, k] - 2*SPD[k, pp] + SPD[pp, pp])))"}, {"fcitTIDMTests-ID2", "TID[GSD[z].GA[5] FAD[{z,M},{k+z,M},{-k+pp-z,MD}] \ SPD[k,z],z]//FCE", @@ -202,5 +130,995 @@ M}, {-pp + z, MD}]*(-(GSD[pp] . GA[5]*SPD[k, k]*SPD[k, pp]*SPD[pp, \ pp]) + GSD[k] . GA[5]*SPD[k, k]*SPD[pp, pp]^2 - 2*GSD[k] . \ GA[5]*SPD[pp, pp]*(SPD[k, pp]^2 - SPD[k, k]*SPD[pp, pp]) + GSD[pp] . \ GA[5]*(M^2 - MD^2 + SPD[pp, pp])*(SPD[k, pp]^2 - SPD[k, k]*SPD[pp, \ -pp])))/(4*SPD[pp, pp]*(SPD[k, pp]^2 - SPD[k, k]*SPD[pp, pp]))"} +pp])))/(4*SPD[pp, pp]*(SPD[k, pp]^2 - SPD[k, k]*SPD[pp, pp]))"}, + +{"fcitTIDMTests-ID3", +"TimeConstrained[TID[(-4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] - +8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] - +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 + +(32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 + +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 - +(16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 + +4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] - +8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] - +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (4*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (4*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p3, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p3, D]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . + Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]* +Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 + +(32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 + +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . + Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]* +Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . + Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]* +Pair[LorentzIndex[Lor2, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 + +2*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] - +4*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] - +(CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(2*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +2*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] + +4*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] + +(CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(2*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +2*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] + +4*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]] + +(CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(2*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[l, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p3, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p3, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 - (4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p3, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p3, D]]*Pair[Momentum[l, D], Momentum[l, D]]* +SUNT[SUNIndex[Cola1]])/3 + (4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . + Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]* +Pair[Momentum[l, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 + +(16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 - +(32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 - +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p1, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p2, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 - 8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]] + 16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]] + (4*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p2, D]]*Pair[Momentum[l, D], Momentum[p1, D]]* +SUNT[SUNIndex[Cola1]])/3 + (4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[l, D], D] . + Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]* +Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[l, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[l, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[p1, D]]*Pair[Momentum[l, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . + Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]* +Pair[Momentum[l, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 - +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 - +(4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[p2, D], D] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[l, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 + +(16*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[p1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(32*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[p1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 - +(2*CA*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[p1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(4*CF*D*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[p1, D], Momentum[p2, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[p1, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 - (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[Momentum[l, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], LorentzIndex[Lor2, D]]*Pair[Momentum[p1, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[Momentum[p1, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor1, D], Momentum[l, D]]*Pair[Momentum[p1, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 - (8*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[p1, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 + (16*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[LorentzIndex[Lor2, D], Momentum[l, D]]*Pair[Momentum[p1, D], Momentum[p2, D]]* +SUNT[SUNIndex[Cola1]])/3 - (4*CA*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . + Spinor[-Momentum[p3, D], 0, 1]*FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], + PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]* +Pair[Momentum[p2, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3 + +(8*CF*Spinor[Momentum[p1, D], 0, 1] . DiracGamma[LorentzIndex[Lor2, D], D] . DiracGamma[Momentum[l, D], D] . DiracGamma[LorentzIndex[Lor1, D], D] . Spinor[-Momentum[p3, D], 0, 1]* +FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p2, D], 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D], + 0], PropagatorDenominator[Momentum[l, D] - Momentum[p1, D] - Momentum[p2, D] - Momentum[p3, D], 0]]*Pair[Momentum[p2, D], Momentum[p3, D]]*SUNT[SUNIndex[Cola1]])/3,l, + ToPaVe -> True, UsePaVeBasis -> True, FCE->True], 15, $Failed]", + "((-2*I)/3)*(CA - 2*CF)*Pi^2*C0[0, 0, 2*SPD[p1, p2], 0, 0, 0]*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SUNT[Cola1] - +(I/3)*(CA - 2*CF)*Pi^2*C0[0, 2*SPD[p1, p2], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 0, 0, 0]* +(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1] + +10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - +10*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + 16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + 12*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2])*SUNT[Cola1] + (I/3)*(CA - 2*CF)*Pi^2*C0[0, 0, 2*SPD[p1, p3], 0, 0, 0]* +(8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1] + +10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - +10*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - 16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + 28*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +4*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2])*SUNT[Cola1] - +(I/3)*(CA - 2*CF)*Pi^2*C0[0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 0, 0, 0]* +(10*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2])* +SUNT[Cola1] + ((2*I)/3)*(CA - 2*CF)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1 - p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + +Spinor[Momentum[p1, D], 0, 1] . GSD[p1 - p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1])*PaVe[1, {0, 2*SPD[p1, p2], 0}, {0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* +SUNT[Cola1] - ((2*I)/3)*(CA - 2*CF)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1] + +Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + 6*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2])*PaVe[1, {0, 2*SPD[p1, p2], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3]}, {0, 0, 0}, +PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + (I/3)*(CA - 2*CF)*Pi^2*(8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1 - p3] . Spinor[-Momentum[p3, D], 0, 1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1 - p3] . Spinor[-Momentum[p3, D], 0, 1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1 - p3] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1] + 16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - 16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p3, Lor2] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1 - p3] . Spinor[-Momentum[p3, D], 0, 1]* + MTD[Lor1, Lor2])*PaVe[1, {0, 2*SPD[p1, p3], 0}, {0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*(6 - D)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]* +PaVe[1, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3]}, {0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[-p1 - p2 - p3] . Spinor[-Momentum[p3, D], 0, 1] + +Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[-p1 - p2 - p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - 6*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2] + D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 6*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p2, Lor2] + D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - 6*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p3, Lor2] + D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2])*PaVe[2, {0, 2*SPD[p1, p2], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3]}, {0, 0, 0}, +PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - ((2*I)/3)*(CA - 2*CF)*(6 - D)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]* +(FVD[p1, Lor2] + FVD[p2, Lor2] + FVD[p3, Lor2])*PaVe[2, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3]}, {0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] - +4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] + +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2])*PaVe[0, 0, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, +{0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p1, Lor2] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1])* +PaVe[1, 1, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]* + FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + +8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]* + FVD[p3, Lor1] - 6*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]* + FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]*FVD[p3, Lor2])* +PaVe[1, 2, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[-p1 - p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +6*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[-p1 - p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] - 6*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + 16*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] - 6*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - +8*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p2, Lor2] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] - +8*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p2, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + 16*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p2, Lor1]*FVD[p2, Lor2] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1])* +PaVe[1, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + +8*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]* + FVD[p3, Lor1] + 2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p3, Lor2] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]* + FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]*FVD[p3, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]*FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]* + FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]*FVD[p3, Lor2])* +PaVe[2, 2, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] + 2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + 12*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + +16*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p2, Lor1]*FVD[p2, Lor2] - 2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[-p1 - p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]* + FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] - 8*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p2, Lor2]*FVD[p3, Lor1] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]* + FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] + +6*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[-p1 - p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]* + FVD[p3, Lor2] - 8*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] + +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p2, Lor1]*FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]*FVD[p3, Lor2])* +PaVe[2, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[-p1 - p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[-p1 - p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[-p1 - p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + +12*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[-p1 - p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p2, Lor2] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p2, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]* + FVD[p2, Lor2] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] + +16*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p2, Lor1]*FVD[p2, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] + +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1])* +PaVe[3, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2])* +PaVe[0, 0, 1, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2])* +PaVe[0, 0, 2, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(-(Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]) - +Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2])* +PaVe[0, 0, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2]* +PaVe[1, 1, 1, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + +Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p3, Lor2])*PaVe[1, 1, 2, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] - +Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]* + FVD[p2, Lor1] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2])* +PaVe[1, 1, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + +Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]* + FVD[p3, Lor2])*PaVe[1, 2, 2, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + +Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p2, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] - +Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]* + FVD[p3, Lor1] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] - +Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]* + FVD[p3, Lor2])*PaVe[1, 2, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] - Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + +Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] - Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p2, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2])* +PaVe[1, 3, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]*FVD[p3, Lor2]* +PaVe[2, 2, 2, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + +Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] + Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p3, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] - +Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]*FVD[p3, Lor2])* +PaVe[2, 2, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*(Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + +Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p2, Lor2] + Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - +Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] - Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p2, Lor2]*FVD[p3, Lor1] - Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] - +Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2])* +PaVe[2, 3, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*(2 - D)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*(FVD[p1, Lor1] + FVD[p2, Lor1])*(FVD[p1, Lor2] + FVD[p2, Lor2])* +PaVe[3, 3, 3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*Pi^2*(8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2])*PaVe[1, {0, 2*SPD[p1, p2], 0, 2*SPD[p1, p3], 0, 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3]}, +{0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SPD[p1, p2]*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*(8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] - 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*MTD[Lor1, Lor2])*PaVe[2, {0, 2*SPD[p1, p2], 0, 2*SPD[p1, p3], 0, 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3]}, +{0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SPD[p1, p2]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*Pi^2*(8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[-p1 - p3] . Spinor[-Momentum[p3, D], 0, 1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[-p1 - p3] . Spinor[-Momentum[p3, D], 0, 1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p3] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1] + 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1] - 16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - 16*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p3, Lor2] + 2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p3] . Spinor[-Momentum[p3, D], 0, 1]* + MTD[Lor1, Lor2])*PaVe[3, {0, 2*SPD[p1, p2], 0, 2*SPD[p1, p3], 0, 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3]}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SPD[p1, p2]* +SUNT[Cola1] - ((2*I)/3)*(CA - 2*CF)*Pi^2*PaVe[1, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, +PaVeAutoReduce -> True]*(4*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +12*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +12*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] - +8*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p1, Lor2] + 10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +8*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + 20*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] - 4*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]* + FVD[p2, Lor1] + 2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]* + FVD[p2, Lor2] + 12*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] - +10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + 8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*SPD[p1, p2] - 2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p3] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p3] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p2, p3])*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*Pi^2*D0[0, 0, 0, 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 2*SPD[p1, p3], 0, 0, 0, 0]* +(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +10*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +10*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] - 12*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p1, Lor2] + +10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +8*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + 12*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]* + FVD[p2, Lor1] + 2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p2, Lor2] - 12*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p2, Lor2] + +12*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p2, Lor1]*FVD[p2, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]* + FVD[p3, Lor1] - 2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] - +10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] - +10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] - +10*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + 8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*SPD[p1, p2] + 20*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*SPD[p1, p2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*SPD[p1, p2] - +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p3] - +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p3] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p3] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p2, p3])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*PaVe[2, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* +(2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +10*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p1, Lor2] + 10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] - +8*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1] + 12*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p2, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p2, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p2, Lor2] + 12*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p2, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor2]*FVD[p3, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]* + FVD[p3, Lor1] + 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]* + FVD[p3, Lor1] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] + +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor2]*FVD[p3, Lor1] - +6*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] + +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor2] - 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p1, Lor1]*FVD[p3, Lor2] - 8*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*FVD[p3, Lor2] + +8*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] - 2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]* + FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] - +2*D*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]* + FVD[p3, Lor2] + 4*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p3, Lor1]*FVD[p3, Lor2] - +8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[p3] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] - +10*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + +D*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2] + 8*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]* + FVD[p3, Lor1]*SPD[p1, p2] - 2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p3] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p3] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p3] - +2*Spinor[Momentum[p1, D], 0, 1] . GSD[p3] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p2, p3])*SUNT[Cola1] + +PaVe[3, {0, 2*SPD[p1, p3], 2*SPD[p1, p2] + 2*SPD[p1, p3] + 2*SPD[p2, p3], 2*SPD[p1, p2], 0, 0}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* +(((2*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[-p1 - p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] - +(4*I)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] - +((8*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] + +((8*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor2]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[-p1 - p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(FVD[p1, Lor1] + FVD[p2, Lor1])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[-p1 - p2] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(2*FVD[p1, Lor1] + 10*FVD[p2, Lor1])*SUNT[Cola1] - +(4*I)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] - +((8*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p1] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] - +((8*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] - +((16*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p1, Lor1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] + +((16*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] + +((8*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*SUNT[Cola1] + +((16*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*FVD[p2, Lor2]*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*FVD[p2, Lor2]*SUNT[Cola1] + +((8*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*FVD[p2, Lor2]*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*FVD[p2, Lor2]*SUNT[Cola1] + +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*(FVD[p1, Lor2] + FVD[p2, Lor2])*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*D*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*FVD[p2, Lor1]*(FVD[p1, Lor2] + FVD[p2, Lor2])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-6*FVD[p1, Lor2] + 2*FVD[p2, Lor2])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GAD[Lor2] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*(2*FVD[p1, Lor1] - 8*FVD[p2, Lor1] - 2*FVD[p3, Lor1])*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*(FVD[p1, Lor2] + FVD[p2, Lor2])*(2*FVD[p1, Lor1] - 6*FVD[p2, Lor1] - 2*FVD[p3, Lor1])* + SUNT[Cola1] + ((8*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p1] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*FVD[p3, Lor1]*SUNT[Cola1] + +((8*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor2] - FVD[p2, Lor2])*FVD[p3, Lor1]*SUNT[Cola1] - +((2*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[p2] . GSD[-p1 - p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*(-10*FVD[p1, Lor2] + 2*FVD[p3, Lor2])*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*(-8 + D)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GAD[Lor1] . GSD[-p1 - p2] . Spinor[-Momentum[p3, D], 0, 1]*SPD[p1, p2]*SUNT[Cola1] + +((16*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . Spinor[-Momentum[p3, D], 0, 1]*(-FVD[p1, Lor1] - FVD[p2, Lor1])*SPD[p1, p2]*SUNT[Cola1] + +((2*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GAD[Lor2] . GSD[-p1 - p2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*(-10*SPD[p1, p2] + D*SPD[p1, p2] - 2*SPD[p1, p3])*SUNT[Cola1] - +((4*I)/3)*(CA - 2*CF)*Pi^2*Spinor[Momentum[p1, D], 0, 1] . GSD[-p1 - p2] . GAD[Lor2] . GAD[Lor1] . Spinor[-Momentum[p3, D], 0, 1]*(SPD[p1, p3] + SPD[p2, p3])*SUNT[Cola1])"} }) diff --git a/Tests/LoopIntegrals/IntegrationTests/TIDPTests.test b/Tests/LoopIntegrals/IntegrationTests/TIDPTests.test index fe96e796e..e58f5f36e 100644 --- a/Tests/LoopIntegrals/IntegrationTests/TIDPTests.test +++ b/Tests/LoopIntegrals/IntegrationTests/TIDPTests.test @@ -1,26 +1,25 @@ Tests`LoopIntegrals`fcitTIDPTests = ({ {"fcitTIDPTests-ID1"," -$Larin = True; \n $BreitMaison = False; \n exp = +FCSetDiracGammaScheme[\"Larin\"]; \n exp = Spinor[-Momentum[pv1, D], 0, 1].GAD[i1].GA[5].Spinor[ Momentum[pv2, D], 0, 1] Spinor[Momentum[pv4, D], 0, 1].GAD[ i2].GSD[q].GAD[i1].GA[5].GSD[q].GAD[i2].Spinor[-Momentum[pv3, D], 0, 1] FAD[q, pv3 + q, -(pv1 + pv2 - pv3) + q] Spinor[Momentum[pv2, D], 0, 1].GAD[n2].Spinor[-Momentum[pv1, D], 0, 1] Spinor[-Momentum[pv3, D], 0, 1].GAD[n2].Spinor[Momentum[pv4, D], 0, 1]; \n -Factor2[TID[(FermionSpinSum[exp] /. DiracTrace -> Tr /. pv4 -> pv1 + pv2 - pv3), q, ToPaVe -> True] //PropagatorDenominatorExplicit // Simplify] - +Factor2[TID[(FermionSpinSum[exp] /. DiracTrace -> Tr /. pv4 -> pv1 + pv2 - pv3), q, ToPaVe -> True] //FeynAmpDenominatorExplicit // Simplify] - Factor2[(((FermionSpinSum[TID[exp, q, ToPaVe -> True]] /. DiracTrace -> Tr /. pv4 -> pv1 + pv2 - pv3) // Contract)) // Simplify]", "0"}, -{"fcitTIDPTests-ID2"," -$Larin = False; \n $BreitMaison = True; \n +{"fcitTIDPTests-ID2","FCSetDiracGammaScheme[\"BMHV\"]; \n exp = Spinor[-Momentum[pv1, D], 0, 1].GAD[i1].GA[5].Spinor[Momentum[pv2, D], 0, 1] Spinor[Momentum[pv4, D], 0, 1].GAD[i2].GSD[q].GAD[i1].GA[5].GSD[q].GAD[i2].Spinor[-Momentum[pv3, D],0, 1] FAD[q,pv3 + q, -(pv1 + pv2 - pv3) + q] Spinor[Momentum[pv2, D], 0,1].GAD[n2].Spinor[-Momentum[pv1, D], 0,1] Spinor[-Momentum[pv3, D], 0, 1].GAD[n2].Spinor[Momentum[pv4, D], 0, 1]; Factor2[TID[(FermionSpinSum[exp] /. DiracTrace -> Tr /. -pv4 -> pv1 + pv2 - pv3), q, ToPaVe -> True] // PropagatorDenominatorExplicit // Simplify] - Factor2[(((FermionSpinSum[TID[exp, q, ToPaVe -> True]] /. +pv4 -> pv1 + pv2 - pv3), q, ToPaVe -> True] // FeynAmpDenominatorExplicit // Simplify] - Factor2[(((FermionSpinSum[TID[exp, q, ToPaVe -> True]] /. DiracTrace -> Tr /. pv4 -> pv1 + pv2 - pv3) // Contract) /. Momentum[(a : pv1 | pv2 | pv3 | pv4), D | D - 4] :> Momentum[a]) // Simplify]", "0"}, {"fcitTIDPTests-ID3"," -$Larin = False; \n $BreitMaison = False; \n OneLoop[q,(CA*gc^2*SD[b, c]*(-(FAD[q, q, q, -p + q, -p + q]*FVD[q, mu]*FVD[q, nu]*SPD[p, p]^3) + FAD[q, q, q, -p + q, -p + q, -p + q]*FVD[q, mu]*FVD[q, nu]* +FCSetDiracGammaScheme[\"NDR\"]; \n OneLoop[q,(CA*gc^2*SD[b, c]*(-(FAD[q, q, q, -p + q, -p + q]*FVD[q, mu]*FVD[q, nu]*SPD[p, p]^3) + FAD[q, q, q, -p + q, -p + q, -p + q]*FVD[q, mu]*FVD[q, nu]* SPD[p, p]^4 + 3*FAD[q, q, q, -p + q, -p + q]*FVD[p, nu]*FVD[q, mu]*SPD[p, p]^2*SPD[p, q] + 3*FAD[q, q, q, -p + q, -p + q]*FVD[p, mu]*FVD[q, nu]* SPD[p, p]^2*SPD[p, q] - 2*FAD[q, q, q, -p + q, -p + q]*FVD[q, mu]*FVD[q, nu]*SPD[p, p]^2*SPD[p, q] - FAD[q, q, q, -p + q, -p + q, -p + q]*FVD[p, nu]*FVD[q, mu]*SPD[p, p]^3*SPD[p, q] - FAD[q, q, q, -p + q, -p + q, -p + q]*FVD[p, mu]*FVD[q, nu]* @@ -60,46 +59,95 @@ FAD[q, q, -p + q, -p + q]*(MTD[mu, nu]*(5*SPD[p, p]^3 + SPD[p, p]^2*(-12*SPD[p, FVD[q, mu]*(FVD[p, nu]*(-((-3 + D)*SPD[p, p]^2) + SPD[p, p]*(2*(-5 + 2*D)*SPD[p, q] + (5 - 3*D)*SPD[q, q]) - (2*SPD[p, q] - SPD[q, q])*(2*(-2 + D)*SPD[p, q] + (3 - 2*D)*SPD[q, q])) + FVD[q, nu]*((-2 + D)*SPD[p, p]^2 + 4*(-2 + D)*SPD[p, q]^2 + 4*(3 - 2*D)*SPD[p, q]*SPD[q, q] + 2*(-3 + 2*D)*SPD[q, q]^2 + SPD[p, p]*(-4*(-2 + D)*SPD[p, q] + 2*(-3 + 2*D)*SPD[q, q]))))))/2]//FCE", -"I*Pi^2*(2*CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[1, {0, SP[p, p], SP[p, p]}, {0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p] + -(CA*gc^2*D0[0, 0, SP[p, p], SP[p, p], 0, SP[p, p], 0, 0, 0, 0]*FV[p, mu]*FV[p, nu]*SD[b, c]*SP[p, p]^2)/4 - -2*CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[2, {0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* -SD[b, c]*SP[p, p]^2 - 2*CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, - PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - 2*CA*gc^2*FV[p, mu]*FV[p, nu]* -PaVe[4, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* -SD[b, c]*SP[p, p]^3 - CA*gc^2*MT[mu, nu]*PaVe[0, 0, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, - PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - CA*gc^2*FV[p, mu]*FV[p, nu]* -PaVe[3, 3, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* -SD[b, c]*SP[p, p]^3 - 2*CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 4, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - -CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, 4, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, - PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 + -(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[0, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/8 + -(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + -(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + -(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[5, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + -(CA*gc^2*MT[mu, nu]*PaVe[0, 0, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + -(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 3, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + -CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 4, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4 + -CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 5, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4 + -(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, 4, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + -CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, 5, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4 + -(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[5, 5, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, - {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + -(CA*gc^2*B0[SP[p, p], 0, 0]*SD[b, c]*(2*FV[p, mu]*FV[p, nu] - D*FV[p, mu]*FV[p, nu] - 3*MT[mu, nu]*SP[p, p]))/4 - -(CA*gc^2*D0[0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], 0, 0, 0, 0]*SD[b, c]*SP[p, p]^2*(5*FV[p, mu]*FV[p, nu] - 2*MT[mu, nu]*SP[p, p]))/4 - -(CA*gc^2*PaVe[0, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, PaVeAutoOrder -> True, - PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3*(2*FV[p, mu]*FV[p, nu] + MT[mu, nu]*SP[p, p]))/4 + -(CA*gc^2*C0[0, SP[p, p], SP[p, p], 0, 0, 0]*SD[b, c]*SP[p, p]*(-4*FV[p, mu]*FV[p, nu] + 5*MT[mu, nu]*SP[p, p]))/4)"}, +"I*Pi^2*((CA*gc^2*B0[SP[p, p], 0, 0]*FV[p, mu]*FV[p, nu]*SD[b, c])/2 - +(CA*D*gc^2*B0[SP[p, p], 0, 0]*FV[p, mu]*FV[p, nu]*SD[b, c])/2 + +(CA*D*gc^2*B0[SP[p, p], 0, 0]*FV[p, mu]*FV[p, nu]*SD[b, c])/(4*(1 - D)) - +(CA*D^2*gc^2*B0[SP[p, p], 0, 0]*FV[p, mu]*FV[p, nu]*SD[b, c])/ +(4*(1 - D)) - CA*gc^2*C0[0, SP[p, p], SP[p, p], 0, 0, 0]*FV[p, mu]* +FV[p, nu]*SD[b, c]*SP[p, p] - (CA*gc^2*B0[SP[p, p], 0, 0]*MT[mu, nu]* + SD[b, c]*SP[p, p])/2 - (CA*gc^2*B0[SP[p, p], 0, 0]*MT[mu, nu]*SD[b, c]* + SP[p, p])/(4*(1 - D)) + (CA*D*gc^2*B0[SP[p, p], 0, 0]*MT[mu, nu]* + SD[b, c]*SP[p, p])/(4*(1 - D)) + 2*CA*gc^2*FV[p, mu]*FV[p, nu]* +PaVe[1, {0, SP[p, p], SP[p, p]}, {0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p] + +(CA*gc^2*D0[0, 0, SP[p, p], SP[p, p], 0, SP[p, p], 0, 0, 0, 0]*FV[p, mu]* + FV[p, nu]*SD[b, c]*SP[p, p]^2)/4 - +(5*CA*gc^2*D0[0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], 0, 0, 0, 0]* + FV[p, mu]*FV[p, nu]*SD[b, c]*SP[p, p]^2)/4 + +(5*CA*gc^2*C0[0, SP[p, p], SP[p, p], 0, 0, 0]*MT[mu, nu]*SD[b, c]* + SP[p, p]^2)/4 - 2*CA*gc^2*FV[p, mu]*FV[p, nu]* +PaVe[2, {0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^2 + +(CA*gc^2*D0[0, SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], 0, 0, 0, 0]* + MT[mu, nu]*SD[b, c]*SP[p, p]^3)/2 - +(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[0, {0, 0, SP[p, p], 0, SP[p, p], 0, + SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3)/ +2 - 2*CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, {0, 0, SP[p, p], 0, SP[p, p], + 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - +2*CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, {0, 0, SP[p, p], 0, SP[p, p], 0, + SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - +CA*gc^2*MT[mu, nu]*PaVe[0, 0, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], + SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - +CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 3, {0, 0, SP[p, p], 0, SP[p, p], 0, + SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - +2*CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 4, {0, 0, SP[p, p], 0, SP[p, p], 0, + SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - +CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, 4, {0, 0, SP[p, p], 0, SP[p, p], 0, + SP[p, p], SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^3 - +(CA*gc^2*MT[mu, nu]*PaVe[0, {0, 0, SP[p, p], 0, SP[p, p], 0, SP[p, p], + SP[p, p], SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0}, + PaVeAutoOrder -> True, PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/ +4 + (CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[0, {0, 0, SP[p, p], 0, 0, + SP[p, p], 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], + SP[p, p], SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/8 + +(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, + SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + +(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, + SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + +(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[5, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, + SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + +(CA*gc^2*MT[mu, nu]*PaVe[0, 0, {0, 0, SP[p, p], 0, 0, SP[p, p], 0, + SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + +(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 3, {0, 0, SP[p, p], 0, 0, SP[p, p], + 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + +CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 4, {0, 0, SP[p, p], 0, 0, SP[p, p], + 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4 + +CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[3, 5, {0, 0, SP[p, p], 0, 0, SP[p, p], + 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4 + +(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, 4, {0, 0, SP[p, p], 0, 0, SP[p, p], + 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2 + +CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[4, 5, {0, 0, SP[p, p], 0, 0, SP[p, p], + 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4 + +(CA*gc^2*FV[p, mu]*FV[p, nu]*PaVe[5, 5, {0, 0, SP[p, p], 0, 0, SP[p, p], + 0, SP[p, p], SP[p, p], 0, SP[p, p], SP[p, p], SP[p, p], SP[p, p], + SP[p, p]}, {0, 0, 0, 0, 0, 0}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True]*SD[b, c]*SP[p, p]^4)/2)"}, {"fcitTIDPTests-ID4","OneLoop[q,(CA*gc^2*SD[b, c]*(-(FAD[q, q, q, -p + q, -p + q]*FVD[q, mu]*FVD[q, nu]*SPD[p, p]^3) + FAD[q, q, q, -p + q, -p + q, -p + q]*FVD[q, mu]*FVD[q, nu]* SPD[p, p]^4 + 3*FAD[q, q, q, -p + q, -p + q]*FVD[p, nu]*FVD[q, mu]*SPD[p, p]^2*SPD[p, q] + 3*FAD[q, q, q, -p + q, -p + q]*FVD[p, mu]*FVD[q, nu]* diff --git a/Tests/LoopIntegrals/IntegrationTests/TIDSTests.test b/Tests/LoopIntegrals/IntegrationTests/TIDSTests.test index 88bef92f8..5a536e5ff 100644 --- a/Tests/LoopIntegrals/IntegrationTests/TIDSTests.test +++ b/Tests/LoopIntegrals/IntegrationTests/TIDSTests.test @@ -489,114 +489,89 @@ j]*FVD[qst, \[Alpha]] + 4*(2 - D)*FVD[qst, j]*FVD[qst, \[Alpha]] + \ "TID[GA[7].GSD[p-q].GAD[\[Nu]].GAD[\[Alpha]]FVD[q,\[Mu]] \ FVD[pst-qst-kst,\[Alpha]]FVD[kst,\[Mu]]FVD[kst,\[Nu]]FAD[pst-qst-kst,\ kst+qst,kst,kst],kst]//FCE", -"((2*(2 - D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6] + 2*(-2 + \ -D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6] + (2 - D)*GSD[p] . GSD[qst] . \ -GSD[qst] . GA[6] + 2*(-2 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6] - \ -2*(2 - D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6] - 2*(-2 + D)*GSD[q] . \ -GSD[qst] . GSD[pst] . GA[6] - (2 - D)*GSD[q] . GSD[qst] . GSD[qst] . \ -GA[6] - 2*(-2 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6])*FAD[kst, \ -kst, kst - qst]*SPD[q, qst])/((2 - D)*m^2) + (FAD[kst, kst - pst + \ -qst]*((-2 + D)*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[pst, q] + (-2 \ -+ D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - 2*(-1 + \ -D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + D*GSD[p] . \ -GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - 2*(-1 + D)*GSD[p] . \ -GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + D*GSD[p] . GSD[qst] . \ -GSD[qst] . GA[6]*SPD[pst, q] - (-2 + D)*GSD[q] . GSD[pst] . GSD[pst] \ -. GA[6]*SPD[pst, q] - (-2 + D)*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] + 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] - D*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, \ -q] + 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - \ -D*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - 2*(-1 + \ -D)*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + D*GSD[p] . \ -GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] - 2*(-1 + D)*GSD[p] . \ -GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + D*GSD[p] . GSD[qst] . \ -GSD[pst] . GA[6]*SPD[q, qst] + 2*(-1 + D)*GSD[q] . GSD[pst] . \ -GSD[pst] . GA[6]*SPD[q, qst] - D*GSD[q] . GSD[pst] . GSD[pst] . \ -GA[6]*SPD[q, qst] + 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[q, qst] - D*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, \ -qst]))/((2 - D)*m^4) - (FAD[kst, kst - pst]*(m^2*GSD[p] . GSD[q] . \ -GSD[pst] . GA[6] + m^2*GSD[p] . GSD[qst] . GSD[q] . GA[6] - \ -m^2*GSD[q] . GSD[q] . GSD[pst] . GA[6] - m^2*GSD[q] . GSD[qst] . \ -GSD[q] . GA[6] + (-2 + D)*GSD[p] . GSD[pst] . GSD[pst] . \ -GA[6]*SPD[pst, q] + (-2 + D)*GSD[p] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] - 2*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] - 2*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[pst, q] - (-2 + D)*GSD[q] . GSD[pst] . GSD[pst] . \ -GA[6]*SPD[pst, q] - (-2 + D)*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] + 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] + 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[pst, q] - 2*(-1 + D)*GSD[p] . GSD[pst] . GSD[pst] . \ -GA[6]*SPD[q, qst] + 2*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[q, qst] + 2*(-1 + D)*GSD[q] . GSD[pst] . GSD[pst] . \ -GA[6]*SPD[q, qst] - 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[q, qst] - 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[q, qst]))/((2 - D)*m^4) + (FAD[kst, kst - qst]*(m^2*GSD[p] \ -. GSD[q] . GSD[pst] . GA[6] + m^2*GSD[p] . GSD[qst] . GSD[q] . GA[6] \ -- m^2*GSD[q] . GSD[q] . GSD[pst] . GA[6] - m^2*GSD[q] . GSD[qst] . \ -GSD[q] . GA[6] - D*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - \ -D*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + D*GSD[q] . \ -GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + D*GSD[q] . GSD[qst] . \ -GSD[qst] . GA[6]*SPD[pst, q] - D*GSD[p] . GSD[pst] . GSD[pst] . \ -GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[q, qst] - D*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, \ -qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] + \ -D*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] - 4*(-1 + \ -D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + D*GSD[q] . \ -GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - 4*(-1 + D)*GSD[q] . \ -GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst]))/((2 - D)*m^4) - (FAD[kst, \ -kst - pst, kst - qst]*(m^2*GSD[p] . GSD[q] . GSD[pst] . GA[6] + \ -m^2*GSD[p] . GSD[qst] . GSD[q] . GA[6] - m^2*GSD[q] . GSD[q] . \ -GSD[pst] . GA[6] - m^2*GSD[q] . GSD[qst] . GSD[q] . GA[6] - (2 - \ -D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - D*GSD[p] . \ -GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - D*GSD[p] . GSD[qst] . \ -GSD[qst] . GA[6]*SPD[pst, q] + (2 - D)*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] + D*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, \ -q] + D*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - (2 - \ -D)*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] - D*GSD[p] . \ -GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + 3*(2 - D)*GSD[p] . GSD[qst] \ -. GSD[pst] . GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . \ -GSD[pst] . GA[6]*SPD[q, qst] - D*GSD[p] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[q, qst] + 2*(2 - D)*GSD[p] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[q, qst] + (2 - D)*GSD[q] . GSD[pst] . GSD[pst] . \ -GA[6]*SPD[q, qst] + D*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, \ -qst] - 3*(2 - D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - \ -4*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + \ -D*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - 2*(2 - D)*GSD[q] \ -. GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] - 4*(-1 + D)*GSD[q] . \ -GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst]))/((2 - D)*m^2) + (FAD[kst, \ -kst, kst - pst + qst]*(2*GSD[p] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] - (2 - D)*GSD[p] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] - D*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, \ -q] + 2*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - D*GSD[p] . \ -GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - 2*GSD[q] . GSD[qst] . \ -GSD[pst] . GA[6]*SPD[pst, q] + (2 - D)*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[pst, q] + D*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, \ -q] - 2*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + D*GSD[q] . \ -GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + 2*GSD[p] . GSD[pst] . \ -GSD[pst] . GA[6]*SPD[q, qst] - (2 - D)*GSD[p] . GSD[pst] . GSD[pst] . \ -GA[6]*SPD[q, qst] - D*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, \ -qst] - 2*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + (2 - \ -D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - 2*(-2 + \ -D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + 4*(-1 + \ -D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - D*GSD[p] . \ -GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - 4*GSD[p] . GSD[qst] . \ -GSD[qst] . GA[6]*SPD[q, qst] + (2 - D)*GSD[p] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[q, qst] - 2*(-2 + D)*GSD[p] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . \ -GA[6]*SPD[q, qst] - 2*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, \ -qst] + (2 - D)*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + \ -D*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + 2*GSD[q] . \ -GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - (2 - D)*GSD[q] . GSD[qst] . \ -GSD[pst] . GA[6]*SPD[q, qst] + 2*(-2 + D)*GSD[q] . GSD[qst] . \ -GSD[pst] . GA[6]*SPD[q, qst] - 4*(-1 + D)*GSD[q] . GSD[qst] . \ -GSD[pst] . GA[6]*SPD[q, qst] + D*GSD[q] . GSD[qst] . GSD[pst] . \ -GA[6]*SPD[q, qst] + 4*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, \ -qst] - (2 - D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] + \ -2*(-2 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] - 4*(-1 + \ -D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst]))/((2 - \ -D)*m^2)"}, +"(GSD[p] . GSD[qst] . GSD[pst] . GA[6] - GSD[p] . GSD[qst] . GSD[qst] . GA[6] - GSD[q] . GSD[qst] . GSD[pst] . GA[6] + +GSD[q] . GSD[qst] . GSD[qst] . GA[6])*FAD[kst, kst - pst, kst - qst, kst - qst]*SPD[q, qst] - +((-2 + 2*(2 - D) + D)*(GSD[p] . GSD[qst] . GSD[pst] . GA[6] - GSD[p] . GSD[qst] . GSD[qst] . GA[6] - + GSD[q] . GSD[qst] . GSD[pst] . GA[6] + GSD[q] . GSD[qst] . GSD[qst] . GA[6])* +FAD[kst, kst - qst, kst - qst, kst - pst]*SPD[q, qst])/(2 - D) - +(FAD[kst, kst - pst]*(m^2*GSD[p] . GSD[q] . GSD[pst] . GA[6] - m^2*GSD[p] . GSD[q] . GSD[qst] . GA[6] - + m^2*GSD[q] . GSD[q] . GSD[pst] . GA[6] + m^2*GSD[q] . GSD[q] . GSD[qst] . GA[6] - + (2 - D)*m^2*GSD[p] . GA[6]*SPD[pst, q] + (2 - D)*m^2*GSD[q] . GA[6]*SPD[pst, q] + + (-2 + D)*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[pst, q] - (-2 + D)*GSD[p] . GSD[pst] . GSD[qst] . GA[6]* + SPD[pst, q] - 2*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + + 2*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - (-2 + D)*GSD[q] . GSD[pst] . GSD[pst] . GA[6]* + SPD[pst, q] + (-2 + D)*GSD[q] . GSD[pst] . GSD[qst] . GA[6]*SPD[pst, q] + + 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]* + SPD[pst, q] + 2*(2 - D)*m^2*GSD[p] . GA[6]*SPD[q, qst] - 2*(2 - D)*m^2*GSD[q] . GA[6]*SPD[q, qst] - + 2*(-1 + D)*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + 2*(-1 + D)*GSD[p] . GSD[pst] . GSD[qst] . GA[6]* + SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] + 2*(-1 + D)*GSD[q] . GSD[pst] . GSD[pst] . GA[6]* + SPD[q, qst] - 2*(-1 + D)*GSD[q] . GSD[pst] . GSD[qst] . GA[6]*SPD[q, qst] - + 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]* + SPD[q, qst]))/((2 - D)*m^4) + (FAD[kst, kst - pst + qst]*(m^2*GSD[p] . GSD[q] . GSD[pst] . GA[6] - + m^2*GSD[p] . GSD[q] . GSD[qst] . GA[6] - m^2*GSD[q] . GSD[q] . GSD[pst] . GA[6] + + m^2*GSD[q] . GSD[q] . GSD[qst] . GA[6] - (2 - D)*m^2*GSD[p] . GA[6]*SPD[pst, q] + + (2 - D)*m^2*GSD[q] . GA[6]*SPD[pst, q] + (-2 + D)*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[pst, q] - + (-2 + D)*GSD[p] . GSD[pst] . GSD[qst] . GA[6]*SPD[pst, q] - 2*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]* + SPD[pst, q] + 2*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - + (-2 + D)*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[pst, q] + (-2 + D)*GSD[q] . GSD[pst] . GSD[qst] . GA[6]* + SPD[pst, q] + 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - + 2*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + (2 - D)*m^2*GSD[p] . GA[6]*SPD[q, qst] - + (2 - D)*m^2*GSD[q] . GA[6]*SPD[q, qst] - 2*(-1 + D)*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + + 2*(-1 + D)*GSD[p] . GSD[pst] . GSD[qst] . GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]* + SPD[q, qst] - 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] + + 2*(-1 + D)*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] - 2*(-1 + D)*GSD[q] . GSD[pst] . GSD[qst] . GA[6]* + SPD[q, qst] - 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + + 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst]))/((2 - D)*m^4) + +(FAD[kst, kst - qst]*(m^2*GSD[p] . GSD[q] . GSD[pst] . GA[6] - m^2*GSD[p] . GSD[q] . GSD[qst] . GA[6] - + m^2*GSD[q] . GSD[q] . GSD[pst] . GA[6] + m^2*GSD[q] . GSD[q] . GSD[qst] . GA[6] - + D*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + D*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + + D*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - D*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + + (2 - D)*m^2*GSD[p] . GA[6]*SPD[q, qst] - (2 - D)*m^2*GSD[q] . GA[6]*SPD[q, qst] - + D*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + D*GSD[p] . GSD[pst] . GSD[qst] . GA[6]*SPD[q, qst] + + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]* + SPD[q, qst] + D*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] - D*GSD[q] . GSD[pst] . GSD[qst] . GA[6]* + SPD[q, qst] - 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + + 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst]))/((2 - D)*m^4) - +(FAD[kst, kst - qst, kst - pst]*(m^2*GSD[p] . GSD[q] . GSD[pst] . GA[6] - m^2*GSD[p] . GSD[q] . GSD[qst] . GA[6] - + m^2*GSD[q] . GSD[q] . GSD[pst] . GA[6] + m^2*GSD[q] . GSD[q] . GSD[qst] . GA[6] - + (2 - D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - D*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + + (2 - D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + D*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + + (2 - D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + D*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - + (2 - D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - D*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - + D*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + D*GSD[p] . GSD[pst] . GSD[qst] . GA[6]*SPD[q, qst] - + (2 - D)*GSD[p] . GSD[pst - 2*qst] . GSD[pst] . GA[6]*SPD[q, qst] + + (2 - D)*GSD[p] . GSD[pst - 2*qst] . GSD[qst] . GA[6]*SPD[q, qst] + 2*(2 - D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]* + SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - + 2*(2 - D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] - 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]* + SPD[q, qst] + D*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] - D*GSD[q] . GSD[pst] . GSD[qst] . GA[6]* + SPD[q, qst] + (2 - D)*GSD[q] . GSD[pst - 2*qst] . GSD[pst] . GA[6]*SPD[q, qst] - + (2 - D)*GSD[q] . GSD[pst - 2*qst] . GSD[qst] . GA[6]*SPD[q, qst] - 2*(2 - D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]* + SPD[q, qst] - 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + + 2*(2 - D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]* + SPD[q, qst]))/((2 - D)*m^2) + (FAD[kst, kst, kst - pst + qst]*(2*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - + (2 - D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - D*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] - + 2*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + (2 - D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + + D*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - 2*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + + (2 - D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + D*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[pst, q] + + 2*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - (2 - D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] - + D*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[pst, q] + 2*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] - + D*GSD[p] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] - 2*GSD[p] . GSD[pst] . GSD[qst] . GA[6]*SPD[q, qst] + + D*GSD[p] . GSD[pst] . GSD[qst] . GA[6]*SPD[q, qst] - (2 - D)*GSD[p] . GSD[pst - qst] . GSD[pst] . GA[6]*SPD[q, qst] + + (2 - D)*GSD[p] . GSD[pst - qst] . GSD[qst] . GA[6]*SPD[q, qst] - 4*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + + (2 - D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - 2*(-2 + D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]* + SPD[q, qst] + 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + + 4*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] - (2 - D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] + + 2*(-2 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] - 4*(-1 + D)*GSD[p] . GSD[qst] . GSD[qst] . GA[6]* + SPD[q, qst] - 2*GSD[q] . GSD[pst] . GSD[pst] . GA[6]*SPD[q, qst] + D*GSD[q] . GSD[pst] . GSD[pst] . GA[6]* + SPD[q, qst] + 2*GSD[q] . GSD[pst] . GSD[qst] . GA[6]*SPD[q, qst] - D*GSD[q] . GSD[pst] . GSD[qst] . GA[6]* + SPD[q, qst] + (2 - D)*GSD[q] . GSD[pst - qst] . GSD[pst] . GA[6]*SPD[q, qst] - + (2 - D)*GSD[q] . GSD[pst - qst] . GSD[qst] . GA[6]*SPD[q, qst] + 4*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - + (2 - D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] + 2*(-2 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]* + SPD[q, qst] - 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[pst] . GA[6]*SPD[q, qst] - + 4*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] + (2 - D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] - + 2*(-2 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]*SPD[q, qst] + 4*(-1 + D)*GSD[q] . GSD[qst] . GSD[qst] . GA[6]* + SPD[q, qst]))/((2 - D)*m^2)"}, {"fcitTIDSTests-ID11", "TID[FVD[pst-qst-kst,\[Alpha]]FAD[pst-qst-kst,{pst-qst-kst,m},kst+\ qst,kst],kst]//FCE", diff --git a/Tests/LoopIntegrals/IntegrationTests/fcstTID.tost b/Tests/LoopIntegrals/IntegrationTests/fcstTID.tost deleted file mode 100644 index e9c12b06b..000000000 --- a/Tests/LoopIntegrals/IntegrationTests/fcstTID.tost +++ /dev/null @@ -1,28 +0,0 @@ -Tests`LoopIntegrals`fcstTID = -{ -{"fcstTID-ID1", "TID[FAD[{k, m}, k - q, k + p - q] FVD[k + p - q, \[Mu]], k]//FCE", - "FAD[k, k - p, {k - q, m}] (2 FVD[p, \[Mu]] - 3 FVD[q, \[Mu]]) + ( - FAD[k, {k - q, m}] FVD[q, \[Mu]])/m^2 + - FAD[k, k - p] (FVD[p, \[Mu]]/m^2 - (2 FVD[q, \[Mu]])/m^2) + - FAD[k, {k - p + q, m}] (-(FVD[p, \[Mu]]/m^2) + FVD[q, \[Mu]]/m^2)"} - - -{"fcstTID-ID2", "TID[FAD[{k, m}, k - q, k + p - q],k]//FCE","FAD[k, k - p, {k - q, m}]"}, -{"fcstTID-ID3", "TID[FVD[k + p, \[Alpha]] FAD[p + k, k, k],k]//FCE","-((FAD[k, k - p] FVD[p, \[Alpha]])/(2 m^2)) + -1/2 FAD[k, k, k - p] FVD[p, \[Alpha]]"}, -{"fcstTID-ID4", "TID[FVD[k, \[Beta]] FAD[k + q, {k + q, m}, k, k + p],k]//FCE","(FAD[k, k - q, {k, m}] FVD[q, \[Beta]])/m^2 - -FAD[k, k - p, k - q, {k - q, m}] FVD[q, \[Beta]] + FAD[k, k - p, {k - q, m}] (FVD[p, \[Beta]]/m^2 - (2 FVD[q, \[Beta]])/ - m^2) + FAD[k, k - p + q, {k, m}] (-(FVD[p, \[Beta]]/m^2) + FVD[q, \[Beta]]/m^2)f"}, -{"fcstTID-ID5", "TID[FVD[k + p, \[Mu]] FAD[k, k, {k + q, m}, k + p],k]//FCE","FAD[k, k, k - p, {k - q, m}] (2 FVD[p, \[Mu]] - 3 FVD[q, \[Mu]]) + ( -FAD[k, k, {k - q, m}] FVD[q, \[Mu]])/m^2 + FAD[k, k, k - p] (FVD[p, \[Mu]]/m^2 - (2 FVD[q, \[Mu]])/m^2) + -FAD[k, k - p, {k - q, m}] (-(FVD[p, \[Mu]]/m^2) + FVD[q, \[Mu]]/m^2)"}(*, -{"fcstTID-ID6", "TID[,k]//FCE",""}, -{"fcstTID-ID7", "TID[,k]//FCE",""}, -{"fcstTID-ID8", "TID[,k]//FCE",""}, -{"fcstTID-ID9", "",""}, -{"fcstTID-ID10", "",""}, -{"fcstTID-ID11", "",""}, -{"fcstTID-ID12", "",""}, -{"fcstTID-ID13", "",""}, -{"fcstTID-ID14", "",""}*) -}; diff --git a/Tests/LoopIntegrals/IntegrationTests/iTestsLoopIntegrals.mt b/Tests/LoopIntegrals/IntegrationTests/iTestsLoopIntegrals.mt new file mode 100644 index 000000000..918b215bf --- /dev/null +++ b/Tests/LoopIntegrals/IntegrationTests/iTestsLoopIntegrals.mt @@ -0,0 +1,171 @@ +(* :Title: LoopIntegrals.mt *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Unit tests for functions in the "LoopIntegrals" directory *) + +(* ------------------------------------------------------------------------ *) + +Needs["FeynCalc`"]; + +(*$FCAdvice = False;*) + +ClearAll[itests]; +itests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "LoopIntegrals", "IntegrationTests"}]] +Get/@itests; + + +If[ $OnlySubTest=!="", + testNames = "Tests`LoopIntegrals`fcit*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + +ClearAll[p,k1,k2,k3,m0,m1,m2,m3,k1z,k2z,k1g,k2g,kst,qst,pst,m,p1,p2,p3,p4,p5]; +FCClearScalarProducts[]; +ScalarProduct[k1z, k1z] = 0; +ScalarProduct[k2z, k2z] = 0; +ScalarProduct[k1g, k2g] = 0; +ScalarProduct[k1g, k1g] = 0; +ScalarProduct[k2g, k2g] = 0; + +ScalarProduct[qst, qst] = 0; +ScalarProduct[pst, pst] = m^2; +ScalarProduct[qst, pst] = (m^2)/2; + +ScalarProduct[pv1, pv1] = 0; +ScalarProduct[pv2, pv2] = 0; +ScalarProduct[pv3, pv3] = 0; +ScalarProduct[pv4, pv4] = 0; +ScalarProduct[pv1, pv2] = s/2; +ScalarProduct[pv1, pv3] = 0; +ScalarProduct[pv2, pv3] = s/2; + +SPD[p1] = 0; +SPD[p2] = 0; +SPD[p3] = 0; +SPD[p4] = 0; +SPD[p5] = 0; + +(* Isolate checks DownValues before generating new abbreviations, which is why + the results we get from TID can have slightly different form depending on the + integrals that TID had to work out before. Of course all those are exactly the + same (just written in a different way) and we use Simplify to check the equivalence *) + +If[ Names["Tests`LoopIntegrals`fcitTIDUsePaVeBasisA"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p], + {B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDUsePaVeBasisA"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDUsePaVeBasisB"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p], + {B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDUsePaVeBasisB"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDUsePaVeBasisC"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p], + {B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDUsePaVeBasisC"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDUsePaVeBasisD"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p], + {B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDUsePaVeBasisD"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDFullRedA"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p], + {B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDFullRedA"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDFullRedB"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p], + {B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDFullRedB"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDFullRedCR1"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p], + {B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDFullRedCR1"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDFullRedCR2"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p], + {B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDFullRedCR2"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + + +If[ Names["Tests`LoopIntegrals`fcitTIDSTests"]=!={}, + $LimitTo4=True; + tmpTest = Map[test[ Simplify[ReplaceAll[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],kst],{B0[x__] :> B0[x, BReduce -> True], + PaVe[x__, PaVeAutoReduce -> False, y___] :> PaVe[x, PaVeAutoReduce -> True, y]}]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDSTests"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $LimitTo4=False +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDMTests"]=!={}, + tmpTest = Map[test[ DiracSimplify[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]]],0,testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDMTests"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + +]; + +If[ Names["Tests`LoopIntegrals`fcitTIDPTests"]=!={}, + $LimitTo4=False; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDPTests"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + +If[ Names["Tests`LoopIntegrals`fcitOneLoopMiscTests"]=!={}, + $LimitTo4=False; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitOneLoopMiscTests"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + + + + +If[ Names["Tests`LoopIntegrals`fcitTIDL"]=!={}, + $LimitTo4=False; + FCClearScalarProducts[]; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcitTIDL"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; diff --git a/Tests/LoopIntegrals/IntegrationTests/iTestsTID.mt b/Tests/LoopIntegrals/IntegrationTests/iTestsTID.mt deleted file mode 100644 index c662c5b60..000000000 --- a/Tests/LoopIntegrals/IntegrationTests/iTestsTID.mt +++ /dev/null @@ -1,88 +0,0 @@ -(* :Title: LoopIntegrals.mt *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Unit tests for functions in the "LoopIntegrals" directory *) - -(* ------------------------------------------------------------------------ *) - -Needs["FeynCalc`"]; - -(*$FCAdvice = False;*) - -ClearAll[itests]; -itests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "LoopIntegrals", "IntegrationTests"}]] -Get/@itests; -ClearAll[p,k1,k2,k3,m0,m1,m2,m3,k1z,k2z,k1g,k2g,kst,qst,pst,m]; -FCClearScalarProducts[]; -ScalarProduct[k1z, k1z] = 0; -ScalarProduct[k2z, k2z] = 0; -ScalarProduct[k1g, k2g] = 0; -ScalarProduct[k1g, k1g] = 0; -ScalarProduct[k2g, k2g] = 0; - -ScalarProduct[qst, qst] = 0; -ScalarProduct[pst, pst] = m^2; -ScalarProduct[qst, pst] = (m^2)/2; - -ScalarProduct[pv1, pv1] = 0; -ScalarProduct[pv2, pv2] = 0; -ScalarProduct[pv3, pv3] = 0; -ScalarProduct[pv4, pv4] = 0; -ScalarProduct[pv1, pv2] = s/2; -ScalarProduct[pv1, pv3] = 0; -ScalarProduct[pv2, pv3] = s/2; - -(* Isolate checks DownValues before generating new abbreviations, which is why - the results we get from TID can have slightly different form depending on the - integrals that TID had to work out before. Of course all those are exactly the - same (just written in a different way) and we use Simplify to check the equivalence *) -$LimitTo4=True; -Map[Test[ Simplify[ReplaceRepeated[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],p],{B1[x__]/;FreeQ[{x},BReduce] :> B1[x, BReduce -> True],B0[x__]/;FreeQ[{x},BReduce] :> B0[x, BReduce -> True]}]],0,TestID->#[[1]]]&, - Join[ - Tests`LoopIntegrals`fcitTIDUsePaVeBasisA, - Tests`LoopIntegrals`fcitTIDUsePaVeBasisB, - Tests`LoopIntegrals`fcitTIDUsePaVeBasisC, - Tests`LoopIntegrals`fcitTIDUsePaVeBasisD, - Tests`LoopIntegrals`fcitTIDFullRedA, - Tests`LoopIntegrals`fcitTIDFullRedB, - Tests`LoopIntegrals`fcitTIDFullRedCR1, - Tests`LoopIntegrals`fcitTIDFullRedCR2 - ]]; - -Map[Test[ Simplify[ReplaceAll[ToPaVe[Simplify[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],kst],{B0[x__] :> B0[x, BReduce -> True], - PaVe[x__, PaVeAutoReduce -> False, y___] :> PaVe[x, PaVeAutoReduce -> True, y]}]],0,TestID->#[[1]]]&, - Join[ - Tests`LoopIntegrals`fcitTIDSTests - ]]; - - - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join[ - Tests`LoopIntegrals`fcitTIDMTests - ]]; -$LimitTo4=False; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join[ - Tests`LoopIntegrals`fcitTIDPTests - ]]; - - - - - - - - - - - - - diff --git a/Tests/LoopIntegrals/LogDivergentScaleless.test b/Tests/LoopIntegrals/LogDivergentScaleless.test index d6b5fb0a5..a4a8d1d6d 100644 --- a/Tests/LoopIntegrals/LogDivergentScaleless.test +++ b/Tests/LoopIntegrals/LogDivergentScaleless.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for LogDivergentScaleless *) diff --git a/Tests/LoopIntegrals/LoopIntegrals.mt b/Tests/LoopIntegrals/LoopIntegrals.mt index 688792f29..6aa197a24 100644 --- a/Tests/LoopIntegrals/LoopIntegrals.mt +++ b/Tests/LoopIntegrals/LoopIntegrals.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "LoopIntegrals" directory *) @@ -13,22 +13,37 @@ Needs["FeynCalc`"]; $FCAdvice = False; +$VeryVerbose = -1; + ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "LoopIntegrals"}]]; Get/@tests; +If[ $OnlySubTest=!="", + testNames = "Tests`LoopIntegrals`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + FCClearScalarProducts[]; -SetOptions[Tdec,UseParallelization->False]; +SetOptions[Tdec,UseParallelization->False]; +SetOptions[CTdec,UseParallelization->False]; Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, Join@@(ToExpression/@Select[Names["Tests`LoopIntegrals`*"], !StringMatchQ[#, "*fcstLogDivergentScaleless"] &])]; -$FCAdvice = True; -$KeepLogDivergentScalelessIntegrals=True; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcstLogDivergentScaleless"])]; -$KeepLogDivergentScalelessIntegrals=False; +$FCAdvice = True; + +If[ Names["Tests`LoopIntegrals`fcstLogDivergentScaleless"]=!={}, + $KeepLogDivergentScalelessIntegrals=True; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`LoopIntegrals`fcstLogDivergentScaleless"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + $KeepLogDivergentScalelessIntegrals=False +]; +$VeryVerbose = 0; diff --git a/Tests/LoopIntegrals/NPointTo4Point.test b/Tests/LoopIntegrals/NPointTo4Point.test new file mode 100644 index 000000000..c6e29a6b9 --- /dev/null +++ b/Tests/LoopIntegrals/NPointTo4Point.test @@ -0,0 +1,518 @@ + + +(* :Title: NPointTo4Point.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for NPointTo4Point *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`NPointTo4Point = +({ +{"fcstNPointTo4Point-ID1", "FCClearScalarProducts[]; \n NPointTo4Point[ +FCI@FAD[{q, m0}, {q + p1, 0}, {q + p2, 0}, {q + p3, 0}, {q + p4, + 0}], q, FCE -> True,FCVerbose->-1]", "(8 FAD[{q, m0}, p1 + q, p2 + q, + p3 + q] (m0^2 SPD[p1, p3]^2 SPD[p2, p2] - + m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] - + 2 m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p2, p3] + + m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p2, p3] + + m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p3] + + SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p2, p3] + + m0^2 SPD[p1, p1] SPD[p2, p3]^2 - + m0^2 SPD[p1, p4] SPD[p2, p3]^2 - + SPD[p1, p1] SPD[p1, p4] SPD[p2, p3]^2 + + m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p2, p4] - + m0^2 SPD[p1, p3]^2 SPD[p2, p4] - + SPD[p1, p3]^2 SPD[p2, p2] SPD[p2, p4] - + m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] + + m0^2 SPD[p1, p3] SPD[p2, p3] SPD[p2, p4] + + SPD[p1, p1] SPD[p1, p3] SPD[p2, p3] SPD[p2, p4] + + m0^2 SPD[p1, p2]^2 SPD[p3, p3] - + m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p3, p3] - + m0^2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] + + m0^2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] + + SPD[p1, p1] SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] - + SPD[p1, p2] SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] - + SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] + + SPD[p1, p2] SPD[p1, p4] SPD[p2, p3] SPD[p3, p3] + + m0^2 SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] - + m0^2 SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p1] SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] + + SPD[p1, p2] SPD[p1, p3] SPD[p2, p4] SPD[p3, p3] + + SPD[p1, p1] SPD[p2, p2] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] SPD[p3, p3] - + m0^2 SPD[p1, p2]^2 SPD[p3, p4] + + m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p3, p4] + + m0^2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p4] - + m0^2 SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] - + SPD[p1, p1] SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] + + SPD[p1, p2] SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] - + m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p3, p4] + + m0^2 SPD[p1, p2] SPD[p2, p3] SPD[p3, p4] + + SPD[p1, p1] SPD[p1, p2] SPD[p2, p3] SPD[p3, p4] - + SPD[p1, p1] SPD[p2, p2] SPD[p2, p3] SPD[p3, p4] - + SPD[p1, p2]^2 SPD[p3, p3] SPD[p3, p4] + + SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] SPD[p3, p4] + + SPD[p1, p3]^2 SPD[p2, p2] SPD[p4, p4] - + 2 SPD[p1, p2] SPD[p1, p3] SPD[p2, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p3]^2 SPD[p4, p4] + + SPD[p1, p2]^2 SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4]) - +8 FAD[{q, m0}, p1 + q, p2 + q, + p4 + q] (m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] - + m0^2 SPD[p1, p4]^2 SPD[p2, p2] - + m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p2, p3] + + m0^2 SPD[p1, p4]^2 SPD[p2, p3] + + SPD[p1, p4]^2 SPD[p2, p2] SPD[p2, p3] - + m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p2, p4] + + 2 m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p2, p4] - + m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p4] - + SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p2, p4] + + m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] - + m0^2 SPD[p1, p4] SPD[p2, p3] SPD[p2, p4] - + SPD[p1, p1] SPD[p1, p4] SPD[p2, p3] SPD[p2, p4] - + m0^2 SPD[p1, p1] SPD[p2, p4]^2 + + m0^2 SPD[p1, p3] SPD[p2, p4]^2 + + SPD[p1, p1] SPD[p1, p3] SPD[p2, p4]^2 - + SPD[p1, p4]^2 SPD[p2, p2] SPD[p3, p3] + + 2 SPD[p1, p2] SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p1] SPD[p2, p4]^2 SPD[p3, p3] + + m0^2 SPD[p1, p2]^2 SPD[p3, p4] - + m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p3, p4] - + m0^2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p4] + + m0^2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] + + SPD[p1, p1] SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] - + SPD[p1, p2] SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] + + m0^2 SPD[p1, p1] SPD[p2, p4] SPD[p3, p4] - + m0^2 SPD[p1, p2] SPD[p2, p4] SPD[p3, p4] - + SPD[p1, p1] SPD[p1, p2] SPD[p2, p4] SPD[p3, p4] + + SPD[p1, p1] SPD[p2, p2] SPD[p2, p4] SPD[p3, p4] - + m0^2 SPD[p1, p2]^2 SPD[p4, p4] + + m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p4, p4] + + m0^2 SPD[p1, p1] SPD[p2, p2] SPD[p4, p4] - + m0^2 SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] - + SPD[p1, p1] SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] + + SPD[p1, p2] SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] + + SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p4, p4] - + m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p4, p4] + + m0^2 SPD[p1, p2] SPD[p2, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p1, p2] SPD[p2, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p1, p4] SPD[p2, p3] SPD[p4, p4] - + SPD[p1, p1] SPD[p2, p2] SPD[p2, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p1, p3] SPD[p2, p4] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] SPD[p4, p4] - + SPD[p1, p2]^2 SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p2]^2 SPD[p3, p4] SPD[p4, p4] - + SPD[p1, p1] SPD[p2, p2] SPD[p3, p4] SPD[p4, p4]) + +8 FAD[{q, m0}, p1 + q, p3 + q, + p4 + q] (m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p3] - + m0^2 SPD[p1, p4]^2 SPD[p2, p3] - + m0^2 SPD[p1, p3]^2 SPD[p2, p4] + + m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p4] - + m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p3, p3] + + m0^2 SPD[p1, p4]^2 SPD[p3, p3] + + SPD[p1, p4]^2 SPD[p2, p2] SPD[p3, p3] - + SPD[p1, p4]^2 SPD[p2, p3] SPD[p3, p3] + + m0^2 SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] - + m0^2 SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p1] SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] + + SPD[p1, p3] SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] + + m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p3, p4] + + m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p3, p4] - + 2 m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p3, p4] - + 2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] - + m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p3, p4] + + m0^2 SPD[p1, p4] SPD[p2, p3] SPD[p3, p4] + + SPD[p1, p1] SPD[p1, p4] SPD[p2, p3] SPD[p3, p4] - + m0^2 SPD[p1, p1] SPD[p2, p4] SPD[p3, p4] + + m0^2 SPD[p1, p3] SPD[p2, p4] SPD[p3, p4] + + SPD[p1, p1] SPD[p1, p3] SPD[p2, p4] SPD[p3, p4] + + SPD[p1, p2] SPD[p1, p4] SPD[p3, p3] SPD[p3, p4] - + SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] SPD[p3, p4] + + m0^2 SPD[p1, p1] SPD[p3, p4]^2 - + m0^2 SPD[p1, p2] SPD[p3, p4]^2 - + SPD[p1, p1] SPD[p1, p2] SPD[p3, p4]^2 + + SPD[p1, p1] SPD[p2, p2] SPD[p3, p4]^2 - + m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p4, p4] + + m0^2 SPD[p1, p3]^2 SPD[p4, p4] + + SPD[p1, p3]^2 SPD[p2, p2] SPD[p4, p4] + + m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p4, p4] - + m0^2 SPD[p1, p3] SPD[p2, p3] SPD[p4, p4] - + SPD[p1, p1] SPD[p1, p3] SPD[p2, p3] SPD[p4, p4] + + SPD[p1, p3] SPD[p1, p4] SPD[p2, p3] SPD[p4, p4] - + SPD[p1, p3]^2 SPD[p2, p4] SPD[p4, p4] - + m0^2 SPD[p1, p1] SPD[p3, p3] SPD[p4, p4] + + m0^2 SPD[p1, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p1, p2] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p1, p3] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p1, p4] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p3] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p2] SPD[p1, p3] SPD[p3, p4] SPD[p4, p4] - + SPD[p1, p1] SPD[p2, p3] SPD[p3, p4] SPD[p4, p4]) - +8 FAD[{q, m0}, p2 + q, p3 + q, + p4 + q] (m0^2 SPD[p1, p4] SPD[p2, p3]^2 - + m0^2 SPD[p1, p3] SPD[p2, p3] SPD[p2, p4] - + m0^2 SPD[p1, p4] SPD[p2, p3] SPD[p2, p4] + + m0^2 SPD[p1, p3] SPD[p2, p4]^2 - + m0^2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] + + m0^2 SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] + + m0^2 SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] + + SPD[p1, p4] SPD[p2, p2] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p4] SPD[p2, p3] SPD[p2, p4] SPD[p3, p3] - + m0^2 SPD[p2, p4]^2 SPD[p3, p3] - + SPD[p1, p1] SPD[p2, p4]^2 SPD[p3, p3] + + SPD[p1, p3] SPD[p2, p4]^2 SPD[p3, p3] + + m0^2 SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] + + m0^2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] - + m0^2 SPD[p1, p2] SPD[p2, p3] SPD[p3, p4] - + m0^2 SPD[p1, p4] SPD[p2, p3] SPD[p3, p4] - + SPD[p1, p4] SPD[p2, p2] SPD[p2, p3] SPD[p3, p4] - + m0^2 SPD[p1, p2] SPD[p2, p4] SPD[p3, p4] - + m0^2 SPD[p1, p3] SPD[p2, p4] SPD[p3, p4] - + SPD[p1, p3] SPD[p2, p2] SPD[p2, p4] SPD[p3, p4] + + 2 m0^2 SPD[p2, p3] SPD[p2, p4] SPD[p3, p4] + + 2 SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] SPD[p3, p4] + + SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] SPD[p3, p4] - + SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] SPD[p3, p4] + + m0^2 SPD[p1, p2] SPD[p3, p4]^2 - + m0^2 SPD[p2, p2] SPD[p3, p4]^2 - + SPD[p1, p1] SPD[p2, p2] SPD[p3, p4]^2 + + SPD[p1, p2] SPD[p2, p2] SPD[p3, p4]^2 - + m0^2 SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] + + m0^2 SPD[p1, p2] SPD[p2, p3] SPD[p4, p4] + + m0^2 SPD[p1, p3] SPD[p2, p3] SPD[p4, p4] + + SPD[p1, p3] SPD[p2, p2] SPD[p2, p3] SPD[p4, p4] - + m0^2 SPD[p2, p3]^2 SPD[p4, p4] - + SPD[p1, p1] SPD[p2, p3]^2 SPD[p4, p4] + + SPD[p1, p4] SPD[p2, p3]^2 SPD[p4, p4] - + SPD[p1, p3] SPD[p2, p3] SPD[p2, p4] SPD[p4, p4] - + m0^2 SPD[p1, p2] SPD[p3, p3] SPD[p4, p4] + + m0^2 SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p3] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p2] SPD[p2, p3] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] SPD[p4, p4] - + SPD[p1, p2] SPD[p2, p3] SPD[p3, p4] SPD[p4, p4]) - +8 FAD[p1 + q, p2 + q, p3 + q, + p4 + q] (m0^2 SPD[p1, p3]^2 SPD[p2, p2] - + 2 m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] + + m0^2 SPD[p1, p4]^2 SPD[p2, p2] - + 2 m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p2, p3] + + 2 m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p2, p3] + + 2 m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p3] - + 2 m0^2 SPD[p1, p4]^2 SPD[p2, p3] + + SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p2, p3] - + SPD[p1, p4]^2 SPD[p2, p2] SPD[p2, p3] + + m0^2 SPD[p1, p1] SPD[p2, p3]^2 - + 2 m0^2 SPD[p1, p4] SPD[p2, p3]^2 - + SPD[p1, p1] SPD[p1, p4] SPD[p2, p3]^2 + + 2 SPD[p1, p4]^2 SPD[p2, p3]^2 + + 2 m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p2, p4] - + 2 m0^2 SPD[p1, p3]^2 SPD[p2, p4] - + 2 m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p2, p4] + + 2 m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p4] - + SPD[p1, p3]^2 SPD[p2, p2] SPD[p2, p4] + + SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p2, p4] - + 2 m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] + + 2 m0^2 SPD[p1, p3] SPD[p2, p3] SPD[p2, p4] + + SPD[p1, p1] SPD[p1, p3] SPD[p2, p3] SPD[p2, p4] + + 2 m0^2 SPD[p1, p4] SPD[p2, p3] SPD[p2, p4] + + SPD[p1, p1] SPD[p1, p4] SPD[p2, p3] SPD[p2, p4] - + 4 SPD[p1, p3] SPD[p1, p4] SPD[p2, p3] SPD[p2, p4] + + m0^2 SPD[p1, p1] SPD[p2, p4]^2 - + 2 m0^2 SPD[p1, p3] SPD[p2, p4]^2 - + SPD[p1, p1] SPD[p1, p3] SPD[p2, p4]^2 + + 2 SPD[p1, p3]^2 SPD[p2, p4]^2 + + m0^2 SPD[p1, p2]^2 SPD[p3, p3] - + 2 m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p3, p3] + + m0^2 SPD[p1, p4]^2 SPD[p3, p3] - + m0^2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] + + 2 m0^2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] + + SPD[p1, p1] SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] - + SPD[p1, p2] SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] - + SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] + + SPD[p1, p2] SPD[p1, p4] SPD[p2, p3] SPD[p3, p3] - + SPD[p1, p4]^2 SPD[p2, p3] SPD[p3, p3] + + 2 m0^2 SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] - + 2 m0^2 SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p1] SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] + + SPD[p1, p2] SPD[p1, p3] SPD[p2, p4] SPD[p3, p3] - + 2 m0^2 SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p1] SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] + + 2 SPD[p1, p2] SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] + + SPD[p1, p3] SPD[p1, p4] SPD[p2, p4] SPD[p3, p3] + + SPD[p1, p1] SPD[p2, p2] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p4] SPD[p2, p2] SPD[p2, p4] SPD[p3, p3] - + SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] SPD[p3, p3] + + SPD[p1, p4] SPD[p2, p3] SPD[p2, p4] SPD[p3, p3] + + m0^2 SPD[p2, p4]^2 SPD[p3, p3] - + SPD[p1, p3] SPD[p2, p4]^2 SPD[p3, p3] - + 2 m0^2 SPD[p1, p2]^2 SPD[p3, p4] + + 2 m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p3, p4] + + 2 m0^2 SPD[p1, p2] SPD[p1, p4] SPD[p3, p4] - + 2 m0^2 SPD[p1, p3] SPD[p1, p4] SPD[p3, p4] + + 2 m0^2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p4] - + 2 m0^2 SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] - + SPD[p1, p1] SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] + + SPD[p1, p2] SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] - + 2 m0^2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] - + SPD[p1, p1] SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] + + SPD[p1, p2] SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] + + 2 SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p3, p4] - + 2 m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p3, p4] + + 2 m0^2 SPD[p1, p2] SPD[p2, p3] SPD[p3, p4] + + SPD[p1, p1] SPD[p1, p2] SPD[p2, p3] SPD[p3, p4] + + 2 m0^2 SPD[p1, p4] SPD[p2, p3] SPD[p3, p4] + + SPD[p1, p1] SPD[p1, p4] SPD[p2, p3] SPD[p3, p4] - + 4 SPD[p1, p2] SPD[p1, p4] SPD[p2, p3] SPD[p3, p4] - + SPD[p1, p1] SPD[p2, p2] SPD[p2, p3] SPD[p3, p4] + + SPD[p1, p4] SPD[p2, p2] SPD[p2, p3] SPD[p3, p4] - + 2 m0^2 SPD[p1, p1] SPD[p2, p4] SPD[p3, p4] + + 2 m0^2 SPD[p1, p2] SPD[p2, p4] SPD[p3, p4] + + SPD[p1, p1] SPD[p1, p2] SPD[p2, p4] SPD[p3, p4] + + 2 m0^2 SPD[p1, p3] SPD[p2, p4] SPD[p3, p4] + + SPD[p1, p1] SPD[p1, p3] SPD[p2, p4] SPD[p3, p4] - + 4 SPD[p1, p2] SPD[p1, p3] SPD[p2, p4] SPD[p3, p4] - + SPD[p1, p1] SPD[p2, p2] SPD[p2, p4] SPD[p3, p4] + + SPD[p1, p3] SPD[p2, p2] SPD[p2, p4] SPD[p3, p4] - + 2 m0^2 SPD[p2, p3] SPD[p2, p4] SPD[p3, p4] + + 2 SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] SPD[p3, p4] - + SPD[p1, p2]^2 SPD[p3, p3] SPD[p3, p4] + + SPD[p1, p2] SPD[p1, p4] SPD[p3, p3] SPD[p3, p4] + + SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] SPD[p3, p4] - + SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] SPD[p3, p4] - + SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] SPD[p3, p4] + + SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] SPD[p3, p4] + + m0^2 SPD[p1, p1] SPD[p3, p4]^2 - + 2 m0^2 SPD[p1, p2] SPD[p3, p4]^2 - + SPD[p1, p1] SPD[p1, p2] SPD[p3, p4]^2 + + 2 SPD[p1, p2]^2 SPD[p3, p4]^2 + m0^2 SPD[p2, p2] SPD[p3, p4]^2 - + SPD[p1, p2] SPD[p2, p2] SPD[p3, p4]^2 + + m0^2 SPD[p1, p2]^2 SPD[p4, p4] - + 2 m0^2 SPD[p1, p2] SPD[p1, p3] SPD[p4, p4] + + m0^2 SPD[p1, p3]^2 SPD[p4, p4] - + m0^2 SPD[p1, p1] SPD[p2, p2] SPD[p4, p4] + + 2 m0^2 SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] + + SPD[p1, p1] SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] - + SPD[p1, p2] SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] - + SPD[p1, p3] SPD[p1, p4] SPD[p2, p2] SPD[p4, p4] + + 2 m0^2 SPD[p1, p1] SPD[p2, p3] SPD[p4, p4] - + 2 m0^2 SPD[p1, p2] SPD[p2, p3] SPD[p4, p4] - + SPD[p1, p1] SPD[p1, p2] SPD[p2, p3] SPD[p4, p4] - + 2 m0^2 SPD[p1, p3] SPD[p2, p3] SPD[p4, p4] - + SPD[p1, p1] SPD[p1, p3] SPD[p2, p3] SPD[p4, p4] + + 2 SPD[p1, p2] SPD[p1, p3] SPD[p2, p3] SPD[p4, p4] + + SPD[p1, p2] SPD[p1, p4] SPD[p2, p3] SPD[p4, p4] + + SPD[p1, p3] SPD[p1, p4] SPD[p2, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p2] SPD[p2, p3] SPD[p4, p4] - + SPD[p1, p3] SPD[p2, p2] SPD[p2, p3] SPD[p4, p4] + + m0^2 SPD[p2, p3]^2 SPD[p4, p4] - + SPD[p1, p4] SPD[p2, p3]^2 SPD[p4, p4] + + SPD[p1, p2] SPD[p1, p3] SPD[p2, p4] SPD[p4, p4] - + SPD[p1, p3]^2 SPD[p2, p4] SPD[p4, p4] - + SPD[p1, p1] SPD[p2, p3] SPD[p2, p4] SPD[p4, p4] + + SPD[p1, p3] SPD[p2, p3] SPD[p2, p4] SPD[p4, p4] - + m0^2 SPD[p1, p1] SPD[p3, p3] SPD[p4, p4] + + 2 m0^2 SPD[p1, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p1, p2] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p1, p3] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p1, p4] SPD[p3, p3] SPD[p4, p4] - + m0^2 SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] - + 2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p2] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p3] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p3] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p2, p3] SPD[p3, p3] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p2] SPD[p2, p4] SPD[p3, p3] SPD[p4, p4] - + SPD[p1, p2]^2 SPD[p3, p4] SPD[p4, p4] + + SPD[p1, p2] SPD[p1, p3] SPD[p3, p4] SPD[p4, p4] + + SPD[p1, p1] SPD[p2, p2] SPD[p3, p4] SPD[p4, p4] - + SPD[p1, p3] SPD[p2, p2] SPD[p3, p4] SPD[p4, p4] - + SPD[p1, p1] SPD[p2, p3] SPD[p3, p4] SPD[p4, p4] + + SPD[p1, p2] SPD[p2, p3] SPD[p3, p4] SPD[p4, + p4]))/(-(-SPD[p1, p1] + 2 SPD[p1, p4] - + SPD[p4, p4]) ((-2 m0^4 SPD[p1, p2] + 2 m0^4 SPD[p1, p3] + + 2 m0^4 SPD[p2, p2] + 2 m0^2 SPD[p1, p1] SPD[p2, p2] - + 2 m0^2 SPD[p1, p2] SPD[p2, p2] - + 4 m0^2 SPD[p1, p3] SPD[p2, p2] + + 2 SPD[p1, p3] SPD[p2, p2]^2 - 2 m0^4 SPD[p2, p3] - + 2 m0^2 SPD[p1, p1] SPD[p2, p3] + + 8 m0^2 SPD[p1, p2] SPD[p2, p3] - + 2 m0^2 SPD[p2, p2] SPD[p2, p3] - + 2 SPD[p1, p1] SPD[p2, p2] SPD[p2, p3] - + 2 m0^2 SPD[p1, p2] SPD[p3, p3] + + 2 m0^2 SPD[p2, p2] SPD[p3, p3] + + 2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p3] - + 2 SPD[p1, p2] SPD[p2, p2] SPD[p3, p3]) (-SPD[p3, p3] + + 2 SPD[p3, p4] - SPD[p4, p4]) + (-SPD[p2, p2] + + 2 SPD[p2, p3] - SPD[p3, p3]) (-2 m0^4 SPD[p1, p3] + + 2 m0^4 SPD[p1, p4] - 2 m0^2 SPD[p1, p3] SPD[p2, p2] + + 2 m0^2 SPD[p1, p4] SPD[p2, p2] + 2 m0^4 SPD[p2, p3] + + 2 m0^2 SPD[p1, p1] SPD[p2, p3] - + 8 m0^2 SPD[p1, p4] SPD[p2, p3] - 2 m0^4 SPD[p2, p4] - + 2 m0^2 SPD[p1, p1] SPD[p2, p4] + + 8 m0^2 SPD[p1, p3] SPD[p2, p4] + + 2 m0^2 SPD[p1, p4] SPD[p3, p3] + + 2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] - + 2 m0^2 SPD[p2, p4] SPD[p3, p3] - + 2 SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] - + 2 m0^2 SPD[p1, p3] SPD[p4, p4] - + 2 SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] + + 2 m0^2 SPD[p2, p3] SPD[p4, p4] + + 2 SPD[p1, p1] SPD[p2, p3] SPD[p4, p4]) - (m0^2 - + SPD[p3, p3]) ((-2 m0^2 SPD[p1, p2] + 2 m0^2 SPD[p1, p3] + + m0^2 SPD[p2, p2] + SPD[p1, p1] SPD[p2, p2] - + 2 SPD[p1, p3] SPD[p2, p2] - m0^2 SPD[p3, p3] - + SPD[p1, p1] SPD[p3, p3] + + 2 SPD[p1, p2] SPD[p3, p3]) (-SPD[p2, p2] + 2 SPD[p2, p4] - + SPD[p4, p4]) - (-SPD[p2, p2] + 2 SPD[p2, p3] - + SPD[p3, p3]) (-2 m0^2 SPD[p1, p2] + 2 m0^2 SPD[p1, p4] + + m0^2 SPD[p2, p2] + SPD[p1, p1] SPD[p2, p2] - + 2 SPD[p1, p4] SPD[p2, p2] - m0^2 SPD[p4, p4] - + SPD[p1, p1] SPD[p4, p4] + + 2 SPD[p1, p2] SPD[p4, p4]))) + (-SPD[p2, p2] + + 2 SPD[p2, p4] - + SPD[p4, p4]) ((-2 m0^4 SPD[p1, p1] + 2 m0^4 SPD[p1, p2] + + 2 m0^2 SPD[p1, p1] SPD[p1, p2] + 2 m0^4 SPD[p1, p3] + + 2 m0^2 SPD[p1, p1] SPD[p1, p3] - + 8 m0^2 SPD[p1, p2] SPD[p1, p3] - + 2 m0^2 SPD[p1, p1] SPD[p2, p2] + + 2 m0^2 SPD[p1, p3] SPD[p2, p2] + + 2 SPD[p1, p1] SPD[p1, p3] SPD[p2, p2] - 2 m0^4 SPD[p2, p3] + + 4 m0^2 SPD[p1, p1] SPD[p2, p3] - + 2 SPD[p1, p1]^2 SPD[p2, p3] - + 2 m0^2 SPD[p1, p1] SPD[p3, p3] + + 2 m0^2 SPD[p1, p2] SPD[p3, p3] + + 2 SPD[p1, p1] SPD[p1, p2] SPD[p3, p3] - + 2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p3]) (-SPD[p3, p3] + + 2 SPD[p3, p4] - SPD[p4, p4]) + (-SPD[p1, p1] + + 2 SPD[p1, p3] - SPD[p3, p3]) (-2 m0^4 SPD[p1, p3] + + 2 m0^4 SPD[p1, p4] - 2 m0^2 SPD[p1, p3] SPD[p2, p2] + + 2 m0^2 SPD[p1, p4] SPD[p2, p2] + 2 m0^4 SPD[p2, p3] + + 2 m0^2 SPD[p1, p1] SPD[p2, p3] - + 8 m0^2 SPD[p1, p4] SPD[p2, p3] - 2 m0^4 SPD[p2, p4] - + 2 m0^2 SPD[p1, p1] SPD[p2, p4] + + 8 m0^2 SPD[p1, p3] SPD[p2, p4] + + 2 m0^2 SPD[p1, p4] SPD[p3, p3] + + 2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] - + 2 m0^2 SPD[p2, p4] SPD[p3, p3] - + 2 SPD[p1, p1] SPD[p2, p4] SPD[p3, p3] - + 2 m0^2 SPD[p1, p3] SPD[p4, p4] - + 2 SPD[p1, p3] SPD[p2, p2] SPD[p4, p4] + + 2 m0^2 SPD[p2, p3] SPD[p4, p4] + + 2 SPD[p1, p1] SPD[p2, p3] SPD[p4, p4]) - (m0^2 - + SPD[p3, p3]) (-(m0^2 SPD[p1, p1] - 2 m0^2 SPD[p1, p2] + + SPD[p1, p1] SPD[p2, p2] + 2 m0^2 SPD[p2, p3] - + 2 SPD[p1, p1] SPD[p2, p3] - m0^2 SPD[p3, p3] + + 2 SPD[p1, p2] SPD[p3, p3] - + SPD[p2, p2] SPD[p3, p3]) (-SPD[p1, p1] + 2 SPD[p1, p4] - + SPD[p4, p4]) + (-SPD[p1, p1] + 2 SPD[p1, p3] - + SPD[p3, p3]) (m0^2 SPD[p1, p1] - 2 m0^2 SPD[p1, p2] + + SPD[p1, p1] SPD[p2, p2] + 2 m0^2 SPD[p2, p4] - + 2 SPD[p1, p1] SPD[p2, p4] - m0^2 SPD[p4, p4] + + 2 SPD[p1, p2] SPD[p4, p4] - + SPD[p2, p2] SPD[p4, p4]))) + (m0^2 - + SPD[p4, p4]) (((m0^2 - SPD[p1, p1]) (-SPD[p1, p1] + + 2 SPD[p1, p2] - SPD[p2, p2]) (-SPD[p2, p2] + + 2 SPD[p2, p3] - SPD[p3, p3]) + (-SPD[p1, p1] + + 2 SPD[p1, p2] - SPD[p2, p2]) (-2 m0^2 SPD[p1, p2] + + 2 m0^2 SPD[p1, p3] + m0^2 SPD[p2, p2] + + SPD[p1, p1] SPD[p2, p2] - 2 SPD[p1, p3] SPD[p2, p2] - + m0^2 SPD[p3, p3] - SPD[p1, p1] SPD[p3, p3] + + 2 SPD[p1, p2] SPD[p3, p3])) (-SPD[p3, p3] + + 2 SPD[p3, p4] - SPD[p4, p4]) - (-SPD[p1, p1] + + 2 SPD[p1, p3] - + SPD[p3, p3]) ((-2 m0^2 SPD[p1, p2] + 2 m0^2 SPD[p1, p3] + + m0^2 SPD[p2, p2] + SPD[p1, p1] SPD[p2, p2] - + 2 SPD[p1, p3] SPD[p2, p2] - m0^2 SPD[p3, p3] - + SPD[p1, p1] SPD[p3, p3] + + 2 SPD[p1, p2] SPD[p3, p3]) (-SPD[p2, p2] + 2 SPD[p2, p4] - + SPD[p4, p4]) - (-SPD[p2, p2] + 2 SPD[p2, p3] - + SPD[p3, p3]) (-2 m0^2 SPD[p1, p2] + 2 m0^2 SPD[p1, p4] + + m0^2 SPD[p2, p2] + SPD[p1, p1] SPD[p2, p2] - + 2 SPD[p1, p4] SPD[p2, p2] - m0^2 SPD[p4, p4] - + SPD[p1, p1] SPD[p4, p4] + + 2 SPD[p1, p2] SPD[p4, p4])) + (-SPD[p2, p2] + + 2 SPD[p2, p3] - + SPD[p3, p3]) (-(m0^2 SPD[p1, p1] - 2 m0^2 SPD[p1, p2] + + SPD[p1, p1] SPD[p2, p2] + 2 m0^2 SPD[p2, p3] - + 2 SPD[p1, p1] SPD[p2, p3] - m0^2 SPD[p3, p3] + + 2 SPD[p1, p2] SPD[p3, p3] - + SPD[p2, p2] SPD[p3, p3]) (-SPD[p1, p1] + 2 SPD[p1, p4] - + SPD[p4, p4]) + (-SPD[p1, p1] + 2 SPD[p1, p3] - + SPD[p3, p3]) (m0^2 SPD[p1, p1] - 2 m0^2 SPD[p1, p2] + + SPD[p1, p1] SPD[p2, p2] + 2 m0^2 SPD[p2, p4] - + 2 SPD[p1, p1] SPD[p2, p4] - m0^2 SPD[p4, p4] + + 2 SPD[p1, p2] SPD[p4, p4] - + SPD[p2, p2] SPD[p4, p4]))) - (-SPD[p3, p3] + + 2 SPD[p3, p4] - + SPD[p4, p4]) (-(-2 m0^4 SPD[p1, p1] + 2 m0^4 SPD[p1, p2] + + 2 m0^2 SPD[p1, p1] SPD[p1, p2] + 2 m0^4 SPD[p1, p3] + + 2 m0^2 SPD[p1, p1] SPD[p1, p3] - + 8 m0^2 SPD[p1, p2] SPD[p1, p3] - + 2 m0^2 SPD[p1, p1] SPD[p2, p2] + + 2 m0^2 SPD[p1, p3] SPD[p2, p2] + + 2 SPD[p1, p1] SPD[p1, p3] SPD[p2, p2] - + 2 m0^4 SPD[p2, p3] + 4 m0^2 SPD[p1, p1] SPD[p2, p3] - + 2 SPD[p1, p1]^2 SPD[p2, p3] - + 2 m0^2 SPD[p1, p1] SPD[p3, p3] + + 2 m0^2 SPD[p1, p2] SPD[p3, p3] + + 2 SPD[p1, p1] SPD[p1, p2] SPD[p3, p3] - + 2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p3]) (-SPD[p2, p2] + + 2 SPD[p2, p4] - SPD[p4, p4]) - (-SPD[p1, p1] + + 2 SPD[p1, p2] - SPD[p2, p2]) (-2 m0^4 SPD[p1, p2] + + 2 m0^4 SPD[p1, p4] + 2 m0^2 SPD[p1, p4] SPD[p2, p2] + + 2 m0^4 SPD[p2, p3] + 2 m0^2 SPD[p1, p1] SPD[p2, p3] - + 8 m0^2 SPD[p1, p4] SPD[p2, p3] - + 2 m0^2 SPD[p1, p2] SPD[p3, p3] + + 2 m0^2 SPD[p1, p4] SPD[p3, p3] + + 2 SPD[p1, p4] SPD[p2, p2] SPD[p3, p3] - 2 m0^4 SPD[p3, p4] - + 2 m0^2 SPD[p1, p1] SPD[p3, p4] + + 8 m0^2 SPD[p1, p2] SPD[p3, p4] - + 2 m0^2 SPD[p2, p2] SPD[p3, p4] - + 2 SPD[p1, p1] SPD[p2, p2] SPD[p3, p4] - + 2 m0^2 SPD[p1, p2] SPD[p4, p4] + + 2 m0^2 SPD[p2, p3] SPD[p4, p4] + + 2 SPD[p1, p1] SPD[p2, p3] SPD[p4, p4] - + 2 SPD[p1, p2] SPD[p3, p3] SPD[p4, p4]) + (m0^2 - + SPD[p2, p2]) (-(m0^2 SPD[p1, p1] - 2 m0^2 SPD[p1, p3] - + m0^2 SPD[p2, p2] + 2 SPD[p1, p3] SPD[p2, p2] + + 2 m0^2 SPD[p2, p3] - 2 SPD[p1, p1] SPD[p2, p3] + + SPD[p1, p1] SPD[p3, p3] - + SPD[p2, p2] SPD[p3, p3]) (-SPD[p1, p1] + 2 SPD[p1, p4] - + SPD[p4, p4]) + (-SPD[p1, p1] + 2 SPD[p1, p2] - + SPD[p2, p2]) (m0^2 SPD[p1, p1] - 2 m0^2 SPD[p1, p3] + + SPD[p1, p1] SPD[p3, p3] + 2 m0^2 SPD[p3, p4] - + 2 SPD[p1, p1] SPD[p3, p4] - m0^2 SPD[p4, p4] + + 2 SPD[p1, p3] SPD[p4, p4] - SPD[p3, p3] SPD[p4, p4]))))"}, +{"fcstNPointTo4Point-ID2", "NPointTo4Point[FCI@FAD[{q, m0}, {q, 0}, {q, 0}, {q, 0}, {q, 0}], q, +FCE -> True]", "FeynAmpDenominator[PropagatorDenominator[Momentum[q, D], m0], +PropagatorDenominator[Momentum[q, D], 0], +PropagatorDenominator[Momentum[q, D], 0], +PropagatorDenominator[Momentum[q, D], 0], +PropagatorDenominator[Momentum[q, D], 0]]"}, +{"fcstNPointTo4Point-ID3", "NPointTo4Point[0, q]", "0"}, +{"fcstNPointTo4Point-ID4", +"NPointTo4Point[ +FCI[FVD[q, mu] FAD[{q, m0}, {q + p1, m1}, {q + p2, m2}, {q + p3,m3}, {q + p4, m4}]], q]", " +FeynAmpDenominator[PropagatorDenominator[Momentum[q, D], m0], +PropagatorDenominator[Momentum[p1, D] + Momentum[q, D], m1], +PropagatorDenominator[Momentum[p2, D] + Momentum[q, D], m2], +PropagatorDenominator[Momentum[p3, D] + Momentum[q, D], m3], +PropagatorDenominator[Momentum[p4, D] + Momentum[q, D], m4]] Pair[ +LorentzIndex[mu, D], Momentum[q, D]]"} +}) diff --git a/Tests/LoopIntegrals/OneLoop.test b/Tests/LoopIntegrals/OneLoop.test index 47200f7cf..77bc41dc5 100644 --- a/Tests/LoopIntegrals/OneLoop.test +++ b/Tests/LoopIntegrals/OneLoop.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for OneLoop *) @@ -15,22 +15,17 @@ Tests`LoopIntegrals`fcstOneLoop = { -{"fcstOneLoop-ID1","OneLoop[q, -I/Pi^ 2 FeynAmpDenominator[PropagatorDenominator[q, m]]]","A0[m^2]"}, -{"fcstOneLoop-ID2","OneLoop[q, (I el^2)/(16 Pi^4)/(1 - D)* - FeynAmpDenominator[PropagatorDenominator[q, mf], - PropagatorDenominator[q - k, mf]]* - DiracTrace[(mf + DiracSlash[q - k]).DiracMatrix[ - mu].(mf + DiracSlash[q]).DiracMatrix[mu]], - Factoring -> True] /. ScalarProduct[k, k] -> k2 /. - mf^2 -> mf2 // Simplify","-(el^2*(2*(-2 + D)*A0[mf2] - ((-2 + D)*k2 + 4*mf2)*B0[k2, mf2, mf2]))/(8*(-1 + D)*Pi^2)"}, +{"fcstOneLoop-ID1","OneLoop[q, -I/Pi^ 2 FAD[{q, m}]]","A0[m^2]"}, +{"fcstOneLoop-ID2","OneLoop[q, (I el^2)/(16 Pi^4)/(1 - D)*FAD[{q, mf}, {q - k, mf}]* + DiracTrace[(mf + GSD[-k + q]).GAD[mu].(mf + GSD[q]).GAD[mu]], + Factoring -> True] /. ScalarProduct[k, k] -> k2 /. mf^2 -> mf2 // FullSimplify", + "(el^2*(-2*(-2 + D)*A0[mf2] + ((-2 + D)*k2 + 4*mf2)*B0[k2, mf2, mf2]))/(8*(-1 + D)*Pi^2)"}, {"fcstOneLoop-ID3","OneLoop[q, xxx + FAD[{q,m}]]","xxx + I \[Pi]^2 A0[m^2]"}, {"fcstOneLoop-ID4","OneLoop[k, -32 M FeynAmpDenominator[PropagatorDenominator[k, M], -PropagatorDenominator[k - q1 - q2, M], -PropagatorDenominator[k - q1, M]] Pair[Momentum[k], -Momentum[Polarization[q1, I, Transversality -> True]]] Pair[ -Momentum[k], -Momentum[Polarization[q2, I, Transversality -> True]]]]","(32*I)*M*Pi^2*(-(Pair[Momentum[q1], +32 M FAD[{k, M}, {k - q1 - q2, M}, {k - q1, M}] Pair[Momentum[k, D], +Momentum[Polarization[q1, I, Transversality -> True], D]] Pair[ +Momentum[k, D], +Momentum[Polarization[q2, I, Transversality -> True], D]]]","(32*I)*M*Pi^2*(-(Pair[Momentum[q1], Momentum[Polarization[q2, I, Transversality -> True]]]*Pair[Momentum[q2], Momentum[Polarization[q1, I, Transversality -> True]]]*PaVe[2, {Pair[Momentum[q1], Momentum[q1]], Pair[Momentum[q1], Momentum[q1]] + 2*Pair[Momentum[q1], Momentum[q2]] + @@ -46,8 +41,8 @@ Momentum[q1]], Pair[Momentum[q1], Momentum[q1]] + 2*Pair[Momentum[q1], Momentum[ Pair[Momentum[q2], Momentum[q2]], Pair[Momentum[q2], Momentum[q2]]}, {M^2, M^2, M^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True])"}, {"fcstOneLoop-ID5","OneLoop[q, FAD[q, q - p1]]","I Pi^2 B0[Pair[Momentum[p1], Momentum[p1]], 0, 0]"}, -{"fcstOneLoop-ID6","OneLoop[q1, ((-I)*GA[mu]).(m + GS[q1]).GA[nu].(m + -GS[q1]).((-I)*GA[mu])*FAD[{q1, 0}, {q1, 0}, {-p + q1, 0}]]//FCE", +{"fcstOneLoop-ID6","OneLoop[q1, ((-I)*GAD[mu]).(m + GSD[q1]).GAD[nu].(m + GSD[q1]).((-I)*GAD[mu])* +FAD[{q1, 0}, {q1, 0}, {-p + q1, 0}]] // FCE", "-I \[Pi]^2 (2 D m C0[0, SP[p, p], SP[p, p], 0, 0, 0] FV[p, nu] - (2 - D) B0[SP[p, p], 0, 0] GA[nu] + (2 - D) m^2 C0[0, SP[p, p], SP[p, p], 0, 0, 0] GA[nu] + @@ -63,13 +58,850 @@ GS[q1]).((-I)*GA[mu])*FAD[{q1, 0}, {q1, 0}, {-p + q1, 0}]]//FCE", 0, {0, 0, SP[p1, p1], SP[p1, p1] - 2 SP[p1, p2] + SP[p2, p2], SP[p2, p2], 0, SP[p1, p1], SP[p2, p2], SP[p1, p1], SP[p2, p2]}, {0, 0, 0, 0, m^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]"}, -{"fcstOneLoop-ID8","Simplify[ChangeDimension[ -OneLoop[q, - FVD[q, mu] FAD[{q, 0}, {q + p1, 0}, {q + p2, 0}, {q + p3, - 0}, {q + p4, 0}]], D] - -TID[FVD[q, - mu] FAD[{q, 0}, {q + p1, 0}, {q + p2, 0}, {q + p3, 0}, {q + p4, - 0}], q, UsePaVeBasis -> True]]", -"0"}, -{"fcstOneLoop-ID9","OneLoop[k, FVD[k1, al] FAD[k, m]]","0"} +{"fcstOneLoop-ID8","OneLoop[q,FCI@FAD[{q, m0}, {q + p1, m1}, {q + p2, m2}, {q + p3, m3}, +{q + p4, m4}]] // PaVeOrder // FCE", +"(I \[Pi]^2 (8 D0[SP[p1, p1], SP[p2, p2], + SP[p2, p2] - 2 SP[p2, p3] + SP[p3, p3], + SP[p1, p1] - 2 SP[p1, p3] + SP[p3, p3], + SP[p1, p1] - 2 SP[p1, p2] + SP[p2, p2], SP[p3, p3], m1^2, m0^2, + m2^2, m3^2] (m0^2 SP[p1, p3]^2 SP[p2, p2] - + m4^2 SP[p1, p3]^2 SP[p2, p2] - + m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p2] + + m3^2 SP[p1, p3] SP[p1, p4] SP[p2, p2] - + 2 m0^2 SP[p1, p2] SP[p1, p3] SP[p2, p3] + + 2 m4^2 SP[p1, p2] SP[p1, p3] SP[p2, p3] + + m0^2 SP[p1, p2] SP[p1, p4] SP[p2, p3] - + m3^2 SP[p1, p2] SP[p1, p4] SP[p2, p3] + + m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p3] - + m2^2 SP[p1, p3] SP[p1, p4] SP[p2, p3] + + SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p2, p3] + + m0^2 SP[p1, p1] SP[p2, p3]^2 - m4^2 SP[p1, p1] SP[p2, p3]^2 - + m0^2 SP[p1, p4] SP[p2, p3]^2 + m1^2 SP[p1, p4] SP[p2, p3]^2 - + SP[p1, p1] SP[p1, p4] SP[p2, p3]^2 + + m0^2 SP[p1, p2] SP[p1, p3] SP[p2, p4] - + m3^2 SP[p1, p2] SP[p1, p3] SP[p2, p4] - + m0^2 SP[p1, p3]^2 SP[p2, p4] + m2^2 SP[p1, p3]^2 SP[p2, p4] - + SP[p1, p3]^2 SP[p2, p2] SP[p2, p4] - + m0^2 SP[p1, p1] SP[p2, p3] SP[p2, p4] + + m3^2 SP[p1, p1] SP[p2, p3] SP[p2, p4] + + m0^2 SP[p1, p3] SP[p2, p3] SP[p2, p4] - + m1^2 SP[p1, p3] SP[p2, p3] SP[p2, p4] + + SP[p1, p1] SP[p1, p3] SP[p2, p3] SP[p2, p4] + + m0^2 SP[p1, p2]^2 SP[p3, p3] - m4^2 SP[p1, p2]^2 SP[p3, p3] - + m0^2 SP[p1, p2] SP[p1, p4] SP[p3, p3] + + m2^2 SP[p1, p2] SP[p1, p4] SP[p3, p3] - + m0^2 SP[p1, p1] SP[p2, p2] SP[p3, p3] + + m4^2 SP[p1, p1] SP[p2, p2] SP[p3, p3] + + m0^2 SP[p1, p4] SP[p2, p2] SP[p3, p3] - + m1^2 SP[p1, p4] SP[p2, p2] SP[p3, p3] + + SP[p1, p1] SP[p1, p4] SP[p2, p2] SP[p3, p3] - + SP[p1, p2] SP[p1, p4] SP[p2, p2] SP[p3, p3] - + SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p3, p3] + + SP[p1, p2] SP[p1, p4] SP[p2, p3] SP[p3, p3] + + m0^2 SP[p1, p1] SP[p2, p4] SP[p3, p3] - + m2^2 SP[p1, p1] SP[p2, p4] SP[p3, p3] - + m0^2 SP[p1, p2] SP[p2, p4] SP[p3, p3] + + m1^2 SP[p1, p2] SP[p2, p4] SP[p3, p3] - + SP[p1, p1] SP[p1, p2] SP[p2, p4] SP[p3, p3] + + SP[p1, p2] SP[p1, p3] SP[p2, p4] SP[p3, p3] + + SP[p1, p1] SP[p2, p2] SP[p2, p4] SP[p3, p3] - + SP[p1, p1] SP[p2, p3] SP[p2, p4] SP[p3, p3] - + m0^2 SP[p1, p2]^2 SP[p3, p4] + m3^2 SP[p1, p2]^2 SP[p3, p4] + + m0^2 SP[p1, p2] SP[p1, p3] SP[p3, p4] - + m2^2 SP[p1, p2] SP[p1, p3] SP[p3, p4] + + m0^2 SP[p1, p1] SP[p2, p2] SP[p3, p4] - + m3^2 SP[p1, p1] SP[p2, p2] SP[p3, p4] - + m0^2 SP[p1, p3] SP[p2, p2] SP[p3, p4] + + m1^2 SP[p1, p3] SP[p2, p2] SP[p3, p4] - + SP[p1, p1] SP[p1, p3] SP[p2, p2] SP[p3, p4] + + SP[p1, p2] SP[p1, p3] SP[p2, p2] SP[p3, p4] - + m0^2 SP[p1, p1] SP[p2, p3] SP[p3, p4] + + m2^2 SP[p1, p1] SP[p2, p3] SP[p3, p4] + + m0^2 SP[p1, p2] SP[p2, p3] SP[p3, p4] - + m1^2 SP[p1, p2] SP[p2, p3] SP[p3, p4] + + SP[p1, p1] SP[p1, p2] SP[p2, p3] SP[p3, p4] - + SP[p1, p1] SP[p2, p2] SP[p2, p3] SP[p3, p4] - + SP[p1, p2]^2 SP[p3, p3] SP[p3, p4] + + SP[p1, p1] SP[p2, p2] SP[p3, p3] SP[p3, p4] + + SP[p1, p3]^2 SP[p2, p2] SP[p4, p4] - + 2 SP[p1, p2] SP[p1, p3] SP[p2, p3] SP[p4, p4] + + SP[p1, p1] SP[p2, p3]^2 SP[p4, p4] + + SP[p1, p2]^2 SP[p3, p3] SP[p4, p4] - + SP[p1, p1] SP[p2, p2] SP[p3, p3] SP[p4, p4]) - + 8 D0[SP[p1, p1], SP[p2, p2], + SP[p2, p2] - 2 SP[p2, p4] + SP[p4, p4], + SP[p1, p1] - 2 SP[p1, p4] + SP[p4, p4], + SP[p1, p1] - 2 SP[p1, p2] + SP[p2, p2], SP[p4, p4], m1^2, m0^2, + m2^2, m4^2] (m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p2] - + m4^2 SP[p1, p3] SP[p1, p4] SP[p2, p2] - + m0^2 SP[p1, p4]^2 SP[p2, p2] + m3^2 SP[p1, p4]^2 SP[p2, p2] - + m0^2 SP[p1, p2] SP[p1, p4] SP[p2, p3] + + m4^2 SP[p1, p2] SP[p1, p4] SP[p2, p3] + + m0^2 SP[p1, p4]^2 SP[p2, p3] - m2^2 SP[p1, p4]^2 SP[p2, p3] + + SP[p1, p4]^2 SP[p2, p2] SP[p2, p3] - + m0^2 SP[p1, p2] SP[p1, p3] SP[p2, p4] + + m4^2 SP[p1, p2] SP[p1, p3] SP[p2, p4] + + 2 m0^2 SP[p1, p2] SP[p1, p4] SP[p2, p4] - + 2 m3^2 SP[p1, p2] SP[p1, p4] SP[p2, p4] - + m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p4] + + m2^2 SP[p1, p3] SP[p1, p4] SP[p2, p4] - + SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p2, p4] + + m0^2 SP[p1, p1] SP[p2, p3] SP[p2, p4] - + m4^2 SP[p1, p1] SP[p2, p3] SP[p2, p4] - + m0^2 SP[p1, p4] SP[p2, p3] SP[p2, p4] + + m1^2 SP[p1, p4] SP[p2, p3] SP[p2, p4] - + SP[p1, p1] SP[p1, p4] SP[p2, p3] SP[p2, p4] - + m0^2 SP[p1, p1] SP[p2, p4]^2 + m3^2 SP[p1, p1] SP[p2, p4]^2 + + m0^2 SP[p1, p3] SP[p2, p4]^2 - m1^2 SP[p1, p3] SP[p2, p4]^2 + + SP[p1, p1] SP[p1, p3] SP[p2, p4]^2 - + SP[p1, p4]^2 SP[p2, p2] SP[p3, p3] + + 2 SP[p1, p2] SP[p1, p4] SP[p2, p4] SP[p3, p3] - + SP[p1, p1] SP[p2, p4]^2 SP[p3, p3] + + m0^2 SP[p1, p2]^2 SP[p3, p4] - m4^2 SP[p1, p2]^2 SP[p3, p4] - + m0^2 SP[p1, p2] SP[p1, p4] SP[p3, p4] + + m2^2 SP[p1, p2] SP[p1, p4] SP[p3, p4] - + m0^2 SP[p1, p1] SP[p2, p2] SP[p3, p4] + + m4^2 SP[p1, p1] SP[p2, p2] SP[p3, p4] + + m0^2 SP[p1, p4] SP[p2, p2] SP[p3, p4] - + m1^2 SP[p1, p4] SP[p2, p2] SP[p3, p4] + + SP[p1, p1] SP[p1, p4] SP[p2, p2] SP[p3, p4] - + SP[p1, p2] SP[p1, p4] SP[p2, p2] SP[p3, p4] + + m0^2 SP[p1, p1] SP[p2, p4] SP[p3, p4] - + m2^2 SP[p1, p1] SP[p2, p4] SP[p3, p4] - + m0^2 SP[p1, p2] SP[p2, p4] SP[p3, p4] + + m1^2 SP[p1, p2] SP[p2, p4] SP[p3, p4] - + SP[p1, p1] SP[p1, p2] SP[p2, p4] SP[p3, p4] + + SP[p1, p1] SP[p2, p2] SP[p2, p4] SP[p3, p4] - + m0^2 SP[p1, p2]^2 SP[p4, p4] + m3^2 SP[p1, p2]^2 SP[p4, p4] + + m0^2 SP[p1, p2] SP[p1, p3] SP[p4, p4] - + m2^2 SP[p1, p2] SP[p1, p3] SP[p4, p4] + + m0^2 SP[p1, p1] SP[p2, p2] SP[p4, p4] - + m3^2 SP[p1, p1] SP[p2, p2] SP[p4, p4] - + m0^2 SP[p1, p3] SP[p2, p2] SP[p4, p4] + + m1^2 SP[p1, p3] SP[p2, p2] SP[p4, p4] - + SP[p1, p1] SP[p1, p3] SP[p2, p2] SP[p4, p4] + + SP[p1, p2] SP[p1, p3] SP[p2, p2] SP[p4, p4] + + SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p4, p4] - + m0^2 SP[p1, p1] SP[p2, p3] SP[p4, p4] + + m2^2 SP[p1, p1] SP[p2, p3] SP[p4, p4] + + m0^2 SP[p1, p2] SP[p2, p3] SP[p4, p4] - + m1^2 SP[p1, p2] SP[p2, p3] SP[p4, p4] + + SP[p1, p1] SP[p1, p2] SP[p2, p3] SP[p4, p4] - + SP[p1, p2] SP[p1, p4] SP[p2, p3] SP[p4, p4] - + SP[p1, p1] SP[p2, p2] SP[p2, p3] SP[p4, p4] - + SP[p1, p2] SP[p1, p3] SP[p2, p4] SP[p4, p4] + + SP[p1, p1] SP[p2, p3] SP[p2, p4] SP[p4, p4] - + SP[p1, p2]^2 SP[p3, p3] SP[p4, p4] + + SP[p1, p1] SP[p2, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p2]^2 SP[p3, p4] SP[p4, p4] - + SP[p1, p1] SP[p2, p2] SP[p3, p4] SP[p4, p4]) + + 8 D0[SP[p1, p1], SP[p3, p3], + SP[p3, p3] - 2 SP[p3, p4] + SP[p4, p4], + SP[p1, p1] - 2 SP[p1, p4] + SP[p4, p4], + SP[p1, p1] - 2 SP[p1, p3] + SP[p3, p3], SP[p4, p4], m1^2, m0^2, + m3^2, m4^2] (m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p3] - + m4^2 SP[p1, p3] SP[p1, p4] SP[p2, p3] - + m0^2 SP[p1, p4]^2 SP[p2, p3] + m3^2 SP[p1, p4]^2 SP[p2, p3] - + m0^2 SP[p1, p3]^2 SP[p2, p4] + m4^2 SP[p1, p3]^2 SP[p2, p4] + + m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p4] - + m3^2 SP[p1, p3] SP[p1, p4] SP[p2, p4] - + m0^2 SP[p1, p2] SP[p1, p4] SP[p3, p3] + + m4^2 SP[p1, p2] SP[p1, p4] SP[p3, p3] + + m0^2 SP[p1, p4]^2 SP[p3, p3] - m2^2 SP[p1, p4]^2 SP[p3, p3] + + SP[p1, p4]^2 SP[p2, p2] SP[p3, p3] - + SP[p1, p4]^2 SP[p2, p3] SP[p3, p3] + + m0^2 SP[p1, p1] SP[p2, p4] SP[p3, p3] - + m4^2 SP[p1, p1] SP[p2, p4] SP[p3, p3] - + m0^2 SP[p1, p4] SP[p2, p4] SP[p3, p3] + + m1^2 SP[p1, p4] SP[p2, p4] SP[p3, p3] - + SP[p1, p1] SP[p1, p4] SP[p2, p4] SP[p3, p3] + + SP[p1, p3] SP[p1, p4] SP[p2, p4] SP[p3, p3] + + m0^2 SP[p1, p2] SP[p1, p3] SP[p3, p4] - + m4^2 SP[p1, p2] SP[p1, p3] SP[p3, p4] + + m0^2 SP[p1, p2] SP[p1, p4] SP[p3, p4] - + m3^2 SP[p1, p2] SP[p1, p4] SP[p3, p4] - + 2 m0^2 SP[p1, p3] SP[p1, p4] SP[p3, p4] + + 2 m2^2 SP[p1, p3] SP[p1, p4] SP[p3, p4] - + 2 SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p3, p4] - + m0^2 SP[p1, p1] SP[p2, p3] SP[p3, p4] + + m4^2 SP[p1, p1] SP[p2, p3] SP[p3, p4] + + m0^2 SP[p1, p4] SP[p2, p3] SP[p3, p4] - + m1^2 SP[p1, p4] SP[p2, p3] SP[p3, p4] + + SP[p1, p1] SP[p1, p4] SP[p2, p3] SP[p3, p4] - + m0^2 SP[p1, p1] SP[p2, p4] SP[p3, p4] + + m3^2 SP[p1, p1] SP[p2, p4] SP[p3, p4] + + m0^2 SP[p1, p3] SP[p2, p4] SP[p3, p4] - + m1^2 SP[p1, p3] SP[p2, p4] SP[p3, p4] + + SP[p1, p1] SP[p1, p3] SP[p2, p4] SP[p3, p4] + + SP[p1, p2] SP[p1, p4] SP[p3, p3] SP[p3, p4] - + SP[p1, p1] SP[p2, p4] SP[p3, p3] SP[p3, p4] + + m0^2 SP[p1, p1] SP[p3, p4]^2 - m2^2 SP[p1, p1] SP[p3, p4]^2 - + m0^2 SP[p1, p2] SP[p3, p4]^2 + m1^2 SP[p1, p2] SP[p3, p4]^2 - + SP[p1, p1] SP[p1, p2] SP[p3, p4]^2 + + SP[p1, p1] SP[p2, p2] SP[p3, p4]^2 - + m0^2 SP[p1, p2] SP[p1, p3] SP[p4, p4] + + m3^2 SP[p1, p2] SP[p1, p3] SP[p4, p4] + + m0^2 SP[p1, p3]^2 SP[p4, p4] - m2^2 SP[p1, p3]^2 SP[p4, p4] + + SP[p1, p3]^2 SP[p2, p2] SP[p4, p4] + + m0^2 SP[p1, p1] SP[p2, p3] SP[p4, p4] - + m3^2 SP[p1, p1] SP[p2, p3] SP[p4, p4] - + m0^2 SP[p1, p3] SP[p2, p3] SP[p4, p4] + + m1^2 SP[p1, p3] SP[p2, p3] SP[p4, p4] - + SP[p1, p1] SP[p1, p3] SP[p2, p3] SP[p4, p4] + + SP[p1, p3] SP[p1, p4] SP[p2, p3] SP[p4, p4] - + SP[p1, p3]^2 SP[p2, p4] SP[p4, p4] - + m0^2 SP[p1, p1] SP[p3, p3] SP[p4, p4] + + m2^2 SP[p1, p1] SP[p3, p3] SP[p4, p4] + + m0^2 SP[p1, p2] SP[p3, p3] SP[p4, p4] - + m1^2 SP[p1, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p1] SP[p1, p2] SP[p3, p3] SP[p4, p4] - + SP[p1, p2] SP[p1, p3] SP[p3, p3] SP[p4, p4] - + SP[p1, p2] SP[p1, p4] SP[p3, p3] SP[p4, p4] - + SP[p1, p1] SP[p2, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p1] SP[p2, p3] SP[p3, p3] SP[p4, p4] + + SP[p1, p1] SP[p2, p4] SP[p3, p3] SP[p4, p4] + + SP[p1, p2] SP[p1, p3] SP[p3, p4] SP[p4, p4] - + SP[p1, p1] SP[p2, p3] SP[p3, p4] SP[p4, p4]) - + 8 D0[SP[p2, p2], SP[p3, p3], + SP[p3, p3] - 2 SP[p3, p4] + SP[p4, p4], + SP[p2, p2] - 2 SP[p2, p4] + SP[p4, p4], + SP[p2, p2] - 2 SP[p2, p3] + SP[p3, p3], SP[p4, p4], m2^2, m0^2, + m3^2, m4^2] (m0^2 SP[p1, p4] SP[p2, p3]^2 - + m4^2 SP[p1, p4] SP[p2, p3]^2 - + m0^2 SP[p1, p3] SP[p2, p3] SP[p2, p4] + + m4^2 SP[p1, p3] SP[p2, p3] SP[p2, p4] - + m0^2 SP[p1, p4] SP[p2, p3] SP[p2, p4] + + m3^2 SP[p1, p4] SP[p2, p3] SP[p2, p4] + + m0^2 SP[p1, p3] SP[p2, p4]^2 - m3^2 SP[p1, p3] SP[p2, p4]^2 - + m0^2 SP[p1, p4] SP[p2, p2] SP[p3, p3] + + m4^2 SP[p1, p4] SP[p2, p2] SP[p3, p3] + + m0^2 SP[p1, p2] SP[p2, p4] SP[p3, p3] - + m4^2 SP[p1, p2] SP[p2, p4] SP[p3, p3] + + m0^2 SP[p1, p4] SP[p2, p4] SP[p3, p3] - + m2^2 SP[p1, p4] SP[p2, p4] SP[p3, p3] + + SP[p1, p4] SP[p2, p2] SP[p2, p4] SP[p3, p3] - + SP[p1, p4] SP[p2, p3] SP[p2, p4] SP[p3, p3] - + m0^2 SP[p2, p4]^2 SP[p3, p3] + m1^2 SP[p2, p4]^2 SP[p3, p3] - + SP[p1, p1] SP[p2, p4]^2 SP[p3, p3] + + SP[p1, p3] SP[p2, p4]^2 SP[p3, p3] + + m0^2 SP[p1, p3] SP[p2, p2] SP[p3, p4] - + m4^2 SP[p1, p3] SP[p2, p2] SP[p3, p4] + + m0^2 SP[p1, p4] SP[p2, p2] SP[p3, p4] - + m3^2 SP[p1, p4] SP[p2, p2] SP[p3, p4] - + m0^2 SP[p1, p2] SP[p2, p3] SP[p3, p4] + + m4^2 SP[p1, p2] SP[p2, p3] SP[p3, p4] - + m0^2 SP[p1, p4] SP[p2, p3] SP[p3, p4] + + m2^2 SP[p1, p4] SP[p2, p3] SP[p3, p4] - + SP[p1, p4] SP[p2, p2] SP[p2, p3] SP[p3, p4] - + m0^2 SP[p1, p2] SP[p2, p4] SP[p3, p4] + + m3^2 SP[p1, p2] SP[p2, p4] SP[p3, p4] - + m0^2 SP[p1, p3] SP[p2, p4] SP[p3, p4] + + m2^2 SP[p1, p3] SP[p2, p4] SP[p3, p4] - + SP[p1, p3] SP[p2, p2] SP[p2, p4] SP[p3, p4] + + 2 m0^2 SP[p2, p3] SP[p2, p4] SP[p3, p4] - + 2 m1^2 SP[p2, p3] SP[p2, p4] SP[p3, p4] + + 2 SP[p1, p1] SP[p2, p3] SP[p2, p4] SP[p3, p4] + + SP[p1, p4] SP[p2, p2] SP[p3, p3] SP[p3, p4] - + SP[p1, p2] SP[p2, p4] SP[p3, p3] SP[p3, p4] + + m0^2 SP[p1, p2] SP[p3, p4]^2 - m2^2 SP[p1, p2] SP[p3, p4]^2 - + m0^2 SP[p2, p2] SP[p3, p4]^2 + m1^2 SP[p2, p2] SP[p3, p4]^2 - + SP[p1, p1] SP[p2, p2] SP[p3, p4]^2 + + SP[p1, p2] SP[p2, p2] SP[p3, p4]^2 - + m0^2 SP[p1, p3] SP[p2, p2] SP[p4, p4] + + m3^2 SP[p1, p3] SP[p2, p2] SP[p4, p4] + + m0^2 SP[p1, p2] SP[p2, p3] SP[p4, p4] - + m3^2 SP[p1, p2] SP[p2, p3] SP[p4, p4] + + m0^2 SP[p1, p3] SP[p2, p3] SP[p4, p4] - + m2^2 SP[p1, p3] SP[p2, p3] SP[p4, p4] + + SP[p1, p3] SP[p2, p2] SP[p2, p3] SP[p4, p4] - + m0^2 SP[p2, p3]^2 SP[p4, p4] + m1^2 SP[p2, p3]^2 SP[p4, p4] - + SP[p1, p1] SP[p2, p3]^2 SP[p4, p4] + + SP[p1, p4] SP[p2, p3]^2 SP[p4, p4] - + SP[p1, p3] SP[p2, p3] SP[p2, p4] SP[p4, p4] - + m0^2 SP[p1, p2] SP[p3, p3] SP[p4, p4] + + m2^2 SP[p1, p2] SP[p3, p3] SP[p4, p4] + + m0^2 SP[p2, p2] SP[p3, p3] SP[p4, p4] - + m1^2 SP[p2, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p1] SP[p2, p2] SP[p3, p3] SP[p4, p4] - + SP[p1, p2] SP[p2, p2] SP[p3, p3] SP[p4, p4] - + SP[p1, p3] SP[p2, p2] SP[p3, p3] SP[p4, p4] - + SP[p1, p4] SP[p2, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p2] SP[p2, p3] SP[p3, p3] SP[p4, p4] + + SP[p1, p2] SP[p2, p4] SP[p3, p3] SP[p4, p4] + + SP[p1, p3] SP[p2, p2] SP[p3, p4] SP[p4, p4] - + SP[p1, p2] SP[p2, p3] SP[p3, p4] SP[p4, p4]) - + 8 D0[SP[p1, p1] - 2 SP[p1, p2] + SP[p2, p2], + SP[p1, p1] - 2 SP[p1, p3] + SP[p3, p3], + SP[p3, p3] - 2 SP[p3, p4] + SP[p4, p4], + SP[p2, p2] - 2 SP[p2, p4] + SP[p4, p4], + SP[p2, p2] - 2 SP[p2, p3] + SP[p3, p3], + SP[p1, p1] - 2 SP[p1, p4] + SP[p4, p4], m2^2, m1^2, m3^2, + m4^2] (m0^2 SP[p1, p3]^2 SP[p2, p2] - + m4^2 SP[p1, p3]^2 SP[p2, p2] - + 2 m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p2] + + m3^2 SP[p1, p3] SP[p1, p4] SP[p2, p2] + + m4^2 SP[p1, p3] SP[p1, p4] SP[p2, p2] + + m0^2 SP[p1, p4]^2 SP[p2, p2] - m3^2 SP[p1, p4]^2 SP[p2, p2] - + 2 m0^2 SP[p1, p2] SP[p1, p3] SP[p2, p3] + + 2 m4^2 SP[p1, p2] SP[p1, p3] SP[p2, p3] + + 2 m0^2 SP[p1, p2] SP[p1, p4] SP[p2, p3] - + m3^2 SP[p1, p2] SP[p1, p4] SP[p2, p3] - + m4^2 SP[p1, p2] SP[p1, p4] SP[p2, p3] + + 2 m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p3] - + m2^2 SP[p1, p3] SP[p1, p4] SP[p2, p3] - + m4^2 SP[p1, p3] SP[p1, p4] SP[p2, p3] - + 2 m0^2 SP[p1, p4]^2 SP[p2, p3] + + m2^2 SP[p1, p4]^2 SP[p2, p3] + m3^2 SP[p1, p4]^2 SP[p2, p3] + + SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p2, p3] - + SP[p1, p4]^2 SP[p2, p2] SP[p2, p3] + + m0^2 SP[p1, p1] SP[p2, p3]^2 - m4^2 SP[p1, p1] SP[p2, p3]^2 - + 2 m0^2 SP[p1, p4] SP[p2, p3]^2 + + m1^2 SP[p1, p4] SP[p2, p3]^2 + m4^2 SP[p1, p4] SP[p2, p3]^2 - + SP[p1, p1] SP[p1, p4] SP[p2, p3]^2 + + 2 SP[p1, p4]^2 SP[p2, p3]^2 + + 2 m0^2 SP[p1, p2] SP[p1, p3] SP[p2, p4] - + m3^2 SP[p1, p2] SP[p1, p3] SP[p2, p4] - + m4^2 SP[p1, p2] SP[p1, p3] SP[p2, p4] - + 2 m0^2 SP[p1, p3]^2 SP[p2, p4] + + m2^2 SP[p1, p3]^2 SP[p2, p4] + m4^2 SP[p1, p3]^2 SP[p2, p4] - + 2 m0^2 SP[p1, p2] SP[p1, p4] SP[p2, p4] + + 2 m3^2 SP[p1, p2] SP[p1, p4] SP[p2, p4] + + 2 m0^2 SP[p1, p3] SP[p1, p4] SP[p2, p4] - + m2^2 SP[p1, p3] SP[p1, p4] SP[p2, p4] - + m3^2 SP[p1, p3] SP[p1, p4] SP[p2, p4] - + SP[p1, p3]^2 SP[p2, p2] SP[p2, p4] + + SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p2, p4] - + 2 m0^2 SP[p1, p1] SP[p2, p3] SP[p2, p4] + + m3^2 SP[p1, p1] SP[p2, p3] SP[p2, p4] + + m4^2 SP[p1, p1] SP[p2, p3] SP[p2, p4] + + 2 m0^2 SP[p1, p3] SP[p2, p3] SP[p2, p4] - + m1^2 SP[p1, p3] SP[p2, p3] SP[p2, p4] - + m4^2 SP[p1, p3] SP[p2, p3] SP[p2, p4] + + SP[p1, p1] SP[p1, p3] SP[p2, p3] SP[p2, p4] + + 2 m0^2 SP[p1, p4] SP[p2, p3] SP[p2, p4] - + m1^2 SP[p1, p4] SP[p2, p3] SP[p2, p4] - + m3^2 SP[p1, p4] SP[p2, p3] SP[p2, p4] + + SP[p1, p1] SP[p1, p4] SP[p2, p3] SP[p2, p4] - + 4 SP[p1, p3] SP[p1, p4] SP[p2, p3] SP[p2, p4] + + m0^2 SP[p1, p1] SP[p2, p4]^2 - m3^2 SP[p1, p1] SP[p2, p4]^2 - + 2 m0^2 SP[p1, p3] SP[p2, p4]^2 + + m1^2 SP[p1, p3] SP[p2, p4]^2 + m3^2 SP[p1, p3] SP[p2, p4]^2 - + SP[p1, p1] SP[p1, p3] SP[p2, p4]^2 + + 2 SP[p1, p3]^2 SP[p2, p4]^2 + m0^2 SP[p1, p2]^2 SP[p3, p3] - + m4^2 SP[p1, p2]^2 SP[p3, p3] - + 2 m0^2 SP[p1, p2] SP[p1, p4] SP[p3, p3] + + m2^2 SP[p1, p2] SP[p1, p4] SP[p3, p3] + + m4^2 SP[p1, p2] SP[p1, p4] SP[p3, p3] + + m0^2 SP[p1, p4]^2 SP[p3, p3] - m2^2 SP[p1, p4]^2 SP[p3, p3] - + m0^2 SP[p1, p1] SP[p2, p2] SP[p3, p3] + + m4^2 SP[p1, p1] SP[p2, p2] SP[p3, p3] + + 2 m0^2 SP[p1, p4] SP[p2, p2] SP[p3, p3] - + m1^2 SP[p1, p4] SP[p2, p2] SP[p3, p3] - + m4^2 SP[p1, p4] SP[p2, p2] SP[p3, p3] + + SP[p1, p1] SP[p1, p4] SP[p2, p2] SP[p3, p3] - + SP[p1, p2] SP[p1, p4] SP[p2, p2] SP[p3, p3] - + SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p3, p3] + + SP[p1, p2] SP[p1, p4] SP[p2, p3] SP[p3, p3] - + SP[p1, p4]^2 SP[p2, p3] SP[p3, p3] + + 2 m0^2 SP[p1, p1] SP[p2, p4] SP[p3, p3] - + m2^2 SP[p1, p1] SP[p2, p4] SP[p3, p3] - + m4^2 SP[p1, p1] SP[p2, p4] SP[p3, p3] - + 2 m0^2 SP[p1, p2] SP[p2, p4] SP[p3, p3] + + m1^2 SP[p1, p2] SP[p2, p4] SP[p3, p3] + + m4^2 SP[p1, p2] SP[p2, p4] SP[p3, p3] - + SP[p1, p1] SP[p1, p2] SP[p2, p4] SP[p3, p3] + + SP[p1, p2] SP[p1, p3] SP[p2, p4] SP[p3, p3] - + 2 m0^2 SP[p1, p4] SP[p2, p4] SP[p3, p3] + + m1^2 SP[p1, p4] SP[p2, p4] SP[p3, p3] + + m2^2 SP[p1, p4] SP[p2, p4] SP[p3, p3] - + SP[p1, p1] SP[p1, p4] SP[p2, p4] SP[p3, p3] + + 2 SP[p1, p2] SP[p1, p4] SP[p2, p4] SP[p3, p3] + + SP[p1, p3] SP[p1, p4] SP[p2, p4] SP[p3, p3] + + SP[p1, p1] SP[p2, p2] SP[p2, p4] SP[p3, p3] - + SP[p1, p4] SP[p2, p2] SP[p2, p4] SP[p3, p3] - + SP[p1, p1] SP[p2, p3] SP[p2, p4] SP[p3, p3] + + SP[p1, p4] SP[p2, p3] SP[p2, p4] SP[p3, p3] + + m0^2 SP[p2, p4]^2 SP[p3, p3] - m1^2 SP[p2, p4]^2 SP[p3, p3] - + SP[p1, p3] SP[p2, p4]^2 SP[p3, p3] - + 2 m0^2 SP[p1, p2]^2 SP[p3, p4] + + m3^2 SP[p1, p2]^2 SP[p3, p4] + m4^2 SP[p1, p2]^2 SP[p3, p4] + + 2 m0^2 SP[p1, p2] SP[p1, p3] SP[p3, p4] - + m2^2 SP[p1, p2] SP[p1, p3] SP[p3, p4] - + m4^2 SP[p1, p2] SP[p1, p3] SP[p3, p4] + + 2 m0^2 SP[p1, p2] SP[p1, p4] SP[p3, p4] - + m2^2 SP[p1, p2] SP[p1, p4] SP[p3, p4] - + m3^2 SP[p1, p2] SP[p1, p4] SP[p3, p4] - + 2 m0^2 SP[p1, p3] SP[p1, p4] SP[p3, p4] + + 2 m2^2 SP[p1, p3] SP[p1, p4] SP[p3, p4] + + 2 m0^2 SP[p1, p1] SP[p2, p2] SP[p3, p4] - + m3^2 SP[p1, p1] SP[p2, p2] SP[p3, p4] - + m4^2 SP[p1, p1] SP[p2, p2] SP[p3, p4] - + 2 m0^2 SP[p1, p3] SP[p2, p2] SP[p3, p4] + + m1^2 SP[p1, p3] SP[p2, p2] SP[p3, p4] + + m4^2 SP[p1, p3] SP[p2, p2] SP[p3, p4] - + SP[p1, p1] SP[p1, p3] SP[p2, p2] SP[p3, p4] + + SP[p1, p2] SP[p1, p3] SP[p2, p2] SP[p3, p4] - + 2 m0^2 SP[p1, p4] SP[p2, p2] SP[p3, p4] + + m1^2 SP[p1, p4] SP[p2, p2] SP[p3, p4] + + m3^2 SP[p1, p4] SP[p2, p2] SP[p3, p4] - + SP[p1, p1] SP[p1, p4] SP[p2, p2] SP[p3, p4] + + SP[p1, p2] SP[p1, p4] SP[p2, p2] SP[p3, p4] + + 2 SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p3, p4] - + 2 m0^2 SP[p1, p1] SP[p2, p3] SP[p3, p4] + + m2^2 SP[p1, p1] SP[p2, p3] SP[p3, p4] + + m4^2 SP[p1, p1] SP[p2, p3] SP[p3, p4] + + 2 m0^2 SP[p1, p2] SP[p2, p3] SP[p3, p4] - + m1^2 SP[p1, p2] SP[p2, p3] SP[p3, p4] - + m4^2 SP[p1, p2] SP[p2, p3] SP[p3, p4] + + SP[p1, p1] SP[p1, p2] SP[p2, p3] SP[p3, p4] + + 2 m0^2 SP[p1, p4] SP[p2, p3] SP[p3, p4] - + m1^2 SP[p1, p4] SP[p2, p3] SP[p3, p4] - + m2^2 SP[p1, p4] SP[p2, p3] SP[p3, p4] + + SP[p1, p1] SP[p1, p4] SP[p2, p3] SP[p3, p4] - + 4 SP[p1, p2] SP[p1, p4] SP[p2, p3] SP[p3, p4] - + SP[p1, p1] SP[p2, p2] SP[p2, p3] SP[p3, p4] + + SP[p1, p4] SP[p2, p2] SP[p2, p3] SP[p3, p4] - + 2 m0^2 SP[p1, p1] SP[p2, p4] SP[p3, p4] + + m2^2 SP[p1, p1] SP[p2, p4] SP[p3, p4] + + m3^2 SP[p1, p1] SP[p2, p4] SP[p3, p4] + + 2 m0^2 SP[p1, p2] SP[p2, p4] SP[p3, p4] - + m1^2 SP[p1, p2] SP[p2, p4] SP[p3, p4] - + m3^2 SP[p1, p2] SP[p2, p4] SP[p3, p4] + + SP[p1, p1] SP[p1, p2] SP[p2, p4] SP[p3, p4] + + 2 m0^2 SP[p1, p3] SP[p2, p4] SP[p3, p4] - + m1^2 SP[p1, p3] SP[p2, p4] SP[p3, p4] - + m2^2 SP[p1, p3] SP[p2, p4] SP[p3, p4] + + SP[p1, p1] SP[p1, p3] SP[p2, p4] SP[p3, p4] - + 4 SP[p1, p2] SP[p1, p3] SP[p2, p4] SP[p3, p4] - + SP[p1, p1] SP[p2, p2] SP[p2, p4] SP[p3, p4] + + SP[p1, p3] SP[p2, p2] SP[p2, p4] SP[p3, p4] - + 2 m0^2 SP[p2, p3] SP[p2, p4] SP[p3, p4] + + 2 m1^2 SP[p2, p3] SP[p2, p4] SP[p3, p4] + + 2 SP[p1, p1] SP[p2, p3] SP[p2, p4] SP[p3, p4] - + SP[p1, p2]^2 SP[p3, p3] SP[p3, p4] + + SP[p1, p2] SP[p1, p4] SP[p3, p3] SP[p3, p4] + + SP[p1, p1] SP[p2, p2] SP[p3, p3] SP[p3, p4] - + SP[p1, p4] SP[p2, p2] SP[p3, p3] SP[p3, p4] - + SP[p1, p1] SP[p2, p4] SP[p3, p3] SP[p3, p4] + + SP[p1, p2] SP[p2, p4] SP[p3, p3] SP[p3, p4] + + m0^2 SP[p1, p1] SP[p3, p4]^2 - m2^2 SP[p1, p1] SP[p3, p4]^2 - + 2 m0^2 SP[p1, p2] SP[p3, p4]^2 + + m1^2 SP[p1, p2] SP[p3, p4]^2 + m2^2 SP[p1, p2] SP[p3, p4]^2 - + SP[p1, p1] SP[p1, p2] SP[p3, p4]^2 + + 2 SP[p1, p2]^2 SP[p3, p4]^2 + m0^2 SP[p2, p2] SP[p3, p4]^2 - + m1^2 SP[p2, p2] SP[p3, p4]^2 - + SP[p1, p2] SP[p2, p2] SP[p3, p4]^2 + + m0^2 SP[p1, p2]^2 SP[p4, p4] - m3^2 SP[p1, p2]^2 SP[p4, p4] - + 2 m0^2 SP[p1, p2] SP[p1, p3] SP[p4, p4] + + m2^2 SP[p1, p2] SP[p1, p3] SP[p4, p4] + + m3^2 SP[p1, p2] SP[p1, p3] SP[p4, p4] + + m0^2 SP[p1, p3]^2 SP[p4, p4] - m2^2 SP[p1, p3]^2 SP[p4, p4] - + m0^2 SP[p1, p1] SP[p2, p2] SP[p4, p4] + + m3^2 SP[p1, p1] SP[p2, p2] SP[p4, p4] + + 2 m0^2 SP[p1, p3] SP[p2, p2] SP[p4, p4] - + m1^2 SP[p1, p3] SP[p2, p2] SP[p4, p4] - + m3^2 SP[p1, p3] SP[p2, p2] SP[p4, p4] + + SP[p1, p1] SP[p1, p3] SP[p2, p2] SP[p4, p4] - + SP[p1, p2] SP[p1, p3] SP[p2, p2] SP[p4, p4] - + SP[p1, p3] SP[p1, p4] SP[p2, p2] SP[p4, p4] + + 2 m0^2 SP[p1, p1] SP[p2, p3] SP[p4, p4] - + m2^2 SP[p1, p1] SP[p2, p3] SP[p4, p4] - + m3^2 SP[p1, p1] SP[p2, p3] SP[p4, p4] - + 2 m0^2 SP[p1, p2] SP[p2, p3] SP[p4, p4] + + m1^2 SP[p1, p2] SP[p2, p3] SP[p4, p4] + + m3^2 SP[p1, p2] SP[p2, p3] SP[p4, p4] - + SP[p1, p1] SP[p1, p2] SP[p2, p3] SP[p4, p4] - + 2 m0^2 SP[p1, p3] SP[p2, p3] SP[p4, p4] + + m1^2 SP[p1, p3] SP[p2, p3] SP[p4, p4] + + m2^2 SP[p1, p3] SP[p2, p3] SP[p4, p4] - + SP[p1, p1] SP[p1, p3] SP[p2, p3] SP[p4, p4] + + 2 SP[p1, p2] SP[p1, p3] SP[p2, p3] SP[p4, p4] + + SP[p1, p2] SP[p1, p4] SP[p2, p3] SP[p4, p4] + + SP[p1, p3] SP[p1, p4] SP[p2, p3] SP[p4, p4] + + SP[p1, p1] SP[p2, p2] SP[p2, p3] SP[p4, p4] - + SP[p1, p3] SP[p2, p2] SP[p2, p3] SP[p4, p4] + + m0^2 SP[p2, p3]^2 SP[p4, p4] - m1^2 SP[p2, p3]^2 SP[p4, p4] - + SP[p1, p4] SP[p2, p3]^2 SP[p4, p4] + + SP[p1, p2] SP[p1, p3] SP[p2, p4] SP[p4, p4] - + SP[p1, p3]^2 SP[p2, p4] SP[p4, p4] - + SP[p1, p1] SP[p2, p3] SP[p2, p4] SP[p4, p4] + + SP[p1, p3] SP[p2, p3] SP[p2, p4] SP[p4, p4] - + m0^2 SP[p1, p1] SP[p3, p3] SP[p4, p4] + + m2^2 SP[p1, p1] SP[p3, p3] SP[p4, p4] + + 2 m0^2 SP[p1, p2] SP[p3, p3] SP[p4, p4] - + m1^2 SP[p1, p2] SP[p3, p3] SP[p4, p4] - + m2^2 SP[p1, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p1] SP[p1, p2] SP[p3, p3] SP[p4, p4] - + SP[p1, p2] SP[p1, p3] SP[p3, p3] SP[p4, p4] - + SP[p1, p2] SP[p1, p4] SP[p3, p3] SP[p4, p4] - + m0^2 SP[p2, p2] SP[p3, p3] SP[p4, p4] + + m1^2 SP[p2, p2] SP[p3, p3] SP[p4, p4] - + 2 SP[p1, p1] SP[p2, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p2] SP[p2, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p3] SP[p2, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p4] SP[p2, p2] SP[p3, p3] SP[p4, p4] + + SP[p1, p1] SP[p2, p3] SP[p3, p3] SP[p4, p4] - + SP[p1, p2] SP[p2, p3] SP[p3, p3] SP[p4, p4] + + SP[p1, p1] SP[p2, p4] SP[p3, p3] SP[p4, p4] - + SP[p1, p2] SP[p2, p4] SP[p3, p3] SP[p4, p4] - + SP[p1, p2]^2 SP[p3, p4] SP[p4, p4] + + SP[p1, p2] SP[p1, p3] SP[p3, p4] SP[p4, p4] + + SP[p1, p1] SP[p2, p2] SP[p3, p4] SP[p4, p4] - + SP[p1, p3] SP[p2, p2] SP[p3, p4] SP[p4, p4] - + SP[p1, p1] SP[p2, p3] SP[p3, p4] SP[p4, p4] + + SP[p1, p2] SP[p2, p3] SP[p3, p4] SP[p4, + p4])))/(2 m4^2 (4 m0^4 SP[p1, p2]^2 - + 8 m0^2 m3^2 SP[p1, p2]^2 + 4 m3^4 SP[p1, p2]^2 - + 8 m0^4 SP[p1, p2] SP[p1, p3] + + 8 m0^2 m2^2 SP[p1, p2] SP[p1, p3] + + 8 m0^2 m3^2 SP[p1, p2] SP[p1, p3] - + 8 m2^2 m3^2 SP[p1, p2] SP[p1, p3] + 4 m0^4 SP[p1, p3]^2 - + 8 m0^2 m2^2 SP[p1, p3]^2 + 4 m2^4 SP[p1, p3]^2 - + 4 m0^4 SP[p1, p1] SP[p2, p2] + + 8 m0^2 m3^2 SP[p1, p1] SP[p2, p2] - + 4 m3^4 SP[p1, p1] SP[p2, p2] + 8 m0^4 SP[p1, p3] SP[p2, p2] - + 8 m0^2 m1^2 SP[p1, p3] SP[p2, p2] - + 8 m0^2 m3^2 SP[p1, p3] SP[p2, p2] + + 8 m1^2 m3^2 SP[p1, p3] SP[p2, p2] + + 8 m0^2 SP[p1, p1] SP[p1, p3] SP[p2, p2] - + 8 m3^2 SP[p1, p1] SP[p1, p3] SP[p2, p2] - + 8 m0^2 SP[p1, p2] SP[p1, p3] SP[p2, p2] + + 8 m3^2 SP[p1, p2] SP[p1, p3] SP[p2, p2] - + 8 m0^2 SP[p1, p3]^2 SP[p2, p2] - + 8 m2^2 SP[p1, p3]^2 SP[p2, p2] + 4 SP[p1, p3]^2 SP[p2, p2]^2 + + 8 m0^4 SP[p1, p1] SP[p2, p3] - + 8 m0^2 m2^2 SP[p1, p1] SP[p2, p3] - + 8 m0^2 m3^2 SP[p1, p1] SP[p2, p3] + + 8 m2^2 m3^2 SP[p1, p1] SP[p2, p3] - + 8 m0^4 SP[p1, p2] SP[p2, p3] + + 8 m0^2 m1^2 SP[p1, p2] SP[p2, p3] + + 8 m0^2 m3^2 SP[p1, p2] SP[p2, p3] - + 8 m1^2 m3^2 SP[p1, p2] SP[p2, p3] - + 8 m0^2 SP[p1, p1] SP[p1, p2] SP[p2, p3] + + 8 m3^2 SP[p1, p1] SP[p1, p2] SP[p2, p3] - + 8 m0^4 SP[p1, p3] SP[p2, p3] + + 8 m0^2 m1^2 SP[p1, p3] SP[p2, p3] + + 8 m0^2 m2^2 SP[p1, p3] SP[p2, p3] - + 8 m1^2 m2^2 SP[p1, p3] SP[p2, p3] - + 8 m0^2 SP[p1, p1] SP[p1, p3] SP[p2, p3] + + 8 m2^2 SP[p1, p1] SP[p1, p3] SP[p2, p3] + + 32 m0^2 SP[p1, p2] SP[p1, p3] SP[p2, p3] + + 8 m0^2 SP[p1, p1] SP[p2, p2] SP[p2, p3] - + 8 m3^2 SP[p1, p1] SP[p2, p2] SP[p2, p3] - + 8 m0^2 SP[p1, p3] SP[p2, p2] SP[p2, p3] + + 8 m1^2 SP[p1, p3] SP[p2, p2] SP[p2, p3] - + 8 SP[p1, p1] SP[p1, p3] SP[p2, p2] SP[p2, p3] + + 4 m0^4 SP[p2, p3]^2 - 8 m0^2 m1^2 SP[p2, p3]^2 + + 4 m1^4 SP[p2, p3]^2 - 8 m0^2 SP[p1, p1] SP[p2, p3]^2 - + 8 m1^2 SP[p1, p1] SP[p2, p3]^2 + 4 SP[p1, p1]^2 SP[p2, p3]^2 - + 4 m0^4 SP[p1, p1] SP[p3, p3] + + 8 m0^2 m2^2 SP[p1, p1] SP[p3, p3] - + 4 m2^4 SP[p1, p1] SP[p3, p3] + 8 m0^4 SP[p1, p2] SP[p3, p3] - + 8 m0^2 m1^2 SP[p1, p2] SP[p3, p3] - + 8 m0^2 m2^2 SP[p1, p2] SP[p3, p3] + + 8 m1^2 m2^2 SP[p1, p2] SP[p3, p3] + + 8 m0^2 SP[p1, p1] SP[p1, p2] SP[p3, p3] - + 8 m2^2 SP[p1, p1] SP[p1, p2] SP[p3, p3] - + 8 m0^2 SP[p1, p2]^2 SP[p3, p3] - + 8 m3^2 SP[p1, p2]^2 SP[p3, p3] - + 8 m0^2 SP[p1, p2] SP[p1, p3] SP[p3, p3] + + 8 m2^2 SP[p1, p2] SP[p1, p3] SP[p3, p3] - + 4 m0^4 SP[p2, p2] SP[p3, p3] + + 8 m0^2 m1^2 SP[p2, p2] SP[p3, p3] - + 4 m1^4 SP[p2, p2] SP[p3, p3] - + 8 m0^2 SP[p1, p1] SP[p2, p2] SP[p3, p3] + + 8 m1^2 SP[p1, p1] SP[p2, p2] SP[p3, p3] + + 8 m2^2 SP[p1, p1] SP[p2, p2] SP[p3, p3] + + 8 m3^2 SP[p1, p1] SP[p2, p2] SP[p3, p3] - + 4 SP[p1, p1]^2 SP[p2, p2] SP[p3, p3] + + 8 m0^2 SP[p1, p2] SP[p2, p2] SP[p3, p3] - + 8 m1^2 SP[p1, p2] SP[p2, p2] SP[p3, p3] + + 8 SP[p1, p1] SP[p1, p2] SP[p2, p2] SP[p3, p3] + + 8 m0^2 SP[p1, p3] SP[p2, p2] SP[p3, p3] - + 8 m1^2 SP[p1, p3] SP[p2, p2] SP[p3, p3] + + 8 SP[p1, p1] SP[p1, p3] SP[p2, p2] SP[p3, p3] - + 8 SP[p1, p2] SP[p1, p3] SP[p2, p2] SP[p3, p3] - + 4 SP[p1, p1] SP[p2, p2]^2 SP[p3, p3] + + 8 m0^2 SP[p1, p1] SP[p2, p3] SP[p3, p3] - + 8 m2^2 SP[p1, p1] SP[p2, p3] SP[p3, p3] - + 8 m0^2 SP[p1, p2] SP[p2, p3] SP[p3, p3] + + 8 m1^2 SP[p1, p2] SP[p2, p3] SP[p3, p3] - + 8 SP[p1, p1] SP[p1, p2] SP[p2, p3] SP[p3, p3] + + 8 SP[p1, p1] SP[p2, p2] SP[p2, p3] SP[p3, p3] + + 4 SP[p1, p2]^2 SP[p3, p3]^2 - + 4 SP[p1, p1] SP[p2, p2] SP[p3, + p3]^2) + (-2 m3^2 (-2 m2^2 (-2 m1^2 (m0^2 + m4^2 - + SP[p4, p4]) + (m0^2 + m1^2 - SP[p1, p1]) (m1^2 + m4^2 - + SP[p1, p1] + 2 SP[p1, p4] - SP[p4, p4])) + (m1^2 + + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + + SP[p2, p2]) (-(m1^2 + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m2^2 - SP[p2, p2]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (-2 m1^2 (m0^2 + m2^2 - + SP[p2, p2]) + (m0^2 + m1^2 - SP[p1, p1]) (m1^2 + m2^2 - + SP[p1, p1] + 2 SP[p1, p2] - SP[p2, p2])) (m2^2 + + m4^2 - SP[p2, p2] + 2 SP[p2, p4] - SP[p4, p4])) + (m2^2 + + m3^2 - SP[p2, p2] + 2 SP[p2, p3] - + SP[p3, p3]) (-(m2^2 + m3^2 - SP[p2, p2] + 2 SP[p2, p3] - + SP[p3, p3]) (-2 m1^2 (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m1^2 - SP[p1, p1]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (m1^2 + m2^2 - + SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (-(m1^2 + m3^2 - SP[p1, p1] + 2 SP[p1, p3] - + SP[p3, p3]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m3^2 - SP[p3, p3]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (-2 m1^2 (m0^2 + m3^2 - + SP[p3, p3]) + (m0^2 + m1^2 - SP[p1, p1]) (m1^2 + m3^2 - + SP[p1, p1] + 2 SP[p1, p3] - SP[p3, p3])) (m2^2 + + m4^2 - SP[p2, p2] + 2 SP[p2, p4] - SP[p4, p4])) - (m1^2 + + m3^2 - SP[p1, p1] + 2 SP[p1, p3] - + SP[p3, p3]) (-(m2^2 + m3^2 - SP[p2, p2] + 2 SP[p2, p3] - + SP[p3, p3]) (-(m1^2 + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m2^2 - SP[p2, p2]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + + 2 m2^2 (-(m1^2 + m3^2 - SP[p1, p1] + 2 SP[p1, p3] - + SP[p3, p3]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m3^2 - SP[p3, p3]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - + SP[p4, p4])) + (-(m1^2 + m2^2 - SP[p1, p1] + + 2 SP[p1, p2] - SP[p2, p2]) (m0^2 + m3^2 - + SP[p3, p3]) + (m0^2 + m2^2 - SP[p2, p2]) (m1^2 + m3^2 - + SP[p1, p1] + 2 SP[p1, p3] - SP[p3, p3])) (m2^2 + + m4^2 - SP[p2, p2] + 2 SP[p2, p4] - + SP[p4, p4])) + (-2 m2^2 (-2 m1^2 (m0^2 + m3^2 - + SP[p3, p3]) + (m0^2 + m1^2 - SP[p1, p1]) (m1^2 + m3^2 - + SP[p1, p1] + 2 SP[p1, p3] - SP[p3, p3])) + (m1^2 + + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (-(m1^2 + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (m0^2 + m3^2 - SP[p3, p3]) + (m0^2 + + m2^2 - SP[p2, p2]) (m1^2 + m3^2 - SP[p1, p1] + + 2 SP[p1, p3] - SP[p3, p3])) + (-2 m1^2 (m0^2 + m2^2 - + SP[p2, p2]) + (m0^2 + m1^2 - SP[p1, p1]) (m1^2 + m2^2 - + SP[p1, p1] + 2 SP[p1, p2] - SP[p2, p2])) (m2^2 + + m3^2 - SP[p2, p2] + 2 SP[p2, p3] - SP[p3, p3])) (m3^2 + + m4^2 - SP[p3, p3] + 2 SP[p3, p4] - SP[p4, p4])) (m0^2 + + m4^2 - SP[p4, p4]) - (m3^2 + m4^2 - SP[p3, p3] + 2 SP[p3, p4] - + SP[p4, p4]) (-(m0^2 + m3^2 - + SP[p3, p3]) (-2 m2^2 (-2 m1^2 (m0^2 + m4^2 - + SP[p4, p4]) + (m0^2 + m1^2 - SP[p1, p1]) (m1^2 + m4^2 - + SP[p1, p1] + 2 SP[p1, p4] - SP[p4, p4])) + (m1^2 + + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (-(m1^2 + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m2^2 - SP[p2, p2]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (-2 m1^2 (m0^2 + m2^2 - + SP[p2, p2]) + (m0^2 + m1^2 - SP[p1, p1]) (m1^2 + m2^2 - + SP[p1, p1] + 2 SP[p1, p2] - SP[p2, p2])) (m2^2 + + m4^2 - SP[p2, p2] + 2 SP[p2, p4] - + SP[p4, p4])) + (-2 m0^4 SP[p1, p1] + + 4 m0^2 m2^2 SP[p1, p1] - 2 m2^4 SP[p1, p1] + + 4 m0^4 SP[p1, p2] - 4 m0^2 m1^2 SP[p1, p2] - + 4 m0^2 m2^2 SP[p1, p2] + 4 m1^2 m2^2 SP[p1, p2] + + 4 m0^2 SP[p1, p1] SP[p1, p2] - + 4 m2^2 SP[p1, p1] SP[p1, p2] - 8 m0^2 SP[p1, p2]^2 - + 2 m0^4 SP[p2, p2] + 4 m0^2 m1^2 SP[p2, p2] - + 2 m1^4 SP[p2, p2] + 4 m1^2 SP[p1, p1] SP[p2, p2] + + 4 m2^2 SP[p1, p1] SP[p2, p2] - 2 SP[p1, p1]^2 SP[p2, p2] + + 4 m0^2 SP[p1, p2] SP[p2, p2] - + 4 m1^2 SP[p1, p2] SP[p2, p2] + + 4 SP[p1, p1] SP[p1, p2] SP[p2, p2] - + 2 SP[p1, p1] SP[p2, p2]^2) (m3^2 + m4^2 - SP[p3, p3] + + 2 SP[p3, p4] - SP[p4, p4]) + (m1^2 + m3^2 - SP[p1, p1] + + 2 SP[p1, p3] - + SP[p3, p3]) ((m0^2 + m2^2 - + SP[p2, p2]) (-(m1^2 + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m2^2 - SP[p2, p2]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (-m0^4 + m0^2 m1^2 + + m0^2 m2^2 - m1^2 m2^2 - m0^2 SP[p1, p1] + + m2^2 SP[p1, p1] + 4 m0^2 SP[p1, p2] - m0^2 SP[p2, p2] + + m1^2 SP[p2, p2] - SP[p1, p1] SP[p2, p2]) (m2^2 + m4^2 - + SP[p2, p2] + 2 SP[p2, p4] - SP[p4, p4]) - + 2 m2^2 (-m0^4 + m0^2 m1^2 + m0^2 m4^2 - m1^2 m4^2 - + m0^2 SP[p1, p1] + m4^2 SP[p1, p1] + 4 m0^2 SP[p1, p4] - + m0^2 SP[p4, p4] + m1^2 SP[p4, p4] - + SP[p1, p1] SP[p4, p4])) - (m2^2 + m3^2 - SP[p2, p2] + + 2 SP[p2, p3] - + SP[p3, p3]) ((m0^2 + m2^2 - + SP[p2, p2]) (-2 m1^2 (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m1^2 - SP[p1, p1]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (4 m0^2 m1^2 - (m0^2 + + m1^2 - SP[p1, p1])^2) (m2^2 + m4^2 - SP[p2, p2] + + 2 SP[p2, p4] - SP[p4, p4]) - (m1^2 + m2^2 - SP[p1, p1] + + 2 SP[p1, p2] - SP[p2, p2]) (-m0^4 + m0^2 m1^2 + + m0^2 m4^2 - m1^2 m4^2 - m0^2 SP[p1, p1] + + m4^2 SP[p1, p1] + 4 m0^2 SP[p1, p4] - m0^2 SP[p4, p4] + + m1^2 SP[p4, p4] - SP[p1, p1] SP[p4, p4]))) + (m2^2 + + m4^2 - SP[p2, p2] + 2 SP[p2, p4] - + SP[p4, p4]) (-(m0^2 + m3^2 - + SP[p3, p3]) (-(m2^2 + m3^2 - SP[p2, p2] + 2 SP[p2, p3] - + SP[p3, p3]) (-2 m1^2 (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m1^2 - SP[p1, p1]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (m1^2 + m2^2 - + SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (-(m1^2 + m3^2 - SP[p1, p1] + 2 SP[p1, p3] - + SP[p3, p3]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m3^2 - SP[p3, p3]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (-2 m1^2 (m0^2 + m3^2 - + SP[p3, p3]) + (m0^2 + m1^2 - SP[p1, p1]) (m1^2 + m3^2 - + SP[p1, p1] + 2 SP[p1, p3] - SP[p3, p3])) (m2^2 + + m4^2 - SP[p2, p2] + 2 SP[p2, p4] - SP[p4, p4])) + ((m0^2 + + m2^2 - + SP[p2, p2]) (-2 m1^2 (m0^2 + m3^2 - SP[p3, p3]) + (m0^2 + + m1^2 - SP[p1, p1]) (m1^2 + m3^2 - SP[p1, p1] + + 2 SP[p1, p3] - SP[p3, p3])) + (4 m0^2 m1^2 - (m0^2 + + m1^2 - SP[p1, p1])^2) (m2^2 + m3^2 - SP[p2, p2] + + 2 SP[p2, p3] - SP[p3, p3]) - (m1^2 + m2^2 - SP[p1, p1] + + 2 SP[p1, p2] - SP[p2, p2]) (-m0^4 + m0^2 m1^2 + + m0^2 m3^2 - m1^2 m3^2 - m0^2 SP[p1, p1] + + m3^2 SP[p1, p1] + 4 m0^2 SP[p1, p3] - m0^2 SP[p3, p3] + + m1^2 SP[p3, p3] - SP[p1, p1] SP[p3, p3])) (m3^2 + m4^2 - + SP[p3, p3] + 2 SP[p3, p4] - SP[p4, p4]) - + 2 m3^2 ((m0^2 + m2^2 - + SP[p2, p2]) (-2 m1^2 (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m1^2 - SP[p1, p1]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (4 m0^2 m1^2 - (m0^2 + + m1^2 - SP[p1, p1])^2) (m2^2 + m4^2 - SP[p2, p2] + + 2 SP[p2, p4] - SP[p4, p4]) - (m1^2 + m2^2 - SP[p1, p1] + + 2 SP[p1, p2] - SP[p2, p2]) (-m0^4 + m0^2 m1^2 + + m0^2 m4^2 - m1^2 m4^2 - m0^2 SP[p1, p1] + + m4^2 SP[p1, p1] + 4 m0^2 SP[p1, p4] - m0^2 SP[p4, p4] + + m1^2 SP[p4, p4] - SP[p1, p1] SP[p4, p4])) + (m1^2 + m3^2 - + SP[p1, p1] + 2 SP[p1, p3] - + SP[p3, p3]) ((m0^2 + m2^2 - + + SP[p2, p2]) (-(m1^2 + m3^2 - SP[p1, p1] + 2 SP[p1, p3] - + SP[p3, p3]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m3^2 - SP[p3, p3]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (-m0^4 + m0^2 m1^2 + + m0^2 m3^2 - m1^2 m3^2 - m0^2 SP[p1, p1] + + m3^2 SP[p1, p1] + 4 m0^2 SP[p1, p3] - m0^2 SP[p3, p3] + + m1^2 SP[p3, p3] - SP[p1, p1] SP[p3, p3]) (m2^2 + m4^2 - + SP[p2, p2] + 2 SP[p2, p4] - SP[p4, p4]) - (m2^2 + m3^2 - + SP[p2, p2] + 2 SP[p2, p3] - SP[p3, p3]) (-m0^4 + + m0^2 m1^2 + m0^2 m4^2 - m1^2 m4^2 - m0^2 SP[p1, p1] + + m4^2 SP[p1, p1] + 4 m0^2 SP[p1, p4] - m0^2 SP[p4, p4] + + m1^2 SP[p4, p4] - SP[p1, p1] SP[p4, p4]))) - (m1^2 + + m4^2 - SP[p1, p1] + 2 SP[p1, p4] - + SP[p4, p4]) (-(m0^2 + m3^2 - + SP[p3, p3]) (-(m2^2 + m3^2 - SP[p2, p2] + 2 SP[p2, p3] - + SP[p3, p3]) (-(m1^2 + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m2^2 - SP[p2, p2]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + + 2 m2^2 (-(m1^2 + m3^2 - SP[p1, p1] + 2 SP[p1, p3] - + SP[p3, p3]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m3^2 - SP[p3, p3]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - + SP[p4, p4])) + (-(m1^2 + m2^2 - SP[p1, p1] + + 2 SP[p1, p2] - SP[p2, p2]) (m0^2 + m3^2 - + SP[p3, p3]) + (m0^2 + m2^2 - SP[p2, p2]) (m1^2 + m3^2 - + SP[p1, p1] + 2 SP[p1, p3] - SP[p3, p3])) (m2^2 + + m4^2 - SP[p2, p2] + 2 SP[p2, p4] - SP[p4, p4])) + ((m0^2 + + m2^2 - + SP[p2, p2]) (-(m1^2 + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (m0^2 + m3^2 - SP[p3, p3]) + (m0^2 + + m2^2 - SP[p2, p2]) (m1^2 + m3^2 - SP[p1, p1] + + 2 SP[p1, p3] - SP[p3, p3])) + (-m0^4 + m0^2 m1^2 + + m0^2 m2^2 - m1^2 m2^2 - m0^2 SP[p1, p1] + + m2^2 SP[p1, p1] + 4 m0^2 SP[p1, p2] - m0^2 SP[p2, p2] + + m1^2 SP[p2, p2] - SP[p1, p1] SP[p2, p2]) (m2^2 + m3^2 - + SP[p2, p2] + 2 SP[p2, p3] - SP[p3, p3]) - + 2 m2^2 (-m0^4 + m0^2 m1^2 + m0^2 m3^2 - m1^2 m3^2 - + m0^2 SP[p1, p1] + m3^2 SP[p1, p1] + 4 m0^2 SP[p1, p3] - + m0^2 SP[p3, p3] + m1^2 SP[p3, p3] - + SP[p1, p1] SP[p3, p3])) (m3^2 + m4^2 - SP[p3, p3] + + 2 SP[p3, p4] - SP[p4, p4]) - + 2 m3^2 ((m0^2 + m2^2 - + SP[p2, p2]) (-(m1^2 + m2^2 - SP[p1, p1] + 2 SP[p1, p2] - + SP[p2, p2]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m2^2 - SP[p2, p2]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (-m0^4 + m0^2 m1^2 + + m0^2 m2^2 - m1^2 m2^2 - m0^2 SP[p1, p1] + + m2^2 SP[p1, p1] + 4 m0^2 SP[p1, p2] - m0^2 SP[p2, p2] + + m1^2 SP[p2, p2] - SP[p1, p1] SP[p2, p2]) (m2^2 + m4^2 - + SP[p2, p2] + 2 SP[p2, p4] - SP[p4, p4]) - + 2 m2^2 (-m0^4 + m0^2 m1^2 + m0^2 m4^2 - m1^2 m4^2 - + m0^2 SP[p1, p1] + m4^2 SP[p1, p1] + 4 m0^2 SP[p1, p4] - + m0^2 SP[p4, p4] + m1^2 SP[p4, p4] - + SP[p1, p1] SP[p4, p4])) + (m2^2 + m3^2 - SP[p2, p2] + + 2 SP[p2, p3] - + SP[p3, p3]) ((m0^2 + m2^2 - + SP[p2, p2]) (-(m1^2 + m3^2 - SP[p1, p1] + 2 SP[p1, p3] - + SP[p3, p3]) (m0^2 + m4^2 - SP[p4, p4]) + (m0^2 + + m3^2 - SP[p3, p3]) (m1^2 + m4^2 - SP[p1, p1] + + 2 SP[p1, p4] - SP[p4, p4])) + (-m0^4 + m0^2 m1^2 + + m0^2 m3^2 - m1^2 m3^2 - m0^2 SP[p1, p1] + + m3^2 SP[p1, p1] + 4 m0^2 SP[p1, p3] - m0^2 SP[p3, p3] + + m1^2 SP[p3, p3] - SP[p1, p1] SP[p3, p3]) (m2^2 + m4^2 - + SP[p2, p2] + 2 SP[p2, p4] - SP[p4, p4]) - (m2^2 + m3^2 - + SP[p2, p2] + 2 SP[p2, p3] - SP[p3, p3]) (-m0^4 + + m0^2 m1^2 + m0^2 m4^2 - m1^2 m4^2 - m0^2 SP[p1, p1] + + m4^2 SP[p1, p1] + 4 m0^2 SP[p1, p4] - m0^2 SP[p4, p4] + + m1^2 SP[p4, p4] - SP[p1, p1] SP[p4, p4]))))"}, +{"fcstOneLoop-ID9","OneLoop[k, 1/(I Pi^2) FAD[{k}, {k, mW}] GSD[k]]","0"}, +{"fcstOneLoop-ID10","PaVeReduce[(OneLoop[q, Contract[MTD[mu, nu] FVD[q, mu] FVD[q,nu] FAD[{q, Subscript[m, 0]}, {q + p1, m1}]], +OneLoopSimplify -> False] //ChangeDimension[#, D] &) - (Contract[MTD[mu, nu] ChangeDimension[ +OneLoop[q, FVD[q, mu] FVD[q, nu] FAD[{q, Subscript[m, 0]}, {q + p1, m1}], OneLoopSimplify -> False], D]])]","0"}, +{"fcstOneLoop-ID11","OneLoop[q1, FAD[{q1, MG}, {p3 + q1, MB}, {p3 + p4 + q1, MT}] FVD[q1, mu]] // FCE", +"-I \[Pi]^2 (C0[SP[p3, p3], SP[p4, p4], + SP[p3, p3] + 2 SP[p3, p4] + SP[p4, p4], MG^2, MB^2, MT^2] FV[p3, + mu] + FV[p3, mu] PaVe[ 1, {SP[p3, p3], SP[p3, p3] + 2 SP[p3, p4] + SP[p4, p4], + SP[p4, p4]}, {MB^2, MG^2, MT^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True] - FV[p4, mu] PaVe[ + 2, {SP[p3, p3], SP[p3, p3] + 2 SP[p3, p4] + SP[p4, p4], + SP[p4, p4]}, {MB^2, MG^2, MT^2}, PaVeAutoOrder -> True, + PaVeAutoReduce -> True])"}, + +{"fcstOneLoop-ID11","FCSetDiracGammaScheme[\"BMHV\"]; \n +res= FCE[OneLoop[q, +SpinorUBar[p3, ms].GA[6].(GS[q] + mt).GA[7].PolarizationVector[p2, + mu].(2*FV[q, mu] + 2*FV[p1, mu] + FV[p2, mu]).SpinorU[p1, + mb] FAD[{q, mt}, {q + p1, mh}, {q + p1 + p2, mh}]]] \n + FCSetDiracGammaScheme[\"NDR\"]; \n res", + "I*Pi^2*(2*PaVe[0, 0, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GS[Polarization[p2, I]] . GA[7] . Spinor[Momentum[p1], mb, 1]] + +(2*mb*PaVe[1, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] + + 2*mb*PaVe[1, 1, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True])* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GA[6] . Spinor[Momentum[p1], mb, 1]*SP[p1, Polarization[p2, I]]] - +2*PaVe[1, 2, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GS[p2] . GA[7] . Spinor[Momentum[p1], mb, 1]*SP[p1, Polarization[p2, I]]] + +(-(mb*C0[SP[p1, p1], SP[p2, p2], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], mt^2, mh^2, mh^2]) - + mb*PaVe[1, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] - + 2*mb*PaVe[2, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] - + 2*mb*PaVe[1, 2, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True])* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GA[6] . Spinor[Momentum[p1], mb, 1]*SP[p2, Polarization[p2, I]]] + +(PaVe[2, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] + + 2*PaVe[2, 2, {SP[p1, p1], SP[p1, p1] + 2*SP[p1, p2] + SP[p2, p2], SP[p2, p2]}, {mh^2, mt^2, mh^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True])* +StandardMatrixElement[Spinor[Momentum[p3], ms, 1] . GS[p2] . GA[7] . Spinor[Momentum[p1], mb, 1]*SP[p2, Polarization[p2, I]]])"}, +{"fcstOneLoop-ID12","OneLoop[k, +FVD[k, a] SPD[k, p] SPD[k] FAD[{k, my}, {k + p - q, mw}, {k + p + q, mw}], FCE -> True] // +Collect2[#, FeynCalc`Package`PaVeHeadsList] &","((I/8)*my^2*Pi^2*B0[SP[p, p] - 2*SP[p, q] + SP[q, q], mw^2, my^2]*(FV[p, a] - FV[q, a])*(mw^2 - my^2 - SP[p, p] + 2*SP[p, q] - SP[q, q]))/ +(SP[p, p] - 2*SP[p, q] + SP[q, q]) + ((I/8)*my^2*Pi^2*B0[SP[p, p] + 2*SP[p, q] + SP[q, q], mw^2, my^2]*(FV[p, a] + FV[q, a])* +(mw^2 - my^2 - SP[p, p] - 2*SP[p, q] - SP[q, q]))/(SP[p, p] + 2*SP[p, q] + SP[q, q]) - +(2*I)*Pi^2*FV[q, a]*PaVe[1, {4*SP[q, q], SP[p, p] + 2*SP[p, q] + SP[q, q], SP[p, p] - 2*SP[p, q] + SP[q, q]}, {mw^2, mw^2, my^2}, PaVeAutoOrder -> True, +PaVeAutoReduce -> True]*(SP[p, p] + SP[p, q])*(SP[p, p] + 2*SP[p, q] + SP[q, q]) + +I*Pi^2*(FV[p, a] - FV[q, a])*PaVe[2, {4*SP[q, q], SP[p, p] + 2*SP[p, q] + SP[q, q], SP[p, p] - 2*SP[p, q] + SP[q, q]}, {mw^2, mw^2, my^2}, +PaVeAutoOrder -> True, PaVeAutoReduce -> True]*(SP[p, p] + SP[p, q])*(SP[p, p] + 2*SP[p, q] + SP[q, q]) + +((I/4)*my^2*Pi^2*A0[my^2]*(FV[p, a]*SP[p, p] - 2*FV[q, a]*SP[p, q] + FV[p, a]*SP[q, q]))/ +((SP[p, p] - 2*SP[p, q] + SP[q, q])*(SP[p, p] + 2*SP[p, q] + SP[q, q])) + +I*Pi^2*FV[q, a]*PaVe[1, {4*SP[q, q], SP[p, p] - 2*SP[p, q] + SP[q, q], SP[p, p] + 2*SP[p, q] + SP[q, q]}, {mw^2, mw^2, my^2}, PaVeAutoOrder -> True, +PaVeAutoReduce -> True]*(-(mw^2*my^2) + my^4 + my^2*SP[p, p] - 2*SP[p, p]^2 - 6*SP[p, p]*SP[p, q] - 4*SP[p, q]^2 + my^2*SP[q, q] - 2*SP[p, p]*SP[q, q] - +2*SP[p, q]*SP[q, q]) + (I/2)*Pi^2*(FV[p, a] + FV[q, a])*PaVe[2, {4*SP[q, q], SP[p, p] - 2*SP[p, q] + SP[q, q], SP[p, p] + 2*SP[p, q] + SP[q, q]}, +{mw^2, mw^2, my^2}, PaVeAutoOrder -> True, PaVeAutoReduce -> True]*(-(mw^2*my^2) + my^4 + my^2*SP[p, p] - 2*SP[p, p]^2 - 6*SP[p, p]*SP[p, q] - +4*SP[p, q]^2 + my^2*SP[q, q] - 2*SP[p, p]*SP[q, q] - 2*SP[p, q]*SP[q, q]) + +(I/2)*Pi^2*C0[4*SP[q, q], SP[p, p] - 2*SP[p, q] + SP[q, q], SP[p, p] + 2*SP[p, q] + SP[q, q], mw^2, mw^2, my^2]* +(-(mw^2*my^2*FV[p, a]) + my^4*FV[p, a] - mw^2*my^2*FV[q, a] + my^4*FV[q, a] + my^2*FV[p, a]*SP[p, p] + my^2*FV[q, a]*SP[p, p] - 4*FV[q, a]*SP[p, p]^2 - +12*FV[q, a]*SP[p, p]*SP[p, q] - 8*FV[q, a]*SP[p, q]^2 + my^2*FV[p, a]*SP[q, q] + my^2*FV[q, a]*SP[q, q] - 4*FV[q, a]*SP[p, p]*SP[q, q] - +4*FV[q, a]*SP[p, q]*SP[q, q]) + ((I/2)*Pi^2*B0[4*SP[q, q], mw^2, mw^2]*(-2*mw^2*FV[q, a]*SP[p, q] + 2*mw^2*FV[p, a]*SP[q, q] - my^2*FV[p, a]*SP[q, q] + + D*my^2*FV[p, a]*SP[q, q] - 2*FV[p, a]*SP[p, p]*SP[q, q] + 2*D*FV[p, a]*SP[p, p]*SP[q, q] + 2*FV[q, a]*SP[p, q]*SP[q, q] - 2*FV[p, a]*SP[q, q]^2))/ +((-1 + D)*SP[q, q]) + ((I/4)*Pi^2*A0[mw^2]*(4*FV[q, a]*SP[p, p]^2*SP[p, q] - 2*D*FV[q, a]*SP[p, p]^2*SP[p, q] - 16*FV[q, a]*SP[p, q]^3 + + 8*D*FV[q, a]*SP[p, q]^3 - my^2*FV[p, a]*SP[p, p]*SP[q, q] + D*my^2*FV[p, a]*SP[p, p]*SP[q, q] - 2*FV[p, a]*SP[p, p]^2*SP[q, q] + + 2*my^2*FV[q, a]*SP[p, q]*SP[q, q] - 2*D*my^2*FV[q, a]*SP[p, q]*SP[q, q] + 8*FV[q, a]*SP[p, p]*SP[p, q]*SP[q, q] - + 4*D*FV[q, a]*SP[p, p]*SP[p, q]*SP[q, q] + 8*FV[p, a]*SP[p, q]^2*SP[q, q] - my^2*FV[p, a]*SP[q, q]^2 + D*my^2*FV[p, a]*SP[q, q]^2 - + 4*FV[p, a]*SP[p, p]*SP[q, q]^2 + 4*FV[q, a]*SP[p, q]*SP[q, q]^2 - 2*D*FV[q, a]*SP[p, q]*SP[q, q]^2 - 2*FV[p, a]*SP[q, q]^3))/ +((-1 + D)*(-SP[p, p] + 2*SP[p, q] - SP[q, q])*SP[q, q]*(SP[p, p] + 2*SP[p, q] + SP[q, q]))"}, +{"fcstOneLoop-ID13","OneLoop[q, FAD[{q, m1}, {p + q - k, m2}]]//FCE","I \[Pi]^2 B0[SP[k, k] - 2 SP[k, p] + SP[p, p], m1^2, m2^2]"} } diff --git a/Tests/LoopIntegrals/OneLoopSimplify.test b/Tests/LoopIntegrals/OneLoopSimplify.test index f9baba23d..46e276105 100644 --- a/Tests/LoopIntegrals/OneLoopSimplify.test +++ b/Tests/LoopIntegrals/OneLoopSimplify.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for OneLoopSimplify *) @@ -39,7 +39,7 @@ HoldForm[_]) Pair[LorentzIndex[mu, D], LorentzIndex[nu, D]]]","True"}, "OneLoopSimplify[FVD[p, i] SPD[p, k] FAD[{p}, {p, m}], p] // FCE", "(FAD[{p, m}] FVD[k, i])/D"}, {"fcstOneLoopSimplify-ID8", -"OneLoopSimplify[FV[p, i] FV[p, j] FAD[{p}, {p, m}], p] // FCE", +"OneLoopSimplify[FVD[p, i] FVD[p, j] FAD[{p}, {p, m}], p] // FCE", "(FAD[{p, m}] MTD[i, j])/D"}, {"fcstOneLoopSimplify-ID9", " OneLoopSimplify[ @@ -49,23 +49,32 @@ GAD[mu].(1/2 Fal (1 - GA[5]) + nu].(1/2 Fbe (1 - GA[5]) + 1/2 FbeCC (1 + GA[5])) FAD[{k - p, mF}, {k, mV}, k] (-FVD[k, mu] FVD[k, nu] + MTD[mu, nu] SPD[k, k]), k] // FCE", -"-((-2 + D)*FAD[{k, mF}]*(-(Fal*Fbe*GSD[p] . GA[5]) + FalCC*FbeCC*GSD[p] . GA[5] + Fal*Fbe*GSD[p] + FalCC*FbeCC*GSD[p]))/ -(4*SPD[p, p]) - (FAD[k, {k - p, mF}]*(-(Fal*Fbe*GSD[p] . GA[5]) + FalCC*FbeCC*GSD[p] . GA[5] + Fal*Fbe*GSD[p] + FalCC*FbeCC*GSD[p])* -(mF^2 - SPD[p, p])^2)/(4*mV^2*SPD[p, p]) + -(FAD[{k, mV}]*(-(Fal*Fbe*GSD[p] . GA[5]) + FalCC*FbeCC*GSD[p] . GA[5] + Fal*Fbe*GSD[p] + FalCC*FbeCC*GSD[p])* -(mF^2 - 2*mV^2 + D*mV^2 - SPD[p, p]))/(4*mV^2*SPD[p, p]) - -(FAD[{k, mF}, {k - p, mV}]*(Fal*Fbe*mF^4*GSD[p] . GA[5] - FalCC*FbeCC*mF^4*GSD[p] . GA[5] - 3*Fal*Fbe*mF^2*mV^2*GSD[p] . GA[5] + - D*Fal*Fbe*mF^2*mV^2*GSD[p] . GA[5] + 3*FalCC*FbeCC*mF^2*mV^2*GSD[p] . GA[5] - D*FalCC*FbeCC*mF^2*mV^2*GSD[p] . GA[5] + - 2*Fal*Fbe*mV^4*GSD[p] . GA[5] - D*Fal*Fbe*mV^4*GSD[p] . GA[5] - 2*FalCC*FbeCC*mV^4*GSD[p] . GA[5] + - D*FalCC*FbeCC*mV^4*GSD[p] . GA[5] - Fal*Fbe*mF^4*GSD[p] - FalCC*FbeCC*mF^4*GSD[p] + 3*Fal*Fbe*mF^2*mV^2*GSD[p] - - D*Fal*Fbe*mF^2*mV^2*GSD[p] + 3*FalCC*FbeCC*mF^2*mV^2*GSD[p] - D*FalCC*FbeCC*mF^2*mV^2*GSD[p] - 2*Fal*Fbe*mV^4*GSD[p] + - D*Fal*Fbe*mV^4*GSD[p] - 2*FalCC*FbeCC*mV^4*GSD[p] + D*FalCC*FbeCC*mV^4*GSD[p] + 2*FalCC*Fbe*M*mV^2*SPD[p, p] - - 2*D*FalCC*Fbe*M*mV^2*SPD[p, p] + 2*Fal*FbeCC*Mcc*mV^2*SPD[p, p] - 2*D*Fal*FbeCC*Mcc*mV^2*SPD[p, p] - - 2*Fal*Fbe*mF^2*GSD[p] . GA[5]*SPD[p, p] + 2*FalCC*FbeCC*mF^2*GSD[p] . GA[5]*SPD[p, p] - 3*Fal*Fbe*mV^2*GSD[p] . GA[5]*SPD[p, p] + - D*Fal*Fbe*mV^2*GSD[p] . GA[5]*SPD[p, p] + 3*FalCC*FbeCC*mV^2*GSD[p] . GA[5]*SPD[p, p] - - D*FalCC*FbeCC*mV^2*GSD[p] . GA[5]*SPD[p, p] - 2*FalCC*Fbe*M*mV^2*GA[5]*SPD[p, p] + 2*D*FalCC*Fbe*M*mV^2*GA[5]*SPD[p, p] + - 2*Fal*FbeCC*Mcc*mV^2*GA[5]*SPD[p, p] - 2*D*Fal*FbeCC*Mcc*mV^2*GA[5]*SPD[p, p] + 2*Fal*Fbe*mF^2*GSD[p]*SPD[p, p] + - 2*FalCC*FbeCC*mF^2*GSD[p]*SPD[p, p] + 3*Fal*Fbe*mV^2*GSD[p]*SPD[p, p] - D*Fal*Fbe*mV^2*GSD[p]*SPD[p, p] + - 3*FalCC*FbeCC*mV^2*GSD[p]*SPD[p, p] - D*FalCC*FbeCC*mV^2*GSD[p]*SPD[p, p] + Fal*Fbe*GSD[p] . GA[5]*SPD[p, p]^2 - - FalCC*FbeCC*GSD[p] . GA[5]*SPD[p, p]^2 - Fal*Fbe*GSD[p]*SPD[p, p]^2 - FalCC*FbeCC*GSD[p]*SPD[p, p]^2))/(4*mV^2*SPD[p, p])"} +"((2 - D)*(FalCC*FbeCC*GSD[p] . GA[6] + Fal*Fbe*GSD[p] . GA[7])*FAD[{k, mF}])/(2*SPD[p, p]) - +((FalCC*FbeCC*GSD[p] . GA[6] + Fal*Fbe*GSD[p] . GA[7])*FAD[k, {k - p, mF}]*(mF^2 - SPD[p, p])^2)/(2*mV^2*SPD[p, p]) + +((FalCC*FbeCC*GSD[p] . GA[6] + Fal*Fbe*GSD[p] . GA[7])*FAD[{k, mV}]*(mF^2 - 2*mV^2 + D*mV^2 - SPD[p, p]))/(2*mV^2*SPD[p, p]) + +(FAD[{k, mF}, {k - p, mV}]*(FalCC*FbeCC*mF^4*GSD[p] . GA[6] - 3*FalCC*FbeCC*mF^2*mV^2*GSD[p] . GA[6] + + D*FalCC*FbeCC*mF^2*mV^2*GSD[p] . GA[6] + 2*FalCC*FbeCC*mV^4*GSD[p] . GA[6] - D*FalCC*FbeCC*mV^4*GSD[p] . GA[6] + + Fal*Fbe*mF^4*GSD[p] . GA[7] - 3*Fal*Fbe*mF^2*mV^2*GSD[p] . GA[7] + D*Fal*Fbe*mF^2*mV^2*GSD[p] . GA[7] + + 2*Fal*Fbe*mV^4*GSD[p] . GA[7] - D*Fal*Fbe*mV^4*GSD[p] . GA[7] - 2*FalCC*FbeCC*mF^2*GSD[p] . GA[6]*SPD[p, p] - + 3*FalCC*FbeCC*mV^2*GSD[p] . GA[6]*SPD[p, p] + D*FalCC*FbeCC*mV^2*GSD[p] . GA[6]*SPD[p, p] - + 2*Fal*Fbe*mF^2*GSD[p] . GA[7]*SPD[p, p] - 3*Fal*Fbe*mV^2*GSD[p] . GA[7]*SPD[p, p] + D*Fal*Fbe*mV^2*GSD[p] . GA[7]*SPD[p, p] - + 2*Fal*FbeCC*Mcc*mV^2*GA[6]*SPD[p, p] + 2*D*Fal*FbeCC*Mcc*mV^2*GA[6]*SPD[p, p] - 2*FalCC*Fbe*M*mV^2*GA[7]*SPD[p, p] + + 2*D*FalCC*Fbe*M*mV^2*GA[7]*SPD[p, p] + FalCC*FbeCC*GSD[p] . GA[6]*SPD[p, p]^2 + Fal*Fbe*GSD[p] . GA[7]*SPD[p, p]^2))/ +(2*mV^2*SPD[p, p])"}, +{"fcstOneLoopSimplify-ID10", +"$KeepLogDivergentScalelessIntegrals = True; \n +res=OneLoopSimplify[(-I GAD[Lor2] SMP[\"g_s\"] SUNTF[{Glu3}, Col2, +Col3]).(M + GSD[q]).(-I GAD[Lor1] SMP[\"g_s\"] SUNTF[{Glu3}, Col3, +Col1]) ((1 - GaugeXi) FAD[{q, M}, -p + q, -p + q] FVD[p - q, +Lor2] FVD[-p + q, Lor1] + FAD[{q, M}, -p + q] MTD[Lor1, Lor2]), q, FCE -> True]; +$KeepLogDivergentScalelessIntegrals = False; \n res", +"(CF*(2 - D)*FAD[{q, M}]*GSD[p]*SDF[Col1, Col2]*SMP[\"g_s\"]^2)/ +(2*SPD[p, p]) + (CF*(1 - GaugeXi)*FAD[q, q]*GSD[p]*SDF[Col1, Col2]* +SMP[\"g_s\"]^2*(M^2 - SPD[p, p]))/(2*SPD[p, p]) + +(CF*(1 - GaugeXi)*FAD[q, q, {-p + q, M}]*GSD[p]*SDF[Col1, Col2]* +SMP[\"g_s\"]^2*(M^2 - SPD[p, p])^2)/(2*SPD[p, p]) - +(CF*FAD[q, {-p + q, M}]*SDF[Col1, Col2]*SMP[\"g_s\"]^2* +(3*M^2*GSD[p] - D*M^2*GSD[p] - GaugeXi*M^2*GSD[p] - 2*M*SPD[p, p] + +2*D*M*SPD[p, p] + 2*GaugeXi*M*SPD[p, p] + 3*GSD[p]*SPD[p, p] - +D*GSD[p]*SPD[p, p] - GaugeXi*GSD[p]*SPD[p, p]))/(2*SPD[p, p])"} } diff --git a/Tests/LoopIntegrals/PaVe.test b/Tests/LoopIntegrals/PaVe.test index 082c786f7..32c5ca80d 100644 --- a/Tests/LoopIntegrals/PaVe.test +++ b/Tests/LoopIntegrals/PaVe.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for PaVe *) diff --git a/Tests/LoopIntegrals/PaVeIntegrals.test b/Tests/LoopIntegrals/PaVeIntegrals.test index a54663095..474f67bbb 100644 --- a/Tests/LoopIntegrals/PaVeIntegrals.test +++ b/Tests/LoopIntegrals/PaVeIntegrals.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Passarino-Veltman diff --git a/Tests/LoopIntegrals/PaVeOrder.test b/Tests/LoopIntegrals/PaVeOrder.test index 130bd2fba..be0b42ef5 100644 --- a/Tests/LoopIntegrals/PaVeOrder.test +++ b/Tests/LoopIntegrals/PaVeOrder.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for PaVeOrder *) diff --git a/Tests/LoopIntegrals/PaVeReduce.test b/Tests/LoopIntegrals/PaVeReduce.test index dfeb7581f..9275ffd35 100644 --- a/Tests/LoopIntegrals/PaVeReduce.test +++ b/Tests/LoopIntegrals/PaVeReduce.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for PaVeReduce *) @@ -330,7 +330,26 @@ m2^2}])/(D*(2 + D)) + ((1 + 2*D)*m1^2*(m1^2 - m2^2)*PaVe[1, 1, {0}, \ "PaVe[0,0,1,1,1,{0},{m1^2,m2^2}]//PaVeReduce", "-PaVe[0, {}, {m2^2}]/(2*(2 + D)) + (m1^2*PaVe[1, 1, 1, {0}, \ {m1^2, m2^2}])/(2 + D) + ((m1^2 - m2^2)*PaVe[1, 1, 1, 1, {0}, {m1^2, \ -m2^2}])/(2*(2 + D))"} +m2^2}])/(2*(2 + D))"}, +{"fcstPaVeReduceBFunctions-ID25", +"PaVeReduce[PaVe[1, 1, 1, {-CSPD[p, p]}, {m1^2, m2^2}], FCE -> True]", +"((2 D m1^4 + D^2 m1^4 - 4 D m1^2 m2^2 - 2 D^2 m1^2 m2^2 + 2 D m2^4 + + D^2 m2^4 - 8 m1^2 CSPD[p, p] + 4 D m1^2 CSPD[p, p] - + 2 D^2 m1^2 CSPD[p, p] + 4 D m2^2 CSPD[p, p] + + 2 D^2 m2^2 CSPD[p, p] + 2 D CSPD[p, p]^2 + D^2 CSPD[p, p]^2) PaVe[ +0, {}, {m1^2}])/(8 (1 - D) D CSPD[p, p]^3) - (1/( +8 (1 - D) D CSPD[p, +p]^3))(2 D m1^4 + D^2 m1^4 - 4 D m1^2 m2^2 - 2 D^2 m1^2 m2^2 + + 2 D m2^4 + D^2 m2^4 + 4 D m1^2 CSPD[p, p] - + 4 D^2 m1^2 CSPD[p, p] - 8 m2^2 CSPD[p, p] + 4 D m2^2 CSPD[p, p] + + 4 D^2 m2^2 CSPD[p, p] - 10 D CSPD[p, p]^2 + + 7 D^2 CSPD[p, p]^2) PaVe[0, {}, {m2^2}] - (1/( +8 (1 - D) CSPD[p, +p]^3))(m1^2 - m2^2 - CSPD[p, p]) (2 m1^4 + D m1^4 - 4 m1^2 m2^2 - + 2 D m1^2 m2^2 + 2 m2^4 + D m2^4 + 8 m1^2 CSPD[p, p] - + 2 D m1^2 CSPD[p, p] + 4 m2^2 CSPD[p, p] + 2 D m2^2 CSPD[p, p] + + 2 CSPD[p, p]^2 + D CSPD[p, p]^2) PaVe[ +0, {-CSPD[p, p]}, {m1^2, m2^2}]"} }); Tests`LoopIntegrals`fcstPaVeReduceCFunctions = @@ -955,7 +974,18 @@ PaVe[2, {p10, p12, p20}, {m1^2, m2^2, "0"}, {"fcstPaVeReduce-ID9", "PaVe[0, 0, {0}, {0, m^2}, PaVeAutoOrder -> True] // PaVeReduce", "-(PaVe[0, {}, {m^2}]/(2 (1 - D))) + (m^2 PaVe[1, {0}, {0, m^2}])/( -2 (1 - D))"} +2 (1 - D))"}, +{"fcstPaVeReduce-ID10", "PaVeReduce[PaVe[0, 0, 1, {pp}, {mm1, mm2}], MaxIterations -> 1]", +"(mm1 PaVe[0, {}, {mm1}])/( +2 D pp) - ((mm1 + mm2 + pp) PaVe[0, {}, {mm2}])/(4 D pp) - ( +mm1 (mm1 - mm2 + pp) PaVe[0, {pp}, {mm1, mm2}])/( +2 D pp) - ((mm1 - mm2 + pp)^2 PaVe[1, {pp}, {mm1, mm2}])/( +4 D pp) - ((mm1 - mm2 + pp) PaVe[0, 0, {pp}, {mm1, mm2}])/(2 D pp)"}, +{"fcstPaVeReduce-ID11", "MatchQ[PaVeReduce[ +Collect2[Expand[Sum[a[i], {i, 1, 5}] B0[0, mm, mm]], B0, +IsolateNames -> KK], +BReduce -> True], -(((2 - D) HoldForm[_] PaVe[0, {}, {mm}])/(2 mm))]", +"True"} }) diff --git a/Tests/LoopIntegrals/PaVeUVPart.test b/Tests/LoopIntegrals/PaVeUVPart.test new file mode 100644 index 000000000..0c963fc85 --- /dev/null +++ b/Tests/LoopIntegrals/PaVeUVPart.test @@ -0,0 +1,1696 @@ + + +(* :Title: PaVeUVPart.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for PaVeUVPart *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`PaVeUVPart = +({ +{"fcstPaVeUVPart-ID1", "PaVeUVPart[A0[m^2]]", "(-2*m^2)/(-4 + D)"}, +{"fcstPaVeUVPart-ID2", +"PaVeUVPart[A0[m^2],FCLoopExtract\[Rule]False,Prefactor\[Rule]cc]", + "(-2*cc*m^2)/(-4 + D)"}, +{"fcstPaVeUVPart-ID3", +"PaVeUVPart[x+y B0[SPD[p,p],0,\!\(\*SuperscriptBox[\(M\), \ +\(2\)]\)]]", "(-4*x + D*x - 2*y)/(-4 + D)"}, +{"fcstPaVeUVPart-ID4", +"PaVeUVPart[x+ y \ +C0[0,SPD[p,p],SPD[p,p],0,0,\!\(\*SuperscriptBox[\(M\), \(2\)]\)]]", +"x"}, +{"fcstPaVeUVPart-ID5", +"PaVeUVPart[PaVe[0,0,{p10,p12,p20},{m1^2,m2^2,m3^2}]]", +"-1/(2*(-4 + D))"}, +{"fcstPaVeUVPart-ID6", +"PaVeUVPart[PaVe[0,0,0,0,0,0,{p10,p12,p23,0,p20,p13},{m1^2,m2^2,m3^\ +2,m4^2}]]", +"(-5*m1^2 - 5*m2^2 - 5*m3^2 - 5*m4^2 + p10 + p12 + p13 + p20 + \ +p23)/(480*(-4 + D))"}, +{"fcstPaVeUVPart-ID7", +"PaVeUVPart[PaVe[0, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"-2/(-4 + D)"}, +{"fcstPaVeUVPart-ID8", +"PaVeUVPart[PaVe[1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(-4 + D)^(-1)"}, +{"fcstPaVeUVPart-ID9", +"PaVeUVPart[PaVe[0, 0, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(-3*m0^2 - 3*m1^2 + Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(6*(-4 + D))"}, +{"fcstPaVeUVPart-ID10", +"PaVeUVPart[PaVe[1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"-2/(3*(-4 + D))"}, +{"fcstPaVeUVPart-ID11", +"PaVeUVPart[PaVe[0, 0, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(2*m0^2 + 4*m1^2 - Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(12*(-4 + D))"}, +{"fcstPaVeUVPart-ID12", +"PaVeUVPart[PaVe[1, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"1/(2*(-4 + D))"}, +{"fcstPaVeUVPart-ID13", +"PaVeUVPart[PaVe[0, 0, 0, 0, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(-10*m0^4 - 10*m0^2*m1^2 - 10*m1^4 + 5*m0^2*Pair[Momentum[p1, D], \ +Momentum[p1, D]] + 5*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +Pair[Momentum[p1, D], Momentum[p1, D]]^2)/(120*(-4 + D))"}, +{"fcstPaVeUVPart-ID14", +"PaVeUVPart[PaVe[0, 0, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(-5*m0^2 - 15*m1^2 + 3*Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(60*(-4 + D))"}, +{"fcstPaVeUVPart-ID15", +"PaVeUVPart[PaVe[1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"-2/(5*(-4 + D))"}, +{"fcstPaVeUVPart-ID16", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(5*m0^4 + 10*m0^2*m1^2 + 15*m1^4 - 4*m0^2*Pair[Momentum[p1, D], \ +Momentum[p1, D]] - 6*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +Pair[Momentum[p1, D], Momentum[p1, D]]^2)/(240*(-4 + D))"}, +{"fcstPaVeUVPart-ID17", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(3*m0^2 + 12*m1^2 - 2*Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(60*(-4 + D))"}, +{"fcstPaVeUVPart-ID18", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"1/(3*(-4 + D))"}, +{"fcstPaVeUVPart-ID19", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(-35*m0^6 - 35*m0^4*m1^2 - 35*m0^2*m1^4 - 35*m1^6 + \ +21*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +28*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +21*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +7*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +7*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + Pair[Momentum[p1, \ +D], Momentum[p1, D]]^3)/(3360*(-4 + D))"}, +{"fcstPaVeUVPart-ID20", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(-7*m0^4 - 21*m0^2*m1^2 - 42*m1^4 + 7*m0^2*Pair[Momentum[p1, D], \ +Momentum[p1, D]] + 14*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +2*Pair[Momentum[p1, D], Momentum[p1, D]]^2)/(840*(-4 + D))"}, +{"fcstPaVeUVPart-ID21", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"(-7*m0^2 - 35*m1^2 + 5*Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(210*(-4 + D))"}, +{"fcstPaVeUVPart-ID22", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, m1^2}]]", +"-2/(7*(-4 + D))"}, +{"fcstPaVeUVPart-ID23", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(14*m0^6 + 28*m0^4*m1^2 + 42*m0^2*m1^4 + 56*m1^6 - \ +14*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +28*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +28*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +6*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +8*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - Pair[Momentum[p1, \ +D], Momentum[p1, D]]^3)/(6720*(-4 + D))"}, +{"fcstPaVeUVPart-ID24", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(14*m0^4 + 56*m0^2*m1^2 + 140*m1^4 - 16*m0^2*Pair[Momentum[p1, \ +D], Momentum[p1, D]] - 40*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] \ ++ 5*Pair[Momentum[p1, D], Momentum[p1, D]]^2)/(3360*(-4 + D))"}, +{"fcstPaVeUVPart-ID25", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(4*m0^2 + 24*m1^2 - 3*Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(168*(-4 + D))"}, +{"fcstPaVeUVPart-ID26", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", "1/(4*(-4 + D))"}, +{"fcstPaVeUVPart-ID27", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 0, 0, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(-126*m0^8 - 126*m0^6*m1^2 - 126*m0^4*m1^4 - 126*m0^2*m1^6 - \ +126*m1^8 + 84*m0^6*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +126*m0^4*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +126*m0^2*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +84*m1^6*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +36*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +54*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +36*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +9*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^3 + \ +9*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^3 - Pair[Momentum[p1, \ +D], Momentum[p1, D]]^4)/(120960*(-4 + D))"}, +{"fcstPaVeUVPart-ID28", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(-42*m0^6 - 126*m0^4*m1^2 - 252*m0^2*m1^4 - 420*m1^6 + \ +54*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +144*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +180*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +27*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +45*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +5*Pair[Momentum[p1, D], Momentum[p1, D]]^3)/(60480*(-4 + D))"}, +{"fcstPaVeUVPart-ID29", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(-12*m0^4 - 60*m0^2*m1^2 - 180*m1^4 + 15*m0^2*Pair[Momentum[p1, \ +D], Momentum[p1, D]] + 45*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] \ +- 5*Pair[Momentum[p1, D], Momentum[p1, D]]^2)/(5040*(-4 + D))"}, +{"fcstPaVeUVPart-ID30", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(-9*m0^2 - 63*m1^2 + 7*Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(504*(-4 + D))"}, +{"fcstPaVeUVPart-ID31", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", "-2/(9*(-4 + D))"}, +{"fcstPaVeUVPart-ID32", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 0, 0, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(42*m0^8 + 84*m0^6*m1^2 + 126*m0^4*m1^4 + 168*m0^2*m1^6 + \ +210*m1^8 - 48*m0^6*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +108*m0^4*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +144*m0^2*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +120*m1^6*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +27*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +54*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +45*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +8*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^3 - \ +10*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^3 + Pair[Momentum[p1, \ +D], Momentum[p1, D]]^4)/(241920*(-4 + D))"}, +{"fcstPaVeUVPart-ID33", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(6*m0^6 + 24*m0^4*m1^2 + 60*m0^2*m1^4 + 120*m1^6 - \ +9*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +30*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +45*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +5*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +10*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - Pair[Momentum[p1, \ +D], Momentum[p1, D]]^3)/(20160*(-4 + D))"}, +{"fcstPaVeUVPart-ID34", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(15*m0^4 + 90*m0^2*m1^2 + 315*m1^4 - 20*m0^2*Pair[Momentum[p1, \ +D], Momentum[p1, D]] - 70*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] \ ++ 7*Pair[Momentum[p1, D], Momentum[p1, D]]^2)/(10080*(-4 + D))"}, +{"fcstPaVeUVPart-ID35", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", +"(5*m0^2 + 40*m1^2 - 4*Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(360*(-4 + D))"}, +{"fcstPaVeUVPart-ID36", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, {m0^2, \ +m1^2}]]", "1/(5*(-4 + D))"}, +{"fcstPaVeUVPart-ID37", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, {SPD[p1, p1]}, \ +{m0^2, m1^2}]]", +"(-462*m0^10 - 462*m0^8*m1^2 - 462*m0^6*m1^4 - 462*m0^4*m1^6 - \ +462*m0^2*m1^8 - 462*m1^10 + 330*m0^8*Pair[Momentum[p1, D], \ +Momentum[p1, D]] + 528*m0^6*m1^2*Pair[Momentum[p1, D], Momentum[p1, \ +D]] + 594*m0^4*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +528*m0^2*m1^6*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +330*m1^8*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +165*m0^6*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +297*m0^4*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +297*m0^2*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +165*m1^6*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +55*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]]^3 + \ +88*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^3 + \ +55*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]]^3 - \ +11*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^4 - \ +11*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^4 + Pair[Momentum[p1, \ +D], Momentum[p1, D]]^5)/(5322240*(-4 + D))"}, +{"fcstPaVeUVPart-ID38", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 0, 0, 1, 1, {SPD[p1, p1]}, \ +{m0^2, m1^2}]]", +"(-66*m0^8 - 198*m0^6*m1^2 - 396*m0^4*m1^4 - 660*m0^2*m1^6 - \ +990*m1^8 + 99*m0^6*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +297*m0^4*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +495*m0^2*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +495*m1^6*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +66*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +165*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +165*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +22*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^3 + \ +33*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^3 - \ +3*Pair[Momentum[p1, D], Momentum[p1, D]]^4)/(1330560*(-4 + D))"}, +{"fcstPaVeUVPart-ID39", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, {SPD[p1, p1]}, \ +{m0^2, m1^2}]]", +"(-33*m0^6 - 165*m0^4*m1^2 - 495*m0^2*m1^4 - 1155*m1^6 + \ +55*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +220*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +385*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +33*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +77*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +7*Pair[Momentum[p1, D], Momentum[p1, D]]^3)/(221760*(-4 + D))"}, +{"fcstPaVeUVPart-ID40", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, \ +{m0^2, m1^2}]]", +"(-55*m0^4 - 385*m0^2*m1^2 - 1540*m1^4 + 77*m0^2*Pair[Momentum[p1, \ +D], Momentum[p1, D]] + 308*m1^2*Pair[Momentum[p1, D], Momentum[p1, \ +D]] - 28*Pair[Momentum[p1, D], Momentum[p1, D]]^2)/(55440*(-4 + \ +D))"}, +{"fcstPaVeUVPart-ID41", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, \ +{m0^2, m1^2}]]", +"(-11*m0^2 - 99*m1^2 + 9*Pair[Momentum[p1, D], Momentum[p1, \ +D]])/(990*(-4 + D))"}, +{"fcstPaVeUVPart-ID42", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1]}, \ +{m0^2, m1^2}]]", "-2/(11*(-4 + D))"}, +{"fcstPaVeUVPart-ID43", +"PaVeUVPart[PaVe[1, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, m1^2, \ +m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID44", +"PaVeUVPart[PaVe[2, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, m1^2, \ +m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID45", +"PaVeUVPart[PaVe[0, 0, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "-1/(2*(-4 + D))"}, +{"fcstPaVeUVPart-ID46", +"PaVeUVPart[PaVe[1, 1, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID47", +"PaVeUVPart[PaVe[1, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID48", +"PaVeUVPart[PaVe[2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID49", +"PaVeUVPart[PaVe[0, 0, 1, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "1/(6*(-4 + D))"}, +{"fcstPaVeUVPart-ID50", +"PaVeUVPart[PaVe[0, 0, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "1/(6*(-4 + D))"}, +{"fcstPaVeUVPart-ID51", +"PaVeUVPart[PaVe[1, 1, 1, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID52", +"PaVeUVPart[PaVe[1, 1, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID53", +"PaVeUVPart[PaVe[1, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID54", +"PaVeUVPart[PaVe[2, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, {m0^2, \ +m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID55", +"PaVeUVPart[PaVe[0, 0, 0, 0, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", +"(-4*m0^2 - 4*m1^2 - 4*m2^2 + p12 + Pair[Momentum[p1, D], \ +Momentum[p1, D]] + Pair[Momentum[p2, D], Momentum[p2, D]])/(48*(-4 + \ +D))"}, +{"fcstPaVeUVPart-ID56", +"PaVeUVPart[PaVe[0, 0, 1, 1, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "-1/(12*(-4 + D))"}, +{"fcstPaVeUVPart-ID57", +"PaVeUVPart[PaVe[0, 0, 1, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "-1/(24*(-4 + D))"}, +{"fcstPaVeUVPart-ID58", +"PaVeUVPart[PaVe[0, 0, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "-1/(12*(-4 + D))"}, +{"fcstPaVeUVPart-ID59", +"PaVeUVPart[PaVe[1, 1, 1, 1, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID60", +"PaVeUVPart[PaVe[1, 1, 1, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID61", +"PaVeUVPart[PaVe[1, 1, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID62", +"PaVeUVPart[PaVe[1, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID63", +"PaVeUVPart[PaVe[2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID64", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", +"(5*m0^2 + 10*m1^2 + 5*m2^2 - 2*p12 - 2*Pair[Momentum[p1, D], \ +Momentum[p1, D]] - Pair[Momentum[p2, D], Momentum[p2, D]])/(240*(-4 + \ +D))"}, +{"fcstPaVeUVPart-ID65", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", +"(5*m0^2 + 5*m1^2 + 10*m2^2 - 2*p12 - Pair[Momentum[p1, D], \ +Momentum[p1, D]] - 2*Pair[Momentum[p2, D], Momentum[p2, D]])/(240*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID66", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "1/(20*(-4 + D))"}, +{"fcstPaVeUVPart-ID67", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "1/(60*(-4 + D))"}, +{"fcstPaVeUVPart-ID68", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "1/(60*(-4 + D))"}, +{"fcstPaVeUVPart-ID69", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "1/(20*(-4 + D))"}, +{"fcstPaVeUVPart-ID70", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID71", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID72", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID73", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID74", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID75", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, p2]}, \ +{m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID76", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(-15*m0^4 - 15*m0^2*m1^2 - 15*m1^4 - 15*m0^2*m2^2 - 15*m1^2*m2^2 \ +- 15*m2^4 + 3*m0^2*p12 + 6*m1^2*p12 + 6*m2^2*p12 - p12^2 + \ +6*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +6*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +3*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] - p12*Pair[Momentum[p1, \ +D], Momentum[p1, D]] - Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +6*m0^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +3*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +6*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] - p12*Pair[Momentum[p2, \ +D], Momentum[p2, D]] - Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p2, D]] - Pair[Momentum[p2, D], \ +Momentum[p2, D]]^2)/(1440*(-4 + D))"}, +{"fcstPaVeUVPart-ID77", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(-6*m0^2 - 18*m1^2 - 6*m2^2 + 3*p12 + 3*Pair[Momentum[p1, D], \ +Momentum[p1, D]] + Pair[Momentum[p2, D], Momentum[p2, D]])/(720*(-4 + \ +D))"}, +{"fcstPaVeUVPart-ID78", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(-3*m0^2 - 6*m1^2 - 6*m2^2 + 2*p12 + Pair[Momentum[p1, D], \ +Momentum[p1, D]] + Pair[Momentum[p2, D], Momentum[p2, D]])/(720*(-4 + \ +D))"}, +{"fcstPaVeUVPart-ID79", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(-6*m0^2 - 6*m1^2 - 18*m2^2 + 3*p12 + Pair[Momentum[p1, D], \ +Momentum[p1, D]] + 3*Pair[Momentum[p2, D], Momentum[p2, D]])/(720*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID80", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "-1/(30*(-4 + D))"}, +{"fcstPaVeUVPart-ID81", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "-1/(120*(-4 + D))"}, +{"fcstPaVeUVPart-ID82", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "-1/(180*(-4 + D))"}, +{"fcstPaVeUVPart-ID83", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "-1/(120*(-4 + D))"}, +{"fcstPaVeUVPart-ID84", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "-1/(30*(-4 + D))"}, +{"fcstPaVeUVPart-ID85", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID86", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID87", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID88", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID89", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID90", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID91", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID92", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(21*m0^4 + 42*m0^2*m1^2 + 63*m1^4 + 21*m0^2*m2^2 + 42*m1^2*m2^2 + \ +21*m2^4 - 7*m0^2*p12 - 21*m1^2*p12 - 14*m2^2*p12 + 3*p12^2 - \ +14*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +21*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +7*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +3*p12*Pair[Momentum[p1, D], Momentum[p1, D]] + 3*Pair[Momentum[p1, \ +D], Momentum[p1, D]]^2 - 7*m0^2*Pair[Momentum[p2, D], Momentum[p2, \ +D]] - 7*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +7*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +2*p12*Pair[Momentum[p2, D], Momentum[p2, D]] + 2*Pair[Momentum[p1, \ +D], Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +Pair[Momentum[p2, D], Momentum[p2, D]]^2)/(10080*(-4 + D))"}, +{"fcstPaVeUVPart-ID93", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(21*m0^4 + 21*m0^2*m1^2 + 21*m1^4 + 42*m0^2*m2^2 + 42*m1^2*m2^2 + \ +63*m2^4 - 7*m0^2*p12 - 14*m1^2*p12 - 21*m2^2*p12 + 3*p12^2 - \ +7*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +7*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +7*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +2*p12*Pair[Momentum[p1, D], Momentum[p1, D]] + Pair[Momentum[p1, D], \ +Momentum[p1, D]]^2 - 14*m0^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +7*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +21*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +3*p12*Pair[Momentum[p2, D], Momentum[p2, D]] + 2*Pair[Momentum[p1, \ +D], Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +3*Pair[Momentum[p2, D], Momentum[p2, D]]^2)/(10080*(-4 + D))"}, +{"fcstPaVeUVPart-ID94", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(7*m0^2 + 28*m1^2 + 7*m2^2 - 4*p12 - 4*Pair[Momentum[p1, D], \ +Momentum[p1, D]] - Pair[Momentum[p2, D], Momentum[p2, D]])/(1680*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID95", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(7*m0^2 + 21*m1^2 + 14*m2^2 - 6*p12 - 3*Pair[Momentum[p1, D], \ +Momentum[p1, D]] - 2*Pair[Momentum[p2, D], Momentum[p2, \ +D]])/(5040*(-4 + D))"}, +{"fcstPaVeUVPart-ID96", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(7*m0^2 + 14*m1^2 + 21*m2^2 - 6*p12 - 2*Pair[Momentum[p1, D], \ +Momentum[p1, D]] - 3*Pair[Momentum[p2, D], Momentum[p2, \ +D]])/(5040*(-4 + D))"}, +{"fcstPaVeUVPart-ID97", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", +"(7*m0^2 + 7*m1^2 + 28*m2^2 - 4*p12 - Pair[Momentum[p1, D], \ +Momentum[p1, D]] - 4*Pair[Momentum[p2, D], Momentum[p2, \ +D]])/(1680*(-4 + D))"}, +{"fcstPaVeUVPart-ID98", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "1/(42*(-4 + D))"}, +{"fcstPaVeUVPart-ID99", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "1/(210*(-4 + D))"}, +{"fcstPaVeUVPart-ID100", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "1/(420*(-4 + D))"}, +{"fcstPaVeUVPart-ID101", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "1/(420*(-4 + D))"}, +{"fcstPaVeUVPart-ID102", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "1/(210*(-4 + D))"}, +{"fcstPaVeUVPart-ID103", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "1/(42*(-4 + D))"}, +{"fcstPaVeUVPart-ID104", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID105", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID106", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID107", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID108", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID109", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID110", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID111", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, SPD[p2, \ +p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID112", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 0, 0, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-168*m0^6 - 168*m0^4*m1^2 - 168*m0^2*m1^4 - 168*m1^6 - \ +168*m0^4*m2^2 - 168*m0^2*m1^2*m2^2 - 168*m1^4*m2^2 - 168*m0^2*m2^4 - \ +168*m1^2*m2^4 - 168*m2^6 + 28*m0^4*p12 + 56*m0^2*m1^2*p12 + \ +84*m1^4*p12 + 56*m0^2*m2^2*p12 + 112*m1^2*m2^2*p12 + 84*m2^4*p12 - \ +8*m0^2*p12^2 - 24*m1^2*p12^2 - 24*m2^2*p12^2 + 3*p12^3 + \ +84*m0^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +112*m0^2*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +84*m1^4*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +56*m0^2*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +56*m1^2*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +28*m2^4*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +16*m0^2*p12*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +24*m1^2*p12*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +16*m2^2*p12*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +3*p12^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +24*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +24*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 - \ +8*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +3*p12*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + 3*Pair[Momentum[p1, \ +D], Momentum[p1, D]]^3 + 84*m0^4*Pair[Momentum[p2, D], Momentum[p2, \ +D]] + 56*m0^2*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +28*m1^4*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +112*m0^2*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +56*m1^2*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +84*m2^4*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +16*m0^2*p12*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +16*m1^2*p12*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +24*m2^2*p12*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +3*p12^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +24*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]] - 16*m1^2*Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +16*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]] + 4*p12*Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p2, D]] + 3*Pair[Momentum[p1, D], \ +Momentum[p1, D]]^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +24*m0^2*Pair[Momentum[p2, D], Momentum[p2, D]]^2 - \ +8*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]]^2 - \ +24*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]]^2 + \ +3*p12*Pair[Momentum[p2, D], Momentum[p2, D]]^2 + 3*Pair[Momentum[p1, \ +D], Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, D]]^2 + \ +3*Pair[Momentum[p2, D], Momentum[p2, D]]^3)/(161280*(-4 + D))"}, +{"fcstPaVeUVPart-ID113", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, 1, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-28*m0^4 - 84*m0^2*m1^2 - 168*m1^4 - 28*m0^2*m2^2 - 84*m1^2*m2^2 \ +- 28*m2^4 + 12*m0^2*p12 + 48*m1^2*p12 + 24*m2^2*p12 - 6*p12^2 + \ +24*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +48*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +12*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +6*p12*Pair[Momentum[p1, D], Momentum[p1, D]] - 6*Pair[Momentum[p1, \ +D], Momentum[p1, D]]^2 + 8*m0^2*Pair[Momentum[p2, D], Momentum[p2, \ +D]] + 12*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +8*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +3*p12*Pair[Momentum[p2, D], Momentum[p2, D]] - 3*Pair[Momentum[p1, \ +D], Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +Pair[Momentum[p2, D], Momentum[p2, D]]^2)/(40320*(-4 + D))"}, +{"fcstPaVeUVPart-ID114", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-28*m0^4 - 56*m0^2*m1^2 - 84*m1^4 - 56*m0^2*m2^2 - 112*m1^2*m2^2 \ +- 84*m2^4 + 16*m0^2*p12 + 48*m1^2*p12 + 48*m2^2*p12 - 9*p12^2 + \ +16*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +24*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +16*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +6*p12*Pair[Momentum[p1, D], Momentum[p1, D]] - 3*Pair[Momentum[p1, \ +D], Momentum[p1, D]]^2 + 16*m0^2*Pair[Momentum[p2, D], Momentum[p2, \ +D]] + 16*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +24*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +6*p12*Pair[Momentum[p2, D], Momentum[p2, D]] - 4*Pair[Momentum[p1, \ +D], Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +3*Pair[Momentum[p2, D], Momentum[p2, D]]^2)/(80640*(-4 + D))"}, +{"fcstPaVeUVPart-ID115", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-28*m0^4 - 28*m0^2*m1^2 - 28*m1^4 - 84*m0^2*m2^2 - 84*m1^2*m2^2 \ +- 168*m2^4 + 12*m0^2*p12 + 24*m1^2*p12 + 48*m2^2*p12 - 6*p12^2 + \ +8*m0^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +8*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +12*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +3*p12*Pair[Momentum[p1, D], Momentum[p1, D]] - Pair[Momentum[p1, D], \ +Momentum[p1, D]]^2 + 24*m0^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +12*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +48*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +6*p12*Pair[Momentum[p2, D], Momentum[p2, D]] - 3*Pair[Momentum[p1, \ +D], Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +6*Pair[Momentum[p2, D], Momentum[p2, D]]^2)/(40320*(-4 + D))"}, +{"fcstPaVeUVPart-ID116", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, 1, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-8*m0^2 - 40*m1^2 - 8*m2^2 + 5*p12 + 5*Pair[Momentum[p1, D], \ +Momentum[p1, D]] + Pair[Momentum[p2, D], Momentum[p2, D]])/(3360*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID117", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-4*m0^2 - 16*m1^2 - 8*m2^2 + 4*p12 + 2*Pair[Momentum[p1, D], \ +Momentum[p1, D]] + Pair[Momentum[p2, D], Momentum[p2, D]])/(6720*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID118", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-8*m0^2 - 24*m1^2 - 24*m2^2 + 9*p12 + 3*Pair[Momentum[p1, D], \ +Momentum[p1, D]] + 3*Pair[Momentum[p2, D], Momentum[p2, \ +D]])/(20160*(-4 + D))"}, +{"fcstPaVeUVPart-ID119", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-4*m0^2 - 8*m1^2 - 16*m2^2 + 4*p12 + Pair[Momentum[p1, D], \ +Momentum[p1, D]] + 2*Pair[Momentum[p2, D], Momentum[p2, \ +D]])/(6720*(-4 + D))"}, +{"fcstPaVeUVPart-ID120", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", +"(-8*m0^2 - 8*m1^2 - 40*m2^2 + 5*p12 + Pair[Momentum[p1, D], \ +Momentum[p1, D]] + 5*Pair[Momentum[p2, D], Momentum[p2, \ +D]])/(3360*(-4 + D))"}, +{"fcstPaVeUVPart-ID121", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "-1/(56*(-4 + D))"}, +{"fcstPaVeUVPart-ID122", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "-1/(336*(-4 + D))"}, +{"fcstPaVeUVPart-ID123", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "-1/(840*(-4 + D))"}, +{"fcstPaVeUVPart-ID124", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "-1/(1120*(-4 + D))"}, +{"fcstPaVeUVPart-ID125", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "-1/(840*(-4 + D))"}, +{"fcstPaVeUVPart-ID126", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "-1/(336*(-4 + D))"}, +{"fcstPaVeUVPart-ID127", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "-1/(56*(-4 + D))"}, +{"fcstPaVeUVPart-ID128", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID129", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID130", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID131", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID132", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID133", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID134", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID135", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID136", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, \ +SPD[p2, p2]}, {m0^2, m1^2, m2^2}]]", "0"}, +{"fcstPaVeUVPart-ID137", +"PaVeUVPart[PaVe[1, {SPD[p1, p1], p12, p23, SPD[p3, p3], SPD[p2, \ +p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID138", +"PaVeUVPart[PaVe[2, {SPD[p1, p1], p12, p23, SPD[p3, p3], SPD[p2, \ +p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID139", +"PaVeUVPart[PaVe[3, {SPD[p1, p1], p12, p23, SPD[p3, p3], SPD[p2, \ +p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID140", +"PaVeUVPart[PaVe[0, 0, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID141", +"PaVeUVPart[PaVe[1, 1, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID142", +"PaVeUVPart[PaVe[1, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID143", +"PaVeUVPart[PaVe[2, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID144", +"PaVeUVPart[PaVe[2, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID145", +"PaVeUVPart[PaVe[3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID146", +"PaVeUVPart[PaVe[0, 0, 1, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID147", +"PaVeUVPart[PaVe[0, 0, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID148", +"PaVeUVPart[PaVe[0, 0, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID149", +"PaVeUVPart[PaVe[1, 1, 1, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID150", +"PaVeUVPart[PaVe[1, 1, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID151", +"PaVeUVPart[PaVe[1, 1, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID152", +"PaVeUVPart[PaVe[1, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID153", +"PaVeUVPart[PaVe[1, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID154", +"PaVeUVPart[PaVe[1, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID155", +"PaVeUVPart[PaVe[2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID156", +"PaVeUVPart[PaVe[2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID157", +"PaVeUVPart[PaVe[2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID158", +"PaVeUVPart[PaVe[3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID159", +"PaVeUVPart[PaVe[0, 0, 0, 0, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "-1/(12*(-4 + D))"}, +{"fcstPaVeUVPart-ID160", +"PaVeUVPart[PaVe[0, 0, 1, 1, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID161", +"PaVeUVPart[PaVe[0, 0, 1, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID162", +"PaVeUVPart[PaVe[0, 0, 1, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID163", +"PaVeUVPart[PaVe[0, 0, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID164", +"PaVeUVPart[PaVe[0, 0, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID165", +"PaVeUVPart[PaVe[0, 0, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID166", +"PaVeUVPart[PaVe[1, 1, 1, 1, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID167", +"PaVeUVPart[PaVe[1, 1, 1, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID168", +"PaVeUVPart[PaVe[1, 1, 1, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID169", +"PaVeUVPart[PaVe[1, 1, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID170", +"PaVeUVPart[PaVe[1, 1, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID171", +"PaVeUVPart[PaVe[1, 1, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID172", +"PaVeUVPart[PaVe[1, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID173", +"PaVeUVPart[PaVe[1, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID174", +"PaVeUVPart[PaVe[1, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID175", +"PaVeUVPart[PaVe[1, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID176", +"PaVeUVPart[PaVe[2, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID177", +"PaVeUVPart[PaVe[2, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID178", +"PaVeUVPart[PaVe[2, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID179", +"PaVeUVPart[PaVe[2, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID180", +"PaVeUVPart[PaVe[3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, p3], \ +SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID181", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(48*(-4 + D))"}, +{"fcstPaVeUVPart-ID182", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(48*(-4 + D))"}, +{"fcstPaVeUVPart-ID183", +"PaVeUVPart[PaVe[0, 0, 0, 0, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(48*(-4 + D))"}, +{"fcstPaVeUVPart-ID184", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID185", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID186", +"PaVeUVPart[PaVe[0, 0, 1, 1, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID187", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID188", +"PaVeUVPart[PaVe[0, 0, 1, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID189", +"PaVeUVPart[PaVe[0, 0, 1, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID190", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID191", +"PaVeUVPart[PaVe[0, 0, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID192", +"PaVeUVPart[PaVe[0, 0, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID193", +"PaVeUVPart[PaVe[0, 0, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID194", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID195", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID196", +"PaVeUVPart[PaVe[1, 1, 1, 1, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID197", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID198", +"PaVeUVPart[PaVe[1, 1, 1, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID199", +"PaVeUVPart[PaVe[1, 1, 1, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID200", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID201", +"PaVeUVPart[PaVe[1, 1, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID202", +"PaVeUVPart[PaVe[1, 1, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID203", +"PaVeUVPart[PaVe[1, 1, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID204", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID205", +"PaVeUVPart[PaVe[1, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID206", +"PaVeUVPart[PaVe[1, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID207", +"PaVeUVPart[PaVe[1, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID208", +"PaVeUVPart[PaVe[1, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID209", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID210", +"PaVeUVPart[PaVe[2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID211", +"PaVeUVPart[PaVe[2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID212", +"PaVeUVPart[PaVe[2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID213", +"PaVeUVPart[PaVe[2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID214", +"PaVeUVPart[PaVe[3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID215", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(-5*m0^2 - 5*m1^2 - 5*m2^2 - 5*m3^2 + p12 + p13 + p23 + \ +Pair[Momentum[p1, D], Momentum[p1, D]] + Pair[Momentum[p2, D], \ +Momentum[p2, D]] + Pair[Momentum[p3, D], Momentum[p3, D]])/(480*(-4 + \ +D))"}, +{"fcstPaVeUVPart-ID216", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(120*(-4 + D))"}, +{"fcstPaVeUVPart-ID217", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(240*(-4 + D))"}, +{"fcstPaVeUVPart-ID218", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(240*(-4 + D))"}, +{"fcstPaVeUVPart-ID219", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(120*(-4 + D))"}, +{"fcstPaVeUVPart-ID220", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(240*(-4 + D))"}, +{"fcstPaVeUVPart-ID221", +"PaVeUVPart[PaVe[0, 0, 0, 0, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(120*(-4 + D))"}, +{"fcstPaVeUVPart-ID222", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID223", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID224", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID225", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID226", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID227", +"PaVeUVPart[PaVe[0, 0, 1, 1, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID228", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID229", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID230", +"PaVeUVPart[PaVe[0, 0, 1, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID231", +"PaVeUVPart[PaVe[0, 0, 1, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID232", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID233", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID234", +"PaVeUVPart[PaVe[0, 0, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID235", +"PaVeUVPart[PaVe[0, 0, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID236", +"PaVeUVPart[PaVe[0, 0, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID237", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID238", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID239", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID240", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID241", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID242", +"PaVeUVPart[PaVe[1, 1, 1, 1, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID243", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID244", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID245", +"PaVeUVPart[PaVe[1, 1, 1, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID246", +"PaVeUVPart[PaVe[1, 1, 1, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID247", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID248", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID249", +"PaVeUVPart[PaVe[1, 1, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID250", +"PaVeUVPart[PaVe[1, 1, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID251", +"PaVeUVPart[PaVe[1, 1, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID252", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID253", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID254", +"PaVeUVPart[PaVe[1, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID255", +"PaVeUVPart[PaVe[1, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID256", +"PaVeUVPart[PaVe[1, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID257", +"PaVeUVPart[PaVe[1, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID258", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID259", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID260", +"PaVeUVPart[PaVe[2, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID261", +"PaVeUVPart[PaVe[2, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID262", +"PaVeUVPart[PaVe[2, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID263", +"PaVeUVPart[PaVe[2, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID264", +"PaVeUVPart[PaVe[3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, SPD[p3, \ +p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID265", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(6*m0^2 + 12*m1^2 + 6*m2^2 + 6*m3^2 - 2*p12 - 2*p13 - p23 - \ +2*Pair[Momentum[p1, D], Momentum[p1, D]] - Pair[Momentum[p2, D], \ +Momentum[p2, D]] - Pair[Momentum[p3, D], Momentum[p3, D]])/(2880*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID266", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(6*m0^2 + 6*m1^2 + 12*m2^2 + 6*m3^2 - 2*p12 - p13 - 2*p23 - \ +Pair[Momentum[p1, D], Momentum[p1, D]] - 2*Pair[Momentum[p2, D], \ +Momentum[p2, D]] - Pair[Momentum[p3, D], Momentum[p3, D]])/(2880*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID267", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(6*m0^2 + 6*m1^2 + 6*m2^2 + 12*m3^2 - p12 - 2*p13 - 2*p23 - \ +Pair[Momentum[p1, D], Momentum[p1, D]] - Pair[Momentum[p2, D], \ +Momentum[p2, D]] - 2*Pair[Momentum[p3, D], Momentum[p3, \ +D]])/(2880*(-4 + D))"}, +{"fcstPaVeUVPart-ID268", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(240*(-4 + D))"}, +{"fcstPaVeUVPart-ID269", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(720*(-4 + D))"}, +{"fcstPaVeUVPart-ID270", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(720*(-4 + D))"}, +{"fcstPaVeUVPart-ID271", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(720*(-4 + D))"}, +{"fcstPaVeUVPart-ID272", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(1440*(-4 + D))"}, +{"fcstPaVeUVPart-ID273", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(720*(-4 + D))"}, +{"fcstPaVeUVPart-ID274", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(240*(-4 + D))"}, +{"fcstPaVeUVPart-ID275", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(720*(-4 + D))"}, +{"fcstPaVeUVPart-ID276", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(720*(-4 + D))"}, +{"fcstPaVeUVPart-ID277", +"PaVeUVPart[PaVe[0, 0, 0, 0, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"1/(240*(-4 + D))"}, +{"fcstPaVeUVPart-ID278", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID279", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID280", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID281", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID282", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID283", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID284", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID285", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID286", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID287", +"PaVeUVPart[PaVe[0, 0, 1, 1, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID288", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID289", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID290", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID291", +"PaVeUVPart[PaVe[0, 0, 1, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID292", +"PaVeUVPart[PaVe[0, 0, 1, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID293", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID294", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID295", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID296", +"PaVeUVPart[PaVe[0, 0, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID297", +"PaVeUVPart[PaVe[0, 0, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID298", +"PaVeUVPart[PaVe[0, 0, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID299", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID300", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID301", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID302", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID303", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID304", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID305", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID306", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID307", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID308", +"PaVeUVPart[PaVe[1, 1, 1, 1, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID309", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID310", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID311", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID312", +"PaVeUVPart[PaVe[1, 1, 1, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID313", +"PaVeUVPart[PaVe[1, 1, 1, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID314", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID315", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID316", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID317", +"PaVeUVPart[PaVe[1, 1, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID318", +"PaVeUVPart[PaVe[1, 1, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID319", +"PaVeUVPart[PaVe[1, 1, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID320", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID321", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID322", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID323", +"PaVeUVPart[PaVe[1, 2, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID324", +"PaVeUVPart[PaVe[1, 2, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID325", +"PaVeUVPart[PaVe[1, 2, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID326", +"PaVeUVPart[PaVe[1, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID327", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID328", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID329", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID330", +"PaVeUVPart[PaVe[2, 2, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID331", +"PaVeUVPart[PaVe[2, 2, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID332", +"PaVeUVPart[PaVe[2, 2, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID333", +"PaVeUVPart[PaVe[2, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID334", +"PaVeUVPart[PaVe[3, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID335", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 0, 0, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(-42*m0^4 - 42*m0^2*m1^2 - 42*m1^4 - 42*m0^2*m2^2 - 42*m1^2*m2^2 \ +- 42*m2^4 - 42*m0^2*m3^2 - 42*m1^2*m3^2 - 42*m2^2*m3^2 - 42*m3^4 + \ +7*m0^2*p12 + 14*m1^2*p12 + 14*m2^2*p12 + 7*m3^2*p12 - 2*p12^2 + \ +7*m0^2*p13 + 14*m1^2*p13 + 7*m2^2*p13 + 14*m3^2*p13 - 2*p12*p13 - \ +2*p13^2 + 7*m0^2*p23 + 7*m1^2*p23 + 14*m2^2*p23 + 14*m3^2*p23 - \ +2*p12*p23 - 2*p13*p23 - 2*p23^2 + 14*m0^2*Pair[Momentum[p1, D], \ +Momentum[p1, D]] + 14*m1^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +7*m2^2*Pair[Momentum[p1, D], Momentum[p1, D]] + \ +7*m3^2*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +2*p12*Pair[Momentum[p1, D], Momentum[p1, D]] - \ +2*p13*Pair[Momentum[p1, D], Momentum[p1, D]] - p23*Pair[Momentum[p1, \ +D], Momentum[p1, D]] - 2*Pair[Momentum[p1, D], Momentum[p1, D]]^2 + \ +14*m0^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +7*m1^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +14*m2^2*Pair[Momentum[p2, D], Momentum[p2, D]] + \ +7*m3^2*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +2*p12*Pair[Momentum[p2, D], Momentum[p2, D]] - p13*Pair[Momentum[p2, \ +D], Momentum[p2, D]] - 2*p23*Pair[Momentum[p2, D], Momentum[p2, D]] - \ +2*Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]] - 2*Pair[Momentum[p2, D], Momentum[p2, D]]^2 + \ +14*m0^2*Pair[Momentum[p3, D], Momentum[p3, D]] + \ +7*m1^2*Pair[Momentum[p3, D], Momentum[p3, D]] + \ +7*m2^2*Pair[Momentum[p3, D], Momentum[p3, D]] + \ +14*m3^2*Pair[Momentum[p3, D], Momentum[p3, D]] - \ +p12*Pair[Momentum[p3, D], Momentum[p3, D]] - 2*p13*Pair[Momentum[p3, \ +D], Momentum[p3, D]] - 2*p23*Pair[Momentum[p3, D], Momentum[p3, D]] - \ +2*Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p3, D], \ +Momentum[p3, D]] - 2*Pair[Momentum[p2, D], Momentum[p2, \ +D]]*Pair[Momentum[p3, D], Momentum[p3, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p3, D]]^2)/(40320*(-4 + D))"}, +{"fcstPaVeUVPart-ID336", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, 1, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(-7*m0^2 - 21*m1^2 - 7*m2^2 - 7*m3^2 + 3*p12 + 3*p13 + p23 + \ +3*Pair[Momentum[p1, D], Momentum[p1, D]] + Pair[Momentum[p2, D], \ +Momentum[p2, D]] + Pair[Momentum[p3, D], Momentum[p3, D]])/(10080*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID337", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(-7*m0^2 - 14*m1^2 - 14*m2^2 - 7*m3^2 + 4*p12 + 2*p13 + 2*p23 + \ +2*Pair[Momentum[p1, D], Momentum[p1, D]] + 2*Pair[Momentum[p2, D], \ +Momentum[p2, D]] + Pair[Momentum[p3, D], Momentum[p3, D]])/(20160*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID338", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 1, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(-7*m0^2 - 14*m1^2 - 7*m2^2 - 14*m3^2 + 2*p12 + 4*p13 + 2*p23 + \ +2*Pair[Momentum[p1, D], Momentum[p1, D]] + Pair[Momentum[p2, D], \ +Momentum[p2, D]] + 2*Pair[Momentum[p3, D], Momentum[p3, \ +D]])/(20160*(-4 + D))"}, +{"fcstPaVeUVPart-ID339", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(-7*m0^2 - 7*m1^2 - 21*m2^2 - 7*m3^2 + 3*p12 + p13 + 3*p23 + \ +Pair[Momentum[p1, D], Momentum[p1, D]] + 3*Pair[Momentum[p2, D], \ +Momentum[p2, D]] + Pair[Momentum[p3, D], Momentum[p3, D]])/(10080*(-4 \ ++ D))"}, +{"fcstPaVeUVPart-ID340", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(-7*m0^2 - 7*m1^2 - 14*m2^2 - 14*m3^2 + 2*p12 + 2*p13 + 4*p23 + \ +Pair[Momentum[p1, D], Momentum[p1, D]] + 2*Pair[Momentum[p2, D], \ +Momentum[p2, D]] + 2*Pair[Momentum[p3, D], Momentum[p3, \ +D]])/(20160*(-4 + D))"}, +{"fcstPaVeUVPart-ID341", +"PaVeUVPart[PaVe[0, 0, 0, 0, 0, 0, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"(-7*m0^2 - 7*m1^2 - 7*m2^2 - 21*m3^2 + p12 + 3*p13 + 3*p23 + \ +Pair[Momentum[p1, D], Momentum[p1, D]] + Pair[Momentum[p2, D], \ +Momentum[p2, D]] + 3*Pair[Momentum[p3, D], Momentum[p3, \ +D]])/(10080*(-4 + D))"}, +{"fcstPaVeUVPart-ID342", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, 1, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(420*(-4 + D))"}, +{"fcstPaVeUVPart-ID343", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(1680*(-4 + D))"}, +{"fcstPaVeUVPart-ID344", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 1, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(1680*(-4 + D))"}, +{"fcstPaVeUVPart-ID345", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(2520*(-4 + D))"}, +{"fcstPaVeUVPart-ID346", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(5040*(-4 + D))"}, +{"fcstPaVeUVPart-ID347", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 1, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(2520*(-4 + D))"}, +{"fcstPaVeUVPart-ID348", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(1680*(-4 + D))"}, +{"fcstPaVeUVPart-ID349", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(5040*(-4 + D))"}, +{"fcstPaVeUVPart-ID350", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(5040*(-4 + D))"}, +{"fcstPaVeUVPart-ID351", +"PaVeUVPart[PaVe[0, 0, 0, 0, 1, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(1680*(-4 + D))"}, +{"fcstPaVeUVPart-ID352", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(420*(-4 + D))"}, +{"fcstPaVeUVPart-ID353", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(1680*(-4 + D))"}, +{"fcstPaVeUVPart-ID354", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(2520*(-4 + D))"}, +{"fcstPaVeUVPart-ID355", +"PaVeUVPart[PaVe[0, 0, 0, 0, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(1680*(-4 + D))"}, +{"fcstPaVeUVPart-ID356", +"PaVeUVPart[PaVe[0, 0, 0, 0, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", +"-1/(420*(-4 + D))"}, +{"fcstPaVeUVPart-ID357", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID358", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID359", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 1, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID360", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID361", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID362", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 1, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID363", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID364", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID365", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID366", +"PaVeUVPart[PaVe[0, 0, 1, 1, 1, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID367", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID368", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID369", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID370", +"PaVeUVPart[PaVe[0, 0, 1, 1, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID371", +"PaVeUVPart[PaVe[0, 0, 1, 1, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID372", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID373", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID374", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID375", +"PaVeUVPart[PaVe[0, 0, 1, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID376", +"PaVeUVPart[PaVe[0, 0, 1, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID377", +"PaVeUVPart[PaVe[0, 0, 1, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID378", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID379", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID380", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID381", +"PaVeUVPart[PaVe[0, 0, 2, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID382", +"PaVeUVPart[PaVe[0, 0, 2, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID383", +"PaVeUVPart[PaVe[0, 0, 2, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID384", +"PaVeUVPart[PaVe[0, 0, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID385", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, 1, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID386", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID387", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 1, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID388", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID389", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID390", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 1, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID391", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID392", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID393", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID394", +"PaVeUVPart[PaVe[1, 1, 1, 1, 1, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID395", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID396", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID397", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID398", +"PaVeUVPart[PaVe[1, 1, 1, 1, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID399", +"PaVeUVPart[PaVe[1, 1, 1, 1, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID400", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID401", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID402", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID403", +"PaVeUVPart[PaVe[1, 1, 1, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID404", +"PaVeUVPart[PaVe[1, 1, 1, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID405", +"PaVeUVPart[PaVe[1, 1, 1, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID406", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID407", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID408", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID409", +"PaVeUVPart[PaVe[1, 1, 2, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID410", +"PaVeUVPart[PaVe[1, 1, 2, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID411", +"PaVeUVPart[PaVe[1, 1, 2, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID412", +"PaVeUVPart[PaVe[1, 1, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID413", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID414", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID415", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID416", +"PaVeUVPart[PaVe[1, 2, 2, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID417", +"PaVeUVPart[PaVe[1, 2, 2, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID418", +"PaVeUVPart[PaVe[1, 2, 2, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID419", +"PaVeUVPart[PaVe[1, 2, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID420", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, 2, 2, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID421", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, 2, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID422", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 2, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID423", +"PaVeUVPart[PaVe[2, 2, 2, 2, 2, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID424", +"PaVeUVPart[PaVe[2, 2, 2, 2, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID425", +"PaVeUVPart[PaVe[2, 2, 2, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID426", +"PaVeUVPart[PaVe[2, 2, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID427", +"PaVeUVPart[PaVe[2, 3, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID428", +"PaVeUVPart[PaVe[3, 3, 3, 3, 3, 3, 3, 3, {SPD[p1, p1], p12, p23, \ +SPD[p3, p3], SPD[p2, p2], p13}, {m0^2, m1^2, m2^2, m3^2}]]", "0"}, +{"fcstPaVeUVPart-ID429", +"TID[SPD[k] FAD[{k + q1, m1}, {k + q2, m2}]/(I Pi^2), k, +UsePaVeBasis -> True, ToPaVe -> True] //PaVeUVPart[#, FCE -> True] &", +"-((2 (m1^2 + m2^2 + SPD[q1, q2]))/(-4 + D))"}, +{"fcstPaVeUVPart-ID430", +"TID[SPD[k, p1]^3 FAD[k, {k + q1, m1}, {k + q2, m2}]/(I Pi^2), k, +UsePaVeBasis -> True, ToPaVe -> True] // +PaVeUVPart[#, FCE -> True] &", +"(SPD[p1, p1] SPD[p1, q1] + SPD[p1, p1] SPD[p1, q2])/(2 (-4 + D))"}, +{"fcstPaVeUVPart-ID431", +"TID[SPD[k, p1]^8 FAD[{k, m0}, {k, m1, 2}, {k, m2}]/(I Pi^2), k, +UsePaVeBasis -> True, ToPaVe -> True] // +PaVeUVPart[#, FCE -> True] &", +"-((7 (m0^4 + 2 m0^2 m1^2 + 3 m1^4 + m0^2 m2^2 + 2 m1^2 m2^2 + +m2^4) SPD[p1, p1]^4)/(64 (-4 + D)))"} +}); diff --git a/Tests/LoopIntegrals/PropagatorDenominatorExplicit.test b/Tests/LoopIntegrals/PropagatorDenominatorExplicit.test deleted file mode 100644 index 0219270c7..000000000 --- a/Tests/LoopIntegrals/PropagatorDenominatorExplicit.test +++ /dev/null @@ -1,36 +0,0 @@ - - -(* :Title: PropagatorDenominatorExplicit.test *) - -(* - This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko -*) - -(* :Summary: Framework independent unit tests for - PropagatorDenominatorExplicit *) - -(* ------------------------------------------------------------------------ *) - -Tests`LoopIntegrals`fcstPropagatorDenominatorExplicit = { - -{"fcstPropagatorDenominatorExplicit-ID1", - "PropagatorDenominatorExplicit[FAD[{q, m}, {q - p, 0}] // FCI] // FCE", - "1/((-m^2 + SPD[q, q]) (SPD[p, p] - 2 SPD[p, q] + SPD[q, q]))"}, -{"fcstPropagatorDenominatorExplicit-ID2","PropagatorDenominatorExplicit[FAD[{q, m}, {q - p, 0}] // FCI, - PDEHead -> dummy] // FCE","dummy[1/((-m^2 + SPD[q, q]) (SPD[p, p] - 2 SPD[p, q] + SPD[q, q]))]"}, -{"fcstPropagatorDenominatorExplicit-ID3","PropagatorDenominatorExplicit[ - FAD[{q, m}, {q - p, 0}] // FCI // FeynAmpDenominatorSplit, - PDEHead -> dummy] // FCE","dummy[1/(-m^2 + SPD[q, q])] dummy[1/( - SPD[p, p] - 2 SPD[p, q] + SPD[q, q])]"}, -{"fcstPropagatorDenominatorExplicit-ID4", - "PropagatorDenominatorExplicit[FAD[{q, m}, {q + p}]] // FCE", - "1/((-m^2 + SPD[q, q]) (SPD[p, p] + 2 SPD[p, q] + SPD[q, q]))" -}, -{"fcstPropagatorDenominatorExplicit-ID5", - "PropagatorDenominatorExplicit[FAD[{q, m}, {q + p}], Dimension -> 4]//FCE", - "1/((-m^2 + SP[q, q]) (SP[p, p] + 2 SP[p, q] + SP[q, q]))" -} -} diff --git a/Tests/LoopIntegrals/ScalarProductCancel.test b/Tests/LoopIntegrals/ScalarProductCancel.test index 75aa708e9..7b4220910 100644 --- a/Tests/LoopIntegrals/ScalarProductCancel.test +++ b/Tests/LoopIntegrals/ScalarProductCancel.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (*:Summary:FrameworkindependentunittestsforScalarProductCancel *) @@ -21,10 +21,10 @@ Tests`LoopIntegrals`fcstSPC={ {"fcstSPC-ID2", "SPC[SPD[q2,p]SPD[q1,p]FAD[{q1,m},{q2,m},q1-p,q2-p, q2-q1],q1,q2,FDS->True]//FCE", - "-FAD[{q1, m}, q1 - q2, -p + q2]/2 + FAD[{q1, m}, - {q2, m}, -q1 + q2]/4 + (FAD[{q1, m}, {q2, m}, -p + q1, q1 - q2]*(-m^2 - - SPD[p, p]))/2 + (FAD[q1, q2, {-p + q1, m}, q1 - q2]*(m^2 + SPD[p, p]))/2 + - (FAD[{q1, m}, {q2, m}, -p + q1, q1 - q2, -p + q2]*(m^2 + SPD[p, p])^2)/4"}, + "-FAD[{q1, m}, q1 - q2, -p + q2]/2 + FAD[{q1, m}, {q2, m}, q1 - q2]/4 + +(FAD[q1, q2, {-p + q1, m}, q1 - q2]*(m^2 + SPD[p, p]))/2 - +(FAD[{q1, m}, {q2, m}, -p + q1, q1 - q2]*(m^2 + SPD[p, p]))/2 + +(FAD[{q1, m}, {q2, m}, -p + q1, q1 - q2, -p + q2]*(m^2 + SPD[p, p])^2)/4"}, {"fcstSPC-ID3", "SPC[SPD[l,-p1+p3+p2]FAD[{l,m1},{l-p1+p3+p2,m3}, l-p1+p2,l-k1],l]//FCE", diff --git a/Tests/LoopIntegrals/TFIOrder.test b/Tests/LoopIntegrals/TFIOrder.test index ad561265d..b837b7884 100644 --- a/Tests/LoopIntegrals/TFIOrder.test +++ b/Tests/LoopIntegrals/TFIOrder.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for TFIOrder *) diff --git a/Tests/LoopIntegrals/TID.test b/Tests/LoopIntegrals/TID.test index 4113ea3c6..a7159cc0e 100644 --- a/Tests/LoopIntegrals/TID.test +++ b/Tests/LoopIntegrals/TID.test @@ -775,11 +775,340 @@ GenPaVe[{0, 0}, {{0, m0}, {p1, m1}, {p2, m2}}] MTD[mu, nu]"}, I m0^2 \[Pi]^2 B0[SPD[p, p], m0^2, m1^2] FVD[p, mu] (m0^2 - m1^2 + SPD[p, p]))/(2 SPD[p, p]) - ( I \[Pi]^2 A0[m1^2] FVD[p, mu] (m0^2 + 2 SPD[p, p]))/(2 SPD[p, p])"}, -{"fcstTID-ID20", "$BreitMaison=True; \n tmp = FCE[ +{"fcstTID-ID20", "FCSetDiracGammaScheme[\"BMHV\"]; \n tmp = FCE[ TID[FVD[q, mu] FVD[q, nu] FAD[{q, m}] - FVE[q, mu] FVE[q, nu] FAD[{q, m}], q]]; \n -$BreitMaison=False; \n tmp","-((m^2 FAD[{q, m}] (-MTD[mu, nu] + MTE[mu, nu]))/D)"}, -{"fcstTID-ID21", "$BreitMaison=True; \n tmp = +FCSetDiracGammaScheme[\"NDR\"]; \n tmp","-((m^2 FAD[{q, m}] (-MTD[mu, nu] + MTE[mu, nu]))/D)"}, +{"fcstTID-ID21", "FCSetDiracGammaScheme[\"BMHV\"]; \n tmp = FCE[TID[ FAD[l, k + l] MTE[mu, nu] (SPE[k, l] + SPE[l, l]), l]]; \n -$BreitMaison=False; \n tmp","-((FAD[l, -k + l] MTE[mu, nu] (4 SPD[k, k] - -D SPD[k, k] + 2 (1 - D) SPE[k, k] + D SPE[k, k]))/(4 (1 - D)))"} +FCSetDiracGammaScheme[\"NDR\"]; \n tmp","-((FAD[l, -k + l] MTE[mu, nu] (4 SPD[k, k] - +D SPD[k, k] + 2 (1 - D) SPE[k, k] + D SPE[k, k]))/(4 (1 - D)))"}, +{"fcstTID-ID22", "TID[8 (-FAD[{q, mA}, {p + q, mS2}] SPD[p,p] + +(1 - GaugeXi) FAD[{q, mA}, {p + q, mS2}, {q,mA Sqrt[GaugeXi]}] SPD[p, q]^2) , q,FCE->True]", +"2 (1 - GaugeXi) FAD[{q, mS2}] + ( +2 FAD[{q, mA}, {-p + q, mS2}] (mA^2 - 2 mA mS2 + mS2^2 - + SPD[p, p]) (mA^2 + 2 mA mS2 + mS2^2 - SPD[p, p]))/mA^2 - ( +2 FAD[{q, mA}] (mA^2 - mS2^2 + SPD[p, p]))/mA^2 + ( +2 FAD[{q, Sqrt[GaugeXi] mA}] (GaugeXi mA^2 - mS2^2 + + SPD[p, p]))/mA^2 - ( +2 FAD[{q, Sqrt[GaugeXi] mA}, {-p + q, mS2}] (GaugeXi mA^2 - mS2^2 + + SPD[p, p])^2)/mA^2"}, +{"fcstTID-ID23", "TID[4 m^2 ((4 - Epsilon) FAD[{q, mA}, {p + q, mA}] + (1 - + GaugeXi)^2 FAD[{q, mA}, {p + q, mA}, {q, + mA Sqrt[GaugeXi]}, {p + q, mA Sqrt[GaugeXi]}] (-SPD[p, q] - + SPD[q, q])^2 + (1 - + GaugeXi) (-FAD[{q, mA}, {p + q, mA}, {q, + mA Sqrt[GaugeXi]}] SPD[q, q] - + FAD[{q, mA}, {p + q, mA}, {p + q, mA Sqrt[GaugeXi]}] SPD[p + q, + p + q])) , q, FCE -> True]", +"(2 (1 - GaugeXi) m^2 FAD[{q, mA}])/mA^2 - ( +2 (1 - GaugeXi) m^2 FAD[{q, Sqrt[GaugeXi] mA}])/mA^2 + ( +m^2 FAD[{q, Sqrt[GaugeXi] mA}, {-p + q, + Sqrt[GaugeXi] mA}] (2 GaugeXi mA^2 - SPD[p, p])^2)/mA^4 + ( +m^2 FAD[{q, mA}, {-p + q, mA}] (12 mA^4 - 4 Epsilon mA^4 - + 4 mA^2 SPD[p, p] + SPD[p, p]^2))/mA^4 - ( +2 m^2 FAD[{q, mA}, {-p + q, Sqrt[GaugeXi] mA}] (mA^4 - + 2 GaugeXi mA^4 + GaugeXi^2 mA^4 - 2 mA^2 SPD[p, p] - + 2 GaugeXi mA^2 SPD[p, p] + SPD[p, p]^2))/mA^4"}, +{"fcstTID-ID24", "TID[((DiracGamma[LorentzIndex[b, d], d] . + DiracGamma[Momentum[k + p, d], d] . + DiracGamma[LorentzIndex[b, d], d]* + FeynAmpDenominator[PropagatorDenominator[Momentum[k, d], m1]]* + FeynAmpDenominator[ + PropagatorDenominator[Momentum[k, d] + Momentum[p, d], m2]])/ +cw^2), k, Dimension -> d]", +"((2 - d)*DiracGamma[Momentum[p, d], d]*FeynAmpDenominator[PropagatorDenominator[Momentum[k, d], m1]])/(2*cw^2*Pair[Momentum[p, d], Momentum[p, d]]) - +((2 - d)*DiracGamma[Momentum[p, d], d]*FeynAmpDenominator[PropagatorDenominator[Momentum[k, d], m2]])/(2*cw^2*Pair[Momentum[p, d], Momentum[p, d]]) - +((2 - d)*DiracGamma[Momentum[p, d], d]*FeynAmpDenominator[PropagatorDenominator[Momentum[k, d], m1], PropagatorDenominator[Momentum[k, d] - Momentum[p, d], m2]]* +(m1^2 - m2^2 - Pair[Momentum[p, d], Momentum[p, d]]))/(2*cw^2*Pair[Momentum[p, d], Momentum[p, d]])"}, +{"fcstTID-ID25", "SPD[k1] = 0; SPD[k2] = 0; SPD[k1, k2] = 2 m^2; res = TID[ FeynAmpDenominator[PropagatorDenominator[Momentum[l, D], 0], +PropagatorDenominator[1/2 Momentum[k1 + k2, D] + Momentum[l, D], m], PropagatorDenominator[-Momentum[k2, D] + +1/2 Momentum[k1 + k2, D] + Momentum[l, D], m], PropagatorDenominator[-Momentum[k1, D] - Momentum[k2, D] + 1/2 Momentum[k1 + k2, D] + +Momentum[l, D], m]] Pair[LorentzIndex[mu, D], Momentum[l, D]], l, FCE->True]; FCClearScalarProducts[]; res", +"(FAD[l, {-k1/2 + k2/2 + l, m}, {k1/2 + k2/2 + l, m}]*FVD[k1, mu])/(4*m^2) - +(FAD[l, l, {-k1/2 - k2/2 + l, m}]*(FVD[k1, mu] - FVD[k2, mu]))/(4*m^2) - +(FAD[l, l, {-k1/2 - k2/2 + l, m}, {-k1/2 + k2/2 + l, m}]*(FVD[k1, mu] - FVD[k2, mu]))/4 - +(FAD[l, l, {-k1/2 + k2/2 + l, m}, {k1/2 + k2/2 + l, m}]*(FVD[k1, mu] - FVD[k2, mu]))/4 - +(FAD[l, {-k1/2 - k2/2 + l, m}, {-k1/2 + k2/2 + l, m}]*FVD[k2, mu])/(4*m^2)"}, +{"fcstTID-ID26", "TID[CVD[q,i]CVD[q,j]CFAD[{q,m}],q,FCE->True]", +"-((m*CFAD[{{q, 0}, {m, -1}, 1}]*KDD[i, j])/(-1 + D))"}, +{"fcstTID-ID27", "TID[CVD[q,i]CFAD[{q,m}],q,FCE->True]", "0"}, +{"fcstTID-ID28", +"TID[CVD[q,i]CVD[q,j]CVD[q,k]CVD[q,l]CFAD[{q,m}],q,FCE->True]", +"(m^2*CFAD[{{q, 0}, {m, -1}, 1}]*(KDD[i, l]*KDD[j, k] + KDD[i, \ +k]*KDD[j, l] + KDD[i, j]*KDD[k, l]))/((-1 + D)*(1 + D))"}, +{"fcstTID-ID29", "TID[CVD[q,i]CVD[q,j]CFAD[q,q+p],q,FCE->True]", +"(CFAD[{{q, 0}, {0, -1}, 1}, {{p + q, 0}, {0, -1}, +1}] (-(-1 + D) CVD[p, i] CVD[p, j] + CSPD[p, p] KDD[i, j]))/(4 (2 - + D))"}, +{"fcstTID-ID30", "TID[CVD[q,i]CVD[q,j]CFAD[{q,m,2}],q,FCE->True]", +"(CFAD[{{q, 0}, {m, -1}, 1}]*KDD[i, j])/(-1 + D) - (m*CFAD[{{q, \ +0}, {m, -1}, 1}, {{q, 0}, {m, -1}, 1}]*KDD[i, j])/(-1 + D)"}, +{"fcstTID-ID31", "TID[CVD[q,i]CVD[q,j]CFAD[{q,m,-1}],q,FCE->True]", +"0"}, +{"fcstTID-ID32", "TID[FVD[q,i]FVD[q,j]SFAD[{q,m}],q,FCE->True]", +"(m*MTD[i, j]*SFAD[{{q, 0}, {m, 1}, 1}])/D"}, +{"fcstTID-ID33", "TID[FVD[q,i]SFAD[{q,m}],q,FCE->True]", "0"}, +{"fcstTID-ID34", +"TID[FVD[q,i]FVD[q,j]FVD[q,k]FVD[q,l]SFAD[{q,m}],q,FCE->True]", +"(m^2*(MTD[i, l]*MTD[j, k] + MTD[i, k]*MTD[j, l] + MTD[i, \ +j]*MTD[k, l])*SFAD[{{q, 0}, {m, 1}, 1}])/(D*(2 + D))"}, +{"fcstTID-ID35", "TID[FVD[q,i]FVD[q,j]SFAD[{q,m,2}],q,FCE->True]", +"(MTD[i, j]*SFAD[{{q, 0}, {m, 1}, 1}])/D + (m*MTD[i, j]*SFAD[{{q, \ +0}, {m, 1}, 1}, {{q, 0}, {m, 1}, 1}])/D"}, +{"fcstTID-ID36", +"TID[FVD[q,i]SFAD[{q,m,2},q+p],q,UsePaVeBasis\[Rule]True,FCE->True]\ +", "(-2*I)*Pi^2*FVD[p, i]*PaVe[1, {SPD[p, p], 0, SPD[p, p]}, {0, m, \ +m}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] - FVD[p, \ +i]*SFAD[{{q, 0}, {0, 1}, 1}, {{-p + q, 0}, {m, 1}, 2}]"}, +{"fcstTID-ID37", +"TID[FVD[q,i]SFAD[{q,m,3},q+p],q,UsePaVeBasis\[Rule]True,FCE->True]\ +", "(-3*I)*Pi^2*FVD[p, i]*PaVe[1, {SPD[p, p], 0, 0, SPD[p, p], SPD[p, \ +p], 0}, {0, m, m, m}, PaVeAutoOrder -> True, PaVeAutoReduce -> True] \ +- FVD[p, i]*SFAD[{{q, 0}, {0, 1}, 1}, {{-p + q, 0}, {m, 1}, 3}]"}, +{"fcstTID-ID38", +"TID[FCI[FVD[q,mu] FVD[q,nu] \ +SFAD[{q,m0^2},{q+p1,m1^2},{q+p2,m2^2}]]/(I*Pi^2),q,UsePaVeBasis\[Rule]\ +True,GenPaVe\[Rule]True,FCE\[Rule]True]", +"FVD[p1, mu]*FVD[p1, nu]*GenPaVe[{1, 1}, {{0, m0}, {-p1, m1}, \ +{-p2, m2}}] + (FVD[p1, nu]*FVD[p2, mu] + FVD[p1, mu]*FVD[p2, \ +nu])*GenPaVe[{1, 2}, {{0, m0}, {-p1, m1}, {-p2, m2}}] + FVD[p2, \ +mu]*FVD[p2, nu]*GenPaVe[{2, 2}, {{0, m0}, {-p1, m1}, {-p2, m2}}] + \ +GenPaVe[{0, 0}, {{0, m0}, {-p1, m1}, {-p2, m2}}]*MTD[mu, nu]"}, +{"fcstTID-ID39", "TID[FVD[q,mu]SFAD[-q,q-p]FAD[q-p],q,FCE->True]", +"FAD[-p + q]*FVD[q, mu]*SFAD[{{q, 0}, {0, 1}, 1}, {{-p + q, 0}, \ +{0, 1}, 1}]"}, +{"fcstTID-ID40", "TID[FVD[q,mu]SFAD[q,q-p]FAD[q-p],q,FCE->True]", +"FAD[-p + q]*FVD[q, mu]*SFAD[{{q, 0}, {0, 1}, 1}, {{-p + q, 0}, \ +{0, 1}, 1}]"}, +{"fcstTID-ID41", "TID[FVD[q,mu]SFAD[q,q-p,{{0,q.k}}],q,FCE->True]", +"FVD[q, mu]*SFAD[{{0, k . q}, {0, 1}, 1}, {{q, 0}, {0, 1}, 1}, {{p \ +- q, 0}, {0, 1}, 1}]"}, +{"fcstTID-ID42", +"TID[FCI[CVD[q,i]CVD[q,j]SFAD[{q,m^2,2}]],q,FCE->True]", +"(CFAD[{{q, 0}, {m^2 - TC[q]^2, -1}, 1}]*KDD[i, j])/(-1 + D) - \ +(m^2*CFAD[{{q, 0}, {m^2 - TC[q]^2, -1}, 1}, {{q, 0}, {m^2 - TC[q]^2, \ +-1}, 1}]*KDD[i, j])/(-1 + D) + (CFAD[{{q, 0}, {m^2 - TC[q]^2, -1}, \ +1}, {{q, 0}, {m^2 - TC[q]^2, -1}, 1}]*KDD[i, j]*TC[q]^2)/(-1 + D)"}, +{"fcstTID-ID43", +"TID[(-(-1/2 \ +GA[5].(GAD[mu].GSD[v]-FVD[v,mu])FVD[k,mu]))SFAD[{{0,v.(r-k)}},{k,-M^2}\ +]*\[IndentingNewLine](-1/2 \ +GA[5].(GAD[nu].GSD[v]-FVD[v,nu]))FVD[k,nu],k,FCE->True]", +"(SFAD[{{k, 0}, {-M^2, 1}, 1}]*SPD[r, v])/4 - (SFAD[{{k, 0}, \ +{-M^2, 1}, 1}, {{0, (-k + r) . v}, {0, 1}, 1}]*(SPD[r, v]^2 + \ +M^2*SPD[v, v]))/4"}, +{"fcstTID-ID44", +"TID[TC[q]^2SFAD[q]CVD[q,i]CVD[q,j],q,FCE\[Rule]True]", +"-((CFAD[{{q, 0}, {-TC[q]^2, -1}, 1}]*KDD[i, j]*TC[q]^4)/(-1 + \ +D))"}, +{"fcstTID-ID45", +"TID[SFAD[q]CVD[q,i]CVD[q,j]CVD[q,k]CVD[q,l],q,FCE\[Rule]True]", +"-((CFAD[{{q, 0}, {-TC[q]^2, -1}, 1}]*(KDD[i, l]*KDD[j, k] + \ +KDD[i, k]*KDD[j, l] + KDD[i, j]*KDD[k, l])*TC[q]^4)/((-1 + D)*(1 + \ +D)))"}, +{"fcstTID-ID46", "TID[TC[q]^2*SFAD[q]CVD[q,i],q]", "0"}, +{"fcstTID-ID47", "TID[CVD[k, i] CVD[k, j] SFAD[k, k - q], k, FCE -> True]", +"(CFAD[{{k, 0}, {-TC[k - q]^2, -1}, 1}]*(4*CVD[q, i]*CVD[q, j] - 3*(-1 + D)*CVD[q, i]*CVD[q, j] - + CSPD[q, q]*KDD[i, j]))/(4*(2 - D)*CSPD[q, q]) + +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - q, 0}, {-TC[k - q]^2, -1}, 1}]* +(-((-1 + D)*CVD[q, i]*CVD[q, j]) + CSPD[q, q]*KDD[i, j]))/(4*(2 - D)) - +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}]*(-((-1 + D)*CVD[q, i]*CVD[q, j]) + CSPD[q, q]*KDD[i, j]))/ +(4*(2 - D)*CSPD[q, q]) + (CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - q, 0}, {-TC[k - q]^2, -1}, 1}]* +(2*CVD[q, i]*CVD[q, j] - (-1 + D)*CVD[q, i]*CVD[q, j] - CSPD[q, q]*KDD[i, j])*TC[k]^2)/(2*(2 - D)*CSPD[q, q]) - +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}]*(-((-1 + D)*CVD[q, i]*CVD[q, j]) + CSPD[q, q]*KDD[i, j])*TC[k]^2)/ +(4*(2 - D)*CSPD[q, q]^2) + (CFAD[{{k, 0}, {-TC[k - q]^2, -1}, 1}]*(-((-1 + D)*CVD[q, i]*CVD[q, j]) + + CSPD[q, q]*KDD[i, j])*TC[k]^2)/(4*(2 - D)*CSPD[q, q]^2) + +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - q, 0}, {-TC[k - q]^2, -1}, 1}]* +(-((-1 + D)*CVD[q, i]*CVD[q, j]) + CSPD[q, q]*KDD[i, j])*TC[k]^4)/(4*(2 - D)*CSPD[q, q]^2) + +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}]*(-((-1 + D)*CVD[q, i]*CVD[q, j]) + CSPD[q, q]*KDD[i, j])*(TC[k] - TC[q])^2)/ +(4*(2 - D)*CSPD[q, q]^2) - (CFAD[{{k, 0}, {-TC[k - q]^2, -1}, 1}]*(-((-1 + D)*CVD[q, i]*CVD[q, j]) + + CSPD[q, q]*KDD[i, j])*(TC[k] - TC[q])^2)/(4*(2 - D)*CSPD[q, q]^2) - +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - q, 0}, {-TC[k - q]^2, -1}, 1}]* +(-((-1 + D)*CVD[q, i]*CVD[q, j]) + CSPD[q, q]*KDD[i, j])*(TC[k] - TC[q])^2)/(2*(2 - D)*CSPD[q, q]) - +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - q, 0}, {-TC[k - q]^2, -1}, 1}]* +(-((-1 + D)*CVD[q, i]*CVD[q, j]) + CSPD[q, q]*KDD[i, j])*TC[k]^2*(TC[k] - TC[q])^2)/(2*(2 - D)*CSPD[q, q]^2) + +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - q, 0}, {-TC[k - q]^2, -1}, 1}]* +(-((-1 + D)*CVD[q, i]*CVD[q, j]) + CSPD[q, q]*KDD[i, j])*(TC[k] - TC[q])^4)/(4*(2 - D)*CSPD[q, q]^2)"}, +{"fcstTID-ID48", "FCClearScalarProducts[]; \n CSPD[p] = 0; \n TID[CVD[q, i] CVD[q, j] CFAD[{q, m^2}, {q - p, m^2}], q, FCE -> True]", +"(CFAD[{{q, 0}, {m^2, -1}, 1}] KDD[i, j])/(-1 + D) - ( +m^2 CFAD[{{q, 0}, {m^2, -1}, 1}, {{q, 0}, {m^2, -1}, 1}] KDD[i,j])/(-1 + D)"}, +{"fcstTID-ID49", "FCClearScalarProducts[]; \n TID[TC[k] FVD[k,mu] FAD[k,k+p],k,FCE->True]", +"-(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - p, 0}, {-TC[k - p]^2, -1}, 1}]* + Pair[CartesianMomentum[p, -1 + D], LorentzIndex[mu, D]]*TC[k])/2 + +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}]*Pair[CartesianMomentum[p, -1 + D], + LorentzIndex[mu, D]]*TC[k])/(2*CSPD[p, p]) - +(CFAD[{{k, 0}, {-TC[k - p]^2, -1}, 1}]*Pair[CartesianMomentum[p, -1 + D], + LorentzIndex[mu, D]]*TC[k])/(2*CSPD[p, p]) + +CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - p, 0}, {-TC[k - p]^2, -1}, 1}]* +MT[0, mu]*TC[k]^2 - +(CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, {{k - p, 0}, {-TC[k - p]^2, -1}, 1}]* +Pair[CartesianMomentum[p, -1 + D], LorentzIndex[mu, D]]*TC[k]^3)/ +(2*CSPD[p, p]) + (CFAD[{{k, 0}, {-TC[k]^2, -1}, 1}, + {{k - p, 0}, {-TC[k - p]^2, -1}, 1}]*Pair[CartesianMomentum[p, -1 + D], + LorentzIndex[mu, D]]*TC[k]*(TC[k] - TC[p])^2)/(2*CSPD[p, p])"}, +{"fcstTID-ID50", +"TID[GSD[k] FAD[-pE1-pPh] \ +FAD[{k,m2},k+pE1-pH+pPh,{k-pH,m2},{k-pH,m3}] TC[k],k,FCE\[Rule]True]", + "(CFAD[{{k, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}, {{k + pE1 - pH + \ +pPh, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}]*(CGSD[pH] - CGSD[-pE1 - pPh] \ +- CGSD[pE1 + pH + pPh])*(CSPD[pE1, pH] + CSPD[pH, pPh])*FAD[pE1 + \ +pPh]*TC[k])/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ +CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - \ +(CFAD[{{k, 0}, {-m2^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k \ +- pH]^2, -1}, 1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, \ +pH] + CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - \ +m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, \ +pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + (CFAD[{{k, 0}, {-m3^2 - \ +TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k - pH]^2, -1}, \ +1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + \ +CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - \ +m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, \ +pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + (CFAD[{{k, 0}, {-TC[k - \ +pE1 - pPh]^2, -1}, 1}, {{k + pE1 + pPh, 0}, {-m2^2 - TC[k]^2, -1}, \ +1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + \ +2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + \ +CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - \ +m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, \ +pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - (CFAD[{{k, 0}, {-TC[k - \ +pE1 - pPh]^2, -1}, 1}, {{k + pE1 + pPh, 0}, {-m3^2 - TC[k]^2, -1}, \ +1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + \ +2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + \ +CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - \ +m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, \ +pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - (CFAD[{{k, 0}, {-m2^2 - \ +TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m2^2 - TC[k]^2, -1}, 1}, {{k - \ +pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, \ +1}]*(CGSD[pH]*CSPD[pE1, pE1]*CSPD[pH, pH] + CGSD[-pE1 - \ +pPh]*CSPD[pE1, pH]*CSPD[pH, pH] + 2*CGSD[pH]*CSPD[pE1, pPh]*CSPD[pH, \ +pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pH, \ +pH]*CSPD[pPh, pPh] - CGSD[pH]*CSPD[pE1, pH]*(m2^2 + CSPD[pE1, pE1] + \ +2*CSPD[pE1, pPh] + CSPD[pPh, pPh]) - CGSD[-pE1 - pPh]*CSPD[pH, \ +pH]*(m2^2 + CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]) - \ +CGSD[pH]*CSPD[pH, pPh]*(m2^2 + CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + \ +CSPD[pPh, pPh]))*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - m3^2)*((-CSPD[pE1, \ +pH] - CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, \ +pPh] + CSPD[pPh, pPh]))) - (CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, \ +1}, {{k + pH, 0}, {-m3^2 - TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, \ +0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1]*(m2^2 - \ +m3^2 - CSPD[pH, pH]) + CGSD[-pE1 - pPh]*CSPD[pE1, pH]*(m2^2 - m3^2 - \ +CSPD[pH, pH]) + 2*CGSD[pH]*CSPD[pE1, pPh]*(m2^2 - m3^2 - CSPD[pH, \ +pH]) + CGSD[-pE1 - pPh]*(m2^2 - m3^2 - CSPD[pH, pH])*CSPD[pH, pPh] + \ +CGSD[pH]*(m2^2 - m3^2 - CSPD[pH, pH])*CSPD[pPh, pPh] + \ +CGSD[pH]*CSPD[pE1, pH]*(m3^2 + CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + \ +CSPD[pPh, pPh]) + CGSD[-pE1 - pPh]*CSPD[pH, pH]*(m3^2 + CSPD[pE1, \ +pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]) + CGSD[pH]*CSPD[pH, \ +pPh]*(m3^2 + CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, \ +pPh]))*FAD[pE1 + pPh]*TC[k])/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - \ +CSPD[pH, pPh])^2 - CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + \ +CSPD[pPh, pPh]))) + (CFAD[{{k, 0}, {-m2^2 - TC[k]^2, -1}, 1}, {{k - \ +pH, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - \ +pE1 - pPh]^2, -1}, 1}]*FAD[pE1 + pPh]*GSD[pH]*TC[k])/(m2^2 - m3^2) - \ +(CFAD[{{k, 0}, {-m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k \ +- pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, \ +1}]*FAD[pE1 + pPh]*GSD[pH]*TC[k])/(m2^2 - m3^2) - (CFAD[{{k, 0}, \ +{-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m2^2 - TC[k]^2, -1}, \ +1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, \ +1}]*(CGSD[pH]*CSPD[pE1, pE1] - CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - \ +pPh]*CSPD[pE1, pH] + 2*CGSD[pH]*CSPD[pE1, pPh] - CGSD[-pE1 - \ +pPh]*CSPD[pH, pH] - CGSD[pH]*CSPD[pH, pPh] + CGSD[-pE1 - \ +pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + \ +pPh]*TC[k]^3)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ +CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + \ +(CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m3^2 - \ +TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ +-1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1] - CGSD[pE1 + pH + pPh]*CSPD[pE1, \ +pH] + 2*CGSD[pH]*CSPD[pE1, pPh] - CGSD[-pE1 - pPh]*CSPD[pH, pH] - \ +CGSD[pE1 + pH + pPh]*CSPD[pH, pPh] + CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 \ ++ pPh]*TC[k]^3)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 \ +- CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) \ ++ (CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m2^2 \ +- TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ +-1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + \ +2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + \ +CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - \ +TC[pH])^2)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ +CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - \ +(CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m3^2 - \ +TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ +-1}, 1}]*(CGSD[pH]*CSPD[pE1, pE1] + CGSD[-pE1 - pPh]*CSPD[pE1, pH] + \ +2*CGSD[pH]*CSPD[pE1, pPh] + CGSD[-pE1 - pPh]*CSPD[pH, pPh] + \ +CGSD[pH]*CSPD[pPh, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - \ +TC[pH])^2)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ +CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + \ +(FAD[pE1 + pPh]*FAD[{k, m2}, {k - pH, m2}]*(GSD[pH]*SPD[pE1, pH] + \ +GSD[-pE1 - pPh]*SPD[pH, pH] + GSD[pH]*SPD[pH, pPh])*TC[pH])/(2*(m2^2 \ +- m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, \ +pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - (FAD[pE1 + pPh]*FAD[{k, \ +m2}, {k - pH, m3}]*(GSD[pH]*SPD[pE1, pH] + GSD[-pE1 - pPh]*SPD[pH, \ +pH] + GSD[pH]*SPD[pH, pPh])*TC[pH])/(2*(m2^2 - m3^2)*((-SPD[pE1, pH] \ +- SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + \ +SPD[pPh, pPh]))) - (FAD[pE1 + pPh]*FAD[{k, m2}, k - pE1 - \ +pPh]*(GSD[pH]*SPD[pE1, pE1] + GSD[-pE1 - pPh]*SPD[pE1, pH] + \ +2*GSD[pH]*SPD[pE1, pPh] + GSD[-pE1 - pPh]*SPD[pH, pPh] + \ +GSD[pH]*SPD[pPh, pPh])*TC[pH])/(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - \ +SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + \ +SPD[pPh, pPh]))) + (FAD[pE1 + pPh]*FAD[{k, m3}, k - pE1 - \ +pPh]*(GSD[pH]*SPD[pE1, pE1] + GSD[-pE1 - pPh]*SPD[pE1, pH] + \ +2*GSD[pH]*SPD[pE1, pPh] + GSD[-pE1 - pPh]*SPD[pH, pPh] + \ +GSD[pH]*SPD[pPh, pPh])*TC[pH])/(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - \ +SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + \ +SPD[pPh, pPh]))) + (FAD[pE1 + pPh]*FAD[{k, m2}, {k - pH, m2}, k - pE1 \ +- pPh]*(GSD[pH]*SPD[pE1, pE1]*SPD[pH, pH] + GSD[-pE1 - pPh]*SPD[pE1, \ +pH]*SPD[pH, pH] + 2*GSD[pH]*SPD[pE1, pPh]*SPD[pH, pH] + GSD[-pE1 - \ +pPh]*SPD[pH, pH]*SPD[pH, pPh] + GSD[pH]*SPD[pH, pH]*SPD[pPh, pPh] - \ +GSD[pH]*SPD[pE1, pH]*(m2^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + \ +SPD[pPh, pPh]) - GSD[-pE1 - pPh]*SPD[pH, pH]*(m2^2 + SPD[pE1, pE1] + \ +2*SPD[pE1, pPh] + SPD[pPh, pPh]) - GSD[pH]*SPD[pH, pPh]*(m2^2 + \ +SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) + \ +2*GSD[pH]*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, \ +pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh])))*TC[pH])/(2*(m2^2 - \ +m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - SPD[pH, pH]*(SPD[pE1, pE1] \ ++ 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - (FAD[pE1 + pPh]*FAD[{k, m3}, \ +{k - pH, m2}, k - pE1 - pPh]*(-(GSD[pH]*SPD[pE1, pE1]*(m2^2 - m3^2 - \ +SPD[pH, pH])) - GSD[-pE1 - pPh]*SPD[pE1, pH]*(m2^2 - m3^2 - SPD[pH, \ +pH]) - 2*GSD[pH]*SPD[pE1, pPh]*(m2^2 - m3^2 - SPD[pH, pH]) - GSD[-pE1 \ +- pPh]*(m2^2 - m3^2 - SPD[pH, pH])*SPD[pH, pPh] - GSD[pH]*(m2^2 - \ +m3^2 - SPD[pH, pH])*SPD[pPh, pPh] - GSD[pH]*SPD[pE1, pH]*(m3^2 + \ +SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]) - GSD[-pE1 - \ +pPh]*SPD[pH, pH]*(m3^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, \ +pPh]) - GSD[pH]*SPD[pH, pPh]*(m3^2 + SPD[pE1, pE1] + 2*SPD[pE1, pPh] \ ++ SPD[pPh, pPh]) + 2*GSD[pH]*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - \ +SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, \ +pPh])))*TC[pH])/(2*(m2^2 - m3^2)*((-SPD[pE1, pH] - SPD[pH, pPh])^2 - \ +SPD[pH, pH]*(SPD[pE1, pE1] + 2*SPD[pE1, pPh] + SPD[pPh, pPh]))) - \ +(CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m2^2 - \ +TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ +-1}, 1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + \ +CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - TC[pE1] - \ +TC[pPh])^2)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ +CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) + \ +(CFAD[{{k, 0}, {-m2^2 - TC[k - pH]^2, -1}, 1}, {{k + pH, 0}, {-m3^2 - \ +TC[k]^2, -1}, 1}, {{k - pE1 + pH - pPh, 0}, {-TC[k - pE1 - pPh]^2, \ +-1}, 1}]*(CGSD[pH]*CSPD[pE1, pH] + CGSD[-pE1 - pPh]*CSPD[pH, pH] + \ +CGSD[pH]*CSPD[pH, pPh])*FAD[pE1 + pPh]*TC[k]*(TC[k] - TC[pE1] - \ +TC[pPh])^2)/(2*(m2^2 - m3^2)*((-CSPD[pE1, pH] - CSPD[pH, pPh])^2 - \ +CSPD[pH, pH]*(CSPD[pE1, pE1] + 2*CSPD[pE1, pPh] + CSPD[pPh, pPh]))) - \ +(CFAD[{{k, 0}, {-m2^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k \ +- pH]^2, -1}, 1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, \ +1}]*FAD[pE1 + pPh]*TC[k]^2*TGA[])/(m2^2 - m3^2) + (CFAD[{{k, 0}, \ +{-m3^2 - TC[k]^2, -1}, 1}, {{k - pH, 0}, {-m2^2 - TC[k - pH]^2, -1}, \ +1}, {{k - pE1 - pPh, 0}, {-TC[k - pE1 - pPh]^2, -1}, 1}]*FAD[pE1 + \ +pPh]*TC[k]^2*TGA[])/(m2^2 - m3^2)"}, +{"fcstTID-ID51","TID[DCHN[-GSD[k] + me, Dir3, Dir4] FAD[{k, me}, k - q], k, +FCE -> True]","(DCHN[GSD[q], Dir3, Dir4] FAD[{k, me}])/(2 SPD[q, q]) - (1/( +2 SPD[q, q]))*FAD[k, {k - q, me}] (DCHN[GSD[q], Dir3, Dir4] (me^2 - SPD[q, q]) - +2 me DCHN[1, Dir3, Dir4] SPD[q, q] + 2 DCHN[GSD[q], Dir3, Dir4] SPD[q, q])"}, +{"fcstTID-ID52","TID[DCHN[GAD[mu].(-GSD[k] + me).GAD[nu], Dir3, Dir4] FAD[{k, me}, +k - q], k, FCE -> True]","(DCHN[GAD[mu].GSD[q].GAD[nu], Dir3, Dir4] FAD[{k, me}])/( +2 SPD[q, q]) - (1/(2 SPD[q, q]))* FAD[k, {k - q, me}] (DCHN[GAD[mu].GSD[q].GAD[nu], Dir3, Dir4] (me^2 - SPD[q, q]) - +2 me DCHN[GAD[mu].GAD[nu], Dir3, Dir4] SPD[q, q] + 2 DCHN[GAD[mu].GSD[q].GAD[nu], Dir3, Dir4] SPD[q, q])"}, +{"fcstTID-ID52","TID[FVD[p, mu] FAD[p, p + q], {p}, FCE -> True]", +"-(1/2) FAD[p, p - q] FVD[q, mu]"}, +{"fcstTID-ID53","TID[DiracTrace[GAD[mu].(GSD[q]).GAD[nu, rho, 5]] FAD[q, q - p], q, +DiracSimplify -> False, FCE -> True]", +"1/2 DiracTrace[GAD[mu].GSD[p].GAD[nu].GAD[rho].GA[5]] FAD[q, -p + q]"}, +{"fcstTID-ID54","TID[DiracTrace[GAD[mu].(GSD[q] + m).GAD[nu, rho, 5]] FAD[q, q - p], q, +DiracSimplify -> False, FCE -> True]", +"1/2 (2 m DiracTrace[GAD[mu].GAD[nu].GAD[rho].GA[5]] + +DiracTrace[GAD[mu].GSD[p].GAD[nu].GAD[rho].GA[5]]) FAD[q, -p + q]"} }; diff --git a/Tests/LoopIntegrals/TarcerToFC.test b/Tests/LoopIntegrals/TarcerToFC.test index 61db46bff..a0a75cd72 100644 --- a/Tests/LoopIntegrals/TarcerToFC.test +++ b/Tests/LoopIntegrals/TarcerToFC.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for TarcerToFC *) @@ -25,10 +25,31 @@ q2]^2"}, "TarcerToFC[Tarcer`TJI[D, Pair[Momentum[p, D], Momentum[p, D]], \ {{1, 0}, {1, 0}, {1, 0}}],{q1,q2}]//FCE", "FAD[q1, q1 - q2, -p + q2]"}, {"fcstTarcerToFC-ID3", -"TarcerToFC[Tarcer`TBI[D, pp^2, {{1, 0}, {1, 0}}],{q1,q2}]//FCE", -"FAD[q1, -pp + q1]"}, +"TarcerToFC[Tarcer`TBI[D, pp^2, {{1, 0}, {1, 0}}],{q1,q2}]", +"Tarcer`TBI[D, pp^2, {{1, 0}, {1, 0}}]"}, {"fcstTarcerToFC-ID4", "TarcerToFC[Tarcer`TAI[D, 0, {{1, m}}],{q1,q2}]//FCE", -"FAD[{q1, m}]"} +"FAD[{q1, m}]"}, +{"fcstTarcerToFC-ID5", +"TarcerToFC[Tarcer`TFI[d, M^2, OPEDelta, {1, 3}, {{2, M}, {1, 0}, {1, 0}, {1, M}, {1, M}}], {q1, q2}]", +"TarcerToFC[Tarcer`TFI[d, M^2, OPEDelta, {1, 3}, {{2, M}, {1, 0}, {1, 0}, {1, M}, {1, M}}], {q1, q2}]"}, +{"fcstTarcerToFC-ID6", +"TarcerToFC[(mG^2*(FVD[q, Lor1]*FVD[q, Lor2] - + MTD[Lor1, Lor2]*SPD[q, q])* Tarcer`TFI[2 + D, + SPD[q, q], {{5, I*mG}, {2, mM}, {0, 0}, {0, 0}, {0,0}}])/(2*(-1 + D)), {q1, q2}] // FCE", +"(1/(2 (-1 + D)))mG^2 FAD[{q1, I mG}, {q1, I mG}, {q1, I mG}, {q1, +I mG}, {q1, I mG}, {q2, mM}, {q2, mM}, +Dimension -> 2 + D] (FVD[q, Lor1] FVD[q, Lor2] - +MTD[Lor1, Lor2] SPD[q, q])"}, +{"fcstTarcerToFC-ID7", +"TarcerToFC[Tarcer`TBI[D, pp^2, {{1, 0}, {1, 0}}], {q1, q2}, +ScalarProduct -> {{pp^2, p1}}, FCE -> True]", +"FAD[q1, -p1 + q1]"}, +{"fcstTarcerToFC-ID8", +"TarcerToFC[a1 Tarcer`TBI[D, pp^2, {{1, 0}, {1, 0}}] + +b1 Tarcer`TBI[D, mm1, {{1, 0}, {1, 0}}], {q1, q2}, +ScalarProduct -> {{pp^2, p1}, {mm1, p1}}, +FCE -> True]", +"a1 FAD[q1, -p1 + q1] + b1 FAD[q1, -p1 + q1]"} }); diff --git a/Tests/LoopIntegrals/Tdec.test b/Tests/LoopIntegrals/Tdec.test index 53e8227aa..3d871dd9d 100644 --- a/Tests/LoopIntegrals/Tdec.test +++ b/Tests/LoopIntegrals/Tdec.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Tdec *) @@ -85,7 +85,13 @@ Dimension -> D, List -> False, UseTIDL -> False, FCE -> True]", (FVD[k1, $3047]*FVD[k1, $3488]*MTD[$3050, $3489]*(4*SPD[k1, q1]^2*SPD[k1, q2]^2 - D^2*SPD[k1, q1]^2*SPD[k1, q2]^2 - 2*SPD[k1, k1]*SPD[k1, q2]^2*SPD[q1, q1] + D^2*SPD[k1, k1]*SPD[k1, q2]^2*SPD[q1, q1] - 4*SPD[k1, k1]*SPD[k1, q1]*SPD[k1, q2]*SPD[q1, q2] + 2*SPD[k1, k1]^2*SPD[q1, q2]^2 + D*SPD[k1, k1]*SPD[k1, q1]^2*SPD[q2, q2] - D*SPD[k1, k1]^2*SPD[q1, q1]*SPD[q2, q2]))/((2 - D)*(1 - D^2)*SPD[k1, k1]^3) + (FVD[k1, $3050]*FVD[k1, $3489]*MTD[$3047, $3488]*(4*SPD[k1, q1]^2*SPD[k1, q2]^2 - D^2*SPD[k1, q1]^2*SPD[k1, q2]^2 + D*SPD[k1, k1]*SPD[k1, q2]^2*SPD[q1, q1] - 4*SPD[k1, k1]*SPD[k1, q1]*SPD[k1, q2]*SPD[q1, q2] + - 2*SPD[k1, k1]^2*SPD[q1, q2]^2 - 2*SPD[k1, k1]*SPD[k1, q1]^2*SPD[q2, q2] + D^2*SPD[k1, k1]*SPD[k1, q1]^2*SPD[q2, q2] - D*SPD[k1, k1]^2*SPD[q1, q1]*SPD[q2, q2]))/((2 - D)*(1 - D^2)*SPD[k1, k1]^3)"} + 2*SPD[k1, k1]^2*SPD[q1, q2]^2 - 2*SPD[k1, k1]*SPD[k1, q1]^2*SPD[q2, q2] + D^2*SPD[k1, k1]*SPD[k1, q1]^2*SPD[q2, q2] - D*SPD[k1, k1]^2*SPD[q1, q1]*SPD[q2, q2]))/((2 - D)*(1 - D^2)*SPD[k1, k1]^3)"}, +{"fcstTdec-ID17","Tdec[{{l, i1}, {l, i2}}, {p1}, Head -> mom]", + "{{X1 -> D, X2 -> SPD[l, l], X3 -> SPD[l, mom[p1]], +X4 -> SPD[mom[p1], + mom[p1]]}, -(((X1 X3^2 - X2 X4) FVD[mom[p1], i1] FVD[mom[p1], + i2])/((1 - X1) X4^2)) + ((X3^2 - X2 X4) MTD[i1, + i2])/((1 - X1) X4)}"} }; Tests`LoopIntegrals`fcstTdecNegativeMomenta = ({ diff --git a/Tests/LoopIntegrals/ToPaVe.test b/Tests/LoopIntegrals/ToPaVe.test index 56863eeeb..2c5bb789d 100644 --- a/Tests/LoopIntegrals/ToPaVe.test +++ b/Tests/LoopIntegrals/ToPaVe.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ToPaVe *) @@ -74,5 +74,53 @@ PaVeAutoReduce -> True]"}, {"fcstToPaVe-ID20","FCClearScalarProducts[];\n SPD[p, p] = ma^2; \n ToPaVe[FAD[q, q + p], q]", "I Pi^2 B0[ma^2, 0, 0]"}, {"fcstToPaVe-ID21","FCClearScalarProducts[];\n SPD[p, p] = mb^2; \n ToPaVe[FAD[q, q + p], q]", -"I Pi^2 B0[mb^2, 0, 0]"} +"I Pi^2 B0[mb^2, 0, 0]"}, +{"fcstToPaVe-ID22","ToPaVe[FAD[{l, m}, {l + p, m}] GFAD[{SPD[l, p], 1}], l] // FCE", +"FAD[{l, m}, {l + p, m}] GFAD[{{SPD[l, p], 1}, 1}]"}, +{"fcstToPaVe-ID23","ToPaVe[FAD[{l, m}, {l + p, m}] CFAD[{{0, l.p}, m^2}], l] // FCE", +"CFAD[{{0, l.p}, {m^2, -1}, 1}] FAD[{l, m}, {l + p, m}]"}, +{"fcstToPaVe-ID25", "ToPaVe[SFAD[{q,m1^2}],q,FCE->True]", +"I*Pi^2*A0[m1^2]"}, +{"fcstToPaVe-ID26", "ToPaVe[SFAD[{q,m1^2,2}],q,FCE->True]", +"I*Pi^2*B0[0, m1^2, m1^2]"}, +{"fcstToPaVe-ID27", "ToPaVe[SFAD[{{q,q.p},m^2}],q,FCE->True]", +"SFAD[{{q, p . q}, {m^2, 1}, 1}]"}, +{"fcstToPaVe-ID28", "ToPaVe[SFAD[{q,m1^2},{q-p,m2^2}],q,FCE->True]", + "I*Pi^2*B0[SPD[p, p], m1^2, m2^2]"}, +{"fcstToPaVe-ID29", +"ToPaVe[SFAD[{q,m1^2},{q+p1,m2^2}],q,FCE->True]", +"I*Pi^2*B0[SPD[p1, p1], m1^2, m2^2]"}, +{"fcstToPaVe-ID30", +"ToPaVe[SFAD[{q,mm1},{q+p1,mm2},{q+p2,mm3}],q,FCE->True]", +"I*Pi^2*C0[SPD[p1, p1], SPD[p2, p2], SPD[p1, p1] - 2*SPD[p1, p2] + \ +SPD[p2, p2], mm2, mm1, mm3]"}, +{"fcstToPaVe-ID31", +"ToPaVe[SFAD[{q, mm1}, {q + p1, mm2}, {q + p2, mm3}, {q + p3, \ +mm4}], q,FCE->True]", +"I*Pi^2*D0[SPD[p1, p1], SPD[p2, p2], SPD[p2, p2] - 2*SPD[p2, p3] + \ +SPD[p3, p3], SPD[p1, p1] - 2*SPD[p1, p3] + SPD[p3, p3], SPD[p1, p1] - \ +2*SPD[p1, p2] + SPD[p2, p2], SPD[p3, p3], mm2, mm1, mm3, mm4]"}, +{"fcstToPaVe-ID32", "ToPaVe[SFAD[{q,m1^2,2}],q,FCE->True]", +"I*Pi^2*B0[0, m1^2, m1^2]"}, +{"fcstToPaVe-ID33", "ToPaVe[SFAD[{q,m1^2,3}],q,FCE->True]", +"I*Pi^2*C0[0, 0, 0, m1^2, m1^2, m1^2]"}, +{"fcstToPaVe-ID34", "ToPaVe[SFAD[{q,m1^2,4}],q,FCE->True]", +"I*Pi^2*D0[0, 0, 0, 0, 0, 0, m1^2, m1^2, m1^2, m1^2]"}, +{"fcstToPaVe-ID35", +"FCClearScalarProducts[]; \n ToPaVe[SFAD[{q,m1^2},{q-p,m2^2,3}],q,FCE->True]", +"I*Pi^2*D0[0, 0, SPD[p, p], SPD[p, p], 0, SPD[p, p], m2^2, m2^2, \ +m2^2, m1^2]"}, +{"fcstToPaVe-ID36", "ToPaVe[FAD[{q, m0}, {q - p1, m1}, {q - p2, m2}], q, +PaVeAutoOrder -> False, PaVeOrder -> False, FCE -> True]", +"I \[Pi]^2 PaVe[ +0, {SPD[p1, p1], SPD[p1, p1] - 2 SPD[p1, p2] + SPD[p2, p2], +SPD[p2, p2]}, {m0^2, m1^2, m2^2}, PaVeAutoOrder -> False, +PaVeAutoReduce -> True]"}, +{"fcstToPaVe-ID37", "ToPaVe[FAD[{q, m0}, {q - p1, m1}, {q - p2, m2}, {q - p2, m3}], q, +PaVeAutoOrder -> False, PaVeOrder -> False, FCE -> True]", +"I \[Pi]^2 PaVe[ +0, {SPD[p1, p1], SPD[p1, p1] - 2 SPD[p1, p2] + SPD[p2, p2], 0, +SPD[p2, p2], SPD[p2, p2], +SPD[p1, p1] - 2 SPD[p1, p2] + SPD[p2, p2]}, {m0^2, m1^2, m2^2, +m3^2}, PaVeAutoOrder -> False, PaVeAutoReduce -> True]"} }; diff --git a/Tests/LoopIntegrals/ToPaVe2.test b/Tests/LoopIntegrals/ToPaVe2.test index 25a12d7be..1201b65bd 100644 --- a/Tests/LoopIntegrals/ToPaVe2.test +++ b/Tests/LoopIntegrals/ToPaVe2.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ToPaVe2 *) diff --git a/Tests/LoopIntegrals/ToSFAD.test b/Tests/LoopIntegrals/ToSFAD.test new file mode 100644 index 000000000..8c8414cfc --- /dev/null +++ b/Tests/LoopIntegrals/ToSFAD.test @@ -0,0 +1,81 @@ + + +(* :Title: ToSFAD.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for ToSFAD *) + +(* ------------------------------------------------------------------------ *) + +Tests`LoopIntegrals`ToSFAD = +({ +{"fcstToSFAD-ID1", "ToSFAD[0]", "0"}, +{"fcstToSFAD-ID2", "ToSFAD[a]", "a"}, +{"fcstToSFAD-ID3", "ToSFAD[FAD[p]]", "SFAD[{{p, 0}, {0, 1}, 1}]"}, +{"fcstToSFAD-ID4", "ToSFAD[FAD[{p,m}]]", +"SFAD[{{p, 0}, {m^2, 1}, 1}]"}, +{"fcstToSFAD-ID5", "ToSFAD[FAD[{p,m,2}]]", +"SFAD[{{p, 0}, {m^2, 1}, 1}, {{p, 0}, {m^2, 1}, 1}]"}, +{"fcstToSFAD-ID6", "ToSFAD[FAD[{p,m},q]]", +"SFAD[{{p, 0}, {m^2, 1}, 1}, {{q, 0}, {0, 1}, 1}]"}, +{"fcstToSFAD-ID7", "ToSFAD[FAD[{p,m1},q,{r-q,m2,2}]]", +"SFAD[{{p, 0}, {m1^2, 1}, 1}, {{q, 0}, {0, 1}, 1}, {{-q + r, 0}, \ +{m2^2, 1}, 1}, {{-q + r, 0}, {m2^2, 1}, 1}]"}, +{"fcstToSFAD-ID8", "ToSFAD[FAD[{p,m},q]FAD[{p,m1},q,{r-q,m2,2}]]", +"SFAD[{{p, 0}, {m^2, 1}, 1}, {{q, 0}, {0, 1}, 1}]*SFAD[{{p, 0}, \ +{m1^2, 1}, 1}, {{q, 0}, {0, 1}, 1}, {{-q + r, 0}, {m2^2, 1}, 1}, {{-q \ ++ r, 0}, {m2^2, 1}, 1}]"}, +{"fcstToSFAD-ID9", "ToSFAD[x+FAD[{p,m},q]FAD[{p,m1},q,{r-q,m2,2}]]", + "x + SFAD[{{p, 0}, {m^2, 1}, 1}, {{q, 0}, {0, 1}, 1}]*SFAD[{{p, \ +0}, {m1^2, 1}, 1}, {{q, 0}, {0, 1}, 1}, {{-q + r, 0}, {m2^2, 1}, 1}, \ +{{-q + r, 0}, {m2^2, 1}, 1}]"}, +{"fcstToSFAD-ID10", "ToSFAD[FCI[FAD[p]]]", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ +0, 0, {1, 1}]]"}, +{"fcstToSFAD-ID11", "ToSFAD[FCI[FAD[{p,m}]]]", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ +0, m^2, {1, 1}]]"}, +{"fcstToSFAD-ID12", "ToSFAD[FCI[FAD[{p,m,2}]]]", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ +0, m^2, {1, 1}], StandardPropagatorDenominator[Momentum[p, D], 0, \ +m^2, {1, 1}]]"}, +{"fcstToSFAD-ID13", "ToSFAD[FCI[FAD[{p,m},q]]]", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ +0, m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ +{1, 1}]]"}, +{"fcstToSFAD-ID14", "ToSFAD[FCI[FAD[{p,m1},q,{r-q,m2,2}]]]", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ +0, m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ +{1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + Momentum[r, \ +D], 0, m2^2, {1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + \ +Momentum[r, D], 0, m2^2, {1, 1}]]"}, +{"fcstToSFAD-ID15", +"ToSFAD[FCI[FAD[{p,m},q]FAD[{p,m1},q,{r-q,m2,2}]]]", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, D], \ +0, m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, 0, \ +{1, 1}]]*FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, \ +D], 0, m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + \ +Momentum[r, D], 0, m2^2, {1, 1}], \ +StandardPropagatorDenominator[-Momentum[q, D] + Momentum[r, D], 0, \ +m2^2, {1, 1}]]"}, +{"fcstToSFAD-ID16", +"ToSFAD[FCI[x+FAD[{p,m},q]FAD[{p,m1},q,{r-q,m2,2}]]]", +"x + FeynAmpDenominator[StandardPropagatorDenominator[Momentum[p, \ +D], 0, m^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, D], 0, \ +0, {1, 1}]]*FeynAmpDenominator[StandardPropagatorDenominator[Momentum[\ +p, D], 0, m1^2, {1, 1}], StandardPropagatorDenominator[Momentum[q, \ +D], 0, 0, {1, 1}], StandardPropagatorDenominator[-Momentum[q, D] + \ +Momentum[r, D], 0, m2^2, {1, 1}], \ +StandardPropagatorDenominator[-Momentum[q, D] + Momentum[r, D], 0, \ +m2^2, {1, 1}]]"}, +{"fcstToSFAD-ID17", +"ToSFAD[FAD[p, Dimension -> X]]", +"SFAD[{{p, 0}, {0, 1}, 1}, Dimension -> X]"} +}); diff --git a/Tests/LoopIntegrals/ToTFI.test b/Tests/LoopIntegrals/ToTFI.test index d9fe6a6d7..1f897a407 100644 --- a/Tests/LoopIntegrals/ToTFI.test +++ b/Tests/LoopIntegrals/ToTFI.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ToTFI *) diff --git a/Tests/Lorentz/Amputate.test b/Tests/Lorentz/Amputate.test index 3636f6b8d..10ea4f68a 100644 --- a/Tests/Lorentz/Amputate.test +++ b/Tests/Lorentz/Amputate.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Amputate *) diff --git a/Tests/Lorentz/CartesianToLorentz.test b/Tests/Lorentz/CartesianToLorentz.test new file mode 100644 index 000000000..237194369 --- /dev/null +++ b/Tests/Lorentz/CartesianToLorentz.test @@ -0,0 +1,52 @@ + + +(* :Title: CartesianToLorentz.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for CartesianToLorentz *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstCartesianToLorentz = +({ +{"fcstCartesianToLorentz-ID1", "CartesianToLorentz[CSP[p,q]]", +"-Pair[Momentum[p], Momentum[q]] + TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]]"}, +{"fcstCartesianToLorentz-ID2", "CartesianToLorentz[CSPD[p,q]]", +"-Pair[Momentum[p, D], Momentum[q, D]] + TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]]"}, +{"fcstCartesianToLorentz-ID3", "CartesianToLorentz[CSPE[p,q]]", +"-Pair[Momentum[p, -4 + D], Momentum[q, -4 + D]]"}, +{"fcstCartesianToLorentz-ID4", "CartesianToLorentz[CGS[p]]", +"-DiracGamma[Momentum[p]] + DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]]"}, +{"fcstCartesianToLorentz-ID5", "CartesianToLorentz[CGSD[p]]", +"-DiracGamma[Momentum[p, D], D] + \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstCartesianToLorentz-ID6", "CartesianToLorentz[CGSE[p]]", +"-DiracGamma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstCartesianToLorentz-ID7", +"LorentzToCartesian[CartesianToLorentz[CSP[p,q]]]", +"CartesianPair[CartesianMomentum[p], CartesianMomentum[q]]"}, +{"fcstCartesianToLorentz-ID8", +"LorentzToCartesian[CartesianToLorentz[CSPD[p,q]]]", +"CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D]]"}, +{"fcstCartesianToLorentz-ID9", +"LorentzToCartesian[CartesianToLorentz[CSPE[p,q]]]", +"CartesianPair[CartesianMomentum[p, -4 + D], CartesianMomentum[q, -4 + D]]"}, +{"fcstCartesianToLorentz-ID10", +"LorentzToCartesian[CartesianToLorentz[CGS[p]]]", +"DiracGamma[CartesianMomentum[p]]"}, +{"fcstCartesianToLorentz-ID11", +"LorentzToCartesian[CartesianToLorentz[CGSD[p]]]", +"DiracGamma[CartesianMomentum[p, -1 + D], D]"}, +{"fcstCartesianToLorentz-ID12", +"LorentzToCartesian[CartesianToLorentz[CGSE[p]]]", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]"} +}); diff --git a/Tests/Lorentz/ChangeDimension.test b/Tests/Lorentz/ChangeDimension.test index 2c9e0d09b..54bbe33eb 100644 --- a/Tests/Lorentz/ChangeDimension.test +++ b/Tests/Lorentz/ChangeDimension.test @@ -2,37 +2,197 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ChangeDimension *) (* ------------------------------------------------------------------------ *) -Tests`Lorentz`fcstChangeDimension = { -{"ChangeDimension-ID1", - "ChangeDimension[{LorentzIndex[\[Mu]], Momentum[p]}, D]", - "{LorentzIndex[\[Mu], D], Momentum[p, D]}"}, -{"ChangeDimension-ID2", - "ChangeDimension[{LorentzIndex[\[Mu],D],Momentum[p,D]},4]", - "{LorentzIndex[\[Mu]], Momentum[p]}"}, -{"ChangeDimension-ID3", - "ChangeDimension[LeviCivita[\[Mu],\[Nu],\[Rho],\[Sigma],Dimension\ - \[Rule]D],D]", - "Eps[LorentzIndex[\[Mu], D], LorentzIndex[\[Nu], D], LorentzIndex[\ - \[Rho], D], LorentzIndex[\[Sigma], D], Dimension -> D]"}, -{"ChangeDimension-ID4", - "DiracTrick /@ (ChangeDimension[{GA[\[Mu], \[Nu]] MT[\[Mu], \[Nu]], - GAD[\[Mu], \[Nu]] MTD[\[Mu], \[Nu]] f[D]}, n] // Contract)", - "{n, n*f[D]}"}, -{"ChangeDimension-ID5", - "ChangeDimension[FCI[LCD[i1,i2,i3,i4]],4]", - "Eps[LorentzIndex[i1], LorentzIndex[i2], LorentzIndex[i3], -LorentzIndex[i4]]"}, -{"ChangeDimension-ID6", - "ChangeDimension[FCI[LC[i1,i2,i3,i4]],D]", - "Eps[LorentzIndex[i1,D], LorentzIndex[i2,D], LorentzIndex[i3,D], -LorentzIndex[i4,D],Dimension->D]"} -}; +Tests`Lorentz`fcstChangeDimension = +({ +{"fcstChangeDimension-ID1", +"ChangeDimension[{LorentzIndex[\[Mu]],Momentum[p]},D]", +"{LorentzIndex[\[Mu], D], Momentum[p, D]}"}, +{"fcstChangeDimension-ID2", +"ChangeDimension[{LorentzIndex[\[Mu],D],Momentum[p,D]},4]", +"{LorentzIndex[\[Mu]], Momentum[p]}"}, +{"fcstChangeDimension-ID3", +"ChangeDimension[LCD[\[Mu],\[Nu],\[Rho],\[Sigma]],D,FCE\[Rule]True]\ +", "LCD[\[Mu], \[Nu], \[Rho], \[Sigma]]"}, +{"fcstChangeDimension-ID4", +"DiracTrick/@(ChangeDimension[{GA[mu,nu] MT[mu,nu],GAD[mu,nu] \ +MTD[mu,nu] f[D]},n]//Contract)", "{n, n*f[D]}"}, +{"fcstChangeDimension-ID5", +"ChangeDimension[LCD[i1,i2,i3,i4],4,FCE\[Rule]True]", +"LC[i1, i2, i3, i4]"}, +{"fcstChangeDimension-ID6", +"ChangeDimension[LC[i1,i2,i3,i4],D,FCE\[Rule]True]", +"LCD[i1, i2, i3, i4]"}, +{"fcstChangeDimension-ID7", +"ChangeDimension[GS[p].GA[i,j,5],4,FCE\[Rule]True]", +"GS[p] . GA[i] . GA[j] . GA[5]"}, +{"fcstChangeDimension-ID8", +"ChangeDimension[GS[p].GA[i,j,5],D,FCE\[Rule]True]", +"GSD[p] . GAD[i] . GAD[j] . GA[5]"}, +{"fcstChangeDimension-ID9", +"ChangeDimension[GS[p].GA[i,j,5],D-4,FCE\[Rule]True]", +"GSE[p] . GAE[i] . GAE[j] . GA[5]"}, +{"fcstChangeDimension-ID10", +"ChangeDimension[CGS[p].CGA[i,j],4,FCE->True]", +"CGS[p] . CGA[i] . CGA[j]"}, +{"fcstChangeDimension-ID11", +"ChangeDimension[CGS[p].CGA[i,j],D,FCE->True]", +"CGSD[p] . CGAD[i] . CGAD[j]"}, +{"fcstChangeDimension-ID12", +"ChangeDimension[CGS[p].CGA[i,j],D-4,FCE->True]", +"CGSE[p] . CGAE[i] . CGAE[j]"}, +{"fcstChangeDimension-ID13", +"ChangeDimension[SIS[p].SI[i,j],4,FCE->True]", +"SIS[p] . SI[i] . SI[j]"}, +{"fcstChangeDimension-ID14", +"ChangeDimension[SIS[p].SI[i,j],D,FCE->True]", +"SISD[p] . SID[i] . SID[j]"}, +{"fcstChangeDimension-ID15", +"ChangeDimension[SIS[p].SI[i,j],D-4,FCE->True]", +"SISE[p] . SIE[i] . SIE[j]"}, +{"fcstChangeDimension-ID16", +"ChangeDimension[SISD[p].SID[i,j],4,FCE->True]", +"SIS[p] . SI[i] . SI[j]"}, +{"fcstChangeDimension-ID17", +"ChangeDimension[SISD[p].SID[i,j],D,FCE->True]", +"SISD[p] . SID[i] . SID[j]"}, +{"fcstChangeDimension-ID18", +"ChangeDimension[SISD[p].SID[i,j],D-4,FCE->True]", +"SISE[p] . SIE[i] . SIE[j]"}, +{"fcstChangeDimension-ID19", +"ChangeDimension[SISE[p].SIE[i,j],4,FCE->True]", +"SIS[p] . SI[i] . SI[j]"}, +{"fcstChangeDimension-ID20", +"ChangeDimension[SISE[p].SIE[i,j],D,FCE->True]", +"SISD[p] . SID[i] . SID[j]"}, +{"fcstChangeDimension-ID21", +"ChangeDimension[SISE[p].SIE[i,j],D-4,FCE->True]", +"SISE[p] . SIE[i] . SIE[j]"}, +{"fcstChangeDimension-ID22", +"ChangeDimension[CSIS[p].CSI[i,j],4,FCE->True]", +"CSIS[p] . CSI[i] . CSI[j]"}, +{"fcstChangeDimension-ID23", +"ChangeDimension[CSIS[p].CSI[i,j],D,FCE->True]", +"CSISD[p] . CSID[i] . CSID[j]"}, +{"fcstChangeDimension-ID24", +"ChangeDimension[CSIS[p].CSI[i,j],D-4,FCE->True]", +"CSISE[p] . CSIE[i] . CSIE[j]"}, +{"fcstChangeDimension-ID25", +"ChangeDimension[CSISD[p].CSID[i,j],4,FCE->True]", +"CSIS[p] . CSI[i] . CSI[j]"}, +{"fcstChangeDimension-ID26", +"ChangeDimension[CSISD[p].CSID[i,j],D,FCE->True]", +"CSISD[p] . CSID[i] . CSID[j]"}, +{"fcstChangeDimension-ID27", +"ChangeDimension[CSISD[p].CSID[i,j],D-4,FCE->True]", +"CSISE[p] . CSIE[i] . CSIE[j]"}, +{"fcstChangeDimension-ID28", +"ChangeDimension[CSISE[p].CSIE[i,j],4,FCE->True]", +"CSIS[p] . CSI[i] . CSI[j]"}, +{"fcstChangeDimension-ID29", +"ChangeDimension[CSISE[p].CSIE[i,j],D,FCE->True]", +"CSISD[p] . CSID[i] . CSID[j]"}, +{"fcstChangeDimension-ID30", +"ChangeDimension[CSISE[p].CSIE[i,j],D-4,FCE->True]", +"CSISE[p] . CSIE[i] . CSIE[j]"}, +{"fcstChangeDimension-ID31", +"ChangeDimension[SP[p,q](a+b),4,FCE->True]", "(a + b)*SP[p, q]"}, +{"fcstChangeDimension-ID32", +"ChangeDimension[SP[p,q](a+b),D,FCE->True]", "(a + b)*SPD[p, q]"}, +{"fcstChangeDimension-ID33", +"ChangeDimension[SP[p,q](a+b),D-4,FCE->True]", "(a + b)*SPE[p, q]"}, +{"fcstChangeDimension-ID34", +"ChangeDimension[SPD[p,q](a+b),4,FCE->True]", "(a + b)*SP[p, q]"}, +{"fcstChangeDimension-ID35", +"ChangeDimension[SPD[p,q](a+b),D,FCE->True]", +"(a + b)*SPD[p, q]"}, +{"fcstChangeDimension-ID36", +"ChangeDimension[SPD[p,q](a+b),D-4,FCE->True]", +"(a + b)*SPE[p, q]"}, +{"fcstChangeDimension-ID37", +"ChangeDimension[SPE[p,q](a+b),4,FCE->True]", "(a + b)*SP[p, q]"}, +{"fcstChangeDimension-ID38", +"ChangeDimension[SPE[p,q](a+b),D,FCE->True]", +"(a + b)*SPD[p, q]"}, +{"fcstChangeDimension-ID39", +"ChangeDimension[SPE[p,q](a+b),D-4,FCE->True]", +"(a + b)*SPE[p, q]"}, +{"fcstChangeDimension-ID40", +"ChangeDimension[CSP[p,q](a+b),4,FCE->True]", +"(a + b)*CSP[p, q]"}, +{"fcstChangeDimension-ID41", +"ChangeDimension[CSP[p,q](a+b),D,FCE->True]", "(a + b)*CSPD[p, q]"}, +{"fcstChangeDimension-ID42", +"ChangeDimension[CSP[p,q](a+b),D-4,FCE->True]", +"(a + b)*CSPE[p, q]"}, +{"fcstChangeDimension-ID43", +"ChangeDimension[CSPD[p,q](a+b),4,FCE->True]", "(a + b)*CSP[p, q]"}, +{"fcstChangeDimension-ID44", +"ChangeDimension[CSPD[p,q](a+b),D,FCE->True]", +"(a + b)*CSPD[p, q]"}, +{"fcstChangeDimension-ID45", +"ChangeDimension[CSPD[p,q](a+b),D-4,FCE->True]", +"(a + b)*CSPE[p, q]"}, +{"fcstChangeDimension-ID46", +"ChangeDimension[CSPE[p,q](a+b),4,FCE->True]", "(a + b)*CSP[p, q]"}, +{"fcstChangeDimension-ID47", +"ChangeDimension[CSPE[p,q](a+b),D,FCE->True]", +"(a + b)*CSPD[p, q]"}, +{"fcstChangeDimension-ID48", +"ChangeDimension[CSPE[p,q](a+b),D-4,FCE->True]", +"(a + b)*CSPE[p, q]"}, +{"fcstChangeDimension-ID49", +"ChangeDimension[FV[p,q](a+b),4,FCE->True]", "(a + b)*FV[p, q]"}, +{"fcstChangeDimension-ID50", +"ChangeDimension[FV[p,q](a+b),D,FCE->True]", "(a + b)*FVD[p, q]"}, +{"fcstChangeDimension-ID51", +"ChangeDimension[FV[p,q](a+b),D-4,FCE->True]", "(a + b)*FVE[p, q]"}, +{"fcstChangeDimension-ID52", +"ChangeDimension[FVD[p,q](a+b),4,FCE->True]", "(a + b)*FV[p, q]"}, +{"fcstChangeDimension-ID53", +"ChangeDimension[FVD[p,q](a+b),D,FCE->True]", +"(a + b)*FVD[p, q]"}, +{"fcstChangeDimension-ID54", +"ChangeDimension[FVD[p,q](a+b),D-4,FCE->True]", +"(a + b)*FVE[p, q]"}, +{"fcstChangeDimension-ID55", +"ChangeDimension[FVE[p,q](a+b),4,FCE->True]", "(a + b)*FV[p, q]"}, +{"fcstChangeDimension-ID56", +"ChangeDimension[FVE[p,q](a+b),D,FCE->True]", +"(a + b)*FVD[p, q]"}, +{"fcstChangeDimension-ID57", +"ChangeDimension[FVE[p,q](a+b),D-4,FCE->True]", +"(a + b)*FVE[p, q]"}, +{"fcstChangeDimension-ID58", +"ChangeDimension[CV[p,q](a+b),4,FCE->True]", "(a + b)*CV[p, q]"}, +{"fcstChangeDimension-ID59", +"ChangeDimension[CV[p,q](a+b),D,FCE->True]", "(a + b)*CVD[p, q]"}, +{"fcstChangeDimension-ID60", +"ChangeDimension[CV[p,q](a+b),D-4,FCE->True]", "(a + b)*CVE[p, q]"}, +{"fcstChangeDimension-ID61", +"ChangeDimension[CVD[p,q](a+b),4,FCE->True]", "(a + b)*CV[p, q]"}, +{"fcstChangeDimension-ID62", +"ChangeDimension[CVD[p,q](a+b),D,FCE->True]", +"(a + b)*CVD[p, q]"}, +{"fcstChangeDimension-ID63", +"ChangeDimension[CVD[p,q](a+b),D-4,FCE->True]", +"(a + b)*CVE[p, q]"}, +{"fcstChangeDimension-ID64", +"ChangeDimension[CVE[p,q](a+b),4,FCE->True]", "(a + b)*CV[p, q]"}, +{"fcstChangeDimension-ID65", +"ChangeDimension[CVE[p,q](a+b),D,FCE->True]", +"(a + b)*CVD[p, q]"}, +{"fcstChangeDimension-ID66", +"ChangeDimension[CVE[p,q](a+b),D-4,FCE->True]", "(a + b)*CVE[p, q]"}, +{"fcstChangeDimension-ID67", +"ChangeDimension[DiracChain[DiracGamma[LorentzIndex[Lor1, D], D], +DiracIndex[QGIDirMinus2], DiracIndex[QGIDirMinus1]],4,FCE->True]", "DCHN[GA[Lor1], QGIDirMinus2, QGIDirMinus1]"} +}); diff --git a/Tests/Lorentz/Contract.test b/Tests/Lorentz/Contract.test index 389f952a3..cb81c66a1 100644 --- a/Tests/Lorentz/Contract.test +++ b/Tests/Lorentz/Contract.test @@ -3,9 +3,9 @@ (* :Title: Contract.test *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Contract *) @@ -33,8 +33,10 @@ Tests`Lorentz`fcstContractContractionsIn4dims = { "-6*Pair[LorentzIndex[a], LorentzIndex[b]]"}, {"fcstContractContractionsIn4dims-ID11", "Contract[MetricTensor[a, sigma]*FourVector[p, a] FourVector[p,sigma]*(FourVector[q, b] + FourVector[r, b])*(FourVector[p, b] - -FourVector[q, b]), Expanding -> False]", "Pair[Momentum[p], Momentum[p]]*(Pair[Momentum[p], Momentum[q]] + - Pair[Momentum[p], Momentum[r]] - Pair[Momentum[q], Momentum[q]] - Pair[Momentum[q], Momentum[r]])"}, + -FourVector[q, b]), Expanding -> False]", "Pair[Momentum[p], +Momentum[p]]*(Pair[Momentum[p], Momentum[q]] + +Pair[Momentum[p], Momentum[r]] - Pair[Momentum[q], Momentum[q]] - +Pair[Momentum[q], Momentum[r]])"}, {"fcstContractContractionsIn4dims-ID12", "Contract[FourVector[k, mu] PolarizationVector[k, mu]]", "Contract[FourVector[k, mu] PolarizationVector[k, mu]]"}, {"fcstContractContractionsIn4dims-ID13", "Contract[FourVector[k, mu] @@ -143,7 +145,19 @@ MT[i1, i4] MT[i10, i7] MT[i11, i9] MT[i12, i8] MT[i2, i5] MT[i3, i6] - MT[i1, i4] MT[i10, i8] MT[i11, i7] MT[i12, i9] MT[i2, i5] MT[ i3, i6] + MT[i1, i4] MT[i10, i7] MT[i11, i8] MT[i12, i9] MT[i2, i5] MT[i3, i6]"}, -{"fcstContractContractionsIn4dims-ID27","Contract[PairContract[LorentzIndex[i], Momentum[p]]] // FCE","FV[p, i]"} +{"fcstContractContractionsIn4dims-ID27","Contract[PairContract[LorentzIndex[i], Momentum[p]]] // FCE","FV[p, i]"}, +{"fcstContractContractionsIn4dims-ID28","Contract[LC[mu, nu, rho, sigma] FV[k, mu] FV[P, rho]] // FCE","-LC[nu, sigma][k, P]"}, +{"fcstContractContractionsIn4dims-ID29","Contract[Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], + LorentzIndex[d]]*FV[p, a]*FV[p + q, b]] // FCE","LC[c, d][p, q]"}, +{"fcstContractContractionsIn4dims-ID30","Contract[FV[p1 + p2 + p3 + p4, i] FV[q1 + q2 + q3 + q4, i], +ExpandScalarProduct -> False] // FCE","SP[p1 + p2 + p3 + p4, q1 + q2 + q3 + q4]"}, +{"fcstContractContractionsIn4dims-ID31","FCE[Contract[ +DiracChain[GA[mu].(GS[p] + m).GA[nu], DiracIndex[i], + DiracIndex[j]] FV[p, mu]]]","DCHN[GS[p].(m + GS[p]).GA[nu], i, j]"}, +{"fcstContractContractionsIn4dims-ID32","Contract[DCHN[FV[p, mu] GA[nu, mu, rho], i, j], FCE -> True]", + "DCHN[GA[nu].GS[p].GA[rho], i, j]"}, +{"fcstContractContractionsIn4dims-ID33","Contract[FV[p, mu] DCHN[GA[nu, mu, rho], i, j], FCE -> True]", + "DCHN[GA[nu].GS[p].GA[rho], i, j]"} }; Tests`Lorentz`fcstContractDDims = { @@ -267,13 +281,13 @@ Pair[LorentzIndex[i1], LorentzIndex[j2]]*Pair[LorentzIndex[i2], LorentzIndex[j1] Pair[LorentzIndex[i1, D], LorentzIndex[j1, D]]*Pair[LorentzIndex[i2, D], LorentzIndex[j2, D]]* Pair[LorentzIndex[i3, D], LorentzIndex[j3, D]]*Pair[LorentzIndex[i4, D], LorentzIndex[j4, D]]"}, {"fcstContractDDims-ID11","LCD[i1, i2, i3, i4] MT[i4, i5] // Contract", - "-Eps[LorentzIndex[i5], LorentzIndex[i1, D], LorentzIndex[i2, D], LorentzIndex[i3, D], Dimension -> D]"}, + "Eps[LorentzIndex[i1], LorentzIndex[i2], LorentzIndex[i3], LorentzIndex[i5]]"}, {"fcstContractDDims-ID12","LCD[i1, i2, i3, i4] MTD[i4, i5] // Contract", - "Eps[LorentzIndex[i1, D], LorentzIndex[i2, D], LorentzIndex[i3, D], LorentzIndex[i5, D], Dimension -> D]"}, + "Eps[LorentzIndex[i1, D], LorentzIndex[i2, D], LorentzIndex[i3, D], LorentzIndex[i5, D]]"}, {"fcstContractDDims-ID13","LCD[i1, i2, i3, i4] FV[p, i4] // Contract", - "Eps[LorentzIndex[i1, D], LorentzIndex[i2, D], LorentzIndex[i3, D], Momentum[p], Dimension -> D]"}, + "Eps[LorentzIndex[i1, D], LorentzIndex[i2, D], LorentzIndex[i3, D], Momentum[p]]"}, {"fcstContractDDims-ID14","LCD[i1, i2, i3, i4] FVD[p, i4] // Contract", - "Eps[LorentzIndex[i1, D], LorentzIndex[i2, D], LorentzIndex[i3, D], Momentum[p, D], Dimension -> D]"}, + "Eps[LorentzIndex[i1, D], LorentzIndex[i2, D], LorentzIndex[i3, D], Momentum[p, D]]"}, {"fcstContractDDims-ID15","Contract[PairContract[LorentzIndex[i, D], Momentum[p, D]]] // FCE","FVD[p, i]"} }; @@ -339,26 +353,23 @@ Lor6] (FVE[k, Lor5] MTE[Lor3, i] + FVD[k, Lor3] MTE[Lor5, i])]//FCE", "(-4 + D) SPD[k, k] + 2 SPE[k, k] + (-4 + D) SPE[k, k]"} }; -Tests`Lorentz`fcstContractContractionsUpperLower = { +Tests`Lorentz`fcstContractCartesian = { +{"fcstContractCartesian-ID1","FCE[Contract[FVD[v1, mu] FVD[v2, nu] Pair[LorentzIndex[mu], CartesianIndex[i]] Pair[ LorentzIndex[nu], CartesianIndex[i]]]]","CSP[v1, v2]"}, +{"fcstContractCartesian-ID2","Contract[3 +I CLC[i, j,aa] (CSI[j] KD[i, aa] + I CLC[aa, i, bb] (I CLC[bb, j, cc] CSI[cc] + KD[j, bb]))]","-3"}, +{"fcstContractCartesian-ID3","Simplify[LorentzToCartesian[ +Contract[LC[0][p1, p2, p3] LC[0][q1, q2, q3]]] - Contract[EpsEvaluate[LC[0][p1, p2, p3] LC[0][q1, q2, q3]]]]","0"} +} + + + + + -{"fcstContractContractionsNR-ID1","Contract[Pair[Momentum[p], LorentzIndex[Upper[mu]]], -Pair[Momentum[q], LorentzIndex[Upper[mu]]]]","Pair[LorentzIndex[Upper[mu]], Momentum[p]]*Pair[LorentzIndex[Upper[mu]], Momentum[q]]"}, -{"fcstContractContractionsNR-ID2","Contract[Pair[Momentum[p], LorentzIndex[Upper[mu]]], -Pair[Momentum[p], LorentzIndex[Upper[mu]]]]","Pair[LorentzIndex[Upper[mu]], Momentum[p]]^2"}, -{"fcstContractContractionsNR-ID3","Contract[Pair[Momentum[p], LorentzIndex[Lower[mu]]], -Pair[Momentum[q], LorentzIndex[Lower[mu]]]]","Pair[LorentzIndex[Lower[mu]], Momentum[p]]*Pair[LorentzIndex[Lower[mu]], Momentum[q]]"}, -{"fcstContractContractionsNR-ID4","Contract[Pair[Momentum[p], LorentzIndex[Lower[mu]]], -Pair[Momentum[p], LorentzIndex[Lower[mu]]]]","Pair[LorentzIndex[Lower[mu]], Momentum[p]]^2"}, -{"fcstContractContractionsNR-ID5","Contract[Pair[Momentum[p], LorentzIndex[Upper[mu]]], -Pair[Momentum[q], LorentzIndex[Lower[mu]]]]","Pair[Momentum[p], Momentum[q]]"}, -{"fcstContractContractionsNR-ID6","Contract[Pair[Momentum[p], LorentzIndex[Upper[mu]]], -Pair[Momentum[p], LorentzIndex[Lower[mu]]]]","Pair[Momentum[p], Momentum[p]]"} -} diff --git a/Tests/Lorentz/DummyIndexFreeQ.test b/Tests/Lorentz/DummyIndexFreeQ.test new file mode 100644 index 000000000..ad33da8bd --- /dev/null +++ b/Tests/Lorentz/DummyIndexFreeQ.test @@ -0,0 +1,57 @@ + + +(* :Title: DummyIndexFreeQ.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for DummyIndexFreeQ *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstLorentzDummyIndexFreeQ = +({ +{"fcstLorentzDummyIndexFreeQ-ID1", "DummyIndexFreeQ[0,{LorentzIndex}]", +"True"}, +{"fcstLorentzDummyIndexFreeQ-ID2", "DummyIndexFreeQ[a,{LorentzIndex}]", +"True"}, +{"fcstLorentzDummyIndexFreeQ-ID3", +"DummyIndexFreeQ[FCI[FV[p,i]],{LorentzIndex}]", "True"}, +{"fcstLorentzDummyIndexFreeQ-ID4", +"DummyIndexFreeQ[FCI[FV[p,i]^2],{LorentzIndex}]", "False"}, +{"fcstLorentzDummyIndexFreeQ-ID5", +"DummyIndexFreeQ[xxx(Sum[Pair[Momentum[p[i]],LorentzIndex[\ +li]],{i,1,50000}]),{LorentzIndex}]", "True"}, +{"fcstLorentzDummyIndexFreeQ-ID6", +"DummyIndexFreeQ[xxx(Sum[Pair[Momentum[p[i]],LorentzIndex[\ +li]],{i,1,50000}])+FCI[FV[q,i]MT[j,j]],{LorentzIndex}]", "False"}, +{"fcstLorentzDummyIndexFreeQ-ID7", +"DummyIndexFreeQ[FCI[FV[p1,i]+FV[p2,i]+FV[p3,i]MT[j,j]],{LorentzIndex}]", +"False"} +}); + + +Tests`Lorentz`fcstCartesianDummyIndexFreeQ = +({ +{"fcstCartesianDummyIndexFreeQ-ID1", "DummyIndexFreeQ[0,{CartesianIndex}]", +"True"}, +{"fcstCartesianDummyIndexFreeQ-ID2", "DummyIndexFreeQ[a,{CartesianIndex}]", +"True"}, +{"fcstCartesianDummyIndexFreeQ-ID3", +"DummyIndexFreeQ[CartesianPair[CartesianIndex[i],CartesianMomentum[p]],{CartesianIndex}]", "True"}, +{"fcstCartesianDummyIndexFreeQ-ID4", +"DummyIndexFreeQ[CartesianPair[CartesianIndex[i],CartesianMomentum[p]]^2,{CartesianIndex}]", "False"}, +{"fcstCartesianDummyIndexFreeQ-ID5", +"DummyIndexFreeQ[xxx(Sum[CartesianPair[CartesianMomentum[p[i]],CartesianIndex[\ +li]],{i,1,50000}]),{CartesianIndex}]", "True"}, +{"fcstCartesianDummyIndexFreeQ-ID6", +"DummyIndexFreeQ[xxx(Sum[Pair[CartesianMomentum[p[i]],CartesianIndex[\ +li]],{i,1,50000}])+ CartesianPair[CartesianIndex[i],CartesianMomentum[q]] CartesianPair[CartesianIndex[j],CartesianIndex[j]],{CartesianIndex}]", "False"}, +{"fcstCartesianDummyIndexFreeQ-ID7", +"DummyIndexFreeQ[CartesianPair[CartesianIndex[i],CartesianMomentum[p1]]+CartesianPair[CartesianIndex[i],CartesianMomentum[p2]]+CartesianPair[CartesianIndex[i],CartesianMomentum[p3]] CartesianPair[CartesianIndex[j],CartesianIndex[j]],{CartesianIndex}]", +"False"} +}); diff --git a/Tests/Lorentz/EpsContract.test b/Tests/Lorentz/EpsContract.test new file mode 100644 index 000000000..8acd722a9 --- /dev/null +++ b/Tests/Lorentz/EpsContract.test @@ -0,0 +1,971 @@ + + +(* :Title: EpsContract.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for EpsContract *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstEpsContract = +({ +{"fcstEpsContract-ID1", "EpsContract[0]", "0"}, +{"fcstEpsContract-ID2", "EpsContract[a LC[i1,i2,i3,i4]^2 + b]", +"-24*a + b"}, +{"fcstEpsContract-ID3", "EpsContract[Eps[p1,p2,p3,p4]]", +"Eps[p1, p2, p3, p4]"}, +{"fcstEpsContract-ID4", +"EpsContract[LCD[i1,i2,i3,i4]LCD[i5,i6,i7,i8]]", +"-(Pair[LorentzIndex[i1, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i2, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i5, D]]) + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i5, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i5, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i5, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i5, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i5, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i5, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i5, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i5, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i5, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i8, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i5, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i5, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i7, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] + \ +Pair[LorentzIndex[i1, D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] - \ +Pair[LorentzIndex[i1, D], LorentzIndex[i5, D]]*Pair[LorentzIndex[i2, \ +D], LorentzIndex[i6, D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]]"}, +{"fcstEpsContract-ID5", +"EpsContract[LCD[i1,i2,i3,i4]LCD[i1,i6,i7,i8]]", +"-3*Pair[LorentzIndex[i2, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] + \ +D*Pair[LorentzIndex[i2, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] + \ +3*Pair[LorentzIndex[i2, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] - \ +D*Pair[LorentzIndex[i2, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i6, D]] + \ +3*Pair[LorentzIndex[i2, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] - \ +D*Pair[LorentzIndex[i2, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] - \ +3*Pair[LorentzIndex[i2, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] + \ +D*Pair[LorentzIndex[i2, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] - \ +3*Pair[LorentzIndex[i2, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] + \ +D*Pair[LorentzIndex[i2, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] + \ +3*Pair[LorentzIndex[i2, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] - \ +D*Pair[LorentzIndex[i2, D], LorentzIndex[i6, \ +D]]*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]]"}, +{"fcstEpsContract-ID6", +"EpsContract[LCD[i1,i2,i3,i4]LCD[i1,i2,i7,i8]]", +"6*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] - \ +5*D*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] + \ +D^2*Pair[LorentzIndex[i3, D], LorentzIndex[i8, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i7, D]] - \ +6*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] + \ +5*D*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] - \ +D^2*Pair[LorentzIndex[i3, D], LorentzIndex[i7, \ +D]]*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]]"}, +{"fcstEpsContract-ID7", +"EpsContract[LCD[i1,i2,i3,i4]LCD[i1,i2,i3,i8]]", +"6*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] - \ +11*D*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] + \ +6*D^2*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]] - \ +D^3*Pair[LorentzIndex[i4, D], LorentzIndex[i8, D]]"}, +{"fcstEpsContract-ID8", +"EpsContract[LCD[i1,i2,i3,i4]LCD[i1,i2,i3,i4]]", +"6*D - 11*D^2 + 6*D^3 - D^4"}, +{"fcstEpsContract-ID9", +"EpsContract[LCD[][p1,p2,p3,p4]LCD[][p5,p6,p7,p8]]", +"-(Pair[Momentum[p1, D], Momentum[p8, D]]*Pair[Momentum[p2, D], \ +Momentum[p7, D]]*Pair[Momentum[p3, D], Momentum[p6, \ +D]]*Pair[Momentum[p4, D], Momentum[p5, D]]) + Pair[Momentum[p1, D], \ +Momentum[p7, D]]*Pair[Momentum[p2, D], Momentum[p8, \ +D]]*Pair[Momentum[p3, D], Momentum[p6, D]]*Pair[Momentum[p4, D], \ +Momentum[p5, D]] + Pair[Momentum[p1, D], Momentum[p8, \ +D]]*Pair[Momentum[p2, D], Momentum[p6, D]]*Pair[Momentum[p3, D], \ +Momentum[p7, D]]*Pair[Momentum[p4, D], Momentum[p5, D]] - \ +Pair[Momentum[p1, D], Momentum[p6, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]]*Pair[Momentum[p3, D], Momentum[p7, \ +D]]*Pair[Momentum[p4, D], Momentum[p5, D]] - Pair[Momentum[p1, D], \ +Momentum[p7, D]]*Pair[Momentum[p2, D], Momentum[p6, \ +D]]*Pair[Momentum[p3, D], Momentum[p8, D]]*Pair[Momentum[p4, D], \ +Momentum[p5, D]] + Pair[Momentum[p1, D], Momentum[p6, \ +D]]*Pair[Momentum[p2, D], Momentum[p7, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]]*Pair[Momentum[p4, D], Momentum[p5, D]] + \ +Pair[Momentum[p1, D], Momentum[p8, D]]*Pair[Momentum[p2, D], \ +Momentum[p7, D]]*Pair[Momentum[p3, D], Momentum[p5, \ +D]]*Pair[Momentum[p4, D], Momentum[p6, D]] - Pair[Momentum[p1, D], \ +Momentum[p7, D]]*Pair[Momentum[p2, D], Momentum[p8, \ +D]]*Pair[Momentum[p3, D], Momentum[p5, D]]*Pair[Momentum[p4, D], \ +Momentum[p6, D]] - Pair[Momentum[p1, D], Momentum[p8, \ +D]]*Pair[Momentum[p2, D], Momentum[p5, D]]*Pair[Momentum[p3, D], \ +Momentum[p7, D]]*Pair[Momentum[p4, D], Momentum[p6, D]] + \ +Pair[Momentum[p1, D], Momentum[p5, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]]*Pair[Momentum[p3, D], Momentum[p7, \ +D]]*Pair[Momentum[p4, D], Momentum[p6, D]] + Pair[Momentum[p1, D], \ +Momentum[p7, D]]*Pair[Momentum[p2, D], Momentum[p5, \ +D]]*Pair[Momentum[p3, D], Momentum[p8, D]]*Pair[Momentum[p4, D], \ +Momentum[p6, D]] - Pair[Momentum[p1, D], Momentum[p5, \ +D]]*Pair[Momentum[p2, D], Momentum[p7, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]]*Pair[Momentum[p4, D], Momentum[p6, D]] - \ +Pair[Momentum[p1, D], Momentum[p8, D]]*Pair[Momentum[p2, D], \ +Momentum[p6, D]]*Pair[Momentum[p3, D], Momentum[p5, \ +D]]*Pair[Momentum[p4, D], Momentum[p7, D]] + Pair[Momentum[p1, D], \ +Momentum[p6, D]]*Pair[Momentum[p2, D], Momentum[p8, \ +D]]*Pair[Momentum[p3, D], Momentum[p5, D]]*Pair[Momentum[p4, D], \ +Momentum[p7, D]] + Pair[Momentum[p1, D], Momentum[p8, \ +D]]*Pair[Momentum[p2, D], Momentum[p5, D]]*Pair[Momentum[p3, D], \ +Momentum[p6, D]]*Pair[Momentum[p4, D], Momentum[p7, D]] - \ +Pair[Momentum[p1, D], Momentum[p5, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]]*Pair[Momentum[p3, D], Momentum[p6, \ +D]]*Pair[Momentum[p4, D], Momentum[p7, D]] - Pair[Momentum[p1, D], \ +Momentum[p6, D]]*Pair[Momentum[p2, D], Momentum[p5, \ +D]]*Pair[Momentum[p3, D], Momentum[p8, D]]*Pair[Momentum[p4, D], \ +Momentum[p7, D]] + Pair[Momentum[p1, D], Momentum[p5, \ +D]]*Pair[Momentum[p2, D], Momentum[p6, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]]*Pair[Momentum[p4, D], Momentum[p7, D]] + \ +Pair[Momentum[p1, D], Momentum[p7, D]]*Pair[Momentum[p2, D], \ +Momentum[p6, D]]*Pair[Momentum[p3, D], Momentum[p5, \ +D]]*Pair[Momentum[p4, D], Momentum[p8, D]] - Pair[Momentum[p1, D], \ +Momentum[p6, D]]*Pair[Momentum[p2, D], Momentum[p7, \ +D]]*Pair[Momentum[p3, D], Momentum[p5, D]]*Pair[Momentum[p4, D], \ +Momentum[p8, D]] - Pair[Momentum[p1, D], Momentum[p7, \ +D]]*Pair[Momentum[p2, D], Momentum[p5, D]]*Pair[Momentum[p3, D], \ +Momentum[p6, D]]*Pair[Momentum[p4, D], Momentum[p8, D]] + \ +Pair[Momentum[p1, D], Momentum[p5, D]]*Pair[Momentum[p2, D], \ +Momentum[p7, D]]*Pair[Momentum[p3, D], Momentum[p6, \ +D]]*Pair[Momentum[p4, D], Momentum[p8, D]] + Pair[Momentum[p1, D], \ +Momentum[p6, D]]*Pair[Momentum[p2, D], Momentum[p5, \ +D]]*Pair[Momentum[p3, D], Momentum[p7, D]]*Pair[Momentum[p4, D], \ +Momentum[p8, D]] - Pair[Momentum[p1, D], Momentum[p5, \ +D]]*Pair[Momentum[p2, D], Momentum[p6, D]]*Pair[Momentum[p3, D], \ +Momentum[p7, D]]*Pair[Momentum[p4, D], Momentum[p8, D]]"}, +{"fcstEpsContract-ID10", +"EpsContract[LCD[][p1,p2,p3,p4]LCD[][p1,p6,p7,p8]]", +"-(Pair[Momentum[p1, D], Momentum[p4, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p7, \ +D]]*Pair[Momentum[p3, D], Momentum[p6, D]]) + Pair[Momentum[p1, D], \ +Momentum[p4, D]]*Pair[Momentum[p1, D], Momentum[p7, \ +D]]*Pair[Momentum[p2, D], Momentum[p8, D]]*Pair[Momentum[p3, D], \ +Momentum[p6, D]] + Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p1, D], Momentum[p8, D]]*Pair[Momentum[p2, D], \ +Momentum[p6, D]]*Pair[Momentum[p3, D], Momentum[p7, D]] - \ +Pair[Momentum[p1, D], Momentum[p4, D]]*Pair[Momentum[p1, D], \ +Momentum[p6, D]]*Pair[Momentum[p2, D], Momentum[p8, \ +D]]*Pair[Momentum[p3, D], Momentum[p7, D]] - Pair[Momentum[p1, D], \ +Momentum[p4, D]]*Pair[Momentum[p1, D], Momentum[p7, \ +D]]*Pair[Momentum[p2, D], Momentum[p6, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]] + Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p1, D], Momentum[p6, D]]*Pair[Momentum[p2, D], \ +Momentum[p7, D]]*Pair[Momentum[p3, D], Momentum[p8, D]] + \ +Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p7, \ +D]]*Pair[Momentum[p4, D], Momentum[p6, D]] - Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p1, D], Momentum[p7, \ +D]]*Pair[Momentum[p2, D], Momentum[p8, D]]*Pair[Momentum[p4, D], \ +Momentum[p6, D]] - Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p8, D]]*Pair[Momentum[p3, D], \ +Momentum[p7, D]]*Pair[Momentum[p4, D], Momentum[p6, D]] + \ +Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]]*Pair[Momentum[p3, D], Momentum[p7, \ +D]]*Pair[Momentum[p4, D], Momentum[p6, D]] + Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p7, \ +D]]*Pair[Momentum[p3, D], Momentum[p8, D]]*Pair[Momentum[p4, D], \ +Momentum[p6, D]] - Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p7, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]]*Pair[Momentum[p4, D], Momentum[p6, D]] - \ +Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p6, \ +D]]*Pair[Momentum[p4, D], Momentum[p7, D]] + Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p1, D], Momentum[p6, \ +D]]*Pair[Momentum[p2, D], Momentum[p8, D]]*Pair[Momentum[p4, D], \ +Momentum[p7, D]] + Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p8, D]]*Pair[Momentum[p3, D], \ +Momentum[p6, D]]*Pair[Momentum[p4, D], Momentum[p7, D]] - \ +Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]]*Pair[Momentum[p3, D], Momentum[p6, \ +D]]*Pair[Momentum[p4, D], Momentum[p7, D]] - Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p6, \ +D]]*Pair[Momentum[p3, D], Momentum[p8, D]]*Pair[Momentum[p4, D], \ +Momentum[p7, D]] + Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p6, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]]*Pair[Momentum[p4, D], Momentum[p7, D]] + \ +Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p1, D], \ +Momentum[p7, D]]*Pair[Momentum[p2, D], Momentum[p6, \ +D]]*Pair[Momentum[p4, D], Momentum[p8, D]] - Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p1, D], Momentum[p6, \ +D]]*Pair[Momentum[p2, D], Momentum[p7, D]]*Pair[Momentum[p4, D], \ +Momentum[p8, D]] - Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p7, D]]*Pair[Momentum[p3, D], \ +Momentum[p6, D]]*Pair[Momentum[p4, D], Momentum[p8, D]] + \ +Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p7, D]]*Pair[Momentum[p3, D], Momentum[p6, \ +D]]*Pair[Momentum[p4, D], Momentum[p8, D]] + Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p6, \ +D]]*Pair[Momentum[p3, D], Momentum[p7, D]]*Pair[Momentum[p4, D], \ +Momentum[p8, D]] - Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p6, D]]*Pair[Momentum[p3, D], \ +Momentum[p7, D]]*Pair[Momentum[p4, D], Momentum[p8, D]]"}, +{"fcstEpsContract-ID11", +"EpsContract[LCD[][p1,p2,p3,p4]LCD[][p1,p2,p7,p8]]", +"-(Pair[Momentum[p1, D], Momentum[p4, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p3, \ +D]]*Pair[Momentum[p2, D], Momentum[p7, D]]) + Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p1, D], Momentum[p8, \ +D]]*Pair[Momentum[p2, D], Momentum[p4, D]]*Pair[Momentum[p2, D], \ +Momentum[p7, D]] + Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p1, D], Momentum[p7, D]]*Pair[Momentum[p2, D], \ +Momentum[p3, D]]*Pair[Momentum[p2, D], Momentum[p8, D]] - \ +Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p1, D], \ +Momentum[p7, D]]*Pair[Momentum[p2, D], Momentum[p4, \ +D]]*Pair[Momentum[p2, D], Momentum[p8, D]] + Pair[Momentum[p1, D], \ +Momentum[p4, D]]*Pair[Momentum[p1, D], Momentum[p8, \ +D]]*Pair[Momentum[p2, D], Momentum[p2, D]]*Pair[Momentum[p3, D], \ +Momentum[p7, D]] - Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p8, D]]*Pair[Momentum[p2, D], \ +Momentum[p4, D]]*Pair[Momentum[p3, D], Momentum[p7, D]] - \ +Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p1, D], \ +Momentum[p4, D]]*Pair[Momentum[p2, D], Momentum[p8, \ +D]]*Pair[Momentum[p3, D], Momentum[p7, D]] + Pair[Momentum[p1, D], \ +Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p4, \ +D]]*Pair[Momentum[p2, D], Momentum[p8, D]]*Pair[Momentum[p3, D], \ +Momentum[p7, D]] - Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p1, D], Momentum[p7, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]]*Pair[Momentum[p3, D], Momentum[p8, D]] + \ +Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p1, D], \ +Momentum[p7, D]]*Pair[Momentum[p2, D], Momentum[p4, \ +D]]*Pair[Momentum[p3, D], Momentum[p8, D]] + Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p2, D], Momentum[p7, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]] - Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p4, D]]*Pair[Momentum[p2, D], \ +Momentum[p7, D]]*Pair[Momentum[p3, D], Momentum[p8, D]] - \ +Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p2, \ +D]]*Pair[Momentum[p4, D], Momentum[p7, D]] + Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p8, \ +D]]*Pair[Momentum[p2, D], Momentum[p3, D]]*Pair[Momentum[p4, D], \ +Momentum[p7, D]] + Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]]*Pair[Momentum[p4, D], Momentum[p7, D]] - \ +Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p3, D]]*Pair[Momentum[p2, D], Momentum[p8, \ +D]]*Pair[Momentum[p4, D], Momentum[p7, D]] - Pair[Momentum[p1, D], \ +Momentum[p2, D]]^2*Pair[Momentum[p3, D], Momentum[p8, \ +D]]*Pair[Momentum[p4, D], Momentum[p7, D]] + Pair[Momentum[p1, D], \ +Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, \ +D]]*Pair[Momentum[p3, D], Momentum[p8, D]]*Pair[Momentum[p4, D], \ +Momentum[p7, D]] + Pair[Momentum[p1, D], Momentum[p3, \ +D]]*Pair[Momentum[p1, D], Momentum[p7, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]]*Pair[Momentum[p4, D], Momentum[p8, D]] - \ +Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p1, D], \ +Momentum[p7, D]]*Pair[Momentum[p2, D], Momentum[p3, \ +D]]*Pair[Momentum[p4, D], Momentum[p8, D]] - Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p3, \ +D]]*Pair[Momentum[p2, D], Momentum[p7, D]]*Pair[Momentum[p4, D], \ +Momentum[p8, D]] + Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p3, D]]*Pair[Momentum[p2, D], \ +Momentum[p7, D]]*Pair[Momentum[p4, D], Momentum[p8, D]] + \ +Pair[Momentum[p1, D], Momentum[p2, D]]^2*Pair[Momentum[p3, D], \ +Momentum[p7, D]]*Pair[Momentum[p4, D], Momentum[p8, D]] - \ +Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]]*Pair[Momentum[p3, D], Momentum[p7, \ +D]]*Pair[Momentum[p4, D], Momentum[p8, D]]"}, +{"fcstEpsContract-ID12", +"EpsContract[LCD[][p1,p2,p3,p4]LCD[][p1,p2,p3,p8]]", +"-(Pair[Momentum[p1, D], Momentum[p4, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p3, D]]^2) + \ +Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p3, \ +D]]*Pair[Momentum[p2, D], Momentum[p4, D]] + Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p2, D], Momentum[p3, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]] - Pair[Momentum[p1, D], Momentum[p3, \ +D]]^2*Pair[Momentum[p2, D], Momentum[p4, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]] + Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p1, D], Momentum[p8, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]]*Pair[Momentum[p3, D], Momentum[p3, D]] - \ +Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p4, \ +D]]*Pair[Momentum[p3, D], Momentum[p3, D]] - Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p2, D], Momentum[p8, D]]*Pair[Momentum[p3, D], \ +Momentum[p3, D]] + Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p4, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]]*Pair[Momentum[p3, D], Momentum[p3, D]] - \ +Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p1, D], \ +Momentum[p8, D]]*Pair[Momentum[p2, D], Momentum[p2, \ +D]]*Pair[Momentum[p3, D], Momentum[p4, D]] + Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p8, \ +D]]*Pair[Momentum[p2, D], Momentum[p3, D]]*Pair[Momentum[p3, D], \ +Momentum[p4, D]] + Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p2, D], \ +Momentum[p8, D]]*Pair[Momentum[p3, D], Momentum[p4, D]] - \ +Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p3, D]]*Pair[Momentum[p2, D], Momentum[p8, \ +D]]*Pair[Momentum[p3, D], Momentum[p4, D]] - Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p2, D], Momentum[p2, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]] + Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p4, D]]*Pair[Momentum[p2, D], \ +Momentum[p3, D]]*Pair[Momentum[p3, D], Momentum[p8, D]] + \ +Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p2, D], Momentum[p4, \ +D]]*Pair[Momentum[p3, D], Momentum[p8, D]] - Pair[Momentum[p1, D], \ +Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p3, \ +D]]*Pair[Momentum[p2, D], Momentum[p4, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]] - Pair[Momentum[p1, D], Momentum[p2, \ +D]]^2*Pair[Momentum[p3, D], Momentum[p4, D]]*Pair[Momentum[p3, D], \ +Momentum[p8, D]] + Pair[Momentum[p1, D], Momentum[p1, \ +D]]*Pair[Momentum[p2, D], Momentum[p2, D]]*Pair[Momentum[p3, D], \ +Momentum[p4, D]]*Pair[Momentum[p3, D], Momentum[p8, D]] + \ +Pair[Momentum[p1, D], Momentum[p3, D]]^2*Pair[Momentum[p2, D], \ +Momentum[p2, D]]*Pair[Momentum[p4, D], Momentum[p8, D]] - \ +2*Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p2, D], Momentum[p3, \ +D]]*Pair[Momentum[p4, D], Momentum[p8, D]] + Pair[Momentum[p1, D], \ +Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p3, \ +D]]^2*Pair[Momentum[p4, D], Momentum[p8, D]] + Pair[Momentum[p1, D], \ +Momentum[p2, D]]^2*Pair[Momentum[p3, D], Momentum[p3, \ +D]]*Pair[Momentum[p4, D], Momentum[p8, D]] - Pair[Momentum[p1, D], \ +Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, \ +D]]*Pair[Momentum[p3, D], Momentum[p3, D]]*Pair[Momentum[p4, D], \ +Momentum[p8, D]]"}, +{"fcstEpsContract-ID13", +"EpsContract[LCD[][p1,p2,p3,p4]LCD[][p1,p2,p3,p4]]", +"-(Pair[Momentum[p1, D], Momentum[p4, D]]^2*Pair[Momentum[p2, D], \ +Momentum[p3, D]]^2) + 2*Pair[Momentum[p1, D], Momentum[p3, \ +D]]*Pair[Momentum[p1, D], Momentum[p4, D]]*Pair[Momentum[p2, D], \ +Momentum[p3, D]]*Pair[Momentum[p2, D], Momentum[p4, D]] - \ +Pair[Momentum[p1, D], Momentum[p3, D]]^2*Pair[Momentum[p2, D], \ +Momentum[p4, D]]^2 + Pair[Momentum[p1, D], Momentum[p4, \ +D]]^2*Pair[Momentum[p2, D], Momentum[p2, D]]*Pair[Momentum[p3, D], \ +Momentum[p3, D]] - 2*Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p4, D]]*Pair[Momentum[p2, D], \ +Momentum[p4, D]]*Pair[Momentum[p3, D], Momentum[p3, D]] + \ +Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p4, D]]^2*Pair[Momentum[p3, D], Momentum[p3, D]] - \ +2*Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p1, D], \ +Momentum[p4, D]]*Pair[Momentum[p2, D], Momentum[p2, \ +D]]*Pair[Momentum[p3, D], Momentum[p4, D]] + 2*Pair[Momentum[p1, D], \ +Momentum[p2, D]]*Pair[Momentum[p1, D], Momentum[p4, \ +D]]*Pair[Momentum[p2, D], Momentum[p3, D]]*Pair[Momentum[p3, D], \ +Momentum[p4, D]] + 2*Pair[Momentum[p1, D], Momentum[p2, \ +D]]*Pair[Momentum[p1, D], Momentum[p3, D]]*Pair[Momentum[p2, D], \ +Momentum[p4, D]]*Pair[Momentum[p3, D], Momentum[p4, D]] - \ +2*Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p3, D]]*Pair[Momentum[p2, D], Momentum[p4, \ +D]]*Pair[Momentum[p3, D], Momentum[p4, D]] - Pair[Momentum[p1, D], \ +Momentum[p2, D]]^2*Pair[Momentum[p3, D], Momentum[p4, D]]^2 + \ +Pair[Momentum[p1, D], Momentum[p1, D]]*Pair[Momentum[p2, D], \ +Momentum[p2, D]]*Pair[Momentum[p3, D], Momentum[p4, D]]^2 + \ +Pair[Momentum[p1, D], Momentum[p3, D]]^2*Pair[Momentum[p2, D], \ +Momentum[p2, D]]*Pair[Momentum[p4, D], Momentum[p4, D]] - \ +2*Pair[Momentum[p1, D], Momentum[p2, D]]*Pair[Momentum[p1, D], \ +Momentum[p3, D]]*Pair[Momentum[p2, D], Momentum[p3, \ +D]]*Pair[Momentum[p4, D], Momentum[p4, D]] + Pair[Momentum[p1, D], \ +Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p3, \ +D]]^2*Pair[Momentum[p4, D], Momentum[p4, D]] + Pair[Momentum[p1, D], \ +Momentum[p2, D]]^2*Pair[Momentum[p3, D], Momentum[p3, \ +D]]*Pair[Momentum[p4, D], Momentum[p4, D]] - Pair[Momentum[p1, D], \ +Momentum[p1, D]]*Pair[Momentum[p2, D], Momentum[p2, \ +D]]*Pair[Momentum[p3, D], Momentum[p3, D]]*Pair[Momentum[p4, D], \ +Momentum[p4, D]]"}, +{"fcstEpsContract-ID14", +"EpsContract[LC[i1,i2,i3,i4]LC[i5,i6,i7,i8]]", +"-(Pair[LorentzIndex[i1], LorentzIndex[i8]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i4], LorentzIndex[i5]]) + \ +Pair[LorentzIndex[i1], LorentzIndex[i7]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i4], LorentzIndex[i5]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i8]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i5]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i6]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i5]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i7]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i4], LorentzIndex[i5]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i6]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i4], LorentzIndex[i5]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i8]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i4], LorentzIndex[i6]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i7]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i4], LorentzIndex[i6]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i8]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i6]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i5]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i6]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i7]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i4], LorentzIndex[i6]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i5]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i4], LorentzIndex[i6]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i8]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i4], LorentzIndex[i7]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i6]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i4], LorentzIndex[i7]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i8]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i4], LorentzIndex[i7]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i5]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i4], LorentzIndex[i7]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i6]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i4], LorentzIndex[i7]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i5]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i4], LorentzIndex[i7]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i7]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i4], LorentzIndex[i8]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i6]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i4], LorentzIndex[i8]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i7]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i4], LorentzIndex[i8]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i5]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i4], LorentzIndex[i8]] + \ +Pair[LorentzIndex[i1], LorentzIndex[i6]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i5]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i8]] - \ +Pair[LorentzIndex[i1], LorentzIndex[i5]]*Pair[LorentzIndex[i2], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i8]]"}, +{"fcstEpsContract-ID15", +"EpsContract[LC[i1,i2,i3,i4]LC[i1,i6,i7,i8]]", +"Pair[LorentzIndex[i2], LorentzIndex[i8]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i6]] - \ +Pair[LorentzIndex[i2], LorentzIndex[i7]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i4], LorentzIndex[i6]] - \ +Pair[LorentzIndex[i2], LorentzIndex[i8]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i4], LorentzIndex[i7]] + \ +Pair[LorentzIndex[i2], LorentzIndex[i6]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i8]]*Pair[LorentzIndex[i4], LorentzIndex[i7]] + \ +Pair[LorentzIndex[i2], LorentzIndex[i7]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i6]]*Pair[LorentzIndex[i4], LorentzIndex[i8]] - \ +Pair[LorentzIndex[i2], LorentzIndex[i6]]*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i8]]"}, +{"fcstEpsContract-ID16", +"EpsContract[LC[i1,i2,i3,i4]LC[i1,i2,i7,i8]]", +"2*Pair[LorentzIndex[i3], LorentzIndex[i8]]*Pair[LorentzIndex[i4], \ +LorentzIndex[i7]] - 2*Pair[LorentzIndex[i3], \ +LorentzIndex[i7]]*Pair[LorentzIndex[i4], LorentzIndex[i8]]"}, +{"fcstEpsContract-ID17", +"EpsContract[LC[i1,i2,i3,i4]LC[i1,i2,i3,i8]]", +"-6*Pair[LorentzIndex[i4], LorentzIndex[i8]]"}, +{"fcstEpsContract-ID18", +"EpsContract[LC[i1,i2,i3,i4]LC[i1,i2,i3,i4]]", "-24"}, +{"fcstEpsContract-ID19", +"EpsContract[LC[][p1,p2,p3,p4]LC[][p5,p6,p7,p8]]", +"-(Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p5]]) + Pair[Momentum[p1], Momentum[p7]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p5]] + Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p5]] - Pair[Momentum[p1], Momentum[p6]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p5]] - Pair[Momentum[p1], Momentum[p7]]*Pair[Momentum[p2], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p5]] + Pair[Momentum[p1], Momentum[p6]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p5]] + Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p5]]*Pair[Momentum[p4], \ +Momentum[p6]] - Pair[Momentum[p1], Momentum[p7]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p5]]*Pair[Momentum[p4], \ +Momentum[p6]] - Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p5]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p6]] + Pair[Momentum[p1], Momentum[p5]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p6]] + Pair[Momentum[p1], Momentum[p7]]*Pair[Momentum[p2], \ +Momentum[p5]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p6]] - Pair[Momentum[p1], Momentum[p5]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p6]] - Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p5]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p6]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p5]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p5]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p5]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p6]]*Pair[Momentum[p2], \ +Momentum[p5]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p5]]*Pair[Momentum[p2], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p7]]*Pair[Momentum[p2], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p5]]*Pair[Momentum[p4], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p6]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p5]]*Pair[Momentum[p4], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p7]]*Pair[Momentum[p2], \ +Momentum[p5]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p5]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p6]]*Pair[Momentum[p2], \ +Momentum[p5]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p5]]*Pair[Momentum[p2], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p8]]"}, +{"fcstEpsContract-ID20", +"EpsContract[LC[][p1,p2,p3,p4]LC[][p1,p6,p7,p8]]", +"-(Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p7]]*Pair[Momentum[p3], \ +Momentum[p6]]) + Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p2], Momentum[p8]]*Pair[Momentum[p3], \ +Momentum[p6]] + Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p6]]*Pair[Momentum[p3], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p6]]*Pair[Momentum[p2], Momentum[p8]]*Pair[Momentum[p3], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p2], Momentum[p6]]*Pair[Momentum[p3], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p6]]*Pair[Momentum[p2], Momentum[p7]]*Pair[Momentum[p3], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p6]] - Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p2], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p6]] - Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p6]] + Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p6]] + Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p6]] - Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p6]] - Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p6]]*Pair[Momentum[p2], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p2], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p6]]*Pair[Momentum[p2], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p3], Momentum[p6]]*Pair[Momentum[p4], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p6]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p8]]"}, +{"fcstEpsContract-ID21", +"EpsContract[LC[][p1,p2,p3,p4]LC[][p1,p2,p7,p8]]", +"-(Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p7]]) + Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p4]]*Pair[Momentum[p2], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p2], Momentum[p4]]*Pair[Momentum[p2], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p2]]*Pair[Momentum[p3], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p4]]*Pair[Momentum[p3], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p4]]*Pair[Momentum[p2], Momentum[p8]]*Pair[Momentum[p3], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p4]]*Pair[Momentum[p2], Momentum[p8]]*Pair[Momentum[p3], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p2], Momentum[p2]]*Pair[Momentum[p3], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p7]]*Pair[Momentum[p2], Momentum[p4]]*Pair[Momentum[p3], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p4]]*Pair[Momentum[p2], Momentum[p7]]*Pair[Momentum[p3], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p4]]*Pair[Momentum[p2], Momentum[p7]]*Pair[Momentum[p3], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p2]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p4], \ +Momentum[p7]] + Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p3]]*Pair[Momentum[p2], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p3]]*Pair[Momentum[p2], Momentum[p8]]*Pair[Momentum[p4], \ +Momentum[p7]] - Pair[Momentum[p1], Momentum[p2]]^2*Pair[Momentum[p3], \ +Momentum[p8]]*Pair[Momentum[p4], Momentum[p7]] + Pair[Momentum[p1], \ +Momentum[p1]]*Pair[Momentum[p2], Momentum[p2]]*Pair[Momentum[p3], \ +Momentum[p8]]*Pair[Momentum[p4], Momentum[p7]] + Pair[Momentum[p1], \ +Momentum[p3]]*Pair[Momentum[p1], Momentum[p7]]*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p4], Momentum[p8]] - Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p7]]*Pair[Momentum[p2], \ +Momentum[p3]]*Pair[Momentum[p4], Momentum[p8]] - Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p4], Momentum[p8]] + Pair[Momentum[p1], \ +Momentum[p1]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p7]]*Pair[Momentum[p4], Momentum[p8]] + Pair[Momentum[p1], \ +Momentum[p2]]^2*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p3], Momentum[p7]]*Pair[Momentum[p4], \ +Momentum[p8]]"}, +{"fcstEpsContract-ID22", +"EpsContract[LC[][p1,p2,p3,p4]LC[][p1,p2,p3,p8]]", +"-(Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p3]]^2) + \ +Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p8]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p4]] + Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p4]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p8]] - Pair[Momentum[p1], Momentum[p3]]^2*Pair[Momentum[p2], \ +Momentum[p4]]*Pair[Momentum[p2], Momentum[p8]] + Pair[Momentum[p1], \ +Momentum[p4]]*Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p3], Momentum[p3]] - Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p4]]*Pair[Momentum[p3], Momentum[p3]] - Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p3]] + Pair[Momentum[p1], \ +Momentum[p1]]*Pair[Momentum[p2], Momentum[p4]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p3]] - Pair[Momentum[p1], \ +Momentum[p3]]*Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p3], Momentum[p4]] + Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p8]]*Pair[Momentum[p2], \ +Momentum[p3]]*Pair[Momentum[p3], Momentum[p4]] + Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p4]] - Pair[Momentum[p1], \ +Momentum[p1]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p8]]*Pair[Momentum[p3], Momentum[p4]] - Pair[Momentum[p1], \ +Momentum[p3]]*Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p3], Momentum[p8]] + Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p2], \ +Momentum[p3]]*Pair[Momentum[p3], Momentum[p8]] + Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p4]]*Pair[Momentum[p3], Momentum[p8]] - Pair[Momentum[p1], \ +Momentum[p1]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p4]]*Pair[Momentum[p3], Momentum[p8]] - Pair[Momentum[p1], \ +Momentum[p2]]^2*Pair[Momentum[p3], Momentum[p4]]*Pair[Momentum[p3], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p3], Momentum[p4]]*Pair[Momentum[p3], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p3]]^2*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p4], Momentum[p8]] - 2*Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p2], \ +Momentum[p3]]*Pair[Momentum[p4], Momentum[p8]] + Pair[Momentum[p1], \ +Momentum[p1]]*Pair[Momentum[p2], Momentum[p3]]^2*Pair[Momentum[p4], \ +Momentum[p8]] + Pair[Momentum[p1], Momentum[p2]]^2*Pair[Momentum[p3], \ +Momentum[p3]]*Pair[Momentum[p4], Momentum[p8]] - Pair[Momentum[p1], \ +Momentum[p1]]*Pair[Momentum[p2], Momentum[p2]]*Pair[Momentum[p3], \ +Momentum[p3]]*Pair[Momentum[p4], Momentum[p8]]"}, +{"fcstEpsContract-ID23", +"EpsContract[LC[][p1,p2,p3,p4]LC[][p1,p2,p3,p4]]", +"-(Pair[Momentum[p1], Momentum[p4]]^2*Pair[Momentum[p2], \ +Momentum[p3]]^2) + 2*Pair[Momentum[p1], \ +Momentum[p3]]*Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p2], \ +Momentum[p3]]*Pair[Momentum[p2], Momentum[p4]] - Pair[Momentum[p1], \ +Momentum[p3]]^2*Pair[Momentum[p2], Momentum[p4]]^2 + \ +Pair[Momentum[p1], Momentum[p4]]^2*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p3], Momentum[p3]] - 2*Pair[Momentum[p1], \ +Momentum[p2]]*Pair[Momentum[p1], Momentum[p4]]*Pair[Momentum[p2], \ +Momentum[p4]]*Pair[Momentum[p3], Momentum[p3]] + Pair[Momentum[p1], \ +Momentum[p1]]*Pair[Momentum[p2], Momentum[p4]]^2*Pair[Momentum[p3], \ +Momentum[p3]] - 2*Pair[Momentum[p1], Momentum[p3]]*Pair[Momentum[p1], \ +Momentum[p4]]*Pair[Momentum[p2], Momentum[p2]]*Pair[Momentum[p3], \ +Momentum[p4]] + 2*Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p4]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p3], \ +Momentum[p4]] + 2*Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p3]]*Pair[Momentum[p2], Momentum[p4]]*Pair[Momentum[p3], \ +Momentum[p4]] - 2*Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p3]]*Pair[Momentum[p2], Momentum[p4]]*Pair[Momentum[p3], \ +Momentum[p4]] - Pair[Momentum[p1], Momentum[p2]]^2*Pair[Momentum[p3], \ +Momentum[p4]]^2 + Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p3], Momentum[p4]]^2 + Pair[Momentum[p1], \ +Momentum[p3]]^2*Pair[Momentum[p2], Momentum[p2]]*Pair[Momentum[p4], \ +Momentum[p4]] - 2*Pair[Momentum[p1], Momentum[p2]]*Pair[Momentum[p1], \ +Momentum[p3]]*Pair[Momentum[p2], Momentum[p3]]*Pair[Momentum[p4], \ +Momentum[p4]] + Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p3]]^2*Pair[Momentum[p4], Momentum[p4]] + Pair[Momentum[p1], \ +Momentum[p2]]^2*Pair[Momentum[p3], Momentum[p3]]*Pair[Momentum[p4], \ +Momentum[p4]] - Pair[Momentum[p1], Momentum[p1]]*Pair[Momentum[p2], \ +Momentum[p2]]*Pair[Momentum[p3], Momentum[p3]]*Pair[Momentum[p4], \ +Momentum[p4]]"}, +{"fcstEpsContract-ID24", "EpsContract[CLC[i1,i2,i3]CLC[i4,i5,i6]]", +"-(CartesianPair[CartesianIndex[i1], CartesianIndex[i6]]*CartesianPair[CartesianIndex[i2], \ +CartesianIndex[i5]]*CartesianPair[CartesianIndex[i3], CartesianIndex[i4]]) + CartesianPair[CartesianIndex[i1], \ +CartesianIndex[i5]]*CartesianPair[CartesianIndex[i2], CartesianIndex[i6]]*CartesianPair[CartesianIndex[i3], \ +CartesianIndex[i4]] + CartesianPair[CartesianIndex[i1], CartesianIndex[i6]]*CartesianPair[CartesianIndex[i2], \ +CartesianIndex[i4]]*CartesianPair[CartesianIndex[i3], CartesianIndex[i5]] - CartesianPair[CartesianIndex[i1], \ +CartesianIndex[i4]]*CartesianPair[CartesianIndex[i2], CartesianIndex[i6]]*CartesianPair[CartesianIndex[i3], \ +CartesianIndex[i5]] - CartesianPair[CartesianIndex[i1], CartesianIndex[i5]]*CartesianPair[CartesianIndex[i2], \ +CartesianIndex[i4]]*CartesianPair[CartesianIndex[i3], CartesianIndex[i6]] + CartesianPair[CartesianIndex[i1], \ +CartesianIndex[i4]]*CartesianPair[CartesianIndex[i2], CartesianIndex[i5]]*CartesianPair[CartesianIndex[i3], \ +CartesianIndex[i6]]"}, +{"fcstEpsContract-ID25", "EpsContract[CLC[i1,i2,i3]CLC[i1,i5,i6]]", +"-(CartesianPair[CartesianIndex[i2], CartesianIndex[i6]]*CartesianPair[CartesianIndex[i3], CartesianIndex[i5]]) + \ +CartesianPair[CartesianIndex[i2], CartesianIndex[i5]]*CartesianPair[CartesianIndex[i3], CartesianIndex[i6]]"}, +{"fcstEpsContract-ID26", "EpsContract[CLC[i1,i2,i3]CLC[i1,i2,i6]]", +"2*CartesianPair[CartesianIndex[i3], CartesianIndex[i6]]"}, +{"fcstEpsContract-ID27", "EpsContract[CLC[i1,i2,i3]CLC[i1,i2,i3]]", +"6"}, +{"fcstEpsContract-ID28", +"EpsContract[CLC[][p1,p2,p3]CLC[][p4,p5,p6]]", +"-(CartesianPair[CartesianMomentum[p1], CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p5]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]]) + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p5]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]] + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p4]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p5]] - \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p4]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p5]] - \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p5]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p4]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p6]] + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p4]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p5]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p6]]"}, +{"fcstEpsContract-ID29", +"EpsContract[CLC[][p1,p2,p3]CLC[][p1,p5,p6]]", +"-(CartesianPair[CartesianMomentum[p1], CartesianMomentum[p3]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p2], CartesianMomentum[p5]]) + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p3]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p5]]*CartesianPair[CartesianMomentum[p2], CartesianMomentum[p6]] + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p5]] - \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p1]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p5]] - \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p5]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p6]] + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p1]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p5]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p6]]"}, +{"fcstEpsContract-ID30", +"EpsContract[CLC[][p1,p2,p3]CLC[][p1,p2,p6]]", +"-(CartesianPair[CartesianMomentum[p1], CartesianMomentum[p3]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p2], CartesianMomentum[p2]]) + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p6]]*CartesianPair[CartesianMomentum[p2], CartesianMomentum[p3]] + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p3]]*CartesianPair[CartesianMomentum[p2], CartesianMomentum[p6]] - \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p1]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p3]]*CartesianPair[CartesianMomentum[p2], CartesianMomentum[p6]] - \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]]^2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p6]] + CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p1]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p2]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p6]]"}, +{"fcstEpsContract-ID31", +"EpsContract[CLC[][p1,p2,p3]CLC[][p1,p2,p3]]", +"-(CartesianPair[CartesianMomentum[p1], CartesianMomentum[p3]]^2*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p2]]) + 2*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]]*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p3]]*CartesianPair[CartesianMomentum[p2], CartesianMomentum[p3]] - \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p1]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p3]]^2 - CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]]^2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p3]] + \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p1]]*CartesianPair[CartesianMomentum[p2], \ +CartesianMomentum[p2]]*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p3]]"}, +{"fcstEpsContract-ID32", +"EpsContract[CLCD[i1,i2,i3]CLCD[i4,i5,i6]]", +"-(CartesianPair[CartesianIndex[i1, -1 + D], CartesianIndex[i6, -1 + D]]*CartesianPair[CartesianIndex[i2, \ +-1 + D], CartesianIndex[i5, -1 + D]]*CartesianPair[CartesianIndex[i3, -1 + D], CartesianIndex[i4, -1 \ ++ D]]) + CartesianPair[CartesianIndex[i1, -1 + D], CartesianIndex[i5, -1 + \ +D]]*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i6, -1 + D]]*CartesianPair[CartesianIndex[i3, -1 \ ++ D], CartesianIndex[i4, -1 + D]] + CartesianPair[CartesianIndex[i1, -1 + D], CartesianIndex[i6, -1 + \ +D]]*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i4, -1 + D]]*CartesianPair[CartesianIndex[i3, -1 \ ++ D], CartesianIndex[i5, -1 + D]] - CartesianPair[CartesianIndex[i1, -1 + D], CartesianIndex[i4, -1 + \ +D]]*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i6, -1 + D]]*CartesianPair[CartesianIndex[i3, -1 \ ++ D], CartesianIndex[i5, -1 + D]] - CartesianPair[CartesianIndex[i1, -1 + D], CartesianIndex[i5, -1 + \ +D]]*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i4, -1 + D]]*CartesianPair[CartesianIndex[i3, -1 \ ++ D], CartesianIndex[i6, -1 + D]] + CartesianPair[CartesianIndex[i1, -1 + D], CartesianIndex[i4, -1 + \ +D]]*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i5, -1 + D]]*CartesianPair[CartesianIndex[i3, -1 \ ++ D], CartesianIndex[i6, -1 + D]]"}, +{"fcstEpsContract-ID33", +"EpsContract[CLCD[i1,i2,i3]CLCD[i1,i5,i6]]", +"3*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i6, -1 + D]]*CartesianPair[CartesianIndex[i3, \ +-1 + D], CartesianIndex[i5, -1 + D]] - D*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i6, \ +-1 + D]]*CartesianPair[CartesianIndex[i3, -1 + D], CartesianIndex[i5, -1 + D]] - \ +3*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i5, -1 + D]]*CartesianPair[CartesianIndex[i3, -1 + \ +D], CartesianIndex[i6, -1 + D]] + D*CartesianPair[CartesianIndex[i2, -1 + D], CartesianIndex[i5, -1 + \ +D]]*CartesianPair[CartesianIndex[i3, -1 + D], CartesianIndex[i6, -1 + D]]"}, +{"fcstEpsContract-ID34", +"EpsContract[CLCD[i1,i2,i3]CLCD[i1,i2,i6]]", +"6*CartesianPair[CartesianIndex[i3, -1 + D], CartesianIndex[i6, -1 + D]] - \ +5*D*CartesianPair[CartesianIndex[i3, -1 + D], CartesianIndex[i6, -1 + D]] + \ +D^2*CartesianPair[CartesianIndex[i3, -1 + D], CartesianIndex[i6, -1 + D]]"}, +{"fcstEpsContract-ID35", +"EpsContract[CLCD[i1,i2,i3]CLCD[i1,i2,i3]]", +"-6 + 11*D - 6*D^2 + D^3"}, +{"fcstEpsContract-ID36", +"EpsContract[CLCD[][p1,p2,p3]CLCD[][p4,p5,p6]]", +"-(CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p5, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, -1 + D]]) + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p5, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, -1 + D]] + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p4, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p5, -1 + D]] - \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p4, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p5, -1 + D]] - \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p5, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p4, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p6, -1 + D]] + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p4, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p5, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p6, -1 + D]]"}, +{"fcstEpsContract-ID37", +"EpsContract[CLCD[][p1,p2,p3]CLCD[][p1,p5,p6]]", +"-(CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p3, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p5, -1 + D]]) + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p3, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p5, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p6, -1 + D]] + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p5, -1 + D]] - \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p5, -1 + D]] - \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p5, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p6, -1 + D]] + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p5, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p6, -1 + D]]"}, +{"fcstEpsContract-ID38", +"EpsContract[CLCD[][p1,p2,p3]CLCD[][p1,p2,p6]]", +"-(CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p3, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p2, -1 + D]]) + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p6, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p3, -1 + D]] + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p3, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p6, -1 + D]] - \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p3, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p6, -1 + D]] - \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + \ +D]]^2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p6, -1 + D]] + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p2, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p6, -1 + D]]"}, +{"fcstEpsContract-ID39", +"EpsContract[CLCD[][p1,p2,p3]CLCD[][p1,p2,p3]]", +"-(CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p3, -1 + \ +D]]^2*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p2, -1 + D]]) + \ +2*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + \ +D]]*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p3, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p3, -1 + D]] - \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p3, -1 + D]]^2 - \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + \ +D]]^2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p3, -1 + D]] + \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p1, -1 + \ +D]]*CartesianPair[CartesianMomentum[p2, -1 + D], CartesianMomentum[p2, -1 + \ +D]]*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p3, -1 + D]]"}, +{"fcstEpsContract-ID40", +"LC[0][p1, p2, p3] LC[0][q1, q2, q3]// EpsContract // FCE", +"-(CSP[p1, q3]*CSP[p2, q2]*CSP[p3, q1]) + CSP[p1, q2]*CSP[p2, q3]*CSP[p3, q1] + +CSP[p1, q3]*CSP[p2, q1]*CSP[p3, q2] - CSP[p1, q1]*CSP[p2, q3]*CSP[p3, q2] - + CSP[p1, q2]*CSP[p2, q1]*CSP[p3, q3] + CSP[p1, q1]*CSP[p2, q2]*CSP[p3, q3]"}, +{"fcstEpsContract-ID41", +"LC[0][p1, p2, p3] LC[0][q1, q2, q3] // LorentzToCartesian // EpsContract // FCE","-CSP[p1, q3] CSP[p2, q2] CSP[p3, q1] + +CSP[p1, q2] CSP[p2, q3] CSP[p3, q1] + +CSP[p1, q3] CSP[p2, q1] CSP[p3, q2] - +CSP[p1, q1] CSP[p2, q3] CSP[p3, q2] - +CSP[p1, q2] CSP[p2, q1] CSP[p3, q3] + +CSP[p1, q1] CSP[p2, q2] CSP[p3, q3]"} +}) diff --git a/Tests/Lorentz/EpsContractFreeQ.test b/Tests/Lorentz/EpsContractFreeQ.test new file mode 100644 index 000000000..ae1b8fb67 --- /dev/null +++ b/Tests/Lorentz/EpsContractFreeQ.test @@ -0,0 +1,33 @@ + + +(* :Title: EpsContractFreeQ.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for EpsContractFreeQ *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstEpsContractFreeQ = +({ +{"fcstEpsContractFreeQ-ID1", "EpsContractFreeQ[0]", "True"}, +{"fcstEpsContractFreeQ-ID2", +"EpsContractFreeQ[FCI[LC[p1,p2,p3,p4]]]", "True"}, +{"fcstEpsContractFreeQ-ID3", +"EpsContractFreeQ[FCI[LC[p1,p2,p3,p4]^2]]", "False"}, +{"fcstEpsContractFreeQ-ID4", +"EpsContractFreeQ[xxx \ +Sum[Eps[LorentzIndex[i[s]],LorentzIndex[j[s]],LorentzIndex[k[s]],\ +LorentzIndex[l[s]]],{s,1,5000}]]", "True"}, +{"fcstEpsContractFreeQ-ID5", +"EpsContractFreeQ[xxx \ +Sum[Eps[LorentzIndex[i[s]],LorentzIndex[j[s]],LorentzIndex[k[s]],\ +LorentzIndex[l[s]]],{s,1,5000}]+FCI[LC[][p1,p2,p3,p4]LC[][p5,p6,p7,p8]\ +]]", "False"}, +{"fcstEpsContractFreeQ-ID6", Null, "Null"} +}); diff --git a/Tests/Lorentz/EpsEvaluate.test b/Tests/Lorentz/EpsEvaluate.test index d1beff2fe..956d47ac3 100644 --- a/Tests/Lorentz/EpsEvaluate.test +++ b/Tests/Lorentz/EpsEvaluate.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for EpsEvaluate *) @@ -38,5 +38,27 @@ Tests`Lorentz`fcstEpsEvaluate = { 0] // EpsEvaluate","0"}, {"fcstEpsEvaluate-ID8","EpsEvaluate[LC[a, b][p1 + p2, p3 + p4] + LC[a, b][q1 + q2, q3 + q4], Momentum -> {p1}] // FCE","LC[a, b][p1, p3] + LC[a, b][p1, p4] + LC[a, b][p2, p3] + -LC[a, b][p2, p4] + LC[a, b][q1 + q2, q3 + q4]"} +LC[a, b][p2, p4] + LC[a, b][q1 + q2, q3 + q4]"}, +{"fcstEpsEvaluate-ID9","EpsEvaluate[ +Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p2] + CartesianMomentum[p3]]]","Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p2]] + +Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p3]]"}, +{"fcstEpsEvaluate-ID10","EpsEvaluate[Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p2 + p3]]]","Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p2]] + +Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p3]]"}, +{"fcstEpsEvaluate-ID11","EpsEvaluate[ +Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p1] + CartesianMomentum[p2]]]","Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p2]]"}, +{"fcstEpsEvaluate-ID12","EpsEvaluate[Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p1 + p2]]]","Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p2]]"}, +{"fcstEpsEvaluate-ID13","EpsEvaluate[Eps[CartesianIndex[i], x CartesianMomentum[p1], CartesianMomentum[p2]]]","x Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p2]]"}, +{"fcstEpsEvaluate-ID14","Eps[ExplicitLorentzIndex[0], CartesianMomentum[p1, D - 1], CartesianMomentum[p2, D - 1], CartesianMomentum[p3, D - 1]] // EpsEvaluate", +"Eps[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + D], CartesianMomentum[p3, -1 + D]]"}, +{"fcstEpsEvaluate-ID15","Eps[ExplicitLorentzIndex[0], CartesianMomentum[p1], CartesianMomentum[p2], +CartesianMomentum[p3]] // EpsEvaluate", +"Eps[CartesianMomentum[p1], CartesianMomentum[p2], CartesianMomentum[p3]]"}, +{"fcstEpsEvaluate-ID16","Eps[ExplicitLorentzIndex[0], Momentum[p1, D], Momentum[p2, D], +Momentum[p3, D]] // EpsEvaluate", +"-Eps[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + D], +CartesianMomentum[p3, -1 + D]]"}, +{"fcstEpsEvaluate-ID17","Eps[ExplicitLorentzIndex[0], Momentum[p1], Momentum[p2], Momentum[p3]] // EpsEvaluate", +"-Eps[CartesianMomentum[p1], CartesianMomentum[p2], CartesianMomentum[p3]]"} } + + diff --git a/Tests/Lorentz/ExpandScalarProduct.test b/Tests/Lorentz/ExpandScalarProduct.test index 8cb1ddc0b..f7f65225d 100644 --- a/Tests/Lorentz/ExpandScalarProduct.test +++ b/Tests/Lorentz/ExpandScalarProduct.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ExpandScalarProduct *) @@ -62,6 +62,27 @@ myTens[z, Momentum[b], Momentum[d]]"}, myTens[z, Momentum[a + b], Momentum[c + d]]]","myTens[z, Momentum[a + b], Momentum[c + d]]"}, {"fcstExpandScalarProduct-ID12","SP[p, p] = (a + b)^2; \n tmp = ExpandScalarProduct[Pair[Momentum[p], Momentum[p]]]; \n FCClearScalarProducts[]; \n tmp","(a + b)^2"}, +{"fcstExpandScalarProduct-ID13","ExpandScalarProduct[CartesianPair[CartesianMomentum[p], CartesianMomentum[q]]]","CartesianPair[CartesianMomentum[p], CartesianMomentum[q]]"}, +{"fcstExpandScalarProduct-ID14","ExpandScalarProduct[CartesianPair[CartesianMomentum[p1 + p2], CartesianMomentum[q]]]","CartesianPair[CartesianMomentum[p1], CartesianMomentum[q]] + +CartesianPair[CartesianMomentum[p2], CartesianMomentum[q]]"}, +{"fcstExpandScalarProduct-ID15","ExpandScalarProduct[CartesianPair[CartesianMomentum[p1 + p2], CartesianMomentum[q1 + q2]]]","CartesianPair[CartesianMomentum[p1], CartesianMomentum[q1]] + +CartesianPair[CartesianMomentum[p1], CartesianMomentum[q2]] + CartesianPair[CartesianMomentum[p2], CartesianMomentum[q1]] + CartesianPair[CartesianMomentum[p2], CartesianMomentum[q2]]"}, +{"fcstExpandScalarProduct-ID16","ExpandScalarProduct[CartesianPair[CartesianMomentum[p1 + p2], CartesianIndex[i]]]","CartesianPair[CartesianIndex[i], CartesianMomentum[p1]] + CartesianPair[CartesianIndex[i], CartesianMomentum[p2]]"}, +{"fcstExpandScalarProduct-ID17","ExpandScalarProduct[CartesianPair[CartesianMomentum[p1 + p2], CartesianMomentum[q1 + q2]] + CartesianPair[CartesianMomentum[p3 + p4], CartesianMomentum[q1 + q2]], Momentum -> {p3}]", +"CartesianPair[CartesianMomentum[p1 + p2], CartesianMomentum[q1 + q2]] +CartesianPair[CartesianMomentum[p3], CartesianMomentum[q1]] +CartesianPair[CartesianMomentum[p3], CartesianMomentum[q2]] +CartesianPair[CartesianMomentum[p4], CartesianMomentum[q1]] +CartesianPair[CartesianMomentum[p4], CartesianMomentum[q2]]"}, +{"fcstExpandScalarProduct-ID18","ExpandScalarProduct[TemporalPair[TemporalMomentum[p1 + p2], ExplicitLorentzIndex[0]]]", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p1]] + TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p2]]"}, +{"fcstExpandScalarProduct-ID19", +"ExpandScalarProduct[FV[-l+p2+p3+p4,mu],Momentum->{l},Full->True,FCE->True]", +"-FV[l, mu] + FV[p2, mu] + FV[p3, mu] + FV[p4, mu]"}, {"fcstExpandScalarProduct-ID20", +"ExpandScalarProduct[FV[-l+p2+p3+p4,mu],Momentum->{l},Full->False,FCE->True]", +"-FV[l, mu] + FV[p2 + p3 + p4, mu]"}, {"fcstExpandScalarProduct-ID21", +"ExpandScalarProduct[SP[l+p1+p2+p3,q1+q2+q3+q4],Momentum->l,Full->True,FCE->True]", "SP[l, \ +q1] + SP[l, q2] + SP[l, q3] + SP[l, q4] + SP[p1, q1] + SP[p1, q2] + SP[p1, q3] + SP[p1, q4] + \ +SP[p2, q1] + SP[p2, q2] + SP[p2, q3] + SP[p2, q4] + SP[p3, q1] + SP[p3, q2] + SP[p3, q3] + \ +SP[p3, q4]"}, {"fcstExpandScalarProduct-ID22", +"ExpandScalarProduct[SP[l+p1+p2+p3,q1+q2+q3+q4],Momentum->l,Full->False,FCE->True]", +"SP[l, q1 + q2 + q3 + q4] + SP[p1 + p2 + p3, q1 + q2 + q3 + q4]"}, {"fcstExpandScalarProduct-ID22", "ExpandScalarProduct[Pair[Momentum[k + P], Momentum[Polarization[k + P, I]]]]", "Pair[Momentum[k], Momentum[Polarization[k + P, I]]] + diff --git a/Tests/Lorentz/FCCanonicalizeDummyIndices.test b/Tests/Lorentz/FCCanonicalizeDummyIndices.test index c6804e927..a4ba2b392 100644 --- a/Tests/Lorentz/FCCanonicalizeDummyIndices.test +++ b/Tests/Lorentz/FCCanonicalizeDummyIndices.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for @@ -92,7 +92,53 @@ QuantumField[FCPartialD[LorentzIndex[\[Nu]]], GaugeField, LorentzIndex[c_], SUNIndex[b_]].QuantumField[ FCPartialD[LorentzIndex[a_]], GaugeField, LorentzIndex[c_], SUNIndex[b_]]]","True"}, -{"fcstFCCanonicalizeDummyIndices-ID12","FCCanonicalizeDummyIndices[ +{"fcstFCCanonicalizeDummyIndices-ID14","MatchQ[tmp = +FCCanonicalizeDummyIndices[ +CVD[q, mu] CVD[p, mu] + CVD[q, nu] CVD[p, nu]]; FCE[tmp], +2 CVD[p, i_] CVD[q, i_]]","True"}, +{"fcstFCCanonicalizeDummyIndices-ID15","FCCanonicalizeDummyIndices[ +Uncontract[CSP[q, p]^4, q, p, CartesianPair -> All], +CartesianIndexNames -> {i, j, k, l}, FCE -> True]","CV[p, i] CV[p, j] CV[p, k] CV[p, l] CV[q, i] CV[q, j] CV[q, k] CV[q,l]"}, +{"fcstFCCanonicalizeDummyIndices-ID16","MatchQ[FCCanonicalizeDummyIndices[ +CV[p1, mu] (CV[p2, nu] CV[p3, nu] + CV[p2, rho] CV[p3, rho]), +FCE -> True], 2 CV[p1, mu] CV[p2, a_] CV[p3, a_]]","True"}, +{"fcstFCCanonicalizeDummyIndices-ID17","MatchQ[FCCanonicalizeDummyIndices[ +FV[p, i] FV[q, i] CV[p, i] CV[q, i] + +CV[p, j] CV[q, j] FV[p, j] FV[q, j], FCE -> True], +2 CV[p, b_] CV[q, b_] FV[p, a_] FV[q, a_]]","True"}, +{"fcstFCCanonicalizeDummyIndices-ID18","MatchQ[FCCanonicalizeDummyIndices[ +FV[p, i] FV[p, i] CV[p, i] CV[p, i] + +CV[p, j] CV[p, j] FV[p, j] FV[p, j], FCE -> True], +2 CV[p, a_]^2 FV[p, b_]^2]","True"}, +{"fcstFCCanonicalizeDummyIndices-ID19","MatchQ[FCCanonicalizeDummyIndices[SUNT[a, a].GA[i].(GS[p] + m).GA[i], +DotSimplify -> False, Head -> {SUNIndex}, FCE -> True], +SUNT[a_].SUNT[a_].GA[i].(m + GS[p]).GA[i]]","True"}, +{"fcstFCCanonicalizeDummyIndices-ID20","MatchQ[FCCanonicalizeDummyIndices[ +SUNT[a, a].CGA[i].(CGS[p] + m).CGA[i], DotSimplify -> False, +Head -> {SUNIndex}, FCE -> True], +SUNT[a_].SUNT[a_].CGA[i].(m + CGS[p]).CGA[i]]","True"}, +{"fcstFCCanonicalizeDummyIndices-ID21", +"MatchQ[FCCanonicalizeDummyIndices[GAD[i].GAD[i] + GAD[i].GAE[i], FCE -> True], +GAD[FCGV[a_]].GAD[FCGV[a_]] + GAD[FCGV[a_]].GAE[FCGV[a_]]]","True"}, +{"fcstFCCanonicalizeDummyIndices-ID22", +"MatchQ[FCCanonicalizeDummyIndices[CGAD[i].CGAD[i] + CGAD[i].CGAE[i], +FCE -> True], CGAD[FCGV[a_]].CGAD[FCGV[a_]] + CGAD[FCGV[a_]].CGAE[FCGV[a_]]]","True"}, +{"fcstFCCanonicalizeDummyIndices-ID23", +"FCCanonicalizeDummyIndices[ +DiracTrace[(- GAD[Lor2].GSD[a1].GA[6] - GAD[Lor2].GSD[a1].GA[7] + + GAD[Lor2].GSD[pPh].GSD[a1].GA[6])] Spinor[Momentum[p1, D], 0, + 1].GAD[Lor2].GA[6].Spinor[-Momentum[p2, D], 0, 1], +LorentzIndexNames -> {lor}, FCE -> True]","-DiracTrace[GAD[lor].GSD[a1].GA[6]] Spinor[Momentum[p1, D], 0, 1].GAD[ + lor].GA[6].Spinor[-Momentum[p2, D], 0, 1] - +DiracTrace[ +GAD[lor].GSD[a1].GA[7]] Spinor[Momentum[p1, D], 0, 1].GAD[lor].GA[ + 6].Spinor[-Momentum[p2, D], 0, 1] + +DiracTrace[ +GAD[lor].GSD[pPh].GSD[a1].GA[6]] Spinor[Momentum[p1, D], 0, 1].GAD[ + lor].GA[6].Spinor[-Momentum[p2, D], 0, 1]"}, + +{"fcstFCCanonicalizeDummyIndices-ID24", +"FCCanonicalizeDummyIndices[ Spinor[Momentum[pE2, D], 0, 1].(-((I EL GA[6] me)/(Sqrt[2] me sw))).(GSD[-k + pE2 - pS] + me).(-((I EL GA[7] me)/( @@ -103,124 +149,42 @@ Spinor[Momentum[pE2, D], 0, I EL mU VUb GA[7])/(Sqrt[2] me sw) - (I EL VUb GA[6] mb)/( Sqrt[2] me sw)).Spinor[Momentum[pB, D], mb, 1] FAD[{k, mU}, {k + pS, Sqrt[GaugeXi[W]] me}, {k - pE2 + pS, - me}, {k - pE1 - pE2 + pS, Sqrt[GaugeXi[W]] me}]]","(EL^2*mb*mU^2*VUb*Spinor[-Momentum[pS, D], ms, 1] . DiracGamma[6] . - DiracGamma[6] . Spinor[Momentum[pB, D], mb, 1]* -(-(EL^2*me*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[7] . Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2) - - (EL^2*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[Momentum[-k + pE2 - pS, D], D] . DiracGamma[7] . - Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2))* -FeynAmpDenominator[PropagatorDenominator[Momentum[k, D], mU], - PropagatorDenominator[Momentum[k, D] + Momentum[pS, D], - me*Sqrt[GaugeXi[W]]], PropagatorDenominator[ - Momentum[k, D] - Momentum[pE2, D] + Momentum[pS, D], me], - PropagatorDenominator[Momentum[k, D] - Momentum[pE1, D] - - Momentum[pE2, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]]]* -SUNFDelta[SUNFIndex[Col1], SUNFIndex[Col2]])/(2*me^2*sw^2) - -(EL^2*mU^3*VUb*Spinor[-Momentum[pS, D], ms, 1] . DiracGamma[6] . - DiracGamma[7] . Spinor[Momentum[pB, D], mb, 1]* -(-(EL^2*me*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[7] . Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2) - - (EL^2*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[Momentum[-k + pE2 - pS, D], D] . DiracGamma[7] . - Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2))* -FeynAmpDenominator[PropagatorDenominator[Momentum[k, D], mU], - PropagatorDenominator[Momentum[k, D] + Momentum[pS, D], - me*Sqrt[GaugeXi[W]]], PropagatorDenominator[ - Momentum[k, D] - Momentum[pE2, D] + Momentum[pS, D], me], - PropagatorDenominator[Momentum[k, D] - Momentum[pE1, D] - - Momentum[pE2, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]]]* -SUNFDelta[SUNFIndex[Col1], SUNFIndex[Col2]])/(2*me^2*sw^2) - -(EL^2*mb*ms*mU*VUb*Spinor[-Momentum[pS, D], ms, 1] . DiracGamma[7] . - DiracGamma[6] . Spinor[Momentum[pB, D], mb, 1]* -(-(EL^2*me*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[7] . Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2) - - (EL^2*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[Momentum[-k + pE2 - pS, D], D] . DiracGamma[7] . - Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2))* -FeynAmpDenominator[PropagatorDenominator[Momentum[k, D], mU], - PropagatorDenominator[Momentum[k, D] + Momentum[pS, D], - me*Sqrt[GaugeXi[W]]], PropagatorDenominator[ - Momentum[k, D] - Momentum[pE2, D] + Momentum[pS, D], me], - PropagatorDenominator[Momentum[k, D] - Momentum[pE1, D] - - Momentum[pE2, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]]]* -SUNFDelta[SUNFIndex[Col1], SUNFIndex[Col2]])/(2*me^2*sw^2) + -(EL^2*ms*mU^2*VUb*Spinor[-Momentum[pS, D], ms, 1] . DiracGamma[7] . - DiracGamma[7] . Spinor[Momentum[pB, D], mb, 1]* -(-(EL^2*me*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[7] . Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2) - - (EL^2*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[Momentum[-k + pE2 - pS, D], D] . DiracGamma[7] . - Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2))* -FeynAmpDenominator[PropagatorDenominator[Momentum[k, D], mU], - PropagatorDenominator[Momentum[k, D] + Momentum[pS, D], - me*Sqrt[GaugeXi[W]]], PropagatorDenominator[ - Momentum[k, D] - Momentum[pE2, D] + Momentum[pS, D], me], - PropagatorDenominator[Momentum[k, D] - Momentum[pE1, D] - - Momentum[pE2, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]]]* -SUNFDelta[SUNFIndex[Col1], SUNFIndex[Col2]])/(2*me^2*sw^2) + -(EL^2*mb*mU*VUb* -(-(EL^2*me*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[7] . Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2) - - (EL^2*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[Momentum[-k + pE2 - pS, D], D] . DiracGamma[7] . - Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2))* -Spinor[-Momentum[pS, D], ms, 1] . DiracGamma[6] . - DiracGamma[Momentum[k, D], D] . DiracGamma[6] . - Spinor[Momentum[pB, D], mb, 1]*FeynAmpDenominator[ - PropagatorDenominator[Momentum[k, D], mU], PropagatorDenominator[ - Momentum[k, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]], - PropagatorDenominator[Momentum[k, D] - Momentum[pE2, D] + - Momentum[pS, D], me], PropagatorDenominator[ - Momentum[k, D] - Momentum[pE1, D] - Momentum[pE2, D] + - Momentum[pS, D], me*Sqrt[GaugeXi[W]]]]*SUNFDelta[SUNFIndex[Col1], - SUNFIndex[Col2]])/(2*me^2*sw^2) - -(EL^2*mU^2*VUb*(-(EL^2*me*Spinor[Momentum[pE2, D], 0, 1] . - DiracGamma[6] . DiracGamma[7] . Spinor[-Momentum[pE1, D], 0, 1])/ - (2*sw^2) - (EL^2*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[Momentum[-k + pE2 - pS, D], D] . DiracGamma[7] . - Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2))* -Spinor[-Momentum[pS, D], ms, 1] . DiracGamma[6] . - DiracGamma[Momentum[k, D], D] . DiracGamma[7] . - Spinor[Momentum[pB, D], mb, 1]*FeynAmpDenominator[ - PropagatorDenominator[Momentum[k, D], mU], PropagatorDenominator[ - Momentum[k, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]], - PropagatorDenominator[Momentum[k, D] - Momentum[pE2, D] + - Momentum[pS, D], me], PropagatorDenominator[ - Momentum[k, D] - Momentum[pE1, D] - Momentum[pE2, D] + - Momentum[pS, D], me*Sqrt[GaugeXi[W]]]]*SUNFDelta[SUNFIndex[Col1], - SUNFIndex[Col2]])/(2*me^2*sw^2) - -(EL^2*mb*ms*VUb* -(-(EL^2*me*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[7] . Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2) - - (EL^2*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[Momentum[-k + pE2 - pS, D], D] . DiracGamma[7] . - Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2))* -Spinor[-Momentum[pS, D], ms, 1] . DiracGamma[7] . - DiracGamma[Momentum[k, D], D] . DiracGamma[6] . - Spinor[Momentum[pB, D], mb, 1]*FeynAmpDenominator[ - PropagatorDenominator[Momentum[k, D], mU], PropagatorDenominator[ - Momentum[k, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]], - PropagatorDenominator[Momentum[k, D] - Momentum[pE2, D] + + me}, {k - pE1 - pE2 + pS, Sqrt[GaugeXi[W]] me}], FCE -> True]", +"Spinor[Momentum[pE2, D], 0, 1] . (((-I)*EL*DiracGamma[6])/(Sqrt[2]*sw)) . +(me + DiracGamma[Momentum[-k + pE2 - pS, D], D]) . +(((-I)*EL*DiracGamma[7])/(Sqrt[2]*sw)) . Spinor[-Momentum[pE1, D], 0, 1]* +Spinor[-Momentum[pS, D], ms, 1] . +((I*EL*mU*DiracGamma[6]*SUNFDelta[SUNFIndex[Col1], SUNFIndex[Col2]])/ + (Sqrt[2]*me*sw) - (I*EL*ms*DiracGamma[7]*SUNFDelta[SUNFIndex[Col1], + SUNFIndex[Col2]])/(Sqrt[2]*me*sw)) . +(mU + DiracGamma[Momentum[k, D], D]) . +(((-I)*EL*mb*VUb*DiracGamma[6])/(Sqrt[2]*me*sw) + +(I*EL*mU*VUb*DiracGamma[7])/(Sqrt[2]*me*sw)) . +Spinor[Momentum[pB, D], mb, 1]*FeynAmpDenominator[ +PropagatorDenominator[Momentum[k, D], mU], PropagatorDenominator[ +Momentum[k, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]], +PropagatorDenominator[Momentum[k, D] - Momentum[pE2, D] + Momentum[pS, D], me], PropagatorDenominator[ - Momentum[k, D] - Momentum[pE1, D] - Momentum[pE2, D] + - Momentum[pS, D], me*Sqrt[GaugeXi[W]]]]*SUNFDelta[SUNFIndex[Col1], - SUNFIndex[Col2]])/(2*me^2*sw^2) + -(EL^2*ms*mU*VUb* -(-(EL^2*me*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[7] . Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2) - - (EL^2*Spinor[Momentum[pE2, D], 0, 1] . DiracGamma[6] . - DiracGamma[Momentum[-k + pE2 - pS, D], D] . DiracGamma[7] . - Spinor[-Momentum[pE1, D], 0, 1])/(2*sw^2))* -Spinor[-Momentum[pS, D], ms, 1] . DiracGamma[7] . - DiracGamma[Momentum[k, D], D] . DiracGamma[7] . - Spinor[Momentum[pB, D], mb, 1]*FeynAmpDenominator[ - PropagatorDenominator[Momentum[k, D], mU], PropagatorDenominator[ - Momentum[k, D] + Momentum[pS, D], me*Sqrt[GaugeXi[W]]], - PropagatorDenominator[Momentum[k, D] - Momentum[pE2, D] + - Momentum[pS, D], me], PropagatorDenominator[ - Momentum[k, D] - Momentum[pE1, D] - Momentum[pE2, D] + - Momentum[pS, D], me*Sqrt[GaugeXi[W]]]]*SUNFDelta[SUNFIndex[Col1], - SUNFIndex[Col2]])/(2*me^2*sw^2)"} - +Momentum[k, D] - Momentum[pE1, D] - Momentum[pE2, D] + Momentum[pS, D], +me*Sqrt[GaugeXi[W]]]]"}, +{"fcstFCCanonicalizeDummyIndices-ID25", +"MatchQ[FCCanonicalizeDummyIndices[ +DCHN[SpinorUBar[p1], i] DCHN[SpinorV[p1], j] DIDelta[i, j], +FCE -> True], +DIDelta[a_FCGV, b_FCGV] DCHN[Spinor[-Momentum[p1], 0, 1], +b_FCGV] DCHN[Spinor[Momentum[p1], 0, 1], a_FCGV]]", "True"}, +{"fcstFCCanonicalizeDummyIndices-ID26", +"FCCanonicalizeDummyIndices[DiracChain[DiracGamma[LorentzIndex[mu]].(m + + DiracGamma[LorentzIndex[j]] Pair[LorentzIndex[j], + Momentum[p]]).DiracGamma[LorentzIndex[nu]], DiracIndex[i], +DiracIndex[j]], LorentzIndexNames -> {al}, FCE -> True]", +"m DCHN[GA[mu].GA[nu], i, j] + DCHN[GA[mu].GA[al].GA[nu], i, j] FV[p, al]"}, +{"fcstFCCanonicalizeDummyIndices-ID27", +"FCCanonicalizeDummyIndices[ +DCHN[Spinor[-Momentum[p1], m1, 1], $AL[$42]] DCHN[ +Spinor[Momentum[p2], m2, 1], $AL[$43]] DCHN[ +GA[5].GA[nu].GA[mu], $AL[$42], $AL[$43]], +DiracIndexNames -> {i, j}, FCE -> True]", +"DCHN[Spinor[-Momentum[p1], m1, 1], i] DCHN[ +Spinor[Momentum[p2], m2, 1], j] DCHN[GA[5].GA[nu].GA[mu], i, j]"} }); diff --git a/Tests/Lorentz/FCGetDimensions.test b/Tests/Lorentz/FCGetDimensions.test index 10c3cd525..6aff44cfa 100644 --- a/Tests/Lorentz/FCGetDimensions.test +++ b/Tests/Lorentz/FCGetDimensions.test @@ -4,16 +4,16 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCGetDimensions *) (* ------------------------------------------------------------------------ *) -Tests`Lorenz`fcstFCGetDimensions = +Tests`Lorentz`fcstFCGetDimensions = ({ {"fcstFCGetDimensions-ID1", "FCGetDimensions[0]", "{}"}, {"fcstFCGetDimensions-ID2", "FCGetDimensions[x]", "{}"}, @@ -28,5 +28,20 @@ Tests`Lorenz`fcstFCGetDimensions = {"fcstFCGetDimensions-ID8", "FCGetDimensions[GAD[p]]", "{D}"}, {"fcstFCGetDimensions-ID9", "FCGetDimensions[GAE[p]]", "{-4 + D}"}, {"fcstFCGetDimensions-ID10", "FCGetDimensions[GSD[p]+GA[x]]", -"{4, D}"} +"{4, D}"}, +{"fcstFCGetDimensions-ID11", "FCGetDimensions[DiracGamma[CartesianIndex[i]]]", "{3,4}"}, +{"fcstFCGetDimensions-ID12", "FCGetDimensions[DiracGamma[CartesianIndex[i, D - 1], D]]", "{D-1,D}"}, +{"fcstFCGetDimensions-ID13", "FCGetDimensions[DiracGamma[CartesianIndex[i, D - 4], D - 4]]", "{D-4}"}, +{"fcstFCGetDimensions-ID14", "FCGetDimensions[DiracGamma[CartesianMomentum[p]]]", "{3,4}"}, +{"fcstFCGetDimensions-ID15", "FCGetDimensions[DiracGamma[CartesianMomentum[p, D - 1], D]]", "{D-1,D}"}, +{"fcstFCGetDimensions-ID16", "FCGetDimensions[DiracGamma[CartesianMomentum[p, D - 4], D - 4]]", "{D-4}"}, +{"fcstFCGetDimensions-ID17", "FCGetDimensions[DiracGamma[CartesianPair[CartesianMomentum[p], CartesianIndex[i]]]]", "{3,4}"}, +{"fcstFCGetDimensions-ID18", "FCGetDimensions[PauliSigma[CartesianMomentum[p]]]", "{3}"}, +{"fcstFCGetDimensions-ID19", "FCGetDimensions[PauliSigma[Momentum[p]]]", "{3,4}"}, +{"fcstFCGetDimensions-ID20", "FCGetDimensions[CV[p, i], ChangeDimension -> True]", "{4}"}, +{"fcstFCGetDimensions-ID21", "FCGetDimensions[CVD[p, i], ChangeDimension -> True]", "{D}"}, +{"fcstFCGetDimensions-ID22", "FCGetDimensions[PauliSigma[CartesianMomentum[p]], ChangeDimension -> True]", "{3,4}"}, +{"fcstFCGetDimensions-ID23", "FCGetDimensions[GAD[5, mu], FreeQ -> {DiracGamma[5]}]", "{D}"}, +{"fcstFCGetDimensions-ID23", "FCGetDimensions[GAD[5, mu,6,nu,7], FreeQ -> {DiracGamma[5],DiracGamma[6],DiracGamma[7]}]", "{D}"}, +{"fcstFCGetDimensions-ID24", "FCGetDimensions[TC[p] GAD[mu], FreeQ -> {TemporalPair[__]}]", "{D}"} }); diff --git a/Tests/Lorentz/FCPermuteMomentaRules.test b/Tests/Lorentz/FCPermuteMomentaRules.test new file mode 100644 index 000000000..c0e8d9483 --- /dev/null +++ b/Tests/Lorentz/FCPermuteMomentaRules.test @@ -0,0 +1,117 @@ + + +(* :Title: FCPermuteMomentaRules.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCPermuteMomentaRules *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstFCPermuteMomentaRules = +({ +{"fcstFCPermuteMomentaRules-ID1", "FCPermuteMomentaRules[{}]", +"{{}}"}, +{"fcstFCPermuteMomentaRules-ID2", "FCPermuteMomentaRules[{p1}]", +"{{}}"}, +{"fcstFCPermuteMomentaRules-ID3", "FCPermuteMomentaRules[{p1,p2}]", +"{{}, {p1 -> p2, p2 -> p1}}"}, +{"fcstFCPermuteMomentaRules-ID4", +"FCPermuteMomentaRules[{p1,p2,p3}]", +"{{}, {p1 -> p2, p2 -> p1}, {p1 -> p3, p3 -> p1}, {p2 -> p3, p3 -> \ +p2}, {p1 -> p2, p2 -> p3, p3 -> p1}, {p1 -> p3, p2 -> p1, p3 -> p2}}"}, +{"fcstFCPermuteMomentaRules-ID5", +"FCPermuteMomentaRules[{p1,p2,p3,p4}]", +"{{}, {p1 -> p2, p2 -> p1}, {p1 -> p3, p3 -> p1}, {p1 -> p4, p4 -> \ +p1}, {p2 -> p3, p3 -> p2}, {p2 -> p4, p4 -> p2}, {p3 -> p4, p4 -> \ +p3}, {p1 -> p2, p2 -> p3, p3 -> p1}, {p1 -> p2, p2 -> p4, p4 -> p1}, \ +{p1 -> p3, p2 -> p1, p3 -> p2}, {p1 -> p3, p3 -> p4, p4 -> p1}, {p1 -> \ +p4, p2 -> p1, p4 -> p2}, {p1 -> p4, p3 -> p1, p4 -> p3}, {p2 -> p3, \ +p3 -> p4, p4 -> p2}, {p2 -> p4, p3 -> p2, p4 -> p3}, {p1 -> p2, p2 -> \ +p1, p3 -> p4, p4 -> p3}, {p1 -> p2, p2 -> p3, p3 -> p4, p4 -> p1}, \ +{p1 -> p2, p2 -> p4, p3 -> p1, p4 -> p3}, {p1 -> p3, p2 -> p1, p3 -> \ +p4, p4 -> p2}, {p1 -> p3, p2 -> p4, p3 -> p1, p4 -> p2}, {p1 -> p3, \ +p2 -> p4, p3 -> p2, p4 -> p1}, {p1 -> p4, p2 -> p1, p3 -> p2, p4 -> \ +p3}, {p1 -> p4, p2 -> p3, p3 -> p1, p4 -> p2}, {p1 -> p4, p2 -> p3, \ +p3 -> p2, p4 -> p1}}"}, +{"fcstFCPermuteMomentaRules-ID6", +"FCPermuteMomentaRules[{p1,p2,p3,p4,p5}]", +"{{}, {p1 -> p2, p2 -> p1}, {p1 -> p3, p3 -> p1}, {p1 -> p4, p4 -> \ +p1}, {p1 -> p5, p5 -> p1}, {p2 -> p3, p3 -> p2}, {p2 -> p4, p4 -> \ +p2}, {p2 -> p5, p5 -> p2}, {p3 -> p4, p4 -> p3}, {p3 -> p5, p5 -> \ +p3}, {p4 -> p5, p5 -> p4}, {p1 -> p2, p2 -> p3, p3 -> p1}, {p1 -> p2, \ +p2 -> p4, p4 -> p1}, {p1 -> p2, p2 -> p5, p5 -> p1}, {p1 -> p3, p2 -> \ +p1, p3 -> p2}, {p1 -> p3, p3 -> p4, p4 -> p1}, {p1 -> p3, p3 -> p5, \ +p5 -> p1}, {p1 -> p4, p2 -> p1, p4 -> p2}, {p1 -> p4, p3 -> p1, p4 -> \ +p3}, {p1 -> p4, p4 -> p5, p5 -> p1}, {p1 -> p5, p2 -> p1, p5 -> p2}, \ +{p1 -> p5, p3 -> p1, p5 -> p3}, {p1 -> p5, p4 -> p1, p5 -> p4}, {p2 -> \ +p3, p3 -> p4, p4 -> p2}, {p2 -> p3, p3 -> p5, p5 -> p2}, {p2 -> p4, \ +p3 -> p2, p4 -> p3}, {p2 -> p4, p4 -> p5, p5 -> p2}, {p2 -> p5, p3 -> \ +p2, p5 -> p3}, {p2 -> p5, p4 -> p2, p5 -> p4}, {p3 -> p4, p4 -> p5, \ +p5 -> p3}, {p3 -> p5, p4 -> p3, p5 -> p4}, {p1 -> p2, p2 -> p1, p3 -> \ +p4, p4 -> p3}, {p1 -> p2, p2 -> p1, p3 -> p5, p5 -> p3}, {p1 -> p2, \ +p2 -> p1, p4 -> p5, p5 -> p4}, {p1 -> p2, p2 -> p3, p3 -> p4, p4 -> \ +p1}, {p1 -> p2, p2 -> p3, p3 -> p5, p5 -> p1}, {p1 -> p2, p2 -> p4, \ +p3 -> p1, p4 -> p3}, {p1 -> p2, p2 -> p4, p4 -> p5, p5 -> p1}, {p1 -> \ +p2, p2 -> p5, p3 -> p1, p5 -> p3}, {p1 -> p2, p2 -> p5, p4 -> p1, p5 -> \ +p4}, {p1 -> p3, p2 -> p1, p3 -> p4, p4 -> p2}, {p1 -> p3, p2 -> p1, \ +p3 -> p5, p5 -> p2}, {p1 -> p3, p2 -> p4, p3 -> p1, p4 -> p2}, {p1 -> \ +p3, p2 -> p4, p3 -> p2, p4 -> p1}, {p1 -> p3, p2 -> p5, p3 -> p1, p5 -> \ +p2}, {p1 -> p3, p2 -> p5, p3 -> p2, p5 -> p1}, {p1 -> p3, p3 -> p1, \ +p4 -> p5, p5 -> p4}, {p1 -> p3, p3 -> p4, p4 -> p5, p5 -> p1}, {p1 -> \ +p3, p3 -> p5, p4 -> p1, p5 -> p4}, {p1 -> p4, p2 -> p1, p3 -> p2, p4 -> \ +p3}, {p1 -> p4, p2 -> p1, p4 -> p5, p5 -> p2}, {p1 -> p4, p2 -> p3, \ +p3 -> p1, p4 -> p2}, {p1 -> p4, p2 -> p3, p3 -> p2, p4 -> p1}, {p1 -> \ +p4, p2 -> p5, p4 -> p1, p5 -> p2}, {p1 -> p4, p2 -> p5, p4 -> p2, p5 -> \ +p1}, {p1 -> p4, p3 -> p1, p4 -> p5, p5 -> p3}, {p1 -> p4, p3 -> p5, \ +p4 -> p1, p5 -> p3}, {p1 -> p4, p3 -> p5, p4 -> p3, p5 -> p1}, {p1 -> \ +p5, p2 -> p1, p3 -> p2, p5 -> p3}, {p1 -> p5, p2 -> p1, p4 -> p2, p5 -> \ +p4}, {p1 -> p5, p2 -> p3, p3 -> p1, p5 -> p2}, {p1 -> p5, p2 -> p3, \ +p3 -> p2, p5 -> p1}, {p1 -> p5, p2 -> p4, p4 -> p1, p5 -> p2}, {p1 -> \ +p5, p2 -> p4, p4 -> p2, p5 -> p1}, {p1 -> p5, p3 -> p1, p4 -> p3, p5 -> \ +p4}, {p1 -> p5, p3 -> p4, p4 -> p1, p5 -> p3}, {p1 -> p5, p3 -> p4, \ +p4 -> p3, p5 -> p1}, {p2 -> p3, p3 -> p2, p4 -> p5, p5 -> p4}, {p2 -> \ +p3, p3 -> p4, p4 -> p5, p5 -> p2}, {p2 -> p3, p3 -> p5, p4 -> p2, p5 -> \ +p4}, {p2 -> p4, p3 -> p2, p4 -> p5, p5 -> p3}, {p2 -> p4, p3 -> p5, \ +p4 -> p2, p5 -> p3}, {p2 -> p4, p3 -> p5, p4 -> p3, p5 -> p2}, {p2 -> \ +p5, p3 -> p2, p4 -> p3, p5 -> p4}, {p2 -> p5, p3 -> p4, p4 -> p2, p5 -> \ +p3}, {p2 -> p5, p3 -> p4, p4 -> p3, p5 -> p2}, {p1 -> p2, p2 -> p1, \ +p3 -> p4, p4 -> p5, p5 -> p3}, {p1 -> p2, p2 -> p1, p3 -> p5, p4 -> \ +p3, p5 -> p4}, {p1 -> p2, p2 -> p3, p3 -> p1, p4 -> p5, p5 -> p4}, \ +{p1 -> p2, p2 -> p3, p3 -> p4, p4 -> p5, p5 -> p1}, {p1 -> p2, p2 -> \ +p3, p3 -> p5, p4 -> p1, p5 -> p4}, {p1 -> p2, p2 -> p4, p3 -> p1, p4 -> \ +p5, p5 -> p3}, {p1 -> p2, p2 -> p4, p3 -> p5, p4 -> p1, p5 -> p3}, \ +{p1 -> p2, p2 -> p4, p3 -> p5, p4 -> p3, p5 -> p1}, {p1 -> p2, p2 -> \ +p5, p3 -> p1, p4 -> p3, p5 -> p4}, {p1 -> p2, p2 -> p5, p3 -> p4, p4 -> \ +p1, p5 -> p3}, {p1 -> p2, p2 -> p5, p3 -> p4, p4 -> p3, p5 -> p1}, \ +{p1 -> p3, p2 -> p1, p3 -> p2, p4 -> p5, p5 -> p4}, {p1 -> p3, p2 -> \ +p1, p3 -> p4, p4 -> p5, p5 -> p2}, {p1 -> p3, p2 -> p1, p3 -> p5, p4 -> \ +p2, p5 -> p4}, {p1 -> p3, p2 -> p4, p3 -> p1, p4 -> p5, p5 -> p2}, \ +{p1 -> p3, p2 -> p4, p3 -> p2, p4 -> p5, p5 -> p1}, {p1 -> p3, p2 -> \ +p4, p3 -> p5, p4 -> p1, p5 -> p2}, {p1 -> p3, p2 -> p4, p3 -> p5, p4 -> \ +p2, p5 -> p1}, {p1 -> p3, p2 -> p5, p3 -> p1, p4 -> p2, p5 -> p4}, \ +{p1 -> p3, p2 -> p5, p3 -> p2, p4 -> p1, p5 -> p4}, {p1 -> p3, p2 -> \ +p5, p3 -> p4, p4 -> p1, p5 -> p2}, {p1 -> p3, p2 -> p5, p3 -> p4, p4 -> \ +p2, p5 -> p1}, {p1 -> p4, p2 -> p1, p3 -> p2, p4 -> p5, p5 -> p3}, \ +{p1 -> p4, p2 -> p1, p3 -> p5, p4 -> p2, p5 -> p3}, {p1 -> p4, p2 -> \ +p1, p3 -> p5, p4 -> p3, p5 -> p2}, {p1 -> p4, p2 -> p3, p3 -> p1, p4 -> \ +p5, p5 -> p2}, {p1 -> p4, p2 -> p3, p3 -> p2, p4 -> p5, p5 -> p1}, \ +{p1 -> p4, p2 -> p3, p3 -> p5, p4 -> p1, p5 -> p2}, {p1 -> p4, p2 -> \ +p3, p3 -> p5, p4 -> p2, p5 -> p1}, {p1 -> p4, p2 -> p5, p3 -> p1, p4 -> \ +p2, p5 -> p3}, {p1 -> p4, p2 -> p5, p3 -> p1, p4 -> p3, p5 -> p2}, \ +{p1 -> p4, p2 -> p5, p3 -> p2, p4 -> p1, p5 -> p3}, {p1 -> p4, p2 -> \ +p5, p3 -> p2, p4 -> p3, p5 -> p1}, {p1 -> p5, p2 -> p1, p3 -> p2, p4 -> \ +p3, p5 -> p4}, {p1 -> p5, p2 -> p1, p3 -> p4, p4 -> p2, p5 -> p3}, \ +{p1 -> p5, p2 -> p1, p3 -> p4, p4 -> p3, p5 -> p2}, {p1 -> p5, p2 -> \ +p3, p3 -> p1, p4 -> p2, p5 -> p4}, {p1 -> p5, p2 -> p3, p3 -> p2, p4 -> \ +p1, p5 -> p4}, {p1 -> p5, p2 -> p3, p3 -> p4, p4 -> p1, p5 -> p2}, \ +{p1 -> p5, p2 -> p3, p3 -> p4, p4 -> p2, p5 -> p1}, {p1 -> p5, p2 -> \ +p4, p3 -> p1, p4 -> p2, p5 -> p3}, {p1 -> p5, p2 -> p4, p3 -> p1, p4 -> \ +p3, p5 -> p2}, {p1 -> p5, p2 -> p4, p3 -> p2, p4 -> p1, p5 -> p3}, \ +{p1 -> p5, p2 -> p4, p3 -> p2, p4 -> p3, p5 -> p1}}"} +}); diff --git a/Tests/Lorentz/FCRenameDummyIndices.test b/Tests/Lorentz/FCRenameDummyIndices.test index ca98c5489..f5bccd31e 100644 --- a/Tests/Lorentz/FCRenameDummyIndices.test +++ b/Tests/Lorentz/FCRenameDummyIndices.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCRenameDummyIndices *) @@ -15,7 +15,7 @@ Tests`Lorentz`fcstFCRenameDummyIndices = { {"FCRenameDummyIndices-ID1", "MatchQ[FieldStrength[a,b].FieldStrength[a,b]\ - //Explicit//Expand//FCRenameDummyIndices,(QuantumField[FCPartialD[\ + //Explicit//ChangeDimension[#,D]&//Expand//FCRenameDummyIndices,(QuantumField[FCPartialD[\ LorentzIndex[$AL[i_],D]],GaugeField,LorentzIndex[$AL[j_],D]]-\ QuantumField[FCPartialD[LorentzIndex[$AL[j_],D]],GaugeField,\ LorentzIndex[$AL[i_],D]]).(QuantumField[FCPartialD[LorentzIndex[$AL[$i_]\ @@ -36,7 +36,27 @@ Tests`Lorentz`fcstFCRenameDummyIndices = SUNIndex[b]].SUNT[SUNIndex[$AL[$x_]]].SUNT[SUNIndex[$AL[y_]]].SUNT[\ SUNIndex[k]]]", "True"}, {"FCRenameDummyIndices-ID5", - "MatchQ[FCRenameDummyIndices[FCI[FVD[p, mu] FVD[q, mu]]], -Pair[LorentzIndex[a_$AL, D], Momentum[p, D]] Pair[ -LorentzIndex[a_$AL, D], Momentum[q, D]]]", "True"} -} + "MatchQ[FCRenameDummyIndices[FVD[p, mu] FVD[q, mu], FCE -> True], +FVD[p, $AL[a_]] FVD[q, $AL[a_]]]", "True"}, +{"FCRenameDummyIndices-ID6", + "MatchQ[FCRenameDummyIndices[CVD[p, i] CVD[q, i], FCE -> True], +CVD[p, $AL[a_]] CVD[q, $AL[a_]]]", "True"}, +{"FCRenameDummyIndices-ID7", + "MatchQ[ +FCRenameDummyIndices[ +Spinor[Momentum[k], m, 1].GA[k].Spinor[Momentum[k], m, 1] Spinor[ + Momentum[p], m, 1].GA[k].Spinor[Momentum[p], m, 1], +FCE -> True], +Spinor[Momentum[k], m, 1].GA[a_].Spinor[Momentum[k], m, 1] Spinor[ + Momentum[p], m, 1].GA[a_].Spinor[Momentum[p], m, 1]]", "True"}, +{"FCRenameDummyIndices-ID8","MatchQ[FCRenameDummyIndices[ +DCHN[SpinorUBar[p1], i] DCHN[SpinorV[p1], j] DIDelta[i, j], +FCE -> True], +DIDelta[$AL[a_], $AL[b_]] DCHN[ +Spinor[-Momentum[p1], 0, 1], $AL[b_]] DCHN[ +Spinor[Momentum[p1], 0, 1], $AL[a_]]]","True"}, +{"FCRenameDummyIndices-ID9", + "MatchQ[FCRenameDummyIndices[ +tr[GA[mu].(1 - GA[5]), GA[mu].(1 - GA[5])], DotSimplify -> False, FCE -> True], +tr[GA[$AL[a_]].(1 - GA[5]), GA[$AL[a_]].(1 - GA[5])]]", "True"} +}; diff --git a/Tests/Lorentz/FCReplaceMomenta.test b/Tests/Lorentz/FCReplaceMomenta.test new file mode 100644 index 000000000..766e2093c --- /dev/null +++ b/Tests/Lorentz/FCReplaceMomenta.test @@ -0,0 +1,88 @@ + + +(* :Title: FCReplaceMomenta.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCReplaceMomenta *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstFCReplaceMomenta = +({ +{"fcstFCReplaceMomenta-ID1", +"FCReplaceMomenta[SPD[p,q],{p\[Rule]a}]", +"Pair[Momentum[a, D], Momentum[q, D]]"}, +{"fcstFCReplaceMomenta-ID2", +"FCReplaceMomenta[SPD[p,q],{p\[Rule]a},Dimensions\[Rule]{4}]", +"Pair[Momentum[p, D], Momentum[q, D]]"}, +{"fcstFCReplaceMomenta-ID3", +"FCReplaceMomenta[SPD[p,q],{p\[Rule]a},Dimensions\[Rule]{4,D}]", +"Pair[Momentum[a, D], Momentum[q, D]]"}, +{"fcstFCReplaceMomenta-ID4", +"FCReplaceMomenta[SPD[p,q],{p\[Rule]2a},Dimensions\[Rule]{4,D}]", +"2*Pair[Momentum[a, D], Momentum[q, D]]"}, +{"fcstFCReplaceMomenta-ID5", +"FCReplaceMomenta[SPD[p,q],{p\[Rule]a q1 +c q2 \ +},Dimensions\[Rule]{4,D},Variables\[Rule]{a,c}]", +"Pair[Momentum[q, D], a*Momentum[q1, D] + c*Momentum[q2, D]]"}, +{"fcstFCReplaceMomenta-ID6", +"FCReplaceMomenta[SPD[p,q],{p\[Rule]a q1 +c q2 \ +},Dimensions\[Rule]{4,D},Variables\[Rule]{a,c},Head\[Rule]{DiracGamma}\ +]", "Pair[Momentum[p, D], Momentum[q, D]]"}, +{"fcstFCReplaceMomenta-ID7", +"FCReplaceMomenta[GSD[p]SPD[p,q],{p\[Rule]a q1 +c q2 },Dimensions\ +\[Rule]{4,D},Variables\[Rule]{a,c},Head\[Rule]{DiracGamma}]", +"(a*DiracGamma[Momentum[q1, D], D] + c*DiracGamma[Momentum[q2, D], \ +D])*Pair[Momentum[p, D], Momentum[q, D]]"}, +{"fcstFCReplaceMomenta-ID8", +"FCReplaceMomenta[Spinor[p,m],{p\[Rule]a},Dimensions\[Rule]{4,D}]", + "Spinor[Momentum[p], m, 1]"}, +{"fcstFCReplaceMomenta-ID9", +"FCReplaceMomenta[Spinor[p,m],{p\[Rule]a},Dimensions\[Rule]{4,D},\ +Head->Join[OptionValue[FCReplaceMomenta, Head],{Spinor}]]", +"Spinor[Momentum[a], m, 1]"}, +{"fcstFCReplaceMomenta-ID10", +"FCReplaceMomenta[PolarizationVector[p,mu],{p\[Rule]a},Dimensions\ +\[Rule]{4,D}]", +"Pair[LorentzIndex[mu], Momentum[Polarization[p, I]]]"}, +{"fcstFCReplaceMomenta-ID11", +"FCReplaceMomenta[PolarizationVector[p,mu],{p\[Rule]a},Dimensions\ +\[Rule]{4,D},Polarization\[Rule]True]", +"Pair[LorentzIndex[mu], Momentum[Polarization[a, I]]]"}, +{"fcstFCReplaceMomenta-ID12", +"FCReplaceMomenta[ +SFAD[{{p1, 0}, {0, 1}, 1}] SFAD[{{p2, 0}, {0, 1}, + 1}] SFAD[{{p1 + p2, 0}, {0, 1}, 1}] SFAD[{{p4, 0}, {0, 1}, + 1}] SFAD[{{p1 + p4, 0}, {0, 1}, + 1}] SFAD[{{-p1 - p2 - p4 + Q, 0}, {0, 1}, 1}] SPD[-p1 - p4 + +Q, -p1 - p4 + Q], {Q -> p1 + p2 + p3 + p4}, FCE -> True]", +"SFAD[{{p1, 0}, {0, 1}, 1}] SFAD[{{p2, 0}, {0, 1}, +1}] SFAD[{{p1 + p2, 0}, {0, 1}, 1}] SFAD[{{p3, 0}, {0, 1}, +1}] SFAD[{{p4, 0}, {0, 1}, 1}] SFAD[{{p1 + p4, 0}, {0, 1}, 1}] SPD[ +p2 + p3, p2 + p3]"}, +{"fcstFCReplaceMomenta-ID13", +"FCReplaceMomenta[ +GFAD[{{-Q2 SPD[p2, p4] + (1 - c) SPD[p2, Q] SPD[p4, Q], 1}, + 1}] SFAD[{{p1, 0}, {0, 1}, 1}] SFAD[{{p2, 0}, {0, 1}, + 1}] SFAD[{{p1 + p2, 0}, {0, 1}, 1}] SFAD[{{p4, 0}, {0, 1}, + 1}] SFAD[{{p1 + p4, 0}, {0, 1}, + 1}] SFAD[{{-p1 - p2 - p4 + Q, 0}, {0, 1}, 1}], {Q -> +p1 + p2 + p3 + p4}, SelectFree -> {GenericPropagatorDenominator}, +FCE -> True]", +"GFAD[{{-Q2 SPD[p2, p4] + (1 - c) SPD[p2, Q] SPD[p4, Q], 1}, +1}] SFAD[{{p1, 0}, {0, 1}, 1}] SFAD[{{p2, 0}, {0, 1}, +1}] SFAD[{{p1 + p2, 0}, {0, 1}, 1}] SFAD[{{p3, 0}, {0, 1}, +1}] SFAD[{{p4, 0}, {0, 1}, 1}] SFAD[{{p1 + p4, 0}, {0, 1}, 1}]"}, +{"fcstFCReplaceMomenta-ID9", +"FCReplaceMomenta[ +CartesianPair[CartesianMomentum[kphat], +CartesianMomentum[p2]], {p2 -> 1/2 P - Q}, +ExpandScalarProduct -> True,FCE->True]", +"1/2 CSP[kphat, P] - CSP[kphat, Q]"} +}); diff --git a/Tests/Lorentz/FCRerouteMomenta.test b/Tests/Lorentz/FCRerouteMomenta.test new file mode 100644 index 000000000..37c0faf3e --- /dev/null +++ b/Tests/Lorentz/FCRerouteMomenta.test @@ -0,0 +1,127 @@ +(* :Title: FCRerouteMomenta.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCRerouteMomenta *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstFCRerouteMomenta = +({ +{"fcstRerouteMomenta-ID1", +"FCRerouteMomenta[GS[p1]+GS[p2+p3],{k1,k2},{p1,p2,p3}]", +"DiracGamma[Momentum[p1]] + DiracGamma[Momentum[p2 + p3]]"}, +{"fcstRerouteMomenta-ID2", +"FCRerouteMomenta[GS[p1]+GS[p2+p3],{k1,k2},{p1,p2,p3},\ +DiracGammaCombine\[Rule]True]", "DiracGamma[Momentum[k1 + k2]]"}, +{"fcstRerouteMomenta-ID3", +"FCRerouteMomenta[CGS[p1]+CGS[p2+p3],{k1,k2},{p1,p2,p3}]", +"DiracGamma[CartesianMomentum[p1]] + \ +DiracGamma[CartesianMomentum[p2 + p3]]"}, +{"fcstRerouteMomenta-ID4", +"FCRerouteMomenta[CGS[p1]+CGS[p2+p3],{k1,k2},{p1,p2,p3},\ +DiracGammaCombine\[Rule]True]", +"DiracGamma[CartesianMomentum[p1 + p2 + p3]]"}, +{"fcstRerouteMomenta-ID5", +"FCRerouteMomenta[FV[p1,mu]+FV[p2+p3,mu],{k1,k2},{p1,p2,p3}]", +"Pair[LorentzIndex[mu], Momentum[p1]] + Pair[LorentzIndex[mu], \ +Momentum[p2 + p3]]"}, +{"fcstRerouteMomenta-ID6", +"FCRerouteMomenta[FV[p1,mu]+FV[p2+p3,mu],{k1,k2},{p1,p2,p3},\ +MomentumCombine\[Rule]True]", +"Pair[LorentzIndex[mu], Momentum[k1 + k2]]"}, +{"fcstRerouteMomenta-ID7", +"FCRerouteMomenta[CV[p1,mu]+CV[p2+p3,mu],{k1,k2},{p1,p2,p3}]", +"CartesianPair[CartesianIndex[mu], CartesianMomentum[p1]] + \ +CartesianPair[CartesianIndex[mu], CartesianMomentum[p2 + p3]]"}, +{"fcstRerouteMomenta-ID8", +"FCRerouteMomenta[CV[p1,mu]+CV[p2+p3,mu],{k1,k2},{p1,p2,p3},\ +MomentumCombine\[Rule]True]", +"CartesianPair[CartesianIndex[mu], CartesianMomentum[k1 + k2]]"}, +{"fcstRerouteMomenta-ID9", +"FCRerouteMomenta[FAD[p1+p2+p3],{k1,k2},{p1,p2,p3}]", +"FeynAmpDenominator[PropagatorDenominator[Momentum[k1, D] + \ +Momentum[k2, D], 0]]"}, +{"fcstRerouteMomenta-ID10", +"FCRerouteMomenta[FAD[p1+p2+p3],{k1,k2},{p1,p2,p3},Eliminate\[Rule]\ +{k2}]", "FeynAmpDenominator[PropagatorDenominator[Momentum[p1, D] + \ +Momentum[p2, D] + Momentum[p3, D], 0]]"}, +{"fcstRerouteMomenta-ID11", +"FCRerouteMomenta[FAD[pH],{k1,k2},{p1,p2,p3},InitialSubstitutions\ +\[Rule]{pH\[Rule]p1+p2+p3}]", +"FeynAmpDenominator[PropagatorDenominator[Momentum[k1, D] + \ +Momentum[k2, D], 0]]"}, +{"fcstRerouteMomenta-ID12", +"FCRerouteMomenta[FAD[p1+p2],{k1,k2},{p1,p2},Eliminate\[Rule]{p2}]\ +", "FeynAmpDenominator[PropagatorDenominator[Momentum[k1, D] + \ +Momentum[k2, D], 0]]"}, +{"fcstRerouteMomenta-ID13", +"FCRerouteMomenta[FAD[p1+p2],{k1,k2},{p1,p2},Eliminate\[Rule]{p1,\ +p2}]", "FeynAmpDenominator[PropagatorDenominator[Momentum[k1, D] + \ +Momentum[k2, D], 0]]"}, +{"fcstRerouteMomenta-ID14", +"FCRerouteMomenta[FAD[p1+p2],{k1,k2},{p1,p2},Eliminate\[Rule]{k1,\ +p2}]", "FeynAmpDenominator[PropagatorDenominator[Momentum[p1, D] + \ +Momentum[p2, D], 0]]"}, +{"fcstRerouteMomenta-ID15", +"FCRerouteMomenta[Spinor[-Momentum[p2],m,1].GS[Polarization[k2,-\ +\[ImaginaryI]]].(GS[k2-p2]+m).GS[Polarization[k4,-\[ImaginaryI]]].(GS[\ +k2+k4-p2]+m).GS[Polarization[k3,-\[ImaginaryI]]].(GS[k2+k3+k4-p2]+m).\ +GS[Polarization[k1,-\[ImaginaryI]]].Spinor[Momentum[p1],m,1] \ +FAD[{-k2+p2,m}] FAD[{-k2-k4+p2,m}] FAD[{-k2-k3-k4+p2,m}] \ +,{p1,p2},{k1,k2,k3,k4},FCE->True]", +"Spinor[-Momentum[p2], m, 1] . GS[Polarization[k2, -I]] . (m + \ +GS[k2 - p2]) . GS[Polarization[k4, -I]] . (m + GS[k2 + k4 - p2]) . \ +GS[Polarization[k3, -I]] . (m + GS[-k1 + p1]) . GS[Polarization[k1, \ +-I]] . Spinor[Momentum[p1], m, 1]*FAD[{k1 - p1, m}]*FAD[{-k2 + p2, \ +m}]*FAD[{-k2 - k4 + p2, m}]"}, +{"fcstRerouteMomenta-ID16", +"FCRerouteMomenta[Spinor[-Momentum[p2],m,1].GS[Polarization[k2,-\ +\[ImaginaryI]]].(GS[k2-p2]+m).GS[Polarization[k4,-\[ImaginaryI]]].(GS[\ +k2+k4-p2]+m).GS[Polarization[k3,-\[ImaginaryI]]].(GS[k2+k3+k4-p2]+m).\ +GS[Polarization[k1,-\[ImaginaryI]]].Spinor[Momentum[p1],m,1] \ +FAD[{-k2+p2,m}] FAD[{-k2-k4+p2,m}] FAD[{-k2-k3-k4+p2,m}] \ +,{p1,p2},{k1,k2,k3,k4},Eliminate\[Rule]{p2},FCE->True]", +"Spinor[-Momentum[p2], m, 1] . GS[Polarization[k2, -I]] . (m + \ +GS[k2 - p2]) . GS[Polarization[k4, -I]] . (m + GS[-k1 - k3 + p1]) . \ +GS[Polarization[k3, -I]] . (m + GS[-k1 + p1]) . GS[Polarization[k1, \ +-I]] . Spinor[Momentum[p1], m, 1]*FAD[{k1 - p1, m}]*FAD[{k1 + k3 - \ +p1, m}]*FAD[{-k2 + p2, m}]"}, +{"fcstRerouteMomenta-ID17", +"FCRerouteMomenta[Spinor[-Momentum[p2],m,1].GS[Polarization[k2,-\ +\[ImaginaryI]]].(GS[k2-p2]+m).GS[Polarization[k4,-\[ImaginaryI]]].(GS[\ +k2+k4-p2]+m).GS[Polarization[k3,-\[ImaginaryI]]].(GS[k2+k3+k4-p2]+m).\ +GS[Polarization[k1,-\[ImaginaryI]]].Spinor[Momentum[p1],m,1] \ +FAD[{-k2+p2,m}] FAD[{-k2-k4+p2,m}] FAD[{-k2-k3-k4+p2,m}] \ +,{p1,p2},{k1,k2,k3,k4},Eliminate\[Rule]{p2},InitialSubstitutions\ +\[Rule]{p2\[Rule]k1+k2+k3+k4-p1},FCE->True]", +"Spinor[-Momentum[p2], m, 1] . GS[Polarization[k2, -I]] . (m + \ +GS[-k1 - k3 - k4 + p1]) . GS[Polarization[k4, -I]] . (m + GS[-k1 - k3 \ ++ p1]) . GS[Polarization[k3, -I]] . (m + GS[-k1 + p1]) . \ +GS[Polarization[k1, -I]] . Spinor[Momentum[p1], m, 1]*FAD[{k1 - p1, \ +m}]*FAD[{k1 + k3 - p1, m}]*FAD[{k1 + k3 + k4 - p1, m}]"}, +{"fcstRerouteMomenta-ID18", +"FCRerouteMomenta[FAD[p1,p2,p3,p1+p2+p3-Q] \ +SPD[-p2-p3+Q,-p2-p3+Q],{Q},{p1,p2,p3,p4},FCE->True]", +"FAD[p1, p2, p3, -p4]*SPD[p1 + p4, p1 + p4]"}, +{"fcstRerouteMomenta-ID19", +"FCRerouteMomenta[FAD[p1,p2,p3,p3-Q,p1+p2+p3-Q] \ +SPD[-p2-p3+Q,-p2-p3+Q],{Q},{p1,p2,p3,p4},FCE->True]", +"FAD[p1, p2, p3, p3 - Q, -p4]*SPD[p1 + p4, p1 + p4]"}, +{"fcstRerouteMomenta-ID20", +"FCRerouteMomenta[FAD[p1,p2,p3,p1+p2+p3-Q],{Q},{p1,p2,p3,p4},\ +FCE->True]", "FAD[p1, p2, p3, -p4]"}, +{"fcstRerouteMomenta-ID21", +"FCRerouteMomenta[GFAD[{{-Q2 SPD[p2,p4]+(1-c) SPD[p2,Q] SPD[p4,Q],1},1}] SFAD[{{p1,0},{0,1},1}] * +SFAD[{{p2,0},{0,1},1}] SFAD[{{p1+p2,0},{0,1},1}] SFAD[{{p4,0},{0,1},1}] SFAD[{{p1+p4,0},{0,1},1}] * +SFAD[{{-p1-p2-p4+Q,0},{0,1},1}],{Q},{p1,p2,p3,p4},FCE->True]", "GFAD[{{-Q2 SPD[p2, p4] + SPD[p2, Q] SPD[p4, Q] - + c SPD[p2, Q] SPD[p4, Q], 1}, 1}] SFAD[{{p1, 0}, {0, 1}, +1}] SFAD[{{p2, 0}, {0, 1}, 1}] SFAD[{{p1 + p2, 0}, {0, 1}, +1}] SFAD[{{p3, 0}, {0, 1}, 1}] SFAD[{{p4, 0}, {0, 1}, +1}] SFAD[{{p1 + p4, 0}, {0, 1}, 1}]"} +}); diff --git a/Tests/Lorentz/FCSchoutenBruteForce.test b/Tests/Lorentz/FCSchoutenBruteForce.test new file mode 100644 index 000000000..bff72f9a3 --- /dev/null +++ b/Tests/Lorentz/FCSchoutenBruteForce.test @@ -0,0 +1,69 @@ +(* :Title: FCSchoutenBruteForce.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCSchoutenBruteForce *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstFCSchoutenBruteForce = +({ +{"fcstFCSchoutenBruteForce-ID1", "FCSchoutenBruteForce[1,{},{}]", +"1"}, +{"fcstFCSchoutenBruteForce-ID2", +"FCSchoutenBruteForce[LC[][p1,p2,p3,p4]SP[p5,p6]+LC[][p2,p3,p4,p5]\ +SP[p1,p6]+LC[][p3,p4,p5,p1]SP[p2,p6]+LC[][p4,p5,p1,p2]SP[p3,p6],{},{},\ +Rule\[Rule]False,Information\[Rule]False]", +"Eps[Momentum[p1], Momentum[p2], Momentum[p3], \ +Momentum[p5]]*Pair[Momentum[p4], Momentum[p6]]"}, +{"fcstFCSchoutenBruteForce-ID3", +"FCSchoutenBruteForce[LC[][p1,p2,p3,p4]SP[p5,p6]+LC[][p2,p3,p4,p5]\ +SP[p1,p6]+LC[][p3,p4,p5,p1]SP[p2,p6]+LC[][p4,p5,p1,p2]SP[p3,p6],{},{},\ +Rule\[Rule]False,Information\[Rule]False,Take\[Rule]2]", +"Eps[Momentum[p1], Momentum[p2], Momentum[p3], \ +Momentum[p5]]*Pair[Momentum[p4], Momentum[p6]]"}, +{"fcstFCSchoutenBruteForce-ID4", +"FCSchoutenBruteForce[LC[][p1,p2,p3,p4]SP[p5,p6]+LC[][p2,p3,p4,p5]\ +SP[p1,p6]+LC[][p3,p4,p5,p1]SP[p2,p6]+LC[][p4,p5,p1,p2]SP[p3,p6]+LC[][\ +p5,p1,p2,p3]SP[p4,p6],{},{},Rule\[Rule]False,Information\[Rule]False]\ +", "0"}, +{"fcstFCSchoutenBruteForce-ID5", +"4 I (SP[p5, p6] LC[][p1, p2, p3, p4] - + SP[p4, p6] LC[][p1, p2, p3, p5] + + SP[p3, p5] LC[][p1, p2, p4, p6] - + SP[p3, p4] LC[][p1, p2, p5, p6] - + SP[p2, p6] LC[][p1, p3, p4, p5] + + SP[p2, p3] LC[][p1, p4, p5, p6] + + SP[p1, p6] LC[][p2, p3, p4, p5] - + SP[p1, p3] LC[][p2, p4, p5, p6]) // +FCSchoutenBruteForce[#, {}, {}, Rule -> False, +Information -> False] & // FCSchoutenBruteForce[#, {}, {}, +Rule -> False, Information -> False]&", "0"}, +{"fcstFCSchoutenBruteForce-ID6", +"rule@@Last[list@@(FCSchoutenBruteForce[ +4 I (SP[p5, p6] LC[][p1, p2, p3, p4] - + SP[p4, p6] LC[][p1, p2, p3, p5] + + SP[p3, p5] LC[][p1, p2, p4, p6] - + SP[p3, p4] LC[][p1, p2, p5, p6] - + SP[p2, p6] LC[][p1, p3, p4, p5] + + SP[p2, p3] LC[][p1, p4, p5, p6] + + SP[p1, p6] LC[][p2, p3, p4, p5] - + SP[p1, p3] LC[][p2, p4, p5, p6]), {}, {}, Rule -> False, +Information -> False, List -> True, FCE -> True])]", +"rule[SP[p5, p6]*LC[][p1, p2, p3, p4], +-(LC[][p2, p3, p4, p5]*SP[p1, p6]) + LC[][p1, p3, p4, p5]*SP[p2, p6] - +LC[][p1, p2, p4, p5]*SP[p3, p6] + LC[][p1, p2, p3, p5]*SP[p4, p6]]"}, +{"fcstFCSchoutenBruteForce-ID7", +"FCSchoutenBruteForce[ +4 I (SP[p, z] LC[][c, d, k, t] - SP[p, t] LC[][c, d, k, z] + + SP[k, p] LC[][c, d, t, z] - SP[d, p] LC[][c, k, t, z] - + SP[c, z] LC[][d, k, p, t] + SP[c, t] LC[][d, k, p, z] + + SP[c, k] LC[][d, p, t, z] - SP[c, d] LC[][k, p, t, z]), {}, {}, +Schouten -> True, Information -> 0]", +"0"} +}); diff --git a/Tests/Lorentz/FourDivergence.test b/Tests/Lorentz/FourDivergence.test index 767f848b3..0eb7604cc 100644 --- a/Tests/Lorentz/FourDivergence.test +++ b/Tests/Lorentz/FourDivergence.test @@ -3,9 +3,9 @@ (* :Title: FourDivergence.test *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FourDivergence *) @@ -14,53 +14,58 @@ Tests`Lorentz`fcstFourDivergence = { -{"fcstFourDivergence-ID1","FourDivergence[ScalarProduct[p, q], FV[p, mu]]","Pair[LorentzIndex[mu], Momentum[q]]"}, -{"fcstFourDivergence-ID2","FourDivergence[ScalarProduct[p - k, q], FV[p - k, mu]]","Pair[LorentzIndex[mu], Momentum[q]]"}, -{"fcstFourDivergence-ID3","FourDivergence[ScalarProduct[p - k, q] // ExpandScalarProduct, -FV[p, mu]]","Pair[LorentzIndex[mu], Momentum[q]]"}, -{"fcstFourDivergence-ID4","FourDivergence[1/ScalarProduct[p, q], FV[p, mu]] // -FourDivergence[#, FV[p, mu]] &","(2*Pair[Momentum[q], Momentum[q]])/Pair[Momentum[p], Momentum[q]]^3"}, -{"fcstFourDivergence-ID5","FourDivergence[ +{"fcstFourDivergence-ID1","FourDivergence[SP[p, q], FV[p, mu], FCE->True]","FV[q,mu]"}, +{"fcstFourDivergence-ID2","FourDivergence[ScalarProduct[p - k, q], FV[p, mu], FCE->True]","FV[q,mu]"}, +{"fcstFourDivergence-ID3","FourDivergence[1/SP[p, q], FV[p, mu], FV[p, mu], FCE -> True]","(2 SP[q, q])/SP[p, q]^3"}, +{"fcstFourDivergence-ID4","FourDivergence[ Uncontract[SP[p, w] SpinorUBar[p2, m].GS[w].SpinorU[p1, m], w, Pair -> All], FV[w, a]]","Spinor[Momentum[p2], m, 1] . DiracGamma[Momentum[w]] . Spinor[Momentum[p1], m, 1]*Pair[LorentzIndex[a], Momentum[p]] + Spinor[Momentum[p2], m, 1] . DiracGamma[LorentzIndex[a]] . Spinor[Momentum[p1], m, 1]*Pair[Momentum[p], Momentum[w]]"}, -{"fcstFourDivergence-ID6","FourDivergence[FV[k1, a] FV[k1, b] (SP[k1, q] + 2 SP[k2, q]), - FV[q, c]]","Pair[LorentzIndex[a], Momentum[k1]]*Pair[LorentzIndex[b], Momentum[k1]]* - Pair[LorentzIndex[c], Momentum[k1]] + 2*Pair[LorentzIndex[a], Momentum[k1]]* - Pair[LorentzIndex[b], Momentum[k1]]*Pair[LorentzIndex[c], Momentum[k2]]"}, -{"fcstFourDivergence-ID7","FourDivergence[FV[k1, a] FV[k1, b] (SP[k1, q] + SP[k2, q]), FV[q, c]]", - "Pair[LorentzIndex[a], Momentum[k1]]*Pair[LorentzIndex[b], Momentum[k1]]*Pair[LorentzIndex[c], Momentum[k1]] + - Pair[LorentzIndex[a], Momentum[k1]]*Pair[LorentzIndex[b], Momentum[k1]]*Pair[LorentzIndex[c], Momentum[k2]]"}, -{"fcstFourDivergence-ID8","FourDivergence[ScalarProduct[p - k, q + b], FV[k, mu]]", +{"fcstFourDivergence-ID5","FourDivergence[FV[k1, a] FV[k1, b] (SP[k1, q] + 2 SP[k2, q]), + FV[q, c],FCE->True]","FV[k1, a]*FV[k1, b]*(FV[k1, c] + 2*FV[k2, c])"}, +{"fcstFourDivergence-ID6","FourDivergence[FV[k1, a] FV[k1, b] (SP[k1, q] + SP[k2, q]), FV[q, c], FCE->True]", + "FV[k1, a]*FV[k1, b]*(FV[k1, c] + FV[k2, c])"}, +{"fcstFourDivergence-ID7","FourDivergence[ScalarProduct[p - k, q + b], FV[k, mu]]", "-Pair[LorentzIndex[mu], Momentum[b]] - Pair[LorentzIndex[mu], Momentum[q]]"}, -{"fcstFourDivergence-ID9","FourDivergence[FAD[p - k], FV[k, mu]]","0"}, -{"fcstFourDivergence-ID10","FourDivergence[FAD[p - k], FVD[k, mu]]", - "2 FeynAmpDenominator[PropagatorDenominator[-Momentum[k, D] + Momentum[p, D], 0], - PropagatorDenominator[-Momentum[k, D] + Momentum[p, D], 0]] (-Pair[LorentzIndex[mu, D], Momentum[k, D]] + - Pair[LorentzIndex[mu, D], Momentum[p, D]])"}, -{"fcstFourDivergence-ID11","FourDivergence[FAD[{p + q, m}], FVD[p, mu]] // FCE", - "-2 FAD[{p + q, m}, {p + q, m}] (FVD[p, mu] + FVD[q, mu])"}, -{"fcstFourDivergence-ID12","FourDivergence[FAD[{p + k, m}, {k - l, m}], FVD[k, mu]] // FCE", - "-2 FAD[{k + p, m}, {k - l, m}, {k - l, m}] (FVD[k, mu] - - FVD[l, mu]) - 2 FAD[{k - l, m}, {k + p, m}, {k + p, m}] (FVD[k, mu] + FVD[p, mu])"}, -{"fcstFourDivergence-ID11","FourDivergence[ScalarProduct[p - k, q],FourVector[k - p, mu]] // FCE", - "-FV[q, mu]"}, -{"fcstFourDivergence-ID12","FourDivergence[GSD[p], FVD[p, mu]]//FCE", +{"fcstFourDivergence-ID8","Off[FourDivergence::warn]; tmp=FourDivergence[FAD[p - k], FV[k, mu]]; On[FourDivergence::warn]; tmp","0"}, +{"fcstFourDivergence-ID9","FourDivergence[FAD[p - k], FVD[k, mu], FCE->True]", + "FAD[-k + p, -k + p]*(-2*FVD[k, mu] + 2*FVD[p, mu])"}, +{"fcstFourDivergence-ID10","FourDivergence[FAD[{p + q, m}], FVD[p, mu], FCE->True]", + "FAD[{p + q, m}, {p + q, m}]*(-2*FVD[p, mu] - 2*FVD[q, mu])"}, +{"fcstFourDivergence-ID11","FourDivergence[FAD[{p + k, m}, {k - l, m}], FVD[k, mu], FCE->True]", + "FAD[{k + p, m}, {k - l, m}, {k - l, m}] (-2 FVD[k, mu] + + 2 FVD[l, mu]) + FAD[{k - l, m}, {k + p, m}, {k + p, m}] (-2 FVD[k, mu] - 2 FVD[p, mu])"}, +{"fcstFourDivergence-ID12","FourDivergence[GSD[p], FVD[p, mu], FCE->True]", "GAD[mu]"}, -{"fcstFourDivergence-ID13","FourDivergence[GS[p], FV[p, mu]]//FCE", +{"fcstFourDivergence-ID13","FourDivergence[GS[p], FV[p, mu], FCE->True]", "GA[mu]"}, -{"fcstFourDivergence-ID14","FourDivergence[GSD[p+q], FVD[p, mu]]//FCE", +{"fcstFourDivergence-ID14","FourDivergence[GSD[p+q], FVD[p, mu], FCE->True]", "GAD[mu]"}, -{"fcstFourDivergence-ID15","FourDivergence[GS[p+q], FV[p, mu]]//FCE", +{"fcstFourDivergence-ID15","FourDivergence[GS[p+q], FV[p, mu], FCE->True]", "GA[mu]"}, -{"fcstFourDivergence-ID16","FourDivergence[FVD[l, mu] FAD[{l, 0}, {l - p, 0}], FVD[l, mu]]//FCE", - "D FAD[l, l - p] - 2 FAD[l, l, l - p] SPD[l, l] -2 FAD[l, l - p, l - p] (SPD[l, l] - SPD[l, p])"} - - - - - - - +{"fcstFourDivergence-ID16","FourDivergence[FVD[l, mu] FAD[{l, 0}, {l - p, 0}], FVD[l, mu], FCE->True]", + "D FAD[l, l - p] - 2 FAD[l, l, l - p] SPD[l, l] +FAD[l, l - p, l - p] (-2 SPD[l, l] + 2 SPD[l, p])"}, +{"fcstFourDivergence-ID17","FourDivergence[FVD[l, mu] FAD[{l, 0}, {l - p, 0}], FVD[l, mu], FCE->True, ApartFF->True]", + "(-3 + D) FAD[l, l - p] - FAD[l - p, l - p] + FAD[l, l - p, l - p] SPD[p, p]"}, +{"fcstFourDivergence-ID18","FourDivergence[ +FeynAmpDenominator[ +PropagatorDenominator[ +Momentum[q, D] - Sqrt[m^2 - SPD[q, q]] Momentum[k1hat, D] + + 2 Sqrt[m^2 - SPD[q, q]] Momentum[Phat, D], m]], FVD[q, nu], +FCE -> True]//Simplify", + "(2*FAD[{q - (k1hat - 2*Phat)*Sqrt[m^2 - SPD[q, q]], m}, + {q - (k1hat - 2*Phat)*Sqrt[m^2 - SPD[q, q]], m}]* + (FVD[q, nu]*(-SPD[k1hat, q] + 2*SPD[Phat, q] + + (-1 + SPD[k1hat, k1hat] - 4*SPD[k1hat, Phat] + 4*SPD[Phat, Phat])* + Sqrt[m^2 - SPD[q, q]]) + FVD[k1hat, nu]*(m^2 - SPD[q, q]) - + 2*FVD[Phat, nu]*(m^2 - SPD[q, q])))/Sqrt[m^2 - SPD[q, q]]"}, +{"fcstFourDivergence-ID15","FourDivergence[ScalarProduct[p, w]*SpinorUBar[p2, m].GS[w].SpinorU[p1, m], FV[w, a],FCE -> True]", + "Spinor[Momentum[p2], m, 1].GS[w].Spinor[Momentum[p1], m, 1] FV[p, a] + +Spinor[Momentum[p2], m, 1].GA[a].Spinor[Momentum[p1], m, 1] SP[p, w]"}, +{"fcstFourDivergence-ID16","Off[FourDivergence::warnCartesian]; tmp = +FourDivergence[CSP[p, q], FV[p, mu]]; On[FourDivergence::warnCartesian]; tmp","0"}, +{"fcstFourDivergence-ID17","FourDivergence[SFAD[{{p + q, p.l}}], FVD[p, mu], FCE -> True]", +"(-FVD[l, mu] - 2 FVD[p, mu] -2 FVD[q, mu]) SFAD[{{p + q, l.p}, {0, 1}, +1}, {{p + q, l.p}, {0, 1}, 1}]"} }; diff --git a/Tests/Lorentz/FourLaplacian.test b/Tests/Lorentz/FourLaplacian.test index bade370d9..e749685e7 100644 --- a/Tests/Lorentz/FourLaplacian.test +++ b/Tests/Lorentz/FourLaplacian.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FourLaplacian *) @@ -17,18 +17,11 @@ Tests`Lorentz`fcstFourLaplacian = ({ {"fcstFourLaplacian-ID1", "FourLaplacian[SP[q,q],q,q]", "2*D"}, {"fcstFourLaplacian-ID2", "FourLaplacian[SOD[q]^OPEm FAD[q,q-p]//FCI,q,q]//FCE//FCI//FCE", -"2 OPEm FAD[q, -p + q, -p + q] SOD[p] SOD[q]^(-1 + OPEm) - -2 D FAD[q, q, -p + q] SOD[q]^OPEm - -4 OPEm FAD[q, q, -p + q] SOD[q]^OPEm - -2 D FAD[q, -p + q, -p + q] SOD[q]^OPEm - -2 OPEm FAD[q, -p + q, -p + q] SOD[q]^OPEm - -2 OPEm FAD[q, -p + q, -p + q] SOD[q]^(-1 + -OPEm) (-SOD[p] + SOD[q]) - -4 FAD[q, q, -p + q, -p + q] SOD[q]^OPEm SPD[p, q] - -8 FAD[q, -p + q, -p + q, -p + q] SOD[q]^ -OPEm (-SPD[p, p] + SPD[p, q]) + -8 FAD[q, q, q, -p + q] SOD[q]^OPEm SPD[q, q] + -4 FAD[q, q, -p + q, -p + q] SOD[q]^OPEm SPD[q, q] + -4 FAD[q, q, -p + q, -p + q] SOD[q]^OPEm (-SPD[p, q] + SPD[q, q]) + -8 FAD[q, -p + q, -p + q, -p + q] SOD[q]^OPEm (-SPD[p, q] + SPD[q, q])"} +"-2*(D + 2*OPEm)*FAD[q, q, -p + q]*SOD[q]^OPEm + +FAD[q, -p + q, -p + q]*(4*OPEm*SOD[p]*SOD[q]^(-1 + OPEm) - +2*D*SOD[q]^OPEm - 4*OPEm*SOD[q]^OPEm) + 8*FAD[q, q, q, -p + q]* +SOD[q]^OPEm*SPD[q, q] + FAD[q, -p + q, -p + q, -p + q]* +(8*SOD[q]^OPEm*SPD[p, p] - 16*SOD[q]^OPEm*SPD[p, q] + +8*SOD[q]^OPEm*SPD[q, q]) + FAD[q, q, -p + q, -p + q]* +(-8*SOD[q]^OPEm*SPD[p, q] + 8*SOD[q]^OPEm*SPD[q, q])"} }) diff --git a/Tests/Lorentz/FreeIndexFreeQ.test b/Tests/Lorentz/FreeIndexFreeQ.test new file mode 100644 index 000000000..7d107f9f4 --- /dev/null +++ b/Tests/Lorentz/FreeIndexFreeQ.test @@ -0,0 +1,40 @@ + + +(* :Title: FreeIndexFreeQ.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FreeIndexFreeQ *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstFreeIndexFreeQ = +({ +{"fcstFreeIndexFreeQ-ID1", "FreeIndexFreeQ[0,{LorentzIndex}]", +"True"}, +{"fcstFreeIndexFreeQ-ID2", "FreeIndexFreeQ[a,{LorentzIndex}]", +"True"}, +{"fcstFreeIndexFreeQ-ID3", +"FreeIndexFreeQ[FCI[FV[p,i]],{LorentzIndex}]", "False"}, +{"fcstFreeIndexFreeQ-ID4", +"FreeIndexFreeQ[FCI[FV[p,i]],{CartesianIndex}]", "True"}, +{"fcstFreeIndexFreeQ-ID5", +"FreeIndexFreeQ[FCI[FV[p,i]^2],{LorentzIndex}]", "True"}, +{"fcstFreeIndexFreeQ-ID6", +"FreeIndexFreeQ[FCI[FV[p1,i]+FV[p2,i]+FV[p3,i]MT[j,j]],{\ +LorentzIndex}]", "False"}, +{"fcstFreeIndexFreeQ-ID7", +"FreeIndexFreeQ[FCI[FV[p,mu]FV[q,mu]FV[t,bh].GA[bh]+GS[nh]],{\ +LorentzIndex}]", "True"}, +{"fcstFreeIndexFreeQ-ID8", +"FreeIndexFreeQ[FCI[FV[p,mu]FV[q,mu]FV[t,bh]+GA[nh]],{LorentzIndex}\ +]", "False"}, +{"fcstFreeIndexFreeQ-ID9", +"FreeIndexFreeQ[FCI[FV[p,mu]FV[q,mu]FV[t,bh].GA[bh]+GS[nh]],{\ +LorentzIndex}]", "True"} +}); diff --git a/Tests/Lorentz/IntegrationTests/Contract.test b/Tests/Lorentz/IntegrationTests/Contract.test new file mode 100644 index 000000000..3c8b04e7b --- /dev/null +++ b/Tests/Lorentz/IntegrationTests/Contract.test @@ -0,0 +1,568 @@ +Tests`Lorentz`fcitContract = +({ +{"fcitContract-ID1", +"Y[k_, mu_, nu_, al_, be_, ga_] := +FVD[k, mu] (MTD[nu, be] MTD[al, ga] - MTD[nu, ga] MTD[al, be]) + +FVD[k, be] (MTD[mu, al] MTD[nu, ga] - + 1/2 MTD[mu, nu] MTD[al, ga]) - +FVD[k, ga] (MTD[mu, al] MTD[nu, be] - + 1/2 MTD[mu, nu] MTD[al, be]); \n +Z[k1_, k2_, k3_, mu_, nu_, al_, be_, ga_] := +Y[k1, mu, nu, al, be, ga] + Y[k2, mu, nu, be, ga, al] + +Y[k3, nu, mu, ga, al, be] + Y[k1, nu, mu, al, be, ga] + +Y[k2, nu, mu, be, ga, al] + Y[k3, nu, mu, ga, al, be]; \n +gps[mu_, nu_, rho_, si_] := (MTD[mu, rho] - (FVD[k, mu] FVD[k, rho])/SPD[k, k]) (MTD[ + nu, si] - (FVD[k, nu] FVD[k, si])/SPD[k, k]) + (MTD[mu, + si] - (FVD[k, mu] FVD[k, si])/SPD[k, k]) (MTD[nu, + rho] - (FVD[k, nu] FVD[k, rho])/SPD[k, k]) - +2/3 (MTD[mu, nu] - (FVD[k, mu] FVD[k, nu])/SPD[k, k]) (MTD[rho, + si] - (FVD[k, rho] FVD[k, si]/SPD[k, k])); \n +xyz[k1_, k2_, k3_, al_, be_, ga_] := +MTD[al, be] FVD[(k1 - k2), ga] + MTD[be, ga] FVD[(k2 - k3), al] + MTD[ga, al] FVD[(k3 - k1), be]; +gp = (GSD[p3] + m).GAD[ga].(GSD[p4 + k] + m).(FVD[2 p4 + k, mu] GAD[nu] + + FVD[2 p4 + k, nu].GAD[mu]).gps[mu, nu, rho, si].(GSD[p4] - m); \n +cp = xyz[k1, k2, -k1 + k2, al, be, ga]; \n +cpc = Z[-k1, -k2, k1 + k2 - k, rho, si, al, be, eps]; \n +TimeConstrained[(res = Contract[TR[gp.GAD[eps]] cp cpc];), If[$VersionNumber>=9,5,10]]; \n FCE[res]", +"-192*m^2*SPD[k, k1]*SPD[k, p4] + 128*D*m^2*SPD[k, k1]*SPD[k, p4] + +(128*m^2*SPD[k, k1]^2*SPD[k, p4])/(3*SPD[k, k]) - +(256*D*m^2*SPD[k, k1]^2*SPD[k, p4])/(3*SPD[k, k]) + +(32*D^2*m^2*SPD[k, k1]^2*SPD[k, p4])/SPD[k, k] + +64*m^2*SPD[k, k2]*SPD[k, p4] - (128*D*m^2*SPD[k, k2]*SPD[k, p4])/3 - +(256*m^2*SPD[k, k1]*SPD[k, k2]*SPD[k, p4])/(3*SPD[k, k]) + +(512*D*m^2*SPD[k, k1]*SPD[k, k2]*SPD[k, p4])/(3*SPD[k, k]) - +(64*D^2*m^2*SPD[k, k1]*SPD[k, k2]*SPD[k, p4])/SPD[k, k] + +(128*m^2*SPD[k, k2]^2*SPD[k, p4])/(3*SPD[k, k]) - +(256*D*m^2*SPD[k, k2]^2*SPD[k, p4])/(3*SPD[k, k]) + +(32*D^2*m^2*SPD[k, k2]^2*SPD[k, p4])/SPD[k, k] + +(576*m^2*SPD[k, k1]*SPD[k, p3]*SPD[k, p4])/SPD[k, k] - +(352*D*m^2*SPD[k, k1]*SPD[k, p3]*SPD[k, p4])/SPD[k, k] + +(32*D^2*m^2*SPD[k, k1]*SPD[k, p3]*SPD[k, p4])/SPD[k, k] - +(192*m^2*SPD[k, k2]*SPD[k, p3]*SPD[k, p4])/SPD[k, k] + +(352*D*m^2*SPD[k, k2]*SPD[k, p3]*SPD[k, p4])/(3*SPD[k, k]) - +(32*D^2*m^2*SPD[k, k2]*SPD[k, p3]*SPD[k, p4])/(3*SPD[k, k]) - +(384*m^2*SPD[k, k1]*SPD[k, p4]^2)/SPD[k, k] + +(256*D*m^2*SPD[k, k1]*SPD[k, p4]^2)/SPD[k, k] - +(512*m^2*SPD[k, k1]^2*SPD[k, p4]^2)/(3*SPD[k, k]^2) + +(256*D*m^2*SPD[k, k1]^2*SPD[k, p4]^2)/(3*SPD[k, k]^2) + +(128*m^2*SPD[k, k2]*SPD[k, p4]^2)/SPD[k, k] - +(256*D*m^2*SPD[k, k2]*SPD[k, p4]^2)/(3*SPD[k, k]) + +(1024*m^2*SPD[k, k1]*SPD[k, k2]*SPD[k, p4]^2)/(3*SPD[k, k]^2) - +(512*D*m^2*SPD[k, k1]*SPD[k, k2]*SPD[k, p4]^2)/(3*SPD[k, k]^2) - +(512*m^2*SPD[k, k2]^2*SPD[k, p4]^2)/(3*SPD[k, k]^2) + +(256*D*m^2*SPD[k, k2]^2*SPD[k, p4]^2)/(3*SPD[k, k]^2) + +(384*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]^2)/SPD[k, k] - +(192*D*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]^2)/SPD[k, k] - +(128*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]^2)/SPD[k, k] + +(64*D*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]^2)/SPD[k, k] - +(2048*m^2*SPD[k, p3]*SPD[k, p4]*SPD[k1, k1])/SPD[k, k] + +(928*D*m^2*SPD[k, p3]*SPD[k, p4]*SPD[k1, k1])/SPD[k, k] - +(64*D^2*m^2*SPD[k, p3]*SPD[k, p4]*SPD[k1, k1])/SPD[k, k] + +(128*m^2*SPD[k, p4]^2*SPD[k1, k1])/SPD[k, k] - +(64*D*m^2*SPD[k, p4]^2*SPD[k1, k1])/SPD[k, k] - +(1984*SPD[k, p3]*SPD[k, p4]^2*SPD[k1, k1])/(3*SPD[k, k]) + +(384*D*SPD[k, p3]*SPD[k, p4]^2*SPD[k1, k1])/SPD[k, k] + +(2560*SPD[k, p3]*SPD[k, p4]^3*SPD[k1, k1])/(3*SPD[k, k]^2) - +(256*m^2*SPD[k, p3]*SPD[k, p4]*SPD[k1, k2])/SPD[k, k] + +(64*D*m^2*SPD[k, p3]*SPD[k, p4]*SPD[k1, k2])/SPD[k, k] - +(256*m^2*SPD[k, p4]^2*SPD[k1, k2])/SPD[k, k] + +(128*D*m^2*SPD[k, p4]^2*SPD[k1, k2])/SPD[k, k] + +(128*SPD[k, p3]*SPD[k, p4]^2*SPD[k1, k2])/(3*SPD[k, k]) + +(1024*SPD[k, p3]*SPD[k, p4]^3*SPD[k1, k2])/(3*SPD[k, k]^2) + +(4736*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k1, p3])/(3*SPD[k, k]) - +(2144*D*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k1, p3])/(3*SPD[k, k]) + +(160*D^2*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k1, p3])/(3*SPD[k, k]) - +(512*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k1, p3])/(3*SPD[k, k]) + +(608*D*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k1, p3])/(3*SPD[k, k]) - +(160*D^2*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k1, p3])/(3*SPD[k, k]) + +96*SPD[k, p4]^2*SPD[k1, p3] - 32*D*SPD[k, p4]^2*SPD[k1, p3] + +(704*SPD[k, k1]*SPD[k, p4]^2*SPD[k1, p3])/SPD[k, k] - +(1408*D*SPD[k, k1]*SPD[k, p4]^2*SPD[k1, p3])/(3*SPD[k, k]) + +(32*D^2*SPD[k, k1]*SPD[k, p4]^2*SPD[k1, p3])/SPD[k, k] + +(128*SPD[k, k2]*SPD[k, p4]^2*SPD[k1, p3])/SPD[k, k] + +(256*D*SPD[k, k2]*SPD[k, p4]^2*SPD[k1, p3])/(3*SPD[k, k]) - +(32*D^2*SPD[k, k2]*SPD[k, p4]^2*SPD[k1, p3])/SPD[k, k] + +(384*SPD[k, p4]^3*SPD[k1, p3])/SPD[k, k] - (64*D*SPD[k, p4]^3*SPD[k1, p3])/ +SPD[k, k] - (1024*SPD[k, k1]*SPD[k, p4]^3*SPD[k1, p3])/SPD[k, k]^2 + +(256*D*SPD[k, k1]*SPD[k, p4]^3*SPD[k1, p3])/(3*SPD[k, k]^2) - +(256*D*SPD[k, k2]*SPD[k, p4]^3*SPD[k1, p3])/(3*SPD[k, k]^2) + +192*m^2*SPD[k, k]*SPD[k1, p4] - 128*D*m^2*SPD[k, k]*SPD[k1, p4] - +(128*m^2*SPD[k, k1]*SPD[k1, p4])/3 + (256*D*m^2*SPD[k, k1]*SPD[k1, p4])/3 - +32*D^2*m^2*SPD[k, k1]*SPD[k1, p4] - (1024*m^2*SPD[k, k2]*SPD[k1, p4])/3 + +(512*D*m^2*SPD[k, k2]*SPD[k1, p4])/3 + 32*D^2*m^2*SPD[k, k2]*SPD[k1, p4] + +192*m^2*SPD[k, p3]*SPD[k1, p4] - 128*D*m^2*SPD[k, p3]*SPD[k1, p4] + +(640*m^2*SPD[k, k1]*SPD[k, p3]*SPD[k1, p4])/SPD[k, k] - +(160*D*m^2*SPD[k, k1]*SPD[k, p3]*SPD[k1, p4])/(3*SPD[k, k]) + +(160*D*m^2*SPD[k, k2]*SPD[k, p3]*SPD[k1, p4])/(3*SPD[k, k]) + +384*m^2*SPD[k, p4]*SPD[k1, p4] - 256*D*m^2*SPD[k, p4]*SPD[k1, p4] + +(512*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k1, p4])/(3*SPD[k, k]) - +(640*D*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k1, p4])/(3*SPD[k, k]) + +(64*D^2*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k1, p4])/SPD[k, k] - +(2816*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k1, p4])/(3*SPD[k, k]) + +(2176*D*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k1, p4])/(3*SPD[k, k]) - +(64*D^2*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k1, p4])/SPD[k, k] - +96*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4] - 32*D*SPD[k, p3]*SPD[k, p4]* +SPD[k1, p4] - (192*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4])/ +SPD[k, k] + (320*D*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4])/ +(3*SPD[k, k]) - (32*D^2*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4])/ +SPD[k, k] + (256*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4])/SPD[k, k] - +(896*D*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4])/(3*SPD[k, k]) + +(32*D^2*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4])/SPD[k, k] - +(384*SPD[k, p3]*SPD[k, p4]^2*SPD[k1, p4])/SPD[k, k] - +(64*D*SPD[k, p3]*SPD[k, p4]^2*SPD[k1, p4])/SPD[k, k] - +(1024*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]^2*SPD[k1, p4])/SPD[k, k]^2 + +(256*D*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]^2*SPD[k1, p4])/(3*SPD[k, k]^2) - +(256*D*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]^2*SPD[k1, p4])/(3*SPD[k, k]^2) - +(4736*m^2*SPD[k1, p3]*SPD[k1, p4])/3 + (2144*D*m^2*SPD[k1, p3]*SPD[k1, p4])/ +3 - (160*D^2*m^2*SPD[k1, p3]*SPD[k1, p4])/3 - +(4736*SPD[k, p4]*SPD[k1, p3]*SPD[k1, p4])/3 + +(2144*D*SPD[k, p4]*SPD[k1, p3]*SPD[k1, p4])/3 - +(160*D^2*SPD[k, p4]*SPD[k1, p3]*SPD[k1, p4])/3 - +(2560*SPD[k, p4]^2*SPD[k1, p3]*SPD[k1, p4])/(3*SPD[k, k]) + +(1408*D*SPD[k, p4]^2*SPD[k1, p3]*SPD[k1, p4])/(3*SPD[k, k]) - +(128*D^2*SPD[k, p4]^2*SPD[k1, p3]*SPD[k1, p4])/(3*SPD[k, k]) - +128*m^2*SPD[k1, p4]^2 + 192*D*m^2*SPD[k1, p4]^2 - 64*D^2*m^2*SPD[k1, p4]^2 + +832*SPD[k, p3]*SPD[k1, p4]^2 - 160*D*SPD[k, p3]*SPD[k1, p4]^2 + +32*D^2*SPD[k, p3]*SPD[k1, p4]^2 + (1536*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4]^2)/ +SPD[k, k] - (128*D*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4]^2)/SPD[k, k] + +(128*m^2*SPD[k, p3]*SPD[k, p4]*SPD[k2, k2])/SPD[k, k] - +(32*D*m^2*SPD[k, p3]*SPD[k, p4]*SPD[k2, k2])/SPD[k, k] + +(128*m^2*SPD[k, p4]^2*SPD[k2, k2])/SPD[k, k] - +(64*D*m^2*SPD[k, p4]^2*SPD[k2, k2])/SPD[k, k] - +(64*SPD[k, p3]*SPD[k, p4]^2*SPD[k2, k2])/(3*SPD[k, k]) - +(512*SPD[k, p3]*SPD[k, p4]^3*SPD[k2, k2])/(3*SPD[k, k]^2) - +(512*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k2, p3])/(3*SPD[k, k]) + +(608*D*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k2, p3])/(3*SPD[k, k]) - +(160*D^2*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k2, p3])/(3*SPD[k, k]) + +(512*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k2, p3])/(3*SPD[k, k]) - +(608*D*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k2, p3])/(3*SPD[k, k]) + +(160*D^2*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k2, p3])/(3*SPD[k, k]) - +32*SPD[k, p4]^2*SPD[k2, p3] + (32*D*SPD[k, p4]^2*SPD[k2, p3])/3 - +(256*SPD[k, k1]*SPD[k, p4]^2*SPD[k2, p3])/SPD[k, k] + +(256*D*SPD[k, k1]*SPD[k, p4]^2*SPD[k2, p3])/(3*SPD[k, k]) - +(32*D^2*SPD[k, k1]*SPD[k, p4]^2*SPD[k2, p3])/SPD[k, k] + +(64*SPD[k, k2]*SPD[k, p4]^2*SPD[k2, p3])/SPD[k, k] - +(256*D*SPD[k, k2]*SPD[k, p4]^2*SPD[k2, p3])/(3*SPD[k, k]) + +(32*D^2*SPD[k, k2]*SPD[k, p4]^2*SPD[k2, p3])/SPD[k, k] - +(128*SPD[k, p4]^3*SPD[k2, p3])/SPD[k, k] + (64*D*SPD[k, p4]^3*SPD[k2, p3])/ +(3*SPD[k, k]) - (256*D*SPD[k, k1]*SPD[k, p4]^3*SPD[k2, p3])/ +(3*SPD[k, k]^2) + (256*D*SPD[k, k2]*SPD[k, p4]^3*SPD[k2, p3])/ +(3*SPD[k, k]^2) + (512*m^2*SPD[k1, p4]*SPD[k2, p3])/3 - +(608*D*m^2*SPD[k1, p4]*SPD[k2, p3])/3 + +(160*D^2*m^2*SPD[k1, p4]*SPD[k2, p3])/3 + +(512*SPD[k, p4]*SPD[k1, p4]*SPD[k2, p3])/3 - +(608*D*SPD[k, p4]*SPD[k1, p4]*SPD[k2, p3])/3 + +(160*D^2*SPD[k, p4]*SPD[k1, p4]*SPD[k2, p3])/3 + +(1024*SPD[k, p4]^2*SPD[k1, p4]*SPD[k2, p3])/(3*SPD[k, k]) - +(640*D*SPD[k, p4]^2*SPD[k1, p4]*SPD[k2, p3])/(3*SPD[k, k]) + +(128*D^2*SPD[k, p4]^2*SPD[k1, p4]*SPD[k2, p3])/(3*SPD[k, k]) - +64*m^2*SPD[k, k]*SPD[k2, p4] + (128*D*m^2*SPD[k, k]*SPD[k2, p4])/3 + +(1280*m^2*SPD[k, k1]*SPD[k2, p4])/3 - (1024*D*m^2*SPD[k, k1]*SPD[k2, p4])/ +3 + 32*D^2*m^2*SPD[k, k1]*SPD[k2, p4] - (128*m^2*SPD[k, k2]*SPD[k2, p4])/ +3 + (256*D*m^2*SPD[k, k2]*SPD[k2, p4])/3 - +32*D^2*m^2*SPD[k, k2]*SPD[k2, p4] - 64*m^2*SPD[k, p3]*SPD[k2, p4] + +(128*D*m^2*SPD[k, p3]*SPD[k2, p4])/3 + +(160*D*m^2*SPD[k, k1]*SPD[k, p3]*SPD[k2, p4])/(3*SPD[k, k]) - +(160*D*m^2*SPD[k, k2]*SPD[k, p3]*SPD[k2, p4])/(3*SPD[k, k]) - +128*m^2*SPD[k, p4]*SPD[k2, p4] + (256*D*m^2*SPD[k, p4]*SPD[k2, p4])/3 + +(1792*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k2, p4])/(3*SPD[k, k]) - +(896*D*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k2, p4])/(3*SPD[k, k]) - +(64*D^2*m^2*SPD[k, k1]*SPD[k, p4]*SPD[k2, p4])/SPD[k, k] + +(512*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k2, p4])/(3*SPD[k, k]) - +(640*D*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k2, p4])/(3*SPD[k, k]) + +(64*D^2*m^2*SPD[k, k2]*SPD[k, p4]*SPD[k2, p4])/SPD[k, k] + +32*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4] + +(32*D*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4])/3 - +(128*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4])/SPD[k, k] + +(256*D*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4])/(3*SPD[k, k]) + +(32*D^2*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4])/SPD[k, k] - +(64*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4])/SPD[k, k] + +(320*D*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4])/(3*SPD[k, k]) - +(32*D^2*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4])/SPD[k, k] + +(128*SPD[k, p3]*SPD[k, p4]^2*SPD[k2, p4])/SPD[k, k] + +(64*D*SPD[k, p3]*SPD[k, p4]^2*SPD[k2, p4])/(3*SPD[k, k]) - +(256*D*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]^2*SPD[k2, p4])/(3*SPD[k, k]^2) + +(256*D*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]^2*SPD[k2, p4])/(3*SPD[k, k]^2) + +(512*m^2*SPD[k1, p3]*SPD[k2, p4])/3 - (608*D*m^2*SPD[k1, p3]*SPD[k2, p4])/ +3 + (160*D^2*m^2*SPD[k1, p3]*SPD[k2, p4])/3 + +(512*SPD[k, p4]*SPD[k1, p3]*SPD[k2, p4])/3 - +(608*D*SPD[k, p4]*SPD[k1, p3]*SPD[k2, p4])/3 + +(160*D^2*SPD[k, p4]*SPD[k1, p3]*SPD[k2, p4])/3 + +(1024*SPD[k, p4]^2*SPD[k1, p3]*SPD[k2, p4])/(3*SPD[k, k]) - +(640*D*SPD[k, p4]^2*SPD[k1, p3]*SPD[k2, p4])/(3*SPD[k, k]) + +(128*D^2*SPD[k, p4]^2*SPD[k1, p3]*SPD[k2, p4])/(3*SPD[k, k]) + +256*m^2*SPD[k1, p4]*SPD[k2, p4] - 384*D*m^2*SPD[k1, p4]*SPD[k2, p4] + +128*D^2*m^2*SPD[k1, p4]*SPD[k2, p4] - 128*SPD[k, p3]*SPD[k1, p4]* +SPD[k2, p4] + 320*D*SPD[k, p3]*SPD[k1, p4]*SPD[k2, p4] - +64*D^2*SPD[k, p3]*SPD[k1, p4]*SPD[k2, p4] + +(256*D*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4]*SPD[k2, p4])/SPD[k, k] - +(512*m^2*SPD[k2, p3]*SPD[k2, p4])/3 + (608*D*m^2*SPD[k2, p3]*SPD[k2, p4])/ +3 - (160*D^2*m^2*SPD[k2, p3]*SPD[k2, p4])/3 - +(512*SPD[k, p4]*SPD[k2, p3]*SPD[k2, p4])/3 + +(608*D*SPD[k, p4]*SPD[k2, p3]*SPD[k2, p4])/3 - +(160*D^2*SPD[k, p4]*SPD[k2, p3]*SPD[k2, p4])/3 - +(1024*SPD[k, p4]^2*SPD[k2, p3]*SPD[k2, p4])/(3*SPD[k, k]) + +(640*D*SPD[k, p4]^2*SPD[k2, p3]*SPD[k2, p4])/(3*SPD[k, k]) - +(128*D^2*SPD[k, p4]^2*SPD[k2, p3]*SPD[k2, p4])/(3*SPD[k, k]) - +128*m^2*SPD[k2, p4]^2 + 192*D*m^2*SPD[k2, p4]^2 - 64*D^2*m^2*SPD[k2, p4]^2 + +64*SPD[k, p3]*SPD[k2, p4]^2 - 160*D*SPD[k, p3]*SPD[k2, p4]^2 + +32*D^2*SPD[k, p3]*SPD[k2, p4]^2 - +(128*D*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4]^2)/SPD[k, k] - +768*m^2*SPD[k, k1]*SPD[p3, p4] + 480*D*m^2*SPD[k, k1]*SPD[p3, p4] - +32*D^2*m^2*SPD[k, k1]*SPD[p3, p4] - (640*m^2*SPD[k, k1]^2*SPD[p3, p4])/ +SPD[k, k] + (160*D*m^2*SPD[k, k1]^2*SPD[p3, p4])/(3*SPD[k, k]) + +256*m^2*SPD[k, k2]*SPD[p3, p4] - 160*D*m^2*SPD[k, k2]*SPD[p3, p4] + +(32*D^2*m^2*SPD[k, k2]*SPD[p3, p4])/3 - +(320*D*m^2*SPD[k, k1]*SPD[k, k2]*SPD[p3, p4])/(3*SPD[k, k]) + +(160*D*m^2*SPD[k, k2]^2*SPD[p3, p4])/(3*SPD[k, k]) - +1056*SPD[k, k1]*SPD[k, p4]*SPD[p3, p4] + 576*D*SPD[k, k1]*SPD[k, p4]* +SPD[p3, p4] - 32*D^2*SPD[k, k1]*SPD[k, p4]*SPD[p3, p4] + +(192*SPD[k, k1]^2*SPD[k, p4]*SPD[p3, p4])/SPD[k, k] - +(320*D*SPD[k, k1]^2*SPD[k, p4]*SPD[p3, p4])/(3*SPD[k, k]) + +(32*D^2*SPD[k, k1]^2*SPD[k, p4]*SPD[p3, p4])/SPD[k, k] + +352*SPD[k, k2]*SPD[k, p4]*SPD[p3, p4] - 192*D*SPD[k, k2]*SPD[k, p4]* +SPD[p3, p4] + (32*D^2*SPD[k, k2]*SPD[k, p4]*SPD[p3, p4])/3 - +(128*SPD[k, k1]*SPD[k, k2]*SPD[k, p4]*SPD[p3, p4])/SPD[k, k] + +(640*D*SPD[k, k1]*SPD[k, k2]*SPD[k, p4]*SPD[p3, p4])/(3*SPD[k, k]) - +(64*D^2*SPD[k, k1]*SPD[k, k2]*SPD[k, p4]*SPD[p3, p4])/SPD[k, k] + +(64*SPD[k, k2]^2*SPD[k, p4]*SPD[p3, p4])/SPD[k, k] - +(320*D*SPD[k, k2]^2*SPD[k, p4]*SPD[p3, p4])/(3*SPD[k, k]) + +(32*D^2*SPD[k, k2]^2*SPD[k, p4]*SPD[p3, p4])/SPD[k, k] - +(1152*SPD[k, k1]*SPD[k, p4]^2*SPD[p3, p4])/SPD[k, k] + +(576*D*SPD[k, k1]*SPD[k, p4]^2*SPD[p3, p4])/SPD[k, k] - +(64*D^2*SPD[k, k1]*SPD[k, p4]^2*SPD[p3, p4])/SPD[k, k] + +(1024*SPD[k, k1]^2*SPD[k, p4]^2*SPD[p3, p4])/SPD[k, k]^2 - +(256*D*SPD[k, k1]^2*SPD[k, p4]^2*SPD[p3, p4])/(3*SPD[k, k]^2) + +(384*SPD[k, k2]*SPD[k, p4]^2*SPD[p3, p4])/SPD[k, k] - +(192*D*SPD[k, k2]*SPD[k, p4]^2*SPD[p3, p4])/SPD[k, k] + +(64*D^2*SPD[k, k2]*SPD[k, p4]^2*SPD[p3, p4])/(3*SPD[k, k]) + +(512*D*SPD[k, k1]*SPD[k, k2]*SPD[k, p4]^2*SPD[p3, p4])/(3*SPD[k, k]^2) - +(256*D*SPD[k, k2]^2*SPD[k, p4]^2*SPD[p3, p4])/(3*SPD[k, k]^2) + +2048*m^2*SPD[k1, k1]*SPD[p3, p4] - 928*D*m^2*SPD[k1, k1]*SPD[p3, p4] + +64*D^2*m^2*SPD[k1, k1]*SPD[p3, p4] + 2048*SPD[k, p4]*SPD[k1, k1]* +SPD[p3, p4] - 928*D*SPD[k, p4]*SPD[k1, k1]*SPD[p3, p4] + +64*D^2*SPD[k, p4]*SPD[k1, k1]*SPD[p3, p4] + +(2048*SPD[k, p4]^2*SPD[k1, k1]*SPD[p3, p4])/SPD[k, k] - +(1152*D*SPD[k, p4]^2*SPD[k1, k1]*SPD[p3, p4])/SPD[k, k] + +(128*D^2*SPD[k, p4]^2*SPD[k1, k1]*SPD[p3, p4])/SPD[k, k] + +256*m^2*SPD[k1, k2]*SPD[p3, p4] - 64*D*m^2*SPD[k1, k2]*SPD[p3, p4] + +256*SPD[k, p4]*SPD[k1, k2]*SPD[p3, p4] - 64*D*SPD[k, p4]*SPD[k1, k2]* +SPD[p3, p4] + 288*SPD[k, k]*SPD[k1, p4]*SPD[p3, p4] - +96*D*SPD[k, k]*SPD[k1, p4]*SPD[p3, p4] - 832*SPD[k, k1]*SPD[k1, p4]* +SPD[p3, p4] + 160*D*SPD[k, k1]*SPD[k1, p4]*SPD[p3, p4] - +32*D^2*SPD[k, k1]*SPD[k1, p4]*SPD[p3, p4] - 128*SPD[k, k2]*SPD[k1, p4]* +SPD[p3, p4] + 32*D*SPD[k, k2]*SPD[k1, p4]*SPD[p3, p4] + +32*D^2*SPD[k, k2]*SPD[k1, p4]*SPD[p3, p4] + 384*SPD[k, p4]*SPD[k1, p4]* +SPD[p3, p4] - (1536*SPD[k, k1]*SPD[k, p4]*SPD[k1, p4]*SPD[p3, p4])/ +SPD[k, k] + (128*D*SPD[k, k1]*SPD[k, p4]*SPD[k1, p4]*SPD[p3, p4])/ +SPD[k, k] - (128*D*SPD[k, k2]*SPD[k, p4]*SPD[k1, p4]*SPD[p3, p4])/ +SPD[k, k] - 128*m^2*SPD[k2, k2]*SPD[p3, p4] + +32*D*m^2*SPD[k2, k2]*SPD[p3, p4] - 128*SPD[k, p4]*SPD[k2, k2]*SPD[p3, p4] + +32*D*SPD[k, p4]*SPD[k2, k2]*SPD[p3, p4] - 96*SPD[k, k]*SPD[k2, p4]* +SPD[p3, p4] + 32*D*SPD[k, k]*SPD[k2, p4]*SPD[p3, p4] + +256*SPD[k, k1]*SPD[k2, p4]*SPD[p3, p4] - 352*D*SPD[k, k1]*SPD[k2, p4]* +SPD[p3, p4] + 32*D^2*SPD[k, k1]*SPD[k2, p4]*SPD[p3, p4] - +64*SPD[k, k2]*SPD[k2, p4]*SPD[p3, p4] + 160*D*SPD[k, k2]*SPD[k2, p4]* +SPD[p3, p4] - 32*D^2*SPD[k, k2]*SPD[k2, p4]*SPD[p3, p4] - +128*SPD[k, p4]*SPD[k2, p4]*SPD[p3, p4] - +(128*D*SPD[k, k1]*SPD[k, p4]*SPD[k2, p4]*SPD[p3, p4])/SPD[k, k] + +(128*D*SPD[k, k2]*SPD[k, p4]*SPD[k2, p4]*SPD[p3, p4])/SPD[k, k] + +(128*m^2*SPD[k, k1]^2*SPD[p4, p4])/SPD[k, k] - +(64*D*m^2*SPD[k, k1]^2*SPD[p4, p4])/SPD[k, k] - +(256*m^2*SPD[k, k1]*SPD[k, k2]*SPD[p4, p4])/SPD[k, k] + +(128*D*m^2*SPD[k, k1]*SPD[k, k2]*SPD[p4, p4])/SPD[k, k] + +(128*m^2*SPD[k, k2]^2*SPD[p4, p4])/SPD[k, k] - +(64*D*m^2*SPD[k, k2]^2*SPD[p4, p4])/SPD[k, k] + +480*SPD[k, k1]*SPD[k, p3]*SPD[p4, p4] - 256*D*SPD[k, k1]*SPD[k, p3]* +SPD[p4, p4] + 32*D^2*SPD[k, k1]*SPD[k, p3]*SPD[p4, p4] - +160*SPD[k, k2]*SPD[k, p3]*SPD[p4, p4] + +(256*D*SPD[k, k2]*SPD[k, p3]*SPD[p4, p4])/3 - +(32*D^2*SPD[k, k2]*SPD[k, p3]*SPD[p4, p4])/3 + +(960*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[p4, p4])/SPD[k, k] - +(352*D*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[p4, p4])/SPD[k, k] + +(32*D^2*SPD[k, k1]*SPD[k, p3]*SPD[k, p4]*SPD[p4, p4])/SPD[k, k] - +(320*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[p4, p4])/SPD[k, k] + +(352*D*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[p4, p4])/(3*SPD[k, k]) - +(32*D^2*SPD[k, k2]*SPD[k, p3]*SPD[k, p4]*SPD[p4, p4])/(3*SPD[k, k]) - +128*m^2*SPD[k1, k1]*SPD[p4, p4] + 64*D*m^2*SPD[k1, k1]*SPD[p4, p4] - +(4160*SPD[k, p3]*SPD[k1, k1]*SPD[p4, p4])/3 + +544*D*SPD[k, p3]*SPD[k1, k1]*SPD[p4, p4] - 64*D^2*SPD[k, p3]*SPD[k1, k1]* +SPD[p4, p4] - (8704*SPD[k, p3]*SPD[k, p4]*SPD[k1, k1]*SPD[p4, p4])/ +(3*SPD[k, k]) + (928*D*SPD[k, p3]*SPD[k, p4]*SPD[k1, k1]*SPD[p4, p4])/ +SPD[k, k] - (64*D^2*SPD[k, p3]*SPD[k, p4]*SPD[k1, k1]*SPD[p4, p4])/ +SPD[k, k] + 256*m^2*SPD[k1, k2]*SPD[p4, p4] - +128*D*m^2*SPD[k1, k2]*SPD[p4, p4] - (896*SPD[k, p3]*SPD[k1, k2]*SPD[p4, p4])/ +3 + 64*D*SPD[k, p3]*SPD[k1, k2]*SPD[p4, p4] - +(1792*SPD[k, p3]*SPD[k, p4]*SPD[k1, k2]*SPD[p4, p4])/(3*SPD[k, k]) + +(64*D*SPD[k, p3]*SPD[k, p4]*SPD[k1, k2]*SPD[p4, p4])/SPD[k, k] - +96*SPD[k, k]*SPD[k1, p3]*SPD[p4, p4] + 32*D*SPD[k, k]*SPD[k1, p3]* +SPD[p4, p4] + (2624*SPD[k, k1]*SPD[k1, p3]*SPD[p4, p4])/3 - +(736*D*SPD[k, k1]*SPD[k1, p3]*SPD[p4, p4])/3 + +(64*D^2*SPD[k, k1]*SPD[k1, p3]*SPD[p4, p4])/3 - +(896*SPD[k, k2]*SPD[k1, p3]*SPD[p4, p4])/3 + +(352*D*SPD[k, k2]*SPD[k1, p3]*SPD[p4, p4])/3 - +(64*D^2*SPD[k, k2]*SPD[k1, p3]*SPD[p4, p4])/3 - +384*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4] + 64*D*SPD[k, p4]*SPD[k1, p3]* +SPD[p4, p4] + (7808*SPD[k, k1]*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4])/ +(3*SPD[k, k]) - (800*D*SPD[k, k1]*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4])/ +SPD[k, k] + (160*D^2*SPD[k, k1]*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4])/ +(3*SPD[k, k]) - (512*SPD[k, k2]*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4])/ +(3*SPD[k, k]) + (288*D*SPD[k, k2]*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4])/ +SPD[k, k] - (160*D^2*SPD[k, k2]*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4])/ +(3*SPD[k, k]) + 192*SPD[k, p3]*SPD[k1, p4]*SPD[p4, p4] - +64*D*SPD[k, p3]*SPD[k1, p4]*SPD[p4, p4] + +(128*SPD[k, k1]*SPD[k, p3]*SPD[k1, p4]*SPD[p4, p4])/SPD[k, k] - +(32*D*SPD[k, k1]*SPD[k, p3]*SPD[k1, p4]*SPD[p4, p4])/(3*SPD[k, k]) + +(32*D*SPD[k, k2]*SPD[k, p3]*SPD[k1, p4]*SPD[p4, p4])/(3*SPD[k, k]) - +(2176*SPD[k1, p3]*SPD[k1, p4]*SPD[p4, p4])/3 + +(736*D*SPD[k1, p3]*SPD[k1, p4]*SPD[p4, p4])/3 - +(32*D^2*SPD[k1, p3]*SPD[k1, p4]*SPD[p4, p4])/3 - +128*m^2*SPD[k2, k2]*SPD[p4, p4] + 64*D*m^2*SPD[k2, k2]*SPD[p4, p4] + +(448*SPD[k, p3]*SPD[k2, k2]*SPD[p4, p4])/3 - 32*D*SPD[k, p3]*SPD[k2, k2]* +SPD[p4, p4] + (896*SPD[k, p3]*SPD[k, p4]*SPD[k2, k2]*SPD[p4, p4])/ +(3*SPD[k, k]) - (32*D*SPD[k, p3]*SPD[k, p4]*SPD[k2, k2]*SPD[p4, p4])/ +SPD[k, k] + 32*SPD[k, k]*SPD[k2, p3]*SPD[p4, p4] - +(32*D*SPD[k, k]*SPD[k2, p3]*SPD[p4, p4])/3 + +(256*SPD[k, k1]*SPD[k2, p3]*SPD[p4, p4])/3 + +(352*D*SPD[k, k1]*SPD[k2, p3]*SPD[p4, p4])/3 - +(64*D^2*SPD[k, k1]*SPD[k2, p3]*SPD[p4, p4])/3 + +(320*SPD[k, k2]*SPD[k2, p3]*SPD[p4, p4])/3 - +(352*D*SPD[k, k2]*SPD[k2, p3]*SPD[p4, p4])/3 + +(64*D^2*SPD[k, k2]*SPD[k2, p3]*SPD[p4, p4])/3 + +128*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4] - +(64*D*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4])/3 - +(512*SPD[k, k1]*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4])/(3*SPD[k, k]) + +(288*D*SPD[k, k1]*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4])/SPD[k, k] - +(160*D^2*SPD[k, k1]*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4])/(3*SPD[k, k]) + +(512*SPD[k, k2]*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4])/(3*SPD[k, k]) - +(288*D*SPD[k, k2]*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4])/SPD[k, k] + +(160*D^2*SPD[k, k2]*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4])/(3*SPD[k, k]) - +(512*SPD[k1, p4]*SPD[k2, p3]*SPD[p4, p4])/3 + +(32*D*SPD[k1, p4]*SPD[k2, p3]*SPD[p4, p4])/3 + +(32*D^2*SPD[k1, p4]*SPD[k2, p3]*SPD[p4, p4])/3 - +64*SPD[k, p3]*SPD[k2, p4]*SPD[p4, p4] + +(64*D*SPD[k, p3]*SPD[k2, p4]*SPD[p4, p4])/3 + +(32*D*SPD[k, k1]*SPD[k, p3]*SPD[k2, p4]*SPD[p4, p4])/(3*SPD[k, k]) - +(32*D*SPD[k, k2]*SPD[k, p3]*SPD[k2, p4]*SPD[p4, p4])/(3*SPD[k, k]) - +(512*SPD[k1, p3]*SPD[k2, p4]*SPD[p4, p4])/3 + +(32*D*SPD[k1, p3]*SPD[k2, p4]*SPD[p4, p4])/3 + +(32*D^2*SPD[k1, p3]*SPD[k2, p4]*SPD[p4, p4])/3 + +(512*SPD[k2, p3]*SPD[k2, p4]*SPD[p4, p4])/3 - +(32*D*SPD[k2, p3]*SPD[k2, p4]*SPD[p4, p4])/3 - +(32*D^2*SPD[k2, p3]*SPD[k2, p4]*SPD[p4, p4])/3 - +96*D*SPD[k, k1]*SPD[p3, p4]*SPD[p4, p4] + 32*D^2*SPD[k, k1]*SPD[p3, p4]* +SPD[p4, p4] - (128*SPD[k, k1]^2*SPD[p3, p4]*SPD[p4, p4])/SPD[k, k] + +(32*D*SPD[k, k1]^2*SPD[p3, p4]*SPD[p4, p4])/(3*SPD[k, k]) + +32*D*SPD[k, k2]*SPD[p3, p4]*SPD[p4, p4] - +(32*D^2*SPD[k, k2]*SPD[p3, p4]*SPD[p4, p4])/3 - +(64*D*SPD[k, k1]*SPD[k, k2]*SPD[p3, p4]*SPD[p4, p4])/(3*SPD[k, k]) + +(32*D*SPD[k, k2]^2*SPD[p3, p4]*SPD[p4, p4])/(3*SPD[k, k]) + +224*D*SPD[k1, k1]*SPD[p3, p4]*SPD[p4, p4] - 64*D^2*SPD[k1, k1]*SPD[p3, p4]* +SPD[p4, p4] + 256*SPD[k1, k2]*SPD[p3, p4]*SPD[p4, p4] - +64*D*SPD[k1, k2]*SPD[p3, p4]*SPD[p4, p4] - 128*SPD[k2, k2]*SPD[p3, p4]* +SPD[p4, p4] + 32*D*SPD[k2, k2]*SPD[p3, p4]*SPD[p4, p4] - +6*((-16*SPD[k, k1]*(SPD[k, k] + 2*SPD[k, p4])*(D*m^2*SPD[k, k] + + 2*m^2*SPD[k, p3] - D*m^2*SPD[k, p3] - 2*SPD[k, k]*SPD[p3, p4] + + D*SPD[k, k]*SPD[p3, p4] - 4*SPD[k, p4]*SPD[p3, p4] + + 2*D*SPD[k, p4]*SPD[p3, p4] + 2*SPD[k, p3]*SPD[p4, p4] - + D*SPD[k, p3]*SPD[p4, p4]))/SPD[k, k] + +(8*SPD[k, k1]*(2*D*m^2*SPD[k, k]^2 + 4*m^2*SPD[k, k]*SPD[k, p3] - + 2*D*m^2*SPD[k, k]*SPD[k, p3] + 4*D*m^2*SPD[k, k]*SPD[k, p4] + + 8*m^2*SPD[k, p3]*SPD[k, p4] - 4*D*m^2*SPD[k, p3]*SPD[k, p4] - + 4*SPD[k, k]^2*SPD[p3, p4] + 2*D*SPD[k, k]^2*SPD[p3, p4] - + 16*SPD[k, k]*SPD[k, p4]*SPD[p3, p4] + 8*D*SPD[k, k]*SPD[k, p4]* + SPD[p3, p4] - 16*SPD[k, p4]^2*SPD[p3, p4] + 8*D*SPD[k, p4]^2* + SPD[p3, p4] + 4*SPD[k, k]*SPD[k, p3]*SPD[p4, p4] - + 2*D*SPD[k, k]*SPD[k, p3]*SPD[p4, p4] + 8*SPD[k, p3]*SPD[k, p4]* + SPD[p4, p4] - 4*D*SPD[k, p3]*SPD[k, p4]*SPD[p4, p4]))/SPD[k, k]) + +2*((-16*SPD[k, k2]*(SPD[k, k] + 2*SPD[k, p4])*(D*m^2*SPD[k, k] + + 2*m^2*SPD[k, p3] - D*m^2*SPD[k, p3] - 2*SPD[k, k]*SPD[p3, p4] + + D*SPD[k, k]*SPD[p3, p4] - 4*SPD[k, p4]*SPD[p3, p4] + + 2*D*SPD[k, p4]*SPD[p3, p4] + 2*SPD[k, p3]*SPD[p4, p4] - + D*SPD[k, p3]*SPD[p4, p4]))/SPD[k, k] + +(8*SPD[k, k2]*(2*D*m^2*SPD[k, k]^2 + 4*m^2*SPD[k, k]*SPD[k, p3] - + 2*D*m^2*SPD[k, k]*SPD[k, p3] + 4*D*m^2*SPD[k, k]*SPD[k, p4] + + 8*m^2*SPD[k, p3]*SPD[k, p4] - 4*D*m^2*SPD[k, p3]*SPD[k, p4] - + 4*SPD[k, k]^2*SPD[p3, p4] + 2*D*SPD[k, k]^2*SPD[p3, p4] - + 16*SPD[k, k]*SPD[k, p4]*SPD[p3, p4] + 8*D*SPD[k, k]*SPD[k, p4]* + SPD[p3, p4] - 16*SPD[k, p4]^2*SPD[p3, p4] + 8*D*SPD[k, p4]^2* + SPD[p3, p4] + 4*SPD[k, k]*SPD[k, p3]*SPD[p4, p4] - + 2*D*SPD[k, k]*SPD[k, p3]*SPD[p4, p4] + 8*SPD[k, p3]*SPD[k, p4]* + SPD[p4, p4] - 4*D*SPD[k, p3]*SPD[k, p4]*SPD[p4, p4]))/SPD[k, k]) + +10*((-16*(SPD[k, k] + 2*SPD[k, p4])*(2*SPD[k, k1]^2 + SPD[k, k]*SPD[k1, k1])* + (D*m^2*SPD[k, k] + 2*m^2*SPD[k, p3] - D*m^2*SPD[k, p3] - + 2*SPD[k, k]*SPD[p3, p4] + D*SPD[k, k]*SPD[p3, p4] - + 4*SPD[k, p4]*SPD[p3, p4] + 2*D*SPD[k, p4]*SPD[p3, p4] + + 2*SPD[k, p3]*SPD[p4, p4] - D*SPD[k, p3]*SPD[p4, p4]))/(3*SPD[k, k]^2) + +(16*SPD[k, k1]*(2*D*m^2*SPD[k, k]*SPD[k, k1] + 2*m^2*SPD[k, k1]* + SPD[k, p3] - D*m^2*SPD[k, k1]*SPD[k, p3] + 2*D*m^2*SPD[k, k1]* + SPD[k, p4] + 2*m^2*SPD[k, k]*SPD[k1, p3] - D*m^2*SPD[k, k]* + SPD[k1, p3] + 4*m^2*SPD[k, p4]*SPD[k1, p3] - 2*D*m^2*SPD[k, p4]* + SPD[k1, p3] + 2*SPD[k, k]*SPD[k, p4]*SPD[k1, p3] - + D*SPD[k, k]*SPD[k, p4]*SPD[k1, p3] + 4*SPD[k, p4]^2*SPD[k1, p3] - + 2*D*SPD[k, p4]^2*SPD[k1, p3] + 2*D*m^2*SPD[k, k]*SPD[k1, p4] + + 4*m^2*SPD[k, p3]*SPD[k1, p4] - 2*D*m^2*SPD[k, p3]*SPD[k1, p4] - + 2*SPD[k, k]*SPD[k, p3]*SPD[k1, p4] + D*SPD[k, k]*SPD[k, p3]* + SPD[k1, p4] - 4*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4] + + 2*D*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4] - 4*SPD[k, k]*SPD[k, k1]* + SPD[p3, p4] + 2*D*SPD[k, k]*SPD[k, k1]*SPD[p3, p4] - + 8*SPD[k, k1]*SPD[k, p4]*SPD[p3, p4] + 4*D*SPD[k, k1]*SPD[k, p4]* + SPD[p3, p4] - 8*SPD[k, k]*SPD[k1, p4]*SPD[p3, p4] + + 4*D*SPD[k, k]*SPD[k1, p4]*SPD[p3, p4] - 16*SPD[k, p4]*SPD[k1, p4]* + SPD[p3, p4] + 8*D*SPD[k, p4]*SPD[k1, p4]*SPD[p3, p4] + + 2*SPD[k, k1]*SPD[k, p3]*SPD[p4, p4] - D*SPD[k, k1]*SPD[k, p3]* + SPD[p4, p4] + 2*SPD[k, k]*SPD[k1, p3]*SPD[p4, p4] - + D*SPD[k, k]*SPD[k1, p3]*SPD[p4, p4] + 4*SPD[k, p4]*SPD[k1, p3]* + SPD[p4, p4] - 2*D*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4] + + 4*SPD[k, p3]*SPD[k1, p4]*SPD[p4, p4] - 2*D*SPD[k, p3]*SPD[k1, p4]* + SPD[p4, p4]))/SPD[k, k] - 8*(2*D*m^2*SPD[k, k1]^2 + + 4*m^2*SPD[k, k1]*SPD[k1, p3] - 2*D*m^2*SPD[k, k1]*SPD[k1, p3] + + 4*SPD[k, k1]*SPD[k, p4]*SPD[k1, p3] - 2*D*SPD[k, k1]*SPD[k, p4]* + SPD[k1, p3] + 4*D*m^2*SPD[k, k1]*SPD[k1, p4] - + 4*SPD[k, k1]*SPD[k, p3]*SPD[k1, p4] + 2*D*SPD[k, k1]*SPD[k, p3]* + SPD[k1, p4] + 8*m^2*SPD[k1, p3]*SPD[k1, p4] - + 4*D*m^2*SPD[k1, p3]*SPD[k1, p4] + 8*SPD[k, p4]*SPD[k1, p3]*SPD[k1, p4] - + 4*D*SPD[k, p4]*SPD[k1, p3]*SPD[k1, p4] - 8*SPD[k, p3]*SPD[k1, p4]^2 + + 4*D*SPD[k, p3]*SPD[k1, p4]^2 - 4*SPD[k, k1]^2*SPD[p3, p4] + + 2*D*SPD[k, k1]^2*SPD[p3, p4] - 16*SPD[k, k1]*SPD[k1, p4]*SPD[p3, p4] + + 8*D*SPD[k, k1]*SPD[k1, p4]*SPD[p3, p4] - 16*SPD[k1, p4]^2*SPD[p3, p4] + + 8*D*SPD[k1, p4]^2*SPD[p3, p4] + 4*SPD[k, k1]*SPD[k1, p3]*SPD[p4, p4] - + 2*D*SPD[k, k1]*SPD[k1, p3]*SPD[p4, p4] + 8*SPD[k1, p3]*SPD[k1, p4]* + SPD[p4, p4] - 4*D*SPD[k1, p3]*SPD[k1, p4]*SPD[p4, p4]) + +(16*(-SPD[k, k1]^2 + SPD[k, k]*SPD[k1, k1])*(D*m^2*SPD[k, k] + + 2*m^2*SPD[k, p3] - D*m^2*SPD[k, p3] + 2*D*m^2*SPD[k, p4] + + 4*m^2*SPD[p3, p4] - 2*D*m^2*SPD[p3, p4] - 2*SPD[k, k]*SPD[p3, p4] + + D*SPD[k, k]*SPD[p3, p4] - 4*SPD[k, p4]*SPD[p3, p4] + + 2*D*SPD[k, p4]*SPD[p3, p4] - 2*SPD[k, p3]*SPD[p4, p4] + + D*SPD[k, p3]*SPD[p4, p4] - 4*SPD[p3, p4]*SPD[p4, p4] + + 2*D*SPD[p3, p4]*SPD[p4, p4]))/(3*SPD[k, k])) + +4*((-16*(SPD[k, k] + 2*SPD[k, p4])*(2*SPD[k, k1]*SPD[k, k2] + + SPD[k, k]*SPD[k1, k2])*(D*m^2*SPD[k, k] + 2*m^2*SPD[k, p3] - + D*m^2*SPD[k, p3] - 2*SPD[k, k]*SPD[p3, p4] + D*SPD[k, k]*SPD[p3, p4] - + 4*SPD[k, p4]*SPD[p3, p4] + 2*D*SPD[k, p4]*SPD[p3, p4] + + 2*SPD[k, p3]*SPD[p4, p4] - D*SPD[k, p3]*SPD[p4, p4]))/(3*SPD[k, k]^2) + +(8*SPD[k, k2]*(2*D*m^2*SPD[k, k]*SPD[k, k1] + 2*m^2*SPD[k, k1]* + SPD[k, p3] - D*m^2*SPD[k, k1]*SPD[k, p3] + 2*D*m^2*SPD[k, k1]* + SPD[k, p4] + 2*m^2*SPD[k, k]*SPD[k1, p3] - D*m^2*SPD[k, k]* + SPD[k1, p3] + 4*m^2*SPD[k, p4]*SPD[k1, p3] - 2*D*m^2*SPD[k, p4]* + SPD[k1, p3] + 2*SPD[k, k]*SPD[k, p4]*SPD[k1, p3] - + D*SPD[k, k]*SPD[k, p4]*SPD[k1, p3] + 4*SPD[k, p4]^2*SPD[k1, p3] - + 2*D*SPD[k, p4]^2*SPD[k1, p3] + 2*D*m^2*SPD[k, k]*SPD[k1, p4] + + 4*m^2*SPD[k, p3]*SPD[k1, p4] - 2*D*m^2*SPD[k, p3]*SPD[k1, p4] - + 2*SPD[k, k]*SPD[k, p3]*SPD[k1, p4] + D*SPD[k, k]*SPD[k, p3]* + SPD[k1, p4] - 4*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4] + + 2*D*SPD[k, p3]*SPD[k, p4]*SPD[k1, p4] - 4*SPD[k, k]*SPD[k, k1]* + SPD[p3, p4] + 2*D*SPD[k, k]*SPD[k, k1]*SPD[p3, p4] - + 8*SPD[k, k1]*SPD[k, p4]*SPD[p3, p4] + 4*D*SPD[k, k1]*SPD[k, p4]* + SPD[p3, p4] - 8*SPD[k, k]*SPD[k1, p4]*SPD[p3, p4] + + 4*D*SPD[k, k]*SPD[k1, p4]*SPD[p3, p4] - 16*SPD[k, p4]*SPD[k1, p4]* + SPD[p3, p4] + 8*D*SPD[k, p4]*SPD[k1, p4]*SPD[p3, p4] + + 2*SPD[k, k1]*SPD[k, p3]*SPD[p4, p4] - D*SPD[k, k1]*SPD[k, p3]* + SPD[p4, p4] + 2*SPD[k, k]*SPD[k1, p3]*SPD[p4, p4] - + D*SPD[k, k]*SPD[k1, p3]*SPD[p4, p4] + 4*SPD[k, p4]*SPD[k1, p3]* + SPD[p4, p4] - 2*D*SPD[k, p4]*SPD[k1, p3]*SPD[p4, p4] + + 4*SPD[k, p3]*SPD[k1, p4]*SPD[p4, p4] - 2*D*SPD[k, p3]*SPD[k1, p4]* + SPD[p4, p4]))/SPD[k, k] + +(8*SPD[k, k1]*(2*D*m^2*SPD[k, k]*SPD[k, k2] + 2*m^2*SPD[k, k2]* + SPD[k, p3] - D*m^2*SPD[k, k2]*SPD[k, p3] + 2*D*m^2*SPD[k, k2]* + SPD[k, p4] + 2*m^2*SPD[k, k]*SPD[k2, p3] - D*m^2*SPD[k, k]* + SPD[k2, p3] + 4*m^2*SPD[k, p4]*SPD[k2, p3] - 2*D*m^2*SPD[k, p4]* + SPD[k2, p3] + 2*SPD[k, k]*SPD[k, p4]*SPD[k2, p3] - + D*SPD[k, k]*SPD[k, p4]*SPD[k2, p3] + 4*SPD[k, p4]^2*SPD[k2, p3] - + 2*D*SPD[k, p4]^2*SPD[k2, p3] + 2*D*m^2*SPD[k, k]*SPD[k2, p4] + + 4*m^2*SPD[k, p3]*SPD[k2, p4] - 2*D*m^2*SPD[k, p3]*SPD[k2, p4] - + 2*SPD[k, k]*SPD[k, p3]*SPD[k2, p4] + D*SPD[k, k]*SPD[k, p3]* + SPD[k2, p4] - 4*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4] + + 2*D*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4] - 4*SPD[k, k]*SPD[k, k2]* + SPD[p3, p4] + 2*D*SPD[k, k]*SPD[k, k2]*SPD[p3, p4] - + 8*SPD[k, k2]*SPD[k, p4]*SPD[p3, p4] + 4*D*SPD[k, k2]*SPD[k, p4]* + SPD[p3, p4] - 8*SPD[k, k]*SPD[k2, p4]*SPD[p3, p4] + + 4*D*SPD[k, k]*SPD[k2, p4]*SPD[p3, p4] - 16*SPD[k, p4]*SPD[k2, p4]* + SPD[p3, p4] + 8*D*SPD[k, p4]*SPD[k2, p4]*SPD[p3, p4] + + 2*SPD[k, k2]*SPD[k, p3]*SPD[p4, p4] - D*SPD[k, k2]*SPD[k, p3]* + SPD[p4, p4] + 2*SPD[k, k]*SPD[k2, p3]*SPD[p4, p4] - + D*SPD[k, k]*SPD[k2, p3]*SPD[p4, p4] + 4*SPD[k, p4]*SPD[k2, p3]* + SPD[p4, p4] - 2*D*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4] + + 4*SPD[k, p3]*SPD[k2, p4]*SPD[p4, p4] - 2*D*SPD[k, p3]*SPD[k2, p4]* + SPD[p4, p4]))/SPD[k, k] - 8*(2*D*m^2*SPD[k, k1]*SPD[k, k2] + + 2*m^2*SPD[k, k2]*SPD[k1, p3] - D*m^2*SPD[k, k2]*SPD[k1, p3] + + 2*SPD[k, k2]*SPD[k, p4]*SPD[k1, p3] - D*SPD[k, k2]*SPD[k, p4]* + SPD[k1, p3] + 2*D*m^2*SPD[k, k2]*SPD[k1, p4] - + 2*SPD[k, k2]*SPD[k, p3]*SPD[k1, p4] + D*SPD[k, k2]*SPD[k, p3]* + SPD[k1, p4] + 2*m^2*SPD[k, k1]*SPD[k2, p3] - + D*m^2*SPD[k, k1]*SPD[k2, p3] + 2*SPD[k, k1]*SPD[k, p4]*SPD[k2, p3] - + D*SPD[k, k1]*SPD[k, p4]*SPD[k2, p3] + 4*m^2*SPD[k1, p4]*SPD[k2, p3] - + 2*D*m^2*SPD[k1, p4]*SPD[k2, p3] + 4*SPD[k, p4]*SPD[k1, p4]*SPD[k2, p3] - + 2*D*SPD[k, p4]*SPD[k1, p4]*SPD[k2, p3] + 2*D*m^2*SPD[k, k1]* + SPD[k2, p4] - 2*SPD[k, k1]*SPD[k, p3]*SPD[k2, p4] + + D*SPD[k, k1]*SPD[k, p3]*SPD[k2, p4] + 4*m^2*SPD[k1, p3]*SPD[k2, p4] - + 2*D*m^2*SPD[k1, p3]*SPD[k2, p4] + 4*SPD[k, p4]*SPD[k1, p3]*SPD[k2, p4] - + 2*D*SPD[k, p4]*SPD[k1, p3]*SPD[k2, p4] - 8*SPD[k, p3]*SPD[k1, p4]* + SPD[k2, p4] + 4*D*SPD[k, p3]*SPD[k1, p4]*SPD[k2, p4] - + 4*SPD[k, k1]*SPD[k, k2]*SPD[p3, p4] + 2*D*SPD[k, k1]*SPD[k, k2]* + SPD[p3, p4] - 8*SPD[k, k2]*SPD[k1, p4]*SPD[p3, p4] + + 4*D*SPD[k, k2]*SPD[k1, p4]*SPD[p3, p4] - 8*SPD[k, k1]*SPD[k2, p4]* + SPD[p3, p4] + 4*D*SPD[k, k1]*SPD[k2, p4]*SPD[p3, p4] - + 16*SPD[k1, p4]*SPD[k2, p4]*SPD[p3, p4] + 8*D*SPD[k1, p4]*SPD[k2, p4]* + SPD[p3, p4] + 2*SPD[k, k2]*SPD[k1, p3]*SPD[p4, p4] - + D*SPD[k, k2]*SPD[k1, p3]*SPD[p4, p4] + 2*SPD[k, k1]*SPD[k2, p3]* + SPD[p4, p4] - D*SPD[k, k1]*SPD[k2, p3]*SPD[p4, p4] + + 4*SPD[k1, p4]*SPD[k2, p3]*SPD[p4, p4] - 2*D*SPD[k1, p4]*SPD[k2, p3]* + SPD[p4, p4] + 4*SPD[k1, p3]*SPD[k2, p4]*SPD[p4, p4] - + 2*D*SPD[k1, p3]*SPD[k2, p4]*SPD[p4, p4]) + +(16*(-(SPD[k, k1]*SPD[k, k2]) + SPD[k, k]*SPD[k1, k2])* + (D*m^2*SPD[k, k] + 2*m^2*SPD[k, p3] - D*m^2*SPD[k, p3] + + 2*D*m^2*SPD[k, p4] + 4*m^2*SPD[p3, p4] - 2*D*m^2*SPD[p3, p4] - + 2*SPD[k, k]*SPD[p3, p4] + D*SPD[k, k]*SPD[p3, p4] - + 4*SPD[k, p4]*SPD[p3, p4] + 2*D*SPD[k, p4]*SPD[p3, p4] - + 2*SPD[k, p3]*SPD[p4, p4] + D*SPD[k, p3]*SPD[p4, p4] - + 4*SPD[p3, p4]*SPD[p4, p4] + 2*D*SPD[p3, p4]*SPD[p4, p4]))/ + (3*SPD[k, k])) - +2*((-16*(SPD[k, k] + 2*SPD[k, p4])*(2*SPD[k, k2]^2 + SPD[k, k]*SPD[k2, k2])* + (D*m^2*SPD[k, k] + 2*m^2*SPD[k, p3] - D*m^2*SPD[k, p3] - + 2*SPD[k, k]*SPD[p3, p4] + D*SPD[k, k]*SPD[p3, p4] - + 4*SPD[k, p4]*SPD[p3, p4] + 2*D*SPD[k, p4]*SPD[p3, p4] + + 2*SPD[k, p3]*SPD[p4, p4] - D*SPD[k, p3]*SPD[p4, p4]))/(3*SPD[k, k]^2) + +(16*SPD[k, k2]*(2*D*m^2*SPD[k, k]*SPD[k, k2] + 2*m^2*SPD[k, k2]* + SPD[k, p3] - D*m^2*SPD[k, k2]*SPD[k, p3] + 2*D*m^2*SPD[k, k2]* + SPD[k, p4] + 2*m^2*SPD[k, k]*SPD[k2, p3] - D*m^2*SPD[k, k]* + SPD[k2, p3] + 4*m^2*SPD[k, p4]*SPD[k2, p3] - 2*D*m^2*SPD[k, p4]* + SPD[k2, p3] + 2*SPD[k, k]*SPD[k, p4]*SPD[k2, p3] - + D*SPD[k, k]*SPD[k, p4]*SPD[k2, p3] + 4*SPD[k, p4]^2*SPD[k2, p3] - + 2*D*SPD[k, p4]^2*SPD[k2, p3] + 2*D*m^2*SPD[k, k]*SPD[k2, p4] + + 4*m^2*SPD[k, p3]*SPD[k2, p4] - 2*D*m^2*SPD[k, p3]*SPD[k2, p4] - + 2*SPD[k, k]*SPD[k, p3]*SPD[k2, p4] + D*SPD[k, k]*SPD[k, p3]* + SPD[k2, p4] - 4*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4] + + 2*D*SPD[k, p3]*SPD[k, p4]*SPD[k2, p4] - 4*SPD[k, k]*SPD[k, k2]* + SPD[p3, p4] + 2*D*SPD[k, k]*SPD[k, k2]*SPD[p3, p4] - + 8*SPD[k, k2]*SPD[k, p4]*SPD[p3, p4] + 4*D*SPD[k, k2]*SPD[k, p4]* + SPD[p3, p4] - 8*SPD[k, k]*SPD[k2, p4]*SPD[p3, p4] + + 4*D*SPD[k, k]*SPD[k2, p4]*SPD[p3, p4] - 16*SPD[k, p4]*SPD[k2, p4]* + SPD[p3, p4] + 8*D*SPD[k, p4]*SPD[k2, p4]*SPD[p3, p4] + + 2*SPD[k, k2]*SPD[k, p3]*SPD[p4, p4] - D*SPD[k, k2]*SPD[k, p3]* + SPD[p4, p4] + 2*SPD[k, k]*SPD[k2, p3]*SPD[p4, p4] - + D*SPD[k, k]*SPD[k2, p3]*SPD[p4, p4] + 4*SPD[k, p4]*SPD[k2, p3]* + SPD[p4, p4] - 2*D*SPD[k, p4]*SPD[k2, p3]*SPD[p4, p4] + + 4*SPD[k, p3]*SPD[k2, p4]*SPD[p4, p4] - 2*D*SPD[k, p3]*SPD[k2, p4]* + SPD[p4, p4]))/SPD[k, k] - 8*(2*D*m^2*SPD[k, k2]^2 + + 4*m^2*SPD[k, k2]*SPD[k2, p3] - 2*D*m^2*SPD[k, k2]*SPD[k2, p3] + + 4*SPD[k, k2]*SPD[k, p4]*SPD[k2, p3] - 2*D*SPD[k, k2]*SPD[k, p4]* + SPD[k2, p3] + 4*D*m^2*SPD[k, k2]*SPD[k2, p4] - + 4*SPD[k, k2]*SPD[k, p3]*SPD[k2, p4] + 2*D*SPD[k, k2]*SPD[k, p3]* + SPD[k2, p4] + 8*m^2*SPD[k2, p3]*SPD[k2, p4] - + 4*D*m^2*SPD[k2, p3]*SPD[k2, p4] + 8*SPD[k, p4]*SPD[k2, p3]*SPD[k2, p4] - + 4*D*SPD[k, p4]*SPD[k2, p3]*SPD[k2, p4] - 8*SPD[k, p3]*SPD[k2, p4]^2 + + 4*D*SPD[k, p3]*SPD[k2, p4]^2 - 4*SPD[k, k2]^2*SPD[p3, p4] + + 2*D*SPD[k, k2]^2*SPD[p3, p4] - 16*SPD[k, k2]*SPD[k2, p4]*SPD[p3, p4] + + 8*D*SPD[k, k2]*SPD[k2, p4]*SPD[p3, p4] - 16*SPD[k2, p4]^2*SPD[p3, p4] + + 8*D*SPD[k2, p4]^2*SPD[p3, p4] + 4*SPD[k, k2]*SPD[k2, p3]*SPD[p4, p4] - + 2*D*SPD[k, k2]*SPD[k2, p3]*SPD[p4, p4] + 8*SPD[k2, p3]*SPD[k2, p4]* + SPD[p4, p4] - 4*D*SPD[k2, p3]*SPD[k2, p4]*SPD[p4, p4]) + +(16*(-SPD[k, k2]^2 + SPD[k, k]*SPD[k2, k2])*(D*m^2*SPD[k, k] + + 2*m^2*SPD[k, p3] - D*m^2*SPD[k, p3] + 2*D*m^2*SPD[k, p4] + + 4*m^2*SPD[p3, p4] - 2*D*m^2*SPD[p3, p4] - 2*SPD[k, k]*SPD[p3, p4] + + D*SPD[k, k]*SPD[p3, p4] - 4*SPD[k, p4]*SPD[p3, p4] + + 2*D*SPD[k, p4]*SPD[p3, p4] - 2*SPD[k, p3]*SPD[p4, p4] + + D*SPD[k, p3]*SPD[p4, p4] - 4*SPD[p3, p4]*SPD[p4, p4] + + 2*D*SPD[p3, p4]*SPD[p4, p4]))/(3*SPD[k, k]))"} +}); diff --git a/Tests/Lorentz/IntegrationTests/Uncontract.test b/Tests/Lorentz/IntegrationTests/Uncontract.test index 8f9825e9e..d29d126c4 100644 --- a/Tests/Lorentz/IntegrationTests/Uncontract.test +++ b/Tests/Lorentz/IntegrationTests/Uncontract.test @@ -1,10 +1,11 @@ Tests`Lorentz`fcitUncontract = ({ -{"fcitContract-ID1", -"MatchQ[Uncontract[LC[][a, b, c, d]^3, a, b, c, d, Pair -> All], -FCI[FV[a, i1_] FV[a, i2_] FV[a, i3_] FV[b, j1_] FV[b, j2_] FV[b, - j3_] FV[c, k1_] FV[c, k2_] FV[c, k3_] FV[d, l1_] FV[d, l2_] FV[d, - l3_] LC[i1_, j1_, k1_, l1_] -LC[i2_, j2_, k2_, l2_] LC[i3_, j3_, k3_, l3_]]]", -"True"} +{"fcitUncontract-ID1", +"FCCanonicalizeDummyIndices[ +Uncontract[LC[][a, b, c, d]^3, a, b, c, d, Pair -> All], +LorentzIndexNames -> {i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, +i12}, FCE -> True]", +"FV[a, i11] FV[a, i4] FV[a, i7] FV[b, i10] FV[b, i3] FV[b, i6] FV[c, +i2] FV[c, i5] FV[c, i9] FV[d, i1] FV[d, i12] FV[d, i8] LC[i1, i5, +i6, i7] LC[i10, i11, i8, i9] LC[i12, i2, i3, i4]"} }); diff --git a/Tests/Lorentz/IntegrationTests/iTestsLorentz.mt b/Tests/Lorentz/IntegrationTests/iTestsLorentz.mt index 72d628d1a..8ee359c37 100644 --- a/Tests/Lorentz/IntegrationTests/iTestsLorentz.mt +++ b/Tests/Lorentz/IntegrationTests/iTestsLorentz.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Integration tests for functions in the "Lorentz" directory *) @@ -21,7 +21,10 @@ Get/@itestsLorentz; FCClearScalarProducts[]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, + + +Map[Test[ExpandAll[ToExpression[(#[[2]])]-ToExpression[(#[[3]])]],0,TestID->#[[1]]]&, Join[ - Tests`Lorentz`fcitUncontract + Tests`Lorentz`fcitUncontract, + Tests`Lorentz`fcitContract ]]; diff --git a/Tests/Lorentz/Lorentz.mt b/Tests/Lorentz/Lorentz.mt index 283589d00..d00af34f3 100644 --- a/Tests/Lorentz/Lorentz.mt +++ b/Tests/Lorentz/Lorentz.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "Lorentz" directory *) @@ -17,8 +17,16 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "Lorentz"}]] Get/@tests; +If[ $OnlySubTest=!="", + testNames = "Tests`Lorentz`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + FCClearScalarProducts[]; -ClearAll[xsp1,xsp2,ysp,zsp,X,abval,abval2,abval3,a,b,a1,a2,b1,b2]; +ClearAll[xsp1,xsp2,ysp,zsp,X,abval,abval2,abval3,a,b,a1,a2,b1,b2,p,q,xxx,tmp,i,li]; Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`Lorentz`*"])]; diff --git a/Tests/Lorentz/LorentzToCartesian.test b/Tests/Lorentz/LorentzToCartesian.test new file mode 100644 index 000000000..3ac5e5190 --- /dev/null +++ b/Tests/Lorentz/LorentzToCartesian.test @@ -0,0 +1,289 @@ + + +(* :Title: LorentzToCartesian.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for LorentzToCartesian *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstLorentzToCartesian = +({ +{"fcstLorentzToCartesian-ID1", "LorentzToCartesian[FVD[p,mu]]", +"-Pair[CartesianMomentum[p, -1 + D], LorentzIndex[mu, D]] + \ +Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstLorentzToCartesian-ID2", "LorentzToCartesian[FV[p,mu]]", +"-Pair[CartesianMomentum[p], LorentzIndex[mu]] + Pair[LorentzIndex[mu], \ +ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstLorentzToCartesian-ID3", "LorentzToCartesian[FVE[p,mu]]", +"-Pair[CartesianMomentum[p, -4 + D], LorentzIndex[mu, -4 + D]]"}, +{"fcstLorentzToCartesian-ID4", +"LorentzToCartesian[Pair[LorentzIndex[mu],x Momentum[p1]+y \ +Momentum[p2]]]", +"x*(-Pair[CartesianMomentum[p1], LorentzIndex[mu]] + \ +Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p1]]) + \ +y*(-Pair[CartesianMomentum[p2], LorentzIndex[mu]] + Pair[LorentzIndex[mu], \ +ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p2]])"}, +{"fcstLorentzToCartesian-ID5", +"LorentzToCartesian[Pair[LorentzIndex[mu],x Momentum[p1+p2]+y \ +Momentum[p3]]]", +"x*(-Pair[CartesianMomentum[p1], LorentzIndex[mu]] + \ +Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p1]]) + \ +x*(-Pair[CartesianMomentum[p2], LorentzIndex[mu]] + Pair[LorentzIndex[mu], \ +ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p2]]) + y*(-Pair[CartesianMomentum[p3], \ +LorentzIndex[mu]] + Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p3]])"}, +{"fcstLorentzToCartesian-ID6", "LorentzToCartesian[SP[p,q]]", +"-CartesianPair[CartesianMomentum[p], CartesianMomentum[q]] + TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]]"}, +{"fcstLorentzToCartesian-ID7", "LorentzToCartesian[SPD[p,q]]", +"-CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D]] + \ +TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]]"}, +{"fcstLorentzToCartesian-ID8", "LorentzToCartesian[SPE[p,q]]", +"-CartesianPair[CartesianMomentum[p, -4 + D], CartesianMomentum[q, -4 + D]]"}, +{"fcstLorentzToCartesian-ID9", +"LorentzToCartesian[Pair[c1 Momentum[p1]+c2 Momentum[p2],c3 \ +Momentum[q1]+c4 Momentum[q2]]]", +"c1*c3*(-CartesianPair[CartesianMomentum[p1], CartesianMomentum[q1]] + TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p1]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q1]]) + \ +c2*c3*(-CartesianPair[CartesianMomentum[p2], CartesianMomentum[q1]] + TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p2]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q1]]) + \ +c1*c4*(-CartesianPair[CartesianMomentum[p1], CartesianMomentum[q2]] + TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p1]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q2]]) + \ +c2*c4*(-CartesianPair[CartesianMomentum[p2], CartesianMomentum[q2]] + TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p2]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q2]])"}, +{"fcstLorentzToCartesian-ID10", +"LorentzToCartesian[LC[mu,nu,rho,si],LorentzIndex -> False]", +"Eps[LorentzIndex[mu], LorentzIndex[nu], LorentzIndex[rho], \ +LorentzIndex[si]]"}, +{"fcstLorentzToCartesian-ID11", +"LorentzToCartesian[LC[mu,nu,rho][p],LorentzIndex -> False]", +"Eps[CartesianMomentum[p], LorentzIndex[mu], LorentzIndex[nu], \ +LorentzIndex[rho]] + Eps[LorentzIndex[mu], LorentzIndex[nu], \ +LorentzIndex[rho],ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstLorentzToCartesian-ID12", +"LorentzToCartesian[LC[mu,nu][p,q],LorentzIndex -> False]", +"Eps[CartesianMomentum[p], CartesianMomentum[q], LorentzIndex[mu], \ +LorentzIndex[nu]] + Eps[CartesianMomentum[q], LorentzIndex[mu], \ +LorentzIndex[nu], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]] - \ +Eps[CartesianMomentum[p], LorentzIndex[mu], LorentzIndex[nu], \ +ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]]"}, +{"fcstLorentzToCartesian-ID13", "LorentzToCartesian[LC[mu][p,q,r],LorentzIndex -> False]", + "Eps[CartesianMomentum[p], CartesianMomentum[q], CartesianMomentum[r], LorentzIndex[mu]] \ ++ Eps[CartesianMomentum[q], CartesianMomentum[r], LorentzIndex[mu], \ +ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]] - Eps[CartesianMomentum[p], \ +CartesianMomentum[r], LorentzIndex[mu], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[q]] + Eps[CartesianMomentum[p], CartesianMomentum[q], LorentzIndex[mu], \ +ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[r]]"}, +{"fcstLorentzToCartesian-ID14", "LorentzToCartesian[LC[][a,x,y,z],LorentzIndex -> False]", + "-(Eps[CartesianMomentum[x], CartesianMomentum[y], CartesianMomentum[z]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[a]]) + Eps[CartesianMomentum[a], CartesianMomentum[y], \ +CartesianMomentum[z]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[x]] - Eps[CartesianMomentum[a], \ +CartesianMomentum[x], CartesianMomentum[z]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[y]] + \ +Eps[CartesianMomentum[a], CartesianMomentum[x], CartesianMomentum[y]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[z]]"}, +{"fcstLorentzToCartesian-ID15", +"LorentzToCartesian[LCD[mu,nu,rho,si],LorentzIndex -> False]", +"Eps[LorentzIndex[mu, D], LorentzIndex[nu, D], LorentzIndex[rho, \ +D], LorentzIndex[si, D]]"}, +{"fcstLorentzToCartesian-ID16", +"LorentzToCartesian[LCD[mu,nu,rho][p],LorentzIndex -> False]", +"Eps[CartesianMomentum[p, -1 + D], LorentzIndex[mu, D], LorentzIndex[nu, \ +D], LorentzIndex[rho, D]] + Eps[LorentzIndex[mu, D], LorentzIndex[nu, \ +D], LorentzIndex[rho, D],ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstLorentzToCartesian-ID17", +"LorentzToCartesian[LCD[mu,nu][p,q],LorentzIndex -> Falses]", +"Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D], LorentzIndex[mu, \ +D], LorentzIndex[nu, D]] + Eps[CartesianMomentum[q, -1 + D], LorentzIndex[mu, \ +D], LorentzIndex[nu, D], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]] - \ +Eps[CartesianMomentum[p, -1 + D], LorentzIndex[mu, D], LorentzIndex[nu, D], \ +ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]]"}, +{"fcstLorentzToCartesian-ID18", +"LorentzToCartesian[LCD[mu][p,q,r],LorentzIndex -> False]", +"Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D], CartesianMomentum[r, -1 + \ +D], LorentzIndex[mu, D]] + Eps[CartesianMomentum[q, -1 + D], CartesianMomentum[r, -1 \ ++ D], LorentzIndex[mu, D], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]] - \ +Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[r, -1 + D], LorentzIndex[mu, D], \ +ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[q]] + Eps[CartesianMomentum[p, -1 + D], \ +CartesianMomentum[q, -1 + D], LorentzIndex[mu, D], ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[r]]"}, +{"fcstLorentzToCartesian-ID19", +"LorentzToCartesian[LCD[][a,x,y,z],LorentzIndex -> False]", +"-(Eps[CartesianMomentum[x, -1 + D], CartesianMomentum[y, -1 + D], CartesianMomentum[z, -1 \ ++ D]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[a]]) + Eps[CartesianMomentum[a, -1 + D], \ +CartesianMomentum[y, -1 + D], CartesianMomentum[z, -1 + D]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[x]] - Eps[CartesianMomentum[a, -1 + D], CartesianMomentum[x, -1 + D], \ +CartesianMomentum[z, -1 + D]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[y]] + \ +Eps[CartesianMomentum[a, -1 + D], CartesianMomentum[x, -1 + D], CartesianMomentum[y, -1 + \ +D]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[z]]"}, +{"fcstLorentzToCartesian-ID20", +"MatchQ[LorentzToCartesian[ +DiracGamma[ +LorentzIndex[mu]]], -DiracGamma[CartesianIndex[$MU[a_]]] Pair[ + CartesianIndex[$MU[a_]], LorentzIndex[mu]] + +DiracGamma[ExplicitLorentzIndex[0]] Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]]]", +"True"}, +{"fcstLorentzToCartesian-ID21", +"MatchQ[LorentzToCartesian[ +DiracGamma[LorentzIndex[mu, D], +D]], -DiracGamma[CartesianIndex[$MU[a_], -1 + D], D] Pair[ + CartesianIndex[$MU[a_], -1 + D], LorentzIndex[mu, D]] + +DiracGamma[ExplicitLorentzIndex[0]] Pair[LorentzIndex[mu], ExplicitLorentzIndex[0]]]", +"True"}, +{"fcstLorentzToCartesian-ID22", +"MatchQ[LorentzToCartesian[ +DiracGamma[LorentzIndex[mu, D - 4], +D - 4]], -DiracGamma[CartesianIndex[$MU[a_], -4 + D], -4 + D] Pair[ +CartesianIndex[$MU[a_], -4 + D], LorentzIndex[mu, -4 + D]]]", +"True"}, +{"fcstLorentzToCartesian-ID23", +"LorentzToCartesian[DiracGamma[Momentum[p]]]", +"-DiracGamma[CartesianMomentum[p]] + DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p]]"}, +{"fcstLorentzToCartesian-ID24", +"LorentzToCartesian[DiracGamma[Momentum[p,D],D]]", +"-DiracGamma[CartesianMomentum[p, -1 + D], D] + \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstLorentzToCartesian-ID25", +"LorentzToCartesian[DiracGamma[Momentum[p,D-4],D-4]]", +"-DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstLorentzToCartesian-ID26", "MatchQ[LorentzToCartesian[ +GA[mu, rho, +si]], -DiracGamma[CartesianIndex[$MU[a_]]].DiracGamma[ + CartesianIndex[$MU[b_]]].DiracGamma[CartesianIndex[$MU[c_]]] Pair[ + CartesianIndex[$MU[a_]], LorentzIndex[mu]] Pair[CartesianIndex[$MU[b_]], + LorentzIndex[rho]] Pair[CartesianIndex[$MU[c_]], LorentzIndex[si]] + +DiracGamma[ExplicitLorentzIndex[0]].DiracGamma[CartesianIndex[$MU[b_]]].DiracGamma[ + CartesianIndex[$MU[c_]]] Pair[CartesianIndex[$MU[b_]], LorentzIndex[rho]] Pair[ + CartesianIndex[$MU[c_]], LorentzIndex[si]] Pair[LorentzIndex[mu], + ExplicitLorentzIndex[0]] + +DiracGamma[CartesianIndex[$MU[a_]]].DiracGamma[ExplicitLorentzIndex[0]].DiracGamma[ + CartesianIndex[$MU[c_]]] Pair[CartesianIndex[$MU[a_]], LorentzIndex[mu]] Pair[ + CartesianIndex[$MU[c_]], LorentzIndex[si]] Pair[LorentzIndex[rho], + ExplicitLorentzIndex[0]] - +DiracGamma[ExplicitLorentzIndex[0]].DiracGamma[ExplicitLorentzIndex[0]].DiracGamma[ + CartesianIndex[$MU[c_]]] Pair[CartesianIndex[$MU[c_]], LorentzIndex[si]] Pair[ + LorentzIndex[mu], ExplicitLorentzIndex[0]] Pair[LorentzIndex[rho], ExplicitLorentzIndex[0]] + +DiracGamma[CartesianIndex[$MU[a_]]].DiracGamma[CartesianIndex[$MU[b_]]].DiracGamma[ + ExplicitLorentzIndex[0]] Pair[CartesianIndex[$MU[a_]], LorentzIndex[mu]] Pair[ + CartesianIndex[$MU[b_]], LorentzIndex[rho]] Pair[LorentzIndex[si], + ExplicitLorentzIndex[0]] - +DiracGamma[ExplicitLorentzIndex[0]].DiracGamma[CartesianIndex[$MU[b_]]].DiracGamma[ + ExplicitLorentzIndex[0]] Pair[CartesianIndex[$MU[b_]], LorentzIndex[rho]] Pair[ + LorentzIndex[mu], ExplicitLorentzIndex[0]] Pair[LorentzIndex[si], ExplicitLorentzIndex[0]] - +DiracGamma[CartesianIndex[$MU[a_]]].DiracGamma[ExplicitLorentzIndex[0]].DiracGamma[ + ExplicitLorentzIndex[0]] Pair[CartesianIndex[$MU[a_]], LorentzIndex[mu]] Pair[ + LorentzIndex[rho], ExplicitLorentzIndex[0]] Pair[LorentzIndex[si], ExplicitLorentzIndex[0]] + +DiracGamma[ExplicitLorentzIndex[0]].DiracGamma[ExplicitLorentzIndex[0]].DiracGamma[ExplicitLorentzIndex[0]] Pair[ + LorentzIndex[mu], ExplicitLorentzIndex[0]] Pair[LorentzIndex[rho], + ExplicitLorentzIndex[0]] Pair[LorentzIndex[si], ExplicitLorentzIndex[0]]]", + "True"}, +{"fcstLorentzToCartesian-ID27", "LorentzToCartesian[GS[p1,p2,p3]]", +"-DiracGamma[CartesianMomentum[p1]] . DiracGamma[CartesianMomentum[p2]] . \ +DiracGamma[CartesianMomentum[p3]] + DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[CartesianMomentum[p2]] . DiracGamma[CartesianMomentum[p3]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p1]] + DiracGamma[CartesianMomentum[p1]] . DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[CartesianMomentum[p3]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p2]] - \ +DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[CartesianMomentum[p3]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p1]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p2]] + \ +DiracGamma[CartesianMomentum[p1]] . DiracGamma[CartesianMomentum[p2]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p3]] - \ +DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[CartesianMomentum[p2]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p1]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p3]] - DiracGamma[CartesianMomentum[p1]] . DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p2]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p3]] + DiracGamma[ExplicitLorentzIndex[0]] . DiracGamma[ExplicitLorentzIndex[0]] . \ +DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p1]]*TemporalPair[ExplicitLorentzIndex[0], \ +TemporalMomentum[p2]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p3]]"}, +{"fcstLorentzToCartesian-ID28", "MatchQ[LorentzToCartesian[GA[j].GA[i]^2, DotSimplify -> False, +FCE -> True], (-CGA[a_] Pair[CartesianIndex[a_], LorentzIndex[j]] + + MT[0,j] TGA[]).(-CGA[b_] Pair[CartesianIndex[b_], + LorentzIndex[i]] + + MT[0,i] TGA[]).(-CGA[c_] Pair[CartesianIndex[c_], + LorentzIndex[i]] + MT[0,i] TGA[]) /; +a =!= b && b =!= c]","True"}, +{"fcstLorentzToCartesian-ID29", "DataType[mytensor, FCTensor] = True; \n +MatchQ[LorentzToCartesian[ +mytensor[bla, bla, Momentum[p], + LorentzIndex[ + mu]]^2], (-Pair[CartesianIndex[a_], + LorentzIndex[ + mu]] (-mytensor[bla, bla, CartesianMomentum[p], CartesianIndex[a_]] + + mytensor[bla, bla, ExplicitLorentzIndex[0], CartesianIndex[a_]] TemporalPair[ExplicitLorentzIndex[0], + TemporalMomentum[p]]) + + Pair[LorentzIndex[mu], + ExplicitLorentzIndex[0]] (-mytensor[bla, bla, CartesianMomentum[p], ExplicitLorentzIndex[0]] + + mytensor[bla, bla, ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]] TemporalPair[ExplicitLorentzIndex[0], + TemporalMomentum[p]])) (-Pair[CartesianIndex[b_], + LorentzIndex[ + mu]] (-mytensor[bla, bla, CartesianMomentum[p], CartesianIndex[b_]] + + mytensor[bla, bla, ExplicitLorentzIndex[0], CartesianIndex[b_]] TemporalPair[ExplicitLorentzIndex[0], + TemporalMomentum[p]]) + + Pair[LorentzIndex[mu], + ExplicitLorentzIndex[0]] (-mytensor[bla, bla, CartesianMomentum[p], ExplicitLorentzIndex[0]] + + mytensor[bla, bla, ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]] TemporalPair[ExplicitLorentzIndex[0], + TemporalMomentum[p]])) /; a =!= b]","True"}, +{"fcstLorentzToCartesian-ID30", "MatchQ[LorentzToCartesian[LC[mu, nu, rho, si], LorentzIndex -> True, +FCE -> True] // Expand2, +Eps[CartesianIndex[i1_], CartesianIndex[i2_], CartesianIndex[i5_], CartesianIndex[i6_]] Pair[ + CartesianIndex[i1_], LorentzIndex[mu]] Pair[CartesianIndex[i2_], + LorentzIndex[nu]] Pair[CartesianIndex[i5_], LorentzIndex[rho]] Pair[ + CartesianIndex[i6_], LorentzIndex[si]] - +CLC[i3_, i4_, i1_] Pair[CartesianIndex[i3_], LorentzIndex[nu]] Pair[ + CartesianIndex[i4_], LorentzIndex[rho]] Pair[CartesianIndex[i1_], + LorentzIndex[si]] MT[0,mu] + +CLC[i1_, i7_, i2_] Pair[CartesianIndex[i1_], LorentzIndex[mu]] Pair[ + CartesianIndex[i7_], LorentzIndex[rho]] Pair[CartesianIndex[i2_], + LorentzIndex[si]] MT[0,nu] - +CLC[i1_, i2_, i5_] Pair[CartesianIndex[i1_], LorentzIndex[mu]] Pair[ + CartesianIndex[i2_], LorentzIndex[nu]] Pair[CartesianIndex[i5_], + LorentzIndex[si]] MT[0,rho] + +CLC[i1_, i2_, i5_] Pair[CartesianIndex[i1_], LorentzIndex[mu]] Pair[ + CartesianIndex[i2_], LorentzIndex[nu]] Pair[CartesianIndex[i5_], + LorentzIndex[rho]] MT[0,si]]","True"}, +{"fcstLorentzToCartesian-ID31", +"MatchQ[LorentzToCartesian[SI[mu], FCE -> True], +MT[0, mu] - CSI[a_] Pair[CartesianIndex[a_], LorentzIndex[mu]]]","True"}, +{"fcstLorentzToCartesian-ID32", +"MatchQ[LorentzToCartesian[SID[mu], FCE -> True], +MT[0, mu] - CSID[a_] Pair[CartesianIndex[a_, D - 1], LorentzIndex[mu, D]]]","True"}, +{"fcstLorentzToCartesian-ID33", +"MatchQ[LorentzToCartesian[SIE[mu], FCE -> True], +-CSIE[a_] Pair[CartesianIndex[a_, -4 + D], LorentzIndex[mu, -4 + D]]]","True"}, +{"fcstLorentzToCartesian-ID34", +"LorentzToCartesian[SIS[p], FCE -> True]","-CSIS[p] + TC[p]"}, +{"fcstLorentzToCartesian-ID35", +"LorentzToCartesian[SISD[p], FCE -> True]","-CSISD[p] + TC[p]"}, +{"fcstLorentzToCartesian-ID36", +"LorentzToCartesian[SISE[p], FCE -> True]","-CSISE[p]"} +}); + + + + + + + + + + + + + + + + + + + + + + + diff --git a/Tests/Lorentz/MomentumCombine.test b/Tests/Lorentz/MomentumCombine.test index 42b0b0d87..1447dc7bd 100644 --- a/Tests/Lorentz/MomentumCombine.test +++ b/Tests/Lorentz/MomentumCombine.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for MomentumCombine *) @@ -19,39 +19,166 @@ Tests`Lorentz`fcstMomentumCombine = { {"fcstMomentumCombine-ID2","MomentumCombine[FV[p, mu] + 2 FV[q, mu]]", "Pair[LorentzIndex[mu], Momentum[p + 2*q]]"}, {"fcstMomentumCombine-ID3","MomentumCombine[ Pair[Momentum[a], Momentum[c]] - 2*Pair[Momentum[a], Momentum[d]] + - Pair[Momentum[b], Momentum[c]] - 2*Pair[Momentum[b], Momentum[d]]]", "Pair[Momentum[a + b], Momentum[c - 2*d]]"} + Pair[Momentum[b], Momentum[c]] - 2*Pair[Momentum[b], Momentum[d]]]", "Pair[Momentum[a + b], Momentum[c - 2*d]]"}, +{"fcstMomentumCombine-ID4","MomentumCombine[n FV[p, mu] + m FV[q, mu]]", "n Pair[LorentzIndex[mu], Momentum[p]] + +m Pair[LorentzIndex[mu], Momentum[q]]"}, +{"fcstMomentumCombine-ID5","MomentumCombine[n FV[p, mu] + m FV[q, mu], FV -> False]", "n Pair[LorentzIndex[mu], Momentum[p]] + +m Pair[LorentzIndex[mu], Momentum[q]]"}, +{"fcstMomentumCombine-ID6","MomentumCombine[SP[a, b] + SP[a, c]]", "Pair[Momentum[a], Momentum[b + c]]"}, +{"fcstMomentumCombine-ID7","MomentumCombine[SP[a, b] + SP[a, c], SP -> False]", "Pair[Momentum[a], Momentum[b]] + Pair[Momentum[a], Momentum[c]]"}, +{"fcstMomentumCombine-ID8","MomentumCombine[Pair[LorentzIndex[Lor1, D], Momentum[p1, D]] PaVe[1, {m^2, q2, m^2}, {0, m^2, m^2}] - +Pair[LorentzIndex[Lor1, D], Momentum[p1, D]] PaVe[0, 0, {m^2, q2, m^2}, {0, m^2, m^2}]]", "Pair[LorentzIndex[Lor1, D], Momentum[p1, D]] PaVe[ +1, {m^2, q2, m^2}, {0, m^2, m^2}] - Pair[LorentzIndex[Lor1, D], Momentum[p1, D]] PaVe[0,0, {m^2, q2, m^2}, {0, m^2, m^2}]"}, +{"fcstMomentumCombine-ID9","MomentumCombine[CartesianMomentum[p] - 2 CartesianMomentum[q]]", "CartesianMomentum[p - 2 q]"}, +{"fcstMomentumCombine-ID10","MomentumCombine[ +CartesianPair[CartesianMomentum[p], CartesianIndex[i]] + 2 CartesianPair[CartesianMomentum[q], CartesianIndex[i]]]", "CartesianPair[CartesianIndex[i], CartesianMomentum[p + 2 q]]"}, +{"fcstMomentumCombine-ID11","MomentumCombine[CartesianPair[CartesianMomentum[a], CartesianMomentum[c]] - 2*CartesianPair[CartesianMomentum[a], CartesianMomentum[d]] + +CartesianPair[CartesianMomentum[b], CartesianMomentum[c]] - 2*CartesianPair[CartesianMomentum[b], CartesianMomentum[d]]]", "CartesianPair[CartesianMomentum[a + b], CartesianMomentum[c - 2 d]]"}, +{"fcstMomentumCombine-ID12","MomentumCombine[ +n CartesianPair[CartesianMomentum[p], CartesianIndex[i]] + m CartesianPair[CartesianMomentum[q], CartesianIndex[i]]]", "n CartesianPair[CartesianIndex[i], CartesianMomentum[p]] + m CartesianPair[CartesianIndex[i], CartesianMomentum[q]]"}, +{"fcstMomentumCombine-ID13","MomentumCombine[ +CartesianPair[CartesianMomentum[a], CartesianMomentum[b]] + +CartesianPair[CartesianMomentum[a], CartesianMomentum[c]]]", "CartesianPair[CartesianMomentum[a], CartesianMomentum[b + c]]"}, +{"fcstMomentumCombine-ID14","MomentumCombine[ +CartesianPair[CartesianMomentum[a], CartesianMomentum[b]] + +CartesianPair[CartesianMomentum[a], CartesianMomentum[c]], SP -> False]", "CartesianPair[CartesianMomentum[a], CartesianMomentum[b]] + CartesianPair[CartesianMomentum[a], CartesianMomentum[c]]"}, +{"fcstMomentumCombine-ID15","FCE[MomentumCombine[ +CartesianPair[CartesianIndex[i], CartesianMomentum[q1]] c1 + +CartesianPair[CartesianIndex[i], CartesianMomentum[q2]] c1 + +CartesianPair[CartesianIndex[i], CartesianMomentum[q2]] + +CartesianPair[CartesianIndex[i], CartesianMomentum[q1]] ]]", "CV[q1 + q2, i] + c1 CV[q1 + q2, i]"}, +{"fcstMomentumCombine-ID16", +"MomentumCombine[5LC[][p1,q,r,s]+4LC[][p2,q,r,s],FCE->True]", +"LC[][5*p1 + 4*p2, q, r, s]"}, +{"fcstMomentumCombine-ID17", +"MomentumCombine[5LC[][p,q1,r,s]+4LC[][p,q2,r,s],FCE->True]", +"LC[][p, 5*q1 + 4*q2, r, s]"}, +{"fcstMomentumCombine-ID18", +"MomentumCombine[5LC[][p,q,r,s1]+4LC[][p,q,r,s2],FCE->True]", +"LC[][p, q, r, 5*s1 + 4*s2]"}, +{"fcstMomentumCombine-ID19", +"MomentumCombine[3LC[][p1,q,r,s]+3LC[][p2,q,r,s],FCE->True]", +"3*LC[][p1 + p2, q, r, s]"}, +{"fcstMomentumCombine-ID20", +"MomentumCombine[3LC[][p,q1,r,s]+3LC[][p,q2,r,s],FCE->True]", +"3*LC[][p, q1 + q2, r, s]"}, +{"fcstMomentumCombine-ID21", +"MomentumCombine[3LC[][p,q,r,s1]+3LC[][p,q,r,s2],FCE->True]", +"3*LC[][p, q, r, s1 + s2]"}, +{"fcstMomentumCombine-ID22", +"MomentumCombine[5LC[][p1,q,r,s]+4LC[][p2,q,r,s],LC\[Rule]False,\ +FCE->True]", "5*LC[][p1, q, r, s] + 4*LC[][p2, q, r, s]"}, +{"fcstMomentumCombine-ID23", +"MomentumCombine[5CLC[][p1,q,r]+4CLC[][p2,q,r],FCE->True]", +"CLC[][5*p1 + 4*p2, q, r]"}, +{"fcstMomentumCombine-ID24", +"MomentumCombine[5CLC[][p,q1,r]+4CLC[][p,q2,r],FCE->True]", +"CLC[][p, 5*q1 + 4*q2, r]"}, +{"fcstMomentumCombine-ID25", +"MomentumCombine[5CLC[][p,q,s1]+4CLC[][p,q,s2],FCE->True]", +"CLC[][p, q, 5*s1 + 4*s2]"}, +{"fcstMomentumCombine-ID26", +"MomentumCombine[3CLC[][p1,q,r]+3CLC[][p2,q,r],FCE->True]", +"3*CLC[][p1 + p2, q, r]"}, +{"fcstMomentumCombine-ID27", +"MomentumCombine[3CLC[][p,q1,r]+3CLC[][p,q2,r],FCE->True]", +"3*CLC[][p, q1 + q2, r]"}, +{"fcstMomentumCombine-ID28", +"MomentumCombine[3CLC[][q,r,s1]+3CLC[][q,r,s2],FCE->True]", +"3*CLC[][q, r, s1 + s2]"}, +{"fcstMomentumCombine-ID29", +"MomentumCombine[5CLC[][p1,r,s]+4CLC[][p2,r,s],LC\[Rule]False,\ +FCE->True]", "5*CLC[][p1, r, s] + 4*CLC[][p2, r, s]"}, +{"fcstMomentumCombine-ID30", +"MomentumCombine[Spinor[Momentum[q] + Momentum[p], 0, 1]]", "Spinor[Momentum[p + q], 0, 1]"}, +{"fcstMomentumCombine-ID31", +"MomentumCombine[c1 SP[p1,p2]-c1 SP[p1,p3]]", +"c1*Pair[Momentum[p1], Momentum[p2 - p3]]"}, +{"fcstMomentumCombine-ID32", +"MomentumCombine[-c1 SP[p1,p2]+c1 SP[p1,p3]]", +"c1*Pair[Momentum[p1], Momentum[-p2 + p3]]"}, +{"fcstMomentumCombine-ID33", +"MomentumCombine[-c1 SP[p1,p2]-c1 SP[p1,p3]]", +"-(c1*Pair[Momentum[p1], Momentum[p2 + p3]])"}, +{"fcstMomentumCombine-ID34", +"MomentumCombine[c1 CSP[p1,p2]-c1 CSP[p1,p3]]", +"c1*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2 - \ +p3]]"}, +{"fcstMomentumCombine-ID35", +"MomentumCombine[-c1 CSP[p1,p2]+c1 CSP[p1,p3]]", +"c1*CartesianPair[CartesianMomentum[p1], CartesianMomentum[-p2 + \ +p3]]"}, +{"fcstMomentumCombine-ID36", +"MomentumCombine[-c1 CSP[p1,p2]-c1 CSP[p1,p3]]", +"-(c1*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2 + \ +p3]])"}, +{"fcstMomentumCombine-ID37", +"MomentumCombine[c1 FV[p1,mu]-c1 FV[p2,mu]]", +"c1*Pair[LorentzIndex[mu], Momentum[p1 - p2]]"}, +{"fcstMomentumCombine-ID38", +"MomentumCombine[-c1 FV[p1,mu]+c1 FV[p2,mu]]", +"c1*Pair[LorentzIndex[mu], Momentum[-p1 + p2]]"}, +{"fcstMomentumCombine-ID39", +"MomentumCombine[c1 CV[p1,mu]-c1 CV[p2,mu]]", +"c1*CartesianPair[CartesianIndex[mu], CartesianMomentum[p1 - p2]]"}, +{"fcstMomentumCombine-ID40", +"MomentumCombine[-c1 CV[p1,mu]+c1 CV[p2,mu]]", +"c1*CartesianPair[CartesianIndex[mu], CartesianMomentum[-p1 + \ +p2]]"}, +{"fcstMomentumCombine-ID41", "MomentumCombine[c1 TC[p1]-c1 TC[p2]]", + "c1*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p1 - p2]]"}, +{"fcstMomentumCombine-ID42", +"MomentumCombine[-c1 TC[p1]+c1 TC[p2]]", +"c1*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[-p1 + p2]]"}, +{"fcstMomentumCombine-ID43", +"MomentumCombine[c1 LC[][a,p1,b,c]+c1 LC[][a,p2,b,c]]", +"c1*Eps[Momentum[a], Momentum[p1 + p2], Momentum[b], Momentum[c]]"}, +{"fcstMomentumCombine-ID44", +"MomentumCombine[c1 LC[][a,p1,b,c]-c1 LC[][a,p2,b,c]]", +"c1*Eps[Momentum[a], Momentum[p1 - p2], Momentum[b], Momentum[c]]"}, +{"fcstMomentumCombine-ID45", +"MomentumCombine[-c1 LC[][a,p1,b,c]+c1 LC[][a,p2,b,c]]", +"c1*Eps[Momentum[a], Momentum[-p1 + p2], Momentum[b], \ +Momentum[c]]"}, +{"fcstMomentumCombine-ID46", +"MomentumCombine[c1 CLC[][a,p1,b]+c1 CLC[][a,p2,b]]", +"c1*Eps[CartesianMomentum[a], CartesianMomentum[p1 + p2], \ +CartesianMomentum[b]]"}, +{"fcstMomentumCombine-ID47", +"MomentumCombine[c1 CLC[][a,p1,b]-c1 CLC[][a,p2,b]]", +"c1*Eps[CartesianMomentum[a], CartesianMomentum[p1 - p2], \ +CartesianMomentum[b]]"}, +{"fcstMomentumCombine-ID48", +"MomentumCombine[-c1 CLC[][a,p1,b]+c1 CLC[][a,p2,b]]", +"c1*Eps[CartesianMomentum[a], CartesianMomentum[-p1 + p2], \ +CartesianMomentum[b]]"}, +{"fcstMomentumCombine-ID49", +"MomentumCombine[SP[p,p] (SP[p,q]+SP[p,r]-SP[q,q]-SP[q,r])]", +"Pair[Momentum[p], Momentum[p]]*Pair[Momentum[p - q], Momentum[q + \ +r]]"}, +{"fcstMomentumCombine-ID50", +"MomentumCombine[SP[p,p] (CSP[p,q]+CSP[p,r]-CSP[q,q]-CSP[q,r])]", +"CartesianPair[CartesianMomentum[p - q], CartesianMomentum[q + \ +r]]*Pair[Momentum[p], Momentum[p]]"}, +{"fcstMomentumCombine-ID51", +"MomentumCombine[c1 SP[p1,p2]-c1 SP[p1,p3]]", +"c1*Pair[Momentum[p1], Momentum[p2 - p3]]"}, +{"fcstMomentumCombine-ID52", +"MomentumCombine[-c1 SP[p1,p2]+c1 SP[p1,p3]]", +"c1*Pair[Momentum[p1], Momentum[-p2 + p3]]"}, +{"fcstMomentumCombine-ID53", +"MomentumCombine[-c1 SP[p1,p2]-c1 SP[p1,p3]]", +"-(c1*Pair[Momentum[p1], Momentum[p2 + p3]])"}, +{"fcstMomentumCombine-ID54", +"MomentumCombine[c1 CSP[p1,p2]-c1 CSP[p1,p3]]", +"c1*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2 - \ +p3]]"}, +{"fcstMomentumCombine-ID55", +"MomentumCombine[-c1 CSP[p1,p2]+c1 CSP[p1,p3]]", +"c1*CartesianPair[CartesianMomentum[p1], CartesianMomentum[-p2 + \ +p3]]"}, +{"fcstMomentumCombine-ID56", +"MomentumCombine[-c1 CSP[p1,p2]-c1 CSP[p1,p3]]", +"-(c1*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2 + \ +p3]])"} }; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/Tests/Lorentz/MomentumExpand.test b/Tests/Lorentz/MomentumExpand.test index e3f2b6e0e..416a34af3 100644 --- a/Tests/Lorentz/MomentumExpand.test +++ b/Tests/Lorentz/MomentumExpand.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for MomentumExpand *) @@ -41,11 +41,62 @@ Tests`Lorentz`fcstMomentumExpand = { {"fcstMomentumExpand-ID13","Momentum[p + Momentum[3 q], D]//MomentumExpand", "Momentum[p, D] + 3*Momentum[q, {4, D}]"}, {"fcstMomentumExpand-ID14","Momentum[p + Momentum[3 q], D - 4]//MomentumExpand", - "Momentum[p, -4 + D] + 3*Momentum[q, {4, -4 + D}]"} + "Momentum[p, -4 + D] + 3*Momentum[q, {4, -4 + D}]"}, +{"fcstMomentumExpand-ID15","Pair[LorentzIndex[mu, D], Momentum[l - q, D]] // MomentumExpand", + "Pair[LorentzIndex[mu, D], Momentum[l, D] - Momentum[q, D]]"} }; - - +Tests`Lorentz`fcstMomentumExpandNR = +{{"fcstMomentumExpandNR-ID1", "MomentumExpand[TemporalMomentum[p]]", +"TemporalMomentum[p]"}, {"fcstMomentumExpandNR-ID2", +"MomentumExpand[TemporalMomentum[p+3q]]", +"TemporalMomentum[p] + 3*TemporalMomentum[q]"}, {"fcstMomentumExpandNR-ID4", +"MomentumExpand[TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[p+3q]]]", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p] + 3*TemporalMomentum[q]]"}, \ +{"fcstMomentumExpandNR-ID5", "MomentumExpand[CartesianMomentum[p]]", +"CartesianMomentum[p]"}, {"fcstMomentumExpandNR-ID6", +"MomentumExpand[CartesianMomentum[p,D-1]]", +"CartesianMomentum[p, -1 + D]"}, {"fcstMomentumExpandNR-ID7", +"MomentumExpand[CartesianMomentum[p,D-4]]", +"CartesianMomentum[p, -4 + D]"}, {"fcstMomentumExpandNR-ID8", +"MomentumExpand[CartesianMomentum[p+3q]]", +"CartesianMomentum[p] + 3*CartesianMomentum[q]"}, {"fcstMomentumExpandNR-ID9", +"MomentumExpand[CartesianMomentum[p+3q,D-1]]", +"CartesianMomentum[p, -1 + D] + 3*CartesianMomentum[q, -1 + D]"}, \ +{"fcstMomentumExpandNR-ID10", "MomentumExpand[CartesianMomentum[p+3q,D-4]]", +"CartesianMomentum[p, -4 + D] + 3*CartesianMomentum[q, -4 + D]"}, \ +{"fcstMomentumExpandNR-ID11", +"MomentumExpand[CartesianMomentum[p+CartesianMomentum[3 q]]]", +"CartesianMomentum[p] + 3*CartesianMomentum[q]"}, {"fcstMomentumExpandNR-ID12", +"MomentumExpand[CartesianMomentum[p+CartesianMomentum[3 q,D-1],D-1]]", +"CartesianMomentum[p, -1 + D] + 3*CartesianMomentum[q, -1 + D]"}, \ +{"fcstMomentumExpandNR-ID13", +"MomentumExpand[CartesianMomentum[p+CartesianMomentum[3 q,D-4],D-4]]", +"CartesianMomentum[p, -4 + D] + 3*CartesianMomentum[q, -4 + D]"}, \ +{"fcstMomentumExpandNR-ID14", +"MomentumExpand[CartesianMomentum[p+CartesianMomentum[3 q],D-1]]", +"CartesianMomentum[p, -1 + D] + 3*CartesianMomentum[q, {3, -1 + D}]"}, \ +{"fcstMomentumExpandNR-ID15", +"MomentumExpand[CartesianMomentum[p+CartesianMomentum[3 q],D-4]]", +"CartesianMomentum[p, -4 + D] + 3*CartesianMomentum[q, {3, -4 + D}]"}, \ +{"fcstMomentumExpandNR-ID16", +"MomentumExpand[CartesianMomentum[p+CartesianMomentum[3 q,D-1]]]", +"CartesianMomentum[p] + 3*CartesianMomentum[q, {-1 + D, 3}]"}, \ +{"fcstMomentumExpandNR-ID17", +"MomentumExpand[CartesianMomentum[p+CartesianMomentum[3 q],D-1]]", +"CartesianMomentum[p, -1 + D] + 3*CartesianMomentum[q, {3, -1 + D}]"}, \ +{"fcstMomentumExpandNR-ID18", +"MomentumExpand[CartesianMomentum[p+CartesianMomentum[3 q],D-4]]", +"CartesianMomentum[p, -4 + D] + 3*CartesianMomentum[q, {3, -4 + D}]"}, \ +{"fcstMomentumExpandNR-ID19", +"MomentumExpand[CartesianPair[CartesianIndex[i,D-1],CartesianMomentum[l-q,D-1]]]", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[l, -1 + D] - CartesianMomentum[q, -1 + \ +D]]"}, {"fcstMomentumExpandNR-ID20", "MomentumExpand[TemporalMomentum[p]]", +"TemporalMomentum[p]"}, {"fcstMomentumExpandNR-ID21", +"MomentumExpand[TemporalMomentum[p+3q]]", +"TemporalMomentum[p] + 3*TemporalMomentum[q]"}, {"fcstMomentumExpandNR-ID23", +"MomentumExpand[TemporalPair[ExplicitLorentzIndex[0],TemporalMomentum[p+3q]]]", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p] + 3*TemporalMomentum[q]]"}}; diff --git a/Tests/Lorentz/PairContract.test b/Tests/Lorentz/PairContract.test index e2b7c04ba..37f328384 100644 --- a/Tests/Lorentz/PairContract.test +++ b/Tests/Lorentz/PairContract.test @@ -4,20 +4,251 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for PairContract *) (* ------------------------------------------------------------------------ *) -Tests`Lorentz`fcstPairContract = { -{"fcstPairContract-ID1","PairContract[0,x]","0"} -} +Tests`Lorentz`fcstPairContract = +({ +{"fcstPairContract-ID1", "PairContract[0,x]", "0"}, +{"fcstPairContract-ID2", +"PairContract[LorentzIndex[i],LorentzIndex[i]]", "4"}, +{"fcstPairContract-ID3", +"PairContract[LorentzIndex[i,D],LorentzIndex[i,D]]", "D"}, +{"fcstPairContract-ID4", +"PairContract[LorentzIndex[i,D-4],LorentzIndex[i,D-4]]", +"-4 + D"}, +{"fcstPairContract-ID5", +"PairContract[LorentzIndex[i,D],LorentzIndex[i]]", "4"}, +{"fcstPairContract-ID6", +"PairContract[LorentzIndex[i,D-4],LorentzIndex[i]]", "0"}, +{"fcstPairContract-ID7", +"PairContract[LorentzIndex[i,D-4],LorentzIndex[i,D]]", "-4 + D"}, +{"fcstPairContract-ID8", +"PairContract[LorentzIndex[i,D1],LorentzIndex[i,D2]]", +"PairContract[LorentzIndex[i, D1], LorentzIndex[i, D2]]"}, +{"fcstPairContract-ID9", "PairContract[Momentum[p],Momentum[p]]", +"Pair[Momentum[p], Momentum[p]]"}, +{"fcstPairContract-ID10", +"PairContract[Momentum[p,D],Momentum[p,D]]", +"Pair[Momentum[p, D], Momentum[p, D]]"}, +{"fcstPairContract-ID11", +"PairContract[Momentum[p,D-4],Momentum[p,D-4]]", +"Pair[Momentum[p, -4 + D], Momentum[p, -4 + D]]"}, +{"fcstPairContract-ID12", "PairContract[Momentum[p,D],Momentum[p]]", + "Pair[Momentum[p], Momentum[p]]"}, +{"fcstPairContract-ID13", +"PairContract[Momentum[p,D-4],Momentum[p]]", "0"}, +{"fcstPairContract-ID14", +"PairContract[Momentum[p,D-4],Momentum[p,D]]", +"Pair[Momentum[p, -4 + D], Momentum[p, -4 + D]]"}, +{"fcstPairContract-ID15", +"PairContract[Momentum[p,D1],Momentum[p,D2]]", +"Pair[Momentum[p, D1], Momentum[p, D2]]"} +}); Tests`Lorentz`fcstPairContract3 = { {"fcstPairContract3-ID1","SP[p, p] = (a + b)^2; \n tmp = PairContract3[Momentum[p], Momentum[p]]; \n FCClearScalarProducts[]; \n tmp","(a + b)^2"} } + +Tests`Lorentz`fcstCartesianPairContract = +({ +{"fcstCartesianPairContract-ID1", +"CartesianPair[CartesianIndex[i],CartesianIndex[i]]/.CartesianPair\[Rule]CartesianPairContract", "3"}, +{"fcstCartesianPairContract-ID2", +"CartesianPair[CartesianIndex[i,D-1],CartesianIndex[i,D-1]]/.CartesianPair\[Rule]CartesianPairContract", +"-1 + D"}, +{"fcstCartesianPairContract-ID3", +"CartesianPair[CartesianIndex[i,D-4],CartesianIndex[i,D-4]]/.CartesianPair\[Rule]CartesianPairContract", +"-4 + D"}, +{"fcstCartesianPairContract-ID4", +"CartesianPair[CartesianIndex[i],CartesianIndex[j]]^2/.CartesianPair\[Rule]CartesianPairContract", "3"}, +{"fcstCartesianPairContract-ID5", +"CartesianPair[CartesianIndex[i],CartesianIndex[j]]CartesianPair[CartesianIndex[j],CartesianIndex[k]]/.CartesianPair\[Rule]\ +CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i], CartesianIndex[k]]"}, +{"fcstCartesianPairContract-ID6", +"CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]CartesianPair[CartesianIndex[j],CartesianIndex[k]]\ +/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i], CartesianIndex[k]]"}, +{"fcstCartesianPairContract-ID7", +"CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]CartesianPair[CartesianIndex[j,D-1],CartesianIndex[k,D-\ +1]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianIndex[k, -1 + D]]"}, +{"fcstCartesianPairContract-ID8", +"CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]CartesianPair[CartesianIndex[j,D-4],CartesianIndex[k,D-\ +4]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[k, -4 + D]]"}, +{"fcstCartesianPairContract-ID9", +"CartesianPair[CartesianIndex[i,D-4],CartesianIndex[j,D-4]]CartesianPair[CartesianIndex[j,D-4],CartesianIndex[k,D-\ +4]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[k, -4 + D]]"}, +{"fcstCartesianPairContract-ID10", +"CartesianPair[CartesianIndex[i,D-4],CartesianIndex[j,D-4]]CartesianPair[CartesianIndex[j],CartesianIndex[k]]\ +/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", "0"}, +{"fcstCartesianPairContract-ID11", +"CartesianPair[CartesianIndex[i],CartesianIndex[j]]CartesianPair[CartesianIndex[j],CartesianMomentum[k]]/.CartesianPair\ +\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i], CartesianMomentum[k]]"}, +{"fcstCartesianPairContract-ID12", +"CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]CartesianPair[CartesianIndex[j],CartesianMomentum[k]]\ +/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i], CartesianMomentum[k]]"}, +{"fcstCartesianPairContract-ID13", +"CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]CartesianPair[CartesianIndex[j,D-1],CartesianMomentum[k,\ +D-1]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[k, -1 + D]]"}, +{"fcstCartesianPairContract-ID14", +"CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]CartesianPair[CartesianIndex[j,D-4],CartesianMomentum[k,\ +D-4]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianMomentum[k, -4 + D]]"}, +{"fcstCartesianPairContract-ID15", +"CartesianPair[CartesianIndex[i,D-4],CartesianIndex[j,D-4]]CartesianPair[CartesianIndex[j,D-4],CartesianMomentum[k,\ +D-4]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianMomentum[k, -4 + D]]"}, +{"fcstCartesianPairContract-ID16", +"CartesianPair[CartesianIndex[i],CartesianIndex[j]]CartesianPair[CartesianIndex[j,D-4],CartesianMomentum[k,D-4]]\ +/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", "0"}, +{"fcstCartesianPairContract-ID17", +"CartesianPair[CartesianIndex[i],CartesianMomentum[p]]CartesianPair[CartesianIndex[i],CartesianMomentum[k]]/.CartesianPair\ +\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianMomentum[k], CartesianMomentum[p]]"}, +{"fcstCartesianPairContract-ID18", +"CartesianPair[CartesianIndex[i,D-1],CartesianMomentum[p,D-1]]CartesianPair[CartesianIndex[i],CartesianMomentum[k]]\ +/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", +"CartesianPair[CartesianMomentum[k], CartesianMomentum[p]]"}, +{"fcstCartesianPairContract-ID19", +"CartesianPair[CartesianIndex[i,D-1],CartesianMomentum[p,D-1]]CartesianPair[CartesianIndex[i,D-1],\ +CartesianMomentum[k,D-1]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]\ +CartesianPair", "CartesianPair[CartesianMomentum[k, -1 + D], CartesianMomentum[p, -1 + D]]"}, +{"fcstCartesianPairContract-ID20", +"CartesianPair[CartesianIndex[i,D-4],CartesianMomentum[p,D-4]]CartesianPair[CartesianIndex[i,D-1],\ +CartesianMomentum[k,D-1]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]\ +CartesianPair", "CartesianPair[CartesianMomentum[k, -4 + D], CartesianMomentum[p, -4 + D]]"}, +{"fcstCartesianPairContract-ID21", +"CartesianPair[CartesianIndex[i,D-4],CartesianMomentum[p,D-4]]CartesianPair[CartesianIndex[i,D-4],\ +CartesianMomentum[k,D-4]]/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]\ +CartesianPair", "CartesianPair[CartesianMomentum[k, -4 + D], CartesianMomentum[p, -4 + D]]"}, +{"fcstCartesianPairContract-ID22", +"CartesianPair[CartesianIndex[i],CartesianMomentum[p]]CartesianPair[CartesianIndex[i,D-4],CartesianMomentum[k,D-4]]\ +/.CartesianPair\[Rule]CartesianPairContract/.CartesianPairContract\[Rule]CartesianPair", "0"}, +{"fcstCartesianPairContract-ID23", +"DiracGamma[CartesianIndex[i]]CartesianPair[CartesianIndex[i],CartesianIndex[j]]/.CartesianPair\[Rule]\ +CartesianPairContract", "DiracGamma[CartesianIndex[j]]"}, +{"fcstCartesianPairContract-ID24", +"DiracGamma[CartesianIndex[i]]CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]/.CartesianPair\ +\[Rule]CartesianPairContract", "DiracGamma[CartesianIndex[j]]"}, +{"fcstCartesianPairContract-ID25", +"DiracGamma[CartesianIndex[i,D-1],D]CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]\ +/.CartesianPair\[Rule]CartesianPairContract", "DiracGamma[CartesianIndex[j, -1 + D], D]"}, +{"fcstCartesianPairContract-ID26", +"DiracGamma[CartesianIndex[i,D-4],D-4]CartesianPair[CartesianIndex[i,D-4],CartesianIndex[j,D-4]]\ +/.CartesianPair\[Rule]CartesianPairContract", "DiracGamma[CartesianIndex[j, -4 + D], -4 + D]"}, +{"fcstCartesianPairContract-ID27", +"DiracGamma[CartesianIndex[i]]CartesianPair[CartesianIndex[i,D-4],CartesianIndex[j,D-4]]/.CartesianPair\ +\[Rule]CartesianPairContract", "0"}, +{"fcstCartesianPairContract-ID28", +"DiracGamma[CartesianIndex[i]]CartesianPair[CartesianIndex[i],CartesianMomentum[j]]/.CartesianPair\[Rule]\ +CartesianPairContract", "DiracGamma[CartesianMomentum[j]]"}, +{"fcstCartesianPairContract-ID29", +"DiracGamma[CartesianIndex[i]]CartesianPair[CartesianIndex[i,D-1],CartesianMomentum[p,D-1]]/.CartesianPair\ +\[Rule]CartesianPairContract", "DiracGamma[CartesianMomentum[p]]"}, +{"fcstCartesianPairContract-ID30", +"DiracGamma[CartesianIndex[i,D-1],D]CartesianPair[CartesianIndex[i,D-1],CartesianMomentum[p,D-1]]\ +/.CartesianPair\[Rule]CartesianPairContract", "DiracGamma[CartesianMomentum[p, -1 + D], D]"}, +{"fcstCartesianPairContract-ID31", +"DiracGamma[CartesianIndex[i,D-4],D-4]CartesianPair[CartesianIndex[i,D-4],CartesianMomentum[p,D-4]]\ +/.CartesianPair\[Rule]CartesianPairContract", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstCartesianPairContract-ID32", +"DiracGamma[CartesianIndex[i]]CartesianPair[CartesianIndex[i,D-4],CartesianMomentum[p,D-4]]/.CartesianPair\ +\[Rule]CartesianPairContract", "0"}, +{"fcstCartesianPairContract-ID33", +"Pair[LorentzIndex[i],CartesianIndex[i]]/.Pair\[Rule]\ +PairContract/.PairContract\[Rule]Pair", +"Pair[CartesianIndex[i], LorentzIndex[i]]"}, +{"fcstCartesianPairContract-ID34", +"Pair[LorentzIndex[i],CartesianIndex[i]]^2/.Pair\[Rule]PairContract/.CartesianPair\ +\[Rule]CartesianPairContract", "-3"}, +{"fcstCartesianPairContract-ID35", +"Pair[LorentzIndex[i],CartesianIndex[i,D-1]]^2/.Pair\[Rule]\ +PairContract/.CartesianPair\[Rule]CartesianPairContract", "-3"}, +{"fcstCartesianPairContract-ID36", +"Pair[LorentzIndex[i,D-4],CartesianIndex[i,D-1]]^2/.Pair\[Rule]\ +PairContract/.CartesianPair\[Rule]CartesianPairContract", "4 - D"}, +{"fcstCartesianPairContract-ID37", +"Pair[LorentzIndex[i,D-4],CartesianIndex[i]]^2/.Pair\[Rule]\ +PairContract/.CartesianPair\[Rule]CartesianPairContract", "0"}, +{"fcstCartesianPairContract-ID38", +"Pair[CartesianIndex[i],LorentzIndex[\[Mu]]] \ +CartesianPair[CartesianIndex[i],CartesianMomentum[p]]/.CartesianPair\[Rule]CartesianPairContract/.Pair\[Rule]\ +PairContract/.CartesianPairContract\[Rule]CartesianPair/.PairContract\[Rule]Pair", +"Pair[CartesianMomentum[p], LorentzIndex[\[Mu]]]"}, +{"fcstCartesianPairContract-ID39", +"Pair[CartesianIndex[i],LorentzIndex[\[Mu]]] \ +CartesianPair[CartesianIndex[i,D-1],CartesianMomentum[p,D-1]]/.CartesianPair\[Rule]\ +CartesianPairContract/.Pair\[Rule]PairContract/.CartesianPairContract\[Rule]\ +CartesianPair/.PairContract\[Rule]Pair", +"Pair[CartesianMomentum[p, -1 + D], LorentzIndex[\[Mu]]]"}, +{"fcstCartesianPairContract-ID40", +"Pair[CartesianIndex[i,D-1],LorentzIndex[\[Mu],D]] \ +CartesianPair[CartesianIndex[i,D-1],CartesianMomentum[p,D-1]]/.CartesianPair\[Rule]\ +CartesianPairContract/.Pair\[Rule]PairContract/.CartesianPairContract\[Rule]\ +CartesianPair/.PairContract\[Rule]Pair", +"Pair[CartesianMomentum[p, -1 + D], LorentzIndex[\[Mu], D]]"}, +{"fcstCartesianPairContract-ID41", +"Pair[CartesianIndex[i],LorentzIndex[\[Mu]]] \ +CartesianPair[CartesianIndex[i],CartesianIndex[j]]/.CartesianPair\[Rule]CartesianPairContract/.Pair\[Rule]\ +PairContract/.CartesianPairContract\[Rule]CartesianPair/.PairContract\[Rule]Pair", +"Pair[CartesianIndex[j], LorentzIndex[\[Mu]]]"}, +{"fcstCartesianPairContract-ID42", +"Pair[CartesianIndex[i],LorentzIndex[\[Mu]]] \ +CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]/.CartesianPair\[Rule]CartesianPairContract/.Pair\ +\[Rule]PairContract/.CartesianPairContract\[Rule]CartesianPair/.PairContract\[Rule]\ +Pair", "Pair[CartesianIndex[j], LorentzIndex[\[Mu]]]"}, +{"fcstCartesianPairContract-ID43", +"Pair[CartesianIndex[i],LorentzIndex[\[Mu]]] \ +CartesianPair[CartesianIndex[i,D-4],CartesianIndex[j,D-4]]/.CartesianPair\[Rule]CartesianPairContract/.Pair\ +\[Rule]PairContract/.CartesianPairContract\[Rule]CartesianPair/.PairContract\[Rule]\ +Pair", "0"}, +{"fcstCartesianPairContract-ID44", +"Pair[CartesianIndex[i,D-1],LorentzIndex[\[Mu],D]] \ +CartesianPair[CartesianIndex[i],CartesianIndex[j]]/.CartesianPair\[Rule]CartesianPairContract/.Pair\[Rule]\ +PairContract/.CartesianPairContract\[Rule]CartesianPair/.PairContract\[Rule]Pair", +"Pair[CartesianIndex[j], LorentzIndex[\[Mu]]]"}, +{"fcstCartesianPairContract-ID45", +"Pair[CartesianIndex[i,D-1],LorentzIndex[\[Mu],D]] \ +CartesianPair[CartesianIndex[i,D-4],CartesianIndex[j,D-4]]/.CartesianPair\[Rule]CartesianPairContract/.Pair\ +\[Rule]PairContract/.CartesianPairContract\[Rule]CartesianPair/.PairContract\[Rule]\ +Pair", "Pair[CartesianIndex[j, -4 + D], LorentzIndex[\[Mu], -4 + D]]"}, +{"fcstCartesianPairContract-ID46", +"Pair[CartesianIndex[i,D-4],LorentzIndex[\[Mu],D-4]] \ +CartesianPair[CartesianIndex[i],CartesianIndex[j]]/.CartesianPair\[Rule]CartesianPairContract/.Pair\[Rule]\ +PairContract/.CartesianPairContract\[Rule]CartesianPair/.PairContract\[Rule]Pair", +"0"}, +{"fcstCartesianPairContract-ID47", +"Pair[CartesianIndex[i,D-4],LorentzIndex[\[Mu],D-4]] \ +CartesianPair[CartesianIndex[i,D-1],CartesianIndex[j,D-1]]/.CartesianPair\[Rule]CartesianPairContract/.Pair\ +\[Rule]PairContract/.CartesianPairContract\[Rule]CartesianPair/.PairContract\[Rule]\ +Pair", "Pair[CartesianIndex[j, -4 + D], LorentzIndex[\[Mu], -4 + D]]"}, +{"fcstCartesianPairContract-ID48", +"Pair[CartesianIndex[i],LorentzIndex[\[Mu]]] DiracGamma[CartesianIndex[i]]/.CartesianPair\ +\[Rule]CartesianPairContract/.Pair\[Rule]PairContract/.CartesianPairContract\[Rule]\ +CartesianPair/.PairContract\[Rule]Pair", +"DiracGamma[CartesianIndex[i]]*Pair[CartesianIndex[i], LorentzIndex[\[Mu]]]"}, +{"fcstCartesianPairContract-ID49", +"PairContract[CartesianIndex[mu], CartesianIndex[mu]]","-3"}, +{"fcstCartesianPairContract-ID50", +"PairContract[CartesianIndex[mu, D - 1], CartesianIndex[mu, D - 1]]","1-D"}, +{"fcstCartesianPairContract-ID51", +"PairContract[CartesianIndex[mu], CartesianMomentum[p]]","PairContract[CartesianIndex[mu], CartesianMomentum[p]]"}, +{"fcstCartesianPairContract-ID52","CartesianPairContract[CartesianIndex[i], CartesianIndex[i,D-1]]","3"}, +{"fcstCartesianPairContract-ID53","CartesianPairContract[CartesianIndex[i], CartesianIndex[i,D-4]]","0"}, +{"fcstCartesianPairContract-ID54","CartesianPairContract[CartesianIndex[i,D-1], CartesianIndex[i,D-4]]","D-4"} +}); diff --git a/Tests/Lorentz/PartialFourVector.test b/Tests/Lorentz/PartialFourVector.test index e257724ad..e428fcd28 100644 --- a/Tests/Lorentz/PartialFourVector.test +++ b/Tests/Lorentz/PartialFourVector.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for PartialFourVector *) diff --git a/Tests/Lorentz/ScalarProduct.test b/Tests/Lorentz/ScalarProduct.test index d82e987df..d6c53b6bb 100644 --- a/Tests/Lorentz/ScalarProduct.test +++ b/Tests/Lorentz/ScalarProduct.test @@ -1,12 +1,12 @@ -(* :Title: ScalarProduct.test *) +(* :Title: CartesianScalarProduct.test *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ScalarProduct *) @@ -830,3 +830,865 @@ Tests`Lorentz`fsctSPSet = ({ {"fsctSPSet-ID101", "FCClearScalarProducts[]; \n SP[p]=xxx; \n SP[p,p]", "xxx"}, {"fsctSPSet-ID102", "FCClearScalarProducts[]; \n SPE[p]=xxx; \n SPE[p,p]", "xxx"} }); + +Tests`Lorentz`fcstCartesianScalarProduct = { +{"fcstCartesianScalarProduct-ID1","CartesianScalarProduct[a, a]", + "CartesianPair[CartesianMomentum[a], CartesianMomentum[a]]"}, +{"fcstCartesianScalarProduct-ID2","CartesianScalarProduct[a, a, Dimension -> D-1]", + "CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[a, D-1]]"}, +{"fcstCartesianScalarProduct-ID3","CartesianScalarProduct[a, a, Dimension -> D - 4]", + "CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[a, -4 + D]]"}, +{"fcstCartesianScalarProduct-ID4","CartesianScalarProduct[a, b]", + "CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProduct-ID5","CartesianScalarProduct[a, b, Dimension -> D-1]", + "CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProduct-ID6","CartesianScalarProduct[a, b, Dimension -> D - 4]", + "CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProduct-ID7","CartesianScalarProduct[a, a, FCI -> False]", + "CartesianScalarProduct[a, a, FCI -> False]"}, +{"fcstCartesianScalarProduct-ID8","CartesianScalarProduct[a, a, Dimension -> D, FCI -> False]", + "CartesianScalarProduct[a, a, Dimension -> D, FCI -> False]"}, +{"fcstCartesianScalarProduct-ID9","CartesianScalarProduct[a, a, Dimension -> D - 4, FCI -> False]", + "CartesianScalarProduct[a, a, Dimension -> D - 4, FCI -> False]"}, +{"fcstCartesianScalarProduct-ID10","CartesianScalarProduct[a, b, FCI -> False]", + "CartesianScalarProduct[a, b, FCI -> False]"}, +{"fcstCartesianScalarProduct-ID11","CartesianScalarProduct[a, b, Dimension -> D, FCI -> False]", + "CartesianScalarProduct[a, b, Dimension -> D, FCI -> False]"}, +{"fcstCartesianScalarProduct-ID12","CartesianScalarProduct[a, b, Dimension -> D - 4, FCI -> False]", + "CartesianScalarProduct[a, b, Dimension -> D - 4, FCI -> False]"}, +{"fcstCartesianScalarProduct-ID13","CartesianScalarProduct[xsp1, xsp2]= ysp \n CartesianScalarProduct[xsp1, xsp2]= zsp", + "zsp"} +}; + + +Tests`Lorentz`fsctCSPSet = ({ +{"fsctCSPSet-ID1", "FCClearScalarProducts[] \n + CSP[a+b,c+d]=abval", "abval"}, +{"fsctCSPSet-ID2", "CSP[a+b,c+d]", "abval"}, +{"fsctCSPSet-ID3", "CSP[-a-b,c+d]", "-abval"}, +{"fsctCSPSet-ID4", "CSP[a+b,-c-d]", "-abval"}, +{"fsctCSPSet-ID5", "CSP[-a-b,-c-d]", "abval"}, +{"fsctCSPSet-ID6", "CSP[a+b,c+d]//FCI", "abval"}, +{"fsctCSPSet-ID7", "CSP[-a-b,c+d]//FCI", "-abval"}, +{"fsctCSPSet-ID8", "CSP[a+b,-c-d]//FCI", "-abval"}, +{"fsctCSPSet-ID9", "CSP[-a-b,-c-d]//FCI", "abval"}, +{"fsctCSPSet-ID10", "CSPD[a+b,c+d]", "CSPD[a + b, c + d]"}, +{"fsctCSPSet-ID11", "CSPD[-a-b,c+d]", "CSPD[-a - b, c + d]"}, +{"fsctCSPSet-ID12", "CSPD[a+b,-c-d]", "CSPD[a + b, -c - d]"}, +{"fsctCSPSet-ID13", "CSPD[-a-b,-c-d]", "CSPD[-a - b, -c - d]"}, +{"fsctCSPSet-ID14", "CSPD[a+b,c+d]//FCI", +"CartesianPair[CartesianMomentum[a + b, D-1], CartesianMomentum[c + d, D-1]]"}, +{"fsctCSPSet-ID15", "CSPD[-a-b,c+d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, D-1], CartesianMomentum[c + d, D-1]]"}, +{"fsctCSPSet-ID16", "CSPD[a+b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[a + b, D-1], CartesianMomentum[-c - d, D-1]]"}, +{"fsctCSPSet-ID17", "CSPD[-a-b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, D-1], CartesianMomentum[-c - d, D-1]]"}, +{"fsctCSPSet-ID18", "CSPE[a+b,c+d]", "CSPE[a + b, c + d]"}, +{"fsctCSPSet-ID19", "CSPE[-a-b,c+d]", "CSPE[-a - b, c + d]"}, +{"fsctCSPSet-ID20", "CSPE[a+b,-c-d]", "CSPE[a + b, -c - d]"}, +{"fsctCSPSet-ID21", "CSPE[-a-b,-c-d]", "CSPE[-a - b, -c - d]"}, +{"fsctCSPSet-ID22", "CSPE[a+b,c+d]//FCI", +"CartesianPair[CartesianMomentum[a + b, -4 + D], CartesianMomentum[c + d, -4 + D]]"}, +{"fsctCSPSet-ID23", "CSPE[-a-b,c+d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, -4 + D], CartesianMomentum[c + d, -4 + D]]"}, +{"fsctCSPSet-ID24", "CSPE[a+b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[a + b, -4 + D], CartesianMomentum[-c - d, -4 + D]]"}, +{"fsctCSPSet-ID25", "CSPE[-a-b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, -4 + D], CartesianMomentum[-c - d, -4 + D]]"}, +{"fsctCSPSet-ID26", "FCClearScalarProducts[] + CSP[a+b,c+d]=abval2", "abval2"}, +{"fsctCSPSet-ID27", "CSP[-a-b,c+d]", "-abval2"}, +{"fsctCSPSet-ID28", "CSP[a+b,-c-d]", "-abval2"}, +{"fsctCSPSet-ID29", "CSP[-a-b,-c-d]", "abval2"}, +{"fsctCSPSet-ID30", "CSP[a+b,c+d]//FCI", "abval2"}, +{"fsctCSPSet-ID31", "CSP[-a-b,c+d]//FCI", "-abval2"}, +{"fsctCSPSet-ID32", "CSP[a+b,-c-d]//FCI", "-abval2"}, +{"fsctCSPSet-ID33", "CSP[-a-b,-c-d]//FCI", "abval2"}, +{"fsctCSPSet-ID34", "CSPD[a+b,c+d]", "CSPD[a + b, c + d]"}, +{"fsctCSPSet-ID35", "CSPD[-a-b,c+d]", "CSPD[-a - b, c + d]"}, +{"fsctCSPSet-ID36", "CSPD[a+b,-c-d]", "CSPD[a + b, -c - d]"}, +{"fsctCSPSet-ID37", "CSPD[-a-b,-c-d]", "CSPD[-a - b, -c - d]"}, +{"fsctCSPSet-ID38", "CSPD[a+b,c+d]//FCI", +"CartesianPair[CartesianMomentum[a + b, D-1], CartesianMomentum[c + d, D-1]]"}, +{"fsctCSPSet-ID39", "CSPD[-a-b,c+d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, D-1], CartesianMomentum[c + d, D-1]]"}, +{"fsctCSPSet-ID40", "CSPD[a+b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[a + b, D-1], CartesianMomentum[-c - d, D-1]]"}, +{"fsctCSPSet-ID41", "CSPD[-a-b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, D-1], CartesianMomentum[-c - d, D-1]]"}, +{"fsctCSPSet-ID42", "CSPE[a+b,c+d]", "CSPE[a + b, c + d]"}, +{"fsctCSPSet-ID43", "CSPE[-a-b,c+d]", "CSPE[-a - b, c + d]"}, +{"fsctCSPSet-ID44", "CSPE[a+b,-c-d]", "CSPE[a + b, -c - d]"}, +{"fsctCSPSet-ID45", "CSPE[-a-b,-c-d]", "CSPE[-a - b, -c - d]"}, +{"fsctCSPSet-ID46", "CSPE[a+b,c+d]//FCI", +"CartesianPair[CartesianMomentum[a + b, -4 + D], CartesianMomentum[c + d, -4 + D]]"}, +{"fsctCSPSet-ID47", "CSPE[-a-b,c+d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, -4 + D], CartesianMomentum[c + d, -4 + D]]"}, +{"fsctCSPSet-ID48", "CSPE[a+b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[a + b, -4 + D], CartesianMomentum[-c - d, -4 + D]]"}, +{"fsctCSPSet-ID49", "CSPE[-a-b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, -4 + D], CartesianMomentum[-c - d, -4 + D]]"}, +{"fsctCSPSet-ID50", "FCClearScalarProducts[]; \n + CSPD[a+b,c+d]=abval", "abval"}, +{"fsctCSPSet-ID51", "CSP[a+b,c+d]", "CSP[a + b, c + d]"}, +{"fsctCSPSet-ID52", "CSP[-a-b,c+d]", "CSP[-a - b, c + d]"}, +{"fsctCSPSet-ID53", "CSP[a+b,-c-d]", "CSP[a + b, -c - d]"}, +{"fsctCSPSet-ID54", "CSP[-a-b,-c-d]", "CSP[-a - b, -c - d]"}, +{"fsctCSPSet-ID55", "CSP[a+b,c+d]//FCI", +"CartesianPair[CartesianMomentum[a + b], CartesianMomentum[c + d]]"}, +{"fsctCSPSet-ID56", "CSP[-a-b,c+d]//FCI", +"CartesianPair[CartesianMomentum[-a - b], CartesianMomentum[c + d]]"}, +{"fsctCSPSet-ID57", "CSP[a+b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[a + b], CartesianMomentum[-c - d]]"}, +{"fsctCSPSet-ID58", "CSP[-a-b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[-a - b], CartesianMomentum[-c - d]]"}, +{"fsctCSPSet-ID59", "CSPD[a+b,c+d]", "abval"}, +{"fsctCSPSet-ID60", "CSPD[-a-b,c+d]", "-abval"}, +{"fsctCSPSet-ID61", "CSPD[a+b,-c-d]", "-abval"}, +{"fsctCSPSet-ID62", "CSPD[-a-b,-c-d]", "abval"}, +{"fsctCSPSet-ID63", "CSPD[a+b,c+d]//FCI", "abval"}, +{"fsctCSPSet-ID64", "CSPD[-a-b,c+d]//FCI", "-abval"}, +{"fsctCSPSet-ID65", "CSPD[a+b,-c-d]//FCI", "-abval"}, +{"fsctCSPSet-ID66", "CSPD[-a-b,-c-d]//FCI", "abval"}, +{"fsctCSPSet-ID67", "CSPE[a+b,c+d]", "CSPE[a + b, c + d]"}, +{"fsctCSPSet-ID68", "CSPE[-a-b,c+d]", "CSPE[-a - b, c + d]"}, +{"fsctCSPSet-ID69", "CSPE[a+b,-c-d]", "CSPE[a + b, -c - d]"}, +{"fsctCSPSet-ID70", "CSPE[-a-b,-c-d]", "CSPE[-a - b, -c - d]"}, +{"fsctCSPSet-ID71", "CSPE[a+b,c+d]//FCI", +"CartesianPair[CartesianMomentum[a + b, -4 + D], CartesianMomentum[c + d, -4 + D]]"}, +{"fsctCSPSet-ID72", "CSPE[-a-b,c+d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, -4 + D], CartesianMomentum[c + d, -4 + D]]"}, +{"fsctCSPSet-ID73", "CSPE[a+b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[a + b, -4 + D], CartesianMomentum[-c - d, -4 + D]]"}, +{"fsctCSPSet-ID74", "CSPE[-a-b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, -4 + D], CartesianMomentum[-c - d, -4 + D]]"}, +{"fsctCSPSet-ID75", "FCClearScalarProducts[]; + CSPE[a+b,c+d]=abval", "abval"}, +{"fsctCSPSet-ID76", "CSP[a+b,c+d]", "CSP[a + b, c + d]"}, +{"fsctCSPSet-ID77", "CSP[-a-b,c+d]", "CSP[-a - b, c + d]"}, +{"fsctCSPSet-ID78", "CSP[a+b,-c-d]", "CSP[a + b, -c - d]"}, +{"fsctCSPSet-ID79", "CSP[-a-b,-c-d]", "CSP[-a - b, -c - d]"}, +{"fsctCSPSet-ID80", "CSP[a+b,c+d]//FCI", +"CartesianPair[CartesianMomentum[a + b], CartesianMomentum[c + d]]"}, +{"fsctCSPSet-ID81", "CSP[-a-b,c+d]//FCI", +"CartesianPair[CartesianMomentum[-a - b], CartesianMomentum[c + d]]"}, +{"fsctCSPSet-ID82", "CSP[a+b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[a + b], CartesianMomentum[-c - d]]"}, +{"fsctCSPSet-ID83", "CSP[-a-b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[-a - b], CartesianMomentum[-c - d]]"}, +{"fsctCSPSet-ID84", "CSPD[a+b,c+d]", "CSPD[a + b, c + d]"}, +{"fsctCSPSet-ID85", "CSPD[-a-b,c+d]", "CSPD[-a - b, c + d]"}, +{"fsctCSPSet-ID86", "CSPD[a+b,-c-d]", "CSPD[a + b, -c - d]"}, +{"fsctCSPSet-ID87", "CSPD[-a-b,-c-d]", "CSPD[-a - b, -c - d]"}, +{"fsctCSPSet-ID88", "CSPD[a+b,c+d]//FCI", +"CartesianPair[CartesianMomentum[a + b, D-1], CartesianMomentum[c + d, D-1]]"}, +{"fsctCSPSet-ID89", "CSPD[-a-b,c+d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, D-1], CartesianMomentum[c + d, D-1]]"}, +{"fsctCSPSet-ID90", "CSPD[a+b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[a + b, D-1], CartesianMomentum[-c - d, D-1]]"}, +{"fsctCSPSet-ID91", "CSPD[-a-b,-c-d]//FCI", +"CartesianPair[CartesianMomentum[-a - b, D-1], CartesianMomentum[-c - d, D-1]]"}, +{"fsctCSPSet-ID92", "CSPE[a+b,c+d]", "abval"}, +{"fsctCSPSet-ID93", "CSPE[-a-b,c+d]", "-abval"}, +{"fsctCSPSet-ID94", "CSPE[a+b,-c-d]", "-abval"}, +{"fsctCSPSet-ID95", "CSPE[-a-b,-c-d]", "abval"}, +{"fsctCSPSet-ID96", "CSPE[a+b,c+d]//FCI", "abval"}, +{"fsctCSPSet-ID97", "CSPE[-a-b,c+d]//FCI", "-abval"}, +{"fsctCSPSet-ID98", "CSPE[a+b,-c-d]//FCI", "-abval"}, +{"fsctCSPSet-ID99", "CSPE[-a-b,-c-d]//FCI", "abval"}, +{"fsctCSPSet-ID100", "FCClearScalarProducts[]; \n CSPD[p]=xxx; \n CSPD[p,p]", "xxx"}, +{"fsctCSPSet-ID101", "FCClearScalarProducts[]; \n CSP[p]=xxx; \n CSP[p,p]", "xxx"}, +{"fsctCSPSet-ID102", "FCClearScalarProducts[]; \n CSPE[p]=xxx; \n CSPE[p,p]", "xxx"} +}); + + +Tests`Lorentz`fcstCartesianScalarProductSet = ({ +{"fcstCartesianScalarProductSet-ID1", "FCClearScalarProducts[]; \n + CartesianScalarProduct[a,b]=abval; \n + CartesianScalarProduct[a,b]", "abval"}, +{"fcstCartesianScalarProductSet-ID2", "CartesianScalarProduct[a,-b]", "-abval"}, +{"fcstCartesianScalarProductSet-ID3", "CartesianScalarProduct[-a,b]", "-abval"}, +{"fcstCartesianScalarProductSet-ID4", "CartesianScalarProduct[-a,-b]", "abval"}, +{"fcstCartesianScalarProductSet-ID5", "CartesianScalarProduct[a,b,Dimension\[Rule]D-1]", + "abval"}, +{"fcstCartesianScalarProductSet-ID6", +"CartesianScalarProduct[a,-b,Dimension\[Rule]D-1]", "-abval"}, +{"fcstCartesianScalarProductSet-ID7", +"CartesianScalarProduct[-a,b,Dimension\[Rule]D-1]", "-abval"}, +{"fcstCartesianScalarProductSet-ID8", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]D-1]", "abval"}, +{"fcstCartesianScalarProductSet-ID9", +"CartesianScalarProduct[a,b,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID10", +"CartesianScalarProduct[a,-b,Dimension\[Rule]D-4]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID11", +"CartesianScalarProduct[-a,b,Dimension\[Rule]D-4]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID12", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID13", "CartesianPair[CartesianMomentum[a],CartesianMomentum[b]]", +"abval"}, +{"fcstCartesianScalarProductSet-ID14", "CartesianPair[CartesianMomentum[a],CartesianMomentum[-b]]", +"-abval"}, +{"fcstCartesianScalarProductSet-ID15", "CartesianPair[CartesianMomentum[-a],CartesianMomentum[b]]", +"-abval"}, +{"fcstCartesianScalarProductSet-ID16", "CartesianPair[CartesianMomentum[-a],CartesianMomentum[-b]]", +"abval"}, +{"fcstCartesianScalarProductSet-ID17", "CartesianPair[CartesianMomentum[a,D-1],CartesianMomentum[b,D-1]]", +"abval"}, +{"fcstCartesianScalarProductSet-ID18", "CartesianPair[CartesianMomentum[a,D-1],CartesianMomentum[-b,D-1]]", +"-abval"}, +{"fcstCartesianScalarProductSet-ID19", "CartesianPair[CartesianMomentum[-a,D-1],CartesianMomentum[b,D-1]]", +"-abval"}, +{"fcstCartesianScalarProductSet-ID20", "CartesianPair[CartesianMomentum[-a,D-1],CartesianMomentum[-b,D-1]]", + "abval"}, +{"fcstCartesianScalarProductSet-ID21", +"CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[b,D-4]]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID22", +"CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[-b,D-4]]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID23", +"CartesianPair[CartesianMomentum[-a,D-4],CartesianMomentum[b,D-4]]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID24", +"CartesianPair[CartesianMomentum[-a,D-4],CartesianMomentum[-b,D-4]]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID25", "CSP[a,b]", "abval"}, +{"fcstCartesianScalarProductSet-ID26", "CSP[a,-b]", "-abval"}, +{"fcstCartesianScalarProductSet-ID27", "CSP[-a,b]", "-abval"}, +{"fcstCartesianScalarProductSet-ID28", "CSP[-a,-b]", "abval"}, +{"fcstCartesianScalarProductSet-ID29", "CSPD[a,b]", "abval"}, +{"fcstCartesianScalarProductSet-ID30", "CSPD[a,-b]", "-abval"}, +{"fcstCartesianScalarProductSet-ID31", "CSPD[-a,b]", "-abval"}, +{"fcstCartesianScalarProductSet-ID32", "CSPD[-a,-b]", "abval"}, +{"fcstCartesianScalarProductSet-ID33", "CSPE[a,b]", "CSPE[a, b]"}, +{"fcstCartesianScalarProductSet-ID34", "CSPE[a,-b]", "CSPE[a, -b]"}, +{"fcstCartesianScalarProductSet-ID35", "CSPE[-a,b]", "CSPE[-a, b]"}, +{"fcstCartesianScalarProductSet-ID36", "CSPE[-a,-b]", "CSPE[-a, -b]"}, +{"fcstCartesianScalarProductSet-ID37", "CartesianScalarProduct[a,b]=abva2 + CartesianScalarProduct[a,b]", "abva2"}, +{"fcstCartesianScalarProductSet-ID38", "CartesianScalarProduct[a,-b]", "-abva2"}, +{"fcstCartesianScalarProductSet-ID39", "CartesianScalarProduct[-a,b]", "-abva2"}, +{"fcstCartesianScalarProductSet-ID40", "CartesianScalarProduct[-a,-b]", "abva2"}, +{"fcstCartesianScalarProductSet-ID41", +"CartesianScalarProduct[a,b,Dimension\[Rule]D-1]", "abva2"}, +{"fcstCartesianScalarProductSet-ID42", +"CartesianScalarProduct[a,-b,Dimension\[Rule]D-1]", "-abva2"}, +{"fcstCartesianScalarProductSet-ID43", +"CartesianScalarProduct[-a,b,Dimension\[Rule]D-1]", "-abva2"}, +{"fcstCartesianScalarProductSet-ID44", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]D-1]", "abva2"}, +{"fcstCartesianScalarProductSet-ID45", +"CartesianScalarProduct[a,b,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID46", +"CartesianScalarProduct[a,-b,Dimension\[Rule]D-4]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID47", +"CartesianScalarProduct[-a,b,Dimension\[Rule]D-4]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID48", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID49", "CartesianPair[CartesianMomentum[a],CartesianMomentum[b]]", +"abva2"}, +{"fcstCartesianScalarProductSet-ID50", "CartesianPair[CartesianMomentum[a],CartesianMomentum[-b]]", +"-abva2"}, +{"fcstCartesianScalarProductSet-ID51", "CartesianPair[CartesianMomentum[-a],CartesianMomentum[b]]", +"-abva2"}, +{"fcstCartesianScalarProductSet-ID52", "CartesianPair[CartesianMomentum[-a],CartesianMomentum[-b]]", +"abva2"}, +{"fcstCartesianScalarProductSet-ID53", "CartesianPair[CartesianMomentum[a,D-1],CartesianMomentum[b,D-1]]", +"abva2"}, +{"fcstCartesianScalarProductSet-ID54", "CartesianPair[CartesianMomentum[a,D-1],CartesianMomentum[-b,D-1]]", +"-abva2"}, +{"fcstCartesianScalarProductSet-ID55", "CartesianPair[CartesianMomentum[-a,D-1],CartesianMomentum[b,D-1]]", +"-abva2"}, +{"fcstCartesianScalarProductSet-ID56", "CartesianPair[CartesianMomentum[-a,D-1],CartesianMomentum[-b,D-1]]", + "abva2"}, +{"fcstCartesianScalarProductSet-ID57", +"CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[b,D-4]]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID58", +"CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[-b,D-4]]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID59", +"CartesianPair[CartesianMomentum[-a,D-4],CartesianMomentum[b,D-4]]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID60", +"CartesianPair[CartesianMomentum[-a,D-4],CartesianMomentum[-b,D-4]]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID61", "CSP[a,b]", "abva2"}, +{"fcstCartesianScalarProductSet-ID62", "CSP[a,-b]", "-abva2"}, +{"fcstCartesianScalarProductSet-ID63", "CSP[-a,b]", "-abva2"}, +{"fcstCartesianScalarProductSet-ID64", "CSP[-a,-b]", "abva2"}, +{"fcstCartesianScalarProductSet-ID65", "CSPD[a,b]", "abva2"}, +{"fcstCartesianScalarProductSet-ID66", "CSPD[a,-b]", "-abva2"}, +{"fcstCartesianScalarProductSet-ID67", "CSPD[-a,b]", "-abva2"}, +{"fcstCartesianScalarProductSet-ID68", "CSPD[-a,-b]", "abva2"}, +{"fcstCartesianScalarProductSet-ID69", "CSPE[a,b]", "CSPE[a, b]"}, +{"fcstCartesianScalarProductSet-ID70", "CSPE[a,-b]", "CSPE[a, -b]"}, +{"fcstCartesianScalarProductSet-ID71", "CSPE[-a,b]", "CSPE[-a, b]"}, +{"fcstCartesianScalarProductSet-ID72", "CSPE[-a,-b]", "CSPE[-a, -b]"}, +{"fcstCartesianScalarProductSet-ID73", "abval", "abval"}, +{"fcstCartesianScalarProductSet-ID74", "FCClearScalarProducts[] + CartesianScalarProduct[a,b]", "CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID75", "CartesianScalarProduct[a,-b]", +"-CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID76", "CartesianScalarProduct[-a,b]", +"-CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID77", "CartesianScalarProduct[-a,-b]", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID78", +"CartesianScalarProduct[a,b,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID79", +"CartesianScalarProduct[a,-b,Dimension\[Rule]D-1]", +"-CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID80", +"CartesianScalarProduct[-a,b,Dimension\[Rule]D-1]", +"-CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID81", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID82", +"CartesianScalarProduct[a,b,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID83", +"CartesianScalarProduct[a,-b,Dimension\[Rule]D-4]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID84", +"CartesianScalarProduct[-a,b,Dimension\[Rule]D-4]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID85", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID86", "CartesianPair[CartesianMomentum[a],CartesianMomentum[b]]", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID87", "CartesianPair[CartesianMomentum[a],CartesianMomentum[-b]]", +"-CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID88", "CartesianPair[CartesianMomentum[-a],CartesianMomentum[b]]", +"-CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID89", "CartesianPair[CartesianMomentum[-a],CartesianMomentum[-b]]", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID90", "CartesianPair[CartesianMomentum[a,D-1],CartesianMomentum[b,D-1]]", +"CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID91", "CartesianPair[CartesianMomentum[a,D-1],CartesianMomentum[-b,D-1]]", +"-CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID92", "CartesianPair[CartesianMomentum[-a,D-1],CartesianMomentum[b,D-1]]", +"-CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID93", "CartesianPair[CartesianMomentum[-a,D-1],CartesianMomentum[-b,D-1]]", + "CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID94", +"CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[b,D-4]]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID95", +"CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[-b,D-4]]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID96", +"CartesianPair[CartesianMomentum[-a,D-4],CartesianMomentum[b,D-4]]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID97", +"CartesianPair[CartesianMomentum[-a,D-4],CartesianMomentum[-b,D-4]]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID98", "CSP[a,b]", "CSP[a, b]"}, +{"fcstCartesianScalarProductSet-ID99", "CSP[a,-b]", "CSP[a, -b]"}, +{"fcstCartesianScalarProductSet-ID100", "CSP[-a,b]", "CSP[-a, b]"}, +{"fcstCartesianScalarProductSet-ID101", "CSP[-a,-b]", "CSP[-a, -b]"}, +{"fcstCartesianScalarProductSet-ID102", "CSPD[a,b]", "CSPD[a, b]"}, +{"fcstCartesianScalarProductSet-ID103", "CSPD[a,-b]", "CSPD[a, -b]"}, +{"fcstCartesianScalarProductSet-ID104", "CSPD[-a,b]", "CSPD[-a, b]"}, +{"fcstCartesianScalarProductSet-ID105", "CSPD[-a,-b]", "CSPD[-a, -b]"}, +{"fcstCartesianScalarProductSet-ID106", "CSPE[a,b]", "CSPE[a, b]"}, +{"fcstCartesianScalarProductSet-ID107", "CSPE[a,-b]", "CSPE[a, -b]"}, +{"fcstCartesianScalarProductSet-ID108", "CSPE[-a,b]", "CSPE[-a, b]"}, +{"fcstCartesianScalarProductSet-ID109", "CSPE[-a,-b]", "CSPE[-a, -b]"}, +{"fcstCartesianScalarProductSet-ID110", +"CartesianScalarProduct[a,b,SetDimensions\[Rule]{X}]=abval3 \n + CartesianScalarProduct[a,b]", "CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID111", "CartesianScalarProduct[a,-b]", +"-CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID112", "CartesianScalarProduct[-a,b]", +"-CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID113", "CartesianScalarProduct[-a,-b]", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID114", +"CartesianScalarProduct[a,b,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID115", +"CartesianScalarProduct[a,-b,Dimension\[Rule]D-1]", +"-CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID116", +"CartesianScalarProduct[-a,b,Dimension\[Rule]D-1]", +"-CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID117", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[a, D-1], CartesianMomentum[b, D-1]]"}, +{"fcstCartesianScalarProductSet-ID118", +"CartesianScalarProduct[a,b,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID119", +"CartesianScalarProduct[a,-b,Dimension\[Rule]D-4]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID120", +"CartesianScalarProduct[-a,b,Dimension\[Rule]D-4]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID121", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID122", +"CartesianScalarProduct[a,b,Dimension\[Rule]X]", "abval3"}, +{"fcstCartesianScalarProductSet-ID123", +"CartesianScalarProduct[a,-b,Dimension\[Rule]X]", "-abval3"}, +{"fcstCartesianScalarProductSet-ID124", +"CartesianScalarProduct[-a,b,Dimension\[Rule]X]", "-abval3"}, +{"fcstCartesianScalarProductSet-ID125", +"CartesianScalarProduct[-a,-b,Dimension\[Rule]X]", "abval3"}, +{"fcstCartesianScalarProductSet-ID126", "CartesianPair[CartesianMomentum[a],CartesianMomentum[b]]", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID127", "CartesianPair[CartesianMomentum[a],CartesianMomentum[-b]]", +"-CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID128", "CartesianPair[CartesianMomentum[-a],CartesianMomentum[b]]", +"-CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID129", "CartesianPair[CartesianMomentum[-a],CartesianMomentum[-b]]", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianScalarProductSet-ID130", "CartesianPair[CartesianMomentum[a,D],CartesianMomentum[b,D]]", +"CartesianPair[CartesianMomentum[a, D], CartesianMomentum[b, D]]"}, +{"fcstCartesianScalarProductSet-ID131", "CartesianPair[CartesianMomentum[a,D],CartesianMomentum[-b,D]]", + "-CartesianPair[CartesianMomentum[a, D], CartesianMomentum[b, D]]"}, +{"fcstCartesianScalarProductSet-ID132", "CartesianPair[CartesianMomentum[-a,D],CartesianMomentum[b,D]]", + "-CartesianPair[CartesianMomentum[a, D], CartesianMomentum[b, D]]"}, +{"fcstCartesianScalarProductSet-ID133", +"CartesianPair[CartesianMomentum[-a,D],CartesianMomentum[-b,D]]", +"CartesianPair[CartesianMomentum[a, D], CartesianMomentum[b, D]]"}, +{"fcstCartesianScalarProductSet-ID134", +"CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[b,D-4]]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID135", +"CartesianPair[CartesianMomentum[a,D-4],CartesianMomentum[-b,D-4]]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID136", +"CartesianPair[CartesianMomentum[-a,D-4],CartesianMomentum[b,D-4]]", +"-CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID137", +"CartesianPair[CartesianMomentum[-a,D-4],CartesianMomentum[-b,D-4]]", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID138", "CartesianPair[CartesianMomentum[a,X],CartesianMomentum[b,X]]", +"abval3"}, +{"fcstCartesianScalarProductSet-ID139", "CartesianPair[CartesianMomentum[a,X],CartesianMomentum[-b,X]]", + "-abval3"}, +{"fcstCartesianScalarProductSet-ID140", "CartesianPair[CartesianMomentum[-a,X],CartesianMomentum[b,X]]", + "-abval3"}, +{"fcstCartesianScalarProductSet-ID141", +"CartesianPair[CartesianMomentum[-a,X],CartesianMomentum[-b,X]]", "abval3"}, +{"fcstCartesianScalarProductSet-ID142", "CSP[a,b]", "CSP[a, b]"}, +{"fcstCartesianScalarProductSet-ID143", "CSP[a,-b]", "CSP[a, -b]"}, +{"fcstCartesianScalarProductSet-ID144", "CSP[-a,b]", "CSP[-a, b]"}, +{"fcstCartesianScalarProductSet-ID145", "CSP[-a,-b]", "CSP[-a, -b]"}, +{"fcstCartesianScalarProductSet-ID146", "CSPD[a,b]", "CSPD[a, b]"}, +{"fcstCartesianScalarProductSet-ID147", "CSPD[a,-b]", "CSPD[a, -b]"}, +{"fcstCartesianScalarProductSet-ID148", "CSPD[-a,b]", "CSPD[-a, b]"}, +{"fcstCartesianScalarProductSet-ID149", "CSPD[-a,-b]", "CSPD[-a, -b]"}, +{"fcstCartesianScalarProductSet-ID150", "CSPE[a,b]", "CSPE[a, b]"}, +{"fcstCartesianScalarProductSet-ID151", "CSPE[a,-b]", "CSPE[a, -b]"}, +{"fcstCartesianScalarProductSet-ID152", "CSPE[-a,b]", "CSPE[-a, b]"}, +{"fcstCartesianScalarProductSet-ID153", "CSPE[-a,-b]", "CSPE[-a, -b]"}, +{"fcstCartesianScalarProductSet-ID154", "FCClearScalarProducts[] \n + CartesianScalarProduct[a1+a2,b1+b2]=abval \n + CartesianScalarProduct[a1+a2,b1+b2,FCI\[Rule]False]", +"CartesianScalarProduct[a1 + a2, b1 + b2, FeynCalcInternal -> False]"}, +{"fcstCartesianScalarProductSet-ID155", "CartesianScalarProduct[a1+a2,-b1-b2]", +"-abval"}, +{"fcstCartesianScalarProductSet-ID156", "CartesianScalarProduct[-a1-a2,b1+b2]", +"-abval"}, +{"fcstCartesianScalarProductSet-ID157", "CartesianScalarProduct[-a1-a2,-b1-b2]", +"abval"}, +{"fcstCartesianScalarProductSet-ID158", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]D-1]", "abval"}, +{"fcstCartesianScalarProductSet-ID159", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]D-1]", "-abval"}, +{"fcstCartesianScalarProductSet-ID160", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]D-1]", "-abval"}, +{"fcstCartesianScalarProductSet-ID161", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]D-1]", "abval"}, +{"fcstCartesianScalarProductSet-ID162", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID163", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID164", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID165", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID166", +"CartesianPair[CartesianMomentum[a1+a2],CartesianMomentum[b1+b2]]", "abval"}, +{"fcstCartesianScalarProductSet-ID167", +"CartesianPair[CartesianMomentum[a1+a2],CartesianMomentum[-b1-b2]]", "-abval"}, +{"fcstCartesianScalarProductSet-ID168", +"CartesianPair[CartesianMomentum[-a1-a2],CartesianMomentum[b1+b2]]", "-abval"}, +{"fcstCartesianScalarProductSet-ID169", +"CartesianPair[CartesianMomentum[-a1-a2],CartesianMomentum[-b1-b2]]", "abval"}, +{"fcstCartesianScalarProductSet-ID170", +"CartesianPair[CartesianMomentum[a1+a2,D-1],CartesianMomentum[b1+b2,D-1]]", "abval"}, +{"fcstCartesianScalarProductSet-ID171", +"CartesianPair[CartesianMomentum[a1+a2,D-1],CartesianMomentum[-b1-b2,D-1]]", "-abval"}, +{"fcstCartesianScalarProductSet-ID172", +"CartesianPair[CartesianMomentum[-a1-a2,D-1],CartesianMomentum[b1+b2,D-1]]", "-abval"}, +{"fcstCartesianScalarProductSet-ID173", +"CartesianPair[CartesianMomentum[-a1-a2,D-1],CartesianMomentum[-b1-b2,D-1]]", "abval"}, +{"fcstCartesianScalarProductSet-ID174", +"CartesianPair[CartesianMomentum[a1+a2,D-4],CartesianMomentum[b1+b2,D-4]]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID175", +"CartesianPair[CartesianMomentum[a1+a2,D-4],CartesianMomentum[-b1-b2,D-4]]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID176", +"CartesianPair[CartesianMomentum[-a1-a2,D-4],CartesianMomentum[b1+b2,D-4]]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID177", +"CartesianPair[CartesianMomentum[-a1-a2,D-4],CartesianMomentum[-b1-b2,D-4]]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID178", "CSP[a1+a2,b1+b2]", "abval"}, +{"fcstCartesianScalarProductSet-ID179", "CSP[a1+a2,-b1-b2]", "-abval"}, +{"fcstCartesianScalarProductSet-ID180", "CSP[-a1-a2,b1+b2]", "-abval"}, +{"fcstCartesianScalarProductSet-ID181", "CSP[-a1-a2,-b1-b2]", "abval"}, +{"fcstCartesianScalarProductSet-ID182", "CSPD[a1+a2,b1+b2]", "abval"}, +{"fcstCartesianScalarProductSet-ID183", "CSPD[a1+a2,-b1-b2]", "-abval"}, +{"fcstCartesianScalarProductSet-ID184", "CSPD[-a1-a2,b1+b2]", "-abval"}, +{"fcstCartesianScalarProductSet-ID185", "CSPD[-a1-a2,-b1-b2]", "abval"}, +{"fcstCartesianScalarProductSet-ID186", "CSPE[a1+a2,b1+b2]", +"CSPE[a1 + a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID187", "CSPE[a1+a2,-b1-b2]", +"CSPE[a1 + a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID188", "CSPE[-a1-a2,b1+b2]", +"CSPE[-a1 - a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID189", "CSPE[-a1-a2,-b1-b2]", +"CSPE[-a1 - a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID190", "CartesianScalarProduct[a1+a2,b1+b2]=abval2 \n + CartesianScalarProduct[a1+a2,b1+b2]", "abval2"}, +{"fcstCartesianScalarProductSet-ID191", "CartesianScalarProduct[a1+a2,-b1-b2]", +"-abval2"}, +{"fcstCartesianScalarProductSet-ID192", "CartesianScalarProduct[-a1-a2,b1+b2]", +"-abval2"}, +{"fcstCartesianScalarProductSet-ID193", "CartesianScalarProduct[-a1-a2,-b1-b2]", +"abval2"}, +{"fcstCartesianScalarProductSet-ID194", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]D-1]", "abval2"}, +{"fcstCartesianScalarProductSet-ID195", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]D-1]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID196", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]D-1]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID197", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]D-1]", "abval2"}, +{"fcstCartesianScalarProductSet-ID198", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID199", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID200", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID201", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID202", +"CartesianPair[CartesianMomentum[a1+a2],CartesianMomentum[b1+b2]]", "abval2"}, +{"fcstCartesianScalarProductSet-ID203", +"CartesianPair[CartesianMomentum[a1+a2],CartesianMomentum[-b1-b2]]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID204", +"CartesianPair[CartesianMomentum[-a1-a2],CartesianMomentum[b1+b2]]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID205", +"CartesianPair[CartesianMomentum[-a1-a2],CartesianMomentum[-b1-b2]]", "abval2"}, +{"fcstCartesianScalarProductSet-ID206", +"CartesianPair[CartesianMomentum[a1+a2,D-1],CartesianMomentum[b1+b2,D-1]]", "abval2"}, +{"fcstCartesianScalarProductSet-ID207", +"CartesianPair[CartesianMomentum[a1+a2,D-1],CartesianMomentum[-b1-b2,D-1]]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID208", +"CartesianPair[CartesianMomentum[-a1-a2,D-1],CartesianMomentum[b1+b2,D-1]]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID209", +"CartesianPair[CartesianMomentum[-a1-a2,D-1],CartesianMomentum[-b1-b2,D-1]]", "abval2"}, +{"fcstCartesianScalarProductSet-ID210", +"CartesianPair[CartesianMomentum[a1+a2,D-4],CartesianMomentum[b1+b2,D-4]]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID211", +"CartesianPair[CartesianMomentum[a1+a2,D-4],CartesianMomentum[-b1-b2,D-4]]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID212", +"CartesianPair[CartesianMomentum[-a1-a2,D-4],CartesianMomentum[b1+b2,D-4]]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID213", +"CartesianPair[CartesianMomentum[-a1-a2,D-4],CartesianMomentum[-b1-b2,D-4]]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID214", "CSP[a1+a2,b1+b2]", "abval2"}, +{"fcstCartesianScalarProductSet-ID215", "CSP[a1+a2,-b1-b2]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID216", "CSP[-a1-a2,b1+b2]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID217", "CSP[-a1-a2,-b1-b2]", "abval2"}, +{"fcstCartesianScalarProductSet-ID218", "CSPD[a1+a2,b1+b2]", "abval2"}, +{"fcstCartesianScalarProductSet-ID219", "CSPD[a1+a2,-b1-b2]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID220", "CSPD[-a1-a2,b1+b2]", "-abval2"}, +{"fcstCartesianScalarProductSet-ID221", "CSPD[-a1-a2,-b1-b2]", "abval2"}, +{"fcstCartesianScalarProductSet-ID222", "CSPE[a1+a2,b1+b2]", +"CSPE[a1 + a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID223", "CSPE[a1+a2,-b1-b2]", +"CSPE[a1 + a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID224", "CSPE[-a1-a2,b1+b2]", +"CSPE[-a1 - a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID225", "CSPE[-a1-a2,-b1-b2]", +"CSPE[-a1 - a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID226", "abval", "abval"}, +{"fcstCartesianScalarProductSet-ID227", "FCClearScalarProducts[] \n + CartesianScalarProduct[a1+a2,b1+b2,FCI\[Rule]False]", +"CartesianScalarProduct[a1 + a2, b1 + b2, FeynCalcInternal -> False]"}, +{"fcstCartesianScalarProductSet-ID228", "CartesianScalarProduct[a1+a2,-b1-b2]", +"CartesianPair[CartesianMomentum[a1 + a2], CartesianMomentum[-b1 - b2]]"}, +{"fcstCartesianScalarProductSet-ID229", "CartesianScalarProduct[-a1-a2,b1+b2]", +"CartesianPair[CartesianMomentum[-a1 - a2], CartesianMomentum[b1 + b2]]"}, +{"fcstCartesianScalarProductSet-ID230", "CartesianScalarProduct[-a1-a2,-b1-b2]", +"CartesianPair[CartesianMomentum[-a1 - a2], CartesianMomentum[-b1 - b2]]"}, +{"fcstCartesianScalarProductSet-ID231", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[a1 + a2, D-1], CartesianMomentum[b1 + b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID232", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[a1 + a2, D-1], CartesianMomentum[-b1 - b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID233", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[-a1 - a2, D-1], CartesianMomentum[b1 + b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID234", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[-a1 - a2, D-1], CartesianMomentum[-b1 - b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID235", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID236", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID237", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID238", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID239", +"CartesianPair[CartesianMomentum[a1+a2],CartesianMomentum[b1+b2]]", +"CartesianPair[CartesianMomentum[a1 + a2], CartesianMomentum[b1 + b2]]"}, +{"fcstCartesianScalarProductSet-ID240", +"CartesianPair[CartesianMomentum[a1+a2],CartesianMomentum[-b1-b2]]", +"CartesianPair[CartesianMomentum[a1 + a2], CartesianMomentum[-b1 - b2]]"}, +{"fcstCartesianScalarProductSet-ID241", +"CartesianPair[CartesianMomentum[-a1-a2],CartesianMomentum[b1+b2]]", +"CartesianPair[CartesianMomentum[-a1 - a2], CartesianMomentum[b1 + b2]]"}, +{"fcstCartesianScalarProductSet-ID242", +"CartesianPair[CartesianMomentum[-a1-a2],CartesianMomentum[-b1-b2]]", +"CartesianPair[CartesianMomentum[-a1 - a2], CartesianMomentum[-b1 - b2]]"}, +{"fcstCartesianScalarProductSet-ID243", +"CartesianPair[CartesianMomentum[a1+a2,D-1],CartesianMomentum[b1+b2,D-1]]", +"CartesianPair[CartesianMomentum[a1 + a2, D-1], CartesianMomentum[b1 + b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID244", +"CartesianPair[CartesianMomentum[a1+a2,D-1],CartesianMomentum[-b1-b2,D-1]]", +"CartesianPair[CartesianMomentum[a1 + a2, D-1], CartesianMomentum[-b1 - b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID245", +"CartesianPair[CartesianMomentum[-a1-a2,D-1],CartesianMomentum[b1+b2,D-1]]", +"CartesianPair[CartesianMomentum[-a1 - a2, D-1], CartesianMomentum[b1 + b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID246", +"CartesianPair[CartesianMomentum[-a1-a2,D-1],CartesianMomentum[-b1-b2,D-1]]", +"CartesianPair[CartesianMomentum[-a1 - a2, D-1], CartesianMomentum[-b1 - b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID247", +"CartesianPair[CartesianMomentum[a1+a2,D-4],CartesianMomentum[b1+b2,D-4]]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID248", +"CartesianPair[CartesianMomentum[a1+a2,D-4],CartesianMomentum[-b1-b2,D-4]]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID249", +"CartesianPair[CartesianMomentum[-a1-a2,D-4],CartesianMomentum[b1+b2,D-4]]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID250", +"CartesianPair[CartesianMomentum[-a1-a2,D-4],CartesianMomentum[-b1-b2,D-4]]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID251", "CSP[a1+a2,b1+b2]", +"CSP[a1 + a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID252", "CSP[a1+a2,-b1-b2]", +"CSP[a1 + a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID253", "CSP[-a1-a2,b1+b2]", +"CSP[-a1 - a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID254", "CSP[-a1-a2,-b1-b2]", +"CSP[-a1 - a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID255", "CSPD[a1+a2,b1+b2]", +"CSPD[a1 + a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID256", "CSPD[a1+a2,-b1-b2]", +"CSPD[a1 + a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID257", "CSPD[-a1-a2,b1+b2]", +"CSPD[-a1 - a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID258", "CSPD[-a1-a2,-b1-b2]", +"CSPD[-a1 - a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID259", "CSPE[a1+a2,b1+b2]", +"CSPE[a1 + a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID260", "CSPE[a1+a2,-b1-b2]", +"CSPE[a1 + a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID261", "CSPE[-a1-a2,b1+b2]", +"CSPE[-a1 - a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID262", "CSPE[-a1-a2,-b1-b2]", +"CSPE[-a1 - a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID263", "FCClearScalarProducts[] \n + CartesianScalarProduct[a1+a2,b1+b2,SetDimensions\[Rule]{X}]=abval3 \n + CartesianScalarProduct[a1+a2,b1+b2]", +"CartesianPair[CartesianMomentum[a1 + a2], CartesianMomentum[b1 + b2]]"}, +{"fcstCartesianScalarProductSet-ID264", "CartesianScalarProduct[a1+a2,-b1-b2]", +"CartesianPair[CartesianMomentum[a1 + a2], CartesianMomentum[-b1 - b2]]"}, +{"fcstCartesianScalarProductSet-ID265", "CartesianScalarProduct[-a1-a2,b1+b2]", +"CartesianPair[CartesianMomentum[-a1 - a2], CartesianMomentum[b1 + b2]]"}, +{"fcstCartesianScalarProductSet-ID266", "CartesianScalarProduct[-a1-a2,-b1-b2]", +"CartesianPair[CartesianMomentum[-a1 - a2], CartesianMomentum[-b1 - b2]]"}, +{"fcstCartesianScalarProductSet-ID267", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[a1 + a2, D-1], CartesianMomentum[b1 + b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID268", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[a1 + a2, D-1], CartesianMomentum[-b1 - b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID269", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[-a1 - a2, D-1], CartesianMomentum[b1 + b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID270", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]D-1]", +"CartesianPair[CartesianMomentum[-a1 - a2, D-1], CartesianMomentum[-b1 - b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID271", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID272", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID273", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID274", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]D-4]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID275", +"CartesianScalarProduct[a1+a2,b1+b2,Dimension\[Rule]X]", "abval3"}, +{"fcstCartesianScalarProductSet-ID276", +"CartesianScalarProduct[a1+a2,-b1-b2,Dimension\[Rule]X]", "-abval3"}, +{"fcstCartesianScalarProductSet-ID277", +"CartesianScalarProduct[-a1-a2,b1+b2,Dimension\[Rule]X]", "-abval3"}, +{"fcstCartesianScalarProductSet-ID278", +"CartesianScalarProduct[-a1-a2,-b1-b2,Dimension\[Rule]X]", "abval3"}, +{"fcstCartesianScalarProductSet-ID279", +"CartesianPair[CartesianMomentum[a1+a2],CartesianMomentum[b1+b2]]", +"CartesianPair[CartesianMomentum[a1 + a2], CartesianMomentum[b1 + b2]]"}, +{"fcstCartesianScalarProductSet-ID280", +"CartesianPair[CartesianMomentum[a1+a2],CartesianMomentum[-b1-b2]]", +"CartesianPair[CartesianMomentum[a1 + a2], CartesianMomentum[-b1 - b2]]"}, +{"fcstCartesianScalarProductSet-ID281", +"CartesianPair[CartesianMomentum[-a1-a2],CartesianMomentum[b1+b2]]", +"CartesianPair[CartesianMomentum[-a1 - a2], CartesianMomentum[b1 + b2]]"}, +{"fcstCartesianScalarProductSet-ID282", +"CartesianPair[CartesianMomentum[-a1-a2],CartesianMomentum[-b1-b2]]", +"CartesianPair[CartesianMomentum[-a1 - a2], CartesianMomentum[-b1 - b2]]"}, +{"fcstCartesianScalarProductSet-ID283", +"CartesianPair[CartesianMomentum[a1+a2,D-1],CartesianMomentum[b1+b2,D-1]]", +"CartesianPair[CartesianMomentum[a1 + a2, D-1], CartesianMomentum[b1 + b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID284", +"CartesianPair[CartesianMomentum[a1+a2,D-1],CartesianMomentum[-b1-b2,D-1]]", +"CartesianPair[CartesianMomentum[a1 + a2, D-1], CartesianMomentum[-b1 - b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID285", +"CartesianPair[CartesianMomentum[-a1-a2,D-1],CartesianMomentum[b1+b2,D-1]]", +"CartesianPair[CartesianMomentum[-a1 - a2, D-1], CartesianMomentum[b1 + b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID286", +"CartesianPair[CartesianMomentum[-a1-a2,D-1],CartesianMomentum[-b1-b2,D-1]]", +"CartesianPair[CartesianMomentum[-a1 - a2, D-1], CartesianMomentum[-b1 - b2, D-1]]"}, +{"fcstCartesianScalarProductSet-ID287", +"CartesianPair[CartesianMomentum[a1+a2,D-4],CartesianMomentum[b1+b2,D-4]]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID288", +"CartesianPair[CartesianMomentum[a1+a2,D-4],CartesianMomentum[-b1-b2,D-4]]", +"CartesianPair[CartesianMomentum[a1 + a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID289", +"CartesianPair[CartesianMomentum[-a1-a2,D-4],CartesianMomentum[b1+b2,D-4]]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[b1 + b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID290", +"CartesianPair[CartesianMomentum[-a1-a2,D-4],CartesianMomentum[-b1-b2,D-4]]", +"CartesianPair[CartesianMomentum[-a1 - a2, -4 + D], CartesianMomentum[-b1 - b2, -4 + D]]"}, +{"fcstCartesianScalarProductSet-ID291", +"CartesianPair[CartesianMomentum[a1+a2,X],CartesianMomentum[b1+b2,X]]", "abval3"}, +{"fcstCartesianScalarProductSet-ID292", +"CartesianPair[CartesianMomentum[a1+a2,X],CartesianMomentum[-b1-b2,X]]", "-abval3"}, +{"fcstCartesianScalarProductSet-ID293", +"CartesianPair[CartesianMomentum[-a1-a2,X],CartesianMomentum[b1+b2,X]]", "-abval3"}, +{"fcstCartesianScalarProductSet-ID294", +"CartesianPair[CartesianMomentum[-a1-a2,X],CartesianMomentum[-b1-b2,X]]", "abval3"}, +{"fcstCartesianScalarProductSet-ID295", "CSP[a1+a2,b1+b2]", +"CSP[a1 + a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID296", "CSP[a1+a2,-b1-b2]", +"CSP[a1 + a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID297", "CSP[-a1-a2,b1+b2]", +"CSP[-a1 - a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID298", "CSP[-a1-a2,-b1-b2]", +"CSP[-a1 - a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID299", "CSPD[a1+a2,b1+b2]", +"CSPD[a1 + a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID300", "CSPD[a1+a2,-b1-b2]", +"CSPD[a1 + a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID301", "CSPD[-a1-a2,b1+b2]", +"CSPD[-a1 - a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID302", "CSPD[-a1-a2,-b1-b2]", +"CSPD[-a1 - a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID303", "CSPE[a1+a2,b1+b2]", +"CSPE[a1 + a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID304", "CSPE[a1+a2,-b1-b2]", +"CSPE[a1 + a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID305", "CSPE[-a1-a2,b1+b2]", +"CSPE[-a1 - a2, b1 + b2]"}, +{"fcstCartesianScalarProductSet-ID306", "CSPE[-a1-a2,-b1-b2]", +"CSPE[-a1 - a2, -b1 - b2]"}, +{"fcstCartesianScalarProductSet-ID307", +"FCClearScalarProducts[];CartesianScalarProduct[p,p]=0; \ +{CartesianMomentum[p],CartesianMomentum[p,D-1],CartesianMomentum[p,D-\ +4]}", "{0, 0, CartesianMomentum[p, -4 + D]}"}, +{"fcstCartesianScalarProductSet-ID308", +"FCClearScalarProducts[];CSP[p,p]=0; \ +{CartesianMomentum[p],CartesianMomentum[p,D-1],CartesianMomentum[p,D-\ +4]}", "{0, CartesianMomentum[p, -1 + D], CartesianMomentum[p, -4 + \ +D]}"}, +{"fcstCartesianScalarProductSet-ID309", +"FCClearScalarProducts[];CSPD[p,p]=0; \ +{CartesianMomentum[p],CartesianMomentum[p,D-1],CartesianMomentum[p,D-\ +4]}", "{CartesianMomentum[p], 0, CartesianMomentum[p, -4 + D]}"}, +{"fcstCartesianScalarProductSet-ID310", +"FCClearScalarProducts[];CSPE[p,p]=0; \ +{CartesianMomentum[p],CartesianMomentum[p,D-1],CartesianMomentum[p,D-\ +4]}", "{CartesianMomentum[p], CartesianMomentum[p, -1 + D], 0}"}, +{"fcstCartesianScalarProductSet-ID311", +"FCClearScalarProducts[];CartesianMomentum[p]=ab;CSP[p,p]=0; \ +{CartesianMomentum[p],CartesianMomentum[p,D-1],CartesianMomentum[p,D-\ +4]}", "{0, CartesianMomentum[p, -1 + D], CartesianMomentum[p, -4 + \ +D]}"}, +{"fcstCartesianScalarProductSet-ID312", +"FCClearScalarProducts[];CartesianMomentum[p,D-1]=ab;CSPD[p,p]=0; \ +{CartesianMomentum[p],CartesianMomentum[p,D-1],CartesianMomentum[p,D-\ +4]}", "{CartesianMomentum[p], 0, CartesianMomentum[p, -4 + D]}"}, +{"fcstCartesianScalarProductSet-ID313", +"FCClearScalarProducts[];CartesianMomentum[p,D-4]=ab;CSPE[p,p]=0; \ +tmp = {CartesianMomentum[p],CartesianMomentum[p,D-1],CartesianMomentum[p,D-\ +4]}; \n FCClearScalarProducts[]; \n tmp", "{CartesianMomentum[p], CartesianMomentum[p, -1 + D], 0}"} +}); + +Tests`Lorentz`fcstSetTemporalComponent = { +{"fcstSetTemporalComponent-ID1", "SetTemporalComponent[p, a]; \n TC[p]", +"a"}, +{"fcstSetTemporalComponent-ID2", "SetTemporalComponent[p, b]; \n TC[p]", +"b"}, +{"fcstSetTemporalComponent-ID3", "TC[p] = c; TemporalPair[TemporalMomentum[p], ExplicitLorentzIndex[0]]", +"c"}, +{"fcstSetTemporalComponent-ID4", "FCClearScalarProducts[]; \n Head[TC[p]]", +"TC"} +}; + + diff --git a/Tests/Lorentz/Schouten.test b/Tests/Lorentz/Schouten.test new file mode 100644 index 000000000..2d5d228ac --- /dev/null +++ b/Tests/Lorentz/Schouten.test @@ -0,0 +1,28 @@ +(* :Title: Schouten.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for Schouten *) + +(* ------------------------------------------------------------------------ *) + +Tests`Lorentz`fcstSchouten = ({ +{"fcstSchouten-ID1", +"Schouten[-FV[k,mu] LC[][q[1],q[2],q[3],q[4]]-SP[k,q[4]] \ +LC[mu][q[1],q[2],q[3]]+SP[k,q[3]] LC[mu][q[1],q[2],q[4]]-SP[k,q[2]] \ +LC[mu][q[1],q[3],q[4]]+SP[k,q[1]] LC[mu][q[2],q[3],q[4]]]", "0"}, +{"fcstSchouten-ID2", +"Schouten[8 \[ImaginaryI] (-LC[b,c,d,f] MT[a,e]+LC[b,c,d,e] \ +MT[a,f]+LC[a,c,d,f] MT[b,e]-LC[a,c,d,e] MT[b,f]-LC[a,b,d,f] \ +MT[c,e]+LC[a,b,d,e] MT[c,f]+LC[a,b,c,f] MT[d,e]-LC[a,b,c,e] \ +MT[d,f])]", "0"}, +{"fcstSchouten-ID3", +"Schouten[(-32*I)*(MT[b,c]*LC[a][k,p,y]-MT[a,c]*LC[b][k,p,y]+FV[p,\ +c]*LC[a,b][k,y]-FV[k,c]*LC[a,b][p,y]-FV[y,b]*LC[a,c][k,p]+FV[y,a]*LC[\ +b,c][k,p]+SP[p,y]*LC[a,b,c][k]-SP[k,y]*LC[a,b,c][p])]", "0"} +}); diff --git a/Tests/Lorentz/TensorFunction.test b/Tests/Lorentz/TensorFunction.test index c181875b8..c47282ac8 100644 --- a/Tests/Lorentz/TensorFunction.test +++ b/Tests/Lorentz/TensorFunction.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for TensorFunction *) diff --git a/Tests/Lorentz/ThreeDivergence.test b/Tests/Lorentz/ThreeDivergence.test new file mode 100644 index 000000000..83100c74d --- /dev/null +++ b/Tests/Lorentz/ThreeDivergence.test @@ -0,0 +1,74 @@ + + +(* :Title: .test *) + +(* This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for *) + +(* ------------------------------------------------------------------------ *) + + +Tests`Lorentz`fcstThreeDivergence = +({ +{"fcstThreeDivergence-ID1", +"ThreeDivergence[CSP[p,q],CV[p,i],FCE->True]", "CV[q, i]"}, +{"fcstThreeDivergence-ID2", +"ThreeDivergence[CSP[p-r,q],CV[p,i],FCE->True]", "CV[q, i]"}, +{"fcstThreeDivergence-ID3", +"ThreeDivergence[CSP[p,q]^2,CV[p,i],FCE->True]", +"2*CSP[p, q]*CV[q, i]"}, +{"fcstThreeDivergence-ID4", +"ThreeDivergence[CGS[p],CV[p,i],FCE->True]", "CGA[i]"}, +{"fcstThreeDivergence-ID5", +"ThreeDivergence[1/CSP[p,q]^2,CV[p,i],FCE->True]", +"(-2*CV[q, i])/CSP[p, q]^3"}, +{"fcstThreeDivergence-ID6", +"Off[ThreeDivergence::warn];tmp=ThreeDivergence[CFAD[p-k],CV[k,mu]]\ +;On[ThreeDivergence::warn];tmp", "0"}, +{"fcstThreeDivergence-ID7", +"ThreeDivergence[CFAD[{p+q,m}],CVD[p,mu],FCE\[Rule]True]", +"CFAD[{{p + q, 0}, {m, -1}, 1}, {{p + q, 0}, {m, -1}, \ +1}]*(-2*CVD[p, mu] - 2*CVD[q, mu])"}, +{"fcstThreeDivergence-ID8", +"ThreeDivergence[CFAD[{p+k,m},{k-l,m}],CVD[k,mu],FCE\[Rule]True]", +"CFAD[{{k - l, 0}, {m, -1}, 1}, {{k - l, 0}, {m, -1}, 1}, {{k + p, \ +0}, {m, -1}, 1}]*(-2*CVD[k, mu] + 2*CVD[l, mu]) + CFAD[{{k - l, 0}, \ +{m, -1}, 1}, {{k + p, 0}, {m, -1}, 1}, {{k + p, 0}, {m, -1}, \ +1}]*(-2*CVD[k, mu] - 2*CVD[p, mu])"}, +{"fcstThreeDivergence-ID9", +"ThreeDivergence[CGSD[p],CVD[p,i],FCE\[Rule]True]", "CGAD[i]"}, +{"fcstThreeDivergence-ID10", +"ThreeDivergence[CGSE[p+q],CVE[p,i],FCE\[Rule]True]", "CGAE[i]"}, +{"fcstThreeDivergence-ID11", +"ThreeDivergence[CVD[l,mu] \ +CFAD[{l,0},{l-p,0}],CVD[l,mu],FCE\[Rule]True]", +"(-1 + D)*CFAD[{{l, 0}, {0, -1}, 1}, {{l - p, 0}, {0, -1}, 1}] - \ +2*CFAD[{{l, 0}, {0, -1}, 1}, {{l, 0}, {0, -1}, 1}, {{l - p, 0}, {0, \ +-1}, 1}]*CSPD[l, l] + CFAD[{{l, 0}, {0, -1}, 1}, {{l - p, 0}, {0, \ +-1}, 1}, {{l - p, 0}, {0, -1}, 1}]*(-2*CSPD[l, l] + 2*CSPD[l, p])"}, +{"fcstThreeDivergence-ID12", +"ThreeDivergence[CFAD[{p,m^2}],CVD[p,i],FCE->True]", +"-2*CFAD[{{p, 0}, {m^2, -1}, 1}, {{p, 0}, {m^2, -1}, 1}]*CVD[p, \ +i]"}, +{"fcstThreeDivergence-ID13", +"ThreeDivergence[CFAD[{{p+q,p.r},m^2}],CVD[p,i],FCE->True]", +"CFAD[{{p + q, p . r}, {m^2, -1}, 1}, {{p + q, p . r}, {m^2, -1}, \ +1}]*(-2*CVD[p, i] - 2*CVD[q, i] - CVD[r, i])"}, +{"fcstThreeDivergence-ID14", +"ThreeDivergence[GFAD[CSPD[p,q]+x],CVD[p,i],FCE->True]", +"-(CVD[q, i]*GFAD[{{x + CSPD[p, q], 1}, 1}, {{x + CSPD[p, q], 1}, \ +1}])"}, +{"fcstThreeDivergence-ID15", +"ThreeDivergence[CLC[][p,q,r],CV[p,i],FCE->True]", +"CLC[i][q, r]"}, +{"fcstThreeDivergence-ID16", +"ThreeDivergence[CLC[][q,p,r],CV[p,i],FCE->True]", "-CLC[i][q, r]"}, +{"fcstThreeDivergence-ID17", +"Off[ThreeDivergence::warnLorentz];tmp=ThreeDivergence[SP[p,q],CV[\ +p,i],FCE->True];On[ThreeDivergence::warn];tmp", "0"} +}); diff --git a/Tests/Lorentz/TrickMandelstam.test b/Tests/Lorentz/TrickMandelstam.test index 9fe2f0ffc..f7bde75bf 100644 --- a/Tests/Lorentz/TrickMandelstam.test +++ b/Tests/Lorentz/TrickMandelstam.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for TrickMandelstam *) diff --git a/Tests/Lorentz/Uncontract.test b/Tests/Lorentz/Uncontract.test index 0fd48db4a..1c91003bf 100644 --- a/Tests/Lorentz/Uncontract.test +++ b/Tests/Lorentz/Uncontract.test @@ -3,64 +3,207 @@ (* :Title: Uncontract.test *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) -(* :Summary: Framework independent unit tests for Unconctract *) +(* :Summary: Framework independent unit tests for Uncontract *) (* ------------------------------------------------------------------------ *) -Tests`Lorentz`fcstUncontract = { -{"fcstUncontract-ID1","(Uncontract[LeviCivita[mu, nu][p, q], p] //FCRenameDummyIndices) /. {$AL[_] -> rho}", - "Eps[LorentzIndex[mu], LorentzIndex[nu], LorentzIndex[rho], Momentum[q]]*Pair[LorentzIndex[rho], Momentum[p]]"}, -{"fcstUncontract-ID2","(Uncontract[DiracSlash[p], p, Pair -> All] // FCRenameDummyIndices) /. {$AL[_] -> mu}", - "DiracGamma[LorentzIndex[mu]]*Pair[LorentzIndex[mu], Momentum[p]]"}, -{"fcstUncontract-ID3","(Uncontract[DiracSlash[p], p] // FCRenameDummyIndices) /. {$AL[_] -> mu}", - "DiracGamma[LorentzIndex[mu]]*Pair[LorentzIndex[mu], Momentum[p]]"}, -{"fcstUncontract-ID4","(Uncontract[LeviCivita[mu, nu][p, q], p, q]) /. {Eps[LorentzIndex[mu], - LorentzIndex[nu], LorentzIndex[a_], LorentzIndex[b_]]*Pair[LorentzIndex[b_], Momentum[q]]* - Pair[LorentzIndex[a_], Momentum[p]] -> Eps[LorentzIndex[mu], LorentzIndex[nu], LorentzIndex[rho], - LorentzIndex[sigma]]*Pair[LorentzIndex[sigma], Momentum[q]]* Pair[LorentzIndex[rho], Momentum[p]]}", - "Eps[LorentzIndex[mu], LorentzIndex[nu], LorentzIndex[rho], LorentzIndex[sigma]]*Pair[LorentzIndex[rho], Momentum[p]]* - Pair[LorentzIndex[sigma], Momentum[q]]"}, -{"fcstUncontract-ID5","Uncontract[SP[p, w] , p]1", - "Pair[Momentum[p], Momentum[w]]"}, -{"fcstUncontract-ID6","(Uncontract[SP[p, w] , p, Pair -> All] // - FCRenameDummyIndices) /. {$AL[_] -> mu}", - "Pair[LorentzIndex[mu], Momentum[p]]*Pair[LorentzIndex[mu], Momentum[w]]"}, -{"fcstUncontract-ID7","Uncontract[SP[p, w]^2 , p, Pair -> All] /. {Pair[LorentzIndex[a_], - Momentum[p]]*Pair[LorentzIndex[a_], Momentum[w]]* Pair[LorentzIndex[b_], Momentum[p]]* - Pair[LorentzIndex[b_], Momentum[w]] -> Pair[LorentzIndex[mu], Momentum[p]]* Pair[LorentzIndex[mu], - Momentum[w]]* Pair[LorentzIndex[nu], Momentum[p]]* Pair[LorentzIndex[nu], Momentum[w]]}", - "Pair[LorentzIndex[mu], Momentum[p]]*Pair[LorentzIndex[mu], Momentum[w]]*Pair[LorentzIndex[nu], Momentum[p]]* - Pair[LorentzIndex[nu], Momentum[w]]"}, -{"fcstUncontract-ID8","MatchQ[Pair[Momentum[p], Momentum[Polarization[p, I]]] // - Uncontract[#, p, Pair -> {p}] &, Pair[LorentzIndex[a_], LorentzIndex[b_]]* - Pair[LorentzIndex[a_], Momentum[p]]*Pair[LorentzIndex[b_], Momentum[Polarization[p, I]]]]","True"}, -{"fcstUncontract-ID9","MatchQ[-Eps[LorentzIndex[nu], LorentzIndex[rho], LorentzIndex[si], - Momentum[Polarization[p, I]]] // Uncontract[#,p] &, - -(Eps[LorentzIndex[nu], LorentzIndex[rho], LorentzIndex[si], LorentzIndex[a_]]* - Pair[LorentzIndex[a_], Momentum[Polarization[p, I]]])]","True"}, -{"fcstUncontract-ID10","MatchQ[Uncontract[FCI[GS[p + q + l]], l, Pair -> All] // FCE, - GS[p] + GS[q] + DiracGamma[LorentzIndex[x_]] Pair[LorentzIndex[x_], Momentum[l]]]","True"}, -{"fcstUncontract-ID11","MatchQ[Uncontract[ExpandScalarProduct[SP[q + p, a + b]], q, -Pair -> All] // FCE, -Pair[LorentzIndex[x_], Momentum[a]] Pair[LorentzIndex[x_], - Momentum[q]] + -Pair[LorentzIndex[y_], Momentum[b]] Pair[LorentzIndex[y_], - Momentum[q]] + SP[a, p] + SP[b, p]]","True"}, -{"fcstUncontract-ID11","DataType[mytensor, FCTensor] = True; \n -MatchQ[Uncontract[mytensor[Momentum[x], Momentum[y]]^3, x, y, -Pair -> All], -FCI[FV[x, i1_] FV[x, i2_]] FCI[FV[x, i3_]] FCI[ - FV[y, j1_] FV[y, j2_]] FCI[FV[y, j3_]] -mytensor[LorentzIndex[i1_], LorentzIndex[j1_]] mytensor[ - LorentzIndex[i2_], LorentzIndex[j2_]] -mytensor[LorentzIndex[i3_], LorentzIndex[j3_]] /; -i1 =!= i2 && i2 =!= i3 && j1 =!= j2 && j2 =!= j3]","True"}, -{"fcstUncontract-ID12","MatchQ[Uncontract[SP[x, y]^3, x, y, Pair -> All], -FCI[FV[x, i1_] FV[x, i2_]] FCI[FV[x, i3_]] FCI[ - FV[y, i1_] FV[y, i2_]] FCI[FV[y, i3_]] /; i1 =!= i2 && i2 =!= i3]","True"} -}; +Tests`Lorentz`fcstUncontract = +({ +{"fcstUncontract-ID1", "Uncontract[SP[p,q],p,FCE\[Rule]True]", +"SP[p, q]"}, +{"fcstUncontract-ID2", +"MatchQ[Uncontract[SP[p,q],p,Pair\[Rule]All,FCE\[Rule]True],FV[p,a_\ +] FV[q,a_]]", "True"}, +{"fcstUncontract-ID3", +"MatchQ[Uncontract[SP[p,q]^2,p,Pair\[Rule]All,FCE\[Rule]True],FV[p,\ +b_] FV[p,a_] FV[q,b_] FV[q,a_]]", "True"}, +{"fcstUncontract-ID4", +"MatchQ[Uncontract[SP[p,q],p,Pair\[Rule]All,Dimension\[Rule]D,FCE\ +\[Rule]True],FVD[p,a_] FVD[q,a_]]", "True"}, +{"fcstUncontract-ID5", +"MatchQ[Uncontract[SP[p,q],p,Pair\[Rule]All,Dimension\[Rule]D-4,\ +FCE\[Rule]True],FVE[p,a_] FVE[q,a_]]", "True"}, +{"fcstUncontract-ID6", +"MatchQ[Uncontract[SPD[p,q],p,Pair\[Rule]All,FCE\[Rule]True],FVD[p,\ +a_] FVD[q,a_]]", "True"}, +{"fcstUncontract-ID7", "Uncontract[CSP[p,q],p,FCE\[Rule]True]", +"CSP[p, q]"}, +{"fcstUncontract-ID8", +"MatchQ[Uncontract[CSP[p,q],p,CartesianPair\[Rule]All,FCE\[Rule]True],CV[p,\ +a_]CV[q,a_]]", "True"}, +{"fcstUncontract-ID9", +"MatchQ[Uncontract[CSP[p,q]^2,p,CartesianPair\[Rule]All,FCE\[Rule]True],CV[\ +p,b_] CV[p,a_] CV[q,b_]CV[q,a_]]", "True"}, +{"fcstUncontract-ID10", +"MatchQ[Uncontract[CSP[p,q],p,CartesianPair\[Rule]All,Dimension\[Rule]D,\ +FCE\[Rule]True],CVD[p,a_] CVD[q,a_]]", "True"}, +{"fcstUncontract-ID11", +"MatchQ[Uncontract[CSP[p,q],p,CartesianPair\[Rule]All,Dimension\[Rule]D-4,\ +FCE\[Rule]True],CVE[p,a_] CVE[q,a_]]", "True"}, +{"fcstUncontract-ID12", +"MatchQ[Uncontract[CSPD[p,q],p,CartesianPair\[Rule]All,FCE\[Rule]True],CVD[\ +p,a_] CVD[q,a_]]", "True"}, +{"fcstUncontract-ID13", +"MatchQ[Uncontract[Pair[CartesianMomentum[p],LorentzIndex[mu]],p,Pair\ +\[Rule]All,FCE\[Rule]True],\[IndentingNewLine]CV[p,a_] \ +Pair[CartesianIndex[a_],LorentzIndex[mu]]]", "True"}, +{"fcstUncontract-ID14", +"Uncontract[GS[p],p,FCE\[Rule]True,DiracGamma\[Rule]False]", +"GS[p]"}, +{"fcstUncontract-ID15", +"MatchQ[Uncontract[GS[p],p,FCE\[Rule]True],FV[p,a_] GA[a_]]", +"True"}, +{"fcstUncontract-ID16", +"MatchQ[Uncontract[GSD[p],p,FCE\[Rule]True],FVD[p,a_] GAD[a_]]", +"True"}, +{"fcstUncontract-ID17", +"MatchQ[Uncontract[GSE[p],p,FCE\[Rule]True],FVE[p,a_] GAE[a_]]", +"True"}, +{"fcstUncontract-ID18", +"MatchQ[Uncontract[GS[p],p,Dimension\[Rule]D,FCE\[Rule]True],FVD[p,\ +a_] GAD[a_]]", "True"}, +{"fcstUncontract-ID19", +"MatchQ[Uncontract[GS[p],p,Dimension\[Rule]D-4,FCE\[Rule]True],FVE[\ +p,a_] GAE[a_]]", "True"}, +{"fcstUncontract-ID20", +"MatchQ[Uncontract[GS[p]^2,p,FCE\[Rule]True],FV[p,a_] FV[p,b_] \ +GA[a_].GA[b_]]", "True"}, +{"fcstUncontract-ID21", +"MatchQ[Uncontract[CGS[p],p,FCE\[Rule]True],CV[p,a_] CGA[a_]]", +"True"}, +{"fcstUncontract-ID22", +"MatchQ[Uncontract[CGSD[p],p,FCE\[Rule]True],CVD[p,a_] CGAD[a_]]", +"True"}, +{"fcstUncontract-ID23", +"MatchQ[Uncontract[CGSE[p],p,FCE\[Rule]True],CVE[p,a_] CGAE[a_]]", +"True"}, +{"fcstUncontract-ID24", +"MatchQ[Uncontract[CGS[p],p,Dimension\[Rule]D,FCE\[Rule]True],CVD[\ +p,a_] CGAD[a_]]", "True"}, +{"fcstUncontract-ID25", +"MatchQ[Uncontract[CGS[p],p,Dimension\[Rule]D-4,FCE\[Rule]True],\ +CVE[p,a_] CGAE[a_]]", "True"}, +{"fcstUncontract-ID26", +"MatchQ[Uncontract[CGS[p]^2,p,FCE\[Rule]True],CV[p,a_] \ +CV[p,b_]CGA[a_].CGA[b_]]", "True"}, +{"fcstUncontract-ID27", +"MatchQ[Uncontract[SIS[p],p,FCE\[Rule]True],FV[p,a_] SI[a_]]", +"True"}, +{"fcstUncontract-ID28", +"MatchQ[Uncontract[SISD[p],p,FCE\[Rule]True],FVD[p,a_] SID[a_]]", +"True"}, +{"fcstUncontract-ID29", +"MatchQ[Uncontract[SISE[p],p,FCE\[Rule]True],FVE[p,a_] SIE[a_]]", +"True"}, +{"fcstUncontract-ID30", +"MatchQ[Uncontract[SIS[p],p,Dimension\[Rule]D,FCE\[Rule]True],FVD[\ +p,a_] SID[a_]]", "True"}, +{"fcstUncontract-ID31", +"MatchQ[Uncontract[SIS[p],p,Dimension\[Rule]D-4,FCE\[Rule]True],\ +FVE[p,a_] SIE[a_]]", "True"}, +{"fcstUncontract-ID32", +"MatchQ[Uncontract[SIS[p]^2,p,FCE\[Rule]True],FV[p,a_] FV[p,b_] \ +SI[a_].SI[b_]]", "True"}, +{"fcstUncontract-ID33", +"MatchQ[Uncontract[CSIS[p],p,FCE\[Rule]True],CV[p,a_] CSI[a_]]", +"True"}, +{"fcstUncontract-ID34", +"MatchQ[Uncontract[CSISD[p],p,FCE\[Rule]True],CVD[p,a_] CSID[a_]]", + "True"}, +{"fcstUncontract-ID35", +"MatchQ[Uncontract[CSISE[p],p,FCE\[Rule]True],CVE[p,a_] CSIE[a_]]", + "True"}, +{"fcstUncontract-ID36", +"MatchQ[Uncontract[CSIS[p],p,Dimension\[Rule]D,FCE\[Rule]True],CVD[\ +p,a_] CSID[a_]]", "True"}, +{"fcstUncontract-ID37", +"MatchQ[Uncontract[CSIS[p],p,Dimension\[Rule]D-4,FCE\[Rule]True],\ +CVE[p,a_] CSIE[a_]]", "True"}, +{"fcstUncontract-ID38", +"MatchQ[Uncontract[CSIS[p]^2,p,FCE\[Rule]True],CV[p,a_] \ +CV[p,b_]CSI[a_].CSI[b_]]", "True"}, +{"fcstUncontract-ID39", +"MatchQ[Uncontract[LC[mu,nu][p,q],p,FCE\[Rule]True],FV[p,a_] \ +LC[mu,nu,a_][q]]", "True"}, +{"fcstUncontract-ID40", +"Uncontract[LC[mu,nu][p,q],p,FCE\[Rule]True,Eps\[Rule]False]", +"LC[mu, nu][p, q]"}, +{"fcstUncontract-ID41", +"MatchQ[Uncontract[CLC[i][p,q],p,FCE\[Rule]True],CV[p,a_] \ +CLC[i,a_][q]]", "True"}, +{"fcstUncontract-ID42", +"Uncontract[CLC[i][p,q],p,FCE\[Rule]True,Eps\[Rule]False]", +"CLC[i][p, q]"}, +{"fcstUncontract-ID43", +"MatchQ[Uncontract[LC[mu,nu][p,q],p,q,FCE\[Rule]True],-FV[p,a_] \ +FV[q,b_] LC[mu,nu,b_,a_]]", "True"}, +{"fcstUncontract-ID44", +"MatchQ[Uncontract[Pair[Momentum[p], Momentum[Polarization[p, I]]], p, +Pair -> {p}, FCE -> True], +FV[p, $AL[b_]] FV[Polarization[p, I], $AL[a_]] MT[$AL[a_], $AL[b_]]]", "True"}, +{"fcstUncontract-ID45", +"MatchQ[Uncontract[CartesianPair[CartesianMomentum[p], CartesianMomentum[Polarization[p, I]]], +p, CartesianPair -> {p}, FCE -> True], +CV[p, $AL[b_]] CV[Polarization[p, I], $AL[a_]] KD[$AL[a_], $AL[b_]]]", "True"}, +{"fcstUncontract-ID46", +"MatchQ[Uncontract[Eps[LorentzIndex[nu],LorentzIndex[rho],\ +LorentzIndex[si],Momentum[Polarization[p,I]]],p,FCE\[Rule]True],FV[\ +Polarization[p,\[ImaginaryI]],a_] LC[nu,rho,si,a_]]", "True"}, +{"fcstUncontract-ID47", +"MatchQ[Uncontract[FCI[GS[p+q+l]],l,Pair\[Rule]All,FCE\[Rule]True],\ +FV[l,a_] GA[a_]+GS[p]+GS[q]]", "True"}, +{"fcstUncontract-ID48", +"MatchQ[Uncontract[ExpandScalarProduct[SP[q+p,a+b]],q,Pair\[Rule]\ +All,FCE\[Rule]True],\[IndentingNewLine]FV[a,b_] FV[q,b_]+FV[b,c_] \ +FV[q,c_]+SP[a,p]+SP[b,p]]", "True"}, +{"fcstUncontract-ID49", "DataType[mytensor,FCTensor]=True; +MatchQ[Uncontract[mytensor[Momentum[x],Momentum[y]]^3,x,y,Pair\ +\[Rule]All],FCI[FV[x,i1_] FV[x,i2_]] FCI[FV[x,i3_]] FCI[FV[y,j1_] \ +FV[y,j2_]] FCI[FV[y,j3_]] \ +mytensor[LorentzIndex[i1_],LorentzIndex[j1_]] \ +mytensor[LorentzIndex[i2_],LorentzIndex[j2_]] \ +mytensor[LorentzIndex[i3_],LorentzIndex[j3_]]\ +/;i1=!=i2&&i2=!=i3&&j1=!=j2&&j2=!=j3]", "True"}, +{"fcstUncontract-ID50", +"MatchQ[Uncontract[SP[x,y]^3,x,y,Pair\[Rule]All],FCI[FV[x,i1_] \ +FV[x,i2_]] FCI[FV[x,i3_]] FCI[FV[y,i1_] FV[y,i2_]] \ +FCI[FV[y,i3_]]/;i1=!=i2&&i2=!=i3]", "True"}, +{"fcstUncontract-ID51", +"MatchQ[Uncontract[SPD[l, l], l, Pair -> All, FCE -> True], +FVD[l, $AL[a_]] FVD[l, $AL[b_]] MTD[$AL[a_], $AL[b_]]]", "True"}, +{"fcstUncontract-ID52", +"MatchQ[Uncontract[CSPD[l, l], l, CartesianPair -> All, FCE -> True], +CVD[l, $AL[a_]] CVD[l, $AL[b_]] KDD[$AL[a_], $AL[b_]]]", "True"}, +{"fcstUncontract-ID53", +"Uncontract[SPD[l, l], l, Pair -> All, Square -> False, FCE -> True]", "SPD[l, l]"}, +{"fcstUncontract-ID54", +"Uncontract[CSPD[l, l], l, CartesianPair -> All, Square -> False, FCE -> True]", "CSPD[l, l]"}, +{"fcstUncontract-ID55", +"MatchQ[Uncontract[GSD[l, q, l], l, FCE -> True],GAD[b_].GSD[q].GAD[a_] FVD[l, b_] FVD[l, a_]]", "True"}, +{"fcstUncontract-ID56", +"MatchQ[Uncontract[SP[q, p]^2 GS[r1].GA[mu].GS[r2], All, Pair -> All, FCE -> True], +GA[b_].GA[mu].GA[a_] FV[p, c_] FV[p, d_] FV[q, c_] FV[q, d_] FV[r1, b_] FV[r2, a_]]", "True"}, +{"fcstUncontract-ID55", +"Uncontract[aaa, All]", "aaa"}, +{"fcstUncontract-ID56", +"FCCanonicalizeDummyIndices[ +Uncontract[DCHN[GA[mu].(GS[p]).GA[nu], i, j], p], +LorentzIndexNames -> {al}, FCE -> True]", "DCHN[GA[mu].GA[al].GA[nu], i, j] FV[p, al]"}, +{"fcstUncontract-ID57", +"FCCanonicalizeDummyIndices[ +Uncontract[DCHN[GA[mu].(GS[p] + m).GA[nu], i, j], p], +LorentzIndexNames -> {al}, FCE -> True]", "m DCHN[ GA[mu].GA[nu], i, j] + +DCHN[GA[mu].GA[al].GA[nu], i, j] FV[p, al]"}, +{"fcstUncontract-ID58", "FCCanonicalizeDummyIndices[ +Uncontract[DCHN[-GSD[k] + me, Dir3, Dir4], k], +LorentzIndexNames -> {mu}, FCE -> True]", "me DCHN[1, Dir3, Dir4] - DCHN[GAD[mu], Dir3, Dir4] FVD[k, mu]"}, +{"fcstUncontract-ID59", "FCCanonicalizeDummyIndices[ +Uncontract[DCHN[GA[mu].(-GSD[k] + me).GA[nu], Dir3, Dir4], k], +LorentzIndexNames -> {la}, FCE -> True]", "me DCHN[GA[mu].GA[nu], Dir3, Dir4] - +DCHN[GA[mu].GAD[la].GA[nu], Dir3, Dir4] FVD[k, la]"} +}); diff --git a/Tests/NonCommAlgebra/AntiCommutator.test b/Tests/NonCommAlgebra/AntiCommutator.test index 7886e0f88..a7824acc8 100644 --- a/Tests/NonCommAlgebra/AntiCommutator.test +++ b/Tests/NonCommAlgebra/AntiCommutator.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for AntiCommutator *) @@ -18,5 +18,14 @@ Tests`NonCommAlgebra`fcstAntiCommutator = { "CommutatorExplicit[AntiCommutator[a+b,a-2b]]", "(a - 2*b) . (a + b) + (a + b) . (a - 2*b)"}, {"AntiCommutator-ID3", "Do[AntiCommutator[a, b] = 1, {i, 1, 5}] \n DownValues[AntiCommutator]", -"{HoldPattern[AntiCommutator[a, b]] :> 1}"} +"{HoldPattern[AntiCommutator[a, b]] :> 1}"}, +{"Commutator-ID4", "AntiCommutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A1], +QuantumField[A1]] = 0; DotSimplify[ +ExpandPartialD[QuantumField[A1].QuantumField[A1].LeftPartialD[nu]]]; +UnDeclareAntiCommutator[ +QuantumField[FCPartialD[LorentzIndex[xxx_]], A1], +QuantumField[A1]]; DotSimplify[ +ExpandPartialD[QuantumField[A1].QuantumField[A1].LeftPartialD[nu]]]", +"QuantumField[A1].QuantumField[FCPartialD[LorentzIndex[nu]], A1] + +QuantumField[FCPartialD[LorentzIndex[nu]], A1].QuantumField[A1]"} }; diff --git a/Tests/NonCommAlgebra/Calc.test b/Tests/NonCommAlgebra/Calc.test index 37ad7fa98..23c3bb9da 100644 --- a/Tests/NonCommAlgebra/Calc.test +++ b/Tests/NonCommAlgebra/Calc.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Calc *) @@ -14,5 +14,7 @@ (* ------------------------------------------------------------------------ *) Tests`NonCommAlgebra`fcstCalc = { -{"fcstCalc-ID1","Calc[Sqrt[a - 1]] // Simplify[#, Assumptions -> {a > 1}]& ","Sqrt[a - 1]"} +{"fcstCalc-ID1","Calc[Sqrt[a - 1]] // Simplify[#, Assumptions -> {a > 1}]& ","Sqrt[a - 1]"}, +{"fcstCalc-ID2","Calc[FV[p + r, mu MT[mu, nu] FV[q - p, nu]]] // FCE","FV[p, -mu FV[p - q, mu]] + FV[r, -mu FV[p - q, mu]]"}, +{"fcstCalc-ID3","Calc[CV[p + r, i] KD[i, j] CV[q - p, j]] // FCE","-CSP[p, p] + CSP[p, q] - CSP[p, r] + CSP[q, r]"} }; diff --git a/Tests/NonCommAlgebra/Commutator.test b/Tests/NonCommAlgebra/Commutator.test index 7b51e7217..398fe02d5 100644 --- a/Tests/NonCommAlgebra/Commutator.test +++ b/Tests/NonCommAlgebra/Commutator.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Commutator *) @@ -18,5 +18,13 @@ Tests`NonCommAlgebra`fcstCommutator = { "-(a - 2*b) . (a + b) + (a + b) . (a - 2*b)"}, {"Commutator-ID3", "Do[Commutator[a, b] = 1, {i, 1, 5}] \n DownValues[Commutator]", "{HoldPattern[Commutator[a, b]] :> 1, -HoldPattern[Commutator[RightPartialD[FeynCalc`SharedObjects`Private`x_], LeftPartialD[FeynCalc`SharedObjects`Private`y_]]] :> 0}"} +HoldPattern[Commutator[RightPartialD[FeynCalc`SharedObjects`Private`x_], LeftPartialD[FeynCalc`SharedObjects`Private`y_]]] :> 0}"}, +{"Commutator-ID4", "Commutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A1], +QuantumField[A1]] = 0; DotSimplify[ +ExpandPartialD[QuantumField[A1].QuantumField[A1].LeftPartialD[nu]]]; +UnDeclareCommutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A1], +QuantumField[A1]]; DotSimplify[ +ExpandPartialD[QuantumField[A1].QuantumField[A1].LeftPartialD[nu]]]", +"QuantumField[A1].QuantumField[FCPartialD[LorentzIndex[nu]], A1] + +QuantumField[FCPartialD[LorentzIndex[nu]], A1].QuantumField[A1]"} }; diff --git a/Tests/NonCommAlgebra/CommutatorExplicit.test b/Tests/NonCommAlgebra/CommutatorExplicit.test index cec471699..2e25ea70b 100644 --- a/Tests/NonCommAlgebra/CommutatorExplicit.test +++ b/Tests/NonCommAlgebra/CommutatorExplicit.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for CommutatorExplicit *) diff --git a/Tests/NonCommAlgebra/CommutatorOrder.test b/Tests/NonCommAlgebra/CommutatorOrder.test index f2170eb75..22dfd6c6e 100644 --- a/Tests/NonCommAlgebra/CommutatorOrder.test +++ b/Tests/NonCommAlgebra/CommutatorOrder.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for CommutatorOrder *) diff --git a/Tests/NonCommAlgebra/DotExpand.test b/Tests/NonCommAlgebra/DotExpand.test index e8745ec20..148583368 100644 --- a/Tests/NonCommAlgebra/DotExpand.test +++ b/Tests/NonCommAlgebra/DotExpand.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DotExpand *) diff --git a/Tests/NonCommAlgebra/DotSimplify.test b/Tests/NonCommAlgebra/DotSimplify.test index 80e7edcbe..babb3b90f 100644 --- a/Tests/NonCommAlgebra/DotSimplify.test +++ b/Tests/NonCommAlgebra/DotSimplify.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DotSimplify *) @@ -33,29 +33,93 @@ b*DiracGamma[LorentzIndex[mu]] . DiracGamma[Momentum[q]] . DiracGamma[Momentum[q QuantumField[A, LorentzIndex[mu]].RightPartialD[ Momentum[OPEDelta]].RightPartialD[ Momentum[OPEDelta]].QuantumField[A, LorentzIndex[rho]])"}, -{"fcstDotSimplify-ID7","DotSimplify[DiracTrace[SUNT[a,b]GA[c,d]SUNT[e,f]]]","DiracTrace[ - DiracGamma[LorentzIndex[c]].DiracGamma[LorentzIndex[d]]] SUNT[ - SUNIndex[a]].SUNT[SUNIndex[b]].SUNT[SUNIndex[e]].SUNT[SUNIndex[f]]"}, +{"fcstDotSimplify-ID7","DotSimplify[DiracTrace[SUNT[a,b]GA[c,d]SUNT[e,f]]]//FCE", +"DiracTrace[GA[c].GA[d]] SUNT[a].SUNT[b] SUNT[e].SUNT[f]"}, {"fcstDotSimplify-ID8","DotSimplify[ RightPartialD[Momentum[OPEDelta]].LeftPartialD[Momentum[OPEDelta]]]", "LeftPartialD[Momentum[OPEDelta]].RightPartialD[Momentum[OPEDelta]]"}, -{"fcstDotSimplify-ID9","DotSimplify[(GA[i].SUNT[a] (GS[p] + M).GA[j].GA[6].GA[k].GA[j] FAD[ +{"fcstDotSimplify-ID9","DotSimplify[SUNT[a](GA[i].(GS[p] + M).GA[j].GA[6].GA[k].GA[j] FAD[ p + k, M] + GA[i].(GS[p1] + M).GA[j].GA[7].GA[j].GA[k] FAD[p1 + k, M]).(GS[q] + m).(GA[l].(GS[p] + M).GA[n] + GA[n].(GS[p] + M).GA[l]), PreservePropagatorStructures -> True] // FCE", -"GA[i] . (M + GS[p1]) . GA[j] . GA[7] . GA[j] . GA[k] . (m + -GS[q]) . GA[l] . (M + GS[p]) . GA[n]*FAD[k + p1, M] + -GA[i] . (M + GS[p1]) . GA[j] . GA[7] . GA[j] . GA[k] . (m + -GS[q]) . GA[n] . (M + GS[p]) . GA[l]*FAD[k + p1, M] + GA[i] . (M + -GS[p]) . GA[j] . GA[6] . GA[k] . GA[j] . (m + -GS[q]) . GA[l] . (M + GS[p]) . GA[n]*FAD[k + p, -M]*SUNT[a] + GA[i] . (M + -GS[p]) . GA[j] . GA[6] . GA[k] . GA[j] . (m + -GS[q]) . GA[n] . (M + GS[p]) . GA[l]*FAD[k + p, -M]*SUNT[a]"}, +"(GA[i].(M + GS[p]).GA[j].GA[6].GA[k].GA[j].(m + GS[q]).GA[ + l].(M + GS[p]).GA[n] FAD[k + p, M] + +GA[i].(M + GS[p]).GA[j].GA[6].GA[k].GA[j].(m + GS[q]).GA[ + n].(M + GS[p]).GA[l] FAD[k + p, M] + +GA[i].(M + GS[p1]).GA[j].GA[7].GA[j].GA[k].(m + GS[q]).GA[ + l].(M + GS[p]).GA[n] FAD[k + p1, M] + +GA[i].(M + GS[p1]).GA[j].GA[7].GA[j].GA[k].(m + GS[q]).GA[ + n].(M + GS[p]).GA[l] FAD[k + p1, M]) SUNT[a]"}, {"fcstDotSimplify-ID10","DotSimplify[GA[5].(1/2).GA[5]]","1/2 DiracGamma[5].DiracGamma[5]"}, +{"fcstDotSimplify-ID11","DotSimplify[SpinorUBar[p1, m1].GA[i].SpinorU[p2, +m2].(a.SUNT[a] + b.SUNT[a] + c.SUNT[a]), Expanding -> False]", +"(a + b + c) Spinor[Momentum[p1], m1, 1].DiracGamma[LorentzIndex[i]].Spinor[Momentum[p2], m2, 1] SUNT[SUNIndex[a]]"}, +{"fcstDotSimplify-ID12","DotSimplify[PauliEta[-I].SIS[p].GA[k, l].SUNT[a, b, c].PauliXi[I]]", +"DiracGamma[LorentzIndex[k]].DiracGamma[ +LorentzIndex[l]] PauliEta[-I].PauliSigma[Momentum[p]].PauliXi[ +I] SUNT[SUNIndex[a]].SUNT[SUNIndex[b]].SUNT[SUNIndex[c]]"}, +{"fcstDotSimplify-ID13","DotSimplify[ +PauliEta[-I].SIS[p].SpinorU[p1, m].GA[k, l].SUNT[a, b, c].SpinorV[ +p2].PauliXi[I]]","PauliEta[-I].PauliSigma[Momentum[p]].PauliXi[I] SUNT[ +SUNIndex[a]].SUNT[SUNIndex[b]].SUNT[SUNIndex[c]] Spinor[ +Momentum[p1], m, 1].DiracGamma[LorentzIndex[k]].DiracGamma[ +LorentzIndex[l]].Spinor[-Momentum[p2], 0, 1]"}, +{"fcstDotSimplify-ID14","DotSimplify[SUNT[a, b] SUNT[c, d]]","SUNT[SUNIndex[a]].SUNT[SUNIndex[b]] SUNT[SUNIndex[c]].SUNT[ +SUNIndex[d]]"}, +{"fcstDotSimplify-ID15","DotSimplify[ +m Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1] + +Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[l].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1] + +Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[p3].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1], Expanding -> False] // FCE", + "m Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1] + +Spinor[Momentum[p3, D], m, 1].GAD[Lor4].(GSD[l] + GSD[p3]).GAD[ +Lor1].Spinor[Momentum[p1, D], 0, 1]"}, +{"fcstDotSimplify-ID16","DotSimplify[ +m Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1] + +Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[l].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1] + +Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[p3].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1], Expanding -> False, +FCJoinDOTs -> False] // FCE","m Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GAD[Lor1].Spinor[ + Momentum[p1, D], 0, 1] + +Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[l].GAD[Lor1].Spinor[ +Momentum[p1, D], 0, 1] + +Spinor[Momentum[p3, D], m, 1].GAD[Lor4].GSD[p3].GAD[Lor1].Spinor[ +Momentum[p1, D], 0, 1]"}, +{"fcstDotSimplify-ID17","DotSimplify[GA[i, j1, k] + GA[i, j2, k], Expanding -> False, +FCE -> True]","GA[i].(GA[j1] + GA[j2]).GA[k]"}, +{"fcstDotSimplify-ID18","DotSimplify[GA[i, j1, k] + GA[i, j2, k], Expanding -> False, +FCJoinDOTs -> False, FCE -> True]","GA[i].GA[j1].GA[k] + GA[i].GA[j2].GA[k]"}, +{"fcstDotSimplify-ID19","DataType[f, g, NonCommutative] = True; \n DotSimplify[f.g - g.(2 a).f]","f.g - 2 a g.f"}, +{"fcstDotSimplify-ID20","DataType[f, g, NonCommutative] = False; \n tmp = DotSimplify[f.g - g.(2 a).f]; \n + UnDeclareNonCommutative[f, g]; \n tmp","f g-2 a f g"}, +{"fcstDotSimplify-ID21","DotSimplify[DiracGamma[ +Momentum[q]].(DiracGamma[LorentzIndex[mu]].DiracGamma[6] c1).(DiracGamma[Momentum[k]] + + DiracGamma[Momentum[q]]).(DiracGamma[LorentzIndex[mu]].DiracGamma[7] c2)]", + "c1 c2 DiracGamma[Momentum[q]].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 6].DiracGamma[Momentum[k]].DiracGamma[ + LorentzIndex[mu]].DiracGamma[7] + +c1 c2 DiracGamma[Momentum[q]].DiracGamma[ + LorentzIndex[mu]].DiracGamma[6].DiracGamma[ + Momentum[q]].DiracGamma[LorentzIndex[mu]].DiracGamma[7]"}, +{"fcstDotSimplify-ID22","DotSimplify[ +DiracGamma[Momentum[q]].(DiracGamma[LorentzIndex[mu]].DiracGamma[6] SUNT[SUNIndex[b]]).(DiracGamma[Momentum[k]] + + DiracGamma[Momentum[q]]).(DiracGamma[LorentzIndex[mu]].DiracGamma[7] SUNT[SUNIndex[a]])]", + "SUNT[SUNIndex[b]].SUNT[SUNIndex[a]] DiracGamma[Momentum[q]].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 6].DiracGamma[Momentum[k]].DiracGamma[ + LorentzIndex[mu]].DiracGamma[7] + +SUNT[SUNIndex[b]].SUNT[SUNIndex[a]] DiracGamma[ + Momentum[q]].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 6].DiracGamma[Momentum[q]].DiracGamma[ + LorentzIndex[mu]].DiracGamma[7]"}, {"fcstDotSimplify-ID23","Commutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A1], QuantumField[A1]] = 0; DotSimplify[ExpandPartialD[QuantumField[A1].QuantumField[A1].LeftPartialD[nu]]]","2 QuantumField[A1].QuantumField[FCPartialD[LorentzIndex[nu]], A1]"}, {"fcstDotSimplify-ID24","AntiCommutator[QuantumField[FCPartialD[LorentzIndex[xxx_]], A2], QuantumField[A2]] = 0; -DotSimplify[ExpandPartialD[QuantumField[A2].QuantumField[A2].LeftPartialD[nu]]]","0"} +DotSimplify[ExpandPartialD[QuantumField[A2].QuantumField[A2].LeftPartialD[nu]]]","0"}, +{"fcstDotSimplify-ID25","DotSimplify[DCHN[GA[mu].(x GS[p]).GA[nu], i, j], FCE -> True]", +"x DCHN[GA[mu].GS[p].GA[nu], i, j]"} } diff --git a/Tests/NonCommAlgebra/FCMatrixIsolate.test b/Tests/NonCommAlgebra/FCMatrixIsolate.test new file mode 100644 index 000000000..1762f1b51 --- /dev/null +++ b/Tests/NonCommAlgebra/FCMatrixIsolate.test @@ -0,0 +1,142 @@ +(* :Title: FCMatrixIsolate.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCMatrixIsolate *) + +(* ------------------------------------------------------------------------ *) + +Tests`NonCommAlgebra`fcstFCMatrixIsolate = +({ +{"fcstFCMatrixIsolate-ID1", "FCMatrixIsolate[0]", "0"}, +{"fcstFCMatrixIsolate-ID2", "FCMatrixIsolate[1]", "1"}, +{"fcstFCMatrixIsolate-ID3", "FCMatrixIsolate[1,Head\[Rule]re]", +"re[1]"}, +{"fcstFCMatrixIsolate-ID4", +"FCMatrixIsolate[x1 \ +SpinorUBar[p1,m1].GA[mu].(GS[p]+m).GA[nu].SpinorV[p2,m2]+\ +\[IndentingNewLine]x2 \ +SpinorUBar[p1,m1].GA[rho].(GS[p]+m).GA[si,5].SpinorV[p2,m2],\ +FCDiracIsolate\[Rule]{dch},FCE\[Rule]True]", +"x1*dch[Spinor[Momentum[p1], m1, 1] . GA[mu] . (m + GS[p]) . \ +GA[nu] . Spinor[-Momentum[p2], m2, 1]] + x2*dch[Spinor[Momentum[p1], \ +m1, 1] . GA[rho] . (m + GS[p]) . GA[si] . GA[5] . \ +Spinor[-Momentum[p2], m2, 1]]"}, +{"fcstFCMatrixIsolate-ID5", +"FCMatrixIsolate[x1 SUNT[a] \ +SpinorUBar[p1,m1].GA[mu].(GS[p]+m).GA[nu].SpinorV[p2,m2]+\ +\[IndentingNewLine]x2 \ +SpinorUBar[p1,m1].GA[rho].(GS[p]+m).GA[si,5].SpinorV[p2,m2],\ +FCDiracIsolate\[Rule]{dch},FCColorIsolate\[Rule]{cch},FCE\[Rule]True]\ +", "x1*cch[SUNT[a]]*dch[Spinor[Momentum[p1], m1, 1] . GA[mu] . (m + \ +GS[p]) . GA[nu] . Spinor[-Momentum[p2], m2, 1]] + \ +x2*dch[Spinor[Momentum[p1], m1, 1] . GA[rho] . (m + GS[p]) . GA[si] . \ +GA[5] . Spinor[-Momentum[p2], m2, 1]]"}, +{"fcstFCMatrixIsolate-ID6", +"FCMatrixIsolate[x1 SUNT[a] \ +SpinorUBar[p1,m1].GA[mu].(GS[p]+m).GA[nu].SpinorV[p2,m2]+\ +\[IndentingNewLine]x2 SI[i,j] \ +SpinorUBar[p1,m1].GA[rho].(GS[p]+m).GA[si,5].SpinorV[p2,m2],\ +FCDiracIsolate\[Rule]{dch},FCColorIsolate\[Rule]{cch},FCPauliIsolate\ +\[Rule]{pch},FCE\[Rule]True]", +"x1*cch[SUNT[a]]*dch[Spinor[Momentum[p1], m1, 1] . GA[mu] . (m + \ +GS[p]) . GA[nu] . Spinor[-Momentum[p2], m2, 1]] + \ +x2*dch[Spinor[Momentum[p1], m1, 1] . GA[rho] . (m + GS[p]) . GA[si] . \ +GA[5] . Spinor[-Momentum[p2], m2, 1]]*pch[SI[i] . SI[j]]"}, +{"fcstFCMatrixIsolate-ID7", +"FCMatrixIsolate[x1 SUNT[a] \ +SpinorUBar[p1,m1].GA[mu].(GS[p]+m).GA[nu].SpinorV[p2,m2]+\ +\[IndentingNewLine]x2 SI[i,j] \ +SpinorUBar[p1,m1].GA[rho].(GS[p]+m).GA[si,5].SpinorV[p2,m2],\ +FCDiracIsolate\[Rule]{dch},FCColorIsolate\[Rule]{cch},FCPauliIsolate\ +\[Rule]{pch},FCE\[Rule]True,Ordering\[Rule]{FCPauliIsolate}]", +"x2*Spinor[Momentum[p1], m1, 1] . GA[rho] . (m + GS[p]) . GA[si] . \ +GA[5] . Spinor[-Momentum[p2], m2, 1]*pch[SI[i] . SI[j]] + \ +x1*Spinor[Momentum[p1], m1, 1] . GA[mu] . (m + GS[p]) . GA[nu] . \ +Spinor[-Momentum[p2], m2, 1]*SUNT[a]"}, +{"fcstFCMatrixIsolate-ID8", +"FCMatrixIsolate[x1 SUNT[a] \ +SpinorUBar[p1,m1].GA[mu].(GS[p]+m).GA[nu].SpinorV[p2,m2]+\ +\[IndentingNewLine]x2 SI[i,j] \ +SpinorUBar[p1,m1].GA[rho].(GS[p]+m).GA[si,5].SpinorV[p2,m2],\ +FCDiracIsolate\[Rule]{dch},FCColorIsolate\[Rule]{cch},FCPauliIsolate\ +\[Rule]{pch},FCE\[Rule]True,Ordering\[Rule]{FCDiracIsolate}]", +"x2*dch[Spinor[Momentum[p1], m1, 1] . GA[rho] . (m + GS[p]) . \ +GA[si] . GA[5] . Spinor[-Momentum[p2], m2, 1]]*SI[i] . SI[j] + \ +x1*dch[Spinor[Momentum[p1], m1, 1] . GA[mu] . (m + GS[p]) . GA[nu] . \ +Spinor[-Momentum[p2], m2, 1]]*SUNT[a]"}, +{"fcstFCMatrixIsolate-ID9", +"FCMatrixIsolate[x1 SUNT[a] \ +SpinorUBar[p1,m1].GA[mu].(GS[p]+m).GA[nu].SpinorV[p2,m2]+\ +\[IndentingNewLine]x2 SI[i,j] \ +SpinorUBar[p1,m1].GA[rho].(GS[p]+m).GA[si,5].SpinorV[p2,m2],\ +FCDiracIsolate\[Rule]{dch},FCColorIsolate\[Rule]{cch},FCPauliIsolate\ +\[Rule]{pch},FCE\[Rule]True,Ordering\[Rule]{FCColorIsolate}]", +"x1*cch[SUNT[a]]*Spinor[Momentum[p1], m1, 1] . GA[mu] . (m + \ +GS[p]) . GA[nu] . Spinor[-Momentum[p2], m2, 1] + x2*SI[i] . \ +SI[j]*Spinor[Momentum[p1], m1, 1] . GA[rho] . (m + GS[p]) . GA[si] . \ +GA[5] . Spinor[-Momentum[p2], m2, 1]"}, +{"fcstFCMatrixIsolate-ID10", +"FCMatrixIsolate[x1 SUNT[a] \ +SpinorUBar[p1,m1].GA[mu].(GS[p]+m).GA[nu].SpinorV[p2,m2]+\ +\[IndentingNewLine]x2 SI[i,j] \ +SpinorUBar[p1,m1].GA[rho].(GS[p]+m).GA[si,5].SpinorV[p2,m2],\ +FCDiracIsolate\[Rule]{dch},FCColorIsolate\[Rule]{cch},FCPauliIsolate\ +\[Rule]{pch},FCE\[Rule]True,Ordering\[Rule]{FCColorIsolate,\ +FCPauliIsolate,FCDiracIsolate}]", +"x1*cch[SUNT[a]]*dch[Spinor[Momentum[p1], m1, 1] . GA[mu] . (m + \ +GS[p]) . GA[nu] . Spinor[-Momentum[p2], m2, 1]] + \ +x2*dch[Spinor[Momentum[p1], m1, 1] . GA[rho] . (m + GS[p]) . GA[si] . \ +GA[5] . Spinor[-Momentum[p2], m2, 1]]*pch[SI[i] . SI[j]]"}, +{"fcstFCMatrixIsolate-ID11", +"FCMatrixIsolate[-e eQ gs \ +Spinor[Momentum[k2],mu,1].GS[Polarization[k1,-\[ImaginaryI],\ +Transversality\[Rule]True]].(mu+GS[k1+k2]).GS[Polarization[p2,\ +\[ImaginaryI]]].Spinor[Momentum[p1],mu,1] FAD[{-k1-k2,mu},Dimension\ +\[Rule]4] SUNTF[{Glu3},Col4,Col1]-e eQ gs \ +Spinor[Momentum[k2],mu,1].GS[Polarization[p2,\[ImaginaryI]]].(mu+GS[\ +k2-p2]).GS[Polarization[k1,-\[ImaginaryI],Transversality\[Rule]True]].\ +Spinor[Momentum[p1],mu,1] FAD[{-k2+p2,mu},Dimension\[Rule]4] \ +SUNTF[{Glu3},Col4,Col1],FCDiracIsolate\[Rule]{dch},\[IndentingNewLine]\ +FCColorIsolate\[Rule]{cch},FCPauliIsolate\[Rule]{pch},Head\[Rule]re,\ +FCE\[Rule]True]", +"cch[SUNTF[{Glu3}, Col4, Col1]]*dch[Spinor[Momentum[k2], mu, 1] . \ +GS[Polarization[k1, -I, Transversality -> True]] . (mu + GS[k1 + k2]) \ +. GS[Polarization[p2, I]] . Spinor[Momentum[p1], mu, \ +1]]*re[-(e*eQ*gs*FAD[{-k1 - k2, mu}, Dimension -> 4])] + \ +cch[SUNTF[{Glu3}, Col4, Col1]]*dch[Spinor[Momentum[k2], mu, 1] . \ +GS[Polarization[p2, I]] . (mu + GS[k2 - p2]) . GS[Polarization[k1, \ +-I, Transversality -> True]] . Spinor[Momentum[p1], mu, \ +1]]*re[-(e*eQ*gs*FAD[{-k2 + p2, mu}, Dimension -> 4])]"}, +{"fcstFCMatrixIsolate-ID12", "FCMatrixIsolate[-e eQ gs Spinor[Momentum[k2], mu, 1].GS[ + Polarization[k1, -I, Transversality -> True]].(mu + + GS[k1 + k2]).GS[Polarization[p2, I]].Spinor[Momentum[p1], mu, + 1] FAD[{-k1 - k2, mu}, Dimension -> 4] SUNTF[{Glu3}, Col4, + Col1] - e eQ gs DCHN[Spinor[Momentum[k2], mu, 1], i] DCHN[ + GS[Polarization[p2, I]].(mu + GS[k2 - p2]).GS[ + Polarization[k1, -I, Transversality -> True]], i, j] DCHN[ + Spinor[Momentum[p1], mu, 1], j] FAD[{-k2 + p2, mu}, + Dimension -> 4] SUNTF[{Glu3}, Col4, Col1], FCDiracIsolate -> {dch}, +FCColorIsolate -> {cch}, FCPauliIsolate -> {pch}, Head -> re, +FCE -> True]", "cch[SUNTF[{Glu3}, Col4, Col1]] dch[ +Spinor[Momentum[k2], mu, 1].GS[ + Polarization[k1, -I, Transversality -> True]].(mu + + GS[k1 + k2]).GS[Polarization[p2, I]].Spinor[Momentum[p1], mu, + 1]] re[-e eQ gs FAD[{-k1 - k2, mu}, Dimension -> 4]] + +cch[SUNTF[{Glu3}, Col4, Col1]] dch[ +DCHN[Spinor[Momentum[k2], mu, 1], i] DCHN[ + Spinor[Momentum[p1], mu, 1], j] DCHN[ + GS[Polarization[p2, I]].(mu + GS[k2 - p2]).GS[ + Polarization[k1, -I, Transversality -> True]], i, + j]] re[-e eQ gs FAD[{-k2 + p2, mu}, Dimension -> 4]]"}, +{"fcstFCMatrixIsolate-ID12", "FCMatrixIsolate[{GA[mu], SI[j], SUNT[a]}, +FCColorIsolate -> {col}, +FCDiracIsolate -> {di}, +FCPauliIsolate -> {pau}, +FCE -> True]", "{di[GA[mu]], pau[SI[j]], col[SUNT[a]]}"} +}); diff --git a/Tests/NonCommAlgebra/FCTraceExpand.test b/Tests/NonCommAlgebra/FCTraceExpand.test index 3b531799a..3f7c77d77 100644 --- a/Tests/NonCommAlgebra/FCTraceExpand.test +++ b/Tests/NonCommAlgebra/FCTraceExpand.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCTraceExpand *) @@ -84,5 +84,39 @@ FCTraceExpand[#, DiracGammaExpand -> False, PreservePropagatorStructures -> True] & // FCE", "DiracTrace[(M + GSD[k + p]).GA[5].GSD[l - p].GAD[nu].(M + GSD[l]).GAD[la].GSD[k + l].(M + GSD[x])] + DiracTrace[(M + GSD[k1 + p1]).GA[6].GSD[l1 - p1].GAD[nu].(M + -GSD[l]).GAD[la].GSD[k1 + l1].(M + GSD[x])]"} +GSD[l]).GAD[la].GSD[k1 + l1].(M + GSD[x])]"}, +{"fcstFCTraceExpand-ID17", +"FCTraceExpand[ +DiracTrace[ +SI[x1, x2].((GSD[k + p] + M).GA[5].GSD[l - p].GAD[ + nu].(GSD[l] + M).GAD[la].GSD[k + l] + (GSD[k1 + p1] + M).GA[ + 6].GSD[l1 - p1].GAD[nu].(GSD[l] + M).GAD[la].GSD[ + k1 + l1]).(GSD[x] + M)], DiracGammaExpand -> False, +PreservePropagatorStructures -> True, FCE -> True]", +"DiracTrace[ +SI[x1].SI[x2] (M + GSD[k + p]).GA[5].GSD[l - p].GAD[ + nu].(M + GSD[l]).GAD[la].GSD[k + l].(M + GSD[x])] + +DiracTrace[ +SI[x1].SI[x2] (M + GSD[k1 + p1]).GA[6].GSD[l1 - p1].GAD[ + nu].(M + GSD[l]).GAD[la].GSD[k1 + l1].(M + GSD[x])]"}, +{"fcstFCTraceExpand-ID18", +"FCTraceExpand[ +DiracTrace[ +DiracGamma[ + Momentum[ + q]].(DiracGamma[LorentzIndex[mu]].DiracGamma[6] SUNT[ + SUNIndex[b]]).(DiracGamma[Momentum[k]] + + DiracGamma[ + Momentum[q]]).(DiracGamma[LorentzIndex[mu]].DiracGamma[7] SUNT[ + SUNIndex[a]])]]", +"DiracTrace[ +SUNT[SUNIndex[b]].SUNT[SUNIndex[a]] DiracGamma[ + Momentum[q]].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 6].DiracGamma[Momentum[k]].DiracGamma[ + LorentzIndex[mu]].DiracGamma[7]] + +DiracTrace[ +SUNT[SUNIndex[b]].SUNT[SUNIndex[a]] DiracGamma[ + Momentum[q]].DiracGamma[LorentzIndex[mu]].DiracGamma[ + 6].DiracGamma[Momentum[q]].DiracGamma[ + LorentzIndex[mu]].DiracGamma[7]]"} }) diff --git a/Tests/NonCommAlgebra/FCTraceFactor.test b/Tests/NonCommAlgebra/FCTraceFactor.test index 5732b9aeb..49bdbd505 100644 --- a/Tests/NonCommAlgebra/FCTraceFactor.test +++ b/Tests/NonCommAlgebra/FCTraceFactor.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCTraceFactor *) @@ -36,5 +36,10 @@ b)]]//FCE", "(a - b)*(a + b)^2*c*DiracTrace[1]*DiracTrace[GA[i] . GA[j]]"}, {"fcstFCTraceFactor-ID8", "DiracTrace[DiracTrace[GA[i, j]] GA[k, l]] // FCTraceFactor // FCE", -"DiracTrace[GA[i].GA[j]] DiracTrace[GA[k].GA[l]]"} +"DiracTrace[GA[i].GA[j]] DiracTrace[GA[k].GA[l]]"}, +{"fcstFCTraceFactor-ID9", +"FCTraceFactor[ +DiracTrace[(x*(GS[p1] + M)).GA[mu].SI[xx].SUNT[ + a].(y*(GS[p2] + M).GA[nu])], FCE -> True]", +"x y DiracTrace[(M + GS[p1]).GA[mu].SI[xx].SUNT[a].(M + GS[p2]).GA[nu]]"} }) diff --git a/Tests/NonCommAlgebra/NonCommAlgebra.mt b/Tests/NonCommAlgebra/NonCommAlgebra.mt index d569fa0c3..fa4690bb1 100644 --- a/Tests/NonCommAlgebra/NonCommAlgebra.mt +++ b/Tests/NonCommAlgebra/NonCommAlgebra.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "NonCommAlgebra" directory *) @@ -17,27 +17,34 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "NonCommAlgebra"}]] Get/@tests; -DeclareNonCommutative[a,b]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, +If[ $OnlySubTest=!="", + testNames = "Tests`NonCommAlgebra`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + +If[ Names["Tests`NonCommAlgebra`fcstAntiCommutator*"]=!={}, + DeclareNonCommutative[a,b]; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`NonCommAlgebra`fcstAntiCommutator*"])]; -UnDeclareNonCommutative[a,b]; - -DeclareNonCommutative[a,b]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`NonCommAlgebra`fcstCommutator"])]; -UnDeclareNonCommutative[a,b]; - -DeclareNonCommutative[a,b,c,d]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`NonCommAlgebra`fcstCommutatorExplicit"])]; -UnDeclareNonCommutative[a,b,c,d]; - -DeclareNonCommutative[a,b,c,d]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Names["Tests`NonCommAlgebra`fcstCommutatorOrder"])]; -UnDeclareNonCommutative[a,b,c,d]; - -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Select[Names["Tests`NonCommAlgebra`*"], - !StringMatchQ[#, "*fcstCommutator" | "*fcstAntiCommutator" | "*fcstCommutatorExplicit" ] &])]; - + tmpTest = tmpTest /. testID->TestID /. test -> Test; + UnDeclareNonCommutative[a,b] + +]; + +If[ Names["Tests`NonCommAlgebra`fcstCommutator*"]=!={}, + DeclareNonCommutative[a,b,c,d]; + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`NonCommAlgebra`fcstCommutator*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; + UnDeclareNonCommutative[a,b,c,d] +]; + +If[ Names["Tests`NonCommAlgebra`*"]=!={} && + Select[Names["Tests`NonCommAlgebra`*"], !StringMatchQ[#, "*fcstCommutator" | "*fcstAntiCommutator" | "*fcstCommutatorExplicit" ] &]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Select[Names["Tests`NonCommAlgebra`*"], !StringMatchQ[#, "*fcstCommutator" | "*fcstAntiCommutator" | "*fcstCommutatorExplicit" ] &])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; diff --git a/Tests/NonCommAlgebra/Tr2.test b/Tests/NonCommAlgebra/Tr2.test index dcc8046c3..cf3750b13 100644 --- a/Tests/NonCommAlgebra/Tr2.test +++ b/Tests/NonCommAlgebra/Tr2.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Tr2 *) @@ -14,5 +14,7 @@ Tests`NonCommAlgebra`fcstTr2 = { {"Tr2-ID1", "DiracTrace[a]//Tr2", "4*a"}, {"Tr2-ID2", "DiracTrace[a[SUNFIndex[i]]Tf ]//Tr2", - "4*Tf*a[SUNFIndex[i]]"} + "4*Tf*a[SUNFIndex[i]]"}, +{"Tr2-ID3", "Tr[GA[i, j]]// FCE", "4 MT[i, j]"}, +{"Tr2-ID4", "Tr[CGA[i, j]] // FCE", "-4 KD[i, j]"} }; diff --git a/Tests/NonCommAlgebra/Trick.test b/Tests/NonCommAlgebra/Trick.test index b67940be2..bbc79b6e0 100644 --- a/Tests/NonCommAlgebra/Trick.test +++ b/Tests/NonCommAlgebra/Trick.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Trick *) @@ -19,5 +19,7 @@ Tests`NonCommAlgebra`fcstTrick = { "-Pair[Momentum[p], Momentum[p]] + Pair[Momentum[p], Momentum[q]] \ - Pair[Momentum[p], Momentum[r]] + Pair[Momentum[q], Momentum[r]]"}, {"Trick-ID3", "Trick[c.b.a . GA[d].GA[e]]", - "a*b*c*DiracGamma[LorentzIndex[d]] . DiracGamma[LorentzIndex[e]]"} + "a*b*c*DiracGamma[LorentzIndex[d]] . DiracGamma[LorentzIndex[e]]"}, +{"Trick-ID4", "Trick[{CGA[i] KD[i, j], KDD[\[Nu], \[Nu]]}]", + "{DiracGamma[CartesianIndex[j]], -1 + D}"} }; diff --git a/Tests/Pauli/FCPauliIsolate.test b/Tests/Pauli/FCPauliIsolate.test new file mode 100644 index 000000000..eeed579b6 --- /dev/null +++ b/Tests/Pauli/FCPauliIsolate.test @@ -0,0 +1,88 @@ + + +(* :Title: FCPauliIsolate.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCPauliIsolate *) + +(* ------------------------------------------------------------------------ *) + +Tests`Pauli`fcstFCPauliIsolate = +({ +{"fcstFCPauiliIsolate-ID1", "FCPauliIsolate[1]", "1"}, +{"fcstFCPauiliIsolate-ID2", "FCPauliIsolate[0]", "0"}, +{"fcstFCPauiliIsolate-ID3", "FCPauliIsolate[xx+yy]", "xx + yy"}, +{"fcstFCPauiliIsolate-ID4", "FCPauliIsolate[SI[i]]", +"FCGV[\"PauliChain\"][PauliSigma[LorentzIndex[i]]]"}, +{"fcstFCPauiliIsolate-ID5", "FCPauliIsolate[SI[i]+xx]", +"xx + FCGV[\"PauliChain\"][PauliSigma[LorentzIndex[i]]]"}, +{"fcstFCPauiliIsolate-ID6", "FCPauliIsolate[yy SI[i]+xx]", +"xx + yy*FCGV[\"PauliChain\"][PauliSigma[LorentzIndex[i]]]"}, +{"fcstFCPauiliIsolate-ID7", +"FCPauliIsolate[yy SI[i]+xx PauliXi[-I].SIS[p].PauliEta[I]]", +"xx*FCGV[\"PauliChain\"][PauliXi[-I] . PauliSigma[Momentum[p]] . \ +PauliEta[I]] + \ +yy*FCGV[\"PauliChain\"][PauliSigma[LorentzIndex[i]]]"}, +{"fcstFCPauiliIsolate-ID8", +"FCPauliIsolate[yy SI[i]+xx \ +PauliXi[-I].SIS[p].PauliEta[I].PauliEta[-I].SIS[p2].PauliXi[I],\ +PauliSigma\[Rule]False]", +"xx*PauliEta[-I] . PauliSigma[Momentum[p2]] . \ +PauliXi[I]*PauliXi[-I] . PauliSigma[Momentum[p]] . PauliEta[I] + \ +yy*PauliSigma[LorentzIndex[i]]"}, +{"fcstFCPauiliIsolate-ID9", +"FCPauliIsolate[yy SI[i]+xx \ +PauliXi[-I].SIS[p].PauliEta[I].PauliEta[-I].SIS[p2].PauliXi[I]]", +"xx*FCGV[\"PauliChain\"][PauliEta[-I] . PauliSigma[Momentum[p2]] . \ +PauliXi[I]]*FCGV[\"PauliChain\"][PauliXi[-I] . \ +PauliSigma[Momentum[p]] . PauliEta[I]] + \ +yy*FCGV[\"PauliChain\"][PauliSigma[LorentzIndex[i]]]"}, +{"fcstFCPauiliIsolate-ID10", +"FCPauliIsolate[yy SI[i]+xx \ +PauliXi[-I].SIS[p].PauliEta[I].PauliEta[-I].SIS[p2].PauliXi[I],\ +Split->False]", +"xx*FCGV[\"PauliChain\"][PauliXi[-I] . PauliSigma[Momentum[p]] . \ +PauliEta[I] . PauliEta[-I] . PauliSigma[Momentum[p2]] . PauliXi[I]] + \ +yy*FCGV[\"PauliChain\"][PauliSigma[LorentzIndex[i]]]"}, +{"fcstFCPauiliIsolate-ID11", +"FCPauliIsolate[SI[i,j,k]SI[l,m,n],Split\[Rule]False]", +"FCGV[\"PauliChain\"][PauliSigma[LorentzIndex[i]] . \ +PauliSigma[LorentzIndex[j]] . \ +PauliSigma[LorentzIndex[k]]*PauliSigma[LorentzIndex[l]] . \ +PauliSigma[LorentzIndex[m]] . PauliSigma[LorentzIndex[n]]]"}, +{"fcstFCPauiliIsolate-ID12", "FCPauliIsolate[SI[i,j,k]SI[l,m,n]]", +"FCGV[\"PauliChain\"][PauliSigma[LorentzIndex[i]] . \ +PauliSigma[LorentzIndex[j]] . \ +PauliSigma[LorentzIndex[k]]]*FCGV[\"PauliChain\"][PauliSigma[\ +LorentzIndex[l]] . PauliSigma[LorentzIndex[m]] . \ +PauliSigma[LorentzIndex[n]]]"}, +{"fcstFCPauiliIsolate-ID13", +"FCPauliIsolate[SI[nu].(SIS[p] + SIS[q] + SIS[k] + m).SI[mu], Head \ +-> dch]//FCE", "dch[SI[nu] . (m + SIS[k + p + q]) . SI[mu]]"}, +{"fcstFCPauiliIsolate-ID14", +"FCPauliIsolate[PauliXi[-I].SI[i].PauliXi[I].PauliEta[-I].SI[i].\ +PauliEta[I], Head -> dch] // FCE", +"dch[PauliEta[-I] . SI[i] . PauliEta[I]]*dch[PauliXi[-I] . SI[i] . \ +PauliXi[I]]"}, +{"fcstFCPauiliIsolate-ID15", +"FCPauliIsolate[MT[mu, nu] SI[i, j, k] + SIS[p, l] + MT[mu, nu] \ +SI[mu, j, k],LorentzIndex -> False, Head -> dch] // FCE", +"dch[SIS[p] . SIS[l]] + dch[SI[i] . SI[j] . SI[k]]*MT[mu, nu] + \ +dch[SI[mu] . SI[j] . SI[k]]*MT[mu, nu]"}, +{"fcstFCPauiliIsolate-ID16", +"FCPauliIsolate[ +MT[mu, nu] SI[i, j, k] + SIS[p, l] + MT[mu, nu] SI[mu, j, k], +LorentzIndex -> False, Head -> {dch, re}, FCE -> True]", +"dch[SIS[p].SIS[l]] re[1] + dch[SI[i].SI[j].SI[k]] re[MT[mu, nu]] + +dch[SI[mu].SI[j].SI[k]] re[MT[mu, nu]]"}, +{"fcstFCPauiliIsolate-ID17", "FCPauliIsolate[x,Head->{pa,re}]", "re[x]"}, +{"fcstFCPauiliIsolate-ID18", "FCPauliIsolate[{SI[i], SI[j]}, Head -> pau, FCE -> True]", +"{pau[SI[i]], pau[SI[j]]}"} +}); + diff --git a/Tests/Pauli/Pauli.mt b/Tests/Pauli/Pauli.mt new file mode 100644 index 000000000..d8e3281cb --- /dev/null +++ b/Tests/Pauli/Pauli.mt @@ -0,0 +1,62 @@ +(* :Title: Pauli.mt *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Unit tests for functions in the "Pauli" directory *) + +(* ------------------------------------------------------------------------ *) + +Needs["FeynCalc`"]; + +ClearAll[tests]; +tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "Pauli"}]] +Get/@tests; + +If[ $OnlySubTest=!="", + testNames = "Tests`Pauli`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + +If[ Names["Tests`Pauli`fcstPauliSigmaCombine*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Pauli`fcstPauliSigmaCombine*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Pauli`fcstPauliSigmaExpand*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Pauli`fcstPauliSigmaExpand*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Pauli`fcstFCPauliIsolate*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Pauli`fcstFCPauliIsolate*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Pauli`fcstPauliTrick*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Pauli`fcstPauliTrick*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Pauli`fcstPauliSimplify*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Pauli`fcstPauliSimplify*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Pauli`fcstPauliOrder*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Pauli`fcstPauliOrder*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; diff --git a/Tests/Pauli/PauliOrder.test b/Tests/Pauli/PauliOrder.test new file mode 100644 index 000000000..aba6fc669 --- /dev/null +++ b/Tests/Pauli/PauliOrder.test @@ -0,0 +1,94 @@ + + +(* :Title: PauliOrder.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for PauliOrder *) + +(* ------------------------------------------------------------------------ *) + +Tests`Pauli`fcstPauliOrder = +({ +{"fcstPauliOrder-ID1", "PauliOrder[0]", "0"}, +{"fcstPauliOrder-ID2", "PauliOrder[CSI[i],FCE\[Rule]True]", +"CSI[i]"}, +{"fcstPauliOrder-ID3", "PauliOrder[CSI[j,i],FCE\[Rule]True]", +"-CSI[i] . CSI[j] + 2*KD[i, j]"}, +{"fcstPauliOrder-ID4", "PauliOrder[CSID[j,i],FCE\[Rule]True]", +"-CSID[i] . CSID[j] + 2*KDD[i, j]"}, +{"fcstPauliOrder-ID5", "PauliOrder[CSI[i,j],{j,i},FCE\[Rule]True]", +"-CSI[j] . CSI[i] + 2*KD[i, j]"}, +{"fcstPauliOrder-ID6", "PauliOrder[CSID[i,j],{j,i},FCE\[Rule]True]", + "-CSID[j] . CSID[i] + 2*KDD[i, j]"}, +{"fcstPauliOrder-ID7", +"PauliOrder[-CSI[a,b]+2 KD[a,b],{b,a},FCE\[Rule]True]", +"CSI[b] . CSI[a]"}, +{"fcstPauliOrder-ID8", +"PauliOrder[-CSID[a,b]+2 KDD[a,b],{b,a},FCE\[Rule]True]", +"CSID[b] . CSID[a]"}, +{"fcstPauliOrder-ID9", +"PauliOrder[CSI[i,i].CSIS[p,p],FCE\[Rule]True]", "3*CSP[p, p]"}, +{"fcstPauliOrder-ID10", +"PauliOrder[CSID[i,i].CSISD[p,p],FCE\[Rule]True]", +"(-1 + D)*CSPD[p, p]"}, +{"fcstPauliOrder-ID11", +"PauliOrder[CSI[i,j].CSI[i,j],FCE\[Rule]True]", "-3"}, +{"fcstPauliOrder-ID12", "PauliOrder[CSI[i,j,i],FCE\[Rule]True]", +"-CSI[j]"}, +{"fcstPauliOrder-ID13", "PauliOrder[CSID[i,j,i],FCE\[Rule]True]", +"(3 - D)*CSID[j]"}, +{"fcstPauliOrder-ID14", "PauliOrder[CSIS[-p,q,p],FCE\[Rule]True]", +"CSIS[q]*CSP[p, p] - 2*CSIS[p]*CSP[p, q]"}, +{"fcstPauliOrder-ID15", "PauliOrder[CSISD[-p,q,p],FCE\[Rule]True]", +"CSISD[q]*CSPD[p, p] - 2*CSISD[p]*CSPD[p, q]"}, +{"fcstPauliOrder-ID16", +"PauliOrder[CSI[i],FCE\[Rule]True,FCPauliIsolate\[Rule]False]", +"CSI[i]"}, +{"fcstPauliOrder-ID17", +"PauliOrder[CSI[j,i],FCE\[Rule]True,FCPauliIsolate\[Rule]False]", +"-CSI[i] . CSI[j] + 2*KD[i, j]"}, +{"fcstPauliOrder-ID18", +"PauliOrder[CSID[j,i],FCE\[Rule]True,FCPauliIsolate\[Rule]False]", +"-CSID[i] . CSID[j] + 2*KDD[i, j]"}, +{"fcstPauliOrder-ID19", +"PauliOrder[CSI[i,j],{j,i},FCE\[Rule]True,FCPauliIsolate\[Rule]\ +False]", "-CSI[j] . CSI[i] + 2*KD[i, j]"}, +{"fcstPauliOrder-ID20", +"PauliOrder[CSID[i,j],{j,i},FCE\[Rule]True,FCPauliIsolate\[Rule]\ +False]", "-CSID[j] . CSID[i] + 2*KDD[i, j]"}, +{"fcstPauliOrder-ID21", +"PauliOrder[-CSI[a,b]+2 \ +KD[a,b],{b,a},FCE\[Rule]True,FCPauliIsolate\[Rule]False]", +"CSI[b] . CSI[a]"}, +{"fcstPauliOrder-ID22", +"PauliOrder[-CSID[a,b]+2 \ +KDD[a,b],{b,a},FCE\[Rule]True,FCPauliIsolate\[Rule]False]", +"CSID[b] . CSID[a]"}, +{"fcstPauliOrder-ID23", +"PauliOrder[CSI[i,i].CSIS[p,p],FCE\[Rule]True,FCPauliIsolate\[Rule]\ +False]", "3*CSP[p, p]"}, +{"fcstPauliOrder-ID24", +"PauliOrder[CSID[i,i].CSISD[p,p],FCE\[Rule]True,FCPauliIsolate\ +\[Rule]False]", "(-1 + D)*CSPD[p, p]"}, +{"fcstPauliOrder-ID25", +"PauliOrder[CSI[i,j].CSI[i,j],FCE\[Rule]True,FCPauliIsolate\[Rule]\ +False]", "-3"}, +{"fcstPauliOrder-ID26", +"PauliOrder[CSI[i,j,i],FCE\[Rule]True,FCPauliIsolate\[Rule]False]", + "-CSI[j]"}, +{"fcstPauliOrder-ID27", +"PauliOrder[CSID[i,j,i],FCE\[Rule]True,FCPauliIsolate\[Rule]False]\ +", "(3 - D)*CSID[j]"}, +{"fcstPauliOrder-ID28", +"PauliOrder[CSIS[-p,q,p],FCE\[Rule]True,FCPauliIsolate\[Rule]False]\ +", "CSIS[q]*CSP[p, p] - 2*CSIS[p]*CSP[p, q]"}, +{"fcstPauliOrder-ID29", +"PauliOrder[CSISD[-p,q,p],FCE\[Rule]True,FCPauliIsolate\[Rule]\ +False]", "CSISD[q]*CSPD[p, p] - 2*CSISD[p]*CSPD[p, q]"} +}); diff --git a/Tests/Pauli/PauliSigmaCombine.test b/Tests/Pauli/PauliSigmaCombine.test new file mode 100644 index 000000000..87cae72b8 --- /dev/null +++ b/Tests/Pauli/PauliSigmaCombine.test @@ -0,0 +1,47 @@ + + +(* :Title: PauliSigmaCombine.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for PauliSigmaCombine *) + +(* ------------------------------------------------------------------------ *) + +Tests`Pauli`fcstPauliSigmaCombine = +({ +{"fcstPauliSigmaCombine-ID1", +"PauliSigmaCombine[SIS[p]+SIS[q],FCE\[Rule]True]", "SIS[p + q]"}, +{"fcstPauliSigmaCombine-ID2", +"PauliSigmaCombine[SIS[p]+SISD[q],FCE\[Rule]True]", "SIS[p] + SISD[q]"}, +{"fcstPauliSigmaCombine-ID3", +"PauliSigmaCombine[SIS[p]+SIS[q]+m,FCE\[Rule]True]", "m + SIS[p + q]"}, +{"fcstPauliSigmaCombine-ID4", +"PauliSigmaCombine[SI[i].(SIS[p]+SIS[q]+m).SI[j],FCE\[Rule]True]", +"SI[i] . (m + SIS[p + q]) . SI[j]"}, +{"fcstPauliSigmaCombine-ID5", +"PauliSigmaCombine[SI[i].(2SIS[p]+3SIS[q]+m).SI[j],FCE\[Rule]True]", +"SI[i] . (m + SIS[2*p + 3*q]) . SI[j]"}, +{"fcstPauliSigmaCombine-ID6", +"PauliSigmaCombine[SI[i].(2SIS[p]+3SIS[p]+m).SI[j],FCE\[Rule]True]", +"SI[i] . (m + 5*SIS[p]) . SI[j]"}, +{"fcstPauliSigmaCombine-ID7", +"PauliSigmaCombine[CSIS[p] + CSIS[q], FCE -> True]", "CSIS[p + q]"}, +{"fcstPauliSigmaCombine-ID8", +"PauliSigmaCombine[CSIS[p] + CSISD[q], FCE -> True]", "CSIS[p] + CSISD[q]"}, +{"fcstPauliSigmaCombine-ID9", +"PauliSigmaCombine[CSIS[p] + CSIS[q] + m, FCE -> True]", "m + CSIS[p + q]"}, +{"fcstPauliSigmaCombine-ID10", +"PauliSigmaCombine[CSI[i].(CSIS[p] + CSIS[q] + m).CSI[j], FCE -> True]", "CSI[i].(m + CSIS[p + q]).CSI[j]"}, +{"fcstPauliSigmaCombine-ID11", +"PauliSigmaCombine[CSI[i].(2 CSIS[p] + 3 CSIS[q] + m).CSI[j], +FCE -> True]", "CSI[i].(m + CSIS[2 p + 3 q]).CSI[j]"}, +{"fcstPauliSigmaCombine-ID12", +"PauliSigmaCombine[CSI[i].(2 CSIS[p] + 3 CSIS[p] + m).CSI[j], +FCE -> True]", "CSI[i].(m + 5 CSIS[p]).CSI[j]"} +}); diff --git a/Tests/Pauli/PauliSigmaExpand.test b/Tests/Pauli/PauliSigmaExpand.test new file mode 100644 index 000000000..a08d0c261 --- /dev/null +++ b/Tests/Pauli/PauliSigmaExpand.test @@ -0,0 +1,45 @@ + + +(* :Title: PauliSigmaExpand.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for PauliSigmaExpand *) + +(* ------------------------------------------------------------------------ *) + +Tests`Pauli`fcstPauliSigmaExpand = { +{"fcstPauliSigmaExpand-ID1","PauliSigmaExpand[SIS[q].SIS[p - q]] // FCE", + "SIS[q].(SIS[p] - SIS[q])"}, +{"fcstPauliSigmaExpand-ID2","PauliSigmaExpand[SIS[a + b].SIS[c + d], Momentum -> {a}] // FCE", + "(SIS[a] + SIS[b]).SIS[c + d]"}, +{"fcstPauliSigmaExpand-ID3","PauliSigmaExpand[SIS[a + b].SIS[c + d], Momentum -> {c}] // FCE", + "SIS[a + b].(SIS[c] + SIS[d])"}, +{"fcstPauliSigmaExpand-ID4","PauliSigmaExpand[SIS[a + b].SIS[c + d], Momentum -> All] // FCE", + "(SIS[a] + SIS[b]).(SIS[c] + SIS[d])"}, +{"fcstPauliSigmaExpand-ID5","PauliSigmaExpand[ +PauliSigma[5 Momentum[a] + c Momentum[b + d] + Momentum[e]]] // FCE","5 SIS[a] + c (SIS[b] + SIS[d]) + SIS[e]"}, +{"fcstPauliSigmaExpand-ID6","PauliSigmaExpand[PauliSigma[5 Momentum[a, D] + + c Momentum[b + d, D] + Momentum[e, D], D-1]] // FCE", + "5*SISD[a] + c*(SISD[b] + SISD[d]) + SISD[e]"}, +{"fcstPauliSigmaExpand-ID7","PauliSigmaExpand[CSIS[q].CSIS[p - q]] // FCE", + "CSIS[q].(CSIS[p] - CSIS[q])"}, +{"fcstPauliSigmaExpand-ID8","PauliSigmaExpand[CSIS[a + b].CSIS[c + d], Momentum -> {a}] // FCE", + "(CSIS[a] + CSIS[b]).CSIS[c + d]"}, +{"fcstPauliSigmaExpand-ID9","PauliSigmaExpand[CSIS[a + b].CSIS[c + d], Momentum -> {c}] // FCE", + "CSIS[a + b].(CSIS[c] + CSIS[d])"}, +{"fcstPauliSigmaExpand-ID10","PauliSigmaExpand[CSIS[a + b].CSIS[c + d], Momentum -> All] // FCE", + "(CSIS[a] + CSIS[b]).(CSIS[c] + CSIS[d])"}, +{"fcstPauliSigmaExpand-ID11","PauliSigmaExpand[PauliSigma[5 CartesianMomentum[a] + c CartesianMomentum[b + d] + CartesianMomentum[e]]] // FCE", + "5 CSIS[a] + c (CSIS[b] + CSIS[d]) + CSIS[e]"}, +{"fcstPauliSigmaExpand-ID12","PauliSigmaExpand[ +PauliSigma[ +5 CartesianMomentum[a, D - 1] + c CartesianMomentum[b + d, D - 1] + + CartesianMomentum[e, D - 1], D-1]] // FCE", + "5 CSISD[a] + c (CSISD[b] + CSISD[d]) + CSISD[e]"} +}; diff --git a/Tests/Pauli/PauliSimplify.test b/Tests/Pauli/PauliSimplify.test new file mode 100644 index 000000000..37b2935e2 --- /dev/null +++ b/Tests/Pauli/PauliSimplify.test @@ -0,0 +1,365 @@ + + +(* :Title: PauliSimplify.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for PauliSimplify *) + +(* ------------------------------------------------------------------------ *) + +Tests`Pauli`fcstPauliSimplfyChains = +({ +{"fcstPauliSimplfyChains-ID1", +"PauliSimplify[CSIS[p].CSI[j1].CSIS[p],PauliReduce\[Rule]False,\ +FCE->True]", "-(CSI[j1]*CSP[p, p]) + 2*CSIS[p]*CV[p, j1]"}, +{"fcstPauliSimplfyChains-ID2", +"PauliSimplify[CSIS[p].CSI[j1,j2].CSIS[p],PauliReduce\[Rule]False,\ +FCE->True]", +"CSP[p, p]*CSI[j1] . CSI[j2] - 2*CV[p, j2]*CSI[j1] . CSIS[p] + \ +2*CV[p, j1]*CSI[j2] . CSIS[p]"}, +{"fcstPauliSimplfyChains-ID3", +"PauliSimplify[CSIS[p].CSI[j1,j2,j3].CSIS[p],PauliReduce\[Rule]\ +False,FCE->True]", +"-(CSP[p, p]*CSI[j1] . CSI[j2] . CSI[j3]) + 2*CV[p, j3]*CSI[j1] . \ +CSI[j2] . CSIS[p] - 2*CV[p, j2]*CSI[j1] . CSI[j3] . CSIS[p] + 2*CV[p, \ +j1]*CSI[j2] . CSI[j3] . CSIS[p]"}, +{"fcstPauliSimplfyChains-ID4", +"PauliSimplify[CSIS[p].CSI[j1,j2,j3,j4].CSIS[p],PauliReduce\[Rule]\ +False,FCE->True]", +"CSP[p, p]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] - 2*CV[p, \ +j4]*CSI[j1] . CSI[j2] . CSI[j3] . CSIS[p] + 2*CV[p, j3]*CSI[j1] . \ +CSI[j2] . CSI[j4] . CSIS[p] - 2*CV[p, j2]*CSI[j1] . CSI[j3] . CSI[j4] \ +. CSIS[p] + 2*CV[p, j1]*CSI[j2] . CSI[j3] . CSI[j4] . CSIS[p]"}, +{"fcstPauliSimplfyChains-ID5", +"PauliSimplify[CSIS[p].CSI[j1,j2,j3,j4,j5].CSIS[p],PauliReduce\ +\[Rule]False,FCE->True]", +"-(CSP[p, p]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5]) + \ +2*CV[p, j5]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSIS[p] - 2*CV[p, \ +j4]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j5] . CSIS[p] + 2*CV[p, \ +j3]*CSI[j1] . CSI[j2] . CSI[j4] . CSI[j5] . CSIS[p] - 2*CV[p, \ +j2]*CSI[j1] . CSI[j3] . CSI[j4] . CSI[j5] . CSIS[p] + 2*CV[p, \ +j1]*CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSIS[p]"}, +{"fcstPauliSimplfyChains-ID6", +"PauliSimplify[CSIS[p].CSI[j1,j2,j3,j4,j5,j6,j7].CSIS[p],\ +PauliReduce\[Rule]False,FCE->True]", +"-(CSP[p, p]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . \ +CSI[j6] . CSI[j7]) + 2*CV[p, j7]*CSI[j1] . CSI[j2] . CSI[j3] . \ +CSI[j4] . CSI[j5] . CSI[j6] . CSIS[p] - 2*CV[p, j6]*CSI[j1] . CSI[j2] \ +. CSI[j3] . CSI[j4] . CSI[j5] . CSI[j7] . CSIS[p] + 2*CV[p, \ +j5]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j6] . CSI[j7] . \ +CSIS[p] - 2*CV[p, j4]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j5] . CSI[j6] \ +. CSI[j7] . CSIS[p] + 2*CV[p, j3]*CSI[j1] . CSI[j2] . CSI[j4] . \ +CSI[j5] . CSI[j6] . CSI[j7] . CSIS[p] - 2*CV[p, j2]*CSI[j1] . CSI[j3] \ +. CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSIS[p] + 2*CV[p, \ +j1]*CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . \ +CSIS[p]"}, +{"fcstPauliSimplfyChains-ID7", +"PauliSimplify[CSIS[p].CSI[j1,j2,j3,j4,j5,j6,j7,j8].CSIS[p],\ +PauliReduce\[Rule]False,FCE->True]", +"CSP[p, p]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . \ +CSI[j6] . CSI[j7] . CSI[j8] - 2*CV[p, j8]*CSI[j1] . CSI[j2] . CSI[j3] \ +. CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSIS[p] + 2*CV[p, \ +j7]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . \ +CSI[j8] . CSIS[p] - 2*CV[p, j6]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] \ +. CSI[j5] . CSI[j7] . CSI[j8] . CSIS[p] + 2*CV[p, j5]*CSI[j1] . \ +CSI[j2] . CSI[j3] . CSI[j4] . CSI[j6] . CSI[j7] . CSI[j8] . CSIS[p] - \ +2*CV[p, j4]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j5] . CSI[j6] . CSI[j7] \ +. CSI[j8] . CSIS[p] + 2*CV[p, j3]*CSI[j1] . CSI[j2] . CSI[j4] . \ +CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSIS[p] - 2*CV[p, j2]*CSI[j1] \ +. CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSIS[p] \ ++ 2*CV[p, j1]*CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . \ +CSI[j7] . CSI[j8] . CSIS[p]"}, +{"fcstPauliSimplfyChains-ID8", +"PauliSimplify[CSIS[p].CSI[j1,j2,j3,j4,j5,j6,j7,j8,j9].CSIS[p],\ +PauliReduce\[Rule]False,FCE->True]", +"-(CSP[p, p]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . \ +CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9]) + 2*CV[p, j9]*CSI[j1] . \ +CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . \ +CSIS[p] - 2*CV[p, j8]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] \ +. CSI[j6] . CSI[j7] . CSI[j9] . CSIS[p] + 2*CV[p, j7]*CSI[j1] . \ +CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j8] . CSI[j9] . \ +CSIS[p] - 2*CV[p, j6]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] \ +. CSI[j7] . CSI[j8] . CSI[j9] . CSIS[p] + 2*CV[p, j5]*CSI[j1] . \ +CSI[j2] . CSI[j3] . CSI[j4] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] . \ +CSIS[p] - 2*CV[p, j4]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j5] . CSI[j6] \ +. CSI[j7] . CSI[j8] . CSI[j9] . CSIS[p] + 2*CV[p, j3]*CSI[j1] . \ +CSI[j2] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] . \ +CSIS[p] - 2*CV[p, j2]*CSI[j1] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] \ +. CSI[j7] . CSI[j8] . CSI[j9] . CSIS[p] + 2*CV[p, j1]*CSI[j2] . \ +CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] . \ +CSIS[p]"}, +{"fcstPauliSimplfyChains-ID9", +"PauliSimplify[CSIS[p].CSI[j1,j2,j3,j4,j5,j6,j7,j8,j9,j10].CSIS[p],\ +PauliReduce\[Rule]False,FCE->True]", +"2*CV[p, j9]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . \ +CSI[j6] . CSI[j7] . CSI[j8] . CSI[j10] . CSIS[p] + CSP[p, p]*CSI[j1] \ +. CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] \ +. CSI[j9] . CSI[j10] - 2*CV[p, j10]*CSI[j1] . CSI[j2] . CSI[j3] . \ +CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] . CSIS[p] - \ +2*CV[p, j8]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] \ +. CSI[j7] . CSI[j9] . CSI[j10] . CSIS[p] + 2*CV[p, j7]*CSI[j1] . \ +CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j8] . CSI[j9] . \ +CSI[j10] . CSIS[p] - 2*CV[p, j6]*CSI[j1] . CSI[j2] . CSI[j3] . \ +CSI[j4] . CSI[j5] . CSI[j7] . CSI[j8] . CSI[j9] . CSI[j10] . CSIS[p] \ ++ 2*CV[p, j5]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j6] . \ +CSI[j7] . CSI[j8] . CSI[j9] . CSI[j10] . CSIS[p] - 2*CV[p, \ +j4]*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j5] . CSI[j6] . CSI[j7] . \ +CSI[j8] . CSI[j9] . CSI[j10] . CSIS[p] + 2*CV[p, j3]*CSI[j1] . \ +CSI[j2] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] . \ +CSI[j10] . CSIS[p] - 2*CV[p, j2]*CSI[j1] . CSI[j3] . CSI[j4] . \ +CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] . CSI[j10] . CSIS[p] \ ++ 2*CV[p, j1]*CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . \ +CSI[j7] . CSI[j8] . CSI[j9] . CSI[j10] . CSIS[p]"}, +{"fcstPauliSimplfyChains-ID10", +"PauliSimplify[CSISD[p].CSID[j1].CSISD[p],PauliReduce\[Rule]False,\ +FCE->True]", "-(CSID[j1]*CSPD[p, p]) + 2*CSISD[p]*CVD[p, j1]"}, +{"fcstPauliSimplfyChains-ID11", +"PauliSimplify[CSISD[p].CSID[j1,j2].CSISD[p],PauliReduce\[Rule]\ +False,FCE->True]", +"CSPD[p, p]*CSID[j1] . CSID[j2] - 2*CVD[p, j2]*CSID[j1] . CSISD[p] \ ++ 2*CVD[p, j1]*CSID[j2] . CSISD[p]"}, +{"fcstPauliSimplfyChains-ID12", +"PauliSimplify[CSISD[p].CSID[j1,j2,j3].CSISD[p],PauliReduce\[Rule]\ +False,FCE->True]", +"-(CSPD[p, p]*CSID[j1] . CSID[j2] . CSID[j3]) + 2*CVD[p, \ +j3]*CSID[j1] . CSID[j2] . CSISD[p] - 2*CVD[p, j2]*CSID[j1] . CSID[j3] \ +. CSISD[p] + 2*CVD[p, j1]*CSID[j2] . CSID[j3] . CSISD[p]"}, +{"fcstPauliSimplfyChains-ID13", +"PauliSimplify[CSISD[p].CSID[j1,j2,j3,j4].CSISD[p],PauliReduce\ +\[Rule]False,FCE->True]", +"CSPD[p, p]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] - 2*CVD[p, \ +j4]*CSID[j1] . CSID[j2] . CSID[j3] . CSISD[p] + 2*CVD[p, j3]*CSID[j1] \ +. CSID[j2] . CSID[j4] . CSISD[p] - 2*CVD[p, j2]*CSID[j1] . CSID[j3] . \ +CSID[j4] . CSISD[p] + 2*CVD[p, j1]*CSID[j2] . CSID[j3] . CSID[j4] . \ +CSISD[p]"}, +{"fcstPauliSimplfyChains-ID14", +"PauliSimplify[CSISD[p].CSID[j1,j2,j3,j4,j5].CSISD[p],PauliReduce\ +\[Rule]False,FCE->True]", +"-(CSPD[p, p]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . \ +CSID[j5]) + 2*CVD[p, j5]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . \ +CSISD[p] - 2*CVD[p, j4]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j5] . \ +CSISD[p] + 2*CVD[p, j3]*CSID[j1] . CSID[j2] . CSID[j4] . CSID[j5] . \ +CSISD[p] - 2*CVD[p, j2]*CSID[j1] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSISD[p] + 2*CVD[p, j1]*CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSISD[p]"}, +{"fcstPauliSimplfyChains-ID15", +"PauliSimplify[CSISD[p].CSID[j1,j2,j3,j4,j5,j6,j7].CSISD[p],\ +PauliReduce\[Rule]False,FCE->True]", +"-(CSPD[p, p]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] \ +. CSID[j6] . CSID[j7]) + 2*CVD[p, j7]*CSID[j1] . CSID[j2] . CSID[j3] \ +. CSID[j4] . CSID[j5] . CSID[j6] . CSISD[p] - 2*CVD[p, j6]*CSID[j1] . \ +CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j7] . CSISD[p] + \ +2*CVD[p, j5]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j6] . \ +CSID[j7] . CSISD[p] - 2*CVD[p, j4]*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j5] . CSID[j6] . CSID[j7] . CSISD[p] + 2*CVD[p, j3]*CSID[j1] . \ +CSID[j2] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSISD[p] - \ +2*CVD[p, j2]*CSID[j1] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSISD[p] + 2*CVD[p, j1]*CSID[j2] . CSID[j3] . CSID[j4] . \ +CSID[j5] . CSID[j6] . CSID[j7] . CSISD[p]"}, +{"fcstPauliSimplfyChains-ID16", +"PauliSimplify[CSISD[p].CSID[j1,j2,j3,j4,j5,j6,j7,j8].CSISD[p],\ +PauliReduce\[Rule]False,FCE->True]", +"CSPD[p, p]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSID[j6] . CSID[j7] . CSID[j8] - 2*CVD[p, j8]*CSID[j1] . CSID[j2] . \ +CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSISD[p] + \ +2*CVD[p, j7]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSID[j6] . CSID[j8] . CSISD[p] - 2*CVD[p, j6]*CSID[j1] . CSID[j2] . \ +CSID[j3] . CSID[j4] . CSID[j5] . CSID[j7] . CSID[j8] . CSISD[p] + \ +2*CVD[p, j5]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j6] . \ +CSID[j7] . CSID[j8] . CSISD[p] - 2*CVD[p, j4]*CSID[j1] . CSID[j2] . \ +CSID[j3] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSISD[p] + \ +2*CVD[p, j3]*CSID[j1] . CSID[j2] . CSID[j4] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSID[j8] . CSISD[p] - 2*CVD[p, j2]*CSID[j1] . CSID[j3] . \ +CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSISD[p] + \ +2*CVD[p, j1]*CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSID[j8] . CSISD[p]"}, +{"fcstPauliSimplfyChains-ID17", +"PauliSimplify[CSISD[p].CSID[j1,j2,j3,j4,j5,j6,j7,j8,j9].CSISD[p],\ +PauliReduce\[Rule]False,FCE->True]", +"-(CSPD[p, p]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] \ +. CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9]) + 2*CVD[p, j9]*CSID[j1] \ +. CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . \ +CSID[j8] . CSISD[p] - 2*CVD[p, j8]*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j9] . CSISD[p] + \ +2*CVD[p, j7]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSID[j6] . CSID[j8] . CSID[j9] . CSISD[p] - 2*CVD[p, j6]*CSID[j1] . \ +CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j7] . CSID[j8] . \ +CSID[j9] . CSISD[p] + 2*CVD[p, j5]*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9] . CSISD[p] - \ +2*CVD[p, j4]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSID[j8] . CSID[j9] . CSISD[p] + 2*CVD[p, j3]*CSID[j1] . \ +CSID[j2] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . \ +CSID[j9] . CSISD[p] - 2*CVD[p, j2]*CSID[j1] . CSID[j3] . CSID[j4] . \ +CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9] . CSISD[p] + \ +2*CVD[p, j1]*CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSID[j8] . CSID[j9] . CSISD[p]"}, +{"fcstPauliSimplfyChains-ID18", +"PauliSimplify[CSISD[p].CSID[j1,j2,j3,j4,j5,j6,j7,j8,j9,j10].CSISD[\ +p],PauliReduce\[Rule]False,FCE->True]", +"2*CVD[p, j9]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] \ +. CSID[j6] . CSID[j7] . CSID[j8] . CSID[j10] . CSISD[p] + CSPD[p, \ +p]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSID[j8] . CSID[j9] . CSID[j10] - 2*CVD[p, j10]*CSID[j1] . \ +CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . \ +CSID[j8] . CSID[j9] . CSISD[p] - 2*CVD[p, j8]*CSID[j1] . CSID[j2] . \ +CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j9] . \ +CSID[j10] . CSISD[p] + 2*CVD[p, j7]*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j5] . CSID[j6] . CSID[j8] . CSID[j9] . CSID[j10] . \ +CSISD[p] - 2*CVD[p, j6]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . \ +CSID[j5] . CSID[j7] . CSID[j8] . CSID[j9] . CSID[j10] . CSISD[p] + \ +2*CVD[p, j5]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j6] . \ +CSID[j7] . CSID[j8] . CSID[j9] . CSID[j10] . CSISD[p] - 2*CVD[p, \ +j4]*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j5] . CSID[j6] . CSID[j7] . \ +CSID[j8] . CSID[j9] . CSID[j10] . CSISD[p] + 2*CVD[p, j3]*CSID[j1] . \ +CSID[j2] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . \ +CSID[j9] . CSID[j10] . CSISD[p] - 2*CVD[p, j2]*CSID[j1] . CSID[j3] . \ +CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9] . \ +CSID[j10] . CSISD[p] + 2*CVD[p, j1]*CSID[j2] . CSID[j3] . CSID[j4] . \ +CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9] . CSID[j10] . \ +CSISD[p]"}, +{"fcstPauliSimplfyChains-ID19", +"PauliSimplify[CSI[i,j1,i],PauliReduce\[Rule]False,FCE->True]", +"-CSI[j1]"}, +{"fcstPauliSimplfyChains-ID20", +"PauliSimplify[CSI[i,j1,j2,i],PauliReduce\[Rule]False,FCE->True]", +"CSI[j1] . CSI[j2] + 2*CSI[j2] . CSI[j1]"}, +{"fcstPauliSimplfyChains-ID21", +"PauliSimplify[CSI[i,j1,j2,j3,i],PauliReduce\[Rule]False,FCE->True]\ +", "-CSI[j1] . CSI[j2] . CSI[j3] - 2*CSI[j1] . CSI[j3] . CSI[j2] + \ +2*CSI[j2] . CSI[j3] . CSI[j1]"}, +{"fcstPauliSimplfyChains-ID22", +"PauliSimplify[CSI[i,j1,j2,j3,j4,i],PauliReduce\[Rule]False,\ +FCE->True]", +"CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] + 2*CSI[j1] . CSI[j2] . \ +CSI[j4] . CSI[j3] - 2*CSI[j1] . CSI[j3] . CSI[j4] . CSI[j2] + \ +2*CSI[j2] . CSI[j3] . CSI[j4] . CSI[j1]"}, +{"fcstPauliSimplfyChains-ID23", +"PauliSimplify[CSI[i,j1,j2,j3,j4,j5,i],PauliReduce\[Rule]False,\ +FCE->True]", +"-CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] - 2*CSI[j1] . \ +CSI[j2] . CSI[j3] . CSI[j5] . CSI[j4] + 2*CSI[j1] . CSI[j2] . CSI[j4] \ +. CSI[j5] . CSI[j3] - 2*CSI[j1] . CSI[j3] . CSI[j4] . CSI[j5] . \ +CSI[j2] + 2*CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j1]"}, +{"fcstPauliSimplfyChains-ID24", +"PauliSimplify[CSI[i,j1,j2,j3,j4,j5,j6,j7,i],PauliReduce\[Rule]\ +False,FCE->True]", +"-CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . \ +CSI[j7] - 2*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j7] \ +. CSI[j6] + 2*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j6] . \ +CSI[j7] . CSI[j5] - 2*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j5] . CSI[j6] \ +. CSI[j7] . CSI[j4] + 2*CSI[j1] . CSI[j2] . CSI[j4] . CSI[j5] . \ +CSI[j6] . CSI[j7] . CSI[j3] - 2*CSI[j1] . CSI[j3] . CSI[j4] . CSI[j5] \ +. CSI[j6] . CSI[j7] . CSI[j2] + 2*CSI[j2] . CSI[j3] . CSI[j4] . \ +CSI[j5] . CSI[j6] . CSI[j7] . CSI[j1]"}, +{"fcstPauliSimplfyChains-ID25", +"PauliSimplify[CSI[i,j1,j2,j3,j4,j5,j6,j7,j8,i],PauliReduce\[Rule]\ +False,FCE->True]", +"CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . \ +CSI[j7] . CSI[j8] + 2*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] \ +. CSI[j6] . CSI[j8] . CSI[j7] - 2*CSI[j1] . CSI[j2] . CSI[j3] . \ +CSI[j4] . CSI[j5] . CSI[j7] . CSI[j8] . CSI[j6] + 2*CSI[j1] . CSI[j2] \ +. CSI[j3] . CSI[j4] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j5] - \ +2*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] \ +. CSI[j4] + 2*CSI[j1] . CSI[j2] . CSI[j4] . CSI[j5] . CSI[j6] . \ +CSI[j7] . CSI[j8] . CSI[j3] - 2*CSI[j1] . CSI[j3] . CSI[j4] . CSI[j5] \ +. CSI[j6] . CSI[j7] . CSI[j8] . CSI[j2] + 2*CSI[j2] . CSI[j3] . \ +CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j1]"}, +{"fcstPauliSimplfyChains-ID26", +"PauliSimplify[CSI[i,j1,j2,j3,j4,j5,j6,j7,j8,j9,i],PauliReduce\ +\[Rule]False,FCE->True]", +"-CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . \ +CSI[j7] . CSI[j8] . CSI[j9] - 2*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] \ +. CSI[j5] . CSI[j6] . CSI[j7] . CSI[j9] . CSI[j8] + 2*CSI[j1] . \ +CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j8] . CSI[j9] . \ +CSI[j7] - 2*CSI[j1] . CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j7] \ +. CSI[j8] . CSI[j9] . CSI[j6] + 2*CSI[j1] . CSI[j2] . CSI[j3] . \ +CSI[j4] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] . CSI[j5] - 2*CSI[j1] \ +. CSI[j2] . CSI[j3] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] \ +. CSI[j4] + 2*CSI[j1] . CSI[j2] . CSI[j4] . CSI[j5] . CSI[j6] . \ +CSI[j7] . CSI[j8] . CSI[j9] . CSI[j3] - 2*CSI[j1] . CSI[j3] . CSI[j4] \ +. CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] . CSI[j9] . CSI[j2] + \ +2*CSI[j2] . CSI[j3] . CSI[j4] . CSI[j5] . CSI[j6] . CSI[j7] . CSI[j8] \ +. CSI[j9] . CSI[j1]"}, +{"fcstPauliSimplfyChains-ID27", +"PauliSimplify[CSID[i,j1,i],PauliReduce\[Rule]False,FCE->True]", +"3*CSID[j1] - D*CSID[j1]"}, +{"fcstPauliSimplfyChains-ID28", +"PauliSimplify[CSID[i,j1,j2,i],PauliReduce\[Rule]False,FCE->True]", + "-3*CSID[j1] . CSID[j2] + D*CSID[j1] . CSID[j2] + 2*CSID[j2] . \ +CSID[j1]"}, +{"fcstPauliSimplfyChains-ID29", +"PauliSimplify[CSID[i,j1,j2,j3,i],PauliReduce\[Rule]False,\ +FCE->True]", +"3*CSID[j1] . CSID[j2] . CSID[j3] - D*CSID[j1] . CSID[j2] . \ +CSID[j3] - 2*CSID[j1] . CSID[j3] . CSID[j2] + 2*CSID[j2] . CSID[j3] . \ +CSID[j1]"}, +{"fcstPauliSimplfyChains-ID30", +"PauliSimplify[CSID[i,j1,j2,j3,j4,i],PauliReduce\[Rule]False,\ +FCE->True]", +"-3*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] + D*CSID[j1] . \ +CSID[j2] . CSID[j3] . CSID[j4] + 2*CSID[j1] . CSID[j2] . CSID[j4] . \ +CSID[j3] - 2*CSID[j1] . CSID[j3] . CSID[j4] . CSID[j2] + 2*CSID[j2] . \ +CSID[j3] . CSID[j4] . CSID[j1]"}, +{"fcstPauliSimplfyChains-ID31", +"PauliSimplify[CSID[i,j1,j2,j3,j4,j5,i],PauliReduce\[Rule]False,\ +FCE->True]", +"3*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] - \ +D*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] - 2*CSID[j1] . \ +CSID[j2] . CSID[j3] . CSID[j5] . CSID[j4] + 2*CSID[j1] . CSID[j2] . \ +CSID[j4] . CSID[j5] . CSID[j3] - 2*CSID[j1] . CSID[j3] . CSID[j4] . \ +CSID[j5] . CSID[j2] + 2*CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSID[j1]"}, +{"fcstPauliSimplfyChains-ID32", +"PauliSimplify[CSID[i,j1,j2,j3,j4,j5,j6,j7,i],PauliReduce\[Rule]\ +False,FCE->True]", +"3*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] \ +. CSID[j7] - D*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSID[j6] . CSID[j7] - 2*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . \ +CSID[j5] . CSID[j7] . CSID[j6] + 2*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j6] . CSID[j7] . CSID[j5] - 2*CSID[j1] . CSID[j2] . \ +CSID[j3] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j4] + 2*CSID[j1] . \ +CSID[j2] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j3] - \ +2*CSID[j1] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . \ +CSID[j2] + 2*CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSID[j1]"}, +{"fcstPauliSimplfyChains-ID33", +"PauliSimplify[CSID[i,j1,j2,j3,j4,j5,j6,j7,j8,i],PauliReduce\[Rule]\ +False,FCE->True]", +"-3*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSID[j6] . CSID[j7] . CSID[j8] + D*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] + 2*CSID[j1] . \ +CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j8] . \ +CSID[j7] - 2*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . \ +CSID[j7] . CSID[j8] . CSID[j6] + 2*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j5] - 2*CSID[j1] . \ +CSID[j2] . CSID[j3] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . \ +CSID[j4] + 2*CSID[j1] . CSID[j2] . CSID[j4] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSID[j8] . CSID[j3] - 2*CSID[j1] . CSID[j3] . CSID[j4] . \ +CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j2] + 2*CSID[j2] . \ +CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . \ +CSID[j1]"}, +{"fcstPauliSimplfyChains-ID34", +"PauliSimplify[CSID[i,j1,j2,j3,j4,j5,j6,j7,j8,j9,i],PauliReduce\ +\[Rule]False,FCE->True]", +"3*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] \ +. CSID[j7] . CSID[j8] . CSID[j9] - D*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9] - \ +2*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . \ +CSID[j7] . CSID[j9] . CSID[j8] + 2*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j5] . CSID[j6] . CSID[j8] . CSID[j9] . CSID[j7] - \ +2*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j7] . \ +CSID[j8] . CSID[j9] . CSID[j6] + 2*CSID[j1] . CSID[j2] . CSID[j3] . \ +CSID[j4] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9] . CSID[j5] - \ +2*CSID[j1] . CSID[j2] . CSID[j3] . CSID[j5] . CSID[j6] . CSID[j7] . \ +CSID[j8] . CSID[j9] . CSID[j4] + 2*CSID[j1] . CSID[j2] . CSID[j4] . \ +CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9] . CSID[j3] - \ +2*CSID[j1] . CSID[j3] . CSID[j4] . CSID[j5] . CSID[j6] . CSID[j7] . \ +CSID[j8] . CSID[j9] . CSID[j2] + 2*CSID[j2] . CSID[j3] . CSID[j4] . \ +CSID[j5] . CSID[j6] . CSID[j7] . CSID[j8] . CSID[j9] . CSID[j1]"} +}); diff --git a/Tests/Pauli/PauliTrick.test b/Tests/Pauli/PauliTrick.test new file mode 100644 index 000000000..cc32f362e --- /dev/null +++ b/Tests/Pauli/PauliTrick.test @@ -0,0 +1,169 @@ + + +(* :Title: PauliTrick.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for PauliTrick *) + +(* ------------------------------------------------------------------------ *) + +Tests`Pauli`fcstPauliTrick = +({ +{"fcstPauliTrick-ID1", "PauliTrick[0]", "0"}, +{"fcstPauliTrick-ID2", "PauliTrick[a]", "a"}, +{"fcstPauliTrick-ID3", "PauliTrick[SI[mu,mu]]", "-2"}, +{"fcstPauliTrick-ID4", "PauliTrick[CSI[i,i]]", "3"}, +{"fcstPauliTrick-ID5", "PauliTrick[SID[mu,mu]]", "2 - D"}, +{"fcstPauliTrick-ID6", "PauliTrick[CSID[i,i]]", "-1 + D"}, +{"fcstPauliTrick-ID7", "PauliTrick[SIE[mu,mu]]", "4 - D"}, +{"fcstPauliTrick-ID8", "PauliTrick[CSIE[i,i]]", "-4 + D"}, +{"fcstPauliTrick-ID9", "PauliTrick[SIS[p,p]]", +"Pair[Momentum[p], Momentum[p]]"}, +{"fcstPauliTrick-ID10", "PauliTrick[CSIS[p,p]]", +"CartesianPair[CartesianMomentum[p], CartesianMomentum[p]]"}, +{"fcstPauliTrick-ID11", "PauliTrick[SISD[p,p]]", +"Pair[Momentum[p, D], Momentum[p, D]]"}, +{"fcstPauliTrick-ID12", "PauliTrick[CSISD[p,p]]", +"CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[p, -1 + D]]"}, +{"fcstPauliTrick-ID13", "PauliTrick[SISE[p,p]]", +"Pair[Momentum[p, -4 + D], Momentum[p, -4 + D]]"}, +{"fcstPauliTrick-ID14", "PauliTrick[CSISE[p,p]]", +"CartesianPair[CartesianMomentum[p, -4 + D], CartesianMomentum[p, -4 + D]]"}, +{"fcstPauliTrick-ID15", +"MatchQ[PauliTrick[CSI[i,j]]//Contract,\[IndentingNewLine]CartesianPair[\ +CartesianIndex[i],CartesianIndex[j]]+\[ImaginaryI] \ +Eps[CartesianIndex[i],CartesianIndex[j],CartesianIndex[a_]] PauliSigma[CartesianIndex[a_]]]", +"True"}, +{"fcstPauliTrick-ID16", "PauliTrick[CSI[i,j,i,j]]//Contract", +"-3"}, +{"fcstPauliTrick-ID17", "PauliTrick[CSI[i,j,i]]//Contract", +"-PauliSigma[CartesianIndex[j]]"}, +{"fcstPauliTrick-ID18", +"PauliTrick[CSIS[p1].CSI[i].CSIS[p2]]//Contract", +"(-I)*Eps[CartesianIndex[i], CartesianMomentum[p1], CartesianMomentum[p2]] - \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]]*PauliSigma[CartesianIndex[i]] + \ +CartesianPair[CartesianIndex[i], CartesianMomentum[p2]]*PauliSigma[CartesianMomentum[p1]] + \ +CartesianPair[CartesianIndex[i], CartesianMomentum[p1]]*PauliSigma[CartesianMomentum[p2]]"}, +{"fcstPauliTrick-ID19", "PauliTrick[CSI[a,i,b]]//Contract", +"(-I)*Eps[CartesianIndex[a], CartesianIndex[b], CartesianIndex[i]] + CartesianPair[CartesianIndex[b], \ +CartesianIndex[i]]*PauliSigma[CartesianIndex[a]] + CartesianPair[CartesianIndex[a], \ +CartesianIndex[i]]*PauliSigma[CartesianIndex[b]] - CartesianPair[CartesianIndex[a], \ +CartesianIndex[b]]*PauliSigma[CartesianIndex[i]]"}, +{"fcstPauliTrick-ID20", +"MatchQ[FCSetPauliSigmaScheme[\"Naive\"]; PauliTrick[CSID[i,j]],\ +\[IndentingNewLine]CartesianPair[CartesianIndex[i,-1+D],CartesianIndex[j,-1+D]]+\[ImaginaryI] \ +Eps[CartesianIndex[i,-1+D],CartesianIndex[j,-1+D],CartesianIndex[a_,-1+D]] \ +PauliSigma[CartesianIndex[a_,D-1],D-1]]", "True"}, +{"fcstPauliTrick-ID21", +"FCSetPauliSigmaScheme[\"None\"]; PauliTrick[CSID[i,j]]", +"PauliSigma[CartesianIndex[i, -1 + D], -1 + D] . PauliSigma[CartesianIndex[j, -1 + \ +D], -1 + D]"}, +{"fcstPauliTrick-ID22", "PauliTrick[CSI[i, j, i], PauliReduce -> False, FCE -> True]", +"-CSI[j]"} +}); + +Tests`Pauli`fcstPauliTrickAnticommutator = +({ +{"fcstPauliTrickAnticommutator-ID1", +"CSID[i,j,i]//PauliTrick//Contract//Simplify", +"-((-3 + D)*PauliSigma[CartesianIndex[j, -1 + D], -1 + D])"}, +{"fcstPauliTrickAnticommutator-ID2", +"CSID[i,j,k,i]//PauliTrick//Contract//Simplify", +"(-3 + D)*PauliSigma[CartesianIndex[j, -1 + D], -1 + D] . \ +PauliSigma[CartesianIndex[k, -1 + D], -1 + D] + 2*PauliSigma[CartesianIndex[k, -1 + \ +D], -1 + D] . PauliSigma[CartesianIndex[j, -1 + D], -1 + D]"}, +{"fcstPauliTrickAnticommutator-ID3", +"CSID[i,j,k,l,i]//PauliTrick//Contract//Simplify", +"-((-3 + D)*PauliSigma[CartesianIndex[j, -1 + D], -1 + D] . \ +PauliSigma[CartesianIndex[k, -1 + D], -1 + D] . PauliSigma[CartesianIndex[l, -1 + D], \ +-1 + D]) - 2*PauliSigma[CartesianIndex[j, -1 + D], -1 + D] . \ +PauliSigma[CartesianIndex[l, -1 + D], -1 + D] . PauliSigma[CartesianIndex[k, -1 + D], \ +-1 + D] + 2*PauliSigma[CartesianIndex[k, -1 + D], -1 + D] . \ +PauliSigma[CartesianIndex[l, -1 + D], -1 + D] . PauliSigma[CartesianIndex[j, -1 + D], \ +-1 + D]"}, +{"fcstPauliTrickAnticommutator-ID4", +"CSISD[p].CSID[j].CSISD[p]//PauliTrick", +"-(CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[p, -1 + \ +D]]*PauliSigma[CartesianIndex[j, -1 + D], -1 + D]) + 2*CartesianPair[CartesianIndex[j, -1 + \ +D], CartesianMomentum[p, -1 + D]]*PauliSigma[CartesianMomentum[p, -1 + D], -1 + D]"}, +{"fcstPauliTrickAnticommutator-ID5", +"CSISD[p].CSID[j,k].CSISD[p]//PauliTrick", +"CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[p, -1 + D]]*PauliSigma[CartesianIndex[j, -1 + D], +-1 + D] . PauliSigma[CartesianIndex[k, -1 + D], -1 + D] + 2*(-(CartesianPair[CartesianIndex[k, -1 + D], +CartesianMomentum[p, -1 + D]]*PauliSigma[CartesianIndex[j, -1 + D], -1 + D] . PauliSigma[CartesianMomentum[p, +-1 + D], -1 + D]) + CartesianPair[CartesianIndex[j, -1 + D], CartesianMomentum[p, +-1 + D]]*PauliSigma[CartesianIndex[k, -1 + D], -1 + D] . PauliSigma[CartesianMomentum[p, -1 + D], -1 + D])"}, +{"fcstPauliTrickAnticommutator-ID6", +"CSISD[p].CSID[j,k,l].CSISD[p]//PauliTrick", +"-(CartesianPair[CartesianMomentum[p, -1 + D], CartesianMomentum[p, -1 + D]]*PauliSigma[CartesianIndex[j, +-1 + D], -1 + D] . PauliSigma[CartesianIndex[k, -1 + D], -1 + D] . PauliSigma[CartesianIndex[l, +-1 + D], -1 + D]) + 2*(CartesianPair[CartesianIndex[l, -1 + D], CartesianMomentum[p, +-1 + D]]*PauliSigma[CartesianIndex[j, -1 + D], -1 + D] . PauliSigma[CartesianIndex[k, +-1 + D], -1 + D] . PauliSigma[CartesianMomentum[p, -1 + D], -1 + D] - +CartesianPair[CartesianIndex[k, -1 + D], CartesianMomentum[p, -1 + D]]*PauliSigma[CartesianIndex[j, +-1 + D], -1 + D] . PauliSigma[CartesianIndex[l, -1 + D], -1 + D] . PauliSigma[CartesianMomentum[p, +-1 + D], -1 + D] + CartesianPair[CartesianIndex[j, -1 + D], CartesianMomentum[p, +-1 + D]]*PauliSigma[CartesianIndex[k, -1 + D], -1 + D] . PauliSigma[CartesianIndex[l, +-1 + D], -1 + D] . PauliSigma[CartesianMomentum[p, -1 + D], -1 + D])"}, +{"fcstPauliTrickAnticommutator-ID7", +"CSI[i,j,i]//PauliTrick[#,PauliReduce\[Rule]False]&\ +//Contract//Simplify", "-PauliSigma[CartesianIndex[j]]"}, +{"fcstPauliTrickAnticommutator-ID8", +"CSI[i,j,k,i]//PauliTrick[#,PauliReduce\[Rule]False]&\ +//Contract//Simplify", +"PauliSigma[CartesianIndex[j]] . PauliSigma[CartesianIndex[k]] + \ +2*PauliSigma[CartesianIndex[k]] . PauliSigma[CartesianIndex[j]]"}, +{"fcstPauliTrickAnticommutator-ID9", +"CSI[i,j,k,l,i]//PauliTrick[#,PauliReduce\[Rule]False]&\ +//Contract//Simplify", +"-PauliSigma[CartesianIndex[j]] . PauliSigma[CartesianIndex[k]] . \ +PauliSigma[CartesianIndex[l]] - 2*PauliSigma[CartesianIndex[j]] . \ +PauliSigma[CartesianIndex[l]] . PauliSigma[CartesianIndex[k]] + \ +2*PauliSigma[CartesianIndex[k]] . PauliSigma[CartesianIndex[l]] . \ +PauliSigma[CartesianIndex[j]]"}, +{"fcstPauliTrickAnticommutator-ID10", +"CSIS[p].CSI[j].CSIS[p]//PauliTrick[#,PauliReduce\[Rule]False]&\ +//Contract//Simplify", +"-(CartesianPair[CartesianMomentum[p], CartesianMomentum[p]]*PauliSigma[CartesianIndex[j]]) + \ +2*CartesianPair[CartesianIndex[j], CartesianMomentum[p]]*PauliSigma[CartesianMomentum[p]]"}, +{"fcstPauliTrickAnticommutator-ID11", +"CSIS[p].CSI[j,k].CSIS[p]//PauliTrick[#,PauliReduce\[Rule]False]&\ +//Contract//Simplify", +"CartesianPair[CartesianMomentum[p], CartesianMomentum[p]]*PauliSigma[CartesianIndex[j]] . \ +PauliSigma[CartesianIndex[k]] - 2*CartesianPair[CartesianIndex[k], \ +CartesianMomentum[p]]*PauliSigma[CartesianIndex[j]] . PauliSigma[CartesianMomentum[p]] + \ +2*CartesianPair[CartesianIndex[j], CartesianMomentum[p]]*PauliSigma[CartesianIndex[k]] . \ +PauliSigma[CartesianMomentum[p]]"}, +{"fcstPauliTrickAnticommutator-ID12", +"CSIS[p].CSI[j,k,l].CSIS[p]//PauliTrick[#,PauliReduce\[Rule]False]&\ +//Contract//Simplify", +"-(CartesianPair[CartesianMomentum[p], CartesianMomentum[p]]*PauliSigma[CartesianIndex[j]] . \ +PauliSigma[CartesianIndex[k]] . PauliSigma[CartesianIndex[l]]) + 2*CartesianPair[CartesianIndex[l], \ +CartesianMomentum[p]]*PauliSigma[CartesianIndex[j]] . PauliSigma[CartesianIndex[k]] . \ +PauliSigma[CartesianMomentum[p]] - 2*CartesianPair[CartesianIndex[k], \ +CartesianMomentum[p]]*PauliSigma[CartesianIndex[j]] . PauliSigma[CartesianIndex[l]] . \ +PauliSigma[CartesianMomentum[p]] + 2*CartesianPair[CartesianIndex[j], \ +CartesianMomentum[p]]*PauliSigma[CartesianIndex[k]] . PauliSigma[CartesianIndex[l]] . \ +PauliSigma[CartesianMomentum[p]]"}, +{"fcstPauliTrickAnticommutator-ID13", +"Contract[PauliTrick[PauliTrick[CSI[i,j,i],PauliReduce\[Rule]False]\ +-CSI[i,j,i]]]//FCCanonicalizeDummyIndices//EpsEvaluate", "0"}, +{"fcstPauliTrickAnticommutator-ID14", +"Contract[PauliTrick[PauliTrick[CSI[i,j,k,i],PauliReduce\[Rule]\ +False]-CSI[i,j,k,i]]]//FCCanonicalizeDummyIndices//EpsEvaluate", +"0"}, +{"fcstPauliTrickAnticommutator-ID15", +"Contract[PauliTrick[PauliTrick[CSI[i,j,k,l,i],PauliReduce\[Rule]\ +False]-CSI[i,j,k,l,i]]]//FCCanonicalizeDummyIndices//EpsEvaluate", +"0"}, +{"fcstPauliTrickAnticommutator-ID16", +"Contract[PauliTrick[PauliTrick[CSIS[p].CSI[j].CSIS[p],PauliReduce\ +\[Rule]False]-CSIS[p].CSI[j].CSIS[p]]]\ +//FCCanonicalizeDummyIndices//EpsEvaluate", "0"} +}); diff --git a/Tests/QCD/QCD.mt b/Tests/QCD/QCD.mt index a5e7cb2ff..c76020513 100644 --- a/Tests/QCD/QCD.mt +++ b/Tests/QCD/QCD.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "QCD" directory *) @@ -17,6 +17,14 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "QCD"}]] Get/@tests; +If[ $OnlySubTest=!="", + testNames = "Tests`QCD`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + FCClearScalarProducts[]; Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, diff --git a/Tests/QCD/Twist2GluonOperator.test b/Tests/QCD/Twist2GluonOperator.test index 660c2b84d..4778760fa 100644 --- a/Tests/QCD/Twist2GluonOperator.test +++ b/Tests/QCD/Twist2GluonOperator.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for GluonVertex *) diff --git a/Tests/SUN/FCColorIsolate.test b/Tests/SUN/FCColorIsolate.test index b8fc903e6..f53236d1f 100644 --- a/Tests/SUN/FCColorIsolate.test +++ b/Tests/SUN/FCColorIsolate.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FCColorIsolate *) @@ -53,5 +53,22 @@ SUNIndex[k]]*FCGV[\"ColorObject\"][SUNT[SUNIndex[c]]]"}, {"fcstFCColorIsolate-ID9", "FCColorIsolate[SUNTrace[SUNT[a,b,c]]x+y]", "y + x*FCGV[\"ColorObject\"][SUNTrace[SUNT[SUNIndex[a]] . \ -SUNT[SUNIndex[b]] . SUNT[SUNIndex[c]]]]"} +SUNT[SUNIndex[b]] . SUNT[SUNIndex[c]]]]"}, +{"fcstFCColorIsolate-ID10", +"FCColorIsolate[SUNF[x, y, z]^2 SUNT[a, b] x + y SUNT[c] SUND[i, j, k], +Head -> {col, re}, FCE -> True]", +"col[SUNT[a].SUNT[b] SUNF[x, y, z]^2] re[x] + +col[SUND[i, j, k] SUNT[c]] re[y]"}, +{"fcstFCColorIsolate-ID11", "FCColorIsolate[x,Head->{col,re}]", "re[x]"}, +{"fcstFCColorIsolate-ID12", "FCColorIsolate[ +Spinor[Momentum[p1, D], mb, 1].GAD[FCGV[mu]].GA[7].Spinor[ + Momentum[p3, D], ms, 1] Spinor[-Momentum[p1, D], mb, 1].GAD[ + mu].GSD[p1].GSD[p1].GA[7].Spinor[-Momentum[p2, D], ms, 1] SDF[ +colInB, colOutS] SDF[colInS, colOutB], ExceptHeads -> {CA}, +Head -> col, FCE -> True]", "col[SDF[colInB, colOutS] SDF[colInS, colOutB]] Spinor[Momentum[p1, D], + mb, 1].GAD[FCGV[mu]].GA[7].Spinor[Momentum[p3, D], ms, +1] Spinor[-Momentum[p1, D], mb, 1].GAD[mu].GSD[p1].GSD[p1].GA[ +7].Spinor[-Momentum[p2, D], ms, 1]"}, +{"fcstFCColorIsolate-ID13", "FCColorIsolate[{SUNT[a], SUNT[b]}, Head -> col, FCE -> True]", +"{col[SUNT[a]], col[SUNT[b]]}"} }); diff --git a/Tests/SUN/SUN.mt b/Tests/SUN/SUN.mt index 917c26998..1abd9d36d 100644 --- a/Tests/SUN/SUN.mt +++ b/Tests/SUN/SUN.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "SUN" directory *) @@ -17,5 +17,13 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "SUN"}]] Get/@tests; +If[ $OnlySubTest=!="", + testNames = "Tests`SUN`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`SUN`*"])]; diff --git a/Tests/SUN/SUNFDeltaContract.test b/Tests/SUN/SUNFDeltaContract.test index 52da87baf..29da77d7c 100644 --- a/Tests/SUN/SUNFDeltaContract.test +++ b/Tests/SUN/SUNFDeltaContract.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for SUNFDeltaContract. *) diff --git a/Tests/SUN/SUNFSimplify.test b/Tests/SUN/SUNFSimplify.test index 139f770d3..3d9d81c47 100644 --- a/Tests/SUN/SUNFSimplify.test +++ b/Tests/SUN/SUNFSimplify.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for SUNFSimplify *) diff --git a/Tests/SUN/SUNSimplify.test b/Tests/SUN/SUNSimplify.test index 2bbc4a1b0..9352148ae 100644 --- a/Tests/SUN/SUNSimplify.test +++ b/Tests/SUN/SUNSimplify.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for SUNSimplify *) @@ -16,7 +16,7 @@ Tests`SUN`fcstSUNSimplify = { {"fcstSUNSimplify-ID1","SUNSimplify[1]","1"}, {"fcstSUNSimplify-ID2","SUNSimplify[SUNT[a].SUNT[b].SUNT[a]]", - "-(1/2) (CA - 2 CF) SUNT[SUNIndex[b]]"}, + "-((CA - 2*CF)*SUNT[SUNIndex[b]])/2"}, {"fcstSUNSimplify-ID3","SUNSimplify[SUNF[a, c, d].SUNF[b, c, d]]", "CA SUNDelta[SUNIndex[a], SUNIndex[b]]"}, {"fcstSUNSimplify-ID4","SUNSimplify[SUNF[a, b, c].SUNT[b].SUNT[c]]", @@ -72,6 +72,20 @@ Tests`SUN`fcstSUNSimplify = { {"fcstSUNSimplify-ID25","SUNSimplify[ SUNTrace[SUNF[a, c, g] SUNF[b, e, h] SUNF[d, g, h] SUNT[a].SUNT[b].SUNT[c].SUNT[d].SUNT[e]], Explicit -> True]", - "1/4 I CA^2 CF"} + "1/4 I CA^2 CF"}, +{"fcstSUNSimplify-ID26","SUNSimplify[SUND[a, e, r] SUND[b, d, r] SUND[a, b, s] SUND[d, e, s], +Explicit -> True]", + "(4 - CA^2) (12 - CA^2) (CA - 2 CF) CF"}, +{"fcstSUNSimplify-ID27","SUNSimplify[SUNF[a, b, c]^2]", + "2 CA^2 CF"}, +{"fcstSUNSimplify-ID28","SUNSimplify[SUND[a, b, c]^2]", + "-2 (4 - CA^2) CF"}, +{"fcstSUNSimplify-ID27","SUNSimplify[SUNF[a, b, c]^2, SUNNToCACF -> False]", + "SUNN (-1 + SUNN^2)"}, +{"fcstSUNSimplify-ID28","SUNSimplify[SUND[a, b, c]^2, SUNNToCACF -> False]", + "-(((4 - SUNN^2) (-1 + SUNN^2))/SUNN)"}, +{"fcstSUNSimplify-ID29","SUNSimplify[SUNF[a, b, c] SUNT[b]]", + "I (SUNT[SUNIndex[a]].SUNT[SUNIndex[c]] - +SUNT[SUNIndex[c]].SUNT[SUNIndex[a]])"} }; diff --git a/Tests/SUN/SUNTrace.test b/Tests/SUN/SUNTrace.test index 4457f5ac7..da0a5a0ba 100644 --- a/Tests/SUN/SUNTrace.test +++ b/Tests/SUN/SUNTrace.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for SUNTrace *) @@ -29,6 +29,8 @@ Tests`SUN`fcstSUNTraceColorTraces = { {"fcstSUNTraceColorTraces-ID7","SUNTrace[SUNF[a, b, c] SUNT[a, b, c]] // SUNSimplify", "(I/2)*CA^2*CF"}, {"fcstSUNTraceColorTraces-ID8","SUNTrace[SUNF[a, r, s] SUNF[b, r, s]] // SUNSimplify", - "CA^2*SUNDelta[SUNIndex[a], SUNIndex[b]]"} + "CA^2*SUNDelta[SUNIndex[a], SUNIndex[b]]"}, +{"fcstSUNTraceColorTraces-ID9","SUNTrace[SUNT[a, b, c, a, b, c]]", + "-(1/(8 SUNN^2)) + SUNN^2/8"} }; diff --git a/Tests/Shared/CacheManagement.test b/Tests/Shared/CacheManagement.test index 36e56151a..e3d913a61 100644 --- a/Tests/Shared/CacheManagement.test +++ b/Tests/Shared/CacheManagement.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for cache management *) @@ -20,8 +20,8 @@ Tests`Shared`fcstCacheManagement = { "SP[a, c] + SP[a, d] + SP[b, c] + SP[b, d]"}, {"fcstCacheManagement-ID4","FCClearScalarProducts[] \n FCUseCache[ExpandScalarProduct, {SP[a + b, c + d]}, {Momentum -> {e}}] // FCE", "SP[a + b, c + d]"}, -{"fcstCacheManagement-ID5","FCClearScalarProducts[] \n (Table[FCUseCache[ - ExpandScalarProduct, {SP[a + b + c (d + e), c + e + 2 (h + j)]}], {i, 1, 15000}] // AbsoluteTiming)[[1]] < 1.0", "True"}, +{"fcstCacheManagement-ID5","FCClearScalarProducts[] \n ((Table[FCUseCache[ + ExpandScalarProduct, {SP[a + b + c (d + e), c + e + 2 (h + j)]}], {i, 1, 10000}] // AbsoluteTiming)[[1]] < 2.0 || $VersionNumber<10.)", "True"}, {"fcstCacheManagement-ID6","FCClearCache[ExpandScalarProduct] \n FCShowCache[ExpandScalarProduct]", "{}"} }; diff --git a/Tests/Shared/Collect.test b/Tests/Shared/Collect.test index dabde2230..05644c792 100644 --- a/Tests/Shared/Collect.test +++ b/Tests/Shared/Collect.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Collect2 *) @@ -57,5 +57,105 @@ VAR^2 (Sum[xy[i], {i, 1, 10}] + Sum[xz[i], {i, 1, 10}])]", "True"}, {"fcstCollect2-ID13","Collect2[Together[a (1 + x) + 4 b (1 + y)], {a, b}, FCFactorOut -> 4]", - "4 (1/4 a (x+1)+b (y+1))"} + "4 (1/4 a (x+1)+b (y+1))"}, +{"fcstCollect2-ID14","Collect2[a PolyLog[2, z] + +s^2 PolyLog[2, z] + (1 - z) Log[2] + (2 + Pi^2) Log[1/(1 - z)] + +f Log[1/(1 - z)], Log[1/(1 - z)], PolyLog[2, z]]", + "-(-1 + z) Log[2] + (2 + f + \[Pi]^2) Log[1/( +1 - z)] + (a + s^2) PolyLog[2, z]"}, +{"fcstCollect2-ID15","Collect2[a PolyLog[2, z] + +s^2 PolyLog[2, z] + (1 - z) Log[2] + (2 + Pi^2) Log[1/(1 - z)] + +f Log[1/(1 - z)], Log[1/(1 - z)], PolyLog[2, z], Head -> {h1, h2}]", + "h2[2 + f + \[Pi]^2, h1[Log[1/(1 - z)]]] + +h2[a + s^2, h1[PolyLog[2, z]]] + h2[-(-1 + z) Log[2], 1]"}, +{"fcstCollect2-ID16","Collect2[(a - b)^2 - a^2 - b^2, a, b, InitialFunction -> fu]", + "fu[-a^2 + (a - b)^2 - b^2]"}, +{"fcstCollect2-ID17","Collect2[(a - b)^2 - a^2 - b^2, a, b, +InitialFunction -> {fu1, fu2, fu3}]", + "fu1[fu2[fu3[-a^2 + (a - b)^2 - b^2]]]"}, +{"fcstCollect2-ID18","Collect2[(a - b)^2 - a^2 - b^2, a, b, +IntermediateSubstitutions -> {a - b -> c}]", + "-a^2 - b^2 + c^2"}, +{"fcstCollect2-ID19","MatchQ[FCE[ +Collect2[Isolate[ + FCI[Isolate[(a + b + c + d)*FVD[p, mu]*FVD[p, nu]*FAD[p, {p, m}] + + (e + f + g)*FVD[p, mu]*FVD[p, nu]*FAD[{p, m}], p]], p, + IsolateNames -> loopisolate], FeynAmpDenominator[__]]], +FAD[{p, m}]*FVD[p, mu]*FVD[p, nu]*HoldForm[KK[a_]] + +FAD[p, {p, m}]*FVD[p, mu]*FVD[p, nu]*HoldForm[KK[b_]]]", + "True"}, +{"fcstCollect2-ID19","Collect2[a^2 + 2 a b + b^2, c]", + "(a + b)^2"}, +{"fcstCollect2-ID20","Collect2[(x1 a^2 + y 1 a^2 + 2 a b + x2 b^2 + y2 b^2)/(a + b + c^2 + +2 c d + d^2), a, b, Numerator -> True]", +"(2 a b + a^2 (x1 + y) + b^2 (x2 + y2))/(a + b + c^2 + 2 c d + d^2)"}, +{"fcstCollect2-ID21","Collect2[(x1 a^2 + y 1 a^2 + 2 a b + x2 b^2 + y2 b^2)/(a + b + c^2 + + 2 c d + d^2), a, b, Numerator->True, FactoringDenominator -> Simplify]", +"(2 a b + a^2 (x1 + y) + b^2 (x2 + y2))/(a + b + (c + d)^2)"}, +{"fcstCollect2-ID22","Collect2[{x1 -> a^2 + (2 a^2 + 3 b^2)/4 + 5 b^2}, a, b, c, d]", +"{x1 -> (3 a^2)/2 + (23 b^2)/4}"}, +{"fcstCollect2-ID23","Collect2[{x1 -> a^2 + (2 a^2 + 3 b^2)/4 + 5 b^2, +x2 -> c^2 + (c^2 + 4 d^2)/7 + 6 d^2}, a, b, c, d]", +"{x1 -> (3 a^2)/2 + (23 b^2)/4, x2 -> (8 c^2)/7 + (46 d^2)/7}"}, +{"fcstCollect2-ID24","Collect2[{x1 :> a^2 + (2 a^2 + 3 b^2)/4 + 5 b^2, +x2 -> c^2 + (c^2 + 4 d^2)/7 + 6 d^2}, a, b, c, d]/.RuleDelayed->rd", +"{rd[x1 , (3*a^2)/2 + (23*b^2)/4], x2 -> (8*c^2)/7 + (46*d^2)/7}"}, +{"fcstCollect2-ID25","Collect2[{{x1 -> a^2 + (2 a^2 + 3 b^2)/4 + 5 b^2, +x2 -> c^2 + (c^2 + 4 d^2)/7 + 6 d^2}}, a, b, c, d]", +"{{x1 -> (3 a^2)/2 + (23 b^2)/4, x2 -> (8 c^2)/7 + (46 d^2)/7}}"}, + + +{"fcstCollect2-ID26","Collect2[Sum[a b[i, c1 + c2, c3 + c4], {i, 1, 50}], d, +Factoring -> {Factor2, 400}]", +"a b[1, c1 + c2, c3 + c4] + a b[2, c1 + c2, c3 + c4] + +a b[3, c1 + c2, c3 + c4] + a b[4, c1 + c2, c3 + c4] + +a b[5, c1 + c2, c3 + c4] + a b[6, c1 + c2, c3 + c4] + +a b[7, c1 + c2, c3 + c4] + a b[8, c1 + c2, c3 + c4] + +a b[9, c1 + c2, c3 + c4] + a b[10, c1 + c2, c3 + c4] + +a b[11, c1 + c2, c3 + c4] + a b[12, c1 + c2, c3 + c4] + +a b[13, c1 + c2, c3 + c4] + a b[14, c1 + c2, c3 + c4] + +a b[15, c1 + c2, c3 + c4] + a b[16, c1 + c2, c3 + c4] + +a b[17, c1 + c2, c3 + c4] + a b[18, c1 + c2, c3 + c4] + +a b[19, c1 + c2, c3 + c4] + a b[20, c1 + c2, c3 + c4] + +a b[21, c1 + c2, c3 + c4] + a b[22, c1 + c2, c3 + c4] + +a b[23, c1 + c2, c3 + c4] + a b[24, c1 + c2, c3 + c4] + +a b[25, c1 + c2, c3 + c4] + a b[26, c1 + c2, c3 + c4] + +a b[27, c1 + c2, c3 + c4] + a b[28, c1 + c2, c3 + c4] + +a b[29, c1 + c2, c3 + c4] + a b[30, c1 + c2, c3 + c4] + +a b[31, c1 + c2, c3 + c4] + a b[32, c1 + c2, c3 + c4] + +a b[33, c1 + c2, c3 + c4] + a b[34, c1 + c2, c3 + c4] + +a b[35, c1 + c2, c3 + c4] + a b[36, c1 + c2, c3 + c4] + +a b[37, c1 + c2, c3 + c4] + a b[38, c1 + c2, c3 + c4] + +a b[39, c1 + c2, c3 + c4] + a b[40, c1 + c2, c3 + c4] + +a b[41, c1 + c2, c3 + c4] + a b[42, c1 + c2, c3 + c4] + +a b[43, c1 + c2, c3 + c4] + a b[44, c1 + c2, c3 + c4] + +a b[45, c1 + c2, c3 + c4] + a b[46, c1 + c2, c3 + c4] + +a b[47, c1 + c2, c3 + c4] + a b[48, c1 + c2, c3 + c4] + +a b[49, c1 + c2, c3 + c4] + a b[50, c1 + c2, c3 + c4]"}, +{"fcstCollect2-ID27","Collect2[Sum[a b[i, c1 + c2, c3 + c4], {i, 1, 50}], d, +Factoring -> {Factor2, 600}]","a (b[1, c1 + c2, c3 + c4] + b[2, c1 + c2, c3 + c4] + +b[3, c1 + c2, c3 + c4] + b[4, c1 + c2, c3 + c4] + +b[5, c1 + c2, c3 + c4] + b[6, c1 + c2, c3 + c4] + +b[7, c1 + c2, c3 + c4] + b[8, c1 + c2, c3 + c4] + +b[9, c1 + c2, c3 + c4] + b[10, c1 + c2, c3 + c4] + +b[11, c1 + c2, c3 + c4] + b[12, c1 + c2, c3 + c4] + +b[13, c1 + c2, c3 + c4] + b[14, c1 + c2, c3 + c4] + +b[15, c1 + c2, c3 + c4] + b[16, c1 + c2, c3 + c4] + +b[17, c1 + c2, c3 + c4] + b[18, c1 + c2, c3 + c4] + +b[19, c1 + c2, c3 + c4] + b[20, c1 + c2, c3 + c4] + +b[21, c1 + c2, c3 + c4] + b[22, c1 + c2, c3 + c4] + +b[23, c1 + c2, c3 + c4] + b[24, c1 + c2, c3 + c4] + +b[25, c1 + c2, c3 + c4] + b[26, c1 + c2, c3 + c4] + +b[27, c1 + c2, c3 + c4] + b[28, c1 + c2, c3 + c4] + +b[29, c1 + c2, c3 + c4] + b[30, c1 + c2, c3 + c4] + +b[31, c1 + c2, c3 + c4] + b[32, c1 + c2, c3 + c4] + +b[33, c1 + c2, c3 + c4] + b[34, c1 + c2, c3 + c4] + +b[35, c1 + c2, c3 + c4] + b[36, c1 + c2, c3 + c4] + +b[37, c1 + c2, c3 + c4] + b[38, c1 + c2, c3 + c4] + +b[39, c1 + c2, c3 + c4] + b[40, c1 + c2, c3 + c4] + +b[41, c1 + c2, c3 + c4] + b[42, c1 + c2, c3 + c4] + +b[43, c1 + c2, c3 + c4] + b[44, c1 + c2, c3 + c4] + +b[45, c1 + c2, c3 + c4] + b[46, c1 + c2, c3 + c4] + +b[47, c1 + c2, c3 + c4] + b[48, c1 + c2, c3 + c4] + +b[49, c1 + c2, c3 + c4] + b[50, c1 + c2, c3 + c4])"} }; diff --git a/Tests/Shared/DataType.test b/Tests/Shared/DataType.test index 58a386bbe..a914bd4c1 100644 --- a/Tests/Shared/DataType.test +++ b/Tests/Shared/DataType.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for DataType *) @@ -15,5 +15,9 @@ Tests`Shared`fcstDataType = { {"fcstDataType-ID1","ClearAll[f, g]; \n DataType[f, g, NonCommutative] = True; \n DotExpand[f.g - g.(2 a).f]", "f.g - 2 a g.f"}, {"fcstDataType-ID2","DataType[f, g, NonCommutative] = False; \n DotExpand[f.g - g.(2 a).f]", - "f g - 2 a f g"} + "f g - 2 a f g"}, +{"fcstDataType-ID3","DataType[z, FCVariable] = True; \n tmp=FCI[FAD[q - z p]]; \n DataType[z, FCVariable] = True; \n tmp", +"FeynAmpDenominator[PropagatorDenominator[-z Momentum[p, D] + Momentum[q, D], 0]]"}, +{"fcstDataType-ID4","DataType[z, FCVariable] = True; \n tmp=FCI[SFAD[{{0, (z p).q}}]]; \n DataType[z, FCVariable] = True; \n tmp", +"FeynAmpDenominator[StandardPropagatorDenominator[0, z Pair[Momentum[p, D], Momentum[q, D]], 0, {1, 1}]]"} }; diff --git a/Tests/Shared/Explicit.test b/Tests/Shared/Explicit.test index 70b2b1fb5..4f562560d 100644 --- a/Tests/Shared/Explicit.test +++ b/Tests/Shared/Explicit.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Explicit *) @@ -74,7 +74,7 @@ Pair[LorentzIndex[la, D], Pair[LorentzIndex[la], LorentzIndex[mu]] (Pair[LorentzIndex[nu], Momentum[k]] - Pair[LorentzIndex[nu], Momentum[p]]))"}, -{"fcstExplicit-ID17","Explicit[FieldStrength[mu, nu]]", +{"fcstExplicit-ID17","Explicit[FieldStrength[mu, nu]]//ChangeDimension[#,D]&", "QuantumField[FCPartialD[LorentzIndex[mu, D]], GaugeField, LorentzIndex[nu, D]] - QuantumField[FCPartialD[LorentzIndex[nu, D]], GaugeField, diff --git a/Tests/Shared/FCCheckSyntax.test b/Tests/Shared/FCCheckSyntax.test new file mode 100644 index 000000000..5341fbf8d --- /dev/null +++ b/Tests/Shared/FCCheckSyntax.test @@ -0,0 +1,112 @@ + + +(* :Title: FCCheckSyntax.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for FCCheckSyntax *) + +(* ------------------------------------------------------------------------ *) + + + +Tests`Shared`fcstFCCheckSyntaxLorentz = +({ +{"fcstFCCheckSyntaxLorentz-ID1", +"CheckAbort[FCCheckSyntax[FV[p,mu]],True]", "FV[p, mu]"}, +{"fcstFCCheckSyntaxLorentz-ID2", +"CheckAbort[FCCheckSyntax[FV[p,mu]+FV[p,nu]],True]", "True"}, +{"fcstFCCheckSyntaxLorentz-ID3", +"CheckAbort[FCCheckSyntax[FV[p,mu]FV[p,mu]],True]", +"FV[p, mu]^2"}, +{"fcstFCCheckSyntaxLorentz-ID4", +"CheckAbort[FCCheckSyntax[FV[p,mu]FV[p,mu]FV[p,mu]],True]", "True"}, +{"fcstFCCheckSyntaxLorentz-ID5", +"CheckAbort[FCCheckSyntax[FV[p,mu]FV[p,mu]+FV[p,nu]FV[p,nu]],True]\ +", "FV[p, mu]^2 + FV[p, nu]^2"}, +{"fcstFCCheckSyntaxLorentz-ID6", +"CheckAbort[FCCheckSyntax[FV[p,mu]FV[p,mu]+FV[p,nu]FV[p,nu]FV[p,\ +rho]],True]", "True"} +}); + +Tests`Shared`fcstFCCheckSyntaxCartesian = +({ +{"fcstFCCheckSyntaxCartesian-ID1", +"CheckAbort[FCCheckSyntax[CV[p,i]],True]", "CV[p, i]"}, +{"fcstFCCheckSyntaxCartesian-ID2", +"CheckAbort[FCCheckSyntax[CV[p,i]+CV[p,j]],True]", "True"}, +{"fcstFCCheckSyntaxCartesian-ID3", +"CheckAbort[FCCheckSyntax[CV[p,i]CV[p,i]],True]", "CV[p, i]^2"}, +{"fcstFCCheckSyntaxCartesian-ID4", +"CheckAbort[FCCheckSyntax[CV[p,i]CV[p,i]CV[p,i]],True]", +"CV[p, i]^3"}, +{"fcstFCCheckSyntaxCartesian-ID5", +"CheckAbort[FCCheckSyntax[CV[p,i]CV[p,i]+CV[p,j]CV[p,j]],True]", +"True"}, +{"fcstFCCheckSyntaxCartesian-ID6", +"CheckAbort[FCCheckSyntax[CV[p,i]CV[p,i]+CV[p,j]CV[p,j]CV[p,k]],\ +True]", "True"} +}) + +Tests`Shared`fcstFCCheckSyntaxColor = +({ +{"fcstFCCheckSyntaxColor-ID1", +"CheckAbort[FCCheckSyntax[SUNT[a]],True]", "SUNT[a]"}, +{"fcstFCCheckSyntaxColor-ID2", +"CheckAbort[FCCheckSyntax[SUNT[a]+SUNT[b]],True]", "True"}, +{"fcstFCCheckSyntaxColor-ID3", +"CheckAbort[FCCheckSyntax[SUNT[mu]SUNT[mu]],True]", "SUNT[mu]^2"}, +{"fcstFCCheckSyntaxColor-ID4", +"CheckAbort[FCCheckSyntax[SUNT[mu]^2SUNT[nu]],True]", "True"}, +{"fcstFCCheckSyntaxColor-ID5", +"CheckAbort[FCCheckSyntax[SUNT[nu].(SUNT[mu]^2).SUNT[rho]],True]", +"SUNT[nu] . SUNT[mu]^2 . SUNT[rho]"}, +{"fcstFCCheckSyntaxColor-ID6", +"CheckAbort[FCCheckSyntax[SUNT[nu].(SUNT[mu]^3).SUNT[rho]],True]", +"True"}, +{"fcstFCCheckSyntaxColor-ID7", +"CheckAbort[FCCheckSyntax[SUNT[a, b] SUNT[c]],True]", "True"} +}) + +Tests`Shared`fcstFCCheckSyntaxDirac = +({ +{"fcstFCCheckSyntaxDirac-ID1", +"CheckAbort[FCCheckSyntax[GA[mu]],True]", "GA[mu]"}, +{"fcstFCCheckSyntaxDirac-ID2", +"CheckAbort[FCCheckSyntax[GA[mu]+GA[nu]],True]", "True"}, +{"fcstFCCheckSyntaxDirac-ID3", +"CheckAbort[FCCheckSyntax[GA[mu]GA[mu]],True]", "GA[mu]^2"}, +{"fcstFCCheckSyntaxDirac-ID4", +"CheckAbort[FCCheckSyntax[GA[mu]^2GA[nu]],True]", "True"}, +{"fcstFCCheckSyntaxDirac-ID5", +"CheckAbort[FCCheckSyntax[GA[nu].(GA[mu]^2).GA[rho]],True]", +"GA[nu] . GA[mu]^2 . GA[rho]"}, +{"fcstFCCheckSyntaxDirac-ID6", +"CheckAbort[FCCheckSyntax[GA[nu].(GA[mu]^3).GA[rho]],True]", "True"}, +{"fcstFCCheckSyntaxDirac-ID7", +"CheckAbort[FCCheckSyntax[GA[a, b] GA[c]],True]", "True"} +}) + +Tests`Shared`fcstFCCheckSyntaxPauli = +({ +{"fcstFCCheckSyntaxPauli-ID1", +"CheckAbort[FCCheckSyntax[SI[mu]],True]", "SI[mu]"}, +{"fcstFCCheckSyntaxPauli-ID2", +"CheckAbort[FCCheckSyntax[SI[mu]+SI[nu]],True]", "True"}, +{"fcstFCCheckSyntaxPauli-ID3", +"CheckAbort[FCCheckSyntax[SI[mu]SI[mu]],True]", "SI[mu]^2"}, +{"fcstFCCheckSyntaxPauli-ID4", +"CheckAbort[FCCheckSyntax[SI[mu]^2SI[nu]],True]", "True"}, +{"fcstFCCheckSyntaxPauli-ID5", +"CheckAbort[FCCheckSyntax[SI[nu].(SI[mu]^2).SI[rho]],True]", +"SI[nu] . SI[mu]^2 . SI[rho]"}, +{"fcstFCCheckSyntaxPauli-ID6", +"CheckAbort[FCCheckSyntax[SI[nu].(SI[mu]^3).SI[rho]],True]", "True"}, +{"fcstFCCheckSyntaxPauli-ID7", +"CheckAbort[FCCheckSyntax[SI[a, b] SI[c]],True]", "True"} +}) diff --git a/Tests/Shared/FCCompareResults.test b/Tests/Shared/FCCompareResults.test new file mode 100644 index 000000000..92f4664c4 --- /dev/null +++ b/Tests/Shared/FCCompareResults.test @@ -0,0 +1,18 @@ +(* :Title: Factor2.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for Factor2 *) + +(* ------------------------------------------------------------------------ *) + +Tests`Shared`fcstFCCompareResults = { +{"fcstFCCompareResults-ID1","FCCompareResults[{{D}, {D}}, {{D}, {D}},Function->False]", "True"}, +{"fcstFCCompareResults-ID2","FCCompareResults[{}, {},Function->False]", "True"}, +{"fcstFCCompareResults-ID3","FCCompareResults[{1,2}, {1,2},Function->False]", "True"} +}; diff --git a/Tests/Shared/Factor2.test b/Tests/Shared/Factor2.test index af66f9c0a..aae3970c2 100644 --- a/Tests/Shared/Factor2.test +++ b/Tests/Shared/Factor2.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Factor2 *) diff --git a/Tests/Shared/FeynCalcExternal.test b/Tests/Shared/FeynCalcExternal.test index 4d81f600b..c626081c2 100644 --- a/Tests/Shared/FeynCalcExternal.test +++ b/Tests/Shared/FeynCalcExternal.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. -Copyright (C) 1990-2016 Rolf Mertig -Copyright (C) 1997-2016 Frederik Orellana -Copyright (C) 2014-2016 Vladyslav Shtabovenko +Copyright (C) 1990-2018 Rolf Mertig +Copyright (C) 1997-2018 Frederik Orellana +Copyright (C) 2014-2018 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FeynCalcExternal *) @@ -14,7 +14,7 @@ Copyright (C) 2014-2016 Vladyslav Shtabovenko (* ------------------------------------------------------------------------ *) Tests`Shared`fcstFeynCalcExternal = { - {"fcstFeynCalcExternal-ID1", "$BreitMaison=False;\nFCE[DiracGamma[LorentzIndex[mu]]]", "GA[mu]"}, + {"fcstFeynCalcExternal-ID1", "FCSetDiracGammaScheme[\"NDR\"];\nFCE[DiracGamma[LorentzIndex[mu]]]", "GA[mu]"}, {"fcstFeynCalcExternal-ID1.1", "FCE[DiracGamma[LorentzIndex[mu,D],D]]", "GAD[mu]"}, {"fcstFeynCalcExternal-ID1.2", "FCE[DiracGamma[LorentzIndex[mu,D-4],D-4]]", "GAE[mu]"}, {"fcstFeynCalcExternal-ID2", "FCE[DiracGamma[LM[mu, V], D]]", "DiracGamma[LM[mu, V], D]"}, @@ -36,44 +36,48 @@ Tests`Shared`fcstFeynCalcExternal = { "LC[a, b, c][d]"}, {"fcstFeynCalcExternal-ID12", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]//FCE", "LC[a, b, c, d]"}, - {"fcstFeynCalcExternal-ID13", "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension->4]//FCE", + {"fcstFeynCalcExternal-ID13", "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]//FCE", "LC[][a, b, c, d]"}, - {"fcstFeynCalcExternal-ID14", "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension->4]//FCE", + {"fcstFeynCalcExternal-ID14", "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]//FCE", "LC[a][b, c, d]"}, - {"fcstFeynCalcExternal-ID15", "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension->4]//FCE", + {"fcstFeynCalcExternal-ID15", "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]//FCE", "LC[a, b][c, d]"}, - {"fcstFeynCalcExternal-ID16", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension->4]//FCE", + {"fcstFeynCalcExternal-ID16", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]//FCE", "LC[a, b, c][d]"}, - {"fcstFeynCalcExternal-ID17", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension->4]//FCE", + {"fcstFeynCalcExternal-ID17", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]//FCE", "LC[a, b, c, d]"}, - {"fcstFeynCalcExternal-ID13", "Eps[Momentum[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE", + {"fcstFeynCalcExternal-ID13", "Eps[Momentum[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]//FCE", "LCD[][a, b, c, d]"}, - {"fcstFeynCalcExternal-ID14", "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE", + {"fcstFeynCalcExternal-ID14", "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]//FCE", "LCD[a][b, c, d]"}, - {"fcstFeynCalcExternal-ID15", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE", + {"fcstFeynCalcExternal-ID15", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]//FCE", "LCD[a, b][c, d]"}, - {"fcstFeynCalcExternal-ID16", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension->D]//FCE", + {"fcstFeynCalcExternal-ID16", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]//FCE", "LCD[a, b, c][d]"}, - {"fcstFeynCalcExternal-ID17", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension->D]//FCE", + {"fcstFeynCalcExternal-ID17", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]//FCE", "LCD[a, b, c, d]"}, - {"fcstFeynCalcExternal-ID18", "Eps[Momentum[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE", + {"fcstFeynCalcExternal-ID18", "Eps[Momentum[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n]]//FCE", "LeviCivita[Dimension->n][a, b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternal-ID19", "Eps[LorentzIndex[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE", + {"fcstFeynCalcExternal-ID19", "Eps[LorentzIndex[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n]]//FCE", "LeviCivita[a,Dimension->n][b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternal-ID20", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE", + {"fcstFeynCalcExternal-ID20", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], Momentum[c,n], Momentum[d,n]]//FCE", "LeviCivita[a, b,Dimension->n][c, d,Dimension->n]"}, - {"fcstFeynCalcExternal-ID21", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], Momentum[d,n], Dimension->n]//FCE", + {"fcstFeynCalcExternal-ID21", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], Momentum[d,n]]//FCE", "LeviCivita[a, b, c,Dimension->n][d,Dimension->n]"}, - {"fcstFeynCalcExternal-ID22", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], LorentzIndex[d,n], Dimension->n]//FCE", + {"fcstFeynCalcExternal-ID22", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], LorentzIndex[d,n]]//FCE", "LeviCivita[a, b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternal-ID23", "FCE[FeynAmpDenominator[PropagatorDenominator[x, 0], PropagatorDenominator[x2, 0]]]", + {"fcstFeynCalcExternal-ID23", "FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[x,D], 0], PropagatorDenominator[Momentum[x2,D], 0]]]", "FAD[x, x2]"}, - {"fcstFeynCalcExternal-ID24", "FCE[FeynAmpDenominator[PropagatorDenominator[x, m], PropagatorDenominator[x2, m2]]]", + {"fcstFeynCalcExternal-ID24", "FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[x,D], m], PropagatorDenominator[Momentum[x2,D], m2]]]", "FAD[{x, m}, {x2, m2}]"}, + {"fcstFeynCalcExternal-ID24.1", "ChangeDimension[FCI[FAD[{p, m}, {p - k, m}]], 4] // FCE", "FAD[{p, m}, {-k + p, m}, Dimension -> 4]"}, + {"fcstFeynCalcExternal-ID24.2", "FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[p1, 2 + D], m1], PropagatorDenominator[Momentum[p1, 2 + D], m1], + PropagatorDenominator[Momentum[p2, 2 + D], m2], PropagatorDenominator[Momentum[p2, 2 + D], m2]] ]", + "FAD[{p1, m1}, {p1, m1}, {p2, m2}, {p2, m2}, Dimension -> 2 + D]"}, {"fcstFeynCalcExternal-ID25", "FCE[Pair[LorentzIndex[a], LorentzIndex[b]]]", "MT[a, b]"}, - {"fcstFeynCalcExternal-ID25.1", "FCE[Pair[ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]]]", "MT[0, 0]"}, + {"fcstFeynCalcExternal-ID25.1", "FCE[Pair[ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]]]", "1"}, {"fcstFeynCalcExternal-ID26", "FCE[Pair[LorentzIndex[a, D], LorentzIndex[b, D]]]", "MTD[a, b]"}, {"fcstFeynCalcExternal-ID29", "FCE[Pair[LorentzIndex[a, -4 + D], LorentzIndex[b, -4 + D]]]", "MTE[a,b]"}, {"fcstFeynCalcExternal-ID30", "FCE[Pair[LorentzIndex[a], Momentum[p]]]", "FV[p, a]"}, @@ -81,7 +85,7 @@ Tests`Shared`fcstFeynCalcExternal = { {"fcstFeynCalcExternal-ID32", "FCE[Pair[LorentzIndex[a, -4 + D], Momentum[p, -4 + D]]]", "FVE[p,a]"}, {"fcstFeynCalcExternal-ID32.1", "FCE[Pair[ExplicitLorentzIndex[0], Momentum[a]]]", - "FV[a, 0]"}, + "TC[a]"}, {"fcstFeynCalcExternal-ID32.2", "FCE[Pair[ExplicitLorentzIndex[0], LorentzIndex[a]]]", "MT[a, 0]"}, {"fcstFeynCalcExternal-ID33", "FCE[Pair[Momentum[OPEDelta], Momentum[p]]]", "SO[p]"}, @@ -97,7 +101,7 @@ Tests`Shared`fcstFeynCalcExternal = { {"fcstFeynCalcExternal-ID41", "FCE[Pair[Momentum[k, -4 + D], Momentum[p, -4 + D]]]", "SPE[k,p]"}, {"fcstFeynCalcExternal-ID41.1", "FCE[Pair[Momentum[p, D], -Momentum[q1, D] + Momentum[q2, D]]]", "SPD[p, -q1 + q2]"}, - + {"fcstFeynCalcExternal-ID41.2", "FCE[Pair[CartesianIndex[i], LorentzIndex[mu]]]", "Pair[CartesianIndex[i], LorentzIndex[mu]]"}, {"fcstFeynCalcExternal-ID43", "FCE[SUND[SUNIndex[a], SUNIndex[b], SUNIndex[c]]]", "SUND[a, b, c]"}, {"fcstFeynCalcExternal-ID44", "FCE[SUNDelta[a, b]]", "SD[a, b]"}, {"fcstFeynCalcExternal-ID44-1", "FCE[SUNFDelta[a, b]]", "SDF[a, b]"}, @@ -117,7 +121,1535 @@ Tests`Shared`fcstFeynCalcExternal = { {"fcstFeynCalcExternal-ID50-1", "FCE[SUNFDeltaContract[SUNFIndex[a], SUNFIndex[b]]]", "SDF[a, b]"}, {"fcstFeynCalcExternal-ID51-1", "FCE[SUNFDeltaContract[a, b]]", "SDF[a, b]"}, {"fcstFeynCalcExternal-ID53", "FCE[Pair[Momentum[a, -4 + D], Momentum[b, -4 + D]]]", "SPE[a, b]"}, - {"fcstFeynCalcExternal-ID54", "FCE[Power2[x, y]]", "x^y"} + {"fcstFeynCalcExternal-ID54", "FCE[Power2[x, y]]", "x^y"}, + + {"fcstFeynCalcExternal-ID55", "FCE /@ {Eps[LorentzIndex[mu, D], LorentzIndex[nu, D], +LorentzIndex[al, D], LorentzIndex[be, D]], +Eps[LorentzIndex[mu, D], LorentzIndex[nu, D], LorentzIndex[al, D], +Momentum[be, D]], +Eps[LorentzIndex[mu, D], LorentzIndex[nu, D], Momentum[al, D], +LorentzIndex[be, D]], +Eps[LorentzIndex[mu, D], LorentzIndex[nu, D], Momentum[al, D], +Momentum[be, D]], +Eps[LorentzIndex[mu, D], Momentum[nu, D], LorentzIndex[al, D], +LorentzIndex[be, D]], +Eps[LorentzIndex[mu, D], Momentum[nu, D], LorentzIndex[al, D], +Momentum[be, D]], +Eps[LorentzIndex[mu, D], Momentum[nu, D], Momentum[al, D], +LorentzIndex[be, D]], +Eps[LorentzIndex[mu, D], Momentum[nu, D], Momentum[al, D], +Momentum[be, D]], +Eps[Momentum[mu, D], LorentzIndex[nu, D], LorentzIndex[al, D], +LorentzIndex[be, D]], +Eps[Momentum[mu, D], LorentzIndex[nu, D], LorentzIndex[al, D], +Momentum[be, D]], +Eps[Momentum[mu, D], LorentzIndex[nu, D], Momentum[al, D], +LorentzIndex[be, D]], +Eps[Momentum[mu, D], LorentzIndex[nu, D], Momentum[al, D], +Momentum[be, D]], +Eps[Momentum[mu, D], Momentum[nu, D], LorentzIndex[al, D], +LorentzIndex[be, D]], +Eps[Momentum[mu, D], Momentum[nu, D], LorentzIndex[al, D], +Momentum[be, D]], +Eps[Momentum[mu, D], Momentum[nu, D], Momentum[al, D], +LorentzIndex[be, D]], +Eps[Momentum[mu, D], Momentum[nu, D], Momentum[al, D], +Momentum[be, D]]}", "{LCD[al, be, mu, nu], LCD[al, mu, nu][be], -LCD[be, mu, nu][al], +LCD[mu, nu][al, be], LCD[al, be, mu][nu], -LCD[al, mu][be, nu], +LCD[be, mu][al, nu], LCD[mu][al, be, nu], -LCD[al, be, nu][mu], +LCD[al, nu][be, mu], -LCD[be, nu][al, mu], -LCD[nu][al, be, mu], +LCD[al, be][mu, nu], LCD[al][be, mu, nu], -LCD[be][al, mu, nu], +LCD[][al, be, mu, nu]}"}, +{"fcstFeynCalcExternal-ID56", +"DiracIndexDelta[DiracIndex[i],DiracIndex[j]]//FCE", +"DIDelta[i, j]"}, +{"fcstFeynCalcExternal-ID57", +"DiracIndexDelta[DiracIndex[1],DiracIndex[j]]//FCE", +"DIDelta[1, j]"}, +{"fcstFeynCalcExternal-ID58", +"DiracIndexDelta[DiracIndex[3],DiracIndex[1]]//FCE", +"DIDelta[1, 3]"}, +{"fcstFeynCalcExternal-ID59", +"DiracIndexDelta[DiracIndex[3],DiracIndex[3]]//FCE", +"DIDelta[3, 3]"}, +{"fcstFeynCalcExternal-ID60", +"DiracIndexDelta[ExplicitDiracIndex[1],ExplicitDiracIndex[2]]\ +//FCE", "DIDelta[1, 2]"}, +{"fcstFeynCalcExternal-ID61", +"DiracIndexDelta[ExplicitDiracIndex[3],ExplicitDiracIndex[3]]\ +//FCE", "DIDelta[3, 3]"}, +{"fcstFeynCalcExternal-ID62", +"DiracIndexDelta[DiracIndex[i],DiracIndex[i]]//FCE", +"DIDelta[i, i]"}, +{"fcstFeynCalcExternal-ID63", +"DiracIndexDelta[DiracIndex[i],0]//FCE", "DIDelta[0, i]"}, +{"fcstFeynCalcExternal-ID64", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],\ +DiracIndex[j]]//FCE", "DCHN[GA[mu], i, j]"}, +{"fcstFeynCalcExternal-ID65", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[1],\ +DiracIndex[j]]//FCE", "DCHN[GA[mu], 1, j]"}, +{"fcstFeynCalcExternal-ID66", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[3],\ +DiracIndex[1]]//FCE", "DCHN[GA[mu], 3, 1]"}, +{"fcstFeynCalcExternal-ID67", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[3],\ +DiracIndex[3]]//FCE", "DCHN[GA[mu], 3, 3]"}, +{"fcstFeynCalcExternal-ID68", +"DiracChain[DiracGamma[LorentzIndex[mu]],ExplicitDiracIndex[1],\ +ExplicitDiracIndex[2]]//FCE", "DCHN[GA[mu], 1, 2]"}, +{"fcstFeynCalcExternal-ID69", +"DiracChain[DiracGamma[LorentzIndex[mu]],ExplicitDiracIndex[3],\ +ExplicitDiracIndex[3]]//FCE", "DCHN[GA[mu], 3, 3]"}, +{"fcstFeynCalcExternal-ID70", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],\ +DiracIndex[i]]//FCE", "DCHN[GA[mu], i, i]"}, +{"fcstFeynCalcExternal-ID71", +"DiracChain[Spinor[Momentum[p],m],DiracIndex[i]]//FCE", +"DCHN[Spinor[Momentum[p], m, 1], i]"}, +{"fcstFeynCalcExternal-ID72", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],Spinor[Momentum[p],m],DiracIndex[j]]//FCE", +"DCHN[GA[mu] . GSD[p], Spinor[Momentum[p], m, 1], j]"}, +{"fcstFeynCalcExternal-ID73", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[i],Spinor[Momentum[p],m]]//FCE", +"DCHN[GA[mu] . GSD[p], i, Spinor[Momentum[p], m, 1]]"}, +{"fcstFeynCalcExternal-ID74", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]//FCE", +"DCHN[GA[mu] . GSD[p], Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcExternal-ID75", +"DiracChain[1,Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]\ +//FCE", "DCHN[1, Spinor[Momentum[p1], m1, 1], Spinor[Momentum[p2], \ +m2, 1]]"}, +{"fcstFeynCalcExternal-ID75", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}]]//FCE", "GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}]"}, +{"fcstFeynCalcExternal-ID76", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}]]//FCE", "GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}]"}, +{"fcstFeynCalcExternal-ID77", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}]]//FCE", "GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}]"}, +{"fcstFeynCalcExternal-ID78", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}]]//FCE", "GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}]"}, +{"fcstFeynCalcExternal-ID79", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, 1}]]//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, 4}]"}, +{"fcstFeynCalcExternal-ID80", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, -1}]]//FCE", + "GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, 4}]"}, +{"fcstFeynCalcExternal-ID81", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, 1}]]//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, n}]"}, +{"fcstFeynCalcExternal-ID82", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, -1}]]//FCE", + "GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, n}]"}, +{"fcstFeynCalcExternal-ID83", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {2, -1}], PropagatorDenominator[Momentum[p, D], m], \ +GenericPropagatorDenominator[1 + Pair[Momentum[p, D], Momentum[q, \ +D]]*Pair[Momentum[r, D], Momentum[s, D]], {2, -1}]]//FCE", +"FAD[{p, m}]*GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 2}, {{1 + SPD[p, \ +q]*SPD[r, s], -1}, 2}]"}, +{"fcstFeynCalcExternal-ID84", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {2, -1}], PropagatorDenominator[Momentum[p, D], m], \ +GenericPropagatorDenominator[1 + Pair[Momentum[p, D], Momentum[q, \ +D]]*Pair[Momentum[r, D], Momentum[s, D]], {2, -1}]]//FCE", +"FAD[{p, m}]*GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 2}, {{1 + SPD[p, \ +q]*SPD[r, s], -1}, 2}]"}, +{"fcstFeynCalcExternal-ID86", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID87", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, 1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID88", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID89", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID90", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID91", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID92", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID93", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID94", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID95", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID96", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID97", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID98", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID99", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID100", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {1, -1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID101", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {2, -1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID102", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {n, -1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID103", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID104", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID105", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID106", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID107", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID108", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID109", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID110", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID111", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID112", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID113", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID114", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID115", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID116", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID117", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID118", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID119", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID120", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID121", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID122", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID123", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID124", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID125", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID126", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID127", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {1, \ +-1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID128", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {2, \ +-1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID129", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {n, \ +-1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID130", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID131", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID132", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID133", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID134", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID135", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID136", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID137", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID138", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID139", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{1, -1}]]//FCE", "CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID140", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{2, -1}]]//FCE", "CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID141", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{n, -1}]]//FCE", "CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID142", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID143", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID144", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID145", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID146", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID147", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID148", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternal-ID149", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternal-ID150", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternal-ID151", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID152", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID153", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID154", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {1, -1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID155", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {2, -1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID156", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {n, -1}]]//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID157", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID158", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID159", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID160", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID161", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID162", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID163", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID164", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID165", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID166", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ 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\ +{2, -1}]]//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID228", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]//FCE", "CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID229", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE", "CFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternal-ID230", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]//FCE", "CFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID231", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID232", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]//FCE", "CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternal-ID233", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE", "CFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternal-ID234", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE", "CFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID235", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, 1}]]//FCE", "CFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID236", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, 1}]]//FCE", "CFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternal-ID237", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE", "CFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternal-ID238", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]//FCE", "CFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID239", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID240", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]//FCE", "CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternal-ID241", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID242", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1, -1 + D], 0, 0, \ +{1, -1}]]//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, {{q1, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID243", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}]]//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID244", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, m^2, {1, -1}]]//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID245", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4, -1 + D], 0, 0, \ +{1, -1}]]//FCE", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, {0, \ +-1}, 1}, {{q4, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID246", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}]]//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID247", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1], 0, 0, {1, \ +-1}]]//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, {{q1, 0}, {0, -1}, 1}, Dimension -> \ +3]"}, +{"fcstFeynCalcExternal-ID248", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, \ +-1}]]//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID249", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, m^2, {1, \ +-1}]]//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID250", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4], 0, 0, {1, \ +-1}]]//FCE", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, {0, \ +-1}, 1}, {{q4, 0}, {0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID251", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID252", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1, -1 + D], 0, 0, \ +{1, -1}]]//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, {{q1, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID253", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}]]//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID254", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, m^2, {1, -1}]]//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID255", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4, -1 + D], 0, 0, \ +{1, -1}]]//FCE", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, {0, \ +-1}, 1}, {{q4, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID256", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}]]//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID257", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1], 0, 0, {1, \ +-1}]]//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, {{q1, 0}, {0, -1}, 1}, Dimension -> \ +3]"}, +{"fcstFeynCalcExternal-ID258", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, \ +-1}]]//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID259", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, m^2, {1, \ +-1}]]//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID260", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4], 0, 0, {1, \ +-1}]]//FCE", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, {0, \ +-1}, 1}, {{q4, 0}, {0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternal-ID261", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID262", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID263", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, -1}]]//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID264", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID265", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID266", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID267", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID268", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID269", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID270", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID271", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID272", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID273", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID274", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID275", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID276", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID277", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID278", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID279", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID280", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID281", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID282", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID283", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID284", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID285", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID286", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID287", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID288", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID289", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID290", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}, Dimension -> 4]"}, +{"fcstFeynCalcExternal-ID291", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}, Dimension -> 4]"}, +{"fcstFeynCalcExternal-ID292", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, n}, Dimension -> 4]"}, +{"fcstFeynCalcExternal-ID293", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}, Dimension -> 4]"}, +{"fcstFeynCalcExternal-ID294", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}, Dimension -> 4]"}, +{"fcstFeynCalcExternal-ID295", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}, Dimension -> 4]"}, +{"fcstFeynCalcExternal-ID296", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternal-ID297", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternal-ID298", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternal-ID299", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID300", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID301", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID302", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID303", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID304", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID305", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID306", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID307", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID308", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID309", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID310", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID311", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID312", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID313", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID314", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID315", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID316", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID317", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE", "SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID318", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE", "SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID319", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE", "SFAD[{{q, -p1 . p2}, {m^2, 1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID320", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID321", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID322", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternal-ID323", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, \ +1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternal-ID324", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, \ +1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternal-ID325", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, \ +1}]]//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternal-ID326", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID327", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID328", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID329", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID330", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID331", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID332", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID333", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID334", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID335", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID336", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID337", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID338", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID339", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID340", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID341", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, \ +1}]]//FCE", "SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID342", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, \ +1}]]//FCE", "SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID343", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, \ +1}]]//FCE", "SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID344", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]//FCE", "SFAD[{{q, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID345", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID346", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID347", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID348", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]//FCE", "SFAD[{{q, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID349", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID350", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID351", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID352", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, -1}]]//FCE", "SFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID353", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, -1}]]//FCE", "SFAD[{{q, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID354", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, -1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID355", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, -1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID356", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]//FCE", "SFAD[{{q, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID357", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID358", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID359", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID360", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]//FCE", "SFAD[{{q, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID361", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID362", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID363", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID364", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, -1}]]//FCE", "SFAD[{{q, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID365", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, -1}]]//FCE", "SFAD[{{q, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID366", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, -1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID367", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, -1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID368", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]//FCE", "SFAD[{{q, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternal-ID369", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]//FCE", "SFAD[{{q, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID370", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID371", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternal-ID372", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]//FCE", "SFAD[{{q, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternal-ID373", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]//FCE", "SFAD[{{q, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID374", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID375", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternal-ID376", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, -1}]]//FCE", "SFAD[{{q, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternal-ID377", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, -1}]]//FCE", "SFAD[{{q, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID378", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, -1}]]//FCE", "SFAD[{{q, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID379", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, -1}]]//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternal-ID380", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID381", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID382", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID383", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID384", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID385", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID386", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID387", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternal-ID388", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +-1}]]//FCE", "SFAD[{{0, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID389", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE", "SFAD[{{0, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID390", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +-1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID391", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, -1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternal-ID392", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID393", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID394", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID395", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID396", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID397", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID398", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID399", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternal-ID400", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +-1}]]//FCE", "SFAD[{{0, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID401", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE", "SFAD[{{0, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID402", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +-1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID403", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, -1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternal-ID404", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternal-ID405", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID406", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID407", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternal-ID408", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternal-ID409", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID410", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternal-ID411", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternal-ID412", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE", "SFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternal-ID413", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE", "SFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID414", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +-1}]]//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternal-ID415", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, -1}]]//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"} + }; @@ -144,44 +1676,47 @@ Tests`Shared`fcstFeynCalcExternalDouble = { "LC[a, b, c][d]"}, {"fcstFeynCalcExternalDouble-ID12", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]//FCE//FCE", "LC[a, b, c, d]"}, - {"fcstFeynCalcExternalDouble-ID13", "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension->4]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID13", "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]//FCE//FCE", "LC[][a, b, c, d]"}, - {"fcstFeynCalcExternalDouble-ID14", "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension->4]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID14", "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]//FCE//FCE", "LC[a][b, c, d]"}, - {"fcstFeynCalcExternalDouble-ID15", "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension->4]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID15", "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]//FCE//FCE", "LC[a, b][c, d]"}, - {"fcstFeynCalcExternalDouble-ID16", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension->4]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID16", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]//FCE//FCE", "LC[a, b, c][d]"}, - {"fcstFeynCalcExternalDouble-ID17", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension->4]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID17", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]//FCE//FCE", "LC[a, b, c, d]"}, - {"fcstFeynCalcExternalDouble-ID13", "Eps[Momentum[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID13", "Eps[Momentum[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]//FCE//FCE", "LCD[][a, b, c, d]"}, - {"fcstFeynCalcExternalDouble-ID14", "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID14", "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]//FCE//FCE", "LCD[a][b, c, d]"}, - {"fcstFeynCalcExternalDouble-ID15", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID15", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]//FCE//FCE", "LCD[a, b][c, d]"}, - {"fcstFeynCalcExternalDouble-ID16", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension->D]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID16", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]//FCE//FCE", "LCD[a, b, c][d]"}, - {"fcstFeynCalcExternalDouble-ID17", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension->D]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID17", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]//FCE//FCE", "LCD[a, b, c, d]"}, - {"fcstFeynCalcExternalDouble-ID18", "Eps[Momentum[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID18", "Eps[Momentum[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n]]//FCE//FCE", "LeviCivita[Dimension->n][a, b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternalDouble-ID19", "Eps[LorentzIndex[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID19", "Eps[LorentzIndex[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n]]//FCE//FCE", "LeviCivita[a,Dimension->n][b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternalDouble-ID20", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID20", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], Momentum[c,n], Momentum[d,n]]//FCE//FCE", "LeviCivita[a, b,Dimension->n][c, d,Dimension->n]"}, - {"fcstFeynCalcExternalDouble-ID21", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], Momentum[d,n], Dimension->n]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID21", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], Momentum[d,n]]//FCE//FCE", "LeviCivita[a, b, c,Dimension->n][d,Dimension->n]"}, - {"fcstFeynCalcExternalDouble-ID22", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], LorentzIndex[d,n], Dimension->n]//FCE//FCE", + {"fcstFeynCalcExternalDouble-ID22", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], LorentzIndex[d,n]]//FCE//FCE", "LeviCivita[a, b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternalDouble-ID23", "FCE[FCE[FeynAmpDenominator[PropagatorDenominator[x, 0], - PropagatorDenominator[x2, 0]]]]", "FAD[x, x2]"}, - {"fcstFeynCalcExternalDouble-ID24", "FCE[FCE[FeynAmpDenominator[PropagatorDenominator[x, m], - PropagatorDenominator[x2, m2]]]]", "FAD[{x, m}, {x2, m2}]"}, - {"fcstFeynCalcExternalDouble-ID24.2", "ChangeDimension[FCI[FAD[{p, m}, {p - k, m}]], 4] // FCE //FCE ", + {"fcstFeynCalcExternalDouble-ID23", "FCE[FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[x,D], 0], + PropagatorDenominator[Momentum[x2,D], 0]]]]", "FAD[x, x2]"}, + {"fcstFeynCalcExternalDouble-ID24", "FCE[FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[x,D], m], + PropagatorDenominator[Momentum[x2,D], m2]]]]", "FAD[{x, m}, {x2, m2}]"}, + {"fcstFeynCalcExternalDouble-ID24.1", "ChangeDimension[FCI[FAD[{p, m}, {p - k, m}]], 4] // FCE //FCE ", "FAD[{p, m}, {-k + p, m}, Dimension -> 4]"}, + {"fcstFeynCalcExternalDouble-ID24.2", "FCE[FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[p1, 2 + D], m1], PropagatorDenominator[Momentum[p1, 2 + D], m1], + PropagatorDenominator[Momentum[p2, 2 + D], m2], PropagatorDenominator[Momentum[p2, 2 + D], m2]] ]]", + "FAD[{p1, m1}, {p1, m1}, {p2, m2}, {p2, m2}, Dimension -> 2 + D]"}, {"fcstFeynCalcExternalDouble-ID25", "FCE[FCE[Pair[LorentzIndex[a], LorentzIndex[b]]]]", "MT[a, b]"}, - {"fcstFeynCalcExternalDouble-ID25.1", "FCE[FCE[Pair[ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]]]]", "MT[0, 0]"}, + {"fcstFeynCalcExternalDouble-ID25.1", "FCE[FCE[Pair[ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]]]]", "1"}, {"fcstFeynCalcExternalDouble-ID26", "FCE[FCE[Pair[LorentzIndex[a, D], LorentzIndex[b, D]]]]", "MTD[a, b]"}, {"fcstFeynCalcExternalDouble-ID29", "FCE[FCE[Pair[LorentzIndex[a, -4 + D], LorentzIndex[b, -4 + D]]]]", "MTE[a,b]"}, @@ -189,7 +1724,7 @@ Tests`Shared`fcstFeynCalcExternalDouble = { {"fcstFeynCalcExternalDouble-ID31", "FCE[FCE[Pair[LorentzIndex[a, D], Momentum[p, D]]]]", "FVD[p, a]"}, {"fcstFeynCalcExternalDouble-ID32", "FCE[FCE[Pair[LorentzIndex[a, -4 + D], Momentum[p, -4 + D]]]]", "FVE[p,a]"}, - {"fcstFeynCalcExternalDouble-ID32.1", "FCE[FCE[Pair[ExplicitLorentzIndex[0], Momentum[a]]]]", "FV[a, 0]"}, + {"fcstFeynCalcExternalDouble-ID32.1", "FCE[FCE[Pair[ExplicitLorentzIndex[0], Momentum[a]]]]", "TC[a]"}, {"fcstFeynCalcExternalDouble-ID32.2", "FCE[FCE[Pair[ExplicitLorentzIndex[0], LorentzIndex[a]]]]", "MT[a, 0]"}, {"fcstFeynCalcExternalDouble-ID33", "FCE[FCE[Pair[Momentum[OPEDelta], Momentum[p]]]]", "SO[p]"}, {"fcstFeynCalcExternalDouble-ID34", "FCE[FCE[Pair[Momentum[OPEDelta], Momentum[p]]]]", "SO[p]"}, @@ -203,6 +1738,7 @@ Tests`Shared`fcstFeynCalcExternalDouble = { {"fcstFeynCalcExternalDouble-ID40", "FCE[FCE[Pair[Momentum[k, D], Momentum[p, D]]]]", "SPD[k, p]"}, {"fcstFeynCalcExternalDouble-ID41", "FCE[FCE[Pair[Momentum[k, -4 + D], Momentum[p, -4 + D]]]]", "SPE[k,p]"}, {"fcstFeynCalcExternalDouble-ID41.1", "FCE[FCE[Pair[Momentum[p, D], -Momentum[q1, D] + Momentum[q2, D]]]]", "SPD[p, -q1 + q2]"}, + {"fcstFeynCalcExternalDouble-ID41.2", "FCE[FCE[Pair[CartesianIndex[i], LorentzIndex[mu]]]]", "Pair[CartesianIndex[i], LorentzIndex[mu]]"}, {"fcstFeynCalcExternalDouble-ID43", "FCE[FCE[SUND[SUNIndex[a], SUNIndex[b], SUNIndex[c]]]]", "SUND[a, b, c]"}, {"fcstFeynCalcExternalDouble-ID44", "FCE[FCE[SUNDelta[a, b]]]", "SD[a, b]"}, {"fcstFeynCalcExternalDouble-ID44-1", "FCE[FCE[SUNFDelta[a, b]]]", "SDF[a, b]"}, @@ -222,7 +1758,1469 @@ Tests`Shared`fcstFeynCalcExternalDouble = { {"fcstFeynCalcExternalDouble-ID51", "FCE[FCE[SUNDeltaContract[a, b]]]", "SD[a, b]"}, {"fcstFeynCalcExternalDouble-ID51-1", "FCE[FCE[SUNFDeltaContract[a, b]]]", "SDF[a, b]"}, {"fcstFeynCalcExternalDouble-ID53", "FCE[FCE[Pair[Momentum[a, -4 + D], Momentum[b, -4 + D]]]]", "SPE[a,b]"}, - {"fcstFeynCalcExternalDouble-ID54", "FCE[FCE[Power2[x, y]]]", "x^y"} + {"fcstFeynCalcExternalDouble-ID54", "FCE[FCE[Power2[x, y]]]", "x^y"}, +{"fcstFeynCalcExternalDouble-ID55", +"DiracIndexDelta[DiracIndex[i],DiracIndex[j]]//FCE//FCE", +"DIDelta[i, j]"}, +{"fcstFeynCalcExternalDouble-ID56", +"DiracIndexDelta[DiracIndex[1],DiracIndex[j]]//FCE//FCE", +"DIDelta[1, j]"}, +{"fcstFeynCalcExternalDouble-ID57", +"DiracIndexDelta[DiracIndex[3],DiracIndex[1]]//FCE//FCE", +"DIDelta[1, 3]"}, +{"fcstFeynCalcExternalDouble-ID58", +"DiracIndexDelta[DiracIndex[3],DiracIndex[3]]//FCE//FCE", +"DIDelta[3, 3]"}, +{"fcstFeynCalcExternalDouble-ID59", +"DiracIndexDelta[ExplicitDiracIndex[1],ExplicitDiracIndex[2]]\ +//FCE//FCE", "DIDelta[1, 2]"}, +{"fcstFeynCalcExternalDouble-ID60", +"DiracIndexDelta[ExplicitDiracIndex[3],ExplicitDiracIndex[3]]\ +//FCE//FCE", "DIDelta[3, 3]"}, +{"fcstFeynCalcExternalDouble-ID61", +"DiracIndexDelta[DiracIndex[i],DiracIndex[i]]//FCE//FCE", +"DIDelta[i, i]"}, +{"fcstFeynCalcExternalDouble-ID62", +"DiracIndexDelta[DiracIndex[i],0]//FCE//FCE", "DIDelta[0, i]"}, +{"fcstFeynCalcExternalDouble-ID63", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],\ +DiracIndex[j]]//FCE//FCE", "DCHN[GA[mu], i, j]"}, +{"fcstFeynCalcExternalDouble-ID64", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[1],\ +DiracIndex[j]]//FCE//FCE", "DCHN[GA[mu], 1, j]"}, +{"fcstFeynCalcExternalDouble-ID65", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[3],\ +DiracIndex[1]]//FCE//FCE", "DCHN[GA[mu], 3, 1]"}, +{"fcstFeynCalcExternalDouble-ID66", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[3],\ +DiracIndex[3]]//FCE//FCE", "DCHN[GA[mu], 3, 3]"}, +{"fcstFeynCalcExternalDouble-ID67", +"DiracChain[DiracGamma[LorentzIndex[mu]],ExplicitDiracIndex[1],\ +ExplicitDiracIndex[2]]//FCE//FCE", "DCHN[GA[mu], 1, 2]"}, +{"fcstFeynCalcExternalDouble-ID68", +"DiracChain[DiracGamma[LorentzIndex[mu]],ExplicitDiracIndex[3],\ +ExplicitDiracIndex[3]]//FCE//FCE", "DCHN[GA[mu], 3, 3]"}, +{"fcstFeynCalcExternalDouble-ID69", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],\ +DiracIndex[i]]//FCE//FCE", "DCHN[GA[mu], i, i]"}, +{"fcstFeynCalcExternalDouble-ID70", +"DiracChain[Spinor[Momentum[p],m],DiracIndex[i]]//FCE//FCE", +"DCHN[Spinor[Momentum[p], m, 1], i]"}, +{"fcstFeynCalcExternalDouble-ID71", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],Spinor[Momentum[p],m],DiracIndex[j]]//FCE//FCE", +"DCHN[GA[mu] . GSD[p], Spinor[Momentum[p], m, 1], j]"}, +{"fcstFeynCalcExternalDouble-ID72", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[i],Spinor[Momentum[p],m]]//FCE//FCE", +"DCHN[GA[mu] . GSD[p], i, Spinor[Momentum[p], m, 1]]"}, +{"fcstFeynCalcExternalDouble-ID73", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]//FCE//FCE", +"DCHN[GA[mu] . GSD[p], Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcExternalDouble-ID74", +"DiracChain[1,Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]\ +//FCE//FCE", +"DCHN[1, Spinor[Momentum[p1], m1, 1], Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcExternalDouble-ID75", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}]]//FCE//FCE", "GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}]"}, +{"fcstFeynCalcExternalDouble-ID76", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}]]//FCE//FCE", "GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}]"}, +{"fcstFeynCalcExternalDouble-ID77", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}]]//FCE//FCE", "GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID78", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}]]//FCE//FCE", "GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID79", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, \ +1}]]//FCE//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, 4}]"}, +{"fcstFeynCalcExternalDouble-ID80", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, \ +-1}]]//FCE//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, 4}]"}, +{"fcstFeynCalcExternalDouble-ID81", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, \ +1}]]//FCE//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID82", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, \ +-1}]]//FCE//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID83", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {2, -1}], PropagatorDenominator[Momentum[p, D], m], \ +GenericPropagatorDenominator[1 + Pair[Momentum[p, D], Momentum[q, \ +D]]*Pair[Momentum[r, D], Momentum[s, D]], {2, -1}]]//FCE//FCE", +"FAD[{p, m}]*GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 2}, {{1 + SPD[p, \ +q]*SPD[r, s], -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID84", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {2, -1}], PropagatorDenominator[Momentum[p, D], m], \ +GenericPropagatorDenominator[1 + Pair[Momentum[p, D], Momentum[q, \ +D]]*Pair[Momentum[r, D], Momentum[s, D]], {2, -1}]]//FCE//FCE", +"FAD[{p, m}]*GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 2}, {{1 + SPD[p, \ +q]*SPD[r, s], -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID86", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID87", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, 1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID88", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID89", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID90", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID91", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID92", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID93", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID94", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID95", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID96", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID97", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID98", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID99", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID100", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID101", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID102", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID103", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID104", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID105", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID106", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID107", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID108", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID109", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID110", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID111", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID112", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID113", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID114", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID115", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID116", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID117", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID118", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID119", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID120", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID121", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID122", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID123", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID124", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID125", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID126", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID127", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {1, \ +-1}]]//FCE//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID128", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {2, \ +-1}]]//FCE//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID129", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {n, \ +-1}]]//FCE//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID130", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID131", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID132", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID133", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID134", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID135", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID136", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID137", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID138", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID139", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{1, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID140", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{2, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID141", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{n, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID142", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID143", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID144", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID145", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID146", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID147", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID148", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternalDouble-ID149", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternalDouble-ID150", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternalDouble-ID151", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID152", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID153", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID154", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID155", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID156", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID157", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID158", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID159", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID160", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID161", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID162", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID163", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID164", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID165", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID166", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID167", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID168", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID169", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID170", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID171", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID172", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID173", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID174", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID175", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID176", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID177", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID178", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID179", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID180", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID181", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID182", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID183", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID184", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID185", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID186", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID187", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID188", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID189", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID190", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID191", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID192", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID193", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID194", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID195", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID196", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID197", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID198", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID199", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID200", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, 1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID201", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID202", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID203", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID204", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID205", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID206", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID207", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID208", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]//FCE//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID209", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID210", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID211", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, 1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID212", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, 1}]]//FCE//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID213", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID214", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID215", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID216", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]//FCE//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID217", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID218", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID219", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID220", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]//FCE//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID221", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID222", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID223", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, 1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID224", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, 1}]]//FCE//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID225", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID226", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID227", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID228", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]//FCE//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID229", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID230", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID231", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID232", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]//FCE//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID233", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID234", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID235", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, 1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID236", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, 1}]]//FCE//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID237", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID238", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]//FCE//FCE", "CFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID239", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]//FCE//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID240", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]//FCE//FCE", "CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID251", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID252", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1, -1 + D], 0, 0, \ +{1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, {{q1, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID253", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}]]//FCE//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID254", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, m^2, {1, -1}]]//FCE//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID255", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4, -1 + D], 0, 0, \ +{1, -1}]]//FCE//FCE", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, {0, \ +-1}, 1}, {{q4, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID256", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID257", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1], 0, 0, {1, \ +-1}]]//FCE//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, {{q1, 0}, {0, -1}, 1}, Dimension -> \ +3]"}, +{"fcstFeynCalcExternalDouble-ID258", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, \ +-1}]]//FCE//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID259", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, m^2, {1, \ +-1}]]//FCE//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID260", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4], 0, 0, {1, \ +-1}]]//FCE//FCE", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, {0, \ +-1}, 1}, {{q4, 0}, {0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalDouble-ID261", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID262", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID263", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, -1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID264", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID265", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID266", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID267", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID268", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID269", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID270", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID271", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID272", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID273", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID274", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID275", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID276", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID277", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID278", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID279", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID280", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID281", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID282", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID283", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID284", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID285", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID286", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID287", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID288", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID289", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID290", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}, Dimension -> 4]"}, +{"fcstFeynCalcExternalDouble-ID291", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}, Dimension -> 4]"}, +{"fcstFeynCalcExternalDouble-ID292", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, n}, Dimension -> 4]"}, +{"fcstFeynCalcExternalDouble-ID293", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}, Dimension -> 4]"}, +{"fcstFeynCalcExternalDouble-ID294", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}, Dimension -> 4]"}, +{"fcstFeynCalcExternalDouble-ID295", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}, Dimension -> 4]"}, +{"fcstFeynCalcExternalDouble-ID296", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternalDouble-ID297", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternalDouble-ID298", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternalDouble-ID299", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID300", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID301", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID302", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID303", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID304", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID305", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID306", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID307", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID308", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID309", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID310", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID311", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID312", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID313", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID314", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID315", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID316", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]//FCE//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID317", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID318", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID319", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID320", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID321", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID322", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalDouble-ID323", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternalDouble-ID324", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternalDouble-ID325", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternalDouble-ID326", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID327", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID328", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID329", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID330", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID331", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID332", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID333", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID334", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID335", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID336", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID337", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID338", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID339", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID340", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID341", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID342", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID343", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID344", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID345", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID346", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID347", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID348", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID349", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID350", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID351", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID352", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID353", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID354", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID355", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, -1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID356", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID357", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID358", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID359", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID360", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID361", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID362", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID363", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID364", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID365", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID366", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID367", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, -1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID368", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID369", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID370", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID371", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID372", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID373", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID374", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID375", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID376", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID377", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID378", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, -1}]]//FCE//FCE", "SFAD[{{q, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID379", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, -1}]]//FCE//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID380", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID381", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID382", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID383", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]//FCE//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID384", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID385", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID386", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID387", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]//FCE//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID388", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID389", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID390", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID391", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, -1}]]//FCE//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalDouble-ID392", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID393", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID394", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID395", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]//FCE//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID396", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID397", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID398", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID399", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]//FCE//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID400", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID401", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID402", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID403", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, -1}]]//FCE//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalDouble-ID404", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID405", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID406", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID407", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]//FCE//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID408", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID409", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID410", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID411", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]//FCE//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID412", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID413", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID414", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +-1}]]//FCE//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalDouble-ID415", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, -1}]]//FCE//FCE", "SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"} + }; @@ -249,44 +3247,47 @@ Tests`Shared`fcstFeynCalcExternalTriple = { "LC[a, b, c][d]"}, {"fcstFeynCalcExternalTriple-ID12", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]//FCE//FCI//FCE", "LC[a, b, c, d]"}, - {"fcstFeynCalcExternalTriple-ID13", "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension->4]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID13", "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]//FCE//FCI//FCE", "LC[][a, b, c, d]"}, - {"fcstFeynCalcExternalTriple-ID14", "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension->4]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID14", "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]//FCE//FCI//FCE", "LC[a][b, c, d]"}, - {"fcstFeynCalcExternalTriple-ID15", "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension->4]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID15", "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]//FCE//FCI//FCE", "LC[a, b][c, d]"}, - {"fcstFeynCalcExternalTriple-ID16", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension->4]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID16", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]//FCE//FCI//FCE", "LC[a, b, c][d]"}, - {"fcstFeynCalcExternalTriple-ID17", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension->4]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID17", "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]//FCE//FCI//FCE", "LC[a, b, c, d]"}, - {"fcstFeynCalcExternalTriple-ID13", "Eps[Momentum[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID13", "Eps[Momentum[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]//FCE//FCI//FCE", "LCD[][a, b, c, d]"}, - {"fcstFeynCalcExternalTriple-ID14", "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID14", "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]//FCE//FCI//FCE", "LCD[a][b, c, d]"}, - {"fcstFeynCalcExternalTriple-ID15", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension->D]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID15", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]//FCE//FCI//FCE", "LCD[a, b][c, d]"}, - {"fcstFeynCalcExternalTriple-ID16", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension->D]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID16", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]//FCE//FCI//FCE", "LCD[a, b, c][d]"}, - {"fcstFeynCalcExternalTriple-ID17", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension->D]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID17", "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]//FCE//FCI//FCE", "LCD[a, b, c, d]"}, - {"fcstFeynCalcExternalTriple-ID18", "Eps[Momentum[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID18", "Eps[Momentum[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n]]//FCE//FCI//FCE", "LeviCivita[Dimension->n][a, b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternalTriple-ID19", "Eps[LorentzIndex[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID19", "Eps[LorentzIndex[a,n], Momentum[b,n], Momentum[c,n], Momentum[d,n]]//FCE//FCI//FCE", "LeviCivita[a,Dimension->n][b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternalTriple-ID20", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], Momentum[c,n], Momentum[d,n], Dimension->n]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID20", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], Momentum[c,n], Momentum[d,n]]//FCE//FCI//FCE", "LeviCivita[a, b,Dimension->n][c, d,Dimension->n]"}, - {"fcstFeynCalcExternalTriple-ID21", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], Momentum[d,n], Dimension->n]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID21", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], Momentum[d,n]]//FCE//FCI//FCE", "LeviCivita[a, b, c,Dimension->n][d,Dimension->n]"}, - {"fcstFeynCalcExternalTriple-ID22", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], LorentzIndex[d,n], Dimension->n]//FCE//FCI//FCE", + {"fcstFeynCalcExternalTriple-ID22", "Eps[LorentzIndex[a,n], LorentzIndex[b,n], LorentzIndex[c,n], LorentzIndex[d,n]]//FCE//FCI//FCE", "LeviCivita[a, b, c, d,Dimension->n]"}, - {"fcstFeynCalcExternalTriple-ID23", "FCE[FCI[FCE[FeynAmpDenominator[PropagatorDenominator[x, 0], - PropagatorDenominator[x2, 0]]]]]", "FAD[x, x2]"}, - {"fcstFeynCalcExternalTriple-ID24", "FCE[FCI[FCE[FeynAmpDenominator[PropagatorDenominator[x, m], - PropagatorDenominator[x2, m2]]]]]", "FAD[{x, m}, {x2, m2}]"}, + {"fcstFeynCalcExternalTriple-ID23", "FCE[FCI[FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[x,D], 0], + PropagatorDenominator[Momentum[x2,D], 0]]]]]", "FAD[x, x2]"}, + {"fcstFeynCalcExternalTriple-ID24", "FCE[FCI[FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[x,D], m], + PropagatorDenominator[Momentum[x2,D], m2]]]]]", "FAD[{x, m}, {x2, m2}]"}, {"fcstFeynCalcExternalTriple-ID24.1", "ChangeDimension[FCI[FAD[{p, m}, {p - k, m}]], 4] // FCE //FCI //FCE", "FAD[{p, m}, {-k + p, m}, Dimension -> 4]"}, + {"fcstFeynCalcExternalTriple-ID24.2", "FCE[FCI[FCE[FeynAmpDenominator[PropagatorDenominator[Momentum[p1, 2 + D], m1], PropagatorDenominator[Momentum[p1, 2 + D], m1], + PropagatorDenominator[Momentum[p2, 2 + D], m2], PropagatorDenominator[Momentum[p2, 2 + D], m2]] ]]]", + "FAD[{p1, m1}, {p1, m1}, {p2, m2}, {p2, m2}, Dimension -> 2 + D]"}, {"fcstFeynCalcExternalTriple-ID25", "FCE[FCI[FCE[Pair[LorentzIndex[a], LorentzIndex[b]]]]]", "MT[a, b]"}, - {"fcstFeynCalcExternalTriple-ID25.1", "FCE[FCI[FCE[Pair[ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]]]]]", "MT[0, 0]"}, + {"fcstFeynCalcExternalTriple-ID25.1", "FCE[FCI[FCE[Pair[ExplicitLorentzIndex[0], ExplicitLorentzIndex[0]]]]]", "1"}, {"fcstFeynCalcExternalTriple-ID26", "FCE[FCI[FCE[Pair[LorentzIndex[a, D], LorentzIndex[b, D]]]]]", "MTD[a, b]"}, {"fcstFeynCalcExternalTriple-ID29", "FCE[FCI[FCE[Pair[LorentzIndex[a, -4 + D], LorentzIndex[b, -4 + D]]]]]", "MTE[a,b]"}, @@ -295,7 +3296,7 @@ Tests`Shared`fcstFeynCalcExternalTriple = { {"fcstFeynCalcExternalTriple-ID31", "FCE[FCI[FCE[Pair[LorentzIndex[a, D], Momentum[p, D]]]]]", "FVD[p, a]"}, {"fcstFeynCalcExternalTriple-ID32", "FCE[FCI[FCE[Pair[LorentzIndex[a, -4 + D], Momentum[p, -4 + D]]]]]", "FVE[p,a]"}, - {"fcstFeynCalcExternalTriple-ID32.1", "FCE[FCI[FCE[Pair[ExplicitLorentzIndex[0], Momentum[a]]]]]", "FV[a, 0]"}, + {"fcstFeynCalcExternalTriple-ID32.1", "FCE[FCI[FCE[Pair[ExplicitLorentzIndex[0], Momentum[a]]]]]", "TC[a]"}, {"fcstFeynCalcExternalTriple-ID32.1", "FCE[FCI[FCE[Pair[ExplicitLorentzIndex[0], LorentzIndex[a]]]]]", "MT[a, 0]"}, {"fcstFeynCalcExternalTriple-ID33", "FCE[FCI[FCE[Pair[Momentum[OPEDelta], Momentum[p]]]]]", "SO[p]"}, {"fcstFeynCalcExternalTriple-ID34", "FCE[FCI[FCE[Pair[Momentum[OPEDelta], Momentum[p]]]]]", "SO[p]"}, @@ -309,6 +3310,7 @@ Tests`Shared`fcstFeynCalcExternalTriple = { {"fcstFeynCalcExternalTriple-ID40", "FCE[FCI[FCE[Pair[Momentum[k, D], Momentum[p, D]]]]]", "SPD[k, p]"}, {"fcstFeynCalcExternalTriple-ID41", "FCE[FCI[FCE[Pair[Momentum[k, -4 + D], Momentum[p, -4 + D]]]]]", "SPE[k,p]"}, {"fcstFeynCalcExternalTriple-ID41.1", "FCE[FCI[FCE[Pair[Momentum[p, D], -Momentum[q1, D] + Momentum[q2, D]]]]]", "SPD[p, -q1 + q2]"}, + {"fcstFeynCalcExternalTriple-ID41.2", "FCE[FCI[FCE[Pair[CartesianIndex[i], LorentzIndex[mu]]]]]", "Pair[CartesianIndex[i], LorentzIndex[mu]]"}, {"fcstFeynCalcExternalTriple-ID43", "FCE[FCI[FCE[SUND[SUNIndex[a], SUNIndex[b], SUNIndex[c]]]]]", "SUND[a, b, c]"}, {"fcstFeynCalcExternalTriple-ID44", "FCE[FCI[FCE[SUNDelta[a, b]]]]", "SD[a, b]"}, {"fcstFeynCalcExternalTriple-ID44-1", "FCE[FCI[FCE[SUNFDelta[a, b]]]]", "SDF[a, b]"}, @@ -328,5 +3330,1802 @@ Tests`Shared`fcstFeynCalcExternalTriple = { {"fcstFeynCalcExternalTriple-ID51", "FCE[FCI[FCE[SUNDeltaContract[a, b]]]]", "SD[a, b]"}, {"fcstFeynCalcExternalTriple-ID51-1", "FCE[FCI[FCE[SUNFDeltaContract[a, b]]]]", "SDF[a, b]"}, {"fcstFeynCalcExternalTriple-ID53", "FCE[FCI[FCE[Pair[Momentum[a, -4 + D], Momentum[b, -4 + D]]]]]", "SPE[a,b]"}, - {"fcstFeynCalcExternalTriple-ID54", "FCE[FCI[FCE[Power2[x, y]]]]", "x^y"} + {"fcstFeynCalcExternalTriple-ID54", "FCE[FCI[FCE[Power2[x, y]]]]", "x^y"}, +{"fcstFeynCalcExternalTriple-ID55", +"DiracIndexDelta[DiracIndex[i],DiracIndex[j]]//FCE//FCI//FCE", +"DIDelta[i, j]"}, +{"fcstFeynCalcExternalTriple-ID56", +"DiracIndexDelta[DiracIndex[1],DiracIndex[j]]//FCE//FCI//FCE", +"DIDelta[1, j]"}, +{"fcstFeynCalcExternalTriple-ID57", +"DiracIndexDelta[DiracIndex[3],DiracIndex[1]]//FCE//FCI//FCE", +"DIDelta[1, 3]"}, +{"fcstFeynCalcExternalTriple-ID58", +"DiracIndexDelta[DiracIndex[3],DiracIndex[3]]//FCE//FCI//FCE", +"DIDelta[3, 3]"}, +{"fcstFeynCalcExternalTriple-ID59", +"DiracIndexDelta[ExplicitDiracIndex[1],ExplicitDiracIndex[2]]\ +//FCE//FCI//FCE", "DIDelta[1, 2]"}, +{"fcstFeynCalcExternalTriple-ID60", +"DiracIndexDelta[ExplicitDiracIndex[3],ExplicitDiracIndex[3]]\ +//FCE//FCI//FCE", "DIDelta[3, 3]"}, +{"fcstFeynCalcExternalTriple-ID61", +"DiracIndexDelta[DiracIndex[i],DiracIndex[i]]//FCE//FCI//FCE", +"DIDelta[i, i]"}, +{"fcstFeynCalcExternalTriple-ID62", +"DiracIndexDelta[DiracIndex[i],0]//FCE//FCI//FCE", "DIDelta[0, i]"}, +{"fcstFeynCalcExternalTriple-ID63", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],\ +DiracIndex[j]]//FCE//FCI//FCE", "DCHN[GA[mu], i, j]"}, +{"fcstFeynCalcExternalTriple-ID64", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[1],\ +DiracIndex[j]]//FCE//FCI//FCE", "DCHN[GA[mu], 1, j]"}, +{"fcstFeynCalcExternalTriple-ID65", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[3],\ +DiracIndex[1]]//FCE//FCI//FCE", "DCHN[GA[mu], 3, 1]"}, +{"fcstFeynCalcExternalTriple-ID66", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[3],\ +DiracIndex[3]]//FCE//FCI//FCE", "DCHN[GA[mu], 3, 3]"}, +{"fcstFeynCalcExternalTriple-ID67", +"DiracChain[DiracGamma[LorentzIndex[mu]],ExplicitDiracIndex[1],\ +ExplicitDiracIndex[2]]//FCE//FCI//FCE", "DCHN[GA[mu], 1, 2]"}, +{"fcstFeynCalcExternalTriple-ID68", +"DiracChain[DiracGamma[LorentzIndex[mu]],ExplicitDiracIndex[3],\ +ExplicitDiracIndex[3]]//FCE//FCI//FCE", "DCHN[GA[mu], 3, 3]"}, +{"fcstFeynCalcExternalTriple-ID69", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],\ +DiracIndex[i]]//FCE//FCI//FCE", "DCHN[GA[mu], i, i]"}, +{"fcstFeynCalcExternalTriple-ID70", +"DiracChain[Spinor[Momentum[p],m],DiracIndex[i]]\ +//FCE//FCI//FCE", "DCHN[Spinor[Momentum[p], m, 1], i]"}, +{"fcstFeynCalcExternalTriple-ID71", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],Spinor[Momentum[p],m],DiracIndex[j]]//FCE//FCI//FCE", +"DCHN[GA[mu] . GSD[p], Spinor[Momentum[p], m, 1], j]"}, +{"fcstFeynCalcExternalTriple-ID72", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[i],Spinor[Momentum[p],m]]//FCE//FCI//FCE", +"DCHN[GA[mu] . GSD[p], i, Spinor[Momentum[p], m, 1]]"}, +{"fcstFeynCalcExternalTriple-ID73", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]\ +//FCE//FCI//FCE", +"DCHN[GA[mu] . GSD[p], Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcExternalTriple-ID74", +"DiracChain[1,Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]\ +//FCE//FCI//FCE", +"DCHN[1, Spinor[Momentum[p1], m1, 1], Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcExternalTriple-ID75", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}]]//FCE//FCI//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}]"}, +{"fcstFeynCalcExternalTriple-ID76", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}]]//FCE//FCI//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}]"}, +{"fcstFeynCalcExternalTriple-ID77", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}]]//FCE//FCI//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID78", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}]]//FCE//FCI//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID79", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, \ +1}]]//FCE//FCI//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, 4}]"}, +{"fcstFeynCalcExternalTriple-ID80", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, \ +-1}]]//FCE//FCI//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, 4}]"}, +{"fcstFeynCalcExternalTriple-ID81", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, \ +1}]]//FCE//FCI//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID82", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, \ +-1}]]//FCE//FCI//FCE", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID83", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {2, -1}], PropagatorDenominator[Momentum[p, D], m], \ +GenericPropagatorDenominator[1 + Pair[Momentum[p, D], Momentum[q, \ +D]]*Pair[Momentum[r, D], Momentum[s, D]], {2, -1}]]//FCE//FCI//FCE", +"FAD[{p, m}]*GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 2}, {{1 + SPD[p, \ +q]*SPD[r, s], -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID84", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {2, -1}], PropagatorDenominator[Momentum[p, D], m], \ +GenericPropagatorDenominator[1 + Pair[Momentum[p, D], Momentum[q, \ +D]]*Pair[Momentum[r, D], Momentum[s, D]], {2, -1}]]//FCE//FCI//FCE", +"FAD[{p, m}]*GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 2}, {{1 + SPD[p, \ +q]*SPD[r, s], -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID86", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID87", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID88", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID89", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID90", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID91", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID92", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID93", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID94", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID95", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID96", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID97", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID98", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID99", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID100", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID101", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID102", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID103", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID104", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID105", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID106", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID107", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID108", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID109", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID110", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID111", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID112", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID113", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID114", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID115", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID116", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID117", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID118", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID119", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID120", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID121", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID122", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID123", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID124", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID125", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID126", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID127", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID128", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID129", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID130", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE//FCI//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID131", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE//FCI//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID132", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE//FCI//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID133", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE//FCI//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID134", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE//FCI//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID135", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE//FCI//FCE", "CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID136", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]//FCE//FCI//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID137", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]//FCE//FCI//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID138", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]//FCE//FCI//FCE", "CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID139", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID140", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID141", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID142", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID143", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID144", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, -p1 . p2}, {m^2, -1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID145", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {1, \ +-1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID146", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {2, \ +-1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID147", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {n, \ +-1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2}, {m^2, -1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID148", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternalTriple-ID149", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternalTriple-ID150", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}, Dimension -> -4 \ ++ D]"}, +{"fcstFeynCalcExternalTriple-ID151", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID152", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID153", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID154", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID155", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID156", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID157", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID158", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID159", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID160", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID161", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID162", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, -p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID163", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID164", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID165", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID166", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID167", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID168", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID169", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID170", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID171", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID172", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID173", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID174", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID175", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID176", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, \ +1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID177", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID178", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID179", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID180", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID181", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID182", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID183", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID184", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID185", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID186", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID187", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID188", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, \ +1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID189", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID190", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID191", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID192", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID193", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID194", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID195", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID196", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID197", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID198", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID199", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, 1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID200", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, \ +1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID201", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID202", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID203", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID204", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID205", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID206", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID207", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID208", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID209", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID210", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID211", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, 1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID212", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, 1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID213", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID214", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID215", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID216", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID217", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID218", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID219", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID220", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID221", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID222", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID223", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, 1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID224", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, 1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID225", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID226", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID227", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID228", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID229", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID230", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID231", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID232", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID233", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID234", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID235", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, 1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID236", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, 1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID237", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID238", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID239", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]//FCE//FCI//FCE", "CFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID240", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]//FCE//FCI//FCE", +"CFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID251", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID252", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1, -1 + D], 0, 0, \ +{1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, {{q1, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID253", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID254", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, m^2, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID255", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4, -1 + D], 0, 0, \ +{1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, {0, \ +-1}, 1}, {{q4, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID256", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID257", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1], 0, 0, {1, \ +-1}]]//FCE//FCI//FCE", +"CFAD[{{q, 0}, {0, -1}, 1}, {{q1, 0}, {0, -1}, 1}, Dimension -> \ +3]"}, +{"fcstFeynCalcExternalTriple-ID258", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, \ +-1}]]//FCE//FCI//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID259", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, m^2, {1, \ +-1}]]//FCE//FCI//FCE", +"CFAD[{{q1, 0}, {m^2, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, \ +{m^2, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID260", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4], 0, 0, {1, \ +-1}]]//FCE//FCI//FCE", +"CFAD[{{q1, 0}, {0, -1}, 1}, {{q2, 0}, {0, -1}, 1}, {{q3, 0}, {0, \ +-1}, 1}, {{q4, 0}, {0, -1}, 1}, Dimension -> 3]"}, +{"fcstFeynCalcExternalTriple-ID261", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID262", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID263", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{q, -p1 . p2}, {m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID264", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID265", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{q, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID266", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID267", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID268", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID269", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID270", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID271", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID272", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID273", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID274", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID275", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID276", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID277", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID278", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID279", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID280", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID281", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID282", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID283", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID284", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID285", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID286", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID287", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID288", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID289", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID290", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}, Dimension -> 4]"}, +{"fcstFeynCalcExternalTriple-ID291", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}, Dimension -> 4]"}, +{"fcstFeynCalcExternalTriple-ID292", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, n}, Dimension -> 4]"}, +{"fcstFeynCalcExternalTriple-ID293", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}, Dimension -> 4]"}, +{"fcstFeynCalcExternalTriple-ID294", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}, Dimension -> 4]"}, +{"fcstFeynCalcExternalTriple-ID295", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}, Dimension -> 4]"}, +{"fcstFeynCalcExternalTriple-ID296", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternalTriple-ID297", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternalTriple-ID298", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}, Dimension -> \ +4]"}, +{"fcstFeynCalcExternalTriple-ID299", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID300", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID301", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID302", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID303", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID304", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID305", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID306", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID307", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID308", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID309", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID310", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID311", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID312", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID313", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID314", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID315", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID316", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID317", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID318", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID319", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, -p1 . p2}, {m^2, 1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID320", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 1}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID321", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, 2}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID322", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2}, {m^2, 1}, n}, Dimension -> -4 + D]"}, +{"fcstFeynCalcExternalTriple-ID323", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternalTriple-ID324", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternalTriple-ID325", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{q, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}, Dimension -> -4 + \ +D]"}, +{"fcstFeynCalcExternalTriple-ID326", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID327", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID328", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID329", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID330", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID331", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID332", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID333", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID334", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID335", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID336", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID337", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, -p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID338", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID339", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID340", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, x*p1 . p2}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID341", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID342", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID343", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, \ +1}]]//FCE//FCI//FCE", +"SFAD[{{0, x*p1 . p2 - 2*p3 . p4}, {m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID344", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID345", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID346", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID347", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID348", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID349", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID350", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID351", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID352", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, -1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID353", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, -1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID354", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, -1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID355", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, -1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID356", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID357", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID358", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID359", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID360", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID361", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID362", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID363", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID364", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, -1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID365", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, -1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID366", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, -1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID367", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, -1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID368", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID369", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID370", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID371", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID372", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID373", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID374", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID375", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID376", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, -1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID377", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, -1}]]//FCE//FCI//FCE", "SFAD[{{q, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID378", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, -1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID379", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, -1}]]//FCE//FCI//FCE", +"SFAD[{{q, 0}, {m2^2 - m1^2*x, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID380", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID381", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID382", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID383", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID384", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID385", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID386", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID387", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID388", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID389", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID390", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID391", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, -1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 1}]"}, +{"fcstFeynCalcExternalTriple-ID392", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID393", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID394", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID395", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID396", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID397", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID398", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID399", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID400", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID401", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID402", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID403", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, -1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, 2}]"}, +{"fcstFeynCalcExternalTriple-ID404", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID405", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID406", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID407", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID408", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID409", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID410", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID411", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, 1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID412", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {0, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID413", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID414", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +-1}]]//FCE//FCI//FCE", "SFAD[{{0, 0}, {-2*m^2, -1}, n}]"}, +{"fcstFeynCalcExternalTriple-ID415", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, -1}]]//FCE//FCI//FCE", +"SFAD[{{0, 0}, {m2^2 - m1^2*x, -1}, n}]"} + }; + +Tests`Shared`fcstCartesianFeynCalcExternal = +({ +{"fcstCartesianFeynCalcExternal-ID1", +"CartesianPair[CartesianIndex[i], CartesianMomentum[p]]//FCE", "CV[p, i]"}, +{"fcstCartesianFeynCalcExternal-ID2", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D]]//FCE", "CVD[p, i]"}, +{"fcstCartesianFeynCalcExternal-ID3", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianMomentum[p, -4 + D]]//FCE", "CVE[p, i]"}, +{"fcstCartesianFeynCalcExternal-ID4", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]//FCE", "TC[p]"}, +{"fcstCartesianFeynCalcExternal-ID5", +"CartesianPair[CartesianIndex[i], CartesianIndex[j]]//FCE", "KD[i, j]"}, +{"fcstCartesianFeynCalcExternal-ID6", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D]]//FCE", "KDD[i, j]"}, +{"fcstCartesianFeynCalcExternal-ID7", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[j, -4 + D]]//FCE", "KDE[i, j]"}, +{"fcstCartesianFeynCalcExternal-ID8", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]//FCE", "CSP[a, b]"}, +{"fcstCartesianFeynCalcExternal-ID9", +"CartesianPair[CartesianMomentum[a, -1 + D], CartesianMomentum[b, -1 + D]]//FCE", +"CSPD[a, b]"}, +{"fcstCartesianFeynCalcExternal-ID10", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]//FCE", +"CSPE[a, b]"}, +{"fcstCartesianFeynCalcExternal-ID11", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]//FCE", "CLC[i, j, k]"}, +{"fcstCartesianFeynCalcExternal-ID12", +"Eps[CartesianIndex[p], CartesianMomentum[i], CartesianMomentum[j]]//FCE", +"CLC[p][i, j]"}, +{"fcstCartesianFeynCalcExternal-ID13", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]//FCE", "CLC[i, j, k]"}, +{"fcstCartesianFeynCalcExternal-ID14", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianMomentum[p]]//FCE", "CLC[i, j][p]"}, +{"fcstCartesianFeynCalcExternal-ID15", +"Eps[CartesianIndex[i], CartesianMomentum[p], CartesianMomentum[q]]//FCE", +"CLC[i][p, q]"}, +{"fcstCartesianFeynCalcExternal-ID16", +"Eps[CartesianMomentum[p], CartesianMomentum[q], CartesianMomentum[r]]//FCE", +"CLC[][p, q, r]"}, +{"fcstCartesianFeynCalcExternal-ID17", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + \ +D]]//FCE", "CLCD[i, j, k]"}, +{"fcstCartesianFeynCalcExternal-ID18", +"Eps[CartesianIndex[p, -1 + D], CartesianMomentum[i, -1 + D], CartesianMomentum[j, -1 + \ +D]]//FCE", "CLCD[p][i, j]"}, +{"fcstCartesianFeynCalcExternal-ID19", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + \ +D]]//FCE", "CLCD[i, j, k]"}, +{"fcstCartesianFeynCalcExternal-ID20", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianMomentum[p, -1 + \ +D]]//FCE", "CLCD[i, j][p]"}, +{"fcstCartesianFeynCalcExternal-ID21", +"Eps[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + \ +D]]//FCE", "CLCD[i][p, q]"}, +{"fcstCartesianFeynCalcExternal-ID22", +"Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D], CartesianMomentum[r, -1 + \ +D]]//FCE", "CLCD[][p, q, r]"}, +{"fcstCartesianFeynCalcExternal-ID23", "DiracGamma[CartesianIndex[i]]//FCE", + "CGA[i]"}, +{"fcstCartesianFeynCalcExternal-ID24", +"DiracGamma[CartesianIndex[i, -1 + D], D]//FCE", "CGAD[i]"}, +{"fcstCartesianFeynCalcExternal-ID25", +"DiracGamma[CartesianIndex[i, -4 + D], -4 + D]//FCE", "CGAE[i]"}, +{"fcstCartesianFeynCalcExternal-ID26", "DiracGamma[ExplicitLorentzIndex[0]]//FCE", +"TGA[]"}, +{"fcstCartesianFeynCalcExternal-ID27", +"DiracGamma[CartesianMomentum[p]]//FCE", "CGS[p]"}, +{"fcstCartesianFeynCalcExternal-ID28", +"DiracGamma[CartesianMomentum[p, -1 + D], D]//FCE", "CGSD[p]"}, +{"fcstCartesianFeynCalcExternal-ID29", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]//FCE", "CGSE[p]"}, +{"fcstCartesianFeynCalcExternal-ID30", +"PauliSigma[LorentzIndex[mu]]//FCE", "SI[mu]"}, +{"fcstCartesianFeynCalcExternal-ID31", +"PauliSigma[LorentzIndex[mu, D], -1 + D]//FCE", "SID[mu]"}, +{"fcstCartesianFeynCalcExternal-ID32", +"PauliSigma[LorentzIndex[mu, -4 + D], -4 + D]//FCE", "SIE[mu]"}, +{"fcstCartesianFeynCalcExternal-ID33", +"PauliSigma[Momentum[p]]//FCE", "SIS[p]"}, +{"fcstCartesianFeynCalcExternal-ID34", +"PauliSigma[Momentum[p, D], -1 + D]//FCE", "SISD[p]"}, +{"fcstCartesianFeynCalcExternal-ID35", +"PauliSigma[Momentum[p, -4 + D], -4 + D]//FCE", "SISE[p]"}, +{"fcstCartesianFeynCalcExternal-ID36", "PauliSigma[CartesianIndex[i]]//FCE", + "CSI[i]"}, +{"fcstCartesianFeynCalcExternal-ID37", +"PauliSigma[CartesianIndex[i, -1 + D], -1 + D]//FCE", "CSID[i]"}, +{"fcstCartesianFeynCalcExternal-ID38", +"PauliSigma[CartesianIndex[i, -4 + D], -4 + D]//FCE", "CSIE[i]"}, +{"fcstCartesianFeynCalcExternal-ID39", +"PauliSigma[CartesianMomentum[p]]//FCE", "CSIS[p]"}, +{"fcstCartesianFeynCalcExternal-ID40", +"PauliSigma[CartesianMomentum[p, -1 + D], -1 + D]//FCE", "CSISD[p]"}, +{"fcstCartesianFeynCalcExternal-ID41", +"PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]//FCE", "CSISE[p]"} +}) + +Tests`Shared`fcstCartesianFeynCalcExternalDouble = +({ +{"fcstCartesianFeynCalcExternalDouble-ID1", +"CartesianPair[CartesianIndex[i], CartesianMomentum[p]]//FCE//FCE", "CV[p, i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID2", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D]]//FCE//FCE", +"CVD[p, i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID3", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianMomentum[p, -4 + D]]//FCE//FCE", +"CVE[p, i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID4", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]//FCE//FCE", "TC[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID5", +"CartesianPair[CartesianIndex[i], CartesianIndex[j]]//FCE//FCE", "KD[i, j]"}, +{"fcstCartesianFeynCalcExternalDouble-ID6", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D]]//FCE//FCE", +"KDD[i, j]"}, +{"fcstCartesianFeynCalcExternalDouble-ID7", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[j, -4 + D]]//FCE//FCE", +"KDE[i, j]"}, +{"fcstCartesianFeynCalcExternalDouble-ID8", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]//FCE//FCE", "CSP[a, b]"}, +{"fcstCartesianFeynCalcExternalDouble-ID9", +"CartesianPair[CartesianMomentum[a, -1 + D], CartesianMomentum[b, -1 + D]]//FCE//FCE", +"CSPD[a, b]"}, +{"fcstCartesianFeynCalcExternalDouble-ID10", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]//FCE//FCE", +"CSPE[a, b]"}, +{"fcstCartesianFeynCalcExternalDouble-ID11", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]//FCE//FCE", "CLC[i, j, k]"}, +{"fcstCartesianFeynCalcExternalDouble-ID12", +"Eps[CartesianIndex[p], CartesianMomentum[i], CartesianMomentum[j]]//FCE//FCE", +"CLC[p][i, j]"}, +{"fcstCartesianFeynCalcExternalDouble-ID13", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]//FCE//FCE", "CLC[i, j, k]"}, +{"fcstCartesianFeynCalcExternalDouble-ID14", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianMomentum[p]]//FCE//FCE", +"CLC[i, j][p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID15", +"Eps[CartesianIndex[i], CartesianMomentum[p], CartesianMomentum[q]]//FCE//FCE", +"CLC[i][p, q]"}, +{"fcstCartesianFeynCalcExternalDouble-ID16", +"Eps[CartesianMomentum[p], CartesianMomentum[q], CartesianMomentum[r]]//FCE//FCE", +"CLC[][p, q, r]"}, +{"fcstCartesianFeynCalcExternalDouble-ID17", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + \ +D]]//FCE//FCE", "CLCD[i, j, k]"}, +{"fcstCartesianFeynCalcExternalDouble-ID18", +"Eps[CartesianIndex[p, -1 + D], CartesianMomentum[i, -1 + D], CartesianMomentum[j, -1 + \ +D]]//FCE//FCE", "CLCD[p][i, j]"}, +{"fcstCartesianFeynCalcExternalDouble-ID19", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + \ +D]]//FCE//FCE", "CLCD[i, j, k]"}, +{"fcstCartesianFeynCalcExternalDouble-ID20", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianMomentum[p, -1 + \ +D]]//FCE//FCE", "CLCD[i, j][p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID21", +"Eps[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + \ +D]]//FCE//FCE", "CLCD[i][p, q]"}, +{"fcstCartesianFeynCalcExternalDouble-ID22", +"Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D], CartesianMomentum[r, -1 + \ +D]]//FCE//FCE", "CLCD[][p, q, r]"}, +{"fcstCartesianFeynCalcExternalDouble-ID23", +"DiracGamma[CartesianIndex[i]]//FCE//FCE", "CGA[i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID24", +"DiracGamma[CartesianIndex[i, -1 + D], D]//FCE//FCE", "CGAD[i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID25", +"DiracGamma[CartesianIndex[i, -4 + D], -4 + D]//FCE//FCE", "CGAE[i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID26", +"DiracGamma[ExplicitLorentzIndex[0]]//FCE//FCE", "TGA[]"}, +{"fcstCartesianFeynCalcExternalDouble-ID27", +"DiracGamma[CartesianMomentum[p]]//FCE//FCE", "CGS[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID28", +"DiracGamma[CartesianMomentum[p, -1 + D], D]//FCE//FCE", "CGSD[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID29", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]//FCE//FCE", "CGSE[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID30", +"PauliSigma[LorentzIndex[mu]]//FCE//FCE", "SI[mu]"}, +{"fcstCartesianFeynCalcExternalDouble-ID31", +"PauliSigma[LorentzIndex[mu, D], -1 + D]//FCE//FCE", "SID[mu]"}, +{"fcstCartesianFeynCalcExternalDouble-ID32", +"PauliSigma[LorentzIndex[mu, -4 + D], -4 + D]//FCE//FCE", +"SIE[mu]"}, +{"fcstCartesianFeynCalcExternalDouble-ID33", +"PauliSigma[Momentum[p]]//FCE//FCE", "SIS[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID34", +"PauliSigma[Momentum[p, D], -1 + D]//FCE//FCE", "SISD[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID35", +"PauliSigma[Momentum[p, -4 + D], -4 + D]//FCE//FCE", "SISE[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID36", +"PauliSigma[CartesianIndex[i]]//FCE//FCE", "CSI[i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID37", +"PauliSigma[CartesianIndex[i, -1 + D], -1 + D]//FCE//FCE", "CSID[i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID38", +"PauliSigma[CartesianIndex[i, -4 + D], -4 + D]//FCE//FCE", "CSIE[i]"}, +{"fcstCartesianFeynCalcExternalDouble-ID39", +"PauliSigma[CartesianMomentum[p]]//FCE//FCE", "CSIS[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID40", +"PauliSigma[CartesianMomentum[p, -1 + D], -1 + D]//FCE//FCE", "CSISD[p]"}, +{"fcstCartesianFeynCalcExternalDouble-ID41", +"PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]//FCE//FCE", "CSISE[p]"} +}) + +Tests`Shared`fcstCartesianFeynCalcExternalTriple = +({ +{"fcstCartesianFeynCalcExternalTriple-ID1", +"CartesianPair[CartesianIndex[i], CartesianMomentum[p]]//FCE//FCI//FCE", "CV[p, i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID2", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D]]//FCE//FCI//FCE", +"CVD[p, i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID3", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianMomentum[p, -4 + D]]//FCE//FCI//FCE", +"CVE[p, i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID4", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]//FCE//FCI//FCE", "TC[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID5", +"CartesianPair[CartesianIndex[i], CartesianIndex[j]]//FCE//FCI//FCE", "KD[i, j]"}, +{"fcstCartesianFeynCalcExternalTriple-ID6", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D]]//FCE//FCI//FCE", +"KDD[i, j]"}, +{"fcstCartesianFeynCalcExternalTriple-ID7", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[j, -4 + D]]//FCE//FCI//FCE", +"KDE[i, j]"}, +{"fcstCartesianFeynCalcExternalTriple-ID8", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]//FCE//FCI//FCE", "CSP[a, b]"}, +{"fcstCartesianFeynCalcExternalTriple-ID9", +"CartesianPair[CartesianMomentum[a, -1 + D], CartesianMomentum[b, -1 + D]]//FCE//FCI//FCE", + "CSPD[a, b]"}, +{"fcstCartesianFeynCalcExternalTriple-ID10", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]//FCE//FCI//FCE", + "CSPE[a, b]"}, +{"fcstCartesianFeynCalcExternalTriple-ID11", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]//FCE//FCI//FCE", +"CLC[i, j, k]"}, +{"fcstCartesianFeynCalcExternalTriple-ID12", +"Eps[CartesianIndex[p], CartesianMomentum[i], CartesianMomentum[j]]//FCE//FCI//FCE", +"CLC[p][i, j]"}, +{"fcstCartesianFeynCalcExternalTriple-ID13", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]//FCE//FCI//FCE", +"CLC[i, j, k]"}, +{"fcstCartesianFeynCalcExternalTriple-ID14", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianMomentum[p]]//FCE//FCI//FCE", +"CLC[i, j][p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID15", +"Eps[CartesianIndex[i], CartesianMomentum[p], CartesianMomentum[q]]//FCE//FCI//FCE", +"CLC[i][p, q]"}, +{"fcstCartesianFeynCalcExternalTriple-ID16", +"Eps[CartesianMomentum[p], CartesianMomentum[q], CartesianMomentum[r]]//FCE//FCI//FCE", +"CLC[][p, q, r]"}, +{"fcstCartesianFeynCalcExternalTriple-ID17", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + \ +D]]//FCE//FCI//FCE", "CLCD[i, j, k]"}, +{"fcstCartesianFeynCalcExternalTriple-ID18", +"Eps[CartesianIndex[p, -1 + D], CartesianMomentum[i, -1 + D], CartesianMomentum[j, -1 + \ +D]]//FCE//FCI//FCE", "CLCD[p][i, j]"}, +{"fcstCartesianFeynCalcExternalTriple-ID19", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + \ +D]]//FCE//FCI//FCE", "CLCD[i, j, k]"}, +{"fcstCartesianFeynCalcExternalTriple-ID20", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianMomentum[p, -1 + \ +D]]//FCE//FCI//FCE", "CLCD[i, j][p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID21", +"Eps[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + \ +D]]//FCE//FCI//FCE", "CLCD[i][p, q]"}, +{"fcstCartesianFeynCalcExternalTriple-ID22", +"Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D], CartesianMomentum[r, -1 + \ +D]]//FCE//FCI//FCE", "CLCD[][p, q, r]"}, +{"fcstCartesianFeynCalcExternalTriple-ID23", +"DiracGamma[CartesianIndex[i]]//FCE//FCI//FCE", "CGA[i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID24", +"DiracGamma[CartesianIndex[i, -1 + D], D]//FCE//FCI//FCE", "CGAD[i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID25", +"DiracGamma[CartesianIndex[i, -4 + D], -4 + D]//FCE//FCI//FCE", +"CGAE[i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID26", +"DiracGamma[ExplicitLorentzIndex[0]]//FCE//FCI//FCE", "TGA[]"}, +{"fcstCartesianFeynCalcExternalTriple-ID27", +"DiracGamma[CartesianMomentum[p]]//FCE//FCI//FCE", "CGS[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID28", +"DiracGamma[CartesianMomentum[p, -1 + D], D]//FCE//FCI//FCE", "CGSD[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID29", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]//FCE//FCI//FCE", +"CGSE[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID30", +"PauliSigma[LorentzIndex[mu]]//FCE//FCI//FCE", "SI[mu]"}, +{"fcstCartesianFeynCalcExternalTriple-ID31", +"PauliSigma[LorentzIndex[mu, D], -1 + D]//FCE//FCI//FCE", +"SID[mu]"}, +{"fcstCartesianFeynCalcExternalTriple-ID32", +"PauliSigma[LorentzIndex[mu, -4 + D], -4 + D]//FCE//FCI//FCE", +"SIE[mu]"}, +{"fcstCartesianFeynCalcExternalTriple-ID33", +"PauliSigma[Momentum[p]]//FCE//FCI//FCE", "SIS[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID34", +"PauliSigma[Momentum[p, D], -1 + D]//FCE//FCI//FCE", "SISD[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID35", +"PauliSigma[Momentum[p, -4 + D], -4 + D]//FCE//FCI//FCE", +"SISE[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID36", +"PauliSigma[CartesianIndex[i]]//FCE//FCI//FCE", "CSI[i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID37", +"PauliSigma[CartesianIndex[i, -1 + D], -1 + D]//FCE//FCI//FCE", +"CSID[i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID38", +"PauliSigma[CartesianIndex[i, -4 + D], -4 + D]//FCE//FCI//FCE", +"CSIE[i]"}, +{"fcstCartesianFeynCalcExternalTriple-ID39", +"PauliSigma[CartesianMomentum[p]]//FCE//FCI//FCE", "CSIS[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID40", +"PauliSigma[CartesianMomentum[p, -1 + D], -1 + D]//FCE//FCI//FCE", +"CSISD[p]"}, +{"fcstCartesianFeynCalcExternalTriple-ID41", +"PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]//FCE//FCI//FCE", +"CSISE[p]"} +}); diff --git a/Tests/Shared/FeynCalcInternal.test b/Tests/Shared/FeynCalcInternal.test index f7c43bdf5..5a679fbbf 100644 --- a/Tests/Shared/FeynCalcInternal.test +++ b/Tests/Shared/FeynCalcInternal.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. -Copyright (C) 1990-2016 Rolf Mertig -Copyright (C) 1997-2016 Frederik Orellana -Copyright (C) 2014-2016 Vladyslav Shtabovenko +Copyright (C) 1990-2018 Rolf Mertig +Copyright (C) 1997-2018 Frederik Orellana +Copyright (C) 2014-2018 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for FeynCalcInternal *) @@ -14,7 +14,7 @@ Copyright (C) 2014-2016 Vladyslav Shtabovenko (* ------------------------------------------------------------------------ *) Tests`Shared`fcstFeynCalcInternal = { - {"fcstFeynCalcInternal-ID1", "$BreitMaison=False;\nFCI[SpinorU[p]]", "Spinor[Momentum[p], 0, 1]"}, + {"fcstFeynCalcInternal-ID1", "FCSetDiracGammaScheme[\"NDR\"];\nFCI[SpinorU[p]]", "Spinor[Momentum[p], 0, 1]"}, {"fcstFeynCalcInternal-ID2", "FCI[SpinorU[p, 0]]", "Spinor[Momentum[p], 0, 1]"}, {"fcstFeynCalcInternal-ID3", "FCI[SpinorU[p, 0, 1]]", "Spinor[Momentum[p], 0, 1]"}, {"fcstFeynCalcInternal-ID4", "FCI[SpinorU[p, m]]", "Spinor[Momentum[p], m, 1]"}, @@ -134,59 +134,64 @@ Tests`Shared`fcstFeynCalcInternal = { {"fcstFeynCalcInternal-ID64.1", "FCI[FAD[q1, {-p + q1, m},Dimension->4]]", "FeynAmpDenominator[PropagatorDenominator[Momentum[q1], 0], PropagatorDenominator[-Momentum[p] + Momentum[q1], m]]"}, + {"fcstFeynCalcInternal-ID64.2", "FCI[FAD[0]]", "FeynAmpDenominator[PropagatorDenominator[0, 0]]"}, + + + {"fcstFeynCalcInternal-ID64.3", "FCI[FAD[{p, m}, Dimension -> ss]]", "FeynAmpDenominator[PropagatorDenominator[Momentum[p, ss], m]]"}, + {"fcstFeynCalcInternal-ID65", "FCI[FVD[p, mu]]", "Pair[LorentzIndex[mu, D], Momentum[p, D]]"}, {"fcstFeynCalcInternal-ID66", "FCI[FV[p, mu]]", "Pair[LorentzIndex[mu], Momentum[p]]"}, {"fcstFeynCalcInternal-ID66.1", "FCI[FVE[p, mu]]", "Pair[LorentzIndex[mu,D-4], Momentum[p,D-4]]"}, {"fcstFeynCalcInternal-ID67", "LC[a, b, c, d]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternal-ID67.1", "LCD[a, b, c, d]//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]"}, {"fcstFeynCalcInternal-ID67.2", "LC[][a, b, c, d]//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.3", "LCD[][a, b, c, d]//FCI", - "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D], Dimension -> D]"}, + "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D]]"}, {"fcstFeynCalcInternal-ID67.4", "LC[a][ b, c, d]//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.5", "LC[a, b][ c, d]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.6", "LC[a, b, c][ d]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.7", "LCD[a][ b, c, d]//FCI", - "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternal-ID67.8", "LCD[a, b][ c, d]//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternal-ID67.9", "LCD[a, b, c][ d]//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternal-ID67.10", "LeviCivita[a, b, c, d, FCI->False]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternal-ID67.11", "LeviCivita[a, b, c, d, Dimension->4, FCI->False]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternal-ID67.12", "LeviCivita[a, b, c, d, Dimension->D, FCI->False]//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]"}, {"fcstFeynCalcInternal-ID67.13", "LeviCivita[FCI->False][a, b, c, d, FCI->False]//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.14", "LeviCivita[FCI->False][a, b, c, d, Dimension->4, FCI->False]//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.15", "LeviCivita[Dimension->D, FCI->False][a, b, c, d, Dimension->D, FCI->False]//FCI", - "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D], Dimension -> D]"}, + "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D]]"}, {"fcstFeynCalcInternal-ID67.16", "LeviCivita[a, FCI->False][ b, c, d, FCI->False]//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.17", "LeviCivita[a, Dimension->4, FCI->False][ b, c, d, Dimension->4, FCI->False]//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.18", "LeviCivita[a, Dimension->D, FCI->False][ b, c, d, Dimension->D, FCI->False]//FCI", - "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternal-ID67.19", "LeviCivita[a, b, FCI->False][ c, d, FCI->False]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.20", "LeviCivita[a, b, Dimension->4, FCI->False][ c, d, Dimension->4, FCI->False]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.21", "LeviCivita[a, b, Dimension->D, FCI->False][ c, d, Dimension->D, FCI->False]//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternal-ID67.22", "LeviCivita[a, b, c, FCI->False][ d, FCI->False]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.23", "LeviCivita[a, b, c, Dimension->4, FCI->False][d, Dimension->4, FCI->False]//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternal-ID67.24", "LeviCivita[a, b, c, Dimension->D, FCI->False][d, Dimension->D, FCI->False]//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternal-ID71", "FCI[MT[a, b]]", "Pair[LorentzIndex[a], LorentzIndex[b]]"}, {"fcstFeynCalcInternal-ID72", "FCI[MTD[a, b]]", "Pair[LorentzIndex[a, D], LorentzIndex[b, D]]"}, {"fcstFeynCalcInternal-ID72.1", "FCI[MTE[a, b]]", "Pair[LorentzIndex[a, D-4], LorentzIndex[b, D-4]]"}, @@ -205,8 +210,1473 @@ PropagatorDenominator[-Momentum[p] + Momentum[q1], m]]"}, {"fcstFeynCalcInternal-ID84.1", "FCI[SPE[a, b]]", "Pair[Momentum[a, D-4], Momentum[b, D-4]]"}, {"fcstFeynCalcInternal-ID85", "FCI[SO[a]]", "Pair[Momentum[a], Momentum[OPEDelta]]"}, {"fcstFeynCalcInternal-ID86", "FCI[SOD[a]]", "Pair[Momentum[a, D], Momentum[OPEDelta, D]]"}, - {"fcstFeynCalcInternal-ID87", "FCI[PropagatorDenominator[p, m]]", "PropagatorDenominator[Momentum[p, D], m]"}, - {"fcstFeynCalcInternal-ID88", "FCI[PropagatorDenominator[Momentum[p + q], m]]", "PropagatorDenominator[Momentum[p] + Momentum[q], m]"} + {"fcstFeynCalcInternal-ID87", "FCI[PropagatorDenominator[Momentum[p,D], m]]", "PropagatorDenominator[Momentum[p, D], m]"}, + {"fcstFeynCalcInternal-ID88", "FCI[PropagatorDenominator[Momentum[p + q], m]]", "PropagatorDenominator[Momentum[p + q], m]"}, +{"fcstFeynCalcInternal-ID89", "DIDelta[i,j]//FCI", +"DiracIndexDelta[DiracIndex[i], DiracIndex[j]]"}, +{"fcstFeynCalcInternal-ID90", "DIDelta[i,2]//FCI", +"DiracIndexDelta[DiracIndex[i], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternal-ID91", "DIDelta[1,2]//FCI", +"DiracIndexDelta[ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternal-ID92", "DIDelta[2,2]//FCI", +"DiracIndexDelta[ExplicitDiracIndex[2], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternal-ID93", "DIDelta[i,i]//FCI", +"DiracIndexDelta[DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternal-ID94", "DCHN[GA[mu],i,j]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], \ +DiracIndex[j]]"}, +{"fcstFeynCalcInternal-ID95", "DCHN[GA[mu],1,j]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternal-ID96", "DCHN[GA[mu],3,1]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternal-ID97", "DCHN[GA[mu],3,3]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternal-ID98", "DCHN[GA[mu],1,2]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternal-ID99", "DCHN[GA[mu],i,i]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], \ +DiracIndex[i]]"}, +{"fcstFeynCalcInternal-ID100", "DCHN[GA[mu].GSD[p],i,j]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], DiracIndex[j]]"}, +{"fcstFeynCalcInternal-ID101", "DCHN[GA[mu].GSD[p],1,j]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternal-ID102", "DCHN[GA[mu].GSD[p],3,1]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternal-ID103", "DCHN[GA[mu].GSD[p],3,3]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternal-ID104", "DCHN[GA[mu].GSD[p],1,2]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[1], \ +ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternal-ID105", "DCHN[GA[mu].GSD[p],i,i]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternal-ID106", +"DCHN[GA[mu].(m+GS[p]).GA[nu],1,j]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternal-ID107", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,1]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternal-ID108", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,3]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternal-ID109", +"DCHN[GA[mu].(m+GS[p]).GA[nu],1,2]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternal-ID110", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,3]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternal-ID111", +"DCHN[GA[mu].(m+GS[p]).GA[nu],i,i]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternal-ID112", "DCHN[Spinor[Momentum[p],m],i]//FCI", + "DiracChain[Spinor[Momentum[p], m, 1], DiracIndex[i]]"}, +{"fcstFeynCalcInternal-ID112.1", "DCHN[i, Spinor[Momentum[p],m]]//FCI", + "DiracChain[DiracIndex[i], Spinor[Momentum[p], m, 1]]"}, +{"fcstFeynCalcInternal-ID113", +"DCHN[GA[mu].GSD[p],Spinor[Momentum[p],m],j]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], Spinor[Momentum[p], m, 1], \ +DiracIndex[j]]"}, +{"fcstFeynCalcInternal-ID114", +"DCHN[GA[mu].GSD[p],i,Spinor[Momentum[p],m]]//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], Spinor[Momentum[p], m, \ +1]]"}, +{"fcstFeynCalcInternal-ID115", +"DCHN[GA[mu].GSD[p],Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]\ +]//FCI", "DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcInternal-ID116", +"DCHN[1,Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]//FCI", +"DiracChain[1, Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, + +{"fcstFeynCalcInternal-ID117", "GFAD[{{SPD[q, q]}, 2}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {2, 1}]]"}, +{"fcstFeynCalcInternal-ID118", "GFAD[{{SPD[q, q], -1}}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, -1}]]"}, +{"fcstFeynCalcInternal-ID119", "GFAD[{{SPD[q, q]}, 1}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternal-ID120", "GFAD[{{SPD[q, q], 1}}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternal-ID121", "GFAD[{{SPD[q, q]}}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternal-ID122", "GFAD[{SPD[q, q]}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternal-ID123", "GFAD[{SPD[q, q]}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternal-ID124", +"GFAD[{SPD[q, q]}, EtaSign -> -1]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, -1}]]"}, +{"fcstFeynCalcInternal-ID125", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}]]"}, +{"fcstFeynCalcInternal-ID126", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}]]"}, +{"fcstFeynCalcInternal-ID127", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}]]"}, +{"fcstFeynCalcInternal-ID128", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}]]"}, +{"fcstFeynCalcInternal-ID129", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, 4}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, 1}]]"}, +{"fcstFeynCalcInternal-ID130", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, 4}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, -1}]]"}, +{"fcstFeynCalcInternal-ID131", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, n}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, 1}]]"}, +{"fcstFeynCalcInternal-ID132", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, n}]//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, -1}]]"}, + +{"fcstFeynCalcInternal-ID125", "CFAD[{{q, -p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID126", +"CFAD[{{q, -p1 . p2}, m^2}, EtaSign -> 1]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID127", +"CFAD[{{q, -p1 . p2}, {m^2, -1}}, EtaSign -> 1]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID128", "CFAD[{{q, -p1 . p2}, m^2, 2}]//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID129", "CFAD[{{q, -p1 . p2}, m^2, n}]//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID130", "CFAD[{{q, x*p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID131", +"CFAD[{{q, x*p1 . p2}, m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID132", +"CFAD[{{q, x*p1 . p2}, m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID133", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID134", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID135", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID136", "CFAD[{0, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID137", "CFAD[{0, m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID138", "CFAD[{0, m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID139", "CFAD[{{0, p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID140", "CFAD[{{0, p1 . p2}, m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID141", "CFAD[{{0, p1 . p2}, m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID142", "CFAD[{{0, -p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID143", "CFAD[{{0, -p1 . p2}, m^2, 2}]//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID144", "CFAD[{{0, -p1 . p2}, m^2, n}]//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID145", "CFAD[{{0, -p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID146", "CFAD[{{0, -p1 . p2}, m^2, 2}]//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID147", "CFAD[{{0, -p1 . p2}, m^2, n}]//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID148", "CFAD[{{0, x*p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID149", +"CFAD[{{0, x*p1 . p2}, m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID150", +"CFAD[{{0, x*p1 . p2}, m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID151", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID152", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID153", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID154", +"CFAD[{{q, -p1 . p2}, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID155", +"CFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID156", +"CFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID157", +"CFAD[{{q, x*p1 . p2}, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID158", +"CFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID159", +"CFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID160", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID161", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID162", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID163", +"CFAD[{0, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID164", +"CFAD[{0, m^2, 2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID165", +"CFAD[{0, m^2, n}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID166", +"CFAD[{{0, p1 . p2}, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID167", +"CFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID168", +"CFAD[{{0, p1 . p2}, m^2, n}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID169", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternal-ID170", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternal-ID171", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternal-ID172", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternal-ID173", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternal-ID174", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternal-ID175", +"CFAD[{{0, x*p1 . p2}, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternal-ID176", +"CFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternal-ID177", +"CFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternal-ID178", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternal-ID179", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternal-ID180", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternal-ID181", +"CFAD[{{q, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID182", +"CFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID183", +"CFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID184", +"CFAD[{{q, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID185", +"CFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID186", +"CFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID187", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID188", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID189", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID190", +"CFAD[{0, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID191", +"CFAD[{0, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID192", +"CFAD[{0, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID193", +"CFAD[{{0, p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID194", +"CFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID195", +"CFAD[{{0, p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID196", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID197", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID198", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID199", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID200", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID201", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID202", +"CFAD[{{0, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID203", +"CFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID204", +"CFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID205", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID206", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID207", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID208", "CFAD[{q, 0}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID209", "CFAD[{q, -m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID210", "CFAD[{q, -2*m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID211", "CFAD[{q, m2^2 - m1^2*x}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID212", "CFAD[{q, {0, 1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID213", "CFAD[{q, {-m^2, 1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID214", "CFAD[{q, {-2*m^2, 1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID215", "CFAD[{q, {m2^2 - m1^2*x, 1}}]//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID216", "CFAD[{q, {0, -1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID217", "CFAD[{q, {-m^2, -1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID218", "CFAD[{q, {-2*m^2, -1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID219", +"CFAD[{q, {m2^2 - m1^2*x, -1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID220", "CFAD[{q, 0, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID221", "CFAD[{q, -m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID222", "CFAD[{q, -2*m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID223", "CFAD[{q, m2^2 - m1^2*x, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID224", "CFAD[{q, {0, 1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID225", "CFAD[{q, {-m^2, 1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID226", "CFAD[{q, {-2*m^2, 1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID227", +"CFAD[{q, {m2^2 - m1^2*x, 1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID228", "CFAD[{q, {0, -1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID229", "CFAD[{q, {-m^2, -1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID230", "CFAD[{q, {-2*m^2, -1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID231", +"CFAD[{q, {m2^2 - m1^2*x, -1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID232", "CFAD[{q, 0, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID233", "CFAD[{q, -m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID234", "CFAD[{q, -2*m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID235", "CFAD[{q, m2^2 - m1^2*x, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID236", "CFAD[{q, {0, 1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID237", "CFAD[{q, {-m^2, 1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID238", "CFAD[{q, {-2*m^2, 1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID239", +"CFAD[{q, {m2^2 - m1^2*x, 1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID240", "CFAD[{q, {0, -1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID241", "CFAD[{q, {-m^2, -1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID242", "CFAD[{q, {-2*m^2, -1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID243", +"CFAD[{q, {m2^2 - m1^2*x, -1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID244", "CFAD[{0, 0}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID245", "CFAD[{0, -m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID246", "CFAD[{0, -2*m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternal-ID247", "CFAD[{0, m2^2 - m1^2*x}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID248", "CFAD[{0, {0, 1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID249", "CFAD[{0, {-m^2, 1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID250", "CFAD[{0, {-2*m^2, 1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, 1}]]"}, +{"fcstFeynCalcInternal-ID251", "CFAD[{0, {m2^2 - m1^2*x, 1}}]//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID252", "CFAD[{0, {0, -1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID253", "CFAD[{0, {-m^2, -1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID254", "CFAD[{0, {-2*m^2, -1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternal-ID255", +"CFAD[{0, {m2^2 - m1^2*x, -1}}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID256", "CFAD[{0, 0, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID257", "CFAD[{0, -m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID258", "CFAD[{0, -2*m^2, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternal-ID259", "CFAD[{0, m2^2 - m1^2*x, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID260", "CFAD[{0, {0, 1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID261", "CFAD[{0, {-m^2, 1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID262", "CFAD[{0, {-2*m^2, 1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, 1}]]"}, +{"fcstFeynCalcInternal-ID263", +"CFAD[{0, {m2^2 - m1^2*x, 1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID264", "CFAD[{0, {0, -1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID265", "CFAD[{0, {-m^2, -1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID266", "CFAD[{0, {-2*m^2, -1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternal-ID267", +"CFAD[{0, {m2^2 - m1^2*x, -1}, 2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID268", "CFAD[{0, 0, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID269", "CFAD[{0, -m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID270", "CFAD[{0, -2*m^2, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternal-ID271", "CFAD[{0, m2^2 - m1^2*x, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID272", "CFAD[{0, {0, 1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID273", "CFAD[{0, {-m^2, 1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID274", "CFAD[{0, {-2*m^2, 1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, 1}]]"}, +{"fcstFeynCalcInternal-ID275", +"CFAD[{0, {m2^2 - m1^2*x, 1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID276", "CFAD[{0, {0, -1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID277", "CFAD[{0, {-m^2, -1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID278", "CFAD[{0, {-2*m^2, -1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternal-ID279", +"CFAD[{0, {m2^2 - m1^2*x, -1}, n}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID280", "CFAD[q]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID281", "CFAD[q, q1]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1, -1 + D], 0, 0, \ +{1, -1}]]"}, +{"fcstFeynCalcInternal-ID282", "CFAD[{q1, m^2}, q2, q3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID283", +"CFAD[{q1, m^2}, q2, {q3, m^2}]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID284", "CFAD[q1, q2, q3, q4]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4, -1 + D], 0, 0, \ +{1, -1}]]"}, +{"fcstFeynCalcInternal-ID285", "CFAD[q, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID286", "CFAD[q, q1, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1], 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID287", +"CFAD[{q1, m^2}, q2, q3, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID288", +"CFAD[{q1, m^2}, q2, {q3, m^2}, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID289", +"CFAD[q1, q2, q3, q4, Dimension -> 3]//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID290", +"CFAD[{{p1, p1.p2}}] // FCI", +"FeynAmpDenominator[ +CartesianPropagatorDenominator[CartesianMomentum[p1, -1 + D], +CartesianPair[CartesianMomentum[p1, -1 + D], +CartesianMomentum[p2, -1 + D]], 0, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID290", "SFAD[{{q, -p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID291", +"SFAD[{{q, -p1 . p2}, m^2}, EtaSign -> 1]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID292", +"SFAD[{{q, -p1 . p2}, {m^2, -1}}, EtaSign -> 1]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID293", "SFAD[{{q, -p1 . p2}, m^2, 2}]//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID294", "SFAD[{{q, -p1 . p2}, m^2, n}]//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID295", "SFAD[{{q, x*p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID296", +"SFAD[{{q, x*p1 . p2}, m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID297", +"SFAD[{{q, x*p1 . p2}, m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID298", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID299", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID300", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID301", "SFAD[{0, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID302", "SFAD[{0, m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID303", "SFAD[{0, m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID304", "SFAD[{{0, p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID305", "SFAD[{{0, p1 . p2}, m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID306", "SFAD[{{0, p1 . p2}, m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID307", "SFAD[{{0, -p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID308", "SFAD[{{0, -p1 . p2}, m^2, 2}]//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID309", "SFAD[{{0, -p1 . p2}, m^2, n}]//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID310", "SFAD[{{0, -p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID311", "SFAD[{{0, -p1 . p2}, m^2, 2}]//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID312", "SFAD[{{0, -p1 . p2}, m^2, n}]//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID313", "SFAD[{{0, x*p1 . p2}, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID314", +"SFAD[{{0, x*p1 . p2}, m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID315", +"SFAD[{{0, x*p1 . p2}, m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID316", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID317", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID318", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID319", +"SFAD[{{q, -p1 . p2}, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID320", +"SFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID321", +"SFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID322", +"SFAD[{{q, x*p1 . p2}, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID323", +"SFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID324", +"SFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID325", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID326", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID327", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID328", +"SFAD[{0, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID329", +"SFAD[{0, m^2, 2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID330", +"SFAD[{0, m^2, n}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID331", +"SFAD[{{0, p1 . p2}, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID332", +"SFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID333", +"SFAD[{{0, p1 . p2}, m^2, n}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID334", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID335", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID336", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID337", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID338", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID339", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID340", +"SFAD[{{0, x*p1 . p2}, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID341", +"SFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID342", +"SFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID343", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> 4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID344", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID345", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +4]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID346", +"SFAD[{{q, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID347", +"SFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID348", +"SFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID349", +"SFAD[{{q, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID350", +"SFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID351", +"SFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID352", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID353", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID354", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID355", +"SFAD[{0, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID356", +"SFAD[{0, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID357", +"SFAD[{0, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID358", +"SFAD[{{0, p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID359", +"SFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID360", +"SFAD[{{0, p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID361", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID362", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID363", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID364", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID365", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID366", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID367", +"SFAD[{{0, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID368", +"SFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID369", +"SFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID370", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID371", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID372", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID373", "SFAD[{q, 0}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID374", "SFAD[{q, -m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID375", "SFAD[{q, -2*m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID376", "SFAD[{q, m2^2 - m1^2*x}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID377", "SFAD[{q, {0, 1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID378", "SFAD[{q, {-m^2, 1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID379", "SFAD[{q, {-2*m^2, 1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID380", "SFAD[{q, {m2^2 - m1^2*x, 1}}]//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID381", "SFAD[{q, {0, -1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID382", "SFAD[{q, {-m^2, -1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID383", "SFAD[{q, {-2*m^2, -1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID384", +"SFAD[{q, {m2^2 - m1^2*x, -1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID385", "SFAD[{q, 0, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID386", "SFAD[{q, -m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID387", "SFAD[{q, -2*m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID388", "SFAD[{q, m2^2 - m1^2*x, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID389", "SFAD[{q, {0, 1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID390", "SFAD[{q, {-m^2, 1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID391", "SFAD[{q, {-2*m^2, 1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID392", +"SFAD[{q, {m2^2 - m1^2*x, 1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID393", "SFAD[{q, {0, -1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID394", "SFAD[{q, {-m^2, -1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID395", "SFAD[{q, {-2*m^2, -1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID396", +"SFAD[{q, {m2^2 - m1^2*x, -1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID397", "SFAD[{q, 0, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID398", "SFAD[{q, -m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID399", "SFAD[{q, -2*m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID400", "SFAD[{q, m2^2 - m1^2*x, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID401", "SFAD[{q, {0, 1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID402", "SFAD[{q, {-m^2, 1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID403", "SFAD[{q, {-2*m^2, 1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID404", +"SFAD[{q, {m2^2 - m1^2*x, 1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID405", "SFAD[{q, {0, -1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID406", "SFAD[{q, {-m^2, -1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID407", "SFAD[{q, {-2*m^2, -1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID408", +"SFAD[{q, {m2^2 - m1^2*x, -1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternal-ID409", "SFAD[{0, 0}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID410", "SFAD[{0, -m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID411", "SFAD[{0, -2*m^2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID412", "SFAD[{0, m2^2 - m1^2*x}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID413", "SFAD[{0, {0, 1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID414", "SFAD[{0, {-m^2, 1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID415", "SFAD[{0, {-2*m^2, 1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternal-ID416", "SFAD[{0, {m2^2 - m1^2*x, 1}}]//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternal-ID417", "SFAD[{0, {0, -1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID418", "SFAD[{0, {-m^2, -1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID419", "SFAD[{0, {-2*m^2, -1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID420", +"SFAD[{0, {m2^2 - m1^2*x, -1}}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternal-ID421", "SFAD[{0, 0, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID422", "SFAD[{0, -m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID423", "SFAD[{0, -2*m^2, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID424", "SFAD[{0, m2^2 - m1^2*x, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID425", "SFAD[{0, {0, 1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID426", "SFAD[{0, {-m^2, 1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID427", "SFAD[{0, {-2*m^2, 1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternal-ID428", +"SFAD[{0, {m2^2 - m1^2*x, 1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternal-ID429", "SFAD[{0, {0, -1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID430", "SFAD[{0, {-m^2, -1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID431", "SFAD[{0, {-2*m^2, -1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID432", +"SFAD[{0, {m2^2 - m1^2*x, -1}, 2}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternal-ID433", "SFAD[{0, 0, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID434", "SFAD[{0, -m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID435", "SFAD[{0, -2*m^2, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID436", "SFAD[{0, m2^2 - m1^2*x, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID437", "SFAD[{0, {0, 1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID438", "SFAD[{0, {-m^2, 1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID439", "SFAD[{0, {-2*m^2, 1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternal-ID440", +"SFAD[{0, {m2^2 - m1^2*x, 1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternal-ID441", "SFAD[{0, {0, -1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID442", "SFAD[{0, {-m^2, -1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID443", "SFAD[{0, {-2*m^2, -1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternal-ID444", +"SFAD[{0, {m2^2 - m1^2*x, -1}, n}]//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, -1}]]"} }; @@ -330,59 +1800,61 @@ Tests`Shared`fcstFeynCalcInternalDouble = { PropagatorDenominator[-Momentum[p, D] + Momentum[q1, D], m]]"}, {"fcstFeynCalcInternalDouble-ID64.1", "FCI[FCI[FAD[q1, {-p + q1, m},Dimension->4]]]", "FeynAmpDenominator[PropagatorDenominator[Momentum[q1], 0], PropagatorDenominator[-Momentum[p] + Momentum[q1], m]]"}, + {"fcstFeynCalcInternalDouble-ID64.2", "FCI[FCI[FAD[0]]]", "FeynAmpDenominator[PropagatorDenominator[0, 0]]"}, + {"fcstFeynCalcInternalDouble-ID64.3", "FCI[FCI[FAD[{p, m}, Dimension -> ss]]]", "FeynAmpDenominator[PropagatorDenominator[Momentum[p, ss], m]]"}, {"fcstFeynCalcInternalDouble-ID65", "FCI[FCI[FVD[p, mu]]]", "Pair[LorentzIndex[mu, D], Momentum[p, D]]"}, {"fcstFeynCalcInternalDouble-ID66", "FCI[FCI[FV[p, mu]]]", "Pair[LorentzIndex[mu], Momentum[p]]"}, {"fcstFeynCalcInternalDouble-ID66.1", "FCI[FCI[FVE[p, mu]]]", "Pair[LorentzIndex[mu, D-4], Momentum[p, D-4]]"}, {"fcstFeynCalcInternalDouble-ID67", "LC[a, b, c, d]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternalDouble-ID67.1", "LCD[a, b, c, d]//FCI//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]"}, {"fcstFeynCalcInternalDouble-ID67.2", "LC[][a, b, c, d]//FCI//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.3", "LCD[][a, b, c, d]//FCI//FCI", - "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D], Dimension -> D]"}, + "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D]]"}, {"fcstFeynCalcInternalDouble-ID67.4", "LC[a][ b, c, d]//FCI//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.5", "LC[a, b][ c, d]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.6", "LC[a, b, c][ d]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.7", "LCD[a][ b, c, d]//FCI//FCI", - "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalDouble-ID67.8", "LCD[a, b][ c, d]//FCI//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalDouble-ID67.9", "LCD[a, b, c][ d]//FCI//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalDouble-ID67.10", "LeviCivita[a, b, c, d, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternalDouble-ID67.11", "LeviCivita[a, b, c, d, Dimension->4, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternalDouble-ID67.12", "LeviCivita[a, b, c, d, Dimension->D, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]"}, {"fcstFeynCalcInternalDouble-ID67.13", "LeviCivita[FCI->False][a, b, c, d, FCI->False]//FCI//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.14", "LeviCivita[FCI->False][a, b, c, d, Dimension->4, FCI->False]//FCI//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.15", "LeviCivita[Dimension->D, FCI->False][a, b, c, d, Dimension->D, FCI->False]//FCI//FCI", - "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D], Dimension -> D]"}, + "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D]]"}, {"fcstFeynCalcInternalDouble-ID67.16", "LeviCivita[a, FCI->False][ b, c, d, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.17", "LeviCivita[a, Dimension->4, FCI->False][ b, c, d, Dimension->4, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.18", "LeviCivita[a, Dimension->D, FCI->False][ b, c, d, Dimension->D, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalDouble-ID67.19", "LeviCivita[a, b, FCI->False][ c, d, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.20", "LeviCivita[a, b, Dimension->4, FCI->False][ c, d, Dimension->4, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.21", "LeviCivita[a, b, Dimension->D, FCI->False][ c, d, Dimension->D, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalDouble-ID67.22", "LeviCivita[a, b, c, FCI->False][ d, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.23", "LeviCivita[a, b, c, Dimension->4, FCI->False][d, Dimension->4, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternalDouble-ID67.24", "LeviCivita[a, b, c, Dimension->D, FCI->False][d, Dimension->D, FCI->False]//FCI//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalDouble-ID71", "FCI[FCI[MT[a, b]]]", "Pair[LorentzIndex[a], LorentzIndex[b]]"}, {"fcstFeynCalcInternalDouble-ID72", "FCI[FCI[MTD[a, b]]]", "Pair[LorentzIndex[a, D], LorentzIndex[b, D]]"}, {"fcstFeynCalcInternalDouble-ID72.1", "FCI[FCI[MTE[a, b]]]", "Pair[LorentzIndex[a, D-4], LorentzIndex[b, D-4]]"}, @@ -401,9 +1873,1610 @@ Tests`Shared`fcstFeynCalcInternalDouble = { {"fcstFeynCalcInternalDouble-ID84.1", "FCI[FCI[SPE[a, b]]]", "Pair[Momentum[a, D-4], Momentum[b, D-4]]"}, {"fcstFeynCalcInternalDouble-ID85", "FCI[FCI[SO[a]]]", "Pair[Momentum[a], Momentum[OPEDelta]]"}, {"fcstFeynCalcInternalDouble-ID86", "FCI[FCI[SOD[a]]]", "Pair[Momentum[a, D], Momentum[OPEDelta, D]]"}, - {"fcstFeynCalcInternalDouble-ID87", "FCI[FCI[PropagatorDenominator[p, m]]]", "PropagatorDenominator[Momentum[p, D], m]"}, - {"fcstFeynCalcInternalDouble-ID88", "FCI[FCI[PropagatorDenominator[Momentum[p + q], m]]]", "PropagatorDenominator[Momentum[p] + Momentum[q], m]"} + {"fcstFeynCalcInternalDouble-ID87", "FCI[FCI[PropagatorDenominator[Momentum[p,D], m]]]", "PropagatorDenominator[Momentum[p, D], m]"}, + {"fcstFeynCalcInternalDouble-ID88", "FCI[FCI[PropagatorDenominator[Momentum[p + q], m]]]", "PropagatorDenominator[Momentum[p + q], m]"}, +{"fcstFeynCalcInternalDouble-ID89", "DIDelta[i,j]//FCI//FCI", +"DiracIndexDelta[DiracIndex[i], DiracIndex[j]]"}, +{"fcstFeynCalcInternalDouble-ID90", "DIDelta[i,2]//FCI//FCI", +"DiracIndexDelta[DiracIndex[i], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalDouble-ID91", "DIDelta[1,2]//FCI//FCI", +"DiracIndexDelta[ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalDouble-ID92", "DIDelta[2,2]//FCI//FCI", +"DiracIndexDelta[ExplicitDiracIndex[2], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalDouble-ID93", "DIDelta[i,i]//FCI//FCI", +"DiracIndexDelta[DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternalDouble-ID94", "DCHN[GA[mu],i,j]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], \ +DiracIndex[j]]"}, +{"fcstFeynCalcInternalDouble-ID95", "DCHN[GA[mu],1,j]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternalDouble-ID96", "DCHN[GA[mu],3,1]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternalDouble-ID97", "DCHN[GA[mu],3,3]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternalDouble-ID98", "DCHN[GA[mu],1,2]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalDouble-ID99", "DCHN[GA[mu],i,i]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], \ +DiracIndex[i]]"}, +{"fcstFeynCalcInternalDouble-ID100", +"DCHN[GA[mu].GSD[p],i,j]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], DiracIndex[j]]"}, +{"fcstFeynCalcInternalDouble-ID101", +"DCHN[GA[mu].GSD[p],1,j]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternalDouble-ID102", +"DCHN[GA[mu].GSD[p],3,1]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternalDouble-ID103", +"DCHN[GA[mu].GSD[p],3,3]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternalDouble-ID104", +"DCHN[GA[mu].GSD[p],1,2]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[1], \ +ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalDouble-ID105", +"DCHN[GA[mu].GSD[p],i,i]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternalDouble-ID106", +"DCHN[GA[mu].(m+GS[p]).GA[nu],1,j]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternalDouble-ID107", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,1]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternalDouble-ID108", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,3]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternalDouble-ID109", +"DCHN[GA[mu].(m+GS[p]).GA[nu],1,2]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalDouble-ID110", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,3]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternalDouble-ID111", +"DCHN[GA[mu].(m+GS[p]).GA[nu],i,i]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternalDouble-ID112", +"DCHN[Spinor[Momentum[p],m],i]//FCI//FCI", +"DiracChain[Spinor[Momentum[p], m, 1], DiracIndex[i]]"}, +{"fcstFeynCalcInternalDouble-ID112.1", "DCHN[i, Spinor[Momentum[p],m]]//FCI//FCI", + "DiracChain[DiracIndex[i], Spinor[Momentum[p], m, 1]]"}, +{"fcstFeynCalcInternalDouble-ID113", +"DCHN[GA[mu].GSD[p],Spinor[Momentum[p],m],j]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], Spinor[Momentum[p], m, 1], \ +DiracIndex[j]]"}, +{"fcstFeynCalcInternalDouble-ID114", +"DCHN[GA[mu].GSD[p],i,Spinor[Momentum[p],m]]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], Spinor[Momentum[p], m, \ +1]]"}, +{"fcstFeynCalcInternalDouble-ID115", +"DCHN[GA[mu].GSD[p],Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]\ +]//FCI//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcInternalDouble-ID116", +"DCHN[1,Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]\ +//FCI//FCI", +"DiracChain[1, Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcInternalDouble-ID117", +"GFAD[{{SPD[q, q]}, 2}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID118", +"GFAD[{{SPD[q, q], -1}}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID119", +"GFAD[{{SPD[q, q]}, 1}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID120", +"GFAD[{{SPD[q, q], 1}}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID121", +"GFAD[{{SPD[q, q]}}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID122", "GFAD[{SPD[q, q]}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID123", "GFAD[{SPD[q, q]}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID124", +"GFAD[{SPD[q, q]}, EtaSign -> -1]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID125", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID126", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID127", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID128", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID129", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, 4}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID130", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, 4}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID131", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, n}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID132", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, n}]//FCI//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID125", +"CFAD[{{q, -p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID126", +"CFAD[{{q, -p1 . p2}, m^2}, EtaSign -> 1]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID127", +"CFAD[{{q, -p1 . p2}, {m^2, -1}}, EtaSign -> 1]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID128", +"CFAD[{{q, -p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID129", +"CFAD[{{q, -p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID130", +"CFAD[{{q, x*p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID131", +"CFAD[{{q, x*p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID132", +"CFAD[{{q, x*p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID133", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID134", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID135", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID136", "CFAD[{0, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID137", "CFAD[{0, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID138", "CFAD[{0, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID139", +"CFAD[{{0, p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID140", +"CFAD[{{0, p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID141", +"CFAD[{{0, p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID142", +"CFAD[{{0, -p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID143", +"CFAD[{{0, -p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID144", +"CFAD[{{0, -p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID145", +"CFAD[{{0, -p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID146", +"CFAD[{{0, -p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID147", +"CFAD[{{0, -p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID148", +"CFAD[{{0, x*p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID149", +"CFAD[{{0, x*p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID150", +"CFAD[{{0, x*p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID151", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID152", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID153", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID154", +"CFAD[{{q, -p1 . p2}, m^2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID155", +"CFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID156", +"CFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID157", +"CFAD[{{q, x*p1 . p2}, m^2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID158", +"CFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID159", +"CFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID160", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> \ +3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID161", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID162", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID163", +"CFAD[{0, m^2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID164", +"CFAD[{0, m^2, 2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID165", +"CFAD[{0, m^2, n}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID166", +"CFAD[{{0, p1 . p2}, m^2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID167", +"CFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID168", +"CFAD[{{0, p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID169", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID170", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID171", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID172", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID173", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID174", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID175", +"CFAD[{{0, x*p1 . p2}, m^2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID176", +"CFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID177", +"CFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]], m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID178", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> \ +3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID179", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID180", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1], CartesianMomentum[p2]] - \ +2*CartesianPair[CartesianMomentum[p3], CartesianMomentum[p4]], m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID181", +"CFAD[{{q, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID182", +"CFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID183", +"CFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID184", +"CFAD[{{q, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID185", +"CFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID186", +"CFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID187", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID188", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID189", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID190", +"CFAD[{0, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID191", +"CFAD[{0, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID192", +"CFAD[{0, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID193", +"CFAD[{{0, p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID194", +"CFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID195", +"CFAD[{{0, p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, -4 \ ++ D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID196", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID197", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID198", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID199", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID200", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID201", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID202", +"CFAD[{{0, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID203", +"CFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID204", +"CFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID205", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID206", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID207", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -4 + D], CartesianMomentum[p2, \ +-4 + D]] - 2*CartesianPair[CartesianMomentum[p3, -4 + D], \ +CartesianMomentum[p4, -4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID208", "CFAD[{q, 0}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID209", "CFAD[{q, -m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID210", "CFAD[{q, -2*m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID211", +"CFAD[{q, m2^2 - m1^2*x}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID212", "CFAD[{q, {0, 1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID213", +"CFAD[{q, {-m^2, 1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID214", +"CFAD[{q, {-2*m^2, 1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID215", +"CFAD[{q, {m2^2 - m1^2*x, 1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID216", "CFAD[{q, {0, -1}}]//FCI//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID217", +"CFAD[{q, {-m^2, -1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID218", +"CFAD[{q, {-2*m^2, -1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID219", +"CFAD[{q, {m2^2 - m1^2*x, -1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID220", "CFAD[{q, 0, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID221", "CFAD[{q, -m^2, 2}]//FCI//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID222", +"CFAD[{q, -2*m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID223", +"CFAD[{q, m2^2 - m1^2*x, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID224", +"CFAD[{q, {0, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID225", +"CFAD[{q, {-m^2, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID226", +"CFAD[{q, {-2*m^2, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID227", +"CFAD[{q, {m2^2 - m1^2*x, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID228", +"CFAD[{q, {0, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID229", +"CFAD[{q, {-m^2, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID230", +"CFAD[{q, {-2*m^2, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID231", +"CFAD[{q, {m2^2 - m1^2*x, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID232", "CFAD[{q, 0, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID233", "CFAD[{q, -m^2, n}]//FCI//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID234", +"CFAD[{q, -2*m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID235", +"CFAD[{q, m2^2 - m1^2*x, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID236", +"CFAD[{q, {0, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID237", +"CFAD[{q, {-m^2, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID238", +"CFAD[{q, {-2*m^2, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID239", +"CFAD[{q, {m2^2 - m1^2*x, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID240", +"CFAD[{q, {0, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID241", +"CFAD[{q, {-m^2, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID242", +"CFAD[{q, {-2*m^2, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID243", +"CFAD[{q, {m2^2 - m1^2*x, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID244", "CFAD[{0, 0}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID245", "CFAD[{0, -m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID246", "CFAD[{0, -2*m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID247", +"CFAD[{0, m2^2 - m1^2*x}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID248", "CFAD[{0, {0, 1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID249", +"CFAD[{0, {-m^2, 1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID250", +"CFAD[{0, {-2*m^2, 1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID251", +"CFAD[{0, {m2^2 - m1^2*x, 1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID252", "CFAD[{0, {0, -1}}]//FCI//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID253", +"CFAD[{0, {-m^2, -1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID254", +"CFAD[{0, {-2*m^2, -1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID255", +"CFAD[{0, {m2^2 - m1^2*x, -1}}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID256", "CFAD[{0, 0, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID257", "CFAD[{0, -m^2, 2}]//FCI//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID258", +"CFAD[{0, -2*m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID259", +"CFAD[{0, m2^2 - m1^2*x, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID260", +"CFAD[{0, {0, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID261", +"CFAD[{0, {-m^2, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID262", +"CFAD[{0, {-2*m^2, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID263", +"CFAD[{0, {m2^2 - m1^2*x, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID264", +"CFAD[{0, {0, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID265", +"CFAD[{0, {-m^2, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID266", +"CFAD[{0, {-2*m^2, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID267", +"CFAD[{0, {m2^2 - m1^2*x, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID268", "CFAD[{0, 0, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID269", "CFAD[{0, -m^2, n}]//FCI//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID270", +"CFAD[{0, -2*m^2, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID271", +"CFAD[{0, m2^2 - m1^2*x, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID272", +"CFAD[{0, {0, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID273", +"CFAD[{0, {-m^2, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID274", +"CFAD[{0, {-2*m^2, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID275", +"CFAD[{0, {m2^2 - m1^2*x, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID276", +"CFAD[{0, {0, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID277", +"CFAD[{0, {-m^2, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID278", +"CFAD[{0, {-2*m^2, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID279", +"CFAD[{0, {m2^2 - m1^2*x, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID280", "CFAD[q]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID281", "CFAD[q, q1]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1, -1 + D], 0, 0, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID282", +"CFAD[{q1, m^2}, q2, q3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID283", +"CFAD[{q1, m^2}, q2, {q3, m^2}]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID284", +"CFAD[q1, q2, q3, q4]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4, -1 + D], 0, 0, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID285", +"CFAD[q, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID286", +"CFAD[q, q1, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1], 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID287", +"CFAD[{q1, m^2}, q2, q3, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID288", +"CFAD[{q1, m^2}, q2, {q3, m^2}, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID289", +"CFAD[q1, q2, q3, q4, Dimension -> 3]//FCI//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID290", +"CFAD[{{p1, p1.p2}}] // FCI// FCI", +"FeynAmpDenominator[ +CartesianPropagatorDenominator[CartesianMomentum[p1, -1 + D], +CartesianPair[CartesianMomentum[p1, -1 + D], +CartesianMomentum[p2, -1 + D]], 0, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID290", +"SFAD[{{q, -p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID291", +"SFAD[{{q, -p1 . p2}, m^2}, EtaSign -> 1]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID292", +"SFAD[{{q, -p1 . p2}, {m^2, -1}}, EtaSign -> 1]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID293", +"SFAD[{{q, -p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID294", +"SFAD[{{q, -p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID295", +"SFAD[{{q, x*p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID296", +"SFAD[{{q, x*p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID297", +"SFAD[{{q, x*p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID298", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID299", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID300", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID301", "SFAD[{0, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID302", "SFAD[{0, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID303", "SFAD[{0, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID304", +"SFAD[{{0, p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID305", +"SFAD[{{0, p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID306", +"SFAD[{{0, p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID307", +"SFAD[{{0, -p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID308", +"SFAD[{{0, -p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID309", +"SFAD[{{0, -p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID310", +"SFAD[{{0, -p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID311", +"SFAD[{{0, -p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID312", +"SFAD[{{0, -p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID313", +"SFAD[{{0, x*p1 . p2}, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID314", +"SFAD[{{0, x*p1 . p2}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID315", +"SFAD[{{0, x*p1 . p2}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID316", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID317", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID318", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID319", +"SFAD[{{q, -p1 . p2}, m^2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID320", +"SFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID321", +"SFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID322", +"SFAD[{{q, x*p1 . p2}, m^2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID323", +"SFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID324", +"SFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID325", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> \ +4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID326", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID327", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID328", +"SFAD[{0, m^2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID329", +"SFAD[{0, m^2, 2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID330", +"SFAD[{0, m^2, n}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID331", +"SFAD[{{0, p1 . p2}, m^2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID332", +"SFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID333", +"SFAD[{{0, p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID334", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID335", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID336", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID337", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID338", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID339", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID340", +"SFAD[{{0, x*p1 . p2}, m^2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID341", +"SFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID342", +"SFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID343", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> \ +4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID344", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID345", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +4]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID346", +"SFAD[{{q, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID347", +"SFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID348", +"SFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID349", +"SFAD[{{q, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID350", +"SFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID351", +"SFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID352", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID353", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID354", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID355", +"SFAD[{0, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID356", +"SFAD[{0, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID357", +"SFAD[{0, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID358", +"SFAD[{{0, p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID359", +"SFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID360", +"SFAD[{{0, p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID361", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID362", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID363", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID364", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID365", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID366", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID367", +"SFAD[{{0, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID368", +"SFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID369", +"SFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID370", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID371", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID372", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID373", "SFAD[{q, 0}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID374", "SFAD[{q, -m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID375", "SFAD[{q, -2*m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID376", +"SFAD[{q, m2^2 - m1^2*x}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID377", "SFAD[{q, {0, 1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID378", +"SFAD[{q, {-m^2, 1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID379", +"SFAD[{q, {-2*m^2, 1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID380", +"SFAD[{q, {m2^2 - m1^2*x, 1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID381", "SFAD[{q, {0, -1}}]//FCI//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID382", +"SFAD[{q, {-m^2, -1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID383", +"SFAD[{q, {-2*m^2, -1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID384", +"SFAD[{q, {m2^2 - m1^2*x, -1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID385", "SFAD[{q, 0, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID386", "SFAD[{q, -m^2, 2}]//FCI//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID387", +"SFAD[{q, -2*m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID388", +"SFAD[{q, m2^2 - m1^2*x, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID389", +"SFAD[{q, {0, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID390", +"SFAD[{q, {-m^2, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID391", +"SFAD[{q, {-2*m^2, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID392", +"SFAD[{q, {m2^2 - m1^2*x, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID393", +"SFAD[{q, {0, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID394", +"SFAD[{q, {-m^2, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID395", +"SFAD[{q, {-2*m^2, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID396", +"SFAD[{q, {m2^2 - m1^2*x, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID397", "SFAD[{q, 0, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID398", "SFAD[{q, -m^2, n}]//FCI//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID399", +"SFAD[{q, -2*m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID400", +"SFAD[{q, m2^2 - m1^2*x, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID401", +"SFAD[{q, {0, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID402", +"SFAD[{q, {-m^2, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID403", +"SFAD[{q, {-2*m^2, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID404", +"SFAD[{q, {m2^2 - m1^2*x, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID405", +"SFAD[{q, {0, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID406", +"SFAD[{q, {-m^2, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID407", +"SFAD[{q, {-2*m^2, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID408", +"SFAD[{q, {m2^2 - m1^2*x, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID409", "SFAD[{0, 0}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID410", "SFAD[{0, -m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID411", "SFAD[{0, -2*m^2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID412", +"SFAD[{0, m2^2 - m1^2*x}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID413", "SFAD[{0, {0, 1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID414", +"SFAD[{0, {-m^2, 1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID415", +"SFAD[{0, {-2*m^2, 1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID416", +"SFAD[{0, {m2^2 - m1^2*x, 1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID417", "SFAD[{0, {0, -1}}]//FCI//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID418", +"SFAD[{0, {-m^2, -1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID419", +"SFAD[{0, {-2*m^2, -1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID420", +"SFAD[{0, {m2^2 - m1^2*x, -1}}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID421", "SFAD[{0, 0, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID422", "SFAD[{0, -m^2, 2}]//FCI//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID423", +"SFAD[{0, -2*m^2, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID424", +"SFAD[{0, m2^2 - m1^2*x, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID425", +"SFAD[{0, {0, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID426", +"SFAD[{0, {-m^2, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID427", +"SFAD[{0, {-2*m^2, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID428", +"SFAD[{0, {m2^2 - m1^2*x, 1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID429", +"SFAD[{0, {0, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID430", +"SFAD[{0, {-m^2, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID431", +"SFAD[{0, {-2*m^2, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID432", +"SFAD[{0, {m2^2 - m1^2*x, -1}, 2}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalDouble-ID433", "SFAD[{0, 0, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID434", "SFAD[{0, -m^2, n}]//FCI//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID435", +"SFAD[{0, -2*m^2, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID436", +"SFAD[{0, m2^2 - m1^2*x, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID437", +"SFAD[{0, {0, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID438", +"SFAD[{0, {-m^2, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID439", +"SFAD[{0, {-2*m^2, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalDouble-ID440", +"SFAD[{0, {m2^2 - m1^2*x, 1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalDouble-ID441", +"SFAD[{0, {0, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID442", +"SFAD[{0, {-m^2, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID443", +"SFAD[{0, {-2*m^2, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalDouble-ID444", +"SFAD[{0, {m2^2 - m1^2*x, -1}, n}]//FCI//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, -1}]]"} }; Tests`Shared`fcstFeynCalcInternalTriple = { @@ -525,59 +3598,61 @@ Tests`Shared`fcstFeynCalcInternalTriple = { PropagatorDenominator[-Momentum[p, D] + Momentum[q1, D], m]]"}, {"fcstFeynCalcInternalTriple-ID64.1", "FCI[FCE[FCI[FAD[q1, {-p + q1, m},Dimension->4]]]]", "FeynAmpDenominator[PropagatorDenominator[Momentum[q1], 0], PropagatorDenominator[-Momentum[p] + Momentum[q1], m]]"}, + {"fcstFeynCalcInternalTriple-ID64.2", "FCI[FCE[FCI[FAD[0]]]]", "FeynAmpDenominator[PropagatorDenominator[0, 0]]"}, + {"fcstFeynCalcInternalDouble-ID64.3", "FCI[FCE[FCI[FAD[{p, m}, Dimension -> ss]]]]", "FeynAmpDenominator[PropagatorDenominator[Momentum[p, ss], m]]"}, {"fcstFeynCalcInternalTriple-ID65", "FCI[FCE[FCI[FVD[p, mu]]]]", "Pair[LorentzIndex[mu, D], Momentum[p, D]]"}, {"fcstFeynCalcInternalTriple-ID66", "FCI[FCE[FCI[FV[p, mu]]]]", "Pair[LorentzIndex[mu], Momentum[p]]"}, {"fcstFeynCalcInternalTriple-ID66.1", "FCI[FCE[FCI[FVE[p, mu]]]]", "Pair[LorentzIndex[mu,D-4], Momentum[p,D-4]]"}, {"fcstFeynCalcInternalTriple-ID67", "LC[a, b, c, d]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternalTriple-ID67.1", "LCD[a, b, c, d]//FCI//FCE//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]"}, {"fcstFeynCalcInternalTriple-ID67.2", "LC[][a, b, c, d]//FCI//FCE//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.3", "LCD[][a, b, c, d]//FCI//FCE//FCI", - "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D], Dimension -> D]"}, + "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D]]"}, {"fcstFeynCalcInternalTriple-ID67.4", "LC[a][ b, c, d]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.5", "LC[a, b][ c, d]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.6", "LC[a, b, c][ d]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.7", "LCD[a][ b, c, d]//FCI//FCE//FCI", - "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalTriple-ID67.8", "LCD[a, b][ c, d]//FCI//FCE//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalTriple-ID67.9", "LCD[a, b, c][ d]//FCI//FCE//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalTriple-ID67.10", "LeviCivita[a, b, c, d, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternalTriple-ID67.11", "LeviCivita[a, b, c, d, Dimension->4, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstFeynCalcInternalTriple-ID67.12", "LeviCivita[a, b, c, d, Dimension->D, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]"}, {"fcstFeynCalcInternalTriple-ID67.13", "LeviCivita[FCI->False][a, b, c, d, FCI->False]//FCI//FCE//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.14", "LeviCivita[FCI->False][a, b, c, d, Dimension->4, FCI->False]//FCI//FCE//FCI", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.15", "LeviCivita[Dimension->D, FCI->False][a, b, c, d, Dimension->D, FCI->False]//FCI//FCE//FCI", - "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D], Dimension -> D]"}, + "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D]]"}, {"fcstFeynCalcInternalTriple-ID67.16", "LeviCivita[a, FCI->False][ b, c, d, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.17", "LeviCivita[a, Dimension->4, FCI->False][ b, c, d, Dimension->4, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.18", "LeviCivita[a, Dimension->D, FCI->False][ b, c, d, Dimension->D, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalTriple-ID67.19", "LeviCivita[a, b, FCI->False][ c, d, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.20", "LeviCivita[a, b, Dimension->4, FCI->False][ c, d, Dimension->4, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.21", "LeviCivita[a, b, Dimension->D, FCI->False][ c, d, Dimension->D, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalTriple-ID67.22", "LeviCivita[a, b, c, FCI->False][ d, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.23", "LeviCivita[a, b, c, Dimension->4, FCI->False][d, Dimension->4, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstFeynCalcInternalTriple-ID67.24", "LeviCivita[a, b, c, Dimension->D, FCI->False][d, Dimension->D, FCI->False]//FCI//FCE//FCI", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]"}, {"fcstFeynCalcInternalTriple-ID71", "FCI[FCE[FCI[MT[a, b]]]]", "Pair[LorentzIndex[a], LorentzIndex[b]]"}, {"fcstFeynCalcInternalTriple-ID72", "FCI[FCE[FCI[MTD[a, b]]]]", "Pair[LorentzIndex[a, D], LorentzIndex[b, D]]"}, {"fcstFeynCalcInternalTriple-ID72.1", "FCI[FCE[FCI[MTE[a, b]]]]", "Pair[LorentzIndex[a, D-4], LorentzIndex[b, D-4]]"}, @@ -596,5 +3671,1977 @@ Tests`Shared`fcstFeynCalcInternalTriple = { {"fcstFeynCalcInternalTriple-ID84.1", "FCI[FCE[FCI[SPE[a, b]]]]", "Pair[Momentum[a, D-4], Momentum[b, D-4]]"}, {"fcstFeynCalcInternalTriple-ID85", "FCI[FCE[FCI[SO[a]]]]", "Pair[Momentum[a], Momentum[OPEDelta]]"}, {"fcstFeynCalcInternalTriple-ID86", "FCI[FCE[FCI[SOD[a]]]]", "Pair[Momentum[a, D], Momentum[OPEDelta, D]]"}, - {"fcstFeynCalcInternalTriple-ID87", "FCI[FCE[FCI[PropagatorDenominator[p, m]]]]", "PropagatorDenominator[Momentum[p, D], m]"} + {"fcstFeynCalcInternalTriple-ID87", "FCI[FCE[FCI[PropagatorDenominator[Momentum[p,D], m]]]]", "PropagatorDenominator[Momentum[p, D], m]"}, +{"fcstFeynCalcInternalTriple-ID88", "DIDelta[i,j]//FCI//FCE//FCI", +"DiracIndexDelta[DiracIndex[i], DiracIndex[j]]"}, +{"fcstFeynCalcInternalTriple-ID89", "DIDelta[i,2]//FCI//FCE//FCI", +"DiracIndexDelta[DiracIndex[i], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalTriple-ID90", "DIDelta[1,2]//FCI//FCE//FCI", +"DiracIndexDelta[ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalTriple-ID91", "DIDelta[2,2]//FCI//FCE//FCI", +"DiracIndexDelta[ExplicitDiracIndex[2], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalTriple-ID92", "DIDelta[i,i]//FCI//FCE//FCI", +"DiracIndexDelta[DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternalTriple-ID93", +"DCHN[GA[mu],i,j]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], \ +DiracIndex[j]]"}, +{"fcstFeynCalcInternalTriple-ID94", +"DCHN[GA[mu],1,j]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternalTriple-ID95", +"DCHN[GA[mu],3,1]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternalTriple-ID96", +"DCHN[GA[mu],3,3]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternalTriple-ID97", +"DCHN[GA[mu],1,2]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalTriple-ID98", +"DCHN[GA[mu],i,i]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], \ +DiracIndex[i]]"}, +{"fcstFeynCalcInternalTriple-ID99", +"DCHN[GA[mu].GSD[p],i,j]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], DiracIndex[j]]"}, +{"fcstFeynCalcInternalTriple-ID100", +"DCHN[GA[mu].GSD[p],1,j]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternalTriple-ID101", +"DCHN[GA[mu].GSD[p],3,1]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternalTriple-ID102", +"DCHN[GA[mu].GSD[p],3,3]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternalTriple-ID103", +"DCHN[GA[mu].GSD[p],1,2]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[1], \ +ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalTriple-ID104", +"DCHN[GA[mu].GSD[p],i,i]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternalTriple-ID105", +"DCHN[GA[mu].(m+GS[p]).GA[nu],1,j]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstFeynCalcInternalTriple-ID106", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,1]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[1]]"}, +{"fcstFeynCalcInternalTriple-ID107", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,3]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternalTriple-ID108", +"DCHN[GA[mu].(m+GS[p]).GA[nu],1,2]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstFeynCalcInternalTriple-ID109", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,3]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstFeynCalcInternalTriple-ID110", +"DCHN[GA[mu].(m+GS[p]).GA[nu],i,i]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +DiracIndex[i], DiracIndex[i]]"}, +{"fcstFeynCalcInternalTriple-ID111", +"DCHN[Spinor[Momentum[p],m],i]//FCI//FCE//FCI", +"DiracChain[Spinor[Momentum[p], m, 1], DiracIndex[i]]"}, +{"fcstFeynCalcInternalTriple-ID112", +"DCHN[GA[mu].GSD[p],Spinor[Momentum[p],m],j]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], Spinor[Momentum[p], m, 1], \ +DiracIndex[j]]"}, +{"fcstFeynCalcInternalTriple-ID112.1", "DCHN[i, Spinor[Momentum[p],m]]//FCI//FCE//FCI", + "DiracChain[DiracIndex[i], Spinor[Momentum[p], m, 1]]"}, +{"fcstFeynCalcInternalTriple-ID113", +"DCHN[GA[mu].GSD[p],i,Spinor[Momentum[p],m]]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], Spinor[Momentum[p], m, \ +1]]"}, +{"fcstFeynCalcInternalTriple-ID114", +"DCHN[GA[mu].GSD[p],Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]\ +]//FCI//FCE//FCI", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcInternalTriple-ID115", +"DCHN[1,Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]\ +//FCI//FCE//FCI", +"DiracChain[1, Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstFeynCalcInternalTriple-ID117", +"GFAD[{{SPD[q, q]}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID118", +"GFAD[{{SPD[q, q], -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID119", +"GFAD[{{SPD[q, q]}, 1}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID120", +"GFAD[{{SPD[q, q], 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID121", +"GFAD[{{SPD[q, q]}}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID122", +"GFAD[{SPD[q, q]}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID123", +"GFAD[{SPD[q, q]}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID124", +"GFAD[{SPD[q, q]}, EtaSign -> -1]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[q, \ +D], Momentum[q, D]], {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID125", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID126", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID127", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID128", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID129", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, 4}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID130", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, 4}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, 4}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {4, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {4, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID131", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], 1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, 1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID132", +"GFAD[{{1 - SPD[p, q]*SPD[r, s], -1}, n}, {{1 + SPD[p, q]*SPD[r, \ +s], -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[GenericPropagatorDenominator[1 - \ +Pair[Momentum[p, D], Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, \ +D]], {n, -1}], GenericPropagatorDenominator[1 + Pair[Momentum[p, D], \ +Momentum[q, D]]*Pair[Momentum[r, D], Momentum[s, D]], {n, -1}]]"}, + +{"fcstFeynCalcInternalTriple-ID125", +"CFAD[{{q, -p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID126", +"CFAD[{{q, -p1 . p2}, m^2}, EtaSign -> 1]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID127", +"CFAD[{{q, -p1 . p2}, {m^2, -1}}, EtaSign -> 1]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID128", +"CFAD[{{q, -p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID129", +"CFAD[{{q, -p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], -CartesianPair[CartesianMomentum[p1, -1 \ ++ D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID130", +"CFAD[{{q, x*p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID131", +"CFAD[{{q, x*p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID132", +"CFAD[{{q, x*p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID133", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID134", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID135", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], x*CartesianPair[CartesianMomentum[p1, \ +-1 + D], CartesianMomentum[p2, -1 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -1 + D], CartesianMomentum[p4, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID136", +"CFAD[{0, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID137", +"CFAD[{0, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID138", +"CFAD[{0, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID139", +"CFAD[{{0, p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID140", +"CFAD[{{0, p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID141", +"CFAD[{{0, p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID142", +"CFAD[{{0, -p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID143", +"CFAD[{{0, -p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID144", +"CFAD[{{0, -p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID145", +"CFAD[{{0, -p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID146", +"CFAD[{{0, -p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID147", +"CFAD[{{0, -p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID148", +"CFAD[{{0, x*p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID149", +"CFAD[{{0, x*p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID150", +"CFAD[{{0, x*p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID151", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID152", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID153", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID154", +"CFAD[{{q, -p1 . p2}, m^2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID155", +"CFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID156", +"CFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], -CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID157", +"CFAD[{{q, x*p1 . p2}, m^2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID158", +"CFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID159", +"CFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID160", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> \ +3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID161", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID162", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], x*CartesianPair[CartesianMomentum[p1], \ +CartesianMomentum[p2]] - 2*CartesianPair[CartesianMomentum[p3], \ +CartesianMomentum[p4]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID163", +"CFAD[{0, m^2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID164", +"CFAD[{0, m^2, 2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID165", +"CFAD[{0, m^2, n}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID166", +"CFAD[{{0, p1 . p2}, m^2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID167", +"CFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID168", +"CFAD[{{0, p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID169", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID170", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID171", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID172", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID173", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID174", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID175", +"CFAD[{{0, x*p1 . p2}, m^2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID176", +"CFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID177", +"CFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID178", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> \ +3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID179", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID180", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID181", +"CFAD[{{q, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID182", +"CFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID183", +"CFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], -CartesianPair[CartesianMomentum[p1, -4 \ ++ D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID184", +"CFAD[{{q, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID185", +"CFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID186", +"CFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID187", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID188", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID189", +"CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -4 + D], x*CartesianPair[CartesianMomentum[p1, \ +-4 + D], CartesianMomentum[p2, -4 + D]] - \ +2*CartesianPair[CartesianMomentum[p3, -4 + D], CartesianMomentum[p4, \ +-4 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID190", +"CFAD[{0, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID191", +"CFAD[{0, m^2, 2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID192", +"CFAD[{0, m^2, n}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID193", +"CFAD[{{0, p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID194", +"CFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCE//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID195", +"CFAD[{{0, p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCE//FCI", + "FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 \ ++ D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID196", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID197", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID198", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID199", +"CFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID200", +"CFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID201", +"CFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +-CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID202", +"CFAD[{{0, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID203", +"CFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID204", +"CFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID205", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID206", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID207", +"CFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, \ +x*CartesianPair[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, \ +-1 + D]] - 2*CartesianPair[CartesianMomentum[p3, -1 + D], \ +CartesianMomentum[p4, -1 + D]], m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID208", "CFAD[{q, 0}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID209", +"CFAD[{q, -m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID210", +"CFAD[{q, -2*m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID211", +"CFAD[{q, m2^2 - m1^2*x}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID212", +"CFAD[{q, {0, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID213", +"CFAD[{q, {-m^2, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID214", +"CFAD[{q, {-2*m^2, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID215", +"CFAD[{q, {m2^2 - m1^2*x, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID216", +"CFAD[{q, {0, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID217", +"CFAD[{q, {-m^2, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID218", +"CFAD[{q, {-2*m^2, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID219", +"CFAD[{q, {m2^2 - m1^2*x, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID220", +"CFAD[{q, 0, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID221", +"CFAD[{q, -m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID222", +"CFAD[{q, -2*m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID223", +"CFAD[{q, m2^2 - m1^2*x, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID224", +"CFAD[{q, {0, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID225", +"CFAD[{q, {-m^2, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID226", +"CFAD[{q, {-2*m^2, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID227", +"CFAD[{q, {m2^2 - m1^2*x, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID228", +"CFAD[{q, {0, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID229", +"CFAD[{q, {-m^2, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID230", +"CFAD[{q, {-2*m^2, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID231", +"CFAD[{q, {m2^2 - m1^2*x, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID232", +"CFAD[{q, 0, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID233", +"CFAD[{q, -m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID234", +"CFAD[{q, -2*m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID235", +"CFAD[{q, m2^2 - m1^2*x, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID236", +"CFAD[{q, {0, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID237", +"CFAD[{q, {-m^2, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID238", +"CFAD[{q, {-2*m^2, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID239", +"CFAD[{q, {m2^2 - m1^2*x, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID240", +"CFAD[{q, {0, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID241", +"CFAD[{q, {-m^2, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID242", +"CFAD[{q, {-2*m^2, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, -2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID243", +"CFAD[{q, {m2^2 - m1^2*x, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, m2^2 - m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID244", "CFAD[{0, 0}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID245", +"CFAD[{0, -m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID246", +"CFAD[{0, -2*m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID247", +"CFAD[{0, m2^2 - m1^2*x}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID248", +"CFAD[{0, {0, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID249", +"CFAD[{0, {-m^2, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID250", +"CFAD[{0, {-2*m^2, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID251", +"CFAD[{0, {m2^2 - m1^2*x, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID252", +"CFAD[{0, {0, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID253", +"CFAD[{0, {-m^2, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID254", +"CFAD[{0, {-2*m^2, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID255", +"CFAD[{0, {m2^2 - m1^2*x, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID256", +"CFAD[{0, 0, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID257", +"CFAD[{0, -m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID258", +"CFAD[{0, -2*m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID259", +"CFAD[{0, m2^2 - m1^2*x, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID260", +"CFAD[{0, {0, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID261", +"CFAD[{0, {-m^2, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID262", +"CFAD[{0, {-2*m^2, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID263", +"CFAD[{0, {m2^2 - m1^2*x, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID264", +"CFAD[{0, {0, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID265", +"CFAD[{0, {-m^2, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID266", +"CFAD[{0, {-2*m^2, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID267", +"CFAD[{0, {m2^2 - m1^2*x, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID268", +"CFAD[{0, 0, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID269", +"CFAD[{0, -m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID270", +"CFAD[{0, -2*m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID271", +"CFAD[{0, m2^2 - m1^2*x, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID272", +"CFAD[{0, {0, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID273", +"CFAD[{0, {-m^2, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID274", +"CFAD[{0, {-2*m^2, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID275", +"CFAD[{0, {m2^2 - m1^2*x, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID276", +"CFAD[{0, {0, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID277", +"CFAD[{0, {-m^2, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID278", +"CFAD[{0, {-2*m^2, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, -2*m^2, \ +{n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID279", +"CFAD[{0, {m2^2 - m1^2*x, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, m2^2 - \ +m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID280", "CFAD[q]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID281", "CFAD[q, q1]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1, -1 + D], 0, 0, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID282", +"CFAD[{q1, m^2}, q2, q3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID283", +"CFAD[{q1, m^2}, q2, {q3, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID284", +"CFAD[q1, q2, q3, q4]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1, -1 + D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2, -1 + D], 0, 0, \ +{1, -1}], CartesianPropagatorDenominator[CartesianMomentum[q3, -1 + \ +D], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4, -1 + D], 0, 0, \ +{1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID285", +"CFAD[q, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID286", +"CFAD[q, q1, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q1], 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID287", +"CFAD[{q1, m^2}, q2, q3, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID288", +"CFAD[{q1, m^2}, q2, {q3, m^2}, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, m^2, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID289", +"CFAD[q1, q2, q3, q4, Dimension -> 3]//FCI//FCE//FCI", +"FeynAmpDenominator[CartesianPropagatorDenominator[\ +CartesianMomentum[q1], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q2], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q3], 0, 0, {1, -1}], \ +CartesianPropagatorDenominator[CartesianMomentum[q4], 0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID290", +"CFAD[{{p1, p1.p2}}] // FCI//FCE//FCI", +"FeynAmpDenominator[ +CartesianPropagatorDenominator[CartesianMomentum[p1, -1 + D], +CartesianPair[CartesianMomentum[p1, -1 + D], +CartesianMomentum[p2, -1 + D]], 0, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID290", +"SFAD[{{q, -p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID291", +"SFAD[{{q, -p1 . p2}, m^2}, EtaSign -> 1]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID292", +"SFAD[{{q, -p1 . p2}, {m^2, -1}}, EtaSign -> 1]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID293", +"SFAD[{{q, -p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID294", +"SFAD[{{q, -p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID295", +"SFAD[{{q, x*p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID296", +"SFAD[{{q, x*p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID297", +"SFAD[{{q, x*p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID298", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID299", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID300", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID301", +"SFAD[{0, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID302", +"SFAD[{0, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID303", +"SFAD[{0, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID304", +"SFAD[{{0, p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID305", +"SFAD[{{0, p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID306", +"SFAD[{{0, p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID307", +"SFAD[{{0, -p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID308", +"SFAD[{{0, -p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID309", +"SFAD[{{0, -p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID310", +"SFAD[{{0, -p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID311", +"SFAD[{{0, -p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID312", +"SFAD[{{0, -p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID313", +"SFAD[{{0, x*p1 . p2}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID314", +"SFAD[{{0, x*p1 . p2}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID315", +"SFAD[{{0, x*p1 . p2}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID316", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID317", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID318", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID319", +"SFAD[{{q, -p1 . p2}, m^2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID320", +"SFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID321", +"SFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +-Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID322", +"SFAD[{{q, x*p1 . p2}, m^2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID323", +"SFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID324", +"SFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID325", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> \ +4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID326", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID327", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q], \ +x*Pair[Momentum[p1], Momentum[p2]] - 2*Pair[Momentum[p3], \ +Momentum[p4]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID328", +"SFAD[{0, m^2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID329", +"SFAD[{0, m^2, 2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID330", +"SFAD[{0, m^2, n}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID331", +"SFAD[{{0, p1 . p2}, m^2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID332", +"SFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID333", +"SFAD[{{0, p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID334", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID335", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID336", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID337", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID338", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID339", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID340", +"SFAD[{{0, x*p1 . p2}, m^2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID341", +"SFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID342", +"SFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> 4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID343", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> \ +4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID344", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> \ +4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID345", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> \ +4]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID346", +"SFAD[{{q, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID347", +"SFAD[{{q, -p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID348", +"SFAD[{{q, -p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], -Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID349", +"SFAD[{{q, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID350", +"SFAD[{{q, x*p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID351", +"SFAD[{{q, x*p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]], -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID352", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID353", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID354", +"SFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, -4 + \ +D], x*Pair[Momentum[p1, -4 + D], Momentum[p2, -4 + D]] - \ +2*Pair[Momentum[p3, -4 + D], Momentum[p4, -4 + D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID355", +"SFAD[{0, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID356", +"SFAD[{0, m^2, 2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID357", +"SFAD[{0, m^2, n}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID358", +"SFAD[{{0, p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID359", +"SFAD[{{0, p1 . p2}, m^2, 2}, Dimension -> -4 + D]//FCI//FCE//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID360", +"SFAD[{{0, p1 . p2}, m^2, n}, Dimension -> -4 + D]//FCI//FCE//FCI", + "FeynAmpDenominator[StandardPropagatorDenominator[0, \ +Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID361", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID362", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID363", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID364", +"SFAD[{{0, -p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID365", +"SFAD[{{0, -p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID366", +"SFAD[{{0, -p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +-Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID367", +"SFAD[{{0, x*p1 . p2}, m^2}, Dimension -> -4 + D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID368", +"SFAD[{{0, x*p1 . p2}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID369", +"SFAD[{{0, x*p1 . p2}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID370", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID371", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, 2}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID372", +"SFAD[{{0, x*p1 . p2 - (2*p3) . p4}, m^2, n}, Dimension -> -4 + \ +D]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, \ +x*Pair[Momentum[p1, D], Momentum[p2, D]] - 2*Pair[Momentum[p3, D], \ +Momentum[p4, D]], -m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID373", "SFAD[{q, 0}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID374", +"SFAD[{q, -m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID375", +"SFAD[{q, -2*m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID376", +"SFAD[{q, m2^2 - m1^2*x}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID377", +"SFAD[{q, {0, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID378", +"SFAD[{q, {-m^2, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID379", +"SFAD[{q, {-2*m^2, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID380", +"SFAD[{q, {m2^2 - m1^2*x, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID381", +"SFAD[{q, {0, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID382", +"SFAD[{q, {-m^2, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID383", +"SFAD[{q, {-2*m^2, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID384", +"SFAD[{q, {m2^2 - m1^2*x, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID385", +"SFAD[{q, 0, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID386", +"SFAD[{q, -m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID387", +"SFAD[{q, -2*m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID388", +"SFAD[{q, m2^2 - m1^2*x, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID389", +"SFAD[{q, {0, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID390", +"SFAD[{q, {-m^2, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID391", +"SFAD[{q, {-2*m^2, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID392", +"SFAD[{q, {m2^2 - m1^2*x, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID393", +"SFAD[{q, {0, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID394", +"SFAD[{q, {-m^2, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID395", +"SFAD[{q, {-2*m^2, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID396", +"SFAD[{q, {m2^2 - m1^2*x, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID397", +"SFAD[{q, 0, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID398", +"SFAD[{q, -m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID399", +"SFAD[{q, -2*m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID400", +"SFAD[{q, m2^2 - m1^2*x, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID401", +"SFAD[{q, {0, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID402", +"SFAD[{q, {-m^2, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID403", +"SFAD[{q, {-2*m^2, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID404", +"SFAD[{q, {m2^2 - m1^2*x, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID405", +"SFAD[{q, {0, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 0, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID406", +"SFAD[{q, {-m^2, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID407", +"SFAD[{q, {-2*m^2, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, 2*m^2, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID408", +"SFAD[{q, {m2^2 - m1^2*x, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[Momentum[q, D], \ +0, -m2^2 + m1^2*x, {n, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID409", "SFAD[{0, 0}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID410", +"SFAD[{0, -m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID411", +"SFAD[{0, -2*m^2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID412", +"SFAD[{0, m2^2 - m1^2*x}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID413", +"SFAD[{0, {0, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID414", +"SFAD[{0, {-m^2, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID415", +"SFAD[{0, {-2*m^2, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID416", +"SFAD[{0, {m2^2 - m1^2*x, 1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID417", +"SFAD[{0, {0, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID418", +"SFAD[{0, {-m^2, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID419", +"SFAD[{0, {-2*m^2, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {1, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID420", +"SFAD[{0, {m2^2 - m1^2*x, -1}}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {1, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID421", +"SFAD[{0, 0, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID422", +"SFAD[{0, -m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID423", +"SFAD[{0, -2*m^2, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID424", +"SFAD[{0, m2^2 - m1^2*x, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID425", +"SFAD[{0, {0, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID426", +"SFAD[{0, {-m^2, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID427", +"SFAD[{0, {-2*m^2, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID428", +"SFAD[{0, {m2^2 - m1^2*x, 1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID429", +"SFAD[{0, {0, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID430", +"SFAD[{0, {-m^2, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID431", +"SFAD[{0, {-2*m^2, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {2, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID432", +"SFAD[{0, {m2^2 - m1^2*x, -1}, 2}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {2, -1}]]"}, +{"fcstFeynCalcInternalTriple-ID433", +"SFAD[{0, 0, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID434", +"SFAD[{0, -m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID435", +"SFAD[{0, -2*m^2, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID436", +"SFAD[{0, m2^2 - m1^2*x, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID437", +"SFAD[{0, {0, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID438", +"SFAD[{0, {-m^2, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID439", +"SFAD[{0, {-2*m^2, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +1}]]"}, +{"fcstFeynCalcInternalTriple-ID440", +"SFAD[{0, {m2^2 - m1^2*x, 1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, 1}]]"}, +{"fcstFeynCalcInternalTriple-ID441", +"SFAD[{0, {0, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 0, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID442", +"SFAD[{0, {-m^2, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID443", +"SFAD[{0, {-2*m^2, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, 2*m^2, {n, \ +-1}]]"}, +{"fcstFeynCalcInternalTriple-ID444", +"SFAD[{0, {m2^2 - m1^2*x, -1}, n}]//FCI//FCE//FCI", +"FeynAmpDenominator[StandardPropagatorDenominator[0, 0, -m2^2 + \ +m1^2*x, {n, -1}]]"} + }; + + +Tests`Shared`fcstCartesianFeynCalcInternal = +({ +{"fcstCartesianFeynCalcInternal-ID1", "CV[p,i]//FCI", +"CartesianPair[CartesianIndex[i], CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternal-ID2", "CVD[p,i]//FCI", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D]]"}, +{"fcstCartesianFeynCalcInternal-ID3", "CVE[p,i]//FCI", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianMomentum[p, -4 + D]]"}, +{"fcstCartesianFeynCalcInternal-ID4", "TC[p]//FCI", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstCartesianFeynCalcInternal-ID5", "KD[i,j]//FCI", +"CartesianPair[CartesianIndex[i], CartesianIndex[j]]"}, +{"fcstCartesianFeynCalcInternal-ID6", "KDD[i,j]//FCI", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D]]"}, +{"fcstCartesianFeynCalcInternal-ID7", "KDE[i,j]//FCI", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[j, -4 + D]]"}, +{"fcstCartesianFeynCalcInternal-ID8", "CSP[a,b]//FCI", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianFeynCalcInternal-ID9", "CSPD[a,b]//FCI", +"CartesianPair[CartesianMomentum[a, -1 + D], CartesianMomentum[b, -1 + D]]"}, +{"fcstCartesianFeynCalcInternal-ID10", "CSPE[a,b]//FCI", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianFeynCalcInternal-ID11", "CLC[i,j,k]//FCI", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]"}, +{"fcstCartesianFeynCalcInternal-ID12", "CLC[p][i,j]//FCI", +"Eps[CartesianIndex[p], CartesianMomentum[i], CartesianMomentum[j]]"}, +{"fcstCartesianFeynCalcInternal-ID13", "CLC[i,j,k]//FCI", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]"}, +{"fcstCartesianFeynCalcInternal-ID14", "CLC[i,j][p]//FCI", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternal-ID15", "CLC[i][p,q]//FCI", +"Eps[CartesianIndex[i], CartesianMomentum[p], CartesianMomentum[q]]"}, +{"fcstCartesianFeynCalcInternal-ID16", "CLC[][p,q,r]//FCI", +"Eps[CartesianMomentum[p], CartesianMomentum[q], CartesianMomentum[r]]"}, +{"fcstCartesianFeynCalcInternal-ID17", "CLCD[i,j,k]//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + D]]"}, +{"fcstCartesianFeynCalcInternal-ID18", "CLCD[p][i,j]//FCI", +"Eps[CartesianIndex[p, -1 + D], CartesianMomentum[i, -1 + D], CartesianMomentum[j, -1 + \ +D]]"}, +{"fcstCartesianFeynCalcInternal-ID19", "CLCD[i,j,k]//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + D]]"}, +{"fcstCartesianFeynCalcInternal-ID20", "CLCD[i,j][p]//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianMomentum[p, -1 + \ +D]]"}, +{"fcstCartesianFeynCalcInternal-ID21", "CLCD[i][p,q]//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + \ +D]]"}, +{"fcstCartesianFeynCalcInternal-ID22", "CLCD[][p,q,r]//FCI", +"Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D], CartesianMomentum[r, -1 + \ +D]]"}, +{"fcstCartesianFeynCalcInternal-ID23", "CGA[i]//FCI", +"DiracGamma[CartesianIndex[i]]"}, +{"fcstCartesianFeynCalcInternal-ID24", "CGAD[i]//FCI", +"DiracGamma[CartesianIndex[i, -1 + D], D]"}, +{"fcstCartesianFeynCalcInternal-ID25", "CGAE[i]//FCI", +"DiracGamma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternal-ID26", "TGA[]//FCI", +"DiracGamma[ExplicitLorentzIndex[0]]"}, +{"fcstCartesianFeynCalcInternal-ID27", "CGS[p]//FCI", +"DiracGamma[CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternal-ID28", "CGSD[p]//FCI", +"DiracGamma[CartesianMomentum[p, -1 + D], D]"}, +{"fcstCartesianFeynCalcInternal-ID29", "CGSE[p]//FCI", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternal-ID30", "SI[mu]//FCI", +"PauliSigma[LorentzIndex[mu]]"}, +{"fcstCartesianFeynCalcInternal-ID31", "SID[mu]//FCI", +"PauliSigma[LorentzIndex[mu, D], -1 + D]"}, +{"fcstCartesianFeynCalcInternal-ID32", "SIE[mu]//FCI", +"PauliSigma[LorentzIndex[mu, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternal-ID33", "SIS[p]//FCI", +"PauliSigma[Momentum[p]]"}, +{"fcstCartesianFeynCalcInternal-ID34", "SISD[p]//FCI", +"PauliSigma[Momentum[p, D], -1 + D]"}, +{"fcstCartesianFeynCalcInternal-ID35", "SISE[p]//FCI", +"PauliSigma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternal-ID36", "CSI[i]//FCI", +"PauliSigma[CartesianIndex[i]]"}, +{"fcstCartesianFeynCalcInternal-ID37", "CSID[i]//FCI", +"PauliSigma[CartesianIndex[i, -1 + D], -1 + D]"}, +{"fcstCartesianFeynCalcInternal-ID38", "CSIE[i]//FCI", +"PauliSigma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternal-ID39", "CSIS[p]//FCI", +"PauliSigma[CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternal-ID40", "CSISD[p]//FCI", +"PauliSigma[CartesianMomentum[p, -1 + D], -1 + D]"}, +{"fcstCartesianFeynCalcInternal-ID41", "CSISE[p]//FCI", +"PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]"} +}); + +Tests`Shared`fcstCartesianFeynCalcInternalDouble = +({ +{"fcstCartesianFeynCalcInternalDouble-ID1", "CV[p,i]//FCI//FCI", +"CartesianPair[CartesianIndex[i], CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID2", "CVD[p,i]//FCI//FCI", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID3", "CVE[p,i]//FCI//FCI", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianMomentum[p, -4 + D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID4", "TC[p]//FCI//FCI", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID5", "KD[i,j]//FCI//FCI", +"CartesianPair[CartesianIndex[i], CartesianIndex[j]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID6", "KDD[i,j]//FCI//FCI", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID7", "KDE[i,j]//FCI//FCI", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[j, -4 + D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID8", "CSP[a,b]//FCI//FCI", +"CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID9", "CSPD[a,b]//FCI//FCI", +"CartesianPair[CartesianMomentum[a, -1 + D], CartesianMomentum[b, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID10", "CSPE[a,b]//FCI//FCI", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID11", "CLC[i,j,k]//FCI//FCI", + "Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID12", +"CLC[p][i,j]//FCI//FCI", +"Eps[CartesianIndex[p], CartesianMomentum[i], CartesianMomentum[j]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID13", "CLC[i,j,k]//FCI//FCI", + "Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID14", +"CLC[i,j][p]//FCI//FCI", "Eps[CartesianIndex[i], CartesianIndex[j], CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID15", +"CLC[i][p,q]//FCI//FCI", +"Eps[CartesianIndex[i], CartesianMomentum[p], CartesianMomentum[q]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID16", +"CLC[][p,q,r]//FCI//FCI", +"Eps[CartesianMomentum[p], CartesianMomentum[q], CartesianMomentum[r]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID17", +"CLCD[i,j,k]//FCI//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID18", +"CLCD[p][i,j]//FCI//FCI", +"Eps[CartesianIndex[p, -1 + D], CartesianMomentum[i, -1 + D], CartesianMomentum[j, -1 + \ +D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID19", +"CLCD[i,j,k]//FCI//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID20", +"CLCD[i,j][p]//FCI//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianMomentum[p, -1 + \ +D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID21", +"CLCD[i][p,q]//FCI//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + \ +D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID22", +"CLCD[][p,q,r]//FCI//FCI", +"Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D], CartesianMomentum[r, -1 + \ +D]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID23", "CGA[i]//FCI//FCI", +"DiracGamma[CartesianIndex[i]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID24", "CGAD[i]//FCI//FCI", +"DiracGamma[CartesianIndex[i, -1 + D], D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID25", "CGAE[i]//FCI//FCI", +"DiracGamma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID26", "TGA[]//FCI//FCI", +"DiracGamma[ExplicitLorentzIndex[0]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID27", "CGS[p]//FCI//FCI", +"DiracGamma[CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID28", "CGSD[p]//FCI//FCI", +"DiracGamma[CartesianMomentum[p, -1 + D], D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID29", "CGSE[p]//FCI//FCI", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID30", "SI[mu]//FCI//FCI", +"PauliSigma[LorentzIndex[mu]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID31", "SID[mu]//FCI//FCI", +"PauliSigma[LorentzIndex[mu, D], -1 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID32", "SIE[mu]//FCI//FCI", +"PauliSigma[LorentzIndex[mu, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID33", "SIS[p]//FCI//FCI", +"PauliSigma[Momentum[p]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID34", "SISD[p]//FCI//FCI", +"PauliSigma[Momentum[p, D], -1 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID35", "SISE[p]//FCI//FCI", +"PauliSigma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID36", "CSI[i]//FCI//FCI", +"PauliSigma[CartesianIndex[i]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID37", "CSID[i]//FCI//FCI", +"PauliSigma[CartesianIndex[i, -1 + D], -1 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID38", "CSIE[i]//FCI//FCI", +"PauliSigma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID39", "CSIS[p]//FCI//FCI", +"PauliSigma[CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalDouble-ID40", "CSISD[p]//FCI//FCI", +"PauliSigma[CartesianMomentum[p, -1 + D], -1 + D]"}, +{"fcstCartesianFeynCalcInternalDouble-ID41", "CSISE[p]//FCI//FCI", +"PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]"} +}) + +Tests`Shared`fcstCartesianFeynCalcInternalTriple = +({ +{"fcstCartesianFeynCalcInternalTriple-ID1", +"CV[p,i]//FCI//FCE//FCI", "CartesianPair[CartesianIndex[i], CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID2", +"CVD[p,i]//FCI//FCE//FCI", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID3", +"CVE[p,i]//FCI//FCE//FCI", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianMomentum[p, -4 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID4", "TC[p]//FCI//FCE//FCI", +"TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID5", +"KD[i,j]//FCI//FCE//FCI", "CartesianPair[CartesianIndex[i], CartesianIndex[j]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID6", +"KDD[i,j]//FCI//FCE//FCI", +"CartesianPair[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID7", +"KDE[i,j]//FCI//FCE//FCI", +"CartesianPair[CartesianIndex[i, -4 + D], CartesianIndex[j, -4 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID8", +"CSP[a,b]//FCI//FCE//FCI", "CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID9", +"CSPD[a,b]//FCI//FCE//FCI", +"CartesianPair[CartesianMomentum[a, -1 + D], CartesianMomentum[b, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID10", +"CSPE[a,b]//FCI//FCE//FCI", +"CartesianPair[CartesianMomentum[a, -4 + D], CartesianMomentum[b, -4 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID11", +"CLC[i,j,k]//FCI//FCE//FCI", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID12", +"CLC[p][i,j]//FCI//FCE//FCI", +"Eps[CartesianIndex[p], CartesianMomentum[i], CartesianMomentum[j]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID13", +"CLC[i,j,k]//FCI//FCE//FCI", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID14", +"CLC[i,j][p]//FCI//FCE//FCI", +"Eps[CartesianIndex[i], CartesianIndex[j], CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID15", +"CLC[i][p,q]//FCI//FCE//FCI", +"Eps[CartesianIndex[i], CartesianMomentum[p], CartesianMomentum[q]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID16", +"CLC[][p,q,r]//FCI//FCE//FCI", +"Eps[CartesianMomentum[p], CartesianMomentum[q], CartesianMomentum[r]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID17", +"CLCD[i,j,k]//FCI//FCE//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID18", +"CLCD[p][i,j]//FCI//FCE//FCI", +"Eps[CartesianIndex[p, -1 + D], CartesianMomentum[i, -1 + D], CartesianMomentum[j, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID19", +"CLCD[i,j,k]//FCI//FCE//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID20", +"CLCD[i,j][p]//FCI//FCE//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianMomentum[p, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID21", +"CLCD[i][p,q]//FCI//FCE//FCI", +"Eps[CartesianIndex[i, -1 + D], CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID22", +"CLCD[][p,q,r]//FCI//FCE//FCI", +"Eps[CartesianMomentum[p, -1 + D], CartesianMomentum[q, -1 + D], CartesianMomentum[r, -1 + D]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID23", +"CGA[i]//FCI//FCE//FCI", "DiracGamma[CartesianIndex[i]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID24", +"CGAD[i]//FCI//FCE//FCI", "DiracGamma[CartesianIndex[i, -1 + D], D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID25", +"CGAE[i]//FCI//FCE//FCI", +"DiracGamma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID26", "TGA[]//FCI//FCE//FCI", + "DiracGamma[ExplicitLorentzIndex[0]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID27", +"CGS[p]//FCI//FCE//FCI", "DiracGamma[CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID28", +"CGSD[p]//FCI//FCE//FCI", "DiracGamma[CartesianMomentum[p, -1 + D], D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID29", +"CGSE[p]//FCI//FCE//FCI", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID30", +"SI[mu]//FCI//FCE//FCI", "PauliSigma[LorentzIndex[mu]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID31", +"SID[mu]//FCI//FCE//FCI", +"PauliSigma[LorentzIndex[mu, D], -1 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID32", +"SIE[mu]//FCI//FCE//FCI", +"PauliSigma[LorentzIndex[mu, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID33", +"SIS[p]//FCI//FCE//FCI", "PauliSigma[Momentum[p]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID34", +"SISD[p]//FCI//FCE//FCI", "PauliSigma[Momentum[p, D], -1 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID35", +"SISE[p]//FCI//FCE//FCI", +"PauliSigma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID36", +"CSI[i]//FCI//FCE//FCI", "PauliSigma[CartesianIndex[i]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID37", +"CSID[i]//FCI//FCE//FCI", +"PauliSigma[CartesianIndex[i, -1 + D], -1 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID38", +"CSIE[i]//FCI//FCE//FCI", +"PauliSigma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID39", +"CSIS[p]//FCI//FCE//FCI", "PauliSigma[CartesianMomentum[p]]"}, +{"fcstCartesianFeynCalcInternalTriple-ID40", +"CSISD[p]//FCI//FCE//FCI", +"PauliSigma[CartesianMomentum[p, -1 + D], -1 + D]"}, +{"fcstCartesianFeynCalcInternalTriple-ID41", +"CSISE[p]//FCI//FCE//FCI", +"PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]"} +}); diff --git a/Tests/Shared/Isolate.test b/Tests/Shared/Isolate.test index bde48ea24..27230532f 100644 --- a/Tests/Shared/Isolate.test +++ b/Tests/Shared/Isolate.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Isolate *) diff --git a/Tests/Shared/Series2.test b/Tests/Shared/Series2.test index 41c8d0b61..ff676becf 100644 --- a/Tests/Shared/Series2.test +++ b/Tests/Shared/Series2.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Series2 *) diff --git a/Tests/Shared/Shared.mt b/Tests/Shared/Shared.mt index d3b454381..2aa8650aa 100644 --- a/Tests/Shared/Shared.mt +++ b/Tests/Shared/Shared.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "Shared" directory *) @@ -19,16 +19,42 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "Shared"}]] Get/@tests; -stingCompare[a_,b_]:=If[ToString[a]===ToString[b],True,False]; +If[ $OnlySubTest=!="", + testNames = "Tests`Shared`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + +stringCompare[a_,b_]:=If[ToString[a]===ToString[b],True,False]; + +stringCompareIgnore[_,_]:= + True; + +If[ Names["Tests`Shared`fcstSharedObjectsCheckAbort"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],(#[[4]]),testID->#[[1]], + MessagesEquivalenceFunction->stringCompareIgnore]&, + Join@@(ToExpression/@Names["Tests`Shared`fcstSharedObjectsCheckAbort"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; + +If[ Names["Tests`Shared`fcstSharedObjectsTypesetting*"]=!={} && $VersionNumber >= 10, + tmpTest = Map[test[StringReplace[ToString[(ToExpression[#[[2]]]),InputForm, CharacterEncoding -> "Unicode"]," " ->""],StringReplace[(#[[3]])," " ->""],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Shared`fcstSharedObjectsTypesetting*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; -Map[Test[InputForm[ToExpression[(#[[2]])]],InputForm[ToExpression[(#[[3]])]],(#[[4]]),TestID->#[[1]], - MessagesEquivalenceFunction->stingCompare]&, - Join[Tests`Shared`fcstSharedObjectsMessages]]; -If [$VersionNumber >= 10, -Map[Test[StringReplace[ToString[(ToExpression[#[[2]]]),InputForm, CharacterEncoding -> "Unicode"]," " ->""],StringReplace[(#[[3]])," " ->""],TestID->#[[1]]]&, - Join[Tests`Shared`fcstSharedObjectsTypesetting]]; +If[ Names["Tests`Shared`fcstFCCheckSyntax*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],(#[[4]]),testID->#[[1]], + MessagesEquivalenceFunction->stringCompareIgnore]&, + Join@@(ToExpression/@Names["Tests`Shared`fcstFCCheckSyntax*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test ]; -Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, - Join@@(ToExpression/@Select[Names["Tests`Shared`*"], - !StringMatchQ[#, "*fcstSharedObjectsMessages" | "*fcstSharedObjectsTypesetting"] &])]; +nms=Names["Tests`Shared`*"]; +If[ nms=!={} && Select[nms, !StringMatchQ[#, "*fcstSharedObjectsMessages" | "*fcstSharedObjectsTypesetting*" | "*fcstSharedObjectsCheckAbort" | "*fcstFCCheckSyntax*" ] &]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Select[nms, !StringMatchQ[#, "*fcstSharedObjectsMessages" | "*fcstSharedObjectsTypesetting*" | "*fcstSharedObjectsCheckAbort" | "*fcstFCCheckSyntax*" ] &])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test +]; diff --git a/Tests/Shared/SharedObjects.test b/Tests/Shared/SharedObjects.test index e11bd5c4a..29f2c01de 100644 --- a/Tests/Shared/SharedObjects.test +++ b/Tests/Shared/SharedObjects.test @@ -3,9 +3,9 @@ (* :Title: SharedObjects.test *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for the properties of the *) @@ -22,7 +22,6 @@ Tests`Shared`fcstSharedObjectsOwnValues = { {"fcstSharedObjectsOwnValues-ID6", "OwnValues[DeltaFunctionDoublePrime]", "{}"}, {"fcstSharedObjectsOwnValues-ID7", "OwnValues[DeltaFunctionPrime]", "{}"}, {"fcstSharedObjectsOwnValues-ID8", "OwnValues[DiracGamma]", "{}"}, -{"fcstSharedObjectsOwnValues-ID9", "OwnValues[DiracGammaT]", "{}"}, {"fcstSharedObjectsOwnValues-ID10", "OwnValues[DiracMatrix]", "{}"}, {"fcstSharedObjectsOwnValues-ID11", "OwnValues[DiracSigma]", "{}"}, {"fcstSharedObjectsOwnValues-ID12", "OwnValues[DiracSlash]", "{}"}, @@ -40,34 +39,60 @@ Tests`Shared`fcstSharedObjectsOwnValues = { {"fcstSharedObjectsOwnValues-ID24", "OwnValues[FVD]", "{}"}, {"fcstSharedObjectsOwnValues-ID24.1", "OwnValues[FVE]", "{}"}, {"fcstSharedObjectsOwnValues-ID25", "OwnValues[GA]", "{}"}, +{"fcstSharedObjectsOwnValues-ID25.1", "OwnValues[CGA]", "{}"}, {"fcstSharedObjectsOwnValues-ID26", "OwnValues[GA5]", "{HoldPattern[GA5] :> DiracGamma[5]}"}, {"fcstSharedObjectsOwnValues-ID27", "OwnValues[GAD]", "{}"}, -{"fcstSharedObjectsOwnValues-ID27.1", "OwnValues[GAE]", "{}"}, +{"fcstSharedObjectsOwnValues-ID27.1", "OwnValues[CGAD]", "{}"}, +{"fcstSharedObjectsOwnValues-ID27.2", "OwnValues[GAE]", "{}"}, +{"fcstSharedObjectsOwnValues-ID27.3", "OwnValues[CGAE]", "{}"}, {"fcstSharedObjectsOwnValues-ID28", "OwnValues[GaugeField]", "{}"}, {"fcstSharedObjectsOwnValues-ID29", "OwnValues[GS]", "{}"}, +{"fcstSharedObjectsOwnValues-ID29.1", "OwnValues[CGS]", "{}"}, {"fcstSharedObjectsOwnValues-ID30", "OwnValues[GSD]", "{}"}, -{"fcstSharedObjectsOwnValues-ID30.1", "OwnValues[GSE]", "{}"}, +{"fcstSharedObjectsOwnValues-ID30.1", "OwnValues[CGSD]", "{}"}, +{"fcstSharedObjectsOwnValues-ID30.2", "OwnValues[GSE]", "{}"}, +{"fcstSharedObjectsOwnValues-ID30.3", "OwnValues[CGSE]", "{}"}, {"fcstSharedObjectsOwnValues-ID31", "OwnValues[Gstrong]", "{HoldPattern[Gstrong] :> SMP[\"g_s\"]}"}, {"fcstSharedObjectsOwnValues-ID32", "OwnValues[IFPD]", "{}"}, {"fcstSharedObjectsOwnValues-ID33", "OwnValues[Integratedx]", "{}"}, {"fcstSharedObjectsOwnValues-ID34", "OwnValues[LC]", "{}"}, +{"fcstSharedObjectsOwnValues-ID34.1", "OwnValues[CLC]", "{}"}, {"fcstSharedObjectsOwnValues-ID35", "OwnValues[LCD]", "{}"}, +{"fcstSharedObjectsOwnValues-ID35.1", "OwnValues[CLCD]", "{}"}, {"fcstSharedObjectsOwnValues-ID36", "OwnValues[LeftPartialD]", "{}"}, {"fcstSharedObjectsOwnValues-ID37", "OwnValues[LeftRightPartialD]", "{}"}, {"fcstSharedObjectsOwnValues-ID38", "OwnValues[LeftRightPartialD2]", "{}"}, {"fcstSharedObjectsOwnValues-ID38.1", "OwnValues[LeviCivita]", "{}"}, {"fcstSharedObjectsOwnValues-ID39", "OwnValues[LorentzIndex]", "{}"}, -{"fcstSharedObjectsOwnValues-ID40", "OwnValues[Lower]", "{}"}, {"fcstSharedObjectsOwnValues-ID41", "OwnValues[MetricTensor]", "{}"}, {"fcstSharedObjectsOwnValues-ID42", "OwnValues[Momentum]", "{}"}, +{"fcstSharedObjectsOwnValues-ID42.1", "OwnValues[CartesianMomentum]", "{}"}, +{"fcstSharedObjectsOwnValues-ID42.2", "OwnValues[TemporalMomentum]", "{}"}, +{"fcstSharedObjectsOwnValues-ID42.3", "OwnValues[KD]", "{}"}, +{"fcstSharedObjectsOwnValues-ID42.4", "OwnValues[KDD]", "{}"}, +{"fcstSharedObjectsOwnValues-ID42.5", "OwnValues[KDE]", "{}"}, {"fcstSharedObjectsOwnValues-ID43", "OwnValues[MT]", "{}"}, {"fcstSharedObjectsOwnValues-ID44", "OwnValues[MTD]", "{}"}, {"fcstSharedObjectsOwnValues-ID44.1", "OwnValues[MTE]", "{}"}, {"fcstSharedObjectsOwnValues-ID45", "OwnValues[NegativeInteger]", "{}"}, {"fcstSharedObjectsOwnValues-ID46", "OwnValues[Nf]", "{}"}, {"fcstSharedObjectsOwnValues-ID47", "OwnValues[Pair]", "{}"}, +{"fcstSharedObjectsOwnValues-ID47.1", "OwnValues[CartesianPair]", "{}"}, +{"fcstSharedObjectsOwnValues-ID47.2", "OwnValues[TemporalPair]", "{}"}, {"fcstSharedObjectsOwnValues-ID48", "OwnValues[PartialD]", "{}"}, -{"fcstSharedObjectsOwnValues-ID49", "OwnValues[PauliSigma]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48", "OwnValues[PauliSigma]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.1", "OwnValues[SI]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.2", "OwnValues[SID]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.3", "OwnValues[SIE]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.4", "OwnValues[SIS]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.5", "OwnValues[SISD]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.6", "OwnValues[SISE]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.7", "OwnValues[CSI]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.8", "OwnValues[CSID]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.9", "OwnValues[CSIE]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.10", "OwnValues[CSIS]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.11", "OwnValues[CSISD]", "{}"}, +{"fcstSharedObjectsOwnValues-ID48.12", "OwnValues[CSISE]", "{}"}, {"fcstSharedObjectsOwnValues-ID50", "OwnValues[Polarization]", "{}"}, {"fcstSharedObjectsOwnValues-ID51", "OwnValues[PolarizationVector]", "{}"}, {"fcstSharedObjectsOwnValues-ID52", "OwnValues[PlusDistribution]", "{}"}, @@ -85,8 +110,11 @@ Tests`Shared`fcstSharedObjectsOwnValues = { {"fcstSharedObjectsOwnValues-ID64", "OwnValues[SO]", "{}"}, {"fcstSharedObjectsOwnValues-ID65", "OwnValues[SOD]", "{}"}, {"fcstSharedObjectsOwnValues-ID66", "OwnValues[SP]", "{}"}, +{"fcstSharedObjectsOwnValues-ID66.1", "OwnValues[CSP]", "{}"}, {"fcstSharedObjectsOwnValues-ID67", "OwnValues[SPD]", "{}"}, +{"fcstSharedObjectsOwnValues-ID67.1", "OwnValues[CSPD]", "{}"}, {"fcstSharedObjectsOwnValues-ID67.1", "OwnValues[SPE]", "{}"}, +{"fcstSharedObjectsOwnValues-ID67.2", "OwnValues[CSPE]", "{}"}, {"fcstSharedObjectsOwnValues-ID68", "OwnValues[Spinor]", "{}"}, {"fcstSharedObjectsOwnValues-ID69", "OwnValues[SpinorU]", "{}"}, {"fcstSharedObjectsOwnValues-ID70", "OwnValues[SpinorUBar]", "{}"}, @@ -108,7 +136,11 @@ Tests`Shared`fcstSharedObjectsOwnValues = { {"fcstSharedObjectsOwnValues-ID82", "OwnValues[SUNTF]", "{}"}, {"fcstSharedObjectsOwnValues-ID83", "OwnValues[SUNFIndex]", "{}"}, {"fcstSharedObjectsOwnValues-ID84", "OwnValues[ExplicitSUNFIndex]", "{}"}, -{"fcstSharedObjectsOwnValues-ID85", "OwnValues[Zeta2]", "{}"} +{"fcstSharedObjectsOwnValues-ID85", "OwnValues[Zeta2]", "{}"}, +{"fcstSharedObjectsOwnValues-ID86", "OwnValues[Zeta4]", "{}"}, +{"fcstSharedObjectsOwnValues-ID87", "OwnValues[Zeta6]", "{}"}, +{"fcstSharedObjectsOwnValues-ID88", "OwnValues[Zeta8]", "{}"}, +{"fcstSharedObjectsOwnValues-ID89", "OwnValues[Zeta10]", "{}"} }; @@ -124,10 +156,7 @@ Tests`Shared`fcstSharedObjectsUpValues = { {"fcstSharedObjectsUpValues-ID5", "UpValues[DeltaFunction]", "{}"}, {"fcstSharedObjectsUpValues-ID6", "UpValues[DeltaFunctionDoublePrime]", "{}"}, {"fcstSharedObjectsUpValues-ID7", "UpValues[DeltaFunctionPrime]", "{}"}, -{"fcstSharedObjectsUpValues-ID8", "UpValues[DiracGamma]", "{HoldPattern[Transpose[DiracGamma[FeynCalc`SharedObjects`Private`a__\ -]]] :> \n\n \n DiracGammaT[FeynCalc`SharedObjects`Private`a]}"}, -{"fcstSharedObjectsUpValues-ID9", "UpValues[DiracGammaT]", "{HoldPattern[Transpose[DiracGammaT[FeynCalc`SharedObjects`Private`a__]]] :> \n\n \n \ -DiracGamma[FeynCalc`SharedObjects`Private`a]}"}, +{"fcstSharedObjectsUpValues-ID8", "UpValues[DiracGamma]", "{}"}, {"fcstSharedObjectsUpValues-ID10", "UpValues[DiracMatrix]", "{}"}, {"fcstSharedObjectsUpValues-ID11", "UpValues[DiracSigma]", "{}"}, {"fcstSharedObjectsUpValues-ID12", "UpValues[DiracSlash]", "{}"}, @@ -146,13 +175,19 @@ DiracGamma[FeynCalc`SharedObjects`Private`a]}"}, {"fcstSharedObjectsUpValues-ID24", "UpValues[FVD]", "{}"}, {"fcstSharedObjectsUpValues-ID24.1", "UpValues[FVE]", "{}"}, {"fcstSharedObjectsUpValues-ID25", "UpValues[GA]", "{}"}, +{"fcstSharedObjectsUpValues-ID25.1", "UpValues[CGA]", "{}"}, {"fcstSharedObjectsUpValues-ID26", "UpValues[GA5]", "{}"}, {"fcstSharedObjectsUpValues-ID27", "UpValues[GAD]", "{}"}, -{"fcstSharedObjectsUpValues-ID27.1", "UpValues[GAE]", "{}"}, +{"fcstSharedObjectsUpValues-ID27.1", "UpValues[CGAD]", "{}"}, +{"fcstSharedObjectsUpValues-ID27.2", "UpValues[GAE]", "{}"}, +{"fcstSharedObjectsUpValues-ID27.3", "UpValues[CGAE]", "{}"}, {"fcstSharedObjectsUpValues-ID28", "UpValues[GaugeField]", "{}"}, {"fcstSharedObjectsUpValues-ID29", "UpValues[GS]", "{}"}, +{"fcstSharedObjectsUpValues-ID29.1", "UpValues[CGS]", "{}"}, {"fcstSharedObjectsUpValues-ID30", "UpValues[GSD]", "{}"}, -{"fcstSharedObjectsUpValues-ID30.1", "UpValues[GSE]", "{}"}, +{"fcstSharedObjectsUpValues-ID30.1", "UpValues[CGSD]", "{}"}, +{"fcstSharedObjectsUpValues-ID30.2", "UpValues[GSE]", "{}"}, +{"fcstSharedObjectsUpValues-ID30.3", "UpValues[CGSE]", "{}"}, {"fcstSharedObjectsUpValues-ID31", "UpValues[Gstrong]", "{}"}, {"fcstSharedObjectsUpValues-ID32", "UpValues[IFPD]", "{}"}, {"fcstSharedObjectsUpValues-ID33", "UpValues[Integratedx]", "{}"}, @@ -163,17 +198,32 @@ DiracGamma[FeynCalc`SharedObjects`Private`a]}"}, {"fcstSharedObjectsUpValues-ID38", "UpValues[LeftRightPartialD2]", "{}"}, {"fcstSharedObjectsUpValues-ID38.1", "UpValues[LeviCivita]", "{}"}, {"fcstSharedObjectsUpValues-ID39", "UpValues[LorentzIndex]", "{}"}, -{"fcstSharedObjectsUpValues-ID40", "UpValues[Lower]", "{}"}, {"fcstSharedObjectsUpValues-ID41", "UpValues[MetricTensor]", "{}"}, {"fcstSharedObjectsUpValues-ID42", "UpValues[Momentum]", "{}"}, +{"fcstSharedObjectsUpValues-ID42.1", "UpValues[CartesianMomentum]", "{}"}, +{"fcstSharedObjectsUpValues-ID42.2", "UpValues[TemporalMomentum]", "{}"}, {"fcstSharedObjectsUpValues-ID43", "UpValues[MT]", "{}"}, {"fcstSharedObjectsUpValues-ID44", "UpValues[MTD]", "{}"}, {"fcstSharedObjectsUpValues-ID44.1", "UpValues[MTE]", "{}"}, {"fcstSharedObjectsUpValues-ID45", "UpValues[NegativeInteger]", "{}"}, {"fcstSharedObjectsUpValues-ID46", "UpValues[Nf]", "{}"}, {"fcstSharedObjectsUpValues-ID47", "UpValues[Pair]", "{}"}, +{"fcstSharedObjectsUpValues-ID47.1", "UpValues[CartesianPair]", "{}"}, +{"fcstSharedObjectsUpValues-ID47.2", "UpValues[TemporalPair]", "{}"}, {"fcstSharedObjectsUpValues-ID48", "UpValues[PartialD]", "{}"}, {"fcstSharedObjectsUpValues-ID49", "UpValues[PauliSigma]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.1", "UpValues[SI]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.2", "UpValues[SID]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.3", "UpValues[SIE]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.4", "UpValues[SIS]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.5", "UpValues[SISD]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.6", "UpValues[SISE]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.7", "UpValues[CSI]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.8", "UpValues[CSID]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.9", "UpValues[CSIE]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.10", "UpValues[CSIS]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.11", "UpValues[CSISD]", "{}"}, +{"fcstSharedObjectsUpValues-ID49.12", "UpValues[CSISE]", "{}"}, {"fcstSharedObjectsUpValues-ID50", "UpValues[Polarization]", "{}"}, {"fcstSharedObjectsUpValues-ID51", "UpValues[PolarizationVector]", "{}"}, {"fcstSharedObjectsUpValues-ID52", "UpValues[PlusDistribution]", "{}"}, @@ -213,38 +263,328 @@ DiracGamma[FeynCalc`SharedObjects`Private`a]}"}, {"fcstSharedObjectsUpValues-ID84", "UpValues[ExplicitSUNFIndex]", "{HoldPattern[SUNFIndex[FeynCalc`SharedObjects`Private`i_ExplicitSUNFIndex]] :> ExplicitSUNFIndex[FeynCalc`SharedObjects`Private`i]}"}, -{"fcstSharedObjectsUpValues-ID85", "UpValues[Zeta2]", "{}"} +{"fcstSharedObjectsUpValues-ID85", "UpValues[Zeta2]", "{HoldPattern[Conjugate[Zeta2]] :> Zeta2}"}, +{"fcstSharedObjectsUpValues-ID86", "UpValues[Zeta4]", "{HoldPattern[Conjugate[Zeta4]] :> Zeta4}"}, +{"fcstSharedObjectsUpValues-ID87", "UpValues[Zeta6]", "{HoldPattern[Conjugate[Zeta6]] :> Zeta6}"}, +{"fcstSharedObjectsUpValues-ID88", "UpValues[Zeta8]", "{HoldPattern[Conjugate[Zeta8]] :> Zeta8}"}, +{"fcstSharedObjectsUpValues-ID89", "UpValues[Zeta10]", "{HoldPattern[Conjugate[Zeta10]] :> Zeta10}"} } +Tests`Shared`fcstSharedObjectsCheckAbort = { +{"fcstSharedObjectsCheckAbort-ID1", "CheckAbort[DiracGamma[2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID2", "CheckAbort[DiracGamma[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID2.1", "CheckAbort[DiracGamma[a,b,c],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID3", "CheckAbort[GA[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID4", "CheckAbort[GA[8],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID5", "CheckAbort[GAD[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID6", "CheckAbort[GAD[8],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID7", "CheckAbort[GAE[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID8", "CheckAbort[GAE[8],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID9", "CheckAbort[GS[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID10", "CheckAbort[GS[2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID11", "CheckAbort[GSD[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID12", "CheckAbort[GSD[2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID13", "CheckAbort[GSE[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID14", "CheckAbort[GSE[2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID15", "CheckAbort[DiracMatrix[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID16", "CheckAbort[DiracMatrix[8],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID17", "CheckAbort[DiracSlash[1.2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID18", "CheckAbort[DiracSlash[2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID19", "CheckAbort[Eps[i1,i2],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID20", "CheckAbort[Eps[i1,i2,i3,i4,i5],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID21", "CheckAbort[GAE[5],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID22", "CheckAbort[GAE[6],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID23", "CheckAbort[GAE[7],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID24", "CheckAbort[DiracGamma[5,D-4],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID25", "CheckAbort[DiracGamma[6,D-4],True]", "True"}, +{"fcstSharedObjectsCheckAbort-ID26", "CheckAbort[DiracGamma[7,D-4],True]", "True"} +} +Tests`Shared`fcstSharedObjectsBehaviorDiracGamma = +({ +{"fcstSharedObjectsBehaviorDiracGamma-ID1", "DiracGamma[x,0]", +"0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID2", "DiracGamma[0]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID3", "DiracGamma[0,D]", +"0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID4", "DiracGamma[0,D-4]", +"0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID5", "DiracGamma[a+b+c]", +"DiracGamma[a] + DiracGamma[b] + DiracGamma[c]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID6", "DiracGamma[a+b+c,D]", +"DiracGamma[a, D] + DiracGamma[b, D] + DiracGamma[c, D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID7", +"DiracGamma[a TemporalMomentum[p,dim1],dim2]", +"a*DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID8", +"DiracGamma[a TemporalMomentum[p,dim1],dim2-4]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID9", +"DiracGamma[a CartesianMomentum[p,dim1],dim2]", +"a*DiracGamma[CartesianMomentum[p, dim1], dim2]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID10", +"DiracGamma[a CartesianMomentum[p,dim1],dim2-4]", +"a*DiracGamma[CartesianMomentum[p, dim1], -4 + dim2]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID11", +"DiracGamma[ a Momentum[p,dim1],dim2]", +"a*DiracGamma[Momentum[p, dim1], dim2]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID12", +"DiracGamma[a Momentum[p,dim1],dim2-4]", +"a*DiracGamma[Momentum[p, dim1], -4 + dim2]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID13", +"DiracGamma[ExplicitLorentzIndex[2]]", +"DiracGamma[ExplicitLorentzIndex[2]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID14", +"DiracGamma[ExplicitLorentzIndex[2],D]", +"DiracGamma[ExplicitLorentzIndex[2]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID15", +"DiracGamma[ExplicitLorentzIndex[2],D-4]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID16", +"DiracGamma[LorentzIndex[i],D-4]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID17", +"DiracGamma[CartesianIndex[i],D-4]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID18", +"DiracGamma[Momentum[p],D-4]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID19", +"DiracGamma[CartesianMomentum[p],D-4]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID20", +"DiracGamma[TemporalMomentum[p],D-4]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID21", +"DiracGamma[ExplicitLorentzIndex[0],D-4]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID22", +"DiracGamma[LorentzIndex[i,D-4]]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID23", +"DiracGamma[CartesianIndex[i,D-4]]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID24", +"DiracGamma[Momentum[p,D-4]]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID25", +"DiracGamma[CartesianMomentum[p,D-4]]", "0"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID26", +"DiracGamma[LorentzIndex[i,D],D-4]", +"DiracGamma[LorentzIndex[i, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID27", +"DiracGamma[Momentum[p,D],D-4]", +"DiracGamma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID28", +"DiracGamma[CartesianIndex[i,D-1],D-4]", +"DiracGamma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID29", +"DiracGamma[CartesianMomentum[p,D-1],D-4]", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID30", +"DiracGamma[LorentzIndex[i,D-4],D]", +"DiracGamma[LorentzIndex[i, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID31", +"DiracGamma[Momentum[p,D-4],D]", +"DiracGamma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID32", +"DiracGamma[CartesianIndex[i,D-4],D]", +"DiracGamma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID33", +"DiracGamma[CartesianMomentum[p,D-4],D]", +"DiracGamma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID34", +"DiracGamma[LorentzIndex[i],D]", "DiracGamma[LorentzIndex[i]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID35", +"DiracGamma[Momentum[p],D]", "DiracGamma[Momentum[p]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID36", +"DiracGamma[CartesianIndex[i],D]", "DiracGamma[CartesianIndex[i]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID37", +"DiracGamma[CartesianMomentum[p],D]", "DiracGamma[CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID38", +"DiracGamma[LorentzIndex[i,D]]", "DiracGamma[LorentzIndex[i]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID39", +"DiracGamma[Momentum[p,D]]", "DiracGamma[Momentum[p]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID40", +"DiracGamma[CartesianIndex[i,D-1]]", "DiracGamma[CartesianIndex[i]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID41", +"DiracGamma[CartesianMomentum[p,D-1]]", "DiracGamma[CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID42", +"DiracGamma[ExplicitLorentzIndex[0],D]", "DiracGamma[ExplicitLorentzIndex[0]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID43", +"DiracGamma[TemporalMomentum[p],D]", +"DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID44", +"DiracGamma[TemporalMomentum[p]]", +"DiracGamma[ExplicitLorentzIndex[0]]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID45", "DiracGamma[5]", +"DiracGamma[5]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID46", "DiracGamma[6]", +"DiracGamma[6]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID47", "DiracGamma[7]", +"DiracGamma[7]"}, +{"fcstSharedObjectsBehaviorDiracGamma-ID50", +"DataType[SoftScale, FCVariable] = True; \n DiracGamma[ +SoftScale*(qvabs*CartesianMomentum[qhat] - +qvabs*CartesianMomentum[kphat]* +CartesianPair[CartesianMomentum[kphat], +CartesianMomentum[qhat]] + (qvabs*CartesianMomentum[kphat]* +CartesianPair[CartesianMomentum[kphat], CartesianMomentum[qhat]]*m1)/m2)] // FCE", +"SoftScale (qvabs CGS[qhat] - qvabs CGS[kphat] CSP[kphat, qhat] + (m1 qvabs CGS[kphat] CSP[kphat, qhat])/m2)"} +}); + +Tests`Shared`fcstSharedObjectsBehaviorEps = +({ +{"fcstSharedObjectsBehaviorEps-ID1", "Eps[0, 1, 2, 3]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID2", "Eps[0,1,3,2]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID3", "Eps[a,b,a]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID4", "Eps[a,CartesianMomentum[p,D-4],b,c]", +"0"}, +{"fcstSharedObjectsBehaviorEps-ID5", "Eps[a,Momentum[p,D-4],b,c]", +"0"}, +{"fcstSharedObjectsBehaviorEps-ID6", +"Eps[a,LorentzIndex[i,D-4],b,c]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID7", "Eps[a,CartesianIndex[i,D-4],b,c]", +"0"}, +{"fcstSharedObjectsBehaviorEps-ID8", "Eps[a,ExplicitLorentzIndex[0],b]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID9", "Eps[a,TemporalMomentum[],b]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID10", "Eps[a,ff Momentum[p],b,c]", +"ff*Eps[a, Momentum[p], b, c]"}, +{"fcstSharedObjectsBehaviorEps-ID11", "Eps[a,ff CartesianMomentum[p],b,c]", +"ff*Eps[a, CartesianMomentum[p], b, c]"}, +{"fcstSharedObjectsBehaviorEps-ID12", +"Eps[LorentzIndex[i1], Momentum[p,D],LorentzIndex[i2], \ +Momentum[q,D]]", +"Eps[LorentzIndex[i1], Momentum[p], LorentzIndex[i2], \ +Momentum[q]]"}, +{"fcstSharedObjectsBehaviorEps-ID13", +"Eps[CartesianIndex[i1], Momentum[p,D],CartesianIndex[i2], Momentum[q,D]]", +"Eps[CartesianIndex[i1], Momentum[p], CartesianIndex[i2], Momentum[q]]"}, +{"fcstSharedObjectsBehaviorEps-ID14", "Eps[a,TemporalMomentum[p],b,c]", +"Eps[a, ExplicitLorentzIndex[0], b, c]*TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstSharedObjectsBehaviorEps-ID15", "Eps[a,Momentum[p],b]", +"-Eps[a, CartesianMomentum[p], b]"}, +{"fcstSharedObjectsBehaviorEps-ID16", "Eps[CartesianMomentum[p1], CartesianMomentum[p2], CartesianMomentum[p3], ExplicitLorentzIndex[0]]","-Eps[CartesianMomentum[p1], CartesianMomentum[p2], CartesianMomentum[p3]]"}, +{"fcstSharedObjectsBehaviorEps-ID17", "Eps[CartesianMomentum[p1, D - 1], CartesianMomentum[p2, D - 1], CartesianMomentum[p3, D - 1], +ExplicitLorentzIndex[0]]","-Eps[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + D], +CartesianMomentum[p3, -1 + D]]"}, +{"fcstSharedObjectsBehaviorEps-ID18", "Eps[Momentum[p1], Momentum[p2], Momentum[p3], ExplicitLorentzIndex[0]]","Eps[CartesianMomentum[p1], CartesianMomentum[p2], CartesianMomentum[p3]]"}, +{"fcstSharedObjectsBehaviorEps-ID19", "Eps[Momentum[p1, D], Momentum[p2, D], Momentum[p3, D], ExplicitLorentzIndex[0]]","Eps[CartesianMomentum[p1, -1 + D], CartesianMomentum[p2, -1 + D], +CartesianMomentum[p3, -1 + D]]"}, +{"fcstSharedObjectsBehaviorEps-ID20", "Eps[LorentzIndex[i1], 0, LorentzIndex[i2], LorentzIndex[i3]]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID21", "Eps[0, CartesianMomentum[x], CartesianMomentum[y]]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID22", "Eps[CartesianIndex[i], CartesianIndex[j], CartesianIndex[k], CartesianIndex[l]]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID23", "Eps[CartesianMomentum[p], CartesianIndex[j], CartesianMomentum[k],CartesianIndex[l]]", "0"}, +{"fcstSharedObjectsBehaviorEps-ID24", "Eps[CartesianIndex[c1], CartesianIndex[c2], ExplicitLorentzIndex[0]]", "0"} +}) + +Tests`Shared`fcstSharedObjectsBehaviorPauliSigma = +({ +{"fcstSharedObjectsBehaviorPauliSigma-ID1", "PauliSigma[x,0]", +"0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID2", "PauliSigma[0]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID3", "PauliSigma[0,D-1]", +"0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID4", "PauliSigma[0,D-4]", +"0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID5", "PauliSigma[a+b+c]", +"PauliSigma[a] + PauliSigma[b] + PauliSigma[c]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID6", "PauliSigma[a+b+c,D-1]", + "PauliSigma[a, -1 + D] + PauliSigma[b, -1 + D] + PauliSigma[c, -1 \ ++ D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID7", +"PauliSigma[a TemporalMomentum[p,dim1],dim2]", +"a*PauliSigma[TemporalMomentum[p], dim2]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID8", +"PauliSigma[a TemporalMomentum[p,dim1],dim2-4]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID9", +"PauliSigma[a CartesianMomentum[p,dim1],dim2]", +"a*PauliSigma[CartesianMomentum[p, dim1], dim2]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID10", +"PauliSigma[a CartesianMomentum[p,dim1],dim2-4]", +"a*PauliSigma[CartesianMomentum[p, dim1], -4 + dim2]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID11", +"PauliSigma[ a Momentum[p,dim1],dim2]", +"a*PauliSigma[Momentum[p, dim1], dim2]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID12", +"PauliSigma[a Momentum[p,dim1],dim2-4]", +"a*PauliSigma[Momentum[p, dim1], -4 + dim2]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID13", +"PauliSigma[ExplicitLorentzIndex[2]]", +"PauliSigma[ExplicitLorentzIndex[2]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID14", +"PauliSigma[ExplicitLorentzIndex[2],D-1]", +"PauliSigma[ExplicitLorentzIndex[2]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID15", +"PauliSigma[ExplicitLorentzIndex[2],D-4]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID16", +"PauliSigma[LorentzIndex[i],D-4]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID17", +"PauliSigma[CartesianIndex[i],D-4]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID18", +"PauliSigma[Momentum[p],D-4]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID19", +"PauliSigma[CartesianMomentum[p],D-4]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID20", +"PauliSigma[TemporalMomentum[p],D-4]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID21", +"PauliSigma[ExplicitLorentzIndex[0],D-4]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID22", +"PauliSigma[LorentzIndex[i,D-4]]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID23", +"PauliSigma[CartesianIndex[i,D-4]]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID24", +"PauliSigma[Momentum[p,D-4]]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID25", +"PauliSigma[CartesianMomentum[p,D-4]]", "0"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID26", +"PauliSigma[LorentzIndex[i,D],D-4]", +"PauliSigma[LorentzIndex[i, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID27", +"PauliSigma[Momentum[p,D],D-4]", +"PauliSigma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID28", +"PauliSigma[CartesianIndex[i,D-1],D-4]", +"PauliSigma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID29", +"PauliSigma[CartesianMomentum[p,D-1],D-4]", +"PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID30", +"PauliSigma[LorentzIndex[i,D-4],D-1]", +"PauliSigma[LorentzIndex[i, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID31", +"PauliSigma[Momentum[p,D-4],D-1]", +"PauliSigma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID32", +"PauliSigma[CartesianIndex[i,D-4],D-1]", +"PauliSigma[CartesianIndex[i, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID33", +"PauliSigma[CartesianMomentum[p,D-4],D-1]", +"PauliSigma[CartesianMomentum[p, -4 + D], -4 + D]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID34", +"PauliSigma[LorentzIndex[i],D-1]", "PauliSigma[LorentzIndex[i]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID35", +"PauliSigma[Momentum[p],D-1]", "PauliSigma[Momentum[p]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID36", +"PauliSigma[CartesianIndex[i],D-1]", "PauliSigma[CartesianIndex[i]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID37", +"PauliSigma[CartesianMomentum[p],D-1]", "PauliSigma[CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID38", +"PauliSigma[LorentzIndex[i,D]]", "PauliSigma[LorentzIndex[i]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID39", +"PauliSigma[Momentum[p,D]]", "PauliSigma[Momentum[p]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID40", +"PauliSigma[CartesianIndex[i,D-1]]", "PauliSigma[CartesianIndex[i]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID41", +"PauliSigma[CartesianMomentum[p,D-1]]", "PauliSigma[CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID42", +"PauliSigma[ExplicitLorentzIndex[0],D-1]", "1"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID43", +"PauliSigma[TemporalMomentum[p],D-1]", "TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID44", +"PauliSigma[TemporalMomentum[p]]", "TemporalPair[ExplicitLorentzIndex[0], TemporalMomentum[p]]"}, +{"fcstSharedObjectsBehaviorPauliSigma-ID45", +"DataType[SoftScale, FCVariable] = True; \n PauliSigma[ +SoftScale*(qvabs*CartesianMomentum[qhat] - + qvabs*CartesianMomentum[kphat]* + CartesianPair[CartesianMomentum[kphat], + CartesianMomentum[qhat]] + + (qvabs*CartesianMomentum[kphat]* + CartesianPair[CartesianMomentum[kphat], + CartesianMomentum[qhat]]*m1)/m2)] // FCE", "SoftScale (qvabs CSIS[qhat] - qvabs CSIS[kphat] CSP[kphat, qhat] + ( +m1 qvabs CSIS[kphat] CSP[kphat, qhat])/m2)"} +}); -Tests`Shared`fcstSharedObjectsMessages = { -{"fcstSharedObjectsMessages-I1", "DiracGamma[5, D]", "Null", "{Message[DiracGamma::gamma5fail, DiracGamma[5, D]]}"}, -{"fcstSharedObjectsMessages-I2", "DiracGamma[6, D]", "Null", "{Message[DiracGamma::gamma5fail, DiracGamma[6, D]]}"}, -{"fcstSharedObjectsMessages-I3", "DiracGamma[7, D]", "Null", "{Message[DiracGamma::gamma5fail, DiracGamma[7, D]]}"}, -{"fcstSharedObjectsMessages-I4", "GAD[5]", "Null", "{Message[DiracGamma::gamma5fail, GAD[5]]}"}, -{"fcstSharedObjectsMessages-I5", "GAD[6]", "Null", "{Message[DiracGamma::gamma5fail, GAD[6]]}"}, -{"fcstSharedObjectsMessages-I6", "GAD[7]", "Null", "{Message[DiracGamma::gamma5fail, GAD[7]]}"}, -{"fcstSharedObjectsMessages-I7", "DiracMatrix[5, Dimension->D]", "Null", "{Message[DiracGamma::gamma5fail, DiracGamma[5, Dimension -> D]]}"}, -{"fcstSharedObjectsMessages-I8", "DiracMatrix[6, Dimension->D]", "Null", "{Message[DiracGamma::gamma5fail, DiracGamma[6, Dimension -> D]]}"}, -{"fcstSharedObjectsMessages-I9", "DiracMatrix[7, Dimension->D]", "Null", "{Message[DiracGamma::gamma5fail, DiracGamma[7, Dimension -> D]]}"}, -{"fcstSharedObjectsMessages-I10", "Eps[i1,i2]", "Null", "{Message[Eps::argrx, Eps[{i1, i2}], 2, 4]}"}, -{"fcstSharedObjectsMessages-I11", "Eps[i1,i2,i3]", "Null", "{Message[Eps::argrx, Eps[{i1, i2, i3}], 3, 4]}"}, -{"fcstSharedObjectsMessages-I12", "Eps[i1,i2,i3,i4,i5]", "Null", "{Message[Eps::argrx, Eps[{i1, i2, i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I13", "Eps[1,2]", "Null", "{Message[Eps::argrx, Eps[{1, 2}], 2, 4]}"}, -{"fcstSharedObjectsMessages-I14", "Eps[1,2,3]", "Null", "{Message[Eps::argrx, Eps[{1, 2, 3}], 3, 4]}"}, -{"fcstSharedObjectsMessages-I15", "Eps[1,2,3,4,5]", "Null", "{Message[Eps::argrx, Eps[{1, 2, 3, 4, 5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I16", "LC[i1,i2,i3,i4,i5]", "Null", "{Message[LC::argrx, LC[{i1, i2, i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I17", "LCD[i1,i2,i3,i4,i5]", "Null", "{Message[LCD::argrx, LCD[{i1, i2, i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I18", "LC[i1][i2,i3,i4,i5]", "Null", "{Message[LC::argrx, LC[{i1}][{i2, i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I19", "LCD[i1][i2,i3,i4,i5]", "Null", "{Message[LCD::argrx, LCD[{i1}][{i2, i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I20", "LC[i1,i2][i3,i4,i5]", "Null", "{Message[LC::argrx, LC[{i1, i2}][{i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I21", "LCD[i1,i2][i3,i4,i5]", "Null", "{Message[LCD::argrx, LCD[{i1, i2}][{i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I22", "LeviCivita[i1,i2,i3,i4,i5]", "Null", "{Message[LeviCivita::argrx, LeviCivita[{i1, i2, i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I23", "LeviCivita[i1][i2,i3,i4,i5]", "Null", "{Message[LeviCivita::argrx, LeviCivita[{i1}][{i2, i3, i4, i5}], 5, 4]}"}, -{"fcstSharedObjectsMessages-I24", "LeviCivita[i1,i2][i3,i4,i5]", "Null", "{Message[LeviCivita::argrx, LeviCivita[{i1, i2}][{i3, i4, i5}], 5, 4]}"} -} Tests`Shared`fcstSharedObjectsBehavior = { {"fcstSharedObjectsBehavior-ID1", "ChiralityProjector[1]", "DiracGamma[6]"}, @@ -253,64 +593,11 @@ Tests`Shared`fcstSharedObjectsBehavior = { {"fcstSharedObjectsBehavior-ID4", "DeltaFunction[x]", "DeltaFunction[x]"}, {"fcstSharedObjectsBehavior-ID5", "DeltaFunction[0.7]", "0"}, {"fcstSharedObjectsBehavior-ID6", "DeltaFunction[-0.3]", "0"}, -{"fcstSharedObjectsBehavior-ID7", "Transpose[DiracGamma[x]]", "DiracGammaT[x]"}, -{"fcstSharedObjectsBehavior-ID8", "DiracGamma[]", "1"}, -{"fcstSharedObjectsBehavior-ID9", "DiracGamma[a*Momentum[p, D1], D2]", "a DiracGamma[Momentum[p, D1], D2]"}, -{"fcstSharedObjectsBehavior-ID10", "DiracGamma[a LorentzIndex[mu, D1], D2]","a DiracGamma[LorentzIndex[mu, D1], D2]"}, - {"fcstSharedObjectsBehavior-ID10.1","DiracGamma[LorentzIndex[p, D], 4]"," DiracGamma[LorentzIndex[p, D]]"}, - {"fcstSharedObjectsBehavior-ID10.2","DiracGamma[ExplicitLorentzIndex[p, D], 4]"," DiracGamma[ExplicitLorentzIndex[p, D]]"}, - {"fcstSharedObjectsBehavior-ID10.3","DiracGamma[Momentum[p, D], 4]"," DiracGamma[Momentum[p, D]]"}, - {"fcstSharedObjectsBehavior-ID10.4","DiracGamma[func[p, D], 4]"," DiracGamma[func[p, D],4]"}, -{"fcstSharedObjectsBehavior-ID14", "DiracGamma[x, 0]", "0"}, -{"fcstSharedObjectsBehavior-ID14.1", "DiracGamma[0]", "0"}, -{"fcstSharedObjectsBehavior-ID14.2", "DiracGamma[0,x]", "0"}, -{"fcstSharedObjectsBehavior-ID15", "DiracGamma[Momentum[a] + Momentum[b] + Momentum[c]]", -"DiracGamma[Momentum[a]] + DiracGamma[Momentum[b]] + DiracGamma[Momentum[c]]"}, -{"fcstSharedObjectsBehavior-ID15.1", "DiracGamma[Momentum[a,D] + Momentum[b,D] + Momentum[c,D],D]", -"DiracGamma[Momentum[a,D],D] + DiracGamma[Momentum[b,D],D] + DiracGamma[Momentum[c,D],D]"}, -{"fcstSharedObjectsBehavior-ID16", "DiracGamma[Momentum[p1, D1], Momentum[p2, D2]]", "DiracGamma[Momentum[p1, D1], D1].DiracGamma[Momentum[p2, D2], D2]"}, -{"fcstSharedObjectsBehavior-ID17", "DiracGamma[Momentum[p1, D1], Momentum[p2, D2], LorentzIndex[mu]]", - "DiracGamma[Momentum[p1, D1], D1].DiracGamma[Momentum[p2, D2], D2].DiracGamma[LorentzIndex[mu]]"}, -{"fcstSharedObjectsBehavior-ID18", "DiracGamma[LorentzIndex[p1, D1], LorentzIndex[p2, D2]]", - "DiracGamma[LorentzIndex[p1, D1], D1] . DiracGamma[LorentzIndex[p2, D2], D2]"}, -{"fcstSharedObjectsBehavior-ID19", "DiracGamma[LorentzIndex[p1, D1], LorentzIndex[p2, D2], Momentum[p, 4]]", - "DiracGamma[LorentzIndex[p1, D1], D1].DiracGamma[LorentzIndex[p2, D2], D2].DiracGamma[Momentum[p]]"}, -{"fcstSharedObjectsBehavior-ID20", "DiracGamma[LorentzIndex[p1, D1],Momentum[p2, D2]]", " DiracGamma[LorentzIndex[p1, D1], D1] . DiracGamma[Momentum[p2, D2], D2]"}, -{"fcstSharedObjectsBehavior-ID21", "DiracGamma[LorentzIndex[p1, D1], Momentum[p2, D2], Momentum[p, 4]]", - "DiracGamma[LorentzIndex[p1, D1], D1] . DiracGamma[Momentum[p2, D2], D2] . DiracGamma[Momentum[p]]"}, -{"fcstSharedObjectsBehavior-ID22", "DiracGamma[Momentum[p1, D1], LorentzIndex[p2, D2]]", - "DiracGamma[Momentum[p1, D1], D1] . DiracGamma[LorentzIndex[p2, D2], D2]"}, -{"fcstSharedObjectsBehavior-ID23", "DiracGamma[Momentum[p1, D1], LorentzIndex[p2, D2], Momentum[p, 4]]", - "DiracGamma[Momentum[p1, D1], D1] . DiracGamma[LorentzIndex[p2, D2], D2] . DiracGamma[Momentum[p]]"}, -{"fcstSharedObjectsBehavior-ID24", "DiracGamma[LorentzIndex[mu], D - 4]", "0"}, -{"fcstSharedObjectsBehavior-ID25", "DiracGamma[Momentum[p], D - 4]", "0"}, -{"fcstSharedObjectsBehavior-ID26", "DiracGamma[Momentum[p, D - 4]]", "0"}, -{"fcstSharedObjectsBehavior-ID27", "DiracGamma[LorentzIndex[mu, D - 4]]", "0"}, -{"fcstSharedObjectsBehavior-ID28", "DiracGamma[LorentzIndex[mu, D], D - 4]", - "DiracGamma[LorentzIndex[mu, -4 + D], -4 + D]"}, -{"fcstSharedObjectsBehavior-ID29", "DiracGamma[Momentum[p, D], D - 4]", " DiracGamma[Momentum[p, -4 + D], -4 + D]"}, -{"fcstSharedObjectsBehavior-ID30", "DiracGamma[LorentzIndex[mu, D - 4], D]", "DiracGamma[LorentzIndex[mu, -4 + D], -4 + D]"}, -{"fcstSharedObjectsBehavior-ID31", "DiracGamma[Momentum[p, D - 4], D]", "DiracGamma[Momentum[p, -4 + D], -4 + D]"}, -{"fcstSharedObjectsBehavior-ID32", "DiracGamma[LorentzIndex[mu, D]]", - "DiracGamma[LorentzIndex[mu]]"}, -{"fcstSharedObjectsBehavior-ID33", "DiracGamma[2 Momentum[p], D]", "2*DiracGamma[Momentum[p], D]"}, -{"fcstSharedObjectsBehavior-ID34", "DiracGamma[Momentum[p, D]]", " DiracGamma[Momentum[p]]"}, -{"fcstSharedObjectsBehavior-ID35", "DiracGamma[LorentzIndex[mu, D]]", "DiracGamma[LorentzIndex[mu]]"}, -{"fcstSharedObjectsBehavior-ID35.1", "DiracGamma[LorentzIndex[mu, D], DD]", "DiracGamma[LorentzIndex[mu, D], DD]"}, -{"fcstSharedObjectsBehavior-ID35.2", "DiracGamma[LorentzIndex[mu, D], 5]", "DiracGamma[LorentzIndex[mu, D], 5]"}, -{"fcstSharedObjectsBehavior-ID35.3", "DiracGamma[LorentzIndex[mu, D], D - 2]", "DiracGamma[LorentzIndex[mu, D], D - 2]"}, -{"fcstSharedObjectsBehavior-ID35.4", "DiracGamma[LorentzIndex[mu, 4], 5]", "DiracGamma[LorentzIndex[mu, 4], 5]"}, -{"fcstSharedObjectsBehavior-ID35.5", "DiracGamma[LorentzIndex[mu, 4], D - 2]", "DiracGamma[LorentzIndex[mu, 4], D - 2]"}, -{"fcstSharedObjectsBehavior-ID35.6", "DiracGamma[LorentzIndex[mu, D - 4], DD]", "DiracGamma[LorentzIndex[mu, D - 4], DD]"}, -{"fcstSharedObjectsBehavior-ID35.7", "DiracGamma[LorentzIndex[mu, D - 4], 5]", "DiracGamma[LorentzIndex[mu, D - 4], 5]"}, -{"fcstSharedObjectsBehavior-ID35.8", "DiracGamma[LorentzIndex[mu, D - 4], 2]", "DiracGamma[LorentzIndex[mu, D - 4], 2]"}, -{"fcstSharedObjectsBehavior-ID36", "Transpose[DiracGammaT[x]]", "DiracGamma[x]"}, {"fcstSharedObjectsBehavior-ID37", "DiracMatrix[0]", "DiracGamma[ExplicitLorentzIndex[0]]"}, {"fcstSharedObjectsBehavior-ID38", "DiracMatrix[1]", "DiracGamma[ExplicitLorentzIndex[1]]"}, {"fcstSharedObjectsBehavior-ID39", "DiracMatrix[2]", "DiracGamma[ExplicitLorentzIndex[2]]"}, {"fcstSharedObjectsBehavior-ID40", "DiracMatrix[3]", "DiracGamma[ExplicitLorentzIndex[3]]"}, -{"fcstSharedObjectsBehavior-ID41", "DiracMatrix[4]", "DiracGamma[ExplicitLorentzIndex[4]]"}, -{"fcstSharedObjectsBehavior-ID41.1", "DiracMatrix[mu]", "DiracGamma[LorentzIndex[mu]]"}, +{"fcstSharedObjectsBehavior-ID41", "DiracMatrix[mu]", "DiracGamma[LorentzIndex[mu]]"}, {"fcstSharedObjectsBehavior-ID41.2", "DiracMatrix[mu, nu, rho]", "DiracGamma[LorentzIndex[mu]].DiracGamma[LorentzIndex[nu]].DiracGamma[ LorentzIndex[rho]]"}, {"fcstSharedObjectsBehavior-ID41.3", "DiracMatrix[mu, nu, rho, Dimension -> D]", "DiracGamma[LorentzIndex[mu, D], D].DiracGamma[LorentzIndex[nu, D], @@ -321,6 +608,9 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID45", "DiracSigma[2, 1] ", " - DiracSigma[1, 2]"}, {"fcstSharedObjectsBehavior-ID46", "DiracSigma[a, b] ", " DiracSigma[a, b]"}, {"fcstSharedObjectsBehavior-ID47", "DiracSigma[b, a] ", " - DiracSigma[a, b]"}, +{"fcstSharedObjectsBehavior-ID47.1", "DiracSigma[a, a] ", "0"}, +{"fcstSharedObjectsBehavior-ID47.2", "DiracSigma[GA[mu], GA[mu]] ", "0"}, +{"fcstSharedObjectsBehavior-ID47.3", "Head[DiracSigma[a_, a_]]", "DiracSigma"}, {"fcstSharedObjectsBehavior-ID48", "DiracSigma[DiracMatrix[1, 3]]", " DiracSigma[DiracMatrix[1, 3]]"}, {"fcstSharedObjectsBehavior-ID49", "DiracSigma[DiracMatrix[2, 1]]", " - DiracSigma[DiracMatrix[1, 2]]"}, @@ -330,37 +620,10 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, "x DiracSigma[DiracGamma[i], DiracGamma[j]]"}, {"fcstSharedObjectsBehavior-ID53", "DiracSigma[x DiracGamma[i], y z DiracGamma[j]]", "x y z DiracSigma[DiracGamma[i], DiracGamma[j]]"}, {"fcstSharedObjectsBehavior-ID54", "DiracSlash[p]", "DiracGamma[Momentum[p]]"}, +{"fcstSharedObjectsBehavior-ID54.1", "DiracSlash[0]", "0"}, {"fcstSharedObjectsBehavior-ID55", "DiracSlash[p, Dimension -> D]", "DiracGamma[Momentum[p, D], D]"}, {"fcstSharedObjectsBehavior-ID56", "DiracSlash[p , l, k]", "DiracGamma[Momentum[p]].DiracGamma[Momentum[l]].DiracGamma[Momentum[k]]"}, {"fcstSharedObjectsBehavior-ID57", "DiracSlash[p , l, k, Dimension -> D]", "DiracGamma[Momentum[p, D], D].DiracGamma[Momentum[l, D], D].DiracGamma[Momentum[k, D], D]"}, -{"fcstSharedObjectsBehavior-ID57.1", "DiracSpinor[p, 0]", "Spinor[Momentum[p], 0, 1]"}, -{"fcstSharedObjectsBehavior-ID57.2", "DiracSpinor[p, m]", "Spinor[Momentum[p], m, 1]"}, -{"fcstSharedObjectsBehavior-ID58", "Head[Eps[0, 1, 2, 3]]", "Eps"}, -{"fcstSharedObjectsBehavior-ID59", "Head[Eps[0, 1, 3,2]]", "Eps"}, -{"fcstSharedObjectsBehavior-ID63", "Eps[a, a, b, c]", "0"}, -{"fcstSharedObjectsBehavior-ID64", "Head[Eps[ExplicitLorentzIndex[1], ExplicitLorentzIndex[2], ExplicitLorentzIndex[3], ExplicitLorentzIndex[0]]]", "Eps"}, -{"fcstSharedObjectsBehavior-ID65", "Head[Eps[ExplicitLorentzIndex[0], ExplicitLorentzIndex[1], ExplicitLorentzIndex[3], ExplicitLorentzIndex[2]]]", "Eps"}, -{"fcstSharedObjectsBehavior-ID66", "Eps[ExplicitLorentzIndex[1], ExplicitLorentzIndex[1], ExplicitLorentzIndex[3], ExplicitLorentzIndex[2]]", "0"}, -{"fcstSharedObjectsBehavior-ID67", "Eps[a, LorentzIndex[mu], b, LorentzIndex[nu]]", " Eps[a, LorentzIndex[mu], b, LorentzIndex[nu]]"}, -{"fcstSharedObjectsBehavior-ID68", "Eps[a, LorentzIndex[mu], b, LorentzIndex[mu]]", " 0"}, -{"fcstSharedObjectsBehavior-ID69", "Eps[a, 5 ExplicitLorentzIndex[mu], b, ExplicitLorentzIndex[nu]]", " Eps[a, 5 ExplicitLorentzIndex[mu], b, ExplicitLorentzIndex[nu]]"}, -{"fcstSharedObjectsBehavior-ID70", "Eps[a, ExplicitLorentzIndex[mu], d, ExplicitLorentzIndex[mu]]", " 0"}, -{"fcstSharedObjectsBehavior-ID71", "Eps[a, 2 LorentzIndex[mu], b, 4 LorentzIndex[mu]]", " 0"}, -{"fcstSharedObjectsBehavior-ID72", "Eps[a, 2 LorentzIndex[mu], b,f LorentzIndex[mu]]", " Eps[a, 2 LorentzIndex[mu], b, f LorentzIndex[mu]]"}, -{"fcstSharedObjectsBehavior-ID73", "Eps[a,2 ExplicitLorentzIndex[mu], b, 4 ExplicitLorentzIndex[mu]]", " 0"}, -{"fcstSharedObjectsBehavior-ID74", "Eps[a,2 ExplicitLorentzIndex[mu], b, f ExplicitLorentzIndex[mu]]", " Eps[a,2 ExplicitLorentzIndex[mu],b, f ExplicitLorentzIndex[mu]]"}, -{"fcstSharedObjectsBehavior-ID75", "Eps[a, Momentum[p], Momentum[q], e]", " Eps[a, Momentum[p], Momentum[q], e]"}, -{"fcstSharedObjectsBehavior-ID76", "Eps[a, Momentum[p], b, Momentum[p]]", " 0"}, -{"fcstSharedObjectsBehavior-ID77", "Eps[a, 2 Momentum[p], b, 4 Momentum[p]]", " 0"}, -{"fcstSharedObjectsBehavior-ID78", "Eps[a, 2 Momentum[p], b, f Momentum[p]]", " Eps[a, 2 Momentum[p], b, f Momentum[p]]"}, -{"fcstSharedObjectsBehavior-ID79", "Eps[a, LorentzIndex[mu, D - 4], b, c]", " 0"}, -{"fcstSharedObjectsBehavior-ID80", "Eps[a, Momentum[p, D - 4], b, c]", " 0"}, -{"fcstSharedObjectsBehavior-ID81", "Eps[a, LorentzIndex[mu, D], b ,c]", " Eps[a, LorentzIndex[mu], b, c]"}, -{"fcstSharedObjectsBehavior-ID82", "Eps[a, LorentzIndex[mu, D1], b, c, Dimension -> D2]", - " Eps[a, LorentzIndex[mu, D1], b, c, Dimension -> D2]"}, -{"fcstSharedObjectsBehavior-ID83", "Eps[a, Momentum[mu, D], b, c]", " Eps[a, Momentum[mu], b ,c]"}, -{"fcstSharedObjectsBehavior-ID84", "Eps[a, Momentum[mu, D1], b, c, Dimension -> D2]", " Eps[a, Momentum[mu, D1], b, c, Dimension -> D2]"}, -{"fcstSharedObjectsBehavior-ID84.1", "Eps[a, Momentum[mu, D], b, Momentum[mu, D], Dimension->D]", "0"}, {"fcstSharedObjectsBehavior-ID85", "SUNIndex[ExplicitSUNIndex[a]]", " ExplicitSUNIndex[a]"}, {"fcstSharedObjectsBehavior-ID86", "SUNIndex[ExplicitSUNIndex[2]]", " ExplicitSUNIndex[2]"}, {"fcstSharedObjectsBehavior-ID87", "FAD[-a]", " FAD[a]"}, @@ -372,8 +635,7 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID87.5", "FAD[{q1, m}, {q1 - p, 0, 0}]", "FAD[{q1, m}]"}, {"fcstSharedObjectsBehavior-ID87.6", "FAD[{q1 - p, 0, 0}, {q1, m}]", "FAD[{q1, m}]"}, {"fcstSharedObjectsBehavior-ID87.7", "FAD[{q1, m}, {q1 - p, 0, 0}, {q2, m}]", "FAD[{q1, m}, {q2, m}]"}, -{"fcstSharedObjectsBehavior-ID88", "FeynAmpDenominator[{a, b}]", "FeynAmpDenominator[PropagatorDenominator[Momentum[a, D], b]]"}, -{"fcstSharedObjectsBehavior-ID89", "FeynAmpDenominator[{a}]", " FeynAmpDenominator[PropagatorDenominator[Momentum[a, D], 0]]"}, +{"fcstSharedObjectsBehavior-ID89.1", "FeynAmpDenominator[PD[0, 0]]", "FeynAmpDenominator[PD[0, 0]]"}, {"fcstSharedObjectsBehavior-ID90", "FourVector[p, mu]", " Pair[LorentzIndex[mu], Momentum[p]]"}, {"fcstSharedObjectsBehavior-ID91", "FourVector[p, mu, Dimension -> D]", " Pair[LorentzIndex[mu, D], Momentum[p, D]]"}, @@ -382,15 +644,25 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID94", "FourVector[p, mu, FCI -> False]", " FourVector[p, mu, FeynCalcInternal -> False]"}, {"fcstSharedObjectsBehavior-ID95", "FV[p, l]", " FV[p, l]"}, -{"fcstSharedObjectsBehavior-ID96", "FV[p, Momentum[l]]", " SP[l, p]"}, -{"fcstSharedObjectsBehavior-ID97", "FV[Momentum[p], Momentum[l]]", " SP[l, p]"}, -{"fcstSharedObjectsBehavior-ID98", "FV[Momentum[l], p]", " FV[Momentum[l], p]"}, +{"fcstSharedObjectsBehavior-ID95.1", "FV[-p, l]", "-FV[p, l]"}, +{"fcstSharedObjectsBehavior-ID95.2", "FVD[-p, l]", "-FVD[p, l]"}, +{"fcstSharedObjectsBehavior-ID95.3", "FVE[-p, l]", "-FVE[p, l]"}, {"fcstSharedObjectsBehavior-ID98.1", "FV[0, mu]", "0"}, {"fcstSharedObjectsBehavior-ID98.2", "FVD[0, mu]", "0"}, {"fcstSharedObjectsBehavior-ID98.3", "FVE[0, mu]", "0"}, +{"fcstSharedObjectsBehavior-ID98.4", "CV[0, mu]", "0"}, +{"fcstSharedObjectsBehavior-ID98.5", "CVD[0, mu]", "0"}, +{"fcstSharedObjectsBehavior-ID98.6", "CVE[0, mu]", "0"}, +{"fcstSharedObjectsBehavior-ID98.6", "TC[0]", "0"}, +{"fcstSharedObjectsBehavior-ID98.7", "CV[-p, l]", "-CV[p, l]"}, +{"fcstSharedObjectsBehavior-ID98.8", "CVD[-p, l]", "-CVD[p, l]"}, +{"fcstSharedObjectsBehavior-ID98.9", "CVE[-p, l]", "-CVE[p, l]"}, {"fcstSharedObjectsBehavior-ID99", "GA[a.b.c]", " GA[a].GA[b].GA[c]"}, {"fcstSharedObjectsBehavior-ID100", "GA[a, b, c]", " GA[a].GA[b].GA[c]"}, {"fcstSharedObjectsBehavior-ID101", "GA5", " DiracGamma[5]"}, +{"fcstSharedObjectsBehavior-ID101.1", "GAD[5]", "GA[5]"}, +{"fcstSharedObjectsBehavior-ID101.2", "GAD[6]", "GA[6]"}, +{"fcstSharedObjectsBehavior-ID101.3", "GAD[7]", "GA[7]"}, {"fcstSharedObjectsBehavior-ID102", "GAD[a.b.c]", " GAD[a].GAD[b].GAD[c]"}, {"fcstSharedObjectsBehavior-ID103", "GAD[a, b, c]", " GAD[a].GAD[b].GAD[c]"}, {"fcstSharedObjectsBehavior-ID103.1", "GAE[a.b.c]", " GAE[a].GAE[b].GAE[c]"}, @@ -401,6 +673,36 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID107", "GSD[a, b, c]", " GSD[a].GSD[b].GSD[c]"}, {"fcstSharedObjectsBehavior-ID107.1", "GSE[a.b.c]", " GSE[a].GSE[b].GSE[c]"}, {"fcstSharedObjectsBehavior-ID107.2", "GSE[a, b, c]", " GSE[a].GSE[b].GSE[c]"}, +{"fcstSharedObjectsBehavior-ID107.3", "GS[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.4", "GSD[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.5", "GSE[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.6", "CGA[a,b,c]", " CGA[a].CGA[b].CGA[c]"}, +{"fcstSharedObjectsBehavior-ID107.7", "CGAD[a,b,c]", " CGAD[a].CGAD[b].CGAD[c]"}, +{"fcstSharedObjectsBehavior-ID107.8", "CGAE[a,b,c]", " CGAE[a].CGAE[b].CGAE[c]"}, +{"fcstSharedObjectsBehavior-ID107.9", "CGS[a,b,c]", " CGS[a].CGS[b].CGS[c]"}, +{"fcstSharedObjectsBehavior-ID107.10", "CGSD[a,b,c]", " CGSD[a].CGSD[b].CGSD[c]"}, +{"fcstSharedObjectsBehavior-ID107.11", "CGSE[a,b,c]", " CGSE[a].CGSE[b].CGSE[c]"}, +{"fcstSharedObjectsBehavior-ID107.12", "CGS[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.13", "CGSD[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.14", "CGSE[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.15", "SI[a,b,c]", " SI[a].SI[b].SI[c]"}, +{"fcstSharedObjectsBehavior-ID107.16", "SID[a,b,c]", " SID[a].SID[b].SID[c]"}, +{"fcstSharedObjectsBehavior-ID107.17", "SIE[a,b,c]", " SIE[a].SIE[b].SIE[c]"}, +{"fcstSharedObjectsBehavior-ID107.18", "CSI[a,b,c]", " CSI[a].CSI[b].CSI[c]"}, +{"fcstSharedObjectsBehavior-ID107.19", "CSID[a,b,c]", " CSID[a].CSID[b].CSID[c]"}, +{"fcstSharedObjectsBehavior-ID107.20", "CSIE[a,b,c]", " CSIE[a].CSIE[b].CSIE[c]"}, +{"fcstSharedObjectsBehavior-ID107.21", "SIS[a,b,c]", " SIS[a].SIS[b].SIS[c]"}, +{"fcstSharedObjectsBehavior-ID107.22", "SISD[a,b,c]", " SISD[a].SISD[b].SISD[c]"}, +{"fcstSharedObjectsBehavior-ID107.23", "SISE[a,b,c]", " SISE[a].SISE[b].SISE[c]"}, +{"fcstSharedObjectsBehavior-ID107.24", "CSIS[a,b,c]", " CSIS[a].CSIS[b].CSIS[c]"}, +{"fcstSharedObjectsBehavior-ID107.25", "CSISD[a,b,c]", " CSISD[a].CSISD[b].CSISD[c]"}, +{"fcstSharedObjectsBehavior-ID107.26", "CSISE[a,b,c]", " CSISE[a].CSISE[b].CSISE[c]"}, +{"fcstSharedObjectsBehavior-ID107.27", "SIS[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.28", "SISD[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.29", "SISE[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.30", "CSIS[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.31", "CSISD[0]", "0"}, +{"fcstSharedObjectsBehavior-ID107.32", "CSISE[0]", "0"}, {"fcstSharedObjectsBehavior-ID108", "IFPD[Momentum[OPEDelta, a], 0]", " 0"}, {"fcstSharedObjectsBehavior-ID109", "LeftPartialD[(1)]", " 1"}, {"fcstSharedObjectsBehavior-ID110", "LeftPartialD[(1), (1), (1)]", "1"}, @@ -434,40 +736,43 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID129", "LeftRightPartialD2[nu, mu, rho]", " LeftRightPartialD2[LorentzIndex[nu]].LeftRightPartialD2[LorentzIndex[mu]].LeftRightPartialD2[LorentzIndex[rho]]"}, {"fcstSharedObjectsBehavior-ID129.1", "LeviCivita[a, b, c, d]", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstSharedObjectsBehavior-ID129.2", "LeviCivita[a, b, c, d, Dimension->4]", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], LorentzIndex[d]]"}, {"fcstSharedObjectsBehavior-ID129.3", "LeviCivita[a, b, c, d, Dimension->D]", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], LorentzIndex[d,D]]"}, {"fcstSharedObjectsBehavior-ID129.4", "LeviCivita[][a, b, c, d]", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstSharedObjectsBehavior-ID129.5", "LeviCivita[][a, b, c, d, Dimension->4]", - "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[Momentum[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstSharedObjectsBehavior-ID129.6", "LeviCivita[Dimension->D][a, b, c, d, Dimension->D]", - "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D], Dimension -> D]"}, + "Eps[Momentum[a, D], Momentum[b, D], Momentum[c, D], Momentum[d, D]]"}, {"fcstSharedObjectsBehavior-ID129.7", "LeviCivita[a][ b, c, d]", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstSharedObjectsBehavior-ID129.8", "LeviCivita[a, Dimension->4][ b, c, d, Dimension->4]", - "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], Momentum[b], Momentum[c], Momentum[d]]"}, {"fcstSharedObjectsBehavior-ID129.9", "LeviCivita[a, Dimension->D][ b, c, d, Dimension->D]", - "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], Momentum[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstSharedObjectsBehavior-ID129.10", "LeviCivita[a, b][ c, d]", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstSharedObjectsBehavior-ID129.11", "LeviCivita[a, b, Dimension->4][ c, d, Dimension->4]", - "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], Momentum[c], Momentum[d]]"}, {"fcstSharedObjectsBehavior-ID129.12", "LeviCivita[a, b, Dimension->D][ c, d, Dimension->D]", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], Momentum[c,D], Momentum[d,D]]"}, {"fcstSharedObjectsBehavior-ID129.13", "LeviCivita[a, b, c][ d]", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstSharedObjectsBehavior-ID129.14", "LeviCivita[a, b, c, Dimension->4][d, Dimension->4]", - "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d], Dimension -> 4]"}, + "Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], Momentum[d]]"}, {"fcstSharedObjectsBehavior-ID129.15", "LeviCivita[a, b, c, Dimension->D][d, Dimension->D]", - "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D], Dimension -> D]"}, + "Eps[LorentzIndex[a,D], LorentzIndex[b,D], LorentzIndex[c,D], Momentum[d,D]]"}, {"fcstSharedObjectsBehavior-ID130", "LorentzIndex[LorentzIndex[mu, D], D]", " LorentzIndex[mu, D]"}, {"fcstSharedObjectsBehavior-ID131", "LorentzIndex[mu, 4]", " LorentzIndex[mu]"}, {"fcstSharedObjectsBehavior-ID132", "LorentzIndex[mu, 0]", " 0"}, {"fcstSharedObjectsBehavior-ID133", "LorentzIndex[3, 4]", " ExplicitLorentzIndex[3]"}, {"fcstSharedObjectsBehavior-ID134", "LorentzIndex[3, D]", " ExplicitLorentzIndex[3, D]"}, +{"fcstSharedObjectsBehavior-ID134.0", "ExplicitLorentzIndex[0]", "ExplicitLorentzIndex[0]"}, +{"fcstSharedObjectsBehavior-ID134.1", "CartesianIndex[mu, 3]", " CartesianIndex[mu]"}, +{"fcstSharedObjectsBehavior-ID134.2", "CartesianIndex[mu, 0]", " 0"}, {"fcstSharedObjectsBehavior-ID135", "MetricTensor[a, b]", " Pair[LorentzIndex[a], LorentzIndex[b]]"}, {"fcstSharedObjectsBehavior-ID136", "MetricTensor[a, b, Dimension -> D]", " Pair[LorentzIndex[a, D], LorentzIndex[b, D]]"}, {"fcstSharedObjectsBehavior-ID137", "MetricTensor[a, b, Dimension -> D, FCI -> False]", " MetricTensor[a, b, Dimension -> D, FeynCalcInternal -> False]"}, @@ -479,10 +784,15 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID143", "Momentum[Momentum[x, D], D]", "Momentum[x, D]"}, {"fcstSharedObjectsBehavior-ID143-1", "Momentum[Momentum[x]]", "Momentum[x]"}, {"fcstSharedObjectsBehavior-ID143-2", "Momentum[Momentum[x,D],D-4]", "Momentum[x,{D,D-4}]"}, -{"fcstSharedObjectsBehavior-ID144", "MT[Momentum[a], Momentum[b]]", " SP[a, b]"}, -{"fcstSharedObjectsBehavior-ID145", "MT[Momentum[a, D], Momentum[b, D]]", " SPD[a, b]"}, -{"fcstSharedObjectsBehavior-ID145.1", "MT[Momentum[a, D-4], Momentum[b, D-4]]", " SPE[a, b]"}, -{"fcstSharedObjectsBehavior-ID146", "MT[Momentum[a, D], Momentum[b]]", " MT[Momentum[a, D], Momentum[b]]"}, +{"fcstSharedObjectsBehavior-ID143.3", "CartesianMomentum[5 x , D-1]", " 5*CartesianMomentum[x, D-1]"}, +{"fcstSharedObjectsBehavior-ID143.4", "CartesianMomentum[ x , 3]", " CartesianMomentum[x]"}, +{"fcstSharedObjectsBehavior-ID143.5", "CartesianMomentum[ 0 , a]", " 0"}, +{"fcstSharedObjectsBehavior-ID143.6", "CartesianMomentum[ a, 0]", " 0"}, +{"fcstSharedObjectsBehavior-ID143.7", "TemporalMomentum[0]", " TemporalMomentum[0]"}, +{"fcstSharedObjectsBehavior-ID143.8", "TemporalMomentum[ x , 4]", " TemporalMomentum[x]"}, +{"fcstSharedObjectsBehavior-ID143.9", "TemporalMomentum[ x , D]", " TemporalMomentum[x]"}, +{"fcstSharedObjectsBehavior-ID143.10", "TemporalMomentum[ x , D-4]", "0"}, +{"fcstSharedObjectsBehavior-ID143.11", "TemporalMomentum[2 x]", "2 TemporalMomentum[x]"}, {"fcstSharedObjectsBehavior-ID146.1", "MT[b, a]", "MT[a, b]"}, {"fcstSharedObjectsBehavior-ID146.2", "MTD[b, a]", "MTD[a, b]"}, {"fcstSharedObjectsBehavior-ID146.3", "MTE[b, a]", "MTE[a, b]"}, @@ -535,6 +845,35 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID155", "Pair[Momentum[p, D1], Momentum[Polarization[p1 + p2 + p3, I], D2]]", " Pair[Momentum[p, D1], Momentum[Polarization[p1 + p2 + p3, I], D2]]"}, {"fcstSharedObjectsBehavior-ID155.1", "Pair[Momentum[p, D1], Momentum[Polarization[p1 + p2 + p3, I, Transversality->True], D2]]", " Pair[Momentum[p, D1], Momentum[Polarization[p1 + p2 + p3, I, Transversality->True], D2]]"}, {"fcstSharedObjectsBehavior-ID155.2", "Pair[Momentum[p, D1], Momentum[Polarization[p1 + p2 + p3, I, Transversality->False], D2]]", " Pair[Momentum[p, D1], Momentum[Polarization[p1 + p2 + p3, I, Transversality->False], D2]]"}, +{"fcstSharedObjectsBehavior-ID156.0.1", "Pair[LorentzIndex[i, D], CartesianIndex[p]]", "Pair[CartesianIndex[p], LorentzIndex[i]]"}, +{"fcstSharedObjectsBehavior-ID156.0.2", "Pair[LorentzIndex[i, D - 4], CartesianIndex[p]]", "0"}, +{"fcstSharedObjectsBehavior-ID156.0.3", "Pair[ExplicitLorentzIndex[0], Momentum[p, D - 4]]", "0"}, +{"fcstSharedObjectsBehavior-ID156.0.4", "Pair[ExplicitLorentzIndex[0], CartesianIndex[i, D - 4]]", "0"}, +{"fcstSharedObjectsBehavior-ID156.0.5", "Pair[ExplicitLorentzIndex[0], LorentzIndex[i, D - 4]]", "0"}, +{"fcstSharedObjectsBehavior-ID156.0.6", "Pair[ExplicitLorentzIndex[0], Momentum[p, D]]", "Pair[ExplicitLorentzIndex[0], Momentum[p]]"}, +{"fcstSharedObjectsBehavior-ID156.0.6.1", "Pair[ExplicitLorentzIndex[0], CartesianMomentum[p]]", "0"}, +{"fcstSharedObjectsBehavior-ID156.0.6.2", "Pair[ExplicitLorentzIndex[0], CartesianMomentum[p,D-1]]", "0"}, +{"fcstSharedObjectsBehavior-ID156.0.6.3", "Pair[ExplicitLorentzIndex[0], CartesianIndex[i]]", "0"}, +{"fcstSharedObjectsBehavior-ID156.0.6.4", "Pair[ExplicitLorentzIndex[0], CartesianIndex[i,D-1]]", "0"}, +{"fcstSharedObjectsBehavior-ID156.0.7", "Pair[CartesianIndex[i, D - 1], ExplicitLorentzIndex[0]]", "Pair[CartesianIndex[i], ExplicitLorentzIndex[0]]"}, +{"fcstSharedObjectsBehavior-ID156.0.8", "Pair[CartesianIndex[i], CartesianIndex[j, D - 1]]", "-CartesianPair[CartesianIndex[i], CartesianIndex[j]]"}, +{"fcstSharedObjectsBehavior-ID156.0.9", "Pair[LorentzIndex[i], CartesianIndex[j, D - 1]]", "Pair[LorentzIndex[i], CartesianIndex[j]]"}, +{"fcstSharedObjectsBehavior-ID156.0.10", "Pair[CartesianIndex[i, D - 1], CartesianIndex[j, D - 4]]", "-CartesianPair[CartesianIndex[i, D - 4], CartesianIndex[j, D - 4]]"}, +{"fcstSharedObjectsBehavior-ID156.0.11", "Pair[LorentzIndex[i, D], CartesianIndex[j, D - 4]]", "Pair[LorentzIndex[i, D-4], CartesianIndex[j, D - 4]]"}, +{"fcstSharedObjectsBehavior-ID156.0.12", "Pair[CartesianIndex[i, D - 4], CartesianIndex[j, D - 1]]", "-CartesianPair[CartesianIndex[i, D - 4], CartesianIndex[j, D - 4]]"}, +{"fcstSharedObjectsBehavior-ID156.0.13", "Pair[LorentzIndex[i, D - 4], CartesianIndex[j, D - 1]]", "Pair[LorentzIndex[i, D - 4], CartesianIndex[j, D - 4]]"}, +{"fcstSharedObjectsBehavior-ID156.0.14", "Pair[CartesianIndex[i], CartesianMomentum[p]]", "-CartesianPair[CartesianIndex[i], CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehavior-ID156.0.15", "Pair[CartesianIndex[i, D - 1], CartesianMomentum[p, D - 1]]", "-CartesianPair[CartesianIndex[i, D - 1], CartesianMomentum[p, D - 1]]"}, +{"fcstSharedObjectsBehavior-ID156.0.16", "Pair[CartesianIndex[i, D - 4], CartesianMomentum[p, D - 4]]", "-CartesianPair[CartesianIndex[i, D - 4], CartesianMomentum[p, D - 4]]"}, +{"fcstSharedObjectsBehavior-ID156.0.17", "Pair[LorentzIndex[i], CartesianMomentum[p]]", "Pair[LorentzIndex[i], CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehavior-ID156.0.18", "Pair[LorentzIndex[i, D], CartesianMomentum[p, D - 1]]", "Pair[LorentzIndex[i, D], CartesianMomentum[p, D - 1]]"}, +{"fcstSharedObjectsBehavior-ID156.0.19", "Pair[LorentzIndex[i, D - 4], CartesianMomentum[p, D - 4]]", "Pair[LorentzIndex[i, D - 4], CartesianMomentum[p, D - 4]]"}, +{"fcstSharedObjectsBehavior-ID156.0.20", "Pair[Momentum[q], CartesianMomentum[p]]", "CartesianPair[CartesianMomentum[q], CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehavior-ID156.0.21", "Pair[Momentum[q, D], CartesianMomentum[p, D - 1]]", "CartesianPair[CartesianMomentum[q, D-1], CartesianMomentum[p, D - 1]]"}, +{"fcstSharedObjectsBehavior-ID156.0.22", "Pair[Momentum[q, D - 4], CartesianMomentum[p, D - 4]]", "CartesianPair[CartesianMomentum[q, D - 4], CartesianMomentum[p, D - 4]]"}, +{"fcstSharedObjectsBehavior-ID156.0.23", "Pair[CartesianMomentum[q], CartesianMomentum[p]]", "-CartesianPair[CartesianMomentum[q], CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehavior-ID156.0.24", "Pair[CartesianMomentum[q, D - 1], CartesianMomentum[p, D - 1]]", "-CartesianPair[CartesianMomentum[q, D - 1], CartesianMomentum[p, D - 1]]"}, +{"fcstSharedObjectsBehavior-ID156.0.25", "Pair[CartesianMomentum[q, D - 4], CartesianMomentum[p, D - 4]]", "-CartesianPair[CartesianMomentum[q, D - 4], CartesianMomentum[p, D - 4]]"}, {"fcstSharedObjectsBehavior-ID156", "Pair[Momentum[p, D1], Momentum[Polarization[a + b - p, I], D2]]", "Pair[Momentum[p, D1], Momentum[Polarization[a + b - p, I], D2]]"}, {"fcstSharedObjectsBehavior-ID156.1", "Pair[Momentum[p, D1], Momentum[Polarization[a + b - p, I, Transversality->True], D2]]", @@ -548,6 +887,18 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID157.2", "Pair[Momentum[p, D1], Momentum[Polarization[a + b + p, I, Transversality->False], D2]]", "Pair[Momentum[p, D1], Momentum[Polarization[a + b + p, I, Transversality -> False], D2]]"}, {"fcstSharedObjectsBehavior-ID158", "Pair[Momentum[Polarization[p, I], D1], Momentum[Polarization[p, -I], D2]]", "Pair[Momentum[Polarization[p, I], D1], Momentum[Polarization[p, -I], D2]]"}, +{"fcstSharedObjectsBehavior-ID158.1", "CartesianPair[0, x]", "0"}, +{"fcstSharedObjectsBehavior-ID158.2", "CartesianPair[CartesianIndex[i], CartesianIndex[j, D - 1]]", "CartesianPair[CartesianIndex[i], CartesianIndex[j]]"}, +{"fcstSharedObjectsBehavior-ID158.3", "CartesianPair[CartesianIndex[i], CartesianMomentum[p, D - 1]]", "CartesianPair[CartesianIndex[i], CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehavior-ID158.4", "CartesianPair[CartesianMomentum[q], CartesianIndex[j, D - 1]]", "CartesianPair[CartesianMomentum[q], CartesianIndex[j]]"}, +{"fcstSharedObjectsBehavior-ID158.5", "CartesianPair[CartesianMomentum[q], CartesianMomentum[p, D - 1]]", "CartesianPair[CartesianMomentum[q], CartesianMomentum[p]]"}, +{"fcstSharedObjectsBehavior-ID158.6", "CartesianPair[CartesianIndex[i], CartesianIndex[j, D - 4]]", "0"}, +{"fcstSharedObjectsBehavior-ID158.7", "CartesianPair[CartesianIndex[i], CartesianMomentum[p, D - 4]]", "0"}, +{"fcstSharedObjectsBehavior-ID158.8", "CartesianPair[CartesianMomentum[q], CartesianIndex[j, D - 4]]", "0"}, +{"fcstSharedObjectsBehavior-ID158.9", "CartesianPair[CartesianMomentum[q], CartesianMomentum[p, D - 4]]", "0"}, +{"fcstSharedObjectsBehavior-ID158.10", "CartesianPair[n CartesianMomentum[p], x]", "n CartesianPair[CartesianMomentum[p], x]"}, +{"fcstSharedObjectsBehavior-ID158.11", "TemporalPair[0, x]", "0"}, +{"fcstSharedObjectsBehavior-ID158.12", "TemporalPair[n TemporalMomentum[p], x]", "n TemporalPair[ TemporalMomentum[p], x]"}, {"fcstSharedObjectsBehavior-ID159", "FCPartialD[(1)]", "1"}, {"fcstSharedObjectsBehavior-ID160", "FCPartialD[(1), (1), (1)]", "1"}, {"fcstSharedObjectsBehavior-ID161", "FCPartialD[OPEDelta]", "FCPartialD[Momentum[OPEDelta]]"}, @@ -555,10 +906,6 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID163", "FCPartialD[Momentum[p1], Momentum[p2], Momentum[p3]]", "FCPartialD[Momentum[p1]].FCPartialD[Momentum[p2]].FCPartialD[Momentum[p3]]"}, {"fcstSharedObjectsBehavior-ID164", "FCPartialD[nu, mu, LorentzIndex[rho]]", " FCPartialD[nu, mu, LorentzIndex[rho]]"}, {"fcstSharedObjectsBehavior-ID165", "FCPartialD[nu, mu, rho]", "FCPartialD[LorentzIndex[nu]].FCPartialD[LorentzIndex[mu]].FCPartialD[LorentzIndex[rho]]"}, -{"fcstSharedObjectsBehavior-ID166", "PauliSigma[1]", "{ {0, 1}, {1,0} }"}, -{"fcstSharedObjectsBehavior-ID167", "PauliSigma[2]", "{ {0,-I}, {I,0} }"}, -{"fcstSharedObjectsBehavior-ID168", "PauliSigma[3]", "{ {1, 0}, {0,-1} }"}, -{"fcstSharedObjectsBehavior-ID169", "PauliSigma[]", "{PauliSigma[1], PauliSigma[2], PauliSigma[3]}"}, {"fcstSharedObjectsBehavior-ID170", "PlusDistribution[Log[z (1 - z)]/(1 - z)]", " Log[z]/(1 - z) + PlusDistribution[Log[1 - z]/(1 - z)]"}, {"fcstSharedObjectsBehavior-ID171", "Polarization[p]", "Polarization[p, I]"}, {"fcstSharedObjectsBehavior-ID171.1", "Polarization[p, Transversality->True]", "Polarization[p, I, Transversality->True]"}, @@ -575,8 +922,9 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID175", "PolarizationVector[p, {mu, c}]","Pair[LorentzIndex[mu], Momentum[Polarization[p, I, SUNIndex[c]]]]"}, {"fcstSharedObjectsBehavior-ID175.1", "PolarizationVector[p, {mu, c}, Transversality->True]","Pair[LorentzIndex[{mu, c}], Momentum[Polarization[p, I, Transversality -> True]]]"}, {"fcstSharedObjectsBehavior-ID175.2", "PolarizationVector[p, {mu, c}, Transversality->False]","Pair[LorentzIndex[{mu, c}], Momentum[Polarization[p, I, Transversality -> False]]]"}, -{"fcstSharedObjectsBehavior-ID176", "PropagatorDenominator[x]", "PropagatorDenominator[x, 0]"}, +{"fcstSharedObjectsBehavior-ID176", "PropagatorDenominator[Momentum[x]]", "PropagatorDenominator[Momentum[x], 0]"}, {"fcstSharedObjectsBehavior-ID177", "PD", "PropagatorDenominator"}, +{"fcstSharedObjectsBehavior-ID177.1", "PD[0, 0]", "PropagatorDenominator[0, 0]"}, {"fcstSharedObjectsBehavior-ID178", "QuantumField[A, {mu, SUNIndex[a]}]", " QuantumField[A, LorentzIndex[mu], SUNIndex[a]]"}, {"fcstSharedObjectsBehavior-ID179", "QuantumField[QuantumField[A, {mu, SUNIndex[a]}]]", " QuantumField[A, LorentzIndex[mu], SUNIndex[a]]"}, {"fcstSharedObjectsBehavior-ID180", "RightPartialD[(1)]", " 1"}, {"fcstSharedObjectsBehavior-ID181", "RightPartialD[(1), (1), (1)]", "1"}, @@ -594,12 +942,19 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID190.1", "SP[a,0]", "0"}, {"fcstSharedObjectsBehavior-ID190.2", "SPD[a,0]", "0"}, {"fcstSharedObjectsBehavior-ID190.3", "SPE[a,0]", "0"}, +{"fcstSharedObjectsBehavior-ID190.4", "CSP[a]", "CSP[a,a]"}, +{"fcstSharedObjectsBehavior-ID190.5", "CSPE[a]", "CSPE[a,a]"}, +{"fcstSharedObjectsBehavior-ID190.6", "CSPD[a]", "CSPD[a,a]"}, +{"fcstSharedObjectsBehavior-ID190.7", "CSP[a,0]", "0"}, +{"fcstSharedObjectsBehavior-ID190.8", "CSPD[a,0]", "0"}, +{"fcstSharedObjectsBehavior-ID190.9", "CSPE[a,0]", "0"}, {"fcstSharedObjectsBehavior-ID191", "Spinor[Momentum[p], m]", "Spinor[Momentum[p], m, 1]"}, {"fcstSharedObjectsBehavior-ID192", "Spinor[p, m]", "Spinor[Momentum[p], m, 1]"}, +{"fcstSharedObjectsBehavior-ID192.1", "Spinor[HoldForm[p], m]", "Spinor[HoldForm[p], m, 1]"}, {"fcstSharedObjectsBehavior-ID193", "Spinor[Momentum[p, D], m]", " Spinor[Momentum[p,D], m, 1]"}, {"fcstSharedObjectsBehavior-ID194", "Spinor[Momentum[-p, D], m]", "Spinor[-Momentum[p,D], m, 1]"}, {"fcstSharedObjectsBehavior-ID195", "Spinor[a + b Momentum[p1 + p2], m]", - "Spinor[a + b (Momentum[p1] + Momentum[p2]), m, 1]"}, + "Spinor[a + b (Momentum[p1+p2]), m, 1]"}, {"fcstSharedObjectsBehavior-ID196", "Spinor[a, b SmallVariable[c]]", "Spinor[Momentum[a], 0, 1]"}, {"fcstSharedObjectsBehavior-ID197", "Spinor[p]", "Spinor[Momentum[p], 0, 1]"}, {"fcstSharedObjectsBehavior-ID198", "SUND[SUNIndex[a], SUNIndex[a], b]", " 0"}, @@ -625,5 +980,260 @@ D].DiracGamma[LorentzIndex[rho, D], D]"}, {"fcstSharedObjectsBehavior-ID215", "SUNIndex[4]", "ExplicitSUNIndex[4]"}, {"fcstSharedObjectsBehavior-ID216", "SUNFIndex[4]", "ExplicitSUNFIndex[4]"}, {"fcstSharedObjectsBehavior-ID217", "SUNTF[a,b,c]", "SUNTF[{a},b,c]"}, -{"fcstSharedObjectsBehavior-ID218", "FCI[SUNTF[a,x,x]]", "0"} +{"fcstSharedObjectsBehavior-ID217.1", "SUNTF[{SUNIndex[a1], SUNIndex[a2]}, SUNFIndex[b], SUNFIndex[c]] /. +SUNTF[a_List, _, _] :> SUNT @@ a", "SUNT[SUNIndex[a1], SUNIndex[a2]]"}, +{"fcstSharedObjectsBehavior-ID218", "FCI[SUNTF[a,x,x]]", "0"}, +{"fcstSharedObjectsBehavior-ID219", "Conjugate[Zeta2]", "Zeta2"}, +{"fcstSharedObjectsBehavior-ID220", "Conjugate[Zeta4]", "Zeta4"}, +{"fcstSharedObjectsBehavior-ID221", "Conjugate[Zeta6]", "Zeta6"}, +{"fcstSharedObjectsBehavior-ID222", "Conjugate[Zeta8]", "Zeta8"}, +{"fcstSharedObjectsBehavior-ID223", "Conjugate[Zeta10]", "Zeta10"} } + +Tests`Shared`fcstSharedObjectsDiracIndex = +({ +{"fcstSharedObjectsDiracIndex-ID1", "DiracIndex[i]", +"DiracIndex[i]"}, +{"fcstSharedObjectsDiracIndex-ID2", "DiracIndex[5]", +"ExplicitDiracIndex[5]"}, +{"fcstSharedObjectsDiracIndex-ID3", "ExplicitDiracIndex[4]", +"ExplicitDiracIndex[4]"}, +{"fcstSharedObjectsDiracIndex-ID4", +"DiracIndexDelta[DiracIndex[i],DiracIndex[j]]", +"DiracIndexDelta[DiracIndex[i], DiracIndex[j]]"}, +{"fcstSharedObjectsDiracIndex-ID5", +"DiracIndexDelta[DiracIndex[1],DiracIndex[j]]", +"DiracIndexDelta[DiracIndex[j], ExplicitDiracIndex[1]]"}, +{"fcstSharedObjectsDiracIndex-ID6", +"DiracIndexDelta[DiracIndex[3],DiracIndex[1]]", +"DiracIndexDelta[ExplicitDiracIndex[1], ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID7", +"DiracIndexDelta[DiracIndex[3],DiracIndex[3]]", +"DiracIndexDelta[ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID8", +"DiracIndexDelta[ExplicitDiracIndex[1],ExplicitDiracIndex[2]]", +"DiracIndexDelta[ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstSharedObjectsDiracIndex-ID9", +"DiracIndexDelta[ExplicitDiracIndex[3],ExplicitDiracIndex[3]]", +"DiracIndexDelta[ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID10", +"DiracIndexDelta[DiracIndex[i],DiracIndex[i]]", +"DiracIndexDelta[DiracIndex[i], DiracIndex[i]]"}, +{"fcstSharedObjectsDiracIndex-ID11", +"DiracIndexDelta[DiracIndex[i],0]", +"DiracIndexDelta[0, DiracIndex[i]]"}, +{"fcstSharedObjectsDiracIndex-ID12", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],\ +DiracIndex[j]]", +"DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], \ +DiracIndex[j]]"}, +{"fcstSharedObjectsDiracIndex-ID13", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[1],\ +DiracIndex[j]]", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstSharedObjectsDiracIndex-ID14", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[3],\ +DiracIndex[1]]", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[1]]"}, +{"fcstSharedObjectsDiracIndex-ID15", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[3],\ +DiracIndex[3]]", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID16", +"DiracChain[DiracGamma[LorentzIndex[mu]],ExplicitDiracIndex[1],\ +ExplicitDiracIndex[2]]", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstSharedObjectsDiracIndex-ID17", +"DiracChain[DiracGamma[LorentzIndex[mu]],ExplicitDiracIndex[3],\ +ExplicitDiracIndex[3]]", +"DiracChain[DiracGamma[LorentzIndex[mu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID18", +"DiracChain[DiracGamma[LorentzIndex[mu]],DiracIndex[i],\ +DiracIndex[i]]", +"DiracChain[DiracGamma[LorentzIndex[mu]], DiracIndex[i], \ +DiracIndex[i]]"}, +{"fcstSharedObjectsDiracIndex-ID19", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[i],DiracIndex[j]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], DiracIndex[j]]"}, +{"fcstSharedObjectsDiracIndex-ID20", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[1],DiracIndex[j]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstSharedObjectsDiracIndex-ID21", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[3],DiracIndex[1]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[1]]"}, +{"fcstSharedObjectsDiracIndex-ID22", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[3],DiracIndex[3]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID23", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],ExplicitDiracIndex[1],ExplicitDiracIndex[2]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[1], \ +ExplicitDiracIndex[2]]"}, +{"fcstSharedObjectsDiracIndex-ID24", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],ExplicitDiracIndex[3],ExplicitDiracIndex[3]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], ExplicitDiracIndex[3], \ +ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID25", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[i],DiracIndex[i]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], DiracIndex[i]]"}, +{"fcstSharedObjectsDiracIndex-ID26", +"DiracChain[DiracGamma[LorentzIndex[mu]].(m+DiracGamma[\ +Momentum[p]]).DiracGamma[LorentzIndex[nu]],DiracIndex[1],DiracIndex[j]\ +]", "DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[1], DiracIndex[j]]"}, +{"fcstSharedObjectsDiracIndex-ID27", +"DiracChain[DiracGamma[LorentzIndex[mu]].(m+DiracGamma[\ +Momentum[p]]).DiracGamma[LorentzIndex[nu]],DiracIndex[3],DiracIndex[1]\ +]", "DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[1]]"}, +{"fcstSharedObjectsDiracIndex-ID28", +"DiracChain[DiracGamma[LorentzIndex[mu]].(m+DiracGamma[\ +Momentum[p]]).DiracGamma[LorentzIndex[nu]],DiracIndex[3],DiracIndex[3]\ +]", "DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID29", +"DiracChain[DiracGamma[LorentzIndex[mu]].(m+DiracGamma[\ +Momentum[p]]).DiracGamma[LorentzIndex[nu]],ExplicitDiracIndex[1],\ +ExplicitDiracIndex[2]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[1], ExplicitDiracIndex[2]]"}, +{"fcstSharedObjectsDiracIndex-ID30", +"DiracChain[DiracGamma[LorentzIndex[mu]].(m+DiracGamma[\ +Momentum[p]]).DiracGamma[LorentzIndex[nu]],ExplicitDiracIndex[3],\ +ExplicitDiracIndex[3]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +ExplicitDiracIndex[3], ExplicitDiracIndex[3]]"}, +{"fcstSharedObjectsDiracIndex-ID31", +"DiracChain[DiracGamma[LorentzIndex[mu]].(m+DiracGamma[\ +Momentum[p]]).DiracGamma[LorentzIndex[nu]],DiracIndex[i],DiracIndex[i]\ +]", "DiracChain[DiracGamma[LorentzIndex[mu]] . (m + \ +DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[nu]], \ +DiracIndex[i], DiracIndex[i]]"}, +{"fcstSharedObjectsDiracIndex-ID32", +"DiracChain[Spinor[Momentum[p],m],DiracIndex[i]]", +"DiracChain[Spinor[Momentum[p], m, 1], DiracIndex[i]]"}, +{"fcstSharedObjectsDiracIndex-ID33", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],Spinor[Momentum[p],m],DiracIndex[j]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], Spinor[Momentum[p], m, 1], \ +DiracIndex[j]]"}, +{"fcstSharedObjectsDiracIndex-ID34", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],DiracIndex[i],Spinor[Momentum[p],m]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], DiracIndex[i], Spinor[Momentum[p], m, \ +1]]"}, +{"fcstSharedObjectsDiracIndex-ID35", +"DiracChain[DiracGamma[LorentzIndex[mu]].DiracGamma[Momentum[p,\ +D],D],Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]", +"DiracChain[DiracGamma[LorentzIndex[mu]] . \ +DiracGamma[Momentum[p, D], D], Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstSharedObjectsDiracIndex-ID36", +"DiracChain[1,Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]\ +", "DiracChain[1, Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstSharedObjectsDiracIndex-ID37", "DIDelta[i,j]", +"DIDelta[i, j]"}, +{"fcstSharedObjectsDiracIndex-ID38", "DIDelta[i,2]", +"DIDelta[2, i]"}, +{"fcstSharedObjectsDiracIndex-ID39", "DIDelta[1,2]", +"DIDelta[1, 2]"}, +{"fcstSharedObjectsDiracIndex-ID40", "DIDelta[2,2]", +"DIDelta[2, 2]"}, +{"fcstSharedObjectsDiracIndex-ID41", "DIDelta[i,i]", +"DIDelta[i, i]"}, +{"fcstSharedObjectsDiracIndex-ID42", "DCHN[GA[mu],i,j]", +"DCHN[GA[mu], i, j]"}, +{"fcstSharedObjectsDiracIndex-ID43", "DCHN[GA[mu],1,j]", +"DCHN[GA[mu], 1, j]"}, +{"fcstSharedObjectsDiracIndex-ID44", "DCHN[GA[mu],3,1]", +"DCHN[GA[mu], 3, 1]"}, +{"fcstSharedObjectsDiracIndex-ID45", "DCHN[GA[mu],3,3]", +"DCHN[GA[mu], 3, 3]"}, +{"fcstSharedObjectsDiracIndex-ID46", "DCHN[GA[mu],1,2]", +"DCHN[GA[mu], 1, 2]"}, +{"fcstSharedObjectsDiracIndex-ID47", "DCHN[GA[mu],i,i]", +"DCHN[GA[mu], i, i]"}, +{"fcstSharedObjectsDiracIndex-ID48", "DCHN[GA[mu].GSD[p],i,j]", +"DCHN[GA[mu] . GSD[p], i, j]"}, +{"fcstSharedObjectsDiracIndex-ID49", "DCHN[GA[mu].GSD[p],1,j]", +"DCHN[GA[mu] . GSD[p], 1, j]"}, +{"fcstSharedObjectsDiracIndex-ID50", "DCHN[GA[mu].GSD[p],3,1]", +"DCHN[GA[mu] . GSD[p], 3, 1]"}, +{"fcstSharedObjectsDiracIndex-ID51", "DCHN[GA[mu].GSD[p],3,3]", +"DCHN[GA[mu] . GSD[p], 3, 3]"}, +{"fcstSharedObjectsDiracIndex-ID52", "DCHN[GA[mu].GSD[p],1,2]", +"DCHN[GA[mu] . GSD[p], 1, 2]"}, +{"fcstSharedObjectsDiracIndex-ID53", "DCHN[GA[mu].GSD[p],i,i]", +"DCHN[GA[mu] . GSD[p], i, i]"}, +{"fcstSharedObjectsDiracIndex-ID54", +"DCHN[GA[mu].(m+GS[p]).GA[nu],1,j]", +"DCHN[GA[mu] . (m + GS[p]) . GA[nu], 1, j]"}, +{"fcstSharedObjectsDiracIndex-ID55", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,1]", +"DCHN[GA[mu] . (m + GS[p]) . GA[nu], 3, 1]"}, +{"fcstSharedObjectsDiracIndex-ID56", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,3]", +"DCHN[GA[mu] . (m + GS[p]) . GA[nu], 3, 3]"}, +{"fcstSharedObjectsDiracIndex-ID57", +"DCHN[GA[mu].(m+GS[p]).GA[nu],1,2]", +"DCHN[GA[mu] . (m + GS[p]) . GA[nu], 1, 2]"}, +{"fcstSharedObjectsDiracIndex-ID58", +"DCHN[GA[mu].(m+GS[p]).GA[nu],3,3]", +"DCHN[GA[mu] . (m + GS[p]) . GA[nu], 3, 3]"}, +{"fcstSharedObjectsDiracIndex-ID59", +"DCHN[GA[mu].(m+GS[p]).GA[nu],i,i]", +"DCHN[GA[mu] . (m + GS[p]) . GA[nu], i, i]"}, +{"fcstSharedObjectsDiracIndex-ID60", +"DCHN[Spinor[Momentum[p],m],i]", +"DCHN[Spinor[Momentum[p], m, 1], i]"}, +{"fcstSharedObjectsDiracIndex-ID61", +"DCHN[GA[mu].GSD[p],Spinor[Momentum[p],m],j]", +"DCHN[GA[mu] . GSD[p], Spinor[Momentum[p], m, 1], j]"}, +{"fcstSharedObjectsDiracIndex-ID62", +"DCHN[GA[mu].GSD[p],i,Spinor[Momentum[p],m]]", +"DCHN[GA[mu] . GSD[p], i, Spinor[Momentum[p], m, 1]]"}, +{"fcstSharedObjectsDiracIndex-ID63", +"DCHN[GA[mu].GSD[p],Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]\ +]", "DCHN[GA[mu] . GSD[p], Spinor[Momentum[p1], m1, 1], \ +Spinor[Momentum[p2], m2, 1]]"}, +{"fcstSharedObjectsDiracIndex-ID64", +"DCHN[1,Spinor[Momentum[p1],m1],Spinor[Momentum[p2],m2]]", +"DCHN[Spinor[Momentum[p1], m1, 1], Spinor[Momentum[p2], m2, 1]]"}, +{"fcstSharedObjectsDiracIndex-ID65", +"DCHN[a, Spinor[Momentum[p1], m1, 1], Spinor[Momentum[p2], m1, 1]] // +FCI // FCE", +"a DCHN[1, Spinor[Momentum[p1], m1, 1], Spinor[Momentum[p2], m1, 1]]"}, +{"fcstSharedObjectsDiracIndex-ID66", +"DCHN[a, Spinor[Momentum[p1], m1, 1], DiracIndex[i]] // FCI // FCE", +"a DCHN[Spinor[Momentum[p1], m1, 1], i]"}, +{"fcstSharedObjectsDiracIndex-ID67", "Head[DCHN[1,i,j]//FCI]", +"DiracChain"} +}); diff --git a/Tests/Shared/SharedObjectsTypesetting.test b/Tests/Shared/SharedObjectsTypesetting.test index 8de5b0f7b..5d3b147d6 100644 --- a/Tests/Shared/SharedObjectsTypesetting.test +++ b/Tests/Shared/SharedObjectsTypesetting.test @@ -3,9 +3,9 @@ (* :Title: SharedObjectsTypesetting.test *) (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for the typesetting of the *) @@ -13,6 +13,16 @@ (* ------------------------------------------------------------------------ *) +(* Fast way to update those tests + +FUnitCreateUnitTestsTypesetting["fcstSharedObjectsTypesettingNrCFAD", \ +(ToExpression /@ (StringReplace[ + FUnitExtractUnitTests[{"Shared", "SharedObjectsTypesetting"}, + "fcstSharedObjectsTypesettingNrCFAD"], + {"MakeBoxes[" -> "", ", TraditionalForm]" -> ""}]))] + +*) + Tests`Shared`fcstSharedObjectsTypesetting = ({ {"fcstSharedObjectsTypesetting-ID1", @@ -125,412 +135,132 @@ TraditionalForm]", "SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"^\"]}], \ FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm]]"}, {"fcstSharedObjectsTypesetting-ID23", -"MakeBoxes[DiracGamma[LorentzIndex[Upper[a]]], TraditionalForm]", +"MakeBoxes[DiracGamma[ExplicitLorentzIndex[3]], TraditionalForm]", "SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"]}], \ -FormBox[FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm], \ -TraditionalForm]]"}, +FormBox[FormBox[\"3\", TraditionalForm], TraditionalForm]]"}, {"fcstSharedObjectsTypesetting-ID24", -"MakeBoxes[DiracGamma[LorentzIndex[Upper[a], D], D], \ -TraditionalForm]", -"SuperscriptBox[RowBox[{\"\[Gamma]\"}], \ -FormBox[FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm], \ -TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID25", -"MakeBoxes[DiracGamma[LorentzIndex[Upper[a], -4 + D], -4 + D], \ -TraditionalForm]", -"SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"^\"]}], \ -FormBox[FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm], \ -TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID26", -"MakeBoxes[DiracGamma[LorentzIndex[Lower[a]]], TraditionalForm]", -"SubscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"]}], \ -FormBox[FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm], \ -TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID27", -"MakeBoxes[DiracGamma[LorentzIndex[Lower[a], D], D], \ -TraditionalForm]", -"SubscriptBox[RowBox[{\"\[Gamma]\"}], \ -FormBox[FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm], \ -TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID28", -"MakeBoxes[DiracGamma[LorentzIndex[Lower[a], -4 + D], -4 + D], \ -TraditionalForm]", -"SubscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"^\"]}], \ -FormBox[FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm], \ -TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID29", "MakeBoxes[DiracGamma[ExplicitLorentzIndex[3]], TraditionalForm]", "SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"]}], \ FormBox[FormBox[\"3\", TraditionalForm], TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID30", -"MakeBoxes[DiracGamma[ExplicitLorentzIndex[3, D], D], \ -TraditionalForm]", -"SuperscriptBox[RowBox[{\"\[Gamma]\"}], FormBox[FormBox[\"3\", \ -TraditionalForm], TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID31", -"MakeBoxes[DiracGamma[ExplicitLorentzIndex[3, -4 + D], -4 + D], \ -TraditionalForm]", -"SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"^\"]}], \ -FormBox[FormBox[\"3\", TraditionalForm], TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID32", -"MakeBoxes[DiracGamma[ExplicitLorentzIndex[Upper[3]]], \ -TraditionalForm]", -"SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"]}], \ -FormBox[FormBox[FormBox[\"3\", TraditionalForm], TraditionalForm], \ -TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID33", -"MakeBoxes[DiracGamma[ExplicitLorentzIndex[Upper[3], D], D], \ -TraditionalForm]", -"SuperscriptBox[RowBox[{\"\[Gamma]\"}], \ -FormBox[FormBox[FormBox[\"3\", TraditionalForm], TraditionalForm], \ 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TraditionalForm]", "SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"]}], \ FormBox[\"7\", TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID79", +{"fcstSharedObjectsTypesetting-ID52", "MakeBoxes[DiracMatrix[i, FeynCalcInternal -> False], \ TraditionalForm]", "FormBox[SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \ \"_\"]}], FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]], \ TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID80", +{"fcstSharedObjectsTypesetting-ID53", "MakeBoxes[DiracMatrix[i, FeynCalcInternal -> False, Dimension -> \ D], TraditionalForm]", "FormBox[SuperscriptBox[RowBox[{\"\[Gamma]\"}], \ FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]], \ TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID81", +{"fcstSharedObjectsTypesetting-ID54", "MakeBoxes[DiracMatrix[i, FeynCalcInternal -> False, Dimension -> \ -4 + D], TraditionalForm]", "FormBox[SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \ \"^\"]}], FormBox[FormBox[\"i\", 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TraditionalForm]", "FormBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"], \ @@ -565,14 +295,14 @@ FormBox[FormBox[RowBox[{OverscriptBox[FormBox[\"p\", \ TraditionalForm], \"_\"], \"+\", OverscriptBox[FormBox[\"q\", \ TraditionalForm], \"_\"]}], TraditionalForm], TraditionalForm], \ \")\"}], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID98", +{"fcstSharedObjectsTypesetting-ID70", "MakeBoxes[DiracSlash[p + q, FeynCalcInternal -> False, Dimension -> \ D], TraditionalForm]", "FormBox[RowBox[{\"\[Gamma]\", \"\[CenterDot]\", \"(\", \ FormBox[FormBox[RowBox[{FormBox[\"p\", TraditionalForm], \"+\", \ FormBox[\"q\", TraditionalForm]}], TraditionalForm], \ TraditionalForm], \")\"}], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID99", +{"fcstSharedObjectsTypesetting-ID71", "MakeBoxes[DiracSlash[p + q, FeynCalcInternal -> False, Dimension -> \ -4 + D], TraditionalForm]", "FormBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"^\"], \ @@ -581,124 +311,124 @@ FormBox[FormBox[RowBox[{OverscriptBox[FormBox[\"p\", \ TraditionalForm], \"^\"], \"+\", OverscriptBox[FormBox[\"q\", \ TraditionalForm], \"^\"]}], TraditionalForm], TraditionalForm], \ \")\"}], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID100", +{"fcstSharedObjectsTypesetting-ID72", "MakeBoxes[DiracGamma[Momentum[Polarization[p, I]]], \ TraditionalForm]", "RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"], \"\[CenterDot]\", \ FormBox[RowBox[{OverscriptBox[\"\[CurlyEpsilon]\", \"_\"], \"(\", \ FormBox[\"p\", TraditionalForm], \")\"}], TraditionalForm]}]"}, -{"fcstSharedObjectsTypesetting-ID101", +{"fcstSharedObjectsTypesetting-ID73", "MakeBoxes[DiracGamma[Momentum[Polarization[p, I], D], D], \ TraditionalForm]", "RowBox[{\"\[Gamma]\", \"\[CenterDot]\", \ FormBox[RowBox[{FormBox[\"\\\"\[CurlyEpsilon]\\\"\", \ TraditionalForm], \"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ TraditionalForm]}]"}, -{"fcstSharedObjectsTypesetting-ID102", +{"fcstSharedObjectsTypesetting-ID74", "MakeBoxes[DiracGamma[Momentum[Polarization[p, I], -4 + D], -4 + \ D], TraditionalForm]", "RowBox[{OverscriptBox[\"\[Gamma]\", \"^\"], \"\[CenterDot]\", \ FormBox[RowBox[{OverscriptBox[\"\[CurlyEpsilon]\", \"^\"], \"(\", \ FormBox[\"p\", TraditionalForm], \")\"}], TraditionalForm]}]"}, -{"fcstSharedObjectsTypesetting-ID103", +{"fcstSharedObjectsTypesetting-ID75", "MakeBoxes[DiracSlash[Polarization[p, I], FeynCalcInternal -> \ False], TraditionalForm]", "FormBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"], \ \"\[CenterDot]\", FormBox[RowBox[{OverscriptBox[\"\[CurlyEpsilon]\", \ \"_\"], \"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ TraditionalForm]}], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID104", +{"fcstSharedObjectsTypesetting-ID76", "MakeBoxes[DiracSlash[Polarization[p, I], FeynCalcInternal -> \ False, Dimension -> D], TraditionalForm]", "FormBox[RowBox[{\"\[Gamma]\", \"\[CenterDot]\", \ FormBox[RowBox[{FormBox[\"\\\"\[CurlyEpsilon]\\\"\", \ TraditionalForm], \"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ TraditionalForm]}], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID105", +{"fcstSharedObjectsTypesetting-ID77", "MakeBoxes[DiracSlash[Polarization[p, I], FeynCalcInternal -> \ False, Dimension -> -4 + D], TraditionalForm]", "FormBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"^\"], \ \"\[CenterDot]\", FormBox[RowBox[{OverscriptBox[\"\[CurlyEpsilon]\", \ \"^\"], \"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ TraditionalForm]}], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID106", +{"fcstSharedObjectsTypesetting-ID78", "MakeBoxes[DiracSigma[DiracGamma[LorentzIndex[a]], \ DiracGamma[LorentzIndex[b]]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", RowBox[{FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm], FormBox[FormBox[\"b\", \ TraditionalForm], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID107", +{"fcstSharedObjectsTypesetting-ID79", "MakeBoxes[DiracSigma[DiracGamma[LorentzIndex[a, D], D], \ DiracGamma[LorentzIndex[b, D], D]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", RowBox[{FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm], FormBox[FormBox[\"b\", \ TraditionalForm], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID108", +{"fcstSharedObjectsTypesetting-ID80", "MakeBoxes[DiracSigma[DiracGamma[LorentzIndex[a, -4 + D], -4 + D], \ DiracGamma[LorentzIndex[b, -4 + D], -4 + D]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", RowBox[{FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm], FormBox[FormBox[\"b\", \ TraditionalForm], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID109", +{"fcstSharedObjectsTypesetting-ID81", "MakeBoxes[DiracSigma[DiracGamma[LorentzIndex[a]], \ DiracGamma[LorentzIndex[b]]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", RowBox[{FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm], FormBox[FormBox[\"b\", \ TraditionalForm], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID110", +{"fcstSharedObjectsTypesetting-ID82", "MakeBoxes[DiracSigma[DiracGamma[LorentzIndex[a, D], D], \ DiracGamma[LorentzIndex[b, D], D]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", RowBox[{FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm], FormBox[FormBox[\"b\", \ TraditionalForm], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID111", +{"fcstSharedObjectsTypesetting-ID83", "MakeBoxes[DiracSigma[DiracGamma[LorentzIndex[a, -4 + D], -4 + D], \ DiracGamma[LorentzIndex[b, -4 + D], -4 + D]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", RowBox[{FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm], FormBox[FormBox[\"b\", \ TraditionalForm], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID112", +{"fcstSharedObjectsTypesetting-ID84", "MakeBoxes[DiracSigma[DiracGamma[Momentum[a]], \ DiracGamma[Momentum[b]]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", \ RowBox[{FormBox[OverscriptBox[FormBox[\"a\", TraditionalForm], \ \"_\"], TraditionalForm], FormBox[OverscriptBox[FormBox[\"b\", \ TraditionalForm], \"_\"], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID113", +{"fcstSharedObjectsTypesetting-ID85", "MakeBoxes[DiracSigma[DiracGamma[Momentum[a, D], D], \ DiracGamma[Momentum[b, D], D]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", RowBox[{FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm], FormBox[FormBox[\"b\", \ TraditionalForm], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID114", +{"fcstSharedObjectsTypesetting-ID86", "MakeBoxes[DiracSigma[DiracGamma[Momentum[a, -4 + D], -4 + D], \ DiracGamma[Momentum[b, -4 + D], -4 + D]], TraditionalForm]", "SuperscriptBox[\"\[Sigma]\", \ RowBox[{FormBox[OverscriptBox[FormBox[\"a\", TraditionalForm], \ \"^\"], TraditionalForm], FormBox[OverscriptBox[FormBox[\"b\", \ TraditionalForm], \"^\"], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID115", +{"fcstSharedObjectsTypesetting-ID87", "MakeBoxes[Eps[LorentzIndex[a], LorentzIndex[b], LorentzIndex[c], \ LorentzIndex[d]], TraditionalForm]", -"SuperscriptBox[\"\[Epsilon]\", RowBox[{FormBox[FormBox[\"a\", \ -TraditionalForm], TraditionalForm], FormBox[FormBox[\"b\", \ -TraditionalForm], TraditionalForm], FormBox[FormBox[\"c\", \ -TraditionalForm], TraditionalForm], FormBox[FormBox[\"d\", \ -TraditionalForm], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID116", +"SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"_\"], \ +RowBox[{FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm], \ +FormBox[FormBox[\"b\", TraditionalForm], TraditionalForm], \ +FormBox[FormBox[\"c\", TraditionalForm], TraditionalForm], \ +FormBox[FormBox[\"d\", TraditionalForm], TraditionalForm]}]]"}, +{"fcstSharedObjectsTypesetting-ID88", "MakeBoxes[Eps[Momentum[a], Momentum[b], Momentum[c], \ Momentum[d]], TraditionalForm]", -"SuperscriptBox[\"\[Epsilon]\", \ +"SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"_\"], \ RowBox[{FormBox[OverscriptBox[FormBox[\"a\", TraditionalForm], \ \"_\"], TraditionalForm], FormBox[OverscriptBox[FormBox[\"b\", \ TraditionalForm], \"_\"], TraditionalForm], \ FormBox[OverscriptBox[FormBox[\"c\", TraditionalForm], \"_\"], \ TraditionalForm], FormBox[OverscriptBox[FormBox[\"d\", \ TraditionalForm], \"_\"], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID117", +{"fcstSharedObjectsTypesetting-ID89", "MakeBoxes[Eps[Momentum[Polarization[a, I]], Momentum[b], \ Momentum[c], Momentum[Polarization[d, I]]], TraditionalForm]", -"SuperscriptBox[\"\[Epsilon]\", \ +"SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"_\"], \ RowBox[{FormBox[RowBox[{OverscriptBox[\"\[CurlyEpsilon]\", \"_\"], \ \"(\", FormBox[\"a\", TraditionalForm], \")\"}], TraditionalForm], \ FormBox[OverscriptBox[FormBox[\"b\", TraditionalForm], \"_\"], \ @@ -706,135 +436,280 @@ TraditionalForm], FormBox[OverscriptBox[FormBox[\"c\", \ TraditionalForm], \"_\"], TraditionalForm], \ FormBox[RowBox[{OverscriptBox[\"\[CurlyEpsilon]\", \"_\"], \"(\", \ FormBox[\"d\", TraditionalForm], \")\"}], TraditionalForm]}]]"}, -{"fcstSharedObjectsTypesetting-ID118", +{"fcstSharedObjectsTypesetting-ID90", "MakeBoxes[Epsilon, TraditionalForm]", "TagBox[\"\[CurlyEpsilon]\", TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID119", +{"fcstSharedObjectsTypesetting-ID91", "MakeBoxes[ExplicitLorentzIndex[i], TraditionalForm]", "FormBox[\"i\", TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID120", -"MakeBoxes[ExplicitLorentzIndex[Upper[i]], TraditionalForm]", -"FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID121", -"MakeBoxes[ExplicitLorentzIndex[Lower[i]], TraditionalForm]", -"FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID122", +{"fcstSharedObjectsTypesetting-ID92", "MakeBoxes[ExplicitLorentzIndex[i, D], TraditionalForm]", "FormBox[\"i\", TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID123", -"MakeBoxes[ExplicitLorentzIndex[Upper[i], D], TraditionalForm]", -"FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID124", -"MakeBoxes[ExplicitLorentzIndex[Lower[i], D], TraditionalForm]", -"FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID125", +{"fcstSharedObjectsTypesetting-ID93", "MakeBoxes[ExplicitSUNIndex[i], TraditionalForm]", "FormBox[\"i\", TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID126", +{"fcstSharedObjectsTypesetting-ID94", "MakeBoxes[ExplicitSUNFIndex[i], TraditionalForm]", "FormBox[\"i\", TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID127", +{"fcstSharedObjectsTypesetting-ID95", "MakeBoxes[FAD[p], TraditionalForm]", "FormBox[FractionBox[\"1\", \ -InterpretationBox[RowBox[{\"\\\"[\\\"\", \"\[InvisibleSpace]\", \ -SuperscriptBox[\"p\", \"2\"], \"\[InvisibleSpace]\", \"\\\"]\\\"\"}], \ -\"[\"p^2\"]\", Editable -> False]], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID128", +InterpretationBox[SuperscriptBox[FormBox[FormBox[\"p\", \ 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TraditionalForm], 2], Pair[Momentum[q, D], \ +Momentum[q, D]], Editable -> False]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID97", "MakeBoxes[FAD[p, -l + q], TraditionalForm]", -"FormBox[FractionBox[\"1\", RowBox[{RowBox[{\"(\", \ -InterpretationBox[RowBox[{\"\\\"[\\\"\", \"\[InvisibleSpace]\", \ -SuperscriptBox[\"p\", \"2\"], \"\[InvisibleSpace]\", \"\\\"]\\\"\"}], \ -\"[\"p^2\"]\", Editable -> False], \")\"}], \".\", RowBox[{\"(\", \ -InterpretationBox[RowBox[{\"\\\"[\\\"\", \"\[InvisibleSpace]\", \ -SuperscriptBox[RowBox[{\"(\", RowBox[{\"q\", \"-\", \"l\"}], \")\"}], \ -\"2\"], \"\[InvisibleSpace]\", \"\\\"]\\\"\"}], \"[\"(-l + q)^2\"]\", \ -Editable -> False], \")\"}]}]], TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID130", +"FormBox[FractionBox[\"1\", \ +RowBox[{InterpretationBox[SuperscriptBox[FormBox[FormBox[\"p\", \ +TraditionalForm], TraditionalForm], 2], Pair[Momentum[p, D], \ +Momentum[p, D]], Editable -> False], \".\", \ 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-{"fcstSharedObjectsTypesetting-ID398", +{"fcstSharedObjectsTypesetting-ID254", "MakeBoxes[FCPartialD[LorentzIndex[x]], TraditionalForm]", "SubscriptBox[\"\[PartialD]\", FormBox[FormBox[\"x\", \ TraditionalForm], TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID399", +{"fcstSharedObjectsTypesetting-ID255", "MakeBoxes[FCPartialD[x, LorentzIndex[mu]], TraditionalForm]", "RowBox[{\"\[PartialD]\", \"/\", \"\[PartialD]\", \ SuperscriptBox[FormBox[\"x\", TraditionalForm], \ FormBox[FormBox[\"mu\", TraditionalForm], TraditionalForm]]}]"}, -{"fcstSharedObjectsTypesetting-ID400", +{"fcstSharedObjectsTypesetting-ID256", "MakeBoxes[PlusDistribution[x], TraditionalForm]", "SubscriptBox[RowBox[{\"(\", \"x\", \")\"}], \"+\"]"}, -{"fcstSharedObjectsTypesetting-ID401", -"MakeBoxes[PropagatorDenominator[a, 0], TraditionalForm]", -"FormBox[FractionBox[\"1\", SuperscriptBox[\"a\", \"2\"]], \ -TraditionalForm]"}, -{"fcstSharedObjectsTypesetting-ID402", -"MakeBoxes[PropagatorDenominator[a, b], 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TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID407", +{"fcstSharedObjectsTypesetting-ID260", "MakeBoxes[QuantumField[f, LorentzIndex[mu], SUNIndex[a]], \ TraditionalForm]", "SubsuperscriptBox[FormBox[\"f\", TraditionalForm], \ FormBox[FormBox[\"mu\", TraditionalForm], TraditionalForm], \ FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID408", +{"fcstSharedObjectsTypesetting-ID261", "MakeBoxes[QuantumField[f, LorentzIndex[mu], Momentum[p], \ SUNIndex[a]], TraditionalForm]", "SubsuperscriptBox[FormBox[\"f\", TraditionalForm], \ @@ -2656,14 +1584,14 @@ RowBox[{FormBox[FormBox[\"mu\", TraditionalForm], TraditionalForm], \ FormBox[OverscriptBox[FormBox[\"p\", TraditionalForm], \"_\"], \ TraditionalForm]}], FormBox[FormBox[\"a\", TraditionalForm], \ TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID409", +{"fcstSharedObjectsTypesetting-ID262", "MakeBoxes[QuantumField[f, LorentzIndex[mu], SUNIndex[a]][q], \ TraditionalForm]", "RowBox[{SubsuperscriptBox[FormBox[\"f\", TraditionalForm], \ FormBox[FormBox[\"mu\", TraditionalForm], TraditionalForm], \ FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm]], \"(\", \ FormBox[\"q\", TraditionalForm], \")\"}]"}, -{"fcstSharedObjectsTypesetting-ID410", +{"fcstSharedObjectsTypesetting-ID263", "MakeBoxes[QuantumField[f, LorentzIndex[mu], Momentum[p], \ SUNIndex[a]][q], TraditionalForm]", "RowBox[{SubsuperscriptBox[FormBox[\"f\", TraditionalForm], \ @@ -2671,7 +1599,7 @@ RowBox[{FormBox[FormBox[\"mu\", TraditionalForm], TraditionalForm], \ FormBox[OverscriptBox[FormBox[\"p\", TraditionalForm], \"_\"], \ TraditionalForm]}], FormBox[FormBox[\"a\", TraditionalForm], \ TraditionalForm]], \"(\", FormBox[\"q\", TraditionalForm], \")\"}]"}, -{"fcstSharedObjectsTypesetting-ID411", +{"fcstSharedObjectsTypesetting-ID264", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], f, \ LorentzIndex[mu], SUNIndex[a]][q], TraditionalForm]", "RowBox[{RowBox[{\"(\", RowBox[{SubscriptBox[\"(\[PartialD]\", \ @@ -2681,7 +1609,7 @@ FormBox[FormBox[\"mu\", TraditionalForm], TraditionalForm], \ FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm]], \")\"}], \ \")\"}], \"\[InvisibleApplication]\", RowBox[{\"(\", \"q\", \ \")\"}]}]"}, -{"fcstSharedObjectsTypesetting-ID412", +{"fcstSharedObjectsTypesetting-ID265", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], f, \ ExplicitLorentzIndex[2], SUNIndex[a]][q], TraditionalForm]", "RowBox[{RowBox[{\"(\", RowBox[{SubscriptBox[\"(\[PartialD]\", \ @@ -2691,7 +1619,7 @@ FormBox[FormBox[\"2\", TraditionalForm], TraditionalForm], \ FormBox[FormBox[\"a\", TraditionalForm], TraditionalForm]], \")\"}], \ \")\"}], \"\[InvisibleApplication]\", RowBox[{\"(\", \"q\", \ \")\"}]}]"}, -{"fcstSharedObjectsTypesetting-ID413", +{"fcstSharedObjectsTypesetting-ID266", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], f, \ LorentzIndex[mu]][q], TraditionalForm]", "RowBox[{RowBox[{\"(\", RowBox[{SubscriptBox[\"(\[PartialD]\", \ @@ -2699,8 +1627,8 @@ FormBox[FormBox[\"f\", TraditionalForm], TraditionalForm]], \ SubscriptBox[FormBox[\"f\", TraditionalForm], FormBox[FormBox[\"mu\", \ TraditionalForm], TraditionalForm]], \")\"}], \")\"}], \"\ \[InvisibleApplication]\", RowBox[{\"(\", \"q\", \")\"}]}]"}, -{"fcstSharedObjectsTypesetting-ID414", -"MakeBoxes[2 QuantumField[FCPartialD[LorentzIndex[f]], f, \ +{"fcstSharedObjectsTypesetting-ID267", +"MakeBoxes[2*QuantumField[FCPartialD[LorentzIndex[f]], f, \ LorentzIndex[mu], SUNIndex[a]][q], TraditionalForm]", "RowBox[{\"2\", \" \", RowBox[{RowBox[{\"(\", \ RowBox[{SubscriptBox[\"(\[PartialD]\", FormBox[FormBox[\"f\", \ @@ -2709,8 +1637,8 @@ TraditionalForm], FormBox[FormBox[\"mu\", TraditionalForm], \ TraditionalForm], FormBox[FormBox[\"a\", TraditionalForm], \ TraditionalForm]], \")\"}], \")\"}], \"\[InvisibleApplication]\", \ RowBox[{\"(\", \"q\", \")\"}]}]}]"}, -{"fcstSharedObjectsTypesetting-ID415", -"MakeBoxes[2 QuantumField[FCPartialD[LorentzIndex[f]], f, \ +{"fcstSharedObjectsTypesetting-ID268", +"MakeBoxes[2*QuantumField[FCPartialD[LorentzIndex[f]], f, \ ExplicitLorentzIndex[2], SUNIndex[a]][q], TraditionalForm]", "RowBox[{\"2\", \" \", RowBox[{RowBox[{\"(\", \ RowBox[{SubscriptBox[\"(\[PartialD]\", FormBox[FormBox[\"f\", \ @@ -2719,8 +1647,8 @@ TraditionalForm], FormBox[FormBox[\"2\", TraditionalForm], \ TraditionalForm], FormBox[FormBox[\"a\", TraditionalForm], \ TraditionalForm]], \")\"}], \")\"}], \"\[InvisibleApplication]\", \ RowBox[{\"(\", \"q\", \")\"}]}]}]"}, -{"fcstSharedObjectsTypesetting-ID416", -"MakeBoxes[2 QuantumField[FCPartialD[LorentzIndex[f]], f, \ +{"fcstSharedObjectsTypesetting-ID269", +"MakeBoxes[2*QuantumField[FCPartialD[LorentzIndex[f]], f, \ LorentzIndex[mu]][q], TraditionalForm]", "RowBox[{\"2\", \" \", RowBox[{RowBox[{\"(\", \ RowBox[{SubscriptBox[\"(\[PartialD]\", FormBox[FormBox[\"f\", \ @@ -2728,7 +1656,7 @@ TraditionalForm], TraditionalForm]], SubscriptBox[FormBox[\"f\", \ TraditionalForm], FormBox[FormBox[\"mu\", TraditionalForm], \ TraditionalForm]], \")\"}], \")\"}], \"\[InvisibleApplication]\", \ RowBox[{\"(\", \"q\", \")\"}]}]}]"}, -{"fcstSharedObjectsTypesetting-ID417", +{"fcstSharedObjectsTypesetting-ID270", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], f, \ Momentum[p], SUNIndex[a]], TraditionalForm]", "RowBox[{SubscriptBox[\"(\[PartialD]\", FormBox[FormBox[\"f\", \ @@ -2736,14 +1664,14 @@ TraditionalForm], TraditionalForm]], SubsuperscriptBox[FormBox[\"f\", \ TraditionalForm], FormBox[OverscriptBox[FormBox[\"p\", \ TraditionalForm], \"_\"], TraditionalForm], FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm]], \")\"}]"}, -{"fcstSharedObjectsTypesetting-ID418", +{"fcstSharedObjectsTypesetting-ID271", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], f, \ Momentum[p]], TraditionalForm]", "RowBox[{SubscriptBox[\"(\[PartialD]\", FormBox[FormBox[\"f\", \ TraditionalForm], TraditionalForm]], SubscriptBox[FormBox[\"f\", \ TraditionalForm], FormBox[OverscriptBox[FormBox[\"p\", \ TraditionalForm], \"_\"], TraditionalForm]], \")\"}]"}, -{"fcstSharedObjectsTypesetting-ID419", +{"fcstSharedObjectsTypesetting-ID272", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], \ FCPartialD[LorentzIndex[g]], f, Momentum[p], SUNIndex[a]], \ TraditionalForm]", @@ -2755,7 +1683,7 @@ TraditionalForm]}], SubsuperscriptBox[FormBox[\"f\", \ TraditionalForm], FormBox[OverscriptBox[FormBox[\"p\", \ TraditionalForm], \"_\"], TraditionalForm], FormBox[FormBox[\"a\", \ TraditionalForm], TraditionalForm]], \")\"}]"}, -{"fcstSharedObjectsTypesetting-ID420", +{"fcstSharedObjectsTypesetting-ID273", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], \ FCPartialD[LorentzIndex[g]], f, Momentum[p]], TraditionalForm]", "RowBox[{\"(\", RowBox[{FormBox[SubscriptBox[\"\[PartialD]\", \ @@ -2765,7 +1693,7 @@ FormBox[FormBox[\"g\", TraditionalForm], TraditionalForm]], \ TraditionalForm]}], SubscriptBox[FormBox[\"f\", TraditionalForm], \ FormBox[OverscriptBox[FormBox[\"p\", TraditionalForm], \"_\"], \ TraditionalForm]], \")\"}]"}, -{"fcstSharedObjectsTypesetting-ID421", +{"fcstSharedObjectsTypesetting-ID274", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], \ FCPartialD[LorentzIndex[g]], f, LorentzIndex[mu], SUNIndex[a]], \ TraditionalForm]", @@ -2777,7 +1705,7 @@ TraditionalForm]}], SubsuperscriptBox[FormBox[\"f\", \ TraditionalForm], FormBox[FormBox[\"mu\", TraditionalForm], \ TraditionalForm], FormBox[FormBox[\"a\", TraditionalForm], \ TraditionalForm]], \")\"}]"}, -{"fcstSharedObjectsTypesetting-ID422", +{"fcstSharedObjectsTypesetting-ID275", "MakeBoxes[QuantumField[FCPartialD[LorentzIndex[f]], \ FCPartialD[LorentzIndex[g]], f, LorentzIndex[mu]], TraditionalForm]", "RowBox[{\"(\", RowBox[{FormBox[SubscriptBox[\"\[PartialD]\", \ @@ -2786,80 +1714,80 @@ TraditionalForm], FormBox[SubscriptBox[\"\[PartialD]\", \ FormBox[FormBox[\"g\", TraditionalForm], TraditionalForm]], \ TraditionalForm]}], SubscriptBox[FormBox[\"f\", TraditionalForm], \ FormBox[FormBox[\"mu\", TraditionalForm], TraditionalForm]], \")\"}]"}, -{"fcstSharedObjectsTypesetting-ID423", +{"fcstSharedObjectsTypesetting-ID276", "MakeBoxes[QuarkField, TraditionalForm]", "\"\[Psi]\""}, -{"fcstSharedObjectsTypesetting-ID424", +{"fcstSharedObjectsTypesetting-ID277", "MakeBoxes[RightPartialD[LorentzIndex[x]], TraditionalForm]", "SubscriptBox[RowBox[{OverscriptBox[\"\[PartialD]\", \"\ \[RightArrow]\"]}], FormBox[FormBox[\"x\", TraditionalForm], \ TraditionalForm]]"}, -{"fcstSharedObjectsTypesetting-ID425", -"MakeBoxes[2 RightPartialD[Momentum[x]], TraditionalForm]", +{"fcstSharedObjectsTypesetting-ID278", +"MakeBoxes[2*RightPartialD[Momentum[x]], TraditionalForm]", "RowBox[{\"2\", \" \", SubscriptBox[RowBox[{OverscriptBox[\"\ \[PartialD]\", \"\[RightArrow]\"]}], \ FormBox[OverscriptBox[FormBox[\"x\", TraditionalForm], \"_\"], \ TraditionalForm]]}]"}, 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+\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID678", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +-m2^2 + m1^2*x, {1, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{SuperscriptBox[\"m1\", \"2\"], \" \", \"x\"}], \"-\", \ +SuperscriptBox[\"m2\", \"2\"]}], \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID679", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +0, {1, -1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +\"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \ +\"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \"RowDefault\"]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID680", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +m^2, {1, -1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID681", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +2*m^2, {1, -1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{\"2\", \" \", SuperscriptBox[\"m\", \"2\"]}], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID682", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +-m2^2 + m1^2*x, {1, -1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{SuperscriptBox[\"m1\", \"2\"], \" \", \"x\"}], \"-\", \ +SuperscriptBox[\"m2\", \"2\"]}], \"\\\"-\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID683", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +0, {2, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID684", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +m^2, {2, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", SuperscriptBox[\"m\", \ +\"2\"], \"\\\"+\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\ +\\\"\"}], \"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID685", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +2*m^2, {2, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", RowBox[{\"2\", \" \", \ +SuperscriptBox[\"m\", \"2\"]}], \"\\\"+\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID686", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +-m2^2 + m1^2*x, {2, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{SuperscriptBox[\"m1\", \"2\"], \" \", \"x\"}], \"-\", \ +SuperscriptBox[\"m2\", \"2\"]}], \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID687", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +0, {2, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID688", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +m^2, {2, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", SuperscriptBox[\"m\", \ +\"2\"], \"\\\"+\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\ +\\\"\"}], \"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID689", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +2*m^2, {2, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", RowBox[{\"2\", \" \", \ +SuperscriptBox[\"m\", \"2\"]}], \"\\\"+\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID690", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +-m2^2 + m1^2*x, {2, 1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{SuperscriptBox[\"m1\", \"2\"], \" \", \"x\"}], \"-\", \ +SuperscriptBox[\"m2\", \"2\"]}], \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID691", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +0, {2, -1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"-\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID692", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +m^2, {2, -1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", SuperscriptBox[\"m\", \ +\"2\"], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\ +\\\"\"}], \"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID693", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +2*m^2, {2, -1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", RowBox[{\"2\", \" \", \ +SuperscriptBox[\"m\", \"2\"]}], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID694", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +-m2^2 + m1^2*x, {2, -1}]], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{SuperscriptBox[\"m1\", \"2\"], \" \", \"x\"}], \"-\", \ +SuperscriptBox[\"m2\", \"2\"]}], \"\\\"-\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID695", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +0, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"+\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID696", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +m^2, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"+\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID697", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +2*m^2, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", RowBox[{\"2\", \ +\" \", SuperscriptBox[\"m\", \"2\"]}], \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID698", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +-m2^2 + m1^2*x, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{SuperscriptBox[\"m1\", \"2\"], \" \", \"x\"}], \"-\", \ +SuperscriptBox[\"m2\", \"2\"]}], \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID699", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +0, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"+\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID700", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +m^2, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"+\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID701", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +2*m^2, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", RowBox[{\"2\", \ +\" \", SuperscriptBox[\"m\", \"2\"]}], \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID702", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +-m2^2 + m1^2*x, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{SuperscriptBox[\"m1\", \"2\"], \" \", \"x\"}], \"-\", \ +SuperscriptBox[\"m2\", \"2\"]}], \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID703", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +0, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID704", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +m^2, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID705", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +2*m^2, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", RowBox[{\"2\", \ +\" \", SuperscriptBox[\"m\", \"2\"]}], \"\\\"-\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID706", +"MakeBoxes[FeynAmpDenominator[StandardPropagatorDenominator[0, 0, \ +-m2^2 + m1^2*x, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{SuperscriptBox[\"m1\", \"2\"], \" \", \"x\"}], \"-\", \ +SuperscriptBox[\"m2\", \"2\"]}], \"\\\"-\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesetting-ID707", +"MakeBoxes[SFAD[{{0, p1 . p2}}], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{FormBox[FormBox[\"p1\", TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[\"p2\", TraditionalForm], TraditionalForm]}], \"\\\"+\ +\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"} +}); + +Tests`Shared`fcstSharedObjectsTypesettingNr = +({ +{"fcstSharedObjectsTypesettingNr-ID1", +"MakeBoxes[CartesianIndex[i], TraditionalForm]", +"FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNr-ID2", +"MakeBoxes[CartesianIndex[i], TraditionalForm]", +"FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNr-ID3", +"MakeBoxes[CartesianIndex[i, -1 + D], TraditionalForm]", +"FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNr-ID4", +"MakeBoxes[CartesianIndex[i, -4 + D], TraditionalForm]", +"FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNr-ID5", +"MakeBoxes[CartesianMomentum[p], TraditionalForm]", +"OverscriptBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> \ +False], TraditionalForm], \"_\"]"}, +{"fcstSharedObjectsTypesettingNr-ID6", +"MakeBoxes[CartesianMomentum[p], TraditionalForm]", +"OverscriptBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> \ +False], TraditionalForm], \"_\"]"}, +{"fcstSharedObjectsTypesettingNr-ID7", +"MakeBoxes[CartesianMomentum[p, -1 + D], TraditionalForm]", +"FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNr-ID8", +"MakeBoxes[CartesianMomentum[p, -4 + D], TraditionalForm]", +"OverscriptBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> \ +False], TraditionalForm], \"^\"]"}, +{"fcstSharedObjectsTypesettingNr-ID9", +"MakeBoxes[CartesianMomentum[Polarization[p, I]], \ +TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[CurlyEpsilon]\\\"\"\ +, Bold, StripOnInput -> False], TraditionalForm], \"_\"], \"(\", \ +FormBox[\"p\", TraditionalForm], \")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID10", +"MakeBoxes[CartesianMomentum[Polarization[p, I], -4 + D], \ +TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[CurlyEpsilon]\\\"\"\ +, Bold, StripOnInput -> False], TraditionalForm], \"^\"], \"(\", \ +FormBox[\"p\", TraditionalForm], \")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID11", +"MakeBoxes[CartesianMomentum[Polarization[p, I]], \ +TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[CurlyEpsilon]\\\"\"\ +, Bold, StripOnInput -> False], TraditionalForm], \"_\"], \"(\", \ +FormBox[\"p\", TraditionalForm], \")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID12", +"MakeBoxes[TemporalMomentum[Polarization[p, I]], TraditionalForm]", + "FormBox[RowBox[{FormBox[\"\\\"\[CurlyEpsilon]\\\"\", \ +TraditionalForm], \"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNr-ID13", +"MakeBoxes[CartesianPair[CartesianIndex[a], CartesianMomentum[p]], \ +TraditionalForm]", +"SuperscriptBox[RowBox[{FormBox[OverscriptBox[FormBox[StyleBox[\"p\ +\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], \ +TraditionalForm]}], FormBox[FormBox[StyleBox[\"a\", Bold, \ +StripOnInput -> False], TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID14", +"MakeBoxes[CartesianPair[CartesianIndex[a, -1 + D], \ +CartesianMomentum[p, -1 + D]], TraditionalForm]", +"SuperscriptBox[RowBox[{FormBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], TraditionalForm]}], \ +FormBox[FormBox[StyleBox[\"a\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID15", +"MakeBoxes[CartesianPair[CartesianIndex[a, -4 + D], \ +CartesianMomentum[p, -4 + D]], TraditionalForm]", +"SuperscriptBox[RowBox[{FormBox[OverscriptBox[FormBox[StyleBox[\"p\ +\", Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +TraditionalForm]}], FormBox[FormBox[StyleBox[\"a\", Bold, \ +StripOnInput -> False], TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID16", +"MakeBoxes[CartesianPair[CartesianIndex[a], CartesianMomentum[p + \ +q]], TraditionalForm]", +"SuperscriptBox[RowBox[{\"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"]}], TraditionalForm], TraditionalForm], \ +\")\"}], FormBox[FormBox[StyleBox[\"a\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID17", +"MakeBoxes[CartesianPair[CartesianIndex[a, -1 + D], \ +CartesianMomentum[p + q, -1 + D]], TraditionalForm]", +"SuperscriptBox[RowBox[{\"(\", \ +FormBox[FormBox[RowBox[{FormBox[StyleBox[\"p\", Bold, StripOnInput -> \ +False], TraditionalForm], \"+\", FormBox[StyleBox[\"q\", Bold, \ +StripOnInput -> False], TraditionalForm]}], TraditionalForm], \ +TraditionalForm], \")\"}], FormBox[FormBox[StyleBox[\"a\", Bold, \ +StripOnInput -> False], TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID18", +"MakeBoxes[CartesianPair[CartesianIndex[a, -4 + D], \ +CartesianMomentum[p + q, -4 + D]], TraditionalForm]", +"SuperscriptBox[RowBox[{\"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"]}], TraditionalForm], TraditionalForm], \ +\")\"}], FormBox[FormBox[StyleBox[\"a\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID19", +"MakeBoxes[CartesianPair[CartesianIndex[a], CartesianMomentum[p + \ +q] + CartesianMomentum[r]], TraditionalForm]", +"SuperscriptBox[RowBox[{\"(\", FormBox[RowBox[{RowBox[{\"(\", \ +FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"]}], TraditionalForm], \")\"}], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"r\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"]}], TraditionalForm], \")\"}], \ +FormBox[FormBox[StyleBox[\"a\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID20", +"MakeBoxes[CartesianPair[CartesianIndex[a, -1 + D], \ +CartesianMomentum[p + q, -1 + D] + CartesianMomentum[r, -1 + D]], \ +TraditionalForm]", +"SuperscriptBox[RowBox[{\"(\", FormBox[RowBox[{RowBox[{\"(\", \ +FormBox[RowBox[{FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], \ +TraditionalForm], \"+\", FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm]}], TraditionalForm], \")\"}], \"+\", \ +FormBox[StyleBox[\"r\", Bold, StripOnInput -> False], \ +TraditionalForm]}], TraditionalForm], \")\"}], \ +FormBox[FormBox[StyleBox[\"a\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID21", +"MakeBoxes[CartesianPair[CartesianIndex[a, -4 + D], \ +CartesianMomentum[p + q, -4 + D] + CartesianMomentum[r, -4 + D]], \ +TraditionalForm]", +"SuperscriptBox[RowBox[{\"(\", FormBox[RowBox[{RowBox[{\"(\", \ +FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"]}], TraditionalForm], \")\"}], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"r\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"]}], TraditionalForm], \")\"}], \ +FormBox[FormBox[StyleBox[\"a\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID22", +"MakeBoxes[CartesianPair[CartesianIndex[a], \ +CartesianMomentum[Polarization[p, I]]], TraditionalForm]", +"RowBox[{SuperscriptBox[OverscriptBox[FormBox[StyleBox[\"\\\"\ +\[CurlyEpsilon]\\\"\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"], FormBox[FormBox[StyleBox[\"a\", Bold, \ +StripOnInput -> False], TraditionalForm], TraditionalForm]], \"(\", \ +FormBox[\"p\", TraditionalForm], \")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID23", +"MakeBoxes[CartesianPair[CartesianIndex[a, -1 + D], \ +CartesianMomentum[Polarization[p, I], -1 + D]], TraditionalForm]", +"RowBox[{SuperscriptBox[FormBox[StyleBox[\"\\\"\[CurlyEpsilon]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm], \ +FormBox[FormBox[StyleBox[\"a\", Bold, StripOnInput -> False], \ +TraditionalForm], 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+"MakeBoxes[DiracGamma[CartesianMomentum[p + q + r, -1 + D], D], \ +TraditionalForm]", +"RowBox[{FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", Bold, StripOnInput \ +-> False], TraditionalForm], \"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{FormBox[StyleBox[\"p\", Bold, StripOnInput -> \ +False], TraditionalForm], \"+\", FormBox[StyleBox[\"q\", Bold, \ +StripOnInput -> False], TraditionalForm], \"+\", FormBox[StyleBox[\"r\ +\", Bold, StripOnInput -> False], TraditionalForm]}], \ +TraditionalForm], TraditionalForm], \")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID66", +"MakeBoxes[DiracGamma[CartesianMomentum[p + q + r, -4 + D], -4 + \ +D], TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +\"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"r\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"]}], TraditionalForm], TraditionalForm], \ +\")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID67", +"MakeBoxes[DiracGamma[CartesianMomentum[p, 4]] + \ +DiracGamma[CartesianMomentum[q, 4]], TraditionalForm]", +"RowBox[{RowBox[{SubscriptBox[FormBox[StyleBox[\"\\\"\[Gamma]\\\"\"\ +, Bold, StripOnInput -> False], TraditionalForm], FormBox[\"4\", \ +TraditionalForm]], \"\[CenterDot]\", \ +FormBox[SubscriptBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> \ +False], TraditionalForm], FormBox[\"4\", TraditionalForm]], \ +TraditionalForm]}], \"+\", RowBox[{SubscriptBox[FormBox[StyleBox[\"\\\ +\"\[Gamma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \ +FormBox[\"4\", TraditionalForm]], \"\[CenterDot]\", \ +FormBox[SubscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], FormBox[\"4\", TraditionalForm]], \ +TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID68", +"MakeBoxes[DiracGamma[CartesianMomentum[p, -1 + D], D] + \ +DiracGamma[CartesianMomentum[q, -1 + D], D], TraditionalForm]", +"RowBox[{RowBox[{FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", Bold, \ +StripOnInput -> False], TraditionalForm], \"\[CenterDot]\", \ +FormBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \"+\", \ +RowBox[{FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", Bold, StripOnInput -> \ +False], TraditionalForm], \"\[CenterDot]\", FormBox[FormBox[StyleBox[\ +\"q\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID69", +"MakeBoxes[DiracGamma[CartesianMomentum[p, -4 + D], -4 + D] + \ +DiracGamma[CartesianMomentum[q, -4 + D], -4 + D], TraditionalForm]", +"RowBox[{RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Gamma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm], \"^\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], TraditionalForm]}], \ +\"+\", RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +\"\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"q\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], \ +TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID70", +"MakeBoxes[DiracGamma[CartesianMomentum[Polarization[p, I]]], \ +TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"_\"], \ +\"\[CenterDot]\", FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\ +\"\[CurlyEpsilon]\\\"\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"], \"(\", FormBox[\"p\", TraditionalForm], \")\ +\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID71", +"MakeBoxes[DiracGamma[CartesianMomentum[Polarization[p, I], -1 + \ +D], D], TraditionalForm]", +"RowBox[{FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", Bold, StripOnInput \ +-> False], TraditionalForm], \"\[CenterDot]\", \ +FormBox[RowBox[{FormBox[StyleBox[\"\\\"\[CurlyEpsilon]\\\"\", Bold, \ +StripOnInput -> False], TraditionalForm], \"(\", FormBox[\"p\", \ +TraditionalForm], \")\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID72", +"MakeBoxes[DiracGamma[CartesianMomentum[Polarization[p, I], -4 + \ +D], -4 + D], TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +\"\[CenterDot]\", FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\ +\"\[CurlyEpsilon]\\\"\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"], \"(\", FormBox[\"p\", TraditionalForm], \")\ +\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID73", +"MakeBoxes[DiracGamma[CartesianIndex[i]], TraditionalForm]", +"SuperscriptBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\ +\[Gamma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \ +\"_\"]}], FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID74", +"MakeBoxes[DiracGamma[ExplicitLorentzIndex[0]], TraditionalForm]", +"SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"]}], \ +FormBox[FormBox[\"0\", TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID75", +"MakeBoxes[PauliSigma[LorentzIndex[i]], TraditionalForm]", +"SuperscriptBox[RowBox[{OverscriptBox[\"\[Sigma]\", \"_\"]}], \ +FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID76", +"MakeBoxes[PauliSigma[LorentzIndex[i, D], -1 + D], \ +TraditionalForm]", +"SuperscriptBox[RowBox[{\"\[Sigma]\"}], FormBox[FormBox[\"i\", \ +TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID77", +"MakeBoxes[PauliSigma[LorentzIndex[i, -4 + D], -4 + D], \ +TraditionalForm]", +"SuperscriptBox[RowBox[{OverscriptBox[\"\[Sigma]\", \"^\"]}], \ +FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID78", +"MakeBoxes[PauliSigma[Momentum[p]], TraditionalForm]", +"RowBox[{OverscriptBox[\"\[Sigma]\", \"_\"], \"\[CenterDot]\", \ +FormBox[OverscriptBox[FormBox[\"p\", TraditionalForm], \"_\"], \ +TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID79", +"MakeBoxes[PauliSigma[Momentum[p, D], -1 + D], TraditionalForm]", +"RowBox[{\"\[Sigma]\", \"\[CenterDot]\", FormBox[FormBox[\"p\", \ +TraditionalForm], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID80", +"MakeBoxes[PauliSigma[Momentum[p, -4 + D], -4 + D], \ +TraditionalForm]", +"RowBox[{OverscriptBox[\"\[Sigma]\", \"^\"], \"\[CenterDot]\", \ +FormBox[OverscriptBox[FormBox[\"p\", TraditionalForm], \"^\"], \ +TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID81", +"MakeBoxes[PauliSigma[Momentum[p + q]], TraditionalForm]", +"RowBox[{OverscriptBox[\"\[Sigma]\", \"_\"], \"\[CenterDot]\", \"(\ +\", FormBox[FormBox[RowBox[{OverscriptBox[FormBox[\"p\", \ +TraditionalForm], \"_\"], \"+\", OverscriptBox[FormBox[\"q\", \ +TraditionalForm], \"_\"]}], TraditionalForm], TraditionalForm], \ +\")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID82", +"MakeBoxes[PauliSigma[Momentum[p + q, D], -1 + D], \ +TraditionalForm]", +"RowBox[{\"\[Sigma]\", \"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{FormBox[\"p\", TraditionalForm], \"+\", \ +FormBox[\"q\", TraditionalForm]}], TraditionalForm], \ +TraditionalForm], \")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID83", +"MakeBoxes[PauliSigma[Momentum[p + q, -4 + D], -4 + D], \ +TraditionalForm]", +"RowBox[{OverscriptBox[\"\[Sigma]\", \"^\"], \"\[CenterDot]\", \"(\ +\", FormBox[FormBox[RowBox[{OverscriptBox[FormBox[\"p\", \ +TraditionalForm], \"^\"], \"+\", OverscriptBox[FormBox[\"q\", \ +TraditionalForm], \"^\"]}], TraditionalForm], TraditionalForm], \ +\")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID84", +"MakeBoxes[PauliSigma[Momentum[p + q]] + PauliSigma[Momentum[r]], \ +TraditionalForm]", +"RowBox[{RowBox[{OverscriptBox[\"\[Sigma]\", \"_\"], \ +\"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[\"p\", \ +TraditionalForm], \"_\"], \"+\", OverscriptBox[FormBox[\"q\", \ +TraditionalForm], \"_\"]}], TraditionalForm], TraditionalForm], \ +\")\"}], \"+\", RowBox[{OverscriptBox[\"\[Sigma]\", \"_\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[\"r\", \ +TraditionalForm], \"_\"], TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID85", +"MakeBoxes[PauliSigma[Momentum[p + q, D], -1 + D] + \ +PauliSigma[Momentum[r, D], -1 + D], TraditionalForm]", +"RowBox[{RowBox[{\"\[Sigma]\", \"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{FormBox[\"p\", TraditionalForm], \"+\", \ +FormBox[\"q\", TraditionalForm]}], TraditionalForm], \ +TraditionalForm], \")\"}], \"+\", RowBox[{\"\[Sigma]\", \ +\"\[CenterDot]\", FormBox[FormBox[\"r\", TraditionalForm], \ +TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID86", +"MakeBoxes[PauliSigma[Momentum[p + q, -4 + D], -4 + D] + \ +PauliSigma[Momentum[r, -4 + D], -4 + D], TraditionalForm]", +"RowBox[{RowBox[{OverscriptBox[\"\[Sigma]\", \"^\"], \ +\"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[\"p\", \ +TraditionalForm], \"^\"], \"+\", OverscriptBox[FormBox[\"q\", \ +TraditionalForm], \"^\"]}], TraditionalForm], TraditionalForm], \ +\")\"}], \"+\", RowBox[{OverscriptBox[\"\[Sigma]\", \"^\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[\"r\", \ +TraditionalForm], \"^\"], TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID87", +"MakeBoxes[PauliSigma[Momentum[Polarization[p, I]]], \ +TraditionalForm]", +"RowBox[{OverscriptBox[\"\[Sigma]\", \"_\"], \"\[CenterDot]\", \ +FormBox[RowBox[{OverscriptBox[\"\[CurlyEpsilon]\", \"_\"], \"(\", \ +FormBox[\"p\", TraditionalForm], \")\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID88", +"MakeBoxes[PauliSigma[Momentum[Polarization[p, I], D], -1 + D], \ +TraditionalForm]", +"RowBox[{\"\[Sigma]\", \"\[CenterDot]\", \ +FormBox[RowBox[{FormBox[\"\\\"\[CurlyEpsilon]\\\"\", \ +TraditionalForm], \"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ +TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID89", +"MakeBoxes[PauliSigma[Momentum[Polarization[p, I], -4 + D], -4 + \ +D], TraditionalForm]", +"RowBox[{OverscriptBox[\"\[Sigma]\", \"^\"], \"\[CenterDot]\", \ +FormBox[RowBox[{OverscriptBox[\"\[CurlyEpsilon]\", \"^\"], \"(\", \ +FormBox[\"p\", TraditionalForm], \")\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID90", +"MakeBoxes[PauliSigma[Momentum[Polarization[p, -I]]], \ +TraditionalForm]", +"RowBox[{OverscriptBox[\"\[Sigma]\", \"_\"], \"\[CenterDot]\", \ +FormBox[RowBox[{SuperscriptBox[OverscriptBox[\"\[CurlyEpsilon]\", \"_\ +\"], \"*\"], \"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ +TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID91", +"MakeBoxes[PauliSigma[Momentum[Polarization[p, -I], D], -1 + D], \ +TraditionalForm]", +"RowBox[{\"\[Sigma]\", \"\[CenterDot]\", \ +FormBox[RowBox[{SuperscriptBox[FormBox[\"\\\"\[CurlyEpsilon]\\\"\", \ +TraditionalForm], \"*\"], \"(\", FormBox[\"p\", TraditionalForm], \")\ +\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID92", +"MakeBoxes[PauliSigma[Momentum[Polarization[p, -I], -4 + D], -4 + \ +D], TraditionalForm]", +"RowBox[{OverscriptBox[\"\[Sigma]\", \"^\"], \"\[CenterDot]\", \ +FormBox[RowBox[{SuperscriptBox[OverscriptBox[\"\[CurlyEpsilon]\", \"^\ +\"], \"*\"], \"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ +TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID93", +"MakeBoxes[PauliSigma[CartesianIndex[i]], TraditionalForm]", +"SuperscriptBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\ +\[Sigma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \ +\"_\"]}], FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID94", +"MakeBoxes[PauliSigma[CartesianIndex[i, -1 + D], -1 + D], \ +TraditionalForm]", +"SuperscriptBox[RowBox[{FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm]}], \ +FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID95", +"MakeBoxes[PauliSigma[CartesianIndex[i, -4 + D], -4 + D], \ +TraditionalForm]", +"SuperscriptBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\ +\[Sigma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \ +\"^\"]}], FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm]]"}, +{"fcstSharedObjectsTypesettingNr-ID96", +"MakeBoxes[PauliSigma[CartesianMomentum[p]], TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"_\"], \ +\"\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID97", +"MakeBoxes[PauliSigma[CartesianMomentum[p, -1 + D], -1 + D], \ +TraditionalForm]", +"RowBox[{FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", Bold, StripOnInput \ +-> False], TraditionalForm], \"\[CenterDot]\", \ +FormBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID98", +"MakeBoxes[PauliSigma[CartesianMomentum[p, -4 + D], -4 + D], \ +TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +\"\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID99", +"MakeBoxes[PauliSigma[CartesianMomentum[p + q]], TraditionalForm]", + "RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"_\"], \ +\"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"]}], TraditionalForm], TraditionalForm], \ +\")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID100", +"MakeBoxes[PauliSigma[CartesianMomentum[p + q, -1 + D], -1 + D], \ +TraditionalForm]", +"RowBox[{FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", Bold, StripOnInput \ +-> False], TraditionalForm], \"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{FormBox[StyleBox[\"p\", Bold, StripOnInput -> \ +False], TraditionalForm], \"+\", FormBox[StyleBox[\"q\", Bold, \ +StripOnInput -> False], TraditionalForm]}], TraditionalForm], \ +TraditionalForm], \")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID101", +"MakeBoxes[PauliSigma[CartesianMomentum[p + q, -4 + D], -4 + D], \ +TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +\"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"]}], TraditionalForm], TraditionalForm], \ +\")\"}]"}, +{"fcstSharedObjectsTypesettingNr-ID102", +"MakeBoxes[PauliSigma[CartesianMomentum[p + q]] + \ +PauliSigma[CartesianMomentum[r]], TraditionalForm]", +"RowBox[{RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], \"\ +\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"]}], TraditionalForm], TraditionalForm], \ +\")\"}], \"+\", RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\ +\\\"\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"r\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], \ +TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID103", +"MakeBoxes[PauliSigma[CartesianMomentum[p + q, -1 + D], -1 + D] + \ +PauliSigma[CartesianMomentum[r, -1 + D], -1 + D], TraditionalForm]", +"RowBox[{RowBox[{FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", Bold, \ +StripOnInput -> False], TraditionalForm], \"\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{FormBox[StyleBox[\"p\", Bold, StripOnInput -> \ +False], TraditionalForm], \"+\", FormBox[StyleBox[\"q\", Bold, \ +StripOnInput -> False], TraditionalForm]}], TraditionalForm], \ +TraditionalForm], \")\"}], \"+\", RowBox[{FormBox[StyleBox[\"\\\"\ +\[Sigma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \"\ +\[CenterDot]\", FormBox[FormBox[StyleBox[\"r\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID104", +"MakeBoxes[PauliSigma[CartesianMomentum[p + q, -4 + D], -4 + D] + \ +PauliSigma[CartesianMomentum[r, -4 + D], -4 + D], TraditionalForm]", +"RowBox[{RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm], \"^\"], \"\ +\[CenterDot]\", \"(\", \ +FormBox[FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], \"+\", \ +OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"]}], TraditionalForm], TraditionalForm], \ +\")\"}], \"+\", RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\ +\\\"\", Bold, StripOnInput -> False], TraditionalForm], \"^\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"r\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], \ +TraditionalForm]}]}]"}, +{"fcstSharedObjectsTypesettingNr-ID105", +"MakeBoxes[PauliSigma[CartesianMomentum[Polarization[p, I]]], \ +TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"_\"], \ +\"\[CenterDot]\", FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\ +\"\[CurlyEpsilon]\\\"\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"], \"(\", FormBox[\"p\", TraditionalForm], \")\ +\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID106", +"MakeBoxes[PauliSigma[CartesianMomentum[Polarization[p, I], -1 + \ +D], -1 + D], TraditionalForm]", +"RowBox[{FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", Bold, StripOnInput \ +-> False], TraditionalForm], \"\[CenterDot]\", \ +FormBox[RowBox[{FormBox[StyleBox[\"\\\"\[CurlyEpsilon]\\\"\", Bold, \ +StripOnInput -> False], TraditionalForm], \"(\", FormBox[\"p\", \ +TraditionalForm], \")\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID107", +"MakeBoxes[PauliSigma[CartesianMomentum[Polarization[p, I], -4 + \ +D], -4 + D], TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +\"\[CenterDot]\", FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\ +\"\[CurlyEpsilon]\\\"\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"], \"(\", FormBox[\"p\", TraditionalForm], \")\ +\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID108", +"MakeBoxes[PauliSigma[CartesianMomentum[Polarization[p, -I]]], \ +TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"_\"], \ +\"\[CenterDot]\", \ +FormBox[RowBox[{SuperscriptBox[OverscriptBox[FormBox[StyleBox[\"\\\"\ +\[CurlyEpsilon]\\\"\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"], \"*\"], \"(\", FormBox[\"p\", \ +TraditionalForm], \")\"}], TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID109", +"MakeBoxes[PauliSigma[CartesianMomentum[Polarization[p, -I], -1 + \ +D], -1 + D], TraditionalForm]", +"RowBox[{FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", Bold, StripOnInput \ +-> False], TraditionalForm], \"\[CenterDot]\", \ +FormBox[RowBox[{SuperscriptBox[FormBox[StyleBox[\"\\\"\[CurlyEpsilon]\ +\\\"\", Bold, StripOnInput -> False], TraditionalForm], \"*\"], \ +\"(\", FormBox[\"p\", TraditionalForm], \")\"}], \ +TraditionalForm]}]"}, +{"fcstSharedObjectsTypesettingNr-ID110", +"MakeBoxes[PauliSigma[CartesianMomentum[Polarization[p, -I], -4 + \ +D], -4 + D], TraditionalForm]", +"RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", \ +Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +\"\[CenterDot]\", \ +FormBox[RowBox[{SuperscriptBox[OverscriptBox[FormBox[StyleBox[\"\\\"\ +\[CurlyEpsilon]\\\"\", Bold, StripOnInput -> False], \ +TraditionalForm], \"^\"], \"*\"], \"(\", FormBox[\"p\", \ +TraditionalForm], \")\"}], TraditionalForm]}]"} +}); + +Tests`Shared`fcstSharedObjectsTypesettingNrFCE = +({ +{"fcstSharedObjectsTypesettingNrFCE-ID1", +"MakeBoxes[TC[p], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{FormBox[FormBox[FormBox[\"p\", \ +TraditionalForm], TraditionalForm], TraditionalForm]}], 0], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID2", +"MakeBoxes[CV[p, i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{FormBox[OverscriptBox[FormBox[\ +StyleBox[\"p\", Bold, StripOnInput -> False], TraditionalForm], \ +\"_\"], TraditionalForm]}], FormBox[FormBox[StyleBox[\"i\", Bold, \ +StripOnInput -> False], TraditionalForm], TraditionalForm]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID3", +"MakeBoxes[CVD[p, i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{FormBox[FormBox[StyleBox[\"p\", \ +Bold, StripOnInput -> False], TraditionalForm], TraditionalForm]}], \ +FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID4", +"MakeBoxes[CVE[p, i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{FormBox[OverscriptBox[FormBox[\ +StyleBox[\"p\", Bold, StripOnInput -> False], TraditionalForm], \ +\"^\"], TraditionalForm]}], FormBox[FormBox[StyleBox[\"i\", Bold, \ +StripOnInput -> False], TraditionalForm], TraditionalForm]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID5", +"MakeBoxes[KD[i, j], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[\"\[Delta]\", \ +\"_\"]}], RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], FormBox[FormBox[StyleBox[\ +\"j\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID6", +"MakeBoxes[KDD[i, j], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{\"\[Delta]\"}], \ +RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm], FormBox[FormBox[StyleBox[\"j\", \ +Bold, StripOnInput -> False], TraditionalForm], TraditionalForm]}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID7", +"MakeBoxes[KDE[i, j], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[\"\[Delta]\", \ +\"^\"]}], RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], FormBox[FormBox[StyleBox[\ +\"j\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID8", +"MakeBoxes[CSP[a, b], TraditionalForm]", +"FormBox[RowBox[{FormBox[OverscriptBox[FormBox[StyleBox[\"a\", \ +Bold, StripOnInput -> False], TraditionalForm], \"_\"], \ +TraditionalForm], FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[OverscriptBox[FormBox[StyleBox[\"b\", Bold, StripOnInput -> \ +False], TraditionalForm], \"_\"], TraditionalForm]}], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID9", +"MakeBoxes[CSPD[a, b], TraditionalForm]", +"FormBox[RowBox[{FormBox[FormBox[StyleBox[\"a\", Bold, \ +StripOnInput -> False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"b\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID10", +"MakeBoxes[CSPE[a, b], TraditionalForm]", +"FormBox[RowBox[{FormBox[OverscriptBox[FormBox[StyleBox[\"a\", \ +Bold, StripOnInput -> False], TraditionalForm], \"^\"], \ +TraditionalForm], FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[OverscriptBox[FormBox[StyleBox[\"b\", Bold, StripOnInput -> \ +False], TraditionalForm], \"^\"], TraditionalForm]}], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID11", +"MakeBoxes[TGA[], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[\"\[Gamma]\", \"_\"]}], FormBox[FormBox[\"0\", TraditionalForm], \ +TraditionalForm]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID12", +"MakeBoxes[CGA[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\ +\"\[Gamma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \"_\ +\"]}], FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID13", +"MakeBoxes[CGAD[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{FormBox[StyleBox[\"\\\"\[Gamma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm]}], \ +FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID14", +"MakeBoxes[CGAE[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\ +\"\[Gamma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \"^\ +\"]}], FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID15", +"MakeBoxes[CGS[p], TraditionalForm]", +"FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Gamma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm]}], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID16", +"MakeBoxes[CGSD[p], TraditionalForm]", +"FormBox[RowBox[{FormBox[StyleBox[\"\\\"\[Gamma]\\\"\", Bold, \ +StripOnInput -> False], TraditionalForm], \"\[CenterDot]\", \ +FormBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID17", +"MakeBoxes[CGSE[p], TraditionalForm]", +"FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Gamma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm], \"^\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], TraditionalForm]}], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID18", +"MakeBoxes[SI[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[\"\[Sigma]\", \ +\"_\"]}], FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID19", +"MakeBoxes[SID[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{\"\[Sigma]\"}], \ +FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID20", +"MakeBoxes[SIE[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[\"\[Sigma]\", \ +\"^\"]}], FormBox[FormBox[\"i\", TraditionalForm], TraditionalForm]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID21", +"MakeBoxes[SIS[p], TraditionalForm]", +"FormBox[RowBox[{OverscriptBox[\"\[Sigma]\", \"_\"], \ +\"\[CenterDot]\", FormBox[OverscriptBox[FormBox[\"p\", \ +TraditionalForm], \"_\"], TraditionalForm]}], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID22", +"MakeBoxes[SISD[p], TraditionalForm]", +"FormBox[RowBox[{\"\[Sigma]\", \"\[CenterDot]\", \ +FormBox[FormBox[\"p\", TraditionalForm], TraditionalForm]}], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID23", +"MakeBoxes[SISE[p], TraditionalForm]", +"FormBox[RowBox[{OverscriptBox[\"\[Sigma]\", \"^\"], \ +\"\[CenterDot]\", FormBox[OverscriptBox[FormBox[\"p\", \ +TraditionalForm], \"^\"], TraditionalForm]}], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID24", +"MakeBoxes[CSI[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\ +\"\[Sigma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \"_\ +\"]}], FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID25", +"MakeBoxes[CSID[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{FormBox[StyleBox[\"\\\"\[Sigma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm]}], \ +FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID26", +"MakeBoxes[CSIE[i], TraditionalForm]", +"FormBox[SuperscriptBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\ +\"\[Sigma]\\\"\", Bold, StripOnInput -> False], TraditionalForm], \"^\ +\"]}], FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID27", +"MakeBoxes[CSIS[p], TraditionalForm]", +"FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm]}], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID28", +"MakeBoxes[CSISD[p], TraditionalForm]", +"FormBox[RowBox[{FormBox[StyleBox[\"\\\"\[Sigma]\\\"\", Bold, \ +StripOnInput -> False], TraditionalForm], \"\[CenterDot]\", \ +FormBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID29", +"MakeBoxes[CSISE[p], TraditionalForm]", +"FormBox[RowBox[{OverscriptBox[FormBox[StyleBox[\"\\\"\[Sigma]\\\"\ +\", Bold, StripOnInput -> False], TraditionalForm], \"^\"], \"\ +\[CenterDot]\", FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, \ +StripOnInput -> False], TraditionalForm], \"^\"], TraditionalForm]}], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID30", +"MakeBoxes[CLC[i, j, k], TraditionalForm]", +"FormBox[SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"_\"], RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm], FormBox[FormBox[StyleBox[\"j\", Bold, StripOnInput -> False], TraditionalForm], TraditionalForm], FormBox[FormBox[StyleBox[\"k\", \ +Bold, StripOnInput -> False], TraditionalForm], TraditionalForm]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID31", +"MakeBoxes[CLC[i, j][p], TraditionalForm]", +"FormBox[SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"_\"], RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm], FormBox[FormBox[StyleBox[\"j\", Bold, StripOnInput -> False], TraditionalForm], TraditionalForm], \ +FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID32", +"MakeBoxes[CLC[i][p, q], TraditionalForm]", +"FormBox[SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"_\"], RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm], FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +FormBox[OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID33", +"MakeBoxes[CLC[][p, q, r], TraditionalForm]", +"FormBox[SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"_\"], RowBox[{FormBox[OverscriptBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], \ +TraditionalForm], \"_\"], TraditionalForm], FormBox[OverscriptBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], \ +TraditionalForm], FormBox[OverscriptBox[FormBox[StyleBox[\"r\", Bold, StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm]}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID34", +"MakeBoxes[CLCD[i, j, k], TraditionalForm]", +"FormBox[SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"\"], RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm], FormBox[FormBox[StyleBox[\"j\", Bold, StripOnInput -> False], TraditionalForm], TraditionalForm], FormBox[FormBox[StyleBox[\"k\", \ +Bold, StripOnInput -> False], TraditionalForm], TraditionalForm]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID35", +"MakeBoxes[CLCD[i, j][p], TraditionalForm]", +"FormBox[SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"\"], RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm], FormBox[FormBox[StyleBox[\"j\", Bold, StripOnInput -> False], TraditionalForm], TraditionalForm], FormBox[FormBox[StyleBox[\"p\", \ +Bold, StripOnInput -> False], TraditionalForm], TraditionalForm]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID36", +"MakeBoxes[CLCD[i][p, q], TraditionalForm]", +"FormBox[SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"\"], RowBox[{FormBox[FormBox[StyleBox[\"i\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm], FormBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], TraditionalForm], TraditionalForm], FormBox[FormBox[StyleBox[\"q\", \ +Bold, StripOnInput -> False], TraditionalForm], TraditionalForm]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrFCE-ID37", +"MakeBoxes[CLCD[][p, q, r], TraditionalForm]", +"FormBox[SuperscriptBox[OverscriptBox[\"\[Epsilon]\", \"\"], RowBox[{FormBox[FormBox[StyleBox[\"p\", Bold, StripOnInput -> False], TraditionalForm], \ +TraditionalForm], FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> False], TraditionalForm], TraditionalForm], FormBox[FormBox[StyleBox[\"r\", \ +Bold, StripOnInput -> False], TraditionalForm], TraditionalForm]}]], TraditionalForm]"} +}); + +Tests`Shared`fcstSharedObjectsTypesettingNrCFAD = +({ +{"fcstSharedObjectsTypesettingNrCFAD-ID1", +"MakeBoxes[CFAD[{{q, -p1 . p2}, m^2}], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID2", +"MakeBoxes[CFAD[{{q, -p1 . p2}, m^2}, EtaSign -> 1], \ +TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"+\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID3", +"MakeBoxes[CFAD[{{q, -p1 . p2}, {m^2, -1}}, EtaSign -> 1], \ +TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID4", +"MakeBoxes[CFAD[{{q, -p1 . p2}, m^2, 2}], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID5", +"MakeBoxes[CFAD[{{q, -p1 . p2}, m^2, n}], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID6", +"MakeBoxes[CFAD[{{q, x*p1 . p2}, m^2}], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +RowBox[{\"x\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID7", +"MakeBoxes[CFAD[{{q, x*p1 . p2}, m^2, 2}], TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +RowBox[{\"x\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID8", +"MakeBoxes[CFAD[{{q, x*p1 . p2}, m^2, n}], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +RowBox[{\"x\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID9", +"MakeBoxes[CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2}], \ +TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +RowBox[{RowBox[{\"x\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}], \"-\", \ +RowBox[{\"2\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p3\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p4\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID10", +"MakeBoxes[CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, 2}], \ +TraditionalForm]", +"FormBox[FractionBox[\"1\", \ +SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +RowBox[{RowBox[{\"x\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}], \"-\", \ +RowBox[{\"2\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p3\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p4\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID11", +"MakeBoxes[CFAD[{{q, x*p1 . p2 - (2*p3) . p4}, m^2, n}], \ +TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +RowBox[{RowBox[{\"x\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}], \"-\", \ +RowBox[{\"2\", \" \", RowBox[{\"(\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p3\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p4\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \")\"}]}]}], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ 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\ +\"RowDefault\"], \"2\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID299", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +0, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID300", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +-m^2, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", RowBox[{\"-\", \ +SuperscriptBox[\"m\", \"2\"]}], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID301", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +-2*m^2, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{\"-\", \"2\"}], \" \", SuperscriptBox[\"m\", \ +\"2\"]}], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\ +\[Eta]\\\"\"}], \"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \ +\"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID302", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +m2^2 - m1^2*x, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{SuperscriptBox[\"m2\", \"2\"], \"-\", RowBox[{SuperscriptBox[\ +\"m1\", \"2\"], \" \", \"x\"}]}], \"\\\"-\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID303", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +0, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"+\\\"\", \ 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+{"fcstSharedObjectsTypesettingNrCFAD-ID306", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +m2^2 - m1^2*x, {n, 1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{SuperscriptBox[\"m2\", \"2\"], \"-\", RowBox[{SuperscriptBox[\ +\"m1\", \"2\"], \" \", \"x\"}]}], \"\\\"+\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID307", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +0, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID308", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +-m^2, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", RowBox[{\"-\", \ +SuperscriptBox[\"m\", \"2\"]}], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \"n\"}]], \ +TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID309", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +-2*m^2, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{RowBox[{\"-\", \"2\"}], \" \", SuperscriptBox[\"m\", \ +\"2\"]}], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\ +\[Eta]\\\"\"}], \"\\\")\\\"\"}, \"RowDefault\"], RowBox[{\"-\", \ +\"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID310", +"MakeBoxes[FeynAmpDenominator[CartesianPropagatorDenominator[0, 0, \ +m2^2 - m1^2*x, {n, -1}]], TraditionalForm]", +"FormBox[SuperscriptBox[TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{SuperscriptBox[\"m2\", \"2\"], \"-\", RowBox[{SuperscriptBox[\ +\"m1\", \"2\"], \" \", \"x\"}]}], \"\\\"-\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"], RowBox[{\"-\", \"n\"}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID311", +"MakeBoxes[CFAD[q, q1], TraditionalForm]", +"FormBox[FractionBox[\"1\", RowBox[{TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID312", +"MakeBoxes[CFAD[{q1, m^2}, q2, q3], TraditionalForm]", +"FormBox[FractionBox[\"1\", RowBox[{TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q2\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q3\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID313", +"MakeBoxes[CFAD[{q1, m^2}, q2, {q3, m^2}], TraditionalForm]", +"FormBox[FractionBox[\"1\", RowBox[{TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q2\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q3\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"+\\\"\", \ +SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID314", +"MakeBoxes[CFAD[q1, q2, q3, q4], TraditionalForm]", +"FormBox[FractionBox[\"1\", RowBox[{TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q2\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q3\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[FormBox[StyleBox[\"q4\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], 2], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID315", +"MakeBoxes[CFAD[q, Dimension -> 3], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID316", +"MakeBoxes[CFAD[q, q1, Dimension -> 3], TraditionalForm]", +"FormBox[FractionBox[\"1\", RowBox[{TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"], \".\", \ +TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q1\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID317", +"MakeBoxes[CFAD[{q1, m^2}, q2, q3, Dimension -> 3], \ +TraditionalForm]", +"FormBox[FractionBox[\"1\", RowBox[{TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q1\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"+\\\"\", SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q2\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"], \".\", \ +TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q3\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID318", +"MakeBoxes[CFAD[{q1, m^2}, q2, {q3, m^2}, Dimension -> 3], \ +TraditionalForm]", +"FormBox[FractionBox[\"1\", RowBox[{TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q1\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"+\\\"\", SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"], \".\", TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q2\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"], \".\", \ +TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q3\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"+\\\"\", SuperscriptBox[\"m\", \"2\"], \"\\\"-\\\"\", \ +RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \ +\"\\\")\\\"\"}, \"RowDefault\"]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID319", +"MakeBoxes[CFAD[q1, q2, q3, q4, Dimension -> 3], TraditionalForm]", + "FormBox[FractionBox[\"1\", RowBox[{TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q1\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"], \".\", \ +TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q2\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"], \".\", \ +TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q3\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"], \".\", \ +TemplateBox[{\"\\\"(\\\"\", \ +SuperscriptBox[FormBox[OverscriptBox[FormBox[StyleBox[\"q4\", Bold, \ +StripOnInput -> False], TraditionalForm], \"_\"], TraditionalForm], \ +2], \"\\\"-\\\"\", RowBox[{\"\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\ +\"}], \"\\\")\\\"\"}, \"RowDefault\"]}]], TraditionalForm]"}, +{"fcstSharedObjectsTypesettingNrCFAD-ID320", +"MakeBoxes[CFAD[{{0, p1 . p2}}], TraditionalForm]", +"FormBox[FractionBox[\"1\", TemplateBox[{\"\\\"(\\\"\", \ +RowBox[{FormBox[FormBox[StyleBox[\"p1\", Bold, StripOnInput -> \ +False], TraditionalForm], TraditionalForm], \ +FormBox[\"\\\"\[CenterDot]\\\"\", TraditionalForm], \ +FormBox[FormBox[StyleBox[\"p2\", Bold, StripOnInput -> False], \ +TraditionalForm], TraditionalForm]}], \"\\\"-\\\"\", RowBox[{\"\ +\[ImaginaryI]\", \" \", \"\\\"\[Eta]\\\"\"}], \"\\\")\\\"\"}, \ +\"RowDefault\"]], TraditionalForm]"} +}); diff --git a/Tests/Shared/SharedTools.test b/Tests/Shared/SharedTools.test index db3bb85f6..1f25d5536 100644 --- a/Tests/Shared/SharedTools.test +++ b/Tests/Shared/SharedTools.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for SharedTools *) @@ -15,9 +15,12 @@ Tests`Shared`fcstSharedToolsCases2 = { {"fcstSharedToolsCases2-ID1","Cases2[f[a] + f[b]^2 + f[c, d], f]","{f[a], f[b], f[c, d]}"}, {"fcstSharedToolsCases2-ID2","Cases2[Sin[x] Sin[y - z] + g[y], Sin, g]","{g[y], Sin[x], Sin[y - z]}"}, {"fcstSharedToolsCases2-ID3","Cases2[Sin[x] Sin[y - z] + g[x] + g[a, b, c], {Sin, g}]","{g[x], g[a, b, c], Sin[x], Sin[y - z]}"}, -{"fcstSharedToolsCases2-ID4","Cases2[DiracSlash[p].DiracSlash[q] + ScalarProduct[p, p], Dot]","{DiracGamma[Momentum[p]].DiracGamma[Momentum[q]]}"} +{"fcstSharedToolsCases2-ID4","Cases2[DiracSlash[p].DiracSlash[q] + ScalarProduct[p, p], Dot]","{DiracGamma[Momentum[p]].DiracGamma[Momentum[q]]}"}, +{"fcstSharedToolsCases2-ID5","Cases2[a PolyLog[2, x] + Log[y] b + c PolyLog[2, x] Log[z], Log, PolyLog]","{Log[y], Log[z], PolyLog[2, x]}"} }; + + Tests`Shared`fcstSharedToolsCombine = { {"fcstSharedToolsCombine-ID1","Combine[((a - b) (c - d))/e + g]","((a-b) (c-d)+e g)/e"}, {"fcstSharedToolsCombine-ID2","Combine[((a - b) (c - d))/e + g, Expanding -> True]", @@ -40,6 +43,52 @@ Tests`Shared`fcstSharedToolsComplement1 = { "{}"} }; +Tests`Shared`fcstSharedToolsExpandAll2 = +({ +{"fcstSharedToolsExpandAll2-ID1", "ExpandAll2[a]", "a"}, +{"fcstSharedToolsExpandAll2-ID2", "ExpandAll2[a b]", "a*b"}, +{"fcstSharedToolsExpandAll2-ID3", "ExpandAll2[a+b]", "a + b"}, +{"fcstSharedToolsExpandAll2-ID4", "ExpandAll2[c(a+b)]", "a*c + b*c"}, +{"fcstSharedToolsExpandAll2-ID5", "ExpandAll2[c(a+b)+e]", +"a*c + b*c + e"}, +{"fcstSharedToolsExpandAll2-ID6", "ExpandAll2[c(a+b)+e(f+g)]", +"a*c + b*c + e*f + e*g"}, +{"fcstSharedToolsExpandAll2-ID7", "ExpandAll2[h(c(a+b)+e(f+g))]", +"a*c*h + b*c*h + e*f*h + e*g*h"}, +{"fcstSharedToolsExpandAll2-ID8", +"ExpandAll2[h(c(a(i1+i2)+b(i3+i4))+e(f+g))]", +"e*f*h + e*g*h + a*c*h*i1 + a*c*h*i2 + b*c*h*i3 + b*c*h*i4"}, +{"fcstSharedToolsExpandAll2-ID9", +"ExpandAll2[h(c(a(i1(i5+i6)+i2)+b(i3+i4))+e(f+g))]", +"e*f*h + e*g*h + a*c*h*i2 + b*c*h*i3 + b*c*h*i4 + a*c*h*i1*i5 + \ +a*c*h*i1*i6"}, +{"fcstSharedToolsExpandAll2-ID10", "ExpandAll2[FCI[GS[p]]]", +"DiracGamma[Momentum[p]]"}, +{"fcstSharedToolsExpandAll2-ID11", "ExpandAll2[FCI[GSD[p]]]", +"DiracGamma[Momentum[p, D], D]"}, +{"fcstSharedToolsExpandAll2-ID12", "ExpandAll2[FCI[GSE[p]]]", +"DiracGamma[Momentum[p, -4 + D], -4 + D]"}, +{"fcstSharedToolsExpandAll2-ID13", "ExpandAll2[FCI[GS[p]+GS[q]]]", +"DiracGamma[Momentum[p]] + DiracGamma[Momentum[q]]"}, +{"fcstSharedToolsExpandAll2-ID14", "ExpandAll2[FCI[GSD[p]+GSD[q]]]", + "DiracGamma[Momentum[p, D], D] + DiracGamma[Momentum[q, D], D]"}, +{"fcstSharedToolsExpandAll2-ID15", "ExpandAll2[FCI[GSE[p]+GSE[q]]]", + "DiracGamma[Momentum[p, -4 + D], -4 + D] + DiracGamma[Momentum[q, \ +-4 + D], -4 + D]"}, +{"fcstSharedToolsExpandAll2-ID16", +"ExpandAll2[FCI[LC[i1,i2,i3,i4](GS[p]+GS[q])]]", +"DiracGamma[Momentum[p]]*Eps[LorentzIndex[i1], LorentzIndex[i2], \ +LorentzIndex[i3], LorentzIndex[i4]] + \ +DiracGamma[Momentum[q]]*Eps[LorentzIndex[i1], LorentzIndex[i2], \ +LorentzIndex[i3], LorentzIndex[i4]]"}, +{"fcstSharedToolsExpandAll2-ID17", "ExpandAll2[{a,b,c}]", +"{a, b, c}"}, +{"fcstSharedToolsExpandAll2-ID18", "ExpandAll2[{e(a+d),b,c}]", +"{(a + d)*e, b, c}"}, +{"fcstSharedToolsExpandAll2-ID19", "ExpandAll2[-2 a + 2 b + 2 (a - b)]", +"0"} +}); + Tests`Shared`fcstSharedToolsExpand2 = { {"fcstSharedToolsExpand2-ID1","Expand2[(x1 + x2 + x3) (2 x1 + 3 x2) + (y1 + y2 + y3) (2 y1 + 3 y2), {x1, x2}]","2 x1^2+5 x1 x2+2 x1 x3+3 x2^2+3 x2 x3+(2 y1+3 y2) (y1+y2+y3)"}, @@ -64,6 +113,52 @@ Tests`Shared`fcstSharedToolsFCAntiSymmetrize = { f[d, b, a, c] - f[d, b, c, a] - f[d, c, a, b] + f[d, c, b, a])"} }; +Tests`Shared`fcstFCMakeIndex = +{ +{"fcstFCMakeIndex-ID1", "FCMakeIndex[\"Lor\",\"1\"]", "Lor1"}, +{"fcstFCMakeIndex-ID2", "FCMakeIndex[\"Lor\",2]", "Lor2"}, +{"fcstFCMakeIndex-ID3", "FCMakeIndex[\"Lor\",0]", "Lor0"}, +{"fcstFCMakeIndex-ID4", "FCMakeIndex[\"Lor\",-2]", "LorMinus2"}, +{"fcstFCMakeIndex-ID5", "FCMakeIndex[\"Sun\",\"1\",SUNIndex]", +"SUNIndex[Sun1]"}, +{"fcstFCMakeIndex-ID6", "FCMakeIndex[\"Sun\",2,SUNIndex]", +"SUNIndex[Sun2]"}, +{"fcstFCMakeIndex-ID7", "FCMakeIndex[\"Sun\",0,SUNIndex]", +"SUNIndex[Sun0]"}, +{"fcstFCMakeIndex-ID8", "FCMakeIndex[\"Sun\",-2,SUNIndex]", +"SUNIndex[SunMinus2]"}, +{"fcstFCMakeIndex-ID9", "FCMakeIndex[\"Lor\",{3,1,4},LorentzIndex]", + "{LorentzIndex[Lor3], LorentzIndex[Lor1], LorentzIndex[Lor4]}"}, +{"fcstFCMakeIndex-ID10", "FCMakeIndex[\"Sun\",{\"a\",1,-4}]", +"{Suna, Sun1, SunMinus4}"} +}; + +Tests`Shared`fcstSharedToolsFCPatternFreeQ = { +{"fcstSharedToolsFCPatternFreeQ-ID1","FCPatternFreeQ[{0}]","True"}, +{"fcstSharedToolsFCPatternFreeQ-ID2","FCPatternFreeQ[{a_}]","False"}, +{"fcstSharedToolsFCPatternFreeQ-ID3","FCPatternFreeQ[{g[x]},{g}]","False"} +}; + +Tests`Shared`fcstSharedToolsFCProductSplit = +({ +{"fcstSharedToolsFCProductSplit-ID1", "FCProductSplit[0,{a}]", +"{0, 0}"}, +{"fcstSharedToolsFCProductSplit-ID2", "FCProductSplit[c,{a}]", +"{c, 1}"}, +{"fcstSharedToolsFCProductSplit-ID3", "FCProductSplit[c^2,{a}]", +"{c^2, 1}"}, +{"fcstSharedToolsFCProductSplit-ID4", "FCProductSplit[a*b,{a}]", +"{b, a}"}, +{"fcstSharedToolsFCProductSplit-ID5", "FCProductSplit[a^2*b,{a}]", +"{b, a^2}"}, +{"fcstSharedToolsFCProductSplit-ID6", +"FCProductSplit[(a^2+b)*b,{a}]", "{b, a^2 + b}"}, +{"fcstSharedToolsFCProductSplit-ID7", +"FCProductSplit[(a^2+b)*b*(c+d),{a,c}]", "{b, (a^2 + b)*(c + d)}"}, +{"fcstSharedToolsFCProductSplit-ID8", +"FCProductSplit[1/(-1+2 eps),{Foo}]", "{1/(2 eps-1),1}"} +}); + Tests`Shared`fcstSharedToolsFCSplit = { {"fcstSharedToolsFCSplit-ID1","FCSplit[0, {z}]","{0,0}"}, {"fcstSharedToolsFCSplit-ID2","FCSplit[1, {z}]","{1,0}"}, @@ -78,6 +173,34 @@ Tests`Shared`fcstSharedToolsFCSplit = { "{{b^2, a^2 + 2 a b}, {d^2, a^2 + 2 a d}}"} }; +Tests`Shared`fcstSharedToolsFCReplaceAll = { +{"fcstSharedToolsFCReplaceAll-ID1", "FCReplaceAll[a,a\[Rule]b]", +"b"}, +{"fcstSharedToolsFCReplaceAll-ID2", +"FCReplaceAll[a c,{a\[Rule]b,c\[Rule]d}]", "b*d"}, +{"fcstSharedToolsFCReplaceAll-ID3", +"FCReplaceAll[a c,a\[Rule]b,c\[Rule]d]", "b*d"}, +{"fcstSharedToolsFCReplaceAll-ID4", +"FCReplaceAll[a c,a\[Rule]b,c\[Rule]d,d\[Rule]e,b\[Rule]f]", "e*f"} +}; + +Tests`Shared`fcstSharedToolsFCReplaceRepeated ={ +{"fcstSharedToolsFCReplaceRepeated-ID1", +"FCReplaceRepeated[a,a\[Rule]b]", "b"}, +{"fcstSharedToolsFCReplaceRepeated-ID2", +"FCReplaceRepeated[a c,{a\[Rule]b,c\[Rule]d}]", "b*d"}, +{"fcstSharedToolsFCReplaceRepeated-ID3", +"FCReplaceRepeated[a c,a\[Rule]b,c\[Rule]d]", "b*d"}, +{"fcstSharedToolsFCReplaceRepeated-ID4", +"FCReplaceRepeated[a c,a\[Rule]b,c\[Rule]d,d\[Rule]e,b\[Rule]f]", +"e*f"} +}; + + + + + + Tests`Shared`fcstSharedToolsFCSymmetrize = { {"fcstSharedToolsFCSymmetrize-ID1","FCSymmetrize[f[a, b], {a, b}]","1/2 (f[a, b] + f[b, a])"}, {"fcstSharedToolsFCSymmetrize-ID2","FCSymmetrize[f[a, b, c], {a, b, c}]", @@ -101,7 +224,7 @@ Tests`Shared`fcstSharedToolsFreeQ2 = { Tests`Shared`fcstSharedToolsFRH = { {"fcstSharedToolsFRH-ID1","FRH[Hold[1 - 1 - Hold[2 - 2]]]","0"}, -{"fcstSharedToolsFRH-ID2","FRH[Isolate[Solve[x^3 - x - 1 == 0], x, IsolateNames -> H]][[1]]", +{"fcstSharedToolsFRH-ID2","FRH[Isolate[Solve[x^3 - x - 1 == 0, Cubics -> True], x, IsolateNames -> H]][[1]]", "{x -> 1/3 (27/2 - (3 Sqrt[69])/2)^(1/3) + (1/2 (9 + Sqrt[69]))^(1/3)/3^(2/3)}"}, {"fcstSharedToolsFRH-ID3","MatchQ[FRH[ Isolate[(a + b) F[q], q, IsolateNames -> KK1] + @@ -136,7 +259,8 @@ Tests`Shared`fcstSharedToolsNTerms = { {"fcstSharedToolsNTerms-ID2","NTerms[a b c]","1"}, {"fcstSharedToolsNTerms-ID3","NTerms[9]","1"}, {"fcstSharedToolsNTerms-ID4","NTerms[0]","0"}, -{"fcstSharedToolsNTerms-ID5","NTerms[a (b + c (d + e))]","3"} +{"fcstSharedToolsNTerms-ID5","NTerms[a (b + c (d + e))]","3"}, +{"fcstSharedToolsNTerms-ID6","NTerms[(a^2 + b)*b, Expand -> False]","1"} }; Tests`Shared`fcstSharedToolsNumericalFactor = { @@ -269,5 +393,34 @@ Tests`Shared`fcstSharedToolsFCFactorOut = { {"fcstSharedToolsFCFactorOut-ID2","FCFactorOut[0, 1]", "0"}, {"fcstSharedToolsFCFactorOut-ID3","FCFactorOut[(a + 3 b), 3 b]", - "3 (1 + a/(3 b)) b"} + "3 (1 + a/(3 b)) b"}, +{"fcstSharedToolsFCFactorOut-ID4","FCFactorOut[(a + 3 b), 3 b, Head -> head]", + "3 b head[1 + a/(3 b)]"} }; + +Tests`Shared`fcstSharedToolsFCSubsetQ = +({ +{"fcstSharedToolsFCSubsetQ-ID1", "FCSubsetQ[{a,b,c,d},{a,d,e}]", +"False"}, +{"fcstSharedToolsFCSubsetQ-ID2", "FCSubsetQ[{a,b,c,d},{a,d}]", +"True"}, +{"fcstSharedToolsFCSubsetQ-ID3", "FCSubsetQ[{a,b,c,d},{}]", +"True"}, +{"fcstSharedToolsFCSubsetQ-ID4", "FCSubsetQ[{},{}]", "True"}, +{"fcstSharedToolsFCSubsetQ-ID5", "FCSubsetQ[{},{a}]", "False"} +}); + +Tests`Shared`fcstFCDuplicateFreeQ = +({ +{"fcstFCDuplicateFreeQ-ID1", "FCDuplicateFreeQ[{}]", "True"}, +{"fcstFCDuplicateFreeQ-ID2", "FCDuplicateFreeQ[{a}]", "True"}, +{"fcstFCDuplicateFreeQ-ID3", "FCDuplicateFreeQ[{a,b,c}]", "True"}, +{"fcstFCDuplicateFreeQ-ID4", "FCDuplicateFreeQ[{a,b,c,d}]", +"True"}, +{"fcstFCDuplicateFreeQ-ID5", "FCDuplicateFreeQ[{a,b,c,a}]", "False"}, +{"fcstFCDuplicateFreeQ-ID6", "FCDuplicateFreeQ[{{a,b},{a,c}}]", +"True"}, +{"fcstFCDuplicateFreeQ-ID7", +"FCDuplicateFreeQ[{{a,b},{a,c}},Function[{x,y},First[x]===First[y]]\ +]", "False"} +}); diff --git a/Tests/Shared/Solve.test b/Tests/Shared/Solve.test index 0af919ceb..a57866883 100644 --- a/Tests/Shared/Solve.test +++ b/Tests/Shared/Solve.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for Solve2 and Solve3 *) diff --git a/Tests/Shared/Sum.test b/Tests/Shared/Sum.test index f3aa735c8..b495a178d 100644 --- a/Tests/Shared/Sum.test +++ b/Tests/Shared/Sum.test @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for SumP, SumS and SumT *) diff --git a/Tests/TARCER/TAR.test b/Tests/TARCER/TAR.test new file mode 100644 index 000000000..994698229 --- /dev/null +++ b/Tests/TARCER/TAR.test @@ -0,0 +1,18 @@ + + +(* :Title: TAR.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for TAR *) + +(* ------------------------------------------------------------------------ *) + +Tests`TARCER`TAR = ({ +{"fcstTAR-ID1", "FreeQ2[DownValues[TAR], {Tarcer`Private`Schiebe}]", "True"} +}); diff --git a/Tests/TARCER/TARCER.mt b/Tests/TARCER/TARCER.mt index 9454ae6dc..76cb604ab 100644 --- a/Tests/TARCER/TARCER.mt +++ b/Tests/TARCER/TARCER.mt @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Unit tests for functions in the "SUN" directory *) @@ -17,5 +17,13 @@ ClearAll[tests]; tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "TARCER"}]] Get/@tests; +If[ $OnlySubTest=!="", + testNames = "Tests`TARCER`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + Map[Test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],TestID->#[[1]]]&, Join@@(ToExpression/@Names["Tests`TARCER`*"])]; diff --git a/Tests/TARCER/TBR.test b/Tests/TARCER/TBR.test new file mode 100644 index 000000000..3229b6c90 --- /dev/null +++ b/Tests/TARCER/TBR.test @@ -0,0 +1,18 @@ + + +(* :Title: TBR.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for TBR *) + +(* ------------------------------------------------------------------------ *) + +Tests`TARCER`TBR = ({ +{"fcstTBR-ID1", "FreeQ2[DownValues[TBR], {Tarcer`Private`Schiebe}]", "True"} +}); diff --git a/Tests/TARCER/TFR.test b/Tests/TARCER/TFR.test index 82d34331e..473cfa6ff 100644 --- a/Tests/TARCER/TFR.test +++ b/Tests/TARCER/TFR.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for TFR *) @@ -16,5 +16,6 @@ Tests`TARCER`TFR = ({ {"fcstTFR-ID1", "(TFI[D, SPD[q, q], {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {1, 0}}] /. TFI -> TFR)", "TFI[D, SPD[q, q], {{0, 0}, {2, 0}, {1, 0}, {1, 0}, {1, 0}}]/(4 - D) + TFI[D, SPD[q, q], {{1, 0}, {1, 0}, {0, 0}, {2, 0}, {1, 0}}]/(4 - D) - -TFI[D, SPD[q, q], {{1, 0}, {1, 0}, {1, 0}, {2, 0}, {0, 0}}]/(4 - D) - TFI[D, SPD[q, q], {{1, 0}, {2, 0}, {1, 0}, {1, 0}, {0, 0}}]/(4 - D)"} +TFI[D, SPD[q, q], {{1, 0}, {1, 0}, {1, 0}, {2, 0}, {0, 0}}]/(4 - D) - TFI[D, SPD[q, q], {{1, 0}, {2, 0}, {1, 0}, {1, 0}, {0, 0}}]/(4 - D)"}, +{"fcstTFR-ID2", "FreeQ2[DownValues[TJR], {Tarcer`Private`Schiebe}]", "True"} }); diff --git a/Tests/TARCER/TJR.test b/Tests/TARCER/TJR.test new file mode 100644 index 000000000..b733a5d6b --- /dev/null +++ b/Tests/TARCER/TJR.test @@ -0,0 +1,18 @@ + + +(* :Title: TJR.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for TJR *) + +(* ------------------------------------------------------------------------ *) + +Tests`TARCER`TJR = ({ +{"fcstTJR-ID1", "FreeQ2[DownValues[TJR], {Tarcer`Private`Schiebe}]", "True"} +}); diff --git a/Tests/TARCER/TVR.test b/Tests/TARCER/TVR.test new file mode 100644 index 000000000..a58ba8938 --- /dev/null +++ b/Tests/TARCER/TVR.test @@ -0,0 +1,18 @@ + + +(* :Title: TVR.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for TVR *) + +(* ------------------------------------------------------------------------ *) + +Tests`TARCER`TVR = ({ +{"fcstTVR-ID1", "FreeQ2[DownValues[TVR], {Tarcer`Private`Schiebe}]", "True"} +}); diff --git a/Tests/TARCER/TarcerRecurse.test b/Tests/TARCER/TarcerRecurse.test index c14f6def9..d22f98506 100644 --- a/Tests/TARCER/TarcerRecurse.test +++ b/Tests/TARCER/TarcerRecurse.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for TarcerRecurse *) @@ -44,5 +44,16 @@ d, M^2, {{1, M}, {1, M}, {1, M}}])/(128 (-4 + d)^2 M^6)"}, TFI[D, SPD[q, q], {0, 0, 2, 1, 1}, {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {2, 0}}]]", "((-3 + D)*SPD[q, q]^2*TBI[D, SPD[q, q], {{1, 0}, {1, 0}}]^2)/(8*(-4 + D)) - -((72 - 253*D + 206*D^2 - 61*D^3 + 6*D^4)*SPD[q, q]*TJI[D, SPD[q, q], {{1, 0}, {1, 0}, {1, 0}}])/(6*(-6 + D)*(-4 + D)^2)"} +((72 - 253*D + 206*D^2 - 61*D^3 + 6*D^4)*SPD[q, q]*TJI[D, SPD[q, q], {{1, 0}, {1, 0}, {1, 0}}])/(6*(-6 + D)*(-4 + D)^2)"}, +{"fcstTarcerRecurse-ID7", "TarcerRecurse[TFI[d, M1^2, { 0, 0, 1, 0, 0}, {{1, M2}, {1, 0}, {0, 0}, {1, M1}, {1, M2}}]] ", +"-((-2 + d)^2*(M1 - M2)*(M1 + M2)*TAI[d, 0, {{1, M1}}]*TAI[d, 0, {{1, M2}}])/(4*(-4 + d)*(-8 + 3*d)*M1^2*M2^2) - +((-2 + d)*TAI[d, 0, {{1, M2}}]^2)/(4*(-8 + 3*d)*M2^2) + ((-7*M1^2 + 2*d*M1^2 + 3*M2^2 - d*M2^2)*TJI[d, M1^2, {{2, M1}, {1, M2}, {1, M2}}])/ +((-4 + d)*(-8 + 3*d)) + ((-7*M1^2 + 2*d*M1^2 + 3*M2^2 - d*M2^2)*TJI[d, M1^2, {{2, M2}, {1, M2}, {1, M1}}])/((-4 + d)*(-8 + 3*d)) - +(4*(M1 - M2)*M2^2*(M1 + M2)*TJI[d, M1^2, {{2, M2}, {2, M1}, {1, M2}}])/((-4 + d)*(-8 + 3*d)) + +(2*M2^2*(-M1 + M2)*(M1 + M2)*TJI[d, M1^2, {{2, M2}, {2, M2}, {1, M1}}])/((-4 + d)*(-8 + 3*d)) + +(4*M2^2*(-M1 + M2)*(M1 + M2)*TJI[d, M1^2, {{3, M2}, {1, M2}, {1, M1}}])/((-4 + d)*(-8 + 3*d))"}, +{"fcstTarcerRecurse-ID8", "TarcerRecurse[TFI[d, s, {0, 0, 0, 0, 1}, {{2, 0}, {1, M2}, {1, M1}, {0, 0}, {1, M2}}]]", +"-((-2 + d)^2*TAI[d, 0, {{1, M2}}]^2)/(4*(-3 + d)*M2^2*(M1^2 - s)) + ((-2 + d)*TAI[d, 0, {{1, M2}}]*TBI[d, s, {{1, M1}, {1, 0}}])/(4*M2^2) + +((-8 + 3*d)*TJI[d, s, {{1, M2}, {1, M2}, {1, M1}}])/(2*(M1^2 - s)) - (2*M1^2*TJI[d, s, {{2, M1}, {1, M2}, {1, M2}}])/(M1^2 - s) - +((M1^2 + 4*M2^2 - s)*TJI[d, s, {{2, M2}, {1, M2}, {1, M1}}])/(2*(M1^2 - s))"} }); diff --git a/Tests/TARCER/ToFI.test b/Tests/TARCER/ToFI.test index fd0e6370b..b1e82761a 100644 --- a/Tests/TARCER/ToFI.test +++ b/Tests/TARCER/ToFI.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ToFI *) @@ -14,5 +14,14 @@ (* ------------------------------------------------------------------------ *) Tests`TARCER`ToFI = { -{"fcstToFI-ID1","ToFI[FAD[{q1, m1}, {-p + q1, m2}], {q1}, {p}]", "TBI[D, SPD[p, p], {{1, m2}, {1, m1}}]"} +{"fcstToFI-ID1","ToFI[FAD[{q1, m1}, {-p + q1, m2}], {q1}, {p}]", "TBI[D, SPD[p, p], {{1, m2}, {1, m1}}]"}, +{"fcstToFI-ID2","ToFI[1/((-1 + D) SPD[q, q]) +32 CA^3 mE^2 FAD[ +p1, {p2, I mE}, {-p1 + p2, I mE}, {-p1 + p2, I mE}, {-p1 + p2, + I mE}] SD[a, b] SPD[p1, q] SPD[p2, +q] (-FVD[q, Lor1] FVD[q, Lor2] + + MTD[Lor1, Lor2] SPD[q, q]) Subscript[zeta, 1], {p1, p2}, {q}]", "(32*CA^3*mE^2*SD[a, b]*(-(FVD[q, Lor1]*FVD[q, Lor2]) + +MTD[Lor1, Lor2]*SPD[q, q])*Subscript[zeta, 1]* +TFI[D, SPD[q, q], {0, 0, 1, 1, 0}, {{1, 0}, {1, I*mE}, {0, 0}, {0, 0}, + {3, I*mE}}])/((-1 + D)*SPD[q, q])"} }; diff --git a/Tests/TARCER/ToTFI.test b/Tests/TARCER/ToTFI.test index 7a1f4dbee..cefe10ba1 100644 --- a/Tests/TARCER/ToTFI.test +++ b/Tests/TARCER/ToTFI.test @@ -4,9 +4,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Framework independent unit tests for ToTFI *) @@ -20,8 +20,9 @@ Tests`TARCER`ToTFI = ({ "TBI[D, SPD[p, p], {{2, 0}, {1, 0}}]"}, {"fcstToTFI-ID3", "ToTFI[FAD[q,q,-p+q,-p+q],q,p]", "TBI[D, SPD[p, p], {{2, 0}, {2, 0}}]"}, - -{"fcstToTFI-ID4", "tmp1 = ToTFI[ +{"fcstToTFI-ID4", "ToTFI[-((8 CA^3 FAD[{p2, mE}, {p2, mE}] MTD[Lor1, Lor2] SD[a, b])/D), {p1, p2}, {q}]", +"-((8 CA^3 MTD[Lor1, Lor2] SD[a, b] Tarcer`TAI[D, 0, {{2, mE}}])/D)"}, +{"fcstToTFI-ID5", "tmp1 = ToTFI[ 1/((-1 + D) SPD[q, q]) 32 CA^3 mE^2 FAD[p1, {p2, mE}, {-p1 + p2, mE}, {-p1 + p2, mE}, {-p1 + p2, mE}] SD[ @@ -32,5 +33,41 @@ tmp2 = ToTFI[FAD[{p2, mE}, {p2, mE}] MTD[Lor1, Lor2] SD[a, b], {p1, p2}, {q}]; \ "{(32*CA^3*mE^2*SD[a, b]*(-(FVD[q, Lor1]*FVD[q, Lor2]) + MTD[Lor1, Lor2]*SPD[q, q])*TFI[D, SPD[q, q], {0, 0, 1, 1, 0}, {{1, 0}, {1, mE}, {0, 0}, {0, 0}, {3, mE}}])/((-1 + D)*SPD[q, q]), -MTD[Lor1, Lor2]*SD[a, b]*TAI[D, 0, {{2, mE}}]}"} +MTD[Lor1, Lor2]*SD[a, b]*TAI[D, 0, {{2, mE}}]}"}, + +{"fcstToTFI-ID6", "ToTFI[1/((-1 + D) SPD[q, q]^2) + FAD[{p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, I mG}, {p2, + I mG}] SPD[p1, q]^2 SPD[p2, + q]^2 (D FVD[q, Lor1] FVD[q, Lor2] - MTD[Lor1, Lor2] SPD[q, q]) - +1/((-1 + D) SPD[q, q]^2) + mG^2 FAD[{p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, + I mG}, {p2, I mG}] SPD[p1, q]^2 SPD[p2, + q]^2 (D FVD[q, Lor1] FVD[q, Lor2] - MTD[Lor1, Lor2] SPD[q, q]) + +1/((-1 + D) SPD[q, q]) + FAD[{p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, I mG}] SPD[p1, + q]^2 (-FVD[q, Lor1] FVD[q, Lor2] + MTD[Lor1, Lor2] SPD[q, q]) - +1/((-1 + D) SPD[q, q]) + mG^2 FAD[{p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, + I mG}] SPD[p1, + q]^2 (-FVD[q, Lor1] FVD[q, Lor2] + MTD[Lor1, Lor2] SPD[q, q]) - +1/((-1 + D) SPD[q, q]) + mG^2 FAD[{p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, I mG}, {p2, + I mG}] SPD[p1, + q]^2 (-FVD[q, Lor1] FVD[q, Lor2] + MTD[Lor1, Lor2] SPD[q, q]) + +1/((-1 + D) SPD[q, q]) + mG^4 FAD[{p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, I mG}, {p1, + I mG}, {p2, I mG}] SPD[p1, + q]^2 (-FVD[q, Lor1] FVD[q, Lor2] + MTD[Lor1, Lor2] SPD[q, q]), +p1, p2, q, TID -> True] // FCE", +"((-(FVD[q, Lor1]*FVD[q, Lor2]) + MTD[Lor1, Lor2]*SPD[q, q])*(TAI[D, 0, {{3, I*mG}}] - + 2*mG^2*TAI[D, 0, {{4, I*mG}}] + mG^4*TAI[D, 0, {{5, I*mG}}]))/((-1 + D)*D) - +(mG^2*(-(FVD[q, Lor1]*FVD[q, Lor2]) + MTD[Lor1, Lor2]*SPD[q, q])* +TFI[D, SPD[q, q], {0, 0, 2, 0, 0}, {{4, I*mG}, {1, I*mG}, {0, 0}, {0, 0}, {0, 0}}])/ +((-1 + D)*SPD[q, q]) + (mG^4*(-(FVD[q, Lor1]*FVD[q, Lor2]) + MTD[Lor1, Lor2]*SPD[q, q])* +TFI[D, SPD[q, q], {0, 0, 2, 0, 0}, {{5, I*mG}, {1, I*mG}, {0, 0}, {0, 0}, {0, 0}}])/ +((-1 + D)*SPD[q, q]) + ((D*FVD[q, Lor1]*FVD[q, Lor2] - MTD[Lor1, Lor2]*SPD[q, q])* +TFI[D, SPD[q, q], {0, 0, 2, 2, 0}, {{4, I*mG}, {1, I*mG}, {0, 0}, {0, 0}, {0, 0}}])/ +((-1 + D)*SPD[q, q]^2) - (mG^2*(D*FVD[q, Lor1]*FVD[q, Lor2] - MTD[Lor1, Lor2]*SPD[q, q])* +TFI[D, SPD[q, q], {0, 0, 2, 2, 0}, {{5, I*mG}, {1, I*mG}, {0, 0}, {0, 0}, {0, 0}}])/ +((-1 + D)*SPD[q, q]^2)"} }); diff --git a/Tests/Tables/Hill.test b/Tests/Tables/Hill.test new file mode 100644 index 000000000..93e605c96 --- /dev/null +++ b/Tests/Tables/Hill.test @@ -0,0 +1,29 @@ + + +(* :Title: Hill.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for Hill *) + +(* ------------------------------------------------------------------------ *) + +Tests`Tables`fcstHill = +({ +{"fcstHill-ID1", "Hill[a,b]", +"-Pi^2/6 + Log[a]*(Log[1 - a] - Log[1 - b]) + Log[(1 - a)/(1 - \ +b)]*(-Log[a] + Log[1 - b] - Log[(a - b)/a] + Log[(a - b)/(1 - b)]) - \ +(Log[1 - b] - Log[(a - b)/a] + Log[(a - b)/(a*(1 - b))])*Log[((1 - \ +a)*b)/(a*(1 - b))] + PolyLog[2, a] + PolyLog[2, (1 - a)/(1 - b)] - \ +PolyLog[2, b] + PolyLog[2, b/a] - PolyLog[2, ((1 - a)*b)/(a*(1 - \ +b))]"}, +{"fcstHill-ID2", "Chop[Hill[a,b]/.a\[Rule].123/.b\[Rule].656]", "0"}, +{"fcstHill-ID3", +"Chop[N[(Hill[x,x y]//SimplifyPolyLog)/.x\[Rule].34/.y\[Rule].6]]", + "0"} +}); diff --git a/Tests/Tables/Kummer.test b/Tests/Tables/Kummer.test new file mode 100644 index 000000000..9120ed09f --- /dev/null +++ b/Tests/Tables/Kummer.test @@ -0,0 +1,127 @@ + + +(* :Title: Kummer.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for Kummer *) + +(* ------------------------------------------------------------------------ *) + +Tests`Tables`fcstKummer = +({ +{"fcstKummer-ID1", "Kummer[2][Hypergeometric2F1[a,b,c,z]]", +"(1 - z)^(-a - b + c)*Hypergeometric2F1[-a + c, -b + c, c, z]"}, +{"fcstKummer-ID2", "Kummer[3][Hypergeometric2F1[a,b,c,z]]", +"Hypergeometric2F1[a, -b + c, c, -(z/(1 - z))]/(1 - z)^a"}, +{"fcstKummer-ID3", "Kummer[4][Hypergeometric2F1[a,b,c,z]]", +"Hypergeometric2F1[b, -a + c, c, -(z/(1 - z))]/(1 - z)^b"}, +{"fcstKummer-ID4", "Kummer[6][Hypergeometric2F1[a,b,c,1-z]]", +"z^(-a - b + c)*Hypergeometric2F1[-a + c, -b + c, c, 1 - z]"}, +{"fcstKummer-ID5", "Kummer[6][Hypergeometric2F1[a,b,a+b+1-c,1-z]]", +"z^(1 - c)*Hypergeometric2F1[1 + a - c, 1 + b - c, 1 + a + b - c, \ +1 - z]"}, +{"fcstKummer-ID6", "Kummer[7][Hypergeometric2F1[a,b,c,1-z]]", +"Hypergeometric2F1[a, -b + c, c, -((1 - z)/z)]/z^a"}, +{"fcstKummer-ID7", "Kummer[7][Hypergeometric2F1[a,b,a+b+1-c,1-z]]", +"Hypergeometric2F1[a, 1 + a - c, 1 + a + b - c, -((1 - z)/z)]/z^a"}, +{"fcstKummer-ID8", "Kummer[8][Hypergeometric2F1[a,b,c,1-z]]", +"Hypergeometric2F1[b, -a + c, c, -((1 - z)/z)]/z^b"}, +{"fcstKummer-ID9", "Kummer[8][Hypergeometric2F1[a,b,a+b+1-c,1-z]]", +"Hypergeometric2F1[b, 1 + b - c, 1 + a + b - c, -((1 - z)/z)]/z^b"}, +{"fcstKummer-ID10", "Kummer[10][Hypergeometric2F1[a,b,c,z^(-1)]]", +"(1 - z)^(-a - b + c)*(-z)^(a + b - c)*Hypergeometric2F1[-a + c, \ +-b + c, c, z^(-1)]"}, +{"fcstKummer-ID11", +"Kummer[10][Hypergeometric2F1[a,a+1-c,a-b+1,z^(-1)]]", +"(1 - z)^(-a - b + c)*(-z)^(a + b - c)*Hypergeometric2F1[1 - b, -b \ ++ c, 1 + a - b, z^(-1)]"}, +{"fcstKummer-ID12", "Kummer[11][Hypergeometric2F1[a,b,c,z^(-1)]]", +"((-z)^a*Hypergeometric2F1[a, -b + c, c, (1 - z)^(-1)])/(-((1 - \ +z)/z))^a"}, +{"fcstKummer-ID13", +"Kummer[11][Hypergeometric2F1[a,a+1-c,a-b+1,z^(-1)]]", +"((-z)^a*Hypergeometric2F1[a, -b + c, 1 + a - b, (1 - \ +z)^(-1)])/(-((1 - z)/z))^a"}, +{"fcstKummer-ID14", "Kummer[12][Hypergeometric2F1[a,b,c,z^(-1)]]", +"((-z)^(-a + b)*Hypergeometric2F1[b, -a + c, c, (1 - z)^(-1)])/(1 \ +- z)^b"}, +{"fcstKummer-ID15", +"Kummer[12][Hypergeometric2F1[a,a+1-c,a-b+1,z^(-1)]]", +"(1 - z)^(-1 - a + c)*(-z)^(1 - c)*Hypergeometric2F1[1 - b, 1 + a \ +- c, 1 + a - b, (1 - z)^(-1)]"}, +{"fcstKummer-ID16", "Kummer[14][Hypergeometric2F1[a,b,c,z^(-1)]]", +"(1 - z)^(-a - b + c)*(-z)^(a + b - c)*Hypergeometric2F1[-a + c, \ +-b + c, c, z^(-1)]"}, +{"fcstKummer-ID17", +"Kummer[14][Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]]", +"(1 - z)^(-a - b + c)*(-z)^(a + b - c)*Hypergeometric2F1[1 - a, -a \ ++ c, 1 - a + b, z^(-1)]"}, +{"fcstKummer-ID18", "Kummer[15][Hypergeometric2F1[a,b,c,z^(-1)]]", +"((-z)^b*Hypergeometric2F1[b, -a + c, c, (1 - z)^(-1)])/(1 - z)^b"}, +{"fcstKummer-ID19", +"Kummer[15][Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]]", +"(1 - z)^(-1 - b + c)*(-z)^(1 + b - c)*Hypergeometric2F1[1 - a, 1 \ ++ b - c, 1 - a + b, (1 - z)^(-1)]"}, +{"fcstKummer-ID20", "Kummer[16][Hypergeometric2F1[a,b,c,z^(-1)]]", +"((-z)^a*Hypergeometric2F1[a, -b + c, c, (1 - z)^(-1)])/(1 - z)^a"}, +{"fcstKummer-ID21", +"Kummer[16][Hypergeometric2F1[b+1-c,b,b+1-a,z^(-1)]]", +"((-z)^b*Hypergeometric2F1[b, -a + c, 1 - a + b, (1 - z)^(-1)])/(1 \ +- z)^b"}, +{"fcstKummer-ID22", "Kummer[18][Hypergeometric2F1[a,b,c,z]]", +"(1 - z)^(-a - b + c)*Hypergeometric2F1[-a + c, -b + c, c, z]"}, +{"fcstKummer-ID23", +"Kummer[18][Hypergeometric2F1[a+1-c,b+1-c,2-c,z]]", +"(1 - z)^(-a - b + c)*Hypergeometric2F1[1 - a, 1 - b, 2 - c, z]"}, +{"fcstKummer-ID24", "Kummer[19][Hypergeometric2F1[a,b,c,z]]", +"Hypergeometric2F1[a, -b + c, c, z/(-1 + z)]/(1 - z)^a"}, +{"fcstKummer-ID25", +"Kummer[19][Hypergeometric2F1[a+1-c,b+1-c,2-c,z]]", +"(1 - z)^(-1 - a + c)*Hypergeometric2F1[1 - b, 1 + a - c, 2 - c, \ +z/(-1 + z)]"}, +{"fcstKummer-ID26", "Kummer[20][Hypergeometric2F1[a,b,c,z]]", +"Hypergeometric2F1[b, -a + c, c, z/(-1 + z)]/(1 - z)^b"}, +{"fcstKummer-ID27", +"Kummer[20][Hypergeometric2F1[a+1-c,b+1-c,2-c,z]]", +"(1 - z)^(-1 - b + c)*Hypergeometric2F1[1 - a, 1 + b - c, 2 - c, \ +z/(-1 + z)]"}, +{"fcstKummer-ID28", "Kummer[22][Hypergeometric2F1[a,b,c,1-z]]", +"z^(-a - b + c)*Hypergeometric2F1[-a + c, -b + c, c, 1 - z]"}, +{"fcstKummer-ID29", +"Kummer[22][Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]]", +"z^(1 - c)*Hypergeometric2F1[1 - a, 1 - b, 1 - a - b + c, 1 - \ +z]"}, +{"fcstKummer-ID30", "Kummer[23][Hypergeometric2F1[a,b,c,1-z]]", +"Hypergeometric2F1[a, -b + c, c, 1 - (1 - z)^(-1)]/(1 - z)^a"}, +{"fcstKummer-ID31", +"Kummer[23][Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]]", +"(1 - z)^(a - c)*Hypergeometric2F1[1 - a, -a + c, 1 - a - b + c, 1 \ +- (1 - z)^(-1)]"}, +{"fcstKummer-ID32", "Kummer[24][Hypergeometric2F1[a,b,c,1-z]]", +"Hypergeometric2F1[b, -a + c, c, -((1 - z)/z)]/z^b"}, +{"fcstKummer-ID33", +"Kummer[24][Hypergeometric2F1[c-a,c-b,c+1-a-b,1-z]]", +"z^(b - c)*Hypergeometric2F1[1 - b, -b + c, 1 - a - b + c, -((1 - \ +z)/z)]"}, +{"fcstKummer-ID34", "Kummer[94][Hypergeometric2F1[a,b,c,z]]", +"(Gamma[c]*Gamma[-a - b + c]*Hypergeometric2F1[a, b, 1 + a + b - \ +c, 1 - z])/(Gamma[-a + c]*Gamma[-b + c]) + ((1 - z)^(-a - b + \ +c)*Gamma[a + b - c]*Gamma[c]*Hypergeometric2F1[-a + c, -b + c, 1 - a \ +- b + c, 1 - z])/(Gamma[a]*Gamma[b])"}, +{"fcstKummer-ID35", "Kummer[95][Hypergeometric2F1[a,b,c,z]]", +"(Gamma[-a + b]*Gamma[c]*Hypergeometric2F1[a, -b + c, 1 + a - b, \ +(1 - z)^(-1)])/((1 - z)^a*Gamma[b]*Gamma[-a + c]) + (Gamma[a - \ +b]*Gamma[c]*Hypergeometric2F1[b, -a + c, 1 - a + b, (1 - \ +z)^(-1)])/((1 - z)^b*Gamma[a]*Gamma[-b + c])"}, +{"fcstKummer-ID36", "Kummer[96][Hypergeometric2F1[a,b,c,z]]", +"((-1)^a*Gamma[-a + b]*Gamma[c]*Hypergeometric2F1[a, 1 + a - c, 1 \ ++ a - b, z^(-1)])/(z^a*Gamma[b]*Gamma[-a + c]) + ((-1)^b*Gamma[a - \ +b]*Gamma[c]*Hypergeometric2F1[b, 1 + b - c, 1 - a + b, \ +z^(-1)])/(z^b*Gamma[a]*Gamma[-b + c])"} +}); diff --git a/Tests/Tables/Nielsen.test b/Tests/Tables/Nielsen.test new file mode 100644 index 000000000..faf238eb2 --- /dev/null +++ b/Tests/Tables/Nielsen.test @@ -0,0 +1,33 @@ + + +(* :Title: Nielsen.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for Nielsen *) + +(* ------------------------------------------------------------------------ *) + +Tests`Tables`fcstNielsen = +({ +{"fcstNielsen-ID1", "Nielsen[1,2,x]", "Nielsen[1, 2, x]"}, +{"fcstNielsen-ID2", +"N[Nielsen[1,2,0.45]]\[Equal]0.07287162612104658`", "True"}, +{"fcstNielsen-ID3", "Nielsen[1,2,0]", "0"}, +{"fcstNielsen-ID4", "Nielsen[1,2,-1]", "Zeta[3]/8"}, +{"fcstNielsen-ID5", "Nielsen[1,2,1/2]", "Zeta[3]/8"}, +{"fcstNielsen-ID6", "Nielsen[1,2,1]", "Zeta[3]"}, +{"fcstNielsen-ID7", "Nielsen[1,2,x,PolyLog\[Rule]True]", +"(Log[1 - x]^2*Log[x])/2 + Log[1 - x]*PolyLog[2, 1 - x] - \ +PolyLog[3, 1 - x] + Zeta[3]"}, +{"fcstNielsen-ID8", "Nielsen[1,3,x,PolyLog\[Rule]True]", +"Pi^4/90 - (Log[1 - x]^3*Log[x])/6 - (Log[1 - x]^2*PolyLog[2, 1 - \ +x])/2 + Log[1 - x]*PolyLog[3, 1 - x] - PolyLog[4, 1 - x]"}, +{"fcstNielsen-ID9", "Nielsen[3,1,x,PolyLog\[Rule]True]", +"PolyLog[4, x]"} +}) diff --git a/Tests/Tables/SimplifyPolyLog.test b/Tests/Tables/SimplifyPolyLog.test new file mode 100644 index 000000000..ed4a89633 --- /dev/null +++ b/Tests/Tables/SimplifyPolyLog.test @@ -0,0 +1,499 @@ + + +(* :Title: SimplifyPolyLog.test *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko +*) + +(* :Summary: Framework independent unit tests for SimplifyPolyLog *) + +(* ------------------------------------------------------------------------ *) + +Tests`Tables`fcstSimplifyPolyLog = +({ +{"fcstSimplifyPolyLog-ID1", "SimplifyPolyLog[PolyLog[2,1/x]]", +"Zeta2 + I*Pi*Log[x] + Log[1 - x]*Log[x] - Log[x]^2/2 + PolyLog[2, \ +1 - x]"}, +{"fcstSimplifyPolyLog-ID2", "SimplifyPolyLog[PolyLog[2,x]]", +"Zeta2 - Log[1 - x]*Log[x] - PolyLog[2, 1 - x]"}, +{"fcstSimplifyPolyLog-ID3", "SimplifyPolyLog[PolyLog[2,1-x^2]]", +"-Zeta2 - 2*Log[x]*Log[1 + x] + 2*PolyLog[2, 1 - x] - 2*PolyLog[2, \ +-x]"}, +{"fcstSimplifyPolyLog-ID4", "SimplifyPolyLog[PolyLog[2,x^2]]", +"2*Zeta2 - 2*Log[1 - x]*Log[x] - 2*PolyLog[2, 1 - x] + \ +2*PolyLog[2, -x]"}, +{"fcstSimplifyPolyLog-ID5", "SimplifyPolyLog[PolyLog[2,-x/(1-x)]]", +"-Zeta2 - Log[1 - x]^2/2 + Log[1 - x]*Log[x] + PolyLog[2, 1 - \ +x]"}, +{"fcstSimplifyPolyLog-ID6", "SimplifyPolyLog[PolyLog[2,x/(x-1)]]", +"-Zeta2 - Log[1 - x]^2/2 + Log[1 - x]*Log[x] + PolyLog[2, 1 - \ +x]"}, +{"fcstSimplifyPolyLog-ID7", +"SimplifyPolyLog[Nielsen[1,2,-x/(1-x)]]", +"-Log[1 - x]^3/6 + Nielsen[1, 2, x]"}, +{"fcstSimplifyPolyLog-ID8", "SimplifyPolyLog[PolyLog[3,-1/x]]", +"Zeta2*Log[x] + Log[x]^3/6 + PolyLog[3, -x]"}, +{"fcstSimplifyPolyLog-ID9", "SimplifyPolyLog[PolyLog[3,1-x]]", +"PolyLog[3, 1 - x]"}, +{"fcstSimplifyPolyLog-ID10", "SimplifyPolyLog[PolyLog[3,x^2]]", +"4*Zeta2*Log[x] - 2*Log[1 - x]*Log[x]^2 - 4*Nielsen[1, 2, 1 - x] - \ +4*Log[x]*PolyLog[2, 1 - x] + 4*PolyLog[3, -x] + 4*Zeta[3]"}, +{"fcstSimplifyPolyLog-ID11", "SimplifyPolyLog[PolyLog[3,-x/(1-x)]]", + "Zeta2*Log[1 - x] + Log[1 - x]^3/6 - Zeta2*Log[x] - (Log[1 - \ +x]^2*Log[x])/2 + (Log[1 - x]*Log[x]^2)/2 + Nielsen[1, 2, 1 - x] + \ +Log[x]*PolyLog[2, 1 - x] - PolyLog[3, 1 - x]"}, +{"fcstSimplifyPolyLog-ID12", "SimplifyPolyLog[PolyLog[3,1-1/x]]", +"-(Log[1 - x]^2*Log[x])/2 + Log[x]^3/6 + Nielsen[1, 2, 1 - x] + \ +Nielsen[1, 2, x] - Log[1 - x]*PolyLog[2, 1 - x] + Log[x]*PolyLog[2, 1 \ +- x] - Zeta[3]"}, +{"fcstSimplifyPolyLog-ID13", "SimplifyPolyLog[PolyLog[4,-x/(1-x)]]", + "-(Zeta2*Log[1 - x]^2)/2 - Log[1 - x]^4/24 + Zeta2*Log[1 - \ +x]*Log[x] + (Log[1 - x]^3*Log[x])/2 - (Log[1 - x]^2*Log[x]^2)/2 - \ +Log[1 - x]*Nielsen[1, 2, 1 - x] - Log[1 - x]*Nielsen[1, 2, x] - \ +Nielsen[1, 3, x] + Nielsen[2, 2, x] + (Log[1 - x]^2*PolyLog[2, 1 - \ +x])/2 - Log[1 - x]*Log[x]*PolyLog[2, 1 - x] - PolyLog[4, x] + Log[1 - \ +x]*Zeta[3]"}, +{"fcstSimplifyPolyLog-ID14", "SimplifyPolyLog[Log[a+b/c]]", +"Log[(b + a*c)/c]"}, +{"fcstSimplifyPolyLog-ID15", "SimplifyPolyLog[Log[1/x]]", "-Log[x]"}, +{"fcstSimplifyPolyLog-ID16", "SimplifyPolyLog[ArcTanh[x]]", +"Log[-((1 + x)/(1 - x))]/2"}, +{"fcstSimplifyPolyLog-ID17", "SimplifyPolyLog[ArcSinh[x]]", +"Log[x + Sqrt[1 + x^2]]"}, +{"fcstSimplifyPolyLog-ID18", "SimplifyPolyLog[ArcCosh[x]]", +"Log[x + Sqrt[-1 + x^2]]"}, +{"fcstSimplifyPolyLog-ID19", "SimplifyPolyLog[Pi^4]", +"90 Zeta4"}, +{"fcstSimplifyPolyLog-ID20", "SimplifyPolyLog[Nielsen[3, 1, 1 - z], Nielsen -> False]", +"PolyLog[4, 1 - z]"}, + +{"fcstSimplifyPolyLog-ID21", "SimplifyPolyLog[Log[Sqrt[z]]]", +"Log[z]/2"}, +{"fcstSimplifyPolyLog-ID22", +"SimplifyPolyLog[Log[1+Sqrt[z]]+Log[1-Sqrt[z]]]", "Log[1 - z]"}, +{"fcstSimplifyPolyLog-ID23", +"SimplifyPolyLog[PolyLog[2,Sqrt[z]]+PolyLog[2,-Sqrt[z]]]", +"Zeta2/2 - (Log[1 - z]*Log[z])/2 - PolyLog[2, 1 - z]/2"}, +{"fcstSimplifyPolyLog-ID24", +"SimplifyPolyLog[PolyLog[3,Sqrt[z]]+PolyLog[3,-Sqrt[z]], Nielsen -> False]", +"1/4 PolyLog[3, z]"}, +{"fcstSimplifyPolyLog-ID25", +"SimplifyPolyLog[PolyLog[4,Sqrt[z]]+PolyLog[4,-Sqrt[z]], Nielsen -> False]", +"1/8 PolyLog[4, z]"}, +{"fcstSimplifyPolyLog-ID26", +"SimplifyPolyLog[Log[Sqrt[z]],Sqrt\[Rule]False]", "Log[Sqrt[z]]"}, +{"fcstSimplifyPolyLog-ID27", +"SimplifyPolyLog[Log[1+Sqrt[z]]+Log[1-Sqrt[z]],Sqrt\[Rule]False]", +"Log[1 - Sqrt[z]] + Log[1 + Sqrt[z]]"}, +{"fcstSimplifyPolyLog-ID28", +"SimplifyPolyLog[PolyLog[2,Sqrt[z]]+PolyLog[2,-Sqrt[z]],Sqrt\[Rule]\ +False]", "PolyLog[2, -Sqrt[z]] + PolyLog[2, Sqrt[z]]"}, +{"fcstSimplifyPolyLog-ID29", +"SimplifyPolyLog[PolyLog[3,Sqrt[z]]+PolyLog[3,-Sqrt[z]],Sqrt\[Rule]\ +False]", "PolyLog[3, -Sqrt[z]] + PolyLog[3, Sqrt[z]]"}, +{"fcstSimplifyPolyLog-ID30", +"SimplifyPolyLog[PolyLog[4,Sqrt[z]]+PolyLog[4,-Sqrt[z]],Sqrt\[Rule]\ +False]", "PolyLog[4, -Sqrt[z]] + PolyLog[4, Sqrt[z]]"}, +{"fcstSimplifyPolyLog-ID31", +"SimplifyPolyLog[ +-((-1 + zz)*(312*Zeta2*Log[2] - 104*Log[2]^3 - 276*Zeta2*Log[1 + Sqrt[zz]] - 312*Log[2]*Log[1 + Sqrt[zz]]^2 - 52*Log[1 + Sqrt[zz]]^3 + 288*Zeta2*Log[1 - zz] + + 156*Log[2]^2*Log[1 - zz] + 312*Log[2]*Log[1 + Sqrt[zz]]*Log[1 - zz] + 156*Log[1 + Sqrt[zz]]^2*Log[1 - zz] - 156*Log[2]*Log[1 - zz]^2 - + 156*Log[1 + Sqrt[zz]]*Log[1 - zz]^2 + 52*Log[1 - zz]^3 - 180*Log[1 + Sqrt[zz]]^2*Log[-Sqrt[zz]] + 78*Zeta2*Log[zz] - 144*Log[1 + Sqrt[zz]]^2*Log[zz] + + 300*Log[1 + Sqrt[zz]]*Log[1 - zz]*Log[zz] - 66*Log[1 - zz]^2*Log[zz] - 39*Log[1 - zz]*Log[zz]^2 - 78*Nielsen[1, 2, 1 - zz] - + 24*(Log[1 + Sqrt[zz]] - Log[1 - zz])*PolyLog[2, 1 - Sqrt[zz]] - 24*Log[1 + Sqrt[zz]]*PolyLog[2, 1 + Sqrt[zz]] + 12*Log[1 + Sqrt[zz]]*PolyLog[2, 1 - zz] - + 78*Log[zz]*PolyLog[2, 1 - zz] + 24*Log[1 - zz]*PolyLog[2, Sqrt[zz]] + 312*PolyLog[3, (1 - Sqrt[zz])/2] - 624*PolyLog[3, 1 - Sqrt[zz]] + + 312*PolyLog[3, (1 + Sqrt[zz])/2] - 312*PolyLog[3, 1 + Sqrt[zz]] + 156*PolyLog[3, 1 - zz] - 312*PolyLog[3, Sqrt[zz]] - + 312*PolyLog[3, (2*Sqrt[zz])/(-1 + Sqrt[zz])] + 312*PolyLog[3, Sqrt[zz]/(1 + Sqrt[zz])] - 312*PolyLog[3, (2*Sqrt[zz])/(1 + Sqrt[zz])] + 312*Zeta[3]))/(6*zz^2) +] +", "0"}, +{"fcstSimplifyPolyLog-ID32", "SimplifyPolyLog[Log[1048576]]", +"20*Log[2]"}, +{"fcstSimplifyPolyLog-ID33", "SimplifyPolyLog[Log[16 1048576]]", +"24*Log[2]"}, +{"fcstSimplifyPolyLog-ID34", "SimplifyPolyLog[Li2[(1-Sqrt[x])/2]]", +"-Log[2]^2/2 + Log[2]*Log[1 + Sqrt[x]] - Log[1 + Sqrt[x]]^2/2 + +2*PolyLog[2, 1 - Sqrt[x]] - PolyLog[2, (1 - Sqrt[x])/(1 + Sqrt[x])] - PolyLog[2, 1 - x]/2"}, +{"fcstSimplifyPolyLog-ID35", +"Chop[N[(Li2[(1-Sqrt[x])/2]-SimplifyPolyLog[Li2[(1-Sqrt[x])/2]])\ +/.x\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID36", "SimplifyPolyLog[Li2[(1+Sqrt[x])]]", +"(3*Zeta2)/2 - I*Pi*Log[1 + Sqrt[x]] - PolyLog[2, 1 - Sqrt[x]] + \ +PolyLog[2, 1 - x]/2"}, +{"fcstSimplifyPolyLog-ID37", +"Chop[N[(Li2[(1+Sqrt[x])]-SimplifyPolyLog[Li2[(1+Sqrt[x])]])/.x\ +\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID38", "SimplifyPolyLog[Li2[(Sqrt[x])]]", +"Zeta2 + (Log[1 + Sqrt[x]]*Log[x])/2 - (Log[1 - x]*Log[x])/2 - \ +PolyLog[2, 1 - Sqrt[x]]"}, +{"fcstSimplifyPolyLog-ID39", +"Chop[N[(Li2[(Sqrt[x])]-SimplifyPolyLog[Li2[(Sqrt[x])]])/.x\[Rule]\ +1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID40", "SimplifyPolyLog[Li2[2x/(1+x)]]", +"Zeta2 - Log[2]*Log[1 - x] - Log[1 - x]*Log[x] + Log[2]*Log[1 + x] \ ++ Log[1 - x]*Log[1 + x] + Log[x]*Log[1 + x] - Log[1 + x]^2 - \ +PolyLog[2, (1 - x)/(1 + x)]"}, +{"fcstSimplifyPolyLog-ID41", +"Chop[N[(Li2[2x/(1+x)]-SimplifyPolyLog[Li2[2x/(1+x)]])/.x\[Rule]1/\ +3]]", "0"}, +{"fcstSimplifyPolyLog-ID42", "SimplifyPolyLog[Li3[(1+Sqrt[x])]]", +"2*Zeta2*Log[1 + Sqrt[x]] - (I/2)*Pi*Log[1 + Sqrt[x]]^2 - Log[1 + \ +Sqrt[x]]^3/6 + PolyLog[3, (1 + Sqrt[x])^(-1)]"}, +{"fcstSimplifyPolyLog-ID43", +"Chop[N[(Li3[(1+Sqrt[x])]-SimplifyPolyLog[Li3[(1+Sqrt[x])]])/.x\ +\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID44", +"SimplifyPolyLog[Li3[2Sqrt[x]/(Sqrt[x]-1)]]", +"-(Zeta2*Log[2]) - Log[2]^3/6 - Zeta2*Log[1 + Sqrt[x]] - \ +(Log[2]^2*Log[1 + Sqrt[x]])/2 - (Log[2]*Log[1 + Sqrt[x]]^2)/2 - Log[1 \ ++ Sqrt[x]]^3/6 + Zeta2*Log[1 - x] + (Log[2]^2*Log[1 - x])/2 + \ +Log[2]*Log[1 + Sqrt[x]]*Log[1 - x] + (Log[1 + Sqrt[x]]^2*Log[1 - \ +x])/2 - (Log[2]*Log[1 - x]^2)/2 - (Log[1 + Sqrt[x]]*Log[1 - x]^2)/2 + \ +Log[1 - x]^3/6 - (Zeta2*Log[x])/2 - (Log[2]^2*Log[x])/4 - \ +(Log[2]*Log[1 + Sqrt[x]]*Log[x])/2 - (Log[1 + Sqrt[x]]^2*Log[x])/4 + \ +(Log[2]*Log[1 - x]*Log[x])/2 + (Log[1 + Sqrt[x]]*Log[1 - x]*Log[x])/2 \ +- (Log[1 - x]^2*Log[x])/4 - (Log[2]*Log[x]^2)/8 - (Log[1 + \ +Sqrt[x]]*Log[x]^2)/8 + (Log[1 - x]*Log[x]^2)/8 - Log[x]^3/48 + \ +PolyLog[3, -(1 - Sqrt[x])/(2*Sqrt[x])]"}, +{"fcstSimplifyPolyLog-ID45", +"Chop[N[(Li3[2Sqrt[x]/(Sqrt[x]-1)]-SimplifyPolyLog[Li3[2Sqrt[x]/(\ +Sqrt[x]-1)]])/.x\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID46", "SimplifyPolyLog[Li3[(x-1)/(x+1)]]", +"-(Zeta2*Log[2]) + Log[2]^3/3 - (Log[2]^2*Log[1 - x])/2 + \ +Zeta2*Log[1 + x] - (Log[2]^2*Log[1 + x])/2 + Log[2]*Log[1 - x]*Log[1 \ ++ x] - (Log[1 - x]*Log[1 + x]^2)/2 + Log[1 + x]^3/6 - PolyLog[3, (1 - \ +x)/2] - PolyLog[3, (1 + x)/2] + Zeta[3]"}, +{"fcstSimplifyPolyLog-ID47", +"Chop[N[(Li3[(x-1)/(x+1)]-SimplifyPolyLog[Li3[(x-1)/(x+1)]])/.x\ +\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID48", +"SimplifyPolyLog[Li3[(Sqrt[x]-1)/(Sqrt[x]+1)]]", +"-(Zeta2*Log[2]) + Log[2]^3/3 + Zeta2*Log[1 + Sqrt[x]] - \ +Log[2]*Log[1 + Sqrt[x]]^2 + (2*Log[1 + Sqrt[x]]^3)/3 - \ +(Log[2]^2*Log[1 - x])/2 + Log[2]*Log[1 + Sqrt[x]]*Log[1 - x] - (Log[1 \ ++ Sqrt[x]]^2*Log[1 - x])/2 - PolyLog[3, (1 - Sqrt[x])/2] - PolyLog[3, \ +(1 + Sqrt[x])/2] + Zeta[3]"}, +{"fcstSimplifyPolyLog-ID49", +"Chop[N[(Li3[(Sqrt[x]-1)/(Sqrt[x]+1)]-SimplifyPolyLog[Li3[(Sqrt[x]-\ +1)/(Sqrt[x]+1)]])/.x\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID50", +"SimplifyPolyLog[Li3[(Sqrt[x])/(Sqrt[x]+1)]]", +"-(Zeta2*Log[1 + Sqrt[x]]) + Log[1 + Sqrt[x]]^3/3 - \ +(Zeta2*Log[x])/4 - (Log[1 + Sqrt[x]]^2*Log[x])/4 + (Log[1 - \ +x]*Log[x]^2)/8 + Nielsen[1, 2, 1 - x]/4 + (Log[x]*PolyLog[2, 1 - \ +x])/4 - PolyLog[3, (1 + Sqrt[x])^(-1)] + PolyLog[3, Sqrt[x]] + \ +(3*Zeta[3])/4"}, +{"fcstSimplifyPolyLog-ID51", +"Chop[N[(Li3[(Sqrt[x])/(Sqrt[x]+1)]-SimplifyPolyLog[Li3[(Sqrt[x])/(\ +Sqrt[x]+1)]])/.x\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID52", "SimplifyPolyLog[Li3[2x/(1+x)]]", +"Zeta2*Log[2] + Log[2]^3/6 - (Log[2]^2*Log[1 - x])/2 + \ +Zeta2*Log[x] + (Log[2]^2*Log[x])/2 - Log[2]*Log[1 - x]*Log[x] + \ +(Log[2]*Log[x]^2)/2 - (Log[1 - x]*Log[x]^2)/2 + Log[x]^3/6 - \ +Zeta2*Log[1 + x] + Log[2]*Log[1 - x]*Log[1 + x] + Log[1 - \ +x]*Log[x]*Log[1 + x] - (Log[2]*Log[1 + x]^2)/2 - (Log[1 - x]*Log[1 + \ +x]^2)/2 - (Log[x]*Log[1 + x]^2)/2 + Log[1 + x]^3/3 - PolyLog[3, -(1 - \ +x)/(2*x)] - PolyLog[3, (1 - x)/(1 + x)] + Zeta[3]"}, +{"fcstSimplifyPolyLog-ID53", +"Chop[N[(Li3[2x/(1+x)]-SimplifyPolyLog[Li3[2x/(1+x)]])/.x\[Rule]1/\ +3]]", "0"}, +{"fcstSimplifyPolyLog-ID54", +"SimplifyPolyLog[Li3[2Sqrt[x]/(1+Sqrt[x])]]", +"2*Zeta2*Log[2] - Log[2]^3/6 - 3*Zeta2*Log[1 + Sqrt[x]] + \ +(Log[2]^2*Log[1 + Sqrt[x]])/2 - (Log[2]*Log[1 + Sqrt[x]]^2)/2 + Log[1 \ ++ Sqrt[x]]^3/2 + (Zeta2*Log[x])/2 + (Log[2]^2*Log[x])/4 + \ +(Log[2]*Log[1 + Sqrt[x]]*Log[x])/2 - (3*Log[1 + Sqrt[x]]^2*Log[x])/4 \ +- (Log[2]*Log[1 - x]*Log[x])/2 + (Log[1 + Sqrt[x]]*Log[1 - \ +x]*Log[x])/2 + (Log[2]*Log[x]^2)/8 + (Log[1 + Sqrt[x]]*Log[x]^2)/8 - \ +(Log[1 - x]*Log[x]^2)/8 + Log[x]^3/48 + PolyLog[3, (1 - Sqrt[x])/2] - \ +2*PolyLog[3, 1 - Sqrt[x]] - 2*PolyLog[3, (1 + Sqrt[x])^(-1)] + \ +PolyLog[3, (1 + Sqrt[x])/2] + PolyLog[3, 1 - x]/2 - PolyLog[3, -(1 - \ +Sqrt[x])/(2*Sqrt[x])] + (7*Zeta[3])/4"}, +{"fcstSimplifyPolyLog-ID55", +"Chop[N[(Li3[2Sqrt[x]/(1+Sqrt[x])]-SimplifyPolyLog[Li3[2Sqrt[x]/(1+\ +Sqrt[x])]])/.x\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID56", +"SimplifyPolyLog[Li3[(1-Sqrt[x])/(Sqrt[x]+1)]]", +"-(Zeta2*Log[2]) + Log[2]^3/3 + 2*Zeta2*Log[1 + Sqrt[x]] - \ +Log[2]*Log[1 + Sqrt[x]]^2 + Log[1 + Sqrt[x]]^3/3 - (Log[2]^2*Log[1 - \ +x])/2 + Log[2]*Log[1 + Sqrt[x]]*Log[1 - x] - (Log[1 + \ +Sqrt[x]]^2*Log[1 - x])/2 - PolyLog[3, (1 - Sqrt[x])/2] + 2*PolyLog[3, \ +1 - Sqrt[x]] + 2*PolyLog[3, (1 + Sqrt[x])^(-1)] - PolyLog[3, (1 + \ +Sqrt[x])/2] - PolyLog[3, 1 - x]/2 - (3*Zeta[3])/4"}, +{"fcstSimplifyPolyLog-ID57", +"Chop[N[(Li3[(1-Sqrt[x])/(Sqrt[x]+1)]-SimplifyPolyLog[Li3[(1-Sqrt[\ +x])/(Sqrt[x]+1)]])/.x\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID58", "SimplifyPolyLog[Li3[(x)/(x+1)]]", +"-(Zeta2*Log[1 + x]) - (Log[x]*Log[1 + x]^2)/2 + Log[1 + x]^3/3 - \ +PolyLog[3, -x] - PolyLog[3, (1 + x)^(-1)] + Zeta[3]"}, +{"fcstSimplifyPolyLog-ID59", +"Chop[N[(Li3[(x)/(x+1)]-SimplifyPolyLog[Li3[(x)/(x+1)]])/.x\[Rule]\ +1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID60", "SimplifyPolyLog[Log[1/(1+x)]]", +"-Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID61", "SimplifyPolyLog[Log[1/(1+x)^2]]", +"2*Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID62", "SimplifyPolyLog[Log[1/(1+x)^3]]", +"3*Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID63", "SimplifyPolyLog[Log[1/(1+x)^4]]", +"4*Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID64", "SimplifyPolyLog[Log[1/(1+x^2)]]", +"Log[1 + x^2]"}, +{"fcstSimplifyPolyLog-ID65", "SimplifyPolyLog[Log[1/(1+x^2)^2]]", +"2*Log[1 + x^2]"}, +{"fcstSimplifyPolyLog-ID66", "SimplifyPolyLog[Log[1/(1+x^2)^3]]", +"3*Log[1 + x^2]"}, +{"fcstSimplifyPolyLog-ID67", "SimplifyPolyLog[Log[1/(1+x^2)^4]]", +"4*Log[1 + x^2]"}, +{"fcstSimplifyPolyLog-ID68", "SimplifyPolyLog[Log[1/(1-x)]]", +"-Log[1 - x]"}, +{"fcstSimplifyPolyLog-ID69", "SimplifyPolyLog[Log[1/(1-x)^2]]", +"2*Log[1 - x]"}, +{"fcstSimplifyPolyLog-ID70", "SimplifyPolyLog[Log[1/(1-x)^3]]", +"3*Log[1 - x]"}, +{"fcstSimplifyPolyLog-ID71", "SimplifyPolyLog[Log[1/(1-x)^4]]", +"4*Log[1 - x]"}, +{"fcstSimplifyPolyLog-ID72", "SimplifyPolyLog[Log[1/(1-x^2)]]", +"Log[1 - x] + Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID73", "SimplifyPolyLog[Log[1/(1-x^2)^2]]", +"2*Log[1 - x] + 2*Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID74", "SimplifyPolyLog[Log[1/(1-x^2)^3]]", +"3*Log[1 - x] + 3*Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID75", "SimplifyPolyLog[Log[1/(1-x^2)^4]]", +"4*Log[1 - x] + 4*Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID76", "SimplifyPolyLog[Log[-Sqrt[x]]]", +"I*Pi + Log[x]/2"}, +{"fcstSimplifyPolyLog-ID77", "SimplifyPolyLog[Li2[1/2(1+Sqrt[x])]]", + "Zeta2 - Log[2]^2/2 - Log[2]*Log[1 + Sqrt[x]] + (3*Log[1 + \ +Sqrt[x]]^2)/2 + Log[2]*Log[1 - x] - Log[1 + Sqrt[x]]*Log[1 - x] - \ +2*PolyLog[2, 1 - Sqrt[x]] + PolyLog[2, (1 - Sqrt[x])/(1 + Sqrt[x])] + \ +PolyLog[2, 1 - x]/2"}, +{"fcstSimplifyPolyLog-ID78", +"Chop[N[(Li2[1/2(1+Sqrt[x])]-SimplifyPolyLog[Li2[1/2(1+Sqrt[x])]])\ +/.x\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID79", "SimplifyPolyLog[Li2[1/2(1-Sqrt[x])]]", + "-Log[2]^2/2 + Log[2]*Log[1 + Sqrt[x]] - Log[1 + Sqrt[x]]^2/2 + \ +2*PolyLog[2, 1 - Sqrt[x]] - PolyLog[2, (1 - Sqrt[x])/(1 + Sqrt[x])] - \ +PolyLog[2, 1 - x]/2"}, +{"fcstSimplifyPolyLog-ID80", +"Chop[N[(Li2[1/2(1-Sqrt[x])]-SimplifyPolyLog[Li2[1/2(1-Sqrt[x])]])\ +/.x\[Rule]1/3]]", "0"}, +{"fcstSimplifyPolyLog-ID81", +"SimplifyPolyLog[Zeta2 - Log[2]^2/2 - Log[2]*Log[1 + Sqrt[x]] + (3*Log[1 + Sqrt[x]]^2)/2 + +Log[2]*Log[1 - x] - Log[1 + Sqrt[x]]*Log[1 - x] - 2*PolyLog[2, 1 - Sqrt[x]] + +PolyLog[2, (1 - Sqrt[x])/(1 + Sqrt[x])] - PolyLog[2, (1 + Sqrt[x])/2] + PolyLog[2, 1 - x]/2]", "0"}, +{"fcstSimplifyPolyLog-ID82", +"SimplifyPolyLog[Log[x^4]]", "4 Log[x]"}, +{"fcstSimplifyPolyLog-ID83", +"SimplifyPolyLog[Log[x^10]]", "10 Log[x]"}, +{"fcstSimplifyPolyLog-ID84", +"SimplifyPolyLog[4 Zeta2^2]", "10 Zeta4"}, +{"fcstSimplifyPolyLog-ID85", +"SimplifyPolyLog[Zeta2^2 - 5 Zeta[4]/2]", "0"}, +{"fcstSimplifyPolyLog-ID86", +"SimplifyPolyLog[PolyLog[2, 2, x]]", "Nielsen[2, 2, x]"}, +{"fcstSimplifyPolyLog-ID87", +"SimplifyPolyLog[(250 PolyGamma[2, 3])/(3 (2 - 2 zz) zz) - ( +250 Log[1 - (2 zz)/(-2 + 2 zz)] PolyGamma[2, 3])/(3 (2 - 2 zz))]", "(250 (9/4 - 2 Zeta[3]))/(3 (2 - 2 zz) zz) + ( +250 Log[1 - zz] (9/4 - 2 Zeta[3]))/(3 (2 - 2 zz))"}, +{"fcstSimplifyPolyLog-ID88", +"SimplifyPolyLog[Log[-2 x]]", "I \[Pi] + Log[2] + Log[x]"}, +{"fcstSimplifyPolyLog-ID89", +"SimplifyPolyLog[Log[-4 x]]", "I \[Pi] + 2 Log[2] + Log[x]"}, +{"fcstSimplifyPolyLog-ID90", +"SimplifyPolyLog[Log[-10 x]]", "I \[Pi] + Log[2] + Log[5] + Log[x]"}, +{"fcstSimplifyPolyLog-ID91", "SimplifyPolyLog[Li2[2/(1+x)]]", +"(3*Zeta2)/2 - I*Pi*Log[2] - Log[2]*Log[1 - x] + I*Pi*Log[1 + x] + \ +Log[2]*Log[1 + x] + Log[1 - x]*Log[1 + x] + Log[x]*Log[1 + x] - Log[1 \ ++ x]^2 + PolyLog[2, 1 - x] + PolyLog[2, -x] - PolyLog[2, (1 - x)/(1 + \ +x)]"}, +{"fcstSimplifyPolyLog-ID92", +"N[(SimplifyPolyLog[Li2[2/(1+x)]]-Li2[2/(1+x)])/.x\[Rule]0.3]\ +//Chop", "0"}, +{"fcstSimplifyPolyLog-ID93", "SimplifyPolyLog[Li3[2/(1+x)]]", +"(Zeta2*Log[2])/2 - Log[2]^3/6 - 2*Zeta2*Log[1 + x] + \ +I*Pi*Log[2]*Log[1 + x] + (Log[2]^2*Log[1 + x])/2 - (I/2)*Pi*Log[1 + \ +x]^2 - (Log[2]*Log[1 + x]^2)/2 + Log[1 + x]^3/6 + PolyLog[3, 2] + \ +PolyLog[3, (1 + x)/2] - (7*Zeta[3])/8"}, +{"fcstSimplifyPolyLog-ID94", +"N[(SimplifyPolyLog[Li3[2/(1+x)]]-Li3[2/(1+x)])/.x\[Rule]0.3]\ +//Chop", "0"}, +{"fcstSimplifyPolyLog-ID95", "SimplifyPolyLog[Log[2/(1+x)]]", +"Log[2] - Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID96", "SimplifyPolyLog[Log[6/(1+x)]]", +"Log[2] + Log[3] - Log[1 + x]"}, +{"fcstSimplifyPolyLog-ID97", +"SimplifyPolyLog[Log[-(Sqrt[1-x]-Sqrt[-x])/Sqrt[-x]]]", +"(I/2)*Pi - Log[Sqrt[1 - x] + Sqrt[-x]] - Log[x]/2"}, +{"fcstSimplifyPolyLog-ID98", +"N[(SimplifyPolyLog[Log[-(Sqrt[1-x]-Sqrt[-x])/Sqrt[-x]]]-Log[-(\ +Sqrt[1-x]-Sqrt[-x])/Sqrt[-x]])/.x\[Rule]0.3]//Chop", "0"}, +{"fcstSimplifyPolyLog-ID99", +"SimplifyPolyLog[Log[(Sqrt[1-x]+Sqrt[-x])/Sqrt[-x]]]", +"(-I/2)*Pi + Log[Sqrt[1 - x] + Sqrt[-x]] - Log[x]/2"}, +{"fcstSimplifyPolyLog-ID100", +"N[(SimplifyPolyLog[Log[(Sqrt[1-x]+Sqrt[-x])/Sqrt[-x]]]-Log[(Sqrt[\ +1-x]+Sqrt[-x])/Sqrt[-x]])/.x\[Rule]0.3]//Chop", "0"}, +{"fcstSimplifyPolyLog-ID101", +"SimplifyPolyLog[Log[Sqrt[-x]-Sqrt[1-x]]]", +"I*Pi - Log[Sqrt[1 - x] + Sqrt[-x]]"}, +{"fcstSimplifyPolyLog-ID102", +"N[(SimplifyPolyLog[Log[Sqrt[-x]-Sqrt[1-x]]]-Log[Sqrt[-x]-Sqrt[1-x]\ +])/.x\[Rule]0.3]//Chop", "0"}, +{"fcstSimplifyPolyLog-ID103", +"SimplifyPolyLog[Log[Sqrt[1-x]/Sqrt[-x]]]", +"(-I/2)*Pi + Log[1 - x]/2 - Log[x]/2"}, +{"fcstSimplifyPolyLog-ID104", +"N[(SimplifyPolyLog[Log[Sqrt[1-x]/Sqrt[-x]]]-Log[Sqrt[1-x]/Sqrt[-x]\ +])/.x\[Rule]0.3]//Chop", "0"}, +{"fcstSimplifyPolyLog-ID105", "SimplifyPolyLog[Log[Sqrt[-x]]]", +"(I/2)*Pi + Log[x]/2"}, +{"fcstSimplifyPolyLog-ID106", +"N[(SimplifyPolyLog[Log[Sqrt[-x]]]-Log[Sqrt[-x]])/.x\[Rule]0.3]\ +//Chop", "0"}, +{"fcstSimplifyPolyLog-ID107", "SimplifyPolyLog[Log[Sqrt[1-x]]]", +"Log[1 - x]/2"}, +{"fcstSimplifyPolyLog-ID108", +"N[(SimplifyPolyLog[Log[Sqrt[1-x]]]-Log[Sqrt[1-x]])/.x\[Rule]0.3]\ +//Chop", "0"}, +{"fcstSimplifyPolyLog-ID109", "SimplifyPolyLog[Log[-Sqrt[1-x]]]", +"I*Pi + Log[1 - x]/2"}, +{"fcstSimplifyPolyLog-ID110", +"N[(SimplifyPolyLog[Log[-Sqrt[1-x]]]-Log[-Sqrt[1-x]])/.x\[Rule]0.3]\ +//Chop", "0"}, +{"fcstSimplifyPolyLog-ID111", +"SimplifyPolyLog[Log[Sqrt[1-x]/Sqrt[-x]]]", +"(-I/2)*Pi + Log[1 - x]/2 - Log[x]/2"}, +{"fcstSimplifyPolyLog-ID112", +"N[(SimplifyPolyLog[Log[Sqrt[1-x]/Sqrt[-x]]]-Log[Sqrt[1-x]/Sqrt[-x]\ +])/.x\[Rule]0.3]//Chop", "0"}, +{"fcstSimplifyPolyLog-ID113", +"SimplifyPolyLog[Log[(3 - x)/(1 - x)]]", "-Log[1 - x] + Log[3 - x]"}, +{"fcstSimplifyPolyLog-ID114", +"SimplifyPolyLog[Log[(2 - x)/(1 - x)]]", "-Log[1 - x] + Log[2 - x]"}, +{"fcstSimplifyPolyLog-ID115", +"SimplifyPolyLog[Log[(-Sqrt[1 - x] + Sqrt[-x])/(8 Sqrt[-x])]]", + "(I \[Pi])/2 - 3 Log[2] - Log[Sqrt[1 - x] + Sqrt[-x]] - Log[x]/2"}, +{"fcstSimplifyPolyLog-ID116", +"SimplifyPolyLog[Li2[x], PolyLog -> False]", + "PolyLog[2, x]"}, +{"fcstSimplifyPolyLog-ID117", +"SimplifyPolyLog[Log[Sqrt[1 - zz] - Sqrt[-zz]]]", + "-Log[Sqrt[1 - zz] + Sqrt[-zz]]"}, +{"fcstSimplifyPolyLog-ID118", +"SimplifyPolyLog[Log[Sqrt[-zz]/(Sqrt[1 - zz] + Sqrt[-zz])]]", + "(I \[Pi])/2 - Log[Sqrt[1 - zz] + Sqrt[-zz]] + Log[zz]/2"}, +{"fcstSimplifyPolyLog-ID119", +"SimplifyPolyLog[Log[Sqrt[1 - zz]/(Sqrt[1 - zz] + Sqrt[-zz])]]", + "-Log[Sqrt[1 - zz] + Sqrt[-zz]] + 1/2 Log[1 - zz]"}, +{"fcstSimplifyPolyLog-ID120", +"SimplifyPolyLog[Log[(Sqrt[1 - x] - Sqrt[-x])/Sqrt[1 - x]]]", + "-Log[Sqrt[1 - x] + Sqrt[-x]] - Log[1 - x]/2"}, +{"fcstSimplifyPolyLog-ID121", +"SimplifyPolyLog[Log[(Sqrt[1 - x] + Sqrt[-x])/Sqrt[1 - x]]]", + "Log[Sqrt[1 - x] + Sqrt[-x]] - Log[1 - x]/2"}, +{"fcstSimplifyPolyLog-ID122", +"SimplifyPolyLog[Log[Sqrt[-x]/Sqrt[1 - x]]]", + "(I/2)*Pi - Log[1 - x]/2 + Log[x]/2"}, + {"fcstSimplifyPolyLog-ID123", +"SimplifyPolyLog[Log[Sqrt[-x]/Sqrt[1 - x]]]", + "(I \[Pi])/2 - 1/2 Log[1 - x] + Log[x]/2"}, +{"fcstSimplifyPolyLog-ID124", +"SimplifyPolyLog[Log[-Sqrt[-x]]]", + "(-I/2)*Pi + Log[x]/2"}, +{"fcstSimplifyPolyLog-ID125", +"SimplifyPolyLog[Log[(1 - Sqrt[x])/(1 + Sqrt[x])]]", + "-2*Log[1 + Sqrt[x]] + Log[1 - x]"}, +{"fcstSimplifyPolyLog-ID126", +"SimplifyPolyLog[Log[1/(1 - Sqrt[x])]]", + "Log[1 + Sqrt[x]] - Log[1 - x]"}, +{"fcstSimplifyPolyLog-ID127", +"SimplifyPolyLog[Log[1/(1 + Sqrt[x])]]", + "-Log[1 + Sqrt[x]]"}, +{"fcstSimplifyPolyLog-ID128", +"SimplifyPolyLog[Log[-(Sqrt[x]/(1 - Sqrt[x]))]]", + "I*Pi + Log[1 + Sqrt[x]] - Log[1 - x] + Log[x]/2"}, +{"fcstSimplifyPolyLog-ID129", +"SimplifyPolyLog[Log[(1 - 2 Sqrt[x])/(1 - Sqrt[x])]]", + "Log[1 - 2*Sqrt[x]] + Log[1 + Sqrt[x]] - Log[1 - x]"}, +{"fcstSimplifyPolyLog-ID130", +"SimplifyPolyLog[Log[1 - Complex[0, 1]]]", + "(-I/4)*Pi + Log[2]/2"}, +{"fcstSimplifyPolyLog-ID131", +"SimplifyPolyLog[Log[1 + Complex[0, 1]]]", + "(I/4)*Pi + Log[2]/2"}, +{"fcstSimplifyPolyLog-ID132", +"SimplifyPolyLog[PolyLog[3, Complex[Rational[1, 2], Rational[1, 2]]]]", + "((21*I)/64)*Pi*Zeta2 + (Zeta2*Log[2])/32 + ((3*I)/32)*Pi*Log[2]^2 + + Log[2]^3/48 - PolyLog[3, 1 + I] + (35*Zeta[3])/32"}, +{"fcstSimplifyPolyLog-ID133", +"SimplifyPolyLog[PolyLog[3, Complex[1, -1]]]", + "(3*Zeta2*Log[2])/8 - PolyLog[3, 1 + I] + (35*Zeta[3])/32"}, +{"fcstSimplifyPolyLog-ID134", +"SimplifyPolyLog[PolyLog[3, Complex[0, 1]]]", + "((3*I)/16)*Pi*Zeta2 - (3*Zeta[3])/32"}, +{"fcstSimplifyPolyLog-ID135", +"SimplifyPolyLog[Log[I*Sqrt[z/(1 - z)]]]", + "Log[I*Sqrt[z/(1 - z)]]"}, +{"fcstSimplifyPolyLog-ID136", +"SimplifyPolyLog[PolyGamma[0, 3/2], EulerGamma -> False]", + "2 - 2 Log[2]"}, +{"fcstSimplifyPolyLog-ID137", +"SimplifyPolyLog[PolyGamma[0, 3/2]]", + "2 - 2 Log[2] - EulerGamma"}, +{"fcstSimplifyPolyLog-ID138", +"SimplifyPolyLog[(23*Pi^6)/8640 - (23*Zeta2*Zeta4)/16]", + "0"}, +{"fcstSimplifyPolyLog-ID139", +"SimplifyPolyLog[Zeta[2]^3]", + "(35 Zeta6)/8"}, +{"fcstSimplifyPolyLog-ID140", +"SimplifyPolyLog[Zeta2^3]", + "(35 Zeta6)/8"}, +{"fcstSimplifyPolyLog-ID141", +"SimplifyPolyLog[Pi^8/9450]", + "Zeta8"}, +{"fcstSimplifyPolyLog-ID142", +"SimplifyPolyLog[Zeta[2]^4]", + "(175 Zeta8)/24"}, +{"fcstSimplifyPolyLog-ID143", +"SimplifyPolyLog[Zeta[2]Zeta[6]]", + "(5 Zeta8)/3"}, +{"fcstSimplifyPolyLog-ID144", +"SimplifyPolyLog[Zeta[4]^2]", + "(7 Zeta8)/6"}, +{"fcstSimplifyPolyLog-ID145", "SimplifyPolyLog[Zeta[2]^5]", +"(385*Zeta10)/32"}, +{"fcstSimplifyPolyLog-ID146", "SimplifyPolyLog[Zeta2^5]", +"(385*Zeta10)/32"}, +{"fcstSimplifyPolyLog-ID147", "SimplifyPolyLog[Zeta[4]Zeta[6]]", +"(11*Zeta10)/10"}, +{"fcstSimplifyPolyLog-ID148", "SimplifyPolyLog[Zeta4 Zeta6]", +"(11*Zeta10)/10"}, +{"fcstSimplifyPolyLog-ID149", "SimplifyPolyLog[Zeta[4]^2Zeta[2]]", +"(77*Zeta10)/40"}, +{"fcstSimplifyPolyLog-ID150", "SimplifyPolyLog[Zeta4^2 Zeta2]", +"(77*Zeta10)/40"}, +{"fcstSimplifyPolyLog-ID151", "SimplifyPolyLog[ArcTanh[z]]", +"Log[-((1 + z)/(1 - z))]/2"}, +{"fcstSimplifyPolyLog-ID152", "SimplifyPolyLog[ArcTanh[1+z]]", +"ArcTanh[1 + z]"}, +{"fcstSimplifyPolyLog-ID153", +"SimplifyPolyLog[ArcTanh[z],Trig\[Rule]False]", "ArcTanh[z]"}, +{"fcstSimplifyPolyLog-ID154", +"SimplifyPolyLog[Log[y-1],Log\[Rule]False]", "Log[-1 + y]"}, +{"fcstSimplifyPolyLog-ID155", +"SimplifyPolyLog[Log[-x^2],Log\[Rule]False]", "Log[-x^2]"}, +{"fcstSimplifyPolyLog-ID156", +"Head[SimplifyPolyLog[Log[-x_Symbol^2]]]", "SimplifyPolyLog"}, +{"fcstSimplifyPolyLog-ID157", +"SimplifyPolyLog[PolyLog[2, 2, x], Nielsen -> False]", "Zeta4 + 1/2 Zeta2 Log[1 - x]^2 + 1/24 Log[1 - x]^4 - +1/6 Log[1 - x]^3 Log[x] - Log[1 - x] PolyLog[3, x] - +PolyLog[4, 1 - x] + PolyLog[4, x] + PolyLog[4, x/(-1 + x)] + +Log[1 - x] Zeta[3]"}, +{"fcstSimplifyPolyLog-ID157", +"SimplifyPolyLog[PolyLog[4, 4, x]]", "Nielsen[4, 4, x]"} +}) diff --git a/Tests/Tables/Tables.mt b/Tests/Tables/Tables.mt new file mode 100644 index 000000000..a54ab048b --- /dev/null +++ b/Tests/Tables/Tables.mt @@ -0,0 +1,50 @@ +(* :Title: Tables.mt *) + +(* + This software is covered by the GNU General Public License 3. + Copyright (C) 1990-2017 Rolf Mertig + Copyright (C) 1997-2017 Frederik Orellana + Copyright (C) 2014-2017 Vladyslav Shtabovenko +*) + +(* :Summary: Unit tests for functions in the "Tables" directory *) + +(* ------------------------------------------------------------------------ *) + +Needs["FeynCalc`"]; + +ClearAll[tests]; +tests = FileNames["*.test",FileNameJoin[{ParentDirectory@$FeynCalcDirectory, "Tests", "Tables"}]] +Get/@tests; + +If[ $OnlySubTest=!="", + testNames = "Tests`Tables`*"; + removeTests=Complement[Names[testNames],Flatten[StringCases[Names[testNames],Alternatives@@$OnlySubTest]]]; + Remove/@removeTests; + Print["Only following subtests will be checked: ", Names[testNames]]; + Remove[testNames] +]; + +If[ Names["Tests`Tables`fcstSimplifyPolyLog*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Tables`fcstSimplifyPolyLog*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Tables`fcstNielsen*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Tables`fcstNielsen*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Tables`fcstKummer*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Tables`fcstKummer*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; + +If[ Names["Tests`Tables`fcstHill*"]=!={}, + tmpTest = Map[test[ToExpression[(#[[2]])],ToExpression[(#[[3]])],testID->#[[1]]]&, + Join@@(ToExpression/@Names["Tests`Tables`fcstHill*"])]; + tmpTest = tmpTest /. testID->TestID /. test -> Test; +]; diff --git a/Tests/TestSuite.m b/Tests/TestSuite.m index c98455e53..8a21ace81 100644 --- a/Tests/TestSuite.m +++ b/Tests/TestSuite.m @@ -2,9 +2,9 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Test Suite for FeynCalc via MUnit. Doesn't require Wolfram @@ -16,10 +16,18 @@ $FeynCalcStartupMessages = False; If[testType===3, - $LoadTARCER=True; + If[ !ValueQ[$LoadAddOns], + $LoadAddOns={"TARCER"}, + $LoadAddOns=Join[$LoadAddOns,{"TARCER"}] + ]; WriteString["stdout","Tests for TARCER.\n"] ]; +If[testType===4, + $LoadPhi=True; + WriteString["stdout","Tests for PHI.\n"] +]; + <True]; Exit[] ]; -If [onlyTest=!="" && Head[onlyTest]===String, -str = ".*"<>ToString[onlyTest]<>".*"; -fcTestList = StringCases[fcTestList,RegularExpression[str]]//Flatten; -FCPrint[0,"Only following tests will be checked: ", fcTestList,UseWriteString->True]; -FCPrint[0,"\n",UseWriteString->True] -] +If[ onlyTest=!="" && Head[onlyTest]===String, + strList = StringSplit[ToString[onlyTest],"|"]; + str = RegularExpression[(".*" <> # <> ".*")]& /@ strList; + fcTestList = StringCases[fcTestList,Alternatives@@str]//Flatten; + FCPrint[0,"Only following tests will be checked: ", fcTestList,UseWriteString->True]; + FCPrint[0,"\n",UseWriteString->True] +]; + +If[ onlySubTest=!="" && Head[onlySubTest]===String, + strList = StringSplit[ToString[onlySubTest],"|"]; + $OnlySubTest = RegularExpression[(".*" <> # <> ".*")]& /@ strList, + $OnlySubTest="" +]; + +SetAttributes[test, HoldAllComplete]; testRunner/@fcTestList; FCPrint[0,"\n",UseWriteString->True]; diff --git a/Tests/examples.sh b/Tests/examples.sh index 54c4e41bc..9b1bd6ae8 100755 --- a/Tests/examples.sh +++ b/Tests/examples.sh @@ -1,58 +1,140 @@ #!/bin/bash # This software is covered by the GNU General Public License 3. -# Copyright (C) 1990-2016 Rolf Mertig -# Copyright (C) 1997-2016 Frederik Orellana -# Copyright (C) 2014-2016 Vladyslav Shtabovenko +# Copyright (C) 1990-2018 Rolf Mertig +# Copyright (C) 1997-2018 Frederik Orellana +# Copyright (C) 2014-2018 Vladyslav Shtabovenko # Description: # Checks FeynCalc using real-life calculations. +# Stop if any of the examples fails +set -e + DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )" cd $DIR -if [ -z ${MATH+x} ]; then MATH=math; else echo $MATH; fi -#Misc Examples -$MATH -nopromt -script ../FeynCalc/Examples/Misc/Integrate2.m && -#Tdec Examples -$MATH -nopromt -script ../FeynCalc/Examples/Tdec/GrossNeveuMultiloopTID.m && +MATH=$1 + + +##Misc Examples +#$MATH -nopromt -script ../FeynCalc/Examples/Misc/Integrate2.m && + +##Tdec Examples +#$MATH -nopromt -script ../FeynCalc/Examples/Tdec/GrossNeveuMultiloopTID.m && + +#MSSM Examples +#------------------------------------------------------------------------------- +for exFile in 'MnelEl-MnelEl.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/MSSM/Tree/$exFile +done + +#Phi3 Examples +#------------------------------------------------------------------------------- +for exFile in 'Renormalization.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/Phi3/OneLoop/$exFile +done + + +#Phi^4 Examples +#------------------------------------------------------------------------------- +for exFile in 'PhiPhi-PhiPhi.m' 'Renormalization.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/Phi4/OneLoop/$exFile +done +#------------------------------------------------------------------------------- + #QED Examples -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDABJAxialAnomaly.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDElectronGMinusTwoOneLoop.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDBhabhaScatteringTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDComptonScatteringTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDElectronMuonScatteringTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDMoellerScatteringTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDMuonProductionTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDPairAnnihilationTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDOnePhotonTadpoleOneLoop.m && -$MATH -nopromt -script ../FeynCalc/Examples/QED/QEDThreePhotonDiagramsOneLoop.m && - -#EW Examples -$MATH -nopromt -script ../FeynCalc/Examples/EW/EWMuonDecayTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/EW/EWElectronMuonNeutrinoToMuonElectronNeutrinoTree.m -$MATH -nopromt -script ../FeynCalc/Examples/EW/EWHiggsToTwoFermionsTree.m -$MATH -nopromt -script ../FeynCalc/Examples/EW/EWHiggsToWPlusWMinusTree.m -$MATH -nopromt -script ../FeynCalc/Examples/EW/EWHiggsToZZTree.m +#------------------------------------------------------------------------------- +for exFile in 'ElAel-ElAel.m' 'ElAel-GaGa.m' 'ElAel-MuAmu.m' 'ElEl-ElEl.m' \ +'ElGa-ElGa.m' 'ElMu-ElMu.m' 'Ga-MuAmu.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/QED/Tree/$exFile +done + +for exFile in 'El-El.m' 'El-GaEl.m' 'Ga.m' 'Ga-Ga.m' 'Ga-GaGa.m' 'Ga-GaGaGaGa.m' \ +'PiToGaGa.m' 'Renormalization.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/QED/OneLoop/$exFile +done +#------------------------------------------------------------------------------- + #QCD Examples -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDGammaStarGToQiQBari.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQiGammaStarToQiGTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQiQBariToGammaStarGTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQiQjToQiQjTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQiQBarjToQiQBarjTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQiQiToQiQiTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQiQBariToQjQBarjTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQiQBariToQiQBariTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQiQBariToGGTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDGGToQiQBariTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDGQiToGQi.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDGGToGGTree.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDQuarkSelfEnergyOneLoop.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDGluonSelfEnergyOneLoop.m && -$MATH -nopromt -script ../FeynCalc/Examples/QCD/QCDGhostSelfEnergyTwoLoops.m -$MATH -nopromt -script ../FeynCalc/Examples/FeynRules/QCDBGF/PureYMSelfEnergyInQCDBGFAtOneLoop.m +#------------------------------------------------------------------------------- +for exFile in 'ElAel-QQbar.m' 'GaGl-QQbar.m' 'Ga-QQbar.m' 'Ga-QQbarGl.m' \ +'GlGl-GlGl.m' 'GlGl-QQbar.m' 'MuAmu-QQbar.m' 'QGa-GlQ.m' 'QGl-QGl.m' \ +'QiQibar-QiQibar.m' 'QiQibar-QjQjbar.m' 'QiQi-QiQi.m' 'QiQjbar-QiQjbar.m' \ +'QiQj-QiQj.m' 'QQbar-ElAel.m' 'QQbar-GaGa.m' 'QQbar-GaGl.m' 'QQbar-GlGl.m' \ +'QQbar-MuAmu.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/QCD/Tree/$exFile +done + +for exFile in 'Gh-Gh.m' 'GhGl-Gh.m' 'Gl-Gl.m' 'Gl-Gl-BackgroundFieldGauge.m' \ +'Gl-GlGl.m' 'Q-Q.m' 'Renormalization.m' 'RenormalizationMassless.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/QCD/OneLoop/$exFile +done + +for exFile in 'Gh-Gh.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/QCD/TwoLoops/$exFile +done +#------------------------------------------------------------------------------- + + +##EW Examples +#------------------------------------------------------------------------------- +for exFile in 'AnelEl-AnmuMu.m' 'AnelEl-QubarQd.m' 'AnelEl-WW.m' 'AnelEl-ZZ.m' \ +'ElNmu-MuNel.m' 'H-FFbar.m' 'H-WW.m' 'H-ZZ.m' 'Mu-ElAnelNmu.m' 'NleQdt-LeQut.m' \ +'QQbar-ZZ.m' 'Qt-QbW.m' 'QuQdbar-AelNel.m' 'QutbarQdt-NelAnel.m' 'W-ElAnel.m' \ +'W-QiQjbar.m' 'Z-FFbar.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/EW/Tree/$exFile +done + +for exFile in 'H-GG.m' + +do + echo + echo -e "* \c" + $MATH -nopromt -script ../FeynCalc/Examples/EW/OneLoop/$exFile +done +#------------------------------------------------------------------------------- + + +notify-send --urgency=low -i "$([ $? = 0 ] && echo sunny || echo error)" "Finished running examples for FeynCalc." diff --git a/Tests/inttests.sh b/Tests/inttests.sh index c560e4c06..9d805356f 100755 --- a/Tests/inttests.sh +++ b/Tests/inttests.sh @@ -1,9 +1,9 @@ #!/bin/bash # This software is covered by the GNU General Public License 3. -# Copyright (C) 1990-2016 Rolf Mertig -# Copyright (C) 1997-2016 Frederik Orellana -# Copyright (C) 2014-2016 Vladyslav Shtabovenko +# Copyright (C) 1990-2018 Rolf Mertig +# Copyright (C) 1997-2018 Frederik Orellana +# Copyright (C) 2014-2018 Vladyslav Shtabovenko # Description: @@ -18,4 +18,13 @@ set -o pipefail DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )" cd $DIR -$1 -nopromt -script TestSuite.m -run testType=2 -run onlyTest=\"$2\" +$1 -nopromt -script TestSuite.m -run testType=2 -run onlyTest=\"$2\" -run onlySubTest=\"$3\" + +if [ -z "$2" ] + then + outtxt="Finished running integration tests for FeynCalc." + else + outtxt="Finished running integration tests for FeynCalc ($2)." +fi + +notify-send --urgency=low -i "$([ $? = 0 ] && echo sunny || echo error)" "$outtxt" diff --git a/Tests/runtests.sh b/Tests/runtests.sh index c9a47da3f..b52dbd297 100755 --- a/Tests/runtests.sh +++ b/Tests/runtests.sh @@ -1,9 +1,9 @@ #!/bin/bash # This software is covered by the GNU General Public License 3. -# Copyright (C) 1990-2016 Rolf Mertig -# Copyright (C) 1997-2016 Frederik Orellana -# Copyright (C) 2014-2016 Vladyslav Shtabovenko +# Copyright (C) 1990-2018 Rolf Mertig +# Copyright (C) 1997-2018 Frederik Orellana +# Copyright (C) 2014-2018 Vladyslav Shtabovenko # Description: diff --git a/Tests/runtests_short.sh b/Tests/runtests_short.sh index 068e3f974..857c58fd2 100755 --- a/Tests/runtests_short.sh +++ b/Tests/runtests_short.sh @@ -1,9 +1,9 @@ #!/bin/bash # This software is covered by the GNU General Public License 3. -# Copyright (C) 1990-2016 Rolf Mertig -# Copyright (C) 1997-2016 Frederik Orellana -# Copyright (C) 2014-2016 Vladyslav Shtabovenko +# Copyright (C) 1990-2018 Rolf Mertig +# Copyright (C) 1997-2018 Frederik Orellana +# Copyright (C) 2014-2018 Vladyslav Shtabovenko # Description: diff --git a/Tests/tarcertests.sh b/Tests/tarcertests.sh index cb25dbdee..0d75c3801 100755 --- a/Tests/tarcertests.sh +++ b/Tests/tarcertests.sh @@ -1,9 +1,9 @@ #!/bin/bash # This software is covered by the GNU General Public License 3. -# Copyright (C) 1990-2016 Rolf Mertig -# Copyright (C) 1997-2016 Frederik Orellana -# Copyright (C) 2014-2016 Vladyslav Shtabovenko +# Copyright (C) 1990-2018 Rolf Mertig +# Copyright (C) 1997-2018 Frederik Orellana +# Copyright (C) 2014-2018 Vladyslav Shtabovenko # Description: @@ -18,3 +18,12 @@ DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )" cd $DIR $1 -nopromt -script TestSuite.m -run testType=3 -run onlyTest=\"$2\" + +if [ -z "$2" ] + then + outtxt="Finished running unit tests for TARCER." + else + outtxt="Finished running unit tests for TARCER ($2)." +fi + +notify-send --urgency=low -i "$([ $? = 0 ] && echo sunny || echo error)" "$outtxt" diff --git a/Tests/unittests.sh b/Tests/unittests.sh index f3200b199..787390947 100755 --- a/Tests/unittests.sh +++ b/Tests/unittests.sh @@ -1,9 +1,9 @@ #!/bin/bash # This software is covered by the GNU General Public License 3. -# Copyright (C) 1990-2016 Rolf Mertig -# Copyright (C) 1997-2016 Frederik Orellana -# Copyright (C) 2014-2016 Vladyslav Shtabovenko +# Copyright (C) 1990-2018 Rolf Mertig +# Copyright (C) 1997-2018 Frederik Orellana +# Copyright (C) 2014-2018 Vladyslav Shtabovenko # Description: @@ -17,4 +17,13 @@ set -o pipefail DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )" cd $DIR -$1 -nopromt -script TestSuite.m -run testType=1 -run onlyTest=\"$2\" +$1 -nopromt -script TestSuite.m -run testType=1 -run onlyTest=\"$2\" -run onlySubTest=\"$3\" + +if [ -z "$2" ] + then + outtxt="Finished running unit tests for FeynCalc." + else + outtxt="Finished running unit tests for FeynCalc ($2)." +fi + +notify-send --urgency=low -i "$([ $? = 0 ] && echo sunny || echo error)" "$outtxt" diff --git a/install.m b/install.m index 1173ce14f..1d59c0b04 100644 --- a/install.m +++ b/install.m @@ -4,22 +4,43 @@ (* This software is covered by the GNU General Public License 3. - Copyright (C) 1990-2016 Rolf Mertig - Copyright (C) 1997-2016 Frederik Orellana - Copyright (C) 2014-2016 Vladyslav Shtabovenko + Copyright (C) 1990-2020 Rolf Mertig + Copyright (C) 1997-2020 Frederik Orellana + Copyright (C) 2014-2020 Vladyslav Shtabovenko *) (* :Summary: Installs FeynCalc and FeynArts *) (* ------------------------------------------------------------------------ *) +If[ !FreeQ[$ContextPath,"WolframLanguageForJupyter`"], + Print["It seems that your are trying to install FeynCalc from a ", + "Wolfram Language kernel for Jupyter notebooks.", + "Unfortunately, graphical installation using a Jupyter frontend is currently not possible.", + "If you only have access to the Free Wolfram Engine, please start the kernel with a text-based interface", + "and run the installer again.", "\n\nInstallation aborted!"]; + Abort[] +]; + +BeginPackage["FeynCalcInstaller`"]; + InstallFeynCalc::notcomp = "Your Mathematica version is too old. FeynCalc requires at least Mathematica 8. Installation aborted!"; + InstallFeynCalc::failed = "Download of `1` failed. Installation aborted!"; +InstallFeynCalcQuiet::usage="InstallFeynCalcQuiet is the silent mode of installing FeynCalc, where the \ +installer does not ask you any questions but silently overwrites any existing FeynCalc installation and \ +modifies Mathematica's options accordingly. FeynArts is not installed. The main purpose of this mode is \ +to facilitate the installation of FeynCalc on Mathematica Online."; + +AutoEnableTraditionalForm::usage="AutoEnableTraditionalForm is an option of InstallFeynCalc. If \ +set to True, the format type of new output cells will be set to TraditionalForm. False means that \ +the current value will not be changed."; + AutoOverwriteFeynCalcDirectory::usage="AutoOverwriteFeynCalcDirectory is an option of InstallFeynCalc. If \ -set to True, the existing FeynCalc directory will be deleted without any further notice. The default +set to True, the existing FeynCalc directory will be deleted without any further notice. The default \ value None means that the user will be asked by a dialog. False means that the directory will be overwritten."; AutoDisableInsufficientVersionWarning::usage="AutoDisableInsufficientVersionWarning is an option of InstallFeynCalc. If \ @@ -59,6 +80,10 @@ If the value is not empty, the installer will use the specified file instead of downloading it from the official \ website." +Begin["`Private`"] + +testConnection::usage=""; + If[ !ValueQ[$PathToFCArc], $PathToFCArc = "" ]; @@ -67,38 +92,101 @@ $PathToFAArc = "" ]; -If[ $VersionNumber == 8, -(*To use FetchURL in MMA8 we need to load URLTools first *) -Needs["Utilities`URLTools`"]; +If[ $VersionNumber < 8, + Message[InstallFeynCalc::notcomp]; + Abort[] ]; -Options[InstallFeynCalc]={ - AutoDisableInsufficientVersionWarning->None, - AutoInstallFeynArts->None, - AutoOverwriteFeynCalcDirectory->None, - FeynCalcDevelopmentVersionLink->"https://github.com/FeynCalc/feyncalc/archive/master.zip", - FeynCalcStableVersionLink->"https://github.com/FeynCalc/feyncalc/archive/hotfix-stable.zip", - InstallFeynCalcDevelopmentVersion->False, - InstallFeynCalcTo->FileNameJoin[{$UserBaseDirectory, "Applications","FeynCalc"}] + +If[ 8.0 <=$VersionNumber < 9.0, + (*To use FetchURL in MMA8 we need to load URLTools first *) + Needs["Utilities`URLTools`"]; +]; + +Which[ + (*Mma 8*) + 8.0 <=$VersionNumber < 9.0, + (*To use FetchURL we need to load URLTools first *) + FCGetUrl[x_]:= Utilities`URLTools`FetchURL[x], + (*Mma 9 or 10 *) + 9.0 <=$VersionNumber < 11.0, + FCGetUrl[x_]:= URLSave[x,CreateTemporary[]], + (*Mma 11 and above *) + $VersionNumber >= 11.0, + FCGetUrl[x_]:= First[URLDownload[x,CreateTemporary[]]] +]; + +If[ $PathToFCArc==="", + (*Test that we can access the FeynCalc repository*) + Quiet[testConnection = FCGetUrl["https://github.com/FeynCalc/feyncalc"];]; + If[ testConnection===$Failed || !FileExistsQ[testConnection], + WriteString["stdout", + "It seems that your Mathematica version is unable to ", + "connect to the FeynCalc repository on GitHub.\n", + "This might be a network connectivity problem or an issue with Mathematica.\n", + "Especially some older versions of Mathematica (8, 9 or 10) and known to cause such problems\n", + "on recent versions of Linux, MacOS and Windows when accessing SSL-encrypted urls.\n\n", + "Please check the wiki for ", + "possible workarounds.\n", + "Notice that it is also possible to download all the necessary files by hand and install FeynCalc\n", + "without an existing internet connection. The required steps are described in the wiki.", "\n\nInstallation aborted!" + ]; + Abort[] + ]; +]; + +fancyText[Column[li_List]] := + Column[(TextCell[#, "Text"] & /@ li)] /; $Notebooks + +fancyText[x_] := + x /; !$Notebooks; + +choiceDialog2[x__] := + ChoiceDialog[x]/; $Notebooks; + +choiceDialog2[text_,rest__] := + ( + WriteString["stdout","\n\n"]; + MessageDialog[text]; + ChoiceDialog["",rest] + )/; !$Notebooks; + +(*Greeter*) +Print["Welcome to the automatic FeynCalc installer brought to you by the FeynCalc developer team!"]; +Print[" \[Bullet] To install the current stable version of FeynCalc (recommended for productive use), please evaluate"]; +Print["\t", If[$Notebooks,TextCell["InstallFeynCalc[]", "Code"],"InstallFeynCalc[]"]]; +Print[" \[Bullet] To install the development version of FeynCalc (only for experts or beta testers), please evaluate "]; +Print["\t", If[$Notebooks,TextCell["InstallFeynCalc[InstallFeynCalcDevelopmentVersion->True]", "Code"], + "InstallFeynCalc[InstallFeynCalcDevelopmentVersion->True]" ]]; + +Options[InstallFeynCalc] = { + AutoDisableInsufficientVersionWarning -> None, + AutoEnableTraditionalForm -> None, + AutoInstallFeynArts -> None, + AutoOverwriteFeynCalcDirectory -> None, + FeynCalcDevelopmentVersionLink -> "https://github.com/FeynCalc/feyncalc/archive/master.zip", + FeynCalcStableVersionLink -> "https://github.com/FeynCalc/feyncalc/archive/hotfix-stable.zip", + InstallFeynCalcDevelopmentVersion -> False, + InstallFeynCalcTo -> FileNameJoin[{$UserBaseDirectory, "Applications","FeynCalc"}] }; -Options[InstallFeynArts]={ - FeynArtsMirrorLink->"https://github.com/FeynCalc/feynarts-mirror/archive/master.zip", - InstallFeynArtsTo->FileNameJoin[{$UserBaseDirectory, "Applications","FeynCalc","FeynArts"}] +Options[InstallFeynCalcQuiet]= + Options[InstallFeynCalc]; + +Options[InstallFeynArts] = { + FeynArtsMirrorLink -> "https://github.com/FeynCalc/feynarts-mirror/archive/master.zip", + InstallFeynArtsTo -> FileNameJoin[{$UserBaseDirectory, "Applications","FeynCalc","FeynArts"}] }; + + + InstallFeynArts[OptionsPattern[]]:= - Module[{tmpzip,fazip,FCGetUrl,unzipDir,faDir}, + Module[{tmpzip,fazip,unzipDir,faDir}, (* Install FeynArts *) - faDir=OptionValue[InstallFeynArtsTo]; - fazip = OptionValue[FeynArtsMirrorLink]; - - If[$VersionNumber == 8, - (*To use FetchURL in MMA8 we need to load URLTools first *) - FCGetUrl[x_]:= Utilities`URLTools`FetchURL[x], - FCGetUrl[x_]:= URLSave[x,CreateTemporary[]] - ]; + faDir = OptionValue[InstallFeynArtsTo]; + fazip = OptionValue[FeynArtsMirrorLink]; (* Download FeynArts tarball *) If[ $PathToFAArc=!="", @@ -131,131 +219,217 @@ ]; - -InstallFeynCalc[OptionsPattern[]]:= - Module[{ unzipDir, tmpzip, gitzip, packageName, packageDir, - strDisableWarning,strFeynArts,FCGetUrl, - strOverwriteFCdit, faInstalled, zipDir}, - - If[OptionValue[InstallFeynCalcDevelopmentVersion], - gitzip = OptionValue[FeynCalcDevelopmentVersionLink]; - zipDir = "feyncalc-master", - gitzip = OptionValue[FeynCalcStableVersionLink]; - zipDir = "feyncalc-hotfix-stable" +InstallFeynCalcQuiet[]:= + InstallFeynCalc[ + AutoDisableInsufficientVersionWarning-> True, + AutoEnableTraditionalForm -> True, + AutoInstallFeynArts-> False, + AutoOverwriteFeynCalcDirectory-> True ]; - faInstalled=False; - packageName = "FeynCalc"; - packageDir = OptionValue[InstallFeynCalcTo]; +InstallFeynCalc[OptionsPattern[]]:= + Module[ {unzipDir, tmpzip, gitzip, packageName, packageDir, fullPath, + strFeynArts, configFileProlog, strOverwriteFC, + strDisableWarning, strEnableTraditionalForm, faInstalled, zipDir, + useTraditionalForm, configFile}, + + If[ OptionValue[InstallFeynCalcDevelopmentVersion], + gitzip = OptionValue[FeynCalcDevelopmentVersionLink], + gitzip = OptionValue[FeynCalcStableVersionLink] + ]; -strDisableWarning="To make the documentation work, we need to disable the warning that appears \ -when you open a notebook that was created with a newer Mathematica version. Otherwise this \ -warning will pop up every time you use the Documentation Center to read info on FeynCalc functions \ -in Mathematica 8 and 9. This setting is harmless and can be always undone via \ -\"SetOptions[$FrontEnd, MessageOptions -> {\"InsufficientVersionWarning\" -> True}]\". Should we do this now?"; + faInstalled = False; + useTraditionalForm = False; + packageName = "FeynCalc"; + packageDir = OptionValue[InstallFeynCalcTo]; + + strDisableWarning = + Column[{ + StringJoin["To make the documentation work, we need to disable the warning ", + "that appears when you open a notebook that was created with a newer Mathematica version."], + " ", + StringJoin["Otherwise this warning will appear every time you use the Documentation Center ", + "to check FeynCalc documentation in Mathematica 8 and 9."], + " ", + "This setting is harmless and can be always undone via", + " ", + "\"SetOptions[$FrontEnd, MessageOptions -> \ {\"InsufficientVersionWarning\" -> True}]\"", + "", + "Should we do this now?"} + ]; + + + strEnableTraditionalForm = + Column[{ + StringJoin["FeynCalc makes an extensive use of Mathematica's typesetting capabilities ", + "to format the output in a nice and easily readable manner."], + " ", + StringJoin["However, the built-in typesetting is available only if the format type of ", + "new output cells is set to TraditionalForm. The default value is StandardForm."], + " ", + StringJoin["Do you want to allow FeynCalc to change the default output format to ", + "TraditionalForm whenever it is loaded?"], + " ", + StringJoin["This will only affect the current FeynCalc front end session and will not ", + "modify the default behavior of Mathematica."] + } + ]; + strFeynArts = + Column[{ + "Do you want to install FeynArts from "<> OptionValue[InstallFeynArts,FeynArtsMirrorLink] <> "?", + "", + "FeynArts is a Feynman diagram generator developed by Thomas Hahn (www.feynarts.de).", + "It is not part of FeynCalc but it can be used together with FeynCalc after some adjustments.", + "", + "The modified version of FeynArts will be placed into " <> FileNameJoin[{packageDir,"FeynArts"}]<>"." + } + ]; + + strOverwriteFC = + Column[{ + "Looks like you already have a version of FeynCalc installed in " <> packageDir, + "", + "The installer can overwrite the content of this directory with the downloaded version of FeynCalc.", + "", + "However, in this case all custom configuration files or add-ons located there will be lost.", + "", + "How should we proceed?" + } + ]; + + configFileProlog = StringJoin[ + "(* ", + "Here you can put some commands and settings to be evaluated on every start of FeynCalc.\n", + "This can be used to customize your FeynCalc installation. ", + "*)" + ]; -strFeynArts="Do you want to install FeynArts from "<> OptionValue[InstallFeynArts,FeynArtsMirrorLink] <> "? FeynArts is a Feynman diagram \ -generator which is currently developed by Thomas Hahn (www.feynarts.de). It is not a part of FeynCalc but it \ -can be used together with FeynCalc after some patching. The patched version will be located in the directory \"FeynArts\" -inside your FeynCalc installation."; -strOverwriteFCdit="Looks like FeynCalc is already installed. Do you want to replace the content \ -of " <> packageDir <> " with the downloaded version of FeynCalc? If you are using any custom configuration \ -files or add-ons that are located in that directory, please backup them in advance."; + (* If the package directory already exists, ask the user about overwriting *) + If[ DirectoryQ[packageDir], - If[$VersionNumber < 8, - Message[InstallFeynCalc::notcomp]; - Abort[] - ]; + If[ OptionValue[AutoOverwriteFeynCalcDirectory], - If[$VersionNumber == 8, - (*To use FetchURL in MMA8 we need to load URLTools first *) - FCGetUrl[x_]:= Utilities`URLTools`FetchURL[x], - FCGetUrl[x_]:= URLSave[x,CreateTemporary[]] - ]; + Quiet@DeleteDirectory[packageDir, DeleteContents -> True], + Null, + If[ choiceDialog2[fancyText[strOverwriteFC],{"Yes, overwrite the " <> packageName <>" directory"->True, + "No, I need to do a backup first. Abort installation."->False}, WindowFloating->True, WindowTitle->"Existing FeynCalc installation detected"], + Quiet@DeleteDirectory[packageDir, DeleteContents -> True], + Abort[] + ] + ] + ]; - (* If the package directory already exists, ask the user about overwriting *) - If[ DirectoryQ[packageDir], + (* Download FeynCalc zip file *) + If[ $PathToFCArc=!="", + tmpzip = $PathToFCArc; + WriteString["stdout", "Installing FeynCalc from ", tmpzip," ..."], + WriteString["stdout", "Downloading FeynCalc from ", gitzip," ..."]; + tmpzip=FCGetUrl[gitzip]; + ]; - If[ OptionValue[AutoOverwriteFeynCalcDirectory], + If[tmpzip===$Failed || !FileExistsQ[tmpzip], + WriteString["stdout", "\nFailed to download the FeynCalc zip file. Please check your interent connection.\nInstallation aborted!"]; + Abort[], - Quiet@DeleteDirectory[packageDir, DeleteContents -> True], + unzipDir= tmpzip<>".dir"; + WriteString["stdout", "done! \n"]; + ]; - Null, - If[ ChoiceDialog[strOverwriteFCdit,{"Yes, overwrite the " <> packageName <>" directory"->True, - "No! I need to do a backup first."->False}], - Quiet@DeleteDirectory[packageDir, DeleteContents -> True], - Abort[] + (* Extract the content *) + WriteString["stdout", "FeynCalc zip file was saved to ", tmpzip,".\n"]; + WriteString["stdout", "Extracting FeynCalc zip file to ", unzipDir, " ..."]; + + If[ ExtractArchive[tmpzip, unzipDir]===$Failed, + WriteString["stdout", "\nFailed to extract the FeynCalc zip. The file might be corrupted.\nInstallation aborted!"]; + Abort[], + WriteString["stdout", "done! \n"]; + (* Delete the downloaded file *) + If[ $PathToFCArc==="", + Quiet@DeleteFile[tmpzip]; ] - ] - ]; + ]; - (* Download FeynCalc tarball *) - If[ $PathToFCArc=!="", - tmpzip = $PathToFCArc; - WriteString["stdout", "Installing FeynCalc from ", tmpzip," ..."], - WriteString["stdout", "Downloading FeynCalc from ", gitzip," ..."]; - tmpzip=FCGetUrl[gitzip]; - ]; - unzipDir= tmpzip<>".dir"; - WriteString["stdout", "done! \n"]; - - (* Extract to the content *) - WriteString["stdout", "FeynCalc zip file was saved to ", tmpzip,".\n"]; - WriteString["stdout", "Extracting FeynCalc zip file to ", unzipDir, " ..."]; - ExtractArchive[tmpzip, unzipDir]; - WriteString["stdout", "done! \n"]; - - (* Delete the downloaded file *) - If[ $PathToFCArc==="", - Quiet@DeleteFile[tmpzip]; - ]; + WriteString["stdout", "Checking the directory structure..."]; + zipDir = FileNames["FeynCalc.m", unzipDir, Infinity]; + If[ Length[zipDir]===1, + fullPath = DirectoryName[zipDir[[1]]]; + zipDir = Last[FileNameSplit[DirectoryName[zipDir[[1]]]]]; + WriteString["stdout", "done! \n"], + WriteString["stdout", "\nFailed to recognize the directory structure of the downloaded zip file. \nInstallation aborted!"]; + Abort[] + ]; + + (* Move the files to the final destination *) + WriteString["stdout", "Copying "<>packageName<>" to ", packageDir, " ..."]; + + If[ CopyDirectory[fullPath,packageDir]===$Failed, + WriteString["stdout", "\nFailed to copy " <>fullPath<>" to ", packageDir <>". \nInstallation aborted!"]; + Abort[], + WriteString["stdout", "done! \n"]; + (* Delete the extracted archive *) + Quiet@DeleteDirectory[unzipDir, DeleteContents -> True]; + ]; + (* Activate the documentation *) + WriteString["stdout", "Setting up the help system ... "]; + RenameDirectory[FileNameJoin[{packageDir,"DocOutput"}],FileNameJoin[{packageDir,"Documentation"}]]; + Quiet@DeleteDirectory[FileNameJoin[{packageDir,"DocSource"}], DeleteContents -> True]; + (* Disable InsufficientVersionWarning?*) + If[ OptionValue[AutoDisableInsufficientVersionWarning] && $Notebooks, - (* Move the files to the final destination *) - WriteString["stdout", "Copying "<>packageName<>" to ", packageDir, " ..."]; - CopyDirectory[FileNameJoin[{unzipDir,zipDir,"FeynCalc"}],packageDir]; - WriteString["stdout", "done! \n"]; - (* Delete the extracted archive *) - Quiet@DeleteDirectory[unzipDir, DeleteContents -> True]; + SetOptions[$FrontEnd, MessageOptions -> {"InsufficientVersionWarning" -> False}], - (* Activate the documentation *) - WriteString["stdout", "Setting up the help system... "]; - RenameDirectory[FileNameJoin[{packageDir,"DocOutput"}],FileNameJoin[{packageDir,"Documentation"}]]; - Quiet@DeleteDirectory[FileNameJoin[{packageDir,"DocSource"}], DeleteContents -> True]; + Null, + If[ choiceDialog2[fancyText[strDisableWarning], WindowFloating->True, WindowTitle->"Documentation system"] && $Notebooks, + SetOptions[$FrontEnd, MessageOptions -> {"InsufficientVersionWarning" -> False}] + ] + ]; - If[ OptionValue[AutoDisableInsufficientVersionWarning], + (* Activate TraditionalForm? *) + WriteString["stdout", "Setting up the format type of new output cells ... "]; + If[ OptionValue[AutoEnableTraditionalForm], - SetOptions[$FrontEnd, MessageOptions -> {"InsufficientVersionWarning" -> False}], + useTraditionalForm = True, + Null, + If[ choiceDialog2[fancyText[strEnableTraditionalForm], WindowFloating->True, WindowTitle -> "TraditionalForm typesetting"], + useTraditionalForm = True + ] + ]; - Null, - If[ ChoiceDialog[strDisableWarning], - SetOptions[$FrontEnd, MessageOptions -> {"InsufficientVersionWarning" -> False}] - ] - ]; + WriteString["stdout", "done! \n"]; + (* To have the documentation available immediately after installing FeynCalc (following the advice of Szabolcs Horv'at) *) + RebuildPacletData[]; - WriteString["stdout", "done! \n"]; + (* Generate FCConfig.m *) + WriteString["stdout", "Creating the configuration file ... "]; + configFile = StringJoin[configFileProlog, "\n\n(* Activate TraditionalForm output for each FeynCalc session *) \n$FCTraditionalFormOutput="<>ToString[useTraditionalForm]<>";"]; + Export[FileNameJoin[{packageDir,"FCConfig.m"}], configFile, "Text"]; + WriteString["stdout", "done! \n"]; - If[ OptionValue[AutoInstallFeynArts], + If[ OptionValue[AutoInstallFeynArts], - faInstalled=True; - InstallFeynArts[InstallFeynArtsTo->FileNameJoin[{packageDir,"FeynArts"}]], - Null, - If[ ChoiceDialog[strFeynArts], faInstalled=True; - InstallFeynArts[InstallFeynArtsTo->FileNameJoin[{packageDir,"FeynArts"}]] - ] - ]; - + InstallFeynArts[InstallFeynArtsTo->FileNameJoin[{packageDir,"FeynArts"}]], + Null, + If[ choiceDialog2[fancyText[strFeynArts], WindowFloating->True, WindowTitle->"Install FeynArts"], + faInstalled=True; + InstallFeynArts[InstallFeynArtsTo->FileNameJoin[{packageDir,"FeynArts"}]] + ] + ]; - WriteString["stdout", "\nInstallation complete! Loading FeynCalc... \n"]; + WriteString["stdout", "\nInstallation complete! Loading FeynCalc ... \n"]; - If[ faInstalled, - Global`$LoadFeynArts=True; - ]; - Get["FeynCalc`"]; + If[ faInstalled, + Global`$LoadAddOns={"FeynArts"} + ]; + Get["FeynCalc`"]; ]; + +End[]; + +EndPackage[]; diff --git a/issue_template.md b/issue_template.md new file mode 100644 index 000000000..12faf9c27 --- /dev/null +++ b/issue_template.md @@ -0,0 +1,19 @@ +* Your Mathematica version + + ```Evaluate $Version in your Mathematica session and paste the output here``` + +* Your FeynCalc version + + ```Load FeynCalc, evaluate $FeynCalcVersion and paste the output here``` + +* Did you try to reinstall FeynCalc (stable version) using the automatic installer to make sure that you have the latest bugfixes? + + ```Yes/No``` + +* Does your Mathematica initialization file contain statements that might influence the behavior of FeynCalc? Sometimes external packages may modify `init.m` in unusual ways, causing troubles for other codes. + + ```Check the output of Import[FileNameJoin[{$UserBaseDirectory, "Kernel", "init.m"}], "String"]``` + +* Please provide a minimal working example that illustrates the problem and works on a fresh kernel. Please explain the difference between the current behavior and the expected behavior. + + ```Paste your code here```